|\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428240051 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 3 2 4 2 F := [-9 x + 12 z + 16, -2 x y - 17 x y + 6 y z, -2 z - 20 y z + 9 x] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 2 3 2 G := [7 z - 8 x - 11 y , 3 x y - 3 x + 6 y , -y + 16 y z + 18 z ] > Problem := [F,G]; Problem := [ 4 2 2 3 2 4 2 [-9 x + 12 z + 16, -2 x y - 17 x y + 6 y z, -2 z - 20 y z + 9 x], 3 2 2 2 2 2 3 2 [7 z - 8 x - 11 y , 3 x y - 3 x + 6 y , -y + 16 y z + 18 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.8MB, alloc=32.3MB, time=0.53 memory used=48.2MB, alloc=32.3MB, time=0.86 memory used=66.8MB, alloc=56.3MB, time=1.15 memory used=108.2MB, alloc=60.3MB, time=1.79 memory used=148.3MB, alloc=84.3MB, time=2.42 memory used=210.1MB, alloc=92.3MB, time=3.39 memory used=275.6MB, alloc=116.3MB, time=4.33 memory used=351.7MB, alloc=116.3MB, time=5.48 memory used=419.3MB, alloc=372.3MB, time=6.44 memory used=508.8MB, alloc=396.3MB, time=7.73 memory used=624.7MB, alloc=396.3MB, time=9.36 memory used=738.8MB, alloc=420.3MB, time=10.78 memory used=873.0MB, alloc=444.3MB, time=12.82 memory used=1016.2MB, alloc=444.3MB, time=15.06 memory used=1138.3MB, alloc=468.3MB, time=16.82 memory used=1254.7MB, alloc=468.3MB, time=18.31 memory used=1369.9MB, alloc=468.3MB, time=20.24 memory used=1484.8MB, alloc=492.3MB, time=22.07 memory used=1639.1MB, alloc=492.3MB, time=23.44 memory used=1869.9MB, alloc=492.3MB, time=24.96 memory used=2031.2MB, alloc=492.3MB, time=26.52 memory used=2119.8MB, alloc=492.3MB, time=26.90 memory used=2204.9MB, alloc=492.3MB, time=27.39 memory used=2352.6MB, alloc=492.3MB, time=28.93 memory used=2488.7MB, alloc=492.3MB, time=30.12 memory used=2688.9MB, alloc=516.3MB, time=31.52 memory used=2792.7MB, alloc=516.3MB, time=33.00 memory used=2867.9MB, alloc=516.3MB, time=34.24 memory used=2953.7MB, alloc=516.3MB, time=35.56 memory used=3053.6MB, alloc=516.3MB, time=36.86 memory used=3210.0MB, alloc=516.3MB, time=38.13 memory used=3302.2MB, alloc=516.3MB, time=39.64 memory used=3467.6MB, alloc=540.3MB, time=40.93 memory used=3562.0MB, alloc=540.3MB, time=42.43 memory used=3634.4MB, alloc=540.3MB, time=43.75 memory used=3700.9MB, alloc=540.3MB, time=45.11 memory used=3785.4MB, alloc=540.3MB, time=46.43 memory used=3878.5MB, alloc=540.3MB, time=47.41 memory used=3923.1MB, alloc=540.3MB, time=48.46 memory used=4076.3MB, alloc=540.3MB, time=49.68 memory used=4191.0MB, alloc=540.3MB, time=50.31 memory used=4281.7MB, alloc=540.3MB, time=51.35 memory used=4564.0MB, alloc=564.3MB, time=54.17 memory used=4756.3MB, alloc=564.3MB, time=55.86 memory used=4999.4MB, alloc=564.3MB, time=57.70 memory used=5257.2MB, alloc=564.3MB, time=59.90 memory used=5390.3MB, alloc=564.3MB, time=61.02 memory used=5554.4MB, alloc=564.3MB, time=62.96 memory used=5660.5MB, alloc=564.3MB, time=63.52 memory used=5799.5MB, alloc=564.3MB, time=64.89 memory used=5903.5MB, alloc=564.3MB, time=65.42 memory used=6037.3MB, alloc=564.3MB, time=66.31 memory used=6164.4MB, alloc=564.3MB, time=66.89 memory used=6296.7MB, alloc=564.3MB, time=68.41 memory used=6565.2MB, alloc=564.3MB, time=70.83 memory used=6836.4MB, alloc=588.3MB, time=73.32 memory used=7045.7MB, alloc=612.3MB, time=77.39 memory used=7233.0MB, alloc=636.3MB, time=80.83 memory used=7377.6MB, alloc=660.3MB, time=83.14 memory used=7569.4MB, alloc=684.3MB, time=86.72 memory used=7747.3MB, alloc=684.3MB, time=90.56 memory used=7881.8MB, alloc=684.3MB, time=92.91 memory used=8021.3MB, alloc=708.3MB, time=95.11 memory used=8177.9MB, alloc=708.3MB, time=98.45 memory used=8342.0MB, alloc=708.3MB, time=100.99 memory used=8499.7MB, alloc=732.3MB, time=103.29 memory used=8682.4MB, alloc=732.3MB, time=106.37 memory used=8799.0MB, alloc=732.3MB, time=109.28 memory used=8916.1MB, alloc=756.3MB, time=112.14 memory used=9035.5MB, alloc=756.3MB, time=114.41 memory used=9134.1MB, alloc=756.3MB, time=116.41 memory used=9563.8MB, alloc=780.3MB, time=124.17 memory used=9952.2MB, alloc=804.3MB, time=131.32 memory used=10329.2MB, alloc=828.3MB, time=137.19 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428240351 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 2 3 4 3 4 3 F := [8 x z + 19 x z - 13 z , -5 x y - 6 y z + z , 7 x y + y + 15 y ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 2 G := [11 x z - 20 x y z - 8 x z , -2 x y - 9 x y z + 19 x y z, 2 3 17 x y z + 11 x + 13 z] > Problem := [F,G]; Problem := [ 3 3 2 2 2 3 4 3 4 3 [8 x z + 19 x z - 13 z , -5 x y - 6 y z + z , 7 x y + y + 15 y ], [ 2 2 2 2 2 2 11 x z - 20 x y z - 8 x z , -2 x y - 9 x y z + 19 x y z, 2 3 17 x y z + 11 x + 13 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.20 memory used=26.5MB, alloc=32.3MB, time=0.55 memory used=46.8MB, alloc=32.3MB, time=0.87 memory used=66.0MB, alloc=56.3MB, time=1.19 memory used=106.7MB, alloc=60.3MB, time=1.84 memory used=145.9MB, alloc=60.3MB, time=2.45 memory used=184.3MB, alloc=84.3MB, time=3.10 memory used=228.5MB, alloc=84.3MB, time=3.83 memory used=289.8MB, alloc=116.3MB, time=4.81 memory used=356.6MB, alloc=372.3MB, time=5.87 memory used=443.0MB, alloc=372.3MB, time=7.30 memory used=527.0MB, alloc=396.3MB, time=8.67 memory used=638.3MB, alloc=420.3MB, time=10.35 memory used=774.4MB, alloc=420.3MB, time=12.43 memory used=911.1MB, alloc=444.3MB, time=14.59 memory used=1038.1MB, alloc=444.3MB, time=16.80 memory used=1169.9MB, alloc=468.3MB, time=18.98 memory used=1295.0MB, alloc=492.3MB, time=21.21 memory used=1412.7MB, alloc=492.3MB, time=23.10 memory used=1541.9MB, alloc=492.3MB, time=25.41 memory used=1654.5MB, alloc=492.3MB, time=27.47 memory used=1764.4MB, alloc=492.3MB, time=29.36 memory used=1862.4MB, alloc=516.3MB, time=31.35 memory used=1957.9MB, alloc=516.3MB, time=33.26 memory used=2044.4MB, alloc=516.3MB, time=35.21 memory used=2121.4MB, alloc=516.3MB, time=36.92 memory used=2199.0MB, alloc=516.3MB, time=38.47 memory used=2282.8MB, alloc=516.3MB, time=40.09 memory used=2367.0MB, alloc=516.3MB, time=41.78 memory used=2441.0MB, alloc=516.3MB, time=43.25 memory used=2507.8MB, alloc=516.3MB, time=44.63 memory used=2571.5MB, alloc=516.3MB, time=46.10 memory used=2632.2MB, alloc=540.3MB, time=47.22 memory used=2695.3MB, alloc=540.3MB, time=48.70 memory used=2754.2MB, alloc=540.3MB, time=50.01 memory used=2808.9MB, alloc=540.3MB, time=51.30 memory used=2856.8MB, alloc=540.3MB, time=52.52 memory used=2919.3MB, alloc=540.3MB, time=53.71 memory used=2965.4MB, alloc=540.3MB, time=54.77 memory used=3191.5MB, alloc=564.3MB, time=59.14 memory used=3368.8MB, alloc=588.3MB, time=62.41 memory used=3544.1MB, alloc=612.3MB, time=66.13 memory used=3723.3MB, alloc=636.3MB, time=69.13 memory used=3898.6MB, alloc=636.3MB, time=72.60 memory used=4064.8MB, alloc=660.3MB, time=75.53 memory used=4262.7MB, alloc=660.3MB, time=79.38 memory used=4460.2MB, alloc=684.3MB, time=84.65 memory used=4651.5MB, alloc=684.3MB, time=89.43 memory used=4785.0MB, alloc=684.3MB, time=92.48 memory used=4935.1MB, alloc=708.3MB, time=96.38 memory used=5065.9MB, alloc=708.3MB, time=99.38 memory used=5191.1MB, alloc=708.3MB, time=102.71 memory used=5317.3MB, alloc=708.3MB, time=105.44 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428240651 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; F := 4 2 3 4 2 3 3 4 [-3 x - 2 x z - 8 y z, 2 x y - 18 z + 11 z , -17 x z - 13 x y + 4 y ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 4 2 4 G := [17 x y - 10 y z - 15 y z , -20 x + 5 x y z - 14 x z , 3 z + 12 y z] > Problem := [F,G]; Problem := [ 4 2 3 4 2 3 3 4 [-3 x - 2 x z - 8 y z, 2 x y - 18 z + 11 z , -17 x z - 13 x y + 4 y ] 3 3 2 4 2 4 , [17 x y - 10 y z - 15 y z , -20 x + 5 x y z - 14 x z , 3 z + 12 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=25.0MB, alloc=32.3MB, time=0.47 memory used=42.8MB, alloc=56.3MB, time=0.75 memory used=82.5MB, alloc=56.3MB, time=3.90 memory used=114.4MB, alloc=56.3MB, time=12.90 memory used=159.1MB, alloc=68.2MB, time=18.70 memory used=181.3MB, alloc=68.2MB, time=18.77 memory used=206.4MB, alloc=68.2MB, time=18.83 memory used=237.9MB, alloc=68.2MB, time=18.99 memory used=273.1MB, alloc=68.2MB, time=22.17 memory used=304.7MB, alloc=68.2MB, time=31.29 memory used=348.2MB, alloc=68.2MB, time=36.94 memory used=370.5MB, alloc=68.2MB, time=37.00 memory used=394.7MB, alloc=68.2MB, time=37.06 memory used=436.5MB, alloc=68.2MB, time=37.53 memory used=479.5MB, alloc=68.2MB, time=42.64 memory used=507.8MB, alloc=68.2MB, time=43.07 memory used=534.7MB, alloc=68.2MB, time=43.17 memory used=581.9MB, alloc=68.2MB, time=43.71 memory used=626.4MB, alloc=68.2MB, time=44.65 memory used=664.5MB, alloc=68.2MB, time=45.48 memory used=707.6MB, alloc=68.2MB, time=46.00 memory used=751.1MB, alloc=92.2MB, time=46.55 memory used=796.3MB, alloc=92.2MB, time=46.96 memory used=853.5MB, alloc=92.2MB, time=51.52 memory used=899.1MB, alloc=92.2MB, time=55.93 memory used=933.1MB, alloc=92.2MB, time=56.04 memory used=967.5MB, alloc=92.2MB, time=56.14 memory used=996.8MB, alloc=92.2MB, time=56.22 memory used=1034.4MB, alloc=92.2MB, time=56.32 memory used=1087.9MB, alloc=92.2MB, time=57.00 memory used=1135.8MB, alloc=116.2MB, time=59.95 memory used=1335.6MB, alloc=124.2MB, time=61.54 memory used=1412.7MB, alloc=148.2MB, time=81.36 memory used=1478.4MB, alloc=148.2MB, time=144.09 memory used=1541.4MB, alloc=172.2MB, time=148.68 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428240951 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; F := 3 3 2 2 3 2 [6 x y - 6 x y z + 11 y , 2 x y z - 8 x y z + 3 z , 11 y z - 19 x - 12] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 2 2 3 2 2 4 G := [5 x + 16 z - 20, -8 y z + 14 x - x y, -20 x y z + 19 y - 3 z] > Problem := [F,G]; Problem := [ 3 3 2 2 3 2 [6 x y - 6 x y z + 11 y , 2 x y z - 8 x y z + 3 z , 11 y z - 19 x - 12] 4 3 2 2 3 2 2 4 , [5 x + 16 z - 20, -8 y z + 14 x - x y, -20 x y z + 19 y - 3 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.18 memory used=25.6MB, alloc=32.3MB, time=0.50 memory used=45.1MB, alloc=32.3MB, time=0.75 memory used=64.5MB, alloc=60.3MB, time=1.04 memory used=105.9MB, alloc=60.3MB, time=1.62 memory used=143.8MB, alloc=60.3MB, time=2.17 memory used=188.6MB, alloc=92.3MB, time=2.80 memory used=251.8MB, alloc=92.3MB, time=3.41 memory used=319.6MB, alloc=92.3MB, time=4.00 memory used=387.8MB, alloc=348.3MB, time=4.70 memory used=442.5MB, alloc=348.3MB, time=5.47 memory used=481.1MB, alloc=348.3MB, time=5.69 memory used=561.8MB, alloc=348.3MB, time=6.55 memory used=632.0MB, alloc=348.3MB, time=7.36 memory used=700.5MB, alloc=372.3MB, time=8.20 memory used=794.2MB, alloc=372.3MB, time=9.56 memory used=844.9MB, alloc=372.3MB, time=9.84 memory used=934.6MB, alloc=372.3MB, time=10.82 memory used=1019.3MB, alloc=396.3MB, time=11.79 memory used=1120.7MB, alloc=396.3MB, time=12.59 memory used=1197.8MB, alloc=396.3MB, time=13.03 memory used=1270.5MB, alloc=396.3MB, time=14.67 memory used=1380.8MB, alloc=396.3MB, time=15.66 memory used=1488.5MB, alloc=396.3MB, time=16.86 memory used=1602.1MB, alloc=396.3MB, time=21.21 memory used=1649.5MB, alloc=396.3MB, time=21.45 memory used=1699.5MB, alloc=396.3MB, time=21.68 memory used=1738.0MB, alloc=396.3MB, time=21.89 memory used=1781.6MB, alloc=420.3MB, time=22.13 memory used=1851.0MB, alloc=420.3MB, time=22.38 memory used=1932.6MB, alloc=420.3MB, time=22.64 memory used=1982.7MB, alloc=420.3MB, time=22.84 memory used=2032.2MB, alloc=420.3MB, time=23.08 memory used=2085.9MB, alloc=420.3MB, time=23.28 memory used=2143.8MB, alloc=420.3MB, time=23.50 memory used=2207.3MB, alloc=420.3MB, time=23.70 memory used=2275.1MB, alloc=420.3MB, time=23.91 memory used=2351.6MB, alloc=420.3MB, time=24.11 memory used=2510.7MB, alloc=420.3MB, time=25.79 memory used=2638.1MB, alloc=420.3MB, time=26.97 memory used=2716.3MB, alloc=420.3MB, time=27.37 memory used=2840.0MB, alloc=420.3MB, time=29.91 memory used=2896.2MB, alloc=420.3MB, time=30.17 memory used=2960.2MB, alloc=420.3MB, time=30.42 memory used=3020.3MB, alloc=420.3MB, time=30.64 memory used=3067.4MB, alloc=420.3MB, time=30.84 memory used=3139.5MB, alloc=420.3MB, time=31.25 memory used=3289.1MB, alloc=420.3MB, time=32.48 memory used=3390.0MB, alloc=420.3MB, time=33.97 memory used=3469.7MB, alloc=444.3MB, time=34.34 memory used=3538.2MB, alloc=444.3MB, time=34.66 memory used=3625.6MB, alloc=444.3MB, time=34.99 memory used=3693.6MB, alloc=444.3MB, time=35.29 memory used=3748.8MB, alloc=444.3MB, time=35.55 memory used=3809.3MB, alloc=444.3MB, time=35.83 memory used=3876.4MB, alloc=444.3MB, time=36.14 memory used=3949.9MB, alloc=444.3MB, time=36.43 memory used=4029.6MB, alloc=444.3MB, time=36.72 memory used=4115.4MB, alloc=444.3MB, time=37.01 memory used=4207.1MB, alloc=444.3MB, time=37.31 memory used=4281.7MB, alloc=444.3MB, time=37.57 memory used=4331.0MB, alloc=444.3MB, time=37.81 memory used=4382.1MB, alloc=444.3MB, time=38.04 memory used=4434.1MB, alloc=444.3MB, time=38.28 memory used=4488.5MB, alloc=444.3MB, time=38.50 memory used=4545.9MB, alloc=444.3MB, time=38.76 memory used=4604.6MB, alloc=444.3MB, time=38.99 memory used=4667.6MB, alloc=444.3MB, time=39.22 memory used=4731.7MB, alloc=444.3MB, time=39.45 memory used=4799.2MB, alloc=444.3MB, time=39.68 memory used=4869.2MB, alloc=444.3MB, time=39.93 memory used=4943.1MB, alloc=444.3MB, time=40.16 memory used=5020.8MB, alloc=444.3MB, time=40.39 memory used=5103.5MB, alloc=444.3MB, time=40.63 memory used=5210.5MB, alloc=444.3MB, time=41.62 memory used=5295.3MB, alloc=444.3MB, time=41.99 memory used=5370.9MB, alloc=444.3MB, time=42.32 memory used=5462.7MB, alloc=444.3MB, time=42.64 memory used=5516.5MB, alloc=444.3MB, time=42.91 memory used=5575.2MB, alloc=444.3MB, time=43.19 memory used=5640.5MB, alloc=444.3MB, time=43.47 memory used=5709.4MB, alloc=444.3MB, time=43.75 memory used=5784.1MB, alloc=444.3MB, time=44.03 memory used=5865.1MB, alloc=444.3MB, time=44.34 memory used=5954.8MB, alloc=444.3MB, time=44.65 memory used=6050.9MB, alloc=444.3MB, time=44.94 memory used=6105.1MB, alloc=444.3MB, time=45.18 memory used=6155.6MB, alloc=444.3MB, time=45.42 memory used=6206.8MB, alloc=444.3MB, time=45.65 memory used=6261.5MB, alloc=444.3MB, time=45.88 memory used=6317.1MB, alloc=444.3MB, time=46.12 memory used=6375.0MB, alloc=444.3MB, time=46.35 memory used=6435.6MB, alloc=444.3MB, time=46.62 memory used=6498.6MB, alloc=444.3MB, time=46.86 memory used=6564.6MB, alloc=444.3MB, time=47.12 memory used=6633.5MB, alloc=444.3MB, time=47.37 memory used=6705.8MB, alloc=444.3MB, time=47.62 memory used=6783.2MB, alloc=444.3MB, time=47.87 memory used=6864.2MB, alloc=444.3MB, time=48.11 memory used=6950.6MB, alloc=444.3MB, time=48.35 memory used=7072.4MB, alloc=444.3MB, time=56.71 memory used=7147.9MB, alloc=444.3MB, time=57.01 memory used=7216.0MB, alloc=444.3MB, time=57.29 memory used=7301.6MB, alloc=444.3MB, time=57.57 memory used=7372.8MB, alloc=444.3MB, time=57.83 memory used=7428.3MB, alloc=444.3MB, time=58.06 memory used=7490.2MB, alloc=444.3MB, time=58.30 memory used=7557.1MB, alloc=444.3MB, time=58.53 memory used=7630.7MB, alloc=444.3MB, time=58.77 memory used=7712.4MB, alloc=444.3MB, time=59.01 memory used=7801.9MB, alloc=444.3MB, time=59.26 memory used=8006.7MB, alloc=444.3MB, time=59.82 memory used=8118.2MB, alloc=444.3MB, time=60.30 memory used=8187.3MB, alloc=444.3MB, time=60.57 memory used=8282.5MB, alloc=444.3MB, time=61.66 memory used=8355.2MB, alloc=444.3MB, time=61.94 memory used=8424.7MB, alloc=444.3MB, time=62.18 memory used=8552.1MB, alloc=444.3MB, time=63.56 memory used=8683.7MB, alloc=444.3MB, time=64.63 memory used=8772.7MB, alloc=444.3MB, time=65.46 memory used=8861.4MB, alloc=444.3MB, time=65.90 memory used=8949.0MB, alloc=444.3MB, time=66.67 memory used=9021.2MB, alloc=444.3MB, time=66.97 memory used=9118.7MB, alloc=444.3MB, time=67.59 memory used=9191.0MB, alloc=444.3MB, time=67.91 memory used=9276.6MB, alloc=444.3MB, time=68.28 memory used=9350.3MB, alloc=444.3MB, time=68.60 memory used=9436.4MB, alloc=444.3MB, time=69.03 memory used=9510.0MB, alloc=444.3MB, time=69.33 memory used=9624.1MB, alloc=444.3MB, time=70.18 memory used=9751.3MB, alloc=444.3MB, time=71.17 memory used=9814.7MB, alloc=444.3MB, time=71.45 memory used=9908.3MB, alloc=444.3MB, time=72.46 memory used=9979.1MB, alloc=444.3MB, time=72.78 memory used=10040.3MB, alloc=444.3MB, time=73.05 memory used=10155.3MB, alloc=444.3MB, time=74.55 memory used=10231.5MB, alloc=444.3MB, time=74.90 memory used=10296.7MB, alloc=444.3MB, time=75.23 memory used=10351.6MB, alloc=444.3MB, time=75.56 memory used=10413.3MB, alloc=444.3MB, time=75.86 memory used=10482.5MB, alloc=444.3MB, time=76.17 memory used=10559.1MB, alloc=444.3MB, time=76.49 memory used=10643.0MB, alloc=444.3MB, time=76.85 memory used=10709.8MB, alloc=468.3MB, time=77.17 memory used=10768.6MB, alloc=468.3MB, time=77.44 memory used=10831.1MB, alloc=468.3MB, time=77.72 memory used=10897.9MB, alloc=468.3MB, time=78.01 memory used=10968.9MB, alloc=468.3MB, time=78.31 memory used=11043.8MB, alloc=468.3MB, time=78.58 memory used=11122.2MB, alloc=468.3MB, time=78.87 memory used=11207.0MB, alloc=468.3MB, time=79.17 memory used=11297.3MB, alloc=468.3MB, time=79.47 memory used=11395.1MB, alloc=468.3MB, time=79.78 memory used=11498.5MB, alloc=468.3MB, time=80.08 memory used=11745.5MB, alloc=468.3MB, time=81.47 memory used=11836.0MB, alloc=468.3MB, time=81.88 memory used=11926.7MB, alloc=468.3MB, time=82.26 memory used=11996.2MB, alloc=468.3MB, time=82.65 memory used=12077.8MB, alloc=468.3MB, time=83.06 memory used=12169.8MB, alloc=468.3MB, time=83.40 memory used=12275.1MB, alloc=468.3MB, time=83.76 memory used=12357.8MB, alloc=468.3MB, time=84.09 memory used=12416.9MB, alloc=468.3MB, time=84.37 memory used=12479.5MB, alloc=468.3MB, time=84.66 memory used=12546.5MB, alloc=468.3MB, time=84.95 memory used=12617.5MB, alloc=468.3MB, time=85.25 memory used=12692.3MB, alloc=468.3MB, time=85.55 memory used=12771.4MB, alloc=468.3MB, time=85.85 memory used=12855.8MB, alloc=468.3MB, time=86.19 memory used=12945.9MB, alloc=468.3MB, time=86.50 memory used=13042.6MB, alloc=468.3MB, time=86.80 memory used=13148.1MB, alloc=468.3MB, time=87.12 memory used=13411.9MB, alloc=468.3MB, time=97.72 memory used=13500.0MB, alloc=468.3MB, time=98.08 memory used=13593.1MB, alloc=468.3MB, time=98.42 memory used=13672.0MB, alloc=468.3MB, time=98.73 memory used=13742.8MB, alloc=468.3MB, time=99.01 memory used=13825.1MB, alloc=468.3MB, time=99.30 memory used=13918.1MB, alloc=468.3MB, time=99.59 memory used=14024.1MB, alloc=468.3MB, time=99.91 memory used=14197.3MB, alloc=468.3MB, time=100.32 memory used=14360.8MB, alloc=468.3MB, time=100.74 memory used=14481.2MB, alloc=468.3MB, time=101.24 memory used=14595.4MB, alloc=468.3MB, time=102.64 memory used=14686.7MB, alloc=468.3MB, time=103.01 memory used=14762.8MB, alloc=468.3MB, time=103.31 memory used=14882.2MB, alloc=468.3MB, time=107.19 memory used=15018.4MB, alloc=468.3MB, time=111.09 memory used=15094.2MB, alloc=468.3MB, time=111.42 memory used=15197.8MB, alloc=468.3MB, time=111.79 memory used=15262.7MB, alloc=468.3MB, time=112.10 memory used=15331.7MB, alloc=468.3MB, time=112.43 memory used=15408.7MB, alloc=468.3MB, time=112.73 memory used=15495.6MB, alloc=468.3MB, time=113.06 memory used=15590.3MB, alloc=468.3MB, time=113.40 memory used=15695.9MB, alloc=468.3MB, time=113.72 memory used=15877.1MB, alloc=468.3MB, time=114.17 memory used=16024.1MB, alloc=468.3MB, time=114.58 memory used=16193.1MB, alloc=468.3MB, time=115.01 memory used=16476.4MB, alloc=468.3MB, time=116.63 memory used=16688.9MB, alloc=468.3MB, time=118.64 memory used=16880.9MB, alloc=468.3MB, time=121.51 memory used=17075.4MB, alloc=468.3MB, time=125.83 memory used=17272.2MB, alloc=468.3MB, time=131.09 memory used=17390.6MB, alloc=468.3MB, time=134.29 memory used=17478.9MB, alloc=468.3MB, time=135.39 memory used=17601.2MB, alloc=468.3MB, time=136.42 memory used=17691.9MB, alloc=468.3MB, time=136.81 memory used=17761.2MB, alloc=468.3MB, time=137.17 memory used=17863.3MB, alloc=468.3MB, time=137.72 memory used=17946.8MB, alloc=468.3MB, time=138.09 memory used=18023.3MB, alloc=468.3MB, time=138.43 memory used=18123.9MB, alloc=468.3MB, time=139.04 memory used=18217.3MB, alloc=468.3MB, time=139.50 memory used=18341.4MB, alloc=468.3MB, time=141.24 memory used=18422.5MB, alloc=468.3MB, time=141.66 memory used=18500.7MB, alloc=468.3MB, time=142.03 memory used=18596.9MB, alloc=468.3MB, time=142.41 memory used=18671.3MB, alloc=468.3MB, time=142.81 memory used=18730.9MB, alloc=468.3MB, time=143.16 memory used=18797.3MB, alloc=468.3MB, time=143.53 memory used=18867.7MB, alloc=468.3MB, time=143.88 memory used=18945.7MB, alloc=468.3MB, time=144.23 memory used=19031.0MB, alloc=468.3MB, time=144.58 memory used=19122.2MB, alloc=468.3MB, time=144.93 memory used=19223.9MB, alloc=468.3MB, time=145.29 memory used=19289.0MB, alloc=468.3MB, time=145.59 memory used=19346.0MB, alloc=468.3MB, time=145.88 memory used=19408.0MB, alloc=468.3MB, time=146.18 memory used=19493.8MB, alloc=468.3MB, time=147.42 memory used=19595.7MB, alloc=468.3MB, time=147.88 memory used=19670.0MB, alloc=468.3MB, time=148.28 memory used=19761.0MB, alloc=468.3MB, time=148.69 memory used=19848.7MB, alloc=468.3MB, time=149.10 memory used=19907.5MB, alloc=468.3MB, time=149.44 memory used=19970.8MB, alloc=468.3MB, time=149.79 memory used=20040.7MB, alloc=468.3MB, time=150.15 memory used=20116.3MB, alloc=468.3MB, time=150.53 memory used=20199.4MB, alloc=468.3MB, time=150.91 memory used=20288.8MB, alloc=468.3MB, time=151.27 memory used=20387.3MB, alloc=468.3MB, time=151.63 memory used=20466.8MB, alloc=468.3MB, time=151.96 memory used=20523.1MB, alloc=468.3MB, time=152.28 memory used=20584.2MB, alloc=468.3MB, time=152.56 memory used=20651.1MB, alloc=468.3MB, time=152.87 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428241251 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; F := [ 2 2 3 2 2 2 2 3 x y z - 20 y z, x y z - 13 x y - 16 x z, -10 y z + 11 x z + 18 x y ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 2 3 4 2 G := [5 x y - 18 z + 10, 4 x y + 20 x z - 14 y , 9 x y - 10 y - 10 x z] > Problem := [F,G]; Problem := [[ 2 2 3 2 2 2 2 3 x y z - 20 y z, x y z - 13 x y - 16 x z, -10 y z + 11 x z + 18 x y ], 2 2 2 2 2 2 3 4 2 [5 x y - 18 z + 10, 4 x y + 20 x z - 14 y , 9 x y - 10 y - 10 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.18 memory used=26.6MB, alloc=32.3MB, time=0.50 memory used=46.1MB, alloc=56.3MB, time=0.80 memory used=86.3MB, alloc=60.3MB, time=1.37 memory used=125.6MB, alloc=60.3MB, time=1.96 memory used=165.4MB, alloc=84.3MB, time=2.54 memory used=228.6MB, alloc=94.9MB, time=4.22 memory used=283.7MB, alloc=94.9MB, time=4.89 memory used=337.8MB, alloc=94.9MB, time=5.30 memory used=410.2MB, alloc=94.9MB, time=11.68 memory used=457.9MB, alloc=94.9MB, time=11.94 memory used=493.9MB, alloc=94.9MB, time=12.06 memory used=528.3MB, alloc=94.9MB, time=12.16 memory used=555.2MB, alloc=94.9MB, time=12.26 memory used=585.4MB, alloc=94.9MB, time=12.36 memory used=619.5MB, alloc=94.9MB, time=12.46 memory used=657.4MB, alloc=94.9MB, time=12.56 memory used=698.8MB, alloc=94.9MB, time=12.67 memory used=731.7MB, alloc=94.9MB, time=12.76 memory used=754.7MB, alloc=94.9MB, time=12.84 memory used=778.9MB, alloc=94.9MB, time=12.93 memory used=805.0MB, alloc=94.9MB, time=13.01 memory used=832.0MB, alloc=94.9MB, time=13.08 memory used=860.7MB, alloc=94.9MB, time=13.16 memory used=891.6MB, alloc=94.9MB, time=13.25 memory used=924.3MB, alloc=94.9MB, time=13.33 memory used=958.4MB, alloc=94.9MB, time=13.42 memory used=994.2MB, alloc=94.9MB, time=13.50 memory used=1034.3MB, alloc=94.9MB, time=13.59 memory used=1112.7MB, alloc=94.9MB, time=14.45 memory used=1174.9MB, alloc=94.9MB, time=21.73 memory used=1217.0MB, alloc=94.9MB, time=32.51 memory used=1255.6MB, alloc=94.9MB, time=32.67 memory used=1289.0MB, alloc=94.9MB, time=32.78 memory used=1323.0MB, alloc=94.9MB, time=32.88 memory used=1347.1MB, alloc=94.9MB, time=32.98 memory used=1373.8MB, alloc=94.9MB, time=33.09 memory used=1403.7MB, alloc=94.9MB, time=33.20 memory used=1436.6MB, alloc=94.9MB, time=33.29 memory used=1473.0MB, alloc=94.9MB, time=33.40 memory used=1513.2MB, alloc=94.9MB, time=33.52 memory used=1535.7MB, alloc=94.9MB, time=33.59 memory used=1558.2MB, alloc=94.9MB, time=33.68 memory used=1582.6MB, alloc=94.9MB, time=33.79 memory used=1609.0MB, alloc=94.9MB, time=33.88 memory used=1643.0MB, alloc=94.9MB, time=34.05 memory used=1681.1MB, alloc=94.9MB, time=34.44 memory used=1741.4MB, alloc=118.9MB, time=35.32 memory used=1814.7MB, alloc=118.9MB, time=36.42 memory used=1885.3MB, alloc=374.9MB, time=37.45 memory used=1972.5MB, alloc=398.9MB, time=38.59 memory used=2083.0MB, alloc=422.9MB, time=40.14 memory used=2213.7MB, alloc=446.9MB, time=42.04 memory used=2350.0MB, alloc=446.9MB, time=43.87 memory used=2442.5MB, alloc=446.9MB, time=44.81 memory used=2541.5MB, alloc=446.9MB, time=46.64 memory used=2696.1MB, alloc=446.9MB, time=49.22 memory used=2832.0MB, alloc=446.9MB, time=51.56 memory used=2968.0MB, alloc=470.9MB, time=53.60 memory used=3119.1MB, alloc=470.9MB, time=55.32 memory used=3238.1MB, alloc=470.9MB, time=58.28 memory used=3308.5MB, alloc=470.9MB, time=58.62 memory used=3397.8MB, alloc=470.9MB, time=58.97 memory used=3456.8MB, alloc=470.9MB, time=59.26 memory used=3532.8MB, alloc=470.9MB, time=59.56 memory used=3721.7MB, alloc=470.9MB, time=63.53 memory used=3809.1MB, alloc=470.9MB, time=63.90 memory used=3874.3MB, alloc=470.9MB, time=64.18 memory used=3949.6MB, alloc=470.9MB, time=64.48 memory used=4041.3MB, alloc=470.9MB, time=64.79 memory used=4106.4MB, alloc=470.9MB, time=65.06 memory used=4164.0MB, alloc=470.9MB, time=65.32 memory used=4226.9MB, alloc=470.9MB, time=65.60 memory used=4295.5MB, alloc=470.9MB, time=65.86 memory used=4371.3MB, alloc=470.9MB, time=66.13 memory used=4455.0MB, alloc=470.9MB, time=66.42 memory used=4547.7MB, alloc=470.9MB, time=66.70 memory used=4729.9MB, alloc=470.9MB, time=68.12 memory used=4873.8MB, alloc=494.9MB, time=69.65 memory used=4983.1MB, alloc=494.9MB, time=70.44 memory used=5091.0MB, alloc=494.9MB, time=74.05 memory used=5213.8MB, alloc=494.9MB, time=93.50 memory used=5312.5MB, alloc=494.9MB, time=93.93 memory used=5395.9MB, alloc=494.9MB, time=94.30 memory used=5469.7MB, alloc=494.9MB, time=94.67 memory used=5550.5MB, alloc=494.9MB, time=95.03 memory used=5642.3MB, alloc=494.9MB, time=95.38 memory used=5744.8MB, alloc=494.9MB, time=95.75 memory used=5855.4MB, alloc=494.9MB, time=96.14 memory used=5917.9MB, alloc=494.9MB, time=96.44 memory used=5981.4MB, alloc=494.9MB, time=96.74 memory used=6049.6MB, alloc=494.9MB, time=97.05 memory used=6121.3MB, alloc=494.9MB, time=97.35 memory used=6197.1MB, alloc=494.9MB, time=97.66 memory used=6277.2MB, alloc=494.9MB, time=97.97 memory used=6363.5MB, alloc=494.9MB, time=98.28 memory used=6456.0MB, alloc=494.9MB, time=98.59 memory used=6556.9MB, alloc=494.9MB, time=98.91 memory used=6675.9MB, alloc=494.9MB, time=108.47 memory used=6770.4MB, alloc=494.9MB, time=108.85 memory used=6846.4MB, alloc=494.9MB, time=109.22 memory used=6940.5MB, alloc=494.9MB, time=109.60 memory used=7041.6MB, alloc=494.9MB, time=109.95 memory used=7108.6MB, alloc=494.9MB, time=110.26 memory used=7210.1MB, alloc=494.9MB, time=111.00 memory used=7336.3MB, alloc=494.9MB, time=112.26 memory used=7425.5MB, alloc=494.9MB, time=112.68 memory used=7519.7MB, alloc=494.9MB, time=113.09 memory used=7620.5MB, alloc=494.9MB, time=113.48 memory used=7689.3MB, alloc=494.9MB, time=113.83 memory used=7770.9MB, alloc=494.9MB, time=114.16 memory used=7900.5MB, alloc=494.9MB, time=115.38 memory used=7980.9MB, alloc=494.9MB, time=115.79 memory used=8082.5MB, alloc=494.9MB, time=116.19 memory used=8170.9MB, alloc=494.9MB, time=116.55 memory used=8244.0MB, alloc=494.9MB, time=116.90 memory used=8354.0MB, alloc=494.9MB, time=126.18 memory used=8462.5MB, alloc=494.9MB, time=141.39 memory used=8556.8MB, alloc=494.9MB, time=141.79 memory used=8631.2MB, alloc=494.9MB, time=142.14 memory used=8722.4MB, alloc=494.9MB, time=142.51 memory used=8827.5MB, alloc=494.9MB, time=142.87 memory used=8892.2MB, alloc=494.9MB, time=143.16 memory used=8993.4MB, alloc=494.9MB, time=143.67 memory used=9088.8MB, alloc=494.9MB, time=144.60 memory used=9202.5MB, alloc=494.9MB, time=145.16 memory used=9331.5MB, alloc=494.9MB, time=146.65 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428241551 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; F := [ 2 3 2 2 2 2 2 3 10 x y z + 7 x - 15 x y, -3 x z + x y + 4 z, -2 x z - 11 y z - 5 z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 G := [-20 x y z - 9 y z + 4 x, 18 x y z - 4 x z - 14 x , -5 y z + 3] > Problem := [F,G]; Problem := [[ 2 3 2 2 2 2 2 3 10 x y z + 7 x - 15 x y, -3 x z + x y + 4 z, -2 x z - 11 y z - 5 z ] 2 2 3 2 2 , [-20 x y z - 9 y z + 4 x, 18 x y z - 4 x z - 14 x , -5 y z + 3]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.3MB, alloc=32.3MB, time=0.50 memory used=46.5MB, alloc=32.3MB, time=0.79 memory used=65.6MB, alloc=56.3MB, time=1.08 memory used=106.5MB, alloc=60.3MB, time=1.68 memory used=146.9MB, alloc=84.3MB, time=2.27 memory used=210.9MB, alloc=92.3MB, time=3.20 memory used=272.0MB, alloc=116.3MB, time=4.09 memory used=342.0MB, alloc=116.3MB, time=5.14 memory used=407.1MB, alloc=396.3MB, time=6.15 memory used=518.9MB, alloc=396.3MB, time=7.74 memory used=626.4MB, alloc=420.3MB, time=9.37 memory used=742.8MB, alloc=444.3MB, time=11.11 memory used=851.3MB, alloc=444.3MB, time=12.75 memory used=962.2MB, alloc=468.3MB, time=14.44 memory used=1054.8MB, alloc=468.3MB, time=15.98 memory used=1148.0MB, alloc=468.3MB, time=17.54 memory used=1239.2MB, alloc=468.3MB, time=19.07 memory used=1320.4MB, alloc=468.3MB, time=20.42 memory used=1399.6MB, alloc=468.3MB, time=21.89 memory used=1473.5MB, alloc=492.3MB, time=23.34 memory used=1533.0MB, alloc=492.3MB, time=24.56 memory used=1587.9MB, alloc=492.3MB, time=25.66 memory used=1645.8MB, alloc=492.3MB, time=26.91 memory used=1690.4MB, alloc=492.3MB, time=27.87 memory used=1743.6MB, alloc=492.3MB, time=29.11 memory used=1928.7MB, alloc=516.3MB, time=32.02 memory used=2131.1MB, alloc=540.3MB, time=34.69 memory used=2315.6MB, alloc=564.3MB, time=37.71 memory used=2486.7MB, alloc=564.3MB, time=40.84 memory used=2631.0MB, alloc=588.3MB, time=43.11 memory used=2791.1MB, alloc=588.3MB, time=45.67 memory used=2944.9MB, alloc=612.3MB, time=48.71 memory used=3076.6MB, alloc=612.3MB, time=51.22 memory used=3198.8MB, alloc=612.3MB, time=53.60 memory used=3321.4MB, alloc=612.3MB, time=56.46 memory used=3431.7MB, alloc=636.3MB, time=58.83 memory used=3539.7MB, alloc=636.3MB, time=60.89 memory used=3615.1MB, alloc=636.3MB, time=62.83 memory used=3712.2MB, alloc=636.3MB, time=65.52 memory used=4018.2MB, alloc=660.3MB, time=71.19 memory used=4332.0MB, alloc=684.3MB, time=77.36 memory used=4665.9MB, alloc=708.3MB, time=83.07 memory used=5011.1MB, alloc=732.3MB, time=90.58 memory used=5357.6MB, alloc=756.3MB, time=96.65 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428241851 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 2 2 2 4 F := [12 x z - 14 x z, 12 x y + 14 x y z + 20 y z , 15 x y z + 6 y ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 3 2 2 G := [-5 x y z + 8 x z - 12 y z , 15 x y z - 16 y z - 9 x z, 3 2 -2 x z - 8 y z + 3 z] > Problem := [F,G]; Problem := [ 2 2 2 2 2 2 2 2 4 [12 x z - 14 x z, 12 x y + 14 x y z + 20 y z , 15 x y z + 6 y ], [ 2 3 3 2 2 -5 x y z + 8 x z - 12 y z , 15 x y z - 16 y z - 9 x z, 3 2 -2 x z - 8 y z + 3 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.17 memory used=26.5MB, alloc=32.3MB, time=0.50 memory used=47.7MB, alloc=32.3MB, time=0.81 memory used=66.7MB, alloc=56.3MB, time=1.10 memory used=106.5MB, alloc=60.3MB, time=1.71 memory used=146.1MB, alloc=84.3MB, time=2.31 memory used=208.2MB, alloc=92.3MB, time=3.26 memory used=268.7MB, alloc=116.3MB, time=4.21 memory used=350.1MB, alloc=116.3MB, time=5.48 memory used=423.8MB, alloc=396.3MB, time=6.66 memory used=525.8MB, alloc=420.3MB, time=8.36 memory used=654.5MB, alloc=444.3MB, time=10.48 memory used=800.3MB, alloc=468.3MB, time=13.03 memory used=933.7MB, alloc=468.3MB, time=15.18 memory used=1039.0MB, alloc=492.3MB, time=17.00 memory used=1159.8MB, alloc=492.3MB, time=19.20 memory used=1273.4MB, alloc=492.3MB, time=21.38 memory used=1370.9MB, alloc=492.3MB, time=23.29 memory used=1477.8MB, alloc=516.3MB, time=25.33 memory used=1572.4MB, alloc=516.3MB, time=27.23 memory used=1657.4MB, alloc=516.3MB, time=28.99 memory used=1718.4MB, alloc=516.3MB, time=30.44 memory used=1758.9MB, alloc=516.3MB, time=31.37 memory used=1808.5MB, alloc=516.3MB, time=32.71 memory used=1868.4MB, alloc=516.3MB, time=34.06 memory used=1939.9MB, alloc=516.3MB, time=35.87 memory used=1988.5MB, alloc=516.3MB, time=37.00 memory used=2040.6MB, alloc=516.3MB, time=38.62 memory used=2246.4MB, alloc=540.3MB, time=43.06 memory used=2465.4MB, alloc=564.3MB, time=47.76 memory used=2667.3MB, alloc=588.3MB, time=52.20 memory used=2841.9MB, alloc=612.3MB, time=56.14 memory used=3025.8MB, alloc=636.3MB, time=60.55 memory used=3186.5MB, alloc=660.3MB, time=64.54 memory used=3357.5MB, alloc=684.3MB, time=68.84 memory used=3515.3MB, alloc=684.3MB, time=72.90 memory used=3658.7MB, alloc=684.3MB, time=76.55 memory used=3775.6MB, alloc=684.3MB, time=79.66 memory used=3883.9MB, alloc=684.3MB, time=83.16 memory used=4228.6MB, alloc=708.3MB, time=91.91 memory used=4592.7MB, alloc=732.3MB, time=101.07 memory used=4974.7MB, alloc=756.3MB, time=110.52 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428242151 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 4 3 3 4 3 F := [x y - 8 x y + 10 z , -7 x + 6 x y - 16 z , -6 x + 19 y z - 20] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 3 G := [4 x + 5 y z - 20 y, -11 y z + 8 y z - 20 y, x z + 17 y + 12 x y] > Problem := [F,G]; Problem := [ 2 2 2 3 4 3 3 4 3 [x y - 8 x y + 10 z , -7 x + 6 x y - 16 z , -6 x + 19 y z - 20], 3 2 2 2 3 [4 x + 5 y z - 20 y, -11 y z + 8 y z - 20 y, x z + 17 y + 12 x y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.18 memory used=24.5MB, alloc=32.3MB, time=0.46 memory used=44.3MB, alloc=56.3MB, time=0.74 memory used=88.0MB, alloc=60.3MB, time=1.27 memory used=135.8MB, alloc=68.3MB, time=1.72 memory used=176.8MB, alloc=68.6MB, time=2.01 memory used=221.2MB, alloc=68.6MB, time=2.55 memory used=264.3MB, alloc=68.6MB, time=2.96 memory used=315.2MB, alloc=68.6MB, time=3.56 memory used=356.6MB, alloc=68.6MB, time=4.09 memory used=399.6MB, alloc=68.6MB, time=4.56 memory used=446.3MB, alloc=68.6MB, time=5.17 memory used=488.5MB, alloc=92.6MB, time=5.79 memory used=543.8MB, alloc=92.6MB, time=6.08 memory used=584.6MB, alloc=92.6MB, time=6.33 memory used=624.0MB, alloc=92.6MB, time=6.47 memory used=671.1MB, alloc=92.6MB, time=7.37 memory used=704.0MB, alloc=92.6MB, time=7.48 memory used=761.1MB, alloc=92.6MB, time=8.51 memory used=810.9MB, alloc=92.6MB, time=8.74 memory used=854.2MB, alloc=92.6MB, time=8.92 memory used=893.5MB, alloc=92.6MB, time=9.06 memory used=965.3MB, alloc=92.6MB, time=16.06 memory used=1003.0MB, alloc=92.6MB, time=16.19 memory used=1040.8MB, alloc=92.6MB, time=16.30 memory used=1067.7MB, alloc=92.6MB, time=16.39 memory used=1101.0MB, alloc=92.6MB, time=16.49 memory used=1167.8MB, alloc=93.8MB, time=17.20 memory used=1209.6MB, alloc=93.8MB, time=17.40 memory used=1246.4MB, alloc=93.8MB, time=17.53 memory used=1296.7MB, alloc=93.8MB, time=19.33 memory used=1352.8MB, alloc=93.8MB, time=19.75 memory used=1437.2MB, alloc=93.8MB, time=21.11 memory used=1507.3MB, alloc=349.8MB, time=22.05 memory used=1567.3MB, alloc=373.8MB, time=22.97 memory used=1662.3MB, alloc=373.8MB, time=24.41 memory used=1742.0MB, alloc=373.8MB, time=26.00 memory used=1811.3MB, alloc=373.8MB, time=26.37 memory used=1886.5MB, alloc=373.8MB, time=26.82 memory used=1965.9MB, alloc=373.8MB, time=30.04 memory used=2050.2MB, alloc=373.8MB, time=39.31 memory used=2111.4MB, alloc=373.8MB, time=39.54 memory used=2152.5MB, alloc=373.8MB, time=39.70 memory used=2189.2MB, alloc=373.8MB, time=39.84 memory used=2292.0MB, alloc=397.8MB, time=41.80 memory used=2396.0MB, alloc=397.8MB, time=43.29 memory used=2451.9MB, alloc=397.8MB, time=43.49 memory used=2516.2MB, alloc=397.8MB, time=43.68 memory used=2561.0MB, alloc=397.8MB, time=43.86 memory used=2612.4MB, alloc=397.8MB, time=44.03 memory used=2670.9MB, alloc=397.8MB, time=44.21 memory used=2737.5MB, alloc=397.8MB, time=44.40 memory used=2807.8MB, alloc=397.8MB, time=44.57 memory used=2847.8MB, alloc=397.8MB, time=44.70 memory used=2890.6MB, alloc=397.8MB, time=44.84 memory used=2937.0MB, alloc=397.8MB, time=44.97 memory used=2986.8MB, alloc=397.8MB, time=45.12 memory used=3059.9MB, alloc=397.8MB, time=45.72 memory used=3117.9MB, alloc=397.8MB, time=45.94 memory used=3179.0MB, alloc=397.8MB, time=46.14 memory used=3224.5MB, alloc=397.8MB, time=46.32 memory used=3277.4MB, alloc=397.8MB, time=46.50 memory used=3336.7MB, alloc=397.8MB, time=46.70 memory used=3404.2MB, alloc=397.8MB, time=46.89 memory used=3470.5MB, alloc=397.8MB, time=47.06 memory used=3511.2MB, alloc=397.8MB, time=47.21 memory used=3554.1MB, alloc=397.8MB, time=47.36 memory used=3600.7MB, alloc=397.8MB, time=47.50 memory used=3651.0MB, alloc=397.8MB, time=47.65 memory used=3736.4MB, alloc=397.8MB, time=56.69 memory used=3794.0MB, alloc=397.8MB, time=56.89 memory used=3850.6MB, alloc=397.8MB, time=57.07 memory used=3920.1MB, alloc=397.8MB, time=57.26 memory used=3962.4MB, alloc=397.8MB, time=57.41 memory used=4009.8MB, alloc=397.8MB, time=57.56 memory used=4061.8MB, alloc=397.8MB, time=57.73 memory used=4119.9MB, alloc=397.8MB, time=57.88 memory used=4184.2MB, alloc=397.8MB, time=58.05 memory used=4255.1MB, alloc=397.8MB, time=58.22 memory used=4459.2MB, alloc=397.8MB, time=61.06 memory used=4518.4MB, alloc=397.8MB, time=61.27 memory used=4571.8MB, alloc=397.8MB, time=61.47 memory used=4631.9MB, alloc=397.8MB, time=61.64 memory used=4678.4MB, alloc=397.8MB, time=61.78 memory used=4758.5MB, alloc=397.8MB, time=62.20 memory used=4813.2MB, alloc=397.8MB, time=62.41 memory used=4879.6MB, alloc=397.8MB, time=62.61 memory used=4922.9MB, alloc=397.8MB, time=62.78 memory used=4972.8MB, alloc=397.8MB, time=62.96 memory used=5050.2MB, alloc=397.8MB, time=63.47 memory used=5112.1MB, alloc=397.8MB, time=63.71 memory used=5171.0MB, alloc=397.8MB, time=63.92 memory used=5231.0MB, alloc=397.8MB, time=64.12 memory used=5275.1MB, alloc=397.8MB, time=64.30 memory used=5327.2MB, alloc=397.8MB, time=64.47 memory used=5426.3MB, alloc=397.8MB, time=83.14 memory used=5520.1MB, alloc=397.8MB, time=86.09 memory used=5582.6MB, alloc=397.8MB, time=86.30 memory used=5628.5MB, alloc=397.8MB, time=86.49 memory used=5680.0MB, alloc=397.8MB, time=86.68 memory used=5739.7MB, alloc=397.8MB, time=86.86 memory used=5809.0MB, alloc=397.8MB, time=87.06 memory used=5854.5MB, alloc=397.8MB, time=87.22 memory used=5895.0MB, alloc=397.8MB, time=87.37 memory used=5938.5MB, alloc=397.8MB, time=87.54 memory used=5985.1MB, alloc=397.8MB, time=87.71 memory used=6035.2MB, alloc=397.8MB, time=87.86 memory used=6090.0MB, alloc=397.8MB, time=88.03 memory used=6148.4MB, alloc=397.8MB, time=88.21 memory used=6211.5MB, alloc=397.8MB, time=88.38 memory used=6294.2MB, alloc=397.8MB, time=88.56 memory used=6427.3MB, alloc=397.8MB, time=89.54 memory used=6530.0MB, alloc=397.8MB, time=90.33 memory used=6603.8MB, alloc=397.8MB, time=90.66 memory used=6662.2MB, alloc=397.8MB, time=90.86 memory used=6769.1MB, alloc=397.8MB, time=93.53 memory used=6821.6MB, alloc=397.8MB, time=93.72 memory used=6938.3MB, alloc=397.8MB, time=95.22 memory used=7063.3MB, alloc=397.8MB, time=96.95 memory used=7131.6MB, alloc=397.8MB, time=97.36 memory used=7186.7MB, alloc=397.8MB, time=97.61 memory used=7243.6MB, alloc=397.8MB, time=97.87 memory used=7321.1MB, alloc=397.8MB, time=99.49 memory used=7367.2MB, alloc=397.8MB, time=99.72 memory used=7410.6MB, alloc=397.8MB, time=99.94 memory used=7460.3MB, alloc=421.8MB, time=100.17 memory used=7537.8MB, alloc=421.8MB, time=100.43 memory used=7606.6MB, alloc=421.8MB, time=100.68 memory used=7656.4MB, alloc=421.8MB, time=100.90 memory used=7704.5MB, alloc=421.8MB, time=101.12 memory used=7757.1MB, alloc=421.8MB, time=101.34 memory used=7811.8MB, alloc=421.8MB, time=101.56 memory used=7868.9MB, alloc=421.8MB, time=101.77 memory used=7931.4MB, alloc=421.8MB, time=102.00 memory used=7996.3MB, alloc=421.8MB, time=102.22 memory used=8063.6MB, alloc=421.8MB, time=102.44 memory used=8136.3MB, alloc=421.8MB, time=102.67 memory used=8211.3MB, alloc=421.8MB, time=102.90 memory used=8293.1MB, alloc=421.8MB, time=103.13 memory used=8370.4MB, alloc=421.8MB, time=103.36 memory used=8418.1MB, alloc=445.8MB, time=103.56 memory used=8470.2MB, alloc=445.8MB, time=103.75 memory used=8524.8MB, alloc=445.8MB, time=103.96 memory used=8580.9MB, alloc=445.8MB, time=104.16 memory used=8638.5MB, alloc=445.8MB, time=104.36 memory used=8699.4MB, alloc=445.8MB, time=104.56 memory used=8761.5MB, alloc=445.8MB, time=104.76 memory used=8825.2MB, alloc=445.8MB, time=104.96 memory used=8891.2MB, alloc=445.8MB, time=105.16 memory used=8959.6MB, alloc=445.8MB, time=105.36 memory used=9031.0MB, alloc=445.8MB, time=105.57 memory used=9104.1MB, alloc=445.8MB, time=105.77 memory used=9180.4MB, alloc=445.8MB, time=105.97 memory used=9259.9MB, alloc=445.8MB, time=106.17 memory used=9344.3MB, alloc=445.8MB, time=106.38 memory used=9431.8MB, alloc=445.8MB, time=106.59 memory used=9521.6MB, alloc=445.8MB, time=106.80 memory used=9614.7MB, alloc=445.8MB, time=107.03 memory used=9713.3MB, alloc=445.8MB, time=107.25 memory used=9817.3MB, alloc=445.8MB, time=107.47 memory used=9940.5MB, alloc=445.8MB, time=109.16 memory used=10037.3MB, alloc=445.8MB, time=109.53 memory used=10118.1MB, alloc=445.8MB, time=109.83 memory used=10217.8MB, alloc=445.8MB, time=110.14 memory used=10293.8MB, alloc=445.8MB, time=110.40 memory used=10353.8MB, alloc=445.8MB, time=110.64 memory used=10419.1MB, alloc=445.8MB, time=110.89 memory used=10488.9MB, alloc=445.8MB, time=111.13 memory used=10564.5MB, alloc=445.8MB, time=111.39 memory used=10645.3MB, alloc=445.8MB, time=111.64 memory used=10731.8MB, alloc=445.8MB, time=111.90 memory used=10827.3MB, alloc=445.8MB, time=112.16 memory used=10926.3MB, alloc=445.8MB, time=112.42 memory used=11027.6MB, alloc=445.8MB, time=112.70 memory used=11088.5MB, alloc=445.8MB, time=112.90 memory used=11144.3MB, alloc=445.8MB, time=113.09 memory used=11200.2MB, alloc=445.8MB, time=113.27 memory used=11256.4MB, alloc=445.8MB, time=113.47 memory used=11314.3MB, alloc=445.8MB, time=113.67 memory used=11374.9MB, alloc=445.8MB, time=113.88 memory used=11437.1MB, alloc=445.8MB, time=114.08 memory used=11500.7MB, alloc=445.8MB, time=114.28 memory used=11566.7MB, alloc=445.8MB, time=114.47 memory used=11635.1MB, alloc=445.8MB, time=114.67 memory used=11706.3MB, alloc=445.8MB, time=114.87 memory used=11779.4MB, alloc=445.8MB, time=115.10 memory used=11855.5MB, alloc=445.8MB, time=115.30 memory used=11934.8MB, alloc=445.8MB, time=115.50 memory used=12019.0MB, alloc=445.8MB, time=115.72 memory used=12106.1MB, alloc=445.8MB, time=115.92 memory used=12195.6MB, alloc=445.8MB, time=116.13 memory used=12288.6MB, alloc=445.8MB, time=116.36 memory used=12386.3MB, alloc=445.8MB, time=116.56 memory used=12489.9MB, alloc=445.8MB, time=116.78 memory used=12616.4MB, alloc=445.8MB, time=127.14 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428242451 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 3 4 3 2 F := [7 x z - 12 y z - 19 x z, 11 y z + 17 z - 10 x y, -15 x - 19 x ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; G := [ 3 2 2 2 3 2 2 2 -x z + 5 y z - 13 y, -x y z - 4 y z + 10 y , 4 x y - 8 x y z - 14 z ] > Problem := [F,G]; Problem := [ 3 3 2 3 4 3 2 [7 x z - 12 y z - 19 x z, 11 y z + 17 z - 10 x y, -15 x - 19 x ], [ 3 2 2 2 3 2 2 2 -x z + 5 y z - 13 y, -x y z - 4 y z + 10 y , 4 x y - 8 x y z - 14 z ] ] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.8MB, alloc=32.3MB, time=0.51 memory used=46.8MB, alloc=32.3MB, time=0.80 memory used=65.5MB, alloc=56.3MB, time=1.09 memory used=106.9MB, alloc=68.3MB, time=1.68 memory used=144.0MB, alloc=68.3MB, time=1.92 memory used=179.6MB, alloc=68.3MB, time=2.33 memory used=214.7MB, alloc=68.3MB, time=2.64 memory used=252.2MB, alloc=68.3MB, time=2.96 memory used=297.5MB, alloc=68.3MB, time=3.45 memory used=340.9MB, alloc=68.3MB, time=3.78 memory used=376.2MB, alloc=68.3MB, time=4.17 memory used=417.8MB, alloc=68.3MB, time=4.74 memory used=460.0MB, alloc=92.3MB, time=5.31 memory used=522.7MB, alloc=92.3MB, time=6.08 memory used=589.2MB, alloc=92.3MB, time=6.95 memory used=646.3MB, alloc=116.3MB, time=7.84 memory used=721.2MB, alloc=372.3MB, time=8.91 memory used=807.3MB, alloc=372.3MB, time=10.07 memory used=897.2MB, alloc=396.3MB, time=11.22 memory used=1004.6MB, alloc=396.3MB, time=12.23 memory used=1081.8MB, alloc=396.3MB, time=12.97 memory used=1161.4MB, alloc=396.3MB, time=13.96 memory used=1243.5MB, alloc=396.3MB, time=14.71 memory used=1331.2MB, alloc=396.3MB, time=15.44 memory used=1409.4MB, alloc=396.3MB, time=15.94 memory used=1460.9MB, alloc=396.3MB, time=16.14 memory used=1520.0MB, alloc=396.3MB, time=16.37 memory used=1605.5MB, alloc=396.3MB, time=16.90 memory used=1651.2MB, alloc=396.3MB, time=17.08 memory used=1725.4MB, alloc=396.3MB, time=19.53 memory used=1798.7MB, alloc=396.3MB, time=20.16 memory used=1847.7MB, alloc=396.3MB, time=20.35 memory used=1931.5MB, alloc=396.3MB, time=20.86 memory used=1977.0MB, alloc=396.3MB, time=21.05 memory used=2049.9MB, alloc=396.3MB, time=21.48 memory used=2114.9MB, alloc=396.3MB, time=21.73 memory used=2164.9MB, alloc=396.3MB, time=21.92 memory used=2256.4MB, alloc=396.3MB, time=24.80 memory used=2310.2MB, alloc=396.3MB, time=25.01 memory used=2375.0MB, alloc=396.3MB, time=26.43 memory used=2454.8MB, alloc=396.3MB, time=26.75 memory used=2527.8MB, alloc=396.3MB, time=27.04 memory used=2595.7MB, alloc=396.3MB, time=27.30 memory used=2637.3MB, alloc=420.3MB, time=27.54 memory used=2690.0MB, alloc=420.3MB, time=27.78 memory used=2749.0MB, alloc=420.3MB, time=28.04 memory used=2812.5MB, alloc=420.3MB, time=28.29 memory used=2880.3MB, alloc=420.3MB, time=28.56 memory used=2954.3MB, alloc=420.3MB, time=28.80 memory used=3034.7MB, alloc=420.3MB, time=29.05 memory used=3122.9MB, alloc=420.3MB, time=29.31 memory used=3182.6MB, alloc=420.3MB, time=29.53 memory used=3229.6MB, alloc=420.3MB, time=29.74 memory used=3278.4MB, alloc=420.3MB, time=29.94 memory used=3329.9MB, alloc=420.3MB, time=30.14 memory used=3385.1MB, alloc=420.3MB, time=30.35 memory used=3443.1MB, alloc=420.3MB, time=30.56 memory used=3505.6MB, alloc=420.3MB, time=30.76 memory used=3588.8MB, alloc=420.3MB, time=33.14 memory used=3693.0MB, alloc=420.3MB, time=34.14 memory used=3775.2MB, alloc=420.3MB, time=34.45 memory used=3834.3MB, alloc=420.3MB, time=34.72 memory used=3890.6MB, alloc=420.3MB, time=34.96 memory used=3949.5MB, alloc=420.3MB, time=35.21 memory used=4012.2MB, alloc=420.3MB, time=35.45 memory used=4080.8MB, alloc=420.3MB, time=35.71 memory used=4155.2MB, alloc=420.3MB, time=35.96 memory used=4232.5MB, alloc=420.3MB, time=36.22 memory used=4315.7MB, alloc=420.3MB, time=36.49 memory used=4396.3MB, alloc=420.3MB, time=36.74 memory used=4449.7MB, alloc=420.3MB, time=36.95 memory used=4496.7MB, alloc=420.3MB, time=37.15 memory used=4544.2MB, alloc=420.3MB, time=37.35 memory used=4590.6MB, alloc=420.3MB, time=37.55 memory used=4640.7MB, alloc=420.3MB, time=37.75 memory used=4691.3MB, alloc=420.3MB, time=37.96 memory used=4742.5MB, alloc=420.3MB, time=38.17 memory used=4797.4MB, alloc=420.3MB, time=38.38 memory used=4852.6MB, alloc=420.3MB, time=38.59 memory used=4908.2MB, alloc=420.3MB, time=38.79 memory used=4967.5MB, alloc=420.3MB, time=39.01 memory used=5027.2MB, alloc=420.3MB, time=39.23 memory used=5090.4MB, alloc=420.3MB, time=39.44 memory used=5153.7MB, alloc=420.3MB, time=39.65 memory used=5220.5MB, alloc=420.3MB, time=39.86 memory used=5287.1MB, alloc=420.3MB, time=40.09 memory used=5357.1MB, alloc=420.3MB, time=40.31 memory used=5430.1MB, alloc=420.3MB, time=40.52 memory used=5502.5MB, alloc=420.3MB, time=40.73 memory used=5577.6MB, alloc=420.3MB, time=40.95 memory used=5655.1MB, alloc=420.3MB, time=41.16 memory used=5734.7MB, alloc=420.3MB, time=41.40 memory used=5819.1MB, alloc=420.3MB, time=41.63 memory used=5904.6MB, alloc=420.3MB, time=41.86 memory used=5962.8MB, alloc=420.3MB, time=42.05 memory used=6006.0MB, alloc=420.3MB, time=42.22 memory used=6049.9MB, alloc=420.3MB, time=42.38 memory used=6095.3MB, alloc=420.3MB, time=42.54 memory used=6142.0MB, alloc=420.3MB, time=42.70 memory used=6189.7MB, alloc=420.3MB, time=42.87 memory used=6237.8MB, alloc=420.3MB, time=43.04 memory used=6288.3MB, alloc=420.3MB, time=43.21 memory used=6340.0MB, alloc=420.3MB, time=43.37 memory used=6392.3MB, alloc=420.3MB, time=43.53 memory used=6446.6MB, alloc=420.3MB, time=43.70 memory used=6504.2MB, alloc=420.3MB, time=43.86 memory used=6716.0MB, alloc=420.3MB, time=52.99 memory used=6923.5MB, alloc=420.3MB, time=54.33 memory used=7061.5MB, alloc=420.3MB, time=56.07 memory used=7190.3MB, alloc=420.3MB, time=57.48 memory used=7335.6MB, alloc=420.3MB, time=58.68 memory used=7444.5MB, alloc=420.3MB, time=59.57 memory used=7538.1MB, alloc=420.3MB, time=60.03 memory used=7630.5MB, alloc=420.3MB, time=61.10 memory used=7734.0MB, alloc=420.3MB, time=62.03 memory used=7863.8MB, alloc=420.3MB, time=63.45 memory used=7994.3MB, alloc=420.3MB, time=64.77 memory used=8089.8MB, alloc=420.3MB, time=65.33 memory used=8182.0MB, alloc=420.3MB, time=66.39 memory used=8289.3MB, alloc=420.3MB, time=67.69 memory used=8382.1MB, alloc=420.3MB, time=68.19 memory used=8435.7MB, alloc=420.3MB, time=68.42 memory used=8528.4MB, alloc=420.3MB, time=68.88 memory used=8589.9MB, alloc=420.3MB, time=69.14 memory used=8688.8MB, alloc=420.3MB, time=72.07 memory used=8756.4MB, alloc=420.3MB, time=72.33 memory used=8834.1MB, alloc=420.3MB, time=72.78 memory used=8899.3MB, alloc=420.3MB, time=73.05 memory used=8977.6MB, alloc=420.3MB, time=73.51 memory used=9056.1MB, alloc=420.3MB, time=73.82 memory used=9117.1MB, alloc=420.3MB, time=74.06 memory used=9215.8MB, alloc=420.3MB, time=77.00 memory used=9273.9MB, alloc=420.3MB, time=77.21 memory used=9381.3MB, alloc=420.3MB, time=78.72 memory used=9466.8MB, alloc=420.3MB, time=79.06 memory used=9543.0MB, alloc=444.3MB, time=79.37 memory used=9604.9MB, alloc=444.3MB, time=79.68 memory used=9669.7MB, alloc=444.3MB, time=79.97 memory used=9741.0MB, alloc=444.3MB, time=80.26 memory used=9817.3MB, alloc=444.3MB, time=80.56 memory used=9900.7MB, alloc=444.3MB, time=80.85 memory used=9992.6MB, alloc=444.3MB, time=81.15 memory used=10089.5MB, alloc=444.3MB, time=81.44 memory used=10143.9MB, alloc=444.3MB, time=81.69 memory used=10199.3MB, alloc=444.3MB, time=81.93 memory used=10256.7MB, alloc=444.3MB, time=82.18 memory used=10318.0MB, alloc=444.3MB, time=82.42 memory used=10383.3MB, alloc=444.3MB, time=82.67 memory used=10454.4MB, alloc=444.3MB, time=82.91 memory used=10562.0MB, alloc=444.3MB, time=86.04 memory used=10673.7MB, alloc=444.3MB, time=86.46 memory used=10747.7MB, alloc=444.3MB, time=86.78 memory used=10810.1MB, alloc=444.3MB, time=87.08 memory used=10876.2MB, alloc=444.3MB, time=87.37 memory used=10947.3MB, alloc=444.3MB, time=87.67 memory used=11025.1MB, alloc=444.3MB, time=87.97 memory used=11109.5MB, alloc=444.3MB, time=88.26 memory used=11197.7MB, alloc=444.3MB, time=88.56 memory used=11292.4MB, alloc=444.3MB, time=88.87 memory used=11365.5MB, alloc=444.3MB, time=89.14 memory used=11419.6MB, alloc=444.3MB, time=89.38 memory used=11471.2MB, alloc=444.3MB, time=89.61 memory used=11524.5MB, alloc=444.3MB, time=89.86 memory used=11578.5MB, alloc=444.3MB, time=90.09 memory used=11636.5MB, alloc=444.3MB, time=90.34 memory used=11695.1MB, alloc=444.3MB, time=90.59 memory used=11757.6MB, alloc=444.3MB, time=90.83 memory used=11820.6MB, alloc=444.3MB, time=91.06 memory used=11883.9MB, alloc=444.3MB, time=91.31 memory used=11951.0MB, alloc=444.3MB, time=91.55 memory used=12021.9MB, alloc=444.3MB, time=91.79 memory used=12092.9MB, alloc=444.3MB, time=92.04 memory used=12167.5MB, alloc=444.3MB, time=92.28 memory used=12245.3MB, alloc=444.3MB, time=92.53 memory used=12322.8MB, alloc=444.3MB, time=92.78 memory used=12403.2MB, alloc=444.3MB, time=93.03 memory used=12486.4MB, alloc=444.3MB, time=93.28 memory used=12572.0MB, alloc=444.3MB, time=93.54 memory used=12662.6MB, alloc=444.3MB, time=93.81 memory used=12754.7MB, alloc=444.3MB, time=94.08 memory used=12850.7MB, alloc=444.3MB, time=94.34 memory used=12911.7MB, alloc=444.3MB, time=94.55 memory used=12961.9MB, alloc=444.3MB, time=94.75 memory used=13011.2MB, alloc=444.3MB, time=94.94 memory used=13061.8MB, alloc=444.3MB, time=95.13 memory used=13113.4MB, alloc=444.3MB, time=95.32 memory used=13167.4MB, alloc=444.3MB, time=95.52 memory used=13223.5MB, alloc=444.3MB, time=95.74 memory used=13280.5MB, alloc=444.3MB, time=95.94 memory used=13340.9MB, alloc=444.3MB, time=96.15 memory used=13403.5MB, alloc=444.3MB, time=96.35 memory used=13469.0MB, alloc=444.3MB, time=96.55 memory used=13650.8MB, alloc=444.3MB, time=105.32 memory used=13887.3MB, alloc=444.3MB, time=106.89 memory used=14044.0MB, alloc=444.3MB, time=108.72 memory used=14194.7MB, alloc=444.3MB, time=110.41 memory used=14310.0MB, alloc=444.3MB, time=112.01 memory used=14447.5MB, alloc=468.3MB, time=114.17 memory used=14572.5MB, alloc=468.3MB, time=116.03 memory used=14686.4MB, alloc=468.3MB, time=116.76 memory used=14794.1MB, alloc=468.3MB, time=117.39 memory used=14901.0MB, alloc=468.3MB, time=117.98 memory used=15018.3MB, alloc=468.3MB, time=118.92 memory used=15125.1MB, alloc=468.3MB, time=119.67 memory used=15201.7MB, alloc=468.3MB, time=120.04 memory used=15290.7MB, alloc=468.3MB, time=120.39 memory used=15362.5MB, alloc=468.3MB, time=120.70 memory used=15427.5MB, alloc=468.3MB, time=120.99 memory used=15504.7MB, alloc=468.3MB, time=121.28 memory used=15617.6MB, alloc=468.3MB, time=122.11 memory used=15692.2MB, alloc=468.3MB, time=122.44 memory used=15783.9MB, alloc=468.3MB, time=122.78 memory used=15843.1MB, alloc=468.3MB, time=123.07 memory used=15912.9MB, alloc=468.3MB, time=123.37 memory used=16027.1MB, alloc=468.3MB, time=127.93 memory used=16110.6MB, alloc=468.3MB, time=128.27 memory used=16177.3MB, alloc=468.3MB, time=128.56 memory used=16265.4MB, alloc=468.3MB, time=128.86 memory used=16348.2MB, alloc=468.3MB, time=129.46 memory used=16440.5MB, alloc=468.3MB, time=129.86 memory used=16521.0MB, alloc=468.3MB, time=130.19 memory used=16604.5MB, alloc=468.3MB, time=130.52 memory used=16666.8MB, alloc=468.3MB, time=130.80 memory used=16740.0MB, alloc=468.3MB, time=131.09 memory used=16857.0MB, alloc=468.3MB, time=131.87 memory used=16928.6MB, alloc=468.3MB, time=132.21 memory used=17021.3MB, alloc=468.3MB, time=132.54 memory used=17087.3MB, alloc=468.3MB, time=132.84 memory used=17154.1MB, alloc=468.3MB, time=133.11 memory used=17249.1MB, alloc=468.3MB, time=136.70 memory used=17349.4MB, alloc=468.3MB, time=137.89 memory used=17419.6MB, alloc=468.3MB, time=138.18 memory used=17502.1MB, alloc=468.3MB, time=138.46 memory used=17573.8MB, alloc=468.3MB, time=138.72 memory used=17667.1MB, alloc=468.3MB, time=140.71 memory used=17793.1MB, alloc=468.3MB, time=141.77 memory used=17893.1MB, alloc=492.3MB, time=142.21 memory used=17974.6MB, alloc=492.3MB, time=142.61 memory used=18054.0MB, alloc=492.3MB, time=142.99 memory used=18140.7MB, alloc=492.3MB, time=143.38 memory used=18237.4MB, alloc=492.3MB, time=143.79 memory used=18344.4MB, alloc=492.3MB, time=144.19 memory used=18461.5MB, alloc=492.3MB, time=144.59 memory used=18563.9MB, alloc=492.3MB, time=144.96 memory used=18630.4MB, alloc=492.3MB, time=145.28 memory used=18695.6MB, alloc=492.3MB, time=145.62 memory used=18763.9MB, alloc=492.3MB, time=145.93 memory used=18833.2MB, alloc=492.3MB, time=146.25 memory used=18903.5MB, alloc=492.3MB, time=146.57 memory used=18979.6MB, alloc=492.3MB, time=146.89 memory used=19056.6MB, alloc=492.3MB, time=147.23 memory used=19139.4MB, alloc=492.3MB, time=147.55 memory used=19222.9MB, alloc=492.3MB, time=147.90 memory used=19311.9MB, alloc=492.3MB, time=148.23 memory used=19401.1MB, alloc=492.3MB, time=148.58 memory used=19495.8MB, alloc=492.3MB, time=148.92 memory used=19595.4MB, alloc=492.3MB, time=149.26 memory used=19695.6MB, alloc=492.3MB, time=149.60 memory used=19803.3MB, alloc=492.3MB, time=149.94 memory used=19915.6MB, alloc=492.3MB, time=150.28 memory used=20030.9MB, alloc=492.3MB, time=150.62 memory used=20149.3MB, alloc=492.3MB, time=150.97 memory used=20212.8MB, alloc=492.3MB, time=151.24 memory used=20273.3MB, alloc=492.3MB, time=151.50 memory used=20336.3MB, alloc=492.3MB, time=151.76 memory used=20401.5MB, alloc=492.3MB, time=152.03 memory used=20468.4MB, alloc=492.3MB, time=152.29 memory used=20536.3MB, alloc=492.3MB, time=152.56 memory used=20607.8MB, alloc=492.3MB, time=152.82 memory used=20681.2MB, alloc=492.3MB, time=153.09 memory used=20758.6MB, alloc=492.3MB, time=153.35 memory used=20853.3MB, alloc=492.3MB, time=154.66 memory used=20991.9MB, alloc=492.3MB, time=158.87 memory used=21080.3MB, alloc=492.3MB, time=159.28 memory used=21162.5MB, alloc=492.3MB, time=159.66 memory used=21249.6MB, alloc=492.3MB, time=160.05 memory used=21346.0MB, alloc=492.3MB, time=160.45 memory used=21449.5MB, alloc=492.3MB, time=160.86 memory used=21563.2MB, alloc=492.3MB, time=161.27 memory used=21647.6MB, alloc=492.3MB, time=161.64 memory used=21720.4MB, alloc=516.3MB, time=162.01 memory used=21801.3MB, alloc=516.3MB, time=162.38 memory used=21882.9MB, alloc=516.3MB, time=162.74 memory used=21967.7MB, alloc=516.3MB, time=163.11 memory used=22054.8MB, alloc=516.3MB, time=163.48 memory used=22144.1MB, alloc=516.3MB, time=163.85 memory used=22235.7MB, alloc=516.3MB, time=164.23 memory used=22335.2MB, alloc=516.3MB, time=164.61 memory used=22437.0MB, alloc=516.3MB, time=164.97 memory used=22540.8MB, alloc=516.3MB, time=165.37 memory used=22646.8MB, alloc=516.3MB, time=165.76 memory used=22761.1MB, alloc=516.3MB, time=166.15 memory used=22877.5MB, alloc=516.3MB, time=166.53 memory used=22995.8MB, alloc=516.3MB, time=166.93 memory used=23122.7MB, alloc=516.3MB, time=167.33 memory used=23251.5MB, alloc=516.3MB, time=167.73 memory used=23381.9MB, alloc=516.3MB, time=168.13 memory used=23521.1MB, alloc=516.3MB, time=168.54 memory used=23621.7MB, alloc=516.3MB, time=168.90 memory used=23699.6MB, alloc=516.3MB, time=169.24 memory used=23770.1MB, alloc=516.3MB, time=169.56 memory used=23836.0MB, alloc=516.3MB, time=169.86 memory used=23903.0MB, alloc=516.3MB, time=170.17 memory used=23976.9MB, alloc=516.3MB, time=170.49 memory used=24051.7MB, alloc=516.3MB, time=170.79 memory used=24126.7MB, alloc=516.3MB, time=171.09 memory used=24201.8MB, alloc=516.3MB, time=171.39 memory used=24277.1MB, alloc=516.3MB, time=171.69 memory used=24352.5MB, alloc=516.3MB, time=171.99 memory used=24428.0MB, alloc=516.3MB, time=172.29 memory used=24504.4MB, alloc=516.3MB, time=172.60 memory used=24586.8MB, alloc=516.3MB, time=172.90 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428242751 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 3 3 2 4 4 3 F := [-20 y - 13 y z - 20 y, 6 x z - 11 z - 17 z , 10 x - 6 z + z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 2 G := [17 x y z + 17 x z - 2 z, -6 x y z - 9 y z - 19 x y , 3 2 2 -13 y z - 19 x z + 15 x ] > Problem := [F,G]; Problem := [ 4 3 3 3 2 4 4 3 [-20 y - 13 y z - 20 y, 6 x z - 11 z - 17 z , 10 x - 6 z + z ], [ 2 2 2 2 2 2 17 x y z + 17 x z - 2 z, -6 x y z - 9 y z - 19 x y , 3 2 2 -13 y z - 19 x z + 15 x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.18 memory used=26.4MB, alloc=32.3MB, time=0.50 memory used=47.0MB, alloc=32.3MB, time=0.81 memory used=66.3MB, alloc=56.3MB, time=1.13 memory used=105.3MB, alloc=60.3MB, time=1.72 memory used=142.1MB, alloc=84.3MB, time=2.30 memory used=207.8MB, alloc=92.3MB, time=3.25 memory used=271.3MB, alloc=116.3MB, time=4.22 memory used=344.1MB, alloc=116.3MB, time=5.27 memory used=408.3MB, alloc=372.3MB, time=6.15 memory used=498.1MB, alloc=396.3MB, time=7.41 memory used=608.9MB, alloc=396.3MB, time=9.04 memory used=715.7MB, alloc=420.3MB, time=10.58 memory used=840.1MB, alloc=420.3MB, time=12.11 memory used=977.8MB, alloc=420.3MB, time=15.29 memory used=1034.6MB, alloc=420.3MB, time=15.53 memory used=1082.1MB, alloc=420.3MB, time=15.76 memory used=1146.5MB, alloc=420.3MB, time=16.15 memory used=1278.1MB, alloc=444.3MB, time=18.16 memory used=1407.3MB, alloc=468.3MB, time=20.16 memory used=1566.7MB, alloc=468.3MB, time=25.32 memory used=1645.7MB, alloc=468.3MB, time=25.62 memory used=1740.1MB, alloc=468.3MB, time=26.26 memory used=1867.1MB, alloc=468.3MB, time=27.39 memory used=1956.1MB, alloc=468.3MB, time=29.20 memory used=2040.4MB, alloc=468.3MB, time=29.73 memory used=2177.0MB, alloc=468.3MB, time=31.64 memory used=2303.6MB, alloc=468.3MB, time=32.74 memory used=2434.7MB, alloc=492.3MB, time=34.27 memory used=2538.8MB, alloc=492.3MB, time=34.83 memory used=2645.4MB, alloc=492.3MB, time=36.68 memory used=2799.5MB, alloc=492.3MB, time=42.33 memory used=2891.6MB, alloc=492.3MB, time=42.69 memory used=2969.0MB, alloc=492.3MB, time=42.98 memory used=3115.9MB, alloc=492.3MB, time=43.85 memory used=3254.4MB, alloc=492.3MB, time=46.12 memory used=3394.4MB, alloc=492.3MB, time=47.35 memory used=3497.0MB, alloc=492.3MB, time=47.93 memory used=3608.0MB, alloc=492.3MB, time=50.39 memory used=3717.4MB, alloc=492.3MB, time=51.52 memory used=3823.4MB, alloc=492.3MB, time=52.87 memory used=3974.0MB, alloc=492.3MB, time=59.40 memory used=4055.7MB, alloc=492.3MB, time=59.79 memory used=4133.3MB, alloc=492.3MB, time=60.14 memory used=4208.0MB, alloc=492.3MB, time=60.49 memory used=4359.1MB, alloc=492.3MB, time=61.63 memory used=4492.2MB, alloc=492.3MB, time=62.87 memory used=4583.0MB, alloc=492.3MB, time=63.35 memory used=4684.3MB, alloc=492.3MB, time=65.45 memory used=4814.8MB, alloc=516.3MB, time=66.87 memory used=4920.2MB, alloc=516.3MB, time=67.38 memory used=5039.7MB, alloc=516.3MB, time=71.87 memory used=5141.7MB, alloc=516.3MB, time=72.33 memory used=5227.8MB, alloc=516.3MB, time=72.71 memory used=5463.0MB, alloc=516.3MB, time=76.85 memory used=5598.8MB, alloc=516.3MB, time=103.54 memory used=5691.1MB, alloc=516.3MB, time=103.98 memory used=5782.3MB, alloc=516.3MB, time=104.42 memory used=5860.3MB, alloc=516.3MB, time=104.81 memory used=5951.4MB, alloc=516.3MB, time=105.20 memory used=6054.8MB, alloc=516.3MB, time=105.63 memory used=6175.9MB, alloc=516.3MB, time=106.11 memory used=6323.4MB, alloc=516.3MB, time=106.71 memory used=6474.2MB, alloc=516.3MB, time=107.21 memory used=6642.2MB, alloc=516.3MB, time=107.72 memory used=6834.5MB, alloc=516.3MB, time=108.26 memory used=7057.5MB, alloc=516.3MB, time=108.83 memory used=7338.3MB, alloc=516.3MB, time=110.55 memory used=7431.4MB, alloc=516.3MB, time=111.83 memory used=7550.7MB, alloc=516.3MB, time=112.72 memory used=7656.4MB, alloc=516.3MB, time=113.66 memory used=7772.8MB, alloc=516.3MB, time=116.06 memory used=7881.0MB, alloc=516.3MB, time=118.18 memory used=7967.3MB, alloc=516.3MB, time=119.32 memory used=8058.6MB, alloc=516.3MB, time=120.75 memory used=8134.1MB, alloc=516.3MB, time=122.35 memory used=8206.5MB, alloc=516.3MB, time=123.68 memory used=8287.6MB, alloc=516.3MB, time=125.29 memory used=8339.8MB, alloc=540.3MB, time=126.30 memory used=8392.4MB, alloc=540.3MB, time=127.27 memory used=8445.3MB, alloc=540.3MB, time=128.16 memory used=8515.8MB, alloc=540.3MB, time=129.87 memory used=8731.3MB, alloc=564.3MB, time=133.75 memory used=8933.1MB, alloc=588.3MB, time=136.96 memory used=9096.7MB, alloc=612.3MB, time=139.44 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428243051 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; F := [ 2 2 3 2 4 3 2 2 x y - 10 y - 5 x z, 20 x y z + 8 z - 18, -16 x z + 6 x y + 14 x z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 3 2 2 G := [-9 x y + 19 y z - 7, 12 y z + 14 x - 16 x z , 7 x y z - x + 19] > Problem := [F,G]; Problem := [[ 2 2 3 2 4 3 2 2 x y - 10 y - 5 x z, 20 x y z + 8 z - 18, -16 x z + 6 x y + 14 x z] 2 3 3 2 2 , [-9 x y + 19 y z - 7, 12 y z + 14 x - 16 x z , 7 x y z - x + 19]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=24.9MB, alloc=32.3MB, time=0.47 memory used=43.7MB, alloc=32.3MB, time=0.74 memory used=60.0MB, alloc=32.3MB, time=0.88 memory used=80.8MB, alloc=36.3MB, time=1.16 memory used=102.8MB, alloc=60.3MB, time=1.45 memory used=151.5MB, alloc=68.3MB, time=2.02 memory used=192.2MB, alloc=68.3MB, time=2.36 memory used=238.9MB, alloc=68.3MB, time=2.92 memory used=284.5MB, alloc=92.3MB, time=3.52 memory used=350.6MB, alloc=92.3MB, time=4.51 memory used=401.2MB, alloc=92.3MB, time=4.94 memory used=449.9MB, alloc=92.3MB, time=5.30 memory used=503.5MB, alloc=92.5MB, time=6.63 memory used=534.4MB, alloc=92.5MB, time=6.74 memory used=569.9MB, alloc=92.5MB, time=6.96 memory used=603.3MB, alloc=92.5MB, time=7.18 memory used=634.7MB, alloc=92.5MB, time=7.30 memory used=672.8MB, alloc=92.5MB, time=7.65 memory used=723.0MB, alloc=92.5MB, time=8.94 memory used=754.2MB, alloc=92.5MB, time=9.06 memory used=782.9MB, alloc=92.5MB, time=9.16 memory used=856.4MB, alloc=92.5MB, time=10.28 memory used=936.3MB, alloc=92.5MB, time=11.05 memory used=1017.5MB, alloc=92.6MB, time=12.40 memory used=1092.9MB, alloc=93.5MB, time=13.39 memory used=1153.3MB, alloc=117.5MB, time=14.21 memory used=1205.4MB, alloc=117.5MB, time=14.66 memory used=1273.2MB, alloc=117.5MB, time=15.49 memory used=1335.1MB, alloc=373.5MB, time=16.33 memory used=1418.5MB, alloc=373.5MB, time=17.14 memory used=1475.6MB, alloc=373.5MB, time=17.68 memory used=1530.4MB, alloc=373.5MB, time=19.56 memory used=1616.3MB, alloc=373.5MB, time=20.55 memory used=1696.8MB, alloc=373.5MB, time=21.26 memory used=1734.2MB, alloc=373.5MB, time=21.40 memory used=1779.9MB, alloc=373.5MB, time=22.07 memory used=1820.2MB, alloc=373.5MB, time=22.27 memory used=1903.7MB, alloc=373.5MB, time=23.07 memory used=1966.0MB, alloc=373.5MB, time=23.93 memory used=2007.8MB, alloc=373.5MB, time=24.20 memory used=2101.7MB, alloc=373.5MB, time=25.12 memory used=2191.6MB, alloc=397.5MB, time=26.19 memory used=2259.8MB, alloc=397.5MB, time=26.95 memory used=2331.1MB, alloc=397.5MB, time=27.66 memory used=2411.7MB, alloc=397.5MB, time=28.24 memory used=2522.8MB, alloc=397.5MB, time=29.75 memory used=2627.5MB, alloc=421.5MB, time=31.28 memory used=2731.6MB, alloc=421.5MB, time=32.89 memory used=2792.0MB, alloc=421.5MB, time=33.12 memory used=2861.2MB, alloc=421.5MB, time=33.33 memory used=2908.7MB, alloc=421.5MB, time=33.51 memory used=2978.3MB, alloc=421.5MB, time=33.97 memory used=3056.0MB, alloc=421.5MB, time=34.37 memory used=3131.3MB, alloc=421.5MB, time=34.61 memory used=3207.9MB, alloc=421.5MB, time=35.12 memory used=3270.6MB, alloc=421.5MB, time=35.37 memory used=3362.2MB, alloc=421.5MB, time=43.57 memory used=3429.8MB, alloc=421.5MB, time=43.84 memory used=3481.3MB, alloc=421.5MB, time=44.06 memory used=3547.6MB, alloc=421.5MB, time=44.30 memory used=3612.7MB, alloc=421.5MB, time=44.51 memory used=3657.4MB, alloc=421.5MB, time=44.72 memory used=3706.7MB, alloc=421.5MB, time=44.90 memory used=3761.8MB, alloc=421.5MB, time=45.12 memory used=3822.2MB, alloc=421.5MB, time=45.31 memory used=3890.0MB, alloc=421.5MB, time=45.52 memory used=3966.1MB, alloc=421.5MB, time=45.73 memory used=4159.7MB, alloc=421.5MB, time=47.03 memory used=4249.6MB, alloc=421.5MB, time=48.41 memory used=4378.3MB, alloc=421.5MB, time=50.01 memory used=4544.3MB, alloc=421.5MB, time=51.47 memory used=4648.8MB, alloc=445.5MB, time=73.50 memory used=4765.5MB, alloc=445.5MB, time=80.65 memory used=4986.0MB, alloc=445.5MB, time=83.52 memory used=5097.8MB, alloc=445.5MB, time=84.98 memory used=5203.6MB, alloc=445.5MB, time=86.57 memory used=5328.5MB, alloc=445.5MB, time=87.93 memory used=5427.7MB, alloc=469.5MB, time=89.25 memory used=5513.5MB, alloc=469.5MB, time=90.37 memory used=5607.3MB, alloc=469.5MB, time=91.52 memory used=5720.8MB, alloc=493.5MB, time=92.57 memory used=5835.2MB, alloc=493.5MB, time=93.64 memory used=5925.6MB, alloc=493.5MB, time=94.94 memory used=5996.0MB, alloc=493.5MB, time=95.87 memory used=6070.1MB, alloc=517.5MB, time=96.85 memory used=6131.0MB, alloc=517.5MB, time=97.79 memory used=6202.6MB, alloc=517.5MB, time=98.61 memory used=6244.4MB, alloc=517.5MB, time=99.46 memory used=6328.7MB, alloc=517.5MB, time=100.32 memory used=6392.8MB, alloc=517.5MB, time=101.44 memory used=6449.0MB, alloc=517.5MB, time=102.72 memory used=6494.6MB, alloc=517.5MB, time=103.70 memory used=6680.6MB, alloc=541.5MB, time=106.24 memory used=6881.6MB, alloc=565.5MB, time=108.81 memory used=7023.6MB, alloc=589.5MB, time=110.09 memory used=7180.9MB, alloc=589.5MB, time=111.70 memory used=7315.3MB, alloc=589.5MB, time=112.62 memory used=7470.6MB, alloc=589.5MB, time=113.79 memory used=7617.6MB, alloc=589.5MB, time=114.76 memory used=7776.6MB, alloc=589.5MB, time=119.04 memory used=7937.7MB, alloc=589.5MB, time=121.05 memory used=8097.9MB, alloc=589.5MB, time=122.35 memory used=8244.2MB, alloc=589.5MB, time=123.24 memory used=8403.7MB, alloc=589.5MB, time=127.57 memory used=8532.3MB, alloc=589.5MB, time=128.31 memory used=8704.5MB, alloc=589.5MB, time=129.59 memory used=8846.7MB, alloc=589.5MB, time=130.47 memory used=8996.6MB, alloc=589.5MB, time=133.22 memory used=9166.6MB, alloc=589.5MB, time=134.64 memory used=9477.0MB, alloc=589.5MB, time=139.64 memory used=9745.1MB, alloc=613.5MB, time=142.93 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428243351 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 2 2 F := [14 x y + y z - 17 y z, 11 x z - 3 y z - 9 x y, 2 2 3 2 14 x y - 11 y z + 12 x y] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 2 2 3 2 G := [-11 x z + 4 y , 5 x y - 20 x y z + 7 y z , -10 x y + 9 x y + 3 x y] > Problem := [F,G]; 3 2 2 2 2 2 2 Problem := [[14 x y + y z - 17 y z, 11 x z - 3 y z - 9 x y, 2 2 3 2 14 x y - 11 y z + 12 x y], 2 3 2 2 2 2 3 2 [-11 x z + 4 y , 5 x y - 20 x y z + 7 y z , -10 x y + 9 x y + 3 x y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.18 memory used=26.7MB, alloc=32.3MB, time=0.52 memory used=46.3MB, alloc=56.3MB, time=0.81 memory used=88.1MB, alloc=60.3MB, time=1.44 memory used=127.8MB, alloc=60.3MB, time=2.03 memory used=166.9MB, alloc=84.3MB, time=2.64 memory used=232.1MB, alloc=92.3MB, time=3.49 memory used=300.0MB, alloc=92.3MB, time=4.35 memory used=353.5MB, alloc=92.3MB, time=4.84 memory used=422.7MB, alloc=92.3MB, time=5.68 memory used=488.6MB, alloc=116.3MB, time=6.59 memory used=555.7MB, alloc=372.3MB, time=7.65 memory used=637.8MB, alloc=372.3MB, time=8.94 memory used=686.9MB, alloc=372.3MB, time=9.38 memory used=749.6MB, alloc=372.3MB, time=10.17 memory used=817.1MB, alloc=372.3MB, time=10.74 memory used=907.9MB, alloc=396.3MB, time=12.01 memory used=1022.1MB, alloc=396.3MB, time=13.61 memory used=1135.2MB, alloc=420.3MB, time=15.28 memory used=1256.3MB, alloc=420.3MB, time=16.96 memory used=1401.6MB, alloc=420.3MB, time=18.46 memory used=1541.1MB, alloc=444.3MB, time=20.63 memory used=1686.5MB, alloc=444.3MB, time=22.76 memory used=1777.4MB, alloc=444.3MB, time=23.71 memory used=1906.4MB, alloc=444.3MB, time=25.53 memory used=2066.9MB, alloc=444.3MB, time=27.72 memory used=2149.2MB, alloc=468.3MB, time=28.49 memory used=2230.3MB, alloc=468.3MB, time=28.83 memory used=2305.3MB, alloc=468.3MB, time=29.14 memory used=2401.8MB, alloc=468.3MB, time=29.47 memory used=2465.3MB, alloc=468.3MB, time=29.73 memory used=2528.4MB, alloc=468.3MB, time=29.97 memory used=2599.0MB, alloc=468.3MB, time=30.23 memory used=2678.9MB, alloc=468.3MB, time=30.49 memory used=2769.9MB, alloc=468.3MB, time=30.75 memory used=2880.6MB, alloc=468.3MB, time=31.46 memory used=2961.9MB, alloc=468.3MB, time=31.79 memory used=3036.5MB, alloc=468.3MB, time=32.10 memory used=3132.2MB, alloc=468.3MB, time=32.43 memory used=3197.3MB, alloc=468.3MB, time=32.68 memory used=3259.6MB, alloc=468.3MB, time=32.93 memory used=3329.6MB, alloc=468.3MB, time=33.18 memory used=3409.7MB, alloc=468.3MB, time=33.43 memory used=3499.3MB, alloc=468.3MB, time=33.69 memory used=3622.0MB, alloc=468.3MB, time=37.58 memory used=3707.5MB, alloc=468.3MB, time=37.90 memory used=3777.0MB, alloc=468.3MB, time=38.17 memory used=3855.8MB, alloc=468.3MB, time=38.43 memory used=4098.7MB, alloc=468.3MB, time=39.10 memory used=4233.4MB, alloc=468.3MB, time=40.38 memory used=4314.8MB, alloc=468.3MB, time=40.71 memory used=4455.2MB, alloc=468.3MB, time=42.39 memory used=4603.5MB, alloc=468.3MB, time=44.23 memory used=4719.1MB, alloc=468.3MB, time=49.38 memory used=4849.2MB, alloc=468.3MB, time=50.94 memory used=4971.6MB, alloc=468.3MB, time=52.65 memory used=5095.5MB, alloc=492.3MB, time=54.56 memory used=5216.2MB, alloc=492.3MB, time=56.76 memory used=5343.9MB, alloc=492.3MB, time=58.05 memory used=5484.5MB, alloc=492.3MB, time=59.62 memory used=5608.0MB, alloc=516.3MB, time=61.46 memory used=5709.1MB, alloc=516.3MB, time=62.92 memory used=5806.0MB, alloc=516.3MB, time=64.75 memory used=5903.1MB, alloc=516.3MB, time=66.53 memory used=5983.9MB, alloc=516.3MB, time=67.76 memory used=6074.5MB, alloc=516.3MB, time=69.81 memory used=6163.0MB, alloc=540.3MB, time=71.42 memory used=6240.9MB, alloc=540.3MB, time=72.95 memory used=6309.4MB, alloc=540.3MB, time=74.20 memory used=6369.8MB, alloc=540.3MB, time=75.26 memory used=6429.4MB, alloc=540.3MB, time=76.30 memory used=6482.6MB, alloc=540.3MB, time=77.08 memory used=6580.8MB, alloc=540.3MB, time=78.49 memory used=6670.5MB, alloc=540.3MB, time=80.06 memory used=6753.6MB, alloc=540.3MB, time=81.47 memory used=6966.6MB, alloc=564.3MB, time=84.16 memory used=7192.4MB, alloc=588.3MB, time=86.90 memory used=7404.3MB, alloc=612.3MB, time=91.17 memory used=7600.7MB, alloc=636.3MB, time=94.64 memory used=7868.4MB, alloc=660.3MB, time=98.47 memory used=8062.4MB, alloc=684.3MB, time=100.28 memory used=8323.7MB, alloc=684.3MB, time=104.58 memory used=8473.4MB, alloc=684.3MB, time=106.85 memory used=8626.2MB, alloc=708.3MB, time=108.95 memory used=8764.1MB, alloc=708.3MB, time=112.09 memory used=8902.2MB, alloc=708.3MB, time=115.26 memory used=9031.4MB, alloc=708.3MB, time=118.18 memory used=9156.5MB, alloc=708.3MB, time=120.38 memory used=9271.3MB, alloc=732.3MB, time=122.53 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428243651 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 3 4 2 F := [19 x y + 15 x - 6, 14 x y z + 13 y z , -14 y z - 11 z + 14 x z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 2 2 G := [2 x y + 10 y z + 4 y z , -15 y z - 6 y z + 9 x, 2 x + 20 y z - 8 z] > Problem := [F,G]; Problem := [ 2 2 2 2 3 4 2 [19 x y + 15 x - 6, 14 x y z + 13 y z , -14 y z - 11 z + 14 x z ], 3 3 2 2 2 2 [2 x y + 10 y z + 4 y z , -15 y z - 6 y z + 9 x, 2 x + 20 y z - 8 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.5MB, alloc=32.3MB, time=0.50 memory used=47.4MB, alloc=32.3MB, time=0.81 memory used=66.7MB, alloc=56.3MB, time=1.12 memory used=104.7MB, alloc=60.3MB, time=1.71 memory used=142.4MB, alloc=84.3MB, time=2.29 memory used=202.2MB, alloc=92.3MB, time=3.23 memory used=293.0MB, alloc=124.3MB, time=4.65 memory used=375.9MB, alloc=124.3MB, time=5.95 memory used=461.1MB, alloc=148.3MB, time=7.31 memory used=546.4MB, alloc=148.3MB, time=8.77 memory used=621.6MB, alloc=404.3MB, time=10.07 memory used=728.8MB, alloc=428.3MB, time=11.98 memory used=864.9MB, alloc=452.3MB, time=14.31 memory used=1019.3MB, alloc=476.3MB, time=17.05 memory used=1154.9MB, alloc=476.3MB, time=19.42 memory used=1291.9MB, alloc=500.3MB, time=22.03 memory used=1419.3MB, alloc=500.3MB, time=24.39 memory used=1549.7MB, alloc=500.3MB, time=26.97 memory used=1676.7MB, alloc=524.3MB, time=29.39 memory used=1805.1MB, alloc=524.3MB, time=32.03 memory used=1921.4MB, alloc=524.3MB, time=34.50 memory used=2036.4MB, alloc=524.3MB, time=37.06 memory used=2130.0MB, alloc=524.3MB, time=39.05 memory used=2234.2MB, alloc=548.3MB, time=41.41 memory used=2332.0MB, alloc=548.3MB, time=43.63 memory used=2415.7MB, alloc=548.3MB, time=45.48 memory used=2486.4MB, alloc=548.3MB, time=47.12 memory used=2556.3MB, alloc=548.3MB, time=48.75 memory used=2629.1MB, alloc=548.3MB, time=50.56 memory used=2695.6MB, alloc=548.3MB, time=52.17 memory used=2763.2MB, alloc=548.3MB, time=53.92 memory used=2809.1MB, alloc=572.3MB, time=54.95 memory used=2860.4MB, alloc=572.3MB, time=56.46 memory used=2908.4MB, alloc=572.3MB, time=57.81 memory used=2966.6MB, alloc=572.3MB, time=59.57 memory used=3210.3MB, alloc=596.3MB, time=65.20 memory used=3426.6MB, alloc=620.3MB, time=69.86 memory used=3640.1MB, alloc=644.3MB, time=74.36 memory used=3853.8MB, alloc=668.3MB, time=78.72 memory used=4055.1MB, alloc=692.3MB, time=82.88 memory used=4303.0MB, alloc=716.3MB, time=88.06 memory used=4546.5MB, alloc=740.3MB, time=93.15 memory used=4804.3MB, alloc=764.3MB, time=98.56 memory used=5023.7MB, alloc=788.3MB, time=103.39 memory used=5230.4MB, alloc=812.3MB, time=108.02 memory used=5432.6MB, alloc=836.3MB, time=112.51 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428243951 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 F := [-14 x y + 6 y z + 17 x y, 20 x z + 8 x + 10 x y, 2 2 2 -4 y z + 16 x + 16 y] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 2 G := [-18 x y + 3 x z - 17 y z , 9 x y - 7 x y - 11 z , 2 2 2 17 x z - 10 x y z + 17 x z] > Problem := [F,G]; 2 2 3 2 Problem := [[-14 x y + 6 y z + 17 x y, 20 x z + 8 x + 10 x y, 2 2 2 3 2 2 -4 y z + 16 x + 16 y], [-18 x y + 3 x z - 17 y z , 2 2 2 2 2 2 9 x y - 7 x y - 11 z , 17 x z - 10 x y z + 17 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.17 memory used=26.7MB, alloc=32.3MB, time=0.51 memory used=47.7MB, alloc=32.3MB, time=0.82 memory used=66.2MB, alloc=56.3MB, time=1.11 memory used=105.4MB, alloc=60.3MB, time=1.70 memory used=143.1MB, alloc=84.3MB, time=2.28 memory used=204.3MB, alloc=92.3MB, time=3.23 memory used=265.2MB, alloc=116.3MB, time=4.18 memory used=343.2MB, alloc=116.3MB, time=5.37 memory used=424.2MB, alloc=372.3MB, time=6.59 memory used=510.4MB, alloc=396.3MB, time=7.93 memory used=615.0MB, alloc=420.3MB, time=9.66 memory used=745.8MB, alloc=444.3MB, time=11.73 memory used=894.8MB, alloc=468.3MB, time=14.23 memory used=1023.8MB, alloc=468.3MB, time=16.26 memory used=1167.4MB, alloc=492.3MB, time=18.29 memory used=1288.1MB, alloc=492.3MB, time=20.27 memory used=1398.9MB, alloc=492.3MB, time=22.19 memory used=1506.7MB, alloc=516.3MB, time=24.10 memory used=1611.0MB, alloc=516.3MB, time=26.06 memory used=1697.3MB, alloc=516.3MB, time=27.48 memory used=1810.4MB, alloc=516.3MB, time=29.86 memory used=1889.7MB, alloc=516.3MB, time=31.47 memory used=1949.4MB, alloc=516.3MB, time=32.54 memory used=2026.7MB, alloc=540.3MB, time=34.26 memory used=2089.6MB, alloc=540.3MB, time=35.60 memory used=2147.4MB, alloc=540.3MB, time=36.79 memory used=2199.2MB, alloc=540.3MB, time=38.14 memory used=2239.4MB, alloc=540.3MB, time=39.11 memory used=2448.8MB, alloc=564.3MB, time=42.68 memory used=2655.0MB, alloc=588.3MB, time=46.46 memory used=2841.5MB, alloc=612.3MB, time=50.35 memory used=3001.5MB, alloc=636.3MB, time=53.69 memory used=3148.0MB, alloc=636.3MB, time=56.99 memory used=3280.1MB, alloc=636.3MB, time=59.88 memory used=3426.7MB, alloc=660.3MB, time=63.04 memory used=3538.6MB, alloc=660.3MB, time=65.46 memory used=3698.9MB, alloc=660.3MB, time=69.33 memory used=3803.6MB, alloc=660.3MB, time=71.74 memory used=3921.9MB, alloc=660.3MB, time=74.99 memory used=4244.5MB, alloc=684.3MB, time=81.94 memory used=4596.1MB, alloc=708.3MB, time=89.13 memory used=4971.3MB, alloc=732.3MB, time=95.67 memory used=5305.0MB, alloc=756.3MB, time=102.47 memory used=5675.1MB, alloc=780.3MB, time=110.52 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428244251 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 2 3 3 3 2 F := [7 y z - 8 x - 6 y , 9 x z - 12 y z - 5 x, -5 y z + 2 z - 6 y ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 2 2 2 2 G := [-x - 11 y + y z, 2 x y - 14 x y + 4, 10 x y + 7 y z - 2 z ] > Problem := [F,G]; Problem := [ 2 2 2 2 2 2 3 3 3 2 [7 y z - 8 x - 6 y , 9 x z - 12 y z - 5 x, -5 y z + 2 z - 6 y ], 4 3 2 2 2 2 [-x - 11 y + y z, 2 x y - 14 x y + 4, 10 x y + 7 y z - 2 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.17 memory used=26.0MB, alloc=37.0MB, time=0.47 memory used=46.8MB, alloc=61.0MB, time=0.76 memory used=87.6MB, alloc=61.0MB, time=1.24 memory used=130.5MB, alloc=69.0MB, time=1.69 memory used=182.2MB, alloc=69.0MB, time=2.31 memory used=232.4MB, alloc=69.0MB, time=2.82 memory used=278.1MB, alloc=93.0MB, time=3.38 memory used=345.1MB, alloc=93.0MB, time=4.22 memory used=417.6MB, alloc=355.1MB, time=6.89 memory used=460.5MB, alloc=355.1MB, time=7.04 memory used=521.4MB, alloc=355.1MB, time=8.33 memory used=596.3MB, alloc=355.1MB, time=9.02 memory used=665.8MB, alloc=355.1MB, time=10.35 memory used=714.5MB, alloc=355.1MB, time=10.67 memory used=786.5MB, alloc=355.1MB, time=11.56 memory used=843.2MB, alloc=379.1MB, time=12.00 memory used=904.9MB, alloc=379.1MB, time=12.33 memory used=960.4MB, alloc=379.1MB, time=12.55 memory used=1003.8MB, alloc=379.1MB, time=12.70 memory used=1057.1MB, alloc=379.1MB, time=12.95 memory used=1120.6MB, alloc=379.1MB, time=13.32 memory used=1166.2MB, alloc=379.1MB, time=13.48 memory used=1220.7MB, alloc=379.1MB, time=13.71 memory used=1266.5MB, alloc=379.1MB, time=13.87 memory used=1324.2MB, alloc=379.1MB, time=14.76 memory used=1371.1MB, alloc=379.1MB, time=14.92 memory used=1413.2MB, alloc=379.1MB, time=15.06 memory used=1459.1MB, alloc=379.1MB, time=15.19 memory used=1550.8MB, alloc=379.1MB, time=16.02 memory used=1596.2MB, alloc=379.1MB, time=16.19 memory used=1644.3MB, alloc=379.1MB, time=16.35 memory used=1684.8MB, alloc=379.1MB, time=16.48 memory used=1767.8MB, alloc=379.1MB, time=29.36 memory used=1839.8MB, alloc=379.1MB, time=30.12 memory used=1882.8MB, alloc=379.1MB, time=30.29 memory used=1936.5MB, alloc=379.1MB, time=30.47 memory used=1971.4MB, alloc=379.1MB, time=30.62 memory used=2006.9MB, alloc=379.1MB, time=30.77 memory used=2046.1MB, alloc=379.1MB, time=30.91 memory used=2088.7MB, alloc=379.1MB, time=31.06 memory used=2136.0MB, alloc=379.1MB, time=31.22 memory used=2186.7MB, alloc=379.1MB, time=31.36 memory used=2238.7MB, alloc=379.1MB, time=31.52 memory used=2284.0MB, alloc=379.1MB, time=31.65 memory used=2314.1MB, alloc=379.1MB, time=31.78 memory used=2344.9MB, alloc=379.1MB, time=31.90 memory used=2377.4MB, alloc=379.1MB, time=32.02 memory used=2411.6MB, alloc=379.1MB, time=32.15 memory used=2447.3MB, alloc=379.1MB, time=32.27 memory used=2484.3MB, alloc=379.1MB, time=32.40 memory used=2522.7MB, alloc=379.1MB, time=32.52 memory used=2562.2MB, alloc=379.1MB, time=32.64 memory used=2603.9MB, alloc=379.1MB, time=32.76 memory used=2647.7MB, alloc=379.1MB, time=32.89 memory used=2693.1MB, alloc=379.1MB, time=33.01 memory used=2741.0MB, alloc=379.1MB, time=33.15 memory used=2791.6MB, alloc=379.1MB, time=33.29 memory used=2849.8MB, alloc=379.1MB, time=33.43 memory used=2980.8MB, alloc=379.1MB, time=33.96 memory used=3026.4MB, alloc=379.1MB, time=34.23 memory used=3080.1MB, alloc=379.1MB, time=34.65 memory used=3131.8MB, alloc=379.1MB, time=34.82 memory used=3192.5MB, alloc=379.1MB, time=35.31 memory used=3275.4MB, alloc=379.1MB, time=40.95 memory used=3317.3MB, alloc=379.1MB, time=41.12 memory used=3368.9MB, alloc=379.1MB, time=41.29 memory used=3403.4MB, alloc=379.1MB, time=41.44 memory used=3442.0MB, alloc=379.1MB, time=41.59 memory used=3484.9MB, alloc=379.1MB, time=41.74 memory used=3533.2MB, alloc=379.1MB, time=41.88 memory used=3586.0MB, alloc=379.1MB, time=42.03 memory used=3633.9MB, alloc=379.1MB, time=42.18 memory used=3665.8MB, alloc=379.1MB, time=42.32 memory used=3698.9MB, alloc=379.1MB, time=42.44 memory used=3733.4MB, alloc=379.1MB, time=42.57 memory used=3770.4MB, alloc=379.1MB, time=42.71 memory used=3809.7MB, alloc=379.1MB, time=42.83 memory used=3851.5MB, alloc=379.1MB, time=42.98 memory used=3895.6MB, alloc=379.1MB, time=43.10 memory used=3944.2MB, alloc=379.1MB, time=43.22 memory used=4005.5MB, alloc=379.1MB, time=43.56 memory used=4048.7MB, alloc=379.1MB, time=43.86 memory used=4119.3MB, alloc=379.1MB, time=44.40 memory used=4183.8MB, alloc=379.1MB, time=44.60 memory used=4228.7MB, alloc=379.1MB, time=44.73 memory used=4337.3MB, alloc=379.1MB, time=48.05 memory used=4403.2MB, alloc=379.1MB, time=48.57 memory used=4453.6MB, alloc=379.1MB, time=48.76 memory used=4498.4MB, alloc=379.1MB, time=48.92 memory used=4560.6MB, alloc=379.1MB, time=54.97 memory used=4630.4MB, alloc=403.1MB, time=86.11 memory used=4746.2MB, alloc=403.1MB, time=87.92 memory used=4802.7MB, alloc=403.1MB, time=88.14 memory used=4866.5MB, alloc=403.1MB, time=88.36 memory used=4933.8MB, alloc=403.1MB, time=88.56 memory used=4978.3MB, alloc=403.1MB, time=88.74 memory used=5025.2MB, alloc=403.1MB, time=88.92 memory used=5076.7MB, alloc=403.1MB, time=89.09 memory used=5131.2MB, alloc=403.1MB, time=89.27 memory used=5190.7MB, alloc=403.1MB, time=89.45 memory used=5253.1MB, alloc=403.1MB, time=89.64 memory used=5320.6MB, alloc=403.1MB, time=89.83 memory used=5393.2MB, alloc=403.1MB, time=90.02 memory used=5462.3MB, alloc=403.1MB, time=90.21 memory used=5510.0MB, alloc=403.1MB, time=90.36 memory used=5550.3MB, alloc=403.1MB, time=90.51 memory used=5591.8MB, alloc=403.1MB, time=90.65 memory used=5634.3MB, alloc=403.1MB, time=90.79 memory used=5677.4MB, alloc=403.1MB, time=90.95 memory used=5721.0MB, alloc=403.1MB, time=91.09 memory used=5765.2MB, alloc=403.1MB, time=91.23 memory used=5812.6MB, alloc=403.1MB, time=91.39 memory used=5860.6MB, alloc=403.1MB, time=91.53 memory used=5908.9MB, alloc=403.1MB, time=91.73 memory used=5957.8MB, alloc=403.1MB, time=91.88 memory used=6009.9MB, alloc=403.1MB, time=92.02 memory used=6062.4MB, alloc=403.1MB, time=92.16 memory used=6115.3MB, alloc=403.1MB, time=92.31 memory used=6171.4MB, alloc=403.1MB, time=92.46 memory used=6227.9MB, alloc=403.1MB, time=92.61 memory used=6287.5MB, alloc=403.1MB, time=92.77 memory used=6347.3MB, alloc=403.1MB, time=92.92 memory used=6407.5MB, alloc=403.1MB, time=93.07 memory used=6470.5MB, alloc=403.1MB, time=93.24 memory used=6533.9MB, alloc=403.1MB, time=93.39 memory used=6599.9MB, alloc=403.1MB, time=93.55 memory used=6668.9MB, alloc=403.1MB, time=93.71 memory used=6739.4MB, alloc=403.1MB, time=93.87 memory used=6822.1MB, alloc=403.1MB, time=94.05 memory used=6906.1MB, alloc=403.1MB, time=94.23 memory used=7017.2MB, alloc=403.1MB, time=94.44 memory used=7150.6MB, alloc=403.1MB, time=94.80 memory used=7290.0MB, alloc=403.1MB, time=95.07 memory used=7435.5MB, alloc=403.1MB, time=95.34 memory used=7590.3MB, alloc=403.1MB, time=95.63 memory used=7753.5MB, alloc=403.1MB, time=95.92 memory used=7928.7MB, alloc=403.1MB, time=96.22 memory used=8124.8MB, alloc=403.1MB, time=96.53 memory used=8307.2MB, alloc=403.1MB, time=98.34 memory used=8427.7MB, alloc=403.1MB, time=99.54 memory used=8548.4MB, alloc=403.1MB, time=100.75 memory used=8670.4MB, alloc=403.1MB, time=102.49 memory used=8790.8MB, alloc=403.1MB, time=104.43 memory used=8915.4MB, alloc=403.1MB, time=106.89 memory used=9037.5MB, alloc=403.1MB, time=109.59 memory used=9157.2MB, alloc=403.1MB, time=112.78 memory used=9278.6MB, alloc=403.1MB, time=116.09 memory used=9399.7MB, alloc=403.1MB, time=120.22 memory used=9521.6MB, alloc=403.1MB, time=124.52 memory used=9643.0MB, alloc=403.1MB, time=129.32 memory used=9764.7MB, alloc=403.1MB, time=134.51 memory used=9889.4MB, alloc=403.1MB, time=140.80 memory used=10012.2MB, alloc=403.1MB, time=147.04 memory used=10136.7MB, alloc=403.1MB, time=153.25 memory used=10258.8MB, alloc=403.1MB, time=155.17 memory used=10381.9MB, alloc=403.1MB, time=157.59 memory used=10464.5MB, alloc=403.1MB, time=158.05 memory used=10520.3MB, alloc=403.1MB, time=158.26 memory used=10579.1MB, alloc=403.1MB, time=158.45 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428244551 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 2 3 3 2 F := [14 x - x z - 14 x y z , -10 x y - 3 y z + 9 y z, 3 3 8 x y + 19 y z - 18 x y] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 2 G := [-17 y + 12 y z + 3 y , 19 x y - 2 x y + 9 y, 2 2 2 15 x z - 11 x y z - 9 z ] > Problem := [F,G]; 4 3 2 3 3 2 Problem := [[14 x - x z - 14 x y z , -10 x y - 3 y z + 9 y z, 3 3 3 2 2 8 x y + 19 y z - 18 x y], [-17 y + 12 y z + 3 y , 2 2 2 2 2 2 19 x y - 2 x y + 9 y, 15 x z - 11 x y z - 9 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.4MB, alloc=32.3MB, time=0.49 memory used=47.5MB, alloc=32.3MB, time=0.78 memory used=67.9MB, alloc=32.3MB, time=1.08 memory used=86.9MB, alloc=56.3MB, time=1.38 memory used=125.7MB, alloc=60.3MB, time=1.96 memory used=164.0MB, alloc=84.3MB, time=2.55 memory used=218.8MB, alloc=84.3MB, time=3.37 memory used=277.0MB, alloc=92.3MB, time=4.28 memory used=336.0MB, alloc=116.3MB, time=5.22 memory used=416.8MB, alloc=116.3MB, time=6.53 memory used=497.8MB, alloc=116.3MB, time=7.77 memory used=577.5MB, alloc=140.3MB, time=9.04 memory used=659.9MB, alloc=396.3MB, time=10.41 memory used=759.6MB, alloc=420.3MB, time=12.14 memory used=882.2MB, alloc=420.3MB, time=14.13 memory used=1006.7MB, alloc=420.3MB, time=16.26 memory used=1069.1MB, alloc=420.3MB, time=16.64 memory used=1188.1MB, alloc=444.3MB, time=18.80 memory used=1314.3MB, alloc=444.3MB, time=20.31 memory used=1464.9MB, alloc=468.3MB, time=22.83 memory used=1621.7MB, alloc=468.3MB, time=25.75 memory used=1774.4MB, alloc=492.3MB, time=28.51 memory used=1895.4MB, alloc=516.3MB, time=30.25 memory used=2019.0MB, alloc=540.3MB, time=32.42 memory used=2137.1MB, alloc=540.3MB, time=34.54 memory used=2229.7MB, alloc=540.3MB, time=35.84 memory used=2333.9MB, alloc=540.3MB, time=37.87 memory used=2421.0MB, alloc=564.3MB, time=39.32 memory used=2521.3MB, alloc=564.3MB, time=41.31 memory used=2623.5MB, alloc=564.3MB, time=43.67 memory used=2712.7MB, alloc=564.3MB, time=45.71 memory used=2787.3MB, alloc=564.3MB, time=47.34 memory used=2856.4MB, alloc=564.3MB, time=48.98 memory used=2916.1MB, alloc=564.3MB, time=50.18 memory used=2973.5MB, alloc=564.3MB, time=51.29 memory used=3029.9MB, alloc=564.3MB, time=52.23 memory used=3097.2MB, alloc=564.3MB, time=53.79 memory used=3339.2MB, alloc=588.3MB, time=58.74 memory used=3539.1MB, alloc=612.3MB, time=62.08 memory used=3779.3MB, alloc=636.3MB, time=67.33 memory used=3949.1MB, alloc=660.3MB, time=70.89 memory used=4089.8MB, alloc=684.3MB, time=73.66 memory used=4244.2MB, alloc=684.3MB, time=76.73 memory used=4420.5MB, alloc=708.3MB, time=80.59 memory used=4567.8MB, alloc=708.3MB, time=84.45 memory used=4735.0MB, alloc=708.3MB, time=88.52 memory used=4878.7MB, alloc=708.3MB, time=92.37 memory used=5038.0MB, alloc=708.3MB, time=96.86 memory used=5143.2MB, alloc=708.3MB, time=99.32 memory used=5248.8MB, alloc=708.3MB, time=101.74 memory used=5377.5MB, alloc=732.3MB, time=104.33 memory used=5523.5MB, alloc=732.3MB, time=106.84 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428244851 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; F := 2 2 3 4 2 3 3 2 [-6 x y z + 6 x y - 5 x, 16 y z + 15 z - 16 y z, -y z - 13 x - 9 y ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 3 2 G := [-9 y z + 17 y z - 9 y z , -9 y z - 4 x y - 15 x, 4 2 3 -9 x + 17 x y z - 10 y z] > Problem := [F,G]; Problem := [ 2 2 3 4 2 3 3 2 [-6 x y z + 6 x y - 5 x, 16 y z + 15 z - 16 y z, -y z - 13 x - 9 y ] 3 2 2 2 3 2 , [-9 y z + 17 y z - 9 y z , -9 y z - 4 x y - 15 x, 4 2 3 -9 x + 17 x y z - 10 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.1MB, alloc=32.3MB, time=0.49 memory used=46.7MB, alloc=56.3MB, time=0.81 memory used=87.3MB, alloc=60.3MB, time=1.42 memory used=131.2MB, alloc=68.3MB, time=1.91 memory used=171.7MB, alloc=68.3MB, time=2.45 memory used=216.9MB, alloc=92.3MB, time=3.05 memory used=281.1MB, alloc=92.3MB, time=4.03 memory used=343.3MB, alloc=116.3MB, time=4.99 memory used=408.5MB, alloc=372.3MB, time=5.91 memory used=483.7MB, alloc=372.3MB, time=6.61 memory used=582.3MB, alloc=396.3MB, time=7.74 memory used=699.8MB, alloc=396.3MB, time=9.11 memory used=816.6MB, alloc=420.3MB, time=10.64 memory used=943.8MB, alloc=444.3MB, time=12.62 memory used=1046.7MB, alloc=444.3MB, time=14.19 memory used=1160.3MB, alloc=444.3MB, time=15.58 memory used=1270.5MB, alloc=468.3MB, time=17.02 memory used=1372.6MB, alloc=468.3MB, time=18.59 memory used=1465.2MB, alloc=468.3MB, time=20.04 memory used=1568.2MB, alloc=468.3MB, time=21.27 memory used=1656.8MB, alloc=492.3MB, time=22.64 memory used=1740.9MB, alloc=492.3MB, time=23.88 memory used=1819.9MB, alloc=492.3MB, time=25.16 memory used=1901.4MB, alloc=492.3MB, time=26.30 memory used=1967.2MB, alloc=492.3MB, time=27.45 memory used=2044.0MB, alloc=492.3MB, time=28.77 memory used=2104.4MB, alloc=492.3MB, time=29.87 memory used=2165.6MB, alloc=492.3MB, time=31.00 memory used=2216.3MB, alloc=492.3MB, time=31.99 memory used=2268.9MB, alloc=492.3MB, time=33.12 memory used=2332.6MB, alloc=492.3MB, time=34.26 memory used=2372.8MB, alloc=516.3MB, time=35.14 memory used=2430.7MB, alloc=516.3MB, time=36.14 memory used=2500.5MB, alloc=516.3MB, time=37.39 memory used=2557.3MB, alloc=516.3MB, time=38.58 memory used=2768.2MB, alloc=540.3MB, time=42.12 memory used=2949.8MB, alloc=564.3MB, time=45.29 memory used=3122.4MB, alloc=588.3MB, time=48.14 memory used=3300.3MB, alloc=612.3MB, time=51.06 memory used=3453.2MB, alloc=612.3MB, time=53.55 memory used=3665.3MB, alloc=612.3MB, time=55.37 memory used=3847.8MB, alloc=612.3MB, time=57.02 memory used=3999.7MB, alloc=612.3MB, time=58.16 memory used=4158.1MB, alloc=612.3MB, time=62.95 memory used=4383.1MB, alloc=612.3MB, time=65.25 memory used=4567.7MB, alloc=636.3MB, time=70.67 memory used=4742.0MB, alloc=636.3MB, time=72.85 memory used=4884.8MB, alloc=660.3MB, time=74.92 memory used=5076.7MB, alloc=660.3MB, time=76.47 memory used=5268.6MB, alloc=660.3MB, time=80.59 memory used=5486.9MB, alloc=660.3MB, time=82.89 memory used=5622.0MB, alloc=660.3MB, time=86.20 memory used=5737.0MB, alloc=660.3MB, time=91.01 memory used=5919.0MB, alloc=660.3MB, time=92.67 memory used=6039.0MB, alloc=660.3MB, time=94.88 memory used=6122.1MB, alloc=660.3MB, time=96.90 memory used=6453.3MB, alloc=684.3MB, time=102.15 memory used=6806.0MB, alloc=708.3MB, time=108.06 memory used=7131.1MB, alloc=732.3MB, time=114.04 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428245151 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 4 2 3 2 2 F := [7 y z + 4 x - 10 y z , 13 y - 3 x + 18, 7 x z - 2 y z - 13 x y] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 3 4 2 G := [-12 x y - 6 y z + 13 y , 14 y - 18 x z + x y, 3 2 2 -3 x y + 4 x y z - 20 y z] > Problem := [F,G]; Problem := [ 3 3 2 4 2 3 2 2 [7 y z + 4 x - 10 y z , 13 y - 3 x + 18, 7 x z - 2 y z - 13 x y], [ 3 3 3 4 2 -12 x y - 6 y z + 13 y , 14 y - 18 x z + x y, 3 2 2 -3 x y + 4 x y z - 20 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=25.7MB, alloc=32.3MB, time=0.49 memory used=46.2MB, alloc=60.3MB, time=0.79 memory used=87.2MB, alloc=60.3MB, time=1.35 memory used=129.2MB, alloc=68.3MB, time=1.92 memory used=201.8MB, alloc=100.3MB, time=2.83 memory used=272.1MB, alloc=100.3MB, time=3.70 memory used=338.2MB, alloc=380.3MB, time=4.59 memory used=437.0MB, alloc=380.3MB, time=5.90 memory used=503.6MB, alloc=380.3MB, time=6.40 memory used=569.6MB, alloc=380.3MB, time=6.87 memory used=610.9MB, alloc=380.3MB, time=7.02 memory used=664.8MB, alloc=380.3MB, time=7.27 memory used=733.6MB, alloc=380.3MB, time=9.06 memory used=773.2MB, alloc=380.3MB, time=9.22 memory used=834.0MB, alloc=380.3MB, time=9.72 memory used=940.0MB, alloc=404.3MB, time=10.81 memory used=1059.2MB, alloc=428.3MB, time=12.46 memory used=1197.5MB, alloc=428.3MB, time=13.90 memory used=1292.1MB, alloc=428.3MB, time=15.09 memory used=1430.7MB, alloc=428.3MB, time=16.38 memory used=1563.3MB, alloc=452.3MB, time=17.87 memory used=1689.0MB, alloc=452.3MB, time=19.31 memory used=1782.3MB, alloc=452.3MB, time=20.64 memory used=1857.6MB, alloc=452.3MB, time=20.93 memory used=1914.8MB, alloc=452.3MB, time=21.21 memory used=1985.5MB, alloc=452.3MB, time=21.49 memory used=2146.7MB, alloc=452.3MB, time=23.77 memory used=2220.6MB, alloc=452.3MB, time=24.09 memory used=2352.1MB, alloc=452.3MB, time=25.20 memory used=2490.6MB, alloc=452.3MB, time=26.67 memory used=2591.9MB, alloc=476.3MB, time=28.06 memory used=2677.5MB, alloc=476.3MB, time=29.18 memory used=2826.3MB, alloc=476.3MB, time=30.86 memory used=2934.8MB, alloc=476.3MB, time=32.23 memory used=3015.4MB, alloc=476.3MB, time=33.51 memory used=3102.3MB, alloc=476.3MB, time=34.68 memory used=3169.2MB, alloc=476.3MB, time=35.73 memory used=3243.1MB, alloc=500.3MB, time=36.85 memory used=3313.4MB, alloc=500.3MB, time=37.91 memory used=3380.3MB, alloc=500.3MB, time=39.06 memory used=3469.8MB, alloc=500.3MB, time=39.93 memory used=3555.0MB, alloc=500.3MB, time=40.38 memory used=3664.0MB, alloc=500.3MB, time=41.06 memory used=3786.5MB, alloc=500.3MB, time=44.62 memory used=3874.7MB, alloc=500.3MB, time=45.07 memory used=3990.3MB, alloc=500.3MB, time=46.11 memory used=4083.3MB, alloc=500.3MB, time=47.05 memory used=4135.9MB, alloc=500.3MB, time=47.94 memory used=4216.3MB, alloc=500.3MB, time=49.27 memory used=4325.2MB, alloc=500.3MB, time=50.72 memory used=4395.1MB, alloc=500.3MB, time=51.90 memory used=4449.8MB, alloc=500.3MB, time=52.80 memory used=4546.2MB, alloc=500.3MB, time=54.06 memory used=4750.0MB, alloc=524.3MB, time=57.14 memory used=4947.7MB, alloc=548.3MB, time=59.77 memory used=5111.6MB, alloc=572.3MB, time=62.88 memory used=5227.2MB, alloc=572.3MB, time=63.50 memory used=5382.2MB, alloc=572.3MB, time=70.85 memory used=5517.1MB, alloc=572.3MB, time=71.66 memory used=5643.6MB, alloc=572.3MB, time=72.32 memory used=5734.8MB, alloc=572.3MB, time=72.89 memory used=5851.4MB, alloc=572.3MB, time=73.47 memory used=6158.7MB, alloc=596.3MB, time=76.23 memory used=6376.4MB, alloc=596.3MB, time=78.78 memory used=6505.2MB, alloc=596.3MB, time=79.84 memory used=6641.9MB, alloc=596.3MB, time=81.32 memory used=6819.7MB, alloc=596.3MB, time=84.98 memory used=6943.5MB, alloc=596.3MB, time=85.76 memory used=7055.4MB, alloc=596.3MB, time=86.45 memory used=7291.6MB, alloc=596.3MB, time=87.41 memory used=7444.4MB, alloc=596.3MB, time=89.42 memory used=7626.7MB, alloc=596.3MB, time=90.84 memory used=7950.4MB, alloc=620.3MB, time=102.66 memory used=8082.1MB, alloc=620.3MB, time=103.41 memory used=8226.0MB, alloc=620.3MB, time=104.14 memory used=8345.4MB, alloc=620.3MB, time=104.80 memory used=8459.1MB, alloc=620.3MB, time=105.41 memory used=8596.0MB, alloc=620.3MB, time=106.03 memory used=8780.1MB, alloc=620.3MB, time=106.92 memory used=8999.5MB, alloc=620.3MB, time=109.09 memory used=9217.5MB, alloc=620.3MB, time=111.50 memory used=9395.9MB, alloc=620.3MB, time=114.03 memory used=9542.7MB, alloc=644.3MB, time=116.93 memory used=9675.6MB, alloc=644.3MB, time=119.33 memory used=9800.3MB, alloc=668.3MB, time=121.48 memory used=9940.6MB, alloc=692.3MB, time=123.30 memory used=10073.2MB, alloc=692.3MB, time=125.20 memory used=10182.5MB, alloc=716.3MB, time=127.03 memory used=10270.3MB, alloc=716.3MB, time=129.10 memory used=10674.3MB, alloc=740.3MB, time=133.98 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428245451 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 4 2 2 F := [9 y - 10 x - 6 y z, -5 x - 10 x z - 14 y z, 3 3 2 17 x y + 20 y z + 20 y z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; G := [ 3 3 3 3 3 4 2 13 x y z + 20 y - 15 z , 10 x y + 11 y + 16 x z, -9 x z + 6 y - 12 z ] > Problem := [F,G]; 4 3 4 2 2 Problem := [[9 y - 10 x - 6 y z, -5 x - 10 x z - 14 y z, 3 3 2 17 x y + 20 y z + 20 y z ], [ 3 3 3 3 3 4 2 13 x y z + 20 y - 15 z , 10 x y + 11 y + 16 x z, -9 x z + 6 y - 12 z ] ] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.18 memory used=25.8MB, alloc=32.3MB, time=0.44 memory used=42.7MB, alloc=32.3MB, time=0.53 memory used=64.3MB, alloc=32.3MB, time=0.83 memory used=76.2MB, alloc=32.3MB, time=0.87 memory used=96.7MB, alloc=32.3MB, time=1.01 memory used=120.6MB, alloc=36.4MB, time=1.31 memory used=140.7MB, alloc=60.4MB, time=1.59 memory used=189.6MB, alloc=68.4MB, time=2.67 memory used=249.4MB, alloc=68.8MB, time=3.18 memory used=275.2MB, alloc=68.8MB, time=3.26 memory used=301.8MB, alloc=68.8MB, time=3.34 memory used=323.5MB, alloc=68.8MB, time=3.42 memory used=348.5MB, alloc=68.8MB, time=3.50 memory used=378.5MB, alloc=68.8MB, time=3.57 memory used=414.5MB, alloc=68.8MB, time=3.82 memory used=470.9MB, alloc=68.8MB, time=4.45 memory used=501.2MB, alloc=68.8MB, time=4.58 memory used=522.6MB, alloc=68.8MB, time=4.66 memory used=547.6MB, alloc=68.8MB, time=4.73 memory used=600.2MB, alloc=68.8MB, time=5.54 memory used=625.0MB, alloc=68.8MB, time=5.63 memory used=647.8MB, alloc=68.8MB, time=5.70 memory used=669.3MB, alloc=68.8MB, time=5.78 memory used=695.0MB, alloc=68.8MB, time=5.85 memory used=720.6MB, alloc=68.8MB, time=5.92 memory used=739.0MB, alloc=68.8MB, time=5.98 memory used=775.9MB, alloc=68.8MB, time=6.46 memory used=823.6MB, alloc=68.8MB, time=6.83 memory used=863.1MB, alloc=68.8MB, time=7.29 memory used=895.9MB, alloc=68.8MB, time=7.51 memory used=947.1MB, alloc=68.8MB, time=9.18 memory used=969.8MB, alloc=68.8MB, time=9.26 memory used=987.3MB, alloc=68.8MB, time=9.33 memory used=1019.2MB, alloc=68.8MB, time=9.47 memory used=1060.0MB, alloc=68.8MB, time=12.22 memory used=1095.8MB, alloc=68.8MB, time=14.60 memory used=1118.8MB, alloc=68.8MB, time=14.68 memory used=1137.2MB, alloc=68.8MB, time=14.76 memory used=1156.3MB, alloc=68.8MB, time=14.83 memory used=1179.6MB, alloc=68.8MB, time=14.90 memory used=1198.8MB, alloc=68.8MB, time=14.96 memory used=1233.7MB, alloc=68.8MB, time=15.12 memory used=1277.6MB, alloc=68.8MB, time=19.94 memory used=1305.5MB, alloc=68.8MB, time=20.28 memory used=1329.1MB, alloc=68.8MB, time=20.35 memory used=1346.1MB, alloc=68.8MB, time=20.42 memory used=1366.2MB, alloc=68.8MB, time=20.50 memory used=1390.8MB, alloc=68.8MB, time=20.58 memory used=1413.2MB, alloc=68.8MB, time=20.86 memory used=1446.9MB, alloc=68.8MB, time=21.13 memory used=1498.6MB, alloc=68.8MB, time=21.62 memory used=1548.4MB, alloc=92.8MB, time=22.11 memory used=1621.9MB, alloc=92.8MB, time=22.98 memory used=1688.7MB, alloc=92.8MB, time=28.86 memory used=1723.9MB, alloc=92.8MB, time=28.98 memory used=1752.9MB, alloc=92.8MB, time=29.07 memory used=1790.0MB, alloc=92.8MB, time=29.17 memory used=1837.5MB, alloc=92.8MB, time=29.56 memory used=1919.8MB, alloc=92.8MB, time=30.17 memory used=1995.7MB, alloc=92.8MB, time=30.85 memory used=2054.1MB, alloc=372.8MB, time=31.64 memory used=2144.1MB, alloc=372.8MB, time=32.76 memory used=2238.8MB, alloc=396.8MB, time=33.74 memory used=2311.0MB, alloc=396.8MB, time=34.11 memory used=2388.1MB, alloc=396.8MB, time=34.56 memory used=2451.0MB, alloc=396.8MB, time=34.91 memory used=2518.6MB, alloc=396.8MB, time=35.22 memory used=2599.9MB, alloc=396.8MB, time=35.83 memory used=2707.4MB, alloc=396.8MB, time=46.92 memory used=2794.1MB, alloc=396.8MB, time=47.36 memory used=2851.7MB, alloc=396.8MB, time=47.55 memory used=2893.7MB, alloc=396.8MB, time=47.72 memory used=2943.7MB, alloc=396.8MB, time=47.90 memory used=3002.6MB, alloc=396.8MB, time=48.07 memory used=3058.1MB, alloc=396.8MB, time=48.24 memory used=3095.5MB, alloc=396.8MB, time=48.39 memory used=3135.9MB, alloc=396.8MB, time=48.55 memory used=3180.1MB, alloc=396.8MB, time=48.69 memory used=3227.8MB, alloc=396.8MB, time=48.83 memory used=3282.8MB, alloc=396.8MB, time=48.98 memory used=3355.3MB, alloc=396.8MB, time=49.40 memory used=3409.5MB, alloc=396.8MB, time=49.59 memory used=3477.7MB, alloc=396.8MB, time=50.01 memory used=3534.5MB, alloc=396.8MB, time=50.22 memory used=3593.1MB, alloc=396.8MB, time=50.41 memory used=3674.3MB, alloc=396.8MB, time=62.36 memory used=3738.7MB, alloc=420.8MB, time=93.64 memory used=3848.8MB, alloc=420.8MB, time=115.80 memory used=3972.8MB, alloc=420.8MB, time=116.71 memory used=4043.4MB, alloc=420.8MB, time=116.96 memory used=4105.6MB, alloc=420.8MB, time=117.18 memory used=4163.9MB, alloc=420.8MB, time=117.39 memory used=4232.6MB, alloc=420.8MB, time=117.61 memory used=4311.6MB, alloc=420.8MB, time=117.82 memory used=4384.6MB, alloc=420.8MB, time=118.03 memory used=4432.5MB, alloc=420.8MB, time=118.20 memory used=4483.4MB, alloc=420.8MB, time=118.36 memory used=4537.1MB, alloc=420.8MB, time=118.52 memory used=4594.2MB, alloc=420.8MB, time=118.69 memory used=4654.4MB, alloc=420.8MB, time=118.87 memory used=4718.9MB, alloc=420.8MB, time=119.04 memory used=4788.3MB, alloc=420.8MB, time=119.22 memory used=4862.9MB, alloc=420.8MB, time=119.41 memory used=4943.6MB, alloc=420.8MB, time=119.60 memory used=5143.6MB, alloc=420.8MB, time=120.20 memory used=5214.3MB, alloc=420.8MB, time=120.51 memory used=5299.3MB, alloc=420.8MB, time=121.00 memory used=5373.0MB, alloc=420.8MB, time=121.25 memory used=5462.7MB, alloc=420.8MB, time=121.76 memory used=5536.7MB, alloc=420.8MB, time=122.01 memory used=5635.7MB, alloc=420.8MB, time=131.65 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428245751 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 4 2 F := [-20 x y z - 16 x y + 7 y z, -18 x y - 7 z + 20 x , 3 3 2 20 x y + 13 x + 9 y z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 G := [-6 y z - 17 z, 15 x z + 10 x y z - 5, -20 x z + 11 x y + 18 x y z] > Problem := [F,G]; 2 2 2 4 2 Problem := [[-20 x y z - 16 x y + 7 y z, -18 x y - 7 z + 20 x , 3 3 2 20 x y + 13 x + 9 y z ], 2 2 2 2 2 [-6 y z - 17 z, 15 x z + 10 x y z - 5, -20 x z + 11 x y + 18 x y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.18 memory used=26.8MB, alloc=32.3MB, time=0.51 memory used=47.5MB, alloc=32.3MB, time=0.82 memory used=66.2MB, alloc=56.3MB, time=1.12 memory used=104.9MB, alloc=60.3MB, time=1.71 memory used=143.1MB, alloc=84.3MB, time=2.31 memory used=204.3MB, alloc=92.3MB, time=3.28 memory used=264.5MB, alloc=116.3MB, time=4.23 memory used=347.4MB, alloc=116.3MB, time=5.51 memory used=428.4MB, alloc=140.3MB, time=6.79 memory used=505.3MB, alloc=140.3MB, time=8.09 memory used=567.0MB, alloc=396.3MB, time=9.10 memory used=669.5MB, alloc=420.3MB, time=10.79 memory used=792.7MB, alloc=444.3MB, time=12.85 memory used=938.4MB, alloc=468.3MB, time=15.47 memory used=1072.0MB, alloc=492.3MB, time=17.85 memory used=1190.1MB, alloc=492.3MB, time=19.95 memory used=1313.4MB, alloc=516.3MB, time=22.03 memory used=1423.2MB, alloc=516.3MB, time=23.95 memory used=1529.3MB, alloc=516.3MB, time=25.94 memory used=1641.3MB, alloc=516.3MB, time=28.08 memory used=1725.5MB, alloc=516.3MB, time=29.65 memory used=1814.9MB, alloc=516.3MB, time=31.49 memory used=1901.8MB, alloc=516.3MB, time=33.41 memory used=1974.5MB, alloc=516.3MB, time=34.85 memory used=2046.6MB, alloc=540.3MB, time=36.13 memory used=2111.0MB, alloc=540.3MB, time=37.64 memory used=2162.9MB, alloc=540.3MB, time=38.70 memory used=2210.2MB, alloc=540.3MB, time=39.60 memory used=2263.0MB, alloc=540.3MB, time=40.86 memory used=2326.6MB, alloc=540.3MB, time=42.48 memory used=2366.7MB, alloc=540.3MB, time=43.53 memory used=2573.8MB, alloc=564.3MB, time=47.27 memory used=2793.2MB, alloc=588.3MB, time=52.00 memory used=2997.0MB, alloc=612.3MB, time=56.19 memory used=3182.5MB, alloc=636.3MB, time=60.08 memory used=3364.5MB, alloc=660.3MB, time=63.65 memory used=3549.8MB, alloc=684.3MB, time=67.35 memory used=3697.7MB, alloc=684.3MB, time=70.57 memory used=3861.7MB, alloc=684.3MB, time=74.57 memory used=3997.1MB, alloc=684.3MB, time=77.65 memory used=4122.2MB, alloc=684.3MB, time=80.15 memory used=4222.9MB, alloc=708.3MB, time=82.11 memory used=4361.0MB, alloc=708.3MB, time=85.91 memory used=4481.7MB, alloc=708.3MB, time=89.03 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428246051 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 3 2 F := [13 x y z + 20 x - 15 z, -4 y z + 5 y + 9 x , 3 2 2 2 -5 x y + 9 x y z - 12 y z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; G := [ 2 2 3 2 2 2 3 2 2 4 x z + x y - 2 z, 7 x z - 18 x y + 12 x z, 18 y z - 12 x z + 20 y ] > Problem := [F,G]; 2 3 3 2 Problem := [[13 x y z + 20 x - 15 z, -4 y z + 5 y + 9 x , 3 2 2 2 -5 x y + 9 x y z - 12 y z ], [ 2 2 3 2 2 2 3 2 2 4 x z + x y - 2 z, 7 x z - 18 x y + 12 x z, 18 y z - 12 x z + 20 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.18 memory used=25.8MB, alloc=32.3MB, time=0.51 memory used=45.5MB, alloc=56.3MB, time=0.80 memory used=90.2MB, alloc=60.3MB, time=1.36 memory used=136.7MB, alloc=68.3MB, time=1.93 memory used=178.8MB, alloc=68.3MB, time=2.54 memory used=222.3MB, alloc=92.3MB, time=3.15 memory used=282.7MB, alloc=92.3MB, time=4.00 memory used=338.9MB, alloc=92.3MB, time=4.67 memory used=377.5MB, alloc=92.3MB, time=4.83 memory used=435.5MB, alloc=92.3MB, time=5.53 memory used=518.4MB, alloc=92.3MB, time=6.51 memory used=600.9MB, alloc=92.3MB, time=8.41 memory used=655.4MB, alloc=92.3MB, time=8.94 memory used=726.4MB, alloc=92.3MB, time=9.82 memory used=792.2MB, alloc=116.3MB, time=11.04 memory used=850.4MB, alloc=116.3MB, time=11.43 memory used=918.2MB, alloc=116.3MB, time=12.33 memory used=962.1MB, alloc=116.3MB, time=12.47 memory used=1034.4MB, alloc=372.3MB, time=13.43 memory used=1089.2MB, alloc=372.3MB, time=13.70 memory used=1132.8MB, alloc=372.3MB, time=13.85 memory used=1172.7MB, alloc=372.3MB, time=13.97 memory used=1208.0MB, alloc=372.3MB, time=14.07 memory used=1251.2MB, alloc=372.3MB, time=14.19 memory used=1325.6MB, alloc=372.3MB, time=14.89 memory used=1369.6MB, alloc=372.3MB, time=15.03 memory used=1449.3MB, alloc=372.3MB, time=15.77 memory used=1516.3MB, alloc=372.3MB, time=16.56 memory used=1602.7MB, alloc=396.3MB, time=17.75 memory used=1709.7MB, alloc=396.3MB, time=19.28 memory used=1824.5MB, alloc=396.3MB, time=20.78 memory used=1934.9MB, alloc=420.3MB, time=22.34 memory used=2058.2MB, alloc=444.3MB, time=24.18 memory used=2177.0MB, alloc=444.3MB, time=25.56 memory used=2297.2MB, alloc=444.3MB, time=27.29 memory used=2417.7MB, alloc=468.3MB, time=28.48 memory used=2528.8MB, alloc=468.3MB, time=30.13 memory used=2640.2MB, alloc=468.3MB, time=31.47 memory used=2738.6MB, alloc=468.3MB, time=32.03 memory used=2817.4MB, alloc=468.3MB, time=32.36 memory used=2901.2MB, alloc=468.3MB, time=32.65 memory used=3001.6MB, alloc=468.3MB, time=33.31 memory used=3075.1MB, alloc=468.3MB, time=33.62 memory used=3185.7MB, alloc=468.3MB, time=38.99 memory used=3269.2MB, alloc=468.3MB, time=39.31 memory used=3340.5MB, alloc=468.3MB, time=39.60 memory used=3430.3MB, alloc=468.3MB, time=39.97 memory used=3525.4MB, alloc=468.3MB, time=40.63 memory used=3602.9MB, alloc=468.3MB, time=40.97 memory used=3701.0MB, alloc=468.3MB, time=41.46 memory used=3780.3MB, alloc=468.3MB, time=41.79 memory used=3864.1MB, alloc=468.3MB, time=42.11 memory used=3996.6MB, alloc=468.3MB, time=47.75 memory used=4079.7MB, alloc=468.3MB, time=48.08 memory used=4143.3MB, alloc=468.3MB, time=48.36 memory used=4239.0MB, alloc=468.3MB, time=48.89 memory used=4318.1MB, alloc=468.3MB, time=49.23 memory used=4402.0MB, alloc=468.3MB, time=49.53 memory used=4502.2MB, alloc=468.3MB, time=50.18 memory used=4574.3MB, alloc=468.3MB, time=50.47 memory used=4702.7MB, alloc=468.3MB, time=56.11 memory used=4783.3MB, alloc=468.3MB, time=56.44 memory used=4860.5MB, alloc=468.3MB, time=56.71 memory used=4933.8MB, alloc=468.3MB, time=56.97 memory used=5026.9MB, alloc=468.3MB, time=57.45 memory used=5201.3MB, alloc=468.3MB, time=60.48 memory used=5380.6MB, alloc=468.3MB, time=63.31 memory used=5506.2MB, alloc=468.3MB, time=64.57 memory used=5675.9MB, alloc=468.3MB, time=70.91 memory used=5759.8MB, alloc=468.3MB, time=71.37 memory used=5838.4MB, alloc=468.3MB, time=71.78 memory used=5930.7MB, alloc=492.3MB, time=80.11 memory used=6032.6MB, alloc=492.3MB, time=82.41 memory used=6129.7MB, alloc=492.3MB, time=82.74 memory used=6207.8MB, alloc=492.3MB, time=83.05 memory used=6308.1MB, alloc=492.3MB, time=83.37 memory used=6500.6MB, alloc=492.3MB, time=85.24 memory used=6668.9MB, alloc=492.3MB, time=88.03 memory used=6789.8MB, alloc=492.3MB, time=89.08 memory used=6875.6MB, alloc=492.3MB, time=89.46 memory used=6966.6MB, alloc=492.3MB, time=89.81 memory used=7068.5MB, alloc=492.3MB, time=90.35 memory used=7157.9MB, alloc=492.3MB, time=90.71 memory used=7270.1MB, alloc=492.3MB, time=96.09 memory used=7358.9MB, alloc=492.3MB, time=96.45 memory used=7435.9MB, alloc=492.3MB, time=96.79 memory used=7538.6MB, alloc=492.3MB, time=97.33 memory used=7640.3MB, alloc=492.3MB, time=97.88 memory used=7733.1MB, alloc=492.3MB, time=98.24 memory used=7838.8MB, alloc=492.3MB, time=98.98 memory used=7921.7MB, alloc=492.3MB, time=99.35 memory used=8055.6MB, alloc=492.3MB, time=104.93 memory used=8159.3MB, alloc=492.3MB, time=105.39 memory used=8241.5MB, alloc=492.3MB, time=105.71 memory used=8342.0MB, alloc=492.3MB, time=106.28 memory used=8434.9MB, alloc=492.3MB, time=106.70 memory used=8527.9MB, alloc=492.3MB, time=107.04 memory used=8629.4MB, alloc=492.3MB, time=107.63 memory used=8711.1MB, alloc=492.3MB, time=107.99 memory used=8842.6MB, alloc=492.3MB, time=113.67 memory used=8934.7MB, alloc=492.3MB, time=114.04 memory used=9010.9MB, alloc=492.3MB, time=114.39 memory used=9122.5MB, alloc=492.3MB, time=114.95 memory used=9281.5MB, alloc=492.3MB, time=116.56 memory used=9433.5MB, alloc=492.3MB, time=127.27 memory used=9520.0MB, alloc=492.3MB, time=127.63 memory used=9592.0MB, alloc=492.3MB, time=127.94 memory used=9672.1MB, alloc=492.3MB, time=128.25 memory used=9839.6MB, alloc=492.3MB, time=129.15 memory used=9969.6MB, alloc=492.3MB, time=130.36 memory used=10092.3MB, alloc=492.3MB, time=132.02 memory used=10159.9MB, alloc=492.3MB, time=133.02 memory used=10238.7MB, alloc=516.3MB, time=134.32 memory used=10296.5MB, alloc=516.3MB, time=135.29 memory used=10361.9MB, alloc=516.3MB, time=136.48 memory used=10409.6MB, alloc=516.3MB, time=137.42 memory used=10468.7MB, alloc=516.3MB, time=138.53 memory used=10518.2MB, alloc=516.3MB, time=139.54 memory used=10603.8MB, alloc=516.3MB, time=140.61 memory used=10638.0MB, alloc=516.3MB, time=141.33 memory used=10679.0MB, alloc=516.3MB, time=142.12 memory used=10724.7MB, alloc=516.3MB, time=142.89 memory used=10787.0MB, alloc=516.3MB, time=144.96 memory used=10834.6MB, alloc=516.3MB, time=145.75 memory used=10966.8MB, alloc=516.3MB, time=146.89 memory used=11095.8MB, alloc=516.3MB, time=149.21 memory used=11193.9MB, alloc=516.3MB, time=149.71 memory used=11266.7MB, alloc=516.3MB, time=150.16 memory used=11358.1MB, alloc=516.3MB, time=150.61 memory used=11573.9MB, alloc=516.3MB, time=153.12 memory used=11665.1MB, alloc=516.3MB, time=153.66 memory used=11754.3MB, alloc=516.3MB, time=154.16 memory used=11834.3MB, alloc=516.3MB, time=154.61 memory used=11933.9MB, alloc=516.3MB, time=155.09 memory used=12216.6MB, alloc=516.3MB, time=162.95 memory used=12318.1MB, alloc=540.3MB, time=163.55 memory used=12436.3MB, alloc=540.3MB, time=164.08 memory used=12520.6MB, alloc=540.3MB, time=164.54 memory used=12621.2MB, alloc=540.3MB, time=165.03 memory used=12740.6MB, alloc=540.3MB, time=165.55 memory used=12963.7MB, alloc=540.3MB, time=166.19 memory used=13111.4MB, alloc=540.3MB, time=166.72 memory used=13372.4MB, alloc=540.3MB, time=168.35 memory used=13474.6MB, alloc=540.3MB, time=168.83 memory used=13608.5MB, alloc=540.3MB, time=169.79 memory used=13701.5MB, alloc=540.3MB, time=170.36 memory used=13826.0MB, alloc=540.3MB, time=170.92 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428246351 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 F := [16 x z - 4 x z - 18 y z, 10 x z + 20 y z + 8 y, 2 2 2 2 -4 x z + 2 y z - 16 y ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 3 3 G := [-3 x - y z + 10 y, -15 x y - 5 y z + 3, -3 x y + 16 y z - 17 x ] > Problem := [F,G]; 3 2 2 2 2 Problem := [[16 x z - 4 x z - 18 y z, 10 x z + 20 y z + 8 y, 2 2 2 2 -4 x z + 2 y z - 16 y ], 2 2 2 3 3 3 [-3 x - y z + 10 y, -15 x y - 5 y z + 3, -3 x y + 16 y z - 17 x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.5MB, alloc=32.3MB, time=0.50 memory used=47.4MB, alloc=32.3MB, time=0.80 memory used=65.4MB, alloc=56.3MB, time=1.09 memory used=104.8MB, alloc=60.3MB, time=1.64 memory used=143.0MB, alloc=84.3MB, time=2.23 memory used=207.2MB, alloc=92.3MB, time=3.21 memory used=273.1MB, alloc=92.3MB, time=4.12 memory used=335.9MB, alloc=116.3MB, time=5.10 memory used=420.5MB, alloc=372.3MB, time=6.44 memory used=505.4MB, alloc=396.3MB, time=7.75 memory used=612.7MB, alloc=396.3MB, time=9.36 memory used=719.6MB, alloc=420.3MB, time=11.05 memory used=851.1MB, alloc=444.3MB, time=13.17 memory used=976.4MB, alloc=444.3MB, time=14.59 memory used=1077.0MB, alloc=444.3MB, time=16.04 memory used=1219.6MB, alloc=444.3MB, time=17.75 memory used=1312.7MB, alloc=444.3MB, time=19.29 memory used=1390.7MB, alloc=444.3MB, time=19.64 memory used=1494.4MB, alloc=444.3MB, time=20.64 memory used=1627.8MB, alloc=444.3MB, time=22.62 memory used=1765.5MB, alloc=444.3MB, time=24.51 memory used=1874.8MB, alloc=444.3MB, time=26.21 memory used=2021.5MB, alloc=468.3MB, time=28.02 memory used=2127.5MB, alloc=468.3MB, time=29.86 memory used=2239.7MB, alloc=468.3MB, time=31.55 memory used=2360.5MB, alloc=492.3MB, time=33.62 memory used=2449.7MB, alloc=492.3MB, time=34.95 memory used=2546.8MB, alloc=516.3MB, time=36.52 memory used=2637.8MB, alloc=516.3MB, time=38.16 memory used=2707.5MB, alloc=516.3MB, time=39.20 memory used=2780.1MB, alloc=540.3MB, time=40.12 memory used=2845.2MB, alloc=540.3MB, time=41.38 memory used=2904.3MB, alloc=540.3MB, time=42.54 memory used=2962.4MB, alloc=540.3MB, time=43.56 memory used=3005.7MB, alloc=540.3MB, time=44.45 memory used=3043.8MB, alloc=540.3MB, time=45.28 memory used=3238.3MB, alloc=564.3MB, time=48.25 memory used=3435.8MB, alloc=588.3MB, time=51.42 memory used=3606.3MB, alloc=612.3MB, time=54.14 memory used=3744.0MB, alloc=636.3MB, time=56.46 memory used=3892.9MB, alloc=660.3MB, time=59.21 memory used=4020.0MB, alloc=660.3MB, time=61.07 memory used=4139.7MB, alloc=684.3MB, time=63.53 memory used=4255.3MB, alloc=684.3MB, time=65.93 memory used=4358.2MB, alloc=684.3MB, time=67.96 memory used=4436.1MB, alloc=684.3MB, time=70.02 memory used=4511.0MB, alloc=684.3MB, time=71.96 memory used=4866.6MB, alloc=708.3MB, time=77.63 memory used=5237.3MB, alloc=732.3MB, time=83.14 memory used=5633.4MB, alloc=756.3MB, time=88.24 memory used=5993.7MB, alloc=780.3MB, time=95.12 memory used=6289.4MB, alloc=804.3MB, time=100.58 memory used=6631.6MB, alloc=828.3MB, time=110.45 memory used=6803.9MB, alloc=852.3MB, time=112.08 memory used=7031.3MB, alloc=876.3MB, time=114.22 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428246651 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; F := 3 2 2 2 2 2 2 2 [-4 x y + 4 x y + 2 y, -20 x y + 11 x y + 2 y , -17 x z - 5 x - 6 y] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; G := [ 4 2 2 3 2 2 2 2 x + 18 x z - 3 y, -19 x z + 17 x y z - 4 y , 15 x y z - 18 x y z + 7 ] > Problem := [F,G]; Problem := [ 3 2 2 2 2 2 2 2 [-4 x y + 4 x y + 2 y, -20 x y + 11 x y + 2 y , -17 x z - 5 x - 6 y] , [ 4 2 2 3 2 2 2 2 x + 18 x z - 3 y, -19 x z + 17 x y z - 4 y , 15 x y z - 18 x y z + 7 ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.8MB, alloc=32.3MB, time=0.51 memory used=47.4MB, alloc=32.3MB, time=0.81 memory used=65.0MB, alloc=56.3MB, time=1.08 memory used=106.5MB, alloc=60.3MB, time=1.66 memory used=141.3MB, alloc=60.3MB, time=2.13 memory used=185.0MB, alloc=92.3MB, time=2.74 memory used=252.1MB, alloc=92.3MB, time=3.57 memory used=319.3MB, alloc=92.3MB, time=4.48 memory used=357.9MB, alloc=116.3MB, time=4.81 memory used=444.6MB, alloc=116.3MB, time=5.95 memory used=519.1MB, alloc=372.3MB, time=7.10 memory used=617.9MB, alloc=372.3MB, time=8.27 memory used=706.5MB, alloc=396.3MB, time=9.59 memory used=819.2MB, alloc=420.3MB, time=11.21 memory used=941.2MB, alloc=444.3MB, time=12.71 memory used=1068.4MB, alloc=444.3MB, time=14.62 memory used=1204.0MB, alloc=468.3MB, time=16.20 memory used=1305.8MB, alloc=468.3MB, time=17.50 memory used=1408.4MB, alloc=468.3MB, time=18.82 memory used=1502.7MB, alloc=468.3MB, time=20.28 memory used=1588.3MB, alloc=468.3MB, time=21.72 memory used=1699.0MB, alloc=492.3MB, time=23.11 memory used=1825.7MB, alloc=492.3MB, time=24.11 memory used=1965.4MB, alloc=492.3MB, time=25.41 memory used=2056.1MB, alloc=492.3MB, time=26.99 memory used=2167.0MB, alloc=492.3MB, time=28.41 memory used=2249.3MB, alloc=492.3MB, time=29.88 memory used=2335.8MB, alloc=492.3MB, time=31.75 memory used=2404.4MB, alloc=492.3MB, time=33.00 memory used=2471.5MB, alloc=492.3MB, time=34.21 memory used=2536.6MB, alloc=492.3MB, time=35.42 memory used=2593.6MB, alloc=516.3MB, time=36.52 memory used=2660.9MB, alloc=516.3MB, time=37.50 memory used=2793.7MB, alloc=516.3MB, time=38.59 memory used=2919.7MB, alloc=516.3MB, time=39.76 memory used=3038.2MB, alloc=516.3MB, time=40.43 memory used=3170.6MB, alloc=516.3MB, time=41.57 memory used=3300.9MB, alloc=516.3MB, time=43.11 memory used=3398.0MB, alloc=516.3MB, time=43.61 memory used=3528.2MB, alloc=516.3MB, time=44.51 memory used=3600.7MB, alloc=516.3MB, time=45.66 memory used=3658.4MB, alloc=516.3MB, time=46.47 memory used=3891.3MB, alloc=540.3MB, time=49.43 memory used=4087.2MB, alloc=564.3MB, time=52.36 memory used=4260.9MB, alloc=588.3MB, time=55.11 memory used=4420.2MB, alloc=588.3MB, time=57.98 memory used=4567.2MB, alloc=612.3MB, time=60.74 memory used=4757.5MB, alloc=612.3MB, time=63.64 memory used=4912.0MB, alloc=612.3MB, time=66.95 memory used=5070.1MB, alloc=636.3MB, time=70.45 memory used=5217.8MB, alloc=636.3MB, time=73.32 memory used=5423.9MB, alloc=660.3MB, time=76.81 memory used=5615.9MB, alloc=660.3MB, time=78.87 memory used=5834.4MB, alloc=660.3MB, time=80.97 memory used=6042.6MB, alloc=660.3MB, time=83.43 memory used=6169.5MB, alloc=660.3MB, time=85.21 memory used=6252.8MB, alloc=660.3MB, time=87.14 memory used=6439.8MB, alloc=684.3MB, time=88.64 memory used=6609.1MB, alloc=684.3MB, time=89.72 memory used=6794.5MB, alloc=684.3MB, time=91.69 memory used=6936.3MB, alloc=684.3MB, time=92.57 memory used=7160.4MB, alloc=684.3MB, time=93.69 memory used=7355.7MB, alloc=684.3MB, time=95.30 memory used=7533.2MB, alloc=684.3MB, time=96.41 memory used=7703.1MB, alloc=684.3MB, time=97.97 memory used=7855.6MB, alloc=684.3MB, time=98.89 memory used=7955.9MB, alloc=684.3MB, time=100.67 memory used=8326.8MB, alloc=708.3MB, time=106.77 memory used=8728.8MB, alloc=732.3MB, time=112.32 memory used=9117.3MB, alloc=756.3MB, time=116.97 memory used=9452.0MB, alloc=780.3MB, time=118.86 memory used=9981.9MB, alloc=804.3MB, time=121.10 memory used=10347.5MB, alloc=804.3MB, time=122.80 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428246951 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 3 2 2 2 2 3 F := [-7 x + x y z - 17 y , -5 x y - 3 x y + 3 y, -9 y z - z + 7 y z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 3 3 G := [-17 x y z - 5 z + 3, 18 x y - 3 x y + 20 y z , 2 3 -18 x y z + 4 y z - 18 y z] > Problem := [F,G]; Problem := [ 4 2 3 2 2 2 2 3 [-7 x + x y z - 17 y , -5 x y - 3 x y + 3 y, -9 y z - z + 7 y z], [ 2 2 3 3 3 -17 x y z - 5 z + 3, 18 x y - 3 x y + 20 y z , 2 3 -18 x y z + 4 y z - 18 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.8MB, alloc=32.3MB, time=0.50 memory used=47.8MB, alloc=32.3MB, time=0.80 memory used=67.6MB, alloc=32.3MB, time=1.10 memory used=85.3MB, alloc=56.3MB, time=1.38 memory used=127.0MB, alloc=60.3MB, time=1.92 memory used=172.3MB, alloc=60.3MB, time=2.53 memory used=210.8MB, alloc=60.3MB, time=3.02 memory used=251.8MB, alloc=60.3MB, time=3.59 memory used=292.2MB, alloc=84.3MB, time=4.06 memory used=334.7MB, alloc=84.3MB, time=6.27 memory used=377.2MB, alloc=84.3MB, time=6.95 memory used=417.1MB, alloc=84.3MB, time=7.06 memory used=442.1MB, alloc=84.3MB, time=7.12 memory used=472.4MB, alloc=84.3MB, time=7.21 memory used=516.1MB, alloc=84.3MB, time=7.53 memory used=552.7MB, alloc=84.3MB, time=7.72 memory used=587.3MB, alloc=84.3MB, time=7.83 memory used=638.0MB, alloc=107.8MB, time=8.18 memory used=666.8MB, alloc=107.8MB, time=8.28 memory used=699.2MB, alloc=107.8MB, time=8.37 memory used=735.2MB, alloc=107.8MB, time=8.46 memory used=792.6MB, alloc=107.8MB, time=8.58 memory used=820.6MB, alloc=107.8MB, time=8.67 memory used=852.2MB, alloc=107.8MB, time=8.76 memory used=887.6MB, alloc=107.8MB, time=8.85 memory used=931.4MB, alloc=107.8MB, time=8.94 memory used=982.5MB, alloc=107.8MB, time=9.58 memory used=1057.8MB, alloc=107.8MB, time=10.57 memory used=1126.6MB, alloc=107.8MB, time=11.49 memory used=1187.4MB, alloc=131.8MB, time=12.34 memory used=1254.1MB, alloc=387.8MB, time=13.28 memory used=1340.2MB, alloc=387.8MB, time=14.51 memory used=1429.9MB, alloc=411.8MB, time=15.70 memory used=1546.4MB, alloc=435.8MB, time=17.18 memory used=1675.8MB, alloc=435.8MB, time=18.91 memory used=1798.5MB, alloc=459.8MB, time=20.55 memory used=1901.6MB, alloc=459.8MB, time=21.95 memory used=2003.8MB, alloc=459.8MB, time=23.26 memory used=2096.8MB, alloc=483.8MB, time=24.55 memory used=2197.4MB, alloc=483.8MB, time=25.92 memory used=2338.8MB, alloc=483.8MB, time=28.62 memory used=2420.0MB, alloc=483.8MB, time=28.99 memory used=2518.2MB, alloc=483.8MB, time=29.66 memory used=2643.4MB, alloc=483.8MB, time=32.01 memory used=2721.2MB, alloc=483.8MB, time=32.38 memory used=2841.9MB, alloc=483.8MB, time=34.51 memory used=2917.9MB, alloc=483.8MB, time=34.84 memory used=3015.1MB, alloc=483.8MB, time=35.65 memory used=3127.8MB, alloc=483.8MB, time=37.86 memory used=3214.4MB, alloc=483.8MB, time=38.38 memory used=3321.9MB, alloc=483.8MB, time=39.15 memory used=3415.2MB, alloc=483.8MB, time=39.73 memory used=3555.0MB, alloc=483.8MB, time=40.95 memory used=3708.0MB, alloc=483.8MB, time=43.46 memory used=3872.1MB, alloc=483.8MB, time=45.73 memory used=4024.7MB, alloc=507.8MB, time=47.26 memory used=4163.7MB, alloc=507.8MB, time=49.23 memory used=4294.6MB, alloc=507.8MB, time=50.66 memory used=4470.7MB, alloc=507.8MB, time=52.80 memory used=4594.3MB, alloc=507.8MB, time=54.86 memory used=4702.6MB, alloc=507.8MB, time=55.56 memory used=4840.9MB, alloc=507.8MB, time=58.03 memory used=4933.0MB, alloc=507.8MB, time=58.50 memory used=5052.9MB, alloc=507.8MB, time=59.41 memory used=5189.7MB, alloc=507.8MB, time=60.45 memory used=5294.1MB, alloc=507.8MB, time=61.64 memory used=5380.5MB, alloc=507.8MB, time=62.71 memory used=5484.1MB, alloc=507.8MB, time=64.35 memory used=5576.6MB, alloc=507.8MB, time=66.10 memory used=5641.7MB, alloc=531.8MB, time=67.17 memory used=5733.6MB, alloc=531.8MB, time=68.36 memory used=5854.5MB, alloc=531.8MB, time=69.04 memory used=5992.9MB, alloc=531.8MB, time=75.47 memory used=6087.2MB, alloc=531.8MB, time=75.94 memory used=6191.4MB, alloc=531.8MB, time=76.36 memory used=6269.3MB, alloc=531.8MB, time=76.77 memory used=6375.8MB, alloc=531.8MB, time=77.35 memory used=6488.1MB, alloc=531.8MB, time=78.53 memory used=6601.7MB, alloc=531.8MB, time=79.13 memory used=6726.6MB, alloc=531.8MB, time=80.00 memory used=6869.4MB, alloc=531.8MB, time=86.44 memory used=6958.8MB, alloc=531.8MB, time=86.90 memory used=7054.1MB, alloc=531.8MB, time=87.34 memory used=7136.6MB, alloc=531.8MB, time=87.72 memory used=7264.5MB, alloc=531.8MB, time=88.53 memory used=7382.5MB, alloc=531.8MB, time=89.36 memory used=7499.9MB, alloc=531.8MB, time=90.43 memory used=7569.8MB, alloc=531.8MB, time=91.38 memory used=7641.8MB, alloc=531.8MB, time=92.29 memory used=7693.7MB, alloc=531.8MB, time=93.20 memory used=7781.5MB, alloc=531.8MB, time=94.38 memory used=7850.7MB, alloc=531.8MB, time=95.73 memory used=7910.4MB, alloc=531.8MB, time=97.08 memory used=7957.8MB, alloc=531.8MB, time=98.11 memory used=8154.2MB, alloc=555.8MB, time=101.32 memory used=8333.9MB, alloc=579.8MB, time=104.56 memory used=8501.0MB, alloc=603.8MB, time=107.26 memory used=8669.7MB, alloc=627.8MB, time=110.32 memory used=8861.5MB, alloc=651.8MB, time=114.02 memory used=9069.8MB, alloc=675.8MB, time=116.99 memory used=9253.7MB, alloc=675.8MB, time=119.20 memory used=9458.5MB, alloc=675.8MB, time=123.94 memory used=9634.1MB, alloc=675.8MB, time=129.70 memory used=9863.8MB, alloc=675.8MB, time=133.86 memory used=10016.6MB, alloc=675.8MB, time=140.60 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428247251 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 3 3 2 2 F := [-14 x z - 17 x y - 8 y , 19 y z + 3 y + 3 y z , 12 x y - 20] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 3 2 3 3 G := [-11 y z - 5 x - 7 y, 12 x y - 7 x y - 14 y z, 3 x y + x z + 14 y z] > Problem := [F,G]; 3 2 2 3 3 2 2 Problem := [[-14 x z - 17 x y - 8 y , 19 y z + 3 y + 3 y z , 12 x y - 20], 3 3 3 2 3 3 [-11 y z - 5 x - 7 y, 12 x y - 7 x y - 14 y z, 3 x y + x z + 14 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.6MB, alloc=32.3MB, time=0.53 memory used=47.5MB, alloc=32.3MB, time=0.84 memory used=66.4MB, alloc=56.3MB, time=1.14 memory used=107.1MB, alloc=60.3MB, time=1.76 memory used=145.7MB, alloc=84.3MB, time=2.37 memory used=212.5MB, alloc=92.3MB, time=3.33 memory used=276.8MB, alloc=92.3MB, time=4.31 memory used=338.5MB, alloc=116.3MB, time=5.19 memory used=403.5MB, alloc=372.3MB, time=6.13 memory used=492.8MB, alloc=372.3MB, time=7.44 memory used=584.6MB, alloc=396.3MB, time=8.70 memory used=697.7MB, alloc=420.3MB, time=10.34 memory used=835.2MB, alloc=420.3MB, time=12.40 memory used=967.3MB, alloc=444.3MB, time=14.46 memory used=1102.2MB, alloc=468.3MB, time=16.34 memory used=1246.4MB, alloc=468.3MB, time=18.12 memory used=1361.4MB, alloc=468.3MB, time=19.80 memory used=1453.1MB, alloc=468.3MB, time=21.27 memory used=1553.5MB, alloc=468.3MB, time=22.83 memory used=1664.2MB, alloc=468.3MB, time=23.68 memory used=1787.4MB, alloc=468.3MB, time=24.94 memory used=1894.6MB, alloc=468.3MB, time=26.54 memory used=2004.1MB, alloc=468.3MB, time=28.50 memory used=2097.6MB, alloc=468.3MB, time=29.96 memory used=2174.1MB, alloc=468.3MB, time=31.21 memory used=2288.8MB, alloc=492.3MB, time=32.24 memory used=2427.3MB, alloc=492.3MB, time=34.07 memory used=2536.7MB, alloc=492.3MB, time=35.39 memory used=2691.7MB, alloc=492.3MB, time=36.92 memory used=2809.7MB, alloc=492.3MB, time=38.41 memory used=2934.2MB, alloc=492.3MB, time=39.81 memory used=3045.4MB, alloc=492.3MB, time=43.35 memory used=3181.0MB, alloc=492.3MB, time=45.58 memory used=3273.4MB, alloc=492.3MB, time=46.11 memory used=3365.8MB, alloc=492.3MB, time=46.62 memory used=3463.1MB, alloc=492.3MB, time=47.08 memory used=3551.1MB, alloc=492.3MB, time=47.48 memory used=3659.9MB, alloc=492.3MB, time=48.27 memory used=3737.2MB, alloc=492.3MB, time=48.65 memory used=3872.5MB, alloc=492.3MB, time=50.04 memory used=3974.7MB, alloc=492.3MB, time=50.58 memory used=4048.6MB, alloc=492.3MB, time=50.96 memory used=4143.6MB, alloc=492.3MB, time=51.35 memory used=4213.0MB, alloc=492.3MB, time=51.69 memory used=4319.4MB, alloc=492.3MB, time=53.48 memory used=4405.8MB, alloc=492.3MB, time=53.86 memory used=4480.1MB, alloc=492.3MB, time=54.19 memory used=4575.9MB, alloc=492.3MB, time=54.54 memory used=4717.7MB, alloc=492.3MB, time=55.85 memory used=4817.5MB, alloc=492.3MB, time=57.06 memory used=4903.7MB, alloc=492.3MB, time=58.31 memory used=4985.4MB, alloc=492.3MB, time=59.89 memory used=5075.7MB, alloc=492.3MB, time=60.90 memory used=5149.7MB, alloc=492.3MB, time=62.25 memory used=5273.2MB, alloc=516.3MB, time=63.56 memory used=5380.8MB, alloc=516.3MB, time=64.13 memory used=5522.5MB, alloc=516.3MB, time=65.94 memory used=5619.5MB, alloc=516.3MB, time=66.37 memory used=5704.3MB, alloc=516.3MB, time=66.74 memory used=5837.7MB, alloc=516.3MB, time=68.23 memory used=5938.6MB, alloc=516.3MB, time=68.67 memory used=6018.0MB, alloc=516.3MB, time=69.06 memory used=6183.1MB, alloc=516.3MB, time=70.27 memory used=6264.1MB, alloc=516.3MB, time=71.33 memory used=6336.5MB, alloc=516.3MB, time=72.64 memory used=6396.0MB, alloc=516.3MB, time=73.65 memory used=6461.0MB, alloc=516.3MB, time=74.89 memory used=6517.2MB, alloc=516.3MB, time=75.96 memory used=6573.7MB, alloc=516.3MB, time=77.00 memory used=6621.9MB, alloc=516.3MB, time=78.02 memory used=6668.5MB, alloc=516.3MB, time=79.03 memory used=6715.2MB, alloc=516.3MB, time=80.06 memory used=6766.9MB, alloc=516.3MB, time=81.18 memory used=6806.8MB, alloc=516.3MB, time=82.18 memory used=7014.0MB, alloc=540.3MB, time=86.02 memory used=7200.0MB, alloc=564.3MB, time=89.53 memory used=7402.5MB, alloc=588.3MB, time=92.03 memory used=7625.5MB, alloc=588.3MB, time=94.80 memory used=7815.9MB, alloc=588.3MB, time=96.41 memory used=7935.8MB, alloc=588.3MB, time=97.12 memory used=8081.9MB, alloc=588.3MB, time=98.04 memory used=8200.1MB, alloc=588.3MB, time=98.78 memory used=8311.5MB, alloc=588.3MB, time=99.46 memory used=8443.5MB, alloc=612.3MB, time=100.16 memory used=8641.5MB, alloc=612.3MB, time=120.59 memory used=8773.8MB, alloc=612.3MB, time=121.35 memory used=8904.3MB, alloc=612.3MB, time=122.06 memory used=9066.4MB, alloc=612.3MB, time=122.81 memory used=9164.9MB, alloc=612.3MB, time=123.43 memory used=9271.8MB, alloc=612.3MB, time=124.06 memory used=9388.6MB, alloc=612.3MB, time=124.71 memory used=9512.9MB, alloc=612.3MB, time=125.34 memory used=9648.7MB, alloc=612.3MB, time=126.00 memory used=9796.4MB, alloc=612.3MB, time=126.65 memory used=9951.3MB, alloc=612.3MB, time=127.34 memory used=10117.9MB, alloc=612.3MB, time=127.99 memory used=10335.5MB, alloc=612.3MB, time=128.89 memory used=10452.0MB, alloc=612.3MB, time=129.53 memory used=10573.0MB, alloc=612.3MB, time=130.17 memory used=10701.4MB, alloc=612.3MB, time=130.81 memory used=10832.5MB, alloc=612.3MB, time=131.45 memory used=10971.6MB, alloc=612.3MB, time=132.09 memory used=11112.8MB, alloc=612.3MB, time=132.77 memory used=11261.9MB, alloc=612.3MB, time=133.45 memory used=11413.3MB, alloc=612.3MB, time=134.15 memory used=11571.4MB, alloc=612.3MB, time=134.83 memory used=11737.6MB, alloc=612.3MB, time=135.51 memory used=11905.9MB, alloc=612.3MB, time=136.18 memory used=12080.5MB, alloc=612.3MB, time=136.87 memory used=12261.9MB, alloc=612.3MB, time=137.58 memory used=12450.6MB, alloc=612.3MB, time=138.26 memory used=12645.9MB, alloc=612.3MB, time=138.95 memory used=12847.3MB, alloc=612.3MB, time=139.66 memory used=13060.3MB, alloc=612.3MB, time=140.37 memory used=13278.0MB, alloc=612.3MB, time=141.09 memory used=13474.3MB, alloc=612.3MB, time=141.79 memory used=13625.2MB, alloc=612.3MB, time=142.45 memory used=13780.1MB, alloc=612.3MB, time=143.09 memory used=13943.1MB, alloc=612.3MB, time=143.74 memory used=14110.1MB, alloc=612.3MB, time=144.41 memory used=14279.3MB, alloc=612.3MB, time=145.06 memory used=14455.4MB, alloc=612.3MB, time=145.74 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428247551 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 4 2 3 3 F := [-13 z - 13 x y - 8 y , -18 x - 10 y - 4, 8 x y z + 20 x z + 18 y ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 3 2 2 G := [15 x y + 20 z + 4 z, 14 x y z - 20 x y , -8 x y - 10 x y z - 15 z ] > Problem := [F,G]; Problem := [ 3 2 4 2 3 3 [-13 z - 13 x y - 8 y , -18 x - 10 y - 4, 8 x y z + 20 x z + 18 y ], 3 3 2 3 2 2 [15 x y + 20 z + 4 z, 14 x y z - 20 x y , -8 x y - 10 x y z - 15 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=27.1MB, alloc=32.3MB, time=0.52 memory used=46.5MB, alloc=56.3MB, time=0.82 memory used=87.9MB, alloc=60.3MB, time=1.43 memory used=128.8MB, alloc=68.3MB, time=2.04 memory used=169.5MB, alloc=68.3MB, time=2.57 memory used=215.8MB, alloc=92.3MB, time=3.17 memory used=281.0MB, alloc=92.3MB, time=4.13 memory used=347.9MB, alloc=92.3MB, time=4.94 memory used=411.6MB, alloc=116.3MB, time=5.90 memory used=472.6MB, alloc=116.3MB, time=6.75 memory used=536.8MB, alloc=372.3MB, time=7.67 memory used=618.9MB, alloc=396.3MB, time=8.99 memory used=732.5MB, alloc=396.3MB, time=10.55 memory used=846.6MB, alloc=420.3MB, time=12.18 memory used=954.9MB, alloc=420.3MB, time=13.20 memory used=1040.2MB, alloc=420.3MB, time=13.81 memory used=1161.2MB, alloc=420.3MB, time=15.27 memory used=1287.4MB, alloc=420.3MB, time=16.50 memory used=1405.0MB, alloc=444.3MB, time=17.66 memory used=1511.6MB, alloc=444.3MB, time=19.27 memory used=1623.8MB, alloc=468.3MB, time=20.98 memory used=1762.3MB, alloc=468.3MB, time=22.42 memory used=1857.4MB, alloc=468.3MB, time=23.00 memory used=1950.8MB, alloc=468.3MB, time=23.49 memory used=2047.7MB, alloc=468.3MB, time=24.14 memory used=2114.9MB, alloc=468.3MB, time=24.49 memory used=2199.6MB, alloc=468.3MB, time=24.84 memory used=2273.8MB, alloc=468.3MB, time=25.13 memory used=2336.6MB, alloc=468.3MB, time=25.41 memory used=2415.9MB, alloc=468.3MB, time=26.50 memory used=2485.8MB, alloc=468.3MB, time=26.82 memory used=2578.8MB, alloc=468.3MB, time=27.78 memory used=2672.4MB, alloc=468.3MB, time=28.28 memory used=2766.3MB, alloc=468.3MB, time=28.85 memory used=2854.4MB, alloc=468.3MB, time=29.25 memory used=2940.4MB, alloc=468.3MB, time=29.68 memory used=3035.4MB, alloc=468.3MB, time=30.21 memory used=3129.4MB, alloc=468.3MB, time=30.72 memory used=3220.6MB, alloc=468.3MB, time=31.20 memory used=3307.8MB, alloc=468.3MB, time=31.71 memory used=3386.6MB, alloc=468.3MB, time=32.02 memory used=3527.5MB, alloc=468.3MB, time=33.42 memory used=3655.2MB, alloc=468.3MB, time=34.97 memory used=3760.8MB, alloc=468.3MB, time=36.23 memory used=3854.9MB, alloc=468.3MB, time=37.51 memory used=3944.2MB, alloc=492.3MB, time=38.97 memory used=4032.9MB, alloc=492.3MB, time=40.48 memory used=4114.1MB, alloc=492.3MB, time=41.92 memory used=4196.9MB, alloc=492.3MB, time=43.36 memory used=4279.3MB, alloc=492.3MB, time=44.71 memory used=4363.7MB, alloc=492.3MB, time=45.81 memory used=4439.5MB, alloc=492.3MB, time=46.81 memory used=4517.5MB, alloc=492.3MB, time=47.94 memory used=4579.7MB, alloc=492.3MB, time=49.05 memory used=4648.0MB, alloc=492.3MB, time=50.07 memory used=4729.2MB, alloc=492.3MB, time=51.47 memory used=4817.5MB, alloc=492.3MB, time=52.54 memory used=4895.3MB, alloc=492.3MB, time=53.84 memory used=4950.6MB, alloc=492.3MB, time=54.90 memory used=5006.1MB, alloc=492.3MB, time=56.10 memory used=5054.5MB, alloc=516.3MB, time=57.16 memory used=5106.1MB, alloc=516.3MB, time=58.29 memory used=5151.8MB, alloc=516.3MB, time=59.33 memory used=5369.0MB, alloc=540.3MB, time=63.73 memory used=5541.4MB, alloc=540.3MB, time=65.33 memory used=5703.9MB, alloc=540.3MB, time=66.68 memory used=5817.2MB, alloc=540.3MB, time=67.57 memory used=5930.6MB, alloc=540.3MB, time=68.17 memory used=6013.0MB, alloc=540.3MB, time=68.69 memory used=6115.0MB, alloc=540.3MB, time=69.22 memory used=6276.9MB, alloc=540.3MB, time=74.60 memory used=6468.3MB, alloc=540.3MB, time=75.49 memory used=6719.5MB, alloc=540.3MB, time=77.49 memory used=6896.6MB, alloc=540.3MB, time=79.21 memory used=7097.3MB, alloc=540.3MB, time=82.93 memory used=7244.5MB, alloc=564.3MB, time=84.11 memory used=7491.0MB, alloc=564.3MB, time=86.77 memory used=7624.9MB, alloc=564.3MB, time=87.73 memory used=7752.2MB, alloc=564.3MB, time=88.52 memory used=7871.9MB, alloc=564.3MB, time=89.23 memory used=7991.5MB, alloc=564.3MB, time=90.02 memory used=8117.9MB, alloc=564.3MB, time=90.75 memory used=8250.8MB, alloc=564.3MB, time=91.53 memory used=8352.8MB, alloc=564.3MB, time=92.12 memory used=8494.3MB, alloc=564.3MB, time=93.15 memory used=8604.2MB, alloc=564.3MB, time=93.77 memory used=8779.1MB, alloc=564.3MB, time=94.96 memory used=8899.2MB, alloc=564.3MB, time=95.73 memory used=9015.7MB, alloc=564.3MB, time=96.35 memory used=9141.5MB, alloc=564.3MB, time=98.59 memory used=9252.4MB, alloc=564.3MB, time=99.22 memory used=9373.4MB, alloc=564.3MB, time=99.82 memory used=9687.7MB, alloc=564.3MB, time=102.60 memory used=9837.3MB, alloc=564.3MB, time=103.81 memory used=9962.2MB, alloc=564.3MB, time=104.64 memory used=10183.2MB, alloc=564.3MB, time=107.84 memory used=10448.1MB, alloc=588.3MB, time=110.30 memory used=10584.7MB, alloc=588.3MB, time=111.30 memory used=10800.3MB, alloc=588.3MB, time=113.65 memory used=11045.9MB, alloc=588.3MB, time=116.94 memory used=11277.5MB, alloc=588.3MB, time=119.56 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428247852 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 2 3 2 2 F := [12 y - 12 y z + 16 x, 19 z - 14 x - 10 y , -18 x z - 5 x z - 20] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 3 2 G := [11 x y z + 9 x y + 19 y z, 16 x y - 11 y z + 10 y , 4 2 -3 y + 20 y z + 5 z] > Problem := [F,G]; Problem := [ 3 2 3 2 2 3 2 2 [12 y - 12 y z + 16 x, 19 z - 14 x - 10 y , -18 x z - 5 x z - 20], [ 2 3 3 2 11 x y z + 9 x y + 19 y z, 16 x y - 11 y z + 10 y , 4 2 -3 y + 20 y z + 5 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.17 memory used=24.6MB, alloc=32.3MB, time=0.48 memory used=46.5MB, alloc=34.0MB, time=0.65 memory used=67.7MB, alloc=34.0MB, time=1.23 memory used=78.1MB, alloc=58.0MB, time=1.28 memory used=125.1MB, alloc=62.0MB, time=1.72 memory used=187.2MB, alloc=73.3MB, time=2.70 memory used=222.6MB, alloc=73.3MB, time=2.87 memory used=266.6MB, alloc=73.3MB, time=4.11 memory used=294.5MB, alloc=73.3MB, time=4.19 memory used=318.1MB, alloc=73.3MB, time=4.25 memory used=348.7MB, alloc=73.3MB, time=4.33 memory used=371.2MB, alloc=73.3MB, time=4.39 memory used=393.7MB, alloc=73.3MB, time=4.45 memory used=437.7MB, alloc=73.3MB, time=4.88 memory used=481.6MB, alloc=73.3MB, time=5.47 memory used=524.1MB, alloc=73.3MB, time=6.04 memory used=557.3MB, alloc=73.3MB, time=6.26 memory used=588.5MB, alloc=73.3MB, time=6.42 memory used=620.4MB, alloc=73.3MB, time=7.10 memory used=648.7MB, alloc=73.3MB, time=7.26 memory used=686.0MB, alloc=73.3MB, time=7.90 memory used=710.8MB, alloc=73.3MB, time=7.99 memory used=764.5MB, alloc=73.3MB, time=8.62 memory used=823.7MB, alloc=73.3MB, time=9.57 memory used=881.3MB, alloc=73.3MB, time=10.56 memory used=936.6MB, alloc=97.3MB, time=11.04 memory used=1018.4MB, alloc=97.3MB, time=14.08 memory used=1053.8MB, alloc=97.3MB, time=14.18 memory used=1108.1MB, alloc=97.3MB, time=16.36 memory used=1143.1MB, alloc=97.3MB, time=16.46 memory used=1208.1MB, alloc=97.3MB, time=17.32 memory used=1242.3MB, alloc=97.3MB, time=17.44 memory used=1282.9MB, alloc=97.3MB, time=17.58 memory used=1337.1MB, alloc=97.3MB, time=19.35 memory used=1375.9MB, alloc=97.3MB, time=19.47 memory used=1407.1MB, alloc=97.3MB, time=19.59 memory used=1443.9MB, alloc=97.3MB, time=19.69 memory used=1470.2MB, alloc=97.3MB, time=19.77 memory used=1531.5MB, alloc=97.3MB, time=20.28 memory used=1614.3MB, alloc=97.3MB, time=25.99 memory used=1649.5MB, alloc=97.3MB, time=26.11 memory used=1676.9MB, alloc=97.3MB, time=26.22 memory used=1707.2MB, alloc=97.3MB, time=26.33 memory used=1744.2MB, alloc=97.3MB, time=26.43 memory used=1774.2MB, alloc=97.3MB, time=26.52 memory used=1797.7MB, alloc=97.3MB, time=26.60 memory used=1823.1MB, alloc=97.3MB, time=26.69 memory used=1851.0MB, alloc=97.3MB, time=26.77 memory used=1881.2MB, alloc=97.3MB, time=26.85 memory used=1914.5MB, alloc=97.3MB, time=26.94 memory used=1967.3MB, alloc=97.3MB, time=27.26 memory used=2030.6MB, alloc=97.3MB, time=28.01 memory used=2091.5MB, alloc=97.3MB, time=29.06 memory used=2151.4MB, alloc=97.3MB, time=29.61 memory used=2201.2MB, alloc=97.3MB, time=29.98 memory used=2246.6MB, alloc=97.3MB, time=30.33 memory used=2302.9MB, alloc=97.3MB, time=30.75 memory used=2338.6MB, alloc=97.3MB, time=30.93 memory used=2376.0MB, alloc=97.3MB, time=31.08 memory used=2429.9MB, alloc=121.3MB, time=33.41 memory used=2474.6MB, alloc=121.3MB, time=33.58 memory used=2545.5MB, alloc=121.3MB, time=34.24 memory used=2607.7MB, alloc=377.3MB, time=35.09 memory used=2681.0MB, alloc=377.3MB, time=35.69 memory used=2732.1MB, alloc=377.3MB, time=35.89 memory used=2779.0MB, alloc=377.3MB, time=36.05 memory used=2818.8MB, alloc=377.3MB, time=36.20 memory used=2855.6MB, alloc=377.3MB, time=36.34 memory used=2915.8MB, alloc=377.3MB, time=36.61 memory used=2960.5MB, alloc=377.3MB, time=36.78 memory used=3004.3MB, alloc=377.3MB, time=36.94 memory used=3040.8MB, alloc=377.3MB, time=37.08 memory used=3120.7MB, alloc=377.3MB, time=42.84 memory used=3164.6MB, alloc=377.3MB, time=43.03 memory used=3205.7MB, alloc=377.3MB, time=43.19 memory used=3241.7MB, alloc=377.3MB, time=43.33 memory used=3283.5MB, alloc=377.3MB, time=43.48 memory used=3331.3MB, alloc=377.3MB, time=43.63 memory used=3386.1MB, alloc=377.3MB, time=43.78 memory used=3417.7MB, alloc=377.3MB, time=43.91 memory used=3448.8MB, alloc=377.3MB, time=44.03 memory used=3481.9MB, alloc=377.3MB, time=44.18 memory used=3516.7MB, alloc=377.3MB, time=44.31 memory used=3553.3MB, alloc=377.3MB, time=44.45 memory used=3592.2MB, alloc=377.3MB, time=44.62 memory used=3633.6MB, alloc=377.3MB, time=44.75 memory used=3678.5MB, alloc=377.3MB, time=44.89 memory used=3726.2MB, alloc=377.3MB, time=45.04 memory used=3776.5MB, alloc=377.3MB, time=45.18 memory used=3829.9MB, alloc=377.3MB, time=45.31 memory used=3981.4MB, alloc=377.3MB, time=46.08 memory used=4030.1MB, alloc=377.3MB, time=46.26 memory used=4066.5MB, alloc=377.3MB, time=46.40 memory used=4108.6MB, alloc=377.3MB, time=46.54 memory used=4165.2MB, alloc=377.3MB, time=46.82 memory used=4214.2MB, alloc=377.3MB, time=46.99 memory used=4248.8MB, alloc=377.3MB, time=47.14 memory used=4291.7MB, alloc=377.3MB, time=47.27 memory used=4357.4MB, alloc=377.3MB, time=48.30 memory used=4397.3MB, alloc=377.3MB, time=48.44 memory used=4444.3MB, alloc=377.3MB, time=48.58 memory used=4483.6MB, alloc=377.3MB, time=48.70 memory used=4528.3MB, alloc=377.3MB, time=49.07 memory used=4581.2MB, alloc=377.3MB, time=49.26 memory used=4626.1MB, alloc=377.3MB, time=49.45 memory used=4675.5MB, alloc=377.3MB, time=49.62 memory used=4707.7MB, alloc=377.3MB, time=49.77 memory used=4744.2MB, alloc=377.3MB, time=49.94 memory used=4785.2MB, alloc=377.3MB, time=50.10 memory used=4830.4MB, alloc=377.3MB, time=50.24 memory used=4880.7MB, alloc=377.3MB, time=50.39 memory used=4932.4MB, alloc=377.3MB, time=50.53 memory used=4962.9MB, alloc=377.3MB, time=50.64 memory used=4994.8MB, alloc=377.3MB, time=50.77 memory used=5029.2MB, alloc=377.3MB, time=50.88 memory used=5087.2MB, alloc=377.3MB, time=51.33 memory used=5128.0MB, alloc=377.3MB, time=51.50 memory used=5178.1MB, alloc=377.3MB, time=51.67 memory used=5218.8MB, alloc=377.3MB, time=51.83 memory used=5253.2MB, alloc=377.3MB, time=51.97 memory used=5290.6MB, alloc=377.3MB, time=52.13 memory used=5333.4MB, alloc=377.3MB, time=52.28 memory used=5380.4MB, alloc=377.3MB, time=52.43 memory used=5432.7MB, alloc=377.3MB, time=52.58 memory used=5475.7MB, alloc=377.3MB, time=52.71 memory used=5506.2MB, alloc=377.3MB, time=52.83 memory used=5538.9MB, alloc=377.3MB, time=52.95 memory used=5574.4MB, alloc=377.3MB, time=53.11 memory used=5641.9MB, alloc=377.3MB, time=55.34 memory used=5688.6MB, alloc=377.3MB, time=55.54 memory used=5725.2MB, alloc=377.3MB, time=55.75 memory used=5770.0MB, alloc=377.3MB, time=55.92 memory used=5823.5MB, alloc=377.3MB, time=56.07 memory used=5858.2MB, alloc=377.3MB, time=56.19 memory used=5891.7MB, alloc=377.3MB, time=56.31 memory used=5928.1MB, alloc=377.3MB, time=56.45 memory used=5967.1MB, alloc=377.3MB, time=56.62 memory used=6010.6MB, alloc=377.3MB, time=56.77 memory used=6060.9MB, alloc=377.3MB, time=56.89 memory used=6160.7MB, alloc=377.3MB, time=58.54 memory used=6272.5MB, alloc=377.3MB, time=59.54 memory used=6352.0MB, alloc=377.3MB, time=60.56 memory used=6389.4MB, alloc=377.3MB, time=60.74 memory used=6437.6MB, alloc=377.3MB, time=60.93 memory used=6470.4MB, alloc=401.3MB, time=61.10 memory used=6516.2MB, alloc=401.3MB, time=61.30 memory used=6569.3MB, alloc=401.3MB, time=61.50 memory used=6629.1MB, alloc=401.3MB, time=61.71 memory used=6698.1MB, alloc=401.3MB, time=61.91 memory used=6758.8MB, alloc=401.3MB, time=62.10 memory used=6798.6MB, alloc=401.3MB, time=62.26 memory used=6838.9MB, alloc=401.3MB, time=62.41 memory used=6881.9MB, alloc=401.3MB, time=62.56 memory used=6927.2MB, alloc=401.3MB, time=62.72 memory used=6975.6MB, alloc=401.3MB, time=62.88 memory used=7027.2MB, alloc=401.3MB, time=63.05 memory used=7083.8MB, alloc=401.3MB, time=63.22 memory used=7144.4MB, alloc=401.3MB, time=63.38 memory used=7209.5MB, alloc=401.3MB, time=63.56 memory used=7289.6MB, alloc=401.3MB, time=64.19 memory used=7349.4MB, alloc=401.3MB, time=64.43 memory used=7405.3MB, alloc=401.3MB, time=64.64 memory used=7451.2MB, alloc=401.3MB, time=64.85 memory used=7504.3MB, alloc=401.3MB, time=65.05 memory used=7564.1MB, alloc=401.3MB, time=65.26 memory used=7633.1MB, alloc=401.3MB, time=65.48 memory used=7693.8MB, alloc=401.3MB, time=65.68 memory used=7733.5MB, alloc=401.3MB, time=65.84 memory used=7773.8MB, alloc=401.3MB, time=66.01 memory used=7816.8MB, alloc=401.3MB, time=66.17 memory used=7862.1MB, alloc=401.3MB, time=66.34 memory used=7910.5MB, alloc=401.3MB, time=66.50 memory used=7962.1MB, alloc=401.3MB, time=66.68 memory used=8018.9MB, alloc=401.3MB, time=66.85 memory used=8079.5MB, alloc=401.3MB, time=67.03 memory used=8144.6MB, alloc=401.3MB, time=67.19 memory used=8243.7MB, alloc=401.3MB, time=87.14 memory used=8323.1MB, alloc=401.3MB, time=88.35 memory used=8373.6MB, alloc=401.3MB, time=88.55 memory used=8434.2MB, alloc=401.3MB, time=88.76 memory used=8492.2MB, alloc=401.3MB, time=88.96 memory used=8533.6MB, alloc=401.3MB, time=89.12 memory used=8578.6MB, alloc=401.3MB, time=89.29 memory used=8628.0MB, alloc=401.3MB, time=89.46 memory used=8681.7MB, alloc=401.3MB, time=89.62 memory used=8741.5MB, alloc=401.3MB, time=89.81 memory used=8805.7MB, alloc=401.3MB, time=89.99 memory used=8876.0MB, alloc=401.3MB, time=90.18 memory used=9055.8MB, alloc=401.3MB, time=90.63 memory used=9210.2MB, alloc=401.3MB, time=90.95 memory used=9389.7MB, alloc=401.3MB, time=91.31 memory used=9602.4MB, alloc=401.3MB, time=91.69 memory used=9753.6MB, alloc=401.3MB, time=92.69 memory used=9817.1MB, alloc=401.3MB, time=92.92 memory used=9876.8MB, alloc=401.3MB, time=93.11 memory used=9921.8MB, alloc=401.3MB, time=93.28 memory used=9993.6MB, alloc=401.3MB, time=93.60 memory used=10050.1MB, alloc=401.3MB, time=93.81 memory used=10101.6MB, alloc=401.3MB, time=94.00 memory used=10151.5MB, alloc=401.3MB, time=94.17 memory used=10250.0MB, alloc=401.3MB, time=99.36 memory used=10306.5MB, alloc=401.3MB, time=99.56 memory used=10357.4MB, alloc=401.3MB, time=99.75 memory used=10419.9MB, alloc=401.3MB, time=99.94 memory used=10478.4MB, alloc=401.3MB, time=100.11 memory used=10519.5MB, alloc=401.3MB, time=100.25 memory used=10563.6MB, alloc=401.3MB, time=100.40 memory used=10611.8MB, alloc=401.3MB, time=100.57 memory used=10663.9MB, alloc=401.3MB, time=100.73 memory used=10721.0MB, alloc=401.3MB, time=100.89 memory used=10782.9MB, alloc=401.3MB, time=101.05 memory used=10850.3MB, alloc=401.3MB, time=101.22 memory used=11038.7MB, alloc=401.3MB, time=101.53 memory used=11125.2MB, alloc=401.3MB, time=102.08 memory used=11178.6MB, alloc=401.3MB, time=102.26 memory used=11232.9MB, alloc=401.3MB, time=102.42 memory used=11303.1MB, alloc=401.3MB, time=102.71 memory used=11359.9MB, alloc=401.3MB, time=102.90 memory used=11411.2MB, alloc=401.3MB, time=103.08 memory used=11489.5MB, alloc=401.3MB, time=104.04 memory used=11544.4MB, alloc=401.3MB, time=104.22 memory used=11606.1MB, alloc=401.3MB, time=104.40 memory used=11650.5MB, alloc=401.3MB, time=104.54 memory used=11721.8MB, alloc=401.3MB, time=104.96 memory used=11777.8MB, alloc=401.3MB, time=105.18 memory used=11832.8MB, alloc=401.3MB, time=105.39 memory used=11879.8MB, alloc=401.3MB, time=105.58 memory used=11934.7MB, alloc=401.3MB, time=105.76 memory used=11998.1MB, alloc=401.3MB, time=105.94 memory used=12065.0MB, alloc=401.3MB, time=106.12 memory used=12105.6MB, alloc=401.3MB, time=106.27 memory used=12147.5MB, alloc=401.3MB, time=106.43 memory used=12193.2MB, alloc=401.3MB, time=106.59 memory used=12253.1MB, alloc=401.3MB, time=106.94 memory used=12315.5MB, alloc=401.3MB, time=107.17 memory used=12378.8MB, alloc=401.3MB, time=107.38 memory used=12422.6MB, alloc=401.3MB, time=107.56 memory used=12474.3MB, alloc=401.3MB, time=107.74 memory used=12533.4MB, alloc=401.3MB, time=107.93 memory used=12602.0MB, alloc=401.3MB, time=108.11 memory used=12651.2MB, alloc=401.3MB, time=108.28 memory used=12692.7MB, alloc=401.3MB, time=108.44 memory used=12737.4MB, alloc=401.3MB, time=108.58 memory used=12786.0MB, alloc=401.3MB, time=108.75 memory used=12863.5MB, alloc=401.3MB, time=110.68 memory used=12917.1MB, alloc=401.3MB, time=110.88 memory used=12973.6MB, alloc=401.3MB, time=111.07 memory used=13035.2MB, alloc=401.3MB, time=111.24 memory used=13076.7MB, alloc=401.3MB, time=111.42 memory used=13123.4MB, alloc=401.3MB, time=111.59 memory used=13175.4MB, alloc=401.3MB, time=111.77 memory used=13234.0MB, alloc=401.3MB, time=111.93 memory used=13325.0MB, alloc=401.3MB, time=112.38 memory used=13429.4MB, alloc=401.3MB, time=113.31 memory used=13498.6MB, alloc=401.3MB, time=113.62 memory used=13579.1MB, alloc=401.3MB, time=117.07 memory used=13638.4MB, alloc=401.3MB, time=117.34 memory used=13753.4MB, alloc=401.3MB, time=118.93 memory used=13858.3MB, alloc=401.3MB, time=120.19 memory used=13954.3MB, alloc=401.3MB, time=121.15 memory used=14017.9MB, alloc=401.3MB, time=121.42 memory used=14066.5MB, alloc=401.3MB, time=121.63 memory used=14120.6MB, alloc=401.3MB, time=121.84 memory used=14160.3MB, alloc=401.3MB, time=122.03 memory used=14234.1MB, alloc=401.3MB, time=122.38 memory used=14277.6MB, alloc=401.3MB, time=122.59 memory used=14336.4MB, alloc=401.3MB, time=122.80 memory used=14375.8MB, alloc=401.3MB, time=123.00 memory used=14447.3MB, alloc=401.3MB, time=124.62 memory used=14497.7MB, alloc=401.3MB, time=124.84 memory used=14544.0MB, alloc=401.3MB, time=125.03 memory used=14589.3MB, alloc=401.3MB, time=125.23 memory used=14668.7MB, alloc=401.3MB, time=125.88 memory used=14746.1MB, alloc=401.3MB, time=126.19 memory used=14792.4MB, alloc=401.3MB, time=126.42 memory used=14835.5MB, alloc=425.3MB, time=126.65 memory used=14906.4MB, alloc=425.3MB, time=126.91 memory used=14984.3MB, alloc=425.3MB, time=127.18 memory used=15033.6MB, alloc=425.3MB, time=127.40 memory used=15088.9MB, alloc=425.3MB, time=127.62 memory used=15166.0MB, alloc=425.3MB, time=128.08 memory used=15263.5MB, alloc=425.3MB, time=128.44 memory used=15319.3MB, alloc=425.3MB, time=128.70 memory used=15388.4MB, alloc=425.3MB, time=128.96 memory used=15471.1MB, alloc=425.3MB, time=129.22 memory used=15520.5MB, alloc=425.3MB, time=129.43 memory used=15575.5MB, alloc=425.3MB, time=129.65 memory used=15643.0MB, alloc=425.3MB, time=129.90 memory used=15779.0MB, alloc=425.3MB, time=149.12 memory used=15841.5MB, alloc=425.3MB, time=149.38 memory used=15917.6MB, alloc=425.3MB, time=149.64 memory used=15967.8MB, alloc=425.3MB, time=149.85 memory used=16024.7MB, alloc=425.3MB, time=150.09 memory used=16089.5MB, alloc=425.3MB, time=150.33 memory used=16162.9MB, alloc=425.3MB, time=150.57 memory used=16245.2MB, alloc=425.3MB, time=150.82 memory used=16298.9MB, alloc=425.3MB, time=151.03 memory used=16346.6MB, alloc=425.3MB, time=151.22 memory used=16397.4MB, alloc=425.3MB, time=151.45 memory used=16452.2MB, alloc=425.3MB, time=151.65 memory used=16511.4MB, alloc=425.3MB, time=151.87 memory used=16575.3MB, alloc=425.3MB, time=152.08 memory used=16706.3MB, alloc=425.3MB, time=153.98 memory used=16869.0MB, alloc=449.3MB, time=156.76 memory used=16996.5MB, alloc=449.3MB, time=158.65 memory used=17151.5MB, alloc=449.3MB, time=160.78 memory used=17253.3MB, alloc=449.3MB, time=162.24 memory used=17368.9MB, alloc=449.3MB, time=163.69 memory used=17473.5MB, alloc=449.3MB, time=164.83 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428248152 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 F := [-8 y z + 18 x z - 19 y z, -6 x - 13 x z - 8 x y, 3 2 2 -14 x z - 13 x y z + 6 x y ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 3 2 3 G := [-18 x z - x - 10 x z, 20 x y + 9 x y z - 11 y , 2 2 3 2 18 x z - 19 x z + 9 x z ] > Problem := [F,G]; 3 2 3 2 Problem := [[-8 y z + 18 x z - 19 y z, -6 x - 13 x z - 8 x y, 3 2 2 2 2 3 2 -14 x z - 13 x y z + 6 x y ], [-18 x z - x - 10 x z, 3 2 3 2 2 3 2 20 x y + 9 x y z - 11 y , 18 x z - 19 x z + 9 x z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.17 memory used=26.2MB, alloc=32.3MB, time=0.49 memory used=47.3MB, alloc=56.3MB, time=0.82 memory used=87.1MB, alloc=60.3MB, time=1.41 memory used=126.1MB, alloc=84.3MB, time=2.00 memory used=170.7MB, alloc=84.3MB, time=2.68 memory used=230.6MB, alloc=92.3MB, time=3.59 memory used=290.9MB, alloc=116.3MB, time=4.47 memory used=368.9MB, alloc=116.3MB, time=5.61 memory used=439.7MB, alloc=396.3MB, time=6.65 memory used=552.5MB, alloc=420.3MB, time=8.21 memory used=681.9MB, alloc=444.3MB, time=10.27 memory used=809.4MB, alloc=468.3MB, time=12.13 memory used=943.7MB, alloc=468.3MB, time=14.35 memory used=1056.5MB, alloc=468.3MB, time=16.12 memory used=1166.6MB, alloc=492.3MB, time=17.89 memory used=1268.6MB, alloc=492.3MB, time=19.60 memory used=1379.8MB, alloc=492.3MB, time=20.98 memory used=1487.2MB, alloc=516.3MB, time=22.60 memory used=1577.6MB, alloc=516.3MB, time=23.94 memory used=1666.9MB, alloc=516.3MB, time=25.54 memory used=1747.8MB, alloc=516.3MB, time=26.76 memory used=1836.6MB, alloc=516.3MB, time=28.03 memory used=1915.6MB, alloc=516.3MB, time=29.62 memory used=1988.1MB, alloc=516.3MB, time=31.14 memory used=2054.3MB, alloc=516.3MB, time=32.41 memory used=2109.7MB, alloc=516.3MB, time=33.72 memory used=2165.6MB, alloc=540.3MB, time=34.75 memory used=2234.9MB, alloc=540.3MB, time=36.32 memory used=2278.6MB, alloc=540.3MB, time=37.33 memory used=2483.1MB, alloc=564.3MB, time=41.16 memory used=2696.9MB, alloc=588.3MB, time=45.12 memory used=2893.1MB, alloc=612.3MB, time=49.03 memory used=3084.4MB, alloc=636.3MB, time=53.10 memory used=3253.5MB, alloc=660.3MB, time=56.49 memory used=3429.8MB, alloc=684.3MB, time=60.51 memory used=3589.3MB, alloc=684.3MB, time=63.85 memory used=3865.1MB, alloc=684.3MB, time=67.61 memory used=3977.2MB, alloc=684.3MB, time=70.06 memory used=4130.4MB, alloc=708.3MB, time=73.76 memory used=4255.0MB, alloc=708.3MB, time=76.78 memory used=4338.4MB, alloc=708.3MB, time=79.30 memory used=4457.0MB, alloc=708.3MB, time=82.28 memory used=4569.2MB, alloc=708.3MB, time=85.24 memory used=4946.4MB, alloc=732.3MB, time=92.44 memory used=5327.6MB, alloc=756.3MB, time=101.03 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428248452 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; F := [ 3 2 3 2 3 -4 x z + 15 x y - 5 y, 8 x z + 12 x z + 11 x z, 12 x z - 15 y z + 12 z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 4 2 3 3 2 G := [20 x y z - 4 y z + 4 z , -7 y - x z + x y, -x z + 4 y z - 17 y z ] > Problem := [F,G]; Problem := [[ 3 2 3 2 3 -4 x z + 15 x y - 5 y, 8 x z + 12 x z + 11 x z, 12 x z - 15 y z + 12 z 2 3 4 2 3 3 2 ], [20 x y z - 4 y z + 4 z , -7 y - x z + x y, -x z + 4 y z - 17 y z ] ] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.5MB, alloc=32.3MB, time=0.50 memory used=46.4MB, alloc=32.3MB, time=0.78 memory used=65.0MB, alloc=56.3MB, time=1.07 memory used=107.1MB, alloc=60.3MB, time=1.69 memory used=147.6MB, alloc=84.3MB, time=2.27 memory used=213.0MB, alloc=92.3MB, time=3.16 memory used=284.3MB, alloc=92.3MB, time=3.98 memory used=348.9MB, alloc=116.3MB, time=4.89 memory used=429.6MB, alloc=396.3MB, time=6.04 memory used=544.3MB, alloc=420.3MB, time=7.56 memory used=679.0MB, alloc=444.3MB, time=9.56 memory used=784.1MB, alloc=444.3MB, time=11.01 memory used=899.0MB, alloc=468.3MB, time=12.70 memory used=1013.5MB, alloc=468.3MB, time=14.35 memory used=1118.1MB, alloc=468.3MB, time=15.69 memory used=1220.1MB, alloc=468.3MB, time=17.31 memory used=1325.1MB, alloc=492.3MB, time=18.89 memory used=1442.7MB, alloc=492.3MB, time=20.20 memory used=1523.7MB, alloc=492.3MB, time=21.29 memory used=1607.2MB, alloc=492.3MB, time=22.70 memory used=1684.8MB, alloc=492.3MB, time=24.06 memory used=1748.6MB, alloc=492.3MB, time=25.33 memory used=1800.1MB, alloc=492.3MB, time=26.43 memory used=1858.0MB, alloc=516.3MB, time=27.69 memory used=1910.8MB, alloc=516.3MB, time=28.88 memory used=2119.6MB, alloc=540.3MB, time=32.38 memory used=2281.3MB, alloc=564.3MB, time=34.92 memory used=2471.5MB, alloc=588.3MB, time=38.45 memory used=2685.1MB, alloc=612.3MB, time=41.16 memory used=2868.0MB, alloc=636.3MB, time=43.58 memory used=3058.9MB, alloc=636.3MB, time=45.56 memory used=3298.1MB, alloc=636.3MB, time=48.78 memory used=3429.5MB, alloc=636.3MB, time=51.03 memory used=3582.4MB, alloc=660.3MB, time=53.72 memory used=3727.3MB, alloc=660.3MB, time=56.11 memory used=3841.1MB, alloc=660.3MB, time=58.43 memory used=4021.4MB, alloc=684.3MB, time=62.46 memory used=4141.3MB, alloc=684.3MB, time=64.50 memory used=4237.9MB, alloc=684.3MB, time=66.46 memory used=4344.5MB, alloc=684.3MB, time=68.74 memory used=4677.4MB, alloc=708.3MB, time=75.26 memory used=5033.6MB, alloc=732.3MB, time=81.33 memory used=5383.7MB, alloc=756.3MB, time=87.10 memory used=5725.1MB, alloc=780.3MB, time=94.11 memory used=6041.1MB, alloc=804.3MB, time=99.99 memory used=6310.3MB, alloc=828.3MB, time=105.33 memory used=6573.8MB, alloc=852.3MB, time=110.90 memory used=6881.5MB, alloc=876.3MB, time=116.23 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428248752 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 3 2 F := [-7 x z + 15 x y z, 17 x y + 14 x z + 11, 7 y z + 9 x y + 8 y z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 4 3 2 2 2 G := [17 z - 14 y z + 10, -2 x z + 4 z + 18 x , 10 x y + 4 x y z - 3 z] > Problem := [F,G]; Problem := [ 2 2 2 2 3 2 [-7 x z + 15 x y z, 17 x y + 14 x z + 11, 7 y z + 9 x y + 8 y z], 4 2 2 4 3 2 2 2 [17 z - 14 y z + 10, -2 x z + 4 z + 18 x , 10 x y + 4 x y z - 3 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.18 memory used=26.9MB, alloc=32.3MB, time=0.51 memory used=48.3MB, alloc=32.3MB, time=0.82 memory used=66.5MB, alloc=56.3MB, time=1.11 memory used=106.4MB, alloc=60.3MB, time=1.69 memory used=146.9MB, alloc=84.3MB, time=2.27 memory used=211.2MB, alloc=92.3MB, time=3.23 memory used=277.6MB, alloc=116.3MB, time=4.20 memory used=351.4MB, alloc=116.3MB, time=5.20 memory used=420.7MB, alloc=372.3MB, time=6.17 memory used=511.8MB, alloc=396.3MB, time=7.36 memory used=621.3MB, alloc=396.3MB, time=8.98 memory used=729.9MB, alloc=420.3MB, time=10.64 memory used=862.2MB, alloc=420.3MB, time=12.47 memory used=996.3MB, alloc=444.3MB, time=14.37 memory used=1129.7MB, alloc=468.3MB, time=16.13 memory used=1285.7MB, alloc=468.3MB, time=17.68 memory used=1373.6MB, alloc=468.3MB, time=18.03 memory used=1466.1MB, alloc=468.3MB, time=18.67 memory used=1619.6MB, alloc=468.3MB, time=20.09 memory used=1717.0MB, alloc=468.3MB, time=20.95 memory used=1832.5MB, alloc=468.3MB, time=22.25 memory used=1978.2MB, alloc=468.3MB, time=23.84 memory used=2107.4MB, alloc=468.3MB, time=24.84 memory used=2296.1MB, alloc=468.3MB, time=27.26 memory used=2442.7MB, alloc=468.3MB, time=28.80 memory used=2522.7MB, alloc=468.3MB, time=29.20 memory used=2654.2MB, alloc=468.3MB, time=30.73 memory used=2789.8MB, alloc=492.3MB, time=32.53 memory used=2884.0MB, alloc=492.3MB, time=33.88 memory used=2995.0MB, alloc=492.3MB, time=35.25 memory used=3106.4MB, alloc=492.3MB, time=36.76 memory used=3243.3MB, alloc=492.3MB, time=38.44 memory used=3382.0MB, alloc=492.3MB, time=39.72 memory used=3508.6MB, alloc=492.3MB, time=41.78 memory used=3597.6MB, alloc=492.3MB, time=43.04 memory used=3676.0MB, alloc=492.3MB, time=44.40 memory used=3764.7MB, alloc=516.3MB, time=46.02 memory used=3838.7MB, alloc=516.3MB, time=47.30 memory used=3927.5MB, alloc=516.3MB, time=48.93 memory used=4002.8MB, alloc=516.3MB, time=50.25 memory used=4063.2MB, alloc=516.3MB, time=51.25 memory used=4139.5MB, alloc=516.3MB, time=52.39 memory used=4215.3MB, alloc=516.3MB, time=53.88 memory used=4283.6MB, alloc=516.3MB, time=55.16 memory used=4351.8MB, alloc=516.3MB, time=56.40 memory used=4422.1MB, alloc=516.3MB, time=57.86 memory used=4482.9MB, alloc=516.3MB, time=59.14 memory used=4526.5MB, alloc=516.3MB, time=60.20 memory used=4577.1MB, alloc=516.3MB, time=61.32 memory used=4798.3MB, alloc=540.3MB, time=64.20 memory used=4987.1MB, alloc=564.3MB, time=67.39 memory used=5159.7MB, alloc=588.3MB, time=69.99 memory used=5375.2MB, alloc=612.3MB, time=72.97 memory used=5535.2MB, alloc=636.3MB, time=75.62 memory used=5681.0MB, alloc=660.3MB, time=77.78 memory used=5889.5MB, alloc=660.3MB, time=80.46 memory used=6070.8MB, alloc=660.3MB, time=83.12 memory used=6226.0MB, alloc=660.3MB, time=84.06 memory used=6389.3MB, alloc=660.3MB, time=85.08 memory used=6601.5MB, alloc=660.3MB, time=91.09 memory used=6736.8MB, alloc=660.3MB, time=91.87 memory used=6902.8MB, alloc=660.3MB, time=92.88 memory used=7070.5MB, alloc=660.3MB, time=93.99 memory used=7278.4MB, alloc=660.3MB, time=100.18 memory used=7416.0MB, alloc=660.3MB, time=100.96 memory used=7598.0MB, alloc=660.3MB, time=102.25 memory used=7742.5MB, alloc=660.3MB, time=103.18 memory used=7875.5MB, alloc=660.3MB, time=103.99 memory used=8053.9MB, alloc=660.3MB, time=105.23 memory used=8200.2MB, alloc=660.3MB, time=106.18 memory used=8355.3MB, alloc=660.3MB, time=107.07 memory used=8486.8MB, alloc=660.3MB, time=107.86 memory used=8646.6MB, alloc=660.3MB, time=117.19 memory used=8830.1MB, alloc=660.3MB, time=118.56 memory used=9009.9MB, alloc=660.3MB, time=121.18 memory used=9236.8MB, alloc=660.3MB, time=124.67 memory used=9377.9MB, alloc=684.3MB, time=127.83 memory used=9615.1MB, alloc=684.3MB, time=130.21 memory used=9774.1MB, alloc=684.3MB, time=132.99 memory used=9870.0MB, alloc=684.3MB, time=135.01 memory used=9985.5MB, alloc=684.3MB, time=136.99 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428249052 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; F := [ 2 2 3 2 2 2 2 4 2 6 x y + 2 y + 5 z, 17 y z + 17 y z - 11 x z , 17 x y z + 16 y - 7 z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 4 2 G := [-12 x z + 10 x y z + 18 y z, 15 y - 17 y z, 15 z + 5 x y z - 6 y ] > Problem := [F,G]; Problem := [[ 2 2 3 2 2 2 2 4 2 6 x y + 2 y + 5 z, 17 y z + 17 y z - 11 x z , 17 x y z + 16 y - 7 z 3 2 3 2 4 2 ], [-12 x z + 10 x y z + 18 y z, 15 y - 17 y z, 15 z + 5 x y z - 6 y ] ] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.18 memory used=26.5MB, alloc=32.3MB, time=0.51 memory used=47.7MB, alloc=32.3MB, time=0.83 memory used=67.6MB, alloc=56.3MB, time=1.14 memory used=107.5MB, alloc=60.3MB, time=1.75 memory used=146.0MB, alloc=60.3MB, time=2.32 memory used=184.5MB, alloc=84.3MB, time=2.92 memory used=233.7MB, alloc=84.3MB, time=3.68 memory used=293.0MB, alloc=92.3MB, time=4.63 memory used=349.2MB, alloc=116.3MB, time=5.51 memory used=430.3MB, alloc=116.3MB, time=6.76 memory used=501.7MB, alloc=396.3MB, time=7.80 memory used=612.7MB, alloc=396.3MB, time=9.43 memory used=720.8MB, alloc=420.3MB, time=11.07 memory used=840.1MB, alloc=420.3MB, time=12.81 memory used=958.7MB, alloc=444.3MB, time=14.54 memory used=1056.7MB, alloc=444.3MB, time=16.00 memory used=1173.6MB, alloc=468.3MB, time=17.82 memory used=1281.4MB, alloc=468.3MB, time=19.61 memory used=1392.8MB, alloc=468.3MB, time=21.48 memory used=1496.3MB, alloc=468.3MB, time=23.34 memory used=1592.6MB, alloc=492.3MB, time=25.10 memory used=1689.4MB, alloc=492.3MB, time=26.68 memory used=1811.8MB, alloc=492.3MB, time=27.70 memory used=1924.6MB, alloc=492.3MB, time=28.39 memory used=2060.9MB, alloc=492.3MB, time=29.81 memory used=2139.8MB, alloc=492.3MB, time=31.08 memory used=2222.7MB, alloc=492.3MB, time=32.20 memory used=2302.3MB, alloc=492.3MB, time=33.80 memory used=2377.2MB, alloc=492.3MB, time=35.26 memory used=2445.1MB, alloc=492.3MB, time=36.54 memory used=2494.6MB, alloc=492.3MB, time=37.47 memory used=2573.4MB, alloc=492.3MB, time=39.17 memory used=2629.1MB, alloc=492.3MB, time=40.25 memory used=2695.2MB, alloc=492.3MB, time=41.76 memory used=2747.5MB, alloc=492.3MB, time=42.90 memory used=2784.8MB, alloc=492.3MB, time=43.80 memory used=2836.7MB, alloc=492.3MB, time=45.08 memory used=3020.2MB, alloc=516.3MB, time=48.37 memory used=3231.9MB, alloc=540.3MB, time=51.91 memory used=3425.3MB, alloc=564.3MB, time=55.44 memory used=3644.4MB, alloc=588.3MB, time=58.31 memory used=3864.1MB, alloc=588.3MB, time=60.88 memory used=3987.2MB, alloc=588.3MB, time=61.65 memory used=4108.7MB, alloc=588.3MB, time=62.40 memory used=4209.9MB, alloc=588.3MB, time=63.08 memory used=4328.3MB, alloc=588.3MB, time=63.74 memory used=4468.6MB, alloc=588.3MB, time=64.42 memory used=4585.9MB, alloc=588.3MB, time=65.07 memory used=4726.5MB, alloc=588.3MB, time=66.15 memory used=4849.9MB, alloc=588.3MB, time=66.89 memory used=4964.4MB, alloc=588.3MB, time=67.62 memory used=5073.1MB, alloc=588.3MB, time=68.32 memory used=5207.8MB, alloc=588.3MB, time=68.99 memory used=5395.6MB, alloc=588.3MB, time=78.44 memory used=5515.3MB, alloc=588.3MB, time=79.14 memory used=5641.7MB, alloc=588.3MB, time=79.79 memory used=5743.0MB, alloc=588.3MB, time=80.39 memory used=5885.3MB, alloc=588.3MB, time=81.19 memory used=6032.3MB, alloc=588.3MB, time=82.05 memory used=6150.7MB, alloc=588.3MB, time=83.28 memory used=6402.1MB, alloc=588.3MB, time=94.21 memory used=6519.7MB, alloc=588.3MB, time=94.95 memory used=6645.8MB, alloc=588.3MB, time=95.65 memory used=6759.7MB, alloc=588.3MB, time=96.31 memory used=6856.5MB, alloc=588.3MB, time=96.92 memory used=6969.8MB, alloc=588.3MB, time=97.59 memory used=7103.4MB, alloc=588.3MB, time=98.27 memory used=7329.2MB, alloc=612.3MB, time=100.18 memory used=7483.2MB, alloc=612.3MB, time=101.18 memory used=7740.2MB, alloc=612.3MB, time=104.40 memory used=7915.0MB, alloc=612.3MB, time=106.01 memory used=8053.6MB, alloc=612.3MB, time=106.87 memory used=8183.1MB, alloc=612.3MB, time=107.71 memory used=8290.2MB, alloc=636.3MB, time=108.49 memory used=8426.8MB, alloc=636.3MB, time=109.31 memory used=8583.7MB, alloc=636.3MB, time=110.14 memory used=8764.0MB, alloc=636.3MB, time=110.98 memory used=8900.5MB, alloc=636.3MB, time=111.74 memory used=9002.0MB, alloc=636.3MB, time=112.46 memory used=9110.9MB, alloc=636.3MB, time=113.16 memory used=9226.9MB, alloc=636.3MB, time=113.86 memory used=9349.5MB, alloc=636.3MB, time=114.58 memory used=9483.9MB, alloc=636.3MB, time=115.30 memory used=9623.9MB, alloc=636.3MB, time=116.02 memory used=9776.3MB, alloc=636.3MB, time=116.74 memory used=9941.0MB, alloc=636.3MB, time=117.49 memory used=10117.0MB, alloc=636.3MB, time=118.22 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428249352 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; F := [ 2 2 3 2 2 4 2 2 -9 y z - 17 x + 15 z, 8 y z - 15 y z - 10 y, -12 y - 15 x z - 7 y z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 2 G := [-15 x y z + 4 x y + 7 z, -5 x z - 13 x y - 6 y z , 3 2 -4 x + 18 x z - 2 y z] > Problem := [F,G]; Problem := [[ 2 2 3 2 2 4 2 2 -9 y z - 17 x + 15 z, 8 y z - 15 y z - 10 y, -12 y - 15 x z - 7 y z 2 2 3 2 2 2 ], [-15 x y z + 4 x y + 7 z, -5 x z - 13 x y - 6 y z , 3 2 -4 x + 18 x z - 2 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.18 memory used=26.9MB, alloc=32.3MB, time=0.52 memory used=47.4MB, alloc=56.3MB, time=0.76 memory used=88.3MB, alloc=60.3MB, time=1.32 memory used=130.6MB, alloc=60.3MB, time=1.90 memory used=166.9MB, alloc=63.4MB, time=2.06 memory used=204.9MB, alloc=63.4MB, time=2.70 memory used=226.1MB, alloc=63.4MB, time=2.77 memory used=267.9MB, alloc=71.4MB, time=3.21 memory used=314.6MB, alloc=71.4MB, time=3.83 memory used=357.3MB, alloc=95.4MB, time=4.45 memory used=418.9MB, alloc=95.4MB, time=5.19 memory used=481.7MB, alloc=95.4MB, time=5.80 memory used=542.9MB, alloc=95.4MB, time=6.70 memory used=608.2MB, alloc=119.4MB, time=7.51 memory used=681.2MB, alloc=375.4MB, time=8.35 memory used=772.2MB, alloc=399.4MB, time=9.48 memory used=878.8MB, alloc=399.4MB, time=11.13 memory used=988.6MB, alloc=423.4MB, time=12.69 memory used=1092.4MB, alloc=423.4MB, time=13.41 memory used=1172.1MB, alloc=423.4MB, time=14.05 memory used=1258.9MB, alloc=423.4MB, time=14.82 memory used=1355.0MB, alloc=423.4MB, time=15.48 memory used=1437.3MB, alloc=423.4MB, time=15.91 memory used=1529.7MB, alloc=423.4MB, time=16.73 memory used=1647.8MB, alloc=423.4MB, time=17.90 memory used=1784.0MB, alloc=447.4MB, time=19.41 memory used=1928.6MB, alloc=447.4MB, time=20.56 memory used=2031.9MB, alloc=447.4MB, time=21.56 memory used=2131.3MB, alloc=447.4MB, time=22.24 memory used=2252.2MB, alloc=447.4MB, time=23.88 memory used=2364.1MB, alloc=447.4MB, time=24.80 memory used=2487.6MB, alloc=447.4MB, time=26.44 memory used=2588.6MB, alloc=471.4MB, time=27.97 memory used=2696.4MB, alloc=471.4MB, time=29.54 memory used=2805.2MB, alloc=471.4MB, time=31.41 memory used=2921.3MB, alloc=471.4MB, time=32.37 memory used=3019.1MB, alloc=471.4MB, time=32.92 memory used=3126.2MB, alloc=471.4MB, time=34.08 memory used=3254.8MB, alloc=471.4MB, time=35.48 memory used=3366.7MB, alloc=495.4MB, time=36.79 memory used=3471.6MB, alloc=495.4MB, time=38.00 memory used=3602.5MB, alloc=495.4MB, time=38.83 memory used=3724.9MB, alloc=495.4MB, time=40.36 memory used=3796.0MB, alloc=495.4MB, time=41.52 memory used=3883.9MB, alloc=495.4MB, time=42.81 memory used=3953.3MB, alloc=495.4MB, time=44.03 memory used=4025.6MB, alloc=495.4MB, time=45.53 memory used=4099.1MB, alloc=495.4MB, time=47.00 memory used=4168.6MB, alloc=495.4MB, time=48.43 memory used=4225.4MB, alloc=495.4MB, time=49.37 memory used=4284.1MB, alloc=495.4MB, time=50.38 memory used=4339.2MB, alloc=495.4MB, time=51.62 memory used=4393.5MB, alloc=495.4MB, time=52.66 memory used=4454.4MB, alloc=495.4MB, time=53.83 memory used=4507.6MB, alloc=495.4MB, time=54.99 memory used=4557.9MB, alloc=519.4MB, time=55.92 memory used=4692.8MB, alloc=519.4MB, time=57.26 memory used=4817.8MB, alloc=519.4MB, time=58.36 memory used=5010.7MB, alloc=519.4MB, time=61.05 memory used=5143.8MB, alloc=519.4MB, time=63.42 memory used=5240.2MB, alloc=519.4MB, time=63.95 memory used=5360.4MB, alloc=519.4MB, time=64.79 memory used=5496.0MB, alloc=519.4MB, time=66.06 memory used=5746.6MB, alloc=519.4MB, time=68.92 memory used=5919.6MB, alloc=519.4MB, time=71.28 memory used=6098.1MB, alloc=519.4MB, time=73.56 memory used=6212.1MB, alloc=519.4MB, time=75.70 memory used=6303.1MB, alloc=519.4MB, time=76.22 memory used=6402.7MB, alloc=519.4MB, time=77.03 memory used=6505.6MB, alloc=519.4MB, time=77.75 memory used=6618.3MB, alloc=519.4MB, time=78.66 memory used=6827.4MB, alloc=543.4MB, time=80.93 memory used=6970.4MB, alloc=543.4MB, time=82.15 memory used=7065.2MB, alloc=543.4MB, time=82.74 memory used=7277.0MB, alloc=567.4MB, time=85.89 memory used=7396.7MB, alloc=567.4MB, time=86.83 memory used=7525.9MB, alloc=567.4MB, time=87.65 memory used=7662.2MB, alloc=567.4MB, time=88.68 memory used=7862.3MB, alloc=567.4MB, time=91.69 memory used=8011.6MB, alloc=591.4MB, time=94.30 memory used=8162.7MB, alloc=591.4MB, time=96.99 memory used=8284.3MB, alloc=591.4MB, time=99.38 memory used=8419.9MB, alloc=615.4MB, time=101.98 memory used=8596.8MB, alloc=615.4MB, time=103.84 memory used=8756.6MB, alloc=615.4MB, time=104.87 memory used=8913.0MB, alloc=615.4MB, time=107.01 memory used=9043.0MB, alloc=615.4MB, time=107.83 memory used=9265.5MB, alloc=615.4MB, time=110.15 memory used=9440.3MB, alloc=615.4MB, time=113.15 memory used=9684.6MB, alloc=615.4MB, time=115.44 memory used=9890.7MB, alloc=615.4MB, time=117.71 memory used=10038.6MB, alloc=639.4MB, time=119.13 memory used=10178.1MB, alloc=639.4MB, time=120.03 memory used=10320.2MB, alloc=639.4MB, time=120.89 memory used=10430.7MB, alloc=639.4MB, time=121.67 memory used=10559.4MB, alloc=639.4MB, time=122.46 memory used=10705.8MB, alloc=639.4MB, time=123.27 memory used=10875.6MB, alloc=639.4MB, time=124.10 memory used=11088.0MB, alloc=639.4MB, time=125.15 memory used=11222.5MB, alloc=639.4MB, time=125.92 memory used=11494.1MB, alloc=639.4MB, time=127.52 memory used=11644.2MB, alloc=639.4MB, time=128.41 memory used=11774.1MB, alloc=639.4MB, time=129.22 memory used=11889.1MB, alloc=639.4MB, time=130.02 memory used=12021.5MB, alloc=639.4MB, time=130.82 memory used=12175.4MB, alloc=639.4MB, time=131.62 memory used=12352.1MB, alloc=639.4MB, time=132.46 memory used=12518.5MB, alloc=639.4MB, time=133.31 memory used=12652.7MB, alloc=639.4MB, time=134.09 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428249652 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; F := 4 3 4 2 2 2 2 2 3 [-8 x + 15 x z - 17 z , -7 x z + 2 y z + 13 y, 2 y z - 10 z - 10 z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 4 3 2 G := [12 x z - 20 y z + 12 z , 16 x y + 7 y z + 10 y, 2 2 -15 x z + 7 y z - 11 y z] > Problem := [F,G]; Problem := [ 4 3 4 2 2 2 2 2 3 [-8 x + 15 x z - 17 z , -7 x z + 2 y z + 13 y, 2 y z - 10 z - 10 z] 3 2 2 4 3 2 , [12 x z - 20 y z + 12 z , 16 x y + 7 y z + 10 y, 2 2 -15 x z + 7 y z - 11 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.18 memory used=26.1MB, alloc=32.3MB, time=0.49 memory used=46.2MB, alloc=60.3MB, time=0.79 memory used=88.5MB, alloc=60.3MB, time=1.36 memory used=130.0MB, alloc=68.3MB, time=1.89 memory used=180.7MB, alloc=68.3MB, time=2.43 memory used=220.9MB, alloc=92.3MB, time=3.02 memory used=288.6MB, alloc=92.3MB, time=3.81 memory used=351.7MB, alloc=92.3MB, time=4.59 memory used=409.3MB, alloc=116.3MB, time=5.47 memory used=481.5MB, alloc=116.3MB, time=6.49 memory used=547.5MB, alloc=396.3MB, time=7.54 memory used=652.6MB, alloc=396.3MB, time=8.95 memory used=753.7MB, alloc=396.3MB, time=10.05 memory used=875.8MB, alloc=396.3MB, time=11.39 memory used=977.1MB, alloc=420.3MB, time=13.02 memory used=1105.1MB, alloc=420.3MB, time=14.90 memory used=1215.9MB, alloc=420.3MB, time=16.01 memory used=1301.1MB, alloc=420.3MB, time=16.69 memory used=1397.7MB, alloc=444.3MB, time=18.29 memory used=1543.0MB, alloc=444.3MB, time=20.35 memory used=1685.9MB, alloc=444.3MB, time=22.44 memory used=1815.4MB, alloc=468.3MB, time=24.49 memory used=1950.2MB, alloc=468.3MB, time=26.93 memory used=2083.2MB, alloc=492.3MB, time=29.45 memory used=2199.3MB, alloc=492.3MB, time=31.57 memory used=2294.1MB, alloc=492.3MB, time=33.23 memory used=2402.2MB, alloc=516.3MB, time=34.90 memory used=2503.6MB, alloc=516.3MB, time=36.64 memory used=2601.6MB, alloc=516.3MB, time=38.17 memory used=2677.2MB, alloc=516.3MB, time=39.59 memory used=2760.9MB, alloc=516.3MB, time=40.96 memory used=2883.1MB, alloc=516.3MB, time=42.48 memory used=2996.4MB, alloc=516.3MB, time=43.49 memory used=3095.4MB, alloc=516.3MB, time=44.54 memory used=3191.7MB, alloc=516.3MB, time=46.17 memory used=3270.2MB, alloc=516.3MB, time=47.65 memory used=3398.1MB, alloc=516.3MB, time=49.39 memory used=3512.4MB, alloc=516.3MB, time=50.82 memory used=3640.7MB, alloc=540.3MB, time=52.67 memory used=3770.5MB, alloc=540.3MB, time=54.11 memory used=3846.8MB, alloc=540.3MB, time=55.26 memory used=3951.1MB, alloc=540.3MB, time=56.95 memory used=4046.7MB, alloc=540.3MB, time=59.22 memory used=4116.0MB, alloc=540.3MB, time=60.76 memory used=4208.8MB, alloc=540.3MB, time=61.98 memory used=4278.1MB, alloc=540.3MB, time=63.45 memory used=4349.8MB, alloc=540.3MB, time=65.00 memory used=4408.3MB, alloc=540.3MB, time=66.41 memory used=4469.9MB, alloc=540.3MB, time=67.96 memory used=4533.1MB, alloc=540.3MB, time=69.43 memory used=4588.5MB, alloc=540.3MB, time=70.96 memory used=4634.6MB, alloc=540.3MB, time=72.22 memory used=4853.6MB, alloc=564.3MB, time=76.78 memory used=5077.2MB, alloc=588.3MB, time=79.99 memory used=5297.8MB, alloc=612.3MB, time=82.82 memory used=5535.0MB, alloc=612.3MB, time=85.59 memory used=5765.7MB, alloc=612.3MB, time=88.99 memory used=5955.1MB, alloc=636.3MB, time=92.78 memory used=6107.3MB, alloc=636.3MB, time=95.44 memory used=6271.0MB, alloc=660.3MB, time=97.81 memory used=6444.7MB, alloc=684.3MB, time=101.75 memory used=6641.3MB, alloc=684.3MB, time=105.75 memory used=6782.6MB, alloc=708.3MB, time=108.43 memory used=6925.5MB, alloc=708.3MB, time=110.79 memory used=7059.5MB, alloc=708.3MB, time=113.09 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428249952 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 3 2 2 F := [8 x z - 15 x y - 20 y z , 4 y z + 14 y z + 5 y z , 3 2 2 12 x y - 5 x z - 8 x] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; G := 3 3 3 3 3 2 [10 y z - 13 x + 9 x y, -7 y z + 3 z - 7 x z, -6 x z + 18 x z - 10 y] > Problem := [F,G]; 3 3 2 2 3 2 2 Problem := [[8 x z - 15 x y - 20 y z , 4 y z + 14 y z + 5 y z , 3 2 2 12 x y - 5 x z - 8 x], 3 3 3 3 3 2 [10 y z - 13 x + 9 x y, -7 y z + 3 z - 7 x z, -6 x z + 18 x z - 10 y] ] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.8MB, alloc=32.3MB, time=0.51 memory used=46.9MB, alloc=32.3MB, time=0.80 memory used=66.4MB, alloc=56.3MB, time=1.11 memory used=106.2MB, alloc=60.3MB, time=1.70 memory used=143.7MB, alloc=84.3MB, time=2.25 memory used=208.0MB, alloc=92.3MB, time=3.19 memory used=266.4MB, alloc=116.3MB, time=4.08 memory used=351.6MB, alloc=116.3MB, time=5.35 memory used=425.5MB, alloc=372.3MB, time=6.41 memory used=506.8MB, alloc=396.3MB, time=7.70 memory used=617.3MB, alloc=396.3MB, time=9.31 memory used=726.5MB, alloc=420.3MB, time=10.80 memory used=821.8MB, alloc=420.3MB, time=11.82 memory used=946.6MB, alloc=420.3MB, time=13.22 memory used=1074.1MB, alloc=420.3MB, time=14.76 memory used=1160.8MB, alloc=420.3MB, time=15.50 memory used=1248.1MB, alloc=420.3MB, time=16.31 memory used=1367.7MB, alloc=420.3MB, time=17.93 memory used=1499.9MB, alloc=444.3MB, time=19.62 memory used=1645.1MB, alloc=444.3MB, time=21.82 memory used=1782.1MB, alloc=468.3MB, time=24.02 memory used=1905.4MB, alloc=468.3MB, time=26.08 memory used=2024.0MB, alloc=468.3MB, time=28.02 memory used=2124.7MB, alloc=492.3MB, time=29.72 memory used=2240.0MB, alloc=492.3MB, time=31.66 memory used=2330.6MB, alloc=492.3MB, time=33.04 memory used=2475.6MB, alloc=492.3MB, time=35.70 memory used=2556.4MB, alloc=492.3MB, time=36.09 memory used=2666.1MB, alloc=492.3MB, time=36.69 memory used=2752.6MB, alloc=492.3MB, time=37.08 memory used=2858.5MB, alloc=492.3MB, time=42.07 memory used=2940.7MB, alloc=492.3MB, time=42.46 memory used=3031.7MB, alloc=492.3MB, time=42.81 memory used=3115.1MB, alloc=492.3MB, time=43.23 memory used=3214.9MB, alloc=492.3MB, time=44.28 memory used=3367.4MB, alloc=492.3MB, time=46.70 memory used=3440.0MB, alloc=516.3MB, time=47.12 memory used=3552.7MB, alloc=516.3MB, time=47.58 memory used=3654.8MB, alloc=516.3MB, time=48.02 memory used=3733.7MB, alloc=516.3MB, time=48.42 memory used=3822.1MB, alloc=516.3MB, time=48.82 memory used=3921.6MB, alloc=516.3MB, time=49.20 memory used=4032.7MB, alloc=516.3MB, time=49.59 memory used=4159.9MB, alloc=516.3MB, time=49.99 memory used=4232.4MB, alloc=516.3MB, time=50.30 memory used=4340.1MB, alloc=516.3MB, time=63.41 memory used=4464.4MB, alloc=516.3MB, time=81.02 memory used=4562.5MB, alloc=516.3MB, time=81.47 memory used=4656.1MB, alloc=516.3MB, time=81.89 memory used=4774.2MB, alloc=516.3MB, time=82.32 memory used=4858.2MB, alloc=516.3MB, time=82.69 memory used=4935.4MB, alloc=516.3MB, time=83.06 memory used=5021.9MB, alloc=516.3MB, time=83.43 memory used=5119.2MB, alloc=516.3MB, time=83.81 memory used=5228.4MB, alloc=516.3MB, time=84.17 memory used=5363.5MB, alloc=516.3MB, time=84.72 memory used=5495.9MB, alloc=516.3MB, time=87.38 memory used=5593.4MB, alloc=516.3MB, time=87.78 memory used=5744.7MB, alloc=516.3MB, time=88.85 memory used=5947.3MB, alloc=516.3MB, time=92.96 memory used=6092.3MB, alloc=516.3MB, time=95.83 memory used=6292.9MB, alloc=516.3MB, time=98.72 memory used=6432.4MB, alloc=516.3MB, time=102.78 memory used=6579.8MB, alloc=516.3MB, time=105.46 memory used=6672.9MB, alloc=516.3MB, time=105.89 memory used=6795.7MB, alloc=516.3MB, time=106.56 memory used=6901.6MB, alloc=516.3MB, time=110.20 memory used=7016.1MB, alloc=516.3MB, time=112.10 memory used=7113.6MB, alloc=516.3MB, time=112.49 memory used=7216.3MB, alloc=516.3MB, time=112.98 memory used=7364.2MB, alloc=516.3MB, time=114.71 memory used=7455.5MB, alloc=516.3MB, time=115.96 memory used=7558.4MB, alloc=516.3MB, time=118.19 memory used=7657.1MB, alloc=516.3MB, time=118.72 memory used=7754.3MB, alloc=540.3MB, time=119.23 memory used=7876.6MB, alloc=540.3MB, time=119.72 memory used=7961.6MB, alloc=540.3MB, time=120.17 memory used=8058.2MB, alloc=540.3MB, time=120.63 memory used=8166.6MB, alloc=540.3MB, time=121.07 memory used=8291.6MB, alloc=540.3MB, time=121.53 memory used=8416.7MB, alloc=540.3MB, time=121.96 memory used=8496.8MB, alloc=540.3MB, time=122.34 memory used=8650.3MB, alloc=540.3MB, time=152.65 memory used=8768.0MB, alloc=540.3MB, time=153.17 memory used=8863.4MB, alloc=540.3MB, time=153.60 memory used=8987.8MB, alloc=540.3MB, time=154.06 memory used=9090.4MB, alloc=540.3MB, time=154.51 memory used=9176.2MB, alloc=540.3MB, time=154.89 memory used=9273.4MB, alloc=540.3MB, time=155.31 memory used=9383.6MB, alloc=540.3MB, time=155.72 memory used=9510.3MB, alloc=540.3MB, time=156.10 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428250252 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 4 2 2 2 F := [13 z + 3 x z + 15 z , -3 y - 19 x z + 12 x , -3 x + 3 y z - 12 y] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; G := [ 3 2 3 4 2 2 2 13 x y - 15 x + 4 x y, 11 x y - 12 y - 9 x z, -2 y z - 2 x z + 14 z] > Problem := [F,G]; Problem := [ 3 2 4 2 2 2 [13 z + 3 x z + 15 z , -3 y - 19 x z + 12 x , -3 x + 3 y z - 12 y], [ 3 2 3 4 2 2 2 13 x y - 15 x + 4 x y, 11 x y - 12 y - 9 x z, -2 y z - 2 x z + 14 z] ] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.17 memory used=26.8MB, alloc=32.3MB, time=0.51 memory used=47.7MB, alloc=32.3MB, time=0.81 memory used=68.2MB, alloc=32.3MB, time=1.11 memory used=87.6MB, alloc=56.3MB, time=1.43 memory used=127.7MB, alloc=60.3MB, time=2.01 memory used=166.7MB, alloc=84.3MB, time=2.59 memory used=201.2MB, alloc=84.3MB, time=3.08 memory used=263.9MB, alloc=92.3MB, time=4.02 memory used=323.9MB, alloc=116.3MB, time=4.92 memory used=398.5MB, alloc=116.3MB, time=6.03 memory used=461.7MB, alloc=372.3MB, time=6.95 memory used=542.3MB, alloc=396.3MB, time=8.17 memory used=650.3MB, alloc=420.3MB, time=9.75 memory used=779.6MB, alloc=444.3MB, time=11.59 memory used=882.2MB, alloc=468.3MB, time=13.04 memory used=988.2MB, alloc=468.3MB, time=14.71 memory used=1080.2MB, alloc=468.3MB, time=16.10 memory used=1161.5MB, alloc=468.3MB, time=17.37 memory used=1244.8MB, alloc=468.3MB, time=18.79 memory used=1320.0MB, alloc=492.3MB, time=20.16 memory used=1382.7MB, alloc=492.3MB, time=21.32 memory used=1443.3MB, alloc=492.3MB, time=22.43 memory used=1511.6MB, alloc=492.3MB, time=23.48 memory used=1565.5MB, alloc=492.3MB, time=24.48 memory used=1634.1MB, alloc=516.3MB, time=25.60 memory used=1684.5MB, alloc=516.3MB, time=26.74 memory used=1738.2MB, alloc=516.3MB, time=27.62 memory used=1774.4MB, alloc=516.3MB, time=28.51 memory used=1970.1MB, alloc=540.3MB, time=31.42 memory used=2143.5MB, alloc=564.3MB, time=34.11 memory used=2325.9MB, alloc=588.3MB, time=37.46 memory used=2527.2MB, alloc=612.3MB, time=41.30 memory used=2665.7MB, alloc=612.3MB, time=43.80 memory used=2832.5MB, alloc=636.3MB, time=46.52 memory used=2978.6MB, alloc=636.3MB, time=48.80 memory used=3113.7MB, alloc=636.3MB, time=51.50 memory used=3232.6MB, alloc=660.3MB, time=53.62 memory used=3337.9MB, alloc=660.3MB, time=55.70 memory used=3485.6MB, alloc=660.3MB, time=58.17 memory used=3617.7MB, alloc=660.3MB, time=60.26 memory used=3704.9MB, alloc=684.3MB, time=62.00 memory used=3797.7MB, alloc=684.3MB, time=64.33 memory used=3928.9MB, alloc=684.3MB, time=67.77 memory used=4286.2MB, alloc=708.3MB, time=73.61 memory used=4638.2MB, alloc=732.3MB, time=80.10 memory used=4951.3MB, alloc=756.3MB, time=85.73 memory used=5238.4MB, alloc=780.3MB, time=91.63 memory used=5505.0MB, alloc=804.3MB, time=97.09 memory used=5706.9MB, alloc=828.3MB, time=101.90 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428250552 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; F := [ 4 3 3 2 2 3 2 2 12 y + 2 y z + 7 x y, 7 x y - 20 x z - 2 z , -12 x y + 2 y z - 5 x y ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 3 2 2 G := [18 x z + 14 y - 20 z , 20 x z + 13 x y + 16 z, 2 2 2 -6 y z + 5 y z + 4 x z] > Problem := [F,G]; Problem := [[ 4 3 3 2 2 3 2 2 12 y + 2 y z + 7 x y, 7 x y - 20 x z - 2 z , -12 x y + 2 y z - 5 x y 2 2 3 2 3 2 2 ], [18 x z + 14 y - 20 z , 20 x z + 13 x y + 16 z, 2 2 2 -6 y z + 5 y z + 4 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=27.0MB, alloc=32.3MB, time=0.51 memory used=46.3MB, alloc=56.3MB, time=0.79 memory used=84.8MB, alloc=60.3MB, time=1.29 memory used=126.7MB, alloc=68.3MB, time=1.88 memory used=167.1MB, alloc=68.3MB, time=2.44 memory used=208.7MB, alloc=92.3MB, time=3.00 memory used=276.8MB, alloc=92.3MB, time=3.75 memory used=345.0MB, alloc=92.3MB, time=4.62 memory used=397.4MB, alloc=92.3MB, time=5.06 memory used=468.8MB, alloc=116.3MB, time=5.82 memory used=541.0MB, alloc=372.3MB, time=6.78 memory used=626.2MB, alloc=372.3MB, time=7.99 memory used=699.8MB, alloc=372.3MB, time=8.60 memory used=746.7MB, alloc=372.3MB, time=8.84 memory used=822.8MB, alloc=396.3MB, time=9.45 memory used=878.6MB, alloc=396.3MB, time=9.65 memory used=950.1MB, alloc=396.3MB, time=10.00 memory used=1036.1MB, alloc=396.3MB, time=17.24 memory used=1177.4MB, alloc=396.3MB, time=19.66 memory used=1232.4MB, alloc=396.3MB, time=19.85 memory used=1281.4MB, alloc=396.3MB, time=20.03 memory used=1341.2MB, alloc=396.3MB, time=20.20 memory used=1400.7MB, alloc=396.3MB, time=20.37 memory used=1440.4MB, alloc=396.3MB, time=20.51 memory used=1484.2MB, alloc=396.3MB, time=20.64 memory used=1532.3MB, alloc=396.3MB, time=20.78 memory used=1585.5MB, alloc=396.3MB, time=20.95 memory used=1670.8MB, alloc=396.3MB, time=21.40 memory used=1790.7MB, alloc=396.3MB, time=23.03 memory used=1906.3MB, alloc=396.3MB, time=24.77 memory used=2022.9MB, alloc=420.3MB, time=26.32 memory used=2092.1MB, alloc=420.3MB, time=26.64 memory used=2151.8MB, alloc=420.3MB, time=26.89 memory used=2206.3MB, alloc=420.3MB, time=27.13 memory used=2274.7MB, alloc=420.3MB, time=27.37 memory used=2334.0MB, alloc=420.3MB, time=27.57 memory used=2408.1MB, alloc=420.3MB, time=28.03 memory used=2473.6MB, alloc=420.3MB, time=28.30 memory used=2526.0MB, alloc=420.3MB, time=28.54 memory used=2590.7MB, alloc=420.3MB, time=28.77 memory used=2658.3MB, alloc=420.3MB, time=29.01 memory used=2747.1MB, alloc=420.3MB, time=48.35 memory used=2999.0MB, alloc=420.3MB, time=54.26 memory used=3058.3MB, alloc=420.3MB, time=54.52 memory used=3119.2MB, alloc=420.3MB, time=54.78 memory used=3192.2MB, alloc=420.3MB, time=55.05 memory used=3236.1MB, alloc=420.3MB, time=55.26 memory used=3284.1MB, alloc=420.3MB, time=55.47 memory used=3335.9MB, alloc=420.3MB, time=55.69 memory used=3392.3MB, alloc=420.3MB, time=55.91 memory used=3453.3MB, alloc=420.3MB, time=56.13 memory used=3518.9MB, alloc=420.3MB, time=56.36 memory used=3591.2MB, alloc=420.3MB, time=56.59 memory used=3671.6MB, alloc=420.3MB, time=56.84 memory used=3826.7MB, alloc=420.3MB, time=57.38 memory used=3974.8MB, alloc=420.3MB, time=57.74 memory used=4141.1MB, alloc=420.3MB, time=58.12 memory used=4332.2MB, alloc=420.3MB, time=58.52 memory used=4554.0MB, alloc=420.3MB, time=58.92 memory used=4688.1MB, alloc=420.3MB, time=60.14 memory used=4819.4MB, alloc=420.3MB, time=62.43 memory used=4939.7MB, alloc=420.3MB, time=63.75 memory used=5069.6MB, alloc=444.3MB, time=65.44 memory used=5189.8MB, alloc=444.3MB, time=67.26 memory used=5295.1MB, alloc=468.3MB, time=68.73 memory used=5396.6MB, alloc=468.3MB, time=70.09 memory used=5482.1MB, alloc=468.3MB, time=71.23 memory used=5578.2MB, alloc=492.3MB, time=72.43 memory used=5661.6MB, alloc=492.3MB, time=73.61 memory used=5749.2MB, alloc=492.3MB, time=74.70 memory used=5832.2MB, alloc=492.3MB, time=76.03 memory used=5903.4MB, alloc=492.3MB, time=77.00 memory used=5971.8MB, alloc=492.3MB, time=78.33 memory used=6028.7MB, alloc=492.3MB, time=79.35 memory used=6094.9MB, alloc=516.3MB, time=80.58 memory used=6162.5MB, alloc=516.3MB, time=81.67 memory used=6231.3MB, alloc=516.3MB, time=82.60 memory used=6339.5MB, alloc=516.3MB, time=83.59 memory used=6465.1MB, alloc=516.3MB, time=84.44 memory used=6611.6MB, alloc=516.3MB, time=91.63 memory used=6692.0MB, alloc=540.3MB, time=92.16 memory used=6810.0MB, alloc=540.3MB, time=92.69 memory used=6896.1MB, alloc=540.3MB, time=93.14 memory used=7000.7MB, alloc=540.3MB, time=93.59 memory used=7138.0MB, alloc=540.3MB, time=94.27 memory used=7270.8MB, alloc=540.3MB, time=95.11 memory used=7336.5MB, alloc=540.3MB, time=103.65 memory used=7452.7MB, alloc=540.3MB, time=104.28 memory used=7570.0MB, alloc=540.3MB, time=104.84 memory used=7663.9MB, alloc=540.3MB, time=105.35 memory used=7760.2MB, alloc=540.3MB, time=105.83 memory used=7894.9MB, alloc=540.3MB, time=106.51 memory used=8134.9MB, alloc=540.3MB, time=109.02 memory used=8320.0MB, alloc=540.3MB, time=110.61 memory used=8441.5MB, alloc=540.3MB, time=111.34 memory used=8552.2MB, alloc=540.3MB, time=112.02 memory used=8693.9MB, alloc=540.3MB, time=113.21 memory used=8788.3MB, alloc=540.3MB, time=113.79 memory used=8920.5MB, alloc=540.3MB, time=114.71 memory used=9020.5MB, alloc=540.3MB, time=115.27 memory used=9170.6MB, alloc=540.3MB, time=134.17 memory used=9280.7MB, alloc=564.3MB, time=135.27 memory used=9406.1MB, alloc=564.3MB, time=135.88 memory used=9506.7MB, alloc=564.3MB, time=136.40 memory used=9611.3MB, alloc=564.3MB, time=136.91 memory used=9735.1MB, alloc=564.3MB, time=137.46 memory used=9919.0MB, alloc=564.3MB, time=138.06 memory used=10068.3MB, alloc=564.3MB, time=138.65 memory used=10227.6MB, alloc=564.3MB, time=139.22 memory used=10420.2MB, alloc=564.3MB, time=140.34 memory used=10562.5MB, alloc=564.3MB, time=141.18 memory used=10678.2MB, alloc=564.3MB, time=141.79 memory used=10849.3MB, alloc=564.3MB, time=159.17 memory used=10964.3MB, alloc=564.3MB, time=159.78 memory used=11094.0MB, alloc=564.3MB, time=160.37 memory used=11186.4MB, alloc=564.3MB, time=160.88 memory used=11295.1MB, alloc=564.3MB, time=161.39 memory used=11424.7MB, alloc=564.3MB, time=161.92 memory used=11676.7MB, alloc=564.3MB, time=162.61 memory used=11826.7MB, alloc=564.3MB, time=163.17 memory used=12123.1MB, alloc=564.3MB, time=164.78 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428250852 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 4 3 3 F := [8 x - 18 x y z , -12 x + 9 z - 20, 19 x z + 6 z - 2 z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 G := [-4 x z - 2 x - 20 x y z, -19 x y - 14 x z - 3 x z, 2 2 3 2 -20 x z + 7 z + 18 x ] > Problem := [F,G]; 4 2 4 3 3 Problem := [[8 x - 18 x y z , -12 x + 9 z - 20, 19 x z + 6 z - 2 z], [ 3 3 2 2 -4 x z - 2 x - 20 x y z, -19 x y - 14 x z - 3 x z, 2 2 3 2 -20 x z + 7 z + 18 x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.4MB, alloc=32.3MB, time=0.50 memory used=47.2MB, alloc=56.3MB, time=0.83 memory used=89.9MB, alloc=60.3MB, time=1.46 memory used=133.1MB, alloc=60.3MB, time=2.05 memory used=174.0MB, alloc=84.3MB, time=2.64 memory used=238.6MB, alloc=92.3MB, time=3.58 memory used=299.0MB, alloc=116.3MB, time=4.51 memory used=363.8MB, alloc=116.3MB, time=5.42 memory used=439.3MB, alloc=372.3MB, time=6.27 memory used=523.1MB, alloc=396.3MB, time=7.49 memory used=637.4MB, alloc=396.3MB, time=8.99 memory used=746.1MB, alloc=420.3MB, time=10.53 memory used=870.5MB, alloc=444.3MB, time=12.51 memory used=1002.4MB, alloc=444.3MB, time=14.37 memory used=1130.0MB, alloc=468.3MB, time=16.10 memory used=1261.7MB, alloc=468.3MB, time=18.04 memory used=1362.2MB, alloc=468.3MB, time=19.69 memory used=1474.1MB, alloc=492.3MB, time=21.65 memory used=1570.9MB, alloc=492.3MB, time=23.17 memory used=1692.0MB, alloc=492.3MB, time=24.61 memory used=1816.7MB, alloc=492.3MB, time=25.99 memory used=1930.2MB, alloc=492.3MB, time=27.57 memory used=2030.0MB, alloc=516.3MB, time=28.86 memory used=2107.1MB, alloc=516.3MB, time=30.26 memory used=2199.9MB, alloc=516.3MB, time=31.69 memory used=2264.8MB, alloc=516.3MB, time=33.06 memory used=2346.4MB, alloc=516.3MB, time=34.51 memory used=2429.7MB, alloc=516.3MB, time=35.76 memory used=2507.9MB, alloc=516.3MB, time=37.16 memory used=2577.0MB, alloc=516.3MB, time=38.55 memory used=2641.0MB, alloc=516.3MB, time=39.88 memory used=2698.2MB, alloc=516.3MB, time=41.02 memory used=2771.5MB, alloc=516.3MB, time=42.12 memory used=2838.4MB, alloc=516.3MB, time=43.01 memory used=2890.3MB, alloc=516.3MB, time=43.99 memory used=2943.5MB, alloc=516.3MB, time=44.96 memory used=3156.1MB, alloc=540.3MB, time=48.21 memory used=3367.1MB, alloc=564.3MB, time=52.15 memory used=3561.9MB, alloc=588.3MB, time=55.89 memory used=3768.0MB, alloc=612.3MB, time=59.85 memory used=3945.4MB, alloc=636.3MB, time=63.15 memory used=4122.1MB, alloc=636.3MB, time=66.50 memory used=4287.3MB, alloc=660.3MB, time=69.82 memory used=4457.9MB, alloc=660.3MB, time=73.67 memory used=4610.9MB, alloc=660.3MB, time=76.62 memory used=4767.4MB, alloc=660.3MB, time=79.62 memory used=4926.5MB, alloc=660.3MB, time=83.13 memory used=5042.7MB, alloc=684.3MB, time=85.75 memory used=5172.0MB, alloc=684.3MB, time=88.24 memory used=5317.0MB, alloc=684.3MB, time=91.60 memory used=5453.6MB, alloc=684.3MB, time=95.33 memory used=5556.4MB, alloc=684.3MB, time=97.90 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428251152 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 3 3 2 2 3 2 2 F := [13 x - 4 x z, 20 x y + 20 x y + 12 y z , -3 x - 3 x y + 13 y z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 4 2 G := [7 y - 13 y z + 4 x z, -10 x y + 4 y , -18 x - 17 y - 13 y] > Problem := [F,G]; Problem := [ 4 3 3 3 2 2 3 2 2 [13 x - 4 x z, 20 x y + 20 x y + 12 y z , -3 x - 3 x y + 13 y z], 3 2 2 2 4 2 [7 y - 13 y z + 4 x z, -10 x y + 4 y , -18 x - 17 y - 13 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.3MB, alloc=32.3MB, time=0.50 memory used=48.0MB, alloc=32.3MB, time=0.83 memory used=68.3MB, alloc=60.3MB, time=1.16 memory used=110.2MB, alloc=60.3MB, time=1.76 memory used=147.1MB, alloc=60.3MB, time=2.27 memory used=188.8MB, alloc=92.3MB, time=2.88 memory used=252.1MB, alloc=92.3MB, time=3.81 memory used=316.2MB, alloc=116.3MB, time=4.77 memory used=378.5MB, alloc=372.3MB, time=5.71 memory used=469.4MB, alloc=396.3MB, time=6.93 memory used=581.3MB, alloc=420.3MB, time=8.57 memory used=717.4MB, alloc=420.3MB, time=10.32 memory used=849.1MB, alloc=444.3MB, time=12.26 memory used=986.3MB, alloc=444.3MB, time=13.84 memory used=1106.0MB, alloc=468.3MB, time=15.61 memory used=1217.9MB, alloc=468.3MB, time=17.31 memory used=1321.8MB, alloc=468.3MB, time=18.99 memory used=1417.6MB, alloc=468.3MB, time=20.49 memory used=1505.1MB, alloc=492.3MB, time=21.99 memory used=1602.9MB, alloc=492.3MB, time=23.67 memory used=1691.5MB, alloc=492.3MB, time=25.10 memory used=1776.8MB, alloc=492.3MB, time=26.65 memory used=1863.2MB, alloc=516.3MB, time=27.82 memory used=1959.8MB, alloc=516.3MB, time=29.13 memory used=2080.2MB, alloc=516.3MB, time=30.86 memory used=2216.3MB, alloc=516.3MB, time=32.19 memory used=2340.0MB, alloc=516.3MB, time=33.89 memory used=2441.0MB, alloc=540.3MB, time=37.71 memory used=2509.3MB, alloc=540.3MB, time=38.64 memory used=2662.9MB, alloc=540.3MB, time=41.72 memory used=2762.8MB, alloc=540.3MB, time=42.81 memory used=2908.9MB, alloc=540.3MB, time=51.27 memory used=2996.6MB, alloc=540.3MB, time=52.25 memory used=3068.5MB, alloc=564.3MB, time=53.65 memory used=3280.3MB, alloc=564.3MB, time=56.96 memory used=3388.0MB, alloc=564.3MB, time=57.57 memory used=3514.0MB, alloc=564.3MB, time=59.04 memory used=3620.3MB, alloc=564.3MB, time=60.17 memory used=3823.5MB, alloc=564.3MB, time=63.09 memory used=3997.9MB, alloc=564.3MB, time=95.62 memory used=4111.3MB, alloc=564.3MB, time=96.24 memory used=4206.9MB, alloc=564.3MB, time=96.78 memory used=4348.9MB, alloc=588.3MB, time=102.07 memory used=4621.9MB, alloc=588.3MB, time=105.68 memory used=4861.1MB, alloc=612.3MB, time=108.37 memory used=5154.9MB, alloc=612.3MB, time=111.16 memory used=5460.4MB, alloc=612.3MB, time=116.19 memory used=5771.8MB, alloc=612.3MB, time=123.86 memory used=6069.6MB, alloc=612.3MB, time=131.92 memory used=6282.9MB, alloc=612.3MB, time=135.04 memory used=6520.0MB, alloc=636.3MB, time=138.24 memory used=6785.0MB, alloc=660.3MB, time=140.86 memory used=7083.8MB, alloc=660.3MB, time=144.08 memory used=7372.2MB, alloc=660.3MB, time=145.33 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428251452 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; F := [ 3 2 2 2 3 2 2 9 x y + 6 x y z - y , 3 x y - 14 y + 18 x y, 12 x y + 5 x y - 20 x z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 2 G := [10 x y - 19 x y z + x , -19 x y z - 19 y z - 11 x z, 2 2 -4 x y + 6 x y + 20 y z] > Problem := [F,G]; Problem := [[ 3 2 2 2 3 2 2 9 x y + 6 x y z - y , 3 x y - 14 y + 18 x y, 12 x y + 5 x y - 20 x z] 2 2 2 2 2 2 , [10 x y - 19 x y z + x , -19 x y z - 19 y z - 11 x z, 2 2 -4 x y + 6 x y + 20 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.5MB, alloc=32.3MB, time=0.48 memory used=47.6MB, alloc=32.3MB, time=0.79 memory used=66.0MB, alloc=56.3MB, time=1.09 memory used=106.1MB, alloc=60.3MB, time=1.69 memory used=143.7MB, alloc=60.3MB, time=2.26 memory used=180.5MB, alloc=84.3MB, time=2.84 memory used=226.2MB, alloc=84.3MB, time=3.56 memory used=284.2MB, alloc=116.3MB, time=4.54 memory used=365.1MB, alloc=116.3MB, time=5.84 memory used=445.8MB, alloc=140.3MB, time=7.12 memory used=527.8MB, alloc=396.3MB, time=8.56 memory used=634.4MB, alloc=420.3MB, time=10.41 memory used=760.5MB, alloc=444.3MB, time=12.69 memory used=905.0MB, alloc=444.3MB, time=15.36 memory used=1048.6MB, alloc=468.3MB, time=18.04 memory used=1213.8MB, alloc=492.3MB, time=21.29 memory used=1363.4MB, alloc=516.3MB, time=23.98 memory used=1499.7MB, alloc=516.3MB, time=26.73 memory used=1634.4MB, alloc=540.3MB, time=29.85 memory used=1738.8MB, alloc=540.3MB, time=32.00 memory used=1845.9MB, alloc=540.3MB, time=34.44 memory used=1959.1MB, alloc=540.3MB, time=36.96 memory used=2027.6MB, alloc=540.3MB, time=38.42 memory used=2118.0MB, alloc=564.3MB, time=40.60 memory used=2199.0MB, alloc=564.3MB, time=42.33 memory used=2277.1MB, alloc=564.3MB, time=44.50 memory used=2329.4MB, alloc=564.3MB, time=45.80 memory used=2388.3MB, alloc=564.3MB, time=47.26 memory used=2464.8MB, alloc=564.3MB, time=49.55 memory used=2535.1MB, alloc=564.3MB, time=51.77 memory used=2591.9MB, alloc=564.3MB, time=53.39 memory used=2839.8MB, alloc=588.3MB, time=58.78 memory used=3070.9MB, alloc=612.3MB, time=63.88 memory used=3290.2MB, alloc=636.3MB, time=69.22 memory used=3514.5MB, alloc=660.3MB, time=75.44 memory used=3726.0MB, alloc=684.3MB, time=81.56 memory used=3904.6MB, alloc=708.3MB, time=86.32 memory used=4096.8MB, alloc=708.3MB, time=92.60 memory used=4261.7MB, alloc=708.3MB, time=97.06 memory used=4427.4MB, alloc=708.3MB, time=102.07 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428251752 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; F := [ 2 2 2 2 3 2 2 2 -10 x y - 13 y z - 8 y z, 7 x - 5 x - 10 z, 7 x y z - 14 x z + 10 z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; G := 3 2 2 2 3 2 2 2 [-12 x y + 11 x z - 2 z , 18 x - y z - 9 x z, 7 x y - 4 x y z + 7 y ] > Problem := [F,G]; Problem := [[ 2 2 2 2 3 2 2 2 -10 x y - 13 y z - 8 y z, 7 x - 5 x - 10 z, 7 x y z - 14 x z + 10 z ], 3 2 2 2 3 2 2 2 [-12 x y + 11 x z - 2 z , 18 x - y z - 9 x z, 7 x y - 4 x y z + 7 y ] ] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.2MB, alloc=32.3MB, time=0.50 memory used=47.1MB, alloc=32.3MB, time=0.81 memory used=67.5MB, alloc=32.3MB, time=1.12 memory used=87.0MB, alloc=56.3MB, time=1.43 memory used=127.4MB, alloc=60.3MB, time=2.04 memory used=165.7MB, alloc=84.3MB, time=2.63 memory used=213.1MB, alloc=84.3MB, time=3.35 memory used=274.3MB, alloc=92.3MB, time=4.26 memory used=332.6MB, alloc=116.3MB, time=5.18 memory used=413.2MB, alloc=116.3MB, time=6.43 memory used=486.6MB, alloc=396.3MB, time=7.60 memory used=591.8MB, alloc=396.3MB, time=9.29 memory used=694.1MB, alloc=420.3MB, time=10.96 memory used=818.9MB, alloc=420.3MB, time=13.18 memory used=941.5MB, alloc=444.3MB, time=15.24 memory used=1088.9MB, alloc=468.3MB, time=17.93 memory used=1234.0MB, alloc=492.3MB, time=20.67 memory used=1345.6MB, alloc=492.3MB, time=22.45 memory used=1468.6MB, alloc=516.3MB, time=24.43 memory used=1559.1MB, alloc=516.3MB, time=25.85 memory used=1669.6MB, alloc=516.3MB, time=27.90 memory used=1755.1MB, alloc=516.3MB, time=29.47 memory used=1849.6MB, alloc=516.3MB, time=31.47 memory used=1920.7MB, alloc=540.3MB, time=32.76 memory used=2009.0MB, alloc=540.3MB, time=34.42 memory used=2098.9MB, alloc=540.3MB, time=36.48 memory used=2159.5MB, alloc=540.3MB, time=37.84 memory used=2218.7MB, alloc=540.3MB, time=39.16 memory used=2286.9MB, alloc=540.3MB, time=40.82 memory used=2488.7MB, alloc=564.3MB, time=44.71 memory used=2668.0MB, alloc=588.3MB, time=47.91 memory used=2834.4MB, alloc=612.3MB, time=51.00 memory used=3003.6MB, alloc=636.3MB, time=54.16 memory used=3149.3MB, alloc=636.3MB, time=57.61 memory used=3277.6MB, alloc=636.3MB, time=60.50 memory used=3402.0MB, alloc=660.3MB, time=62.84 memory used=3546.6MB, alloc=660.3MB, time=66.03 memory used=3662.6MB, alloc=660.3MB, time=68.20 memory used=3788.3MB, alloc=660.3MB, time=71.39 memory used=3880.7MB, alloc=660.3MB, time=73.96 memory used=3972.6MB, alloc=660.3MB, time=76.44 memory used=4299.8MB, alloc=684.3MB, time=83.18 memory used=4656.6MB, alloc=708.3MB, time=89.52 memory used=5019.9MB, alloc=732.3MB, time=96.92 memory used=5394.3MB, alloc=756.3MB, time=104.26 memory used=5710.8MB, alloc=780.3MB, time=111.14 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428252052 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 3 2 2 3 4 3 F := [-7 x + 16 x y + 7 z , 11 x y - 11 x - 6 y z, 10 y z - 6 z + 19 z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 2 G := [-17 y + 3 x y + 8 x z, 7 x y + 19 x y z - 16 y z , 2 2 -17 x y z + 14 x y - 20 x] > Problem := [F,G]; Problem := [ 4 2 3 2 2 3 4 3 [-7 x + 16 x y + 7 z , 11 x y - 11 x - 6 y z, 10 y z - 6 z + 19 z ], 4 2 2 2 [-17 y + 3 x y + 8 x z, 7 x y + 19 x y z - 16 y z , 2 2 -17 x y z + 14 x y - 20 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.4MB, alloc=32.3MB, time=0.50 memory used=46.6MB, alloc=32.3MB, time=0.79 memory used=65.3MB, alloc=56.3MB, time=1.08 memory used=104.6MB, alloc=60.3MB, time=1.66 memory used=142.9MB, alloc=84.3MB, time=2.23 memory used=207.4MB, alloc=92.3MB, time=3.21 memory used=271.1MB, alloc=116.3MB, time=4.16 memory used=338.5MB, alloc=116.3MB, time=5.00 memory used=407.5MB, alloc=372.3MB, time=6.01 memory used=494.0MB, alloc=396.3MB, time=7.28 memory used=599.9MB, alloc=396.3MB, time=8.93 memory used=708.4MB, alloc=420.3MB, time=10.56 memory used=836.6MB, alloc=444.3MB, time=12.59 memory used=975.0MB, alloc=444.3MB, time=14.47 memory used=1095.7MB, alloc=468.3MB, time=16.28 memory used=1234.1MB, alloc=468.3MB, time=18.30 memory used=1339.5MB, alloc=492.3MB, time=20.05 memory used=1446.7MB, alloc=492.3MB, time=21.62 memory used=1548.1MB, alloc=492.3MB, time=23.25 memory used=1653.4MB, alloc=516.3MB, time=25.00 memory used=1738.6MB, alloc=516.3MB, time=26.70 memory used=1812.6MB, alloc=516.3MB, time=27.88 memory used=1897.3MB, alloc=516.3MB, time=29.64 memory used=1973.2MB, alloc=516.3MB, time=30.92 memory used=2049.4MB, alloc=516.3MB, time=32.29 memory used=2105.2MB, alloc=516.3MB, time=33.26 memory used=2158.0MB, alloc=516.3MB, time=34.24 memory used=2207.4MB, alloc=516.3MB, time=35.18 memory used=2273.7MB, alloc=516.3MB, time=36.58 memory used=2482.4MB, alloc=540.3MB, time=40.04 memory used=2686.8MB, alloc=564.3MB, time=43.29 memory used=2875.3MB, alloc=588.3MB, time=46.67 memory used=3055.6MB, alloc=612.3MB, time=49.98 memory used=3224.9MB, alloc=636.3MB, time=53.30 memory used=3390.6MB, alloc=660.3MB, time=56.54 memory used=3531.5MB, alloc=660.3MB, time=59.37 memory used=3671.4MB, alloc=660.3MB, time=62.48 memory used=3811.8MB, alloc=660.3MB, time=65.33 memory used=3933.7MB, alloc=684.3MB, time=67.59 memory used=4062.8MB, alloc=684.3MB, time=70.38 memory used=4155.1MB, alloc=684.3MB, time=72.64 memory used=4499.6MB, alloc=708.3MB, time=79.64 memory used=4863.8MB, alloc=732.3MB, time=86.11 memory used=5192.7MB, alloc=756.3MB, time=91.50 memory used=5582.7MB, alloc=780.3MB, time=98.34 memory used=5967.7MB, alloc=804.3MB, time=104.88 memory used=6370.5MB, alloc=828.3MB, time=111.59 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428252352 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 3 2 3 F := [x z + 18 x z + 3 z, x - 19 x y z - 10 y z, -3 x z + 10 x y - 5 y ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 3 2 2 3 G := [-7 x y + 8 x - 11 x y, -7 x z + 11 x z + 8 x , 11 z + 7 x + 5] > Problem := [F,G]; Problem := [ 2 2 2 3 2 3 2 3 [x z + 18 x z + 3 z, x - 19 x y z - 10 y z, -3 x z + 10 x y - 5 y ], 3 3 3 2 2 3 [-7 x y + 8 x - 11 x y, -7 x z + 11 x z + 8 x , 11 z + 7 x + 5]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=31.9MB, alloc=40.3MB, time=0.59 memory used=59.3MB, alloc=44.3MB, time=0.98 memory used=85.5MB, alloc=68.3MB, time=1.36 memory used=135.3MB, alloc=76.3MB, time=2.09 memory used=185.7MB, alloc=76.3MB, time=2.78 memory used=232.9MB, alloc=100.3MB, time=3.48 memory used=306.1MB, alloc=100.3MB, time=4.47 memory used=378.2MB, alloc=124.3MB, time=5.47 memory used=446.5MB, alloc=380.3MB, time=6.36 memory used=539.8MB, alloc=380.3MB, time=7.37 memory used=609.9MB, alloc=380.3MB, time=7.85 memory used=681.1MB, alloc=380.3MB, time=9.42 memory used=772.6MB, alloc=380.3MB, time=10.13 memory used=864.0MB, alloc=404.3MB, time=11.38 memory used=985.6MB, alloc=404.3MB, time=13.05 memory used=1106.1MB, alloc=428.3MB, time=14.66 memory used=1219.9MB, alloc=428.3MB, time=15.68 memory used=1342.6MB, alloc=428.3MB, time=16.57 memory used=1469.8MB, alloc=428.3MB, time=19.99 memory used=1530.5MB, alloc=428.3MB, time=20.21 memory used=1592.2MB, alloc=428.3MB, time=20.44 memory used=1647.6MB, alloc=428.3MB, time=20.63 memory used=1790.6MB, alloc=428.3MB, time=22.47 memory used=1910.6MB, alloc=428.3MB, time=24.17 memory used=2060.4MB, alloc=452.3MB, time=27.91 memory used=2147.1MB, alloc=452.3MB, time=28.29 memory used=2321.5MB, alloc=476.3MB, time=31.07 memory used=2537.7MB, alloc=476.3MB, time=32.60 memory used=2731.0MB, alloc=476.3MB, time=33.52 memory used=2921.3MB, alloc=476.3MB, time=35.54 memory used=3016.3MB, alloc=476.3MB, time=36.07 memory used=3108.1MB, alloc=476.3MB, time=36.48 memory used=3213.4MB, alloc=476.3MB, time=37.03 memory used=3329.2MB, alloc=476.3MB, time=37.50 memory used=3438.4MB, alloc=500.3MB, time=75.63 memory used=3555.9MB, alloc=500.3MB, time=158.10 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428252652 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 3 3 2 F := [-10 x y - 2 x y z - 6, -5 x z - 8 x y z + 13 x y , 18 x y + 8 y ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; G := 2 2 2 2 2 3 2 [-x y z + 20 x y - 17 z, y z - 4 x y - 10 x, -20 x z + 8 x y + 11 y ] > Problem := [F,G]; Problem := [ 2 3 2 3 3 2 [-10 x y - 2 x y z - 6, -5 x z - 8 x y z + 13 x y , 18 x y + 8 y ], 2 2 2 2 2 3 2 [-x y z + 20 x y - 17 z, y z - 4 x y - 10 x, -20 x z + 8 x y + 11 y ] ] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.18 memory used=27.1MB, alloc=32.3MB, time=0.51 memory used=48.0MB, alloc=32.3MB, time=0.82 memory used=68.3MB, alloc=56.3MB, time=1.13 memory used=109.4MB, alloc=60.3MB, time=1.72 memory used=145.4MB, alloc=60.3MB, time=2.23 memory used=184.6MB, alloc=84.3MB, time=2.83 memory used=221.7MB, alloc=84.3MB, time=3.38 memory used=287.4MB, alloc=92.3MB, time=4.34 memory used=352.6MB, alloc=116.3MB, time=5.31 memory used=416.0MB, alloc=116.3MB, time=6.28 memory used=482.2MB, alloc=372.3MB, time=7.22 memory used=575.4MB, alloc=396.3MB, time=8.30 memory used=687.8MB, alloc=420.3MB, time=9.96 memory used=816.5MB, alloc=444.3MB, time=11.81 memory used=924.3MB, alloc=444.3MB, time=13.55 memory used=1009.9MB, alloc=444.3MB, time=14.92 memory used=1125.2MB, alloc=444.3MB, time=16.59 memory used=1238.3MB, alloc=468.3MB, time=18.13 memory used=1338.1MB, alloc=468.3MB, time=19.63 memory used=1419.4MB, alloc=468.3MB, time=20.94 memory used=1538.5MB, alloc=468.3MB, time=22.13 memory used=1640.2MB, alloc=468.3MB, time=23.56 memory used=1741.9MB, alloc=468.3MB, time=24.46 memory used=1828.3MB, alloc=468.3MB, time=25.64 memory used=1906.1MB, alloc=468.3MB, time=26.35 memory used=1999.2MB, alloc=492.3MB, time=27.63 memory used=2079.3MB, alloc=492.3MB, time=28.89 memory used=2139.5MB, alloc=492.3MB, time=30.00 memory used=2200.1MB, alloc=492.3MB, time=31.18 memory used=2266.4MB, alloc=492.3MB, time=32.51 memory used=2317.4MB, alloc=492.3MB, time=33.54 memory used=2382.2MB, alloc=492.3MB, time=34.38 memory used=2445.3MB, alloc=492.3MB, time=35.36 memory used=2493.4MB, alloc=492.3MB, time=36.30 memory used=2542.4MB, alloc=492.3MB, time=37.17 memory used=2672.0MB, alloc=492.3MB, time=38.35 memory used=2854.9MB, alloc=516.3MB, time=40.56 memory used=3054.1MB, alloc=540.3MB, time=44.02 memory used=3254.8MB, alloc=564.3MB, time=47.47 memory used=3427.6MB, alloc=588.3MB, time=50.19 memory used=3566.9MB, alloc=612.3MB, time=52.62 memory used=3738.7MB, alloc=636.3MB, time=56.00 memory used=3865.9MB, alloc=636.3MB, time=58.29 memory used=3998.6MB, alloc=636.3MB, time=60.98 memory used=4131.5MB, alloc=660.3MB, time=63.59 memory used=4228.0MB, alloc=660.3MB, time=65.52 memory used=4338.3MB, alloc=660.3MB, time=67.39 memory used=4427.2MB, alloc=660.3MB, time=69.33 memory used=4755.8MB, alloc=684.3MB, time=75.33 memory used=5096.9MB, alloc=708.3MB, time=80.90 memory used=5466.5MB, alloc=732.3MB, time=87.43 memory used=5771.4MB, alloc=756.3MB, time=93.26 memory used=6060.1MB, alloc=780.3MB, time=99.06 memory used=6285.6MB, alloc=804.3MB, time=104.00 memory used=6653.8MB, alloc=828.3MB, time=110.31 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428252952 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 3 2 F := [-13 x y z - 14 x y + 4 x z , 2 y + 4 y z, -3 y z + 19 z + 15 y ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; G := [ 3 2 2 4 2 2 14 x y z - 20 x + 9 z, 15 x z + 10 x z + 8 x y , 13 z - 11 x z - 16 y ] > Problem := [F,G]; Problem := [ 2 2 2 2 2 3 2 [-13 x y z - 14 x y + 4 x z , 2 y + 4 y z, -3 y z + 19 z + 15 y ], [ 3 2 2 4 2 2 14 x y z - 20 x + 9 z, 15 x z + 10 x z + 8 x y , 13 z - 11 x z - 16 y ] ] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.7MB, alloc=32.3MB, time=0.51 memory used=47.4MB, alloc=32.3MB, time=0.81 memory used=64.7MB, alloc=56.3MB, time=1.08 memory used=104.3MB, alloc=60.3MB, time=1.69 memory used=143.6MB, alloc=84.3MB, time=2.31 memory used=206.8MB, alloc=92.3MB, time=3.18 memory used=271.3MB, alloc=92.3MB, time=3.94 memory used=334.7MB, alloc=92.3MB, time=4.90 memory used=395.5MB, alloc=116.3MB, time=5.87 memory used=466.4MB, alloc=116.3MB, time=6.85 memory used=552.4MB, alloc=116.3MB, time=8.20 memory used=631.9MB, alloc=140.3MB, time=9.48 memory used=714.0MB, alloc=396.3MB, time=10.82 memory used=805.0MB, alloc=396.3MB, time=11.79 memory used=882.4MB, alloc=396.3MB, time=12.57 memory used=1006.4MB, alloc=420.3MB, time=14.08 memory used=1155.9MB, alloc=420.3MB, time=15.90 memory used=1284.1MB, alloc=444.3MB, time=17.88 memory used=1429.4MB, alloc=444.3MB, time=20.14 memory used=1572.0MB, alloc=468.3MB, time=22.04 memory used=1685.4MB, alloc=468.3MB, time=23.61 memory used=1761.3MB, alloc=468.3MB, time=23.89 memory used=1841.4MB, alloc=468.3MB, time=24.14 memory used=1973.5MB, alloc=468.3MB, time=25.01 memory used=2075.1MB, alloc=468.3MB, time=25.47 memory used=2239.8MB, alloc=468.3MB, time=26.34 memory used=2411.0MB, alloc=468.3MB, time=26.68 memory used=2618.9MB, alloc=468.3MB, time=27.21 memory used=2881.9MB, alloc=468.3MB, time=28.68 memory used=2995.7MB, alloc=468.3MB, time=29.76 memory used=3106.7MB, alloc=468.3MB, time=30.78 memory used=3245.6MB, alloc=468.3MB, time=32.01 memory used=3417.8MB, alloc=492.3MB, time=34.66 memory used=3561.2MB, alloc=516.3MB, time=37.21 memory used=3711.8MB, alloc=516.3MB, time=39.81 memory used=3874.9MB, alloc=516.3MB, time=41.86 memory used=3974.2MB, alloc=540.3MB, time=43.38 memory used=4097.7MB, alloc=540.3MB, time=45.47 memory used=4219.9MB, alloc=540.3MB, time=47.66 memory used=4345.3MB, alloc=540.3MB, time=49.49 memory used=4423.0MB, alloc=540.3MB, time=50.80 memory used=4538.1MB, alloc=564.3MB, time=52.34 memory used=4698.9MB, alloc=564.3MB, time=53.38 memory used=4834.9MB, alloc=564.3MB, time=54.77 memory used=4974.8MB, alloc=564.3MB, time=55.58 memory used=5116.1MB, alloc=564.3MB, time=56.33 memory used=5230.5MB, alloc=564.3MB, time=56.82 memory used=5363.7MB, alloc=564.3MB, time=57.49 memory used=5478.6MB, alloc=564.3MB, time=57.97 memory used=5636.2MB, alloc=564.3MB, time=60.31 memory used=5754.7MB, alloc=564.3MB, time=60.83 memory used=5861.3MB, alloc=564.3MB, time=61.31 memory used=5967.0MB, alloc=564.3MB, time=61.78 memory used=6105.4MB, alloc=564.3MB, time=63.02 memory used=6228.9MB, alloc=564.3MB, time=63.58 memory used=6329.7MB, alloc=564.3MB, time=64.05 memory used=6427.6MB, alloc=564.3MB, time=64.53 memory used=6543.8MB, alloc=564.3MB, time=65.01 memory used=6675.8MB, alloc=564.3MB, time=65.49 memory used=6779.5MB, alloc=564.3MB, time=65.92 memory used=6864.8MB, alloc=564.3MB, time=66.30 memory used=6963.6MB, alloc=564.3MB, time=66.70 memory used=7165.5MB, alloc=564.3MB, time=71.24 memory used=7262.1MB, alloc=564.3MB, time=72.59 memory used=7353.4MB, alloc=564.3MB, time=73.97 memory used=7431.3MB, alloc=564.3MB, time=75.53 memory used=7496.1MB, alloc=564.3MB, time=76.75 memory used=7565.4MB, alloc=564.3MB, time=78.22 memory used=7630.1MB, alloc=564.3MB, time=79.69 memory used=7692.9MB, alloc=564.3MB, time=81.09 memory used=7755.0MB, alloc=564.3MB, time=82.47 memory used=7799.4MB, alloc=564.3MB, time=83.53 memory used=7852.2MB, alloc=564.3MB, time=84.95 memory used=7898.7MB, alloc=564.3MB, time=86.21 memory used=8129.6MB, alloc=588.3MB, time=90.79 memory used=8365.8MB, alloc=612.3MB, time=95.61 memory used=8569.7MB, alloc=636.3MB, time=98.49 memory used=8733.2MB, alloc=636.3MB, time=99.60 memory used=8901.7MB, alloc=660.3MB, time=102.26 memory used=9062.1MB, alloc=660.3MB, time=103.13 memory used=9194.0MB, alloc=660.3MB, time=103.88 memory used=9357.2MB, alloc=660.3MB, time=104.64 memory used=9520.0MB, alloc=660.3MB, time=105.35 memory used=9637.5MB, alloc=660.3MB, time=105.98 memory used=9790.8MB, alloc=660.3MB, time=107.57 memory used=9951.4MB, alloc=660.3MB, time=108.40 memory used=10089.6MB, alloc=660.3MB, time=109.16 memory used=10267.8MB, alloc=660.3MB, time=109.94 memory used=10394.9MB, alloc=660.3MB, time=110.61 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428253252 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 3 3 F := [18 x y - 8 x y z - 5 x y z , -x y + 7 x z - 18 y, 2 2 3 4 -20 x z + 16 x z + 13 z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 2 2 2 3 G := [12 x y z + 3 x z + 13 y , 13 x z + 14 x + 16 y z, -18 y z - 9 y ] > Problem := [F,G]; 3 2 2 3 3 Problem := [[18 x y - 8 x y z - 5 x y z , -x y + 7 x z - 18 y, 2 2 3 4 -20 x z + 16 x z + 13 z ], 2 3 2 2 2 2 2 3 [12 x y z + 3 x z + 13 y , 13 x z + 14 x + 16 y z, -18 y z - 9 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.17 memory used=26.6MB, alloc=32.3MB, time=0.48 memory used=47.3MB, alloc=32.3MB, time=0.78 memory used=66.0MB, alloc=56.3MB, time=1.07 memory used=104.9MB, alloc=60.3MB, time=1.66 memory used=143.3MB, alloc=84.3MB, time=2.27 memory used=204.9MB, alloc=92.3MB, time=3.24 memory used=263.6MB, alloc=116.3MB, time=4.21 memory used=347.0MB, alloc=140.3MB, time=5.60 memory used=431.7MB, alloc=396.3MB, time=6.98 memory used=531.1MB, alloc=420.3MB, time=8.63 memory used=651.8MB, alloc=420.3MB, time=10.60 memory used=775.1MB, alloc=444.3MB, time=12.74 memory used=926.6MB, alloc=468.3MB, time=15.39 memory used=1083.0MB, alloc=492.3MB, time=18.47 memory used=1261.5MB, alloc=516.3MB, time=22.32 memory used=1413.9MB, alloc=540.3MB, time=25.76 memory used=1575.3MB, alloc=564.3MB, time=29.62 memory used=1708.9MB, alloc=588.3MB, time=32.35 memory used=1849.3MB, alloc=588.3MB, time=35.90 memory used=2001.0MB, alloc=588.3MB, time=40.15 memory used=2125.7MB, alloc=588.3MB, time=43.27 memory used=2279.4MB, alloc=612.3MB, time=47.60 memory used=2398.6MB, alloc=612.3MB, time=51.07 memory used=2515.3MB, alloc=612.3MB, time=54.28 memory used=2621.0MB, alloc=612.3MB, time=57.11 memory used=2731.5MB, alloc=612.3MB, time=60.35 memory used=2818.9MB, alloc=612.3MB, time=62.58 memory used=2902.2MB, alloc=612.3MB, time=64.33 memory used=2992.6MB, alloc=612.3MB, time=66.36 memory used=3074.9MB, alloc=612.3MB, time=68.83 memory used=3141.3MB, alloc=612.3MB, time=70.57 memory used=3213.0MB, alloc=636.3MB, time=72.18 memory used=3281.5MB, alloc=636.3MB, time=73.76 memory used=3366.0MB, alloc=636.3MB, time=76.29 memory used=3436.8MB, alloc=636.3MB, time=78.33 memory used=3488.8MB, alloc=636.3MB, time=79.70 memory used=3783.3MB, alloc=660.3MB, time=87.16 memory used=4097.2MB, alloc=684.3MB, time=95.18 memory used=4393.2MB, alloc=708.3MB, time=101.97 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428253552 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 3 3 F := [-9 y z + 19 y + 15, -12 x z - 3 y z - 11 z , 2 2 2 2 9 x y + 7 x y z + 10 y z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 4 3 G := [13 x y + 2 y z + 5 y, -19 x y - 10 x y z - 13 x z, 17 x + 4 x ] > Problem := [F,G]; 2 2 3 2 2 3 3 Problem := [[-9 y z + 19 y + 15, -12 x z - 3 y z - 11 z , 2 2 2 2 9 x y + 7 x y z + 10 y z], 3 2 2 2 2 4 3 [13 x y + 2 y z + 5 y, -19 x y - 10 x y z - 13 x z, 17 x + 4 x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.1MB, alloc=32.3MB, time=0.48 memory used=46.9MB, alloc=32.3MB, time=0.79 memory used=65.6MB, alloc=56.3MB, time=1.08 memory used=106.5MB, alloc=60.3MB, time=1.68 memory used=145.0MB, alloc=84.3MB, time=2.26 memory used=210.0MB, alloc=92.3MB, time=3.18 memory used=270.4MB, alloc=116.3MB, time=4.13 memory used=336.9MB, alloc=116.3MB, time=5.13 memory used=397.6MB, alloc=372.3MB, time=5.98 memory used=482.6MB, alloc=396.3MB, time=7.28 memory used=592.9MB, alloc=420.3MB, time=8.94 memory used=720.3MB, alloc=420.3MB, time=11.05 memory used=850.3MB, alloc=444.3MB, time=13.12 memory used=979.0MB, alloc=468.3MB, time=15.08 memory used=1095.4MB, alloc=468.3MB, time=16.92 memory used=1220.5MB, alloc=468.3MB, time=18.73 memory used=1325.4MB, alloc=468.3MB, time=20.38 memory used=1432.5MB, alloc=492.3MB, time=22.19 memory used=1549.4MB, alloc=492.3MB, time=24.37 memory used=1651.2MB, alloc=516.3MB, time=26.66 memory used=1743.4MB, alloc=516.3MB, time=29.53 memory used=1823.3MB, alloc=516.3MB, time=31.85 memory used=1906.1MB, alloc=516.3MB, time=34.43 memory used=1989.5MB, alloc=516.3MB, time=37.07 memory used=2067.8MB, alloc=516.3MB, time=39.79 memory used=2129.0MB, alloc=516.3MB, time=41.63 memory used=2194.1MB, alloc=516.3MB, time=43.65 memory used=2271.4MB, alloc=516.3MB, time=46.56 memory used=2338.9MB, alloc=540.3MB, time=48.91 memory used=2407.2MB, alloc=540.3MB, time=51.47 memory used=2459.7MB, alloc=540.3MB, time=53.36 memory used=2502.4MB, alloc=540.3MB, time=54.97 memory used=2709.7MB, alloc=564.3MB, time=60.64 memory used=2868.0MB, alloc=588.3MB, time=64.66 memory used=3076.8MB, alloc=612.3MB, time=71.80 memory used=3230.2MB, alloc=612.3MB, time=76.21 memory used=3414.9MB, alloc=636.3MB, time=82.33 memory used=3609.6MB, alloc=660.3MB, time=88.60 memory used=3783.6MB, alloc=660.3MB, time=94.67 memory used=3947.7MB, alloc=660.3MB, time=100.65 memory used=4096.4MB, alloc=684.3MB, time=106.37 memory used=4242.7MB, alloc=684.3MB, time=111.28 memory used=4362.9MB, alloc=684.3MB, time=115.63 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428253852 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 F := [-12 x y z - 12 x y z + 15 x z , -10 y z + 10 x z - 8 z, 2 2 2 2 3 -5 x y + 14 x z + 8 y z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [-2 x y z - 18 x, -8 x z - 16 x z - 4 x , 17 x y + 9] > Problem := [F,G]; 2 2 3 Problem := [[-12 x y z - 12 x y z + 15 x z , -10 y z + 10 x z - 8 z, 2 2 2 2 3 -5 x y + 14 x z + 8 y z], 2 2 2 2 [-2 x y z - 18 x, -8 x z - 16 x z - 4 x , 17 x y + 9]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.31 memory used=26.6MB, alloc=32.3MB, time=0.87 memory used=47.3MB, alloc=32.3MB, time=1.41 memory used=65.3MB, alloc=56.3MB, time=1.89 memory used=105.9MB, alloc=60.3MB, time=2.94 memory used=144.8MB, alloc=60.3MB, time=3.94 memory used=183.6MB, alloc=84.3MB, time=4.96 memory used=213.7MB, alloc=84.3MB, time=5.61 memory used=270.6MB, alloc=92.3MB, time=6.50 memory used=337.2MB, alloc=92.3MB, time=7.68 memory used=399.7MB, alloc=92.3MB, time=9.07 memory used=455.9MB, alloc=92.3MB, time=10.08 memory used=497.0MB, alloc=92.3MB, time=11.36 memory used=547.8MB, alloc=92.3MB, time=12.70 memory used=586.8MB, alloc=92.3MB, time=13.27 memory used=638.0MB, alloc=92.3MB, time=14.19 memory used=726.3MB, alloc=92.3MB, time=16.44 memory used=774.4MB, alloc=92.3MB, time=16.91 memory used=822.6MB, alloc=116.8MB, time=18.67 memory used=891.5MB, alloc=120.2MB, time=19.03 memory used=957.6MB, alloc=120.2MB, time=19.36 memory used=1016.3MB, alloc=120.2MB, time=19.66 memory used=1053.8MB, alloc=120.2MB, time=19.89 memory used=1092.0MB, alloc=120.2MB, time=20.12 memory used=1132.5MB, alloc=120.2MB, time=20.35 memory used=1176.4MB, alloc=120.2MB, time=20.61 memory used=1224.2MB, alloc=120.2MB, time=20.85 memory used=1278.4MB, alloc=120.2MB, time=26.72 memory used=1354.1MB, alloc=120.2MB, time=29.41 memory used=1415.5MB, alloc=120.2MB, time=29.66 memory used=1452.7MB, alloc=120.2MB, time=29.87 memory used=1485.5MB, alloc=120.2MB, time=30.07 memory used=1519.6MB, alloc=120.2MB, time=30.27 memory used=1554.5MB, alloc=120.2MB, time=30.48 memory used=1590.5MB, alloc=120.2MB, time=30.67 memory used=1627.6MB, alloc=120.2MB, time=30.88 memory used=1665.3MB, alloc=120.2MB, time=31.08 memory used=1704.4MB, alloc=120.2MB, time=31.30 memory used=1745.0MB, alloc=120.2MB, time=31.50 memory used=1787.3MB, alloc=120.2MB, time=31.69 memory used=1831.6MB, alloc=120.2MB, time=31.90 memory used=1877.5MB, alloc=120.2MB, time=32.11 memory used=1925.5MB, alloc=120.2MB, time=32.32 memory used=1995.1MB, alloc=120.2MB, time=33.40 memory used=2073.6MB, alloc=120.2MB, time=35.25 memory used=2153.6MB, alloc=376.2MB, time=37.35 memory used=2235.5MB, alloc=400.2MB, time=39.31 memory used=2338.1MB, alloc=400.2MB, time=42.07 memory used=2438.6MB, alloc=400.2MB, time=44.75 memory used=2517.1MB, alloc=400.2MB, time=47.33 memory used=2573.1MB, alloc=400.2MB, time=47.86 memory used=2647.8MB, alloc=400.2MB, time=48.52 memory used=2726.5MB, alloc=400.2MB, time=52.81 memory used=2775.8MB, alloc=400.2MB, time=53.13 memory used=2843.5MB, alloc=424.2MB, time=54.94 memory used=2939.1MB, alloc=424.2MB, time=55.46 memory used=2994.7MB, alloc=424.2MB, time=55.84 memory used=3052.3MB, alloc=424.2MB, time=56.21 memory used=3118.2MB, alloc=424.2MB, time=56.59 memory used=3193.6MB, alloc=424.2MB, time=56.98 memory used=3270.5MB, alloc=424.2MB, time=57.36 memory used=3317.5MB, alloc=424.2MB, time=57.69 memory used=3368.2MB, alloc=424.2MB, time=58.00 memory used=3423.1MB, alloc=424.2MB, time=58.31 memory used=3483.0MB, alloc=424.2MB, time=58.63 memory used=3565.6MB, alloc=424.2MB, time=60.62 memory used=3664.7MB, alloc=424.2MB, time=61.17 memory used=3728.5MB, alloc=424.2MB, time=61.56 memory used=3785.4MB, alloc=424.2MB, time=61.94 memory used=3850.7MB, alloc=424.2MB, time=62.32 memory used=3925.7MB, alloc=424.2MB, time=62.70 memory used=4007.1MB, alloc=424.2MB, time=63.09 memory used=4055.4MB, alloc=424.2MB, time=63.41 memory used=4105.2MB, alloc=424.2MB, time=63.72 memory used=4159.1MB, alloc=424.2MB, time=64.03 memory used=4218.7MB, alloc=424.2MB, time=64.34 memory used=4286.0MB, alloc=424.2MB, time=65.00 memory used=4567.4MB, alloc=424.2MB, time=157.10 memory used=4768.7MB, alloc=424.2MB, time=157.62 memory used=4925.8MB, alloc=424.2MB, time=159.34 memory used=4993.5MB, alloc=424.2MB, time=159.70 memory used=5098.1MB, alloc=424.2MB, time=160.28 memory used=5270.8MB, alloc=424.2MB, time=160.85 memory used=5459.2MB, alloc=424.2MB, time=161.98 memory used=5677.4MB, alloc=424.2MB, time=162.60 memory used=5889.8MB, alloc=424.2MB, time=163.15 memory used=6088.2MB, alloc=424.2MB, time=163.63 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428254152 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 4 2 F := [-x y z + 18 x y + 13 x z, 9 x y + y , 7 x - 9 x y z - 2 x y z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 4 2 2 G := [-19 x y + 7 y z + 2 x y z, -4 y - 12 x z - 6 z , 3 3 -6 x z - 19 x - 20 y z] > Problem := [F,G]; Problem := [ 2 3 2 2 4 2 [-x y z + 18 x y + 13 x z, 9 x y + y , 7 x - 9 x y z - 2 x y z], [ 3 3 4 2 2 -19 x y + 7 y z + 2 x y z, -4 y - 12 x z - 6 z , 3 3 -6 x z - 19 x - 20 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.31 memory used=26.8MB, alloc=32.3MB, time=0.90 memory used=47.1MB, alloc=60.3MB, time=1.41 memory used=87.8MB, alloc=60.3MB, time=2.33 memory used=129.5MB, alloc=68.3MB, time=3.37 memory used=173.1MB, alloc=92.3MB, time=4.43 memory used=233.7MB, alloc=92.3MB, time=5.48 memory used=274.5MB, alloc=92.3MB, time=5.75 memory used=308.8MB, alloc=92.3MB, time=5.90 memory used=356.9MB, alloc=92.3MB, time=7.31 memory used=397.6MB, alloc=92.3MB, time=7.80 memory used=432.5MB, alloc=92.3MB, time=8.01 memory used=476.2MB, alloc=95.9MB, time=8.29 memory used=509.5MB, alloc=95.9MB, time=8.45 memory used=550.2MB, alloc=95.9MB, time=8.64 memory used=591.6MB, alloc=95.9MB, time=8.82 memory used=626.9MB, alloc=95.9MB, time=8.99 memory used=680.3MB, alloc=95.9MB, time=9.82 memory used=739.9MB, alloc=95.9MB, time=11.34 memory used=807.8MB, alloc=95.9MB, time=14.10 memory used=839.9MB, alloc=95.9MB, time=14.35 memory used=893.7MB, alloc=95.9MB, time=15.08 memory used=960.8MB, alloc=119.9MB, time=16.52 memory used=1022.0MB, alloc=375.9MB, time=17.95 memory used=1110.5MB, alloc=399.9MB, time=20.14 memory used=1224.2MB, alloc=399.9MB, time=23.01 memory used=1334.6MB, alloc=399.9MB, time=25.04 memory used=1420.6MB, alloc=423.9MB, time=28.33 memory used=1550.4MB, alloc=423.9MB, time=30.35 memory used=1682.8MB, alloc=423.9MB, time=32.56 memory used=1823.4MB, alloc=423.9MB, time=35.66 memory used=1951.5MB, alloc=447.9MB, time=38.44 memory used=2062.0MB, alloc=471.9MB, time=41.22 memory used=2172.1MB, alloc=471.9MB, time=43.79 memory used=2269.5MB, alloc=471.9MB, time=44.78 memory used=2383.3MB, alloc=471.9MB, time=49.13 memory used=2475.2MB, alloc=471.9MB, time=49.96 memory used=2593.6MB, alloc=471.9MB, time=52.52 memory used=2718.0MB, alloc=471.9MB, time=55.43 memory used=2817.8MB, alloc=471.9MB, time=57.54 memory used=2919.0MB, alloc=471.9MB, time=59.59 memory used=3008.9MB, alloc=471.9MB, time=60.64 memory used=3109.3MB, alloc=471.9MB, time=61.84 memory used=3195.4MB, alloc=495.9MB, time=62.89 memory used=3282.8MB, alloc=495.9MB, time=63.53 memory used=3379.1MB, alloc=495.9MB, time=64.12 memory used=3477.2MB, alloc=495.9MB, time=65.21 memory used=3564.4MB, alloc=495.9MB, time=65.82 memory used=3659.0MB, alloc=495.9MB, time=66.43 memory used=3802.7MB, alloc=495.9MB, time=83.47 memory used=3895.2MB, alloc=495.9MB, time=84.11 memory used=3980.7MB, alloc=495.9MB, time=84.65 memory used=4064.0MB, alloc=495.9MB, time=85.15 memory used=4201.4MB, alloc=495.9MB, time=86.42 memory used=4308.8MB, alloc=495.9MB, time=88.40 memory used=4410.7MB, alloc=495.9MB, time=90.60 memory used=4511.8MB, alloc=495.9MB, time=92.10 memory used=4584.3MB, alloc=495.9MB, time=94.02 memory used=4678.1MB, alloc=495.9MB, time=96.74 memory used=4742.7MB, alloc=495.9MB, time=98.43 memory used=4806.2MB, alloc=495.9MB, time=100.16 memory used=4867.5MB, alloc=495.9MB, time=102.04 memory used=4916.8MB, alloc=495.9MB, time=103.61 memory used=4973.0MB, alloc=495.9MB, time=105.46 memory used=5038.1MB, alloc=519.9MB, time=107.46 memory used=5136.1MB, alloc=519.9MB, time=108.39 memory used=5226.2MB, alloc=519.9MB, time=109.18 memory used=5344.6MB, alloc=519.9MB, time=110.73 memory used=5462.7MB, alloc=519.9MB, time=111.73 memory used=5562.8MB, alloc=519.9MB, time=112.53 memory used=5687.5MB, alloc=519.9MB, time=124.69 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428254452 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 3 F := [15 y - 17 y z + 12 z , -15 x z - 12 y z + 13 x, 2 2 3 12 x y - 9 x z + 11 y z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 4 3 3 2 G := [16 x z + 5 y - 20, -15 x z - y z + 19 z, 16 x z + 16 y z - 19 x] > Problem := [F,G]; 3 2 3 3 Problem := [[15 y - 17 y z + 12 z , -15 x z - 12 y z + 13 x, 2 2 3 12 x y - 9 x z + 11 y z], 3 4 3 3 2 [16 x z + 5 y - 20, -15 x z - y z + 19 z, 16 x z + 16 y z - 19 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.31 memory used=25.0MB, alloc=32.3MB, time=0.84 memory used=47.5MB, alloc=56.3MB, time=1.33 memory used=95.6MB, alloc=61.0MB, time=2.28 memory used=127.5MB, alloc=62.1MB, time=2.55 memory used=150.8MB, alloc=62.1MB, time=2.66 memory used=182.0MB, alloc=62.1MB, time=2.78 memory used=203.0MB, alloc=62.1MB, time=2.87 memory used=223.5MB, alloc=62.1MB, time=2.96 memory used=246.6MB, alloc=62.1MB, time=3.05 memory used=272.7MB, alloc=62.1MB, time=3.15 memory used=301.8MB, alloc=62.1MB, time=3.25 memory used=339.8MB, alloc=83.8MB, time=3.41 memory used=353.0MB, alloc=83.8MB, time=3.48 memory used=415.3MB, alloc=83.8MB, time=4.85 memory used=466.1MB, alloc=83.8MB, time=5.47 memory used=508.9MB, alloc=83.8MB, time=6.53 memory used=551.4MB, alloc=83.8MB, time=8.03 memory used=580.6MB, alloc=83.8MB, time=8.29 memory used=600.7MB, alloc=83.8MB, time=8.42 memory used=624.2MB, alloc=83.8MB, time=8.54 memory used=648.9MB, alloc=83.8MB, time=8.64 memory used=665.6MB, alloc=83.8MB, time=8.73 memory used=684.5MB, alloc=83.8MB, time=8.82 memory used=706.5MB, alloc=83.8MB, time=8.91 memory used=747.4MB, alloc=83.8MB, time=11.28 memory used=782.6MB, alloc=83.8MB, time=13.59 memory used=807.4MB, alloc=83.8MB, time=13.71 memory used=825.2MB, alloc=83.8MB, time=13.82 memory used=846.1MB, alloc=83.8MB, time=13.93 memory used=870.4MB, alloc=83.8MB, time=14.05 memory used=898.2MB, alloc=83.8MB, time=14.17 memory used=913.5MB, alloc=83.8MB, time=14.25 memory used=930.0MB, alloc=83.8MB, time=14.36 memory used=947.5MB, alloc=83.8MB, time=14.46 memory used=966.1MB, alloc=83.8MB, time=14.55 memory used=985.7MB, alloc=83.8MB, time=14.64 memory used=1006.1MB, alloc=83.8MB, time=14.74 memory used=1028.0MB, alloc=83.8MB, time=14.85 memory used=1051.5MB, alloc=83.8MB, time=14.96 memory used=1076.9MB, alloc=83.8MB, time=15.05 memory used=1105.0MB, alloc=83.8MB, time=15.15 memory used=1122.3MB, alloc=83.8MB, time=15.23 memory used=1136.1MB, alloc=83.8MB, time=15.37 memory used=1189.2MB, alloc=83.8MB, time=16.21 memory used=1231.0MB, alloc=83.8MB, time=17.97 memory used=1253.1MB, alloc=83.8MB, time=18.09 memory used=1273.1MB, alloc=83.8MB, time=18.20 memory used=1297.8MB, alloc=83.8MB, time=18.32 memory used=1317.5MB, alloc=83.8MB, time=18.42 memory used=1334.1MB, alloc=83.8MB, time=18.51 memory used=1352.6MB, alloc=83.8MB, time=18.61 memory used=1373.6MB, alloc=83.8MB, time=18.74 memory used=1418.6MB, alloc=83.8MB, time=19.42 memory used=1460.1MB, alloc=107.8MB, time=20.37 memory used=1530.3MB, alloc=107.8MB, time=49.76 memory used=1580.3MB, alloc=107.8MB, time=56.17 memory used=1617.7MB, alloc=107.8MB, time=56.39 memory used=1645.5MB, alloc=107.8MB, time=56.57 memory used=1677.6MB, alloc=107.8MB, time=56.76 memory used=1715.7MB, alloc=107.8MB, time=56.94 memory used=1757.8MB, alloc=107.8MB, time=57.14 memory used=1781.8MB, alloc=107.8MB, time=57.29 memory used=1805.8MB, alloc=107.8MB, time=57.43 memory used=1830.4MB, alloc=107.8MB, time=57.56 memory used=1857.7MB, alloc=107.8MB, time=57.71 memory used=1886.1MB, alloc=107.8MB, time=57.85 memory used=1915.4MB, alloc=107.8MB, time=58.00 memory used=1947.7MB, alloc=107.8MB, time=58.17 memory used=1981.0MB, alloc=107.8MB, time=58.32 memory used=2015.2MB, alloc=107.8MB, time=58.48 memory used=2052.5MB, alloc=107.8MB, time=58.63 memory used=2090.7MB, alloc=107.8MB, time=58.80 memory used=2129.8MB, alloc=107.8MB, time=58.96 memory used=2171.9MB, alloc=107.8MB, time=59.13 memory used=2211.0MB, alloc=107.8MB, time=59.30 memory used=2217.7MB, alloc=107.8MB, time=59.38 memory used=2225.2MB, alloc=107.8MB, time=59.49 memory used=2232.6MB, alloc=107.8MB, time=59.58 memory used=2240.1MB, alloc=107.8MB, time=59.70 memory used=2247.6MB, alloc=107.8MB, time=59.81 memory used=2255.1MB, alloc=107.8MB, time=59.90 memory used=2262.7MB, alloc=107.8MB, time=59.99 memory used=2270.2MB, alloc=107.8MB, time=60.09 memory used=2277.8MB, alloc=107.8MB, time=60.19 memory used=2285.3MB, alloc=107.8MB, time=60.28 memory used=2292.9MB, alloc=107.8MB, time=60.38 memory used=2300.5MB, alloc=107.8MB, time=60.49 memory used=2308.1MB, alloc=107.8MB, time=60.59 memory used=2315.7MB, alloc=107.8MB, time=60.69 memory used=2323.5MB, alloc=107.8MB, time=60.79 memory used=2333.5MB, alloc=107.8MB, time=60.89 memory used=2341.3MB, alloc=107.8MB, time=61.01 memory used=2351.3MB, alloc=107.8MB, time=61.12 memory used=2361.6MB, alloc=107.8MB, time=61.21 memory used=2371.8MB, alloc=107.8MB, time=61.31 memory used=2382.0MB, alloc=107.8MB, time=61.44 memory used=2392.2MB, alloc=107.8MB, time=61.55 memory used=2402.5MB, alloc=107.8MB, time=61.65 memory used=2412.7MB, alloc=107.8MB, time=61.75 memory used=2423.0MB, alloc=107.8MB, time=61.88 memory used=2433.3MB, alloc=107.8MB, time=61.97 memory used=2443.5MB, alloc=107.8MB, time=62.08 memory used=2453.8MB, alloc=107.8MB, time=62.18 memory used=2464.0MB, alloc=107.8MB, time=62.28 memory used=2474.3MB, alloc=107.8MB, time=62.39 memory used=2484.6MB, alloc=107.8MB, time=62.49 memory used=2494.8MB, alloc=107.8MB, time=62.59 memory used=2505.1MB, alloc=107.8MB, time=62.70 memory used=2515.3MB, alloc=107.8MB, time=62.80 memory used=2525.6MB, alloc=107.8MB, time=62.91 memory used=2535.8MB, alloc=107.8MB, time=63.01 memory used=2546.0MB, alloc=107.8MB, time=63.11 memory used=2556.2MB, alloc=107.8MB, time=63.22 memory used=2566.6MB, alloc=107.8MB, time=63.34 memory used=2579.2MB, alloc=107.8MB, time=63.49 memory used=2591.9MB, alloc=107.8MB, time=63.59 memory used=2604.6MB, alloc=107.8MB, time=63.70 memory used=2617.2MB, alloc=107.8MB, time=63.80 memory used=2629.9MB, alloc=107.8MB, time=63.91 memory used=2642.5MB, alloc=107.8MB, time=64.01 memory used=2655.0MB, alloc=107.8MB, time=64.11 memory used=2667.6MB, alloc=107.8MB, time=64.22 memory used=2680.0MB, alloc=107.8MB, time=64.32 memory used=2692.5MB, alloc=107.8MB, time=64.42 memory used=2704.9MB, alloc=107.8MB, time=64.52 memory used=2717.3MB, alloc=107.8MB, time=64.65 memory used=2729.6MB, alloc=107.8MB, time=64.77 memory used=2742.0MB, alloc=107.8MB, time=64.88 memory used=2756.5MB, alloc=107.8MB, time=64.99 memory used=2771.0MB, alloc=107.8MB, time=65.11 memory used=2785.5MB, alloc=107.8MB, time=65.23 memory used=2799.9MB, alloc=107.8MB, time=65.33 memory used=2814.2MB, alloc=107.8MB, time=65.44 memory used=2828.4MB, alloc=107.8MB, time=65.55 memory used=2842.5MB, alloc=107.8MB, time=65.67 memory used=2856.5MB, alloc=107.8MB, time=65.78 memory used=2870.6MB, alloc=107.8MB, time=65.90 memory used=2886.4MB, alloc=107.8MB, time=66.01 memory used=2902.3MB, alloc=107.8MB, time=66.14 memory used=2918.0MB, alloc=107.8MB, time=66.27 memory used=2933.6MB, alloc=107.8MB, time=66.38 memory used=2949.0MB, alloc=107.8MB, time=66.51 memory used=2964.5MB, alloc=107.8MB, time=66.62 memory used=2981.4MB, alloc=107.8MB, time=66.74 memory used=2998.4MB, alloc=107.8MB, time=66.89 memory used=3015.0MB, alloc=107.8MB, time=67.02 memory used=3033.4MB, alloc=107.8MB, time=67.15 memory used=3051.4MB, alloc=107.8MB, time=67.26 memory used=3069.0MB, alloc=107.8MB, time=67.38 memory used=3088.1MB, alloc=107.8MB, time=67.50 memory used=3106.7MB, alloc=107.8MB, time=67.62 memory used=3126.5MB, alloc=107.8MB, time=67.76 memory used=3145.9MB, alloc=107.8MB, time=67.89 memory used=3161.2MB, alloc=107.8MB, time=68.00 memory used=3174.3MB, alloc=107.8MB, time=68.10 memory used=3187.1MB, alloc=107.8MB, time=68.20 memory used=3200.2MB, alloc=107.8MB, time=68.30 memory used=3212.5MB, alloc=107.8MB, time=68.40 memory used=3227.0MB, alloc=107.8MB, time=68.50 memory used=3240.5MB, alloc=107.8MB, time=68.62 memory used=3254.9MB, alloc=107.8MB, time=68.73 memory used=3269.8MB, alloc=107.8MB, time=68.83 memory used=3285.5MB, alloc=107.8MB, time=68.94 memory used=3301.5MB, alloc=107.8MB, time=69.04 memory used=3346.4MB, alloc=107.8MB, time=69.40 memory used=3382.3MB, alloc=107.8MB, time=69.59 memory used=3420.5MB, alloc=107.8MB, time=69.90 memory used=3461.1MB, alloc=107.8MB, time=70.13 memory used=3496.1MB, alloc=107.8MB, time=70.31 memory used=3538.7MB, alloc=107.8MB, time=74.39 memory used=3599.7MB, alloc=131.8MB, time=100.96 memory used=3654.6MB, alloc=131.8MB, time=159.91 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428254752 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 4 2 3 4 F := [6 x y z - 7 x z + 6 z, -10 z - 14 x + 3, 9 x y z - 13 x z + 12 z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 4 2 2 2 3 2 G := [11 x z + 19 y + 4 y z , -12 x z - 19 y + 18 x , 2 2 -6 x y z + 13 y z - 6] > Problem := [F,G]; Problem := [ 2 4 2 3 4 [6 x y z - 7 x z + 6 z, -10 z - 14 x + 3, 9 x y z - 13 x z + 12 z ], [ 2 2 4 2 2 2 3 2 11 x z + 19 y + 4 y z , -12 x z - 19 y + 18 x , 2 2 -6 x y z + 13 y z - 6]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=25.8MB, alloc=32.3MB, time=0.86 memory used=45.8MB, alloc=32.3MB, time=1.35 memory used=65.3MB, alloc=56.3MB, time=1.86 memory used=109.4MB, alloc=68.3MB, time=2.93 memory used=151.6MB, alloc=92.3MB, time=3.95 memory used=219.8MB, alloc=92.3MB, time=5.54 memory used=284.0MB, alloc=348.3MB, time=6.93 memory used=348.8MB, alloc=372.3MB, time=8.47 memory used=438.1MB, alloc=372.3MB, time=10.27 memory used=504.7MB, alloc=372.3MB, time=11.51 memory used=586.6MB, alloc=372.3MB, time=12.93 memory used=684.9MB, alloc=396.3MB, time=15.05 memory used=798.8MB, alloc=396.3MB, time=17.50 memory used=900.2MB, alloc=420.3MB, time=19.64 memory used=1041.1MB, alloc=420.3MB, time=22.46 memory used=1150.8MB, alloc=444.3MB, time=25.18 memory used=1265.9MB, alloc=444.3MB, time=28.06 memory used=1396.9MB, alloc=444.3MB, time=31.67 memory used=1461.1MB, alloc=444.3MB, time=32.12 memory used=1555.4MB, alloc=444.3MB, time=33.13 memory used=1652.7MB, alloc=444.3MB, time=35.10 memory used=1764.1MB, alloc=468.3MB, time=37.82 memory used=1858.1MB, alloc=468.3MB, time=40.24 memory used=1946.2MB, alloc=468.3MB, time=42.44 memory used=2031.7MB, alloc=468.3MB, time=44.92 memory used=2103.5MB, alloc=492.3MB, time=46.71 memory used=2186.5MB, alloc=492.3MB, time=48.52 memory used=2244.2MB, alloc=492.3MB, time=49.81 memory used=2319.9MB, alloc=492.3MB, time=51.90 memory used=2374.3MB, alloc=492.3MB, time=53.58 memory used=2436.7MB, alloc=492.3MB, time=55.21 memory used=2501.3MB, alloc=492.3MB, time=56.76 memory used=2576.3MB, alloc=516.3MB, time=58.77 memory used=2622.8MB, alloc=516.3MB, time=60.46 memory used=2680.5MB, alloc=516.3MB, time=62.08 memory used=2726.7MB, alloc=516.3MB, time=63.63 memory used=2944.5MB, alloc=540.3MB, time=67.74 memory used=3139.9MB, alloc=564.3MB, time=72.72 memory used=3298.2MB, alloc=588.3MB, time=76.12 memory used=3464.4MB, alloc=612.3MB, time=80.61 memory used=3617.9MB, alloc=636.3MB, time=84.13 memory used=3758.3MB, alloc=636.3MB, time=87.78 memory used=3897.8MB, alloc=660.3MB, time=91.13 memory used=4022.4MB, alloc=660.3MB, time=94.27 memory used=4135.6MB, alloc=660.3MB, time=97.07 memory used=4303.7MB, alloc=660.3MB, time=101.07 memory used=4488.0MB, alloc=684.3MB, time=104.16 memory used=4692.5MB, alloc=684.3MB, time=109.36 memory used=4924.4MB, alloc=684.3MB, time=115.66 memory used=5122.8MB, alloc=684.3MB, time=117.51 memory used=5331.8MB, alloc=684.3MB, time=123.05 memory used=5485.6MB, alloc=684.3MB, time=126.82 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428255052 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 4 3 4 2 2 2 F := [15 y z - 16 z - 13 x, 3 x + 2 y - 3 z, 13 y + 16 y z - 4 y ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 4 3 2 G := [-18 x y - 18 x y z, 4 x z + 14 z + 14, 12 z + 6 x + 18 x z] > Problem := [F,G]; Problem := [ 2 2 4 3 4 2 2 2 [15 y z - 16 z - 13 x, 3 x + 2 y - 3 z, 13 y + 16 y z - 4 y ], 3 2 2 4 3 2 [-18 x y - 18 x y z, 4 x z + 14 z + 14, 12 z + 6 x + 18 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.31 memory used=27.0MB, alloc=32.3MB, time=0.90 memory used=48.2MB, alloc=32.3MB, time=1.46 memory used=67.9MB, alloc=60.3MB, time=1.99 memory used=106.5MB, alloc=60.3MB, time=3.01 memory used=144.2MB, alloc=60.3MB, time=4.02 memory used=184.4MB, alloc=92.3MB, time=5.08 memory used=248.2MB, alloc=92.3MB, time=6.68 memory used=311.6MB, alloc=92.3MB, time=8.29 memory used=369.7MB, alloc=116.3MB, time=9.92 memory used=450.1MB, alloc=116.3MB, time=12.05 memory used=528.2MB, alloc=372.3MB, time=14.09 memory used=607.7MB, alloc=396.3MB, time=16.21 memory used=710.8MB, alloc=396.3MB, time=18.96 memory used=809.9MB, alloc=420.3MB, time=21.79 memory used=946.4MB, alloc=444.3MB, time=25.14 memory used=1071.6MB, alloc=444.3MB, time=28.35 memory used=1200.9MB, alloc=468.3MB, time=31.38 memory used=1336.0MB, alloc=468.3MB, time=35.06 memory used=1452.4MB, alloc=492.3MB, time=38.33 memory used=1581.2MB, alloc=492.3MB, time=42.03 memory used=1719.1MB, alloc=492.3MB, time=44.94 memory used=1818.7MB, alloc=492.3MB, time=47.46 memory used=1949.3MB, alloc=516.3MB, time=50.17 memory used=2060.8MB, alloc=516.3MB, time=52.93 memory used=2138.8MB, alloc=516.3MB, time=55.22 memory used=2247.0MB, alloc=516.3MB, time=57.68 memory used=2330.6MB, alloc=516.3MB, time=59.61 memory used=2439.6MB, alloc=516.3MB, time=62.39 memory used=2518.3MB, alloc=516.3MB, time=64.83 memory used=2591.4MB, alloc=516.3MB, time=67.09 memory used=2663.5MB, alloc=516.3MB, time=69.43 memory used=2732.5MB, alloc=516.3MB, time=71.87 memory used=2792.8MB, alloc=516.3MB, time=74.06 memory used=2850.1MB, alloc=516.3MB, time=75.93 memory used=2932.1MB, alloc=516.3MB, time=78.23 memory used=2998.7MB, alloc=516.3MB, time=79.82 memory used=3057.0MB, alloc=516.3MB, time=81.45 memory used=3111.3MB, alloc=516.3MB, time=83.11 memory used=3321.0MB, alloc=540.3MB, time=88.64 memory used=3543.4MB, alloc=564.3MB, time=95.82 memory used=3714.0MB, alloc=588.3MB, time=100.38 memory used=3866.5MB, alloc=612.3MB, time=104.71 memory used=4044.3MB, alloc=612.3MB, time=109.81 memory used=4254.6MB, alloc=612.3MB, time=114.35 memory used=4475.1MB, alloc=612.3MB, time=119.64 memory used=4715.0MB, alloc=612.3MB, time=123.42 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428255352 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 4 2 F := [-4 x y z + x y z - 7 x z , 2 x y + 5 y z + 5 y, 17 x - 2 x y z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 2 G := [5 x z + 15 x y - 8 y , 10 x y z + 13 x y z - 18 z , 3 3 2 13 y z + 2 x + 2 y z] > Problem := [F,G]; Problem := [ 2 2 2 4 2 [-4 x y z + x y z - 7 x z , 2 x y + 5 y z + 5 y, 17 x - 2 x y z ], [ 2 2 2 3 2 2 5 x z + 15 x y - 8 y , 10 x y z + 13 x y z - 18 z , 3 3 2 13 y z + 2 x + 2 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.30 memory used=26.1MB, alloc=32.3MB, time=0.84 memory used=46.5MB, alloc=32.3MB, time=1.34 memory used=66.3MB, alloc=56.3MB, time=1.88 memory used=105.9MB, alloc=60.3MB, time=2.89 memory used=144.7MB, alloc=84.3MB, time=3.89 memory used=205.8MB, alloc=92.3MB, time=5.49 memory used=265.7MB, alloc=116.3MB, time=7.09 memory used=346.3MB, alloc=116.3MB, time=9.20 memory used=427.0MB, alloc=140.3MB, time=11.43 memory used=499.7MB, alloc=140.3MB, time=13.34 memory used=566.6MB, alloc=396.3MB, time=15.15 memory used=675.2MB, alloc=420.3MB, time=17.86 memory used=805.2MB, alloc=444.3MB, time=21.41 memory used=933.9MB, alloc=444.3MB, time=24.80 memory used=1062.9MB, alloc=468.3MB, time=28.40 memory used=1181.3MB, alloc=468.3MB, time=31.70 memory used=1297.0MB, alloc=492.3MB, time=34.97 memory used=1424.4MB, alloc=492.3MB, time=39.00 memory used=1533.8MB, alloc=492.3MB, time=42.50 memory used=1651.5MB, alloc=516.3MB, time=46.13 memory used=1746.9MB, alloc=516.3MB, time=49.05 memory used=1848.4MB, alloc=516.3MB, time=52.15 memory used=1925.8MB, alloc=516.3MB, time=54.47 memory used=2009.3MB, alloc=516.3MB, time=57.25 memory used=2088.0MB, alloc=516.3MB, time=59.94 memory used=2169.4MB, alloc=516.3MB, time=62.78 memory used=2229.0MB, alloc=516.3MB, time=64.70 memory used=2298.9MB, alloc=516.3MB, time=67.26 memory used=2359.6MB, alloc=516.3MB, time=69.56 memory used=2411.5MB, alloc=516.3MB, time=71.46 memory used=2479.0MB, alloc=540.3MB, time=74.09 memory used=2527.0MB, alloc=540.3MB, time=76.15 memory used=2749.6MB, alloc=564.3MB, time=83.13 memory used=2981.2MB, alloc=588.3MB, time=91.11 memory used=3190.1MB, alloc=612.3MB, time=98.29 memory used=3381.4MB, alloc=636.3MB, time=104.46 memory used=3631.6MB, alloc=660.3MB, time=110.19 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428255652 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 3 2 2 3 3 F := [x y z - x - 6 y z , 5 x y - 9 y z - 5, -8 x y - 9 x z + 12 y z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 2 3 2 G := [3 y z + 19 x + y , -12 y z + x + 9 y , -2 x y + 7 x z - 13 x y] > Problem := [F,G]; Problem := [ 2 3 2 3 2 2 3 3 [x y z - x - 6 y z , 5 x y - 9 y z - 5, -8 x y - 9 x z + 12 y z], 2 2 2 3 2 2 3 2 [3 y z + 19 x + y , -12 y z + x + 9 y , -2 x y + 7 x z - 13 x y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.31 memory used=26.4MB, alloc=32.3MB, time=0.90 memory used=46.9MB, alloc=36.3MB, time=1.35 memory used=69.4MB, alloc=60.7MB, time=1.82 memory used=112.8MB, alloc=68.7MB, time=2.84 memory used=156.0MB, alloc=68.7MB, time=3.78 memory used=199.7MB, alloc=68.7MB, time=4.50 memory used=234.2MB, alloc=68.7MB, time=5.06 memory used=274.7MB, alloc=68.7MB, time=5.69 memory used=314.3MB, alloc=68.7MB, time=6.52 memory used=349.6MB, alloc=68.7MB, time=7.15 memory used=388.4MB, alloc=92.7MB, time=8.17 memory used=452.8MB, alloc=92.7MB, time=9.43 memory used=524.4MB, alloc=92.7MB, time=10.75 memory used=599.9MB, alloc=116.7MB, time=12.12 memory used=662.2MB, alloc=372.7MB, time=13.62 memory used=754.2MB, alloc=372.7MB, time=15.44 memory used=845.7MB, alloc=396.7MB, time=17.53 memory used=948.3MB, alloc=396.7MB, time=20.23 memory used=1063.7MB, alloc=396.7MB, time=22.66 memory used=1144.7MB, alloc=420.7MB, time=23.73 memory used=1213.6MB, alloc=420.7MB, time=24.16 memory used=1312.7MB, alloc=420.7MB, time=26.09 memory used=1387.4MB, alloc=420.7MB, time=26.82 memory used=1477.9MB, alloc=420.7MB, time=27.39 memory used=1563.0MB, alloc=420.7MB, time=28.12 memory used=1660.6MB, alloc=420.7MB, time=29.62 memory used=1735.0MB, alloc=420.7MB, time=30.07 memory used=1789.0MB, alloc=420.7MB, time=30.46 memory used=1851.6MB, alloc=420.7MB, time=30.85 memory used=1925.1MB, alloc=420.7MB, time=31.26 memory used=1992.6MB, alloc=420.7MB, time=31.63 memory used=2043.8MB, alloc=420.7MB, time=31.96 memory used=2134.0MB, alloc=420.7MB, time=33.06 memory used=2206.3MB, alloc=420.7MB, time=33.52 memory used=2265.7MB, alloc=420.7MB, time=33.90 memory used=2331.4MB, alloc=420.7MB, time=34.27 memory used=2444.7MB, alloc=420.7MB, time=42.80 memory used=2507.4MB, alloc=420.7MB, time=43.22 memory used=2572.2MB, alloc=420.7MB, time=43.59 memory used=2644.1MB, alloc=420.7MB, time=44.20 memory used=2733.9MB, alloc=420.7MB, time=44.90 memory used=2824.3MB, alloc=420.7MB, time=46.15 memory used=2915.4MB, alloc=420.7MB, time=47.22 memory used=2999.3MB, alloc=420.7MB, time=47.74 memory used=3057.1MB, alloc=420.7MB, time=48.13 memory used=3121.2MB, alloc=420.7MB, time=48.49 memory used=3213.0MB, alloc=420.7MB, time=49.38 memory used=3275.2MB, alloc=420.7MB, time=49.76 memory used=3374.9MB, alloc=420.7MB, time=54.55 memory used=3439.9MB, alloc=420.7MB, time=54.94 memory used=3565.5MB, alloc=420.7MB, time=57.24 memory used=3676.3MB, alloc=420.7MB, time=60.17 memory used=3800.4MB, alloc=420.7MB, time=62.25 memory used=3924.0MB, alloc=420.7MB, time=65.18 memory used=4046.5MB, alloc=420.7MB, time=67.34 memory used=4162.3MB, alloc=444.7MB, time=69.86 memory used=4269.9MB, alloc=444.7MB, time=72.14 memory used=4365.3MB, alloc=444.7MB, time=74.62 memory used=4453.8MB, alloc=444.7MB, time=76.94 memory used=4541.1MB, alloc=468.7MB, time=79.25 memory used=4614.8MB, alloc=468.7MB, time=81.28 memory used=4692.3MB, alloc=468.7MB, time=83.53 memory used=4762.5MB, alloc=468.7MB, time=85.62 memory used=4823.8MB, alloc=468.7MB, time=87.21 memory used=4928.1MB, alloc=468.7MB, time=88.35 memory used=5027.2MB, alloc=468.7MB, time=89.74 memory used=5124.1MB, alloc=468.7MB, time=91.14 memory used=5234.6MB, alloc=468.7MB, time=92.97 memory used=5308.3MB, alloc=468.7MB, time=93.63 memory used=5384.8MB, alloc=468.7MB, time=94.27 memory used=5456.2MB, alloc=468.7MB, time=94.88 memory used=5554.7MB, alloc=468.7MB, time=96.05 memory used=5635.4MB, alloc=468.7MB, time=96.99 memory used=5739.6MB, alloc=468.7MB, time=100.84 memory used=5812.4MB, alloc=468.7MB, time=101.49 memory used=5896.7MB, alloc=468.7MB, time=102.64 memory used=6007.1MB, alloc=468.7MB, time=104.72 memory used=6095.0MB, alloc=468.7MB, time=106.33 memory used=6164.8MB, alloc=468.7MB, time=109.17 memory used=6227.2MB, alloc=492.7MB, time=110.46 memory used=6294.5MB, alloc=492.7MB, time=112.47 memory used=6401.8MB, alloc=492.7MB, time=113.33 memory used=6493.8MB, alloc=492.7MB, time=114.03 memory used=6603.2MB, alloc=492.7MB, time=115.02 memory used=6724.5MB, alloc=492.7MB, time=117.79 memory used=6801.2MB, alloc=492.7MB, time=119.41 memory used=6861.8MB, alloc=492.7MB, time=120.78 memory used=6920.8MB, alloc=492.7MB, time=122.52 memory used=6976.4MB, alloc=492.7MB, time=124.74 memory used=7030.3MB, alloc=492.7MB, time=126.16 memory used=7084.3MB, alloc=492.7MB, time=127.81 memory used=7143.3MB, alloc=492.7MB, time=129.27 memory used=7248.6MB, alloc=492.7MB, time=130.43 memory used=7353.6MB, alloc=492.7MB, time=132.08 memory used=7467.5MB, alloc=492.7MB, time=133.42 memory used=7555.3MB, alloc=492.7MB, time=134.20 memory used=7648.0MB, alloc=492.7MB, time=135.24 memory used=7749.8MB, alloc=492.7MB, time=136.09 memory used=7858.8MB, alloc=492.7MB, time=139.33 memory used=7956.0MB, alloc=492.7MB, time=140.67 memory used=8052.7MB, alloc=492.7MB, time=142.04 memory used=8148.1MB, alloc=492.7MB, time=142.85 memory used=8301.0MB, alloc=492.7MB, time=146.02 memory used=8478.8MB, alloc=492.7MB, time=148.51 memory used=8592.6MB, alloc=492.7MB, time=149.69 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428255953 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 3 3 3 F := [-20 x y + 2 y z - 14 z , 8 x y - 16 y z + 17 y z , 2 4 3 -6 x y z + 10 y - 12 x ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; G := [ 3 2 3 2 2 17 y z + 13 x y - 19 x y z, -4 x z - 15 y z - 15 y, -6 x y + x - 16 y] > Problem := [F,G]; 2 2 3 2 3 3 3 Problem := [[-20 x y + 2 y z - 14 z , 8 x y - 16 y z + 17 y z , 2 4 3 -6 x y z + 10 y - 12 x ], [ 3 2 3 2 2 17 y z + 13 x y - 19 x y z, -4 x z - 15 y z - 15 y, -6 x y + x - 16 y] ] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=31.6MB, alloc=44.3MB, time=0.95 memory used=59.9MB, alloc=44.3MB, time=1.59 memory used=85.8MB, alloc=44.3MB, time=1.96 memory used=114.5MB, alloc=46.7MB, time=2.37 memory used=137.7MB, alloc=46.7MB, time=2.49 memory used=158.9MB, alloc=46.7MB, time=2.59 memory used=174.8MB, alloc=46.7MB, time=2.67 memory used=186.0MB, alloc=46.7MB, time=2.74 memory used=198.1MB, alloc=46.7MB, time=2.81 memory used=211.2MB, alloc=46.7MB, time=2.88 memory used=225.9MB, alloc=46.7MB, time=2.96 memory used=241.4MB, alloc=46.7MB, time=3.03 memory used=258.7MB, alloc=46.7MB, time=3.11 memory used=274.6MB, alloc=46.7MB, time=3.19 memory used=289.5MB, alloc=46.7MB, time=3.26 memory used=300.5MB, alloc=46.7MB, time=3.32 memory used=317.2MB, alloc=46.7MB, time=3.66 memory used=343.2MB, alloc=47.2MB, time=3.81 memory used=365.7MB, alloc=47.2MB, time=3.93 memory used=386.6MB, alloc=47.2MB, time=4.03 memory used=400.7MB, alloc=47.2MB, time=4.11 memory used=412.5MB, alloc=47.2MB, time=4.18 memory used=425.5MB, alloc=47.2MB, time=4.26 memory used=439.4MB, alloc=47.2MB, time=4.34 memory used=454.9MB, alloc=47.2MB, time=4.41 memory used=471.9MB, alloc=47.2MB, time=4.50 memory used=489.6MB, alloc=47.2MB, time=4.57 memory used=504.9MB, alloc=47.2MB, time=4.65 memory used=517.9MB, alloc=47.2MB, time=4.72 memory used=530.0MB, alloc=47.2MB, time=4.78 memory used=559.5MB, alloc=47.2MB, time=10.85 memory used=589.8MB, alloc=47.2MB, time=16.80 memory used=626.8MB, alloc=47.2MB, time=17.29 memory used=656.2MB, alloc=47.2MB, time=17.55 memory used=671.6MB, alloc=47.2MB, time=17.64 memory used=685.3MB, alloc=47.2MB, time=17.72 memory used=702.1MB, alloc=47.2MB, time=17.80 memory used=719.3MB, alloc=47.2MB, time=17.88 memory used=730.2MB, alloc=47.2MB, time=17.94 memory used=741.8MB, alloc=47.2MB, time=18.00 memory used=754.7MB, alloc=47.2MB, time=18.07 memory used=769.1MB, alloc=47.2MB, time=18.14 memory used=786.7MB, alloc=47.2MB, time=18.25 memory used=818.1MB, alloc=47.2MB, time=19.22 memory used=833.8MB, alloc=47.2MB, time=19.33 memory used=867.7MB, alloc=47.2MB, time=20.05 memory used=893.8MB, alloc=71.2MB, time=20.95 memory used=929.4MB, alloc=71.2MB, time=21.34 memory used=974.3MB, alloc=71.2MB, time=21.89 memory used=1028.7MB, alloc=79.2MB, time=22.92 memory used=1056.8MB, alloc=79.2MB, time=23.07 memory used=1088.8MB, alloc=79.2MB, time=23.37 memory used=1118.3MB, alloc=79.2MB, time=23.53 memory used=1146.8MB, alloc=79.2MB, time=24.38 memory used=1167.1MB, alloc=81.9MB, time=29.83 memory used=1201.2MB, alloc=91.8MB, time=33.97 memory used=1212.3MB, alloc=91.8MB, time=34.05 memory used=1224.1MB, alloc=91.8MB, time=34.14 memory used=1276.8MB, alloc=91.8MB, time=34.90 memory used=1333.0MB, alloc=91.8MB, time=38.25 memory used=1368.0MB, alloc=91.8MB, time=48.81 memory used=1396.8MB, alloc=91.8MB, time=49.29 memory used=1424.3MB, alloc=91.8MB, time=49.41 memory used=1474.3MB, alloc=91.8MB, time=50.55 memory used=1521.2MB, alloc=91.8MB, time=51.18 memory used=1557.4MB, alloc=91.8MB, time=52.02 memory used=1583.4MB, alloc=91.8MB, time=52.25 memory used=1623.1MB, alloc=91.8MB, time=52.72 memory used=1662.8MB, alloc=91.8MB, time=53.20 memory used=1732.3MB, alloc=115.8MB, time=70.26 memory used=1791.0MB, alloc=115.8MB, time=120.99 memory used=1879.2MB, alloc=115.8MB, time=125.68 memory used=1998.5MB, alloc=115.8MB, time=127.83 memory used=2079.6MB, alloc=115.8MB, time=128.85 memory used=2116.1MB, alloc=115.8MB, time=129.06 memory used=2161.3MB, alloc=115.8MB, time=129.29 memory used=2201.7MB, alloc=115.8MB, time=129.48 memory used=2230.7MB, alloc=115.8MB, time=129.65 memory used=2262.5MB, alloc=115.8MB, time=129.82 memory used=2295.4MB, alloc=115.8MB, time=129.98 memory used=2331.7MB, alloc=115.8MB, time=130.17 memory used=2370.1MB, alloc=115.8MB, time=130.36 memory used=2410.3MB, alloc=115.8MB, time=130.54 memory used=2454.2MB, alloc=115.8MB, time=130.73 memory used=2500.0MB, alloc=115.8MB, time=130.93 memory used=2549.9MB, alloc=115.8MB, time=131.12 memory used=2589.5MB, alloc=115.8MB, time=131.30 memory used=2615.6MB, alloc=115.8MB, time=131.44 memory used=2642.2MB, alloc=115.8MB, time=131.58 memory used=2669.0MB, alloc=115.8MB, time=131.71 memory used=2696.2MB, alloc=115.8MB, time=131.85 memory used=2723.8MB, alloc=115.8MB, time=131.99 memory used=2751.7MB, alloc=115.8MB, time=132.12 memory used=2779.9MB, alloc=115.8MB, time=132.27 memory used=2808.6MB, alloc=115.8MB, time=132.40 memory used=2840.1MB, alloc=115.8MB, time=132.56 memory used=2872.0MB, alloc=115.8MB, time=132.71 memory used=2904.3MB, alloc=115.8MB, time=132.84 memory used=2936.9MB, alloc=115.8MB, time=132.98 memory used=2969.8MB, alloc=115.8MB, time=133.12 memory used=3003.0MB, alloc=115.8MB, time=133.26 memory used=3036.6MB, alloc=115.8MB, time=133.41 memory used=3073.1MB, alloc=115.8MB, time=133.55 memory used=3109.9MB, alloc=115.8MB, time=133.69 memory used=3147.0MB, alloc=115.8MB, time=133.84 memory used=3184.4MB, alloc=115.8MB, time=134.00 memory used=3222.2MB, alloc=115.8MB, time=134.15 memory used=3262.8MB, alloc=115.8MB, time=134.31 memory used=3303.7MB, alloc=115.8MB, time=134.46 memory used=3344.9MB, alloc=115.8MB, time=134.60 memory used=3386.2MB, alloc=115.8MB, time=134.76 memory used=3430.6MB, alloc=115.8MB, time=134.92 memory used=3475.2MB, alloc=115.8MB, time=135.07 memory used=3519.8MB, alloc=115.8MB, time=135.23 memory used=3568.7MB, alloc=115.8MB, time=135.39 memory used=3621.1MB, alloc=115.8MB, time=135.56 memory used=3675.3MB, alloc=115.8MB, time=135.74 memory used=3733.8MB, alloc=115.8MB, time=135.92 memory used=3743.7MB, alloc=115.8MB, time=136.02 memory used=3750.1MB, alloc=115.8MB, time=136.13 memory used=3758.0MB, alloc=115.8MB, time=136.23 memory used=3764.0MB, alloc=115.8MB, time=136.32 memory used=3769.9MB, alloc=115.8MB, time=136.42 memory used=3778.4MB, alloc=115.8MB, time=136.53 memory used=3784.4MB, alloc=115.8MB, time=136.63 memory used=3792.9MB, alloc=115.8MB, time=136.72 memory used=3799.0MB, alloc=115.8MB, time=136.81 memory used=3807.4MB, alloc=115.8MB, time=136.93 memory used=3816.1MB, alloc=115.8MB, time=137.02 memory used=3824.8MB, alloc=115.8MB, time=137.11 memory used=3833.5MB, alloc=115.8MB, time=137.21 memory used=3842.2MB, alloc=115.8MB, time=137.31 memory used=3850.9MB, alloc=115.8MB, time=137.40 memory used=3859.5MB, alloc=115.8MB, time=137.51 memory used=3868.2MB, alloc=115.8MB, time=137.61 memory used=3876.8MB, alloc=115.8MB, time=137.72 memory used=3885.4MB, alloc=115.8MB, time=137.81 memory used=3894.1MB, alloc=115.8MB, time=137.91 memory used=3902.7MB, alloc=115.8MB, time=138.01 memory used=3911.3MB, alloc=115.8MB, time=138.11 memory used=3919.9MB, alloc=115.8MB, time=138.20 memory used=3928.4MB, alloc=115.8MB, time=138.30 memory used=3937.0MB, alloc=115.8MB, time=138.39 memory used=3945.6MB, alloc=115.8MB, time=138.49 memory used=3954.1MB, alloc=115.8MB, time=138.59 memory used=3962.7MB, alloc=115.8MB, time=138.68 memory used=3971.2MB, alloc=115.8MB, time=138.78 memory used=3979.7MB, alloc=115.8MB, time=138.87 memory used=3988.2MB, alloc=115.8MB, time=138.97 memory used=3996.7MB, alloc=115.8MB, time=139.06 memory used=4005.2MB, alloc=115.8MB, time=139.16 memory used=4013.7MB, alloc=115.8MB, time=139.25 memory used=4022.1MB, alloc=115.8MB, time=139.34 memory used=4030.6MB, alloc=115.8MB, time=139.50 memory used=4039.0MB, alloc=115.8MB, time=139.60 memory used=4047.4MB, alloc=115.8MB, time=139.70 memory used=4055.8MB, alloc=115.8MB, time=139.81 memory used=4064.2MB, alloc=115.8MB, time=139.91 memory used=4072.6MB, alloc=115.8MB, time=140.03 memory used=4080.9MB, alloc=115.8MB, time=140.13 memory used=4089.3MB, alloc=115.8MB, time=140.22 memory used=4097.6MB, alloc=115.8MB, time=140.31 memory used=4105.9MB, alloc=115.8MB, time=140.41 memory used=4114.2MB, alloc=115.8MB, time=140.51 memory used=4122.5MB, alloc=115.8MB, time=140.62 memory used=4130.8MB, alloc=115.8MB, time=140.73 memory used=4139.0MB, alloc=115.8MB, time=140.84 memory used=4147.3MB, alloc=115.8MB, time=140.93 memory used=4155.5MB, alloc=115.8MB, time=141.04 memory used=4163.7MB, alloc=115.8MB, time=141.13 memory used=4171.9MB, alloc=115.8MB, time=141.23 memory used=4180.3MB, alloc=115.8MB, time=141.34 memory used=4190.9MB, alloc=115.8MB, time=141.45 memory used=4199.4MB, alloc=115.8MB, time=141.54 memory used=4209.9MB, alloc=115.8MB, time=141.64 memory used=4220.6MB, alloc=115.8MB, time=141.75 memory used=4231.4MB, alloc=115.8MB, time=141.85 memory used=4242.1MB, alloc=115.8MB, time=141.95 memory used=4252.7MB, alloc=115.8MB, time=142.06 memory used=4263.4MB, alloc=115.8MB, time=142.16 memory used=4273.9MB, alloc=115.8MB, time=142.26 memory used=4284.5MB, alloc=115.8MB, time=142.36 memory used=4295.0MB, alloc=115.8MB, time=142.48 memory used=4305.5MB, alloc=115.8MB, time=142.59 memory used=4315.9MB, alloc=115.8MB, time=142.69 memory used=4326.3MB, alloc=115.8MB, time=142.78 memory used=4336.7MB, alloc=115.8MB, time=142.87 memory used=4347.0MB, alloc=115.8MB, time=142.98 memory used=4357.3MB, alloc=115.8MB, time=143.09 memory used=4367.5MB, alloc=115.8MB, time=143.21 memory used=4377.7MB, alloc=115.8MB, time=143.31 memory used=4387.8MB, alloc=115.8MB, time=143.41 memory used=4397.9MB, alloc=115.8MB, time=143.51 memory used=4408.0MB, alloc=115.8MB, time=143.61 memory used=4418.0MB, alloc=115.8MB, time=143.75 memory used=4428.2MB, alloc=115.8MB, time=143.88 memory used=4440.4MB, alloc=115.8MB, time=143.97 memory used=4452.7MB, alloc=115.8MB, time=144.08 memory used=4465.0MB, alloc=115.8MB, time=144.18 memory used=4477.2MB, alloc=115.8MB, time=144.28 memory used=4489.3MB, alloc=115.8MB, time=144.38 memory used=4501.3MB, alloc=115.8MB, time=144.48 memory used=4513.2MB, alloc=115.8MB, time=144.58 memory used=4525.1MB, alloc=115.8MB, time=144.69 memory used=4536.8MB, alloc=115.8MB, time=144.80 memory used=4548.5MB, alloc=115.8MB, time=144.92 memory used=4560.2MB, alloc=115.8MB, time=145.03 memory used=4571.7MB, alloc=115.8MB, time=145.14 memory used=4583.1MB, alloc=115.8MB, time=145.25 memory used=4594.7MB, alloc=115.8MB, time=145.34 memory used=4608.0MB, alloc=115.8MB, time=145.44 memory used=4621.4MB, alloc=115.8MB, time=145.57 memory used=4634.6MB, alloc=115.8MB, time=145.67 memory used=4647.8MB, alloc=115.8MB, time=145.77 memory used=4660.7MB, alloc=115.8MB, time=145.87 memory used=4673.6MB, alloc=115.8MB, time=145.98 memory used=4686.3MB, alloc=115.8MB, time=146.09 memory used=4698.9MB, alloc=115.8MB, time=146.20 memory used=4711.6MB, alloc=115.8MB, time=146.30 memory used=4725.6MB, alloc=115.8MB, time=146.40 memory used=4739.7MB, alloc=115.8MB, time=146.51 memory used=4753.6MB, alloc=115.8MB, time=146.62 memory used=4767.3MB, alloc=115.8MB, time=146.72 memory used=4780.9MB, alloc=115.8MB, time=146.83 memory used=4796.1MB, alloc=115.8MB, time=146.93 memory used=4811.0MB, alloc=115.8MB, time=147.03 memory used=4825.6MB, alloc=115.8MB, time=147.15 memory used=4840.2MB, alloc=115.8MB, time=147.26 memory used=4855.7MB, alloc=115.8MB, time=147.37 memory used=4871.0MB, alloc=115.8MB, time=147.49 memory used=4886.3MB, alloc=115.8MB, time=147.59 memory used=4902.1MB, alloc=115.8MB, time=147.70 memory used=4918.1MB, alloc=115.8MB, time=147.80 memory used=4934.5MB, alloc=115.8MB, time=147.90 memory used=4950.9MB, alloc=115.8MB, time=147.99 memory used=4967.6MB, alloc=115.8MB, time=148.11 memory used=4984.8MB, alloc=115.8MB, time=148.23 memory used=5002.4MB, alloc=115.8MB, time=148.35 memory used=5020.8MB, alloc=115.8MB, time=148.46 memory used=5039.6MB, alloc=115.8MB, time=148.57 memory used=5059.0MB, alloc=115.8MB, time=148.67 memory used=5117.5MB, alloc=115.8MB, time=149.43 memory used=5136.8MB, alloc=115.8MB, time=149.89 memory used=5180.4MB, alloc=115.8MB, time=150.08 memory used=5247.0MB, alloc=115.8MB, time=172.06 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428256253 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 2 3 4 3 F := [10 y z - 5 x z + 8 z , 3 y z - 9 y z - 9 x z, -19 x y + y + 20 x ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; G := [ 2 4 2 2 4 2 3 2 9 x y z + 18 y + 3 z, 20 x z + 19 z - 17 x z , -3 x - 19 x y - 15 y ] > Problem := [F,G]; Problem := [ 3 2 3 2 2 3 4 3 [10 y z - 5 x z + 8 z , 3 y z - 9 y z - 9 x z, -19 x y + y + 20 x ], 2 4 2 2 4 2 3 2 [9 x y z + 18 y + 3 z, 20 x z + 19 z - 17 x z , -3 x - 19 x y - 15 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.31 memory used=26.0MB, alloc=32.3MB, time=0.87 memory used=46.7MB, alloc=32.3MB, time=1.39 memory used=66.0MB, alloc=60.3MB, time=1.90 memory used=108.7MB, alloc=68.3MB, time=3.09 memory used=150.9MB, alloc=68.3MB, time=4.05 memory used=192.3MB, alloc=68.3MB, time=4.97 memory used=232.4MB, alloc=92.3MB, time=5.95 memory used=294.5MB, alloc=92.3MB, time=7.45 memory used=360.3MB, alloc=92.3MB, time=9.16 memory used=404.1MB, alloc=92.3MB, time=9.58 memory used=440.0MB, alloc=92.3MB, time=10.13 memory used=503.1MB, alloc=92.3MB, time=12.65 memory used=537.2MB, alloc=92.3MB, time=12.86 memory used=579.2MB, alloc=92.3MB, time=13.49 memory used=640.5MB, alloc=372.3MB, time=15.06 memory used=725.5MB, alloc=372.3MB, time=17.66 memory used=794.7MB, alloc=372.3MB, time=18.69 memory used=885.4MB, alloc=372.3MB, time=20.54 memory used=976.0MB, alloc=396.3MB, time=22.86 memory used=1079.0MB, alloc=396.3MB, time=25.54 memory used=1190.3MB, alloc=420.3MB, time=28.13 memory used=1309.9MB, alloc=444.3MB, time=31.18 memory used=1412.2MB, alloc=444.3MB, time=33.89 memory used=1518.1MB, alloc=468.3MB, time=36.56 memory used=1603.0MB, alloc=468.3MB, time=38.52 memory used=1695.8MB, alloc=468.3MB, time=41.17 memory used=1803.8MB, alloc=468.3MB, time=42.89 memory used=1917.1MB, alloc=492.3MB, time=44.86 memory used=2035.1MB, alloc=492.3MB, time=47.16 memory used=2120.5MB, alloc=492.3MB, time=49.15 memory used=2190.3MB, alloc=492.3MB, time=50.99 memory used=2265.6MB, alloc=492.3MB, time=53.28 memory used=2344.0MB, alloc=492.3MB, time=55.71 memory used=2424.5MB, alloc=492.3MB, time=58.02 memory used=2488.3MB, alloc=492.3MB, time=59.89 memory used=2541.3MB, alloc=492.3MB, time=61.38 memory used=2590.1MB, alloc=492.3MB, time=62.82 memory used=2652.0MB, alloc=492.3MB, time=64.98 memory used=2703.6MB, alloc=492.3MB, time=66.76 memory used=2746.7MB, alloc=492.3MB, time=68.27 memory used=2903.0MB, alloc=492.3MB, time=71.74 memory used=3010.3MB, alloc=492.3MB, time=73.48 memory used=3119.4MB, alloc=516.3MB, time=75.35 memory used=3346.8MB, alloc=540.3MB, time=81.31 memory used=3539.2MB, alloc=540.3MB, time=84.25 memory used=3721.1MB, alloc=564.3MB, time=88.75 memory used=3884.1MB, alloc=588.3MB, time=91.08 memory used=4033.4MB, alloc=588.3MB, time=93.25 memory used=4161.6MB, alloc=588.3MB, time=94.40 memory used=4293.7MB, alloc=588.3MB, time=95.93 memory used=4436.5MB, alloc=588.3MB, time=97.74 memory used=4617.3MB, alloc=588.3MB, time=102.59 memory used=4747.1MB, alloc=588.3MB, time=103.74 memory used=4865.7MB, alloc=588.3MB, time=104.70 memory used=5057.3MB, alloc=588.3MB, time=106.27 memory used=5180.7MB, alloc=588.3MB, time=107.30 memory used=5284.5MB, alloc=588.3MB, time=108.23 memory used=5447.8MB, alloc=588.3MB, time=112.11 memory used=5567.8MB, alloc=588.3MB, time=113.23 memory used=5692.3MB, alloc=588.3MB, time=114.28 memory used=5880.3MB, alloc=588.3MB, time=115.89 memory used=6009.9MB, alloc=588.3MB, time=116.95 memory used=6119.4MB, alloc=588.3MB, time=118.14 memory used=6275.8MB, alloc=588.3MB, time=121.91 memory used=6392.0MB, alloc=588.3MB, time=122.96 memory used=6582.6MB, alloc=588.3MB, time=124.77 memory used=6756.6MB, alloc=588.3MB, time=126.65 memory used=6905.2MB, alloc=588.3MB, time=128.63 memory used=7131.6MB, alloc=588.3MB, time=133.31 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428256553 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 2 2 F := [13 x y - 3 x y z - y z, 20 x z - 11 x + y , 2 2 2 2 -17 x y - 4 y z + 16 y ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; G := [ 3 3 2 3 2 2 3 2 -2 y z + 4 y + 20 y z, -8 x + 4 x y + 2 x y , 20 x y + 14 x y + 17 z ] > Problem := [F,G]; 2 2 2 2 2 2 2 Problem := [[13 x y - 3 x y z - y z, 20 x z - 11 x + y , 2 2 2 2 -17 x y - 4 y z + 16 y ], [ 3 3 2 3 2 2 3 2 -2 y z + 4 y + 20 y z, -8 x + 4 x y + 2 x y , 20 x y + 14 x y + 17 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.31 memory used=26.4MB, alloc=32.3MB, time=0.89 memory used=47.1MB, alloc=32.3MB, time=1.43 memory used=66.8MB, alloc=56.3MB, time=1.98 memory used=107.5MB, alloc=60.3MB, time=3.04 memory used=145.6MB, alloc=60.3MB, time=4.00 memory used=185.0MB, alloc=92.3MB, time=5.08 memory used=249.4MB, alloc=92.3MB, time=6.73 memory used=311.1MB, alloc=92.3MB, time=8.37 memory used=374.5MB, alloc=116.3MB, time=10.03 memory used=446.1MB, alloc=116.3MB, time=11.91 memory used=517.5MB, alloc=372.3MB, time=13.77 memory used=602.7MB, alloc=396.3MB, time=15.99 memory used=707.1MB, alloc=396.3MB, time=18.79 memory used=829.7MB, alloc=420.3MB, time=21.29 memory used=969.1MB, alloc=444.3MB, time=24.42 memory used=1101.4MB, alloc=468.3MB, time=28.05 memory used=1204.8MB, alloc=468.3MB, time=30.80 memory used=1307.1MB, alloc=468.3MB, time=33.31 memory used=1401.6MB, alloc=492.3MB, time=35.82 memory used=1498.6MB, alloc=492.3MB, time=38.45 memory used=1577.3MB, alloc=492.3MB, time=40.58 memory used=1665.6MB, alloc=492.3MB, time=43.18 memory used=1743.8MB, alloc=492.3MB, time=45.47 memory used=1819.4MB, alloc=492.3MB, time=48.03 memory used=1888.1MB, alloc=492.3MB, time=49.98 memory used=1966.3MB, alloc=492.3MB, time=52.04 memory used=2013.0MB, alloc=492.3MB, time=53.66 memory used=2061.4MB, alloc=492.3MB, time=55.17 memory used=2120.6MB, alloc=492.3MB, time=56.83 memory used=2179.6MB, alloc=516.3MB, time=58.41 memory used=2398.1MB, alloc=540.3MB, time=64.39 memory used=2591.6MB, alloc=564.3MB, time=69.26 memory used=2773.8MB, alloc=588.3MB, time=75.17 memory used=2979.4MB, alloc=612.3MB, time=80.15 memory used=3140.6MB, alloc=612.3MB, time=84.45 memory used=3380.5MB, alloc=612.3MB, time=88.78 memory used=3541.1MB, alloc=636.3MB, time=92.84 memory used=3708.1MB, alloc=636.3MB, time=97.52 memory used=3828.2MB, alloc=636.3MB, time=101.42 memory used=3965.2MB, alloc=636.3MB, time=105.52 memory used=4099.4MB, alloc=636.3MB, time=109.46 memory used=4211.8MB, alloc=636.3MB, time=113.31 memory used=4331.6MB, alloc=636.3MB, time=117.30 memory used=4428.4MB, alloc=636.3MB, time=120.85 memory used=4507.8MB, alloc=636.3MB, time=123.89 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428256853 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; F := [ 2 2 2 2 3 2 2 3 3 15 x y - x y z - 2 z , 7 x z + 2 y z - 3 x, 3 x z - 2 y z - 17 y z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 2 2 2 2 G := [20 x z - x z , -4 y z - 4 x z - 20 x , 15 x y - 5 x z - 19 x y] > Problem := [F,G]; Problem := [[ 2 2 2 2 3 2 2 3 3 15 x y - x y z - 2 z , 7 x z + 2 y z - 3 x, 3 x z - 2 y z - 17 y z ] 2 2 3 2 2 2 2 2 2 , [20 x z - x z , -4 y z - 4 x z - 20 x , 15 x y - 5 x z - 19 x y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.32 memory used=26.7MB, alloc=32.3MB, time=0.89 memory used=47.9MB, alloc=32.3MB, time=1.45 memory used=66.8MB, alloc=60.3MB, time=1.98 memory used=108.1MB, alloc=60.3MB, time=3.06 memory used=144.1MB, alloc=84.3MB, time=3.97 memory used=209.6MB, alloc=92.3MB, time=5.64 memory used=275.5MB, alloc=116.3MB, time=7.29 memory used=362.7MB, alloc=116.3MB, time=9.43 memory used=435.0MB, alloc=396.3MB, time=11.42 memory used=544.9MB, alloc=420.3MB, time=14.15 memory used=685.2MB, alloc=444.3MB, time=17.40 memory used=804.9MB, alloc=444.3MB, time=19.81 memory used=927.8MB, alloc=468.3MB, time=22.87 memory used=1049.2MB, alloc=468.3MB, time=25.68 memory used=1169.3MB, alloc=492.3MB, time=28.06 memory used=1298.8MB, alloc=492.3MB, time=30.68 memory used=1400.6MB, alloc=516.3MB, time=33.36 memory used=1507.1MB, alloc=516.3MB, time=36.07 memory used=1604.1MB, alloc=516.3MB, time=38.28 memory used=1677.3MB, alloc=516.3MB, time=39.94 memory used=1769.4MB, alloc=540.3MB, time=42.74 memory used=1846.9MB, alloc=540.3MB, time=44.77 memory used=1939.3MB, alloc=540.3MB, time=47.20 memory used=2017.2MB, alloc=540.3MB, time=49.44 memory used=2113.3MB, alloc=540.3MB, time=51.61 memory used=2218.7MB, alloc=540.3MB, time=53.50 memory used=2301.1MB, alloc=540.3MB, time=55.34 memory used=2392.6MB, alloc=540.3MB, time=57.55 memory used=2516.3MB, alloc=564.3MB, time=59.98 memory used=2581.7MB, alloc=564.3MB, time=61.52 memory used=2702.6MB, alloc=564.3MB, time=63.26 memory used=2767.1MB, alloc=564.3MB, time=65.64 memory used=2829.9MB, alloc=564.3MB, time=67.97 memory used=3060.6MB, alloc=588.3MB, time=74.05 memory used=3280.0MB, alloc=612.3MB, time=81.02 memory used=3474.6MB, alloc=636.3MB, time=86.84 memory used=3624.7MB, alloc=660.3MB, time=91.64 memory used=3776.6MB, alloc=684.3MB, time=96.31 memory used=3913.3MB, alloc=684.3MB, time=100.65 memory used=4073.2MB, alloc=708.3MB, time=105.80 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428257153 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 3 2 2 2 F := [-9 x - 3 x y + 20 x z , 5 x z + 20 y z - 4 x , 4 2 2 3 -20 x + 20 x y - 20 x y ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 3 4 G := [-10 x z - 4 x z - 7 y z, -4 x z + 19 x - 11 z, 14 y - 5] > Problem := [F,G]; 3 2 2 3 2 2 2 Problem := [[-9 x - 3 x y + 20 x z , 5 x z + 20 y z - 4 x , 4 2 2 3 -20 x + 20 x y - 20 x y ], 3 2 3 3 4 [-10 x z - 4 x z - 7 y z, -4 x z + 19 x - 11 z, 14 y - 5]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=31.7MB, alloc=44.3MB, time=1.01 memory used=59.2MB, alloc=44.3MB, time=1.70 memory used=83.7MB, alloc=68.3MB, time=2.33 memory used=136.0MB, alloc=76.3MB, time=3.54 memory used=185.6MB, alloc=100.3MB, time=4.73 memory used=254.9MB, alloc=100.3MB, time=6.34 memory used=327.4MB, alloc=100.3MB, time=8.01 memory used=399.1MB, alloc=124.3MB, time=9.84 memory used=478.6MB, alloc=380.3MB, time=11.83 memory used=578.0MB, alloc=380.3MB, time=13.77 memory used=683.0MB, alloc=404.3MB, time=16.12 memory used=802.2MB, alloc=404.3MB, time=18.65 memory used=930.9MB, alloc=428.3MB, time=21.52 memory used=1062.8MB, alloc=428.3MB, time=24.41 memory used=1164.3MB, alloc=428.3MB, time=27.81 memory used=1230.5MB, alloc=428.3MB, time=28.57 memory used=1363.9MB, alloc=428.3MB, time=31.55 memory used=1520.6MB, alloc=452.3MB, time=35.91 memory used=1673.7MB, alloc=452.3MB, time=40.61 memory used=1791.8MB, alloc=452.3MB, time=43.73 memory used=1957.4MB, alloc=452.3MB, time=46.01 memory used=2074.7MB, alloc=452.3MB, time=48.82 memory used=2156.2MB, alloc=452.3MB, time=49.69 memory used=2324.3MB, alloc=476.3MB, time=52.24 memory used=2462.8MB, alloc=476.3MB, time=56.30 memory used=2567.3MB, alloc=476.3MB, time=59.15 memory used=2645.3MB, alloc=476.3MB, time=61.01 memory used=2739.6MB, alloc=476.3MB, time=63.54 memory used=2831.6MB, alloc=500.3MB, time=66.26 memory used=2918.4MB, alloc=500.3MB, time=68.80 memory used=2992.6MB, alloc=500.3MB, time=70.69 memory used=3071.4MB, alloc=500.3MB, time=73.05 memory used=3138.1MB, alloc=500.3MB, time=74.94 memory used=3219.0MB, alloc=500.3MB, time=77.44 memory used=3278.5MB, alloc=500.3MB, time=79.21 memory used=3349.5MB, alloc=500.3MB, time=81.53 memory used=3417.8MB, alloc=500.3MB, time=83.85 memory used=3471.6MB, alloc=500.3MB, time=85.60 memory used=3528.5MB, alloc=500.3MB, time=87.09 memory used=3650.8MB, alloc=500.3MB, time=93.32 memory used=3741.8MB, alloc=500.3MB, time=94.59 memory used=4397.9MB, alloc=524.3MB, time=101.94 memory used=4457.9MB, alloc=524.3MB, time=107.20 memory used=4511.3MB, alloc=524.3MB, time=108.96 memory used=4559.6MB, alloc=524.3MB, time=110.38 memory used=4600.1MB, alloc=524.3MB, time=111.69 memory used=4802.3MB, alloc=524.3MB, time=116.63 memory used=4946.4MB, alloc=524.3MB, time=126.63 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428257453 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 4 4 F := [10 x y + 4 x y z - 15 x y , -z, 10 y - 17 z - 8 x y] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 3 2 2 2 G := [5 z + 13 y z + 2 z , -4 x y z + 4 x y + 19 y z, 2 3 -11 x y z + 12 y z - 7 x y] > Problem := [F,G]; 2 2 2 2 4 4 Problem := [[10 x y + 4 x y z - 15 x y , -z, 10 y - 17 z - 8 x y], [ 4 2 3 2 2 2 5 z + 13 y z + 2 z , -4 x y z + 4 x y + 19 y z, 2 3 -11 x y z + 12 y z - 7 x y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.5MB, alloc=32.3MB, time=0.86 memory used=47.1MB, alloc=32.3MB, time=1.40 memory used=65.8MB, alloc=56.3MB, time=1.92 memory used=104.5MB, alloc=84.3MB, time=2.98 memory used=150.6MB, alloc=84.3MB, time=4.23 memory used=211.4MB, alloc=92.3MB, time=5.81 memory used=272.0MB, alloc=116.3MB, time=7.39 memory used=354.6MB, alloc=116.3MB, time=9.61 memory used=426.0MB, alloc=372.3MB, time=11.55 memory used=506.1MB, alloc=396.3MB, time=13.83 memory used=610.1MB, alloc=420.3MB, time=16.75 memory used=735.2MB, alloc=420.3MB, time=19.80 memory used=855.9MB, alloc=444.3MB, time=22.95 memory used=1001.8MB, alloc=468.3MB, time=27.17 memory used=1147.9MB, alloc=468.3MB, time=30.99 memory used=1299.0MB, alloc=492.3MB, time=35.27 memory used=1429.5MB, alloc=492.3MB, time=38.82 memory used=1559.9MB, alloc=516.3MB, time=42.24 memory used=1683.7MB, alloc=516.3MB, time=44.22 memory used=1804.7MB, alloc=516.3MB, time=47.05 memory used=1934.4MB, alloc=540.3MB, time=50.29 memory used=2045.2MB, alloc=540.3MB, time=53.26 memory used=2143.2MB, alloc=540.3MB, time=56.20 memory used=2259.6MB, alloc=540.3MB, time=59.01 memory used=2358.6MB, alloc=540.3MB, time=61.61 memory used=2465.9MB, alloc=564.3MB, time=64.34 memory used=2558.7MB, alloc=564.3MB, time=67.30 memory used=2642.0MB, alloc=564.3MB, time=69.58 memory used=2763.0MB, alloc=564.3MB, time=72.44 memory used=2854.1MB, alloc=564.3MB, time=74.87 memory used=2927.3MB, alloc=564.3MB, time=76.92 memory used=3004.2MB, alloc=588.3MB, time=78.98 memory used=3080.5MB, alloc=588.3MB, time=81.77 memory used=3144.6MB, alloc=588.3MB, time=84.04 memory used=3193.1MB, alloc=588.3MB, time=85.61 memory used=3250.7MB, alloc=588.3MB, time=87.45 memory used=3315.2MB, alloc=588.3MB, time=90.00 memory used=3369.5MB, alloc=588.3MB, time=92.05 memory used=3405.8MB, alloc=588.3MB, time=93.66 memory used=3648.8MB, alloc=588.3MB, time=99.23 memory used=3805.1MB, alloc=588.3MB, time=100.72 memory used=4047.7MB, alloc=612.3MB, time=106.19 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428257753 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 4 3 2 3 3 3 F := [-12 y - 9 x y - 4 z , -17 y - y z + 3 x , 14 x y + 7 x z - 2 x ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 G := [y z + 11 z + 12 x, -14 x z - 15 x y - 9 y z , 3 3 2 -12 x z + 9 y z + 7 x y] > Problem := [F,G]; Problem := [ 4 2 4 3 2 3 3 3 [-12 y - 9 x y - 4 z , -17 y - y z + 3 x , 14 x y + 7 x z - 2 x ], [ 2 2 3 2 2 y z + 11 z + 12 x, -14 x z - 15 x y - 9 y z , 3 3 2 -12 x z + 9 y z + 7 x y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.31 memory used=26.1MB, alloc=32.3MB, time=0.88 memory used=45.9MB, alloc=56.3MB, time=1.40 memory used=88.0MB, alloc=60.3MB, time=2.47 memory used=128.4MB, alloc=60.3MB, time=3.44 memory used=165.0MB, alloc=84.3MB, time=4.26 memory used=232.5MB, alloc=92.3MB, time=5.82 memory used=305.4MB, alloc=92.3MB, time=7.52 memory used=370.6MB, alloc=92.3MB, time=9.09 memory used=435.9MB, alloc=116.3MB, time=10.69 memory used=516.2MB, alloc=116.3MB, time=12.72 memory used=586.1MB, alloc=372.3MB, time=14.24 memory used=634.4MB, alloc=372.3MB, time=14.77 memory used=688.5MB, alloc=372.3MB, time=15.43 memory used=771.6MB, alloc=372.3MB, time=22.46 memory used=813.2MB, alloc=372.3MB, time=22.70 memory used=845.7MB, alloc=372.3MB, time=22.91 memory used=885.3MB, alloc=372.3MB, time=23.12 memory used=924.8MB, alloc=372.3MB, time=23.32 memory used=955.3MB, alloc=372.3MB, time=23.49 memory used=1002.9MB, alloc=372.3MB, time=24.03 memory used=1094.4MB, alloc=396.3MB, time=25.44 memory used=1229.7MB, alloc=396.3MB, time=27.65 memory used=1353.2MB, alloc=396.3MB, time=35.60 memory used=1405.9MB, alloc=396.3MB, time=35.91 memory used=1451.1MB, alloc=396.3MB, time=36.18 memory used=1506.2MB, alloc=396.3MB, time=36.44 memory used=1550.1MB, alloc=396.3MB, time=36.73 memory used=1664.0MB, alloc=396.3MB, time=38.49 memory used=1777.2MB, alloc=420.3MB, time=40.67 memory used=1913.0MB, alloc=420.3MB, time=43.59 memory used=2040.6MB, alloc=444.3MB, time=46.39 memory used=2172.3MB, alloc=444.3MB, time=49.47 memory used=2288.4MB, alloc=444.3MB, time=51.89 memory used=2415.0MB, alloc=468.3MB, time=62.07 memory used=2491.4MB, alloc=468.3MB, time=62.52 memory used=2568.2MB, alloc=468.3MB, time=62.93 memory used=2799.2MB, alloc=468.3MB, time=64.06 memory used=2965.7MB, alloc=468.3MB, time=66.83 memory used=3081.2MB, alloc=468.3MB, time=69.60 memory used=3214.2MB, alloc=492.3MB, time=71.51 memory used=3306.3MB, alloc=492.3MB, time=72.23 memory used=3439.7MB, alloc=492.3MB, time=76.76 memory used=3575.4MB, alloc=492.3MB, time=79.47 memory used=3702.9MB, alloc=492.3MB, time=84.45 memory used=3798.4MB, alloc=492.3MB, time=85.29 memory used=3917.9MB, alloc=492.3MB, time=88.42 memory used=4077.2MB, alloc=492.3MB, time=90.96 memory used=4221.3MB, alloc=492.3MB, time=95.50 memory used=4335.3MB, alloc=516.3MB, time=98.78 memory used=4442.7MB, alloc=516.3MB, time=101.67 memory used=4557.3MB, alloc=516.3MB, time=102.86 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428258053 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 4 3 3 2 3 2 2 F := [11 x z + 6 y - 14 y z , 20 x y + 17 x + 14, 10 y z + 19 y z + 1] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 4 2 2 2 2 4 2 G := [18 x y + 3 z + 2 x z , 17 x y - x y z + 15 z , 9 x y] > Problem := [F,G]; Problem := [ 3 4 3 3 2 3 2 2 [11 x z + 6 y - 14 y z , 20 x y + 17 x + 14, 10 y z + 19 y z + 1], 3 4 2 2 2 2 4 2 [18 x y + 3 z + 2 x z , 17 x y - x y z + 15 z , 9 x y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=24.6MB, alloc=32.3MB, time=0.82 memory used=43.9MB, alloc=60.3MB, time=1.32 memory used=97.4MB, alloc=60.3MB, time=2.15 memory used=127.2MB, alloc=60.3MB, time=2.43 memory used=164.7MB, alloc=60.3MB, time=7.08 memory used=190.4MB, alloc=60.3MB, time=7.20 memory used=216.9MB, alloc=60.3MB, time=7.31 memory used=244.4MB, alloc=60.3MB, time=7.43 memory used=263.7MB, alloc=60.3MB, time=7.51 memory used=285.9MB, alloc=60.3MB, time=7.60 memory used=310.3MB, alloc=60.3MB, time=7.70 memory used=338.0MB, alloc=60.3MB, time=7.80 memory used=368.6MB, alloc=60.3MB, time=7.91 memory used=412.1MB, alloc=83.8MB, time=8.07 memory used=424.5MB, alloc=83.8MB, time=8.16 memory used=437.9MB, alloc=83.8MB, time=8.25 memory used=452.3MB, alloc=83.8MB, time=8.33 memory used=467.3MB, alloc=83.8MB, time=8.42 memory used=482.8MB, alloc=83.8MB, time=8.50 memory used=499.5MB, alloc=83.8MB, time=8.58 memory used=516.4MB, alloc=83.8MB, time=8.67 memory used=535.4MB, alloc=83.8MB, time=8.75 memory used=585.7MB, alloc=83.8MB, time=9.25 memory used=612.3MB, alloc=83.8MB, time=9.39 memory used=638.4MB, alloc=83.8MB, time=9.69 memory used=664.9MB, alloc=83.8MB, time=9.84 memory used=697.5MB, alloc=83.8MB, time=9.96 memory used=722.3MB, alloc=83.8MB, time=10.06 memory used=749.3MB, alloc=83.8MB, time=10.71 memory used=772.2MB, alloc=83.8MB, time=10.81 memory used=796.7MB, alloc=83.8MB, time=10.92 memory used=822.7MB, alloc=83.8MB, time=11.03 memory used=864.2MB, alloc=83.8MB, time=11.16 memory used=909.7MB, alloc=83.8MB, time=11.29 memory used=958.9MB, alloc=83.8MB, time=11.42 memory used=984.6MB, alloc=83.8MB, time=11.50 memory used=999.3MB, alloc=83.8MB, time=11.58 memory used=1014.4MB, alloc=83.8MB, time=11.65 memory used=1029.7MB, alloc=83.8MB, time=11.72 memory used=1046.4MB, alloc=83.8MB, time=12.05 memory used=1110.5MB, alloc=83.8MB, time=13.52 memory used=1172.4MB, alloc=83.8MB, time=14.49 memory used=1251.1MB, alloc=83.8MB, time=15.54 memory used=1287.1MB, alloc=83.8MB, time=22.38 memory used=1329.5MB, alloc=83.8MB, time=28.06 memory used=1352.1MB, alloc=83.8MB, time=28.16 memory used=1375.5MB, alloc=83.8MB, time=28.27 memory used=1401.5MB, alloc=83.8MB, time=28.39 memory used=1425.2MB, alloc=83.8MB, time=28.50 memory used=1439.8MB, alloc=83.8MB, time=28.59 memory used=1454.8MB, alloc=83.8MB, time=28.68 memory used=1470.7MB, alloc=83.8MB, time=28.78 memory used=1486.9MB, alloc=83.8MB, time=28.91 memory used=1503.3MB, alloc=83.8MB, time=29.01 memory used=1521.2MB, alloc=83.8MB, time=29.11 memory used=1539.2MB, alloc=83.8MB, time=29.21 memory used=1558.6MB, alloc=83.8MB, time=29.31 memory used=1578.2MB, alloc=83.8MB, time=29.41 memory used=1599.1MB, alloc=83.8MB, time=29.52 memory used=1620.0MB, alloc=83.8MB, time=29.63 memory used=1642.2MB, alloc=83.8MB, time=29.72 memory used=1665.6MB, alloc=83.8MB, time=29.81 memory used=1690.1MB, alloc=83.8MB, time=29.91 memory used=1715.4MB, alloc=83.8MB, time=30.01 memory used=1741.6MB, alloc=83.8MB, time=30.11 memory used=1769.6MB, alloc=83.8MB, time=30.22 memory used=1787.4MB, alloc=83.8MB, time=30.30 memory used=1798.0MB, alloc=83.8MB, time=30.38 memory used=1808.7MB, alloc=83.8MB, time=30.49 memory used=1819.1MB, alloc=83.8MB, time=30.57 memory used=1830.2MB, alloc=83.8MB, time=30.65 memory used=1841.1MB, alloc=83.8MB, time=30.73 memory used=1852.5MB, alloc=83.8MB, time=30.82 memory used=1864.3MB, alloc=83.8MB, time=30.89 memory used=1876.5MB, alloc=83.8MB, time=30.97 memory used=1888.0MB, alloc=83.8MB, time=31.06 memory used=1900.2MB, alloc=83.8MB, time=31.14 memory used=1913.7MB, alloc=83.8MB, time=31.23 memory used=1927.9MB, alloc=83.8MB, time=31.31 memory used=1943.2MB, alloc=83.8MB, time=31.41 memory used=1977.5MB, alloc=107.8MB, time=45.30 memory used=2037.8MB, alloc=107.8MB, time=78.92 memory used=2073.6MB, alloc=107.8MB, time=79.05 memory used=2103.7MB, alloc=107.8MB, time=79.17 memory used=2136.6MB, alloc=107.8MB, time=79.28 memory used=2174.2MB, alloc=107.8MB, time=79.41 memory used=2215.6MB, alloc=107.8MB, time=79.53 memory used=2261.1MB, alloc=107.8MB, time=79.67 memory used=2284.5MB, alloc=107.8MB, time=79.77 memory used=2296.5MB, alloc=107.8MB, time=79.85 memory used=2380.7MB, alloc=107.8MB, time=84.06 memory used=2443.5MB, alloc=107.8MB, time=93.25 memory used=2484.1MB, alloc=107.8MB, time=93.43 memory used=2510.1MB, alloc=107.8MB, time=93.56 memory used=2540.6MB, alloc=107.8MB, time=93.69 memory used=2574.0MB, alloc=107.8MB, time=93.83 memory used=2611.7MB, alloc=107.8MB, time=93.98 memory used=2653.8MB, alloc=107.8MB, time=94.14 memory used=2706.5MB, alloc=107.8MB, time=94.32 memory used=2714.7MB, alloc=107.8MB, time=94.40 memory used=2722.8MB, alloc=107.8MB, time=94.48 memory used=2730.9MB, alloc=107.8MB, time=94.56 memory used=2739.1MB, alloc=107.8MB, time=94.67 memory used=2749.4MB, alloc=107.8MB, time=94.76 memory used=2759.7MB, alloc=107.8MB, time=94.87 memory used=2770.2MB, alloc=107.8MB, time=94.98 memory used=2780.7MB, alloc=107.8MB, time=95.08 memory used=2791.2MB, alloc=107.8MB, time=95.17 memory used=2801.8MB, alloc=107.8MB, time=95.26 memory used=2812.4MB, alloc=107.8MB, time=95.36 memory used=2823.1MB, alloc=107.8MB, time=95.45 memory used=2833.9MB, alloc=107.8MB, time=95.56 memory used=2844.6MB, alloc=107.8MB, time=95.66 memory used=2855.4MB, alloc=107.8MB, time=95.76 memory used=2866.3MB, alloc=107.8MB, time=95.86 memory used=2877.1MB, alloc=107.8MB, time=95.96 memory used=2888.1MB, alloc=107.8MB, time=96.05 memory used=2901.1MB, alloc=107.8MB, time=96.14 memory used=2914.3MB, alloc=107.8MB, time=96.23 memory used=2927.4MB, alloc=107.8MB, time=96.34 memory used=2940.5MB, alloc=107.8MB, time=96.42 memory used=2953.7MB, alloc=107.8MB, time=96.51 memory used=2966.8MB, alloc=107.8MB, time=96.62 memory used=2980.0MB, alloc=107.8MB, time=96.72 memory used=2993.1MB, alloc=107.8MB, time=96.81 memory used=3008.4MB, alloc=107.8MB, time=96.91 memory used=3023.6MB, alloc=107.8MB, time=97.00 memory used=3038.8MB, alloc=107.8MB, time=97.09 memory used=3053.9MB, alloc=107.8MB, time=97.18 memory used=3069.0MB, alloc=107.8MB, time=97.29 memory used=3083.9MB, alloc=107.8MB, time=97.38 memory used=3100.9MB, alloc=107.8MB, time=97.48 memory used=3117.8MB, alloc=107.8MB, time=97.58 memory used=3134.5MB, alloc=107.8MB, time=97.69 memory used=3151.1MB, alloc=107.8MB, time=97.79 memory used=3169.5MB, alloc=107.8MB, time=97.89 memory used=3187.9MB, alloc=107.8MB, time=97.99 memory used=3204.0MB, alloc=107.8MB, time=98.09 memory used=3221.0MB, alloc=107.8MB, time=98.18 memory used=3237.1MB, alloc=107.8MB, time=98.28 memory used=3249.2MB, alloc=107.8MB, time=98.37 memory used=3261.0MB, alloc=107.8MB, time=98.45 memory used=3271.8MB, alloc=107.8MB, time=98.54 memory used=3284.3MB, alloc=107.8MB, time=98.66 memory used=3296.5MB, alloc=107.8MB, time=98.76 memory used=3308.4MB, alloc=107.8MB, time=98.88 memory used=3320.2MB, alloc=107.8MB, time=98.96 memory used=3333.0MB, alloc=107.8MB, time=99.07 memory used=3345.6MB, alloc=107.8MB, time=99.16 memory used=3359.2MB, alloc=107.8MB, time=99.26 memory used=3372.4MB, alloc=107.8MB, time=99.35 memory used=3386.4MB, alloc=107.8MB, time=99.44 memory used=3402.6MB, alloc=107.8MB, time=99.54 memory used=3418.8MB, alloc=107.8MB, time=99.63 memory used=3436.8MB, alloc=107.8MB, time=99.73 memory used=3454.7MB, alloc=107.8MB, time=99.82 memory used=3476.8MB, alloc=107.8MB, time=100.84 memory used=3521.7MB, alloc=107.8MB, time=101.69 memory used=3560.2MB, alloc=107.8MB, time=101.93 memory used=3604.9MB, alloc=107.8MB, time=102.12 memory used=3640.6MB, alloc=107.8MB, time=102.26 memory used=3658.1MB, alloc=107.8MB, time=102.60 memory used=3680.8MB, alloc=107.8MB, time=102.72 memory used=3709.4MB, alloc=107.8MB, time=102.85 memory used=3740.5MB, alloc=107.8MB, time=102.97 memory used=3774.1MB, alloc=107.8MB, time=103.09 memory used=3810.1MB, alloc=107.8MB, time=103.22 memory used=3848.5MB, alloc=107.8MB, time=103.34 memory used=3871.3MB, alloc=107.8MB, time=103.44 memory used=3882.8MB, alloc=107.8MB, time=103.52 memory used=3929.1MB, alloc=107.8MB, time=104.28 memory used=3963.7MB, alloc=107.8MB, time=104.48 memory used=4004.0MB, alloc=107.8MB, time=104.76 memory used=4047.3MB, alloc=107.8MB, time=104.94 memory used=4096.0MB, alloc=107.8MB, time=105.12 memory used=4131.1MB, alloc=107.8MB, time=105.28 memory used=4179.3MB, alloc=107.8MB, time=105.46 memory used=4217.3MB, alloc=107.8MB, time=105.92 memory used=4237.0MB, alloc=107.8MB, time=106.04 memory used=4257.7MB, alloc=107.8MB, time=106.15 memory used=4279.6MB, alloc=107.8MB, time=106.26 memory used=4302.5MB, alloc=107.8MB, time=106.37 memory used=4337.7MB, alloc=107.8MB, time=106.50 memory used=4376.7MB, alloc=107.8MB, time=106.63 memory used=4418.1MB, alloc=107.8MB, time=106.77 memory used=4451.0MB, alloc=107.8MB, time=106.88 memory used=4463.5MB, alloc=107.8MB, time=106.97 memory used=4476.2MB, alloc=107.8MB, time=107.07 memory used=4489.2MB, alloc=107.8MB, time=107.15 memory used=4502.3MB, alloc=107.8MB, time=107.24 memory used=4515.6MB, alloc=107.8MB, time=107.32 memory used=4530.7MB, alloc=107.8MB, time=107.44 memory used=4549.7MB, alloc=107.8MB, time=107.55 memory used=4569.7MB, alloc=107.8MB, time=107.66 memory used=4590.8MB, alloc=107.8MB, time=107.77 memory used=4613.0MB, alloc=107.8MB, time=107.88 memory used=4639.2MB, alloc=107.8MB, time=107.99 memory used=4676.7MB, alloc=107.8MB, time=108.13 memory used=4716.7MB, alloc=107.8MB, time=108.25 memory used=4759.0MB, alloc=107.8MB, time=108.38 memory used=4779.6MB, alloc=107.8MB, time=108.47 memory used=4792.2MB, alloc=107.8MB, time=108.55 memory used=4804.9MB, alloc=107.8MB, time=108.63 memory used=4817.9MB, alloc=107.8MB, time=108.71 memory used=4831.1MB, alloc=107.8MB, time=108.82 memory used=4844.4MB, alloc=107.8MB, time=108.92 memory used=4903.3MB, alloc=107.8MB, time=149.82 memory used=4959.6MB, alloc=107.8MB, time=157.23 memory used=4990.0MB, alloc=107.8MB, time=157.37 memory used=5026.3MB, alloc=107.8MB, time=157.53 memory used=5069.7MB, alloc=107.8MB, time=157.69 memory used=5104.4MB, alloc=107.8MB, time=157.84 memory used=5114.9MB, alloc=107.8MB, time=157.93 memory used=5124.9MB, alloc=107.8MB, time=158.01 memory used=5136.1MB, alloc=107.8MB, time=158.10 memory used=5147.4MB, alloc=107.8MB, time=158.18 memory used=5158.6MB, alloc=107.8MB, time=158.27 memory used=5170.8MB, alloc=107.8MB, time=158.36 memory used=5183.0MB, alloc=107.8MB, time=158.47 memory used=5196.3MB, alloc=107.8MB, time=158.57 memory used=5210.5MB, alloc=107.8MB, time=158.66 memory used=5224.4MB, alloc=107.8MB, time=158.77 memory used=5239.1MB, alloc=107.8MB, time=158.87 memory used=5254.4MB, alloc=107.8MB, time=158.98 memory used=5271.2MB, alloc=107.8MB, time=159.07 memory used=5288.9MB, alloc=107.8MB, time=159.18 memory used=5307.0MB, alloc=107.8MB, time=159.28 memory used=5326.7MB, alloc=107.8MB, time=159.38 memory used=5420.5MB, alloc=107.8MB, time=171.99 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428258353 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 4 3 3 4 3 F := [-14 x y z + 15 y z - 8 z , -9 y z - 3 x + 9 x z, -15 y + 18 z - 8] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; G := 4 4 3 2 2 2 4 2 3 [2 x - 11 y + 8 x , -12 y z - 8 x y + 6 y z, -4 x - 19 x y z + 5 y ] > Problem := [F,G]; Problem := [ 2 3 4 3 3 4 3 [-14 x y z + 15 y z - 8 z , -9 y z - 3 x + 9 x z, -15 y + 18 z - 8], 4 4 3 2 2 2 4 2 3 [2 x - 11 y + 8 x , -12 y z - 8 x y + 6 y z, -4 x - 19 x y z + 5 y ] ] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.31 memory used=26.3MB, alloc=32.3MB, time=0.87 memory used=45.5MB, alloc=56.3MB, time=1.37 memory used=91.8MB, alloc=60.3MB, time=2.40 memory used=123.3MB, alloc=60.3MB, time=2.67 memory used=155.5MB, alloc=61.6MB, time=3.29 memory used=180.9MB, alloc=61.6MB, time=3.40 memory used=202.7MB, alloc=61.6MB, time=3.50 memory used=242.5MB, alloc=61.6MB, time=4.27 memory used=277.5MB, alloc=61.6MB, time=5.13 memory used=324.5MB, alloc=69.6MB, time=6.38 memory used=371.5MB, alloc=69.6MB, time=7.45 memory used=408.7MB, alloc=69.6MB, time=8.04 memory used=438.5MB, alloc=69.6MB, time=8.34 memory used=463.6MB, alloc=69.6MB, time=8.53 memory used=490.8MB, alloc=69.6MB, time=8.76 memory used=518.8MB, alloc=69.6MB, time=9.01 memory used=544.7MB, alloc=69.6MB, time=9.27 memory used=564.3MB, alloc=69.6MB, time=9.39 memory used=581.9MB, alloc=69.6MB, time=9.49 memory used=607.0MB, alloc=69.6MB, time=9.65 memory used=630.3MB, alloc=69.6MB, time=9.79 memory used=652.3MB, alloc=69.6MB, time=10.04 memory used=677.7MB, alloc=69.6MB, time=10.19 memory used=694.5MB, alloc=69.6MB, time=10.30 memory used=717.3MB, alloc=69.6MB, time=10.43 memory used=748.5MB, alloc=69.6MB, time=11.22 memory used=768.7MB, alloc=93.6MB, time=11.38 memory used=805.1MB, alloc=93.6MB, time=11.55 memory used=837.9MB, alloc=93.6MB, time=11.68 memory used=886.9MB, alloc=93.6MB, time=12.15 memory used=923.5MB, alloc=93.6MB, time=12.32 memory used=961.5MB, alloc=93.6MB, time=12.49 memory used=989.9MB, alloc=93.6MB, time=12.64 memory used=1022.9MB, alloc=93.6MB, time=12.79 memory used=1062.0MB, alloc=93.6MB, time=12.95 memory used=1113.7MB, alloc=93.6MB, time=13.42 memory used=1149.6MB, alloc=93.6MB, time=13.61 memory used=1190.0MB, alloc=93.6MB, time=13.78 memory used=1218.7MB, alloc=93.6MB, time=13.92 memory used=1251.7MB, alloc=93.6MB, time=14.08 memory used=1291.0MB, alloc=93.6MB, time=14.23 memory used=1361.5MB, alloc=93.6MB, time=37.96 memory used=1410.8MB, alloc=93.6MB, time=60.23 memory used=1453.9MB, alloc=93.6MB, time=61.19 memory used=1491.7MB, alloc=93.6MB, time=61.38 memory used=1521.5MB, alloc=93.6MB, time=61.54 memory used=1555.6MB, alloc=93.6MB, time=61.70 memory used=1595.6MB, alloc=93.6MB, time=61.88 memory used=1640.3MB, alloc=93.6MB, time=62.06 memory used=1666.0MB, alloc=93.6MB, time=62.18 memory used=1691.7MB, alloc=93.6MB, time=62.30 memory used=1719.0MB, alloc=93.6MB, time=62.43 memory used=1748.3MB, alloc=93.6MB, time=62.55 memory used=1778.3MB, alloc=93.6MB, time=62.68 memory used=1810.3MB, alloc=93.6MB, time=62.82 memory used=1844.2MB, alloc=93.6MB, time=62.95 memory used=1880.1MB, alloc=93.6MB, time=63.08 memory used=1917.7MB, alloc=93.6MB, time=63.22 memory used=1958.4MB, alloc=93.6MB, time=63.37 memory used=2000.7MB, alloc=93.6MB, time=63.51 memory used=2045.9MB, alloc=93.6MB, time=63.65 memory used=2073.9MB, alloc=107.8MB, time=63.79 memory used=2084.2MB, alloc=107.8MB, time=63.88 memory used=2093.7MB, alloc=107.8MB, time=63.99 memory used=2103.4MB, alloc=107.8MB, time=64.09 memory used=2113.1MB, alloc=107.8MB, time=64.18 memory used=2123.6MB, alloc=107.8MB, time=64.31 memory used=2134.2MB, alloc=107.8MB, time=64.40 memory used=2144.7MB, alloc=107.8MB, time=64.49 memory used=2155.2MB, alloc=107.8MB, time=64.58 memory used=2166.4MB, alloc=107.8MB, time=64.67 memory used=2177.6MB, alloc=107.8MB, time=64.77 memory used=2188.8MB, alloc=107.8MB, time=64.88 memory used=2200.5MB, alloc=107.8MB, time=64.97 memory used=2212.4MB, alloc=107.8MB, time=65.06 memory used=2224.6MB, alloc=107.8MB, time=65.15 memory used=2237.0MB, alloc=107.8MB, time=65.24 memory used=2249.7MB, alloc=107.8MB, time=65.34 memory used=2262.9MB, alloc=107.8MB, time=65.43 memory used=2276.5MB, alloc=107.8MB, time=65.54 memory used=2290.8MB, alloc=107.8MB, time=65.66 memory used=2305.4MB, alloc=107.8MB, time=65.77 memory used=2320.8MB, alloc=107.8MB, time=65.87 memory used=2384.5MB, alloc=107.8MB, time=67.43 memory used=2416.8MB, alloc=107.8MB, time=67.61 memory used=2448.2MB, alloc=107.8MB, time=67.78 memory used=2483.8MB, alloc=107.8MB, time=67.98 memory used=2524.7MB, alloc=107.8MB, time=68.16 memory used=2564.5MB, alloc=107.8MB, time=68.35 memory used=2588.7MB, alloc=107.8MB, time=68.49 memory used=2612.0MB, alloc=107.8MB, time=68.64 memory used=2636.7MB, alloc=107.8MB, time=68.78 memory used=2664.4MB, alloc=107.8MB, time=68.93 memory used=2693.1MB, alloc=107.8MB, time=69.08 memory used=2722.6MB, alloc=107.8MB, time=69.23 memory used=2752.6MB, alloc=107.8MB, time=69.39 memory used=2784.0MB, alloc=107.8MB, time=69.54 memory used=2818.0MB, alloc=107.8MB, time=69.69 memory used=2853.2MB, alloc=107.8MB, time=69.86 memory used=2889.6MB, alloc=107.8MB, time=70.02 memory used=2928.6MB, alloc=107.8MB, time=70.19 memory used=2968.7MB, alloc=107.8MB, time=70.37 memory used=3012.6MB, alloc=107.8MB, time=70.55 memory used=3045.4MB, alloc=107.8MB, time=70.69 memory used=3068.3MB, alloc=107.8MB, time=70.81 memory used=3088.8MB, alloc=107.8MB, time=70.92 memory used=3110.3MB, alloc=107.8MB, time=71.03 memory used=3131.8MB, alloc=107.8MB, time=71.14 memory used=3153.8MB, alloc=107.8MB, time=71.25 memory used=3178.1MB, alloc=107.8MB, time=71.36 memory used=3202.7MB, alloc=107.8MB, time=71.48 memory used=3227.2MB, alloc=107.8MB, time=71.59 memory used=3251.6MB, alloc=107.8MB, time=71.71 memory used=3276.7MB, alloc=107.8MB, time=71.82 memory used=3302.9MB, alloc=107.8MB, time=71.93 memory used=3329.8MB, alloc=107.8MB, time=72.05 memory used=3357.4MB, alloc=107.8MB, time=72.17 memory used=3386.3MB, alloc=107.8MB, time=72.29 memory used=3417.2MB, alloc=107.8MB, time=72.41 memory used=3448.1MB, alloc=107.8MB, time=72.53 memory used=3481.0MB, alloc=107.8MB, time=72.65 memory used=3515.5MB, alloc=107.8MB, time=72.77 memory used=3551.1MB, alloc=107.8MB, time=72.89 memory used=3588.0MB, alloc=107.8MB, time=73.02 memory used=3626.4MB, alloc=107.8MB, time=73.14 memory used=3667.2MB, alloc=107.8MB, time=73.27 memory used=3722.5MB, alloc=107.8MB, time=74.91 memory used=3765.5MB, alloc=107.8MB, time=75.13 memory used=3794.3MB, alloc=107.8MB, time=75.30 memory used=3827.7MB, alloc=107.8MB, time=75.50 memory used=3866.9MB, alloc=107.8MB, time=75.70 memory used=3910.3MB, alloc=107.8MB, time=75.89 memory used=3939.4MB, alloc=107.8MB, time=76.05 memory used=3963.4MB, alloc=107.8MB, time=76.20 memory used=3987.4MB, alloc=107.8MB, time=76.35 memory used=4012.6MB, alloc=107.8MB, time=76.49 memory used=4040.5MB, alloc=107.8MB, time=76.65 memory used=4069.5MB, alloc=107.8MB, time=76.81 memory used=4099.3MB, alloc=107.8MB, time=76.98 memory used=4130.2MB, alloc=107.8MB, time=77.13 memory used=4164.0MB, alloc=107.8MB, time=77.29 memory used=4199.0MB, alloc=107.8MB, time=77.47 memory used=4234.9MB, alloc=107.8MB, time=77.64 memory used=4273.9MB, alloc=107.8MB, time=77.82 memory used=4313.9MB, alloc=107.8MB, time=78.00 memory used=4357.7MB, alloc=107.8MB, time=78.17 memory used=4396.5MB, alloc=107.8MB, time=78.33 memory used=4421.9MB, alloc=131.8MB, time=78.48 memory used=4454.9MB, alloc=131.8MB, time=78.63 memory used=4490.5MB, alloc=131.8MB, time=78.77 memory used=4526.7MB, alloc=131.8MB, time=78.92 memory used=4563.6MB, alloc=131.8MB, time=79.08 memory used=4602.4MB, alloc=131.8MB, time=79.22 memory used=4643.9MB, alloc=131.8MB, time=79.38 memory used=4686.1MB, alloc=131.8MB, time=79.53 memory used=4730.0MB, alloc=131.8MB, time=79.69 memory used=4776.2MB, alloc=131.8MB, time=79.85 memory used=4826.1MB, alloc=131.8MB, time=80.01 memory used=4877.4MB, alloc=131.8MB, time=80.17 memory used=4932.0MB, alloc=131.8MB, time=80.34 memory used=4990.3MB, alloc=131.8MB, time=80.50 memory used=5058.3MB, alloc=131.8MB, time=80.78 memory used=5135.1MB, alloc=131.8MB, time=122.03 memory used=5189.2MB, alloc=131.8MB, time=181.31 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428258653 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; F := 4 3 2 3 2 [-2 x - 9 x y z - 12 z , x y z + 19 z + 13 x y, 15 x z - 18 x y - 20 x] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; G := 2 2 3 3 4 2 2 2 3 [-12 x z + 19 y z + 6 z , 10 y - 14 y z - 8 x z, 18 x z - 3 z + 10] > Problem := [F,G]; Problem := [ 4 3 2 3 2 [-2 x - 9 x y z - 12 z , x y z + 19 z + 13 x y, 15 x z - 18 x y - 20 x] , 2 2 3 3 4 2 2 2 3 [-12 x z + 19 y z + 6 z , 10 y - 14 y z - 8 x z, 18 x z - 3 z + 10] ] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.31 memory used=26.6MB, alloc=32.3MB, time=0.90 memory used=47.2MB, alloc=56.3MB, time=1.47 memory used=87.9MB, alloc=60.3MB, time=2.53 memory used=127.2MB, alloc=60.3MB, time=3.51 memory used=166.1MB, alloc=84.3MB, time=4.54 memory used=232.6MB, alloc=92.3MB, time=6.26 memory used=297.4MB, alloc=92.3MB, time=7.89 memory used=363.3MB, alloc=116.3MB, time=9.41 memory used=426.8MB, alloc=372.3MB, time=11.04 memory used=513.7MB, alloc=372.3MB, time=13.33 memory used=603.5MB, alloc=396.3MB, time=15.40 memory used=717.1MB, alloc=396.3MB, time=17.81 memory used=833.7MB, alloc=396.3MB, time=20.45 memory used=944.7MB, alloc=420.3MB, time=23.43 memory used=1068.9MB, alloc=444.3MB, time=26.88 memory used=1185.8MB, alloc=444.3MB, time=29.81 memory used=1301.5MB, alloc=444.3MB, time=32.54 memory used=1430.9MB, alloc=444.3MB, time=35.27 memory used=1534.5MB, alloc=444.3MB, time=36.83 memory used=1613.3MB, alloc=444.3MB, time=38.13 memory used=1694.6MB, alloc=444.3MB, time=39.19 memory used=1821.4MB, alloc=444.3MB, time=41.73 memory used=1903.2MB, alloc=468.3MB, time=42.55 memory used=1985.3MB, alloc=468.3MB, time=43.05 memory used=2105.2MB, alloc=468.3MB, time=62.87 memory used=2185.8MB, alloc=468.3MB, time=63.39 memory used=2263.2MB, alloc=468.3MB, time=63.88 memory used=2358.5MB, alloc=468.3MB, time=64.37 memory used=2418.7MB, alloc=468.3MB, time=64.79 memory used=2487.0MB, alloc=468.3MB, time=65.19 memory used=2564.2MB, alloc=468.3MB, time=65.62 memory used=2653.0MB, alloc=468.3MB, time=66.05 memory used=2795.3MB, alloc=468.3MB, time=67.09 memory used=2884.5MB, alloc=468.3MB, time=67.82 memory used=3026.2MB, alloc=468.3MB, time=69.68 memory used=3212.0MB, alloc=468.3MB, time=72.61 memory used=3313.3MB, alloc=468.3MB, time=73.55 memory used=3397.7MB, alloc=468.3MB, time=74.14 memory used=3523.6MB, alloc=468.3MB, time=76.15 memory used=3623.3MB, alloc=468.3MB, time=77.01 memory used=3700.5MB, alloc=468.3MB, time=77.48 memory used=3792.0MB, alloc=468.3MB, time=78.12 memory used=3920.5MB, alloc=468.3MB, time=79.70 memory used=4041.1MB, alloc=468.3MB, time=81.22 memory used=4183.4MB, alloc=468.3MB, time=84.25 memory used=4268.2MB, alloc=468.3MB, time=84.81 memory used=4337.6MB, alloc=468.3MB, time=85.28 memory used=4455.3MB, alloc=468.3MB, time=104.94 memory used=4529.8MB, alloc=468.3MB, time=105.47 memory used=4601.3MB, alloc=468.3MB, time=105.99 memory used=4690.3MB, alloc=468.3MB, time=106.49 memory used=4745.1MB, alloc=468.3MB, time=106.91 memory used=4806.5MB, alloc=468.3MB, time=107.36 memory used=4876.0MB, alloc=468.3MB, time=107.80 memory used=4954.0MB, alloc=468.3MB, time=108.26 memory used=5042.9MB, alloc=468.3MB, time=108.73 memory used=5300.9MB, alloc=468.3MB, time=111.78 memory used=5394.3MB, alloc=468.3MB, time=114.22 memory used=5499.8MB, alloc=468.3MB, time=115.43 memory used=5608.0MB, alloc=468.3MB, time=116.63 memory used=5696.5MB, alloc=468.3MB, time=117.38 memory used=5769.5MB, alloc=468.3MB, time=117.93 memory used=5841.1MB, alloc=468.3MB, time=118.43 memory used=5940.2MB, alloc=468.3MB, time=119.89 memory used=6011.5MB, alloc=468.3MB, time=120.38 memory used=6099.3MB, alloc=468.3MB, time=121.18 memory used=6165.4MB, alloc=468.3MB, time=121.70 memory used=6250.5MB, alloc=468.3MB, time=122.80 memory used=6350.2MB, alloc=492.3MB, time=124.88 memory used=6454.3MB, alloc=492.3MB, time=126.98 memory used=6589.1MB, alloc=492.3MB, time=128.64 memory used=6708.2MB, alloc=492.3MB, time=130.17 memory used=6824.6MB, alloc=492.3MB, time=131.32 memory used=6926.3MB, alloc=492.3MB, time=131.97 memory used=6998.4MB, alloc=492.3MB, time=132.54 memory used=7077.8MB, alloc=492.3MB, time=133.12 memory used=7171.5MB, alloc=492.3MB, time=133.69 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428258953 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 3 2 F := [14 y z - 14 x y + 3 y , x y z - 2 x + 12 y z, 3 2 12 x z + 15 x y + 19 z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 4 3 2 3 G := [-7 x z + 13 x - 6 z , 14 x - 20 x z - y, -x y z + 5 y - 18] > Problem := [F,G]; 2 2 2 3 2 3 2 Problem := [[14 y z - 14 x y + 3 y , x y z - 2 x + 12 y z, 3 2 12 x z + 15 x y + 19 z], 2 2 2 4 3 2 3 [-7 x z + 13 x - 6 z , 14 x - 20 x z - y, -x y z + 5 y - 18]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.31 memory used=25.0MB, alloc=32.3MB, time=0.80 memory used=45.7MB, alloc=36.3MB, time=1.29 memory used=65.1MB, alloc=36.3MB, time=1.67 memory used=81.5MB, alloc=36.3MB, time=1.82 memory used=102.6MB, alloc=36.3MB, time=2.22 memory used=123.6MB, alloc=60.3MB, time=2.75 memory used=161.3MB, alloc=60.3MB, time=3.54 memory used=208.4MB, alloc=68.3MB, time=4.63 memory used=258.3MB, alloc=92.3MB, time=5.60 memory used=324.6MB, alloc=92.3MB, time=6.98 memory used=374.8MB, alloc=92.3MB, time=7.50 memory used=425.9MB, alloc=92.3MB, time=8.05 memory used=475.0MB, alloc=92.3MB, time=8.47 memory used=530.3MB, alloc=94.4MB, time=10.08 memory used=561.1MB, alloc=94.4MB, time=10.26 memory used=590.4MB, alloc=94.4MB, time=10.42 memory used=638.8MB, alloc=94.4MB, time=10.87 memory used=674.5MB, alloc=94.4MB, time=11.21 memory used=717.1MB, alloc=94.4MB, time=11.46 memory used=760.7MB, alloc=94.4MB, time=14.32 memory used=797.4MB, alloc=94.4MB, time=14.54 memory used=830.2MB, alloc=94.4MB, time=14.73 memory used=855.7MB, alloc=94.4MB, time=14.89 memory used=895.3MB, alloc=94.4MB, time=15.22 memory used=931.2MB, alloc=94.4MB, time=15.43 memory used=992.0MB, alloc=94.4MB, time=16.33 memory used=1055.4MB, alloc=350.4MB, time=17.71 memory used=1132.5MB, alloc=374.4MB, time=19.42 memory used=1245.3MB, alloc=374.4MB, time=21.20 memory used=1340.9MB, alloc=398.4MB, time=23.27 memory used=1424.1MB, alloc=398.4MB, time=24.13 memory used=1504.0MB, alloc=398.4MB, time=24.84 memory used=1572.7MB, alloc=398.4MB, time=25.31 memory used=1646.2MB, alloc=398.4MB, time=26.01 memory used=1718.5MB, alloc=398.4MB, time=26.66 memory used=1791.5MB, alloc=398.4MB, time=27.08 memory used=1871.5MB, alloc=398.4MB, time=27.69 memory used=1956.6MB, alloc=398.4MB, time=32.59 memory used=2013.9MB, alloc=398.4MB, time=32.93 memory used=2070.1MB, alloc=398.4MB, time=33.22 memory used=2117.0MB, alloc=398.4MB, time=33.50 memory used=2190.6MB, alloc=398.4MB, time=34.30 memory used=2267.5MB, alloc=398.4MB, time=34.72 memory used=2314.1MB, alloc=398.4MB, time=35.01 memory used=2372.5MB, alloc=398.4MB, time=35.31 memory used=2435.9MB, alloc=398.4MB, time=36.18 memory used=2524.7MB, alloc=398.4MB, time=36.67 memory used=2571.8MB, alloc=398.4MB, time=36.97 memory used=2628.0MB, alloc=398.4MB, time=37.26 memory used=2684.8MB, alloc=398.4MB, time=37.55 memory used=2778.4MB, alloc=398.4MB, time=49.24 memory used=2831.7MB, alloc=398.4MB, time=49.56 memory used=2889.9MB, alloc=398.4MB, time=49.85 memory used=2933.2MB, alloc=398.4MB, time=50.10 memory used=2983.2MB, alloc=398.4MB, time=50.37 memory used=3041.8MB, alloc=398.4MB, time=50.65 memory used=3099.0MB, alloc=398.4MB, time=50.89 memory used=3173.1MB, alloc=398.4MB, time=51.76 memory used=3236.0MB, alloc=398.4MB, time=52.12 memory used=3285.2MB, alloc=398.4MB, time=52.42 memory used=3348.6MB, alloc=398.4MB, time=52.73 memory used=3434.7MB, alloc=398.4MB, time=53.78 memory used=3572.6MB, alloc=398.4MB, time=55.81 memory used=3707.8MB, alloc=398.4MB, time=57.65 memory used=3816.9MB, alloc=422.4MB, time=60.10 memory used=3939.6MB, alloc=446.4MB, time=62.98 memory used=4067.1MB, alloc=446.4MB, time=65.78 memory used=4206.6MB, alloc=446.4MB, time=69.71 memory used=4347.0MB, alloc=446.4MB, time=73.33 memory used=4446.3MB, alloc=446.4MB, time=75.96 memory used=4544.3MB, alloc=470.4MB, time=78.10 memory used=4688.6MB, alloc=470.4MB, time=80.00 memory used=4774.3MB, alloc=470.4MB, time=80.61 memory used=4898.8MB, alloc=470.4MB, time=82.61 memory used=5027.6MB, alloc=470.4MB, time=84.62 memory used=5148.2MB, alloc=470.4MB, time=86.80 memory used=5256.3MB, alloc=470.4MB, time=88.69 memory used=5345.0MB, alloc=470.4MB, time=90.03 memory used=5431.1MB, alloc=470.4MB, time=91.09 memory used=5537.6MB, alloc=494.4MB, time=92.95 memory used=5625.3MB, alloc=494.4MB, time=93.58 memory used=5729.4MB, alloc=494.4MB, time=94.22 memory used=5796.8MB, alloc=494.4MB, time=94.76 memory used=5872.8MB, alloc=494.4MB, time=95.32 memory used=5958.3MB, alloc=494.4MB, time=95.92 memory used=6054.2MB, alloc=494.4MB, time=96.49 memory used=6162.2MB, alloc=494.4MB, time=97.08 memory used=6262.2MB, alloc=494.4MB, time=97.66 memory used=6328.4MB, alloc=494.4MB, time=98.13 memory used=6393.0MB, alloc=494.4MB, time=98.59 memory used=6462.4MB, alloc=494.4MB, time=99.07 memory used=6536.0MB, alloc=494.4MB, time=99.53 memory used=6613.5MB, alloc=494.4MB, time=100.00 memory used=6697.4MB, alloc=494.4MB, time=100.47 memory used=6786.4MB, alloc=494.4MB, time=100.97 memory used=6890.9MB, alloc=494.4MB, time=101.70 memory used=7011.7MB, alloc=494.4MB, time=103.46 memory used=7102.1MB, alloc=494.4MB, time=104.10 memory used=7202.1MB, alloc=494.4MB, time=104.73 memory used=7269.7MB, alloc=494.4MB, time=105.28 memory used=7346.0MB, alloc=494.4MB, time=105.85 memory used=7431.9MB, alloc=494.4MB, time=106.42 memory used=7528.1MB, alloc=494.4MB, time=107.01 memory used=7636.3MB, alloc=494.4MB, time=107.60 memory used=7734.2MB, alloc=494.4MB, time=108.17 memory used=7799.3MB, alloc=494.4MB, time=108.63 memory used=7863.6MB, alloc=494.4MB, time=109.10 memory used=7932.8MB, alloc=494.4MB, time=109.56 memory used=8006.4MB, alloc=494.4MB, time=110.03 memory used=8083.7MB, alloc=494.4MB, time=110.51 memory used=8166.0MB, alloc=494.4MB, time=110.98 memory used=8254.7MB, alloc=494.4MB, time=111.47 memory used=8369.9MB, alloc=494.4MB, time=114.85 memory used=8502.8MB, alloc=494.4MB, time=140.23 memory used=8587.0MB, alloc=494.4MB, time=140.84 memory used=8674.0MB, alloc=494.4MB, time=141.43 memory used=8781.4MB, alloc=494.4MB, time=142.05 memory used=8858.5MB, alloc=494.4MB, time=142.57 memory used=8925.3MB, alloc=494.4MB, time=143.05 memory used=8999.2MB, alloc=494.4MB, time=143.54 memory used=9078.9MB, alloc=494.4MB, time=144.05 memory used=9164.0MB, alloc=494.4MB, time=144.56 memory used=9256.7MB, alloc=494.4MB, time=145.07 memory used=9356.8MB, alloc=494.4MB, time=145.60 memory used=9464.1MB, alloc=494.4MB, time=146.13 memory used=9589.7MB, alloc=494.4MB, time=146.69 memory used=9743.3MB, alloc=494.4MB, time=147.60 memory used=9885.9MB, alloc=494.4MB, time=148.24 memory used=10039.8MB, alloc=494.4MB, time=148.89 memory used=10209.9MB, alloc=494.4MB, time=149.55 memory used=10399.7MB, alloc=494.4MB, time=150.25 memory used=10603.8MB, alloc=494.4MB, time=153.07 memory used=10721.2MB, alloc=494.4MB, time=155.12 memory used=10856.0MB, alloc=494.4MB, time=155.88 memory used=10985.4MB, alloc=494.4MB, time=159.13 memory used=11068.6MB, alloc=494.4MB, time=159.78 memory used=11176.4MB, alloc=494.4MB, time=160.45 memory used=11243.7MB, alloc=494.4MB, time=160.99 memory used=11318.9MB, alloc=494.4MB, time=161.58 memory used=11402.8MB, alloc=494.4MB, time=162.16 memory used=11495.6MB, alloc=494.4MB, time=162.77 memory used=11598.3MB, alloc=494.4MB, time=163.39 memory used=11704.1MB, alloc=494.4MB, time=164.00 memory used=11773.2MB, alloc=494.4MB, time=164.50 memory used=11836.4MB, alloc=494.4MB, time=164.97 memory used=11903.2MB, alloc=494.4MB, time=165.43 memory used=11973.4MB, alloc=494.4MB, time=165.92 memory used=12048.1MB, alloc=494.4MB, time=166.39 memory used=12128.5MB, alloc=494.4MB, time=166.87 memory used=12215.2MB, alloc=494.4MB, time=167.36 memory used=12307.7MB, alloc=494.4MB, time=167.86 memory used=12422.4MB, alloc=494.4MB, time=168.96 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428259253 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 2 F := [-6 x y z + x y z - 12 x y z , 6 x y + 9 x z + y z , 3 2 -3 x y + 3 x z + 16 z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 2 2 2 G := [-9 x z - 15 x z + 7 y , -8 x z - 13 z - 7 x, -3 y z - 15 y z + 3 y ] > Problem := [F,G]; 2 2 2 3 2 2 Problem := [[-6 x y z + x y z - 12 x y z , 6 x y + 9 x z + y z , 3 2 -3 x y + 3 x z + 16 z], 3 2 3 2 2 2 2 [-9 x z - 15 x z + 7 y , -8 x z - 13 z - 7 x, -3 y z - 15 y z + 3 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.31 memory used=26.3MB, alloc=32.3MB, time=0.87 memory used=47.0MB, alloc=32.3MB, time=1.42 memory used=66.2MB, alloc=56.3MB, time=1.95 memory used=106.7MB, alloc=60.3MB, time=3.03 memory used=144.2MB, alloc=84.3MB, time=4.05 memory used=203.9MB, alloc=92.3MB, time=5.72 memory used=263.7MB, alloc=116.3MB, time=7.38 memory used=339.0MB, alloc=116.3MB, time=9.37 memory used=413.9MB, alloc=372.3MB, time=11.41 memory used=497.8MB, alloc=396.3MB, time=13.76 memory used=603.9MB, alloc=420.3MB, time=16.94 memory used=733.9MB, alloc=444.3MB, time=20.86 memory used=884.4MB, alloc=444.3MB, time=25.46 memory used=1035.9MB, alloc=468.3MB, time=30.10 memory used=1178.8MB, alloc=492.3MB, time=34.53 memory used=1309.4MB, alloc=492.3MB, time=38.38 memory used=1427.3MB, alloc=492.3MB, time=42.32 memory used=1571.3MB, alloc=516.3MB, time=47.45 memory used=1679.4MB, alloc=516.3MB, time=51.14 memory used=1805.2MB, alloc=540.3MB, time=55.78 memory used=1912.3MB, alloc=540.3MB, time=59.73 memory used=2009.4MB, alloc=540.3MB, time=63.51 memory used=2109.0MB, alloc=540.3MB, time=67.14 memory used=2186.5MB, alloc=540.3MB, time=70.12 memory used=2255.8MB, alloc=540.3MB, time=72.58 memory used=2336.5MB, alloc=564.3MB, time=75.08 memory used=2411.7MB, alloc=564.3MB, time=78.30 memory used=2473.2MB, alloc=564.3MB, time=80.55 memory used=2521.7MB, alloc=564.3MB, time=82.31 memory used=2567.0MB, alloc=564.3MB, time=84.03 memory used=2633.2MB, alloc=564.3MB, time=86.44 memory used=2685.4MB, alloc=564.3MB, time=88.77 memory used=2738.8MB, alloc=564.3MB, time=90.95 memory used=2785.3MB, alloc=564.3MB, time=92.81 memory used=2991.1MB, alloc=588.3MB, time=99.52 memory used=3191.3MB, alloc=612.3MB, time=106.59 memory used=3396.8MB, alloc=636.3MB, time=114.40 memory used=3555.6MB, alloc=660.3MB, time=119.25 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428259553 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 3 2 F := [9 x z + 19 x, -17 x y z - 7 x y - 18 y z, 3 x y + 16 y z + 16 x z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 4 2 3 3 3 G := [-7 y z - 2 x z - 3, 16 y z - 8 z + 18 x y , 13 x + 9 y - z ] > Problem := [F,G]; Problem := [ 2 2 2 2 3 2 [9 x z + 19 x, -17 x y z - 7 x y - 18 y z, 3 x y + 16 y z + 16 x z], 3 2 3 4 2 3 3 3 [-7 y z - 2 x z - 3, 16 y z - 8 z + 18 x y , 13 x + 9 y - z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.30 memory used=25.3MB, alloc=32.3MB, time=0.84 memory used=44.3MB, alloc=56.3MB, time=1.35 memory used=83.1MB, alloc=60.3MB, time=2.26 memory used=127.1MB, alloc=68.3MB, time=3.33 memory used=169.3MB, alloc=92.3MB, time=4.38 memory used=237.1MB, alloc=92.3MB, time=6.20 memory used=321.2MB, alloc=92.3MB, time=8.43 memory used=390.9MB, alloc=92.3MB, time=9.87 memory used=458.2MB, alloc=372.3MB, time=11.39 memory used=547.2MB, alloc=372.3MB, time=13.57 memory used=616.1MB, alloc=396.3MB, time=14.59 memory used=694.7MB, alloc=396.3MB, time=15.99 memory used=783.5MB, alloc=396.3MB, time=17.89 memory used=879.6MB, alloc=396.3MB, time=19.31 memory used=998.4MB, alloc=396.3MB, time=22.14 memory used=1138.0MB, alloc=420.3MB, time=26.41 memory used=1266.7MB, alloc=420.3MB, time=29.99 memory used=1408.7MB, alloc=420.3MB, time=32.95 memory used=1520.2MB, alloc=444.3MB, time=35.67 memory used=1657.0MB, alloc=444.3MB, time=38.97 memory used=1777.4MB, alloc=468.3MB, time=41.36 memory used=1905.7MB, alloc=468.3MB, time=44.24 memory used=2024.7MB, alloc=468.3MB, time=46.85 memory used=2138.1MB, alloc=492.3MB, time=49.34 memory used=2252.8MB, alloc=492.3MB, time=52.36 memory used=2356.3MB, alloc=492.3MB, time=54.99 memory used=2492.2MB, alloc=492.3MB, time=56.78 memory used=2616.7MB, alloc=492.3MB, time=77.10 memory used=2698.0MB, alloc=492.3MB, time=77.71 memory used=2780.2MB, alloc=492.3MB, time=78.28 memory used=2890.2MB, alloc=492.3MB, time=81.88 memory used=2982.8MB, alloc=492.3MB, time=82.58 memory used=3076.4MB, alloc=516.3MB, time=83.26 memory used=3161.6MB, alloc=516.3MB, time=83.88 memory used=3286.7MB, alloc=516.3MB, time=85.17 memory used=3395.5MB, alloc=516.3MB, time=85.85 memory used=3489.4MB, alloc=516.3MB, time=86.58 memory used=3631.6MB, alloc=516.3MB, time=146.96 memory used=3725.7MB, alloc=516.3MB, time=147.54 memory used=3825.8MB, alloc=516.3MB, time=148.08 memory used=3943.3MB, alloc=516.3MB, time=149.28 memory used=4143.6MB, alloc=516.3MB, time=150.51 memory used=4311.0MB, alloc=516.3MB, time=153.26 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428259853 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 4 2 2 2 2 2 F := [18 y z - 5 z + 16 z , -8 y - 7 x - 17 z , 19 y z - 20 x + 1] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 3 2 G := [12 x y z - 5 y z - 17 y z, -3 x y - 17 x z + 19 y , 2 -4 x z + 12 x y + 17 x z] > Problem := [F,G]; Problem := [ 2 3 2 4 2 2 2 2 2 [18 y z - 5 z + 16 z , -8 y - 7 x - 17 z , 19 y z - 20 x + 1], [ 2 3 2 3 2 12 x y z - 5 y z - 17 y z, -3 x y - 17 x z + 19 y , 2 -4 x z + 12 x y + 17 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.31 memory used=25.4MB, alloc=32.3MB, time=0.82 memory used=46.2MB, alloc=32.3MB, time=1.29 memory used=60.2MB, alloc=32.3MB, time=1.41 memory used=83.4MB, alloc=33.3MB, time=2.62 memory used=97.6MB, alloc=33.3MB, time=2.71 memory used=109.2MB, alloc=33.3MB, time=2.77 memory used=119.1MB, alloc=33.3MB, time=2.82 memory used=139.9MB, alloc=33.3MB, time=3.16 memory used=164.3MB, alloc=61.3MB, time=3.69 memory used=203.9MB, alloc=61.3MB, time=4.49 memory used=241.4MB, alloc=61.3MB, time=5.39 memory used=283.2MB, alloc=61.3MB, time=6.52 memory used=306.1MB, alloc=61.3MB, time=6.69 memory used=340.1MB, alloc=61.3MB, time=7.16 memory used=374.7MB, alloc=61.3MB, time=7.83 memory used=399.2MB, alloc=61.3MB, time=8.00 memory used=426.9MB, alloc=61.3MB, time=8.91 memory used=467.5MB, alloc=61.3MB, time=11.42 memory used=488.9MB, alloc=61.3MB, time=11.53 memory used=505.2MB, alloc=85.3MB, time=11.66 memory used=546.9MB, alloc=85.3MB, time=11.83 memory used=575.5MB, alloc=85.3MB, time=11.95 memory used=613.8MB, alloc=85.3MB, time=12.18 memory used=663.3MB, alloc=85.3MB, time=12.96 memory used=729.4MB, alloc=93.4MB, time=14.75 memory used=775.9MB, alloc=93.4MB, time=15.39 memory used=841.1MB, alloc=93.4MB, time=16.92 memory used=897.2MB, alloc=93.4MB, time=17.93 memory used=943.2MB, alloc=93.4MB, time=18.72 memory used=983.0MB, alloc=93.4MB, time=19.04 memory used=1014.0MB, alloc=93.4MB, time=19.21 memory used=1064.5MB, alloc=93.4MB, time=24.02 memory used=1093.0MB, alloc=93.4MB, time=24.20 memory used=1125.0MB, alloc=93.4MB, time=24.37 memory used=1180.7MB, alloc=93.4MB, time=25.47 memory used=1242.3MB, alloc=117.4MB, time=26.59 memory used=1304.8MB, alloc=373.4MB, time=27.86 memory used=1390.9MB, alloc=397.4MB, time=29.92 memory used=1503.8MB, alloc=421.4MB, time=32.57 memory used=1619.3MB, alloc=445.4MB, time=35.18 memory used=1753.4MB, alloc=445.4MB, time=37.46 memory used=1844.2MB, alloc=445.4MB, time=41.54 memory used=1969.0MB, alloc=445.4MB, time=43.90 memory used=2098.5MB, alloc=469.4MB, time=45.85 memory used=2205.4MB, alloc=469.4MB, time=47.93 memory used=2305.3MB, alloc=469.4MB, time=49.91 memory used=2399.5MB, alloc=469.4MB, time=50.58 memory used=2495.5MB, alloc=469.4MB, time=51.60 memory used=2574.8MB, alloc=469.4MB, time=52.12 memory used=2686.0MB, alloc=469.4MB, time=66.32 memory used=2778.6MB, alloc=469.4MB, time=67.88 memory used=2859.8MB, alloc=469.4MB, time=68.35 memory used=2931.0MB, alloc=469.4MB, time=68.81 memory used=3022.1MB, alloc=469.4MB, time=69.27 memory used=3163.5MB, alloc=469.4MB, time=71.67 memory used=3241.7MB, alloc=469.4MB, time=72.15 memory used=3348.4MB, alloc=469.4MB, time=73.15 memory used=3448.3MB, alloc=469.4MB, time=75.14 memory used=3544.8MB, alloc=469.4MB, time=76.16 memory used=3677.6MB, alloc=469.4MB, time=79.18 memory used=3785.6MB, alloc=469.4MB, time=82.00 memory used=3931.0MB, alloc=469.4MB, time=85.63 memory used=4043.0MB, alloc=469.4MB, time=100.58 memory used=4121.8MB, alloc=469.4MB, time=101.12 memory used=4193.6MB, alloc=469.4MB, time=101.58 memory used=4264.3MB, alloc=469.4MB, time=102.02 memory used=4410.0MB, alloc=469.4MB, time=103.34 memory used=4552.2MB, alloc=469.4MB, time=105.91 memory used=4673.1MB, alloc=469.4MB, time=108.75 memory used=4798.8MB, alloc=493.4MB, time=113.66 memory used=4873.0MB, alloc=493.4MB, time=115.57 memory used=4947.5MB, alloc=493.4MB, time=117.60 memory used=5024.4MB, alloc=493.4MB, time=119.84 memory used=5088.7MB, alloc=493.4MB, time=121.81 memory used=5148.0MB, alloc=493.4MB, time=123.76 memory used=5203.6MB, alloc=493.4MB, time=125.46 memory used=5250.7MB, alloc=493.4MB, time=127.09 memory used=5304.2MB, alloc=493.4MB, time=128.80 memory used=5346.2MB, alloc=493.4MB, time=130.39 memory used=5516.2MB, alloc=517.4MB, time=135.74 memory used=5723.5MB, alloc=541.4MB, time=140.77 memory used=5945.3MB, alloc=541.4MB, time=147.15 memory used=6157.0MB, alloc=565.4MB, time=152.99 memory used=6296.8MB, alloc=565.4MB, time=156.88 memory used=6556.8MB, alloc=589.4MB, time=161.46 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428260153 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 3 3 3 2 2 2 F := [16 z + 19 z , 4 x z - 12 x z - 8 y z , 9 x y - 11 x y + z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; G := [ 3 2 2 2 3 3 3 2 2 -2 x y - 16 x y + 7 y , -9 x y z + 2 x z - 5 y , -17 x y - 2 x z - z ] > Problem := [F,G]; 4 2 3 3 3 2 2 2 Problem := [[16 z + 19 z , 4 x z - 12 x z - 8 y z , 9 x y - 11 x y + z], [ 3 2 2 2 3 3 3 2 2 -2 x y - 16 x y + 7 y , -9 x y z + 2 x z - 5 y , -17 x y - 2 x z - z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.31 memory used=26.2MB, alloc=32.3MB, time=0.88 memory used=47.5MB, alloc=32.3MB, time=1.43 memory used=66.9MB, alloc=32.3MB, time=1.93 memory used=85.6MB, alloc=56.3MB, time=2.44 memory used=126.4MB, alloc=60.3MB, time=3.49 memory used=166.9MB, alloc=92.3MB, time=4.56 memory used=231.1MB, alloc=92.3MB, time=6.15 memory used=294.7MB, alloc=116.3MB, time=7.78 memory used=373.1MB, alloc=372.3MB, time=9.84 memory used=457.8MB, alloc=396.3MB, time=12.09 memory used=566.6MB, alloc=420.3MB, time=14.95 memory used=691.1MB, alloc=420.3MB, time=18.24 memory used=819.8MB, alloc=444.3MB, time=21.11 memory used=947.1MB, alloc=468.3MB, time=24.43 memory used=1060.2MB, alloc=468.3MB, time=27.27 memory used=1164.8MB, alloc=468.3MB, time=30.01 memory used=1270.2MB, alloc=492.3MB, time=32.65 memory used=1388.2MB, alloc=492.3MB, time=35.98 memory used=1470.6MB, alloc=492.3MB, time=38.20 memory used=1557.3MB, alloc=492.3MB, time=40.71 memory used=1646.6MB, alloc=492.3MB, time=43.32 memory used=1719.6MB, alloc=492.3MB, time=45.44 memory used=1796.8MB, alloc=492.3MB, time=47.91 memory used=1881.0MB, alloc=492.3MB, time=50.54 memory used=1944.4MB, alloc=492.3MB, time=52.58 memory used=2011.4MB, alloc=492.3MB, time=54.49 memory used=2076.9MB, alloc=492.3MB, time=56.46 memory used=2134.9MB, alloc=492.3MB, time=58.19 memory used=2192.1MB, alloc=492.3MB, time=59.99 memory used=2249.7MB, alloc=492.3MB, time=62.18 memory used=2298.4MB, alloc=516.3MB, time=63.76 memory used=2347.5MB, alloc=516.3MB, time=65.44 memory used=2389.3MB, alloc=516.3MB, time=66.85 memory used=2603.2MB, alloc=540.3MB, time=72.41 memory used=2804.8MB, alloc=564.3MB, time=78.34 memory used=2981.9MB, alloc=564.3MB, time=83.21 memory used=3187.4MB, alloc=588.3MB, time=89.15 memory used=3366.6MB, alloc=612.3MB, time=94.95 memory used=3531.4MB, alloc=636.3MB, time=100.28 memory used=3698.5MB, alloc=636.3MB, time=105.66 memory used=3837.8MB, alloc=636.3MB, time=110.16 memory used=3983.4MB, alloc=660.3MB, time=114.95 memory used=4125.9MB, alloc=660.3MB, time=119.58 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428260453 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 3 F := [-x y z + 20 x y z + 10 x z , 5 x y z + 17 x y z - 15 z , 2 -19 x z + 12 x y - 20] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 3 3 2 2 3 G := [2 x y - 3 x y z - 10 y , 2 x z - 13 y z - 3 y z, 11 x y + 3 z ] > Problem := [F,G]; 2 2 2 2 3 Problem := [[-x y z + 20 x y z + 10 x z , 5 x y z + 17 x y z - 15 z , 2 -19 x z + 12 x y - 20], 3 2 3 3 3 2 2 3 [2 x y - 3 x y z - 10 y , 2 x z - 13 y z - 3 y z, 11 x y + 3 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.32 memory used=27.1MB, alloc=32.3MB, time=0.90 memory used=47.5MB, alloc=32.3MB, time=1.43 memory used=66.0MB, alloc=56.3MB, time=1.93 memory used=106.7MB, alloc=60.3MB, time=3.00 memory used=145.1MB, alloc=84.3MB, time=4.02 memory used=205.7MB, alloc=92.3MB, time=5.68 memory used=266.4MB, alloc=116.3MB, time=7.32 memory used=345.1MB, alloc=116.3MB, time=9.38 memory used=426.3MB, alloc=396.3MB, time=11.78 memory used=534.0MB, alloc=396.3MB, time=14.74 memory used=640.2MB, alloc=420.3MB, time=17.81 memory used=769.3MB, alloc=444.3MB, time=21.65 memory used=923.1MB, alloc=444.3MB, time=26.06 memory used=1070.0MB, alloc=468.3MB, time=30.63 memory used=1220.2MB, alloc=468.3MB, time=34.78 memory used=1374.8MB, alloc=492.3MB, time=38.95 memory used=1491.1MB, alloc=492.3MB, time=42.43 memory used=1617.0MB, alloc=516.3MB, time=46.66 memory used=1735.9MB, alloc=516.3MB, time=50.26 memory used=1859.2MB, alloc=516.3MB, time=54.11 memory used=1978.4MB, alloc=540.3MB, time=58.00 memory used=2078.1MB, alloc=540.3MB, time=61.34 memory used=2160.5MB, alloc=540.3MB, time=64.09 memory used=2252.3MB, alloc=540.3MB, time=67.21 memory used=2331.7MB, alloc=540.3MB, time=69.82 memory used=2388.5MB, alloc=540.3MB, time=71.54 memory used=2475.5MB, alloc=540.3MB, time=74.81 memory used=2562.7MB, alloc=540.3MB, time=78.08 memory used=2631.2MB, alloc=540.3MB, time=80.68 memory used=2687.2MB, alloc=564.3MB, time=82.72 memory used=2761.3MB, alloc=564.3MB, time=85.89 memory used=2835.8MB, alloc=564.3MB, time=88.98 memory used=2881.8MB, alloc=564.3MB, time=90.90 memory used=3085.4MB, alloc=588.3MB, time=97.29 memory used=3287.1MB, alloc=612.3MB, time=103.68 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428260753 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 3 2 F := [-8 y z - 13 x z - 20 y , -20 x y z - y - 11, -2 x + 8 x y - 16] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 4 G := [-11 x y z - 20 x y - 12 y , -15 x y z + 15 x y z + 12 z , 3 2 2 -10 x z + 2 x y z + 16 z ] > Problem := [F,G]; Problem := [ 3 2 2 2 2 3 2 [-8 y z - 13 x z - 20 y , -20 x y z - y - 11, -2 x + 8 x y - 16], [ 2 2 2 2 4 -11 x y z - 20 x y - 12 y , -15 x y z + 15 x y z + 12 z , 3 2 2 -10 x z + 2 x y z + 16 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.31 memory used=26.4MB, alloc=32.3MB, time=0.86 memory used=47.9MB, alloc=32.3MB, time=1.41 memory used=67.3MB, alloc=56.3MB, time=1.95 memory used=107.1MB, alloc=60.3MB, time=2.99 memory used=145.6MB, alloc=60.3MB, time=3.98 memory used=183.4MB, alloc=84.3MB, time=5.00 memory used=230.1MB, alloc=84.3MB, time=6.23 memory used=290.0MB, alloc=92.3MB, time=7.80 memory used=345.8MB, alloc=116.3MB, time=9.32 memory used=420.2MB, alloc=116.3MB, time=11.24 memory used=490.8MB, alloc=396.3MB, time=13.02 memory used=595.4MB, alloc=396.3MB, time=15.72 memory used=698.8MB, alloc=420.3MB, time=18.52 memory used=825.6MB, alloc=444.3MB, time=21.92 memory used=957.5MB, alloc=444.3MB, time=25.28 memory used=1092.6MB, alloc=468.3MB, time=29.02 memory used=1235.7MB, alloc=468.3MB, time=32.12 memory used=1346.6MB, alloc=468.3MB, time=35.10 memory used=1482.6MB, alloc=468.3MB, time=37.53 memory used=1606.7MB, alloc=492.3MB, time=39.89 memory used=1733.1MB, alloc=492.3MB, time=42.59 memory used=1852.6MB, alloc=492.3MB, time=45.92 memory used=1950.1MB, alloc=492.3MB, time=48.76 memory used=2060.1MB, alloc=492.3MB, time=52.21 memory used=2162.5MB, alloc=492.3MB, time=55.29 memory used=2235.1MB, alloc=492.3MB, time=57.59 memory used=2310.8MB, alloc=516.3MB, time=60.04 memory used=2403.6MB, alloc=516.3MB, time=63.13 memory used=2478.1MB, alloc=516.3MB, time=65.37 memory used=2547.4MB, alloc=516.3MB, time=67.19 memory used=2610.1MB, alloc=516.3MB, time=69.32 memory used=2669.4MB, alloc=516.3MB, time=71.27 memory used=2734.2MB, alloc=516.3MB, time=73.69 memory used=2799.6MB, alloc=516.3MB, time=76.00 memory used=2859.6MB, alloc=516.3MB, time=78.21 memory used=2894.4MB, alloc=516.3MB, time=79.36 memory used=2946.4MB, alloc=516.3MB, time=81.46 memory used=3000.6MB, alloc=516.3MB, time=83.44 memory used=3088.4MB, alloc=516.3MB, time=84.29 memory used=3192.3MB, alloc=516.3MB, time=86.09 memory used=3250.0MB, alloc=516.3MB, time=87.71 memory used=3449.3MB, alloc=540.3MB, time=92.68 memory used=3557.4MB, alloc=540.3MB, time=93.73 memory used=3668.3MB, alloc=540.3MB, time=95.25 memory used=3778.2MB, alloc=540.3MB, time=96.24 memory used=3899.7MB, alloc=540.3MB, time=98.07 memory used=4014.3MB, alloc=540.3MB, time=99.42 memory used=4185.0MB, alloc=564.3MB, time=102.60 memory used=4444.2MB, alloc=564.3MB, time=109.42 memory used=4647.9MB, alloc=564.3MB, time=114.72 memory used=4762.7MB, alloc=564.3MB, time=115.69 memory used=4928.7MB, alloc=564.3MB, time=117.98 memory used=5129.8MB, alloc=564.3MB, time=122.16 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428261053 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 2 3 F := [15 x y + 9 y z - 15 x y , -x z + 6 z - 17 y, 3 2 2 3 -10 x y - 12 y z + 14 y z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; G := 2 2 3 2 2 2 2 2 [-14 x y z - 7 z + 8 z, -5 x y + 11 x y + 16 z , -8 y z + 4 y z - 4] > Problem := [F,G]; 3 3 2 2 2 3 Problem := [[15 x y + 9 y z - 15 x y , -x z + 6 z - 17 y, 3 2 2 3 -10 x y - 12 y z + 14 y z ], 2 2 3 2 2 2 2 2 [-14 x y z - 7 z + 8 z, -5 x y + 11 x y + 16 z , -8 y z + 4 y z - 4] ] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=25.7MB, alloc=32.3MB, time=0.85 memory used=45.9MB, alloc=56.3MB, time=1.35 memory used=90.2MB, alloc=60.3MB, time=2.30 memory used=142.2MB, alloc=68.7MB, time=3.18 memory used=200.9MB, alloc=68.7MB, time=4.04 memory used=255.7MB, alloc=68.7MB, time=4.88 memory used=295.8MB, alloc=68.7MB, time=5.85 memory used=329.4MB, alloc=68.7MB, time=6.31 memory used=358.4MB, alloc=68.7MB, time=6.53 memory used=396.7MB, alloc=68.7MB, time=7.33 memory used=440.5MB, alloc=92.7MB, time=8.28 memory used=506.7MB, alloc=92.7MB, time=9.62 memory used=575.2MB, alloc=92.7MB, time=11.19 memory used=639.9MB, alloc=92.7MB, time=12.64 memory used=701.4MB, alloc=116.7MB, time=13.88 memory used=763.1MB, alloc=116.7MB, time=14.59 memory used=831.6MB, alloc=116.7MB, time=15.37 memory used=879.5MB, alloc=116.7MB, time=15.64 memory used=923.1MB, alloc=116.7MB, time=15.87 memory used=977.7MB, alloc=116.7MB, time=16.21 memory used=1024.0MB, alloc=116.7MB, time=16.46 memory used=1063.7MB, alloc=116.7MB, time=16.67 memory used=1113.7MB, alloc=116.7MB, time=17.58 memory used=1167.5MB, alloc=119.8MB, time=18.00 memory used=1212.3MB, alloc=119.8MB, time=18.21 memory used=1231.7MB, alloc=131.8MB, time=18.56 memory used=1254.9MB, alloc=131.8MB, time=18.72 memory used=1284.1MB, alloc=131.8MB, time=18.88 memory used=1315.9MB, alloc=131.8MB, time=19.05 memory used=1350.3MB, alloc=131.8MB, time=19.22 memory used=1387.2MB, alloc=131.8MB, time=19.38 memory used=1426.5MB, alloc=131.8MB, time=19.55 memory used=1445.2MB, alloc=131.8MB, time=19.68 memory used=1462.2MB, alloc=131.8MB, time=20.09 memory used=1514.2MB, alloc=131.8MB, time=20.39 memory used=1559.2MB, alloc=131.8MB, time=20.62 memory used=1613.9MB, alloc=131.8MB, time=20.97 memory used=1660.6MB, alloc=131.8MB, time=21.21 memory used=1701.4MB, alloc=131.8MB, time=21.42 memory used=1750.8MB, alloc=131.8MB, time=22.32 memory used=1801.6MB, alloc=131.8MB, time=22.59 memory used=1846.5MB, alloc=131.8MB, time=22.81 memory used=1900.5MB, alloc=131.8MB, time=23.15 memory used=1946.6MB, alloc=131.8MB, time=23.39 memory used=1987.4MB, alloc=131.8MB, time=23.61 memory used=2035.6MB, alloc=131.8MB, time=24.46 memory used=2090.1MB, alloc=131.8MB, time=24.92 memory used=2136.1MB, alloc=131.8MB, time=25.14 memory used=2157.6MB, alloc=131.8MB, time=25.48 memory used=2180.6MB, alloc=131.8MB, time=25.64 memory used=2209.7MB, alloc=131.8MB, time=25.81 memory used=2241.4MB, alloc=131.8MB, time=25.98 memory used=2275.6MB, alloc=131.8MB, time=26.14 memory used=2312.6MB, alloc=131.8MB, time=26.32 memory used=2352.2MB, alloc=131.8MB, time=26.50 memory used=2370.5MB, alloc=131.8MB, time=26.63 memory used=2393.9MB, alloc=131.8MB, time=27.10 memory used=2458.5MB, alloc=131.8MB, time=28.01 memory used=2503.4MB, alloc=131.8MB, time=28.24 memory used=2549.7MB, alloc=131.8MB, time=28.65 memory used=2600.4MB, alloc=131.8MB, time=29.04 memory used=2649.3MB, alloc=131.8MB, time=29.30 memory used=2694.1MB, alloc=131.8MB, time=29.65 memory used=2738.6MB, alloc=131.8MB, time=29.96 memory used=2796.2MB, alloc=131.8MB, time=33.51 memory used=2849.1MB, alloc=131.8MB, time=33.84 memory used=2895.2MB, alloc=131.8MB, time=34.09 memory used=2939.8MB, alloc=131.8MB, time=34.47 memory used=2983.1MB, alloc=131.8MB, time=34.76 memory used=3036.2MB, alloc=131.8MB, time=35.14 memory used=3077.1MB, alloc=131.8MB, time=35.35 memory used=3125.2MB, alloc=131.8MB, time=35.79 memory used=3183.2MB, alloc=131.8MB, time=39.44 memory used=3224.7MB, alloc=131.8MB, time=39.61 memory used=3276.0MB, alloc=131.8MB, time=39.99 memory used=3316.5MB, alloc=131.8MB, time=40.20 memory used=3365.3MB, alloc=131.8MB, time=40.64 memory used=3416.0MB, alloc=131.8MB, time=41.02 memory used=3459.5MB, alloc=131.8MB, time=41.24 memory used=3506.6MB, alloc=131.8MB, time=41.66 memory used=3553.0MB, alloc=131.8MB, time=43.83 memory used=3604.2MB, alloc=131.8MB, time=45.47 memory used=3653.8MB, alloc=131.8MB, time=45.93 memory used=3695.1MB, alloc=131.8MB, time=46.16 memory used=3734.3MB, alloc=131.8MB, time=46.51 memory used=3756.5MB, alloc=131.8MB, time=46.67 memory used=3781.3MB, alloc=131.8MB, time=46.82 memory used=3834.4MB, alloc=131.8MB, time=47.02 memory used=3933.4MB, alloc=131.8MB, time=48.59 memory used=4020.1MB, alloc=131.8MB, time=49.81 memory used=4103.1MB, alloc=131.8MB, time=51.20 memory used=4195.3MB, alloc=131.8MB, time=52.33 memory used=4252.7MB, alloc=131.8MB, time=54.07 memory used=4305.8MB, alloc=131.8MB, time=61.88 memory used=4360.5MB, alloc=131.8MB, time=62.27 memory used=4394.0MB, alloc=155.8MB, time=62.49 memory used=4466.9MB, alloc=155.8MB, time=63.20 memory used=4548.9MB, alloc=155.8MB, time=64.19 memory used=4615.0MB, alloc=155.8MB, time=64.56 memory used=4666.5MB, alloc=155.8MB, time=64.82 memory used=4733.1MB, alloc=155.8MB, time=65.24 memory used=4787.7MB, alloc=155.8MB, time=65.52 memory used=4848.6MB, alloc=155.8MB, time=66.52 memory used=4910.9MB, alloc=155.8MB, time=66.93 memory used=4957.7MB, alloc=155.8MB, time=67.34 memory used=4983.7MB, alloc=155.8MB, time=67.54 memory used=5012.4MB, alloc=155.8MB, time=67.76 memory used=5043.6MB, alloc=155.8MB, time=67.95 memory used=5077.3MB, alloc=155.8MB, time=68.14 memory used=5113.6MB, alloc=155.8MB, time=68.35 memory used=5151.9MB, alloc=155.8MB, time=68.55 memory used=5193.4MB, alloc=155.8MB, time=69.08 memory used=5250.6MB, alloc=155.8MB, time=69.39 memory used=5308.6MB, alloc=155.8MB, time=69.77 memory used=5369.7MB, alloc=155.8MB, time=70.10 memory used=5419.0MB, alloc=155.8MB, time=70.36 memory used=5485.8MB, alloc=155.8MB, time=71.36 memory used=5542.8MB, alloc=155.8MB, time=71.65 memory used=5606.1MB, alloc=155.8MB, time=72.04 memory used=5664.2MB, alloc=155.8MB, time=72.36 memory used=5712.0MB, alloc=155.8MB, time=72.71 memory used=5788.3MB, alloc=155.8MB, time=74.31 memory used=5855.1MB, alloc=155.8MB, time=74.70 memory used=5913.3MB, alloc=155.8MB, time=75.11 memory used=5966.6MB, alloc=155.8MB, time=75.39 memory used=6034.0MB, alloc=155.8MB, time=79.09 memory used=6096.1MB, alloc=155.8MB, time=79.47 memory used=6149.2MB, alloc=155.8MB, time=79.75 memory used=6212.3MB, alloc=155.8MB, time=80.17 memory used=6266.5MB, alloc=155.8MB, time=81.55 memory used=6330.6MB, alloc=155.8MB, time=84.11 memory used=6393.4MB, alloc=155.8MB, time=84.51 memory used=6452.6MB, alloc=155.8MB, time=84.91 memory used=6509.9MB, alloc=155.8MB, time=85.22 memory used=6574.2MB, alloc=155.8MB, time=88.91 memory used=6639.5MB, alloc=155.8MB, time=89.44 memory used=6733.7MB, alloc=411.8MB, time=90.99 memory used=6850.2MB, alloc=411.8MB, time=92.72 memory used=6953.1MB, alloc=411.8MB, time=95.23 memory used=7010.1MB, alloc=411.8MB, time=97.42 memory used=7086.7MB, alloc=411.8MB, time=103.79 memory used=7132.8MB, alloc=411.8MB, time=104.05 memory used=7187.9MB, alloc=411.8MB, time=104.48 memory used=7276.5MB, alloc=411.8MB, time=106.33 memory used=7340.1MB, alloc=411.8MB, time=107.04 memory used=7410.1MB, alloc=411.8MB, time=108.03 memory used=7468.0MB, alloc=435.8MB, time=108.55 memory used=7537.8MB, alloc=435.8MB, time=108.91 memory used=7592.2MB, alloc=435.8MB, time=109.22 memory used=7660.8MB, alloc=435.8MB, time=109.55 memory used=7739.0MB, alloc=435.8MB, time=110.33 memory used=7806.4MB, alloc=435.8MB, time=110.69 memory used=7864.3MB, alloc=435.8MB, time=111.01 memory used=7936.2MB, alloc=435.8MB, time=112.07 memory used=8021.4MB, alloc=435.8MB, time=113.31 memory used=8093.2MB, alloc=435.8MB, time=113.67 memory used=8145.8MB, alloc=435.8MB, time=113.98 memory used=8213.7MB, alloc=435.8MB, time=114.29 memory used=8291.2MB, alloc=435.8MB, time=115.09 memory used=8361.1MB, alloc=435.8MB, time=115.45 memory used=8415.5MB, alloc=435.8MB, time=115.75 memory used=8484.0MB, alloc=435.8MB, time=116.06 memory used=8572.3MB, alloc=435.8MB, time=117.97 memory used=8637.1MB, alloc=435.8MB, time=118.33 memory used=8694.8MB, alloc=435.8MB, time=118.63 memory used=8756.6MB, alloc=435.8MB, time=118.95 memory used=8838.6MB, alloc=435.8MB, time=119.80 memory used=8906.5MB, alloc=435.8MB, time=120.16 memory used=8961.5MB, alloc=435.8MB, time=120.47 memory used=9025.6MB, alloc=435.8MB, time=120.79 memory used=9097.3MB, alloc=435.8MB, time=121.86 memory used=9171.9MB, alloc=435.8MB, time=122.92 memory used=9239.6MB, alloc=435.8MB, time=123.29 memory used=9367.8MB, alloc=435.8MB, time=124.04 memory used=9492.5MB, alloc=435.8MB, time=124.49 memory used=9614.2MB, alloc=435.8MB, time=124.92 memory used=9715.9MB, alloc=435.8MB, time=126.58 memory used=9790.5MB, alloc=435.8MB, time=127.28 memory used=9855.9MB, alloc=435.8MB, time=127.64 memory used=9914.6MB, alloc=435.8MB, time=127.95 memory used=9993.5MB, alloc=435.8MB, time=128.70 memory used=10060.3MB, alloc=435.8MB, time=129.06 memory used=10116.1MB, alloc=435.8MB, time=129.38 memory used=10219.8MB, alloc=435.8MB, time=137.28 memory used=10293.9MB, alloc=435.8MB, time=137.57 memory used=10387.3MB, alloc=435.8MB, time=139.40 memory used=10450.6MB, alloc=435.8MB, time=139.74 memory used=10510.7MB, alloc=435.8MB, time=140.06 memory used=10588.8MB, alloc=435.8MB, time=140.85 memory used=10654.6MB, alloc=435.8MB, time=141.20 memory used=10711.1MB, alloc=435.8MB, time=141.51 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428261353 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 3 3 4 2 F := [12 x y + 19 y z - 10 z, -18 y z + 9 y z + 2 x , 5 x + x + 12] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 2 2 G := [16 x z + 16 x z - 10 x y , -4 x z + 9 x y z - 4 y z, 3 2 2 3 -5 x z + 13 x z - 17 x ] > Problem := [F,G]; Problem := [ 2 2 3 2 2 3 3 4 2 [12 x y + 19 y z - 10 z, -18 y z + 9 y z + 2 x , 5 x + x + 12], [ 3 2 2 2 2 2 2 16 x z + 16 x z - 10 x y , -4 x z + 9 x y z - 4 y z, 3 2 2 3 -5 x z + 13 x z - 17 x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.31 memory used=26.2MB, alloc=32.3MB, time=0.87 memory used=47.0MB, alloc=32.3MB, time=1.40 memory used=66.4MB, alloc=60.3MB, time=1.94 memory used=107.3MB, alloc=60.3MB, time=2.93 memory used=139.8MB, alloc=60.3MB, time=3.63 memory used=185.7MB, alloc=68.3MB, time=4.62 memory used=226.5MB, alloc=92.3MB, time=5.60 memory used=292.4MB, alloc=92.3MB, time=7.21 memory used=359.5MB, alloc=372.3MB, time=8.82 memory used=449.8MB, alloc=372.3MB, time=10.96 memory used=537.0MB, alloc=396.3MB, time=13.17 memory used=652.7MB, alloc=396.3MB, time=15.85 memory used=755.9MB, alloc=420.3MB, time=17.72 memory used=850.7MB, alloc=420.3MB, time=18.76 memory used=978.8MB, alloc=420.3MB, time=20.81 memory used=1110.5MB, alloc=444.3MB, time=23.10 memory used=1248.7MB, alloc=444.3MB, time=25.24 memory used=1347.7MB, alloc=444.3MB, time=26.25 memory used=1474.4MB, alloc=444.3MB, time=28.55 memory used=1606.7MB, alloc=444.3MB, time=30.78 memory used=1702.6MB, alloc=444.3MB, time=33.19 memory used=1808.0MB, alloc=468.3MB, time=35.81 memory used=1944.0MB, alloc=468.3MB, time=37.77 memory used=2053.3MB, alloc=468.3MB, time=39.00 memory used=2164.8MB, alloc=468.3MB, time=40.99 memory used=2255.4MB, alloc=468.3MB, time=42.92 memory used=2333.6MB, alloc=468.3MB, time=44.90 memory used=2413.0MB, alloc=468.3MB, time=46.98 memory used=2508.8MB, alloc=492.3MB, time=49.50 memory used=2599.6MB, alloc=492.3MB, time=51.95 memory used=2672.2MB, alloc=492.3MB, time=53.93 memory used=2741.5MB, alloc=492.3MB, time=55.72 memory used=2840.7MB, alloc=492.3MB, time=57.66 memory used=2963.2MB, alloc=492.3MB, time=60.65 memory used=3069.1MB, alloc=492.3MB, time=62.93 memory used=3177.0MB, alloc=492.3MB, time=64.72 memory used=3277.8MB, alloc=492.3MB, time=66.44 memory used=3381.1MB, alloc=492.3MB, time=68.03 memory used=3480.8MB, alloc=492.3MB, time=70.27 memory used=3554.6MB, alloc=492.3MB, time=72.84 memory used=3669.0MB, alloc=516.3MB, time=75.41 memory used=3762.5MB, alloc=516.3MB, time=77.93 memory used=3844.7MB, alloc=516.3MB, time=79.71 memory used=3951.2MB, alloc=516.3MB, time=81.45 memory used=4090.5MB, alloc=516.3MB, time=83.54 memory used=4154.9MB, alloc=516.3MB, time=85.06 memory used=4227.0MB, alloc=516.3MB, time=86.63 memory used=4337.6MB, alloc=516.3MB, time=87.95 memory used=4442.7MB, alloc=516.3MB, time=89.21 memory used=4539.6MB, alloc=516.3MB, time=90.04 memory used=4621.2MB, alloc=516.3MB, time=90.75 memory used=4713.9MB, alloc=516.3MB, time=91.45 memory used=4865.7MB, alloc=516.3MB, time=92.73 memory used=4954.2MB, alloc=516.3MB, time=93.46 memory used=5103.2MB, alloc=516.3MB, time=95.74 memory used=5171.3MB, alloc=540.3MB, time=98.83 memory used=5291.7MB, alloc=540.3MB, time=100.45 memory used=5396.2MB, alloc=540.3MB, time=101.23 memory used=5588.6MB, alloc=540.3MB, time=102.41 memory used=5756.7MB, alloc=540.3MB, time=103.88 memory used=5876.7MB, alloc=540.3MB, time=104.76 memory used=5960.6MB, alloc=540.3MB, time=105.47 memory used=6062.1MB, alloc=540.3MB, time=106.20 memory used=6184.9MB, alloc=540.3MB, time=106.94 memory used=6367.0MB, alloc=540.3MB, time=117.13 memory used=6476.9MB, alloc=540.3MB, time=118.00 memory used=6569.3MB, alloc=540.3MB, time=118.74 memory used=6684.8MB, alloc=540.3MB, time=119.56 memory used=6932.4MB, alloc=540.3MB, time=120.72 memory used=7074.1MB, alloc=540.3MB, time=121.61 memory used=7234.9MB, alloc=540.3MB, time=122.53 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428261653 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 3 F := [-8 y z + 15 y + 1, 16 x y z + 12 x z - 4 x y z, 3 3 2 -20 x y - 5 x z - 4 x y z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 4 4 2 2 2 2 2 G := [8 z - 6 x z - 11 z, 7 x - 20 z + 11 x y , 16 x z - 11 x z - 19 y ] > Problem := [F,G]; 2 2 3 2 3 Problem := [[-8 y z + 15 y + 1, 16 x y z + 12 x z - 4 x y z, 3 3 2 -20 x y - 5 x z - 4 x y z], 3 4 4 2 2 2 2 2 [8 z - 6 x z - 11 z, 7 x - 20 z + 11 x y , 16 x z - 11 x z - 19 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.30 memory used=26.3MB, alloc=32.3MB, time=0.87 memory used=45.3MB, alloc=56.3MB, time=1.37 memory used=85.7MB, alloc=60.3MB, time=2.40 memory used=127.7MB, alloc=68.3MB, time=3.46 memory used=171.4MB, alloc=92.3MB, time=4.53 memory used=244.8MB, alloc=92.3MB, time=5.90 memory used=311.8MB, alloc=116.3MB, time=7.51 memory used=384.2MB, alloc=116.3MB, time=9.29 memory used=442.5MB, alloc=372.3MB, time=10.64 memory used=517.3MB, alloc=372.3MB, time=13.60 memory used=554.0MB, alloc=372.3MB, time=13.85 memory used=604.0MB, alloc=372.3MB, time=14.41 memory used=644.2MB, alloc=372.3MB, time=14.64 memory used=700.0MB, alloc=372.3MB, time=18.01 memory used=742.1MB, alloc=372.3MB, time=18.25 memory used=779.2MB, alloc=372.3MB, time=18.62 memory used=830.0MB, alloc=372.3MB, time=19.02 memory used=870.6MB, alloc=372.3MB, time=19.25 memory used=933.9MB, alloc=396.3MB, time=20.15 memory used=1006.2MB, alloc=396.3MB, time=22.54 memory used=1102.3MB, alloc=396.3MB, time=23.79 memory used=1198.2MB, alloc=396.3MB, time=25.44 memory used=1327.6MB, alloc=396.3MB, time=27.47 memory used=1445.3MB, alloc=420.3MB, time=29.90 memory used=1591.8MB, alloc=420.3MB, time=32.71 memory used=1726.7MB, alloc=444.3MB, time=35.68 memory used=1857.8MB, alloc=444.3MB, time=38.55 memory used=1971.3MB, alloc=468.3MB, time=41.33 memory used=2099.3MB, alloc=492.3MB, time=44.01 memory used=2255.1MB, alloc=492.3MB, time=46.88 memory used=2381.7MB, alloc=492.3MB, time=49.21 memory used=2474.5MB, alloc=492.3MB, time=51.52 memory used=2565.4MB, alloc=492.3MB, time=53.67 memory used=2668.4MB, alloc=516.3MB, time=56.68 memory used=2763.2MB, alloc=516.3MB, time=59.55 memory used=2828.1MB, alloc=516.3MB, time=61.41 memory used=2901.8MB, alloc=516.3MB, time=63.52 memory used=2984.7MB, alloc=516.3MB, time=65.65 memory used=3054.3MB, alloc=516.3MB, time=67.49 memory used=3117.6MB, alloc=540.3MB, time=69.11 memory used=3202.2MB, alloc=540.3MB, time=71.42 memory used=3269.5MB, alloc=540.3MB, time=73.37 memory used=3316.5MB, alloc=540.3MB, time=74.65 memory used=3370.0MB, alloc=540.3MB, time=76.55 memory used=3423.3MB, alloc=540.3MB, time=78.69 memory used=3648.2MB, alloc=564.3MB, time=84.23 memory used=3860.8MB, alloc=588.3MB, time=88.93 memory used=3985.9MB, alloc=612.3MB, time=90.60 memory used=4155.8MB, alloc=612.3MB, time=103.94 memory used=4372.5MB, alloc=612.3MB, time=106.19 memory used=4526.2MB, alloc=612.3MB, time=109.08 memory used=4654.5MB, alloc=612.3MB, time=110.21 memory used=4808.4MB, alloc=612.3MB, time=112.81 memory used=4936.4MB, alloc=612.3MB, time=113.89 memory used=5173.6MB, alloc=612.3MB, time=132.95 memory used=5431.4MB, alloc=612.3MB, time=135.45 memory used=5743.2MB, alloc=612.3MB, time=137.22 memory used=6019.6MB, alloc=612.3MB, time=138.48 memory used=6183.8MB, alloc=612.3MB, time=139.51 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428261953 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 3 2 F := [13 x y - 9 z + 8, -13 x - 4 z + 2 y, -5 x y + 18 y z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 3 3 G := [6 x y - 10 x z - 8 x y z, 3 x y z - 3 x z + 19 z , 4 2 20 z - 9 x y + 13 x y z] > Problem := [F,G]; 2 3 2 3 2 Problem := [[13 x y - 9 z + 8, -13 x - 4 z + 2 y, -5 x y + 18 y z ], [ 3 3 2 3 3 6 x y - 10 x z - 8 x y z, 3 x y z - 3 x z + 19 z , 4 2 20 z - 9 x y + 13 x y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.4MB, alloc=32.3MB, time=0.89 memory used=45.6MB, alloc=56.3MB, time=1.39 memory used=87.1MB, alloc=60.3MB, time=2.45 memory used=126.7MB, alloc=60.3MB, time=3.43 memory used=163.9MB, alloc=84.3MB, time=4.35 memory used=229.8MB, alloc=92.3MB, time=6.00 memory used=297.2MB, alloc=116.3MB, time=7.52 memory used=364.4MB, alloc=116.3MB, time=9.17 memory used=432.9MB, alloc=372.3MB, time=10.77 memory used=516.1MB, alloc=396.3MB, time=12.96 memory used=624.9MB, alloc=420.3MB, time=15.70 memory used=744.0MB, alloc=420.3MB, time=18.54 memory used=869.4MB, alloc=444.3MB, time=21.86 memory used=1003.6MB, alloc=468.3MB, time=24.62 memory used=1109.8MB, alloc=468.3MB, time=27.10 memory used=1213.0MB, alloc=468.3MB, time=29.69 memory used=1311.4MB, alloc=492.3MB, time=32.48 memory used=1396.9MB, alloc=492.3MB, time=34.57 memory used=1468.5MB, alloc=492.3MB, time=36.60 memory used=1550.0MB, alloc=492.3MB, time=38.63 memory used=1631.8MB, alloc=492.3MB, time=41.28 memory used=1689.3MB, alloc=492.3MB, time=43.05 memory used=1745.7MB, alloc=516.3MB, time=44.48 memory used=1801.8MB, alloc=516.3MB, time=46.59 memory used=1853.8MB, alloc=516.3MB, time=48.34 memory used=2045.8MB, alloc=540.3MB, time=52.95 memory used=2243.1MB, alloc=564.3MB, time=57.89 memory used=2432.0MB, alloc=588.3MB, time=63.40 memory used=2582.2MB, alloc=612.3MB, time=67.67 memory used=2738.6MB, alloc=636.3MB, time=71.91 memory used=2893.1MB, alloc=636.3MB, time=76.56 memory used=3037.9MB, alloc=636.3MB, time=80.42 memory used=3157.0MB, alloc=636.3MB, time=83.74 memory used=3261.4MB, alloc=636.3MB, time=86.63 memory used=3376.0MB, alloc=660.3MB, time=90.52 memory used=3463.7MB, alloc=660.3MB, time=93.95 memory used=3549.4MB, alloc=660.3MB, time=97.13 memory used=3873.9MB, alloc=684.3MB, time=106.35 memory used=4184.8MB, alloc=708.3MB, time=112.52 memory used=4564.3MB, alloc=732.3MB, time=122.23 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428262253 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 3 2 2 2 3 F := [15 x - 15 x z + 4 y , -3 y - 3 y z - 2 x, 3 y z + x y z - 3 y ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 4 G := [-10 x y z + 18 z + 4, 15 x y z - x y + 18 y, 10 x y - 11 z ] > Problem := [F,G]; Problem := [ 3 2 3 3 2 2 2 3 [15 x - 15 x z + 4 y , -3 y - 3 y z - 2 x, 3 y z + x y z - 3 y ], 3 3 4 [-10 x y z + 18 z + 4, 15 x y z - x y + 18 y, 10 x y - 11 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=24.3MB, alloc=32.3MB, time=0.76 memory used=46.7MB, alloc=36.3MB, time=1.26 memory used=66.9MB, alloc=60.3MB, time=1.74 memory used=116.2MB, alloc=61.9MB, time=2.48 memory used=145.8MB, alloc=61.9MB, time=2.59 memory used=167.8MB, alloc=61.9MB, time=2.68 memory used=196.6MB, alloc=61.9MB, time=2.79 memory used=246.3MB, alloc=61.9MB, time=3.53 memory used=289.1MB, alloc=61.9MB, time=4.45 memory used=332.1MB, alloc=61.9MB, time=5.29 memory used=366.1MB, alloc=61.9MB, time=5.73 memory used=415.2MB, alloc=93.9MB, time=6.77 memory used=487.0MB, alloc=93.9MB, time=8.02 memory used=551.9MB, alloc=93.9MB, time=9.56 memory used=607.4MB, alloc=117.9MB, time=10.41 memory used=668.7MB, alloc=117.9MB, time=10.92 memory used=721.0MB, alloc=117.9MB, time=11.29 memory used=765.4MB, alloc=117.9MB, time=11.53 memory used=818.6MB, alloc=117.9MB, time=12.04 memory used=879.1MB, alloc=117.9MB, time=12.57 memory used=934.9MB, alloc=117.9MB, time=13.05 memory used=984.0MB, alloc=117.9MB, time=13.30 memory used=1036.4MB, alloc=117.9MB, time=13.77 memory used=1085.8MB, alloc=117.9MB, time=14.04 memory used=1138.3MB, alloc=117.9MB, time=18.95 memory used=1214.0MB, alloc=117.9MB, time=43.93 memory used=1314.0MB, alloc=117.9MB, time=45.48 memory used=1376.2MB, alloc=117.9MB, time=46.07 memory used=1425.1MB, alloc=117.9MB, time=46.32 memory used=1468.2MB, alloc=117.9MB, time=46.54 memory used=1504.1MB, alloc=117.9MB, time=46.74 memory used=1544.0MB, alloc=117.9MB, time=46.95 memory used=1589.2MB, alloc=117.9MB, time=47.15 memory used=1639.6MB, alloc=117.9MB, time=47.36 memory used=1695.3MB, alloc=117.9MB, time=47.58 memory used=1740.4MB, alloc=117.9MB, time=47.77 memory used=1770.6MB, alloc=117.9MB, time=47.96 memory used=1802.3MB, alloc=117.9MB, time=48.13 memory used=1835.7MB, alloc=117.9MB, time=48.29 memory used=1870.7MB, alloc=117.9MB, time=48.46 memory used=1907.2MB, alloc=117.9MB, time=48.63 memory used=1945.3MB, alloc=117.9MB, time=48.80 memory used=1985.9MB, alloc=117.9MB, time=48.98 memory used=2029.0MB, alloc=117.9MB, time=49.14 memory used=2074.2MB, alloc=117.9MB, time=49.32 memory used=2121.1MB, alloc=117.9MB, time=49.50 memory used=2170.4MB, alloc=117.9MB, time=49.69 memory used=2223.6MB, alloc=117.9MB, time=49.88 memory used=2278.5MB, alloc=117.9MB, time=50.06 memory used=2315.9MB, alloc=131.8MB, time=50.24 memory used=2326.2MB, alloc=131.8MB, time=50.35 memory used=2336.9MB, alloc=131.8MB, time=50.48 memory used=2347.8MB, alloc=131.8MB, time=50.60 memory used=2359.1MB, alloc=131.8MB, time=50.73 memory used=2370.9MB, alloc=131.8MB, time=50.85 memory used=2383.2MB, alloc=131.8MB, time=50.99 memory used=2447.5MB, alloc=131.8MB, time=51.73 memory used=2495.4MB, alloc=131.8MB, time=51.97 memory used=2548.1MB, alloc=131.8MB, time=52.46 memory used=2595.4MB, alloc=131.8MB, time=52.69 memory used=2650.5MB, alloc=131.8MB, time=60.01 memory used=2722.9MB, alloc=131.8MB, time=82.68 memory used=2821.2MB, alloc=131.8MB, time=84.24 memory used=2880.2MB, alloc=131.8MB, time=84.74 memory used=2929.3MB, alloc=131.8MB, time=84.99 memory used=2971.4MB, alloc=131.8MB, time=85.22 memory used=3006.7MB, alloc=131.8MB, time=85.44 memory used=3046.7MB, alloc=131.8MB, time=85.66 memory used=3091.8MB, alloc=131.8MB, time=85.87 memory used=3140.9MB, alloc=131.8MB, time=86.10 memory used=3195.2MB, alloc=131.8MB, time=86.33 memory used=3241.3MB, alloc=131.8MB, time=86.55 memory used=3272.2MB, alloc=131.8MB, time=86.72 memory used=3303.9MB, alloc=131.8MB, time=86.89 memory used=3337.2MB, alloc=131.8MB, time=87.07 memory used=3372.2MB, alloc=131.8MB, time=87.24 memory used=3408.7MB, alloc=131.8MB, time=87.41 memory used=3446.7MB, alloc=131.8MB, time=87.59 memory used=3487.3MB, alloc=131.8MB, time=87.78 memory used=3529.0MB, alloc=131.8MB, time=87.97 memory used=3572.8MB, alloc=131.8MB, time=88.15 memory used=3619.7MB, alloc=131.8MB, time=88.35 memory used=3669.1MB, alloc=131.8MB, time=88.54 memory used=3721.2MB, alloc=131.8MB, time=88.74 memory used=3775.3MB, alloc=131.8MB, time=88.93 memory used=3817.8MB, alloc=131.8MB, time=89.10 memory used=3828.0MB, alloc=131.8MB, time=89.22 memory used=3838.7MB, alloc=131.8MB, time=89.36 memory used=3849.6MB, alloc=131.8MB, time=89.49 memory used=3860.7MB, alloc=131.8MB, time=89.63 memory used=3871.9MB, alloc=131.8MB, time=89.74 memory used=3884.0MB, alloc=131.8MB, time=89.87 memory used=3953.1MB, alloc=131.8MB, time=90.53 memory used=3993.3MB, alloc=131.8MB, time=90.73 memory used=4087.3MB, alloc=387.8MB, time=92.31 memory used=4199.5MB, alloc=387.8MB, time=102.06 memory used=4263.3MB, alloc=411.8MB, time=141.69 memory used=4369.3MB, alloc=411.8MB, time=143.95 memory used=4430.2MB, alloc=411.8MB, time=144.25 memory used=4484.9MB, alloc=411.8MB, time=144.53 memory used=4534.5MB, alloc=411.8MB, time=144.80 memory used=4591.8MB, alloc=411.8MB, time=145.08 memory used=4656.4MB, alloc=411.8MB, time=145.37 memory used=4729.7MB, alloc=411.8MB, time=145.65 memory used=4775.2MB, alloc=411.8MB, time=145.86 memory used=4817.8MB, alloc=411.8MB, time=146.07 memory used=4861.7MB, alloc=411.8MB, time=146.29 memory used=4908.9MB, alloc=411.8MB, time=146.50 memory used=4959.4MB, alloc=411.8MB, time=146.71 memory used=5012.8MB, alloc=411.8MB, time=146.93 memory used=5068.8MB, alloc=411.8MB, time=147.16 memory used=5128.2MB, alloc=411.8MB, time=147.37 memory used=5191.7MB, alloc=411.8MB, time=147.61 memory used=5260.6MB, alloc=411.8MB, time=147.84 memory used=5334.0MB, alloc=411.8MB, time=148.07 memory used=5563.9MB, alloc=411.8MB, time=150.35 memory used=5653.5MB, alloc=411.8MB, time=152.41 memory used=5731.9MB, alloc=411.8MB, time=154.14 memory used=5846.0MB, alloc=411.8MB, time=157.56 memory used=5954.6MB, alloc=411.8MB, time=159.61 memory used=6053.6MB, alloc=411.8MB, time=162.06 memory used=6173.7MB, alloc=435.8MB, time=164.55 memory used=6304.6MB, alloc=435.8MB, time=167.10 memory used=6425.5MB, alloc=435.8MB, time=169.41 memory used=6550.4MB, alloc=459.8MB, time=171.26 memory used=6667.4MB, alloc=459.8MB, time=173.12 memory used=6743.3MB, alloc=459.8MB, time=173.61 memory used=6799.5MB, alloc=459.8MB, time=174.04 memory used=6869.3MB, alloc=459.8MB, time=174.48 memory used=6954.5MB, alloc=459.8MB, time=174.93 memory used=7006.4MB, alloc=459.8MB, time=175.27 memory used=7081.5MB, alloc=459.8MB, time=177.25 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428262553 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; F := [ 3 2 3 4 2 3 11 x z + 2 x z + 9 x z, -10 x z - 2 z + 14 z, 2 x z - 2 x y z + 19 y ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 4 3 2 2 4 2 2 G := [7 x z - 9 z - 18 y , -4 x y z + z + 17 z, 11 z + 12 x z - 10 x z ] > Problem := [F,G]; Problem := [[ 3 2 3 4 2 3 11 x z + 2 x z + 9 x z, -10 x z - 2 z + 14 z, 2 x z - 2 x y z + 19 y ] 3 4 3 2 2 4 2 2 , [7 x z - 9 z - 18 y , -4 x y z + z + 17 z, 11 z + 12 x z - 10 x z ] ] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.0MB, alloc=32.3MB, time=0.87 memory used=45.4MB, alloc=56.3MB, time=1.37 memory used=88.6MB, alloc=60.3MB, time=2.41 memory used=129.9MB, alloc=68.3MB, time=3.42 memory used=170.8MB, alloc=68.3MB, time=4.24 memory used=211.5MB, alloc=68.3MB, time=5.00 memory used=243.8MB, alloc=68.3MB, time=5.67 memory used=275.2MB, alloc=68.3MB, time=5.87 memory used=304.9MB, alloc=68.3MB, time=6.03 memory used=322.2MB, alloc=92.3MB, time=6.18 memory used=356.4MB, alloc=92.3MB, time=6.36 memory used=398.1MB, alloc=92.3MB, time=6.54 memory used=447.9MB, alloc=92.3MB, time=7.25 memory used=507.3MB, alloc=95.5MB, time=7.55 memory used=544.0MB, alloc=95.5MB, time=7.74 memory used=580.1MB, alloc=95.5MB, time=7.94 memory used=625.2MB, alloc=95.5MB, time=8.16 memory used=685.2MB, alloc=95.5MB, time=21.37 memory used=768.2MB, alloc=95.5MB, time=24.20 memory used=803.8MB, alloc=95.5MB, time=24.38 memory used=848.4MB, alloc=95.5MB, time=24.57 memory used=877.6MB, alloc=95.5MB, time=24.72 memory used=911.6MB, alloc=95.5MB, time=24.89 memory used=951.9MB, alloc=95.5MB, time=25.05 memory used=1014.2MB, alloc=96.5MB, time=25.81 memory used=1058.7MB, alloc=96.5MB, time=26.05 memory used=1092.9MB, alloc=96.5MB, time=26.25 memory used=1134.8MB, alloc=96.5MB, time=26.44 memory used=1184.5MB, alloc=96.5MB, time=27.14 memory used=1244.0MB, alloc=96.5MB, time=27.45 memory used=1281.4MB, alloc=96.5MB, time=27.65 memory used=1317.6MB, alloc=96.5MB, time=27.82 memory used=1362.4MB, alloc=96.5MB, time=28.03 memory used=1423.1MB, alloc=96.5MB, time=40.18 memory used=1507.2MB, alloc=96.5MB, time=44.22 memory used=1543.0MB, alloc=96.5MB, time=44.40 memory used=1588.0MB, alloc=96.5MB, time=44.60 memory used=1617.2MB, alloc=96.5MB, time=44.76 memory used=1651.2MB, alloc=96.5MB, time=44.91 memory used=1690.8MB, alloc=96.5MB, time=45.10 memory used=1762.3MB, alloc=96.5MB, time=46.48 memory used=1828.1MB, alloc=96.5MB, time=47.43 memory used=1883.0MB, alloc=96.5MB, time=47.95 memory used=1919.7MB, alloc=96.5MB, time=48.15 memory used=1952.8MB, alloc=96.5MB, time=48.34 memory used=1995.6MB, alloc=96.5MB, time=48.53 memory used=2033.9MB, alloc=96.5MB, time=48.98 memory used=2086.1MB, alloc=96.5MB, time=49.25 memory used=2116.1MB, alloc=96.5MB, time=49.43 memory used=2153.5MB, alloc=96.5MB, time=49.62 memory used=2190.2MB, alloc=96.5MB, time=49.80 memory used=2251.1MB, alloc=96.5MB, time=65.86 memory used=2299.1MB, alloc=96.5MB, time=67.18 memory used=2334.1MB, alloc=96.5MB, time=67.36 memory used=2371.8MB, alloc=96.5MB, time=67.54 memory used=2398.8MB, alloc=96.5MB, time=67.71 memory used=2429.8MB, alloc=96.5MB, time=67.88 memory used=2465.3MB, alloc=96.5MB, time=68.04 memory used=2505.9MB, alloc=96.5MB, time=68.21 memory used=2535.1MB, alloc=96.5MB, time=68.35 memory used=2583.3MB, alloc=96.5MB, time=68.82 memory used=2624.4MB, alloc=96.5MB, time=69.04 memory used=2656.1MB, alloc=96.5MB, time=69.23 memory used=2696.6MB, alloc=96.5MB, time=69.41 memory used=2730.9MB, alloc=96.5MB, time=69.76 memory used=2787.5MB, alloc=96.5MB, time=70.09 memory used=2819.5MB, alloc=96.5MB, time=70.29 memory used=2854.2MB, alloc=96.5MB, time=70.47 memory used=2894.2MB, alloc=96.5MB, time=70.64 memory used=2940.9MB, alloc=96.5MB, time=78.11 memory used=3001.5MB, alloc=96.5MB, time=88.20 memory used=3033.8MB, alloc=96.5MB, time=88.38 memory used=3075.3MB, alloc=96.5MB, time=88.58 memory used=3102.3MB, alloc=96.5MB, time=88.74 memory used=3131.4MB, alloc=96.5MB, time=88.89 memory used=3165.2MB, alloc=96.5MB, time=89.04 memory used=3203.6MB, alloc=96.5MB, time=89.21 memory used=3239.4MB, alloc=96.5MB, time=89.37 memory used=3286.8MB, alloc=96.5MB, time=89.99 memory used=3358.5MB, alloc=96.5MB, time=91.21 memory used=3422.1MB, alloc=96.5MB, time=93.56 memory used=3478.7MB, alloc=96.5MB, time=94.31 memory used=3518.9MB, alloc=96.5MB, time=94.71 memory used=3585.2MB, alloc=96.5MB, time=96.22 memory used=3645.2MB, alloc=120.5MB, time=97.71 memory used=3698.2MB, alloc=120.5MB, time=98.01 memory used=3749.2MB, alloc=120.5MB, time=98.34 memory used=3801.6MB, alloc=120.5MB, time=98.77 memory used=3882.2MB, alloc=120.5MB, time=100.44 memory used=3950.0MB, alloc=120.5MB, time=102.11 memory used=4021.0MB, alloc=120.5MB, time=103.17 memory used=4069.7MB, alloc=120.5MB, time=103.60 memory used=4116.4MB, alloc=120.5MB, time=104.03 memory used=4155.7MB, alloc=120.5MB, time=104.28 memory used=4204.2MB, alloc=120.5MB, time=104.72 memory used=4248.4MB, alloc=120.5MB, time=105.03 memory used=4287.9MB, alloc=120.5MB, time=105.27 memory used=4331.3MB, alloc=120.5MB, time=105.60 memory used=4393.2MB, alloc=144.5MB, time=107.72 memory used=4449.2MB, alloc=144.5MB, time=108.10 memory used=4503.3MB, alloc=144.5MB, time=108.43 memory used=4569.7MB, alloc=144.5MB, time=108.79 memory used=4620.7MB, alloc=144.5MB, time=109.10 memory used=4658.0MB, alloc=144.5MB, time=109.37 memory used=4699.7MB, alloc=144.5MB, time=109.64 memory used=4743.6MB, alloc=144.5MB, time=109.91 memory used=4789.6MB, alloc=144.5MB, time=110.19 memory used=4838.3MB, alloc=144.5MB, time=110.47 memory used=4892.5MB, alloc=144.5MB, time=110.78 memory used=4949.6MB, alloc=144.5MB, time=111.08 memory used=5008.8MB, alloc=144.5MB, time=111.38 memory used=5070.0MB, alloc=144.5MB, time=111.68 memory used=5134.2MB, alloc=144.5MB, time=111.99 memory used=5197.2MB, alloc=144.5MB, time=112.30 memory used=5235.2MB, alloc=168.5MB, time=112.55 memory used=5278.7MB, alloc=168.5MB, time=112.79 memory used=5327.9MB, alloc=168.5MB, time=113.05 memory used=5377.9MB, alloc=168.5MB, time=113.30 memory used=5428.5MB, alloc=168.5MB, time=113.55 memory used=5479.8MB, alloc=168.5MB, time=113.80 memory used=5531.8MB, alloc=168.5MB, time=114.06 memory used=5584.4MB, alloc=168.5MB, time=114.32 memory used=5638.8MB, alloc=168.5MB, time=114.58 memory used=5697.9MB, alloc=168.5MB, time=114.85 memory used=5758.8MB, alloc=168.5MB, time=115.12 memory used=5820.3MB, alloc=168.5MB, time=115.39 memory used=5882.3MB, alloc=168.5MB, time=115.67 memory used=5946.0MB, alloc=168.5MB, time=115.94 memory used=6014.4MB, alloc=168.5MB, time=116.23 memory used=6084.5MB, alloc=168.5MB, time=116.51 memory used=6154.9MB, alloc=168.5MB, time=116.80 memory used=6227.0MB, alloc=168.5MB, time=117.09 memory used=6303.3MB, alloc=168.5MB, time=117.39 memory used=6381.2MB, alloc=168.5MB, time=117.69 memory used=6460.6MB, alloc=168.5MB, time=117.98 memory used=6543.7MB, alloc=168.5MB, time=118.29 memory used=6628.0MB, alloc=168.5MB, time=118.60 memory used=6714.5MB, alloc=168.5MB, time=118.90 memory used=6804.0MB, alloc=168.5MB, time=119.22 memory used=6847.0MB, alloc=179.8MB, time=119.45 memory used=6850.1MB, alloc=179.8MB, time=119.58 memory used=6853.4MB, alloc=179.8MB, time=119.74 memory used=6855.2MB, alloc=179.8MB, time=119.90 memory used=6856.2MB, alloc=179.8MB, time=120.05 memory used=6860.0MB, alloc=179.8MB, time=120.24 memory used=6861.8MB, alloc=179.8MB, time=120.38 memory used=6862.8MB, alloc=179.8MB, time=120.53 memory used=6866.6MB, alloc=179.8MB, time=120.66 memory used=6868.4MB, alloc=179.8MB, time=120.80 memory used=6869.4MB, alloc=179.8MB, time=120.94 memory used=6873.2MB, alloc=179.8MB, time=121.08 memory used=6875.0MB, alloc=179.8MB, time=121.22 memory used=6876.0MB, alloc=179.8MB, time=121.37 memory used=6879.8MB, alloc=179.8MB, time=121.53 memory used=6881.6MB, alloc=179.8MB, time=121.67 memory used=6882.6MB, alloc=179.8MB, time=121.81 memory used=6886.4MB, alloc=179.8MB, time=121.94 memory used=6888.2MB, alloc=179.8MB, time=122.08 memory used=6889.1MB, alloc=179.8MB, time=122.23 memory used=6892.9MB, alloc=179.8MB, time=122.36 memory used=6894.8MB, alloc=179.8MB, time=122.50 memory used=6895.7MB, alloc=179.8MB, time=122.64 memory used=6899.5MB, alloc=179.8MB, time=122.78 memory used=6901.3MB, alloc=179.8MB, time=122.93 memory used=6902.3MB, alloc=179.8MB, time=123.07 memory used=6906.1MB, alloc=179.8MB, time=123.22 memory used=6907.9MB, alloc=179.8MB, time=123.36 memory used=6912.6MB, alloc=179.8MB, time=123.52 memory used=6914.5MB, alloc=179.8MB, time=123.67 memory used=6919.2MB, alloc=179.8MB, time=123.83 memory used=6921.0MB, alloc=179.8MB, time=123.98 memory used=6925.7MB, alloc=179.8MB, time=124.13 memory used=6927.6MB, alloc=179.8MB, time=124.28 memory used=6932.2MB, alloc=179.8MB, time=124.42 memory used=6934.1MB, alloc=179.8MB, time=124.58 memory used=6938.7MB, alloc=179.8MB, time=124.72 memory used=6940.7MB, alloc=179.8MB, time=124.85 memory used=6945.2MB, alloc=179.8MB, time=125.00 memory used=6947.2MB, alloc=179.8MB, time=125.14 memory used=6951.7MB, alloc=179.8MB, time=125.30 memory used=6953.7MB, alloc=179.8MB, time=125.44 memory used=6958.2MB, alloc=179.8MB, time=125.60 memory used=6960.2MB, alloc=179.8MB, time=125.75 memory used=6964.7MB, alloc=179.8MB, time=125.91 memory used=6966.8MB, alloc=179.8MB, time=126.04 memory used=6971.2MB, alloc=179.8MB, time=126.19 memory used=6973.3MB, alloc=179.8MB, time=126.33 memory used=6977.6MB, alloc=179.8MB, time=126.47 memory used=6979.7MB, alloc=179.8MB, time=126.60 memory used=6984.1MB, alloc=179.8MB, time=126.73 memory used=6986.2MB, alloc=179.8MB, time=126.87 memory used=6990.5MB, alloc=179.8MB, time=127.01 memory used=6992.7MB, alloc=179.8MB, time=127.14 memory used=6997.0MB, alloc=179.8MB, time=127.29 memory used=6999.2MB, alloc=179.8MB, time=127.43 memory used=7003.4MB, alloc=179.8MB, time=127.58 memory used=7005.6MB, alloc=179.8MB, time=127.71 memory used=7009.8MB, alloc=179.8MB, time=127.86 memory used=7012.1MB, alloc=179.8MB, time=128.01 memory used=7016.3MB, alloc=179.8MB, time=128.14 memory used=7018.5MB, alloc=179.8MB, time=128.28 memory used=7022.7MB, alloc=179.8MB, time=128.42 memory used=7024.9MB, alloc=179.8MB, time=128.57 memory used=7029.1MB, alloc=179.8MB, time=128.71 memory used=7031.4MB, alloc=179.8MB, time=128.85 memory used=7035.5MB, alloc=179.8MB, time=129.01 memory used=7037.8MB, alloc=179.8MB, time=129.17 memory used=7041.8MB, alloc=179.8MB, time=129.33 memory used=7044.2MB, alloc=179.8MB, time=129.50 memory used=7048.2MB, alloc=179.8MB, time=129.63 memory used=7050.6MB, alloc=179.8MB, time=129.77 memory used=7054.6MB, alloc=179.8MB, time=129.91 memory used=7057.5MB, alloc=179.8MB, time=130.05 memory used=7060.9MB, alloc=179.8MB, time=130.19 memory used=7063.8MB, alloc=179.8MB, time=130.32 memory used=7067.3MB, alloc=179.8MB, time=130.46 memory used=7070.2MB, alloc=179.8MB, time=130.59 memory used=7073.6MB, alloc=179.8MB, time=130.74 memory used=7076.5MB, alloc=179.8MB, time=130.88 memory used=7079.9MB, alloc=179.8MB, time=131.07 memory used=7082.8MB, alloc=179.8MB, time=131.22 memory used=7086.2MB, alloc=179.8MB, 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used=7151.8MB, alloc=179.8MB, time=134.37 memory used=7155.0MB, alloc=179.8MB, time=134.50 memory used=7158.0MB, alloc=179.8MB, time=134.64 memory used=7161.2MB, alloc=179.8MB, time=134.77 memory used=7164.2MB, alloc=179.8MB, time=134.90 memory used=7167.4MB, alloc=179.8MB, time=135.04 memory used=7170.4MB, alloc=179.8MB, time=135.20 memory used=7173.6MB, alloc=179.8MB, time=135.34 memory used=7176.6MB, alloc=179.8MB, time=135.48 memory used=7179.8MB, alloc=179.8MB, time=135.61 memory used=7182.8MB, alloc=179.8MB, time=135.76 memory used=7186.0MB, alloc=179.8MB, time=135.89 memory used=7189.0MB, alloc=179.8MB, time=136.05 memory used=7192.1MB, alloc=179.8MB, time=136.18 memory used=7198.2MB, alloc=179.8MB, time=136.36 memory used=7204.3MB, alloc=179.8MB, time=136.50 memory used=7210.4MB, alloc=179.8MB, time=136.65 memory used=7216.5MB, alloc=179.8MB, time=136.79 memory used=7222.6MB, alloc=179.8MB, time=136.93 memory used=7228.7MB, alloc=179.8MB, time=137.07 memory used=7234.7MB, alloc=179.8MB, time=137.21 memory used=7240.8MB, alloc=179.8MB, time=137.37 memory used=7246.8MB, alloc=179.8MB, time=137.51 memory used=7252.8MB, alloc=179.8MB, time=137.64 memory used=7258.9MB, alloc=179.8MB, time=137.78 memory used=7264.9MB, alloc=179.8MB, time=137.93 memory used=7270.8MB, alloc=179.8MB, time=138.07 memory used=7276.8MB, alloc=179.8MB, time=138.22 memory used=7282.8MB, alloc=179.8MB, time=138.39 memory used=7288.7MB, alloc=179.8MB, time=138.57 memory used=7294.7MB, alloc=179.8MB, time=138.74 memory used=7300.6MB, alloc=179.8MB, time=138.92 memory used=7306.5MB, alloc=179.8MB, time=139.07 memory used=7312.4MB, alloc=179.8MB, time=139.21 memory used=7318.3MB, alloc=179.8MB, time=139.37 memory used=7324.2MB, alloc=179.8MB, time=139.50 memory used=7330.1MB, alloc=179.8MB, time=139.66 memory used=7335.9MB, alloc=179.8MB, time=139.82 memory used=7341.8MB, alloc=179.8MB, time=139.97 memory used=7347.6MB, alloc=179.8MB, time=140.14 memory used=7353.4MB, alloc=179.8MB, time=140.29 memory used=7359.2MB, alloc=179.8MB, time=140.43 memory used=7365.0MB, alloc=179.8MB, time=140.57 memory used=7370.8MB, alloc=179.8MB, time=140.71 memory used=7376.5MB, alloc=179.8MB, time=140.86 memory used=7382.3MB, alloc=179.8MB, time=141.03 memory used=7388.0MB, alloc=179.8MB, time=141.18 memory used=7393.7MB, alloc=179.8MB, time=141.31 memory used=7399.4MB, alloc=179.8MB, time=141.46 memory used=7405.1MB, alloc=179.8MB, time=141.61 memory used=7410.8MB, alloc=179.8MB, time=141.76 memory used=7416.5MB, alloc=179.8MB, time=141.91 memory used=7422.1MB, alloc=179.8MB, time=142.04 memory used=7427.8MB, alloc=179.8MB, time=142.18 memory used=7433.4MB, alloc=179.8MB, time=142.32 memory used=7439.0MB, alloc=179.8MB, time=142.49 memory used=7444.6MB, alloc=179.8MB, time=142.63 memory used=7450.2MB, alloc=179.8MB, time=142.77 memory used=7455.8MB, alloc=179.8MB, time=142.92 memory used=7461.3MB, alloc=179.8MB, time=143.07 memory used=7466.9MB, alloc=179.8MB, time=143.22 memory used=7474.5MB, alloc=179.8MB, time=143.37 memory used=7481.2MB, alloc=179.8MB, time=143.53 memory used=7488.9MB, alloc=179.8MB, time=143.69 memory used=7496.5MB, alloc=179.8MB, time=143.82 memory used=7503.0MB, alloc=179.8MB, time=143.97 memory used=7510.6MB, alloc=179.8MB, time=144.11 memory used=7518.2MB, alloc=179.8MB, time=144.28 memory used=7524.7MB, alloc=179.8MB, time=144.44 memory used=7532.1MB, alloc=179.8MB, time=144.60 memory used=7539.7MB, alloc=179.8MB, time=144.74 memory used=7546.1MB, alloc=179.8MB, time=144.89 memory used=7553.4MB, alloc=179.8MB, time=145.03 memory used=7560.9MB, alloc=179.8MB, time=145.17 memory used=7569.2MB, alloc=179.8MB, time=145.32 memory used=7576.8MB, alloc=179.8MB, time=145.46 memory used=7584.8MB, alloc=179.8MB, time=145.61 memory used=7592.5MB, alloc=179.8MB, time=145.76 memory used=7600.3MB, alloc=179.8MB, time=145.92 memory used=7608.0MB, alloc=179.8MB, time=146.07 memory used=7615.6MB, alloc=179.8MB, time=146.22 memory used=7623.4MB, alloc=179.8MB, time=146.36 memory used=7630.8MB, alloc=179.8MB, time=146.52 memory used=7639.2MB, alloc=179.8MB, time=146.66 memory used=7648.1MB, alloc=179.8MB, time=146.84 memory used=7655.8MB, alloc=179.8MB, time=146.99 memory used=7664.1MB, alloc=179.8MB, time=147.13 memory used=7673.0MB, alloc=179.8MB, time=147.29 memory used=7682.6MB, alloc=179.8MB, time=147.45 memory used=7692.3MB, alloc=179.8MB, time=147.60 memory used=7701.9MB, alloc=179.8MB, time=147.75 memory used=7711.5MB, alloc=179.8MB, time=147.91 memory used=7721.0MB, alloc=179.8MB, time=148.07 memory used=7730.6MB, alloc=179.8MB, time=148.23 memory used=7740.1MB, alloc=179.8MB, time=148.37 memory used=7749.6MB, alloc=179.8MB, time=148.53 memory used=7759.1MB, alloc=179.8MB, time=148.68 memory used=7768.5MB, alloc=179.8MB, time=148.83 memory used=7778.1MB, alloc=179.8MB, time=148.97 memory used=7787.6MB, alloc=179.8MB, time=149.12 memory used=7797.1MB, alloc=179.8MB, time=149.27 memory used=7806.7MB, alloc=179.8MB, time=149.44 memory used=7816.3MB, alloc=179.8MB, time=149.60 memory used=7826.0MB, alloc=179.8MB, time=149.76 memory used=7835.7MB, alloc=179.8MB, time=149.93 memory used=7845.4MB, alloc=179.8MB, time=150.09 memory used=7855.1MB, alloc=179.8MB, time=150.26 memory used=7864.8MB, alloc=179.8MB, time=150.42 memory used=7874.6MB, alloc=179.8MB, time=150.57 memory used=7884.5MB, alloc=179.8MB, time=150.72 memory used=7894.3MB, alloc=179.8MB, time=150.89 memory used=7904.2MB, alloc=179.8MB, time=151.03 memory used=7936.0MB, alloc=179.8MB, time=153.07 memory used=8019.7MB, alloc=179.8MB, time=153.57 memory used=8095.5MB, alloc=179.8MB, time=153.99 memory used=8176.8MB, alloc=179.8MB, time=154.39 memory used=8230.3MB, alloc=179.8MB, time=154.71 memory used=8288.1MB, alloc=179.8MB, time=155.04 memory used=8351.8MB, alloc=179.8MB, time=155.38 memory used=8419.5MB, alloc=179.8MB, time=155.73 memory used=8491.7MB, alloc=179.8MB, time=156.10 memory used=8571.3MB, alloc=179.8MB, time=156.47 memory used=8655.7MB, alloc=179.8MB, time=156.84 memory used=8748.4MB, alloc=179.8MB, time=157.24 memory used=8805.3MB, alloc=179.8MB, time=157.53 memory used=8853.3MB, alloc=179.8MB, time=157.78 memory used=8902.6MB, alloc=179.8MB, time=158.04 memory used=8952.6MB, alloc=179.8MB, time=158.30 memory used=9003.4MB, alloc=179.8MB, time=158.56 memory used=9054.8MB, alloc=179.8MB, time=158.82 memory used=9106.9MB, alloc=179.8MB, time=159.08 memory used=9160.7MB, alloc=179.8MB, time=159.34 memory used=9219.5MB, alloc=179.8MB, time=159.62 memory used=9280.0MB, alloc=179.8MB, time=159.89 memory used=9341.0MB, alloc=179.8MB, time=160.17 memory used=9402.6MB, alloc=179.8MB, time=160.46 memory used=9464.7MB, alloc=179.8MB, time=160.74 memory used=9528.8MB, alloc=179.8MB, time=161.02 memory used=9597.0MB, alloc=179.8MB, time=161.32 memory used=9667.2MB, alloc=179.8MB, time=161.61 memory used=9737.6MB, alloc=179.8MB, time=161.89 memory used=9810.0MB, alloc=179.8MB, time=162.18 memory used=9886.1MB, alloc=179.8MB, time=162.49 memory used=9964.0MB, alloc=179.8MB, time=162.80 memory used=10043.5MB, alloc=179.8MB, time=163.10 memory used=10126.4MB, alloc=179.8MB, time=163.41 memory used=10210.8MB, alloc=179.8MB, time=163.72 memory used=10301.5MB, alloc=179.8MB, time=164.04 memory used=10391.6MB, alloc=179.8MB, time=164.36 memory used=10415.3MB, alloc=179.8MB, time=164.57 memory used=10418.3MB, alloc=179.8MB, time=164.71 memory used=10421.6MB, alloc=179.8MB, time=164.85 memory used=10423.4MB, alloc=179.8MB, time=164.98 memory used=10424.3MB, alloc=179.8MB, time=165.12 memory used=10428.2MB, alloc=179.8MB, time=165.27 memory used=10430.0MB, alloc=179.8MB, time=165.41 memory used=10430.9MB, alloc=179.8MB, time=165.55 memory used=10434.8MB, alloc=179.8MB, time=165.69 memory used=10436.6MB, alloc=179.8MB, time=165.84 memory used=10437.5MB, alloc=179.8MB, time=165.99 memory used=10441.4MB, alloc=179.8MB, time=166.13 memory used=10443.2MB, alloc=179.8MB, time=166.27 memory used=10444.1MB, alloc=179.8MB, time=166.40 memory used=10448.0MB, alloc=179.8MB, time=166.55 memory used=10449.8MB, alloc=179.8MB, time=166.70 memory used=10450.7MB, alloc=179.8MB, time=166.84 memory used=10454.5MB, alloc=179.8MB, time=166.98 memory used=10456.3MB, alloc=179.8MB, time=167.11 memory used=10457.3MB, alloc=179.8MB, time=167.27 memory used=10461.1MB, alloc=179.8MB, time=167.43 memory used=10462.9MB, alloc=179.8MB, time=167.57 memory used=10463.9MB, alloc=179.8MB, time=167.70 memory used=10467.7MB, alloc=179.8MB, time=167.84 memory used=10469.5MB, alloc=179.8MB, time=167.97 memory used=10470.4MB, alloc=179.8MB, time=168.10 memory used=10474.2MB, alloc=179.8MB, time=168.26 memory used=10476.1MB, alloc=179.8MB, time=168.40 memory used=10480.8MB, alloc=179.8MB, time=168.55 memory used=10482.6MB, alloc=179.8MB, time=168.74 memory used=10487.3MB, alloc=179.8MB, time=168.88 memory used=10489.2MB, alloc=179.8MB, time=169.01 memory used=10493.8MB, alloc=179.8MB, time=169.16 memory used=10495.8MB, alloc=179.8MB, time=169.30 memory used=10500.4MB, alloc=179.8MB, time=169.44 memory used=10502.3MB, alloc=179.8MB, time=169.59 memory used=10506.9MB, alloc=179.8MB, time=169.73 memory used=10508.8MB, alloc=179.8MB, time=169.87 memory used=10513.4MB, alloc=179.8MB, time=170.02 memory used=10515.4MB, alloc=179.8MB, time=170.15 memory used=10519.9MB, alloc=179.8MB, time=170.28 memory used=10521.9MB, alloc=179.8MB, time=170.41 memory used=10526.4MB, alloc=179.8MB, time=170.56 memory used=10528.4MB, alloc=179.8MB, time=170.72 memory used=10532.9MB, alloc=179.8MB, time=170.87 memory used=10534.9MB, alloc=179.8MB, time=171.02 memory used=10539.3MB, alloc=179.8MB, time=171.16 memory used=10541.4MB, alloc=179.8MB, time=171.29 memory used=10545.8MB, alloc=179.8MB, time=171.44 memory used=10547.9MB, alloc=179.8MB, time=171.58 memory used=10552.3MB, alloc=179.8MB, time=171.73 memory used=10554.4MB, alloc=179.8MB, time=171.86 memory used=10558.7MB, alloc=179.8MB, time=172.03 memory used=10560.9MB, alloc=179.8MB, time=172.17 memory used=10565.2MB, alloc=179.8MB, time=172.33 memory used=10567.3MB, alloc=179.8MB, time=172.46 memory used=10571.6MB, alloc=179.8MB, time=172.60 memory used=10573.8MB, alloc=179.8MB, time=172.74 memory used=10578.0MB, alloc=179.8MB, time=172.87 memory used=10580.2MB, alloc=179.8MB, time=173.03 memory used=10584.4MB, alloc=179.8MB, time=173.17 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428262853 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 4 2 2 2 2 3 F := [-11 x y + 14 y + 2 y z , -6 x z + 7 z , -20 x y z + 9 x y + 19 y] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; G := [ 3 2 3 2 3 3 2 17 y z - 17 x z + 14 z , 2 x y + 11 y - 5 y, 19 x z - 20 x y - 6 x z ] > Problem := [F,G]; Problem := [ 2 2 4 2 2 2 2 3 [-11 x y + 14 y + 2 y z , -6 x z + 7 z , -20 x y z + 9 x y + 19 y], [ 3 2 3 2 3 3 2 17 y z - 17 x z + 14 z , 2 x y + 11 y - 5 y, 19 x z - 20 x y - 6 x z ] ] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.31 memory used=26.6MB, alloc=32.3MB, time=0.87 memory used=47.7MB, alloc=32.3MB, time=1.41 memory used=67.6MB, alloc=32.3MB, time=1.91 memory used=86.6MB, alloc=56.3MB, time=2.42 memory used=123.9MB, alloc=60.3MB, time=3.39 memory used=164.8MB, alloc=92.3MB, time=4.43 memory used=227.2MB, alloc=92.3MB, time=6.01 memory used=288.8MB, alloc=116.3MB, time=7.60 memory used=371.6MB, alloc=372.3MB, time=9.78 memory used=455.9MB, alloc=396.3MB, time=11.91 memory used=561.7MB, alloc=396.3MB, time=14.65 memory used=666.5MB, alloc=420.3MB, time=17.21 memory used=797.3MB, alloc=444.3MB, time=20.24 memory used=918.6MB, alloc=444.3MB, time=23.31 memory used=1020.8MB, alloc=468.3MB, time=25.40 memory used=1130.8MB, alloc=468.3MB, time=28.35 memory used=1234.3MB, alloc=492.3MB, time=30.34 memory used=1352.7MB, alloc=516.3MB, time=33.86 memory used=1451.8MB, alloc=516.3MB, time=36.85 memory used=1528.6MB, alloc=516.3MB, time=38.88 memory used=1612.4MB, alloc=516.3MB, time=41.29 memory used=1688.7MB, alloc=516.3MB, time=43.90 memory used=1759.2MB, alloc=516.3MB, time=46.23 memory used=1826.2MB, alloc=516.3MB, time=48.45 memory used=1871.2MB, alloc=516.3MB, time=49.90 memory used=1934.3MB, alloc=516.3MB, time=52.16 memory used=1977.7MB, alloc=516.3MB, time=53.75 memory used=2022.2MB, alloc=516.3MB, time=55.45 memory used=2218.8MB, alloc=540.3MB, time=60.56 memory used=2439.0MB, alloc=564.3MB, time=65.11 memory used=2631.1MB, alloc=588.3MB, time=70.89 memory used=2792.6MB, alloc=612.3MB, time=76.06 memory used=2937.1MB, alloc=636.3MB, time=80.69 memory used=3066.6MB, alloc=660.3MB, time=84.63 memory used=3203.3MB, alloc=660.3MB, time=89.71 memory used=3324.1MB, alloc=660.3MB, time=93.81 memory used=3436.1MB, alloc=660.3MB, time=96.83 memory used=3531.8MB, alloc=660.3MB, time=100.78 memory used=3611.6MB, alloc=660.3MB, time=103.83 memory used=3932.1MB, alloc=684.3MB, time=113.62 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428263153 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; F := [ 3 2 2 4 3 3 10 y z + 16 x z - 5 x z, -17 x y + 11 x z - 13 z , -7 x + 6 x y + 3 x ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; G := [ 4 2 4 2 2 3 3 -15 z - 4 x y - 15 x, 20 x + 13 x z - 11 y , -18 x y + 20 y z + 13 x] > Problem := [F,G]; Problem := [[ 3 2 2 4 3 3 10 y z + 16 x z - 5 x z, -17 x y + 11 x z - 13 z , -7 x + 6 x y + 3 x ] , [ 4 2 4 2 2 3 3 -15 z - 4 x y - 15 x, 20 x + 13 x z - 11 y , -18 x y + 20 y z + 13 x] ] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.30 memory used=26.3MB, alloc=32.3MB, time=0.84 memory used=47.9MB, alloc=32.3MB, time=1.42 memory used=68.0MB, alloc=56.3MB, time=1.95 memory used=107.8MB, alloc=60.3MB, time=2.97 memory used=146.1MB, alloc=84.3MB, time=3.97 memory used=209.3MB, alloc=92.3MB, time=5.58 memory used=272.4MB, alloc=92.3MB, time=6.96 memory used=336.9MB, alloc=92.3MB, time=8.17 memory used=378.8MB, alloc=92.3MB, time=8.61 memory used=422.5MB, alloc=92.3MB, time=9.16 memory used=462.4MB, alloc=92.3MB, time=9.42 memory used=503.8MB, alloc=92.3MB, time=10.03 memory used=538.7MB, alloc=92.3MB, time=10.27 memory used=574.9MB, alloc=92.3MB, time=10.50 memory used=615.4MB, alloc=92.3MB, time=11.14 memory used=649.6MB, alloc=92.3MB, time=11.37 memory used=686.7MB, alloc=92.3MB, time=11.63 memory used=726.9MB, alloc=92.3MB, time=12.28 memory used=774.6MB, alloc=92.3MB, time=13.04 memory used=832.2MB, alloc=92.3MB, time=14.27 memory used=865.5MB, alloc=92.3MB, time=14.64 memory used=928.5MB, alloc=116.3MB, time=16.07 memory used=998.0MB, alloc=116.3MB, time=16.96 memory used=1056.2MB, alloc=116.3MB, time=17.59 memory used=1114.7MB, alloc=116.3MB, time=18.25 memory used=1173.3MB, alloc=116.3MB, time=18.90 memory used=1256.8MB, alloc=116.3MB, time=20.67 memory used=1333.9MB, alloc=116.3MB, time=22.38 memory used=1410.8MB, alloc=372.3MB, time=24.21 memory used=1490.3MB, alloc=396.3MB, time=25.87 memory used=1574.1MB, alloc=396.3MB, time=27.14 memory used=1651.3MB, alloc=396.3MB, time=32.73 memory used=1701.3MB, alloc=396.3MB, time=33.00 memory used=1796.2MB, alloc=396.3MB, time=34.65 memory used=1907.1MB, alloc=396.3MB, time=37.17 memory used=1966.8MB, alloc=396.3MB, time=37.88 memory used=2044.5MB, alloc=396.3MB, time=39.11 memory used=2089.9MB, alloc=396.3MB, time=39.42 memory used=2167.0MB, alloc=396.3MB, time=46.56 memory used=2218.2MB, alloc=396.3MB, time=46.92 memory used=2265.3MB, alloc=396.3MB, time=47.20 memory used=2307.2MB, alloc=396.3MB, time=47.46 memory used=2391.1MB, alloc=396.3MB, time=48.40 memory used=2499.0MB, alloc=420.3MB, time=50.95 memory used=2626.8MB, alloc=420.3MB, time=53.95 memory used=2768.7MB, alloc=420.3MB, time=56.67 memory used=2842.2MB, alloc=420.3MB, time=57.26 memory used=2908.0MB, alloc=444.3MB, time=61.22 memory used=2993.2MB, alloc=444.3MB, time=63.33 memory used=3067.4MB, alloc=444.3MB, time=63.80 memory used=3156.6MB, alloc=444.3MB, time=64.27 memory used=3212.3MB, alloc=444.3MB, time=64.66 memory used=3269.5MB, alloc=444.3MB, time=65.05 memory used=3331.8MB, alloc=444.3MB, time=65.44 memory used=3398.6MB, alloc=444.3MB, time=65.84 memory used=3471.4MB, alloc=444.3MB, time=66.24 memory used=3550.2MB, alloc=444.3MB, time=66.66 memory used=3634.9MB, alloc=444.3MB, time=67.07 memory used=3725.2MB, alloc=444.3MB, time=67.50 memory used=3800.9MB, alloc=444.3MB, time=67.87 memory used=3850.1MB, alloc=444.3MB, time=68.20 memory used=3901.2MB, alloc=444.3MB, time=68.53 memory used=3954.3MB, alloc=444.3MB, time=68.86 memory used=4009.0MB, alloc=444.3MB, time=69.19 memory used=4065.2MB, alloc=444.3MB, time=69.53 memory used=4124.6MB, alloc=444.3MB, time=69.87 memory used=4185.1MB, alloc=444.3MB, time=70.22 memory used=4248.1MB, alloc=444.3MB, time=70.56 memory used=4313.2MB, alloc=444.3MB, time=70.89 memory used=4381.5MB, alloc=444.3MB, time=71.24 memory used=4453.9MB, alloc=444.3MB, time=71.59 memory used=4528.9MB, alloc=444.3MB, time=71.94 memory used=4607.9MB, alloc=444.3MB, time=72.31 memory used=4691.7MB, alloc=444.3MB, time=72.67 memory used=4780.0MB, alloc=444.3MB, time=73.03 memory used=4900.1MB, alloc=444.3MB, time=78.63 memory used=4967.0MB, alloc=444.3MB, time=79.09 memory used=5051.6MB, alloc=444.3MB, time=79.56 memory used=5121.3MB, alloc=444.3MB, time=80.00 memory used=5175.8MB, alloc=444.3MB, time=80.41 memory used=5235.3MB, alloc=444.3MB, time=80.80 memory used=5299.2MB, alloc=444.3MB, time=81.21 memory used=5369.1MB, alloc=444.3MB, time=81.62 memory used=5443.3MB, alloc=444.3MB, time=82.03 memory used=5523.2MB, alloc=444.3MB, time=82.45 memory used=5608.9MB, alloc=444.3MB, time=82.88 memory used=5700.8MB, alloc=444.3MB, time=83.31 memory used=5754.6MB, alloc=444.3MB, time=83.66 memory used=5804.2MB, alloc=444.3MB, time=84.00 memory used=5855.4MB, alloc=444.3MB, time=84.35 memory used=5908.4MB, alloc=444.3MB, time=84.71 memory used=5963.0MB, alloc=444.3MB, time=85.04 memory used=6019.1MB, alloc=444.3MB, time=85.41 memory used=6078.2MB, alloc=444.3MB, time=85.75 memory used=6140.0MB, alloc=444.3MB, time=86.09 memory used=6204.2MB, alloc=444.3MB, time=86.45 memory used=6270.3MB, alloc=444.3MB, time=86.81 memory used=6339.4MB, alloc=444.3MB, time=87.15 memory used=6412.1MB, alloc=444.3MB, time=87.52 memory used=6487.0MB, alloc=444.3MB, time=87.90 memory used=6566.5MB, alloc=444.3MB, time=88.26 memory used=6650.4MB, alloc=444.3MB, time=88.63 memory used=6738.4MB, alloc=444.3MB, time=89.00 memory used=6856.8MB, alloc=444.3MB, time=89.95 memory used=6941.3MB, alloc=444.3MB, time=90.44 memory used=7000.1MB, alloc=444.3MB, time=90.84 memory used=7064.4MB, alloc=444.3MB, time=91.25 memory used=7139.3MB, alloc=444.3MB, time=91.67 memory used=7228.0MB, alloc=444.3MB, time=92.11 memory used=7284.3MB, alloc=444.3MB, time=92.46 memory used=7340.6MB, alloc=444.3MB, time=92.81 memory used=7421.4MB, alloc=444.3MB, time=93.31 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428263453 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 2 2 F := [8 x z - 2 y + 5 x , 6 x z + 12 x z, 5 x y - 19 x + 13 y z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 4 2 G := [3 x y z - 15 y + 4 y, -10 x y - 6 y + 14 y z , 2 3 2 -15 x y z - 15 y z - 8 x ] > Problem := [F,G]; 2 3 2 2 2 2 Problem := [[8 x z - 2 y + 5 x , 6 x z + 12 x z, 5 x y - 19 x + 13 y z], [ 3 2 2 4 2 3 x y z - 15 y + 4 y, -10 x y - 6 y + 14 y z , 2 3 2 -15 x y z - 15 y z - 8 x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.31 memory used=26.6MB, alloc=32.3MB, time=0.87 memory used=47.5MB, alloc=32.3MB, time=1.42 memory used=67.6MB, alloc=56.3MB, time=1.97 memory used=107.1MB, alloc=60.3MB, time=2.99 memory used=143.9MB, alloc=84.3MB, time=3.93 memory used=204.6MB, alloc=92.3MB, time=5.50 memory used=270.7MB, alloc=116.3MB, time=7.08 memory used=344.1MB, alloc=116.3MB, time=8.91 memory used=408.4MB, alloc=372.3MB, time=10.50 memory used=496.9MB, alloc=396.3MB, time=12.60 memory used=612.2MB, alloc=396.3MB, time=14.96 memory used=723.9MB, alloc=420.3MB, time=17.54 memory used=856.9MB, alloc=444.3MB, time=20.88 memory used=959.0MB, alloc=444.3MB, time=23.33 memory used=1079.5MB, alloc=444.3MB, time=26.28 memory used=1213.7MB, alloc=468.3MB, time=29.70 memory used=1334.4MB, alloc=468.3MB, time=32.13 memory used=1450.6MB, alloc=468.3MB, time=34.27 memory used=1569.1MB, alloc=492.3MB, time=37.61 memory used=1660.1MB, alloc=492.3MB, time=40.01 memory used=1760.4MB, alloc=492.3MB, time=42.62 memory used=1842.5MB, alloc=492.3MB, time=44.40 memory used=1915.0MB, alloc=492.3MB, time=46.56 memory used=2034.7MB, alloc=492.3MB, time=49.25 memory used=2163.1MB, alloc=492.3MB, time=51.25 memory used=2307.0MB, alloc=492.3MB, time=53.62 memory used=2396.0MB, alloc=492.3MB, time=54.74 memory used=2514.1MB, alloc=516.3MB, time=56.64 memory used=2640.1MB, alloc=516.3MB, time=58.64 memory used=2719.0MB, alloc=516.3MB, time=60.80 memory used=2798.7MB, alloc=516.3MB, time=62.85 memory used=2858.6MB, alloc=516.3MB, time=64.56 memory used=2960.5MB, alloc=516.3MB, time=66.44 memory used=3079.7MB, alloc=516.3MB, time=68.15 memory used=3207.5MB, alloc=516.3MB, time=71.43 memory used=3319.9MB, alloc=516.3MB, time=72.89 memory used=3375.2MB, alloc=516.3MB, time=74.47 memory used=3434.3MB, alloc=516.3MB, time=76.06 memory used=3502.7MB, alloc=516.3MB, time=77.91 memory used=3566.1MB, alloc=516.3MB, time=79.48 memory used=3626.1MB, alloc=516.3MB, time=81.39 memory used=3693.2MB, alloc=516.3MB, time=83.40 memory used=3768.1MB, alloc=516.3MB, time=86.11 memory used=3812.2MB, alloc=516.3MB, time=87.71 memory used=3860.5MB, alloc=516.3MB, time=89.32 memory used=4081.1MB, alloc=540.3MB, time=94.04 memory used=4313.9MB, alloc=564.3MB, time=99.47 memory used=4505.4MB, alloc=588.3MB, time=104.94 memory used=4657.1MB, alloc=612.3MB, time=108.66 memory used=4819.1MB, alloc=636.3MB, time=112.66 memory used=4978.4MB, alloc=660.3MB, time=116.75 memory used=5140.6MB, alloc=660.3MB, time=121.43 memory used=5281.7MB, alloc=660.3MB, time=125.15 memory used=5405.9MB, alloc=684.3MB, time=128.48 memory used=5498.2MB, alloc=684.3MB, time=131.30 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428263753 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; F := [ 3 3 2 3 2 4 3 3 3 -12 x z - 15 x - 8 x y, x y + 7 x y z - 5 y , 6 x z - 20 y z - 2 y ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 3 2 G := [-13 x z - 3 y z - 13 y, -6 x y - 14 x y + 5 x z , 2 2 3 2 -11 x z + 16 x + 5 y z] > Problem := [F,G]; Problem := [[ 3 3 2 3 2 4 3 3 3 -12 x z - 15 x - 8 x y, x y + 7 x y z - 5 y , 6 x z - 20 y z - 2 y ] 3 2 2 2 3 2 , [-13 x z - 3 y z - 13 y, -6 x y - 14 x y + 5 x z , 2 2 3 2 -11 x z + 16 x + 5 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=25.4MB, alloc=32.3MB, time=0.74 memory used=50.0MB, alloc=36.3MB, time=1.26 memory used=72.2MB, alloc=36.3MB, time=1.64 memory used=92.7MB, alloc=60.3MB, time=2.10 memory used=126.4MB, alloc=60.3MB, time=2.84 memory used=173.5MB, alloc=68.3MB, time=3.66 memory used=219.2MB, alloc=68.3MB, time=4.56 memory used=251.9MB, alloc=68.3MB, time=4.91 memory used=287.2MB, alloc=68.3MB, time=5.18 memory used=310.3MB, alloc=68.3MB, time=5.31 memory used=344.1MB, alloc=68.3MB, time=6.86 memory used=391.1MB, alloc=68.3MB, time=9.66 memory used=415.4MB, alloc=68.3MB, time=9.79 memory used=433.8MB, alloc=68.3MB, time=9.92 memory used=463.9MB, alloc=68.3MB, time=10.11 memory used=488.1MB, alloc=68.3MB, time=10.26 memory used=525.7MB, alloc=68.3MB, time=10.69 memory used=580.1MB, alloc=68.3MB, time=11.66 memory used=632.3MB, alloc=92.3MB, time=12.51 memory used=715.1MB, alloc=92.3MB, time=13.79 memory used=779.8MB, alloc=372.3MB, time=15.10 memory used=874.1MB, alloc=372.3MB, time=17.10 memory used=945.1MB, alloc=396.3MB, time=18.02 memory used=1004.9MB, alloc=396.3MB, time=18.38 memory used=1067.1MB, alloc=396.3MB, time=18.87 memory used=1139.4MB, alloc=396.3MB, time=19.63 memory used=1215.4MB, alloc=396.3MB, time=20.21 memory used=1263.6MB, alloc=396.3MB, time=20.53 memory used=1322.3MB, alloc=396.3MB, time=20.86 memory used=1380.3MB, alloc=396.3MB, time=21.17 memory used=1420.6MB, alloc=396.3MB, time=21.44 memory used=1465.2MB, alloc=396.3MB, time=21.71 memory used=1516.3MB, alloc=396.3MB, time=22.00 memory used=1572.7MB, alloc=396.3MB, time=22.29 memory used=1636.8MB, alloc=396.3MB, time=22.58 memory used=1687.2MB, alloc=396.3MB, time=22.84 memory used=1751.6MB, alloc=396.3MB, time=23.40 memory used=1808.1MB, alloc=396.3MB, time=23.71 memory used=1854.5MB, alloc=396.3MB, time=23.99 memory used=1950.3MB, alloc=396.3MB, time=57.15 memory used=2045.6MB, alloc=396.3MB, time=58.10 memory used=2106.0MB, alloc=396.3MB, time=58.44 memory used=2147.3MB, alloc=396.3MB, time=58.71 memory used=2195.4MB, alloc=396.3MB, time=59.01 memory used=2251.6MB, alloc=396.3MB, time=59.30 memory used=2317.1MB, alloc=396.3MB, time=59.61 memory used=2361.1MB, alloc=396.3MB, time=59.86 memory used=2400.2MB, alloc=396.3MB, time=60.09 memory used=2442.0MB, alloc=396.3MB, time=60.36 memory used=2486.6MB, alloc=396.3MB, time=60.59 memory used=2535.4MB, alloc=396.3MB, time=60.84 memory used=2587.9MB, alloc=396.3MB, time=61.08 memory used=2644.0MB, alloc=396.3MB, time=61.33 memory used=2718.2MB, alloc=396.3MB, time=61.82 memory used=2782.6MB, alloc=396.3MB, time=62.21 memory used=2834.0MB, alloc=396.3MB, time=62.53 memory used=2899.2MB, alloc=396.3MB, time=62.88 memory used=2943.0MB, alloc=396.3MB, time=63.18 memory used=2985.6MB, alloc=396.3MB, time=63.46 memory used=3033.4MB, alloc=396.3MB, time=63.74 memory used=3085.8MB, alloc=396.3MB, time=64.03 memory used=3145.6MB, alloc=396.3MB, time=64.33 memory used=3210.1MB, alloc=396.3MB, time=64.62 memory used=3254.5MB, alloc=396.3MB, time=64.94 memory used=3381.2MB, alloc=396.3MB, time=67.03 memory used=3506.1MB, alloc=396.3MB, time=68.90 memory used=3565.1MB, alloc=420.3MB, time=69.39 memory used=3628.2MB, alloc=420.3MB, time=69.76 memory used=3708.0MB, alloc=420.3MB, time=70.44 memory used=3810.6MB, alloc=420.3MB, time=75.67 memory used=3875.7MB, alloc=420.3MB, time=76.01 memory used=3928.7MB, alloc=420.3MB, time=76.30 memory used=4011.6MB, alloc=420.3MB, time=76.81 memory used=4073.8MB, alloc=420.3MB, time=77.27 memory used=4199.2MB, alloc=420.3MB, time=79.53 memory used=4319.3MB, alloc=420.3MB, time=81.88 memory used=4434.2MB, alloc=444.3MB, time=84.20 memory used=4531.2MB, alloc=444.3MB, time=86.42 memory used=4633.9MB, alloc=468.3MB, time=88.85 memory used=4742.3MB, alloc=468.3MB, time=91.05 memory used=4857.7MB, alloc=468.3MB, time=93.06 memory used=4957.5MB, alloc=468.3MB, time=94.79 memory used=5038.8MB, alloc=468.3MB, time=96.71 memory used=5144.5MB, alloc=492.3MB, time=98.53 memory used=5243.2MB, alloc=492.3MB, time=99.20 memory used=5312.3MB, alloc=492.3MB, time=99.78 memory used=5394.9MB, alloc=492.3MB, time=100.38 memory used=5496.7MB, alloc=492.3MB, time=101.01 memory used=5578.7MB, alloc=492.3MB, time=101.57 memory used=5646.1MB, alloc=492.3MB, time=102.06 memory used=5744.6MB, alloc=492.3MB, time=103.11 memory used=5835.0MB, alloc=492.3MB, time=103.78 memory used=5911.6MB, alloc=492.3MB, time=104.39 memory used=6034.1MB, alloc=492.3MB, time=112.92 memory used=6168.4MB, alloc=492.3MB, time=124.99 memory used=6259.4MB, alloc=492.3MB, time=125.63 memory used=6334.0MB, alloc=492.3MB, time=126.19 memory used=6414.4MB, alloc=492.3MB, time=126.74 memory used=6512.9MB, alloc=492.3MB, time=127.29 memory used=6695.0MB, alloc=492.3MB, time=128.93 memory used=6791.1MB, alloc=492.3MB, time=129.63 memory used=6861.7MB, alloc=492.3MB, time=130.26 memory used=6946.8MB, alloc=492.3MB, time=130.89 memory used=7050.2MB, alloc=492.3MB, time=131.53 memory used=7125.2MB, alloc=492.3MB, time=132.09 memory used=7193.9MB, alloc=492.3MB, time=132.59 memory used=7303.4MB, alloc=492.3MB, time=133.84 memory used=7400.3MB, alloc=492.3MB, time=134.57 memory used=7526.4MB, alloc=492.3MB, time=136.47 memory used=7641.0MB, alloc=492.3MB, time=138.18 memory used=7726.4MB, alloc=492.3MB, time=138.83 memory used=7837.8MB, alloc=492.3MB, time=140.72 memory used=7912.9MB, alloc=492.3MB, time=142.53 memory used=7972.0MB, alloc=492.3MB, time=144.22 memory used=8030.0MB, alloc=492.3MB, time=145.86 memory used=8077.4MB, alloc=492.3MB, time=147.38 memory used=8129.4MB, alloc=492.3MB, time=148.92 memory used=8204.7MB, alloc=492.3MB, time=150.46 memory used=8392.4MB, alloc=516.3MB, time=156.28 memory used=8593.3MB, alloc=540.3MB, time=159.78 memory used=8769.7MB, alloc=540.3MB, time=162.41 memory used=8939.9MB, alloc=540.3MB, time=171.49 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428264053 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 4 3 3 2 F := [18 x y - 8 x z + x y, 11 x z - 18 y - 10 y, 5 x y - 15 y z + 7 y ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 3 2 2 3 3 G := [-x z + 16 y z + 18 x, -12 x z - 9 x y - 18 z , 7 x y + 15 y + 11 z] > Problem := [F,G]; Problem := [ 2 2 3 4 3 3 2 [18 x y - 8 x z + x y, 11 x z - 18 y - 10 y, 5 x y - 15 y z + 7 y ], 3 3 3 2 2 3 3 [-x z + 16 y z + 18 x, -12 x z - 9 x y - 18 z , 7 x y + 15 y + 11 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=24.5MB, alloc=32.3MB, time=0.83 memory used=45.2MB, alloc=36.3MB, time=1.31 memory used=64.1MB, alloc=60.3MB, time=1.80 memory used=105.4MB, alloc=60.3MB, time=2.43 memory used=141.7MB, alloc=60.3MB, time=3.13 memory used=182.1MB, alloc=60.3MB, time=3.87 memory used=217.1MB, alloc=60.3MB, time=4.49 memory used=266.5MB, alloc=63.1MB, time=6.02 memory used=292.0MB, alloc=63.1MB, time=6.15 memory used=316.9MB, alloc=63.1MB, time=6.27 memory used=336.0MB, alloc=63.1MB, time=6.37 memory used=359.3MB, alloc=63.1MB, time=6.47 memory used=401.1MB, alloc=63.1MB, time=7.13 memory used=446.2MB, alloc=64.5MB, time=8.05 memory used=467.0MB, alloc=64.5MB, time=8.17 memory used=493.5MB, alloc=64.5MB, time=8.51 memory used=528.4MB, alloc=64.5MB, time=9.27 memory used=573.5MB, alloc=96.5MB, time=10.37 memory used=640.8MB, alloc=96.5MB, time=11.93 memory used=714.0MB, alloc=96.5MB, time=17.25 memory used=749.8MB, alloc=96.5MB, time=17.45 memory used=776.8MB, alloc=96.5MB, time=17.61 memory used=809.3MB, alloc=96.5MB, time=17.80 memory used=847.3MB, alloc=96.5MB, time=17.99 memory used=883.1MB, alloc=96.5MB, time=18.18 memory used=905.3MB, alloc=96.5MB, time=18.31 memory used=929.6MB, alloc=96.5MB, time=18.45 memory used=955.0MB, alloc=96.5MB, time=18.58 memory used=982.4MB, alloc=96.5MB, time=18.72 memory used=1011.0MB, alloc=96.5MB, time=18.86 memory used=1041.5MB, alloc=96.5MB, time=19.01 memory used=1074.2MB, alloc=96.5MB, time=19.16 memory used=1109.2MB, alloc=96.5MB, time=19.32 memory used=1146.5MB, alloc=96.5MB, time=19.48 memory used=1185.7MB, alloc=96.5MB, time=19.64 memory used=1226.9MB, alloc=96.5MB, time=19.80 memory used=1259.4MB, alloc=107.8MB, time=19.96 memory used=1268.9MB, alloc=107.8MB, time=20.06 memory used=1278.6MB, alloc=107.8MB, time=20.16 memory used=1288.3MB, alloc=107.8MB, time=20.26 memory used=1297.9MB, alloc=107.8MB, time=20.37 memory used=1307.5MB, alloc=107.8MB, time=20.48 memory used=1317.1MB, alloc=107.8MB, time=20.58 memory used=1327.0MB, alloc=107.8MB, time=20.68 memory used=1337.8MB, alloc=107.8MB, time=20.80 memory used=1348.7MB, alloc=107.8MB, time=20.91 memory used=1359.6MB, alloc=107.8MB, time=21.02 memory used=1370.4MB, alloc=107.8MB, time=21.11 memory used=1381.1MB, alloc=107.8MB, time=21.22 memory used=1392.1MB, alloc=107.8MB, time=21.32 memory used=1403.8MB, alloc=107.8MB, time=21.44 memory used=1415.6MB, alloc=107.8MB, time=21.55 memory used=1427.3MB, alloc=107.8MB, time=21.67 memory used=1439.3MB, alloc=107.8MB, time=21.82 memory used=1451.7MB, alloc=107.8MB, time=21.93 memory used=1464.3MB, alloc=107.8MB, time=22.03 memory used=1477.0MB, alloc=107.8MB, time=22.14 memory used=1490.1MB, alloc=107.8MB, time=22.26 memory used=1503.5MB, alloc=107.8MB, time=22.37 memory used=1517.2MB, alloc=107.8MB, time=22.51 memory used=1531.3MB, alloc=107.8MB, time=22.63 memory used=1545.7MB, alloc=107.8MB, time=22.75 memory used=1560.5MB, alloc=107.8MB, time=22.87 memory used=1575.8MB, alloc=107.8MB, time=23.03 memory used=1591.8MB, alloc=107.8MB, time=23.14 memory used=1676.1MB, alloc=107.8MB, time=24.33 memory used=1718.0MB, alloc=107.8MB, time=24.92 memory used=1787.0MB, alloc=107.8MB, time=27.52 memory used=1819.3MB, alloc=107.8MB, time=27.71 memory used=1850.4MB, alloc=107.8MB, time=27.88 memory used=1879.8MB, alloc=107.8MB, time=28.03 memory used=1906.9MB, alloc=107.8MB, time=28.18 memory used=1986.6MB, alloc=107.8MB, time=30.27 memory used=2049.4MB, alloc=131.8MB, time=31.61 memory used=2116.3MB, alloc=131.8MB, time=32.39 memory used=2201.1MB, alloc=155.8MB, time=34.46 memory used=2277.2MB, alloc=411.8MB, time=36.61 memory used=2373.4MB, alloc=411.8MB, time=38.18 memory used=2494.5MB, alloc=411.8MB, time=40.66 memory used=2598.0MB, alloc=411.8MB, time=42.63 memory used=2720.7MB, alloc=435.8MB, time=44.63 memory used=2841.1MB, alloc=435.8MB, time=46.05 memory used=2975.7MB, alloc=435.8MB, time=47.89 memory used=3137.2MB, alloc=459.8MB, time=50.17 memory used=3273.5MB, alloc=459.8MB, time=52.66 memory used=3376.6MB, alloc=483.8MB, time=55.05 memory used=3471.5MB, alloc=483.8MB, time=56.92 memory used=3578.7MB, alloc=483.8MB, time=58.78 memory used=3719.7MB, alloc=507.8MB, time=60.37 memory used=3836.7MB, alloc=507.8MB, time=64.11 memory used=3996.1MB, alloc=507.8MB, time=69.79 memory used=4081.4MB, alloc=507.8MB, time=70.38 memory used=4185.1MB, alloc=507.8MB, time=70.99 memory used=4253.3MB, alloc=507.8MB, time=71.47 memory used=4349.7MB, alloc=507.8MB, time=72.28 memory used=4459.8MB, alloc=507.8MB, time=74.25 memory used=4561.4MB, alloc=507.8MB, time=76.12 memory used=4672.5MB, alloc=507.8MB, time=77.91 memory used=4796.9MB, alloc=507.8MB, time=82.51 memory used=4884.9MB, alloc=507.8MB, time=83.10 memory used=5007.8MB, alloc=507.8MB, time=84.99 memory used=5100.0MB, alloc=507.8MB, time=86.78 memory used=5216.0MB, alloc=531.8MB, time=88.58 memory used=5306.5MB, alloc=531.8MB, time=90.34 memory used=5404.2MB, alloc=531.8MB, time=93.29 memory used=5520.2MB, alloc=531.8MB, time=97.28 memory used=5583.4MB, alloc=531.8MB, time=98.97 memory used=5662.1MB, alloc=531.8MB, time=103.57 memory used=5767.5MB, alloc=531.8MB, time=105.09 memory used=5810.5MB, alloc=531.8MB, time=106.43 memory used=5869.4MB, alloc=531.8MB, time=107.73 memory used=5914.0MB, alloc=531.8MB, time=109.19 memory used=6097.6MB, alloc=531.8MB, time=111.75 memory used=6209.3MB, alloc=531.8MB, time=112.79 memory used=6364.7MB, alloc=531.8MB, time=115.06 memory used=6465.4MB, alloc=531.8MB, time=115.88 memory used=6546.0MB, alloc=531.8MB, time=116.59 memory used=6653.2MB, alloc=531.8MB, time=117.32 memory used=6726.2MB, alloc=531.8MB, time=117.96 memory used=6837.7MB, alloc=531.8MB, time=119.09 memory used=6934.7MB, alloc=531.8MB, time=119.87 memory used=7021.7MB, alloc=531.8MB, time=120.60 memory used=7124.6MB, alloc=531.8MB, time=121.33 memory used=7196.3MB, alloc=531.8MB, time=121.98 memory used=7333.4MB, alloc=531.8MB, time=128.45 memory used=7415.8MB, alloc=531.8MB, time=129.23 memory used=7525.0MB, alloc=531.8MB, time=130.03 memory used=7606.7MB, alloc=531.8MB, time=130.76 memory used=7682.6MB, alloc=531.8MB, time=131.44 memory used=7768.2MB, alloc=531.8MB, time=132.14 memory used=7864.7MB, alloc=531.8MB, time=132.83 memory used=7974.5MB, alloc=531.8MB, time=133.53 memory used=8160.9MB, alloc=531.8MB, time=134.64 memory used=8270.2MB, alloc=531.8MB, time=135.53 memory used=8395.0MB, alloc=531.8MB, time=138.67 memory used=8490.8MB, alloc=531.8MB, time=139.45 memory used=8576.2MB, alloc=531.8MB, time=140.13 memory used=8660.8MB, alloc=531.8MB, time=140.80 memory used=8775.9MB, alloc=531.8MB, time=141.79 memory used=8904.9MB, alloc=531.8MB, time=145.01 memory used=8997.3MB, alloc=531.8MB, time=145.79 memory used=9102.9MB, alloc=531.8MB, time=146.57 memory used=9176.3MB, alloc=531.8MB, time=147.23 memory used=9283.3MB, alloc=531.8MB, time=148.20 memory used=9488.0MB, alloc=531.8MB, time=151.29 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428264353 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; F := [ 3 2 4 2 4 2 2 -13 x y + 7 x y + 18 y, -20 x - 13 x y z - 16 z, -4 z - 20 y z + 7 x ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 4 3 G := [20 x y + 20 x y z + 4 x y , 15 x - 5 x y - 10 x z, 2 2 2 3 18 x y + 8 x y - 7 y ] > Problem := [F,G]; Problem := [[ 3 2 4 2 4 2 2 -13 x y + 7 x y + 18 y, -20 x - 13 x y z - 16 z, -4 z - 20 y z + 7 x 3 2 3 4 3 ], [20 x y + 20 x y z + 4 x y , 15 x - 5 x y - 10 x z, 2 2 2 3 18 x y + 8 x y - 7 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.9MB, alloc=32.3MB, time=0.88 memory used=47.5MB, alloc=32.3MB, time=1.40 memory used=67.3MB, alloc=60.3MB, time=1.94 memory used=108.9MB, alloc=60.3MB, time=2.96 memory used=146.9MB, alloc=60.3MB, time=3.88 memory used=186.9MB, alloc=92.3MB, time=4.95 memory used=253.1MB, alloc=92.3MB, time=6.54 memory used=320.7MB, alloc=92.3MB, time=8.09 memory used=381.5MB, alloc=92.3MB, time=9.14 memory used=443.5MB, alloc=116.3MB, time=10.48 memory used=509.0MB, alloc=372.3MB, time=12.14 memory used=606.9MB, alloc=372.3MB, time=14.40 memory used=695.1MB, alloc=396.3MB, time=16.48 memory used=810.8MB, alloc=396.3MB, time=19.32 memory used=925.2MB, alloc=420.3MB, time=21.84 memory used=1035.2MB, alloc=420.3MB, time=24.38 memory used=1146.4MB, alloc=444.3MB, time=26.76 memory used=1252.2MB, alloc=444.3MB, time=29.22 memory used=1363.4MB, alloc=468.3MB, time=32.01 memory used=1462.1MB, alloc=468.3MB, time=34.97 memory used=1553.8MB, alloc=468.3MB, time=37.18 memory used=1654.4MB, alloc=468.3MB, time=39.57 memory used=1731.8MB, alloc=468.3MB, time=41.95 memory used=1814.2MB, alloc=468.3MB, time=43.99 memory used=1894.7MB, alloc=468.3MB, time=46.36 memory used=1966.0MB, alloc=468.3MB, time=48.15 memory used=2074.6MB, alloc=492.3MB, time=50.20 memory used=2179.1MB, alloc=492.3MB, time=53.45 memory used=2273.2MB, alloc=492.3MB, time=57.26 memory used=2343.7MB, alloc=492.3MB, time=59.03 memory used=2423.1MB, alloc=492.3MB, time=61.36 memory used=2498.5MB, alloc=492.3MB, time=62.84 memory used=2556.7MB, alloc=492.3MB, time=64.48 memory used=2613.6MB, alloc=492.3MB, time=66.08 memory used=2670.8MB, alloc=492.3MB, time=67.73 memory used=2716.7MB, alloc=492.3MB, time=68.97 memory used=2763.3MB, alloc=492.3MB, time=70.48 memory used=2951.0MB, alloc=516.3MB, time=73.96 memory used=3077.7MB, alloc=516.3MB, time=75.28 memory used=3194.6MB, alloc=516.3MB, time=78.33 memory used=3365.3MB, alloc=516.3MB, time=79.58 memory used=3518.7MB, alloc=516.3MB, time=82.22 memory used=3687.1MB, alloc=516.3MB, time=87.90 memory used=3902.7MB, alloc=540.3MB, time=92.91 memory used=4085.5MB, alloc=540.3MB, time=97.15 memory used=4254.0MB, alloc=564.3MB, time=101.03 memory used=4378.2MB, alloc=564.3MB, time=102.20 memory used=4481.7MB, alloc=564.3MB, time=103.23 memory used=4619.4MB, alloc=564.3MB, time=104.76 memory used=4726.2MB, alloc=564.3MB, time=105.84 memory used=4876.6MB, alloc=564.3MB, time=114.60 memory used=4987.6MB, alloc=564.3MB, time=115.69 memory used=5090.4MB, alloc=564.3MB, time=116.66 memory used=5228.1MB, alloc=564.3MB, time=118.18 memory used=5359.7MB, alloc=564.3MB, time=121.39 memory used=5564.3MB, alloc=588.3MB, time=125.29 memory used=5755.3MB, alloc=588.3MB, time=129.75 memory used=5913.2MB, alloc=588.3MB, time=133.85 memory used=6059.1MB, alloc=612.3MB, time=138.17 memory used=6180.6MB, alloc=612.3MB, time=141.94 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428264654 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 2 2 2 4 2 2 F := [9 x + 19 y - 16 y, 16 x z - 13 y z + 4 x y, 17 y + 17 y z - 5 x ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; G := [ 3 2 2 3 3 3 3 3 2 -5 x y + 2 x y z + 9 x y, 18 y z - 3 x + 7 y , 11 x y + 17 y - 3 x ] > Problem := [F,G]; Problem := [ 4 3 2 2 2 4 2 2 [9 x + 19 y - 16 y, 16 x z - 13 y z + 4 x y, 17 y + 17 y z - 5 x ], 3 2 2 3 3 3 3 3 2 [-5 x y + 2 x y z + 9 x y, 18 y z - 3 x + 7 y , 11 x y + 17 y - 3 x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=29.9MB, alloc=44.3MB, time=0.97 memory used=56.0MB, alloc=44.3MB, time=1.59 memory used=82.9MB, alloc=44.3MB, time=2.20 memory used=110.2MB, alloc=68.3MB, time=2.72 memory used=148.8MB, alloc=68.3MB, time=3.61 memory used=197.5MB, alloc=76.3MB, time=4.79 memory used=246.6MB, alloc=76.3MB, time=5.93 memory used=301.0MB, alloc=100.3MB, time=7.02 memory used=375.4MB, alloc=100.3MB, time=8.58 memory used=435.4MB, alloc=124.3MB, time=9.77 memory used=520.9MB, alloc=124.3MB, time=11.02 memory used=579.7MB, alloc=124.3MB, time=12.27 memory used=632.9MB, alloc=380.3MB, time=13.26 memory used=730.5MB, alloc=404.3MB, time=15.40 memory used=847.5MB, alloc=428.3MB, time=17.88 memory used=962.7MB, alloc=428.3MB, time=20.34 memory used=1048.1MB, alloc=428.3MB, time=21.27 memory used=1139.0MB, alloc=428.3MB, time=22.21 memory used=1223.1MB, alloc=428.3MB, time=24.62 memory used=1368.5MB, alloc=428.3MB, time=28.55 memory used=1429.9MB, alloc=428.3MB, time=28.95 memory used=1557.0MB, alloc=452.3MB, time=31.67 memory used=1670.1MB, alloc=452.3MB, time=34.34 memory used=1796.6MB, alloc=452.3MB, time=36.68 memory used=1871.6MB, alloc=452.3MB, time=37.24 memory used=1990.9MB, alloc=452.3MB, time=39.56 memory used=2106.1MB, alloc=476.3MB, time=42.34 memory used=2208.9MB, alloc=476.3MB, time=44.85 memory used=2298.8MB, alloc=476.3MB, time=46.82 memory used=2388.4MB, alloc=476.3MB, time=49.05 memory used=2501.9MB, alloc=476.3MB, time=50.39 memory used=2579.8MB, alloc=476.3MB, time=51.00 memory used=2668.3MB, alloc=476.3MB, time=51.73 memory used=2746.5MB, alloc=476.3MB, time=52.29 memory used=2826.7MB, alloc=476.3MB, time=53.09 memory used=2905.3MB, alloc=476.3MB, time=53.70 memory used=3001.6MB, alloc=476.3MB, time=55.93 memory used=3083.9MB, alloc=500.3MB, time=56.63 memory used=3176.6MB, alloc=500.3MB, time=57.26 memory used=3258.1MB, alloc=500.3MB, time=57.86 memory used=3358.8MB, alloc=500.3MB, time=58.48 memory used=3453.4MB, alloc=500.3MB, time=59.04 memory used=3556.0MB, alloc=500.3MB, time=60.05 memory used=3658.3MB, alloc=500.3MB, time=60.80 memory used=3732.8MB, alloc=500.3MB, time=61.40 memory used=3824.8MB, alloc=500.3MB, time=62.02 memory used=3937.5MB, alloc=500.3MB, time=62.67 memory used=4017.3MB, alloc=500.3MB, time=64.69 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428264954 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; F := [ 3 2 3 2 2 2 3 -11 x + 7 x - 7 x z, 11 x y + 11 x y z - x , 19 x y z + 14 x + 3 x y] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 3 2 G := [13 x z - 18 x y z + 12 y , 6 x y - 10 x y + 10 y , 3 2 2 -7 y z + 8 x z - 5 x ] > Problem := [F,G]; Problem := [[ 3 2 3 2 2 2 3 -11 x + 7 x - 7 x z, 11 x y + 11 x y z - x , 19 x y z + 14 x + 3 x y] 2 2 2 2 3 2 , [13 x z - 18 x y z + 12 y , 6 x y - 10 x y + 10 y , 3 2 2 -7 y z + 8 x z - 5 x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.30 memory used=26.8MB, alloc=32.3MB, time=0.87 memory used=47.8MB, alloc=32.3MB, time=1.41 memory used=66.8MB, alloc=56.3MB, time=1.94 memory used=109.0MB, alloc=68.3MB, time=3.03 memory used=150.0MB, alloc=68.3MB, time=4.07 memory used=192.9MB, alloc=92.3MB, time=5.12 memory used=260.6MB, alloc=92.3MB, time=6.77 memory used=324.5MB, alloc=116.3MB, time=8.46 memory used=395.4MB, alloc=372.3MB, time=10.34 memory used=484.2MB, alloc=372.3MB, time=12.59 memory used=570.5MB, alloc=396.3MB, time=14.80 memory used=681.5MB, alloc=396.3MB, time=17.58 memory used=779.5MB, alloc=420.3MB, time=21.58 memory used=855.9MB, alloc=420.3MB, time=22.23 memory used=957.8MB, alloc=420.3MB, time=23.51 memory used=1051.6MB, alloc=420.3MB, time=25.29 memory used=1150.1MB, alloc=420.3MB, time=27.07 memory used=1280.6MB, alloc=420.3MB, time=30.12 memory used=1397.0MB, alloc=444.3MB, time=32.68 memory used=1541.6MB, alloc=444.3MB, time=36.38 memory used=1666.3MB, alloc=444.3MB, time=38.64 memory used=1805.2MB, alloc=444.3MB, time=41.37 memory used=1893.0MB, alloc=444.3MB, time=44.47 memory used=2029.8MB, alloc=444.3MB, time=46.86 memory used=2118.3MB, alloc=444.3MB, time=48.30 memory used=2200.7MB, alloc=444.3MB, time=49.61 memory used=2326.5MB, alloc=444.3MB, time=51.55 memory used=2410.8MB, alloc=444.3MB, time=55.42 memory used=2475.9MB, alloc=444.3MB, time=55.89 memory used=2539.3MB, alloc=444.3MB, time=56.29 memory used=2631.4MB, alloc=444.3MB, time=57.44 memory used=2703.1MB, alloc=444.3MB, time=58.16 memory used=2801.4MB, alloc=444.3MB, time=66.37 memory used=2864.3MB, alloc=444.3MB, time=66.84 memory used=2928.7MB, alloc=444.3MB, time=67.27 memory used=2983.3MB, alloc=444.3MB, time=67.66 memory used=3048.9MB, alloc=444.3MB, time=68.09 memory used=3202.5MB, alloc=468.3MB, time=70.63 memory used=3303.0MB, alloc=468.3MB, time=71.78 memory used=3406.0MB, alloc=468.3MB, time=74.46 memory used=3478.5MB, alloc=468.3MB, time=74.91 memory used=3584.8MB, alloc=468.3MB, time=76.18 memory used=3704.1MB, alloc=468.3MB, time=82.12 memory used=3786.4MB, alloc=468.3MB, time=82.64 memory used=3851.2MB, alloc=468.3MB, time=83.06 memory used=3991.5MB, alloc=468.3MB, time=84.79 memory used=4090.0MB, alloc=468.3MB, time=87.66 memory used=4178.3MB, alloc=468.3MB, time=90.13 memory used=4254.4MB, alloc=492.3MB, time=92.13 memory used=4326.3MB, alloc=492.3MB, time=93.97 memory used=4411.0MB, alloc=492.3MB, time=96.50 memory used=4473.4MB, alloc=492.3MB, time=98.26 memory used=4535.1MB, alloc=492.3MB, time=99.86 memory used=4573.3MB, alloc=492.3MB, time=100.89 memory used=4620.9MB, alloc=492.3MB, time=102.32 memory used=4674.3MB, alloc=492.3MB, time=104.25 memory used=4707.6MB, alloc=492.3MB, time=105.57 memory used=4891.1MB, alloc=516.3MB, time=109.75 memory used=5065.2MB, alloc=540.3MB, time=114.29 memory used=5233.1MB, alloc=564.3MB, time=119.14 memory used=5378.9MB, alloc=588.3MB, time=123.26 memory used=5534.9MB, alloc=612.3MB, time=128.24 memory used=5682.0MB, alloc=612.3MB, time=132.90 memory used=5815.7MB, alloc=636.3MB, time=136.59 memory used=5960.5MB, alloc=636.3MB, time=140.60 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428265254 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 4 3 2 3 2 F := [-4 y - x z - 16 y, 8 x - 4 y z + 10 x y , -10 y z - 11 x z + 2 x z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 G := [-6 x y + 13 x z - 10 x, -20 x y + 13 x z - 12 x y z , 2 2 2 13 x y + x y z + 2 x] > Problem := [F,G]; Problem := [ 4 2 4 3 2 3 2 [-4 y - x z - 16 y, 8 x - 4 y z + 10 x y , -10 y z - 11 x z + 2 x z], 3 2 2 2 [-6 x y + 13 x z - 10 x, -20 x y + 13 x z - 12 x y z , 2 2 2 13 x y + x y z + 2 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.29 memory used=26.0MB, alloc=32.3MB, time=0.86 memory used=46.0MB, alloc=32.3MB, time=1.37 memory used=64.8MB, alloc=56.3MB, time=1.88 memory used=105.4MB, alloc=60.3MB, time=2.83 memory used=140.5MB, alloc=60.3MB, time=3.27 memory used=177.6MB, alloc=60.3MB, time=4.01 memory used=206.9MB, alloc=60.3MB, time=4.65 memory used=246.6MB, alloc=92.3MB, time=5.69 memory used=310.8MB, alloc=92.3MB, time=7.27 memory used=374.4MB, alloc=116.3MB, time=8.86 memory used=432.5MB, alloc=372.3MB, time=10.12 memory used=521.9MB, alloc=372.3MB, time=12.26 memory used=613.5MB, alloc=396.3MB, time=14.14 memory used=718.3MB, alloc=396.3MB, time=16.56 memory used=779.0MB, alloc=396.3MB, time=17.07 memory used=896.3MB, alloc=396.3MB, time=19.77 memory used=996.4MB, alloc=420.3MB, time=22.57 memory used=1123.0MB, alloc=444.3MB, time=25.60 memory used=1269.0MB, alloc=444.3MB, time=28.46 memory used=1387.9MB, alloc=444.3MB, time=31.35 memory used=1509.3MB, alloc=468.3MB, time=34.36 memory used=1631.8MB, alloc=468.3MB, time=37.06 memory used=1713.8MB, alloc=468.3MB, time=39.00 memory used=1821.1MB, alloc=468.3MB, time=40.45 memory used=1908.8MB, alloc=468.3MB, time=41.28 memory used=2035.3MB, alloc=468.3MB, time=43.98 memory used=2155.2MB, alloc=468.3MB, time=47.26 memory used=2249.6MB, alloc=468.3MB, time=48.33 memory used=2350.4MB, alloc=468.3MB, time=49.57 memory used=2438.9MB, alloc=468.3MB, time=51.81 memory used=2526.2MB, alloc=492.3MB, time=54.05 memory used=2605.5MB, alloc=492.3MB, time=56.30 memory used=2719.1MB, alloc=492.3MB, time=58.01 memory used=2822.8MB, alloc=492.3MB, time=59.04 memory used=2911.4MB, alloc=492.3MB, time=60.70 memory used=2983.9MB, alloc=492.3MB, time=63.05 memory used=3053.6MB, alloc=492.3MB, time=64.92 memory used=3110.3MB, alloc=492.3MB, time=66.56 memory used=3161.9MB, alloc=516.3MB, time=67.92 memory used=3206.2MB, alloc=516.3MB, time=69.47 memory used=3261.2MB, alloc=516.3MB, time=71.56 memory used=3316.7MB, alloc=516.3MB, time=73.34 memory used=3350.0MB, alloc=516.3MB, time=74.70 memory used=3553.8MB, alloc=540.3MB, time=80.78 memory used=3764.9MB, alloc=564.3MB, time=86.44 memory used=3923.5MB, alloc=588.3MB, time=90.48 memory used=4115.5MB, alloc=612.3MB, time=93.89 memory used=4333.9MB, alloc=612.3MB, time=100.48 memory used=4500.7MB, alloc=636.3MB, time=104.13 memory used=4658.5MB, alloc=660.3MB, time=107.98 memory used=4819.1MB, alloc=684.3MB, time=110.99 memory used=4970.7MB, alloc=684.3MB, time=115.56 memory used=5113.3MB, alloc=684.3MB, time=119.78 memory used=5327.6MB, alloc=684.3MB, time=125.75 memory used=5515.7MB, alloc=708.3MB, time=129.83 memory used=5605.7MB, alloc=708.3MB, time=132.75 memory used=5704.0MB, alloc=708.3MB, time=135.65 memory used=5799.7MB, alloc=708.3MB, time=138.82 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428265554 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 2 2 2 3 2 F := [-4 y + 11 z + 2 y , 15 x y - 10 y z - 2 x, y z + 13 x y - 16 z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 3 3 2 G := [12 x + 16 x y z + 12 y z , -17 x z - 12 y z + 14 y , 3 2 5 x y + 18 x y z + 2 x z] > Problem := [F,G]; Problem := [ 4 3 2 2 2 3 2 [-4 y + 11 z + 2 y , 15 x y - 10 y z - 2 x, y z + 13 x y - 16 z ], [ 4 2 2 3 3 2 12 x + 16 x y z + 12 y z , -17 x z - 12 y z + 14 y , 3 2 5 x y + 18 x y z + 2 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.31 memory used=26.0MB, alloc=32.3MB, time=0.87 memory used=45.7MB, alloc=60.3MB, time=1.39 memory used=85.0MB, alloc=60.3MB, time=2.34 memory used=130.3MB, alloc=68.3MB, time=3.33 memory used=170.2MB, alloc=68.3MB, time=3.83 memory used=192.4MB, alloc=68.3MB, time=3.96 memory used=219.1MB, alloc=68.3MB, time=4.14 memory used=242.4MB, alloc=68.3MB, time=4.27 memory used=270.1MB, alloc=68.3MB, time=5.43 memory used=296.8MB, alloc=68.3MB, time=5.67 memory used=328.5MB, alloc=68.3MB, time=6.21 memory used=373.7MB, alloc=68.3MB, time=8.10 memory used=398.2MB, alloc=68.3MB, time=8.23 memory used=422.1MB, alloc=68.3MB, time=8.46 memory used=474.2MB, alloc=68.3MB, time=9.26 memory used=521.2MB, alloc=68.3MB, time=10.43 memory used=570.0MB, alloc=68.3MB, time=12.33 memory used=616.4MB, alloc=92.3MB, time=13.64 memory used=669.7MB, alloc=92.3MB, time=14.36 memory used=739.2MB, alloc=92.3MB, time=15.71 memory used=779.7MB, alloc=92.3MB, time=15.97 memory used=820.3MB, alloc=92.3MB, time=16.96 memory used=887.1MB, alloc=92.3MB, time=18.07 memory used=923.7MB, alloc=92.3MB, time=18.25 memory used=952.8MB, alloc=92.3MB, time=18.40 memory used=985.8MB, alloc=92.3MB, time=18.57 memory used=1022.8MB, alloc=92.3MB, time=18.74 memory used=1048.0MB, alloc=92.3MB, time=18.87 memory used=1095.6MB, alloc=92.3MB, time=21.19 memory used=1127.6MB, alloc=92.3MB, time=21.36 memory used=1177.8MB, alloc=92.3MB, time=21.99 memory used=1222.1MB, alloc=92.3MB, time=23.36 memory used=1267.1MB, alloc=92.3MB, time=28.66 memory used=1297.8MB, alloc=92.3MB, time=28.83 memory used=1333.1MB, alloc=92.3MB, time=29.01 memory used=1364.1MB, alloc=92.3MB, time=29.15 memory used=1389.7MB, alloc=92.3MB, time=29.29 memory used=1420.6MB, alloc=92.3MB, time=29.42 memory used=1461.1MB, alloc=92.3MB, time=29.84 memory used=1493.3MB, alloc=92.3MB, time=30.15 memory used=1550.7MB, alloc=92.3MB, time=31.01 memory used=1611.2MB, alloc=92.3MB, time=32.16 memory used=1653.0MB, alloc=92.3MB, time=32.89 memory used=1704.6MB, alloc=92.3MB, time=36.10 memory used=1740.7MB, alloc=92.3MB, time=36.32 memory used=1773.8MB, alloc=92.3MB, time=36.48 memory used=1799.6MB, alloc=92.3MB, time=36.61 memory used=1843.3MB, alloc=92.3MB, time=38.27 memory used=1912.7MB, alloc=92.3MB, time=39.76 memory used=1975.6MB, alloc=116.3MB, time=41.12 memory used=2041.1MB, alloc=372.3MB, time=42.59 memory used=2129.6MB, alloc=396.3MB, time=44.57 memory used=2242.4MB, alloc=396.3MB, time=46.67 memory used=2301.3MB, alloc=396.3MB, time=47.10 memory used=2366.1MB, alloc=396.3MB, time=51.85 memory used=2467.2MB, alloc=396.3MB, time=53.41 memory used=2581.7MB, alloc=420.3MB, time=55.92 memory used=2705.3MB, alloc=420.3MB, time=58.05 memory used=2794.5MB, alloc=420.3MB, time=59.33 memory used=2877.6MB, alloc=420.3MB, time=61.03 memory used=2939.4MB, alloc=420.3MB, time=61.45 memory used=2986.8MB, alloc=420.3MB, time=61.81 memory used=3052.2MB, alloc=420.3MB, time=62.32 memory used=3123.2MB, alloc=420.3MB, time=63.00 memory used=3179.3MB, alloc=420.3MB, time=63.40 memory used=3236.5MB, alloc=420.3MB, time=63.76 memory used=3317.0MB, alloc=420.3MB, time=68.80 memory used=3388.2MB, alloc=420.3MB, time=70.59 memory used=3450.0MB, alloc=420.3MB, time=71.16 memory used=3524.3MB, alloc=420.3MB, time=71.75 memory used=3604.7MB, alloc=444.3MB, time=78.55 memory used=3698.6MB, alloc=444.3MB, time=79.88 memory used=3790.9MB, alloc=444.3MB, time=81.84 memory used=3883.7MB, alloc=444.3MB, time=82.42 memory used=3952.6MB, alloc=444.3MB, time=82.88 memory used=4037.2MB, alloc=444.3MB, time=83.36 memory used=4116.9MB, alloc=444.3MB, time=83.83 memory used=4169.7MB, alloc=444.3MB, time=84.22 memory used=4225.8MB, alloc=444.3MB, time=84.63 memory used=4287.5MB, alloc=444.3MB, time=85.03 memory used=4351.9MB, alloc=444.3MB, time=85.44 memory used=4422.0MB, alloc=444.3MB, time=85.85 memory used=4494.7MB, alloc=444.3MB, time=86.26 memory used=4573.1MB, alloc=444.3MB, time=86.69 memory used=4657.4MB, alloc=444.3MB, time=87.11 memory used=4747.5MB, alloc=444.3MB, time=87.55 memory used=4836.7MB, alloc=444.3MB, time=87.97 memory used=4885.5MB, alloc=444.3MB, time=88.29 memory used=4932.8MB, alloc=444.3MB, time=88.62 memory used=4982.6MB, alloc=444.3MB, time=88.94 memory used=5032.7MB, alloc=468.3MB, time=89.30 memory used=5097.2MB, alloc=468.3MB, time=89.66 memory used=5167.3MB, alloc=468.3MB, time=90.03 memory used=5237.6MB, alloc=468.3MB, time=90.38 memory used=5311.6MB, alloc=468.3MB, time=90.74 memory used=5389.1MB, alloc=468.3MB, time=91.13 memory used=5469.9MB, alloc=468.3MB, time=91.51 memory used=5553.7MB, alloc=468.3MB, time=91.91 memory used=5639.9MB, alloc=468.3MB, time=92.29 memory used=5728.2MB, alloc=468.3MB, time=92.70 memory used=5821.4MB, alloc=468.3MB, time=93.09 memory used=5918.5MB, alloc=468.3MB, time=93.49 memory used=6021.4MB, alloc=468.3MB, time=93.91 memory used=6130.8MB, alloc=468.3MB, time=94.31 memory used=6261.2MB, alloc=468.3MB, time=94.79 memory used=6427.0MB, alloc=468.3MB, time=95.58 memory used=6568.5MB, alloc=468.3MB, time=97.76 memory used=6651.8MB, alloc=468.3MB, time=98.29 memory used=6759.5MB, alloc=468.3MB, time=98.86 memory used=6844.6MB, alloc=468.3MB, time=99.34 memory used=6912.4MB, alloc=468.3MB, time=99.78 memory used=6986.5MB, alloc=468.3MB, time=100.23 memory used=7067.7MB, alloc=468.3MB, time=100.69 memory used=7156.3MB, alloc=468.3MB, time=101.17 memory used=7252.1MB, alloc=468.3MB, time=101.65 memory used=7355.1MB, alloc=468.3MB, time=102.13 memory used=7465.3MB, alloc=468.3MB, time=102.60 memory used=7559.4MB, alloc=468.3MB, time=103.03 memory used=7620.7MB, alloc=468.3MB, time=103.39 memory used=7682.5MB, alloc=468.3MB, time=103.74 memory used=7748.3MB, alloc=468.3MB, time=104.12 memory used=7814.5MB, alloc=468.3MB, time=104.48 memory used=7884.7MB, alloc=468.3MB, time=104.85 memory used=7954.9MB, alloc=468.3MB, time=105.22 memory used=8028.8MB, alloc=468.3MB, time=105.59 memory used=8106.3MB, alloc=468.3MB, time=105.96 memory used=8187.0MB, alloc=468.3MB, time=106.32 memory used=8270.5MB, alloc=468.3MB, time=106.70 memory used=8356.5MB, alloc=468.3MB, time=107.08 memory used=8448.0MB, alloc=468.3MB, time=107.45 memory used=8540.8MB, alloc=468.3MB, time=107.84 memory used=8640.5MB, alloc=468.3MB, time=108.24 memory used=8742.7MB, alloc=468.3MB, time=108.63 memory used=8850.7MB, alloc=468.3MB, time=109.03 memory used=8990.6MB, alloc=468.3MB, time=109.49 memory used=9138.9MB, alloc=468.3MB, time=110.01 memory used=9260.7MB, alloc=468.3MB, time=161.14 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428265854 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 3 2 F := [7 x + 8 x z - 10 y z, 14 x z + 2 x z, -11 x y + 20 x z + 7 z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 3 4 2 2 2 G := [20 x y z - 7 z + 10 x , 15 x z + 17 y - 2 y z , -7 x y + 13 x z] > Problem := [F,G]; Problem := [ 3 2 2 2 3 2 [7 x + 8 x z - 10 y z, 14 x z + 2 x z, -11 x y + 20 x z + 7 z], 2 3 2 3 4 2 2 2 [20 x y z - 7 z + 10 x , 15 x z + 17 y - 2 y z , -7 x y + 13 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.7MB, alloc=32.3MB, time=0.87 memory used=47.0MB, alloc=32.3MB, time=1.39 memory used=65.6MB, alloc=56.3MB, time=1.90 memory used=106.1MB, alloc=60.3MB, time=2.97 memory used=144.8MB, alloc=84.3MB, time=4.00 memory used=206.2MB, alloc=92.3MB, time=5.63 memory used=265.5MB, alloc=92.3MB, time=7.17 memory used=324.6MB, alloc=116.3MB, time=8.72 memory used=404.6MB, alloc=116.3MB, time=10.89 memory used=482.5MB, alloc=140.3MB, time=13.09 memory used=555.9MB, alloc=396.3MB, time=15.17 memory used=666.4MB, alloc=420.3MB, time=17.74 memory used=790.2MB, alloc=444.3MB, time=21.23 memory used=917.6MB, alloc=468.3MB, time=24.56 memory used=1044.9MB, alloc=468.3MB, time=27.79 memory used=1166.8MB, alloc=468.3MB, time=30.92 memory used=1281.3MB, alloc=492.3MB, time=34.03 memory used=1380.5MB, alloc=492.3MB, time=36.73 memory used=1479.2MB, alloc=492.3MB, time=39.49 memory used=1579.2MB, alloc=492.3MB, time=42.29 memory used=1671.8MB, alloc=492.3MB, time=44.86 memory used=1743.6MB, alloc=492.3MB, time=47.03 memory used=1829.5MB, alloc=492.3MB, time=49.15 memory used=1901.1MB, alloc=492.3MB, time=51.19 memory used=1964.7MB, alloc=516.3MB, time=52.99 memory used=2049.2MB, alloc=516.3MB, time=55.58 memory used=2118.0MB, alloc=516.3MB, time=57.68 memory used=2195.0MB, alloc=516.3MB, time=60.44 memory used=2272.5MB, alloc=516.3MB, time=63.09 memory used=2335.4MB, alloc=516.3MB, time=65.25 memory used=2397.4MB, alloc=516.3MB, time=66.97 memory used=2459.8MB, alloc=516.3MB, time=69.53 memory used=2508.3MB, alloc=516.3MB, time=71.47 memory used=2712.1MB, alloc=540.3MB, time=77.75 memory used=2902.0MB, alloc=564.3MB, time=83.30 memory used=3092.3MB, alloc=588.3MB, time=88.72 memory used=3256.4MB, alloc=612.3MB, time=93.42 memory used=3453.7MB, alloc=612.3MB, time=99.89 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428266154 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; F := [ 3 2 2 2 2 2 2 3 2 2 -8 x y - 6 x y z + 7 y z, -9 x y - 20 x y - x z , -3 x y + 17 x y ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 4 G := [15 y z - 11 y z - 15 y, 5 x y + 17 x z, -10 x y + 9 z + 14 x z] > Problem := [F,G]; Problem := [[ 3 2 2 2 2 2 2 3 2 2 -8 x y - 6 x y z + 7 y z, -9 x y - 20 x y - x z , -3 x y + 17 x y ] 3 3 2 2 4 , [15 y z - 11 y z - 15 y, 5 x y + 17 x z, -10 x y + 9 z + 14 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.31 memory used=27.2MB, alloc=32.3MB, time=0.91 memory used=48.2MB, alloc=32.3MB, time=1.45 memory used=67.8MB, alloc=56.3MB, time=1.98 memory used=113.1MB, alloc=68.5MB, time=3.08 memory used=153.7MB, alloc=68.5MB, time=4.10 memory used=192.5MB, alloc=92.5MB, time=5.11 memory used=256.3MB, alloc=92.5MB, time=6.72 memory used=320.2MB, alloc=116.5MB, time=8.33 memory used=406.1MB, alloc=116.5MB, time=10.14 memory used=467.0MB, alloc=116.5MB, time=10.82 memory used=530.7MB, alloc=116.5MB, time=11.68 memory used=586.5MB, alloc=116.5MB, time=12.92 memory used=662.4MB, alloc=372.5MB, time=14.48 memory used=748.8MB, alloc=396.5MB, time=16.72 memory used=856.0MB, alloc=420.5MB, time=19.56 memory used=985.0MB, alloc=420.5MB, time=22.85 memory used=1078.3MB, alloc=420.5MB, time=24.45 memory used=1204.1MB, alloc=444.5MB, time=27.18 memory used=1350.3MB, alloc=444.5MB, time=30.60 memory used=1484.8MB, alloc=468.5MB, time=34.28 memory used=1610.4MB, alloc=468.5MB, time=37.13 memory used=1701.9MB, alloc=468.5MB, time=37.83 memory used=1788.8MB, alloc=468.5MB, time=39.10 memory used=1923.1MB, alloc=468.5MB, time=41.09 memory used=2024.3MB, alloc=468.5MB, time=42.55 memory used=2153.3MB, alloc=468.5MB, time=45.00 memory used=2295.6MB, alloc=492.5MB, time=47.42 memory used=2403.9MB, alloc=492.5MB, time=50.85 memory used=2492.2MB, alloc=492.5MB, time=53.24 memory used=2611.8MB, alloc=492.5MB, time=55.51 memory used=2738.4MB, alloc=492.5MB, time=58.19 memory used=2871.7MB, alloc=492.5MB, time=60.77 memory used=2966.2MB, alloc=492.5MB, time=63.22 memory used=3058.6MB, alloc=516.5MB, time=65.45 memory used=3144.5MB, alloc=516.5MB, time=67.46 memory used=3233.4MB, alloc=516.5MB, time=70.13 memory used=3323.4MB, alloc=516.5MB, time=72.56 memory used=3395.4MB, alloc=516.5MB, time=74.68 memory used=3461.4MB, alloc=516.5MB, time=77.03 memory used=3529.4MB, alloc=516.5MB, time=79.08 memory used=3581.8MB, alloc=516.5MB, time=80.69 memory used=3641.3MB, alloc=516.5MB, time=82.63 memory used=3698.7MB, alloc=516.5MB, time=84.78 memory used=3756.4MB, alloc=516.5MB, time=86.75 memory used=3806.3MB, alloc=516.5MB, time=88.42 memory used=3860.0MB, alloc=516.5MB, time=90.12 memory used=3913.1MB, alloc=516.5MB, time=92.00 memory used=4115.6MB, alloc=540.5MB, time=97.89 memory used=4310.4MB, alloc=564.5MB, time=101.45 memory used=4447.5MB, alloc=564.5MB, time=103.26 memory used=4585.4MB, alloc=564.5MB, time=104.38 memory used=4734.2MB, alloc=564.5MB, time=106.60 memory used=4888.7MB, alloc=564.5MB, time=108.33 memory used=5009.8MB, alloc=564.5MB, time=109.61 memory used=5139.6MB, alloc=564.5MB, time=110.66 memory used=5277.4MB, alloc=564.5MB, time=114.50 memory used=5445.6MB, alloc=564.5MB, time=117.40 memory used=5656.1MB, alloc=564.5MB, time=122.09 memory used=5873.6MB, alloc=588.5MB, time=128.23 memory used=6057.0MB, alloc=588.5MB, time=132.04 memory used=6211.4MB, alloc=612.5MB, time=136.10 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428266454 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 4 3 3 2 2 F := [4 x y + 6 x y, 10 y - 14 y z - z, -9 x z + 5 x z - 9] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; G := [ 3 3 2 2 2 2 2 2 2 2 2 -18 y - z + 8 x, -4 x y + 5 y z - 8 z , -9 x y - 16 x y z - 7 y z ] > Problem := [F,G]; 2 4 3 3 2 2 Problem := [[4 x y + 6 x y, 10 y - 14 y z - z, -9 x z + 5 x z - 9], [ 3 3 2 2 2 2 2 2 2 2 2 -18 y - z + 8 x, -4 x y + 5 y z - 8 z , -9 x y - 16 x y z - 7 y z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.6MB, alloc=32.3MB, time=0.89 memory used=45.9MB, alloc=56.3MB, time=1.39 memory used=87.0MB, alloc=60.3MB, time=2.33 memory used=125.4MB, alloc=60.3MB, time=2.83 memory used=166.5MB, alloc=60.3MB, time=3.42 memory used=208.6MB, alloc=60.3MB, time=4.27 memory used=255.5MB, alloc=61.2MB, time=5.41 memory used=303.7MB, alloc=61.8MB, time=6.37 memory used=325.9MB, alloc=61.8MB, time=6.49 memory used=362.6MB, alloc=61.8MB, time=7.18 memory used=393.5MB, alloc=61.8MB, time=7.96 memory used=439.3MB, alloc=93.8MB, time=8.95 memory used=504.7MB, alloc=93.8MB, time=10.53 memory used=567.4MB, alloc=119.2MB, time=11.61 memory used=646.0MB, alloc=384.1MB, time=12.34 memory used=738.9MB, alloc=384.1MB, time=14.06 memory used=835.8MB, alloc=384.1MB, time=18.52 memory used=923.8MB, alloc=384.1MB, time=20.52 memory used=1011.5MB, alloc=384.1MB, time=21.91 memory used=1064.0MB, alloc=384.1MB, time=22.40 memory used=1116.5MB, alloc=384.1MB, time=22.82 memory used=1167.8MB, alloc=384.1MB, time=23.24 memory used=1236.5MB, alloc=384.1MB, time=24.79 memory used=1294.4MB, alloc=384.1MB, time=25.14 memory used=1334.4MB, alloc=408.1MB, time=25.44 memory used=1380.0MB, alloc=408.1MB, time=25.75 memory used=1433.5MB, alloc=408.1MB, time=26.06 memory used=1491.3MB, alloc=408.1MB, time=26.39 memory used=1556.6MB, alloc=408.1MB, time=26.73 memory used=1629.3MB, alloc=408.1MB, time=27.07 memory used=1682.5MB, alloc=408.1MB, time=27.36 memory used=1720.3MB, alloc=408.1MB, time=27.62 memory used=1760.6MB, alloc=408.1MB, time=27.88 memory used=1801.9MB, alloc=408.1MB, time=28.14 memory used=1847.5MB, alloc=408.1MB, time=28.41 memory used=1893.7MB, alloc=408.1MB, time=28.68 memory used=1940.5MB, alloc=408.1MB, time=28.95 memory used=1991.6MB, alloc=408.1MB, time=29.21 memory used=2043.2MB, alloc=408.1MB, time=29.50 memory used=2098.8MB, alloc=408.1MB, time=29.77 memory used=2154.7MB, alloc=408.1MB, time=30.05 memory used=2214.4MB, alloc=408.1MB, time=30.34 memory used=2277.9MB, alloc=408.1MB, time=30.63 memory used=2344.7MB, alloc=408.1MB, time=30.94 memory used=2414.4MB, alloc=408.1MB, time=31.24 memory used=2484.8MB, alloc=408.1MB, time=31.54 memory used=2536.8MB, alloc=408.1MB, time=31.79 memory used=2572.9MB, alloc=408.1MB, time=32.04 memory used=2609.8MB, alloc=408.1MB, time=32.26 memory used=2649.5MB, alloc=408.1MB, time=32.50 memory used=2688.7MB, alloc=408.1MB, time=32.75 memory used=2729.3MB, alloc=408.1MB, time=32.97 memory used=2772.7MB, alloc=408.1MB, time=33.22 memory used=2817.4MB, alloc=408.1MB, time=33.43 memory used=2864.2MB, alloc=408.1MB, time=33.65 memory used=2913.5MB, alloc=408.1MB, time=33.87 memory used=2987.1MB, alloc=408.1MB, time=34.96 memory used=3069.7MB, alloc=408.1MB, time=35.42 memory used=3117.6MB, alloc=408.1MB, time=35.74 memory used=3174.2MB, alloc=408.1MB, time=36.07 memory used=3241.7MB, alloc=408.1MB, time=36.41 memory used=3309.8MB, alloc=408.1MB, time=36.74 memory used=3351.2MB, alloc=408.1MB, time=37.01 memory used=3394.9MB, alloc=408.1MB, time=37.29 memory used=3442.1MB, alloc=408.1MB, time=37.57 memory used=3493.4MB, alloc=408.1MB, time=37.84 memory used=3549.1MB, alloc=408.1MB, time=38.13 memory used=3610.2MB, alloc=408.1MB, time=38.42 memory used=3677.0MB, alloc=408.1MB, time=38.72 memory used=3746.6MB, alloc=408.1MB, time=38.99 memory used=3839.8MB, alloc=408.1MB, time=69.79 memory used=3944.8MB, alloc=408.1MB, time=118.74 memory used=4002.5MB, alloc=408.1MB, time=119.07 memory used=4070.4MB, alloc=408.1MB, time=119.41 memory used=4114.9MB, alloc=408.1MB, time=119.69 memory used=4162.5MB, alloc=408.1MB, time=119.96 memory used=4216.5MB, alloc=408.1MB, time=120.25 memory used=4276.1MB, alloc=408.1MB, time=120.54 memory used=4343.0MB, alloc=408.1MB, time=120.84 memory used=4415.3MB, alloc=408.1MB, time=121.16 memory used=4463.3MB, alloc=408.1MB, time=121.40 memory used=4503.3MB, alloc=408.1MB, time=121.63 memory used=4544.5MB, alloc=408.1MB, time=121.85 memory used=4588.4MB, alloc=408.1MB, time=122.07 memory used=4633.0MB, alloc=408.1MB, time=122.29 memory used=4680.1MB, alloc=408.1MB, time=122.52 memory used=4729.7MB, alloc=408.1MB, time=122.76 memory used=4779.9MB, alloc=408.1MB, time=122.99 memory used=4832.4MB, alloc=408.1MB, time=123.23 memory used=4887.2MB, alloc=408.1MB, time=123.48 memory used=4944.1MB, alloc=408.1MB, time=123.71 memory used=5003.1MB, alloc=408.1MB, time=123.95 memory used=5066.0MB, alloc=408.1MB, time=124.20 memory used=5130.4MB, alloc=408.1MB, time=124.46 memory used=5198.0MB, alloc=408.1MB, time=124.71 memory used=5268.3MB, alloc=408.1MB, time=124.96 memory used=5356.6MB, alloc=408.1MB, time=125.24 memory used=5496.6MB, alloc=408.1MB, time=125.94 memory used=5649.9MB, alloc=408.1MB, time=126.39 memory used=5873.7MB, alloc=408.1MB, time=128.48 memory used=5940.7MB, alloc=408.1MB, time=128.87 memory used=5987.3MB, alloc=408.1MB, time=129.17 memory used=6040.8MB, alloc=408.1MB, time=129.50 memory used=6098.7MB, alloc=408.1MB, time=129.83 memory used=6163.7MB, alloc=408.1MB, time=130.17 memory used=6236.3MB, alloc=408.1MB, time=130.50 memory used=6289.2MB, alloc=408.1MB, time=130.80 memory used=6326.9MB, alloc=408.1MB, time=131.06 memory used=6366.9MB, alloc=408.1MB, time=131.32 memory used=6408.2MB, alloc=408.1MB, time=131.60 memory used=6453.7MB, alloc=408.1MB, time=131.86 memory used=6499.8MB, alloc=408.1MB, time=132.12 memory used=6546.8MB, alloc=408.1MB, time=132.40 memory used=6597.5MB, alloc=408.1MB, time=132.67 memory used=6648.9MB, alloc=408.1MB, time=132.94 memory used=6704.5MB, alloc=408.1MB, time=133.21 memory used=6760.7MB, alloc=408.1MB, time=133.49 memory used=6819.8MB, alloc=408.1MB, time=133.77 memory used=6883.1MB, alloc=408.1MB, time=134.06 memory used=6949.7MB, alloc=408.1MB, time=134.36 memory used=7019.3MB, alloc=408.1MB, time=134.66 memory used=7089.5MB, alloc=408.1MB, time=134.95 memory used=7141.0MB, alloc=408.1MB, time=135.20 memory used=7177.5MB, alloc=408.1MB, time=135.40 memory used=7214.3MB, alloc=408.1MB, time=135.60 memory used=7253.3MB, alloc=408.1MB, time=135.82 memory used=7294.9MB, alloc=408.1MB, time=136.04 memory used=7337.9MB, alloc=408.1MB, time=136.27 memory used=7381.7MB, alloc=408.1MB, time=136.49 memory used=7426.6MB, alloc=408.1MB, time=136.71 memory used=7474.4MB, alloc=408.1MB, time=136.93 memory used=7524.6MB, alloc=408.1MB, time=137.15 memory used=7596.0MB, alloc=408.1MB, time=139.04 memory used=7688.4MB, alloc=408.1MB, time=139.56 memory used=7749.7MB, alloc=408.1MB, time=139.92 memory used=7797.8MB, alloc=408.1MB, time=140.23 memory used=7852.2MB, alloc=408.1MB, time=140.56 memory used=7913.8MB, alloc=408.1MB, time=140.89 memory used=7979.9MB, alloc=408.1MB, time=141.23 memory used=8052.5MB, alloc=408.1MB, time=141.56 memory used=8099.3MB, alloc=408.1MB, time=141.85 memory used=8140.1MB, alloc=408.1MB, time=142.10 memory used=8180.7MB, alloc=408.1MB, time=142.37 memory used=8222.5MB, alloc=408.1MB, time=142.63 memory used=8267.8MB, alloc=408.1MB, time=142.89 memory used=8314.2MB, alloc=408.1MB, time=143.16 memory used=8364.8MB, alloc=408.1MB, time=143.44 memory used=8416.1MB, alloc=408.1MB, time=143.71 memory used=8471.4MB, alloc=408.1MB, time=143.98 memory used=8527.1MB, alloc=408.1MB, time=144.24 memory used=8586.8MB, alloc=408.1MB, time=144.53 memory used=8650.3MB, alloc=408.1MB, time=144.82 memory used=8713.8MB, alloc=408.1MB, time=145.13 memory used=8780.3MB, alloc=408.1MB, time=145.42 memory used=8852.7MB, alloc=408.1MB, time=145.73 memory used=8917.5MB, alloc=408.1MB, time=146.02 memory used=8962.1MB, alloc=408.1MB, time=146.25 memory used=8999.2MB, alloc=408.1MB, time=146.47 memory used=9036.8MB, alloc=408.1MB, time=146.69 memory used=9075.7MB, alloc=408.1MB, time=146.91 memory used=9116.0MB, alloc=408.1MB, time=147.13 memory used=9158.2MB, alloc=408.1MB, time=147.35 memory used=9202.0MB, alloc=408.1MB, time=147.58 memory used=9247.6MB, alloc=408.1MB, time=147.80 memory used=9296.0MB, alloc=408.1MB, time=148.03 memory used=9348.0MB, alloc=408.1MB, time=148.25 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428266754 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 4 4 2 3 2 3 F := [-8 y z - 6 x, -10 x - 17 z - y z, 7 x z - x y z - 2 x ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 3 3 G := [11 x y - 11 y z - 17 x y, -13 x y - 6 y z - 5 y z , 2 2 -19 x y z + 11 x z - 4 y z ] > Problem := [F,G]; 2 2 4 4 2 3 2 3 Problem := [[-8 y z - 6 x, -10 x - 17 z - y z, 7 x z - x y z - 2 x ], [ 3 3 2 2 3 3 11 x y - 11 y z - 17 x y, -13 x y - 6 y z - 5 y z , 2 2 -19 x y z + 11 x z - 4 y z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.32 memory used=26.6MB, alloc=32.3MB, time=0.90 memory used=47.1MB, alloc=32.3MB, time=1.43 memory used=66.4MB, alloc=56.3MB, time=1.96 memory used=106.7MB, alloc=60.3MB, time=3.01 memory used=140.5MB, alloc=84.3MB, time=3.88 memory used=206.5MB, alloc=92.3MB, time=5.55 memory used=269.5MB, alloc=116.3MB, time=7.20 memory used=340.7MB, alloc=116.3MB, time=8.85 memory used=413.2MB, alloc=372.3MB, time=10.58 memory used=501.5MB, alloc=396.3MB, time=12.70 memory used=610.9MB, alloc=420.3MB, time=15.48 memory used=738.7MB, alloc=444.3MB, time=19.05 memory used=888.5MB, alloc=444.3MB, time=22.94 memory used=1011.5MB, alloc=468.3MB, time=26.06 memory used=1128.4MB, alloc=468.3MB, time=28.81 memory used=1229.9MB, alloc=492.3MB, time=30.89 memory used=1351.9MB, alloc=492.3MB, time=33.95 memory used=1432.0MB, alloc=492.3MB, time=35.92 memory used=1540.9MB, alloc=516.3MB, time=38.66 memory used=1640.6MB, alloc=516.3MB, time=41.22 memory used=1718.9MB, alloc=516.3MB, time=43.14 memory used=1816.3MB, alloc=516.3MB, time=46.07 memory used=1899.5MB, alloc=516.3MB, time=48.73 memory used=1969.6MB, alloc=516.3MB, time=50.89 memory used=2042.7MB, alloc=516.3MB, time=52.71 memory used=2105.0MB, alloc=516.3MB, time=54.89 memory used=2175.0MB, alloc=516.3MB, time=56.89 memory used=2280.0MB, alloc=516.3MB, time=58.99 memory used=2343.2MB, alloc=516.3MB, time=60.98 memory used=2402.9MB, alloc=516.3MB, time=62.62 memory used=2463.2MB, alloc=540.3MB, time=64.08 memory used=2520.7MB, alloc=540.3MB, time=66.02 memory used=2733.0MB, alloc=540.3MB, time=69.92 memory used=2924.8MB, alloc=564.3MB, time=74.04 memory used=3125.2MB, alloc=588.3MB, time=78.24 memory used=3355.8MB, alloc=612.3MB, time=83.22 memory used=3587.0MB, alloc=636.3MB, time=88.01 memory used=3801.4MB, alloc=660.3MB, time=92.38 memory used=3972.5MB, alloc=660.3MB, time=97.25 memory used=4096.3MB, alloc=684.3MB, time=100.79 memory used=4270.3MB, alloc=684.3MB, time=105.09 memory used=4408.7MB, alloc=684.3MB, time=108.73 memory used=4550.7MB, alloc=708.3MB, time=112.01 memory used=4675.5MB, alloc=708.3MB, time=116.17 memory used=4781.5MB, alloc=708.3MB, time=119.70 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428267054 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 2 F := [-6 x y - 11 y z + 14 x y, -10 y z + 15 x z + 15 y z, 3 2 3 -2 y z + 15 x z - 6 y ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 3 2 2 2 4 G := [-7 y z + 12 x z , 13 x y + 5 y z + 20 y z, 13 x y + 7 y + 10 y] > Problem := [F,G]; 3 3 2 2 2 Problem := [[-6 x y - 11 y z + 14 x y, -10 y z + 15 x z + 15 y z, 3 2 3 -2 y z + 15 x z - 6 y ], 2 2 2 2 2 3 2 2 2 4 [-7 y z + 12 x z , 13 x y + 5 y z + 20 y z, 13 x y + 7 y + 10 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.6MB, alloc=32.3MB, time=0.88 memory used=47.2MB, alloc=32.3MB, time=1.41 memory used=65.8MB, alloc=56.3MB, time=1.90 memory used=106.7MB, alloc=60.3MB, time=2.98 memory used=146.3MB, alloc=60.3MB, time=3.99 memory used=185.4MB, alloc=84.3MB, time=5.04 memory used=226.6MB, alloc=84.3MB, time=6.13 memory used=287.4MB, alloc=92.3MB, time=7.76 memory used=346.9MB, alloc=116.3MB, time=9.35 memory used=410.9MB, alloc=116.3MB, time=10.98 memory used=478.1MB, alloc=372.3MB, time=12.67 memory used=563.1MB, alloc=396.3MB, time=14.82 memory used=669.3MB, alloc=420.3MB, time=17.72 memory used=794.5MB, alloc=444.3MB, time=20.62 memory used=929.9MB, alloc=444.3MB, time=24.27 memory used=1057.0MB, alloc=468.3MB, time=27.59 memory used=1167.0MB, alloc=468.3MB, time=30.42 memory used=1282.0MB, alloc=468.3MB, time=33.10 memory used=1374.6MB, alloc=468.3MB, time=35.80 memory used=1466.0MB, alloc=468.3MB, time=38.49 memory used=1561.8MB, alloc=492.3MB, time=41.36 memory used=1648.0MB, alloc=492.3MB, time=43.82 memory used=1730.4MB, alloc=492.3MB, time=46.36 memory used=1817.6MB, alloc=492.3MB, time=49.25 memory used=1887.4MB, alloc=492.3MB, time=51.67 memory used=1959.0MB, alloc=492.3MB, time=54.03 memory used=2009.6MB, alloc=492.3MB, time=55.60 memory used=2067.5MB, alloc=492.3MB, time=57.43 memory used=2128.1MB, alloc=492.3MB, time=59.42 memory used=2191.2MB, alloc=492.3MB, time=61.33 memory used=2247.6MB, alloc=492.3MB, time=63.39 memory used=2294.0MB, alloc=492.3MB, time=65.19 memory used=2365.6MB, alloc=516.3MB, time=66.63 memory used=2468.9MB, alloc=516.3MB, time=69.70 memory used=2592.4MB, alloc=516.3MB, time=71.18 memory used=2790.5MB, alloc=516.3MB, time=75.31 memory used=2945.3MB, alloc=516.3MB, time=78.98 memory used=3038.0MB, alloc=516.3MB, time=79.85 memory used=3231.1MB, alloc=540.3MB, time=83.70 memory used=3435.0MB, alloc=564.3MB, time=89.61 memory used=3672.0MB, alloc=588.3MB, time=96.61 memory used=3870.2MB, alloc=588.3MB, time=99.89 memory used=4035.2MB, alloc=588.3MB, time=102.98 memory used=4233.1MB, alloc=588.3MB, time=109.08 memory used=4402.2MB, alloc=612.3MB, time=114.12 memory used=4581.8MB, alloc=612.3MB, time=118.56 memory used=4727.0MB, alloc=612.3MB, time=122.89 memory used=4907.8MB, alloc=612.3MB, time=125.29 memory used=5069.1MB, alloc=612.3MB, time=129.08 memory used=5188.0MB, alloc=612.3MB, time=130.12 memory used=5410.4MB, alloc=612.3MB, time=133.56 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428267354 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 4 3 2 F := [12 x z + 15 x y - 11 x y, 16 x + 2 x z + 9 x y, 4 2 10 y - 12 x z + 3 y z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 3 2 2 2 G := [-9 x y - 16 y z + 20 z , -8 x y + 5 x y - 7 x , -x y z - 19 y - 3] > Problem := [F,G]; 3 3 2 4 3 2 Problem := [[12 x z + 15 x y - 11 x y, 16 x + 2 x z + 9 x y, 4 2 10 y - 12 x z + 3 y z], 3 2 3 3 2 2 2 [-9 x y - 16 y z + 20 z , -8 x y + 5 x y - 7 x , -x y z - 19 y - 3]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.31 memory used=25.7MB, alloc=32.3MB, time=0.88 memory used=44.5MB, alloc=56.3MB, time=1.34 memory used=85.9MB, alloc=60.3MB, time=2.37 memory used=128.4MB, alloc=68.3MB, time=3.41 memory used=168.7MB, alloc=68.3MB, time=4.33 memory used=210.2MB, alloc=68.3MB, time=5.24 memory used=248.8MB, alloc=68.3MB, time=5.84 memory used=278.4MB, alloc=68.3MB, time=6.52 memory used=301.8MB, alloc=68.3MB, time=6.75 memory used=344.3MB, alloc=68.3MB, time=7.69 memory used=376.5MB, alloc=68.3MB, time=8.13 memory used=419.3MB, alloc=92.3MB, time=9.07 memory used=486.0MB, alloc=92.3MB, time=10.41 memory used=549.7MB, alloc=92.3MB, time=11.55 memory used=618.7MB, alloc=116.3MB, time=12.97 memory used=683.9MB, alloc=116.3MB, time=14.50 memory used=747.2MB, alloc=372.3MB, time=16.01 memory used=844.7MB, alloc=396.3MB, time=17.93 memory used=951.8MB, alloc=396.3MB, time=20.32 memory used=1066.7MB, alloc=420.3MB, time=23.25 memory used=1190.4MB, alloc=420.3MB, time=24.85 memory used=1284.3MB, alloc=420.3MB, time=29.16 memory used=1364.8MB, alloc=420.3MB, time=29.78 memory used=1445.4MB, alloc=420.3MB, time=30.47 memory used=1545.6MB, alloc=420.3MB, time=48.91 memory used=1637.6MB, alloc=420.3MB, time=51.47 memory used=1723.4MB, alloc=420.3MB, time=54.63 memory used=1849.7MB, alloc=420.3MB, time=66.59 memory used=1906.7MB, alloc=420.3MB, time=66.94 memory used=2026.7MB, alloc=420.3MB, time=69.84 memory used=2158.5MB, alloc=444.3MB, time=71.77 memory used=2261.3MB, alloc=444.3MB, time=72.75 memory used=2366.6MB, alloc=444.3MB, time=75.64 memory used=2464.2MB, alloc=444.3MB, time=76.61 memory used=2539.3MB, alloc=444.3MB, time=77.08 memory used=2627.4MB, alloc=444.3MB, time=77.84 memory used=2706.3MB, alloc=444.3MB, time=78.34 memory used=2791.6MB, alloc=444.3MB, time=83.59 memory used=2877.7MB, alloc=444.3MB, time=85.16 memory used=2982.6MB, alloc=444.3MB, time=86.26 memory used=3051.5MB, alloc=444.3MB, time=86.76 memory used=3130.2MB, alloc=444.3MB, time=87.23 memory used=3193.7MB, alloc=444.3MB, time=87.65 memory used=3300.6MB, alloc=444.3MB, time=88.75 memory used=3370.1MB, alloc=444.3MB, time=89.22 memory used=3446.4MB, alloc=444.3MB, time=89.68 memory used=3508.4MB, alloc=444.3MB, time=90.07 memory used=3627.2MB, alloc=444.3MB, time=107.52 memory used=3699.2MB, alloc=444.3MB, time=107.97 memory used=3763.7MB, alloc=444.3MB, time=108.40 memory used=3839.3MB, alloc=444.3MB, time=108.83 memory used=3898.7MB, alloc=444.3MB, time=109.19 memory used=4009.7MB, alloc=444.3MB, time=110.52 memory used=4075.6MB, alloc=444.3MB, time=110.98 memory used=4156.2MB, alloc=444.3MB, time=111.46 memory used=4226.8MB, alloc=444.3MB, time=111.88 memory used=4286.1MB, alloc=444.3MB, time=112.27 memory used=4357.1MB, alloc=444.3MB, time=112.67 memory used=4472.3MB, alloc=444.3MB, time=114.09 memory used=4539.6MB, alloc=444.3MB, time=114.57 memory used=4617.4MB, alloc=444.3MB, time=115.05 memory used=4693.2MB, alloc=444.3MB, time=115.49 memory used=4749.2MB, alloc=444.3MB, time=115.91 memory used=4815.1MB, alloc=444.3MB, time=116.31 memory used=4911.4MB, alloc=444.3MB, time=118.62 memory used=5039.9MB, alloc=444.3MB, time=184.16 memory used=5113.4MB, alloc=444.3MB, time=184.65 memory used=5183.1MB, alloc=444.3MB, time=185.08 memory used=5242.6MB, alloc=444.3MB, time=185.49 memory used=5312.9MB, alloc=444.3MB, time=185.91 memory used=5391.2MB, alloc=444.3MB, time=186.33 memory used=5464.1MB, alloc=444.3MB, time=186.72 memory used=5515.6MB, alloc=444.3MB, time=187.07 memory used=5572.5MB, alloc=444.3MB, time=187.41 memory used=5634.9MB, alloc=444.3MB, time=187.76 memory used=5705.0MB, alloc=444.3MB, time=188.12 memory used=5811.9MB, alloc=444.3MB, time=189.18 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428267654 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 2 2 3 2 F := [x y z - 2 y z - 6 y z , 3 x z + 7 y z + 12 x , 2 2 2 2 2 -8 x y - 7 y z + 4 x y] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 3 2 2 3 G := [2 y z - 8 x + 16 x z, -5 y z + 19 x , 14 x y z + 3 x y z - 12 x ] > Problem := [F,G]; 2 3 2 2 2 2 3 2 Problem := [[x y z - 2 y z - 6 y z , 3 x z + 7 y z + 12 x , 2 2 2 2 2 -8 x y - 7 y z + 4 x y], 3 2 2 2 3 2 2 3 [2 y z - 8 x + 16 x z, -5 y z + 19 x , 14 x y z + 3 x y z - 12 x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.30 memory used=26.4MB, alloc=32.3MB, time=0.89 memory used=45.3MB, alloc=56.3MB, time=1.40 memory used=86.3MB, alloc=60.3MB, time=2.44 memory used=125.1MB, alloc=84.3MB, time=3.47 memory used=166.2MB, alloc=84.3MB, time=4.47 memory used=234.4MB, alloc=92.3MB, time=6.01 memory used=297.9MB, alloc=116.3MB, time=7.60 memory used=370.7MB, alloc=116.3MB, time=9.25 memory used=435.7MB, alloc=396.3MB, time=10.69 memory used=547.4MB, alloc=396.3MB, time=13.51 memory used=651.8MB, alloc=420.3MB, time=16.23 memory used=775.9MB, alloc=444.3MB, time=19.73 memory used=922.2MB, alloc=444.3MB, time=23.33 memory used=1037.0MB, alloc=468.3MB, time=25.78 memory used=1166.9MB, alloc=468.3MB, time=28.38 memory used=1290.7MB, alloc=492.3MB, time=30.89 memory used=1413.7MB, alloc=492.3MB, time=33.48 memory used=1529.0MB, alloc=492.3MB, time=35.76 memory used=1626.8MB, alloc=516.3MB, time=38.45 memory used=1732.4MB, alloc=516.3MB, time=41.58 memory used=1817.1MB, alloc=516.3MB, time=43.77 memory used=1924.3MB, alloc=516.3MB, time=45.99 memory used=2004.9MB, alloc=516.3MB, time=47.94 memory used=2087.8MB, alloc=516.3MB, time=49.90 memory used=2176.9MB, alloc=516.3MB, time=51.87 memory used=2242.6MB, alloc=516.3MB, time=53.59 memory used=2304.5MB, alloc=516.3MB, time=55.21 memory used=2379.5MB, alloc=516.3MB, time=57.13 memory used=2464.8MB, alloc=516.3MB, time=59.21 memory used=2539.2MB, alloc=516.3MB, time=61.00 memory used=2600.8MB, alloc=516.3MB, time=62.47 memory used=2664.2MB, alloc=540.3MB, time=64.16 memory used=2721.7MB, alloc=540.3MB, time=65.72 memory used=2777.3MB, alloc=540.3MB, time=67.03 memory used=2845.8MB, alloc=540.3MB, time=69.16 memory used=2904.1MB, alloc=540.3MB, time=71.29 memory used=2960.1MB, alloc=540.3MB, time=73.31 memory used=3012.8MB, alloc=540.3MB, time=75.43 memory used=3231.3MB, alloc=564.3MB, time=81.72 memory used=3466.7MB, alloc=588.3MB, time=92.10 memory used=3676.2MB, alloc=612.3MB, time=98.21 memory used=3881.0MB, alloc=636.3MB, time=105.11 memory used=4079.2MB, alloc=636.3MB, time=115.23 memory used=4298.5MB, alloc=636.3MB, time=132.83 memory used=4485.0MB, alloc=636.3MB, time=136.51 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428267954 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 F := [-17 x z + 8 y z - 20 y z, 7 x y + 13 x y - 5 y z, 2 2 2 -4 x y z + 6 x y + 7 y z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 2 3 2 2 G := [-10 y z - 7 y z + y, -18 x y - 19 y z - y , 3 x z - 5 x z - 7 x] > Problem := [F,G]; 2 2 3 2 2 Problem := [[-17 x z + 8 y z - 20 y z, 7 x y + 13 x y - 5 y z, 2 2 2 -4 x y z + 6 x y + 7 y z], 3 2 2 2 2 2 3 2 2 [-10 y z - 7 y z + y, -18 x y - 19 y z - y , 3 x z - 5 x z - 7 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.8MB, alloc=32.3MB, time=0.87 memory used=47.3MB, alloc=32.3MB, time=1.40 memory used=66.5MB, alloc=56.3MB, time=1.90 memory used=107.6MB, alloc=60.3MB, time=2.94 memory used=146.1MB, alloc=84.3MB, time=3.96 memory used=211.2MB, alloc=92.3MB, time=5.55 memory used=275.7MB, alloc=116.3MB, time=7.19 memory used=349.2MB, alloc=116.3MB, time=9.09 memory used=418.3MB, alloc=396.3MB, time=10.76 memory used=526.5MB, alloc=396.3MB, time=13.60 memory used=633.4MB, alloc=420.3MB, time=16.40 memory used=761.8MB, alloc=444.3MB, time=19.86 memory used=905.9MB, alloc=444.3MB, time=23.18 memory used=1026.6MB, alloc=468.3MB, time=26.31 memory used=1166.5MB, alloc=468.3MB, time=29.11 memory used=1290.7MB, alloc=468.3MB, time=31.80 memory used=1390.0MB, alloc=492.3MB, time=34.73 memory used=1534.2MB, alloc=492.3MB, time=36.96 memory used=1654.1MB, alloc=492.3MB, time=39.23 memory used=1751.6MB, alloc=492.3MB, time=41.80 memory used=1849.3MB, alloc=492.3MB, time=44.99 memory used=1917.1MB, alloc=516.3MB, time=46.80 memory used=1993.7MB, alloc=516.3MB, time=49.27 memory used=2056.7MB, alloc=516.3MB, time=51.02 memory used=2115.8MB, alloc=516.3MB, time=52.99 memory used=2183.6MB, alloc=516.3MB, time=55.28 memory used=2243.4MB, alloc=516.3MB, time=57.33 memory used=2299.0MB, alloc=516.3MB, time=59.09 memory used=2337.5MB, alloc=516.3MB, time=60.53 memory used=2541.8MB, alloc=540.3MB, time=66.36 memory used=2729.6MB, alloc=564.3MB, time=71.66 memory used=2900.9MB, alloc=588.3MB, time=76.79 memory used=3042.3MB, alloc=612.3MB, time=81.42 memory used=3206.6MB, alloc=636.3MB, time=87.10 memory used=3314.0MB, alloc=636.3MB, time=90.50 memory used=3443.3MB, alloc=636.3MB, time=94.90 memory used=3582.8MB, alloc=660.3MB, time=99.74 memory used=3689.0MB, alloc=660.3MB, time=103.68 memory used=3800.7MB, alloc=660.3MB, time=107.74 memory used=3878.9MB, alloc=660.3MB, time=110.92 memory used=4185.9MB, alloc=684.3MB, time=119.58 memory used=4492.2MB, alloc=708.3MB, time=125.87 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428268254 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 4 2 F := [-17 x y - 18 x y z - 6 y z, -19 y z - 14 z + 15 x y, 2 2 -6 y z + 14 z + x] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 3 2 2 3 2 G := [8 x z - 14 y z - 14 y z , 13 x z - 8 x + 7 y z, 3 2 -12 x z - 8 y z - 11] > Problem := [F,G]; 3 2 3 4 2 Problem := [[-17 x y - 18 x y z - 6 y z, -19 y z - 14 z + 15 x y, 2 2 2 2 2 2 3 -6 y z + 14 z + x], [8 x z - 14 y z - 14 y z , 2 2 3 2 3 2 13 x z - 8 x + 7 y z, -12 x z - 8 y z - 11]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.2MB, alloc=32.3MB, time=0.88 memory used=47.0MB, alloc=56.3MB, time=1.42 memory used=89.0MB, alloc=60.3MB, time=2.22 memory used=141.6MB, alloc=68.3MB, time=3.56 memory used=183.6MB, alloc=68.3MB, time=4.48 memory used=226.1MB, alloc=92.3MB, time=5.44 memory used=294.5MB, alloc=92.3MB, time=7.06 memory used=362.1MB, alloc=116.3MB, time=8.56 memory used=416.0MB, alloc=372.3MB, time=9.56 memory used=499.2MB, alloc=372.3MB, time=11.02 memory used=560.4MB, alloc=372.3MB, time=11.74 memory used=621.3MB, alloc=372.3MB, time=12.48 memory used=694.0MB, alloc=372.3MB, time=13.47 memory used=803.4MB, alloc=396.3MB, time=15.88 memory used=933.2MB, alloc=396.3MB, time=18.24 memory used=1047.0MB, alloc=420.3MB, time=20.96 memory used=1169.8MB, alloc=420.3MB, time=23.59 memory used=1281.1MB, alloc=444.3MB, time=25.97 memory used=1391.0MB, alloc=444.3MB, time=28.20 memory used=1488.5MB, alloc=444.3MB, time=30.40 memory used=1584.3MB, alloc=468.3MB, time=32.92 memory used=1674.3MB, alloc=468.3MB, time=35.09 memory used=1737.8MB, alloc=468.3MB, time=36.82 memory used=1839.8MB, alloc=468.3MB, time=39.40 memory used=1926.7MB, alloc=468.3MB, time=41.40 memory used=2009.3MB, alloc=468.3MB, time=43.38 memory used=2110.3MB, alloc=492.3MB, time=45.92 memory used=2180.3MB, alloc=492.3MB, time=47.79 memory used=2249.7MB, alloc=492.3MB, time=49.72 memory used=2303.3MB, alloc=492.3MB, time=51.25 memory used=2364.9MB, alloc=492.3MB, time=53.28 memory used=2416.8MB, alloc=492.3MB, time=54.98 memory used=2499.3MB, alloc=492.3MB, time=56.77 memory used=2582.1MB, alloc=492.3MB, time=58.11 memory used=2692.5MB, alloc=492.3MB, time=59.67 memory used=2804.9MB, alloc=492.3MB, time=61.12 memory used=2856.4MB, alloc=492.3MB, time=62.61 memory used=2904.4MB, alloc=492.3MB, time=64.36 memory used=2952.8MB, alloc=492.3MB, time=65.81 memory used=3011.6MB, alloc=492.3MB, time=67.44 memory used=3155.0MB, alloc=492.3MB, time=70.24 memory used=3257.9MB, alloc=492.3MB, time=71.56 memory used=3357.4MB, alloc=492.3MB, time=73.17 memory used=3522.6MB, alloc=516.3MB, time=75.80 memory used=3722.6MB, alloc=516.3MB, time=79.57 memory used=3816.3MB, alloc=516.3MB, time=80.58 memory used=3914.9MB, alloc=516.3MB, time=81.88 memory used=4016.3MB, alloc=516.3MB, time=83.03 memory used=4138.3MB, alloc=516.3MB, time=84.62 memory used=4252.9MB, alloc=516.3MB, time=87.11 memory used=4338.4MB, alloc=516.3MB, time=87.95 memory used=4454.5MB, alloc=516.3MB, time=89.57 memory used=4540.6MB, alloc=516.3MB, time=90.43 memory used=4660.1MB, alloc=516.3MB, time=92.43 memory used=4790.7MB, alloc=516.3MB, time=94.30 memory used=4973.1MB, alloc=540.3MB, time=97.60 memory used=5135.9MB, alloc=540.3MB, time=100.34 memory used=5324.3MB, alloc=540.3MB, time=103.77 memory used=5499.9MB, alloc=540.3MB, time=107.89 memory used=5679.4MB, alloc=564.3MB, time=112.19 memory used=5852.0MB, alloc=588.3MB, time=116.33 memory used=6009.4MB, alloc=588.3MB, time=120.65 memory used=6229.6MB, alloc=612.3MB, time=124.75 memory used=6406.6MB, alloc=612.3MB, time=128.41 memory used=6605.8MB, alloc=612.3MB, time=131.84 memory used=6779.7MB, alloc=612.3MB, time=135.66 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428268554 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 4 2 2 F := [-2 y z - 18 y z + 3 y, -2 y - 5 y z - 2 x y z, 3 2 2 4 6 x z - 9 x y - 18 y ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 2 2 3 2 4 G := [-7 x y z + 18 z , -15 y z - 19 x y + 18 x , 7 x z - 3 x y z - 4 z ] > Problem := [F,G]; 2 2 4 2 2 Problem := [[-2 y z - 18 y z + 3 y, -2 y - 5 y z - 2 x y z, 3 2 2 4 6 x z - 9 x y - 18 y ], 2 3 2 2 2 2 3 2 4 [-7 x y z + 18 z , -15 y z - 19 x y + 18 x , 7 x z - 3 x y z - 4 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.31 memory used=25.9MB, alloc=32.3MB, time=0.86 memory used=45.2MB, alloc=56.3MB, time=1.35 memory used=88.1MB, alloc=60.3MB, time=2.30 memory used=134.2MB, alloc=68.3MB, time=3.11 memory used=177.1MB, alloc=68.3MB, time=4.08 memory used=217.7MB, alloc=92.3MB, time=5.12 memory used=285.1MB, alloc=92.3MB, time=7.49 memory used=333.1MB, alloc=92.3MB, time=8.85 memory used=388.0MB, alloc=92.3MB, time=9.64 memory used=458.1MB, alloc=92.3MB, time=11.17 memory used=525.6MB, alloc=92.3MB, time=12.72 memory used=587.3MB, alloc=116.3MB, time=14.19 memory used=664.5MB, alloc=116.3MB, time=15.43 memory used=727.2MB, alloc=116.3MB, time=22.27 memory used=768.7MB, alloc=116.3MB, time=22.52 memory used=808.0MB, alloc=116.3MB, time=22.75 memory used=842.8MB, alloc=116.3MB, time=22.97 memory used=884.8MB, alloc=116.3MB, time=23.19 memory used=950.9MB, alloc=116.3MB, time=29.99 memory used=994.9MB, alloc=116.3MB, time=30.27 memory used=1040.8MB, alloc=116.3MB, time=30.53 memory used=1073.3MB, alloc=116.3MB, time=30.75 memory used=1111.5MB, alloc=116.3MB, time=30.98 memory used=1168.5MB, alloc=116.3MB, time=31.61 memory used=1242.1MB, alloc=116.3MB, time=32.68 memory used=1313.0MB, alloc=119.8MB, time=36.94 memory used=1354.2MB, alloc=119.8MB, time=37.19 memory used=1393.9MB, alloc=119.8MB, time=37.41 memory used=1427.4MB, alloc=119.8MB, time=37.63 memory used=1466.2MB, alloc=119.8MB, time=37.84 memory used=1531.1MB, alloc=119.8MB, time=38.53 memory used=1612.3MB, alloc=120.8MB, time=41.41 memory used=1654.9MB, alloc=120.8MB, time=41.65 memory used=1688.3MB, alloc=120.8MB, time=41.86 memory used=1725.3MB, alloc=120.8MB, time=42.08 memory used=1786.6MB, alloc=120.8MB, time=43.35 memory used=1852.8MB, alloc=144.8MB, time=62.21 memory used=1912.5MB, alloc=144.8MB, time=72.30 memory used=1961.0MB, alloc=144.8MB, time=72.57 memory used=2027.3MB, alloc=144.8MB, time=75.63 memory used=2093.2MB, alloc=144.8MB, time=100.93 memory used=2139.0MB, alloc=144.8MB, time=101.18 memory used=2190.0MB, alloc=144.8MB, time=101.45 memory used=2250.1MB, alloc=144.8MB, time=101.99 memory used=2327.0MB, alloc=400.8MB, time=106.18 memory used=2428.9MB, alloc=400.8MB, time=110.36 memory used=2533.5MB, alloc=400.8MB, time=113.25 memory used=2638.6MB, alloc=424.8MB, time=116.96 memory used=2760.4MB, alloc=448.8MB, time=120.19 memory used=2881.9MB, alloc=448.8MB, time=131.74 memory used=2952.7MB, alloc=448.8MB, time=132.19 memory used=3030.9MB, alloc=448.8MB, time=133.41 memory used=3192.5MB, alloc=448.8MB, time=136.05 memory used=3295.7MB, alloc=472.8MB, time=138.29 memory used=3401.0MB, alloc=472.8MB, time=141.03 memory used=3536.8MB, alloc=472.8MB, time=145.02 memory used=3610.6MB, alloc=472.8MB, time=145.49 memory used=3745.0MB, alloc=472.8MB, time=147.70 memory used=3848.1MB, alloc=496.8MB, time=150.50 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428268854 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 3 2 4 F := [13 x y + 12 x y z - 19 y z , x + 17 x y + 2, 5 x + 20] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 2 2 3 G := [-9 x - 12 x z, 14 x y - 7 x - 16 x, -6 x z + 20 z] > Problem := [F,G]; 3 2 3 3 2 4 Problem := [[13 x y + 12 x y z - 19 y z , x + 17 x y + 2, 5 x + 20], 4 3 2 2 3 [-9 x - 12 x z, 14 x y - 7 x - 16 x, -6 x z + 20 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.30 memory used=26.2MB, alloc=32.3MB, time=0.82 memory used=47.9MB, alloc=32.3MB, time=1.37 memory used=68.5MB, alloc=32.3MB, time=1.90 memory used=89.4MB, alloc=56.3MB, time=2.55 N1 := 569 > GB := Basis(F, plex(op(vars))); 4 3 2 2 3 2 3 GB := [x + 4, -x + 2 x + 34 y , 13 x - 204 x z + 323 z + 26] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=132.0MB, alloc=60.3MB, time=4.05 memory used=171.4MB, alloc=60.3MB, time=5.06 N2 := 501 > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 3 2 3 4 H := [13 x y + 12 x y z - 19 y z , 17 y x + x + 2, 5 x + 20, 4 3 2 2 3 -9 x - 12 x z, 14 x y - 7 x - 16 x, -6 x z + 20 z] > J:=[op(GB),op(G)]; 4 3 2 2 3 2 3 J := [x + 4, -x + 2 x + 34 y , 323 z - 204 z x + 13 x + 26, 4 3 2 2 3 -9 x - 12 x z, 14 x y - 7 x - 16 x, -6 x z + 20 z] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; 11 featureList := [6, 12, 21, 4, 4, 3, 3, 1, 1/2, 1/2, --, 1/3, 1/3, 6, 11, 20, 4, 15 11 4, 2, 3, 1, 1/3, 1/2, --, 1/8, 5/16, 1, 1, 0] 16 > save(F, G, cat("ranSet/34", convert(F, string),".txt")); > quit memory used=206.1MB, alloc=60.3MB, time=6.22 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428268871 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 2 3 F := [4 y z - 12 x + 13 x z, 18 x y z - 9 y z - 13 x y, -12 x - 20 y] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 2 2 G := [-14 x y z + 15 y z - 3 y z, -9 x y + 5 x y + 13 y , 2 2 2 15 x y - 6 x - 13 y ] > Problem := [F,G]; Problem := [ 2 2 3 2 2 2 3 [4 y z - 12 x + 13 x z, 18 x y z - 9 y z - 13 x y, -12 x - 20 y], [ 2 3 2 2 2 2 -14 x y z + 15 y z - 3 y z, -9 x y + 5 x y + 13 y , 2 2 2 15 x y - 6 x - 13 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.31 memory used=26.6MB, alloc=32.3MB, time=0.87 memory used=47.7MB, alloc=32.3MB, time=1.39 memory used=67.9MB, alloc=32.3MB, time=1.91 memory used=87.4MB, alloc=56.3MB, time=2.42 memory used=126.7MB, alloc=60.3MB, time=3.44 memory used=164.9MB, alloc=84.3MB, time=4.43 memory used=203.4MB, alloc=84.3MB, time=5.37 memory used=265.5MB, alloc=92.3MB, time=6.96 memory used=327.1MB, alloc=116.3MB, time=8.54 memory used=404.6MB, alloc=116.3MB, time=10.59 memory used=484.6MB, alloc=396.3MB, time=12.80 memory used=591.2MB, alloc=396.3MB, time=15.60 memory used=699.9MB, alloc=420.3MB, time=18.36 memory used=829.8MB, alloc=420.3MB, time=21.32 memory used=957.9MB, alloc=444.3MB, time=24.64 memory used=1078.1MB, alloc=444.3MB, time=26.73 memory used=1217.5MB, alloc=468.3MB, time=30.25 memory used=1395.2MB, alloc=468.3MB, time=33.43 memory used=1571.5MB, alloc=492.3MB, time=37.74 memory used=1762.8MB, alloc=516.3MB, time=41.37 memory used=1951.0MB, alloc=540.3MB, time=47.54 memory used=2159.1MB, alloc=564.3MB, time=54.23 memory used=2370.4MB, alloc=588.3MB, time=61.21 memory used=2582.2MB, alloc=612.3MB, time=67.72 memory used=2813.3MB, alloc=636.3MB, time=74.64 memory used=3007.3MB, alloc=660.3MB, time=80.73 memory used=3191.3MB, alloc=684.3MB, time=86.61 memory used=3368.3MB, alloc=708.3MB, time=92.67 memory used=3544.7MB, alloc=732.3MB, time=98.91 memory used=3702.1MB, alloc=756.3MB, time=104.60 memory used=3871.9MB, alloc=780.3MB, time=110.48 memory used=4045.7MB, alloc=804.3MB, time=116.40 memory used=4226.9MB, alloc=828.3MB, time=122.34 memory used=4362.2MB, alloc=852.3MB, time=128.25 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428269171 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 3 F := [-3 x y + 13 x y z + 14 y z, -20 x z - 20 z - 3 x z, 2 2 -13 x z + 13 y z + 19] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; G := [ 3 2 2 2 3 2 2 2 2 3 2 -2 x z - 19 x y + 17 x y z , 17 x y + 13 y z , 16 y z + 9 y + 18 y ] > Problem := [F,G]; 2 2 2 2 2 3 Problem := [[-3 x y + 13 x y z + 14 y z, -20 x z - 20 z - 3 x z, 2 2 -13 x z + 13 y z + 19], [ 3 2 2 2 3 2 2 2 2 3 2 -2 x z - 19 x y + 17 x y z , 17 x y + 13 y z , 16 y z + 9 y + 18 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.8MB, alloc=32.3MB, time=0.87 memory used=47.2MB, alloc=32.3MB, time=1.38 memory used=65.7MB, alloc=56.3MB, time=1.89 memory used=104.6MB, alloc=60.3MB, time=2.87 memory used=142.2MB, alloc=84.3MB, time=3.84 memory used=203.7MB, alloc=92.3MB, time=5.37 memory used=264.4MB, alloc=92.3MB, time=6.88 memory used=324.5MB, alloc=116.3MB, time=8.37 memory used=404.9MB, alloc=372.3MB, time=10.24 memory used=486.6MB, alloc=396.3MB, time=12.27 memory used=590.7MB, alloc=396.3MB, time=14.87 memory used=693.4MB, alloc=420.3MB, time=17.44 memory used=813.8MB, alloc=444.3MB, time=20.74 memory used=952.6MB, alloc=468.3MB, time=24.37 memory used=1093.0MB, alloc=468.3MB, time=28.25 memory used=1199.3MB, alloc=492.3MB, time=31.04 memory used=1312.5MB, alloc=492.3MB, time=33.92 memory used=1418.6MB, alloc=492.3MB, time=36.85 memory used=1538.7MB, alloc=492.3MB, time=40.46 memory used=1638.0MB, alloc=516.3MB, time=43.56 memory used=1715.1MB, alloc=516.3MB, time=46.00 memory used=1798.6MB, alloc=516.3MB, time=48.63 memory used=1862.1MB, alloc=516.3MB, time=50.68 memory used=1931.0MB, alloc=516.3MB, time=53.00 memory used=1999.4MB, alloc=516.3MB, time=55.31 memory used=2070.9MB, alloc=516.3MB, time=57.68 memory used=2133.1MB, alloc=516.3MB, time=59.78 memory used=2177.7MB, alloc=516.3MB, time=61.26 memory used=2235.4MB, alloc=516.3MB, time=63.54 memory used=2432.4MB, alloc=540.3MB, time=69.58 memory used=2647.7MB, alloc=564.3MB, time=76.28 memory used=2857.4MB, alloc=588.3MB, time=82.83 memory used=3047.7MB, alloc=612.3MB, time=89.01 memory used=3188.2MB, alloc=636.3MB, time=93.73 memory used=3345.2MB, alloc=660.3MB, time=98.69 memory used=3478.2MB, alloc=684.3MB, time=102.97 memory used=3622.2MB, alloc=684.3MB, time=107.10 memory used=3754.7MB, alloc=708.3MB, time=110.88 memory used=3866.2MB, alloc=708.3MB, time=114.88 memory used=3974.7MB, alloc=708.3MB, time=118.90 memory used=4081.2MB, alloc=708.3MB, time=122.93 memory used=4431.2MB, alloc=732.3MB, time=135.41 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428269471 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 2 2 2 2 2 F := [-12 y + 18 y z - 2 x y, 19 x z + 6 y z - 14 z , 2 3 2 -17 x y z - 10 y z + 7 y ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 2 3 2 2 G := [4 x - 12 x y - 17 y z, -20 y z + 3 x z + 15 y z, 2 2 3 -13 y z - x - 12 y z] > Problem := [F,G]; 4 3 2 2 2 2 2 Problem := [[-12 y + 18 y z - 2 x y, 19 x z + 6 y z - 14 z , 2 3 2 4 2 2 2 -17 x y z - 10 y z + 7 y ], [4 x - 12 x y - 17 y z, 3 2 2 2 2 3 -20 y z + 3 x z + 15 y z, -13 y z - x - 12 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.31 memory used=26.5MB, alloc=32.3MB, time=0.89 memory used=46.4MB, alloc=32.3MB, time=1.39 memory used=65.4MB, alloc=56.3MB, time=1.91 memory used=106.4MB, alloc=68.3MB, time=2.97 memory used=147.8MB, alloc=92.3MB, time=3.96 memory used=212.0MB, alloc=92.3MB, time=5.53 memory used=276.1MB, alloc=92.3MB, time=6.77 memory used=340.6MB, alloc=116.3MB, time=8.36 memory used=408.0MB, alloc=118.7MB, time=8.97 memory used=478.6MB, alloc=118.7MB, time=10.17 memory used=550.1MB, alloc=118.7MB, time=11.07 memory used=612.1MB, alloc=118.7MB, time=12.16 memory used=671.1MB, alloc=118.7MB, time=12.82 memory used=738.4MB, alloc=118.7MB, time=13.97 memory used=815.4MB, alloc=374.7MB, time=15.48 memory used=895.9MB, alloc=374.7MB, time=17.44 memory used=979.0MB, alloc=398.7MB, time=19.54 memory used=1091.6MB, alloc=398.7MB, time=22.13 memory used=1199.0MB, alloc=422.7MB, time=24.77 memory used=1318.6MB, alloc=446.7MB, time=27.83 memory used=1460.9MB, alloc=446.7MB, time=30.93 memory used=1576.7MB, alloc=446.7MB, time=33.28 memory used=1700.1MB, alloc=470.7MB, time=35.72 memory used=1799.9MB, alloc=470.7MB, time=37.87 memory used=1898.6MB, alloc=470.7MB, time=40.27 memory used=1986.1MB, alloc=470.7MB, time=42.56 memory used=2083.9MB, alloc=470.7MB, time=44.47 memory used=2188.9MB, alloc=470.7MB, time=45.44 memory used=2313.1MB, alloc=470.7MB, time=47.59 memory used=2389.6MB, alloc=494.7MB, time=49.29 memory used=2481.2MB, alloc=494.7MB, time=51.70 memory used=2558.0MB, alloc=494.7MB, time=53.82 memory used=2671.1MB, alloc=494.7MB, time=55.21 memory used=2788.9MB, alloc=494.7MB, time=56.37 memory used=2899.9MB, alloc=494.7MB, time=58.12 memory used=3030.0MB, alloc=494.7MB, time=59.59 memory used=3151.9MB, alloc=494.7MB, time=62.11 memory used=3256.3MB, alloc=494.7MB, time=62.99 memory used=3377.1MB, alloc=494.7MB, time=65.47 memory used=3504.8MB, alloc=494.7MB, time=67.23 memory used=3583.2MB, alloc=494.7MB, time=69.96 memory used=3696.7MB, alloc=494.7MB, time=72.55 memory used=3768.4MB, alloc=494.7MB, time=74.39 memory used=3854.0MB, alloc=494.7MB, time=77.10 memory used=3971.9MB, alloc=494.7MB, time=80.28 memory used=4091.4MB, alloc=494.7MB, time=82.30 memory used=4169.4MB, alloc=494.7MB, time=83.99 memory used=4229.9MB, alloc=494.7MB, time=85.50 memory used=4322.4MB, alloc=494.7MB, time=87.10 memory used=4430.9MB, alloc=518.7MB, time=88.42 memory used=4538.6MB, alloc=518.7MB, time=89.23 memory used=4622.8MB, alloc=518.7MB, time=89.96 memory used=4747.2MB, alloc=518.7MB, time=90.95 memory used=4883.2MB, alloc=518.7MB, time=93.31 memory used=4983.0MB, alloc=518.7MB, time=94.08 memory used=5111.2MB, alloc=518.7MB, time=96.19 memory used=5208.9MB, alloc=518.7MB, time=97.07 memory used=5322.6MB, alloc=518.7MB, time=97.91 memory used=5418.8MB, alloc=518.7MB, time=98.74 memory used=5497.5MB, alloc=518.7MB, time=99.49 memory used=5584.2MB, alloc=518.7MB, time=100.27 memory used=5682.3MB, alloc=518.7MB, time=101.05 memory used=5789.0MB, alloc=518.7MB, time=101.83 memory used=5907.7MB, alloc=518.7MB, time=102.60 memory used=6014.0MB, alloc=518.7MB, time=103.34 memory used=6083.1MB, alloc=518.7MB, time=103.96 memory used=6156.3MB, alloc=518.7MB, time=104.59 memory used=6235.2MB, alloc=518.7MB, time=105.22 memory used=6321.3MB, alloc=518.7MB, time=105.86 memory used=6416.6MB, alloc=518.7MB, time=106.50 memory used=6525.0MB, alloc=518.7MB, time=108.05 memory used=6630.6MB, alloc=518.7MB, time=108.90 memory used=6725.5MB, alloc=518.7MB, time=109.67 memory used=6808.8MB, alloc=518.7MB, time=110.44 memory used=6906.6MB, alloc=518.7MB, time=111.21 memory used=7022.8MB, alloc=518.7MB, time=111.99 memory used=7114.2MB, alloc=518.7MB, time=112.66 memory used=7249.8MB, alloc=518.7MB, time=123.70 memory used=7356.8MB, alloc=518.7MB, time=124.53 memory used=7448.5MB, alloc=518.7MB, time=125.26 memory used=7564.0MB, alloc=518.7MB, time=126.02 memory used=7639.2MB, alloc=518.7MB, time=126.67 memory used=7727.0MB, alloc=518.7MB, time=127.32 memory used=7832.8MB, alloc=518.7MB, time=127.99 memory used=7954.5MB, alloc=518.7MB, time=129.19 memory used=8053.4MB, alloc=518.7MB, time=129.96 memory used=8147.5MB, alloc=518.7MB, time=130.69 memory used=8274.7MB, alloc=518.7MB, time=131.70 memory used=8408.9MB, alloc=518.7MB, time=134.07 memory used=8507.6MB, alloc=518.7MB, time=134.81 memory used=8623.5MB, alloc=518.7MB, time=135.84 memory used=8757.6MB, alloc=518.7MB, time=138.20 memory used=8854.3MB, alloc=518.7MB, time=139.02 memory used=8951.0MB, alloc=518.7MB, time=139.74 memory used=9047.3MB, alloc=518.7MB, time=141.42 memory used=9137.9MB, alloc=518.7MB, time=142.28 memory used=9257.6MB, alloc=518.7MB, time=143.16 memory used=9335.0MB, alloc=518.7MB, time=143.89 memory used=9419.3MB, alloc=518.7MB, time=144.66 memory used=9515.9MB, alloc=518.7MB, time=145.43 memory used=9627.9MB, alloc=518.7MB, time=146.22 memory used=9734.5MB, alloc=518.7MB, time=146.99 memory used=9809.1MB, alloc=518.7MB, time=147.62 memory used=9921.2MB, alloc=518.7MB, time=149.00 memory used=10034.1MB, alloc=518.7MB, time=149.84 memory used=10114.1MB, alloc=518.7MB, time=150.57 memory used=10217.4MB, alloc=518.7MB, time=151.34 memory used=10321.6MB, alloc=518.7MB, time=164.13 memory used=10422.9MB, alloc=518.7MB, time=164.94 memory used=10514.2MB, alloc=518.7MB, time=165.67 memory used=10631.7MB, alloc=518.7MB, time=166.43 memory used=10705.9MB, alloc=518.7MB, time=167.09 memory used=10790.6MB, alloc=518.7MB, time=167.75 memory used=10889.5MB, alloc=518.7MB, time=168.40 memory used=11033.1MB, alloc=518.7MB, time=170.26 memory used=11123.9MB, alloc=518.7MB, time=171.10 memory used=11244.8MB, alloc=518.7MB, time=171.95 memory used=11322.4MB, alloc=518.7MB, time=172.68 memory used=11406.1MB, alloc=518.7MB, time=173.45 memory used=11502.4MB, alloc=518.7MB, time=174.17 memory used=11614.4MB, alloc=518.7MB, time=174.96 memory used=11722.1MB, alloc=518.7MB, time=175.69 memory used=11796.7MB, alloc=518.7MB, time=176.32 memory used=11903.2MB, alloc=518.7MB, time=177.69 memory used=12014.6MB, alloc=518.7MB, time=178.53 memory used=12096.8MB, alloc=518.7MB, time=179.28 memory used=12197.7MB, alloc=518.7MB, time=180.02 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428269771 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 4 2 F := [-x z + 12 y z - 6 x z, -16 x y z - 14 y - 17 x y, 3 3 5 x y + 12 x y + 9 z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 4 2 2 3 2 G := [x z + 18 x y - 14 y , -4 x + 7 x z + 5 z , -2 x y - 3 x z - 7 y] > Problem := [F,G]; 3 2 2 2 2 4 2 Problem := [[-x z + 12 y z - 6 x z, -16 x y z - 14 y - 17 x y, 3 3 5 x y + 12 x y + 9 z], 3 2 4 2 2 3 2 [x z + 18 x y - 14 y , -4 x + 7 x z + 5 z , -2 x y - 3 x z - 7 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.31 memory used=26.8MB, alloc=32.3MB, time=0.88 memory used=47.6MB, alloc=32.3MB, time=1.40 memory used=66.1MB, alloc=56.3MB, time=1.90 memory used=104.7MB, alloc=60.3MB, time=2.92 memory used=144.0MB, alloc=84.3MB, time=3.92 memory used=208.7MB, alloc=92.3MB, time=5.55 memory used=271.2MB, alloc=92.3MB, time=7.15 memory used=333.3MB, alloc=116.3MB, time=8.81 memory used=409.8MB, alloc=372.3MB, time=10.84 memory used=496.3MB, alloc=396.3MB, time=13.00 memory used=607.6MB, alloc=420.3MB, time=15.81 memory used=743.7MB, alloc=420.3MB, time=19.25 memory used=871.4MB, alloc=444.3MB, time=22.30 memory used=1007.4MB, alloc=468.3MB, time=25.53 memory used=1145.4MB, alloc=468.3MB, time=29.53 memory used=1249.1MB, alloc=492.3MB, time=32.41 memory used=1344.5MB, alloc=492.3MB, time=34.92 memory used=1437.9MB, alloc=516.3MB, time=36.86 memory used=1531.1MB, alloc=516.3MB, time=39.71 memory used=1599.6MB, alloc=516.3MB, time=41.62 memory used=1682.5MB, alloc=516.3MB, time=44.29 memory used=1756.3MB, alloc=516.3MB, time=46.24 memory used=1831.0MB, alloc=516.3MB, time=48.16 memory used=1895.1MB, alloc=516.3MB, time=50.43 memory used=1943.9MB, alloc=516.3MB, time=52.06 memory used=1988.9MB, alloc=516.3MB, time=53.46 memory used=2041.4MB, alloc=516.3MB, time=55.21 memory used=2236.3MB, alloc=540.3MB, time=60.27 memory used=2455.4MB, alloc=564.3MB, time=67.01 memory used=2629.8MB, alloc=588.3MB, time=72.24 memory used=2799.3MB, alloc=612.3MB, time=77.20 memory used=2935.8MB, alloc=636.3MB, time=81.07 memory used=3104.4MB, alloc=660.3MB, time=85.84 memory used=3240.3MB, alloc=660.3MB, time=89.62 memory used=3397.5MB, alloc=660.3MB, time=94.20 memory used=3522.0MB, alloc=660.3MB, time=97.74 memory used=3658.0MB, alloc=684.3MB, time=100.95 memory used=3769.0MB, alloc=684.3MB, time=105.19 memory used=3883.5MB, alloc=684.3MB, time=108.84 memory used=4246.8MB, alloc=708.3MB, time=118.48 memory used=4622.4MB, alloc=732.3MB, time=129.64 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428270071 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 4 4 3 3 2 2 F := [18 x y z + 20 y z - 19 x, 5 x + 13 z - 12 x , x + 6 x y - 16 x z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 3 2 G := [-4 x y + 10 x y z + 2 y , x y z - 19 z + 5 y , 3 3 2 -15 x z - y z - 20 y z ] > Problem := [F,G]; Problem := [ 2 2 2 4 4 3 3 2 2 [18 x y z + 20 y z - 19 x, 5 x + 13 z - 12 x , x + 6 x y - 16 x z ], 2 2 2 2 2 3 2 [-4 x y + 10 x y z + 2 y , x y z - 19 z + 5 y , 3 3 2 -15 x z - y z - 20 y z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.31 memory used=26.6MB, alloc=32.3MB, time=0.87 memory used=47.9MB, alloc=60.3MB, time=1.45 memory used=89.9MB, alloc=60.3MB, time=2.39 memory used=140.9MB, alloc=68.5MB, time=3.59 memory used=190.2MB, alloc=68.5MB, time=4.61 memory used=235.1MB, alloc=92.5MB, time=5.62 memory used=299.6MB, alloc=92.5MB, time=7.18 memory used=365.4MB, alloc=92.5MB, time=8.50 memory used=428.0MB, alloc=372.5MB, time=9.68 memory used=529.0MB, alloc=372.5MB, time=11.49 memory used=615.4MB, alloc=396.5MB, time=13.36 memory used=693.4MB, alloc=396.5MB, time=13.95 memory used=765.4MB, alloc=396.5MB, time=15.58 memory used=836.3MB, alloc=396.5MB, time=16.03 memory used=909.2MB, alloc=396.5MB, time=17.61 memory used=999.2MB, alloc=396.5MB, time=19.44 memory used=1076.2MB, alloc=396.5MB, time=20.92 memory used=1138.2MB, alloc=396.5MB, time=21.37 memory used=1222.6MB, alloc=396.5MB, time=22.46 memory used=1332.8MB, alloc=396.5MB, time=27.06 memory used=1383.3MB, alloc=396.5MB, time=27.32 memory used=1511.0MB, alloc=396.5MB, time=29.76 memory used=1640.5MB, alloc=396.5MB, time=32.36 memory used=1743.6MB, alloc=420.5MB, time=34.46 memory used=1810.6MB, alloc=420.5MB, time=35.06 memory used=1894.0MB, alloc=420.5MB, time=36.84 memory used=1973.4MB, alloc=420.5MB, time=38.18 memory used=2041.6MB, alloc=420.5MB, time=38.72 memory used=2117.8MB, alloc=420.5MB, time=39.39 memory used=2198.9MB, alloc=420.5MB, time=41.87 memory used=2279.3MB, alloc=420.5MB, time=44.35 memory used=2354.7MB, alloc=420.5MB, time=45.16 memory used=2425.1MB, alloc=420.5MB, time=45.76 memory used=2511.4MB, alloc=420.5MB, time=48.32 memory used=2619.0MB, alloc=420.5MB, time=56.09 memory used=2688.2MB, alloc=420.5MB, time=56.81 memory used=2746.4MB, alloc=420.5MB, time=57.10 memory used=2883.1MB, alloc=444.5MB, time=59.60 memory used=3033.6MB, alloc=444.5MB, time=61.81 memory used=3116.3MB, alloc=444.5MB, time=62.33 memory used=3198.8MB, alloc=444.5MB, time=62.78 memory used=3259.5MB, alloc=444.5MB, time=63.18 memory used=3323.1MB, alloc=444.5MB, time=63.57 memory used=3401.1MB, alloc=444.5MB, time=63.96 memory used=3492.6MB, alloc=444.5MB, time=64.73 memory used=3567.1MB, alloc=444.5MB, time=65.16 memory used=3669.1MB, alloc=444.5MB, time=74.39 memory used=3739.6MB, alloc=444.5MB, time=74.83 memory used=3813.7MB, alloc=444.5MB, time=75.24 memory used=3879.0MB, alloc=444.5MB, time=75.60 memory used=3963.1MB, alloc=444.5MB, time=76.34 memory used=4036.5MB, alloc=444.5MB, time=76.82 memory used=4122.1MB, alloc=444.5MB, time=77.29 memory used=4178.8MB, alloc=444.5MB, time=77.70 memory used=4245.5MB, alloc=444.5MB, time=78.10 memory used=4336.9MB, alloc=444.5MB, time=78.72 memory used=4419.1MB, alloc=444.5MB, time=79.23 memory used=4489.5MB, alloc=444.5MB, time=79.64 memory used=4594.6MB, alloc=444.5MB, time=88.87 memory used=4663.4MB, alloc=444.5MB, time=89.29 memory used=4745.4MB, alloc=444.5MB, time=89.72 memory used=4801.0MB, alloc=444.5MB, time=90.06 memory used=4895.6MB, alloc=444.5MB, time=97.67 memory used=5001.8MB, alloc=444.5MB, time=100.37 memory used=5066.3MB, alloc=444.5MB, time=100.78 memory used=5146.2MB, alloc=444.5MB, time=101.20 memory used=5201.0MB, alloc=444.5MB, time=101.53 memory used=5291.9MB, alloc=444.5MB, time=102.32 memory used=5365.4MB, alloc=444.5MB, time=102.79 memory used=5435.1MB, alloc=444.5MB, time=103.22 memory used=5496.8MB, alloc=444.5MB, time=103.60 memory used=5574.5MB, alloc=444.5MB, time=104.00 memory used=5657.7MB, alloc=444.5MB, time=104.93 memory used=5754.0MB, alloc=444.5MB, time=105.88 memory used=5828.6MB, alloc=444.5MB, time=106.33 memory used=5904.1MB, alloc=444.5MB, time=109.04 memory used=6006.8MB, alloc=444.5MB, time=115.97 memory used=6070.4MB, alloc=444.5MB, time=116.36 memory used=6147.8MB, alloc=444.5MB, time=116.76 memory used=6204.8MB, alloc=444.5MB, time=117.07 memory used=6300.5MB, alloc=444.5MB, time=118.06 memory used=6375.2MB, alloc=444.5MB, time=118.49 memory used=6439.2MB, alloc=444.5MB, time=118.90 memory used=6539.9MB, alloc=444.5MB, time=122.31 memory used=6608.8MB, alloc=444.5MB, time=122.71 memory used=6693.4MB, alloc=444.5MB, time=123.47 memory used=6791.9MB, alloc=444.5MB, time=124.48 memory used=6874.6MB, alloc=444.5MB, time=125.03 memory used=6978.9MB, alloc=444.5MB, time=126.14 memory used=7077.9MB, alloc=444.5MB, time=127.22 memory used=7240.9MB, alloc=444.5MB, time=130.55 memory used=7384.0MB, alloc=444.5MB, time=132.71 memory used=7488.4MB, alloc=444.5MB, time=135.21 memory used=7591.9MB, alloc=468.5MB, time=137.72 memory used=7690.5MB, alloc=468.5MB, time=140.39 memory used=7777.0MB, alloc=492.5MB, time=142.57 memory used=7863.1MB, alloc=492.5MB, time=144.74 memory used=7936.4MB, alloc=492.5MB, time=146.65 memory used=8013.6MB, alloc=492.5MB, time=148.75 memory used=8073.5MB, alloc=492.5MB, time=150.35 memory used=8145.2MB, alloc=492.5MB, time=152.34 memory used=8284.4MB, alloc=492.5MB, time=157.07 memory used=8382.0MB, alloc=492.5MB, time=158.27 memory used=8451.1MB, alloc=492.5MB, time=159.58 memory used=8531.0MB, alloc=492.5MB, time=161.73 memory used=8629.6MB, alloc=492.5MB, time=163.89 memory used=8729.1MB, alloc=492.5MB, time=166.20 memory used=8820.0MB, alloc=492.5MB, time=169.77 memory used=8914.3MB, alloc=516.5MB, time=171.71 memory used=9002.1MB, alloc=516.5MB, time=173.30 memory used=9092.5MB, alloc=516.5MB, time=175.68 memory used=9171.0MB, alloc=516.5MB, time=179.06 memory used=9223.6MB, alloc=516.5MB, time=180.88 memory used=9270.9MB, alloc=516.5MB, time=182.42 memory used=9315.9MB, alloc=516.5MB, time=183.73 memory used=9365.0MB, alloc=516.5MB, time=185.44 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428270371 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 2 4 3 2 F := [-6 x z + 2 x y z - 7 x , -12 x z - 8 y - 17 x , 11 x z + 8 y - 15] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 4 2 3 G := [16 x y z + 20 y + 14 y z , -8 x + 14 x y z + 20 x z , 2 2 2 4 x y z - 11 y z + 13 x ] > Problem := [F,G]; Problem := [ 3 2 3 2 2 4 3 2 [-6 x z + 2 x y z - 7 x , -12 x z - 8 y - 17 x , 11 x z + 8 y - 15], 3 2 4 2 3 [16 x y z + 20 y + 14 y z , -8 x + 14 x y z + 20 x z , 2 2 2 4 x y z - 11 y z + 13 x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.30 memory used=26.3MB, alloc=32.3MB, time=0.88 memory used=47.0MB, alloc=60.3MB, time=1.41 memory used=88.5MB, alloc=60.3MB, time=2.48 memory used=130.4MB, alloc=92.3MB, time=3.54 memory used=201.9MB, alloc=92.3MB, time=5.12 memory used=267.3MB, alloc=116.3MB, time=6.76 memory used=335.9MB, alloc=372.3MB, time=8.50 memory used=430.1MB, alloc=396.3MB, time=10.67 memory used=544.3MB, alloc=420.3MB, time=13.61 memory used=672.0MB, alloc=420.3MB, time=16.89 memory used=755.6MB, alloc=420.3MB, time=18.32 memory used=855.5MB, alloc=420.3MB, time=20.03 memory used=946.4MB, alloc=420.3MB, time=22.18 memory used=1082.5MB, alloc=444.3MB, time=24.53 memory used=1192.8MB, alloc=444.3MB, time=26.30 memory used=1275.1MB, alloc=444.3MB, time=27.33 memory used=1395.2MB, alloc=444.3MB, time=29.29 memory used=1489.6MB, alloc=444.3MB, time=31.18 memory used=1622.5MB, alloc=468.3MB, time=33.86 memory used=1755.4MB, alloc=468.3MB, time=37.01 memory used=1872.8MB, alloc=468.3MB, time=39.90 memory used=1987.8MB, alloc=468.3MB, time=43.00 memory used=2107.1MB, alloc=492.3MB, time=45.41 memory used=2265.2MB, alloc=492.3MB, time=48.42 memory used=2366.4MB, alloc=492.3MB, time=50.60 memory used=2465.2MB, alloc=492.3MB, time=52.86 memory used=2541.2MB, alloc=492.3MB, time=54.96 memory used=2635.8MB, alloc=492.3MB, time=57.85 memory used=2729.6MB, alloc=492.3MB, time=60.42 memory used=2800.0MB, alloc=516.3MB, time=62.57 memory used=2894.0MB, alloc=516.3MB, time=65.76 memory used=3023.1MB, alloc=516.3MB, time=69.87 memory used=3155.0MB, alloc=516.3MB, time=73.57 memory used=3331.6MB, alloc=516.3MB, time=76.88 memory used=3474.1MB, alloc=540.3MB, time=79.03 memory used=3636.8MB, alloc=540.3MB, time=81.81 memory used=3706.5MB, alloc=540.3MB, time=83.44 memory used=3860.3MB, alloc=540.3MB, time=85.97 memory used=4024.4MB, alloc=540.3MB, time=89.25 memory used=4104.7MB, alloc=540.3MB, time=91.51 memory used=4184.9MB, alloc=540.3MB, time=93.35 memory used=4237.9MB, alloc=540.3MB, time=94.80 memory used=4319.9MB, alloc=540.3MB, time=96.53 memory used=4372.2MB, alloc=540.3MB, time=98.43 memory used=4591.5MB, alloc=564.3MB, time=104.51 memory used=4826.9MB, alloc=588.3MB, time=113.35 memory used=5044.2MB, alloc=612.3MB, time=119.25 memory used=5289.1MB, alloc=636.3MB, time=125.35 memory used=5527.7MB, alloc=636.3MB, time=130.47 memory used=5719.4MB, alloc=636.3MB, time=134.64 memory used=5879.1MB, alloc=636.3MB, time=136.67 memory used=6025.3MB, alloc=636.3MB, time=138.35 memory used=6169.7MB, alloc=636.3MB, time=139.96 memory used=6320.6MB, alloc=636.3MB, time=141.72 memory used=6493.4MB, alloc=660.3MB, time=144.74 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428270671 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 2 2 3 F := [15 x y z - 11 x y z + 5 x , 3 x y + 2 x z + 6 x y , 3 3 -6 x y + 16 y z + 15 x] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; G := [ 3 3 4 2 2 3 3 -14 x y - 19 z - 10 x y, 9 z - 10 x z + 18 y , 6 x y + 11 y + 15 y z] > Problem := [F,G]; 2 2 3 2 2 2 2 3 Problem := [[15 x y z - 11 x y z + 5 x , 3 x y + 2 x z + 6 x y , 3 3 -6 x y + 16 y z + 15 x], [ 3 3 4 2 2 3 3 -14 x y - 19 z - 10 x y, 9 z - 10 x z + 18 y , 6 x y + 11 y + 15 y z] ] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.31 memory used=25.5MB, alloc=32.3MB, time=0.74 memory used=44.7MB, alloc=32.3MB, time=0.97 memory used=68.3MB, alloc=36.3MB, time=1.65 memory used=85.1MB, alloc=36.3MB, time=1.78 memory used=106.6MB, alloc=36.3MB, time=2.21 memory used=128.2MB, alloc=36.3MB, time=2.57 memory used=142.6MB, alloc=36.3MB, time=2.68 memory used=157.4MB, alloc=36.3MB, time=2.92 memory used=171.8MB, alloc=36.3MB, time=3.08 memory used=184.3MB, alloc=36.3MB, time=3.24 memory used=195.8MB, alloc=36.3MB, time=3.32 memory used=213.4MB, alloc=60.3MB, time=3.66 memory used=250.7MB, alloc=62.3MB, time=3.92 memory used=280.0MB, alloc=62.3MB, time=4.04 memory used=305.5MB, alloc=62.3MB, time=4.13 memory used=356.0MB, alloc=62.3MB, time=7.07 memory used=387.3MB, alloc=62.3MB, time=7.19 memory used=410.0MB, alloc=62.3MB, time=7.28 memory used=440.0MB, alloc=62.3MB, time=7.39 memory used=477.7MB, alloc=62.3MB, time=7.91 memory used=529.8MB, alloc=62.6MB, time=9.46 memory used=560.0MB, alloc=62.6MB, time=9.59 memory used=581.9MB, alloc=62.6MB, time=9.69 memory used=605.7MB, alloc=62.6MB, time=9.79 memory used=633.6MB, alloc=62.6MB, time=9.89 memory used=666.7MB, alloc=62.6MB, time=10.00 memory used=687.8MB, alloc=62.6MB, time=10.08 memory used=707.6MB, alloc=62.6MB, time=10.16 memory used=729.2MB, alloc=62.6MB, time=10.24 memory used=753.4MB, alloc=62.6MB, time=10.32 memory used=785.6MB, alloc=62.6MB, time=10.71 memory used=823.7MB, alloc=62.6MB, time=11.27 memory used=881.7MB, alloc=62.6MB, time=12.22 memory used=943.2MB, alloc=62.6MB, time=13.05 memory used=1005.5MB, alloc=62.6MB, time=14.29 memory used=1067.0MB, alloc=62.6MB, time=15.91 memory used=1114.7MB, alloc=62.6MB, time=17.54 memory used=1165.2MB, alloc=62.7MB, time=18.72 memory used=1192.4MB, alloc=62.7MB, time=18.85 memory used=1214.7MB, alloc=62.7MB, time=18.95 memory used=1236.1MB, alloc=62.7MB, time=19.06 memory used=1261.3MB, alloc=62.7MB, time=19.17 memory used=1290.4MB, alloc=62.7MB, time=19.28 memory used=1316.7MB, alloc=62.7MB, time=19.38 memory used=1334.3MB, alloc=62.7MB, time=19.47 memory used=1353.3MB, alloc=62.7MB, time=19.55 memory used=1374.0MB, alloc=62.7MB, time=19.63 memory used=1397.2MB, alloc=62.7MB, time=19.71 memory used=1457.1MB, alloc=62.7MB, time=20.55 memory used=1503.7MB, alloc=70.7MB, time=21.52 memory used=1541.8MB, alloc=70.7MB, time=22.34 memory used=1573.9MB, alloc=70.7MB, time=22.74 memory used=1592.6MB, alloc=70.7MB, time=22.88 memory used=1615.7MB, alloc=70.7MB, time=23.01 memory used=1632.8MB, alloc=70.7MB, time=23.12 memory used=1658.0MB, alloc=70.7MB, time=25.05 memory used=1687.0MB, alloc=70.7MB, time=26.57 memory used=1707.6MB, alloc=70.7MB, time=26.71 memory used=1724.7MB, alloc=70.7MB, time=26.82 memory used=1746.0MB, alloc=70.7MB, time=26.94 memory used=1764.7MB, alloc=70.7MB, time=27.04 memory used=1801.1MB, alloc=70.7MB, time=27.61 memory used=1845.3MB, alloc=94.7MB, time=28.46 memory used=1879.9MB, alloc=94.7MB, time=28.64 memory used=1918.1MB, alloc=94.7MB, time=28.83 memory used=1946.4MB, alloc=94.7MB, time=28.96 memory used=2009.7MB, alloc=94.7MB, time=30.66 memory used=2069.0MB, alloc=94.7MB, time=31.23 memory used=2101.6MB, alloc=94.7MB, time=31.42 memory used=2136.6MB, alloc=94.7MB, time=31.62 memory used=2179.2MB, alloc=94.7MB, time=31.83 memory used=2206.7MB, alloc=94.7MB, time=31.98 memory used=2233.7MB, alloc=94.7MB, time=32.12 memory used=2263.1MB, alloc=94.7MB, time=32.26 memory used=2294.6MB, alloc=94.7MB, time=32.41 memory used=2329.1MB, alloc=94.7MB, time=32.57 memory used=2366.5MB, alloc=94.7MB, time=32.73 memory used=2407.4MB, alloc=94.7MB, time=32.90 memory used=2451.2MB, alloc=94.7MB, time=33.06 memory used=2466.7MB, alloc=107.8MB, time=33.19 memory used=2476.6MB, alloc=107.8MB, time=33.29 memory used=2486.8MB, alloc=107.8MB, time=33.39 memory used=2496.9MB, alloc=107.8MB, time=33.49 memory used=2507.6MB, alloc=107.8MB, time=33.59 memory used=2518.2MB, alloc=107.8MB, time=33.71 memory used=2529.9MB, alloc=107.8MB, time=33.82 memory used=2541.6MB, alloc=107.8MB, time=33.94 memory used=2553.3MB, alloc=107.8MB, time=34.04 memory used=2566.5MB, alloc=107.8MB, time=34.14 memory used=2580.2MB, alloc=107.8MB, time=34.24 memory used=2594.3MB, alloc=107.8MB, time=34.34 memory used=2678.7MB, alloc=107.8MB, time=35.39 memory used=2749.3MB, alloc=107.8MB, time=36.62 memory used=2812.9MB, alloc=107.8MB, time=37.69 memory used=2864.6MB, alloc=107.8MB, time=38.28 memory used=2909.8MB, alloc=107.8MB, time=38.95 memory used=2972.6MB, alloc=107.8MB, time=40.31 memory used=3035.0MB, alloc=131.8MB, time=41.58 memory used=3104.5MB, alloc=387.8MB, time=43.11 memory used=3188.3MB, alloc=387.8MB, time=44.48 memory used=3259.9MB, alloc=411.8MB, time=45.69 memory used=3332.5MB, alloc=411.8MB, time=46.44 memory used=3401.0MB, alloc=411.8MB, time=47.22 memory used=3478.1MB, alloc=411.8MB, time=47.98 memory used=3531.8MB, alloc=411.8MB, time=48.26 memory used=3601.1MB, alloc=411.8MB, time=49.75 memory used=3662.6MB, alloc=411.8MB, time=50.35 memory used=3736.2MB, alloc=411.8MB, time=51.11 memory used=3805.2MB, alloc=411.8MB, time=52.46 memory used=3888.3MB, alloc=411.8MB, time=54.83 memory used=3947.3MB, alloc=411.8MB, time=55.16 memory used=4019.0MB, alloc=411.8MB, time=55.72 memory used=4090.7MB, alloc=411.8MB, time=57.25 memory used=4179.0MB, alloc=435.8MB, time=105.11 memory used=4262.6MB, alloc=435.8MB, time=115.58 memory used=4336.1MB, alloc=435.8MB, time=115.93 memory used=4395.7MB, alloc=435.8MB, time=116.25 memory used=4466.0MB, alloc=435.8MB, time=116.57 memory used=4547.8MB, alloc=435.8MB, time=116.91 memory used=4622.4MB, alloc=435.8MB, time=117.21 memory used=4670.9MB, alloc=435.8MB, time=117.45 memory used=4722.7MB, alloc=435.8MB, time=117.70 memory used=4778.1MB, alloc=435.8MB, time=117.95 memory used=4837.0MB, alloc=435.8MB, time=118.20 memory used=4899.3MB, alloc=435.8MB, time=118.45 memory used=4965.1MB, alloc=435.8MB, time=118.71 memory used=5036.2MB, alloc=435.8MB, time=118.99 memory used=5110.3MB, alloc=435.8MB, time=119.26 memory used=5189.4MB, alloc=435.8MB, time=119.55 memory used=5273.1MB, alloc=435.8MB, time=119.83 memory used=5363.0MB, alloc=435.8MB, time=120.13 memory used=5531.6MB, alloc=435.8MB, time=120.88 memory used=5683.7MB, alloc=435.8MB, time=121.34 memory used=5853.1MB, alloc=435.8MB, time=121.82 memory used=6096.9MB, alloc=435.8MB, time=123.31 memory used=6193.3MB, alloc=435.8MB, time=124.03 memory used=6278.5MB, alloc=435.8MB, time=137.41 memory used=6351.0MB, alloc=435.8MB, time=137.83 memory used=6402.6MB, alloc=435.8MB, time=138.20 memory used=6457.8MB, alloc=435.8MB, time=138.55 memory used=6518.6MB, alloc=435.8MB, time=138.91 memory used=6583.4MB, alloc=435.8MB, time=139.29 memory used=6652.4MB, alloc=435.8MB, time=139.65 memory used=6725.2MB, alloc=435.8MB, time=140.03 memory used=6802.0MB, alloc=435.8MB, time=140.41 memory used=6880.7MB, alloc=435.8MB, time=140.78 memory used=6930.2MB, alloc=459.8MB, time=141.10 memory used=6984.8MB, alloc=459.8MB, time=141.42 memory used=7038.8MB, alloc=459.8MB, time=141.74 memory used=7095.7MB, alloc=459.8MB, time=142.06 memory used=7154.0MB, alloc=459.8MB, time=142.39 memory used=7213.7MB, alloc=459.8MB, time=142.72 memory used=7274.7MB, alloc=459.8MB, time=143.06 memory used=7336.9MB, alloc=459.8MB, time=143.40 memory used=7400.5MB, alloc=459.8MB, time=143.73 memory used=7465.3MB, alloc=459.8MB, time=144.07 memory used=7531.3MB, alloc=459.8MB, time=144.40 memory used=7598.5MB, alloc=459.8MB, time=144.75 memory used=7667.0MB, alloc=459.8MB, time=145.10 memory used=7737.1MB, alloc=459.8MB, time=145.44 memory used=7817.6MB, alloc=459.8MB, time=145.82 memory used=7899.8MB, alloc=459.8MB, time=146.18 memory used=7983.5MB, alloc=459.8MB, time=146.53 memory used=8068.5MB, alloc=459.8MB, time=146.89 memory used=8154.9MB, alloc=459.8MB, time=147.25 memory used=8242.5MB, alloc=459.8MB, time=147.62 memory used=8331.4MB, alloc=459.8MB, time=147.98 memory used=8421.5MB, alloc=459.8MB, time=148.34 memory used=8512.8MB, alloc=459.8MB, time=148.69 memory used=8605.2MB, alloc=459.8MB, time=149.07 memory used=8698.8MB, alloc=459.8MB, time=149.45 memory used=8782.6MB, alloc=459.8MB, time=149.80 memory used=8833.1MB, alloc=483.8MB, time=150.08 memory used=8889.2MB, alloc=483.8MB, time=150.35 memory used=8949.2MB, alloc=483.8MB, time=150.64 memory used=9009.5MB, alloc=483.8MB, time=150.92 memory used=9070.2MB, alloc=483.8MB, time=151.19 memory used=9131.3MB, alloc=483.8MB, time=151.47 memory used=9192.7MB, alloc=483.8MB, time=151.75 memory used=9254.5MB, alloc=483.8MB, time=152.02 memory used=9316.6MB, alloc=483.8MB, time=152.30 memory used=9379.0MB, alloc=483.8MB, time=152.58 memory used=9441.7MB, alloc=483.8MB, time=152.87 memory used=9504.7MB, alloc=483.8MB, time=153.15 memory used=9568.0MB, alloc=483.8MB, time=153.43 memory used=9631.6MB, alloc=483.8MB, time=153.71 memory used=9695.4MB, alloc=483.8MB, time=153.99 memory used=9759.6MB, alloc=483.8MB, time=154.27 memory used=9823.9MB, alloc=483.8MB, time=154.55 memory used=9888.6MB, alloc=483.8MB, time=154.83 memory used=9953.4MB, alloc=483.8MB, time=155.10 memory used=10018.5MB, alloc=483.8MB, time=155.38 memory used=10083.9MB, alloc=483.8MB, time=155.67 memory used=10150.4MB, alloc=483.8MB, time=155.96 memory used=10228.6MB, alloc=483.8MB, time=156.26 memory used=10307.8MB, alloc=483.8MB, time=156.57 memory used=10387.2MB, alloc=483.8MB, time=156.87 memory used=10466.9MB, alloc=483.8MB, time=157.17 memory used=10546.8MB, alloc=483.8MB, time=157.47 memory used=10626.9MB, alloc=483.8MB, time=157.77 memory used=10707.2MB, alloc=483.8MB, time=158.07 memory used=10787.8MB, alloc=483.8MB, time=158.36 memory used=10868.4MB, alloc=483.8MB, time=158.66 memory used=10949.3MB, alloc=483.8MB, time=158.96 memory used=11030.3MB, alloc=483.8MB, time=159.27 memory used=11111.4MB, alloc=483.8MB, time=159.56 memory used=11192.6MB, alloc=483.8MB, time=159.86 memory used=11273.9MB, alloc=483.8MB, time=160.17 memory used=11356.3MB, alloc=483.8MB, time=160.47 memory used=11450.5MB, alloc=483.8MB, time=160.79 memory used=11545.6MB, alloc=483.8MB, time=161.11 memory used=11640.7MB, alloc=483.8MB, time=161.43 memory used=11735.8MB, alloc=483.8MB, time=161.75 memory used=11830.9MB, alloc=483.8MB, time=162.06 memory used=11926.0MB, alloc=483.8MB, time=162.38 memory used=12021.0MB, alloc=483.8MB, time=162.70 memory used=12115.9MB, alloc=483.8MB, time=163.02 memory used=12210.7MB, alloc=483.8MB, time=163.33 memory used=12305.6MB, alloc=483.8MB, time=163.67 memory used=12413.6MB, alloc=483.8MB, time=164.00 memory used=12521.3MB, alloc=483.8MB, time=164.34 memory used=12628.8MB, alloc=483.8MB, time=164.66 memory used=12735.9MB, alloc=483.8MB, time=164.99 memory used=12842.7MB, alloc=483.8MB, time=165.33 memory used=12949.1MB, alloc=483.8MB, time=165.65 memory used=13055.3MB, alloc=483.8MB, time=165.99 memory used=13173.9MB, alloc=483.8MB, time=166.34 memory used=13292.0MB, alloc=483.8MB, time=166.68 memory used=13409.3MB, alloc=483.8MB, time=167.02 memory used=13525.9MB, alloc=483.8MB, time=167.37 memory used=13655.8MB, alloc=483.8MB, time=167.74 memory used=13879.3MB, alloc=483.8MB, time=168.34 memory used=14004.1MB, alloc=483.8MB, time=168.75 memory used=14128.3MB, alloc=483.8MB, time=169.17 memory used=14251.2MB, alloc=483.8MB, time=169.59 memory used=14373.9MB, alloc=483.8MB, time=170.01 memory used=14504.7MB, alloc=483.8MB, time=170.44 memory used=14634.8MB, alloc=483.8MB, time=170.87 memory used=14764.4MB, alloc=483.8MB, time=171.28 memory used=14900.4MB, alloc=483.8MB, time=171.70 memory used=15035.4MB, alloc=483.8MB, time=172.14 memory used=15178.4MB, alloc=483.8MB, time=172.59 memory used=15319.5MB, alloc=483.8MB, time=173.02 memory used=15465.0MB, alloc=483.8MB, time=173.47 memory used=15617.5MB, alloc=483.8MB, time=173.93 memory used=15774.6MB, alloc=483.8MB, time=174.39 memory used=15934.8MB, alloc=483.8MB, time=174.86 memory used=16096.7MB, alloc=483.8MB, time=175.32 memory used=16260.5MB, alloc=483.8MB, time=175.78 memory used=16433.3MB, alloc=483.8MB, time=176.26 memory used=16609.6MB, alloc=483.8MB, time=176.73 memory used=16796.1MB, alloc=483.8MB, time=177.22 memory used=17075.2MB, alloc=483.8MB, time=179.09 memory used=17236.1MB, alloc=483.8MB, time=180.60 memory used=17459.4MB, alloc=483.8MB, time=188.92 memory used=17568.3MB, alloc=483.8MB, time=194.81 memory used=17651.4MB, alloc=483.8MB, time=195.28 memory used=17747.7MB, alloc=483.8MB, time=195.79 memory used=17854.3MB, alloc=483.8MB, time=196.31 memory used=17977.1MB, alloc=483.8MB, time=196.83 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428270971 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 4 2 2 F := [-11 y - 20 x y - 20 x y, -17 x + 19 x y z - 5 y z, 3 2 2 10 x z + 3 y z - 13 z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 3 2 2 2 3 G := [-18 x - 3 x z + 2 x y , 12 x y - 7 y + 11 y z, 11 y z + 6 x] > Problem := [F,G]; 4 2 4 2 2 Problem := [[-11 y - 20 x y - 20 x y, -17 x + 19 x y z - 5 y z, 3 2 2 10 x z + 3 y z - 13 z ], 4 3 3 2 2 2 3 [-18 x - 3 x z + 2 x y , 12 x y - 7 y + 11 y z, 11 y z + 6 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.30 memory used=25.9MB, alloc=32.3MB, time=0.85 memory used=46.3MB, alloc=32.3MB, time=1.38 memory used=65.4MB, alloc=56.3MB, time=1.89 memory used=106.5MB, alloc=68.3MB, time=2.98 memory used=146.4MB, alloc=68.3MB, time=3.96 memory used=185.2MB, alloc=92.3MB, time=5.01 memory used=247.8MB, alloc=92.3MB, time=6.58 memory used=307.8MB, alloc=92.3MB, time=8.17 memory used=371.6MB, alloc=116.3MB, time=9.69 memory used=436.2MB, alloc=116.3MB, time=11.22 memory used=507.2MB, alloc=396.3MB, time=13.17 memory used=618.4MB, alloc=396.3MB, time=15.86 memory used=727.3MB, alloc=420.3MB, time=18.64 memory used=848.7MB, alloc=420.3MB, time=21.74 memory used=965.1MB, alloc=444.3MB, time=24.66 memory used=1084.7MB, alloc=468.3MB, time=27.67 memory used=1189.8MB, alloc=468.3MB, time=30.53 memory used=1296.5MB, alloc=468.3MB, time=33.34 memory used=1387.4MB, alloc=468.3MB, time=35.69 memory used=1471.2MB, alloc=468.3MB, time=38.11 memory used=1549.2MB, alloc=492.3MB, time=40.23 memory used=1634.4MB, alloc=492.3MB, time=42.55 memory used=1720.3MB, alloc=492.3MB, time=45.01 memory used=1791.7MB, alloc=492.3MB, time=47.24 memory used=1872.6MB, alloc=492.3MB, time=49.86 memory used=1932.6MB, alloc=492.3MB, time=51.63 memory used=1993.5MB, alloc=492.3MB, time=53.20 memory used=2056.4MB, alloc=492.3MB, time=55.40 memory used=2100.6MB, alloc=516.3MB, time=56.89 memory used=2144.3MB, alloc=516.3MB, time=58.21 memory used=2192.5MB, alloc=516.3MB, time=60.15 memory used=2412.5MB, alloc=540.3MB, time=65.56 memory used=2604.6MB, alloc=564.3MB, time=70.66 memory used=2784.7MB, alloc=588.3MB, time=75.43 memory used=2948.4MB, alloc=612.3MB, time=79.91 memory used=3096.8MB, alloc=636.3MB, time=84.32 memory used=3240.7MB, alloc=636.3MB, time=89.03 memory used=3359.3MB, alloc=636.3MB, time=92.50 memory used=3464.7MB, alloc=636.3MB, time=96.08 memory used=3586.0MB, alloc=660.3MB, time=99.71 memory used=3672.6MB, alloc=660.3MB, time=102.88 memory used=3771.2MB, alloc=660.3MB, time=105.98 memory used=3860.4MB, alloc=660.3MB, time=109.70 memory used=4197.9MB, alloc=684.3MB, time=119.01 memory used=4548.9MB, alloc=708.3MB, time=128.27 memory used=4916.0MB, alloc=732.3MB, time=137.82 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428271271 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 4 2 3 2 F := [-3 x y z + 3 z + 5 x z, -8 x y + 9 y - 15 y, 2 2 3 2 -17 x z - 13 y z + 6 x z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; G := [ 2 2 3 4 3 3 2 2 -6 x z + 7 x y z + 19 y , 4 x - 2 y - 15 z , -16 x y - 14 x z + 3 x z ] > Problem := [F,G]; 2 4 2 3 2 Problem := [[-3 x y z + 3 z + 5 x z, -8 x y + 9 y - 15 y, 2 2 3 2 -17 x z - 13 y z + 6 x z], [ 2 2 3 4 3 3 2 2 -6 x z + 7 x y z + 19 y , 4 x - 2 y - 15 z , -16 x y - 14 x z + 3 x z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.31 memory used=25.6MB, alloc=32.3MB, time=0.86 memory used=47.4MB, alloc=36.3MB, time=1.37 memory used=64.8MB, alloc=60.3MB, time=1.80 memory used=106.4MB, alloc=68.3MB, time=2.88 memory used=150.5MB, alloc=68.3MB, time=3.78 memory used=190.6MB, alloc=68.3MB, time=4.30 memory used=224.1MB, alloc=68.3MB, time=5.65 memory used=244.0MB, alloc=68.3MB, time=5.76 memory used=274.2MB, alloc=68.3MB, time=6.02 memory used=310.6MB, alloc=68.3MB, time=7.59 memory used=331.5MB, alloc=68.3MB, time=7.72 memory used=358.7MB, alloc=68.3MB, time=8.02 memory used=399.0MB, alloc=68.3MB, time=8.67 memory used=432.0MB, alloc=68.3MB, time=9.19 memory used=477.2MB, alloc=92.3MB, time=10.23 memory used=538.2MB, alloc=92.3MB, time=11.63 memory used=596.7MB, alloc=92.3MB, time=12.57 memory used=663.4MB, alloc=92.3MB, time=14.04 memory used=731.6MB, alloc=92.3MB, time=15.36 memory used=795.7MB, alloc=116.3MB, time=16.95 memory used=886.3MB, alloc=116.3MB, time=20.13 memory used=937.2MB, alloc=116.3MB, time=20.48 memory used=1014.9MB, alloc=372.3MB, time=21.90 memory used=1125.3MB, alloc=372.3MB, time=24.42 memory used=1218.8MB, alloc=396.3MB, time=26.54 memory used=1322.2MB, alloc=396.3MB, time=29.38 memory used=1438.6MB, alloc=420.3MB, time=31.87 memory used=1560.6MB, alloc=444.3MB, time=34.86 memory used=1669.5MB, alloc=444.3MB, time=37.35 memory used=1795.2MB, alloc=444.3MB, time=39.18 memory used=1876.9MB, alloc=444.3MB, time=39.80 memory used=1975.3MB, alloc=444.3MB, time=46.89 memory used=2039.7MB, alloc=444.3MB, time=47.30 memory used=2108.9MB, alloc=444.3MB, time=47.82 memory used=2196.0MB, alloc=444.3MB, time=48.44 memory used=2294.4MB, alloc=444.3MB, time=55.55 memory used=2360.3MB, alloc=444.3MB, time=55.99 memory used=2425.5MB, alloc=444.3MB, time=56.38 memory used=2502.3MB, alloc=444.3MB, time=56.99 memory used=2601.9MB, alloc=444.3MB, time=64.71 memory used=2663.4MB, alloc=444.3MB, time=65.13 memory used=2723.0MB, alloc=444.3MB, time=65.51 memory used=2838.9MB, alloc=468.3MB, time=68.07 memory used=2961.8MB, alloc=468.3MB, time=70.29 memory used=3074.9MB, alloc=468.3MB, time=73.39 memory used=3217.5MB, alloc=492.3MB, time=77.40 memory used=3324.3MB, alloc=492.3MB, time=80.14 memory used=3463.1MB, alloc=492.3MB, time=83.40 memory used=3563.7MB, alloc=492.3MB, time=85.37 memory used=3698.5MB, alloc=492.3MB, time=90.76 memory used=3783.0MB, alloc=492.3MB, time=93.06 memory used=3880.7MB, alloc=492.3MB, time=95.42 memory used=3995.7MB, alloc=492.3MB, time=96.34 memory used=4104.4MB, alloc=492.3MB, time=101.69 memory used=4224.4MB, alloc=492.3MB, time=102.81 memory used=4335.2MB, alloc=492.3MB, time=108.16 memory used=4427.1MB, alloc=492.3MB, time=110.14 memory used=4500.4MB, alloc=492.3MB, time=111.91 memory used=4580.8MB, alloc=492.3MB, time=115.92 memory used=4683.6MB, alloc=492.3MB, time=119.10 memory used=4812.7MB, alloc=516.3MB, time=121.35 memory used=4942.8MB, alloc=516.3MB, time=123.01 memory used=5048.7MB, alloc=516.3MB, time=124.83 memory used=5118.8MB, alloc=516.3MB, time=126.68 memory used=5179.2MB, alloc=516.3MB, time=128.40 memory used=5260.3MB, alloc=516.3MB, time=130.44 memory used=5367.5MB, alloc=516.3MB, time=132.33 memory used=5447.0MB, alloc=516.3MB, time=133.58 memory used=5504.1MB, alloc=516.3MB, time=135.23 memory used=5558.2MB, alloc=516.3MB, time=136.76 memory used=5627.9MB, alloc=516.3MB, time=138.71 memory used=5700.2MB, alloc=516.3MB, time=140.86 memory used=5771.8MB, alloc=516.3MB, time=142.55 memory used=5880.8MB, alloc=516.3MB, time=143.51 memory used=6027.2MB, alloc=516.3MB, time=155.98 memory used=6129.7MB, alloc=516.3MB, time=156.92 memory used=6239.1MB, alloc=516.3MB, time=158.06 memory used=6383.7MB, alloc=516.3MB, time=170.63 memory used=6486.2MB, alloc=516.3MB, time=171.53 memory used=6644.3MB, alloc=516.3MB, time=184.78 memory used=6734.4MB, alloc=516.3MB, time=185.50 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428271571 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; F := [ 3 2 2 2 2 2 4 2 4 2 2 -3 x y + 6 y z + 16 y z , 6 x z + 3 y - 15 x y , -7 y - 4 x + 15 z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 3 2 2 2 4 G := [3 z + 11 y z - 15 z , 4 x y z - 10 x y + y z, -8 y - 19 x y z] > Problem := [F,G]; Problem := [[ 3 2 2 2 2 2 4 2 4 2 2 -3 x y + 6 y z + 16 y z , 6 x z + 3 y - 15 x y , -7 y - 4 x + 15 z 4 2 3 2 2 2 4 ], [3 z + 11 y z - 15 z , 4 x y z - 10 x y + y z, -8 y - 19 x y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.31 memory used=27.0MB, alloc=32.3MB, time=0.90 memory used=46.7MB, alloc=56.3MB, time=1.39 memory used=92.0MB, alloc=60.3MB, time=4.17 memory used=130.7MB, alloc=60.3MB, time=4.84 memory used=177.4MB, alloc=60.3MB, time=5.77 memory used=212.1MB, alloc=60.3MB, time=6.21 memory used=242.9MB, alloc=60.3MB, time=7.52 memory used=299.2MB, alloc=68.3MB, time=8.65 memory used=345.5MB, alloc=68.3MB, time=9.25 memory used=394.5MB, alloc=68.3MB, time=10.09 memory used=441.4MB, alloc=68.3MB, time=10.96 memory used=489.8MB, alloc=92.3MB, time=11.73 memory used=566.6MB, alloc=92.3MB, time=13.02 memory used=641.5MB, alloc=92.3MB, time=15.89 memory used=675.9MB, alloc=92.3MB, time=16.08 memory used=710.0MB, alloc=92.3MB, time=16.25 memory used=755.4MB, alloc=92.3MB, time=18.41 memory used=818.1MB, alloc=92.3MB, time=19.73 memory used=874.8MB, alloc=116.3MB, time=21.13 memory used=955.6MB, alloc=116.3MB, time=22.75 memory used=1035.5MB, alloc=116.3MB, time=26.16 memory used=1125.3MB, alloc=116.3MB, time=27.49 memory used=1216.9MB, alloc=140.3MB, time=28.95 memory used=1300.7MB, alloc=140.3MB, time=30.44 memory used=1381.3MB, alloc=140.3MB, time=32.68 memory used=1433.0MB, alloc=140.3MB, time=33.14 memory used=1464.8MB, alloc=155.8MB, time=33.48 memory used=1523.3MB, alloc=155.8MB, time=33.75 memory used=1595.6MB, alloc=155.8MB, time=38.01 memory used=1644.5MB, alloc=155.8MB, time=38.25 memory used=1689.5MB, alloc=155.8MB, time=38.45 memory used=1750.8MB, alloc=155.8MB, time=39.06 memory used=1809.2MB, alloc=155.8MB, time=39.57 memory used=1884.2MB, alloc=179.8MB, time=67.45 memory used=1965.4MB, alloc=203.8MB, time=153.88 memory used=2073.8MB, alloc=203.8MB, time=159.19 memory used=2144.9MB, alloc=203.8MB, time=159.54 memory used=2234.4MB, alloc=203.8MB, time=159.88 memory used=2316.7MB, alloc=203.8MB, time=160.20 memory used=2378.8MB, alloc=203.8MB, time=160.46 memory used=2449.2MB, alloc=203.8MB, time=160.72 memory used=2527.2MB, alloc=203.8MB, time=160.99 memory used=2615.2MB, alloc=203.8MB, time=161.27 memory used=2724.8MB, alloc=203.8MB, time=161.59 memory used=2751.0MB, alloc=203.8MB, time=161.76 memory used=2762.1MB, alloc=203.8MB, time=161.90 memory used=2773.0MB, alloc=203.8MB, time=162.05 memory used=2784.5MB, alloc=203.8MB, time=162.20 memory used=2796.3MB, alloc=203.8MB, time=162.36 memory used=2808.8MB, alloc=203.8MB, time=162.51 memory used=2879.1MB, alloc=203.8MB, time=163.13 memory used=2994.4MB, alloc=203.8MB, time=190.93 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428271871 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 4 2 2 F := [6 x y - 20 x y z - 18 x z , 2 y + 12 y z - 10 y z, 3 2 10 x z - 2 x y + 9 y z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 2 2 G := [15 x + 4 x y - 9 y , 14 x y z + 14 x z - 7 y z, 2 2 -6 x y z - 16 x z - 2 z ] > Problem := [F,G]; 2 2 2 2 4 2 2 Problem := [[6 x y - 20 x y z - 18 x z , 2 y + 12 y z - 10 y z, 3 2 4 2 10 x z - 2 x y + 9 y z], [15 x + 4 x y - 9 y , 2 2 2 2 2 14 x y z + 14 x z - 7 y z, -6 x y z - 16 x z - 2 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=31.9MB, alloc=40.3MB, time=1.01 memory used=59.2MB, alloc=40.3MB, time=1.72 memory used=84.9MB, alloc=68.3MB, time=2.43 memory used=132.1MB, alloc=76.3MB, time=3.69 memory used=178.1MB, alloc=76.3MB, time=4.89 memory used=224.1MB, alloc=100.3MB, time=6.06 memory used=293.3MB, alloc=100.3MB, time=7.81 memory used=362.1MB, alloc=124.3MB, time=9.60 memory used=447.4MB, alloc=380.3MB, time=11.96 memory used=539.6MB, alloc=404.3MB, time=14.38 memory used=652.0MB, alloc=404.3MB, time=17.45 memory used=762.2MB, alloc=428.3MB, time=20.48 memory used=886.2MB, alloc=428.3MB, time=23.69 memory used=1010.6MB, alloc=452.3MB, time=27.27 memory used=1112.7MB, alloc=452.3MB, time=29.93 memory used=1221.9MB, alloc=452.3MB, time=33.00 memory used=1343.4MB, alloc=476.3MB, time=36.74 memory used=1441.0MB, alloc=476.3MB, time=39.25 memory used=1551.9MB, alloc=476.3MB, time=42.36 memory used=1653.9MB, alloc=476.3MB, time=45.22 memory used=1767.9MB, alloc=476.3MB, time=48.75 memory used=1874.1MB, alloc=500.3MB, time=51.55 memory used=1975.6MB, alloc=500.3MB, time=54.77 memory used=2073.8MB, alloc=500.3MB, time=58.06 memory used=2155.9MB, alloc=500.3MB, time=60.57 memory used=2233.2MB, alloc=500.3MB, time=63.03 memory used=2335.5MB, alloc=500.3MB, time=65.07 memory used=2413.7MB, alloc=500.3MB, time=67.59 memory used=2498.4MB, alloc=524.3MB, time=70.93 memory used=2583.7MB, alloc=524.3MB, time=73.82 memory used=2659.9MB, alloc=524.3MB, time=75.68 memory used=2756.0MB, alloc=524.3MB, time=78.12 memory used=2843.5MB, alloc=524.3MB, time=80.19 memory used=2908.9MB, alloc=524.3MB, time=82.33 memory used=2971.5MB, alloc=524.3MB, time=84.48 memory used=3059.8MB, alloc=524.3MB, time=86.49 memory used=3129.1MB, alloc=524.3MB, time=88.47 memory used=3180.2MB, alloc=524.3MB, time=90.35 memory used=3236.8MB, alloc=524.3MB, time=91.85 memory used=3308.1MB, alloc=524.3MB, time=93.21 memory used=3347.3MB, alloc=524.3MB, time=94.78 memory used=3394.3MB, alloc=524.3MB, time=96.57 memory used=3439.1MB, alloc=548.3MB, time=98.34 memory used=3497.3MB, alloc=548.3MB, time=99.87 memory used=3735.6MB, alloc=572.3MB, time=106.74 memory used=3929.3MB, alloc=596.3MB, time=112.80 memory used=4141.9MB, alloc=596.3MB, time=116.88 memory used=4367.5MB, alloc=620.3MB, time=122.36 memory used=4545.1MB, alloc=620.3MB, time=127.28 memory used=4763.2MB, alloc=644.3MB, time=135.48 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428272171 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 3 2 2 F := [-15 x - 2 y z + y z , 12 x y - 7 y z - 10 x z, 20 x y z + 2 z + 5] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 G := [10 y z - 10 y z - 12, 2 x y z + 14 x - 2 x z , 2 16 x y z - 4 x y z + 11 x] > Problem := [F,G]; Problem := [ 3 2 2 2 2 3 2 2 [-15 x - 2 y z + y z , 12 x y - 7 y z - 10 x z, 20 x y z + 2 z + 5], 2 2 3 2 [10 y z - 10 y z - 12, 2 x y z + 14 x - 2 x z , 2 16 x y z - 4 x y z + 11 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.30 memory used=26.4MB, alloc=32.3MB, time=0.88 memory used=47.3MB, alloc=32.3MB, time=1.43 memory used=67.1MB, alloc=60.3MB, time=1.99 memory used=108.1MB, alloc=68.3MB, time=3.05 memory used=151.1MB, alloc=92.3MB, time=4.06 memory used=214.3MB, alloc=92.3MB, time=5.70 memory used=280.5MB, alloc=116.3MB, time=7.38 memory used=346.2MB, alloc=116.3MB, time=9.03 memory used=416.8MB, alloc=372.3MB, time=10.82 memory used=502.4MB, alloc=396.3MB, time=13.07 memory used=614.4MB, alloc=396.3MB, time=15.38 memory used=723.1MB, alloc=420.3MB, time=17.99 memory used=858.6MB, alloc=420.3MB, time=21.15 memory used=989.4MB, alloc=444.3MB, time=24.42 memory used=1117.1MB, alloc=444.3MB, time=27.42 memory used=1240.1MB, alloc=468.3MB, time=29.99 memory used=1371.8MB, alloc=468.3MB, time=32.54 memory used=1492.0MB, alloc=492.3MB, time=35.96 memory used=1584.6MB, alloc=492.3MB, time=38.21 memory used=1688.4MB, alloc=492.3MB, time=40.85 memory used=1776.8MB, alloc=516.3MB, time=43.13 memory used=1869.5MB, alloc=516.3MB, time=45.79 memory used=1943.2MB, alloc=516.3MB, time=48.02 memory used=2046.1MB, alloc=516.3MB, time=51.55 memory used=2113.3MB, alloc=516.3MB, time=53.87 memory used=2183.4MB, alloc=516.3MB, time=56.33 memory used=2244.5MB, alloc=516.3MB, time=58.24 memory used=2298.3MB, alloc=516.3MB, time=59.91 memory used=2350.0MB, alloc=516.3MB, time=61.35 memory used=2416.9MB, alloc=516.3MB, time=63.86 memory used=2467.8MB, alloc=516.3MB, time=65.79 memory used=2679.6MB, alloc=540.3MB, time=71.39 memory used=2880.6MB, alloc=564.3MB, time=76.81 memory used=3075.7MB, alloc=588.3MB, time=82.63 memory used=3248.7MB, alloc=612.3MB, time=88.28 memory used=3432.0MB, alloc=636.3MB, time=94.21 memory used=3601.9MB, alloc=636.3MB, time=99.02 memory used=3725.8MB, alloc=660.3MB, time=102.51 memory used=3929.8MB, alloc=660.3MB, time=107.00 memory used=4014.0MB, alloc=660.3MB, time=110.05 memory used=4127.2MB, alloc=660.3MB, time=113.44 memory used=4242.3MB, alloc=660.3MB, time=117.57 memory used=4352.0MB, alloc=660.3MB, time=121.29 memory used=4466.1MB, alloc=660.3MB, time=125.44 memory used=4553.4MB, alloc=660.3MB, time=128.78 memory used=4637.4MB, alloc=660.3MB, time=131.76 memory used=4876.8MB, alloc=684.3MB, time=136.71 memory used=5089.5MB, alloc=684.3MB, time=142.34 memory used=5269.5MB, alloc=684.3MB, time=144.31 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428272471 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 4 4 F := [7 y z - 16 x y + 3 x z, 19 x y z - 12 y + 4 z , 2 2 -8 x y z + 16 x z - 11 z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 2 2 G := [-8 x y + 7 x z - 19, 4 x z - 2 y + 12, 12 y z + 16 x y + 4 z ] > Problem := [F,G]; 3 2 2 2 4 4 Problem := [[7 y z - 16 x y + 3 x z, 19 x y z - 12 y + 4 z , 2 2 -8 x y z + 16 x z - 11 z ], 2 2 3 2 2 2 2 [-8 x y + 7 x z - 19, 4 x z - 2 y + 12, 12 y z + 16 x y + 4 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.4MB, alloc=32.3MB, time=0.87 memory used=46.4MB, alloc=56.3MB, time=1.41 memory used=86.5MB, alloc=60.3MB, time=2.46 memory used=124.0MB, alloc=60.3MB, time=3.43 memory used=161.3MB, alloc=84.3MB, time=4.45 memory used=225.9MB, alloc=92.3MB, time=6.10 memory used=290.9MB, alloc=116.3MB, time=7.68 memory used=359.2MB, alloc=116.3MB, time=9.28 memory used=425.4MB, alloc=372.3MB, time=10.90 memory used=512.7MB, alloc=396.3MB, time=13.00 memory used=623.2MB, alloc=396.3MB, time=15.75 memory used=731.5MB, alloc=420.3MB, time=18.48 memory used=863.0MB, alloc=444.3MB, time=21.85 memory used=989.6MB, alloc=444.3MB, time=25.11 memory used=1127.5MB, alloc=468.3MB, time=28.34 memory used=1250.6MB, alloc=468.3MB, time=31.35 memory used=1389.3MB, alloc=468.3MB, time=33.75 memory used=1500.7MB, alloc=468.3MB, time=36.55 memory used=1582.6MB, alloc=468.3MB, time=37.11 memory used=1725.9MB, alloc=468.3MB, time=39.58 memory used=1867.3MB, alloc=492.3MB, time=41.81 memory used=2035.2MB, alloc=492.3MB, time=45.96 memory used=2172.4MB, alloc=492.3MB, time=47.51 memory used=2256.1MB, alloc=492.3MB, time=48.05 memory used=2366.5MB, alloc=492.3MB, time=48.93 memory used=2449.2MB, alloc=492.3MB, time=49.47 memory used=2572.6MB, alloc=492.3MB, time=55.80 memory used=2660.3MB, alloc=492.3MB, time=56.34 memory used=2741.5MB, alloc=492.3MB, time=56.84 memory used=2818.9MB, alloc=492.3MB, time=57.29 memory used=2954.3MB, alloc=492.3MB, time=58.48 memory used=3068.6MB, alloc=492.3MB, time=60.97 memory used=3230.8MB, alloc=492.3MB, time=63.33 memory used=3332.7MB, alloc=492.3MB, time=65.87 memory used=3442.6MB, alloc=492.3MB, time=67.99 memory used=3597.3MB, alloc=492.3MB, time=70.02 memory used=3698.2MB, alloc=492.3MB, time=72.95 memory used=3838.1MB, alloc=492.3MB, time=75.30 memory used=3949.9MB, alloc=492.3MB, time=77.33 memory used=4041.7MB, alloc=492.3MB, time=80.19 memory used=4120.1MB, alloc=516.3MB, time=82.46 memory used=4175.3MB, alloc=516.3MB, time=84.11 memory used=4256.0MB, alloc=516.3MB, time=85.95 memory used=4339.7MB, alloc=516.3MB, time=88.02 memory used=4441.1MB, alloc=516.3MB, time=89.87 memory used=4515.6MB, alloc=516.3MB, time=91.75 memory used=4595.2MB, alloc=516.3MB, time=93.44 memory used=4655.8MB, alloc=516.3MB, time=95.57 memory used=4755.2MB, alloc=516.3MB, time=98.31 memory used=4840.3MB, alloc=516.3MB, time=99.99 memory used=4936.0MB, alloc=516.3MB, time=101.86 memory used=5036.8MB, alloc=540.3MB, time=103.22 memory used=5149.1MB, alloc=540.3MB, time=104.09 memory used=5283.5MB, alloc=540.3MB, time=105.41 memory used=5438.0MB, alloc=540.3MB, time=117.49 memory used=5557.1MB, alloc=540.3MB, time=118.41 memory used=5647.7MB, alloc=540.3MB, time=119.19 memory used=5763.6MB, alloc=540.3MB, time=119.97 memory used=5877.1MB, alloc=540.3MB, time=120.73 memory used=5956.8MB, alloc=540.3MB, time=121.40 memory used=6046.1MB, alloc=540.3MB, time=122.05 memory used=6146.3MB, alloc=540.3MB, time=122.72 memory used=6258.4MB, alloc=540.3MB, time=123.40 memory used=6385.8MB, alloc=540.3MB, time=124.10 memory used=6517.9MB, alloc=540.3MB, time=141.12 memory used=6637.5MB, alloc=540.3MB, time=142.00 memory used=6727.3MB, alloc=540.3MB, time=142.77 memory used=6842.5MB, alloc=540.3MB, time=143.56 memory used=6959.1MB, alloc=540.3MB, time=144.32 memory used=7038.8MB, alloc=540.3MB, time=144.96 memory used=7127.8MB, alloc=540.3MB, time=145.63 memory used=7226.8MB, alloc=540.3MB, time=146.29 memory used=7338.6MB, alloc=540.3MB, time=146.98 memory used=7464.2MB, alloc=540.3MB, time=147.68 memory used=7585.4MB, alloc=540.3MB, time=149.40 memory used=7647.3MB, alloc=540.3MB, time=151.03 memory used=7853.2MB, alloc=564.3MB, time=157.48 memory used=8060.0MB, alloc=588.3MB, time=163.31 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428272771 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; F := [ 3 2 2 2 2 2 2 4 -13 x y + 20 x y z - 3 y z, 8 x y + 20 x y + 15 y, -17 x y z - 18 z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 4 2 4 2 2 G := [-13 y z + x + 18 y , 15 x - x y z + 13 y z, -z + 7 x z - 3 y z ] > Problem := [F,G]; Problem := [[ 3 2 2 2 2 2 2 4 -13 x y + 20 x y z - 3 y z, 8 x y + 20 x y + 15 y, -17 x y z - 18 z 3 3 2 4 2 4 2 2 ], [-13 y z + x + 18 y , 15 x - x y z + 13 y z, -z + 7 x z - 3 y z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.31 memory used=26.6MB, alloc=32.3MB, time=0.89 memory used=47.4MB, alloc=32.3MB, time=1.42 memory used=66.0MB, alloc=56.3MB, time=1.91 memory used=106.5MB, alloc=60.3MB, time=2.95 memory used=146.5MB, alloc=60.3MB, time=3.97 memory used=184.9MB, alloc=84.3MB, time=4.88 memory used=218.6MB, alloc=84.3MB, time=5.76 memory used=276.9MB, alloc=92.3MB, time=6.59 memory used=325.5MB, alloc=93.3MB, time=7.40 memory used=357.9MB, alloc=93.3MB, time=7.56 memory used=418.8MB, alloc=93.3MB, time=9.17 memory used=477.8MB, alloc=117.3MB, time=10.59 memory used=541.1MB, alloc=373.3MB, time=12.09 memory used=630.6MB, alloc=397.3MB, time=14.15 memory used=743.1MB, alloc=421.3MB, time=16.89 memory used=872.2MB, alloc=445.3MB, time=19.77 memory used=984.8MB, alloc=445.3MB, time=22.34 memory used=1092.1MB, alloc=469.3MB, time=25.06 memory used=1198.4MB, alloc=469.3MB, time=27.81 memory used=1328.8MB, alloc=469.3MB, time=31.11 memory used=1436.0MB, alloc=469.3MB, time=33.67 memory used=1565.2MB, alloc=469.3MB, time=36.21 memory used=1709.4MB, alloc=493.3MB, time=38.83 memory used=1804.7MB, alloc=493.3MB, time=40.98 memory used=1899.7MB, alloc=493.3MB, time=43.22 memory used=2030.2MB, alloc=493.3MB, time=45.37 memory used=2145.1MB, alloc=493.3MB, time=48.93 memory used=2253.9MB, alloc=493.3MB, time=52.55 memory used=2362.7MB, alloc=493.3MB, time=54.03 memory used=2512.7MB, alloc=493.3MB, time=56.26 memory used=2634.0MB, alloc=493.3MB, time=59.39 memory used=2724.0MB, alloc=493.3MB, time=60.31 memory used=2850.9MB, alloc=517.3MB, time=62.38 memory used=3020.6MB, alloc=517.3MB, time=66.88 memory used=3143.5MB, alloc=517.3MB, time=70.11 memory used=3260.5MB, alloc=517.3MB, time=71.10 memory used=3374.0MB, alloc=517.3MB, time=73.35 memory used=3487.3MB, alloc=517.3MB, time=75.80 memory used=3625.2MB, alloc=517.3MB, time=77.70 memory used=3714.5MB, alloc=517.3MB, time=80.12 memory used=3774.3MB, alloc=517.3MB, time=81.90 memory used=3830.7MB, alloc=517.3MB, time=83.86 memory used=3881.9MB, alloc=517.3MB, time=85.47 memory used=3930.0MB, alloc=517.3MB, time=87.24 memory used=3975.5MB, alloc=517.3MB, time=88.84 memory used=4169.2MB, alloc=541.3MB, time=94.02 memory used=4350.2MB, alloc=565.3MB, time=98.97 memory used=4549.3MB, alloc=589.3MB, time=103.38 memory used=4744.9MB, alloc=589.3MB, time=108.26 memory used=4940.7MB, alloc=613.3MB, time=113.05 memory used=5092.8MB, alloc=637.3MB, time=117.80 memory used=5239.5MB, alloc=637.3MB, time=122.58 memory used=5383.7MB, alloc=637.3MB, time=126.67 memory used=5547.0MB, alloc=637.3MB, time=130.54 memory used=5684.2MB, alloc=661.3MB, time=135.05 memory used=5897.3MB, alloc=661.3MB, time=138.36 memory used=6070.1MB, alloc=661.3MB, time=143.85 memory used=6222.7MB, alloc=661.3MB, time=145.27 memory used=6395.1MB, alloc=661.3MB, time=147.02 memory used=6688.6MB, alloc=661.3MB, time=153.40 memory used=6828.6MB, alloc=661.3MB, time=154.86 memory used=7099.1MB, alloc=661.3MB, time=156.59 memory used=7394.5MB, alloc=661.3MB, time=159.60 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428273071 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 3 2 F := [11 x z + 4 y z + 19 z , x y + 8 y - 16, 18 x z + 19 y z + 10] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 4 3 2 G := [17 y - 15 x z - 8 y z , -10 z + 14 x y + 3, 5 x y + 10 y z - 5] > Problem := [F,G]; Problem := [ 2 2 2 3 2 3 2 [11 x z + 4 y z + 19 z , x y + 8 y - 16, 18 x z + 19 y z + 10], 4 2 2 4 3 2 [17 y - 15 x z - 8 y z , -10 z + 14 x y + 3, 5 x y + 10 y z - 5]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.31 memory used=25.3MB, alloc=32.3MB, time=0.85 memory used=44.6MB, alloc=56.3MB, time=1.37 memory used=85.6MB, alloc=60.3MB, time=2.42 memory used=128.0MB, alloc=68.3MB, time=3.40 memory used=168.4MB, alloc=68.3MB, time=4.30 memory used=214.7MB, alloc=92.3MB, time=5.34 memory used=279.6MB, alloc=92.3MB, time=6.84 memory used=345.4MB, alloc=92.3MB, time=8.27 memory used=416.7MB, alloc=116.3MB, time=9.71 memory used=486.4MB, alloc=116.3MB, time=10.55 memory used=540.6MB, alloc=116.3MB, time=10.98 memory used=588.1MB, alloc=116.3MB, time=11.38 memory used=662.7MB, alloc=372.3MB, time=13.09 memory used=746.6MB, alloc=396.3MB, time=15.19 memory used=859.9MB, alloc=420.3MB, time=17.79 memory used=977.5MB, alloc=420.3MB, time=20.26 memory used=1096.8MB, alloc=444.3MB, time=22.99 memory used=1205.3MB, alloc=444.3MB, time=25.44 memory used=1314.2MB, alloc=468.3MB, time=27.50 memory used=1436.1MB, alloc=468.3MB, time=29.07 memory used=1555.0MB, alloc=468.3MB, time=30.14 memory used=1679.7MB, alloc=468.3MB, time=36.73 memory used=1772.0MB, alloc=468.3MB, time=37.35 memory used=1879.2MB, alloc=468.3MB, time=38.38 memory used=1995.8MB, alloc=468.3MB, time=39.42 memory used=2118.0MB, alloc=468.3MB, time=45.90 memory used=2222.2MB, alloc=468.3MB, time=46.80 memory used=2305.2MB, alloc=468.3MB, time=47.38 memory used=2406.4MB, alloc=468.3MB, time=49.70 memory used=2547.3MB, alloc=468.3MB, time=65.01 memory used=2630.4MB, alloc=468.3MB, time=65.61 memory used=2706.4MB, alloc=468.3MB, time=66.14 memory used=2776.0MB, alloc=468.3MB, time=66.65 memory used=2888.9MB, alloc=468.3MB, time=68.68 memory used=2973.4MB, alloc=468.3MB, time=70.93 memory used=3061.5MB, alloc=468.3MB, time=73.01 memory used=3138.2MB, alloc=492.3MB, time=74.75 memory used=3198.3MB, alloc=492.3MB, time=76.65 memory used=3279.6MB, alloc=492.3MB, time=78.46 memory used=3407.0MB, alloc=492.3MB, time=80.80 memory used=3481.1MB, alloc=492.3MB, time=82.62 memory used=3564.4MB, alloc=492.3MB, time=84.85 memory used=3641.0MB, alloc=492.3MB, time=86.41 memory used=3690.1MB, alloc=492.3MB, time=88.09 memory used=3741.6MB, alloc=492.3MB, time=89.87 memory used=3786.7MB, alloc=492.3MB, time=91.30 memory used=3837.9MB, alloc=492.3MB, time=92.86 memory used=3934.1MB, alloc=492.3MB, time=94.28 memory used=4027.0MB, alloc=492.3MB, time=95.09 memory used=4127.0MB, alloc=492.3MB, time=96.07 memory used=4220.7MB, alloc=492.3MB, time=97.08 memory used=4318.1MB, alloc=492.3MB, time=98.19 memory used=4421.7MB, alloc=492.3MB, time=99.23 memory used=4523.8MB, alloc=492.3MB, time=100.84 memory used=4609.5MB, alloc=516.3MB, time=101.70 memory used=4728.1MB, alloc=516.3MB, time=102.54 memory used=4810.5MB, alloc=516.3MB, time=103.28 memory used=4899.4MB, alloc=516.3MB, time=104.03 memory used=5007.4MB, alloc=516.3MB, time=104.78 memory used=5143.0MB, alloc=516.3MB, time=106.40 memory used=5242.3MB, alloc=516.3MB, time=107.25 memory used=5357.8MB, alloc=516.3MB, time=108.08 memory used=5436.4MB, alloc=516.3MB, time=108.82 memory used=5528.7MB, alloc=516.3MB, time=109.57 memory used=5641.8MB, alloc=516.3MB, time=110.31 memory used=5763.8MB, alloc=516.3MB, time=138.03 memory used=5882.0MB, alloc=516.3MB, time=138.94 memory used=5966.3MB, alloc=516.3MB, time=139.72 memory used=6068.0MB, alloc=516.3MB, time=140.51 memory used=6190.8MB, alloc=516.3MB, time=141.31 memory used=6263.7MB, alloc=516.3MB, time=141.95 memory used=6342.9MB, alloc=516.3MB, time=142.61 memory used=6429.3MB, alloc=516.3MB, time=143.29 memory used=6525.5MB, alloc=516.3MB, time=143.97 memory used=6633.8MB, alloc=516.3MB, time=144.66 memory used=6789.5MB, alloc=516.3MB, time=146.10 memory used=6883.7MB, alloc=516.3MB, time=147.03 memory used=6981.2MB, alloc=516.3MB, time=147.89 memory used=7088.2MB, alloc=516.3MB, time=148.72 memory used=7168.8MB, alloc=516.3MB, time=149.46 memory used=7266.0MB, alloc=516.3MB, time=150.23 memory used=7377.7MB, alloc=516.3MB, time=150.97 memory used=7478.9MB, alloc=516.3MB, time=152.42 memory used=7572.8MB, alloc=516.3MB, time=153.26 memory used=7684.0MB, alloc=516.3MB, time=154.10 memory used=7762.9MB, alloc=516.3MB, time=154.84 memory used=7856.9MB, alloc=516.3MB, time=155.62 memory used=7972.6MB, alloc=516.3MB, time=156.40 memory used=8083.2MB, alloc=516.3MB, time=184.65 memory used=8200.1MB, alloc=516.3MB, time=185.56 memory used=8285.0MB, alloc=516.3MB, time=186.31 memory used=8384.2MB, alloc=516.3MB, time=187.08 memory used=8506.2MB, alloc=516.3MB, time=187.90 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428273371 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 4 2 F := [11 x y - 8 x y z - 17 y, 19 x y z + 4 x z, 5 x - 15 x z + 11 x] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 G := [-14 x y z + 4 x y - 6 y z, -7 x y z - 15 x z - 2 y z , 4 3 3 -17 x - 12 x z + 20 y z] > Problem := [F,G]; Problem := [ 2 2 4 2 [11 x y - 8 x y z - 17 y, 19 x y z + 4 x z, 5 x - 15 x z + 11 x], [ 2 3 2 -14 x y z + 4 x y - 6 y z, -7 x y z - 15 x z - 2 y z , 4 3 3 -17 x - 12 x z + 20 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.31 memory used=26.6MB, alloc=32.3MB, time=0.87 memory used=48.1MB, alloc=32.3MB, time=1.42 memory used=68.3MB, alloc=56.3MB, time=1.99 memory used=109.2MB, alloc=60.3MB, time=3.06 memory used=149.6MB, alloc=60.3MB, time=4.09 memory used=189.5MB, alloc=84.3MB, time=5.15 memory used=228.4MB, alloc=84.3MB, time=6.16 memory used=288.9MB, alloc=92.3MB, time=7.78 memory used=348.7MB, alloc=116.3MB, time=9.31 memory used=427.9MB, alloc=116.3MB, time=11.38 memory used=507.2MB, alloc=372.3MB, time=13.43 memory used=584.8MB, alloc=396.3MB, time=15.55 memory used=693.3MB, alloc=420.3MB, time=18.26 memory used=829.4MB, alloc=420.3MB, time=21.67 memory used=943.4MB, alloc=444.3MB, time=24.68 memory used=1070.4MB, alloc=468.3MB, time=27.92 memory used=1183.8MB, alloc=468.3MB, time=30.56 memory used=1321.3MB, alloc=492.3MB, time=33.76 memory used=1436.6MB, alloc=492.3MB, time=36.51 memory used=1542.3MB, alloc=492.3MB, time=38.97 memory used=1651.2MB, alloc=492.3MB, time=41.67 memory used=1741.4MB, alloc=492.3MB, time=44.08 memory used=1836.8MB, alloc=516.3MB, time=46.48 memory used=1919.9MB, alloc=516.3MB, time=48.30 memory used=2013.3MB, alloc=516.3MB, time=51.33 memory used=2082.5MB, alloc=516.3MB, time=53.36 memory used=2160.4MB, alloc=516.3MB, time=55.32 memory used=2240.6MB, alloc=540.3MB, time=57.10 memory used=2326.4MB, alloc=540.3MB, time=59.99 memory used=2396.7MB, alloc=540.3MB, time=62.44 memory used=2463.1MB, alloc=540.3MB, time=64.70 memory used=2519.6MB, alloc=540.3MB, time=66.42 memory used=2573.3MB, alloc=540.3MB, time=68.13 memory used=2627.3MB, alloc=540.3MB, time=69.73 memory used=2685.6MB, alloc=540.3MB, time=71.19 memory used=2753.9MB, alloc=540.3MB, time=73.15 memory used=2811.4MB, alloc=540.3MB, time=75.11 memory used=2860.6MB, alloc=540.3MB, time=77.01 memory used=3052.2MB, alloc=564.3MB, time=81.78 memory used=3259.2MB, alloc=588.3MB, time=87.23 memory used=3446.0MB, alloc=612.3MB, time=91.44 memory used=3617.5MB, alloc=636.3MB, time=97.11 memory used=3806.5MB, alloc=636.3MB, time=101.79 memory used=3972.3MB, alloc=636.3MB, time=106.96 memory used=4138.7MB, alloc=660.3MB, time=110.75 memory used=4290.3MB, alloc=660.3MB, time=115.85 memory used=4439.3MB, alloc=684.3MB, time=120.24 memory used=4580.6MB, alloc=684.3MB, time=123.86 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428273671 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 4 2 3 3 2 F := [4 x + 16 y z + 12 z , 13 y + 16 x z + 19, -3 x y - 6 x y + 4 x ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 4 2 G := [-x z - 17 y z - 4 y z, -11 z - 8 x y - 11 z , 4 2 2 20 x - 3 x y z - 11 x y ] > Problem := [F,G]; Problem := [ 3 2 3 4 2 3 3 2 [4 x + 16 y z + 12 z , 13 y + 16 x z + 19, -3 x y - 6 x y + 4 x ], [ 2 2 3 2 4 2 -x z - 17 y z - 4 y z, -11 z - 8 x y - 11 z , 4 2 2 20 x - 3 x y z - 11 x y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.31 memory used=25.6MB, alloc=32.3MB, time=0.85 memory used=45.2MB, alloc=32.3MB, time=1.35 memory used=63.6MB, alloc=56.3MB, time=1.83 memory used=104.0MB, alloc=60.3MB, time=2.87 memory used=143.2MB, alloc=60.3MB, time=3.75 memory used=184.4MB, alloc=68.3MB, time=4.76 memory used=226.8MB, alloc=68.3MB, time=5.73 memory used=268.4MB, alloc=92.3MB, time=6.62 memory used=330.2MB, alloc=92.3MB, time=8.83 memory used=383.7MB, alloc=92.3MB, time=9.42 memory used=449.5MB, alloc=92.3MB, time=11.02 memory used=507.7MB, alloc=92.3MB, time=12.09 memory used=562.3MB, alloc=92.3MB, time=12.88 memory used=629.0MB, alloc=92.3MB, time=14.09 memory used=681.0MB, alloc=92.3MB, time=16.58 memory used=711.9MB, alloc=92.3MB, time=16.76 memory used=752.8MB, alloc=92.3MB, time=17.32 memory used=812.2MB, alloc=116.3MB, time=18.56 memory used=884.6MB, alloc=116.3MB, time=21.20 memory used=978.4MB, alloc=116.3MB, time=22.96 memory used=1046.4MB, alloc=372.3MB, time=24.55 memory used=1136.3MB, alloc=372.3MB, time=26.60 memory used=1217.6MB, alloc=396.3MB, time=28.70 memory used=1335.9MB, alloc=396.3MB, time=31.21 memory used=1441.1MB, alloc=396.3MB, time=33.02 memory used=1553.5MB, alloc=420.3MB, time=35.54 memory used=1687.6MB, alloc=444.3MB, time=38.16 memory used=1820.1MB, alloc=444.3MB, time=41.24 memory used=1944.5MB, alloc=444.3MB, time=44.01 memory used=2056.8MB, alloc=468.3MB, time=46.46 memory used=2151.8MB, alloc=468.3MB, time=48.53 memory used=2236.2MB, alloc=468.3MB, time=50.39 memory used=2384.1MB, alloc=492.3MB, time=52.38 memory used=2517.2MB, alloc=492.3MB, time=53.96 memory used=2630.2MB, alloc=492.3MB, time=54.86 memory used=2772.6MB, alloc=492.3MB, time=62.59 memory used=2904.5MB, alloc=492.3MB, time=65.02 memory used=3029.4MB, alloc=492.3MB, time=66.04 memory used=3165.8MB, alloc=492.3MB, time=73.70 memory used=3289.8MB, alloc=492.3MB, time=76.01 memory used=3374.3MB, alloc=492.3MB, time=77.95 memory used=3450.5MB, alloc=492.3MB, time=79.96 memory used=3583.5MB, alloc=492.3MB, time=104.59 memory used=3668.4MB, alloc=492.3MB, time=105.19 memory used=3804.5MB, alloc=492.3MB, time=106.93 memory used=3889.6MB, alloc=492.3MB, time=108.65 memory used=4012.8MB, alloc=492.3MB, time=109.99 memory used=4102.7MB, alloc=492.3MB, time=111.77 memory used=4212.8MB, alloc=492.3MB, time=112.72 memory used=4322.1MB, alloc=492.3MB, time=116.45 memory used=4416.8MB, alloc=492.3MB, time=117.41 memory used=4541.2MB, alloc=492.3MB, time=120.16 memory used=4608.4MB, alloc=492.3MB, time=121.80 memory used=4669.7MB, alloc=492.3MB, time=123.31 memory used=4749.7MB, alloc=492.3MB, time=126.73 memory used=4825.7MB, alloc=492.3MB, time=128.53 memory used=4895.9MB, alloc=492.3MB, time=129.85 memory used=4965.4MB, alloc=492.3MB, time=132.01 memory used=5014.3MB, alloc=492.3MB, time=133.53 memory used=5069.0MB, alloc=492.3MB, time=135.09 memory used=5124.4MB, alloc=492.3MB, time=136.84 memory used=5168.7MB, alloc=492.3MB, time=138.31 memory used=5206.8MB, alloc=492.3MB, time=139.59 memory used=5248.7MB, alloc=492.3MB, time=140.91 memory used=5382.5MB, alloc=516.3MB, time=143.52 memory used=5575.2MB, alloc=516.3MB, time=148.20 memory used=5759.1MB, alloc=540.3MB, time=151.20 memory used=5905.0MB, alloc=540.3MB, time=153.42 memory used=6102.5MB, alloc=564.3MB, time=157.48 memory used=6321.9MB, alloc=588.3MB, time=161.56 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428273971 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 4 2 2 4 F := [16 x z - 2 x z - 12 y , 17 x y z + 10 x y z - 5 z , 2 2 2 4 x y z - 15 x y - 8 x y ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 3 3 G := [-10 x z - 16 x y - 11, 16 x y z - 5 y z - 18 y z , 2 3 15 x y z + 17 x z + 19 x y z] > Problem := [F,G]; 2 2 3 4 2 2 4 Problem := [[16 x z - 2 x z - 12 y , 17 x y z + 10 x y z - 5 z , 2 2 2 3 2 4 x y z - 15 x y - 8 x y ], [-10 x z - 16 x y - 11, 2 3 3 2 3 16 x y z - 5 y z - 18 y z , 15 x y z + 17 x z + 19 x y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.30 memory used=27.0MB, alloc=32.3MB, time=0.89 memory used=47.2MB, alloc=60.3MB, time=1.43 memory used=88.4MB, alloc=60.3MB, time=2.45 memory used=129.1MB, alloc=60.3MB, time=3.45 memory used=159.0MB, alloc=60.3MB, time=4.16 memory used=199.4MB, alloc=92.3MB, time=5.13 memory used=264.9MB, alloc=92.3MB, time=6.71 memory used=329.4MB, alloc=116.3MB, time=8.24 memory used=404.1MB, alloc=372.3MB, time=10.08 memory used=495.0MB, alloc=396.3MB, time=12.17 memory used=603.2MB, alloc=396.3MB, time=14.68 memory used=725.1MB, alloc=420.3MB, time=16.94 memory used=853.1MB, alloc=420.3MB, time=19.53 memory used=940.7MB, alloc=420.3MB, time=20.74 memory used=1064.3MB, alloc=420.3MB, time=23.13 memory used=1190.0MB, alloc=444.3MB, time=26.26 memory used=1301.1MB, alloc=468.3MB, time=29.09 memory used=1412.1MB, alloc=468.3MB, time=32.21 memory used=1490.9MB, alloc=468.3MB, time=34.26 memory used=1587.3MB, alloc=468.3MB, time=36.63 memory used=1677.1MB, alloc=492.3MB, time=39.11 memory used=1765.6MB, alloc=492.3MB, time=41.45 memory used=1847.1MB, alloc=492.3MB, time=43.69 memory used=1934.5MB, alloc=492.3MB, time=45.69 memory used=2022.1MB, alloc=492.3MB, time=47.63 memory used=2097.0MB, alloc=492.3MB, time=49.67 memory used=2216.0MB, alloc=492.3MB, time=51.26 memory used=2327.6MB, alloc=492.3MB, time=52.77 memory used=2395.2MB, alloc=492.3MB, time=54.46 memory used=2448.0MB, alloc=492.3MB, time=56.13 memory used=2513.6MB, alloc=516.3MB, time=57.82 memory used=2566.4MB, alloc=516.3MB, time=59.38 memory used=2621.5MB, alloc=516.3MB, time=60.92 memory used=2672.0MB, alloc=516.3MB, time=62.47 memory used=2742.2MB, alloc=516.3MB, time=64.89 memory used=2784.6MB, alloc=516.3MB, time=66.54 memory used=2991.9MB, alloc=540.3MB, time=72.05 memory used=3195.0MB, alloc=564.3MB, time=76.57 memory used=3353.7MB, alloc=588.3MB, time=80.97 memory used=3531.5MB, alloc=612.3MB, time=85.73 memory used=3682.4MB, alloc=636.3MB, time=90.27 memory used=3838.1MB, alloc=636.3MB, time=94.30 memory used=3977.4MB, alloc=660.3MB, time=97.70 memory used=4096.2MB, alloc=660.3MB, time=101.46 memory used=4201.7MB, alloc=660.3MB, time=104.97 memory used=4305.4MB, alloc=660.3MB, time=108.17 memory used=4408.7MB, alloc=684.3MB, time=111.33 memory used=4501.0MB, alloc=684.3MB, time=114.93 memory used=4843.5MB, alloc=708.3MB, time=122.58 memory used=5227.8MB, alloc=732.3MB, time=130.84 memory used=5568.6MB, alloc=756.3MB, time=139.38 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428274271 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 3 F := [x - 8 y z - 9 z , 19 y z - 9 y + 16 y, 16 x y z + 9 x z + 4 z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 3 2 2 2 2 G := [3 x y - 2 z + 13 y , -4 x + 9 x y + 8 z, 12 x z - 2 y z + 19 z ] > Problem := [F,G]; Problem := [ 2 2 3 2 2 3 [x - 8 y z - 9 z , 19 y z - 9 y + 16 y, 16 x y z + 9 x z + 4 z], 2 2 3 2 3 2 2 2 2 [3 x y - 2 z + 13 y , -4 x + 9 x y + 8 z, 12 x z - 2 y z + 19 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.4MB, alloc=32.3MB, time=0.86 memory used=46.7MB, alloc=32.3MB, time=1.38 memory used=65.1MB, alloc=56.3MB, time=1.81 memory used=104.4MB, alloc=60.3MB, time=2.82 memory used=143.6MB, alloc=84.3MB, time=3.84 memory used=207.8MB, alloc=92.3MB, time=5.46 memory used=273.7MB, alloc=92.3MB, time=6.91 memory used=347.7MB, alloc=116.3MB, time=8.36 memory used=410.5MB, alloc=372.3MB, time=9.98 memory used=494.7MB, alloc=396.3MB, time=12.21 memory used=603.1MB, alloc=396.3MB, time=14.97 memory used=715.4MB, alloc=420.3MB, time=17.80 memory used=844.5MB, alloc=444.3MB, time=21.23 memory used=977.3MB, alloc=444.3MB, time=23.89 memory used=1089.2MB, alloc=468.3MB, time=26.66 memory used=1188.5MB, alloc=468.3MB, time=29.12 memory used=1290.3MB, alloc=468.3MB, time=31.70 memory used=1396.5MB, alloc=492.3MB, time=34.64 memory used=1481.9MB, alloc=492.3MB, time=36.83 memory used=1584.3MB, alloc=492.3MB, time=40.00 memory used=1678.8MB, alloc=492.3MB, time=42.83 memory used=1773.6MB, alloc=516.3MB, time=45.97 memory used=1848.0MB, alloc=516.3MB, time=48.03 memory used=1921.4MB, alloc=516.3MB, time=50.27 memory used=1977.5MB, alloc=516.3MB, time=52.12 memory used=2029.3MB, alloc=516.3MB, time=53.85 memory used=2098.1MB, alloc=516.3MB, time=55.90 memory used=2150.4MB, alloc=516.3MB, time=57.65 memory used=2206.7MB, alloc=516.3MB, time=59.35 memory used=2255.7MB, alloc=516.3MB, time=60.83 memory used=2305.6MB, alloc=516.3MB, time=62.19 memory used=2516.7MB, alloc=540.3MB, time=67.47 memory used=2739.9MB, alloc=564.3MB, time=74.15 memory used=2946.3MB, alloc=588.3MB, time=81.15 memory used=3107.0MB, alloc=612.3MB, time=86.17 memory used=3255.5MB, alloc=636.3MB, time=91.06 memory used=3407.1MB, alloc=660.3MB, time=96.06 memory used=3551.4MB, alloc=660.3MB, time=100.51 memory used=3761.2MB, alloc=660.3MB, time=104.05 memory used=3852.8MB, alloc=660.3MB, time=107.01 memory used=3953.2MB, alloc=660.3MB, time=110.09 memory used=4065.7MB, alloc=660.3MB, time=114.66 memory used=4173.1MB, alloc=684.3MB, time=118.60 memory used=4263.7MB, alloc=684.3MB, time=122.42 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428274571 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 4 4 4 2 2 3 F := [2 x y + 16 y + 16 z , 3 y + 6 x y - 10 z , x y - 17 x y z + 2 x] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 2 2 G := [-11 x z - 12 x y + 7 x y z, -8 y z - 5 y z - 7 x z, 2 2 4 2 18 x z + 10 z - 8 x y] > Problem := [F,G]; Problem := [ 3 4 4 4 2 2 3 [2 x y + 16 y + 16 z , 3 y + 6 x y - 10 z , x y - 17 x y z + 2 x], [ 3 3 2 2 2 2 -11 x z - 12 x y + 7 x y z, -8 y z - 5 y z - 7 x z, 2 2 4 2 18 x z + 10 z - 8 x y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.30 memory used=26.2MB, alloc=32.3MB, time=0.87 memory used=46.4MB, alloc=56.3MB, time=1.41 memory used=88.0MB, alloc=60.3MB, time=2.43 memory used=131.0MB, alloc=68.3MB, time=3.30 memory used=182.5MB, alloc=68.3MB, time=4.64 memory used=224.6MB, alloc=68.3MB, time=5.46 memory used=265.9MB, alloc=92.3MB, time=6.40 memory used=332.2MB, alloc=92.3MB, time=7.97 memory used=396.4MB, alloc=116.3MB, time=9.53 memory used=454.0MB, alloc=116.3MB, time=10.91 memory used=515.3MB, alloc=372.3MB, time=12.42 memory used=604.0MB, alloc=396.3MB, time=14.44 memory used=711.8MB, alloc=396.3MB, time=16.52 memory used=793.3MB, alloc=396.3MB, time=17.61 memory used=878.5MB, alloc=396.3MB, time=18.76 memory used=973.5MB, alloc=396.3MB, time=21.37 memory used=1109.2MB, alloc=396.3MB, time=24.55 memory used=1205.4MB, alloc=420.3MB, time=27.08 memory used=1333.2MB, alloc=420.3MB, time=29.82 memory used=1441.9MB, alloc=420.3MB, time=32.08 memory used=1536.1MB, alloc=444.3MB, time=34.09 memory used=1673.1MB, alloc=444.3MB, time=38.02 memory used=1773.4MB, alloc=444.3MB, time=40.68 memory used=1861.3MB, alloc=468.3MB, time=43.04 memory used=1960.3MB, alloc=468.3MB, time=45.77 memory used=2053.4MB, alloc=468.3MB, time=48.05 memory used=2129.2MB, alloc=468.3MB, time=50.11 memory used=2203.8MB, alloc=468.3MB, time=52.22 memory used=2282.4MB, alloc=492.3MB, time=54.17 memory used=2396.2MB, alloc=492.3MB, time=62.95 memory used=2480.1MB, alloc=492.3MB, time=63.63 memory used=2594.2MB, alloc=492.3MB, time=64.73 memory used=2705.7MB, alloc=492.3MB, time=65.68 memory used=2819.3MB, alloc=492.3MB, time=70.72 memory used=2907.3MB, alloc=492.3MB, time=72.92 memory used=3030.8MB, alloc=492.3MB, time=73.93 memory used=3180.3MB, alloc=492.3MB, time=94.22 memory used=3271.6MB, alloc=492.3MB, time=94.94 memory used=3347.4MB, alloc=492.3MB, time=95.61 memory used=3447.1MB, alloc=492.3MB, time=96.30 memory used=3518.8MB, alloc=492.3MB, time=96.89 memory used=3618.5MB, alloc=492.3MB, time=98.83 memory used=3764.5MB, alloc=492.3MB, time=101.94 memory used=3890.5MB, alloc=492.3MB, time=107.16 memory used=3947.5MB, alloc=492.3MB, time=109.04 memory used=4015.6MB, alloc=492.3MB, time=110.91 memory used=4070.6MB, alloc=492.3MB, time=112.57 memory used=4134.1MB, alloc=492.3MB, time=114.06 memory used=4231.2MB, alloc=492.3MB, time=115.03 memory used=4328.2MB, alloc=492.3MB, time=115.86 memory used=4429.3MB, alloc=492.3MB, time=117.98 memory used=4511.6MB, alloc=492.3MB, time=118.65 memory used=4625.3MB, alloc=492.3MB, time=120.26 memory used=4745.2MB, alloc=516.3MB, time=138.51 memory used=4836.2MB, alloc=516.3MB, time=139.28 memory used=4949.8MB, alloc=516.3MB, time=140.06 memory used=5024.9MB, alloc=516.3MB, time=140.70 memory used=5112.4MB, alloc=516.3MB, time=141.36 memory used=5215.8MB, alloc=516.3MB, time=142.06 memory used=5361.1MB, alloc=516.3MB, time=143.08 memory used=5491.8MB, alloc=516.3MB, time=148.72 memory used=5578.1MB, alloc=516.3MB, time=150.08 memory used=5629.7MB, alloc=516.3MB, time=151.47 memory used=5673.2MB, alloc=516.3MB, time=152.61 memory used=5741.0MB, alloc=516.3MB, time=155.03 memory used=5780.0MB, alloc=516.3MB, time=156.67 memory used=5915.5MB, alloc=516.3MB, time=158.76 memory used=6015.4MB, alloc=516.3MB, time=159.59 memory used=6098.1MB, alloc=516.3MB, time=160.34 memory used=6200.1MB, alloc=516.3MB, time=161.08 memory used=6296.9MB, alloc=516.3MB, time=161.81 memory used=6410.1MB, alloc=516.3MB, time=163.17 memory used=6514.1MB, alloc=516.3MB, time=164.01 memory used=6593.6MB, alloc=516.3MB, time=164.77 memory used=6692.7MB, alloc=516.3MB, time=165.54 memory used=6796.7MB, alloc=516.3MB, time=166.29 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428274871 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 2 2 3 3 2 2 F := [2 x + 17 x y - 7 y z , -18 z - 14 x z, -16 y + 13 x + 12 z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; G := [ 3 2 2 2 2 3 -11 x + 15 y - 17 y, 11 x z - 13 x z + 12 x y, 10 x z - 2 x y z + 7 x ] > Problem := [F,G]; Problem := [ 4 3 2 2 3 3 2 2 [2 x + 17 x y - 7 y z , -18 z - 14 x z, -16 y + 13 x + 12 z ], [ 3 2 2 2 2 3 -11 x + 15 y - 17 y, 11 x z - 13 x z + 12 x y, 10 x z - 2 x y z + 7 x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.30 memory used=26.7MB, alloc=32.3MB, time=0.87 memory used=48.0MB, alloc=32.3MB, time=1.42 memory used=67.2MB, alloc=56.3MB, time=1.92 memory used=111.8MB, alloc=68.3MB, time=2.97 memory used=153.2MB, alloc=68.3MB, time=3.97 memory used=195.2MB, alloc=92.3MB, time=4.97 memory used=257.4MB, alloc=92.3MB, time=6.25 memory used=323.2MB, alloc=116.3MB, time=7.90 memory used=394.4MB, alloc=372.3MB, time=9.71 memory used=487.0MB, alloc=396.3MB, time=11.88 memory used=607.7MB, alloc=420.3MB, time=14.85 memory used=746.9MB, alloc=420.3MB, time=17.68 memory used=872.2MB, alloc=444.3MB, time=20.79 memory used=983.2MB, alloc=468.3MB, time=23.55 memory used=1083.8MB, alloc=468.3MB, time=26.06 memory used=1190.1MB, alloc=468.3MB, time=28.17 memory used=1282.5MB, alloc=468.3MB, time=30.50 memory used=1424.9MB, alloc=468.3MB, time=33.34 memory used=1509.2MB, alloc=468.3MB, time=35.53 memory used=1598.4MB, alloc=468.3MB, time=37.95 memory used=1679.4MB, alloc=468.3MB, time=40.29 memory used=1776.2MB, alloc=492.3MB, time=42.67 memory used=1851.3MB, alloc=492.3MB, time=44.73 memory used=1914.9MB, alloc=492.3MB, time=46.66 memory used=1983.3MB, alloc=492.3MB, time=48.86 memory used=2042.7MB, alloc=492.3MB, time=50.79 memory used=2103.8MB, alloc=492.3MB, time=52.59 memory used=2158.5MB, alloc=492.3MB, time=54.51 memory used=2199.7MB, alloc=492.3MB, time=56.02 memory used=2249.0MB, alloc=492.3MB, time=57.62 memory used=2311.7MB, alloc=492.3MB, time=59.55 memory used=2497.1MB, alloc=516.3MB, time=64.42 memory used=2689.1MB, alloc=540.3MB, time=69.42 memory used=2925.9MB, alloc=564.3MB, time=74.15 memory used=3100.1MB, alloc=588.3MB, time=78.68 memory used=3305.5MB, alloc=612.3MB, time=83.65 memory used=3466.4MB, alloc=612.3MB, time=88.17 memory used=3619.0MB, alloc=636.3MB, time=93.16 memory used=3764.2MB, alloc=636.3MB, time=97.74 memory used=3929.9MB, alloc=660.3MB, time=101.84 memory used=4072.1MB, alloc=660.3MB, time=105.62 memory used=4281.0MB, alloc=660.3MB, time=109.85 memory used=4402.7MB, alloc=660.3MB, time=113.82 memory used=4522.6MB, alloc=660.3MB, time=118.15 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428275171 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 2 F := [13 x z + 5 x y z - 17 x z, 13 x z - 15 x y + 13 x y z, 2 2 2 -17 x y z + 20 x y - x ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 4 2 G := [20 x z - 13 x y - 4 x z, -19 x y z - 11 z - x z , 2 2 3 2 -6 x y + 17 y + 4 y z ] > Problem := [F,G]; 2 3 2 2 2 Problem := [[13 x z + 5 x y z - 17 x z, 13 x z - 15 x y + 13 x y z, 2 2 2 3 2 -17 x y z + 20 x y - x ], [20 x z - 13 x y - 4 x z, 2 4 2 2 2 3 2 -19 x y z - 11 z - x z , -6 x y + 17 y + 4 y z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.31 memory used=26.6MB, alloc=32.3MB, time=0.89 memory used=47.6MB, alloc=32.3MB, time=1.42 memory used=65.7MB, alloc=56.3MB, time=1.91 memory used=105.3MB, alloc=60.3MB, time=2.96 memory used=144.0MB, alloc=84.3MB, time=4.00 memory used=205.1MB, alloc=92.3MB, time=5.62 memory used=268.7MB, alloc=116.3MB, time=7.18 memory used=352.9MB, alloc=116.3MB, time=9.40 memory used=429.3MB, alloc=396.3MB, time=11.51 memory used=540.0MB, alloc=420.3MB, time=14.31 memory used=675.8MB, alloc=420.3MB, time=17.30 memory used=807.9MB, alloc=444.3MB, time=20.61 memory used=957.4MB, alloc=444.3MB, time=23.93 memory used=1082.5MB, alloc=468.3MB, time=27.33 memory used=1195.7MB, alloc=468.3MB, time=30.47 memory used=1306.4MB, alloc=492.3MB, time=33.22 memory used=1410.5MB, alloc=492.3MB, time=35.93 memory used=1508.3MB, alloc=492.3MB, time=38.78 memory used=1594.9MB, alloc=492.3MB, time=41.40 memory used=1679.9MB, alloc=492.3MB, time=43.87 memory used=1760.4MB, alloc=492.3MB, time=46.16 memory used=1841.1MB, alloc=516.3MB, time=48.44 memory used=1956.7MB, alloc=516.3MB, time=50.84 memory used=2052.7MB, alloc=516.3MB, time=51.58 memory used=2167.4MB, alloc=516.3MB, time=52.87 memory used=2264.5MB, alloc=516.3MB, time=53.59 memory used=2386.0MB, alloc=516.3MB, time=57.79 memory used=2474.5MB, alloc=516.3MB, time=58.48 memory used=2622.1MB, alloc=516.3MB, time=59.61 memory used=2718.4MB, alloc=516.3MB, time=60.36 memory used=2835.8MB, alloc=516.3MB, time=61.85 memory used=2942.4MB, alloc=516.3MB, time=62.79 memory used=3041.8MB, alloc=516.3MB, time=64.54 memory used=3171.7MB, alloc=516.3MB, time=67.21 memory used=3269.7MB, alloc=516.3MB, time=69.00 memory used=3339.4MB, alloc=516.3MB, time=70.99 memory used=3397.9MB, alloc=516.3MB, time=72.76 memory used=3477.5MB, alloc=516.3MB, time=74.43 memory used=3546.6MB, alloc=516.3MB, time=76.01 memory used=3648.7MB, alloc=516.3MB, time=78.39 memory used=3697.5MB, alloc=516.3MB, time=79.99 memory used=3887.8MB, alloc=540.3MB, time=86.02 memory used=4094.5MB, alloc=564.3MB, time=91.46 memory used=4329.2MB, alloc=588.3MB, time=98.64 memory used=4518.9MB, alloc=612.3MB, time=104.67 memory used=4701.1MB, alloc=636.3MB, time=110.54 memory used=4865.7MB, alloc=660.3MB, time=114.94 memory used=5024.6MB, alloc=660.3MB, time=119.72 memory used=5165.0MB, alloc=684.3MB, time=123.75 memory used=5297.7MB, alloc=684.3MB, time=127.36 memory used=5471.7MB, alloc=708.3MB, time=132.63 memory used=5629.6MB, alloc=708.3MB, time=136.56 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428275471 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 2 2 F := [20 x y - 17 x y + 13 z , -19 x y + 7 x z + 5 y z , 3 17 x y - 11 x y - 6 z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 2 2 2 2 G := [-x y + 10 y z - 20 z , -10 x y + 5 x z - 10 x , 2 2 2 -x z - 12 x y z + 14] > Problem := [F,G]; 3 3 2 2 2 2 Problem := [[20 x y - 17 x y + 13 z , -19 x y + 7 x z + 5 y z , 3 3 3 2 17 x y - 11 x y - 6 z], [-x y + 10 y z - 20 z , 2 2 2 2 2 2 2 2 -10 x y + 5 x z - 10 x , -x z - 12 x y z + 14]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.30 memory used=27.3MB, alloc=32.3MB, time=0.88 memory used=46.9MB, alloc=32.3MB, time=1.35 memory used=65.1MB, alloc=56.3MB, time=1.83 memory used=105.9MB, alloc=60.3MB, time=2.89 memory used=140.0MB, alloc=60.3MB, time=3.69 memory used=181.4MB, alloc=68.3MB, time=4.64 memory used=227.7MB, alloc=92.3MB, time=5.57 memory used=297.8MB, alloc=92.3MB, time=7.02 memory used=365.8MB, alloc=92.3MB, time=8.54 memory used=431.7MB, alloc=116.3MB, time=10.07 memory used=493.0MB, alloc=372.3MB, time=11.44 memory used=586.3MB, alloc=396.3MB, time=13.55 memory used=705.3MB, alloc=396.3MB, time=16.19 memory used=784.8MB, alloc=396.3MB, time=17.72 memory used=879.8MB, alloc=396.3MB, time=18.83 memory used=991.9MB, alloc=420.3MB, time=21.45 memory used=1107.9MB, alloc=444.3MB, time=24.03 memory used=1240.1MB, alloc=444.3MB, time=26.07 memory used=1382.1MB, alloc=444.3MB, time=30.01 memory used=1449.2MB, alloc=444.3MB, time=30.44 memory used=1526.2MB, alloc=444.3MB, time=30.87 memory used=1580.3MB, alloc=444.3MB, time=31.20 memory used=1644.0MB, alloc=444.3MB, time=31.55 memory used=1744.5MB, alloc=444.3MB, time=32.15 memory used=1931.1MB, alloc=444.3MB, time=34.62 memory used=2094.1MB, alloc=444.3MB, time=37.42 memory used=2157.8MB, alloc=444.3MB, time=37.87 memory used=2232.3MB, alloc=444.3MB, time=38.34 memory used=2283.3MB, alloc=444.3MB, time=38.73 memory used=2344.8MB, alloc=444.3MB, time=39.11 memory used=2444.9MB, alloc=444.3MB, time=43.42 memory used=2511.3MB, alloc=444.3MB, time=43.87 memory used=2569.5MB, alloc=444.3MB, time=44.26 memory used=2725.7MB, alloc=468.3MB, time=46.77 memory used=2876.1MB, alloc=468.3MB, time=49.48 memory used=2989.3MB, alloc=468.3MB, time=52.04 memory used=3075.3MB, alloc=468.3MB, time=52.55 memory used=3137.1MB, alloc=468.3MB, time=52.99 memory used=3213.3MB, alloc=468.3MB, time=53.46 memory used=3386.1MB, alloc=468.3MB, time=55.18 memory used=3493.6MB, alloc=468.3MB, time=57.22 memory used=3614.9MB, alloc=468.3MB, time=58.78 memory used=3745.0MB, alloc=468.3MB, time=60.56 memory used=3870.3MB, alloc=468.3MB, time=62.46 memory used=3976.5MB, alloc=468.3MB, time=65.09 memory used=4087.5MB, alloc=492.3MB, time=67.66 memory used=4221.3MB, alloc=492.3MB, time=69.95 memory used=4317.6MB, alloc=492.3MB, time=73.15 memory used=4391.6MB, alloc=492.3MB, time=75.09 memory used=4458.9MB, alloc=492.3MB, time=76.89 memory used=4531.6MB, alloc=492.3MB, time=78.92 memory used=4596.9MB, alloc=492.3MB, time=80.61 memory used=4680.5MB, alloc=492.3MB, time=82.18 memory used=4796.4MB, alloc=492.3MB, time=83.33 memory used=4910.0MB, alloc=492.3MB, time=84.85 memory used=5018.6MB, alloc=492.3MB, time=85.76 memory used=5096.1MB, alloc=492.3MB, time=86.40 memory used=5209.1MB, alloc=492.3MB, time=90.48 memory used=5308.0MB, alloc=492.3MB, time=92.14 memory used=5367.9MB, alloc=492.3MB, time=93.53 memory used=5483.3MB, alloc=516.3MB, time=95.11 memory used=5565.6MB, alloc=516.3MB, time=96.85 memory used=5679.4MB, alloc=516.3MB, time=98.06 memory used=5741.6MB, alloc=540.3MB, time=101.18 memory used=5900.1MB, alloc=540.3MB, time=106.65 memory used=5999.3MB, alloc=540.3MB, time=107.47 memory used=6130.7MB, alloc=540.3MB, time=108.28 memory used=6229.6MB, alloc=540.3MB, time=108.98 memory used=6320.6MB, alloc=540.3MB, time=109.64 memory used=6422.7MB, alloc=540.3MB, time=110.32 memory used=6538.2MB, alloc=540.3MB, time=111.02 memory used=6669.6MB, alloc=540.3MB, time=111.72 memory used=6905.5MB, alloc=540.3MB, time=112.85 memory used=7131.0MB, alloc=540.3MB, time=116.38 memory used=7406.2MB, alloc=540.3MB, time=121.50 memory used=7688.2MB, alloc=540.3MB, time=130.84 memory used=7792.6MB, alloc=540.3MB, time=131.68 memory used=7887.2MB, alloc=540.3MB, time=132.44 memory used=8008.1MB, alloc=540.3MB, time=134.43 memory used=8285.8MB, alloc=564.3MB, time=138.76 memory used=8413.1MB, alloc=564.3MB, time=140.58 memory used=8522.3MB, alloc=564.3MB, time=141.41 memory used=8658.5MB, alloc=564.3MB, time=142.58 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428275772 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 2 2 3 3 F := [5 x - 13 y - 10 x y, 13 x y + 3 x y - 19 x z , 4 x y - 10 z + 7 y] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 4 2 2 2 3 G := [-14 x y - 19 z - 17 y z , -8 x z + 5 x y - 10 x y z, 2 2 -2 x y z + 20 x y z - 7 y z] > Problem := [F,G]; Problem := [ 3 3 2 2 2 2 3 3 [5 x - 13 y - 10 x y, 13 x y + 3 x y - 19 x z , 4 x y - 10 z + 7 y], 3 4 2 2 2 3 [-14 x y - 19 z - 17 y z , -8 x z + 5 x y - 10 x y z, 2 2 -2 x y z + 20 x y z - 7 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.5MB, alloc=32.3MB, time=0.86 memory used=47.7MB, alloc=32.3MB, time=1.41 memory used=67.2MB, alloc=56.3MB, time=1.94 memory used=106.6MB, alloc=60.3MB, time=2.99 memory used=145.5MB, alloc=84.3MB, time=3.98 memory used=208.7MB, alloc=92.3MB, time=5.59 memory used=266.1MB, alloc=92.3MB, time=6.51 memory used=329.9MB, alloc=92.3MB, time=8.12 memory used=392.0MB, alloc=116.3MB, time=9.74 memory used=474.3MB, alloc=116.3MB, time=11.90 memory used=533.6MB, alloc=116.3MB, time=12.59 memory used=575.8MB, alloc=116.3MB, time=12.91 memory used=638.7MB, alloc=116.3MB, time=13.76 memory used=707.3MB, alloc=116.3MB, time=14.82 memory used=782.0MB, alloc=372.3MB, time=16.66 memory used=850.2MB, alloc=396.3MB, time=17.76 memory used=950.8MB, alloc=396.3MB, time=19.74 memory used=1060.0MB, alloc=396.3MB, time=22.48 memory used=1150.1MB, alloc=396.3MB, time=24.04 memory used=1249.4MB, alloc=396.3MB, time=25.64 memory used=1308.2MB, alloc=420.3MB, time=26.04 memory used=1403.5MB, alloc=420.3MB, time=30.02 memory used=1476.8MB, alloc=420.3MB, time=30.44 memory used=1545.5MB, alloc=420.3MB, time=30.81 memory used=1625.5MB, alloc=420.3MB, time=31.61 memory used=1698.2MB, alloc=420.3MB, time=32.11 memory used=1776.8MB, alloc=420.3MB, time=33.01 memory used=1838.7MB, alloc=420.3MB, time=33.34 memory used=1908.4MB, alloc=420.3MB, time=33.65 memory used=1957.9MB, alloc=420.3MB, time=33.91 memory used=2029.4MB, alloc=420.3MB, time=34.30 memory used=2092.9MB, alloc=420.3MB, time=34.62 memory used=2175.8MB, alloc=420.3MB, time=38.38 memory used=2235.7MB, alloc=420.3MB, time=38.72 memory used=2301.0MB, alloc=420.3MB, time=39.04 memory used=2367.3MB, alloc=420.3MB, time=39.33 memory used=2415.3MB, alloc=420.3MB, time=39.58 memory used=2469.0MB, alloc=420.3MB, time=39.84 memory used=2529.3MB, alloc=420.3MB, time=40.10 memory used=2597.0MB, alloc=420.3MB, time=40.37 memory used=2673.8MB, alloc=420.3MB, time=40.65 memory used=2858.0MB, alloc=420.3MB, time=43.65 memory used=2989.5MB, alloc=444.3MB, time=46.85 memory used=3113.8MB, alloc=444.3MB, time=50.02 memory used=3237.7MB, alloc=444.3MB, time=53.18 memory used=3375.1MB, alloc=468.3MB, time=56.31 memory used=3517.3MB, alloc=468.3MB, time=59.96 memory used=3626.4MB, alloc=468.3MB, time=62.75 memory used=3724.2MB, alloc=468.3MB, time=65.22 memory used=3834.2MB, alloc=492.3MB, time=68.31 memory used=3945.1MB, alloc=492.3MB, time=71.37 memory used=4052.2MB, alloc=492.3MB, time=74.39 memory used=4150.3MB, alloc=492.3MB, time=77.15 memory used=4246.4MB, alloc=492.3MB, time=80.39 memory used=4321.5MB, alloc=492.3MB, time=82.40 memory used=4433.2MB, alloc=492.3MB, time=86.03 memory used=4556.5MB, alloc=492.3MB, time=91.58 memory used=4634.6MB, alloc=516.3MB, time=93.76 memory used=4699.4MB, alloc=516.3MB, time=95.93 memory used=4765.2MB, alloc=516.3MB, time=98.03 memory used=4905.4MB, alloc=516.3MB, time=99.73 memory used=5010.7MB, alloc=516.3MB, time=100.63 memory used=5135.0MB, alloc=516.3MB, time=101.89 memory used=5251.7MB, alloc=516.3MB, time=103.37 memory used=5371.9MB, alloc=516.3MB, time=104.62 memory used=5483.8MB, alloc=516.3MB, time=105.65 memory used=5598.0MB, alloc=516.3MB, time=106.72 memory used=5697.0MB, alloc=516.3MB, time=107.46 memory used=5780.9MB, alloc=516.3MB, time=108.09 memory used=5901.4MB, alloc=516.3MB, time=113.76 memory used=5962.5MB, alloc=516.3MB, time=115.62 memory used=6014.5MB, alloc=516.3MB, time=117.05 memory used=6084.4MB, alloc=516.3MB, time=118.58 memory used=6200.5MB, alloc=516.3MB, time=120.29 memory used=6305.8MB, alloc=516.3MB, time=121.22 memory used=6416.0MB, alloc=516.3MB, time=122.18 memory used=6530.5MB, alloc=516.3MB, time=123.40 memory used=6639.9MB, alloc=516.3MB, time=124.44 memory used=6767.9MB, alloc=516.3MB, time=128.47 memory used=6878.8MB, alloc=540.3MB, time=129.77 memory used=6996.5MB, alloc=540.3MB, time=130.68 memory used=7108.1MB, alloc=540.3MB, time=131.54 memory used=7190.1MB, alloc=540.3MB, time=132.37 memory used=7281.4MB, alloc=540.3MB, time=133.19 memory used=7382.9MB, alloc=540.3MB, time=134.01 memory used=7495.2MB, alloc=540.3MB, time=134.84 memory used=7618.7MB, alloc=540.3MB, time=135.69 memory used=7753.6MB, alloc=540.3MB, time=136.54 memory used=7843.8MB, alloc=540.3MB, time=137.26 memory used=7918.9MB, alloc=564.3MB, time=137.95 memory used=8007.3MB, alloc=564.3MB, time=138.66 memory used=8100.3MB, alloc=564.3MB, time=139.37 memory used=8199.6MB, alloc=564.3MB, time=140.12 memory used=8305.1MB, alloc=564.3MB, time=140.86 memory used=8416.2MB, alloc=564.3MB, time=141.61 memory used=8532.4MB, alloc=564.3MB, time=142.38 memory used=8653.6MB, alloc=564.3MB, time=143.14 memory used=8782.2MB, alloc=564.3MB, time=143.92 memory used=8918.7MB, alloc=564.3MB, time=144.68 memory used=9065.0MB, alloc=564.3MB, time=145.45 memory used=9221.8MB, alloc=564.3MB, time=146.24 memory used=9416.1MB, alloc=564.3MB, time=147.27 memory used=9635.7MB, alloc=564.3MB, time=151.02 memory used=9788.8MB, alloc=564.3MB, time=152.06 memory used=9887.5MB, alloc=564.3MB, time=152.90 memory used=9992.6MB, alloc=564.3MB, time=153.74 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428276072 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; F := [ 2 2 3 3 2 3 3 -9 y z - 13 x - 2 x y z, 2 y z + 4 y z + 6 z , 6 x y z - 12 y + 19 y] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; G := [ 3 2 3 2 2 2 3 2 11 x y + x y z + 5 x z , 6 x z - 3 x z + 7 z , -4 x - 16 x z - 19 y z ] > Problem := [F,G]; Problem := [[ 2 2 3 3 2 3 3 -9 y z - 13 x - 2 x y z, 2 y z + 4 y z + 6 z , 6 x y z - 12 y + 19 y] , [ 3 2 3 2 2 2 3 2 11 x y + x y z + 5 x z , 6 x z - 3 x z + 7 z , -4 x - 16 x z - 19 y z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.9MB, alloc=32.3MB, time=0.89 memory used=47.3MB, alloc=32.3MB, time=1.40 memory used=66.4MB, alloc=56.3MB, time=1.93 memory used=106.8MB, alloc=60.3MB, time=2.95 memory used=144.4MB, alloc=84.3MB, time=3.93 memory used=208.6MB, alloc=92.3MB, time=5.56 memory used=273.5MB, alloc=116.3MB, time=7.13 memory used=347.1MB, alloc=116.3MB, time=9.01 memory used=409.2MB, alloc=372.3MB, time=10.46 memory used=497.0MB, alloc=396.3MB, time=12.62 memory used=609.9MB, alloc=420.3MB, time=15.25 memory used=752.3MB, alloc=420.3MB, time=18.44 memory used=889.0MB, alloc=444.3MB, time=21.51 memory used=1010.5MB, alloc=468.3MB, time=24.69 memory used=1126.2MB, alloc=468.3MB, time=27.45 memory used=1285.0MB, alloc=468.3MB, time=30.11 memory used=1390.0MB, alloc=468.3MB, time=32.54 memory used=1506.9MB, alloc=468.3MB, time=35.01 memory used=1603.9MB, alloc=492.3MB, time=37.32 memory used=1704.8MB, alloc=492.3MB, time=39.85 memory used=1797.7MB, alloc=492.3MB, time=42.15 memory used=1905.8MB, alloc=492.3MB, time=44.38 memory used=1984.2MB, alloc=492.3MB, time=46.29 memory used=2059.2MB, alloc=492.3MB, time=48.25 memory used=2134.1MB, alloc=516.3MB, time=50.25 memory used=2227.7MB, alloc=516.3MB, time=53.54 memory used=2314.7MB, alloc=516.3MB, time=56.47 memory used=2377.4MB, alloc=516.3MB, time=58.22 memory used=2429.0MB, alloc=516.3MB, time=59.70 memory used=2491.4MB, alloc=516.3MB, time=62.00 memory used=2542.3MB, alloc=516.3MB, time=63.74 memory used=2583.7MB, alloc=516.3MB, time=65.22 memory used=2774.2MB, alloc=540.3MB, time=71.23 memory used=2984.5MB, alloc=564.3MB, time=76.69 memory used=3137.3MB, alloc=588.3MB, time=80.95 memory used=3328.9MB, alloc=612.3MB, time=86.34 memory used=3495.6MB, alloc=636.3MB, time=91.08 memory used=3658.0MB, alloc=636.3MB, time=96.13 memory used=3818.9MB, alloc=636.3MB, time=101.03 memory used=3960.4MB, alloc=660.3MB, time=105.04 memory used=4132.4MB, alloc=660.3MB, time=109.73 memory used=4257.0MB, alloc=660.3MB, time=113.13 memory used=4417.7MB, alloc=660.3MB, time=117.61 memory used=4640.8MB, alloc=660.3MB, time=121.28 memory used=4842.5MB, alloc=660.3MB, time=124.23 memory used=4939.0MB, alloc=660.3MB, time=127.41 memory used=5046.4MB, alloc=660.3MB, time=130.33 memory used=5180.6MB, alloc=660.3MB, time=134.83 memory used=5307.3MB, alloc=660.3MB, time=139.49 memory used=5381.3MB, alloc=660.3MB, time=142.50 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428276372 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; F := [ 2 2 4 3 2 3 2 2 -18 x z - 9 y - 18 y, 11 x - 4 x z + 4 y z, 8 x y + 10 x y - 3 y z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 4 2 2 G := [8 x z + 15 y - 6 z , -17 y z + 15 x y - 19 y z, 3 3 4 x y + 6 x z - 12 x y z] > Problem := [F,G]; Problem := [[ 2 2 4 3 2 3 2 2 -18 x z - 9 y - 18 y, 11 x - 4 x z + 4 y z, 8 x y + 10 x y - 3 y z] 2 2 4 2 2 , [8 x z + 15 y - 6 z , -17 y z + 15 x y - 19 y z, 3 3 4 x y + 6 x z - 12 x y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=25.7MB, alloc=32.3MB, time=0.86 memory used=45.7MB, alloc=56.3MB, time=1.39 memory used=85.8MB, alloc=60.3MB, time=2.43 memory used=129.0MB, alloc=92.3MB, time=3.50 memory used=193.2MB, alloc=92.3MB, time=5.18 memory used=256.4MB, alloc=116.3MB, time=6.83 memory used=331.9MB, alloc=372.3MB, time=8.65 memory used=419.5MB, alloc=396.3MB, time=10.89 memory used=532.7MB, alloc=396.3MB, time=13.71 memory used=639.9MB, alloc=420.3MB, time=16.59 memory used=770.5MB, alloc=444.3MB, time=20.11 memory used=902.9MB, alloc=468.3MB, time=23.28 memory used=1031.7MB, alloc=468.3MB, time=26.44 memory used=1132.1MB, alloc=492.3MB, time=29.23 memory used=1254.0MB, alloc=492.3MB, time=32.97 memory used=1350.2MB, alloc=492.3MB, time=35.38 memory used=1449.2MB, alloc=492.3MB, time=38.07 memory used=1518.1MB, alloc=492.3MB, time=39.95 memory used=1600.7MB, alloc=492.3MB, time=42.40 memory used=1686.8MB, alloc=516.3MB, time=45.01 memory used=1743.1MB, alloc=516.3MB, time=46.91 memory used=1820.7MB, alloc=516.3MB, time=49.14 memory used=1886.9MB, alloc=516.3MB, time=51.17 memory used=1956.7MB, alloc=516.3MB, time=53.44 memory used=2006.3MB, alloc=516.3MB, time=55.22 memory used=2061.3MB, alloc=516.3MB, time=57.16 memory used=2253.3MB, alloc=540.3MB, time=62.43 memory used=2471.6MB, alloc=564.3MB, time=68.66 memory used=2682.1MB, alloc=588.3MB, time=75.34 memory used=2856.8MB, alloc=612.3MB, time=79.99 memory used=3007.6MB, alloc=636.3MB, time=84.76 memory used=3155.1MB, alloc=636.3MB, time=88.94 memory used=3308.2MB, alloc=636.3MB, time=93.96 memory used=3450.0MB, alloc=660.3MB, time=98.49 memory used=3564.7MB, alloc=660.3MB, time=102.63 memory used=3685.3MB, alloc=660.3MB, time=106.97 memory used=3805.0MB, alloc=660.3MB, time=111.43 memory used=3916.4MB, alloc=660.3MB, time=115.65 memory used=4004.0MB, alloc=660.3MB, time=118.86 memory used=4338.0MB, alloc=684.3MB, time=129.29 memory used=4684.4MB, alloc=708.3MB, time=141.17 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428276672 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 3 4 2 2 2 F := [20 x + 15 x z + 17 y z , 14 y + 13 y z + 4 x z, 2 2 3 2 x y - 3 y z - 3 y z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 2 2 G := [17 x y z + 6 y z + 12 z , 8 x y z - 19 x z + 14 x y, 3 4 -11 x y + z + y z] > Problem := [F,G]; 4 2 2 3 4 2 2 2 Problem := [[20 x + 15 x z + 17 y z , 14 y + 13 y z + 4 x z, 2 2 3 2 2 2 3 x y - 3 y z - 3 y z], [17 x y z + 6 y z + 12 z , 2 2 2 2 3 4 8 x y z - 19 x z + 14 x y, -11 x y + z + y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=25.4MB, alloc=32.3MB, time=0.84 memory used=45.2MB, alloc=32.3MB, time=1.37 memory used=63.9MB, alloc=56.3MB, time=1.89 memory used=103.3MB, alloc=60.3MB, time=2.92 memory used=140.4MB, alloc=84.3MB, time=3.91 memory used=204.8MB, alloc=92.3MB, time=5.52 memory used=265.6MB, alloc=116.3MB, time=7.11 memory used=336.6MB, alloc=116.3MB, time=8.98 memory used=417.8MB, alloc=372.3MB, time=11.17 memory used=500.3MB, alloc=396.3MB, time=13.42 memory used=608.5MB, alloc=396.3MB, time=16.30 memory used=710.5MB, alloc=420.3MB, time=19.23 memory used=841.5MB, alloc=420.3MB, time=22.82 memory used=943.6MB, alloc=444.3MB, time=25.51 memory used=1050.1MB, alloc=444.3MB, time=27.17 memory used=1144.4MB, alloc=444.3MB, time=28.12 memory used=1243.5MB, alloc=444.3MB, time=36.69 memory used=1325.4MB, alloc=444.3MB, time=37.24 memory used=1415.8MB, alloc=444.3MB, time=38.01 memory used=1490.7MB, alloc=444.3MB, time=38.67 memory used=1586.1MB, alloc=444.3MB, time=39.25 memory used=1678.0MB, alloc=444.3MB, time=43.09 memory used=1762.7MB, alloc=444.3MB, time=43.83 memory used=1851.7MB, alloc=444.3MB, time=44.46 memory used=1939.1MB, alloc=444.3MB, time=45.12 memory used=2024.5MB, alloc=444.3MB, time=45.51 memory used=2177.6MB, alloc=444.3MB, time=48.46 memory used=2312.5MB, alloc=444.3MB, time=56.44 memory used=2399.6MB, alloc=444.3MB, time=58.94 memory used=2480.9MB, alloc=444.3MB, time=59.79 memory used=2600.1MB, alloc=444.3MB, time=64.53 memory used=2718.1MB, alloc=444.3MB, time=66.37 memory used=2843.1MB, alloc=444.3MB, time=68.82 memory used=2942.7MB, alloc=444.3MB, time=74.33 memory used=3007.8MB, alloc=468.3MB, time=74.76 memory used=3091.2MB, alloc=468.3MB, time=75.50 memory used=3202.8MB, alloc=468.3MB, time=76.28 memory used=3310.2MB, alloc=468.3MB, time=76.74 memory used=3471.4MB, alloc=468.3MB, time=80.49 memory used=3608.8MB, alloc=492.3MB, time=84.64 memory used=3761.5MB, alloc=492.3MB, time=88.90 memory used=3934.4MB, alloc=492.3MB, time=93.66 memory used=4098.2MB, alloc=492.3MB, time=99.30 memory used=4259.8MB, alloc=516.3MB, time=104.72 memory used=4409.1MB, alloc=516.3MB, time=107.76 memory used=4525.8MB, alloc=516.3MB, time=110.92 memory used=4636.3MB, alloc=516.3MB, time=113.71 memory used=4743.8MB, alloc=516.3MB, time=116.62 memory used=4857.1MB, alloc=540.3MB, time=119.98 memory used=4970.4MB, alloc=540.3MB, time=123.53 memory used=5069.2MB, alloc=540.3MB, time=126.85 memory used=5175.9MB, alloc=540.3MB, time=129.24 memory used=5433.3MB, alloc=540.3MB, time=173.30 memory used=5587.9MB, alloc=540.3MB, time=179.37 memory used=5741.7MB, alloc=540.3MB, time=192.42 memory used=5856.4MB, alloc=540.3MB, time=193.42 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428276972 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 4 2 2 2 3 F := [5 x - y + 4 y z , -8 x y z + 5 x y - 6 y , -4 x - 5 y + 8 z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 4 2 G := [11 x y - 15 y - 11 y z, 10 x + 11 y z + 5 y z, 2 4 2 -13 x y z + 12 z - 7 x y ] > Problem := [F,G]; 4 4 2 2 2 3 Problem := [[5 x - y + 4 y z , -8 x y z + 5 x y - 6 y , -4 x - 5 y + 8 z], 3 3 2 4 2 [11 x y - 15 y - 11 y z, 10 x + 11 y z + 5 y z, 2 4 2 -13 x y z + 12 z - 7 x y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.6MB, alloc=32.3MB, time=0.87 memory used=46.4MB, alloc=32.3MB, time=1.37 memory used=65.9MB, alloc=56.3MB, time=1.89 memory used=106.2MB, alloc=68.3MB, time=3.00 memory used=146.4MB, alloc=92.3MB, time=4.04 memory used=212.3MB, alloc=92.3MB, time=5.67 memory used=277.0MB, alloc=116.3MB, time=7.25 memory used=341.9MB, alloc=116.3MB, time=8.91 memory used=411.5MB, alloc=372.3MB, time=10.67 memory used=494.9MB, alloc=396.3MB, time=12.76 memory used=604.0MB, alloc=420.3MB, time=15.67 memory used=732.7MB, alloc=444.3MB, time=18.86 memory used=845.4MB, alloc=444.3MB, time=21.60 memory used=952.1MB, alloc=468.3MB, time=23.93 memory used=1076.0MB, alloc=468.3MB, time=27.24 memory used=1192.8MB, alloc=468.3MB, time=29.93 memory used=1308.8MB, alloc=492.3MB, time=32.49 memory used=1408.3MB, alloc=492.3MB, time=34.85 memory used=1514.6MB, alloc=492.3MB, time=37.47 memory used=1596.7MB, alloc=492.3MB, time=39.59 memory used=1677.4MB, alloc=492.3MB, time=42.10 memory used=1749.6MB, alloc=492.3MB, time=44.01 memory used=1823.9MB, alloc=516.3MB, time=46.06 memory used=1886.1MB, alloc=516.3MB, time=48.02 memory used=1953.8MB, alloc=516.3MB, time=49.99 memory used=2020.7MB, alloc=516.3MB, time=52.00 memory used=2072.9MB, alloc=516.3MB, time=53.85 memory used=2130.7MB, alloc=516.3MB, time=55.72 memory used=2187.1MB, alloc=516.3MB, time=57.80 memory used=2236.3MB, alloc=516.3MB, time=59.40 memory used=2280.3MB, alloc=516.3MB, time=60.88 memory used=2487.1MB, alloc=540.3MB, time=66.69 memory used=2671.1MB, alloc=564.3MB, time=71.64 memory used=2852.1MB, alloc=588.3MB, time=76.83 memory used=3013.9MB, alloc=612.3MB, time=81.74 memory used=3153.3MB, alloc=612.3MB, time=86.14 memory used=3308.6MB, alloc=636.3MB, time=90.83 memory used=3492.3MB, alloc=636.3MB, time=95.44 memory used=3651.4MB, alloc=636.3MB, time=99.78 memory used=3783.0MB, alloc=636.3MB, time=104.01 memory used=3899.3MB, alloc=660.3MB, time=107.36 memory used=4023.9MB, alloc=660.3MB, time=111.47 memory used=4146.6MB, alloc=660.3MB, time=115.29 memory used=4272.0MB, alloc=660.3MB, time=118.86 memory used=4365.5MB, alloc=660.3MB, time=122.27 memory used=4520.0MB, alloc=660.3MB, time=126.26 memory used=4881.5MB, alloc=684.3MB, time=135.28 memory used=5249.9MB, alloc=708.3MB, time=145.49 memory used=5586.8MB, alloc=732.3MB, time=151.83 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428277272 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 3 3 3 3 F := [5 x y - 16 x y - 7 z , x y z - 15 y z + 19 z , -9 x z + 9 y + 2 y] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; G := 2 2 2 4 4 3 2 2 [20 y z + 8 x y - 2 y z, 11 y - 9 z + 4 y, -2 x z - 14 x y z - 8 z ] > Problem := [F,G]; Problem := [ 2 2 2 3 2 3 3 3 3 [5 x y - 16 x y - 7 z , x y z - 15 y z + 19 z , -9 x z + 9 y + 2 y], 2 2 2 4 4 3 2 2 [20 y z + 8 x y - 2 y z, 11 y - 9 z + 4 y, -2 x z - 14 x y z - 8 z ] ] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.31 memory used=24.8MB, alloc=32.3MB, time=0.81 memory used=43.6MB, alloc=56.3MB, time=1.31 memory used=93.8MB, alloc=63.4MB, time=4.13 memory used=123.1MB, alloc=63.4MB, time=4.26 memory used=146.9MB, alloc=63.4MB, time=4.37 memory used=190.3MB, alloc=63.4MB, time=5.13 memory used=225.3MB, alloc=63.4MB, time=5.97 memory used=268.1MB, alloc=95.4MB, time=7.06 memory used=347.3MB, alloc=95.4MB, time=8.61 memory used=432.1MB, alloc=95.4MB, time=9.78 memory used=512.8MB, alloc=95.4MB, time=11.03 memory used=583.4MB, alloc=95.4MB, time=12.58 memory used=660.9MB, alloc=119.4MB, time=13.77 memory used=738.1MB, alloc=119.4MB, time=17.32 memory used=806.6MB, alloc=119.4MB, time=18.87 memory used=850.2MB, alloc=119.4MB, time=19.09 memory used=891.0MB, alloc=119.4MB, time=19.30 memory used=942.2MB, alloc=119.4MB, time=19.52 memory used=980.8MB, alloc=119.4MB, time=19.71 memory used=1014.9MB, alloc=119.4MB, time=19.87 memory used=1055.2MB, alloc=119.4MB, time=20.04 memory used=1130.0MB, alloc=119.4MB, time=21.28 memory used=1191.7MB, alloc=375.4MB, time=22.84 memory used=1264.7MB, alloc=375.4MB, time=24.10 memory used=1328.1MB, alloc=375.4MB, time=24.97 memory used=1388.0MB, alloc=375.4MB, time=26.97 memory used=1425.7MB, alloc=375.4MB, time=27.20 memory used=1521.0MB, alloc=399.4MB, time=29.38 memory used=1603.7MB, alloc=399.4MB, time=31.48 memory used=1712.7MB, alloc=399.4MB, time=33.77 memory used=1823.3MB, alloc=423.4MB, time=36.22 memory used=1926.5MB, alloc=423.4MB, time=38.78 memory used=2032.0MB, alloc=447.4MB, time=41.40 memory used=2162.1MB, alloc=447.4MB, time=43.65 memory used=2261.6MB, alloc=447.4MB, time=45.71 memory used=2404.4MB, alloc=447.4MB, time=58.40 memory used=2489.0MB, alloc=447.4MB, time=59.12 memory used=2567.3MB, alloc=447.4MB, time=59.57 memory used=2621.2MB, alloc=447.4MB, time=59.97 memory used=2684.0MB, alloc=447.4MB, time=60.40 memory used=2756.7MB, alloc=447.4MB, time=60.82 memory used=2839.8MB, alloc=447.4MB, time=61.23 memory used=2896.5MB, alloc=447.4MB, time=61.58 memory used=2948.5MB, alloc=447.4MB, time=61.91 memory used=3004.6MB, alloc=447.4MB, time=62.24 memory used=3066.8MB, alloc=447.4MB, time=62.57 memory used=3167.4MB, alloc=471.4MB, time=71.75 memory used=3284.8MB, alloc=471.4MB, time=72.45 memory used=3356.3MB, alloc=471.4MB, time=72.98 memory used=3420.3MB, alloc=471.4MB, time=73.46 memory used=3489.8MB, alloc=471.4MB, time=73.97 memory used=3563.7MB, alloc=471.4MB, time=74.47 memory used=3641.5MB, alloc=471.4MB, time=74.99 memory used=3727.9MB, alloc=471.4MB, time=75.51 memory used=3818.2MB, alloc=471.4MB, time=76.05 memory used=3912.0MB, alloc=471.4MB, time=76.58 memory used=4009.7MB, alloc=471.4MB, time=77.13 memory used=4116.6MB, alloc=471.4MB, time=77.69 memory used=4192.2MB, alloc=495.4MB, time=78.18 memory used=4258.3MB, alloc=495.4MB, time=78.64 memory used=4323.2MB, alloc=495.4MB, time=79.10 memory used=4390.6MB, alloc=495.4MB, time=79.56 memory used=4459.1MB, alloc=495.4MB, time=80.03 memory used=4529.0MB, alloc=495.4MB, time=80.49 memory used=4606.0MB, alloc=495.4MB, time=80.97 memory used=4684.4MB, alloc=495.4MB, time=81.44 memory used=4763.7MB, alloc=495.4MB, time=81.92 memory used=4844.0MB, alloc=495.4MB, time=82.41 memory used=4925.2MB, alloc=495.4MB, time=82.90 memory used=5007.8MB, alloc=495.4MB, time=83.38 memory used=5097.6MB, alloc=495.4MB, time=83.88 memory used=5188.7MB, alloc=495.4MB, time=84.37 memory used=5280.5MB, alloc=495.4MB, time=84.87 memory used=5373.4MB, alloc=495.4MB, time=85.39 memory used=5474.3MB, alloc=495.4MB, time=85.89 memory used=5575.9MB, alloc=495.4MB, time=86.41 memory used=5678.0MB, alloc=495.4MB, time=86.92 memory used=5780.9MB, alloc=495.4MB, time=87.45 memory used=5891.8MB, alloc=495.4MB, time=87.95 memory used=6003.0MB, alloc=495.4MB, time=88.46 memory used=6114.6MB, alloc=495.4MB, time=88.98 memory used=6234.1MB, alloc=495.4MB, time=89.52 memory used=6353.7MB, alloc=495.4MB, time=90.07 memory used=6467.7MB, alloc=495.4MB, time=90.58 memory used=6577.3MB, alloc=495.4MB, time=91.08 memory used=6657.2MB, alloc=495.4MB, time=91.48 memory used=6717.2MB, alloc=495.4MB, time=91.87 memory used=6778.4MB, alloc=495.4MB, time=92.26 memory used=6840.0MB, alloc=495.4MB, time=92.64 memory used=6901.4MB, alloc=495.4MB, time=93.02 memory used=6962.6MB, alloc=495.4MB, time=93.39 memory used=7024.4MB, alloc=495.4MB, time=93.77 memory used=7091.7MB, alloc=495.4MB, time=94.15 memory used=7159.4MB, alloc=495.4MB, time=94.52 memory used=7226.6MB, alloc=495.4MB, time=94.89 memory used=7293.4MB, alloc=495.4MB, time=95.28 memory used=7360.7MB, alloc=495.4MB, time=95.69 memory used=7432.9MB, alloc=495.4MB, time=96.07 memory used=7505.1MB, alloc=495.4MB, time=96.45 memory used=7576.9MB, alloc=495.4MB, time=96.85 memory used=7654.7MB, alloc=495.4MB, time=97.25 memory used=7731.5MB, alloc=495.4MB, time=97.65 memory used=7807.4MB, alloc=495.4MB, time=98.05 memory used=7888.8MB, alloc=495.4MB, time=98.44 memory used=7968.8MB, alloc=495.4MB, time=98.85 memory used=8048.4MB, alloc=495.4MB, time=99.24 memory used=8131.0MB, alloc=495.4MB, time=99.64 memory used=8218.6MB, alloc=495.4MB, time=100.04 memory used=8304.1MB, alloc=495.4MB, time=100.44 memory used=8392.9MB, alloc=495.4MB, time=100.84 memory used=8484.5MB, alloc=495.4MB, time=101.26 memory used=8578.0MB, alloc=495.4MB, time=101.66 memory used=8672.7MB, alloc=495.4MB, time=102.07 memory used=8772.1MB, alloc=495.4MB, time=102.49 memory used=8874.2MB, alloc=495.4MB, time=102.90 memory used=8980.4MB, alloc=495.4MB, time=103.32 memory used=9091.4MB, alloc=495.4MB, time=103.74 memory used=9211.9MB, alloc=495.4MB, time=104.15 memory used=9365.9MB, alloc=495.4MB, time=113.43 memory used=9482.6MB, alloc=495.4MB, time=114.15 memory used=9561.0MB, alloc=495.4MB, time=114.73 memory used=9647.1MB, alloc=495.4MB, time=115.30 memory used=9741.7MB, alloc=495.4MB, time=115.90 memory used=9842.1MB, alloc=495.4MB, time=116.48 memory used=9948.4MB, alloc=495.4MB, time=117.10 memory used=10065.5MB, alloc=495.4MB, time=117.72 memory used=10188.4MB, alloc=495.4MB, time=118.34 memory used=10314.0MB, alloc=495.4MB, time=118.95 memory used=10385.0MB, alloc=495.4MB, time=119.43 memory used=10451.1MB, alloc=495.4MB, time=119.90 memory used=10518.1MB, alloc=495.4MB, time=120.37 memory used=10586.1MB, alloc=495.4MB, time=120.83 memory used=10655.4MB, alloc=495.4MB, time=121.32 memory used=10732.4MB, alloc=495.4MB, time=121.81 memory used=10810.4MB, alloc=495.4MB, time=122.30 memory used=10889.4MB, alloc=495.4MB, time=122.79 memory used=10969.3MB, alloc=495.4MB, time=123.28 memory used=11050.1MB, alloc=495.4MB, time=123.75 memory used=11132.1MB, alloc=495.4MB, time=124.26 memory used=11222.0MB, alloc=495.4MB, time=124.76 memory used=11312.9MB, alloc=495.4MB, time=125.25 memory used=11404.5MB, alloc=495.4MB, time=125.76 memory used=11497.1MB, alloc=495.4MB, time=126.27 memory used=11597.8MB, alloc=495.4MB, time=126.77 memory used=11699.2MB, alloc=495.4MB, time=127.27 memory used=11801.2MB, alloc=495.4MB, time=127.78 memory used=11903.9MB, alloc=495.4MB, time=128.30 memory used=12014.7MB, alloc=495.4MB, time=128.82 memory used=12125.8MB, alloc=495.4MB, time=129.33 memory used=12237.4MB, alloc=495.4MB, time=129.85 memory used=12356.9MB, alloc=495.4MB, time=130.40 memory used=12476.5MB, alloc=495.4MB, time=130.93 memory used=12593.8MB, alloc=495.4MB, time=131.45 memory used=12707.4MB, alloc=495.4MB, time=131.97 memory used=12794.2MB, alloc=495.4MB, time=132.40 memory used=12857.5MB, alloc=495.4MB, time=132.77 memory used=12917.6MB, alloc=495.4MB, time=133.16 memory used=12979.3MB, alloc=495.4MB, time=133.55 memory used=13040.7MB, alloc=495.4MB, time=133.94 memory used=13102.0MB, alloc=495.4MB, time=134.35 memory used=13163.7MB, alloc=495.4MB, time=134.74 memory used=13231.3MB, alloc=495.4MB, time=135.14 memory used=13299.0MB, alloc=495.4MB, time=135.53 memory used=13366.4MB, alloc=495.4MB, time=135.91 memory used=13433.3MB, alloc=495.4MB, time=136.34 memory used=13500.4MB, alloc=495.4MB, time=136.74 memory used=13573.0MB, alloc=495.4MB, time=137.14 memory used=13645.4MB, alloc=495.4MB, time=137.52 memory used=13717.2MB, alloc=495.4MB, time=137.91 memory used=13789.1MB, alloc=495.4MB, time=138.30 memory used=13865.3MB, alloc=495.4MB, time=138.69 memory used=13941.4MB, alloc=495.4MB, time=139.10 memory used=14017.4MB, alloc=495.4MB, time=139.49 memory used=14096.9MB, alloc=495.4MB, time=139.88 memory used=14176.1MB, alloc=495.4MB, time=140.29 memory used=14260.0MB, alloc=495.4MB, time=140.69 memory used=14342.9MB, alloc=495.4MB, time=141.09 memory used=14428.5MB, alloc=495.4MB, time=141.51 memory used=14518.4MB, alloc=495.4MB, time=141.93 memory used=14611.0MB, alloc=495.4MB, time=142.35 memory used=14705.7MB, alloc=495.4MB, time=142.76 memory used=14801.5MB, alloc=495.4MB, time=143.17 memory used=14898.5MB, alloc=495.4MB, time=143.58 memory used=15001.6MB, alloc=495.4MB, time=144.00 memory used=15106.4MB, alloc=495.4MB, time=144.41 memory used=15216.3MB, alloc=495.4MB, time=144.85 memory used=15334.0MB, alloc=495.4MB, time=145.26 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428277572 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 3 3 2 3 3 3 F := [15 y + 4 z + 1, -9 x z - 15 x - 12 y z, -x y - 3 x z - 8 x z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 3 2 2 2 2 G := [15 x + 20, 20 x y + 8 y - 9 y z, -7 y z + 5 z + 8] > Problem := [F,G]; Problem := [ 4 2 3 3 2 3 3 3 [15 y + 4 z + 1, -9 x z - 15 x - 12 y z, -x y - 3 x z - 8 x z ], 3 3 3 2 2 2 2 [15 x + 20, 20 x y + 8 y - 9 y z, -7 y z + 5 z + 8]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.2MB, alloc=32.3MB, time=0.85 memory used=46.2MB, alloc=56.3MB, time=1.33 memory used=101.0MB, alloc=60.3MB, time=3.05 memory used=166.3MB, alloc=62.0MB, time=5.68 memory used=191.1MB, alloc=62.0MB, time=5.79 memory used=217.5MB, alloc=62.0MB, time=5.88 memory used=279.8MB, alloc=62.0MB, time=6.72 memory used=339.9MB, alloc=62.0MB, time=7.43 memory used=381.0MB, alloc=62.0MB, time=8.39 memory used=424.2MB, alloc=70.0MB, time=9.42 memory used=462.4MB, alloc=94.0MB, time=10.41 memory used=517.5MB, alloc=94.0MB, time=11.35 memory used=583.9MB, alloc=94.0MB, time=12.61 memory used=642.1MB, alloc=94.0MB, time=24.86 memory used=689.4MB, alloc=94.0MB, time=25.17 memory used=719.5MB, alloc=94.0MB, time=25.34 memory used=758.3MB, alloc=94.0MB, time=25.51 memory used=785.2MB, alloc=94.0MB, time=25.63 memory used=812.8MB, alloc=94.0MB, time=25.75 memory used=851.8MB, alloc=94.0MB, time=26.08 memory used=891.1MB, alloc=94.0MB, time=26.37 memory used=928.4MB, alloc=94.0MB, time=26.70 memory used=964.1MB, alloc=94.0MB, time=27.05 memory used=1008.1MB, alloc=94.0MB, time=29.33 memory used=1046.7MB, alloc=94.0MB, time=29.55 memory used=1084.5MB, alloc=94.0MB, time=29.87 memory used=1122.9MB, alloc=94.0MB, time=30.27 memory used=1158.5MB, alloc=94.0MB, time=30.54 memory used=1251.5MB, alloc=94.0MB, time=31.91 memory used=1344.1MB, alloc=94.0MB, time=33.58 memory used=1420.1MB, alloc=94.0MB, time=34.52 memory used=1510.7MB, alloc=94.0MB, time=36.01 memory used=1583.7MB, alloc=118.0MB, time=36.74 memory used=1684.1MB, alloc=118.0MB, time=48.41 memory used=1734.3MB, alloc=118.0MB, time=49.89 memory used=1782.1MB, alloc=118.0MB, time=50.11 memory used=1822.5MB, alloc=118.0MB, time=50.28 memory used=1863.0MB, alloc=118.0MB, time=50.43 memory used=1962.9MB, alloc=118.0MB, time=51.92 memory used=2074.6MB, alloc=118.0MB, time=53.37 memory used=2140.4MB, alloc=374.0MB, time=54.84 memory used=2224.1MB, alloc=398.0MB, time=56.77 memory used=2329.3MB, alloc=422.0MB, time=59.40 memory used=2459.9MB, alloc=422.0MB, time=62.27 memory used=2604.7MB, alloc=446.0MB, time=64.87 memory used=2756.1MB, alloc=446.0MB, time=67.97 memory used=2877.5MB, alloc=470.0MB, time=71.17 memory used=2992.5MB, alloc=470.0MB, time=73.80 memory used=3098.0MB, alloc=494.0MB, time=76.45 memory used=3198.7MB, alloc=494.0MB, time=79.01 memory used=3293.6MB, alloc=494.0MB, time=81.57 memory used=3407.1MB, alloc=494.0MB, time=84.88 memory used=3519.2MB, alloc=494.0MB, time=88.00 memory used=3633.0MB, alloc=518.0MB, time=91.06 memory used=3770.6MB, alloc=518.0MB, time=92.84 memory used=3884.5MB, alloc=518.0MB, time=93.80 memory used=3979.9MB, alloc=518.0MB, time=94.49 memory used=4070.3MB, alloc=518.0MB, time=95.16 memory used=4184.3MB, alloc=518.0MB, time=95.83 memory used=4263.1MB, alloc=518.0MB, time=96.39 memory used=4338.5MB, alloc=518.0MB, time=96.94 memory used=4424.1MB, alloc=518.0MB, time=97.50 memory used=4522.0MB, alloc=518.0MB, time=98.08 memory used=4661.6MB, alloc=518.0MB, time=104.61 memory used=4755.3MB, alloc=518.0MB, time=105.32 memory used=4856.3MB, alloc=518.0MB, time=105.97 memory used=4933.4MB, alloc=518.0MB, time=106.52 memory used=5028.2MB, alloc=518.0MB, time=107.10 memory used=5146.3MB, alloc=518.0MB, time=107.71 memory used=5343.4MB, alloc=518.0MB, time=108.89 memory used=5453.5MB, alloc=518.0MB, time=110.74 memory used=5543.1MB, alloc=518.0MB, time=111.31 memory used=5686.1MB, alloc=518.0MB, time=113.51 memory used=5790.1MB, alloc=518.0MB, time=115.22 memory used=5909.4MB, alloc=518.0MB, time=117.02 memory used=6057.2MB, alloc=518.0MB, time=120.60 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428277872 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 3 2 4 2 F := [2 x z + 9 y - 10 x , -3 x y + 9 x y - 20, -18 y - 6 x z - 9 z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 4 3 4 3 2 G := [-13 x y - 15 x + 2, 19 x - 10 y z - 1, 6 z - 13 y - 2 y z] > Problem := [F,G]; Problem := [ 3 3 2 3 2 4 2 [2 x z + 9 y - 10 x , -3 x y + 9 x y - 20, -18 y - 6 x z - 9 z ], 3 4 3 4 3 2 [-13 x y - 15 x + 2, 19 x - 10 y z - 1, 6 z - 13 y - 2 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=25.2MB, alloc=32.3MB, time=0.79 memory used=45.1MB, alloc=56.3MB, time=1.30 memory used=88.0MB, alloc=60.3MB, time=2.09 memory used=145.8MB, alloc=62.4MB, time=4.41 memory used=172.3MB, alloc=62.4MB, time=4.53 memory used=202.5MB, alloc=62.4MB, time=4.66 memory used=223.2MB, alloc=62.4MB, time=4.76 memory used=244.0MB, alloc=62.4MB, time=4.85 memory used=267.5MB, alloc=62.4MB, time=4.96 memory used=293.9MB, alloc=62.4MB, time=5.06 memory used=323.3MB, alloc=62.4MB, time=5.17 memory used=354.4MB, alloc=62.4MB, time=5.28 memory used=371.8MB, alloc=62.4MB, time=5.36 memory used=390.1MB, alloc=62.4MB, time=5.44 memory used=409.0MB, alloc=62.4MB, time=5.51 memory used=429.1MB, alloc=62.4MB, time=5.59 memory used=449.7MB, alloc=62.4MB, time=5.67 memory used=471.3MB, alloc=62.4MB, time=5.75 memory used=494.4MB, alloc=62.4MB, time=5.83 memory used=519.8MB, alloc=62.4MB, time=5.92 memory used=547.9MB, alloc=62.4MB, time=6.01 memory used=597.9MB, alloc=62.4MB, time=6.74 memory used=630.8MB, alloc=62.4MB, time=7.42 memory used=676.2MB, alloc=70.4MB, time=8.55 memory used=723.8MB, alloc=70.4MB, time=9.78 memory used=771.2MB, alloc=70.4MB, time=10.70 memory used=815.4MB, alloc=94.4MB, time=11.69 memory used=882.5MB, alloc=94.4MB, time=13.31 memory used=936.1MB, alloc=94.4MB, time=14.79 memory used=966.3MB, alloc=94.4MB, time=14.96 memory used=995.3MB, alloc=94.4MB, time=15.13 memory used=1026.7MB, alloc=94.4MB, time=15.29 memory used=1074.4MB, alloc=94.4MB, time=17.08 memory used=1116.3MB, alloc=94.4MB, time=17.46 memory used=1141.9MB, alloc=94.4MB, time=17.62 memory used=1175.3MB, alloc=94.4MB, time=17.79 memory used=1201.0MB, alloc=94.4MB, time=17.95 memory used=1264.5MB, alloc=94.4MB, time=19.24 memory used=1314.8MB, alloc=94.4MB, time=20.63 memory used=1340.3MB, alloc=94.4MB, time=20.81 memory used=1372.5MB, alloc=94.4MB, time=20.97 memory used=1433.8MB, alloc=118.4MB, time=22.20 memory used=1492.5MB, alloc=374.4MB, time=23.58 memory used=1563.9MB, alloc=374.4MB, time=24.46 memory used=1616.1MB, alloc=374.4MB, time=24.85 memory used=1674.9MB, alloc=374.4MB, time=25.36 memory used=1723.4MB, alloc=374.4MB, time=25.64 memory used=1764.3MB, alloc=374.4MB, time=25.87 memory used=1806.8MB, alloc=374.4MB, time=26.11 memory used=1853.1MB, alloc=374.4MB, time=26.32 memory used=1907.7MB, alloc=374.4MB, time=26.71 memory used=1951.6MB, alloc=374.4MB, time=26.97 memory used=1990.7MB, alloc=374.4MB, time=27.20 memory used=2040.5MB, alloc=374.4MB, time=27.45 memory used=2095.3MB, alloc=374.4MB, time=28.01 memory used=2137.0MB, alloc=374.4MB, time=28.27 memory used=2183.7MB, alloc=374.4MB, time=28.50 memory used=2239.6MB, alloc=374.4MB, time=28.92 memory used=2285.4MB, alloc=374.4MB, time=29.19 memory used=2324.4MB, alloc=374.4MB, time=29.43 memory used=2366.3MB, alloc=374.4MB, time=29.67 memory used=2412.9MB, alloc=374.4MB, time=29.90 memory used=2474.9MB, alloc=374.4MB, time=30.55 memory used=2514.2MB, alloc=374.4MB, time=30.77 memory used=2559.6MB, alloc=374.4MB, time=31.00 memory used=2624.6MB, alloc=374.4MB, time=32.37 memory used=2689.0MB, alloc=374.4MB, time=32.76 memory used=2734.3MB, alloc=374.4MB, time=33.04 memory used=2766.7MB, alloc=374.4MB, time=33.29 memory used=2803.4MB, alloc=374.4MB, time=33.55 memory used=2842.8MB, alloc=374.4MB, time=33.81 memory used=2887.6MB, alloc=374.4MB, time=34.08 memory used=2935.0MB, alloc=374.4MB, time=34.36 memory used=2987.9MB, alloc=374.4MB, time=34.63 memory used=3028.2MB, alloc=398.4MB, time=34.90 memory used=3068.5MB, alloc=398.4MB, time=35.16 memory used=3110.1MB, alloc=398.4MB, time=35.42 memory used=3153.3MB, alloc=398.4MB, time=35.69 memory used=3199.7MB, alloc=398.4MB, time=35.95 memory used=3247.9MB, alloc=398.4MB, time=36.22 memory used=3299.4MB, alloc=398.4MB, time=36.49 memory used=3352.9MB, alloc=398.4MB, time=36.76 memory used=3409.5MB, alloc=398.4MB, time=37.02 memory used=3469.6MB, alloc=398.4MB, time=37.31 memory used=3534.0MB, alloc=398.4MB, time=37.59 memory used=3601.6MB, alloc=398.4MB, time=37.87 memory used=3675.6MB, alloc=398.4MB, time=38.17 memory used=3739.0MB, alloc=398.4MB, time=38.42 memory used=3779.7MB, alloc=398.4MB, time=38.64 memory used=3819.3MB, alloc=398.4MB, time=38.85 memory used=3861.0MB, alloc=398.4MB, time=39.05 memory used=3903.8MB, alloc=398.4MB, time=39.27 memory used=3949.5MB, alloc=398.4MB, time=39.47 memory used=3997.8MB, alloc=398.4MB, time=39.68 memory used=4082.2MB, alloc=398.4MB, time=40.95 memory used=4161.4MB, alloc=398.4MB, time=41.37 memory used=4210.3MB, alloc=398.4MB, time=41.68 memory used=4266.8MB, alloc=398.4MB, time=42.02 memory used=4331.8MB, alloc=398.4MB, time=42.36 memory used=4405.5MB, alloc=398.4MB, time=42.71 memory used=4466.7MB, alloc=398.4MB, time=43.01 memory used=4505.7MB, alloc=398.4MB, time=43.27 memory used=4547.2MB, alloc=398.4MB, time=43.55 memory used=4593.6MB, alloc=398.4MB, time=43.82 memory used=4640.7MB, alloc=398.4MB, time=44.10 memory used=4689.2MB, alloc=398.4MB, time=44.37 memory used=4740.9MB, alloc=398.4MB, time=44.66 memory used=4797.4MB, alloc=398.4MB, time=44.95 memory used=4854.8MB, alloc=398.4MB, time=45.25 memory used=4915.6MB, alloc=398.4MB, time=45.54 memory used=4980.0MB, alloc=398.4MB, time=45.84 memory used=5050.5MB, alloc=398.4MB, time=46.13 memory used=5124.1MB, alloc=398.4MB, time=46.43 memory used=5180.7MB, alloc=398.4MB, time=46.68 memory used=5219.7MB, alloc=398.4MB, time=46.89 memory used=5258.9MB, alloc=398.4MB, time=47.10 memory used=5300.4MB, alloc=398.4MB, time=47.31 memory used=5343.6MB, alloc=398.4MB, time=47.51 memory used=5389.2MB, alloc=398.4MB, time=47.73 memory used=5438.0MB, alloc=398.4MB, time=47.94 memory used=5537.4MB, alloc=398.4MB, time=114.37 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428278172 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 2 4 2 F := [-12 x y - 5 x y, -16 x y - 20 x + 20 y, -15 x y + 15 y - 20 x y ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 3 2 2 2 G := [3 x y z - 9 y z + 11 y z, 19 y z + 13 y z + 11 x, 19 x z + 3 z] > Problem := [F,G]; Problem := [ 3 2 2 2 2 2 4 2 [-12 x y - 5 x y, -16 x y - 20 x + 20 y, -15 x y + 15 y - 20 x y ], 2 3 3 2 2 2 [3 x y z - 9 y z + 11 y z, 19 y z + 13 y z + 11 x, 19 x z + 3 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.4MB, alloc=32.3MB, time=0.85 memory used=47.7MB, alloc=32.3MB, time=1.38 memory used=67.7MB, alloc=56.3MB, time=1.92 memory used=108.2MB, alloc=60.3MB, time=2.96 memory used=149.6MB, alloc=60.3MB, time=3.91 memory used=231.9MB, alloc=100.3MB, time=5.82 memory used=308.7MB, alloc=100.3MB, time=7.87 memory used=380.5MB, alloc=124.3MB, time=9.75 memory used=469.4MB, alloc=148.3MB, time=12.28 memory used=575.4MB, alloc=172.3MB, time=15.37 memory used=699.6MB, alloc=196.3MB, time=18.94 memory used=814.9MB, alloc=476.3MB, time=22.71 memory used=946.9MB, alloc=500.3MB, time=28.81 memory used=1087.0MB, alloc=524.3MB, time=35.96 memory used=1236.1MB, alloc=548.3MB, time=44.93 memory used=1408.3MB, alloc=572.3MB, time=55.34 memory used=1604.5MB, alloc=572.3MB, time=67.09 memory used=1800.6MB, alloc=572.3MB, time=78.84 memory used=1996.7MB, alloc=596.3MB, time=90.54 memory used=2216.7MB, alloc=596.3MB, time=103.57 memory used=2436.7MB, alloc=620.3MB, time=116.59 memory used=2680.8MB, alloc=644.3MB, time=131.14 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428278472 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 3 3 F := [9 x y z + 4 x z - 14 y , -4 x y + 7 y z - 18 y, 3 3 2 10 x y + 13 x z - 20 z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 4 3 4 G := [-3 x z - 13 y - 20 x z, -2 x + 16 y z - 17 z , 3 2 3 4 x y + 7 x y z + 14 y z] > Problem := [F,G]; 2 2 2 3 3 3 Problem := [[9 x y z + 4 x z - 14 y , -4 x y + 7 y z - 18 y, 3 3 2 3 3 10 x y + 13 x z - 20 z ], [-3 x z - 13 y - 20 x z, 4 3 4 3 2 3 -2 x + 16 y z - 17 z , 4 x y + 7 x y z + 14 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.30 memory used=25.1MB, alloc=32.3MB, time=0.84 memory used=46.2MB, alloc=60.3MB, time=1.34 memory used=92.8MB, alloc=60.3MB, time=2.29 memory used=133.3MB, alloc=60.3MB, time=2.86 memory used=175.0MB, alloc=60.3MB, time=3.83 memory used=221.3MB, alloc=68.3MB, time=4.78 memory used=265.9MB, alloc=68.3MB, time=5.79 memory used=317.9MB, alloc=68.3MB, time=6.69 memory used=362.2MB, alloc=92.3MB, time=7.66 memory used=430.0MB, alloc=92.3MB, time=9.20 memory used=498.8MB, alloc=372.3MB, time=10.51 memory used=586.5MB, alloc=372.3MB, time=12.14 memory used=651.9MB, alloc=372.3MB, time=12.99 memory used=709.0MB, alloc=372.3MB, time=13.40 memory used=761.3MB, alloc=372.3MB, time=14.88 memory used=806.6MB, alloc=372.3MB, time=15.17 memory used=862.7MB, alloc=372.3MB, time=16.18 memory used=925.2MB, alloc=372.3MB, time=17.40 memory used=974.8MB, alloc=372.3MB, time=17.77 memory used=1053.2MB, alloc=372.3MB, time=19.51 memory used=1164.2MB, alloc=396.3MB, time=21.99 memory used=1288.1MB, alloc=396.3MB, time=24.21 memory used=1403.2MB, alloc=420.3MB, time=26.95 memory used=1537.0MB, alloc=420.3MB, time=29.57 memory used=1671.6MB, alloc=444.3MB, time=32.16 memory used=1789.1MB, alloc=468.3MB, time=34.82 memory used=1940.0MB, alloc=468.3MB, time=36.73 memory used=2049.9MB, alloc=468.3MB, time=37.81 memory used=2140.3MB, alloc=468.3MB, time=38.63 memory used=2233.7MB, alloc=468.3MB, time=39.22 memory used=2338.0MB, alloc=468.3MB, time=45.26 memory used=2416.3MB, alloc=468.3MB, time=45.74 memory used=2498.6MB, alloc=468.3MB, time=46.17 memory used=2604.7MB, alloc=468.3MB, time=46.99 memory used=2711.4MB, alloc=468.3MB, time=50.50 memory used=2789.8MB, alloc=468.3MB, time=50.99 memory used=2900.0MB, alloc=468.3MB, time=51.87 memory used=3008.8MB, alloc=468.3MB, time=52.63 memory used=3118.4MB, alloc=468.3MB, time=58.58 memory used=3197.0MB, alloc=468.3MB, time=59.08 memory used=3283.3MB, alloc=468.3MB, time=59.67 memory used=3384.1MB, alloc=468.3MB, time=60.51 memory used=3482.3MB, alloc=468.3MB, time=61.36 memory used=3562.6MB, alloc=468.3MB, time=61.87 memory used=3674.0MB, alloc=468.3MB, time=67.99 memory used=3747.0MB, alloc=468.3MB, time=68.44 memory used=3895.5MB, alloc=468.3MB, time=70.22 memory used=4031.5MB, alloc=468.3MB, time=72.57 memory used=4135.0MB, alloc=468.3MB, time=74.74 memory used=4233.1MB, alloc=468.3MB, time=77.18 memory used=4351.6MB, alloc=468.3MB, time=79.57 memory used=4432.9MB, alloc=468.3MB, time=81.42 memory used=4516.1MB, alloc=468.3MB, time=83.57 memory used=4619.3MB, alloc=492.3MB, time=85.13 memory used=4724.9MB, alloc=492.3MB, time=87.30 memory used=4853.9MB, alloc=492.3MB, time=89.69 memory used=4932.5MB, alloc=492.3MB, time=91.71 memory used=5013.6MB, alloc=492.3MB, time=94.02 memory used=5094.8MB, alloc=492.3MB, time=95.98 memory used=5174.7MB, alloc=492.3MB, time=97.69 memory used=5234.8MB, alloc=492.3MB, time=99.41 memory used=5280.3MB, alloc=492.3MB, time=100.76 memory used=5334.2MB, alloc=492.3MB, time=102.50 memory used=5400.5MB, alloc=492.3MB, time=104.09 memory used=5455.0MB, alloc=492.3MB, time=105.84 memory used=5502.3MB, alloc=492.3MB, time=107.42 memory used=5685.9MB, alloc=516.3MB, time=110.92 memory used=5805.8MB, alloc=540.3MB, time=114.12 memory used=5945.3MB, alloc=540.3MB, time=116.58 memory used=6106.3MB, alloc=540.3MB, time=119.10 memory used=6350.9MB, alloc=540.3MB, time=123.73 memory used=6461.2MB, alloc=564.3MB, time=125.06 memory used=6576.1MB, alloc=564.3MB, time=126.00 memory used=6709.2MB, alloc=564.3MB, time=127.60 memory used=6828.4MB, alloc=564.3MB, time=128.60 memory used=6960.6MB, alloc=564.3MB, time=135.50 memory used=7085.2MB, alloc=564.3MB, time=136.59 memory used=7195.6MB, alloc=564.3MB, time=137.52 memory used=7561.8MB, alloc=564.3MB, time=143.74 memory used=7677.0MB, alloc=564.3MB, time=144.71 memory used=7788.2MB, alloc=564.3MB, time=145.61 memory used=8067.7MB, alloc=564.3MB, time=147.62 memory used=8367.0MB, alloc=564.3MB, time=151.87 memory used=8597.4MB, alloc=588.3MB, time=156.92 memory used=8767.9MB, alloc=588.3MB, time=161.03 memory used=8930.0MB, alloc=588.3MB, time=163.03 memory used=9076.7MB, alloc=588.3MB, time=170.33 memory used=9197.6MB, alloc=612.3MB, time=171.51 memory used=9326.4MB, alloc=612.3MB, time=172.55 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428278772 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 3 2 F := [-5 x y - 2 x + 18 z, -20 x y + 3 x z - 9 x , 2 2 2 3 17 x z + 5 x y z + 13 x ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 2 4 3 2 G := [-3 z + 5 y z - 10 x , -4 y z - 10 y, 11 z + 19 x - 19 y z] > Problem := [F,G]; 3 2 3 3 2 Problem := [[-5 x y - 2 x + 18 z, -20 x y + 3 x z - 9 x , 2 2 2 3 17 x z + 5 x y z + 13 x ], 4 2 2 2 4 3 2 [-3 z + 5 y z - 10 x , -4 y z - 10 y, 11 z + 19 x - 19 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.5MB, alloc=32.3MB, time=0.88 memory used=47.1MB, alloc=32.3MB, time=1.39 memory used=65.2MB, alloc=56.3MB, time=1.90 memory used=107.7MB, alloc=68.3MB, time=2.97 memory used=152.6MB, alloc=92.3MB, time=4.00 memory used=218.4MB, alloc=92.3MB, time=5.63 memory used=282.4MB, alloc=116.3MB, time=7.26 memory used=350.4MB, alloc=116.3MB, time=8.59 memory used=415.5MB, alloc=372.3MB, time=10.06 memory used=503.4MB, alloc=372.3MB, time=11.93 memory used=595.8MB, alloc=372.3MB, time=13.68 memory used=680.4MB, alloc=396.3MB, time=15.50 memory used=795.6MB, alloc=396.3MB, time=18.00 memory used=859.9MB, alloc=396.3MB, time=18.83 memory used=926.6MB, alloc=396.3MB, time=19.76 memory used=1034.9MB, alloc=420.3MB, time=21.73 memory used=1102.4MB, alloc=420.3MB, time=22.35 memory used=1180.7MB, alloc=420.3MB, time=23.50 memory used=1256.4MB, alloc=420.3MB, time=24.18 memory used=1327.2MB, alloc=420.3MB, time=24.55 memory used=1407.6MB, alloc=420.3MB, time=25.61 memory used=1530.6MB, alloc=420.3MB, time=27.75 memory used=1656.1MB, alloc=444.3MB, time=30.64 memory used=1791.6MB, alloc=444.3MB, time=34.36 memory used=1894.8MB, alloc=468.3MB, time=37.01 memory used=1986.3MB, alloc=468.3MB, time=39.07 memory used=2093.1MB, alloc=492.3MB, time=41.08 memory used=2192.4MB, alloc=492.3MB, time=43.66 memory used=2269.9MB, alloc=492.3MB, time=45.53 memory used=2357.7MB, alloc=492.3MB, time=47.36 memory used=2440.8MB, alloc=516.3MB, time=49.30 memory used=2517.1MB, alloc=516.3MB, time=51.60 memory used=2574.1MB, alloc=516.3MB, time=53.33 memory used=2637.3MB, alloc=516.3MB, time=54.90 memory used=2688.8MB, alloc=516.3MB, time=56.29 memory used=2757.2MB, alloc=516.3MB, time=58.26 memory used=2806.0MB, alloc=516.3MB, time=59.94 memory used=2860.7MB, alloc=516.3MB, time=61.89 memory used=2904.2MB, alloc=516.3MB, time=63.49 memory used=2941.7MB, alloc=516.3MB, time=65.04 memory used=3141.9MB, alloc=540.3MB, time=69.85 memory used=3290.4MB, alloc=540.3MB, time=71.75 memory used=3420.2MB, alloc=540.3MB, time=73.54 memory used=3666.7MB, alloc=540.3MB, time=139.10 memory used=3900.2MB, alloc=540.3MB, time=141.58 memory used=4022.3MB, alloc=540.3MB, time=142.89 memory used=4153.6MB, alloc=540.3MB, time=144.24 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428279072 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 3 F := [-16 x y + 8 x y + 12 x, 7 x z - 12 x y - 12 y z, 2 2 3 5 x y z + 7 x y z + z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 2 3 3 2 G := [-4 x - x y z - 3 y z , -11 y z - 18 x - 12 y z , 3 2 12 x z - 5 x z + 20 x] > Problem := [F,G]; 3 3 3 Problem := [[-16 x y + 8 x y + 12 x, 7 x z - 12 x y - 12 y z, 2 2 3 4 2 2 2 5 x y z + 7 x y z + z ], [-4 x - x y z - 3 y z , 3 3 2 3 2 -11 y z - 18 x - 12 y z , 12 x z - 5 x z + 20 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=24.8MB, alloc=32.3MB, time=0.83 memory used=45.9MB, alloc=32.3MB, time=1.27 memory used=64.6MB, alloc=56.3MB, time=1.76 memory used=107.3MB, alloc=68.3MB, time=2.78 memory used=152.9MB, alloc=68.3MB, time=3.67 memory used=190.9MB, alloc=69.2MB, time=3.96 memory used=230.9MB, alloc=69.2MB, time=4.95 memory used=280.8MB, alloc=70.0MB, time=6.43 memory used=306.5MB, alloc=70.0MB, time=6.59 memory used=329.1MB, alloc=70.0MB, time=6.72 memory used=357.3MB, alloc=70.0MB, time=6.87 memory used=375.9MB, alloc=70.0MB, time=6.98 memory used=405.1MB, alloc=70.0MB, time=7.20 memory used=444.0MB, alloc=70.0MB, time=7.46 memory used=483.8MB, alloc=70.0MB, time=9.15 memory used=540.2MB, alloc=70.0MB, time=12.56 memory used=575.1MB, alloc=70.0MB, time=12.74 memory used=595.7MB, alloc=70.0MB, time=12.88 memory used=617.2MB, alloc=70.0MB, time=13.00 memory used=642.7MB, alloc=70.0MB, time=13.15 memory used=672.1MB, alloc=70.0MB, time=13.29 memory used=688.7MB, alloc=70.0MB, time=13.40 memory used=707.1MB, alloc=70.0MB, time=13.50 memory used=726.3MB, alloc=70.0MB, time=13.62 memory used=747.8MB, alloc=70.0MB, time=13.73 memory used=793.4MB, alloc=70.0MB, time=14.39 memory used=840.4MB, alloc=70.0MB, time=15.30 memory used=883.0MB, alloc=94.0MB, time=16.27 memory used=948.4MB, alloc=94.0MB, time=17.82 memory used=1000.4MB, alloc=94.0MB, time=18.45 memory used=1040.6MB, alloc=94.0MB, time=18.68 memory used=1069.1MB, alloc=94.0MB, time=18.85 memory used=1105.4MB, alloc=94.0MB, time=19.04 memory used=1146.8MB, alloc=94.0MB, time=19.54 memory used=1194.0MB, alloc=94.0MB, time=19.80 memory used=1221.4MB, alloc=94.0MB, time=19.99 memory used=1256.3MB, alloc=94.0MB, time=20.18 memory used=1299.7MB, alloc=94.0MB, time=23.73 memory used=1370.1MB, alloc=94.0MB, time=30.33 memory used=1402.3MB, alloc=94.0MB, time=30.53 memory used=1435.5MB, alloc=94.0MB, time=30.71 memory used=1472.6MB, alloc=94.0MB, time=30.89 memory used=1496.2MB, alloc=94.0MB, time=31.04 memory used=1522.2MB, alloc=94.0MB, time=31.21 memory used=1550.3MB, alloc=94.0MB, time=31.37 memory used=1581.2MB, alloc=94.0MB, time=31.53 memory used=1614.8MB, alloc=94.0MB, time=31.71 memory used=1651.8MB, alloc=94.0MB, time=31.87 memory used=1691.9MB, alloc=94.0MB, time=32.05 memory used=1718.2MB, alloc=94.0MB, time=32.20 memory used=1740.3MB, alloc=94.0MB, time=32.36 memory used=1763.1MB, alloc=94.0MB, time=32.49 memory used=1787.0MB, alloc=94.0MB, time=32.62 memory used=1812.4MB, alloc=94.0MB, time=32.76 memory used=1838.1MB, alloc=94.0MB, time=32.89 memory used=1866.3MB, alloc=94.0MB, time=33.02 memory used=1896.4MB, alloc=94.0MB, time=33.15 memory used=1935.6MB, alloc=94.0MB, time=33.62 memory used=1966.7MB, alloc=94.0MB, time=33.96 memory used=1998.3MB, alloc=94.0MB, time=34.17 memory used=2019.5MB, alloc=107.8MB, time=34.65 memory used=2062.4MB, alloc=107.8MB, time=34.85 memory used=2102.9MB, alloc=107.8MB, time=35.06 memory used=2145.3MB, alloc=107.8MB, time=35.26 memory used=2178.5MB, alloc=107.8MB, time=35.87 memory used=2239.3MB, alloc=107.8MB, time=36.84 memory used=2318.1MB, alloc=107.8MB, time=38.58 memory used=2378.6MB, alloc=131.8MB, time=40.04 memory used=2448.8MB, alloc=131.8MB, time=41.57 memory used=2519.0MB, alloc=131.8MB, time=42.51 memory used=2582.9MB, alloc=387.8MB, time=44.11 memory used=2663.4MB, alloc=387.8MB, time=46.17 memory used=2747.7MB, alloc=411.8MB, time=48.04 memory used=2852.4MB, alloc=435.8MB, time=50.49 memory used=2975.8MB, alloc=435.8MB, time=53.23 memory used=3068.5MB, alloc=435.8MB, time=53.87 memory used=3122.4MB, alloc=435.8MB, time=54.29 memory used=3180.9MB, alloc=435.8MB, time=54.70 memory used=3270.3MB, alloc=435.8MB, time=55.46 memory used=3353.3MB, alloc=435.8MB, time=56.02 memory used=3402.5MB, alloc=435.8MB, time=56.45 memory used=3464.8MB, alloc=435.8MB, time=56.88 memory used=3588.3MB, alloc=435.8MB, time=74.09 memory used=3681.2MB, alloc=435.8MB, time=75.00 memory used=3735.2MB, alloc=435.8MB, time=75.43 memory used=3805.6MB, alloc=435.8MB, time=75.89 memory used=3853.8MB, alloc=435.8MB, time=76.28 memory used=3900.9MB, alloc=435.8MB, time=76.65 memory used=3953.9MB, alloc=435.8MB, time=77.04 memory used=4014.4MB, alloc=435.8MB, time=77.43 memory used=4083.4MB, alloc=435.8MB, time=77.83 memory used=4153.8MB, alloc=435.8MB, time=78.50 memory used=4243.9MB, alloc=435.8MB, time=79.09 memory used=4292.9MB, alloc=435.8MB, time=79.50 memory used=4354.7MB, alloc=435.8MB, time=79.91 memory used=4449.9MB, alloc=435.8MB, time=80.78 memory used=4521.9MB, alloc=435.8MB, time=81.28 memory used=4573.6MB, alloc=435.8MB, time=81.68 memory used=4639.7MB, alloc=435.8MB, time=82.11 memory used=4777.8MB, alloc=435.8MB, time=99.64 memory used=4848.3MB, alloc=435.8MB, time=100.13 memory used=4906.6MB, alloc=435.8MB, time=100.53 memory used=4976.6MB, alloc=435.8MB, time=100.95 memory used=5019.9MB, alloc=435.8MB, time=101.30 memory used=5068.3MB, alloc=435.8MB, time=101.66 memory used=5123.4MB, alloc=435.8MB, time=102.03 memory used=5186.2MB, alloc=435.8MB, time=102.41 memory used=5253.4MB, alloc=435.8MB, time=102.78 memory used=5339.5MB, alloc=435.8MB, time=107.39 memory used=5421.6MB, alloc=435.8MB, time=108.20 memory used=5488.0MB, alloc=435.8MB, time=108.61 memory used=5536.0MB, alloc=435.8MB, time=108.94 memory used=5615.7MB, alloc=435.8MB, time=110.07 memory used=5745.3MB, alloc=435.8MB, time=112.31 memory used=5868.3MB, alloc=459.8MB, time=113.90 memory used=6041.8MB, alloc=459.8MB, time=116.24 memory used=6145.9MB, alloc=459.8MB, time=118.74 memory used=6262.7MB, alloc=483.8MB, time=121.42 memory used=6364.4MB, alloc=483.8MB, time=123.75 memory used=6464.6MB, alloc=483.8MB, time=126.39 memory used=6552.7MB, alloc=507.8MB, time=128.74 memory used=6693.0MB, alloc=507.8MB, time=130.68 memory used=6835.4MB, alloc=507.8MB, time=132.63 memory used=6917.5MB, alloc=507.8MB, time=133.34 memory used=7013.6MB, alloc=507.8MB, time=134.04 memory used=7112.8MB, alloc=507.8MB, time=134.72 memory used=7178.5MB, alloc=507.8MB, time=135.33 memory used=7252.3MB, alloc=507.8MB, time=135.94 memory used=7335.1MB, alloc=507.8MB, time=136.55 memory used=7427.2MB, alloc=507.8MB, time=137.17 memory used=7531.1MB, alloc=507.8MB, time=137.81 memory used=7618.2MB, alloc=507.8MB, time=138.44 memory used=7748.8MB, alloc=507.8MB, time=140.13 memory used=7830.0MB, alloc=507.8MB, time=140.80 memory used=7932.6MB, alloc=507.8MB, time=141.52 memory used=8016.7MB, alloc=507.8MB, time=142.16 memory used=8085.3MB, alloc=507.8MB, time=142.78 memory used=8161.4MB, alloc=507.8MB, time=143.39 memory used=8246.1MB, alloc=507.8MB, time=144.00 memory used=8341.2MB, alloc=507.8MB, time=144.62 memory used=8449.7MB, alloc=507.8MB, time=145.29 memory used=8565.8MB, alloc=507.8MB, time=180.78 memory used=8722.2MB, alloc=507.8MB, time=187.99 memory used=8822.9MB, alloc=507.8MB, time=188.68 memory used=8891.7MB, alloc=507.8MB, time=189.27 memory used=8973.0MB, alloc=507.8MB, time=189.90 memory used=9068.9MB, alloc=507.8MB, time=190.53 memory used=9179.9MB, alloc=507.8MB, time=191.18 memory used=9243.7MB, alloc=507.8MB, time=191.70 memory used=9308.7MB, alloc=507.8MB, time=192.22 memory used=9379.2MB, alloc=507.8MB, time=192.75 memory used=9454.5MB, alloc=507.8MB, time=193.28 memory used=9535.4MB, alloc=507.8MB, time=193.85 memory used=9623.5MB, alloc=507.8MB, time=194.44 memory used=9719.5MB, alloc=507.8MB, time=195.02 memory used=9823.9MB, alloc=507.8MB, time=195.60 memory used=10009.4MB, alloc=507.8MB, time=197.65 memory used=10102.8MB, alloc=507.8MB, time=198.41 memory used=10193.8MB, alloc=507.8MB, time=199.12 memory used=10303.5MB, alloc=507.8MB, time=199.83 memory used=10369.3MB, alloc=507.8MB, time=200.46 memory used=10440.5MB, alloc=507.8MB, time=201.07 memory used=10521.4MB, alloc=507.8MB, time=201.73 memory used=10610.4MB, alloc=507.8MB, time=202.37 memory used=10711.7MB, alloc=507.8MB, time=203.01 memory used=10807.7MB, alloc=507.8MB, time=203.60 memory used=10937.1MB, alloc=507.8MB, time=205.47 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428279372 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 3 F := [-6 x y z - 3 x y + 16 z , 11 x z - 6 x y z + 10 y, 4 3 2 4 y - 6 y z + 8 y z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 G := [-y z - 4 x z - 12 x y, -18 y z - 13 x z - 19 x y, 3 3 2 -14 x y - 7 y z - y ] > Problem := [F,G]; 2 3 2 3 Problem := [[-6 x y z - 3 x y + 16 z , 11 x z - 6 x y z + 10 y, 4 3 2 2 2 2 4 y - 6 y z + 8 y z ], [-y z - 4 x z - 12 x y, 3 2 3 3 2 -18 y z - 13 x z - 19 x y, -14 x y - 7 y z - y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.2MB, alloc=32.3MB, time=0.88 memory used=47.9MB, alloc=60.6MB, time=1.38 memory used=87.8MB, alloc=60.9MB, time=1.70 memory used=140.2MB, alloc=68.9MB, time=2.81 memory used=188.7MB, alloc=68.9MB, time=3.83 memory used=232.8MB, alloc=68.9MB, time=4.77 memory used=272.6MB, alloc=92.9MB, time=5.83 memory used=340.2MB, alloc=92.9MB, time=7.37 memory used=394.7MB, alloc=92.9MB, time=8.07 memory used=438.4MB, alloc=92.9MB, time=8.82 memory used=475.2MB, alloc=92.9MB, time=9.07 memory used=519.2MB, alloc=92.9MB, time=9.45 memory used=565.8MB, alloc=92.9MB, time=10.21 memory used=602.9MB, alloc=92.9MB, time=10.58 memory used=679.5MB, alloc=348.9MB, time=12.19 memory used=753.5MB, alloc=372.9MB, time=13.52 memory used=845.1MB, alloc=372.9MB, time=15.73 memory used=932.3MB, alloc=396.9MB, time=17.65 memory used=1054.0MB, alloc=396.9MB, time=20.04 memory used=1126.1MB, alloc=396.9MB, time=20.77 memory used=1192.1MB, alloc=396.9MB, time=21.25 memory used=1263.1MB, alloc=396.9MB, time=23.95 memory used=1314.6MB, alloc=396.9MB, time=24.27 memory used=1359.8MB, alloc=396.9MB, time=24.57 memory used=1421.6MB, alloc=396.9MB, time=25.01 memory used=1489.4MB, alloc=396.9MB, time=25.61 memory used=1551.9MB, alloc=396.9MB, time=26.10 memory used=1618.7MB, alloc=396.9MB, time=26.59 memory used=1686.4MB, alloc=396.9MB, time=29.15 memory used=1749.3MB, alloc=396.9MB, time=29.74 memory used=1797.5MB, alloc=396.9MB, time=30.04 memory used=1845.9MB, alloc=396.9MB, time=30.34 memory used=1902.1MB, alloc=396.9MB, time=30.90 memory used=1960.5MB, alloc=396.9MB, time=31.49 memory used=2025.8MB, alloc=396.9MB, time=32.03 memory used=2091.7MB, alloc=396.9MB, time=32.57 memory used=2211.6MB, alloc=420.9MB, time=35.34 memory used=2336.5MB, alloc=420.9MB, time=38.44 memory used=2467.8MB, alloc=444.9MB, time=41.52 memory used=2593.9MB, alloc=444.9MB, time=43.91 memory used=2709.5MB, alloc=444.9MB, time=46.94 memory used=2825.2MB, alloc=468.9MB, time=50.05 memory used=2927.1MB, alloc=468.9MB, time=52.61 memory used=3029.2MB, alloc=468.9MB, time=54.79 memory used=3139.0MB, alloc=468.9MB, time=56.89 memory used=3230.0MB, alloc=468.9MB, time=57.69 memory used=3321.2MB, alloc=468.9MB, time=60.08 memory used=3393.0MB, alloc=492.9MB, time=60.69 memory used=3478.7MB, alloc=492.9MB, time=61.26 memory used=3590.8MB, alloc=492.9MB, time=63.20 memory used=3675.4MB, alloc=492.9MB, time=65.51 memory used=3751.4MB, alloc=492.9MB, time=67.73 memory used=3860.9MB, alloc=492.9MB, time=68.89 memory used=3978.9MB, alloc=492.9MB, time=70.31 memory used=4071.8MB, alloc=492.9MB, time=71.05 memory used=4182.5MB, alloc=492.9MB, time=72.41 memory used=4282.3MB, alloc=492.9MB, time=74.38 memory used=4364.1MB, alloc=492.9MB, time=76.09 memory used=4423.2MB, alloc=492.9MB, time=77.94 memory used=4486.3MB, alloc=492.9MB, time=79.93 memory used=4550.2MB, alloc=492.9MB, time=82.05 memory used=4598.9MB, alloc=492.9MB, time=83.63 memory used=4648.1MB, alloc=492.9MB, time=85.34 memory used=4702.6MB, alloc=492.9MB, time=87.37 memory used=4890.8MB, alloc=516.9MB, time=91.69 memory used=5058.3MB, alloc=540.9MB, time=96.01 memory used=5275.3MB, alloc=564.9MB, time=102.75 memory used=5459.9MB, alloc=588.9MB, time=108.06 memory used=5625.6MB, alloc=612.9MB, time=111.68 memory used=5821.4MB, alloc=612.9MB, time=114.42 memory used=5994.9MB, alloc=612.9MB, time=117.36 memory used=6160.2MB, alloc=612.9MB, time=121.13 memory used=6324.3MB, alloc=612.9MB, time=123.37 memory used=6506.3MB, alloc=636.9MB, time=128.02 memory used=6764.9MB, alloc=636.9MB, time=134.29 memory used=6965.0MB, alloc=636.9MB, time=138.40 memory used=7120.2MB, alloc=636.9MB, time=142.28 memory used=7264.8MB, alloc=660.9MB, time=147.06 memory used=7373.0MB, alloc=660.9MB, time=150.10 memory used=7507.9MB, alloc=660.9MB, time=154.78 memory used=7599.7MB, alloc=660.9MB, time=157.86 memory used=7701.3MB, alloc=660.9MB, time=161.09 memory used=7833.2MB, alloc=660.9MB, time=164.89 memory used=7924.7MB, alloc=660.9MB, time=168.69 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428279672 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; F := 3 2 2 2 2 3 [-2 y z - 10 y z - 17 y , 7 x z - 12 y - 4 x, -12 x y + 12 x z + 17 x] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 3 2 2 2 2 G := [-10 x y + 13 x y , 14 x y - 15 x z + 8 y, -2 x z - 20 y z + 18 x ] > Problem := [F,G]; Problem := [ 3 2 2 2 2 3 [-2 y z - 10 y z - 17 y , 7 x z - 12 y - 4 x, -12 x y + 12 x z + 17 x] 3 2 3 3 2 2 2 2 , [-10 x y + 13 x y , 14 x y - 15 x z + 8 y, -2 x z - 20 y z + 18 x ] ] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.7MB, alloc=32.3MB, time=0.88 memory used=46.8MB, alloc=56.3MB, time=1.35 memory used=89.6MB, alloc=60.3MB, time=2.35 memory used=129.4MB, alloc=60.3MB, time=3.33 memory used=167.4MB, alloc=60.3MB, time=4.23 memory used=193.6MB, alloc=60.3MB, time=5.55 memory used=229.0MB, alloc=84.3MB, time=6.28 memory used=300.9MB, alloc=92.3MB, time=7.83 memory used=363.9MB, alloc=92.3MB, time=9.41 memory used=424.0MB, alloc=92.3MB, time=10.73 memory used=491.7MB, alloc=372.3MB, time=12.22 memory used=556.7MB, alloc=372.3MB, time=19.61 memory used=589.9MB, alloc=372.3MB, time=19.77 memory used=649.7MB, alloc=372.3MB, time=27.39 memory used=683.5MB, alloc=372.3MB, time=27.57 memory used=749.8MB, alloc=372.3MB, time=29.30 memory used=837.7MB, alloc=372.3MB, time=31.24 memory used=920.2MB, alloc=396.3MB, time=33.37 memory used=1020.1MB, alloc=396.3MB, time=36.10 memory used=1120.9MB, alloc=420.3MB, time=38.63 memory used=1245.2MB, alloc=420.3MB, time=40.73 memory used=1384.6MB, alloc=420.3MB, time=43.64 memory used=1508.3MB, alloc=444.3MB, time=47.05 memory used=1624.8MB, alloc=444.3MB, time=49.74 memory used=1712.9MB, alloc=444.3MB, time=50.88 memory used=1802.3MB, alloc=444.3MB, time=53.08 memory used=1933.3MB, alloc=444.3MB, time=56.23 memory used=2083.8MB, alloc=444.3MB, time=59.01 memory used=2243.9MB, alloc=444.3MB, time=61.92 memory used=2368.9MB, alloc=444.3MB, time=64.69 memory used=2451.5MB, alloc=444.3MB, time=67.96 memory used=2512.5MB, alloc=444.3MB, time=68.34 memory used=2612.1MB, alloc=444.3MB, time=69.97 memory used=2741.1MB, alloc=444.3MB, time=72.62 memory used=2891.1MB, alloc=468.3MB, time=75.53 memory used=3040.8MB, alloc=492.3MB, time=78.23 memory used=3166.6MB, alloc=492.3MB, time=80.22 memory used=3278.2MB, alloc=492.3MB, time=83.24 memory used=3386.2MB, alloc=492.3MB, time=84.28 memory used=3570.0MB, alloc=492.3MB, time=85.43 memory used=3783.7MB, alloc=492.3MB, time=87.99 memory used=3903.6MB, alloc=492.3MB, time=90.66 memory used=4021.6MB, alloc=492.3MB, time=93.19 memory used=4134.1MB, alloc=492.3MB, time=96.01 memory used=4289.3MB, alloc=492.3MB, time=99.68 memory used=4374.0MB, alloc=492.3MB, time=100.24 memory used=4489.0MB, alloc=492.3MB, time=103.01 memory used=4610.9MB, alloc=492.3MB, time=105.15 memory used=4720.9MB, alloc=492.3MB, time=108.96 memory used=4828.5MB, alloc=492.3MB, time=110.91 memory used=4946.4MB, alloc=492.3MB, time=113.46 memory used=5033.0MB, alloc=492.3MB, time=113.99 memory used=5127.3MB, alloc=492.3MB, time=115.47 memory used=5280.4MB, alloc=516.3MB, time=118.65 memory used=5382.0MB, alloc=516.3MB, time=120.92 memory used=5475.1MB, alloc=516.3MB, time=123.08 memory used=5584.7MB, alloc=516.3MB, time=125.31 memory used=5680.4MB, alloc=516.3MB, time=127.74 memory used=5771.7MB, alloc=516.3MB, time=130.45 memory used=5930.3MB, alloc=540.3MB, time=137.85 memory used=6060.3MB, alloc=540.3MB, time=142.77 memory used=6150.9MB, alloc=540.3MB, time=145.73 memory used=6231.7MB, alloc=540.3MB, time=147.75 memory used=6312.9MB, alloc=540.3MB, time=150.02 memory used=6380.8MB, alloc=564.3MB, time=151.44 memory used=6473.4MB, alloc=564.3MB, time=155.21 memory used=6530.0MB, alloc=564.3MB, time=156.66 memory used=6594.2MB, alloc=588.3MB, time=158.00 memory used=6664.9MB, alloc=588.3MB, time=160.46 memory used=6719.7MB, alloc=588.3MB, time=162.53 memory used=6941.6MB, alloc=612.3MB, time=168.73 memory used=7160.3MB, alloc=636.3MB, time=174.67 memory used=7323.9MB, alloc=660.3MB, time=178.12 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428279972 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 4 3 2 F := [-13 x y - 10 x y z + 11 x y z, 5 y + 6 y z + 4 x y, 4 2 9 y - 6 x z - 5 z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; G := [ 2 2 2 3 3 2 2 2 20 x z + 20 x y z - 5 y z, -y - 7 y z - 4, 14 x z + 5 y z + 11 x z ] > Problem := [F,G]; 3 2 4 3 2 Problem := [[-13 x y - 10 x y z + 11 x y z, 5 y + 6 y z + 4 x y, 4 2 9 y - 6 x z - 5 z], [ 2 2 2 3 3 2 2 2 20 x z + 20 x y z - 5 y z, -y - 7 y z - 4, 14 x z + 5 y z + 11 x z ] ] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.5MB, alloc=32.3MB, time=0.87 memory used=47.4MB, alloc=32.3MB, time=1.42 memory used=65.8MB, alloc=56.3MB, time=1.95 memory used=105.2MB, alloc=60.3MB, time=3.03 memory used=144.9MB, alloc=84.3MB, time=4.10 memory used=210.7MB, alloc=92.3MB, time=5.82 memory used=275.8MB, alloc=372.3MB, time=7.52 memory used=363.8MB, alloc=372.3MB, time=9.74 memory used=453.3MB, alloc=396.3MB, time=11.90 memory used=564.9MB, alloc=396.3MB, time=14.45 memory used=669.6MB, alloc=420.3MB, time=17.23 memory used=799.4MB, alloc=444.3MB, time=20.85 memory used=934.0MB, alloc=468.3MB, time=24.56 memory used=1049.8MB, alloc=468.3MB, time=27.71 memory used=1153.5MB, alloc=492.3MB, time=30.52 memory used=1255.0MB, alloc=492.3MB, time=32.93 memory used=1349.5MB, alloc=492.3MB, time=35.75 memory used=1422.1MB, alloc=492.3MB, time=37.82 memory used=1499.6MB, alloc=492.3MB, time=40.17 memory used=1570.5MB, alloc=516.3MB, time=42.10 memory used=1636.2MB, alloc=516.3MB, time=44.41 memory used=1684.4MB, alloc=516.3MB, time=46.05 memory used=1732.4MB, alloc=516.3MB, time=47.51 memory used=1795.7MB, alloc=516.3MB, time=49.70 memory used=1830.9MB, alloc=516.3MB, time=51.03 memory used=2027.2MB, alloc=540.3MB, time=56.19 memory used=2200.9MB, alloc=564.3MB, time=60.81 memory used=2350.9MB, alloc=564.3MB, time=64.66 memory used=2515.2MB, alloc=588.3MB, time=69.52 memory used=2670.6MB, alloc=612.3MB, time=74.30 memory used=2822.2MB, alloc=612.3MB, time=78.80 memory used=2934.3MB, alloc=612.3MB, time=82.34 memory used=3063.5MB, alloc=612.3MB, time=86.54 memory used=3169.7MB, alloc=612.3MB, time=89.88 memory used=3286.8MB, alloc=612.3MB, time=93.99 memory used=3371.1MB, alloc=636.3MB, time=97.14 memory used=3477.7MB, alloc=636.3MB, time=101.51 memory used=3559.0MB, alloc=636.3MB, time=104.82 memory used=3861.7MB, alloc=660.3MB, time=115.14 memory used=4190.0MB, alloc=684.3MB, time=124.96 memory used=4534.8MB, alloc=708.3MB, time=136.17 memory used=4828.4MB, alloc=732.3MB, time=145.45 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428280272 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; F := [ 3 2 2 3 4 2 2 4 3 -20 x z + 12 y z + 6 z , 2 z - 5 x z - 9 y z , 3 x - 7 y z - 4 x y z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 4 4 3 3 2 G := [11 x y + 5 x y z - y z, 18 x + 8 z - 14 y , -4 x z - 13 x - 7 z] > Problem := [F,G]; Problem := [[ 3 2 2 3 4 2 2 4 3 -20 x z + 12 y z + 6 z , 2 z - 5 x z - 9 y z , 3 x - 7 y z - 4 x y z 3 2 3 4 4 3 3 2 ], [11 x y + 5 x y z - y z, 18 x + 8 z - 14 y , -4 x z - 13 x - 7 z] ] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.31 memory used=25.8MB, alloc=32.3MB, time=0.86 memory used=46.2MB, alloc=32.3MB, time=1.38 memory used=65.2MB, alloc=56.3MB, time=1.89 memory used=105.4MB, alloc=60.3MB, time=2.92 memory used=143.8MB, alloc=84.3MB, time=3.94 memory used=205.6MB, alloc=92.3MB, time=5.56 memory used=268.0MB, alloc=92.3MB, time=7.12 memory used=327.6MB, alloc=116.3MB, time=8.70 memory used=408.9MB, alloc=116.3MB, time=10.87 memory used=480.5MB, alloc=140.3MB, time=12.76 memory used=546.4MB, alloc=396.3MB, time=14.52 memory used=663.7MB, alloc=420.3MB, time=16.74 memory used=798.7MB, alloc=444.3MB, time=19.90 memory used=922.1MB, alloc=468.3MB, time=23.21 memory used=1037.6MB, alloc=468.3MB, time=26.20 memory used=1150.6MB, alloc=492.3MB, time=29.16 memory used=1254.6MB, alloc=492.3MB, time=31.71 memory used=1350.3MB, alloc=492.3MB, time=34.01 memory used=1435.1MB, alloc=492.3MB, time=36.09 memory used=1529.9MB, alloc=492.3MB, time=38.49 memory used=1612.6MB, alloc=516.3MB, time=40.47 memory used=1702.5MB, alloc=516.3MB, time=43.03 memory used=1777.4MB, alloc=516.3MB, time=45.31 memory used=1856.0MB, alloc=516.3MB, time=47.20 memory used=1935.0MB, alloc=540.3MB, time=49.08 memory used=1999.4MB, alloc=540.3MB, time=51.24 memory used=2062.7MB, alloc=540.3MB, time=53.44 memory used=2106.9MB, alloc=540.3MB, time=54.88 memory used=2163.9MB, alloc=540.3MB, time=56.92 memory used=2212.1MB, alloc=540.3MB, time=58.81 memory used=2412.8MB, alloc=564.3MB, time=64.15 memory used=2605.7MB, alloc=588.3MB, time=69.13 memory used=2784.9MB, alloc=612.3MB, time=74.52 memory used=2956.9MB, alloc=636.3MB, time=79.70 memory used=3115.5MB, alloc=636.3MB, time=84.25 memory used=3245.9MB, alloc=636.3MB, time=88.23 memory used=3431.7MB, alloc=636.3MB, time=92.73 memory used=3576.2MB, alloc=660.3MB, time=96.65 memory used=3708.1MB, alloc=660.3MB, time=100.44 memory used=3829.5MB, alloc=660.3MB, time=104.04 memory used=3946.9MB, alloc=660.3MB, time=107.49 memory used=4040.4MB, alloc=660.3MB, time=111.15 memory used=4155.0MB, alloc=660.3MB, time=114.68 memory used=4257.0MB, alloc=684.3MB, time=117.76 memory used=4345.3MB, alloc=684.3MB, time=121.67 memory used=4718.0MB, alloc=708.3MB, time=130.61 memory used=5100.7MB, alloc=732.3MB, time=140.33 memory used=5449.1MB, alloc=756.3MB, time=147.96 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428280572 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 4 2 4 2 2 F := [-2 y z - 8 z - 10 x y, -20 x + 18 y + 10 z, 3 x z - 7 x - 12 y z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 3 3 G := [6 y - 3 y - z , 6 y z + 7 y - 13 x, x z + 4 y z - 13 x y z] > Problem := [F,G]; Problem := [ 2 2 4 2 4 2 2 [-2 y z - 8 z - 10 x y, -20 x + 18 y + 10 z, 3 x z - 7 x - 12 y z], 3 2 2 2 2 3 3 [6 y - 3 y - z , 6 y z + 7 y - 13 x, x z + 4 y z - 13 x y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.30 memory used=26.4MB, alloc=32.3MB, time=0.88 memory used=45.6MB, alloc=56.3MB, time=1.39 memory used=87.3MB, alloc=60.3MB, time=2.43 memory used=127.7MB, alloc=60.3MB, time=3.45 memory used=168.3MB, alloc=60.3MB, time=4.37 memory used=192.0MB, alloc=60.3MB, time=4.54 memory used=241.0MB, alloc=61.5MB, time=5.40 memory used=274.4MB, alloc=61.5MB, time=5.80 memory used=321.1MB, alloc=61.5MB, time=6.55 memory used=360.5MB, alloc=93.5MB, time=7.62 memory used=424.1MB, alloc=93.5MB, time=8.46 memory used=489.8MB, alloc=93.5MB, time=9.69 memory used=549.8MB, alloc=93.5MB, time=11.23 memory used=614.5MB, alloc=117.5MB, time=12.79 memory used=682.5MB, alloc=373.5MB, time=14.45 memory used=766.1MB, alloc=397.5MB, time=16.52 memory used=875.9MB, alloc=421.5MB, time=19.21 memory used=998.4MB, alloc=421.5MB, time=21.56 memory used=1081.5MB, alloc=421.5MB, time=22.35 memory used=1149.8MB, alloc=421.5MB, time=22.82 memory used=1211.7MB, alloc=421.5MB, time=23.23 memory used=1279.2MB, alloc=421.5MB, time=23.62 memory used=1353.8MB, alloc=421.5MB, time=24.32 memory used=1424.3MB, alloc=421.5MB, time=24.78 memory used=1485.1MB, alloc=421.5MB, time=25.17 memory used=1553.9MB, alloc=421.5MB, time=25.55 memory used=1635.9MB, alloc=421.5MB, time=32.19 memory used=1703.7MB, alloc=421.5MB, time=32.64 memory used=1770.7MB, alloc=421.5MB, time=33.03 memory used=1820.6MB, alloc=421.5MB, time=33.38 memory used=1880.7MB, alloc=421.5MB, time=33.73 memory used=1952.0MB, alloc=421.5MB, time=34.10 memory used=2011.4MB, alloc=421.5MB, time=34.43 memory used=2057.6MB, alloc=421.5MB, time=34.71 memory used=2138.2MB, alloc=421.5MB, time=35.45 memory used=2204.7MB, alloc=421.5MB, time=35.88 memory used=2265.9MB, alloc=421.5MB, time=36.27 memory used=2333.0MB, alloc=421.5MB, time=36.64 memory used=2406.7MB, alloc=421.5MB, time=37.35 memory used=2477.2MB, alloc=421.5MB, time=37.80 memory used=2538.2MB, alloc=421.5MB, time=38.19 memory used=2606.6MB, alloc=421.5MB, time=38.57 memory used=2680.3MB, alloc=421.5MB, time=39.30 memory used=2751.4MB, alloc=421.5MB, time=39.76 memory used=2811.7MB, alloc=421.5MB, time=40.14 memory used=2880.2MB, alloc=421.5MB, time=40.52 memory used=2967.5MB, alloc=421.5MB, time=47.30 memory used=3045.4MB, alloc=421.5MB, time=47.88 memory used=3114.9MB, alloc=421.5MB, time=48.27 memory used=3164.1MB, alloc=421.5MB, time=48.60 memory used=3222.4MB, alloc=421.5MB, time=48.94 memory used=3291.4MB, alloc=421.5MB, time=49.29 memory used=3356.0MB, alloc=421.5MB, time=49.62 memory used=3401.0MB, alloc=421.5MB, time=49.89 memory used=3489.3MB, alloc=421.5MB, time=50.89 memory used=3650.8MB, alloc=421.5MB, time=54.22 memory used=3714.5MB, alloc=421.5MB, time=54.62 memory used=3765.4MB, alloc=421.5MB, time=54.95 memory used=3910.7MB, alloc=421.5MB, time=57.56 memory used=3977.3MB, alloc=421.5MB, time=57.97 memory used=4026.1MB, alloc=421.5MB, time=58.33 memory used=4117.6MB, alloc=421.5MB, time=59.50 memory used=4196.2MB, alloc=421.5MB, time=60.30 memory used=4263.8MB, alloc=421.5MB, time=60.74 memory used=4318.6MB, alloc=421.5MB, time=61.13 memory used=4388.0MB, alloc=421.5MB, time=61.52 memory used=4440.3MB, alloc=421.5MB, time=62.15 memory used=4528.5MB, alloc=421.5MB, time=62.70 memory used=4579.3MB, alloc=421.5MB, time=63.08 memory used=4645.3MB, alloc=421.5MB, time=63.45 memory used=4697.4MB, alloc=421.5MB, time=63.78 memory used=4793.3MB, alloc=421.5MB, time=70.49 memory used=4852.9MB, alloc=421.5MB, time=70.89 memory used=4909.0MB, alloc=421.5MB, time=71.27 memory used=4958.7MB, alloc=421.5MB, time=71.61 memory used=5017.2MB, alloc=421.5MB, time=71.97 memory used=5086.2MB, alloc=421.5MB, time=72.34 memory used=5138.7MB, alloc=421.5MB, time=72.66 memory used=5182.6MB, alloc=421.5MB, time=72.95 memory used=5261.1MB, alloc=421.5MB, time=73.77 memory used=5327.0MB, alloc=421.5MB, time=74.23 memory used=5382.3MB, alloc=421.5MB, time=74.63 memory used=5450.9MB, alloc=421.5MB, time=75.01 memory used=5505.1MB, alloc=421.5MB, time=75.71 memory used=5591.6MB, alloc=421.5MB, time=76.26 memory used=5642.6MB, alloc=421.5MB, time=76.63 memory used=5709.6MB, alloc=421.5MB, time=77.01 memory used=5760.4MB, alloc=421.5MB, time=77.35 memory used=5851.3MB, alloc=421.5MB, time=78.14 memory used=5904.2MB, alloc=421.5MB, time=78.52 memory used=5967.2MB, alloc=421.5MB, time=78.91 memory used=6024.8MB, alloc=421.5MB, time=79.27 memory used=6128.1MB, alloc=421.5MB, time=86.19 memory used=6188.4MB, alloc=421.5MB, time=86.59 memory used=6252.0MB, alloc=421.5MB, time=86.97 memory used=6298.7MB, alloc=421.5MB, time=87.31 memory used=6354.2MB, alloc=421.5MB, time=87.66 memory used=6419.2MB, alloc=421.5MB, time=88.01 memory used=6482.9MB, alloc=421.5MB, time=88.36 memory used=6524.7MB, alloc=421.5MB, time=88.65 memory used=6572.4MB, alloc=421.5MB, time=88.95 memory used=6737.4MB, alloc=421.5MB, time=91.89 memory used=6814.0MB, alloc=421.5MB, time=92.97 memory used=6864.0MB, alloc=421.5MB, time=93.31 memory used=6984.5MB, alloc=445.5MB, time=95.64 memory used=7074.6MB, alloc=445.5MB, time=96.26 memory used=7147.0MB, alloc=445.5MB, time=96.89 memory used=7264.9MB, alloc=445.5MB, time=100.07 memory used=7402.4MB, alloc=445.5MB, time=102.38 memory used=7485.7MB, alloc=445.5MB, time=103.21 memory used=7567.5MB, alloc=445.5MB, time=103.76 memory used=7633.6MB, alloc=445.5MB, time=104.22 memory used=7706.6MB, alloc=445.5MB, time=104.72 memory used=7801.4MB, alloc=445.5MB, time=105.66 memory used=7867.1MB, alloc=445.5MB, time=106.14 memory used=7941.6MB, alloc=445.5MB, time=106.60 memory used=8005.9MB, alloc=445.5MB, time=107.08 memory used=8111.2MB, alloc=445.5MB, time=114.07 memory used=8185.3MB, alloc=445.5MB, time=114.55 memory used=8240.7MB, alloc=445.5MB, time=114.98 memory used=8307.7MB, alloc=445.5MB, time=115.42 memory used=8388.6MB, alloc=445.5MB, time=115.89 memory used=8442.3MB, alloc=445.5MB, time=116.29 memory used=8512.7MB, alloc=445.5MB, time=117.01 memory used=8598.6MB, alloc=445.5MB, time=117.60 memory used=8664.5MB, alloc=445.5MB, time=118.09 memory used=8738.8MB, alloc=445.5MB, time=118.54 memory used=8832.8MB, alloc=445.5MB, time=119.53 memory used=8898.1MB, alloc=445.5MB, time=120.05 memory used=8971.1MB, alloc=445.5MB, time=120.53 memory used=9033.0MB, alloc=445.5MB, time=120.97 memory used=9135.9MB, alloc=445.5MB, time=121.97 memory used=9196.5MB, alloc=445.5MB, time=122.45 memory used=9274.7MB, alloc=445.5MB, time=122.93 memory used=9375.8MB, alloc=445.5MB, time=130.08 memory used=9452.6MB, alloc=445.5MB, time=130.62 memory used=9522.8MB, alloc=445.5MB, time=131.08 memory used=9579.9MB, alloc=445.5MB, time=131.50 memory used=9648.8MB, alloc=445.5MB, time=131.94 memory used=9731.2MB, alloc=445.5MB, time=132.39 memory used=9779.5MB, alloc=445.5MB, time=132.74 memory used=9887.9MB, alloc=445.5MB, time=134.27 memory used=10018.9MB, alloc=445.5MB, time=136.69 memory used=10080.0MB, alloc=445.5MB, time=137.14 memory used=10214.3MB, alloc=469.5MB, time=139.82 memory used=10293.1MB, alloc=469.5MB, time=140.31 memory used=10438.5MB, alloc=469.5MB, time=143.23 memory used=10574.5MB, alloc=469.5MB, time=145.31 memory used=10713.0MB, alloc=469.5MB, time=148.17 memory used=10805.5MB, alloc=469.5MB, time=150.11 memory used=10909.7MB, alloc=469.5MB, time=152.63 memory used=10995.5MB, alloc=469.5MB, time=155.10 memory used=11084.5MB, alloc=469.5MB, time=157.75 memory used=11165.5MB, alloc=493.5MB, time=160.18 memory used=11241.7MB, alloc=493.5MB, time=162.62 memory used=11319.8MB, alloc=493.5MB, time=165.12 memory used=11389.1MB, alloc=493.5MB, time=167.19 memory used=11444.9MB, alloc=493.5MB, time=168.61 memory used=11495.0MB, alloc=493.5MB, time=169.94 memory used=11550.3MB, alloc=493.5MB, time=171.43 memory used=11605.5MB, alloc=493.5MB, time=173.34 memory used=11669.6MB, alloc=493.5MB, time=175.44 memory used=11722.3MB, alloc=493.5MB, time=177.27 memory used=11773.6MB, alloc=493.5MB, time=178.83 memory used=11810.2MB, alloc=493.5MB, time=180.32 memory used=11867.9MB, alloc=493.5MB, time=181.88 memory used=11922.7MB, alloc=493.5MB, time=183.29 memory used=11971.0MB, alloc=493.5MB, time=185.19 memory used=12123.9MB, alloc=517.5MB, time=188.25 memory used=12227.3MB, alloc=517.5MB, time=189.21 memory used=12326.3MB, alloc=517.5MB, time=190.06 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428280872 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; F := [ 2 2 3 2 2 2 4 2 2 3 x z - 9 y z + 18 y z , -18 x y z - 6 z + 9 z, 9 x y - 17 y z + 20 ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [-x z - 19 y z - 8 z , -18 x y - 9 x y z - 18 x y z, 2 2 -18 x y - 2 x y - 16 x z] > Problem := [F,G]; Problem := [[ 2 2 3 2 2 2 4 2 2 3 x z - 9 y z + 18 y z , -18 x y z - 6 z + 9 z, 9 x y - 17 y z + 20 2 2 2 2 ], [-x z - 19 y z - 8 z , -18 x y - 9 x y z - 18 x y z, 2 2 -18 x y - 2 x y - 16 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.2MB, alloc=32.3MB, time=0.86 memory used=46.5MB, alloc=32.3MB, time=1.36 memory used=64.2MB, alloc=56.3MB, time=1.86 memory used=101.6MB, alloc=60.3MB, time=2.86 memory used=138.7MB, alloc=84.3MB, time=3.88 memory used=198.7MB, alloc=92.3MB, time=5.50 memory used=257.9MB, alloc=116.3MB, time=7.08 memory used=339.8MB, alloc=116.3MB, time=9.26 memory used=418.3MB, alloc=140.3MB, time=11.42 memory used=500.9MB, alloc=164.3MB, time=13.78 memory used=572.3MB, alloc=420.3MB, time=15.79 memory used=692.9MB, alloc=420.3MB, time=19.25 memory used=821.7MB, alloc=444.3MB, time=22.64 memory used=969.7MB, alloc=468.3MB, time=26.92 memory used=1141.9MB, alloc=492.3MB, time=31.62 memory used=1335.6MB, alloc=516.3MB, time=37.11 memory used=1553.0MB, alloc=540.3MB, time=43.29 memory used=1787.7MB, alloc=564.3MB, time=50.36 memory used=2019.8MB, alloc=588.3MB, time=57.45 memory used=2243.3MB, alloc=612.3MB, time=64.93 memory used=2422.9MB, alloc=636.3MB, time=71.08 memory used=2620.4MB, alloc=660.3MB, time=78.56 memory used=2806.9MB, alloc=684.3MB, time=85.31 memory used=2938.1MB, alloc=684.3MB, time=90.06 memory used=3103.2MB, alloc=684.3MB, time=96.17 memory used=3223.6MB, alloc=684.3MB, time=100.94 memory used=3333.1MB, alloc=684.3MB, time=105.18 memory used=3459.3MB, alloc=684.3MB, time=110.35 memory used=3576.4MB, alloc=708.3MB, time=115.68 memory used=3948.3MB, alloc=732.3MB, time=128.46 memory used=4339.5MB, alloc=756.3MB, time=141.21 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428281172 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 2 4 F := [15 y z + 19 y - 7 y z, 9 x y - 11 y - 16 y, 3 2 2 4 x y + 5 x y z + 18 x y z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 2 3 4 2 G := [y z + 18 y z + y, 19 x z + 16 y z + 5 y , 8 x z - 5 y + 20 y z] > Problem := [F,G]; 3 3 2 2 2 4 Problem := [[15 y z + 19 y - 7 y z, 9 x y - 11 y - 16 y, 3 2 2 4 x y + 5 x y z + 18 x y z ], 3 2 3 2 2 3 4 2 [y z + 18 y z + y, 19 x z + 16 y z + 5 y , 8 x z - 5 y + 20 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=25.8MB, alloc=32.3MB, time=0.85 memory used=44.9MB, alloc=56.3MB, time=1.34 memory used=86.4MB, alloc=60.3MB, time=2.35 memory used=127.3MB, alloc=60.3MB, time=2.99 memory used=164.9MB, alloc=60.3MB, time=3.78 memory used=208.0MB, alloc=68.3MB, time=4.87 memory used=249.3MB, alloc=92.3MB, time=5.62 memory used=318.4MB, alloc=92.3MB, time=6.98 memory used=382.7MB, alloc=92.3MB, time=8.12 memory used=445.1MB, alloc=92.3MB, time=9.44 memory used=516.1MB, alloc=372.3MB, time=10.84 memory used=610.9MB, alloc=372.3MB, time=12.83 memory used=696.9MB, alloc=372.3MB, time=13.92 memory used=760.2MB, alloc=372.3MB, time=14.90 memory used=808.9MB, alloc=372.3MB, time=15.39 memory used=862.0MB, alloc=372.3MB, time=16.50 memory used=899.0MB, alloc=372.3MB, time=16.72 memory used=936.9MB, alloc=372.3MB, time=16.92 memory used=1018.9MB, alloc=396.3MB, time=18.71 memory used=1126.2MB, alloc=396.3MB, time=21.24 memory used=1217.2MB, alloc=396.3MB, time=22.71 memory used=1319.0MB, alloc=420.3MB, time=25.24 memory used=1437.5MB, alloc=420.3MB, time=27.56 memory used=1551.8MB, alloc=444.3MB, time=30.19 memory used=1661.4MB, alloc=444.3MB, time=32.81 memory used=1802.3MB, alloc=468.3MB, time=35.24 memory used=1908.7MB, alloc=468.3MB, time=37.27 memory used=2016.1MB, alloc=468.3MB, time=38.49 memory used=2109.5MB, alloc=468.3MB, time=39.44 memory used=2194.5MB, alloc=468.3MB, time=40.12 memory used=2268.4MB, alloc=468.3MB, time=40.63 memory used=2354.8MB, alloc=468.3MB, time=41.46 memory used=2462.3MB, alloc=468.3MB, time=44.09 memory used=2553.3MB, alloc=492.3MB, time=46.89 memory used=2663.8MB, alloc=492.3MB, time=47.61 memory used=2747.7MB, alloc=492.3MB, time=48.22 memory used=2850.0MB, alloc=492.3MB, time=48.84 memory used=2951.3MB, alloc=492.3MB, time=49.44 memory used=3015.0MB, alloc=492.3MB, time=49.95 memory used=3083.8MB, alloc=492.3MB, time=50.48 memory used=3159.6MB, alloc=492.3MB, time=51.01 memory used=3238.7MB, alloc=492.3MB, time=51.53 memory used=3323.7MB, alloc=492.3MB, time=52.07 memory used=3416.3MB, alloc=492.3MB, time=52.61 memory used=3515.8MB, alloc=492.3MB, time=53.17 memory used=3621.9MB, alloc=492.3MB, time=53.74 memory used=3734.2MB, alloc=492.3MB, time=54.36 memory used=3818.5MB, alloc=492.3MB, time=54.86 memory used=3879.9MB, alloc=492.3MB, time=55.30 memory used=3943.3MB, alloc=492.3MB, time=55.73 memory used=4006.3MB, alloc=492.3MB, time=56.17 memory used=4073.2MB, alloc=492.3MB, time=56.62 memory used=4143.8MB, alloc=492.3MB, time=57.09 memory used=4217.5MB, alloc=492.3MB, time=57.54 memory used=4293.7MB, alloc=492.3MB, time=58.03 memory used=4371.6MB, alloc=492.3MB, time=58.48 memory used=4454.3MB, alloc=492.3MB, time=58.95 memory used=4540.0MB, alloc=492.3MB, time=59.40 memory used=4631.4MB, alloc=492.3MB, time=59.85 memory used=4739.9MB, alloc=492.3MB, time=60.73 memory used=4862.2MB, alloc=492.3MB, time=62.14 memory used=5075.1MB, alloc=492.3MB, time=64.40 memory used=5318.5MB, alloc=492.3MB, time=65.28 memory used=5499.6MB, alloc=492.3MB, time=70.08 memory used=5580.3MB, alloc=492.3MB, time=70.68 memory used=5680.2MB, alloc=492.3MB, time=71.33 memory used=5789.9MB, alloc=492.3MB, time=71.95 memory used=5855.4MB, alloc=492.3MB, time=72.47 memory used=5923.7MB, alloc=492.3MB, time=72.98 memory used=5999.2MB, alloc=492.3MB, time=73.54 memory used=6077.9MB, alloc=492.3MB, time=74.06 memory used=6162.8MB, alloc=492.3MB, time=74.61 memory used=6255.2MB, alloc=492.3MB, time=75.16 memory used=6354.5MB, alloc=492.3MB, time=75.71 memory used=6460.5MB, alloc=492.3MB, time=76.27 memory used=6572.7MB, alloc=492.3MB, time=76.83 memory used=6662.1MB, alloc=516.3MB, time=77.36 memory used=6732.7MB, alloc=516.3MB, time=77.80 memory used=6806.6MB, alloc=516.3MB, time=78.25 memory used=6884.1MB, alloc=516.3MB, time=78.71 memory used=6964.9MB, alloc=516.3MB, time=79.16 memory used=7050.1MB, alloc=516.3MB, time=79.63 memory used=7140.5MB, alloc=516.3MB, time=80.13 memory used=7236.9MB, alloc=516.3MB, time=80.61 memory used=7336.5MB, alloc=516.3MB, time=81.11 memory used=7444.2MB, alloc=516.3MB, time=81.59 memory used=7559.1MB, alloc=516.3MB, time=82.10 memory used=7706.7MB, alloc=516.3MB, time=83.91 memory used=7954.2MB, alloc=516.3MB, time=86.14 memory used=8183.7MB, alloc=516.3MB, time=86.89 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428281472 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 4 2 2 2 3 3 2 F := [2 x y z - 10 y + 16 y , 18 x y - 11 x, 11 y - 6 z + 12 z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 3 3 2 2 2 2 G := [13 x y z - 6 y + 2 z , -6 x y + 6 x z + 20 y , -18 x y + 11 x y] > Problem := [F,G]; 2 4 2 2 2 3 3 2 Problem := [[2 x y z - 10 y + 16 y , 18 x y - 11 x, 11 y - 6 z + 12 z ], 2 3 3 3 2 2 2 2 [13 x y z - 6 y + 2 z , -6 x y + 6 x z + 20 y , -18 x y + 11 x y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.30 memory used=27.1MB, alloc=32.3MB, time=0.91 memory used=46.4MB, alloc=56.3MB, time=1.44 memory used=87.2MB, alloc=60.3MB, time=2.48 memory used=129.3MB, alloc=68.3MB, time=3.47 memory used=171.4MB, alloc=68.3MB, time=4.47 memory used=214.0MB, alloc=92.3MB, time=5.50 memory used=281.2MB, alloc=92.3MB, time=7.07 memory used=345.6MB, alloc=92.3MB, time=8.25 memory used=386.6MB, alloc=92.3MB, time=8.77 memory used=456.5MB, alloc=92.3MB, time=10.31 memory used=516.9MB, alloc=92.3MB, time=11.34 memory used=568.5MB, alloc=116.3MB, time=11.91 memory used=637.8MB, alloc=373.3MB, time=13.81 memory used=698.8MB, alloc=373.3MB, time=14.16 memory used=744.2MB, alloc=373.3MB, time=14.42 memory used=836.3MB, alloc=373.3MB, time=15.61 memory used=941.5MB, alloc=373.3MB, time=17.88 memory used=1025.2MB, alloc=373.3MB, time=19.07 memory used=1066.1MB, alloc=373.3MB, time=19.30 memory used=1137.3MB, alloc=373.3MB, time=20.10 memory used=1236.2MB, alloc=373.3MB, time=21.70 memory used=1322.2MB, alloc=373.3MB, time=23.21 memory used=1397.8MB, alloc=373.3MB, time=24.33 memory used=1439.0MB, alloc=373.3MB, time=24.59 memory used=1483.1MB, alloc=373.3MB, time=24.83 memory used=1518.9MB, alloc=373.3MB, time=25.05 memory used=1567.9MB, alloc=373.3MB, time=25.60 memory used=1610.2MB, alloc=373.3MB, time=25.83 memory used=1643.1MB, alloc=373.3MB, time=26.04 memory used=1685.2MB, alloc=373.3MB, time=26.25 memory used=1776.4MB, alloc=373.3MB, time=29.06 memory used=1812.0MB, alloc=373.3MB, time=29.30 memory used=1856.9MB, alloc=373.3MB, time=29.54 memory used=1894.6MB, alloc=373.3MB, time=29.77 memory used=1925.1MB, alloc=373.3MB, time=29.99 memory used=1958.5MB, alloc=373.3MB, time=30.20 memory used=1994.9MB, alloc=373.3MB, time=30.41 memory used=2035.2MB, alloc=373.3MB, time=30.63 memory used=2078.4MB, alloc=373.3MB, time=30.86 memory used=2125.5MB, alloc=373.3MB, time=31.10 memory used=2174.9MB, alloc=373.3MB, time=31.32 memory used=2201.8MB, alloc=373.3MB, time=31.50 memory used=2229.4MB, alloc=397.3MB, time=31.69 memory used=2271.6MB, alloc=397.3MB, time=31.90 memory used=2316.1MB, alloc=397.3MB, time=32.11 memory used=2363.5MB, alloc=397.3MB, time=32.31 memory used=2414.1MB, alloc=397.3MB, time=32.53 memory used=2468.0MB, alloc=397.3MB, time=32.74 memory used=2525.2MB, alloc=397.3MB, time=32.96 memory used=2586.8MB, alloc=397.3MB, time=33.18 memory used=2691.9MB, alloc=397.3MB, time=34.36 memory used=2818.0MB, alloc=397.3MB, time=36.33 memory used=2906.2MB, alloc=397.3MB, time=37.94 memory used=3013.3MB, alloc=397.3MB, time=40.60 memory used=3114.7MB, alloc=421.3MB, time=43.20 memory used=3238.4MB, alloc=421.3MB, time=46.42 memory used=3356.5MB, alloc=445.3MB, time=49.55 memory used=3470.6MB, alloc=445.3MB, time=52.66 memory used=3583.7MB, alloc=469.3MB, time=55.84 memory used=3710.3MB, alloc=469.3MB, time=58.27 memory used=3861.2MB, alloc=469.3MB, time=60.44 memory used=3978.5MB, alloc=469.3MB, time=64.44 memory used=4097.1MB, alloc=469.3MB, time=67.31 memory used=4191.2MB, alloc=469.3MB, time=69.44 memory used=4282.3MB, alloc=469.3MB, time=86.81 memory used=4407.4MB, alloc=469.3MB, time=89.50 memory used=4513.4MB, alloc=469.3MB, time=91.95 memory used=4599.2MB, alloc=469.3MB, time=93.19 memory used=4718.4MB, alloc=469.3MB, time=94.41 memory used=4849.8MB, alloc=469.3MB, time=96.03 memory used=4932.1MB, alloc=469.3MB, time=96.63 memory used=5039.4MB, alloc=469.3MB, time=99.29 memory used=5162.6MB, alloc=493.3MB, time=100.22 memory used=5299.0MB, alloc=493.3MB, time=101.08 memory used=5415.2MB, alloc=493.3MB, time=101.84 memory used=5488.3MB, alloc=493.3MB, time=102.45 memory used=5564.3MB, alloc=493.3MB, time=103.05 memory used=5648.0MB, alloc=493.3MB, time=103.71 memory used=5736.6MB, alloc=493.3MB, time=104.35 memory used=5834.1MB, alloc=493.3MB, time=104.99 memory used=5937.9MB, alloc=493.3MB, time=105.65 memory used=6049.5MB, alloc=493.3MB, time=106.30 memory used=6170.4MB, alloc=493.3MB, time=106.97 memory used=6255.2MB, alloc=493.3MB, time=107.55 memory used=6322.1MB, alloc=493.3MB, time=108.09 memory used=6390.6MB, alloc=493.3MB, time=108.64 memory used=6464.0MB, alloc=493.3MB, time=109.18 memory used=6540.5MB, alloc=493.3MB, time=109.70 memory used=6622.7MB, alloc=493.3MB, time=110.23 memory used=6746.9MB, alloc=493.3MB, time=112.95 memory used=6892.4MB, alloc=493.3MB, time=113.95 memory used=7026.4MB, alloc=493.3MB, time=114.77 memory used=7136.2MB, alloc=493.3MB, time=115.51 memory used=7210.1MB, alloc=493.3MB, time=116.12 memory used=7288.3MB, alloc=493.3MB, time=116.75 memory used=7372.6MB, alloc=493.3MB, time=117.37 memory used=7463.8MB, alloc=493.3MB, time=118.00 memory used=7561.6MB, alloc=493.3MB, time=118.65 memory used=7665.7MB, alloc=493.3MB, time=119.29 memory used=7779.8MB, alloc=493.3MB, time=119.95 memory used=7902.0MB, alloc=493.3MB, time=120.61 memory used=7976.0MB, alloc=493.3MB, time=121.18 memory used=8042.4MB, alloc=493.3MB, time=121.72 memory used=8112.4MB, alloc=493.3MB, time=122.26 memory used=8185.0MB, alloc=493.3MB, time=122.80 memory used=8262.2MB, alloc=493.3MB, time=123.33 memory used=8346.1MB, alloc=493.3MB, time=123.87 memory used=8494.7MB, alloc=493.3MB, time=188.31 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428281772 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; F := [ 2 2 3 2 2 2 3 5 x y z - 13 y z - 11 z, 5 y z - 13 x y - 2 x , 19 x z + 18 z - 20 y] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 3 2 G := [4 x z - 16 x y z + 17 y z , -12 x + 9 x z + 6 z, 2 2 -15 x + 14 x z + 16 y ] > Problem := [F,G]; Problem := [[ 2 2 3 2 2 2 3 5 x y z - 13 y z - 11 z, 5 y z - 13 x y - 2 x , 19 x z + 18 z - 20 y] 2 2 2 2 2 3 2 , [4 x z - 16 x y z + 17 y z , -12 x + 9 x z + 6 z, 2 2 -15 x + 14 x z + 16 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.31 memory used=26.7MB, alloc=32.3MB, time=0.89 memory used=48.1MB, alloc=36.3MB, time=1.44 memory used=67.9MB, alloc=60.3MB, time=1.97 memory used=111.7MB, alloc=68.3MB, time=3.02 memory used=151.5MB, alloc=68.3MB, time=4.03 memory used=192.7MB, alloc=92.3MB, time=5.03 memory used=259.4MB, alloc=92.3MB, time=6.59 memory used=322.4MB, alloc=92.3MB, time=8.03 memory used=391.7MB, alloc=92.3MB, time=9.30 memory used=458.5MB, alloc=116.3MB, time=10.72 memory used=526.9MB, alloc=372.3MB, time=12.17 memory used=613.1MB, alloc=396.3MB, time=14.22 memory used=726.6MB, alloc=396.3MB, time=16.88 memory used=831.4MB, alloc=420.3MB, time=19.49 memory used=967.1MB, alloc=420.3MB, time=22.58 memory used=1100.2MB, alloc=444.3MB, time=25.67 memory used=1223.8MB, alloc=444.3MB, time=27.77 memory used=1352.6MB, alloc=444.3MB, time=30.13 memory used=1473.6MB, alloc=468.3MB, time=33.23 memory used=1591.0MB, alloc=468.3MB, time=36.08 memory used=1720.3MB, alloc=492.3MB, time=39.60 memory used=1815.2MB, alloc=492.3MB, time=41.83 memory used=1909.7MB, alloc=492.3MB, time=44.48 memory used=1991.3MB, alloc=492.3MB, time=46.55 memory used=2080.4MB, alloc=516.3MB, time=49.09 memory used=2149.2MB, alloc=516.3MB, time=51.07 memory used=2237.3MB, alloc=516.3MB, time=53.77 memory used=2315.8MB, alloc=516.3MB, time=55.72 memory used=2389.4MB, alloc=516.3MB, time=57.66 memory used=2446.2MB, alloc=516.3MB, time=59.15 memory used=2535.0MB, alloc=540.3MB, time=60.86 memory used=2609.3MB, alloc=540.3MB, time=63.15 memory used=2657.0MB, alloc=540.3MB, time=64.80 memory used=2711.5MB, alloc=540.3MB, time=66.36 memory used=2767.1MB, alloc=540.3MB, time=68.32 memory used=2968.0MB, alloc=564.3MB, time=72.70 memory used=3185.4MB, alloc=588.3MB, time=78.71 memory used=3368.0MB, alloc=612.3MB, time=83.65 memory used=3579.6MB, alloc=636.3MB, time=88.51 memory used=3737.9MB, alloc=636.3MB, time=93.23 memory used=3902.9MB, alloc=660.3MB, time=97.93 memory used=4050.6MB, alloc=660.3MB, time=102.36 memory used=4198.5MB, alloc=660.3MB, time=106.62 memory used=4331.9MB, alloc=660.3MB, time=110.37 memory used=4515.2MB, alloc=684.3MB, time=115.02 memory used=4638.9MB, alloc=684.3MB, time=118.47 memory used=4791.1MB, alloc=684.3MB, time=122.64 memory used=4904.5MB, alloc=684.3MB, time=126.54 memory used=5038.6MB, alloc=684.3MB, time=130.96 memory used=5166.4MB, alloc=684.3MB, time=134.29 memory used=5289.0MB, alloc=708.3MB, time=137.39 memory used=5416.1MB, alloc=708.3MB, time=141.92 memory used=5501.0MB, alloc=708.3MB, time=145.27 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428282072 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 3 2 F := [-15 x z + 9 x + 16 x z, -2 x y + 19 y z - 18 x y , 2 3 9 x z - 2 y + 17 x y] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 3 2 2 G := [-13 x y z + 4 x + 5 z , 17 x z + 7 y + 16, -13 x z + 20 y z - 4 y] > Problem := [F,G]; 3 2 3 3 2 Problem := [[-15 x z + 9 x + 16 x z, -2 x y + 19 y z - 18 x y , 2 3 9 x z - 2 y + 17 x y], 2 2 2 3 3 2 2 [-13 x y z + 4 x + 5 z , 17 x z + 7 y + 16, -13 x z + 20 y z - 4 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.32 memory used=24.7MB, alloc=32.3MB, time=0.85 memory used=44.8MB, alloc=56.3MB, time=1.33 memory used=90.1MB, alloc=60.6MB, time=2.08 memory used=125.5MB, alloc=60.6MB, time=3.00 memory used=156.0MB, alloc=60.6MB, time=3.35 memory used=200.7MB, alloc=68.6MB, time=4.38 memory used=260.1MB, alloc=68.9MB, time=5.19 memory used=319.5MB, alloc=68.9MB, time=6.32 memory used=371.4MB, alloc=68.9MB, time=7.52 memory used=416.3MB, alloc=68.9MB, time=8.42 memory used=458.4MB, alloc=68.9MB, time=9.19 memory used=503.2MB, alloc=68.9MB, time=10.22 memory used=528.2MB, alloc=92.9MB, time=10.64 memory used=592.9MB, alloc=92.9MB, time=12.01 memory used=666.1MB, alloc=92.9MB, time=13.40 memory used=707.9MB, alloc=92.9MB, time=13.87 memory used=742.0MB, alloc=92.9MB, time=14.06 memory used=768.2MB, alloc=92.9MB, time=14.20 memory used=815.8MB, alloc=92.9MB, time=16.91 memory used=872.2MB, alloc=92.9MB, time=17.66 memory used=902.8MB, alloc=92.9MB, time=17.85 memory used=937.6MB, alloc=92.9MB, time=18.05 memory used=969.7MB, alloc=92.9MB, time=18.21 memory used=994.4MB, alloc=92.9MB, time=18.36 memory used=1022.1MB, alloc=92.9MB, time=18.51 memory used=1053.5MB, alloc=92.9MB, time=18.66 memory used=1087.8MB, alloc=92.9MB, time=18.82 memory used=1126.5MB, alloc=92.9MB, time=18.99 memory used=1154.5MB, alloc=107.8MB, time=19.15 memory used=1165.6MB, alloc=107.8MB, time=19.26 memory used=1177.4MB, alloc=107.8MB, time=19.36 memory used=1189.6MB, alloc=107.8MB, time=19.48 memory used=1202.3MB, alloc=107.8MB, time=19.59 memory used=1283.9MB, alloc=107.8MB, time=21.19 memory used=1350.5MB, alloc=387.8MB, time=22.57 memory used=1438.9MB, alloc=387.8MB, time=24.50 memory used=1495.5MB, alloc=387.8MB, time=25.05 memory used=1553.9MB, alloc=387.8MB, time=25.75 memory used=1607.8MB, alloc=387.8MB, time=26.54 memory used=1664.1MB, alloc=387.8MB, time=27.23 memory used=1718.7MB, alloc=387.8MB, time=27.95 memory used=1759.7MB, alloc=387.8MB, time=28.21 memory used=1799.5MB, alloc=387.8MB, time=28.45 memory used=1849.6MB, alloc=387.8MB, time=28.69 memory used=1881.9MB, alloc=387.8MB, time=28.90 memory used=1914.1MB, alloc=387.8MB, time=29.10 memory used=1950.7MB, alloc=387.8MB, time=29.30 memory used=1993.4MB, alloc=387.8MB, time=29.51 memory used=2049.6MB, alloc=387.8MB, time=29.98 memory used=2092.8MB, alloc=387.8MB, time=30.19 memory used=2151.6MB, alloc=387.8MB, time=31.01 memory used=2187.1MB, alloc=387.8MB, time=31.26 memory used=2229.6MB, alloc=387.8MB, time=31.51 memory used=2277.1MB, alloc=387.8MB, time=31.75 memory used=2307.3MB, alloc=387.8MB, time=31.94 memory used=2341.0MB, alloc=387.8MB, time=32.15 memory used=2379.8MB, alloc=387.8MB, time=32.34 memory used=2425.5MB, alloc=387.8MB, time=32.56 memory used=2480.8MB, alloc=387.8MB, time=33.04 memory used=2523.9MB, alloc=387.8MB, time=33.72 memory used=2593.1MB, alloc=387.8MB, time=50.24 memory used=2635.2MB, alloc=387.8MB, time=50.50 memory used=2670.9MB, alloc=387.8MB, time=50.72 memory used=2707.6MB, alloc=387.8MB, time=50.94 memory used=2751.0MB, alloc=387.8MB, time=51.16 memory used=2797.7MB, alloc=387.8MB, time=51.38 memory used=2826.8MB, alloc=387.8MB, time=51.55 memory used=2857.6MB, alloc=387.8MB, time=51.73 memory used=2891.8MB, alloc=387.8MB, time=51.90 memory used=2931.8MB, alloc=387.8MB, time=52.08 memory used=2979.1MB, alloc=387.8MB, time=52.83 memory used=3033.3MB, alloc=387.8MB, time=53.31 memory used=3082.7MB, alloc=387.8MB, time=53.55 memory used=3140.8MB, alloc=387.8MB, time=53.83 memory used=3185.5MB, alloc=387.8MB, time=54.79 memory used=3239.0MB, alloc=387.8MB, time=55.09 memory used=3275.5MB, alloc=387.8MB, time=55.33 memory used=3321.8MB, alloc=387.8MB, time=55.58 memory used=3360.8MB, alloc=387.8MB, time=55.80 memory used=3392.4MB, alloc=387.8MB, time=56.00 memory used=3428.1MB, alloc=387.8MB, time=56.21 memory used=3470.0MB, alloc=387.8MB, time=56.42 memory used=3532.7MB, alloc=387.8MB, time=57.35 memory used=3568.3MB, alloc=387.8MB, time=57.58 memory used=3611.8MB, alloc=387.8MB, time=57.82 memory used=3657.3MB, alloc=387.8MB, time=58.07 memory used=3688.3MB, alloc=387.8MB, time=58.27 memory used=3723.2MB, alloc=387.8MB, time=58.49 memory used=3764.1MB, alloc=387.8MB, time=58.70 memory used=3832.1MB, alloc=411.8MB, time=71.96 memory used=4093.4MB, alloc=411.8MB, time=187.13 memory used=4272.0MB, alloc=411.8MB, time=187.59 memory used=4464.4MB, alloc=411.8MB, time=188.07 memory used=4733.3MB, alloc=411.8MB, time=191.05 memory used=4786.7MB, alloc=411.8MB, time=191.35 memory used=4854.6MB, alloc=411.8MB, time=191.64 memory used=4899.0MB, alloc=411.8MB, time=191.90 memory used=4951.5MB, alloc=411.8MB, time=192.15 memory used=5025.6MB, alloc=411.8MB, time=193.02 memory used=5089.0MB, alloc=411.8MB, time=193.36 memory used=5153.2MB, alloc=411.8MB, time=193.68 memory used=5206.4MB, alloc=411.8MB, time=193.94 memory used=5255.3MB, alloc=411.8MB, time=194.19 memory used=5315.4MB, alloc=411.8MB, time=194.44 memory used=5387.2MB, alloc=411.8MB, time=194.96 memory used=5467.4MB, alloc=411.8MB, time=211.80 memory used=5535.1MB, alloc=411.8MB, time=212.69 memory used=5586.0MB, alloc=411.8MB, time=212.96 memory used=5646.5MB, alloc=411.8MB, time=213.22 memory used=5707.1MB, alloc=411.8MB, time=213.47 memory used=5750.8MB, alloc=411.8MB, time=213.67 memory used=5801.6MB, alloc=411.8MB, time=213.87 memory used=5867.7MB, alloc=411.8MB, time=214.45 memory used=5965.9MB, alloc=411.8MB, time=215.85 memory used=6108.7MB, alloc=411.8MB, time=218.70 memory used=6240.4MB, alloc=411.8MB, time=223.86 memory used=6294.7MB, alloc=411.8MB, time=224.14 memory used=6353.1MB, alloc=411.8MB, time=224.39 memory used=6456.4MB, alloc=411.8MB, time=225.98 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428282372 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 3 F := [17 x z - x y - 19 x y z, 20 y z + 13 x + 16 x y, 3 2 2 -18 x y - 19 y z + 15 y z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 2 2 2 3 G := [17 x z - 12 x y + 12 y z , 7 x y z + 8 x z - 8 y , 4 2 2 13 x - 9 y z + 13 z] > Problem := [F,G]; 2 2 2 2 2 3 Problem := [[17 x z - x y - 19 x y z, 20 y z + 13 x + 16 x y, 3 2 2 3 3 2 2 -18 x y - 19 y z + 15 y z], [17 x z - 12 x y + 12 y z , 2 2 2 3 4 2 2 7 x y z + 8 x z - 8 y , 13 x - 9 y z + 13 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.30 memory used=26.0MB, alloc=32.3MB, time=0.84 memory used=46.5MB, alloc=56.3MB, time=1.30 memory used=91.8MB, alloc=60.3MB, time=2.22 memory used=139.2MB, alloc=68.3MB, time=3.26 memory used=183.5MB, alloc=68.3MB, time=4.25 memory used=228.0MB, alloc=92.3MB, time=5.23 memory used=291.0MB, alloc=92.3MB, time=6.31 memory used=346.6MB, alloc=92.3MB, time=7.08 memory used=388.2MB, alloc=92.3MB, time=7.47 memory used=421.2MB, alloc=92.3MB, time=7.63 memory used=454.0MB, alloc=92.3MB, time=7.80 memory used=489.9MB, alloc=92.3MB, time=7.94 memory used=542.4MB, alloc=92.3MB, time=10.86 memory used=574.5MB, alloc=92.3MB, time=11.03 memory used=608.5MB, alloc=92.3MB, time=11.17 memory used=637.0MB, alloc=92.3MB, time=11.29 memory used=717.4MB, alloc=92.3MB, time=13.30 memory used=803.0MB, alloc=92.3MB, time=14.42 memory used=875.9MB, alloc=92.3MB, time=15.56 memory used=948.7MB, alloc=92.3MB, time=17.50 memory used=1020.4MB, alloc=92.3MB, time=19.48 memory used=1058.2MB, alloc=92.3MB, time=19.85 memory used=1090.2MB, alloc=92.3MB, time=20.01 memory used=1118.4MB, alloc=92.3MB, time=20.15 memory used=1154.6MB, alloc=92.3MB, time=20.30 memory used=1201.9MB, alloc=92.3MB, time=23.18 memory used=1232.1MB, alloc=92.3MB, time=23.35 memory used=1264.7MB, alloc=92.3MB, time=23.51 memory used=1290.9MB, alloc=92.3MB, time=23.64 memory used=1330.6MB, alloc=92.3MB, time=24.14 memory used=1383.3MB, alloc=92.3MB, time=27.22 memory used=1412.4MB, alloc=92.3MB, time=27.36 memory used=1446.0MB, alloc=92.3MB, time=27.52 memory used=1469.8MB, alloc=92.3MB, time=27.64 memory used=1527.1MB, alloc=92.3MB, time=28.51 memory used=1596.2MB, alloc=92.3MB, time=29.85 memory used=1667.4MB, alloc=92.3MB, time=30.86 memory used=1730.3MB, alloc=116.3MB, time=32.38 memory used=1796.0MB, alloc=372.3MB, time=34.00 memory used=1879.7MB, alloc=372.3MB, time=35.64 memory used=1985.8MB, alloc=396.3MB, time=38.02 memory used=2047.6MB, alloc=396.3MB, time=38.74 memory used=2102.5MB, alloc=396.3MB, time=39.31 memory used=2190.3MB, alloc=396.3MB, time=40.30 memory used=2273.8MB, alloc=396.3MB, time=40.66 memory used=2335.5MB, alloc=396.3MB, time=41.66 memory used=2399.2MB, alloc=396.3MB, time=42.36 memory used=2470.0MB, alloc=396.3MB, time=43.65 memory used=2538.5MB, alloc=396.3MB, time=43.93 memory used=2622.7MB, alloc=396.3MB, time=44.29 memory used=2758.1MB, alloc=396.3MB, time=46.97 memory used=2842.7MB, alloc=396.3MB, time=48.02 memory used=2948.5MB, alloc=396.3MB, time=52.43 memory used=3003.3MB, alloc=396.3MB, time=52.76 memory used=3049.7MB, alloc=396.3MB, time=53.04 memory used=3109.7MB, alloc=396.3MB, time=53.32 memory used=3154.3MB, alloc=396.3MB, time=53.55 memory used=3193.9MB, alloc=396.3MB, time=53.77 memory used=3237.7MB, alloc=396.3MB, time=53.99 memory used=3285.9MB, alloc=396.3MB, time=54.22 memory used=3339.4MB, alloc=396.3MB, time=54.46 memory used=3399.2MB, alloc=396.3MB, time=54.70 memory used=3468.8MB, alloc=396.3MB, time=54.96 memory used=3618.4MB, alloc=396.3MB, time=55.64 memory used=3784.6MB, alloc=396.3MB, time=60.21 memory used=3833.7MB, alloc=396.3MB, time=60.49 memory used=3886.0MB, alloc=396.3MB, time=60.77 memory used=3944.8MB, alloc=396.3MB, time=61.06 memory used=3981.6MB, alloc=396.3MB, time=61.29 memory used=4023.5MB, alloc=396.3MB, time=61.51 memory used=4068.6MB, alloc=396.3MB, time=61.74 memory used=4119.3MB, alloc=396.3MB, time=61.97 memory used=4175.3MB, alloc=396.3MB, time=62.22 memory used=4236.2MB, alloc=396.3MB, time=62.47 memory used=4429.0MB, alloc=396.3MB, time=63.00 memory used=4601.2MB, alloc=396.3MB, time=64.56 memory used=4723.4MB, alloc=396.3MB, time=66.68 memory used=4835.0MB, alloc=420.3MB, time=68.89 memory used=4968.4MB, alloc=420.3MB, time=71.78 memory used=5104.2MB, alloc=444.3MB, time=74.68 memory used=5262.9MB, alloc=468.3MB, time=77.64 memory used=5382.8MB, alloc=468.3MB, time=80.26 memory used=5515.3MB, alloc=468.3MB, time=82.99 memory used=5637.5MB, alloc=492.3MB, time=85.50 memory used=5756.5MB, alloc=492.3MB, time=87.77 memory used=5861.7MB, alloc=516.3MB, time=89.92 memory used=5996.9MB, alloc=516.3MB, time=91.80 memory used=6123.9MB, alloc=516.3MB, time=93.78 memory used=6235.3MB, alloc=516.3MB, time=94.66 memory used=6342.3MB, alloc=516.3MB, time=95.50 memory used=6442.5MB, alloc=516.3MB, time=96.13 memory used=6648.4MB, alloc=516.3MB, time=99.54 memory used=6744.4MB, alloc=516.3MB, time=100.14 memory used=6846.5MB, alloc=516.3MB, time=100.70 memory used=6945.9MB, alloc=516.3MB, time=107.13 memory used=7066.9MB, alloc=516.3MB, time=108.35 memory used=7153.2MB, alloc=516.3MB, time=108.86 memory used=7267.0MB, alloc=516.3MB, time=109.97 memory used=7378.9MB, alloc=516.3MB, time=110.76 memory used=7493.3MB, alloc=516.3MB, time=112.44 memory used=7653.4MB, alloc=516.3MB, time=179.63 memory used=7757.9MB, alloc=516.3MB, time=180.51 memory used=7867.7MB, alloc=516.3MB, time=181.13 memory used=7939.8MB, alloc=516.3MB, time=181.64 memory used=8023.8MB, alloc=516.3MB, time=182.15 memory used=8119.8MB, alloc=516.3MB, time=182.66 memory used=8231.8MB, alloc=516.3MB, time=183.20 memory used=8445.0MB, alloc=516.3MB, time=183.96 memory used=8600.7MB, alloc=516.3MB, time=184.61 memory used=8864.9MB, alloc=516.3MB, time=187.44 memory used=8966.7MB, alloc=516.3MB, time=188.10 memory used=9044.6MB, alloc=516.3MB, time=188.69 memory used=9136.3MB, alloc=516.3MB, time=189.29 memory used=9244.1MB, alloc=516.3MB, time=189.92 memory used=9355.2MB, alloc=516.3MB, time=190.49 memory used=9422.2MB, alloc=540.3MB, time=190.99 memory used=9508.7MB, alloc=540.3MB, time=191.49 memory used=9605.4MB, alloc=540.3MB, time=192.01 memory used=9716.6MB, alloc=540.3MB, time=192.52 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428282672 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 3 2 2 2 F := [-6 x - 9 x y + 18 y , -12 y z - 10 y z - 16 y , 2 2 2 -7 x y + 10 x z - 20 x ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 4 2 G := [6 x y z - 2 x - 16 x z, 14 x y z + 12 y + 17 x z, 3 2 3 4 x y + 9 x y + 15 y ] > Problem := [F,G]; 3 2 2 3 2 2 2 Problem := [[-6 x - 9 x y + 18 y , -12 y z - 10 y z - 16 y , 2 2 2 2 2 -7 x y + 10 x z - 20 x ], [6 x y z - 2 x - 16 x z, 2 4 2 3 2 3 14 x y z + 12 y + 17 x z, 4 x y + 9 x y + 15 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.8MB, alloc=32.3MB, time=0.86 memory used=47.5MB, alloc=32.3MB, time=1.38 memory used=65.6MB, alloc=56.3MB, time=1.87 memory used=105.3MB, alloc=60.3MB, time=2.90 memory used=145.3MB, alloc=84.3MB, time=3.91 memory used=208.4MB, alloc=92.3MB, time=5.57 memory used=271.2MB, alloc=116.3MB, time=7.18 memory used=350.8MB, alloc=116.3MB, time=9.08 memory used=431.7MB, alloc=396.3MB, time=11.18 memory used=538.1MB, alloc=396.3MB, time=13.99 memory used=645.6MB, alloc=420.3MB, time=16.93 memory used=780.7MB, alloc=444.3MB, time=20.48 memory used=915.5MB, alloc=468.3MB, time=24.16 memory used=1031.2MB, alloc=468.3MB, time=27.35 memory used=1145.5MB, alloc=468.3MB, time=30.40 memory used=1270.5MB, alloc=492.3MB, time=34.27 memory used=1380.5MB, alloc=492.3MB, time=37.60 memory used=1504.5MB, alloc=492.3MB, time=41.25 memory used=1626.8MB, alloc=516.3MB, time=45.20 memory used=1724.3MB, alloc=516.3MB, time=48.39 memory used=1799.7MB, alloc=516.3MB, time=50.82 memory used=1898.3MB, alloc=516.3MB, time=54.06 memory used=1982.5MB, alloc=516.3MB, time=56.48 memory used=2070.0MB, alloc=516.3MB, time=59.29 memory used=2139.7MB, alloc=516.3MB, time=61.79 memory used=2212.3MB, alloc=516.3MB, time=64.54 memory used=2289.9MB, alloc=540.3MB, time=66.57 memory used=2367.6MB, alloc=540.3MB, time=68.67 memory used=2424.3MB, alloc=540.3MB, time=70.84 memory used=2481.1MB, alloc=540.3MB, time=73.06 memory used=2711.1MB, alloc=564.3MB, time=79.80 memory used=2918.0MB, alloc=588.3MB, time=85.53 memory used=3189.8MB, alloc=612.3MB, time=92.98 memory used=3482.9MB, alloc=636.3MB, time=99.69 memory used=3754.4MB, alloc=660.3MB, time=108.31 memory used=4016.8MB, alloc=684.3MB, time=116.77 memory used=4280.6MB, alloc=708.3MB, time=125.05 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428282972 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; F := 3 2 3 2 2 3 2 [7 x y - 6 y z - 10, 17 x z + x y z - 2 x y, 14 x z + 18 x y + 19 z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 G := [-18 z, -14 z + 4 x z - 17 z , 6 z + 2 x - 9 x y] > Problem := [F,G]; Problem := [ 3 2 3 2 2 3 2 [7 x y - 6 y z - 10, 17 x z + x y z - 2 x y, 14 x z + 18 x y + 19 z] 3 2 3 2 , [-18 z, -14 z + 4 x z - 17 z , 6 z + 2 x - 9 x y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.5MB, alloc=32.3MB, time=0.87 memory used=45.4MB, alloc=56.3MB, time=1.36 memory used=85.6MB, alloc=60.3MB, time=2.38 memory used=126.1MB, alloc=60.3MB, time=3.32 memory used=160.9MB, alloc=60.3MB, time=4.05 memory used=204.5MB, alloc=92.3MB, time=5.06 memory used=272.7MB, alloc=92.3MB, time=6.27 memory used=337.3MB, alloc=92.3MB, time=7.26 memory used=404.8MB, alloc=348.3MB, time=8.69 memory used=471.3MB, alloc=372.3MB, time=10.29 memory used=562.4MB, alloc=372.3MB, time=12.32 memory used=649.9MB, alloc=396.3MB, time=14.39 memory used=762.0MB, alloc=420.3MB, time=17.13 memory used=892.5MB, alloc=420.3MB, time=19.82 memory used=1025.6MB, alloc=444.3MB, time=22.65 memory used=1115.0MB, alloc=444.3MB, time=23.46 memory used=1202.2MB, alloc=444.3MB, time=24.51 memory used=1272.9MB, alloc=444.3MB, time=24.96 memory used=1360.4MB, alloc=444.3MB, time=25.73 memory used=1438.5MB, alloc=444.3MB, time=26.29 memory used=1517.0MB, alloc=444.3MB, time=27.31 memory used=1610.6MB, alloc=444.3MB, time=28.20 memory used=1687.3MB, alloc=444.3MB, time=28.74 memory used=1823.7MB, alloc=444.3MB, time=31.26 memory used=1927.0MB, alloc=444.3MB, time=34.05 memory used=2058.6MB, alloc=444.3MB, time=36.44 memory used=2186.8MB, alloc=444.3MB, time=38.64 memory used=2310.2MB, alloc=468.3MB, time=41.14 memory used=2409.6MB, alloc=468.3MB, time=44.09 memory used=2500.6MB, alloc=468.3MB, time=46.64 memory used=2603.7MB, alloc=492.3MB, time=49.20 memory used=2700.8MB, alloc=492.3MB, time=51.35 memory used=2810.1MB, alloc=492.3MB, time=53.39 memory used=2916.2MB, alloc=516.3MB, time=55.58 memory used=2989.6MB, alloc=516.3MB, time=57.80 memory used=3057.5MB, alloc=516.3MB, time=59.48 memory used=3104.1MB, alloc=516.3MB, time=60.86 memory used=3179.8MB, alloc=516.3MB, time=62.78 memory used=3268.4MB, alloc=516.3MB, time=64.40 memory used=3363.0MB, alloc=516.3MB, time=66.36 memory used=3417.2MB, alloc=516.3MB, time=68.10 memory used=3474.3MB, alloc=516.3MB, time=69.66 memory used=3536.1MB, alloc=516.3MB, time=71.15 memory used=3594.7MB, alloc=516.3MB, time=72.59 memory used=3797.0MB, alloc=540.3MB, time=77.81 memory used=4001.7MB, alloc=564.3MB, time=82.92 memory used=4186.4MB, alloc=588.3MB, time=85.66 memory used=4403.4MB, alloc=612.3MB, time=88.35 memory used=4588.4MB, alloc=636.3MB, time=90.74 memory used=4772.8MB, alloc=636.3MB, time=93.74 memory used=4922.5MB, alloc=636.3MB, time=96.04 memory used=5071.6MB, alloc=660.3MB, time=98.84 memory used=5209.3MB, alloc=660.3MB, time=101.09 memory used=5350.1MB, alloc=660.3MB, time=103.86 memory used=5426.6MB, alloc=660.3MB, time=105.52 memory used=5524.6MB, alloc=660.3MB, time=107.64 memory used=5639.4MB, alloc=684.3MB, time=110.03 memory used=5747.8MB, alloc=684.3MB, time=112.06 memory used=6101.5MB, alloc=708.3MB, time=118.04 memory used=6476.5MB, alloc=732.3MB, time=123.08 memory used=6672.1MB, alloc=756.3MB, time=125.14 memory used=6864.1MB, alloc=780.3MB, time=126.65 memory used=7077.2MB, alloc=780.3MB, time=129.96 memory used=7303.0MB, alloc=780.3MB, time=131.66 memory used=7519.1MB, alloc=780.3MB, time=135.00 memory used=7839.3MB, alloc=780.3MB, time=138.35 memory used=8289.5MB, alloc=804.3MB, time=143.57 memory used=8642.8MB, alloc=828.3MB, time=149.06 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428283272 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 2 2 2 F := [18 x y - 6 x y z + 11 y z , 2 x y z - 19 x z - 5 y z, 2 4 11 x y z + 16 z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 G := [12 x y - 17 x z + 7 x y z, 12 x y + 5 y - 20 z, 3 3 2 14 x z - 16 x z - 20 x z] > Problem := [F,G]; 3 2 3 2 2 2 2 Problem := [[18 x y - 6 x y z + 11 y z , 2 x y z - 19 x z - 5 y z, 2 4 3 2 2 11 x y z + 16 z ], [12 x y - 17 x z + 7 x y z, 12 x y + 5 y - 20 z, 3 3 2 14 x z - 16 x z - 20 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.18 memory used=26.4MB, alloc=32.3MB, time=0.50 memory used=47.6MB, alloc=32.3MB, time=0.82 memory used=67.1MB, alloc=56.3MB, time=1.12 memory used=108.4MB, alloc=60.3MB, time=1.75 memory used=146.0MB, alloc=84.3MB, time=2.31 memory used=209.4MB, alloc=92.3MB, time=3.24 memory used=271.1MB, alloc=116.3MB, time=4.16 memory used=351.1MB, alloc=116.3MB, time=5.34 memory used=435.2MB, alloc=140.3MB, time=6.65 memory used=520.8MB, alloc=140.3MB, time=7.92 memory used=598.0MB, alloc=396.3MB, time=9.13 memory used=702.4MB, alloc=396.3MB, time=10.52 memory used=807.6MB, alloc=420.3MB, time=11.85 memory used=936.9MB, alloc=420.3MB, time=13.40 memory used=1064.5MB, alloc=444.3MB, time=15.40 memory used=1186.5MB, alloc=444.3MB, time=16.46 memory used=1334.1MB, alloc=468.3MB, time=18.73 memory used=1457.5MB, alloc=468.3MB, time=20.66 memory used=1563.1MB, alloc=492.3MB, time=22.35 memory used=1657.2MB, alloc=492.3MB, time=23.80 memory used=1767.4MB, alloc=492.3MB, time=25.73 memory used=1844.0MB, alloc=492.3MB, time=27.04 memory used=1924.7MB, alloc=492.3MB, time=28.51 memory used=2005.5MB, alloc=516.3MB, time=29.98 memory used=2072.4MB, alloc=516.3MB, time=31.00 memory used=2149.9MB, alloc=516.3MB, time=32.28 memory used=2214.4MB, alloc=516.3MB, time=33.63 memory used=2267.2MB, alloc=516.3MB, time=34.79 memory used=2335.7MB, alloc=516.3MB, time=36.32 memory used=2387.1MB, alloc=516.3MB, time=37.41 memory used=2438.4MB, alloc=516.3MB, time=38.48 memory used=2495.5MB, alloc=516.3MB, time=39.92 memory used=2700.0MB, alloc=540.3MB, time=43.54 memory used=2912.0MB, alloc=564.3MB, time=47.22 memory used=3081.2MB, alloc=588.3MB, time=50.32 memory used=3248.2MB, alloc=612.3MB, time=53.09 memory used=3402.8MB, alloc=636.3MB, time=56.05 memory used=3576.3MB, alloc=660.3MB, time=59.30 memory used=3707.1MB, alloc=660.3MB, time=61.78 memory used=3851.1MB, alloc=660.3MB, time=64.44 memory used=3960.2MB, alloc=660.3MB, time=66.38 memory used=4150.9MB, alloc=684.3MB, time=69.30 memory used=4396.7MB, alloc=684.3MB, time=74.88 memory used=4623.4MB, alloc=684.3MB, time=80.07 memory used=4731.2MB, alloc=684.3MB, time=82.00 memory used=4847.8MB, alloc=684.3MB, time=84.07 memory used=4982.1MB, alloc=684.3MB, time=86.28 memory used=5315.1MB, alloc=708.3MB, time=91.01 memory used=5674.6MB, alloc=732.3MB, time=96.28 memory used=5985.9MB, alloc=756.3MB, time=100.47 memory used=6222.0MB, alloc=780.3MB, time=102.75 memory used=6468.0MB, alloc=780.3MB, time=109.46 memory used=6731.4MB, alloc=804.3MB, time=116.32 memory used=7185.2MB, alloc=828.3MB, time=121.27 memory used=7608.9MB, alloc=852.3MB, time=128.55 memory used=8030.8MB, alloc=876.3MB, time=135.89 memory used=8352.8MB, alloc=900.3MB, time=138.80 memory used=8701.3MB, alloc=900.3MB, time=144.16 memory used=9040.6MB, alloc=924.3MB, time=147.31 memory used=9376.5MB, alloc=924.3MB, time=151.86 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428283572 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 3 F := [-13 x y z + 6 y z, -9 x y - 13 y - 19 x, 16 y - 6 y + 14] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 2 2 G := [-3 y - 4 z - 10 x z, -18 x y z - 7 x + 17 z , 7 x y + 4 y z + 2 x] > Problem := [F,G]; 2 2 2 3 3 Problem := [[-13 x y z + 6 y z, -9 x y - 13 y - 19 x, 16 y - 6 y + 14], 3 3 2 2 2 2 [-3 y - 4 z - 10 x z, -18 x y z - 7 x + 17 z , 7 x y + 4 y z + 2 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=25.9MB, alloc=32.3MB, time=0.50 memory used=46.2MB, alloc=32.3MB, time=0.78 memory used=66.0MB, alloc=56.3MB, time=1.10 memory used=106.2MB, alloc=60.3MB, time=1.72 memory used=144.8MB, alloc=60.3MB, time=2.33 memory used=183.1MB, alloc=84.3MB, time=2.91 memory used=226.0MB, alloc=84.3MB, time=3.56 memory used=291.8MB, alloc=92.3MB, time=4.53 memory used=355.8MB, alloc=116.3MB, time=5.42 memory used=428.4MB, alloc=116.3MB, time=6.52 memory used=503.3MB, alloc=372.3MB, time=7.75 memory used=589.9MB, alloc=396.3MB, time=9.20 memory used=694.4MB, alloc=396.3MB, time=10.48 memory used=806.6MB, alloc=396.3MB, time=11.98 memory used=914.1MB, alloc=420.3MB, time=13.27 memory used=1048.0MB, alloc=420.3MB, time=15.29 memory used=1179.1MB, alloc=444.3MB, time=17.41 memory used=1323.4MB, alloc=444.3MB, time=19.52 memory used=1399.4MB, alloc=444.3MB, time=19.95 memory used=1495.0MB, alloc=444.3MB, time=20.97 memory used=1611.4MB, alloc=444.3MB, time=21.96 memory used=1731.4MB, alloc=444.3MB, time=23.25 memory used=1871.6MB, alloc=468.3MB, time=25.04 memory used=2008.3MB, alloc=468.3MB, time=27.13 memory used=2087.1MB, alloc=468.3MB, time=27.42 memory used=2192.7MB, alloc=468.3MB, time=28.71 memory used=2325.0MB, alloc=468.3MB, time=29.81 memory used=2477.5MB, alloc=468.3MB, time=31.47 memory used=2624.6MB, alloc=468.3MB, time=33.27 memory used=2770.2MB, alloc=468.3MB, time=34.74 memory used=2880.3MB, alloc=468.3MB, time=35.58 memory used=2983.5MB, alloc=468.3MB, time=38.95 memory used=3056.0MB, alloc=468.3MB, time=39.29 memory used=3136.6MB, alloc=468.3MB, time=39.62 memory used=3196.1MB, alloc=468.3MB, time=39.93 memory used=3295.8MB, alloc=468.3MB, time=42.07 memory used=3383.7MB, alloc=468.3MB, time=42.91 memory used=3463.2MB, alloc=468.3MB, time=43.23 memory used=3525.5MB, alloc=468.3MB, time=43.52 memory used=3664.6MB, alloc=468.3MB, time=45.30 memory used=3791.7MB, alloc=468.3MB, time=47.12 memory used=3950.1MB, alloc=468.3MB, time=49.60 memory used=4104.9MB, alloc=468.3MB, time=53.83 memory used=4238.6MB, alloc=492.3MB, time=55.62 memory used=4377.6MB, alloc=492.3MB, time=57.48 memory used=4481.6MB, alloc=492.3MB, time=58.04 memory used=4629.5MB, alloc=492.3MB, time=59.08 memory used=4740.0MB, alloc=492.3MB, time=60.91 memory used=4880.6MB, alloc=492.3MB, time=62.23 memory used=4978.8MB, alloc=492.3MB, time=63.53 memory used=5084.9MB, alloc=492.3MB, time=64.15 memory used=5216.6MB, alloc=492.3MB, time=68.14 memory used=5317.8MB, alloc=492.3MB, time=68.65 memory used=5410.8MB, alloc=492.3MB, time=69.06 memory used=5480.4MB, alloc=492.3MB, time=69.42 memory used=5559.6MB, alloc=492.3MB, time=69.77 memory used=5708.7MB, alloc=492.3MB, time=71.63 memory used=5842.9MB, alloc=492.3MB, time=72.78 memory used=5927.6MB, alloc=492.3MB, time=73.23 memory used=6019.7MB, alloc=516.3MB, time=74.09 memory used=6116.0MB, alloc=516.3MB, time=74.56 memory used=6209.7MB, alloc=516.3MB, time=74.99 memory used=6327.8MB, alloc=516.3MB, time=75.45 memory used=6405.8MB, alloc=516.3MB, time=75.84 memory used=6482.5MB, alloc=516.3MB, time=76.21 memory used=6565.0MB, alloc=516.3MB, time=76.59 memory used=6657.4MB, alloc=516.3MB, time=76.97 memory used=6759.3MB, alloc=516.3MB, time=77.36 memory used=6870.6MB, alloc=516.3MB, time=77.75 memory used=6994.3MB, alloc=516.3MB, time=78.13 memory used=7153.5MB, alloc=516.3MB, time=78.76 memory used=7383.6MB, alloc=516.3MB, time=118.27 memory used=7478.7MB, alloc=516.3MB, time=118.73 memory used=7577.6MB, alloc=516.3MB, time=119.18 memory used=7684.1MB, alloc=516.3MB, time=119.65 memory used=7753.6MB, alloc=516.3MB, time=120.02 memory used=7832.0MB, alloc=516.3MB, time=120.40 memory used=7916.5MB, alloc=516.3MB, time=120.82 memory used=8007.0MB, alloc=516.3MB, time=121.22 memory used=8106.8MB, alloc=516.3MB, time=121.62 memory used=8212.5MB, alloc=516.3MB, time=122.02 memory used=8328.3MB, alloc=516.3MB, time=122.43 memory used=8454.5MB, alloc=516.3MB, time=122.86 memory used=8600.1MB, alloc=516.3MB, time=123.35 memory used=8731.4MB, alloc=516.3MB, time=123.80 memory used=8873.9MB, alloc=516.3MB, time=124.29 memory used=9021.1MB, alloc=516.3MB, time=124.77 memory used=9178.6MB, alloc=516.3MB, time=125.25 memory used=9340.9MB, alloc=516.3MB, time=125.75 memory used=9512.0MB, alloc=516.3MB, time=126.27 memory used=9693.9MB, alloc=516.3MB, time=126.78 memory used=9885.7MB, alloc=516.3MB, time=127.31 memory used=10087.4MB, alloc=516.3MB, time=127.86 memory used=10298.7MB, alloc=516.3MB, time=128.41 memory used=10519.3MB, alloc=516.3MB, time=128.96 memory used=10746.7MB, alloc=516.3MB, time=129.53 memory used=10950.5MB, alloc=516.3MB, time=130.05 memory used=11116.0MB, alloc=516.3MB, time=130.54 memory used=11283.8MB, alloc=516.3MB, time=131.03 memory used=11457.0MB, alloc=516.3MB, time=131.53 memory used=11636.7MB, alloc=516.3MB, time=132.03 memory used=11821.8MB, alloc=516.3MB, time=132.54 memory used=12018.3MB, alloc=516.3MB, time=133.05 memory used=12219.0MB, alloc=516.3MB, time=133.57 memory used=12429.3MB, alloc=516.3MB, time=134.10 memory used=12647.4MB, alloc=516.3MB, time=134.64 memory used=12871.9MB, alloc=516.3MB, time=135.18 memory used=13106.3MB, alloc=516.3MB, time=135.73 memory used=13324.7MB, alloc=516.3MB, time=136.28 memory used=13516.8MB, alloc=516.3MB, time=136.78 memory used=13713.8MB, alloc=516.3MB, time=137.31 memory used=13917.4MB, alloc=516.3MB, time=137.83 memory used=14132.9MB, alloc=516.3MB, time=138.33 memory used=14416.7MB, alloc=516.3MB, time=141.57 memory used=14532.2MB, alloc=516.3MB, time=142.73 memory used=14633.2MB, alloc=516.3MB, time=143.21 memory used=14737.7MB, alloc=516.3MB, time=143.78 memory used=14836.6MB, alloc=516.3MB, time=144.18 memory used=14922.5MB, alloc=516.3MB, time=144.54 memory used=15042.5MB, alloc=516.3MB, time=146.93 memory used=15271.2MB, alloc=516.3MB, time=151.74 memory used=15360.9MB, alloc=516.3MB, time=152.13 memory used=15457.7MB, alloc=516.3MB, time=152.52 memory used=15699.1MB, alloc=516.3MB, time=153.12 memory used=15871.5MB, alloc=516.3MB, time=154.55 memory used=16027.8MB, alloc=516.3MB, time=156.09 memory used=16102.1MB, alloc=516.3MB, time=157.22 memory used=16175.8MB, alloc=516.3MB, time=158.34 memory used=16256.7MB, alloc=516.3MB, time=159.78 memory used=16351.4MB, alloc=516.3MB, time=161.33 memory used=16523.7MB, alloc=516.3MB, time=162.41 memory used=16713.2MB, alloc=516.3MB, time=164.19 memory used=16847.7MB, alloc=540.3MB, time=164.83 memory used=17011.6MB, alloc=540.3MB, time=165.53 memory used=17170.1MB, alloc=540.3MB, time=169.16 memory used=17355.5MB, alloc=540.3MB, time=170.09 memory used=17513.3MB, alloc=540.3MB, time=170.76 memory used=17674.8MB, alloc=540.3MB, time=171.42 memory used=17833.7MB, alloc=540.3MB, time=172.09 memory used=17991.2MB, alloc=540.3MB, time=172.73 memory used=18154.5MB, alloc=540.3MB, time=173.45 memory used=18349.4MB, alloc=540.3MB, time=177.09 memory used=18550.6MB, alloc=540.3MB, time=178.65 memory used=18708.4MB, alloc=540.3MB, time=179.36 memory used=18899.8MB, alloc=540.3MB, time=182.94 memory used=19088.7MB, alloc=540.3MB, time=183.97 memory used=19246.5MB, alloc=540.3MB, time=184.69 memory used=19418.8MB, alloc=540.3MB, time=187.57 memory used=19513.9MB, alloc=540.3MB, time=189.11 memory used=19686.8MB, alloc=540.3MB, time=189.95 memory used=19842.2MB, alloc=540.3MB, time=190.62 memory used=20012.0MB, alloc=540.3MB, time=191.31 memory used=20147.2MB, alloc=540.3MB, time=194.47 memory used=20350.9MB, alloc=540.3MB, time=195.73 memory used=20498.3MB, alloc=540.3MB, time=197.33 memory used=20647.6MB, alloc=540.3MB, time=198.99 memory used=20830.3MB, alloc=540.3MB, time=200.00 memory used=20985.5MB, alloc=540.3MB, time=200.69 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428283872 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 3 3 2 2 F := [-18 y + 9 x + 5 y , 13 x y - 14 x y + 2 z, 13 y z - 20 y z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; G := 3 2 2 2 2 3 3 [-4 x z - 2 x y - 20 y z, 4 x z + 4 y z - 14 x, 19 x y + 17 x - 3 x] > Problem := [F,G]; 4 3 3 3 2 2 Problem := [[-18 y + 9 x + 5 y , 13 x y - 14 x y + 2 z, 13 y z - 20 y z], 3 2 2 2 2 3 3 [-4 x z - 2 x y - 20 y z, 4 x z + 4 y z - 14 x, 19 x y + 17 x - 3 x] ] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=25.9MB, alloc=32.3MB, time=0.47 memory used=46.8MB, alloc=32.3MB, time=0.76 memory used=66.4MB, alloc=60.3MB, time=1.07 memory used=107.4MB, alloc=60.3MB, time=1.66 memory used=148.0MB, alloc=60.3MB, time=2.24 memory used=188.6MB, alloc=92.3MB, time=2.85 memory used=250.1MB, alloc=92.3MB, time=3.75 memory used=310.9MB, alloc=116.3MB, time=4.68 memory used=378.8MB, alloc=372.3MB, time=5.71 memory used=464.6MB, alloc=396.3MB, time=7.02 memory used=572.9MB, alloc=396.3MB, time=8.60 memory used=681.0MB, alloc=420.3MB, time=10.23 memory used=805.9MB, alloc=444.3MB, time=12.12 memory used=935.2MB, alloc=444.3MB, time=14.03 memory used=1056.4MB, alloc=468.3MB, time=15.96 memory used=1167.8MB, alloc=468.3MB, time=17.79 memory used=1284.5MB, alloc=492.3MB, time=19.68 memory used=1372.6MB, alloc=492.3MB, time=21.16 memory used=1469.3MB, alloc=492.3MB, time=22.63 memory used=1558.9MB, alloc=492.3MB, time=24.13 memory used=1674.8MB, alloc=492.3MB, time=24.91 memory used=1776.6MB, alloc=492.3MB, time=26.09 memory used=1853.7MB, alloc=492.3MB, time=27.45 memory used=1930.5MB, alloc=492.3MB, time=28.70 memory used=1979.8MB, alloc=492.3MB, time=29.72 memory used=2044.8MB, alloc=492.3MB, time=31.00 memory used=2110.6MB, alloc=516.3MB, time=32.25 memory used=2168.6MB, alloc=516.3MB, time=33.47 memory used=2239.9MB, alloc=516.3MB, time=34.82 memory used=2303.6MB, alloc=516.3MB, time=35.92 memory used=2354.4MB, alloc=516.3MB, time=36.98 memory used=2403.4MB, alloc=516.3MB, time=38.17 memory used=2443.1MB, alloc=516.3MB, time=39.23 memory used=2649.0MB, alloc=540.3MB, time=42.73 memory used=2839.7MB, alloc=564.3MB, time=46.00 memory used=3013.4MB, alloc=588.3MB, time=48.38 memory used=3178.6MB, alloc=612.3MB, time=50.59 memory used=3471.6MB, alloc=612.3MB, time=53.84 memory used=3736.9MB, alloc=612.3MB, time=56.21 memory used=4027.5MB, alloc=636.3MB, time=59.23 memory used=4348.5MB, alloc=636.3MB, time=62.33 memory used=4686.7MB, alloc=660.3MB, time=66.61 memory used=4976.3MB, alloc=684.3MB, time=71.45 memory used=5247.9MB, alloc=708.3MB, time=76.31 memory used=5540.3MB, alloc=732.3MB, time=81.58 memory used=5832.1MB, alloc=756.3MB, time=86.75 memory used=6059.0MB, alloc=780.3MB, time=91.20 memory used=6293.1MB, alloc=804.3MB, time=95.71 memory used=6579.8MB, alloc=828.3MB, time=100.64 memory used=6832.9MB, alloc=852.3MB, time=105.08 memory used=7101.4MB, alloc=876.3MB, time=109.96 memory used=7353.8MB, alloc=900.3MB, time=114.32 memory used=7580.2MB, alloc=924.3MB, time=118.41 memory used=7906.3MB, alloc=948.3MB, time=123.34 memory used=8115.3MB, alloc=972.3MB, time=127.83 memory used=8332.9MB, alloc=996.3MB, time=132.33 memory used=8527.5MB, alloc=1020.3MB, time=136.68 memory used=9080.3MB, alloc=1044.3MB, time=146.79 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428284172 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; F := 3 4 2 3 2 2 2 [15 x z + 5 y - 3 y z, -7 y z - 12 x z + 8 y, -15 y z + 5 y z + y z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 4 4 3 G := [-3 x z - z + 20 y, -3 x y z - 3 y z - 18 y z , 17 x + 20 z + 20 z ] > Problem := [F,G]; Problem := [ 3 4 2 3 2 2 2 [15 x z + 5 y - 3 y z, -7 y z - 12 x z + 8 y, -15 y z + 5 y z + y z] 2 2 2 4 4 3 , [-3 x z - z + 20 y, -3 x y z - 3 y z - 18 y z , 17 x + 20 z + 20 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.18 memory used=25.9MB, alloc=32.3MB, time=0.50 memory used=46.3MB, alloc=32.3MB, time=0.81 memory used=65.7MB, alloc=56.3MB, time=1.12 memory used=105.8MB, alloc=60.3MB, time=1.70 memory used=143.1MB, alloc=84.3MB, time=2.26 memory used=204.3MB, alloc=92.3MB, time=3.18 memory used=266.7MB, alloc=116.3MB, time=4.11 memory used=332.7MB, alloc=116.3MB, time=4.98 memory used=386.4MB, alloc=372.3MB, time=5.79 memory used=468.7MB, alloc=396.3MB, time=7.05 memory used=571.6MB, alloc=420.3MB, time=8.66 memory used=704.4MB, alloc=444.3MB, time=10.78 memory used=858.0MB, alloc=468.3MB, time=12.77 memory used=1032.5MB, alloc=468.3MB, time=14.96 memory used=1195.1MB, alloc=492.3MB, time=17.01 memory used=1323.3MB, alloc=492.3MB, time=19.11 memory used=1453.4MB, alloc=516.3MB, time=20.94 memory used=1589.6MB, alloc=516.3MB, time=22.16 memory used=1737.2MB, alloc=516.3MB, time=23.78 memory used=1840.1MB, alloc=540.3MB, time=25.61 memory used=1925.2MB, alloc=540.3MB, time=26.98 memory used=2024.3MB, alloc=540.3MB, time=28.80 memory used=2114.8MB, alloc=540.3MB, time=30.51 memory used=2202.5MB, alloc=540.3MB, time=32.15 memory used=2281.9MB, alloc=540.3MB, time=33.83 memory used=2358.0MB, alloc=540.3MB, time=35.20 memory used=2415.3MB, alloc=540.3MB, time=36.20 memory used=2485.9MB, alloc=564.3MB, time=37.52 memory used=2540.6MB, alloc=564.3MB, time=38.75 memory used=2603.2MB, alloc=564.3MB, time=40.01 memory used=2645.4MB, alloc=564.3MB, time=41.07 memory used=2856.4MB, alloc=588.3MB, time=44.33 memory used=3074.7MB, alloc=612.3MB, time=47.37 memory used=3248.3MB, alloc=636.3MB, time=50.08 memory used=3420.2MB, alloc=660.3MB, time=52.67 memory used=3619.2MB, alloc=684.3MB, time=56.50 memory used=3761.0MB, alloc=684.3MB, time=59.29 memory used=3893.7MB, alloc=684.3MB, time=62.18 memory used=4058.4MB, alloc=708.3MB, time=66.14 memory used=4168.1MB, alloc=708.3MB, time=68.54 memory used=4300.8MB, alloc=708.3MB, time=71.70 memory used=4434.9MB, alloc=708.3MB, time=74.85 memory used=4572.7MB, alloc=708.3MB, time=77.62 memory used=4670.9MB, alloc=708.3MB, time=79.81 memory used=4791.4MB, alloc=708.3MB, time=82.66 memory used=5101.9MB, alloc=732.3MB, time=88.13 memory used=5295.8MB, alloc=756.3MB, time=93.83 memory used=5488.1MB, alloc=756.3MB, time=95.27 memory used=5710.3MB, alloc=756.3MB, time=96.66 memory used=5868.5MB, alloc=756.3MB, time=97.92 memory used=6025.1MB, alloc=780.3MB, time=99.18 memory used=6209.1MB, alloc=780.3MB, time=100.46 memory used=6413.1MB, alloc=780.3MB, time=101.80 memory used=6639.0MB, alloc=780.3MB, time=103.09 memory used=6886.0MB, alloc=780.3MB, time=104.37 memory used=7117.9MB, alloc=780.3MB, time=105.68 memory used=7279.2MB, alloc=780.3MB, time=106.88 memory used=7426.0MB, alloc=780.3MB, time=107.99 memory used=7575.9MB, alloc=780.3MB, time=109.13 memory used=7734.5MB, alloc=780.3MB, time=110.28 memory used=7898.2MB, alloc=780.3MB, time=111.42 memory used=8072.0MB, alloc=780.3MB, time=112.57 memory used=8254.5MB, alloc=780.3MB, time=113.70 memory used=8449.2MB, alloc=780.3MB, time=114.85 memory used=8652.5MB, alloc=780.3MB, time=116.06 memory used=8870.0MB, alloc=780.3MB, time=117.23 memory used=9101.8MB, alloc=780.3MB, time=118.37 memory used=9398.0MB, alloc=780.3MB, time=121.92 memory used=9614.5MB, alloc=780.3MB, time=125.50 memory used=9861.8MB, alloc=780.3MB, time=127.01 memory used=10039.1MB, alloc=780.3MB, time=128.33 memory used=10209.1MB, alloc=780.3MB, time=129.64 memory used=10392.2MB, alloc=780.3MB, time=130.98 memory used=10596.0MB, alloc=780.3MB, time=132.26 memory used=10821.7MB, alloc=780.3MB, time=133.54 memory used=11068.5MB, alloc=780.3MB, time=134.87 memory used=11302.5MB, alloc=780.3MB, time=136.16 memory used=11462.7MB, alloc=780.3MB, time=137.29 memory used=11608.7MB, alloc=780.3MB, time=138.43 memory used=11758.2MB, alloc=780.3MB, time=139.57 memory used=11916.9MB, alloc=780.3MB, time=140.73 memory used=12080.7MB, alloc=780.3MB, time=141.92 memory used=12254.7MB, alloc=780.3MB, time=143.06 memory used=12437.3MB, alloc=780.3MB, time=144.27 memory used=12632.3MB, alloc=780.3MB, time=145.43 memory used=12836.0MB, alloc=780.3MB, time=146.64 memory used=13054.0MB, alloc=780.3MB, time=147.82 memory used=13286.3MB, alloc=780.3MB, time=149.04 memory used=13574.2MB, alloc=780.3MB, time=150.37 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428284472 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 3 F := [4 x z + 13 x z + 11 x, -2 x z - 2 y z - 10 y, 2 2 3 -20 x y z + 18 x z - 17 z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 4 2 2 G := [14 x y z - 9 x z - 8 y z , -z + 3 x z + 5 x , 2 -16 x y z - 4 x z - 12 x y] > Problem := [F,G]; 2 2 2 2 2 3 Problem := [[4 x z + 13 x z + 11 x, -2 x z - 2 y z - 10 y, 2 2 3 2 2 2 -20 x y z + 18 x z - 17 z ], [14 x y z - 9 x z - 8 y z , 4 2 2 2 -z + 3 x z + 5 x , -16 x y z - 4 x z - 12 x y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.18 memory used=26.5MB, alloc=32.3MB, time=0.51 memory used=45.6MB, alloc=56.3MB, time=0.80 memory used=86.0MB, alloc=60.3MB, time=1.39 memory used=125.5MB, alloc=60.3MB, time=1.98 memory used=165.1MB, alloc=60.3MB, time=2.38 memory used=204.1MB, alloc=84.3MB, time=2.97 memory used=248.1MB, alloc=84.3MB, time=3.61 memory used=313.5MB, alloc=92.3MB, time=4.38 memory used=378.7MB, alloc=92.3MB, time=5.24 memory used=437.0MB, alloc=116.3MB, time=6.15 memory used=518.7MB, alloc=372.3MB, time=7.33 memory used=607.2MB, alloc=396.3MB, time=8.51 memory used=708.8MB, alloc=396.3MB, time=9.92 memory used=812.2MB, alloc=420.3MB, time=11.14 memory used=937.2MB, alloc=420.3MB, time=12.77 memory used=1063.4MB, alloc=444.3MB, time=14.70 memory used=1193.4MB, alloc=468.3MB, time=16.66 memory used=1321.9MB, alloc=468.3MB, time=18.59 memory used=1475.6MB, alloc=468.3MB, time=20.56 memory used=1602.3MB, alloc=468.3MB, time=21.78 memory used=1721.6MB, alloc=492.3MB, time=23.19 memory used=1849.5MB, alloc=492.3MB, time=24.62 memory used=1984.8MB, alloc=492.3MB, time=25.87 memory used=2112.9MB, alloc=492.3MB, time=27.41 memory used=2215.7MB, alloc=492.3MB, time=28.71 memory used=2330.7MB, alloc=492.3MB, time=29.57 memory used=2440.7MB, alloc=492.3MB, time=31.00 memory used=2525.2MB, alloc=492.3MB, time=32.38 memory used=2613.0MB, alloc=492.3MB, time=33.98 memory used=2715.3MB, alloc=516.3MB, time=35.47 memory used=2794.2MB, alloc=516.3MB, time=36.71 memory used=2870.4MB, alloc=516.3MB, time=38.03 memory used=2949.4MB, alloc=516.3MB, time=39.54 memory used=3013.5MB, alloc=516.3MB, time=40.64 memory used=3092.7MB, alloc=516.3MB, time=42.18 memory used=3159.9MB, alloc=516.3MB, time=43.39 memory used=3221.7MB, alloc=516.3MB, time=44.61 memory used=3276.2MB, alloc=516.3MB, time=45.63 memory used=3332.3MB, alloc=516.3MB, time=46.85 memory used=3381.6MB, alloc=516.3MB, time=47.80 memory used=3438.2MB, alloc=516.3MB, time=49.06 memory used=3486.2MB, alloc=516.3MB, time=50.09 memory used=3690.5MB, alloc=540.3MB, time=53.46 memory used=3899.8MB, alloc=564.3MB, time=55.76 memory used=4058.8MB, alloc=564.3MB, time=57.36 memory used=4217.2MB, alloc=564.3MB, time=59.00 memory used=4414.0MB, alloc=564.3MB, time=69.27 memory used=4522.3MB, alloc=564.3MB, time=69.91 memory used=4641.5MB, alloc=564.3MB, time=70.54 memory used=4762.0MB, alloc=564.3MB, time=71.15 memory used=4851.6MB, alloc=564.3MB, time=71.67 memory used=4954.6MB, alloc=564.3MB, time=72.21 memory used=5104.7MB, alloc=588.3MB, time=97.95 memory used=5271.3MB, alloc=588.3MB, time=104.12 memory used=5391.1MB, alloc=588.3MB, time=104.78 memory used=5525.8MB, alloc=588.3MB, time=105.43 memory used=5681.1MB, alloc=588.3MB, time=106.08 memory used=5778.2MB, alloc=588.3MB, time=106.62 memory used=5886.3MB, alloc=588.3MB, time=107.20 memory used=6006.8MB, alloc=588.3MB, time=107.77 memory used=6142.5MB, alloc=588.3MB, time=108.33 memory used=6298.7MB, alloc=588.3MB, time=108.91 memory used=6508.4MB, alloc=588.3MB, time=118.27 memory used=6627.7MB, alloc=588.3MB, time=118.98 memory used=6781.7MB, alloc=588.3MB, time=119.65 memory used=6888.4MB, alloc=588.3MB, time=120.21 memory used=7003.9MB, alloc=588.3MB, time=120.78 memory used=7221.9MB, alloc=588.3MB, time=122.40 memory used=7420.6MB, alloc=588.3MB, time=127.20 memory used=7570.0MB, alloc=588.3MB, time=128.11 memory used=7802.3MB, alloc=588.3MB, time=130.73 memory used=8105.2MB, alloc=588.3MB, time=133.81 memory used=8435.3MB, alloc=588.3MB, time=140.94 memory used=8719.8MB, alloc=588.3MB, time=144.31 memory used=9005.3MB, alloc=588.3MB, time=148.22 memory used=9281.8MB, alloc=588.3MB, time=154.28 memory used=9449.7MB, alloc=588.3MB, time=155.99 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428284772 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 4 2 3 2 F := [9 x z - 11 y z, 5 x - x y z + 9 x, -16 x - 18 x y z - 14 y z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 4 2 3 2 3 G := [-4 x y z - 15 y - 15 x z, 17 x y - 13 x y z + 20 y z , 2 3 2 3 x y z + 3 x y + 8 x y ] > Problem := [F,G]; Problem := [ 2 4 2 3 2 [9 x z - 11 y z, 5 x - x y z + 9 x, -16 x - 18 x y z - 14 y z], [ 2 4 2 3 2 3 -4 x y z - 15 y - 15 x z, 17 x y - 13 x y z + 20 y z , 2 3 2 3 x y z + 3 x y + 8 x y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.19 memory used=26.7MB, alloc=32.3MB, time=0.50 memory used=46.8MB, alloc=32.3MB, time=0.79 memory used=64.4MB, alloc=56.3MB, time=1.06 memory used=103.3MB, alloc=60.3MB, time=1.62 memory used=140.2MB, alloc=60.3MB, time=2.11 memory used=179.3MB, alloc=84.3MB, time=2.67 memory used=215.9MB, alloc=84.3MB, time=3.23 memory used=277.1MB, alloc=92.3MB, time=4.13 memory used=339.9MB, alloc=92.3MB, time=4.82 memory used=402.3MB, alloc=92.3MB, time=5.58 memory used=462.0MB, alloc=116.3MB, time=6.49 memory used=538.6MB, alloc=116.3MB, time=7.64 memory used=606.6MB, alloc=396.3MB, time=8.67 memory used=710.0MB, alloc=420.3MB, time=10.26 memory used=843.9MB, alloc=420.3MB, time=12.11 memory used=975.8MB, alloc=444.3MB, time=13.94 memory used=1109.3MB, alloc=468.3MB, time=15.50 memory used=1244.1MB, alloc=468.3MB, time=17.58 memory used=1366.2MB, alloc=492.3MB, time=19.49 memory used=1450.9MB, alloc=492.3MB, time=20.67 memory used=1561.7MB, alloc=492.3MB, time=22.61 memory used=1667.7MB, alloc=492.3MB, time=24.47 memory used=1751.6MB, alloc=516.3MB, time=25.71 memory used=1860.3MB, alloc=516.3MB, time=27.41 memory used=1919.8MB, alloc=516.3MB, time=28.49 memory used=1991.3MB, alloc=516.3MB, time=29.53 memory used=2071.9MB, alloc=516.3MB, time=30.69 memory used=2213.3MB, alloc=516.3MB, time=32.19 memory used=2296.8MB, alloc=516.3MB, time=33.56 memory used=2369.0MB, alloc=516.3MB, time=34.60 memory used=2461.0MB, alloc=540.3MB, time=36.64 memory used=2525.4MB, alloc=540.3MB, time=37.63 memory used=2606.2MB, alloc=540.3MB, time=38.71 memory used=2700.2MB, alloc=540.3MB, time=40.01 memory used=2749.0MB, alloc=540.3MB, time=41.08 memory used=2794.7MB, alloc=540.3MB, time=42.07 memory used=2845.6MB, alloc=540.3MB, time=42.98 memory used=3020.3MB, alloc=540.3MB, time=44.89 memory used=3215.5MB, alloc=540.3MB, time=47.03 memory used=3427.2MB, alloc=564.3MB, time=50.36 memory used=3639.7MB, alloc=588.3MB, time=54.30 memory used=3844.5MB, alloc=612.3MB, time=57.86 memory used=4018.1MB, alloc=612.3MB, time=60.99 memory used=4210.9MB, alloc=636.3MB, time=63.74 memory used=4362.1MB, alloc=636.3MB, time=66.79 memory used=4526.5MB, alloc=636.3MB, time=69.74 memory used=4708.5MB, alloc=636.3MB, time=71.17 memory used=4889.1MB, alloc=636.3MB, time=74.10 memory used=5049.1MB, alloc=636.3MB, time=75.23 memory used=5232.9MB, alloc=636.3MB, time=76.62 memory used=5425.1MB, alloc=636.3MB, time=78.50 memory used=5594.2MB, alloc=660.3MB, time=81.01 memory used=5744.2MB, alloc=660.3MB, time=83.56 memory used=5863.0MB, alloc=660.3MB, time=86.21 memory used=6000.7MB, alloc=660.3MB, time=89.25 memory used=6112.2MB, alloc=660.3MB, time=91.67 memory used=6217.8MB, alloc=660.3MB, time=94.08 memory used=6333.6MB, alloc=684.3MB, time=96.68 memory used=6433.3MB, alloc=684.3MB, time=99.26 memory used=6784.8MB, alloc=708.3MB, time=106.20 memory used=7148.5MB, alloc=732.3MB, time=113.83 memory used=7496.0MB, alloc=756.3MB, time=120.92 memory used=7885.5MB, alloc=780.3MB, time=127.13 memory used=8268.0MB, alloc=804.3MB, time=133.06 memory used=8589.9MB, alloc=828.3MB, time=141.15 memory used=8763.3MB, alloc=852.3MB, time=142.76 memory used=9051.6MB, alloc=891.8MB, time=144.61 memory used=9194.1MB, alloc=891.8MB, time=146.13 memory used=9736.0MB, alloc=915.8MB, time=152.71 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428285072 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 4 2 2 F := [-7 x z - 17 y z - 12 y z , 16 x - x y z - 7 x z , 2 3 2 -12 x y z - 8 y - 5 y z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 2 2 G := [13 x - 7 x z + 4, -15 x y z + 5 x y - 11 x y, 2 2 4 2 -5 x z + 4 y + 11 x y] > Problem := [F,G]; 3 3 2 2 4 2 2 Problem := [[-7 x z - 17 y z - 12 y z , 16 x - x y z - 7 x z , 2 3 2 4 2 2 -12 x y z - 8 y - 5 y z], [13 x - 7 x z + 4, 2 2 2 2 4 2 -15 x y z + 5 x y - 11 x y, -5 x z + 4 y + 11 x y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=23.7MB, alloc=32.3MB, time=0.45 memory used=42.2MB, alloc=32.3MB, time=0.69 memory used=63.2MB, alloc=56.3MB, time=1.25 memory used=100.2MB, alloc=60.3MB, time=1.79 memory used=139.8MB, alloc=60.3MB, time=2.15 memory used=184.9MB, alloc=68.3MB, time=2.77 memory used=229.5MB, alloc=68.6MB, time=4.02 memory used=260.5MB, alloc=68.6MB, time=4.15 memory used=287.4MB, alloc=68.6MB, time=4.31 memory used=325.1MB, alloc=68.6MB, time=4.60 memory used=375.1MB, alloc=68.6MB, time=5.29 memory used=422.0MB, alloc=68.6MB, time=5.82 memory used=464.2MB, alloc=68.6MB, time=6.36 memory used=507.2MB, alloc=92.6MB, time=7.17 memory used=566.5MB, alloc=92.6MB, time=7.73 memory used=635.7MB, alloc=92.6MB, time=8.47 memory used=701.1MB, alloc=92.6MB, time=9.14 memory used=773.3MB, alloc=116.6MB, time=9.95 memory used=829.0MB, alloc=372.6MB, time=10.75 memory used=903.0MB, alloc=372.6MB, time=12.00 memory used=953.8MB, alloc=372.6MB, time=12.36 memory used=1008.3MB, alloc=372.6MB, time=12.72 memory used=1058.7MB, alloc=372.6MB, time=13.01 memory used=1112.7MB, alloc=372.6MB, time=13.32 memory used=1164.7MB, alloc=372.6MB, time=13.86 memory used=1216.6MB, alloc=372.6MB, time=14.17 memory used=1308.2MB, alloc=372.6MB, time=14.97 memory used=1364.2MB, alloc=372.6MB, time=15.60 memory used=1411.6MB, alloc=372.6MB, time=15.87 memory used=1512.7MB, alloc=372.6MB, time=16.64 memory used=1619.0MB, alloc=396.6MB, time=17.52 memory used=1719.0MB, alloc=396.6MB, time=18.46 memory used=1807.8MB, alloc=396.6MB, time=19.75 memory used=1881.5MB, alloc=396.6MB, time=20.28 memory used=1950.7MB, alloc=396.6MB, time=20.95 memory used=2041.3MB, alloc=396.6MB, time=21.93 memory used=2163.1MB, alloc=396.6MB, time=23.15 memory used=2231.5MB, alloc=396.6MB, time=23.66 memory used=2291.9MB, alloc=396.6MB, time=24.03 memory used=2355.4MB, alloc=396.6MB, time=24.46 memory used=2409.0MB, alloc=396.6MB, time=24.75 memory used=2470.6MB, alloc=396.6MB, time=25.40 memory used=2532.3MB, alloc=396.6MB, time=25.77 memory used=2612.5MB, alloc=396.6MB, time=26.85 memory used=2730.1MB, alloc=420.6MB, time=27.92 memory used=2857.8MB, alloc=420.6MB, time=29.62 memory used=2981.5MB, alloc=444.6MB, time=31.39 memory used=3090.6MB, alloc=468.6MB, time=32.92 memory used=3224.2MB, alloc=468.6MB, time=34.36 memory used=3298.8MB, alloc=468.6MB, time=34.63 memory used=3433.5MB, alloc=468.6MB, time=36.15 memory used=3573.9MB, alloc=468.6MB, time=39.14 memory used=3684.7MB, alloc=468.6MB, time=39.78 memory used=3778.4MB, alloc=468.6MB, time=40.44 memory used=3872.4MB, alloc=468.6MB, time=41.23 memory used=3947.9MB, alloc=468.6MB, time=41.52 memory used=4059.0MB, alloc=468.6MB, time=42.67 memory used=4131.7MB, alloc=468.6MB, time=42.97 memory used=4285.7MB, alloc=468.6MB, time=44.37 memory used=4431.0MB, alloc=468.6MB, time=49.11 memory used=4528.0MB, alloc=492.6MB, time=50.62 memory used=4670.8MB, alloc=492.6MB, time=53.38 memory used=4767.2MB, alloc=492.6MB, time=53.92 memory used=4865.0MB, alloc=492.6MB, time=54.47 memory used=4995.2MB, alloc=492.6MB, time=55.96 memory used=5077.4MB, alloc=492.6MB, time=56.28 memory used=5219.7MB, alloc=492.6MB, time=57.05 memory used=5368.5MB, alloc=492.6MB, time=57.79 memory used=5534.1MB, alloc=492.6MB, time=59.25 memory used=5643.5MB, alloc=492.6MB, time=60.52 memory used=5726.0MB, alloc=492.6MB, time=61.83 memory used=5811.2MB, alloc=492.6MB, time=62.99 memory used=5880.0MB, alloc=492.6MB, time=64.19 memory used=5992.5MB, alloc=492.6MB, time=66.73 memory used=6063.8MB, alloc=492.6MB, time=68.09 memory used=6150.1MB, alloc=516.6MB, time=69.42 memory used=6298.5MB, alloc=516.6MB, time=72.66 memory used=6377.2MB, alloc=516.6MB, time=73.83 memory used=6455.5MB, alloc=516.6MB, time=74.97 memory used=6532.9MB, alloc=516.6MB, time=75.84 memory used=6586.0MB, alloc=516.6MB, time=76.74 memory used=6673.1MB, alloc=540.6MB, time=77.67 memory used=6721.3MB, alloc=540.6MB, time=78.58 memory used=6784.1MB, alloc=540.6MB, time=79.46 memory used=7012.6MB, alloc=564.6MB, time=82.20 memory used=7269.8MB, alloc=588.6MB, time=85.03 memory used=7564.9MB, alloc=612.6MB, time=87.76 memory used=7737.7MB, alloc=636.6MB, time=90.78 memory used=7921.0MB, alloc=660.6MB, time=93.22 memory used=8138.9MB, alloc=660.6MB, time=98.60 memory used=8320.2MB, alloc=660.6MB, time=100.67 memory used=8524.9MB, alloc=660.6MB, time=102.72 memory used=8703.1MB, alloc=660.6MB, time=104.87 memory used=8891.0MB, alloc=660.6MB, time=106.80 memory used=9143.2MB, alloc=684.6MB, time=109.57 memory used=9415.3MB, alloc=684.6MB, time=113.10 memory used=9729.9MB, alloc=708.6MB, time=115.90 memory used=9995.7MB, alloc=732.6MB, time=118.77 memory used=10273.8MB, alloc=732.6MB, time=121.94 memory used=10565.9MB, alloc=756.6MB, time=124.59 memory used=10849.7MB, alloc=756.6MB, time=127.10 memory used=11111.5MB, alloc=756.6MB, time=132.98 memory used=11358.0MB, alloc=756.6MB, time=135.85 memory used=11589.2MB, alloc=756.6MB, time=138.84 memory used=11763.4MB, alloc=756.6MB, time=141.16 memory used=11943.6MB, alloc=780.6MB, time=144.07 memory used=12129.4MB, alloc=780.6MB, time=146.43 memory used=12328.9MB, alloc=780.6MB, time=148.85 memory used=12511.8MB, alloc=804.6MB, time=150.97 memory used=12640.6MB, alloc=804.6MB, time=153.34 memory used=12865.1MB, alloc=804.6MB, time=155.39 memory used=13132.7MB, alloc=804.6MB, time=158.26 memory used=13383.5MB, alloc=804.6MB, time=161.03 memory used=13639.7MB, alloc=804.6MB, time=163.37 memory used=13758.7MB, alloc=804.6MB, time=165.39 memory used=13903.0MB, alloc=804.6MB, time=167.42 memory used=14088.0MB, alloc=804.6MB, time=170.54 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428285372 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 3 3 F := [-7 x - 16 x y z + 19 x y, -18 x y - 13 x z + x y , 2 3 2 -x y z + 16 x z - x ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 3 2 2 2 G := [-15 x z - 17 y z - 16 z, -7 x y + 8 x y + 20 x y z, 4 3 2 2 x - 11 x z - 11 x z] > Problem := [F,G]; 3 3 3 3 Problem := [[-7 x - 16 x y z + 19 x y, -18 x y - 13 x z + x y , 2 3 2 3 3 -x y z + 16 x z - x ], [-15 x z - 17 y z - 16 z, 3 2 2 2 4 3 2 -7 x y + 8 x y + 20 x y z, 2 x - 11 x z - 11 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.18 memory used=26.8MB, alloc=32.3MB, time=0.51 memory used=47.4MB, alloc=32.3MB, time=0.80 memory used=66.7MB, alloc=56.3MB, time=1.09 memory used=108.2MB, alloc=60.3MB, time=1.65 memory used=146.4MB, alloc=60.3MB, time=2.16 memory used=187.6MB, alloc=92.3MB, time=2.77 memory used=251.2MB, alloc=92.3MB, time=3.64 memory used=312.8MB, alloc=116.3MB, time=4.53 memory used=379.4MB, alloc=372.3MB, time=5.48 memory used=470.0MB, alloc=396.3MB, time=6.63 memory used=551.9MB, alloc=396.3MB, time=7.34 memory used=667.3MB, alloc=420.3MB, time=8.83 memory used=806.7MB, alloc=444.3MB, time=10.68 memory used=948.4MB, alloc=444.3MB, time=12.30 memory used=1082.7MB, alloc=468.3MB, time=14.22 memory used=1209.6MB, alloc=468.3MB, time=16.08 memory used=1318.4MB, alloc=468.3MB, time=17.59 memory used=1452.1MB, alloc=492.3MB, time=20.04 memory used=1595.5MB, alloc=492.3MB, time=21.36 memory used=1736.0MB, alloc=492.3MB, time=22.71 memory used=1864.2MB, alloc=492.3MB, time=24.26 memory used=1994.2MB, alloc=492.3MB, time=25.44 memory used=2089.0MB, alloc=492.3MB, time=26.61 memory used=2237.4MB, alloc=492.3MB, time=27.82 memory used=2364.7MB, alloc=516.3MB, time=29.10 memory used=2450.9MB, alloc=516.3MB, time=30.49 memory used=2516.5MB, alloc=516.3MB, time=31.60 memory used=2591.2MB, alloc=516.3MB, time=32.86 memory used=2664.0MB, alloc=516.3MB, time=33.97 memory used=2743.4MB, alloc=516.3MB, time=35.11 memory used=2830.0MB, alloc=516.3MB, time=36.51 memory used=2890.4MB, alloc=516.3MB, time=37.68 memory used=2951.2MB, alloc=516.3MB, time=38.83 memory used=3047.8MB, alloc=540.3MB, time=39.99 memory used=3187.8MB, alloc=540.3MB, time=41.50 memory used=3291.1MB, alloc=540.3MB, time=41.98 memory used=3416.0MB, alloc=540.3MB, time=43.10 memory used=3495.3MB, alloc=540.3MB, time=44.25 memory used=3623.7MB, alloc=540.3MB, time=45.41 memory used=3765.6MB, alloc=540.3MB, time=47.13 memory used=3841.7MB, alloc=540.3MB, time=49.98 memory used=3962.9MB, alloc=564.3MB, time=51.58 memory used=4234.6MB, alloc=564.3MB, time=55.06 memory used=4494.2MB, alloc=588.3MB, time=58.87 memory used=5057.6MB, alloc=612.3MB, time=69.21 memory used=5178.3MB, alloc=637.4MB, time=70.75 memory used=5179.4MB, alloc=662.5MB, time=71.19 memory used=5180.5MB, alloc=663.6MB, time=71.65 memory used=5181.6MB, alloc=664.6MB, time=72.06 memory used=5182.7MB, alloc=661.4MB, time=72.53 memory used=5399.4MB, alloc=660.3MB, time=84.07 memory used=5590.3MB, alloc=660.3MB, time=84.70 memory used=5771.3MB, alloc=660.3MB, time=85.48 memory used=5909.5MB, alloc=660.3MB, time=86.09 memory used=6065.9MB, alloc=660.3MB, time=86.70 memory used=6436.8MB, alloc=660.3MB, time=97.28 memory used=6628.0MB, alloc=660.3MB, time=97.91 memory used=6799.6MB, alloc=660.3MB, time=98.60 memory used=6938.1MB, alloc=660.3MB, time=99.22 memory used=7098.0MB, alloc=660.3MB, time=99.82 memory used=7873.7MB, alloc=660.3MB, time=105.25 memory used=8078.4MB, alloc=660.3MB, time=107.01 memory used=8341.1MB, alloc=660.3MB, time=108.96 memory used=8625.2MB, alloc=684.3MB, time=110.47 memory used=8884.6MB, alloc=684.3MB, time=112.12 memory used=8915.6MB, alloc=685.4MB, time=113.04 memory used=8916.7MB, alloc=686.5MB, time=113.49 memory used=8917.8MB, alloc=687.6MB, time=113.93 memory used=8918.9MB, alloc=688.6MB, time=114.35 memory used=8919.9MB, alloc=685.4MB, time=114.79 memory used=9618.9MB, alloc=684.3MB, time=120.76 memory used=9831.8MB, alloc=684.3MB, time=122.65 memory used=10035.4MB, alloc=684.3MB, time=124.54 memory used=10333.1MB, alloc=708.3MB, time=126.25 memory used=10655.2MB, alloc=732.3MB, time=127.80 memory used=10844.5MB, alloc=733.4MB, time=129.52 memory used=10845.6MB, alloc=734.5MB, time=129.96 memory used=10846.7MB, alloc=735.6MB, time=130.40 memory used=10847.7MB, alloc=736.6MB, time=130.86 memory used=10848.8MB, alloc=733.4MB, time=131.32 memory used=11051.5MB, alloc=732.3MB, time=135.64 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428285672 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 4 3 3 2 2 F := [-4 x y + 16 y + 16 y, -3 x z - 7 y z - 8, -5 x y z + 4 z + 5] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 2 2 2 2 2 2 G := [-10 y + 13 x y z, 18 x y - 13 y z + 15 y , -10 y z - 8 y z - 12 y ] > Problem := [F,G]; Problem := [ 3 4 3 3 2 2 [-4 x y + 16 y + 16 y, -3 x z - 7 y z - 8, -5 x y z + 4 z + 5], 4 3 2 2 2 2 2 2 [-10 y + 13 x y z, 18 x y - 13 y z + 15 y , -10 y z - 8 y z - 12 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.7MB, alloc=32.3MB, time=0.51 memory used=46.2MB, alloc=56.3MB, time=0.81 memory used=86.5MB, alloc=60.3MB, time=1.36 memory used=131.1MB, alloc=68.3MB, time=1.88 memory used=178.0MB, alloc=68.3MB, time=2.45 memory used=212.6MB, alloc=68.3MB, time=2.69 memory used=242.9MB, alloc=68.3MB, time=3.33 memory used=264.5MB, alloc=68.3MB, time=3.42 memory used=307.5MB, alloc=92.3MB, time=3.95 memory used=396.0MB, alloc=92.3MB, time=5.00 memory used=463.1MB, alloc=92.3MB, time=5.84 memory used=541.1MB, alloc=92.3MB, time=6.55 memory used=612.6MB, alloc=92.4MB, time=8.34 memory used=642.5MB, alloc=92.4MB, time=8.46 memory used=670.1MB, alloc=92.4MB, time=8.57 memory used=696.6MB, alloc=92.4MB, time=8.67 memory used=728.1MB, alloc=116.4MB, time=8.78 memory used=771.7MB, alloc=116.4MB, time=8.90 memory used=835.3MB, alloc=116.4MB, time=10.84 memory used=887.3MB, alloc=116.4MB, time=11.02 memory used=927.3MB, alloc=116.4MB, time=11.14 memory used=974.5MB, alloc=116.4MB, time=11.28 memory used=1030.0MB, alloc=116.4MB, time=11.42 memory used=1064.3MB, alloc=116.4MB, time=11.52 memory used=1102.1MB, alloc=116.4MB, time=11.62 memory used=1148.9MB, alloc=116.4MB, time=11.77 memory used=1218.2MB, alloc=372.4MB, time=12.76 memory used=1307.1MB, alloc=396.4MB, time=14.05 memory used=1418.5MB, alloc=396.4MB, time=15.52 memory used=1538.6MB, alloc=420.4MB, time=16.97 memory used=1647.4MB, alloc=420.4MB, time=18.68 memory used=1766.8MB, alloc=420.4MB, time=20.02 memory used=1891.4MB, alloc=420.4MB, time=21.35 memory used=1970.0MB, alloc=420.4MB, time=21.96 memory used=2054.6MB, alloc=420.4MB, time=22.80 memory used=2148.2MB, alloc=444.4MB, time=24.63 memory used=2228.0MB, alloc=444.4MB, time=24.96 memory used=2318.9MB, alloc=444.4MB, time=26.41 memory used=2421.0MB, alloc=444.4MB, time=26.92 memory used=2527.4MB, alloc=444.4MB, time=32.61 memory used=2598.2MB, alloc=444.4MB, time=32.88 memory used=2669.1MB, alloc=444.4MB, time=33.11 memory used=2804.6MB, alloc=444.4MB, time=34.50 memory used=2953.9MB, alloc=444.4MB, time=36.22 memory used=3119.2MB, alloc=444.4MB, time=37.78 memory used=3294.1MB, alloc=444.4MB, time=39.56 memory used=3406.4MB, alloc=468.4MB, time=41.13 memory used=3510.5MB, alloc=468.4MB, time=42.58 memory used=3645.4MB, alloc=468.4MB, time=43.85 memory used=3720.9MB, alloc=468.4MB, time=44.18 memory used=3818.3MB, alloc=468.4MB, time=44.64 memory used=3925.4MB, alloc=468.4MB, time=48.21 memory used=3999.4MB, alloc=468.4MB, time=48.55 memory used=4081.1MB, alloc=468.4MB, time=48.86 memory used=4146.8MB, alloc=468.4MB, time=49.24 memory used=4242.7MB, alloc=468.4MB, time=49.65 memory used=4328.7MB, alloc=468.4MB, time=50.15 memory used=4404.7MB, alloc=468.4MB, time=50.48 memory used=4511.9MB, alloc=468.4MB, time=54.08 memory used=4583.1MB, alloc=468.4MB, time=54.40 memory used=4656.0MB, alloc=468.4MB, time=54.70 memory used=4742.7MB, alloc=468.4MB, time=55.12 memory used=4818.4MB, alloc=468.4MB, time=55.44 memory used=4910.5MB, alloc=468.4MB, time=55.93 memory used=5015.0MB, alloc=468.4MB, time=59.37 memory used=5098.4MB, alloc=468.4MB, time=59.73 memory used=5180.8MB, alloc=468.4MB, time=60.05 memory used=5251.1MB, alloc=468.4MB, time=60.41 memory used=5354.4MB, alloc=468.4MB, time=60.99 memory used=5493.3MB, alloc=468.4MB, time=74.48 memory used=5570.6MB, alloc=468.4MB, time=74.84 memory used=5637.9MB, alloc=468.4MB, time=75.16 memory used=5723.6MB, alloc=468.4MB, time=75.50 memory used=5795.9MB, alloc=492.4MB, time=75.81 memory used=5867.2MB, alloc=492.4MB, time=76.11 memory used=5947.7MB, alloc=492.4MB, time=76.41 memory used=6039.2MB, alloc=492.4MB, time=76.72 memory used=6144.1MB, alloc=492.4MB, time=77.04 memory used=6329.1MB, alloc=492.4MB, time=77.69 memory used=6473.0MB, alloc=492.4MB, time=90.92 memory used=6559.1MB, alloc=492.4MB, time=91.31 memory used=6660.5MB, alloc=492.4MB, time=91.70 memory used=6747.4MB, alloc=492.4MB, time=92.04 memory used=6820.4MB, alloc=492.4MB, time=92.36 memory used=6902.3MB, alloc=492.4MB, time=92.66 memory used=6996.6MB, alloc=492.4MB, time=92.98 memory used=7104.4MB, alloc=492.4MB, time=93.30 memory used=7279.3MB, alloc=492.4MB, time=94.38 memory used=7377.9MB, alloc=492.4MB, time=94.81 memory used=7468.3MB, alloc=492.4MB, time=95.18 memory used=7545.3MB, alloc=492.4MB, time=95.53 memory used=7637.5MB, alloc=492.4MB, time=95.89 memory used=7748.9MB, alloc=492.4MB, time=96.25 memory used=7857.3MB, alloc=492.4MB, time=97.15 memory used=7950.4MB, alloc=492.4MB, time=97.58 memory used=8056.3MB, alloc=492.4MB, time=97.97 memory used=8128.5MB, alloc=492.4MB, time=98.32 memory used=8214.0MB, alloc=492.4MB, time=98.67 memory used=8316.4MB, alloc=492.4MB, time=99.03 memory used=8409.9MB, alloc=492.4MB, time=99.36 memory used=8554.3MB, alloc=492.4MB, time=170.45 memory used=8673.2MB, alloc=492.4MB, time=179.44 memory used=8764.1MB, alloc=492.4MB, time=179.82 memory used=8845.1MB, alloc=492.4MB, time=180.19 memory used=8944.6MB, alloc=492.4MB, time=180.56 memory used=9051.0MB, alloc=492.4MB, time=180.94 memory used=9114.6MB, alloc=492.4MB, time=181.26 memory used=9184.8MB, alloc=492.4MB, time=181.58 memory used=9259.4MB, alloc=492.4MB, time=181.91 memory used=9340.2MB, alloc=492.4MB, time=182.25 memory used=9427.0MB, alloc=492.4MB, time=182.57 memory used=9519.5MB, alloc=492.4MB, time=182.92 memory used=9619.2MB, alloc=492.4MB, time=183.25 memory used=9725.4MB, alloc=492.4MB, time=183.60 memory used=9841.3MB, alloc=492.4MB, time=183.98 memory used=10002.7MB, alloc=492.4MB, time=184.51 memory used=10145.5MB, alloc=492.4MB, time=184.93 memory used=10304.9MB, alloc=492.4MB, time=185.37 memory used=10542.3MB, alloc=492.4MB, time=186.79 memory used=10685.9MB, alloc=492.4MB, time=188.10 memory used=10809.6MB, alloc=492.4MB, time=188.92 memory used=10973.1MB, alloc=492.4MB, time=190.22 memory used=11084.0MB, alloc=492.4MB, time=191.55 memory used=11204.7MB, alloc=492.4MB, time=194.13 memory used=11289.9MB, alloc=492.4MB, time=194.53 memory used=11368.8MB, alloc=492.4MB, time=194.87 memory used=11444.6MB, alloc=492.4MB, time=195.20 memory used=11575.1MB, alloc=492.4MB, time=198.96 memory used=11655.4MB, alloc=492.4MB, time=199.35 memory used=11738.9MB, alloc=492.4MB, time=199.71 memory used=11812.8MB, alloc=492.4MB, time=200.05 memory used=11925.3MB, alloc=492.4MB, time=200.70 memory used=12055.9MB, alloc=492.4MB, time=208.19 memory used=12179.8MB, alloc=492.4MB, time=216.55 memory used=12256.7MB, alloc=492.4MB, time=216.94 memory used=12346.9MB, alloc=492.4MB, time=217.32 memory used=12435.9MB, alloc=492.4MB, time=217.66 memory used=12500.0MB, alloc=492.4MB, time=217.98 memory used=12571.5MB, alloc=492.4MB, time=218.31 memory used=12652.8MB, alloc=492.4MB, time=218.63 memory used=12744.8MB, alloc=492.4MB, time=219.00 memory used=12889.9MB, alloc=492.4MB, time=219.47 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428285972 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; F := [ 2 2 3 2 3 2 3 3 3 -3 x z - 8 x + 6 z, -14 x y z - 8 y z - 3 x z , 6 x z - 6 x - 16 y ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 2 3 G := [-19 z + 3 x + 16 x, 3 x y - 16 y z + 3 x , -13 x z - x y + 17 x] > Problem := [F,G]; Problem := [[ 2 2 3 2 3 2 3 3 3 -3 x z - 8 x + 6 z, -14 x y z - 8 y z - 3 x z , 6 x z - 6 x - 16 y ] 3 2 2 2 2 2 3 , [-19 z + 3 x + 16 x, 3 x y - 16 y z + 3 x , -13 x z - x y + 17 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.18 memory used=24.8MB, alloc=32.3MB, time=0.46 memory used=46.5MB, alloc=37.9MB, time=0.73 memory used=66.4MB, alloc=37.9MB, time=0.94 memory used=85.1MB, alloc=37.9MB, time=1.09 memory used=105.9MB, alloc=37.9MB, time=1.33 memory used=126.8MB, alloc=61.9MB, time=1.59 memory used=162.5MB, alloc=61.9MB, time=2.06 memory used=207.3MB, alloc=69.9MB, time=2.62 memory used=252.9MB, alloc=69.9MB, time=2.96 memory used=289.9MB, alloc=69.9MB, time=3.16 memory used=312.6MB, alloc=69.9MB, time=3.23 memory used=344.2MB, alloc=69.9MB, time=3.36 memory used=375.3MB, alloc=69.9MB, time=3.53 memory used=399.4MB, alloc=69.9MB, time=3.61 memory used=430.6MB, alloc=69.9MB, time=3.74 memory used=461.9MB, alloc=69.9MB, time=3.86 memory used=497.9MB, alloc=69.9MB, time=4.57 memory used=526.1MB, alloc=69.9MB, time=4.67 memory used=553.0MB, alloc=69.9MB, time=4.75 memory used=571.2MB, alloc=69.9MB, time=4.82 memory used=593.8MB, alloc=69.9MB, time=4.89 memory used=645.7MB, alloc=69.9MB, time=5.76 memory used=668.1MB, alloc=69.9MB, time=5.84 memory used=696.5MB, alloc=69.9MB, time=5.92 memory used=715.7MB, alloc=69.9MB, time=5.98 memory used=735.5MB, alloc=69.9MB, time=6.06 memory used=757.9MB, alloc=69.9MB, time=6.13 memory used=784.0MB, alloc=69.9MB, time=6.20 memory used=825.3MB, alloc=69.9MB, time=6.57 memory used=878.8MB, alloc=69.9MB, time=8.72 memory used=926.5MB, alloc=69.9MB, time=9.84 memory used=967.1MB, alloc=69.9MB, time=10.85 memory used=986.8MB, alloc=69.9MB, time=10.92 memory used=1016.5MB, alloc=69.9MB, time=11.21 memory used=1037.8MB, alloc=69.9MB, time=11.29 memory used=1086.6MB, alloc=69.9MB, time=11.95 memory used=1133.9MB, alloc=69.9MB, time=13.38 memory used=1167.9MB, alloc=93.9MB, time=13.77 memory used=1226.4MB, alloc=93.9MB, time=14.47 memory used=1286.9MB, alloc=93.9MB, time=15.21 memory used=1346.3MB, alloc=93.9MB, time=15.83 memory used=1410.1MB, alloc=93.9MB, time=16.52 memory used=1471.9MB, alloc=93.9MB, time=17.24 memory used=1514.0MB, alloc=93.9MB, time=17.42 memory used=1557.4MB, alloc=93.9MB, time=17.72 memory used=1606.8MB, alloc=93.9MB, time=18.02 memory used=1664.4MB, alloc=93.9MB, time=18.52 memory used=1724.5MB, alloc=93.9MB, time=19.21 memory used=1785.5MB, alloc=373.9MB, time=20.06 memory used=1840.5MB, alloc=373.9MB, time=20.34 memory used=1895.1MB, alloc=373.9MB, time=20.60 memory used=1946.1MB, alloc=373.9MB, time=20.84 memory used=1995.5MB, alloc=373.9MB, time=21.05 memory used=2054.5MB, alloc=373.9MB, time=21.49 memory used=2103.8MB, alloc=373.9MB, time=21.72 memory used=2160.6MB, alloc=373.9MB, time=22.13 memory used=2218.9MB, alloc=373.9MB, time=22.48 memory used=2259.6MB, alloc=373.9MB, time=22.62 memory used=2316.4MB, alloc=373.9MB, time=23.06 memory used=2356.7MB, alloc=373.9MB, time=23.20 memory used=2433.3MB, alloc=373.9MB, time=24.21 memory used=2473.9MB, alloc=373.9MB, time=24.37 memory used=2526.6MB, alloc=373.9MB, time=24.67 memory used=2600.7MB, alloc=373.9MB, time=25.48 memory used=2655.0MB, alloc=373.9MB, time=25.94 memory used=2695.0MB, alloc=373.9MB, time=26.08 memory used=2766.1MB, alloc=373.9MB, time=26.70 memory used=2802.1MB, alloc=373.9MB, time=26.85 memory used=2846.9MB, alloc=373.9MB, time=27.01 memory used=2899.9MB, alloc=373.9MB, time=27.19 memory used=2931.6MB, alloc=373.9MB, time=27.33 memory used=2965.7MB, alloc=373.9MB, time=27.47 memory used=3002.7MB, alloc=373.9MB, time=27.62 memory used=3044.1MB, alloc=373.9MB, time=27.75 memory used=3091.1MB, alloc=373.9MB, time=27.89 memory used=3158.1MB, alloc=373.9MB, time=28.48 memory used=3204.3MB, alloc=373.9MB, time=28.66 memory used=3245.6MB, alloc=373.9MB, time=28.82 memory used=3296.8MB, alloc=373.9MB, time=29.00 memory used=3337.5MB, alloc=373.9MB, time=29.14 memory used=3370.4MB, alloc=373.9MB, time=29.28 memory used=3407.3MB, alloc=373.9MB, time=29.41 memory used=3448.0MB, alloc=373.9MB, time=29.55 memory used=3493.7MB, alloc=373.9MB, time=29.68 memory used=3560.0MB, alloc=373.9MB, time=33.60 memory used=3639.6MB, alloc=373.9MB, time=59.50 memory used=3731.8MB, alloc=373.9MB, time=60.45 memory used=3775.2MB, alloc=373.9MB, time=60.62 memory used=3816.2MB, alloc=373.9MB, time=60.79 memory used=3866.8MB, alloc=373.9MB, time=60.97 memory used=3901.3MB, alloc=373.9MB, time=61.11 memory used=3932.2MB, alloc=373.9MB, time=61.25 memory used=3966.1MB, alloc=373.9MB, time=61.39 memory used=4003.0MB, alloc=373.9MB, time=61.54 memory used=4042.9MB, alloc=373.9MB, time=61.69 memory used=4085.7MB, alloc=373.9MB, time=61.84 memory used=4131.4MB, alloc=373.9MB, time=62.00 memory used=4180.0MB, alloc=373.9MB, time=62.15 memory used=4231.3MB, alloc=373.9MB, time=62.30 memory used=4271.1MB, alloc=373.9MB, time=62.43 memory used=4298.0MB, alloc=373.9MB, time=62.55 memory used=4326.1MB, alloc=397.9MB, time=62.70 memory used=4368.4MB, alloc=397.9MB, time=62.83 memory used=4413.2MB, alloc=397.9MB, time=62.97 memory used=4459.7MB, alloc=397.9MB, time=63.11 memory used=4509.3MB, alloc=397.9MB, time=63.25 memory used=4560.1MB, alloc=397.9MB, time=63.39 memory used=4613.5MB, alloc=397.9MB, time=63.53 memory used=4670.6MB, alloc=397.9MB, time=63.66 memory used=4730.6MB, alloc=397.9MB, time=63.81 memory used=4794.2MB, alloc=397.9MB, time=63.96 memory used=4861.2MB, alloc=397.9MB, time=64.11 memory used=4930.6MB, alloc=397.9MB, time=64.26 memory used=5074.4MB, alloc=397.9MB, time=65.04 memory used=5140.5MB, alloc=397.9MB, time=65.26 memory used=5204.3MB, alloc=397.9MB, time=65.48 memory used=5265.9MB, alloc=397.9MB, time=65.66 memory used=5313.7MB, alloc=397.9MB, time=65.82 memory used=5368.7MB, alloc=397.9MB, time=65.99 memory used=5433.2MB, alloc=397.9MB, time=66.17 memory used=5525.0MB, alloc=397.9MB, time=66.87 memory used=5579.3MB, alloc=397.9MB, time=67.09 memory used=5650.5MB, alloc=397.9MB, time=67.30 memory used=5700.5MB, alloc=397.9MB, time=67.48 memory used=5750.8MB, alloc=397.9MB, time=67.64 memory used=5808.9MB, alloc=397.9MB, time=67.80 memory used=5878.5MB, alloc=397.9MB, time=68.01 memory used=6006.5MB, alloc=397.9MB, time=98.06 memory used=6107.1MB, alloc=397.9MB, time=98.87 memory used=6164.5MB, alloc=397.9MB, time=99.07 memory used=6230.7MB, alloc=397.9MB, time=99.28 memory used=6275.0MB, alloc=397.9MB, time=99.45 memory used=6323.9MB, alloc=397.9MB, time=99.63 memory used=6378.5MB, alloc=397.9MB, time=99.80 memory used=6439.3MB, alloc=397.9MB, time=99.98 memory used=6506.1MB, alloc=397.9MB, time=100.17 memory used=6580.2MB, alloc=397.9MB, time=100.35 memory used=6630.5MB, alloc=397.9MB, time=100.49 memory used=6671.1MB, alloc=397.9MB, time=100.63 memory used=6714.1MB, alloc=397.9MB, time=100.77 memory used=6759.0MB, alloc=397.9MB, time=100.91 memory used=6805.4MB, alloc=397.9MB, time=101.05 memory used=6853.4MB, alloc=397.9MB, time=101.19 memory used=6904.2MB, alloc=397.9MB, time=101.34 memory used=6957.5MB, alloc=397.9MB, time=101.49 memory used=7013.0MB, alloc=397.9MB, time=101.65 memory used=7071.6MB, alloc=397.9MB, time=101.80 memory used=7133.9MB, alloc=397.9MB, time=101.95 memory used=7199.8MB, alloc=397.9MB, time=102.11 memory used=7269.3MB, alloc=397.9MB, time=102.25 memory used=7408.5MB, alloc=397.9MB, time=103.52 memory used=7495.6MB, alloc=397.9MB, time=103.81 memory used=7544.8MB, alloc=397.9MB, time=104.01 memory used=7598.8MB, alloc=397.9MB, time=104.21 memory used=7661.7MB, alloc=397.9MB, time=104.44 memory used=7733.1MB, alloc=397.9MB, time=104.68 memory used=7800.2MB, alloc=397.9MB, time=104.89 memory used=7840.7MB, alloc=397.9MB, time=105.05 memory used=7882.9MB, alloc=397.9MB, time=105.24 memory used=7927.4MB, alloc=397.9MB, time=105.41 memory used=7973.3MB, alloc=397.9MB, time=105.59 memory used=8022.6MB, alloc=397.9MB, time=105.78 memory used=8073.4MB, alloc=397.9MB, time=105.96 memory used=8128.1MB, alloc=397.9MB, time=106.14 memory used=8183.9MB, alloc=397.9MB, time=106.33 memory used=8243.6MB, alloc=397.9MB, time=106.52 memory used=8304.5MB, alloc=397.9MB, time=106.70 memory used=8368.8MB, alloc=397.9MB, time=106.90 memory used=8437.2MB, alloc=397.9MB, time=107.10 memory used=8509.3MB, alloc=397.9MB, time=107.31 memory used=8582.2MB, alloc=397.9MB, time=107.51 memory used=8644.6MB, alloc=397.9MB, time=107.68 memory used=8683.0MB, alloc=397.9MB, time=107.82 memory used=8721.9MB, alloc=397.9MB, time=107.96 memory used=8760.3MB, alloc=397.9MB, time=108.11 memory used=8801.5MB, alloc=397.9MB, time=108.26 memory used=8842.5MB, alloc=397.9MB, time=108.39 memory used=8883.7MB, alloc=397.9MB, time=108.54 memory used=8926.8MB, alloc=397.9MB, time=108.68 memory used=8970.2MB, alloc=397.9MB, time=108.82 memory used=9015.4MB, alloc=397.9MB, time=108.96 memory used=9063.2MB, alloc=397.9MB, time=109.10 memory used=9110.2MB, alloc=397.9MB, time=109.25 memory used=9159.2MB, alloc=397.9MB, time=109.39 memory used=9209.8MB, alloc=397.9MB, time=109.54 memory used=9261.8MB, alloc=397.9MB, time=109.70 memory used=9315.1MB, alloc=397.9MB, time=109.84 memory used=9370.5MB, alloc=397.9MB, time=109.99 memory used=9428.4MB, alloc=397.9MB, time=110.13 memory used=9488.0MB, alloc=397.9MB, time=110.28 memory used=9550.4MB, alloc=397.9MB, time=110.43 memory used=9616.6MB, alloc=397.9MB, time=110.59 memory used=9705.5MB, alloc=397.9MB, time=111.98 memory used=9773.0MB, alloc=397.9MB, time=112.24 memory used=9824.0MB, alloc=397.9MB, time=112.44 memory used=9881.7MB, alloc=397.9MB, time=112.65 memory used=9947.5MB, alloc=397.9MB, time=112.85 memory used=10021.6MB, alloc=397.9MB, time=113.06 memory used=10074.5MB, alloc=397.9MB, time=113.25 memory used=10116.7MB, alloc=397.9MB, time=113.42 memory used=10160.6MB, alloc=397.9MB, time=113.59 memory used=10205.7MB, alloc=397.9MB, time=113.77 memory used=10254.7MB, alloc=397.9MB, time=113.95 memory used=10305.0MB, alloc=397.9MB, time=114.14 memory used=10359.3MB, alloc=397.9MB, time=114.33 memory used=10414.7MB, alloc=397.9MB, time=114.51 memory used=10474.0MB, alloc=397.9MB, time=114.69 memory used=10534.3MB, alloc=397.9MB, time=114.89 memory used=10598.6MB, alloc=397.9MB, time=115.07 memory used=10666.7MB, alloc=397.9MB, time=115.26 memory used=10735.4MB, alloc=397.9MB, time=115.44 memory used=10807.8MB, alloc=397.9MB, time=115.65 memory used=10878.1MB, alloc=397.9MB, time=115.83 memory used=10923.4MB, alloc=397.9MB, time=115.98 memory used=10961.6MB, alloc=397.9MB, time=116.12 memory used=11000.0MB, alloc=397.9MB, time=116.26 memory used=11038.7MB, alloc=397.9MB, time=116.40 memory used=11079.3MB, alloc=397.9MB, time=116.54 memory used=11120.3MB, alloc=397.9MB, time=116.69 memory used=11163.9MB, alloc=397.9MB, time=116.83 memory used=11207.2MB, alloc=397.9MB, time=116.97 memory used=11252.9MB, alloc=397.9MB, time=117.11 memory used=11298.5MB, alloc=397.9MB, time=117.25 memory used=11345.5MB, alloc=397.9MB, time=117.40 memory used=11394.9MB, alloc=397.9MB, time=117.55 memory used=11446.1MB, alloc=397.9MB, time=117.69 memory used=11498.6MB, alloc=397.9MB, time=117.83 memory used=11552.1MB, alloc=397.9MB, time=117.96 memory used=11606.7MB, alloc=397.9MB, time=118.11 memory used=11663.3MB, alloc=397.9MB, time=118.24 memory used=11722.9MB, alloc=397.9MB, time=118.38 memory used=11785.3MB, alloc=397.9MB, time=118.52 memory used=11850.8MB, alloc=397.9MB, time=118.66 memory used=11935.5MB, alloc=397.9MB, time=130.07 memory used=12011.4MB, alloc=397.9MB, time=131.54 memory used=12073.8MB, alloc=397.9MB, time=131.77 memory used=12138.4MB, alloc=397.9MB, time=131.96 memory used=12184.0MB, alloc=397.9MB, time=132.13 memory used=12235.2MB, alloc=397.9MB, time=132.31 memory used=12291.3MB, alloc=397.9MB, time=132.49 memory used=12352.3MB, alloc=397.9MB, time=132.67 memory used=12419.3MB, alloc=397.9MB, time=132.86 memory used=12492.5MB, alloc=397.9MB, time=133.05 memory used=12554.0MB, alloc=397.9MB, time=133.22 memory used=12594.1MB, alloc=397.9MB, time=133.36 memory used=12635.8MB, alloc=397.9MB, time=133.50 memory used=12680.1MB, alloc=397.9MB, time=133.64 memory used=12726.3MB, alloc=397.9MB, time=133.78 memory used=12774.6MB, alloc=397.9MB, time=133.92 memory used=12824.6MB, alloc=397.9MB, time=134.11 memory used=12876.3MB, alloc=397.9MB, time=134.27 memory used=12929.6MB, alloc=397.9MB, time=134.43 memory used=12985.9MB, alloc=397.9MB, time=134.57 memory used=13044.8MB, alloc=397.9MB, time=134.72 memory used=13106.0MB, alloc=397.9MB, time=134.86 memory used=13170.4MB, alloc=397.9MB, time=135.02 memory used=13237.6MB, alloc=397.9MB, time=135.17 memory used=13308.5MB, alloc=397.9MB, time=135.32 memory used=13390.9MB, alloc=397.9MB, time=135.48 memory used=13584.7MB, alloc=397.9MB, time=136.24 memory used=13654.8MB, alloc=397.9MB, time=136.73 memory used=13721.7MB, alloc=397.9MB, time=136.92 memory used=13788.9MB, alloc=397.9MB, time=137.12 memory used=13876.7MB, alloc=397.9MB, time=138.05 memory used=13929.4MB, alloc=397.9MB, time=138.26 memory used=13998.6MB, alloc=397.9MB, time=138.48 memory used=14052.8MB, alloc=397.9MB, time=138.66 memory used=14100.8MB, alloc=397.9MB, time=138.83 memory used=14154.6MB, alloc=397.9MB, time=139.00 memory used=14216.3MB, alloc=397.9MB, time=139.18 memory used=14288.1MB, alloc=397.9MB, time=139.35 memory used=14368.9MB, alloc=397.9MB, time=139.94 memory used=14421.0MB, alloc=397.9MB, time=140.13 memory used=14489.3MB, alloc=397.9MB, time=140.35 memory used=14544.1MB, alloc=397.9MB, time=140.53 memory used=14591.6MB, alloc=397.9MB, time=140.69 memory used=14645.3MB, alloc=397.9MB, time=140.86 memory used=14706.1MB, alloc=397.9MB, time=141.03 memory used=14776.9MB, alloc=397.9MB, time=141.20 memory used=14869.8MB, alloc=397.9MB, time=143.98 memory used=14930.5MB, alloc=397.9MB, time=144.19 memory used=14986.2MB, alloc=397.9MB, time=144.37 memory used=15038.5MB, alloc=397.9MB, time=144.54 memory used=15100.6MB, alloc=397.9MB, time=144.73 memory used=15173.7MB, alloc=397.9MB, time=144.91 memory used=15222.7MB, alloc=397.9MB, time=145.06 memory used=15268.3MB, alloc=397.9MB, time=145.19 memory used=15317.3MB, alloc=397.9MB, time=145.33 memory used=15373.3MB, alloc=397.9MB, time=145.47 memory used=15459.0MB, alloc=397.9MB, time=146.07 memory used=15513.0MB, alloc=397.9MB, time=146.28 memory used=15584.2MB, alloc=397.9MB, time=146.51 memory used=15634.7MB, alloc=397.9MB, time=146.70 memory used=15683.4MB, alloc=397.9MB, time=146.89 memory used=15739.2MB, alloc=397.9MB, time=147.08 memory used=15802.5MB, alloc=397.9MB, time=147.27 memory used=15868.6MB, alloc=397.9MB, time=147.44 memory used=15950.5MB, alloc=397.9MB, time=147.96 memory used=16005.2MB, alloc=397.9MB, time=148.17 memory used=16078.0MB, alloc=397.9MB, time=148.40 memory used=16127.3MB, alloc=397.9MB, time=148.59 memory used=16176.8MB, alloc=397.9MB, time=148.77 memory used=16232.5MB, alloc=397.9MB, time=148.96 memory used=16297.1MB, alloc=397.9MB, time=149.16 memory used=16361.9MB, alloc=397.9MB, time=149.34 memory used=16469.7MB, alloc=397.9MB, time=152.35 memory used=16531.6MB, alloc=397.9MB, time=152.56 memory used=16585.0MB, alloc=397.9MB, time=152.73 memory used=16637.0MB, alloc=397.9MB, time=152.90 memory used=16698.7MB, alloc=397.9MB, time=153.07 memory used=16771.5MB, alloc=397.9MB, time=153.26 memory used=16821.0MB, alloc=397.9MB, time=153.42 memory used=16865.7MB, alloc=397.9MB, time=153.57 memory used=16914.1MB, alloc=397.9MB, time=153.71 memory used=16968.4MB, alloc=397.9MB, time=153.84 memory used=17036.3MB, alloc=397.9MB, time=154.33 memory used=17115.6MB, alloc=397.9MB, time=154.94 memory used=17173.1MB, alloc=397.9MB, time=155.14 memory used=17236.8MB, alloc=397.9MB, time=155.36 memory used=17298.6MB, alloc=397.9MB, time=155.56 memory used=17344.3MB, alloc=397.9MB, time=155.73 memory used=17395.6MB, alloc=397.9MB, time=155.91 memory used=17454.1MB, alloc=397.9MB, time=156.10 memory used=17521.8MB, alloc=397.9MB, time=156.30 memory used=17599.8MB, alloc=397.9MB, time=156.83 memory used=17660.8MB, alloc=397.9MB, time=157.08 memory used=17722.7MB, alloc=397.9MB, time=157.30 memory used=17787.4MB, alloc=397.9MB, time=157.50 memory used=17832.5MB, alloc=397.9MB, time=157.67 memory used=17883.7MB, alloc=397.9MB, time=157.85 memory used=17941.3MB, alloc=397.9MB, time=158.03 memory used=18008.2MB, alloc=397.9MB, time=158.21 memory used=18095.7MB, alloc=397.9MB, time=160.89 memory used=18163.6MB, alloc=397.9MB, time=161.16 memory used=18227.1MB, alloc=397.9MB, time=161.36 memory used=18275.3MB, alloc=397.9MB, time=161.53 memory used=18333.0MB, alloc=397.9MB, time=161.70 memory used=18400.9MB, alloc=397.9MB, time=161.90 memory used=18462.9MB, alloc=397.9MB, time=162.07 memory used=18506.0MB, alloc=397.9MB, time=162.21 memory used=18553.5MB, alloc=397.9MB, time=162.35 memory used=18605.2MB, alloc=397.9MB, time=162.49 memory used=18704.8MB, alloc=397.9MB, time=163.22 memory used=18833.3MB, alloc=397.9MB, time=165.39 memory used=18962.6MB, alloc=397.9MB, time=169.72 memory used=19094.5MB, alloc=397.9MB, time=176.46 memory used=19236.8MB, alloc=397.9MB, time=178.49 memory used=19361.4MB, alloc=397.9MB, time=180.76 memory used=19486.5MB, alloc=397.9MB, time=185.21 memory used=19613.7MB, alloc=397.9MB, time=191.73 memory used=19732.8MB, alloc=397.9MB, time=198.27 memory used=19790.8MB, alloc=397.9MB, time=198.48 memory used=19841.7MB, alloc=397.9MB, time=198.66 memory used=19891.4MB, alloc=397.9MB, time=198.83 memory used=19951.1MB, alloc=397.9MB, time=199.03 memory used=20020.2MB, alloc=397.9MB, time=199.21 memory used=20061.7MB, alloc=397.9MB, time=199.36 memory used=20104.8MB, alloc=397.9MB, time=199.50 memory used=20153.4MB, alloc=397.9MB, time=199.64 memory used=20239.3MB, alloc=397.9MB, time=202.25 memory used=20299.1MB, alloc=397.9MB, time=202.47 memory used=20350.2MB, alloc=397.9MB, time=202.66 memory used=20399.5MB, alloc=397.9MB, time=202.84 memory used=20458.1MB, alloc=397.9MB, time=203.01 memory used=20527.0MB, alloc=397.9MB, time=203.20 memory used=20575.6MB, alloc=397.9MB, time=203.35 memory used=20618.3MB, alloc=397.9MB, time=203.49 memory used=20663.9MB, alloc=397.9MB, time=203.63 memory used=20715.4MB, alloc=397.9MB, time=203.78 memory used=20797.1MB, alloc=397.9MB, time=204.29 memory used=20867.3MB, alloc=397.9MB, time=204.60 memory used=20947.9MB, alloc=397.9MB, time=205.19 memory used=21017.7MB, alloc=397.9MB, time=205.54 memory used=21099.0MB, alloc=397.9MB, time=206.31 memory used=21165.5MB, alloc=397.9MB, time=206.61 memory used=21257.7MB, alloc=397.9MB, time=207.53 memory used=21337.6MB, alloc=397.9MB, time=208.94 memory used=21408.3MB, alloc=397.9MB, time=209.23 memory used=21453.9MB, alloc=397.9MB, time=209.46 memory used=21507.0MB, alloc=397.9MB, time=209.70 memory used=21565.8MB, alloc=397.9MB, time=209.93 memory used=21632.1MB, alloc=397.9MB, time=210.17 memory used=21695.6MB, alloc=397.9MB, time=210.39 memory used=21733.5MB, alloc=397.9MB, time=210.58 memory used=21772.5MB, alloc=397.9MB, time=210.78 memory used=21813.5MB, alloc=397.9MB, time=210.97 memory used=21855.9MB, alloc=397.9MB, time=211.16 memory used=21901.6MB, alloc=397.9MB, time=211.36 memory used=21948.5MB, alloc=397.9MB, time=211.55 memory used=21999.3MB, alloc=397.9MB, time=211.74 memory used=22050.9MB, alloc=397.9MB, time=211.95 memory used=22103.8MB, alloc=397.9MB, time=212.15 memory used=22159.8MB, alloc=397.9MB, time=212.35 memory used=22220.0MB, alloc=397.9MB, time=212.56 memory used=22280.8MB, alloc=397.9MB, time=212.76 memory used=22345.3MB, alloc=397.9MB, time=212.96 memory used=22413.3MB, alloc=397.9MB, time=213.17 memory used=22481.8MB, alloc=397.9MB, time=213.37 memory used=22536.7MB, alloc=397.9MB, time=213.55 memory used=22572.7MB, alloc=397.9MB, time=213.70 memory used=22609.0MB, alloc=397.9MB, time=213.86 memory used=22646.8MB, alloc=397.9MB, time=214.01 memory used=22684.3MB, alloc=397.9MB, time=214.17 memory used=22721.7MB, alloc=397.9MB, time=214.32 memory used=22761.9MB, alloc=397.9MB, time=214.47 memory used=22801.7MB, alloc=397.9MB, time=214.63 memory used=22841.6MB, alloc=397.9MB, time=214.78 memory used=22883.1MB, alloc=397.9MB, time=214.93 memory used=22925.0MB, alloc=397.9MB, time=215.09 memory used=22968.2MB, alloc=397.9MB, time=215.24 memory used=23013.9MB, alloc=397.9MB, time=215.40 memory used=23061.4MB, alloc=397.9MB, time=215.57 memory used=23108.4MB, alloc=397.9MB, time=215.75 memory used=23158.0MB, alloc=397.9MB, time=215.91 memory used=23209.0MB, alloc=397.9MB, time=216.05 memory used=23260.9MB, alloc=397.9MB, time=216.21 memory used=23315.9MB, alloc=397.9MB, time=216.37 memory used=23372.2MB, alloc=397.9MB, time=216.52 memory used=23431.3MB, alloc=397.9MB, time=216.69 memory used=23493.6MB, alloc=397.9MB, time=216.84 memory used=23578.3MB, alloc=397.9MB, time=218.19 memory used=23641.0MB, alloc=397.9MB, time=218.44 memory used=23687.7MB, alloc=397.9MB, time=218.66 memory used=23740.0MB, alloc=397.9MB, time=218.87 memory used=23799.6MB, alloc=397.9MB, time=219.10 memory used=23866.6MB, alloc=397.9MB, time=219.32 memory used=23926.0MB, alloc=397.9MB, time=219.52 memory used=23963.3MB, alloc=397.9MB, time=219.70 memory used=24002.7MB, alloc=397.9MB, time=219.88 memory used=24043.9MB, alloc=397.9MB, time=220.05 memory used=24086.4MB, alloc=397.9MB, time=220.23 memory used=24132.2MB, alloc=397.9MB, time=220.40 memory used=24179.2MB, alloc=397.9MB, time=220.59 memory used=24230.1MB, alloc=397.9MB, time=220.77 memory used=24281.9MB, alloc=397.9MB, time=220.96 memory used=24334.8MB, alloc=397.9MB, time=221.15 memory used=24390.9MB, alloc=397.9MB, time=221.34 memory used=24451.1MB, alloc=397.9MB, time=221.53 memory used=24512.0MB, alloc=397.9MB, time=221.72 memory used=24576.5MB, alloc=397.9MB, time=221.91 memory used=24644.5MB, alloc=397.9MB, time=222.11 memory used=24713.0MB, alloc=397.9MB, time=222.32 memory used=24765.4MB, alloc=397.9MB, time=222.49 memory used=24800.3MB, alloc=397.9MB, time=222.63 memory used=24837.0MB, alloc=397.9MB, time=222.78 memory used=24874.8MB, alloc=397.9MB, time=222.92 memory used=24912.3MB, alloc=397.9MB, time=223.07 memory used=24949.7MB, alloc=397.9MB, time=223.21 memory used=24989.8MB, alloc=397.9MB, time=223.34 memory used=25029.6MB, alloc=397.9MB, time=223.49 memory used=25069.4MB, alloc=397.9MB, time=223.65 memory used=25110.9MB, alloc=397.9MB, time=223.82 memory used=25152.8MB, alloc=397.9MB, time=223.96 memory used=25195.9MB, alloc=397.9MB, time=224.12 memory used=25241.6MB, alloc=397.9MB, time=224.28 memory used=25289.0MB, alloc=397.9MB, time=224.42 memory used=25335.9MB, alloc=397.9MB, time=224.57 memory used=25385.5MB, alloc=397.9MB, time=224.74 memory used=25436.4MB, alloc=397.9MB, time=224.89 memory used=25488.2MB, alloc=397.9MB, time=225.03 memory used=25542.8MB, alloc=397.9MB, time=225.18 memory used=25598.9MB, alloc=397.9MB, time=225.34 memory used=25658.0MB, alloc=397.9MB, time=225.49 memory used=25719.8MB, alloc=397.9MB, time=225.65 memory used=25812.1MB, alloc=397.9MB, time=238.25 memory used=25868.3MB, alloc=397.9MB, time=238.48 memory used=25932.1MB, alloc=397.9MB, time=238.72 memory used=25986.1MB, alloc=397.9MB, time=238.93 memory used=26029.3MB, alloc=397.9MB, time=239.14 memory used=26077.7MB, alloc=397.9MB, time=239.35 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428286272 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 3 2 3 4 2 2 F := [-3 x z + 15 x y + 5 x z , -2 x y - 16 y , 15 y - 4 x y + 2 y z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 3 2 2 2 G := [-17 x y z + 15 x z - 11 z , 3 y z + 7 z , 2 x y z - 7 x z + 20 y z] > Problem := [F,G]; Problem := [ 2 2 3 3 2 3 4 2 2 [-3 x z + 15 x y + 5 x z , -2 x y - 16 y , 15 y - 4 x y + 2 y z], 2 2 2 3 3 2 2 2 [-17 x y z + 15 x z - 11 z , 3 y z + 7 z , 2 x y z - 7 x z + 20 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.5MB, alloc=32.3MB, time=0.50 memory used=48.2MB, alloc=32.3MB, time=0.82 memory used=68.6MB, alloc=56.3MB, time=1.15 memory used=109.2MB, alloc=60.3MB, time=1.78 memory used=148.6MB, alloc=60.3MB, time=2.37 memory used=185.7MB, alloc=84.3MB, time=2.94 memory used=231.7MB, alloc=84.3MB, time=3.65 memory used=295.0MB, alloc=116.3MB, time=4.57 memory used=375.7MB, alloc=372.3MB, time=5.79 memory used=461.9MB, alloc=396.3MB, time=7.09 memory used=573.5MB, alloc=420.3MB, time=8.80 memory used=713.3MB, alloc=420.3MB, time=10.77 memory used=841.4MB, alloc=444.3MB, time=12.66 memory used=981.5MB, alloc=468.3MB, time=14.83 memory used=1109.2MB, alloc=468.3MB, time=16.89 memory used=1234.4MB, alloc=492.3MB, time=18.96 memory used=1370.7MB, alloc=492.3MB, time=20.70 memory used=1487.8MB, alloc=492.3MB, time=22.65 memory used=1580.5MB, alloc=492.3MB, time=24.27 memory used=1674.8MB, alloc=492.3MB, time=25.96 memory used=1763.1MB, alloc=492.3MB, time=27.53 memory used=1895.3MB, alloc=516.3MB, time=28.90 memory used=1981.5MB, alloc=516.3MB, time=30.20 memory used=2060.7MB, alloc=516.3MB, time=31.67 memory used=2138.1MB, alloc=516.3MB, time=33.06 memory used=2206.2MB, alloc=516.3MB, time=34.27 memory used=2278.0MB, alloc=516.3MB, time=35.58 memory used=2359.3MB, alloc=516.3MB, time=36.89 memory used=2443.8MB, alloc=516.3MB, time=38.19 memory used=2502.0MB, alloc=516.3MB, time=39.29 memory used=2565.6MB, alloc=516.3MB, time=40.59 memory used=2622.7MB, alloc=516.3MB, time=41.88 memory used=2687.0MB, alloc=540.3MB, time=43.01 memory used=2825.8MB, alloc=540.3MB, time=44.10 memory used=2936.2MB, alloc=540.3MB, time=45.25 memory used=3010.0MB, alloc=540.3MB, time=46.54 memory used=3057.5MB, alloc=540.3MB, time=47.55 memory used=3115.9MB, alloc=540.3MB, time=48.56 memory used=3288.6MB, alloc=540.3MB, time=50.35 memory used=3520.1MB, alloc=564.3MB, time=53.42 memory used=3759.5MB, alloc=588.3MB, time=55.92 memory used=3984.6MB, alloc=588.3MB, time=56.85 memory used=4231.7MB, alloc=588.3MB, time=57.82 memory used=4518.9MB, alloc=588.3MB, time=60.54 memory used=4784.8MB, alloc=588.3MB, time=62.53 memory used=5051.5MB, alloc=588.3MB, time=64.94 memory used=5292.3MB, alloc=588.3MB, time=66.67 memory used=5521.8MB, alloc=588.3MB, time=68.36 memory used=5771.4MB, alloc=612.3MB, time=72.87 memory used=6019.7MB, alloc=636.3MB, time=77.55 memory used=6277.5MB, alloc=660.3MB, time=82.64 memory used=6574.0MB, alloc=684.3MB, time=87.37 memory used=6842.1MB, alloc=708.3MB, time=92.29 memory used=7140.8MB, alloc=732.3MB, time=97.83 memory used=7496.4MB, alloc=756.3MB, time=102.86 memory used=7819.6MB, alloc=780.3MB, time=107.52 memory used=8111.2MB, alloc=804.3MB, time=112.74 memory used=8373.2MB, alloc=828.3MB, time=117.39 memory used=8667.2MB, alloc=852.3MB, time=122.68 memory used=8985.0MB, alloc=876.3MB, time=134.23 memory used=9296.1MB, alloc=900.3MB, time=146.59 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428286572 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 4 2 2 3 F := [20 x y - 14 x y - 19 x y z, -16 x + 4 x y + 4 y z, 2 3 3 12 x y z - 12 y z + 20 y ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 2 3 G := [-19 x z - 3 y z , 5 z - 15 x z + 16 z, -18 x y z - 16 x z - 2 z ] > Problem := [F,G]; 3 2 4 2 2 3 Problem := [[20 x y - 14 x y - 19 x y z, -16 x + 4 x y + 4 y z, 2 3 3 12 x y z - 12 y z + 20 y ], 3 2 3 2 2 3 [-19 x z - 3 y z , 5 z - 15 x z + 16 z, -18 x y z - 16 x z - 2 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.16 memory used=26.6MB, alloc=32.3MB, time=0.48 memory used=46.8MB, alloc=32.3MB, time=0.76 memory used=65.0MB, alloc=56.3MB, time=1.04 memory used=104.9MB, alloc=60.3MB, time=1.63 memory used=144.0MB, alloc=84.3MB, time=2.19 memory used=206.0MB, alloc=92.3MB, time=3.12 memory used=265.8MB, alloc=116.3MB, time=4.02 memory used=346.0MB, alloc=140.3MB, time=5.28 memory used=436.2MB, alloc=396.3MB, time=6.70 memory used=536.5MB, alloc=420.3MB, time=8.24 memory used=666.6MB, alloc=444.3MB, time=10.03 memory used=811.1MB, alloc=468.3MB, time=12.25 memory used=948.7MB, alloc=492.3MB, time=14.38 memory used=1082.3MB, alloc=492.3MB, time=16.48 memory used=1216.2MB, alloc=516.3MB, time=18.69 memory used=1330.8MB, alloc=516.3MB, time=20.54 memory used=1426.3MB, alloc=516.3MB, time=22.22 memory used=1524.9MB, alloc=516.3MB, time=23.98 memory used=1612.9MB, alloc=540.3MB, time=25.64 memory used=1695.6MB, alloc=540.3MB, time=27.13 memory used=1781.1MB, alloc=540.3MB, time=28.68 memory used=1834.4MB, alloc=540.3MB, time=29.86 memory used=1967.1MB, alloc=540.3MB, time=31.76 memory used=2039.4MB, alloc=564.3MB, time=33.21 memory used=2099.9MB, alloc=564.3MB, time=34.37 memory used=2168.2MB, alloc=564.3MB, time=35.76 memory used=2234.7MB, alloc=564.3MB, time=37.26 memory used=2297.3MB, alloc=564.3MB, time=38.59 memory used=2356.1MB, alloc=564.3MB, time=40.10 memory used=2599.7MB, alloc=588.3MB, time=44.67 memory used=2809.2MB, alloc=612.3MB, time=48.69 memory used=3007.1MB, alloc=636.3MB, time=52.24 memory used=3201.0MB, alloc=660.3MB, time=55.04 memory used=3390.1MB, alloc=684.3MB, time=58.15 memory used=3524.7MB, alloc=708.3MB, time=60.55 memory used=3646.2MB, alloc=732.3MB, time=62.68 memory used=3801.8MB, alloc=756.3MB, time=65.81 memory used=3919.3MB, alloc=756.3MB, time=68.61 memory used=4049.8MB, alloc=756.3MB, time=71.94 memory used=4182.3MB, alloc=756.3MB, time=75.33 memory used=4273.8MB, alloc=756.3MB, time=77.48 memory used=4703.9MB, alloc=780.3MB, time=84.36 memory used=5100.8MB, alloc=804.3MB, time=90.61 memory used=5521.4MB, alloc=828.3MB, time=99.16 memory used=5889.6MB, alloc=852.3MB, time=106.87 memory used=6232.5MB, alloc=876.3MB, time=113.56 memory used=6548.5MB, alloc=900.3MB, time=119.82 memory used=6802.4MB, alloc=924.3MB, time=124.67 memory used=7073.5MB, alloc=948.3MB, time=130.79 memory used=7316.6MB, alloc=972.3MB, time=135.54 memory used=7520.3MB, alloc=996.3MB, time=141.31 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428286872 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 3 2 3 3 2 2 F := [-13 y z - 6 y , 5 x z + 7 x y z - 19 x z , -x z + 14 x z - 15 x ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 3 3 3 3 2 2 G := [2 x y + 12 x z + 20 x y , 9 x y - x y + 8 x , -18 x y z + 9 x z] > Problem := [F,G]; Problem := [ 3 3 3 2 3 3 2 2 [-13 y z - 6 y , 5 x z + 7 x y z - 19 x z , -x z + 14 x z - 15 x ], 2 2 2 2 3 3 3 3 2 2 [2 x y + 12 x z + 20 x y , 9 x y - x y + 8 x , -18 x y z + 9 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.3MB, alloc=32.3MB, time=0.49 memory used=47.9MB, alloc=32.3MB, time=0.80 memory used=68.5MB, alloc=32.3MB, time=1.10 memory used=87.8MB, alloc=56.3MB, time=1.43 memory used=128.0MB, alloc=60.3MB, time=2.05 memory used=165.9MB, alloc=84.3MB, time=2.64 memory used=218.4MB, alloc=84.3MB, time=3.42 memory used=274.9MB, alloc=116.3MB, time=4.31 memory used=354.1MB, alloc=116.3MB, time=5.49 memory used=431.2MB, alloc=116.3MB, time=6.70 memory used=512.5MB, alloc=140.3MB, time=7.91 memory used=592.1MB, alloc=140.3MB, time=9.07 memory used=668.9MB, alloc=396.3MB, time=10.28 memory used=765.7MB, alloc=420.3MB, time=11.82 memory used=892.1MB, alloc=420.3MB, time=13.47 memory used=1009.0MB, alloc=444.3MB, time=15.16 memory used=1186.2MB, alloc=444.3MB, time=17.14 memory used=1367.5MB, alloc=444.3MB, time=18.45 memory used=1499.1MB, alloc=468.3MB, time=20.75 memory used=1680.4MB, alloc=492.3MB, time=23.16 memory used=1874.7MB, alloc=492.3MB, time=24.79 memory used=2030.7MB, alloc=492.3MB, time=25.32 memory used=2199.4MB, alloc=492.3MB, time=25.85 memory used=2387.0MB, alloc=492.3MB, time=27.16 memory used=2541.8MB, alloc=492.3MB, time=27.70 memory used=2708.8MB, alloc=492.3MB, time=28.22 memory used=2888.7MB, alloc=492.3MB, time=28.75 memory used=3097.5MB, alloc=492.3MB, time=30.43 memory used=3247.6MB, alloc=492.3MB, time=30.97 memory used=3420.8MB, alloc=492.3MB, time=31.50 memory used=3603.4MB, alloc=492.3MB, time=32.03 memory used=3776.0MB, alloc=516.3MB, time=33.19 memory used=3962.8MB, alloc=516.3MB, time=33.80 memory used=4167.6MB, alloc=516.3MB, time=34.40 memory used=4366.5MB, alloc=516.3MB, time=35.69 memory used=4534.3MB, alloc=516.3MB, time=36.28 memory used=4732.1MB, alloc=516.3MB, time=37.23 memory used=4906.3MB, alloc=516.3MB, time=37.93 memory used=5075.6MB, alloc=516.3MB, time=38.51 memory used=5279.6MB, alloc=540.3MB, time=41.64 memory used=5490.3MB, alloc=564.3MB, time=45.54 memory used=5709.7MB, alloc=588.3MB, time=49.68 memory used=5933.5MB, alloc=612.3MB, time=54.04 memory used=6168.9MB, alloc=636.3MB, time=58.62 memory used=6413.8MB, alloc=660.3MB, time=62.98 memory used=6693.3MB, alloc=684.3MB, time=67.48 memory used=6897.0MB, alloc=708.3MB, time=71.34 memory used=7118.3MB, alloc=732.3MB, time=75.62 memory used=7305.0MB, alloc=756.3MB, time=79.47 memory used=7518.4MB, alloc=780.3MB, time=83.77 memory used=7694.5MB, alloc=804.3MB, time=87.25 memory used=8069.8MB, alloc=828.3MB, time=94.23 memory used=8488.6MB, alloc=852.3MB, time=99.52 memory used=8925.7MB, alloc=876.3MB, time=105.48 memory used=9325.8MB, alloc=900.3MB, time=112.02 memory used=9720.4MB, alloc=924.3MB, time=119.29 memory used=10241.0MB, alloc=948.3MB, time=123.87 memory used=10721.2MB, alloc=972.3MB, time=130.84 memory used=11243.0MB, alloc=996.3MB, time=135.70 memory used=11779.9MB, alloc=1020.3MB, time=142.76 memory used=12340.6MB, alloc=1044.3MB, time=149.68 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428287172 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 3 F := [7 x z - 18 x y + 11 z , -16 y z - 2 x y + 13 x, x y z + 3 x - 19] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 2 2 2 2 3 G := [2 x + 7 x z + 7 x y, -11 x z + 14 x y z + 13 x , 2 2 -12 x y - 20 x z + 9 z] > Problem := [F,G]; Problem := [ 3 2 2 2 2 3 [7 x z - 18 x y + 11 z , -16 y z - 2 x y + 13 x, x y z + 3 x - 19], [ 4 3 2 2 2 2 3 2 x + 7 x z + 7 x y, -11 x z + 14 x y z + 13 x , 2 2 -12 x y - 20 x z + 9 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.1MB, alloc=32.3MB, time=0.51 memory used=46.5MB, alloc=60.3MB, time=0.80 memory used=88.7MB, alloc=60.3MB, time=1.39 memory used=130.1MB, alloc=60.3MB, time=1.98 memory used=162.5MB, alloc=84.3MB, time=2.44 memory used=229.7MB, alloc=92.3MB, time=3.35 memory used=299.6MB, alloc=348.3MB, time=4.23 memory used=366.7MB, alloc=372.3MB, time=5.19 memory used=455.2MB, alloc=372.3MB, time=6.44 memory used=548.4MB, alloc=396.3MB, time=7.50 memory used=665.8MB, alloc=396.3MB, time=9.15 memory used=776.8MB, alloc=420.3MB, time=10.78 memory used=891.4MB, alloc=420.3MB, time=12.27 memory used=1026.0MB, alloc=444.3MB, time=14.33 memory used=1150.2MB, alloc=444.3MB, time=15.79 memory used=1252.6MB, alloc=444.3MB, time=17.33 memory used=1378.0MB, alloc=468.3MB, time=19.06 memory used=1504.7MB, alloc=468.3MB, time=20.16 memory used=1619.7MB, alloc=468.3MB, time=21.62 memory used=1738.2MB, alloc=468.3MB, time=23.16 memory used=1844.9MB, alloc=492.3MB, time=24.71 memory used=1946.9MB, alloc=492.3MB, time=26.01 memory used=2032.1MB, alloc=492.3MB, time=27.34 memory used=2108.6MB, alloc=492.3MB, time=28.55 memory used=2186.8MB, alloc=492.3MB, time=29.80 memory used=2256.8MB, alloc=492.3MB, time=30.92 memory used=2323.0MB, alloc=492.3MB, time=31.94 memory used=2401.1MB, alloc=492.3MB, time=33.14 memory used=2468.4MB, alloc=492.3MB, time=34.22 memory used=2532.6MB, alloc=492.3MB, time=35.42 memory used=2611.6MB, alloc=516.3MB, time=36.32 memory used=2688.1MB, alloc=516.3MB, time=37.33 memory used=2740.4MB, alloc=516.3MB, time=38.18 memory used=2799.0MB, alloc=516.3MB, time=39.46 memory used=2848.2MB, alloc=516.3MB, time=40.35 memory used=2896.5MB, alloc=516.3MB, time=41.29 memory used=3104.0MB, alloc=540.3MB, time=44.68 memory used=3293.8MB, alloc=564.3MB, time=47.07 memory used=3480.2MB, alloc=588.3MB, time=49.95 memory used=3648.0MB, alloc=612.3MB, time=52.56 memory used=3822.8MB, alloc=636.3MB, time=56.20 memory used=3937.5MB, alloc=636.3MB, time=58.28 memory used=4090.5MB, alloc=636.3MB, time=60.98 memory used=4199.4MB, alloc=636.3MB, time=62.93 memory used=4344.1MB, alloc=660.3MB, time=64.94 memory used=4482.4MB, alloc=660.3MB, time=67.50 memory used=4569.7MB, alloc=660.3MB, time=69.29 memory used=4666.4MB, alloc=660.3MB, time=71.26 memory used=4762.9MB, alloc=660.3MB, time=73.62 memory used=5107.6MB, alloc=684.3MB, time=78.95 memory used=5462.4MB, alloc=708.3MB, time=84.84 memory used=5659.8MB, alloc=732.3MB, time=89.40 memory used=5841.6MB, alloc=756.3MB, time=90.89 memory used=6087.5MB, alloc=780.3MB, time=96.26 memory used=6399.8MB, alloc=780.3MB, time=99.21 memory used=6685.4MB, alloc=780.3MB, time=104.79 memory used=7090.5MB, alloc=804.3MB, time=110.88 memory used=7489.1MB, alloc=828.3MB, time=117.72 memory used=7747.7MB, alloc=852.3MB, time=125.74 memory used=8032.4MB, alloc=852.3MB, time=127.82 memory used=8303.4MB, alloc=876.3MB, time=137.28 memory used=8811.2MB, alloc=876.3MB, time=149.77 memory used=9265.3MB, alloc=900.3MB, time=154.80 memory used=9568.3MB, alloc=900.3MB, time=160.43 memory used=9866.0MB, alloc=924.3MB, time=168.95 memory used=10150.9MB, alloc=924.3MB, time=171.16 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428287472 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 2 2 3 F := [-17 x y + 18 z , -17 x y + 7 x z - 20, 6 x z + 7 y z + 15 z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 G := [-13 x y - 18 y z - 6 y, -20 x y z - 20 x z + 6 z , 2 2 2 18 x y z + 5 x y - 20 y z] > Problem := [F,G]; Problem := [ 3 2 3 2 2 2 3 [-17 x y + 18 z , -17 x y + 7 x z - 20, 6 x z + 7 y z + 15 z], [ 2 2 2 3 -13 x y - 18 y z - 6 y, -20 x y z - 20 x z + 6 z , 2 2 2 18 x y z + 5 x y - 20 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.16 memory used=26.4MB, alloc=32.3MB, time=0.47 memory used=47.1MB, alloc=32.3MB, time=0.76 memory used=66.0MB, alloc=56.3MB, time=1.05 memory used=103.5MB, alloc=60.3MB, time=1.61 memory used=140.5MB, alloc=84.3MB, time=2.16 memory used=199.8MB, alloc=92.3MB, time=3.07 memory used=258.2MB, alloc=116.3MB, time=4.02 memory used=338.4MB, alloc=116.3MB, time=5.36 memory used=418.4MB, alloc=140.3MB, time=6.75 memory used=505.7MB, alloc=140.3MB, time=8.22 memory used=591.8MB, alloc=420.3MB, time=9.69 memory used=711.2MB, alloc=444.3MB, time=11.81 memory used=854.5MB, alloc=468.3MB, time=14.40 memory used=994.4MB, alloc=492.3MB, time=16.66 memory used=1122.6MB, alloc=492.3MB, time=18.77 memory used=1251.0MB, alloc=516.3MB, time=21.02 memory used=1388.9MB, alloc=516.3MB, time=23.58 memory used=1498.2MB, alloc=516.3MB, time=25.49 memory used=1586.4MB, alloc=516.3MB, time=27.19 memory used=1679.4MB, alloc=516.3MB, time=28.97 memory used=1765.2MB, alloc=540.3MB, time=30.76 memory used=1825.9MB, alloc=540.3MB, time=31.85 memory used=1916.5MB, alloc=540.3MB, time=33.66 memory used=1990.0MB, alloc=540.3MB, time=35.17 memory used=2044.0MB, alloc=540.3MB, time=36.30 memory used=2106.8MB, alloc=540.3MB, time=37.87 memory used=2154.1MB, alloc=540.3MB, time=38.86 memory used=2218.0MB, alloc=540.3MB, time=40.36 memory used=2434.8MB, alloc=564.3MB, time=44.42 memory used=2647.6MB, alloc=588.3MB, time=48.57 memory used=2799.5MB, alloc=612.3MB, time=51.58 memory used=2991.1MB, alloc=636.3MB, time=56.00 memory used=3133.4MB, alloc=636.3MB, time=59.19 memory used=3309.1MB, alloc=660.3MB, time=63.44 memory used=3441.9MB, alloc=660.3MB, time=66.52 memory used=3591.7MB, alloc=660.3MB, time=70.06 memory used=3712.2MB, alloc=684.3MB, time=73.21 memory used=3816.9MB, alloc=684.3MB, time=76.21 memory used=4158.9MB, alloc=708.3MB, time=84.88 memory used=4517.2MB, alloc=732.3MB, time=93.98 memory used=4898.1MB, alloc=756.3MB, time=103.15 memory used=5293.6MB, alloc=780.3MB, time=112.44 memory used=5670.8MB, alloc=804.3MB, time=121.68 memory used=5969.3MB, alloc=828.3MB, time=129.04 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428287773 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 3 4 3 2 F := [15 x y z + 16 x - 8 y, -13 x y + 8 x y + 9 y , 6 z - 10 x - 18 y ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 3 3 2 G := [-x y z + 20 x z , 11 x y z - 11 x , 9 y z - 15 x - 19 y ] > Problem := [F,G]; Problem := [ 2 2 2 2 2 3 4 3 2 [15 x y z + 16 x - 8 y, -13 x y + 8 x y + 9 y , 6 z - 10 x - 18 y ], 2 2 3 3 3 2 [-x y z + 20 x z , 11 x y z - 11 x , 9 y z - 15 x - 19 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.18 memory used=26.4MB, alloc=32.3MB, time=0.49 memory used=47.7MB, alloc=32.3MB, time=0.80 memory used=67.6MB, alloc=56.3MB, time=1.10 memory used=107.2MB, alloc=60.3MB, time=1.70 memory used=147.0MB, alloc=84.3MB, time=2.27 memory used=210.9MB, alloc=92.3MB, time=3.25 memory used=272.2MB, alloc=116.3MB, time=4.24 memory used=353.4MB, alloc=116.3MB, time=5.55 memory used=430.9MB, alloc=396.3MB, time=6.76 memory used=542.6MB, alloc=396.3MB, time=8.46 memory used=646.7MB, alloc=420.3MB, time=10.17 memory used=774.4MB, alloc=444.3MB, time=12.26 memory used=910.4MB, alloc=468.3MB, time=14.39 memory used=1041.8MB, alloc=468.3MB, time=16.55 memory used=1181.4MB, alloc=492.3MB, time=18.08 memory used=1342.0MB, alloc=492.3MB, time=20.32 memory used=1447.8MB, alloc=492.3MB, time=21.83 memory used=1566.3MB, alloc=516.3MB, time=23.74 memory used=1674.8MB, alloc=516.3MB, time=25.64 memory used=1746.6MB, alloc=516.3MB, time=26.85 memory used=1819.0MB, alloc=540.3MB, time=27.92 memory used=1898.8MB, alloc=540.3MB, time=29.43 memory used=1965.1MB, alloc=540.3MB, time=30.68 memory used=2025.3MB, alloc=540.3MB, time=31.65 memory used=2113.7MB, alloc=540.3MB, time=33.29 memory used=2181.3MB, alloc=540.3MB, time=34.81 memory used=2239.6MB, alloc=540.3MB, time=35.93 memory used=2276.2MB, alloc=540.3MB, time=36.71 memory used=2320.9MB, alloc=540.3MB, time=37.67 memory used=2533.4MB, alloc=564.3MB, time=41.02 memory used=2743.5MB, alloc=588.3MB, time=44.65 memory used=2930.1MB, alloc=612.3MB, time=47.90 memory used=3100.1MB, alloc=636.3MB, time=50.81 memory used=3275.0MB, alloc=660.3MB, time=54.14 memory used=3398.3MB, alloc=660.3MB, time=56.32 memory used=3552.3MB, alloc=684.3MB, time=58.66 memory used=3729.6MB, alloc=684.3MB, time=61.48 memory used=3945.8MB, alloc=684.3MB, time=63.03 memory used=4148.4MB, alloc=684.3MB, time=65.88 memory used=4261.2MB, alloc=684.3MB, time=67.81 memory used=4442.2MB, alloc=708.3MB, time=71.08 memory used=4563.8MB, alloc=708.3MB, time=74.19 memory used=4716.3MB, alloc=708.3MB, time=77.27 memory used=4835.3MB, alloc=708.3MB, time=79.26 memory used=4921.4MB, alloc=708.3MB, time=81.19 memory used=5288.4MB, alloc=732.3MB, time=86.86 memory used=5664.2MB, alloc=756.3MB, time=93.69 memory used=6048.2MB, alloc=780.3MB, time=100.80 memory used=6264.3MB, alloc=804.3MB, time=102.93 memory used=6617.5MB, alloc=828.3MB, time=108.31 memory used=6951.0MB, alloc=852.3MB, time=114.57 memory used=7250.6MB, alloc=876.3MB, time=120.67 memory used=7545.3MB, alloc=900.3MB, time=126.58 memory used=7792.6MB, alloc=924.3MB, time=132.15 memory used=8033.1MB, alloc=948.3MB, time=137.82 memory used=8240.7MB, alloc=972.3MB, time=143.45 memory used=8653.1MB, alloc=996.3MB, time=149.12 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428288073 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 3 2 F := [16 x y + 15 x y + 8 y , 19 x y z - 11 y - 11, 3 x y - 6 x - 15 y] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 2 4 2 3 2 G := [10 x - 12 x y + 10 x y , -16 x - 7 y z + 13 x z, 2 y - 8 y - 16 y] > Problem := [F,G]; Problem := [ 2 2 2 2 2 3 2 [16 x y + 15 x y + 8 y , 19 x y z - 11 y - 11, 3 x y - 6 x - 15 y], 4 3 2 4 2 3 2 [10 x - 12 x y + 10 x y , -16 x - 7 y z + 13 x z, 2 y - 8 y - 16 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.5MB, alloc=32.3MB, time=0.50 memory used=47.0MB, alloc=32.3MB, time=0.81 memory used=66.3MB, alloc=56.3MB, time=1.12 memory used=107.1MB, alloc=60.3MB, time=1.72 memory used=149.0MB, alloc=84.3MB, time=2.39 memory used=211.8MB, alloc=92.3MB, time=3.49 memory used=269.1MB, alloc=116.3MB, time=4.50 memory used=346.4MB, alloc=140.3MB, time=5.85 memory used=446.6MB, alloc=140.3MB, time=7.50 memory used=535.9MB, alloc=164.3MB, time=9.78 memory used=634.1MB, alloc=188.3MB, time=13.05 memory used=746.3MB, alloc=212.3MB, time=17.47 memory used=882.7MB, alloc=212.3MB, time=22.91 N1 := 3485 > GB := Basis(F, plex(op(vars))); 2 GB := [16 x + 15 x + 8, 90987 y - 18560 - 36352 x, 2490368 z - 55604131 - 83090128 x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1026.0MB, alloc=212.3MB, time=26.77 memory used=1117.3MB, alloc=492.3MB, time=28.56 memory used=1290.0MB, alloc=516.3MB, time=31.68 memory used=1480.3MB, alloc=540.3MB, time=36.33 memory used=1662.7MB, alloc=564.3MB, time=43.16 memory used=1855.1MB, alloc=588.3MB, time=51.28 memory used=2071.5MB, alloc=612.3MB, time=60.17 N2 := 4651 > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 2 3 2 H := [16 x y + 15 x y + 8 y , 19 z y x - 11 y - 11, 3 x y - 6 x - 15 y, 4 3 2 4 2 3 2 10 x - 12 x y + 10 x y , -16 x - 7 y z + 13 x z, 2 y - 8 y - 16 y] > J:=[op(GB),op(G)]; 2 J := [16 x + 15 x + 8, 90987 y - 18560 - 36352 x, 4 3 2 2490368 z - 55604131 - 83090128 x, 10 x - 12 x y + 10 x y , 4 2 3 2 -16 x - 7 y z + 13 x z, 2 y - 8 y - 16 y] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; 13 featureList := [6, 13, 23, 4, 4, 3, 1, 5/6, 1, 1/3, 5/9, --, 1/6, 6, 11, 15, 4, 18 4, 3, 1, 5/6, 2/3, 1/3, 1/2, 7/18, 1/6, 2, 8, 0] > save(F, G, cat("ranSet/34", convert(F, string),".txt")); > quit memory used=2213.7MB, alloc=612.3MB, time=65.61 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428288210 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 3 2 3 2 F := [-x y + 11 x + 6 y, -4 x z - 12 z + 19 x , -8 y z - 18 x y + z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 2 G := [5 x z - 2 x z + 11, -6 x z - 4 z + 18 z, 16 x y z + 2 x z - 19 x y] > Problem := [F,G]; Problem := [ 3 2 3 3 2 3 2 [-x y + 11 x + 6 y, -4 x z - 12 z + 19 x , -8 y z - 18 x y + z], 3 2 3 2 2 [5 x z - 2 x z + 11, -6 x z - 4 z + 18 z, 16 x y z + 2 x z - 19 x y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.1MB, alloc=32.3MB, time=0.51 memory used=47.3MB, alloc=32.3MB, time=0.83 memory used=65.2MB, alloc=56.3MB, time=1.11 memory used=104.9MB, alloc=60.3MB, time=1.73 memory used=143.0MB, alloc=60.3MB, time=2.32 memory used=180.9MB, alloc=84.3MB, time=2.92 memory used=222.1MB, alloc=84.3MB, time=3.51 memory used=283.3MB, alloc=92.3MB, time=4.51 memory used=344.6MB, alloc=92.3MB, time=5.43 memory used=404.1MB, alloc=116.3MB, time=6.36 memory used=477.4MB, alloc=372.3MB, time=7.51 memory used=563.0MB, alloc=396.3MB, time=8.84 memory used=673.5MB, alloc=396.3MB, time=10.59 memory used=781.7MB, alloc=420.3MB, time=12.28 memory used=910.9MB, alloc=420.3MB, time=14.10 memory used=1049.6MB, alloc=444.3MB, time=16.19 memory used=1184.0MB, alloc=444.3MB, time=18.35 memory used=1313.2MB, alloc=468.3MB, time=20.49 memory used=1443.6MB, alloc=468.3MB, time=22.77 memory used=1583.7MB, alloc=492.3MB, time=25.19 memory used=1695.2MB, alloc=492.3MB, time=27.07 memory used=1829.9MB, alloc=492.3MB, time=28.98 memory used=1926.5MB, alloc=492.3MB, time=30.28 memory used=2046.8MB, alloc=492.3MB, time=31.62 memory used=2143.7MB, alloc=492.3MB, time=32.26 memory used=2271.8MB, alloc=492.3MB, time=33.20 memory used=2419.3MB, alloc=492.3MB, time=35.02 memory used=2533.6MB, alloc=492.3MB, time=36.66 memory used=2637.0MB, alloc=492.3MB, time=38.53 memory used=2776.0MB, alloc=492.3MB, time=39.81 memory used=2891.1MB, alloc=492.3MB, time=41.54 memory used=3009.6MB, alloc=516.3MB, time=44.00 memory used=3102.2MB, alloc=516.3MB, time=46.03 memory used=3193.1MB, alloc=516.3MB, time=47.80 memory used=3284.1MB, alloc=516.3MB, time=49.59 memory used=3360.8MB, alloc=516.3MB, time=51.14 memory used=3439.9MB, alloc=516.3MB, time=52.58 memory used=3531.4MB, alloc=516.3MB, time=54.25 memory used=3619.3MB, alloc=516.3MB, time=55.94 memory used=3689.8MB, alloc=516.3MB, time=57.54 memory used=3769.3MB, alloc=516.3MB, time=59.24 memory used=3847.6MB, alloc=516.3MB, time=60.97 memory used=3915.7MB, alloc=516.3MB, time=62.46 memory used=3987.4MB, alloc=516.3MB, time=64.18 memory used=4039.5MB, alloc=516.3MB, time=65.34 memory used=4106.2MB, alloc=516.3MB, time=67.01 memory used=4157.9MB, alloc=516.3MB, time=68.27 memory used=4217.7MB, alloc=516.3MB, time=69.70 memory used=4258.3MB, alloc=516.3MB, time=70.74 memory used=4321.7MB, alloc=540.3MB, time=72.10 memory used=4365.2MB, alloc=540.3MB, time=73.34 memory used=4405.5MB, alloc=540.3MB, time=74.34 memory used=4456.1MB, alloc=540.3MB, time=75.54 memory used=4504.4MB, alloc=540.3MB, time=76.92 memory used=4549.0MB, alloc=540.3MB, time=78.16 memory used=4603.4MB, alloc=540.3MB, time=79.62 memory used=4651.3MB, alloc=540.3MB, time=80.72 memory used=4873.4MB, alloc=564.3MB, time=85.68 memory used=5083.7MB, alloc=588.3MB, time=89.53 memory used=5273.2MB, alloc=588.3MB, time=93.72 memory used=5481.4MB, alloc=612.3MB, time=98.30 memory used=5692.8MB, alloc=612.3MB, time=102.74 memory used=5866.5MB, alloc=612.3MB, time=104.08 memory used=6033.1MB, alloc=612.3MB, time=105.14 memory used=6197.0MB, alloc=612.3MB, time=106.64 memory used=6420.7MB, alloc=636.3MB, time=108.88 memory used=6612.0MB, alloc=636.3MB, time=110.08 memory used=6791.8MB, alloc=636.3MB, time=111.20 memory used=7011.8MB, alloc=636.3MB, time=114.15 memory used=7201.1MB, alloc=636.3MB, time=115.51 memory used=7395.9MB, alloc=636.3MB, time=116.75 memory used=7572.6MB, alloc=636.3MB, time=117.94 memory used=7734.3MB, alloc=636.3MB, time=118.81 memory used=7926.5MB, alloc=636.3MB, time=120.85 memory used=8169.1MB, alloc=636.3MB, time=123.38 memory used=8328.5MB, alloc=636.3MB, time=124.25 memory used=8450.6MB, alloc=636.3MB, time=125.03 memory used=8607.1MB, alloc=636.3MB, time=125.82 memory used=8773.8MB, alloc=636.3MB, time=127.22 memory used=8900.4MB, alloc=636.3MB, time=128.01 memory used=9053.2MB, alloc=636.3MB, time=128.81 memory used=9188.4MB, alloc=636.3MB, time=129.51 memory used=9303.4MB, alloc=636.3MB, time=130.20 memory used=9498.3MB, alloc=636.3MB, time=132.27 memory used=9667.3MB, alloc=636.3MB, time=135.45 memory used=9838.1MB, alloc=636.3MB, time=137.52 memory used=10078.4MB, alloc=636.3MB, time=142.24 memory used=10248.4MB, alloc=660.3MB, time=146.15 memory used=10393.1MB, alloc=660.3MB, time=149.66 memory used=10548.0MB, alloc=660.3MB, time=153.62 memory used=10703.4MB, alloc=684.3MB, time=157.05 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428288510 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; F := [ 3 2 3 2 2 2 2 7 x z - 12 x y - 6 z , -17 x z + 9 x y - 4 z, 11 x y z + 7 x y + 12 y ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 2 2 G := [16 x y - 4 z + 14 y , 15 x z - 20 x y z + 2 x y, 2 2 3 2 5 x y + 6 x z - 4 y ] > Problem := [F,G]; Problem := [[ 3 2 3 2 2 2 2 7 x z - 12 x y - 6 z , -17 x z + 9 x y - 4 z, 11 x y z + 7 x y + 12 y 3 3 2 2 2 2 ], [16 x y - 4 z + 14 y , 15 x z - 20 x y z + 2 x y, 2 2 3 2 5 x y + 6 x z - 4 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.18 memory used=25.1MB, alloc=32.3MB, time=0.49 memory used=45.8MB, alloc=60.3MB, time=0.80 memory used=86.3MB, alloc=60.3MB, time=1.28 memory used=129.6MB, alloc=68.3MB, time=1.91 memory used=170.9MB, alloc=92.3MB, time=2.52 memory used=237.0MB, alloc=92.3MB, time=3.43 memory used=306.3MB, alloc=348.3MB, time=4.29 memory used=373.7MB, alloc=372.3MB, time=5.20 memory used=442.3MB, alloc=372.3MB, time=5.82 memory used=502.6MB, alloc=372.3MB, time=6.21 memory used=597.8MB, alloc=372.3MB, time=7.34 memory used=698.5MB, alloc=372.3MB, time=8.29 memory used=763.1MB, alloc=396.3MB, time=8.92 memory used=850.0MB, alloc=396.3MB, time=9.65 memory used=972.7MB, alloc=396.3MB, time=10.90 memory used=1085.5MB, alloc=396.3MB, time=12.47 memory used=1199.8MB, alloc=420.3MB, time=14.05 memory used=1329.9MB, alloc=444.3MB, time=16.02 memory used=1475.4MB, alloc=444.3MB, time=17.57 memory used=1561.0MB, alloc=444.3MB, time=18.12 memory used=1690.8MB, alloc=468.3MB, time=19.63 memory used=1810.6MB, alloc=468.3MB, time=21.25 memory used=1958.1MB, alloc=468.3MB, time=22.56 memory used=2076.2MB, alloc=468.3MB, time=23.82 memory used=2200.6MB, alloc=468.3MB, time=24.93 memory used=2339.3MB, alloc=468.3MB, time=26.60 memory used=2499.5MB, alloc=468.3MB, time=28.00 memory used=2631.9MB, alloc=468.3MB, time=29.33 memory used=2737.4MB, alloc=468.3MB, time=30.81 memory used=2857.1MB, alloc=492.3MB, time=32.54 memory used=2959.8MB, alloc=492.3MB, time=34.09 memory used=3042.2MB, alloc=492.3MB, time=35.46 memory used=3121.9MB, alloc=492.3MB, time=36.85 memory used=3200.8MB, alloc=492.3MB, time=38.23 memory used=3271.3MB, alloc=492.3MB, time=39.49 memory used=3376.1MB, alloc=492.3MB, time=40.51 memory used=3510.8MB, alloc=492.3MB, time=42.19 memory used=3633.4MB, alloc=492.3MB, time=43.34 memory used=3720.7MB, alloc=492.3MB, time=45.18 memory used=3849.0MB, alloc=492.3MB, time=46.47 memory used=3986.8MB, alloc=516.3MB, time=49.12 memory used=4130.6MB, alloc=516.3MB, time=50.66 memory used=4267.2MB, alloc=516.3MB, time=51.93 memory used=4375.8MB, alloc=516.3MB, time=52.48 memory used=4491.7MB, alloc=516.3MB, time=53.47 memory used=4563.4MB, alloc=516.3MB, time=54.71 memory used=4628.3MB, alloc=516.3MB, time=55.96 memory used=4705.7MB, alloc=516.3MB, time=57.03 memory used=4763.5MB, alloc=516.3MB, time=58.06 memory used=4881.6MB, alloc=516.3MB, time=58.89 memory used=4985.6MB, alloc=516.3MB, time=59.55 memory used=5085.6MB, alloc=516.3MB, time=60.09 memory used=5175.9MB, alloc=516.3MB, time=60.62 memory used=5275.3MB, alloc=516.3MB, time=61.16 memory used=5370.1MB, alloc=516.3MB, time=61.67 memory used=5467.2MB, alloc=516.3MB, time=62.24 memory used=5567.2MB, alloc=516.3MB, time=62.78 memory used=5659.6MB, alloc=516.3MB, time=63.28 memory used=5753.4MB, alloc=516.3MB, time=63.78 memory used=5868.9MB, alloc=516.3MB, time=64.66 memory used=5971.4MB, alloc=516.3MB, time=65.27 memory used=6075.1MB, alloc=516.3MB, time=65.81 memory used=6188.4MB, alloc=516.3MB, time=67.91 memory used=6277.4MB, alloc=516.3MB, time=68.36 memory used=6379.4MB, alloc=516.3MB, time=68.82 memory used=6556.2MB, alloc=516.3MB, time=69.53 memory used=6621.7MB, alloc=516.3MB, time=70.52 memory used=6685.1MB, alloc=516.3MB, time=71.43 memory used=6748.7MB, alloc=516.3MB, time=72.27 memory used=6862.9MB, alloc=516.3MB, time=73.34 memory used=7074.9MB, alloc=540.3MB, time=76.02 memory used=7287.9MB, alloc=540.3MB, time=78.44 memory used=7508.5MB, alloc=540.3MB, time=81.18 memory used=7717.0MB, alloc=564.3MB, time=84.47 memory used=7915.4MB, alloc=588.3MB, time=86.56 memory used=8067.8MB, alloc=588.3MB, time=87.90 memory used=8320.7MB, alloc=588.3MB, time=90.42 memory used=8443.1MB, alloc=588.3MB, time=91.10 memory used=8586.6MB, alloc=588.3MB, time=94.67 memory used=8716.6MB, alloc=588.3MB, time=95.37 memory used=8815.2MB, alloc=588.3MB, time=95.98 memory used=8943.9MB, alloc=588.3MB, time=96.61 memory used=9146.7MB, alloc=588.3MB, time=97.35 memory used=9307.1MB, alloc=588.3MB, time=98.02 memory used=9507.6MB, alloc=588.3MB, time=99.81 memory used=9623.3MB, alloc=588.3MB, time=100.46 memory used=9747.2MB, alloc=588.3MB, time=101.21 memory used=9949.0MB, alloc=588.3MB, time=102.87 memory used=10214.5MB, alloc=588.3MB, time=106.39 memory used=10373.3MB, alloc=612.3MB, time=108.93 memory used=10596.2MB, alloc=612.3MB, time=111.76 memory used=10783.9MB, alloc=612.3MB, time=114.34 memory used=10942.4MB, alloc=636.3MB, time=116.85 memory used=11063.2MB, alloc=636.3MB, time=118.94 memory used=11186.4MB, alloc=636.3MB, time=120.88 memory used=11340.0MB, alloc=660.3MB, time=123.10 memory used=11452.4MB, alloc=660.3MB, time=125.56 memory used=11563.8MB, alloc=660.3MB, time=127.66 memory used=11690.7MB, alloc=684.3MB, time=129.61 memory used=11848.5MB, alloc=684.3MB, time=131.68 memory used=11928.1MB, alloc=684.3MB, time=133.48 memory used=12027.5MB, alloc=684.3MB, time=135.23 memory used=12156.4MB, alloc=684.3MB, time=137.41 memory used=12544.4MB, alloc=708.3MB, time=141.60 memory used=12954.9MB, alloc=732.3MB, time=146.12 memory used=13281.7MB, alloc=756.3MB, time=150.47 memory used=13738.7MB, alloc=780.3MB, time=155.78 memory used=14211.3MB, alloc=804.3MB, time=160.67 memory used=14624.2MB, alloc=828.3MB, time=167.52 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428288810 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 2 F := [-13 x y - 14 x z - 14 z , -15 x y + 11 x y z - 12 x , 3 2 2 3 4 x y + 12 x y - 4 y z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 3 3 3 G := [12 y z - 14 z - 18 x, -17 y z + 10 y z - 2 z , -13 x y + z + 6] > Problem := [F,G]; 2 2 2 3 2 2 Problem := [[-13 x y - 14 x z - 14 z , -15 x y + 11 x y z - 12 x , 3 2 2 3 4 x y + 12 x y - 4 y z ], 3 2 2 2 3 3 3 [12 y z - 14 z - 18 x, -17 y z + 10 y z - 2 z , -13 x y + z + 6]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=27.0MB, alloc=32.3MB, time=0.50 memory used=46.1MB, alloc=56.3MB, time=0.80 memory used=94.0MB, alloc=60.3MB, time=1.47 memory used=138.3MB, alloc=68.3MB, time=2.09 memory used=184.7MB, alloc=68.3MB, time=2.73 memory used=230.7MB, alloc=68.3MB, time=3.35 memory used=280.8MB, alloc=68.3MB, time=3.85 memory used=320.9MB, alloc=92.3MB, time=4.44 memory used=387.6MB, alloc=92.3MB, time=5.31 memory used=436.9MB, alloc=92.3MB, time=5.93 memory used=482.0MB, alloc=92.3MB, time=7.88 memory used=517.5MB, alloc=92.3MB, time=8.05 memory used=565.6MB, alloc=92.3MB, time=10.40 memory used=599.2MB, alloc=92.3MB, time=10.54 memory used=647.1MB, alloc=92.3MB, time=12.87 memory used=681.6MB, alloc=92.3MB, time=13.21 memory used=742.2MB, alloc=92.3MB, time=13.95 memory used=792.2MB, alloc=92.3MB, time=16.32 memory used=840.8MB, alloc=116.3MB, time=16.72 memory used=908.8MB, alloc=116.3MB, time=17.50 memory used=974.0MB, alloc=372.3MB, time=18.33 memory used=1058.7MB, alloc=396.3MB, time=19.44 memory used=1161.1MB, alloc=396.3MB, time=22.34 memory used=1223.0MB, alloc=396.3MB, time=22.60 memory used=1304.0MB, alloc=396.3MB, time=25.25 memory used=1385.3MB, alloc=396.3MB, time=27.97 memory used=1449.0MB, alloc=396.3MB, time=28.61 memory used=1533.3MB, alloc=396.3MB, time=29.38 memory used=1608.6MB, alloc=396.3MB, time=29.92 memory used=1720.4MB, alloc=396.3MB, time=30.88 memory used=1832.7MB, alloc=396.3MB, time=31.96 memory used=1942.8MB, alloc=420.3MB, time=32.88 memory used=2043.1MB, alloc=420.3MB, time=37.59 memory used=2107.9MB, alloc=420.3MB, time=37.82 memory used=2190.4MB, alloc=420.3MB, time=38.14 memory used=2285.7MB, alloc=420.3MB, time=42.86 memory used=2357.6MB, alloc=420.3MB, time=43.16 memory used=2457.7MB, alloc=420.3MB, time=47.98 memory used=2519.7MB, alloc=420.3MB, time=48.20 memory used=2608.0MB, alloc=420.3MB, time=49.31 memory used=2708.8MB, alloc=420.3MB, time=50.02 memory used=2839.0MB, alloc=420.3MB, time=51.51 memory used=2962.9MB, alloc=444.3MB, time=53.22 memory used=3064.2MB, alloc=444.3MB, time=53.86 memory used=3154.5MB, alloc=444.3MB, time=54.39 memory used=3242.6MB, alloc=444.3MB, time=54.85 memory used=3335.8MB, alloc=444.3MB, time=55.99 memory used=3415.6MB, alloc=444.3MB, time=56.60 memory used=3512.9MB, alloc=444.3MB, time=57.33 memory used=3650.4MB, alloc=444.3MB, time=58.59 memory used=3774.7MB, alloc=468.3MB, time=60.38 memory used=3881.5MB, alloc=468.3MB, time=61.93 memory used=3992.5MB, alloc=468.3MB, time=65.30 memory used=4104.3MB, alloc=492.3MB, time=66.66 memory used=4202.2MB, alloc=492.3MB, time=67.91 memory used=4315.3MB, alloc=492.3MB, time=69.28 memory used=4404.4MB, alloc=492.3MB, time=69.69 memory used=4484.8MB, alloc=492.3MB, time=70.03 memory used=4594.8MB, alloc=492.3MB, time=70.58 memory used=4668.5MB, alloc=492.3MB, time=70.91 memory used=4801.2MB, alloc=492.3MB, time=80.98 memory used=4889.2MB, alloc=492.3MB, time=81.36 memory used=4963.3MB, alloc=492.3MB, time=81.68 memory used=5057.6MB, alloc=492.3MB, time=82.16 memory used=5154.1MB, alloc=492.3MB, time=82.56 memory used=5232.1MB, alloc=492.3MB, time=82.91 memory used=5367.5MB, alloc=492.3MB, time=93.16 memory used=5455.7MB, alloc=492.3MB, time=93.52 memory used=5525.5MB, alloc=492.3MB, time=93.83 memory used=5623.6MB, alloc=492.3MB, time=94.20 memory used=5734.1MB, alloc=492.3MB, time=96.90 memory used=5859.8MB, alloc=492.3MB, time=97.86 memory used=5971.0MB, alloc=492.3MB, time=105.88 memory used=6081.4MB, alloc=492.3MB, time=131.38 memory used=6162.5MB, alloc=492.3MB, time=131.77 memory used=6255.4MB, alloc=492.3MB, time=132.12 memory used=6318.8MB, alloc=492.3MB, time=132.45 memory used=6393.0MB, alloc=492.3MB, time=132.76 memory used=6479.4MB, alloc=492.3MB, time=133.09 memory used=6580.3MB, alloc=492.3MB, time=133.45 memory used=6806.3MB, alloc=492.3MB, time=134.26 memory used=6946.6MB, alloc=492.3MB, time=166.98 memory used=7043.6MB, alloc=516.3MB, time=167.48 memory used=7153.0MB, alloc=516.3MB, time=167.88 memory used=7232.7MB, alloc=516.3MB, time=168.24 memory used=7323.0MB, alloc=516.3MB, time=168.60 memory used=7431.7MB, alloc=516.3MB, time=168.96 memory used=7694.4MB, alloc=516.3MB, time=175.24 memory used=7803.5MB, alloc=516.3MB, time=175.65 memory used=7887.1MB, alloc=516.3MB, time=176.00 memory used=8054.1MB, alloc=516.3MB, time=179.22 memory used=8204.4MB, alloc=516.3MB, time=180.73 memory used=8298.3MB, alloc=516.3MB, time=181.09 memory used=8423.7MB, alloc=516.3MB, time=182.09 memory used=8531.7MB, alloc=516.3MB, time=182.54 memory used=8613.6MB, alloc=516.3MB, time=182.94 memory used=8723.9MB, alloc=516.3MB, time=183.33 memory used=8845.9MB, alloc=516.3MB, time=214.30 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428289110 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 4 4 2 3 2 3 F := [12 x z - 18 y , 7 x + x - 20 x z, 5 x y - 16 y z - 8 z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 3 2 3 G := [15 x + 8 x y + 11 y, -17 x y - 7 y z , 4 y z + 8 x y z - 14 y] > Problem := [F,G]; 2 2 4 4 2 3 2 3 Problem := [[12 x z - 18 y , 7 x + x - 20 x z, 5 x y - 16 y z - 8 z ], 4 2 3 2 3 [15 x + 8 x y + 11 y, -17 x y - 7 y z , 4 y z + 8 x y z - 14 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.17 memory used=27.0MB, alloc=32.3MB, time=0.48 memory used=47.8MB, alloc=32.3MB, time=0.76 memory used=67.6MB, alloc=32.3MB, time=1.04 memory used=86.5MB, alloc=56.3MB, time=1.32 memory used=127.8MB, alloc=60.3MB, time=1.92 memory used=168.2MB, alloc=68.3MB, time=2.48 memory used=208.6MB, alloc=92.3MB, time=3.05 memory used=273.7MB, alloc=92.3MB, time=3.92 memory used=338.5MB, alloc=116.3MB, time=4.79 memory used=414.7MB, alloc=116.3MB, time=5.82 memory used=482.4MB, alloc=372.3MB, time=6.76 memory used=567.6MB, alloc=396.3MB, time=7.93 memory used=675.9MB, alloc=420.3MB, time=9.44 memory used=808.7MB, alloc=444.3MB, time=11.24 memory used=933.8MB, alloc=468.3MB, time=13.11 memory used=1032.0MB, alloc=468.3MB, time=14.55 memory used=1133.4MB, alloc=468.3MB, time=15.80 memory used=1225.6MB, alloc=492.3MB, time=16.91 memory used=1335.0MB, alloc=492.3MB, time=18.04 memory used=1404.3MB, alloc=492.3MB, time=19.21 memory used=1471.7MB, alloc=516.3MB, time=20.26 memory used=1549.5MB, alloc=516.3MB, time=21.29 memory used=1614.1MB, alloc=516.3MB, time=22.11 memory used=1682.5MB, alloc=516.3MB, time=23.17 memory used=1754.2MB, alloc=516.3MB, time=24.56 memory used=1803.2MB, alloc=516.3MB, time=25.44 memory used=1853.8MB, alloc=516.3MB, time=26.38 memory used=2069.5MB, alloc=540.3MB, time=28.61 memory used=2241.0MB, alloc=564.3MB, time=31.26 memory used=2419.6MB, alloc=588.3MB, time=33.49 memory used=2604.3MB, alloc=612.3MB, time=35.78 memory used=2719.1MB, alloc=636.3MB, time=37.92 memory used=2860.4MB, alloc=660.3MB, time=40.02 memory used=2980.3MB, alloc=660.3MB, time=42.47 memory used=3090.8MB, alloc=660.3MB, time=44.67 memory used=3200.5MB, alloc=660.3MB, time=46.65 memory used=3313.4MB, alloc=660.3MB, time=48.64 memory used=3651.4MB, alloc=684.3MB, time=53.75 memory used=4008.5MB, alloc=708.3MB, time=58.56 memory used=4391.3MB, alloc=732.3MB, time=64.14 memory used=4719.7MB, alloc=756.3MB, time=69.18 memory used=5036.0MB, alloc=780.3MB, time=74.64 memory used=5311.2MB, alloc=804.3MB, time=79.47 memory used=5556.1MB, alloc=828.3MB, time=84.52 memory used=5800.5MB, alloc=852.3MB, time=89.90 memory used=6032.3MB, alloc=876.3MB, time=94.81 memory used=6308.5MB, alloc=900.3MB, time=99.27 memory used=6513.6MB, alloc=924.3MB, time=103.68 memory used=6695.0MB, alloc=948.3MB, time=107.86 memory used=7271.5MB, alloc=972.3MB, time=117.87 memory used=7902.1MB, alloc=996.3MB, time=127.15 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428289410 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 4 2 2 3 2 F := [-3 x y z + 16 y - 4, -19 x y + 6 x z - 16 x , 2 -13 x y z - 3 x z + 19 x] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 3 2 4 2 G := [15 x z - 3 x y + y z , 4 x y + 20 x z - 11 y z, 10 z + 8 x y] > Problem := [F,G]; 2 4 2 2 3 2 Problem := [[-3 x y z + 16 y - 4, -19 x y + 6 x z - 16 x , 2 -13 x y z - 3 x z + 19 x], 3 3 2 2 3 2 4 2 [15 x z - 3 x y + y z , 4 x y + 20 x z - 11 y z, 10 z + 8 x y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=27.5MB, alloc=32.3MB, time=0.52 memory used=49.3MB, alloc=60.3MB, time=0.84 memory used=90.8MB, alloc=61.7MB, time=1.14 memory used=134.2MB, alloc=64.3MB, time=1.71 memory used=162.0MB, alloc=64.3MB, time=1.79 memory used=200.7MB, alloc=64.3MB, time=2.25 memory used=240.4MB, alloc=64.3MB, time=2.79 memory used=301.2MB, alloc=72.3MB, time=4.26 memory used=344.0MB, alloc=72.3MB, time=4.64 memory used=374.4MB, alloc=72.3MB, time=4.83 memory used=418.3MB, alloc=72.3MB, time=5.41 memory used=463.0MB, alloc=96.3MB, time=6.04 memory used=519.4MB, alloc=96.3MB, time=6.81 memory used=575.6MB, alloc=96.3MB, time=7.57 memory used=634.7MB, alloc=376.3MB, time=8.26 memory used=702.7MB, alloc=376.3MB, time=8.70 memory used=767.6MB, alloc=376.3MB, time=9.14 memory used=831.1MB, alloc=376.3MB, time=9.49 memory used=892.7MB, alloc=376.3MB, time=10.10 memory used=949.3MB, alloc=376.3MB, time=10.37 memory used=1008.3MB, alloc=376.3MB, time=10.95 memory used=1067.2MB, alloc=376.3MB, time=11.24 memory used=1139.1MB, alloc=376.3MB, time=11.84 memory used=1190.8MB, alloc=376.3MB, time=12.12 memory used=1246.4MB, alloc=376.3MB, time=12.43 memory used=1304.2MB, alloc=376.3MB, time=12.88 memory used=1414.5MB, alloc=376.3MB, time=15.06 memory used=1532.5MB, alloc=376.3MB, time=16.85 memory used=1650.1MB, alloc=376.3MB, time=18.48 memory used=1755.2MB, alloc=376.3MB, time=22.33 memory used=1800.9MB, alloc=376.3MB, time=22.50 memory used=1836.0MB, alloc=376.3MB, time=22.64 memory used=1880.2MB, alloc=376.3MB, time=22.79 memory used=1955.1MB, alloc=376.3MB, time=25.95 memory used=2001.7MB, alloc=376.3MB, time=26.12 memory used=2036.2MB, alloc=376.3MB, time=26.25 memory used=2079.0MB, alloc=376.3MB, time=26.39 memory used=2120.0MB, alloc=376.3MB, time=26.52 memory used=2234.7MB, alloc=376.3MB, time=27.85 memory used=2343.2MB, alloc=376.3MB, time=30.00 memory used=2431.6MB, alloc=400.3MB, time=31.12 memory used=2500.5MB, alloc=400.3MB, time=31.65 memory used=2603.7MB, alloc=400.3MB, time=32.92 memory used=2680.0MB, alloc=400.3MB, time=34.24 memory used=2727.1MB, alloc=400.3MB, time=34.45 memory used=2813.3MB, alloc=400.3MB, time=35.09 memory used=2898.0MB, alloc=400.3MB, time=36.21 memory used=3010.6MB, alloc=424.3MB, time=37.96 memory used=3120.5MB, alloc=424.3MB, time=39.48 memory used=3221.8MB, alloc=448.3MB, time=41.01 memory used=3328.7MB, alloc=448.3MB, time=41.81 memory used=3442.9MB, alloc=448.3MB, time=42.70 memory used=3529.3MB, alloc=448.3MB, time=43.18 memory used=3605.6MB, alloc=448.3MB, time=43.54 memory used=3659.2MB, alloc=448.3MB, time=43.83 memory used=3727.6MB, alloc=448.3MB, time=44.14 memory used=3815.5MB, alloc=448.3MB, time=44.58 memory used=3883.3MB, alloc=448.3MB, time=44.88 memory used=3965.8MB, alloc=448.3MB, time=45.85 memory used=4031.4MB, alloc=448.3MB, time=46.15 memory used=4125.2MB, alloc=448.3MB, time=46.73 memory used=4241.0MB, alloc=448.3MB, time=47.76 memory used=4306.6MB, alloc=448.3MB, time=48.09 memory used=4381.5MB, alloc=448.3MB, time=48.42 memory used=4433.5MB, alloc=448.3MB, time=48.73 memory used=4493.3MB, alloc=448.3MB, time=49.03 memory used=4564.1MB, alloc=448.3MB, time=49.31 memory used=4655.6MB, alloc=448.3MB, time=49.85 memory used=4729.0MB, alloc=448.3MB, time=50.22 memory used=4806.5MB, alloc=448.3MB, time=50.57 memory used=4859.1MB, alloc=448.3MB, time=50.88 memory used=4924.9MB, alloc=448.3MB, time=51.16 memory used=5024.8MB, alloc=448.3MB, time=53.75 memory used=5085.9MB, alloc=448.3MB, time=54.04 memory used=5152.0MB, alloc=448.3MB, time=54.32 memory used=5245.9MB, alloc=448.3MB, time=54.96 memory used=5364.9MB, alloc=448.3MB, time=56.56 memory used=5457.5MB, alloc=448.3MB, time=57.91 memory used=5567.3MB, alloc=448.3MB, time=59.06 memory used=5735.2MB, alloc=448.3MB, time=67.18 memory used=5809.8MB, alloc=472.3MB, time=67.57 memory used=5881.5MB, alloc=472.3MB, time=67.93 memory used=5966.6MB, alloc=472.3MB, time=68.29 memory used=6063.2MB, alloc=472.3MB, time=68.65 memory used=6120.6MB, alloc=472.3MB, time=68.95 memory used=6184.2MB, alloc=472.3MB, time=69.26 memory used=6253.4MB, alloc=472.3MB, time=69.60 memory used=6327.8MB, alloc=472.3MB, time=69.92 memory used=6407.8MB, alloc=472.3MB, time=70.23 memory used=6494.7MB, alloc=472.3MB, time=70.55 memory used=6589.3MB, alloc=472.3MB, time=70.86 memory used=6690.9MB, alloc=472.3MB, time=71.19 memory used=6891.3MB, alloc=472.3MB, time=71.80 memory used=7033.9MB, alloc=472.3MB, time=72.20 memory used=7189.7MB, alloc=472.3MB, time=72.61 memory used=7360.9MB, alloc=472.3MB, time=73.02 memory used=7554.1MB, alloc=472.3MB, time=73.45 memory used=7811.9MB, alloc=472.3MB, time=74.67 memory used=7895.0MB, alloc=472.3MB, time=75.97 memory used=7972.2MB, alloc=472.3MB, time=77.13 memory used=8030.3MB, alloc=472.3MB, time=78.13 memory used=8100.0MB, alloc=472.3MB, time=79.28 memory used=8185.3MB, alloc=472.3MB, time=80.32 memory used=8282.9MB, alloc=472.3MB, time=80.89 memory used=8381.4MB, alloc=472.3MB, time=81.50 memory used=8461.0MB, alloc=472.3MB, time=81.92 memory used=8562.8MB, alloc=472.3MB, time=84.37 memory used=8637.6MB, alloc=472.3MB, time=84.79 memory used=8709.4MB, alloc=472.3MB, time=85.19 memory used=8793.9MB, alloc=472.3MB, time=85.59 memory used=8850.9MB, alloc=472.3MB, time=85.92 memory used=8927.8MB, alloc=472.3MB, time=86.49 memory used=9029.6MB, alloc=472.3MB, time=87.22 memory used=9106.5MB, alloc=472.3MB, time=87.64 memory used=9178.3MB, alloc=496.3MB, time=88.05 memory used=9261.2MB, alloc=496.3MB, time=88.45 memory used=9386.4MB, alloc=496.3MB, time=90.60 memory used=9475.7MB, alloc=496.3MB, time=91.03 memory used=9575.8MB, alloc=496.3MB, time=91.45 memory used=9654.2MB, alloc=496.3MB, time=91.83 memory used=9772.4MB, alloc=496.3MB, time=92.63 memory used=9876.9MB, alloc=496.3MB, time=93.17 memory used=9990.8MB, alloc=496.3MB, time=94.03 memory used=10109.6MB, alloc=496.3MB, time=95.02 memory used=10206.0MB, alloc=496.3MB, time=95.53 memory used=10309.5MB, alloc=496.3MB, time=96.00 memory used=10395.1MB, alloc=496.3MB, time=96.43 memory used=10469.0MB, alloc=496.3MB, time=96.84 memory used=10551.6MB, alloc=496.3MB, time=97.27 memory used=10644.3MB, alloc=496.3MB, time=97.68 memory used=10748.4MB, alloc=496.3MB, time=98.12 memory used=10844.9MB, alloc=496.3MB, time=98.52 memory used=10927.0MB, alloc=496.3MB, time=98.89 memory used=10994.6MB, alloc=496.3MB, time=99.24 memory used=11067.7MB, alloc=496.3MB, time=99.61 memory used=11149.4MB, alloc=496.3MB, time=99.98 memory used=11266.3MB, alloc=496.3MB, time=100.79 memory used=11359.4MB, alloc=496.3MB, time=101.30 memory used=11466.4MB, alloc=496.3MB, time=101.75 memory used=11539.0MB, alloc=496.3MB, time=102.18 memory used=11620.8MB, alloc=496.3MB, time=102.62 memory used=11715.4MB, alloc=496.3MB, time=103.04 memory used=11817.4MB, alloc=496.3MB, time=103.44 memory used=11902.3MB, alloc=496.3MB, time=103.82 memory used=11974.6MB, alloc=496.3MB, time=104.19 memory used=12088.1MB, alloc=496.3MB, time=106.78 memory used=12178.6MB, alloc=496.3MB, time=107.20 memory used=12274.3MB, alloc=496.3MB, time=107.61 memory used=12359.9MB, alloc=496.3MB, time=107.99 memory used=12440.4MB, alloc=496.3MB, time=108.32 memory used=12556.5MB, alloc=496.3MB, time=108.95 memory used=12664.4MB, alloc=496.3MB, time=109.83 memory used=12787.5MB, alloc=496.3MB, time=110.70 memory used=12863.0MB, alloc=496.3MB, time=114.72 memory used=12980.1MB, alloc=496.3MB, time=115.74 memory used=13059.5MB, alloc=496.3MB, time=116.17 memory used=13154.7MB, alloc=496.3MB, time=116.60 memory used=13250.3MB, alloc=496.3MB, time=117.00 memory used=13320.6MB, alloc=496.3MB, time=117.36 memory used=13400.9MB, alloc=496.3MB, time=117.71 memory used=13535.4MB, alloc=496.3MB, time=118.65 memory used=13632.2MB, alloc=496.3MB, time=119.74 memory used=13731.6MB, alloc=496.3MB, time=120.77 memory used=13849.1MB, alloc=496.3MB, time=122.58 memory used=13947.6MB, alloc=496.3MB, time=125.12 memory used=14046.8MB, alloc=496.3MB, time=128.03 memory used=14148.1MB, alloc=496.3MB, time=129.00 memory used=14236.2MB, alloc=496.3MB, time=129.45 memory used=14315.8MB, alloc=496.3MB, time=129.88 memory used=14418.7MB, alloc=496.3MB, time=130.33 memory used=14485.2MB, alloc=496.3MB, time=130.73 memory used=14559.2MB, alloc=496.3MB, time=131.11 memory used=14668.3MB, alloc=496.3MB, time=133.22 memory used=14760.1MB, alloc=496.3MB, time=133.70 memory used=14831.1MB, alloc=496.3MB, time=134.11 memory used=14919.0MB, alloc=496.3MB, time=134.51 memory used=15142.9MB, alloc=496.3MB, time=137.09 memory used=15245.7MB, alloc=496.3MB, time=137.64 memory used=15343.2MB, alloc=496.3MB, time=138.19 memory used=15422.5MB, alloc=520.3MB, time=138.68 memory used=15504.7MB, alloc=520.3MB, time=139.13 memory used=15598.8MB, alloc=520.3MB, time=139.59 memory used=15701.5MB, alloc=520.3MB, time=140.05 memory used=15817.3MB, alloc=520.3MB, time=140.52 memory used=15941.7MB, alloc=520.3MB, time=141.01 memory used=16039.9MB, alloc=544.3MB, time=141.46 memory used=16118.7MB, alloc=544.3MB, time=141.86 memory used=16205.0MB, alloc=544.3MB, time=142.27 memory used=16294.2MB, alloc=544.3MB, time=142.69 memory used=16385.8MB, alloc=544.3MB, time=143.11 memory used=16486.0MB, alloc=544.3MB, time=143.53 memory used=16588.4MB, alloc=544.3MB, time=143.97 memory used=16693.5MB, alloc=544.3MB, time=144.41 memory used=16806.0MB, alloc=544.3MB, time=144.84 memory used=16921.1MB, alloc=544.3MB, time=145.28 memory used=17044.8MB, alloc=544.3MB, time=145.72 memory used=17170.9MB, alloc=544.3MB, time=146.15 memory used=17303.9MB, alloc=544.3MB, time=146.60 memory used=17446.1MB, alloc=544.3MB, time=147.05 memory used=17589.9MB, alloc=544.3MB, time=147.52 memory used=17752.3MB, alloc=544.3MB, time=148.00 memory used=17928.5MB, alloc=544.3MB, time=148.54 memory used=18056.9MB, alloc=544.3MB, time=149.03 memory used=18188.7MB, alloc=544.3MB, time=149.52 memory used=18326.2MB, alloc=544.3MB, time=149.99 memory used=18468.8MB, alloc=544.3MB, time=150.46 memory used=18615.7MB, alloc=544.3MB, time=151.00 memory used=18767.1MB, alloc=544.3MB, time=151.50 memory used=18925.8MB, alloc=544.3MB, time=152.02 memory used=19091.7MB, alloc=544.3MB, time=152.54 memory used=19266.3MB, alloc=544.3MB, time=153.06 memory used=19451.3MB, alloc=544.3MB, time=153.59 memory used=19651.1MB, alloc=544.3MB, time=154.12 memory used=19857.7MB, alloc=544.3MB, time=156.04 memory used=19980.7MB, alloc=544.3MB, time=156.62 memory used=20080.8MB, alloc=544.3MB, time=157.14 memory used=20199.1MB, alloc=544.3MB, time=157.65 memory used=20338.7MB, alloc=544.3MB, time=158.19 memory used=20477.0MB, alloc=544.3MB, time=158.73 memory used=20559.4MB, alloc=544.3MB, time=159.15 memory used=20646.4MB, alloc=544.3MB, time=159.59 memory used=20741.8MB, alloc=544.3MB, time=160.03 memory used=20839.7MB, alloc=544.3MB, time=160.47 memory used=20945.1MB, alloc=544.3MB, time=160.90 memory used=21058.1MB, alloc=544.3MB, time=161.34 memory used=21178.2MB, alloc=544.3MB, time=161.80 memory used=21305.5MB, alloc=544.3MB, time=162.26 memory used=21439.3MB, alloc=544.3MB, time=162.74 memory used=21579.0MB, alloc=544.3MB, time=163.20 memory used=21729.5MB, alloc=544.3MB, time=163.65 memory used=21972.2MB, alloc=544.3MB, time=164.24 memory used=22105.3MB, alloc=544.3MB, time=164.75 memory used=22245.7MB, alloc=544.3MB, time=165.25 memory used=22394.2MB, alloc=544.3MB, time=165.75 memory used=22552.8MB, alloc=544.3MB, time=166.24 memory used=22727.0MB, alloc=544.3MB, time=166.76 memory used=22897.8MB, alloc=544.3MB, time=183.49 memory used=23023.7MB, alloc=544.3MB, time=184.01 memory used=23131.1MB, alloc=544.3MB, time=184.44 memory used=23234.1MB, alloc=544.3MB, time=184.89 memory used=23352.4MB, alloc=544.3MB, time=185.31 memory used=23489.2MB, alloc=544.3MB, time=185.75 memory used=23768.5MB, alloc=544.3MB, time=186.38 memory used=23914.2MB, alloc=544.3MB, time=186.86 memory used=24075.9MB, alloc=544.3MB, time=187.36 memory used=24256.8MB, alloc=544.3MB, time=187.87 memory used=24465.5MB, alloc=544.3MB, time=188.41 memory used=24727.1MB, alloc=544.3MB, time=189.61 memory used=24845.2MB, alloc=544.3MB, time=190.10 memory used=24963.7MB, alloc=544.3MB, time=190.54 memory used=25066.3MB, alloc=544.3MB, time=190.94 memory used=25219.1MB, alloc=544.3MB, time=193.32 memory used=25331.0MB, alloc=544.3MB, time=193.76 memory used=25454.7MB, alloc=544.3MB, time=194.18 memory used=25659.5MB, alloc=544.3MB, time=195.35 memory used=25729.3MB, alloc=544.3MB, time=196.19 memory used=25770.3MB, alloc=544.3MB, time=197.13 memory used=25803.5MB, alloc=544.3MB, time=197.85 memory used=25978.9MB, alloc=544.3MB, time=199.20 memory used=26094.3MB, alloc=544.3MB, time=199.75 memory used=26234.6MB, alloc=544.3MB, time=200.50 memory used=26351.8MB, alloc=544.3MB, time=201.05 memory used=26503.7MB, alloc=544.3MB, time=203.72 memory used=26620.8MB, alloc=544.3MB, time=204.28 memory used=26726.0MB, alloc=544.3MB, time=204.76 memory used=26863.7MB, alloc=544.3MB, time=205.27 memory used=27019.7MB, alloc=544.3MB, time=205.81 memory used=27243.5MB, alloc=544.3MB, time=206.72 memory used=27358.3MB, alloc=544.3MB, time=207.27 memory used=27479.2MB, alloc=544.3MB, time=207.78 memory used=27571.3MB, alloc=544.3MB, time=208.25 memory used=27678.9MB, alloc=544.3MB, time=208.70 memory used=27832.3MB, alloc=544.3MB, time=211.22 memory used=27955.8MB, alloc=544.3MB, time=211.79 memory used=28054.7MB, alloc=544.3MB, time=212.27 memory used=28185.1MB, alloc=544.3MB, time=212.79 memory used=28373.4MB, alloc=544.3MB, time=213.41 memory used=28611.6MB, alloc=544.3MB, time=214.40 memory used=28739.7MB, alloc=544.3MB, time=215.03 memory used=28881.2MB, alloc=544.3MB, time=216.15 memory used=28992.3MB, alloc=544.3MB, time=216.64 memory used=29137.8MB, alloc=544.3MB, time=217.79 memory used=29245.3MB, alloc=544.3MB, time=218.34 memory used=29367.5MB, alloc=544.3MB, time=218.92 memory used=29496.3MB, alloc=544.3MB, time=219.47 memory used=29580.4MB, alloc=544.3MB, time=219.93 memory used=29673.5MB, alloc=544.3MB, time=220.42 memory used=29775.1MB, alloc=544.3MB, time=220.90 memory used=29888.8MB, alloc=544.3MB, time=221.38 memory used=30010.8MB, alloc=544.3MB, time=221.88 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428289710 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 3 2 F := [-13 x y + 18 x y z + 6 y z , -7 x y z - 13 y, 5 y z + 2 x y + 3] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 3 2 2 G := [20 x + 7 x y + 12, -6 x y z - 16 y , -10 x y - 18 x y z - 7] > Problem := [F,G]; Problem := [ 3 2 3 3 2 [-13 x y + 18 x y z + 6 y z , -7 x y z - 13 y, 5 y z + 2 x y + 3], 4 2 3 2 2 [20 x + 7 x y + 12, -6 x y z - 16 y , -10 x y - 18 x y z - 7]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.4MB, alloc=32.3MB, time=0.51 memory used=47.9MB, alloc=32.3MB, time=0.82 memory used=67.5MB, alloc=56.3MB, time=1.14 memory used=109.2MB, alloc=68.3MB, time=1.77 memory used=149.5MB, alloc=68.3MB, time=2.35 memory used=189.9MB, alloc=92.3MB, time=2.96 memory used=254.4MB, alloc=92.3MB, time=3.86 memory used=318.3MB, alloc=92.3MB, time=4.73 memory used=381.0MB, alloc=92.3MB, time=5.44 memory used=446.1MB, alloc=116.3MB, time=6.27 memory used=517.4MB, alloc=372.3MB, time=7.34 memory used=606.2MB, alloc=396.3MB, time=8.57 memory used=716.4MB, alloc=420.3MB, time=10.14 memory used=840.1MB, alloc=420.3MB, time=11.85 memory used=963.4MB, alloc=444.3MB, time=13.70 memory used=1072.3MB, alloc=444.3MB, time=15.26 memory used=1183.4MB, alloc=468.3MB, time=16.76 memory used=1280.7MB, alloc=468.3MB, time=18.14 memory used=1379.6MB, alloc=468.3MB, time=19.53 memory used=1470.7MB, alloc=468.3MB, time=20.89 memory used=1572.3MB, alloc=468.3MB, time=22.23 memory used=1654.1MB, alloc=468.3MB, time=23.37 memory used=1790.7MB, alloc=468.3MB, time=24.80 memory used=1879.7MB, alloc=492.3MB, time=25.91 memory used=1965.4MB, alloc=492.3MB, time=28.42 memory used=2103.1MB, alloc=492.3MB, time=29.73 memory used=2160.8MB, alloc=492.3MB, time=30.68 memory used=2274.0MB, alloc=492.3MB, time=31.96 memory used=2383.4MB, alloc=492.3MB, time=33.02 memory used=2451.9MB, alloc=492.3MB, time=33.95 memory used=2515.0MB, alloc=492.3MB, time=34.99 memory used=2578.2MB, alloc=492.3MB, time=35.87 memory used=2690.8MB, alloc=492.3MB, time=38.03 memory used=2755.7MB, alloc=492.3MB, time=39.21 memory used=2815.6MB, alloc=492.3MB, time=40.36 memory used=2864.7MB, alloc=492.3MB, time=41.26 memory used=2928.8MB, alloc=492.3MB, time=42.28 memory used=2971.7MB, alloc=492.3MB, time=43.18 memory used=3027.1MB, alloc=492.3MB, time=44.19 memory used=3212.6MB, alloc=516.3MB, time=47.12 memory used=3415.4MB, alloc=540.3MB, time=49.94 memory used=3629.5MB, alloc=564.3MB, time=53.27 memory used=3827.1MB, alloc=564.3MB, time=57.05 memory used=3957.5MB, alloc=564.3MB, time=57.90 memory used=4083.4MB, alloc=564.3MB, time=58.71 memory used=4269.5MB, alloc=564.3MB, time=61.29 memory used=4486.6MB, alloc=564.3MB, time=63.49 memory used=4631.2MB, alloc=564.3MB, time=66.11 memory used=4836.8MB, alloc=588.3MB, time=68.04 memory used=4964.9MB, alloc=588.3MB, time=68.82 memory used=5077.6MB, alloc=588.3MB, time=69.54 memory used=5244.5MB, alloc=588.3MB, time=70.57 memory used=5378.3MB, alloc=588.3MB, time=71.39 memory used=5488.0MB, alloc=588.3MB, time=72.13 memory used=5690.4MB, alloc=588.3MB, time=84.59 memory used=5813.9MB, alloc=588.3MB, time=85.33 memory used=5947.2MB, alloc=588.3MB, time=86.06 memory used=6058.9MB, alloc=588.3MB, time=86.73 memory used=6263.9MB, alloc=588.3MB, time=88.65 memory used=6437.5MB, alloc=588.3MB, time=91.82 memory used=6627.6MB, alloc=588.3MB, time=93.72 memory used=6824.8MB, alloc=588.3MB, time=97.01 memory used=6971.6MB, alloc=588.3MB, time=99.75 memory used=7103.0MB, alloc=612.3MB, time=100.66 memory used=7259.7MB, alloc=612.3MB, time=101.53 memory used=7363.8MB, alloc=612.3MB, time=102.32 memory used=7484.6MB, alloc=612.3MB, time=103.15 memory used=7624.9MB, alloc=612.3MB, time=104.00 memory used=7787.6MB, alloc=612.3MB, time=104.87 memory used=7926.1MB, alloc=612.3MB, time=105.66 memory used=8022.2MB, alloc=612.3MB, time=106.39 memory used=8128.1MB, alloc=612.3MB, time=107.07 memory used=8242.4MB, alloc=612.3MB, time=107.78 memory used=8365.2MB, alloc=612.3MB, time=108.48 memory used=8500.6MB, alloc=612.3MB, time=109.23 memory used=8690.9MB, alloc=612.3MB, time=110.93 memory used=8827.3MB, alloc=612.3MB, time=111.86 memory used=8969.1MB, alloc=612.3MB, time=112.78 memory used=9078.8MB, alloc=612.3MB, time=113.66 memory used=9206.3MB, alloc=612.3MB, time=114.45 memory used=9353.1MB, alloc=612.3MB, time=115.24 memory used=9521.9MB, alloc=612.3MB, time=116.04 memory used=9633.0MB, alloc=612.3MB, time=116.73 memory used=9732.8MB, alloc=612.3MB, time=117.42 memory used=9839.1MB, alloc=612.3MB, time=118.12 memory used=9955.0MB, alloc=612.3MB, time=118.81 memory used=10081.8MB, alloc=612.3MB, time=119.51 memory used=10222.4MB, alloc=612.3MB, time=120.25 memory used=10472.3MB, alloc=612.3MB, time=150.57 memory used=10619.6MB, alloc=612.3MB, time=151.43 memory used=10752.5MB, alloc=612.3MB, time=152.21 memory used=10901.4MB, alloc=612.3MB, time=152.97 memory used=11003.5MB, alloc=612.3MB, time=153.67 memory used=11120.2MB, alloc=612.3MB, time=154.40 memory used=11249.5MB, alloc=612.3MB, time=155.11 memory used=11394.6MB, alloc=612.3MB, time=155.86 memory used=11556.9MB, alloc=612.3MB, time=156.57 memory used=11786.7MB, alloc=612.3MB, time=157.53 memory used=11916.5MB, alloc=612.3MB, time=158.25 memory used=12059.3MB, alloc=612.3MB, time=158.98 memory used=12219.8MB, alloc=612.3MB, time=159.76 memory used=12524.3MB, alloc=612.3MB, time=162.59 memory used=12724.1MB, alloc=612.3MB, time=164.65 memory used=12880.6MB, alloc=612.3MB, time=165.62 memory used=13054.0MB, alloc=612.3MB, time=169.81 memory used=13191.6MB, alloc=612.3MB, time=170.57 memory used=13357.4MB, alloc=612.3MB, time=172.61 memory used=13512.4MB, alloc=612.3MB, time=176.35 memory used=13662.7MB, alloc=636.3MB, time=179.73 memory used=13810.6MB, alloc=636.3MB, time=180.70 memory used=13984.8MB, alloc=636.3MB, time=181.66 memory used=14097.6MB, alloc=660.3MB, time=182.58 memory used=14228.8MB, alloc=660.3MB, time=183.50 memory used=14380.6MB, alloc=660.3MB, time=184.38 memory used=14550.6MB, alloc=660.3MB, time=185.28 memory used=14738.8MB, alloc=660.3MB, time=186.19 memory used=14942.6MB, alloc=660.3MB, time=187.12 memory used=15056.5MB, alloc=660.3MB, time=187.88 memory used=15168.4MB, alloc=660.3MB, time=188.63 memory used=15284.3MB, alloc=660.3MB, time=189.40 memory used=15403.1MB, alloc=660.3MB, time=190.14 memory used=15529.3MB, alloc=660.3MB, time=190.90 memory used=15659.4MB, alloc=660.3MB, time=191.66 memory used=15796.2MB, alloc=660.3MB, time=192.44 memory used=15943.1MB, alloc=660.3MB, time=193.22 memory used=16092.0MB, alloc=660.3MB, time=193.99 memory used=16247.5MB, alloc=660.3MB, time=194.79 memory used=16412.0MB, alloc=660.3MB, time=195.56 memory used=16583.9MB, alloc=660.3MB, time=196.37 memory used=16762.9MB, alloc=660.3MB, time=197.15 memory used=16955.1MB, alloc=660.3MB, time=197.96 memory used=17152.1MB, alloc=660.3MB, time=198.80 memory used=17452.0MB, alloc=660.3MB, time=199.76 memory used=17567.9MB, alloc=660.3MB, time=200.50 memory used=17687.3MB, alloc=660.3MB, time=201.24 memory used=17809.3MB, alloc=660.3MB, time=202.00 memory used=17935.0MB, alloc=660.3MB, time=202.74 memory used=18068.4MB, alloc=660.3MB, time=203.51 memory used=18206.6MB, alloc=660.3MB, time=204.29 memory used=18351.4MB, alloc=660.3MB, time=205.04 memory used=18569.8MB, alloc=660.3MB, time=207.50 memory used=18740.5MB, alloc=660.3MB, time=208.56 memory used=18930.0MB, alloc=660.3MB, time=209.56 memory used=19052.5MB, alloc=660.3MB, time=210.47 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428290010 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; F := [ 2 2 2 2 4 2 4 2 -13 x z - 14 x z - 19 y z , -4 z + 8 x y + 12 z , -6 y - 9 x z + 2 y] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 2 2 3 2 2 G := [-6 x - 11 y + 18 y , -16 x y z + 12 x - 19 z, 3 y z - 12 x + 14 y] > Problem := [F,G]; Problem := [[ 2 2 2 2 4 2 4 2 -13 x z - 14 x z - 19 y z , -4 z + 8 x y + 12 z , -6 y - 9 x z + 2 y] 4 3 2 2 3 2 2 , [-6 x - 11 y + 18 y , -16 x y z + 12 x - 19 z, 3 y z - 12 x + 14 y] ] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.18 memory used=26.3MB, alloc=32.3MB, time=0.50 memory used=45.5MB, alloc=32.3MB, time=0.79 memory used=64.4MB, alloc=56.3MB, time=1.07 memory used=105.4MB, alloc=60.3MB, time=1.66 memory used=150.2MB, alloc=60.3MB, time=2.27 memory used=181.0MB, alloc=60.3MB, time=2.47 memory used=216.9MB, alloc=60.3MB, time=2.86 memory used=258.1MB, alloc=92.3MB, time=3.49 memory used=322.6MB, alloc=92.3MB, time=4.42 memory used=389.8MB, alloc=116.3MB, time=5.31 memory used=465.9MB, alloc=372.3MB, time=6.27 memory used=541.3MB, alloc=372.3MB, time=6.90 memory used=590.3MB, alloc=372.3MB, time=7.10 memory used=640.2MB, alloc=372.3MB, time=7.34 memory used=702.7MB, alloc=372.3MB, time=7.73 memory used=763.0MB, alloc=372.3MB, time=9.59 memory used=824.2MB, alloc=396.3MB, time=42.82 memory used=921.2MB, alloc=396.3MB, time=49.73 memory used=1040.7MB, alloc=396.3MB, time=50.51 memory used=1094.8MB, alloc=396.3MB, time=50.71 memory used=1161.1MB, alloc=396.3MB, time=50.91 memory used=1204.6MB, alloc=396.3MB, time=51.07 memory used=1251.7MB, alloc=396.3MB, time=51.24 memory used=1303.8MB, alloc=396.3MB, time=51.39 memory used=1362.0MB, alloc=396.3MB, time=51.56 memory used=1426.3MB, alloc=396.3MB, time=51.74 memory used=1496.7MB, alloc=396.3MB, time=51.94 memory used=1548.2MB, alloc=396.3MB, time=52.09 memory used=1587.0MB, alloc=396.3MB, time=52.22 memory used=1627.9MB, alloc=396.3MB, time=52.35 memory used=1670.8MB, alloc=396.3MB, time=52.48 memory used=1715.5MB, alloc=396.3MB, time=52.61 memory used=1761.9MB, alloc=396.3MB, time=52.74 memory used=1810.0MB, alloc=396.3MB, time=52.88 memory used=1861.0MB, alloc=396.3MB, time=53.01 memory used=1914.7MB, alloc=396.3MB, time=53.15 memory used=1970.7MB, alloc=396.3MB, time=53.29 memory used=2030.1MB, alloc=396.3MB, time=53.44 memory used=2092.0MB, alloc=396.3MB, time=53.58 memory used=2156.9MB, alloc=396.3MB, time=53.72 memory used=2226.9MB, alloc=396.3MB, time=53.86 memory used=2404.7MB, alloc=396.3MB, time=54.33 memory used=2486.4MB, alloc=396.3MB, time=55.88 memory used=2570.5MB, alloc=396.3MB, time=94.85 memory used=2691.3MB, alloc=396.3MB, time=97.16 memory used=2780.9MB, alloc=396.3MB, time=97.66 memory used=2840.1MB, alloc=396.3MB, time=97.87 memory used=2899.2MB, alloc=396.3MB, time=98.07 memory used=2942.5MB, alloc=396.3MB, time=98.23 memory used=2991.0MB, alloc=396.3MB, time=98.39 memory used=3045.6MB, alloc=396.3MB, time=98.57 memory used=3106.3MB, alloc=396.3MB, time=98.76 memory used=3173.1MB, alloc=396.3MB, time=98.94 memory used=3244.8MB, alloc=396.3MB, time=99.14 memory used=3284.5MB, alloc=396.3MB, time=99.29 memory used=3323.1MB, alloc=396.3MB, time=99.42 memory used=3364.2MB, alloc=396.3MB, time=99.56 memory used=3407.1MB, alloc=396.3MB, time=99.71 memory used=3451.8MB, alloc=396.3MB, time=99.85 memory used=3498.3MB, alloc=396.3MB, time=100.01 memory used=3547.8MB, alloc=396.3MB, time=100.15 memory used=3598.7MB, alloc=396.3MB, time=100.29 memory used=3652.2MB, alloc=396.3MB, time=100.43 memory used=3707.9MB, alloc=396.3MB, time=100.58 memory used=3766.9MB, alloc=396.3MB, time=100.74 memory used=3829.7MB, alloc=396.3MB, time=100.89 memory used=3895.3MB, alloc=396.3MB, time=101.03 memory used=3965.0MB, alloc=396.3MB, time=101.18 memory used=4181.4MB, alloc=396.3MB, time=102.22 memory used=4308.2MB, alloc=396.3MB, time=103.38 memory used=4387.5MB, alloc=396.3MB, time=113.00 memory used=4437.6MB, alloc=396.3MB, time=113.17 memory used=4507.8MB, alloc=396.3MB, time=122.69 memory used=4558.4MB, alloc=396.3MB, time=122.86 memory used=4658.4MB, alloc=396.3MB, time=130.05 memory used=4734.7MB, alloc=396.3MB, time=130.40 memory used=4785.9MB, alloc=396.3MB, time=130.56 memory used=4830.8MB, alloc=396.3MB, time=130.69 memory used=4951.3MB, alloc=396.3MB, time=131.83 memory used=5056.5MB, alloc=420.3MB, time=133.26 memory used=5184.9MB, alloc=420.3MB, time=134.60 memory used=5242.6MB, alloc=420.3MB, time=134.82 memory used=5305.2MB, alloc=420.3MB, time=135.02 memory used=5381.1MB, alloc=420.3MB, time=135.51 memory used=5548.7MB, alloc=420.3MB, time=136.97 memory used=5661.5MB, alloc=444.3MB, time=138.44 memory used=5771.5MB, alloc=444.3MB, time=140.06 memory used=5847.8MB, alloc=468.3MB, time=154.06 memory used=5932.3MB, alloc=468.3MB, time=162.69 memory used=6055.0MB, alloc=468.3MB, time=163.66 memory used=6238.2MB, alloc=492.3MB, time=166.18 memory used=6421.1MB, alloc=492.3MB, time=167.62 memory used=6591.9MB, alloc=492.3MB, time=170.41 memory used=6749.8MB, alloc=492.3MB, time=175.38 memory used=6913.8MB, alloc=492.3MB, time=177.08 memory used=7063.0MB, alloc=492.3MB, time=178.73 memory used=7161.8MB, alloc=492.3MB, time=179.12 memory used=7243.5MB, alloc=492.3MB, time=179.44 memory used=7336.3MB, alloc=492.3MB, time=179.76 memory used=7582.4MB, alloc=492.3MB, time=180.31 memory used=7914.1MB, alloc=492.3MB, time=218.35 memory used=8038.8MB, alloc=492.3MB, time=219.03 memory used=8132.9MB, alloc=492.3MB, time=219.40 memory used=8207.4MB, alloc=492.3MB, time=219.72 memory used=8300.0MB, alloc=492.3MB, time=220.06 memory used=8543.4MB, alloc=492.3MB, time=220.62 memory used=8717.7MB, alloc=492.3MB, time=221.08 memory used=8928.2MB, alloc=492.3MB, time=222.70 memory used=9095.7MB, alloc=492.3MB, time=224.02 memory used=9222.7MB, alloc=492.3MB, time=225.34 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428290310 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 3 3 2 F := [16 y z + 6 x z + 14 z, -y z - x - 12 y , 8 x - 18 x y - 8 y z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 3 4 3 G := [-19 x z + 7 x y z - 9 x y, 9 x y - 16 y + 8 y z , 3 2 8 x y + 14 x y z + 4 y] > Problem := [F,G]; Problem := [ 2 2 2 3 3 3 2 [16 y z + 6 x z + 14 z, -y z - x - 12 y , 8 x - 18 x y - 8 y z], [ 3 2 2 3 4 3 -19 x z + 7 x y z - 9 x y, 9 x y - 16 y + 8 y z , 3 2 8 x y + 14 x y z + 4 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.5MB, alloc=32.3MB, time=0.18 memory used=26.3MB, alloc=32.3MB, time=0.50 memory used=46.6MB, alloc=32.3MB, time=0.79 memory used=65.4MB, alloc=56.3MB, time=1.09 memory used=106.7MB, alloc=68.3MB, time=1.72 memory used=146.7MB, alloc=92.3MB, time=2.28 memory used=209.5MB, alloc=92.3MB, time=3.21 memory used=273.0MB, alloc=116.3MB, time=4.13 memory used=352.0MB, alloc=116.3MB, time=5.29 memory used=420.2MB, alloc=396.3MB, time=6.28 memory used=527.8MB, alloc=396.3MB, time=7.89 memory used=631.9MB, alloc=420.3MB, time=9.53 memory used=758.7MB, alloc=444.3MB, time=11.36 memory used=881.2MB, alloc=468.3MB, time=13.21 memory used=1000.2MB, alloc=468.3MB, time=14.92 memory used=1112.3MB, alloc=492.3MB, time=16.53 memory used=1204.5MB, alloc=492.3MB, time=17.76 memory used=1306.5MB, alloc=492.3MB, time=19.43 memory used=1388.9MB, alloc=492.3MB, time=20.89 memory used=1464.9MB, alloc=492.3MB, time=22.06 memory used=1549.6MB, alloc=516.3MB, time=23.38 memory used=1622.2MB, alloc=516.3MB, time=24.56 memory used=1678.1MB, alloc=516.3MB, time=25.50 memory used=1725.8MB, alloc=516.3MB, time=26.23 memory used=1792.9MB, alloc=516.3MB, time=27.58 memory used=1855.8MB, alloc=516.3MB, time=28.72 memory used=1902.1MB, alloc=516.3MB, time=29.55 memory used=1958.2MB, alloc=516.3MB, time=30.92 memory used=2163.5MB, alloc=540.3MB, time=34.44 memory used=2360.6MB, alloc=564.3MB, time=37.76 memory used=2542.2MB, alloc=588.3MB, time=40.14 memory used=2711.5MB, alloc=612.3MB, time=43.04 memory used=2871.9MB, alloc=636.3MB, time=45.96 memory used=3029.8MB, alloc=636.3MB, time=48.78 memory used=3185.1MB, alloc=636.3MB, time=51.52 memory used=3317.1MB, alloc=636.3MB, time=54.07 memory used=3460.0MB, alloc=660.3MB, time=57.11 memory used=3588.3MB, alloc=660.3MB, time=59.93 memory used=3707.9MB, alloc=660.3MB, time=62.73 memory used=3798.1MB, alloc=660.3MB, time=64.93 memory used=3893.9MB, alloc=660.3MB, time=67.62 memory used=4235.7MB, alloc=684.3MB, time=73.31 memory used=4584.6MB, alloc=708.3MB, time=79.88 memory used=4929.6MB, alloc=732.3MB, time=86.71 memory used=5311.1MB, alloc=756.3MB, time=94.38 memory used=5642.5MB, alloc=780.3MB, time=100.25 memory used=5923.3MB, alloc=804.3MB, time=105.26 memory used=6204.8MB, alloc=828.3MB, time=110.53 memory used=6475.2MB, alloc=852.3MB, time=116.20 memory used=6711.8MB, alloc=876.3MB, time=121.68 memory used=6985.4MB, alloc=900.3MB, time=127.09 memory used=7181.5MB, alloc=924.3MB, time=132.01 memory used=7419.3MB, alloc=948.3MB, time=136.82 memory used=7582.0MB, alloc=972.3MB, time=140.83 memory used=7770.6MB, alloc=996.3MB, time=144.86 memory used=8000.1MB, alloc=996.3MB, time=149.32 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428290610 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 3 3 F := [20 x z - 15 y + 9 x, 2 x y z + 11 x y + 14 z, 16 x y - 3 x y + 5] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 2 2 2 G := [11 x z + 11 x + 19 x z, 7 y z - 15 x y, -14 x y + 12 x z - 8 z] > Problem := [F,G]; Problem := [ 2 2 3 2 3 3 [20 x z - 15 y + 9 x, 2 x y z + 11 x y + 14 z, 16 x y - 3 x y + 5], 2 2 3 2 2 2 2 2 [11 x z + 11 x + 19 x z, 7 y z - 15 x y, -14 x y + 12 x z - 8 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.5MB, alloc=32.3MB, time=0.17 memory used=25.3MB, alloc=32.3MB, time=0.48 memory used=45.5MB, alloc=32.3MB, time=0.77 memory used=63.8MB, alloc=56.3MB, time=1.04 memory used=105.9MB, alloc=68.3MB, time=1.66 memory used=147.2MB, alloc=68.3MB, time=2.19 memory used=189.0MB, alloc=68.3MB, time=2.75 memory used=229.6MB, alloc=92.3MB, time=3.35 memory used=299.2MB, alloc=92.3MB, time=4.27 memory used=365.3MB, alloc=116.3MB, time=5.03 memory used=423.5MB, alloc=116.3MB, time=5.81 memory used=484.7MB, alloc=372.3MB, time=6.67 memory used=575.7MB, alloc=396.3MB, time=7.97 memory used=683.0MB, alloc=396.3MB, time=9.14 memory used=793.3MB, alloc=420.3MB, time=10.33 memory used=921.3MB, alloc=420.3MB, time=11.51 memory used=1014.2MB, alloc=420.3MB, time=12.15 memory used=1131.7MB, alloc=420.3MB, time=13.26 memory used=1256.9MB, alloc=420.3MB, time=14.70 memory used=1386.7MB, alloc=444.3MB, time=16.07 memory used=1497.5MB, alloc=444.3MB, time=17.45 memory used=1631.3MB, alloc=444.3MB, time=18.86 memory used=1729.4MB, alloc=444.3MB, time=19.74 memory used=1830.0MB, alloc=444.3MB, time=20.66 memory used=1962.4MB, alloc=444.3MB, time=22.08 memory used=2066.3MB, alloc=468.3MB, time=23.42 memory used=2147.9MB, alloc=468.3MB, time=24.80 memory used=2267.1MB, alloc=468.3MB, time=25.66 memory used=2393.1MB, alloc=468.3MB, time=26.83 memory used=2512.8MB, alloc=468.3MB, time=32.45 memory used=2617.0MB, alloc=468.3MB, time=33.09 memory used=2694.8MB, alloc=468.3MB, time=33.47 memory used=2765.2MB, alloc=468.3MB, time=33.84 memory used=2829.2MB, alloc=468.3MB, time=34.18 memory used=2905.6MB, alloc=468.3MB, time=34.50 memory used=3042.0MB, alloc=468.3MB, time=37.66 memory used=3117.2MB, alloc=468.3MB, time=38.04 memory used=3194.0MB, alloc=468.3MB, time=38.38 memory used=3257.9MB, alloc=468.3MB, time=38.69 memory used=3348.5MB, alloc=468.3MB, time=39.42 memory used=3443.5MB, alloc=468.3MB, time=40.18 memory used=3543.4MB, alloc=468.3MB, time=40.59 memory used=3668.2MB, alloc=468.3MB, time=42.21 memory used=3738.3MB, alloc=468.3MB, time=43.19 memory used=3837.3MB, alloc=468.3MB, time=44.06 memory used=3922.3MB, alloc=468.3MB, time=45.47 memory used=4023.9MB, alloc=492.3MB, time=48.60 memory used=4115.2MB, alloc=492.3MB, time=49.00 memory used=4196.9MB, alloc=492.3MB, time=49.35 memory used=4278.6MB, alloc=492.3MB, time=49.69 memory used=4405.0MB, alloc=492.3MB, time=50.64 memory used=4480.8MB, alloc=492.3MB, time=51.64 memory used=4559.0MB, alloc=492.3MB, time=52.83 memory used=4618.3MB, alloc=492.3MB, time=53.76 memory used=4685.0MB, alloc=492.3MB, time=54.57 memory used=4743.7MB, alloc=492.3MB, time=55.65 memory used=4798.0MB, alloc=492.3MB, time=56.44 memory used=4944.8MB, alloc=492.3MB, time=61.75 memory used=5030.4MB, alloc=492.3MB, time=62.22 memory used=5115.1MB, alloc=492.3MB, time=62.64 memory used=5242.4MB, alloc=492.3MB, time=65.27 memory used=5330.8MB, alloc=492.3MB, time=65.73 memory used=5404.5MB, alloc=492.3MB, time=66.61 memory used=5502.1MB, alloc=492.3MB, time=69.02 memory used=5587.6MB, alloc=492.3MB, time=69.46 memory used=5682.5MB, alloc=492.3MB, time=70.38 memory used=5783.6MB, alloc=492.3MB, time=71.51 memory used=6016.2MB, alloc=492.3MB, time=76.58 memory used=6239.8MB, alloc=516.3MB, time=79.74 memory used=6473.1MB, alloc=516.3MB, time=83.79 memory used=6670.9MB, alloc=540.3MB, time=86.46 memory used=6864.8MB, alloc=564.3MB, time=88.99 memory used=7095.0MB, alloc=564.3MB, time=92.71 memory used=7298.7MB, alloc=588.3MB, time=95.53 memory used=7531.5MB, alloc=588.3MB, time=97.38 memory used=7701.8MB, alloc=588.3MB, time=98.87 memory used=7889.2MB, alloc=588.3MB, time=107.77 memory used=8005.0MB, alloc=588.3MB, time=108.44 memory used=8127.5MB, alloc=588.3MB, time=109.09 memory used=8343.1MB, alloc=588.3MB, time=110.00 memory used=8507.0MB, alloc=588.3MB, time=110.69 memory used=8727.3MB, alloc=588.3MB, time=112.05 memory used=8979.7MB, alloc=588.3MB, time=114.78 memory used=9167.9MB, alloc=612.3MB, time=117.07 memory used=9386.8MB, alloc=612.3MB, time=119.01 memory used=9511.6MB, alloc=612.3MB, time=119.77 memory used=9651.4MB, alloc=612.3MB, time=120.63 memory used=9778.7MB, alloc=612.3MB, time=121.41 memory used=9912.4MB, alloc=612.3MB, time=122.14 memory used=10057.3MB, alloc=612.3MB, time=124.11 memory used=10177.4MB, alloc=612.3MB, time=124.76 memory used=10338.4MB, alloc=612.3MB, time=125.87 memory used=10460.1MB, alloc=612.3MB, time=126.58 memory used=10599.5MB, alloc=612.3MB, time=127.45 memory used=10725.3MB, alloc=612.3MB, time=128.20 memory used=10854.1MB, alloc=612.3MB, time=128.91 memory used=11009.2MB, alloc=612.3MB, time=130.94 memory used=11125.1MB, alloc=612.3MB, time=131.59 memory used=11306.2MB, alloc=612.3MB, time=132.98 memory used=11429.3MB, alloc=612.3MB, time=133.73 memory used=11575.9MB, alloc=612.3MB, time=134.66 memory used=11768.7MB, alloc=612.3MB, time=159.16 memory used=11894.0MB, alloc=612.3MB, time=159.93 memory used=12035.8MB, alloc=612.3MB, time=160.70 memory used=12141.7MB, alloc=636.3MB, time=161.42 memory used=12263.0MB, alloc=636.3MB, time=162.12 memory used=12405.5MB, alloc=636.3MB, time=162.84 memory used=12569.2MB, alloc=636.3MB, time=163.57 memory used=12832.3MB, alloc=636.3MB, time=164.44 memory used=12964.8MB, alloc=636.3MB, time=165.15 memory used=13109.5MB, alloc=636.3MB, time=165.86 memory used=13270.4MB, alloc=636.3MB, time=166.58 memory used=13455.4MB, alloc=636.3MB, time=167.32 memory used=13659.0MB, alloc=636.3MB, time=177.43 memory used=13809.6MB, alloc=636.3MB, time=178.24 memory used=13930.3MB, alloc=636.3MB, time=178.95 memory used=14061.6MB, alloc=636.3MB, time=179.68 memory used=14219.7MB, alloc=636.3MB, time=180.40 memory used=14473.2MB, alloc=636.3MB, time=181.27 memory used=14615.6MB, alloc=636.3MB, time=181.98 memory used=14887.2MB, alloc=636.3MB, time=184.31 memory used=15062.5MB, alloc=636.3MB, time=186.28 memory used=15275.5MB, alloc=636.3MB, time=188.26 memory used=15454.0MB, alloc=636.3MB, time=192.55 memory used=15682.6MB, alloc=636.3MB, time=196.35 memory used=15877.2MB, alloc=636.3MB, time=198.90 memory used=16192.0MB, alloc=636.3MB, time=202.88 memory used=16455.1MB, alloc=636.3MB, time=207.64 memory used=16611.1MB, alloc=660.3MB, time=210.28 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428290910 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 2 3 3 F := [-9 x y - 20 z - 20 z , 3 y z + 14 y z - 9 z , -6 z - 10 x z - 7 z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 4 2 2 3 4 2 2 G := [-19 x y z - x y - 15 z , -10 x y - 14 y z, 16 y + 13 y z ] > Problem := [F,G]; Problem := [ 2 3 2 2 2 3 3 [-9 x y - 20 z - 20 z , 3 y z + 14 y z - 9 z , -6 z - 10 x z - 7 z], 2 3 4 2 2 3 4 2 2 [-19 x y z - x y - 15 z , -10 x y - 14 y z, 16 y + 13 y z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.18 memory used=27.0MB, alloc=32.3MB, time=0.50 memory used=47.6MB, alloc=32.3MB, time=0.81 memory used=67.0MB, alloc=56.3MB, time=1.11 memory used=107.1MB, alloc=60.3MB, time=1.71 memory used=145.7MB, alloc=84.3MB, time=2.28 memory used=211.5MB, alloc=92.3MB, time=3.19 memory used=279.1MB, alloc=116.3MB, time=4.07 memory used=350.0MB, alloc=116.3MB, time=5.03 memory used=421.8MB, alloc=372.3MB, time=6.05 memory used=511.5MB, alloc=396.3MB, time=7.26 memory used=623.2MB, alloc=420.3MB, time=8.87 memory used=757.1MB, alloc=444.3MB, time=10.79 memory used=881.5MB, alloc=444.3MB, time=12.27 memory used=994.3MB, alloc=468.3MB, time=13.91 memory used=1107.0MB, alloc=468.3MB, time=15.49 memory used=1220.8MB, alloc=468.3MB, time=17.12 memory used=1322.5MB, alloc=492.3MB, time=18.55 memory used=1409.3MB, alloc=492.3MB, time=19.95 memory used=1506.4MB, alloc=492.3MB, time=21.50 memory used=1600.0MB, alloc=516.3MB, time=22.66 memory used=1695.4MB, alloc=516.3MB, time=24.01 memory used=1756.9MB, alloc=516.3MB, time=25.10 memory used=1833.6MB, alloc=516.3MB, time=26.43 memory used=1913.0MB, alloc=516.3MB, time=27.56 memory used=1980.8MB, alloc=516.3MB, time=28.69 memory used=2028.8MB, alloc=516.3MB, time=29.80 memory used=2069.6MB, alloc=516.3MB, time=30.62 memory used=2131.4MB, alloc=516.3MB, time=31.89 memory used=2170.4MB, alloc=516.3MB, time=32.79 memory used=2219.4MB, alloc=540.3MB, time=33.87 memory used=2415.9MB, alloc=564.3MB, time=37.03 memory used=2620.4MB, alloc=588.3MB, time=40.14 memory used=2805.7MB, alloc=612.3MB, time=43.25 memory used=3028.5MB, alloc=636.3MB, time=46.18 memory used=3194.3MB, alloc=636.3MB, time=49.05 memory used=3363.8MB, alloc=660.3MB, time=51.80 memory used=3533.1MB, alloc=660.3MB, time=54.46 memory used=3722.7MB, alloc=660.3MB, time=57.02 memory used=3848.4MB, alloc=660.3MB, time=59.31 memory used=3988.1MB, alloc=660.3MB, time=61.74 memory used=4122.7MB, alloc=684.3MB, time=64.32 memory used=4254.1MB, alloc=684.3MB, time=66.73 memory used=4390.0MB, alloc=684.3MB, time=69.30 memory used=4474.2MB, alloc=684.3MB, time=71.22 memory used=4575.7MB, alloc=684.3MB, time=73.49 memory used=4671.8MB, alloc=684.3MB, time=75.72 memory used=5019.3MB, alloc=708.3MB, time=80.78 memory used=5372.6MB, alloc=732.3MB, time=86.22 memory used=5743.0MB, alloc=756.3MB, time=91.96 memory used=6123.7MB, alloc=780.3MB, time=98.82 memory used=6505.5MB, alloc=804.3MB, time=105.12 memory used=6874.6MB, alloc=828.3MB, time=111.96 memory used=7222.3MB, alloc=852.3MB, time=118.26 memory used=7511.8MB, alloc=876.3MB, time=123.42 memory used=7825.9MB, alloc=900.3MB, time=129.09 memory used=8065.7MB, alloc=924.3MB, time=134.36 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428291210 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; F := [ 3 4 4 2 2 3 3 2 2 y z - 11 z + 11 y, -2 x + 11 y z - 15 y z, -2 x z - 2 x + 18 x z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; G := 3 3 2 3 4 2 [-14 y z - 17 x z + 4 z, -10 x z - 8 x y z + 6 x , 8 x - 11 x y + 6 z] > Problem := [F,G]; Problem := [[ 3 4 4 2 2 3 3 2 2 y z - 11 z + 11 y, -2 x + 11 y z - 15 y z, -2 x z - 2 x + 18 x z] , 3 3 2 3 4 2 [-14 y z - 17 x z + 4 z, -10 x z - 8 x y z + 6 x , 8 x - 11 x y + 6 z] ] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.17 memory used=26.2MB, alloc=32.3MB, time=0.48 memory used=47.0MB, alloc=60.3MB, time=0.77 memory used=85.3MB, alloc=60.3MB, time=1.29 memory used=125.9MB, alloc=60.3MB, time=1.87 memory used=163.1MB, alloc=84.3MB, time=2.37 memory used=228.2MB, alloc=92.3MB, time=3.13 memory used=302.4MB, alloc=348.3MB, time=4.03 memory used=373.1MB, alloc=348.3MB, time=4.82 memory used=438.4MB, alloc=372.3MB, time=5.72 memory used=525.3MB, alloc=372.3MB, time=6.99 memory used=617.8MB, alloc=396.3MB, time=8.20 memory used=730.9MB, alloc=396.3MB, time=9.73 memory used=839.8MB, alloc=420.3MB, time=11.31 memory used=969.4MB, alloc=444.3MB, time=13.32 memory used=1110.8MB, alloc=444.3MB, time=15.06 memory used=1247.7MB, alloc=468.3MB, time=17.23 memory used=1358.5MB, alloc=492.3MB, time=18.86 memory used=1460.1MB, alloc=492.3MB, time=20.29 memory used=1565.9MB, alloc=492.3MB, time=21.46 memory used=1675.9MB, alloc=516.3MB, time=23.11 memory used=1770.4MB, alloc=516.3MB, time=24.43 memory used=1885.6MB, alloc=516.3MB, time=26.03 memory used=1989.2MB, alloc=516.3MB, time=27.29 memory used=2055.0MB, alloc=516.3MB, time=28.20 memory used=2135.8MB, alloc=516.3MB, time=29.68 memory used=2197.2MB, alloc=516.3MB, time=30.80 memory used=2277.0MB, alloc=516.3MB, time=32.25 memory used=2339.1MB, alloc=516.3MB, time=33.34 memory used=2418.0MB, alloc=516.3MB, time=34.80 memory used=2469.5MB, alloc=516.3MB, time=35.82 memory used=2500.6MB, alloc=516.3MB, time=36.55 memory used=2550.7MB, alloc=516.3MB, time=37.53 memory used=2601.1MB, alloc=516.3MB, time=38.62 memory used=2647.7MB, alloc=516.3MB, time=39.46 memory used=2704.2MB, alloc=540.3MB, time=40.80 memory used=2755.3MB, alloc=540.3MB, time=41.74 memory used=3008.5MB, alloc=564.3MB, time=45.24 memory used=3188.9MB, alloc=588.3MB, time=48.12 memory used=3388.5MB, alloc=612.3MB, time=51.28 memory used=3549.1MB, alloc=612.3MB, time=54.14 memory used=3719.9MB, alloc=636.3MB, time=57.15 memory used=3879.3MB, alloc=636.3MB, time=60.09 memory used=4044.1MB, alloc=660.3MB, time=62.82 memory used=4213.3MB, alloc=660.3MB, time=65.73 memory used=4390.0MB, alloc=660.3MB, time=69.38 memory used=4521.0MB, alloc=660.3MB, time=72.33 memory used=4653.1MB, alloc=660.3MB, time=75.33 memory used=4809.9MB, alloc=684.3MB, time=77.78 memory used=4905.8MB, alloc=684.3MB, time=79.70 memory used=5035.1MB, alloc=684.3MB, time=82.43 memory used=5149.3MB, alloc=684.3MB, time=84.97 memory used=5268.0MB, alloc=684.3MB, time=87.70 memory used=5621.3MB, alloc=708.3MB, time=94.52 memory used=5986.3MB, alloc=732.3MB, time=101.63 memory used=6359.1MB, alloc=756.3MB, time=109.08 memory used=6774.0MB, alloc=780.3MB, time=116.98 memory used=7147.9MB, alloc=804.3MB, time=123.93 memory used=7519.1MB, alloc=828.3MB, time=130.29 memory used=7865.4MB, alloc=852.3MB, time=136.57 memory used=8164.1MB, alloc=876.3MB, time=142.83 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428291510 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 4 2 F := [-14 x + 19 x + 6 x y, -12 y - 6 x z + 4 x y z, 3 2 6 y z + 20 x y + 16 x y z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; G := [ 3 2 2 3 3 4 2 2 5 y z - 19 x z - 20 x y , 16 y z + 17 x - 5 x z, -16 x + 17 x y + y ] > Problem := [F,G]; 3 2 4 2 Problem := [[-14 x + 19 x + 6 x y, -12 y - 6 x z + 4 x y z, 3 2 6 y z + 20 x y + 16 x y z], [ 3 2 2 3 3 4 2 2 5 y z - 19 x z - 20 x y , 16 y z + 17 x - 5 x z, -16 x + 17 x y + y ] ] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.17 memory used=26.7MB, alloc=32.3MB, time=0.51 memory used=47.4MB, alloc=32.3MB, time=0.80 memory used=65.7MB, alloc=56.3MB, time=1.08 memory used=106.8MB, alloc=60.3MB, time=1.68 memory used=149.8MB, alloc=60.3MB, time=2.25 memory used=193.0MB, alloc=92.3MB, time=2.90 memory used=261.8MB, alloc=92.3MB, time=3.73 memory used=333.3MB, alloc=92.3MB, time=4.40 memory used=364.3MB, alloc=92.3MB, time=4.51 memory used=415.3MB, alloc=92.3MB, time=4.77 memory used=445.2MB, alloc=92.3MB, time=4.89 memory used=508.8MB, alloc=93.1MB, time=6.38 memory used=538.6MB, alloc=93.1MB, time=6.49 memory used=601.2MB, alloc=93.1MB, time=7.18 memory used=658.5MB, alloc=373.1MB, time=7.97 memory used=748.2MB, alloc=373.1MB, time=9.12 memory used=838.5MB, alloc=397.1MB, time=10.25 memory used=946.2MB, alloc=397.1MB, time=11.50 memory used=1067.3MB, alloc=421.1MB, time=37.10 memory used=1183.4MB, alloc=421.1MB, time=43.95 memory used=1309.1MB, alloc=421.1MB, time=45.02 memory used=1386.6MB, alloc=421.1MB, time=45.37 memory used=1444.5MB, alloc=421.1MB, time=45.62 memory used=1510.1MB, alloc=421.1MB, time=45.87 memory used=1580.1MB, alloc=421.1MB, time=46.10 memory used=1634.6MB, alloc=421.1MB, time=46.32 memory used=1683.2MB, alloc=421.1MB, time=46.52 memory used=1733.8MB, alloc=421.1MB, time=46.73 memory used=1785.9MB, alloc=421.1MB, time=46.92 memory used=1843.2MB, alloc=421.1MB, time=47.13 memory used=1903.1MB, alloc=421.1MB, time=47.33 memory used=1968.8MB, alloc=421.1MB, time=47.54 memory used=2036.9MB, alloc=421.1MB, time=47.74 memory used=2107.5MB, alloc=421.1MB, time=47.97 memory used=2183.9MB, alloc=421.1MB, time=48.19 memory used=2286.9MB, alloc=421.1MB, time=48.48 memory used=2436.0MB, alloc=421.1MB, time=48.99 memory used=2574.2MB, alloc=421.1MB, time=49.34 memory used=2722.8MB, alloc=421.1MB, time=49.72 memory used=2884.2MB, alloc=421.1MB, time=50.10 memory used=3057.7MB, alloc=421.1MB, time=50.48 memory used=3242.8MB, alloc=421.1MB, time=50.87 memory used=3438.8MB, alloc=421.1MB, time=51.29 memory used=3648.9MB, alloc=421.1MB, time=51.71 memory used=3872.0MB, alloc=421.1MB, time=52.15 memory used=4100.1MB, alloc=421.1MB, time=52.58 memory used=4278.1MB, alloc=421.1MB, time=52.95 memory used=4457.7MB, alloc=421.1MB, time=53.32 memory used=4647.2MB, alloc=421.1MB, time=53.69 memory used=4849.7MB, alloc=421.1MB, time=54.08 memory used=5068.9MB, alloc=421.1MB, time=54.47 memory used=5352.0MB, alloc=421.1MB, time=55.52 memory used=5527.2MB, alloc=421.1MB, time=57.11 memory used=5651.7MB, alloc=445.1MB, time=58.77 memory used=5811.2MB, alloc=469.1MB, time=85.60 memory used=5942.7MB, alloc=469.1MB, time=92.02 memory used=6077.1MB, alloc=469.1MB, time=92.81 memory used=6156.6MB, alloc=469.1MB, time=93.12 memory used=6255.5MB, alloc=469.1MB, time=93.42 memory used=6322.8MB, alloc=469.1MB, time=93.65 memory used=6393.2MB, alloc=469.1MB, time=93.89 memory used=6473.3MB, alloc=469.1MB, time=94.15 memory used=6564.9MB, alloc=469.1MB, time=94.40 memory used=6787.4MB, alloc=469.1MB, time=94.89 memory used=6886.1MB, alloc=469.1MB, time=95.40 memory used=7073.3MB, alloc=469.1MB, time=97.73 memory used=7274.2MB, alloc=469.1MB, time=99.41 memory used=7486.2MB, alloc=469.1MB, time=103.13 memory used=7643.0MB, alloc=469.1MB, time=115.83 memory used=7716.5MB, alloc=469.1MB, time=116.12 memory used=7796.1MB, alloc=469.1MB, time=116.41 memory used=7955.4MB, alloc=469.1MB, time=117.86 memory used=8093.6MB, alloc=469.1MB, time=119.21 memory used=8184.8MB, alloc=469.1MB, time=119.80 memory used=8285.1MB, alloc=493.1MB, time=120.36 memory used=8367.4MB, alloc=493.1MB, time=120.69 memory used=8622.6MB, alloc=493.1MB, time=121.55 memory used=8710.1MB, alloc=493.1MB, time=121.93 memory used=8806.3MB, alloc=493.1MB, time=122.29 memory used=8984.0MB, alloc=493.1MB, time=122.79 memory used=9137.9MB, alloc=517.1MB, time=175.77 memory used=9337.2MB, alloc=517.1MB, time=179.21 memory used=9537.8MB, alloc=517.1MB, time=180.57 memory used=9643.4MB, alloc=517.1MB, time=180.99 memory used=9730.9MB, alloc=517.1MB, time=181.34 memory used=9818.3MB, alloc=517.1MB, time=181.69 memory used=9919.8MB, alloc=517.1MB, time=182.05 memory used=10036.8MB, alloc=517.1MB, time=182.41 memory used=10256.4MB, alloc=517.1MB, time=182.98 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428291810 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 2 2 2 F := [4 y z + x , 17 x y z - 18 x y - 2 x y z, 17 x y - 5 x + 12 z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 G := [-10 x y + 7 y z - 6 x, -7 x y + 17 x y - 18 x y, 2 2 20 x y z - 18 y z + 9 x ] > Problem := [F,G]; Problem := [ 2 2 2 2 2 2 2 2 [4 y z + x , 17 x y z - 18 x y - 2 x y z, 17 x y - 5 x + 12 z ], [ 3 2 3 2 -10 x y + 7 y z - 6 x, -7 x y + 17 x y - 18 x y, 2 2 20 x y z - 18 y z + 9 x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.18 memory used=26.0MB, alloc=32.3MB, time=0.50 memory used=46.4MB, alloc=56.3MB, time=0.79 memory used=89.8MB, alloc=60.3MB, time=1.35 memory used=134.1MB, alloc=60.3MB, time=1.88 memory used=176.7MB, alloc=60.3MB, time=2.44 memory used=218.0MB, alloc=84.3MB, time=3.02 memory used=260.0MB, alloc=84.3MB, time=3.55 memory used=328.1MB, alloc=92.3MB, time=4.44 memory used=391.1MB, alloc=92.3MB, time=5.35 memory used=455.6MB, alloc=116.3MB, time=6.19 memory used=518.6MB, alloc=372.3MB, time=6.92 memory used=603.3MB, alloc=396.3MB, time=8.17 memory used=699.4MB, alloc=396.3MB, time=9.58 memory used=813.8MB, alloc=396.3MB, time=11.11 memory used=917.6MB, alloc=420.3MB, time=12.68 memory used=1048.5MB, alloc=444.3MB, time=14.49 memory used=1182.3MB, alloc=444.3MB, time=16.40 memory used=1308.5MB, alloc=444.3MB, time=17.57 memory used=1463.5MB, alloc=468.3MB, time=19.07 memory used=1618.6MB, alloc=468.3MB, time=20.60 memory used=1753.4MB, alloc=468.3MB, time=22.04 memory used=1877.7MB, alloc=492.3MB, time=23.54 memory used=1989.7MB, alloc=492.3MB, time=25.13 memory used=2131.6MB, alloc=492.3MB, time=26.48 memory used=2236.7MB, alloc=492.3MB, time=27.98 memory used=2323.0MB, alloc=492.3MB, time=29.20 memory used=2425.6MB, alloc=516.3MB, time=30.97 memory used=2515.2MB, alloc=516.3MB, time=32.40 memory used=2594.1MB, alloc=516.3MB, time=33.85 memory used=2668.3MB, alloc=516.3MB, time=35.17 memory used=2796.7MB, alloc=516.3MB, time=36.70 memory used=2919.8MB, alloc=516.3MB, time=38.07 memory used=3017.6MB, alloc=516.3MB, time=39.73 memory used=3081.7MB, alloc=516.3MB, time=40.78 memory used=3207.8MB, alloc=540.3MB, time=41.72 memory used=3304.8MB, alloc=540.3MB, time=43.09 memory used=3452.7MB, alloc=540.3MB, time=44.67 memory used=3547.8MB, alloc=540.3MB, time=45.67 memory used=3631.2MB, alloc=540.3MB, time=46.85 memory used=3679.0MB, alloc=540.3MB, time=47.77 memory used=3733.0MB, alloc=540.3MB, time=48.83 memory used=3781.9MB, alloc=540.3MB, time=49.74 memory used=4004.9MB, alloc=564.3MB, time=53.48 memory used=4247.1MB, alloc=564.3MB, time=56.48 memory used=4510.9MB, alloc=588.3MB, time=60.58 memory used=4745.0MB, alloc=588.3MB, time=63.14 memory used=4899.4MB, alloc=588.3MB, time=64.51 memory used=5039.2MB, alloc=588.3MB, time=65.52 memory used=5194.0MB, alloc=588.3MB, time=71.62 memory used=5314.2MB, alloc=588.3MB, time=72.28 memory used=5470.3MB, alloc=588.3MB, time=73.16 memory used=5759.2MB, alloc=612.3MB, time=76.29 memory used=5998.7MB, alloc=612.3MB, time=79.16 memory used=6235.5MB, alloc=636.3MB, time=82.16 memory used=6438.4MB, alloc=636.3MB, time=85.28 memory used=6637.2MB, alloc=636.3MB, time=87.96 memory used=6849.4MB, alloc=636.3MB, time=90.78 memory used=6995.0MB, alloc=660.3MB, time=93.66 memory used=7133.7MB, alloc=660.3MB, time=96.33 memory used=7263.7MB, alloc=684.3MB, time=98.39 memory used=7411.6MB, alloc=684.3MB, time=101.75 memory used=7548.4MB, alloc=708.3MB, time=104.56 memory used=7645.8MB, alloc=708.3MB, time=106.35 memory used=7775.4MB, alloc=708.3MB, time=109.39 memory used=7900.6MB, alloc=708.3MB, time=112.47 memory used=8004.7MB, alloc=732.3MB, time=114.99 memory used=8383.6MB, alloc=756.3MB, time=121.99 memory used=8818.5MB, alloc=780.3MB, time=127.83 memory used=9206.6MB, alloc=804.3MB, time=133.78 memory used=9625.7MB, alloc=828.3MB, time=140.49 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428292110 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 3 2 F := [20 x y z + 10 x y + z , -2 x y - 2 y z - 18 x, 2 2 2 -6 x y z - x y z - 14 x ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; G := 2 3 2 2 2 3 2 [-9 x z + 18 y z - 19 y, -x z - 6 x y - 7 x y , 6 x z - 19 y - 9 y z] > Problem := [F,G]; 2 2 3 3 2 Problem := [[20 x y z + 10 x y + z , -2 x y - 2 y z - 18 x, 2 2 2 -6 x y z - x y z - 14 x ], 2 3 2 2 2 3 2 [-9 x z + 18 y z - 19 y, -x z - 6 x y - 7 x y , 6 x z - 19 y - 9 y z] ] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=25.4MB, alloc=32.3MB, time=0.46 memory used=45.7MB, alloc=32.3MB, time=0.69 memory used=71.5MB, alloc=60.3MB, time=0.99 memory used=116.6MB, alloc=68.3MB, time=1.58 memory used=159.7MB, alloc=68.3MB, time=2.13 memory used=207.3MB, alloc=92.3MB, time=2.64 memory used=256.4MB, alloc=92.3MB, time=3.33 memory used=307.5MB, alloc=93.5MB, time=3.57 memory used=354.6MB, alloc=93.5MB, time=4.74 memory used=404.7MB, alloc=93.5MB, time=5.42 memory used=461.1MB, alloc=93.5MB, time=6.20 memory used=533.5MB, alloc=93.5MB, time=7.22 memory used=583.6MB, alloc=93.5MB, time=9.53 memory used=654.7MB, alloc=93.5MB, time=10.08 memory used=722.4MB, alloc=117.5MB, time=10.91 memory used=804.0MB, alloc=117.5MB, time=11.80 memory used=862.0MB, alloc=117.5MB, time=12.74 memory used=926.7MB, alloc=117.5MB, time=13.35 memory used=1013.1MB, alloc=117.5MB, time=14.94 memory used=1091.2MB, alloc=117.5MB, time=17.36 memory used=1182.6MB, alloc=373.5MB, time=18.30 memory used=1256.5MB, alloc=397.5MB, time=19.26 memory used=1369.8MB, alloc=397.5MB, time=20.86 memory used=1480.1MB, alloc=397.5MB, time=22.33 memory used=1578.3MB, alloc=397.5MB, time=23.42 memory used=1707.7MB, alloc=421.5MB, time=25.03 memory used=1843.3MB, alloc=421.5MB, time=26.94 memory used=1954.8MB, alloc=445.5MB, time=28.39 memory used=2064.0MB, alloc=469.5MB, time=29.82 memory used=2156.6MB, alloc=469.5MB, time=31.08 memory used=2267.1MB, alloc=469.5MB, time=32.51 memory used=2351.7MB, alloc=493.5MB, time=33.55 memory used=2464.3MB, alloc=493.5MB, time=35.12 memory used=2545.3MB, alloc=493.5MB, time=36.06 memory used=2637.2MB, alloc=493.5MB, time=37.31 memory used=2717.6MB, alloc=493.5MB, time=38.54 memory used=2822.4MB, alloc=493.5MB, time=39.46 memory used=2922.1MB, alloc=493.5MB, time=40.14 memory used=3022.3MB, alloc=493.5MB, time=40.64 memory used=3140.4MB, alloc=493.5MB, time=43.37 memory used=3238.9MB, alloc=493.5MB, time=43.91 memory used=3331.3MB, alloc=493.5MB, time=44.38 memory used=3445.6MB, alloc=493.5MB, time=45.00 memory used=3580.2MB, alloc=493.5MB, time=48.11 memory used=3660.5MB, alloc=493.5MB, time=48.53 memory used=3769.2MB, alloc=517.5MB, time=49.36 memory used=3900.2MB, alloc=517.5MB, time=50.05 memory used=4032.5MB, alloc=517.5MB, time=52.85 memory used=4153.2MB, alloc=517.5MB, time=53.62 memory used=4240.1MB, alloc=517.5MB, time=54.64 memory used=4308.1MB, alloc=517.5MB, time=55.64 memory used=4445.2MB, alloc=517.5MB, time=56.36 memory used=4601.3MB, alloc=517.5MB, time=59.71 memory used=4702.4MB, alloc=517.5MB, time=60.23 memory used=4790.0MB, alloc=517.5MB, time=61.63 memory used=4916.2MB, alloc=517.5MB, time=62.46 memory used=4974.5MB, alloc=517.5MB, time=63.34 memory used=5048.6MB, alloc=517.5MB, time=65.48 memory used=5178.0MB, alloc=517.5MB, time=66.90 memory used=5277.4MB, alloc=517.5MB, time=68.27 memory used=5370.4MB, alloc=517.5MB, time=70.35 memory used=5443.2MB, alloc=517.5MB, time=71.90 memory used=5497.2MB, alloc=517.5MB, time=72.90 memory used=5532.7MB, alloc=517.5MB, time=73.59 memory used=5742.6MB, alloc=541.5MB, time=76.48 memory used=5957.4MB, alloc=565.5MB, time=79.62 memory used=6180.2MB, alloc=589.5MB, time=83.28 memory used=6302.8MB, alloc=589.5MB, time=84.00 memory used=6522.9MB, alloc=613.5MB, time=86.16 memory used=6692.9MB, alloc=613.5MB, time=88.61 memory used=6896.8MB, alloc=613.5MB, time=92.08 memory used=7021.0MB, alloc=613.5MB, time=92.86 memory used=7187.0MB, alloc=613.5MB, time=95.75 memory used=7345.2MB, alloc=613.5MB, time=97.47 memory used=7589.0MB, alloc=637.5MB, time=99.76 memory used=7817.0MB, alloc=637.5MB, time=103.81 memory used=7972.8MB, alloc=637.5MB, time=106.13 memory used=8094.6MB, alloc=661.5MB, time=108.33 memory used=8231.1MB, alloc=661.5MB, time=110.63 memory used=8367.8MB, alloc=661.5MB, time=112.78 memory used=8587.7MB, alloc=661.5MB, time=116.45 memory used=8748.5MB, alloc=685.5MB, time=119.23 memory used=8940.9MB, alloc=685.5MB, time=123.41 memory used=9130.2MB, alloc=709.5MB, time=125.77 memory used=9365.9MB, alloc=733.5MB, time=127.95 memory used=9475.8MB, alloc=733.5MB, time=129.97 memory used=9651.2MB, alloc=757.5MB, time=132.30 memory used=9886.4MB, alloc=757.5MB, time=136.43 memory used=10008.8MB, alloc=757.5MB, time=138.87 memory used=10164.7MB, alloc=757.5MB, time=142.73 memory used=10581.9MB, alloc=781.5MB, time=147.06 memory used=11009.3MB, alloc=805.5MB, time=153.15 memory used=11466.5MB, alloc=829.5MB, time=158.78 memory used=11855.6MB, alloc=853.5MB, time=168.72 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428292410 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 2 2 2 2 F := [-13 x + 2 x z - x y z, -5 x z - 14 x y z - 17, 6 x y z - x z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 3 3 G := [8 x y + 9 x z - 20 z , 8 x z - 14 x + 4 y, 9 y z - 4 x - 7 y] > Problem := [F,G]; Problem := [ 4 2 2 2 2 2 2 [-13 x + 2 x z - x y z, -5 x z - 14 x y z - 17, 6 x y z - x z], 2 2 3 3 3 [8 x y + 9 x z - 20 z , 8 x z - 14 x + 4 y, 9 y z - 4 x - 7 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=27.0MB, alloc=32.3MB, time=0.51 memory used=47.8MB, alloc=32.3MB, time=0.81 memory used=66.9MB, alloc=56.3MB, time=1.11 memory used=107.1MB, alloc=84.3MB, time=1.74 memory used=148.8MB, alloc=84.3MB, time=2.38 memory used=212.8MB, alloc=92.3MB, time=3.36 memory used=275.4MB, alloc=116.3MB, time=4.35 memory used=351.7MB, alloc=116.3MB, time=5.50 memory used=412.9MB, alloc=372.3MB, time=6.48 memory used=503.8MB, alloc=396.3MB, time=7.69 memory used=613.4MB, alloc=420.3MB, time=9.39 memory used=749.0MB, alloc=420.3MB, time=11.33 memory used=879.1MB, alloc=444.3MB, time=13.43 memory used=1007.0MB, alloc=468.3MB, time=15.58 memory used=1142.3MB, alloc=468.3MB, time=17.42 memory used=1249.1MB, alloc=492.3MB, time=19.00 memory used=1342.3MB, alloc=492.3MB, time=20.52 memory used=1453.1MB, alloc=492.3MB, time=22.46 memory used=1547.2MB, alloc=492.3MB, time=24.19 memory used=1653.8MB, alloc=516.3MB, time=26.33 memory used=1741.7MB, alloc=516.3MB, time=27.93 memory used=1818.8MB, alloc=516.3MB, time=29.05 memory used=1899.3MB, alloc=516.3MB, time=30.77 memory used=1984.3MB, alloc=516.3MB, time=32.67 memory used=2049.9MB, alloc=516.3MB, time=34.27 memory used=2103.5MB, alloc=516.3MB, time=35.38 memory used=2158.9MB, alloc=516.3MB, time=36.49 memory used=2196.3MB, alloc=540.3MB, time=37.22 memory used=2425.5MB, alloc=564.3MB, time=41.64 memory used=2585.4MB, alloc=588.3MB, time=44.52 memory used=2760.8MB, alloc=612.3MB, time=47.23 memory used=2937.9MB, alloc=636.3MB, time=50.55 memory used=3097.7MB, alloc=636.3MB, time=53.63 memory used=3230.3MB, alloc=636.3MB, time=55.96 memory used=3375.2MB, alloc=636.3MB, time=58.54 memory used=3500.7MB, alloc=636.3MB, time=60.99 memory used=3632.2MB, alloc=660.3MB, time=63.01 memory used=3760.8MB, alloc=660.3MB, time=66.09 memory used=3846.2MB, alloc=660.3MB, time=68.09 memory used=3937.7MB, alloc=660.3MB, time=69.92 memory used=4038.9MB, alloc=660.3MB, time=72.89 memory used=4371.0MB, alloc=684.3MB, time=78.58 memory used=4734.9MB, alloc=708.3MB, time=84.49 memory used=5114.4MB, alloc=732.3MB, time=91.72 memory used=5460.9MB, alloc=756.3MB, time=98.29 memory used=5794.8MB, alloc=780.3MB, time=104.59 memory used=6052.2MB, alloc=804.3MB, time=110.33 memory used=6385.1MB, alloc=828.3MB, time=118.44 memory used=6647.1MB, alloc=852.3MB, time=124.64 memory used=6954.2MB, alloc=876.3MB, time=130.48 memory used=7201.8MB, alloc=900.3MB, time=135.22 memory used=7507.6MB, alloc=924.3MB, time=140.17 memory used=7758.5MB, alloc=948.3MB, time=145.33 memory used=8027.8MB, alloc=972.3MB, time=151.05 memory used=8210.1MB, alloc=972.3MB, time=155.70 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428292710 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 4 2 2 2 2 2 2 F := [9 y z + z + 18 y z , -5 x y + 16 y z - 18 x , 4 2 2 2 20 x + 7 x z - 20 x z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 3 3 4 G := [15 y z - 10 y z - 13 x , -3 x y + 19 z + 16 x z, 2 2 -15 x y z + 3 x z - 14 y] > Problem := [F,G]; 3 4 2 2 2 2 2 2 Problem := [[9 y z + z + 18 y z , -5 x y + 16 y z - 18 x , 4 2 2 2 3 3 3 20 x + 7 x z - 20 x z ], [15 y z - 10 y z - 13 x , 3 4 2 2 -3 x y + 19 z + 16 x z, -15 x y z + 3 x z - 14 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.19 memory used=26.7MB, alloc=32.3MB, time=0.53 memory used=46.7MB, alloc=32.3MB, time=0.83 memory used=65.7MB, alloc=56.3MB, time=1.12 memory used=105.8MB, alloc=60.3MB, time=1.74 memory used=144.2MB, alloc=60.3MB, time=2.33 memory used=186.2MB, alloc=92.3MB, time=2.90 memory used=254.9MB, alloc=92.3MB, time=3.83 memory used=323.4MB, alloc=92.3MB, time=4.72 memory used=393.3MB, alloc=92.3MB, time=5.57 memory used=457.4MB, alloc=92.3MB, time=6.30 memory used=525.4MB, alloc=116.3MB, time=7.14 memory used=592.2MB, alloc=116.3MB, time=7.92 memory used=663.4MB, alloc=372.3MB, time=8.78 memory used=758.8MB, alloc=372.3MB, time=9.79 memory used=842.6MB, alloc=396.3MB, time=11.03 memory used=956.8MB, alloc=396.3MB, time=12.60 memory used=1064.7MB, alloc=420.3MB, time=14.21 memory used=1180.8MB, alloc=420.3MB, time=15.88 memory used=1298.8MB, alloc=420.3MB, time=17.02 memory used=1400.4MB, alloc=420.3MB, time=18.03 memory used=1471.7MB, alloc=444.3MB, time=18.35 memory used=1556.2MB, alloc=444.3MB, time=18.63 memory used=1613.0MB, alloc=444.3MB, time=18.88 memory used=1679.8MB, alloc=444.3MB, time=19.13 memory used=1759.0MB, alloc=444.3MB, time=19.38 memory used=1841.3MB, alloc=444.3MB, time=19.64 memory used=1894.4MB, alloc=444.3MB, time=19.83 memory used=2003.4MB, alloc=444.3MB, time=33.93 memory used=2105.4MB, alloc=444.3MB, time=34.38 memory used=2166.8MB, alloc=444.3MB, time=34.62 memory used=2247.5MB, alloc=444.3MB, time=34.88 memory used=2323.9MB, alloc=444.3MB, time=35.11 memory used=2378.1MB, alloc=444.3MB, time=35.31 memory used=2437.5MB, alloc=444.3MB, time=35.52 memory used=2502.9MB, alloc=444.3MB, time=35.74 memory used=2574.2MB, alloc=444.3MB, time=35.95 memory used=2652.9MB, alloc=444.3MB, time=36.15 memory used=2738.5MB, alloc=444.3MB, time=36.37 memory used=2832.1MB, alloc=444.3MB, time=36.61 memory used=2981.5MB, alloc=444.3MB, time=37.09 memory used=3135.2MB, alloc=444.3MB, time=37.44 memory used=3383.5MB, alloc=444.3MB, time=39.26 memory used=3459.0MB, alloc=444.3MB, time=39.59 memory used=3530.6MB, alloc=444.3MB, time=39.89 memory used=3616.1MB, alloc=444.3MB, time=40.18 memory used=3684.7MB, alloc=444.3MB, time=40.44 memory used=3737.1MB, alloc=444.3MB, time=40.69 memory used=3792.2MB, alloc=444.3MB, time=40.92 memory used=3850.3MB, alloc=444.3MB, time=41.16 memory used=3915.3MB, alloc=444.3MB, time=41.40 memory used=3983.1MB, alloc=444.3MB, time=41.65 memory used=4053.6MB, alloc=444.3MB, time=41.90 memory used=4131.7MB, alloc=444.3MB, time=42.15 memory used=4212.2MB, alloc=444.3MB, time=42.40 memory used=4295.7MB, alloc=444.3MB, time=42.67 memory used=4386.0MB, alloc=444.3MB, time=42.92 memory used=4444.4MB, alloc=468.3MB, time=43.15 memory used=4502.9MB, alloc=468.3MB, time=43.36 memory used=4561.5MB, alloc=468.3MB, time=43.57 memory used=4620.9MB, alloc=468.3MB, time=43.78 memory used=4686.6MB, alloc=468.3MB, time=43.99 memory used=4753.0MB, alloc=468.3MB, time=44.21 memory used=4819.8MB, alloc=468.3MB, time=44.42 memory used=4887.3MB, alloc=468.3MB, time=44.64 memory used=4961.0MB, alloc=468.3MB, time=44.85 memory used=5035.1MB, alloc=468.3MB, time=45.06 memory used=5109.5MB, alloc=468.3MB, time=45.28 memory used=5190.1MB, alloc=468.3MB, time=45.50 memory used=5270.7MB, alloc=468.3MB, time=45.72 memory used=5357.3MB, alloc=468.3MB, time=45.94 memory used=5443.6MB, alloc=468.3MB, time=46.17 memory used=5535.3MB, alloc=468.3MB, time=46.40 memory used=5627.0MB, alloc=468.3MB, time=46.62 memory used=5722.2MB, alloc=468.3MB, time=46.85 memory used=5822.6MB, alloc=468.3MB, time=47.09 memory used=5926.8MB, alloc=468.3MB, time=47.31 memory used=6034.1MB, alloc=468.3MB, time=47.56 memory used=6148.9MB, alloc=468.3MB, time=47.80 memory used=6337.9MB, alloc=468.3MB, time=48.16 memory used=6468.2MB, alloc=468.3MB, time=48.45 memory used=6606.1MB, alloc=468.3MB, time=48.75 memory used=6755.2MB, alloc=468.3MB, time=49.05 memory used=6897.5MB, alloc=468.3MB, time=169.45 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428293010 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 3 2 2 2 2 F := [10 x - 6 x y z + 16 z , -6 x y + 13 y z - y z , 2 2 -9 x y - 11 y z - 2 x z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; G := [ 2 2 2 2 3 2 3 2 3 3 2 -5 x y + 3 y z - 6 y , 17 y z - 10 z - 12 x , -x z + 19 y z + 11 z ] > Problem := [F,G]; 4 2 3 2 2 2 2 Problem := [[10 x - 6 x y z + 16 z , -6 x y + 13 y z - y z , 2 2 -9 x y - 11 y z - 2 x z], [ 2 2 2 2 3 2 3 2 3 3 2 -5 x y + 3 y z - 6 y , 17 y z - 10 z - 12 x , -x z + 19 y z + 11 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=27.1MB, alloc=32.3MB, time=0.51 memory used=47.7MB, alloc=56.3MB, time=0.82 memory used=88.6MB, alloc=60.3MB, time=1.42 memory used=128.3MB, alloc=60.3MB, time=1.97 memory used=164.7MB, alloc=84.3MB, time=2.49 memory used=227.2MB, alloc=92.3MB, time=3.36 memory used=292.8MB, alloc=116.3MB, time=4.29 memory used=367.3MB, alloc=116.3MB, time=5.36 memory used=428.4MB, alloc=396.3MB, time=6.27 memory used=537.5MB, alloc=396.3MB, time=7.67 memory used=651.8MB, alloc=396.3MB, time=8.86 memory used=763.2MB, alloc=420.3MB, time=10.45 memory used=881.0MB, alloc=444.3MB, time=12.20 memory used=999.2MB, alloc=444.3MB, time=13.39 memory used=1133.6MB, alloc=444.3MB, time=14.73 memory used=1270.0MB, alloc=444.3MB, time=16.29 memory used=1373.9MB, alloc=468.3MB, time=17.79 memory used=1477.0MB, alloc=468.3MB, time=19.37 memory used=1576.3MB, alloc=468.3MB, time=21.03 memory used=1666.3MB, alloc=468.3MB, time=22.47 memory used=1747.6MB, alloc=492.3MB, time=23.87 memory used=1819.4MB, alloc=492.3MB, time=25.15 memory used=1882.1MB, alloc=492.3MB, time=26.37 memory used=1958.7MB, alloc=492.3MB, time=27.87 memory used=2023.8MB, alloc=492.3MB, time=29.19 memory used=2078.6MB, alloc=492.3MB, time=30.26 memory used=2129.5MB, alloc=492.3MB, time=31.25 memory used=2184.0MB, alloc=492.3MB, time=32.21 memory used=2228.1MB, alloc=492.3MB, time=33.14 memory used=2272.8MB, alloc=492.3MB, time=34.13 memory used=2440.0MB, alloc=516.3MB, time=36.31 memory used=2559.5MB, alloc=516.3MB, time=37.36 memory used=2675.2MB, alloc=516.3MB, time=38.06 memory used=2798.1MB, alloc=516.3MB, time=39.09 memory used=2994.4MB, alloc=540.3MB, time=41.57 memory used=3175.3MB, alloc=564.3MB, time=44.49 memory used=3349.0MB, alloc=564.3MB, time=47.15 memory used=3491.1MB, alloc=588.3MB, time=49.68 memory used=3646.3MB, alloc=612.3MB, time=52.47 memory used=3835.9MB, alloc=612.3MB, time=56.61 memory used=3965.6MB, alloc=636.3MB, time=59.15 memory used=4095.4MB, alloc=660.3MB, time=61.58 memory used=4221.6MB, alloc=660.3MB, time=64.30 memory used=4343.6MB, alloc=660.3MB, time=66.49 memory used=4470.4MB, alloc=684.3MB, time=69.50 memory used=4570.4MB, alloc=684.3MB, time=71.66 memory used=4656.1MB, alloc=684.3MB, time=73.52 memory used=5008.0MB, alloc=708.3MB, time=79.27 memory used=5363.9MB, alloc=732.3MB, time=84.73 memory used=5777.2MB, alloc=756.3MB, time=91.04 memory used=6125.4MB, alloc=780.3MB, time=97.69 memory used=6444.1MB, alloc=804.3MB, time=104.00 memory used=6768.7MB, alloc=828.3MB, time=109.10 memory used=7159.0MB, alloc=852.3MB, time=115.17 memory used=7493.6MB, alloc=876.3MB, time=120.75 memory used=7766.7MB, alloc=900.3MB, time=125.95 memory used=8040.1MB, alloc=924.3MB, time=131.62 memory used=8330.8MB, alloc=948.3MB, time=137.91 memory used=8525.5MB, alloc=972.3MB, time=142.72 memory used=8700.4MB, alloc=996.3MB, time=147.45 memory used=8915.3MB, alloc=1020.3MB, time=152.41 memory used=9076.1MB, alloc=1044.3MB, time=156.55 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428293310 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 2 3 F := [-16 x y z + 10 x y z - 12 z , 9 x y - 11 x z + 10 y , 2 2 2 3 18 x y - 3 x y + 13 y ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 G := [-4 x z - 12 y z - x y, -12 x y + 16 x z - 3 x z, 2 3 2 20 x y + 8 y - 14 y z ] > Problem := [F,G]; 2 3 2 2 2 3 Problem := [[-16 x y z + 10 x y z - 12 z , 9 x y - 11 x z + 10 y , 2 2 2 3 3 2 18 x y - 3 x y + 13 y ], [-4 x z - 12 y z - x y, 2 2 2 2 3 2 -12 x y + 16 x z - 3 x z, 20 x y + 8 y - 14 y z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.18 memory used=26.7MB, alloc=32.3MB, time=0.50 memory used=48.0MB, alloc=32.3MB, time=0.79 memory used=67.4MB, alloc=56.3MB, time=1.09 memory used=108.0MB, alloc=60.3MB, time=1.69 memory used=146.8MB, alloc=60.3MB, time=2.25 memory used=183.9MB, alloc=84.3MB, time=2.81 memory used=222.9MB, alloc=84.3MB, time=3.39 memory used=283.5MB, alloc=92.3MB, time=4.33 memory used=343.0MB, alloc=116.3MB, time=5.28 memory used=425.0MB, alloc=116.3MB, time=6.64 memory used=490.9MB, alloc=396.3MB, time=7.79 memory used=594.6MB, alloc=396.3MB, time=9.54 memory used=699.1MB, alloc=420.3MB, time=11.39 memory used=823.4MB, alloc=444.3MB, time=13.54 memory used=972.8MB, alloc=468.3MB, time=16.32 memory used=1120.1MB, alloc=492.3MB, time=18.97 memory used=1266.3MB, alloc=492.3MB, time=21.70 memory used=1396.7MB, alloc=516.3MB, time=24.20 memory used=1491.4MB, alloc=516.3MB, time=25.73 memory used=1600.1MB, alloc=516.3MB, time=27.60 memory used=1699.8MB, alloc=540.3MB, time=29.22 memory used=1804.1MB, alloc=540.3MB, time=31.29 memory used=1879.2MB, alloc=540.3MB, time=32.92 memory used=1979.6MB, alloc=540.3MB, time=35.11 memory used=2048.9MB, alloc=540.3MB, time=36.53 memory used=2105.7MB, alloc=540.3MB, time=37.59 memory used=2187.4MB, alloc=540.3MB, time=39.46 memory used=2257.7MB, alloc=540.3MB, time=40.93 memory used=2336.1MB, alloc=540.3MB, time=42.79 memory used=2410.8MB, alloc=540.3MB, time=44.70 memory used=2466.1MB, alloc=564.3MB, time=45.86 memory used=2516.7MB, alloc=564.3MB, time=46.99 memory used=2595.7MB, alloc=564.3MB, time=49.17 memory used=2629.4MB, alloc=564.3MB, time=50.28 memory used=2812.1MB, alloc=588.3MB, time=54.08 memory used=3042.8MB, alloc=612.3MB, time=58.32 memory used=3266.5MB, alloc=636.3MB, time=62.84 memory used=3454.7MB, alloc=660.3MB, time=66.68 memory used=3659.5MB, alloc=660.3MB, time=71.74 memory used=3852.5MB, alloc=684.3MB, time=76.09 memory used=4026.2MB, alloc=684.3MB, time=80.08 memory used=4187.1MB, alloc=684.3MB, time=83.80 memory used=4320.5MB, alloc=684.3MB, time=86.90 memory used=4458.0MB, alloc=684.3MB, time=89.86 memory used=4588.3MB, alloc=708.3MB, time=92.89 memory used=4714.9MB, alloc=708.3MB, time=95.57 memory used=4852.4MB, alloc=708.3MB, time=98.85 memory used=4962.5MB, alloc=708.3MB, time=101.47 memory used=5094.0MB, alloc=708.3MB, time=105.16 memory used=5239.6MB, alloc=708.3MB, time=110.19 memory used=5612.0MB, alloc=732.3MB, time=119.98 memory used=5996.6MB, alloc=756.3MB, time=128.38 memory used=6408.5MB, alloc=780.3MB, time=136.86 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428293610 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; F := 2 2 3 3 3 3 2 3 [-2 x z + 8 y z , 6 x y - 19 x z + 13 y z, -6 x y z + 13 x + 18 y z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 G := [15 x y + 9 y z - 20 z , 4 x y + 16 y z + 2, -13 x y z - 15 z + 17] > Problem := [F,G]; Problem := [ 2 2 3 3 3 3 2 3 [-2 x z + 8 y z , 6 x y - 19 x z + 13 y z, -6 x y z + 13 x + 18 y z] 3 2 2 2 2 , [15 x y + 9 y z - 20 z , 4 x y + 16 y z + 2, -13 x y z - 15 z + 17]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.18 memory used=26.4MB, alloc=32.3MB, time=0.51 memory used=47.3MB, alloc=32.3MB, time=0.85 memory used=65.8MB, alloc=56.3MB, time=1.15 memory used=105.8MB, alloc=60.3MB, time=1.78 memory used=145.2MB, alloc=84.3MB, time=2.42 memory used=206.8MB, alloc=92.3MB, time=3.42 memory used=265.3MB, alloc=116.3MB, time=4.40 memory used=345.7MB, alloc=116.3MB, time=5.78 memory used=417.0MB, alloc=396.3MB, time=7.03 memory used=527.2MB, alloc=420.3MB, time=8.86 memory used=657.7MB, alloc=444.3MB, time=11.00 memory used=787.7MB, alloc=444.3MB, time=13.08 memory used=903.1MB, alloc=468.3MB, time=14.92 memory used=1024.6MB, alloc=468.3MB, time=16.89 memory used=1133.7MB, alloc=468.3MB, time=18.75 memory used=1237.6MB, alloc=492.3MB, time=20.67 memory used=1338.9MB, alloc=492.3MB, time=22.47 memory used=1438.9MB, alloc=492.3MB, time=24.39 memory used=1520.2MB, alloc=492.3MB, time=25.98 memory used=1600.1MB, alloc=492.3MB, time=27.62 memory used=1667.6MB, alloc=516.3MB, time=28.95 memory used=1737.0MB, alloc=516.3MB, time=30.50 memory used=1803.3MB, alloc=516.3MB, time=32.00 memory used=1867.6MB, alloc=516.3MB, time=33.45 memory used=1914.1MB, alloc=516.3MB, time=34.53 memory used=2117.8MB, alloc=540.3MB, time=38.63 memory used=2324.4MB, alloc=564.3MB, time=42.44 memory used=2509.2MB, alloc=588.3MB, time=46.10 memory used=2695.5MB, alloc=612.3MB, time=49.18 memory used=2865.1MB, alloc=636.3MB, time=52.47 memory used=3015.4MB, alloc=636.3MB, time=55.48 memory used=3158.7MB, alloc=636.3MB, time=58.22 memory used=3314.0MB, alloc=636.3MB, time=60.88 memory used=3448.3MB, alloc=636.3MB, time=63.89 memory used=3577.5MB, alloc=660.3MB, time=66.63 memory used=3726.0MB, alloc=660.3MB, time=68.84 memory used=3856.7MB, alloc=660.3MB, time=71.35 memory used=3957.3MB, alloc=660.3MB, time=73.59 memory used=4055.9MB, alloc=660.3MB, time=76.02 memory used=4137.1MB, alloc=660.3MB, time=78.43 memory used=4453.7MB, alloc=684.3MB, time=84.59 memory used=4789.0MB, alloc=708.3MB, time=90.00 memory used=5121.6MB, alloc=732.3MB, time=94.91 memory used=5481.1MB, alloc=756.3MB, time=101.04 memory used=5856.7MB, alloc=780.3MB, time=109.52 memory used=6225.1MB, alloc=804.3MB, time=118.08 memory used=6597.2MB, alloc=828.3MB, time=126.42 memory used=6891.6MB, alloc=852.3MB, time=132.56 memory used=7210.6MB, alloc=876.3MB, time=140.02 memory used=7496.7MB, alloc=900.3MB, time=145.35 memory used=7757.8MB, alloc=924.3MB, time=150.41 memory used=7994.7MB, alloc=948.3MB, time=156.92 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428293910 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 2 3 4 2 F := [-6 y z + 10 x z - 20 y , -3 x y - 12 y z - 17 z , -14 y + y + 5] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 3 2 2 G := [-17 x z + 17 x y + 6 x, 9 x y + 8 x y, -4 y z - 12 x y + 8 y z] > Problem := [F,G]; Problem := [ 2 2 2 3 2 2 3 4 2 [-6 y z + 10 x z - 20 y , -3 x y - 12 y z - 17 z , -14 y + y + 5], 3 2 2 3 2 2 [-17 x z + 17 x y + 6 x, 9 x y + 8 x y, -4 y z - 12 x y + 8 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.17 memory used=54.7MB, alloc=68.4MB, time=0.90 memory used=121.1MB, alloc=68.4MB, time=4.22 memory used=152.9MB, alloc=68.4MB, time=4.31 memory used=189.8MB, alloc=68.4MB, time=4.41 memory used=214.0MB, alloc=68.4MB, time=4.49 memory used=243.3MB, alloc=68.4MB, time=4.56 memory used=279.2MB, alloc=68.4MB, time=4.64 memory used=328.0MB, alloc=78.8MB, time=4.88 memory used=393.8MB, alloc=78.8MB, time=5.50 memory used=453.0MB, alloc=78.8MB, time=7.44 memory used=488.4MB, alloc=78.8MB, time=7.66 memory used=572.8MB, alloc=78.8MB, time=8.45 memory used=629.6MB, alloc=78.8MB, time=12.92 memory used=675.5MB, alloc=78.8MB, time=16.19 memory used=702.3MB, alloc=78.8MB, time=16.28 memory used=726.3MB, alloc=78.8MB, time=16.35 memory used=752.6MB, alloc=78.8MB, time=16.43 memory used=783.0MB, alloc=78.8MB, time=16.52 memory used=816.9MB, alloc=78.8MB, time=16.60 memory used=846.8MB, alloc=78.8MB, time=16.69 memory used=868.6MB, alloc=78.8MB, time=16.76 memory used=889.8MB, alloc=78.8MB, time=16.83 memory used=911.8MB, alloc=78.8MB, time=16.90 memory used=936.3MB, alloc=78.8MB, time=16.98 memory used=964.2MB, alloc=78.8MB, time=17.09 memory used=1004.4MB, alloc=78.8MB, time=27.00 memory used=1031.8MB, alloc=78.8MB, time=40.74 memory used=1071.3MB, alloc=78.8MB, time=46.65 memory used=1116.4MB, alloc=78.8MB, time=46.94 memory used=1153.4MB, alloc=78.8MB, time=47.19 memory used=1191.2MB, alloc=78.8MB, time=47.44 memory used=1228.9MB, alloc=78.8MB, time=47.69 memory used=1266.5MB, alloc=78.8MB, time=47.95 memory used=1297.9MB, alloc=78.8MB, time=48.11 memory used=1319.9MB, alloc=78.8MB, time=48.19 memory used=1342.3MB, alloc=78.8MB, time=48.27 memory used=1366.3MB, alloc=78.8MB, time=48.35 memory used=1391.9MB, alloc=78.8MB, time=48.43 memory used=1419.4MB, alloc=78.8MB, time=48.50 memory used=1448.8MB, alloc=78.8MB, time=48.59 memory used=1480.6MB, alloc=78.8MB, time=48.68 memory used=1504.2MB, alloc=78.8MB, time=48.75 memory used=1525.6MB, alloc=78.8MB, time=48.82 memory used=1544.9MB, alloc=78.8MB, time=48.88 memory used=1563.5MB, alloc=78.8MB, time=48.96 memory used=1583.0MB, alloc=78.8MB, time=49.02 memory used=1602.9MB, alloc=78.8MB, time=49.09 memory used=1623.7MB, alloc=78.8MB, time=49.15 memory used=1645.1MB, alloc=78.8MB, time=49.21 memory used=1667.2MB, alloc=78.8MB, time=49.28 memory used=1690.6MB, alloc=78.8MB, time=49.34 memory used=1715.1MB, alloc=78.8MB, time=49.41 memory used=1740.3MB, alloc=78.8MB, time=49.48 memory used=1765.6MB, alloc=78.8MB, time=49.54 memory used=1793.4MB, alloc=78.8MB, time=49.60 memory used=1825.4MB, alloc=79.2MB, time=49.67 memory used=1851.1MB, alloc=81.9MB, time=49.75 memory used=1903.2MB, alloc=81.9MB, time=51.26 memory used=1944.4MB, alloc=81.9MB, time=57.53 memory used=1975.3MB, alloc=81.9MB, time=57.66 memory used=2002.3MB, alloc=81.9MB, time=57.75 memory used=2032.5MB, alloc=81.9MB, time=57.85 memory used=2053.0MB, alloc=81.9MB, time=57.92 memory used=2074.0MB, alloc=81.9MB, time=58.00 memory used=2096.7MB, alloc=81.9MB, time=58.07 memory used=2121.9MB, alloc=81.9MB, time=58.15 memory used=2149.5MB, alloc=81.9MB, time=58.23 memory used=2179.4MB, alloc=81.9MB, time=58.32 memory used=2211.5MB, alloc=81.9MB, time=58.40 memory used=2253.3MB, alloc=91.8MB, time=58.50 memory used=2262.9MB, alloc=91.8MB, time=58.55 memory used=2270.9MB, alloc=91.8MB, time=58.60 memory used=2279.1MB, alloc=91.8MB, time=58.68 memory used=2287.7MB, alloc=91.8MB, time=58.73 memory used=2296.2MB, alloc=91.8MB, time=58.79 memory used=2304.7MB, alloc=91.8MB, time=58.84 memory used=2313.2MB, alloc=91.8MB, time=58.88 memory used=2321.7MB, alloc=91.8MB, time=58.93 memory used=2330.1MB, alloc=91.8MB, time=58.99 memory used=2338.6MB, alloc=91.8MB, time=59.04 memory used=2348.3MB, alloc=91.8MB, time=59.09 memory used=2358.0MB, alloc=91.8MB, time=59.13 memory used=2367.6MB, alloc=91.8MB, time=59.19 memory used=2377.1MB, alloc=91.8MB, time=59.24 memory used=2387.9MB, alloc=91.8MB, time=59.30 memory used=2398.5MB, alloc=91.8MB, time=59.35 memory used=2409.0MB, alloc=91.8MB, time=59.41 memory used=2419.5MB, alloc=91.8MB, time=59.47 memory used=2430.7MB, alloc=91.8MB, time=59.52 memory used=2441.9MB, alloc=91.8MB, time=59.57 memory used=2454.1MB, alloc=91.8MB, time=59.64 memory used=2465.9MB, alloc=91.8MB, time=59.70 memory used=2478.5MB, alloc=91.8MB, time=59.76 memory used=2491.8MB, alloc=91.8MB, time=59.82 memory used=2505.5MB, alloc=91.8MB, time=59.91 memory used=2519.4MB, alloc=91.8MB, time=59.97 memory used=2534.3MB, alloc=91.8MB, time=60.04 memory used=2549.7MB, alloc=91.8MB, time=60.11 memory used=2566.1MB, alloc=91.8MB, time=60.17 memory used=2615.2MB, alloc=115.8MB, time=70.45 memory used=2662.7MB, alloc=115.8MB, time=87.37 memory used=2732.1MB, alloc=115.8MB, time=90.58 memory used=2797.4MB, alloc=115.8MB, time=90.99 memory used=2862.7MB, alloc=115.8MB, time=91.40 memory used=2915.1MB, alloc=115.8MB, time=91.67 memory used=2958.3MB, alloc=115.8MB, time=91.79 memory used=3000.8MB, alloc=115.8MB, time=91.90 memory used=3034.1MB, alloc=115.8MB, time=92.00 memory used=3069.5MB, alloc=115.8MB, time=92.10 memory used=3108.3MB, alloc=115.8MB, time=92.20 memory used=3151.3MB, alloc=115.8MB, time=92.30 memory used=3198.5MB, alloc=115.8MB, time=92.41 memory used=3249.8MB, alloc=115.8MB, time=92.52 memory used=3282.8MB, alloc=115.8MB, time=92.61 memory used=3294.1MB, alloc=115.8MB, time=92.66 memory used=3302.5MB, alloc=115.8MB, time=92.71 memory used=3311.2MB, alloc=115.8MB, time=92.76 memory used=3318.6MB, alloc=115.8MB, time=92.81 memory used=3326.4MB, alloc=115.8MB, time=92.86 memory used=3332.6MB, alloc=115.8MB, time=92.90 memory used=3338.8MB, alloc=115.8MB, time=92.96 memory used=3345.1MB, alloc=115.8MB, time=93.00 memory used=3351.4MB, alloc=115.8MB, time=93.05 memory used=3357.6MB, alloc=115.8MB, time=93.11 memory used=3364.0MB, alloc=115.8MB, time=93.16 memory used=3372.4MB, alloc=115.8MB, time=93.22 memory used=3380.8MB, alloc=115.8MB, time=93.27 memory used=3389.2MB, alloc=115.8MB, time=93.32 memory used=3397.7MB, alloc=115.8MB, time=93.38 memory used=3406.1MB, alloc=115.8MB, time=93.43 memory used=3414.6MB, alloc=115.8MB, time=93.48 memory used=3423.1MB, alloc=115.8MB, time=93.53 memory used=3431.6MB, alloc=115.8MB, time=93.58 memory used=3440.1MB, alloc=115.8MB, time=93.63 memory used=3448.6MB, alloc=115.8MB, time=93.69 memory used=3457.1MB, alloc=115.8MB, time=93.74 memory used=3465.6MB, alloc=115.8MB, time=93.79 memory used=3474.1MB, alloc=115.8MB, time=93.84 memory used=3482.6MB, alloc=115.8MB, time=93.89 memory used=3491.1MB, alloc=115.8MB, time=93.94 memory used=3499.6MB, alloc=115.8MB, time=93.99 memory used=3508.1MB, alloc=115.8MB, time=94.05 memory used=3516.6MB, alloc=115.8MB, time=94.10 memory used=3525.0MB, alloc=115.8MB, time=94.17 memory used=3533.6MB, alloc=115.8MB, time=94.23 memory used=3544.1MB, alloc=115.8MB, time=94.28 memory used=3554.6MB, alloc=115.8MB, time=94.34 memory used=3565.1MB, alloc=115.8MB, time=94.40 memory used=3575.6MB, alloc=115.8MB, time=94.45 memory used=3586.1MB, alloc=115.8MB, time=94.51 memory used=3596.5MB, alloc=115.8MB, time=94.56 memory used=3606.9MB, alloc=115.8MB, time=94.63 memory used=3617.2MB, alloc=115.8MB, time=94.68 memory used=3627.5MB, alloc=115.8MB, time=94.73 memory used=3637.8MB, alloc=115.8MB, time=94.79 memory used=3648.0MB, alloc=115.8MB, time=94.84 memory used=3658.3MB, alloc=115.8MB, time=94.89 memory used=3670.3MB, alloc=115.8MB, time=94.95 memory used=3682.3MB, alloc=115.8MB, time=95.00 memory used=3694.2MB, alloc=115.8MB, time=95.06 memory used=3706.1MB, alloc=115.8MB, time=95.11 memory used=3717.9MB, alloc=115.8MB, time=95.17 memory used=3729.5MB, alloc=115.8MB, time=95.24 memory used=3741.3MB, alloc=115.8MB, time=95.29 memory used=3754.6MB, alloc=115.8MB, time=95.35 memory used=3767.8MB, alloc=115.8MB, time=95.43 memory used=3780.8MB, alloc=115.8MB, time=95.49 memory used=3793.7MB, alloc=115.8MB, time=95.54 memory used=3808.1MB, alloc=115.8MB, time=95.59 memory used=3822.3MB, alloc=115.8MB, time=95.65 memory used=3834.7MB, alloc=115.8MB, time=95.71 memory used=3849.9MB, alloc=115.8MB, time=95.78 memory used=3865.0MB, alloc=115.8MB, time=95.83 memory used=3878.8MB, alloc=115.8MB, time=95.89 memory used=3892.5MB, alloc=115.8MB, time=95.95 memory used=3906.4MB, alloc=115.8MB, time=96.00 memory used=3920.9MB, alloc=115.8MB, time=96.05 memory used=3934.3MB, alloc=115.8MB, time=96.14 memory used=3945.3MB, alloc=115.8MB, time=96.19 memory used=3956.2MB, alloc=115.8MB, time=96.26 memory used=3967.5MB, alloc=115.8MB, time=96.33 memory used=3979.4MB, alloc=115.8MB, time=96.38 memory used=3991.0MB, alloc=115.8MB, time=96.43 memory used=4003.4MB, alloc=115.8MB, time=96.48 memory used=4016.0MB, alloc=115.8MB, time=96.54 memory used=4029.3MB, alloc=115.8MB, time=96.61 memory used=4069.3MB, alloc=115.8MB, time=97.41 memory used=4126.6MB, alloc=115.8MB, time=120.68 memory used=4198.5MB, alloc=115.8MB, time=126.81 memory used=4262.2MB, alloc=115.8MB, time=127.23 memory used=4325.9MB, alloc=115.8MB, time=127.63 memory used=4388.0MB, alloc=115.8MB, time=128.00 memory used=4424.3MB, alloc=115.8MB, time=128.10 memory used=4462.9MB, alloc=115.8MB, time=128.21 memory used=4506.9MB, alloc=115.8MB, time=128.32 memory used=4556.8MB, alloc=115.8MB, time=128.43 memory used=4601.0MB, alloc=115.8MB, time=128.53 memory used=4635.4MB, alloc=115.8MB, time=128.62 memory used=4667.0MB, alloc=115.8MB, time=128.70 memory used=4700.7MB, alloc=115.8MB, time=128.78 memory used=4736.7MB, alloc=115.8MB, time=128.86 memory used=4774.8MB, alloc=115.8MB, time=128.94 memory used=4815.2MB, alloc=115.8MB, time=129.02 memory used=4858.0MB, alloc=115.8MB, time=129.10 memory used=4903.8MB, alloc=115.8MB, time=129.18 memory used=5001.6MB, alloc=115.8MB, time=129.65 memory used=5337.2MB, alloc=115.8MB, time=133.11 memory used=5389.8MB, alloc=115.8MB, time=133.65 memory used=5427.2MB, alloc=115.8MB, time=133.77 memory used=5472.6MB, alloc=115.8MB, time=133.88 memory used=5742.4MB, alloc=115.8MB, time=139.37 memory used=5775.6MB, alloc=139.8MB, time=143.64 memory used=5829.1MB, alloc=163.8MB, time=146.43 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428294210 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 3 3 2 2 F := [-6 x y + 4 y z + 12 x , 20 x y - 19 y z - 19 x z, 3 -9 y z - 12 x y - 2 z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 G := [18 x y z - 3 x y z - 7 y , -12 x y + 12 x z + 14 y , 2 4 -4 x y z - 15 z + 15 y z] > Problem := [F,G]; 3 3 3 3 2 2 Problem := [[-6 x y + 4 y z + 12 x , 20 x y - 19 y z - 19 x z, 3 2 2 -9 y z - 12 x y - 2 z], [18 x y z - 3 x y z - 7 y , 3 2 2 2 4 -12 x y + 12 x z + 14 y , -4 x y z - 15 z + 15 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.17 memory used=26.7MB, alloc=32.3MB, time=0.48 memory used=46.8MB, alloc=32.3MB, time=0.65 memory used=68.6MB, alloc=36.3MB, time=0.95 memory used=86.2MB, alloc=38.2MB, time=1.01 memory used=95.8MB, alloc=38.2MB, time=1.05 memory used=107.0MB, alloc=38.2MB, time=1.09 memory used=125.9MB, alloc=38.3MB, time=1.18 memory used=137.4MB, alloc=38.3MB, time=1.22 memory used=147.9MB, alloc=38.3MB, time=1.25 memory used=167.9MB, alloc=62.3MB, time=2.29 memory used=236.0MB, alloc=64.8MB, time=5.84 memory used=274.8MB, alloc=64.9MB, time=6.00 memory used=302.6MB, alloc=64.9MB, time=6.08 memory used=335.2MB, alloc=64.9MB, time=6.16 memory used=356.3MB, alloc=64.9MB, time=6.23 memory used=379.2MB, alloc=64.9MB, time=6.31 memory used=404.0MB, alloc=64.9MB, time=6.38 memory used=431.2MB, alloc=64.9MB, time=6.45 memory used=461.5MB, alloc=64.9MB, time=6.52 memory used=494.2MB, alloc=64.9MB, time=6.60 memory used=529.0MB, alloc=64.9MB, time=6.68 memory used=549.4MB, alloc=64.9MB, time=6.73 memory used=568.5MB, alloc=64.9MB, time=6.79 memory used=588.6MB, alloc=64.9MB, time=6.84 memory used=608.8MB, alloc=64.9MB, time=6.89 memory used=630.1MB, alloc=64.9MB, time=6.94 memory used=652.5MB, alloc=64.9MB, time=7.00 memory used=675.8MB, alloc=64.9MB, time=7.07 memory used=699.9MB, alloc=64.9MB, time=7.13 memory used=725.6MB, alloc=64.9MB, time=7.19 memory used=751.9MB, alloc=64.9MB, time=7.25 memory used=779.5MB, alloc=64.9MB, time=7.31 memory used=808.3MB, alloc=64.9MB, time=7.37 memory used=838.4MB, alloc=64.9MB, time=7.43 memory used=870.2MB, alloc=64.9MB, time=7.49 memory used=915.9MB, alloc=83.8MB, time=7.58 memory used=959.5MB, alloc=83.8MB, time=7.86 memory used=989.9MB, alloc=83.8MB, time=7.95 memory used=1026.0MB, alloc=83.8MB, time=8.08 memory used=1083.4MB, alloc=83.8MB, time=12.40 memory used=1142.9MB, alloc=83.8MB, time=12.81 memory used=1169.1MB, alloc=83.8MB, time=12.90 memory used=1201.4MB, alloc=83.8MB, time=13.00 memory used=1227.0MB, alloc=83.8MB, time=13.07 memory used=1249.3MB, alloc=83.8MB, time=13.15 memory used=1273.4MB, alloc=83.8MB, time=13.22 memory used=1300.0MB, alloc=83.8MB, time=13.29 memory used=1329.0MB, alloc=83.8MB, time=13.36 memory used=1361.2MB, alloc=83.8MB, time=13.43 memory used=1395.6MB, alloc=83.8MB, time=13.51 memory used=1422.0MB, alloc=83.8MB, time=13.58 memory used=1440.9MB, alloc=83.8MB, time=13.63 memory used=1461.0MB, alloc=83.8MB, time=13.69 memory used=1481.2MB, alloc=83.8MB, time=13.74 memory used=1502.5MB, alloc=83.8MB, time=13.80 memory used=1524.8MB, alloc=83.8MB, time=13.86 memory used=1548.2MB, alloc=83.8MB, time=13.91 memory used=1572.4MB, alloc=83.8MB, time=13.98 memory used=1597.4MB, alloc=83.8MB, time=14.04 memory used=1623.8MB, alloc=83.8MB, time=14.10 memory used=1651.6MB, alloc=83.8MB, time=14.17 memory used=1681.0MB, alloc=83.8MB, time=14.23 memory used=1710.7MB, alloc=83.8MB, time=14.29 memory used=1742.4MB, alloc=83.8MB, time=14.35 memory used=1776.2MB, alloc=83.8MB, time=14.42 memory used=1796.9MB, alloc=83.8MB, time=14.47 memory used=1839.8MB, alloc=83.8MB, time=14.86 memory used=1884.9MB, alloc=83.8MB, time=15.21 memory used=1912.6MB, alloc=83.8MB, time=15.29 memory used=1936.3MB, alloc=83.8MB, time=15.36 memory used=1966.1MB, alloc=83.8MB, time=15.43 memory used=2014.9MB, alloc=83.8MB, time=15.87 memory used=2059.5MB, alloc=83.8MB, time=16.48 memory used=2102.0MB, alloc=83.8MB, time=16.97 memory used=2138.2MB, alloc=83.8MB, time=17.14 memory used=2158.9MB, alloc=83.8MB, time=17.23 memory used=2189.1MB, alloc=83.8MB, time=17.40 memory used=2216.5MB, alloc=83.8MB, time=17.50 memory used=2238.4MB, alloc=83.8MB, time=17.77 memory used=2282.7MB, alloc=83.8MB, time=20.53 memory used=2302.8MB, alloc=83.8MB, time=20.61 memory used=2324.8MB, alloc=83.8MB, time=20.71 memory used=2348.7MB, alloc=83.8MB, time=20.80 memory used=2364.3MB, alloc=83.8MB, time=20.87 memory used=2381.5MB, alloc=83.8MB, time=20.94 memory used=2400.9MB, alloc=83.8MB, time=21.02 memory used=2422.0MB, alloc=83.8MB, time=21.09 memory used=2445.0MB, alloc=83.8MB, time=21.17 memory used=2466.9MB, alloc=83.8MB, time=21.25 memory used=2499.7MB, alloc=83.8MB, time=21.54 memory used=2531.4MB, alloc=83.8MB, time=21.76 memory used=2587.9MB, alloc=83.8MB, time=22.64 memory used=2639.3MB, alloc=83.8MB, time=23.68 memory used=2692.3MB, alloc=83.8MB, time=24.74 memory used=2740.7MB, alloc=107.8MB, time=25.36 memory used=2792.1MB, alloc=107.8MB, time=26.10 memory used=2856.0MB, alloc=107.8MB, time=26.81 memory used=2920.6MB, alloc=107.8MB, time=27.59 memory used=2980.8MB, alloc=107.8MB, time=28.45 memory used=3038.5MB, alloc=131.8MB, time=29.22 memory used=3094.6MB, alloc=131.8MB, time=29.42 memory used=3137.8MB, alloc=131.8MB, time=29.58 memory used=3184.1MB, alloc=131.8MB, time=29.73 memory used=3217.6MB, alloc=131.8MB, time=29.85 memory used=3256.1MB, alloc=131.8MB, time=29.98 memory used=3301.8MB, alloc=131.8MB, time=30.11 memory used=3353.1MB, alloc=131.8MB, time=36.57 memory used=3393.2MB, alloc=155.8MB, time=67.18 memory used=3430.8MB, alloc=155.8MB, time=108.72 memory used=3485.9MB, alloc=179.8MB, time=173.84 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428294510 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 4 2 2 F := [20 x y - 20 x z, y - 3 y z - 11, 9 z - 2 y] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 3 4 G := [-17 x z + 11 x y , -7 x z - x y z - 19, 9 x y - 7 z + 20 x] > Problem := [F,G]; 2 4 2 2 Problem := [[20 x y - 20 x z, y - 3 y z - 11, 9 z - 2 y], 2 2 3 2 3 4 [-17 x z + 11 x y , -7 x z - x y z - 19, 9 x y - 7 z + 20 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.6MB, alloc=32.3MB, time=0.49 memory used=47.6MB, alloc=32.3MB, time=0.79 memory used=66.5MB, alloc=56.3MB, time=1.08 memory used=108.3MB, alloc=60.3MB, time=1.70 memory used=147.4MB, alloc=60.3MB, time=2.25 memory used=185.9MB, alloc=84.3MB, time=2.84 memory used=229.6MB, alloc=84.3MB, time=3.52 memory used=293.8MB, alloc=116.3MB, time=4.43 memory used=360.3MB, alloc=372.3MB, time=5.39 memory used=447.5MB, alloc=396.3MB, time=6.69 memory used=560.9MB, alloc=420.3MB, time=8.38 memory used=672.9MB, alloc=444.3MB, time=10.06 memory used=778.4MB, alloc=444.3MB, time=11.61 memory used=881.7MB, alloc=468.3MB, time=13.19 memory used=970.2MB, alloc=468.3MB, time=14.54 memory used=1046.9MB, alloc=468.3MB, time=15.77 memory used=1128.7MB, alloc=468.3MB, time=17.18 memory used=1208.0MB, alloc=468.3MB, time=18.57 memory used=1279.9MB, alloc=468.3MB, time=19.84 memory used=1348.9MB, alloc=468.3MB, time=21.14 memory used=1420.1MB, alloc=468.3MB, time=22.53 memory used=1481.5MB, alloc=492.3MB, time=23.80 memory used=1551.3MB, alloc=492.3MB, time=25.06 memory used=1594.4MB, alloc=492.3MB, time=25.91 memory used=1637.5MB, alloc=492.3MB, time=26.90 memory used=1826.2MB, alloc=516.3MB, time=30.10 memory used=2007.4MB, alloc=540.3MB, time=33.28 memory used=2178.5MB, alloc=564.3MB, time=36.49 memory used=2332.3MB, alloc=588.3MB, time=39.15 memory used=2484.3MB, alloc=588.3MB, time=41.48 memory used=2657.4MB, alloc=612.3MB, time=44.02 memory used=2796.0MB, alloc=612.3MB, time=46.75 memory used=2909.5MB, alloc=612.3MB, time=49.20 memory used=3030.7MB, alloc=612.3MB, time=51.76 memory used=3152.4MB, alloc=636.3MB, time=54.27 memory used=3264.8MB, alloc=636.3MB, time=56.65 memory used=3398.0MB, alloc=636.3MB, time=58.70 memory used=3509.9MB, alloc=636.3MB, time=60.83 memory used=3853.4MB, alloc=660.3MB, time=66.56 memory used=4180.6MB, alloc=684.3MB, time=72.97 memory used=4517.6MB, alloc=708.3MB, time=79.59 memory used=4862.8MB, alloc=732.3MB, time=86.55 memory used=5173.7MB, alloc=756.3MB, time=92.22 memory used=5401.2MB, alloc=780.3MB, time=95.58 memory used=5730.5MB, alloc=804.3MB, time=100.02 memory used=6061.4MB, alloc=828.3MB, time=104.17 memory used=6295.0MB, alloc=852.3MB, time=106.75 memory used=6547.3MB, alloc=876.3MB, time=110.49 memory used=6765.4MB, alloc=900.3MB, time=112.17 memory used=7171.9MB, alloc=924.3MB, time=117.48 memory used=7458.2MB, alloc=924.3MB, time=122.83 memory used=7680.2MB, alloc=948.3MB, time=127.64 memory used=7887.1MB, alloc=948.3MB, time=131.77 memory used=8123.2MB, alloc=948.3MB, time=136.23 memory used=8463.7MB, alloc=948.3MB, time=141.25 memory used=8835.9MB, alloc=972.3MB, time=145.31 memory used=9170.0MB, alloc=972.3MB, time=148.86 memory used=9452.1MB, alloc=972.3MB, time=152.50 memory used=9754.8MB, alloc=972.3MB, time=154.70 memory used=10040.4MB, alloc=972.3MB, time=157.46 memory used=10297.8MB, alloc=972.3MB, time=162.62 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428294810 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 3 4 2 2 F := [-17 x z - 17 x z + 13, -5 x y + 19 y - 5 x, -3 y + 18 y z + 12 z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 3 2 2 2 3 2 G := [6 x y - 16 x - 2 y z, 15 x z + 6 z , 3 y z - 19 y z + 4 y z ] > Problem := [F,G]; Problem := [ 3 2 2 3 4 2 2 [-17 x z - 17 x z + 13, -5 x y + 19 y - 5 x, -3 y + 18 y z + 12 z ], 3 3 2 3 2 2 2 3 2 [6 x y - 16 x - 2 y z, 15 x z + 6 z , 3 y z - 19 y z + 4 y z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.2MB, alloc=32.3MB, time=0.48 memory used=46.5MB, alloc=32.3MB, time=0.79 memory used=65.9MB, alloc=56.3MB, time=1.10 memory used=106.6MB, alloc=60.3MB, time=1.70 memory used=145.8MB, alloc=60.3MB, time=2.30 memory used=182.5MB, alloc=84.3MB, time=2.87 memory used=223.4MB, alloc=84.3MB, time=3.52 memory used=285.4MB, alloc=92.3MB, time=4.50 memory used=347.6MB, alloc=116.3MB, time=5.44 memory used=412.4MB, alloc=116.3MB, time=6.29 memory used=475.3MB, alloc=372.3MB, time=7.14 memory used=558.7MB, alloc=372.3MB, time=8.43 memory used=641.4MB, alloc=396.3MB, time=9.72 memory used=750.3MB, alloc=420.3MB, time=11.34 memory used=884.3MB, alloc=420.3MB, time=12.88 memory used=985.6MB, alloc=420.3MB, time=13.77 memory used=1114.0MB, alloc=444.3MB, time=15.35 memory used=1254.5MB, alloc=444.3MB, time=17.56 memory used=1375.7MB, alloc=468.3MB, time=19.47 memory used=1489.2MB, alloc=468.3MB, time=21.31 memory used=1600.5MB, alloc=492.3MB, time=22.70 memory used=1737.6MB, alloc=492.3MB, time=24.10 memory used=1871.0MB, alloc=492.3MB, time=25.63 memory used=1970.8MB, alloc=492.3MB, time=27.02 memory used=2035.7MB, alloc=492.3MB, time=27.96 memory used=2124.3MB, alloc=492.3MB, time=29.15 memory used=2215.4MB, alloc=492.3MB, time=30.67 memory used=2302.0MB, alloc=516.3MB, time=31.97 memory used=2393.1MB, alloc=516.3MB, time=33.24 memory used=2475.9MB, alloc=516.3MB, time=34.35 memory used=2584.5MB, alloc=516.3MB, time=35.55 memory used=2669.2MB, alloc=516.3MB, time=36.92 memory used=2730.8MB, alloc=516.3MB, time=38.09 memory used=2816.2MB, alloc=516.3MB, time=39.70 memory used=2892.7MB, alloc=516.3MB, time=41.21 memory used=2955.6MB, alloc=516.3MB, time=42.40 memory used=3020.1MB, alloc=516.3MB, time=43.73 memory used=3087.5MB, alloc=516.3MB, time=45.04 memory used=3148.1MB, alloc=516.3MB, time=46.03 memory used=3211.3MB, alloc=516.3MB, time=47.12 memory used=3256.4MB, alloc=516.3MB, time=48.03 memory used=3307.0MB, alloc=516.3MB, time=48.97 memory used=3357.6MB, alloc=516.3MB, time=49.91 memory used=3423.5MB, alloc=540.3MB, time=50.92 memory used=3467.8MB, alloc=540.3MB, time=51.95 memory used=3688.1MB, alloc=564.3MB, time=55.62 memory used=3905.3MB, alloc=588.3MB, time=59.50 memory used=4107.9MB, alloc=612.3MB, time=63.10 memory used=4288.8MB, alloc=612.3MB, time=66.14 memory used=4480.0MB, alloc=636.3MB, time=68.84 memory used=4658.9MB, alloc=636.3MB, time=71.39 memory used=4858.4MB, alloc=636.3MB, time=73.65 memory used=5077.2MB, alloc=636.3MB, time=76.71 memory used=5266.0MB, alloc=636.3MB, time=78.16 memory used=5454.8MB, alloc=636.3MB, time=79.71 memory used=5618.9MB, alloc=636.3MB, time=80.66 memory used=5816.6MB, alloc=636.3MB, time=106.60 memory used=5954.8MB, alloc=636.3MB, time=107.39 memory used=6080.0MB, alloc=636.3MB, time=108.13 memory used=6207.8MB, alloc=636.3MB, time=108.82 memory used=6392.9MB, alloc=636.3MB, time=109.85 memory used=6553.6MB, alloc=636.3MB, time=110.82 memory used=6753.0MB, alloc=636.3MB, time=136.67 memory used=6890.2MB, alloc=636.3MB, time=137.47 memory used=7013.7MB, alloc=660.3MB, time=138.19 memory used=7161.6MB, alloc=660.3MB, time=138.93 memory used=7350.4MB, alloc=660.3MB, time=141.24 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428295110 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 2 2 3 2 F := [20 y - 7 y , 11 x - 20 x, 8 x y z + 5 z - 17 z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 3 3 G := [13 x z + 17 y z + 6 y z , -4 y z + 10 x + 15, 3 3 2 10 x y - 16 x z - 15 x y z] > Problem := [F,G]; 4 3 2 2 3 2 Problem := [[20 y - 7 y , 11 x - 20 x, 8 x y z + 5 z - 17 z ], [ 2 2 2 2 3 3 13 x z + 17 y z + 6 y z , -4 y z + 10 x + 15, 3 3 2 10 x y - 16 x z - 15 x y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.4MB, alloc=32.3MB, time=0.49 memory used=47.9MB, alloc=32.3MB, time=0.80 memory used=67.3MB, alloc=56.3MB, time=1.10 memory used=109.0MB, alloc=60.3MB, time=1.73 memory used=147.4MB, alloc=60.3MB, time=2.12 memory used=191.7MB, alloc=68.3MB, time=2.76 memory used=229.0MB, alloc=92.3MB, time=3.34 memory used=296.3MB, alloc=92.3MB, time=4.23 memory used=357.4MB, alloc=116.3MB, time=5.17 memory used=423.3MB, alloc=116.3MB, time=6.11 memory used=488.9MB, alloc=372.3MB, time=6.99 memory used=576.1MB, alloc=396.3MB, time=8.26 memory used=667.8MB, alloc=396.3MB, time=9.12 memory used=774.2MB, alloc=420.3MB, time=10.24 memory used=899.1MB, alloc=420.3MB, time=12.05 memory used=1036.0MB, alloc=420.3MB, time=13.58 memory used=1156.8MB, alloc=444.3MB, time=15.27 memory used=1277.1MB, alloc=444.3MB, time=17.09 memory used=1380.6MB, alloc=468.3MB, time=18.72 memory used=1486.5MB, alloc=468.3MB, time=20.47 memory used=1593.1MB, alloc=468.3MB, time=22.28 memory used=1678.9MB, alloc=492.3MB, time=23.71 memory used=1784.0MB, alloc=492.3MB, time=25.04 memory used=1864.1MB, alloc=492.3MB, time=26.24 memory used=1956.0MB, alloc=492.3MB, time=27.54 memory used=2066.5MB, alloc=492.3MB, time=28.83 memory used=2135.2MB, alloc=492.3MB, time=29.99 memory used=2205.4MB, alloc=492.3MB, time=31.22 memory used=2272.0MB, alloc=492.3MB, time=32.30 memory used=2327.8MB, alloc=492.3MB, time=33.35 memory used=2431.3MB, alloc=516.3MB, time=34.14 memory used=2529.6MB, alloc=516.3MB, time=35.01 memory used=2647.0MB, alloc=516.3MB, time=36.03 memory used=2714.9MB, alloc=516.3MB, time=37.21 memory used=2798.6MB, alloc=516.3MB, time=38.43 memory used=2862.9MB, alloc=516.3MB, time=39.59 memory used=2966.2MB, alloc=516.3MB, time=40.22 memory used=3092.8MB, alloc=516.3MB, time=41.62 memory used=3138.5MB, alloc=516.3MB, time=42.41 memory used=3188.8MB, alloc=516.3MB, time=43.48 memory used=3257.0MB, alloc=516.3MB, time=44.41 memory used=3378.2MB, alloc=516.3MB, time=45.25 memory used=3420.3MB, alloc=516.3MB, time=46.20 memory used=3580.6MB, alloc=516.3MB, time=47.70 memory used=3799.1MB, alloc=540.3MB, time=50.59 memory used=4009.8MB, alloc=540.3MB, time=52.93 memory used=4227.9MB, alloc=564.3MB, time=55.96 memory used=4441.5MB, alloc=564.3MB, time=58.70 memory used=4620.8MB, alloc=588.3MB, time=61.56 memory used=4797.0MB, alloc=588.3MB, time=63.94 memory used=5059.0MB, alloc=612.3MB, time=66.46 memory used=5319.6MB, alloc=612.3MB, time=68.32 memory used=5557.7MB, alloc=612.3MB, time=69.35 memory used=5836.7MB, alloc=612.3MB, time=71.28 memory used=6063.8MB, alloc=612.3MB, time=72.53 memory used=6312.5MB, alloc=612.3MB, time=74.04 memory used=6572.5MB, alloc=612.3MB, time=75.18 memory used=6864.2MB, alloc=612.3MB, time=76.32 memory used=7197.6MB, alloc=612.3MB, time=78.48 memory used=7462.9MB, alloc=612.3MB, time=80.57 memory used=7744.0MB, alloc=612.3MB, time=83.47 memory used=8036.8MB, alloc=636.3MB, time=86.61 memory used=8236.7MB, alloc=636.3MB, time=89.92 memory used=8430.1MB, alloc=660.3MB, time=94.05 memory used=8710.0MB, alloc=684.3MB, time=98.23 memory used=9009.0MB, alloc=708.3MB, time=102.47 memory used=9426.2MB, alloc=708.3MB, time=108.85 memory used=9710.5MB, alloc=732.3MB, time=113.20 memory used=9938.3MB, alloc=756.3MB, time=117.43 memory used=10234.7MB, alloc=756.3MB, time=122.45 memory used=10502.0MB, alloc=780.3MB, time=128.05 memory used=10698.2MB, alloc=804.3MB, time=132.41 memory used=10956.7MB, alloc=828.3MB, time=137.55 memory used=11262.0MB, alloc=852.3MB, time=143.36 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428295410 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 2 F := [12 x y + 18 x y z - 20 z, -x - 20 y , -18 x y z - 15 x] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 3 G := [18 x y z - 8 x y + 10 z , -12 x z - 10 y z, 13 x - 18 x y z - 7] > Problem := [F,G]; 2 2 2 2 2 2 Problem := [[12 x y + 18 x y z - 20 z, -x - 20 y , -18 x y z - 15 x], 2 2 2 2 2 3 [18 x y z - 8 x y + 10 z , -12 x z - 10 y z, 13 x - 18 x y z - 7]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.16 memory used=26.2MB, alloc=32.3MB, time=0.49 memory used=47.3MB, alloc=32.3MB, time=0.79 memory used=65.7MB, alloc=56.3MB, time=1.09 memory used=105.9MB, alloc=60.3MB, time=1.69 memory used=144.7MB, alloc=60.3MB, time=2.26 memory used=183.3MB, alloc=84.3MB, time=2.85 memory used=227.5MB, alloc=84.3MB, time=3.54 memory used=286.4MB, alloc=92.3MB, time=4.47 memory used=345.2MB, alloc=116.3MB, time=5.39 memory used=424.7MB, alloc=116.3MB, time=6.69 memory used=494.5MB, alloc=396.3MB, time=7.82 memory used=603.0MB, alloc=420.3MB, time=9.46 memory used=737.1MB, alloc=444.3MB, time=11.56 memory used=874.6MB, alloc=468.3MB, time=13.83 memory used=996.2MB, alloc=468.3MB, time=15.66 memory used=1111.7MB, alloc=468.3MB, time=17.45 memory used=1236.9MB, alloc=492.3MB, time=19.82 memory used=1350.8MB, alloc=492.3MB, time=21.81 memory used=1445.0MB, alloc=492.3MB, time=23.39 memory used=1519.4MB, alloc=492.3MB, time=24.93 memory used=1614.1MB, alloc=492.3MB, time=26.68 memory used=1712.0MB, alloc=516.3MB, time=28.72 memory used=1791.1MB, alloc=516.3MB, time=30.19 memory used=1864.6MB, alloc=516.3MB, time=31.73 memory used=1928.2MB, alloc=516.3MB, time=32.85 memory used=2004.8MB, alloc=516.3MB, time=34.63 memory used=2062.8MB, alloc=516.3MB, time=35.70 memory used=2135.0MB, alloc=516.3MB, time=37.60 memory used=2181.3MB, alloc=516.3MB, time=38.84 memory used=2201.8MB, alloc=516.3MB, time=39.56 memory used=2256.2MB, alloc=516.3MB, time=41.04 memory used=2285.6MB, alloc=516.3MB, time=41.91 memory used=2493.8MB, alloc=540.3MB, time=46.12 memory used=2686.4MB, alloc=564.3MB, time=49.39 memory used=2890.6MB, alloc=588.3MB, time=53.65 memory used=3082.3MB, alloc=612.3MB, time=58.10 memory used=3244.3MB, alloc=636.3MB, time=61.73 memory used=3410.6MB, alloc=636.3MB, time=65.52 memory used=3549.5MB, alloc=660.3MB, time=68.59 memory used=3692.8MB, alloc=660.3MB, time=72.12 memory used=3836.6MB, alloc=660.3MB, time=75.66 memory used=3956.8MB, alloc=660.3MB, time=78.43 memory used=4070.9MB, alloc=660.3MB, time=81.07 memory used=4190.3MB, alloc=660.3MB, time=84.07 memory used=4276.7MB, alloc=660.3MB, time=86.17 memory used=4376.8MB, alloc=660.3MB, time=88.92 memory used=4475.5MB, alloc=684.3MB, time=92.04 memory used=4829.9MB, alloc=708.3MB, time=99.05 memory used=5201.5MB, alloc=732.3MB, time=106.55 memory used=5562.1MB, alloc=756.3MB, time=113.10 memory used=5951.2MB, alloc=780.3MB, time=120.12 memory used=6349.1MB, alloc=804.3MB, time=129.83 memory used=6684.9MB, alloc=828.3MB, time=136.62 memory used=7012.3MB, alloc=852.3MB, time=144.60 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428295710 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 3 2 F := [19 x z - 20 x y - 9 x y z, -10 x y + 2 x y - 2 x , 3 3 2 -8 x z - 14 x + 2 y z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [13 x y z - 19 x y - 6 x z, 10 x y z - 6 y z + 12 x, 2 2 4 2 20 y z + 5 z + 8 x y] > Problem := [F,G]; 2 2 2 3 3 2 Problem := [[19 x z - 20 x y - 9 x y z, -10 x y + 2 x y - 2 x , 3 3 2 2 2 -8 x z - 14 x + 2 y z], [13 x y z - 19 x y - 6 x z, 2 2 2 2 4 2 10 x y z - 6 y z + 12 x, 20 y z + 5 z + 8 x y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=25.4MB, alloc=32.3MB, time=0.50 memory used=44.5MB, alloc=56.3MB, time=0.79 memory used=83.5MB, alloc=60.3MB, time=1.34 memory used=126.8MB, alloc=68.3MB, time=1.96 memory used=168.6MB, alloc=92.3MB, time=2.59 memory used=234.3MB, alloc=92.3MB, time=3.52 memory used=299.9MB, alloc=116.3MB, time=4.49 memory used=362.0MB, alloc=116.3MB, time=5.43 memory used=415.8MB, alloc=372.3MB, time=6.26 memory used=503.2MB, alloc=396.3MB, time=7.60 memory used=613.3MB, alloc=420.3MB, time=9.29 memory used=715.1MB, alloc=420.3MB, time=10.74 memory used=819.2MB, alloc=420.3MB, time=12.29 memory used=928.7MB, alloc=444.3MB, time=14.02 memory used=1030.8MB, alloc=444.3MB, time=15.65 memory used=1125.5MB, alloc=468.3MB, time=17.08 memory used=1211.1MB, alloc=468.3MB, time=18.35 memory used=1299.8MB, alloc=468.3MB, time=19.81 memory used=1378.4MB, alloc=468.3MB, time=21.21 memory used=1446.0MB, alloc=468.3MB, time=22.54 memory used=1517.9MB, alloc=468.3MB, time=23.88 memory used=1604.4MB, alloc=468.3MB, time=25.14 memory used=1670.8MB, alloc=468.3MB, time=26.27 memory used=1736.9MB, alloc=468.3MB, time=27.44 memory used=1793.1MB, alloc=468.3MB, time=28.60 memory used=1853.1MB, alloc=468.3MB, time=29.82 memory used=1897.1MB, alloc=468.3MB, time=30.75 memory used=1943.0MB, alloc=468.3MB, time=31.83 memory used=2106.0MB, alloc=492.3MB, time=34.62 memory used=2286.4MB, alloc=516.3MB, time=37.64 memory used=2481.9MB, alloc=540.3MB, time=40.51 memory used=2663.1MB, alloc=564.3MB, time=43.84 memory used=2814.0MB, alloc=588.3MB, time=46.73 memory used=3028.0MB, alloc=588.3MB, time=49.91 memory used=3168.6MB, alloc=612.3MB, time=52.07 memory used=3295.8MB, alloc=612.3MB, time=54.46 memory used=3444.7MB, alloc=612.3MB, time=57.41 memory used=3558.1MB, alloc=612.3MB, time=59.86 memory used=3692.1MB, alloc=636.3MB, time=62.15 memory used=3785.8MB, alloc=636.3MB, time=64.11 memory used=4005.1MB, alloc=636.3MB, time=66.74 memory used=4157.7MB, alloc=636.3MB, time=68.65 memory used=4237.2MB, alloc=636.3MB, time=70.80 memory used=4558.4MB, alloc=660.3MB, time=76.00 memory used=4890.1MB, alloc=684.3MB, time=82.33 memory used=5154.2MB, alloc=708.3MB, time=85.96 memory used=5520.5MB, alloc=732.3MB, time=91.85 memory used=5871.5MB, alloc=756.3MB, time=98.15 memory used=6198.8MB, alloc=780.3MB, time=103.69 memory used=6556.5MB, alloc=804.3MB, time=110.19 memory used=6894.8MB, alloc=828.3MB, time=116.03 memory used=7188.0MB, alloc=852.3MB, time=121.62 memory used=7463.7MB, alloc=876.3MB, time=126.48 memory used=7746.2MB, alloc=900.3MB, time=131.60 memory used=7950.0MB, alloc=924.3MB, time=136.28 memory used=8138.6MB, alloc=948.3MB, time=140.58 memory used=8373.8MB, alloc=972.3MB, time=146.02 memory used=8540.4MB, alloc=996.3MB, time=150.52 memory used=9154.4MB, alloc=1020.3MB, time=161.78 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428296010 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; F := [ 3 3 2 2 2 2 2 3 2 -11 x y + 3 x + 13 z , -10 x z - 9 y z - 6 y, -4 x + 17 x z - 15 z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 3 3 4 3 3 G := [-8 x y - 19 x z + 13 x, y + 6 z + 15 x, 20 x - 9 y z - 18 x ] > Problem := [F,G]; Problem := [[ 3 3 2 2 2 2 2 3 2 -11 x y + 3 x + 13 z , -10 x z - 9 y z - 6 y, -4 x + 17 x z - 15 z ] 3 2 2 3 3 4 3 3 , [-8 x y - 19 x z + 13 x, y + 6 z + 15 x, 20 x - 9 y z - 18 x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.0MB, alloc=32.3MB, time=0.49 memory used=46.5MB, alloc=32.3MB, time=0.78 memory used=65.9MB, alloc=56.3MB, time=1.21 memory used=108.2MB, alloc=60.3MB, time=1.65 memory used=150.6MB, alloc=60.3MB, time=2.17 memory used=194.1MB, alloc=68.3MB, time=2.80 memory used=237.9MB, alloc=68.3MB, time=3.41 memory used=272.7MB, alloc=92.3MB, time=3.86 memory used=324.6MB, alloc=92.3MB, time=4.20 memory used=398.1MB, alloc=92.3MB, time=4.84 memory used=482.9MB, alloc=92.3MB, time=5.57 memory used=532.9MB, alloc=92.3MB, time=6.04 memory used=595.2MB, alloc=92.3MB, time=6.66 memory used=664.1MB, alloc=116.3MB, time=7.54 memory used=745.0MB, alloc=116.3MB, time=8.25 memory used=827.3MB, alloc=116.3MB, time=9.01 memory used=890.1MB, alloc=372.3MB, time=9.86 memory used=974.9MB, alloc=396.3MB, time=11.03 memory used=1084.3MB, alloc=396.3MB, time=12.26 memory used=1205.7MB, alloc=396.3MB, time=14.00 memory used=1311.4MB, alloc=420.3MB, time=15.57 memory used=1416.0MB, alloc=420.3MB, time=16.33 memory used=1494.7MB, alloc=420.3MB, time=16.95 memory used=1580.9MB, alloc=420.3MB, time=17.58 memory used=1733.9MB, alloc=444.3MB, time=19.81 memory used=1859.5MB, alloc=444.3MB, time=21.23 memory used=1989.0MB, alloc=444.3MB, time=23.01 memory used=2123.5MB, alloc=444.3MB, time=24.25 memory used=2263.8MB, alloc=468.3MB, time=25.73 memory used=2361.6MB, alloc=468.3MB, time=27.16 memory used=2463.3MB, alloc=468.3MB, time=28.62 memory used=2578.7MB, alloc=468.3MB, time=30.37 memory used=2683.5MB, alloc=492.3MB, time=32.04 memory used=2776.9MB, alloc=492.3MB, time=33.34 memory used=2869.1MB, alloc=492.3MB, time=34.67 memory used=3000.1MB, alloc=492.3MB, time=36.62 memory used=3103.7MB, alloc=492.3MB, time=37.94 memory used=3207.6MB, alloc=516.3MB, time=39.15 memory used=3299.7MB, alloc=516.3MB, time=40.25 memory used=3401.5MB, alloc=516.3MB, time=41.38 memory used=3535.6MB, alloc=540.3MB, time=42.54 memory used=3608.2MB, alloc=540.3MB, time=43.47 memory used=3693.0MB, alloc=540.3MB, time=44.41 memory used=3804.3MB, alloc=540.3MB, time=45.40 memory used=3909.7MB, alloc=540.3MB, time=47.10 memory used=3981.0MB, alloc=540.3MB, time=48.33 memory used=4037.6MB, alloc=540.3MB, time=49.26 memory used=4079.4MB, alloc=564.3MB, time=50.07 memory used=4136.5MB, alloc=564.3MB, time=51.08 memory used=4370.6MB, alloc=588.3MB, time=53.60 memory used=4568.6MB, alloc=612.3MB, time=56.51 memory used=4827.5MB, alloc=612.3MB, time=59.16 memory used=5027.3MB, alloc=636.3MB, time=61.67 memory used=5215.3MB, alloc=660.3MB, time=63.70 memory used=5381.3MB, alloc=684.3MB, time=66.49 memory used=5511.3MB, alloc=684.3MB, time=68.98 memory used=5644.9MB, alloc=684.3MB, time=71.12 memory used=5852.6MB, alloc=708.3MB, time=73.92 memory used=5971.0MB, alloc=708.3MB, time=75.96 memory used=6214.6MB, alloc=708.3MB, time=77.86 memory used=6396.9MB, alloc=708.3MB, time=79.22 memory used=6575.7MB, alloc=708.3MB, time=80.30 memory used=6709.0MB, alloc=732.3MB, time=81.29 memory used=6865.9MB, alloc=732.3MB, time=82.25 memory used=7054.2MB, alloc=732.3MB, time=83.23 memory used=7268.9MB, alloc=732.3MB, time=84.62 memory used=7457.6MB, alloc=732.3MB, time=85.75 memory used=7610.9MB, alloc=732.3MB, time=86.74 memory used=7768.9MB, alloc=732.3MB, time=87.70 memory used=7958.2MB, alloc=732.3MB, time=88.67 memory used=8217.8MB, alloc=732.3MB, time=129.07 memory used=8395.6MB, alloc=732.3MB, time=130.19 memory used=8549.3MB, alloc=732.3MB, time=131.21 memory used=8741.5MB, alloc=732.3MB, time=132.28 memory used=9026.3MB, alloc=732.3MB, time=133.65 memory used=9155.0MB, alloc=732.3MB, time=134.63 memory used=9291.6MB, alloc=732.3MB, time=135.62 memory used=9439.2MB, alloc=732.3MB, time=136.60 memory used=9597.9MB, alloc=732.3MB, time=137.59 memory used=9767.5MB, alloc=732.3MB, time=138.59 memory used=9947.9MB, alloc=732.3MB, time=139.58 memory used=10144.3MB, alloc=732.3MB, time=140.60 memory used=10351.0MB, alloc=732.3MB, time=141.65 memory used=10568.9MB, alloc=732.3MB, time=142.68 memory used=10728.6MB, alloc=732.3MB, time=143.64 memory used=10889.3MB, alloc=732.3MB, time=144.61 memory used=11057.6MB, alloc=732.3MB, time=145.60 memory used=11231.3MB, alloc=732.3MB, time=146.58 memory used=11411.7MB, alloc=732.3MB, time=147.56 memory used=11600.3MB, alloc=732.3MB, time=148.60 memory used=11798.1MB, alloc=732.3MB, time=149.62 memory used=12007.9MB, alloc=732.3MB, time=150.68 memory used=12225.5MB, alloc=732.3MB, time=151.71 memory used=12423.0MB, alloc=732.3MB, time=152.73 memory used=12601.4MB, alloc=732.3MB, time=153.72 memory used=12788.4MB, alloc=732.3MB, time=154.71 memory used=12985.7MB, alloc=732.3MB, time=155.70 memory used=13293.7MB, alloc=732.3MB, time=157.38 memory used=13491.2MB, alloc=732.3MB, time=158.53 memory used=13630.3MB, alloc=732.3MB, time=159.50 memory used=13796.7MB, alloc=732.3MB, time=160.50 memory used=14010.9MB, alloc=732.3MB, time=162.60 memory used=14229.3MB, alloc=732.3MB, time=164.53 memory used=14411.8MB, alloc=732.3MB, time=165.56 memory used=14617.6MB, alloc=732.3MB, time=166.65 memory used=14765.2MB, alloc=732.3MB, time=167.64 memory used=14940.8MB, alloc=732.3MB, time=168.70 memory used=15147.8MB, alloc=732.3MB, time=169.70 memory used=15401.9MB, alloc=732.3MB, time=171.24 memory used=15663.2MB, alloc=732.3MB, time=172.33 memory used=15947.5MB, alloc=732.3MB, time=174.26 memory used=16192.5MB, alloc=732.3MB, time=176.88 memory used=16290.3MB, alloc=732.3MB, time=178.70 memory used=16384.5MB, alloc=732.3MB, time=180.41 memory used=16482.2MB, alloc=732.3MB, time=182.67 memory used=16576.7MB, alloc=732.3MB, time=184.70 memory used=16970.2MB, alloc=756.3MB, time=190.17 memory used=17368.5MB, alloc=780.3MB, time=196.64 memory used=17596.5MB, alloc=804.3MB, time=199.16 memory used=17805.8MB, alloc=828.3MB, time=201.09 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428296310 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 4 2 3 F := [-7 y z + 20 x z + 14 z, -9 y + 7 x y + 13 x, -2 x z - 3 z + 15 y] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 3 4 2 2 2 4 3 G := [11 y + 12 y z + y , 6 y + 18 y z + 5 y z, -19 x - 17 x z - 17] > Problem := [F,G]; Problem := [ 2 4 2 3 [-7 y z + 20 x z + 14 z, -9 y + 7 x y + 13 x, -2 x z - 3 z + 15 y], 4 3 3 4 2 2 2 4 3 [11 y + 12 y z + y , 6 y + 18 y z + 5 y z, -19 x - 17 x z - 17]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=31.8MB, alloc=40.3MB, time=0.56 memory used=59.3MB, alloc=44.3MB, time=0.98 memory used=85.5MB, alloc=68.3MB, time=1.38 memory used=132.3MB, alloc=68.3MB, time=2.07 memory used=175.6MB, alloc=92.3MB, time=2.75 memory used=243.5MB, alloc=100.3MB, time=3.83 memory used=310.0MB, alloc=124.3MB, time=4.87 memory used=401.6MB, alloc=124.3MB, time=6.34 memory used=492.0MB, alloc=404.3MB, time=7.84 memory used=603.8MB, alloc=428.3MB, time=9.80 memory used=740.8MB, alloc=428.3MB, time=11.92 memory used=880.9MB, alloc=452.3MB, time=14.20 memory used=1038.3MB, alloc=476.3MB, time=17.15 memory used=1188.9MB, alloc=476.3MB, time=19.83 memory used=1343.9MB, alloc=500.3MB, time=22.50 memory used=1482.6MB, alloc=500.3MB, time=24.80 memory used=1640.2MB, alloc=524.3MB, time=28.00 memory used=1754.5MB, alloc=524.3MB, time=30.01 memory used=1896.0MB, alloc=548.3MB, time=32.67 memory used=2021.2MB, alloc=548.3MB, time=34.65 memory used=2132.4MB, alloc=548.3MB, time=36.60 memory used=2251.5MB, alloc=548.3MB, time=38.93 memory used=2355.9MB, alloc=572.3MB, time=40.75 memory used=2476.1MB, alloc=572.3MB, time=43.24 memory used=2573.2MB, alloc=572.3MB, time=45.18 memory used=2666.3MB, alloc=572.3MB, time=47.12 memory used=2742.3MB, alloc=572.3MB, time=48.27 memory used=2841.5MB, alloc=572.3MB, time=50.45 memory used=2939.5MB, alloc=596.3MB, time=52.75 memory used=3032.5MB, alloc=596.3MB, time=54.91 memory used=3107.2MB, alloc=596.3MB, time=56.67 memory used=3186.8MB, alloc=596.3MB, time=58.35 memory used=3278.7MB, alloc=596.3MB, time=60.58 memory used=3375.9MB, alloc=596.3MB, time=63.16 memory used=3451.0MB, alloc=596.3MB, time=64.73 memory used=3513.0MB, alloc=596.3MB, time=66.09 memory used=3596.1MB, alloc=596.3MB, time=68.40 memory used=3657.8MB, alloc=596.3MB, time=69.83 memory used=3717.1MB, alloc=596.3MB, time=71.18 memory used=3792.1MB, alloc=596.3MB, time=73.16 memory used=3839.9MB, alloc=596.3MB, time=74.22 memory used=3881.5MB, alloc=596.3MB, time=75.27 memory used=4110.9MB, alloc=620.3MB, time=79.33 memory used=4337.5MB, alloc=644.3MB, time=82.73 memory used=4562.0MB, alloc=644.3MB, time=85.62 memory used=4732.9MB, alloc=644.3MB, time=86.72 memory used=4888.0MB, alloc=644.3MB, time=89.41 memory used=5096.1MB, alloc=644.3MB, time=90.65 memory used=5431.8MB, alloc=668.3MB, time=94.05 memory used=5634.4MB, alloc=668.3MB, time=98.43 memory used=5904.7MB, alloc=692.3MB, time=105.20 memory used=6103.1MB, alloc=716.3MB, time=110.35 memory used=6304.9MB, alloc=740.3MB, time=114.70 memory used=6515.9MB, alloc=740.3MB, time=117.95 memory used=6697.1MB, alloc=740.3MB, time=122.22 memory used=6906.1MB, alloc=764.3MB, time=126.81 memory used=7085.2MB, alloc=764.3MB, time=131.13 memory used=7249.1MB, alloc=764.3MB, time=134.97 memory used=7426.4MB, alloc=764.3MB, time=139.11 memory used=7559.7MB, alloc=764.3MB, time=142.81 memory used=7693.2MB, alloc=764.3MB, time=146.18 memory used=7798.2MB, alloc=788.3MB, time=148.53 memory used=7966.1MB, alloc=788.3MB, time=152.28 memory used=8190.3MB, alloc=788.3MB, time=153.94 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428296610 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; F := [ 3 2 3 2 3 3 2 3 x - 8 x y + 5 x y, -8 x y - 2 y z - 16 x z, 15 x z + 12 x - 17 x z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 4 2 4 2 G := [13 y + 11 y z - 6 y, 2 y - 10 x z - 14 x y, 10 y + 17 x z + 16 y z] > Problem := [F,G]; Problem := [[ 3 2 3 2 3 3 2 3 x - 8 x y + 5 x y, -8 x y - 2 y z - 16 x z, 15 x z + 12 x - 17 x z ], 4 2 4 2 4 2 [13 y + 11 y z - 6 y, 2 y - 10 x z - 14 x y, 10 y + 17 x z + 16 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=25.8MB, alloc=32.3MB, time=0.48 memory used=46.4MB, alloc=32.3MB, time=0.77 memory used=66.2MB, alloc=56.3MB, time=1.02 memory used=113.3MB, alloc=69.4MB, time=1.60 memory used=146.6MB, alloc=69.4MB, time=2.05 memory used=173.0MB, alloc=69.4MB, time=2.16 memory used=216.9MB, alloc=69.4MB, time=3.12 memory used=239.7MB, alloc=69.4MB, time=3.19 memory used=286.2MB, alloc=69.4MB, time=3.68 memory used=328.9MB, alloc=69.4MB, time=4.04 memory used=375.9MB, alloc=69.4MB, time=4.60 memory used=420.0MB, alloc=93.4MB, time=5.16 memory used=470.9MB, alloc=93.4MB, time=5.46 memory used=512.9MB, alloc=93.4MB, time=5.64 memory used=554.5MB, alloc=93.4MB, time=5.83 memory used=593.0MB, alloc=93.4MB, time=5.97 memory used=634.3MB, alloc=93.4MB, time=6.49 memory used=684.7MB, alloc=93.4MB, time=6.77 memory used=752.6MB, alloc=93.4MB, time=7.75 memory used=784.9MB, alloc=93.4MB, time=7.85 memory used=819.2MB, alloc=93.4MB, time=7.95 memory used=849.2MB, alloc=93.4MB, time=8.03 memory used=926.7MB, alloc=93.4MB, time=8.53 memory used=1005.3MB, alloc=93.4MB, time=8.98 memory used=1085.7MB, alloc=93.4MB, time=9.58 memory used=1158.6MB, alloc=93.4MB, time=10.52 memory used=1231.8MB, alloc=93.4MB, time=11.38 memory used=1295.2MB, alloc=117.4MB, time=11.90 memory used=1363.8MB, alloc=117.4MB, time=12.52 memory used=1412.8MB, alloc=117.4MB, time=12.67 memory used=1448.6MB, alloc=117.4MB, time=12.79 memory used=1493.3MB, alloc=117.4MB, time=12.89 memory used=1583.3MB, alloc=373.4MB, time=13.73 memory used=1641.1MB, alloc=373.4MB, time=14.08 memory used=1708.4MB, alloc=373.4MB, time=20.05 memory used=1777.7MB, alloc=373.4MB, time=20.43 memory used=1819.5MB, alloc=373.4MB, time=20.58 memory used=1858.4MB, alloc=373.4MB, time=20.71 memory used=1906.1MB, alloc=373.4MB, time=20.86 memory used=1950.7MB, alloc=373.4MB, time=20.99 memory used=1980.6MB, alloc=373.4MB, time=21.11 memory used=2013.9MB, alloc=373.4MB, time=21.21 memory used=2049.6MB, alloc=373.4MB, time=21.33 memory used=2087.6MB, alloc=373.4MB, time=21.45 memory used=2129.1MB, alloc=373.4MB, time=21.55 memory used=2173.9MB, alloc=373.4MB, time=21.68 memory used=2221.7MB, alloc=373.4MB, time=21.80 memory used=2273.8MB, alloc=373.4MB, time=21.92 memory used=2443.6MB, alloc=373.4MB, time=22.37 memory used=2580.5MB, alloc=373.4MB, time=25.82 memory used=2640.3MB, alloc=373.4MB, time=40.18 memory used=2702.6MB, alloc=373.4MB, time=40.49 memory used=2745.3MB, alloc=373.4MB, time=40.67 memory used=2779.7MB, alloc=373.4MB, time=40.81 memory used=2820.0MB, alloc=373.4MB, time=40.96 memory used=2866.5MB, alloc=373.4MB, time=41.10 memory used=2914.2MB, alloc=373.4MB, time=41.26 memory used=2942.8MB, alloc=373.4MB, time=41.38 memory used=2972.7MB, alloc=373.4MB, time=41.51 memory used=3004.3MB, alloc=373.4MB, time=41.64 memory used=3036.9MB, alloc=373.4MB, time=41.76 memory used=3072.2MB, alloc=373.4MB, time=41.89 memory used=3108.3MB, alloc=373.4MB, time=42.00 memory used=3147.2MB, alloc=373.4MB, time=42.12 memory used=3186.8MB, alloc=373.4MB, time=42.25 memory used=3229.0MB, alloc=373.4MB, time=42.37 memory used=3273.9MB, alloc=373.4MB, time=42.51 memory used=3321.3MB, alloc=373.4MB, time=42.63 memory used=3371.0MB, alloc=373.4MB, time=42.76 memory used=3425.9MB, alloc=373.4MB, time=42.90 memory used=3568.5MB, alloc=373.4MB, time=43.18 memory used=3719.0MB, alloc=373.4MB, time=43.47 memory used=3892.3MB, alloc=373.4MB, time=43.76 memory used=4145.8MB, alloc=373.4MB, time=45.04 memory used=4221.4MB, alloc=373.4MB, time=45.95 memory used=4299.1MB, alloc=397.4MB, time=46.89 memory used=4415.1MB, alloc=421.4MB, time=48.23 memory used=4528.6MB, alloc=421.4MB, time=49.52 memory used=4602.4MB, alloc=421.4MB, time=50.01 memory used=4659.3MB, alloc=421.4MB, time=50.25 memory used=4735.2MB, alloc=421.4MB, time=52.46 memory used=4833.2MB, alloc=421.4MB, time=53.38 memory used=4961.3MB, alloc=445.4MB, time=54.87 memory used=5080.1MB, alloc=445.4MB, time=56.14 memory used=5171.5MB, alloc=445.4MB, time=57.53 memory used=5271.5MB, alloc=469.4MB, time=58.78 memory used=5380.0MB, alloc=469.4MB, time=60.45 memory used=5495.9MB, alloc=469.4MB, time=61.62 memory used=5618.9MB, alloc=469.4MB, time=62.90 memory used=5703.3MB, alloc=469.4MB, time=64.14 memory used=5831.6MB, alloc=469.4MB, time=69.56 memory used=5933.6MB, alloc=469.4MB, time=70.87 memory used=5997.5MB, alloc=469.4MB, time=71.98 memory used=6118.4MB, alloc=493.4MB, time=73.03 memory used=6227.3MB, alloc=493.4MB, time=74.23 memory used=6335.2MB, alloc=493.4MB, time=74.95 memory used=6422.3MB, alloc=493.4MB, time=75.36 memory used=6519.7MB, alloc=493.4MB, time=75.76 memory used=6592.5MB, alloc=493.4MB, time=76.08 memory used=6708.7MB, alloc=493.4MB, time=80.37 memory used=6788.6MB, alloc=493.4MB, time=80.69 memory used=6904.6MB, alloc=493.4MB, time=81.47 memory used=7022.0MB, alloc=493.4MB, time=82.21 memory used=7126.3MB, alloc=493.4MB, time=82.90 memory used=7239.0MB, alloc=493.4MB, time=83.47 memory used=7316.2MB, alloc=493.4MB, time=83.86 memory used=7420.6MB, alloc=493.4MB, time=84.35 memory used=7536.4MB, alloc=493.4MB, time=85.04 memory used=7611.6MB, alloc=493.4MB, time=85.42 memory used=7713.6MB, alloc=493.4MB, time=85.86 memory used=7846.8MB, alloc=493.4MB, time=99.71 memory used=7929.8MB, alloc=493.4MB, time=100.07 memory used=8018.9MB, alloc=493.4MB, time=100.44 memory used=8089.3MB, alloc=493.4MB, time=100.78 memory used=8171.9MB, alloc=493.4MB, time=101.09 memory used=8266.6MB, alloc=493.4MB, time=101.43 memory used=8375.6MB, alloc=493.4MB, time=101.77 memory used=8527.8MB, alloc=493.4MB, time=102.22 memory used=8691.3MB, alloc=493.4MB, time=102.64 memory used=8889.8MB, alloc=493.4MB, time=103.42 memory used=8999.0MB, alloc=493.4MB, time=104.91 memory used=9103.6MB, alloc=493.4MB, time=105.34 memory used=9173.0MB, alloc=517.4MB, time=105.76 memory used=9260.3MB, alloc=517.4MB, time=106.16 memory used=9361.1MB, alloc=517.4MB, time=106.57 memory used=9478.3MB, alloc=517.4MB, time=107.01 memory used=9605.2MB, alloc=517.4MB, time=107.43 memory used=9677.2MB, alloc=517.4MB, time=107.77 memory used=9749.7MB, alloc=517.4MB, time=108.11 memory used=9828.5MB, alloc=517.4MB, time=108.45 memory used=9912.7MB, alloc=517.4MB, time=108.79 memory used=10001.5MB, alloc=517.4MB, time=109.16 memory used=10098.6MB, alloc=517.4MB, time=109.51 memory used=10199.2MB, alloc=517.4MB, time=109.88 memory used=10308.1MB, alloc=517.4MB, time=110.26 memory used=10425.6MB, alloc=517.4MB, time=110.61 memory used=10555.3MB, alloc=517.4MB, time=110.97 memory used=10764.8MB, alloc=517.4MB, time=111.87 memory used=10867.6MB, alloc=517.4MB, time=112.29 memory used=10980.3MB, alloc=517.4MB, time=112.71 memory used=11171.9MB, alloc=517.4MB, time=126.55 memory used=11275.6MB, alloc=517.4MB, time=126.99 memory used=11369.7MB, alloc=517.4MB, time=127.37 memory used=11462.1MB, alloc=517.4MB, time=127.74 memory used=11572.2MB, alloc=517.4MB, time=128.11 memory used=11703.8MB, alloc=517.4MB, time=128.51 memory used=11844.0MB, alloc=517.4MB, time=128.94 memory used=12008.9MB, alloc=517.4MB, time=129.37 memory used=12206.9MB, alloc=517.4MB, time=130.23 memory used=12336.2MB, alloc=517.4MB, time=131.77 memory used=12451.8MB, alloc=517.4MB, time=132.25 memory used=12542.8MB, alloc=517.4MB, time=132.68 memory used=12634.0MB, alloc=517.4MB, time=133.07 memory used=12736.2MB, alloc=517.4MB, time=133.50 memory used=12853.8MB, alloc=517.4MB, time=133.93 memory used=12975.0MB, alloc=517.4MB, time=134.34 memory used=13047.4MB, alloc=517.4MB, time=134.69 memory used=13120.7MB, alloc=517.4MB, time=135.04 memory used=13200.0MB, alloc=517.4MB, time=135.40 memory used=13284.2MB, alloc=517.4MB, time=135.75 memory used=13373.0MB, alloc=517.4MB, time=136.12 memory used=13470.0MB, alloc=517.4MB, time=136.49 memory used=13574.0MB, alloc=517.4MB, time=136.85 memory used=13683.2MB, alloc=517.4MB, time=137.25 memory used=13803.2MB, alloc=517.4MB, time=137.63 memory used=13935.3MB, alloc=517.4MB, time=138.01 memory used=14142.6MB, alloc=517.4MB, time=138.89 memory used=14243.2MB, alloc=517.4MB, time=139.30 memory used=14381.1MB, alloc=517.4MB, time=150.28 memory used=14544.4MB, alloc=517.4MB, time=153.56 memory used=14653.9MB, alloc=517.4MB, time=153.99 memory used=14741.7MB, alloc=517.4MB, time=154.35 memory used=14835.1MB, alloc=517.4MB, time=154.71 memory used=14947.7MB, alloc=517.4MB, time=155.10 memory used=15203.5MB, alloc=517.4MB, time=155.65 memory used=15368.1MB, alloc=517.4MB, time=156.10 memory used=15568.6MB, alloc=517.4MB, time=157.83 memory used=15661.2MB, alloc=517.4MB, time=158.19 memory used=15846.1MB, alloc=517.4MB, time=159.36 memory used=16071.4MB, alloc=517.4MB, time=161.77 memory used=16203.1MB, alloc=517.4MB, time=163.03 memory used=16386.6MB, alloc=517.4MB, time=164.84 memory used=16490.5MB, alloc=517.4MB, time=166.27 memory used=16670.3MB, alloc=517.4MB, time=168.25 memory used=16828.7MB, alloc=517.4MB, time=170.14 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428296910 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 2 4 2 2 F := [3 x z + 9 y z - 10 x, -19 x z - 7 y + 19 y z , 4 -7 x + 8 x y z - 7 x y] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 2 2 2 3 G := [-8 x + 15 x y z - 7 x y , -13 y z + 18 x y + 8 z , 2 2 2 19 x y - x y - 17 z] > Problem := [F,G]; 2 2 2 2 2 2 4 2 2 Problem := [[3 x z + 9 y z - 10 x, -19 x z - 7 y + 19 y z , 4 4 2 2 -7 x + 8 x y z - 7 x y], [-8 x + 15 x y z - 7 x y , 2 2 2 3 2 2 2 -13 y z + 18 x y + 8 z , 19 x y - x y - 17 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.17 memory used=23.9MB, alloc=32.3MB, time=0.46 memory used=43.6MB, alloc=36.3MB, time=0.69 memory used=63.7MB, alloc=36.3MB, time=0.83 memory used=90.8MB, alloc=36.3MB, time=1.13 memory used=110.6MB, alloc=60.3MB, time=1.37 memory used=153.3MB, alloc=60.3MB, time=1.74 memory used=192.9MB, alloc=60.3MB, time=2.26 memory used=237.8MB, alloc=68.3MB, time=2.88 memory used=274.3MB, alloc=68.3MB, time=3.13 memory used=306.7MB, alloc=68.3MB, time=3.39 memory used=333.0MB, alloc=68.3MB, time=3.50 memory used=359.3MB, alloc=68.3MB, time=3.71 memory used=396.3MB, alloc=68.3MB, time=4.14 memory used=415.3MB, alloc=68.3MB, time=4.21 memory used=439.2MB, alloc=68.3MB, time=4.40 memory used=467.1MB, alloc=68.3MB, time=4.52 memory used=492.3MB, alloc=68.3MB, time=4.66 memory used=518.4MB, alloc=68.3MB, time=4.80 memory used=567.6MB, alloc=68.3MB, time=5.32 memory used=621.0MB, alloc=92.3MB, time=5.86 memory used=689.5MB, alloc=92.3MB, time=6.48 memory used=768.0MB, alloc=92.3MB, time=7.29 memory used=833.4MB, alloc=92.3MB, time=8.00 memory used=896.0MB, alloc=92.3MB, time=8.56 memory used=954.1MB, alloc=348.3MB, time=9.18 memory used=999.9MB, alloc=348.3MB, time=9.51 memory used=1030.7MB, alloc=372.3MB, time=9.66 memory used=1080.0MB, alloc=372.3MB, time=9.82 memory used=1135.0MB, alloc=372.3MB, time=10.07 memory used=1181.3MB, alloc=372.3MB, time=10.24 memory used=1223.2MB, alloc=372.3MB, time=10.39 memory used=1334.8MB, alloc=372.3MB, time=13.59 memory used=1379.6MB, alloc=372.3MB, time=13.75 memory used=1425.0MB, alloc=372.3MB, time=13.90 memory used=1475.9MB, alloc=372.3MB, time=14.05 memory used=1510.7MB, alloc=372.3MB, time=14.16 memory used=1569.8MB, alloc=372.3MB, time=14.68 memory used=1619.3MB, alloc=372.3MB, time=14.86 memory used=1680.6MB, alloc=372.3MB, time=15.12 memory used=1726.4MB, alloc=372.3MB, time=15.27 memory used=1770.6MB, alloc=372.3MB, time=15.45 memory used=1828.8MB, alloc=372.3MB, time=15.70 memory used=1882.8MB, alloc=372.3MB, time=15.94 memory used=1938.0MB, alloc=372.3MB, time=16.20 memory used=2032.3MB, alloc=372.3MB, time=17.26 memory used=2130.1MB, alloc=372.3MB, time=18.41 memory used=2212.1MB, alloc=372.3MB, time=19.33 memory used=2291.5MB, alloc=372.3MB, time=20.09 memory used=2340.5MB, alloc=372.3MB, time=20.43 memory used=2421.0MB, alloc=396.3MB, time=21.42 memory used=2530.2MB, alloc=396.3MB, time=22.37 memory used=2674.8MB, alloc=396.3MB, time=24.43 memory used=2799.6MB, alloc=396.3MB, time=26.36 memory used=2906.7MB, alloc=420.3MB, time=27.61 memory used=2990.2MB, alloc=420.3MB, time=28.15 memory used=3053.3MB, alloc=420.3MB, time=28.36 memory used=3120.3MB, alloc=420.3MB, time=28.66 memory used=3182.5MB, alloc=420.3MB, time=28.89 memory used=3238.9MB, alloc=420.3MB, time=29.12 memory used=3315.5MB, alloc=420.3MB, time=29.44 memory used=3375.2MB, alloc=420.3MB, time=29.67 memory used=3436.9MB, alloc=420.3MB, time=29.91 memory used=3549.9MB, alloc=420.3MB, time=32.23 memory used=3605.9MB, alloc=420.3MB, time=32.46 memory used=3674.8MB, alloc=420.3MB, time=32.69 memory used=3721.2MB, alloc=420.3MB, time=32.88 memory used=3774.7MB, alloc=420.3MB, time=33.06 memory used=3836.7MB, alloc=420.3MB, time=33.25 memory used=3918.9MB, alloc=420.3MB, time=33.57 memory used=4034.6MB, alloc=420.3MB, time=34.53 memory used=4109.1MB, alloc=420.3MB, time=35.02 memory used=4171.0MB, alloc=420.3MB, time=35.22 memory used=4249.3MB, alloc=420.3MB, time=35.72 memory used=4309.6MB, alloc=420.3MB, time=35.95 memory used=4366.7MB, alloc=420.3MB, time=36.16 memory used=4512.7MB, alloc=420.3MB, time=37.73 memory used=4659.0MB, alloc=420.3MB, time=40.17 memory used=4808.5MB, alloc=420.3MB, time=41.88 memory used=4931.9MB, alloc=420.3MB, time=44.27 memory used=4996.0MB, alloc=420.3MB, time=44.58 memory used=5076.5MB, alloc=420.3MB, time=45.24 memory used=5134.5MB, alloc=420.3MB, time=45.52 memory used=5185.9MB, alloc=444.3MB, time=45.78 memory used=5250.9MB, alloc=444.3MB, time=46.07 memory used=5329.7MB, alloc=444.3MB, time=46.36 memory used=5416.2MB, alloc=444.3MB, time=46.64 memory used=5467.7MB, alloc=444.3MB, time=46.87 memory used=5521.8MB, alloc=444.3MB, time=47.10 memory used=5581.0MB, alloc=444.3MB, time=47.33 memory used=5645.0MB, alloc=444.3MB, time=47.56 memory used=5713.6MB, alloc=444.3MB, time=47.80 memory used=5787.6MB, alloc=444.3MB, time=48.03 memory used=5867.6MB, alloc=444.3MB, time=48.29 memory used=5954.5MB, alloc=444.3MB, time=48.52 memory used=6091.5MB, alloc=444.3MB, time=48.87 memory used=6186.0MB, alloc=444.3MB, time=49.45 memory used=6252.2MB, alloc=444.3MB, time=49.73 memory used=6320.4MB, alloc=444.3MB, time=50.00 memory used=6403.1MB, alloc=444.3MB, time=50.29 memory used=6481.3MB, alloc=444.3MB, time=50.56 memory used=6533.3MB, alloc=444.3MB, time=50.77 memory used=6588.8MB, alloc=444.3MB, time=51.01 memory used=6648.4MB, alloc=444.3MB, time=51.26 memory used=6712.8MB, alloc=444.3MB, time=51.50 memory used=6782.0MB, alloc=444.3MB, time=51.74 memory used=6856.8MB, alloc=444.3MB, time=51.97 memory used=6938.1MB, alloc=444.3MB, time=52.21 memory used=7026.0MB, alloc=444.3MB, time=52.45 memory used=7188.7MB, alloc=444.3MB, time=58.78 memory used=7365.4MB, alloc=444.3MB, time=60.56 memory used=7442.2MB, alloc=444.3MB, time=60.86 memory used=7512.2MB, alloc=444.3MB, time=61.14 memory used=7571.6MB, alloc=444.3MB, time=61.38 memory used=7638.1MB, alloc=444.3MB, time=61.62 memory used=7714.0MB, alloc=444.3MB, time=61.88 memory used=7797.6MB, alloc=444.3MB, time=62.14 memory used=7891.0MB, alloc=444.3MB, time=62.41 memory used=8043.1MB, alloc=444.3MB, time=62.90 memory used=8193.8MB, alloc=444.3MB, time=63.28 memory used=8362.8MB, alloc=444.3MB, time=63.68 memory used=8553.4MB, alloc=444.3MB, time=64.10 memory used=8773.4MB, alloc=444.3MB, time=64.53 memory used=8982.1MB, alloc=444.3MB, time=64.99 memory used=9057.6MB, alloc=444.3MB, time=65.27 memory used=9177.0MB, alloc=444.3MB, time=66.84 memory used=9249.4MB, alloc=444.3MB, time=67.11 memory used=9333.8MB, alloc=444.3MB, time=67.47 memory used=9423.6MB, alloc=444.3MB, time=68.08 memory used=9504.6MB, alloc=444.3MB, time=68.39 memory used=9565.5MB, alloc=444.3MB, time=68.62 memory used=9644.1MB, alloc=444.3MB, time=68.87 memory used=9829.6MB, alloc=444.3MB, time=70.23 memory used=9956.1MB, alloc=444.3MB, time=71.36 memory used=10072.4MB, alloc=444.3MB, time=72.20 memory used=10161.9MB, alloc=444.3MB, time=73.04 memory used=10228.5MB, alloc=444.3MB, time=73.30 memory used=10300.1MB, alloc=444.3MB, time=73.55 memory used=10390.5MB, alloc=444.3MB, time=74.06 memory used=10458.4MB, alloc=444.3MB, time=74.34 memory used=10526.8MB, alloc=444.3MB, time=74.60 memory used=10689.5MB, alloc=444.3MB, time=75.84 memory used=10822.0MB, alloc=444.3MB, time=77.34 memory used=10920.3MB, alloc=444.3MB, time=78.62 memory used=11017.5MB, alloc=444.3MB, time=79.89 memory used=11089.4MB, alloc=468.3MB, time=81.05 memory used=11171.7MB, alloc=468.3MB, time=82.37 memory used=11314.1MB, alloc=468.3MB, time=83.44 memory used=11404.7MB, alloc=468.3MB, time=84.09 memory used=11485.8MB, alloc=468.3MB, time=84.45 memory used=11546.7MB, alloc=468.3MB, time=84.79 memory used=11666.8MB, alloc=468.3MB, time=85.85 memory used=11753.3MB, alloc=468.3MB, time=86.40 memory used=11870.5MB, alloc=468.3MB, time=87.41 memory used=11972.0MB, alloc=468.3MB, time=88.64 memory used=12040.0MB, alloc=468.3MB, time=89.64 memory used=12105.1MB, alloc=468.3MB, time=90.65 memory used=12179.8MB, alloc=492.3MB, time=92.06 memory used=12239.3MB, alloc=492.3MB, time=93.11 memory used=12283.0MB, alloc=492.3MB, time=93.85 memory used=12330.2MB, alloc=492.3MB, time=94.61 memory used=12364.6MB, alloc=492.3MB, time=95.29 memory used=12537.0MB, alloc=516.3MB, time=97.02 memory used=12671.1MB, alloc=516.3MB, time=98.38 memory used=12798.0MB, alloc=516.3MB, time=99.53 memory used=12973.1MB, alloc=516.3MB, time=101.30 memory used=13194.8MB, alloc=540.3MB, time=103.83 memory used=13430.3MB, alloc=564.3MB, time=106.71 memory used=13666.4MB, alloc=564.3MB, time=109.39 memory used=13887.1MB, alloc=588.3MB, time=111.92 memory used=14021.8MB, alloc=612.3MB, time=114.36 memory used=14143.3MB, alloc=636.3MB, time=116.27 memory used=14305.7MB, alloc=636.3MB, time=118.32 memory used=14424.2MB, alloc=636.3MB, time=120.45 memory used=14566.3MB, alloc=660.3MB, time=122.41 memory used=14698.4MB, alloc=660.3MB, time=124.23 memory used=14804.0MB, alloc=660.3MB, time=126.04 memory used=15008.9MB, alloc=660.3MB, time=127.80 memory used=15185.8MB, alloc=660.3MB, time=129.02 memory used=15357.4MB, alloc=660.3MB, time=132.58 memory used=15495.9MB, alloc=660.3MB, time=133.55 memory used=15673.3MB, alloc=660.3MB, time=134.86 memory used=15840.9MB, alloc=660.3MB, time=136.03 memory used=16007.2MB, alloc=660.3MB, time=139.41 memory used=16163.9MB, alloc=660.3MB, time=140.51 memory used=16349.0MB, alloc=660.3MB, time=141.88 memory used=16664.9MB, alloc=684.3MB, time=145.84 memory used=17055.5MB, alloc=708.3MB, time=150.26 memory used=17373.9MB, alloc=732.3MB, time=155.21 memory used=17698.6MB, alloc=756.3MB, time=160.45 memory used=17962.6MB, alloc=780.3MB, time=163.48 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428297210 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 3 2 2 F := [-13 z - 6 y z - 2 z , -5 x y + 19 x y z + 10 x z , 3 2 3 13 x y - 17 x y z + 8 x z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 2 3 G := [19 x y - 5 x z + 18 x y z, 7 y z - 5 x z + 19 z , 2 2 2 16 x y z + 19 y - 10 z ] > Problem := [F,G]; 4 2 2 3 2 2 Problem := [[-13 z - 6 y z - 2 z , -5 x y + 19 x y z + 10 x z , 3 2 3 3 3 13 x y - 17 x y z + 8 x z ], [19 x y - 5 x z + 18 x y z, 2 2 2 3 2 2 2 7 y z - 5 x z + 19 z , 16 x y z + 19 y - 10 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.18 memory used=26.6MB, alloc=32.3MB, time=0.52 memory used=45.7MB, alloc=60.3MB, time=0.78 memory used=88.5MB, alloc=60.3MB, time=1.40 memory used=129.8MB, alloc=60.3MB, time=2.01 memory used=165.8MB, alloc=60.3MB, time=2.39 memory used=210.4MB, alloc=68.3MB, time=2.91 memory used=252.4MB, alloc=68.3MB, time=3.44 memory used=296.9MB, alloc=92.3MB, time=4.06 memory used=364.6MB, alloc=92.3MB, time=4.93 memory used=428.2MB, alloc=92.3MB, time=5.83 memory used=492.0MB, alloc=116.3MB, time=6.72 memory used=559.8MB, alloc=116.3MB, time=7.76 memory used=634.8MB, alloc=372.3MB, time=8.93 memory used=715.8MB, alloc=396.3MB, time=10.21 memory used=801.8MB, alloc=396.3MB, time=11.07 memory used=873.0MB, alloc=396.3MB, time=11.66 memory used=943.5MB, alloc=396.3MB, time=13.75 memory used=998.4MB, alloc=396.3MB, time=14.04 memory used=1057.2MB, alloc=396.3MB, time=14.39 memory used=1118.8MB, alloc=396.3MB, time=14.82 memory used=1188.3MB, alloc=396.3MB, time=17.06 memory used=1246.3MB, alloc=396.3MB, time=17.33 memory used=1308.9MB, alloc=396.3MB, time=17.70 memory used=1374.5MB, alloc=396.3MB, time=21.01 memory used=1431.3MB, alloc=396.3MB, time=21.36 memory used=1496.4MB, alloc=396.3MB, time=21.59 memory used=1553.3MB, alloc=396.3MB, time=21.96 memory used=1619.2MB, alloc=396.3MB, time=22.27 memory used=1683.3MB, alloc=396.3MB, time=22.46 memory used=1746.2MB, alloc=396.3MB, time=22.66 memory used=1800.0MB, alloc=396.3MB, time=22.94 memory used=1908.6MB, alloc=396.3MB, time=24.55 memory used=2007.8MB, alloc=396.3MB, time=27.08 memory used=2104.6MB, alloc=396.3MB, time=27.98 memory used=2180.9MB, alloc=396.3MB, time=28.69 memory used=2250.7MB, alloc=396.3MB, time=29.21 memory used=2309.1MB, alloc=396.3MB, time=29.62 memory used=2368.7MB, alloc=396.3MB, time=31.16 memory used=2428.1MB, alloc=396.3MB, time=31.84 memory used=2486.0MB, alloc=396.3MB, time=32.24 memory used=2544.5MB, alloc=396.3MB, time=32.63 memory used=2605.1MB, alloc=396.3MB, time=33.03 memory used=2661.7MB, alloc=396.3MB, time=33.36 memory used=2720.7MB, alloc=396.3MB, time=35.28 memory used=2781.0MB, alloc=396.3MB, time=35.68 memory used=2841.5MB, alloc=396.3MB, time=36.14 memory used=2900.1MB, alloc=396.3MB, time=36.49 memory used=2954.4MB, alloc=396.3MB, time=36.79 memory used=3014.1MB, alloc=396.3MB, time=37.24 memory used=3078.2MB, alloc=396.3MB, time=40.48 memory used=3161.7MB, alloc=396.3MB, time=41.22 memory used=3221.2MB, alloc=396.3MB, time=42.27 memory used=3298.9MB, alloc=396.3MB, time=44.49 memory used=3394.3MB, alloc=420.3MB, time=45.59 memory used=3509.0MB, alloc=420.3MB, time=46.88 memory used=3629.9MB, alloc=420.3MB, time=48.18 memory used=3758.3MB, alloc=420.3MB, time=49.81 memory used=3848.2MB, alloc=444.3MB, time=50.78 memory used=3949.7MB, alloc=444.3MB, time=53.67 memory used=4036.2MB, alloc=444.3MB, time=54.27 memory used=4127.7MB, alloc=444.3MB, time=56.84 memory used=4262.3MB, alloc=444.3MB, time=59.85 memory used=4394.8MB, alloc=444.3MB, time=61.57 memory used=4543.8MB, alloc=444.3MB, time=64.01 memory used=4682.0MB, alloc=468.3MB, time=66.23 memory used=4794.3MB, alloc=468.3MB, time=67.87 memory used=4912.8MB, alloc=468.3MB, time=69.83 memory used=5037.5MB, alloc=492.3MB, time=72.05 memory used=5153.5MB, alloc=492.3MB, time=73.55 memory used=5256.7MB, alloc=492.3MB, time=78.84 memory used=5361.5MB, alloc=516.3MB, time=80.07 memory used=5478.0MB, alloc=516.3MB, time=81.50 memory used=5630.1MB, alloc=516.3MB, time=87.29 memory used=5714.2MB, alloc=516.3MB, time=88.49 memory used=5819.6MB, alloc=516.3MB, time=89.91 memory used=5911.2MB, alloc=516.3MB, time=91.49 memory used=6008.9MB, alloc=516.3MB, time=93.02 memory used=6095.4MB, alloc=516.3MB, time=94.11 memory used=6217.4MB, alloc=540.3MB, time=95.52 memory used=6361.6MB, alloc=540.3MB, time=101.04 memory used=6488.5MB, alloc=540.3MB, time=101.94 memory used=6574.4MB, alloc=540.3MB, time=103.08 memory used=6662.8MB, alloc=540.3MB, time=104.53 memory used=6740.4MB, alloc=540.3MB, time=105.87 memory used=6887.6MB, alloc=540.3MB, time=107.29 memory used=7008.2MB, alloc=540.3MB, time=108.71 memory used=7126.5MB, alloc=540.3MB, time=110.29 memory used=7250.5MB, alloc=540.3MB, time=112.92 memory used=7354.6MB, alloc=540.3MB, time=114.04 memory used=7402.4MB, alloc=540.3MB, time=114.95 memory used=7524.8MB, alloc=540.3MB, time=117.00 memory used=7673.5MB, alloc=540.3MB, time=120.37 memory used=7810.4MB, alloc=540.3MB, time=126.20 memory used=7879.1MB, alloc=540.3MB, time=127.23 memory used=7984.4MB, alloc=540.3MB, time=129.15 memory used=8079.9MB, alloc=564.3MB, time=130.09 memory used=8211.1MB, alloc=564.3MB, time=132.02 memory used=8363.2MB, alloc=564.3MB, time=135.40 memory used=8518.1MB, alloc=564.3MB, time=141.52 memory used=8632.5MB, alloc=564.3MB, time=142.52 memory used=8686.1MB, alloc=564.3MB, time=143.37 memory used=8741.3MB, alloc=564.3MB, time=144.43 memory used=8813.0MB, alloc=564.3MB, time=145.55 memory used=8862.6MB, alloc=564.3MB, time=146.40 memory used=9074.6MB, alloc=588.3MB, time=149.74 memory used=9306.6MB, alloc=612.3MB, time=152.78 memory used=9483.4MB, alloc=612.3MB, time=154.30 memory used=9645.5MB, alloc=612.3MB, time=159.54 memory used=9792.8MB, alloc=612.3MB, time=160.61 memory used=9935.3MB, alloc=612.3MB, time=161.45 memory used=10220.9MB, alloc=636.3MB, time=164.42 memory used=10452.0MB, alloc=660.3MB, time=167.58 memory used=10661.2MB, alloc=684.3MB, time=171.56 memory used=10824.4MB, alloc=684.3MB, time=174.36 memory used=11016.7MB, alloc=708.3MB, time=178.20 memory used=11166.4MB, alloc=708.3MB, time=181.06 memory used=11282.4MB, alloc=732.3MB, time=183.44 memory used=11428.6MB, alloc=732.3MB, time=186.71 memory used=11568.8MB, alloc=732.3MB, time=189.91 memory used=11742.3MB, alloc=732.3MB, time=192.61 memory used=11974.8MB, alloc=732.3MB, time=196.09 memory used=12168.2MB, alloc=732.3MB, time=197.45 memory used=12346.8MB, alloc=756.3MB, time=198.59 memory used=12548.3MB, alloc=756.3MB, time=199.65 memory used=12748.8MB, alloc=756.3MB, time=200.98 memory used=12932.1MB, alloc=756.3MB, time=202.08 memory used=13152.2MB, alloc=756.3MB, time=215.27 memory used=13360.0MB, alloc=756.3MB, time=216.36 memory used=13522.1MB, alloc=756.3MB, time=217.32 memory used=13798.5MB, alloc=756.3MB, time=220.13 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428297510 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 3 2 F := [16 x z - 10 x z - 14 x y, -14 x z - 16 y z - 19 x y , 2 2 2 15 x y z + 6 x y z + 14 x y] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 2 2 2 3 2 2 G := [-20 y - 16 z - 4 x, x y + 11 x z + 15 z , x z - 8 x z + 7 z ] > Problem := [F,G]; 3 2 3 3 2 Problem := [[16 x z - 10 x z - 14 x y, -14 x z - 16 y z - 19 x y , 2 2 2 15 x y z + 6 x y z + 14 x y], 4 3 2 2 2 3 2 2 [-20 y - 16 z - 4 x, x y + 11 x z + 15 z , x z - 8 x z + 7 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.5MB, alloc=32.3MB, time=0.49 memory used=48.2MB, alloc=36.3MB, time=0.83 memory used=67.1MB, alloc=60.3MB, time=1.12 memory used=107.2MB, alloc=60.3MB, time=1.70 memory used=145.7MB, alloc=60.3MB, time=2.26 memory used=183.2MB, alloc=84.3MB, time=2.83 memory used=219.9MB, alloc=84.3MB, time=3.34 memory used=287.5MB, alloc=92.3MB, time=4.23 memory used=350.1MB, alloc=116.3MB, time=5.13 memory used=419.8MB, alloc=116.3MB, time=6.13 memory used=483.3MB, alloc=372.3MB, time=6.92 memory used=573.4MB, alloc=396.3MB, time=8.15 memory used=688.9MB, alloc=396.3MB, time=9.61 memory used=800.7MB, alloc=420.3MB, time=11.14 memory used=923.4MB, alloc=420.3MB, time=12.80 memory used=1043.3MB, alloc=444.3MB, time=14.43 memory used=1157.9MB, alloc=444.3MB, time=16.13 memory used=1284.8MB, alloc=468.3MB, time=18.05 memory used=1405.6MB, alloc=468.3MB, time=19.98 memory used=1516.2MB, alloc=492.3MB, time=21.53 memory used=1617.7MB, alloc=492.3MB, time=23.17 memory used=1706.7MB, alloc=492.3MB, time=24.71 memory used=1800.1MB, alloc=492.3MB, time=26.03 memory used=1897.9MB, alloc=492.3MB, time=27.71 memory used=1970.2MB, alloc=492.3MB, time=28.86 memory used=2061.0MB, alloc=492.3MB, time=30.33 memory used=2138.6MB, alloc=492.3MB, time=31.51 memory used=2228.2MB, alloc=516.3MB, time=32.69 memory used=2321.6MB, alloc=516.3MB, time=34.05 memory used=2413.0MB, alloc=516.3MB, time=35.11 memory used=2483.7MB, alloc=516.3MB, time=36.14 memory used=2562.7MB, alloc=516.3MB, time=37.44 memory used=2633.5MB, alloc=516.3MB, time=38.50 memory used=2755.6MB, alloc=516.3MB, time=39.39 memory used=2874.2MB, alloc=516.3MB, time=40.55 memory used=2942.5MB, alloc=516.3MB, time=41.61 memory used=3057.3MB, alloc=516.3MB, time=42.46 memory used=3182.2MB, alloc=516.3MB, time=44.88 memory used=3272.6MB, alloc=516.3MB, time=45.38 memory used=3365.6MB, alloc=516.3MB, time=45.84 memory used=3505.8MB, alloc=516.3MB, time=47.01 memory used=3636.8MB, alloc=516.3MB, time=48.22 memory used=3779.6MB, alloc=516.3MB, time=49.71 memory used=3848.9MB, alloc=516.3MB, time=50.86 memory used=3903.3MB, alloc=516.3MB, time=52.10 memory used=3954.6MB, alloc=516.3MB, time=53.17 memory used=4107.2MB, alloc=516.3MB, time=54.68 memory used=4230.2MB, alloc=516.3MB, time=57.13 memory used=4314.5MB, alloc=516.3MB, time=57.64 memory used=4411.3MB, alloc=540.3MB, time=58.15 memory used=4511.6MB, alloc=540.3MB, time=58.71 memory used=4781.2MB, alloc=540.3MB, time=62.10 memory used=5003.4MB, alloc=564.3MB, time=65.80 memory used=5188.0MB, alloc=588.3MB, time=68.74 memory used=5378.8MB, alloc=612.3MB, time=71.69 memory used=5587.0MB, alloc=612.3MB, time=75.29 memory used=5756.7MB, alloc=612.3MB, time=78.27 memory used=5910.9MB, alloc=636.3MB, time=81.00 memory used=6080.0MB, alloc=636.3MB, time=83.70 memory used=6217.1MB, alloc=636.3MB, time=86.32 memory used=6373.9MB, alloc=636.3MB, time=88.97 memory used=6518.4MB, alloc=636.3MB, time=91.62 memory used=6652.3MB, alloc=660.3MB, time=93.97 memory used=6812.1MB, alloc=660.3MB, time=96.50 memory used=6946.5MB, alloc=660.3MB, time=98.88 memory used=7161.4MB, alloc=660.3MB, time=101.63 memory used=7320.3MB, alloc=660.3MB, time=102.81 memory used=7484.3MB, alloc=660.3MB, time=104.57 memory used=7643.8MB, alloc=660.3MB, time=107.11 memory used=7849.5MB, alloc=684.3MB, time=110.18 memory used=8066.4MB, alloc=684.3MB, time=114.44 memory used=8277.1MB, alloc=684.3MB, time=116.54 memory used=8419.9MB, alloc=684.3MB, time=120.85 memory used=8514.4MB, alloc=684.3MB, time=123.22 memory used=8785.0MB, alloc=684.3MB, time=128.48 memory used=8929.8MB, alloc=684.3MB, time=129.46 memory used=9289.5MB, alloc=708.3MB, time=133.66 memory used=9601.0MB, alloc=708.3MB, time=137.44 memory used=9928.6MB, alloc=732.3MB, time=142.21 memory used=10244.7MB, alloc=756.3MB, time=146.30 memory used=10457.5MB, alloc=756.3MB, time=148.24 memory used=10635.3MB, alloc=756.3MB, time=149.65 memory used=10830.7MB, alloc=756.3MB, time=151.00 memory used=10975.1MB, alloc=756.3MB, time=152.25 memory used=11146.6MB, alloc=756.3MB, time=153.50 memory used=11346.7MB, alloc=756.3MB, time=154.79 memory used=11638.4MB, alloc=756.3MB, time=156.28 memory used=11752.8MB, alloc=756.3MB, time=157.47 memory used=12022.2MB, alloc=756.3MB, time=162.46 memory used=12179.4MB, alloc=756.3MB, time=163.79 memory used=12376.1MB, alloc=756.3MB, time=165.13 memory used=12601.0MB, alloc=756.3MB, time=166.41 memory used=12717.2MB, alloc=756.3MB, time=167.57 memory used=12848.0MB, alloc=756.3MB, time=168.74 memory used=12997.4MB, alloc=756.3MB, time=169.93 memory used=13383.3MB, alloc=756.3MB, time=173.92 memory used=13582.0MB, alloc=756.3MB, time=175.35 memory used=13778.7MB, alloc=756.3MB, time=176.85 memory used=13952.8MB, alloc=756.3MB, time=178.05 memory used=14220.1MB, alloc=756.3MB, time=186.46 memory used=14423.5MB, alloc=756.3MB, time=188.86 memory used=14602.7MB, alloc=756.3MB, time=190.16 memory used=14762.4MB, alloc=756.3MB, time=191.36 memory used=14954.0MB, alloc=756.3MB, time=192.55 memory used=15179.0MB, alloc=756.3MB, time=193.83 memory used=15322.7MB, alloc=756.3MB, time=194.98 memory used=15428.8MB, alloc=756.3MB, time=196.10 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428297810 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; F := [ 4 3 2 4 3 2 3 2 2 2 -14 y + 5 y z + 2 y , -6 y - 4 x - 16 x y, -7 x z + 15 y z + 20 z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 3 3 2 2 2 G := [-10 x y + 15 y z + 17 x , 11 x z + 10 x - 5 y, 2 x + 14 y - 20 z ] > Problem := [F,G]; Problem := [[ 4 3 2 4 3 2 3 2 2 2 -14 y + 5 y z + 2 y , -6 y - 4 x - 16 x y, -7 x z + 15 y z + 20 z ] 3 3 2 3 3 2 2 2 , [-10 x y + 15 y z + 17 x , 11 x z + 10 x - 5 y, 2 x + 14 y - 20 z ] ] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=31.9MB, alloc=40.3MB, time=0.60 memory used=58.5MB, alloc=44.3MB, time=1.01 memory used=84.3MB, alloc=68.3MB, time=1.38 memory used=134.5MB, alloc=76.3MB, time=1.95 memory used=185.3MB, alloc=76.3MB, time=2.58 memory used=234.1MB, alloc=76.3MB, time=3.34 memory used=282.7MB, alloc=76.3MB, time=3.81 memory used=306.8MB, alloc=76.3MB, time=3.91 memory used=340.5MB, alloc=76.3MB, time=4.07 memory used=374.5MB, alloc=76.3MB, time=4.47 memory used=401.8MB, alloc=76.3MB, time=4.68 memory used=447.6MB, alloc=76.3MB, time=5.02 memory used=487.8MB, alloc=76.3MB, time=5.92 memory used=509.7MB, alloc=76.3MB, time=6.02 memory used=531.7MB, alloc=76.3MB, time=6.10 memory used=574.3MB, alloc=76.3MB, time=6.50 memory used=622.8MB, alloc=100.3MB, time=7.24 memory used=692.9MB, alloc=100.3MB, time=8.21 memory used=765.0MB, alloc=100.3MB, time=9.33 memory used=836.9MB, alloc=100.3MB, time=10.13 memory used=890.0MB, alloc=100.3MB, time=10.67 memory used=956.7MB, alloc=100.3MB, time=11.94 memory used=993.1MB, alloc=124.3MB, time=12.08 memory used=1037.2MB, alloc=124.3MB, time=12.22 memory used=1092.7MB, alloc=124.3MB, time=12.37 memory used=1129.5MB, alloc=124.3MB, time=12.48 memory used=1173.2MB, alloc=124.3MB, time=12.59 memory used=1237.3MB, alloc=124.3MB, time=16.75 memory used=1308.0MB, alloc=124.3MB, time=18.10 memory used=1356.6MB, alloc=124.3MB, time=18.25 memory used=1398.3MB, alloc=124.3MB, time=18.37 memory used=1478.4MB, alloc=124.3MB, time=19.43 memory used=1532.3MB, alloc=380.3MB, time=20.20 memory used=1626.4MB, alloc=380.3MB, time=21.45 memory used=1720.2MB, alloc=404.3MB, time=22.52 memory used=1815.3MB, alloc=404.3MB, time=23.33 memory used=1930.6MB, alloc=428.3MB, time=24.76 memory used=2067.1MB, alloc=428.3MB, time=26.58 memory used=2201.7MB, alloc=452.3MB, time=28.54 memory used=2338.3MB, alloc=452.3MB, time=29.88 memory used=2427.9MB, alloc=452.3MB, time=30.29 memory used=2523.2MB, alloc=452.3MB, time=31.15 memory used=2603.8MB, alloc=452.3MB, time=31.50 memory used=2683.3MB, alloc=452.3MB, time=31.92 memory used=2765.2MB, alloc=452.3MB, time=32.27 memory used=2849.0MB, alloc=452.3MB, time=33.63 memory used=2934.8MB, alloc=452.3MB, time=34.05 memory used=3038.2MB, alloc=452.3MB, time=34.94 memory used=3154.9MB, alloc=452.3MB, time=37.08 memory used=3235.7MB, alloc=452.3MB, time=37.47 memory used=3329.9MB, alloc=452.3MB, time=37.89 memory used=3432.8MB, alloc=452.3MB, time=43.54 memory used=3504.9MB, alloc=452.3MB, time=43.87 memory used=3565.2MB, alloc=452.3MB, time=44.17 memory used=3643.9MB, alloc=452.3MB, time=44.59 memory used=3795.4MB, alloc=476.3MB, time=47.39 memory used=3904.7MB, alloc=476.3MB, time=48.66 memory used=4038.9MB, alloc=476.3MB, time=49.99 memory used=4151.3MB, alloc=476.3MB, time=50.77 memory used=4259.8MB, alloc=476.3MB, time=51.84 memory used=4380.1MB, alloc=476.3MB, time=52.71 memory used=4505.5MB, alloc=500.3MB, time=62.20 memory used=4618.0MB, alloc=500.3MB, time=63.65 memory used=4719.1MB, alloc=500.3MB, time=64.12 memory used=4848.4MB, alloc=500.3MB, time=64.87 memory used=4953.6MB, alloc=500.3MB, time=65.31 memory used=5039.1MB, alloc=500.3MB, time=65.72 memory used=5168.4MB, alloc=500.3MB, time=66.48 memory used=5264.1MB, alloc=500.3MB, time=66.90 memory used=5358.9MB, alloc=500.3MB, time=67.29 memory used=5502.3MB, alloc=500.3MB, time=94.02 memory used=5619.0MB, alloc=500.3MB, time=108.56 memory used=5709.6MB, alloc=500.3MB, time=108.93 memory used=5810.0MB, alloc=500.3MB, time=109.32 memory used=5896.9MB, alloc=500.3MB, time=109.67 memory used=5990.0MB, alloc=500.3MB, time=110.26 memory used=6107.1MB, alloc=500.3MB, time=110.77 memory used=6214.6MB, alloc=500.3MB, time=111.22 memory used=6296.9MB, alloc=500.3MB, time=111.59 memory used=6426.1MB, alloc=500.3MB, time=112.33 memory used=6523.6MB, alloc=500.3MB, time=112.74 memory used=6616.5MB, alloc=500.3MB, time=113.14 memory used=6766.5MB, alloc=500.3MB, time=143.29 memory used=6886.9MB, alloc=500.3MB, time=154.08 memory used=6973.9MB, alloc=500.3MB, time=154.46 memory used=7077.5MB, alloc=500.3MB, time=154.86 memory used=7158.7MB, alloc=500.3MB, time=155.18 memory used=7290.3MB, alloc=500.3MB, time=156.14 memory used=7398.1MB, alloc=500.3MB, time=157.42 memory used=7509.8MB, alloc=500.3MB, time=159.34 memory used=7658.5MB, alloc=500.3MB, time=160.98 memory used=7782.3MB, alloc=500.3MB, time=163.00 memory used=7851.0MB, alloc=500.3MB, time=164.06 memory used=7923.0MB, alloc=500.3MB, time=164.88 memory used=8000.5MB, alloc=500.3MB, time=166.17 memory used=8067.0MB, alloc=500.3MB, time=167.40 memory used=8123.9MB, alloc=500.3MB, time=168.38 memory used=8191.7MB, alloc=500.3MB, time=169.64 memory used=8232.6MB, alloc=500.3MB, time=170.48 memory used=8277.8MB, alloc=500.3MB, time=171.41 memory used=8347.6MB, alloc=524.3MB, time=172.72 memory used=8465.2MB, alloc=524.3MB, time=175.28 memory used=8540.5MB, alloc=524.3MB, time=175.97 memory used=8651.5MB, alloc=524.3MB, time=176.59 memory used=8754.3MB, alloc=524.3MB, time=177.26 memory used=8857.8MB, alloc=524.3MB, time=181.76 memory used=8995.6MB, alloc=524.3MB, time=201.81 memory used=9094.2MB, alloc=524.3MB, time=202.35 memory used=9211.0MB, alloc=524.3MB, time=203.48 memory used=9323.0MB, alloc=524.3MB, time=204.11 memory used=9422.9MB, alloc=524.3MB, time=204.69 memory used=9545.7MB, alloc=524.3MB, time=205.31 memory used=9649.0MB, alloc=524.3MB, time=205.90 memory used=9727.4MB, alloc=524.3MB, time=206.40 memory used=9813.3MB, alloc=524.3MB, time=206.92 memory used=9909.2MB, alloc=524.3MB, time=207.44 memory used=10015.6MB, alloc=524.3MB, time=207.97 memory used=10136.4MB, alloc=524.3MB, time=208.50 memory used=10269.5MB, alloc=524.3MB, time=209.66 memory used=10381.0MB, alloc=524.3MB, time=210.30 memory used=10481.3MB, alloc=524.3MB, time=210.88 memory used=10604.2MB, alloc=524.3MB, time=211.50 memory used=10706.6MB, alloc=524.3MB, time=212.04 memory used=10785.9MB, alloc=524.3MB, time=212.56 memory used=10871.9MB, alloc=524.3MB, time=213.10 memory used=10967.7MB, alloc=524.3MB, time=213.62 memory used=11074.0MB, alloc=524.3MB, time=214.15 memory used=11194.6MB, alloc=524.3MB, time=214.70 memory used=11322.8MB, alloc=524.3MB, time=232.47 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428298110 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 4 2 2 3 2 2 3 F := [-4 x y + z + 5 y z, -11 x y - 7 x y + y z, -13 y z + 12 z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 G := [-17 x z + 10 y z - 3 x, 18 x y z + 11 x y z - 7 x z, 2 3 20 y z - 19 z - 4 x y] > Problem := [F,G]; Problem := [ 3 4 2 2 3 2 2 3 [-4 x y + z + 5 y z, -11 x y - 7 x y + y z, -13 y z + 12 z ], [ 3 2 2 -17 x z + 10 y z - 3 x, 18 x y z + 11 x y z - 7 x z, 2 3 20 y z - 19 z - 4 x y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.4MB, alloc=32.3MB, time=0.47 memory used=47.5MB, alloc=32.3MB, time=0.79 memory used=67.4MB, alloc=56.3MB, time=1.10 memory used=108.3MB, alloc=60.3MB, time=1.72 memory used=146.3MB, alloc=84.3MB, time=2.30 memory used=204.5MB, alloc=92.3MB, time=3.20 memory used=261.9MB, alloc=116.3MB, time=4.08 memory used=343.6MB, alloc=116.3MB, time=5.37 memory used=415.8MB, alloc=396.3MB, time=6.44 memory used=523.3MB, alloc=396.3MB, time=8.04 memory used=625.2MB, alloc=420.3MB, time=9.64 memory used=755.1MB, alloc=420.3MB, time=11.37 memory used=884.7MB, alloc=444.3MB, time=13.20 memory used=1032.1MB, alloc=468.3MB, time=15.30 memory used=1180.2MB, alloc=468.3MB, time=17.51 memory used=1314.3MB, alloc=492.3MB, time=19.77 memory used=1447.5MB, alloc=492.3MB, time=21.95 memory used=1574.7MB, alloc=516.3MB, time=24.28 memory used=1690.4MB, alloc=516.3MB, time=26.27 memory used=1813.6MB, alloc=516.3MB, time=28.33 memory used=1916.8MB, alloc=516.3MB, time=30.23 memory used=2020.4MB, alloc=516.3MB, time=32.19 memory used=2124.9MB, alloc=516.3MB, time=34.10 memory used=2272.3MB, alloc=540.3MB, time=38.48 memory used=2411.0MB, alloc=540.3MB, time=42.20 memory used=2503.9MB, alloc=540.3MB, time=43.84 memory used=2654.3MB, alloc=540.3MB, time=46.58 memory used=2784.4MB, alloc=540.3MB, time=47.95 memory used=2876.1MB, alloc=540.3MB, time=49.23 memory used=2994.3MB, alloc=540.3MB, time=50.59 memory used=3125.3MB, alloc=564.3MB, time=53.00 memory used=3254.5MB, alloc=564.3MB, time=53.60 memory used=3400.9MB, alloc=564.3MB, time=68.13 memory used=3560.1MB, alloc=564.3MB, time=82.65 memory used=3668.8MB, alloc=564.3MB, time=83.14 memory used=3799.7MB, alloc=564.3MB, time=83.63 memory used=3893.9MB, alloc=564.3MB, time=84.05 memory used=3989.5MB, alloc=564.3MB, time=84.46 memory used=4099.4MB, alloc=564.3MB, time=84.90 memory used=4224.1MB, alloc=564.3MB, time=85.33 memory used=4370.5MB, alloc=564.3MB, time=85.77 memory used=4527.8MB, alloc=564.3MB, time=86.39 memory used=4766.0MB, alloc=564.3MB, time=87.83 memory used=4934.2MB, alloc=564.3MB, time=89.11 memory used=5083.3MB, alloc=564.3MB, time=90.65 memory used=5242.6MB, alloc=564.3MB, time=92.55 memory used=5349.2MB, alloc=564.3MB, time=92.98 memory used=5570.4MB, alloc=564.3MB, time=93.58 memory used=5721.6MB, alloc=564.3MB, time=95.04 memory used=5841.8MB, alloc=564.3MB, time=95.62 memory used=6021.3MB, alloc=564.3MB, time=124.38 memory used=6139.3MB, alloc=564.3MB, time=124.94 memory used=6231.8MB, alloc=564.3MB, time=125.40 memory used=6336.7MB, alloc=564.3MB, time=125.87 memory used=6464.5MB, alloc=564.3MB, time=126.38 memory used=6672.9MB, alloc=564.3MB, time=127.04 memory used=6820.6MB, alloc=564.3MB, time=127.59 memory used=6986.6MB, alloc=564.3MB, time=128.16 memory used=7172.1MB, alloc=564.3MB, time=128.74 memory used=7380.1MB, alloc=564.3MB, time=129.36 memory used=7609.3MB, alloc=564.3MB, time=129.97 memory used=7789.9MB, alloc=564.3MB, time=130.55 memory used=7972.7MB, alloc=564.3MB, time=131.12 memory used=8173.5MB, alloc=564.3MB, time=131.70 memory used=8395.9MB, alloc=564.3MB, time=132.30 memory used=8616.6MB, alloc=564.3MB, time=132.93 memory used=8729.8MB, alloc=564.3MB, time=134.89 memory used=8790.7MB, alloc=564.3MB, time=136.22 memory used=8867.0MB, alloc=564.3MB, time=137.82 memory used=8944.8MB, alloc=564.3MB, time=139.44 memory used=9016.1MB, alloc=564.3MB, time=140.68 memory used=9119.1MB, alloc=564.3MB, time=144.03 memory used=9204.4MB, alloc=564.3MB, time=146.57 memory used=9285.5MB, alloc=564.3MB, time=149.04 memory used=9374.2MB, alloc=588.3MB, time=151.41 memory used=9466.0MB, alloc=588.3MB, time=152.40 memory used=9518.8MB, alloc=588.3MB, time=153.29 memory used=9569.5MB, alloc=588.3MB, time=154.37 memory used=9655.7MB, alloc=588.3MB, time=155.78 memory used=9788.7MB, alloc=588.3MB, time=159.76 memory used=9909.0MB, alloc=588.3MB, time=160.86 memory used=10135.2MB, alloc=612.3MB, time=164.25 memory used=10280.2MB, alloc=612.3MB, time=165.44 memory used=10403.0MB, alloc=612.3MB, time=166.06 memory used=10622.7MB, alloc=612.3MB, time=167.12 memory used=10753.0MB, alloc=612.3MB, time=167.73 memory used=11146.4MB, alloc=612.3MB, time=171.69 memory used=11264.8MB, alloc=612.3MB, time=172.29 memory used=11491.9MB, alloc=612.3MB, time=173.05 memory used=11660.0MB, alloc=612.3MB, time=173.72 memory used=11873.0MB, alloc=612.3MB, time=174.74 memory used=12007.3MB, alloc=612.3MB, time=175.43 memory used=12132.2MB, alloc=612.3MB, time=176.15 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428298410 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 3 F := [-5 x + 11 x y, 15 y z + 11 x - 15, 4 x y z + 5 y + 12 z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 2 2 2 G := [13 x y z - 4 y z + 12 x y z, 10 x y - 3 x z - 7 y z, 2 2 -16 x y z - 5 x y z + 14 y ] > Problem := [F,G]; 2 3 2 3 Problem := [[-5 x + 11 x y, 15 y z + 11 x - 15, 4 x y z + 5 y + 12 z], [ 2 3 2 2 2 2 2 13 x y z - 4 y z + 12 x y z, 10 x y - 3 x z - 7 y z, 2 2 -16 x y z - 5 x y z + 14 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.17 memory used=26.4MB, alloc=32.3MB, time=0.47 memory used=47.1MB, alloc=32.3MB, time=0.77 memory used=66.3MB, alloc=56.3MB, time=1.07 memory used=105.5MB, alloc=60.3MB, time=1.64 memory used=144.3MB, alloc=60.3MB, time=2.16 memory used=186.5MB, alloc=68.3MB, time=2.66 memory used=225.9MB, alloc=92.3MB, time=3.12 memory used=291.9MB, alloc=92.3MB, time=4.05 memory used=359.0MB, alloc=92.3MB, time=4.91 memory used=424.4MB, alloc=116.3MB, time=5.81 memory used=492.2MB, alloc=116.3MB, time=6.35 memory used=536.9MB, alloc=116.3MB, time=6.50 memory used=573.6MB, alloc=116.3MB, time=6.63 memory used=626.2MB, alloc=116.3MB, time=6.86 memory used=669.4MB, alloc=116.3MB, time=7.00 memory used=718.4MB, alloc=116.3MB, time=9.37 memory used=767.8MB, alloc=116.3MB, time=9.62 memory used=806.2MB, alloc=116.3MB, time=9.75 memory used=848.5MB, alloc=116.3MB, time=9.88 memory used=919.4MB, alloc=116.3MB, time=10.56 memory used=1018.0MB, alloc=118.5MB, time=11.90 memory used=1106.7MB, alloc=118.5MB, time=14.12 memory used=1186.3MB, alloc=374.5MB, time=15.32 memory used=1286.9MB, alloc=374.5MB, time=16.44 memory used=1366.2MB, alloc=398.5MB, time=17.66 memory used=1467.2MB, alloc=422.5MB, time=19.28 memory used=1596.2MB, alloc=446.5MB, time=21.26 memory used=1718.2MB, alloc=446.5MB, time=22.96 memory used=1846.4MB, alloc=446.5MB, time=24.76 memory used=1964.8MB, alloc=470.5MB, time=26.41 memory used=2057.6MB, alloc=470.5MB, time=27.85 memory used=2151.3MB, alloc=470.5MB, time=29.32 memory used=2230.7MB, alloc=470.5MB, time=30.64 memory used=2332.9MB, alloc=494.5MB, time=32.13 memory used=2421.5MB, alloc=494.5MB, time=33.55 memory used=2491.3MB, alloc=494.5MB, time=34.51 memory used=2597.1MB, alloc=494.5MB, time=37.01 memory used=2711.4MB, alloc=494.5MB, time=39.13 memory used=2795.1MB, alloc=494.5MB, time=40.38 memory used=2866.6MB, alloc=494.5MB, time=41.33 memory used=2929.7MB, alloc=494.5MB, time=42.17 memory used=2994.8MB, alloc=494.5MB, time=43.46 memory used=3054.8MB, alloc=518.5MB, time=44.63 memory used=3109.3MB, alloc=518.5MB, time=45.75 memory used=3163.1MB, alloc=518.5MB, time=46.86 memory used=3267.6MB, alloc=518.5MB, time=47.83 memory used=3387.7MB, alloc=518.5MB, time=48.58 memory used=3510.5MB, alloc=518.5MB, time=49.35 memory used=3595.9MB, alloc=518.5MB, time=49.84 memory used=3716.3MB, alloc=518.5MB, time=50.51 memory used=3807.2MB, alloc=518.5MB, time=51.01 memory used=3937.1MB, alloc=518.5MB, time=55.20 memory used=4034.0MB, alloc=518.5MB, time=55.70 memory used=4125.2MB, alloc=518.5MB, time=56.28 memory used=4235.2MB, alloc=518.5MB, time=57.02 memory used=4356.5MB, alloc=518.5MB, time=58.69 memory used=4474.8MB, alloc=518.5MB, time=59.70 memory used=4589.9MB, alloc=518.5MB, time=65.77 memory used=4704.5MB, alloc=518.5MB, time=69.84 memory used=4800.3MB, alloc=518.5MB, time=70.34 memory used=4887.6MB, alloc=518.5MB, time=70.80 memory used=4997.7MB, alloc=518.5MB, time=71.41 memory used=5114.8MB, alloc=518.5MB, time=72.15 memory used=5297.4MB, alloc=518.5MB, time=81.92 memory used=5404.0MB, alloc=518.5MB, time=82.63 memory used=5496.0MB, alloc=518.5MB, time=83.09 memory used=5613.7MB, alloc=518.5MB, time=84.02 memory used=5697.5MB, alloc=518.5MB, time=85.10 memory used=5781.1MB, alloc=518.5MB, time=86.91 memory used=5821.9MB, alloc=518.5MB, time=87.98 memory used=6070.5MB, alloc=518.5MB, time=91.66 memory used=6291.1MB, alloc=518.5MB, time=94.79 memory used=6493.2MB, alloc=542.5MB, time=96.76 memory used=6741.3MB, alloc=542.5MB, time=101.14 memory used=6957.4MB, alloc=566.5MB, time=104.49 memory used=7189.1MB, alloc=590.5MB, time=106.92 memory used=7343.4MB, alloc=590.5MB, time=108.14 memory used=7489.5MB, alloc=590.5MB, time=109.19 memory used=7614.8MB, alloc=590.5MB, time=109.93 memory used=7738.7MB, alloc=590.5MB, time=110.59 memory used=7894.9MB, alloc=590.5MB, time=111.64 memory used=8018.7MB, alloc=590.5MB, time=112.32 memory used=8144.6MB, alloc=590.5MB, time=112.96 memory used=8328.9MB, alloc=590.5MB, time=123.85 memory used=8446.4MB, alloc=590.5MB, time=124.52 memory used=8564.5MB, alloc=590.5MB, time=125.19 memory used=8696.3MB, alloc=590.5MB, time=125.96 memory used=8845.3MB, alloc=590.5MB, time=126.84 memory used=9004.0MB, alloc=590.5MB, time=130.41 memory used=9134.7MB, alloc=590.5MB, time=131.13 memory used=9298.4MB, alloc=590.5MB, time=132.88 memory used=9443.1MB, alloc=590.5MB, time=133.71 memory used=9587.5MB, alloc=590.5MB, time=134.56 memory used=9773.8MB, alloc=590.5MB, time=196.04 memory used=9946.8MB, alloc=590.5MB, time=198.02 memory used=10056.9MB, alloc=590.5MB, time=198.69 memory used=10185.7MB, alloc=590.5MB, time=199.39 memory used=10323.0MB, alloc=590.5MB, time=200.04 memory used=10413.9MB, alloc=590.5MB, time=200.65 memory used=10514.2MB, alloc=590.5MB, time=201.28 memory used=10624.9MB, alloc=590.5MB, time=201.85 memory used=10748.0MB, alloc=590.5MB, time=202.42 memory used=10885.5MB, alloc=590.5MB, time=203.00 memory used=11163.2MB, alloc=590.5MB, time=203.87 memory used=11334.4MB, alloc=590.5MB, time=205.13 memory used=11465.7MB, alloc=590.5MB, time=205.82 memory used=11572.9MB, alloc=590.5MB, time=206.46 memory used=11734.8MB, alloc=590.5MB, time=207.63 memory used=11870.2MB, alloc=590.5MB, time=208.35 memory used=11977.4MB, alloc=590.5MB, time=209.00 memory used=12122.2MB, alloc=590.5MB, time=214.83 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428298711 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 2 3 3 F := [6 x z + 19 x y - 13 y z, 5 x z - 20 x + 3 x, -9 x + 19 y - 11 x] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 3 2 G := [-2 x y z + 3 x , -17 x y z + 14 x + 11 x z, -7 y z + 18 x y z + 14 x ] > Problem := [F,G]; Problem := [ 3 2 2 2 2 2 3 3 [6 x z + 19 x y - 13 y z, 5 x z - 20 x + 3 x, -9 x + 19 y - 11 x], 2 2 3 3 2 [-2 x y z + 3 x , -17 x y z + 14 x + 11 x z, -7 y z + 18 x y z + 14 x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.18 memory used=26.3MB, alloc=32.3MB, time=0.50 memory used=45.8MB, alloc=56.3MB, time=0.81 memory used=87.5MB, alloc=60.3MB, time=1.43 memory used=130.5MB, alloc=68.3MB, time=2.04 memory used=172.5MB, alloc=92.3MB, time=2.63 memory used=238.9MB, alloc=92.3MB, time=3.52 memory used=305.1MB, alloc=92.3MB, time=4.44 memory used=369.2MB, alloc=116.3MB, time=5.37 memory used=435.7MB, alloc=372.3MB, time=6.22 memory used=526.1MB, alloc=372.3MB, time=7.37 memory used=608.5MB, alloc=396.3MB, time=8.53 memory used=694.9MB, alloc=396.3MB, time=9.29 memory used=782.0MB, alloc=396.3MB, time=10.16 memory used=888.7MB, alloc=396.3MB, time=11.76 memory used=999.7MB, alloc=420.3MB, time=13.34 memory used=1117.2MB, alloc=420.3MB, time=14.64 memory used=1203.5MB, alloc=420.3MB, time=15.26 memory used=1326.3MB, alloc=420.3MB, time=16.90 memory used=1444.7MB, alloc=444.3MB, time=18.06 memory used=1556.6MB, alloc=444.3MB, time=19.86 memory used=1659.8MB, alloc=444.3MB, time=21.39 memory used=1777.9MB, alloc=468.3MB, time=22.54 memory used=1854.0MB, alloc=468.3MB, time=22.87 memory used=1946.1MB, alloc=468.3MB, time=23.29 memory used=2032.2MB, alloc=468.3MB, time=23.67 memory used=2112.1MB, alloc=468.3MB, time=24.01 memory used=2213.6MB, alloc=468.3MB, time=25.37 memory used=2296.7MB, alloc=468.3MB, time=25.71 memory used=2364.4MB, alloc=468.3MB, time=25.98 memory used=2506.9MB, alloc=468.3MB, time=27.71 memory used=2613.2MB, alloc=468.3MB, time=29.26 memory used=2723.0MB, alloc=468.3MB, time=30.46 memory used=2837.8MB, alloc=492.3MB, time=32.34 memory used=2947.1MB, alloc=492.3MB, time=34.30 memory used=3042.7MB, alloc=492.3MB, time=36.14 memory used=3114.6MB, alloc=492.3MB, time=37.33 memory used=3185.6MB, alloc=492.3MB, time=38.36 memory used=3248.6MB, alloc=516.3MB, time=39.39 memory used=3319.2MB, alloc=516.3MB, time=40.87 memory used=3374.7MB, alloc=516.3MB, time=41.89 memory used=3431.2MB, alloc=516.3MB, time=42.84 memory used=3625.5MB, alloc=540.3MB, time=45.87 memory used=3831.8MB, alloc=564.3MB, time=48.97 memory used=4000.8MB, alloc=588.3MB, time=51.64 memory used=4189.2MB, alloc=612.3MB, time=54.72 memory used=4333.7MB, alloc=636.3MB, time=56.90 memory used=4473.6MB, alloc=636.3MB, time=58.86 memory used=4623.6MB, alloc=660.3MB, time=61.86 memory used=4781.6MB, alloc=660.3MB, time=64.85 memory used=4927.3MB, alloc=660.3MB, time=67.38 memory used=5070.4MB, alloc=660.3MB, time=69.68 memory used=5195.5MB, alloc=684.3MB, time=71.67 memory used=5335.2MB, alloc=684.3MB, time=74.40 memory used=5413.0MB, alloc=684.3MB, time=76.34 memory used=5770.8MB, alloc=708.3MB, time=82.00 memory used=6118.3MB, alloc=732.3MB, time=88.14 memory used=6458.1MB, alloc=756.3MB, time=93.70 memory used=6844.1MB, alloc=780.3MB, time=99.09 memory used=7074.1MB, alloc=804.3MB, time=101.97 memory used=7358.7MB, alloc=828.3MB, time=106.74 memory used=7694.4MB, alloc=852.3MB, time=112.41 memory used=7963.2MB, alloc=876.3MB, time=116.46 memory used=8267.9MB, alloc=900.3MB, time=121.63 memory used=8531.9MB, alloc=924.3MB, time=126.18 memory used=8898.3MB, alloc=948.3MB, time=131.45 memory used=9146.0MB, alloc=972.3MB, time=136.05 memory used=9399.9MB, alloc=996.3MB, time=141.08 memory used=9618.2MB, alloc=1020.3MB, time=146.57 memory used=9787.5MB, alloc=1020.3MB, time=150.74 memory used=10418.1MB, alloc=1044.3MB, time=163.53 memory used=10889.1MB, alloc=1068.3MB, time=171.03 memory used=11169.2MB, alloc=1092.3MB, time=173.72 memory used=11526.5MB, alloc=1116.3MB, time=177.80 memory used=11867.9MB, alloc=1140.3MB, time=180.76 memory used=12221.7MB, alloc=1140.3MB, time=184.10 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428299011 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 4 3 3 2 F := [-15 x y z + 12 z + 14 y z, -5 x y + 5 y z - 7 x , 3 2 2 13 x y - 18 x z + 11 x z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 3 G := [8 x y z - 7 x z + 15 x, -2 x y + 17 y z + 13, 3 2 3 -x z + 12 x y z + 12 x z ] > Problem := [F,G]; 2 4 3 3 2 Problem := [[-15 x y z + 12 z + 14 y z, -5 x y + 5 y z - 7 x , 3 2 2 2 13 x y - 18 x z + 11 x z ], [8 x y z - 7 x z + 15 x, 3 3 3 2 3 -2 x y + 17 y z + 13, -x z + 12 x y z + 12 x z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.17 memory used=25.3MB, alloc=32.3MB, time=0.47 memory used=45.5MB, alloc=32.3MB, time=0.73 memory used=65.6MB, alloc=32.3MB, time=1.54 memory used=76.3MB, alloc=32.3MB, time=1.57 memory used=96.4MB, alloc=56.3MB, time=2.43 memory used=138.1MB, alloc=60.3MB, time=2.79 memory used=182.5MB, alloc=60.3MB, time=3.37 memory used=226.5MB, alloc=68.3MB, time=3.88 memory used=256.7MB, alloc=68.3MB, time=4.09 memory used=289.9MB, alloc=68.3MB, time=5.31 memory used=318.4MB, alloc=68.3MB, time=7.10 memory used=338.2MB, alloc=68.3MB, time=7.17 memory used=360.3MB, alloc=68.3MB, time=7.24 memory used=386.4MB, alloc=68.3MB, time=7.44 memory used=408.0MB, alloc=68.3MB, time=7.55 memory used=429.6MB, alloc=68.3MB, time=7.65 memory used=447.9MB, alloc=81.9MB, time=7.79 memory used=473.6MB, alloc=81.9MB, time=7.87 memory used=496.5MB, alloc=81.9MB, time=7.95 memory used=519.5MB, alloc=83.8MB, time=8.03 memory used=543.9MB, alloc=83.8MB, time=8.11 memory used=566.8MB, alloc=83.8MB, time=8.18 memory used=597.0MB, alloc=83.8MB, time=8.52 memory used=647.8MB, alloc=83.8MB, time=9.16 memory used=695.0MB, alloc=107.8MB, time=9.71 memory used=766.1MB, alloc=107.8MB, time=10.64 memory used=823.1MB, alloc=107.8MB, time=11.49 memory used=886.7MB, alloc=131.8MB, time=12.56 memory used=967.2MB, alloc=387.8MB, time=13.71 memory used=1060.8MB, alloc=411.8MB, time=14.71 memory used=1169.5MB, alloc=435.8MB, time=16.26 memory used=1298.4MB, alloc=435.8MB, time=17.98 memory used=1376.5MB, alloc=435.8MB, time=19.74 memory used=1436.5MB, alloc=435.8MB, time=20.06 memory used=1516.1MB, alloc=435.8MB, time=20.38 memory used=1594.7MB, alloc=435.8MB, time=20.64 memory used=1672.9MB, alloc=435.8MB, time=22.11 memory used=1748.3MB, alloc=435.8MB, time=22.83 memory used=1823.0MB, alloc=435.8MB, time=24.40 memory used=1895.3MB, alloc=435.8MB, time=24.86 memory used=1961.0MB, alloc=435.8MB, time=25.10 memory used=2030.2MB, alloc=435.8MB, time=25.44 memory used=2105.8MB, alloc=435.8MB, time=27.34 memory used=2175.0MB, alloc=435.8MB, time=27.69 memory used=2241.7MB, alloc=435.8MB, time=27.92 memory used=2308.7MB, alloc=435.8MB, time=28.36 memory used=2365.8MB, alloc=435.8MB, time=28.65 memory used=2466.2MB, alloc=435.8MB, time=29.57 memory used=2599.2MB, alloc=459.8MB, time=30.87 memory used=2689.9MB, alloc=459.8MB, time=31.42 memory used=2832.5MB, alloc=459.8MB, time=32.65 memory used=2923.6MB, alloc=459.8MB, time=34.37 memory used=3017.8MB, alloc=459.8MB, time=36.17 memory used=3158.5MB, alloc=483.8MB, time=37.88 memory used=3320.7MB, alloc=483.8MB, time=40.15 memory used=3448.9MB, alloc=483.8MB, time=41.27 memory used=3548.5MB, alloc=507.8MB, time=46.63 memory used=3657.8MB, alloc=507.8MB, time=47.62 memory used=3741.7MB, alloc=507.8MB, time=47.90 memory used=3859.5MB, alloc=507.8MB, time=48.82 memory used=3957.4MB, alloc=507.8MB, time=49.37 memory used=4058.1MB, alloc=507.8MB, time=49.80 memory used=4216.4MB, alloc=507.8MB, time=50.40 memory used=4436.7MB, alloc=507.8MB, time=50.94 memory used=4609.2MB, alloc=507.8MB, time=51.57 memory used=4723.2MB, alloc=507.8MB, time=56.26 memory used=4834.3MB, alloc=507.8MB, time=57.81 memory used=4919.6MB, alloc=507.8MB, time=58.10 memory used=5024.3MB, alloc=507.8MB, time=58.72 memory used=5117.3MB, alloc=507.8MB, time=59.15 memory used=5307.9MB, alloc=507.8MB, time=59.82 memory used=5527.7MB, alloc=507.8MB, time=61.01 memory used=5647.4MB, alloc=507.8MB, time=62.51 memory used=5770.3MB, alloc=507.8MB, time=64.55 memory used=5862.4MB, alloc=531.8MB, time=65.88 memory used=5962.8MB, alloc=531.8MB, time=67.44 memory used=6069.2MB, alloc=531.8MB, time=69.49 memory used=6158.7MB, alloc=531.8MB, time=71.09 memory used=6273.8MB, alloc=555.8MB, time=72.76 memory used=6411.9MB, alloc=555.8MB, time=75.36 memory used=6515.5MB, alloc=555.8MB, time=76.71 memory used=6614.0MB, alloc=555.8MB, time=78.65 memory used=6701.1MB, alloc=555.8MB, time=79.62 memory used=6813.7MB, alloc=555.8MB, time=81.43 memory used=6904.9MB, alloc=555.8MB, time=82.46 memory used=7017.1MB, alloc=555.8MB, time=84.52 memory used=7112.9MB, alloc=555.8MB, time=85.91 memory used=7187.4MB, alloc=555.8MB, time=86.85 memory used=7267.3MB, alloc=555.8MB, time=88.01 memory used=7367.5MB, alloc=555.8MB, time=89.81 memory used=7439.1MB, alloc=555.8MB, time=90.76 memory used=7519.2MB, alloc=555.8MB, time=92.23 memory used=7646.9MB, alloc=579.8MB, time=94.66 memory used=7767.1MB, alloc=579.8MB, time=96.05 memory used=7818.9MB, alloc=579.8MB, time=96.95 memory used=7905.0MB, alloc=603.8MB, time=99.04 memory used=7947.9MB, alloc=603.8MB, time=99.92 memory used=8061.4MB, alloc=603.8MB, time=101.04 memory used=8180.3MB, alloc=603.8MB, time=102.36 memory used=8304.9MB, alloc=603.8MB, time=102.95 memory used=8460.2MB, alloc=603.8MB, time=103.73 memory used=8588.6MB, alloc=603.8MB, time=104.29 memory used=8752.1MB, alloc=603.8MB, time=115.55 memory used=8871.3MB, alloc=603.8MB, time=116.10 memory used=8993.5MB, alloc=603.8MB, time=116.61 memory used=9271.7MB, alloc=603.8MB, time=117.45 memory used=9460.5MB, alloc=603.8MB, time=118.03 memory used=9525.4MB, alloc=603.8MB, time=119.33 memory used=9645.6MB, alloc=603.8MB, time=120.41 memory used=9697.9MB, alloc=603.8MB, time=121.37 memory used=9946.7MB, alloc=603.8MB, time=125.05 memory used=10139.7MB, alloc=603.8MB, time=127.17 memory used=10335.5MB, alloc=603.8MB, time=128.83 memory used=10564.8MB, alloc=627.8MB, time=131.95 memory used=10759.5MB, alloc=651.8MB, time=134.77 memory used=10962.5MB, alloc=675.8MB, time=138.33 memory used=11209.8MB, alloc=675.8MB, time=143.05 memory used=11429.4MB, alloc=675.8MB, time=145.79 memory used=11656.7MB, alloc=699.8MB, time=148.62 memory used=11836.3MB, alloc=699.8MB, time=151.34 memory used=11950.5MB, alloc=699.8MB, time=153.51 memory used=12111.1MB, alloc=723.8MB, time=156.21 memory used=12270.5MB, alloc=723.8MB, time=159.57 memory used=12433.9MB, alloc=747.8MB, time=162.16 memory used=12601.4MB, alloc=747.8MB, time=165.36 memory used=12742.5MB, alloc=747.8MB, time=170.05 memory used=12853.0MB, alloc=747.8MB, time=172.01 memory used=12997.3MB, alloc=771.8MB, time=173.88 memory used=13130.5MB, alloc=795.8MB, time=175.65 memory used=13257.2MB, alloc=795.8MB, time=177.96 memory used=13364.6MB, alloc=795.8MB, time=180.30 memory used=13753.1MB, alloc=819.8MB, time=187.09 memory used=14152.8MB, alloc=843.8MB, time=192.45 memory used=14376.5MB, alloc=867.8MB, time=194.57 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428299311 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 4 3 3 2 2 F := [11 x y - 2 z + 16 x, -17 x - 6 x z , -5 x y + 16 y z - 17 y] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 4 G := [3 x y + 3 x z + 5 y , 6 x y - 20 x y, 2 y + 18 x y z + 11] > Problem := [F,G]; Problem := [ 3 3 4 3 3 2 2 [11 x y - 2 z + 16 x, -17 x - 6 x z , -5 x y + 16 y z - 17 y], 2 2 2 2 4 [3 x y + 3 x z + 5 y , 6 x y - 20 x y, 2 y + 18 x y z + 11]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=25.5MB, alloc=32.3MB, time=0.48 memory used=45.5MB, alloc=36.3MB, time=0.71 memory used=64.2MB, alloc=60.3MB, time=0.99 memory used=114.7MB, alloc=72.5MB, time=1.64 memory used=153.2MB, alloc=72.5MB, time=1.75 memory used=182.4MB, alloc=72.5MB, time=1.84 memory used=203.8MB, alloc=72.5MB, time=1.91 memory used=227.4MB, alloc=72.5MB, time=2.00 memory used=254.4MB, alloc=72.5MB, time=2.09 memory used=284.1MB, alloc=72.5MB, time=2.18 memory used=314.7MB, alloc=72.5MB, time=2.25 memory used=340.0MB, alloc=72.5MB, time=2.33 memory used=359.6MB, alloc=72.5MB, time=2.40 memory used=380.9MB, alloc=72.5MB, time=2.47 memory used=404.2MB, alloc=72.5MB, time=2.55 memory used=442.0MB, alloc=72.5MB, time=2.91 memory used=482.9MB, alloc=72.5MB, time=3.03 memory used=515.9MB, alloc=72.5MB, time=3.14 memory used=537.1MB, alloc=72.5MB, time=3.22 memory used=560.6MB, alloc=72.5MB, time=3.31 memory used=587.4MB, alloc=72.5MB, time=3.41 memory used=617.4MB, alloc=72.5MB, time=3.50 memory used=649.6MB, alloc=72.5MB, time=3.59 memory used=675.3MB, alloc=72.5MB, time=3.71 memory used=695.5MB, alloc=72.5MB, time=3.78 memory used=716.6MB, alloc=72.5MB, time=3.85 memory used=740.0MB, alloc=72.5MB, time=3.93 memory used=780.2MB, alloc=72.5MB, time=6.74 memory used=819.5MB, alloc=72.5MB, time=6.97 memory used=844.3MB, alloc=72.5MB, time=7.04 memory used=876.1MB, alloc=72.5MB, time=7.13 memory used=899.6MB, alloc=72.5MB, time=7.21 memory used=921.5MB, alloc=72.5MB, time=7.28 memory used=946.0MB, alloc=72.5MB, time=7.35 memory used=974.2MB, alloc=72.5MB, time=7.42 memory used=1015.7MB, alloc=72.5MB, time=7.95 memory used=1074.0MB, alloc=72.5MB, time=8.88 memory used=1104.1MB, alloc=72.5MB, time=9.09 memory used=1147.1MB, alloc=72.5MB, time=9.59 memory used=1189.2MB, alloc=72.5MB, time=10.08 memory used=1232.3MB, alloc=72.5MB, time=10.56 memory used=1277.2MB, alloc=96.5MB, time=11.10 memory used=1339.9MB, alloc=96.5MB, time=11.93 memory used=1406.7MB, alloc=96.5MB, time=12.58 memory used=1451.1MB, alloc=96.5MB, time=12.78 memory used=1496.6MB, alloc=96.5MB, time=13.15 memory used=1529.9MB, alloc=96.5MB, time=13.28 memory used=1575.4MB, alloc=96.5MB, time=13.54 memory used=1626.8MB, alloc=96.5MB, time=14.08 memory used=1661.5MB, alloc=96.5MB, time=14.20 memory used=1693.2MB, alloc=96.5MB, time=14.31 memory used=1730.5MB, alloc=96.5MB, time=14.55 memory used=1786.5MB, alloc=96.5MB, time=15.30 memory used=1834.3MB, alloc=96.5MB, time=15.47 memory used=1875.4MB, alloc=96.5MB, time=15.62 memory used=1900.4MB, alloc=96.5MB, time=15.73 memory used=1926.4MB, alloc=96.5MB, time=15.84 memory used=1954.9MB, alloc=96.5MB, time=15.97 memory used=1984.8MB, alloc=96.5MB, time=16.10 memory used=2017.5MB, alloc=96.5MB, time=16.22 memory used=2052.8MB, alloc=96.5MB, time=16.34 memory used=2089.3MB, alloc=96.5MB, time=16.48 memory used=2128.5MB, alloc=96.5MB, time=16.60 memory used=2163.3MB, alloc=96.5MB, time=16.73 memory used=2189.5MB, alloc=96.5MB, time=16.83 memory used=2211.1MB, alloc=96.5MB, time=16.94 memory used=2233.7MB, alloc=120.5MB, time=17.05 memory used=2271.0MB, alloc=120.5MB, time=17.18 memory used=2311.3MB, alloc=120.5MB, time=17.32 memory used=2353.3MB, alloc=120.5MB, time=17.46 memory used=2398.6MB, alloc=120.5MB, time=17.61 memory used=2446.6MB, alloc=120.5MB, time=17.76 memory used=2497.0MB, alloc=120.5MB, time=17.91 memory used=2552.0MB, alloc=120.5MB, time=18.06 memory used=2611.5MB, alloc=120.5MB, time=18.19 memory used=2658.4MB, alloc=120.5MB, time=18.31 memory used=2695.6MB, alloc=120.5MB, time=18.40 memory used=2768.4MB, alloc=121.4MB, time=19.16 memory used=2840.7MB, alloc=121.4MB, time=19.38 memory used=2882.6MB, alloc=121.4MB, time=19.54 memory used=2925.9MB, alloc=121.4MB, time=19.71 memory used=2975.3MB, alloc=121.4MB, time=19.87 memory used=3029.8MB, alloc=121.4MB, time=20.03 memory used=3091.9MB, alloc=121.4MB, time=20.20 memory used=3148.0MB, alloc=121.4MB, time=20.35 memory used=3183.8MB, alloc=121.4MB, time=20.48 memory used=3221.1MB, alloc=121.4MB, time=20.61 memory used=3259.5MB, alloc=121.4MB, time=20.74 memory used=3299.9MB, alloc=121.4MB, time=20.86 memory used=3343.6MB, alloc=121.4MB, time=21.01 memory used=3388.9MB, alloc=121.4MB, time=21.15 memory used=3438.0MB, alloc=121.4MB, time=21.29 memory used=3489.6MB, alloc=121.4MB, time=21.44 memory used=3545.3MB, alloc=121.4MB, time=21.56 memory used=3605.1MB, alloc=121.4MB, time=21.70 memory used=3644.4MB, alloc=121.4MB, time=21.81 memory used=3686.6MB, alloc=121.4MB, time=22.17 memory used=3783.0MB, alloc=121.4MB, time=35.06 memory used=3829.9MB, alloc=121.4MB, time=35.22 memory used=3887.9MB, alloc=121.4MB, time=35.37 memory used=3934.2MB, alloc=121.4MB, time=35.52 memory used=3973.6MB, alloc=121.4MB, time=35.67 memory used=4018.3MB, alloc=121.4MB, time=35.82 memory used=4068.3MB, alloc=121.4MB, time=35.95 memory used=4123.8MB, alloc=121.4MB, time=36.09 memory used=4181.1MB, alloc=121.4MB, time=36.24 memory used=4229.0MB, alloc=121.4MB, time=36.36 memory used=4265.6MB, alloc=121.4MB, time=36.46 memory used=4304.0MB, alloc=121.4MB, time=36.56 memory used=4346.8MB, alloc=121.4MB, time=36.67 memory used=4407.4MB, alloc=121.4MB, time=36.94 memory used=4475.2MB, alloc=121.4MB, time=37.41 memory used=4523.9MB, alloc=121.4MB, time=37.56 memory used=4614.6MB, alloc=121.4MB, time=44.72 memory used=4665.4MB, alloc=121.4MB, time=44.89 memory used=4720.4MB, alloc=121.4MB, time=45.05 memory used=4770.1MB, alloc=121.4MB, time=45.19 memory used=4808.9MB, alloc=121.4MB, time=45.32 memory used=4852.4MB, alloc=121.4MB, time=45.45 memory used=4900.7MB, alloc=121.4MB, time=45.59 memory used=4955.3MB, alloc=121.4MB, time=45.73 memory used=5015.3MB, alloc=121.4MB, time=45.86 memory used=5060.9MB, alloc=121.4MB, time=45.98 memory used=5096.5MB, alloc=121.4MB, time=46.08 memory used=5134.6MB, alloc=121.4MB, time=46.18 memory used=5177.8MB, alloc=121.4MB, time=46.28 memory used=5253.2MB, alloc=121.4MB, time=47.31 memory used=5326.4MB, alloc=121.4MB, time=47.54 memory used=5373.2MB, alloc=121.4MB, time=47.70 memory used=5415.9MB, alloc=121.4MB, time=47.85 memory used=5463.8MB, alloc=121.4MB, time=48.00 memory used=5517.3MB, alloc=121.4MB, time=48.16 memory used=5577.6MB, alloc=121.4MB, time=48.32 memory used=5628.4MB, alloc=121.4MB, time=48.48 memory used=5664.0MB, alloc=121.4MB, time=48.60 memory used=5702.0MB, alloc=121.4MB, time=48.73 memory used=5742.1MB, alloc=121.4MB, time=48.86 memory used=5785.5MB, alloc=121.4MB, time=49.00 memory used=5833.8MB, alloc=121.4MB, time=49.14 memory used=5891.0MB, alloc=121.4MB, time=49.37 memory used=5954.9MB, alloc=121.4MB, time=85.34 memory used=6021.9MB, alloc=145.4MB, time=155.81 memory used=6065.9MB, alloc=155.8MB, time=178.84 memory used=6066.3MB, alloc=155.8MB, time=178.90 memory used=6066.3MB, alloc=411.8MB, time=178.96 memory used=6227.4MB, alloc=411.8MB, time=188.51 memory used=6277.7MB, alloc=411.8MB, time=188.64 memory used=6327.5MB, alloc=411.8MB, time=188.75 memory used=6379.4MB, alloc=411.8MB, time=188.88 memory used=6433.2MB, alloc=411.8MB, time=188.99 memory used=6486.7MB, alloc=411.8MB, time=189.12 memory used=6542.0MB, alloc=411.8MB, time=189.24 memory used=6599.0MB, alloc=411.8MB, time=189.36 memory used=6657.4MB, alloc=411.8MB, time=189.49 memory used=6717.2MB, alloc=411.8MB, time=189.61 memory used=6778.0MB, alloc=411.8MB, time=189.73 memory used=6841.8MB, alloc=411.8MB, time=189.87 memory used=6906.0MB, alloc=411.8MB, time=190.00 memory used=6972.4MB, alloc=411.8MB, time=190.13 memory used=7042.1MB, alloc=411.8MB, time=190.27 memory used=7112.8MB, alloc=411.8MB, time=190.40 memory used=7303.9MB, alloc=411.8MB, time=190.81 memory used=7462.6MB, alloc=411.8MB, time=191.07 memory used=7573.3MB, alloc=411.8MB, time=192.09 memory used=7643.0MB, alloc=411.8MB, time=192.30 memory used=7699.0MB, alloc=411.8MB, time=192.48 memory used=7765.7MB, alloc=411.8MB, time=192.68 memory used=7843.1MB, alloc=411.8MB, time=192.88 memory used=7908.3MB, alloc=411.8MB, time=193.05 memory used=7956.4MB, alloc=411.8MB, time=193.23 memory used=8009.2MB, alloc=411.8MB, time=193.41 memory used=8068.0MB, alloc=411.8MB, time=193.58 memory used=8134.2MB, alloc=411.8MB, time=193.72 memory used=8217.9MB, alloc=435.8MB, time=217.27 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428440545 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 3 2 2 F := [17 x y - x + 4 z, -2 x y - 9 x z + 6 x y z, -4 y z + 12 x - 7 y ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; G := [ 4 3 2 2 2 2 2 3 -18 x - 7 y + 9 y z, -5 x z + 17 y + 4 y z, 4 x y + 15 x z - 4 y z] > Problem := [F,G]; Problem := [ 3 2 2 2 2 3 2 2 [17 x y - x + 4 z, -2 x y - 9 x z + 6 x y z, -4 y z + 12 x - 7 y ], 4 3 2 2 2 2 2 3 [-18 x - 7 y + 9 y z, -5 x z + 17 y + 4 y z, 4 x y + 15 x z - 4 y z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.17 memory used=27.2MB, alloc=32.3MB, time=0.51 memory used=46.9MB, alloc=32.3MB, time=0.72 memory used=69.1MB, alloc=60.3MB, time=1.02 memory used=111.9MB, alloc=68.3MB, time=1.63 memory used=152.3MB, alloc=68.3MB, time=2.23 memory used=192.5MB, alloc=68.3MB, time=2.65 memory used=242.5MB, alloc=92.3MB, time=3.22 memory used=308.3MB, alloc=92.3MB, time=3.86 memory used=375.4MB, alloc=92.3MB, time=4.80 memory used=440.1MB, alloc=92.3MB, time=5.62 memory used=504.1MB, alloc=372.3MB, time=6.48 memory used=601.4MB, alloc=372.3MB, time=7.73 memory used=684.3MB, alloc=372.3MB, time=8.72 memory used=778.0MB, alloc=372.3MB, time=9.87 memory used=830.0MB, alloc=396.3MB, time=10.26 memory used=943.1MB, alloc=396.3MB, time=11.55 memory used=1065.6MB, alloc=396.3MB, time=12.85 memory used=1204.1MB, alloc=396.3MB, time=14.14 memory used=1328.6MB, alloc=396.3MB, time=15.53 memory used=1428.7MB, alloc=420.3MB, time=17.14 memory used=1534.8MB, alloc=444.3MB, time=18.72 memory used=1633.4MB, alloc=444.3MB, time=19.98 memory used=1758.4MB, alloc=444.3MB, time=21.20 memory used=1885.1MB, alloc=444.3MB, time=22.65 memory used=1986.6MB, alloc=468.3MB, time=23.86 memory used=2136.5MB, alloc=468.3MB, time=25.33 memory used=2268.1MB, alloc=468.3MB, time=26.72 memory used=2399.4MB, alloc=468.3MB, time=28.08 memory used=2486.9MB, alloc=492.3MB, time=29.54 memory used=2576.8MB, alloc=492.3MB, time=30.67 memory used=2656.8MB, alloc=492.3MB, time=31.61 memory used=2746.3MB, alloc=492.3MB, time=33.13 memory used=2803.6MB, alloc=492.3MB, time=34.10 memory used=2879.5MB, alloc=492.3MB, time=35.50 memory used=2930.9MB, alloc=492.3MB, time=36.45 memory used=2982.2MB, alloc=492.3MB, time=37.36 memory used=3048.8MB, alloc=492.3MB, time=38.36 memory used=3139.9MB, alloc=516.3MB, time=39.66 memory used=3188.9MB, alloc=516.3MB, time=40.69 memory used=3239.7MB, alloc=516.3MB, time=41.56 memory used=3303.2MB, alloc=516.3MB, time=42.66 memory used=3352.0MB, alloc=516.3MB, time=43.51 memory used=3567.1MB, alloc=540.3MB, time=46.27 memory used=3759.1MB, alloc=564.3MB, time=48.80 memory used=3988.3MB, alloc=588.3MB, time=51.00 memory used=4134.8MB, alloc=588.3MB, time=52.04 memory used=4325.5MB, alloc=588.3MB, time=53.81 memory used=4453.2MB, alloc=588.3MB, time=54.54 memory used=4585.0MB, alloc=588.3MB, time=55.27 memory used=4735.0MB, alloc=588.3MB, time=56.14 memory used=4866.8MB, alloc=588.3MB, time=56.91 memory used=5001.7MB, alloc=588.3MB, time=57.83 memory used=5151.3MB, alloc=588.3MB, time=58.80 memory used=5297.9MB, alloc=588.3MB, time=59.66 memory used=5429.7MB, alloc=588.3MB, time=60.36 memory used=5575.2MB, alloc=588.3MB, time=61.41 memory used=5711.5MB, alloc=588.3MB, time=62.16 memory used=5890.3MB, alloc=588.3MB, time=64.17 memory used=6011.5MB, alloc=588.3MB, time=64.80 memory used=6122.5MB, alloc=588.3MB, time=65.42 memory used=6262.7MB, alloc=588.3MB, time=66.24 memory used=6399.3MB, alloc=588.3MB, time=66.97 memory used=6577.6MB, alloc=588.3MB, time=68.86 memory used=6699.1MB, alloc=588.3MB, time=69.49 memory used=6811.5MB, alloc=588.3MB, time=70.05 memory used=7090.8MB, alloc=588.3MB, time=72.98 memory used=7291.9MB, alloc=588.3MB, time=75.60 memory used=7529.1MB, alloc=612.3MB, time=78.17 memory used=7726.0MB, alloc=612.3MB, time=80.76 memory used=7890.9MB, alloc=636.3MB, time=84.15 memory used=8032.0MB, alloc=636.3MB, time=86.52 memory used=8190.4MB, alloc=660.3MB, time=89.39 memory used=8342.2MB, alloc=660.3MB, time=91.81 memory used=8490.3MB, alloc=684.3MB, time=94.12 memory used=8695.4MB, alloc=684.3MB, time=96.28 memory used=8920.8MB, alloc=684.3MB, time=98.01 memory used=9141.5MB, alloc=684.3MB, time=99.94 memory used=9356.8MB, alloc=684.3MB, time=101.61 memory used=9492.1MB, alloc=684.3MB, time=103.66 memory used=9635.1MB, alloc=684.3MB, time=105.94 memory used=9779.5MB, alloc=684.3MB, time=107.83 memory used=9897.3MB, alloc=684.3MB, time=109.77 memory used=10032.0MB, alloc=684.3MB, time=111.71 memory used=10389.7MB, alloc=708.3MB, time=116.84 memory used=10673.1MB, alloc=732.3MB, time=119.50 memory used=10887.2MB, alloc=732.3MB, time=121.26 memory used=11295.3MB, alloc=756.3MB, time=127.21 memory used=11533.6MB, alloc=780.3MB, time=129.80 memory used=11750.4MB, alloc=804.3MB, time=131.69 memory used=11990.2MB, alloc=804.3MB, time=133.85 memory used=12220.6MB, alloc=804.3MB, time=135.92 memory used=12454.2MB, alloc=804.3MB, time=137.96 memory used=12912.6MB, alloc=828.3MB, time=142.79 memory used=13354.8MB, alloc=828.3MB, time=148.37 memory used=13581.1MB, alloc=828.3MB, time=157.29 memory used=13968.6MB, alloc=852.3MB, time=160.58 memory used=14538.2MB, alloc=876.3MB, time=166.35 memory used=15070.3MB, alloc=900.3MB, time=173.86 memory used=15365.6MB, alloc=924.3MB, time=178.91 memory used=15722.5MB, alloc=948.3MB, time=182.12 memory used=16043.2MB, alloc=948.3MB, time=184.50 memory used=16355.1MB, alloc=948.3MB, time=186.73 memory used=16599.1MB, alloc=948.3MB, time=188.40 memory used=16887.6MB, alloc=948.3MB, time=190.36 memory used=17190.9MB, alloc=948.3MB, time=192.66 memory used=17475.3MB, alloc=948.3MB, time=194.48 memory used=17719.0MB, alloc=948.3MB, time=196.12 memory used=18010.0MB, alloc=948.3MB, time=198.07 memory used=18317.1MB, alloc=948.3MB, time=200.39 memory used=18620.5MB, alloc=948.3MB, time=202.35 memory used=18904.0MB, alloc=948.3MB, time=204.15 memory used=19209.2MB, alloc=948.3MB, time=206.34 memory used=19488.2MB, alloc=948.3MB, time=208.18 memory used=19793.5MB, alloc=948.3MB, time=212.55 memory used=20125.4MB, alloc=948.3MB, time=215.20 memory used=20369.8MB, alloc=948.3MB, time=216.89 memory used=20613.4MB, alloc=948.3MB, time=218.49 memory used=21020.8MB, alloc=948.3MB, time=220.82 memory used=21294.3MB, alloc=948.3MB, time=222.81 memory used=21558.5MB, alloc=948.3MB, time=224.64 memory used=21922.1MB, alloc=948.3MB, time=229.78 memory used=22176.1MB, alloc=948.3MB, time=231.51 memory used=22408.7MB, alloc=948.3MB, time=233.10 memory used=22977.5MB, alloc=948.3MB, time=237.32 memory used=23437.0MB, alloc=948.3MB, time=243.47 memory used=23836.3MB, alloc=948.3MB, time=248.54 memory used=24374.5MB, alloc=972.3MB, time=254.48 memory used=24798.1MB, alloc=972.3MB, time=259.02 memory used=25359.8MB, alloc=996.3MB, time=264.67 memory used=25867.6MB, alloc=1020.3MB, time=270.46 memory used=26573.8MB, alloc=1044.3MB, time=276.15 memory used=27000.8MB, alloc=1044.3MB, time=281.95 memory used=27451.2MB, alloc=1044.3MB, time=285.73 memory used=27843.1MB, alloc=1068.3MB, time=290.60 memory used=28169.7MB, alloc=1324.3MB, time=295.54 memory used=28702.8MB, alloc=1324.3MB, time=302.39 memory used=29362.8MB, alloc=1348.3MB, time=307.18 memory used=30192.2MB, alloc=1372.3MB, time=314.87 memory used=30942.2MB, alloc=1396.3MB, time=328.24 memory used=31713.3MB, alloc=1420.3MB, time=341.86 memory used=32403.2MB, alloc=1444.3MB, time=352.21 memory used=32734.5MB, alloc=1468.3MB, time=355.88 memory used=33056.1MB, alloc=1492.3MB, time=359.24 memory used=33387.4MB, alloc=1516.3MB, time=362.58 memory used=33997.5MB, alloc=1540.3MB, time=369.91 memory used=34995.6MB, alloc=1564.3MB, time=381.97 memory used=35861.1MB, alloc=1588.3MB, time=392.31 memory used=36317.5MB, alloc=1612.3MB, time=397.29 memory used=37185.9MB, alloc=1636.3MB, time=409.92 memory used=37831.5MB, alloc=1660.3MB, time=417.93 memory used=38268.8MB, alloc=1684.3MB, time=421.56 memory used=38703.9MB, alloc=1684.3MB, time=425.33 memory used=39238.2MB, alloc=1684.3MB, time=430.57 memory used=39714.7MB, alloc=1684.3MB, time=434.58 memory used=40117.1MB, alloc=1684.3MB, time=438.04 memory used=40700.2MB, alloc=1699.8MB, time=442.62 memory used=40966.4MB, alloc=1699.8MB, time=445.64 memory used=41413.6MB, alloc=1699.8MB, time=449.30 memory used=42038.3MB, alloc=1699.8MB, time=452.88 memory used=42304.8MB, alloc=1699.8MB, time=455.80 memory used=42784.1MB, alloc=1699.8MB, time=459.82 memory used=43073.5MB, alloc=1699.8MB, time=463.18 memory used=44179.6MB, alloc=1723.8MB, time=475.16 memory used=44874.2MB, alloc=1747.8MB, time=489.50 memory used=45677.1MB, alloc=1771.8MB, time=497.83 memory used=46725.5MB, alloc=1771.8MB, time=508.81 memory used=47792.0MB, alloc=1795.8MB, time=521.69 memory used=48864.1MB, alloc=1795.8MB, time=534.39 memory used=49505.6MB, alloc=1819.8MB, time=547.56 memory used=50455.5MB, alloc=1843.8MB, time=560.86 memory used=50926.5MB, alloc=1843.8MB, time=565.06 memory used=51473.1MB, alloc=1843.8MB, time=569.64 memory used=51938.5MB, alloc=1843.8MB, time=573.78 memory used=52524.4MB, alloc=1843.8MB, time=580.82 memory used=53665.3MB, alloc=1867.8MB, time=595.38 memory used=54368.7MB, alloc=1867.8MB, time=606.24 memory used=54704.0MB, alloc=1867.8MB, time=610.83 memory used=54965.7MB, alloc=1867.8MB, time=615.58 memory used=55273.4MB, alloc=1867.8MB, time=620.08 memory used=55632.1MB, alloc=1867.8MB, time=624.38 memory used=55935.6MB, alloc=1867.8MB, time=628.64 memory used=56234.3MB, alloc=1867.8MB, time=632.90 memory used=56566.0MB, alloc=1867.8MB, time=637.04 memory used=56940.2MB, alloc=1867.8MB, time=641.29 memory used=57535.5MB, alloc=1867.8MB, time=646.14 memory used=58780.5MB, alloc=1891.8MB, time=658.45 memory used=60039.6MB, alloc=1915.8MB, time=675.71 memory used=60538.0MB, alloc=1939.8MB, time=687.10 memory used=61396.4MB, alloc=1963.8MB, time=698.67 memory used=61992.1MB, alloc=1987.8MB, time=709.89 memory used=63008.3MB, alloc=2011.8MB, time=724.13 memory used=63525.5MB, alloc=2035.8MB, time=735.60 memory used=63929.2MB, alloc=2035.8MB, time=745.72 memory used=64636.9MB, alloc=2035.8MB, time=753.17 memory used=64967.3MB, alloc=2035.8MB, time=758.72 memory used=65515.6MB, alloc=2035.8MB, time=764.15 memory used=66077.3MB, alloc=2035.8MB, time=769.74 memory used=66622.8MB, alloc=2035.8MB, time=775.53 memory used=67165.4MB, alloc=2035.8MB, time=781.87 memory used=67723.7MB, alloc=2035.8MB, time=787.87 memory used=68499.5MB, alloc=2035.8MB, time=794.03 memory used=68763.4MB, alloc=2035.8MB, time=798.88 memory used=69027.6MB, alloc=2035.8MB, time=803.74 memory used=69348.2MB, alloc=2035.8MB, time=808.52 memory used=70083.8MB, alloc=2035.8MB, time=815.68 memory used=70595.7MB, alloc=2035.8MB, time=821.07 memory used=71185.8MB, alloc=2059.8MB, time=827.17 memory used=71869.3MB, alloc=2059.8MB, time=832.38 memory used=72099.2MB, alloc=2059.8MB, time=837.16 memory used=72347.0MB, alloc=2059.8MB, time=841.90 memory used=72619.7MB, alloc=2059.8MB, time=846.92 memory used=72921.1MB, alloc=2059.8MB, time=851.93 memory used=73248.8MB, alloc=2059.8MB, time=856.93 memory used=73603.0MB, alloc=2059.8MB, time=861.74 memory used=73941.0MB, alloc=2059.8MB, time=866.52 memory used=74213.2MB, alloc=2059.8MB, time=871.28 memory used=74499.5MB, alloc=2059.8MB, time=875.99 memory used=74805.4MB, alloc=2059.8MB, time=881.07 memory used=75134.1MB, alloc=2059.8MB, time=885.88 memory used=75482.9MB, alloc=2059.8MB, time=891.17 memory used=75859.7MB, alloc=2059.8MB, time=895.94 memory used=76559.2MB, alloc=2059.8MB, time=902.13 memory used=77225.7MB, alloc=2059.8MB, time=907.43 memory used=77455.3MB, alloc=2059.8MB, time=912.25 memory used=77703.1MB, alloc=2059.8MB, time=917.25 memory used=77975.8MB, alloc=2059.8MB, time=922.08 memory used=78277.3MB, alloc=2059.8MB, time=926.92 memory used=78605.0MB, alloc=2059.8MB, time=931.75 memory used=78959.1MB, alloc=2059.8MB, time=936.57 memory used=79297.2MB, alloc=2059.8MB, time=941.67 memory used=79569.3MB, alloc=2059.8MB, time=946.57 memory used=79855.7MB, alloc=2059.8MB, time=951.43 memory used=80161.6MB, alloc=2059.8MB, time=956.09 memory used=80490.3MB, alloc=2059.8MB, time=960.87 memory used=80839.1MB, alloc=2059.8MB, time=965.70 memory used=81215.9MB, alloc=2059.8MB, time=970.57 memory used=82131.3MB, alloc=2059.8MB, time=980.73 memory used=82370.8MB, alloc=2059.8MB, time=985.56 memory used=82651.9MB, alloc=2059.8MB, time=990.30 memory used=82976.6MB, alloc=2059.8MB, time=995.04 memory used=83333.2MB, alloc=2059.8MB, time=999.74 memory used=83611.9MB, alloc=2059.8MB, time=1004.83 memory used=83916.6MB, alloc=2059.8MB, time=1010.06 memory used=84254.9MB, alloc=2059.8MB, time=1014.84 memory used=84628.4MB, alloc=2059.8MB, time=1019.41 memory used=84944.8MB, alloc=2059.8MB, time=1024.17 memory used=85669.5MB, alloc=2059.8MB, time=1030.50 memory used=86336.2MB, alloc=2059.8MB, time=1035.65 memory used=86565.9MB, alloc=2059.8MB, time=1040.19 memory used=86813.7MB, alloc=2059.8MB, time=1045.83 memory used=87086.4MB, alloc=2059.8MB, time=1050.67 memory used=87387.8MB, alloc=2059.8MB, time=1055.39 memory used=87715.5MB, alloc=2059.8MB, time=1060.10 memory used=88069.7MB, alloc=2059.8MB, time=1064.86 memory used=88407.7MB, alloc=2059.8MB, time=1069.56 memory used=88679.9MB, alloc=2059.8MB, time=1074.08 memory used=88966.2MB, alloc=2059.8MB, time=1078.71 memory used=89272.1MB, alloc=2059.8MB, time=1083.53 memory used=89600.8MB, alloc=2059.8MB, time=1088.15 memory used=89949.6MB, alloc=2059.8MB, time=1092.89 memory used=90326.3MB, alloc=2059.8MB, time=1097.60 memory used=91043.2MB, alloc=2059.8MB, time=1103.76 memory used=91709.4MB, alloc=2059.8MB, time=1109.15 memory used=91939.0MB, alloc=2059.8MB, time=1113.84 memory used=92186.8MB, alloc=2059.8MB, time=1118.78 memory used=92459.5MB, alloc=2059.8MB, time=1123.70 memory used=92761.0MB, alloc=2059.8MB, time=1128.70 memory used=93088.7MB, alloc=2059.8MB, time=1133.73 memory used=93442.8MB, alloc=2059.8MB, time=1138.59 memory used=93780.9MB, alloc=2059.8MB, time=1143.43 memory used=94053.0MB, alloc=2059.8MB, time=1148.20 memory used=94339.4MB, alloc=2059.8MB, time=1152.98 memory used=94645.3MB, alloc=2059.8MB, time=1157.79 memory used=94974.0MB, alloc=2059.8MB, time=1162.60 memory used=95322.7MB, alloc=2059.8MB, time=1167.43 memory used=95699.5MB, alloc=2059.8MB, time=1172.26 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428441745 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 4 2 2 F := [-4 x y - 10 z + 14 y, 7 z - 12 z + 16 z, -11 x + 20 x z + 15 z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 3 3 2 2 G := [-12 x + 17 x y z - 12 y , 10 y z + 18 y z + 13 y , 3 4 2 8 x z - 3 y - 17 y z] > Problem := [F,G]; Problem := [ 2 2 2 3 2 4 2 2 [-4 x y - 10 z + 14 y, 7 z - 12 z + 16 z, -11 x + 20 x z + 15 z], [ 4 2 3 3 2 2 -12 x + 17 x y z - 12 y , 10 y z + 18 y z + 13 y , 3 4 2 8 x z - 3 y - 17 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=25.0MB, alloc=32.3MB, time=0.48 memory used=43.6MB, alloc=56.3MB, time=0.78 memory used=89.9MB, alloc=60.4MB, time=1.36 memory used=136.1MB, alloc=68.4MB, time=1.88 memory used=180.1MB, alloc=68.4MB, time=2.49 memory used=224.1MB, alloc=68.4MB, time=3.10 memory used=265.6MB, alloc=68.4MB, time=3.46 memory used=294.7MB, alloc=68.4MB, time=3.57 memory used=310.7MB, alloc=92.4MB, time=3.66 memory used=345.7MB, alloc=92.4MB, time=3.78 memory used=388.3MB, alloc=92.4MB, time=3.89 memory used=431.8MB, alloc=92.4MB, time=4.02 memory used=459.7MB, alloc=92.4MB, time=4.13 memory used=490.3MB, alloc=92.4MB, time=4.23 memory used=524.1MB, alloc=92.4MB, time=4.34 memory used=562.3MB, alloc=92.4MB, time=4.43 memory used=615.9MB, alloc=92.4MB, time=4.76 memory used=665.5MB, alloc=92.4MB, time=4.91 memory used=698.4MB, alloc=92.4MB, time=5.03 memory used=738.4MB, alloc=92.4MB, time=5.14 memory used=787.4MB, alloc=92.4MB, time=5.27 memory used=815.7MB, alloc=92.4MB, time=5.38 memory used=845.1MB, alloc=92.4MB, time=5.48 memory used=877.9MB, alloc=92.4MB, time=5.58 memory used=914.3MB, alloc=92.4MB, time=5.69 memory used=960.8MB, alloc=92.4MB, time=5.88 memory used=1046.9MB, alloc=93.3MB, time=11.84 memory used=1088.1MB, alloc=93.3MB, time=11.98 memory used=1128.4MB, alloc=93.3MB, time=12.09 memory used=1160.1MB, alloc=93.3MB, time=12.18 memory used=1198.0MB, alloc=93.3MB, time=12.29 memory used=1242.9MB, alloc=93.3MB, time=12.38 memory used=1282.2MB, alloc=93.3MB, time=12.48 memory used=1310.1MB, alloc=93.3MB, time=12.55 memory used=1339.8MB, alloc=93.3MB, time=12.62 memory used=1372.8MB, alloc=93.3MB, time=12.70 memory used=1429.8MB, alloc=93.3MB, time=13.02 memory used=1502.4MB, alloc=93.3MB, time=14.08 memory used=1551.5MB, alloc=93.3MB, time=14.57 memory used=1584.6MB, alloc=93.3MB, time=14.67 memory used=1648.1MB, alloc=93.3MB, time=15.32 memory used=1682.8MB, alloc=93.3MB, time=15.43 memory used=1726.0MB, alloc=93.3MB, time=15.78 memory used=1765.6MB, alloc=93.3MB, time=16.01 memory used=1808.6MB, alloc=93.3MB, time=16.21 memory used=1859.5MB, alloc=93.3MB, time=17.25 memory used=1891.9MB, alloc=93.3MB, time=17.35 memory used=1927.2MB, alloc=93.3MB, time=17.45 memory used=1975.5MB, alloc=93.3MB, time=17.80 memory used=2056.8MB, alloc=93.3MB, time=18.91 memory used=2087.7MB, alloc=93.3MB, time=19.02 memory used=2134.6MB, alloc=93.3MB, time=19.35 memory used=2167.7MB, alloc=93.3MB, time=19.46 memory used=2196.0MB, alloc=93.3MB, time=19.55 memory used=2231.8MB, alloc=93.3MB, time=19.67 memory used=2274.1MB, alloc=93.3MB, time=22.74 memory used=2316.7MB, alloc=93.3MB, time=23.17 memory used=2352.0MB, alloc=93.3MB, time=23.29 memory used=2380.0MB, alloc=93.3MB, time=23.40 memory used=2405.6MB, alloc=93.3MB, time=23.50 memory used=2434.8MB, alloc=93.3MB, time=23.61 memory used=2467.7MB, alloc=93.3MB, time=23.73 memory used=2504.5MB, alloc=93.3MB, time=23.84 memory used=2542.8MB, alloc=93.3MB, time=23.95 memory used=2564.4MB, alloc=93.3MB, time=24.03 memory used=2586.5MB, alloc=93.3MB, time=24.12 memory used=2610.5MB, alloc=93.3MB, time=24.21 memory used=2635.7MB, alloc=93.3MB, time=24.30 memory used=2661.7MB, alloc=93.3MB, time=24.39 memory used=2689.4MB, alloc=93.3MB, time=24.47 memory used=2719.5MB, alloc=93.3MB, time=24.56 memory used=2751.1MB, alloc=93.3MB, time=24.64 memory used=2784.1MB, alloc=93.3MB, time=24.74 memory used=2819.6MB, alloc=93.3MB, time=24.82 memory used=2870.9MB, alloc=106.0MB, time=24.99 memory used=2909.2MB, alloc=106.0MB, time=25.39 memory used=2940.3MB, alloc=106.0MB, time=25.51 memory used=2998.8MB, alloc=106.0MB, time=35.69 memory used=3041.6MB, alloc=106.0MB, time=36.23 memory used=3073.4MB, alloc=106.0MB, time=36.36 memory used=3109.8MB, alloc=106.0MB, time=36.48 memory used=3133.3MB, alloc=106.0MB, time=36.59 memory used=3158.7MB, alloc=106.0MB, time=36.70 memory used=3186.9MB, alloc=106.0MB, time=36.81 memory used=3218.0MB, alloc=106.0MB, time=36.91 memory used=3252.1MB, alloc=106.0MB, time=37.03 memory used=3289.0MB, alloc=106.0MB, time=37.15 memory used=3328.8MB, alloc=106.0MB, time=37.27 memory used=3353.3MB, alloc=106.0MB, time=37.35 memory used=3374.8MB, alloc=130.0MB, time=37.45 memory used=3409.9MB, alloc=130.0MB, time=37.55 memory used=3447.9MB, alloc=130.0MB, time=37.66 memory used=3487.9MB, alloc=130.0MB, time=37.76 memory used=3529.7MB, alloc=130.0MB, time=37.87 memory used=3574.7MB, alloc=130.0MB, time=37.98 memory used=3622.5MB, alloc=130.0MB, time=38.09 memory used=3672.9MB, alloc=130.0MB, time=38.21 memory used=3726.6MB, alloc=130.0MB, time=38.32 memory used=3784.5MB, alloc=130.0MB, time=38.44 memory used=3846.2MB, alloc=130.0MB, time=38.57 memory used=3876.0MB, alloc=131.8MB, time=38.66 memory used=3886.1MB, alloc=131.8MB, time=38.73 memory used=3896.3MB, alloc=131.8MB, time=38.80 memory used=3906.2MB, alloc=131.8MB, time=38.86 memory used=3916.8MB, alloc=131.8MB, time=38.93 memory used=3927.9MB, alloc=131.8MB, time=39.00 memory used=3938.6MB, alloc=131.8MB, time=39.07 memory used=3949.6MB, alloc=131.8MB, time=39.14 memory used=3960.9MB, alloc=131.8MB, time=39.21 memory used=3972.7MB, alloc=131.8MB, time=39.28 memory used=3985.0MB, alloc=131.8MB, time=39.35 memory used=3997.8MB, alloc=131.8MB, time=39.42 memory used=4079.6MB, alloc=387.8MB, time=40.57 memory used=4170.1MB, alloc=387.8MB, time=41.62 memory used=4264.7MB, alloc=387.8MB, time=42.65 memory used=4354.1MB, alloc=411.8MB, time=43.78 memory used=4462.3MB, alloc=411.8MB, time=45.12 memory used=4520.5MB, alloc=411.8MB, time=45.50 memory used=4595.2MB, alloc=411.8MB, time=45.97 memory used=4688.9MB, alloc=411.8MB, time=48.31 memory used=4749.9MB, alloc=411.8MB, time=48.62 memory used=4844.4MB, alloc=411.8MB, time=50.87 memory used=4899.6MB, alloc=411.8MB, time=51.18 memory used=4953.2MB, alloc=411.8MB, time=51.45 memory used=5072.9MB, alloc=411.8MB, time=52.77 memory used=5184.7MB, alloc=435.8MB, time=53.98 memory used=5304.6MB, alloc=435.8MB, time=55.00 memory used=5381.1MB, alloc=435.8MB, time=55.40 memory used=5474.3MB, alloc=435.8MB, time=56.76 memory used=5530.8MB, alloc=435.8MB, time=57.02 memory used=5607.6MB, alloc=435.8MB, time=57.50 memory used=5682.3MB, alloc=435.8MB, time=57.90 memory used=5750.3MB, alloc=435.8MB, time=59.20 memory used=5804.6MB, alloc=435.8MB, time=59.44 memory used=5872.4MB, alloc=435.8MB, time=59.82 memory used=5945.0MB, alloc=435.8MB, time=60.17 memory used=6004.7MB, alloc=435.8MB, time=60.46 memory used=6067.4MB, alloc=435.8MB, time=60.72 memory used=6112.2MB, alloc=435.8MB, time=60.96 memory used=6164.6MB, alloc=435.8MB, time=61.18 memory used=6242.5MB, alloc=435.8MB, time=61.64 memory used=6308.8MB, alloc=435.8MB, time=61.97 memory used=6370.4MB, alloc=435.8MB, time=62.25 memory used=6430.2MB, alloc=435.8MB, time=62.51 memory used=6476.2MB, alloc=435.8MB, time=62.76 memory used=6530.6MB, alloc=435.8MB, time=63.01 memory used=6618.9MB, alloc=435.8MB, time=74.04 memory used=6719.3MB, alloc=435.8MB, time=75.20 memory used=6779.7MB, alloc=435.8MB, time=75.50 memory used=6829.9MB, alloc=435.8MB, time=75.75 memory used=6892.2MB, alloc=435.8MB, time=76.03 memory used=6959.2MB, alloc=435.8MB, time=76.30 memory used=7000.8MB, alloc=435.8MB, time=76.52 memory used=7046.9MB, alloc=435.8MB, time=76.73 memory used=7098.2MB, alloc=435.8MB, time=76.94 memory used=7155.0MB, alloc=435.8MB, time=77.15 memory used=7231.3MB, alloc=435.8MB, time=77.50 memory used=7302.2MB, alloc=435.8MB, time=78.86 memory used=7354.3MB, alloc=435.8MB, time=79.11 memory used=7426.7MB, alloc=435.8MB, time=79.43 memory used=7526.1MB, alloc=435.8MB, time=87.20 memory used=7626.8MB, alloc=435.8MB, time=87.88 memory used=7688.6MB, alloc=459.8MB, time=88.17 memory used=7751.3MB, alloc=459.8MB, time=88.45 memory used=7830.7MB, alloc=459.8MB, time=88.72 memory used=7911.7MB, alloc=459.8MB, time=89.02 memory used=7966.2MB, alloc=459.8MB, time=89.25 memory used=8026.8MB, alloc=459.8MB, time=89.49 memory used=8094.4MB, alloc=459.8MB, time=89.73 memory used=8169.9MB, alloc=459.8MB, time=89.97 memory used=8265.2MB, alloc=459.8MB, time=90.44 memory used=8363.9MB, alloc=459.8MB, time=90.87 memory used=8437.6MB, alloc=459.8MB, time=91.21 memory used=8527.5MB, alloc=459.8MB, time=91.54 memory used=8583.0MB, alloc=459.8MB, time=91.82 memory used=8645.8MB, alloc=459.8MB, time=92.09 memory used=8716.4MB, alloc=459.8MB, time=92.38 memory used=8798.6MB, alloc=459.8MB, time=92.68 memory used=8915.3MB, alloc=459.8MB, time=93.30 memory used=8986.2MB, alloc=459.8MB, time=93.61 memory used=9069.4MB, alloc=459.8MB, time=93.95 memory used=9143.9MB, alloc=459.8MB, time=94.26 memory used=9203.4MB, alloc=459.8MB, time=94.55 memory used=9270.2MB, alloc=459.8MB, time=94.83 memory used=9347.2MB, alloc=459.8MB, time=95.10 memory used=9448.5MB, alloc=459.8MB, time=97.88 memory used=9581.7MB, alloc=459.8MB, time=138.85 memory used=9699.6MB, alloc=459.8MB, time=139.64 memory used=9781.2MB, alloc=459.8MB, time=139.99 memory used=9839.5MB, alloc=459.8MB, time=140.27 memory used=9907.7MB, alloc=459.8MB, time=140.56 memory used=9986.6MB, alloc=459.8MB, time=140.86 memory used=10077.3MB, alloc=459.8MB, time=141.17 memory used=10137.0MB, alloc=459.8MB, time=141.44 memory used=10189.6MB, alloc=459.8MB, time=141.69 memory used=10244.7MB, alloc=459.8MB, time=141.93 memory used=10304.6MB, alloc=459.8MB, time=142.17 memory used=10367.2MB, alloc=459.8MB, time=142.40 memory used=10434.3MB, alloc=459.8MB, time=142.64 memory used=10505.5MB, alloc=459.8MB, time=142.91 memory used=10580.4MB, alloc=459.8MB, time=143.16 memory used=10660.3MB, alloc=459.8MB, time=143.42 memory used=10744.5MB, alloc=459.8MB, time=143.67 memory used=10835.3MB, alloc=459.8MB, time=143.92 memory used=11030.8MB, alloc=459.8MB, time=144.50 memory used=11275.0MB, alloc=459.8MB, time=145.27 memory used=11341.1MB, alloc=459.8MB, time=145.61 memory used=11429.0MB, alloc=459.8MB, time=145.98 memory used=11494.7MB, alloc=459.8MB, time=146.28 memory used=11555.0MB, alloc=459.8MB, time=146.56 memory used=11623.6MB, alloc=459.8MB, time=146.85 memory used=11701.8MB, alloc=459.8MB, time=147.15 memory used=11808.3MB, alloc=459.8MB, time=147.74 memory used=11890.8MB, alloc=459.8MB, time=148.12 memory used=11967.1MB, alloc=459.8MB, time=148.43 memory used=12051.2MB, alloc=459.8MB, time=148.77 memory used=12107.3MB, alloc=459.8MB, time=149.06 memory used=12170.0MB, alloc=459.8MB, time=149.34 memory used=12242.0MB, alloc=459.8MB, time=149.61 memory used=12325.4MB, alloc=459.8MB, time=149.91 memory used=12454.6MB, alloc=459.8MB, time=188.14 memory used=12591.3MB, alloc=459.8MB, time=193.98 memory used=12668.7MB, alloc=459.8MB, time=194.30 memory used=12738.4MB, alloc=459.8MB, time=194.61 memory used=12802.6MB, alloc=459.8MB, time=194.91 memory used=12876.6MB, alloc=459.8MB, time=195.19 memory used=12962.6MB, alloc=459.8MB, time=195.47 memory used=13042.4MB, alloc=459.8MB, time=195.73 memory used=13093.0MB, alloc=459.8MB, time=195.95 memory used=13147.5MB, alloc=459.8MB, time=196.19 memory used=13205.1MB, alloc=459.8MB, time=196.43 memory used=13267.4MB, alloc=459.8MB, time=196.69 memory used=13332.3MB, alloc=459.8MB, time=196.93 memory used=13401.6MB, alloc=459.8MB, time=197.15 memory used=13474.7MB, alloc=459.8MB, time=197.38 memory used=13553.2MB, alloc=459.8MB, time=197.63 memory used=13636.3MB, alloc=459.8MB, time=197.91 memory used=13724.8MB, alloc=459.8MB, time=198.18 memory used=13958.5MB, alloc=459.8MB, time=198.61 memory used=14286.7MB, alloc=459.8MB, time=200.26 memory used=14458.4MB, alloc=459.8MB, time=202.37 memory used=14631.5MB, alloc=459.8MB, time=206.07 memory used=14812.5MB, alloc=459.8MB, time=211.82 memory used=14883.1MB, alloc=459.8MB, time=212.12 memory used=14959.7MB, alloc=459.8MB, time=212.37 memory used=15027.0MB, alloc=459.8MB, time=212.69 memory used=15204.4MB, alloc=459.8MB, time=214.52 memory used=15370.0MB, alloc=459.8MB, time=216.18 memory used=15536.4MB, alloc=459.8MB, time=219.41 memory used=15704.3MB, alloc=459.8MB, time=224.10 memory used=15844.3MB, alloc=483.8MB, time=225.92 memory used=16043.9MB, alloc=483.8MB, time=227.28 memory used=16238.2MB, alloc=483.8MB, time=229.20 memory used=16434.5MB, alloc=483.8MB, time=233.23 memory used=16617.3MB, alloc=483.8MB, time=237.88 memory used=16719.8MB, alloc=483.8MB, time=238.94 memory used=16799.0MB, alloc=483.8MB, time=239.29 memory used=16889.0MB, alloc=483.8MB, time=239.60 memory used=16952.9MB, alloc=483.8MB, time=239.85 memory used=17048.5MB, alloc=483.8MB, time=241.22 memory used=17157.3MB, alloc=483.8MB, time=242.55 memory used=17240.1MB, alloc=483.8MB, time=243.10 memory used=17380.8MB, alloc=483.8MB, time=244.38 memory used=17475.3MB, alloc=507.8MB, time=245.42 memory used=17628.8MB, alloc=507.8MB, time=249.66 memory used=17716.4MB, alloc=507.8MB, time=250.07 memory used=17797.8MB, alloc=507.8MB, time=250.40 memory used=17891.2MB, alloc=507.8MB, time=251.87 memory used=17975.1MB, alloc=507.8MB, time=252.87 memory used=18118.7MB, alloc=507.8MB, time=253.89 memory used=18217.0MB, alloc=507.8MB, time=254.45 memory used=18328.1MB, alloc=507.8MB, time=255.14 memory used=18417.1MB, alloc=507.8MB, time=255.61 memory used=18495.1MB, alloc=507.8MB, time=256.04 memory used=18567.9MB, alloc=507.8MB, time=256.46 memory used=18657.4MB, alloc=507.8MB, time=256.87 memory used=18764.4MB, alloc=531.8MB, time=263.78 memory used=18866.6MB, alloc=531.8MB, time=264.23 memory used=18971.6MB, alloc=531.8MB, time=264.63 memory used=19046.9MB, alloc=531.8MB, time=265.00 memory used=19131.4MB, alloc=531.8MB, time=265.38 memory used=19227.5MB, alloc=531.8MB, time=265.77 memory used=19336.5MB, alloc=531.8MB, time=266.16 memory used=19487.8MB, alloc=531.8MB, time=266.94 memory used=19607.3MB, alloc=531.8MB, time=267.64 memory used=19733.7MB, alloc=531.8MB, time=269.69 memory used=19859.5MB, alloc=531.8MB, time=270.30 memory used=19951.7MB, alloc=531.8MB, time=270.82 memory used=20065.9MB, alloc=531.8MB, time=271.37 memory used=20182.2MB, alloc=531.8MB, time=271.87 memory used=20252.9MB, alloc=531.8MB, time=272.33 memory used=20329.2MB, alloc=531.8MB, time=272.77 memory used=20412.9MB, alloc=531.8MB, time=273.24 memory used=20500.0MB, alloc=531.8MB, time=273.68 memory used=20593.9MB, alloc=531.8MB, time=274.15 memory used=20695.4MB, alloc=531.8MB, time=274.65 memory used=20804.1MB, alloc=531.8MB, time=275.14 memory used=20919.9MB, alloc=531.8MB, time=275.63 memory used=21042.3MB, alloc=531.8MB, time=276.13 memory used=21159.9MB, alloc=531.8MB, time=276.61 memory used=21226.2MB, alloc=531.8MB, time=276.97 memory used=21293.3MB, alloc=555.8MB, time=277.36 memory used=21374.5MB, alloc=555.8MB, time=277.78 memory used=21460.6MB, alloc=555.8MB, time=278.19 memory used=21551.0MB, alloc=555.8MB, time=278.57 memory used=21645.1MB, alloc=555.8MB, time=279.01 memory used=21742.2MB, alloc=555.8MB, time=279.44 memory used=21842.2MB, alloc=555.8MB, time=279.85 memory used=21947.0MB, alloc=555.8MB, time=280.25 memory used=22056.8MB, alloc=555.8MB, time=280.67 memory used=22173.0MB, alloc=555.8MB, time=281.12 memory used=22296.1MB, alloc=555.8MB, time=281.52 memory used=22427.5MB, alloc=555.8MB, time=281.94 memory used=22594.0MB, alloc=555.8MB, time=283.73 memory used=22716.7MB, alloc=555.8MB, time=284.37 memory used=22839.7MB, alloc=555.8MB, time=284.91 memory used=22985.1MB, alloc=555.8MB, time=285.53 memory used=23072.1MB, alloc=555.8MB, time=286.02 memory used=23164.6MB, alloc=555.8MB, time=286.52 memory used=23263.0MB, alloc=555.8MB, time=287.05 memory used=23373.3MB, alloc=555.8MB, time=287.54 memory used=23488.9MB, alloc=555.8MB, time=288.04 memory used=23616.4MB, alloc=555.8MB, time=288.59 memory used=23752.6MB, alloc=555.8MB, time=289.11 memory used=23901.1MB, alloc=555.8MB, time=289.63 memory used=24014.7MB, alloc=555.8MB, time=290.12 memory used=24093.0MB, alloc=555.8MB, time=290.51 memory used=24175.2MB, alloc=555.8MB, time=290.90 memory used=24261.7MB, alloc=555.8MB, time=291.31 memory used=24348.4MB, alloc=555.8MB, time=291.71 memory used=24442.1MB, alloc=555.8MB, time=292.13 memory used=24539.6MB, alloc=555.8MB, time=292.53 memory used=24639.6MB, alloc=555.8MB, time=292.94 memory used=24745.7MB, alloc=555.8MB, time=293.38 memory used=24856.4MB, alloc=555.8MB, time=293.80 memory used=24970.6MB, alloc=555.8MB, time=294.20 memory used=25091.8MB, alloc=555.8MB, time=294.65 memory used=25221.6MB, alloc=555.8MB, time=295.08 memory used=25380.7MB, alloc=555.8MB, time=308.91 memory used=25541.3MB, alloc=555.8MB, time=427.51 memory used=25804.0MB, alloc=555.8MB, time=431.13 memory used=25929.5MB, alloc=555.8MB, time=431.74 memory used=26033.1MB, alloc=555.8MB, time=432.24 memory used=26135.9MB, alloc=555.8MB, time=432.74 memory used=26257.5MB, alloc=555.8MB, time=433.25 memory used=26397.8MB, alloc=555.8MB, time=433.76 memory used=26510.6MB, alloc=555.8MB, time=434.21 memory used=26593.1MB, alloc=555.8MB, time=434.63 memory used=26679.9MB, alloc=555.8MB, time=435.03 memory used=26772.5MB, alloc=555.8MB, time=435.43 memory used=26868.1MB, alloc=555.8MB, time=435.85 memory used=26969.3MB, alloc=555.8MB, time=436.26 memory used=27076.5MB, alloc=555.8MB, time=436.67 memory used=27189.5MB, alloc=555.8MB, time=437.09 memory used=27308.2MB, alloc=555.8MB, time=437.53 memory used=27432.5MB, alloc=555.8MB, time=437.95 memory used=27562.4MB, alloc=555.8MB, time=438.38 memory used=27700.5MB, alloc=555.8MB, time=438.83 memory used=27843.8MB, alloc=555.8MB, time=439.26 memory used=28096.1MB, alloc=555.8MB, time=439.88 memory used=28234.9MB, alloc=555.8MB, time=440.35 memory used=28380.7MB, alloc=555.8MB, time=440.83 memory used=28532.1MB, alloc=555.8MB, time=441.31 memory 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time=1280.80 memory used=65757.0MB, alloc=579.8MB, time=1281.26 memory used=65885.1MB, alloc=579.8MB, time=1281.78 memory used=66025.8MB, alloc=579.8MB, time=1282.27 memory used=66178.0MB, alloc=579.8MB, time=1282.78 memory used=66384.9MB, alloc=579.8MB, time=1283.39 memory used=66533.5MB, alloc=579.8MB, time=1283.90 memory used=66693.2MB, alloc=579.8MB, time=1284.43 memory used=66868.9MB, alloc=579.8MB, time=1284.99 memory used=67144.6MB, alloc=579.8MB, time=1286.18 memory used=67279.5MB, alloc=579.8MB, time=1286.80 memory used=67385.2MB, alloc=579.8MB, time=1287.38 memory used=67503.5MB, alloc=579.8MB, time=1287.95 memory used=67649.3MB, alloc=579.8MB, time=1288.48 memory used=67780.1MB, alloc=579.8MB, time=1289.41 memory used=67915.4MB, alloc=579.8MB, time=1290.12 memory used=68038.3MB, alloc=579.8MB, time=1290.73 memory used=68148.1MB, alloc=579.8MB, time=1291.36 memory used=68286.2MB, alloc=579.8MB, time=1291.97 memory used=68398.3MB, alloc=579.8MB, time=1292.44 memory used=68561.3MB, alloc=579.8MB, time=1353.83 memory used=68707.1MB, alloc=579.8MB, time=1354.51 memory used=68814.0MB, alloc=579.8MB, time=1355.07 memory used=68950.6MB, alloc=579.8MB, time=1355.62 memory used=69068.5MB, alloc=579.8MB, time=1356.16 memory used=69160.4MB, alloc=579.8MB, time=1356.62 memory used=69261.6MB, alloc=579.8MB, time=1357.08 memory used=69371.8MB, alloc=579.8MB, time=1357.58 memory used=69493.0MB, alloc=579.8MB, time=1358.07 memory used=69624.6MB, alloc=579.8MB, time=1358.58 memory used=69768.5MB, alloc=579.8MB, time=1359.11 memory used=69925.5MB, alloc=579.8MB, time=1359.61 memory used=70068.2MB, alloc=579.8MB, time=1360.14 memory used=70216.2MB, alloc=579.8MB, time=1360.69 memory used=70375.9MB, alloc=579.8MB, time=1361.23 memory used=70551.6MB, alloc=579.8MB, time=1361.79 memory used=70781.5MB, alloc=579.8MB, time=1363.15 memory used=70860.2MB, alloc=579.8MB, time=1364.13 memory used=70942.3MB, alloc=579.8MB, time=1365.10 memory used=71014.2MB, alloc=579.8MB, time=1366.14 memory used=71077.9MB, alloc=579.8MB, time=1367.01 memory used=71326.3MB, alloc=579.8MB, time=1369.36 memory used=71447.3MB, alloc=579.8MB, time=1369.89 memory used=71544.4MB, alloc=579.8MB, time=1370.35 memory used=71797.6MB, alloc=603.8MB, time=1373.08 memory used=71976.4MB, alloc=627.8MB, time=1375.35 memory used=72191.3MB, alloc=627.8MB, time=1377.19 memory used=72355.6MB, alloc=627.8MB, time=1378.09 memory used=72556.7MB, alloc=627.8MB, time=1385.09 memory used=72689.4MB, alloc=627.8MB, time=1385.73 memory used=72948.2MB, alloc=627.8MB, time=1389.18 memory used=73120.7MB, alloc=627.8MB, time=1390.45 memory used=73471.8MB, alloc=627.8MB, time=1394.40 memory used=73751.9MB, alloc=627.8MB, time=1398.74 memory used=73921.5MB, alloc=651.8MB, time=1401.61 memory used=74178.7MB, alloc=651.8MB, time=1405.61 memory used=74416.2MB, alloc=651.8MB, time=1414.21 memory used=74620.4MB, alloc=651.8MB, time=1416.83 memory used=74733.2MB, alloc=675.8MB, time=1418.79 memory used=74902.4MB, alloc=675.8MB, time=1421.30 memory used=75078.8MB, alloc=699.8MB, time=1422.40 memory used=75259.0MB, alloc=699.8MB, time=1423.51 memory used=75420.5MB, alloc=699.8MB, time=1424.50 memory used=75679.0MB, alloc=699.8MB, time=1438.82 memory used=75836.4MB, alloc=699.8MB, time=1439.81 memory used=76018.4MB, alloc=699.8MB, time=1440.71 memory used=76147.8MB, alloc=699.8MB, time=1441.52 memory used=76299.4MB, alloc=699.8MB, time=1442.32 memory used=76540.4MB, alloc=699.8MB, time=1445.04 memory used=76700.2MB, alloc=699.8MB, time=1446.00 memory used=76893.2MB, alloc=699.8MB, time=1447.10 memory used=77051.6MB, alloc=699.8MB, time=1448.05 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428442945 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 3 3 3 F := [-x + 6 y z - 19 y , 8 y z + 2 y z + 18 x y, -7 x - 6 y + 4 x] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 G := [10 x y z + 12 x z - 18 x y, -12 x y z + 16 y - 5 y z, 3 3 3 -x y + 15 y z + 16 y ] > Problem := [F,G]; Problem := [ 3 2 2 2 2 3 3 3 [-x + 6 y z - 19 y , 8 y z + 2 y z + 18 x y, -7 x - 6 y + 4 x], [ 2 2 3 10 x y z + 12 x z - 18 x y, -12 x y z + 16 y - 5 y z, 3 3 3 -x y + 15 y z + 16 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=31.2MB, alloc=40.3MB, time=0.58 memory used=58.4MB, alloc=44.3MB, time=1.00 memory used=82.4MB, alloc=68.3MB, time=1.41 memory used=130.6MB, alloc=76.3MB, time=2.15 memory used=180.8MB, alloc=100.3MB, time=2.87 memory used=253.9MB, alloc=100.3MB, time=3.85 memory used=323.8MB, alloc=124.3MB, time=4.94 memory used=395.3MB, alloc=124.3MB, time=6.00 memory used=444.1MB, alloc=380.3MB, time=6.76 memory used=537.6MB, alloc=404.3MB, time=8.21 memory used=654.2MB, alloc=428.3MB, time=10.01 memory used=783.2MB, alloc=452.3MB, time=11.95 memory used=909.7MB, alloc=452.3MB, time=13.98 memory used=1031.5MB, alloc=476.3MB, time=16.04 memory used=1133.7MB, alloc=500.3MB, time=17.40 memory used=1235.0MB, alloc=500.3MB, time=19.14 memory used=1314.5MB, alloc=500.3MB, time=20.31 memory used=1408.4MB, alloc=500.3MB, time=21.60 memory used=1487.3MB, alloc=500.3MB, time=23.02 memory used=1557.8MB, alloc=500.3MB, time=24.05 memory used=1617.5MB, alloc=500.3MB, time=24.99 memory used=1698.3MB, alloc=524.3MB, time=26.30 memory used=1760.7MB, alloc=524.3MB, time=27.53 memory used=1814.5MB, alloc=524.3MB, time=28.69 memory used=1872.7MB, alloc=524.3MB, time=30.04 memory used=1919.1MB, alloc=524.3MB, time=31.02 memory used=2102.2MB, alloc=548.3MB, time=33.97 memory used=2289.9MB, alloc=572.3MB, time=36.91 memory used=2458.6MB, alloc=596.3MB, time=39.28 memory used=2630.2MB, alloc=620.3MB, time=42.06 memory used=2781.6MB, alloc=620.3MB, time=44.58 memory used=2914.2MB, alloc=620.3MB, time=46.96 memory used=3055.8MB, alloc=644.3MB, time=49.92 memory used=3192.7MB, alloc=644.3MB, time=52.11 memory used=3313.1MB, alloc=644.3MB, time=54.51 memory used=3429.9MB, alloc=668.3MB, time=56.62 memory used=3541.2MB, alloc=668.3MB, time=59.22 memory used=3884.7MB, alloc=692.3MB, time=64.91 memory used=4247.1MB, alloc=716.3MB, time=71.28 memory used=4607.1MB, alloc=740.3MB, time=77.08 memory used=4979.4MB, alloc=764.3MB, time=83.07 memory used=5268.4MB, alloc=788.3MB, time=89.55 memory used=5578.8MB, alloc=812.3MB, time=95.49 memory used=5882.2MB, alloc=836.3MB, time=101.28 memory used=6206.0MB, alloc=860.3MB, time=108.01 memory used=6448.1MB, alloc=884.3MB, time=112.24 memory used=6814.1MB, alloc=908.3MB, time=118.41 memory used=7085.8MB, alloc=932.3MB, time=123.94 memory used=7317.0MB, alloc=956.3MB, time=128.88 memory used=7505.9MB, alloc=980.3MB, time=133.91 memory used=7707.3MB, alloc=1004.3MB, time=139.19 memory used=8323.4MB, alloc=1028.3MB, time=148.68 memory used=8901.7MB, alloc=1052.3MB, time=159.04 memory used=9551.9MB, alloc=1076.3MB, time=167.94 memory used=10217.1MB, alloc=1100.3MB, time=181.91 memory used=10673.1MB, alloc=1124.3MB, time=190.81 memory used=11117.8MB, alloc=1148.3MB, time=195.85 memory used=11919.7MB, alloc=1172.3MB, time=207.41 memory used=12679.3MB, alloc=1196.3MB, time=221.09 memory used=13326.0MB, alloc=1220.3MB, time=232.68 memory used=14083.1MB, alloc=1244.3MB, time=246.40 memory used=14824.6MB, alloc=1268.3MB, time=261.40 memory used=15286.8MB, alloc=1292.3MB, time=267.53 memory used=15956.2MB, alloc=1316.3MB, time=278.59 memory used=16359.1MB, alloc=1340.3MB, time=284.93 memory used=16764.3MB, alloc=1364.3MB, time=295.79 memory used=17202.0MB, alloc=1388.3MB, time=300.31 memory used=17735.8MB, alloc=1412.3MB, time=308.98 memory used=18415.3MB, alloc=1436.3MB, time=321.84 memory used=19103.3MB, alloc=1460.3MB, time=335.23 memory used=19586.6MB, alloc=1484.3MB, time=346.48 memory used=20077.3MB, alloc=1508.3MB, time=357.47 memory used=20497.3MB, alloc=1532.3MB, time=368.35 memory used=21106.6MB, alloc=1556.3MB, time=380.70 memory used=21561.4MB, alloc=1580.3MB, time=386.51 memory used=22061.0MB, alloc=1604.3MB, time=419.58 memory used=22589.6MB, alloc=1628.3MB, time=426.47 memory used=23084.3MB, alloc=1652.3MB, time=431.69 memory used=23305.0MB, alloc=1691.8MB, time=436.49 memory used=23384.7MB, alloc=1691.8MB, time=441.15 memory used=23468.4MB, alloc=1691.8MB, time=445.83 memory used=23555.6MB, alloc=1691.8MB, time=450.55 memory used=23647.8MB, alloc=1691.8MB, time=455.17 memory used=23746.0MB, alloc=1691.8MB, time=459.86 memory used=23851.1MB, alloc=1691.8MB, time=464.58 memory used=23963.9MB, alloc=1691.8MB, time=469.20 memory used=24088.7MB, alloc=1691.8MB, time=473.84 memory used=24777.5MB, alloc=1691.8MB, time=484.30 memory used=25454.0MB, alloc=1691.8MB, time=549.85 memory used=25943.8MB, alloc=1715.8MB, time=555.37 memory used=26523.4MB, alloc=1715.8MB, time=560.90 memory used=26762.4MB, alloc=1715.8MB, time=565.91 memory used=26836.6MB, alloc=1715.8MB, time=570.75 memory used=26914.5MB, alloc=1715.8MB, time=575.51 memory used=26993.1MB, alloc=1715.8MB, time=580.27 memory used=27074.5MB, alloc=1715.8MB, time=585.12 memory used=27160.0MB, alloc=1715.8MB, time=589.84 memory used=27248.9MB, alloc=1715.8MB, time=594.65 memory used=27341.0MB, alloc=1715.8MB, time=599.47 memory used=27436.1MB, alloc=1715.8MB, time=604.19 memory used=27533.8MB, alloc=1715.8MB, time=609.00 memory used=27634.1MB, alloc=1715.8MB, time=613.81 memory used=27739.6MB, alloc=1715.8MB, time=618.58 memory used=27849.4MB, alloc=1715.8MB, time=623.43 memory used=27963.0MB, alloc=1715.8MB, time=628.20 memory used=28082.2MB, alloc=1715.8MB, time=633.08 memory used=28205.6MB, alloc=1715.8MB, time=637.88 memory used=28336.9MB, alloc=1715.8MB, time=642.72 memory used=28467.3MB, alloc=1715.8MB, time=647.56 memory used=28584.1MB, alloc=1715.8MB, time=652.37 memory used=28699.3MB, alloc=1715.8MB, time=657.17 memory used=29540.0MB, alloc=1715.8MB, time=665.98 memory used=30191.5MB, alloc=1739.8MB, time=677.57 memory used=30737.8MB, alloc=1739.8MB, time=689.68 memory used=31113.5MB, alloc=1763.8MB, time=699.45 memory used=31667.7MB, alloc=1763.8MB, time=711.12 memory used=32160.9MB, alloc=1787.8MB, time=720.31 memory used=32796.1MB, alloc=1787.8MB, time=731.78 memory used=33223.1MB, alloc=1811.8MB, time=741.88 memory used=33496.5MB, alloc=1811.8MB, time=749.52 memory used=33853.9MB, alloc=1835.8MB, time=759.16 memory used=34501.9MB, alloc=1835.8MB, time=766.14 memory used=34901.4MB, alloc=1835.8MB, time=771.95 memory used=35271.8MB, alloc=1835.8MB, time=777.74 memory used=36285.6MB, alloc=1835.8MB, time=787.75 memory used=36705.0MB, alloc=1835.8MB, time=793.52 memory used=37089.8MB, alloc=1835.8MB, time=799.40 memory used=37801.3MB, alloc=1835.8MB, time=809.53 memory used=38373.0MB, alloc=1859.8MB, time=820.01 memory used=39219.3MB, alloc=1859.8MB, time=830.26 memory used=40125.3MB, alloc=1859.8MB, time=839.10 memory used=40869.8MB, alloc=1883.8MB, time=849.96 memory used=41564.3MB, alloc=1883.8MB, time=856.76 memory used=42406.3MB, alloc=1883.8MB, time=867.24 memory used=42794.0MB, alloc=1907.8MB, time=877.14 memory used=43628.7MB, alloc=1907.8MB, time=886.27 memory used=44607.6MB, alloc=1907.8MB, time=895.61 memory used=45069.8MB, alloc=1907.8MB, time=904.73 memory used=45664.2MB, alloc=1931.8MB, time=914.13 memory used=46563.3MB, alloc=1931.8MB, time=924.74 memory used=47549.6MB, alloc=1955.8MB, time=935.90 memory used=48818.3MB, alloc=1955.8MB, time=947.15 memory used=49568.4MB, alloc=1955.8MB, time=955.28 memory used=49974.2MB, alloc=1955.8MB, time=961.35 memory used=50848.0MB, alloc=1955.8MB, time=969.74 memory used=51660.0MB, alloc=1955.8MB, time=977.73 memory used=52522.6MB, alloc=1955.8MB, time=988.92 memory used=52975.0MB, alloc=1979.8MB, time=998.87 memory used=53973.5MB, alloc=1979.8MB, time=1008.08 memory used=54382.6MB, alloc=1979.8MB, time=1014.37 memory used=54677.8MB, alloc=1979.8MB, time=1020.59 memory used=54889.7MB, alloc=1979.8MB, time=1026.34 memory used=55086.6MB, alloc=1979.8MB, time=1032.00 memory used=55276.8MB, alloc=1979.8MB, time=1037.64 memory used=55467.4MB, alloc=1979.8MB, time=1043.61 memory used=55627.6MB, alloc=1979.8MB, time=1049.42 memory used=55822.7MB, alloc=1979.8MB, time=1055.20 memory used=56485.4MB, alloc=1979.8MB, time=1067.82 memory used=57574.1MB, alloc=2003.8MB, time=1078.72 memory used=57997.4MB, alloc=2003.8MB, time=1088.36 memory used=58617.9MB, alloc=2003.8MB, time=1099.92 memory used=58740.8MB, alloc=2003.8MB, time=1108.98 memory used=59169.6MB, alloc=2027.8MB, time=1121.79 memory used=59558.4MB, alloc=2051.8MB, time=1133.58 memory used=59889.5MB, alloc=2075.8MB, time=1144.11 memory used=60307.8MB, alloc=2099.8MB, time=1155.97 memory used=60646.7MB, alloc=2099.8MB, time=1167.11 memory used=61060.0MB, alloc=2123.8MB, time=1180.84 memory used=61452.1MB, alloc=2147.8MB, time=1191.91 memory used=62374.3MB, alloc=2147.8MB, time=1211.72 memory used=62839.9MB, alloc=2171.8MB, time=1223.37 memory used=63263.6MB, alloc=2171.8MB, time=1234.49 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428444146 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 3 4 2 F := [2 x y z + 8 y z - 7 y , 14 y + 10 x y - 3 x y z, 2 2 x y z + 20 y z - 10 y] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 3 4 3 G := [-9 y z + 11 x - y, 19 x y z + 18 x z - 19 z , 18 x + 18 x y] > Problem := [F,G]; 2 3 3 4 2 Problem := [[2 x y z + 8 y z - 7 y , 14 y + 10 x y - 3 x y z, 2 2 x y z + 20 y z - 10 y], 3 3 2 2 3 4 3 [-9 y z + 11 x - y, 19 x y z + 18 x z - 19 z , 18 x + 18 x y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.0MB, alloc=32.3MB, time=0.50 memory used=45.9MB, alloc=32.3MB, time=0.79 memory used=64.8MB, alloc=56.3MB, time=1.08 memory used=107.6MB, alloc=68.3MB, time=1.68 memory used=148.1MB, alloc=92.3MB, time=2.21 memory used=213.1MB, alloc=92.3MB, time=2.97 memory used=290.2MB, alloc=92.3MB, time=3.86 memory used=355.9MB, alloc=116.3MB, time=4.70 memory used=420.6MB, alloc=372.3MB, time=5.50 memory used=506.8MB, alloc=396.3MB, time=6.55 memory used=613.8MB, alloc=396.3MB, time=8.14 memory used=726.4MB, alloc=420.3MB, time=9.67 memory used=851.8MB, alloc=444.3MB, time=11.51 memory used=961.8MB, alloc=444.3MB, time=12.90 memory used=1084.1MB, alloc=468.3MB, time=14.16 memory used=1207.2MB, alloc=468.3MB, time=15.12 memory used=1344.2MB, alloc=468.3MB, time=16.66 memory used=1466.9MB, alloc=468.3MB, time=17.89 memory used=1587.2MB, alloc=468.3MB, time=19.59 memory used=1689.4MB, alloc=492.3MB, time=21.00 memory used=1809.8MB, alloc=492.3MB, time=22.72 memory used=1893.9MB, alloc=492.3MB, time=23.93 memory used=2006.9MB, alloc=492.3MB, time=25.29 memory used=2108.4MB, alloc=492.3MB, time=25.82 memory used=2217.7MB, alloc=492.3MB, time=27.99 memory used=2318.0MB, alloc=492.3MB, time=28.49 memory used=2420.8MB, alloc=492.3MB, time=29.58 memory used=2527.2MB, alloc=492.3MB, time=30.11 memory used=2638.6MB, alloc=492.3MB, time=32.35 memory used=2729.6MB, alloc=492.3MB, time=32.89 memory used=2840.8MB, alloc=492.3MB, time=33.76 memory used=2945.6MB, alloc=492.3MB, time=34.45 memory used=3090.6MB, alloc=492.3MB, time=35.77 memory used=3179.5MB, alloc=492.3MB, time=36.93 memory used=3278.9MB, alloc=516.3MB, time=38.40 memory used=3386.1MB, alloc=516.3MB, time=39.62 memory used=3437.2MB, alloc=516.3MB, time=40.52 memory used=3513.5MB, alloc=516.3MB, time=41.79 memory used=3574.0MB, alloc=516.3MB, time=42.91 memory used=3629.6MB, alloc=516.3MB, time=44.04 memory used=3681.2MB, alloc=516.3MB, time=45.16 memory used=3719.5MB, alloc=516.3MB, time=46.07 memory used=3915.5MB, alloc=540.3MB, time=49.45 memory used=4089.2MB, alloc=564.3MB, time=52.24 memory used=4260.6MB, alloc=588.3MB, time=54.54 memory used=4457.0MB, alloc=612.3MB, time=57.05 memory used=4631.9MB, alloc=612.3MB, time=59.83 memory used=4801.6MB, alloc=636.3MB, time=62.91 memory used=5037.6MB, alloc=636.3MB, time=65.39 memory used=5218.6MB, alloc=636.3MB, time=67.82 memory used=5387.4MB, alloc=660.3MB, time=70.98 memory used=5649.8MB, alloc=660.3MB, time=73.94 memory used=5786.9MB, alloc=660.3MB, time=75.85 memory used=5942.7MB, alloc=660.3MB, time=78.61 memory used=6073.4MB, alloc=684.3MB, time=80.95 memory used=6265.2MB, alloc=684.3MB, time=82.33 memory used=6427.1MB, alloc=684.3MB, time=83.59 memory used=6596.1MB, alloc=684.3MB, time=84.60 memory used=6817.7MB, alloc=684.3MB, time=86.70 memory used=7001.5MB, alloc=684.3MB, time=88.01 memory used=7180.1MB, alloc=684.3MB, time=89.90 memory used=7344.4MB, alloc=684.3MB, time=90.95 memory used=7509.8MB, alloc=684.3MB, time=93.12 memory used=7675.1MB, alloc=708.3MB, time=95.19 memory used=7804.2MB, alloc=708.3MB, time=97.19 memory used=7889.3MB, alloc=708.3MB, time=98.82 memory used=8009.2MB, alloc=708.3MB, time=101.22 memory used=8093.4MB, alloc=708.3MB, time=103.19 memory used=8164.8MB, alloc=708.3MB, time=104.86 memory used=8530.6MB, alloc=732.3MB, time=111.73 memory used=8938.7MB, alloc=756.3MB, time=117.50 memory used=9339.6MB, alloc=780.3MB, time=123.68 memory used=9707.2MB, alloc=804.3MB, time=130.44 memory used=10039.8MB, alloc=828.3MB, time=136.61 memory used=10326.0MB, alloc=852.3MB, time=141.07 memory used=10701.8MB, alloc=876.3MB, time=148.28 memory used=10985.1MB, alloc=900.3MB, time=153.90 memory used=11248.5MB, alloc=924.3MB, time=159.38 memory used=11451.7MB, alloc=948.3MB, time=163.36 memory used=11669.6MB, alloc=972.3MB, time=167.75 memory used=12041.8MB, alloc=996.3MB, time=172.97 memory used=12402.8MB, alloc=1020.3MB, time=177.39 memory used=12758.4MB, alloc=1044.3MB, time=181.23 memory used=13476.2MB, alloc=1068.3MB, time=191.22 memory used=14201.9MB, alloc=1092.3MB, time=201.70 memory used=14898.0MB, alloc=1116.3MB, time=212.73 memory used=15600.4MB, alloc=1140.3MB, time=225.31 memory used=16265.7MB, alloc=1164.3MB, time=235.56 memory used=16518.1MB, alloc=1188.3MB, time=238.54 memory used=16794.1MB, alloc=1212.3MB, time=241.44 memory used=17099.2MB, alloc=1236.3MB, time=245.09 memory used=17378.6MB, alloc=1260.3MB, time=248.31 memory used=17765.5MB, alloc=1284.3MB, time=274.23 memory used=18072.5MB, alloc=1308.3MB, time=277.43 memory used=18511.7MB, alloc=1332.3MB, time=285.28 memory used=18920.9MB, alloc=1356.3MB, time=289.40 memory used=19294.2MB, alloc=1380.3MB, time=292.85 memory used=19716.0MB, alloc=1404.3MB, time=297.00 memory used=20222.5MB, alloc=1428.3MB, time=323.31 memory used=20670.1MB, alloc=1428.3MB, time=326.87 memory used=21192.2MB, alloc=1428.3MB, time=332.00 memory used=21690.7MB, alloc=1428.3MB, time=338.59 memory used=22255.3MB, alloc=1428.3MB, time=345.01 memory used=23018.8MB, alloc=1452.3MB, time=357.46 memory used=23918.8MB, alloc=1476.3MB, time=371.94 memory used=24601.6MB, alloc=1500.3MB, time=386.44 memory used=25055.6MB, alloc=1524.3MB, time=398.18 memory used=25605.5MB, alloc=1548.3MB, time=411.16 memory used=26195.2MB, alloc=1572.3MB, time=424.59 memory used=26739.7MB, alloc=1596.3MB, time=436.85 memory used=27253.6MB, alloc=1620.3MB, time=447.95 memory used=27917.9MB, alloc=1644.3MB, time=459.16 memory used=28414.9MB, alloc=1668.3MB, time=470.00 memory used=28884.6MB, alloc=1692.3MB, time=479.45 memory used=29613.5MB, alloc=1716.3MB, time=488.75 memory used=30146.9MB, alloc=1740.3MB, time=496.28 memory used=30788.1MB, alloc=1764.3MB, time=504.99 memory used=31425.6MB, alloc=1788.3MB, time=514.33 memory used=31788.6MB, alloc=1812.3MB, time=523.20 memory used=32134.3MB, alloc=1836.3MB, time=534.88 memory used=32383.3MB, alloc=1860.3MB, time=544.96 memory used=32629.1MB, alloc=1860.3MB, time=553.66 memory used=32941.2MB, alloc=1860.3MB, time=565.13 memory used=33193.3MB, alloc=1860.3MB, time=573.71 memory used=33654.1MB, alloc=1884.3MB, time=583.48 memory used=34395.2MB, alloc=1884.3MB, time=595.92 memory used=35109.7MB, alloc=1884.3MB, time=608.19 memory used=35857.4MB, alloc=1884.3MB, time=623.12 memory used=36496.5MB, alloc=1884.3MB, time=630.83 memory used=37210.9MB, alloc=1884.3MB, time=639.22 memory used=37429.2MB, alloc=1884.3MB, time=647.64 memory used=37695.1MB, alloc=1884.3MB, time=656.29 memory used=37911.7MB, alloc=1884.3MB, time=664.16 memory used=38253.0MB, alloc=1908.3MB, time=672.26 memory used=38422.0MB, alloc=1908.3MB, time=680.22 memory used=38649.2MB, alloc=1932.3MB, time=688.27 memory used=38924.6MB, alloc=1932.3MB, time=697.10 memory used=39469.7MB, alloc=1932.3MB, time=710.06 memory used=40181.0MB, alloc=1932.3MB, time=723.76 memory used=40805.0MB, alloc=1932.3MB, time=737.25 memory used=41443.6MB, alloc=1947.8MB, time=751.40 memory used=41686.2MB, alloc=1947.8MB, time=760.46 memory used=41791.1MB, alloc=1947.8MB, time=767.61 memory used=41934.9MB, alloc=1947.8MB, time=775.26 memory used=42068.9MB, alloc=1947.8MB, time=783.06 memory used=42242.8MB, alloc=1947.8MB, time=790.70 memory used=42563.1MB, alloc=1947.8MB, time=799.93 memory used=43038.9MB, alloc=1947.8MB, time=811.18 memory used=43449.0MB, alloc=1947.8MB, time=818.60 memory used=43724.4MB, alloc=1947.8MB, time=829.73 memory used=44137.2MB, alloc=1947.8MB, time=837.22 memory used=44516.2MB, alloc=1947.8MB, time=844.82 memory used=44670.0MB, alloc=1947.8MB, time=851.95 memory used=44771.6MB, alloc=1947.8MB, time=859.23 memory used=44914.2MB, alloc=1947.8MB, time=866.88 memory used=44997.7MB, alloc=1947.8MB, time=874.25 memory used=45126.0MB, alloc=1947.8MB, time=882.32 memory used=45232.8MB, alloc=1947.8MB, time=889.72 memory used=45379.5MB, alloc=1971.8MB, time=897.56 memory used=45424.3MB, alloc=1971.8MB, time=904.83 memory used=45513.5MB, alloc=1971.8MB, time=913.95 memory used=45559.2MB, alloc=1971.8MB, time=920.85 memory used=45653.8MB, alloc=1971.8MB, time=928.73 memory used=45747.4MB, alloc=1971.8MB, time=936.69 memory used=45782.3MB, alloc=1971.8MB, time=943.81 memory used=45818.0MB, alloc=1971.8MB, time=950.81 memory used=45887.7MB, alloc=1971.8MB, time=959.01 memory used=46145.9MB, alloc=1971.8MB, time=967.00 memory used=46386.9MB, alloc=1971.8MB, time=974.48 memory used=46457.4MB, alloc=1971.8MB, time=981.13 memory used=47055.7MB, alloc=1971.8MB, time=988.58 memory used=47454.8MB, alloc=1971.8MB, time=996.02 memory used=47836.4MB, alloc=1971.8MB, time=1003.27 memory used=48589.1MB, alloc=1971.8MB, time=1015.78 memory used=48956.2MB, alloc=1971.8MB, time=1022.82 memory used=49131.6MB, alloc=1971.8MB, time=1029.44 memory used=49216.8MB, alloc=1971.8MB, time=1035.97 memory used=49470.5MB, alloc=1971.8MB, time=1043.05 memory used=49930.9MB, alloc=1971.8MB, time=1050.54 memory used=50278.1MB, alloc=1971.8MB, time=1058.81 memory used=50594.6MB, alloc=1971.8MB, time=1065.87 memory used=50942.2MB, alloc=1971.8MB, time=1074.21 memory used=51383.6MB, alloc=1971.8MB, time=1081.91 memory used=51698.8MB, alloc=1971.8MB, time=1089.46 memory used=51904.0MB, alloc=1971.8MB, time=1096.87 memory used=52220.4MB, alloc=1971.8MB, time=1104.16 memory used=52584.4MB, alloc=1971.8MB, time=1111.44 memory used=52878.0MB, alloc=1971.8MB, time=1138.35 memory used=53548.2MB, alloc=1971.8MB, time=1145.80 memory used=53625.4MB, alloc=1971.8MB, time=1152.44 memory used=53707.0MB, alloc=1971.8MB, time=1159.08 memory used=53794.7MB, alloc=1971.8MB, time=1165.72 memory used=53888.6MB, alloc=1971.8MB, time=1172.39 memory used=53989.4MB, alloc=1971.8MB, time=1179.03 memory used=54098.1MB, alloc=1971.8MB, time=1185.66 memory used=54216.1MB, alloc=1971.8MB, time=1192.32 memory used=54432.5MB, alloc=1971.8MB, time=1199.51 memory used=54838.8MB, alloc=1971.8MB, time=1206.96 memory used=55079.7MB, alloc=1971.8MB, time=1214.09 memory used=55392.2MB, alloc=1971.8MB, time=1226.21 memory used=55877.4MB, alloc=1971.8MB, time=1233.44 memory used=56005.6MB, alloc=1971.8MB, time=1241.16 memory used=56284.5MB, alloc=1971.8MB, time=1248.25 memory used=56403.5MB, alloc=1971.8MB, time=1255.04 memory used=56656.4MB, alloc=1971.8MB, time=1262.20 memory used=56775.3MB, alloc=1971.8MB, time=1269.02 memory used=57058.4MB, alloc=1971.8MB, time=1291.82 memory used=57449.4MB, alloc=1971.8MB, time=1303.06 memory used=57997.7MB, alloc=1971.8MB, time=1310.27 memory used=58074.8MB, alloc=1971.8MB, time=1316.91 memory used=58158.1MB, alloc=1971.8MB, time=1323.49 memory used=58245.6MB, alloc=1971.8MB, time=1330.15 memory used=58338.8MB, alloc=1971.8MB, time=1336.74 memory used=58438.8MB, alloc=1971.8MB, time=1343.34 memory used=58548.6MB, alloc=1971.8MB, time=1349.97 memory used=58667.3MB, alloc=1971.8MB, time=1356.57 memory used=58778.9MB, alloc=1971.8MB, time=1363.24 memory used=58858.0MB, alloc=1971.8MB, time=1371.31 memory used=58890.5MB, alloc=1971.8MB, time=1378.19 memory used=58953.4MB, alloc=1971.8MB, time=1385.55 memory used=58997.3MB, alloc=1971.8MB, time=1392.95 memory used=59010.3MB, alloc=1971.8MB, time=1399.77 memory used=59043.2MB, alloc=1971.8MB, time=1406.78 memory used=59161.4MB, alloc=1971.8MB, time=1414.55 memory used=59202.2MB, alloc=1971.8MB, time=1422.07 memory used=59264.7MB, alloc=2227.8MB, time=1436.79 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428445346 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 4 3 2 2 3 2 F := [-12 x z + 16, -13 y + 14 y z - 2 y z , 4 x y + 5 x y z + 14 x y z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 4 2 3 2 G := [-7 x z - 18 y z , -4 y + 13 x y - 14 z , 15 x y z - 4 y z ] > Problem := [F,G]; Problem := [ 2 2 4 3 2 2 3 2 [-12 x z + 16, -13 y + 14 y z - 2 y z , 4 x y + 5 x y z + 14 x y z], 2 2 4 2 3 2 [-7 x z - 18 y z , -4 y + 13 x y - 14 z , 15 x y z - 4 y z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.5MB, alloc=32.3MB, time=0.51 memory used=47.5MB, alloc=32.3MB, time=0.82 memory used=66.2MB, alloc=56.3MB, time=1.10 memory used=106.0MB, alloc=60.3MB, time=1.70 memory used=145.2MB, alloc=84.3MB, time=2.27 memory used=207.9MB, alloc=92.3MB, time=3.20 memory used=267.0MB, alloc=116.3MB, time=4.08 memory used=344.5MB, alloc=116.3MB, time=5.27 memory used=426.6MB, alloc=396.3MB, time=6.46 memory used=538.9MB, alloc=420.3MB, time=8.01 memory used=680.9MB, alloc=444.3MB, time=9.92 memory used=843.7MB, alloc=444.3MB, time=12.07 memory used=994.1MB, alloc=468.3MB, time=13.86 memory used=1129.5MB, alloc=492.3MB, time=15.20 memory used=1281.9MB, alloc=516.3MB, time=17.06 memory used=1391.1MB, alloc=516.3MB, time=18.80 memory used=1484.8MB, alloc=516.3MB, time=20.19 memory used=1586.0MB, alloc=540.3MB, time=22.01 memory used=1659.1MB, alloc=540.3MB, time=23.13 memory used=1749.0MB, alloc=540.3MB, time=24.67 memory used=1825.1MB, alloc=540.3MB, time=25.98 memory used=1886.8MB, alloc=540.3MB, time=26.95 memory used=1961.9MB, alloc=540.3MB, time=28.50 memory used=2022.6MB, alloc=540.3MB, time=29.69 memory used=2077.9MB, alloc=540.3MB, time=30.63 memory used=2119.0MB, alloc=540.3MB, time=31.48 memory used=2171.7MB, alloc=540.3MB, time=32.67 memory used=2223.7MB, alloc=540.3MB, time=33.83 memory used=2420.7MB, alloc=564.3MB, time=36.47 memory used=2619.3MB, alloc=588.3MB, time=39.81 memory used=2800.7MB, alloc=612.3MB, time=43.02 memory used=2968.7MB, alloc=636.3MB, time=45.98 memory used=3116.2MB, alloc=660.3MB, time=48.66 memory used=3272.8MB, alloc=684.3MB, time=51.83 memory used=3402.3MB, alloc=684.3MB, time=54.04 memory used=3571.4MB, alloc=708.3MB, time=57.41 memory used=3706.9MB, alloc=708.3MB, time=60.33 memory used=3804.3MB, alloc=708.3MB, time=62.23 memory used=3913.2MB, alloc=708.3MB, time=64.82 memory used=4021.8MB, alloc=708.3MB, time=67.50 memory used=4398.2MB, alloc=732.3MB, time=73.89 memory used=4787.1MB, alloc=756.3MB, time=81.10 memory used=5199.8MB, alloc=780.3MB, time=88.81 memory used=5605.2MB, alloc=804.3MB, time=95.41 memory used=6041.2MB, alloc=828.3MB, time=112.66 memory used=6435.6MB, alloc=852.3MB, time=117.04 memory used=6747.2MB, alloc=876.3MB, time=136.78 memory used=7182.1MB, alloc=900.3MB, time=143.25 memory used=7482.5MB, alloc=924.3MB, time=149.28 memory used=7785.4MB, alloc=948.3MB, time=155.60 memory used=8044.0MB, alloc=972.3MB, time=161.04 memory used=8300.9MB, alloc=996.3MB, time=166.07 memory used=8636.2MB, alloc=1020.3MB, time=171.82 memory used=8965.3MB, alloc=1044.3MB, time=176.36 memory used=9402.1MB, alloc=1068.3MB, time=181.24 memory used=9616.9MB, alloc=1324.3MB, time=186.81 memory used=10310.0MB, alloc=1348.3MB, time=200.65 memory used=10947.5MB, alloc=1372.3MB, time=212.66 memory used=11450.6MB, alloc=1396.3MB, time=328.37 memory used=11735.3MB, alloc=1435.8MB, time=331.14 memory used=12570.7MB, alloc=1459.8MB, time=358.60 memory used=12923.6MB, alloc=1483.8MB, time=445.96 memory used=13334.5MB, alloc=1507.8MB, time=451.12 memory used=14154.8MB, alloc=1531.8MB, time=467.95 memory used=14980.5MB, alloc=1555.8MB, time=484.11 memory used=15573.0MB, alloc=1579.8MB, time=492.94 memory used=15905.2MB, alloc=1603.8MB, time=496.70 memory used=16281.9MB, alloc=1627.8MB, time=500.85 memory used=16650.7MB, alloc=1651.8MB, time=504.70 memory used=17159.3MB, alloc=1675.8MB, time=511.41 memory used=17460.2MB, alloc=1699.8MB, time=514.83 memory used=18018.4MB, alloc=1723.8MB, time=519.39 memory used=18363.0MB, alloc=1747.8MB, time=522.92 memory used=18967.1MB, alloc=1771.8MB, time=526.82 memory used=19693.0MB, alloc=1795.8MB, time=566.48 memory used=20344.5MB, alloc=1819.8MB, time=570.78 memory used=20588.6MB, alloc=1819.8MB, time=574.44 memory used=20858.9MB, alloc=1819.8MB, time=578.20 memory used=21162.0MB, alloc=1819.8MB, time=581.97 memory used=21503.4MB, alloc=1819.8MB, time=585.76 memory used=21882.4MB, alloc=1819.8MB, time=589.59 memory used=22165.3MB, alloc=1819.8MB, time=593.25 memory used=22457.2MB, alloc=1819.8MB, time=596.90 memory used=22771.0MB, alloc=1819.8MB, time=600.51 memory used=23105.3MB, alloc=1819.8MB, time=604.26 memory used=23466.1MB, alloc=1819.8MB, time=607.97 memory used=23829.7MB, alloc=1819.8MB, time=611.67 memory used=24147.8MB, alloc=1819.8MB, time=615.34 memory used=24492.2MB, alloc=1819.8MB, time=619.02 memory used=25732.8MB, alloc=1843.8MB, time=632.18 memory used=26731.4MB, alloc=1867.8MB, time=648.35 memory used=27355.7MB, alloc=1891.8MB, time=741.38 memory used=28449.1MB, alloc=1915.8MB, time=781.83 memory used=29100.1MB, alloc=1939.8MB, time=924.46 memory used=29915.3MB, alloc=1963.8MB, time=942.83 memory used=30859.0MB, alloc=1987.8MB, time=955.93 memory used=31859.8MB, alloc=2011.8MB, time=998.27 memory used=32495.4MB, alloc=2038.7MB, time=1008.53 memory used=33121.7MB, alloc=2059.8MB, time=1021.97 memory used=34578.5MB, alloc=2083.8MB, time=1038.98 memory used=35451.1MB, alloc=2107.8MB, time=1055.24 memory used=36680.3MB, alloc=2131.8MB, time=1065.97 memory used=37884.1MB, alloc=2155.8MB, time=1076.47 memory used=39350.1MB, alloc=2179.8MB, time=1087.54 memory used=40425.6MB, alloc=2203.8MB, time=1105.22 memory used=42096.5MB, alloc=2227.8MB, time=1125.82 memory used=43668.1MB, alloc=2251.8MB, time=1146.91 memory used=45260.3MB, alloc=2275.8MB, time=1169.35 memory used=46812.6MB, alloc=2299.8MB, time=1192.71 memory used=48350.7MB, alloc=2323.8MB, time=1216.57 memory used=49824.8MB, alloc=2347.8MB, time=1243.57 memory used=51207.4MB, alloc=2371.8MB, time=1272.99 memory used=52454.9MB, alloc=2395.8MB, time=1301.89 memory used=53780.6MB, alloc=2419.8MB, time=1330.66 memory used=55084.2MB, alloc=2443.8MB, time=1359.23 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428446546 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 2 2 F := [-18 x z - 3 x y, -16 x y - 18 x + 6, 15 x y + 7 y z + 4 y z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 2 2 2 2 G := [-6 y - 17 y z + 9 x z, 8 x z - 6 x y - 14 x, 2 2 3 -15 x y z + 5 y z + 18 z ] > Problem := [F,G]; Problem := [ 3 2 2 2 2 2 2 [-18 x z - 3 x y, -16 x y - 18 x + 6, 15 x y + 7 y z + 4 y z ], [ 4 2 2 2 2 2 2 -6 y - 17 y z + 9 x z, 8 x z - 6 x y - 14 x, 2 2 3 -15 x y z + 5 y z + 18 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.8MB, alloc=32.3MB, time=0.51 memory used=47.8MB, alloc=32.3MB, time=0.82 memory used=66.6MB, alloc=56.3MB, time=1.13 memory used=107.1MB, alloc=60.3MB, time=1.74 memory used=145.4MB, alloc=60.3MB, time=2.34 memory used=183.3MB, alloc=84.3MB, time=2.95 memory used=234.5MB, alloc=84.3MB, time=3.77 memory used=293.5MB, alloc=116.3MB, time=4.76 memory used=374.4MB, alloc=116.3MB, time=6.08 memory used=455.8MB, alloc=140.3MB, time=7.40 memory used=525.5MB, alloc=396.3MB, time=8.46 memory used=635.8MB, alloc=420.3MB, time=10.10 memory used=766.8MB, alloc=420.3MB, time=12.12 memory used=894.5MB, alloc=444.3MB, time=14.09 memory used=1013.3MB, alloc=468.3MB, time=15.82 memory used=1139.7MB, alloc=468.3MB, time=17.57 memory used=1263.5MB, alloc=492.3MB, time=19.45 memory used=1378.9MB, alloc=492.3MB, time=21.32 memory used=1473.7MB, alloc=492.3MB, time=22.75 memory used=1566.3MB, alloc=492.3MB, time=24.34 memory used=1664.5MB, alloc=492.3MB, time=25.95 memory used=1747.0MB, alloc=492.3MB, time=27.18 memory used=1838.0MB, alloc=492.3MB, time=28.68 memory used=1910.2MB, alloc=516.3MB, time=29.85 memory used=1997.1MB, alloc=516.3MB, time=31.38 memory used=2066.6MB, alloc=516.3MB, time=32.57 memory used=2136.7MB, alloc=516.3MB, time=33.91 memory used=2211.9MB, alloc=516.3MB, time=35.41 memory used=2274.7MB, alloc=516.3MB, time=36.60 memory used=2332.8MB, alloc=516.3MB, time=37.64 memory used=2398.9MB, alloc=516.3MB, time=39.20 memory used=2447.4MB, alloc=516.3MB, time=40.21 memory used=2507.9MB, alloc=516.3MB, time=41.45 memory used=2556.6MB, alloc=516.3MB, time=42.50 memory used=2601.5MB, alloc=516.3MB, time=43.46 memory used=2800.3MB, alloc=540.3MB, time=45.87 memory used=3025.2MB, alloc=564.3MB, time=48.98 memory used=3208.3MB, alloc=564.3MB, time=51.36 memory used=3397.3MB, alloc=588.3MB, time=54.47 memory used=3568.5MB, alloc=612.3MB, time=57.50 memory used=3739.2MB, alloc=612.3MB, time=60.53 memory used=3894.7MB, alloc=636.3MB, time=63.39 memory used=4069.9MB, alloc=636.3MB, time=66.64 memory used=4228.0MB, alloc=660.3MB, time=69.70 memory used=4367.6MB, alloc=660.3MB, time=72.36 memory used=4504.0MB, alloc=660.3MB, time=75.21 memory used=4630.8MB, alloc=660.3MB, time=77.45 memory used=4752.3MB, alloc=660.3MB, time=79.92 memory used=4840.0MB, alloc=660.3MB, time=81.84 memory used=4942.5MB, alloc=660.3MB, time=84.23 memory used=5031.6MB, alloc=660.3MB, time=86.17 memory used=5116.8MB, alloc=660.3MB, time=88.40 memory used=5443.0MB, alloc=684.3MB, time=94.13 memory used=5788.8MB, alloc=708.3MB, time=100.30 memory used=6150.8MB, alloc=732.3MB, time=107.29 memory used=6469.4MB, alloc=756.3MB, time=111.94 memory used=6661.0MB, alloc=780.3MB, time=113.69 memory used=6899.5MB, alloc=804.3MB, time=116.30 memory used=7117.5MB, alloc=828.3MB, time=118.21 memory used=7325.6MB, alloc=828.3MB, time=119.76 memory used=7536.2MB, alloc=828.3MB, time=121.25 memory used=7743.2MB, alloc=828.3MB, time=122.67 memory used=7983.6MB, alloc=852.3MB, time=160.48 memory used=8226.7MB, alloc=852.3MB, time=167.72 memory used=8450.8MB, alloc=852.3MB, time=169.20 memory used=8649.8MB, alloc=852.3MB, time=170.59 memory used=8894.6MB, alloc=852.3MB, time=171.98 memory used=9200.3MB, alloc=867.8MB, time=173.52 memory used=9322.2MB, alloc=867.8MB, time=174.80 memory used=9454.3MB, alloc=867.8MB, time=176.07 memory used=9600.8MB, alloc=867.8MB, time=177.35 memory used=10006.5MB, alloc=867.8MB, time=179.71 memory used=10214.4MB, alloc=867.8MB, time=181.28 memory used=10456.2MB, alloc=867.8MB, time=182.75 memory used=10689.3MB, alloc=867.8MB, time=214.08 memory used=10965.4MB, alloc=867.8MB, time=283.74 memory used=11211.6MB, alloc=867.8MB, time=285.33 memory used=11392.7MB, alloc=867.8MB, time=286.73 memory used=11597.5MB, alloc=867.8MB, time=288.14 memory used=11838.5MB, alloc=867.8MB, time=289.63 memory used=12122.7MB, alloc=867.8MB, time=291.15 memory used=12250.3MB, alloc=867.8MB, time=292.48 memory used=12367.8MB, alloc=867.8MB, time=293.83 memory used=12490.1MB, alloc=867.8MB, time=295.16 memory used=12619.5MB, alloc=867.8MB, time=296.50 memory used=12759.5MB, alloc=867.8MB, time=297.90 memory used=12907.3MB, alloc=867.8MB, time=299.24 memory used=13064.7MB, alloc=867.8MB, time=300.57 memory used=13236.7MB, alloc=867.8MB, time=301.91 memory used=13652.9MB, alloc=867.8MB, time=304.03 memory used=13932.0MB, alloc=867.8MB, time=320.69 memory used=14154.9MB, alloc=867.8MB, time=322.16 memory used=14361.4MB, alloc=867.8MB, time=323.53 memory used=14738.0MB, alloc=867.8MB, time=325.06 memory used=14871.8MB, alloc=867.8MB, time=326.37 memory used=15360.2MB, alloc=867.8MB, time=334.71 memory used=15643.7MB, alloc=867.8MB, time=373.56 memory used=15885.7MB, alloc=867.8MB, time=375.13 memory used=16059.8MB, alloc=867.8MB, time=376.57 memory used=16260.2MB, alloc=867.8MB, time=377.95 memory used=16495.7MB, alloc=867.8MB, time=379.32 memory used=16772.8MB, alloc=867.8MB, time=380.74 memory used=16895.7MB, alloc=867.8MB, time=382.00 memory used=17013.1MB, alloc=867.8MB, time=383.26 memory used=17137.2MB, alloc=867.8MB, time=384.57 memory used=17270.2MB, alloc=867.8MB, time=385.88 memory used=17409.5MB, alloc=867.8MB, time=387.15 memory used=17560.2MB, alloc=867.8MB, time=388.47 memory used=17721.9MB, alloc=867.8MB, time=389.75 memory used=17902.3MB, alloc=867.8MB, time=391.11 memory used=18457.4MB, alloc=891.8MB, time=397.50 memory used=18972.7MB, alloc=891.8MB, time=403.62 memory used=19482.5MB, alloc=891.8MB, time=414.51 memory used=19989.1MB, alloc=891.8MB, time=434.31 memory used=20501.6MB, alloc=891.8MB, time=461.93 memory used=21031.1MB, alloc=891.8MB, time=494.85 memory used=21309.1MB, alloc=891.8MB, time=497.09 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used=53091.0MB, alloc=963.8MB, time=1063.16 memory used=53414.6MB, alloc=963.8MB, time=1065.24 memory used=53651.9MB, alloc=963.8MB, time=1067.09 memory used=54049.5MB, alloc=963.8MB, time=1069.27 memory used=54284.7MB, alloc=963.8MB, time=1071.09 memory used=54684.9MB, alloc=963.8MB, time=1073.27 memory used=55019.3MB, alloc=963.8MB, time=1075.50 memory used=55269.4MB, alloc=987.8MB, time=1077.36 memory used=55526.7MB, alloc=987.8MB, time=1079.09 memory used=55802.8MB, alloc=987.8MB, time=1080.84 memory used=55929.5MB, alloc=987.8MB, time=1082.39 memory used=56337.1MB, alloc=987.8MB, time=1084.68 memory used=56544.4MB, alloc=987.8MB, time=1086.32 memory used=56925.9MB, alloc=987.8MB, time=1089.35 memory used=57236.2MB, alloc=987.8MB, time=1091.22 memory used=57371.5MB, alloc=987.8MB, time=1092.83 memory used=57530.2MB, alloc=987.8MB, time=1094.43 memory used=57927.0MB, alloc=987.8MB, time=1097.51 memory used=58189.5MB, alloc=987.8MB, time=1099.59 memory used=58473.9MB, alloc=1011.8MB, 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memory used=61955.8MB, alloc=1011.8MB, time=1135.28 memory used=62106.5MB, alloc=1011.8MB, time=1136.87 memory used=62264.8MB, alloc=1011.8MB, time=1138.54 memory used=62429.8MB, alloc=1011.8MB, time=1140.18 memory used=62886.5MB, alloc=1011.8MB, time=1243.34 memory used=63153.6MB, alloc=1011.8MB, time=1245.19 memory used=63415.2MB, alloc=1011.8MB, time=1246.95 memory used=63744.4MB, alloc=1011.8MB, time=1248.77 memory used=63975.1MB, alloc=1011.8MB, time=1250.46 memory used=64082.5MB, alloc=1011.8MB, time=1251.98 memory used=64195.0MB, alloc=1011.8MB, time=1253.51 memory used=64316.3MB, alloc=1011.8MB, time=1255.04 memory used=64441.6MB, alloc=1011.8MB, time=1256.59 memory used=64570.3MB, alloc=1011.8MB, time=1258.13 memory used=64709.3MB, alloc=1011.8MB, time=1259.69 memory used=64851.8MB, alloc=1011.8MB, time=1261.25 memory used=64997.6MB, alloc=1011.8MB, time=1262.91 memory used=65154.0MB, alloc=1011.8MB, time=1264.52 memory used=65313.6MB, alloc=1011.8MB, time=1266.20 memory used=65476.2MB, alloc=1011.8MB, time=1267.84 memory used=65649.8MB, alloc=1011.8MB, time=1269.48 memory used=65826.3MB, alloc=1011.8MB, time=1271.20 memory used=66013.5MB, alloc=1011.8MB, time=1272.87 memory used=66203.5MB, alloc=1011.8MB, time=1274.54 memory used=66404.2MB, alloc=1011.8MB, time=1276.26 memory used=66582.5MB, alloc=1011.8MB, time=1277.92 memory used=66719.9MB, alloc=1011.8MB, time=1279.51 memory used=66855.9MB, alloc=1011.8MB, time=1281.13 memory used=67001.2MB, alloc=1011.8MB, time=1282.74 memory used=67147.1MB, alloc=1011.8MB, time=1284.37 memory used=67293.7MB, alloc=1011.8MB, time=1285.96 memory used=67449.4MB, alloc=1011.8MB, time=1287.57 memory used=67605.5MB, alloc=1011.8MB, time=1289.15 memory used=67762.1MB, alloc=1011.8MB, time=1290.71 memory used=67927.4MB, alloc=1011.8MB, time=1292.32 memory used=68092.8MB, alloc=1011.8MB, time=1293.87 memory used=68266.7MB, alloc=1011.8MB, time=1295.48 memory used=68440.4MB, alloc=1011.8MB, time=1297.08 memory used=68622.2MB, alloc=1011.8MB, time=1298.72 memory used=68803.3MB, alloc=1011.8MB, time=1300.36 memory used=68992.2MB, alloc=1011.8MB, time=1301.95 memory used=69188.3MB, alloc=1011.8MB, time=1303.55 memory used=69382.8MB, alloc=1011.8MB, time=1305.18 memory used=69583.9MB, alloc=1011.8MB, time=1306.79 memory used=69754.3MB, alloc=1011.8MB, time=1308.38 memory used=69908.5MB, alloc=1011.8MB, time=1309.95 memory used=70068.0MB, alloc=1011.8MB, time=1311.53 memory used=70228.0MB, alloc=1011.8MB, time=1313.10 memory used=70391.8MB, alloc=1011.8MB, time=1314.67 memory used=70559.3MB, alloc=1011.8MB, time=1316.26 memory used=70732.4MB, alloc=1011.8MB, time=1317.84 memory used=70909.0MB, alloc=1011.8MB, time=1319.44 memory used=71088.3MB, alloc=1011.8MB, time=1321.05 memory used=71271.5MB, alloc=1011.8MB, time=1322.63 memory used=71459.5MB, alloc=1011.8MB, time=1324.21 memory used=71653.3MB, alloc=1011.8MB, time=1325.80 memory used=71854.9MB, alloc=1011.8MB, time=1327.40 memory used=72063.2MB, alloc=1011.8MB, time=1329.00 memory used=72242.7MB, alloc=1011.8MB, time=1330.56 memory used=72414.7MB, alloc=1011.8MB, time=1332.14 memory used=72862.3MB, alloc=1011.8MB, time=1335.39 memory used=73148.7MB, alloc=1011.8MB, time=1337.47 memory used=73436.0MB, alloc=1011.8MB, time=1339.43 memory used=73648.5MB, alloc=1011.8MB, time=1341.15 memory used=73888.7MB, alloc=1011.8MB, time=1342.91 memory used=74156.4MB, alloc=1011.8MB, time=1344.73 memory used=74455.9MB, alloc=1011.8MB, time=1346.56 memory used=74786.0MB, alloc=1011.8MB, time=1348.42 memory used=75193.3MB, alloc=1011.8MB, time=1350.38 memory used=75294.1MB, alloc=1011.8MB, time=1351.96 memory used=75394.6MB, alloc=1011.8MB, time=1353.51 memory used=75500.5MB, alloc=1011.8MB, time=1355.07 memory used=75609.3MB, alloc=1011.8MB, time=1356.61 memory used=75718.1MB, alloc=1011.8MB, time=1358.19 memory used=75830.9MB, alloc=1011.8MB, time=1359.76 memory used=75948.5MB, alloc=1011.8MB, time=1361.34 memory used=76068.6MB, alloc=1011.8MB, time=1362.90 memory used=76192.6MB, alloc=1011.8MB, time=1364.48 memory used=76319.9MB, alloc=1011.8MB, time=1366.04 memory used=76450.9MB, alloc=1011.8MB, time=1367.65 memory used=76585.9MB, alloc=1011.8MB, time=1369.29 memory used=76727.3MB, alloc=1011.8MB, time=1370.89 memory used=76874.2MB, alloc=1011.8MB, time=1372.50 memory used=77025.1MB, alloc=1011.8MB, time=1374.10 memory used=77182.3MB, alloc=1011.8MB, time=1375.72 memory used=77347.2MB, alloc=1011.8MB, time=1377.34 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428447746 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [-3 x y z + 11 x y z - 4 x y, 20 y z + 4 x y z - 12 x z , 2 3 2 4 x y z + 15 y z - 11 y z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 4 2 2 3 G := [9 x y + 10 z + 7 y z, -19 x z + 4 z - 18 x z, 2 3 19 x y z - 10 x - 7 x y z] > Problem := [F,G]; 2 2 2 2 Problem := [[-3 x y z + 11 x y z - 4 x y, 20 y z + 4 x y z - 12 x z , 2 3 2 3 4 4 x y z + 15 y z - 11 y z], [9 x y + 10 z + 7 y z, 2 2 3 2 3 -19 x z + 4 z - 18 x z, 19 x y z - 10 x - 7 x y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.6MB, alloc=32.3MB, time=0.49 memory used=47.6MB, alloc=32.3MB, time=0.79 memory used=66.7MB, alloc=56.3MB, time=1.09 memory used=106.7MB, alloc=60.3MB, time=1.68 memory used=145.3MB, alloc=84.3MB, time=2.25 memory used=205.1MB, alloc=92.3MB, time=3.16 memory used=265.7MB, alloc=116.3MB, time=4.06 memory used=350.6MB, alloc=116.3MB, time=5.33 memory used=424.0MB, alloc=372.3MB, time=6.34 memory used=505.1MB, alloc=372.3MB, time=7.39 memory used=588.4MB, alloc=396.3MB, time=8.62 memory used=691.2MB, alloc=396.3MB, time=10.20 memory used=793.8MB, alloc=420.3MB, time=11.64 memory used=919.7MB, alloc=420.3MB, time=13.14 memory used=1042.7MB, alloc=444.3MB, time=15.03 memory used=1200.4MB, alloc=468.3MB, time=17.24 memory used=1336.9MB, alloc=468.3MB, time=19.00 memory used=1470.9MB, alloc=468.3MB, time=20.97 memory used=1605.9MB, alloc=492.3MB, time=22.81 memory used=1742.5MB, alloc=492.3MB, time=24.60 memory used=1866.7MB, alloc=516.3MB, time=26.39 memory used=1969.4MB, alloc=516.3MB, time=27.74 memory used=2104.0MB, alloc=516.3MB, time=29.91 memory used=2216.0MB, alloc=516.3MB, time=31.48 memory used=2315.1MB, alloc=516.3MB, time=32.76 memory used=2408.4MB, alloc=540.3MB, time=34.49 memory used=2492.6MB, alloc=540.3MB, time=35.79 memory used=2574.2MB, alloc=540.3MB, time=36.99 memory used=2632.8MB, alloc=540.3MB, time=37.84 memory used=2728.6MB, alloc=540.3MB, time=39.26 memory used=2803.3MB, alloc=540.3MB, time=40.54 memory used=2868.0MB, alloc=540.3MB, time=41.69 memory used=2934.2MB, alloc=540.3MB, time=42.82 memory used=3001.5MB, alloc=540.3MB, time=43.83 memory used=3058.7MB, alloc=564.3MB, time=44.68 memory used=3116.8MB, alloc=564.3MB, time=45.76 memory used=3376.0MB, alloc=588.3MB, time=49.27 memory used=3606.4MB, alloc=612.3MB, time=52.92 memory used=3853.9MB, alloc=636.3MB, time=55.47 memory used=4028.4MB, alloc=636.3MB, time=56.88 memory used=4325.2MB, alloc=636.3MB, time=58.13 memory used=4513.9MB, alloc=636.3MB, time=59.63 memory used=4778.5MB, alloc=636.3MB, time=62.42 memory used=4971.9MB, alloc=660.3MB, time=64.87 memory used=5155.2MB, alloc=684.3MB, time=67.14 memory used=5337.8MB, alloc=684.3MB, time=70.69 memory used=5502.7MB, alloc=708.3MB, time=73.99 memory used=5644.1MB, alloc=708.3MB, time=76.34 memory used=5820.5MB, alloc=708.3MB, time=78.66 memory used=5975.7MB, alloc=732.3MB, time=81.17 memory used=6099.8MB, alloc=732.3MB, time=83.72 memory used=6230.4MB, alloc=732.3MB, time=86.66 memory used=6350.0MB, alloc=732.3MB, time=88.92 memory used=6457.6MB, alloc=732.3MB, time=91.24 memory used=6561.5MB, alloc=732.3MB, time=93.74 memory used=6661.3MB, alloc=732.3MB, time=95.87 memory used=7056.2MB, alloc=756.3MB, time=102.01 memory used=7439.1MB, alloc=780.3MB, time=107.18 memory used=7843.8MB, alloc=804.3MB, time=112.34 memory used=8261.0MB, alloc=828.3MB, time=118.66 memory used=8465.5MB, alloc=852.3MB, time=120.82 memory used=8687.8MB, alloc=876.3MB, time=122.59 memory used=8933.2MB, alloc=900.3MB, time=125.41 memory used=9207.2MB, alloc=924.3MB, time=128.37 memory used=9533.3MB, alloc=924.3MB, time=131.45 memory used=9965.7MB, alloc=924.3MB, time=135.68 memory used=10330.1MB, alloc=948.3MB, time=140.88 memory used=10653.7MB, alloc=972.3MB, time=143.74 memory used=10966.7MB, alloc=972.3MB, time=146.09 memory used=11276.3MB, alloc=972.3MB, time=148.75 memory used=11583.2MB, alloc=972.3MB, time=152.08 memory used=11889.2MB, alloc=972.3MB, time=154.29 memory used=12374.1MB, alloc=996.3MB, time=160.47 memory used=12724.5MB, alloc=1020.3MB, time=166.12 memory used=13219.8MB, alloc=1020.3MB, time=171.94 memory used=13560.7MB, alloc=1020.3MB, time=174.74 memory used=13900.5MB, alloc=1020.3MB, time=177.30 memory used=14273.7MB, alloc=1020.3MB, time=180.51 memory used=14655.2MB, alloc=1044.3MB, time=185.22 memory used=14903.3MB, alloc=1300.3MB, time=189.69 memory used=15587.5MB, alloc=1324.3MB, time=202.15 memory used=16271.9MB, alloc=1348.3MB, time=215.52 memory used=16974.0MB, alloc=1372.3MB, time=230.66 memory used=17282.9MB, alloc=1396.3MB, time=237.44 memory used=17772.2MB, alloc=1420.3MB, time=243.72 memory used=18515.3MB, alloc=1444.3MB, time=254.16 memory used=19287.1MB, alloc=1468.3MB, time=267.64 memory used=19747.3MB, alloc=1492.3MB, time=274.32 memory used=20066.6MB, alloc=1516.3MB, time=278.12 memory used=20478.2MB, alloc=1540.3MB, time=401.02 memory used=20769.7MB, alloc=1564.3MB, time=404.45 memory used=21235.6MB, alloc=1603.8MB, time=408.19 memory used=21808.3MB, alloc=1627.8MB, time=419.54 memory used=22343.1MB, alloc=1651.8MB, time=432.92 memory used=22825.5MB, alloc=1675.8MB, time=445.14 memory used=23388.4MB, alloc=1699.8MB, time=451.87 memory used=24425.8MB, alloc=1723.8MB, time=468.01 memory used=25422.2MB, alloc=1747.8MB, time=485.50 memory used=26396.5MB, alloc=1771.8MB, time=506.02 memory used=27369.7MB, alloc=1795.8MB, time=519.41 memory used=28229.5MB, alloc=1819.8MB, time=530.95 memory used=29106.0MB, alloc=1843.8MB, time=548.35 memory used=29982.6MB, alloc=1867.8MB, time=561.32 memory used=30591.4MB, alloc=1891.8MB, time=568.92 memory used=31192.3MB, alloc=1915.8MB, time=695.04 memory used=31644.8MB, alloc=1939.8MB, time=699.60 memory used=32336.2MB, alloc=1963.8MB, time=708.51 memory used=33238.3MB, alloc=1987.8MB, time=727.00 memory used=34237.5MB, alloc=2011.8MB, time=745.11 memory used=35393.5MB, alloc=2035.8MB, time=762.49 memory used=35919.7MB, alloc=2059.8MB, time=767.18 memory used=36292.9MB, alloc=2083.8MB, time=772.12 memory used=36999.2MB, alloc=2083.8MB, time=778.46 memory used=37440.4MB, alloc=2083.8MB, time=782.94 memory used=38105.9MB, alloc=2083.8MB, time=798.12 memory used=39113.5MB, alloc=2083.8MB, time=809.94 memory used=39760.0MB, alloc=2107.8MB, time=919.88 memory used=40305.4MB, alloc=2107.8MB, time=924.94 memory used=40548.1MB, alloc=2107.8MB, time=929.22 memory used=40826.1MB, alloc=2107.8MB, time=933.46 memory used=41136.7MB, alloc=2107.8MB, time=937.70 memory used=41486.1MB, alloc=2107.8MB, time=942.02 memory used=41826.8MB, alloc=2107.8MB, time=946.46 memory used=42114.1MB, alloc=2107.8MB, time=950.72 memory used=42426.0MB, alloc=2107.8MB, time=955.01 memory used=42771.0MB, alloc=2107.8MB, time=959.32 memory used=43130.4MB, alloc=2107.8MB, time=963.61 memory used=43918.3MB, alloc=2107.8MB, time=1083.08 memory used=44470.8MB, alloc=2107.8MB, time=1088.32 memory used=44713.2MB, alloc=2107.8MB, time=1092.68 memory used=44984.9MB, alloc=2107.8MB, time=1096.99 memory used=45294.1MB, alloc=2107.8MB, time=1101.36 memory used=45639.8MB, alloc=2107.8MB, time=1105.67 memory used=45999.3MB, alloc=2107.8MB, time=1109.94 memory used=46280.0MB, alloc=2107.8MB, time=1114.12 memory used=46584.7MB, alloc=2107.8MB, time=1118.37 memory used=46918.0MB, alloc=2107.8MB, time=1122.69 memory used=47277.3MB, alloc=2107.8MB, time=1126.95 memory used=47620.8MB, alloc=2107.8MB, time=1131.20 memory used=48355.6MB, alloc=2107.8MB, time=1165.16 memory used=48665.4MB, alloc=2107.8MB, time=1169.42 memory used=48924.2MB, alloc=2107.8MB, time=1173.64 memory used=49229.1MB, alloc=2107.8MB, time=1177.84 memory used=49581.6MB, alloc=2107.8MB, time=1182.09 memory used=49888.4MB, alloc=2107.8MB, time=1186.26 memory used=50225.6MB, alloc=2107.8MB, time=1190.46 memory used=51234.9MB, alloc=2131.8MB, time=1203.26 memory used=52198.9MB, alloc=2155.8MB, time=1217.52 memory used=53077.1MB, alloc=2179.8MB, time=1232.24 memory used=53913.1MB, alloc=2203.8MB, time=1240.58 memory used=54887.0MB, alloc=2203.8MB, time=1256.97 memory used=55644.1MB, alloc=2203.8MB, time=1265.86 memory used=55965.5MB, alloc=2203.8MB, time=1270.51 memory used=56666.0MB, alloc=2227.8MB, time=1282.48 memory used=57455.8MB, alloc=2227.8MB, time=1290.34 memory used=58144.8MB, alloc=2227.8MB, time=1296.50 memory used=59020.1MB, alloc=2227.8MB, time=1303.05 memory used=59805.5MB, alloc=2227.8MB, time=1308.99 memory used=60042.8MB, alloc=2227.8MB, time=1313.64 memory used=60658.8MB, alloc=2227.8MB, time=1319.88 memory used=60946.3MB, alloc=2227.8MB, time=1324.62 memory used=61685.3MB, alloc=2227.8MB, time=1330.63 memory used=62473.8MB, alloc=2227.8MB, time=1336.66 memory used=62711.4MB, alloc=2227.8MB, time=1341.31 memory used=63337.6MB, alloc=2227.8MB, time=1347.64 memory used=63614.8MB, alloc=2227.8MB, time=1352.37 memory used=64440.8MB, alloc=2251.8MB, time=1364.96 memory used=65128.1MB, alloc=2275.8MB, time=1371.11 memory used=65671.6MB, alloc=2299.8MB, time=1376.53 memory used=66318.8MB, alloc=2299.8MB, time=1382.04 memory used=67123.1MB, alloc=2299.8MB, time=1387.64 memory used=67443.8MB, alloc=2299.8MB, time=1392.55 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428448946 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 3 2 F := [x y z + 18 x + 5 z , 10 x y - 15 x y z - 6 y, -19 y z + 12 x z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 2 2 2 G := [7 x y - 5 x y - 20 y z, -5 x z + 5 y z - 3 z , 2 2 2 9 y z - 6 x y - 8 y ] > Problem := [F,G]; Problem := [ 2 2 3 2 3 2 [x y z + 18 x + 5 z , 10 x y - 15 x y z - 6 y, -19 y z + 12 x z], [ 2 2 3 2 2 2 2 2 7 x y - 5 x y - 20 y z, -5 x z + 5 y z - 3 z , 2 2 2 9 y z - 6 x y - 8 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.5MB, alloc=32.3MB, time=0.48 memory used=47.7MB, alloc=32.3MB, time=0.79 memory used=67.9MB, alloc=56.3MB, time=1.10 memory used=107.7MB, alloc=60.3MB, time=1.70 memory used=146.7MB, alloc=84.3MB, time=2.31 memory used=208.2MB, alloc=92.3MB, time=3.26 memory used=269.3MB, alloc=116.3MB, time=4.21 memory used=352.1MB, alloc=116.3MB, time=5.47 memory used=427.8MB, alloc=396.3MB, time=6.66 memory used=531.9MB, alloc=396.3MB, time=8.32 memory used=634.4MB, alloc=420.3MB, time=9.91 memory used=759.6MB, alloc=444.3MB, time=12.00 memory used=907.9MB, alloc=468.3MB, time=14.50 memory used=1044.0MB, alloc=492.3MB, time=16.85 memory used=1175.0MB, alloc=492.3MB, time=19.20 memory used=1292.7MB, alloc=492.3MB, time=21.33 memory used=1413.1MB, alloc=492.3MB, time=23.63 memory used=1520.5MB, alloc=516.3MB, time=25.67 memory used=1623.9MB, alloc=516.3MB, time=27.41 memory used=1711.3MB, alloc=516.3MB, time=29.09 memory used=1793.5MB, alloc=516.3MB, time=30.81 memory used=1886.3MB, alloc=516.3MB, time=32.74 memory used=1970.1MB, alloc=516.3MB, time=34.45 memory used=2051.0MB, alloc=516.3MB, time=36.15 memory used=2124.2MB, alloc=516.3MB, time=37.74 memory used=2192.4MB, alloc=516.3MB, time=39.23 memory used=2261.3MB, alloc=516.3MB, time=40.85 memory used=2311.5MB, alloc=516.3MB, time=41.96 memory used=2363.6MB, alloc=516.3MB, time=43.25 memory used=2562.3MB, alloc=540.3MB, time=47.48 memory used=2779.8MB, alloc=564.3MB, time=52.55 memory used=3004.5MB, alloc=588.3MB, time=57.02 memory used=3209.1MB, alloc=612.3MB, time=61.54 memory used=3394.8MB, alloc=636.3MB, time=65.98 memory used=3584.2MB, alloc=660.3MB, time=70.32 memory used=3759.5MB, alloc=684.3MB, time=74.38 memory used=3912.0MB, alloc=684.3MB, time=77.99 memory used=4069.7MB, alloc=684.3MB, time=80.29 memory used=4220.3MB, alloc=684.3MB, time=83.54 memory used=4357.0MB, alloc=684.3MB, time=87.00 memory used=4486.1MB, alloc=708.3MB, time=90.42 memory used=4583.5MB, alloc=708.3MB, time=92.65 memory used=4681.4MB, alloc=708.3MB, time=95.06 memory used=4814.7MB, alloc=708.3MB, time=97.89 memory used=5041.9MB, alloc=732.3MB, time=101.42 memory used=5435.5MB, alloc=756.3MB, time=106.14 memory used=5863.3MB, alloc=780.3MB, time=113.17 memory used=6291.5MB, alloc=804.3MB, time=119.94 memory used=6710.0MB, alloc=828.3MB, time=127.20 memory used=7137.4MB, alloc=852.3MB, time=134.74 memory used=7568.7MB, alloc=876.3MB, time=142.64 memory used=7992.8MB, alloc=900.3MB, time=150.90 memory used=8450.7MB, alloc=924.3MB, time=158.71 memory used=8931.6MB, alloc=948.3MB, time=166.43 memory used=9385.6MB, alloc=972.3MB, time=175.23 memory used=9832.2MB, alloc=996.3MB, time=184.40 memory used=10332.0MB, alloc=1020.3MB, time=192.53 memory used=10853.0MB, alloc=1044.3MB, time=200.87 memory used=11378.1MB, alloc=1068.3MB, time=209.56 memory used=11902.5MB, alloc=1092.3MB, time=218.94 memory used=12389.4MB, alloc=1116.3MB, time=229.28 memory used=12872.1MB, alloc=1140.3MB, time=239.81 memory used=13357.4MB, alloc=1164.3MB, time=250.30 memory used=13846.6MB, alloc=1188.3MB, time=260.69 memory used=14340.4MB, alloc=1212.3MB, time=271.09 memory used=14852.3MB, alloc=1236.3MB, time=281.10 memory used=15251.3MB, alloc=1260.3MB, time=296.16 memory used=15616.9MB, alloc=1284.3MB, time=312.16 memory used=15984.5MB, alloc=1308.3MB, time=328.70 memory used=16360.2MB, alloc=1332.3MB, time=345.79 memory used=16746.4MB, alloc=1356.3MB, time=363.81 memory used=17144.9MB, alloc=1380.3MB, time=382.63 memory used=17557.0MB, alloc=1404.3MB, time=402.10 memory used=17983.3MB, alloc=1428.3MB, time=422.56 memory used=18423.8MB, alloc=1452.3MB, time=443.08 memory used=18879.4MB, alloc=1476.3MB, time=464.41 memory used=19350.8MB, alloc=1500.3MB, time=486.30 memory used=19836.8MB, alloc=1524.3MB, time=508.97 memory used=20336.9MB, alloc=1548.3MB, time=532.37 memory used=20851.1MB, alloc=1572.3MB, time=556.82 memory used=21380.2MB, alloc=1596.3MB, time=581.92 memory used=21925.0MB, alloc=1620.3MB, time=607.95 memory used=22485.6MB, alloc=1644.3MB, time=635.04 memory used=23062.5MB, alloc=1668.3MB, time=662.81 memory used=23656.1MB, alloc=1692.3MB, time=691.18 memory used=24266.2MB, alloc=1716.3MB, time=720.67 memory used=24892.6MB, alloc=1740.3MB, time=750.94 memory used=25535.4MB, alloc=1764.3MB, time=781.87 memory used=26194.8MB, alloc=1788.3MB, time=814.15 memory used=26871.4MB, alloc=1812.3MB, time=847.16 memory used=27564.3MB, alloc=1836.3MB, time=881.46 memory used=28273.4MB, alloc=1860.3MB, time=915.61 memory used=28998.9MB, alloc=1884.3MB, time=950.40 memory used=29741.7MB, alloc=1908.3MB, time=985.82 memory used=30500.4MB, alloc=1932.3MB, time=1022.25 memory used=31275.7MB, alloc=1956.3MB, time=1059.55 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428450146 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 3 4 F := [-17 x - 12 x y z + 13 x y z, 10 x z + z + 3, 2 2 2 -6 x y z + 15 y z - 14 x z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 3 4 G := [-13 x - 12 x y z - 16 y z, -3 x y z - 14 x y + 4 z , 2 2 7 x y z - x z - 15] > Problem := [F,G]; 4 2 3 4 Problem := [[-17 x - 12 x y z + 13 x y z, 10 x z + z + 3, 2 2 2 4 2 -6 x y z + 15 y z - 14 x z], [-13 x - 12 x y z - 16 y z, 2 3 4 2 2 -3 x y z - 14 x y + 4 z , 7 x y z - x z - 15]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.4MB, alloc=32.3MB, time=0.49 memory used=47.0MB, alloc=32.3MB, time=0.81 memory used=66.6MB, alloc=56.3MB, time=1.13 memory used=106.9MB, alloc=60.3MB, time=1.75 memory used=146.0MB, alloc=60.3MB, time=2.34 memory used=184.0MB, alloc=84.3MB, time=2.94 memory used=228.8MB, alloc=84.3MB, time=3.64 memory used=291.1MB, alloc=92.3MB, time=4.44 memory used=352.1MB, alloc=92.3MB, time=5.34 memory used=416.4MB, alloc=116.3MB, time=6.21 memory used=474.5MB, alloc=372.3MB, time=6.95 memory used=565.6MB, alloc=372.3MB, time=8.17 memory used=656.5MB, alloc=396.3MB, time=9.33 memory used=771.3MB, alloc=396.3MB, time=10.85 memory used=890.4MB, alloc=396.3MB, time=12.32 memory used=1007.3MB, alloc=420.3MB, time=13.39 memory used=1136.1MB, alloc=420.3MB, time=14.92 memory used=1261.7MB, alloc=444.3MB, time=16.50 memory used=1376.9MB, alloc=444.3MB, time=17.79 memory used=1498.8MB, alloc=444.3MB, time=19.21 memory used=1617.9MB, alloc=444.3MB, time=20.69 memory used=1721.9MB, alloc=468.3MB, time=21.93 memory used=1824.5MB, alloc=468.3MB, time=23.31 memory used=1902.9MB, alloc=468.3MB, time=24.48 memory used=1992.0MB, alloc=468.3MB, time=25.61 memory used=2082.3MB, alloc=492.3MB, time=26.62 memory used=2162.1MB, alloc=492.3MB, time=27.70 memory used=2241.0MB, alloc=492.3MB, time=28.95 memory used=2320.3MB, alloc=492.3MB, time=30.15 memory used=2384.4MB, alloc=492.3MB, time=31.04 memory used=2442.0MB, alloc=492.3MB, time=31.89 memory used=2504.8MB, alloc=492.3MB, time=32.95 memory used=2576.7MB, alloc=492.3MB, time=33.92 memory used=2639.0MB, alloc=492.3MB, time=34.81 memory used=2706.1MB, alloc=492.3MB, time=35.82 memory used=2758.8MB, alloc=492.3MB, time=36.60 memory used=2805.5MB, alloc=492.3MB, time=37.37 memory used=2854.3MB, alloc=492.3MB, time=38.09 memory used=2922.1MB, alloc=492.3MB, time=39.27 memory used=2985.6MB, alloc=492.3MB, time=40.24 memory used=3022.9MB, alloc=492.3MB, time=40.93 memory used=3082.6MB, alloc=492.3MB, time=42.13 memory used=3124.9MB, alloc=492.3MB, time=43.06 memory used=3316.6MB, alloc=516.3MB, time=45.96 memory used=3532.9MB, alloc=540.3MB, time=49.16 memory used=3728.2MB, alloc=564.3MB, time=51.85 memory used=3920.6MB, alloc=564.3MB, time=54.90 memory used=4101.1MB, alloc=588.3MB, time=57.28 memory used=4327.5MB, alloc=588.3MB, time=59.93 memory used=4487.1MB, alloc=588.3MB, time=60.88 memory used=4646.8MB, alloc=588.3MB, time=62.97 memory used=4851.9MB, alloc=588.3MB, time=64.98 memory used=5036.2MB, alloc=588.3MB, time=66.15 memory used=5193.7MB, alloc=588.3MB, time=68.27 memory used=5420.9MB, alloc=612.3MB, time=71.00 memory used=5618.4MB, alloc=612.3MB, time=73.64 memory used=5817.9MB, alloc=612.3MB, time=75.30 memory used=5967.9MB, alloc=612.3MB, time=76.19 memory used=6132.1MB, alloc=612.3MB, time=78.39 memory used=6291.4MB, alloc=612.3MB, time=79.67 memory used=6447.3MB, alloc=612.3MB, time=81.84 memory used=6652.3MB, alloc=612.3MB, time=84.83 memory used=6875.0MB, alloc=612.3MB, time=87.96 memory used=7056.6MB, alloc=612.3MB, time=89.84 memory used=7222.2MB, alloc=636.3MB, time=91.89 memory used=7373.6MB, alloc=636.3MB, time=94.45 memory used=7502.4MB, alloc=636.3MB, time=96.38 memory used=7685.2MB, alloc=636.3MB, time=99.00 memory used=7860.3MB, alloc=660.3MB, time=100.41 memory used=8032.7MB, alloc=660.3MB, time=101.49 memory used=8181.0MB, alloc=660.3MB, time=102.40 memory used=8369.8MB, alloc=660.3MB, time=105.26 memory used=8542.4MB, alloc=660.3MB, time=107.24 memory used=8623.7MB, alloc=660.3MB, time=108.81 memory used=8752.2MB, alloc=660.3MB, time=111.03 memory used=8932.4MB, alloc=660.3MB, time=112.77 memory used=9113.5MB, alloc=660.3MB, time=113.89 memory used=9296.7MB, alloc=660.3MB, time=116.82 memory used=9446.9MB, alloc=660.3MB, time=118.84 memory used=9644.6MB, alloc=660.3MB, time=120.14 memory used=9835.0MB, alloc=660.3MB, time=123.03 memory used=9991.5MB, alloc=660.3MB, time=125.31 memory used=10325.7MB, alloc=660.3MB, time=129.94 memory used=10592.3MB, alloc=684.3MB, time=132.98 memory used=10938.9MB, alloc=684.3MB, time=137.55 memory used=11296.8MB, alloc=708.3MB, time=143.17 memory used=11665.2MB, alloc=732.3MB, time=149.16 memory used=12036.8MB, alloc=756.3MB, time=155.40 memory used=12430.5MB, alloc=780.3MB, time=160.78 memory used=12652.2MB, alloc=804.3MB, time=163.24 memory used=12876.5MB, alloc=828.3MB, time=164.85 memory used=13178.6MB, alloc=828.3MB, time=175.46 memory used=13380.8MB, alloc=828.3MB, time=176.84 memory used=13685.9MB, alloc=828.3MB, time=178.82 memory used=14102.8MB, alloc=852.3MB, time=184.52 memory used=14398.7MB, alloc=852.3MB, time=188.18 memory used=14630.9MB, alloc=852.3MB, time=189.81 memory used=14900.0MB, alloc=852.3MB, time=195.89 memory used=15308.7MB, alloc=852.3MB, time=200.25 memory used=15760.4MB, alloc=876.3MB, time=205.50 memory used=16048.5MB, alloc=876.3MB, time=211.20 memory used=16279.3MB, alloc=876.3MB, time=213.01 memory used=16617.8MB, alloc=900.3MB, time=218.20 memory used=17004.2MB, alloc=900.3MB, time=223.66 memory used=17366.8MB, alloc=900.3MB, time=230.50 memory used=17697.7MB, alloc=900.3MB, time=232.50 memory used=17989.2MB, alloc=900.3MB, time=240.59 memory used=18220.3MB, alloc=900.3MB, time=242.30 memory used=18417.7MB, alloc=915.8MB, time=243.95 memory used=18820.6MB, alloc=915.8MB, time=247.44 memory used=19056.2MB, alloc=915.8MB, time=249.04 memory used=19322.4MB, alloc=915.8MB, time=250.73 memory used=19662.2MB, alloc=939.8MB, time=254.15 memory used=19945.4MB, alloc=939.8MB, time=256.14 memory used=20138.0MB, alloc=939.8MB, time=257.77 memory used=20366.0MB, alloc=939.8MB, time=259.47 memory used=20647.1MB, alloc=939.8MB, time=261.13 memory used=21007.4MB, alloc=939.8MB, time=263.81 memory used=21259.7MB, alloc=939.8MB, time=265.67 memory used=21484.5MB, alloc=939.8MB, time=267.38 memory used=21702.6MB, alloc=939.8MB, time=269.03 memory used=21966.7MB, alloc=939.8MB, time=270.72 memory used=22372.5MB, alloc=939.8MB, time=334.89 memory used=22691.5MB, alloc=939.8MB, time=337.72 memory used=22932.4MB, alloc=939.8MB, time=339.40 memory used=23185.5MB, alloc=939.8MB, time=341.16 memory used=23311.5MB, alloc=939.8MB, time=342.65 memory used=23453.1MB, alloc=939.8MB, time=344.22 memory used=23615.1MB, alloc=939.8MB, time=345.75 memory used=23804.8MB, alloc=939.8MB, time=347.29 memory used=24299.7MB, alloc=939.8MB, time=352.70 memory used=24782.3MB, alloc=939.8MB, time=376.86 memory used=25014.2MB, alloc=939.8MB, time=378.61 memory used=25244.9MB, alloc=939.8MB, time=380.27 memory used=25597.4MB, alloc=939.8MB, time=382.08 memory used=25717.5MB, alloc=939.8MB, time=383.52 memory used=25847.7MB, alloc=939.8MB, time=384.96 memory used=25986.6MB, alloc=939.8MB, time=386.43 memory used=26139.6MB, alloc=939.8MB, time=387.90 memory used=26304.6MB, alloc=939.8MB, time=389.41 memory used=26485.5MB, alloc=939.8MB, time=390.94 memory used=26683.8MB, alloc=939.8MB, time=392.43 memory used=26848.5MB, alloc=939.8MB, time=393.89 memory used=27006.8MB, alloc=939.8MB, time=395.34 memory used=27661.3MB, alloc=963.8MB, time=401.73 memory used=28239.8MB, alloc=963.8MB, time=407.12 memory used=28821.7MB, alloc=963.8MB, time=418.09 memory used=29297.1MB, alloc=963.8MB, time=425.93 memory used=29565.2MB, alloc=963.8MB, time=427.75 memory used=29827.1MB, alloc=963.8MB, time=429.93 memory used=30155.2MB, alloc=963.8MB, time=449.44 memory used=30390.3MB, alloc=987.8MB, time=451.20 memory used=30676.2MB, alloc=987.8MB, time=452.95 memory used=30869.3MB, alloc=987.8MB, time=454.59 memory used=30992.0MB, alloc=987.8MB, time=456.09 memory used=31126.4MB, alloc=987.8MB, time=457.57 memory used=31272.3MB, alloc=987.8MB, time=459.09 memory used=31432.7MB, alloc=987.8MB, time=460.65 memory used=31610.9MB, alloc=987.8MB, time=462.24 memory used=31810.4MB, alloc=987.8MB, time=463.82 memory used=31966.7MB, alloc=987.8MB, time=465.31 memory used=32356.0MB, alloc=987.8MB, time=469.09 memory used=32600.4MB, alloc=987.8MB, time=470.96 memory used=32915.9MB, alloc=987.8MB, time=472.96 memory used=33129.8MB, alloc=1011.8MB, time=474.70 memory used=33347.1MB, alloc=1011.8MB, time=476.35 memory used=33588.3MB, alloc=1011.8MB, time=478.06 memory used=33854.0MB, alloc=1011.8MB, time=479.77 memory used=34144.4MB, alloc=1011.8MB, time=481.54 memory used=34464.8MB, alloc=1011.8MB, time=483.29 memory used=34819.5MB, alloc=1011.8MB, time=485.09 memory used=35085.3MB, alloc=1011.8MB, time=486.79 memory used=35180.9MB, alloc=1011.8MB, time=488.27 memory used=35279.1MB, alloc=1011.8MB, time=489.76 memory used=35379.3MB, alloc=1011.8MB, time=491.19 memory used=35481.5MB, alloc=1011.8MB, time=492.64 memory used=35590.6MB, alloc=1011.8MB, time=494.13 memory used=35701.4MB, alloc=1011.8MB, time=495.62 memory used=35811.8MB, alloc=1011.8MB, time=497.13 memory used=35924.9MB, alloc=1011.8MB, time=498.56 memory used=36041.8MB, alloc=1011.8MB, time=500.03 memory used=36161.1MB, alloc=1011.8MB, time=501.52 memory used=36289.9MB, alloc=1011.8MB, time=503.01 memory used=36417.3MB, alloc=1011.8MB, time=504.48 memory used=36553.5MB, alloc=1011.8MB, time=506.01 memory used=36687.4MB, alloc=1011.8MB, time=507.54 memory used=36828.9MB, alloc=1011.8MB, time=509.10 memory used=36977.0MB, alloc=1011.8MB, time=510.60 memory used=37125.1MB, alloc=1011.8MB, time=512.08 memory used=37279.2MB, alloc=1011.8MB, time=513.59 memory used=37439.8MB, alloc=1011.8MB, time=515.11 memory used=37605.5MB, alloc=1011.8MB, time=516.63 memory used=37779.8MB, alloc=1011.8MB, time=518.14 memory used=38279.1MB, alloc=1011.8MB, time=522.77 memory used=38543.0MB, alloc=1011.8MB, time=524.68 memory used=38881.1MB, alloc=1011.8MB, time=526.68 memory used=39084.3MB, alloc=1011.8MB, time=528.37 memory used=39304.5MB, alloc=1011.8MB, time=530.09 memory used=39549.0MB, alloc=1011.8MB, time=531.81 memory used=39817.5MB, alloc=1011.8MB, time=533.52 memory used=40117.6MB, alloc=1011.8MB, time=535.31 memory used=40441.8MB, alloc=1011.8MB, time=537.12 memory used=40798.1MB, alloc=1011.8MB, time=538.90 memory used=40996.0MB, alloc=1011.8MB, time=540.51 memory used=41091.2MB, alloc=1011.8MB, time=542.01 memory used=41189.5MB, alloc=1011.8MB, time=543.51 memory used=41289.6MB, alloc=1011.8MB, time=544.99 memory used=41391.8MB, alloc=1011.8MB, time=546.44 memory used=41500.9MB, alloc=1011.8MB, time=547.90 memory used=41611.7MB, alloc=1011.8MB, time=549.36 memory used=41722.1MB, alloc=1011.8MB, time=550.89 memory used=41835.2MB, alloc=1011.8MB, time=552.41 memory used=41952.2MB, alloc=1011.8MB, time=553.87 memory used=42071.4MB, alloc=1011.8MB, time=555.38 memory used=42200.2MB, alloc=1011.8MB, time=556.92 memory used=42327.6MB, alloc=1011.8MB, time=558.44 memory used=42463.8MB, alloc=1011.8MB, time=559.95 memory used=42597.7MB, alloc=1011.8MB, time=561.43 memory used=42739.2MB, alloc=1011.8MB, time=562.93 memory used=42887.3MB, alloc=1011.8MB, time=564.43 memory used=43035.4MB, alloc=1011.8MB, time=565.98 memory used=43189.5MB, alloc=1011.8MB, time=567.52 memory used=43350.1MB, alloc=1011.8MB, time=569.01 memory used=43515.8MB, alloc=1011.8MB, time=570.52 memory used=43690.1MB, alloc=1011.8MB, time=572.05 memory used=44038.1MB, alloc=1011.8MB, time=574.78 memory used=44299.3MB, alloc=1011.8MB, time=576.67 memory used=44554.2MB, alloc=1011.8MB, time=578.37 memory used=44731.1MB, alloc=1011.8MB, time=579.95 memory used=44894.3MB, alloc=1011.8MB, time=581.44 memory used=45071.4MB, alloc=1011.8MB, time=582.99 memory used=45595.2MB, alloc=1011.8MB, time=806.10 memory used=45923.2MB, alloc=1011.8MB, time=808.41 memory used=46160.2MB, alloc=1011.8MB, time=810.19 memory used=46460.5MB, alloc=1011.8MB, time=812.02 memory used=46792.4MB, alloc=1011.8MB, time=813.87 memory used=46903.6MB, alloc=1011.8MB, time=815.40 memory used=47022.2MB, alloc=1011.8MB, time=816.95 memory used=47144.1MB, alloc=1011.8MB, time=818.52 memory used=47274.4MB, alloc=1011.8MB, time=820.12 memory used=47413.2MB, alloc=1011.8MB, time=821.72 memory used=47554.9MB, alloc=1011.8MB, time=823.29 memory used=47704.8MB, alloc=1011.8MB, time=824.86 memory used=47862.9MB, alloc=1011.8MB, time=826.43 memory used=48029.2MB, alloc=1011.8MB, time=828.07 memory used=48203.2MB, alloc=1011.8MB, time=829.65 memory used=48384.6MB, alloc=1011.8MB, time=831.24 memory used=48572.8MB, alloc=1011.8MB, time=832.86 memory used=48773.5MB, alloc=1011.8MB, time=834.49 memory used=48938.9MB, alloc=1011.8MB, time=836.05 memory used=49080.2MB, alloc=1011.8MB, time=837.58 memory used=49223.9MB, alloc=1011.8MB, time=839.13 memory used=49372.2MB, alloc=1011.8MB, time=840.69 memory used=49525.8MB, alloc=1011.8MB, time=842.25 memory used=49686.1MB, alloc=1011.8MB, time=843.82 memory used=49851.0MB, alloc=1011.8MB, time=845.44 memory used=50021.8MB, alloc=1011.8MB, time=847.02 memory used=50202.1MB, alloc=1011.8MB, time=848.64 memory used=50387.0MB, alloc=1011.8MB, time=850.23 memory used=50582.3MB, alloc=1011.8MB, time=851.82 memory used=50784.9MB, alloc=1011.8MB, time=853.40 memory used=50959.2MB, alloc=1011.8MB, time=854.96 memory used=51125.5MB, alloc=1011.8MB, time=856.50 memory used=51661.7MB, alloc=1011.8MB, time=862.26 memory used=51947.5MB, alloc=1011.8MB, time=863.98 memory used=52326.6MB, alloc=1011.8MB, time=867.71 memory used=52654.0MB, alloc=1011.8MB, time=871.05 memory used=52803.0MB, alloc=1011.8MB, time=872.60 memory used=53053.7MB, alloc=1011.8MB, time=874.25 memory used=53477.2MB, alloc=1011.8MB, time=881.25 memory used=53892.4MB, alloc=1267.8MB, time=886.63 memory used=54256.0MB, alloc=1267.8MB, time=890.52 memory used=54547.0MB, alloc=1267.8MB, time=892.73 memory used=54793.5MB, alloc=1267.8MB, time=894.64 memory used=55025.0MB, alloc=1267.8MB, time=896.48 memory used=55293.6MB, alloc=1267.8MB, time=898.31 memory used=55607.8MB, alloc=1267.8MB, time=900.18 memory used=56022.0MB, alloc=1267.8MB, time=902.29 memory used=56260.2MB, alloc=1267.8MB, time=904.07 memory used=56534.3MB, alloc=1267.8MB, time=905.87 memory used=56843.8MB, alloc=1267.8MB, time=907.69 memory used=57318.3MB, alloc=1267.8MB, time=910.54 memory used=57694.5MB, alloc=1267.8MB, time=914.25 memory used=57965.2MB, alloc=1267.8MB, time=916.39 memory used=58273.8MB, alloc=1267.8MB, time=918.45 memory used=58481.5MB, alloc=1267.8MB, time=920.25 memory used=58723.7MB, alloc=1267.8MB, time=922.07 memory used=59008.4MB, alloc=1267.8MB, time=923.92 memory used=59342.8MB, alloc=1267.8MB, time=925.83 memory used=59626.5MB, alloc=1267.8MB, time=927.68 memory used=59866.3MB, alloc=1267.8MB, time=929.47 memory used=60141.1MB, alloc=1267.8MB, time=931.23 memory used=60449.5MB, alloc=1267.8MB, time=933.03 memory used=60923.9MB, alloc=1267.8MB, time=936.00 memory used=61322.4MB, alloc=1267.8MB, time=1026.67 memory used=61655.2MB, alloc=1267.8MB, time=1102.42 memory used=61909.2MB, alloc=1267.8MB, time=1104.32 memory used=62171.4MB, alloc=1267.8MB, time=1106.24 memory used=62496.5MB, alloc=1267.8MB, time=1108.20 memory used=62779.9MB, alloc=1267.8MB, time=1110.13 memory used=63012.4MB, alloc=1267.8MB, time=1111.95 memory used=63264.0MB, alloc=1267.8MB, time=1113.79 memory used=63542.0MB, alloc=1267.8MB, time=1115.66 memory used=63845.6MB, alloc=1267.8MB, time=1117.59 memory used=64174.2MB, alloc=1267.8MB, time=1119.51 memory used=64530.7MB, alloc=1267.8MB, time=1121.48 memory used=64889.8MB, alloc=1267.8MB, time=1123.42 memory used=65163.6MB, alloc=1267.8MB, time=1125.23 memory used=65456.6MB, alloc=1267.8MB, time=1127.07 memory used=65772.2MB, alloc=1267.8MB, time=1128.93 memory used=66108.6MB, alloc=1267.8MB, time=1130.81 memory used=66473.8MB, alloc=1267.8MB, time=1132.73 memory used=66826.8MB, alloc=1267.8MB, time=1134.58 memory used=67270.1MB, alloc=1267.8MB, time=1139.15 memory used=67824.9MB, alloc=1267.8MB, time=1142.21 memory used=68466.2MB, alloc=1267.8MB, time=1149.71 memory used=68968.1MB, alloc=1291.8MB, time=1155.44 memory used=69300.9MB, alloc=1291.8MB, time=1159.21 memory used=69658.0MB, alloc=1291.8MB, time=1163.56 memory used=69964.8MB, alloc=1291.8MB, time=1166.39 memory used=70402.2MB, alloc=1291.8MB, time=1187.05 memory used=70769.1MB, alloc=1291.8MB, time=1189.97 memory used=71046.8MB, alloc=1291.8MB, time=1192.01 memory used=71389.8MB, alloc=1291.8MB, time=1194.17 memory used=71654.0MB, alloc=1291.8MB, time=1196.20 memory used=71967.0MB, alloc=1291.8MB, time=1198.27 memory used=72321.8MB, alloc=1291.8MB, time=1200.33 memory used=72619.3MB, alloc=1291.8MB, time=1202.32 memory used=73002.4MB, alloc=1291.8MB, time=1205.42 memory used=73294.4MB, alloc=1291.8MB, time=1208.20 memory used=73607.3MB, alloc=1291.8MB, time=1210.99 memory used=73881.5MB, alloc=1291.8MB, time=1213.60 memory used=74266.6MB, alloc=1291.8MB, time=1241.68 memory used=74514.7MB, alloc=1315.8MB, time=1243.60 memory used=74995.7MB, alloc=1315.8MB, time=1245.92 memory used=75251.3MB, alloc=1315.8MB, time=1247.91 memory used=75547.7MB, alloc=1315.8MB, time=1249.89 memory used=75892.8MB, alloc=1315.8MB, time=1251.90 memory used=76219.0MB, alloc=1315.8MB, time=1253.88 memory used=76523.6MB, alloc=1315.8MB, time=1255.84 memory used=77077.6MB, alloc=1339.8MB, time=1261.02 memory used=77370.1MB, alloc=1339.8MB, time=1263.34 memory used=77724.3MB, alloc=1339.8MB, time=1265.65 memory used=77950.4MB, alloc=1363.8MB, time=1267.64 memory used=78211.4MB, alloc=1363.8MB, time=1269.61 memory used=78510.0MB, alloc=1363.8MB, time=1271.64 memory used=78839.8MB, alloc=1363.8MB, time=1273.70 memory used=79200.7MB, alloc=1363.8MB, time=1275.83 memory used=79592.0MB, alloc=1363.8MB, time=1277.91 memory used=80065.6MB, alloc=1363.8MB, time=1280.15 memory used=80258.0MB, alloc=1363.8MB, time=1282.03 memory used=80465.4MB, alloc=1363.8MB, time=1283.99 memory used=80677.3MB, alloc=1363.8MB, time=1285.95 memory used=80904.7MB, alloc=1363.8MB, time=1287.91 memory used=81132.9MB, alloc=1363.8MB, time=1289.86 memory used=81375.8MB, alloc=1363.8MB, time=1291.77 memory used=81621.2MB, alloc=1363.8MB, time=1293.68 memory used=81877.1MB, alloc=1363.8MB, time=1295.64 memory used=82143.5MB, alloc=1363.8MB, time=1297.62 memory used=82423.3MB, alloc=1363.8MB, time=1299.59 memory used=82713.2MB, alloc=1363.8MB, time=1301.60 memory used=83024.2MB, alloc=1363.8MB, time=1303.62 memory used=83343.3MB, alloc=1363.8MB, time=1305.63 memory used=83683.5MB, alloc=1363.8MB, time=1307.65 memory used=84037.9MB, alloc=1363.8MB, time=1309.68 memory used=84412.5MB, alloc=1363.8MB, time=1311.75 memory used=84713.0MB, alloc=1363.8MB, time=1313.74 memory used=85179.5MB, alloc=1363.8MB, time=1317.43 memory used=85617.0MB, alloc=1363.8MB, time=1319.78 memory used=85987.2MB, alloc=1363.8MB, time=1321.75 memory used=86325.7MB, alloc=1363.8MB, time=1323.67 memory used=86853.8MB, alloc=1363.8MB, time=1329.01 memory used=87184.9MB, alloc=1363.8MB, time=1331.33 memory used=87526.5MB, alloc=1363.8MB, time=1333.56 memory used=87772.7MB, alloc=1363.8MB, time=1335.54 memory used=88046.4MB, alloc=1363.8MB, time=1337.52 memory used=88351.0MB, alloc=1363.8MB, time=1339.53 memory used=88686.5MB, alloc=1363.8MB, time=1341.62 memory used=89052.6MB, alloc=1363.8MB, time=1343.69 memory used=89461.9MB, alloc=1363.8MB, time=1345.78 memory used=89811.4MB, alloc=1363.8MB, time=1347.86 memory used=90014.2MB, alloc=1363.8MB, time=1349.74 memory used=90224.5MB, alloc=1363.8MB, time=1351.64 memory used=90436.5MB, alloc=1363.8MB, time=1353.54 memory used=90663.9MB, alloc=1363.8MB, time=1355.52 memory used=90892.2MB, alloc=1363.8MB, time=1357.49 memory used=91135.1MB, alloc=1363.8MB, time=1359.48 memory used=91380.8MB, alloc=1363.8MB, time=1361.40 memory used=91636.7MB, alloc=1363.8MB, time=1363.34 memory used=91905.0MB, alloc=1363.8MB, time=1365.29 memory used=92184.8MB, alloc=1363.8MB, time=1367.25 memory used=92475.9MB, alloc=1363.8MB, time=1369.24 memory used=92782.6MB, alloc=1363.8MB, time=1371.23 memory used=93101.5MB, alloc=1363.8MB, time=1373.24 memory used=93440.9MB, alloc=1363.8MB, time=1375.29 memory used=93794.8MB, alloc=1363.8MB, time=1377.36 memory used=94169.9MB, alloc=1363.8MB, time=1379.42 memory used=94465.6MB, alloc=1363.8MB, time=1381.35 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428451346 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 2 2 F := [-6 x z + 5 x z - 13 y , -16 x y + 7 x z - 6 x y z , 3 2 2 -13 x z - 17 x y z + 20 x y] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 3 G := [4 x y - 13 x y z - 8 x, 20 y z - 11 x + 15 x, -11 x y - 2 y] > Problem := [F,G]; 2 2 2 2 2 2 2 Problem := [[-6 x z + 5 x z - 13 y , -16 x y + 7 x z - 6 x y z , 3 2 2 -13 x z - 17 x y z + 20 x y], 2 2 2 2 3 [4 x y - 13 x y z - 8 x, 20 y z - 11 x + 15 x, -11 x y - 2 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=24.6MB, alloc=32.3MB, time=0.47 memory used=44.9MB, alloc=32.3MB, time=0.71 memory used=63.6MB, alloc=32.3MB, time=0.82 memory used=82.7MB, alloc=32.3MB, time=1.04 memory used=103.9MB, alloc=56.3MB, time=1.34 memory used=148.4MB, alloc=68.3MB, time=1.99 memory used=195.3MB, alloc=68.3MB, time=2.58 memory used=232.9MB, alloc=92.3MB, time=2.95 memory used=282.4MB, alloc=92.3MB, time=3.23 memory used=333.7MB, alloc=92.3MB, time=3.50 memory used=393.2MB, alloc=92.3MB, time=3.88 memory used=485.3MB, alloc=95.0MB, time=4.72 memory used=569.2MB, alloc=95.0MB, time=5.49 memory used=631.5MB, alloc=95.0MB, time=6.00 memory used=671.0MB, alloc=95.0MB, time=6.26 memory used=719.1MB, alloc=95.0MB, time=6.58 memory used=756.4MB, alloc=95.0MB, time=6.73 memory used=800.7MB, alloc=95.0MB, time=7.07 memory used=843.0MB, alloc=95.0MB, time=7.26 memory used=884.4MB, alloc=95.0MB, time=7.50 memory used=929.3MB, alloc=95.0MB, time=7.66 memory used=972.5MB, alloc=95.0MB, time=7.90 memory used=1015.3MB, alloc=95.0MB, time=8.14 memory used=1086.3MB, alloc=95.0MB, time=8.83 memory used=1157.8MB, alloc=95.0MB, time=9.60 memory used=1220.5MB, alloc=119.0MB, time=10.40 memory used=1277.1MB, alloc=375.0MB, time=11.05 memory used=1382.8MB, alloc=375.0MB, time=12.13 memory used=1473.7MB, alloc=399.0MB, time=13.32 memory used=1590.8MB, alloc=399.0MB, time=14.65 memory used=1648.6MB, alloc=399.0MB, time=14.92 memory used=1720.0MB, alloc=399.0MB, time=15.45 memory used=1806.0MB, alloc=399.0MB, time=16.15 memory used=1925.2MB, alloc=399.0MB, time=17.23 memory used=2035.4MB, alloc=423.0MB, time=18.66 memory used=2111.0MB, alloc=423.0MB, time=19.06 memory used=2180.5MB, alloc=423.0MB, time=19.43 memory used=2251.2MB, alloc=423.0MB, time=19.82 memory used=2331.7MB, alloc=423.0MB, time=20.32 memory used=2400.2MB, alloc=423.0MB, time=20.68 memory used=2526.0MB, alloc=423.0MB, time=21.84 memory used=2654.3MB, alloc=447.0MB, time=23.45 memory used=2766.8MB, alloc=447.0MB, time=25.07 memory used=2882.1MB, alloc=447.0MB, time=26.37 memory used=2985.3MB, alloc=471.0MB, time=27.91 memory used=3088.5MB, alloc=471.0MB, time=29.47 memory used=3190.2MB, alloc=495.0MB, time=31.20 memory used=3297.9MB, alloc=495.0MB, time=33.03 memory used=3374.6MB, alloc=495.0MB, time=34.20 memory used=3456.0MB, alloc=495.0MB, time=35.27 memory used=3536.1MB, alloc=495.0MB, time=36.39 memory used=3611.4MB, alloc=495.0MB, time=37.28 memory used=3722.7MB, alloc=495.0MB, time=38.21 memory used=3815.1MB, alloc=495.0MB, time=39.57 memory used=3904.5MB, alloc=495.0MB, time=40.87 memory used=3992.6MB, alloc=519.0MB, time=41.80 memory used=4079.1MB, alloc=519.0MB, time=42.97 memory used=4188.7MB, alloc=519.0MB, time=44.28 memory used=4274.3MB, alloc=519.0MB, time=45.23 memory used=4352.9MB, alloc=519.0MB, time=46.34 memory used=4438.6MB, alloc=519.0MB, time=47.15 memory used=4557.4MB, alloc=519.0MB, time=48.27 memory used=4650.6MB, alloc=519.0MB, time=49.08 memory used=4775.5MB, alloc=519.0MB, time=49.98 memory used=4858.6MB, alloc=519.0MB, time=51.18 memory used=4916.9MB, alloc=519.0MB, time=52.11 memory used=4960.8MB, alloc=519.0MB, time=52.95 memory used=5035.2MB, alloc=519.0MB, time=53.92 memory used=5111.1MB, alloc=543.0MB, time=54.84 memory used=5348.1MB, alloc=567.0MB, time=57.82 memory used=5555.0MB, alloc=591.0MB, time=60.36 memory used=5796.4MB, alloc=615.0MB, time=63.01 memory used=6004.6MB, alloc=615.0MB, time=65.39 memory used=6221.1MB, alloc=639.0MB, time=67.81 memory used=6381.6MB, alloc=639.0MB, time=70.06 memory used=6580.4MB, alloc=639.0MB, time=72.84 memory used=6729.0MB, alloc=663.0MB, time=75.17 memory used=6932.3MB, alloc=663.0MB, time=77.60 memory used=7108.6MB, alloc=663.0MB, time=79.83 memory used=7280.1MB, alloc=663.0MB, time=82.06 memory used=7449.3MB, alloc=663.0MB, time=83.99 memory used=7648.6MB, alloc=663.0MB, time=85.88 memory used=7798.5MB, alloc=663.0MB, time=86.82 memory used=7987.0MB, alloc=663.0MB, time=88.56 memory used=8188.9MB, alloc=663.0MB, time=90.37 memory used=8378.9MB, alloc=663.0MB, time=92.58 memory used=8527.1MB, alloc=687.0MB, time=94.63 memory used=8674.5MB, alloc=687.0MB, time=96.62 memory used=8829.5MB, alloc=687.0MB, time=98.64 memory used=8983.6MB, alloc=687.0MB, time=100.85 memory used=9097.0MB, alloc=687.0MB, time=102.88 memory used=9460.8MB, alloc=711.0MB, time=107.89 memory used=9726.9MB, alloc=735.0MB, time=110.66 memory used=9922.6MB, alloc=759.0MB, time=112.28 memory used=10137.8MB, alloc=759.0MB, time=114.00 memory used=10351.3MB, alloc=759.0MB, time=115.54 memory used=10550.6MB, alloc=759.0MB, time=117.33 memory used=10945.9MB, alloc=783.0MB, time=121.66 memory used=11388.5MB, alloc=807.0MB, time=126.83 memory used=11864.2MB, alloc=831.0MB, time=132.68 memory used=12263.0MB, alloc=855.0MB, time=138.43 memory used=12626.8MB, alloc=879.0MB, time=144.45 memory used=12912.6MB, alloc=903.0MB, time=147.48 memory used=13303.7MB, alloc=927.0MB, time=152.60 memory used=13743.8MB, alloc=951.0MB, time=157.40 memory used=14138.4MB, alloc=951.0MB, time=161.92 memory used=14422.6MB, alloc=975.0MB, time=167.07 memory used=14669.3MB, alloc=975.0MB, time=172.16 memory used=14924.4MB, alloc=999.0MB, time=177.96 memory used=15190.5MB, alloc=999.0MB, time=182.46 memory used=15434.7MB, alloc=1023.0MB, time=187.50 memory used=15666.2MB, alloc=1279.0MB, time=193.14 memory used=16324.4MB, alloc=1303.0MB, time=204.33 memory used=17012.3MB, alloc=1327.0MB, time=216.11 memory used=17666.0MB, alloc=1351.0MB, time=226.97 memory used=17965.6MB, alloc=1375.0MB, time=231.08 memory used=18273.7MB, alloc=1399.0MB, time=234.98 memory used=18701.1MB, alloc=1423.0MB, time=240.74 memory used=19028.3MB, alloc=1447.0MB, time=244.60 memory used=19892.4MB, alloc=1471.0MB, time=257.14 memory used=20420.4MB, alloc=1495.0MB, time=263.95 memory used=21228.7MB, alloc=1519.0MB, time=276.21 memory used=22014.2MB, alloc=1543.0MB, time=290.16 memory used=22542.7MB, alloc=1567.0MB, time=296.79 memory used=22911.8MB, alloc=1591.0MB, time=301.78 memory used=23372.3MB, alloc=1615.0MB, time=307.73 memory used=24243.5MB, alloc=1639.0MB, time=320.84 memory used=24957.9MB, alloc=1663.0MB, time=333.29 memory used=25668.2MB, alloc=1687.0MB, time=345.32 memory used=26312.5MB, alloc=1711.0MB, time=358.35 memory used=27129.0MB, alloc=1735.0MB, time=370.58 memory used=27792.1MB, alloc=1759.0MB, time=383.44 memory used=28361.8MB, alloc=1783.0MB, time=396.54 memory used=28810.7MB, alloc=1807.0MB, time=407.24 memory used=29280.1MB, alloc=1831.0MB, time=418.68 memory used=29773.8MB, alloc=1855.0MB, time=428.63 memory used=30116.1MB, alloc=1879.0MB, time=437.34 memory used=30621.2MB, alloc=1903.0MB, time=448.46 memory used=30936.3MB, alloc=1927.0MB, time=457.50 memory used=31394.0MB, alloc=1951.0MB, time=468.20 memory used=31832.3MB, alloc=1975.0MB, time=479.56 memory used=32324.9MB, alloc=1999.0MB, time=490.41 memory used=32822.6MB, alloc=2023.0MB, time=501.80 memory used=33357.5MB, alloc=2047.0MB, time=513.03 memory used=33900.8MB, alloc=2071.0MB, time=523.45 memory used=34217.0MB, alloc=2095.0MB, time=532.25 memory used=34700.0MB, alloc=2119.0MB, time=544.37 memory used=35133.9MB, alloc=2143.0MB, time=558.17 memory used=35593.4MB, alloc=2167.0MB, time=571.71 memory used=35970.7MB, alloc=2191.0MB, time=583.57 memory used=36402.3MB, alloc=2215.0MB, time=596.48 memory used=36881.7MB, alloc=2239.0MB, time=611.02 memory used=37335.3MB, alloc=2263.0MB, time=625.59 memory used=37814.4MB, alloc=2287.0MB, time=640.77 memory used=38269.9MB, alloc=2311.0MB, time=655.36 memory used=38661.9MB, alloc=2335.0MB, time=668.58 memory used=39041.6MB, alloc=2359.0MB, time=681.85 memory used=39476.4MB, alloc=2383.0MB, time=696.21 memory used=39925.3MB, alloc=2407.0MB, time=710.63 memory used=40412.8MB, alloc=2431.0MB, time=725.96 memory used=40817.1MB, alloc=2455.0MB, time=738.86 memory used=41115.6MB, alloc=2479.0MB, time=750.34 memory used=41451.8MB, alloc=2503.0MB, time=762.57 memory used=41879.1MB, alloc=2527.0MB, time=775.34 memory used=42350.8MB, alloc=2551.0MB, time=790.03 memory used=42738.6MB, alloc=2575.0MB, time=803.28 memory used=43028.8MB, alloc=2599.0MB, time=815.15 memory used=43354.7MB, alloc=2623.0MB, time=827.59 memory used=43611.0MB, alloc=2647.0MB, time=839.12 memory used=43966.4MB, alloc=2671.0MB, time=852.15 memory used=44389.8MB, alloc=2695.0MB, time=866.57 memory used=44673.5MB, alloc=2719.0MB, time=878.85 memory used=44963.4MB, alloc=2743.0MB, time=890.84 memory used=45242.6MB, alloc=2767.0MB, time=903.92 memory used=45593.8MB, alloc=2791.0MB, time=917.31 memory used=45866.0MB, alloc=2815.0MB, time=929.30 memory used=46061.4MB, alloc=2839.0MB, time=939.68 memory used=46370.1MB, alloc=2863.0MB, time=952.92 memory used=46606.4MB, alloc=2887.0MB, time=964.01 memory used=46760.2MB, alloc=2911.0MB, time=973.17 memory used=46999.3MB, alloc=2935.0MB, time=984.90 memory used=47283.4MB, alloc=2959.0MB, time=997.10 memory used=47617.7MB, alloc=2983.0MB, time=1010.70 memory used=47786.1MB, alloc=3007.0MB, time=1021.52 memory used=47980.8MB, alloc=3031.0MB, time=1032.07 memory used=48267.7MB, alloc=3055.0MB, time=1045.06 memory used=48539.3MB, alloc=3079.0MB, time=1058.80 memory used=48646.6MB, alloc=3103.0MB, time=1068.88 memory used=48870.6MB, alloc=3127.0MB, time=1080.68 memory used=49063.7MB, alloc=3151.0MB, time=1091.74 memory used=49250.8MB, alloc=3175.0MB, time=1102.94 memory used=49376.9MB, alloc=3175.0MB, time=1112.53 memory used=49540.7MB, alloc=3199.0MB, time=1123.64 memory used=49655.5MB, alloc=3199.0MB, time=1133.29 memory used=49839.4MB, alloc=3223.0MB, time=1144.63 memory used=50058.2MB, alloc=3223.0MB, time=1156.15 memory used=50190.2MB, alloc=3247.0MB, time=1166.11 memory used=50410.0MB, alloc=3247.0MB, time=1177.78 memory used=50519.2MB, alloc=3247.0MB, time=1187.67 memory used=50626.6MB, alloc=3271.0MB, time=1197.70 memory used=50838.3MB, alloc=3271.0MB, time=1209.47 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428452546 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 3 2 2 F := [-7 x z - 2 x, 6 x z - 13 x z - 3 z , -15 x z + 16 x z + 19 x y] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; G := 3 2 2 3 2 2 2 [2 x y + 14 x y - 13 y z, -5 x y z - 17 y - 20, 15 x y + 7 x - 18 x] > Problem := [F,G]; Problem := [ 2 3 2 2 3 2 2 [-7 x z - 2 x, 6 x z - 13 x z - 3 z , -15 x z + 16 x z + 19 x y], 3 2 2 3 2 2 2 [2 x y + 14 x y - 13 y z, -5 x y z - 17 y - 20, 15 x y + 7 x - 18 x] ] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.4MB, alloc=32.3MB, time=0.49 memory used=47.7MB, alloc=32.3MB, time=0.80 memory used=67.3MB, alloc=56.3MB, time=1.11 memory used=107.3MB, alloc=60.3MB, time=1.71 memory used=145.6MB, alloc=60.3MB, time=2.28 memory used=183.2MB, alloc=84.3MB, time=2.87 memory used=226.1MB, alloc=84.3MB, time=3.56 memory used=290.4MB, alloc=92.3MB, time=4.54 memory used=351.7MB, alloc=116.3MB, time=5.54 memory used=431.2MB, alloc=116.3MB, time=6.73 memory used=513.8MB, alloc=140.3MB, time=8.08 memory used=600.6MB, alloc=140.3MB, time=9.48 memory used=683.0MB, alloc=396.3MB, time=10.90 memory used=787.4MB, alloc=420.3MB, time=12.53 memory used=918.7MB, alloc=444.3MB, time=14.55 memory used=1070.4MB, alloc=468.3MB, time=16.98 memory used=1206.7MB, alloc=468.3MB, time=18.81 memory used=1353.8MB, alloc=492.3MB, time=21.42 memory used=1483.8MB, alloc=492.3MB, time=23.67 memory used=1611.6MB, alloc=516.3MB, time=25.82 memory used=1743.8MB, alloc=516.3MB, time=28.26 memory used=1850.3MB, alloc=516.3MB, time=30.10 memory used=1973.5MB, alloc=516.3MB, time=32.53 memory used=2082.4MB, alloc=540.3MB, time=34.69 memory used=2207.1MB, alloc=540.3MB, time=36.53 memory used=2317.9MB, alloc=540.3MB, time=38.48 memory used=2440.9MB, alloc=540.3MB, time=41.41 memory used=2559.7MB, alloc=540.3MB, time=43.96 memory used=2703.6MB, alloc=564.3MB, time=45.71 memory used=2784.2MB, alloc=564.3MB, time=47.00 memory used=2881.1MB, alloc=564.3MB, time=48.96 memory used=2966.6MB, alloc=564.3MB, time=50.90 memory used=3053.1MB, alloc=564.3MB, time=53.01 memory used=3126.6MB, alloc=564.3MB, time=54.86 memory used=3239.3MB, alloc=564.3MB, time=57.07 memory used=3377.3MB, alloc=564.3MB, time=58.32 memory used=3450.2MB, alloc=564.3MB, time=59.51 memory used=3502.8MB, alloc=564.3MB, time=60.45 memory used=3574.4MB, alloc=564.3MB, time=62.19 memory used=3648.0MB, alloc=564.3MB, time=64.02 memory used=3718.5MB, alloc=564.3MB, time=65.78 memory used=3775.7MB, alloc=564.3MB, time=67.18 memory used=3861.3MB, alloc=564.3MB, time=68.78 memory used=3918.0MB, alloc=564.3MB, time=70.09 memory used=3984.2MB, alloc=564.3MB, time=71.64 memory used=4060.7MB, alloc=564.3MB, time=73.76 memory used=4125.9MB, alloc=564.3MB, time=75.68 memory used=4346.0MB, alloc=588.3MB, time=80.82 memory used=4493.1MB, alloc=588.3MB, time=82.96 memory used=4711.8MB, alloc=588.3MB, time=85.31 memory used=4960.9MB, alloc=612.3MB, time=90.95 memory used=5136.6MB, alloc=636.3MB, time=93.45 memory used=5349.5MB, alloc=636.3MB, time=95.88 memory used=5585.9MB, alloc=660.3MB, time=100.88 memory used=5800.8MB, alloc=684.3MB, time=105.29 memory used=6029.7MB, alloc=684.3MB, time=110.62 memory used=6250.0MB, alloc=708.3MB, time=115.60 memory used=6447.7MB, alloc=708.3MB, time=120.06 memory used=6643.0MB, alloc=732.3MB, time=124.26 memory used=6824.6MB, alloc=732.3MB, time=127.34 memory used=6984.2MB, alloc=732.3MB, time=130.68 memory used=7133.0MB, alloc=732.3MB, time=134.16 memory used=7275.6MB, alloc=732.3MB, time=136.84 memory used=7468.3MB, alloc=756.3MB, time=139.64 memory used=7578.7MB, alloc=756.3MB, time=142.12 memory used=7725.9MB, alloc=756.3MB, time=145.43 memory used=7918.3MB, alloc=756.3MB, time=149.26 memory used=8126.2MB, alloc=756.3MB, time=152.45 memory used=8366.3MB, alloc=756.3MB, time=155.61 memory used=8490.6MB, alloc=780.3MB, time=158.17 memory used=8655.1MB, alloc=780.3MB, time=160.45 memory used=8803.2MB, alloc=804.3MB, time=163.97 memory used=9234.4MB, alloc=828.3MB, time=171.53 memory used=9676.0MB, alloc=828.3MB, time=177.99 memory used=10090.1MB, alloc=852.3MB, time=181.72 memory used=10551.0MB, alloc=852.3MB, time=184.58 memory used=10971.9MB, alloc=852.3MB, time=187.48 memory used=11382.7MB, alloc=852.3MB, time=190.23 memory used=11881.7MB, alloc=876.3MB, time=194.53 memory used=12322.4MB, alloc=876.3MB, time=197.63 memory used=12839.7MB, alloc=876.3MB, time=202.83 memory used=13365.6MB, alloc=900.3MB, time=210.21 memory used=13901.9MB, alloc=924.3MB, time=218.06 memory used=14458.4MB, alloc=948.3MB, time=225.42 memory used=14988.4MB, alloc=972.3MB, time=229.93 memory used=15463.3MB, alloc=996.3MB, time=233.03 memory used=15944.0MB, alloc=996.3MB, time=235.85 memory used=16547.9MB, alloc=1020.3MB, time=243.01 memory used=17204.2MB, alloc=1044.3MB, time=251.29 memory used=17858.5MB, alloc=1068.3MB, time=260.85 memory used=18530.8MB, alloc=1092.3MB, time=270.21 memory used=19232.1MB, alloc=1116.3MB, time=279.73 memory used=19939.9MB, alloc=1140.3MB, time=289.74 memory used=20661.5MB, alloc=1164.3MB, time=299.96 memory used=21377.0MB, alloc=1188.3MB, time=310.97 memory used=22118.4MB, alloc=1212.3MB, time=321.70 memory used=22862.8MB, alloc=1236.3MB, time=333.31 memory used=23586.3MB, alloc=1260.3MB, time=345.71 memory used=24243.1MB, alloc=1284.3MB, time=359.24 memory used=24877.8MB, alloc=1308.3MB, time=372.64 memory used=25552.4MB, alloc=1332.3MB, time=385.79 memory used=26182.6MB, alloc=1356.3MB, time=398.88 memory used=26788.5MB, alloc=1380.3MB, time=412.07 memory used=27380.5MB, alloc=1404.3MB, time=425.05 memory used=28004.7MB, alloc=1428.3MB, time=437.19 memory used=28630.3MB, alloc=1452.3MB, time=449.93 memory used=29261.1MB, alloc=1476.3MB, time=463.37 memory used=29870.4MB, alloc=1500.3MB, time=476.36 memory used=30457.4MB, alloc=1524.3MB, time=489.30 memory used=31020.9MB, alloc=1548.3MB, time=502.30 memory used=31585.8MB, alloc=1572.3MB, time=515.35 memory used=32125.7MB, alloc=1596.3MB, time=528.06 memory used=32655.9MB, alloc=1620.3MB, time=540.79 memory used=33170.9MB, alloc=1644.3MB, time=553.33 memory used=33681.8MB, alloc=1668.3MB, time=566.05 memory used=34204.7MB, alloc=1692.3MB, time=578.41 memory used=34714.7MB, alloc=1716.3MB, time=591.05 memory used=35208.8MB, alloc=1740.3MB, time=603.63 memory used=35701.2MB, alloc=1764.3MB, time=616.04 memory used=36213.1MB, alloc=1788.3MB, time=628.21 memory used=36732.3MB, alloc=1812.3MB, time=640.74 memory used=37257.4MB, alloc=1836.3MB, time=652.54 memory used=37813.8MB, alloc=1860.3MB, time=663.96 memory used=38396.0MB, alloc=1884.3MB, time=675.58 memory used=39005.4MB, alloc=1908.3MB, time=687.31 memory used=39643.6MB, alloc=1932.3MB, time=698.98 memory used=40304.8MB, alloc=1956.3MB, time=711.50 memory used=40990.2MB, alloc=1980.3MB, time=724.71 memory used=41583.7MB, alloc=2004.3MB, time=741.13 memory used=41996.9MB, alloc=2028.3MB, time=761.16 memory used=42396.5MB, alloc=2052.3MB, time=781.39 memory used=42800.5MB, alloc=2076.3MB, time=802.14 memory used=43211.9MB, alloc=2100.3MB, time=823.35 memory used=43632.7MB, alloc=2124.3MB, time=844.91 memory used=44063.6MB, alloc=2148.3MB, time=867.18 memory used=44505.9MB, alloc=2172.3MB, time=890.07 memory used=44959.9MB, alloc=2196.3MB, time=913.77 memory used=45426.7MB, alloc=2220.3MB, time=937.93 memory used=45906.2MB, alloc=2244.3MB, time=963.35 memory used=46399.2MB, alloc=2268.3MB, time=989.05 memory used=46905.5MB, alloc=2292.3MB, time=1015.68 memory used=47425.7MB, alloc=2316.3MB, time=1043.06 memory used=47959.9MB, alloc=2340.3MB, time=1070.94 memory used=48508.6MB, alloc=2364.3MB, time=1099.56 memory used=49071.7MB, alloc=2388.3MB, time=1128.89 memory used=49649.4MB, alloc=2412.3MB, time=1159.23 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428453746 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 2 F := [20 x y z - 2 x y z + 18 x z, 5 x y - 5 x y + 8 y z , 3 2 2 3 -x z - 6 y z + 3 x ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 3 2 G := [8 x y + 14 x y + 5 z , -13 y z + x y - 6 x y z, 3 2 2 -3 x y - 10 x y z - 5 y ] > Problem := [F,G]; 2 3 2 2 2 Problem := [[20 x y z - 2 x y z + 18 x z, 5 x y - 5 x y + 8 y z , 3 2 2 3 3 2 2 -x z - 6 y z + 3 x ], [8 x y + 14 x y + 5 z , 3 2 3 2 2 -13 y z + x y - 6 x y z, -3 x y - 10 x y z - 5 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.17 memory used=26.3MB, alloc=32.3MB, time=0.49 memory used=46.8MB, alloc=32.3MB, time=0.79 memory used=65.8MB, alloc=56.3MB, time=1.08 memory used=106.3MB, alloc=60.3MB, time=1.68 memory used=144.3MB, alloc=84.3MB, time=2.27 memory used=208.4MB, alloc=92.3MB, time=3.21 memory used=270.0MB, alloc=116.3MB, time=4.18 memory used=351.4MB, alloc=116.3MB, time=5.44 memory used=420.0MB, alloc=372.3MB, time=6.51 memory used=505.8MB, alloc=396.3MB, time=7.80 memory used=617.8MB, alloc=420.3MB, time=9.43 memory used=743.5MB, alloc=420.3MB, time=11.44 memory used=869.3MB, alloc=444.3MB, time=13.40 memory used=1016.2MB, alloc=468.3MB, time=15.79 memory used=1143.9MB, alloc=468.3MB, time=17.58 memory used=1277.8MB, alloc=492.3MB, time=19.72 memory used=1411.4MB, alloc=492.3MB, time=21.91 memory used=1520.3MB, alloc=516.3MB, time=23.60 memory used=1629.3MB, alloc=516.3MB, time=25.38 memory used=1753.6MB, alloc=516.3MB, time=27.62 memory used=1856.5MB, alloc=516.3MB, time=29.46 memory used=1930.3MB, alloc=540.3MB, time=30.74 memory used=2010.1MB, alloc=540.3MB, time=32.25 memory used=2085.3MB, alloc=540.3MB, time=33.71 memory used=2150.8MB, alloc=540.3MB, time=34.88 memory used=2228.7MB, alloc=540.3MB, time=36.40 memory used=2283.1MB, alloc=540.3MB, time=37.57 memory used=2328.8MB, alloc=540.3MB, time=38.50 memory used=2390.6MB, alloc=540.3MB, time=39.87 memory used=2590.0MB, alloc=564.3MB, time=43.18 memory used=2794.7MB, alloc=588.3MB, time=46.53 memory used=2990.8MB, alloc=612.3MB, time=50.24 memory used=3183.3MB, alloc=636.3MB, time=53.86 memory used=3339.5MB, alloc=660.3MB, time=56.94 memory used=3499.2MB, alloc=660.3MB, time=60.04 memory used=3624.7MB, alloc=660.3MB, time=62.40 memory used=3777.3MB, alloc=684.3MB, time=65.08 memory used=3908.0MB, alloc=684.3MB, time=67.81 memory used=4037.0MB, alloc=684.3MB, time=70.49 memory used=4142.6MB, alloc=684.3MB, time=72.33 memory used=4241.3MB, alloc=684.3MB, time=74.21 memory used=4363.3MB, alloc=684.3MB, time=76.67 memory used=4444.8MB, alloc=684.3MB, time=78.65 memory used=4787.1MB, alloc=708.3MB, time=85.56 memory used=5164.7MB, alloc=732.3MB, time=92.49 memory used=5517.2MB, alloc=756.3MB, time=99.59 memory used=5856.6MB, alloc=780.3MB, time=104.00 memory used=6172.9MB, alloc=804.3MB, time=109.70 memory used=6579.9MB, alloc=828.3MB, time=116.33 memory used=6932.0MB, alloc=852.3MB, time=123.57 memory used=7263.2MB, alloc=876.3MB, time=131.48 memory used=7524.9MB, alloc=900.3MB, time=137.45 memory used=7771.4MB, alloc=924.3MB, time=143.57 memory used=8012.2MB, alloc=948.3MB, time=149.21 memory used=8249.3MB, alloc=972.3MB, time=154.89 memory used=8440.3MB, alloc=972.3MB, time=159.82 memory used=8609.9MB, alloc=972.3MB, time=164.34 memory used=8802.5MB, alloc=996.3MB, time=169.62 memory used=9416.6MB, alloc=1020.3MB, time=183.27 memory used=10058.8MB, alloc=1044.3MB, time=196.23 memory used=10657.1MB, alloc=1068.3MB, time=206.28 memory used=10932.9MB, alloc=1092.3MB, time=209.58 memory used=11377.0MB, alloc=1116.3MB, time=215.21 memory used=12065.5MB, alloc=1140.3MB, time=228.08 memory used=12804.1MB, alloc=1164.3MB, time=244.72 memory used=13531.9MB, alloc=1188.3MB, time=265.05 memory used=14124.3MB, alloc=1212.3MB, time=280.48 memory used=14678.3MB, alloc=1236.3MB, time=293.63 memory used=15264.9MB, alloc=1260.3MB, time=306.64 memory used=15741.0MB, alloc=1284.3MB, time=318.99 memory used=16286.1MB, alloc=1308.3MB, time=333.17 memory used=16729.5MB, alloc=1332.3MB, time=344.20 memory used=17099.6MB, alloc=1356.3MB, time=353.80 memory used=17407.0MB, alloc=1380.3MB, time=364.85 memory used=17687.8MB, alloc=1404.3MB, time=373.10 memory used=18136.7MB, alloc=1428.3MB, time=385.25 memory used=18355.6MB, alloc=1452.3MB, time=394.43 memory used=18620.6MB, alloc=1476.3MB, time=403.07 memory used=18938.5MB, alloc=1500.3MB, time=414.80 memory used=19113.3MB, alloc=1524.3MB, time=422.34 memory used=19445.1MB, alloc=1548.3MB, time=432.40 memory used=19699.0MB, alloc=1572.3MB, time=440.56 memory used=19931.7MB, alloc=1596.3MB, time=448.40 memory used=20181.6MB, alloc=1620.3MB, time=460.89 memory used=20310.2MB, alloc=1644.3MB, time=468.51 memory used=20466.7MB, alloc=1668.3MB, time=477.92 memory used=20572.6MB, alloc=1692.3MB, time=485.82 memory used=20671.3MB, alloc=1716.3MB, time=492.67 memory used=20754.8MB, alloc=1740.3MB, time=499.30 memory used=20821.5MB, alloc=1764.3MB, time=506.04 memory used=20986.0MB, alloc=1788.3MB, time=513.48 memory used=21138.2MB, alloc=1812.3MB, time=521.88 memory used=21274.2MB, alloc=1836.3MB, time=531.40 memory used=21368.9MB, alloc=1860.3MB, time=538.62 memory used=21491.3MB, alloc=1860.3MB, time=545.93 memory used=21634.5MB, alloc=1860.3MB, time=553.61 memory used=21650.3MB, alloc=2116.3MB, time=565.03 memory used=22930.3MB, alloc=2140.3MB, time=599.33 memory used=24216.9MB, alloc=2164.3MB, time=630.27 memory used=25503.6MB, alloc=2188.3MB, time=657.79 memory used=26575.1MB, alloc=2212.3MB, time=685.13 memory used=27820.7MB, alloc=2236.3MB, time=713.58 memory used=29095.1MB, alloc=2260.3MB, time=743.60 memory used=30018.2MB, alloc=2284.3MB, time=772.88 memory used=31040.2MB, alloc=2308.3MB, time=802.68 memory used=32184.7MB, alloc=2332.3MB, time=833.38 memory used=33182.5MB, alloc=2356.3MB, time=863.33 memory used=34143.1MB, alloc=2380.3MB, time=893.75 memory used=34869.1MB, alloc=2404.3MB, time=921.22 memory used=35446.9MB, alloc=2428.3MB, time=945.77 memory used=36044.3MB, alloc=2452.3MB, time=968.31 memory used=36830.7MB, alloc=2476.3MB, time=989.66 memory used=37442.6MB, alloc=2500.3MB, time=1006.00 memory used=38191.7MB, alloc=2524.3MB, time=1029.88 memory used=39045.2MB, alloc=2548.3MB, time=1052.71 memory used=39617.2MB, alloc=2572.3MB, time=1077.92 memory used=40273.9MB, alloc=2596.3MB, time=1102.35 memory used=41068.0MB, alloc=2620.3MB, time=1130.02 memory used=41696.3MB, alloc=2644.3MB, time=1152.10 memory used=42331.8MB, alloc=2668.3MB, time=1176.84 memory used=42892.3MB, alloc=2692.3MB, time=1201.17 memory used=43390.0MB, alloc=2716.3MB, time=1221.66 memory used=43901.7MB, alloc=2740.3MB, time=1247.15 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428454946 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 2 F := [7 x z - 4 x y z - 6 x z , 13 x y z - 15 x y z - 9 y z, 3 2 2 17 x y - 2 x y + 4 x z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 2 G := [-6 y z + 14 x y z - 12 x z, -6 x z + 11 x z , 4 x z - 16 x y - 10] > Problem := [F,G]; 3 2 3 2 2 Problem := [[7 x z - 4 x y z - 6 x z , 13 x y z - 15 x y z - 9 y z, 3 2 2 17 x y - 2 x y + 4 x z ], 3 2 2 2 2 2 [-6 y z + 14 x y z - 12 x z, -6 x z + 11 x z , 4 x z - 16 x y - 10]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.17 memory used=26.4MB, alloc=32.3MB, time=0.48 memory used=47.9MB, alloc=32.3MB, time=0.79 memory used=68.0MB, alloc=56.3MB, time=1.10 memory used=109.0MB, alloc=60.3MB, time=1.72 memory used=147.7MB, alloc=60.3MB, time=2.27 memory used=187.2MB, alloc=84.3MB, time=2.86 memory used=228.7MB, alloc=84.3MB, time=3.48 memory used=291.0MB, alloc=92.3MB, time=4.39 memory used=352.2MB, alloc=116.3MB, time=5.31 memory used=433.6MB, alloc=116.3MB, time=6.44 memory used=511.4MB, alloc=396.3MB, time=7.65 memory used=620.5MB, alloc=396.3MB, time=9.24 memory used=724.1MB, alloc=420.3MB, time=10.71 memory used=855.6MB, alloc=444.3MB, time=12.82 memory used=1006.8MB, alloc=468.3MB, time=15.33 memory used=1159.4MB, alloc=492.3MB, time=18.04 memory used=1322.3MB, alloc=516.3MB, time=21.05 memory used=1496.0MB, alloc=540.3MB, time=24.27 memory used=1679.6MB, alloc=564.3MB, time=27.65 memory used=1876.8MB, alloc=588.3MB, time=31.34 memory used=2064.4MB, alloc=612.3MB, time=34.85 memory used=2249.5MB, alloc=636.3MB, time=38.22 memory used=2453.8MB, alloc=660.3MB, time=44.45 memory used=2655.1MB, alloc=684.3MB, time=51.53 memory used=2866.3MB, alloc=708.3MB, time=59.45 memory used=3091.4MB, alloc=732.3MB, time=68.06 memory used=3333.5MB, alloc=756.3MB, time=77.58 memory used=3592.2MB, alloc=780.3MB, time=88.02 memory used=3866.5MB, alloc=804.3MB, time=99.05 memory used=4156.2MB, alloc=828.3MB, time=110.84 memory used=4456.6MB, alloc=852.3MB, time=123.66 memory used=4775.2MB, alloc=876.3MB, time=137.68 memory used=5117.8MB, alloc=900.3MB, time=152.69 memory used=5484.3MB, alloc=924.3MB, time=168.72 memory used=5874.7MB, alloc=948.3MB, time=185.61 memory used=6289.1MB, alloc=972.3MB, time=203.54 memory used=6727.4MB, alloc=996.3MB, time=222.35 memory used=7189.6MB, alloc=996.3MB, time=242.36 memory used=7651.8MB, alloc=996.3MB, time=262.31 memory used=8114.1MB, alloc=1020.3MB, time=282.29 memory used=8600.1MB, alloc=1020.3MB, time=303.51 memory used=9086.1MB, alloc=1020.3MB, time=324.85 memory used=9572.2MB, alloc=1020.3MB, time=345.74 memory used=10058.2MB, alloc=1044.3MB, time=366.69 memory used=10568.1MB, alloc=1044.3MB, time=388.70 memory used=11078.0MB, alloc=1044.3MB, time=410.61 memory used=11587.9MB, alloc=1068.3MB, time=432.37 memory used=12121.5MB, alloc=1068.3MB, time=455.00 memory used=12655.0MB, alloc=1068.3MB, time=477.80 memory used=13188.4MB, alloc=1092.3MB, time=500.60 memory used=13745.8MB, alloc=1092.3MB, time=524.50 memory used=14303.1MB, alloc=1116.3MB, time=548.04 memory used=14884.3MB, alloc=1116.3MB, time=572.66 memory used=15465.7MB, alloc=1140.3MB, time=597.29 memory used=16071.1MB, alloc=1164.3MB, time=622.79 memory used=16700.7MB, alloc=1188.3MB, time=649.18 N1 := 21709 > GB := Basis(F, plex(op(vars))); 10 9 8 2 8 7 2 GB := [-169065 x y - 13328 x y + 19890 x y + 117045 x y + 1568 x y 7 6 2 5 2 5 3 2 - 55692 x y - 13770 x y + 6552 x y + 19278 x y - 2268 x y , 9 8 7 2 6 2 6 -2197845 x y - 173264 x y + 258570 x y + 20384 x y - 843948 x y 5 4 2 3 2 3 + 1053405 x y + 99288 x y - 413100 x y + 34020 x y , 8 7 6 5 3 7 9945 x z + 784 x z - 6885 x z + 3276 x z - 1134 x z, -7607925 x z 6 5 4 3 + 1210230 x z + 5409713 x z - 2506140 x z + 695016 x z + 238140 y z, 3 2 2 17 x y - 2 x y + 4 x z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=17374.9MB, alloc=1188.3MB, time=665.85 memory used=18139.4MB, alloc=1212.3MB, time=689.70 memory used=18812.9MB, alloc=1236.3MB, time=719.68 memory used=19510.6MB, alloc=1260.3MB, time=750.66 N2 := 7953 > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 3 2 2 H := [7 x z - 4 x y z - 6 x z , 13 x y z - 15 x y z - 9 y z, 3 2 2 3 2 2 2 17 x y - 2 x y + 4 x z , -6 y z + 14 x y z - 12 x z, -6 x z + 11 x z , 2 2 4 x z - 16 x y - 10] > J:=[op(GB),op(G)]; 10 9 8 2 8 7 2 J := [-169065 x y - 13328 x y + 19890 x y + 117045 x y + 1568 x y 7 6 2 5 2 5 3 2 - 55692 x y - 13770 x y + 6552 x y + 19278 x y - 2268 x y , 9 8 7 2 6 2 6 -2197845 x y - 173264 x y + 258570 x y + 20384 x y - 843948 x y 5 4 2 3 2 3 + 1053405 x y + 99288 x y - 413100 x y + 34020 x y , 8 7 6 5 3 7 9945 x z + 784 x z - 6885 x z + 3276 x z - 1134 x z, -7607925 x z 6 5 4 3 + 1210230 x z + 5409713 x z - 2506140 x z + 695016 x z + 238140 y z, 3 2 2 3 2 2 2 17 x y - 2 x y + 4 x z , -6 y z + 14 x y z - 12 x z, -6 x z + 11 x z , 2 2 4 x z - 16 x y - 10] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; 14 13 featureList := [6, 17, 23, 4, 3, 3, 3, 1, 5/6, 1, --, 9/17, --, 8, 20, 53, 11, 17 17 38 25 18 10, 3, 2, 1, 3/4, 3/4, --, --, --, -3, -30, -7] 41 41 41 > save(F, G, cat("ranSet/34", convert(F, string),".txt")); > quit memory used=19807.5MB, alloc=1260.3MB, time=762.90 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428455765 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; F := [ 2 2 3 2 2 2 3 2 3 -18 x z - 6 z + 15 y , 8 x z - 5 y z + 16 x, -9 x z - 15 x z + 19 z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 4 4 2 G := [11 x z + 14 y z, 3 x y - 10 y z - 7 y, 12 y - 15 z + 9 x y] > Problem := [F,G]; Problem := [[ 2 2 3 2 2 2 3 2 3 -18 x z - 6 z + 15 y , 8 x z - 5 y z + 16 x, -9 x z - 15 x z + 19 z 3 3 2 4 4 2 ], [11 x z + 14 y z, 3 x y - 10 y z - 7 y, 12 y - 15 z + 9 x y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.20 memory used=26.9MB, alloc=32.3MB, time=0.53 memory used=47.3MB, alloc=32.3MB, time=0.82 memory used=66.4MB, alloc=56.3MB, time=1.11 memory used=107.4MB, alloc=68.3MB, time=1.72 memory used=149.2MB, alloc=92.3MB, time=2.31 memory used=213.5MB, alloc=92.3MB, time=3.26 memory used=275.9MB, alloc=92.3MB, time=4.17 memory used=342.2MB, alloc=116.3MB, time=5.12 memory used=415.6MB, alloc=372.3MB, time=6.15 memory used=509.9MB, alloc=396.3MB, time=7.40 memory used=614.7MB, alloc=396.3MB, time=8.58 memory used=745.7MB, alloc=396.3MB, time=10.12 memory used=852.8MB, alloc=420.3MB, time=11.68 memory used=975.6MB, alloc=420.3MB, time=12.99 memory used=1086.4MB, alloc=444.3MB, time=14.14 memory used=1226.5MB, alloc=444.3MB, time=15.91 memory used=1351.9MB, alloc=468.3MB, time=17.72 memory used=1469.5MB, alloc=468.3MB, time=19.58 memory used=1576.8MB, alloc=492.3MB, time=21.23 memory used=1655.4MB, alloc=492.3MB, time=22.37 memory used=1755.4MB, alloc=492.3MB, time=23.82 memory used=1836.0MB, alloc=492.3MB, time=24.95 memory used=1916.7MB, alloc=492.3MB, time=26.10 memory used=1998.7MB, alloc=516.3MB, time=27.30 memory used=2067.5MB, alloc=516.3MB, time=28.53 memory used=2148.9MB, alloc=516.3MB, time=30.09 memory used=2217.5MB, alloc=516.3MB, time=31.39 memory used=2287.0MB, alloc=516.3MB, time=32.85 memory used=2343.8MB, alloc=516.3MB, time=34.00 memory used=2405.8MB, alloc=516.3MB, time=35.28 memory used=2462.9MB, alloc=516.3MB, time=36.54 memory used=2510.0MB, alloc=516.3MB, time=37.48 memory used=2700.8MB, alloc=540.3MB, time=40.22 memory used=2912.6MB, alloc=564.3MB, time=42.92 memory used=3094.6MB, alloc=588.3MB, time=45.58 memory used=3253.1MB, alloc=612.3MB, time=48.14 memory used=3496.0MB, alloc=612.3MB, time=50.79 memory used=3703.3MB, alloc=612.3MB, time=53.84 memory used=3863.4MB, alloc=636.3MB, time=56.04 memory used=4078.8MB, alloc=636.3MB, time=58.61 memory used=4249.1MB, alloc=636.3MB, time=59.87 memory used=4388.8MB, alloc=636.3MB, time=62.03 memory used=4547.7MB, alloc=660.3MB, time=64.18 memory used=4687.3MB, alloc=660.3MB, time=66.30 memory used=4795.1MB, alloc=660.3MB, time=68.73 memory used=4876.7MB, alloc=660.3MB, time=70.36 memory used=5048.8MB, alloc=660.3MB, time=72.33 memory used=5216.4MB, alloc=660.3MB, time=73.47 memory used=5428.9MB, alloc=660.3MB, time=78.65 memory used=5602.8MB, alloc=660.3MB, time=79.79 memory used=5772.3MB, alloc=660.3MB, time=81.04 memory used=5983.7MB, alloc=660.3MB, time=86.60 memory used=6172.5MB, alloc=684.3MB, time=88.14 memory used=6340.7MB, alloc=684.3MB, time=89.28 memory used=6486.8MB, alloc=684.3MB, time=90.31 memory used=6689.4MB, alloc=684.3MB, time=91.62 memory used=6865.1MB, alloc=684.3MB, time=92.78 memory used=7008.5MB, alloc=684.3MB, time=93.80 memory used=7210.8MB, alloc=684.3MB, time=103.64 memory used=7451.4MB, alloc=684.3MB, time=112.12 memory used=7608.1MB, alloc=684.3MB, time=113.07 memory used=7822.5MB, alloc=684.3MB, time=114.90 memory used=8034.9MB, alloc=684.3MB, time=116.56 memory used=8233.6MB, alloc=684.3MB, time=119.15 memory used=8604.9MB, alloc=684.3MB, time=123.37 memory used=8907.9MB, alloc=684.3MB, time=127.30 memory used=9293.4MB, alloc=708.3MB, time=132.74 memory used=9656.1MB, alloc=732.3MB, time=138.84 memory used=10041.2MB, alloc=756.3MB, time=144.49 memory used=10346.1MB, alloc=780.3MB, time=149.92 memory used=10629.1MB, alloc=804.3MB, time=153.19 memory used=10875.2MB, alloc=828.3MB, time=159.51 memory used=11107.1MB, alloc=852.3MB, time=161.38 memory used=11373.2MB, alloc=876.3MB, time=166.55 memory used=11652.9MB, alloc=900.3MB, time=169.65 memory used=11972.1MB, alloc=900.3MB, time=172.22 memory used=12202.1MB, alloc=900.3MB, time=173.91 memory used=12512.7MB, alloc=900.3MB, time=176.05 memory used=12747.0MB, alloc=900.3MB, time=177.72 memory used=13106.9MB, alloc=900.3MB, time=197.22 memory used=13348.9MB, alloc=900.3MB, time=198.81 memory used=13761.5MB, alloc=900.3MB, time=203.90 memory used=14157.2MB, alloc=924.3MB, time=209.83 memory used=14505.3MB, alloc=924.3MB, time=213.00 memory used=14834.4MB, alloc=924.3MB, time=223.61 memory used=15068.6MB, alloc=924.3MB, time=225.27 memory used=15363.1MB, alloc=924.3MB, time=227.35 memory used=15691.1MB, alloc=924.3MB, time=238.15 memory used=15935.8MB, alloc=924.3MB, time=239.86 memory used=16233.8MB, alloc=924.3MB, time=242.46 memory used=16474.5MB, alloc=924.3MB, time=244.32 memory used=16742.6MB, alloc=924.3MB, time=246.18 memory used=17024.6MB, alloc=924.3MB, time=248.57 memory used=17256.2MB, alloc=924.3MB, time=250.44 memory used=17515.0MB, alloc=924.3MB, time=252.20 memory used=17861.2MB, alloc=924.3MB, time=287.10 memory used=18110.9MB, alloc=924.3MB, time=288.88 memory used=18324.7MB, alloc=924.3MB, time=290.48 memory used=18759.1MB, alloc=924.3MB, time=295.67 memory used=19147.1MB, alloc=924.3MB, time=300.20 memory used=19420.8MB, alloc=948.3MB, time=302.29 memory used=19636.4MB, alloc=948.3MB, time=304.24 memory used=19902.8MB, alloc=948.3MB, time=306.15 memory used=20206.9MB, alloc=948.3MB, time=308.08 memory used=20395.1MB, alloc=948.3MB, time=309.79 memory used=20608.7MB, alloc=948.3MB, time=311.54 memory used=20855.2MB, alloc=948.3MB, time=313.29 memory used=21177.4MB, alloc=948.3MB, time=316.18 memory used=21452.0MB, alloc=948.3MB, time=318.23 memory used=21678.8MB, alloc=948.3MB, time=320.12 memory used=21963.0MB, alloc=948.3MB, time=322.08 memory used=22228.9MB, alloc=948.3MB, time=323.98 memory used=22424.6MB, alloc=948.3MB, time=325.74 memory used=22647.0MB, alloc=948.3MB, time=327.47 memory used=22904.9MB, alloc=948.3MB, time=329.20 memory used=23390.3MB, alloc=948.3MB, time=409.66 memory used=23661.7MB, alloc=948.3MB, time=411.67 memory used=23935.6MB, alloc=948.3MB, time=413.54 memory used=24145.0MB, alloc=948.3MB, time=415.28 memory used=24396.2MB, alloc=948.3MB, time=417.07 memory used=24696.9MB, alloc=948.3MB, time=418.85 memory used=24961.0MB, alloc=963.8MB, time=420.66 memory used=25077.7MB, alloc=963.8MB, time=422.21 memory used=25201.9MB, alloc=963.8MB, time=423.78 memory used=25334.7MB, alloc=963.8MB, time=425.37 memory used=25480.5MB, alloc=963.8MB, time=427.00 memory used=25921.7MB, alloc=963.8MB, time=430.32 memory used=26153.9MB, alloc=963.8MB, time=432.23 memory used=26412.4MB, alloc=963.8MB, time=434.17 memory used=26728.3MB, alloc=963.8MB, time=436.18 memory used=26914.5MB, alloc=963.8MB, time=437.89 memory used=27124.5MB, alloc=963.8MB, time=439.57 memory used=27365.7MB, alloc=963.8MB, time=441.27 memory used=27691.1MB, alloc=963.8MB, time=444.25 memory used=27968.9MB, alloc=963.8MB, time=446.35 memory used=28190.0MB, alloc=963.8MB, time=448.29 memory used=28466.9MB, alloc=963.8MB, time=450.21 memory used=28748.2MB, alloc=963.8MB, time=452.09 memory used=28942.9MB, alloc=963.8MB, time=453.82 memory used=29162.8MB, alloc=963.8MB, time=455.53 memory used=29416.1MB, alloc=963.8MB, time=457.24 memory used=29869.0MB, alloc=963.8MB, time=537.39 memory used=30173.0MB, alloc=963.8MB, time=539.78 memory used=30452.9MB, alloc=963.8MB, time=541.72 memory used=30656.5MB, alloc=963.8MB, time=543.42 memory used=30903.1MB, alloc=963.8MB, time=545.12 memory used=31197.0MB, alloc=963.8MB, time=546.87 memory used=31495.2MB, alloc=963.8MB, time=548.62 memory used=31612.3MB, alloc=963.8MB, time=550.19 memory used=31736.5MB, alloc=963.8MB, time=551.78 memory used=31869.3MB, alloc=963.8MB, time=553.34 memory used=32015.1MB, alloc=963.8MB, time=554.87 memory used=32417.1MB, alloc=963.8MB, time=557.59 memory used=32734.2MB, alloc=963.8MB, time=563.72 memory used=33046.4MB, alloc=963.8MB, time=565.89 memory used=33252.0MB, alloc=963.8MB, time=567.81 memory used=33473.8MB, alloc=987.8MB, time=569.73 memory used=33739.2MB, alloc=987.8MB, time=571.67 memory used=34038.1MB, alloc=987.8MB, time=573.65 memory used=34374.0MB, alloc=987.8MB, time=575.61 memory used=34647.6MB, alloc=987.8MB, time=577.44 memory used=34840.9MB, alloc=987.8MB, time=579.11 memory used=35043.7MB, alloc=1011.8MB, time=580.83 memory used=35265.1MB, alloc=1011.8MB, time=582.56 memory used=35503.0MB, alloc=1011.8MB, time=584.27 memory used=35753.3MB, alloc=1011.8MB, time=585.99 memory used=36015.6MB, alloc=1011.8MB, time=587.76 memory used=36289.2MB, alloc=1011.8MB, time=589.56 memory used=36582.2MB, alloc=1011.8MB, time=591.30 memory used=36884.8MB, alloc=1011.8MB, time=593.05 memory used=37212.1MB, alloc=1011.8MB, time=594.81 memory used=37554.0MB, alloc=1011.8MB, time=596.61 memory used=37915.5MB, alloc=1011.8MB, time=598.43 memory used=38363.6MB, alloc=1011.8MB, time=600.38 memory used=38469.0MB, alloc=1011.8MB, time=601.94 memory used=38574.1MB, alloc=1011.8MB, time=603.46 memory used=38677.7MB, alloc=1011.8MB, time=604.98 memory used=38783.9MB, alloc=1011.8MB, time=606.50 memory used=38894.8MB, alloc=1011.8MB, time=608.05 memory used=39008.6MB, alloc=1011.8MB, time=609.62 memory used=39124.3MB, alloc=1011.8MB, time=611.14 memory used=39241.6MB, alloc=1011.8MB, time=612.67 memory used=39362.7MB, alloc=1011.8MB, time=614.22 memory used=39487.8MB, alloc=1011.8MB, time=615.79 memory used=39620.5MB, alloc=1011.8MB, time=617.37 memory used=39756.6MB, alloc=1011.8MB, time=618.90 memory used=39901.5MB, alloc=1011.8MB, time=620.43 memory used=40262.2MB, alloc=1011.8MB, time=626.62 memory used=40583.5MB, alloc=1011.8MB, time=628.80 memory used=40818.9MB, alloc=1011.8MB, time=630.82 memory used=41086.2MB, alloc=1011.8MB, time=632.79 memory used=41393.2MB, alloc=1011.8MB, time=634.80 memory used=41740.3MB, alloc=1011.8MB, time=636.84 memory used=42064.4MB, alloc=1011.8MB, time=638.80 memory used=42262.6MB, alloc=1011.8MB, time=640.52 memory used=42474.3MB, alloc=1011.8MB, time=642.23 memory used=42699.0MB, alloc=1011.8MB, time=643.92 memory used=42936.7MB, alloc=1011.8MB, time=645.63 memory used=43186.8MB, alloc=1011.8MB, time=647.38 memory used=43449.0MB, alloc=1011.8MB, time=649.16 memory used=43722.4MB, alloc=1011.8MB, time=650.90 memory used=44015.4MB, alloc=1011.8MB, time=652.64 memory used=44317.5MB, alloc=1011.8MB, time=654.41 memory used=44636.4MB, alloc=1011.8MB, time=656.21 memory used=44978.7MB, alloc=1011.8MB, time=658.03 memory used=45340.8MB, alloc=1011.8MB, time=659.82 memory used=45815.4MB, alloc=1011.8MB, time=661.80 memory used=45914.3MB, alloc=1011.8MB, time=663.36 memory used=46018.6MB, alloc=1011.8MB, time=664.92 memory used=46122.1MB, alloc=1011.8MB, time=666.45 memory used=46228.9MB, alloc=1011.8MB, time=667.97 memory used=46340.0MB, alloc=1011.8MB, time=669.49 memory used=46454.1MB, alloc=1011.8MB, time=671.03 memory used=46570.0MB, alloc=1011.8MB, time=672.60 memory used=46686.9MB, alloc=1011.8MB, time=674.16 memory used=46809.1MB, alloc=1011.8MB, time=675.67 memory used=46933.9MB, alloc=1011.8MB, time=677.20 memory used=47063.1MB, alloc=1011.8MB, time=678.77 memory used=47199.7MB, alloc=1011.8MB, time=680.35 memory used=47343.7MB, alloc=1011.8MB, time=681.90 memory used=47856.4MB, alloc=1011.8MB, time=1021.62 memory used=48263.2MB, alloc=1011.8MB, time=1025.67 memory used=48545.8MB, alloc=1011.8MB, time=1027.68 memory used=48872.5MB, alloc=1011.8MB, time=1029.64 memory used=49090.7MB, alloc=1011.8MB, time=1031.36 memory used=49341.0MB, alloc=1011.8MB, time=1033.13 memory used=49625.9MB, alloc=1011.8MB, time=1034.88 memory used=49949.1MB, alloc=1011.8MB, time=1036.65 memory used=50309.5MB, alloc=1011.8MB, time=1038.46 memory used=50503.8MB, alloc=1011.8MB, time=1040.13 memory used=50611.2MB, alloc=1011.8MB, time=1041.67 memory used=50723.9MB, alloc=1011.8MB, time=1043.21 memory used=50840.8MB, alloc=1011.8MB, time=1044.76 memory used=50961.8MB, alloc=1011.8MB, time=1046.31 memory used=51086.7MB, alloc=1011.8MB, time=1047.86 memory used=51215.1MB, alloc=1011.8MB, time=1049.42 memory used=51347.0MB, alloc=1011.8MB, time=1051.00 memory used=51481.7MB, alloc=1011.8MB, time=1052.54 memory used=51622.3MB, alloc=1011.8MB, time=1054.10 memory used=51768.7MB, alloc=1011.8MB, time=1055.66 memory used=51919.8MB, alloc=1011.8MB, time=1057.22 memory used=52074.6MB, alloc=1011.8MB, time=1058.80 memory used=52235.4MB, alloc=1011.8MB, time=1060.39 memory used=52403.8MB, alloc=1011.8MB, time=1061.99 memory used=52579.4MB, alloc=1011.8MB, time=1063.57 memory used=52763.9MB, alloc=1011.8MB, time=1065.17 memory used=52958.5MB, alloc=1011.8MB, time=1066.78 memory used=53154.4MB, alloc=1011.8MB, time=1068.41 memory used=53555.7MB, alloc=1011.8MB, time=1071.83 memory used=53897.3MB, alloc=1011.8MB, time=1074.24 memory used=54255.3MB, alloc=1011.8MB, time=1077.27 memory used=54580.2MB, alloc=1011.8MB, time=1079.49 memory used=54942.2MB, alloc=1011.8MB, time=1082.81 memory used=55241.5MB, alloc=1011.8MB, time=1084.80 memory used=55511.2MB, alloc=1011.8MB, time=1086.55 memory used=55833.6MB, alloc=1011.8MB, time=1088.95 memory used=56134.0MB, alloc=1011.8MB, time=1090.90 memory used=56496.3MB, alloc=1011.8MB, time=1097.37 memory used=56773.6MB, alloc=1011.8MB, time=1099.16 memory used=57198.0MB, alloc=1267.8MB, time=1104.40 memory used=57640.8MB, alloc=1267.8MB, time=1109.59 memory used=58255.5MB, alloc=1267.8MB, time=1119.10 memory used=58868.4MB, alloc=1291.8MB, time=1130.08 memory used=59509.7MB, alloc=1315.8MB, time=1143.95 memory used=60165.2MB, alloc=1339.8MB, time=1158.80 memory used=60840.7MB, alloc=1363.8MB, time=1173.21 memory used=61504.0MB, alloc=1387.8MB, time=1187.41 memory used=62211.2MB, alloc=1411.8MB, time=1201.70 memory used=62830.0MB, alloc=1435.8MB, time=1213.23 memory used=63554.1MB, alloc=1459.8MB, time=1226.69 memory used=64261.5MB, alloc=1483.8MB, time=1239.82 memory used=64775.0MB, alloc=1507.8MB, time=1251.45 memory used=65303.8MB, alloc=1531.8MB, time=1264.82 memory used=65742.4MB, alloc=1555.8MB, time=1272.47 memory used=65980.8MB, alloc=1579.8MB, time=1277.20 memory used=66288.1MB, alloc=1603.8MB, time=1282.24 memory used=66571.0MB, alloc=1627.8MB, time=1287.01 memory used=67001.4MB, alloc=1651.8MB, time=1306.35 memory used=67299.6MB, alloc=1675.8MB, time=1311.08 memory used=67826.9MB, alloc=1699.8MB, time=1316.56 memory used=68238.7MB, alloc=1723.8MB, time=1322.58 memory used=68608.2MB, alloc=1747.8MB, time=1327.49 memory used=68972.0MB, alloc=1771.8MB, time=1332.29 memory used=69315.4MB, alloc=1795.8MB, time=1336.97 memory used=69766.7MB, alloc=1819.8MB, time=1341.69 memory used=70282.1MB, alloc=1843.8MB, time=1347.89 memory used=70779.8MB, alloc=1867.8MB, time=1353.24 memory used=71158.4MB, alloc=1891.8MB, time=1358.02 memory used=71644.1MB, alloc=1915.8MB, time=1362.82 memory used=72433.8MB, alloc=1915.8MB, time=1425.13 memory used=72911.0MB, alloc=1915.8MB, time=1430.07 memory used=73606.4MB, alloc=1915.8MB, time=1435.25 memory used=73854.8MB, alloc=1915.8MB, time=1439.78 memory used=74487.1MB, alloc=1915.8MB, time=1448.06 memory used=75108.5MB, alloc=1915.8MB, time=1454.61 memory used=75674.6MB, alloc=1915.8MB, time=1477.31 memory used=76144.2MB, alloc=1915.8MB, time=1481.87 memory used=76591.7MB, alloc=1915.8MB, time=1486.40 memory used=76845.9MB, alloc=1915.8MB, time=1490.64 memory used=77796.0MB, alloc=1939.8MB, time=1502.27 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428456965 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 F := [-10 x z - 8 x + 18 z, -13 y z - 7 x z - 12 y z, 4 2 15 x + 12 x y z - 11 y z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; G := 2 2 2 2 2 2 3 3 [2 x z - 14 y z + 15, 2 x y z + 7 y z - 8 x y , -x y + 3 y z - 12 x] > Problem := [F,G]; 3 2 2 2 2 Problem := [[-10 x z - 8 x + 18 z, -13 y z - 7 x z - 12 y z, 4 2 15 x + 12 x y z - 11 y z], 2 2 2 2 2 2 3 3 [2 x z - 14 y z + 15, 2 x y z + 7 y z - 8 x y , -x y + 3 y z - 12 x] ] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.0MB, alloc=32.3MB, time=0.49 memory used=46.9MB, alloc=60.3MB, time=0.76 memory used=87.3MB, alloc=60.3MB, time=1.30 memory used=133.2MB, alloc=68.3MB, time=1.88 memory used=175.0MB, alloc=68.3MB, time=2.35 memory used=214.8MB, alloc=68.3MB, time=2.85 memory used=257.4MB, alloc=92.3MB, time=3.44 memory used=317.6MB, alloc=92.3MB, time=4.11 memory used=381.0MB, alloc=372.3MB, time=5.00 memory used=474.6MB, alloc=396.3MB, time=6.18 memory used=587.1MB, alloc=396.3MB, time=7.45 memory used=654.2MB, alloc=396.3MB, time=7.89 memory used=725.2MB, alloc=396.3MB, time=8.47 memory used=806.4MB, alloc=396.3MB, time=9.07 memory used=920.2MB, alloc=420.3MB, time=10.47 memory used=1029.9MB, alloc=420.3MB, time=11.33 memory used=1157.3MB, alloc=444.3MB, time=13.04 memory used=1289.7MB, alloc=444.3MB, time=14.51 memory used=1415.0MB, alloc=444.3MB, time=15.92 memory used=1533.0MB, alloc=468.3MB, time=17.67 memory used=1641.4MB, alloc=468.3MB, time=19.16 memory used=1733.4MB, alloc=468.3MB, time=20.39 memory used=1853.9MB, alloc=468.3MB, time=21.39 memory used=1959.8MB, alloc=468.3MB, time=22.25 memory used=2084.9MB, alloc=468.3MB, time=23.22 memory used=2204.4MB, alloc=468.3MB, time=24.42 memory used=2299.5MB, alloc=468.3MB, time=25.49 memory used=2391.9MB, alloc=492.3MB, time=26.98 memory used=2502.0MB, alloc=492.3MB, time=28.22 memory used=2590.7MB, alloc=492.3MB, time=29.39 memory used=2660.2MB, alloc=492.3MB, time=30.41 memory used=2732.4MB, alloc=492.3MB, time=31.49 memory used=2773.0MB, alloc=492.3MB, time=32.24 memory used=2829.8MB, alloc=492.3MB, time=33.20 memory used=2872.8MB, alloc=492.3MB, time=33.99 memory used=2927.4MB, alloc=492.3MB, time=35.04 memory used=2978.4MB, alloc=492.3MB, time=36.00 memory used=3023.3MB, alloc=492.3MB, time=36.85 memory used=3153.2MB, alloc=492.3MB, time=37.98 memory used=3280.8MB, alloc=516.3MB, time=39.42 memory used=3504.0MB, alloc=516.3MB, time=42.40 memory used=3718.5MB, alloc=540.3MB, time=45.26 memory used=3844.7MB, alloc=540.3MB, time=45.99 memory used=3965.0MB, alloc=540.3MB, time=46.63 memory used=4073.8MB, alloc=540.3MB, time=47.18 memory used=4197.8MB, alloc=540.3MB, time=48.27 memory used=4309.3MB, alloc=540.3MB, time=48.79 memory used=4408.9MB, alloc=540.3MB, time=49.28 memory used=4580.7MB, alloc=540.3MB, time=51.53 memory used=4753.0MB, alloc=540.3MB, time=52.93 memory used=4882.9MB, alloc=540.3MB, time=54.26 memory used=5096.4MB, alloc=564.3MB, time=56.51 memory used=5319.2MB, alloc=564.3MB, time=58.74 memory used=5571.6MB, alloc=564.3MB, time=61.63 memory used=5733.6MB, alloc=588.3MB, time=63.75 memory used=5927.9MB, alloc=588.3MB, time=65.86 memory used=6052.9MB, alloc=588.3MB, time=66.58 memory used=6205.1MB, alloc=588.3MB, time=67.46 memory used=6359.2MB, alloc=588.3MB, time=70.73 memory used=6475.8MB, alloc=588.3MB, time=71.38 memory used=6601.1MB, alloc=588.3MB, time=72.10 memory used=6767.2MB, alloc=588.3MB, time=73.30 memory used=6911.3MB, alloc=588.3MB, time=74.15 memory used=7052.3MB, alloc=588.3MB, time=75.53 memory used=7235.1MB, alloc=588.3MB, time=77.64 memory used=7412.3MB, alloc=612.3MB, time=79.95 memory used=7556.6MB, alloc=612.3MB, time=82.36 memory used=7687.7MB, alloc=612.3MB, time=84.54 memory used=7864.5MB, alloc=612.3MB, time=86.48 memory used=7998.6MB, alloc=636.3MB, time=88.71 memory used=8199.8MB, alloc=636.3MB, time=91.50 memory used=8351.3MB, alloc=636.3MB, time=92.42 memory used=8534.6MB, alloc=636.3MB, time=95.21 memory used=8677.3MB, alloc=636.3MB, time=96.07 memory used=8865.4MB, alloc=636.3MB, time=97.71 memory used=9004.5MB, alloc=636.3MB, time=99.68 memory used=9110.5MB, alloc=636.3MB, time=101.72 memory used=9230.7MB, alloc=636.3MB, time=104.10 memory used=9331.1MB, alloc=660.3MB, time=105.85 memory used=9412.8MB, alloc=660.3MB, time=107.57 memory used=9749.1MB, alloc=684.3MB, time=111.97 memory used=10075.9MB, alloc=708.3MB, time=117.19 memory used=10437.6MB, alloc=732.3MB, time=121.56 memory used=10771.3MB, alloc=756.3MB, time=126.65 memory used=11041.3MB, alloc=780.3MB, time=130.02 memory used=11389.7MB, alloc=804.3MB, time=134.73 memory used=11717.4MB, alloc=828.3MB, time=139.40 memory used=12053.8MB, alloc=852.3MB, time=143.53 memory used=12356.9MB, alloc=876.3MB, time=148.66 memory used=12608.5MB, alloc=900.3MB, time=153.38 memory used=12869.6MB, alloc=924.3MB, time=157.52 memory used=13102.5MB, alloc=948.3MB, time=162.01 memory used=13313.3MB, alloc=972.3MB, time=165.92 memory used=13510.1MB, alloc=996.3MB, time=169.61 memory used=14092.7MB, alloc=1020.3MB, time=179.60 memory used=14705.3MB, alloc=1044.3MB, time=189.24 memory used=15306.6MB, alloc=1068.3MB, time=196.84 memory used=15643.5MB, alloc=1092.3MB, time=201.51 memory used=15961.2MB, alloc=1116.3MB, time=205.79 memory used=16338.2MB, alloc=1140.3MB, time=209.89 memory used=17087.3MB, alloc=1164.3MB, time=221.12 memory used=17612.9MB, alloc=1188.3MB, time=227.69 memory used=17941.4MB, alloc=1212.3MB, time=231.70 memory used=18337.3MB, alloc=1236.3MB, time=236.38 memory used=18718.6MB, alloc=1260.3MB, time=240.77 memory used=19076.4MB, alloc=1284.3MB, time=244.15 memory used=19482.2MB, alloc=1308.3MB, time=254.38 memory used=19957.7MB, alloc=1332.3MB, time=258.08 memory used=20354.4MB, alloc=1356.3MB, time=261.38 memory used=20744.1MB, alloc=1356.3MB, time=264.95 memory used=21163.2MB, alloc=1356.3MB, time=268.30 memory used=21528.5MB, alloc=1356.3MB, time=271.30 memory used=22058.3MB, alloc=1356.3MB, time=301.26 memory used=22449.7MB, alloc=1356.3MB, time=304.24 memory used=22635.7MB, alloc=1371.8MB, time=307.02 memory used=22720.9MB, alloc=1371.8MB, time=309.62 memory used=22816.6MB, alloc=1371.8MB, time=312.23 memory used=23689.6MB, alloc=1395.8MB, time=322.98 memory used=24379.4MB, alloc=1419.8MB, time=333.43 memory used=25045.3MB, alloc=1443.8MB, time=345.91 memory used=25536.4MB, alloc=1467.8MB, time=355.71 memory used=25963.0MB, alloc=1491.8MB, time=365.08 memory used=26410.4MB, alloc=1515.8MB, time=375.51 memory used=27050.9MB, alloc=1539.8MB, time=385.36 memory used=27630.1MB, alloc=1563.8MB, time=394.15 memory used=28128.0MB, alloc=1587.8MB, time=399.54 memory used=28634.5MB, alloc=1611.8MB, time=405.02 memory used=29202.5MB, alloc=1635.8MB, time=422.43 memory used=29739.1MB, alloc=1659.8MB, time=428.29 memory used=30249.5MB, alloc=1683.8MB, time=433.68 memory used=30802.2MB, alloc=1683.8MB, time=439.02 memory used=31356.9MB, alloc=1683.8MB, time=444.89 memory used=31881.2MB, alloc=1683.8MB, time=450.22 memory used=32458.0MB, alloc=1683.8MB, time=455.32 memory used=33023.8MB, alloc=1683.8MB, time=507.74 memory used=33542.9MB, alloc=1683.8MB, time=512.84 memory used=34014.7MB, alloc=1683.8MB, time=517.52 memory used=34462.8MB, alloc=1683.8MB, time=522.06 memory used=35053.5MB, alloc=1683.8MB, time=533.07 memory used=35619.0MB, alloc=1707.8MB, time=544.75 memory used=36333.3MB, alloc=1707.8MB, time=555.21 memory used=37100.5MB, alloc=1731.8MB, time=566.25 memory used=37799.5MB, alloc=1755.8MB, time=574.42 memory used=38394.5MB, alloc=1755.8MB, time=581.01 memory used=39026.4MB, alloc=1755.8MB, time=587.62 memory used=39641.8MB, alloc=1755.8MB, time=593.92 memory used=40205.5MB, alloc=1755.8MB, time=600.37 memory used=40810.7MB, alloc=1755.8MB, time=606.26 memory used=41380.3MB, alloc=1755.8MB, time=612.50 memory used=41717.2MB, alloc=1755.8MB, time=621.14 memory used=42138.2MB, alloc=1779.8MB, time=628.98 memory used=42510.4MB, alloc=1779.8MB, time=638.91 memory used=42936.5MB, alloc=1779.8MB, time=647.93 memory used=43599.8MB, alloc=1779.8MB, time=656.23 memory used=44105.9MB, alloc=1779.8MB, time=665.66 memory used=44427.7MB, alloc=1803.8MB, time=673.59 memory used=44755.4MB, alloc=1803.8MB, time=682.11 memory used=45175.4MB, alloc=1803.8MB, time=689.18 memory used=45778.4MB, alloc=1803.8MB, time=697.29 memory used=46459.2MB, alloc=1803.8MB, time=709.84 memory used=47085.4MB, alloc=1803.8MB, time=716.50 memory used=47715.3MB, alloc=1803.8MB, time=723.19 memory used=48286.2MB, alloc=1803.8MB, time=729.14 memory used=48989.5MB, alloc=1803.8MB, time=757.34 memory used=49617.2MB, alloc=1803.8MB, time=765.11 memory used=49895.6MB, alloc=1803.8MB, time=773.24 memory used=50260.3MB, alloc=1803.8MB, time=782.00 memory used=50577.3MB, alloc=1827.8MB, time=789.86 memory used=50958.0MB, alloc=1827.8MB, time=798.36 memory used=51299.6MB, alloc=1827.8MB, time=806.55 memory used=51565.4MB, alloc=1827.8MB, time=816.25 memory used=51719.0MB, alloc=1827.8MB, time=823.38 memory used=51927.1MB, alloc=1827.8MB, time=831.10 memory used=52154.5MB, alloc=1851.8MB, time=839.88 memory used=52314.5MB, alloc=1851.8MB, time=847.53 memory used=52505.6MB, alloc=1851.8MB, time=855.17 memory used=52656.7MB, alloc=1851.8MB, time=862.31 memory used=52851.5MB, alloc=1851.8MB, time=869.85 memory used=53314.5MB, alloc=1851.8MB, time=877.70 memory used=53893.4MB, alloc=1851.8MB, time=885.53 memory used=54126.0MB, alloc=1851.8MB, time=892.15 memory used=54738.3MB, alloc=1851.8MB, time=905.00 memory used=55383.5MB, alloc=1851.8MB, time=912.23 memory used=55846.7MB, alloc=1851.8MB, time=921.48 memory used=56242.8MB, alloc=1851.8MB, time=928.76 memory used=56655.9MB, alloc=1851.8MB, time=935.67 memory used=57091.5MB, alloc=1851.8MB, time=943.58 memory used=57359.7MB, alloc=1851.8MB, time=949.95 memory used=57818.9MB, alloc=1851.8MB, time=957.95 memory used=57953.1MB, alloc=1851.8MB, time=965.40 memory used=58082.5MB, alloc=1851.8MB, time=972.46 memory used=58161.0MB, alloc=1851.8MB, time=978.86 memory used=58224.2MB, alloc=1851.8MB, time=985.12 memory used=58286.4MB, alloc=1851.8MB, time=991.39 memory used=58398.8MB, alloc=1851.8MB, time=998.07 memory used=58517.8MB, alloc=1851.8MB, time=1004.65 memory used=58643.7MB, alloc=1851.8MB, time=1012.10 memory used=58830.9MB, alloc=1851.8MB, time=1019.05 memory used=59017.9MB, alloc=1851.8MB, time=1025.47 memory used=59215.7MB, alloc=1851.8MB, time=1032.93 memory used=59318.7MB, alloc=1851.8MB, time=1039.00 memory used=59538.0MB, alloc=1851.8MB, time=1045.37 memory used=59888.6MB, alloc=1851.8MB, time=1058.72 memory used=60253.9MB, alloc=1851.8MB, time=1065.20 memory used=60435.6MB, alloc=1851.8MB, time=1071.47 memory used=60833.2MB, alloc=1851.8MB, time=1078.85 memory used=61124.8MB, alloc=1851.8MB, time=1087.49 memory used=61370.1MB, alloc=1851.8MB, time=1094.65 memory used=61449.8MB, alloc=1851.8MB, time=1102.78 memory used=61742.2MB, alloc=1851.8MB, time=1109.35 memory used=61988.2MB, alloc=1875.8MB, time=1115.72 memory used=62141.2MB, alloc=1875.8MB, time=1121.94 memory used=62485.1MB, alloc=1875.8MB, time=1146.65 memory used=62893.5MB, alloc=1875.8MB, time=1153.22 memory used=63354.8MB, alloc=1875.8MB, time=1160.63 memory used=63442.5MB, alloc=1875.8MB, time=1166.41 memory used=63991.1MB, alloc=1875.8MB, time=1173.33 memory used=64501.0MB, alloc=1875.8MB, time=1180.73 memory used=64684.1MB, alloc=1875.8MB, time=1186.87 memory used=64862.5MB, alloc=1875.8MB, time=1192.86 memory used=65128.8MB, alloc=1875.8MB, time=1199.18 memory used=65431.5MB, alloc=1875.8MB, time=1205.35 memory used=65878.2MB, alloc=1875.8MB, time=1288.34 memory used=66269.4MB, alloc=1875.8MB, time=1295.11 memory used=66814.7MB, alloc=1875.8MB, time=1301.75 memory used=67345.5MB, alloc=1875.8MB, time=1308.29 memory used=67503.7MB, alloc=1875.8MB, time=1315.48 memory used=67581.2MB, alloc=1875.8MB, time=1322.36 memory used=67646.4MB, alloc=1875.8MB, time=1328.70 memory used=67748.4MB, alloc=1875.8MB, time=1335.71 memory used=67788.1MB, alloc=1875.8MB, time=1341.90 memory used=67880.6MB, alloc=1875.8MB, time=1348.57 memory used=67916.5MB, alloc=1875.8MB, time=1354.90 memory used=67956.7MB, alloc=1875.8MB, time=1361.17 memory used=68045.2MB, alloc=1875.8MB, time=1367.71 memory used=68121.4MB, alloc=1875.8MB, time=1374.17 memory used=68127.8MB, alloc=1875.8MB, time=1380.03 memory used=68182.7MB, alloc=1875.8MB, time=1386.95 memory used=68375.8MB, alloc=1875.8MB, time=1393.52 memory used=68380.8MB, alloc=1875.8MB, time=1399.27 memory used=68427.7MB, alloc=1875.8MB, time=1405.76 memory used=68517.3MB, alloc=1875.8MB, time=1412.51 memory used=68585.9MB, alloc=1875.8MB, time=1419.18 memory used=68613.4MB, alloc=1875.8MB, time=1425.40 memory used=68622.7MB, alloc=1875.8MB, time=1431.52 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428458165 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 3 F := [6 x y z - 2 x y z + 12 y z, -9 x z - 18 y z + 20 z , 4 2 -14 z - 2 x y z - 20 z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; G := [ 3 2 3 3 3 2 3 2 2 18 y + 2 y z - 6 z , 12 y z + 4 y z - 12 y z, 16 x - 17 x y + 7 y z ] > Problem := [F,G]; 2 2 2 3 3 Problem := [[6 x y z - 2 x y z + 12 y z, -9 x z - 18 y z + 20 z , 4 2 -14 z - 2 x y z - 20 z ], [ 3 2 3 3 3 2 3 2 2 18 y + 2 y z - 6 z , 12 y z + 4 y z - 12 y z, 16 x - 17 x y + 7 y z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.5MB, alloc=32.3MB, time=0.50 memory used=46.3MB, alloc=32.3MB, time=0.78 memory used=65.0MB, alloc=56.3MB, time=1.06 memory used=104.8MB, alloc=60.3MB, time=1.66 memory used=143.6MB, alloc=84.3MB, time=2.24 memory used=205.2MB, alloc=92.3MB, time=3.22 memory used=266.5MB, alloc=92.3MB, time=4.19 memory used=326.2MB, alloc=116.3MB, time=5.08 memory used=408.4MB, alloc=116.3MB, time=6.35 memory used=491.0MB, alloc=140.3MB, time=7.54 memory used=579.6MB, alloc=396.3MB, time=8.64 memory used=684.3MB, alloc=420.3MB, time=10.21 memory used=807.0MB, alloc=420.3MB, time=11.84 memory used=939.1MB, alloc=444.3MB, time=13.81 memory used=1064.9MB, alloc=468.3MB, time=15.72 memory used=1178.9MB, alloc=468.3MB, time=17.13 memory used=1283.6MB, alloc=492.3MB, time=18.81 memory used=1404.5MB, alloc=492.3MB, time=20.70 memory used=1511.6MB, alloc=492.3MB, time=22.37 memory used=1616.9MB, alloc=492.3MB, time=24.25 memory used=1720.6MB, alloc=516.3MB, time=26.07 memory used=1801.9MB, alloc=516.3MB, time=27.29 memory used=1894.6MB, alloc=516.3MB, time=28.95 memory used=1961.0MB, alloc=516.3MB, time=30.01 memory used=2036.0MB, alloc=516.3MB, time=31.27 memory used=2118.5MB, alloc=516.3MB, time=32.96 memory used=2175.5MB, alloc=516.3MB, time=34.37 memory used=2225.5MB, alloc=516.3MB, time=35.44 memory used=2267.7MB, alloc=516.3MB, time=36.26 memory used=2318.8MB, alloc=516.3MB, time=37.28 memory used=2520.4MB, alloc=540.3MB, time=41.01 memory used=2741.9MB, alloc=564.3MB, time=44.62 memory used=2981.0MB, alloc=588.3MB, time=48.50 memory used=3204.8MB, alloc=612.3MB, time=51.66 memory used=3374.9MB, alloc=636.3MB, time=53.98 memory used=3589.0MB, alloc=636.3MB, time=56.98 memory used=3719.5MB, alloc=636.3MB, time=59.18 memory used=3870.0MB, alloc=660.3MB, time=62.44 memory used=4018.7MB, alloc=660.3MB, time=65.38 memory used=4250.8MB, alloc=660.3MB, time=68.84 memory used=4419.4MB, alloc=684.3MB, time=72.07 memory used=4579.9MB, alloc=684.3MB, time=74.25 memory used=4763.2MB, alloc=684.3MB, time=78.30 memory used=4855.1MB, alloc=684.3MB, time=80.43 memory used=4947.1MB, alloc=684.3MB, time=82.25 memory used=5070.8MB, alloc=708.3MB, time=84.88 memory used=5228.3MB, alloc=708.3MB, time=86.81 memory used=5366.4MB, alloc=708.3MB, time=89.16 memory used=5435.8MB, alloc=708.3MB, time=91.02 memory used=5820.3MB, alloc=732.3MB, time=97.51 memory used=6050.4MB, alloc=756.3MB, time=99.78 memory used=6328.9MB, alloc=780.3MB, time=105.27 memory used=6555.8MB, alloc=780.3MB, time=106.88 memory used=6947.2MB, alloc=780.3MB, time=113.83 memory used=7184.5MB, alloc=780.3MB, time=119.54 memory used=7543.8MB, alloc=804.3MB, time=123.25 memory used=7891.5MB, alloc=804.3MB, time=129.98 memory used=8180.1MB, alloc=804.3MB, time=131.49 memory used=8534.8MB, alloc=804.3MB, time=136.71 memory used=8777.3MB, alloc=804.3MB, time=137.94 memory used=9263.8MB, alloc=828.3MB, time=145.37 memory used=9661.6MB, alloc=852.3MB, time=154.31 memory used=10003.9MB, alloc=876.3MB, time=161.39 memory used=10337.0MB, alloc=900.3MB, time=168.98 memory used=10647.8MB, alloc=924.3MB, time=176.56 memory used=10937.9MB, alloc=948.3MB, time=184.44 memory used=11210.3MB, alloc=972.3MB, time=191.60 memory used=11447.9MB, alloc=996.3MB, time=197.59 memory used=11691.3MB, alloc=1020.3MB, time=203.39 memory used=11918.0MB, alloc=1044.3MB, time=208.79 memory used=12141.0MB, alloc=1324.3MB, time=212.92 memory used=12829.0MB, alloc=1348.3MB, time=227.57 memory used=13553.1MB, alloc=1372.3MB, time=240.55 memory used=14239.5MB, alloc=1396.3MB, time=258.00 memory used=14842.1MB, alloc=1420.3MB, time=268.53 memory used=15556.5MB, alloc=1444.3MB, time=283.37 memory used=16144.9MB, alloc=1468.3MB, time=293.25 memory used=16536.9MB, alloc=1492.3MB, time=303.29 memory used=17022.4MB, alloc=1531.8MB, time=307.02 memory used=17353.6MB, alloc=1555.8MB, time=310.40 memory used=17867.7MB, alloc=1579.8MB, time=317.47 memory used=18625.0MB, alloc=1603.8MB, time=331.21 memory used=18949.5MB, alloc=1627.8MB, time=336.05 memory used=19290.0MB, alloc=1651.8MB, time=340.57 memory used=19730.8MB, alloc=1675.8MB, time=357.19 memory used=20183.6MB, alloc=1699.8MB, time=361.65 memory used=20887.9MB, alloc=1723.8MB, time=366.93 memory used=21349.3MB, alloc=1747.8MB, time=383.56 memory used=22003.2MB, alloc=1771.8MB, time=388.55 memory used=22831.2MB, alloc=1795.8MB, time=395.33 memory used=23362.9MB, alloc=1819.8MB, time=401.26 memory used=24155.0MB, alloc=1843.8MB, time=413.80 memory used=25022.7MB, alloc=1867.8MB, time=428.83 memory used=25618.9MB, alloc=1891.8MB, time=441.99 memory used=26185.8MB, alloc=1915.8MB, time=456.45 memory used=27002.0MB, alloc=1939.8MB, time=468.64 memory used=27645.1MB, alloc=1963.8MB, time=481.68 memory used=28014.8MB, alloc=1963.8MB, time=486.08 memory used=28673.3MB, alloc=1963.8MB, time=492.89 memory used=29163.5MB, alloc=1963.8MB, time=497.41 memory used=30179.3MB, alloc=1987.8MB, time=510.01 memory used=30751.1MB, alloc=2011.8MB, time=522.31 memory used=31530.1MB, alloc=2011.8MB, time=536.33 memory used=31957.5MB, alloc=2035.8MB, time=546.20 memory used=32249.2MB, alloc=2035.8MB, time=555.06 memory used=32669.1MB, alloc=2059.8MB, time=570.17 memory used=33100.5MB, alloc=2059.8MB, time=584.39 memory used=33448.9MB, alloc=2083.8MB, time=594.87 memory used=33770.3MB, alloc=2107.8MB, time=603.77 memory used=34098.9MB, alloc=2107.8MB, time=616.64 memory used=34359.6MB, alloc=2107.8MB, time=626.62 memory used=34828.5MB, alloc=2107.8MB, time=644.42 memory used=35143.4MB, alloc=2131.8MB, time=656.60 memory used=35403.9MB, alloc=2131.8MB, time=667.61 memory used=35682.2MB, alloc=2131.8MB, time=680.43 memory used=35852.0MB, alloc=2131.8MB, time=688.34 memory used=36024.0MB, alloc=2131.8MB, time=696.16 memory used=36175.0MB, alloc=2131.8MB, time=703.70 memory used=36397.2MB, alloc=2131.8MB, time=715.20 memory used=36548.0MB, alloc=2131.8MB, time=723.11 memory used=36682.2MB, alloc=2131.8MB, time=730.55 memory used=36777.4MB, alloc=2131.8MB, time=737.87 memory used=36875.2MB, alloc=2131.8MB, time=744.75 memory used=37046.1MB, alloc=2131.8MB, time=755.08 memory used=37182.3MB, alloc=2131.8MB, time=764.37 memory used=37283.0MB, alloc=2131.8MB, time=772.11 memory used=37430.7MB, alloc=2131.8MB, time=782.90 memory used=37494.9MB, alloc=2131.8MB, time=789.59 memory used=37597.7MB, alloc=2155.8MB, time=797.03 memory used=37636.2MB, alloc=2155.8MB, time=803.35 memory used=37711.9MB, alloc=2155.8MB, time=810.03 memory used=37783.9MB, alloc=2155.8MB, time=817.48 memory used=37802.0MB, alloc=2155.8MB, time=823.86 memory used=37861.8MB, alloc=2155.8MB, time=830.64 memory used=37923.9MB, alloc=2155.8MB, time=837.91 memory used=37986.6MB, alloc=2155.8MB, time=844.64 memory used=38050.3MB, alloc=2155.8MB, time=851.35 memory used=38090.7MB, alloc=2155.8MB, time=858.67 memory used=38139.8MB, alloc=2155.8MB, time=865.77 memory used=38153.1MB, alloc=2155.8MB, time=872.08 memory used=38222.6MB, alloc=2155.8MB, time=880.27 memory used=38246.5MB, alloc=2155.8MB, time=887.20 memory used=38306.0MB, alloc=2155.8MB, time=895.33 memory used=38353.9MB, alloc=2155.8MB, time=902.48 memory used=38393.0MB, alloc=2155.8MB, time=909.29 memory used=38418.9MB, alloc=2155.8MB, time=916.05 memory used=38428.8MB, alloc=2155.8MB, time=922.26 memory used=38453.0MB, alloc=2155.8MB, time=928.68 memory used=38472.4MB, alloc=2155.8MB, time=935.11 memory used=38508.9MB, alloc=2155.8MB, time=942.03 memory used=38546.7MB, alloc=2155.8MB, time=948.42 memory used=38567.2MB, alloc=2155.8MB, time=954.63 memory used=38599.5MB, alloc=2155.8MB, time=961.65 memory used=38627.8MB, alloc=2155.8MB, time=967.93 memory used=38649.6MB, alloc=2411.8MB, time=980.42 memory used=39930.5MB, alloc=2435.8MB, time=1014.61 memory used=40816.0MB, alloc=2459.8MB, time=1037.27 memory used=42051.7MB, alloc=2483.8MB, time=1062.53 memory used=43307.0MB, alloc=2507.8MB, time=1093.24 memory used=44432.5MB, alloc=2531.8MB, time=1118.68 memory used=45624.5MB, alloc=2555.8MB, time=1144.33 memory used=46901.3MB, alloc=2579.8MB, time=1180.65 memory used=47929.8MB, alloc=2603.8MB, time=1203.80 memory used=48991.7MB, alloc=2627.8MB, time=1229.51 memory used=49897.6MB, alloc=2651.8MB, time=1255.70 memory used=50673.1MB, alloc=2675.8MB, time=1274.67 memory used=51245.8MB, alloc=2699.8MB, time=1300.79 memory used=51827.8MB, alloc=2723.8MB, time=1314.74 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428459365 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; F := 3 3 2 2 2 2 2 2 2 [15 x y - 11 x z - 3 x z, 3 x y - 2 x z - 14 z , -4 x z - x - 13 y] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; G := [ 4 3 3 2 2 3 3 2 9 y + 10 y z - 2 x z, 6 y z + 8 y z + 6 x , -18 x y + 7 x y + 14 x y ] > Problem := [F,G]; Problem := [ 3 3 2 2 2 2 2 2 2 [15 x y - 11 x z - 3 x z, 3 x y - 2 x z - 14 z , -4 x z - x - 13 y] , [ 4 3 3 2 2 3 3 2 9 y + 10 y z - 2 x z, 6 y z + 8 y z + 6 x , -18 x y + 7 x y + 14 x y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.18 memory used=25.3MB, alloc=32.3MB, time=0.49 memory used=44.4MB, alloc=56.3MB, time=0.77 memory used=86.9MB, alloc=60.3MB, time=1.35 memory used=132.9MB, alloc=68.6MB, time=2.00 memory used=165.5MB, alloc=68.6MB, time=2.32 memory used=205.3MB, alloc=68.6MB, time=2.96 memory used=247.3MB, alloc=68.6MB, time=3.37 memory used=293.9MB, alloc=92.6MB, time=3.93 memory used=371.7MB, alloc=92.6MB, time=5.57 memory used=415.1MB, alloc=92.6MB, time=5.83 memory used=472.9MB, alloc=92.6MB, time=6.96 memory used=541.3MB, alloc=92.6MB, time=7.67 memory used=605.8MB, alloc=92.6MB, time=8.55 memory used=675.3MB, alloc=116.6MB, time=9.30 memory used=741.4MB, alloc=372.6MB, time=10.26 memory used=828.9MB, alloc=372.6MB, time=11.29 memory used=897.8MB, alloc=372.6MB, time=11.57 memory used=954.4MB, alloc=372.6MB, time=11.78 memory used=993.5MB, alloc=396.6MB, time=11.98 memory used=1041.8MB, alloc=396.6MB, time=12.18 memory used=1098.7MB, alloc=396.6MB, time=12.38 memory used=1164.8MB, alloc=396.6MB, time=12.59 memory used=1224.1MB, alloc=396.6MB, time=12.79 memory used=1282.3MB, alloc=396.6MB, time=13.33 memory used=1377.5MB, alloc=396.6MB, time=13.68 memory used=1444.4MB, alloc=396.6MB, time=13.93 memory used=1491.9MB, alloc=396.6MB, time=14.15 memory used=1547.5MB, alloc=396.6MB, time=14.35 memory used=1613.3MB, alloc=396.6MB, time=14.57 memory used=1674.8MB, alloc=396.6MB, time=14.77 memory used=1726.0MB, alloc=396.6MB, time=15.07 memory used=1836.0MB, alloc=396.6MB, time=50.45 memory used=1949.0MB, alloc=396.6MB, time=51.85 memory used=2004.9MB, alloc=396.6MB, time=52.07 memory used=2059.9MB, alloc=396.6MB, time=52.25 memory used=2126.4MB, alloc=396.6MB, time=52.46 memory used=2180.5MB, alloc=396.6MB, time=52.66 memory used=2222.0MB, alloc=396.6MB, time=52.86 memory used=2267.3MB, alloc=396.6MB, time=53.03 memory used=2315.4MB, alloc=396.6MB, time=53.23 memory used=2367.4MB, alloc=396.6MB, time=53.42 memory used=2423.1MB, alloc=396.6MB, time=53.61 memory used=2483.7MB, alloc=396.6MB, time=53.80 memory used=2548.7MB, alloc=396.6MB, time=53.99 memory used=2617.9MB, alloc=396.6MB, time=54.19 memory used=2674.5MB, alloc=396.6MB, time=54.35 memory used=2712.3MB, alloc=396.6MB, time=54.49 memory used=2751.3MB, alloc=396.6MB, time=54.63 memory used=2792.0MB, alloc=396.6MB, time=54.76 memory used=2834.6MB, alloc=396.6MB, time=54.90 memory used=2879.1MB, alloc=396.6MB, time=55.04 memory used=2926.4MB, alloc=396.6MB, time=55.18 memory used=2976.0MB, alloc=396.6MB, time=55.33 memory used=3027.5MB, alloc=396.6MB, time=55.47 memory used=3088.1MB, alloc=396.6MB, time=55.70 memory used=3175.1MB, alloc=396.6MB, time=56.48 memory used=3268.1MB, alloc=396.6MB, time=57.06 memory used=3409.6MB, alloc=396.6MB, time=60.01 memory used=3543.7MB, alloc=396.6MB, time=60.96 memory used=3668.8MB, alloc=396.6MB, time=62.80 memory used=3768.9MB, alloc=396.6MB, time=63.67 memory used=3826.3MB, alloc=396.6MB, time=64.00 memory used=3873.8MB, alloc=396.6MB, time=64.20 memory used=3962.2MB, alloc=420.6MB, time=86.50 memory used=4037.8MB, alloc=420.6MB, time=87.42 memory used=4099.3MB, alloc=420.6MB, time=87.65 memory used=4156.5MB, alloc=420.6MB, time=87.88 memory used=4225.6MB, alloc=420.6MB, time=88.11 memory used=4304.4MB, alloc=420.6MB, time=88.34 memory used=4350.2MB, alloc=420.6MB, time=88.52 memory used=4397.9MB, alloc=420.6MB, time=88.71 memory used=4449.4MB, alloc=420.6MB, time=88.90 memory used=4504.6MB, alloc=420.6MB, time=89.08 memory used=4564.8MB, alloc=420.6MB, time=89.26 memory used=4629.4MB, alloc=420.6MB, time=89.46 memory used=4699.0MB, alloc=420.6MB, time=89.66 memory used=4775.2MB, alloc=420.6MB, time=89.85 memory used=4988.2MB, alloc=420.6MB, time=90.37 memory used=5096.1MB, alloc=420.6MB, time=91.10 memory used=5252.5MB, alloc=420.6MB, time=92.59 memory used=5388.0MB, alloc=420.6MB, time=94.91 memory used=5501.4MB, alloc=444.6MB, time=96.59 memory used=5638.4MB, alloc=444.6MB, time=97.80 memory used=5745.5MB, alloc=444.6MB, time=98.99 memory used=5824.3MB, alloc=444.6MB, time=103.70 memory used=5905.7MB, alloc=444.6MB, time=104.25 memory used=5980.2MB, alloc=444.6MB, time=104.55 memory used=6082.9MB, alloc=444.6MB, time=105.49 memory used=6174.0MB, alloc=444.6MB, time=106.70 memory used=6282.4MB, alloc=468.6MB, time=108.00 memory used=6393.6MB, alloc=492.6MB, time=109.32 memory used=6471.7MB, alloc=492.6MB, time=110.54 memory used=6546.8MB, alloc=492.6MB, time=111.85 memory used=6635.7MB, alloc=492.6MB, time=112.83 memory used=6764.4MB, alloc=492.6MB, time=115.12 memory used=6888.4MB, alloc=492.6MB, time=117.21 memory used=6994.8MB, alloc=492.6MB, time=118.43 memory used=7072.5MB, alloc=492.6MB, time=119.52 memory used=7153.0MB, alloc=492.6MB, time=120.47 memory used=7214.6MB, alloc=516.6MB, time=121.46 memory used=7284.4MB, alloc=516.6MB, time=122.44 memory used=7344.8MB, alloc=516.6MB, time=123.62 memory used=7388.4MB, alloc=516.6MB, time=124.50 memory used=7442.6MB, alloc=516.6MB, time=125.65 memory used=7623.0MB, alloc=516.6MB, time=127.72 memory used=7729.7MB, alloc=516.6MB, time=128.43 memory used=7877.4MB, alloc=516.6MB, time=132.66 memory used=7968.3MB, alloc=516.6MB, time=133.15 memory used=8066.4MB, alloc=516.6MB, time=133.87 memory used=8188.1MB, alloc=516.6MB, time=134.61 memory used=8304.6MB, alloc=516.6MB, time=137.21 memory used=8433.4MB, alloc=516.6MB, time=139.77 memory used=8520.7MB, alloc=516.6MB, time=140.28 memory used=8637.7MB, alloc=516.6MB, time=141.28 memory used=8860.9MB, alloc=540.6MB, time=144.28 memory used=9021.5MB, alloc=564.6MB, time=145.56 memory used=9197.7MB, alloc=588.6MB, time=147.90 memory used=9365.4MB, alloc=612.6MB, time=150.42 memory used=9563.1MB, alloc=612.6MB, time=152.86 memory used=9706.2MB, alloc=612.6MB, time=155.06 memory used=9831.1MB, alloc=636.6MB, time=157.39 memory used=10048.5MB, alloc=636.6MB, time=159.11 memory used=10263.0MB, alloc=660.6MB, time=162.46 memory used=10449.5MB, alloc=660.6MB, time=163.57 memory used=10587.3MB, alloc=660.6MB, time=164.58 memory used=10740.4MB, alloc=660.6MB, time=165.58 memory used=10914.4MB, alloc=660.6MB, time=166.63 memory used=11110.3MB, alloc=660.6MB, time=167.66 memory used=11300.4MB, alloc=660.6MB, time=168.64 memory used=11420.3MB, alloc=660.6MB, time=169.51 memory used=11535.8MB, alloc=660.6MB, time=170.41 memory used=11655.3MB, alloc=660.6MB, time=171.26 memory used=11782.1MB, alloc=660.6MB, time=172.13 memory used=11910.8MB, alloc=660.6MB, time=172.98 memory used=12046.0MB, alloc=660.6MB, time=173.84 memory used=12188.1MB, alloc=660.6MB, time=174.70 memory used=12336.7MB, alloc=660.6MB, time=175.57 memory used=12491.7MB, alloc=660.6MB, time=176.47 memory used=12656.8MB, alloc=660.6MB, time=177.38 memory used=12827.4MB, alloc=660.6MB, time=178.25 memory used=13006.6MB, alloc=660.6MB, time=179.22 memory used=13194.6MB, alloc=660.6MB, time=180.14 memory used=13393.0MB, alloc=660.6MB, time=181.04 memory used=13545.4MB, alloc=660.6MB, time=181.85 memory used=13649.1MB, alloc=660.6MB, time=182.59 memory used=13755.9MB, alloc=660.6MB, time=183.34 memory used=13867.3MB, alloc=660.6MB, time=184.09 memory used=13981.9MB, alloc=660.6MB, time=184.83 memory used=14101.5MB, alloc=660.6MB, time=185.59 memory used=14226.4MB, alloc=660.6MB, time=186.36 memory used=14358.3MB, alloc=660.6MB, time=187.11 memory used=14519.3MB, alloc=660.6MB, time=188.16 memory used=14748.7MB, alloc=660.6MB, time=190.24 memory used=14901.1MB, alloc=660.6MB, time=191.24 memory used=15061.2MB, alloc=660.6MB, time=192.24 memory used=15252.9MB, alloc=660.6MB, time=193.26 memory used=15417.0MB, alloc=660.6MB, time=194.20 memory used=15536.1MB, alloc=660.6MB, time=195.04 memory used=15665.0MB, alloc=660.6MB, time=195.92 memory used=15806.9MB, alloc=660.6MB, time=196.79 memory used=15962.8MB, alloc=660.6MB, time=197.68 memory used=16137.9MB, alloc=660.6MB, time=198.56 memory used=16394.2MB, alloc=660.6MB, time=253.23 memory used=16634.1MB, alloc=660.6MB, time=272.84 memory used=16812.3MB, alloc=660.6MB, time=273.83 memory used=16940.2MB, alloc=660.6MB, time=274.70 memory used=17092.4MB, alloc=660.6MB, time=275.54 memory used=17271.8MB, alloc=660.6MB, time=276.44 memory used=17439.0MB, alloc=660.6MB, time=277.26 memory used=17554.6MB, alloc=660.6MB, time=278.02 memory used=17680.3MB, alloc=660.6MB, time=278.77 memory used=17818.1MB, alloc=660.6MB, time=279.54 memory used=17971.9MB, alloc=660.6MB, time=280.31 memory used=18174.0MB, alloc=660.6MB, time=283.20 memory used=18407.6MB, alloc=660.6MB, time=284.45 memory used=18549.9MB, alloc=660.6MB, time=285.45 memory used=18694.5MB, alloc=660.6MB, time=286.44 memory used=18858.3MB, alloc=660.6MB, time=287.41 memory used=19043.9MB, alloc=660.6MB, time=288.42 memory used=19247.2MB, alloc=660.6MB, time=289.45 memory used=19394.3MB, alloc=660.6MB, time=290.36 memory used=19505.8MB, alloc=660.6MB, time=291.22 memory used=19624.3MB, alloc=660.6MB, time=292.10 memory used=19744.9MB, alloc=660.6MB, time=292.96 memory used=19872.7MB, alloc=660.6MB, time=293.85 memory used=20007.6MB, alloc=660.6MB, time=294.73 memory used=20149.4MB, alloc=660.6MB, time=295.58 memory used=20297.7MB, alloc=660.6MB, time=296.49 memory used=20452.1MB, alloc=660.6MB, time=297.35 memory used=20612.4MB, alloc=660.6MB, time=298.24 memory used=20783.2MB, alloc=660.6MB, time=299.11 memory used=20958.5MB, alloc=660.6MB, time=300.02 memory used=21147.0MB, alloc=660.6MB, time=300.93 memory used=21342.6MB, alloc=660.6MB, time=301.82 memory used=21529.5MB, alloc=660.6MB, time=302.67 memory used=21633.0MB, alloc=660.6MB, time=303.41 memory used=21739.4MB, alloc=660.6MB, time=304.17 memory used=21848.2MB, alloc=660.6MB, time=304.93 memory used=21961.0MB, alloc=660.6MB, time=305.71 memory used=22079.8MB, alloc=660.6MB, time=306.44 memory used=22202.2MB, alloc=660.6MB, time=307.17 memory used=22332.7MB, alloc=660.6MB, time=307.92 memory used=22469.8MB, alloc=660.6MB, time=308.65 memory used=22686.0MB, alloc=660.6MB, time=311.88 memory used=22901.7MB, alloc=660.6MB, time=313.07 memory used=23040.1MB, alloc=660.6MB, time=314.06 memory used=23185.5MB, alloc=660.6MB, time=315.07 memory used=23350.8MB, alloc=660.6MB, time=316.11 memory used=23538.1MB, alloc=660.6MB, time=317.15 memory used=23746.0MB, alloc=660.6MB, time=318.20 memory used=23877.2MB, alloc=684.6MB, time=319.13 memory used=24000.1MB, alloc=684.6MB, time=320.00 memory used=24130.3MB, alloc=684.6MB, time=320.91 memory used=24268.5MB, alloc=684.6MB, time=321.83 memory used=24414.3MB, alloc=684.6MB, time=322.77 memory used=24567.5MB, alloc=684.6MB, time=323.69 memory used=24727.9MB, alloc=684.6MB, time=324.63 memory used=24900.2MB, alloc=684.6MB, time=325.56 memory used=25078.6MB, alloc=684.6MB, time=326.48 memory used=25267.5MB, alloc=684.6MB, time=327.39 memory used=25466.0MB, alloc=684.6MB, time=328.32 memory used=25677.7MB, alloc=684.6MB, time=329.26 memory used=25900.1MB, alloc=684.6MB, time=330.22 memory used=26057.6MB, alloc=684.6MB, time=331.10 memory used=26175.5MB, alloc=684.6MB, time=331.89 memory used=26296.3MB, alloc=684.6MB, time=332.68 memory used=26423.3MB, alloc=684.6MB, time=333.47 memory used=26555.9MB, alloc=684.6MB, time=334.25 memory used=26693.7MB, alloc=684.6MB, time=335.04 memory used=26840.5MB, alloc=684.6MB, time=335.82 memory used=27017.4MB, alloc=684.6MB, time=336.77 memory used=27245.1MB, alloc=708.6MB, time=453.34 memory used=27510.7MB, alloc=708.6MB, time=697.73 memory used=27857.6MB, alloc=708.6MB, time=701.02 memory used=28074.4MB, alloc=708.6MB, time=702.16 memory used=28234.8MB, alloc=708.6MB, time=703.17 memory used=28401.8MB, alloc=708.6MB, time=704.09 memory used=28592.5MB, alloc=708.6MB, time=705.05 memory used=28810.5MB, alloc=708.6MB, time=706.01 memory used=29037.3MB, alloc=708.6MB, time=706.98 memory used=29173.5MB, alloc=708.6MB, time=707.78 memory used=29312.3MB, alloc=708.6MB, time=708.61 memory used=29458.5MB, alloc=708.6MB, time=709.45 memory used=29614.2MB, alloc=708.6MB, time=710.31 memory used=29778.8MB, alloc=708.6MB, time=711.16 memory used=29954.0MB, alloc=708.6MB, time=711.98 memory used=30138.6MB, alloc=708.6MB, time=712.80 memory used=30336.0MB, alloc=708.6MB, time=713.65 memory used=30545.9MB, alloc=708.6MB, time=714.52 memory used=30771.1MB, alloc=708.6MB, time=715.37 memory used=31019.6MB, alloc=708.6MB, time=716.25 memory used=31157.8MB, alloc=708.6MB, time=717.03 memory used=31285.2MB, alloc=708.6MB, time=717.81 memory used=31690.1MB, alloc=708.6MB, time=727.10 memory used=31880.9MB, alloc=708.6MB, time=728.06 memory used=32090.6MB, alloc=708.6MB, time=729.05 memory used=32349.8MB, alloc=708.6MB, time=734.95 memory used=32540.8MB, alloc=708.6MB, time=735.92 memory used=32739.9MB, alloc=708.6MB, time=736.87 memory used=32986.0MB, alloc=708.6MB, time=740.95 memory used=33199.3MB, alloc=708.6MB, time=742.13 memory used=33365.1MB, alloc=708.6MB, time=743.23 memory used=33553.7MB, alloc=708.6MB, time=744.30 memory used=33765.8MB, alloc=708.6MB, time=745.44 memory used=34004.6MB, alloc=708.6MB, time=746.59 memory used=34214.8MB, alloc=708.6MB, time=747.64 memory used=34353.4MB, alloc=708.6MB, time=748.56 memory used=34496.7MB, alloc=708.6MB, time=749.48 memory used=34644.2MB, alloc=708.6MB, time=750.40 memory used=34800.4MB, alloc=708.6MB, time=751.35 memory used=34965.2MB, alloc=708.6MB, time=752.28 memory used=35138.3MB, alloc=708.6MB, time=753.23 memory used=35319.2MB, alloc=708.6MB, time=754.17 memory used=35507.4MB, alloc=708.6MB, time=755.12 memory used=35702.5MB, alloc=708.6MB, time=756.11 memory used=35910.0MB, alloc=708.6MB, time=757.10 memory used=36128.8MB, alloc=708.6MB, time=758.09 memory used=36357.2MB, alloc=708.6MB, time=759.08 memory used=36599.2MB, alloc=708.6MB, time=760.03 memory used=36798.8MB, alloc=708.6MB, time=760.96 memory used=36924.4MB, alloc=708.6MB, time=761.76 memory used=37056.4MB, alloc=708.6MB, time=762.58 memory used=37193.6MB, alloc=708.6MB, time=763.38 memory used=37334.2MB, alloc=708.6MB, time=764.19 memory used=37480.4MB, alloc=708.6MB, time=765.00 memory used=37633.0MB, alloc=708.6MB, time=765.81 memory used=37794.5MB, alloc=708.6MB, time=766.64 memory used=37988.5MB, alloc=708.6MB, time=767.69 memory used=38186.7MB, alloc=708.6MB, time=769.64 memory used=38384.5MB, alloc=708.6MB, time=770.76 memory used=38579.3MB, alloc=708.6MB, time=771.85 memory used=38821.9MB, alloc=708.6MB, time=773.00 memory used=38988.9MB, alloc=708.6MB, time=773.98 memory used=39141.3MB, alloc=708.6MB, time=774.89 memory used=39310.8MB, alloc=708.6MB, time=775.81 memory used=39502.3MB, alloc=708.6MB, time=776.75 memory used=39736.1MB, alloc=708.6MB, time=777.88 memory used=40108.3MB, alloc=708.6MB, time=917.09 memory used=40315.8MB, alloc=708.6MB, time=918.20 memory used=40496.8MB, alloc=708.6MB, time=919.19 memory used=40665.0MB, alloc=708.6MB, time=920.13 memory used=40864.4MB, alloc=708.6MB, time=921.10 memory used=41096.7MB, alloc=708.6MB, time=922.09 memory used=41261.7MB, alloc=708.6MB, time=922.94 memory used=41403.0MB, alloc=708.6MB, time=923.75 memory used=41555.3MB, alloc=708.6MB, time=924.56 memory used=41719.8MB, alloc=708.6MB, time=925.35 memory used=41896.1MB, alloc=708.6MB, time=926.16 memory used=42088.5MB, alloc=708.6MB, time=926.98 memory used=42299.5MB, alloc=708.6MB, time=927.82 memory used=42610.2MB, alloc=708.6MB, time=932.18 memory used=42846.4MB, alloc=708.6MB, time=933.78 memory used=43038.4MB, alloc=708.6MB, time=934.71 memory used=43280.8MB, alloc=708.6MB, time=938.17 memory used=43529.6MB, alloc=708.6MB, time=939.43 memory used=43694.7MB, alloc=708.6MB, time=940.58 memory used=43876.0MB, alloc=708.6MB, time=941.67 memory used=44083.5MB, alloc=708.6MB, 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time=961.71 memory used=47808.3MB, alloc=708.6MB, time=962.52 memory used=47960.3MB, alloc=708.6MB, time=963.33 memory used=48118.3MB, alloc=708.6MB, time=964.13 memory used=48287.2MB, alloc=708.6MB, time=964.91 memory used=48490.3MB, alloc=708.6MB, time=967.20 memory used=48721.0MB, alloc=708.6MB, time=968.43 memory used=48902.3MB, alloc=708.6MB, time=969.52 memory used=49128.3MB, alloc=708.6MB, time=970.62 memory used=49324.6MB, alloc=708.6MB, time=971.62 memory used=49470.4MB, alloc=708.6MB, time=972.54 memory used=49634.0MB, alloc=708.6MB, time=973.47 memory used=49817.1MB, alloc=708.6MB, time=974.44 memory used=50028.9MB, alloc=708.6MB, time=975.37 memory used=50332.8MB, alloc=708.6MB, time=1112.18 memory used=50605.9MB, alloc=708.6MB, time=1115.48 memory used=50811.1MB, alloc=708.6MB, time=1116.53 memory used=50966.3MB, alloc=708.6MB, time=1117.49 memory used=51150.3MB, alloc=708.6MB, time=1118.45 memory used=51367.3MB, alloc=708.6MB, time=1119.44 memory used=51575.7MB, alloc=708.6MB, time=1120.35 memory used=51710.6MB, alloc=708.6MB, time=1121.16 memory used=51856.1MB, alloc=708.6MB, time=1121.96 memory used=52012.4MB, alloc=708.6MB, time=1122.78 memory used=52181.8MB, alloc=708.6MB, time=1123.61 memory used=52365.3MB, alloc=708.6MB, time=1124.46 memory used=52565.7MB, alloc=708.6MB, time=1125.32 memory used=52787.3MB, alloc=708.6MB, time=1126.17 memory used=53136.8MB, alloc=708.6MB, time=1138.26 memory used=53329.2MB, alloc=708.6MB, time=1139.25 memory used=53517.5MB, alloc=708.6MB, time=1140.18 memory used=53711.0MB, alloc=708.6MB, time=1141.04 memory used=53893.4MB, alloc=708.6MB, time=1142.19 memory used=54104.8MB, alloc=708.6MB, time=1143.48 memory used=54333.0MB, alloc=708.6MB, time=1144.67 memory used=54599.3MB, alloc=708.6MB, time=1147.03 memory used=54756.7MB, alloc=708.6MB, time=1149.37 memory used=54969.7MB, alloc=708.6MB, time=1151.48 memory used=55142.3MB, alloc=708.6MB, time=1154.04 memory used=55300.2MB, alloc=708.6MB, time=1155.93 memory used=55475.1MB, alloc=708.6MB, time=1163.51 memory used=55732.9MB, alloc=708.6MB, time=1170.78 memory used=55897.5MB, alloc=708.6MB, time=1171.77 memory used=56095.3MB, alloc=708.6MB, time=1172.74 memory used=56263.4MB, alloc=708.6MB, time=1173.63 memory used=56467.5MB, alloc=708.6MB, time=1175.26 memory used=56612.5MB, alloc=708.6MB, time=1176.94 memory used=56756.2MB, alloc=708.6MB, time=1178.63 memory used=56926.1MB, alloc=708.6MB, time=1180.47 memory used=57181.6MB, alloc=708.6MB, time=1184.68 memory used=57367.7MB, alloc=708.6MB, time=1185.91 memory used=57551.9MB, alloc=708.6MB, time=1187.10 memory used=57709.1MB, alloc=708.6MB, time=1188.25 memory used=57881.6MB, alloc=708.6MB, time=1189.37 memory used=58076.6MB, alloc=708.6MB, time=1190.46 memory used=58291.8MB, alloc=708.6MB, time=1191.62 memory used=58509.6MB, alloc=708.6MB, time=1192.77 memory used=58652.8MB, alloc=708.6MB, time=1193.78 memory used=58780.8MB, alloc=708.6MB, time=1194.77 memory used=58912.0MB, alloc=732.6MB, time=1195.76 memory used=59061.2MB, alloc=732.6MB, time=1196.77 memory used=59219.0MB, alloc=732.6MB, time=1197.77 memory used=59386.6MB, alloc=732.6MB, time=1198.82 memory used=59563.5MB, alloc=732.6MB, time=1199.87 memory used=59742.9MB, alloc=732.6MB, time=1200.92 memory used=59931.5MB, alloc=732.6MB, time=1201.95 memory used=60129.0MB, alloc=732.6MB, time=1203.00 memory used=60334.9MB, alloc=732.6MB, time=1204.01 memory used=60549.0MB, alloc=732.6MB, time=1205.04 memory used=60777.5MB, alloc=732.6MB, time=1206.13 memory used=61012.6MB, alloc=732.6MB, time=1207.21 memory used=61260.2MB, alloc=732.6MB, time=1208.34 memory used=61452.3MB, alloc=732.6MB, time=1209.33 memory used=61582.6MB, alloc=732.6MB, time=1210.19 memory used=61711.7MB, alloc=732.6MB, time=1211.07 memory used=61845.6MB, alloc=732.6MB, time=1211.93 memory used=61983.7MB, alloc=732.6MB, time=1212.81 memory used=62125.3MB, alloc=732.6MB, time=1213.67 memory used=62269.9MB, alloc=732.6MB, time=1214.55 memory used=62417.3MB, alloc=732.6MB, time=1215.44 memory used=62570.0MB, alloc=732.6MB, time=1216.35 memory used=62728.5MB, alloc=732.6MB, time=1217.22 memory used=62895.1MB, alloc=732.6MB, time=1218.09 memory used=63066.3MB, alloc=732.6MB, time=1218.97 memory used=63242.8MB, alloc=732.6MB, time=1219.86 memory used=63430.6MB, alloc=732.6MB, time=1220.75 memory used=63645.9MB, alloc=732.6MB, time=1221.96 memory used=63859.2MB, alloc=732.6MB, time=1224.65 memory used=64072.6MB, alloc=732.6MB, time=1225.97 memory used=64249.7MB, alloc=732.6MB, time=1227.18 memory used=64466.5MB, alloc=732.6MB, time=1228.34 memory used=64713.4MB, alloc=732.6MB, time=1229.57 memory used=64862.5MB, alloc=732.6MB, time=1230.57 memory used=65017.9MB, alloc=732.6MB, time=1231.59 memory used=65186.2MB, alloc=732.6MB, time=1232.65 memory used=65366.5MB, alloc=732.6MB, time=1233.64 memory used=65563.9MB, alloc=732.6MB, time=1234.66 memory used=65781.3MB, alloc=732.6MB, time=1235.71 memory used=66023.5MB, alloc=732.6MB, time=1236.78 memory used=66195.5MB, alloc=732.6MB, time=1237.71 memory used=66430.0MB, alloc=732.6MB, time=1320.32 memory used=66721.2MB, alloc=732.6MB, time=1348.87 memory used=66933.6MB, alloc=732.6MB, time=1350.00 memory used=67096.2MB, alloc=732.6MB, time=1351.01 memory used=67290.7MB, alloc=732.6MB, time=1352.08 memory used=67521.7MB, alloc=732.6MB, time=1353.16 memory used=67703.9MB, alloc=732.6MB, time=1354.14 memory used=67849.1MB, alloc=732.6MB, time=1355.04 memory used=68006.1MB, alloc=732.6MB, time=1355.94 memory used=68177.1MB, alloc=732.6MB, time=1356.84 memory used=68364.1MB, alloc=732.6MB, time=1357.77 memory used=68570.7MB, alloc=732.6MB, time=1358.73 memory used=68803.1MB, alloc=732.6MB, time=1359.68 memory used=69043.9MB, alloc=732.6MB, time=1364.69 memory used=69285.4MB, alloc=732.6MB, time=1366.07 memory used=69456.0MB, alloc=732.6MB, time=1367.24 memory used=69639.9MB, alloc=732.6MB, time=1368.42 memory used=69849.9MB, alloc=732.6MB, time=1369.65 memory used=70088.2MB, alloc=732.6MB, time=1370.85 memory used=70318.7MB, alloc=732.6MB, time=1372.03 memory used=70472.3MB, alloc=732.6MB, time=1373.08 memory used=70612.6MB, alloc=732.6MB, time=1374.12 memory used=70758.8MB, alloc=732.6MB, time=1375.17 memory used=70914.6MB, alloc=732.6MB, time=1376.16 memory used=71073.4MB, alloc=732.6MB, time=1377.19 memory used=71242.0MB, alloc=732.6MB, time=1378.29 memory used=71420.1MB, alloc=732.6MB, time=1379.38 memory used=71607.3MB, alloc=732.6MB, time=1380.45 memory used=71796.5MB, alloc=732.6MB, time=1381.54 memory used=71994.6MB, alloc=732.6MB, time=1382.61 memory used=72201.3MB, alloc=732.6MB, time=1383.68 memory used=72422.3MB, alloc=732.6MB, time=1384.79 memory used=72650.8MB, alloc=732.6MB, time=1385.91 memory used=72892.7MB, alloc=732.6MB, time=1387.02 memory used=73146.6MB, alloc=732.6MB, time=1388.13 memory used=73294.4MB, alloc=732.6MB, time=1389.09 memory used=73423.5MB, alloc=732.6MB, time=1390.03 memory used=73552.4MB, alloc=732.6MB, time=1390.92 memory used=73685.1MB, alloc=732.6MB, time=1391.83 memory used=73822.4MB, alloc=732.6MB, time=1392.75 memory used=73963.1MB, alloc=732.6MB, time=1393.68 memory used=74106.6MB, alloc=732.6MB, time=1394.60 memory used=74257.9MB, alloc=732.6MB, time=1395.52 memory used=74410.5MB, alloc=732.6MB, time=1396.44 memory used=74571.6MB, alloc=732.6MB, time=1397.38 memory used=74735.6MB, alloc=732.6MB, time=1398.32 memory used=74908.2MB, alloc=732.6MB, time=1399.25 memory used=75088.0MB, alloc=732.6MB, time=1400.18 memory used=75276.9MB, alloc=732.6MB, time=1401.12 memory used=75533.9MB, alloc=732.6MB, time=1405.70 memory used=75765.7MB, alloc=732.6MB, time=1407.08 memory used=75940.1MB, alloc=732.6MB, time=1408.29 memory used=76118.9MB, alloc=732.6MB, time=1409.51 memory used=76324.9MB, alloc=732.6MB, time=1410.68 memory used=76554.1MB, alloc=732.6MB, time=1411.87 memory used=76799.6MB, alloc=732.6MB, time=1413.07 memory used=76964.6MB, alloc=732.6MB, time=1414.15 memory used=77106.5MB, alloc=732.6MB, time=1415.17 memory used=77251.9MB, alloc=732.6MB, time=1416.20 memory used=77407.0MB, alloc=732.6MB, time=1417.24 memory used=77565.4MB, alloc=732.6MB, time=1418.28 memory used=77733.6MB, alloc=732.6MB, time=1419.38 memory used=77911.0MB, alloc=732.6MB, time=1420.47 memory used=78090.9MB, alloc=732.6MB, time=1421.55 memory used=78279.9MB, alloc=732.6MB, time=1422.61 memory used=78477.6MB, alloc=732.6MB, time=1423.66 memory used=78683.7MB, alloc=732.6MB, time=1424.77 memory used=78897.9MB, alloc=732.6MB, time=1425.85 memory used=79126.3MB, alloc=732.6MB, time=1426.93 memory used=79361.2MB, alloc=732.6MB, time=1427.99 memory used=79608.5MB, alloc=732.6MB, time=1429.15 memory used=79782.9MB, alloc=732.6MB, time=1430.11 memory used=79909.3MB, alloc=732.6MB, time=1430.99 memory used=80038.3MB, alloc=732.6MB, time=1431.88 memory used=80172.0MB, alloc=732.6MB, time=1432.78 memory used=80309.9MB, alloc=732.6MB, time=1433.67 memory used=80451.4MB, alloc=732.6MB, time=1434.56 memory used=80595.7MB, alloc=732.6MB, time=1435.46 memory used=80742.8MB, alloc=732.6MB, time=1436.35 memory used=80895.1MB, alloc=732.6MB, time=1437.24 memory used=81053.3MB, alloc=732.6MB, time=1438.16 memory used=81219.4MB, alloc=732.6MB, time=1439.06 memory used=81389.9MB, alloc=732.6MB, time=1439.97 memory used=81565.8MB, alloc=732.6MB, time=1440.88 memory used=81752.3MB, alloc=732.6MB, time=1441.79 memory used=81989.2MB, alloc=732.6MB, time=1486.76 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428460565 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 3 2 3 2 2 F := [2 x z + 4 z + 4 x , -2 y z - 20 x y - 7 y, 10 y + 18 y + 18 z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 3 2 3 G := [10 x y - 12 y z - 9 z , -4 x y + 16 x y z - 2 z , 3 2 -14 y z - 16 x - 20 z] > Problem := [F,G]; Problem := [ 2 3 2 3 2 3 2 2 [2 x z + 4 z + 4 x , -2 y z - 20 x y - 7 y, 10 y + 18 y + 18 z ], [ 2 2 2 2 3 2 3 10 x y - 12 y z - 9 z , -4 x y + 16 x y z - 2 z , 3 2 -14 y z - 16 x - 20 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=27.4MB, alloc=33.5MB, time=0.42 memory used=47.8MB, alloc=33.5MB, time=0.73 memory used=74.1MB, alloc=33.5MB, time=3.31 memory used=89.4MB, alloc=33.5MB, time=3.36 memory used=104.2MB, alloc=33.5MB, time=3.40 memory used=114.4MB, alloc=33.5MB, time=3.43 memory used=125.9MB, alloc=33.5MB, time=3.46 memory used=139.5MB, alloc=33.5MB, time=3.49 memory used=154.7MB, alloc=33.5MB, time=3.52 memory used=168.6MB, alloc=33.5MB, time=3.55 memory used=177.4MB, alloc=33.5MB, time=3.58 memory used=186.8MB, alloc=33.5MB, time=3.60 memory used=197.0MB, alloc=33.5MB, time=3.63 memory used=207.9MB, alloc=33.5MB, time=3.65 memory used=220.0MB, alloc=33.5MB, time=3.68 memory used=233.5MB, alloc=33.5MB, time=3.71 memory used=250.0MB, alloc=33.5MB, time=3.78 memory used=271.8MB, alloc=37.5MB, time=3.98 memory used=295.0MB, alloc=37.5MB, time=4.18 memory used=318.4MB, alloc=37.5MB, time=4.39 memory used=341.2MB, alloc=37.5MB, time=4.65 memory used=362.5MB, alloc=37.5MB, time=4.81 memory used=382.2MB, alloc=37.5MB, time=4.96 memory used=409.0MB, alloc=61.5MB, time=5.26 memory used=458.7MB, alloc=61.5MB, time=6.93 memory used=487.2MB, alloc=61.5MB, time=7.07 memory used=526.7MB, alloc=61.5MB, time=7.43 memory used=569.5MB, alloc=61.5MB, time=8.59 memory used=605.7MB, alloc=61.5MB, time=10.74 memory used=629.2MB, alloc=61.5MB, time=10.80 memory used=651.1MB, alloc=61.5MB, time=10.86 memory used=678.4MB, alloc=61.5MB, time=10.93 memory used=697.4MB, alloc=61.5MB, time=10.98 memory used=715.8MB, alloc=61.5MB, time=11.03 memory used=736.7MB, alloc=61.5MB, time=11.07 memory used=761.8MB, alloc=61.5MB, time=11.13 memory used=798.4MB, alloc=61.5MB, time=11.73 memory used=837.2MB, alloc=61.5MB, time=14.26 memory used=860.6MB, alloc=61.5MB, time=14.32 memory used=881.5MB, alloc=61.5MB, time=14.38 memory used=908.1MB, alloc=61.5MB, time=14.44 memory used=928.0MB, alloc=61.5MB, time=14.49 memory used=945.8MB, alloc=61.5MB, time=14.54 memory used=965.6MB, alloc=61.5MB, time=14.59 memory used=988.7MB, alloc=61.5MB, time=14.64 memory used=1024.6MB, alloc=61.5MB, time=15.69 memory used=1061.7MB, alloc=61.5MB, time=17.79 memory used=1084.9MB, alloc=61.5MB, time=17.85 memory used=1105.8MB, alloc=61.5MB, time=17.91 memory used=1132.3MB, alloc=61.5MB, time=17.97 memory used=1152.0MB, alloc=61.5MB, time=18.02 memory used=1169.6MB, alloc=61.5MB, time=18.07 memory used=1189.3MB, alloc=61.5MB, time=18.12 memory used=1211.9MB, alloc=61.5MB, time=18.17 memory used=1253.1MB, alloc=61.5MB, time=18.63 memory used=1303.3MB, alloc=69.5MB, time=19.46 memory used=1341.4MB, alloc=93.5MB, time=28.92 memory used=1391.9MB, alloc=93.5MB, time=45.36 memory used=1440.3MB, alloc=93.5MB, time=46.48 memory used=1475.8MB, alloc=93.5MB, time=46.59 memory used=1512.5MB, alloc=93.5MB, time=46.68 memory used=1558.1MB, alloc=93.5MB, time=46.79 memory used=1589.0MB, alloc=93.5MB, time=46.87 memory used=1617.4MB, alloc=93.5MB, time=46.95 memory used=1649.1MB, alloc=93.5MB, time=47.03 memory used=1683.8MB, alloc=93.5MB, time=47.10 memory used=1721.1MB, alloc=93.5MB, time=47.19 memory used=1761.9MB, alloc=93.5MB, time=47.27 memory used=1806.3MB, alloc=93.5MB, time=47.35 memory used=1851.1MB, alloc=107.8MB, time=47.45 memory used=1859.2MB, alloc=107.8MB, time=47.49 memory used=1867.8MB, alloc=107.8MB, time=47.55 memory used=1876.8MB, alloc=107.8MB, time=47.61 memory used=1885.5MB, alloc=107.8MB, time=47.68 memory used=1894.6MB, alloc=107.8MB, time=47.73 memory used=1904.0MB, alloc=107.8MB, time=47.79 memory used=1914.1MB, alloc=107.8MB, time=47.83 memory used=1924.6MB, alloc=107.8MB, time=47.88 memory used=1935.5MB, alloc=107.8MB, time=47.94 memory used=1967.3MB, alloc=107.8MB, time=48.12 memory used=2043.3MB, alloc=107.8MB, time=48.94 memory used=2109.6MB, alloc=107.8MB, time=53.25 memory used=2159.7MB, alloc=107.8MB, time=54.37 memory used=2197.4MB, alloc=107.8MB, time=54.50 memory used=2231.9MB, alloc=107.8MB, time=54.61 memory used=2261.8MB, alloc=107.8MB, time=54.72 memory used=2296.5MB, alloc=107.8MB, time=54.83 memory used=2336.6MB, alloc=107.8MB, time=54.92 memory used=2383.7MB, alloc=107.8MB, time=55.13 memory used=2450.0MB, alloc=107.8MB, time=60.11 memory used=2483.9MB, alloc=107.8MB, time=60.22 memory used=2522.1MB, alloc=107.8MB, time=60.33 memory used=2549.8MB, alloc=107.8MB, time=60.42 memory used=2582.0MB, alloc=107.8MB, time=60.53 memory used=2618.7MB, alloc=107.8MB, time=60.62 memory used=2658.7MB, alloc=107.8MB, time=60.76 memory used=2729.1MB, alloc=107.8MB, time=66.17 memory used=2762.7MB, alloc=107.8MB, time=66.28 memory used=2803.0MB, alloc=107.8MB, time=66.39 memory used=2830.7MB, alloc=107.8MB, time=66.48 memory used=2862.0MB, alloc=107.8MB, time=66.58 memory used=2897.6MB, alloc=107.8MB, time=66.67 memory used=2934.3MB, alloc=107.8MB, time=66.77 memory used=2983.4MB, alloc=107.8MB, time=67.04 memory used=3041.7MB, alloc=107.8MB, time=69.65 memory used=3100.0MB, alloc=107.8MB, time=70.47 memory used=3138.8MB, alloc=107.8MB, time=70.59 memory used=3167.3MB, alloc=107.8MB, time=70.68 memory used=3200.5MB, alloc=107.8MB, time=70.77 memory used=3258.2MB, alloc=107.8MB, time=71.29 memory used=3301.0MB, alloc=107.8MB, time=71.43 memory used=3329.6MB, alloc=107.8MB, time=71.54 memory used=3361.7MB, alloc=107.8MB, time=71.66 memory used=3398.3MB, alloc=107.8MB, time=71.77 memory used=3439.5MB, alloc=107.8MB, time=71.88 memory used=3480.4MB, alloc=107.8MB, time=72.00 memory used=3505.8MB, alloc=107.8MB, time=72.10 memory used=3532.1MB, alloc=107.8MB, time=72.20 memory used=3560.8MB, alloc=107.8MB, time=72.29 memory used=3592.6MB, alloc=107.8MB, time=72.40 memory used=3656.6MB, alloc=107.8MB, time=87.19 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time=1365.70 memory used=68128.8MB, alloc=723.8MB, time=1366.37 memory used=68291.0MB, alloc=723.8MB, time=1367.03 memory used=68479.3MB, alloc=723.8MB, time=1367.69 memory used=68796.1MB, alloc=723.8MB, time=1368.51 memory used=69037.3MB, alloc=723.8MB, time=1370.38 memory used=69209.6MB, alloc=723.8MB, time=1371.19 memory used=69372.7MB, alloc=723.8MB, time=1372.00 memory used=69573.8MB, alloc=723.8MB, time=1372.80 memory used=69766.4MB, alloc=723.8MB, time=1374.17 memory used=69953.0MB, alloc=723.8MB, time=1375.05 memory used=70105.7MB, alloc=723.8MB, time=1375.79 memory used=70300.8MB, alloc=723.8MB, time=1376.54 memory used=70516.1MB, alloc=723.8MB, time=1421.11 memory used=70713.6MB, alloc=723.8MB, time=1422.64 memory used=70908.8MB, alloc=723.8MB, time=1423.39 memory used=71046.6MB, alloc=723.8MB, time=1424.03 memory used=71211.7MB, alloc=723.8MB, time=1424.67 memory used=71441.5MB, alloc=723.8MB, time=1425.68 memory used=71684.0MB, alloc=723.8MB, time=1428.87 memory 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time=1444.05 memory used=75264.0MB, alloc=747.8MB, time=1444.70 memory used=75483.0MB, alloc=747.8MB, time=1453.83 memory used=75671.2MB, alloc=747.8MB, time=1458.10 memory used=75879.2MB, alloc=747.8MB, time=1459.04 memory used=76083.4MB, alloc=771.8MB, time=1459.95 memory used=76248.5MB, alloc=771.8MB, time=1460.78 memory used=76412.0MB, alloc=771.8MB, time=1461.57 memory used=76577.5MB, alloc=771.8MB, time=1462.37 memory used=76748.4MB, alloc=771.8MB, time=1463.20 memory used=76930.9MB, alloc=771.8MB, time=1463.97 memory used=77121.3MB, alloc=771.8MB, time=1464.78 memory used=77328.8MB, alloc=771.8MB, time=1465.58 memory used=77543.6MB, alloc=771.8MB, time=1466.40 memory used=77766.4MB, alloc=771.8MB, time=1467.25 memory used=78005.9MB, alloc=771.8MB, time=1468.13 memory used=78249.4MB, alloc=771.8MB, time=1469.00 memory used=78426.8MB, alloc=795.8MB, time=1469.76 memory used=78591.6MB, alloc=795.8MB, time=1470.47 memory used=78755.1MB, alloc=795.8MB, time=1471.18 memory used=78912.9MB, alloc=795.8MB, time=1471.85 memory used=79062.5MB, alloc=795.8MB, time=1472.54 memory used=79216.6MB, alloc=795.8MB, time=1473.21 memory used=79375.8MB, alloc=795.8MB, time=1473.89 memory used=79536.7MB, alloc=795.8MB, time=1474.57 memory used=79699.0MB, alloc=795.8MB, time=1475.25 memory used=79862.8MB, alloc=795.8MB, time=1475.93 memory used=80028.7MB, alloc=795.8MB, time=1476.62 memory used=80207.2MB, alloc=795.8MB, time=1477.32 memory used=80387.6MB, alloc=795.8MB, time=1478.00 memory used=80569.1MB, alloc=795.8MB, time=1478.67 memory used=80752.0MB, alloc=795.8MB, time=1479.38 memory used=80948.9MB, alloc=795.8MB, time=1480.06 memory used=81146.7MB, alloc=795.8MB, time=1480.76 memory used=81345.2MB, alloc=795.8MB, time=1481.46 memory used=81544.8MB, alloc=795.8MB, time=1482.18 memory used=81758.2MB, alloc=795.8MB, time=1482.89 memory used=81971.9MB, alloc=795.8MB, time=1483.58 memory used=82186.3MB, alloc=795.8MB, time=1484.30 memory used=82414.2MB, alloc=795.8MB, time=1485.02 memory used=82641.9MB, alloc=795.8MB, time=1485.75 memory used=82870.5MB, alloc=795.8MB, time=1486.46 memory used=83110.4MB, alloc=795.8MB, time=1487.18 memory used=83350.7MB, alloc=795.8MB, time=1487.90 memory used=83603.1MB, alloc=795.8MB, time=1488.62 memory used=83854.6MB, alloc=795.8MB, time=1489.34 memory used=84117.6MB, alloc=795.8MB, time=1490.08 memory used=84391.5MB, alloc=795.8MB, time=1490.82 memory used=84677.1MB, alloc=795.8MB, time=1491.59 memory used=84926.9MB, alloc=795.8MB, time=1492.39 memory used=85088.3MB, alloc=795.8MB, time=1493.04 memory used=85227.5MB, alloc=795.8MB, time=1493.67 memory used=85344.7MB, alloc=795.8MB, time=1494.30 memory used=85457.2MB, alloc=795.8MB, time=1494.91 memory used=85566.0MB, alloc=795.8MB, time=1495.51 memory used=85684.4MB, alloc=795.8MB, time=1496.12 memory used=85802.7MB, alloc=795.8MB, time=1496.71 memory used=85919.8MB, alloc=795.8MB, time=1497.31 memory used=86035.9MB, alloc=795.8MB, time=1497.92 memory used=86151.9MB, alloc=795.8MB, time=1498.53 memory used=86276.1MB, alloc=795.8MB, time=1499.15 memory used=86399.7MB, alloc=795.8MB, time=1499.76 memory used=86521.8MB, alloc=795.8MB, time=1500.38 memory used=86653.2MB, alloc=795.8MB, time=1500.99 memory used=86782.7MB, alloc=795.8MB, time=1501.59 memory used=86910.2MB, alloc=795.8MB, time=1502.20 memory used=87045.9MB, alloc=795.8MB, time=1502.80 memory used=87179.0MB, alloc=795.8MB, time=1503.42 memory used=87311.0MB, alloc=795.8MB, time=1504.02 memory used=87447.3MB, alloc=795.8MB, time=1504.66 memory used=87591.2MB, alloc=795.8MB, time=1505.27 memory used=87731.2MB, alloc=795.8MB, time=1505.88 memory used=87876.4MB, alloc=795.8MB, time=1506.50 memory used=88025.4MB, alloc=795.8MB, time=1507.13 memory used=88177.2MB, alloc=795.8MB, time=1507.75 memory used=88330.7MB, alloc=795.8MB, time=1508.36 memory used=88484.4MB, alloc=795.8MB, time=1509.00 memory used=88644.0MB, alloc=795.8MB, time=1509.64 memory used=88806.0MB, alloc=795.8MB, time=1510.29 memory used=88973.0MB, alloc=795.8MB, time=1510.93 memory used=89148.7MB, alloc=795.8MB, time=1511.57 memory used=89331.2MB, alloc=795.8MB, time=1512.21 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428461765 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 3 2 F := [15 x y - 2 y z + 9 z , 6 x y z + 18 x y - 2 y z, 17 x z + 7 y] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 4 3 2 G := [-11 x z + 10 x y z - 8 z , -15 z + 14 x - 17 x z, 2 2 2 2 3 -7 x y + 17 x z + x ] > Problem := [F,G]; Problem := [ 2 2 2 3 2 3 2 [15 x y - 2 y z + 9 z , 6 x y z + 18 x y - 2 y z, 17 x z + 7 y], [ 3 3 4 3 2 -11 x z + 10 x y z - 8 z , -15 z + 14 x - 17 x z, 2 2 2 2 3 -7 x y + 17 x z + x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.17 memory used=26.2MB, alloc=32.3MB, time=0.48 memory used=47.1MB, alloc=32.3MB, time=0.78 memory used=65.6MB, alloc=56.3MB, time=1.07 memory used=108.1MB, alloc=68.3MB, time=1.69 memory used=150.5MB, alloc=92.3MB, time=2.27 memory used=215.0MB, alloc=92.3MB, time=2.82 memory used=288.1MB, alloc=92.3MB, time=3.72 memory used=352.9MB, alloc=92.3MB, time=4.63 memory used=415.5MB, alloc=116.3MB, time=5.53 memory used=485.2MB, alloc=116.3MB, time=6.52 memory used=549.1MB, alloc=372.3MB, time=7.47 memory used=635.9MB, alloc=396.3MB, time=8.69 memory used=740.4MB, alloc=396.3MB, time=9.84 memory used=847.6MB, alloc=420.3MB, time=11.36 memory used=973.0MB, alloc=444.3MB, time=13.33 memory used=1100.3MB, alloc=468.3MB, time=14.86 memory used=1212.3MB, alloc=468.3MB, time=16.50 memory used=1308.1MB, alloc=492.3MB, time=17.64 memory used=1413.5MB, alloc=492.3MB, time=19.33 memory used=1510.8MB, alloc=492.3MB, time=20.44 memory used=1640.8MB, alloc=492.3MB, time=21.38 memory used=1745.8MB, alloc=492.3MB, time=22.86 memory used=1837.9MB, alloc=492.3MB, time=24.03 memory used=1919.5MB, alloc=492.3MB, time=25.01 memory used=1983.3MB, alloc=516.3MB, time=25.80 memory used=2056.8MB, alloc=516.3MB, time=27.23 memory used=2122.2MB, alloc=516.3MB, time=28.34 memory used=2181.9MB, alloc=516.3MB, time=29.27 memory used=2249.0MB, alloc=516.3MB, time=30.41 memory used=2295.6MB, alloc=516.3MB, time=31.39 memory used=2332.0MB, alloc=516.3MB, time=32.18 memory used=2533.4MB, alloc=540.3MB, time=35.30 memory used=2737.4MB, alloc=564.3MB, time=38.37 memory used=2908.9MB, alloc=588.3MB, time=41.34 memory used=3064.7MB, alloc=612.3MB, time=43.99 memory used=3233.6MB, alloc=612.3MB, time=47.00 memory used=3388.9MB, alloc=636.3MB, time=49.83 memory used=3520.4MB, alloc=636.3MB, time=52.01 memory used=3637.8MB, alloc=636.3MB, time=54.68 memory used=3758.8MB, alloc=636.3MB, time=56.74 memory used=3859.4MB, alloc=636.3MB, time=59.06 memory used=3953.5MB, alloc=636.3MB, time=60.92 memory used=4061.1MB, alloc=660.3MB, time=62.85 memory used=4206.8MB, alloc=660.3MB, time=64.83 memory used=4356.4MB, alloc=660.3MB, time=66.87 memory used=4719.8MB, alloc=684.3MB, time=71.35 memory used=5068.1MB, alloc=708.3MB, time=76.60 memory used=5404.5MB, alloc=732.3MB, time=81.03 memory used=5810.3MB, alloc=756.3MB, time=87.10 memory used=6180.5MB, alloc=780.3MB, time=94.09 memory used=6537.6MB, alloc=804.3MB, time=101.59 memory used=6836.5MB, alloc=828.3MB, time=107.51 memory used=7104.7MB, alloc=852.3MB, time=112.73 memory used=7399.6MB, alloc=876.3MB, time=119.31 memory used=7651.8MB, alloc=900.3MB, time=125.38 memory used=7892.8MB, alloc=924.3MB, time=130.88 memory used=8119.1MB, alloc=948.3MB, time=136.16 memory used=8366.8MB, alloc=972.3MB, time=140.53 memory used=8716.9MB, alloc=972.3MB, time=145.30 memory used=8923.1MB, alloc=996.3MB, time=149.73 memory used=9584.7MB, alloc=1020.3MB, time=161.01 memory used=10263.7MB, alloc=1044.3MB, time=172.08 memory used=10850.6MB, alloc=1068.3MB, time=180.80 memory used=11476.2MB, alloc=1092.3MB, time=189.82 memory used=12248.5MB, alloc=1116.3MB, time=202.47 memory used=12963.9MB, alloc=1140.3MB, time=217.05 memory used=13692.9MB, alloc=1164.3MB, time=230.64 memory used=14390.5MB, alloc=1188.3MB, time=243.40 memory used=15050.5MB, alloc=1212.3MB, time=257.67 memory used=15613.2MB, alloc=1236.3MB, time=266.48 memory used=15988.8MB, alloc=1260.3MB, time=272.92 memory used=16263.4MB, alloc=1284.3MB, time=277.57 memory used=16770.1MB, alloc=1323.8MB, time=285.61 memory used=17398.9MB, alloc=1347.8MB, time=298.11 memory used=17915.8MB, alloc=1371.8MB, time=309.19 memory used=18488.0MB, alloc=1395.8MB, time=322.02 memory used=18926.6MB, alloc=1419.8MB, time=332.56 memory used=19404.1MB, alloc=1443.8MB, time=345.26 memory used=20031.4MB, alloc=1467.8MB, time=355.72 memory used=20698.0MB, alloc=1491.8MB, time=366.18 memory used=21254.4MB, alloc=1515.8MB, time=377.48 memory used=21620.4MB, alloc=1539.8MB, time=388.02 memory used=22078.3MB, alloc=1563.8MB, time=399.07 memory used=22430.9MB, alloc=1587.8MB, time=407.48 memory used=22844.3MB, alloc=1611.8MB, time=417.85 memory used=23127.0MB, alloc=1635.8MB, time=429.53 memory used=23408.5MB, alloc=1659.8MB, time=438.33 memory used=23671.8MB, alloc=1683.8MB, time=446.55 memory used=23943.3MB, alloc=1707.8MB, time=457.53 memory used=24183.6MB, alloc=1731.8MB, time=466.36 memory used=24384.3MB, alloc=1755.8MB, time=473.99 memory used=24542.0MB, alloc=1779.8MB, time=481.15 memory used=24718.5MB, alloc=1803.8MB, time=488.33 memory used=24877.6MB, alloc=1827.8MB, time=495.68 memory used=25065.6MB, alloc=1827.8MB, time=506.28 memory used=25201.2MB, alloc=1827.8MB, time=514.38 memory used=25299.4MB, alloc=1827.8MB, time=521.45 memory used=25434.5MB, alloc=1827.8MB, time=529.41 memory used=25561.2MB, alloc=1827.8MB, time=536.09 memory used=25976.3MB, alloc=1827.8MB, time=543.64 memory used=26128.6MB, alloc=1827.8MB, time=549.98 memory used=26253.9MB, alloc=1827.8MB, time=557.33 memory used=26371.0MB, alloc=1827.8MB, time=565.85 memory used=26442.3MB, alloc=1827.8MB, time=572.47 memory used=26523.9MB, alloc=1827.8MB, time=579.38 memory used=26618.9MB, alloc=1827.8MB, time=585.83 memory used=26736.1MB, alloc=1827.8MB, time=592.86 memory used=26822.8MB, alloc=1827.8MB, time=599.12 memory used=26868.1MB, alloc=1827.8MB, time=605.28 memory used=26947.3MB, alloc=1827.8MB, time=611.88 memory used=27008.5MB, alloc=1827.8MB, time=618.86 memory used=27060.0MB, alloc=1827.8MB, time=625.18 memory used=27145.5MB, alloc=1827.8MB, time=631.85 memory used=27259.1MB, alloc=1827.8MB, time=638.74 memory used=27375.1MB, alloc=1827.8MB, time=645.80 memory used=27449.0MB, alloc=1827.8MB, time=652.92 memory used=27486.9MB, alloc=1827.8MB, time=659.57 memory used=27522.0MB, alloc=1827.8MB, time=666.10 memory used=27596.3MB, alloc=1851.8MB, time=672.89 memory used=27654.6MB, alloc=1851.8MB, time=679.50 memory used=27719.9MB, alloc=1851.8MB, time=686.25 memory used=27745.4MB, alloc=1851.8MB, time=692.71 memory used=27793.9MB, alloc=1851.8MB, time=699.34 memory used=27837.8MB, alloc=1851.8MB, time=706.13 memory used=27900.5MB, alloc=2107.8MB, time=720.37 memory used=29165.6MB, alloc=2131.8MB, time=745.89 memory used=30390.6MB, alloc=2155.8MB, time=776.17 memory used=31630.6MB, alloc=2179.8MB, time=805.42 memory used=32886.3MB, alloc=2203.8MB, time=832.59 memory used=34043.2MB, alloc=2227.8MB, time=865.89 memory used=35046.3MB, alloc=2251.8MB, time=892.12 memory used=36029.7MB, alloc=2275.8MB, time=919.65 memory used=36928.5MB, alloc=2299.8MB, time=945.11 memory used=37743.1MB, alloc=2323.8MB, time=968.22 memory used=38435.9MB, alloc=2347.8MB, time=987.26 memory used=39392.9MB, alloc=2371.8MB, time=1012.24 memory used=40430.7MB, alloc=2395.8MB, time=1035.97 memory used=41057.2MB, alloc=2419.8MB, time=1060.87 memory used=41777.1MB, alloc=2443.8MB, time=1083.58 memory used=42504.2MB, alloc=2467.8MB, time=1105.46 memory used=43232.5MB, alloc=2491.8MB, time=1128.87 memory used=43695.0MB, alloc=2515.8MB, time=1147.41 memory used=44272.2MB, alloc=2539.8MB, time=1169.09 memory used=44781.7MB, alloc=2563.8MB, time=1191.07 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428462965 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 3 3 3 F := [12 x y + 14 x y z - 6 z , -11 x z - 16 z, 11 x - 17 y - 7] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 4 3 2 2 2 3 2 2 2 G := [-14 x z - 16 y + 7 y z , -14 y z - 9 x y - 16 y , -9 x z - 4 y ] > Problem := [F,G]; 2 2 2 3 3 3 3 Problem := [[12 x y + 14 x y z - 6 z , -11 x z - 16 z, 11 x - 17 y - 7], 3 4 3 2 2 2 3 2 2 2 [-14 x z - 16 y + 7 y z , -14 y z - 9 x y - 16 y , -9 x z - 4 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=32.3MB, alloc=40.3MB, time=0.61 memory used=60.4MB, alloc=44.3MB, time=1.03 memory used=114.9MB, alloc=76.3MB, time=1.86 memory used=170.9MB, alloc=84.3MB, time=2.67 memory used=232.1MB, alloc=108.3MB, time=3.44 memory used=302.2MB, alloc=108.3MB, time=4.29 memory used=369.6MB, alloc=364.3MB, time=5.22 memory used=450.6MB, alloc=388.3MB, time=6.26 memory used=557.3MB, alloc=388.3MB, time=7.77 memory used=657.7MB, alloc=412.3MB, time=9.28 memory used=755.3MB, alloc=412.3MB, time=10.16 memory used=840.6MB, alloc=412.3MB, time=10.80 memory used=905.7MB, alloc=412.3MB, time=11.25 memory used=965.7MB, alloc=412.3MB, time=11.46 memory used=1084.8MB, alloc=412.3MB, time=12.57 memory used=1198.7MB, alloc=436.3MB, time=13.88 memory used=1328.5MB, alloc=436.3MB, time=15.25 memory used=1483.1MB, alloc=436.3MB, time=16.85 memory used=1589.6MB, alloc=460.3MB, time=18.31 memory used=1701.7MB, alloc=460.3MB, time=19.83 memory used=1821.0MB, alloc=460.3MB, time=21.43 memory used=1929.9MB, alloc=484.3MB, time=22.94 memory used=2022.7MB, alloc=484.3MB, time=24.39 memory used=2142.7MB, alloc=484.3MB, time=26.05 memory used=2227.6MB, alloc=484.3MB, time=27.25 memory used=2355.7MB, alloc=484.3MB, time=28.59 memory used=2418.6MB, alloc=484.3MB, time=29.62 memory used=2497.2MB, alloc=484.3MB, time=30.93 memory used=2596.8MB, alloc=508.3MB, time=31.60 memory used=2714.9MB, alloc=508.3MB, time=32.46 memory used=2855.1MB, alloc=508.3MB, time=33.58 memory used=2921.6MB, alloc=508.3MB, time=34.66 memory used=2976.3MB, alloc=508.3MB, time=35.66 memory used=3056.1MB, alloc=508.3MB, time=36.87 memory used=3103.7MB, alloc=508.3MB, time=37.84 memory used=3172.4MB, alloc=508.3MB, time=38.80 memory used=3282.2MB, alloc=508.3MB, time=39.44 memory used=3397.1MB, alloc=508.3MB, time=40.31 memory used=3488.1MB, alloc=508.3MB, time=40.75 memory used=3568.0MB, alloc=508.3MB, time=41.57 memory used=3620.0MB, alloc=508.3MB, time=42.48 memory used=3681.6MB, alloc=508.3MB, time=43.42 memory used=3768.4MB, alloc=532.3MB, time=45.26 memory used=3893.9MB, alloc=532.3MB, time=46.04 memory used=3983.1MB, alloc=532.3MB, time=46.51 memory used=4099.7MB, alloc=532.3MB, time=47.02 memory used=4260.7MB, alloc=532.3MB, time=47.73 memory used=4472.4MB, alloc=532.3MB, time=49.15 memory used=4745.0MB, alloc=532.3MB, time=51.59 memory used=4990.7MB, alloc=556.3MB, time=54.31 memory used=5173.6MB, alloc=556.3MB, time=56.11 memory used=5321.6MB, alloc=556.3MB, time=57.64 memory used=5429.9MB, alloc=556.3MB, time=58.23 memory used=5531.5MB, alloc=556.3MB, time=58.76 memory used=5778.5MB, alloc=580.3MB, time=61.72 memory used=5940.9MB, alloc=604.3MB, time=64.71 memory used=6127.3MB, alloc=628.3MB, time=67.72 memory used=6288.6MB, alloc=652.3MB, time=69.92 memory used=6487.5MB, alloc=652.3MB, time=73.08 memory used=6615.2MB, alloc=652.3MB, time=75.31 memory used=6743.7MB, alloc=676.3MB, time=77.19 memory used=6896.4MB, alloc=676.3MB, time=79.44 memory used=7048.7MB, alloc=676.3MB, time=82.72 memory used=7169.3MB, alloc=700.3MB, time=84.83 memory used=7270.1MB, alloc=700.3MB, time=86.41 memory used=7382.9MB, alloc=724.3MB, time=88.24 memory used=7707.9MB, alloc=724.3MB, time=95.67 memory used=8081.6MB, alloc=748.3MB, time=100.55 memory used=8451.2MB, alloc=772.3MB, time=106.77 memory used=8862.3MB, alloc=796.3MB, time=113.69 memory used=9176.2MB, alloc=820.3MB, time=118.00 memory used=9375.4MB, alloc=844.3MB, time=119.56 memory used=9622.7MB, alloc=868.3MB, time=121.93 memory used=9876.7MB, alloc=892.3MB, time=123.88 memory used=10123.5MB, alloc=916.3MB, time=126.48 memory used=10364.1MB, alloc=916.3MB, time=127.99 memory used=10647.2MB, alloc=916.3MB, time=129.72 memory used=10924.7MB, alloc=916.3MB, time=131.50 memory used=11146.3MB, alloc=916.3MB, time=132.88 memory used=11460.8MB, alloc=916.3MB, time=136.05 memory used=11924.8MB, alloc=940.3MB, time=141.16 memory used=12355.6MB, alloc=964.3MB, time=145.67 memory used=12873.8MB, alloc=988.3MB, time=150.64 memory used=13163.7MB, alloc=1012.3MB, time=155.63 memory used=13589.2MB, alloc=1012.3MB, time=159.38 memory used=13903.9MB, alloc=1012.3MB, time=161.83 memory used=14184.8MB, alloc=1012.3MB, time=163.87 memory used=14563.0MB, alloc=1012.3MB, time=167.72 memory used=14861.3MB, alloc=1012.3MB, time=169.69 memory used=15142.8MB, alloc=1012.3MB, time=184.06 memory used=15477.9MB, alloc=1012.3MB, time=193.31 memory used=15751.6MB, alloc=1012.3MB, time=195.17 memory used=15994.1MB, alloc=1027.8MB, time=196.99 memory used=16119.1MB, alloc=1027.8MB, time=198.62 memory used=16258.0MB, alloc=1027.8MB, time=200.28 memory used=16413.4MB, alloc=1027.8MB, time=201.94 memory used=16589.7MB, alloc=1027.8MB, time=203.63 memory used=16781.7MB, alloc=1027.8MB, time=205.32 memory used=17108.5MB, alloc=1051.8MB, time=208.19 memory used=17406.2MB, alloc=1051.8MB, time=210.27 memory used=17670.9MB, alloc=1051.8MB, time=212.19 memory used=17916.8MB, alloc=1051.8MB, time=214.01 memory used=18207.7MB, alloc=1051.8MB, time=215.91 memory used=18551.6MB, alloc=1051.8MB, time=217.84 memory used=18766.4MB, alloc=1051.8MB, time=219.57 memory used=18880.5MB, alloc=1051.8MB, time=221.17 memory used=19004.9MB, alloc=1051.8MB, time=222.77 memory used=19463.1MB, alloc=1051.8MB, time=229.27 memory used=19751.9MB, alloc=1051.8MB, time=231.18 memory used=19976.4MB, alloc=1051.8MB, time=232.95 memory used=20116.4MB, alloc=1051.8MB, time=234.58 memory used=20540.8MB, alloc=1051.8MB, time=237.78 memory used=20842.9MB, alloc=1051.8MB, time=239.85 memory used=21100.3MB, alloc=1051.8MB, time=241.74 memory used=21345.0MB, alloc=1051.8MB, time=243.57 memory used=21634.4MB, alloc=1051.8MB, time=245.41 memory used=21978.1MB, alloc=1051.8MB, time=247.34 memory used=22187.6MB, alloc=1051.8MB, time=249.05 memory used=22301.6MB, alloc=1051.8MB, time=250.65 memory used=22426.0MB, alloc=1051.8MB, time=252.26 memory used=22884.1MB, alloc=1051.8MB, time=258.79 memory used=23171.8MB, alloc=1051.8MB, time=260.67 memory used=23398.6MB, alloc=1051.8MB, time=262.42 memory used=23538.6MB, alloc=1051.8MB, time=264.08 memory used=23991.5MB, alloc=1051.8MB, time=269.41 memory used=24319.2MB, alloc=1075.8MB, time=271.67 memory used=24556.9MB, alloc=1075.8MB, time=273.71 memory used=24842.9MB, alloc=1075.8MB, time=275.87 memory used=25177.2MB, alloc=1075.8MB, time=278.14 memory used=25560.7MB, alloc=1075.8MB, time=280.39 memory used=25808.4MB, alloc=1099.8MB, time=282.31 memory used=26030.8MB, alloc=1123.8MB, time=284.16 memory used=26278.6MB, alloc=1123.8MB, time=286.06 memory used=26554.3MB, alloc=1123.8MB, time=287.96 memory used=26838.8MB, alloc=1123.8MB, time=289.91 memory used=27149.1MB, alloc=1123.8MB, time=291.85 memory used=27467.3MB, alloc=1123.8MB, time=293.81 memory used=27811.0MB, alloc=1123.8MB, time=295.82 memory used=28164.8MB, alloc=1123.8MB, time=297.78 memory used=28538.8MB, alloc=1123.8MB, time=299.78 memory used=28934.2MB, alloc=1123.8MB, time=301.80 memory used=29355.6MB, alloc=1123.8MB, time=303.83 memory used=29651.5MB, alloc=1123.8MB, time=305.72 memory used=29738.3MB, alloc=1123.8MB, time=307.33 memory used=29819.7MB, alloc=1123.8MB, time=308.95 memory used=29910.7MB, alloc=1123.8MB, time=310.58 memory used=30006.2MB, alloc=1123.8MB, time=312.22 memory used=30101.6MB, alloc=1123.8MB, time=313.85 memory used=30196.6MB, alloc=1123.8MB, time=315.48 memory used=30291.4MB, alloc=1123.8MB, time=317.10 memory used=30385.9MB, alloc=1123.8MB, time=318.74 memory used=30480.1MB, alloc=1123.8MB, time=320.36 memory used=30573.9MB, alloc=1123.8MB, time=321.97 memory used=30667.4MB, alloc=1123.8MB, time=323.59 memory used=30764.1MB, alloc=1123.8MB, time=325.22 memory used=30871.6MB, alloc=1123.8MB, time=326.84 memory used=30969.1MB, alloc=1123.8MB, time=328.44 memory used=31073.5MB, alloc=1123.8MB, time=330.09 memory used=31182.6MB, alloc=1123.8MB, time=331.70 memory used=31290.9MB, alloc=1123.8MB, time=333.32 memory used=31398.3MB, alloc=1123.8MB, time=334.96 memory used=31504.9MB, alloc=1123.8MB, time=336.59 memory used=31614.9MB, alloc=1123.8MB, time=338.24 memory used=31732.6MB, alloc=1123.8MB, time=339.87 memory used=31853.1MB, alloc=1123.8MB, time=341.51 memory used=31972.2MB, alloc=1123.8MB, time=343.17 memory used=32089.9MB, alloc=1123.8MB, time=344.80 memory used=32210.9MB, alloc=1123.8MB, time=346.46 memory used=32336.3MB, alloc=1123.8MB, time=348.10 memory used=32464.4MB, alloc=1123.8MB, time=349.75 memory used=32594.5MB, alloc=1123.8MB, time=351.38 memory used=32728.6MB, alloc=1123.8MB, time=353.05 memory used=32863.7MB, alloc=1123.8MB, time=354.70 memory used=33002.0MB, alloc=1123.8MB, time=356.34 memory used=33144.0MB, alloc=1123.8MB, time=357.99 memory used=33292.4MB, alloc=1123.8MB, time=359.67 memory used=33445.3MB, alloc=1123.8MB, time=361.33 memory used=33602.7MB, alloc=1123.8MB, time=362.98 memory used=33765.7MB, alloc=1123.8MB, time=364.63 memory used=33935.5MB, alloc=1123.8MB, time=366.31 memory used=34107.4MB, alloc=1123.8MB, time=367.95 memory used=34283.4MB, alloc=1123.8MB, time=369.64 memory used=34463.4MB, alloc=1123.8MB, time=371.33 memory used=34966.0MB, alloc=1123.8MB, time=381.97 memory used=35271.0MB, alloc=1123.8MB, time=384.26 memory used=35579.5MB, alloc=1123.8MB, time=386.42 memory used=35944.2MB, alloc=1123.8MB, time=388.73 memory used=36362.8MB, alloc=1123.8MB, time=391.08 memory used=36598.7MB, alloc=1147.8MB, time=393.02 memory used=36847.4MB, alloc=1147.8MB, time=394.95 memory used=37108.9MB, alloc=1147.8MB, time=396.87 memory used=37400.2MB, alloc=1147.8MB, time=398.83 memory used=37704.2MB, alloc=1147.8MB, time=400.78 memory used=38020.5MB, alloc=1147.8MB, time=402.77 memory used=38349.0MB, alloc=1147.8MB, time=404.77 memory used=38710.2MB, alloc=1147.8MB, time=406.81 memory used=39083.9MB, alloc=1147.8MB, time=408.80 memory used=39469.3MB, alloc=1147.8MB, time=410.84 memory used=39866.6MB, alloc=1147.8MB, time=412.92 memory used=40298.6MB, alloc=1147.8MB, time=414.98 memory used=40742.1MB, alloc=1147.8MB, time=417.09 memory used=40963.4MB, alloc=1147.8MB, time=418.90 memory used=41035.3MB, alloc=1147.8MB, time=420.49 memory used=41105.2MB, alloc=1147.8MB, time=422.07 memory used=41180.4MB, alloc=1147.8MB, time=423.64 memory used=41256.0MB, alloc=1147.8MB, time=425.22 memory used=41331.8MB, alloc=1147.8MB, time=426.82 memory used=41407.9MB, alloc=1147.8MB, time=428.41 memory used=41484.3MB, alloc=1147.8MB, time=429.99 memory used=41560.9MB, alloc=1147.8MB, time=431.58 memory used=41637.8MB, alloc=1147.8MB, time=433.18 memory used=41714.9MB, alloc=1147.8MB, time=434.78 memory used=41792.3MB, alloc=1147.8MB, time=436.39 memory used=41870.0MB, alloc=1147.8MB, time=437.98 memory used=41947.9MB, alloc=1147.8MB, time=439.57 memory used=42026.0MB, alloc=1147.8MB, time=441.16 memory used=42104.4MB, alloc=1147.8MB, time=442.76 memory used=42183.0MB, alloc=1147.8MB, time=444.33 memory used=42261.8MB, alloc=1147.8MB, time=445.95 memory used=42340.9MB, alloc=1147.8MB, time=447.54 memory used=42420.2MB, alloc=1147.8MB, time=449.15 memory used=42499.7MB, alloc=1147.8MB, time=450.77 memory used=42579.4MB, alloc=1147.8MB, time=452.36 memory used=42659.4MB, alloc=1147.8MB, time=453.96 memory used=42739.6MB, alloc=1147.8MB, time=455.56 memory used=42820.0MB, alloc=1147.8MB, time=457.16 memory used=42900.6MB, alloc=1147.8MB, time=458.78 memory used=42981.4MB, alloc=1147.8MB, time=460.38 memory used=43062.5MB, alloc=1147.8MB, time=461.96 memory used=43143.7MB, alloc=1147.8MB, time=463.54 memory used=43225.1MB, alloc=1147.8MB, time=465.17 memory used=43306.8MB, alloc=1147.8MB, time=466.77 memory used=43390.5MB, alloc=1147.8MB, time=468.36 memory used=43473.6MB, alloc=1147.8MB, time=469.97 memory used=43580.3MB, alloc=1147.8MB, time=471.60 memory used=43665.2MB, alloc=1147.8MB, time=473.21 memory used=43773.0MB, alloc=1147.8MB, time=474.87 memory used=43858.9MB, alloc=1147.8MB, time=476.47 memory used=43966.7MB, alloc=1147.8MB, time=478.12 memory used=44077.8MB, alloc=1147.8MB, time=479.75 memory used=44189.2MB, alloc=1147.8MB, time=481.38 memory used=44300.8MB, alloc=1147.8MB, time=483.02 memory used=44412.8MB, alloc=1147.8MB, time=484.70 memory used=44525.0MB, alloc=1147.8MB, time=486.33 memory used=44637.5MB, alloc=1147.8MB, time=488.03 memory used=44750.3MB, alloc=1147.8MB, time=489.71 memory used=44863.3MB, alloc=1147.8MB, time=491.34 memory used=44976.6MB, alloc=1147.8MB, time=492.99 memory used=45090.1MB, alloc=1147.8MB, time=494.61 memory used=45203.8MB, alloc=1147.8MB, time=496.24 memory used=45317.9MB, alloc=1147.8MB, time=497.87 memory used=45432.1MB, alloc=1147.8MB, time=499.50 memory used=45546.5MB, alloc=1147.8MB, time=501.13 memory used=45661.2MB, alloc=1147.8MB, time=502.80 memory used=45776.0MB, alloc=1147.8MB, time=504.42 memory used=45891.0MB, alloc=1147.8MB, time=506.06 memory used=46006.3MB, alloc=1147.8MB, time=507.70 memory used=46121.7MB, alloc=1147.8MB, time=509.35 memory used=46237.3MB, alloc=1147.8MB, time=511.01 memory used=46353.0MB, alloc=1147.8MB, time=512.65 memory used=46469.0MB, alloc=1147.8MB, time=514.28 memory used=46585.1MB, alloc=1147.8MB, time=515.91 memory used=46701.3MB, alloc=1147.8MB, time=517.55 memory used=46817.7MB, alloc=1147.8MB, time=519.18 memory used=46934.2MB, alloc=1147.8MB, time=520.85 memory used=47050.8MB, alloc=1147.8MB, time=522.49 memory used=47167.6MB, alloc=1147.8MB, time=524.11 memory used=47284.4MB, alloc=1147.8MB, time=525.76 memory used=47401.4MB, alloc=1147.8MB, time=527.41 memory used=47518.5MB, alloc=1147.8MB, time=529.12 memory used=47635.7MB, alloc=1147.8MB, time=530.77 memory used=47753.0MB, alloc=1147.8MB, time=532.40 memory used=47872.8MB, alloc=1147.8MB, time=534.03 memory used=47991.6MB, alloc=1147.8MB, time=535.67 memory used=48134.7MB, alloc=1147.8MB, time=537.31 memory used=48256.1MB, alloc=1147.8MB, time=538.97 memory used=48399.4MB, alloc=1147.8MB, time=540.64 memory used=48546.5MB, alloc=1147.8MB, time=542.30 memory used=48693.6MB, alloc=1147.8MB, time=543.96 memory used=48840.8MB, alloc=1147.8MB, time=545.62 memory used=48988.1MB, alloc=1147.8MB, time=547.28 memory used=49135.4MB, alloc=1147.8MB, time=548.97 memory used=49282.6MB, alloc=1147.8MB, time=550.64 memory used=49429.9MB, alloc=1147.8MB, time=552.29 memory used=49577.1MB, alloc=1147.8MB, time=553.95 memory used=49724.3MB, alloc=1147.8MB, time=555.61 memory used=49871.4MB, alloc=1147.8MB, time=557.27 memory used=50018.5MB, alloc=1147.8MB, time=558.93 memory used=50165.5MB, alloc=1147.8MB, time=560.59 memory used=50312.5MB, alloc=1147.8MB, time=562.29 memory used=50459.3MB, alloc=1147.8MB, time=563.95 memory used=50606.0MB, alloc=1147.8MB, time=565.60 memory used=50752.5MB, alloc=1147.8MB, time=567.26 memory used=50898.9MB, alloc=1147.8MB, time=568.93 memory used=51045.2MB, alloc=1147.8MB, time=570.63 memory used=51194.2MB, alloc=1147.8MB, time=572.28 memory used=51366.4MB, alloc=1147.8MB, time=573.96 memory used=51516.5MB, alloc=1147.8MB, time=575.64 memory used=51686.8MB, alloc=1147.8MB, time=577.33 memory used=51861.0MB, alloc=1147.8MB, time=579.02 memory used=52034.8MB, alloc=1147.8MB, time=580.72 memory used=52208.3MB, alloc=1147.8MB, time=582.41 memory used=52381.4MB, alloc=1147.8MB, time=584.09 memory used=52554.1MB, alloc=1147.8MB, time=585.78 memory used=52726.3MB, alloc=1147.8MB, time=587.44 memory used=52896.0MB, alloc=1147.8MB, time=589.13 memory used=53050.3MB, alloc=1147.8MB, time=590.82 memory used=53197.0MB, alloc=1147.8MB, time=592.46 memory used=53347.9MB, alloc=1147.8MB, time=594.13 memory used=53459.7MB, alloc=1147.8MB, time=595.75 memory used=53563.3MB, alloc=1147.8MB, time=597.36 memory used=53675.1MB, alloc=1147.8MB, time=598.98 memory used=53787.2MB, alloc=1147.8MB, time=600.58 memory used=53899.0MB, alloc=1147.8MB, time=602.20 memory used=54010.6MB, alloc=1147.8MB, time=603.81 memory used=54121.8MB, alloc=1147.8MB, time=605.44 memory used=54232.8MB, alloc=1147.8MB, time=607.06 memory used=54343.4MB, alloc=1147.8MB, time=608.67 memory used=54453.7MB, alloc=1147.8MB, time=610.28 memory used=54563.7MB, alloc=1147.8MB, time=611.89 memory used=54673.4MB, alloc=1147.8MB, time=613.55 memory used=54782.8MB, alloc=1147.8MB, time=615.16 memory used=54891.8MB, alloc=1147.8MB, time=616.77 memory used=55000.5MB, alloc=1147.8MB, time=618.39 memory used=55108.9MB, alloc=1147.8MB, time=620.00 memory used=55220.3MB, alloc=1147.8MB, time=621.61 memory used=55351.5MB, alloc=1147.8MB, time=623.28 memory used=55463.7MB, alloc=1147.8MB, time=624.90 memory used=55592.1MB, alloc=1147.8MB, time=626.53 memory used=55725.0MB, alloc=1147.8MB, time=628.16 memory used=55857.2MB, alloc=1147.8MB, time=629.79 memory used=55988.7MB, alloc=1147.8MB, time=631.42 memory used=56119.7MB, alloc=1147.8MB, time=633.06 memory used=56250.0MB, alloc=1147.8MB, time=634.69 memory used=56379.6MB, alloc=1147.8MB, time=636.32 memory used=56508.6MB, alloc=1147.8MB, time=637.95 memory used=56636.8MB, alloc=1147.8MB, time=639.58 memory used=56764.3MB, alloc=1147.8MB, time=641.26 memory used=56891.1MB, alloc=1147.8MB, time=642.91 memory used=57017.2MB, alloc=1147.8MB, time=644.54 memory used=57142.6MB, alloc=1147.8MB, time=646.17 memory used=57270.9MB, alloc=1147.8MB, time=647.81 memory used=57415.7MB, alloc=1147.8MB, time=649.47 memory used=57563.1MB, alloc=1147.8MB, time=651.13 memory used=57709.3MB, alloc=1147.8MB, time=652.75 memory used=57854.2MB, alloc=1147.8MB, time=654.42 memory used=57998.0MB, alloc=1147.8MB, time=656.06 memory used=58140.6MB, alloc=1147.8MB, time=657.76 memory used=58281.9MB, alloc=1147.8MB, time=659.38 memory used=58421.9MB, alloc=1147.8MB, time=661.05 memory used=58564.6MB, alloc=1147.8MB, time=662.67 memory used=58721.0MB, alloc=1147.8MB, time=664.33 memory used=58879.4MB, alloc=1147.8MB, time=665.99 memory used=59035.9MB, alloc=1147.8MB, time=667.65 memory used=59190.4MB, alloc=1147.8MB, time=669.30 memory used=59343.1MB, alloc=1147.8MB, time=670.93 memory used=59493.9MB, alloc=1147.8MB, time=672.58 memory used=59647.2MB, alloc=1147.8MB, time=674.22 memory used=59810.0MB, alloc=1147.8MB, time=675.88 memory used=59974.7MB, alloc=1147.8MB, time=677.55 memory used=60136.6MB, alloc=1147.8MB, time=679.21 memory used=60299.8MB, alloc=1147.8MB, time=680.88 memory used=60471.3MB, alloc=1147.8MB, time=682.58 memory used=60643.0MB, alloc=1147.8MB, time=684.25 memory used=60811.1MB, alloc=1147.8MB, time=685.91 memory used=60981.4MB, alloc=1147.8MB, time=687.59 memory used=61157.2MB, alloc=1147.8MB, time=689.25 memory used=61342.6MB, alloc=1147.8MB, time=690.93 memory used=61526.1MB, alloc=1147.8MB, time=692.61 memory used=61710.0MB, alloc=1147.8MB, time=694.28 memory used=61904.6MB, alloc=1147.8MB, time=695.95 memory used=62096.5MB, alloc=1147.8MB, time=697.61 memory used=62292.7MB, alloc=1147.8MB, time=699.30 memory used=62462.5MB, alloc=1147.8MB, time=700.95 memory used=62621.5MB, alloc=1147.8MB, time=702.63 memory used=62777.8MB, alloc=1147.8MB, time=704.30 memory used=62935.6MB, alloc=1147.8MB, time=705.91 memory used=63096.3MB, alloc=1147.8MB, time=707.53 memory used=63260.7MB, alloc=1147.8MB, time=709.14 memory used=63429.6MB, alloc=1147.8MB, time=710.77 memory used=63598.1MB, alloc=1147.8MB, time=712.42 memory used=63768.8MB, alloc=1147.8MB, time=714.05 memory used=63943.9MB, alloc=1147.8MB, time=715.69 memory used=64629.2MB, alloc=1171.8MB, time=1479.80 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428464165 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 2 2 F := [13 y - 16 y + 9 x y, 8 y z - 16 x z - 15 y , 2 3 -8 x y z - 18 y z - 14 x z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 3 2 G := [x y - 10 x y z + 3 y z, -18 x y + 10 y - 20 x , 3 2 3 5 x z + 16 x y z - 19 x y ] > Problem := [F,G]; 4 3 2 2 Problem := [[13 y - 16 y + 9 x y, 8 y z - 16 x z - 15 y , 2 3 2 2 2 3 -8 x y z - 18 y z - 14 x z], [x y - 10 x y z + 3 y z, 2 3 2 3 2 3 -18 x y + 10 y - 20 x , 5 x z + 16 x y z - 19 x y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=31.7MB, alloc=40.3MB, time=0.56 memory used=59.0MB, alloc=44.3MB, time=0.94 memory used=84.3MB, alloc=68.3MB, time=1.33 memory used=137.3MB, alloc=76.3MB, time=1.97 memory used=188.4MB, alloc=76.3MB, time=2.66 memory used=241.0MB, alloc=100.3MB, time=3.34 memory used=317.4MB, alloc=100.3MB, time=4.42 memory used=369.7MB, alloc=100.3MB, time=4.88 memory used=411.0MB, alloc=100.3MB, time=5.24 memory used=450.4MB, alloc=100.3MB, time=6.01 memory used=489.4MB, alloc=100.3MB, time=6.21 memory used=531.2MB, alloc=100.3MB, time=7.06 memory used=568.7MB, alloc=100.3MB, time=7.26 memory used=606.1MB, alloc=100.3MB, time=7.40 memory used=649.8MB, alloc=100.3MB, time=7.71 memory used=718.3MB, alloc=124.3MB, time=10.33 memory used=792.0MB, alloc=124.3MB, time=10.82 memory used=860.1MB, alloc=124.3MB, time=11.67 memory used=941.1MB, alloc=124.3MB, time=12.31 memory used=1011.7MB, alloc=124.3MB, time=13.16 memory used=1076.3MB, alloc=380.3MB, time=14.11 memory used=1157.0MB, alloc=404.3MB, time=15.35 memory used=1280.1MB, alloc=428.3MB, time=16.93 memory used=1421.7MB, alloc=428.3MB, time=18.74 memory used=1549.7MB, alloc=452.3MB, time=20.52 memory used=1689.3MB, alloc=476.3MB, time=22.59 memory used=1874.6MB, alloc=476.3MB, time=24.21 memory used=2095.4MB, alloc=476.3MB, time=25.91 memory used=2306.0MB, alloc=476.3MB, time=28.22 memory used=2497.6MB, alloc=476.3MB, time=29.91 memory used=2670.4MB, alloc=476.3MB, time=32.57 memory used=2809.6MB, alloc=500.3MB, time=34.27 memory used=2961.3MB, alloc=500.3MB, time=35.94 memory used=3120.7MB, alloc=500.3MB, time=37.34 memory used=3233.9MB, alloc=524.3MB, time=39.23 memory used=3340.4MB, alloc=524.3MB, time=40.94 memory used=3433.4MB, alloc=524.3MB, time=42.23 memory used=3523.0MB, alloc=524.3MB, time=43.50 memory used=3613.2MB, alloc=548.3MB, time=45.20 memory used=3707.9MB, alloc=548.3MB, time=46.54 memory used=3864.3MB, alloc=548.3MB, time=49.78 memory used=4028.0MB, alloc=548.3MB, time=53.63 memory used=4183.6MB, alloc=548.3MB, time=56.19 memory used=4311.1MB, alloc=548.3MB, time=61.28 memory used=4411.2MB, alloc=548.3MB, time=62.41 memory used=4515.4MB, alloc=548.3MB, time=64.19 memory used=4630.0MB, alloc=572.3MB, time=65.37 memory used=4693.4MB, alloc=572.3MB, time=66.34 memory used=4845.9MB, alloc=596.3MB, time=67.52 memory used=4945.2MB, alloc=596.3MB, time=69.00 memory used=5000.3MB, alloc=596.3MB, time=70.11 memory used=5056.6MB, alloc=596.3MB, time=71.10 memory used=5116.2MB, alloc=596.3MB, time=72.04 memory used=5219.0MB, alloc=596.3MB, time=73.41 memory used=5276.5MB, alloc=596.3MB, time=74.57 memory used=5323.3MB, alloc=596.3MB, time=75.51 memory used=5551.1MB, alloc=620.3MB, time=78.23 memory used=5739.8MB, alloc=644.3MB, time=81.11 memory used=5974.0MB, alloc=668.3MB, time=84.56 memory used=6189.0MB, alloc=692.3MB, time=87.20 memory used=6408.6MB, alloc=716.3MB, time=90.03 memory used=6585.6MB, alloc=740.3MB, time=92.41 memory used=6764.9MB, alloc=740.3MB, time=95.21 memory used=6970.5MB, alloc=740.3MB, time=98.50 memory used=7119.5MB, alloc=764.3MB, time=100.65 memory used=7291.5MB, alloc=764.3MB, time=103.03 memory used=7506.1MB, alloc=764.3MB, time=105.55 memory used=7628.1MB, alloc=764.3MB, time=107.36 memory used=7742.2MB, alloc=788.3MB, time=109.22 memory used=7864.6MB, alloc=788.3MB, time=111.64 memory used=7963.2MB, alloc=788.3MB, time=113.76 memory used=8356.8MB, alloc=812.3MB, time=119.66 memory used=8608.4MB, alloc=812.3MB, time=121.90 memory used=8831.4MB, alloc=812.3MB, time=123.74 memory used=9051.5MB, alloc=812.3MB, time=125.39 memory used=9287.9MB, alloc=812.3MB, time=126.96 memory used=9538.7MB, alloc=812.3MB, time=128.84 memory used=9764.5MB, alloc=812.3MB, time=130.46 memory used=9985.6MB, alloc=812.3MB, time=132.03 memory used=10269.8MB, alloc=812.3MB, time=134.57 memory used=10669.3MB, alloc=812.3MB, time=141.66 memory used=11050.2MB, alloc=836.3MB, time=144.67 memory used=11484.6MB, alloc=860.3MB, time=149.45 memory used=12008.0MB, alloc=884.3MB, time=154.20 memory used=12498.7MB, alloc=908.3MB, time=158.19 memory used=12988.4MB, alloc=908.3MB, time=163.09 memory used=13251.5MB, alloc=908.3MB, time=165.25 memory used=13504.8MB, alloc=908.3MB, time=167.04 memory used=13773.0MB, alloc=908.3MB, time=168.93 memory used=14112.5MB, alloc=908.3MB, time=170.96 memory used=14396.0MB, alloc=908.3MB, time=173.24 memory used=14650.7MB, alloc=908.3MB, time=175.02 memory used=15158.7MB, alloc=908.3MB, time=179.28 memory used=15466.8MB, alloc=908.3MB, time=185.82 memory used=15963.9MB, alloc=932.3MB, time=190.90 memory used=16499.9MB, alloc=956.3MB, time=196.43 memory used=17024.1MB, alloc=980.3MB, time=202.59 memory used=17461.5MB, alloc=1004.3MB, time=209.35 memory used=17961.7MB, alloc=1028.3MB, time=215.12 memory used=18389.5MB, alloc=1308.3MB, time=222.34 memory used=18725.8MB, alloc=1332.3MB, time=227.39 memory used=19054.7MB, alloc=1356.3MB, time=230.09 memory used=19381.4MB, alloc=1380.3MB, time=232.64 memory used=19825.2MB, alloc=1380.3MB, time=235.74 memory used=20207.8MB, alloc=1380.3MB, time=238.45 memory used=20605.9MB, alloc=1380.3MB, time=241.39 memory used=21039.5MB, alloc=1395.8MB, time=243.66 memory used=21658.1MB, alloc=1395.8MB, time=250.25 memory used=22386.0MB, alloc=1419.8MB, time=257.18 memory used=23128.6MB, alloc=1443.8MB, time=266.70 memory used=23869.4MB, alloc=1467.8MB, time=278.35 memory used=24618.1MB, alloc=1491.8MB, time=291.30 memory used=25401.4MB, alloc=1515.8MB, time=303.60 memory used=26130.2MB, alloc=1539.8MB, time=318.80 memory used=26853.0MB, alloc=1563.8MB, time=330.00 memory used=27669.4MB, alloc=1587.8MB, time=342.38 memory used=28486.4MB, alloc=1611.8MB, time=355.15 memory used=29166.6MB, alloc=1635.8MB, time=368.93 memory used=29872.3MB, alloc=1659.8MB, time=380.49 memory used=30325.5MB, alloc=1683.8MB, time=386.78 memory used=30601.1MB, alloc=1707.8MB, time=391.05 memory used=30920.0MB, alloc=1731.8MB, time=399.40 memory used=31316.4MB, alloc=1755.8MB, time=404.14 memory used=32131.6MB, alloc=1779.8MB, time=416.08 memory used=32853.3MB, alloc=1803.8MB, time=426.00 memory used=33258.2MB, alloc=1827.8MB, time=431.31 memory used=33694.7MB, alloc=1851.8MB, time=439.54 memory used=34200.1MB, alloc=1875.8MB, time=444.64 memory used=34839.8MB, alloc=1899.8MB, time=455.22 memory used=35777.5MB, alloc=1923.8MB, time=465.63 memory used=36743.0MB, alloc=1947.8MB, time=481.15 memory used=37461.2MB, alloc=1971.8MB, time=493.15 memory used=38276.3MB, alloc=1995.8MB, time=509.63 memory used=38970.3MB, alloc=2019.8MB, time=521.19 memory used=39656.4MB, alloc=2043.8MB, time=536.27 memory used=40425.2MB, alloc=2067.8MB, time=549.75 memory used=41335.1MB, alloc=2091.8MB, time=563.86 memory used=41939.4MB, alloc=2115.8MB, time=576.82 memory used=42497.6MB, alloc=2139.8MB, time=588.50 memory used=42925.7MB, alloc=2163.8MB, time=599.14 memory used=43514.6MB, alloc=2187.8MB, time=612.72 memory used=44938.0MB, alloc=2211.8MB, time=625.66 memory used=46252.8MB, alloc=2235.8MB, time=634.63 memory used=46991.6MB, alloc=2259.8MB, time=641.26 memory used=47588.6MB, alloc=2283.8MB, time=647.52 memory used=48167.6MB, alloc=2307.8MB, time=653.75 memory used=48743.9MB, alloc=2331.8MB, time=660.12 memory used=50146.1MB, alloc=2355.8MB, time=676.17 memory used=50775.8MB, alloc=2379.8MB, time=689.18 memory used=51348.3MB, alloc=2403.8MB, time=704.14 memory used=52003.7MB, alloc=2427.8MB, time=722.48 memory used=52593.3MB, alloc=2451.8MB, time=740.74 memory used=53187.6MB, alloc=2475.8MB, time=758.95 memory used=53717.6MB, alloc=2499.8MB, time=775.65 memory used=54288.7MB, alloc=2523.8MB, time=793.23 memory used=54693.8MB, alloc=2547.8MB, time=807.02 memory used=55109.5MB, alloc=2571.8MB, time=821.48 memory used=55627.1MB, alloc=2595.8MB, time=837.50 memory used=56305.6MB, alloc=2619.8MB, time=855.19 memory used=57164.8MB, alloc=2643.8MB, time=872.25 memory used=58066.5MB, alloc=2667.8MB, time=888.29 memory used=58998.6MB, alloc=2691.8MB, time=906.03 memory used=60368.2MB, alloc=2715.8MB, time=923.13 memory used=61074.6MB, alloc=2739.8MB, time=941.14 memory used=61475.1MB, alloc=2763.8MB, time=955.08 memory used=61938.6MB, alloc=2787.8MB, time=970.97 memory used=62257.8MB, alloc=2811.8MB, time=984.13 memory used=62981.1MB, alloc=2835.8MB, time=1002.08 memory used=63503.3MB, alloc=2859.8MB, time=1020.22 memory used=63966.5MB, alloc=2883.8MB, time=1036.56 memory used=64432.7MB, alloc=2907.8MB, time=1052.86 memory used=64824.8MB, alloc=2931.8MB, time=1067.84 memory used=65245.2MB, alloc=2955.8MB, time=1083.69 memory used=65710.3MB, alloc=2979.8MB, time=1099.53 memory used=66165.9MB, alloc=3003.8MB, time=1116.52 memory used=66623.1MB, alloc=3027.8MB, time=1131.91 memory used=67030.8MB, alloc=3051.8MB, time=1146.78 memory used=67474.1MB, alloc=3075.8MB, time=1162.61 memory used=67865.2MB, alloc=3099.8MB, time=1177.64 memory used=68203.0MB, alloc=3123.8MB, time=1191.83 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428465365 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 4 3 2 F := [-18 x z + 8 y z - 19 z, -20 z + 19 x y - 11, -x y - 15 y - 14 y z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 2 2 G := [8 x z + y z + 16 z , 18 x y z + 17 x y - 9 y , -8 x z - 18 y + 4] > Problem := [F,G]; Problem := [ 2 2 3 4 3 2 [-18 x z + 8 y z - 19 z, -20 z + 19 x y - 11, -x y - 15 y - 14 y z], 2 2 3 2 2 2 2 [8 x z + y z + 16 z , 18 x y z + 17 x y - 9 y , -8 x z - 18 y + 4]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.5MB, alloc=32.3MB, time=0.51 memory used=47.3MB, alloc=32.3MB, time=0.82 memory used=66.5MB, alloc=56.3MB, time=1.13 memory used=105.6MB, alloc=60.3MB, time=1.73 memory used=142.5MB, alloc=84.3MB, time=2.31 memory used=204.4MB, alloc=92.3MB, time=3.27 memory used=263.3MB, alloc=116.3MB, time=4.23 memory used=344.8MB, alloc=116.3MB, time=5.53 memory used=425.8MB, alloc=140.3MB, time=6.84 memory used=506.9MB, alloc=140.3MB, time=8.19 memory used=583.2MB, alloc=396.3MB, time=9.45 memory used=684.6MB, alloc=420.3MB, time=11.14 memory used=806.6MB, alloc=444.3MB, time=13.24 memory used=940.1MB, alloc=468.3MB, time=15.36 memory used=1091.9MB, alloc=492.3MB, time=18.08 memory used=1212.6MB, alloc=516.3MB, time=20.01 memory used=1326.9MB, alloc=516.3MB, time=21.97 memory used=1435.4MB, alloc=516.3MB, time=23.86 memory used=1520.9MB, alloc=516.3MB, time=25.31 memory used=1624.7MB, alloc=516.3MB, time=27.27 memory used=1721.5MB, alloc=540.3MB, time=29.25 memory used=1805.3MB, alloc=540.3MB, time=30.92 memory used=1870.6MB, alloc=540.3MB, time=32.22 memory used=1940.4MB, alloc=540.3MB, time=33.78 memory used=2008.9MB, alloc=540.3MB, time=35.43 memory used=2056.2MB, alloc=540.3MB, time=36.54 memory used=2124.8MB, alloc=540.3MB, time=38.28 memory used=2341.3MB, alloc=564.3MB, time=42.30 memory used=2575.1MB, alloc=588.3MB, time=46.74 memory used=2763.3MB, alloc=612.3MB, time=50.79 memory used=2932.9MB, alloc=636.3MB, time=54.21 memory used=3112.2MB, alloc=660.3MB, time=58.17 memory used=3255.5MB, alloc=660.3MB, time=61.08 memory used=3403.4MB, alloc=660.3MB, time=64.44 memory used=3585.9MB, alloc=660.3MB, time=68.79 memory used=3706.2MB, alloc=684.3MB, time=71.60 memory used=3831.4MB, alloc=684.3MB, time=74.66 memory used=3957.2MB, alloc=684.3MB, time=77.71 memory used=4071.6MB, alloc=684.3MB, time=80.89 memory used=4442.8MB, alloc=708.3MB, time=88.87 memory used=4824.6MB, alloc=732.3MB, time=97.68 memory used=5219.6MB, alloc=756.3MB, time=107.69 memory used=5579.6MB, alloc=780.3MB, time=116.01 memory used=5946.4MB, alloc=804.3MB, time=125.22 memory used=6311.3MB, alloc=828.3MB, time=135.28 memory used=6608.7MB, alloc=852.3MB, time=142.82 memory used=6893.4MB, alloc=876.3MB, time=150.19 memory used=7168.0MB, alloc=900.3MB, time=157.35 memory used=7460.2MB, alloc=924.3MB, time=164.94 memory used=7716.4MB, alloc=948.3MB, time=171.67 memory used=7937.1MB, alloc=972.3MB, time=177.86 memory used=8131.2MB, alloc=996.3MB, time=183.94 memory used=8767.2MB, alloc=1020.3MB, time=200.61 memory used=9418.8MB, alloc=1044.3MB, time=216.98 memory used=10086.4MB, alloc=1068.3MB, time=233.07 memory used=10769.1MB, alloc=1092.3MB, time=248.54 memory used=11458.4MB, alloc=1116.3MB, time=265.07 memory used=12143.9MB, alloc=1140.3MB, time=282.82 memory used=12815.1MB, alloc=1164.3MB, time=300.55 memory used=13486.9MB, alloc=1188.3MB, time=320.71 memory used=14020.4MB, alloc=1212.3MB, time=335.38 memory used=14593.5MB, alloc=1236.3MB, time=351.31 memory used=15172.6MB, alloc=1260.3MB, time=365.90 memory used=15604.9MB, alloc=1284.3MB, time=376.18 memory used=16066.3MB, alloc=1308.3MB, time=391.24 memory used=16508.2MB, alloc=1332.3MB, time=406.24 memory used=16912.2MB, alloc=1356.3MB, time=419.95 memory used=17290.0MB, alloc=1380.3MB, time=434.26 memory used=17607.0MB, alloc=1404.3MB, time=447.72 memory used=17924.8MB, alloc=1428.3MB, time=457.30 memory used=18209.2MB, alloc=1452.3MB, time=470.27 memory used=18403.7MB, alloc=1476.3MB, time=478.80 memory used=18603.2MB, alloc=1500.3MB, time=486.28 memory used=18743.7MB, alloc=1524.3MB, time=493.91 memory used=18968.1MB, alloc=1548.3MB, time=506.09 memory used=19081.8MB, alloc=1572.3MB, time=512.93 memory used=19256.7MB, alloc=1596.3MB, time=521.49 memory used=19370.7MB, alloc=1620.3MB, time=528.22 memory used=19488.6MB, alloc=1644.3MB, time=535.55 memory used=19692.6MB, alloc=1668.3MB, time=547.88 memory used=19852.7MB, alloc=1692.3MB, time=556.55 memory used=19985.2MB, alloc=1716.3MB, time=564.55 memory used=20117.9MB, alloc=1740.3MB, time=571.71 memory used=20203.7MB, alloc=1764.3MB, time=578.98 memory used=20228.2MB, alloc=1788.3MB, time=584.86 memory used=20382.3MB, alloc=1812.3MB, time=594.65 memory used=20539.5MB, alloc=1836.3MB, time=604.51 memory used=20578.6MB, alloc=1860.3MB, time=611.26 memory used=20653.0MB, alloc=1884.3MB, time=618.52 memory used=20752.7MB, alloc=1884.3MB, time=625.90 memory used=20788.4MB, alloc=1884.3MB, time=632.31 memory used=20840.4MB, alloc=1884.3MB, time=639.31 memory used=20895.6MB, alloc=1884.3MB, time=645.54 memory used=20952.5MB, alloc=1884.3MB, time=652.31 memory used=21092.4MB, alloc=1884.3MB, time=664.11 memory used=21154.7MB, alloc=1884.3MB, time=671.46 memory used=21225.1MB, alloc=1908.3MB, time=678.71 memory used=21259.0MB, alloc=1908.3MB, time=685.09 memory used=21313.6MB, alloc=1908.3MB, time=692.27 memory used=21335.3MB, alloc=1908.3MB, time=698.52 memory used=21365.5MB, alloc=1908.3MB, time=704.94 memory used=21395.9MB, alloc=1908.3MB, time=711.88 memory used=21405.3MB, alloc=1908.3MB, time=718.04 memory used=21437.0MB, alloc=1908.3MB, time=724.32 memory used=21496.8MB, alloc=1908.3MB, time=730.81 memory used=21542.4MB, alloc=2164.3MB, time=743.51 memory used=22892.8MB, alloc=2188.3MB, time=781.39 memory used=24258.1MB, alloc=2212.3MB, time=818.65 memory used=25597.1MB, alloc=2236.3MB, time=858.97 memory used=26992.5MB, alloc=2260.3MB, time=891.68 memory used=28266.8MB, alloc=2284.3MB, time=930.23 memory used=29293.9MB, alloc=2308.3MB, time=960.73 memory used=30420.6MB, alloc=2332.3MB, time=1000.88 memory used=31365.9MB, alloc=2356.3MB, time=1030.65 memory used=32113.3MB, alloc=2380.3MB, time=1059.16 memory used=33090.4MB, alloc=2404.3MB, time=1096.92 memory used=33962.5MB, alloc=2428.3MB, time=1128.12 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428466565 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 4 2 4 3 2 2 3 2 F := [2 y - 4 z + 20 x y , -12 x + 9 y z + 8 x, 17 x y - 4 y z - 5 x y ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; G := [ 2 3 2 2 3 2 2 15 x y z + 11 x z + 12 x , 16 x y + 12 y - 17 y, 13 x z + 2 x z - 8 x ] > Problem := [F,G]; Problem := [ 4 4 2 4 3 2 2 3 2 [2 y - 4 z + 20 x y , -12 x + 9 y z + 8 x, 17 x y - 4 y z - 5 x y ], [ 2 3 2 2 3 2 2 15 x y z + 11 x z + 12 x , 16 x y + 12 y - 17 y, 13 x z + 2 x z - 8 x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.17 memory used=26.4MB, alloc=32.3MB, time=0.50 memory used=47.2MB, alloc=32.3MB, time=0.81 memory used=65.8MB, alloc=56.3MB, time=1.09 memory used=109.2MB, alloc=68.3MB, time=1.73 memory used=151.3MB, alloc=68.3MB, time=2.31 memory used=195.2MB, alloc=92.3MB, time=2.90 memory used=264.0MB, alloc=92.3MB, time=3.71 memory used=326.1MB, alloc=92.3MB, time=4.44 memory used=386.2MB, alloc=92.3MB, time=5.10 memory used=445.2MB, alloc=92.3MB, time=5.69 memory used=512.6MB, alloc=116.3MB, time=6.59 memory used=593.1MB, alloc=116.3MB, time=7.79 memory used=661.7MB, alloc=372.3MB, time=8.79 memory used=743.8MB, alloc=396.3MB, time=10.06 memory used=855.3MB, alloc=420.3MB, time=11.61 memory used=959.7MB, alloc=420.3MB, time=12.59 memory used=1043.9MB, alloc=420.3MB, time=12.96 memory used=1108.8MB, alloc=420.3MB, time=13.77 memory used=1245.5MB, alloc=420.3MB, time=15.60 memory used=1349.1MB, alloc=420.3MB, time=16.47 memory used=1423.3MB, alloc=420.3MB, time=17.88 memory used=1494.9MB, alloc=420.3MB, time=18.71 memory used=1558.4MB, alloc=420.3MB, time=18.93 memory used=1637.7MB, alloc=420.3MB, time=19.51 memory used=1710.4MB, alloc=420.3MB, time=19.81 memory used=1764.6MB, alloc=420.3MB, time=20.05 memory used=1834.4MB, alloc=420.3MB, time=20.27 memory used=1879.3MB, alloc=420.3MB, time=20.48 memory used=1927.9MB, alloc=420.3MB, time=20.67 memory used=1990.0MB, alloc=420.3MB, time=20.94 memory used=2077.3MB, alloc=420.3MB, time=24.92 memory used=2175.8MB, alloc=420.3MB, time=25.62 memory used=2297.2MB, alloc=444.3MB, time=26.82 memory used=2432.4MB, alloc=444.3MB, time=28.53 memory used=2538.1MB, alloc=444.3MB, time=29.25 memory used=2612.2MB, alloc=444.3MB, time=29.61 memory used=2690.9MB, alloc=444.3MB, time=29.97 memory used=2793.4MB, alloc=444.3MB, time=32.13 memory used=2863.5MB, alloc=444.3MB, time=32.37 memory used=2936.9MB, alloc=444.3MB, time=32.72 memory used=3003.5MB, alloc=444.3MB, time=32.98 memory used=3090.7MB, alloc=444.3MB, time=33.34 memory used=3161.1MB, alloc=444.3MB, time=33.60 memory used=3243.7MB, alloc=444.3MB, time=34.17 memory used=3317.8MB, alloc=444.3MB, time=34.44 memory used=3373.9MB, alloc=444.3MB, time=34.71 memory used=3440.2MB, alloc=444.3MB, time=34.98 memory used=3519.0MB, alloc=444.3MB, time=35.23 memory used=3588.3MB, alloc=444.3MB, time=35.47 memory used=3638.3MB, alloc=444.3MB, time=35.67 memory used=3693.6MB, alloc=444.3MB, time=35.88 memory used=3755.4MB, alloc=444.3MB, time=36.08 memory used=3833.0MB, alloc=444.3MB, time=36.51 memory used=4058.8MB, alloc=444.3MB, time=46.01 memory used=4258.0MB, alloc=444.3MB, time=47.78 memory used=4374.3MB, alloc=444.3MB, time=48.91 memory used=4513.3MB, alloc=444.3MB, time=50.58 memory used=4607.9MB, alloc=468.3MB, time=51.33 memory used=4703.5MB, alloc=468.3MB, time=51.81 memory used=4784.9MB, alloc=468.3MB, time=52.12 memory used=4870.0MB, alloc=468.3MB, time=52.52 memory used=4960.4MB, alloc=468.3MB, time=54.10 memory used=5090.0MB, alloc=468.3MB, time=55.25 memory used=5160.8MB, alloc=468.3MB, time=55.50 memory used=5261.3MB, alloc=468.3MB, time=55.95 memory used=5335.7MB, alloc=468.3MB, time=56.25 memory used=5414.2MB, alloc=468.3MB, time=56.54 memory used=5499.1MB, alloc=468.3MB, time=56.92 memory used=5576.4MB, alloc=468.3MB, time=57.24 memory used=5671.0MB, alloc=468.3MB, time=57.90 memory used=5752.2MB, alloc=468.3MB, time=58.25 memory used=5822.5MB, alloc=468.3MB, time=58.58 memory used=5909.6MB, alloc=468.3MB, time=58.91 memory used=5993.1MB, alloc=468.3MB, time=59.22 memory used=6049.1MB, alloc=468.3MB, time=59.47 memory used=6111.3MB, alloc=468.3MB, time=59.73 memory used=6180.4MB, alloc=468.3MB, time=59.99 memory used=6255.4MB, alloc=468.3MB, time=60.26 memory used=6338.5MB, alloc=468.3MB, time=60.52 memory used=6429.9MB, alloc=468.3MB, time=60.80 memory used=6606.4MB, alloc=468.3MB, time=63.14 memory used=6708.0MB, alloc=468.3MB, time=66.42 memory used=6921.9MB, alloc=468.3MB, time=68.05 memory used=7080.6MB, alloc=468.3MB, time=69.86 memory used=7216.2MB, alloc=468.3MB, time=71.27 memory used=7334.2MB, alloc=468.3MB, time=72.70 memory used=7459.9MB, alloc=468.3MB, time=74.01 memory used=7595.7MB, alloc=492.3MB, time=75.28 memory used=7712.7MB, alloc=492.3MB, time=77.13 memory used=7814.8MB, alloc=492.3MB, time=78.88 memory used=7905.1MB, alloc=492.3MB, time=80.29 memory used=8003.7MB, alloc=492.3MB, time=81.89 memory used=8087.6MB, alloc=492.3MB, time=83.37 memory used=8183.1MB, alloc=492.3MB, time=84.80 memory used=8263.7MB, alloc=492.3MB, time=86.07 memory used=8351.8MB, alloc=492.3MB, time=87.43 memory used=8430.4MB, alloc=492.3MB, time=88.66 memory used=8508.3MB, alloc=492.3MB, time=89.99 memory used=8635.8MB, alloc=516.3MB, time=91.36 memory used=8747.1MB, alloc=516.3MB, time=92.23 memory used=8856.1MB, alloc=516.3MB, time=92.87 memory used=8953.0MB, alloc=516.3MB, time=93.31 memory used=9066.1MB, alloc=516.3MB, time=94.01 memory used=9175.5MB, alloc=516.3MB, time=94.87 memory used=9283.0MB, alloc=516.3MB, time=95.82 memory used=9404.2MB, alloc=516.3MB, time=97.19 memory used=9503.2MB, alloc=516.3MB, time=97.67 memory used=9585.4MB, alloc=516.3MB, time=98.13 memory used=9688.6MB, alloc=516.3MB, time=98.60 memory used=9792.1MB, alloc=516.3MB, time=99.04 memory used=9860.3MB, alloc=516.3MB, time=99.42 memory used=9934.8MB, alloc=516.3MB, time=99.81 memory used=10017.4MB, alloc=516.3MB, time=100.20 memory used=10106.6MB, alloc=516.3MB, time=100.58 memory used=10204.8MB, alloc=516.3MB, time=100.97 memory used=10312.2MB, alloc=516.3MB, time=101.37 memory used=10431.6MB, alloc=516.3MB, time=101.78 memory used=10673.1MB, alloc=516.3MB, time=102.93 memory used=10797.8MB, alloc=516.3MB, time=104.02 memory used=10947.2MB, alloc=516.3MB, time=105.67 memory used=11046.3MB, alloc=516.3MB, time=106.16 memory used=11127.8MB, alloc=516.3MB, time=106.63 memory used=11229.8MB, alloc=516.3MB, time=107.07 memory used=11336.1MB, alloc=516.3MB, time=107.54 memory used=11404.8MB, alloc=516.3MB, time=107.93 memory used=11479.1MB, alloc=516.3MB, time=108.32 memory used=11561.6MB, alloc=516.3MB, time=108.70 memory used=11650.7MB, alloc=516.3MB, time=109.08 memory used=11748.9MB, alloc=516.3MB, time=109.49 memory used=11855.1MB, alloc=516.3MB, time=109.89 memory used=11973.2MB, alloc=516.3MB, time=110.29 memory used=12216.5MB, alloc=516.3MB, time=111.47 memory used=12341.9MB, alloc=516.3MB, time=112.56 memory used=12504.3MB, alloc=516.3MB, time=122.53 memory used=12646.7MB, alloc=516.3MB, time=124.03 memory used=12750.0MB, alloc=516.3MB, time=124.50 memory used=12825.4MB, alloc=516.3MB, time=124.90 memory used=12913.9MB, alloc=516.3MB, time=125.34 memory used=13017.0MB, alloc=516.3MB, time=125.76 memory used=13141.1MB, alloc=516.3MB, time=126.19 memory used=13290.4MB, alloc=516.3MB, time=126.70 memory used=13441.5MB, alloc=516.3MB, time=127.21 memory used=13613.3MB, alloc=516.3MB, time=127.74 memory used=13812.9MB, alloc=516.3MB, time=128.28 memory used=14111.2MB, alloc=516.3MB, time=129.63 memory used=14200.5MB, alloc=516.3MB, time=130.11 memory used=14286.3MB, alloc=516.3MB, time=130.60 memory used=14389.7MB, alloc=516.3MB, time=131.08 memory used=14504.4MB, alloc=516.3MB, time=131.59 memory used=14577.7MB, alloc=516.3MB, time=132.01 memory used=14648.1MB, alloc=540.3MB, time=132.44 memory used=14735.9MB, alloc=540.3MB, time=132.86 memory used=14831.0MB, alloc=540.3MB, time=133.29 memory used=14933.5MB, alloc=540.3MB, time=133.72 memory used=15044.8MB, alloc=540.3MB, time=134.16 memory used=15163.8MB, alloc=540.3MB, time=134.61 memory used=15291.4MB, alloc=540.3MB, time=135.06 memory used=15429.5MB, alloc=540.3MB, time=135.52 memory used=15657.1MB, alloc=540.3MB, time=136.14 memory used=15788.2MB, alloc=540.3MB, time=136.64 memory used=15929.1MB, alloc=540.3MB, time=137.12 memory used=16081.4MB, alloc=540.3MB, time=137.61 memory used=16366.7MB, alloc=540.3MB, time=139.21 memory used=16601.6MB, alloc=540.3MB, time=141.69 memory used=16724.4MB, alloc=540.3MB, time=142.30 memory used=16825.5MB, alloc=540.3MB, time=142.83 memory used=16929.8MB, alloc=540.3MB, time=143.31 memory used=17052.1MB, alloc=540.3MB, time=143.81 memory used=17183.9MB, alloc=540.3MB, time=144.34 memory used=17266.4MB, alloc=540.3MB, time=144.75 memory used=17351.6MB, alloc=540.3MB, time=145.15 memory used=17444.1MB, alloc=540.3MB, time=145.58 memory used=17544.0MB, alloc=540.3MB, time=146.00 memory used=17652.7MB, alloc=540.3MB, time=146.43 memory used=17798.9MB, alloc=540.3MB, time=148.80 memory used=17923.3MB, alloc=540.3MB, time=149.45 memory used=18041.4MB, alloc=540.3MB, time=150.01 memory used=18131.0MB, alloc=540.3MB, time=150.50 memory used=18233.4MB, alloc=540.3MB, time=151.00 memory used=18347.2MB, alloc=540.3MB, time=151.52 memory used=18478.2MB, alloc=540.3MB, time=152.07 memory used=18612.0MB, alloc=540.3MB, time=152.65 memory used=18690.3MB, alloc=564.3MB, time=153.09 memory used=18777.9MB, alloc=564.3MB, time=153.54 memory used=18873.6MB, alloc=564.3MB, time=153.99 memory used=18972.6MB, alloc=564.3MB, time=154.44 memory used=19074.9MB, alloc=564.3MB, time=154.88 memory used=19180.3MB, alloc=564.3MB, time=155.33 memory used=19288.9MB, alloc=564.3MB, time=155.78 memory used=19409.6MB, alloc=564.3MB, time=156.26 memory used=19533.5MB, alloc=564.3MB, time=156.74 memory used=19660.4MB, alloc=564.3MB, time=157.21 memory used=19790.2MB, alloc=564.3MB, time=157.70 memory used=19924.5MB, alloc=564.3MB, time=158.18 memory used=20068.4MB, alloc=564.3MB, time=158.67 memory used=20216.7MB, alloc=564.3MB, time=159.16 memory used=20369.0MB, alloc=564.3MB, time=159.67 memory used=20561.9MB, alloc=564.3MB, time=160.23 memory used=20720.0MB, alloc=564.3MB, time=160.78 memory used=20833.7MB, alloc=564.3MB, time=161.26 memory used=20956.2MB, alloc=564.3MB, time=161.74 memory used=21081.1MB, alloc=564.3MB, time=162.22 memory used=21206.8MB, alloc=564.3MB, time=162.69 memory used=21333.3MB, alloc=564.3MB, time=163.18 memory used=21462.3MB, alloc=564.3MB, time=163.69 memory used=21599.7MB, alloc=564.3MB, time=164.20 memory used=21739.4MB, alloc=564.3MB, time=164.71 memory used=21879.7MB, alloc=564.3MB, time=165.22 memory used=22022.8MB, alloc=564.3MB, time=165.73 memory used=22172.5MB, alloc=564.3MB, time=166.25 memory used=22325.0MB, alloc=564.3MB, time=166.77 memory used=22488.9MB, alloc=564.3MB, time=167.31 memory used=22652.4MB, alloc=564.3MB, time=167.84 memory used=22817.5MB, alloc=564.3MB, time=168.35 memory used=22989.2MB, alloc=564.3MB, time=168.90 memory used=23163.9MB, alloc=564.3MB, time=169.43 memory used=23344.6MB, alloc=564.3MB, time=169.97 memory used=23536.5MB, alloc=564.3MB, time=170.52 memory used=23728.2MB, alloc=564.3MB, time=171.08 memory used=23925.8MB, alloc=564.3MB, time=171.62 memory used=24130.7MB, alloc=564.3MB, time=172.19 memory used=24341.8MB, alloc=564.3MB, time=172.78 memory used=24564.2MB, alloc=564.3MB, time=173.37 memory used=24791.9MB, alloc=564.3MB, time=173.93 memory used=24984.9MB, alloc=564.3MB, time=174.46 memory used=25163.0MB, alloc=564.3MB, time=174.98 memory used=25327.7MB, alloc=564.3MB, time=175.52 memory used=25498.7MB, alloc=564.3MB, time=176.02 memory used=25678.1MB, alloc=564.3MB, time=176.53 memory used=26108.2MB, alloc=564.3MB, time=263.94 memory used=26232.7MB, alloc=564.3MB, time=264.54 memory used=26379.9MB, alloc=564.3MB, time=265.10 memory used=26475.5MB, alloc=564.3MB, time=265.55 memory used=26584.7MB, alloc=564.3MB, time=266.02 memory used=26708.4MB, alloc=564.3MB, time=266.51 memory used=26846.8MB, alloc=564.3MB, time=266.99 memory used=27000.0MB, alloc=564.3MB, time=267.48 memory used=27256.7MB, alloc=564.3MB, time=268.17 memory used=27387.7MB, alloc=564.3MB, time=268.68 memory used=27528.4MB, alloc=564.3MB, time=269.20 memory used=27678.9MB, alloc=564.3MB, time=269.73 memory used=27838.6MB, alloc=564.3MB, time=270.26 memory used=28007.4MB, alloc=564.3MB, time=270.80 memory used=28185.3MB, alloc=564.3MB, time=271.35 memory used=28371.8MB, alloc=564.3MB, time=271.91 memory used=28571.8MB, alloc=564.3MB, time=272.51 memory used=28780.2MB, alloc=564.3MB, time=273.11 memory used=29004.8MB, alloc=564.3MB, time=273.72 memory used=29230.7MB, alloc=564.3MB, time=274.31 memory used=29411.3MB, alloc=564.3MB, time=274.83 memory used=29582.2MB, alloc=564.3MB, time=275.35 memory used=29760.0MB, alloc=564.3MB, time=275.88 memory used=29945.3MB, alloc=564.3MB, time=276.45 memory used=30136.7MB, alloc=564.3MB, time=277.00 memory used=30337.4MB, alloc=564.3MB, time=277.55 memory used=30546.0MB, alloc=564.3MB, time=278.08 memory used=30766.0MB, alloc=564.3MB, time=278.65 memory used=31000.1MB, alloc=564.3MB, time=279.22 memory used=31201.4MB, alloc=564.3MB, time=279.74 memory used=31484.3MB, alloc=564.3MB, time=283.10 memory used=31580.0MB, alloc=564.3MB, time=284.22 memory used=31707.7MB, alloc=564.3MB, time=284.74 memory used=31890.5MB, alloc=564.3MB, time=287.90 memory used=32040.3MB, alloc=564.3MB, time=288.51 memory used=32190.6MB, alloc=564.3MB, time=289.45 memory used=32325.0MB, alloc=564.3MB, time=290.01 memory used=32445.5MB, alloc=564.3MB, time=290.53 memory used=32602.7MB, alloc=564.3MB, time=291.05 memory used=32704.2MB, alloc=564.3MB, time=291.46 memory used=32865.7MB, alloc=564.3MB, time=293.31 memory used=32990.6MB, alloc=564.3MB, time=295.08 memory used=33068.3MB, alloc=564.3MB, time=296.32 memory used=33184.6MB, alloc=564.3MB, time=297.88 memory used=33334.0MB, alloc=564.3MB, time=298.60 memory used=33491.4MB, alloc=564.3MB, time=299.45 memory used=33616.2MB, alloc=564.3MB, time=300.41 memory used=33672.2MB, alloc=564.3MB, time=301.42 memory used=33730.1MB, alloc=564.3MB, time=302.55 memory used=33779.9MB, alloc=564.3MB, time=303.62 memory used=33866.3MB, alloc=564.3MB, time=304.52 memory used=33976.0MB, alloc=588.3MB, time=313.68 memory used=34118.4MB, alloc=612.3MB, time=321.46 memory used=34248.2MB, alloc=612.3MB, time=323.38 memory used=34502.9MB, alloc=612.3MB, time=327.82 memory used=34768.0MB, alloc=612.3MB, time=331.68 memory used=34996.5MB, alloc=612.3MB, time=335.19 memory used=35233.6MB, alloc=636.3MB, time=338.62 memory used=35438.3MB, alloc=636.3MB, time=341.61 memory used=35701.8MB, alloc=660.3MB, time=343.90 memory used=35870.4MB, alloc=684.3MB, time=347.17 memory used=36055.0MB, alloc=708.3MB, time=350.53 memory used=36215.1MB, alloc=708.3MB, time=353.42 memory used=36361.4MB, alloc=732.3MB, time=355.79 memory used=36508.9MB, alloc=732.3MB, time=358.35 memory used=36651.2MB, alloc=732.3MB, time=360.68 memory used=36783.0MB, alloc=732.3MB, time=362.82 memory used=36918.6MB, alloc=732.3MB, time=365.12 memory used=37058.4MB, alloc=756.3MB, time=366.98 memory used=37174.7MB, alloc=756.3MB, time=369.27 memory used=37293.0MB, alloc=780.3MB, time=371.10 memory used=37596.3MB, alloc=780.3MB, time=374.25 memory used=37812.0MB, alloc=780.3MB, time=376.49 memory used=38044.6MB, alloc=780.3MB, time=378.04 memory used=38272.2MB, alloc=780.3MB, time=380.41 memory used=38507.5MB, alloc=780.3MB, time=382.00 memory used=38702.4MB, alloc=780.3MB, time=384.20 memory used=39036.4MB, alloc=780.3MB, time=386.69 memory used=39356.8MB, alloc=780.3MB, time=390.56 memory used=39752.4MB, alloc=804.3MB, time=396.58 memory used=40163.6MB, alloc=828.3MB, time=406.62 memory used=40567.4MB, alloc=852.3MB, time=410.10 memory used=40963.7MB, alloc=876.3MB, time=416.10 memory used=41309.6MB, alloc=900.3MB, time=421.40 memory used=41614.0MB, alloc=924.3MB, time=426.71 memory used=41927.9MB, alloc=948.3MB, time=430.22 memory used=42243.5MB, alloc=948.3MB, time=432.66 memory used=42492.4MB, alloc=948.3MB, time=434.38 memory used=42799.3MB, alloc=963.8MB, time=441.33 memory used=43141.0MB, alloc=963.8MB, time=444.08 memory used=43411.7MB, alloc=963.8MB, time=446.34 memory used=43676.4MB, alloc=963.8MB, time=448.12 memory used=43975.6MB, alloc=963.8MB, time=453.09 memory used=44239.8MB, alloc=963.8MB, time=457.65 memory used=44520.7MB, alloc=963.8MB, time=459.45 memory used=44746.4MB, alloc=963.8MB, time=461.20 memory used=45034.2MB, alloc=963.8MB, time=462.98 memory used=45269.6MB, alloc=963.8MB, time=464.51 memory used=45575.3MB, alloc=963.8MB, time=473.77 memory used=45954.6MB, alloc=963.8MB, time=476.23 memory used=46194.2MB, alloc=963.8MB, time=477.73 memory used=46728.1MB, alloc=963.8MB, time=486.66 memory used=47207.1MB, alloc=987.8MB, time=509.57 memory used=47482.7MB, alloc=987.8MB, time=511.50 memory used=48095.9MB, alloc=1011.8MB, time=587.35 memory used=48379.3MB, alloc=1035.8MB, time=591.51 memory used=48645.1MB, alloc=1035.8MB, time=593.15 memory used=49125.6MB, alloc=1059.8MB, time=597.39 memory used=49657.2MB, alloc=1083.8MB, time=602.94 memory used=50013.9MB, alloc=1363.8MB, time=608.66 memory used=50714.1MB, alloc=1387.8MB, time=616.94 memory used=51111.1MB, alloc=1411.8MB, time=623.34 memory used=51465.8MB, alloc=1435.8MB, time=626.00 memory used=51860.2MB, alloc=1459.8MB, time=629.75 memory used=52252.3MB, alloc=1459.8MB, time=632.82 memory used=52585.9MB, alloc=1459.8MB, time=635.11 memory used=52906.9MB, alloc=1459.8MB, time=637.32 memory used=53630.6MB, alloc=1459.8MB, time=653.42 memory used=53985.2MB, alloc=1459.8MB, time=655.81 memory used=54326.1MB, alloc=1459.8MB, time=658.59 memory used=54702.9MB, alloc=1459.8MB, time=661.14 memory used=54998.8MB, alloc=1459.8MB, time=663.29 memory used=55362.2MB, alloc=1459.8MB, time=665.45 memory used=55883.5MB, alloc=1459.8MB, time=680.91 memory used=56303.5MB, alloc=1459.8MB, time=685.41 memory used=56684.9MB, alloc=1459.8MB, time=687.89 memory used=56951.3MB, alloc=1483.8MB, time=690.03 memory used=57284.7MB, alloc=1483.8MB, time=692.27 memory used=57692.5MB, alloc=1483.8MB, time=694.48 memory used=58079.8MB, alloc=1483.8MB, time=696.71 memory used=58691.6MB, alloc=1483.8MB, time=764.77 memory used=59031.5MB, alloc=1483.8MB, time=766.99 memory used=59525.0MB, alloc=1483.8MB, time=769.37 memory used=60389.0MB, alloc=1483.8MB, time=779.68 memory used=60976.3MB, alloc=1483.8MB, time=802.67 memory used=61696.4MB, alloc=1507.8MB, time=809.34 memory used=62141.5MB, alloc=1507.8MB, time=878.63 memory used=62507.1MB, alloc=1507.8MB, time=880.82 memory used=62799.0MB, alloc=1507.8MB, time=882.98 memory used=63865.5MB, alloc=1531.8MB, time=891.91 memory used=64364.1MB, alloc=1555.8MB, time=897.02 memory used=65219.9MB, alloc=1579.8MB, time=908.02 memory used=65934.8MB, alloc=1603.8MB, time=917.65 memory used=66350.1MB, alloc=1627.8MB, time=921.36 memory used=66834.0MB, alloc=1651.8MB, time=927.87 memory used=67323.4MB, alloc=1675.8MB, time=932.64 memory used=67751.5MB, alloc=1699.8MB, time=935.96 memory used=68261.4MB, alloc=1699.8MB, time=940.05 memory used=68628.3MB, alloc=1699.8MB, time=943.09 memory used=69314.8MB, alloc=1699.8MB, time=946.52 memory used=69558.2MB, alloc=1699.8MB, time=949.32 memory used=70132.4MB, alloc=1699.8MB, time=960.49 memory used=70868.3MB, alloc=1699.8MB, time=965.22 memory used=71272.9MB, alloc=1699.8MB, time=968.38 memory used=71709.3MB, alloc=1699.8MB, time=971.40 memory used=72236.7MB, alloc=1699.8MB, time=975.56 memory used=72608.6MB, alloc=1699.8MB, time=978.59 memory used=73311.2MB, alloc=1699.8MB, time=982.08 memory used=73555.5MB, alloc=1699.8MB, time=984.87 memory used=74235.0MB, alloc=1699.8MB, time=997.04 memory used=74656.7MB, alloc=1723.8MB, time=1000.30 memory used=75055.1MB, alloc=1723.8MB, time=1003.36 memory used=75556.0MB, alloc=1723.8MB, time=1006.52 memory used=75982.1MB, alloc=1723.8MB, time=1009.66 memory used=76198.2MB, alloc=1723.8MB, time=1012.43 memory used=76427.1MB, alloc=1723.8MB, time=1015.20 memory used=76679.9MB, alloc=1723.8MB, time=1018.08 memory used=76955.8MB, alloc=1723.8MB, time=1020.88 memory used=77261.0MB, alloc=1723.8MB, time=1023.66 memory used=77993.3MB, alloc=1723.8MB, time=1094.98 memory used=78571.4MB, alloc=1723.8MB, time=1098.32 memory used=78831.9MB, alloc=1723.8MB, time=1101.16 memory used=79146.6MB, alloc=1723.8MB, time=1104.07 memory used=79907.4MB, alloc=1723.8MB, time=1114.10 memory used=80660.5MB, alloc=1723.8MB, time=1139.51 memory used=81177.0MB, alloc=1723.8MB, time=1142.80 memory used=82120.8MB, alloc=1723.8MB, time=1221.41 memory used=82762.1MB, alloc=1723.8MB, time=1224.84 memory used=83018.5MB, alloc=1723.8MB, time=1227.60 memory used=83324.4MB, alloc=1723.8MB, time=1230.47 memory used=83658.3MB, alloc=1723.8MB, time=1233.35 memory used=84707.3MB, alloc=1747.8MB, time=1242.34 memory used=85608.0MB, alloc=1771.8MB, time=1258.92 memory used=86536.8MB, alloc=1795.8MB, time=1271.64 memory used=87545.6MB, alloc=1819.8MB, time=1293.11 memory used=88485.8MB, alloc=1843.8MB, time=1307.14 memory used=89387.9MB, alloc=1867.8MB, time=1319.70 memory used=90117.1MB, alloc=1891.8MB, time=1333.39 memory used=90788.8MB, alloc=1915.8MB, time=1344.08 memory used=91429.1MB, alloc=1939.8MB, time=1357.83 memory used=92020.8MB, alloc=1963.8MB, time=1364.52 memory used=92889.8MB, alloc=1987.8MB, time=1375.46 memory used=93787.0MB, alloc=2011.8MB, time=1388.95 memory used=94412.9MB, alloc=2035.8MB, time=1401.10 memory used=94996.5MB, alloc=2059.8MB, time=1412.60 memory used=95826.0MB, alloc=2083.8MB, time=1424.59 memory used=96525.8MB, alloc=2107.8MB, time=1433.32 memory used=97198.8MB, alloc=2131.8MB, time=1441.90 memory used=97939.6MB, alloc=2155.8MB, time=1449.81 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428467766 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 3 2 2 2 2 2 F := [15 x y + 14 y z + 8 x, -7 x z - 14 y z , 18 x y + 8 z + 14] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 3 G := [14 x y + 3 x y z + 13 y, 15 x y - 18 x z + 10 z , 3 2 -16 y z + 16 x y + 13 y z] > Problem := [F,G]; Problem := [ 3 3 3 2 2 2 2 2 [15 x y + 14 y z + 8 x, -7 x z - 14 y z , 18 x y + 8 z + 14], [ 3 3 2 2 3 14 x y + 3 x y z + 13 y, 15 x y - 18 x z + 10 z , 3 2 -16 y z + 16 x y + 13 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.20 memory used=26.6MB, alloc=32.3MB, time=0.54 memory used=45.6MB, alloc=32.3MB, time=0.82 memory used=63.8MB, alloc=56.3MB, time=1.09 memory used=109.2MB, alloc=68.3MB, time=1.70 memory used=154.1MB, alloc=68.3MB, time=2.28 memory used=195.1MB, alloc=92.3MB, time=2.87 memory used=262.0MB, alloc=92.3MB, time=3.84 memory used=327.0MB, alloc=92.3MB, time=4.81 memory used=393.7MB, alloc=372.3MB, time=5.76 memory used=482.0MB, alloc=372.3MB, time=6.92 memory used=567.6MB, alloc=372.3MB, time=7.90 memory used=643.0MB, alloc=396.3MB, time=8.65 memory used=731.6MB, alloc=396.3MB, time=9.40 memory used=841.4MB, alloc=396.3MB, time=10.81 memory used=960.1MB, alloc=396.3MB, time=12.37 memory used=1079.5MB, alloc=420.3MB, time=13.88 memory used=1157.1MB, alloc=420.3MB, time=14.34 memory used=1238.7MB, alloc=420.3MB, time=14.90 memory used=1316.1MB, alloc=420.3MB, time=16.10 memory used=1394.1MB, alloc=420.3MB, time=16.67 memory used=1515.9MB, alloc=420.3MB, time=18.36 memory used=1612.9MB, alloc=444.3MB, time=19.45 memory used=1721.3MB, alloc=444.3MB, time=20.84 memory used=1823.0MB, alloc=468.3MB, time=22.26 memory used=1923.8MB, alloc=468.3MB, time=23.82 memory used=2016.9MB, alloc=468.3MB, time=25.28 memory used=2100.2MB, alloc=468.3MB, time=26.56 memory used=2200.3MB, alloc=492.3MB, time=28.05 memory used=2282.9MB, alloc=492.3MB, time=29.14 memory used=2430.9MB, alloc=492.3MB, time=31.46 memory used=2515.9MB, alloc=492.3MB, time=31.85 memory used=2612.2MB, alloc=492.3MB, time=32.25 memory used=2696.5MB, alloc=492.3MB, time=32.79 memory used=2809.5MB, alloc=492.3MB, time=33.33 memory used=2916.3MB, alloc=492.3MB, time=33.89 memory used=3016.1MB, alloc=492.3MB, time=34.32 memory used=3144.8MB, alloc=492.3MB, time=47.18 memory used=3256.2MB, alloc=492.3MB, time=49.29 memory used=3342.0MB, alloc=492.3MB, time=49.71 memory used=3421.5MB, alloc=492.3MB, time=50.11 memory used=3517.5MB, alloc=492.3MB, time=50.50 memory used=3616.7MB, alloc=492.3MB, time=50.88 memory used=3680.1MB, alloc=492.3MB, time=51.21 memory used=3749.2MB, alloc=492.3MB, time=51.55 memory used=3824.7MB, alloc=492.3MB, time=51.88 memory used=3908.1MB, alloc=492.3MB, time=52.23 memory used=4000.1MB, alloc=492.3MB, time=52.57 memory used=4113.2MB, alloc=492.3MB, time=52.93 memory used=4239.4MB, alloc=492.3MB, time=53.53 memory used=4346.3MB, alloc=492.3MB, time=54.09 memory used=4445.2MB, alloc=492.3MB, time=54.54 memory used=4578.0MB, alloc=492.3MB, time=68.44 memory used=4686.7MB, alloc=492.3MB, time=69.62 memory used=4770.8MB, alloc=492.3MB, time=70.05 memory used=4851.4MB, alloc=492.3MB, time=70.44 memory used=4949.2MB, alloc=492.3MB, time=70.85 memory used=5045.8MB, alloc=492.3MB, time=71.23 memory used=5109.2MB, alloc=492.3MB, time=71.59 memory used=5179.5MB, alloc=492.3MB, time=71.93 memory used=5256.4MB, alloc=492.3MB, time=72.28 memory used=5340.8MB, alloc=492.3MB, time=72.62 memory used=5434.4MB, alloc=492.3MB, time=72.97 memory used=5586.0MB, alloc=492.3MB, time=73.67 memory used=5690.6MB, alloc=492.3MB, time=74.83 memory used=5794.3MB, alloc=492.3MB, time=75.97 memory used=5946.3MB, alloc=516.3MB, time=77.17 memory used=6126.3MB, alloc=516.3MB, time=79.65 memory used=6213.4MB, alloc=516.3MB, time=80.07 memory used=6307.0MB, alloc=516.3MB, time=80.45 memory used=6410.5MB, alloc=516.3MB, time=81.72 memory used=6469.5MB, alloc=516.3MB, time=82.63 memory used=6540.1MB, alloc=516.3MB, time=83.79 memory used=6593.2MB, alloc=516.3MB, time=84.76 memory used=6649.1MB, alloc=516.3MB, time=85.87 memory used=6711.9MB, alloc=516.3MB, time=86.92 memory used=6756.8MB, alloc=516.3MB, time=87.74 memory used=6955.0MB, alloc=540.3MB, time=90.49 memory used=7101.4MB, alloc=540.3MB, time=92.14 memory used=7227.1MB, alloc=540.3MB, time=92.85 memory used=7375.3MB, alloc=564.3MB, time=96.22 memory used=7523.3MB, alloc=564.3MB, time=100.58 memory used=7635.5MB, alloc=564.3MB, time=101.13 memory used=7774.4MB, alloc=564.3MB, time=101.92 memory used=7919.9MB, alloc=564.3MB, time=102.68 memory used=8093.9MB, alloc=564.3MB, time=109.70 memory used=8209.9MB, alloc=564.3MB, time=110.26 memory used=8390.0MB, alloc=564.3MB, time=111.62 memory used=8604.9MB, alloc=564.3MB, time=113.98 memory used=8781.8MB, alloc=564.3MB, time=115.66 memory used=9010.7MB, alloc=588.3MB, time=118.08 memory used=9158.5MB, alloc=588.3MB, time=120.59 memory used=9337.4MB, alloc=612.3MB, time=123.21 memory used=9547.8MB, alloc=612.3MB, time=125.38 memory used=9735.0MB, alloc=612.3MB, time=128.91 memory used=9866.3MB, alloc=612.3MB, time=129.68 memory used=10050.8MB, alloc=612.3MB, time=130.76 memory used=10238.7MB, alloc=612.3MB, time=131.86 memory used=10454.0MB, alloc=612.3MB, time=161.03 memory used=10611.2MB, alloc=612.3MB, time=161.92 memory used=10730.2MB, alloc=612.3MB, time=162.68 memory used=10864.3MB, alloc=612.3MB, time=163.43 memory used=11006.5MB, alloc=612.3MB, time=164.20 memory used=11110.2MB, alloc=612.3MB, time=164.84 memory used=11288.2MB, alloc=612.3MB, time=165.90 memory used=11476.7MB, alloc=612.3MB, time=166.99 memory used=11695.4MB, alloc=612.3MB, time=196.15 memory used=11850.1MB, alloc=612.3MB, time=197.02 memory used=11967.6MB, alloc=612.3MB, time=197.74 memory used=12101.9MB, alloc=612.3MB, time=198.54 memory used=12242.5MB, alloc=612.3MB, time=199.25 memory used=12346.2MB, alloc=612.3MB, time=199.94 memory used=12539.1MB, alloc=612.3MB, time=202.14 memory used=12706.2MB, alloc=612.3MB, time=204.28 memory used=12856.3MB, alloc=636.3MB, time=206.51 memory used=12997.8MB, alloc=636.3MB, time=208.45 memory used=13170.6MB, alloc=636.3MB, time=211.57 memory used=13311.9MB, alloc=636.3MB, time=213.61 memory used=13504.6MB, alloc=636.3MB, 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used=70514.7MB, alloc=1011.8MB, time=1225.55 memory used=70678.9MB, alloc=1011.8MB, time=1227.21 memory used=70845.1MB, alloc=1011.8MB, time=1228.90 memory used=71014.9MB, alloc=1011.8MB, time=1230.59 memory used=71192.9MB, alloc=1011.8MB, time=1232.30 memory used=71377.0MB, alloc=1011.8MB, time=1234.02 memory used=71561.0MB, alloc=1011.8MB, time=1235.74 memory used=71754.9MB, alloc=1011.8MB, time=1237.46 memory used=71954.4MB, alloc=1011.8MB, time=1239.15 memory used=72156.2MB, alloc=1011.8MB, time=1240.86 memory used=72317.6MB, alloc=1011.8MB, time=1242.53 memory used=72474.1MB, alloc=1011.8MB, time=1244.24 memory used=72635.9MB, alloc=1011.8MB, time=1245.91 memory used=72800.2MB, alloc=1011.8MB, time=1247.59 memory used=72967.6MB, alloc=1011.8MB, time=1249.25 memory used=73138.9MB, alloc=1011.8MB, time=1250.96 memory used=73316.9MB, alloc=1011.8MB, time=1252.68 memory used=73497.7MB, alloc=1011.8MB, time=1254.39 memory used=73685.7MB, alloc=1011.8MB, time=1256.08 memory 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used=80119.3MB, alloc=1339.8MB, time=1306.39 memory used=80740.5MB, alloc=1339.8MB, time=1308.75 memory used=80938.6MB, alloc=1339.8MB, time=1310.61 memory used=81148.7MB, alloc=1339.8MB, time=1312.46 memory used=81361.4MB, alloc=1339.8MB, time=1314.31 memory used=81582.6MB, alloc=1339.8MB, time=1316.15 memory used=81814.4MB, alloc=1339.8MB, time=1317.96 memory used=82054.6MB, alloc=1339.8MB, time=1319.80 memory used=82305.7MB, alloc=1339.8MB, time=1321.61 memory used=82944.8MB, alloc=1339.8MB, time=1325.54 memory used=83230.7MB, alloc=1339.8MB, time=1327.68 memory used=83532.7MB, alloc=1339.8MB, time=1329.76 memory used=83897.7MB, alloc=1339.8MB, time=1331.98 memory used=84243.5MB, alloc=1339.8MB, time=1334.16 memory used=84466.7MB, alloc=1339.8MB, time=1336.02 memory used=84712.3MB, alloc=1339.8MB, time=1337.89 memory used=84970.7MB, alloc=1339.8MB, time=1339.80 memory used=85247.1MB, alloc=1339.8MB, time=1341.70 memory used=85549.7MB, alloc=1339.8MB, time=1343.62 memory used=85873.4MB, alloc=1339.8MB, time=1345.54 memory used=86214.1MB, alloc=1339.8MB, time=1347.51 memory used=86582.3MB, alloc=1339.8MB, time=1349.46 memory used=86975.8MB, alloc=1339.8MB, time=1351.41 memory used=87547.1MB, alloc=1339.8MB, time=1353.68 memory used=87745.1MB, alloc=1339.8MB, time=1355.54 memory used=87955.0MB, alloc=1339.8MB, time=1357.37 memory used=88167.7MB, alloc=1339.8MB, time=1359.19 memory used=88388.9MB, alloc=1339.8MB, time=1361.03 memory used=88620.8MB, alloc=1339.8MB, time=1362.87 memory used=88860.9MB, alloc=1339.8MB, time=1364.75 memory used=89112.0MB, alloc=1339.8MB, time=1366.61 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428468966 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 4 2 2 2 2 2 F := [9 x + 10 x z + 19 x, -18 z + 5 x z, 20 x y - 13 x - 6 y ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 4 2 2 2 2 3 G := [-x z - 5 y , -17 x + 2 x y - 17 x y , -8 x y z - 14 x + 11 y z] > Problem := [F,G]; 4 2 4 2 2 2 2 2 Problem := [[9 x + 10 x z + 19 x, -18 z + 5 x z, 20 x y - 13 x - 6 y ], 2 3 4 2 2 2 2 3 [-x z - 5 y , -17 x + 2 x y - 17 x y , -8 x y z - 14 x + 11 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.5MB, alloc=32.3MB, time=0.50 memory used=47.4MB, alloc=32.3MB, time=0.80 memory used=67.3MB, alloc=56.3MB, time=1.11 memory used=107.8MB, alloc=60.3MB, time=1.70 memory used=148.8MB, alloc=60.3MB, time=2.29 memory used=189.5MB, alloc=84.3MB, time=2.89 memory used=224.9MB, alloc=84.3MB, time=3.35 memory used=288.5MB, alloc=92.3MB, time=4.21 memory used=354.5MB, alloc=92.3MB, time=5.08 memory used=416.1MB, alloc=116.3MB, time=5.97 memory used=482.7MB, alloc=372.3MB, time=6.90 memory used=570.1MB, alloc=372.3MB, time=8.11 memory used=656.3MB, alloc=396.3MB, time=9.31 memory used=772.8MB, alloc=396.3MB, time=10.83 memory used=874.5MB, alloc=396.3MB, time=11.76 memory used=955.6MB, alloc=396.3MB, time=13.41 memory used=1058.9MB, alloc=420.3MB, time=14.65 memory used=1209.2MB, alloc=420.3MB, time=16.49 memory used=1313.8MB, alloc=420.3MB, time=17.45 memory used=1401.8MB, alloc=420.3MB, time=18.12 memory used=1544.0MB, alloc=420.3MB, time=21.27 memory used=1634.1MB, alloc=420.3MB, time=21.78 memory used=1685.6MB, alloc=420.3MB, time=21.99 memory used=1801.3MB, alloc=420.3MB, time=23.09 memory used=1887.1MB, alloc=420.3MB, time=23.55 memory used=2001.5MB, alloc=420.3MB, time=27.24 memory used=2066.6MB, alloc=420.3MB, time=27.51 memory used=2112.8MB, alloc=420.3MB, time=27.75 memory used=2169.1MB, alloc=420.3MB, time=27.99 memory used=2237.5MB, alloc=420.3MB, time=28.22 memory used=2286.6MB, alloc=420.3MB, time=28.43 memory used=2331.3MB, alloc=420.3MB, time=28.62 memory used=2405.3MB, alloc=420.3MB, time=28.94 memory used=2516.0MB, alloc=420.3MB, time=32.50 memory used=2580.6MB, alloc=420.3MB, time=32.75 memory used=2627.7MB, alloc=420.3MB, time=32.97 memory used=2684.9MB, alloc=420.3MB, time=33.22 memory used=2755.2MB, alloc=420.3MB, time=33.45 memory used=2800.8MB, alloc=420.3MB, time=33.65 memory used=2846.4MB, alloc=420.3MB, time=33.84 memory used=2965.4MB, alloc=420.3MB, time=34.79 memory used=3103.2MB, alloc=444.3MB, time=70.74 memory used=3194.0MB, alloc=444.3MB, time=72.18 memory used=3279.3MB, alloc=444.3MB, time=72.50 memory used=3335.0MB, alloc=444.3MB, time=72.77 memory used=3398.2MB, alloc=444.3MB, time=73.03 memory used=3471.2MB, alloc=444.3MB, time=73.30 memory used=3553.8MB, alloc=444.3MB, time=73.57 memory used=3645.9MB, alloc=444.3MB, time=73.87 memory used=3696.5MB, alloc=444.3MB, time=74.10 memory used=3749.6MB, alloc=444.3MB, time=74.32 memory used=3805.3MB, alloc=444.3MB, time=74.54 memory used=3864.2MB, alloc=444.3MB, time=74.77 memory used=3926.2MB, alloc=444.3MB, time=74.99 memory used=3992.1MB, alloc=444.3MB, time=75.22 memory used=4062.7MB, alloc=444.3MB, time=75.46 memory used=4138.5MB, alloc=444.3MB, time=75.70 memory used=4218.8MB, alloc=444.3MB, time=75.94 memory used=4306.2MB, alloc=444.3MB, time=76.19 memory used=4503.8MB, alloc=444.3MB, time=77.78 memory used=4650.9MB, alloc=444.3MB, time=79.64 memory used=4775.7MB, alloc=444.3MB, time=80.69 memory used=4912.5MB, alloc=444.3MB, time=82.32 memory used=5028.1MB, alloc=468.3MB, time=83.95 memory used=5174.5MB, alloc=468.3MB, time=85.18 memory used=5275.9MB, alloc=468.3MB, time=86.55 memory used=5379.2MB, alloc=468.3MB, time=87.20 memory used=5447.1MB, alloc=468.3MB, time=87.55 memory used=5523.5MB, alloc=468.3MB, time=87.90 memory used=5609.9MB, alloc=468.3MB, time=88.24 memory used=5667.1MB, alloc=468.3MB, time=88.52 memory used=5766.2MB, alloc=468.3MB, time=91.61 memory used=5847.6MB, alloc=468.3MB, time=91.97 memory used=5910.6MB, alloc=468.3MB, time=92.26 memory used=5982.3MB, alloc=468.3MB, time=92.56 memory used=6119.1MB, alloc=468.3MB, time=93.47 memory used=6241.6MB, alloc=468.3MB, time=95.11 memory used=6347.6MB, alloc=468.3MB, time=96.56 memory used=6474.7MB, alloc=492.3MB, time=97.86 memory used=6581.1MB, alloc=492.3MB, time=99.09 memory used=6694.4MB, alloc=492.3MB, time=100.08 memory used=6774.5MB, alloc=492.3MB, time=101.20 memory used=6857.5MB, alloc=492.3MB, time=102.14 memory used=7018.8MB, alloc=516.3MB, time=103.61 memory used=7176.3MB, alloc=516.3MB, time=104.62 memory used=7301.8MB, alloc=516.3MB, time=105.83 memory used=7417.5MB, alloc=516.3MB, time=107.75 memory used=7595.1MB, alloc=516.3MB, time=109.33 memory used=7719.6MB, alloc=516.3MB, time=111.08 memory used=7851.7MB, alloc=516.3MB, time=112.83 memory used=7975.5MB, alloc=516.3MB, time=114.51 memory used=8100.2MB, alloc=516.3MB, time=116.73 memory used=8224.4MB, alloc=540.3MB, time=119.22 memory used=8341.9MB, alloc=564.3MB, time=121.58 memory used=8483.0MB, alloc=588.3MB, time=124.32 memory used=8643.2MB, alloc=612.3MB, time=127.17 memory used=8800.3MB, alloc=612.3MB, time=130.01 memory used=8967.8MB, alloc=636.3MB, time=132.96 memory used=9147.6MB, alloc=660.3MB, time=136.01 memory used=9302.9MB, alloc=684.3MB, time=138.75 memory used=9435.7MB, alloc=684.3MB, time=141.18 memory used=9558.1MB, alloc=708.3MB, time=143.62 memory used=9655.1MB, alloc=708.3MB, time=145.79 memory used=9765.6MB, alloc=732.3MB, time=148.13 memory used=9877.8MB, alloc=756.3MB, time=151.54 memory used=10174.0MB, alloc=780.3MB, time=161.88 memory used=10468.3MB, alloc=804.3MB, time=172.91 memory used=10771.0MB, alloc=828.3MB, time=184.67 memory used=11084.9MB, alloc=852.3MB, time=197.20 memory used=11402.2MB, alloc=876.3MB, time=210.81 memory used=11740.1MB, alloc=900.3MB, time=225.33 memory used=12102.0MB, alloc=924.3MB, time=241.24 memory used=12487.7MB, alloc=948.3MB, time=257.80 memory used=12897.4MB, alloc=972.3MB, time=275.15 memory used=13331.0MB, alloc=972.3MB, time=293.53 memory used=13764.6MB, alloc=972.3MB, time=311.76 memory used=14198.2MB, alloc=972.3MB, time=330.21 memory used=14631.8MB, alloc=996.3MB, time=348.62 memory used=15089.2MB, alloc=996.3MB, time=368.08 memory used=15546.6MB, alloc=996.3MB, time=387.54 memory used=16004.0MB, alloc=1020.3MB, time=406.89 memory used=16485.3MB, alloc=1020.3MB, time=427.20 memory used=16966.6MB, alloc=1020.3MB, time=447.36 memory used=17447.9MB, alloc=1044.3MB, time=467.53 memory used=17953.1MB, alloc=1044.3MB, time=488.71 memory used=18458.3MB, alloc=1068.3MB, time=509.80 memory used=18987.4MB, alloc=1068.3MB, time=531.94 memory used=19516.4MB, alloc=1092.3MB, time=554.19 memory used=20069.7MB, alloc=1116.3MB, time=577.32 memory used=20647.1MB, alloc=1140.3MB, time=601.46 N1 := 18957 > GB := Basis(F, plex(op(vars))); 13 10 9 7 6 4 GB := [59049 x + 498636 x + 22500 x + 1579014 x + 47500 x + 2222316 x 12 11 + 1172889 x, 797652049384448100000 x - 132861972577428000000 x 10 9 + 239295614815334430000 x + 6695869825251000000000 x 8 7 - 746219943084541671000 x + 1958135291205300000000 x 6 5 + 21105940670984694098700 x - 2323742369532068000000 x 4 3 + 6224905815625408229610 x + 29322605172421200000000 x 2 2 - 3132804084714729531117 x + 22929083148180192677946 y 12 9 8 6 + 8796781551726360000000 x, -59049 x - 498636 x - 22500 x - 1579014 x 5 3 4 4 - 47500 x - 1666737 x + 617310 x z, 9 x + 36 z + 19 x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=21223.8MB, alloc=1140.3MB, time=611.11 memory used=21739.6MB, alloc=1140.3MB, time=615.41 memory used=22051.3MB, alloc=1155.8MB, time=617.01 memory used=22271.6MB, alloc=1155.8MB, time=618.52 memory used=22910.8MB, alloc=1155.8MB, time=623.96 memory used=23285.7MB, alloc=1155.8MB, time=626.13 memory used=23539.2MB, alloc=1155.8MB, time=628.01 memory used=24303.2MB, alloc=1155.8MB, time=636.66 memory used=24804.7MB, alloc=1155.8MB, time=640.95 memory used=25359.4MB, alloc=1155.8MB, time=645.78 memory used=25995.0MB, alloc=1155.8MB, time=651.93 memory used=26447.6MB, alloc=1155.8MB, time=654.68 memory used=26722.9MB, alloc=1155.8MB, time=656.68 memory used=26842.0MB, alloc=1155.8MB, time=658.32 memory used=27092.6MB, alloc=1155.8MB, time=660.39 memory used=27244.4MB, alloc=1155.8MB, time=662.11 memory used=27638.0MB, alloc=1155.8MB, time=665.77 memory used=27779.4MB, alloc=1155.8MB, time=667.42 memory used=27923.9MB, alloc=1155.8MB, time=669.03 memory used=28085.7MB, alloc=1155.8MB, time=670.63 memory used=28286.8MB, alloc=1155.8MB, time=672.50 memory used=28436.4MB, alloc=1155.8MB, time=674.15 memory used=28590.4MB, alloc=1155.8MB, time=675.81 memory used=28747.3MB, alloc=1155.8MB, time=677.42 memory used=28956.6MB, alloc=1155.8MB, time=679.34 memory used=29104.9MB, alloc=1155.8MB, time=680.95 memory used=29268.9MB, alloc=1155.8MB, time=682.56 memory used=29467.0MB, alloc=1155.8MB, time=684.38 memory used=29616.7MB, alloc=1155.8MB, time=686.01 memory used=29772.4MB, alloc=1155.8MB, time=687.65 memory used=30002.7MB, alloc=1155.8MB, time=689.62 memory used=30135.7MB, alloc=1155.8MB, time=691.23 memory used=30282.4MB, alloc=1155.8MB, time=692.86 memory used=30446.6MB, alloc=1155.8MB, time=694.50 memory used=30650.3MB, alloc=1155.8MB, time=696.38 memory used=30799.1MB, alloc=1155.8MB, time=698.02 memory used=30947.9MB, alloc=1155.8MB, time=699.63 memory used=31106.2MB, alloc=1155.8MB, time=701.24 memory used=31314.5MB, alloc=1155.8MB, time=703.14 memory used=31463.6MB, alloc=1155.8MB, time=704.77 memory used=31629.0MB, alloc=1155.8MB, time=706.37 memory used=31848.5MB, alloc=1155.8MB, time=708.46 memory used=32079.0MB, alloc=1155.8MB, time=710.60 memory used=32222.8MB, alloc=1155.8MB, time=712.20 memory used=32445.9MB, alloc=1155.8MB, time=714.31 memory used=32684.8MB, alloc=1155.8MB, time=717.48 memory used=33020.3MB, alloc=1155.8MB, time=722.71 memory used=33452.4MB, alloc=1155.8MB, time=725.22 memory used=33522.2MB, alloc=1155.8MB, time=726.69 memory used=33593.1MB, alloc=1155.8MB, time=728.20 memory used=33681.1MB, alloc=1155.8MB, time=729.70 memory used=33760.4MB, alloc=1155.8MB, time=731.20 memory used=33857.8MB, alloc=1155.8MB, time=732.73 memory used=33943.8MB, alloc=1155.8MB, time=734.22 memory used=34047.6MB, alloc=1155.8MB, time=735.79 memory used=34140.2MB, alloc=1155.8MB, time=737.32 memory used=34250.3MB, alloc=1155.8MB, time=738.92 memory used=34350.6MB, alloc=1155.8MB, time=740.46 memory used=34465.7MB, alloc=1155.8MB, time=742.03 memory used=34572.0MB, alloc=1155.8MB, time=743.60 memory used=34693.5MB, alloc=1155.8MB, time=745.20 memory used=34829.1MB, alloc=1155.8MB, time=746.82 memory used=34968.7MB, alloc=1155.8MB, time=748.48 memory used=35112.1MB, alloc=1155.8MB, time=750.11 memory used=35256.5MB, alloc=1155.8MB, time=751.77 memory used=35356.7MB, alloc=1155.8MB, time=753.30 memory used=35429.6MB, alloc=1155.8MB, time=754.78 memory used=35498.4MB, alloc=1155.8MB, time=756.28 memory used=35576.2MB, alloc=1155.8MB, time=757.78 memory used=35654.9MB, alloc=1155.8MB, time=759.29 memory used=35734.6MB, alloc=1155.8MB, time=760.76 memory used=35815.1MB, alloc=1155.8MB, time=762.28 memory used=35896.6MB, alloc=1155.8MB, time=763.77 memory used=35978.9MB, alloc=1155.8MB, time=765.25 memory used=36062.1MB, alloc=1155.8MB, time=766.74 memory used=36146.3MB, alloc=1155.8MB, time=768.25 memory used=36231.3MB, alloc=1155.8MB, time=769.75 memory used=36317.1MB, alloc=1155.8MB, time=771.24 memory used=36403.8MB, alloc=1155.8MB, time=772.72 memory used=36491.4MB, alloc=1155.8MB, time=774.21 memory used=36579.9MB, alloc=1155.8MB, time=775.74 memory used=36669.2MB, alloc=1155.8MB, time=777.25 memory used=36759.3MB, alloc=1155.8MB, time=778.72 memory used=36850.2MB, alloc=1155.8MB, time=780.26 memory used=36942.0MB, alloc=1155.8MB, time=781.78 memory used=37034.7MB, alloc=1155.8MB, time=783.31 memory used=37128.1MB, alloc=1155.8MB, time=784.77 memory used=37222.4MB, alloc=1155.8MB, time=786.32 memory used=37317.4MB, alloc=1155.8MB, time=787.84 memory used=37413.3MB, alloc=1155.8MB, time=789.36 memory used=37521.0MB, alloc=1155.8MB, time=790.91 memory 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time=820.92 memory used=39381.8MB, alloc=1155.8MB, time=822.39 memory used=39456.9MB, alloc=1155.8MB, time=823.87 memory used=39547.9MB, alloc=1155.8MB, time=825.40 memory used=39623.8MB, alloc=1155.8MB, time=826.86 memory used=39715.5MB, alloc=1155.8MB, time=828.37 memory used=39792.2MB, alloc=1155.8MB, time=829.84 memory used=39884.7MB, alloc=1155.8MB, time=831.35 memory used=39962.1MB, alloc=1155.8MB, time=832.80 memory used=40055.2MB, alloc=1155.8MB, time=834.28 memory used=40133.5MB, alloc=1155.8MB, time=835.70 memory used=40227.3MB, alloc=1155.8MB, time=837.21 memory used=40306.3MB, alloc=1155.8MB, time=838.72 memory used=40400.8MB, alloc=1155.8MB, time=840.25 memory used=40480.6MB, alloc=1155.8MB, time=841.73 memory used=40575.8MB, alloc=1155.8MB, time=843.22 memory used=40656.3MB, alloc=1155.8MB, time=844.69 memory used=40752.2MB, alloc=1155.8MB, time=846.22 memory used=40870.7MB, alloc=1155.8MB, time=847.82 memory used=40989.6MB, alloc=1155.8MB, time=849.39 memory 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used=64368.5MB, alloc=1155.8MB, time=1270.16 memory used=64478.1MB, alloc=1155.8MB, time=1271.71 memory used=64578.2MB, alloc=1155.8MB, time=1273.14 memory used=64688.7MB, alloc=1155.8MB, time=1274.57 memory used=64822.0MB, alloc=1155.8MB, time=1276.06 memory used=64926.1MB, alloc=1155.8MB, time=1277.45 memory used=65037.4MB, alloc=1155.8MB, time=1278.93 memory used=65166.6MB, alloc=1155.8MB, time=1280.45 memory used=65260.5MB, alloc=1155.8MB, time=1281.85 memory used=65360.6MB, alloc=1155.8MB, time=1283.26 memory used=65485.1MB, alloc=1155.8MB, time=1285.39 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428470166 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 2 2 F := [-18 x z + 15 y z + 10 x z , 20 x z - 5 x z + 9, 4 3 2 7 x - 19 x y - 10 z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 3 2 3 G := [6 x z + 6 y z + y z, -6 x z + 15 x y - 8 x y, -5 z + 14 y z + 19] > Problem := [F,G]; 2 2 2 2 2 2 2 Problem := [[-18 x z + 15 y z + 10 x z , 20 x z - 5 x z + 9, 4 3 2 7 x - 19 x y - 10 z ], 2 2 3 2 2 3 2 3 [6 x z + 6 y z + y z, -6 x z + 15 x y - 8 x y, -5 z + 14 y z + 19]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.17 memory used=26.4MB, alloc=32.3MB, time=0.49 memory used=45.6MB, alloc=56.3MB, time=0.76 memory used=84.4MB, alloc=60.3MB, time=1.06 memory used=124.9MB, alloc=60.3MB, time=1.42 memory used=165.7MB, alloc=60.3MB, time=1.97 memory used=206.2MB, alloc=60.3MB, time=2.35 memory used=246.6MB, alloc=60.3MB, time=2.76 memory used=289.4MB, alloc=68.3MB, time=3.33 memory used=314.3MB, alloc=68.3MB, time=3.49 memory used=339.5MB, alloc=68.3MB, time=3.62 memory used=366.3MB, alloc=68.3MB, time=3.92 memory used=407.3MB, alloc=68.3MB, time=4.29 memory used=428.5MB, alloc=68.3MB, time=4.36 memory used=446.3MB, alloc=92.3MB, time=4.44 memory used=482.3MB, alloc=92.3MB, time=4.53 memory used=525.2MB, alloc=92.3MB, time=4.63 memory used=552.4MB, alloc=92.3MB, time=4.72 memory used=583.6MB, alloc=92.3MB, time=4.79 memory used=620.7MB, alloc=92.3MB, time=4.86 memory used=682.1MB, alloc=92.3MB, time=5.33 memory used=750.1MB, alloc=92.3MB, time=5.83 memory used=784.8MB, alloc=92.3MB, time=5.92 memory used=846.2MB, alloc=92.3MB, time=6.73 memory used=908.4MB, alloc=92.3MB, time=7.59 memory used=969.7MB, alloc=116.3MB, time=8.31 memory used=1041.8MB, alloc=116.3MB, time=8.76 memory used=1106.4MB, alloc=117.1MB, time=9.45 memory used=1148.7MB, alloc=117.1MB, time=9.60 memory used=1195.0MB, alloc=117.1MB, time=9.74 memory used=1272.9MB, alloc=117.1MB, time=10.50 memory used=1341.6MB, alloc=373.1MB, time=11.33 memory used=1424.9MB, alloc=373.1MB, time=12.48 memory used=1513.2MB, alloc=397.1MB, time=13.58 memory used=1609.1MB, alloc=397.1MB, time=14.47 memory used=1712.7MB, alloc=397.1MB, time=15.57 memory used=1810.2MB, alloc=397.1MB, time=16.40 memory used=1920.2MB, alloc=421.1MB, time=17.82 memory used=2007.8MB, alloc=421.1MB, time=19.28 memory used=2091.7MB, alloc=421.1MB, time=19.72 memory used=2142.8MB, alloc=421.1MB, time=19.95 memory used=2205.9MB, alloc=445.1MB, time=20.21 memory used=2263.2MB, alloc=445.1MB, time=20.43 memory used=2332.3MB, alloc=445.1MB, time=20.65 memory used=2436.1MB, alloc=445.1MB, time=20.92 memory used=2550.2MB, alloc=445.1MB, time=22.34 memory used=2622.2MB, alloc=445.1MB, time=22.61 memory used=2702.8MB, alloc=445.1MB, time=22.87 memory used=2761.5MB, alloc=445.1MB, time=23.08 memory used=2831.7MB, alloc=445.1MB, time=23.29 memory used=2942.1MB, alloc=445.1MB, time=23.59 memory used=3044.1MB, alloc=445.1MB, time=25.80 memory used=3114.8MB, alloc=445.1MB, time=26.07 memory used=3194.2MB, alloc=445.1MB, time=26.29 memory used=3251.9MB, alloc=445.1MB, time=26.48 memory used=3321.1MB, alloc=445.1MB, time=26.69 memory used=3402.9MB, alloc=445.1MB, time=26.91 memory used=3569.4MB, alloc=445.1MB, time=29.63 memory used=3653.0MB, alloc=445.1MB, time=30.18 memory used=3726.9MB, alloc=445.1MB, time=30.45 memory used=3791.1MB, alloc=445.1MB, time=30.68 memory used=3850.6MB, alloc=445.1MB, time=30.89 memory used=3920.4MB, alloc=445.1MB, time=31.14 memory used=4002.3MB, alloc=445.1MB, time=31.38 memory used=4170.8MB, alloc=445.1MB, time=32.96 memory used=4278.0MB, alloc=445.1MB, time=34.19 memory used=4378.0MB, alloc=469.1MB, time=35.55 memory used=4481.0MB, alloc=469.1MB, time=37.02 memory used=4575.6MB, alloc=469.1MB, time=38.37 memory used=4693.9MB, alloc=469.1MB, time=39.70 memory used=4779.1MB, alloc=469.1MB, time=40.77 memory used=4867.7MB, alloc=469.1MB, time=41.95 memory used=4957.2MB, alloc=493.1MB, time=43.03 memory used=5041.4MB, alloc=493.1MB, time=44.03 memory used=5172.1MB, alloc=493.1MB, time=45.68 memory used=5260.1MB, alloc=493.1MB, time=46.12 memory used=5356.8MB, alloc=493.1MB, time=46.56 memory used=5489.5MB, alloc=493.1MB, time=48.15 memory used=5576.1MB, alloc=493.1MB, time=48.54 memory used=5674.3MB, alloc=493.1MB, time=49.00 memory used=5792.6MB, alloc=493.1MB, time=51.00 memory used=5884.9MB, alloc=493.1MB, time=51.40 memory used=5998.5MB, alloc=493.1MB, time=52.35 memory used=6109.2MB, alloc=493.1MB, time=53.06 memory used=6213.2MB, alloc=493.1MB, time=54.02 memory used=6333.6MB, alloc=493.1MB, time=54.98 memory used=6447.6MB, alloc=493.1MB, time=55.62 memory used=6552.7MB, alloc=493.1MB, time=56.50 memory used=6622.3MB, alloc=493.1MB, time=57.43 memory used=6689.9MB, alloc=493.1MB, time=58.35 memory used=6774.1MB, alloc=493.1MB, time=59.30 memory used=6884.6MB, alloc=493.1MB, time=60.33 memory used=6987.5MB, alloc=493.1MB, time=61.47 memory used=7054.2MB, alloc=493.1MB, time=62.38 memory used=7111.8MB, alloc=493.1MB, time=63.21 memory used=7190.0MB, alloc=493.1MB, time=64.33 memory used=7244.8MB, alloc=493.1MB, time=65.41 memory used=7292.6MB, alloc=493.1MB, time=66.33 memory used=7346.5MB, alloc=493.1MB, time=67.38 memory used=7390.9MB, alloc=493.1MB, time=68.25 memory used=7586.5MB, alloc=517.1MB, time=70.65 memory used=7767.4MB, alloc=541.1MB, time=73.01 memory used=7952.6MB, alloc=565.1MB, time=76.11 memory used=8121.0MB, alloc=589.1MB, time=78.47 memory used=8267.8MB, alloc=589.1MB, time=80.69 memory used=8428.8MB, alloc=613.1MB, time=83.05 memory used=8593.6MB, alloc=613.1MB, time=84.62 memory used=8730.0MB, alloc=613.1MB, time=85.36 memory used=8890.4MB, alloc=613.1MB, time=87.04 memory used=9062.9MB, alloc=613.1MB, time=88.37 memory used=9228.8MB, alloc=613.1MB, time=89.52 memory used=9418.2MB, alloc=613.1MB, time=92.09 memory used=9655.6MB, alloc=637.1MB, time=96.68 memory used=9838.0MB, alloc=637.1MB, time=97.97 memory used=10000.4MB, alloc=637.1MB, time=98.94 memory used=10140.5MB, alloc=637.1MB, time=99.68 memory used=10307.4MB, alloc=637.1MB, time=100.65 memory used=10482.5MB, alloc=637.1MB, time=102.85 memory used=10639.6MB, alloc=637.1MB, time=103.69 memory used=10769.2MB, alloc=637.1MB, time=104.42 memory used=10921.1MB, alloc=637.1MB, time=105.13 memory used=11296.5MB, alloc=637.1MB, time=107.65 memory used=11598.4MB, alloc=637.1MB, time=110.78 memory used=11871.3MB, alloc=637.1MB, time=114.58 memory used=12031.1MB, alloc=637.1MB, time=115.88 memory used=12267.2MB, alloc=637.1MB, time=119.78 memory used=12462.0MB, alloc=637.1MB, time=121.74 memory used=12619.2MB, alloc=637.1MB, time=122.66 memory used=12769.4MB, alloc=637.1MB, time=123.65 memory used=12914.5MB, alloc=637.1MB, time=124.46 memory used=13069.2MB, alloc=637.1MB, time=125.37 memory used=13243.1MB, alloc=637.1MB, time=127.55 memory used=13393.4MB, alloc=637.1MB, time=128.37 memory used=13512.8MB, alloc=637.1MB, time=129.08 memory used=13657.0MB, alloc=637.1MB, time=129.82 memory used=13971.2MB, alloc=637.1MB, time=131.95 memory used=14171.9MB, alloc=637.1MB, time=134.65 memory used=14280.6MB, alloc=637.1MB, time=137.10 memory used=14460.7MB, alloc=661.1MB, time=140.49 memory used=14588.5MB, alloc=661.1MB, time=142.19 memory used=14707.4MB, alloc=661.1MB, time=144.21 memory used=14825.4MB, alloc=661.1MB, time=146.22 memory used=14972.1MB, alloc=661.1MB, time=148.29 memory used=15083.8MB, alloc=661.1MB, time=150.01 memory used=15220.7MB, alloc=661.1MB, time=152.45 memory used=15421.2MB, alloc=661.1MB, time=154.11 memory used=15565.6MB, alloc=661.1MB, time=155.01 memory used=15733.2MB, alloc=661.1MB, time=156.36 memory used=15922.7MB, alloc=661.1MB, time=161.00 memory used=16073.1MB, alloc=661.1MB, time=161.99 memory used=16197.2MB, alloc=661.1MB, time=162.91 memory used=16355.6MB, alloc=661.1MB, time=163.82 memory used=16606.8MB, alloc=661.1MB, time=164.93 memory used=16745.1MB, alloc=661.1MB, time=165.90 memory used=16901.9MB, alloc=661.1MB, time=166.85 memory used=17082.4MB, alloc=661.1MB, time=167.79 memory used=17356.9MB, alloc=685.1MB, time=170.36 memory used=17604.3MB, alloc=685.1MB, time=172.67 memory used=17772.3MB, alloc=685.1MB, time=173.78 memory used=17930.7MB, alloc=685.1MB, time=174.75 memory used=18115.4MB, alloc=685.1MB, time=175.90 memory used=18291.0MB, alloc=685.1MB, time=177.90 memory used=18453.0MB, alloc=685.1MB, time=178.92 memory used=18617.4MB, alloc=685.1MB, time=179.86 memory used=18808.9MB, alloc=685.1MB, time=180.80 memory used=19303.6MB, alloc=685.1MB, time=186.19 memory used=19539.6MB, alloc=685.1MB, time=188.25 memory used=19861.2MB, alloc=709.1MB, time=191.39 memory used=20128.9MB, alloc=709.1MB, time=193.96 memory used=20507.3MB, alloc=733.1MB, time=199.18 memory used=20817.9MB, alloc=733.1MB, time=201.91 memory used=21002.1MB, alloc=733.1MB, time=203.25 memory used=21175.1MB, alloc=733.1MB, time=204.51 memory used=21367.2MB, alloc=733.1MB, time=205.82 memory used=21564.7MB, alloc=733.1MB, time=208.63 memory used=21727.9MB, alloc=733.1MB, time=209.78 memory used=21908.2MB, alloc=733.1MB, time=210.85 memory used=22343.9MB, alloc=733.1MB, time=216.15 memory used=22518.0MB, alloc=733.1MB, time=217.30 memory used=22696.6MB, alloc=733.1MB, time=218.65 memory used=22886.3MB, alloc=733.1MB, time=219.95 memory used=23084.6MB, alloc=733.1MB, time=222.51 memory used=23251.7MB, alloc=733.1MB, time=223.56 memory used=23420.2MB, alloc=733.1MB, time=224.58 memory used=23870.2MB, alloc=757.1MB, time=228.50 memory used=24369.5MB, alloc=757.1MB, time=234.22 memory used=24762.8MB, alloc=781.1MB, time=241.53 memory used=25153.3MB, alloc=805.1MB, time=247.55 memory used=25639.1MB, alloc=829.1MB, time=254.50 memory used=26082.1MB, alloc=853.1MB, time=259.32 memory used=26472.6MB, alloc=877.1MB, time=264.46 memory used=26882.7MB, alloc=901.1MB, time=269.37 memory used=27218.1MB, alloc=925.1MB, time=273.44 memory used=27502.1MB, alloc=949.1MB, time=278.91 memory used=27788.1MB, alloc=973.1MB, time=283.21 memory used=28037.4MB, alloc=997.1MB, time=287.36 memory used=28302.9MB, alloc=1021.1MB, time=289.50 memory used=28550.5MB, alloc=1045.1MB, time=291.37 memory used=28860.6MB, alloc=1069.1MB, time=293.73 memory used=29149.2MB, alloc=1093.1MB, time=295.81 memory used=29592.2MB, alloc=1093.1MB, time=312.27 memory used=29885.4MB, alloc=1093.1MB, time=314.34 memory used=30229.7MB, alloc=1093.1MB, time=316.36 memory used=30380.9MB, alloc=1107.8MB, time=318.22 memory used=30504.9MB, alloc=1107.8MB, time=320.02 memory used=30647.9MB, alloc=1107.8MB, time=321.85 memory used=31092.4MB, alloc=1107.8MB, time=324.47 memory used=31420.5MB, alloc=1107.8MB, time=326.70 memory used=31767.1MB, alloc=1107.8MB, time=328.99 memory used=32166.2MB, alloc=1107.8MB, time=345.34 memory used=32501.5MB, alloc=1107.8MB, time=347.63 memory used=32802.9MB, alloc=1107.8MB, time=349.61 memory used=33089.1MB, alloc=1107.8MB, time=351.57 memory used=33212.8MB, alloc=1107.8MB, time=353.27 memory used=33355.8MB, alloc=1107.8MB, time=355.02 memory used=33793.7MB, alloc=1107.8MB, time=357.68 memory used=34096.1MB, alloc=1107.8MB, time=359.75 memory used=34489.5MB, alloc=1107.8MB, time=377.66 memory used=34782.2MB, alloc=1107.8MB, time=379.81 memory used=35113.5MB, alloc=1107.8MB, time=381.90 memory used=35318.2MB, alloc=1107.8MB, time=383.78 memory used=35440.3MB, alloc=1107.8MB, time=385.59 memory used=35576.9MB, alloc=1107.8MB, time=387.42 memory used=35735.5MB, alloc=1107.8MB, time=389.25 memory used=36055.5MB, alloc=1107.8MB, time=394.16 memory used=36396.6MB, alloc=1363.8MB, time=413.21 memory used=36689.0MB, alloc=1363.8MB, time=415.36 memory used=37003.3MB, alloc=1363.8MB, time=417.46 memory used=37340.5MB, alloc=1363.8MB, time=419.64 memory used=37555.2MB, alloc=1363.8MB, time=421.67 memory used=38549.1MB, alloc=1387.8MB, time=431.47 memory used=39311.0MB, alloc=1411.8MB, time=442.37 memory used=40068.2MB, alloc=1435.8MB, time=452.89 memory used=40831.0MB, alloc=1459.8MB, time=464.18 memory used=41512.6MB, alloc=1483.8MB, time=475.33 memory used=42264.9MB, alloc=1507.8MB, time=487.12 memory used=42824.2MB, alloc=1531.8MB, time=496.42 memory used=43441.6MB, alloc=1555.8MB, time=506.29 memory used=44033.2MB, alloc=1579.8MB, time=517.29 memory used=44673.0MB, alloc=1603.8MB, time=526.88 memory used=44943.3MB, alloc=1627.8MB, time=531.26 memory used=45301.6MB, alloc=1651.8MB, time=536.37 memory used=45683.4MB, alloc=1675.8MB, time=553.67 memory used=46021.3MB, alloc=1699.8MB, time=558.43 memory used=46405.6MB, alloc=1723.8MB, time=563.41 memory used=46782.9MB, alloc=1747.8MB, time=568.29 memory used=47207.3MB, alloc=1771.8MB, time=573.62 memory used=47743.6MB, alloc=1795.8MB, time=591.35 memory used=48184.3MB, alloc=1819.8MB, time=596.40 memory used=48707.2MB, alloc=1843.8MB, time=614.44 memory used=49143.3MB, alloc=1867.8MB, time=619.23 memory used=49701.4MB, alloc=1891.8MB, time=624.97 memory used=50265.3MB, alloc=1915.8MB, time=632.91 memory used=50801.1MB, alloc=1939.8MB, time=641.25 memory used=51421.1MB, alloc=1963.8MB, time=649.51 memory used=52021.7MB, alloc=1987.8MB, time=655.48 memory used=52600.9MB, alloc=2011.8MB, time=666.39 memory used=53437.3MB, alloc=2035.8MB, time=678.62 memory used=53949.0MB, alloc=2059.8MB, time=687.63 memory used=54700.9MB, alloc=2083.8MB, time=698.67 memory used=55092.3MB, alloc=2083.8MB, time=707.67 memory used=55501.2MB, alloc=2083.8MB, time=716.63 memory used=55862.1MB, alloc=2107.8MB, time=726.09 memory used=56192.4MB, alloc=2107.8MB, time=736.10 memory used=56421.0MB, alloc=2107.8MB, time=743.89 memory used=56639.3MB, alloc=2107.8MB, time=751.40 memory used=56773.2MB, alloc=2107.8MB, time=758.86 memory used=57026.1MB, alloc=2107.8MB, time=766.89 memory used=57317.1MB, alloc=2131.8MB, time=775.27 memory used=57509.1MB, alloc=2131.8MB, time=782.52 memory used=57868.9MB, alloc=2155.8MB, time=790.60 memory used=58057.2MB, alloc=2179.8MB, time=798.16 memory used=58368.1MB, alloc=2203.8MB, time=806.37 memory used=58632.6MB, alloc=2203.8MB, time=814.99 memory used=58839.0MB, alloc=2203.8MB, time=821.97 memory used=59051.5MB, alloc=2203.8MB, time=829.47 memory used=59190.3MB, alloc=2203.8MB, time=836.95 memory used=59264.7MB, alloc=2203.8MB, time=843.66 memory used=59440.5MB, alloc=2227.8MB, time=851.16 memory used=59564.9MB, alloc=2227.8MB, time=858.60 memory used=59664.5MB, alloc=2227.8MB, time=865.20 memory used=59802.0MB, alloc=2227.8MB, time=872.15 memory used=59873.2MB, alloc=2227.8MB, time=879.00 memory used=60062.7MB, alloc=2227.8MB, time=886.57 memory used=60148.2MB, alloc=2227.8MB, time=893.16 memory used=60232.2MB, alloc=2227.8MB, time=900.48 memory used=60283.0MB, alloc=2227.8MB, time=907.43 memory used=60298.6MB, alloc=2227.8MB, time=913.54 memory used=60352.1MB, alloc=2227.8MB, time=919.87 memory used=60420.9MB, alloc=2227.8MB, time=926.52 memory used=60465.9MB, alloc=2227.8MB, time=933.27 memory used=60530.7MB, alloc=2227.8MB, time=940.21 memory used=60542.9MB, alloc=2227.8MB, time=946.35 memory used=60629.1MB, alloc=2227.8MB, time=953.57 memory used=60670.8MB, alloc=2227.8MB, time=960.16 memory used=60735.2MB, alloc=2227.8MB, time=967.11 memory used=60807.2MB, alloc=2227.8MB, time=974.22 memory used=60843.0MB, alloc=2227.8MB, time=980.69 memory used=60910.0MB, alloc=2227.8MB, time=987.52 memory used=60924.1MB, alloc=2227.8MB, time=993.61 memory used=60957.3MB, alloc=2227.8MB, time=999.98 memory used=60968.6MB, alloc=2227.8MB, time=1006.29 memory used=61024.0MB, alloc=2227.8MB, time=1013.60 memory used=61055.3MB, alloc=2227.8MB, time=1020.30 memory used=61098.4MB, alloc=2227.8MB, time=1027.02 memory used=61190.4MB, alloc=2227.8MB, time=1034.07 memory used=61208.4MB, alloc=2483.8MB, time=1047.17 memory used=62457.3MB, alloc=2507.8MB, time=1073.67 memory used=63737.8MB, alloc=2531.8MB, time=1098.74 memory used=65055.2MB, alloc=2555.8MB, time=1122.75 memory used=66201.6MB, alloc=2579.8MB, time=1147.16 memory used=67382.9MB, alloc=2603.8MB, time=1169.34 memory used=68106.1MB, alloc=2627.8MB, time=1184.12 memory used=68653.6MB, alloc=2651.8MB, time=1203.52 memory used=69064.0MB, alloc=2675.8MB, time=1214.60 memory used=69719.4MB, alloc=2699.8MB, time=1226.54 memory used=70306.1MB, alloc=2723.8MB, time=1245.72 memory used=70945.3MB, alloc=2747.8MB, time=1257.32 memory used=71543.7MB, alloc=2771.8MB, time=1276.68 memory used=72305.3MB, alloc=2795.8MB, time=1289.46 memory used=72959.4MB, alloc=2819.8MB, time=1301.83 memory used=73625.0MB, alloc=2843.8MB, time=1314.48 memory used=74280.5MB, alloc=2867.8MB, time=1326.29 memory used=74945.2MB, alloc=2891.8MB, time=1337.55 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428471366 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 4 2 3 3 F := [-5 y z - 14 x y + 19 y z, -14 z + 19 x y - 3, 15 x z - 11 x z + 7 x] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 4 3 3 3 G := [-x z - 15 x y - 3 x, 3 y + 18 x y z, -17 x z - 18 x z + 14 z ] > Problem := [F,G]; Problem := [ 3 4 2 3 3 [-5 y z - 14 x y + 19 y z, -14 z + 19 x y - 3, 15 x z - 11 x z + 7 x], 3 3 4 3 3 3 [-x z - 15 x y - 3 x, 3 y + 18 x y z, -17 x z - 18 x z + 14 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.5MB, alloc=32.3MB, time=0.52 memory used=46.1MB, alloc=56.3MB, time=0.85 memory used=87.2MB, alloc=60.3MB, time=1.48 memory used=127.9MB, alloc=60.3MB, time=2.09 memory used=168.6MB, alloc=60.3MB, time=2.72 memory used=210.5MB, alloc=84.3MB, time=3.35 memory used=253.6MB, alloc=84.3MB, time=4.04 memory used=318.4MB, alloc=92.3MB, time=4.97 memory used=379.9MB, alloc=92.3MB, time=5.85 memory used=441.0MB, alloc=92.3MB, time=6.75 memory used=505.5MB, alloc=116.3MB, time=7.67 memory used=589.0MB, alloc=116.3MB, time=8.89 memory used=658.2MB, alloc=372.3MB, time=9.87 memory used=745.4MB, alloc=372.3MB, time=11.20 memory used=839.2MB, alloc=396.3MB, time=12.63 memory used=961.8MB, alloc=396.3MB, time=14.59 memory used=1133.7MB, alloc=396.3MB, time=16.87 memory used=1243.9MB, alloc=420.3MB, time=18.51 memory used=1380.7MB, alloc=420.3MB, time=20.65 memory used=1516.9MB, alloc=444.3MB, time=22.85 memory used=1674.1MB, alloc=444.3MB, time=25.75 memory used=1815.8MB, alloc=444.3MB, time=27.93 memory used=1926.4MB, alloc=468.3MB, time=29.31 memory used=2027.1MB, alloc=468.3MB, time=30.46 memory used=2121.6MB, alloc=492.3MB, time=31.54 memory used=2230.0MB, alloc=492.3MB, time=33.18 memory used=2334.8MB, alloc=492.3MB, time=34.80 memory used=2427.3MB, alloc=492.3MB, time=36.04 memory used=2538.9MB, alloc=516.3MB, time=37.23 memory used=2638.2MB, alloc=516.3MB, time=38.88 memory used=2726.9MB, alloc=516.3MB, time=40.42 memory used=2801.5MB, alloc=516.3MB, time=41.53 memory used=2871.1MB, alloc=516.3MB, time=42.44 memory used=2934.7MB, alloc=516.3MB, time=43.40 memory used=3014.1MB, alloc=540.3MB, time=44.28 memory used=3073.6MB, alloc=540.3MB, time=45.24 memory used=3143.2MB, alloc=540.3MB, time=46.60 memory used=3206.9MB, alloc=540.3MB, time=47.84 memory used=3261.9MB, alloc=540.3MB, time=48.84 memory used=3313.1MB, alloc=540.3MB, time=49.73 memory used=3364.7MB, alloc=540.3MB, time=50.59 memory used=3411.7MB, alloc=540.3MB, time=51.41 memory used=3462.3MB, alloc=540.3MB, time=52.23 memory used=3664.9MB, alloc=564.3MB, time=54.49 memory used=3844.6MB, alloc=588.3MB, time=57.55 memory used=4008.2MB, alloc=612.3MB, time=59.79 memory used=4174.6MB, alloc=636.3MB, time=61.90 memory used=4331.7MB, alloc=660.3MB, time=64.60 memory used=4490.2MB, alloc=660.3MB, time=67.31 memory used=4640.0MB, alloc=660.3MB, time=69.81 memory used=4753.4MB, alloc=660.3MB, time=71.38 memory used=4870.2MB, alloc=684.3MB, time=73.07 memory used=5004.9MB, alloc=684.3MB, time=75.11 memory used=5149.4MB, alloc=708.3MB, time=77.00 memory used=5311.1MB, alloc=732.3MB, time=78.84 memory used=5429.4MB, alloc=732.3MB, time=81.28 memory used=5543.4MB, alloc=732.3MB, time=83.55 memory used=5924.9MB, alloc=756.3MB, time=89.24 memory used=6282.0MB, alloc=780.3MB, time=95.09 memory used=6635.4MB, alloc=804.3MB, time=99.47 memory used=6956.5MB, alloc=828.3MB, time=111.73 memory used=7311.2MB, alloc=852.3MB, time=114.09 memory used=7642.4MB, alloc=876.3MB, time=119.18 memory used=7918.7MB, alloc=900.3MB, time=123.31 memory used=8226.5MB, alloc=924.3MB, time=131.61 memory used=8530.3MB, alloc=948.3MB, time=136.65 memory used=8806.8MB, alloc=972.3MB, time=140.60 memory used=9077.6MB, alloc=996.3MB, time=145.03 memory used=9360.0MB, alloc=1020.3MB, time=154.78 memory used=9633.1MB, alloc=1020.3MB, time=164.02 memory used=10260.7MB, alloc=1044.3MB, time=173.11 memory used=10911.7MB, alloc=1068.3MB, time=184.03 memory used=11590.8MB, alloc=1092.3MB, time=194.19 memory used=12180.0MB, alloc=1116.3MB, time=204.51 memory used=12880.2MB, alloc=1140.3MB, time=214.77 memory used=13577.9MB, alloc=1164.3MB, time=227.09 memory used=14223.8MB, alloc=1188.3MB, time=238.63 memory used=14861.9MB, alloc=1212.3MB, time=252.78 memory used=15509.3MB, alloc=1236.3MB, time=263.16 memory used=16170.1MB, alloc=1260.3MB, time=279.45 memory used=16700.3MB, alloc=1284.3MB, time=288.62 memory used=17230.0MB, alloc=1308.3MB, time=310.49 memory used=17603.6MB, alloc=1332.3MB, time=316.81 memory used=18018.0MB, alloc=1356.3MB, time=337.09 memory used=18648.6MB, alloc=1380.3MB, time=346.65 memory used=19300.2MB, alloc=1404.3MB, time=358.47 memory used=19783.2MB, alloc=1428.3MB, time=382.92 memory used=20418.7MB, alloc=1452.3MB, time=409.40 memory used=20907.2MB, alloc=1476.3MB, time=418.52 memory used=21551.6MB, alloc=1500.3MB, time=440.01 memory used=22209.2MB, alloc=1524.3MB, time=460.15 memory used=22520.3MB, alloc=1548.3MB, time=467.99 memory used=22869.1MB, alloc=1572.3MB, time=477.33 memory used=23136.1MB, alloc=1596.3MB, time=485.95 memory used=23445.6MB, alloc=1620.3MB, time=495.70 memory used=23709.2MB, alloc=1644.3MB, time=504.27 memory used=24003.0MB, alloc=1668.3MB, time=514.22 memory used=24239.9MB, alloc=1692.3MB, time=522.30 memory used=24483.7MB, alloc=1716.3MB, time=531.20 memory used=24688.1MB, alloc=1740.3MB, time=539.45 memory used=24889.2MB, alloc=1764.3MB, time=547.05 memory used=25075.8MB, alloc=1788.3MB, time=555.02 memory used=25195.2MB, alloc=1812.3MB, time=562.37 memory used=25368.1MB, alloc=1812.3MB, time=569.85 memory used=25542.2MB, alloc=1812.3MB, time=577.09 memory used=25734.5MB, alloc=1812.3MB, time=584.64 memory used=25933.9MB, alloc=1836.3MB, time=591.92 memory used=26015.8MB, alloc=1836.3MB, time=599.29 memory used=26170.4MB, alloc=1836.3MB, time=607.65 memory used=26303.3MB, alloc=1836.3MB, time=626.00 memory used=26684.9MB, alloc=1836.3MB, time=633.52 memory used=26834.6MB, alloc=1836.3MB, time=640.71 memory used=26949.4MB, alloc=1836.3MB, time=647.95 memory used=27094.4MB, alloc=1836.3MB, time=655.17 memory used=27301.5MB, alloc=1836.3MB, time=663.04 memory used=27464.7MB, alloc=1860.3MB, time=670.55 memory used=27615.1MB, alloc=1860.3MB, time=677.86 memory used=27722.2MB, alloc=1860.3MB, time=685.32 memory used=27741.0MB, alloc=1860.3MB, time=691.59 memory used=27825.8MB, alloc=1860.3MB, time=698.93 memory used=27960.4MB, alloc=1860.3MB, time=706.33 memory used=28031.9MB, alloc=1860.3MB, time=713.44 memory used=28107.1MB, alloc=1860.3MB, time=720.87 memory used=28216.4MB, alloc=1860.3MB, time=728.91 memory used=28286.7MB, alloc=1860.3MB, time=736.10 memory used=28345.2MB, alloc=1860.3MB, time=743.02 memory used=28385.4MB, alloc=1860.3MB, time=749.80 memory used=28474.2MB, alloc=1860.3MB, time=756.77 memory used=28506.6MB, alloc=1860.3MB, time=763.17 memory used=28594.6MB, alloc=1884.3MB, time=770.35 memory used=28650.8MB, alloc=1884.3MB, time=777.30 memory used=28701.3MB, alloc=1884.3MB, time=783.99 memory used=28746.1MB, alloc=1884.3MB, time=790.83 memory used=28826.2MB, alloc=1884.3MB, time=797.83 memory used=28828.0MB, alloc=1884.3MB, time=804.05 memory used=28894.7MB, alloc=1884.3MB, time=811.03 memory used=28907.4MB, alloc=2140.3MB, time=823.93 memory used=29973.0MB, alloc=2164.3MB, time=844.62 memory used=31239.7MB, alloc=2188.3MB, time=867.49 memory used=31973.3MB, alloc=2214.3MB, time=883.89 memory used=33061.8MB, alloc=2236.3MB, time=902.66 memory used=34104.3MB, alloc=2260.3MB, time=992.90 memory used=35153.0MB, alloc=2284.3MB, time=1013.69 memory used=36379.4MB, alloc=2308.3MB, time=1036.97 memory used=37730.7MB, alloc=2332.3MB, time=1067.84 memory used=39265.4MB, alloc=2356.3MB, time=1095.88 memory used=40596.6MB, alloc=2380.3MB, time=1122.56 memory used=41692.6MB, alloc=2404.3MB, time=1144.69 memory used=42892.6MB, alloc=2428.3MB, time=1170.62 memory used=43427.3MB, alloc=2454.6MB, time=1189.37 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428472566 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; F := [ 2 2 2 2 2 3 3 3 2 3 x z - 12 x y - 10 z, -20 x y - 2 y - 18, -15 x z - 7 x + 18 y z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 4 3 2 2 2 G := [-3 x y z + 12 y + 2 y z , 8 x y - 18 y z - 9 z , 2 4 -15 x y z - 13 y + 20 x] > Problem := [F,G]; Problem := [[ 2 2 2 2 2 3 3 3 2 3 x z - 12 x y - 10 z, -20 x y - 2 y - 18, -15 x z - 7 x + 18 y z ] 2 4 3 2 2 2 , [-3 x y z + 12 y + 2 y z , 8 x y - 18 y z - 9 z , 2 4 -15 x y z - 13 y + 20 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=25.3MB, alloc=32.3MB, time=0.46 memory used=49.1MB, alloc=32.3MB, time=0.67 memory used=76.3MB, alloc=36.7MB, time=1.01 memory used=90.7MB, alloc=36.7MB, time=1.11 memory used=110.3MB, alloc=36.8MB, time=1.27 memory used=119.8MB, alloc=36.8MB, time=1.31 memory used=131.7MB, alloc=60.8MB, time=1.36 memory used=158.6MB, alloc=60.8MB, time=1.43 memory used=184.4MB, alloc=60.8MB, time=1.49 memory used=215.9MB, alloc=60.8MB, time=1.55 memory used=247.6MB, alloc=60.8MB, time=1.61 memory used=267.2MB, alloc=60.8MB, time=1.66 memory used=289.0MB, alloc=60.8MB, time=1.70 memory used=313.3MB, alloc=60.8MB, time=1.75 memory used=341.0MB, alloc=60.8MB, time=1.80 memory used=378.7MB, alloc=60.8MB, time=1.98 memory used=420.3MB, alloc=60.8MB, time=2.48 memory used=460.3MB, alloc=60.8MB, time=2.80 memory used=489.9MB, alloc=60.8MB, time=2.91 memory used=521.0MB, alloc=61.0MB, time=3.04 memory used=544.2MB, alloc=61.0MB, time=3.10 memory used=571.4MB, alloc=61.0MB, time=3.20 memory used=599.2MB, alloc=61.0MB, time=3.27 memory used=621.1MB, alloc=61.0MB, time=3.33 memory used=652.1MB, alloc=61.0MB, time=3.48 memory used=674.9MB, alloc=61.0MB, time=3.54 memory used=704.7MB, alloc=61.0MB, time=3.64 memory used=747.4MB, alloc=64.2MB, time=3.93 memory used=771.5MB, alloc=64.2MB, time=4.01 memory used=792.0MB, alloc=64.2MB, time=4.09 memory used=815.5MB, alloc=64.2MB, time=4.17 memory used=842.5MB, alloc=64.2MB, time=4.25 memory used=871.1MB, alloc=64.2MB, time=4.33 memory used=888.6MB, alloc=64.2MB, time=4.41 memory used=905.9MB, alloc=64.2MB, time=4.49 memory used=924.3MB, alloc=64.2MB, time=4.56 memory used=944.3MB, alloc=64.2MB, time=4.63 memory used=965.9MB, alloc=64.2MB, time=4.69 memory used=988.7MB, alloc=64.2MB, time=4.76 memory used=1013.0MB, alloc=64.2MB, time=4.83 memory used=1039.5MB, alloc=64.2MB, time=4.90 memory used=1069.1MB, alloc=64.2MB, time=4.97 memory used=1089.2MB, alloc=64.2MB, time=5.02 memory used=1110.9MB, alloc=64.2MB, time=5.67 memory used=1132.1MB, alloc=88.2MB, time=12.63 memory used=1164.8MB, alloc=88.2MB, time=26.69 memory used=1202.1MB, alloc=112.2MB, time=55.07 memory used=1256.5MB, alloc=112.2MB, time=98.11 memory used=1333.7MB, alloc=136.2MB, time=158.57 memory used=1365.4MB, alloc=155.8MB, time=183.26 memory used=1370.7MB, alloc=155.8MB, time=183.31 memory used=1374.5MB, alloc=155.8MB, time=183.36 memory used=1375.6MB, alloc=411.8MB, time=183.40 memory used=1526.0MB, alloc=411.8MB, time=191.63 memory used=1586.9MB, alloc=411.8MB, time=191.73 memory used=1652.8MB, alloc=411.8MB, time=191.84 memory used=1724.6MB, alloc=411.8MB, time=191.95 memory used=1800.0MB, alloc=411.8MB, time=192.07 memory used=1880.8MB, alloc=411.8MB, time=192.18 memory used=2099.3MB, alloc=411.8MB, time=192.62 memory used=2260.4MB, alloc=411.8MB, time=192.86 memory used=2440.7MB, alloc=411.8MB, time=193.10 memory used=2648.4MB, alloc=411.8MB, time=193.37 memory used=2827.6MB, alloc=411.8MB, time=194.05 memory used=2911.8MB, alloc=411.8MB, time=194.24 memory used=2971.4MB, alloc=411.8MB, time=194.40 memory used=3042.8MB, alloc=411.8MB, time=194.54 memory used=3126.8MB, alloc=411.8MB, time=194.68 memory used=3200.2MB, alloc=411.8MB, time=209.55 memory used=3293.5MB, alloc=411.8MB, time=285.83 memory used=3422.7MB, alloc=411.8MB, time=370.22 memory used=3566.8MB, alloc=411.8MB, time=378.38 memory used=3624.9MB, alloc=411.8MB, time=378.48 memory used=3688.4MB, alloc=411.8MB, time=378.60 memory used=3757.6MB, alloc=411.8MB, time=378.70 memory used=3830.4MB, alloc=411.8MB, time=378.82 memory used=3908.6MB, alloc=411.8MB, time=378.93 memory used=3995.2MB, alloc=411.8MB, time=379.06 memory used=4143.1MB, alloc=411.8MB, time=379.29 memory used=4302.1MB, alloc=411.8MB, time=379.53 memory used=4479.9MB, alloc=411.8MB, time=379.79 memory used=4683.1MB, alloc=411.8MB, time=380.06 memory used=4910.0MB, alloc=411.8MB, time=403.77 memory used=5006.9MB, alloc=411.8MB, time=420.27 memory used=5077.5MB, alloc=411.8MB, time=420.46 memory used=5139.9MB, alloc=411.8MB, time=420.63 memory used=5216.3MB, alloc=411.8MB, time=420.80 memory used=5293.5MB, alloc=411.8MB, time=420.95 memory used=5343.6MB, alloc=411.8MB, time=421.06 memory used=5397.0MB, alloc=411.8MB, time=421.17 memory used=5454.7MB, alloc=411.8MB, time=421.29 memory used=5516.5MB, alloc=411.8MB, time=421.40 memory used=5584.3MB, alloc=411.8MB, time=421.52 memory used=5656.0MB, alloc=411.8MB, time=421.65 memory used=5733.5MB, alloc=411.8MB, time=421.78 memory used=5816.4MB, alloc=411.8MB, time=421.91 memory used=5910.8MB, alloc=411.8MB, time=422.04 memory used=6069.5MB, alloc=411.8MB, time=422.30 memory used=6231.6MB, alloc=411.8MB, time=422.54 memory used=6416.7MB, alloc=411.8MB, time=422.79 memory used=6677.4MB, alloc=411.8MB, time=423.59 memory used=6760.2MB, alloc=411.8MB, time=423.77 memory used=6857.0MB, alloc=411.8MB, time=424.40 memory used=6982.6MB, alloc=411.8MB, time=425.85 memory used=7065.1MB, alloc=411.8MB, time=426.10 memory used=7125.9MB, alloc=411.8MB, time=426.30 memory used=7199.9MB, alloc=411.8MB, time=426.53 memory used=7280.4MB, alloc=411.8MB, time=426.74 memory used=7327.5MB, alloc=411.8MB, time=426.90 memory used=7378.2MB, alloc=411.8MB, time=427.07 memory used=7431.0MB, alloc=411.8MB, time=427.24 memory used=7489.2MB, alloc=411.8MB, time=427.41 memory used=7549.2MB, alloc=411.8MB, time=427.58 memory used=7614.8MB, alloc=411.8MB, time=427.76 memory used=7685.7MB, alloc=411.8MB, time=427.92 memory used=7762.0MB, alloc=411.8MB, time=428.10 memory used=7843.1MB, alloc=411.8MB, time=428.27 memory used=7921.3MB, alloc=411.8MB, time=428.44 memory used=7964.3MB, alloc=411.8MB, time=428.55 memory used=8009.1MB, alloc=411.8MB, time=428.65 memory used=8053.5MB, alloc=411.8MB, time=428.76 memory used=8101.4MB, alloc=411.8MB, time=428.88 memory used=8149.2MB, alloc=411.8MB, time=429.00 memory used=8199.1MB, alloc=411.8MB, time=429.11 memory used=8251.3MB, alloc=411.8MB, time=429.24 memory used=8305.8MB, alloc=411.8MB, time=429.36 memory used=8363.9MB, alloc=411.8MB, time=429.49 memory used=8425.6MB, alloc=411.8MB, time=429.61 memory used=8491.5MB, alloc=411.8MB, time=429.73 memory used=8560.9MB, alloc=411.8MB, time=429.85 memory used=8646.2MB, alloc=411.8MB, time=461.15 memory used=8698.5MB, alloc=435.8MB, time=505.55 memory used=8755.9MB, alloc=459.8MB, time=570.91 memory used=8839.4MB, alloc=459.8MB, time=704.95 memory used=8981.4MB, alloc=459.8MB, time=715.10 memory used=9094.2MB, alloc=459.8MB, time=715.39 memory used=9159.8MB, alloc=459.8MB, time=715.53 memory used=9229.4MB, alloc=459.8MB, time=715.68 memory used=9304.8MB, alloc=459.8MB, time=715.83 memory used=9383.3MB, alloc=459.8MB, time=715.98 memory used=9467.6MB, alloc=459.8MB, time=716.14 memory used=9557.7MB, alloc=459.8MB, time=716.30 memory used=9653.6MB, alloc=459.8MB, time=716.48 memory used=9755.3MB, alloc=459.8MB, time=716.64 memory used=9862.8MB, alloc=459.8MB, time=716.81 memory used=9975.7MB, alloc=459.8MB, time=716.99 memory used=10201.8MB, alloc=459.8MB, time=717.33 memory used=10346.3MB, alloc=459.8MB, time=717.58 memory used=10500.3MB, alloc=459.8MB, time=717.82 memory used=10661.2MB, alloc=459.8MB, time=718.07 memory used=10831.6MB, alloc=459.8MB, time=718.33 memory used=11013.3MB, alloc=459.8MB, time=718.61 memory used=11207.7MB, alloc=459.8MB, time=718.88 memory used=11416.1MB, alloc=459.8MB, time=719.17 memory used=11641.1MB, alloc=459.8MB, time=719.49 memory used=11888.4MB, alloc=459.8MB, time=719.80 memory used=12148.7MB, alloc=459.8MB, time=721.11 memory used=12273.6MB, alloc=459.8MB, time=722.14 memory used=12367.1MB, alloc=459.8MB, time=722.45 memory used=12484.5MB, alloc=459.8MB, time=722.74 memory used=12571.8MB, alloc=459.8MB, time=722.99 memory used=12652.1MB, alloc=459.8MB, time=723.24 memory used=12739.6MB, alloc=459.8MB, time=723.46 memory used=12839.1MB, alloc=459.8MB, time=723.71 memory used=12946.8MB, alloc=459.8MB, time=723.94 memory used=13065.7MB, alloc=459.8MB, time=724.21 memory used=13175.6MB, alloc=459.8MB, time=724.45 memory used=13244.7MB, alloc=459.8MB, time=724.61 memory used=13315.2MB, alloc=459.8MB, time=724.77 memory used=13392.5MB, alloc=459.8MB, time=724.93 memory used=13471.6MB, alloc=459.8MB, time=725.09 memory used=13558.6MB, alloc=459.8MB, time=725.25 memory used=13651.2MB, alloc=459.8MB, time=725.41 memory used=13751.5MB, alloc=459.8MB, time=725.57 memory used=13865.5MB, alloc=459.8MB, time=738.08 memory used=13968.8MB, alloc=459.8MB, time=868.59 memory used=14071.6MB, alloc=483.8MB, time=1004.89 memory used=14174.9MB, alloc=483.8MB, time=1010.63 memory used=14320.6MB, alloc=483.8MB, time=1015.32 memory used=14396.1MB, alloc=483.8MB, time=1015.48 memory used=14479.6MB, alloc=483.8MB, time=1015.65 memory used=14570.1MB, alloc=483.8MB, time=1015.81 memory used=14667.9MB, alloc=483.8MB, time=1015.99 memory used=14772.7MB, alloc=483.8MB, time=1016.17 memory used=14884.6MB, alloc=483.8MB, time=1016.35 memory used=15003.4MB, alloc=483.8MB, time=1016.54 memory used=15132.2MB, alloc=483.8MB, time=1016.73 memory used=15267.3MB, alloc=483.8MB, time=1016.93 memory used=15444.3MB, alloc=483.8MB, time=1017.20 memory used=15588.4MB, alloc=483.8MB, time=1017.45 memory used=15742.3MB, alloc=483.8MB, time=1017.70 memory used=15903.3MB, alloc=483.8MB, time=1017.97 memory used=16073.7MB, alloc=483.8MB, time=1018.24 memory used=16255.3MB, alloc=483.8MB, time=1018.52 memory used=16449.7MB, alloc=483.8MB, time=1018.81 memory used=16658.2MB, alloc=483.8MB, time=1019.11 memory used=16883.1MB, alloc=483.8MB, time=1019.42 memory used=17130.4MB, alloc=483.8MB, time=1019.74 memory used=17463.2MB, alloc=483.8MB, time=1090.55 memory used=17597.6MB, alloc=483.8MB, time=1191.52 memory used=17790.0MB, alloc=483.8MB, time=1193.97 memory used=17902.2MB, alloc=483.8MB, time=1194.27 memory used=18002.3MB, alloc=483.8MB, time=1194.51 memory used=18124.2MB, alloc=483.8MB, time=1194.79 memory used=18260.2MB, alloc=483.8MB, time=1195.05 memory used=18338.7MB, alloc=483.8MB, time=1195.22 memory used=18423.1MB, alloc=483.8MB, time=1195.40 memory used=18512.2MB, alloc=483.8MB, time=1195.58 memory used=18605.3MB, alloc=483.8MB, time=1195.77 memory used=18706.0MB, alloc=483.8MB, time=1195.96 memory used=18810.5MB, alloc=483.8MB, time=1196.14 memory used=18922.6MB, alloc=483.8MB, time=1196.34 memory used=19042.5MB, alloc=483.8MB, time=1196.53 memory used=19166.0MB, alloc=483.8MB, time=1196.73 memory used=19297.3MB, alloc=483.8MB, time=1196.94 memory used=19436.4MB, alloc=483.8MB, time=1197.15 memory used=19677.8MB, alloc=483.8MB, time=1197.50 memory used=19816.9MB, alloc=483.8MB, time=1197.74 memory used=19960.3MB, alloc=483.8MB, time=1198.01 memory used=20110.0MB, alloc=483.8MB, time=1198.27 memory used=20266.1MB, alloc=483.8MB, time=1198.54 memory used=20428.3MB, alloc=483.8MB, time=1198.82 memory used=20596.4MB, alloc=483.8MB, time=1199.10 memory used=20774.4MB, alloc=483.8MB, time=1199.39 memory used=20957.5MB, alloc=483.8MB, time=1199.70 memory used=21150.1MB, alloc=483.8MB, time=1199.99 memory used=21351.0MB, alloc=483.8MB, time=1200.27 memory used=21563.6MB, alloc=483.8MB, time=1200.59 memory used=21782.0MB, alloc=483.8MB, time=1200.90 memory used=22013.4MB, alloc=483.8MB, time=1201.22 memory used=22255.1MB, alloc=483.8MB, time=1201.53 memory used=22511.6MB, alloc=483.8MB, time=1201.84 memory used=22701.2MB, alloc=483.8MB, time=1202.10 memory used=22887.7MB, alloc=483.8MB, time=1202.35 memory used=23081.4MB, alloc=483.8MB, time=1202.62 memory used=23286.5MB, alloc=483.8MB, time=1202.89 memory used=23559.4MB, alloc=483.8MB, time=1203.79 memory used=23738.4MB, alloc=483.8MB, time=1205.44 memory used=23885.6MB, alloc=483.8MB, time=1206.29 memory used=24051.6MB, alloc=483.8MB, time=1207.99 memory used=24217.0MB, alloc=483.8MB, time=1208.83 memory used=24317.0MB, alloc=483.8MB, time=1209.13 memory used=24417.3MB, alloc=483.8MB, time=1209.39 memory used=24687.2MB, alloc=483.8MB, time=1372.56 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428473766 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 3 2 2 F := [12 x y + 10 x y + 3 z , -x y - 11 x - 13 z , 4 2 2 8 x - 15 x y z - 16 x y ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 G := [12 y z - 15 x y + 10 x y , -19 x z - 12 x y z - 11 y z, 2 -10 x z + 5 y + 5 x] > Problem := [F,G]; 2 2 2 3 3 2 2 Problem := [[12 x y + 10 x y + 3 z , -x y - 11 x - 13 z , 4 2 2 3 2 2 8 x - 15 x y z - 16 x y ], [12 y z - 15 x y + 10 x y , 2 2 2 -19 x z - 12 x y z - 11 y z, -10 x z + 5 y + 5 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.17 memory used=26.5MB, alloc=32.3MB, time=0.49 memory used=47.0MB, alloc=32.3MB, time=0.77 memory used=65.9MB, alloc=56.3MB, time=1.07 memory used=107.0MB, alloc=60.3MB, time=1.68 memory used=144.6MB, alloc=84.3MB, time=2.21 memory used=206.4MB, alloc=92.3MB, time=3.12 memory used=266.7MB, alloc=116.3MB, time=4.01 memory used=345.7MB, alloc=116.3MB, time=5.17 memory used=419.4MB, alloc=396.3MB, time=6.24 memory used=542.7MB, alloc=396.3MB, time=7.57 memory used=645.6MB, alloc=420.3MB, time=9.13 memory used=784.7MB, alloc=444.3MB, time=10.87 memory used=913.2MB, alloc=468.3MB, time=12.57 memory used=1044.9MB, alloc=468.3MB, time=14.57 memory used=1166.8MB, alloc=492.3MB, time=16.54 memory used=1268.0MB, alloc=492.3MB, time=18.00 memory used=1370.9MB, alloc=492.3MB, time=19.70 memory used=1472.8MB, alloc=516.3MB, time=21.33 memory used=1572.5MB, alloc=516.3MB, time=23.05 memory used=1659.3MB, alloc=516.3MB, time=24.70 memory used=1738.6MB, alloc=516.3MB, time=26.15 memory used=1816.5MB, alloc=516.3MB, time=27.52 memory used=1871.5MB, alloc=516.3MB, time=28.67 memory used=1938.3MB, alloc=516.3MB, time=30.02 memory used=1996.0MB, alloc=516.3MB, time=31.23 memory used=2060.2MB, alloc=516.3MB, time=32.56 memory used=2115.3MB, alloc=516.3MB, time=33.77 memory used=2163.1MB, alloc=516.3MB, time=34.79 memory used=2218.6MB, alloc=516.3MB, time=36.11 memory used=2412.4MB, alloc=540.3MB, time=39.36 memory used=2584.8MB, alloc=564.3MB, time=41.86 memory used=2801.5MB, alloc=588.3MB, time=45.87 memory used=2969.6MB, alloc=612.3MB, time=48.58 memory used=3169.4MB, alloc=636.3MB, time=51.15 memory used=3335.0MB, alloc=636.3MB, time=53.65 memory used=3531.1MB, alloc=636.3MB, time=56.38 memory used=3722.2MB, alloc=660.3MB, time=58.74 memory used=3858.0MB, alloc=660.3MB, time=60.88 memory used=4034.6MB, alloc=660.3MB, time=64.43 memory used=4211.8MB, alloc=660.3MB, time=68.10 memory used=4365.5MB, alloc=684.3MB, time=71.30 memory used=4506.5MB, alloc=684.3MB, time=74.03 memory used=4697.2MB, alloc=708.3MB, time=76.70 memory used=4878.0MB, alloc=708.3MB, time=80.59 memory used=4999.8MB, alloc=708.3MB, time=83.76 memory used=5099.9MB, alloc=732.3MB, time=85.88 memory used=5181.8MB, alloc=732.3MB, time=87.79 memory used=5590.3MB, alloc=756.3MB, time=94.26 memory used=6022.1MB, alloc=780.3MB, time=101.20 memory used=6423.6MB, alloc=804.3MB, time=109.03 memory used=6758.5MB, alloc=828.3MB, time=115.75 memory used=7097.6MB, alloc=852.3MB, time=122.56 memory used=7425.0MB, alloc=876.3MB, time=127.39 memory used=7764.4MB, alloc=900.3MB, time=135.44 memory used=8080.5MB, alloc=924.3MB, time=142.31 memory used=8388.8MB, alloc=948.3MB, time=150.51 memory used=8659.8MB, alloc=972.3MB, time=157.18 memory used=8902.4MB, alloc=996.3MB, time=161.97 memory used=9184.9MB, alloc=1020.3MB, time=168.38 memory used=9398.9MB, alloc=1044.3MB, time=173.22 memory used=10040.1MB, alloc=1068.3MB, time=184.00 memory used=10688.1MB, alloc=1092.3MB, time=197.61 memory used=11362.5MB, alloc=1116.3MB, time=210.69 memory used=12038.4MB, alloc=1140.3MB, time=224.38 memory used=12717.7MB, alloc=1164.3MB, time=239.01 memory used=13311.8MB, alloc=1188.3MB, time=250.30 memory used=13973.5MB, alloc=1212.3MB, time=261.54 memory used=14355.0MB, alloc=1236.3MB, time=269.26 memory used=15054.3MB, alloc=1260.3MB, time=282.34 memory used=15654.3MB, alloc=1284.3MB, time=299.93 memory used=16136.6MB, alloc=1308.3MB, time=313.82 memory used=16622.8MB, alloc=1332.3MB, time=322.52 memory used=17237.5MB, alloc=1356.3MB, time=333.87 memory used=17831.2MB, alloc=1380.3MB, time=344.40 memory used=18194.0MB, alloc=1404.3MB, time=350.32 memory used=18772.4MB, alloc=1428.3MB, time=360.25 memory used=19232.9MB, alloc=1452.3MB, time=373.02 memory used=19692.7MB, alloc=1476.3MB, time=385.50 memory used=20213.0MB, alloc=1500.3MB, time=396.73 memory used=20710.4MB, alloc=1524.3MB, time=404.57 memory used=21208.7MB, alloc=1548.3MB, time=412.17 memory used=21636.6MB, alloc=1572.3MB, time=422.01 memory used=21989.9MB, alloc=1596.3MB, time=430.50 memory used=22333.8MB, alloc=1620.3MB, time=441.89 memory used=22543.5MB, alloc=1644.3MB, time=449.95 memory used=23140.4MB, alloc=1668.3MB, time=459.72 memory used=23693.1MB, alloc=1692.3MB, time=467.82 memory used=24152.0MB, alloc=1716.3MB, time=476.56 memory used=24369.2MB, alloc=1740.3MB, time=484.45 memory used=24729.9MB, alloc=1764.3MB, time=494.28 memory used=25310.0MB, alloc=1788.3MB, time=502.44 memory used=25948.0MB, alloc=1812.3MB, time=512.59 memory used=26381.9MB, alloc=1836.3MB, time=520.68 memory used=27045.2MB, alloc=1860.3MB, time=532.79 memory used=27487.8MB, alloc=1860.3MB, time=539.22 memory used=27922.2MB, alloc=1860.3MB, time=552.16 memory used=28131.8MB, alloc=1860.3MB, time=559.97 memory used=28338.0MB, alloc=1860.3MB, time=567.84 memory used=28548.9MB, alloc=1860.3MB, time=576.84 memory used=28810.6MB, alloc=1860.3MB, time=585.29 memory used=28925.3MB, alloc=1860.3MB, time=592.38 memory used=29072.4MB, alloc=1860.3MB, time=599.49 memory used=29423.8MB, alloc=1860.3MB, time=609.40 memory used=30006.0MB, alloc=1860.3MB, time=617.83 memory used=30337.4MB, alloc=1860.3MB, time=624.58 memory used=30874.3MB, alloc=1860.3MB, time=633.55 memory used=31309.5MB, alloc=1860.3MB, time=641.36 memory used=31740.7MB, alloc=1860.3MB, time=650.22 memory used=32314.3MB, alloc=1860.3MB, time=659.74 memory used=32955.8MB, alloc=1860.3MB, time=667.20 memory used=33494.1MB, alloc=1860.3MB, time=682.94 memory used=34130.1MB, alloc=1860.3MB, time=690.37 memory used=34821.9MB, alloc=1860.3MB, time=706.42 memory used=35227.4MB, alloc=1860.3MB, time=714.01 memory used=35412.5MB, alloc=1860.3MB, time=721.91 memory used=35555.7MB, alloc=1860.3MB, time=729.23 memory used=35759.4MB, alloc=1884.3MB, time=736.95 memory used=35975.8MB, alloc=1884.3MB, time=744.41 memory used=36062.6MB, alloc=1884.3MB, time=752.53 memory used=36231.2MB, alloc=1884.3MB, time=760.08 memory used=36332.6MB, alloc=1884.3MB, time=766.96 memory used=36374.3MB, alloc=1884.3MB, time=773.22 memory used=36505.9MB, alloc=1884.3MB, time=780.99 memory used=36633.6MB, alloc=1884.3MB, time=788.05 memory used=36723.8MB, alloc=1884.3MB, time=794.56 memory used=36876.2MB, alloc=1884.3MB, time=805.30 memory used=37037.8MB, alloc=1884.3MB, time=814.39 memory used=37144.6MB, alloc=1884.3MB, time=823.69 memory used=37225.6MB, alloc=1884.3MB, time=830.64 memory used=37267.2MB, alloc=1884.3MB, time=836.95 memory used=37329.2MB, alloc=1884.3MB, time=843.72 memory used=37365.5MB, alloc=1884.3MB, time=850.16 memory used=37411.4MB, alloc=2140.3MB, time=862.77 memory used=38532.7MB, alloc=2164.3MB, time=887.22 memory used=39853.3MB, alloc=2188.3MB, time=917.33 memory used=41146.6MB, alloc=2212.3MB, time=947.75 memory used=42410.0MB, alloc=2236.3MB, time=982.45 memory used=43607.7MB, alloc=2260.3MB, time=1011.45 memory used=44188.4MB, alloc=2284.3MB, time=1028.78 memory used=45503.4MB, alloc=2308.3MB, time=1054.26 memory used=46762.7MB, alloc=2332.3MB, time=1089.69 memory used=47932.2MB, alloc=2356.3MB, time=1122.88 memory used=49098.2MB, alloc=2380.3MB, time=1146.94 memory used=49594.0MB, alloc=2404.3MB, time=1159.59 memory used=50177.5MB, alloc=2443.8MB, time=1172.10 memory used=50825.1MB, alloc=2467.8MB, time=1194.01 memory used=52083.1MB, alloc=2491.8MB, time=1217.15 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428474966 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; F := 4 3 2 2 2 3 3 2 [13 x + 17 y z - 14 x y , -10 y z - 5 x - y, 13 x y - 8 x y - 7 x y] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 4 2 4 2 G := [14 x y z - 16 z + 8 x y, 11 x - x y + 18 x, 3 2 2 -15 x z - 10 x y z + 20 z ] > Problem := [F,G]; Problem := [ 4 3 2 2 2 3 3 2 [13 x + 17 y z - 14 x y , -10 y z - 5 x - y, 13 x y - 8 x y - 7 x y] 2 4 2 4 2 , [14 x y z - 16 z + 8 x y, 11 x - x y + 18 x, 3 2 2 -15 x z - 10 x y z + 20 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.18 memory used=26.6MB, alloc=32.3MB, time=0.50 memory used=47.0MB, alloc=32.3MB, time=0.79 memory used=65.5MB, alloc=56.3MB, time=1.07 memory used=106.1MB, alloc=60.3MB, time=1.66 memory used=146.5MB, alloc=60.3MB, time=2.20 memory used=188.2MB, alloc=68.3MB, time=2.78 memory used=231.1MB, alloc=92.3MB, time=3.35 memory used=296.5MB, alloc=92.3MB, time=4.00 memory used=360.3MB, alloc=92.3MB, time=4.90 memory used=423.5MB, alloc=116.3MB, time=5.64 memory used=489.1MB, alloc=117.4MB, time=6.03 memory used=545.1MB, alloc=117.4MB, time=6.23 memory used=611.6MB, alloc=117.4MB, time=6.73 memory used=675.1MB, alloc=117.4MB, time=7.48 memory used=751.3MB, alloc=373.4MB, time=8.56 memory used=840.0MB, alloc=373.4MB, time=9.72 memory used=924.0MB, alloc=397.4MB, time=10.88 memory used=1041.7MB, alloc=397.4MB, time=12.35 memory used=1154.5MB, alloc=421.4MB, time=13.83 memory used=1279.4MB, alloc=421.4MB, time=15.18 memory used=1401.0MB, alloc=421.4MB, time=16.67 memory used=1530.1MB, alloc=421.4MB, time=17.92 memory used=1647.0MB, alloc=445.4MB, time=19.33 memory used=1787.9MB, alloc=445.4MB, time=20.73 memory used=1924.5MB, alloc=445.4MB, time=22.76 memory used=2066.7MB, alloc=469.4MB, time=24.64 memory used=2220.8MB, alloc=469.4MB, time=25.78 memory used=2320.5MB, alloc=469.4MB, time=27.16 memory used=2410.6MB, alloc=493.4MB, time=28.43 memory used=2512.8MB, alloc=493.4MB, time=29.67 memory used=2642.8MB, alloc=493.4MB, time=30.28 memory used=2752.8MB, alloc=493.4MB, time=30.97 memory used=2840.6MB, alloc=493.4MB, time=31.98 memory used=2926.9MB, alloc=493.4MB, time=33.18 memory used=3024.9MB, alloc=493.4MB, time=34.22 memory used=3096.8MB, alloc=493.4MB, time=35.06 memory used=3185.6MB, alloc=493.4MB, time=36.16 memory used=3291.2MB, alloc=493.4MB, time=36.69 memory used=3397.8MB, alloc=493.4MB, time=37.20 memory used=3509.9MB, alloc=493.4MB, time=38.86 memory used=3618.5MB, alloc=493.4MB, time=39.38 memory used=3725.6MB, alloc=493.4MB, time=39.92 memory used=3836.4MB, alloc=493.4MB, time=41.68 memory used=3928.3MB, alloc=493.4MB, time=42.65 memory used=4001.4MB, alloc=493.4MB, time=43.72 memory used=4054.0MB, alloc=493.4MB, time=44.96 memory used=4172.1MB, alloc=517.4MB, time=45.95 memory used=4227.7MB, alloc=517.4MB, time=46.82 memory used=4290.3MB, alloc=517.4MB, time=47.87 memory used=4372.8MB, alloc=517.4MB, time=49.26 memory used=4453.6MB, alloc=517.4MB, time=50.85 memory used=4504.4MB, alloc=517.4MB, time=51.69 memory used=4579.0MB, alloc=517.4MB, time=52.76 memory used=4622.9MB, alloc=517.4MB, time=53.72 memory used=4811.8MB, alloc=517.4MB, time=55.44 memory used=4971.5MB, alloc=517.4MB, time=56.91 memory used=5182.8MB, alloc=541.4MB, time=59.32 memory used=5383.6MB, alloc=565.4MB, time=62.33 memory used=5551.3MB, alloc=565.4MB, time=64.54 memory used=5713.6MB, alloc=589.4MB, time=65.63 memory used=5843.8MB, alloc=589.4MB, time=66.37 memory used=5964.1MB, alloc=589.4MB, time=67.04 memory used=6132.5MB, alloc=589.4MB, time=68.90 memory used=6296.5MB, alloc=589.4MB, time=69.86 memory used=6468.8MB, alloc=589.4MB, time=70.98 memory used=6599.4MB, alloc=589.4MB, time=71.69 memory used=6714.6MB, alloc=589.4MB, time=72.37 memory used=6859.5MB, alloc=589.4MB, time=73.07 memory used=7008.8MB, alloc=589.4MB, time=74.01 memory used=7149.4MB, alloc=589.4MB, time=74.74 memory used=7255.7MB, alloc=589.4MB, time=75.38 memory used=7385.5MB, alloc=589.4MB, time=76.06 memory used=7510.3MB, alloc=589.4MB, time=76.66 memory used=7673.0MB, alloc=589.4MB, time=79.18 memory used=7800.1MB, alloc=589.4MB, time=79.86 memory used=7909.5MB, alloc=589.4MB, time=80.47 memory used=8068.7MB, alloc=589.4MB, time=81.73 memory used=8249.4MB, alloc=589.4MB, time=82.93 memory used=8421.4MB, alloc=589.4MB, time=84.34 memory used=8559.6MB, alloc=589.4MB, time=85.10 memory used=8690.7MB, alloc=589.4MB, time=85.81 memory used=8790.2MB, alloc=589.4MB, time=86.46 memory used=8902.0MB, alloc=589.4MB, time=87.10 memory used=9026.8MB, alloc=589.4MB, time=87.78 memory used=9166.2MB, alloc=589.4MB, time=88.47 memory used=9321.6MB, alloc=589.4MB, time=89.16 memory used=9425.1MB, alloc=589.4MB, time=89.76 memory used=9515.7MB, alloc=589.4MB, time=90.32 memory used=9614.0MB, alloc=589.4MB, time=90.87 memory used=9722.8MB, alloc=589.4MB, time=91.46 memory used=9895.8MB, alloc=589.4MB, time=92.89 memory used=10017.0MB, alloc=589.4MB, time=93.67 memory used=10171.9MB, alloc=589.4MB, time=94.45 memory used=10274.4MB, alloc=589.4MB, time=95.10 memory used=10377.9MB, alloc=589.4MB, time=95.77 memory used=10494.5MB, alloc=589.4MB, time=96.45 memory used=10623.9MB, alloc=589.4MB, time=97.13 memory used=10769.6MB, alloc=589.4MB, time=97.84 memory used=10915.0MB, alloc=589.4MB, time=98.49 memory used=11004.0MB, alloc=589.4MB, time=99.06 memory used=11097.9MB, alloc=589.4MB, time=99.62 memory used=11200.0MB, alloc=589.4MB, time=100.17 memory used=11313.8MB, alloc=589.4MB, time=100.75 memory used=11583.4MB, alloc=589.4MB, time=123.02 memory used=11709.2MB, alloc=589.4MB, time=123.73 memory used=11833.8MB, alloc=589.4MB, time=124.38 memory used=11966.7MB, alloc=589.4MB, time=125.03 memory used=12063.0MB, alloc=589.4MB, time=125.59 memory used=12175.1MB, alloc=589.4MB, time=126.16 memory used=12308.8MB, alloc=589.4MB, time=126.74 memory used=12482.2MB, alloc=589.4MB, time=128.17 memory used=12616.7MB, alloc=589.4MB, time=128.92 memory used=12753.4MB, alloc=589.4MB, time=129.66 memory used=12851.2MB, alloc=589.4MB, time=130.35 memory used=12960.0MB, alloc=589.4MB, time=131.05 memory used=13084.2MB, alloc=589.4MB, time=131.74 memory used=13223.4MB, alloc=589.4MB, time=132.46 memory used=13378.3MB, alloc=589.4MB, 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time=168.95 memory used=16055.9MB, alloc=589.4MB, time=169.63 memory used=16201.4MB, alloc=589.4MB, time=170.27 memory used=16295.3MB, alloc=589.4MB, time=170.82 memory used=16404.1MB, alloc=589.4MB, time=171.40 memory used=16531.6MB, alloc=589.4MB, time=171.97 memory used=16705.4MB, alloc=589.4MB, time=173.24 memory used=16931.9MB, alloc=589.4MB, time=175.88 memory used=17148.6MB, alloc=589.4MB, time=178.45 memory used=17345.7MB, alloc=589.4MB, time=180.89 memory used=17480.3MB, alloc=589.4MB, time=184.10 memory used=17684.2MB, alloc=589.4MB, time=192.96 memory used=17796.1MB, alloc=589.4MB, time=193.68 memory used=17930.5MB, alloc=589.4MB, time=194.37 memory used=18024.2MB, alloc=589.4MB, time=194.95 memory used=18231.8MB, alloc=589.4MB, time=196.47 memory used=18436.5MB, alloc=589.4MB, time=198.94 memory used=18623.1MB, alloc=589.4MB, time=200.28 memory used=18763.2MB, alloc=613.4MB, time=202.41 memory used=18897.5MB, alloc=613.4MB, time=204.05 memory used=19115.3MB, alloc=613.4MB, 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time=240.59 memory used=25138.7MB, alloc=661.4MB, time=241.37 memory used=25327.5MB, alloc=661.4MB, time=242.15 memory used=25521.2MB, alloc=661.4MB, time=242.92 memory used=25719.5MB, alloc=661.4MB, time=243.71 memory used=25947.6MB, alloc=661.4MB, time=244.50 memory used=26218.4MB, alloc=661.4MB, time=245.50 memory used=26332.4MB, alloc=661.4MB, time=246.19 memory used=26446.2MB, alloc=661.4MB, time=246.90 memory used=26562.4MB, alloc=661.4MB, time=247.57 memory used=26682.6MB, alloc=661.4MB, time=248.28 memory used=26805.4MB, alloc=661.4MB, time=249.01 memory used=26930.3MB, alloc=661.4MB, time=249.74 memory used=27061.7MB, alloc=661.4MB, time=250.47 memory used=27192.9MB, alloc=661.4MB, time=251.19 memory used=27327.9MB, alloc=661.4MB, time=251.90 memory used=27469.2MB, alloc=661.4MB, time=252.61 memory used=27613.2MB, alloc=661.4MB, time=253.36 memory used=27763.7MB, alloc=661.4MB, time=254.09 memory used=27922.5MB, alloc=661.4MB, time=254.81 memory used=28284.1MB, alloc=661.4MB, 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time=938.56 memory used=91366.7MB, alloc=685.4MB, time=939.35 memory used=91575.8MB, alloc=685.4MB, time=940.19 memory used=91798.7MB, alloc=685.4MB, time=941.02 memory used=92110.4MB, alloc=685.4MB, time=941.94 memory used=92228.5MB, alloc=685.4MB, time=942.65 memory used=92349.4MB, alloc=685.4MB, time=943.38 memory used=92477.0MB, alloc=685.4MB, time=944.11 memory used=92607.3MB, alloc=685.4MB, time=944.82 memory used=92739.8MB, alloc=685.4MB, time=945.55 memory used=92877.1MB, alloc=685.4MB, time=946.29 memory used=93019.2MB, alloc=685.4MB, time=947.05 memory used=93165.1MB, alloc=685.4MB, time=947.77 memory used=93316.5MB, alloc=685.4MB, time=948.51 memory used=93476.0MB, alloc=685.4MB, time=949.26 memory used=93640.6MB, alloc=685.4MB, time=950.04 memory used=93812.6MB, alloc=685.4MB, time=950.81 memory used=93992.3MB, alloc=685.4MB, time=951.59 memory used=94184.5MB, alloc=685.4MB, time=952.38 memory used=94569.5MB, alloc=685.4MB, time=953.98 memory used=94786.4MB, alloc=685.4MB, 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alloc=685.4MB, time=1051.26 memory used=98785.8MB, alloc=685.4MB, time=1052.03 memory used=98935.1MB, alloc=685.4MB, time=1052.81 memory used=99097.7MB, alloc=685.4MB, time=1053.60 memory used=99416.2MB, alloc=685.4MB, time=1056.18 memory used=99598.4MB, alloc=685.4MB, time=1058.36 memory used=99823.4MB, alloc=685.4MB, time=1060.12 memory used=100073.0MB, alloc=685.4MB, time=1063.10 memory used=100308.2MB, alloc=685.4MB, time=1070.02 memory used=100505.3MB, alloc=685.4MB, time=1073.72 memory used=100654.7MB, alloc=685.4MB, time=1075.82 memory used=100822.1MB, alloc=685.4MB, time=1077.47 memory used=101029.5MB, alloc=685.4MB, time=1078.66 memory used=101230.9MB, alloc=685.4MB, time=1080.28 memory used=101453.7MB, alloc=685.4MB, time=1081.87 memory used=101545.8MB, alloc=685.4MB, time=1083.56 memory used=101639.7MB, alloc=685.4MB, time=1085.11 memory used=101783.2MB, alloc=685.4MB, time=1086.63 memory used=101934.6MB, alloc=685.4MB, time=1088.68 memory used=102084.9MB, alloc=685.4MB, time=1097.22 memory used=102332.9MB, alloc=709.4MB, time=1258.85 memory used=102559.1MB, alloc=733.4MB, time=1554.62 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428476166 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 4 3 2 F := [5 x z + 11 y z - x z, -3 y - 13 x + 16 y z , 3 2 2 -12 x y - 8 x y + 10 x z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; G := [ 2 2 4 2 4 2 2 2 2 -4 y z + 8 z + 3 x z, -16 z - 16 x z - 20 z , 13 x z + 2 x z - 17 x ] > Problem := [F,G]; 3 3 2 4 3 2 Problem := [[5 x z + 11 y z - x z, -3 y - 13 x + 16 y z , 3 2 2 -12 x y - 8 x y + 10 x z ], [ 2 2 4 2 4 2 2 2 2 -4 y z + 8 z + 3 x z, -16 z - 16 x z - 20 z , 13 x z + 2 x z - 17 x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.17 memory used=26.3MB, alloc=32.3MB, time=0.49 memory used=46.2MB, alloc=56.3MB, time=0.76 memory used=91.3MB, alloc=60.5MB, time=1.18 memory used=125.0MB, alloc=60.5MB, time=1.33 memory used=161.6MB, alloc=60.5MB, time=1.59 memory used=191.1MB, alloc=60.5MB, time=1.71 memory used=222.0MB, alloc=60.5MB, time=1.90 memory used=268.6MB, alloc=68.5MB, time=2.49 memory used=308.8MB, alloc=68.5MB, time=3.06 memory used=354.3MB, alloc=68.5MB, time=3.61 memory used=398.2MB, alloc=92.5MB, time=4.13 memory used=463.4MB, alloc=92.5MB, time=4.85 memory used=507.1MB, alloc=92.5MB, time=5.09 memory used=551.3MB, alloc=92.5MB, time=5.33 memory used=599.3MB, alloc=92.5MB, time=5.60 memory used=637.9MB, alloc=92.5MB, time=5.90 memory used=681.8MB, alloc=92.5MB, time=6.12 memory used=722.8MB, alloc=92.5MB, time=6.43 memory used=769.0MB, alloc=92.5MB, time=6.71 memory used=818.8MB, alloc=92.5MB, time=6.99 memory used=860.0MB, alloc=92.5MB, time=7.41 memory used=897.1MB, alloc=92.5MB, time=7.59 memory used=937.6MB, alloc=92.5MB, time=7.82 memory used=979.5MB, alloc=92.5MB, time=8.11 memory used=1051.3MB, alloc=92.5MB, time=8.82 memory used=1109.2MB, alloc=92.5MB, time=9.30 memory used=1168.7MB, alloc=92.5MB, time=9.81 memory used=1217.7MB, alloc=92.5MB, time=10.13 memory used=1258.1MB, alloc=92.5MB, time=10.37 memory used=1307.7MB, alloc=92.5MB, time=10.75 memory used=1347.3MB, alloc=92.5MB, time=10.99 memory used=1402.3MB, alloc=116.5MB, time=11.49 memory used=1480.0MB, alloc=372.5MB, time=12.33 memory used=1564.7MB, alloc=372.5MB, time=13.56 memory used=1651.4MB, alloc=396.5MB, time=14.55 memory used=1720.1MB, alloc=396.5MB, time=14.99 memory used=1787.6MB, alloc=396.5MB, time=15.32 memory used=1857.6MB, alloc=396.5MB, time=15.82 memory used=1926.3MB, alloc=396.5MB, time=16.11 memory used=1992.9MB, alloc=396.5MB, time=16.58 memory used=2096.6MB, alloc=396.5MB, time=17.59 memory used=2205.7MB, alloc=396.5MB, time=18.53 memory used=2268.7MB, alloc=396.5MB, time=18.93 memory used=2320.4MB, alloc=396.5MB, time=19.21 memory used=2376.8MB, alloc=396.5MB, time=19.56 memory used=2443.4MB, alloc=396.5MB, time=19.94 memory used=2501.8MB, alloc=396.5MB, time=20.42 memory used=2568.1MB, alloc=396.5MB, time=21.03 memory used=2628.1MB, alloc=396.5MB, time=21.34 memory used=2706.4MB, alloc=396.5MB, time=21.93 memory used=2767.2MB, alloc=396.5MB, time=22.61 memory used=2825.6MB, alloc=396.5MB, time=22.96 memory used=2947.3MB, alloc=396.5MB, time=26.85 memory used=3011.1MB, alloc=396.5MB, time=28.23 memory used=3057.6MB, alloc=396.5MB, time=28.42 memory used=3103.8MB, alloc=396.5MB, time=28.61 memory used=3157.4MB, alloc=396.5MB, time=28.79 memory used=3208.4MB, alloc=396.5MB, time=28.95 memory used=3244.1MB, alloc=396.5MB, time=29.10 memory used=3283.1MB, alloc=396.5MB, time=29.25 memory used=3326.5MB, alloc=396.5MB, time=29.39 memory used=3373.2MB, alloc=396.5MB, time=29.55 memory used=3431.2MB, alloc=396.5MB, time=29.71 memory used=3505.9MB, alloc=396.5MB, time=29.91 memory used=3705.9MB, alloc=396.5MB, time=30.75 memory used=3831.5MB, alloc=420.5MB, time=31.74 memory used=3980.1MB, alloc=420.5MB, time=32.69 memory used=4135.3MB, alloc=420.5MB, time=33.95 memory used=4256.8MB, alloc=444.5MB, time=35.43 memory used=4368.1MB, alloc=444.5MB, time=39.27 memory used=4439.7MB, alloc=444.5MB, time=39.53 memory used=4531.1MB, alloc=444.5MB, time=39.78 memory used=4593.6MB, alloc=444.5MB, time=39.99 memory used=4661.4MB, alloc=444.5MB, time=40.18 memory used=4739.7MB, alloc=444.5MB, time=40.39 memory used=4841.7MB, alloc=444.5MB, time=40.62 memory used=5117.4MB, alloc=444.5MB, time=41.85 memory used=5258.9MB, alloc=444.5MB, time=43.20 memory used=5378.4MB, alloc=444.5MB, time=44.86 memory used=5517.1MB, alloc=444.5MB, time=46.65 memory used=5584.2MB, alloc=444.5MB, time=46.91 memory used=5662.7MB, alloc=444.5MB, time=47.15 memory used=5746.6MB, alloc=444.5MB, time=47.72 memory used=5847.5MB, alloc=444.5MB, time=48.28 memory used=5944.3MB, alloc=444.5MB, time=48.59 memory used=6082.5MB, alloc=444.5MB, time=50.00 memory used=6223.5MB, alloc=468.5MB, time=51.44 memory used=6344.0MB, alloc=468.5MB, time=52.30 memory used=6439.1MB, alloc=468.5MB, time=53.04 memory used=6588.0MB, alloc=468.5MB, time=54.26 memory used=6725.5MB, alloc=468.5MB, time=56.20 memory used=6831.8MB, alloc=468.5MB, time=59.86 memory used=6912.3MB, alloc=468.5MB, time=60.19 memory used=6980.3MB, alloc=468.5MB, time=60.50 memory used=7057.8MB, alloc=468.5MB, time=60.80 memory used=7148.5MB, alloc=468.5MB, time=61.11 memory used=7223.6MB, alloc=468.5MB, time=61.39 memory used=7291.0MB, alloc=468.5MB, time=61.66 memory used=7378.8MB, alloc=468.5MB, time=61.95 memory used=7485.8MB, alloc=468.5MB, time=62.25 memory used=7698.1MB, alloc=468.5MB, time=63.53 memory used=7847.3MB, alloc=468.5MB, time=64.69 memory used=7969.0MB, alloc=468.5MB, time=66.99 memory used=8047.1MB, alloc=468.5MB, time=67.47 memory used=8131.6MB, alloc=468.5MB, time=68.05 memory used=8265.4MB, alloc=492.5MB, time=69.89 memory used=8397.5MB, alloc=492.5MB, time=73.84 memory used=8490.8MB, alloc=492.5MB, time=74.19 memory used=8575.2MB, alloc=492.5MB, time=74.52 memory used=8675.0MB, alloc=492.5MB, time=74.85 memory used=8777.7MB, alloc=492.5MB, time=75.17 memory used=8855.6MB, alloc=492.5MB, time=75.46 memory used=8963.6MB, alloc=492.5MB, time=75.78 memory used=9104.3MB, alloc=492.5MB, time=76.12 memory used=9388.1MB, alloc=492.5MB, time=77.96 memory used=9502.6MB, alloc=492.5MB, time=79.37 memory used=9614.7MB, alloc=492.5MB, time=80.28 memory used=9756.9MB, alloc=492.5MB, time=82.22 memory used=9855.9MB, alloc=492.5MB, time=82.70 memory used=9988.8MB, alloc=492.5MB, time=90.95 memory used=10080.6MB, alloc=492.5MB, time=91.34 memory used=10162.6MB, alloc=492.5MB, time=91.68 memory used=10262.3MB, alloc=492.5MB, time=92.03 memory used=10361.3MB, alloc=492.5MB, time=92.60 memory used=10511.5MB, alloc=492.5MB, time=94.11 memory used=10597.1MB, alloc=492.5MB, time=94.46 memory used=10711.6MB, alloc=492.5MB, time=95.24 memory used=10816.0MB, alloc=492.5MB, time=95.61 memory used=10937.9MB, alloc=492.5MB, time=97.35 memory used=11038.8MB, alloc=492.5MB, time=98.83 memory used=11140.2MB, alloc=516.5MB, time=100.11 memory used=11227.3MB, alloc=516.5MB, time=101.64 memory used=11294.1MB, alloc=516.5MB, time=102.71 memory used=11438.3MB, alloc=516.5MB, time=103.90 memory used=11567.0MB, alloc=516.5MB, time=104.79 memory used=11719.6MB, alloc=516.5MB, time=106.42 memory used=11823.2MB, alloc=516.5MB, time=106.89 memory used=11938.4MB, alloc=516.5MB, time=108.66 memory used=12043.2MB, alloc=516.5MB, time=109.20 memory used=12175.4MB, alloc=516.5MB, time=110.31 memory used=12272.2MB, alloc=516.5MB, time=110.74 memory used=12389.4MB, alloc=516.5MB, time=112.50 memory used=12508.9MB, alloc=516.5MB, time=113.32 memory used=12620.6MB, alloc=516.5MB, time=113.91 memory used=12710.6MB, alloc=516.5MB, time=115.08 memory used=12782.4MB, alloc=516.5MB, time=116.07 memory used=12850.6MB, alloc=516.5MB, time=117.10 memory used=12921.1MB, alloc=540.5MB, time=117.93 memory used=13001.4MB, alloc=540.5MB, time=119.06 memory used=13095.3MB, alloc=540.5MB, time=120.02 memory used=13193.0MB, alloc=540.5MB, time=121.06 memory used=13332.4MB, alloc=540.5MB, time=122.11 memory used=13472.8MB, alloc=540.5MB, time=123.24 memory used=13526.3MB, alloc=540.5MB, time=124.14 memory used=13566.6MB, alloc=540.5MB, time=124.93 memory used=13616.8MB, alloc=540.5MB, time=125.76 memory used=13830.0MB, alloc=564.5MB, time=129.40 memory used=14041.0MB, alloc=588.5MB, time=132.65 memory used=14233.1MB, alloc=612.5MB, time=134.43 memory used=14401.2MB, alloc=612.5MB, time=135.57 memory used=14583.0MB, alloc=612.5MB, time=137.15 memory used=14750.2MB, alloc=612.5MB, time=138.31 memory used=14905.9MB, alloc=612.5MB, time=140.41 memory used=15065.1MB, alloc=612.5MB, time=141.49 memory used=15283.6MB, alloc=612.5MB, time=144.02 memory used=15511.0MB, alloc=636.5MB, time=145.90 memory used=15698.7MB, alloc=636.5MB, time=147.32 memory used=15867.3MB, alloc=636.5MB, time=148.71 memory used=16084.5MB, alloc=636.5MB, time=151.03 memory used=16245.9MB, alloc=636.5MB, time=151.95 memory used=16409.1MB, alloc=636.5MB, time=154.77 memory used=16581.7MB, alloc=636.5MB, time=155.93 memory used=16752.4MB, alloc=636.5MB, time=157.60 memory used=16919.1MB, alloc=636.5MB, time=160.07 memory used=17084.4MB, alloc=636.5MB, time=160.90 memory used=17199.9MB, alloc=636.5MB, time=161.61 memory used=17323.7MB, alloc=636.5MB, time=162.32 memory used=17465.5MB, alloc=660.5MB, time=163.07 memory used=17624.4MB, alloc=660.5MB, time=163.81 memory used=17798.2MB, alloc=660.5MB, time=164.54 memory used=17935.6MB, alloc=660.5MB, time=165.21 memory used=18056.6MB, alloc=660.5MB, time=165.85 memory used=18188.5MB, alloc=660.5MB, time=166.49 memory used=18333.4MB, alloc=660.5MB, time=167.14 memory used=18494.1MB, alloc=660.5MB, time=167.79 memory used=18749.1MB, alloc=660.5MB, time=168.59 memory used=19031.5MB, alloc=660.5MB, time=174.92 memory used=19249.4MB, alloc=684.5MB, time=400.84 memory used=19411.2MB, alloc=708.5MB, time=615.52 memory used=19637.8MB, alloc=708.5MB, time=940.00 memory used=19853.9MB, alloc=708.5MB, time=945.79 memory used=20041.2MB, alloc=708.5MB, time=946.64 memory used=20234.6MB, alloc=708.5MB, time=947.42 memory used=20367.0MB, alloc=708.5MB, time=948.09 memory used=20514.1MB, alloc=708.5MB, time=948.75 memory used=20675.2MB, alloc=708.5MB, time=949.45 memory used=20850.4MB, alloc=708.5MB, time=950.17 memory used=21039.8MB, alloc=708.5MB, time=950.90 memory used=21257.8MB, alloc=708.5MB, time=951.65 memory used=21492.9MB, alloc=708.5MB, time=952.42 memory used=21743.2MB, alloc=708.5MB, time=953.23 memory used=21860.0MB, alloc=708.5MB, time=953.89 memory used=21980.3MB, alloc=708.5MB, time=954.54 memory used=22107.3MB, alloc=708.5MB, time=955.20 memory used=22235.9MB, alloc=708.5MB, time=955.85 memory used=22370.8MB, alloc=708.5MB, time=956.51 memory used=22512.4MB, alloc=708.5MB, time=957.19 memory used=22655.4MB, alloc=708.5MB, time=957.86 memory used=22804.6MB, alloc=708.5MB, time=958.53 memory used=22960.0MB, alloc=708.5MB, time=959.22 memory used=23121.5MB, alloc=708.5MB, time=959.90 memory used=23288.9MB, alloc=708.5MB, time=960.58 memory used=23461.8MB, alloc=708.5MB, time=961.27 memory used=23634.5MB, alloc=708.5MB, time=961.96 memory used=23810.1MB, alloc=708.5MB, time=962.65 memory used=23991.7MB, alloc=708.5MB, time=963.34 memory used=24176.8MB, alloc=708.5MB, time=964.04 memory used=24370.3MB, alloc=708.5MB, time=964.74 memory used=24571.4MB, alloc=708.5MB, time=965.47 memory used=24778.8MB, alloc=708.5MB, time=966.18 memory used=24991.1MB, alloc=708.5MB, time=966.90 memory used=25203.3MB, alloc=708.5MB, time=967.62 memory used=25364.1MB, alloc=708.5MB, time=968.30 memory used=25529.2MB, alloc=708.5MB, time=968.98 memory used=25700.8MB, alloc=708.5MB, time=969.67 memory used=25872.1MB, alloc=708.5MB, time=970.34 memory used=26046.3MB, alloc=708.5MB, time=971.00 memory used=26229.3MB, alloc=708.5MB, time=971.67 memory used=26423.0MB, alloc=708.5MB, time=972.37 memory used=26785.1MB, alloc=708.5MB, time=976.35 memory used=27119.2MB, alloc=708.5MB, time=977.74 memory used=27395.0MB, alloc=708.5MB, time=978.58 memory used=27613.9MB, alloc=708.5MB, time=979.40 memory used=27837.2MB, alloc=708.5MB, time=981.45 memory used=28100.9MB, alloc=708.5MB, time=982.25 memory used=28323.3MB, alloc=708.5MB, time=982.98 memory used=28505.5MB, alloc=708.5MB, time=983.66 memory used=28701.3MB, alloc=708.5MB, time=984.31 memory used=28890.8MB, alloc=708.5MB, time=984.98 memory used=29080.6MB, alloc=708.5MB, time=985.70 memory used=29335.5MB, alloc=708.5MB, time=986.49 memory used=29578.0MB, alloc=708.5MB, time=987.26 memory used=29757.4MB, alloc=708.5MB, time=987.93 memory used=29950.2MB, alloc=708.5MB, time=988.61 memory used=30143.7MB, alloc=708.5MB, time=989.27 memory used=30329.3MB, alloc=708.5MB, time=989.91 memory used=30573.2MB, alloc=708.5MB, time=1000.34 memory used=30796.6MB, alloc=708.5MB, time=1001.30 memory used=30941.4MB, alloc=708.5MB, time=1002.10 memory used=31094.1MB, alloc=708.5MB, time=1002.88 memory used=31265.8MB, alloc=708.5MB, time=1003.72 memory used=31457.5MB, alloc=708.5MB, time=1004.55 memory used=31665.1MB, alloc=708.5MB, time=1005.42 memory used=31883.6MB, alloc=708.5MB, time=1006.26 memory used=32081.8MB, alloc=708.5MB, time=1007.07 memory used=32205.4MB, alloc=708.5MB, time=1007.74 memory used=32331.5MB, alloc=708.5MB, time=1008.39 memory used=32463.1MB, alloc=708.5MB, time=1009.05 memory used=32597.5MB, alloc=708.5MB, time=1009.72 memory used=32741.9MB, alloc=708.5MB, time=1010.40 memory used=32889.4MB, alloc=708.5MB, time=1011.11 memory used=33048.2MB, alloc=708.5MB, time=1011.79 memory used=33209.0MB, alloc=708.5MB, time=1012.49 memory used=33381.0MB, alloc=708.5MB, time=1013.18 memory used=33554.6MB, alloc=708.5MB, time=1013.88 memory used=33739.0MB, alloc=708.5MB, time=1014.59 memory used=33936.5MB, alloc=708.5MB, time=1015.33 memory used=34144.8MB, alloc=708.5MB, time=1016.08 memory used=34362.2MB, alloc=708.5MB, time=1016.83 memory used=34590.0MB, alloc=708.5MB, time=1017.56 memory used=34835.4MB, alloc=708.5MB, time=1018.33 memory used=35088.9MB, alloc=708.5MB, time=1019.09 memory used=35394.3MB, alloc=708.5MB, time=1019.91 memory used=35505.3MB, alloc=708.5MB, time=1020.54 memory used=35621.1MB, alloc=708.5MB, time=1021.19 memory used=35737.9MB, alloc=708.5MB, time=1021.84 memory used=35853.8MB, alloc=708.5MB, time=1022.48 memory used=35973.6MB, alloc=708.5MB, time=1023.12 memory used=36100.1MB, alloc=708.5MB, time=1023.76 memory used=36231.1MB, alloc=708.5MB, time=1024.41 memory used=36365.7MB, alloc=708.5MB, time=1025.07 memory used=36502.9MB, alloc=708.5MB, time=1025.71 memory used=36648.1MB, alloc=708.5MB, time=1026.38 memory used=36798.5MB, alloc=708.5MB, time=1027.07 memory used=36952.6MB, alloc=708.5MB, time=1027.74 memory used=37118.9MB, alloc=708.5MB, time=1028.42 memory used=37310.7MB, alloc=708.5MB, time=1030.40 memory used=37511.7MB, alloc=708.5MB, time=1076.46 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428477366 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 3 2 2 F := [10 x y z + 17 y z + 3 y z , 12 x y + 11 x y z + 2 y , 3 2 -7 x - 8 x y - 7 x y] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 4 3 3 2 3 G := [6 x z + 19 y z - 20 z , 19 x + 2 y z + 12, 10 x z - 5 x y z - 3 z ] > Problem := [F,G]; 2 3 2 2 3 2 2 Problem := [[10 x y z + 17 y z + 3 y z , 12 x y + 11 x y z + 2 y , 3 2 -7 x - 8 x y - 7 x y], 3 2 2 4 3 3 2 3 [6 x z + 19 y z - 20 z , 19 x + 2 y z + 12, 10 x z - 5 x y z - 3 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.18 memory used=26.7MB, alloc=32.3MB, time=0.50 memory used=47.3MB, alloc=32.3MB, time=0.80 memory used=66.6MB, alloc=56.3MB, time=1.10 memory used=108.5MB, alloc=60.3MB, time=1.70 memory used=144.6MB, alloc=60.3MB, time=2.20 memory used=185.2MB, alloc=92.3MB, time=2.79 memory used=249.0MB, alloc=92.3MB, time=3.73 memory used=311.0MB, alloc=116.3MB, time=4.64 memory used=384.9MB, alloc=372.3MB, time=5.64 memory used=467.5MB, alloc=372.3MB, time=6.98 memory used=551.5MB, alloc=396.3MB, time=8.28 memory used=670.4MB, alloc=420.3MB, time=9.79 memory used=807.0MB, alloc=444.3MB, time=11.64 memory used=937.4MB, alloc=444.3MB, time=13.70 memory used=1065.6MB, alloc=468.3MB, time=15.27 memory used=1181.4MB, alloc=468.3MB, time=17.03 memory used=1299.8MB, alloc=492.3MB, time=19.02 memory used=1416.6MB, alloc=492.3MB, time=20.93 memory used=1508.2MB, alloc=492.3MB, time=22.25 memory used=1601.6MB, alloc=492.3MB, time=23.90 memory used=1700.8MB, alloc=516.3MB, time=25.25 memory used=1780.3MB, alloc=516.3MB, time=26.47 memory used=1871.4MB, alloc=516.3MB, time=27.83 memory used=1947.6MB, alloc=516.3MB, time=29.08 memory used=2027.9MB, alloc=516.3MB, time=30.49 memory used=2099.2MB, alloc=516.3MB, time=31.88 memory used=2157.1MB, alloc=516.3MB, time=33.05 memory used=2219.4MB, alloc=516.3MB, time=34.38 memory used=2280.2MB, alloc=516.3MB, time=35.71 memory used=2328.7MB, alloc=516.3MB, time=36.76 memory used=2391.7MB, alloc=516.3MB, time=37.98 memory used=2438.5MB, alloc=516.3MB, time=39.03 memory used=2634.2MB, alloc=540.3MB, time=42.32 memory used=2817.8MB, alloc=564.3MB, time=45.67 memory used=3005.2MB, alloc=588.3MB, time=49.50 memory used=3177.6MB, alloc=612.3MB, time=52.82 memory used=3325.6MB, alloc=636.3MB, time=55.32 memory used=3473.2MB, alloc=636.3MB, time=57.93 memory used=3632.5MB, alloc=636.3MB, time=60.57 memory used=3777.1MB, alloc=660.3MB, time=63.05 memory used=3904.0MB, alloc=660.3MB, time=65.72 memory used=4038.5MB, alloc=660.3MB, time=68.73 memory used=4145.0MB, alloc=660.3MB, time=71.12 memory used=4251.2MB, alloc=660.3MB, time=73.18 memory used=4379.5MB, alloc=684.3MB, time=75.16 memory used=4492.4MB, alloc=684.3MB, time=76.98 memory used=4578.0MB, alloc=684.3MB, time=78.95 memory used=4680.6MB, alloc=684.3MB, time=81.16 memory used=5038.5MB, alloc=708.3MB, time=87.57 memory used=5416.8MB, alloc=732.3MB, time=93.95 memory used=5809.7MB, alloc=756.3MB, time=101.00 memory used=6195.8MB, alloc=780.3MB, time=109.23 memory used=6588.8MB, alloc=804.3MB, time=115.65 memory used=6962.2MB, alloc=828.3MB, time=120.08 memory used=7348.6MB, alloc=852.3MB, time=127.12 memory used=7751.5MB, alloc=876.3MB, time=134.04 memory used=8151.4MB, alloc=900.3MB, time=140.53 memory used=8463.0MB, alloc=924.3MB, time=146.12 memory used=8782.9MB, alloc=948.3MB, time=150.58 memory used=9052.2MB, alloc=972.3MB, time=156.79 memory used=9286.0MB, alloc=996.3MB, time=161.58 memory used=9565.7MB, alloc=1020.3MB, time=168.12 memory used=9813.9MB, alloc=1044.3MB, time=174.30 memory used=10460.5MB, alloc=1068.3MB, time=187.46 memory used=11124.5MB, alloc=1092.3MB, time=199.34 memory used=11438.0MB, alloc=1116.3MB, time=204.16 memory used=11800.8MB, alloc=1140.3MB, time=209.91 memory used=12495.2MB, alloc=1164.3MB, time=219.90 memory used=13210.6MB, alloc=1188.3MB, time=231.16 memory used=13910.3MB, alloc=1212.3MB, time=246.83 memory used=14644.2MB, alloc=1236.3MB, time=263.10 memory used=15316.8MB, alloc=1260.3MB, time=275.56 memory used=15863.7MB, alloc=1284.3MB, time=286.66 memory used=16429.3MB, alloc=1308.3MB, time=299.74 memory used=16915.0MB, alloc=1332.3MB, time=311.89 memory used=17471.4MB, alloc=1356.3MB, time=325.62 memory used=18026.1MB, alloc=1380.3MB, time=340.66 memory used=18500.1MB, alloc=1404.3MB, time=352.52 memory used=18812.4MB, alloc=1428.3MB, time=361.46 memory used=19290.5MB, alloc=1452.3MB, time=374.15 memory used=19720.8MB, alloc=1476.3MB, time=384.39 memory used=20111.5MB, alloc=1500.3MB, time=393.64 memory used=20581.7MB, alloc=1524.3MB, time=403.59 memory used=20956.0MB, alloc=1548.3MB, time=413.49 memory used=21215.7MB, alloc=1572.3MB, time=421.77 memory used=21489.0MB, alloc=1596.3MB, time=429.81 memory used=22007.9MB, alloc=1620.3MB, time=438.04 memory used=22455.9MB, alloc=1644.3MB, time=445.18 memory used=22924.5MB, alloc=1668.3MB, time=452.41 memory used=23412.9MB, alloc=1692.3MB, time=459.52 memory used=23952.9MB, alloc=1716.3MB, time=468.47 memory used=24469.5MB, alloc=1740.3MB, time=475.73 memory used=25010.7MB, alloc=1764.3MB, time=483.88 memory used=25562.6MB, alloc=1788.3MB, time=490.30 memory used=26139.3MB, alloc=1812.3MB, time=498.11 memory used=26728.4MB, alloc=1836.3MB, time=505.75 memory used=27462.5MB, alloc=1860.3MB, time=516.52 memory used=27778.1MB, alloc=1860.3MB, time=524.84 memory used=28342.6MB, alloc=1884.3MB, time=534.94 memory used=28627.4MB, alloc=1884.3MB, time=545.94 memory used=28835.6MB, alloc=1884.3MB, time=554.08 memory used=29035.1MB, alloc=1884.3MB, time=564.25 memory used=29245.0MB, alloc=1884.3MB, time=572.82 memory used=29410.0MB, alloc=1884.3MB, time=581.56 memory used=29581.8MB, alloc=1884.3MB, time=590.87 memory used=29719.0MB, alloc=1884.3MB, time=598.14 memory used=29873.9MB, alloc=1884.3MB, time=606.89 memory used=29992.8MB, alloc=1884.3MB, time=615.54 memory used=30066.9MB, alloc=1884.3MB, time=622.67 memory used=30173.8MB, alloc=1884.3MB, time=630.03 memory used=30337.1MB, alloc=1884.3MB, time=639.26 memory used=30404.9MB, alloc=1884.3MB, time=645.88 memory used=30677.2MB, alloc=1908.3MB, time=654.48 memory used=30956.4MB, alloc=1908.3MB, time=661.79 memory used=31306.4MB, alloc=1908.3MB, time=669.51 memory used=31476.4MB, alloc=1908.3MB, time=676.25 memory used=31729.5MB, alloc=1908.3MB, time=683.94 memory used=31764.6MB, alloc=1908.3MB, time=690.55 memory used=31897.4MB, alloc=1908.3MB, time=697.82 memory used=31970.0MB, alloc=1908.3MB, time=705.30 memory used=32141.6MB, alloc=2164.3MB, time=718.60 memory used=33256.8MB, alloc=2188.3MB, time=735.84 memory used=33906.6MB, alloc=2212.3MB, time=744.85 memory used=34559.8MB, alloc=2212.3MB, time=753.72 memory used=35227.0MB, alloc=2212.3MB, time=762.55 memory used=35902.3MB, alloc=2212.3MB, time=772.43 memory used=36824.9MB, alloc=2236.3MB, time=785.74 memory used=37944.9MB, alloc=2260.3MB, time=803.43 memory used=38712.8MB, alloc=2284.3MB, time=813.43 memory used=40026.5MB, alloc=2308.3MB, time=838.15 memory used=41345.3MB, alloc=2332.3MB, time=866.17 memory used=42760.1MB, alloc=2356.3MB, time=895.30 memory used=44069.5MB, alloc=2380.3MB, time=927.43 memory used=45417.2MB, alloc=2404.3MB, time=957.25 memory used=46647.9MB, alloc=2428.3MB, time=989.80 memory used=47305.9MB, alloc=2452.3MB, time=1004.60 memory used=47917.1MB, alloc=2476.3MB, time=1018.32 memory used=48516.2MB, alloc=2500.3MB, time=1032.77 memory used=49114.3MB, alloc=2524.3MB, time=1047.33 memory used=49754.2MB, alloc=2548.3MB, time=1061.38 memory used=50414.3MB, alloc=2572.3MB, time=1076.07 memory used=51079.7MB, alloc=2596.3MB, time=1089.35 memory used=51763.3MB, alloc=2620.3MB, time=1103.91 memory used=52486.6MB, alloc=2644.3MB, time=1118.85 memory used=53714.5MB, alloc=2668.3MB, time=1142.56 memory used=54916.6MB, alloc=2692.3MB, time=1176.14 memory used=55864.7MB, alloc=2716.3MB, time=1204.55 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428478566 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; F := [ 2 3 2 2 3 2 2 2 3 x y z + 13 y z + 18 x , -6 x z + 8 y + 9 z, -17 y z - 20 x y - 7 x ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 3 3 G := [3 x y - 2 x z - 16 x , -12 x z - 18 x z - 18, 2 2 2 13 x y z - 7 x z - 19 y z ] > Problem := [F,G]; Problem := [[ 2 3 2 2 3 2 2 2 3 x y z + 13 y z + 18 x , -6 x z + 8 y + 9 z, -17 y z - 20 x y - 7 x 3 3 3 3 ], [3 x y - 2 x z - 16 x , -12 x z - 18 x z - 18, 2 2 2 13 x y z - 7 x z - 19 y z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.5MB, alloc=32.3MB, time=0.52 memory used=46.8MB, alloc=56.3MB, time=0.85 memory used=87.1MB, alloc=60.3MB, time=1.42 memory used=125.8MB, alloc=84.3MB, time=2.00 memory used=161.8MB, alloc=84.3MB, time=2.48 memory used=221.2MB, alloc=92.3MB, time=3.40 memory used=284.2MB, alloc=116.3MB, time=4.27 memory used=367.8MB, alloc=116.3MB, time=5.41 memory used=439.3MB, alloc=372.3MB, time=6.33 memory used=525.7MB, alloc=396.3MB, time=7.57 memory used=633.5MB, alloc=396.3MB, time=9.16 memory used=733.5MB, alloc=396.3MB, time=10.30 memory used=838.2MB, alloc=420.3MB, time=11.72 memory used=969.0MB, alloc=420.3MB, time=13.46 memory used=1097.5MB, alloc=444.3MB, time=15.40 memory used=1238.8MB, alloc=468.3MB, time=17.75 memory used=1359.6MB, alloc=468.3MB, time=18.69 memory used=1454.6MB, alloc=468.3MB, time=25.23 memory used=1586.7MB, alloc=468.3MB, time=32.71 memory used=1674.9MB, alloc=468.3MB, time=34.82 memory used=1805.8MB, alloc=468.3MB, time=36.18 memory used=1949.5MB, alloc=468.3MB, time=38.56 memory used=2104.3MB, alloc=492.3MB, time=40.79 memory used=2234.2MB, alloc=492.3MB, time=42.76 memory used=2335.8MB, alloc=492.3MB, time=43.31 memory used=2429.1MB, alloc=492.3MB, time=43.76 memory used=2544.2MB, alloc=492.3MB, time=58.14 memory used=2629.8MB, alloc=492.3MB, time=58.49 memory used=2705.6MB, alloc=492.3MB, time=58.78 memory used=2819.8MB, alloc=492.3MB, time=59.31 memory used=2984.3MB, alloc=492.3MB, time=60.73 memory used=3100.3MB, alloc=492.3MB, time=62.57 memory used=3219.9MB, alloc=492.3MB, time=63.46 memory used=3319.8MB, alloc=492.3MB, time=64.01 memory used=3416.8MB, alloc=492.3MB, time=65.18 memory used=3554.7MB, alloc=492.3MB, time=66.33 memory used=3644.9MB, alloc=492.3MB, time=66.80 memory used=3777.4MB, alloc=516.3MB, time=68.37 memory used=3883.0MB, alloc=516.3MB, time=68.83 memory used=3965.7MB, alloc=516.3MB, time=69.24 memory used=4066.1MB, alloc=516.3MB, time=69.66 memory used=4187.8MB, alloc=516.3MB, time=70.10 memory used=4263.3MB, alloc=516.3MB, time=70.42 memory used=4338.3MB, alloc=516.3MB, time=70.75 memory used=4421.8MB, alloc=516.3MB, time=71.06 memory used=4513.9MB, alloc=516.3MB, time=71.41 memory used=4617.8MB, alloc=516.3MB, time=71.75 memory used=4750.4MB, alloc=540.3MB, time=109.44 memory used=4912.3MB, alloc=540.3MB, time=150.14 memory used=5024.1MB, alloc=540.3MB, time=150.61 memory used=5138.1MB, alloc=540.3MB, time=151.04 memory used=5231.5MB, alloc=540.3MB, time=151.38 memory used=5339.7MB, alloc=540.3MB, time=151.73 memory used=5466.8MB, alloc=540.3MB, time=152.09 memory used=5740.6MB, alloc=540.3MB, time=152.77 memory used=5888.8MB, alloc=540.3MB, time=153.19 memory used=6057.4MB, alloc=540.3MB, time=153.62 memory used=6253.4MB, alloc=540.3MB, time=154.09 memory used=6477.2MB, alloc=540.3MB, time=158.22 memory used=6577.3MB, alloc=540.3MB, time=160.22 memory used=6724.9MB, alloc=540.3MB, time=162.79 memory used=6836.5MB, alloc=540.3MB, time=164.24 memory used=6985.5MB, alloc=540.3MB, time=168.57 memory used=7128.0MB, alloc=540.3MB, time=169.62 memory used=7216.2MB, alloc=540.3MB, time=170.95 memory used=7333.9MB, alloc=540.3MB, time=172.15 memory used=7482.9MB, alloc=540.3MB, time=173.31 memory used=7593.2MB, alloc=540.3MB, time=173.80 memory used=7744.4MB, alloc=540.3MB, time=186.66 memory used=7901.1MB, alloc=540.3MB, time=187.90 memory used=8048.5MB, alloc=540.3MB, time=221.41 memory used=8149.6MB, alloc=540.3MB, time=221.85 memory used=8258.6MB, alloc=540.3MB, time=222.28 memory used=8384.3MB, alloc=564.3MB, time=223.78 memory used=8506.6MB, alloc=564.3MB, time=225.11 memory used=8654.0MB, alloc=564.3MB, time=226.08 memory used=8769.9MB, alloc=564.3MB, time=226.59 memory used=8898.6MB, alloc=564.3MB, time=227.07 memory used=9065.0MB, alloc=564.3MB, time=261.82 memory used=9187.2MB, alloc=564.3MB, time=262.32 memory used=9296.8MB, alloc=564.3MB, time=262.76 memory used=9410.7MB, alloc=564.3MB, time=263.18 memory used=9622.3MB, alloc=564.3MB, time=264.33 memory used=9726.3MB, alloc=588.3MB, time=266.89 memory used=9858.1MB, alloc=588.3MB, time=269.38 memory used=10035.7MB, alloc=588.3MB, time=270.47 memory used=10185.1MB, alloc=588.3MB, time=271.23 memory used=10348.3MB, alloc=588.3MB, time=272.02 memory used=10467.7MB, alloc=588.3MB, time=272.49 memory used=10716.4MB, alloc=588.3MB, time=273.14 memory used=10889.4MB, alloc=588.3MB, time=274.86 memory used=11018.2MB, alloc=588.3MB, time=275.42 memory used=11140.6MB, alloc=588.3MB, time=275.93 memory used=11293.0MB, alloc=588.3MB, time=276.46 memory used=11493.0MB, alloc=588.3MB, time=277.08 memory used=11644.7MB, alloc=588.3MB, time=277.61 memory used=11819.9MB, alloc=588.3MB, time=278.15 memory used=12020.8MB, alloc=588.3MB, time=278.71 memory used=12234.9MB, alloc=588.3MB, time=279.29 memory used=12435.8MB, alloc=588.3MB, time=280.73 memory used=12553.7MB, alloc=588.3MB, time=281.22 memory used=12681.8MB, alloc=588.3MB, time=281.72 memory used=12841.7MB, alloc=588.3MB, time=282.24 memory used=12996.7MB, alloc=588.3MB, time=282.78 memory used=13149.5MB, alloc=588.3MB, time=283.31 memory used=13324.5MB, alloc=588.3MB, time=283.88 memory used=13529.7MB, alloc=588.3MB, time=284.46 memory used=13739.1MB, alloc=588.3MB, time=285.02 memory used=13933.8MB, alloc=588.3MB, time=292.57 memory used=14077.3MB, alloc=588.3MB, time=293.14 memory used=14179.5MB, alloc=588.3MB, time=293.62 memory used=14300.6MB, alloc=588.3MB, time=294.16 memory used=14442.1MB, alloc=588.3MB, time=294.70 memory used=14604.3MB, alloc=588.3MB, time=295.28 memory used=14770.3MB, alloc=588.3MB, time=295.89 memory used=14908.1MB, alloc=588.3MB, time=296.44 memory used=15059.2MB, alloc=588.3MB, time=296.99 memory used=15222.8MB, alloc=588.3MB, time=297.54 memory used=15398.5MB, alloc=588.3MB, time=298.11 memory used=15589.5MB, alloc=588.3MB, time=298.70 memory used=15798.7MB, alloc=588.3MB, time=299.32 memory used=16024.7MB, alloc=588.3MB, time=299.95 memory used=16234.6MB, alloc=588.3MB, time=300.55 memory used=16408.5MB, alloc=588.3MB, time=301.10 memory used=16590.8MB, alloc=588.3MB, time=301.68 memory used=16789.6MB, alloc=588.3MB, time=302.24 memory used=17006.3MB, alloc=588.3MB, time=302.85 memory used=17318.6MB, alloc=588.3MB, time=304.66 memory used=17441.4MB, alloc=588.3MB, time=305.22 memory used=17564.1MB, alloc=588.3MB, time=305.74 memory used=17717.4MB, alloc=588.3MB, time=306.26 memory used=17909.8MB, alloc=588.3MB, time=306.87 memory used=18062.2MB, alloc=588.3MB, time=307.40 memory used=18235.5MB, alloc=588.3MB, time=307.97 memory used=18433.1MB, alloc=588.3MB, time=308.55 memory used=18653.8MB, alloc=588.3MB, time=309.17 memory used=18945.0MB, alloc=588.3MB, time=443.67 memory used=19132.2MB, alloc=588.3MB, time=446.97 memory used=19247.7MB, alloc=588.3MB, time=447.54 memory used=19394.5MB, alloc=588.3MB, time=448.16 memory used=19492.3MB, alloc=588.3MB, time=448.64 memory used=19591.4MB, alloc=588.3MB, time=449.12 memory used=19699.0MB, alloc=588.3MB, time=449.61 memory used=19819.8MB, alloc=588.3MB, time=450.10 memory used=19949.5MB, alloc=588.3MB, time=450.61 memory used=20092.9MB, alloc=588.3MB, time=451.13 memory used=20245.1MB, alloc=588.3MB, time=451.66 memory used=20474.7MB, alloc=588.3MB, time=452.33 memory used=20604.9MB, alloc=588.3MB, time=452.85 memory used=20741.3MB, alloc=588.3MB, time=453.38 memory used=20881.9MB, alloc=588.3MB, time=453.91 memory used=21026.7MB, alloc=588.3MB, time=454.45 memory used=21182.4MB, alloc=588.3MB, time=454.99 memory used=21342.3MB, alloc=588.3MB, time=455.53 memory used=21506.2MB, alloc=588.3MB, time=456.09 memory used=21681.3MB, alloc=588.3MB, time=456.64 memory used=21860.1MB, alloc=588.3MB, time=457.24 memory used=22050.4MB, alloc=588.3MB, time=457.83 memory used=22244.3MB, alloc=588.3MB, time=458.43 memory used=22449.7MB, alloc=588.3MB, time=459.02 memory used=22658.4MB, alloc=588.3MB, time=459.63 memory used=22878.5MB, alloc=588.3MB, time=460.25 memory used=23101.9MB, alloc=588.3MB, time=460.87 memory used=23328.2MB, alloc=588.3MB, time=461.49 memory used=23489.8MB, alloc=588.3MB, time=462.04 memory used=23652.0MB, alloc=588.3MB, time=462.57 memory used=23818.5MB, alloc=588.3MB, time=463.12 memory used=23985.7MB, alloc=588.3MB, time=463.68 memory used=24162.2MB, alloc=588.3MB, time=464.22 memory used=24339.2MB, alloc=588.3MB, time=464.80 memory used=24525.4MB, alloc=588.3MB, time=465.36 memory used=24711.7MB, alloc=588.3MB, time=465.94 memory used=24906.8MB, alloc=588.3MB, time=466.56 memory used=25101.7MB, alloc=588.3MB, time=467.15 memory used=25305.0MB, alloc=588.3MB, time=467.73 memory used=25507.6MB, alloc=588.3MB, time=468.31 memory used=25718.1MB, alloc=588.3MB, time=468.90 memory used=25935.9MB, alloc=588.3MB, time=469.49 memory used=26160.5MB, alloc=588.3MB, time=470.09 memory used=26391.3MB, alloc=588.3MB, time=470.71 memory used=26627.8MB, alloc=588.3MB, time=471.32 memory used=26831.2MB, alloc=588.3MB, time=471.90 memory used=27009.3MB, alloc=588.3MB, time=472.46 memory used=27193.0MB, alloc=588.3MB, time=473.01 memory used=27381.9MB, alloc=588.3MB, time=473.56 memory used=27574.6MB, alloc=588.3MB, time=474.13 memory used=27771.0MB, alloc=588.3MB, time=474.69 memory used=27976.6MB, alloc=588.3MB, time=475.27 memory used=28183.0MB, alloc=588.3MB, time=475.84 memory used=28395.7MB, alloc=588.3MB, time=476.40 memory used=28612.6MB, alloc=588.3MB, time=476.99 memory used=28837.2MB, alloc=588.3MB, time=477.60 memory used=29071.0MB, alloc=588.3MB, time=478.21 memory used=29307.7MB, alloc=588.3MB, time=478.80 memory used=29506.2MB, alloc=588.3MB, time=479.35 memory used=29715.6MB, alloc=588.3MB, time=479.93 memory used=29953.8MB, alloc=588.3MB, time=481.68 memory used=30027.9MB, alloc=588.3MB, time=483.30 memory used=30098.9MB, alloc=588.3MB, time=484.55 memory used=30181.6MB, alloc=588.3MB, time=486.23 memory used=30233.7MB, alloc=588.3MB, time=487.31 memory used=30295.6MB, alloc=588.3MB, time=488.57 memory used=30348.6MB, alloc=588.3MB, time=489.67 memory used=30409.1MB, alloc=588.3MB, time=490.98 memory used=30471.7MB, alloc=588.3MB, time=492.32 memory used=30669.2MB, alloc=612.3MB, time=495.01 memory used=30894.0MB, alloc=636.3MB, time=498.62 memory used=31089.4MB, alloc=636.3MB, time=502.02 memory used=31279.5MB, alloc=660.3MB, time=505.58 memory used=31448.3MB, alloc=660.3MB, time=508.83 memory used=31631.5MB, alloc=684.3MB, time=511.87 memory used=31792.1MB, alloc=684.3MB, time=514.72 memory used=31930.8MB, alloc=708.3MB, time=516.91 memory used=32101.6MB, alloc=708.3MB, time=520.44 memory used=32257.6MB, alloc=708.3MB, time=523.50 memory used=32378.5MB, alloc=708.3MB, time=525.76 memory used=32521.4MB, alloc=708.3MB, time=528.55 memory used=32640.2MB, alloc=732.3MB, time=531.01 memory used=32738.3MB, alloc=732.3MB, time=532.98 memory used=32852.4MB, alloc=732.3MB, time=535.97 memory used=32946.0MB, alloc=732.3MB, time=538.27 memory used=33070.6MB, alloc=732.3MB, time=541.21 memory used=33443.9MB, alloc=756.3MB, time=548.65 memory used=33672.0MB, alloc=780.3MB, time=556.84 memory used=33995.0MB, alloc=804.3MB, time=561.94 memory used=34395.2MB, alloc=828.3MB, time=571.06 memory used=34737.2MB, alloc=828.3MB, time=574.75 memory used=35025.3MB, alloc=828.3MB, time=577.79 memory used=35268.4MB, alloc=828.3MB, time=595.51 memory used=35523.3MB, alloc=828.3MB, time=608.80 memory used=35704.9MB, alloc=852.3MB, time=610.01 memory used=35962.6MB, alloc=852.3MB, time=611.29 memory used=36098.6MB, alloc=867.8MB, time=612.44 memory used=36225.2MB, alloc=867.8MB, time=613.54 memory used=36365.1MB, alloc=867.8MB, time=614.65 memory used=36524.3MB, alloc=867.8MB, time=615.78 memory used=36708.6MB, alloc=867.8MB, time=616.93 memory used=37039.5MB, alloc=867.8MB, time=623.03 memory used=37245.8MB, alloc=891.8MB, time=624.52 memory used=37455.3MB, alloc=891.8MB, time=625.96 memory used=37699.9MB, alloc=891.8MB, time=627.45 memory used=37981.7MB, alloc=891.8MB, time=628.93 memory used=38192.9MB, alloc=915.8MB, time=630.25 memory used=38367.2MB, alloc=915.8MB, time=631.55 memory used=38560.8MB, alloc=915.8MB, time=632.78 memory used=38761.7MB, alloc=915.8MB, time=634.04 memory used=38980.3MB, alloc=915.8MB, time=635.33 memory used=39216.6MB, alloc=915.8MB, time=636.59 memory used=39458.8MB, alloc=915.8MB, time=637.87 memory used=39716.8MB, alloc=915.8MB, time=639.17 memory used=39990.9MB, alloc=915.8MB, time=640.47 memory used=40291.4MB, alloc=915.8MB, time=641.79 memory used=40606.7MB, alloc=915.8MB, time=643.13 memory used=40872.8MB, alloc=915.8MB, time=644.43 memory used=40970.2MB, alloc=915.8MB, time=645.50 memory used=41067.6MB, alloc=915.8MB, time=646.57 memory used=41164.2MB, alloc=915.8MB, time=647.64 memory used=41262.3MB, alloc=915.8MB, time=648.67 memory used=41366.6MB, alloc=915.8MB, time=649.76 memory used=41471.9MB, alloc=915.8MB, time=650.83 memory used=41577.6MB, alloc=915.8MB, time=651.91 memory used=41689.5MB, alloc=915.8MB, time=653.00 memory used=41801.3MB, alloc=915.8MB, time=654.13 memory used=41921.5MB, alloc=915.8MB, time=655.26 memory used=42039.0MB, alloc=915.8MB, time=656.39 memory used=42163.7MB, alloc=915.8MB, time=657.49 memory used=42294.3MB, alloc=915.8MB, time=658.58 memory used=42429.6MB, alloc=915.8MB, time=659.68 memory used=42567.6MB, alloc=915.8MB, time=660.78 memory used=42708.5MB, alloc=915.8MB, time=661.90 memory used=42854.4MB, alloc=915.8MB, time=663.04 memory used=43007.9MB, alloc=915.8MB, time=664.17 memory used=43433.6MB, alloc=915.8MB, time=670.58 memory used=43694.4MB, alloc=915.8MB, time=672.15 memory used=43914.4MB, alloc=915.8MB, time=673.64 memory used=44177.2MB, alloc=915.8MB, time=675.13 memory used=44491.8MB, alloc=915.8MB, time=676.66 memory used=44697.9MB, alloc=915.8MB, time=677.99 memory used=44875.8MB, alloc=915.8MB, time=679.29 memory used=45071.4MB, alloc=915.8MB, time=680.64 memory used=45273.3MB, alloc=915.8MB, time=681.93 memory used=45492.8MB, alloc=915.8MB, time=683.24 memory used=45730.1MB, alloc=915.8MB, time=684.57 memory used=45984.8MB, alloc=915.8MB, time=685.91 memory used=46256.3MB, alloc=915.8MB, time=687.27 memory used=46543.8MB, alloc=915.8MB, time=688.64 memory used=46845.9MB, alloc=915.8MB, time=690.06 memory used=47162.4MB, alloc=915.8MB, time=691.49 memory used=47348.8MB, alloc=915.8MB, time=692.78 memory used=47445.7MB, alloc=915.8MB, time=693.91 memory used=47543.0MB, alloc=915.8MB, time=695.02 memory used=47639.7MB, alloc=915.8MB, time=696.13 memory used=47737.7MB, alloc=915.8MB, time=697.25 memory used=47842.0MB, alloc=915.8MB, time=698.38 memory used=47947.4MB, alloc=915.8MB, time=699.52 memory used=48053.1MB, alloc=915.8MB, time=700.70 memory used=48165.0MB, alloc=915.8MB, time=701.83 memory used=48276.7MB, alloc=915.8MB, time=702.98 memory used=48397.0MB, alloc=915.8MB, time=704.10 memory used=48514.5MB, alloc=915.8MB, time=705.23 memory used=48639.2MB, alloc=915.8MB, time=706.36 memory used=48769.8MB, alloc=915.8MB, time=707.50 memory used=48905.0MB, alloc=915.8MB, time=708.67 memory used=49043.1MB, alloc=915.8MB, time=709.82 memory used=49184.0MB, alloc=915.8MB, time=710.98 memory used=49329.8MB, alloc=915.8MB, time=712.13 memory used=49483.3MB, alloc=915.8MB, time=713.29 memory used=49765.1MB, alloc=915.8MB, time=715.00 memory used=50086.5MB, alloc=939.8MB, time=981.72 memory used=50303.9MB, alloc=963.8MB, time=1502.47 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428479766 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; F := [ 2 2 2 2 2 2 3 3 -18 x y z + 9 z + 16 x, -5 x y z - 9 x z , -12 x y z - 16 y z - 8 x ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; G := [ 2 2 2 2 2 4 2 2 17 x y z - 19 x y - 9 x z, 8 x y - 13 x z - 19 x , 17 x - 10 x y - 6 ] > Problem := [F,G]; Problem := [[ 2 2 2 2 2 2 3 3 -18 x y z + 9 z + 16 x, -5 x y z - 9 x z , -12 x y z - 16 y z - 8 x ] , [ 2 2 2 2 2 4 2 2 17 x y z - 19 x y - 9 x z, 8 x y - 13 x z - 19 x , 17 x - 10 x y - 6 ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.4MB, alloc=32.3MB, time=0.49 memory used=47.6MB, alloc=32.3MB, time=0.79 memory used=67.6MB, alloc=32.3MB, time=1.06 memory used=86.5MB, alloc=56.3MB, time=1.35 memory used=125.4MB, alloc=60.3MB, time=1.93 memory used=163.0MB, alloc=84.3MB, time=2.50 memory used=206.3MB, alloc=84.3MB, time=3.13 memory used=269.3MB, alloc=92.3MB, time=4.06 memory used=327.9MB, alloc=116.3MB, time=4.99 memory used=410.5MB, alloc=116.3MB, time=6.30 memory used=481.9MB, alloc=372.3MB, time=7.41 memory used=567.0MB, alloc=396.3MB, time=8.67 memory used=669.4MB, alloc=396.3MB, time=10.33 memory used=772.2MB, alloc=420.3MB, time=11.97 memory used=902.0MB, alloc=444.3MB, time=13.94 memory used=1048.1MB, alloc=468.3MB, time=16.26 memory used=1170.2MB, alloc=468.3MB, time=18.16 memory used=1304.7MB, alloc=492.3MB, time=20.42 memory used=1414.1MB, alloc=492.3MB, time=22.05 memory used=1514.2MB, alloc=516.3MB, time=23.75 memory used=1613.3MB, alloc=516.3MB, time=25.20 memory used=1697.4MB, alloc=516.3MB, time=26.75 memory used=1790.0MB, alloc=516.3MB, time=28.43 memory used=1860.6MB, alloc=540.3MB, time=29.59 memory used=1919.3MB, alloc=540.3MB, time=30.52 memory used=1994.5MB, alloc=540.3MB, time=32.13 memory used=2053.7MB, alloc=540.3MB, time=33.24 memory used=2127.5MB, alloc=540.3MB, time=34.89 memory used=2196.7MB, alloc=540.3MB, time=36.44 memory used=2258.5MB, alloc=540.3MB, time=37.86 memory used=2318.4MB, alloc=540.3MB, time=39.20 memory used=2544.4MB, alloc=564.3MB, time=43.69 memory used=2754.5MB, alloc=588.3MB, time=47.53 memory used=2998.2MB, alloc=612.3MB, time=50.55 memory used=3180.3MB, alloc=612.3MB, time=53.42 memory used=3350.8MB, alloc=636.3MB, time=56.70 memory used=3513.7MB, alloc=636.3MB, time=60.00 memory used=3684.7MB, alloc=660.3MB, time=63.75 memory used=3859.7MB, alloc=660.3MB, time=67.59 memory used=4001.8MB, alloc=684.3MB, time=70.81 memory used=4155.3MB, alloc=684.3MB, time=74.29 memory used=4306.2MB, alloc=684.3MB, time=77.80 memory used=4421.7MB, alloc=684.3MB, time=80.29 memory used=4537.7MB, alloc=684.3MB, time=83.40 memory used=4644.1MB, alloc=684.3MB, time=86.56 memory used=4764.9MB, alloc=708.3MB, time=89.88 memory used=5144.8MB, alloc=732.3MB, time=97.22 memory used=5530.8MB, alloc=756.3MB, time=103.63 memory used=5945.9MB, alloc=780.3MB, time=113.52 memory used=6352.3MB, alloc=804.3MB, time=123.01 memory used=6786.6MB, alloc=828.3MB, time=132.02 memory used=7190.6MB, alloc=852.3MB, time=139.82 memory used=7532.0MB, alloc=876.3MB, time=145.59 memory used=7838.5MB, alloc=900.3MB, time=152.48 memory used=8216.9MB, alloc=924.3MB, time=161.10 memory used=8558.0MB, alloc=948.3MB, time=167.91 memory used=8844.9MB, alloc=972.3MB, time=174.40 memory used=9117.0MB, alloc=996.3MB, time=182.06 memory used=9375.1MB, alloc=1020.3MB, time=189.73 memory used=9602.8MB, alloc=1020.3MB, time=195.98 memory used=10256.2MB, alloc=1044.3MB, time=210.83 memory used=10914.4MB, alloc=1068.3MB, time=227.38 memory used=11547.4MB, alloc=1092.3MB, time=241.29 memory used=12174.1MB, alloc=1116.3MB, time=251.23 memory used=12894.6MB, alloc=1140.3MB, time=269.77 memory used=13617.2MB, alloc=1164.3MB, time=287.18 memory used=14200.6MB, alloc=1188.3MB, time=298.33 memory used=14870.6MB, alloc=1212.3MB, time=311.70 memory used=15167.3MB, alloc=1236.3MB, time=317.02 memory used=15488.6MB, alloc=1260.3MB, time=322.25 memory used=16103.9MB, alloc=1284.3MB, time=331.60 memory used=16742.9MB, alloc=1308.3MB, time=344.88 memory used=17374.1MB, alloc=1332.3MB, time=353.68 memory used=17682.7MB, alloc=1356.3MB, time=357.24 memory used=18060.1MB, alloc=1380.3MB, time=360.81 memory used=18179.3MB, alloc=1419.8MB, time=364.00 memory used=18258.7MB, alloc=1443.8MB, time=367.20 memory used=18343.2MB, alloc=1467.8MB, time=370.29 memory used=18434.4MB, alloc=1491.8MB, time=373.44 memory used=18956.7MB, alloc=1515.8MB, time=377.83 memory used=19413.5MB, alloc=1515.8MB, time=381.47 memory used=19491.5MB, alloc=1515.8MB, time=384.60 memory used=19576.0MB, alloc=1515.8MB, time=387.71 memory used=19667.5MB, alloc=1515.8MB, time=390.98 memory used=20222.9MB, alloc=1515.8MB, time=405.27 memory used=20299.8MB, alloc=1515.8MB, time=408.40 memory used=20385.3MB, alloc=1515.8MB, time=411.53 memory used=20479.6MB, alloc=1515.8MB, time=414.84 memory used=20582.2MB, alloc=1515.8MB, time=417.99 memory used=20695.0MB, alloc=1515.8MB, time=421.13 memory used=20819.7MB, alloc=1515.8MB, time=424.30 memory used=20958.7MB, alloc=1515.8MB, time=427.47 memory used=21065.2MB, alloc=1515.8MB, time=430.59 memory used=21175.0MB, alloc=1515.8MB, time=433.72 memory used=21455.2MB, alloc=1515.8MB, time=440.52 memory used=22348.0MB, alloc=1539.8MB, time=453.31 memory used=22960.1MB, alloc=1563.8MB, time=467.62 memory used=23645.8MB, alloc=1563.8MB, time=476.36 memory used=23742.4MB, alloc=1563.8MB, time=480.17 memory used=23861.7MB, alloc=1563.8MB, time=483.94 memory used=24218.0MB, alloc=1563.8MB, time=489.22 memory used=24316.0MB, alloc=1563.8MB, time=492.94 memory used=24774.5MB, alloc=1563.8MB, time=500.11 memory used=25494.5MB, alloc=1587.8MB, time=514.03 memory used=26120.4MB, alloc=1611.8MB, time=532.02 memory used=26990.7MB, alloc=1635.8MB, time=546.84 memory used=27555.0MB, alloc=1659.8MB, time=559.46 memory used=28058.6MB, alloc=1683.8MB, time=570.38 memory used=28730.5MB, alloc=1707.8MB, time=582.81 memory used=29030.8MB, alloc=1731.8MB, time=587.24 memory used=29108.7MB, alloc=1731.8MB, time=591.33 memory used=29189.5MB, alloc=1731.8MB, time=595.45 memory used=29275.9MB, alloc=1731.8MB, time=599.54 memory used=29368.0MB, alloc=1731.8MB, time=603.63 memory used=29465.6MB, alloc=1731.8MB, time=607.73 memory used=29568.5MB, alloc=1731.8MB, time=611.84 memory used=29676.6MB, alloc=1731.8MB, time=615.96 memory used=29793.3MB, alloc=1731.8MB, time=620.07 memory used=29917.9MB, alloc=1731.8MB, time=624.18 memory used=30049.8MB, alloc=1731.8MB, time=628.28 memory used=30188.0MB, alloc=1731.8MB, time=632.42 memory used=30288.2MB, alloc=1731.8MB, time=636.49 memory used=30387.7MB, alloc=1731.8MB, time=640.65 memory used=30492.6MB, alloc=1731.8MB, time=644.74 memory used=30601.2MB, alloc=1731.8MB, time=648.81 memory used=30715.6MB, alloc=1731.8MB, time=652.91 memory used=30836.0MB, alloc=1731.8MB, time=656.98 memory used=30964.0MB, alloc=1731.8MB, time=661.06 memory used=31339.6MB, alloc=1731.8MB, time=665.73 memory used=31495.9MB, alloc=1731.8MB, time=672.14 memory used=32093.7MB, alloc=1731.8MB, time=683.51 memory used=32294.6MB, alloc=1731.8MB, time=687.73 memory used=33036.3MB, alloc=1755.8MB, time=696.86 memory used=33807.2MB, alloc=1779.8MB, time=716.58 memory used=34270.0MB, alloc=1779.8MB, time=729.84 memory used=34716.4MB, alloc=1803.8MB, time=742.32 memory used=35145.1MB, alloc=1827.8MB, time=753.17 memory used=36041.6MB, alloc=1827.8MB, time=765.80 memory used=36794.8MB, alloc=1851.8MB, time=777.85 memory used=37464.0MB, alloc=1875.8MB, time=789.79 memory used=38085.6MB, alloc=1899.8MB, time=801.09 memory used=38878.7MB, alloc=1923.8MB, time=812.91 memory used=39305.3MB, alloc=1947.8MB, time=824.67 memory used=39687.9MB, alloc=1971.8MB, time=837.49 memory used=40116.3MB, alloc=1995.8MB, time=851.04 memory used=40544.5MB, alloc=2019.8MB, time=864.50 memory used=40974.0MB, alloc=2043.8MB, time=877.97 memory used=41365.4MB, alloc=2067.8MB, time=891.21 memory used=41786.0MB, alloc=2091.8MB, time=905.20 memory used=42208.4MB, alloc=2115.8MB, time=916.71 memory used=42540.1MB, alloc=2139.8MB, time=929.32 memory used=42896.5MB, alloc=2163.8MB, time=942.52 memory used=43227.2MB, alloc=2187.8MB, time=954.70 memory used=43617.5MB, alloc=2211.8MB, time=968.64 memory used=44043.2MB, alloc=2235.8MB, time=982.78 memory used=44309.9MB, alloc=2259.8MB, time=994.43 memory used=44567.2MB, alloc=2283.8MB, time=1005.73 memory used=44838.3MB, alloc=2307.8MB, time=1017.41 memory used=45123.7MB, alloc=2331.8MB, time=1029.19 memory used=45509.5MB, alloc=2355.8MB, time=1042.80 memory used=45901.8MB, alloc=2379.8MB, time=1055.72 memory used=46123.1MB, alloc=2403.8MB, time=1066.20 memory used=46421.5MB, alloc=2427.8MB, time=1078.32 memory used=46768.2MB, alloc=2451.8MB, time=1090.68 memory used=46968.0MB, alloc=2475.8MB, time=1100.29 memory used=47259.1MB, alloc=2499.8MB, time=1111.21 memory used=47570.2MB, alloc=2523.8MB, time=1122.03 memory used=48100.6MB, alloc=2547.8MB, time=1135.20 memory used=48488.2MB, alloc=2571.8MB, time=1146.49 memory used=48789.3MB, alloc=2595.8MB, time=1156.34 memory used=49022.6MB, alloc=2619.8MB, time=1164.99 memory used=49551.3MB, alloc=2643.8MB, time=1178.35 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428480966 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 3 F := [12 x y - 17 x y z + 20 y, -15 x y z + 7 z - 6 x z, 2 2 2 2 3 x z + 3 x y + 16 x z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 3 2 2 G := [7 z + 5 y + 4 z, 6 y z - 5 x z + 13 x z, -12 x z - 9 y z + 9] > Problem := [F,G]; 3 2 2 3 Problem := [[12 x y - 17 x y z + 20 y, -15 x y z + 7 z - 6 x z, 2 2 2 2 3 x z + 3 x y + 16 x z ], 3 2 3 2 3 2 2 [7 z + 5 y + 4 z, 6 y z - 5 x z + 13 x z, -12 x z - 9 y z + 9]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.7MB, alloc=32.3MB, time=0.50 memory used=47.9MB, alloc=32.3MB, time=0.81 memory used=68.0MB, alloc=32.3MB, time=1.11 memory used=87.1MB, alloc=56.3MB, time=1.40 memory used=127.8MB, alloc=60.3MB, time=2.00 memory used=167.8MB, alloc=60.3MB, time=2.60 memory used=206.6MB, alloc=84.3MB, time=3.20 memory used=267.3MB, alloc=92.3MB, time=4.14 memory used=327.3MB, alloc=116.3MB, time=5.06 memory used=398.0MB, alloc=116.3MB, time=5.96 memory used=469.4MB, alloc=372.3MB, time=6.91 memory used=563.3MB, alloc=396.3MB, time=8.05 memory used=677.4MB, alloc=420.3MB, time=9.56 memory used=812.2MB, alloc=444.3MB, time=11.48 memory used=932.4MB, alloc=444.3MB, time=12.95 memory used=1062.9MB, alloc=468.3MB, time=14.93 memory used=1174.1MB, alloc=468.3MB, time=16.50 memory used=1287.2MB, alloc=468.3MB, time=18.12 memory used=1388.9MB, alloc=492.3MB, time=19.51 memory used=1488.0MB, alloc=492.3MB, time=20.84 memory used=1582.6MB, alloc=492.3MB, time=22.31 memory used=1664.1MB, alloc=492.3MB, time=23.34 memory used=1753.7MB, alloc=492.3MB, time=24.82 memory used=1838.7MB, alloc=492.3MB, time=26.12 memory used=1920.0MB, alloc=492.3MB, time=27.38 memory used=2001.7MB, alloc=492.3MB, time=28.78 memory used=2079.6MB, alloc=492.3MB, time=30.32 memory used=2141.9MB, alloc=492.3MB, time=31.46 memory used=2212.2MB, alloc=516.3MB, time=32.88 memory used=2273.2MB, alloc=516.3MB, time=34.02 memory used=2335.5MB, alloc=516.3MB, time=35.32 memory used=2386.6MB, alloc=516.3MB, time=36.29 memory used=2433.6MB, alloc=516.3MB, time=37.28 memory used=2647.6MB, alloc=540.3MB, time=40.87 memory used=2854.7MB, alloc=564.3MB, time=44.09 memory used=3054.4MB, alloc=588.3MB, time=47.07 memory used=3265.0MB, alloc=612.3MB, time=49.90 memory used=3472.9MB, alloc=636.3MB, time=53.06 memory used=3659.7MB, alloc=636.3MB, time=56.00 memory used=3803.3MB, alloc=636.3MB, time=58.53 memory used=3953.9MB, alloc=636.3MB, time=61.26 memory used=4103.8MB, alloc=636.3MB, time=63.68 memory used=4269.3MB, alloc=660.3MB, time=66.06 memory used=4403.7MB, alloc=660.3MB, time=68.36 memory used=4515.1MB, alloc=660.3MB, time=70.29 memory used=4642.2MB, alloc=660.3MB, time=72.75 memory used=4759.0MB, alloc=660.3MB, time=74.91 memory used=4855.4MB, alloc=660.3MB, time=76.86 memory used=4965.5MB, alloc=660.3MB, time=79.11 memory used=5308.8MB, alloc=684.3MB, time=84.60 memory used=5677.7MB, alloc=708.3MB, time=90.49 memory used=6000.5MB, alloc=732.3MB, time=94.78 memory used=6422.6MB, alloc=756.3MB, time=100.80 memory used=6837.2MB, alloc=780.3MB, time=107.50 memory used=7242.9MB, alloc=804.3MB, time=113.34 memory used=7621.4MB, alloc=828.3MB, time=119.87 memory used=8039.9MB, alloc=852.3MB, time=125.46 memory used=8485.4MB, alloc=876.3MB, time=131.39 memory used=8731.5MB, alloc=900.3MB, time=135.87 memory used=8936.8MB, alloc=924.3MB, time=137.54 memory used=9166.7MB, alloc=948.3MB, time=139.10 memory used=9685.2MB, alloc=972.3MB, time=144.29 memory used=10111.0MB, alloc=972.3MB, time=149.42 memory used=10514.0MB, alloc=996.3MB, time=155.39 memory used=10945.8MB, alloc=1020.3MB, time=161.07 memory used=11479.0MB, alloc=1020.3MB, time=166.72 memory used=11734.1MB, alloc=1020.3MB, time=168.46 memory used=12116.6MB, alloc=1020.3MB, time=172.43 memory used=12395.3MB, alloc=1020.3MB, time=174.44 memory used=12687.6MB, alloc=1020.3MB, time=176.46 memory used=13268.5MB, alloc=1044.3MB, time=182.11 memory used=13956.0MB, alloc=1068.3MB, time=191.49 memory used=14667.1MB, alloc=1092.3MB, time=205.45 memory used=15401.5MB, alloc=1116.3MB, time=214.53 memory used=16125.5MB, alloc=1140.3MB, time=226.84 memory used=16871.3MB, alloc=1164.3MB, time=238.48 memory used=17615.2MB, alloc=1188.3MB, time=248.04 memory used=18306.2MB, alloc=1212.3MB, time=264.80 memory used=19052.5MB, alloc=1236.3MB, time=275.72 memory used=19684.8MB, alloc=1260.3MB, time=289.00 memory used=20337.0MB, alloc=1284.3MB, time=302.39 memory used=20978.0MB, alloc=1308.3MB, time=314.57 memory used=21508.9MB, alloc=1332.3MB, time=325.33 memory used=22237.0MB, alloc=1356.3MB, time=338.07 memory used=22728.5MB, alloc=1380.3MB, time=348.62 memory used=23224.6MB, alloc=1404.3MB, time=360.53 memory used=23697.6MB, alloc=1428.3MB, time=370.82 memory used=24147.5MB, alloc=1452.3MB, time=379.39 memory used=24576.6MB, alloc=1476.3MB, time=390.79 memory used=24933.5MB, alloc=1500.3MB, time=400.15 memory used=25246.3MB, alloc=1524.3MB, time=408.04 memory used=25632.9MB, alloc=1548.3MB, time=418.63 memory used=25939.7MB, alloc=1572.3MB, time=427.77 memory used=26216.7MB, alloc=1596.3MB, time=435.93 memory used=26609.1MB, alloc=1620.3MB, time=447.16 memory used=26846.4MB, alloc=1644.3MB, time=457.05 memory used=27075.4MB, alloc=1668.3MB, time=467.42 memory used=27302.2MB, alloc=1692.3MB, time=476.60 memory used=27495.5MB, alloc=1716.3MB, time=484.19 memory used=27778.4MB, alloc=1740.3MB, time=495.54 memory used=27931.6MB, alloc=1764.3MB, time=503.91 memory used=28102.7MB, alloc=1788.3MB, time=511.56 memory used=28299.2MB, alloc=1812.3MB, time=519.39 memory used=28429.3MB, alloc=1836.3MB, time=527.16 memory used=28503.8MB, alloc=1860.3MB, time=535.06 memory used=28635.2MB, alloc=1884.3MB, time=543.25 memory used=28740.7MB, alloc=1908.3MB, time=550.46 memory used=28828.8MB, alloc=1932.3MB, time=557.47 memory used=28935.8MB, alloc=1956.3MB, time=564.38 memory used=29054.6MB, alloc=1956.3MB, time=571.68 memory used=29159.2MB, alloc=1956.3MB, time=579.09 memory used=29221.3MB, alloc=1956.3MB, time=585.67 memory used=29244.8MB, alloc=2212.3MB, time=598.19 memory used=30695.7MB, alloc=2236.3MB, time=625.60 memory used=32090.5MB, alloc=2260.3MB, time=658.33 memory used=33378.1MB, alloc=2284.3MB, time=681.63 memory used=34526.6MB, alloc=2308.3MB, time=703.12 memory used=35602.4MB, alloc=2332.3MB, time=722.40 memory used=36924.1MB, alloc=2356.3MB, time=747.25 memory used=37809.1MB, alloc=2380.3MB, time=765.55 memory used=38336.3MB, alloc=2404.3MB, time=776.29 memory used=39325.1MB, alloc=2428.3MB, time=793.58 memory used=40696.7MB, alloc=2452.3MB, time=819.20 memory used=41935.6MB, alloc=2476.3MB, time=844.36 memory used=43173.0MB, alloc=2500.3MB, time=873.63 memory used=44382.2MB, alloc=2524.3MB, time=899.70 memory used=45751.5MB, alloc=2548.3MB, time=926.60 memory used=46322.5MB, alloc=2572.3MB, time=940.00 memory used=47366.4MB, alloc=2596.3MB, time=962.20 memory used=48424.7MB, alloc=2620.3MB, time=985.90 memory used=49565.5MB, alloc=2644.3MB, time=1013.17 memory used=50618.8MB, alloc=2668.3MB, time=1039.59 memory used=51422.3MB, alloc=2692.3MB, time=1063.26 memory used=52284.1MB, alloc=2716.3MB, time=1089.34 memory used=52901.4MB, alloc=2740.3MB, time=1111.44 memory used=53258.2MB, alloc=2764.3MB, time=1128.60 memory used=53841.6MB, alloc=2788.3MB, time=1154.05 memory used=54365.5MB, alloc=2812.3MB, time=1174.05 memory used=54935.3MB, alloc=2836.3MB, time=1198.09 memory used=55413.8MB, alloc=2860.3MB, time=1219.50 memory used=55978.4MB, alloc=2884.3MB, time=1240.24 memory used=56443.3MB, alloc=2908.3MB, time=1264.14 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428482167 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; F := [ 2 2 2 2 4 2 2 2 3 3 4 -x z - 12 x y z + 2 x y, 12 x + 13 x y + 3 z , -x y + 19 y z + z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 3 2 G := [-6 x z + 8 x z - 10, 15 x z + 8 x y + 3 x y z , 2 2 -20 x z + 15 x y - 10 y ] > Problem := [F,G]; Problem := [[ 2 2 2 2 4 2 2 2 3 3 4 -x z - 12 x y z + 2 x y, 12 x + 13 x y + 3 z , -x y + 19 y z + z ] 2 2 2 3 3 2 , [-6 x z + 8 x z - 10, 15 x z + 8 x y + 3 x y z , 2 2 -20 x z + 15 x y - 10 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=25.1MB, alloc=32.3MB, time=0.41 memory used=46.5MB, alloc=32.3MB, time=0.64 memory used=67.8MB, alloc=36.3MB, time=0.86 memory used=86.9MB, alloc=36.3MB, time=0.99 memory used=107.0MB, alloc=36.3MB, time=1.19 memory used=132.9MB, alloc=36.3MB, time=1.52 memory used=146.5MB, alloc=36.3MB, time=1.57 memory used=156.9MB, alloc=36.3MB, time=1.60 memory used=169.4MB, alloc=36.3MB, time=1.64 memory used=177.4MB, alloc=36.3MB, time=1.67 memory used=186.7MB, alloc=36.3MB, time=1.70 memory used=200.7MB, alloc=36.3MB, time=1.79 memory used=211.9MB, alloc=36.3MB, time=1.86 memory used=223.8MB, alloc=36.3MB, time=1.90 memory used=243.9MB, alloc=60.3MB, time=2.13 memory used=303.1MB, alloc=70.8MB, time=2.56 memory used=347.8MB, alloc=71.1MB, time=2.96 memory used=373.8MB, alloc=71.1MB, time=3.04 memory used=412.6MB, alloc=71.1MB, time=3.27 memory used=459.3MB, alloc=71.1MB, time=3.84 memory used=502.2MB, alloc=71.1MB, time=4.41 memory used=543.6MB, alloc=95.1MB, time=4.91 memory used=612.0MB, alloc=95.1MB, time=5.53 memory used=673.1MB, alloc=95.1MB, time=6.07 memory used=708.0MB, alloc=95.1MB, time=6.17 memory used=738.9MB, alloc=95.1MB, time=6.26 memory used=780.9MB, alloc=95.1MB, time=6.81 memory used=828.0MB, alloc=95.1MB, time=7.02 memory used=864.4MB, alloc=95.1MB, time=7.12 memory used=893.5MB, alloc=95.1MB, time=7.22 memory used=928.8MB, alloc=95.1MB, time=7.31 memory used=969.6MB, alloc=95.1MB, time=7.40 memory used=996.0MB, alloc=95.1MB, time=7.48 memory used=1022.7MB, alloc=95.1MB, time=7.55 memory used=1055.5MB, alloc=95.1MB, time=7.65 memory used=1119.0MB, alloc=95.1MB, time=8.29 memory used=1186.0MB, alloc=95.1MB, time=9.12 memory used=1245.7MB, alloc=95.1MB, time=9.64 memory used=1300.8MB, alloc=95.1MB, time=10.32 memory used=1332.4MB, alloc=95.1MB, time=10.45 memory used=1357.6MB, alloc=95.1MB, time=10.55 memory used=1384.6MB, alloc=95.1MB, time=10.67 memory used=1418.0MB, alloc=95.1MB, time=10.76 memory used=1462.1MB, alloc=95.1MB, time=11.34 memory used=1492.4MB, alloc=95.1MB, time=11.46 memory used=1520.5MB, alloc=95.1MB, time=11.56 memory used=1546.2MB, alloc=95.1MB, time=11.66 memory used=1576.5MB, alloc=95.1MB, time=11.77 memory used=1608.2MB, alloc=95.1MB, time=11.87 memory used=1638.6MB, alloc=95.1MB, time=12.12 memory used=1674.6MB, alloc=95.1MB, time=12.29 memory used=1704.1MB, alloc=95.1MB, time=12.40 memory used=1750.1MB, alloc=95.1MB, time=12.84 memory used=1789.2MB, alloc=119.1MB, time=13.00 memory used=1829.2MB, alloc=119.1MB, time=13.16 memory used=1877.1MB, alloc=119.1MB, time=13.32 memory used=1934.6MB, alloc=119.1MB, time=13.48 memory used=1971.9MB, alloc=119.1MB, time=13.61 memory used=2007.9MB, alloc=119.1MB, time=13.74 memory used=2047.1MB, alloc=119.1MB, time=13.88 memory used=2090.3MB, alloc=119.1MB, time=14.02 memory used=2138.1MB, alloc=119.1MB, time=14.18 memory used=2191.2MB, alloc=119.1MB, time=14.31 memory used=2240.9MB, alloc=119.1MB, time=14.45 memory used=2297.1MB, alloc=120.4MB, time=14.78 memory used=2342.9MB, alloc=120.4MB, time=14.90 memory used=2416.5MB, alloc=122.0MB, time=15.41 memory used=2457.3MB, alloc=122.0MB, time=15.57 memory used=2505.2MB, alloc=122.0MB, time=15.72 memory used=2562.7MB, alloc=122.0MB, time=15.87 memory used=2600.0MB, alloc=122.0MB, time=16.01 memory used=2636.0MB, alloc=122.0MB, time=16.15 memory used=2675.2MB, alloc=122.0MB, time=16.29 memory used=2718.4MB, alloc=122.0MB, time=16.43 memory used=2766.2MB, alloc=122.0MB, time=16.57 memory used=2819.2MB, alloc=122.0MB, time=16.72 memory used=2869.0MB, alloc=122.0MB, time=16.85 memory used=2923.9MB, alloc=122.0MB, time=17.13 memory used=2981.3MB, alloc=122.0MB, time=18.59 memory used=3078.0MB, alloc=122.0MB, time=34.98 memory used=3124.9MB, alloc=122.0MB, time=35.15 memory used=3177.7MB, alloc=122.0MB, time=35.30 memory used=3216.5MB, alloc=122.0MB, time=35.44 memory used=3253.1MB, alloc=122.0MB, time=35.57 memory used=3293.7MB, alloc=122.0MB, time=35.70 memory used=3339.3MB, alloc=122.0MB, time=35.84 memory used=3389.9MB, alloc=122.0MB, time=35.98 memory used=3445.3MB, alloc=122.0MB, time=36.13 memory used=3491.6MB, alloc=122.0MB, time=36.25 memory used=3524.0MB, alloc=122.0MB, time=36.36 memory used=3556.8MB, alloc=122.0MB, time=36.47 memory used=3590.0MB, alloc=122.0MB, time=36.58 memory used=3624.7MB, alloc=122.0MB, time=36.69 memory used=3661.9MB, alloc=122.0MB, time=36.80 memory used=3700.3MB, alloc=122.0MB, time=36.90 memory used=3740.9MB, alloc=122.0MB, time=37.01 memory used=3783.5MB, alloc=122.0MB, time=37.12 memory used=3828.8MB, alloc=122.0MB, time=37.23 memory used=3876.2MB, alloc=122.0MB, time=37.35 memory used=3925.9MB, alloc=122.0MB, time=37.46 memory used=3977.8MB, alloc=122.0MB, time=37.58 memory used=4035.2MB, alloc=122.0MB, time=37.69 memory used=4049.2MB, alloc=131.8MB, time=37.78 memory used=4060.0MB, alloc=131.8MB, time=37.86 memory used=4071.3MB, alloc=131.8MB, time=37.94 memory used=4131.1MB, alloc=131.8MB, time=38.42 memory used=4179.2MB, alloc=131.8MB, time=38.67 memory used=4231.1MB, alloc=131.8MB, time=38.83 memory used=4283.4MB, alloc=131.8MB, time=38.98 memory used=4337.2MB, alloc=131.8MB, time=39.15 memory used=4384.5MB, alloc=131.8MB, time=39.52 memory used=4404.5MB, alloc=131.8MB, time=39.62 memory used=4431.4MB, alloc=131.8MB, time=39.72 memory used=4460.7MB, alloc=131.8MB, time=39.83 memory used=4492.2MB, alloc=131.8MB, time=39.93 memory used=4526.0MB, alloc=131.8MB, time=40.03 memory used=4562.2MB, alloc=131.8MB, time=40.13 memory used=4593.6MB, alloc=131.8MB, time=40.23 memory used=4604.6MB, alloc=131.8MB, time=40.31 memory used=4617.5MB, alloc=131.8MB, time=40.40 memory used=4633.3MB, alloc=131.8MB, time=40.49 memory used=4658.8MB, alloc=131.8MB, time=40.59 memory used=4686.9MB, alloc=131.8MB, time=40.69 memory used=4717.3MB, alloc=131.8MB, time=40.79 memory used=4749.9MB, alloc=131.8MB, time=40.89 memory used=4784.9MB, alloc=131.8MB, time=40.99 memory used=4822.4MB, alloc=131.8MB, time=41.10 memory used=4839.6MB, alloc=131.8MB, time=41.18 memory used=4850.7MB, alloc=131.8MB, time=41.26 memory used=4866.3MB, alloc=131.8MB, time=41.34 memory used=4887.7MB, alloc=131.8MB, time=41.44 memory used=4914.8MB, alloc=131.8MB, time=41.55 memory used=4944.3MB, alloc=131.8MB, time=41.64 memory used=4976.0MB, alloc=131.8MB, time=41.74 memory used=5009.8MB, alloc=131.8MB, time=41.85 memory used=5046.1MB, alloc=131.8MB, time=41.95 memory used=5075.6MB, alloc=131.8MB, time=42.03 memory used=5086.6MB, alloc=131.8MB, time=42.11 memory used=5169.5MB, alloc=131.8MB, time=43.19 memory used=5249.2MB, alloc=131.8MB, time=43.84 memory used=5320.8MB, alloc=387.8MB, time=44.53 memory used=5404.4MB, alloc=387.8MB, time=45.40 memory used=5448.0MB, alloc=387.8MB, time=45.55 memory used=5489.3MB, alloc=387.8MB, time=45.68 memory used=5546.1MB, alloc=387.8MB, time=46.01 memory used=5615.6MB, alloc=387.8MB, time=46.74 memory used=5660.1MB, alloc=387.8MB, time=46.89 memory used=5700.1MB, alloc=387.8MB, time=47.04 memory used=5752.3MB, alloc=387.8MB, time=47.30 memory used=5803.7MB, alloc=387.8MB, time=47.54 memory used=5851.5MB, alloc=387.8MB, time=47.68 memory used=5896.8MB, alloc=387.8MB, time=47.81 memory used=5958.3MB, alloc=387.8MB, time=48.56 memory used=6000.7MB, alloc=387.8MB, time=48.71 memory used=6042.5MB, alloc=387.8MB, time=48.84 memory used=6087.2MB, alloc=387.8MB, time=48.97 memory used=6157.4MB, alloc=387.8MB, time=49.45 memory used=6196.4MB, alloc=387.8MB, time=49.61 memory used=6238.0MB, alloc=387.8MB, time=49.77 memory used=6288.8MB, alloc=387.8MB, time=49.93 memory used=6334.8MB, alloc=387.8MB, time=50.08 memory used=6366.3MB, alloc=387.8MB, time=50.22 memory used=6401.1MB, alloc=387.8MB, time=50.36 memory used=6438.9MB, alloc=387.8MB, time=50.49 memory used=6480.1MB, alloc=387.8MB, time=50.64 memory used=6525.1MB, alloc=387.8MB, time=50.78 memory used=6575.7MB, alloc=387.8MB, time=50.92 memory used=6625.8MB, alloc=387.8MB, time=51.15 memory used=6669.7MB, alloc=387.8MB, time=51.37 memory used=6737.8MB, alloc=387.8MB, time=51.89 memory used=6780.4MB, alloc=387.8MB, time=52.08 memory used=6821.7MB, alloc=387.8MB, time=52.26 memory used=6870.6MB, alloc=387.8MB, time=52.43 memory used=6919.2MB, alloc=387.8MB, time=52.62 memory used=6951.4MB, alloc=387.8MB, time=52.79 memory used=6985.9MB, alloc=387.8MB, time=52.93 memory used=7023.7MB, alloc=387.8MB, time=53.07 memory used=7065.0MB, alloc=387.8MB, time=53.20 memory used=7110.3MB, alloc=387.8MB, time=53.35 memory used=7161.0MB, alloc=387.8MB, time=53.50 memory used=7211.7MB, alloc=387.8MB, time=53.72 memory used=7255.5MB, alloc=387.8MB, time=53.94 memory used=7303.6MB, 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memory used=38543.2MB, alloc=651.8MB, time=439.86 memory used=38679.7MB, alloc=651.8MB, time=440.61 memory used=38862.3MB, alloc=651.8MB, time=441.69 memory used=38996.5MB, alloc=651.8MB, time=442.44 memory used=39196.1MB, alloc=651.8MB, time=447.68 memory used=39341.3MB, alloc=651.8MB, time=448.48 memory used=39461.2MB, alloc=651.8MB, time=449.14 memory used=39650.4MB, alloc=651.8MB, time=450.42 memory used=39789.9MB, alloc=651.8MB, time=451.29 memory used=39947.1MB, alloc=651.8MB, time=452.15 memory used=40058.3MB, alloc=651.8MB, time=452.90 memory used=40186.2MB, alloc=651.8MB, time=453.67 memory used=40334.4MB, alloc=651.8MB, time=454.47 memory used=40509.4MB, alloc=651.8MB, time=455.25 memory used=40619.7MB, alloc=651.8MB, time=455.91 memory used=40732.0MB, alloc=651.8MB, time=456.55 memory used=40918.9MB, alloc=651.8MB, time=458.04 memory used=41084.5MB, alloc=651.8MB, time=458.96 memory used=41205.8MB, alloc=651.8MB, time=459.75 memory used=41326.0MB, alloc=651.8MB, time=460.52 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memory used=44640.1MB, alloc=651.8MB, time=507.97 memory used=44748.7MB, alloc=651.8MB, time=508.66 memory used=44983.9MB, alloc=675.8MB, time=510.86 memory used=45224.5MB, alloc=675.8MB, time=522.18 memory used=45375.8MB, alloc=675.8MB, time=523.00 memory used=45514.7MB, alloc=675.8MB, time=523.77 memory used=45646.7MB, alloc=675.8MB, time=524.49 memory used=45880.3MB, alloc=675.8MB, time=526.42 memory used=46029.1MB, alloc=675.8MB, time=528.74 memory used=46168.1MB, alloc=675.8MB, time=530.49 memory used=46323.8MB, alloc=699.8MB, time=532.40 memory used=46536.3MB, alloc=699.8MB, time=534.04 memory used=46663.4MB, alloc=699.8MB, time=536.15 memory used=46770.8MB, alloc=699.8MB, time=538.13 memory used=46863.1MB, alloc=699.8MB, time=539.96 memory used=47230.4MB, alloc=723.8MB, time=544.67 memory used=47597.6MB, alloc=747.8MB, time=549.11 memory used=47964.0MB, alloc=771.8MB, time=555.56 memory used=48319.8MB, alloc=795.8MB, time=559.68 memory used=48574.2MB, alloc=819.8MB, time=563.34 memory used=48795.6MB, alloc=843.8MB, time=564.97 memory used=49069.5MB, alloc=867.8MB, time=568.95 memory used=49339.1MB, alloc=867.8MB, time=570.97 memory used=49578.9MB, alloc=867.8MB, time=572.74 memory used=49846.7MB, alloc=867.8MB, time=574.50 memory used=50197.3MB, alloc=867.8MB, time=662.94 memory used=50383.8MB, alloc=867.8MB, time=664.19 memory used=50548.2MB, alloc=867.8MB, time=665.38 memory used=50722.1MB, alloc=867.8MB, time=666.59 memory used=51025.7MB, alloc=867.8MB, time=669.10 memory used=51296.8MB, alloc=867.8MB, time=670.50 memory used=51521.7MB, alloc=867.8MB, time=672.11 memory used=51755.4MB, alloc=867.8MB, time=673.40 memory used=51893.6MB, alloc=867.8MB, time=674.56 memory used=52076.5MB, alloc=867.8MB, time=676.61 memory used=52288.4MB, alloc=867.8MB, time=677.91 memory used=52517.4MB, alloc=867.8MB, time=679.18 memory used=52706.9MB, alloc=867.8MB, time=680.40 memory used=52869.0MB, alloc=867.8MB, time=681.55 memory used=53038.2MB, alloc=867.8MB, time=682.72 memory used=53214.3MB, alloc=867.8MB, time=683.90 memory used=53388.7MB, alloc=867.8MB, time=685.04 memory used=53553.7MB, alloc=867.8MB, time=686.20 memory used=53724.1MB, alloc=867.8MB, time=687.36 memory used=53899.5MB, alloc=867.8MB, time=688.51 memory used=54082.0MB, alloc=867.8MB, time=689.66 memory used=54254.2MB, alloc=867.8MB, time=690.78 memory used=54423.5MB, alloc=867.8MB, time=691.92 memory used=54884.7MB, alloc=867.8MB, time=697.99 memory used=55354.1MB, alloc=891.8MB, time=704.36 memory used=55763.5MB, alloc=891.8MB, time=712.51 memory used=56143.0MB, alloc=915.8MB, time=718.33 memory used=56521.9MB, alloc=939.8MB, time=723.84 memory used=56774.5MB, alloc=939.8MB, time=725.83 memory used=57056.6MB, alloc=963.8MB, time=727.97 memory used=57352.1MB, alloc=963.8MB, time=729.86 memory used=57613.7MB, alloc=963.8MB, time=731.66 memory used=57956.6MB, alloc=963.8MB, time=739.44 memory used=58208.6MB, alloc=963.8MB, time=741.11 memory used=58459.3MB, alloc=963.8MB, time=742.64 memory used=58821.7MB, alloc=963.8MB, time=744.72 memory used=59118.9MB, alloc=963.8MB, time=746.70 memory used=59387.4MB, alloc=963.8MB, time=748.45 memory used=59724.3MB, alloc=963.8MB, time=756.13 memory used=59972.3MB, alloc=963.8MB, time=757.73 memory used=60231.0MB, alloc=963.8MB, time=759.25 memory used=60608.9MB, alloc=963.8MB, time=761.83 memory used=60866.2MB, alloc=963.8MB, time=763.70 memory used=61104.3MB, alloc=963.8MB, time=765.47 memory used=61396.3MB, alloc=963.8MB, time=767.27 memory used=61648.8MB, alloc=987.8MB, time=769.03 memory used=61856.9MB, alloc=987.8MB, time=770.61 memory used=62093.4MB, alloc=987.8MB, time=772.21 memory used=62368.1MB, alloc=987.8MB, time=773.80 memory used=62723.9MB, alloc=987.8MB, time=776.24 memory used=63013.7MB, alloc=987.8MB, time=778.21 memory used=63259.0MB, alloc=987.8MB, time=780.07 memory used=63564.3MB, alloc=987.8MB, time=781.92 memory used=63840.1MB, alloc=987.8MB, time=783.66 memory used=64049.0MB, alloc=987.8MB, time=785.22 memory used=64285.4MB, alloc=987.8MB, time=786.83 memory used=64560.2MB, alloc=987.8MB, time=788.43 memory used=64992.1MB, alloc=987.8MB, time=819.02 memory used=65279.8MB, alloc=987.8MB, time=820.84 memory used=65526.4MB, alloc=987.8MB, time=822.50 memory used=65779.9MB, alloc=987.8MB, time=824.10 memory used=66093.2MB, alloc=987.8MB, time=825.80 memory used=66323.0MB, alloc=987.8MB, time=827.37 memory used=66438.6MB, alloc=987.8MB, time=828.81 memory used=66564.3MB, alloc=987.8MB, time=830.26 memory used=66782.4MB, alloc=987.8MB, time=832.08 memory used=67118.0MB, alloc=987.8MB, time=840.16 memory used=67383.6MB, alloc=987.8MB, time=841.84 memory used=67661.4MB, alloc=987.8MB, time=843.43 memory used=68265.1MB, alloc=987.8MB, time=850.88 memory used=68582.2MB, alloc=987.8MB, time=853.21 memory used=69083.8MB, alloc=987.8MB, time=870.43 memory used=69360.3MB, alloc=987.8MB, time=872.19 memory used=69581.4MB, alloc=987.8MB, time=873.71 memory used=69869.9MB, alloc=987.8MB, time=875.29 memory used=70091.4MB, alloc=987.8MB, time=876.75 memory used=70503.8MB, alloc=1243.8MB, time=881.58 memory used=71139.6MB, alloc=1267.8MB, time=887.78 memory used=71502.6MB, alloc=1267.8MB, time=898.34 memory used=72110.4MB, alloc=1291.8MB, time=906.53 memory used=72766.8MB, alloc=1315.8MB, time=915.69 memory used=73152.0MB, alloc=1339.8MB, time=919.53 memory used=73476.5MB, alloc=1363.8MB, time=922.43 memory used=73789.7MB, alloc=1387.8MB, time=925.42 memory used=74124.5MB, alloc=1411.8MB, time=928.19 memory used=74542.8MB, alloc=1435.8MB, time=932.12 memory used=74909.9MB, alloc=1435.8MB, time=934.96 memory used=75295.5MB, alloc=1435.8MB, time=937.85 memory used=75669.0MB, alloc=1435.8MB, time=940.44 memory used=76005.9MB, alloc=1435.8MB, time=942.96 memory used=76364.1MB, alloc=1435.8MB, time=946.07 memory used=76718.9MB, alloc=1435.8MB, time=948.51 memory used=77107.8MB, alloc=1435.8MB, time=951.25 memory used=77745.5MB, alloc=1459.8MB, time=957.80 memory used=78435.7MB, alloc=1483.8MB, time=964.47 memory used=79285.9MB, alloc=1507.8MB, time=978.30 memory used=80109.9MB, alloc=1531.8MB, time=991.53 memory used=80854.3MB, alloc=1555.8MB, time=1003.47 memory used=81693.5MB, alloc=1579.8MB, time=1015.87 memory used=82432.1MB, alloc=1603.8MB, time=1025.32 memory used=82795.0MB, alloc=1627.8MB, time=1029.46 memory used=83202.4MB, alloc=1651.8MB, time=1033.52 memory used=83610.0MB, alloc=1675.8MB, time=1040.66 memory used=84068.2MB, alloc=1699.8MB, time=1044.78 memory used=84562.5MB, alloc=1723.8MB, time=1052.56 memory used=84983.6MB, alloc=1747.8MB, time=1056.47 memory used=85494.5MB, alloc=1771.8MB, time=1061.21 memory used=85949.2MB, alloc=1795.8MB, time=1065.17 memory used=86443.4MB, alloc=1795.8MB, time=1069.59 memory used=86929.1MB, alloc=1795.8MB, time=1073.93 memory used=87359.4MB, alloc=1795.8MB, time=1077.72 memory used=87912.7MB, alloc=1795.8MB, time=1097.80 memory used=88361.9MB, alloc=1795.8MB, time=1101.62 memory used=88774.7MB, alloc=1795.8MB, time=1105.44 memory used=89424.6MB, alloc=1795.8MB, time=1114.53 memory used=90025.1MB, alloc=1795.8MB, time=1120.18 memory used=90991.7MB, alloc=1819.8MB, time=1131.57 memory used=91920.3MB, alloc=1843.8MB, time=1141.57 memory used=92480.1MB, alloc=1843.8MB, time=1146.55 memory used=93056.3MB, alloc=1843.8MB, time=1151.41 memory used=93548.2MB, alloc=1843.8MB, time=1155.95 memory used=94161.1MB, alloc=1843.8MB, time=1167.92 memory used=94610.0MB, alloc=1843.8MB, time=1171.99 memory used=95259.5MB, alloc=1843.8MB, time=1176.97 memory used=95815.3MB, alloc=1843.8MB, time=1181.85 memory used=96318.3MB, alloc=1843.8MB, time=1186.21 memory used=96938.2MB, alloc=1843.8MB, time=1197.82 memory used=97372.0MB, alloc=1843.8MB, time=1201.78 memory used=98024.4MB, alloc=1843.8MB, time=1207.72 memory used=98506.6MB, alloc=1867.8MB, time=1212.33 memory used=99016.7MB, alloc=1867.8MB, time=1216.97 memory used=99549.0MB, alloc=1867.8MB, time=1221.22 memory used=99945.0MB, alloc=1867.8MB, time=1225.15 memory used=100429.2MB, alloc=1867.8MB, time=1229.10 memory used=101076.3MB, alloc=1867.8MB, time=1235.31 memory used=101501.4MB, alloc=1867.8MB, time=1239.89 memory used=102069.4MB, alloc=1867.8MB, time=1244.35 memory used=102511.2MB, alloc=1867.8MB, time=1248.45 memory used=102934.7MB, alloc=1867.8MB, time=1252.46 memory used=103609.1MB, alloc=1867.8MB, time=1291.54 memory used=104154.2MB, alloc=1867.8MB, time=1296.09 memory used=104561.2MB, alloc=1867.8MB, time=1299.97 memory used=105073.2MB, alloc=1867.8MB, time=1304.04 memory used=105659.9MB, alloc=1867.8MB, time=1308.29 memory used=105894.5MB, alloc=1867.8MB, time=1311.92 memory used=106609.2MB, alloc=1867.8MB, time=1324.17 memory used=107087.0MB, alloc=1867.8MB, time=1328.30 memory used=107750.0MB, alloc=1867.8MB, time=1333.80 memory used=108364.9MB, alloc=1867.8MB, time=1339.64 memory used=108959.6MB, alloc=1867.8MB, time=1345.26 memory used=109556.3MB, alloc=1867.8MB, time=1351.24 memory used=110109.4MB, alloc=1867.8MB, time=1356.13 memory used=110688.9MB, alloc=1867.8MB, time=1363.63 memory used=111240.8MB, alloc=1867.8MB, time=1368.55 memory used=111851.8MB, alloc=1867.8MB, time=1374.71 memory used=112662.1MB, alloc=1867.8MB, time=1385.56 memory used=113634.6MB, alloc=1891.8MB, time=1396.76 memory used=114279.0MB, alloc=1891.8MB, time=1405.29 memory used=114863.4MB, alloc=1891.8MB, time=1410.26 memory used=115466.5MB, alloc=1891.8MB, time=1418.59 memory used=116000.8MB, alloc=1915.8MB, time=1423.52 memory used=116634.0MB, alloc=1915.8MB, time=1428.82 memory used=117182.7MB, alloc=1915.8MB, time=1440.66 memory used=117790.8MB, alloc=1915.8MB, time=1453.37 memory used=118398.3MB, alloc=1915.8MB, time=1461.41 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428483367 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 3 2 3 2 F := [-8 z - 9 z - 7 x y, 11 x z + 17 x + 1, 5 x y - 6 x y + 4 y z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; G := 2 2 3 2 3 2 2 3 [-15 x y + 16 x y + 12, -5 x y z - 13 y + 3 y, -20 x y + 7 y z + 8] > Problem := [F,G]; Problem := [ 4 3 3 2 3 2 [-8 z - 9 z - 7 x y, 11 x z + 17 x + 1, 5 x y - 6 x y + 4 y z], 2 2 3 2 3 2 2 3 [-15 x y + 16 x y + 12, -5 x y z - 13 y + 3 y, -20 x y + 7 y z + 8] ] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.6MB, alloc=32.3MB, time=0.50 memory used=45.5MB, alloc=56.3MB, time=0.79 memory used=85.8MB, alloc=60.3MB, time=1.37 memory used=128.3MB, alloc=68.3MB, time=1.97 memory used=169.9MB, alloc=92.3MB, time=2.58 memory used=237.7MB, alloc=92.3MB, time=3.40 memory used=307.5MB, alloc=92.3MB, time=4.23 memory used=375.5MB, alloc=92.3MB, time=5.10 memory used=441.3MB, alloc=116.3MB, time=6.07 memory used=521.0MB, alloc=116.3MB, time=6.87 memory used=585.3MB, alloc=116.3MB, time=7.33 memory used=654.5MB, alloc=116.3MB, time=8.04 memory used=699.8MB, alloc=116.3MB, time=8.20 memory used=744.7MB, alloc=116.3MB, time=8.42 memory used=786.9MB, alloc=116.3MB, time=8.61 memory used=848.0MB, alloc=116.3MB, time=9.09 memory used=922.3MB, alloc=372.3MB, time=9.91 memory used=1025.1MB, alloc=372.3MB, time=10.91 memory used=1129.2MB, alloc=372.3MB, time=11.80 memory used=1217.1MB, alloc=396.3MB, time=12.86 memory used=1311.5MB, alloc=396.3MB, time=13.78 memory used=1419.9MB, alloc=396.3MB, time=15.01 memory used=1519.8MB, alloc=420.3MB, time=16.12 memory used=1648.6MB, alloc=420.3MB, time=17.79 memory used=1778.0MB, alloc=444.3MB, time=19.54 memory used=1935.7MB, alloc=444.3MB, time=21.57 memory used=2080.6MB, alloc=444.3MB, time=22.46 memory used=2211.1MB, alloc=444.3MB, time=23.90 memory used=2276.4MB, alloc=444.3MB, time=24.18 memory used=2442.9MB, alloc=468.3MB, time=25.62 memory used=2639.8MB, alloc=468.3MB, time=26.91 memory used=2821.8MB, alloc=468.3MB, time=28.03 memory used=3006.2MB, alloc=468.3MB, time=29.98 memory used=3096.4MB, alloc=468.3MB, time=30.41 memory used=3281.1MB, alloc=468.3MB, time=32.63 memory used=3478.6MB, alloc=468.3MB, time=33.76 memory used=3676.5MB, alloc=468.3MB, time=35.00 memory used=3830.7MB, alloc=468.3MB, time=36.98 memory used=3912.6MB, alloc=468.3MB, time=37.30 memory used=3980.6MB, alloc=468.3MB, time=37.57 memory used=4062.2MB, alloc=468.3MB, time=37.85 memory used=4228.1MB, alloc=468.3MB, time=39.38 memory used=4421.0MB, alloc=468.3MB, time=40.87 memory used=4606.2MB, alloc=468.3MB, time=42.17 memory used=4784.6MB, alloc=468.3MB, time=43.33 memory used=4958.8MB, alloc=468.3MB, time=44.61 memory used=5134.2MB, alloc=468.3MB, time=45.90 memory used=5292.1MB, alloc=468.3MB, time=47.80 memory used=5403.4MB, alloc=468.3MB, time=49.35 memory used=5500.9MB, alloc=492.3MB, time=50.58 memory used=5594.6MB, alloc=492.3MB, time=51.99 memory used=5678.6MB, alloc=492.3MB, time=53.38 memory used=5751.0MB, alloc=492.3MB, time=54.59 memory used=5822.0MB, alloc=492.3MB, time=55.87 memory used=5886.0MB, alloc=492.3MB, time=56.87 memory used=5957.1MB, alloc=516.3MB, time=57.85 memory used=6032.8MB, alloc=516.3MB, time=58.76 memory used=6121.5MB, alloc=516.3MB, time=60.79 memory used=6182.3MB, alloc=516.3MB, time=61.71 memory used=6239.4MB, alloc=516.3MB, time=62.69 memory used=6296.0MB, alloc=516.3MB, time=63.59 memory used=6368.2MB, alloc=540.3MB, time=64.63 memory used=6591.6MB, alloc=564.3MB, time=68.35 memory used=6768.5MB, alloc=588.3MB, time=70.59 memory used=7048.2MB, alloc=588.3MB, time=79.55 memory used=7245.9MB, alloc=612.3MB, time=81.97 memory used=7447.5MB, alloc=636.3MB, time=84.97 memory used=7609.7MB, alloc=636.3MB, time=87.38 memory used=7783.5MB, alloc=660.3MB, time=90.30 memory used=7942.8MB, alloc=660.3MB, time=92.70 memory used=8133.1MB, alloc=684.3MB, time=95.37 memory used=8329.6MB, alloc=684.3MB, time=98.66 memory used=8491.8MB, alloc=684.3MB, time=100.80 memory used=8653.8MB, alloc=684.3MB, time=102.96 memory used=8770.1MB, alloc=684.3MB, time=104.64 memory used=8992.9MB, alloc=684.3MB, time=106.44 memory used=9191.7MB, alloc=684.3MB, time=108.11 memory used=9366.1MB, alloc=684.3MB, time=112.29 memory used=9502.6MB, alloc=684.3MB, time=114.52 memory used=9641.5MB, alloc=684.3MB, time=116.48 memory used=9952.9MB, alloc=708.3MB, time=119.25 memory used=10151.6MB, alloc=708.3MB, time=120.61 memory used=10326.3MB, alloc=708.3MB, time=121.87 memory used=10486.1MB, alloc=708.3MB, time=122.91 memory used=10690.1MB, alloc=708.3MB, time=124.29 memory used=10877.6MB, alloc=708.3MB, time=125.62 memory used=11102.6MB, alloc=708.3MB, time=127.71 memory used=11291.7MB, alloc=708.3MB, time=128.99 memory used=11468.7MB, alloc=708.3MB, time=130.20 memory used=11645.0MB, alloc=708.3MB, time=131.32 memory used=11845.5MB, alloc=732.3MB, time=133.47 memory used=12010.4MB, alloc=732.3MB, time=134.65 memory used=12181.4MB, alloc=732.3MB, time=135.76 memory used=12391.8MB, alloc=732.3MB, time=136.97 memory used=12539.2MB, alloc=732.3MB, time=138.00 memory used=12673.3MB, alloc=756.3MB, time=138.99 memory used=12832.0MB, alloc=756.3MB, time=140.00 memory used=13005.3MB, alloc=756.3MB, time=141.04 memory used=13195.4MB, alloc=756.3MB, time=142.09 memory used=13404.8MB, alloc=756.3MB, time=143.13 memory used=13636.1MB, alloc=756.3MB, time=144.25 memory used=13890.6MB, alloc=756.3MB, time=145.51 memory used=13992.1MB, alloc=756.3MB, time=146.46 memory used=14102.0MB, alloc=756.3MB, time=147.40 memory used=14217.2MB, alloc=756.3MB, time=148.36 memory used=14342.1MB, alloc=756.3MB, time=149.29 memory used=14648.6MB, alloc=756.3MB, time=151.78 memory used=14810.5MB, alloc=756.3MB, time=152.97 memory used=15016.3MB, alloc=756.3MB, time=154.14 memory used=15229.6MB, alloc=756.3MB, time=155.28 memory used=15370.0MB, alloc=756.3MB, time=156.28 memory used=15524.8MB, alloc=756.3MB, time=157.31 memory used=15696.9MB, alloc=756.3MB, time=158.38 memory used=15885.3MB, alloc=756.3MB, time=159.46 memory used=16094.7MB, alloc=756.3MB, time=160.51 memory used=16322.0MB, alloc=756.3MB, time=161.61 memory used=16639.0MB, alloc=756.3MB, time=162.87 memory used=16740.5MB, alloc=756.3MB, time=163.81 memory used=16847.9MB, alloc=756.3MB, time=164.75 memory used=16963.0MB, alloc=756.3MB, time=165.69 memory used=17087.5MB, alloc=756.3MB, time=166.65 memory used=17472.9MB, alloc=780.3MB, time=483.34 memory used=17706.9MB, alloc=780.3MB, time=574.41 memory used=17924.7MB, alloc=780.3MB, time=575.66 memory used=18090.4MB, alloc=780.3MB, time=576.76 memory used=18276.1MB, alloc=780.3MB, time=577.88 memory used=18491.1MB, alloc=780.3MB, time=579.03 memory used=18741.6MB, alloc=780.3MB, time=580.19 memory used=18916.1MB, alloc=780.3MB, time=581.25 memory used=19027.3MB, alloc=795.8MB, time=582.26 memory used=19143.5MB, alloc=795.8MB, time=583.27 memory used=19267.3MB, alloc=795.8MB, time=584.26 memory used=19393.6MB, alloc=795.8MB, time=585.26 memory used=19527.4MB, alloc=795.8MB, time=586.29 memory used=19668.7MB, alloc=795.8MB, time=587.39 memory used=19817.3MB, alloc=795.8MB, time=588.41 memory used=19968.0MB, alloc=795.8MB, time=589.42 memory used=20125.4MB, alloc=795.8MB, time=590.45 memory used=20294.7MB, alloc=795.8MB, time=591.49 memory used=20470.9MB, alloc=795.8MB, time=592.57 memory used=20652.8MB, alloc=795.8MB, time=593.67 memory used=20845.3MB, alloc=795.8MB, time=594.72 memory used=21042.4MB, alloc=795.8MB, time=595.78 memory used=21236.0MB, alloc=795.8MB, time=596.84 memory used=21376.2MB, alloc=795.8MB, time=597.82 memory used=21521.4MB, alloc=795.8MB, time=598.78 memory used=21670.1MB, alloc=795.8MB, time=599.75 memory used=21824.6MB, alloc=795.8MB, time=600.79 memory used=21985.1MB, alloc=795.8MB, time=601.84 memory used=22154.4MB, alloc=795.8MB, time=602.88 memory used=22326.5MB, alloc=795.8MB, time=603.89 memory used=22505.6MB, alloc=795.8MB, time=604.91 memory used=22693.3MB, alloc=795.8MB, time=605.95 memory used=22893.7MB, alloc=795.8MB, time=607.04 memory used=23088.5MB, alloc=795.8MB, time=608.10 memory used=23424.4MB, alloc=795.8MB, time=610.42 memory used=23604.6MB, alloc=795.8MB, time=611.62 memory used=23839.7MB, alloc=795.8MB, time=612.89 memory used=24038.8MB, alloc=795.8MB, time=614.08 memory used=24196.1MB, alloc=795.8MB, time=615.17 memory used=24372.9MB, alloc=795.8MB, time=616.22 memory used=24567.5MB, alloc=795.8MB, time=617.30 memory used=24784.8MB, alloc=795.8MB, time=618.42 memory used=25022.9MB, alloc=795.8MB, time=619.58 memory used=25292.0MB, alloc=795.8MB, time=620.75 memory used=25412.4MB, alloc=795.8MB, time=621.71 memory used=25522.9MB, alloc=795.8MB, time=622.67 memory used=25642.1MB, alloc=795.8MB, time=623.64 memory used=25768.1MB, alloc=795.8MB, time=624.63 memory used=25907.9MB, alloc=795.8MB, time=625.61 memory used=26167.6MB, alloc=795.8MB, time=627.83 memory used=26351.2MB, alloc=795.8MB, time=629.03 memory used=26588.2MB, alloc=795.8MB, time=630.27 memory used=26784.4MB, alloc=795.8MB, time=631.45 memory used=26945.2MB, alloc=795.8MB, time=632.56 memory used=27122.4MB, alloc=795.8MB, time=633.62 memory used=27317.3MB, alloc=795.8MB, time=634.70 memory used=27534.8MB, alloc=795.8MB, time=635.80 memory used=27778.0MB, alloc=795.8MB, time=636.91 memory used=28147.2MB, alloc=795.8MB, time=638.25 memory used=28258.4MB, alloc=795.8MB, time=639.24 memory used=28375.8MB, alloc=795.8MB, time=640.22 memory used=28502.0MB, alloc=795.8MB, time=641.17 memory used=28641.3MB, alloc=795.8MB, time=642.13 memory used=28992.7MB, alloc=795.8MB, time=1022.74 memory used=29212.3MB, alloc=795.8MB, time=1051.45 memory used=29436.6MB, alloc=795.8MB, time=1052.68 memory used=29593.4MB, alloc=795.8MB, time=1053.74 memory used=29778.6MB, alloc=795.8MB, time=1054.83 memory used=29999.4MB, alloc=795.8MB, time=1055.94 memory used=30251.8MB, alloc=795.8MB, time=1057.07 memory used=30412.2MB, alloc=795.8MB, time=1058.11 memory used=30524.6MB, alloc=795.8MB, time=1059.09 memory used=30641.1MB, alloc=795.8MB, time=1060.07 memory used=30765.1MB, alloc=795.8MB, time=1061.04 memory used=30891.6MB, alloc=795.8MB, time=1062.05 memory used=31025.5MB, alloc=795.8MB, time=1063.05 memory used=31166.9MB, alloc=795.8MB, time=1064.05 memory used=31315.7MB, alloc=795.8MB, time=1065.04 memory used=31471.7MB, alloc=795.8MB, time=1066.09 memory used=31634.7MB, alloc=795.8MB, time=1067.12 memory used=31804.4MB, alloc=795.8MB, time=1068.13 memory used=31980.7MB, alloc=795.8MB, time=1069.15 memory used=32162.5MB, alloc=795.8MB, time=1070.18 memory used=32355.0MB, alloc=795.8MB, time=1071.23 memory used=32557.4MB, alloc=795.8MB, time=1072.28 memory used=32745.3MB, alloc=795.8MB, time=1073.33 memory used=32885.1MB, alloc=795.8MB, time=1074.33 memory used=33029.7MB, alloc=795.8MB, time=1075.35 memory used=33182.6MB, alloc=795.8MB, time=1076.37 memory used=33337.5MB, alloc=795.8MB, time=1077.36 memory used=33501.5MB, alloc=795.8MB, time=1078.37 memory used=33669.8MB, alloc=795.8MB, time=1079.39 memory used=33844.3MB, alloc=795.8MB, time=1080.41 memory used=34026.3MB, alloc=795.8MB, time=1081.47 memory used=34215.8MB, alloc=795.8MB, time=1082.54 memory used=34418.5MB, alloc=795.8MB, time=1083.58 memory used=34607.1MB, alloc=795.8MB, time=1084.60 memory used=34922.0MB, alloc=795.8MB, time=1087.66 memory used=35102.0MB, alloc=795.8MB, time=1088.90 memory used=35312.3MB, alloc=795.8MB, time=1090.11 memory used=35565.0MB, alloc=795.8MB, time=1091.35 memory used=35736.3MB, alloc=795.8MB, time=1092.44 memory used=35887.7MB, alloc=795.8MB, time=1093.49 memory used=36053.0MB, alloc=795.8MB, time=1094.54 memory used=36232.0MB, alloc=795.8MB, time=1095.60 memory used=36424.4MB, alloc=795.8MB, time=1096.68 memory used=36630.4MB, alloc=795.8MB, time=1097.75 memory used=36855.6MB, alloc=795.8MB, time=1098.86 memory used=37101.1MB, alloc=795.8MB, time=1099.99 memory used=37364.3MB, alloc=795.8MB, time=1101.13 memory used=37574.4MB, alloc=795.8MB, time=1102.22 memory used=37676.3MB, alloc=795.8MB, time=1103.16 memory used=37780.9MB, alloc=795.8MB, time=1104.11 memory used=37889.2MB, alloc=795.8MB, time=1105.05 memory used=38004.0MB, alloc=795.8MB, time=1106.00 memory used=38123.3MB, alloc=795.8MB, time=1106.98 memory used=38246.0MB, alloc=795.8MB, time=1107.94 memory used=38372.2MB, alloc=795.8MB, time=1108.93 memory used=38504.1MB, alloc=795.8MB, time=1109.90 memory used=38644.9MB, alloc=795.8MB, time=1110.90 memory used=38791.5MB, alloc=795.8MB, time=1111.90 memory used=38949.6MB, alloc=795.8MB, time=1112.91 memory used=39286.2MB, alloc=819.8MB, time=1126.35 memory used=39509.9MB, alloc=819.8MB, time=1127.63 memory used=39765.6MB, alloc=843.8MB, time=1128.97 memory used=39988.5MB, alloc=867.8MB, time=1130.19 memory used=40148.6MB, alloc=867.8MB, time=1131.25 memory used=40322.2MB, alloc=867.8MB, time=1132.31 memory used=40502.2MB, alloc=867.8MB, time=1133.37 memory used=40688.6MB, alloc=867.8MB, time=1134.47 memory used=40894.3MB, alloc=867.8MB, time=1135.57 memory used=41106.3MB, alloc=867.8MB, time=1136.68 memory used=41324.6MB, alloc=867.8MB, time=1137.82 memory used=41563.4MB, alloc=867.8MB, time=1138.97 memory used=41808.1MB, alloc=867.8MB, time=1140.12 memory used=42058.7MB, alloc=867.8MB, time=1141.29 memory used=42330.4MB, alloc=867.8MB, time=1142.46 memory used=42607.5MB, alloc=867.8MB, time=1143.63 memory used=42889.7MB, alloc=867.8MB, time=1144.83 memory used=43193.0MB, alloc=867.8MB, time=1146.03 memory used=43428.2MB, alloc=867.8MB, time=1147.17 memory used=43523.6MB, alloc=867.8MB, time=1148.12 memory used=43608.2MB, alloc=867.8MB, time=1149.07 memory used=43693.0MB, alloc=867.8MB, time=1150.03 memory used=43778.0MB, alloc=867.8MB, time=1150.99 memory used=43863.3MB, alloc=867.8MB, time=1151.92 memory used=43949.9MB, alloc=867.8MB, time=1152.88 memory used=44051.7MB, alloc=867.8MB, time=1153.84 memory used=44154.8MB, alloc=867.8MB, time=1154.84 memory used=44258.0MB, alloc=867.8MB, time=1155.80 memory used=44361.6MB, alloc=867.8MB, time=1156.75 memory used=44465.3MB, alloc=867.8MB, time=1157.75 memory used=44569.1MB, alloc=867.8MB, time=1158.66 memory used=44673.1MB, alloc=867.8MB, time=1159.60 memory used=44777.3MB, alloc=867.8MB, time=1160.53 memory used=44881.6MB, alloc=867.8MB, time=1161.46 memory used=44985.9MB, alloc=867.8MB, time=1162.40 memory used=45090.3MB, alloc=867.8MB, time=1163.34 memory used=45194.7MB, alloc=867.8MB, time=1164.29 memory used=45299.2MB, alloc=867.8MB, time=1165.24 memory used=45404.8MB, alloc=867.8MB, time=1166.17 memory used=45525.5MB, alloc=867.8MB, time=1167.13 memory used=45647.3MB, alloc=867.8MB, time=1168.09 memory used=45769.0MB, alloc=867.8MB, time=1169.05 memory used=45890.5MB, alloc=867.8MB, time=1170.01 memory used=46011.9MB, alloc=867.8MB, time=1170.97 memory used=46133.0MB, alloc=867.8MB, time=1171.90 memory used=46253.9MB, alloc=867.8MB, time=1172.86 memory used=46374.6MB, alloc=867.8MB, time=1173.81 memory used=46495.1MB, alloc=867.8MB, time=1174.77 memory used=46632.2MB, alloc=867.8MB, time=1175.75 memory used=46768.8MB, alloc=867.8MB, time=1176.74 memory used=46904.9MB, alloc=867.8MB, time=1177.71 memory used=47040.4MB, alloc=867.8MB, time=1178.67 memory used=47175.3MB, alloc=867.8MB, time=1179.63 memory used=47309.5MB, alloc=867.8MB, time=1180.61 memory used=47444.5MB, alloc=867.8MB, time=1181.59 memory used=47592.1MB, alloc=867.8MB, time=1182.58 memory used=47740.2MB, alloc=867.8MB, time=1183.57 memory used=47887.1MB, alloc=867.8MB, time=1184.59 memory used=48032.8MB, alloc=867.8MB, time=1185.61 memory used=48179.5MB, alloc=867.8MB, time=1186.63 memory used=48336.1MB, alloc=867.8MB, time=1187.67 memory used=48493.2MB, alloc=867.8MB, time=1188.68 memory used=48648.4MB, alloc=867.8MB, time=1189.68 memory used=48816.8MB, alloc=867.8MB, time=1190.70 memory used=48982.7MB, alloc=867.8MB, time=1191.70 memory used=49147.5MB, alloc=867.8MB, time=1192.71 memory used=49320.8MB, alloc=867.8MB, time=1193.77 memory used=49492.1MB, alloc=867.8MB, time=1194.78 memory used=49673.6MB, alloc=867.8MB, time=1195.81 memory used=49852.6MB, alloc=867.8MB, time=1196.82 memory used=50035.9MB, alloc=867.8MB, time=1197.82 memory used=50228.1MB, alloc=867.8MB, time=1198.88 memory used=50425.4MB, alloc=867.8MB, time=1199.90 memory used=50623.2MB, alloc=867.8MB, time=1200.93 memory used=50759.4MB, alloc=867.8MB, time=1201.88 memory used=50892.4MB, alloc=867.8MB, time=1202.83 memory used=51031.4MB, alloc=867.8MB, time=1203.79 memory used=51173.9MB, alloc=867.8MB, time=1204.76 memory used=51317.9MB, alloc=867.8MB, time=1205.71 memory used=51466.3MB, alloc=867.8MB, time=1206.66 memory used=51620.2MB, alloc=867.8MB, time=1207.62 memory used=51782.4MB, alloc=867.8MB, time=1208.56 memory used=51990.9MB, alloc=867.8MB, time=1243.97 memory used=52183.3MB, alloc=867.8MB, time=1483.19 memory used=52347.7MB, alloc=867.8MB, time=1643.53 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428484567 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 2 2 2 F := [-20 x y + 19 y z - 20 y , -9 x y - 6 y z + 17 y , 3 2 5 x y - 20 x y z + 10 y z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 4 2 2 2 G := [-19 x y z - 20 x y z - x y, 13 y z + 18 z - 5 x , 12 y z + 9 z - 17] > Problem := [F,G]; 2 2 2 2 2 2 2 2 Problem := [[-20 x y + 19 y z - 20 y , -9 x y - 6 y z + 17 y , 3 2 5 x y - 20 x y z + 10 y z ], 2 3 4 2 2 2 [-19 x y z - 20 x y z - x y, 13 y z + 18 z - 5 x , 12 y z + 9 z - 17]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.17 memory used=26.6MB, alloc=32.3MB, time=0.48 memory used=47.9MB, alloc=32.3MB, time=0.78 memory used=67.4MB, alloc=32.3MB, time=1.07 memory used=85.6MB, alloc=56.3MB, time=1.35 memory used=123.9MB, alloc=60.3MB, time=1.91 memory used=163.4MB, alloc=84.3MB, time=2.52 memory used=199.9MB, alloc=84.3MB, time=3.08 memory used=263.9MB, alloc=92.3MB, time=4.05 memory used=327.4MB, alloc=116.3MB, time=5.01 memory used=390.3MB, alloc=116.3MB, time=5.97 memory used=453.2MB, alloc=372.3MB, time=6.91 memory used=538.6MB, alloc=396.3MB, time=8.20 memory used=650.7MB, alloc=420.3MB, time=9.85 memory used=784.4MB, alloc=420.3MB, time=11.87 memory used=917.0MB, alloc=444.3MB, time=13.84 memory used=1051.8MB, alloc=468.3MB, time=15.55 memory used=1180.2MB, alloc=468.3MB, time=16.94 memory used=1304.0MB, alloc=468.3MB, time=18.36 memory used=1419.6MB, alloc=468.3MB, time=20.08 memory used=1534.7MB, alloc=492.3MB, time=21.88 memory used=1643.9MB, alloc=492.3MB, time=23.63 memory used=1770.5MB, alloc=492.3MB, time=24.85 memory used=1859.8MB, alloc=492.3MB, time=26.33 memory used=1988.2MB, alloc=492.3MB, time=27.64 memory used=2085.2MB, alloc=516.3MB, time=28.98 memory used=2164.0MB, alloc=516.3MB, time=30.38 memory used=2250.1MB, alloc=516.3MB, time=31.96 memory used=2327.8MB, alloc=516.3MB, time=33.28 memory used=2407.3MB, alloc=516.3MB, time=34.45 memory used=2496.4MB, alloc=516.3MB, time=36.17 memory used=2563.9MB, alloc=516.3MB, time=37.58 memory used=2636.5MB, alloc=516.3MB, time=39.02 memory used=2696.0MB, alloc=516.3MB, time=40.07 memory used=2745.4MB, alloc=540.3MB, time=40.90 memory used=2800.6MB, alloc=540.3MB, time=41.89 memory used=2858.6MB, alloc=540.3MB, time=42.69 memory used=2921.1MB, alloc=540.3MB, time=44.10 memory used=2965.9MB, alloc=540.3MB, time=45.21 memory used=3011.0MB, alloc=540.3MB, time=46.17 memory used=3193.9MB, alloc=564.3MB, time=48.62 memory used=3361.9MB, alloc=588.3MB, time=51.17 memory used=3537.7MB, alloc=612.3MB, time=54.37 memory used=3694.4MB, alloc=612.3MB, time=56.75 memory used=3883.6MB, alloc=636.3MB, time=60.02 memory used=4050.1MB, alloc=660.3MB, time=62.98 memory used=4216.9MB, alloc=660.3MB, time=66.46 memory used=4350.1MB, alloc=660.3MB, time=68.95 memory used=4487.0MB, alloc=660.3MB, time=71.23 memory used=4610.7MB, alloc=660.3MB, time=73.58 memory used=4762.1MB, alloc=684.3MB, time=75.59 memory used=4882.4MB, alloc=684.3MB, time=77.89 memory used=5004.0MB, alloc=684.3MB, time=79.96 memory used=5135.2MB, alloc=684.3MB, time=81.97 memory used=5284.5MB, alloc=708.3MB, time=84.21 memory used=5389.8MB, alloc=708.3MB, time=86.53 memory used=5462.7MB, alloc=708.3MB, time=88.46 memory used=5547.0MB, alloc=708.3MB, time=90.56 memory used=5923.8MB, alloc=732.3MB, time=95.66 memory used=6315.1MB, alloc=756.3MB, time=101.06 memory used=6734.8MB, alloc=780.3MB, time=106.78 memory used=7080.0MB, alloc=804.3MB, time=112.22 memory used=7441.0MB, alloc=828.3MB, time=118.05 memory used=7791.4MB, alloc=852.3MB, time=123.06 memory used=8116.2MB, alloc=876.3MB, time=129.58 memory used=8436.6MB, alloc=900.3MB, time=134.64 memory used=8766.0MB, alloc=924.3MB, time=141.04 memory used=9062.3MB, alloc=948.3MB, time=146.06 memory used=9352.3MB, alloc=972.3MB, time=152.03 memory used=9580.3MB, alloc=996.3MB, time=156.35 memory used=9850.4MB, alloc=1020.3MB, time=162.39 memory used=10072.4MB, alloc=1044.3MB, time=166.75 memory used=10759.7MB, alloc=1068.3MB, time=178.28 memory used=11264.1MB, alloc=1092.3MB, time=184.28 memory used=11623.1MB, alloc=1116.3MB, time=187.49 memory used=12185.8MB, alloc=1140.3MB, time=194.18 memory used=12956.1MB, alloc=1164.3MB, time=204.18 memory used=13413.4MB, alloc=1188.3MB, time=212.22 memory used=13899.4MB, alloc=1188.3MB, time=220.46 memory used=14335.3MB, alloc=1188.3MB, time=224.51 memory used=14764.9MB, alloc=1188.3MB, time=228.37 memory used=15124.5MB, alloc=1188.3MB, time=231.60 memory used=15554.9MB, alloc=1188.3MB, time=257.34 memory used=15951.8MB, alloc=1188.3MB, time=260.78 memory used=16454.7MB, alloc=1188.3MB, time=272.21 memory used=17271.4MB, alloc=1212.3MB, time=282.33 memory used=18114.7MB, alloc=1236.3MB, time=294.05 memory used=18827.9MB, alloc=1260.3MB, time=305.66 memory used=19346.5MB, alloc=1284.3MB, time=313.80 memory used=19842.8MB, alloc=1284.3MB, time=318.43 memory used=20322.4MB, alloc=1284.3MB, time=322.36 memory used=20715.4MB, alloc=1284.3MB, time=325.61 memory used=21181.1MB, alloc=1284.3MB, time=350.76 memory used=21686.4MB, alloc=1284.3MB, time=361.22 memory used=22518.1MB, alloc=1308.3MB, time=374.07 memory used=23363.0MB, alloc=1332.3MB, time=384.92 memory used=24257.0MB, alloc=1356.3MB, time=398.85 memory used=25106.8MB, alloc=1380.3MB, time=413.07 memory used=25912.0MB, alloc=1409.8MB, time=424.64 memory used=26404.0MB, alloc=1433.8MB, time=430.39 memory used=26821.7MB, alloc=1467.8MB, time=436.07 memory used=27657.5MB, alloc=1491.8MB, time=449.06 memory used=28421.7MB, alloc=1515.8MB, time=464.03 memory used=29244.6MB, alloc=1539.8MB, time=478.82 memory used=29719.9MB, alloc=1563.8MB, time=483.65 memory used=30273.2MB, alloc=1587.8MB, time=496.87 memory used=30789.1MB, alloc=1611.8MB, time=501.81 memory used=31408.2MB, alloc=1611.8MB, time=516.71 memory used=31947.7MB, alloc=1611.8MB, time=521.51 memory used=32352.5MB, alloc=1611.8MB, time=525.74 memory used=32980.4MB, alloc=1611.8MB, time=531.28 memory used=33526.4MB, alloc=1611.8MB, time=536.08 memory used=33930.0MB, alloc=1611.8MB, time=540.42 memory used=34513.1MB, alloc=1611.8MB, time=546.61 memory used=35038.0MB, alloc=1611.8MB, time=551.82 memory used=35843.7MB, alloc=1611.8MB, time=578.75 memory used=36862.3MB, alloc=1635.8MB, time=596.14 memory used=37443.3MB, alloc=1659.8MB, time=610.83 memory used=38133.1MB, alloc=1683.8MB, time=624.50 memory used=38936.1MB, alloc=1707.8MB, time=638.61 memory used=39558.8MB, alloc=1731.8MB, time=646.23 memory used=40084.5MB, alloc=1731.8MB, time=651.32 memory used=40678.5MB, alloc=1731.8MB, time=657.18 memory used=41281.7MB, alloc=1731.8MB, time=675.02 memory used=41887.3MB, alloc=1731.8MB, time=680.49 memory used=42465.6MB, alloc=1731.8MB, time=685.86 memory used=43033.8MB, alloc=1731.8MB, time=691.59 memory used=43557.8MB, alloc=1731.8MB, time=696.67 memory used=44150.9MB, alloc=1731.8MB, time=714.91 memory used=44810.0MB, alloc=1731.8MB, time=723.83 memory used=45348.7MB, alloc=1731.8MB, time=729.52 memory used=45929.9MB, alloc=1731.8MB, time=735.16 memory used=46429.3MB, alloc=1755.8MB, time=740.27 memory used=46883.7MB, alloc=1755.8MB, time=745.30 memory used=47412.1MB, alloc=1755.8MB, time=750.32 memory used=48032.6MB, alloc=1755.8MB, time=755.41 memory used=48496.1MB, alloc=1755.8MB, time=760.41 memory used=48570.2MB, alloc=1755.8MB, time=764.72 memory used=48647.3MB, alloc=1755.8MB, time=769.04 memory used=48943.5MB, alloc=1755.8MB, time=776.02 memory used=49497.7MB, alloc=1755.8MB, time=781.72 memory used=50112.9MB, alloc=1755.8MB, time=787.36 memory used=50600.9MB, alloc=1755.8MB, time=792.44 memory used=51063.8MB, alloc=1755.8MB, time=797.37 memory used=51605.2MB, alloc=1755.8MB, time=802.37 memory used=52241.4MB, alloc=1755.8MB, time=807.40 memory used=52618.9MB, alloc=1755.8MB, time=812.18 memory used=52692.3MB, alloc=1755.8MB, time=816.55 memory used=52769.4MB, alloc=1755.8MB, time=820.98 memory used=53221.4MB, alloc=1755.8MB, time=929.87 memory used=53753.9MB, alloc=1755.8MB, time=935.25 memory used=54292.4MB, alloc=1755.8MB, time=940.24 memory used=54743.6MB, alloc=1755.8MB, time=944.99 memory used=54819.8MB, alloc=1755.8MB, time=949.36 memory used=54898.8MB, alloc=1755.8MB, time=953.71 memory used=54981.5MB, alloc=1755.8MB, time=958.12 memory used=55066.7MB, alloc=1755.8MB, time=962.53 memory used=55156.8MB, alloc=1755.8MB, time=967.02 memory used=55251.3MB, alloc=1755.8MB, time=971.58 memory used=55351.5MB, alloc=1755.8MB, time=976.12 memory used=55984.8MB, alloc=1755.8MB, time=982.43 memory used=56533.6MB, alloc=1755.8MB, time=987.71 memory used=57155.8MB, alloc=1755.8MB, time=1022.08 memory used=57691.8MB, alloc=1755.8MB, time=1027.26 memory used=57947.8MB, alloc=1755.8MB, time=1031.94 memory used=58672.1MB, alloc=1755.8MB, time=1039.48 memory used=59334.6MB, alloc=1755.8MB, time=1049.11 memory used=59937.1MB, alloc=1755.8MB, time=1055.50 memory used=60527.3MB, alloc=1755.8MB, time=1062.06 memory used=61384.5MB, alloc=1755.8MB, time=1075.12 memory used=62034.3MB, alloc=1755.8MB, time=1088.32 memory used=62587.7MB, alloc=1779.8MB, time=1100.78 memory used=63085.8MB, alloc=1803.8MB, time=1119.08 memory used=63457.8MB, alloc=1827.8MB, time=1130.18 memory used=63823.7MB, alloc=1827.8MB, time=1143.50 memory used=64209.8MB, alloc=1851.8MB, time=1158.98 memory used=64588.8MB, alloc=1851.8MB, time=1174.97 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428485767 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 3 4 4 3 F := [-15 x z - 15 y z + 16 x , 12 x + 2 y + 11 z , 2 -12 x y z + 4 x y + 17 y] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; G := [ 2 2 2 3 3 2 2 -18 x y - 16 x z + y z, -17 x y - 10 y + 5 z, -12 y z + 13 x z - 3 y ] > Problem := [F,G]; 2 2 3 3 4 4 3 Problem := [[-15 x z - 15 y z + 16 x , 12 x + 2 y + 11 z , 2 -12 x y z + 4 x y + 17 y], [ 2 2 2 3 3 2 2 -18 x y - 16 x z + y z, -17 x y - 10 y + 5 z, -12 y z + 13 x z - 3 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.18 memory used=24.6MB, alloc=32.3MB, time=0.48 memory used=44.0MB, alloc=32.3MB, time=0.75 memory used=62.2MB, alloc=56.3MB, time=1.04 memory used=105.9MB, alloc=68.3MB, time=1.60 memory used=153.6MB, alloc=92.3MB, time=2.17 memory used=217.6MB, alloc=92.3MB, time=2.71 memory used=281.1MB, alloc=92.3MB, time=3.25 memory used=347.4MB, alloc=92.3MB, time=3.94 memory used=409.3MB, alloc=348.3MB, time=4.83 memory used=473.8MB, alloc=372.3MB, time=5.78 memory used=552.3MB, alloc=372.3MB, time=6.41 memory used=630.5MB, alloc=372.3MB, time=7.03 memory used=677.3MB, alloc=372.3MB, time=7.22 memory used=723.2MB, alloc=372.3MB, time=7.38 memory used=781.3MB, alloc=372.3MB, time=8.10 memory used=822.7MB, alloc=372.3MB, time=8.23 memory used=873.1MB, alloc=372.3MB, time=8.54 memory used=970.2MB, alloc=372.3MB, time=9.95 memory used=1009.2MB, alloc=372.3MB, time=10.10 memory used=1051.2MB, alloc=372.3MB, time=10.25 memory used=1099.3MB, alloc=372.3MB, time=10.47 memory used=1153.1MB, alloc=372.3MB, time=12.15 memory used=1211.9MB, alloc=372.3MB, time=12.88 memory used=1248.3MB, alloc=372.3MB, time=13.02 memory used=1289.0MB, alloc=372.3MB, time=13.18 memory used=1334.4MB, alloc=372.3MB, time=13.32 memory used=1364.3MB, alloc=372.3MB, time=13.44 memory used=1397.0MB, alloc=372.3MB, time=13.55 memory used=1434.5MB, alloc=372.3MB, time=13.68 memory used=1511.7MB, alloc=372.3MB, time=14.28 memory used=1609.2MB, alloc=372.3MB, time=15.06 memory used=1710.2MB, alloc=372.3MB, time=16.30 memory used=1814.5MB, alloc=396.3MB, time=17.27 memory used=1947.1MB, alloc=396.3MB, time=18.48 memory used=2049.9MB, alloc=396.3MB, time=19.58 memory used=2170.3MB, alloc=396.3MB, time=21.07 memory used=2283.1MB, alloc=420.3MB, time=22.62 memory used=2402.7MB, alloc=444.3MB, time=24.34 memory used=2545.5MB, alloc=444.3MB, time=25.90 memory used=2655.1MB, alloc=444.3MB, time=26.94 memory used=2717.9MB, alloc=444.3MB, time=27.20 memory used=2790.6MB, alloc=444.3MB, time=27.45 memory used=2887.2MB, alloc=444.3MB, time=27.83 memory used=2952.1MB, alloc=444.3MB, time=28.11 memory used=3052.1MB, alloc=444.3MB, time=31.26 memory used=3127.4MB, alloc=444.3MB, time=31.57 memory used=3180.4MB, alloc=444.3MB, time=31.81 memory used=3243.2MB, alloc=444.3MB, time=32.07 memory used=3317.7MB, alloc=444.3MB, time=32.34 memory used=3531.6MB, alloc=444.3MB, time=32.97 memory used=3778.1MB, alloc=444.3MB, time=34.40 memory used=3909.3MB, alloc=444.3MB, time=35.71 memory used=3975.4MB, alloc=444.3MB, time=36.05 memory used=4051.6MB, alloc=444.3MB, time=36.49 memory used=4118.7MB, alloc=444.3MB, time=36.84 memory used=4228.6MB, alloc=468.3MB, time=37.60 memory used=4307.5MB, alloc=468.3MB, time=37.92 memory used=4406.7MB, alloc=468.3MB, time=38.34 memory used=4484.0MB, alloc=468.3MB, time=38.63 memory used=4590.3MB, alloc=468.3MB, time=40.19 memory used=4670.7MB, alloc=468.3MB, time=40.49 memory used=4743.8MB, alloc=468.3MB, time=40.76 memory used=4874.6MB, alloc=468.3MB, time=41.98 memory used=5018.0MB, alloc=468.3MB, time=43.28 memory used=5158.0MB, alloc=468.3MB, time=44.48 memory used=5272.5MB, alloc=468.3MB, time=45.51 memory used=5365.1MB, alloc=468.3MB, time=46.05 memory used=5439.3MB, alloc=468.3MB, time=46.34 memory used=5535.3MB, alloc=468.3MB, time=46.78 memory used=5658.7MB, alloc=468.3MB, time=50.56 memory used=5734.7MB, alloc=468.3MB, time=50.91 memory used=5814.6MB, alloc=468.3MB, time=51.24 memory used=5888.8MB, alloc=468.3MB, time=51.53 memory used=5951.8MB, alloc=468.3MB, time=51.81 memory used=6025.4MB, alloc=468.3MB, time=52.09 memory used=6115.5MB, alloc=468.3MB, time=52.36 memory used=6225.8MB, alloc=468.3MB, time=53.84 memory used=6348.3MB, alloc=468.3MB, time=54.92 memory used=6437.0MB, alloc=468.3MB, time=56.17 memory used=6514.7MB, alloc=468.3MB, time=57.38 memory used=6601.4MB, alloc=468.3MB, time=58.45 memory used=6711.3MB, alloc=468.3MB, time=59.10 memory used=6824.5MB, alloc=468.3MB, time=60.24 memory used=6912.9MB, alloc=468.3MB, time=60.75 memory used=7056.6MB, alloc=468.3MB, time=63.76 memory used=7129.4MB, alloc=468.3MB, time=64.11 memory used=7213.2MB, alloc=468.3MB, time=64.79 memory used=7332.4MB, alloc=492.3MB, time=66.58 memory used=7417.7MB, alloc=492.3MB, time=66.98 memory used=7510.8MB, alloc=492.3MB, time=67.35 memory used=7583.7MB, alloc=492.3MB, time=67.68 memory used=7668.9MB, alloc=492.3MB, time=68.01 memory used=7770.2MB, alloc=492.3MB, time=68.35 memory used=7928.8MB, alloc=492.3MB, time=69.03 memory used=8041.2MB, alloc=492.3MB, time=69.73 memory used=8131.1MB, alloc=492.3MB, time=70.15 memory used=8215.4MB, alloc=492.3MB, time=70.53 memory used=8319.9MB, alloc=492.3MB, time=70.90 memory used=8454.3MB, alloc=492.3MB, time=85.05 memory used=8544.6MB, alloc=492.3MB, time=85.47 memory used=8625.8MB, alloc=492.3MB, time=85.86 memory used=8727.9MB, alloc=492.3MB, time=86.23 memory used=8812.5MB, alloc=492.3MB, time=86.58 memory used=8879.0MB, alloc=492.3MB, time=86.91 memory used=8950.7MB, alloc=492.3MB, time=87.24 memory used=9029.7MB, alloc=492.3MB, time=87.58 memory used=9116.1MB, alloc=492.3MB, time=87.92 memory used=9209.6MB, alloc=492.3MB, time=88.25 memory used=9309.9MB, alloc=492.3MB, time=88.59 memory used=9418.8MB, alloc=492.3MB, time=88.94 memory used=9641.8MB, alloc=492.3MB, time=89.45 memory used=9782.3MB, alloc=492.3MB, time=89.86 memory used=9937.7MB, alloc=492.3MB, time=90.28 memory used=10109.5MB, alloc=492.3MB, time=90.69 memory used=10412.3MB, alloc=492.3MB, time=92.22 memory used=10490.4MB, alloc=492.3MB, time=93.19 memory used=10595.4MB, alloc=492.3MB, time=94.34 memory used=10652.7MB, alloc=492.3MB, time=95.39 memory used=10754.2MB, alloc=492.3MB, time=96.36 memory used=10861.8MB, alloc=492.3MB, time=97.03 memory used=10984.7MB, alloc=492.3MB, time=99.59 memory used=11069.1MB, alloc=492.3MB, time=100.02 memory used=11161.6MB, alloc=492.3MB, time=100.44 memory used=11231.6MB, alloc=492.3MB, time=100.80 memory used=11318.2MB, alloc=492.3MB, time=101.13 memory used=11439.8MB, alloc=492.3MB, time=101.92 memory used=11558.5MB, alloc=492.3MB, time=102.82 memory used=11617.0MB, alloc=492.3MB, time=103.67 memory used=11728.0MB, alloc=492.3MB, time=104.61 memory used=11844.4MB, alloc=492.3MB, time=108.73 memory used=11929.4MB, alloc=492.3MB, time=109.18 memory used=12009.3MB, alloc=492.3MB, time=109.58 memory used=12081.6MB, alloc=492.3MB, time=109.95 memory used=12177.2MB, alloc=492.3MB, time=110.40 memory used=12272.4MB, alloc=492.3MB, time=111.39 memory used=12340.2MB, alloc=492.3MB, time=112.30 memory used=12391.5MB, alloc=492.3MB, time=113.15 memory used=12434.9MB, alloc=492.3MB, time=113.89 memory used=12490.3MB, alloc=492.3MB, time=114.83 memory used=12549.5MB, alloc=492.3MB, time=115.79 memory used=12595.2MB, alloc=492.3MB, time=116.71 memory used=12636.8MB, alloc=492.3MB, time=117.46 memory used=12687.1MB, alloc=516.3MB, time=118.34 memory used=12885.5MB, alloc=540.3MB, time=120.94 memory used=13116.6MB, alloc=564.3MB, time=123.58 memory used=13279.2MB, alloc=588.3MB, time=125.50 memory used=13487.6MB, alloc=612.3MB, time=127.38 memory used=13688.8MB, alloc=612.3MB, time=129.57 memory used=13865.5MB, alloc=636.3MB, time=131.77 memory used=14042.3MB, alloc=636.3MB, time=134.01 memory used=14186.8MB, alloc=636.3MB, time=135.83 memory used=14368.8MB, alloc=636.3MB, time=137.96 memory used=14584.3MB, alloc=660.3MB, time=139.89 memory used=14735.3MB, alloc=660.3MB, time=141.87 memory used=14838.8MB, alloc=660.3MB, time=144.05 memory used=14916.9MB, alloc=660.3MB, time=145.66 memory used=15015.8MB, alloc=684.3MB, time=147.49 memory used=15104.7MB, alloc=684.3MB, time=149.10 memory used=15462.4MB, alloc=708.3MB, time=153.49 memory used=15825.3MB, alloc=732.3MB, time=158.44 memory used=16127.1MB, alloc=756.3MB, time=161.79 memory used=16323.1MB, alloc=780.3MB, time=163.44 memory used=16526.5MB, alloc=804.3MB, time=164.99 memory used=16789.1MB, alloc=828.3MB, time=167.23 memory used=17046.1MB, alloc=828.3MB, time=172.00 memory used=17239.3MB, alloc=828.3MB, time=173.45 memory used=17483.1MB, alloc=828.3MB, time=175.05 memory used=17723.4MB, alloc=828.3MB, time=177.63 memory used=17962.0MB, alloc=828.3MB, time=179.96 memory used=18205.0MB, alloc=828.3MB, time=182.21 memory used=18498.7MB, alloc=828.3MB, time=187.61 memory used=18748.2MB, alloc=852.3MB, time=189.61 memory used=18972.8MB, alloc=852.3MB, time=191.11 memory used=19222.2MB, alloc=852.3MB, time=192.56 memory used=19401.1MB, alloc=852.3MB, time=193.83 memory used=19665.8MB, alloc=852.3MB, time=195.74 memory used=19883.3MB, alloc=852.3MB, time=197.53 memory used=20095.8MB, alloc=852.3MB, time=199.05 memory used=20383.5MB, alloc=852.3MB, time=220.81 memory used=20610.9MB, alloc=852.3MB, time=222.23 memory used=20802.7MB, alloc=852.3MB, time=223.65 memory used=21067.3MB, alloc=852.3MB, time=225.04 memory used=21191.2MB, alloc=867.8MB, time=226.22 memory used=21556.4MB, alloc=867.8MB, time=228.23 memory used=21854.3MB, alloc=867.8MB, time=235.55 memory used=22065.3MB, alloc=867.8MB, time=237.12 memory used=22347.5MB, alloc=867.8MB, time=239.16 memory used=22602.3MB, alloc=867.8MB, time=240.96 memory used=22868.0MB, alloc=867.8MB, time=247.88 memory used=23080.3MB, alloc=867.8MB, time=249.16 memory used=23385.5MB, alloc=867.8MB, time=251.82 memory used=23628.4MB, alloc=867.8MB, time=253.66 memory used=23815.2MB, alloc=867.8MB, time=255.32 memory used=24047.7MB, alloc=867.8MB, time=256.94 memory used=24317.9MB, alloc=867.8MB, time=258.61 memory used=24482.8MB, alloc=867.8MB, time=259.82 memory used=24654.4MB, alloc=891.8MB, time=261.04 memory used=24855.4MB, alloc=891.8MB, time=262.33 memory used=25079.8MB, alloc=891.8MB, time=263.91 memory used=25327.1MB, alloc=891.8MB, time=265.45 memory used=25604.4MB, alloc=891.8MB, time=266.91 memory used=25933.7MB, alloc=891.8MB, time=268.32 memory used=26309.6MB, alloc=891.8MB, time=271.06 memory used=26520.0MB, alloc=891.8MB, time=272.51 memory used=26761.4MB, alloc=891.8MB, time=274.00 memory used=27055.3MB, alloc=891.8MB, time=275.65 memory used=27236.0MB, alloc=891.8MB, time=277.01 memory used=27423.2MB, alloc=891.8MB, time=278.36 memory used=27626.4MB, alloc=891.8MB, time=279.62 memory used=27850.7MB, alloc=891.8MB, time=280.91 memory used=28102.0MB, alloc=891.8MB, time=282.29 memory used=28382.4MB, alloc=891.8MB, time=283.87 memory used=28676.8MB, alloc=891.8MB, time=285.40 memory used=29122.7MB, alloc=891.8MB, time=368.56 memory used=29373.9MB, alloc=891.8MB, time=370.03 memory used=29565.8MB, alloc=891.8MB, time=371.36 memory used=29801.5MB, alloc=891.8MB, time=372.63 memory used=30089.7MB, alloc=891.8MB, time=373.94 memory used=30245.4MB, alloc=891.8MB, time=375.20 memory used=30363.7MB, alloc=891.8MB, time=376.41 memory used=30491.7MB, alloc=891.8MB, time=377.81 memory used=30628.3MB, alloc=891.8MB, time=379.00 memory used=30778.0MB, alloc=891.8MB, time=380.20 memory used=30947.3MB, alloc=891.8MB, time=381.37 memory used=31538.1MB, alloc=891.8MB, time=387.79 memory used=32041.3MB, alloc=891.8MB, time=394.17 memory used=32652.5MB, alloc=915.8MB, time=400.76 memory used=33124.1MB, alloc=915.8MB, time=407.46 memory used=33432.8MB, alloc=939.8MB, time=425.31 memory used=33654.6MB, alloc=939.8MB, time=426.75 memory used=34025.4MB, alloc=939.8MB, time=428.36 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428486393 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 3 2 2 F := [-5 x z - 9 y z - 9 z , -3 x y z - 9 x + 4] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 G := [18 x y - 13 x y + 19, -17 x y z + 7 x y z + 3 x z ] > Problem := [F,G]; 2 2 2 2 3 2 2 Problem := [[-5 x z - 9 y z - 9 z , -3 x y z - 9 x + 4], 2 2 2 2 2 [18 x y - 13 x y + 19, -17 x y z + 7 x y z + 3 x z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.15 memory used=26.7MB, alloc=32.3MB, time=0.43 memory used=47.0MB, alloc=32.3MB, time=0.66 memory used=65.9MB, alloc=56.3MB, time=0.92 memory used=106.8MB, alloc=60.3MB, time=1.40 memory used=146.4MB, alloc=60.3MB, time=1.89 memory used=184.6MB, alloc=84.3MB, time=2.38 memory used=227.3MB, alloc=84.3MB, time=2.95 memory used=286.5MB, alloc=116.3MB, time=3.84 memory used=366.5MB, alloc=116.3MB, time=5.14 memory used=435.9MB, alloc=140.3MB, time=6.64 memory used=513.1MB, alloc=164.3MB, time=8.83 memory used=610.6MB, alloc=188.3MB, time=11.57 N1 := 2531 > GB := Basis(F, plex(op(vars))); 8 6 3 6 4 3 6 4 GB := [405 x y + 729 x y - 360 x y - 648 x y - 2187 x + 80 x y 2 3 4 2 6 4 2 4 + 144 x y + 2916 x - 1296 x + 192, 405 x + 729 x y + 729 x z 4 2 2 2 2 2 6 - 360 x - 648 x y - 648 x z + 80 x + 144 y + 144 z, 405 x y 4 3 4 2 3 4 2 3 2 + 729 x y - 360 x y - 648 x y - 2187 x + 80 x y + 144 y + 2916 x 6 2 4 4 6 4 2 + 144 y z - 864, 32805 x y + 59049 x y - 8100 x - 43740 x y 2 4 4 4 2 2 2 2 - 52488 x y - 177147 x y + 7200 x + 19440 x y + 26244 x z 4 2 2 2 2 2 + 11664 y + 157464 x y + 6480 x z - 1600 x - 2880 y - 11664 z 8 2 4 6 6 2 - 34992 y - 2880 z, -1476225 x y + 4782969 x y + 656100 x y 4 4 2 6 4 3 6 - 1180980 x y - 4251528 x y - 28697814 x y + 162000 x 4 2 2 4 6 4 2 3 + 583200 x y + 1049760 x y + 944784 y - 3542940 x y + 25509168 x y 4 2 2 4 2 2 + 42902721 x - 388800 x y - 233280 y + 3149280 x y - 129600 x z 3 3 2 2 2 - 5668704 y + 944784 z - 38231752 x + 57600 y + 233280 z - 699840 y + 57600 z + 8503056] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=704.6MB, alloc=188.3MB, time=12.92 memory used=849.3MB, alloc=444.3MB, time=14.66 memory used=993.4MB, alloc=444.3MB, time=16.46 memory used=1122.4MB, alloc=444.3MB, time=17.70 memory used=1247.7MB, alloc=468.3MB, time=19.00 memory used=1410.5MB, alloc=468.3MB, time=21.14 memory used=1611.3MB, alloc=492.3MB, time=23.23 memory used=1726.7MB, alloc=492.3MB, time=24.67 memory used=1811.0MB, alloc=492.3MB, time=25.01 memory used=1916.2MB, alloc=492.3MB, time=25.36 memory used=1984.4MB, alloc=492.3MB, time=25.66 memory used=2089.1MB, alloc=492.3MB, time=26.11 memory used=2196.7MB, alloc=492.3MB, time=30.11 memory used=2296.3MB, alloc=492.3MB, time=30.46 memory used=2434.2MB, alloc=492.3MB, time=31.66 memory used=2777.8MB, alloc=516.3MB, time=44.80 memory used=2872.9MB, alloc=516.3MB, time=45.19 memory used=2990.0MB, alloc=516.3MB, time=45.59 memory used=3105.1MB, alloc=516.3MB, time=45.96 memory used=3181.8MB, alloc=516.3MB, time=46.32 memory used=3265.7MB, alloc=516.3MB, time=46.66 memory used=3358.7MB, alloc=516.3MB, time=46.97 memory used=3462.5MB, alloc=516.3MB, time=47.27 memory used=3585.1MB, alloc=516.3MB, time=52.53 memory used=3711.8MB, alloc=540.3MB, time=197.64 memory used=3842.7MB, alloc=540.3MB, time=231.51 memory used=4733.9MB, alloc=540.3MB, time=245.65 memory used=4844.6MB, alloc=540.3MB, time=246.07 memory used=4935.8MB, alloc=540.3MB, time=246.46 memory used=5022.9MB, alloc=540.3MB, time=247.03 memory used=5112.8MB, alloc=540.3MB, time=247.51 memory used=5207.4MB, alloc=540.3MB, time=247.89 memory used=5306.8MB, alloc=540.3MB, time=248.29 memory used=5411.0MB, alloc=540.3MB, time=248.66 memory used=5519.6MB, alloc=540.3MB, time=249.08 memory used=5634.3MB, alloc=540.3MB, time=249.54 memory used=5754.3MB, alloc=540.3MB, time=249.93 memory used=5879.3MB, alloc=540.3MB, time=250.51 memory used=6010.2MB, alloc=540.3MB, time=250.93 memory used=6147.7MB, alloc=540.3MB, time=251.35 memory used=6293.8MB, alloc=540.3MB, time=251.79 memory used=6414.2MB, alloc=540.3MB, time=252.16 memory used=6495.1MB, alloc=540.3MB, time=252.58 memory used=6575.8MB, alloc=540.3MB, time=252.88 memory used=6658.7MB, alloc=540.3MB, time=253.18 memory used=6744.4MB, alloc=540.3MB, time=253.52 memory used=6832.7MB, alloc=540.3MB, time=253.83 memory used=6924.9MB, alloc=540.3MB, time=254.25 memory used=7022.0MB, alloc=540.3MB, time=254.65 memory used=7258.9MB, alloc=540.3MB, time=257.55 memory used=7489.8MB, alloc=540.3MB, time=259.05 memory used=7740.8MB, alloc=540.3MB, time=262.63 memory used=7964.3MB, alloc=564.3MB, time=265.97 memory used=8242.9MB, alloc=564.3MB, time=270.08 memory used=8523.7MB, alloc=588.3MB, time=273.39 memory used=8771.5MB, alloc=612.3MB, time=277.38 memory used=9043.6MB, alloc=612.3MB, time=280.72 memory used=9257.0MB, alloc=636.3MB, time=284.04 memory used=9449.9MB, alloc=660.3MB, time=287.10 memory used=9653.7MB, alloc=660.3MB, time=291.27 memory used=9864.3MB, alloc=660.3MB, time=293.03 memory used=10034.0MB, alloc=660.3MB, time=294.30 memory used=10304.2MB, alloc=660.3MB, time=297.19 memory used=10472.3MB, alloc=660.3MB, time=300.04 memory used=10686.7MB, alloc=684.3MB, time=302.95 memory used=10876.0MB, alloc=684.3MB, time=306.15 memory used=11015.1MB, alloc=684.3MB, time=308.91 memory used=11167.7MB, alloc=684.3MB, time=311.64 memory used=11346.0MB, alloc=708.3MB, time=314.48 memory used=11652.6MB, alloc=708.3MB, time=321.81 memory used=11885.6MB, alloc=708.3MB, time=324.93 memory used=12021.0MB, alloc=708.3MB, time=327.77 memory used=12182.5MB, alloc=708.3MB, time=330.92 memory used=12294.8MB, alloc=708.3MB, time=333.28 memory used=12431.8MB, alloc=708.3MB, time=336.02 memory used=12554.8MB, alloc=708.3MB, time=338.85 memory used=12661.7MB, alloc=732.3MB, time=341.10 memory used=12788.4MB, alloc=732.3MB, time=343.85 memory used=12899.0MB, alloc=732.3MB, time=346.24 memory used=12991.3MB, alloc=732.3MB, time=348.47 memory used=13096.1MB, alloc=732.3MB, time=351.19 memory used=13183.1MB, alloc=732.3MB, time=353.66 memory used=13554.3MB, alloc=756.3MB, time=359.69 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428486693 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 4 2 F := [-12 x y + 20 y - 15, 16 y + 8 x y - 18 x z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 3 2 G := [13 x z - 2 x y z - 15 y , -4 x y + 16 y z + 16 y] > Problem := [F,G]; 2 4 2 Problem := [[-12 x y + 20 y - 15, 16 y + 8 x y - 18 x z], 2 2 2 2 3 2 [13 x z - 2 x y z - 15 y , -4 x y + 16 y z + 16 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.19 memory used=25.3MB, alloc=32.3MB, time=0.53 memory used=43.6MB, alloc=56.3MB, time=0.82 memory used=82.9MB, alloc=60.3MB, time=1.42 memory used=125.4MB, alloc=68.3MB, time=2.02 memory used=181.2MB, alloc=68.3MB, time=2.69 memory used=211.9MB, alloc=68.3MB, time=2.86 memory used=238.2MB, alloc=68.3MB, time=3.00 memory used=271.3MB, alloc=68.3MB, time=3.14 memory used=290.1MB, alloc=68.3MB, time=3.22 memory used=314.4MB, alloc=68.3MB, time=3.30 memory used=332.6MB, alloc=68.3MB, time=3.36 memory used=349.9MB, alloc=68.3MB, time=3.43 memory used=381.4MB, alloc=68.3MB, time=3.57 memory used=400.3MB, alloc=68.3MB, time=3.64 memory used=423.8MB, alloc=68.3MB, time=3.71 memory used=448.0MB, alloc=68.3MB, time=3.85 memory used=468.7MB, alloc=68.3MB, time=3.92 memory used=496.3MB, alloc=68.3MB, time=4.12 memory used=529.3MB, alloc=68.3MB, time=4.23 memory used=553.5MB, alloc=68.3MB, time=4.32 memory used=570.2MB, alloc=68.3MB, time=4.40 memory used=589.1MB, alloc=68.3MB, time=4.48 memory used=610.1MB, alloc=68.3MB, time=4.56 memory used=633.5MB, alloc=68.3MB, time=4.64 memory used=659.0MB, alloc=68.3MB, time=4.72 memory used=681.8MB, alloc=92.3MB, time=4.81 memory used=709.4MB, alloc=92.3MB, time=4.91 memory used=739.6MB, alloc=92.3MB, time=5.02 memory used=773.1MB, alloc=92.3MB, time=5.14 memory used=809.6MB, alloc=92.3MB, time=5.23 memory used=849.8MB, alloc=92.3MB, time=5.34 memory used=894.4MB, alloc=92.3MB, time=5.44 memory used=942.9MB, alloc=92.3MB, time=5.66 memory used=992.2MB, alloc=92.3MB, time=5.81 memory used=1028.6MB, alloc=92.3MB, time=5.92 memory used=1075.5MB, alloc=92.3MB, time=6.04 memory used=1108.1MB, alloc=92.3MB, time=6.13 memory used=1140.0MB, alloc=92.3MB, time=6.23 memory used=1176.1MB, alloc=92.3MB, time=6.32 memory used=1230.2MB, alloc=92.3MB, time=7.57 memory used=1274.1MB, alloc=92.3MB, time=7.71 memory used=1317.9MB, alloc=92.3MB, time=7.83 memory used=1348.1MB, alloc=92.3MB, time=7.92 memory used=1383.5MB, alloc=92.3MB, time=8.03 memory used=1425.1MB, alloc=92.3MB, time=8.15 memory used=1469.1MB, alloc=92.3MB, time=8.29 memory used=1496.3MB, alloc=92.3MB, time=8.38 memory used=1547.7MB, alloc=92.3MB, time=8.72 memory used=1626.2MB, alloc=94.6MB, time=9.55 memory used=1707.8MB, alloc=94.6MB, time=13.32 memory used=1762.3MB, alloc=94.6MB, time=13.57 memory used=1793.3MB, alloc=94.6MB, time=13.69 memory used=1833.6MB, alloc=94.6MB, time=13.81 memory used=1860.2MB, alloc=94.6MB, time=13.88 memory used=1918.0MB, alloc=94.6MB, time=14.30 memory used=1994.9MB, alloc=94.6MB, time=15.09 memory used=2053.6MB, alloc=94.6MB, time=15.36 memory used=2123.5MB, alloc=94.6MB, time=15.87 memory used=2186.0MB, alloc=94.6MB, time=16.19 memory used=2259.1MB, alloc=94.6MB, time=16.92 memory used=2333.7MB, alloc=94.6MB, time=17.70 memory used=2385.3MB, alloc=94.6MB, time=17.96 memory used=2434.5MB, alloc=118.6MB, time=18.18 memory used=2512.0MB, alloc=118.6MB, time=18.46 memory used=2593.6MB, alloc=118.6MB, time=19.09 memory used=2682.3MB, alloc=118.6MB, time=19.64 memory used=2759.4MB, alloc=118.6MB, time=19.98 memory used=2834.1MB, alloc=118.6MB, time=20.28 memory used=2925.0MB, alloc=118.6MB, time=21.35 memory used=3018.7MB, alloc=118.6MB, time=22.76 memory used=3103.4MB, alloc=142.6MB, time=24.27 memory used=3205.8MB, alloc=142.6MB, time=26.16 memory used=3312.8MB, alloc=166.6MB, time=27.88 memory used=3449.0MB, alloc=166.6MB, time=29.70 memory used=3572.3MB, alloc=190.6MB, time=31.96 memory used=3689.2MB, alloc=214.6MB, time=35.94 memory used=3813.5MB, alloc=238.6MB, time=40.67 memory used=3952.2MB, alloc=262.6MB, time=46.27 memory used=4114.9MB, alloc=262.6MB, time=52.66 memory used=4277.7MB, alloc=286.6MB, time=59.14 N1 := 4935 > GB := Basis(F, plex(op(vars))); 2 4 2 GB := [12 y x - 20 y + 15, -8 y - 4 x y + 9 x z, 5 3 2 -96 x y - 80 y + 60 y + 180 y z - 135 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=4452.0MB, alloc=286.6MB, time=64.87 memory used=4769.3MB, alloc=542.6MB, time=69.41 memory used=4933.7MB, alloc=566.6MB, time=130.58 memory used=5097.9MB, alloc=566.6MB, time=190.20 memory used=5217.2MB, alloc=566.6MB, time=190.66 memory used=5341.9MB, alloc=566.6MB, time=191.13 memory used=5481.0MB, alloc=566.6MB, time=191.58 memory used=5573.6MB, alloc=566.6MB, time=191.95 memory used=5674.0MB, alloc=566.6MB, time=192.31 memory used=5785.4MB, alloc=566.6MB, time=192.71 memory used=5906.3MB, alloc=566.6MB, time=193.13 memory used=6038.7MB, alloc=566.6MB, time=193.51 memory used=6184.6MB, alloc=566.6MB, time=193.92 memory used=6373.8MB, alloc=566.6MB, time=194.47 memory used=6503.8MB, alloc=579.8MB, time=195.07 memory used=6640.1MB, alloc=579.8MB, time=195.46 memory used=6787.7MB, alloc=579.8MB, time=195.86 memory used=6945.9MB, alloc=579.8MB, time=196.28 memory used=7121.8MB, alloc=579.8MB, time=196.69 memory used=7508.9MB, alloc=579.8MB, time=199.95 memory used=7721.8MB, alloc=579.8MB, time=202.47 memory used=7854.2MB, alloc=579.8MB, time=203.14 memory used=7979.7MB, alloc=579.8MB, time=203.64 memory used=8103.3MB, alloc=579.8MB, time=204.17 memory used=8227.4MB, alloc=579.8MB, time=204.87 memory used=8356.3MB, alloc=579.8MB, time=205.43 memory used=8483.0MB, alloc=579.8MB, time=205.99 memory used=8607.4MB, alloc=579.8MB, time=206.79 memory used=8739.9MB, alloc=579.8MB, time=207.46 memory used=8857.8MB, alloc=579.8MB, time=207.95 memory used=8960.7MB, alloc=579.8MB, time=208.39 memory used=9094.7MB, alloc=579.8MB, time=208.80 memory used=9187.6MB, alloc=579.8MB, time=209.14 memory used=9307.0MB, alloc=579.8MB, time=209.64 memory used=9422.0MB, alloc=579.8MB, time=210.10 memory used=9530.5MB, alloc=579.8MB, time=210.63 memory used=9648.0MB, alloc=579.8MB, time=211.04 memory used=9770.6MB, alloc=579.8MB, time=211.70 memory used=9884.8MB, alloc=579.8MB, time=212.13 memory used=10013.1MB, alloc=579.8MB, time=212.88 memory used=10136.3MB, alloc=579.8MB, time=213.36 memory used=10231.9MB, alloc=579.8MB, time=213.80 memory used=10347.9MB, alloc=579.8MB, time=214.23 memory used=10487.1MB, alloc=579.8MB, time=214.85 memory used=10584.9MB, alloc=579.8MB, time=215.31 memory used=10673.5MB, alloc=579.8MB, time=215.81 memory used=10770.2MB, alloc=579.8MB, time=216.19 memory used=10876.6MB, alloc=579.8MB, time=216.54 memory used=11008.5MB, alloc=579.8MB, time=217.13 memory used=11138.9MB, alloc=579.8MB, time=217.68 memory used=11243.7MB, alloc=579.8MB, time=218.17 memory used=11354.0MB, alloc=579.8MB, time=218.69 memory used=11489.7MB, alloc=579.8MB, time=219.19 memory used=11587.1MB, alloc=579.8MB, time=219.56 memory used=11676.7MB, alloc=579.8MB, time=219.90 memory used=11778.7MB, alloc=579.8MB, time=220.24 memory used=11920.4MB, alloc=579.8MB, time=221.23 memory used=12024.7MB, alloc=579.8MB, time=221.65 memory used=12142.9MB, alloc=579.8MB, time=222.30 memory used=12237.8MB, alloc=579.8MB, time=222.65 memory used=12368.7MB, alloc=579.8MB, time=223.27 memory used=12485.4MB, alloc=579.8MB, time=223.76 memory used=12590.8MB, alloc=579.8MB, time=224.21 memory used=12728.0MB, alloc=579.8MB, time=224.62 memory used=12815.2MB, alloc=579.8MB, time=224.94 memory used=12949.8MB, alloc=579.8MB, time=226.11 memory used=13060.0MB, alloc=579.8MB, time=226.59 memory used=13195.1MB, alloc=579.8MB, time=227.05 memory used=13295.2MB, alloc=579.8MB, time=227.47 memory used=13386.0MB, alloc=579.8MB, time=227.95 memory used=13487.5MB, alloc=579.8MB, time=228.45 memory used=13598.3MB, alloc=579.8MB, time=228.92 memory used=13721.4MB, alloc=579.8MB, time=229.33 memory used=13856.7MB, alloc=579.8MB, time=229.79 memory used=14003.0MB, alloc=579.8MB, time=230.24 memory used=14083.4MB, alloc=603.8MB, time=230.58 memory used=14176.8MB, alloc=603.8MB, time=230.92 memory used=14274.7MB, alloc=603.8MB, time=231.27 memory used=14376.6MB, alloc=603.8MB, time=231.62 memory used=14485.5MB, alloc=603.8MB, time=231.99 memory used=14600.5MB, alloc=603.8MB, time=232.43 memory used=14720.6MB, alloc=603.8MB, time=232.85 memory used=14848.2MB, alloc=603.8MB, time=233.22 memory used=14984.1MB, alloc=603.8MB, time=233.60 memory used=15128.9MB, alloc=603.8MB, time=233.98 memory used=15286.4MB, alloc=603.8MB, time=234.57 memory used=15491.4MB, alloc=603.8MB, time=235.79 memory used=15621.1MB, alloc=603.8MB, time=236.44 memory used=15752.6MB, alloc=603.8MB, time=236.95 memory used=15861.6MB, alloc=603.8MB, time=237.42 memory used=15987.6MB, alloc=603.8MB, time=237.87 memory used=16132.7MB, alloc=603.8MB, time=238.33 memory used=16298.2MB, alloc=603.8MB, time=238.82 memory used=16391.9MB, alloc=603.8MB, time=239.21 memory used=16490.6MB, alloc=603.8MB, time=239.57 memory used=16595.9MB, alloc=603.8MB, time=239.92 memory used=16710.4MB, alloc=603.8MB, time=240.33 memory used=16835.9MB, alloc=603.8MB, time=240.69 memory used=16998.8MB, alloc=603.8MB, time=251.71 memory used=17165.5MB, alloc=603.8MB, time=254.98 memory used=17276.6MB, alloc=603.8MB, time=255.65 memory used=17418.2MB, alloc=603.8MB, time=256.29 memory used=17556.4MB, alloc=603.8MB, time=256.78 memory used=17656.0MB, alloc=603.8MB, time=257.19 memory used=17765.4MB, alloc=603.8MB, time=257.60 memory used=17886.9MB, alloc=603.8MB, time=258.01 memory used=18021.3MB, alloc=603.8MB, time=258.46 memory used=18171.3MB, alloc=603.8MB, time=258.95 memory used=18462.6MB, alloc=603.8MB, time=259.57 memory used=18745.1MB, alloc=603.8MB, time=262.16 memory used=18860.3MB, alloc=603.8MB, time=262.75 memory used=19001.9MB, alloc=603.8MB, time=263.33 memory used=19168.9MB, alloc=603.8MB, time=263.95 memory used=19268.1MB, alloc=603.8MB, time=264.45 memory used=19363.7MB, alloc=603.8MB, time=265.00 memory used=19463.5MB, alloc=603.8MB, time=265.50 memory used=19573.2MB, alloc=603.8MB, time=266.01 memory used=19687.6MB, alloc=603.8MB, time=266.52 memory used=19806.7MB, alloc=603.8MB, time=267.04 memory used=19935.8MB, alloc=603.8MB, time=267.68 memory used=20069.7MB, alloc=603.8MB, time=268.35 memory used=20214.5MB, alloc=603.8MB, time=268.97 memory used=20363.7MB, alloc=603.8MB, time=269.51 memory used=20523.9MB, alloc=603.8MB, time=270.03 memory used=20688.3MB, alloc=603.8MB, time=270.58 memory used=20781.9MB, alloc=627.8MB, time=271.02 memory used=20874.4MB, alloc=627.8MB, time=271.43 memory used=20973.7MB, alloc=627.8MB, time=271.92 memory used=21074.4MB, alloc=627.8MB, time=272.33 memory used=21176.1MB, alloc=627.8MB, time=272.76 memory used=21279.2MB, alloc=627.8MB, time=273.19 memory used=21389.9MB, alloc=627.8MB, time=273.60 memory used=21502.0MB, alloc=627.8MB, time=274.01 memory used=21614.8MB, alloc=627.8MB, time=274.52 memory used=21728.9MB, alloc=627.8MB, time=274.95 memory used=21850.5MB, alloc=627.8MB, time=275.41 memory used=21973.1MB, alloc=627.8MB, time=275.85 memory used=22096.4MB, alloc=627.8MB, time=276.30 memory used=22228.0MB, alloc=627.8MB, time=276.75 memory used=22360.0MB, alloc=627.8MB, time=277.20 memory used=22500.2MB, alloc=627.8MB, time=277.74 memory used=22640.4MB, alloc=627.8MB, time=278.18 memory used=22781.1MB, alloc=627.8MB, time=278.61 memory used=22928.2MB, alloc=627.8MB, time=279.10 memory used=23076.5MB, alloc=627.8MB, time=279.54 memory used=23230.1MB, alloc=627.8MB, time=279.99 memory used=23391.6MB, alloc=627.8MB, time=280.46 memory used=23552.8MB, alloc=627.8MB, time=280.91 memory used=23718.7MB, alloc=627.8MB, time=281.52 memory used=23889.8MB, alloc=627.8MB, time=281.97 memory used=24066.3MB, alloc=627.8MB, time=282.52 memory used=24247.9MB, alloc=627.8MB, time=282.96 memory used=24461.3MB, alloc=627.8MB, time=283.46 memory used=24599.3MB, alloc=627.8MB, time=283.90 memory used=24715.5MB, alloc=627.8MB, time=284.31 memory used=24834.7MB, alloc=627.8MB, time=284.73 memory used=24957.2MB, alloc=627.8MB, time=285.18 memory used=25082.1MB, alloc=627.8MB, time=285.64 memory used=25212.9MB, alloc=627.8MB, time=286.07 memory used=25345.5MB, alloc=627.8MB, time=286.61 memory used=25481.5MB, alloc=627.8MB, time=287.05 memory used=25622.6MB, alloc=627.8MB, time=287.56 memory used=25769.6MB, alloc=627.8MB, time=288.08 memory used=25923.0MB, alloc=627.8MB, time=288.53 memory used=26185.8MB, alloc=627.8MB, time=290.96 memory used=26332.4MB, alloc=627.8MB, time=291.56 memory used=26518.2MB, alloc=627.8MB, time=292.21 memory used=26637.5MB, alloc=627.8MB, time=292.71 memory used=26752.8MB, alloc=627.8MB, time=293.20 memory used=26876.5MB, alloc=627.8MB, time=293.69 memory used=27012.0MB, alloc=627.8MB, time=294.21 memory used=27159.5MB, alloc=627.8MB, time=294.74 memory used=27319.1MB, alloc=627.8MB, time=295.28 memory used=27490.7MB, alloc=627.8MB, time=295.81 memory used=27674.3MB, alloc=627.8MB, time=296.33 memory used=27845.3MB, alloc=627.8MB, time=296.83 memory used=27940.3MB, alloc=627.8MB, time=297.22 memory used=28041.3MB, alloc=627.8MB, time=297.61 memory used=28143.4MB, alloc=627.8MB, time=297.99 memory used=28252.5MB, alloc=627.8MB, time=298.39 memory used=28362.4MB, alloc=627.8MB, time=298.79 memory used=28479.2MB, alloc=627.8MB, time=299.18 memory used=28596.6MB, alloc=627.8MB, time=299.59 memory used=28720.6MB, alloc=627.8MB, time=299.99 memory used=28844.7MB, alloc=627.8MB, time=300.40 memory used=28975.1MB, alloc=627.8MB, time=300.82 memory used=29111.5MB, alloc=627.8MB, time=301.27 memory used=29253.6MB, alloc=627.8MB, time=301.77 memory used=29400.5MB, alloc=627.8MB, time=302.19 memory used=29552.2MB, alloc=627.8MB, time=302.63 memory used=29707.8MB, alloc=627.8MB, time=303.10 memory used=29867.1MB, alloc=627.8MB, time=303.56 memory used=30032.9MB, alloc=627.8MB, time=304.00 memory used=30205.5MB, alloc=627.8MB, time=304.42 memory used=30387.8MB, alloc=627.8MB, time=304.86 memory used=30576.6MB, alloc=627.8MB, time=305.32 memory used=30751.9MB, alloc=627.8MB, time=305.79 memory used=30878.0MB, alloc=627.8MB, time=306.20 memory used=31008.6MB, alloc=627.8MB, time=306.60 memory used=31147.0MB, alloc=627.8MB, time=307.02 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428486993 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 3 F := [8 x y - 10 y + 7 x z, 3 y z - 19 z - x] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 3 2 G := [13 x y + 19 x z - 3 x z, -17 x y z - 17 x - 11 z ] > Problem := [F,G]; 2 2 3 2 3 Problem := [[8 x y - 10 y + 7 x z, 3 y z - 19 z - x], 2 2 3 2 3 2 [13 x y + 19 x z - 3 x z, -17 x y z - 17 x - 11 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.0MB, alloc=32.3MB, time=0.17 memory used=31.8MB, alloc=35.1MB, time=0.64 memory used=49.8MB, alloc=35.1MB, time=0.70 memory used=60.9MB, alloc=59.1MB, time=0.75 memory used=86.6MB, alloc=59.1MB, time=0.83 memory used=119.2MB, alloc=59.1MB, time=0.91 memory used=153.4MB, alloc=59.1MB, time=1.00 memory used=174.5MB, alloc=59.1MB, time=1.06 memory used=197.6MB, alloc=59.1MB, time=1.12 memory used=221.7MB, alloc=59.1MB, time=1.19 memory used=248.7MB, alloc=59.1MB, time=1.26 memory used=276.6MB, alloc=59.1MB, time=1.32 memory used=307.2MB, alloc=59.1MB, time=1.39 memory used=340.8MB, alloc=59.1MB, time=1.47 memory used=377.0MB, alloc=59.1MB, time=1.54 memory used=411.0MB, alloc=59.1MB, time=1.61 memory used=429.5MB, alloc=59.1MB, time=1.66 memory used=448.8MB, alloc=59.1MB, time=1.70 memory used=468.8MB, alloc=59.1MB, time=1.75 memory used=490.6MB, alloc=59.1MB, time=1.80 memory used=513.7MB, alloc=59.1MB, time=1.85 memory used=537.9MB, alloc=59.1MB, time=1.90 memory used=563.0MB, alloc=59.1MB, time=1.95 memory used=589.8MB, alloc=59.1MB, time=2.00 memory used=618.5MB, alloc=59.1MB, time=2.04 memory used=662.4MB, alloc=64.8MB, time=2.30 memory used=691.3MB, alloc=64.8MB, time=2.39 memory used=729.9MB, alloc=64.8MB, time=2.49 memory used=753.6MB, alloc=64.8MB, time=2.57 memory used=780.2MB, alloc=64.8MB, time=2.65 memory used=809.8MB, alloc=64.8MB, time=2.72 memory used=843.7MB, alloc=64.8MB, time=2.80 memory used=882.4MB, alloc=64.8MB, time=2.88 memory used=905.0MB, alloc=64.8MB, time=2.94 memory used=953.9MB, alloc=64.8MB, time=7.96 memory used=1023.4MB, alloc=64.8MB, time=8.90 memory used=1056.0MB, alloc=64.8MB, time=8.99 memory used=1082.5MB, alloc=64.8MB, time=9.08 memory used=1115.4MB, alloc=64.8MB, time=9.16 memory used=1152.1MB, alloc=64.8MB, time=9.25 memory used=1174.5MB, alloc=64.8MB, time=9.31 memory used=1198.0MB, alloc=64.8MB, time=9.37 memory used=1223.4MB, alloc=64.8MB, time=9.44 memory used=1251.6MB, alloc=64.8MB, time=9.50 memory used=1282.5MB, alloc=64.8MB, time=9.57 memory used=1315.9MB, alloc=64.8MB, time=9.64 memory used=1352.3MB, alloc=64.8MB, time=9.71 memory used=1391.1MB, alloc=64.8MB, time=9.78 memory used=1407.1MB, alloc=83.8MB, time=9.84 memory used=1418.4MB, alloc=83.8MB, time=9.88 memory used=1430.2MB, alloc=83.8MB, time=9.92 memory used=1442.4MB, alloc=83.8MB, time=9.96 memory used=1454.9MB, alloc=83.8MB, time=10.01 memory used=1467.7MB, alloc=83.8MB, time=10.05 memory used=1481.0MB, alloc=83.8MB, time=10.10 memory used=1495.5MB, alloc=83.8MB, time=10.14 memory used=1510.7MB, alloc=83.8MB, time=10.18 memory used=1557.0MB, alloc=83.8MB, time=10.61 memory used=1583.5MB, alloc=83.8MB, time=10.69 memory used=1616.4MB, alloc=83.8MB, time=10.79 memory used=1651.7MB, alloc=83.8MB, time=10.88 memory used=1672.8MB, alloc=83.8MB, time=10.95 memory used=1696.0MB, alloc=83.8MB, time=11.03 memory used=1720.4MB, alloc=83.8MB, time=11.10 memory used=1745.4MB, alloc=83.8MB, time=11.18 memory used=1773.1MB, alloc=83.8MB, time=11.25 memory used=1801.6MB, alloc=83.8MB, time=11.33 memory used=1832.4MB, alloc=83.8MB, time=11.40 memory used=1866.1MB, alloc=83.8MB, time=11.49 memory used=1901.9MB, alloc=83.8MB, time=11.57 memory used=1922.1MB, alloc=83.8MB, time=11.62 memory used=1941.2MB, alloc=83.8MB, time=11.67 memory used=1961.2MB, alloc=83.8MB, time=11.72 memory used=1980.8MB, alloc=83.8MB, time=11.78 memory used=2002.0MB, alloc=83.8MB, time=11.83 memory used=2024.6MB, alloc=83.8MB, time=11.89 memory used=2048.2MB, alloc=83.8MB, time=11.94 memory used=2072.8MB, alloc=83.8MB, time=12.00 memory used=2099.7MB, alloc=83.8MB, time=12.06 memory used=2130.3MB, alloc=83.8MB, time=12.18 memory used=2169.7MB, alloc=83.8MB, time=12.42 memory used=2199.8MB, alloc=83.8MB, time=12.52 memory used=2233.2MB, alloc=83.8MB, time=12.61 memory used=2255.7MB, alloc=83.8MB, time=12.68 memory used=2281.3MB, alloc=83.8MB, time=12.76 memory used=2310.4MB, alloc=83.8MB, time=12.83 memory used=2344.1MB, alloc=83.8MB, time=12.91 memory used=2380.8MB, alloc=83.8MB, time=12.98 memory used=2402.1MB, alloc=83.8MB, time=13.03 memory used=2448.1MB, alloc=83.8MB, time=18.00 memory used=2515.6MB, alloc=83.8MB, time=18.88 memory used=2547.2MB, alloc=83.8MB, time=18.97 memory used=2572.2MB, alloc=83.8MB, time=19.05 memory used=2603.9MB, alloc=83.8MB, time=19.13 memory used=2640.6MB, alloc=83.8MB, time=19.21 memory used=2661.9MB, alloc=83.8MB, time=19.27 memory used=2684.5MB, alloc=83.8MB, time=19.33 memory used=2708.7MB, alloc=83.8MB, time=19.39 memory used=2735.5MB, alloc=83.8MB, time=19.45 memory used=2763.9MB, alloc=83.8MB, time=19.52 memory used=2795.0MB, alloc=83.8MB, time=19.58 memory used=2829.3MB, alloc=83.8MB, time=19.66 memory used=2865.9MB, alloc=83.8MB, time=19.73 memory used=2900.4MB, alloc=83.8MB, time=19.80 memory used=2913.5MB, alloc=83.8MB, time=19.84 memory used=2927.1MB, alloc=83.8MB, time=19.88 memory used=2940.2MB, alloc=83.8MB, time=19.92 memory used=2954.8MB, alloc=83.8MB, time=19.97 memory used=2970.1MB, alloc=83.8MB, time=20.01 memory used=2985.4MB, alloc=83.8MB, time=20.05 memory used=3002.7MB, alloc=83.8MB, time=20.10 memory used=3045.2MB, alloc=83.8MB, time=20.58 memory used=3076.2MB, alloc=83.8MB, time=20.67 memory used=3103.8MB, alloc=83.8MB, time=20.74 memory used=3132.6MB, alloc=83.8MB, time=20.80 memory used=3191.9MB, alloc=83.8MB, time=22.18 memory used=3240.5MB, alloc=83.8MB, time=31.89 memory used=3303.2MB, alloc=83.8MB, time=32.49 memory used=3333.2MB, alloc=83.8MB, time=32.59 memory used=3355.4MB, alloc=83.8MB, time=32.66 memory used=3382.0MB, alloc=83.8MB, time=32.74 memory used=3413.7MB, alloc=83.8MB, time=32.83 memory used=3443.2MB, alloc=83.8MB, time=32.91 memory used=3462.6MB, alloc=83.8MB, time=32.96 memory used=3483.2MB, alloc=83.8MB, time=33.03 memory used=3505.5MB, alloc=83.8MB, time=33.10 memory used=3529.4MB, alloc=83.8MB, time=33.16 memory used=3555.1MB, alloc=83.8MB, time=33.22 memory used=3582.4MB, alloc=83.8MB, time=33.29 memory used=3611.1MB, alloc=83.8MB, time=33.36 memory used=3642.3MB, alloc=83.8MB, time=33.44 memory used=3675.7MB, alloc=83.8MB, time=33.51 memory used=3717.6MB, alloc=83.8MB, time=33.60 memory used=3726.0MB, alloc=83.8MB, time=33.64 memory used=3734.5MB, alloc=83.8MB, time=33.68 memory used=3742.9MB, alloc=83.8MB, time=33.72 memory used=3751.3MB, alloc=83.8MB, time=33.76 memory used=3760.3MB, alloc=83.8MB, time=33.80 memory used=3769.2MB, alloc=83.8MB, time=33.84 memory used=3778.9MB, alloc=83.8MB, time=33.88 memory used=3788.3MB, alloc=83.8MB, time=33.92 memory used=3798.3MB, alloc=83.8MB, time=33.96 memory used=3808.8MB, alloc=83.8MB, time=34.00 memory used=3819.0MB, alloc=83.8MB, time=34.04 memory used=3829.9MB, alloc=83.8MB, time=34.08 memory used=3840.9MB, alloc=83.8MB, time=34.13 memory used=3852.5MB, alloc=83.8MB, time=34.17 memory used=3864.9MB, alloc=83.8MB, time=34.21 memory used=3928.5MB, alloc=83.8MB, time=34.81 memory used=3956.9MB, alloc=83.8MB, time=34.91 memory used=3988.7MB, alloc=83.8MB, time=35.29 memory used=4028.7MB, alloc=83.8MB, time=35.74 memory used=4048.6MB, alloc=83.8MB, time=35.83 memory used=4070.1MB, alloc=83.8MB, time=35.95 memory used=4095.9MB, alloc=83.8MB, time=36.07 memory used=4124.3MB, alloc=83.8MB, time=36.18 memory used=4150.5MB, alloc=83.8MB, time=36.26 memory used=4166.1MB, alloc=107.8MB, time=36.35 memory used=4195.1MB, alloc=107.8MB, time=36.46 memory used=4227.6MB, alloc=107.8MB, time=36.59 memory used=4261.9MB, alloc=107.8MB, time=36.71 memory used=4298.2MB, alloc=107.8MB, time=36.87 memory used=4338.9MB, alloc=107.8MB, time=37.04 memory used=4381.7MB, alloc=107.8MB, time=37.26 memory used=4430.0MB, alloc=107.8MB, time=37.43 memory used=4479.9MB, alloc=107.8MB, time=37.55 memory used=4525.4MB, alloc=107.8MB, time=37.67 memory used=4549.6MB, alloc=107.8MB, time=37.75 memory used=4573.4MB, alloc=107.8MB, time=37.83 memory used=4599.4MB, alloc=107.8MB, time=37.91 memory 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memory used=5387.6MB, alloc=107.8MB, time=39.76 memory used=5394.6MB, alloc=107.8MB, time=39.81 memory used=5403.0MB, alloc=107.8MB, time=39.85 memory used=5410.2MB, alloc=107.8MB, time=39.90 memory used=5418.0MB, alloc=107.8MB, time=39.95 memory used=5426.8MB, alloc=107.8MB, time=39.99 memory used=5435.4MB, alloc=107.8MB, time=40.03 memory used=5443.8MB, alloc=107.8MB, time=40.08 memory used=5452.0MB, alloc=107.8MB, time=40.12 memory used=5460.1MB, alloc=107.8MB, time=40.16 memory used=5468.8MB, alloc=107.8MB, time=40.21 memory used=5478.3MB, alloc=107.8MB, time=40.25 memory used=5488.3MB, alloc=107.8MB, time=40.30 memory used=5498.0MB, alloc=107.8MB, time=40.35 memory used=5508.1MB, alloc=107.8MB, time=40.40 memory used=5518.4MB, alloc=107.8MB, time=40.44 memory used=5529.1MB, alloc=107.8MB, time=40.49 memory used=5539.6MB, alloc=107.8MB, time=40.53 memory used=5550.7MB, alloc=107.8MB, time=40.58 memory used=5561.9MB, alloc=107.8MB, time=40.64 memory used=5573.0MB, alloc=107.8MB, time=40.69 memory used=5584.2MB, alloc=107.8MB, time=40.73 memory used=5595.5MB, alloc=107.8MB, time=40.78 memory used=5606.9MB, alloc=107.8MB, time=40.83 memory used=5618.4MB, alloc=107.8MB, time=40.88 memory used=5630.1MB, alloc=107.8MB, time=40.93 memory used=5641.9MB, alloc=107.8MB, time=40.98 memory used=5653.8MB, alloc=107.8MB, time=41.02 memory used=5665.9MB, alloc=107.8MB, time=41.06 memory used=5678.0MB, alloc=107.8MB, time=41.12 memory used=5742.3MB, alloc=107.8MB, time=41.59 memory used=5786.3MB, alloc=107.8MB, time=41.72 memory used=5831.3MB, alloc=107.8MB, time=41.85 memory used=5863.1MB, alloc=107.8MB, time=41.96 memory used=5899.8MB, alloc=107.8MB, time=42.08 memory used=5941.3MB, alloc=107.8MB, time=42.20 memory used=5987.6MB, alloc=107.8MB, time=42.33 memory used=6038.5MB, alloc=107.8MB, time=42.45 memory used=6084.7MB, alloc=107.8MB, time=42.55 memory used=6112.6MB, alloc=107.8MB, time=42.64 memory used=6143.2MB, alloc=107.8MB, time=42.72 memory used=6174.0MB, 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memory used=7400.8MB, alloc=107.8MB, time=59.43 memory used=7408.9MB, alloc=107.8MB, time=59.47 memory used=7417.1MB, alloc=107.8MB, time=59.53 memory used=7425.2MB, alloc=107.8MB, time=59.57 memory used=7433.4MB, alloc=107.8MB, time=59.64 memory used=7441.5MB, alloc=107.8MB, time=59.70 memory used=7449.7MB, alloc=107.8MB, time=59.76 memory used=7457.9MB, alloc=107.8MB, time=59.80 memory used=7466.0MB, alloc=107.8MB, time=59.85 memory used=7474.4MB, alloc=107.8MB, time=59.90 memory used=7485.2MB, alloc=107.8MB, time=59.95 memory used=7493.6MB, alloc=107.8MB, time=60.01 memory used=7504.3MB, alloc=107.8MB, time=60.07 memory used=7515.3MB, alloc=107.8MB, time=60.12 memory used=7526.3MB, alloc=107.8MB, time=60.17 memory used=7537.2MB, alloc=107.8MB, time=60.22 memory used=7548.2MB, alloc=107.8MB, time=60.26 memory used=7559.2MB, alloc=107.8MB, time=60.31 memory used=7570.1MB, alloc=107.8MB, time=60.36 memory used=7581.1MB, alloc=107.8MB, time=60.41 memory used=7592.1MB, alloc=107.8MB, 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memory used=8474.8MB, alloc=107.8MB, time=63.72 memory used=8490.5MB, alloc=107.8MB, time=63.77 memory used=8506.9MB, alloc=107.8MB, time=63.82 memory used=8561.5MB, alloc=107.8MB, time=64.22 memory used=8618.3MB, alloc=107.8MB, time=65.42 memory used=8672.7MB, alloc=107.8MB, time=65.62 memory used=8717.4MB, alloc=107.8MB, time=65.74 memory used=8757.6MB, alloc=107.8MB, time=65.84 memory used=8793.1MB, alloc=107.8MB, time=65.93 memory used=8834.1MB, alloc=107.8MB, time=66.02 memory used=8881.4MB, alloc=107.8MB, time=66.12 memory used=8937.7MB, alloc=107.8MB, time=66.22 memory used=8948.7MB, alloc=107.8MB, time=66.28 memory used=8960.0MB, alloc=107.8MB, time=66.33 memory used=8971.6MB, alloc=107.8MB, time=66.39 memory used=8983.9MB, alloc=107.8MB, time=66.45 memory used=8996.6MB, alloc=107.8MB, time=66.50 memory used=9010.6MB, alloc=107.8MB, time=66.55 memory used=9073.1MB, alloc=107.8MB, time=66.91 memory used=9115.8MB, alloc=107.8MB, time=67.04 memory used=9154.1MB, alloc=107.8MB, 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alloc=107.8MB, time=85.23 memory used=9941.6MB, alloc=107.8MB, time=85.28 memory used=9949.9MB, alloc=107.8MB, time=85.33 memory used=9960.0MB, alloc=107.8MB, time=85.38 memory used=9970.3MB, alloc=107.8MB, time=85.43 memory used=9980.5MB, alloc=107.8MB, time=85.47 memory used=9990.7MB, alloc=107.8MB, time=85.52 memory used=10001.0MB, alloc=107.8MB, time=85.58 memory used=10011.2MB, alloc=107.8MB, time=85.63 memory used=10021.4MB, alloc=107.8MB, time=85.69 memory used=10031.6MB, alloc=107.8MB, time=85.74 memory used=10041.8MB, alloc=107.8MB, time=85.79 memory used=10052.0MB, alloc=107.8MB, time=85.83 memory used=10062.1MB, alloc=107.8MB, time=85.88 memory used=10072.3MB, alloc=107.8MB, time=85.93 memory used=10082.4MB, alloc=107.8MB, time=85.98 memory used=10092.6MB, alloc=107.8MB, time=86.03 memory used=10104.5MB, alloc=107.8MB, time=86.08 memory used=10116.6MB, alloc=107.8MB, time=86.13 memory used=10128.5MB, alloc=107.8MB, time=86.19 memory used=10140.5MB, alloc=107.8MB, time=86.24 memory used=10152.3MB, alloc=107.8MB, time=86.29 memory used=10164.1MB, alloc=107.8MB, time=86.34 memory used=10175.9MB, alloc=107.8MB, time=86.39 memory used=10187.6MB, alloc=107.8MB, time=86.45 memory used=10199.4MB, alloc=107.8MB, time=86.50 memory used=10212.6MB, alloc=107.8MB, time=86.56 memory used=10226.0MB, alloc=107.8MB, time=86.61 memory used=10239.2MB, alloc=107.8MB, time=86.67 memory used=10252.3MB, alloc=107.8MB, time=86.73 memory used=10265.3MB, alloc=107.8MB, time=86.78 memory used=10278.4MB, alloc=107.8MB, time=86.83 memory used=10292.7MB, alloc=107.8MB, time=86.89 memory used=10307.0MB, alloc=107.8MB, time=86.95 memory used=10321.2MB, alloc=107.8MB, time=87.00 memory used=10336.8MB, alloc=107.8MB, time=87.05 memory used=10352.2MB, alloc=107.8MB, time=87.10 memory used=10367.2MB, alloc=107.8MB, time=87.16 memory used=10383.6MB, alloc=107.8MB, time=87.21 memory used=10399.5MB, alloc=107.8MB, time=87.26 memory used=10416.6MB, alloc=107.8MB, time=87.32 memory 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alloc=107.8MB, time=96.66 memory used=11243.3MB, alloc=107.8MB, time=96.79 memory used=11283.2MB, alloc=107.8MB, time=96.89 memory used=11312.2MB, alloc=107.8MB, time=96.98 memory used=11343.0MB, alloc=107.8MB, time=97.07 memory used=11375.3MB, alloc=107.8MB, time=97.16 memory used=11409.0MB, alloc=107.8MB, time=97.25 memory used=11446.0MB, alloc=107.8MB, time=97.35 memory used=11484.4MB, alloc=107.8MB, time=97.45 memory used=11526.3MB, alloc=107.8MB, time=97.54 memory used=11569.6MB, alloc=107.8MB, time=97.64 memory used=11616.4MB, alloc=107.8MB, time=97.74 memory used=11664.4MB, alloc=107.8MB, time=97.85 memory used=11715.9MB, alloc=107.8MB, time=97.96 memory used=11738.9MB, alloc=107.8MB, time=98.04 memory used=11746.7MB, alloc=107.8MB, time=98.09 memory used=11755.5MB, alloc=107.8MB, time=98.15 memory used=11763.2MB, alloc=107.8MB, time=98.20 memory used=11770.9MB, alloc=107.8MB, time=98.25 memory used=11778.6MB, alloc=107.8MB, time=98.31 memory used=11786.4MB, alloc=107.8MB, time=98.36 memory used=11794.2MB, alloc=107.8MB, time=98.41 memory used=11801.9MB, alloc=107.8MB, time=98.46 memory used=11809.7MB, alloc=107.8MB, time=98.51 memory used=11817.5MB, alloc=107.8MB, time=98.56 memory used=11825.4MB, alloc=107.8MB, time=98.61 memory used=11833.2MB, alloc=107.8MB, time=98.66 memory used=11841.0MB, alloc=107.8MB, time=98.71 memory used=11848.9MB, alloc=107.8MB, time=98.76 memory used=11856.8MB, alloc=107.8MB, time=98.81 memory used=11864.6MB, alloc=107.8MB, time=98.86 memory used=11872.5MB, alloc=107.8MB, time=98.91 memory used=11880.4MB, alloc=107.8MB, time=98.97 memory used=11888.3MB, alloc=107.8MB, time=99.02 memory used=11896.2MB, alloc=107.8MB, time=99.07 memory used=11904.2MB, alloc=107.8MB, time=99.12 memory used=11912.2MB, alloc=107.8MB, time=99.18 memory used=11922.7MB, alloc=107.8MB, time=99.23 memory used=11930.8MB, alloc=107.8MB, time=99.29 memory used=11941.2MB, alloc=107.8MB, time=99.35 memory used=11951.9MB, alloc=107.8MB, time=99.40 memory used=11962.5MB, alloc=107.8MB, time=99.46 memory used=11973.1MB, alloc=107.8MB, time=99.52 memory used=11983.7MB, alloc=107.8MB, time=99.58 memory used=11994.3MB, alloc=107.8MB, time=99.64 memory used=12004.9MB, alloc=107.8MB, time=99.70 memory used=12015.6MB, alloc=107.8MB, time=99.75 memory used=12026.2MB, alloc=107.8MB, time=99.81 memory used=12036.8MB, alloc=107.8MB, time=99.87 memory used=12047.4MB, alloc=107.8MB, time=99.92 memory used=12058.1MB, alloc=107.8MB, time=99.98 memory used=12068.7MB, alloc=107.8MB, time=100.04 memory used=12079.3MB, alloc=107.8MB, time=100.09 memory used=12089.9MB, alloc=107.8MB, time=100.15 memory used=12100.5MB, alloc=107.8MB, time=100.21 memory used=12111.0MB, alloc=107.8MB, time=100.27 memory used=12121.6MB, alloc=107.8MB, time=100.33 memory used=12132.1MB, alloc=107.8MB, time=100.38 memory used=12142.7MB, alloc=107.8MB, time=100.44 memory used=12153.2MB, alloc=107.8MB, time=100.50 memory used=12163.9MB, alloc=107.8MB, time=100.56 memory used=12176.8MB, alloc=107.8MB, time=100.62 memory used=12189.9MB, alloc=107.8MB, time=100.68 memory used=12203.0MB, alloc=107.8MB, time=100.74 memory used=12216.0MB, alloc=107.8MB, time=100.81 memory used=12229.0MB, alloc=107.8MB, time=100.85 memory used=12241.9MB, alloc=107.8MB, time=100.91 memory used=12254.8MB, alloc=107.8MB, time=100.96 memory used=12267.7MB, alloc=107.8MB, time=101.02 memory used=12280.5MB, alloc=107.8MB, time=101.08 memory used=12293.3MB, alloc=107.8MB, time=101.13 memory used=12306.0MB, alloc=107.8MB, time=101.19 memory used=12318.7MB, alloc=107.8MB, time=101.25 memory used=12331.3MB, alloc=107.8MB, time=101.31 memory used=12344.1MB, alloc=107.8MB, time=101.37 memory used=12358.9MB, alloc=107.8MB, time=101.43 memory used=12373.8MB, alloc=107.8MB, time=101.50 memory used=12388.6MB, alloc=107.8MB, time=101.57 memory used=12403.3MB, alloc=107.8MB, time=101.64 memory used=12417.9MB, alloc=107.8MB, time=101.71 memory used=12432.4MB, alloc=107.8MB, time=101.79 memory used=12446.8MB, alloc=107.8MB, time=101.86 memory used=12461.1MB, alloc=107.8MB, time=101.93 memory used=12475.5MB, alloc=107.8MB, time=101.99 memory used=12491.7MB, alloc=107.8MB, time=102.05 memory used=12507.9MB, alloc=107.8MB, time=102.12 memory used=12523.9MB, alloc=107.8MB, time=102.18 memory used=12539.8MB, alloc=107.8MB, time=102.24 memory used=12555.4MB, alloc=107.8MB, time=102.30 memory used=12571.2MB, alloc=107.8MB, time=102.36 memory used=12588.5MB, alloc=107.8MB, time=102.42 memory used=12605.6MB, alloc=107.8MB, time=102.47 memory used=12622.6MB, alloc=107.8MB, time=102.53 memory used=12639.5MB, alloc=107.8MB, time=102.59 memory used=12657.5MB, alloc=107.8MB, time=102.66 memory used=12675.4MB, alloc=107.8MB, time=102.72 memory used=12694.8MB, alloc=107.8MB, time=102.79 memory used=12713.7MB, alloc=107.8MB, time=102.86 memory used=12732.5MB, alloc=107.8MB, time=102.93 memory used=12747.3MB, alloc=107.8MB, time=102.99 memory used=12759.6MB, alloc=107.8MB, time=103.05 memory used=12772.6MB, alloc=107.8MB, time=103.11 memory used=12785.5MB, alloc=107.8MB, time=103.17 memory used=12799.5MB, alloc=107.8MB, time=103.23 memory used=12812.9MB, alloc=107.8MB, time=103.29 memory used=12826.3MB, alloc=107.8MB, time=103.34 memory used=12841.0MB, alloc=107.8MB, time=103.41 memory used=12854.3MB, alloc=107.8MB, time=103.46 memory used=12869.0MB, alloc=107.8MB, time=103.52 memory used=12884.3MB, alloc=107.8MB, time=103.58 memory used=12900.5MB, alloc=107.8MB, time=103.64 memory used=13012.8MB, alloc=107.8MB, time=104.73 memory used=13098.2MB, alloc=107.8MB, time=105.13 memory used=13176.2MB, alloc=107.8MB, time=105.56 memory used=13254.8MB, alloc=107.8MB, time=106.03 memory used=13332.6MB, alloc=107.8MB, time=106.59 memory used=13412.2MB, alloc=107.8MB, time=107.27 memory used=13490.5MB, alloc=107.8MB, time=108.02 memory used=13569.7MB, alloc=107.8MB, time=108.93 memory used=13648.8MB, alloc=107.8MB, time=109.92 memory used=13726.0MB, alloc=107.8MB, time=111.16 memory 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used=15084.4MB, alloc=107.8MB, time=141.40 memory used=15095.1MB, alloc=107.8MB, time=141.45 memory used=15105.9MB, alloc=107.8MB, time=141.51 memory used=15117.4MB, alloc=107.8MB, time=141.56 memory used=15129.3MB, alloc=107.8MB, time=141.61 memory used=15141.7MB, alloc=107.8MB, time=141.67 memory used=15155.1MB, alloc=107.8MB, time=141.73 memory used=15242.6MB, alloc=107.8MB, time=142.76 memory used=15288.0MB, alloc=107.8MB, time=145.44 memory used=15365.4MB, alloc=107.8MB, time=147.17 memory used=15405.7MB, alloc=107.8MB, time=147.31 memory used=15437.7MB, alloc=107.8MB, time=147.43 memory used=15471.2MB, alloc=107.8MB, time=147.54 memory used=15511.5MB, alloc=107.8MB, time=147.66 memory used=15555.4MB, alloc=107.8MB, time=147.78 memory used=15581.0MB, alloc=107.8MB, time=147.87 memory used=15606.5MB, alloc=107.8MB, time=147.96 memory used=15633.6MB, alloc=107.8MB, time=148.06 memory used=15661.9MB, alloc=107.8MB, time=148.16 memory used=15693.2MB, alloc=107.8MB, time=148.26 memory 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used=28883.3MB, alloc=411.8MB, time=203.43 memory used=28937.9MB, alloc=411.8MB, time=203.60 memory used=29097.2MB, alloc=411.8MB, time=204.85 memory used=29188.5MB, alloc=411.8MB, time=219.38 memory used=29279.5MB, alloc=411.8MB, time=219.94 memory used=29331.3MB, alloc=411.8MB, time=220.19 memory used=29391.8MB, alloc=411.8MB, time=220.43 memory used=29439.6MB, alloc=411.8MB, time=220.61 memory used=29478.7MB, alloc=411.8MB, time=220.76 memory used=29521.6MB, alloc=411.8MB, time=220.91 memory used=29571.3MB, alloc=411.8MB, time=221.08 memory used=29625.1MB, alloc=411.8MB, time=221.26 memory used=29682.8MB, alloc=411.8MB, time=221.44 memory used=29744.3MB, alloc=411.8MB, time=221.62 memory used=29809.3MB, alloc=411.8MB, time=221.82 memory used=29978.1MB, alloc=411.8MB, time=222.26 memory used=30132.7MB, alloc=411.8MB, time=222.63 memory used=30297.7MB, alloc=411.8MB, time=223.05 memory used=30480.3MB, alloc=411.8MB, time=223.46 memory used=30683.1MB, alloc=411.8MB, time=223.89 memory used=30898.0MB, alloc=411.8MB, time=224.34 memory used=31132.8MB, alloc=411.8MB, time=224.82 memory used=31363.1MB, alloc=411.8MB, time=225.27 memory used=31540.0MB, alloc=411.8MB, time=225.65 memory used=31725.0MB, alloc=411.8MB, time=226.03 memory used=31914.7MB, alloc=411.8MB, time=226.44 memory used=32109.6MB, alloc=411.8MB, time=226.82 memory used=32316.9MB, alloc=411.8MB, time=227.23 memory used=32529.2MB, alloc=411.8MB, time=227.67 memory used=32755.6MB, alloc=411.8MB, time=228.11 memory used=32985.8MB, alloc=411.8MB, time=228.55 memory used=33230.1MB, alloc=411.8MB, time=229.02 memory used=33451.7MB, alloc=411.8MB, time=229.45 memory used=33646.7MB, alloc=411.8MB, time=229.82 memory used=33842.3MB, alloc=411.8MB, time=230.20 memory used=34050.0MB, alloc=411.8MB, time=230.60 memory used=34258.7MB, alloc=411.8MB, time=231.00 memory used=34479.4MB, alloc=411.8MB, time=231.43 memory used=34700.7MB, alloc=411.8MB, time=231.86 memory used=34933.3MB, alloc=411.8MB, time=232.29 memory used=35167.1MB, alloc=411.8MB, time=232.74 memory used=35409.6MB, alloc=411.8MB, time=233.17 memory used=35647.1MB, alloc=411.8MB, time=233.60 memory used=35849.3MB, alloc=411.8MB, time=233.96 memory used=36055.5MB, alloc=411.8MB, time=234.35 memory used=36271.0MB, alloc=411.8MB, time=234.76 memory used=36495.4MB, alloc=411.8MB, time=235.18 memory used=36718.5MB, alloc=411.8MB, time=235.59 memory used=36946.8MB, alloc=411.8MB, time=236.00 memory used=37183.0MB, alloc=411.8MB, time=236.41 memory used=37425.0MB, alloc=411.8MB, time=236.87 memory used=37671.9MB, alloc=411.8MB, time=237.32 memory used=37890.8MB, alloc=411.8MB, time=237.72 memory used=38108.8MB, alloc=411.8MB, time=238.12 memory used=38334.1MB, alloc=411.8MB, time=238.52 memory used=38568.8MB, alloc=411.8MB, time=238.93 memory used=38810.4MB, alloc=411.8MB, time=239.34 memory used=39056.3MB, alloc=411.8MB, time=239.76 memory used=39309.6MB, alloc=411.8MB, time=240.18 memory used=39536.9MB, alloc=411.8MB, time=240.56 memory used=39773.5MB, alloc=411.8MB, time=240.94 memory used=40003.8MB, alloc=411.8MB, time=242.35 memory used=40120.8MB, alloc=411.8MB, time=242.89 memory used=40250.3MB, alloc=411.8MB, time=243.95 memory used=40336.7MB, alloc=411.8MB, time=265.42 memory used=40421.9MB, alloc=411.8MB, time=284.22 memory used=40489.2MB, alloc=411.8MB, time=284.56 memory used=40534.7MB, alloc=411.8MB, time=284.75 memory used=40589.9MB, alloc=411.8MB, time=284.94 memory used=40640.5MB, alloc=411.8MB, time=285.11 memory used=40678.1MB, alloc=411.8MB, time=285.25 memory used=40718.9MB, alloc=411.8MB, time=285.39 memory used=40764.3MB, alloc=411.8MB, time=285.53 memory used=40812.2MB, alloc=411.8MB, time=285.68 memory used=40864.7MB, alloc=411.8MB, time=285.83 memory used=40921.8MB, alloc=411.8MB, time=285.99 memory used=40983.7MB, alloc=411.8MB, time=286.16 memory used=41178.0MB, alloc=411.8MB, time=286.56 memory used=41340.4MB, alloc=411.8MB, time=286.92 memory used=41526.1MB, alloc=411.8MB, time=287.29 memory used=41737.5MB, alloc=411.8MB, time=287.68 memory used=41977.7MB, alloc=411.8MB, time=288.08 memory used=42173.2MB, alloc=411.8MB, time=288.41 memory used=42272.0MB, alloc=411.8MB, time=318.29 memory used=42354.8MB, alloc=411.8MB, time=327.72 memory used=42431.1MB, alloc=411.8MB, time=328.19 memory used=42481.3MB, alloc=411.8MB, time=328.39 memory used=42532.7MB, alloc=411.8MB, time=328.60 memory used=42590.9MB, alloc=411.8MB, time=328.81 memory used=42628.4MB, alloc=411.8MB, time=328.96 memory used=42669.5MB, alloc=411.8MB, time=329.11 memory used=42713.8MB, alloc=411.8MB, time=329.25 memory used=42762.6MB, alloc=411.8MB, time=329.41 memory used=42813.9MB, alloc=411.8MB, time=329.57 memory used=42869.8MB, alloc=411.8MB, time=329.74 memory used=42930.2MB, alloc=411.8MB, time=329.89 memory used=43131.0MB, alloc=411.8MB, time=330.29 memory used=43292.4MB, alloc=411.8MB, time=330.64 memory used=43479.9MB, alloc=411.8MB, time=331.00 memory used=43694.7MB, alloc=411.8MB, time=331.40 memory used=43928.0MB, alloc=411.8MB, time=331.80 memory used=44175.6MB, alloc=411.8MB, time=333.43 memory used=44231.6MB, alloc=411.8MB, time=333.60 memory used=44274.1MB, alloc=411.8MB, time=333.75 memory used=44324.4MB, alloc=411.8MB, time=333.90 memory used=44385.5MB, alloc=411.8MB, time=334.06 memory used=44585.1MB, alloc=411.8MB, time=335.16 memory used=44685.2MB, alloc=411.8MB, time=335.93 memory used=44733.9MB, alloc=411.8MB, time=336.12 memory used=44785.8MB, alloc=435.8MB, time=336.33 memory used=44838.6MB, alloc=435.8MB, time=336.54 memory used=44901.4MB, alloc=435.8MB, time=336.77 memory used=44975.7MB, alloc=435.8MB, time=337.01 memory used=45047.0MB, alloc=435.8MB, time=337.22 memory used=45094.7MB, alloc=435.8MB, time=337.37 memory used=45146.3MB, alloc=435.8MB, time=337.53 memory used=45204.6MB, alloc=435.8MB, time=337.70 memory used=45287.1MB, alloc=435.8MB, time=338.15 memory used=45356.3MB, alloc=435.8MB, time=338.40 memory used=45420.9MB, alloc=435.8MB, time=338.62 memory used=45477.9MB, alloc=435.8MB, time=338.83 memory used=45545.0MB, alloc=435.8MB, time=339.05 memory used=45625.5MB, alloc=435.8MB, time=339.26 memory used=45683.8MB, alloc=435.8MB, time=339.43 memory used=45733.9MB, alloc=435.8MB, time=339.60 memory used=45788.2MB, alloc=435.8MB, time=339.76 memory used=45850.8MB, alloc=435.8MB, time=339.92 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428487293 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [15 x y z - x - 18, -7 x y z - 20 y z - 10 y] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 4 2 2 2 G := [-x y + 9 x y z - 9 z , 3 x y z - 12 y z - 10 y z ] > Problem := [F,G]; 2 2 Problem := [[15 x y z - x - 18, -7 x y z - 20 y z - 10 y], 2 2 2 4 2 2 2 [-x y + 9 x y z - 9 z , 3 x y z - 12 y z - 10 y z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.3MB, alloc=32.3MB, time=0.50 memory used=47.4MB, alloc=32.3MB, time=0.80 memory used=66.0MB, alloc=56.3MB, time=1.09 memory used=108.6MB, alloc=68.3MB, time=1.72 memory used=152.1MB, alloc=68.3MB, time=2.29 memory used=195.8MB, alloc=92.3MB, time=2.91 memory used=266.6MB, alloc=92.3MB, time=3.82 memory used=331.9MB, alloc=92.3MB, time=4.69 memory used=395.8MB, alloc=372.3MB, time=5.58 memory used=488.7MB, alloc=372.3MB, time=6.75 memory used=575.9MB, alloc=372.3MB, time=7.77 memory used=671.4MB, alloc=372.3MB, time=8.71 memory used=745.9MB, alloc=396.3MB, time=9.66 memory used=849.0MB, alloc=396.3MB, time=10.86 memory used=958.9MB, alloc=396.3MB, time=12.15 memory used=1024.7MB, alloc=396.3MB, time=12.59 memory used=1069.7MB, alloc=396.3MB, time=12.76 memory used=1156.8MB, alloc=396.3MB, time=13.35 memory used=1265.4MB, alloc=420.3MB, time=14.87 memory used=1350.7MB, alloc=420.3MB, time=15.44 memory used=1413.1MB, alloc=420.3MB, time=15.65 memory used=1460.1MB, alloc=420.3MB, time=15.83 memory used=1587.5MB, alloc=420.3MB, time=17.02 memory used=1720.8MB, alloc=444.3MB, time=18.43 memory used=1840.1MB, alloc=444.3MB, time=19.00 memory used=1953.6MB, alloc=444.3MB, time=19.43 memory used=2069.3MB, alloc=444.3MB, time=19.85 memory used=2192.5MB, alloc=444.3MB, time=20.30 memory used=2324.2MB, alloc=444.3MB, time=20.76 memory used=2465.8MB, alloc=444.3MB, time=21.22 memory used=2643.1MB, alloc=444.3MB, time=21.91 memory used=2831.9MB, alloc=444.3MB, time=22.69 memory used=3050.3MB, alloc=444.3MB, time=23.61 memory used=3301.1MB, alloc=444.3MB, time=24.76 memory used=3561.8MB, alloc=444.3MB, time=25.91 memory used=3827.9MB, alloc=444.3MB, time=27.16 memory used=4175.5MB, alloc=444.3MB, time=29.10 memory used=4476.5MB, alloc=444.3MB, time=31.68 memory used=4615.8MB, alloc=444.3MB, time=32.61 memory used=4737.9MB, alloc=444.3MB, time=33.05 memory used=4889.0MB, alloc=444.3MB, time=33.50 memory used=5064.0MB, alloc=444.3MB, time=33.96 memory used=5291.8MB, alloc=444.3MB, time=34.54 memory used=5537.6MB, alloc=444.3MB, time=35.12 memory used=5788.5MB, alloc=444.3MB, time=35.70 memory used=6065.4MB, alloc=444.3MB, time=36.39 memory used=6377.0MB, alloc=444.3MB, time=37.14 memory used=6633.9MB, alloc=444.3MB, time=39.12 memory used=6756.7MB, alloc=444.3MB, time=39.79 memory used=6862.7MB, alloc=444.3MB, time=40.21 memory used=6965.6MB, alloc=444.3MB, time=40.61 memory used=7073.9MB, alloc=444.3MB, time=41.01 memory used=7188.3MB, alloc=468.3MB, time=41.43 memory used=7338.9MB, alloc=468.3MB, time=41.90 memory used=7520.6MB, alloc=468.3MB, time=43.95 memory used=7655.8MB, alloc=468.3MB, time=44.62 memory used=7814.9MB, alloc=468.3MB, time=45.50 memory used=7950.8MB, alloc=468.3MB, time=46.05 memory used=8099.0MB, alloc=468.3MB, time=46.59 memory used=8255.6MB, alloc=468.3MB, time=47.10 memory used=8417.6MB, alloc=468.3MB, time=47.62 memory used=8600.7MB, alloc=468.3MB, time=48.16 memory used=8783.5MB, alloc=468.3MB, time=48.73 memory used=8992.9MB, alloc=468.3MB, time=49.30 memory used=9215.5MB, alloc=468.3MB, time=49.88 memory used=9451.5MB, alloc=468.3MB, time=50.46 memory used=9739.8MB, alloc=468.3MB, time=51.16 memory used=10039.7MB, alloc=468.3MB, time=51.94 memory used=10411.9MB, alloc=468.3MB, time=53.03 memory used=10806.3MB, alloc=468.3MB, time=54.24 memory used=11225.9MB, alloc=468.3MB, time=55.66 memory used=11617.3MB, alloc=468.3MB, time=57.06 memory used=11952.6MB, alloc=468.3MB, time=59.42 memory used=12081.3MB, alloc=468.3MB, time=60.03 memory used=12209.9MB, alloc=468.3MB, time=60.54 memory used=12348.3MB, alloc=468.3MB, time=61.04 memory used=12495.3MB, alloc=468.3MB, time=61.56 memory used=12656.8MB, alloc=468.3MB, time=62.15 memory used=12837.1MB, alloc=468.3MB, time=62.77 memory used=13061.7MB, alloc=468.3MB, time=63.74 memory used=13308.7MB, alloc=468.3MB, time=64.73 memory used=13599.6MB, alloc=468.3MB, time=66.04 memory used=13926.3MB, alloc=468.3MB, time=67.62 memory used=14288.0MB, alloc=468.3MB, time=69.40 memory used=14665.5MB, alloc=468.3MB, time=71.36 memory used=15047.4MB, alloc=468.3MB, time=73.61 memory used=15234.0MB, alloc=468.3MB, time=74.73 memory used=15371.7MB, alloc=468.3MB, time=75.20 memory used=15531.9MB, alloc=468.3MB, time=75.69 memory used=15957.6MB, alloc=468.3MB, time=76.90 memory used=16338.6MB, alloc=468.3MB, time=77.72 memory used=16710.9MB, alloc=468.3MB, time=78.51 memory used=17075.1MB, alloc=468.3MB, time=79.28 memory used=17437.5MB, alloc=468.3MB, time=80.04 memory used=17797.4MB, alloc=468.3MB, time=80.81 memory used=18162.9MB, alloc=468.3MB, time=81.60 memory used=18523.2MB, alloc=468.3MB, time=82.38 memory used=18883.3MB, alloc=468.3MB, time=83.21 memory used=19243.7MB, alloc=468.3MB, time=84.03 memory used=19602.2MB, alloc=468.3MB, time=84.83 memory used=19961.7MB, alloc=468.3MB, time=85.64 memory used=20312.8MB, alloc=468.3MB, time=86.41 memory used=20670.4MB, alloc=468.3MB, time=87.19 memory used=21022.2MB, alloc=468.3MB, time=87.98 memory used=21378.8MB, alloc=468.3MB, time=88.79 memory used=21731.7MB, alloc=468.3MB, time=89.60 memory used=22081.0MB, alloc=468.3MB, time=90.39 memory used=22422.5MB, alloc=468.3MB, time=91.16 memory used=22774.9MB, alloc=468.3MB, time=91.90 memory used=23125.0MB, alloc=468.3MB, time=92.70 memory used=23473.7MB, alloc=468.3MB, time=93.52 memory used=23824.6MB, alloc=468.3MB, time=94.34 memory used=24170.9MB, alloc=468.3MB, time=95.14 memory used=24511.1MB, alloc=468.3MB, time=95.88 memory used=24859.5MB, alloc=468.3MB, time=96.73 memory used=25208.7MB, alloc=468.3MB, time=97.58 memory used=25555.9MB, alloc=468.3MB, time=98.42 memory used=25887.8MB, alloc=468.3MB, time=99.10 memory used=26233.5MB, alloc=468.3MB, time=99.93 memory used=26578.5MB, alloc=468.3MB, time=100.77 memory used=26925.5MB, alloc=468.3MB, time=101.62 memory used=27258.6MB, alloc=468.3MB, time=102.31 memory used=27601.2MB, alloc=468.3MB, time=103.14 memory used=27944.6MB, alloc=468.3MB, time=103.99 memory used=28277.9MB, alloc=468.3MB, time=104.71 memory used=28620.5MB, alloc=468.3MB, time=105.61 memory used=28962.9MB, alloc=468.3MB, time=106.50 memory used=29293.5MB, alloc=468.3MB, time=107.19 memory used=29633.7MB, alloc=468.3MB, time=108.04 memory used=29973.9MB, alloc=468.3MB, time=108.92 memory used=30304.6MB, alloc=468.3MB, time=109.60 memory used=30645.0MB, alloc=468.3MB, time=110.46 memory used=30987.0MB, alloc=468.3MB, time=111.67 memory used=31318.5MB, alloc=468.3MB, time=112.44 memory used=31661.8MB, alloc=468.3MB, time=113.95 memory used=31993.2MB, alloc=468.3MB, time=114.89 memory used=32338.4MB, alloc=468.3MB, time=116.58 memory used=32668.5MB, alloc=468.3MB, time=117.63 memory used=33018.2MB, alloc=468.3MB, time=119.50 memory used=33344.9MB, alloc=468.3MB, time=120.38 memory used=33694.2MB, alloc=468.3MB, time=122.79 memory used=34020.2MB, alloc=468.3MB, time=123.54 memory used=34371.3MB, alloc=468.3MB, time=126.25 memory used=34701.2MB, alloc=468.3MB, time=127.02 memory used=35040.3MB, alloc=468.3MB, time=128.99 memory used=35388.6MB, alloc=468.3MB, time=130.68 memory used=35713.0MB, alloc=468.3MB, time=131.35 memory used=36068.4MB, alloc=468.3MB, time=134.66 memory used=36396.2MB, alloc=468.3MB, time=135.40 memory used=36731.6MB, alloc=468.3MB, time=137.09 memory used=37086.9MB, alloc=468.3MB, time=139.72 memory used=37410.5MB, alloc=468.3MB, time=140.42 memory used=37750.8MB, alloc=468.3MB, time=142.82 memory used=38099.3MB, alloc=468.3MB, time=145.29 memory used=38425.9MB, alloc=468.3MB, time=146.00 memory used=38764.5MB, alloc=468.3MB, time=148.44 memory used=39116.1MB, alloc=468.3MB, time=151.06 memory used=39439.5MB, alloc=468.3MB, time=151.75 memory used=39778.8MB, alloc=468.3MB, time=154.09 memory used=40135.4MB, alloc=468.3MB, time=157.25 memory used=40460.4MB, alloc=468.3MB, time=157.98 memory used=40790.1MB, alloc=468.3MB, time=159.65 memory used=41132.9MB, alloc=468.3MB, time=163.04 memory used=41472.1MB, alloc=468.3MB, time=164.59 memory used=41793.8MB, alloc=468.3MB, time=165.30 memory used=42134.8MB, alloc=468.3MB, time=168.60 memory used=42485.2MB, alloc=468.3MB, time=171.69 memory used=42809.0MB, alloc=468.3MB, time=172.42 memory used=43139.2MB, alloc=468.3MB, time=174.16 memory used=43483.6MB, alloc=468.3MB, time=177.61 memory used=43827.3MB, alloc=468.3MB, time=179.91 memory used=44151.6MB, alloc=468.3MB, time=180.65 memory used=44483.8MB, alloc=468.3MB, time=183.11 memory used=44829.2MB, alloc=468.3MB, time=186.70 memory used=45169.6MB, alloc=468.3MB, time=188.73 memory used=45491.4MB, alloc=468.3MB, time=189.42 memory used=45828.6MB, alloc=468.3MB, time=192.14 memory used=46177.6MB, alloc=468.3MB, time=195.73 memory used=46521.1MB, alloc=468.3MB, time=197.85 memory used=46841.7MB, alloc=468.3MB, time=198.56 memory used=47174.8MB, alloc=468.3MB, time=201.13 memory used=47519.1MB, alloc=468.3MB, time=204.74 memory used=47864.4MB, alloc=468.3MB, time=207.63 memory used=48185.8MB, alloc=468.3MB, time=208.34 memory used=48514.0MB, alloc=468.3MB, time=210.24 memory used=48859.0MB, alloc=468.3MB, time=213.93 memory used=49204.1MB, alloc=468.3MB, time=217.69 memory used=49534.4MB, alloc=468.3MB, time=218.76 memory used=49853.9MB, alloc=468.3MB, time=219.45 memory used=50194.7MB, alloc=468.3MB, time=223.05 memory used=50538.6MB, alloc=468.3MB, time=226.75 memory used=50982.1MB, alloc=468.3MB, time=231.19 memory used=51183.3MB, alloc=468.3MB, time=232.56 memory used=51377.6MB, alloc=468.3MB, time=234.20 memory used=51546.3MB, alloc=492.3MB, time=236.54 memory used=51735.4MB, alloc=516.3MB, time=239.26 memory used=51940.2MB, alloc=540.3MB, time=242.44 memory used=52193.8MB, alloc=540.3MB, time=245.04 memory used=52454.5MB, alloc=564.3MB, time=247.68 memory used=52661.0MB, alloc=588.3MB, time=251.30 memory used=52922.4MB, alloc=588.3MB, time=254.70 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428487593 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 4 2 2 4 2 F := [-6 x - 5 z - 17, 14 y z + 10 z + 20 y ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 G := [-4 x y z + 3 y z - 12 z , -6 x y + 18 y z + 11 x] > Problem := [F,G]; 4 4 2 2 4 2 Problem := [[-6 x - 5 z - 17, 14 y z + 10 z + 20 y ], 2 3 [-4 x y z + 3 y z - 12 z , -6 x y + 18 y z + 11 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=24.6MB, alloc=32.3MB, time=0.47 memory used=44.0MB, alloc=56.3MB, time=0.74 memory used=84.6MB, alloc=60.3MB, time=1.08 memory used=116.3MB, alloc=60.3MB, time=1.23 memory used=150.5MB, alloc=60.3MB, time=1.42 memory used=178.4MB, alloc=60.3MB, time=1.58 memory used=203.8MB, alloc=60.3MB, time=1.65 memory used=240.6MB, alloc=83.8MB, time=1.91 memory used=281.2MB, alloc=83.8MB, time=2.00 memory used=305.4MB, alloc=83.8MB, time=2.06 memory used=331.3MB, alloc=83.8MB, time=2.13 memory used=372.7MB, alloc=83.8MB, time=2.23 memory used=397.2MB, alloc=83.8MB, time=2.29 memory used=437.1MB, alloc=83.8MB, time=2.74 memory used=465.8MB, alloc=83.8MB, time=2.90 memory used=521.8MB, alloc=83.8MB, time=3.58 memory used=578.3MB, alloc=83.8MB, time=4.28 memory used=681.9MB, alloc=83.8MB, time=5.35 memory used=732.7MB, alloc=83.8MB, time=6.18 memory used=817.5MB, alloc=83.8MB, time=7.12 memory used=852.5MB, alloc=83.8MB, time=7.42 memory used=888.7MB, alloc=83.8MB, time=7.94 memory used=930.7MB, alloc=83.8MB, time=8.47 memory used=969.9MB, alloc=107.8MB, time=9.02 memory used=1024.6MB, alloc=107.8MB, time=9.52 memory used=1085.8MB, alloc=107.8MB, time=10.14 memory used=1144.2MB, alloc=107.8MB, time=10.71 memory used=1206.6MB, alloc=107.8MB, time=11.36 memory used=1248.1MB, alloc=107.8MB, time=11.67 memory used=1280.0MB, alloc=107.8MB, time=11.79 memory used=1311.7MB, alloc=107.8MB, time=11.90 memory used=1349.7MB, alloc=107.8MB, time=12.22 memory used=1379.2MB, alloc=107.8MB, time=12.34 memory used=1414.0MB, alloc=107.8MB, time=12.46 memory used=1438.5MB, alloc=131.8MB, time=12.59 memory used=1479.3MB, alloc=131.8MB, time=12.74 memory used=1530.7MB, alloc=131.8MB, time=12.87 memory used=1580.2MB, alloc=131.8MB, time=14.36 memory used=1612.3MB, alloc=131.8MB, time=20.40 memory used=1612.5MB, alloc=387.8MB, time=20.47 memory used=1862.3MB, alloc=387.8MB, time=321.66 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428487893 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 3 F := [-12 x z - 14 x y z - 4 y , 18 y - 19 x y + 10 y z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 2 2 G := [-7 y z + 9 x y + 2 y z, y z - 19 x y + 14 z] > Problem := [F,G]; 3 2 2 3 Problem := [[-12 x z - 14 x y z - 4 y , 18 y - 19 x y + 10 y z], 2 2 2 2 2 2 2 [-7 y z + 9 x y + 2 y z, y z - 19 x y + 14 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=24.3MB, alloc=32.3MB, time=0.45 memory used=42.8MB, alloc=56.3MB, time=0.72 memory used=84.5MB, alloc=60.3MB, time=1.26 memory used=126.7MB, alloc=68.3MB, time=1.81 memory used=175.0MB, alloc=92.3MB, time=2.40 memory used=238.4MB, alloc=92.3MB, time=3.19 memory used=295.4MB, alloc=92.3MB, time=3.60 memory used=340.9MB, alloc=92.3MB, time=3.88 memory used=387.8MB, alloc=92.3MB, time=4.13 memory used=438.4MB, alloc=92.3MB, time=4.45 memory used=502.1MB, alloc=92.3MB, time=4.98 memory used=575.8MB, alloc=92.3MB, time=5.70 memory used=642.1MB, alloc=348.3MB, time=6.38 memory used=707.8MB, alloc=372.3MB, time=7.16 memory used=776.6MB, alloc=372.3MB, time=7.63 memory used=834.4MB, alloc=372.3MB, time=7.93 memory used=898.0MB, alloc=372.3MB, time=8.23 memory used=951.8MB, alloc=372.3MB, time=8.61 memory used=1002.3MB, alloc=372.3MB, time=8.81 memory used=1061.7MB, alloc=372.3MB, time=9.16 memory used=1113.1MB, alloc=372.3MB, time=9.38 memory used=1175.3MB, alloc=372.3MB, time=9.85 memory used=1224.6MB, alloc=372.3MB, time=10.07 memory used=1317.2MB, alloc=372.3MB, time=10.98 memory used=1414.4MB, alloc=396.3MB, time=12.12 memory used=1523.7MB, alloc=396.3MB, time=13.11 memory used=1600.9MB, alloc=396.3MB, time=13.87 memory used=1651.6MB, alloc=396.3MB, time=14.07 memory used=1719.6MB, alloc=396.3MB, time=14.49 memory used=1784.3MB, alloc=396.3MB, time=14.90 memory used=1881.9MB, alloc=396.3MB, time=15.99 memory used=1942.4MB, alloc=396.3MB, time=16.27 memory used=2086.5MB, alloc=396.3MB, time=17.82 memory used=2232.3MB, alloc=396.3MB, time=20.68 memory used=2365.8MB, alloc=396.3MB, time=22.17 memory used=2498.5MB, alloc=396.3MB, time=24.88 memory used=2610.2MB, alloc=420.3MB, time=26.28 memory used=2721.0MB, alloc=420.3MB, time=27.80 memory used=2829.9MB, alloc=444.3MB, time=29.42 memory used=2960.0MB, alloc=444.3MB, time=30.80 memory used=3094.2MB, alloc=444.3MB, time=32.18 memory used=3201.7MB, alloc=444.3MB, time=33.04 memory used=3278.0MB, alloc=444.3MB, time=33.49 memory used=3342.5MB, alloc=444.3MB, time=33.84 memory used=3448.6MB, alloc=468.3MB, time=34.88 memory used=3524.7MB, alloc=468.3MB, time=35.16 memory used=3615.7MB, alloc=468.3MB, time=35.64 memory used=3724.1MB, alloc=468.3MB, time=36.93 memory used=3814.7MB, alloc=468.3MB, time=38.02 memory used=3894.4MB, alloc=468.3MB, time=39.18 memory used=3981.1MB, alloc=468.3MB, time=39.74 memory used=4072.3MB, alloc=468.3MB, time=40.30 memory used=4145.2MB, alloc=468.3MB, time=40.67 memory used=4224.9MB, alloc=468.3MB, time=41.02 memory used=4293.2MB, alloc=468.3MB, time=41.32 memory used=4355.1MB, alloc=468.3MB, time=41.61 memory used=4440.8MB, alloc=468.3MB, time=42.04 memory used=4513.8MB, alloc=468.3MB, time=42.41 memory used=4591.7MB, alloc=468.3MB, time=42.76 memory used=4663.5MB, alloc=468.3MB, time=43.07 memory used=4724.6MB, alloc=468.3MB, time=43.36 memory used=4811.7MB, alloc=468.3MB, time=44.12 memory used=4891.7MB, alloc=468.3MB, time=44.48 memory used=4955.8MB, alloc=468.3MB, time=44.77 memory used=5037.7MB, alloc=468.3MB, time=45.07 memory used=5141.5MB, alloc=468.3MB, time=45.85 memory used=5211.5MB, alloc=468.3MB, time=46.21 memory used=5298.1MB, alloc=468.3MB, time=46.56 memory used=5355.6MB, alloc=468.3MB, time=46.86 memory used=5419.9MB, alloc=468.3MB, time=47.15 memory used=5507.1MB, alloc=468.3MB, time=47.64 memory used=5578.5MB, alloc=468.3MB, time=48.00 memory used=5664.7MB, alloc=468.3MB, time=48.36 memory used=5725.2MB, alloc=468.3MB, time=48.66 memory used=5789.6MB, alloc=468.3MB, time=48.96 memory used=5884.1MB, alloc=468.3MB, time=50.21 memory used=5963.8MB, alloc=468.3MB, time=50.58 memory used=6024.6MB, alloc=468.3MB, time=50.90 memory used=6098.9MB, alloc=468.3MB, time=51.21 memory used=6279.4MB, alloc=468.3MB, time=51.82 memory used=6359.6MB, alloc=468.3MB, time=52.26 memory used=6465.1MB, alloc=468.3MB, time=53.24 memory used=6554.4MB, alloc=468.3MB, time=53.65 memory used=6616.2MB, alloc=468.3MB, time=53.99 memory used=6695.8MB, alloc=468.3MB, time=54.35 memory used=6769.7MB, alloc=468.3MB, time=54.67 memory used=6827.0MB, alloc=468.3MB, time=54.95 memory used=6919.4MB, alloc=468.3MB, time=55.45 memory used=6985.0MB, alloc=468.3MB, time=55.79 memory used=7062.6MB, alloc=468.3MB, time=56.14 memory used=7140.2MB, alloc=468.3MB, time=56.45 memory used=7196.7MB, alloc=468.3MB, time=56.74 memory used=7298.0MB, alloc=468.3MB, time=59.83 memory used=7375.1MB, alloc=468.3MB, time=60.20 memory used=7442.8MB, alloc=492.3MB, time=60.54 memory used=7521.0MB, alloc=492.3MB, time=60.88 memory used=7615.2MB, alloc=492.3MB, time=61.22 memory used=7726.6MB, alloc=492.3MB, time=61.59 memory used=7890.2MB, alloc=492.3MB, time=62.12 memory used=8053.8MB, alloc=492.3MB, time=62.57 memory used=8314.1MB, alloc=492.3MB, time=63.96 memory used=8400.0MB, alloc=492.3MB, time=64.32 memory used=8489.4MB, alloc=492.3MB, time=64.67 memory used=8746.4MB, alloc=492.3MB, time=65.45 memory used=8841.0MB, alloc=492.3MB, time=65.84 memory used=8925.2MB, alloc=492.3MB, time=66.17 memory used=9076.7MB, alloc=492.3MB, time=67.39 memory used=9203.0MB, alloc=492.3MB, time=68.58 memory used=9345.2MB, alloc=492.3MB, time=69.66 memory used=9461.1MB, alloc=492.3MB, time=70.70 memory used=9560.1MB, alloc=492.3MB, time=72.19 memory used=9671.8MB, alloc=492.3MB, time=73.67 memory used=9763.6MB, alloc=492.3MB, time=75.09 memory used=9862.4MB, alloc=492.3MB, time=76.06 memory used=9938.6MB, alloc=492.3MB, time=77.14 memory used=9990.3MB, alloc=492.3MB, time=77.93 memory used=10112.3MB, alloc=492.3MB, time=78.92 memory used=10217.3MB, alloc=492.3MB, time=79.82 memory used=10308.7MB, alloc=492.3MB, time=80.91 memory used=10376.2MB, alloc=492.3MB, time=81.87 memory used=10492.4MB, alloc=492.3MB, time=83.77 memory used=10568.6MB, alloc=492.3MB, time=84.18 memory used=10659.3MB, alloc=516.3MB, time=84.61 memory used=10738.5MB, alloc=516.3MB, time=84.98 memory used=10833.6MB, alloc=516.3MB, time=85.38 memory used=10948.0MB, alloc=516.3MB, time=85.77 memory used=11133.5MB, alloc=516.3MB, time=86.59 memory used=11235.5MB, alloc=516.3MB, time=87.02 memory used=11327.7MB, alloc=516.3MB, time=87.40 memory used=11443.2MB, alloc=516.3MB, time=88.80 memory used=11522.0MB, alloc=516.3MB, time=89.92 memory used=11627.4MB, alloc=516.3MB, time=90.38 memory used=11713.8MB, alloc=516.3MB, time=90.75 memory used=11837.3MB, alloc=516.3MB, time=91.37 memory used=11952.4MB, alloc=516.3MB, time=92.07 memory used=12025.7MB, alloc=516.3MB, time=93.06 memory used=12086.8MB, alloc=516.3MB, time=93.88 memory used=12185.1MB, alloc=516.3MB, time=95.08 memory used=12378.2MB, alloc=516.3MB, time=97.01 memory used=12499.0MB, alloc=516.3MB, time=98.24 memory used=12626.4MB, alloc=516.3MB, time=99.20 memory used=12802.0MB, alloc=516.3MB, time=100.78 memory used=12908.1MB, alloc=516.3MB, time=101.67 memory used=13047.5MB, alloc=516.3MB, time=103.15 memory used=13219.9MB, alloc=540.3MB, time=105.27 memory used=13454.5MB, alloc=540.3MB, time=108.50 memory used=13690.9MB, alloc=564.3MB, time=110.75 memory used=13967.7MB, alloc=564.3MB, time=111.67 memory used=14226.6MB, alloc=564.3MB, time=114.66 memory used=14496.2MB, alloc=564.3MB, time=118.01 memory used=14756.9MB, alloc=564.3MB, time=120.84 memory used=15001.0MB, alloc=564.3MB, time=123.26 memory used=15241.8MB, alloc=564.3MB, time=125.46 memory used=15417.8MB, alloc=564.3MB, time=126.37 memory used=15644.9MB, alloc=564.3MB, time=128.28 memory used=15891.5MB, alloc=588.3MB, time=131.35 memory used=16167.9MB, alloc=588.3MB, time=134.62 memory used=16436.0MB, alloc=588.3MB, time=136.99 memory used=16724.2MB, alloc=612.3MB, time=141.93 memory used=17012.3MB, alloc=636.3MB, time=146.52 memory used=17378.3MB, alloc=636.3MB, time=150.86 memory used=17684.6MB, alloc=636.3MB, time=151.98 memory used=18103.0MB, alloc=636.3MB, time=153.85 memory used=18458.8MB, alloc=660.3MB, time=158.58 memory used=18792.4MB, alloc=684.3MB, time=163.23 memory used=19174.7MB, alloc=708.3MB, time=168.50 memory used=19538.8MB, alloc=732.3MB, time=174.52 memory used=19914.8MB, alloc=756.3MB, time=180.69 memory used=20357.9MB, alloc=780.3MB, time=187.18 memory used=20683.1MB, alloc=804.3MB, time=192.68 memory used=21018.9MB, alloc=828.3MB, time=198.19 memory used=21349.9MB, alloc=852.3MB, time=203.62 memory used=21716.8MB, alloc=876.3MB, time=208.52 memory used=22148.6MB, alloc=900.3MB, time=215.00 memory used=22423.1MB, alloc=924.3MB, time=220.24 memory used=22656.5MB, alloc=948.3MB, time=224.90 memory used=22932.5MB, alloc=972.3MB, time=230.12 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428488193 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 4 2 2 F := [6 y z + 6 z + 20 y z, 7 y z + 7 x + 9 x z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 4 3 2 2 2 G := [-20 x y - 12 y - 4 x y z, 11 x z - 17 y z - 3 y z ] > Problem := [F,G]; 3 4 2 2 Problem := [[6 y z + 6 z + 20 y z, 7 y z + 7 x + 9 x z], 2 2 4 3 2 2 2 [-20 x y - 12 y - 4 x y z, 11 x z - 17 y z - 3 y z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.7MB, alloc=32.3MB, time=0.51 memory used=47.0MB, alloc=32.3MB, time=0.81 memory used=65.1MB, alloc=56.3MB, time=1.06 memory used=110.9MB, alloc=60.3MB, time=1.70 memory used=153.4MB, alloc=60.3MB, time=2.20 memory used=201.8MB, alloc=68.3MB, time=2.79 memory used=244.4MB, alloc=92.3MB, time=3.37 memory used=305.6MB, alloc=92.3MB, time=4.23 memory used=367.2MB, alloc=92.3MB, time=5.12 memory used=429.5MB, alloc=92.3MB, time=5.84 memory used=493.6MB, alloc=116.3MB, time=6.67 memory used=582.1MB, alloc=116.3MB, time=7.88 memory used=654.2MB, alloc=116.3MB, time=8.56 memory used=718.8MB, alloc=116.3MB, time=9.32 memory used=781.1MB, alloc=116.3MB, time=10.32 memory used=829.3MB, alloc=116.3MB, time=10.48 memory used=881.6MB, alloc=116.3MB, time=10.70 memory used=953.3MB, alloc=116.3MB, time=18.16 memory used=992.8MB, alloc=116.3MB, time=18.30 memory used=1041.8MB, alloc=116.3MB, time=18.57 memory used=1114.1MB, alloc=116.3MB, time=19.27 memory used=1191.6MB, alloc=116.3MB, time=20.00 memory used=1254.6MB, alloc=116.3MB, time=22.24 memory used=1324.5MB, alloc=116.3MB, time=23.06 memory used=1372.3MB, alloc=116.3MB, time=23.42 memory used=1449.8MB, alloc=116.3MB, time=24.38 memory used=1519.6MB, alloc=396.3MB, time=25.29 memory used=1586.1MB, alloc=396.3MB, time=25.59 memory used=1649.6MB, alloc=396.3MB, time=26.23 memory used=1715.0MB, alloc=396.3MB, time=26.52 memory used=1761.8MB, alloc=396.3MB, time=26.71 memory used=1820.5MB, alloc=396.3MB, time=26.89 memory used=1877.8MB, alloc=396.3MB, time=27.15 memory used=1935.3MB, alloc=396.3MB, time=27.36 memory used=1982.1MB, alloc=396.3MB, time=27.53 memory used=2043.6MB, alloc=396.3MB, time=27.72 memory used=2105.2MB, alloc=396.3MB, time=32.37 memory used=2158.3MB, alloc=396.3MB, time=32.56 memory used=2214.5MB, alloc=396.3MB, time=32.75 memory used=2258.7MB, alloc=396.3MB, time=32.90 memory used=2323.3MB, alloc=396.3MB, time=33.25 memory used=2381.6MB, alloc=396.3MB, time=33.47 memory used=2427.1MB, alloc=396.3MB, time=33.64 memory used=2484.4MB, alloc=396.3MB, time=33.81 memory used=2538.6MB, alloc=396.3MB, time=33.97 memory used=2597.6MB, alloc=396.3MB, time=34.32 memory used=2656.0MB, alloc=396.3MB, time=34.52 memory used=2700.0MB, alloc=396.3MB, time=34.71 memory used=2754.8MB, alloc=396.3MB, time=34.89 memory used=2812.5MB, alloc=396.3MB, time=35.07 memory used=2871.6MB, alloc=396.3MB, time=42.36 memory used=2932.8MB, alloc=396.3MB, time=44.30 memory used=2985.6MB, alloc=396.3MB, time=44.47 memory used=3035.6MB, alloc=396.3MB, time=44.62 memory used=3080.5MB, alloc=396.3MB, time=44.76 memory used=3144.6MB, alloc=396.3MB, time=44.98 memory used=3213.9MB, alloc=396.3MB, time=47.11 memory used=3269.5MB, alloc=396.3MB, time=47.29 memory used=3314.3MB, alloc=396.3MB, time=47.42 memory used=3381.1MB, alloc=396.3MB, time=47.87 memory used=3438.1MB, alloc=396.3MB, time=48.07 memory used=3483.9MB, alloc=396.3MB, time=48.23 memory used=3544.9MB, alloc=396.3MB, time=48.40 memory used=3598.8MB, alloc=396.3MB, time=48.68 memory used=3658.2MB, alloc=396.3MB, time=48.89 memory used=3704.8MB, alloc=396.3MB, time=49.06 memory used=3758.4MB, alloc=396.3MB, time=49.23 memory used=3812.5MB, alloc=396.3MB, time=49.39 memory used=3882.3MB, alloc=396.3MB, time=65.15 memory used=3949.7MB, alloc=396.3MB, time=75.76 memory used=3998.6MB, alloc=396.3MB, time=75.93 memory used=4050.7MB, alloc=396.3MB, time=76.10 memory used=4106.9MB, alloc=396.3MB, time=76.27 memory used=4145.3MB, alloc=396.3MB, time=76.40 memory used=4187.6MB, alloc=396.3MB, time=76.55 memory used=4234.8MB, alloc=396.3MB, time=76.68 memory used=4287.8MB, alloc=396.3MB, time=76.83 memory used=4347.0MB, alloc=396.3MB, time=76.98 memory used=4489.8MB, alloc=396.3MB, time=77.85 memory used=4537.2MB, alloc=396.3MB, time=78.05 memory used=4584.6MB, alloc=396.3MB, time=78.26 memory used=4640.4MB, alloc=396.3MB, time=78.47 memory used=4695.6MB, alloc=396.3MB, time=78.66 memory used=4736.5MB, alloc=420.3MB, time=78.84 memory used=4787.5MB, alloc=420.3MB, time=79.05 memory used=4843.1MB, alloc=420.3MB, time=79.24 memory used=4902.7MB, alloc=420.3MB, time=79.43 memory used=4964.9MB, alloc=420.3MB, time=79.62 memory used=5033.5MB, alloc=420.3MB, time=79.85 memory used=5108.7MB, alloc=420.3MB, time=80.05 memory used=5186.1MB, alloc=420.3MB, time=80.27 memory used=5269.4MB, alloc=420.3MB, time=80.49 memory used=5331.1MB, alloc=420.3MB, time=80.67 memory used=5378.6MB, alloc=420.3MB, time=80.83 memory used=5421.4MB, alloc=420.3MB, time=80.99 memory used=5467.9MB, alloc=420.3MB, time=81.14 memory used=5514.5MB, alloc=420.3MB, time=81.31 memory used=5565.6MB, alloc=420.3MB, time=81.46 memory used=5616.6MB, alloc=420.3MB, time=81.61 memory used=5667.6MB, alloc=420.3MB, time=81.77 memory used=5722.3MB, alloc=420.3MB, time=81.95 memory used=5781.1MB, alloc=420.3MB, time=82.12 memory used=5839.2MB, alloc=420.3MB, time=82.28 memory used=5900.6MB, alloc=420.3MB, time=82.44 memory used=5964.8MB, alloc=420.3MB, time=82.62 memory used=6031.3MB, alloc=420.3MB, time=82.78 memory used=6099.6MB, alloc=420.3MB, time=82.94 memory used=6171.8MB, alloc=420.3MB, time=83.11 memory used=6250.2MB, alloc=420.3MB, time=83.28 memory used=6331.5MB, alloc=420.3MB, time=83.44 memory used=6481.0MB, alloc=420.3MB, time=84.20 memory used=6545.5MB, alloc=420.3MB, time=84.46 memory used=6618.3MB, alloc=420.3MB, time=84.71 memory used=6694.1MB, alloc=420.3MB, time=84.96 memory used=6749.2MB, alloc=420.3MB, time=85.19 memory used=6801.3MB, alloc=420.3MB, time=85.40 memory used=6859.3MB, alloc=420.3MB, time=85.62 memory used=6920.1MB, alloc=420.3MB, time=85.85 memory used=6987.3MB, alloc=420.3MB, time=86.07 memory used=7057.0MB, alloc=420.3MB, time=86.31 memory used=7133.3MB, alloc=420.3MB, time=86.53 memory used=7216.0MB, alloc=420.3MB, time=86.76 memory used=7294.4MB, alloc=420.3MB, time=86.95 memory used=7345.9MB, alloc=420.3MB, time=87.11 memory used=7391.7MB, alloc=420.3MB, time=87.26 memory used=7437.3MB, alloc=420.3MB, time=87.41 memory used=7483.9MB, alloc=420.3MB, time=87.56 memory used=7535.1MB, alloc=420.3MB, time=87.71 memory used=7586.1MB, alloc=420.3MB, time=87.87 memory used=7637.1MB, alloc=420.3MB, time=88.05 memory used=7692.2MB, alloc=420.3MB, time=88.21 memory used=7746.9MB, alloc=420.3MB, time=88.37 memory used=7805.3MB, alloc=420.3MB, time=88.53 memory used=7867.3MB, alloc=420.3MB, time=88.71 memory used=7932.2MB, alloc=420.3MB, time=88.87 memory used=7999.5MB, alloc=420.3MB, time=89.04 memory used=8068.6MB, alloc=420.3MB, time=89.21 memory used=8142.2MB, alloc=420.3MB, time=89.38 memory used=8218.8MB, alloc=420.3MB, time=89.56 memory used=8299.3MB, alloc=420.3MB, time=89.73 memory used=8396.8MB, alloc=420.3MB, time=89.91 memory used=8544.8MB, alloc=444.3MB, time=138.56 memory used=8636.2MB, alloc=444.3MB, time=218.37 memory used=8716.0MB, alloc=444.3MB, time=308.46 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428488494 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 3 2 F := [7 x y - 12 y z - 16 z , 19 x z + 5 x y z + 18 x z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 G := [16 x y + x y z + 4 x , -6 x y + x z - 17 z ] > Problem := [F,G]; 3 3 3 2 Problem := [[7 x y - 12 y z - 16 z , 19 x z + 5 x y z + 18 x z], 3 2 2 2 2 [16 x y + x y z + 4 x , -6 x y + x z - 17 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.4MB, alloc=32.3MB, time=0.48 memory used=45.9MB, alloc=56.3MB, time=0.75 memory used=87.7MB, alloc=60.3MB, time=1.30 memory used=130.5MB, alloc=68.3MB, time=1.77 memory used=177.4MB, alloc=68.3MB, time=2.37 memory used=220.7MB, alloc=68.3MB, time=2.89 memory used=264.2MB, alloc=92.3MB, time=3.42 memory used=332.2MB, alloc=92.3MB, time=4.26 memory used=397.7MB, alloc=92.3MB, time=5.08 memory used=443.4MB, alloc=92.3MB, time=5.30 memory used=485.2MB, alloc=92.3MB, time=5.47 memory used=523.7MB, alloc=92.3MB, time=5.90 memory used=562.0MB, alloc=92.3MB, time=6.04 memory used=602.6MB, alloc=92.3MB, time=6.26 memory used=634.2MB, alloc=92.3MB, time=6.38 memory used=668.6MB, alloc=92.3MB, time=6.49 memory used=697.6MB, alloc=92.3MB, time=6.59 memory used=741.3MB, alloc=92.3MB, time=7.34 memory used=776.1MB, alloc=92.3MB, time=7.47 memory used=803.2MB, alloc=92.3MB, time=7.56 memory used=854.9MB, alloc=92.3MB, time=7.86 memory used=899.8MB, alloc=92.3MB, time=10.82 memory used=952.6MB, alloc=92.3MB, time=11.24 memory used=986.5MB, alloc=92.3MB, time=11.36 memory used=1014.1MB, alloc=92.3MB, time=11.46 memory used=1041.2MB, alloc=92.3MB, time=11.56 memory used=1072.8MB, alloc=92.3MB, time=11.68 memory used=1107.2MB, alloc=92.3MB, time=11.78 memory used=1139.2MB, alloc=92.3MB, time=12.04 memory used=1186.9MB, alloc=92.6MB, time=12.21 memory used=1215.0MB, alloc=92.6MB, time=12.32 memory used=1242.5MB, alloc=92.6MB, time=12.45 memory used=1274.9MB, alloc=92.6MB, time=12.56 memory used=1312.1MB, alloc=92.6MB, time=12.67 memory used=1341.9MB, alloc=92.6MB, time=12.77 memory used=1364.8MB, alloc=92.6MB, time=12.88 memory used=1390.0MB, alloc=92.6MB, time=12.99 memory used=1417.9MB, alloc=92.6MB, time=13.09 memory used=1469.6MB, alloc=92.6MB, time=18.39 memory used=1530.1MB, alloc=92.6MB, time=19.15 memory used=1559.2MB, alloc=92.6MB, time=19.27 memory used=1593.5MB, alloc=92.6MB, time=19.40 memory used=1617.8MB, alloc=92.6MB, time=19.50 memory used=1644.7MB, alloc=92.6MB, time=19.61 memory used=1675.2MB, alloc=92.6MB, time=19.72 memory used=1709.7MB, alloc=92.6MB, time=19.82 memory used=1741.9MB, alloc=92.6MB, time=19.91 memory used=1763.4MB, alloc=92.6MB, time=19.99 memory used=1787.5MB, alloc=92.6MB, time=20.08 memory used=1851.9MB, alloc=92.6MB, time=20.72 memory used=1918.2MB, alloc=94.0MB, time=21.36 memory used=1947.8MB, alloc=94.0MB, time=21.47 memory used=1976.3MB, alloc=94.0MB, time=21.58 memory used=2012.7MB, alloc=94.0MB, time=21.81 memory used=2041.1MB, alloc=94.0MB, time=21.91 memory used=2088.0MB, alloc=94.0MB, time=22.16 memory used=2114.3MB, alloc=94.0MB, time=22.27 memory used=2147.1MB, alloc=94.0MB, time=22.39 memory used=2181.1MB, alloc=94.0MB, time=22.50 memory used=2204.1MB, alloc=94.0MB, time=22.60 memory used=2230.4MB, alloc=94.0MB, time=22.71 memory used=2260.3MB, alloc=94.0MB, time=22.82 memory used=2305.4MB, alloc=94.0MB, time=24.02 memory used=2340.2MB, alloc=94.0MB, time=24.15 memory used=2364.8MB, alloc=94.0MB, time=24.25 memory used=2392.3MB, alloc=94.0MB, time=24.36 memory used=2425.1MB, alloc=94.0MB, time=24.46 memory used=2481.1MB, alloc=94.0MB, time=24.92 memory used=2557.5MB, alloc=94.0MB, time=25.46 memory used=2630.3MB, alloc=94.0MB, time=26.03 memory used=2702.3MB, alloc=94.0MB, time=26.81 memory used=2774.1MB, alloc=94.0MB, time=27.74 memory used=2846.3MB, alloc=94.0MB, time=28.81 memory used=2917.1MB, alloc=94.0MB, time=29.93 memory used=2973.5MB, alloc=118.0MB, time=30.60 memory used=3020.7MB, alloc=118.0MB, time=30.75 memory used=3068.2MB, alloc=118.0MB, time=30.88 memory used=3129.5MB, alloc=118.0MB, time=31.58 memory used=3173.6MB, alloc=118.0MB, time=31.72 memory used=3260.8MB, alloc=118.0MB, time=32.42 memory used=3325.7MB, alloc=118.0MB, time=32.76 memory used=3376.3MB, alloc=118.0MB, time=33.00 memory used=3421.5MB, alloc=118.0MB, time=33.14 memory used=3481.8MB, alloc=118.0MB, time=33.44 memory used=3529.2MB, alloc=118.0MB, time=33.60 memory used=3574.4MB, alloc=118.0MB, time=33.73 memory used=3612.9MB, alloc=118.0MB, time=33.85 memory used=3674.1MB, alloc=118.0MB, time=35.06 memory used=3723.9MB, alloc=118.0MB, time=35.21 memory used=3762.3MB, alloc=118.0MB, time=35.33 memory used=3811.7MB, alloc=118.0MB, time=35.48 memory used=3904.5MB, alloc=118.0MB, time=36.12 memory used=3978.3MB, alloc=374.0MB, time=37.09 memory used=4036.5MB, alloc=374.0MB, time=37.63 memory used=4079.6MB, alloc=374.0MB, time=37.77 memory used=4126.2MB, alloc=374.0MB, time=37.99 memory used=4173.2MB, alloc=374.0MB, time=38.15 memory used=4232.4MB, alloc=374.0MB, time=41.83 memory used=4277.0MB, alloc=374.0MB, time=41.99 memory used=4316.4MB, alloc=374.0MB, time=42.13 memory used=4364.6MB, alloc=374.0MB, time=42.28 memory used=4395.9MB, alloc=374.0MB, time=42.39 memory used=4431.2MB, alloc=374.0MB, time=42.50 memory used=4470.6MB, alloc=374.0MB, time=42.61 memory used=4514.8MB, alloc=374.0MB, time=42.72 memory used=4601.4MB, alloc=374.0MB, time=43.02 memory used=4659.7MB, alloc=374.0MB, time=43.43 memory used=4700.3MB, alloc=374.0MB, time=43.58 memory used=4747.7MB, alloc=374.0MB, time=43.74 memory used=4778.9MB, alloc=374.0MB, time=43.87 memory used=4815.0MB, alloc=374.0MB, time=44.00 memory used=4855.4MB, alloc=374.0MB, time=44.14 memory used=4901.1MB, alloc=374.0MB, time=44.27 memory used=4953.2MB, alloc=374.0MB, time=44.42 memory used=4989.6MB, alloc=374.0MB, time=44.55 memory used=5019.8MB, alloc=374.0MB, time=44.66 memory used=5051.7MB, alloc=374.0MB, time=44.77 memory used=5087.3MB, alloc=374.0MB, time=44.88 memory used=5149.1MB, alloc=374.0MB, time=51.76 memory used=5202.0MB, alloc=374.0MB, time=52.49 memory used=5237.7MB, alloc=374.0MB, time=52.63 memory used=5282.7MB, alloc=374.0MB, time=52.77 memory used=5325.5MB, alloc=374.0MB, time=52.90 memory used=5356.4MB, alloc=374.0MB, time=53.01 memory used=5390.0MB, alloc=374.0MB, time=53.13 memory used=5426.9MB, alloc=374.0MB, time=53.25 memory used=5467.7MB, alloc=374.0MB, time=53.38 memory used=5513.1MB, alloc=374.0MB, time=53.50 memory used=5562.7MB, alloc=374.0MB, time=53.63 memory used=5760.0MB, alloc=374.0MB, time=54.78 memory used=5805.3MB, alloc=374.0MB, time=54.98 memory used=5841.8MB, alloc=374.0MB, time=55.12 memory used=5887.1MB, alloc=374.0MB, time=55.32 memory used=5931.0MB, alloc=374.0MB, time=55.59 memory used=5987.0MB, alloc=398.0MB, time=57.46 memory used=6039.7MB, alloc=398.0MB, time=57.69 memory used=6103.4MB, alloc=398.0MB, time=57.92 memory used=6145.2MB, alloc=398.0MB, time=58.12 memory used=6187.8MB, alloc=398.0MB, time=58.30 memory used=6230.7MB, alloc=398.0MB, time=58.48 memory used=6280.0MB, alloc=398.0MB, time=58.66 memory used=6333.1MB, alloc=398.0MB, time=58.85 memory used=6389.2MB, alloc=398.0MB, time=59.03 memory used=6448.3MB, alloc=398.0MB, time=59.22 memory used=6510.4MB, alloc=398.0MB, time=59.43 memory used=6573.0MB, alloc=422.0MB, time=59.63 memory used=6618.3MB, alloc=422.0MB, time=59.79 memory used=6661.1MB, alloc=422.0MB, time=59.95 memory used=6709.8MB, alloc=422.0MB, time=60.11 memory used=6759.7MB, alloc=422.0MB, time=60.28 memory used=6810.7MB, alloc=422.0MB, time=60.44 memory used=6862.8MB, alloc=422.0MB, time=60.61 memory used=6915.8MB, alloc=422.0MB, time=60.77 memory used=6969.9MB, alloc=422.0MB, time=60.94 memory used=7025.0MB, alloc=422.0MB, time=61.12 memory used=7081.9MB, alloc=422.0MB, time=61.30 memory used=7146.1MB, alloc=422.0MB, time=61.47 memory used=7212.2MB, alloc=422.0MB, time=61.66 memory used=7279.3MB, alloc=422.0MB, time=61.85 memory used=7347.4MB, alloc=422.0MB, time=62.03 memory used=7416.5MB, alloc=422.0MB, time=62.21 memory used=7486.4MB, alloc=422.0MB, time=62.40 memory used=7558.2MB, alloc=422.0MB, time=62.59 memory used=7637.6MB, alloc=422.0MB, time=62.79 memory used=7718.9MB, alloc=422.0MB, time=63.00 memory used=7801.0MB, alloc=422.0MB, time=63.19 memory used=7883.8MB, alloc=422.0MB, time=63.39 memory used=7967.3MB, alloc=422.0MB, time=63.60 memory used=8156.4MB, alloc=422.0MB, time=64.03 memory used=8277.7MB, alloc=422.0MB, time=64.32 memory used=8403.3MB, alloc=422.0MB, time=64.61 memory used=8536.1MB, alloc=422.0MB, time=64.92 memory used=8672.0MB, alloc=422.0MB, time=65.22 memory used=8814.2MB, alloc=422.0MB, time=65.53 memory used=8959.8MB, alloc=422.0MB, time=65.86 memory used=9111.6MB, alloc=422.0MB, time=66.17 memory used=9270.5MB, alloc=422.0MB, time=66.49 memory used=9435.3MB, alloc=422.0MB, time=66.81 memory used=9607.9MB, alloc=422.0MB, time=67.14 memory used=9793.6MB, alloc=422.0MB, time=67.49 memory used=9984.0MB, alloc=422.0MB, time=67.83 memory used=10186.5MB, alloc=422.0MB, time=68.19 memory used=10402.3MB, alloc=422.0MB, time=68.57 memory used=10631.0MB, alloc=422.0MB, time=68.93 memory used=10822.9MB, alloc=422.0MB, time=132.52 memory used=10926.4MB, alloc=422.0MB, time=153.26 memory used=11024.8MB, alloc=422.0MB, time=154.07 memory used=11098.9MB, alloc=422.0MB, time=154.35 memory used=11165.4MB, alloc=422.0MB, time=154.59 memory used=11248.7MB, alloc=422.0MB, time=154.85 memory used=11300.8MB, alloc=422.0MB, time=155.03 memory used=11355.8MB, alloc=422.0MB, time=155.21 memory used=11416.5MB, alloc=422.0MB, time=155.40 memory used=11481.2MB, alloc=422.0MB, time=155.58 memory used=11550.2MB, alloc=422.0MB, time=155.78 memory used=11626.6MB, alloc=422.0MB, time=155.98 memory used=11707.0MB, alloc=422.0MB, time=156.19 memory used=11795.3MB, alloc=422.0MB, time=156.40 memory used=11978.9MB, alloc=422.0MB, time=156.82 memory used=12117.0MB, alloc=422.0MB, time=157.14 memory used=12265.2MB, alloc=422.0MB, time=157.48 memory used=12428.4MB, alloc=422.0MB, time=157.84 memory used=12602.9MB, alloc=422.0MB, time=158.20 memory used=12788.0MB, alloc=422.0MB, time=158.58 memory used=12988.5MB, alloc=422.0MB, time=158.97 memory used=13199.1MB, alloc=422.0MB, time=159.37 memory used=13428.1MB, alloc=422.0MB, time=159.78 memory used=13656.6MB, alloc=422.0MB, time=160.20 memory used=13825.1MB, alloc=422.0MB, time=160.53 memory used=14000.9MB, alloc=422.0MB, time=160.89 memory used=14187.1MB, alloc=422.0MB, time=161.25 memory used=14381.4MB, alloc=422.0MB, time=161.61 memory used=14582.2MB, alloc=422.0MB, time=161.98 memory used=14793.5MB, alloc=422.0MB, time=162.35 memory used=15016.0MB, alloc=422.0MB, time=162.74 memory used=15253.9MB, alloc=422.0MB, time=163.14 memory used=15464.6MB, alloc=422.0MB, time=163.49 memory used=15664.7MB, alloc=422.0MB, time=163.83 memory used=16030.1MB, alloc=422.0MB, time=165.74 memory used=16135.9MB, alloc=422.0MB, time=166.50 memory used=16208.9MB, alloc=422.0MB, time=166.73 memory used=16280.5MB, alloc=422.0MB, time=166.95 memory used=16339.6MB, alloc=422.0MB, time=167.12 memory used=16406.6MB, alloc=422.0MB, time=167.30 memory used=16483.6MB, alloc=422.0MB, time=167.49 memory used=16571.9MB, alloc=422.0MB, time=167.68 memory used=16749.0MB, alloc=422.0MB, time=168.04 memory used=16920.1MB, alloc=422.0MB, time=168.93 memory used=16986.9MB, alloc=422.0MB, time=169.13 memory used=17060.0MB, alloc=422.0MB, time=169.31 memory used=17272.2MB, alloc=422.0MB, time=170.27 memory used=17348.8MB, alloc=422.0MB, time=170.54 memory used=17408.5MB, alloc=422.0MB, time=170.76 memory used=17481.5MB, alloc=422.0MB, time=171.02 memory used=17570.9MB, alloc=422.0MB, time=171.29 memory used=17628.7MB, alloc=422.0MB, time=171.48 memory used=17681.9MB, alloc=422.0MB, time=171.66 memory used=17736.8MB, alloc=422.0MB, time=171.83 memory used=17797.8MB, alloc=422.0MB, time=172.01 memory used=17861.1MB, alloc=422.0MB, time=172.20 memory used=17930.7MB, alloc=422.0MB, time=172.39 memory used=18002.4MB, alloc=422.0MB, time=172.58 memory used=18080.3MB, alloc=422.0MB, time=172.78 memory used=18164.5MB, alloc=422.0MB, time=172.99 memory used=18250.9MB, alloc=422.0MB, time=173.20 memory used=18471.4MB, alloc=422.0MB, time=173.63 memory used=18610.4MB, alloc=422.0MB, time=173.95 memory used=18758.5MB, alloc=422.0MB, time=174.27 memory used=18920.7MB, alloc=422.0MB, time=174.60 memory used=19097.3MB, alloc=422.0MB, time=174.96 memory used=19294.5MB, alloc=422.0MB, time=175.31 memory used=19499.0MB, alloc=422.0MB, time=181.51 memory used=19571.4MB, alloc=422.0MB, time=181.76 memory used=19637.0MB, alloc=422.0MB, time=181.96 memory used=19699.3MB, alloc=422.0MB, time=182.15 memory used=19771.8MB, alloc=422.0MB, time=182.34 memory used=19856.5MB, alloc=422.0MB, time=182.55 memory used=20056.5MB, alloc=422.0MB, time=182.95 memory used=20219.9MB, alloc=422.0MB, time=183.30 memory used=20414.1MB, alloc=422.0MB, time=183.67 memory used=20707.6MB, alloc=422.0MB, time=184.82 memory used=20788.8MB, alloc=422.0MB, time=185.05 memory used=20943.4MB, alloc=422.0MB, time=186.54 memory used=21115.3MB, alloc=422.0MB, time=189.05 memory used=21259.2MB, alloc=422.0MB, time=190.94 memory used=21396.7MB, alloc=422.0MB, time=192.03 memory used=21545.7MB, alloc=422.0MB, time=194.08 memory used=21669.5MB, alloc=422.0MB, time=195.04 memory used=21800.0MB, alloc=422.0MB, time=195.95 memory used=21936.0MB, alloc=422.0MB, time=197.33 memory used=22060.9MB, alloc=422.0MB, time=198.36 memory used=22190.4MB, alloc=422.0MB, time=199.06 memory used=22293.2MB, alloc=422.0MB, time=199.44 memory used=22420.0MB, alloc=422.0MB, time=199.81 memory used=22571.3MB, alloc=422.0MB, time=200.23 memory used=22730.8MB, alloc=422.0MB, time=200.66 memory used=22934.7MB, alloc=422.0MB, time=201.20 memory used=23104.1MB, alloc=422.0MB, time=201.83 memory used=23243.5MB, alloc=422.0MB, time=202.44 memory used=23623.0MB, alloc=422.0MB, time=203.22 memory used=23874.0MB, alloc=422.0MB, time=204.22 memory used=23984.5MB, alloc=422.0MB, time=204.72 memory used=24081.9MB, alloc=422.0MB, time=205.10 memory used=24181.8MB, alloc=422.0MB, time=205.46 memory used=24317.8MB, alloc=422.0MB, time=206.41 memory used=24420.6MB, alloc=422.0MB, time=206.86 memory used=24525.3MB, alloc=422.0MB, time=207.22 memory used=24636.5MB, alloc=422.0MB, time=207.58 memory used=24762.8MB, alloc=422.0MB, time=207.96 memory used=24893.6MB, alloc=422.0MB, time=208.36 memory used=25037.1MB, alloc=422.0MB, time=209.44 memory used=25145.1MB, alloc=422.0MB, time=209.98 memory used=25251.1MB, alloc=422.0MB, time=210.33 memory used=25370.9MB, alloc=422.0MB, time=210.72 memory used=25526.6MB, alloc=422.0MB, time=211.19 memory used=25809.0MB, alloc=422.0MB, time=211.79 memory used=26174.3MB, alloc=422.0MB, time=212.53 memory used=26542.0MB, alloc=422.0MB, time=213.30 memory used=26905.8MB, alloc=422.0MB, time=214.09 memory used=27268.0MB, alloc=422.0MB, time=214.86 memory used=27636.3MB, alloc=422.0MB, time=215.64 memory used=27999.8MB, alloc=422.0MB, time=216.43 memory used=28359.3MB, alloc=422.0MB, time=217.21 memory used=28703.5MB, alloc=422.0MB, time=217.94 memory used=29042.5MB, alloc=422.0MB, time=218.75 memory used=29394.8MB, alloc=422.0MB, time=219.78 memory used=29724.9MB, alloc=422.0MB, time=221.42 memory used=30062.7MB, alloc=422.0MB, time=223.27 memory used=30447.9MB, alloc=422.0MB, time=224.70 memory used=30568.4MB, alloc=422.0MB, time=225.62 memory used=30667.8MB, alloc=422.0MB, time=225.99 memory used=30778.1MB, alloc=422.0MB, time=226.35 memory used=30900.4MB, alloc=422.0MB, time=226.75 memory used=31047.5MB, alloc=422.0MB, time=227.18 memory used=31185.3MB, alloc=422.0MB, time=227.70 memory used=31420.4MB, alloc=422.0MB, time=228.72 memory used=31589.6MB, alloc=422.0MB, time=229.78 memory used=31702.3MB, alloc=422.0MB, time=230.19 memory used=31837.5MB, alloc=422.0MB, time=230.64 memory used=32012.5MB, alloc=422.0MB, time=231.17 memory used=32251.2MB, alloc=422.0MB, time=231.77 memory used=32571.1MB, alloc=422.0MB, time=232.46 memory used=32953.0MB, alloc=422.0MB, time=233.23 memory used=33318.8MB, alloc=422.0MB, time=233.95 memory used=33673.5MB, alloc=422.0MB, time=234.61 memory used=34026.5MB, alloc=422.0MB, time=235.30 memory used=34375.1MB, alloc=422.0MB, time=236.01 memory used=34718.5MB, alloc=422.0MB, time=236.65 memory used=35061.8MB, alloc=422.0MB, time=237.32 memory used=35405.6MB, alloc=422.0MB, time=237.98 memory used=35749.4MB, alloc=422.0MB, time=238.68 memory used=36086.4MB, alloc=422.0MB, time=239.30 memory used=36430.3MB, alloc=422.0MB, time=239.98 memory used=36770.2MB, alloc=422.0MB, time=240.69 memory used=37116.3MB, alloc=422.0MB, time=241.39 memory used=37458.5MB, alloc=422.0MB, time=242.07 memory used=37801.3MB, alloc=422.0MB, time=242.79 memory used=38148.7MB, alloc=422.0MB, time=243.55 memory used=38490.4MB, alloc=422.0MB, time=244.27 memory used=38826.5MB, alloc=422.0MB, time=244.98 memory used=39165.0MB, alloc=422.0MB, time=245.68 memory used=39505.1MB, alloc=422.0MB, time=246.53 memory used=39846.7MB, alloc=422.0MB, time=247.41 memory used=40179.9MB, alloc=422.0MB, time=248.00 memory used=40542.1MB, alloc=422.0MB, time=248.95 memory used=40922.9MB, alloc=422.0MB, time=250.36 memory used=41313.6MB, alloc=422.0MB, time=251.89 memory used=41520.3MB, alloc=422.0MB, time=254.09 memory used=41652.1MB, alloc=446.0MB, time=255.03 memory used=41817.0MB, alloc=446.0MB, time=256.14 memory used=41969.1MB, alloc=446.0MB, time=257.92 memory used=42110.5MB, alloc=470.0MB, time=260.05 memory used=42278.9MB, alloc=470.0MB, time=262.36 memory used=42432.2MB, alloc=494.0MB, time=264.93 memory used=42616.2MB, alloc=518.0MB, time=267.65 memory used=42813.4MB, alloc=542.0MB, time=270.84 memory used=43003.3MB, alloc=566.0MB, time=272.06 memory used=43210.4MB, alloc=566.0MB, time=273.00 memory used=43466.0MB, alloc=566.0MB, time=274.09 memory used=43763.7MB, alloc=566.0MB, time=275.28 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428488794 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 3 F := [-7 x y - 10 x z + 18 z , 15 x y z + 11 x z - 19 z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 G := [-4 x y z - 3 y z - 13, 3 x y + 12 y z + 4 y z] > Problem := [F,G]; 2 2 3 2 2 3 Problem := [[-7 x y - 10 x z + 18 z , 15 x y z + 11 x z - 19 z ], 2 2 2 2 2 [-4 x y z - 3 y z - 13, 3 x y + 12 y z + 4 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.0MB, alloc=32.3MB, time=0.51 memory used=46.6MB, alloc=32.3MB, time=0.82 memory used=65.6MB, alloc=56.3MB, time=1.14 memory used=107.3MB, alloc=60.3MB, time=1.76 memory used=146.4MB, alloc=84.3MB, time=2.38 memory used=208.6MB, alloc=92.3MB, time=3.39 memory used=270.7MB, alloc=348.3MB, time=4.24 memory used=334.0MB, alloc=372.3MB, time=5.21 memory used=425.4MB, alloc=372.3MB, time=6.47 memory used=513.6MB, alloc=396.3MB, time=7.54 memory used=626.7MB, alloc=396.3MB, time=8.93 memory used=741.3MB, alloc=396.3MB, time=10.61 memory used=850.4MB, alloc=420.3MB, time=12.29 memory used=966.2MB, alloc=444.3MB, time=13.88 memory used=1084.1MB, alloc=444.3MB, time=15.70 memory used=1193.4MB, alloc=444.3MB, time=17.33 memory used=1316.5MB, alloc=444.3MB, time=18.98 memory used=1420.5MB, alloc=468.3MB, time=20.51 memory used=1520.7MB, alloc=468.3MB, time=21.91 memory used=1650.8MB, alloc=468.3MB, time=23.36 memory used=1762.4MB, alloc=468.3MB, time=24.62 memory used=1839.1MB, alloc=468.3MB, time=24.98 memory used=1944.9MB, alloc=468.3MB, time=25.79 memory used=2070.8MB, alloc=468.3MB, time=26.97 memory used=2176.8MB, alloc=492.3MB, time=28.26 memory used=2281.1MB, alloc=492.3MB, time=29.85 memory used=2415.5MB, alloc=492.3MB, time=31.57 memory used=2529.5MB, alloc=492.3MB, time=32.66 memory used=2598.3MB, alloc=492.3MB, time=33.92 memory used=2669.1MB, alloc=492.3MB, time=35.14 memory used=2736.4MB, alloc=492.3MB, time=36.23 memory used=2791.4MB, alloc=492.3MB, time=37.27 memory used=2865.5MB, alloc=492.3MB, time=38.45 memory used=2925.5MB, alloc=492.3MB, time=39.54 memory used=2977.5MB, alloc=492.3MB, time=40.59 memory used=3027.1MB, alloc=492.3MB, time=41.60 memory used=3068.9MB, alloc=492.3MB, time=42.43 memory used=3129.9MB, alloc=492.3MB, time=43.47 memory used=3174.2MB, alloc=516.3MB, time=44.51 memory used=3245.9MB, alloc=516.3MB, time=45.47 memory used=3341.4MB, alloc=516.3MB, time=45.99 memory used=3456.5MB, alloc=516.3MB, time=46.58 memory used=3560.4MB, alloc=516.3MB, time=47.16 memory used=3658.8MB, alloc=516.3MB, time=47.75 memory used=3777.1MB, alloc=516.3MB, time=48.33 memory used=3881.8MB, alloc=516.3MB, time=48.96 memory used=3986.1MB, alloc=516.3MB, time=49.94 memory used=4085.7MB, alloc=516.3MB, time=50.82 memory used=4327.4MB, alloc=516.3MB, time=51.78 memory used=4418.6MB, alloc=516.3MB, time=52.29 memory used=4662.9MB, alloc=516.3MB, time=53.23 memory used=4756.2MB, alloc=516.3MB, time=53.76 memory used=5000.1MB, alloc=516.3MB, time=54.74 memory used=5113.3MB, alloc=516.3MB, time=55.31 memory used=5218.0MB, alloc=516.3MB, time=55.95 memory used=5311.6MB, alloc=516.3MB, time=56.47 memory used=5426.6MB, alloc=516.3MB, time=57.07 memory used=5538.8MB, alloc=516.3MB, time=57.74 memory used=5633.8MB, alloc=516.3MB, time=58.25 memory used=5867.4MB, alloc=516.3MB, time=59.13 memory used=5994.7MB, alloc=516.3MB, time=59.69 memory used=6202.7MB, alloc=516.3MB, time=60.58 memory used=6448.5MB, alloc=516.3MB, time=62.05 memory used=6546.4MB, alloc=540.3MB, time=62.70 memory used=6645.5MB, alloc=540.3MB, time=63.34 memory used=6775.9MB, alloc=540.3MB, time=63.98 memory used=6863.7MB, alloc=540.3MB, time=64.57 memory used=6944.9MB, alloc=540.3MB, time=65.08 memory used=7035.8MB, alloc=540.3MB, time=65.61 memory used=7134.0MB, alloc=540.3MB, time=66.15 memory used=7239.4MB, alloc=540.3MB, time=66.68 memory used=7355.0MB, alloc=540.3MB, time=67.24 memory used=7478.0MB, alloc=540.3MB, time=67.85 memory used=7614.8MB, alloc=540.3MB, time=68.44 memory used=7811.5MB, alloc=540.3MB, time=69.17 memory used=7937.9MB, alloc=540.3MB, time=69.79 memory used=8070.5MB, alloc=540.3MB, time=70.41 memory used=8208.0MB, alloc=540.3MB, time=71.03 memory used=8353.9MB, alloc=540.3MB, time=71.66 memory used=8506.5MB, alloc=540.3MB, time=72.29 memory used=8667.2MB, alloc=540.3MB, time=72.95 memory used=8842.2MB, alloc=540.3MB, time=73.62 memory used=9020.9MB, alloc=540.3MB, time=74.33 memory used=9209.0MB, alloc=540.3MB, time=75.02 memory used=9407.5MB, alloc=540.3MB, time=75.71 memory used=9616.5MB, alloc=540.3MB, time=76.41 memory used=9841.0MB, alloc=540.3MB, time=77.14 memory used=10066.9MB, alloc=540.3MB, time=77.87 memory used=10230.1MB, alloc=540.3MB, time=78.47 memory used=10397.2MB, alloc=540.3MB, time=79.09 memory used=10573.0MB, alloc=540.3MB, time=79.75 memory used=10754.9MB, alloc=540.3MB, time=80.38 memory used=10946.2MB, alloc=540.3MB, time=81.00 memory used=11149.3MB, alloc=540.3MB, time=81.62 memory used=11344.4MB, alloc=540.3MB, time=83.12 memory used=11459.0MB, alloc=540.3MB, time=83.76 memory used=11567.3MB, alloc=540.3MB, time=84.35 memory used=11651.4MB, alloc=540.3MB, time=84.88 memory used=11747.3MB, alloc=540.3MB, time=85.44 memory used=11852.8MB, alloc=540.3MB, time=86.01 memory used=11974.2MB, alloc=540.3MB, time=86.58 memory used=12104.2MB, alloc=540.3MB, time=87.16 memory used=12344.5MB, alloc=540.3MB, time=87.96 memory used=12476.8MB, alloc=540.3MB, time=88.58 memory used=12622.2MB, alloc=540.3MB, time=89.21 memory used=12777.0MB, alloc=540.3MB, time=89.85 memory used=12942.5MB, alloc=540.3MB, time=90.52 memory used=13121.1MB, alloc=540.3MB, time=91.20 memory used=13313.5MB, alloc=540.3MB, time=91.87 memory used=13525.7MB, alloc=540.3MB, time=92.56 memory used=13755.8MB, alloc=540.3MB, time=93.24 memory used=14024.6MB, alloc=540.3MB, time=95.04 memory used=14201.6MB, alloc=540.3MB, time=118.02 memory used=14311.2MB, alloc=540.3MB, time=118.63 memory used=14408.4MB, alloc=540.3MB, time=119.17 memory used=14532.0MB, alloc=540.3MB, time=119.74 memory used=14751.8MB, alloc=540.3MB, time=120.51 memory used=14905.0MB, alloc=540.3MB, time=121.18 memory used=15079.6MB, alloc=540.3MB, time=121.84 memory used=15274.5MB, alloc=540.3MB, time=122.54 memory used=15493.8MB, alloc=540.3MB, time=123.26 memory used=15701.9MB, alloc=540.3MB, time=123.96 memory used=15878.0MB, alloc=540.3MB, time=124.59 memory used=16065.1MB, alloc=540.3MB, time=125.30 memory used=16268.9MB, alloc=540.3MB, time=125.98 memory used=16489.7MB, alloc=540.3MB, time=126.68 memory used=16722.1MB, alloc=540.3MB, time=127.39 memory used=16915.4MB, alloc=540.3MB, time=128.03 memory used=17125.6MB, alloc=540.3MB, time=128.67 memory used=17344.0MB, alloc=540.3MB, time=130.18 memory used=17445.0MB, alloc=540.3MB, time=130.77 memory used=17577.3MB, alloc=540.3MB, time=131.41 memory used=17660.4MB, alloc=540.3MB, time=131.96 memory used=17741.7MB, alloc=540.3MB, time=132.47 memory used=17833.3MB, alloc=540.3MB, time=133.05 memory used=17931.9MB, alloc=540.3MB, time=133.61 memory used=18037.4MB, alloc=540.3MB, time=134.15 memory used=18153.7MB, alloc=540.3MB, time=134.69 memory used=18276.9MB, alloc=540.3MB, time=135.25 memory used=18414.1MB, alloc=540.3MB, time=135.83 memory used=18602.6MB, alloc=540.3MB, time=136.53 memory used=18729.0MB, alloc=540.3MB, time=137.14 memory used=18861.6MB, alloc=540.3MB, time=137.74 memory used=18999.1MB, alloc=540.3MB, time=138.35 memory used=19145.0MB, alloc=540.3MB, time=139.00 memory used=19297.5MB, alloc=540.3MB, time=139.64 memory used=19458.3MB, alloc=540.3MB, time=140.26 memory used=19633.3MB, alloc=540.3MB, time=140.93 memory used=19811.9MB, alloc=540.3MB, time=141.59 memory used=20000.0MB, alloc=540.3MB, time=142.26 memory used=20198.6MB, alloc=540.3MB, time=142.93 memory used=20407.5MB, alloc=540.3MB, time=143.62 memory used=20632.1MB, alloc=540.3MB, time=144.33 memory used=20858.0MB, alloc=540.3MB, time=145.06 memory used=21021.2MB, alloc=540.3MB, time=145.70 memory used=21188.3MB, alloc=540.3MB, time=146.32 memory used=21364.1MB, alloc=540.3MB, time=146.94 memory used=21546.0MB, alloc=540.3MB, time=147.59 memory used=21737.3MB, alloc=540.3MB, time=148.20 memory used=21940.4MB, alloc=540.3MB, time=148.81 memory used=22134.9MB, alloc=540.3MB, time=150.28 memory used=22248.5MB, alloc=540.3MB, time=150.93 memory used=22355.9MB, alloc=540.3MB, time=151.49 memory used=22441.1MB, alloc=540.3MB, time=152.00 memory used=22537.6MB, alloc=540.3MB, time=152.53 memory used=22642.5MB, alloc=540.3MB, time=153.08 memory used=22759.1MB, alloc=540.3MB, time=153.63 memory used=22887.6MB, alloc=540.3MB, time=154.21 memory used=23135.8MB, alloc=540.3MB, time=154.98 memory used=23268.1MB, alloc=540.3MB, time=155.56 memory used=23413.5MB, alloc=540.3MB, time=156.18 memory used=23568.3MB, alloc=540.3MB, time=156.80 memory used=23733.8MB, alloc=540.3MB, time=157.47 memory used=23912.4MB, alloc=540.3MB, time=158.10 memory used=24104.8MB, alloc=540.3MB, time=158.75 memory used=24317.0MB, alloc=540.3MB, time=159.41 memory used=24547.1MB, alloc=540.3MB, time=160.08 memory used=24815.1MB, alloc=540.3MB, time=161.87 memory used=25000.9MB, alloc=540.3MB, time=188.44 memory used=25115.0MB, alloc=540.3MB, time=189.11 memory used=25201.6MB, alloc=540.3MB, time=189.69 memory used=25305.5MB, alloc=540.3MB, time=190.35 memory used=25426.5MB, alloc=540.3MB, time=190.94 memory used=25540.2MB, alloc=564.3MB, time=191.54 memory used=25624.0MB, alloc=564.3MB, time=192.09 memory used=25710.0MB, alloc=564.3MB, time=192.62 memory used=25801.4MB, alloc=564.3MB, time=193.15 memory used=25897.3MB, alloc=588.3MB, time=193.70 memory used=26014.8MB, alloc=588.3MB, time=194.27 memory used=26144.6MB, alloc=588.3MB, time=194.87 memory used=26280.6MB, alloc=588.3MB, time=195.47 memory used=26422.9MB, alloc=588.3MB, time=196.09 memory used=26571.3MB, alloc=588.3MB, time=196.70 memory used=26726.9MB, alloc=588.3MB, time=197.34 memory used=26900.4MB, alloc=588.3MB, time=198.01 memory used=27132.9MB, alloc=588.3MB, time=198.82 memory used=27240.1MB, alloc=588.3MB, time=199.38 memory used=27351.4MB, alloc=588.3MB, time=199.98 memory used=27464.6MB, alloc=588.3MB, time=200.59 memory used=27579.9MB, alloc=588.3MB, time=201.18 memory used=27697.1MB, alloc=588.3MB, time=201.77 memory used=27818.1MB, alloc=588.3MB, time=202.37 memory used=27954.7MB, alloc=588.3MB, time=202.99 memory used=28095.4MB, alloc=588.3MB, time=203.62 memory used=28238.4MB, alloc=588.3MB, time=204.28 memory used=28383.7MB, alloc=588.3MB, time=204.91 memory used=28531.2MB, alloc=588.3MB, time=205.56 memory used=28680.7MB, alloc=588.3MB, time=206.20 memory used=28832.4MB, alloc=588.3MB, time=206.82 memory used=28986.0MB, alloc=588.3MB, time=207.46 memory used=29141.5MB, alloc=588.3MB, time=208.10 memory used=29298.9MB, alloc=588.3MB, time=208.75 memory used=29460.1MB, alloc=588.3MB, time=209.39 memory used=29639.1MB, alloc=588.3MB, time=210.11 memory used=29822.3MB, alloc=588.3MB, time=210.79 memory used=30007.5MB, alloc=588.3MB, time=211.46 memory used=30194.6MB, alloc=588.3MB, time=212.13 memory used=30383.6MB, alloc=588.3MB, time=212.81 memory used=30574.2MB, alloc=588.3MB, time=213.51 memory used=30766.5MB, alloc=588.3MB, time=214.19 memory used=30962.8MB, alloc=588.3MB, time=214.87 memory used=31177.4MB, alloc=588.3MB, time=215.60 memory used=31396.1MB, alloc=588.3MB, time=216.36 memory used=31616.4MB, alloc=588.3MB, time=217.07 memory used=31807.4MB, alloc=588.3MB, time=217.75 memory used=31952.5MB, alloc=588.3MB, time=218.37 memory used=32088.5MB, alloc=588.3MB, time=218.97 memory used=32241.7MB, alloc=588.3MB, time=219.58 memory used=32380.0MB, alloc=588.3MB, time=220.18 memory used=32532.6MB, alloc=588.3MB, time=220.79 memory used=32689.9MB, alloc=588.3MB, time=221.42 memory used=32847.6MB, alloc=588.3MB, time=222.05 memory used=33005.6MB, alloc=588.3MB, time=222.70 memory used=33163.9MB, alloc=588.3MB, time=223.33 memory used=33322.4MB, alloc=588.3MB, time=223.97 memory used=33481.1MB, alloc=588.3MB, time=224.61 memory used=33640.0MB, alloc=588.3MB, time=225.24 memory used=33802.2MB, alloc=588.3MB, time=225.88 memory used=33980.9MB, alloc=588.3MB, time=226.54 memory used=34162.8MB, alloc=588.3MB, time=227.21 memory used=34344.5MB, alloc=588.3MB, time=227.91 memory used=34526.3MB, alloc=588.3MB, time=228.58 memory used=34707.9MB, alloc=588.3MB, time=229.25 memory used=34889.3MB, alloc=588.3MB, time=229.92 memory used=35070.3MB, alloc=588.3MB, time=230.60 memory used=35254.5MB, alloc=588.3MB, time=231.26 memory used=35453.9MB, alloc=588.3MB, time=231.95 memory used=35656.1MB, alloc=588.3MB, time=232.64 memory used=35857.5MB, alloc=588.3MB, time=233.34 memory used=36058.3MB, alloc=588.3MB, time=234.02 memory used=36258.1MB, alloc=588.3MB, time=234.71 memory used=36461.3MB, alloc=588.3MB, time=235.41 memory used=36676.6MB, alloc=588.3MB, time=236.10 memory used=36894.8MB, alloc=588.3MB, time=236.80 memory used=37111.5MB, alloc=588.3MB, time=237.51 memory used=37301.2MB, alloc=588.3MB, time=238.16 memory used=37459.0MB, alloc=588.3MB, time=238.78 memory used=37622.6MB, alloc=588.3MB, time=239.41 memory used=37789.9MB, alloc=588.3MB, time=240.06 memory used=37955.8MB, alloc=588.3MB, time=240.68 memory used=38124.6MB, alloc=588.3MB, time=241.31 memory used=38303.6MB, alloc=588.3MB, time=241.96 memory used=38484.9MB, alloc=588.3MB, time=242.60 memory used=38664.1MB, alloc=588.3MB, time=243.23 memory used=38845.7MB, alloc=588.3MB, time=243.87 memory used=39035.3MB, alloc=588.3MB, time=244.51 memory used=39226.4MB, alloc=588.3MB, time=245.17 memory used=39414.7MB, alloc=588.3MB, time=245.85 memory used=39606.6MB, alloc=588.3MB, time=246.50 memory used=39804.3MB, alloc=588.3MB, time=247.16 memory used=40012.7MB, alloc=588.3MB, time=247.82 memory used=40220.7MB, alloc=588.3MB, time=248.48 memory used=40429.3MB, alloc=588.3MB, time=249.15 memory used=40642.6MB, alloc=588.3MB, time=249.81 memory used=40864.0MB, alloc=588.3MB, time=250.46 memory used=41087.8MB, alloc=588.3MB, time=251.13 memory used=41320.9MB, alloc=588.3MB, time=251.81 memory used=41533.6MB, alloc=588.3MB, time=252.45 memory used=41726.5MB, alloc=588.3MB, time=253.07 memory used=41924.6MB, alloc=588.3MB, time=253.67 memory used=42131.0MB, alloc=588.3MB, time=254.42 memory used=42331.9MB, alloc=588.3MB, time=256.67 memory used=42614.7MB, alloc=588.3MB, time=259.17 memory used=42855.1MB, alloc=588.3MB, time=259.87 memory used=43121.8MB, alloc=588.3MB, time=260.57 memory used=43336.6MB, alloc=588.3MB, time=266.89 memory used=43457.9MB, alloc=588.3MB, time=267.58 memory used=43608.4MB, alloc=588.3MB, time=268.32 memory used=43764.3MB, alloc=588.3MB, time=269.04 memory used=43863.1MB, alloc=588.3MB, time=269.66 memory used=43962.6MB, alloc=588.3MB, time=270.29 memory used=44076.0MB, alloc=588.3MB, time=270.89 memory used=44197.4MB, alloc=588.3MB, time=271.47 memory used=44325.4MB, alloc=588.3MB, time=272.09 memory used=44459.8MB, alloc=588.3MB, time=272.71 memory used=44600.4MB, alloc=588.3MB, time=273.33 memory used=44747.2MB, alloc=588.3MB, time=273.96 memory used=44901.3MB, alloc=588.3MB, time=274.60 memory used=45073.2MB, alloc=588.3MB, time=275.29 memory used=45348.7MB, alloc=588.3MB, time=276.16 memory used=45456.3MB, alloc=588.3MB, time=276.73 memory used=45567.5MB, alloc=588.3MB, time=277.35 memory used=45680.8MB, alloc=588.3MB, time=277.94 memory used=45796.0MB, alloc=588.3MB, time=278.54 memory used=45913.2MB, alloc=588.3MB, time=279.15 memory used=46034.2MB, alloc=588.3MB, time=279.76 memory used=46170.8MB, alloc=588.3MB, time=280.40 memory used=46311.5MB, alloc=588.3MB, time=281.04 memory used=46454.6MB, alloc=588.3MB, time=281.70 memory used=46599.8MB, alloc=588.3MB, time=282.33 memory used=46747.3MB, alloc=588.3MB, time=282.97 memory used=46896.9MB, alloc=588.3MB, time=283.61 memory used=47048.5MB, alloc=588.3MB, time=284.25 memory used=47202.1MB, alloc=588.3MB, time=284.90 memory used=47357.6MB, alloc=588.3MB, time=285.56 memory used=47515.0MB, alloc=588.3MB, time=286.22 memory used=47676.3MB, alloc=588.3MB, time=286.88 memory used=47855.2MB, alloc=588.3MB, time=287.60 memory used=48038.4MB, alloc=588.3MB, time=288.29 memory used=48223.6MB, alloc=588.3MB, time=289.01 memory used=48410.7MB, alloc=588.3MB, time=289.70 memory used=48599.7MB, alloc=588.3MB, time=290.40 memory used=48790.3MB, alloc=588.3MB, time=291.15 memory used=48982.6MB, alloc=588.3MB, time=291.86 memory used=49178.9MB, alloc=588.3MB, time=292.54 memory used=49393.5MB, alloc=588.3MB, time=293.31 memory used=49612.2MB, alloc=588.3MB, time=294.04 memory used=49832.5MB, alloc=588.3MB, time=294.77 memory used=50023.5MB, alloc=588.3MB, time=295.47 memory used=50168.6MB, alloc=588.3MB, time=296.11 memory used=50304.6MB, alloc=588.3MB, time=296.74 memory used=50457.8MB, alloc=588.3MB, time=297.37 memory used=50596.2MB, alloc=588.3MB, time=297.97 memory used=50748.8MB, alloc=588.3MB, time=298.61 memory used=50906.1MB, alloc=588.3MB, time=299.27 memory used=51063.7MB, alloc=588.3MB, time=299.91 memory used=51221.7MB, alloc=588.3MB, time=300.55 memory used=51380.0MB, alloc=588.3MB, time=301.18 memory used=51538.5MB, alloc=588.3MB, time=301.81 memory used=51697.3MB, alloc=588.3MB, time=302.45 memory used=51856.1MB, alloc=588.3MB, time=303.08 memory used=52018.3MB, alloc=588.3MB, time=303.71 memory used=52197.0MB, alloc=588.3MB, time=304.36 memory used=52378.9MB, alloc=588.3MB, time=305.04 memory used=52560.7MB, alloc=588.3MB, time=305.75 memory used=52742.5MB, alloc=588.3MB, time=306.42 memory used=52924.0MB, alloc=588.3MB, time=307.09 memory used=53105.4MB, alloc=588.3MB, time=307.76 memory used=53286.4MB, alloc=588.3MB, time=308.43 memory used=53470.7MB, alloc=588.3MB, time=309.10 memory used=53670.0MB, alloc=588.3MB, time=309.79 memory used=53872.2MB, alloc=588.3MB, time=310.47 memory used=54073.7MB, alloc=588.3MB, time=311.18 memory used=54274.4MB, alloc=588.3MB, time=311.87 memory used=54474.2MB, alloc=588.3MB, time=312.56 memory used=54677.4MB, alloc=588.3MB, time=313.29 memory used=54892.7MB, alloc=588.3MB, time=313.98 memory used=55110.9MB, alloc=588.3MB, time=314.68 memory used=55327.6MB, alloc=588.3MB, time=315.38 memory used=55517.3MB, alloc=588.3MB, time=316.04 memory used=55675.0MB, alloc=588.3MB, time=316.66 memory used=55838.8MB, alloc=588.3MB, time=317.31 memory used=56006.0MB, alloc=588.3MB, time=317.98 memory used=56171.9MB, alloc=588.3MB, time=318.60 memory used=56340.7MB, alloc=588.3MB, time=319.22 memory used=56519.7MB, alloc=588.3MB, time=319.87 memory used=56701.0MB, alloc=588.3MB, time=320.51 memory used=56880.2MB, alloc=588.3MB, time=321.17 memory used=57061.8MB, alloc=588.3MB, time=321.81 memory used=57251.4MB, alloc=588.3MB, time=322.47 memory used=57442.6MB, alloc=588.3MB, time=323.14 memory used=57630.7MB, alloc=588.3MB, time=323.79 memory used=57822.7MB, alloc=588.3MB, time=324.44 memory used=58020.3MB, alloc=588.3MB, time=325.09 memory used=58228.8MB, alloc=588.3MB, time=325.76 memory used=58436.8MB, alloc=588.3MB, time=326.42 memory used=58645.4MB, alloc=588.3MB, time=327.08 memory used=58858.7MB, alloc=588.3MB, time=327.75 memory used=59080.1MB, alloc=588.3MB, time=328.42 memory used=59303.9MB, alloc=588.3MB, time=329.14 memory used=59537.1MB, alloc=588.3MB, time=329.85 memory used=59749.7MB, alloc=588.3MB, time=330.57 memory used=59942.6MB, alloc=588.3MB, time=331.20 memory used=60140.7MB, alloc=588.3MB, time=331.86 memory used=60347.0MB, alloc=588.3MB, time=332.65 memory used=60548.6MB, alloc=588.3MB, time=335.02 memory used=60831.2MB, alloc=588.3MB, time=337.47 memory used=61071.4MB, alloc=588.3MB, time=338.16 memory used=61338.0MB, alloc=588.3MB, time=338.86 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428489094 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 2 F := [10 x + 15 x y - 13, -10 x z - 15 y z - 3 x] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 2 2 G := [-5 x y - 6 x y - 16 z , 15 x z + 12 x y z - x y z] > Problem := [F,G]; 4 2 2 2 Problem := [[10 x + 15 x y - 13, -10 x z - 15 y z - 3 x], 3 2 3 2 2 2 [-5 x y - 6 x y - 16 z , 15 x z + 12 x y z - x y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.6MB, alloc=32.3MB, time=0.51 memory used=46.8MB, alloc=32.3MB, time=0.80 memory used=65.4MB, alloc=56.3MB, time=1.08 memory used=106.4MB, alloc=60.3MB, time=1.68 memory used=146.9MB, alloc=60.3MB, time=2.25 memory used=186.4MB, alloc=84.3MB, time=2.84 memory used=226.4MB, alloc=84.3MB, time=3.39 memory used=288.4MB, alloc=92.3MB, time=4.33 memory used=349.2MB, alloc=92.3MB, time=5.23 memory used=410.0MB, alloc=92.3MB, time=5.93 memory used=467.4MB, alloc=116.3MB, time=6.58 memory used=545.8MB, alloc=116.3MB, time=7.60 memory used=620.8MB, alloc=372.3MB, time=8.58 memory used=691.0MB, alloc=372.3MB, time=9.37 memory used=755.4MB, alloc=372.3MB, time=9.87 memory used=818.9MB, alloc=372.3MB, time=10.30 memory used=896.1MB, alloc=372.3MB, time=11.10 memory used=936.1MB, alloc=372.3MB, time=11.36 memory used=1000.8MB, alloc=372.3MB, time=11.86 memory used=1049.8MB, alloc=372.3MB, time=12.06 memory used=1093.1MB, alloc=372.3MB, time=12.33 memory used=1160.7MB, alloc=372.3MB, time=13.22 memory used=1200.4MB, alloc=372.3MB, time=13.38 memory used=1237.8MB, alloc=372.3MB, time=13.52 memory used=1272.2MB, alloc=372.3MB, time=13.66 memory used=1331.1MB, alloc=372.3MB, time=14.14 memory used=1425.8MB, alloc=372.3MB, time=15.67 memory used=1530.4MB, alloc=372.3MB, time=16.59 memory used=1638.8MB, alloc=372.3MB, time=17.22 memory used=1739.1MB, alloc=396.3MB, time=17.86 memory used=1826.1MB, alloc=396.3MB, time=18.20 memory used=1909.8MB, alloc=396.3MB, time=18.49 memory used=2000.1MB, alloc=396.3MB, time=18.80 memory used=2108.5MB, alloc=396.3MB, time=19.68 memory used=2221.6MB, alloc=396.3MB, time=21.15 memory used=2327.2MB, alloc=396.3MB, time=22.15 memory used=2439.6MB, alloc=420.3MB, time=23.61 memory used=2596.3MB, alloc=420.3MB, time=24.82 memory used=2751.9MB, alloc=420.3MB, time=26.02 memory used=2914.7MB, alloc=420.3MB, time=30.35 memory used=3064.9MB, alloc=420.3MB, time=32.27 memory used=3208.5MB, alloc=444.3MB, time=36.86 memory used=3367.7MB, alloc=444.3MB, time=39.35 memory used=3506.1MB, alloc=468.3MB, time=41.56 memory used=3666.9MB, alloc=492.3MB, time=44.09 memory used=3834.2MB, alloc=516.3MB, time=47.06 memory used=4065.2MB, alloc=540.3MB, time=52.97 memory used=4270.4MB, alloc=564.3MB, time=56.83 memory used=4486.0MB, alloc=588.3MB, time=60.68 memory used=4708.2MB, alloc=612.3MB, time=65.42 memory used=4913.7MB, alloc=636.3MB, time=72.63 memory used=5124.1MB, alloc=660.3MB, time=80.63 memory used=5346.5MB, alloc=684.3MB, time=89.19 memory used=5582.2MB, alloc=708.3MB, time=98.56 memory used=5825.3MB, alloc=732.3MB, time=109.24 memory used=6092.3MB, alloc=756.3MB, time=121.00 memory used=6383.3MB, alloc=780.3MB, time=133.84 memory used=6698.2MB, alloc=804.3MB, time=147.66 memory used=7037.1MB, alloc=804.3MB, time=162.32 memory used=7375.8MB, alloc=828.3MB, time=176.94 memory used=7738.5MB, alloc=828.3MB, time=192.63 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428489394 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 4 3 2 2 3 2 F := [-3 x z - 16 y - 19 z , -2 x y - 7 y z + 16 x z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 3 G := [-10 x y + 2 x y z - 11 x , x y - 16 x y z - 11 z ] > Problem := [F,G]; 3 4 3 2 2 3 2 Problem := [[-3 x z - 16 y - 19 z , -2 x y - 7 y z + 16 x z], 3 2 2 3 [-10 x y + 2 x y z - 11 x , x y - 16 x y z - 11 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=35.5MB, alloc=34.3MB, time=0.47 memory used=47.8MB, alloc=34.3MB, time=0.51 memory used=73.8MB, alloc=34.3MB, time=0.68 memory used=90.5MB, alloc=34.3MB, time=0.73 memory used=101.0MB, alloc=34.3MB, time=0.77 memory used=113.5MB, alloc=34.3MB, time=0.80 memory used=127.6MB, alloc=34.3MB, time=0.85 memory used=144.1MB, alloc=34.3MB, time=0.89 memory used=156.0MB, alloc=34.3MB, time=0.92 memory used=165.0MB, alloc=34.3MB, time=0.95 memory used=174.4MB, alloc=34.3MB, time=0.98 memory used=184.5MB, alloc=34.3MB, time=1.02 memory used=195.5MB, alloc=34.3MB, time=1.05 memory used=207.4MB, alloc=34.3MB, time=1.08 memory used=220.7MB, alloc=34.3MB, time=1.12 memory used=238.6MB, alloc=34.3MB, time=1.56 memory used=261.2MB, alloc=58.3MB, time=6.60 memory used=299.2MB, alloc=62.4MB, time=22.24 memory used=332.2MB, alloc=62.4MB, time=33.28 memory used=372.7MB, alloc=86.4MB, time=71.89 memory used=425.6MB, alloc=86.4MB, time=131.95 memory used=470.2MB, alloc=110.4MB, time=195.93 memory used=521.9MB, alloc=110.4MB, time=241.55 memory used=583.5MB, alloc=134.4MB, time=345.63 memory used=652.1MB, alloc=134.4MB, time=379.73 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428489694 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 3 2 2 4 F := [12 z + 18 x y - 15 x , 16 x z - 11 x z - 17 z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 2 G := [11 z + 12 x y + 11 y , -5 x z + 11 z] > Problem := [F,G]; 4 2 2 3 2 2 4 Problem := [[12 z + 18 x y - 15 x , 16 x z - 11 x z - 17 z ], 4 2 2 2 [11 z + 12 x y + 11 y , -5 x z + 11 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.7MB, alloc=36.3MB, time=0.53 memory used=47.2MB, alloc=36.3MB, time=0.83 memory used=84.0MB, alloc=36.3MB, time=1.26 memory used=104.6MB, alloc=60.3MB, time=1.57 memory used=146.6MB, alloc=60.3MB, time=2.06 memory used=219.5MB, alloc=60.3MB, time=2.55 memory used=268.2MB, alloc=60.3MB, time=3.01 memory used=316.8MB, alloc=60.3MB, time=3.48 memory used=343.9MB, alloc=60.3MB, time=3.62 memory used=1281.1MB, alloc=83.8MB, time=6.38 memory used=1616.5MB, alloc=83.8MB, time=10.60 memory used=1653.0MB, alloc=83.8MB, time=10.92 memory used=1698.7MB, alloc=83.8MB, time=11.56 memory used=1742.9MB, alloc=107.8MB, time=12.28 memory used=1806.4MB, alloc=131.8MB, time=13.40 N1 := 1057 > GB := Basis(F, plex(op(vars))); 10 2 11 7 4 8 2 GB := [25165824 x y - 20971520 x + 118730304 x y - 197883840 x y 4 6 9 5 4 8 + 60426432 x y + 82451600 x - 151066080 x y + 108243216 x y 6 2 2 6 7 3 4 + 125888400 x y - 360810720 x y - 34969000 x + 451013400 x y 4 2 5 9 7 2 - 250563000 x y + 52200625 x , 919339008 x z + 3025469280 x y 8 4 4 5 2 6 - 2521224400 x + 222479136 x y - 370798560 x y + 2182904856 x y 6 2 4 3 2 4 + 154499400 x - 5457262140 x y + 4547718450 x y - 1263255125 x , 6 4 2 3 2 5 4 65536 x z + 136392 x y + 143616 x y z - 113660 x - 119680 x z 4 2 2 3 7 + 114444 x y - 190740 x y + 79475 x , -372441088 x z 5 2 6 2 4 4 - 1053156312 x y + 877630260 x + 345735324 x y + 684832896 x y z 3 2 2 2 4 3 - 576225540 x y - 1141388160 x y z + 240093975 x + 475578400 x z, 3 2 2 2 2 5 3 2 -64 x z + 44 x z - 102 x y + 85 x , 65536 x z + 136392 x y 2 2 2 2 4 3 2 + 71808 x y z + 49368 x y z - 113660 x - 119680 x z - 95370 x y 2 4 2 2 + 79475 x , 4 z + 6 x y - 5 x ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1885.4MB, alloc=131.8MB, time=15.09 memory used=1966.6MB, alloc=131.8MB, time=16.28 memory used=2058.8MB, alloc=155.8MB, time=17.61 memory used=2174.5MB, alloc=155.8MB, time=19.18 memory used=2292.4MB, alloc=179.8MB, time=20.77 memory used=2439.8MB, alloc=203.8MB, time=22.65 memory used=2590.3MB, alloc=203.8MB, time=24.62 memory used=2741.9MB, alloc=483.8MB, time=26.76 memory used=2929.1MB, alloc=507.8MB, time=29.23 memory used=3144.6MB, alloc=531.8MB, time=32.37 memory used=3388.2MB, alloc=555.8MB, time=35.77 memory used=3654.4MB, alloc=579.8MB, time=39.06 memory used=3939.5MB, alloc=603.8MB, time=43.14 memory used=4243.7MB, alloc=627.8MB, time=47.18 memory used=4481.1MB, alloc=651.8MB, time=50.22 memory used=4802.5MB, alloc=651.8MB, time=54.91 memory used=5192.0MB, alloc=675.8MB, time=60.34 memory used=5553.9MB, alloc=675.8MB, time=67.28 memory used=5793.1MB, alloc=699.8MB, time=70.42 memory used=6020.9MB, alloc=699.8MB, time=73.60 memory used=6260.0MB, alloc=699.8MB, time=77.04 memory used=6495.0MB, alloc=723.8MB, time=80.21 memory used=6692.9MB, alloc=723.8MB, time=83.00 memory used=6886.3MB, alloc=723.8MB, time=85.88 memory used=7139.5MB, alloc=723.8MB, time=89.31 memory used=7366.8MB, alloc=723.8MB, time=93.11 memory used=7606.9MB, alloc=747.8MB, time=96.64 memory used=7783.9MB, alloc=747.8MB, time=99.75 memory used=8001.6MB, alloc=747.8MB, time=103.87 memory used=8701.7MB, alloc=747.8MB, time=109.14 memory used=9074.3MB, alloc=771.8MB, time=115.24 memory used=9622.0MB, alloc=771.8MB, time=126.98 memory used=10055.0MB, alloc=771.8MB, time=135.78 memory used=10218.5MB, alloc=771.8MB, time=139.72 memory used=10427.8MB, alloc=771.8MB, time=143.88 memory used=10603.5MB, alloc=771.8MB, time=146.79 memory used=10861.7MB, alloc=795.8MB, time=152.47 memory used=11012.1MB, alloc=795.8MB, time=155.15 memory used=11143.2MB, alloc=795.8MB, time=157.69 memory used=11324.7MB, alloc=795.8MB, time=160.50 memory used=11469.5MB, alloc=795.8MB, time=162.95 memory used=11659.9MB, alloc=795.8MB, time=166.67 memory used=11816.0MB, alloc=795.8MB, time=169.47 memory used=12294.8MB, alloc=819.8MB, time=175.82 memory used=12775.4MB, alloc=843.8MB, time=182.76 memory used=13293.7MB, alloc=867.8MB, time=190.69 memory used=13758.5MB, alloc=891.8MB, time=200.02 memory used=14267.7MB, alloc=915.8MB, time=207.41 memory used=14658.2MB, alloc=939.8MB, time=213.43 memory used=14987.3MB, alloc=963.8MB, time=258.07 memory used=15617.5MB, alloc=987.8MB, time=309.06 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428489994 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 4 3 F := [-7 x z + 12 z + 14 x , -x y + 18 y z - 18 x] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 4 2 G := [-20 x y - 7 y z - 9 z, 16 y z - 10 z + 6 x y ] > Problem := [F,G]; 3 4 3 Problem := [[-7 x z + 12 z + 14 x , -x y + 18 y z - 18 x], 2 2 4 2 [-20 x y - 7 y z - 9 z, 16 y z - 10 z + 6 x y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=25.2MB, alloc=32.3MB, time=0.49 memory used=44.8MB, alloc=56.3MB, time=0.79 memory used=90.7MB, alloc=60.3MB, time=1.44 memory used=132.2MB, alloc=68.3MB, time=1.92 memory used=177.7MB, alloc=68.3MB, time=2.44 memory used=216.7MB, alloc=68.3MB, time=2.81 memory used=264.9MB, alloc=92.3MB, time=3.34 memory used=340.8MB, alloc=92.3MB, time=4.28 memory used=387.2MB, alloc=92.3MB, time=4.68 memory used=431.4MB, alloc=92.3MB, time=5.11 memory used=465.0MB, alloc=92.3MB, time=5.24 memory used=507.3MB, alloc=92.3MB, time=5.68 memory used=541.0MB, alloc=92.3MB, time=5.80 memory used=570.1MB, alloc=92.3MB, time=5.91 memory used=605.5MB, alloc=92.3MB, time=6.02 memory used=643.9MB, alloc=92.3MB, time=6.14 memory used=667.4MB, alloc=92.3MB, time=6.23 memory used=693.8MB, alloc=92.3MB, time=6.31 memory used=723.8MB, alloc=92.3MB, time=6.40 memory used=763.6MB, alloc=107.8MB, time=7.44 memory used=826.8MB, alloc=107.8MB, time=8.66 memory used=866.8MB, alloc=107.8MB, time=8.84 memory used=908.0MB, alloc=107.8MB, time=9.25 memory used=944.1MB, alloc=107.8MB, time=9.38 memory used=971.0MB, alloc=107.8MB, time=9.48 memory used=1001.9MB, alloc=107.8MB, time=9.59 memory used=1039.0MB, alloc=107.8MB, time=9.71 memory used=1071.1MB, alloc=107.8MB, time=9.80 memory used=1095.7MB, alloc=107.8MB, time=9.89 memory used=1123.2MB, alloc=107.8MB, time=9.97 memory used=1156.0MB, alloc=107.8MB, time=10.12 memory used=1181.3MB, alloc=107.8MB, time=11.09 memory used=1268.2MB, alloc=107.8MB, time=12.81 memory used=1328.4MB, alloc=107.8MB, time=13.91 memory used=1398.8MB, alloc=107.8MB, time=14.85 memory used=1466.1MB, alloc=107.8MB, time=15.76 memory used=1530.9MB, alloc=131.8MB, time=16.59 memory used=1601.0MB, alloc=131.8MB, time=17.55 memory used=1682.1MB, alloc=131.8MB, time=18.71 memory used=1766.8MB, alloc=131.8MB, time=20.34 memory used=1847.7MB, alloc=387.8MB, time=21.40 memory used=1975.2MB, alloc=387.8MB, time=23.23 memory used=2042.3MB, alloc=387.8MB, time=23.80 memory used=2135.8MB, alloc=411.8MB, time=24.81 memory used=2224.5MB, alloc=411.8MB, time=25.48 memory used=2287.2MB, alloc=411.8MB, time=25.93 memory used=2357.2MB, alloc=411.8MB, time=26.34 memory used=2417.2MB, alloc=411.8MB, time=26.54 memory used=2459.1MB, alloc=411.8MB, time=26.70 memory used=2521.7MB, alloc=411.8MB, time=27.48 memory used=2573.1MB, alloc=411.8MB, time=27.94 memory used=2631.7MB, alloc=411.8MB, time=28.13 memory used=2670.7MB, alloc=411.8MB, time=28.29 memory used=2715.2MB, alloc=411.8MB, time=28.47 memory used=2766.0MB, alloc=411.8MB, time=28.64 memory used=2822.5MB, alloc=411.8MB, time=28.81 memory used=2886.6MB, alloc=411.8MB, time=28.98 memory used=2931.2MB, alloc=435.8MB, time=29.14 memory used=2979.0MB, alloc=435.8MB, time=29.30 memory used=3030.8MB, alloc=435.8MB, time=29.45 memory used=3087.6MB, alloc=435.8MB, time=29.60 memory used=3146.9MB, alloc=435.8MB, time=29.75 memory used=3212.0MB, alloc=435.8MB, time=29.92 memory used=3282.5MB, alloc=435.8MB, time=30.07 memory used=3360.2MB, alloc=435.8MB, time=30.24 memory used=3444.8MB, alloc=435.8MB, time=30.41 memory used=3591.5MB, alloc=435.8MB, time=31.63 memory used=3671.3MB, alloc=435.8MB, time=32.13 memory used=3757.8MB, alloc=435.8MB, time=32.57 memory used=3832.4MB, alloc=435.8MB, time=32.77 memory used=3942.6MB, alloc=435.8MB, time=34.00 memory used=4055.2MB, alloc=435.8MB, time=37.13 memory used=4211.8MB, alloc=435.8MB, time=39.92 memory used=4344.6MB, alloc=435.8MB, time=40.39 memory used=4474.1MB, alloc=435.8MB, time=40.89 memory used=4544.8MB, alloc=435.8MB, time=42.22 memory used=4614.5MB, alloc=435.8MB, time=42.45 memory used=4708.1MB, alloc=459.8MB, time=73.78 memory used=6417.9MB, alloc=459.8MB, time=91.97 memory used=6519.7MB, alloc=459.8MB, time=97.30 memory used=6607.9MB, alloc=459.8MB, time=97.58 memory used=6668.8MB, alloc=459.8MB, time=97.78 memory used=6738.2MB, alloc=459.8MB, time=97.98 memory used=6821.6MB, alloc=459.8MB, time=98.16 memory used=7093.1MB, alloc=459.8MB, time=99.45 memory used=7310.6MB, alloc=459.8MB, time=101.36 memory used=7460.5MB, alloc=459.8MB, time=102.32 memory used=7607.4MB, alloc=459.8MB, time=103.18 memory used=7777.6MB, alloc=459.8MB, time=104.34 memory used=7947.2MB, alloc=459.8MB, time=105.74 memory used=8115.3MB, alloc=459.8MB, time=107.60 memory used=8206.2MB, alloc=459.8MB, time=108.04 memory used=8317.6MB, alloc=459.8MB, time=108.77 memory used=8389.8MB, alloc=459.8MB, time=109.06 memory used=8463.9MB, alloc=459.8MB, time=109.35 memory used=8551.0MB, alloc=459.8MB, time=109.64 memory used=8602.6MB, alloc=459.8MB, time=109.84 memory used=8661.0MB, alloc=459.8MB, time=110.05 memory used=8727.1MB, alloc=459.8MB, time=110.26 memory used=8799.6MB, alloc=459.8MB, time=110.48 memory used=8879.2MB, alloc=459.8MB, time=110.71 memory used=8969.4MB, alloc=459.8MB, time=110.94 memory used=9193.2MB, alloc=459.8MB, time=113.80 memory used=9268.5MB, alloc=459.8MB, time=114.67 memory used=9343.0MB, alloc=459.8MB, time=114.97 memory used=9427.8MB, alloc=459.8MB, time=115.27 memory used=9482.2MB, alloc=459.8MB, time=115.48 memory used=9538.0MB, alloc=459.8MB, time=115.68 memory used=9599.3MB, alloc=459.8MB, time=115.89 memory used=9664.5MB, alloc=459.8MB, time=116.12 memory used=9733.8MB, alloc=459.8MB, time=116.35 memory used=9812.1MB, alloc=459.8MB, time=116.59 memory used=9894.4MB, alloc=459.8MB, time=116.84 memory used=9980.6MB, alloc=459.8MB, time=117.09 memory used=10194.1MB, alloc=459.8MB, time=117.64 memory used=10337.7MB, alloc=459.8MB, time=118.03 memory used=10494.4MB, alloc=459.8MB, time=118.44 memory used=10657.1MB, alloc=459.8MB, time=118.86 memory used=10831.7MB, alloc=459.8MB, time=119.29 memory used=11019.6MB, alloc=459.8MB, time=119.73 memory used=11228.3MB, alloc=459.8MB, time=120.19 memory used=11448.4MB, alloc=459.8MB, time=120.71 memory used=11687.7MB, alloc=459.8MB, time=121.23 memory used=11910.5MB, alloc=459.8MB, time=121.71 memory used=12083.1MB, alloc=459.8MB, time=122.10 memory used=12267.1MB, alloc=459.8MB, time=122.53 memory used=12462.9MB, alloc=459.8MB, time=122.96 memory used=12667.4MB, alloc=459.8MB, time=123.39 memory used=12884.8MB, alloc=459.8MB, time=123.83 memory used=13121.3MB, alloc=459.8MB, time=124.32 memory used=13362.5MB, alloc=459.8MB, time=124.76 memory used=13622.0MB, alloc=459.8MB, time=129.85 memory used=13875.7MB, alloc=459.8MB, time=132.58 memory used=13949.8MB, alloc=459.8MB, time=132.83 memory used=14021.9MB, alloc=459.8MB, time=133.08 memory used=14083.0MB, alloc=459.8MB, time=133.28 memory used=14154.3MB, alloc=459.8MB, time=133.50 memory used=14238.9MB, alloc=459.8MB, time=133.72 memory used=14460.8MB, alloc=459.8MB, time=134.17 memory used=14590.9MB, alloc=459.8MB, time=167.54 memory used=14669.5MB, alloc=459.8MB, time=167.83 memory used=14735.1MB, alloc=459.8MB, time=168.07 memory used=14821.0MB, alloc=459.8MB, time=168.33 memory used=14994.6MB, alloc=459.8MB, time=168.78 memory used=15194.5MB, alloc=459.8MB, time=169.25 memory used=15410.8MB, alloc=459.8MB, time=169.70 memory used=15744.1MB, alloc=459.8MB, time=171.68 memory used=15832.3MB, alloc=459.8MB, time=172.23 memory used=15989.4MB, alloc=459.8MB, time=172.90 memory used=16066.1MB, alloc=459.8MB, time=173.37 memory used=16189.1MB, alloc=459.8MB, time=174.00 memory used=16344.0MB, alloc=459.8MB, time=176.96 memory used=16453.4MB, alloc=459.8MB, time=177.76 memory used=16577.4MB, alloc=459.8MB, time=179.46 memory used=16678.3MB, alloc=483.8MB, time=181.41 memory used=16875.6MB, alloc=483.8MB, time=182.42 memory used=16966.0MB, alloc=483.8MB, time=182.98 memory used=17064.8MB, alloc=483.8MB, time=183.57 memory used=17161.1MB, alloc=483.8MB, time=184.07 memory used=17241.2MB, alloc=483.8MB, time=184.30 memory used=17362.8MB, alloc=483.8MB, time=198.32 memory used=18063.6MB, alloc=483.8MB, time=210.16 memory used=18142.4MB, alloc=483.8MB, time=210.43 memory used=18233.4MB, alloc=483.8MB, time=210.70 memory used=18431.8MB, alloc=483.8MB, time=211.19 memory used=18624.9MB, alloc=483.8MB, time=211.64 memory used=18850.2MB, alloc=483.8MB, time=212.13 memory used=19047.5MB, alloc=483.8MB, time=212.56 memory used=19280.0MB, alloc=483.8MB, time=213.01 memory used=19415.6MB, alloc=483.8MB, time=214.14 memory used=19622.3MB, alloc=483.8MB, time=215.79 memory used=19831.3MB, alloc=483.8MB, time=217.54 memory used=19971.1MB, alloc=483.8MB, time=218.72 memory used=20062.1MB, alloc=483.8MB, time=219.08 memory used=20157.1MB, alloc=483.8MB, time=219.88 memory used=20251.0MB, alloc=483.8MB, time=220.39 memory used=20332.9MB, alloc=483.8MB, time=220.71 memory used=20408.5MB, alloc=483.8MB, time=221.01 memory used=20506.3MB, alloc=483.8MB, time=221.32 memory used=20565.9MB, alloc=483.8MB, time=221.54 memory used=20632.8MB, alloc=483.8MB, time=221.77 memory used=20709.2MB, alloc=483.8MB, time=221.99 memory used=20807.0MB, alloc=483.8MB, time=223.99 memory used=20888.5MB, alloc=483.8MB, time=224.56 memory used=20962.6MB, alloc=483.8MB, time=224.87 memory used=21057.9MB, alloc=483.8MB, time=225.18 memory used=21124.1MB, alloc=483.8MB, time=225.43 memory used=21181.7MB, alloc=483.8MB, time=225.67 memory used=21246.0MB, alloc=483.8MB, time=225.91 memory used=21314.1MB, alloc=483.8MB, time=226.15 memory used=21390.2MB, alloc=483.8MB, time=226.40 memory used=21469.7MB, alloc=483.8MB, time=226.65 memory used=21557.4MB, alloc=483.8MB, time=226.91 memory used=21653.5MB, alloc=483.8MB, time=227.18 memory used=21752.6MB, alloc=483.8MB, time=227.45 memory used=21910.9MB, alloc=483.8MB, time=227.83 memory used=22051.6MB, alloc=483.8MB, time=228.17 memory used=22206.2MB, alloc=483.8MB, time=228.56 memory used=22374.6MB, alloc=483.8MB, time=228.94 memory used=22554.5MB, alloc=483.8MB, time=229.34 memory used=22749.9MB, alloc=483.8MB, time=229.75 memory used=22962.9MB, alloc=483.8MB, time=230.18 memory used=23200.0MB, alloc=483.8MB, time=230.63 memory used=23402.0MB, alloc=483.8MB, time=231.00 memory used=23651.7MB, alloc=483.8MB, time=232.53 memory used=23755.9MB, alloc=483.8MB, time=232.99 memory used=23863.3MB, alloc=483.8MB, time=233.33 memory used=24062.6MB, alloc=483.8MB, time=234.12 memory used=24314.7MB, alloc=483.8MB, time=234.60 memory used=24552.3MB, alloc=483.8MB, time=235.70 memory used=24641.7MB, alloc=483.8MB, time=236.02 memory used=24739.7MB, alloc=483.8MB, time=236.80 memory used=24825.8MB, alloc=483.8MB, time=237.09 memory used=24912.6MB, alloc=483.8MB, time=238.47 memory used=24992.9MB, alloc=483.8MB, time=238.73 memory used=25161.0MB, alloc=483.8MB, time=240.14 memory used=25264.7MB, alloc=483.8MB, time=240.69 memory used=25358.7MB, alloc=483.8MB, time=241.63 memory used=25446.6MB, alloc=483.8MB, time=241.96 memory used=25513.6MB, alloc=483.8MB, time=242.24 memory used=25594.2MB, alloc=483.8MB, time=242.52 memory used=25690.6MB, alloc=483.8MB, time=242.84 memory used=25756.2MB, alloc=483.8MB, time=243.08 memory used=25817.5MB, alloc=483.8MB, time=243.31 memory used=25886.3MB, alloc=483.8MB, time=243.54 memory used=25963.8MB, alloc=483.8MB, time=243.78 memory used=26086.5MB, alloc=483.8MB, time=244.95 memory used=26168.2MB, alloc=483.8MB, time=245.26 memory used=26263.8MB, alloc=483.8MB, time=253.26 memory used=26339.1MB, alloc=483.8MB, time=253.47 memory used=26476.5MB, alloc=483.8MB, time=263.00 memory used=26558.0MB, alloc=483.8MB, time=263.26 memory used=26636.6MB, alloc=483.8MB, time=264.14 memory used=26750.7MB, alloc=507.8MB, time=268.91 memory used=26984.1MB, alloc=507.8MB, time=270.45 memory used=27140.1MB, alloc=507.8MB, time=271.52 memory used=27254.9MB, alloc=507.8MB, time=296.07 memory used=28889.7MB, alloc=507.8MB, time=313.82 memory used=29002.3MB, alloc=507.8MB, time=317.42 memory used=29096.8MB, alloc=507.8MB, time=317.70 memory used=29169.3MB, alloc=507.8MB, time=317.93 memory used=29259.5MB, alloc=507.8MB, time=318.17 memory used=29452.5MB, alloc=507.8MB, time=319.48 memory used=29692.0MB, alloc=507.8MB, time=321.34 memory used=29863.0MB, alloc=507.8MB, time=322.79 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428490294 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 4 2 F := [18 x y - 5 y z - 13 z , 5 z + 17 x y - 16 x y z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 G := [4 x z + 5 x z + 3 x z, 20 x z + 10 y - 14] > Problem := [F,G]; 3 2 2 4 2 Problem := [[18 x y - 5 y z - 13 z , 5 z + 17 x y - 16 x y z], 3 2 2 [4 x z + 5 x z + 3 x z, 20 x z + 10 y - 14]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=26.6MB, alloc=32.3MB, time=0.52 memory used=46.3MB, alloc=56.3MB, time=0.82 memory used=86.7MB, alloc=60.3MB, time=1.42 memory used=126.3MB, alloc=60.3MB, time=2.01 memory used=156.9MB, alloc=60.3MB, time=2.45 memory used=197.3MB, alloc=92.3MB, time=3.14 memory used=262.1MB, alloc=92.3MB, time=4.02 memory used=330.3MB, alloc=92.3MB, time=4.89 memory used=395.9MB, alloc=92.3MB, time=5.86 memory used=459.5MB, alloc=116.3MB, time=6.86 memory used=528.8MB, alloc=372.3MB, time=7.72 memory used=619.4MB, alloc=372.3MB, time=8.96 memory used=706.7MB, alloc=372.3MB, time=10.35 memory used=793.2MB, alloc=396.3MB, time=11.76 memory used=905.8MB, alloc=396.3MB, time=13.27 memory used=1021.1MB, alloc=420.3MB, time=14.96 memory used=1154.2MB, alloc=420.3MB, time=16.98 memory used=1264.1MB, alloc=444.3MB, time=18.22 memory used=1395.0MB, alloc=444.3MB, time=19.92 memory used=1516.3MB, alloc=444.3MB, time=21.69 memory used=1658.8MB, alloc=444.3MB, time=23.24 memory used=1740.1MB, alloc=444.3MB, time=23.68 memory used=1835.6MB, alloc=444.3MB, time=24.30 memory used=1905.5MB, alloc=444.3MB, time=24.59 memory used=1979.3MB, alloc=444.3MB, time=25.00 memory used=2046.7MB, alloc=444.3MB, time=25.27 memory used=2187.3MB, alloc=444.3MB, time=26.91 memory used=2325.1MB, alloc=468.3MB, time=28.65 memory used=2439.8MB, alloc=468.3MB, time=30.57 memory used=2560.9MB, alloc=468.3MB, time=32.35 memory used=2657.5MB, alloc=468.3MB, time=34.15 memory used=2752.6MB, alloc=492.3MB, time=35.73 memory used=2861.2MB, alloc=492.3MB, time=36.43 memory used=2999.7MB, alloc=492.3MB, time=37.77 memory used=3098.0MB, alloc=492.3MB, time=39.15 memory used=3191.0MB, alloc=492.3MB, time=40.74 memory used=3275.0MB, alloc=492.3MB, time=42.30 memory used=3352.8MB, alloc=492.3MB, time=43.65 memory used=3426.7MB, alloc=516.3MB, time=44.80 memory used=3513.0MB, alloc=516.3MB, time=46.30 memory used=3641.6MB, alloc=516.3MB, time=48.27 memory used=3763.4MB, alloc=516.3MB, time=50.15 memory used=3880.9MB, alloc=540.3MB, time=52.30 memory used=4035.5MB, alloc=540.3MB, time=54.82 memory used=4156.2MB, alloc=564.3MB, time=57.14 memory used=4280.6MB, alloc=564.3MB, time=59.33 memory used=4387.7MB, alloc=564.3MB, time=61.36 memory used=4515.2MB, alloc=588.3MB, time=63.47 memory used=4620.4MB, alloc=588.3MB, time=65.52 memory used=4733.3MB, alloc=612.3MB, time=67.73 memory used=4891.4MB, alloc=636.3MB, time=72.83 memory used=5109.7MB, alloc=660.3MB, time=81.45 memory used=5334.8MB, alloc=684.3MB, time=91.30 memory used=5583.8MB, alloc=708.3MB, time=101.95 memory used=5856.8MB, alloc=708.3MB, time=113.63 memory used=6129.7MB, alloc=732.3MB, time=125.48 memory used=6426.7MB, alloc=756.3MB, time=138.05 N1 := 7473 > GB := Basis(F, plex(op(vars))); 11 3 7 4 7 3 7 2 GB := [-2624400 x y - 1377000 x y - 7160400 x y - 9308520 x y 4 5 4 4 3 5 4 3 + 576000 x y + 4492800 x y - 180625 x y + 11681280 x y 3 4 4 2 3 3 3 2 - 1878500 x y + 10123776 x y - 7326150 x y - 12698660 x y 3 11 2 7 3 7 2 - 8254129 x y, -524880 x y - 275400 x y - 1432080 x y 7 6 4 4 4 3 3 4 - 930852 x y + 876096 x y z + 115200 x y + 898560 x y - 36125 x y 4 2 3 3 3 2 3 6 2 + 1557504 x y - 375700 x y - 1221025 x y - 1269866 x y, -1620 x y 2 3 3 2 2 2 2 - 425 x y + 400 x y z - 2210 x y + 2080 x y z - 2873 x y + 2704 x y z, 6 3 2 2 2 2 2 -324 x y + 234 x z - 85 x y + 80 x y z - 221 x y + 208 x y z, 3 2 2 4 2 -18 x y + 5 y z + 13 z , 5 z - 16 z y x + 17 y x ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=6555.4MB, alloc=756.3MB, time=142.34 memory used=6655.9MB, alloc=756.3MB, time=144.21 memory used=6738.6MB, alloc=756.3MB, time=145.65 memory used=6823.2MB, alloc=756.3MB, time=147.39 memory used=6883.2MB, alloc=756.3MB, time=148.73 memory used=6970.5MB, alloc=756.3MB, time=150.10 memory used=7040.4MB, alloc=756.3MB, time=151.55 memory used=7107.2MB, alloc=756.3MB, time=152.83 memory used=7143.8MB, alloc=756.3MB, time=153.84 memory used=7203.6MB, alloc=756.3MB, time=155.15 memory used=7271.5MB, alloc=756.3MB, time=156.29 memory used=7320.1MB, alloc=756.3MB, time=157.41 memory used=7364.1MB, alloc=756.3MB, time=158.57 memory used=7410.0MB, alloc=756.3MB, time=159.88 memory used=7437.8MB, alloc=756.3MB, time=160.83 memory used=7478.8MB, alloc=756.3MB, time=162.04 memory used=7534.3MB, alloc=756.3MB, time=163.35 memory used=7604.8MB, alloc=756.3MB, time=164.47 memory used=7649.7MB, alloc=756.3MB, time=165.44 memory used=7716.6MB, alloc=756.3MB, time=166.67 memory used=7778.5MB, alloc=756.3MB, time=167.93 memory used=7820.4MB, alloc=756.3MB, time=169.10 memory used=7867.3MB, alloc=756.3MB, time=170.39 memory used=8082.4MB, alloc=756.3MB, time=173.60 memory used=8304.1MB, alloc=756.3MB, time=177.02 memory used=8520.7MB, alloc=756.3MB, time=180.47 memory used=8750.4MB, alloc=756.3MB, time=183.76 memory used=8951.2MB, alloc=756.3MB, time=186.91 memory used=9132.2MB, alloc=756.3MB, time=190.39 memory used=9295.3MB, alloc=756.3MB, time=193.69 memory used=9466.7MB, alloc=756.3MB, time=197.13 memory used=9587.5MB, alloc=756.3MB, time=199.96 memory used=9789.1MB, alloc=756.3MB, time=203.19 memory used=10089.3MB, alloc=780.3MB, time=213.07 memory used=10313.5MB, alloc=780.3MB, time=245.27 memory used=10522.0MB, alloc=780.3MB, time=248.41 memory used=10760.3MB, alloc=780.3MB, time=249.59 memory used=10910.3MB, alloc=780.3MB, time=250.59 memory used=11070.4MB, alloc=780.3MB, time=251.59 memory used=11254.5MB, alloc=780.3MB, time=252.62 memory used=11587.0MB, alloc=780.3MB, time=255.12 memory used=12032.2MB, alloc=804.3MB, time=257.51 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428490594 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 3 4 2 2 2 2 F := [14 x y + 16 y z + 15 x , -9 x - 19 x y + 10 y z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 3 G := [-16 x y z + x y z - 13 y , -6 x z + 19 z + 18 z] > Problem := [F,G]; 3 2 2 3 4 2 2 2 2 Problem := [[14 x y + 16 y z + 15 x , -9 x - 19 x y + 10 y z ], 2 2 2 2 3 [-16 x y z + x y z - 13 y , -6 x z + 19 z + 18 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=27.1MB, alloc=32.3MB, time=0.53 memory used=48.4MB, alloc=56.3MB, time=0.86 memory used=88.6MB, alloc=60.3MB, time=1.58 memory used=138.2MB, alloc=68.3MB, time=2.16 memory used=186.9MB, alloc=68.3MB, time=2.71 memory used=230.9MB, alloc=92.3MB, time=3.27 memory used=299.7MB, alloc=92.3MB, time=4.13 memory used=362.5MB, alloc=92.3MB, time=5.08 memory used=431.9MB, alloc=116.3MB, time=5.91 memory used=493.3MB, alloc=116.3MB, time=6.72 memory used=577.2MB, alloc=116.3MB, time=7.53 memory used=627.5MB, alloc=116.3MB, time=7.94 memory used=703.7MB, alloc=116.3MB, time=8.51 memory used=793.6MB, alloc=140.3MB, time=9.51 memory used=892.5MB, alloc=396.3MB, time=10.39 memory used=990.4MB, alloc=396.3MB, time=11.57 memory used=1107.9MB, alloc=396.3MB, time=12.58 memory used=1207.6MB, alloc=396.3MB, time=13.47 memory used=1319.1MB, alloc=420.3MB, time=14.65 memory used=1459.9MB, alloc=444.3MB, time=16.24 memory used=1594.8MB, alloc=444.3MB, time=17.77 memory used=1718.0MB, alloc=444.3MB, time=18.69 memory used=1794.5MB, alloc=444.3MB, time=19.22 memory used=1864.1MB, alloc=444.3MB, time=19.53 memory used=1932.2MB, alloc=444.3MB, time=19.95 memory used=2004.3MB, alloc=444.3MB, time=20.39 memory used=2146.7MB, alloc=444.3MB, time=21.67 memory used=2268.1MB, alloc=444.3MB, time=22.68 memory used=2369.8MB, alloc=444.3MB, time=23.65 memory used=2507.4MB, alloc=468.3MB, time=24.77 memory used=2648.8MB, alloc=468.3MB, time=26.50 memory used=2763.2MB, alloc=492.3MB, time=28.53 memory used=2855.9MB, alloc=492.3MB, time=30.12 memory used=2944.0MB, alloc=492.3MB, time=31.53 memory used=3050.3MB, alloc=492.3MB, time=33.02 memory used=3193.7MB, alloc=492.3MB, time=34.65 memory used=3360.0MB, alloc=516.3MB, time=36.31 memory used=3457.5MB, alloc=516.3MB, time=37.82 memory used=3558.8MB, alloc=516.3MB, time=39.17 memory used=3666.0MB, alloc=516.3MB, time=40.61 memory used=3743.5MB, alloc=516.3MB, time=41.99 memory used=3814.2MB, alloc=516.3MB, time=43.36 memory used=3880.7MB, alloc=516.3MB, time=44.49 memory used=3948.1MB, alloc=516.3MB, time=45.80 memory used=4064.0MB, alloc=516.3MB, time=46.98 memory used=4130.5MB, alloc=516.3MB, time=48.16 memory used=4184.4MB, alloc=516.3MB, time=49.13 memory used=4286.9MB, alloc=540.3MB, time=50.16 memory used=4426.9MB, alloc=540.3MB, time=51.27 memory used=4522.3MB, alloc=540.3MB, time=52.83 memory used=4664.3MB, alloc=540.3MB, time=54.76 memory used=4784.3MB, alloc=540.3MB, time=55.49 memory used=4851.7MB, alloc=540.3MB, time=56.49 memory used=4910.7MB, alloc=540.3MB, time=57.46 memory used=5042.2MB, alloc=540.3MB, time=58.78 memory used=5165.9MB, alloc=540.3MB, time=59.96 memory used=5264.4MB, alloc=540.3MB, time=60.46 memory used=5365.5MB, alloc=540.3MB, time=60.95 memory used=5487.3MB, alloc=540.3MB, time=61.72 memory used=5578.3MB, alloc=540.3MB, time=62.18 memory used=5706.6MB, alloc=540.3MB, time=63.50 memory used=5806.9MB, alloc=540.3MB, time=63.99 memory used=6049.3MB, alloc=540.3MB, time=65.47 memory used=6163.3MB, alloc=540.3MB, time=66.90 memory used=6289.1MB, alloc=540.3MB, time=68.02 memory used=6391.1MB, alloc=540.3MB, time=68.52 memory used=6583.5MB, alloc=540.3MB, time=69.73 memory used=6645.2MB, alloc=540.3MB, time=70.71 memory used=6715.2MB, alloc=540.3MB, time=71.63 memory used=6795.9MB, alloc=540.3MB, time=72.53 memory used=6855.7MB, alloc=540.3MB, time=73.66 memory used=7011.7MB, alloc=540.3MB, time=75.07 memory used=7136.4MB, alloc=540.3MB, time=76.03 memory used=7233.5MB, alloc=540.3MB, time=76.59 memory used=7345.0MB, alloc=540.3MB, time=77.21 memory used=7449.7MB, alloc=540.3MB, time=77.95 memory used=7555.5MB, alloc=540.3MB, time=78.60 memory used=7660.9MB, alloc=540.3MB, time=79.23 memory used=7758.9MB, alloc=540.3MB, time=79.79 memory used=7869.7MB, alloc=540.3MB, time=80.56 memory used=7966.4MB, alloc=540.3MB, time=81.14 memory used=8108.0MB, alloc=540.3MB, time=82.50 memory used=8207.7MB, alloc=540.3MB, time=83.10 memory used=8299.8MB, alloc=540.3MB, time=83.74 memory used=8437.8MB, alloc=540.3MB, time=88.33 memory used=8532.7MB, alloc=540.3MB, time=88.87 memory used=8773.3MB, alloc=540.3MB, time=89.63 memory used=9016.3MB, alloc=540.3MB, time=90.71 memory used=9157.0MB, alloc=540.3MB, time=91.82 memory used=9362.5MB, alloc=564.3MB, time=93.87 memory used=9510.8MB, alloc=564.3MB, time=95.10 memory used=9645.3MB, alloc=564.3MB, time=96.05 memory used=9854.9MB, alloc=564.3MB, time=98.54 memory used=9964.7MB, alloc=564.3MB, time=99.12 memory used=10101.3MB, alloc=564.3MB, time=100.16 memory used=10323.4MB, alloc=564.3MB, time=102.99 memory used=10467.3MB, alloc=564.3MB, time=104.21 memory used=10644.0MB, alloc=588.3MB, time=106.36 memory used=10797.4MB, alloc=588.3MB, time=107.52 memory used=11014.6MB, alloc=588.3MB, time=109.81 memory used=11185.5MB, alloc=588.3MB, time=111.19 memory used=11342.1MB, alloc=588.3MB, time=113.33 memory used=11562.2MB, alloc=588.3MB, time=115.48 memory used=11757.6MB, alloc=588.3MB, time=117.46 memory used=11990.9MB, alloc=588.3MB, time=119.95 memory used=12160.8MB, alloc=588.3MB, time=121.83 memory used=12370.3MB, alloc=612.3MB, time=124.06 memory used=12661.2MB, alloc=612.3MB, time=127.25 memory used=12972.6MB, alloc=636.3MB, time=130.55 memory used=13292.3MB, alloc=636.3MB, time=134.46 memory used=13582.3MB, alloc=660.3MB, time=139.63 memory used=13892.4MB, alloc=684.3MB, time=145.01 memory used=14237.4MB, alloc=708.3MB, time=150.40 memory used=14558.6MB, alloc=732.3MB, time=156.26 memory used=14834.9MB, alloc=756.3MB, time=165.97 memory used=15088.7MB, alloc=780.3MB, time=176.79 memory used=15352.7MB, alloc=804.3MB, time=188.60 memory used=15640.5MB, alloc=828.3MB, time=201.47 memory used=15952.3MB, alloc=852.3MB, time=215.21 memory used=16288.1MB, alloc=876.3MB, time=229.85 memory used=16647.8MB, alloc=900.3MB, time=245.73 memory used=17031.8MB, alloc=924.3MB, time=261.99 N1 := 9005 > GB := Basis(F, plex(op(vars))); 4 2 2 3 3 GB := [72 x + 152 x y + 70 x y + 75 x , 5 4 2 5 3 2 4 2 2 2 2 42 x y + 48 x z - 95 x + 50 x z , -9 x - 19 x y + 10 y z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=17245.1MB, alloc=924.3MB, time=267.85 memory used=17431.9MB, alloc=924.3MB, time=271.66 memory used=17614.6MB, alloc=924.3MB, time=275.27 memory used=17778.8MB, alloc=924.3MB, time=278.15 memory used=17953.8MB, alloc=924.3MB, time=280.94 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428490894 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 4 2 F := [-2 x z - 6 y z + 19 z , -18 x + 17 y z + 10 y z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 4 2 3 2 G := [3 x y - 20 x y z - 4 z , -14 x y z - 6 y - 15 z ] > Problem := [F,G]; 2 2 2 3 4 2 Problem := [[-2 x z - 6 y z + 19 z , -18 x + 17 y z + 10 y z], 3 2 4 2 3 2 [3 x y - 20 x y z - 4 z , -14 x y z - 6 y - 15 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.7MB, alloc=32.3MB, time=0.52 memory used=47.2MB, alloc=60.3MB, time=0.85 memory used=88.2MB, alloc=60.3MB, time=1.43 memory used=130.4MB, alloc=68.3MB, time=2.05 memory used=206.1MB, alloc=68.3MB, time=2.80 memory used=254.2MB, alloc=68.3MB, time=3.08 memory used=302.9MB, alloc=68.3MB, time=3.67 memory used=352.7MB, alloc=92.3MB, time=4.23 memory used=416.9MB, alloc=92.3MB, time=5.12 memory used=495.0MB, alloc=92.3MB, time=5.98 memory used=559.1MB, alloc=92.3MB, time=6.71 memory used=590.7MB, alloc=92.3MB, time=6.82 memory used=618.9MB, alloc=92.3MB, time=7.10 memory used=655.0MB, alloc=92.3MB, time=7.32 memory used=684.5MB, alloc=116.3MB, time=7.43 memory used=747.9MB, alloc=116.3MB, time=7.99 memory used=793.3MB, alloc=116.3MB, time=8.13 memory used=836.8MB, alloc=116.3MB, time=8.23 memory used=887.8MB, alloc=116.3MB, time=8.47 memory used=943.9MB, alloc=116.3MB, time=8.94 memory used=993.0MB, alloc=116.3MB, time=9.07 memory used=1030.0MB, alloc=116.3MB, time=9.19 memory used=1128.6MB, alloc=116.3MB, time=10.02 memory used=1208.8MB, alloc=116.3MB, time=11.15 memory used=1271.2MB, alloc=372.3MB, time=12.01 memory used=1364.3MB, alloc=396.3MB, time=13.15 memory used=1481.2MB, alloc=396.3MB, time=14.59 memory used=1591.5MB, alloc=420.3MB, time=16.18 memory used=1723.4MB, alloc=444.3MB, time=17.71 memory used=1868.1MB, alloc=444.3MB, time=19.72 memory used=1962.4MB, alloc=444.3MB, time=25.97 memory used=2028.5MB, alloc=444.3MB, time=26.24 memory used=2090.0MB, alloc=444.3MB, time=26.48 memory used=2163.8MB, alloc=444.3MB, time=26.76 memory used=2247.6MB, alloc=444.3MB, time=27.04 memory used=2297.5MB, alloc=444.3MB, time=27.26 memory used=2350.5MB, alloc=444.3MB, time=27.48 memory used=2409.8MB, alloc=444.3MB, time=27.71 memory used=2474.3MB, alloc=444.3MB, time=27.93 memory used=2552.6MB, alloc=444.3MB, time=28.33 memory used=2645.2MB, alloc=444.3MB, time=28.71 memory used=2733.3MB, alloc=444.3MB, time=28.99 memory used=2807.9MB, alloc=468.3MB, time=45.61 memory used=2861.9MB, alloc=492.3MB, time=56.14 memory used=2905.3MB, alloc=516.3MB, time=71.09 memory used=2962.4MB, alloc=540.3MB, time=89.46 memory used=3026.8MB, alloc=540.3MB, time=89.83 memory used=3168.2MB, alloc=564.3MB, time=90.32 memory used=3258.4MB, alloc=588.3MB, time=90.68 memory used=3358.8MB, alloc=612.3MB, time=91.10 memory used=3481.1MB, alloc=636.3MB, time=91.54 memory used=3626.0MB, alloc=636.3MB, time=92.00 memory used=3775.2MB, alloc=636.3MB, time=92.43 memory used=3926.2MB, alloc=636.3MB, time=92.90 memory used=4079.1MB, alloc=636.3MB, time=93.33 memory used=4233.8MB, alloc=636.3MB, time=93.77 memory used=4390.2MB, alloc=636.3MB, time=94.24 memory used=4548.5MB, alloc=636.3MB, time=94.67 memory used=4708.5MB, alloc=660.3MB, time=95.15 memory used=4891.6MB, alloc=660.3MB, time=95.65 memory used=5079.0MB, alloc=660.3MB, time=96.17 memory used=5268.5MB, alloc=660.3MB, time=96.66 memory used=5460.3MB, alloc=660.3MB, time=97.25 memory used=5654.2MB, alloc=660.3MB, time=97.73 memory used=5850.3MB, alloc=660.3MB, time=98.26 memory used=6048.5MB, alloc=660.3MB, time=98.77 memory used=6244.3MB, alloc=660.3MB, time=99.29 memory used=6407.9MB, alloc=660.3MB, time=99.77 memory used=6559.4MB, alloc=660.3MB, time=100.20 memory used=6697.6MB, alloc=684.3MB, time=100.62 memory used=6835.8MB, alloc=684.3MB, time=101.06 memory used=6982.2MB, alloc=708.3MB, time=101.48 memory used=7123.4MB, alloc=708.3MB, time=101.90 memory used=7272.7MB, alloc=732.3MB, time=102.33 memory used=7417.4MB, alloc=732.3MB, time=102.77 memory used=7574.2MB, alloc=732.3MB, time=103.21 memory used=7732.1MB, alloc=732.3MB, time=103.64 memory used=7891.2MB, alloc=732.3MB, time=104.08 memory used=8050.7MB, alloc=732.3MB, time=104.51 memory used=8211.0MB, alloc=732.3MB, time=104.91 memory used=8346.2MB, alloc=732.3MB, time=105.30 memory used=8482.0MB, alloc=732.3MB, time=105.69 memory used=8617.8MB, alloc=732.3MB, time=106.09 memory used=8756.5MB, alloc=732.3MB, time=106.49 memory used=8896.5MB, alloc=732.3MB, time=106.88 memory used=9037.2MB, alloc=732.3MB, time=107.26 memory used=9178.6MB, alloc=732.3MB, time=107.66 memory used=9320.7MB, alloc=732.3MB, time=108.05 memory used=9463.4MB, alloc=732.3MB, time=108.44 memory used=9606.8MB, alloc=732.3MB, time=108.82 memory used=9750.8MB, alloc=732.3MB, time=109.19 memory used=9895.4MB, alloc=732.3MB, time=109.60 memory used=10040.7MB, alloc=732.3MB, time=110.00 memory used=10186.6MB, alloc=732.3MB, time=110.38 memory used=10333.1MB, alloc=732.3MB, time=110.76 memory used=10480.3MB, alloc=732.3MB, time=111.14 memory used=10628.0MB, alloc=732.3MB, time=111.53 memory used=10777.1MB, alloc=732.3MB, time=111.95 memory used=10955.8MB, alloc=732.3MB, time=112.38 memory used=11135.5MB, alloc=732.3MB, time=112.81 memory used=11315.9MB, alloc=732.3MB, time=113.25 memory used=11497.3MB, alloc=732.3MB, time=113.68 memory used=11679.4MB, alloc=732.3MB, time=114.12 memory used=11862.3MB, alloc=732.3MB, time=114.55 memory used=12046.1MB, alloc=732.3MB, time=114.98 memory used=12230.6MB, alloc=732.3MB, time=115.42 memory used=12415.9MB, alloc=732.3MB, time=115.86 memory used=12602.0MB, alloc=732.3MB, time=116.29 memory used=12788.8MB, alloc=732.3MB, time=116.75 memory used=12976.4MB, alloc=732.3MB, time=117.18 memory used=13164.7MB, alloc=732.3MB, time=117.62 memory used=13353.7MB, alloc=732.3MB, time=118.06 memory used=13543.5MB, alloc=732.3MB, time=118.52 memory used=13733.9MB, alloc=732.3MB, time=118.96 memory used=13925.0MB, alloc=732.3MB, time=119.38 memory used=14116.8MB, alloc=732.3MB, time=119.80 memory used=14309.3MB, alloc=732.3MB, time=120.26 memory used=14502.4MB, alloc=732.3MB, time=120.69 memory used=14696.1MB, alloc=732.3MB, time=121.13 memory used=14890.5MB, alloc=732.3MB, time=121.57 memory used=15085.5MB, alloc=732.3MB, time=122.02 memory used=15281.1MB, alloc=732.3MB, time=122.47 memory 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used=70910.3MB, alloc=747.8MB, time=321.58 memory used=71149.7MB, alloc=747.8MB, time=322.13 memory used=71389.6MB, alloc=747.8MB, time=322.62 memory used=71630.1MB, alloc=747.8MB, time=323.16 memory used=71871.0MB, alloc=747.8MB, time=323.68 memory used=72112.4MB, alloc=747.8MB, time=324.20 memory used=72354.3MB, alloc=747.8MB, time=324.72 memory used=72596.6MB, alloc=747.8MB, time=325.18 memory used=72839.4MB, alloc=747.8MB, time=325.67 memory used=73082.5MB, alloc=747.8MB, time=326.15 memory used=73326.0MB, alloc=747.8MB, time=326.64 memory used=73569.9MB, alloc=747.8MB, time=327.11 memory used=73814.1MB, alloc=747.8MB, time=327.58 memory used=74058.7MB, alloc=747.8MB, time=328.04 memory used=74303.6MB, alloc=747.8MB, time=328.49 memory used=74548.7MB, alloc=747.8MB, time=328.95 memory used=74794.7MB, alloc=747.8MB, time=329.45 memory used=75075.6MB, alloc=747.8MB, time=329.98 memory used=75356.8MB, alloc=747.8MB, time=330.49 memory used=75638.3MB, alloc=747.8MB, time=330.98 memory used=75920.1MB, alloc=747.8MB, time=331.55 memory used=76202.2MB, alloc=747.8MB, time=332.04 memory used=76529.5MB, alloc=747.8MB, time=332.59 memory used=76759.2MB, alloc=747.8MB, time=333.08 memory used=76916.4MB, alloc=747.8MB, time=333.48 memory used=77039.2MB, alloc=747.8MB, time=333.86 memory used=77161.0MB, alloc=747.8MB, time=334.26 memory used=77261.3MB, alloc=747.8MB, time=334.69 memory used=77362.3MB, alloc=747.8MB, time=335.02 memory used=77463.5MB, alloc=747.8MB, time=335.35 memory used=77565.0MB, alloc=747.8MB, time=335.69 memory used=77667.0MB, alloc=747.8MB, time=336.06 memory used=77769.4MB, alloc=747.8MB, time=336.39 memory used=77839.3MB, alloc=747.8MB, time=336.66 memory used=77909.3MB, alloc=747.8MB, time=336.94 memory used=77979.8MB, alloc=747.8MB, time=337.23 memory used=78050.3MB, alloc=747.8MB, time=337.63 memory used=78121.2MB, alloc=747.8MB, time=337.98 memory used=78226.6MB, alloc=747.8MB, time=338.32 memory used=78332.3MB, alloc=747.8MB, time=338.65 memory used=78437.9MB, alloc=747.8MB, time=338.97 memory used=78543.6MB, alloc=747.8MB, time=339.31 memory used=78649.3MB, alloc=747.8MB, time=339.66 memory used=78754.9MB, alloc=747.8MB, time=340.00 memory used=78860.6MB, alloc=747.8MB, time=340.33 memory used=78966.3MB, alloc=747.8MB, time=340.68 memory used=79071.9MB, alloc=747.8MB, time=341.02 memory used=79177.6MB, alloc=747.8MB, time=341.40 memory used=79283.2MB, alloc=747.8MB, time=341.74 memory used=79388.8MB, alloc=747.8MB, time=342.08 memory used=79494.5MB, alloc=747.8MB, time=342.42 memory used=79600.1MB, alloc=747.8MB, time=342.75 memory used=79705.7MB, alloc=747.8MB, time=343.09 memory used=79811.3MB, alloc=747.8MB, time=343.42 memory used=79916.8MB, alloc=747.8MB, time=343.75 memory used=80022.4MB, alloc=747.8MB, time=344.09 memory used=80127.9MB, alloc=747.8MB, time=344.42 memory used=80233.4MB, alloc=747.8MB, time=344.75 memory used=80338.8MB, alloc=747.8MB, time=345.07 memory used=80444.3MB, alloc=747.8MB, time=345.40 memory used=80549.7MB, alloc=747.8MB, time=345.73 memory used=80655.1MB, alloc=747.8MB, time=346.06 memory used=80760.5MB, alloc=747.8MB, time=346.39 memory used=80865.9MB, alloc=747.8MB, time=346.72 memory used=80971.2MB, alloc=747.8MB, time=347.06 memory used=81076.5MB, alloc=747.8MB, time=347.40 memory used=81181.7MB, alloc=747.8MB, time=347.74 memory used=81286.9MB, alloc=747.8MB, time=348.07 memory used=81392.1MB, alloc=747.8MB, time=348.39 memory used=81497.3MB, alloc=747.8MB, time=348.72 memory used=81602.4MB, alloc=747.8MB, time=349.05 memory used=81707.4MB, alloc=747.8MB, time=349.45 memory used=81812.5MB, alloc=747.8MB, time=349.77 memory used=81917.5MB, alloc=747.8MB, time=350.10 memory used=82022.4MB, alloc=747.8MB, time=350.44 memory used=82127.3MB, alloc=747.8MB, time=350.76 memory used=82232.2MB, alloc=747.8MB, time=351.09 memory used=82337.0MB, alloc=747.8MB, time=351.41 memory used=82441.7MB, alloc=747.8MB, time=351.74 memory used=82546.4MB, alloc=747.8MB, time=352.06 memory used=82651.1MB, alloc=747.8MB, time=352.39 memory used=82755.7MB, alloc=747.8MB, time=352.72 memory used=82860.3MB, alloc=747.8MB, time=353.05 memory used=82964.7MB, alloc=747.8MB, time=353.38 memory used=83069.2MB, alloc=747.8MB, time=353.70 memory used=83173.6MB, alloc=747.8MB, time=354.02 memory used=83277.9MB, alloc=747.8MB, time=354.35 memory used=83382.1MB, alloc=747.8MB, time=354.67 memory used=83486.4MB, alloc=747.8MB, time=354.99 memory used=83590.5MB, alloc=747.8MB, time=355.31 memory used=83694.6MB, alloc=747.8MB, time=355.63 memory used=83798.6MB, alloc=747.8MB, time=355.96 memory used=83902.5MB, alloc=747.8MB, time=356.29 memory used=84006.4MB, alloc=747.8MB, time=356.61 memory used=84110.2MB, alloc=747.8MB, time=356.93 memory used=84213.9MB, alloc=747.8MB, time=357.28 memory used=84317.6MB, alloc=747.8MB, time=357.60 memory used=84421.2MB, alloc=747.8MB, time=357.93 memory used=84524.7MB, alloc=747.8MB, time=358.25 memory used=84628.1MB, alloc=747.8MB, time=358.57 memory used=84731.5MB, alloc=747.8MB, time=358.89 memory used=84834.8MB, alloc=747.8MB, time=359.21 memory used=84938.0MB, alloc=747.8MB, time=359.53 memory used=85041.1MB, alloc=747.8MB, time=359.85 memory used=85144.1MB, alloc=747.8MB, time=360.17 memory used=85247.1MB, alloc=747.8MB, time=360.48 memory used=85349.9MB, alloc=747.8MB, time=360.80 memory used=85452.7MB, alloc=747.8MB, time=361.13 memory used=85555.4MB, alloc=747.8MB, time=361.46 memory used=85658.0MB, alloc=747.8MB, time=361.78 memory used=85760.5MB, alloc=747.8MB, time=362.10 memory used=85862.9MB, alloc=747.8MB, time=362.42 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428491194 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 2 F := [-13 x z - 10 x + 18, x z - 9 x y + 17 y z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 G := [-15 x y z + 8 x - 2 x, -13 x z + 14 y z - 20 z ] > Problem := [F,G]; 3 2 3 2 2 Problem := [[-13 x z - 10 x + 18, x z - 9 x y + 17 y z], 2 3 2 2 [-15 x y z + 8 x - 2 x, -13 x z + 14 y z - 20 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=26.4MB, alloc=32.3MB, time=0.53 memory used=48.0MB, alloc=32.3MB, time=0.86 memory used=68.0MB, alloc=56.3MB, time=1.18 memory used=110.6MB, alloc=68.3MB, time=1.88 memory used=154.0MB, alloc=68.3MB, time=2.50 memory used=197.2MB, alloc=92.3MB, time=3.12 memory used=263.2MB, alloc=92.3MB, time=4.09 memory used=333.2MB, alloc=116.3MB, time=5.02 memory used=399.4MB, alloc=372.3MB, time=6.00 memory used=493.4MB, alloc=396.3MB, time=7.27 memory used=608.4MB, alloc=396.3MB, time=8.94 memory used=721.4MB, alloc=420.3MB, time=10.76 memory used=851.8MB, alloc=444.3MB, time=13.26 memory used=983.6MB, alloc=468.3MB, time=15.89 memory used=1132.8MB, alloc=492.3MB, time=18.64 memory used=1308.9MB, alloc=516.3MB, time=21.54 memory used=1489.6MB, alloc=540.3MB, time=24.99 memory used=1675.2MB, alloc=564.3MB, time=28.68 memory used=1875.3MB, alloc=588.3MB, time=32.62 memory used=2071.9MB, alloc=612.3MB, time=38.45 memory used=2255.8MB, alloc=636.3MB, time=45.31 memory used=2449.7MB, alloc=660.3MB, time=52.49 memory used=2656.4MB, alloc=684.3MB, time=60.35 memory used=2877.2MB, alloc=708.3MB, time=68.98 memory used=3112.1MB, alloc=732.3MB, time=79.04 memory used=3357.0MB, alloc=756.3MB, time=90.06 memory used=3625.8MB, alloc=780.3MB, time=102.16 memory used=3918.6MB, alloc=804.3MB, time=115.48 memory used=4235.2MB, alloc=828.3MB, time=129.23 memory used=4575.9MB, alloc=852.3MB, time=144.22 memory used=4940.5MB, alloc=876.3MB, time=160.49 memory used=5328.9MB, alloc=876.3MB, time=177.98 memory used=5717.4MB, alloc=876.3MB, time=195.50 memory used=6105.9MB, alloc=900.3MB, time=213.17 memory used=6518.3MB, alloc=900.3MB, time=232.48 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428491494 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 4 3 4 F := [-9 x z - 20 y z - 3 z , -6 x - 10 x y - 11 z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 3 4 2 2 G := [17 z + 6 x z - 7 y z , -15 x z + 9 y + 11 y z ] > Problem := [F,G]; 3 2 3 4 3 4 Problem := [[-9 x z - 20 y z - 3 z , -6 x - 10 x y - 11 z ], 4 2 2 3 4 2 2 [17 z + 6 x z - 7 y z , -15 x z + 9 y + 11 y z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.20 memory used=26.1MB, alloc=32.3MB, time=0.52 memory used=45.1MB, alloc=56.3MB, time=0.82 memory used=95.9MB, alloc=60.5MB, time=1.28 memory used=141.6MB, alloc=60.5MB, time=1.71 memory used=186.7MB, alloc=60.5MB, time=2.27 memory used=232.9MB, alloc=68.5MB, time=2.88 memory used=267.6MB, alloc=68.5MB, time=3.20 memory used=311.1MB, alloc=92.5MB, time=3.72 memory used=371.9MB, alloc=92.5MB, time=4.55 memory used=436.7MB, alloc=92.5MB, time=5.66 memory used=503.1MB, alloc=92.5MB, time=6.67 memory used=565.4MB, alloc=92.5MB, time=7.51 memory used=609.2MB, alloc=92.5MB, time=7.83 memory used=651.3MB, alloc=92.5MB, time=8.88 memory used=683.3MB, alloc=92.5MB, time=9.00 memory used=707.8MB, alloc=92.5MB, time=9.10 memory used=736.0MB, alloc=92.5MB, time=9.20 memory used=777.9MB, alloc=116.5MB, time=14.00 memory used=811.7MB, alloc=140.5MB, time=18.35 memory used=867.2MB, alloc=140.5MB, time=21.15 memory used=916.6MB, alloc=140.5MB, time=21.32 memory used=970.4MB, alloc=140.5MB, time=21.52 memory used=1027.3MB, alloc=140.5MB, time=21.72 memory used=1086.2MB, alloc=140.5MB, time=21.91 memory used=1147.0MB, alloc=140.5MB, time=22.10 memory used=1209.8MB, alloc=140.5MB, time=22.29 memory used=1271.0MB, alloc=140.5MB, time=22.49 memory used=1324.2MB, alloc=140.5MB, time=22.66 memory used=1370.3MB, alloc=140.5MB, time=22.81 memory used=1412.7MB, alloc=164.5MB, time=22.98 memory used=1465.9MB, alloc=164.5MB, time=23.18 memory used=1518.2MB, alloc=164.5MB, time=23.36 memory used=1567.4MB, alloc=164.5MB, time=23.56 memory used=1617.8MB, alloc=164.5MB, time=23.74 memory used=1668.8MB, alloc=164.5MB, time=23.91 memory used=1720.7MB, alloc=164.5MB, time=24.10 memory used=1773.1MB, alloc=164.5MB, time=24.26 memory used=1826.2MB, alloc=164.5MB, time=24.42 memory used=1880.4MB, alloc=164.5MB, time=24.59 memory used=1935.5MB, alloc=164.5MB, time=24.77 memory used=1991.3MB, alloc=164.5MB, time=24.95 memory used=2047.6MB, alloc=164.5MB, time=25.11 memory used=2104.6MB, alloc=164.5MB, time=25.28 memory used=2162.1MB, alloc=164.5MB, time=25.45 memory used=2220.1MB, alloc=164.5MB, time=25.63 memory used=2278.6MB, alloc=164.5MB, time=25.80 memory used=2337.7MB, alloc=164.5MB, time=26.00 memory used=2397.8MB, alloc=164.5MB, time=26.22 memory used=2466.3MB, alloc=164.5MB, time=26.41 memory used=2535.6MB, alloc=164.5MB, time=26.59 memory used=2605.6MB, alloc=164.5MB, time=26.76 memory used=2676.0MB, alloc=164.5MB, time=26.95 memory used=2747.0MB, alloc=164.5MB, time=27.13 memory used=2818.6MB, alloc=164.5MB, time=27.34 memory used=2890.5MB, alloc=164.5MB, time=27.53 memory used=2962.8MB, alloc=164.5MB, time=27.71 memory used=3035.7MB, alloc=164.5MB, time=27.91 memory used=3109.3MB, alloc=164.5MB, time=28.09 memory used=3191.9MB, alloc=164.5MB, time=28.28 memory used=3275.1MB, alloc=164.5MB, time=28.46 memory used=3358.8MB, alloc=164.5MB, time=28.65 memory used=3442.8MB, alloc=164.5MB, time=28.84 memory used=3513.6MB, alloc=164.5MB, time=29.01 memory used=3570.4MB, alloc=164.5MB, time=29.17 memory used=3617.8MB, alloc=188.5MB, time=29.37 memory used=3676.8MB, alloc=188.5MB, time=29.56 memory used=3732.1MB, alloc=188.5MB, time=29.70 memory used=3786.4MB, alloc=188.5MB, time=29.85 memory used=3841.9MB, alloc=188.5MB, time=30.03 memory used=3897.4MB, alloc=188.5MB, time=30.18 memory used=3953.0MB, alloc=188.5MB, time=30.32 memory used=4008.6MB, alloc=188.5MB, time=30.46 memory used=4064.3MB, alloc=188.5MB, time=30.64 memory used=4120.0MB, alloc=188.5MB, time=30.83 memory used=4175.7MB, alloc=188.5MB, time=31.03 memory used=4231.5MB, alloc=188.5MB, time=31.20 memory used=4287.9MB, alloc=188.5MB, time=31.35 memory used=4344.3MB, alloc=188.5MB, time=31.49 memory used=4400.7MB, alloc=188.5MB, time=31.64 memory used=4457.0MB, alloc=188.5MB, time=31.78 memory used=4513.3MB, alloc=188.5MB, time=31.93 memory used=4570.0MB, alloc=188.5MB, time=32.08 memory used=4635.2MB, alloc=188.5MB, time=32.23 memory used=4700.5MB, alloc=188.5MB, time=32.44 memory used=4765.7MB, alloc=188.5MB, time=32.63 memory used=4830.7MB, alloc=188.5MB, time=32.78 memory used=4895.5MB, alloc=188.5MB, time=32.94 memory used=4960.0MB, alloc=188.5MB, time=33.12 memory used=5024.3MB, alloc=188.5MB, time=33.30 memory used=5088.3MB, alloc=188.5MB, time=33.47 memory used=5152.6MB, alloc=188.5MB, time=33.62 memory used=5224.9MB, alloc=188.5MB, time=33.79 memory used=5297.1MB, alloc=188.5MB, time=33.97 memory used=5368.9MB, alloc=188.5MB, time=34.16 memory used=5440.2MB, alloc=188.5MB, time=34.31 memory used=5510.9MB, alloc=188.5MB, time=34.47 memory used=5581.4MB, alloc=188.5MB, time=34.63 memory used=5659.9MB, alloc=188.5MB, time=34.78 memory used=5737.7MB, alloc=188.5MB, time=34.94 memory used=5814.7MB, alloc=188.5MB, time=35.10 memory used=5890.9MB, alloc=188.5MB, time=35.26 memory used=5967.0MB, alloc=188.5MB, time=35.41 memory used=6049.3MB, alloc=188.5MB, time=35.57 memory used=6130.9MB, alloc=188.5MB, time=35.73 memory used=6211.5MB, alloc=188.5MB, time=35.90 memory used=6298.7MB, alloc=188.5MB, time=36.07 memory used=6384.2MB, alloc=188.5MB, time=36.24 memory used=6468.8MB, alloc=188.5MB, time=36.40 memory used=6558.0MB, alloc=188.5MB, time=36.57 memory used=6645.8MB, alloc=188.5MB, time=36.73 memory used=6738.4MB, alloc=188.5MB, time=36.91 memory used=6835.0MB, alloc=188.5MB, time=37.09 memory used=6928.5MB, alloc=188.5MB, time=37.25 memory used=7025.0MB, alloc=188.5MB, time=37.43 memory used=7123.6MB, alloc=188.5MB, time=37.61 memory used=7223.6MB, alloc=188.5MB, time=37.78 memory used=7328.0MB, alloc=188.5MB, time=37.96 memory used=7435.6MB, alloc=188.5MB, time=38.13 memory used=7556.2MB, alloc=201.8MB, time=38.34 memory used=7596.0MB, alloc=203.8MB, time=38.44 memory used=7633.3MB, alloc=203.8MB, time=38.54 memory used=7667.4MB, alloc=203.8MB, time=38.64 memory used=7698.0MB, alloc=203.8MB, time=38.73 memory used=7725.0MB, alloc=203.8MB, time=38.83 memory used=7748.2MB, alloc=203.8MB, time=38.91 memory used=7763.7MB, alloc=203.8MB, time=38.99 memory used=7774.0MB, alloc=203.8MB, time=39.06 memory used=7784.7MB, alloc=203.8MB, time=39.13 memory used=7795.8MB, alloc=203.8MB, time=39.20 memory used=7904.4MB, alloc=203.8MB, time=50.90 memory used=7995.4MB, alloc=203.8MB, time=51.18 memory used=8090.2MB, alloc=203.8MB, time=51.48 memory used=8193.0MB, alloc=203.8MB, time=51.77 memory used=8300.7MB, alloc=203.8MB, time=52.06 memory used=8389.5MB, alloc=203.8MB, time=52.31 memory used=8464.2MB, alloc=203.8MB, time=52.55 memory used=8531.3MB, alloc=203.8MB, time=52.78 memory used=8597.6MB, alloc=203.8MB, time=53.00 memory used=8661.9MB, alloc=203.8MB, time=53.22 memory used=8727.5MB, alloc=203.8MB, time=53.41 memory used=8794.3MB, alloc=203.8MB, time=53.60 memory used=8862.1MB, alloc=203.8MB, time=53.82 memory used=8931.8MB, alloc=203.8MB, time=54.03 memory used=9002.9MB, alloc=203.8MB, time=54.26 memory used=9075.1MB, alloc=203.8MB, time=54.50 memory used=9148.3MB, alloc=203.8MB, time=54.71 memory used=9222.3MB, alloc=203.8MB, time=54.93 memory used=9297.6MB, alloc=203.8MB, time=55.17 memory used=9382.0MB, alloc=203.8MB, time=55.38 memory used=9467.5MB, alloc=203.8MB, time=55.59 memory used=9554.0MB, alloc=203.8MB, time=55.80 memory used=9641.4MB, alloc=203.8MB, time=56.03 memory used=9729.7MB, alloc=203.8MB, time=56.23 memory used=9818.7MB, alloc=203.8MB, time=56.43 memory used=9908.9MB, alloc=203.8MB, time=56.65 memory used=10008.6MB, alloc=203.8MB, time=56.89 memory used=10109.0MB, alloc=203.8MB, time=57.12 memory used=10210.3MB, alloc=203.8MB, time=57.33 memory used=10312.2MB, alloc=203.8MB, time=57.54 memory used=10414.9MB, alloc=203.8MB, time=57.83 memory used=10524.2MB, alloc=203.8MB, time=58.06 memory used=10601.5MB, alloc=203.8MB, time=58.24 memory used=10667.4MB, alloc=203.8MB, time=58.46 memory used=10728.1MB, alloc=203.8MB, time=58.66 memory used=10792.1MB, alloc=203.8MB, time=58.85 memory used=10847.0MB, alloc=203.8MB, time=59.03 memory used=10902.2MB, alloc=203.8MB, time=59.18 memory used=10957.8MB, alloc=203.8MB, time=59.32 memory used=11013.3MB, alloc=203.8MB, time=59.50 memory used=11069.0MB, alloc=203.8MB, time=59.65 memory used=11124.6MB, alloc=203.8MB, time=59.79 memory used=11180.3MB, alloc=203.8MB, time=59.93 memory used=11236.0MB, alloc=203.8MB, time=60.12 memory used=11291.9MB, alloc=203.8MB, time=60.30 memory used=11348.3MB, alloc=203.8MB, time=60.44 memory used=11404.8MB, alloc=203.8MB, time=60.58 memory used=11461.1MB, alloc=203.8MB, time=60.75 memory used=11517.4MB, alloc=203.8MB, time=60.89 memory used=11573.9MB, alloc=203.8MB, time=61.05 memory used=11639.5MB, alloc=203.8MB, time=61.21 memory used=11704.9MB, alloc=203.8MB, time=61.37 memory used=11770.2MB, alloc=203.8MB, time=61.53 memory used=11835.3MB, alloc=203.8MB, time=61.72 memory used=11900.3MB, alloc=203.8MB, time=61.89 memory used=11965.0MB, alloc=203.8MB, time=62.05 memory used=12029.4MB, alloc=203.8MB, time=62.21 memory used=12093.6MB, alloc=203.8MB, time=62.36 memory used=12157.8MB, alloc=203.8MB, time=62.52 memory used=12230.7MB, alloc=203.8MB, time=62.71 memory used=12303.1MB, alloc=203.8MB, time=62.88 memory used=12375.2MB, alloc=203.8MB, time=63.04 memory used=12446.8MB, alloc=203.8MB, time=63.20 memory used=12517.8MB, alloc=203.8MB, time=63.35 memory used=12588.3MB, alloc=203.8MB, time=63.52 memory used=12659.1MB, alloc=203.8MB, time=63.67 memory used=12736.9MB, alloc=203.8MB, time=63.83 memory used=12814.4MB, alloc=203.8MB, time=63.99 memory used=12891.1MB, alloc=203.8MB, time=64.15 memory used=12967.2MB, alloc=203.8MB, time=64.31 memory used=13050.7MB, alloc=203.8MB, time=64.48 memory used=13133.1MB, alloc=203.8MB, time=64.64 memory used=13214.2MB, alloc=203.8MB, time=64.81 memory used=13295.0MB, alloc=203.8MB, time=64.97 memory used=13381.0MB, alloc=203.8MB, time=65.14 memory used=13466.1MB, alloc=203.8MB, time=65.30 memory used=13557.1MB, alloc=203.8MB, time=65.47 memory used=13646.0MB, alloc=203.8MB, time=65.64 memory used=13739.9MB, alloc=203.8MB, time=65.81 memory used=13831.1MB, alloc=203.8MB, time=65.98 memory used=13926.5MB, alloc=203.8MB, time=66.15 memory used=14025.0MB, alloc=203.8MB, time=66.33 memory used=14125.9MB, alloc=203.8MB, time=66.50 memory used=14227.9MB, alloc=203.8MB, time=66.67 memory used=14330.2MB, alloc=203.8MB, time=66.86 memory used=14436.5MB, alloc=203.8MB, time=67.04 memory used=14544.4MB, alloc=203.8MB, time=67.21 memory used=14613.0MB, alloc=203.8MB, time=67.35 memory used=14653.2MB, alloc=203.8MB, time=67.46 memory used=14690.0MB, alloc=203.8MB, time=67.56 memory used=14723.5MB, alloc=203.8MB, time=67.67 memory used=14753.6MB, alloc=203.8MB, time=67.77 memory used=14780.0MB, alloc=203.8MB, time=67.86 memory used=14801.7MB, alloc=203.8MB, time=67.94 memory used=14816.1MB, alloc=203.8MB, time=68.02 memory used=14826.2MB, alloc=203.8MB, time=68.09 memory used=14835.6MB, alloc=203.8MB, time=68.16 memory used=14846.0MB, alloc=203.8MB, time=68.24 memory used=14961.1MB, alloc=203.8MB, time=110.50 memory used=15032.3MB, alloc=203.8MB, time=203.52 memory used=15032.8MB, alloc=459.8MB, time=203.59 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428491794 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 4 2 F := [-15 x z + 2 y z + 7 x z , 17 x - 12 y z - 20 y z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 G := [-12 x y z + 9 x z + 11 z, 14 x z - 9 y z + 2 x] > Problem := [F,G]; 3 2 2 2 4 2 Problem := [[-15 x z + 2 y z + 7 x z , 17 x - 12 y z - 20 y z], 2 2 3 2 [-12 x y z + 9 x z + 11 z, 14 x z - 9 y z + 2 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.2MB, alloc=32.3MB, time=0.50 memory used=47.3MB, alloc=32.3MB, time=0.80 memory used=67.2MB, alloc=60.3MB, time=1.12 memory used=109.4MB, alloc=68.3MB, time=1.72 memory used=149.4MB, alloc=92.3MB, time=2.32 memory used=218.0MB, alloc=116.3MB, time=3.21 memory used=281.6MB, alloc=372.3MB, time=4.13 memory used=377.0MB, alloc=396.3MB, time=5.41 memory used=491.7MB, alloc=420.3MB, time=7.10 memory used=617.7MB, alloc=444.3MB, time=8.86 memory used=725.7MB, alloc=444.3MB, time=10.24 memory used=828.8MB, alloc=444.3MB, time=11.76 memory used=925.5MB, alloc=468.3MB, time=13.43 memory used=1021.0MB, alloc=468.3MB, time=14.92 memory used=1102.6MB, alloc=468.3MB, time=16.28 memory used=1179.5MB, alloc=468.3MB, time=17.59 memory used=1254.5MB, alloc=468.3MB, time=18.88 memory used=1312.5MB, alloc=468.3MB, time=19.91 memory used=1370.1MB, alloc=468.3MB, time=20.88 memory used=1427.8MB, alloc=468.3MB, time=21.97 memory used=1492.2MB, alloc=468.3MB, time=23.13 memory used=1543.0MB, alloc=492.3MB, time=24.05 memory used=1594.8MB, alloc=492.3MB, time=25.01 memory used=1641.9MB, alloc=492.3MB, time=26.05 memory used=1809.1MB, alloc=516.3MB, time=28.36 memory used=2000.5MB, alloc=540.3MB, time=31.21 memory used=2166.3MB, alloc=564.3MB, time=33.75 memory used=2393.5MB, alloc=564.3MB, time=36.19 memory used=2600.0MB, alloc=588.3MB, time=38.90 memory used=2820.3MB, alloc=588.3MB, time=41.03 memory used=2966.7MB, alloc=588.3MB, time=43.09 memory used=3111.3MB, alloc=588.3MB, time=45.33 memory used=3246.4MB, alloc=588.3MB, time=47.25 memory used=3373.8MB, alloc=612.3MB, time=49.57 memory used=3475.4MB, alloc=612.3MB, time=51.34 memory used=3558.6MB, alloc=612.3MB, time=53.01 memory used=3650.4MB, alloc=612.3MB, time=54.80 memory used=3724.3MB, alloc=612.3MB, time=56.48 memory used=3837.3MB, alloc=636.3MB, time=58.30 memory used=4137.2MB, alloc=636.3MB, time=61.52 memory used=4473.0MB, alloc=660.3MB, time=66.21 memory used=4814.2MB, alloc=684.3MB, time=70.71 memory used=5175.7MB, alloc=708.3MB, time=76.19 memory used=5509.3MB, alloc=732.3MB, time=80.68 memory used=5908.7MB, alloc=756.3MB, time=86.73 memory used=6311.1MB, alloc=780.3MB, time=93.40 memory used=6642.0MB, alloc=804.3MB, time=100.58 memory used=6984.3MB, alloc=828.3MB, time=107.96 memory used=7351.4MB, alloc=852.3MB, time=115.85 memory used=7791.0MB, alloc=876.3MB, time=124.86 memory used=8226.1MB, alloc=900.3MB, time=133.70 memory used=8645.0MB, alloc=924.3MB, time=141.86 memory used=9093.7MB, alloc=948.3MB, time=150.19 memory used=9504.0MB, alloc=972.3MB, time=159.27 memory used=9882.6MB, alloc=996.3MB, time=168.15 memory used=10268.2MB, alloc=1020.3MB, time=177.23 memory used=10674.7MB, alloc=1044.3MB, time=186.99 memory used=11091.6MB, alloc=1068.3MB, time=196.21 memory used=11467.9MB, alloc=1092.3MB, time=208.91 memory used=11782.9MB, alloc=1116.3MB, time=222.30 memory used=12100.6MB, alloc=1140.3MB, time=236.43 memory used=12426.1MB, alloc=1164.3MB, time=251.18 memory used=12761.9MB, alloc=1188.3MB, time=266.61 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428492094 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 3 4 F := [9 x y z + 7 y z , 5 y z - 13 y z + 10 z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 4 3 2 G := [9 x y + 19 z - y z, 17 x - 16 y z - 19 y z] > Problem := [F,G]; 2 3 3 4 Problem := [[9 x y z + 7 y z , 5 y z - 13 y z + 10 z ], 3 3 4 3 2 [9 x y + 19 z - y z, 17 x - 16 y z - 19 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=25.2MB, alloc=32.3MB, time=0.49 memory used=47.1MB, alloc=56.3MB, time=0.70 memory used=94.4MB, alloc=60.3MB, time=1.29 memory used=150.2MB, alloc=68.3MB, time=1.98 memory used=185.3MB, alloc=68.3MB, time=2.25 memory used=215.3MB, alloc=68.3MB, time=2.66 memory used=240.8MB, alloc=68.3MB, time=2.77 memory used=259.8MB, alloc=68.3MB, time=2.84 memory used=284.3MB, alloc=68.3MB, time=2.92 memory used=304.8MB, alloc=68.3MB, time=2.99 memory used=320.3MB, alloc=68.3MB, time=3.05 memory used=337.4MB, alloc=68.3MB, time=3.11 memory used=356.3MB, alloc=68.3MB, time=3.17 memory used=377.3MB, alloc=68.3MB, time=3.25 memory used=400.1MB, alloc=68.3MB, time=3.32 memory used=424.8MB, alloc=68.3MB, time=3.39 memory used=451.3MB, alloc=68.3MB, time=3.47 memory used=475.1MB, alloc=83.8MB, time=3.55 memory used=485.5MB, alloc=83.8MB, time=3.60 memory used=496.4MB, alloc=83.8MB, time=3.65 memory used=507.2MB, alloc=83.8MB, time=3.70 memory used=518.2MB, alloc=83.8MB, time=3.76 memory used=529.9MB, alloc=83.8MB, time=3.82 memory used=541.7MB, alloc=83.8MB, time=3.87 memory used=554.3MB, alloc=83.8MB, time=3.92 memory used=567.8MB, alloc=83.8MB, time=3.97 memory used=581.1MB, alloc=83.8MB, time=4.03 memory used=595.1MB, alloc=83.8MB, time=4.08 memory used=609.6MB, alloc=83.8MB, time=4.14 memory used=625.4MB, alloc=83.8MB, time=4.20 memory used=641.5MB, alloc=83.8MB, time=4.26 memory used=658.6MB, alloc=83.8MB, time=4.32 memory used=698.5MB, alloc=83.8MB, time=4.62 memory used=722.3MB, alloc=83.8MB, time=4.72 memory used=754.3MB, alloc=83.8MB, time=4.91 memory used=809.1MB, alloc=83.8MB, time=5.49 memory used=851.5MB, alloc=107.8MB, time=6.06 memory used=892.6MB, alloc=107.8MB, time=6.31 memory used=936.9MB, alloc=107.8MB, time=6.47 memory used=978.7MB, alloc=107.8MB, time=6.62 memory used=1016.7MB, alloc=107.8MB, time=7.25 memory used=1066.9MB, alloc=107.8MB, time=13.36 memory used=1100.4MB, alloc=131.8MB, time=19.00 memory used=1148.3MB, alloc=131.8MB, time=37.34 memory used=1202.7MB, alloc=155.8MB, time=58.59 memory used=1268.0MB, alloc=155.8MB, time=130.64 memory used=1343.3MB, alloc=155.8MB, time=178.65 memory used=1415.3MB, alloc=155.8MB, time=265.89 memory used=1492.8MB, alloc=155.8MB, time=272.74 memory used=1558.6MB, alloc=155.8MB, time=273.05 memory used=1609.9MB, alloc=155.8MB, time=273.20 memory used=1667.6MB, alloc=155.8MB, time=273.35 memory used=1730.8MB, alloc=155.8MB, time=273.50 memory used=1799.3MB, alloc=155.8MB, time=273.66 memory used=1870.2MB, alloc=155.8MB, time=273.82 memory used=1920.8MB, alloc=155.8MB, time=273.94 memory used=1964.4MB, alloc=155.8MB, time=274.04 memory used=2006.8MB, alloc=155.8MB, time=274.16 memory used=2050.3MB, alloc=155.8MB, time=274.26 memory used=2095.5MB, alloc=155.8MB, time=274.38 memory used=2141.5MB, alloc=155.8MB, time=274.49 memory used=2190.1MB, alloc=155.8MB, time=274.61 memory used=2239.2MB, alloc=155.8MB, time=274.72 memory used=2290.8MB, alloc=155.8MB, time=274.84 memory used=2345.0MB, alloc=155.8MB, time=274.98 memory used=2399.4MB, alloc=155.8MB, time=275.10 memory used=2456.2MB, alloc=155.8MB, time=275.22 memory used=2515.2MB, alloc=155.8MB, time=275.34 memory used=2576.2MB, alloc=155.8MB, time=275.46 memory used=2639.2MB, alloc=155.8MB, time=275.58 memory used=2706.1MB, alloc=155.8MB, time=275.71 memory used=2774.3MB, alloc=155.8MB, time=275.83 memory used=2845.6MB, alloc=155.8MB, time=275.95 memory used=2919.5MB, alloc=155.8MB, time=276.08 memory used=2954.3MB, alloc=155.8MB, time=276.18 memory used=2971.2MB, alloc=155.8MB, time=276.25 memory used=2986.3MB, alloc=155.8MB, time=276.32 memory used=3000.4MB, alloc=155.8MB, time=276.39 memory used=3014.0MB, alloc=155.8MB, time=276.46 memory used=3026.2MB, alloc=155.8MB, time=276.52 memory used=3038.0MB, alloc=155.8MB, time=276.58 memory used=3048.4MB, alloc=155.8MB, time=276.65 memory used=3058.6MB, alloc=155.8MB, time=276.71 memory used=3068.8MB, alloc=155.8MB, time=276.77 memory used=3078.9MB, alloc=155.8MB, time=276.84 memory used=3089.0MB, alloc=155.8MB, time=276.90 memory used=3097.6MB, alloc=155.8MB, time=276.96 memory used=3106.3MB, alloc=155.8MB, time=277.02 memory used=3116.5MB, alloc=155.8MB, time=277.08 memory used=3126.6MB, alloc=155.8MB, time=277.14 memory used=3136.6MB, alloc=155.8MB, time=277.21 memory used=3146.5MB, alloc=155.8MB, time=277.27 memory used=3156.3MB, alloc=155.8MB, time=277.33 memory used=3166.0MB, alloc=155.8MB, time=277.39 memory used=3175.6MB, alloc=155.8MB, time=277.46 memory used=3185.1MB, alloc=155.8MB, time=277.52 memory used=3196.0MB, alloc=155.8MB, time=277.58 memory used=3206.8MB, alloc=155.8MB, time=277.65 memory used=3217.4MB, alloc=155.8MB, time=277.71 memory used=3227.8MB, alloc=155.8MB, time=277.78 memory used=3238.1MB, alloc=155.8MB, time=277.84 memory used=3248.2MB, alloc=155.8MB, time=277.91 memory used=3259.6MB, alloc=155.8MB, time=277.97 memory used=3270.7MB, alloc=155.8MB, time=278.03 memory used=3281.6MB, alloc=155.8MB, time=278.09 memory used=3292.2MB, alloc=155.8MB, time=278.15 memory used=3304.1MB, alloc=155.8MB, time=278.22 memory used=3314.4MB, alloc=155.8MB, time=278.28 memory used=3325.5MB, alloc=155.8MB, time=278.34 memory used=3336.4MB, alloc=155.8MB, time=278.41 memory used=3348.0MB, alloc=155.8MB, time=278.47 memory used=3359.3MB, alloc=155.8MB, time=278.53 memory used=3371.3MB, alloc=155.8MB, time=278.59 memory used=3382.6MB, alloc=155.8MB, time=278.65 memory used=3394.5MB, alloc=155.8MB, time=278.72 memory used=3407.6MB, alloc=155.8MB, time=278.78 memory used=3419.8MB, alloc=155.8MB, time=278.85 memory used=3432.7MB, alloc=155.8MB, time=278.91 memory used=3446.6MB, alloc=155.8MB, time=278.98 memory used=3461.1MB, alloc=155.8MB, time=279.04 memory used=3484.1MB, alloc=155.8MB, time=279.48 memory used=3579.4MB, alloc=155.8MB, time=280.23 memory used=3643.7MB, alloc=155.8MB, time=280.43 memory used=3707.2MB, alloc=155.8MB, time=280.59 memory used=3776.3MB, alloc=155.8MB, time=280.72 memory used=3827.5MB, alloc=155.8MB, time=280.83 memory used=3886.1MB, alloc=155.8MB, time=280.94 memory used=3955.6MB, alloc=155.8MB, time=284.13 memory used=3998.8MB, alloc=179.8MB, time=286.04 memory used=4085.7MB, alloc=179.8MB, time=287.36 memory used=4174.5MB, alloc=179.8MB, time=287.63 memory used=4247.5MB, alloc=179.8MB, time=287.83 memory used=4333.5MB, alloc=179.8MB, time=288.06 memory used=4435.0MB, alloc=179.8MB, time=288.30 memory used=4500.3MB, alloc=179.8MB, time=288.48 memory used=4561.7MB, alloc=179.8MB, time=288.65 memory used=4630.3MB, alloc=179.8MB, time=288.86 memory used=4704.8MB, alloc=179.8MB, time=289.05 memory used=4787.8MB, alloc=179.8MB, time=289.26 memory used=4882.9MB, alloc=179.8MB, time=289.46 memory used=4954.5MB, alloc=179.8MB, time=289.60 memory used=5033.3MB, alloc=179.8MB, time=289.74 memory used=5130.5MB, alloc=179.8MB, time=289.91 memory used=5159.7MB, alloc=179.8MB, time=290.01 memory used=5170.5MB, alloc=179.8MB, time=290.07 memory used=5181.4MB, alloc=179.8MB, time=290.14 memory used=5192.5MB, alloc=179.8MB, time=290.20 memory used=5203.8MB, alloc=179.8MB, time=290.27 memory used=5215.2MB, alloc=179.8MB, time=290.33 memory used=5226.9MB, alloc=179.8MB, time=290.39 memory used=5238.6MB, alloc=179.8MB, time=290.46 memory used=5250.6MB, alloc=179.8MB, time=290.52 memory used=5262.7MB, alloc=179.8MB, time=290.58 memory used=5275.1MB, alloc=179.8MB, time=290.64 memory used=5287.5MB, alloc=179.8MB, time=290.70 memory used=5300.2MB, alloc=179.8MB, time=290.77 memory used=5312.9MB, alloc=179.8MB, time=290.84 memory used=5325.9MB, alloc=179.8MB, time=290.91 memory used=5339.0MB, alloc=179.8MB, time=290.97 memory used=5352.4MB, alloc=179.8MB, time=291.03 memory used=5365.8MB, alloc=179.8MB, time=291.09 memory used=5379.5MB, alloc=179.8MB, time=291.16 memory used=5393.3MB, alloc=179.8MB, time=291.23 memory used=5407.3MB, alloc=179.8MB, time=291.30 memory used=5421.4MB, alloc=179.8MB, time=291.37 memory used=5435.8MB, alloc=179.8MB, time=291.43 memory used=5450.2MB, alloc=179.8MB, time=291.50 memory used=5464.9MB, alloc=179.8MB, time=291.56 memory used=5479.7MB, alloc=179.8MB, time=291.63 memory used=5494.8MB, alloc=179.8MB, time=291.69 memory used=5509.9MB, alloc=179.8MB, time=291.76 memory used=5525.3MB, alloc=179.8MB, time=291.83 memory used=5540.7MB, alloc=179.8MB, time=291.89 memory used=5556.5MB, alloc=179.8MB, time=291.96 memory used=5572.2MB, alloc=179.8MB, time=292.03 memory used=5588.3MB, alloc=179.8MB, time=292.09 memory used=5604.4MB, alloc=179.8MB, time=292.16 memory used=5620.9MB, alloc=179.8MB, time=292.22 memory used=5637.3MB, alloc=179.8MB, time=292.28 memory used=5662.1MB, alloc=179.8MB, time=292.96 memory used=5673.9MB, alloc=179.8MB, time=293.78 memory used=5685.8MB, alloc=179.8MB, time=293.86 memory used=5690.2MB, alloc=179.8MB, time=293.93 memory used=5691.0MB, alloc=435.8MB, time=293.98 memory used=5958.3MB, alloc=435.8MB, time=392.04 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428492394 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 2 F := [15 x y z + 16 y - 9 y , -7 x y + 20 y - 2] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 3 3 2 G := [20 y z + 13 z + 4 y, -7 x y - 7 x y + 19 x z] > Problem := [F,G]; 2 3 2 2 2 Problem := [[15 x y z + 16 y - 9 y , -7 x y + 20 y - 2], 3 3 3 3 2 [20 y z + 13 z + 4 y, -7 x y - 7 x y + 19 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=30.6MB, alloc=44.3MB, time=0.57 memory used=57.5MB, alloc=44.3MB, time=0.93 memory used=84.0MB, alloc=44.3MB, time=1.19 memory used=109.4MB, alloc=44.3MB, time=1.39 memory used=133.7MB, alloc=45.4MB, time=1.46 memory used=146.8MB, alloc=45.4MB, time=1.50 memory used=169.9MB, alloc=45.4MB, time=1.61 memory used=187.3MB, alloc=45.4MB, time=1.66 memory used=201.7MB, alloc=45.4MB, time=1.72 memory used=228.1MB, alloc=45.4MB, time=2.21 memory used=242.2MB, alloc=45.4MB, time=2.26 memory used=266.9MB, alloc=45.6MB, time=2.36 memory used=280.6MB, alloc=45.6MB, time=2.41 memory used=301.4MB, alloc=45.6MB, time=2.50 memory used=321.0MB, alloc=45.6MB, time=2.56 memory used=334.4MB, alloc=45.6MB, time=2.61 memory used=361.9MB, alloc=45.6MB, time=3.10 memory used=376.0MB, alloc=45.6MB, time=3.15 memory used=399.6MB, alloc=45.6MB, time=3.24 memory used=419.7MB, alloc=45.6MB, time=3.54 memory used=435.6MB, alloc=45.6MB, time=3.59 memory used=460.4MB, alloc=45.6MB, time=3.83 memory used=488.0MB, alloc=45.6MB, time=4.16 memory used=516.8MB, alloc=45.6MB, time=4.47 memory used=545.4MB, alloc=69.6MB, time=4.77 memory used=582.4MB, alloc=69.6MB, time=4.90 memory used=620.1MB, alloc=69.6MB, time=5.35 memory used=662.2MB, alloc=70.4MB, time=5.55 memory used=701.1MB, alloc=70.4MB, time=6.00 memory used=741.4MB, alloc=70.4MB, time=6.33 memory used=788.4MB, alloc=70.4MB, time=6.82 memory used=841.4MB, alloc=78.4MB, time=7.45 memory used=888.5MB, alloc=78.4MB, time=7.88 memory used=952.3MB, alloc=78.4MB, time=11.94 memory used=983.6MB, alloc=78.4MB, time=12.05 memory used=1012.8MB, alloc=78.4MB, time=12.15 memory used=1034.1MB, alloc=78.4MB, time=12.23 memory used=1058.9MB, alloc=78.4MB, time=12.31 memory used=1087.3MB, alloc=78.4MB, time=12.40 memory used=1119.8MB, alloc=78.4MB, time=12.49 memory used=1142.2MB, alloc=78.4MB, time=12.56 memory used=1160.9MB, alloc=78.4MB, time=12.63 memory used=1181.2MB, alloc=78.4MB, time=12.69 memory used=1202.8MB, alloc=78.4MB, time=12.75 memory used=1225.0MB, alloc=78.4MB, time=12.82 memory used=1249.2MB, alloc=78.4MB, time=12.88 memory used=1275.9MB, alloc=78.4MB, time=12.95 memory used=1305.7MB, alloc=78.4MB, time=13.02 memory used=1344.6MB, alloc=78.4MB, time=13.21 memory used=1370.1MB, alloc=78.4MB, time=13.30 memory used=1396.4MB, alloc=78.4MB, time=13.38 memory used=1440.3MB, alloc=78.4MB, time=16.90 memory used=1487.9MB, alloc=78.4MB, time=21.93 memory used=1513.0MB, alloc=78.4MB, time=22.03 memory used=1542.1MB, alloc=78.4MB, time=22.12 memory used=1562.1MB, alloc=78.4MB, time=22.20 memory used=1584.5MB, alloc=78.4MB, time=22.29 memory used=1609.8MB, alloc=78.4MB, time=22.37 memory used=1637.8MB, alloc=78.4MB, time=22.45 memory used=1669.1MB, alloc=78.4MB, time=22.52 memory used=1694.6MB, alloc=78.4MB, time=22.59 memory used=1712.1MB, alloc=78.4MB, time=22.65 memory used=1730.7MB, alloc=78.4MB, time=22.71 memory used=1749.7MB, alloc=78.4MB, time=22.77 memory used=1769.7MB, alloc=78.4MB, time=22.84 memory used=1790.8MB, alloc=78.4MB, time=22.91 memory used=1812.9MB, alloc=78.4MB, time=22.98 memory used=1836.9MB, alloc=78.4MB, time=23.04 memory used=1861.5MB, alloc=78.4MB, time=23.12 memory used=1887.3MB, alloc=78.4MB, time=23.19 memory used=1915.1MB, alloc=78.4MB, time=23.26 memory used=1944.4MB, alloc=78.4MB, time=23.33 memory used=1975.9MB, alloc=78.4MB, time=23.40 memory used=2003.7MB, alloc=91.8MB, time=23.48 memory used=2015.0MB, alloc=91.8MB, time=23.53 memory used=2084.2MB, alloc=91.8MB, time=24.20 memory used=2136.7MB, alloc=91.8MB, time=24.74 memory used=2167.6MB, alloc=91.8MB, time=24.85 memory used=2188.1MB, alloc=91.8MB, time=24.94 memory used=2214.0MB, alloc=91.8MB, time=25.03 memory used=2236.3MB, alloc=91.8MB, time=25.10 memory used=2254.7MB, alloc=91.8MB, time=25.19 memory used=2296.8MB, alloc=91.8MB, time=27.03 memory used=2322.5MB, alloc=91.8MB, time=27.12 memory used=2341.8MB, alloc=91.8MB, time=27.20 memory used=2365.7MB, alloc=91.8MB, time=27.28 memory used=2389.6MB, alloc=91.8MB, time=27.35 memory used=2440.7MB, alloc=91.8MB, time=27.89 memory used=2484.2MB, alloc=115.8MB, time=28.29 memory used=2540.0MB, alloc=115.8MB, time=28.73 memory used=2579.7MB, alloc=115.8MB, time=28.86 memory used=2617.9MB, alloc=115.8MB, time=28.99 memory used=2649.5MB, alloc=115.8MB, time=29.11 memory used=2684.9MB, alloc=115.8MB, time=29.26 memory used=2725.6MB, alloc=115.8MB, time=29.41 memory used=2772.0MB, alloc=115.8MB, time=29.54 memory used=2807.1MB, alloc=115.8MB, time=29.65 memory used=2834.8MB, alloc=115.8MB, time=29.74 memory used=2863.8MB, alloc=115.8MB, time=29.84 memory used=2896.1MB, alloc=115.8MB, time=29.93 memory used=2931.2MB, alloc=115.8MB, time=30.02 memory used=2970.1MB, alloc=115.8MB, time=30.12 memory used=3018.2MB, alloc=115.8MB, time=30.49 memory used=3063.5MB, alloc=115.8MB, time=30.64 memory used=3093.5MB, alloc=115.8MB, time=30.76 memory used=3126.6MB, alloc=115.8MB, time=30.89 memory used=3164.5MB, alloc=115.8MB, time=31.03 memory used=3207.8MB, alloc=115.8MB, time=31.17 memory used=3255.4MB, alloc=115.8MB, time=31.29 memory used=3281.8MB, alloc=115.8MB, time=31.38 memory used=3309.3MB, alloc=115.8MB, time=31.47 memory used=3338.9MB, alloc=115.8MB, time=31.57 memory used=3371.3MB, alloc=115.8MB, time=31.66 memory used=3406.9MB, alloc=115.8MB, time=31.76 memory used=3461.6MB, alloc=115.8MB, time=36.90 memory used=3509.1MB, alloc=115.8MB, time=37.54 memory used=3544.7MB, alloc=115.8MB, time=37.67 memory used=3587.5MB, alloc=115.8MB, time=37.80 memory used=3617.4MB, alloc=115.8MB, time=37.90 memory used=3651.7MB, alloc=115.8MB, time=37.99 memory used=3692.0MB, alloc=115.8MB, time=38.09 memory used=3743.7MB, alloc=115.8MB, time=38.21 memory used=3796.6MB, alloc=115.8MB, time=38.59 memory used=3840.4MB, alloc=115.8MB, time=38.73 memory used=3870.4MB, alloc=115.8MB, time=38.86 memory used=3906.7MB, alloc=115.8MB, time=38.97 memory used=3950.8MB, alloc=115.8MB, time=39.09 memory used=3990.5MB, alloc=115.8MB, time=39.21 memory used=4019.6MB, alloc=115.8MB, time=39.30 memory used=4065.5MB, alloc=115.8MB, time=42.24 memory used=4112.8MB, alloc=115.8MB, time=42.70 memory used=4153.8MB, alloc=115.8MB, time=42.84 memory used=4187.9MB, alloc=115.8MB, time=42.94 memory used=4221.3MB, alloc=115.8MB, time=43.04 memory used=4262.8MB, alloc=115.8MB, time=43.14 memory used=4342.0MB, alloc=115.8MB, time=49.32 memory used=4380.0MB, alloc=115.8MB, time=49.46 memory used=4417.2MB, alloc=115.8MB, time=49.58 memory used=4459.9MB, alloc=115.8MB, time=49.71 memory used=4488.8MB, alloc=115.8MB, time=49.81 memory used=4521.0MB, alloc=115.8MB, time=49.90 memory used=4557.6MB, alloc=115.8MB, time=50.00 memory used=4598.8MB, alloc=115.8MB, time=50.11 memory used=4647.9MB, alloc=115.8MB, time=50.21 memory used=4659.5MB, alloc=115.8MB, time=50.28 memory used=4670.6MB, alloc=115.8MB, time=50.34 memory used=4682.5MB, alloc=115.8MB, time=50.41 memory used=4706.9MB, alloc=115.8MB, time=50.58 memory used=4748.6MB, alloc=115.8MB, time=50.76 memory used=4785.2MB, alloc=115.8MB, time=50.90 memory used=4846.4MB, alloc=115.8MB, time=57.26 memory used=4899.4MB, alloc=115.8MB, time=64.19 memory used=4937.1MB, alloc=115.8MB, time=64.37 memory used=4973.8MB, alloc=115.8MB, time=64.53 memory used=5019.8MB, alloc=115.8MB, time=64.66 memory used=5048.0MB, alloc=115.8MB, time=64.75 memory used=5077.6MB, alloc=115.8MB, time=64.85 memory used=5110.7MB, alloc=115.8MB, time=64.95 memory used=5147.1MB, alloc=115.8MB, time=65.05 memory used=5187.5MB, alloc=115.8MB, time=65.16 memory used=5231.1MB, alloc=115.8MB, time=65.27 memory used=5284.3MB, alloc=115.8MB, time=65.39 memory used=5294.9MB, alloc=115.8MB, time=65.46 memory used=5305.3MB, alloc=115.8MB, time=65.52 memory used=5316.1MB, alloc=115.8MB, time=65.59 memory used=5327.5MB, alloc=115.8MB, time=65.65 memory used=5338.6MB, alloc=115.8MB, time=65.72 memory used=5350.5MB, alloc=115.8MB, time=65.78 memory used=5363.1MB, alloc=115.8MB, time=65.84 memory used=5376.2MB, alloc=115.8MB, time=65.91 memory used=5390.2MB, alloc=115.8MB, time=65.97 memory used=5449.9MB, alloc=115.8MB, time=66.42 memory used=5536.3MB, alloc=115.8MB, time=69.82 memory used=5570.3MB, alloc=115.8MB, time=69.96 memory used=5603.2MB, alloc=115.8MB, time=70.10 memory used=5642.4MB, alloc=115.8MB, time=70.26 memory used=5685.3MB, alloc=115.8MB, time=70.42 memory used=5709.8MB, alloc=139.8MB, time=70.56 memory used=5747.8MB, alloc=139.8MB, time=70.70 memory used=5790.6MB, alloc=139.8MB, time=70.90 memory used=5836.1MB, alloc=139.8MB, time=71.09 memory used=5887.5MB, alloc=139.8MB, time=71.25 memory used=5941.4MB, alloc=139.8MB, time=71.43 memory used=6001.6MB, alloc=139.8MB, time=71.61 memory used=6064.1MB, alloc=139.8MB, time=71.79 memory used=6122.4MB, alloc=139.8MB, time=71.96 memory used=6155.8MB, alloc=139.8MB, time=72.08 memory used=6189.4MB, alloc=139.8MB, time=72.19 memory used=6224.4MB, alloc=139.8MB, time=72.31 memory used=6259.8MB, alloc=139.8MB, time=72.42 memory used=6295.4MB, alloc=139.8MB, time=72.56 memory used=6332.0MB, alloc=139.8MB, time=72.67 memory used=6372.0MB, alloc=139.8MB, time=72.79 memory used=6412.8MB, alloc=139.8MB, time=72.92 memory used=6453.7MB, alloc=139.8MB, time=73.04 memory used=6499.3MB, alloc=139.8MB, time=73.16 memory used=6544.9MB, alloc=139.8MB, time=73.29 memory used=6590.5MB, alloc=139.8MB, time=73.41 memory used=6640.5MB, alloc=139.8MB, time=73.54 memory used=6690.3MB, alloc=139.8MB, time=73.68 memory used=6744.0MB, alloc=139.8MB, time=73.81 memory used=6797.3MB, alloc=139.8MB, time=73.94 memory used=6854.0MB, alloc=139.8MB, time=74.08 memory used=6914.0MB, alloc=139.8MB, time=74.22 memory used=6976.8MB, alloc=139.8MB, time=74.36 memory used=7041.7MB, alloc=139.8MB, time=74.50 memory used=7110.5MB, alloc=139.8MB, time=74.65 memory used=7130.0MB, alloc=139.8MB, time=74.73 memory used=7139.6MB, alloc=139.8MB, time=74.79 memory used=7146.1MB, alloc=139.8MB, time=74.86 memory used=7152.0MB, alloc=139.8MB, time=74.92 memory used=7158.4MB, alloc=139.8MB, time=74.98 memory used=7164.3MB, alloc=139.8MB, time=75.05 memory used=7170.8MB, alloc=139.8MB, time=75.13 memory used=7177.2MB, alloc=139.8MB, time=75.19 memory used=7183.5MB, alloc=139.8MB, time=75.28 memory used=7190.4MB, alloc=139.8MB, time=75.34 memory used=7197.1MB, alloc=139.8MB, time=75.41 memory used=7205.3MB, alloc=139.8MB, time=75.49 memory used=7212.2MB, alloc=139.8MB, time=75.55 memory used=7220.5MB, alloc=139.8MB, time=75.62 memory used=7229.4MB, alloc=139.8MB, time=75.69 memory used=7238.1MB, alloc=139.8MB, time=75.77 memory used=7246.7MB, alloc=139.8MB, time=75.84 memory used=7255.2MB, alloc=139.8MB, time=75.91 memory used=7263.5MB, alloc=139.8MB, time=75.97 memory used=7271.7MB, alloc=139.8MB, time=76.04 memory used=7280.4MB, alloc=139.8MB, time=76.11 memory used=7290.2MB, alloc=139.8MB, time=76.18 memory used=7298.9MB, alloc=139.8MB, time=76.25 memory used=7307.9MB, alloc=139.8MB, time=76.31 memory used=7317.5MB, alloc=139.8MB, time=76.39 memory used=7327.0MB, alloc=139.8MB, time=76.46 memory used=7336.9MB, alloc=139.8MB, time=76.53 memory used=7347.1MB, alloc=139.8MB, time=76.60 memory used=7357.6MB, alloc=139.8MB, time=76.67 memory used=7368.5MB, alloc=139.8MB, time=76.74 memory used=7379.8MB, alloc=139.8MB, time=76.81 memory used=7391.4MB, alloc=139.8MB, time=76.88 memory used=7463.4MB, alloc=139.8MB, time=84.29 memory used=7528.8MB, alloc=139.8MB, time=129.68 memory used=7602.8MB, alloc=139.8MB, time=138.46 memory used=7657.9MB, alloc=139.8MB, time=138.65 memory used=7702.5MB, alloc=139.8MB, time=138.82 memory used=7757.4MB, alloc=139.8MB, time=139.00 memory used=7819.3MB, alloc=139.8MB, time=139.17 memory used=7855.9MB, alloc=139.8MB, time=139.29 memory used=7894.2MB, alloc=139.8MB, time=139.41 memory used=7935.2MB, alloc=139.8MB, time=139.53 memory used=7980.2MB, alloc=139.8MB, time=139.66 memory used=8026.9MB, alloc=139.8MB, time=139.79 memory used=8077.6MB, alloc=139.8MB, time=139.92 memory used=8132.3MB, alloc=139.8MB, time=140.06 memory used=8188.5MB, alloc=139.8MB, time=140.20 memory used=8248.7MB, alloc=139.8MB, time=140.34 memory used=8312.7MB, alloc=139.8MB, time=140.52 memory used=8361.0MB, alloc=139.8MB, time=140.67 memory used=8370.7MB, alloc=139.8MB, time=140.74 memory used=8377.7MB, alloc=139.8MB, time=140.81 memory used=8384.8MB, alloc=139.8MB, time=140.87 memory used=8392.2MB, alloc=139.8MB, time=140.94 memory used=8399.8MB, alloc=139.8MB, time=141.00 memory used=8407.4MB, alloc=139.8MB, time=141.06 memory used=8415.0MB, alloc=139.8MB, time=141.13 memory used=8422.6MB, alloc=139.8MB, time=141.21 memory used=8430.3MB, alloc=139.8MB, time=141.28 memory used=8437.9MB, alloc=139.8MB, time=141.37 memory used=8445.5MB, alloc=139.8MB, time=141.43 memory used=8453.2MB, alloc=139.8MB, time=141.50 memory used=8460.8MB, alloc=139.8MB, time=141.57 memory used=8468.5MB, alloc=139.8MB, time=141.64 memory used=8476.1MB, alloc=139.8MB, time=141.71 memory used=8483.8MB, alloc=139.8MB, time=141.79 memory used=8491.4MB, alloc=139.8MB, time=141.85 memory used=8499.1MB, alloc=139.8MB, time=141.92 memory used=8506.7MB, alloc=139.8MB, time=141.99 memory used=8514.4MB, alloc=139.8MB, time=142.06 memory used=8522.2MB, alloc=139.8MB, time=142.13 memory used=8532.3MB, alloc=139.8MB, time=142.20 memory used=8540.2MB, alloc=139.8MB, time=142.27 memory used=8550.2MB, alloc=139.8MB, time=142.34 memory used=8560.4MB, alloc=139.8MB, time=142.41 memory used=8570.6MB, alloc=139.8MB, time=142.49 memory used=8580.8MB, alloc=139.8MB, time=142.56 memory used=8591.0MB, alloc=139.8MB, time=142.63 memory used=8601.2MB, alloc=139.8MB, time=142.70 memory used=8611.4MB, alloc=139.8MB, time=142.78 memory used=8621.6MB, alloc=139.8MB, time=142.84 memory used=8631.8MB, alloc=139.8MB, time=142.91 memory used=8641.9MB, alloc=139.8MB, time=142.98 memory used=8652.1MB, alloc=139.8MB, time=143.06 memory used=8662.2MB, alloc=139.8MB, time=143.13 memory used=8672.3MB, alloc=139.8MB, time=143.21 memory used=8682.5MB, alloc=139.8MB, time=143.27 memory used=8692.5MB, alloc=139.8MB, time=143.34 memory used=8702.6MB, alloc=139.8MB, time=143.42 memory used=8712.7MB, alloc=139.8MB, time=143.49 memory used=8722.7MB, alloc=139.8MB, time=143.56 memory used=8732.8MB, alloc=139.8MB, time=143.64 memory used=8742.8MB, alloc=139.8MB, time=143.70 memory used=8752.7MB, alloc=139.8MB, time=143.78 memory used=8762.9MB, alloc=139.8MB, time=143.85 memory used=8775.1MB, alloc=139.8MB, time=143.92 memory used=8787.5MB, alloc=139.8MB, time=143.99 memory used=8799.9MB, alloc=139.8MB, time=144.07 memory used=8812.1MB, alloc=139.8MB, time=144.15 memory used=8824.4MB, alloc=139.8MB, time=144.23 memory used=8836.6MB, alloc=139.8MB, time=144.30 memory used=8848.8MB, alloc=139.8MB, time=144.38 memory used=8860.9MB, alloc=139.8MB, time=144.45 memory used=8872.9MB, alloc=139.8MB, time=144.53 memory used=8884.9MB, alloc=139.8MB, time=144.60 memory used=8896.9MB, alloc=139.8MB, time=144.68 memory used=8908.7MB, alloc=139.8MB, time=144.75 memory used=8920.6MB, alloc=139.8MB, time=144.83 memory used=8932.5MB, alloc=139.8MB, time=144.90 memory used=8946.4MB, alloc=139.8MB, time=144.98 memory used=8960.3MB, alloc=139.8MB, time=145.06 memory used=8974.1MB, alloc=139.8MB, time=145.13 memory used=8987.8MB, alloc=139.8MB, time=145.21 memory used=9001.5MB, alloc=139.8MB, time=145.29 memory used=9015.0MB, alloc=139.8MB, time=145.37 memory used=9028.4MB, alloc=139.8MB, time=145.44 memory used=9041.6MB, alloc=139.8MB, time=145.51 memory used=9055.1MB, alloc=139.8MB, time=145.58 memory used=9070.0MB, alloc=139.8MB, time=145.66 memory used=9085.0MB, alloc=139.8MB, time=145.73 memory used=9099.8MB, alloc=139.8MB, time=145.81 memory used=9114.5MB, alloc=139.8MB, time=145.88 memory used=9129.2MB, alloc=139.8MB, time=145.95 memory used=9145.4MB, alloc=139.8MB, time=146.03 memory used=9161.4MB, alloc=139.8MB, time=146.11 memory used=9177.2MB, alloc=139.8MB, time=146.18 memory used=9193.1MB, alloc=139.8MB, time=146.26 memory used=9209.8MB, alloc=139.8MB, time=146.35 memory used=9226.5MB, alloc=139.8MB, time=146.43 memory used=9243.1MB, alloc=139.8MB, time=146.50 memory used=9260.4MB, alloc=139.8MB, time=146.58 memory used=9277.8MB, alloc=139.8MB, time=146.66 memory used=9295.8MB, alloc=139.8MB, time=146.78 memory used=9314.9MB, alloc=139.8MB, time=146.88 memory used=9333.5MB, alloc=139.8MB, time=146.97 memory used=9352.5MB, alloc=139.8MB, time=147.09 memory used=9372.2MB, alloc=139.8MB, time=147.21 memory used=9389.2MB, alloc=139.8MB, time=147.30 memory used=9403.1MB, alloc=139.8MB, time=147.37 memory used=9416.3MB, alloc=139.8MB, time=147.45 memory used=9430.7MB, alloc=139.8MB, time=147.52 memory used=9445.4MB, alloc=139.8MB, time=147.62 memory used=9509.8MB, alloc=139.8MB, time=148.08 memory used=9619.1MB, alloc=139.8MB, time=149.00 memory used=9746.0MB, alloc=139.8MB, time=149.98 memory used=9868.5MB, alloc=139.8MB, time=152.14 memory used=9991.4MB, alloc=139.8MB, time=155.06 memory used=10115.0MB, alloc=139.8MB, time=158.68 memory used=10238.7MB, alloc=139.8MB, time=163.42 memory used=10348.7MB, alloc=139.8MB, time=166.89 memory used=10406.8MB, alloc=139.8MB, time=167.10 memory used=10450.1MB, alloc=139.8MB, time=167.27 memory used=10503.2MB, alloc=139.8MB, time=167.42 memory used=10559.9MB, alloc=139.8MB, time=167.57 memory used=10599.1MB, alloc=139.8MB, time=167.68 memory used=10670.0MB, alloc=139.8MB, time=170.95 memory used=10722.9MB, alloc=139.8MB, time=171.12 memory used=10768.7MB, alloc=139.8MB, time=171.26 memory used=10819.2MB, alloc=139.8MB, time=171.38 memory used=10921.1MB, alloc=139.8MB, time=173.62 memory used=10972.3MB, alloc=139.8MB, time=173.82 memory used=11025.7MB, alloc=139.8MB, time=174.01 memory used=11083.6MB, alloc=139.8MB, time=174.20 memory used=11119.9MB, alloc=139.8MB, time=174.35 memory used=11157.7MB, alloc=139.8MB, time=174.51 memory used=11198.2MB, alloc=139.8MB, time=174.68 memory used=11244.3MB, alloc=139.8MB, time=174.83 memory used=11292.7MB, alloc=139.8MB, time=175.04 memory used=11347.0MB, alloc=139.8MB, time=175.34 memory used=11403.5MB, alloc=139.8MB, time=175.58 memory used=11466.1MB, alloc=139.8MB, time=175.88 memory used=11517.9MB, alloc=139.8MB, time=176.05 memory used=11550.7MB, alloc=139.8MB, time=176.17 memory used=11580.8MB, alloc=139.8MB, time=176.30 memory used=11615.2MB, alloc=139.8MB, time=176.42 memory used=11650.5MB, alloc=139.8MB, time=176.63 memory used=11686.1MB, alloc=139.8MB, time=176.76 memory used=11721.9MB, alloc=139.8MB, time=176.88 memory used=11757.9MB, alloc=139.8MB, time=177.01 memory used=11794.6MB, alloc=139.8MB, time=177.13 memory used=11835.1MB, alloc=139.8MB, time=177.25 memory used=11876.0MB, alloc=139.8MB, time=177.37 memory used=11917.0MB, alloc=139.8MB, time=177.50 memory used=11962.5MB, alloc=139.8MB, time=177.63 memory used=12007.9MB, alloc=139.8MB, time=177.76 memory used=12053.2MB, alloc=139.8MB, time=177.96 memory used=12102.6MB, alloc=139.8MB, time=178.16 memory used=12151.7MB, alloc=139.8MB, time=178.36 memory used=12204.5MB, alloc=139.8MB, time=178.54 memory used=12257.1MB, alloc=139.8MB, time=178.69 memory used=12311.8MB, alloc=139.8MB, time=178.83 memory used=12370.1MB, alloc=139.8MB, time=179.00 memory used=12430.7MB, alloc=139.8MB, time=179.17 memory used=12493.0MB, alloc=139.8MB, time=179.33 memory used=12522.9MB, alloc=139.8MB, time=179.43 memory used=12531.9MB, alloc=139.8MB, time=179.52 memory used=12538.1MB, alloc=139.8MB, time=179.67 memory used=12544.2MB, alloc=139.8MB, time=179.81 memory used=12550.0MB, alloc=139.8MB, time=179.96 memory used=12556.6MB, alloc=139.8MB, time=180.10 memory used=12563.0MB, alloc=139.8MB, time=180.21 memory used=12569.4MB, alloc=139.8MB, time=180.30 memory used=12575.8MB, alloc=139.8MB, time=180.37 memory used=12582.1MB, alloc=139.8MB, time=180.45 memory used=12588.9MB, alloc=139.8MB, time=180.52 memory used=12595.5MB, alloc=139.8MB, time=180.60 memory used=12603.6MB, alloc=139.8MB, time=180.68 memory used=12610.7MB, alloc=139.8MB, time=180.78 memory used=12618.6MB, alloc=139.8MB, time=180.89 memory used=12627.4MB, alloc=139.8MB, time=181.01 memory used=12636.0MB, alloc=139.8MB, time=181.13 memory used=12644.6MB, alloc=139.8MB, time=181.26 memory used=12652.9MB, alloc=139.8MB, time=181.40 memory used=12661.1MB, alloc=139.8MB, time=181.51 memory used=12669.2MB, alloc=139.8MB, time=181.65 memory used=12677.8MB, alloc=139.8MB, time=181.77 memory used=12687.4MB, alloc=139.8MB, time=181.84 memory used=12696.0MB, alloc=139.8MB, time=181.91 memory used=12704.8MB, alloc=139.8MB, time=181.98 memory used=12714.3MB, alloc=139.8MB, time=182.07 memory used=12723.6MB, alloc=139.8MB, time=182.14 memory used=12733.4MB, alloc=139.8MB, time=182.23 memory used=12743.3MB, alloc=139.8MB, time=182.31 memory used=12753.6MB, alloc=139.8MB, time=182.39 memory used=12764.5MB, alloc=139.8MB, time=182.46 memory used=12775.7MB, alloc=139.8MB, time=182.54 memory used=12792.6MB, alloc=139.8MB, time=182.84 memory used=12865.3MB, alloc=139.8MB, time=214.01 memory used=12936.2MB, alloc=163.8MB, time=243.80 memory used=13008.6MB, alloc=163.8MB, time=244.08 memory used=13066.8MB, alloc=163.8MB, time=244.29 memory used=13142.6MB, alloc=163.8MB, time=244.50 memory used=13204.0MB, alloc=163.8MB, time=244.67 memory used=13254.7MB, alloc=163.8MB, time=244.82 memory used=13309.0MB, alloc=163.8MB, time=244.98 memory used=13368.5MB, alloc=163.8MB, time=245.13 memory used=13433.2MB, alloc=163.8MB, time=245.30 memory used=13503.1MB, alloc=163.8MB, time=245.47 memory used=13580.5MB, alloc=163.8MB, time=245.64 memory used=13662.9MB, alloc=163.8MB, time=245.83 memory used=13717.0MB, alloc=163.8MB, time=245.97 memory used=13726.6MB, alloc=163.8MB, time=246.05 memory used=13733.6MB, alloc=163.8MB, time=246.13 memory used=13740.9MB, alloc=163.8MB, time=246.21 memory used=13748.3MB, alloc=163.8MB, time=246.28 memory used=13755.9MB, alloc=163.8MB, time=246.36 memory used=13763.5MB, alloc=163.8MB, time=246.44 memory used=13771.1MB, alloc=163.8MB, time=246.52 memory used=13778.7MB, alloc=163.8MB, time=246.60 memory used=13786.3MB, alloc=163.8MB, time=246.68 memory used=13794.0MB, alloc=163.8MB, time=246.75 memory used=13801.6MB, alloc=163.8MB, time=246.83 memory used=13809.2MB, alloc=163.8MB, time=246.90 memory used=13816.9MB, alloc=163.8MB, time=246.97 memory used=13824.5MB, alloc=163.8MB, time=247.06 memory used=13832.2MB, alloc=163.8MB, time=247.13 memory used=13839.8MB, alloc=163.8MB, time=247.20 memory used=13847.5MB, alloc=163.8MB, time=247.27 memory used=13855.1MB, alloc=163.8MB, time=247.34 memory used=13862.8MB, alloc=163.8MB, time=247.42 memory used=13870.4MB, alloc=163.8MB, time=247.50 memory used=13878.1MB, alloc=163.8MB, time=247.57 memory used=13885.8MB, alloc=163.8MB, time=247.66 memory used=13893.6MB, alloc=163.8MB, time=247.73 memory used=13903.7MB, alloc=163.8MB, time=247.81 memory used=13913.9MB, alloc=163.8MB, time=247.89 memory used=13924.1MB, alloc=163.8MB, time=247.98 memory used=13934.3MB, alloc=163.8MB, time=248.06 memory used=13944.5MB, alloc=163.8MB, time=248.14 memory used=13954.7MB, alloc=163.8MB, time=248.22 memory used=13964.9MB, alloc=163.8MB, time=248.29 memory used=13975.1MB, alloc=163.8MB, time=248.37 memory used=13985.3MB, alloc=163.8MB, time=248.44 memory used=13995.4MB, alloc=163.8MB, time=248.52 memory used=14005.6MB, alloc=163.8MB, time=248.60 memory used=14015.7MB, alloc=163.8MB, time=248.68 memory used=14025.8MB, alloc=163.8MB, time=248.75 memory used=14036.0MB, alloc=163.8MB, time=248.84 memory used=14046.0MB, alloc=163.8MB, time=248.92 memory used=14056.1MB, alloc=163.8MB, time=249.00 memory used=14066.2MB, alloc=163.8MB, time=249.08 memory used=14076.2MB, alloc=163.8MB, time=249.16 memory used=14086.3MB, alloc=163.8MB, time=249.24 memory used=14096.3MB, alloc=163.8MB, time=249.31 memory used=14106.2MB, alloc=163.8MB, time=249.39 memory used=14116.2MB, alloc=163.8MB, time=249.48 memory used=14126.3MB, alloc=163.8MB, time=249.56 memory used=14138.5MB, alloc=163.8MB, time=249.64 memory used=14150.9MB, alloc=163.8MB, time=249.72 memory used=14163.2MB, alloc=163.8MB, time=249.81 memory used=14175.5MB, alloc=163.8MB, time=249.89 memory used=14187.7MB, alloc=163.8MB, time=249.97 memory used=14199.9MB, alloc=163.8MB, time=250.06 memory used=14212.0MB, alloc=163.8MB, time=250.13 memory used=14224.1MB, alloc=163.8MB, time=250.22 memory used=14236.1MB, alloc=163.8MB, time=250.29 memory used=14248.0MB, alloc=163.8MB, time=250.38 memory used=14259.9MB, alloc=163.8MB, time=250.46 memory used=14271.8MB, alloc=163.8MB, time=250.54 memory used=14283.5MB, alloc=163.8MB, time=250.62 memory used=14295.5MB, alloc=163.8MB, time=250.70 memory used=14309.2MB, alloc=163.8MB, time=250.79 memory used=14323.1MB, alloc=163.8MB, time=250.87 memory used=14336.9MB, alloc=163.8MB, time=250.96 memory used=14350.5MB, alloc=163.8MB, time=251.04 memory used=14364.1MB, alloc=163.8MB, time=251.12 memory used=14377.5MB, alloc=163.8MB, time=251.21 memory used=14390.9MB, alloc=163.8MB, time=251.29 memory used=14404.1MB, alloc=163.8MB, time=251.40 memory used=14417.5MB, alloc=163.8MB, time=251.50 memory used=14432.3MB, alloc=163.8MB, time=251.58 memory used=14447.2MB, alloc=163.8MB, time=251.65 memory used=14462.0MB, alloc=163.8MB, time=251.73 memory used=14476.5MB, alloc=163.8MB, time=251.83 memory used=14491.1MB, alloc=163.8MB, time=251.90 memory used=14507.2MB, alloc=163.8MB, time=251.99 memory used=14523.2MB, alloc=163.8MB, time=252.07 memory used=14538.9MB, alloc=163.8MB, time=252.15 memory used=14554.5MB, alloc=163.8MB, time=252.22 memory used=14571.1MB, alloc=163.8MB, time=252.30 memory used=14587.7MB, alloc=163.8MB, time=252.39 memory used=14604.1MB, alloc=163.8MB, time=252.48 memory used=14621.3MB, alloc=163.8MB, time=252.56 memory used=14638.6MB, alloc=163.8MB, time=252.65 memory used=14656.3MB, alloc=163.8MB, time=252.73 memory used=14675.2MB, alloc=163.8MB, time=252.81 memory used=14693.7MB, 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alloc=419.8MB, time=282.11 memory used=16165.6MB, alloc=419.8MB, time=282.31 memory used=16222.5MB, alloc=419.8MB, time=282.50 memory used=16271.5MB, alloc=419.8MB, time=282.73 memory used=16326.8MB, alloc=419.8MB, time=282.90 memory used=16387.7MB, alloc=419.8MB, time=283.08 memory used=16455.9MB, alloc=419.8MB, time=283.26 memory used=16531.5MB, alloc=419.8MB, time=283.44 memory used=16730.5MB, alloc=419.8MB, time=283.85 memory used=16898.2MB, alloc=419.8MB, time=284.21 memory used=17094.0MB, alloc=419.8MB, time=284.58 memory used=17325.6MB, alloc=419.8MB, time=284.98 memory used=17406.6MB, alloc=419.8MB, time=285.47 memory used=17467.8MB, alloc=419.8MB, time=285.66 memory used=17524.8MB, alloc=419.8MB, time=285.87 memory used=17595.7MB, alloc=419.8MB, time=286.06 memory used=17656.6MB, alloc=419.8MB, time=286.24 memory used=17705.4MB, alloc=419.8MB, time=286.40 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428492694 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 2 4 2 F := [-4 x + x z + 10 x z , -16 x - 20 z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 G := [-8 x y z - 18 y - 17 z, 12 y - 13 x y + 16 z] > Problem := [F,G]; 4 3 2 4 2 Problem := [[-4 x + x z + 10 x z , -16 x - 20 z ], 4 2 [-8 x y z - 18 y - 17 z, 12 y - 13 x y + 16 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=24.8MB, alloc=32.3MB, time=0.41 memory used=48.2MB, alloc=36.3MB, time=0.70 memory used=72.7MB, alloc=36.3MB, time=0.97 memory used=97.0MB, alloc=60.3MB, time=1.31 memory used=140.3MB, alloc=60.3MB, time=1.73 memory used=200.0MB, alloc=68.4MB, time=2.41 memory used=243.3MB, alloc=68.4MB, time=2.82 memory used=276.7MB, alloc=68.4MB, time=2.99 memory used=317.6MB, alloc=68.4MB, time=3.42 memory used=359.9MB, alloc=68.4MB, time=3.81 memory used=399.4MB, alloc=68.4MB, time=4.01 memory used=421.3MB, alloc=68.4MB, time=4.08 memory used=448.0MB, alloc=68.4MB, time=4.16 memory used=466.9MB, alloc=68.4MB, time=4.23 memory used=495.0MB, alloc=68.4MB, time=4.33 memory used=522.6MB, alloc=68.4MB, time=4.43 memory used=549.1MB, alloc=68.4MB, time=4.52 memory used=570.4MB, alloc=68.4MB, time=4.60 memory used=591.0MB, alloc=68.4MB, time=4.67 memory used=629.5MB, alloc=68.4MB, time=5.25 memory used=653.6MB, alloc=68.4MB, time=5.34 memory used=675.0MB, alloc=68.4MB, time=5.42 memory used=696.2MB, alloc=68.4MB, time=5.50 memory used=726.6MB, alloc=68.4MB, time=5.63 memory used=770.3MB, alloc=68.4MB, time=6.07 memory used=828.5MB, alloc=68.4MB, time=7.03 memory used=885.3MB, alloc=68.4MB, time=7.98 memory used=916.3MB, alloc=68.4MB, time=8.15 memory used=967.8MB, alloc=68.4MB, time=8.71 memory used=1016.2MB, alloc=68.4MB, time=9.21 memory used=1057.9MB, alloc=92.4MB, time=9.74 memory used=1098.0MB, alloc=92.4MB, time=9.91 memory used=1139.7MB, alloc=92.4MB, time=10.06 memory used=1181.2MB, alloc=92.4MB, time=10.26 memory used=1221.2MB, alloc=92.4MB, time=10.42 memory used=1263.4MB, alloc=92.4MB, time=10.60 memory used=1304.7MB, alloc=92.4MB, time=10.77 memory used=1346.3MB, alloc=92.4MB, time=10.95 memory used=1386.8MB, alloc=92.4MB, time=11.11 memory used=1426.2MB, alloc=92.4MB, time=11.27 memory used=1506.3MB, alloc=92.4MB, time=12.82 memory used=1558.9MB, alloc=92.4MB, time=13.35 memory used=1599.1MB, alloc=92.4MB, time=13.52 memory used=1682.9MB, alloc=92.4MB, time=15.28 memory used=1728.1MB, alloc=92.4MB, time=15.63 memory used=1760.1MB, alloc=92.4MB, time=15.73 memory used=1797.9MB, alloc=92.4MB, time=15.83 memory used=1839.3MB, alloc=92.4MB, time=16.02 memory used=1874.6MB, alloc=92.4MB, time=16.12 memory used=1910.8MB, alloc=92.4MB, time=16.23 memory used=1959.8MB, alloc=92.4MB, time=22.10 memory used=2147.5MB, alloc=92.4MB, time=25.33 memory used=2300.3MB, alloc=348.4MB, time=28.45 memory used=2371.4MB, alloc=348.4MB, time=30.42 memory used=2411.7MB, alloc=348.4MB, time=30.56 memory used=2441.6MB, alloc=348.4MB, time=30.67 memory used=2480.2MB, alloc=348.4MB, time=30.80 memory used=2521.0MB, alloc=348.4MB, time=30.99 memory used=2557.1MB, alloc=348.4MB, time=31.11 memory used=2590.9MB, alloc=348.4MB, time=31.23 memory used=2635.2MB, alloc=348.4MB, time=31.42 memory used=2672.8MB, alloc=348.4MB, time=31.54 memory used=2705.8MB, alloc=348.4MB, time=31.66 memory used=2750.7MB, alloc=348.4MB, time=33.46 memory used=2964.3MB, alloc=348.4MB, time=40.90 memory used=3134.9MB, alloc=372.4MB, time=44.69 memory used=3206.4MB, alloc=372.4MB, time=45.78 memory used=3267.9MB, alloc=372.4MB, time=46.03 memory used=3331.2MB, alloc=372.4MB, time=46.28 memory used=3407.7MB, alloc=372.4MB, time=46.89 memory used=3497.2MB, alloc=372.4MB, time=48.10 memory used=3612.1MB, alloc=372.4MB, time=49.94 memory used=3723.0MB, alloc=372.4MB, time=50.79 memory used=3777.6MB, alloc=372.4MB, time=51.13 memory used=3818.4MB, alloc=372.4MB, time=51.28 memory used=3880.8MB, alloc=372.4MB, time=51.72 memory used=3984.8MB, alloc=372.4MB, time=52.40 memory used=4079.1MB, alloc=396.4MB, time=54.71 memory used=4220.1MB, alloc=396.4MB, time=56.33 memory used=4371.1MB, alloc=396.4MB, time=58.11 memory used=4435.1MB, alloc=396.4MB, time=58.46 memory used=4489.7MB, alloc=396.4MB, time=58.63 memory used=4535.5MB, alloc=396.4MB, time=58.78 memory used=4591.2MB, alloc=396.4MB, time=58.94 memory used=4658.0MB, alloc=396.4MB, time=59.11 memory used=4817.0MB, alloc=396.4MB, time=59.59 memory used=4884.1MB, alloc=396.4MB, time=59.88 memory used=4938.4MB, alloc=396.4MB, time=60.07 memory used=4985.3MB, alloc=396.4MB, time=60.23 memory used=5041.7MB, alloc=396.4MB, time=60.40 memory used=5108.9MB, alloc=396.4MB, time=60.57 memory used=5264.1MB, alloc=396.4MB, time=60.87 memory used=5332.3MB, alloc=396.4MB, time=61.18 memory used=5386.6MB, alloc=396.4MB, time=61.38 memory used=5433.0MB, alloc=396.4MB, time=61.52 memory used=5488.8MB, alloc=396.4MB, time=61.70 memory used=5555.6MB, alloc=396.4MB, time=61.87 memory used=5713.5MB, alloc=396.4MB, time=62.18 memory used=5781.4MB, alloc=396.4MB, time=62.50 memory used=5836.0MB, alloc=396.4MB, time=62.69 memory used=5883.1MB, alloc=396.4MB, time=62.86 memory used=5939.6MB, alloc=396.4MB, time=63.03 memory used=6007.7MB, alloc=396.4MB, time=63.21 memory used=6161.8MB, alloc=396.4MB, time=63.53 memory used=6227.8MB, alloc=396.4MB, time=63.81 memory 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time=77.16 memory used=10190.3MB, alloc=396.4MB, time=77.46 memory used=10364.9MB, alloc=396.4MB, time=77.78 memory used=10563.6MB, alloc=396.4MB, time=78.14 memory used=10793.1MB, alloc=396.4MB, time=78.53 memory used=10981.3MB, alloc=396.4MB, time=78.87 memory used=11544.3MB, alloc=396.4MB, time=90.89 memory used=11790.2MB, alloc=396.4MB, time=95.30 memory used=11823.9MB, alloc=420.4MB, time=96.71 memory used=11907.5MB, alloc=420.4MB, time=97.84 memory used=11975.8MB, alloc=420.4MB, time=98.04 memory used=12041.0MB, alloc=420.4MB, time=98.23 memory used=12123.1MB, alloc=420.4MB, time=98.43 memory used=12292.1MB, alloc=420.4MB, time=98.77 memory used=12450.0MB, alloc=420.4MB, time=102.05 memory used=12524.6MB, alloc=420.4MB, time=102.34 memory used=12606.8MB, alloc=420.4MB, time=102.77 memory used=12696.3MB, alloc=420.4MB, time=103.32 memory used=12775.5MB, alloc=420.4MB, time=103.61 memory used=12854.3MB, alloc=420.4MB, time=103.92 memory used=12929.7MB, alloc=420.4MB, time=104.19 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memory used=24752.1MB, alloc=420.4MB, time=158.79 memory used=24972.2MB, alloc=420.4MB, time=159.18 memory used=25198.4MB, alloc=420.4MB, time=159.56 memory used=25429.7MB, alloc=420.4MB, time=159.96 memory used=25665.4MB, alloc=420.4MB, time=160.35 memory used=25896.0MB, alloc=420.4MB, time=160.74 memory used=26091.0MB, alloc=420.4MB, time=161.08 memory used=26287.9MB, alloc=420.4MB, time=161.43 memory used=26490.0MB, alloc=420.4MB, time=161.79 memory used=26699.6MB, alloc=420.4MB, time=162.15 memory used=26912.8MB, alloc=420.4MB, time=162.50 memory used=27133.2MB, alloc=420.4MB, time=162.86 memory used=27359.1MB, alloc=420.4MB, time=163.20 memory used=27592.8MB, alloc=420.4MB, time=163.54 memory used=27957.5MB, alloc=420.4MB, time=166.16 memory used=28057.9MB, alloc=420.4MB, time=167.95 memory used=28198.4MB, alloc=444.4MB, time=169.59 memory used=28349.0MB, alloc=444.4MB, time=171.94 memory used=28504.6MB, alloc=444.4MB, time=173.87 memory used=28660.9MB, alloc=444.4MB, time=175.61 memory used=28830.2MB, alloc=444.4MB, time=176.92 memory used=28998.1MB, alloc=444.4MB, time=178.20 memory used=29165.9MB, alloc=444.4MB, time=179.68 memory used=29343.2MB, alloc=444.4MB, time=181.18 memory used=29516.7MB, alloc=444.4MB, time=182.73 memory used=29685.8MB, alloc=444.4MB, time=184.35 memory used=29852.5MB, alloc=444.4MB, time=186.10 memory used=30018.9MB, alloc=444.4MB, time=187.86 memory used=30188.9MB, alloc=444.4MB, time=190.18 memory used=30355.7MB, alloc=444.4MB, time=192.24 memory used=30522.9MB, alloc=444.4MB, time=194.71 memory used=30691.8MB, alloc=444.4MB, time=197.26 memory used=30864.7MB, alloc=444.4MB, time=199.57 memory used=31036.9MB, alloc=444.4MB, time=202.03 memory used=31210.0MB, alloc=444.4MB, time=204.79 memory used=31382.3MB, alloc=444.4MB, time=207.22 memory used=31559.7MB, alloc=444.4MB, time=214.10 memory used=31803.8MB, alloc=444.4MB, time=217.07 memory used=31975.3MB, alloc=444.4MB, time=218.71 memory used=32147.3MB, alloc=444.4MB, time=220.57 memory used=32319.1MB, alloc=444.4MB, time=222.60 memory used=32492.6MB, alloc=444.4MB, time=224.83 memory used=32667.8MB, alloc=444.4MB, time=227.22 memory used=32840.9MB, alloc=444.4MB, time=229.74 memory used=33010.8MB, alloc=444.4MB, time=232.53 memory used=33181.1MB, alloc=444.4MB, time=235.49 memory used=33354.6MB, alloc=444.4MB, time=238.12 memory used=33528.7MB, alloc=444.4MB, time=241.64 memory used=33697.5MB, alloc=444.4MB, time=244.43 memory used=33871.6MB, alloc=444.4MB, time=247.11 memory used=34043.4MB, alloc=444.4MB, time=250.04 memory used=34215.3MB, alloc=444.4MB, time=253.54 memory used=34388.3MB, alloc=444.4MB, time=259.89 memory used=34486.3MB, alloc=444.4MB, time=266.26 memory used=34591.4MB, alloc=468.4MB, time=266.58 memory used=34629.2MB, alloc=492.4MB, time=270.84 memory used=34645.8MB, alloc=516.4MB, time=271.07 memory used=34661.7MB, alloc=516.4MB, time=271.37 memory used=34889.6MB, alloc=516.4MB, time=272.74 memory used=35123.5MB, alloc=516.4MB, time=274.61 memory used=35344.5MB, alloc=516.4MB, time=276.19 memory used=35538.1MB, alloc=516.4MB, time=276.81 memory used=35789.5MB, alloc=516.4MB, time=278.64 memory used=36059.1MB, alloc=516.4MB, time=279.22 memory used=36516.8MB, alloc=531.8MB, time=280.10 memory used=36918.1MB, alloc=531.8MB, time=280.86 memory used=37317.6MB, alloc=531.8MB, time=281.60 memory used=37696.4MB, alloc=531.8MB, time=282.30 memory used=38063.8MB, alloc=531.8MB, time=282.99 memory used=38440.1MB, alloc=531.8MB, time=283.67 memory used=38807.9MB, alloc=531.8MB, time=284.30 memory used=39172.3MB, alloc=531.8MB, time=284.93 memory used=39543.9MB, alloc=531.8MB, time=285.64 memory used=39916.8MB, alloc=531.8MB, time=286.34 memory used=40280.1MB, alloc=531.8MB, time=287.00 memory used=40642.2MB, alloc=531.8MB, time=287.67 memory used=41004.4MB, alloc=531.8MB, time=288.30 memory used=41378.3MB, alloc=531.8MB, time=289.03 memory used=41739.7MB, alloc=531.8MB, time=289.68 memory used=42100.0MB, alloc=531.8MB, time=290.32 memory used=42462.1MB, alloc=531.8MB, time=290.95 memory used=42821.5MB, alloc=531.8MB, time=291.59 memory used=43189.4MB, alloc=531.8MB, time=292.29 memory used=43553.0MB, alloc=531.8MB, time=292.92 memory used=43915.2MB, alloc=531.8MB, time=293.55 memory used=44277.7MB, alloc=531.8MB, time=294.19 memory used=44647.8MB, alloc=531.8MB, time=294.90 memory used=45017.1MB, alloc=531.8MB, time=295.55 memory used=45381.5MB, alloc=531.8MB, time=296.19 memory used=45746.7MB, alloc=531.8MB, time=296.83 memory used=46110.2MB, alloc=531.8MB, time=297.46 memory used=46479.2MB, alloc=531.8MB, time=298.15 memory used=46843.6MB, alloc=531.8MB, time=298.78 memory used=47207.1MB, alloc=531.8MB, time=299.42 memory used=47571.4MB, alloc=531.8MB, time=300.07 memory used=47935.1MB, alloc=531.8MB, time=300.70 memory used=48480.4MB, alloc=531.8MB, time=316.58 memory used=48705.1MB, alloc=531.8MB, time=317.72 memory used=48929.8MB, alloc=531.8MB, time=318.28 memory used=49257.8MB, alloc=531.8MB, time=318.98 memory used=49610.7MB, alloc=531.8MB, time=319.74 memory used=49993.2MB, alloc=531.8MB, time=320.54 memory used=50436.1MB, alloc=531.8MB, time=321.44 memory used=50893.9MB, alloc=531.8MB, time=322.33 memory used=51343.6MB, alloc=531.8MB, time=323.21 memory used=51744.3MB, alloc=531.8MB, time=323.99 memory used=52165.9MB, alloc=531.8MB, time=324.82 memory used=52561.4MB, alloc=531.8MB, time=325.58 memory used=52956.9MB, alloc=531.8MB, time=326.33 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428492994 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 3 2 3 F := [-5 x z - 4 x y + 10 x y , -8 x y - 12 x y + 3 z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 4 G := [y z + 19 x y - 20 x y, -11 x y z + 5 z + 15 y z] > Problem := [F,G]; 2 2 2 2 3 2 3 Problem := [[-5 x z - 4 x y + 10 x y , -8 x y - 12 x y + 3 z ], 3 2 2 4 [y z + 19 x y - 20 x y, -11 x y z + 5 z + 15 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=25.5MB, alloc=32.3MB, time=0.48 memory used=44.5MB, alloc=56.3MB, time=0.75 memory used=93.1MB, alloc=64.9MB, time=1.10 memory used=142.8MB, alloc=66.0MB, time=1.97 memory used=168.9MB, alloc=66.0MB, time=2.05 memory used=212.7MB, alloc=66.0MB, time=2.43 memory used=253.9MB, alloc=66.0MB, time=3.03 memory used=303.5MB, alloc=74.0MB, time=3.77 memory used=345.8MB, alloc=74.0MB, time=4.34 memory used=388.0MB, alloc=98.0MB, time=4.90 memory used=450.7MB, alloc=98.0MB, time=5.33 memory used=500.2MB, alloc=98.0MB, time=6.04 memory used=553.3MB, alloc=98.0MB, time=6.27 memory used=605.5MB, alloc=98.0MB, time=7.09 memory used=671.5MB, alloc=98.0MB, time=7.67 memory used=720.6MB, alloc=98.0MB, time=7.90 memory used=767.2MB, alloc=98.0MB, time=8.09 memory used=803.4MB, alloc=98.0MB, time=8.21 memory used=851.2MB, alloc=98.0MB, time=8.81 memory used=888.7MB, alloc=98.0MB, time=8.97 memory used=975.1MB, alloc=98.0MB, time=9.71 memory used=1068.2MB, alloc=98.0MB, time=10.67 memory used=1155.6MB, alloc=98.0MB, time=11.59 memory used=1221.4MB, alloc=98.0MB, time=12.04 memory used=1271.3MB, alloc=98.0MB, time=12.74 memory used=1321.1MB, alloc=98.0MB, time=12.97 memory used=1374.5MB, alloc=98.0MB, time=13.68 memory used=1420.7MB, alloc=98.0MB, time=13.91 memory used=1456.2MB, alloc=98.0MB, time=14.02 memory used=1502.2MB, alloc=98.0MB, time=14.21 memory used=1549.9MB, alloc=98.0MB, time=14.79 memory used=1584.1MB, alloc=98.0MB, time=14.89 memory used=1634.1MB, alloc=98.0MB, time=15.27 memory used=1706.9MB, alloc=98.0MB, time=15.98 memory used=1743.4MB, alloc=98.0MB, time=16.15 memory used=1788.8MB, alloc=98.0MB, time=16.41 memory used=1818.8MB, alloc=98.0MB, time=16.51 memory used=1854.4MB, alloc=98.0MB, time=16.66 memory used=1892.9MB, alloc=98.0MB, time=16.83 memory used=1928.1MB, alloc=98.0MB, time=17.07 memory used=1957.9MB, alloc=98.0MB, time=17.18 memory used=1996.7MB, alloc=98.0MB, time=17.39 memory used=2026.5MB, alloc=98.0MB, time=17.50 memory used=2233.3MB, alloc=98.0MB, time=20.39 memory used=2313.7MB, alloc=98.0MB, time=22.42 memory used=2351.2MB, alloc=98.0MB, time=22.57 memory used=2382.5MB, alloc=98.0MB, time=22.68 memory used=2409.9MB, alloc=98.0MB, time=22.77 memory used=2442.3MB, alloc=98.0MB, time=22.87 memory used=2480.5MB, alloc=98.0MB, time=22.98 memory used=2508.1MB, alloc=98.0MB, time=23.07 memory used=2530.7MB, alloc=98.0MB, time=23.14 memory used=2555.5MB, alloc=98.0MB, time=23.22 memory used=2581.7MB, alloc=98.0MB, time=23.31 memory used=2609.7MB, alloc=98.0MB, time=23.40 memory used=2639.9MB, alloc=98.0MB, time=23.48 memory used=2672.8MB, alloc=98.0MB, time=23.57 memory used=2709.1MB, alloc=98.0MB, time=23.66 memory used=2757.0MB, alloc=98.0MB, time=23.86 memory used=2793.0MB, alloc=98.0MB, time=24.12 memory used=2829.0MB, alloc=98.0MB, time=24.36 memory used=2868.7MB, alloc=98.0MB, time=24.50 memory used=2901.2MB, alloc=98.0MB, time=24.61 memory used=2934.2MB, alloc=98.0MB, time=24.73 memory used=2957.7MB, alloc=98.0MB, time=24.84 memory used=2984.4MB, alloc=98.0MB, time=24.94 memory used=3014.4MB, alloc=98.0MB, time=25.04 memory used=3048.2MB, alloc=98.0MB, time=25.15 memory used=3086.6MB, alloc=98.0MB, time=25.25 memory used=3114.9MB, alloc=98.0MB, time=25.34 memory used=3137.4MB, alloc=98.0MB, time=25.43 memory used=3161.9MB, alloc=98.0MB, time=25.50 memory used=3202.7MB, alloc=98.0MB, time=25.75 memory used=3234.3MB, alloc=98.0MB, time=25.87 memory used=3268.5MB, alloc=98.0MB, time=25.97 memory used=3291.5MB, alloc=98.0MB, time=26.07 memory used=3317.8MB, alloc=98.0MB, time=26.17 memory used=3347.0MB, alloc=98.0MB, time=26.27 memory used=3380.1MB, alloc=98.0MB, time=26.36 memory used=3417.5MB, alloc=98.0MB, time=26.46 memory used=3448.2MB, alloc=98.0MB, time=26.55 memory used=3469.8MB, alloc=98.0MB, time=26.63 memory used=3493.4MB, alloc=98.0MB, time=26.71 memory used=3541.8MB, alloc=98.0MB, time=28.39 memory used=3575.1MB, alloc=98.0MB, time=28.51 memory used=3601.9MB, alloc=98.0MB, time=28.62 memory used=3635.0MB, alloc=98.0MB, time=28.73 memory used=3672.7MB, alloc=98.0MB, time=28.84 memory used=3695.2MB, alloc=98.0MB, time=28.92 memory used=3718.5MB, alloc=98.0MB, time=29.01 memory used=3744.4MB, alloc=98.0MB, time=29.10 memory used=3773.4MB, alloc=98.0MB, time=29.19 memory used=3806.1MB, alloc=98.0MB, time=29.28 memory used=3856.0MB, alloc=98.0MB, time=29.66 memory used=3905.2MB, alloc=98.0MB, time=30.04 memory used=3935.7MB, alloc=98.0MB, time=30.15 memory used=4000.5MB, alloc=98.0MB, time=30.71 memory used=4067.2MB, alloc=122.0MB, time=31.69 memory used=4132.1MB, alloc=378.0MB, time=32.58 memory used=4193.4MB, alloc=378.0MB, time=32.88 memory used=4252.0MB, alloc=378.0MB, time=33.14 memory used=4315.2MB, alloc=378.0MB, time=34.22 memory used=4356.0MB, alloc=378.0MB, time=34.37 memory used=4422.8MB, alloc=378.0MB, time=34.98 memory used=4476.8MB, alloc=378.0MB, time=35.25 memory used=4579.4MB, alloc=378.0MB, time=36.88 memory used=4673.3MB, alloc=378.0MB, time=37.92 memory used=4710.8MB, alloc=378.0MB, time=38.06 memory used=4746.9MB, alloc=378.0MB, time=38.21 memory used=4786.4MB, alloc=378.0MB, time=38.42 memory used=4831.2MB, alloc=378.0MB, time=38.64 memory used=4876.9MB, alloc=378.0MB, time=38.99 memory used=4915.7MB, alloc=378.0MB, time=39.17 memory used=4958.5MB, alloc=378.0MB, time=39.34 memory used=4990.2MB, alloc=378.0MB, time=39.48 memory used=5023.1MB, alloc=378.0MB, time=39.62 memory used=5061.6MB, alloc=378.0MB, time=39.75 memory used=5136.7MB, alloc=378.0MB, time=40.76 memory used=5207.3MB, alloc=378.0MB, time=41.92 memory used=5255.6MB, alloc=378.0MB, time=42.20 memory used=5309.2MB, alloc=378.0MB, time=42.61 memory used=5369.6MB, alloc=378.0MB, time=43.17 memory used=5406.5MB, alloc=378.0MB, time=43.34 memory used=5443.1MB, alloc=378.0MB, time=43.50 memory used=5534.1MB, alloc=402.0MB, time=45.47 memory used=5616.7MB, alloc=402.0MB, time=45.97 memory used=5664.9MB, alloc=402.0MB, time=46.16 memory used=5729.3MB, alloc=402.0MB, time=46.38 memory used=5771.8MB, alloc=402.0MB, time=46.55 memory used=5814.8MB, alloc=402.0MB, time=46.71 memory used=5863.1MB, alloc=402.0MB, time=46.87 memory used=5917.3MB, alloc=402.0MB, time=47.05 memory used=5976.6MB, alloc=402.0MB, time=47.22 memory used=6042.8MB, alloc=402.0MB, time=47.40 memory used=6224.1MB, alloc=402.0MB, time=47.93 memory used=6466.9MB, alloc=402.0MB, time=49.43 memory used=6591.3MB, alloc=402.0MB, time=51.99 memory used=6708.3MB, alloc=402.0MB, time=53.32 memory used=6805.8MB, alloc=426.0MB, time=54.15 memory used=6907.5MB, alloc=426.0MB, time=54.51 memory used=7030.0MB, alloc=426.0MB, time=54.84 memory used=7173.7MB, alloc=426.0MB, time=55.19 memory used=7324.0MB, alloc=426.0MB, time=55.56 memory used=7479.7MB, alloc=426.0MB, time=55.99 memory used=7638.0MB, alloc=426.0MB, time=56.37 memory used=7820.9MB, alloc=426.0MB, time=56.86 memory used=7953.0MB, alloc=426.0MB, time=58.15 memory used=8070.3MB, alloc=426.0MB, time=58.55 memory used=8207.4MB, alloc=426.0MB, time=58.90 memory used=8374.4MB, alloc=426.0MB, time=59.30 memory used=8542.2MB, alloc=426.0MB, time=59.71 memory used=8714.1MB, alloc=426.0MB, time=60.11 memory used=8893.5MB, alloc=426.0MB, time=60.54 memory used=9094.7MB, alloc=426.0MB, time=61.00 memory used=9315.7MB, alloc=426.0MB, time=61.52 memory used=9564.3MB, alloc=426.0MB, time=62.35 memory used=9700.7MB, alloc=426.0MB, time=63.27 memory used=9841.4MB, alloc=426.0MB, time=64.32 memory used=9948.1MB, alloc=426.0MB, time=64.79 memory used=10077.5MB, alloc=426.0MB, time=65.16 memory used=10235.6MB, alloc=426.0MB, time=65.56 memory used=10425.4MB, alloc=426.0MB, time=65.99 memory used=10687.1MB, alloc=426.0MB, time=66.55 memory used=10961.0MB, alloc=426.0MB, time=67.13 memory used=11272.1MB, alloc=426.0MB, time=67.79 memory used=11594.1MB, alloc=426.0MB, time=68.47 memory used=11948.5MB, alloc=426.0MB, time=69.49 memory used=12079.7MB, alloc=426.0MB, time=70.31 memory used=12176.2MB, alloc=426.0MB, time=70.66 memory used=12289.6MB, alloc=426.0MB, time=71.02 memory used=12423.2MB, alloc=426.0MB, time=71.39 memory used=12579.7MB, alloc=426.0MB, time=71.81 memory used=12729.9MB, alloc=426.0MB, time=72.21 memory used=12893.1MB, alloc=426.0MB, time=72.64 memory used=13058.0MB, alloc=426.0MB, time=73.14 memory used=13179.7MB, alloc=426.0MB, time=74.43 memory used=13279.1MB, alloc=426.0MB, time=74.79 memory used=13380.0MB, alloc=426.0MB, time=75.17 memory used=13482.2MB, alloc=426.0MB, time=75.56 memory used=13592.5MB, alloc=426.0MB, time=75.92 memory used=13723.9MB, alloc=426.0MB, time=77.38 memory used=13828.4MB, alloc=426.0MB, time=77.91 memory used=13958.3MB, alloc=426.0MB, time=79.23 memory used=14065.7MB, alloc=450.0MB, time=81.17 memory used=14199.6MB, alloc=474.0MB, time=83.40 memory used=14384.8MB, alloc=474.0MB, time=85.47 memory used=14569.9MB, alloc=474.0MB, time=87.23 memory used=14738.7MB, alloc=498.0MB, time=89.42 memory used=14928.8MB, alloc=522.0MB, time=91.90 memory used=15161.3MB, alloc=522.0MB, time=94.00 memory used=15384.8MB, alloc=546.0MB, time=96.60 memory used=15628.5MB, alloc=546.0MB, time=99.53 memory used=15820.5MB, alloc=570.0MB, time=102.62 memory used=16018.5MB, alloc=594.0MB, time=108.16 memory used=16206.4MB, alloc=618.0MB, time=114.51 memory used=16401.2MB, alloc=642.0MB, time=121.79 memory used=16604.2MB, alloc=666.0MB, time=130.18 memory used=16831.1MB, alloc=690.0MB, time=139.65 memory used=17082.0MB, alloc=714.0MB, time=150.00 memory used=17356.9MB, alloc=738.0MB, time=161.35 memory used=17655.6MB, alloc=738.0MB, time=173.78 memory used=17954.4MB, alloc=762.0MB, time=186.23 memory used=18277.1MB, alloc=762.0MB, time=199.43 memory used=18599.8MB, alloc=762.0MB, time=212.60 memory used=18922.6MB, alloc=786.0MB, time=226.03 memory used=19269.3MB, alloc=810.0MB, time=240.10 N1 := 10715 > GB := Basis(F, plex(op(vars))); 10 9 8 4 2 3 3 2 4 GB := [-1000 x y - 3000 x y - 2250 x y - 72 x y + 540 x y - 1350 x y 5 6 5 3 2 2 3 4 + 1125 x y , 50 x y z + 75 x y z - 12 x y + 60 x y - 75 x y , 5 4 2 2 2 2 2 2 -20 x y - 30 x y - 6 x y z + 15 x y z, 5 x z + 4 x y - 10 x y , 3 2 3 -8 x y - 12 x y + 3 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428493294 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 2 2 F := [8 y z - 4 x z - 8 z , 3 x y + 8 y z + 15 y ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [18 x y z + 2 y z - 11 x, -7 x y z - 8 y z - 8] > Problem := [F,G]; 2 2 2 3 2 2 2 Problem := [[8 y z - 4 x z - 8 z , 3 x y + 8 y z + 15 y ], 2 2 2 2 [18 x y z + 2 y z - 11 x, -7 x y z - 8 y z - 8]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=25.1MB, alloc=32.3MB, time=0.48 memory used=44.6MB, alloc=56.3MB, time=0.77 memory used=87.7MB, alloc=60.3MB, time=1.33 memory used=137.3MB, alloc=68.4MB, time=1.92 memory used=180.3MB, alloc=68.4MB, time=2.50 memory used=220.9MB, alloc=92.4MB, time=3.10 memory used=286.0MB, alloc=116.4MB, time=4.02 memory used=354.2MB, alloc=116.4MB, time=4.92 memory used=426.4MB, alloc=372.4MB, time=5.79 memory used=493.1MB, alloc=372.4MB, time=6.29 memory used=568.0MB, alloc=372.4MB, time=6.84 memory used=672.9MB, alloc=372.4MB, time=7.93 memory used=770.2MB, alloc=396.4MB, time=8.94 memory used=859.1MB, alloc=396.4MB, time=9.55 memory used=982.5MB, alloc=396.4MB, time=10.82 memory used=1090.9MB, alloc=420.4MB, time=12.35 memory used=1196.7MB, alloc=420.4MB, time=13.59 memory used=1282.3MB, alloc=420.4MB, time=14.54 memory used=1359.6MB, alloc=420.4MB, time=15.09 memory used=1444.5MB, alloc=420.4MB, time=15.63 memory used=1567.5MB, alloc=420.4MB, time=16.76 memory used=1674.7MB, alloc=444.4MB, time=18.28 memory used=1786.1MB, alloc=444.4MB, time=20.02 memory used=1892.7MB, alloc=468.4MB, time=21.63 memory used=1997.8MB, alloc=468.4MB, time=23.04 memory used=2103.0MB, alloc=468.4MB, time=24.64 memory used=2206.7MB, alloc=492.4MB, time=26.01 memory used=2317.2MB, alloc=492.4MB, time=27.30 memory used=2401.4MB, alloc=492.4MB, time=28.59 memory used=2503.6MB, alloc=492.4MB, time=29.98 memory used=2603.1MB, alloc=492.4MB, time=30.57 memory used=2698.5MB, alloc=492.4MB, time=31.04 memory used=2799.0MB, alloc=492.4MB, time=31.73 memory used=2892.6MB, alloc=492.4MB, time=32.22 memory used=2987.8MB, alloc=492.4MB, time=32.71 memory used=3082.8MB, alloc=492.4MB, time=33.21 memory used=3195.5MB, alloc=492.4MB, time=34.17 memory used=3294.3MB, alloc=492.4MB, time=34.82 memory used=3379.8MB, alloc=492.4MB, time=35.94 memory used=3477.8MB, alloc=492.4MB, time=36.99 memory used=3549.0MB, alloc=492.4MB, time=38.06 memory used=3633.1MB, alloc=492.4MB, time=39.49 memory used=3691.2MB, alloc=492.4MB, time=40.55 memory used=3749.0MB, alloc=516.4MB, time=41.69 memory used=3806.7MB, alloc=516.4MB, time=42.79 memory used=3884.7MB, alloc=516.4MB, time=43.88 memory used=3934.0MB, alloc=516.4MB, time=44.71 memory used=3994.0MB, alloc=516.4MB, time=45.82 memory used=4045.5MB, alloc=516.4MB, time=46.97 memory used=4272.5MB, alloc=540.4MB, time=49.62 memory used=4504.7MB, alloc=540.4MB, time=51.41 memory used=4751.0MB, alloc=564.4MB, time=54.32 memory used=5020.9MB, alloc=564.4MB, time=58.24 memory used=5277.7MB, alloc=588.4MB, time=61.53 memory used=5553.1MB, alloc=612.4MB, time=65.37 memory used=5858.4MB, alloc=636.4MB, time=69.23 memory used=6169.7MB, alloc=660.4MB, time=74.06 memory used=6506.2MB, alloc=684.4MB, time=79.09 memory used=6863.0MB, alloc=708.4MB, time=84.15 memory used=7230.3MB, alloc=732.4MB, time=89.80 memory used=7531.5MB, alloc=756.4MB, time=95.63 memory used=7803.3MB, alloc=780.4MB, time=101.18 memory used=8103.1MB, alloc=804.4MB, time=107.28 memory used=8389.4MB, alloc=828.4MB, time=113.08 memory used=8670.7MB, alloc=852.4MB, time=118.48 memory used=8938.5MB, alloc=876.4MB, time=123.73 memory used=9211.1MB, alloc=900.4MB, time=129.00 memory used=9481.4MB, alloc=924.4MB, time=134.35 memory used=9736.1MB, alloc=948.4MB, time=139.43 memory used=9965.0MB, alloc=972.4MB, time=143.95 memory used=10460.3MB, alloc=996.4MB, time=152.72 memory used=10870.3MB, alloc=1020.4MB, time=165.81 memory used=11235.5MB, alloc=1044.4MB, time=180.21 memory used=11603.1MB, alloc=1068.4MB, time=195.30 memory used=11977.1MB, alloc=1092.4MB, time=211.00 memory used=12365.4MB, alloc=1116.4MB, time=227.40 memory used=12767.9MB, alloc=1140.4MB, time=244.49 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428493594 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 2 3 F := [-19 y + 6 y z + 2 z , 8 x z + 16 y z - 14 x y z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 3 2 3 G := [-4 x + 15 x y z + 8 y z , -5 x y z + 9 y z - 3 x y z] > Problem := [F,G]; 3 2 3 2 2 3 Problem := [[-19 y + 6 y z + 2 z , 8 x z + 16 y z - 14 x y z], 4 2 3 2 3 [-4 x + 15 x y z + 8 y z , -5 x y z + 9 y z - 3 x y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.5MB, alloc=32.3MB, time=0.50 memory used=46.7MB, alloc=32.3MB, time=0.81 memory used=65.5MB, alloc=56.3MB, time=1.03 memory used=104.2MB, alloc=62.2MB, time=1.50 memory used=136.8MB, alloc=62.2MB, time=2.00 memory used=180.3MB, alloc=62.2MB, time=3.00 memory used=221.8MB, alloc=62.2MB, time=3.41 memory used=260.9MB, alloc=62.2MB, time=3.69 memory used=296.0MB, alloc=62.2MB, time=4.51 memory used=323.2MB, alloc=62.2MB, time=4.65 memory used=365.7MB, alloc=62.2MB, time=5.68 memory used=392.8MB, alloc=62.2MB, time=5.80 memory used=420.6MB, alloc=62.2MB, time=5.94 memory used=468.3MB, alloc=70.2MB, time=6.52 memory used=508.3MB, alloc=70.2MB, time=6.96 memory used=555.5MB, alloc=70.2MB, time=7.68 memory used=600.5MB, alloc=70.2MB, time=8.11 memory used=640.8MB, alloc=70.2MB, time=8.66 memory used=680.3MB, alloc=94.2MB, time=9.27 memory used=743.2MB, alloc=94.2MB, time=10.04 memory used=788.0MB, alloc=94.2MB, time=10.32 memory used=825.8MB, alloc=94.2MB, time=10.43 memory used=866.1MB, alloc=94.2MB, time=10.72 memory used=899.3MB, alloc=94.2MB, time=10.84 memory used=935.2MB, alloc=94.2MB, time=10.96 memory used=980.3MB, alloc=107.8MB, time=18.67 memory used=997.2MB, alloc=107.8MB, time=20.58 memory used=1024.5MB, alloc=107.8MB, time=27.33 memory used=1039.4MB, alloc=107.8MB, time=27.41 memory used=1058.9MB, alloc=107.8MB, time=27.49 memory used=1069.8MB, alloc=107.8MB, time=27.55 memory used=1080.6MB, alloc=107.8MB, time=27.60 memory used=1091.8MB, alloc=107.8MB, time=27.66 memory used=1103.0MB, alloc=107.8MB, time=27.71 memory used=1114.3MB, alloc=107.8MB, time=27.77 memory used=1126.3MB, alloc=107.8MB, time=27.82 memory used=1138.6MB, alloc=107.8MB, time=27.88 memory used=1151.5MB, alloc=107.8MB, time=27.95 memory used=1195.1MB, alloc=107.8MB, time=28.25 memory used=1232.3MB, alloc=107.8MB, time=28.36 memory used=1272.7MB, alloc=107.8MB, time=28.63 memory used=1306.3MB, alloc=107.8MB, time=28.76 memory used=1342.7MB, alloc=107.8MB, time=28.86 memory used=1381.4MB, alloc=107.8MB, time=29.23 memory used=1414.7MB, alloc=107.8MB, time=36.79 memory used=1430.7MB, alloc=107.8MB, time=38.65 memory used=1457.7MB, alloc=107.8MB, time=41.41 memory used=1471.6MB, alloc=107.8MB, time=45.31 memory used=1492.6MB, alloc=107.8MB, time=45.42 memory used=1502.5MB, alloc=107.8MB, time=45.48 memory used=1512.5MB, alloc=107.8MB, time=45.53 memory used=1522.1MB, alloc=107.8MB, time=45.59 memory used=1532.0MB, alloc=107.8MB, time=45.65 memory used=1542.1MB, alloc=107.8MB, time=45.72 memory used=1552.9MB, alloc=107.8MB, time=45.77 memory used=1563.9MB, alloc=107.8MB, time=45.83 memory used=1574.7MB, alloc=107.8MB, time=45.89 memory used=1586.4MB, alloc=107.8MB, time=45.95 memory used=1630.4MB, alloc=107.8MB, time=47.81 memory used=1676.9MB, alloc=107.8MB, time=48.28 memory used=1716.9MB, alloc=107.8MB, time=48.44 memory used=1742.5MB, alloc=107.8MB, time=48.54 memory used=1771.5MB, alloc=107.8MB, time=48.64 memory used=1806.1MB, alloc=107.8MB, time=48.74 memory used=1845.8MB, alloc=107.8MB, time=48.87 memory used=1875.1MB, alloc=107.8MB, time=48.97 memory used=1899.3MB, alloc=107.8MB, time=49.07 memory used=1926.6MB, alloc=107.8MB, time=49.17 memory used=1967.6MB, alloc=107.8MB, time=50.29 memory used=1992.5MB, alloc=131.8MB, time=51.28 memory used=2039.5MB, alloc=131.8MB, time=51.70 memory used=2089.0MB, alloc=131.8MB, time=51.86 memory used=2146.0MB, alloc=131.8MB, time=52.03 memory used=2201.2MB, alloc=131.8MB, time=52.19 memory used=2237.7MB, alloc=131.8MB, time=52.31 memory used=2271.2MB, alloc=131.8MB, time=52.45 memory used=2306.5MB, alloc=131.8MB, time=52.58 memory used=2342.8MB, alloc=131.8MB, time=52.70 memory used=2382.8MB, alloc=131.8MB, time=52.83 memory used=2423.3MB, alloc=131.8MB, time=52.95 memory used=2464.7MB, alloc=131.8MB, time=53.08 memory used=2509.5MB, alloc=131.8MB, time=53.20 memory used=2555.0MB, alloc=131.8MB, time=53.32 memory used=2604.0MB, alloc=131.8MB, time=53.45 memory used=2656.3MB, alloc=131.8MB, time=53.58 memory used=2708.9MB, alloc=131.8MB, time=53.70 memory used=2764.6MB, alloc=131.8MB, time=53.85 memory used=2823.2MB, alloc=131.8MB, time=53.99 memory used=2875.8MB, alloc=131.8MB, time=54.12 memory used=2910.3MB, alloc=131.8MB, time=54.22 memory used=2939.7MB, alloc=131.8MB, time=54.31 memory used=2969.9MB, alloc=131.8MB, time=54.40 memory used=3002.1MB, alloc=131.8MB, time=54.49 memory used=3034.1MB, alloc=131.8MB, time=54.58 memory used=3068.0MB, alloc=131.8MB, time=54.68 memory used=3103.8MB, alloc=131.8MB, time=54.77 memory used=3141.1MB, alloc=131.8MB, time=54.86 memory used=3179.6MB, alloc=131.8MB, time=54.95 memory used=3218.6MB, alloc=131.8MB, time=55.05 memory used=3260.0MB, alloc=131.8MB, time=55.14 memory used=3302.4MB, alloc=131.8MB, time=55.24 memory used=3347.8MB, alloc=131.8MB, time=55.34 memory used=3395.7MB, alloc=131.8MB, time=55.45 memory used=3448.4MB, alloc=131.8MB, time=55.87 memory used=3480.2MB, alloc=131.8MB, time=56.02 memory used=3538.0MB, alloc=131.8MB, time=56.15 memory used=3566.4MB, alloc=131.8MB, time=58.71 memory used=3576.9MB, alloc=131.8MB, time=60.48 memory used=3582.1MB, alloc=131.8MB, time=60.56 memory used=3588.7MB, alloc=131.8MB, time=61.29 memory used=3590.0MB, alloc=387.8MB, time=61.33 memory used=3881.6MB, alloc=387.8MB, time=125.04 memory used=4144.4MB, alloc=387.8MB, time=126.95 memory used=4201.6MB, alloc=387.8MB, time=127.21 memory used=4264.0MB, alloc=387.8MB, time=127.48 memory used=4312.3MB, alloc=387.8MB, time=127.62 memory used=4374.8MB, alloc=387.8MB, time=127.88 memory used=4430.9MB, alloc=387.8MB, time=128.11 memory used=5624.6MB, alloc=387.8MB, time=133.48 memory used=5674.4MB, alloc=387.8MB, time=133.62 memory used=7207.2MB, alloc=387.8MB, time=140.66 memory used=7254.6MB, alloc=387.8MB, time=140.81 memory used=7311.6MB, alloc=387.8MB, time=140.97 memory used=7357.0MB, alloc=387.8MB, time=141.11 memory used=7396.6MB, alloc=387.8MB, time=141.25 memory used=7442.0MB, alloc=387.8MB, time=141.38 memory used=7495.1MB, alloc=387.8MB, time=141.52 memory used=7550.8MB, alloc=387.8MB, time=141.65 memory used=7593.1MB, alloc=387.8MB, time=141.75 memory used=7648.0MB, alloc=387.8MB, time=142.60 memory used=7704.3MB, alloc=387.8MB, time=142.75 memory used=7743.7MB, alloc=387.8MB, time=142.88 memory used=7790.3MB, alloc=387.8MB, time=142.98 memory used=7844.3MB, alloc=387.8MB, time=143.11 memory used=7906.7MB, alloc=387.8MB, time=143.25 memory used=7943.4MB, alloc=387.8MB, time=143.34 memory used=7982.7MB, alloc=387.8MB, time=143.44 memory used=9356.8MB, alloc=387.8MB, time=146.80 memory used=13110.4MB, alloc=387.8MB, time=156.41 memory used=13203.6MB, alloc=387.8MB, time=163.28 memory used=13276.7MB, alloc=387.8MB, time=163.50 memory used=13349.0MB, alloc=387.8MB, time=163.67 memory used=13477.9MB, alloc=387.8MB, time=164.02 memory used=13579.0MB, alloc=387.8MB, time=164.18 memory used=13779.5MB, alloc=387.8MB, time=165.11 memory used=13891.6MB, alloc=387.8MB, time=166.09 memory used=13991.4MB, alloc=387.8MB, time=166.91 memory used=14087.3MB, alloc=387.8MB, time=167.97 memory used=14200.6MB, alloc=387.8MB, time=168.66 memory used=14288.1MB, alloc=387.8MB, time=179.03 memory used=14348.1MB, alloc=387.8MB, time=197.73 memory used=14398.5MB, alloc=387.8MB, time=198.31 memory used=14436.9MB, alloc=387.8MB, time=198.42 memory used=14487.4MB, alloc=387.8MB, time=198.54 memory used=14523.5MB, alloc=387.8MB, time=198.63 memory used=14686.4MB, alloc=387.8MB, time=202.70 memory used=14762.3MB, alloc=387.8MB, time=203.30 memory used=14847.7MB, alloc=387.8MB, time=203.86 memory used=14954.6MB, alloc=387.8MB, time=204.40 memory used=15056.0MB, alloc=387.8MB, time=205.26 memory used=15114.8MB, alloc=387.8MB, time=205.63 memory used=15159.3MB, alloc=387.8MB, time=205.76 memory used=15211.9MB, alloc=387.8MB, time=206.06 memory used=15256.2MB, alloc=387.8MB, time=206.21 memory used=15499.2MB, alloc=387.8MB, time=223.41 memory used=15554.0MB, alloc=387.8MB, time=223.63 memory used=15603.6MB, alloc=387.8MB, time=223.75 memory used=15663.4MB, alloc=387.8MB, time=223.92 memory used=15787.5MB, alloc=387.8MB, time=224.27 memory used=15887.1MB, alloc=387.8MB, time=224.45 memory used=15970.4MB, alloc=387.8MB, time=224.59 memory used=16201.7MB, alloc=387.8MB, time=225.26 memory used=16353.3MB, alloc=387.8MB, time=225.50 memory used=16606.2MB, alloc=387.8MB, time=225.84 memory used=16816.8MB, alloc=387.8MB, time=226.10 memory used=17048.7MB, alloc=387.8MB, time=226.37 memory used=17257.9MB, alloc=387.8MB, time=226.62 memory used=17345.3MB, alloc=387.8MB, time=227.35 memory used=17389.1MB, alloc=387.8MB, time=227.48 memory used=17441.3MB, alloc=387.8MB, time=227.83 memory used=17490.7MB, alloc=387.8MB, time=228.15 memory used=17538.0MB, alloc=387.8MB, time=228.29 memory used=17586.0MB, alloc=387.8MB, time=228.50 memory used=17676.0MB, alloc=387.8MB, time=241.46 memory used=17872.6MB, alloc=387.8MB, time=248.24 memory used=17937.8MB, alloc=387.8MB, time=248.79 memory used=17975.6MB, alloc=387.8MB, time=248.95 memory used=18013.7MB, alloc=387.8MB, time=249.09 memory used=18059.1MB, alloc=387.8MB, time=249.25 memory used=18105.5MB, alloc=387.8MB, time=249.39 memory used=18135.5MB, alloc=387.8MB, time=249.51 memory used=18170.2MB, alloc=387.8MB, time=249.62 memory used=18219.7MB, alloc=411.8MB, time=251.46 memory used=18273.0MB, alloc=411.8MB, time=252.21 memory used=18333.3MB, alloc=411.8MB, time=252.40 memory used=18401.9MB, alloc=411.8MB, time=252.60 memory used=18457.3MB, alloc=411.8MB, time=252.77 memory used=18497.7MB, alloc=411.8MB, time=252.93 memory used=18540.3MB, alloc=411.8MB, time=253.09 memory used=18585.5MB, alloc=411.8MB, time=253.23 memory used=18631.8MB, alloc=411.8MB, time=253.39 memory used=18682.0MB, alloc=411.8MB, time=253.54 memory used=18733.1MB, alloc=411.8MB, time=253.70 memory used=18788.1MB, alloc=411.8MB, time=253.86 memory used=18846.8MB, alloc=411.8MB, time=254.02 memory used=18909.1MB, alloc=411.8MB, time=254.19 memory used=18974.7MB, alloc=411.8MB, time=254.37 memory used=19043.3MB, alloc=411.8MB, time=254.57 memory used=19109.7MB, alloc=411.8MB, time=254.73 memory used=19153.5MB, alloc=411.8MB, time=254.85 memory used=19191.2MB, alloc=411.8MB, time=254.98 memory used=19229.6MB, alloc=411.8MB, time=255.10 memory used=19270.0MB, alloc=411.8MB, time=255.22 memory used=19312.2MB, alloc=411.8MB, time=255.35 memory used=19355.6MB, alloc=411.8MB, time=255.46 memory used=19399.8MB, alloc=411.8MB, time=255.59 memory used=19446.7MB, alloc=411.8MB, time=255.71 memory used=19495.1MB, alloc=411.8MB, time=255.83 memory used=19545.5MB, alloc=411.8MB, time=255.96 memory used=19600.3MB, alloc=411.8MB, time=256.09 memory used=19664.7MB, alloc=411.8MB, time=256.47 memory used=19734.3MB, alloc=411.8MB, time=256.70 memory used=19873.8MB, alloc=411.8MB, time=257.06 memory used=19981.0MB, alloc=411.8MB, time=257.25 memory used=20247.1MB, alloc=411.8MB, time=316.40 memory used=20481.7MB, alloc=411.8MB, time=334.62 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428493894 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 2 F := [-13 x z + 19 x y z + 18 x z , -19 x z + 14 y z + 9 z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 3 2 G := [-5 x z + 8 y z + 18 x y, -17 y z - 11 x z - 20 y] > Problem := [F,G]; 3 2 3 2 2 Problem := [[-13 x z + 19 x y z + 18 x z , -19 x z + 14 y z + 9 z ], 3 3 2 3 2 [-5 x z + 8 y z + 18 x y, -17 y z - 11 x z - 20 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=27.3MB, alloc=32.3MB, time=0.51 memory used=48.2MB, alloc=60.3MB, time=0.83 memory used=89.8MB, alloc=60.3MB, time=1.43 memory used=130.8MB, alloc=92.3MB, time=2.03 memory used=189.1MB, alloc=92.3MB, time=2.47 memory used=234.3MB, alloc=92.3MB, time=2.72 memory used=301.9MB, alloc=92.3MB, time=3.58 memory used=365.5MB, alloc=92.3MB, time=4.50 memory used=431.6MB, alloc=116.3MB, time=5.38 memory used=511.3MB, alloc=116.3MB, time=6.31 memory used=561.1MB, alloc=372.3MB, time=7.00 memory used=650.8MB, alloc=396.3MB, time=8.13 memory used=756.8MB, alloc=396.3MB, time=9.49 memory used=873.5MB, alloc=420.3MB, time=10.92 memory used=1002.0MB, alloc=420.3MB, time=12.19 memory used=1118.1MB, alloc=420.3MB, time=13.44 memory used=1234.3MB, alloc=420.3MB, time=14.42 memory used=1304.7MB, alloc=420.3MB, time=14.93 memory used=1372.2MB, alloc=420.3MB, time=15.35 memory used=1442.3MB, alloc=420.3MB, time=15.77 memory used=1493.6MB, alloc=444.3MB, time=16.02 memory used=1582.7MB, alloc=444.3MB, time=16.79 memory used=1658.2MB, alloc=444.3MB, time=17.11 memory used=1723.5MB, alloc=444.3MB, time=17.39 memory used=1804.2MB, alloc=444.3MB, time=17.70 memory used=1877.9MB, alloc=444.3MB, time=17.97 memory used=1931.0MB, alloc=444.3MB, time=18.20 memory used=1989.5MB, alloc=444.3MB, time=18.44 memory used=2053.7MB, alloc=444.3MB, time=18.67 memory used=2126.0MB, alloc=444.3MB, time=18.91 memory used=2205.8MB, alloc=444.3MB, time=19.16 memory used=2297.5MB, alloc=444.3MB, time=19.41 memory used=2435.8MB, alloc=444.3MB, time=20.33 memory used=2525.8MB, alloc=444.3MB, time=20.87 memory used=2617.1MB, alloc=444.3MB, time=21.41 memory used=2687.7MB, alloc=444.3MB, time=21.70 memory used=2777.0MB, alloc=444.3MB, time=22.47 memory used=2851.9MB, alloc=444.3MB, time=22.78 memory used=2914.3MB, alloc=444.3MB, time=23.06 memory used=2993.4MB, alloc=444.3MB, time=23.36 memory used=3069.1MB, alloc=444.3MB, time=23.64 memory used=3122.8MB, alloc=444.3MB, time=23.87 memory used=3180.6MB, alloc=444.3MB, time=24.11 memory used=3245.7MB, alloc=444.3MB, time=24.35 memory used=3317.3MB, alloc=444.3MB, time=24.60 memory used=3397.7MB, alloc=444.3MB, time=24.86 memory used=3541.4MB, alloc=444.3MB, time=25.21 memory used=3673.3MB, alloc=444.3MB, time=32.96 memory used=3746.2MB, alloc=444.3MB, time=33.26 memory used=3814.7MB, alloc=444.3MB, time=33.52 memory used=3877.7MB, alloc=444.3MB, time=33.76 memory used=3954.8MB, alloc=444.3MB, time=34.02 memory used=4214.4MB, alloc=444.3MB, time=35.14 memory used=4339.3MB, alloc=444.3MB, time=36.29 memory used=4477.3MB, alloc=444.3MB, time=37.40 memory used=4575.6MB, alloc=444.3MB, time=38.14 memory used=4644.5MB, alloc=444.3MB, time=38.44 memory used=4728.3MB, alloc=444.3MB, time=38.75 memory used=4781.7MB, alloc=444.3MB, time=39.00 memory used=4845.0MB, alloc=444.3MB, time=39.26 memory used=4923.3MB, alloc=444.3MB, time=39.65 memory used=5026.2MB, alloc=444.3MB, time=40.14 memory used=5117.9MB, alloc=444.3MB, time=40.68 memory used=5222.7MB, alloc=444.3MB, time=41.86 memory used=5357.6MB, alloc=444.3MB, time=43.05 memory used=5445.6MB, alloc=444.3MB, time=43.62 memory used=5508.6MB, alloc=444.3MB, time=43.93 memory used=5584.2MB, alloc=444.3MB, time=44.24 memory used=5636.6MB, alloc=444.3MB, time=44.53 memory used=5699.0MB, alloc=444.3MB, time=44.82 memory used=5776.9MB, alloc=444.3MB, time=45.26 memory used=5862.0MB, alloc=444.3MB, time=45.72 memory used=5947.6MB, alloc=444.3MB, time=46.28 memory used=6073.1MB, alloc=444.3MB, time=47.57 memory used=6190.4MB, alloc=468.3MB, time=48.86 memory used=6288.1MB, alloc=468.3MB, time=50.09 memory used=6428.9MB, alloc=468.3MB, time=51.40 memory used=6522.1MB, alloc=468.3MB, time=51.91 memory used=6606.1MB, alloc=468.3MB, time=52.28 memory used=6680.4MB, alloc=468.3MB, time=52.62 memory used=6760.9MB, alloc=468.3MB, time=53.10 memory used=6863.1MB, alloc=468.3MB, time=54.22 memory used=6968.9MB, alloc=468.3MB, time=55.47 memory used=7091.7MB, alloc=468.3MB, time=56.50 memory used=7168.9MB, alloc=468.3MB, time=56.91 memory used=7257.7MB, alloc=468.3MB, time=57.30 memory used=7322.7MB, alloc=468.3MB, time=57.65 memory used=7451.7MB, alloc=468.3MB, time=58.81 memory used=7535.7MB, alloc=468.3MB, time=59.98 memory used=7619.5MB, alloc=468.3MB, time=61.21 memory used=7702.0MB, alloc=492.3MB, time=62.57 memory used=7774.8MB, alloc=492.3MB, time=63.71 memory used=7844.6MB, alloc=492.3MB, time=64.97 memory used=7904.6MB, alloc=492.3MB, time=66.04 memory used=7963.2MB, alloc=492.3MB, time=67.11 memory used=8028.9MB, alloc=492.3MB, time=68.30 memory used=8083.2MB, alloc=492.3MB, time=69.23 memory used=8140.9MB, alloc=492.3MB, time=70.17 memory used=8183.8MB, alloc=492.3MB, time=71.14 memory used=8220.9MB, alloc=492.3MB, time=71.96 memory used=8389.2MB, alloc=516.3MB, time=74.06 memory used=8483.6MB, alloc=516.3MB, time=74.62 memory used=8672.3MB, alloc=516.3MB, time=77.63 memory used=8895.6MB, alloc=540.3MB, time=81.29 memory used=9046.3MB, alloc=540.3MB, time=82.54 memory used=9159.1MB, alloc=540.3MB, time=83.25 memory used=9259.8MB, alloc=540.3MB, time=83.79 memory used=9370.4MB, alloc=540.3MB, time=84.90 memory used=9472.1MB, alloc=540.3MB, time=85.49 memory used=9582.7MB, alloc=540.3MB, time=86.07 memory used=9663.1MB, alloc=540.3MB, time=86.58 memory used=9757.0MB, alloc=540.3MB, time=87.12 memory used=9865.7MB, alloc=540.3MB, time=87.67 memory used=9988.6MB, alloc=540.3MB, time=88.21 memory used=10173.4MB, alloc=540.3MB, time=88.89 memory used=10310.6MB, alloc=540.3MB, time=89.49 memory used=10464.3MB, alloc=540.3MB, time=90.12 memory used=10641.7MB, alloc=540.3MB, time=90.73 memory used=10846.3MB, alloc=540.3MB, time=99.85 memory used=10938.7MB, alloc=540.3MB, time=100.38 memory used=11054.7MB, alloc=540.3MB, time=100.92 memory used=11222.0MB, alloc=540.3MB, time=101.57 memory used=11385.2MB, alloc=540.3MB, time=102.19 memory used=11590.8MB, alloc=540.3MB, time=102.84 memory used=11785.7MB, alloc=540.3MB, time=104.03 memory used=12064.1MB, alloc=540.3MB, time=105.31 memory used=12237.7MB, alloc=540.3MB, time=107.21 memory used=12341.2MB, alloc=540.3MB, time=108.08 memory used=12445.8MB, alloc=540.3MB, time=108.60 memory used=12663.6MB, alloc=564.3MB, time=111.33 memory used=12908.6MB, alloc=564.3MB, time=115.22 memory used=13111.4MB, alloc=588.3MB, time=117.56 memory used=13238.2MB, alloc=588.3MB, time=118.50 memory used=13381.0MB, alloc=588.3MB, time=119.76 memory used=13519.6MB, alloc=588.3MB, time=120.73 memory used=13647.3MB, alloc=588.3MB, time=121.43 memory used=13761.8MB, alloc=588.3MB, time=122.31 memory used=13889.8MB, alloc=588.3MB, time=123.24 memory used=14013.9MB, alloc=588.3MB, time=123.95 memory used=14114.4MB, alloc=588.3MB, time=124.58 memory used=14234.4MB, alloc=588.3MB, time=125.22 memory used=14376.2MB, alloc=588.3MB, time=125.86 memory used=14573.3MB, alloc=588.3MB, time=126.62 memory used=14711.2MB, alloc=588.3MB, time=127.28 memory used=14864.8MB, alloc=588.3MB, time=127.95 memory used=15042.7MB, alloc=588.3MB, time=128.65 memory used=15302.0MB, alloc=588.3MB, time=137.42 memory used=15410.8MB, alloc=588.3MB, time=138.04 memory used=15649.0MB, alloc=588.3MB, time=138.87 memory used=15813.6MB, alloc=588.3MB, time=139.56 memory used=16015.8MB, alloc=588.3MB, time=140.26 memory used=16215.6MB, alloc=588.3MB, time=141.71 memory used=16354.8MB, alloc=588.3MB, time=142.93 memory used=16472.7MB, alloc=588.3MB, time=143.56 memory used=16606.3MB, alloc=588.3MB, time=144.62 memory used=16865.3MB, alloc=588.3MB, time=147.16 memory used=17040.2MB, alloc=588.3MB, time=148.82 memory used=17337.3MB, alloc=612.3MB, time=153.36 memory used=17579.3MB, alloc=612.3MB, time=157.62 memory used=17787.1MB, alloc=612.3MB, time=160.17 memory used=17965.2MB, alloc=612.3MB, time=161.59 memory used=18128.6MB, alloc=636.3MB, time=163.63 memory used=18317.1MB, alloc=636.3MB, time=165.04 memory used=18517.5MB, alloc=636.3MB, time=167.29 memory used=18672.2MB, alloc=636.3MB, time=169.82 memory used=18877.9MB, alloc=660.3MB, time=172.08 memory used=19103.9MB, alloc=660.3MB, time=174.47 memory used=19224.6MB, alloc=660.3MB, time=176.78 memory used=19453.9MB, alloc=660.3MB, time=179.04 memory used=19623.7MB, alloc=660.3MB, time=180.42 memory used=19813.6MB, alloc=684.3MB, time=182.46 memory used=19928.4MB, alloc=684.3MB, time=184.76 memory used=20104.6MB, alloc=684.3MB, time=187.59 memory used=20195.8MB, alloc=684.3MB, time=189.23 memory used=20297.3MB, alloc=684.3MB, time=191.11 memory used=20426.9MB, alloc=684.3MB, time=194.01 memory used=20581.3MB, alloc=684.3MB, time=195.81 memory used=20868.4MB, alloc=708.3MB, time=199.10 memory used=21238.0MB, alloc=732.3MB, time=203.51 memory used=21553.1MB, alloc=732.3MB, time=206.22 memory used=21877.0MB, alloc=756.3MB, time=207.75 memory used=22256.2MB, alloc=756.3MB, time=209.96 memory used=22692.7MB, alloc=756.3MB, time=211.56 memory used=23193.1MB, alloc=756.3MB, time=215.26 memory used=23538.5MB, alloc=756.3MB, time=217.74 memory used=23873.7MB, alloc=756.3MB, time=219.96 memory used=24218.5MB, alloc=756.3MB, time=221.50 memory used=24597.1MB, alloc=756.3MB, time=224.48 memory used=25004.9MB, alloc=780.3MB, time=229.68 memory used=25430.8MB, alloc=804.3MB, time=236.22 memory used=25824.7MB, alloc=828.3MB, time=243.84 memory used=26232.6MB, alloc=852.3MB, time=251.58 memory used=26733.6MB, alloc=876.3MB, time=259.12 memory used=27213.5MB, alloc=900.3MB, time=267.49 memory used=27685.7MB, alloc=924.3MB, time=275.93 memory used=28195.7MB, alloc=948.3MB, time=284.55 memory used=28671.8MB, alloc=972.3MB, time=293.06 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428494194 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 2 2 F := [-18 x y + 15 z + 3 y z, -16 y z - 4 y z + 15 x ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 3 2 G := [16 x z + 14 x y + 5 x y, -y z - 8 x - 13 x y ] > Problem := [F,G]; 2 2 3 2 2 2 2 Problem := [[-18 x y + 15 z + 3 y z, -16 y z - 4 y z + 15 x ], 2 2 2 2 3 2 [16 x z + 14 x y + 5 x y, -y z - 8 x - 13 x y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=25.9MB, alloc=32.3MB, time=0.44 memory used=48.2MB, alloc=32.3MB, time=0.70 memory used=68.9MB, alloc=36.3MB, time=0.93 memory used=92.7MB, alloc=36.3MB, time=1.18 memory used=112.9MB, alloc=60.3MB, time=1.43 memory used=165.8MB, alloc=68.3MB, time=1.99 memory used=210.8MB, alloc=68.3MB, time=2.57 memory used=253.0MB, alloc=68.3MB, time=3.07 memory used=290.4MB, alloc=68.3MB, time=3.36 memory used=312.3MB, alloc=68.3MB, time=3.45 memory used=337.2MB, alloc=92.3MB, time=4.80 memory used=384.2MB, alloc=92.3MB, time=5.79 memory used=422.2MB, alloc=92.3MB, time=5.95 memory used=441.4MB, alloc=107.8MB, time=6.08 memory used=487.8MB, alloc=107.8MB, time=6.19 memory used=542.8MB, alloc=107.8MB, time=6.77 memory used=615.6MB, alloc=107.8MB, time=9.99 memory used=649.0MB, alloc=107.8MB, time=10.10 memory used=704.9MB, alloc=107.8MB, time=10.58 memory used=784.3MB, alloc=107.8MB, time=13.44 memory used=825.2MB, alloc=107.8MB, time=13.70 memory used=896.4MB, alloc=107.8MB, time=14.42 memory used=957.2MB, alloc=107.8MB, time=15.06 memory used=1001.0MB, alloc=131.8MB, time=15.36 memory used=1046.6MB, alloc=131.8MB, time=15.51 memory used=1102.5MB, alloc=131.8MB, time=18.36 memory used=1164.0MB, alloc=131.8MB, time=18.80 memory used=1215.6MB, alloc=131.8MB, time=18.96 memory used=1266.8MB, alloc=131.8MB, time=21.76 memory used=1322.0MB, alloc=131.8MB, time=21.95 memory used=1406.5MB, alloc=387.8MB, time=22.71 memory used=1501.7MB, alloc=387.8MB, time=28.19 memory used=1546.1MB, alloc=387.8MB, time=28.34 memory used=1589.0MB, alloc=387.8MB, time=28.46 memory used=1688.9MB, alloc=387.8MB, time=29.33 memory used=1772.8MB, alloc=387.8MB, time=34.17 memory used=1812.7MB, alloc=387.8MB, time=34.35 memory used=1882.7MB, alloc=387.8MB, time=34.86 memory used=1989.1MB, alloc=387.8MB, time=35.66 memory used=2079.8MB, alloc=411.8MB, time=36.78 memory used=2187.1MB, alloc=411.8MB, time=38.19 memory used=2306.3MB, alloc=435.8MB, time=39.51 memory used=2434.6MB, alloc=435.8MB, time=41.28 memory used=2562.1MB, alloc=459.8MB, time=42.90 memory used=2688.2MB, alloc=459.8MB, time=44.33 memory used=2783.1MB, alloc=459.8MB, time=45.03 memory used=2860.4MB, alloc=459.8MB, time=45.35 memory used=2928.5MB, alloc=459.8MB, time=45.62 memory used=2986.0MB, alloc=459.8MB, time=45.86 memory used=3058.5MB, alloc=459.8MB, time=46.12 memory used=3155.4MB, alloc=459.8MB, time=58.63 memory used=3238.2MB, alloc=459.8MB, time=60.79 memory used=3299.1MB, alloc=459.8MB, time=61.03 memory used=3372.8MB, alloc=459.8MB, time=61.29 memory used=3423.7MB, alloc=459.8MB, time=61.51 memory used=3482.6MB, alloc=459.8MB, time=61.73 memory used=3551.4MB, alloc=459.8MB, time=61.96 memory used=3681.8MB, alloc=459.8MB, time=62.64 memory used=3754.8MB, alloc=459.8MB, time=62.93 memory used=3839.6MB, alloc=459.8MB, time=63.94 memory used=3907.6MB, alloc=459.8MB, time=64.20 memory used=3990.5MB, alloc=459.8MB, time=64.63 memory used=4055.6MB, alloc=459.8MB, time=64.89 memory used=4139.7MB, alloc=459.8MB, time=65.93 memory used=4242.0MB, alloc=459.8MB, time=66.82 memory used=4440.2MB, alloc=459.8MB, time=70.32 memory used=4509.7MB, alloc=459.8MB, time=70.61 memory used=4567.8MB, alloc=459.8MB, time=70.86 memory used=4642.5MB, alloc=459.8MB, time=71.16 memory used=4704.1MB, alloc=483.8MB, time=71.41 memory used=4768.6MB, alloc=483.8MB, time=71.64 memory used=4841.5MB, alloc=483.8MB, time=71.87 memory used=4923.4MB, alloc=483.8MB, time=72.12 memory used=5014.7MB, alloc=483.8MB, time=72.36 memory used=5118.0MB, alloc=483.8MB, time=72.62 memory used=5281.9MB, alloc=483.8MB, time=73.12 memory used=5474.8MB, alloc=483.8MB, time=74.89 memory used=5545.9MB, alloc=483.8MB, time=75.22 memory used=5629.7MB, alloc=483.8MB, time=75.57 memory used=5727.1MB, alloc=483.8MB, time=75.92 memory used=5802.4MB, alloc=483.8MB, time=76.23 memory used=5863.0MB, alloc=507.8MB, time=76.52 memory used=5937.4MB, alloc=507.8MB, time=76.82 memory used=6019.0MB, alloc=507.8MB, time=77.12 memory used=6104.8MB, alloc=507.8MB, time=77.43 memory used=6197.9MB, alloc=507.8MB, time=77.75 memory used=6300.4MB, alloc=507.8MB, time=78.08 memory used=6411.4MB, alloc=507.8MB, time=78.41 memory used=6525.7MB, alloc=507.8MB, time=78.75 memory used=6650.3MB, alloc=507.8MB, time=79.11 memory used=6723.8MB, alloc=507.8MB, time=79.38 memory used=6791.9MB, alloc=507.8MB, time=79.61 memory used=6858.0MB, alloc=507.8MB, time=79.85 memory used=6926.0MB, alloc=507.8MB, time=80.08 memory used=6994.7MB, alloc=507.8MB, time=80.32 memory used=7066.7MB, alloc=507.8MB, time=80.58 memory used=7144.8MB, alloc=507.8MB, time=80.83 memory used=7222.4MB, alloc=507.8MB, time=81.10 memory used=7303.5MB, alloc=507.8MB, time=81.35 memory used=7388.2MB, alloc=507.8MB, time=81.60 memory used=7476.1MB, alloc=507.8MB, time=81.84 memory used=7568.9MB, alloc=507.8MB, time=82.11 memory used=7667.6MB, alloc=507.8MB, time=82.35 memory used=7772.7MB, alloc=507.8MB, time=82.62 memory used=7884.8MB, alloc=507.8MB, time=82.88 memory used=8028.5MB, alloc=507.8MB, time=118.92 memory used=8164.1MB, alloc=507.8MB, time=216.18 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428494494 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 4 2 F := [5 x y - 10 x z + 9 y z, -10 x + 4 x y z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 G := [10 x z - 19 x , -12 x y - y z - 5 x y] > Problem := [F,G]; 3 3 2 4 2 Problem := [[5 x y - 10 x z + 9 y z, -10 x + 4 x y z], 3 2 2 2 2 [10 x z - 19 x , -12 x y - y z - 5 x y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.7MB, alloc=32.3MB, time=0.50 memory used=46.2MB, alloc=56.3MB, time=0.80 memory used=87.2MB, alloc=60.3MB, time=1.39 memory used=127.2MB, alloc=84.3MB, time=1.97 memory used=165.7MB, alloc=84.3MB, time=2.53 memory used=232.1MB, alloc=92.3MB, time=3.47 memory used=295.9MB, alloc=116.3MB, time=4.37 memory used=366.8MB, alloc=116.3MB, time=5.36 memory used=433.3MB, alloc=372.3MB, time=6.35 memory used=519.0MB, alloc=396.3MB, time=7.58 memory used=634.8MB, alloc=420.3MB, time=9.09 memory used=768.3MB, alloc=444.3MB, time=11.24 memory used=906.3MB, alloc=468.3MB, time=13.62 memory used=1068.6MB, alloc=492.3MB, time=16.38 memory used=1240.5MB, alloc=516.3MB, time=19.34 memory used=1429.0MB, alloc=540.3MB, time=22.57 memory used=1609.6MB, alloc=564.3MB, time=27.96 memory used=1791.9MB, alloc=588.3MB, time=34.15 memory used=1982.0MB, alloc=612.3MB, time=41.34 memory used=2186.2MB, alloc=636.3MB, time=49.49 memory used=2414.4MB, alloc=660.3MB, time=58.64 memory used=2666.5MB, alloc=684.3MB, time=68.57 memory used=2942.5MB, alloc=684.3MB, time=79.39 memory used=3218.5MB, alloc=684.3MB, time=90.27 memory used=3494.5MB, alloc=708.3MB, time=101.18 memory used=3794.3MB, alloc=708.3MB, time=112.94 memory used=4094.1MB, alloc=732.3MB, time=124.32 N1 := 9183 > GB := Basis(F, plex(op(vars))); 7 5 2 4 2 5 5 4 4 2 GB := [-10 x + 2 x y + 9 x y , -2 x y + 4 x z - 9 x y, -5 x + 2 x y z, 3 3 2 -10 z x + 5 y x + 9 z y ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=4274.6MB, alloc=732.3MB, time=128.17 memory used=4390.5MB, alloc=732.3MB, time=130.29 memory used=4501.1MB, alloc=732.3MB, time=132.25 memory used=4607.6MB, alloc=732.3MB, time=134.30 memory used=4710.1MB, alloc=732.3MB, time=136.22 memory used=4792.7MB, alloc=732.3MB, time=137.97 memory used=4870.7MB, alloc=732.3MB, time=139.71 memory used=4953.2MB, alloc=732.3MB, time=141.49 memory used=5028.1MB, alloc=732.3MB, time=143.15 memory used=5100.3MB, alloc=732.3MB, time=144.76 memory used=5170.1MB, alloc=732.3MB, time=146.37 memory used=5233.0MB, alloc=732.3MB, time=147.97 memory used=5288.4MB, alloc=732.3MB, time=149.34 memory used=5342.2MB, alloc=732.3MB, time=150.68 memory used=5391.4MB, alloc=732.3MB, time=152.10 memory used=5435.6MB, alloc=732.3MB, time=153.38 memory used=5471.0MB, alloc=732.3MB, time=154.53 memory used=5701.1MB, alloc=732.3MB, time=158.11 memory used=5974.5MB, alloc=756.3MB, time=162.78 memory used=6334.0MB, alloc=780.3MB, time=169.12 memory used=6641.6MB, alloc=804.3MB, time=175.23 memory used=6950.5MB, alloc=828.3MB, time=181.29 memory used=7250.0MB, alloc=852.3MB, time=187.41 memory used=7521.0MB, alloc=876.3MB, time=192.99 memory used=7821.9MB, alloc=900.3MB, time=198.88 memory used=8216.3MB, alloc=924.3MB, time=213.25 memory used=8589.4MB, alloc=948.3MB, time=228.77 memory used=8967.6MB, alloc=972.3MB, time=244.89 memory used=9355.4MB, alloc=996.3MB, time=261.82 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428494794 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 3 3 F := [-7 y z - 14 x z + 8 z, -2 y z - 7 x - 4 y ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 3 2 G := [-15 x z - 10 y z - 15 x z, 3 x y z + 19 y z + 18 y ] > Problem := [F,G]; 2 2 2 2 3 3 Problem := [[-7 y z - 14 x z + 8 z, -2 y z - 7 x - 4 y ], 3 2 2 2 3 2 [-15 x z - 10 y z - 15 x z, 3 x y z + 19 y z + 18 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.5MB, alloc=32.3MB, time=0.49 memory used=47.5MB, alloc=32.3MB, time=0.81 memory used=66.8MB, alloc=56.3MB, time=1.11 memory used=108.0MB, alloc=68.3MB, time=1.73 memory used=150.1MB, alloc=92.3MB, time=2.31 memory used=216.7MB, alloc=92.3MB, time=3.15 memory used=287.8MB, alloc=92.3MB, time=3.92 memory used=352.1MB, alloc=116.3MB, time=4.83 memory used=434.5MB, alloc=117.6MB, time=5.50 memory used=504.0MB, alloc=117.6MB, time=5.91 memory used=570.3MB, alloc=373.6MB, time=6.75 memory used=653.4MB, alloc=373.6MB, time=7.55 memory used=705.8MB, alloc=373.6MB, time=7.92 memory used=754.6MB, alloc=373.6MB, time=8.19 memory used=807.6MB, alloc=373.6MB, time=8.56 memory used=889.8MB, alloc=373.6MB, time=9.30 memory used=930.4MB, alloc=373.6MB, time=9.48 memory used=978.1MB, alloc=373.6MB, time=9.71 memory used=1028.3MB, alloc=373.6MB, time=10.37 memory used=1121.2MB, alloc=397.6MB, time=11.49 memory used=1238.8MB, alloc=397.6MB, time=13.08 memory used=1360.1MB, alloc=421.6MB, time=14.49 memory used=1495.9MB, alloc=421.6MB, time=15.65 memory used=1628.4MB, alloc=421.6MB, time=17.55 memory used=1746.0MB, alloc=445.6MB, time=19.55 memory used=1889.8MB, alloc=469.6MB, time=21.86 memory used=2050.9MB, alloc=493.6MB, time=24.41 memory used=2233.9MB, alloc=517.6MB, time=27.03 memory used=2418.1MB, alloc=541.6MB, time=30.20 memory used=2597.5MB, alloc=565.6MB, time=35.20 memory used=2773.4MB, alloc=589.6MB, time=41.24 memory used=2956.1MB, alloc=613.6MB, time=48.24 memory used=3152.8MB, alloc=637.6MB, time=56.23 memory used=3373.4MB, alloc=661.6MB, time=65.27 memory used=3617.9MB, alloc=685.6MB, time=75.26 memory used=3886.4MB, alloc=685.6MB, time=86.09 memory used=4154.8MB, alloc=709.6MB, time=96.90 memory used=4447.2MB, alloc=709.6MB, time=108.67 memory used=4739.5MB, alloc=733.6MB, time=120.43 memory used=5056.0MB, alloc=733.6MB, time=133.14 memory used=5372.5MB, alloc=757.6MB, time=145.94 N1 := 9787 > GB := Basis(F, plex(op(vars))); 6 2 3 5 8 5 2 3 4 GB := [2401 x y + 2744 x y + 784 y + 2744 x + 1568 x y - 3136 x 3 3 3 3 3 5 2 - 1792 x y + 896 x + 512 y , -49 x - 28 y + 28 x z - 16 z, 2401 x y 2 5 4 2 5 5 3 2 5 + 1372 x y + 1372 x y + 784 x y + 784 y z + 784 x y + 448 y 4 3 3 3 2 2 2 3 3 + 2744 x + 1568 x y - 1568 x - 896 y + 256 y z, 2 z y + 4 y + 7 x ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=5533.1MB, alloc=757.6MB, time=149.74 memory used=5642.6MB, alloc=757.6MB, time=151.65 memory used=5746.9MB, alloc=757.6MB, time=153.42 memory used=5874.7MB, alloc=757.6MB, time=155.06 memory used=5948.4MB, alloc=757.6MB, time=156.32 memory used=6043.2MB, alloc=757.6MB, time=157.94 memory used=6138.8MB, alloc=757.6MB, time=159.22 memory used=6234.4MB, alloc=757.6MB, time=160.57 memory used=6359.7MB, alloc=757.6MB, time=162.11 memory used=6463.3MB, alloc=757.6MB, time=163.43 memory used=6532.5MB, alloc=757.6MB, time=164.88 memory used=6612.2MB, alloc=757.6MB, time=166.19 memory used=6675.1MB, alloc=757.6MB, time=167.40 memory used=6745.9MB, alloc=757.6MB, time=168.69 memory used=6802.0MB, alloc=757.6MB, time=170.04 memory used=6852.1MB, alloc=757.6MB, time=171.25 memory used=6916.1MB, alloc=757.6MB, time=172.73 memory used=7007.8MB, alloc=757.6MB, time=173.94 memory used=7128.2MB, alloc=757.6MB, time=175.13 memory used=7191.7MB, alloc=757.6MB, time=176.41 memory used=7235.1MB, alloc=757.6MB, time=177.52 memory used=7478.9MB, alloc=757.6MB, time=180.24 memory used=7692.3MB, alloc=757.6MB, time=183.38 memory used=7886.6MB, alloc=781.6MB, time=186.34 memory used=8085.4MB, alloc=781.6MB, time=189.94 memory used=8344.0MB, alloc=805.6MB, time=193.83 memory used=8565.1MB, alloc=805.6MB, time=195.13 memory used=8809.2MB, alloc=805.6MB, time=197.63 memory used=9037.1MB, alloc=805.6MB, time=200.17 memory used=9201.1MB, alloc=829.6MB, time=202.83 memory used=9358.8MB, alloc=829.6MB, time=205.42 memory used=9484.0MB, alloc=829.6MB, time=207.89 memory used=9587.2MB, alloc=829.6MB, time=210.20 memory used=9693.6MB, alloc=829.6MB, time=212.58 memory used=9812.7MB, alloc=853.6MB, time=214.94 memory used=9948.8MB, alloc=853.6MB, time=217.09 memory used=10177.8MB, alloc=853.6MB, time=218.49 memory used=10433.3MB, alloc=853.6MB, time=220.85 memory used=10659.4MB, alloc=853.6MB, time=222.26 memory used=10810.8MB, alloc=853.6MB, time=224.40 memory used=10931.0MB, alloc=853.6MB, time=226.81 memory used=11013.4MB, alloc=853.6MB, time=228.78 memory used=11107.1MB, alloc=853.6MB, time=231.11 memory used=11371.3MB, alloc=877.6MB, time=233.37 memory used=11769.1MB, alloc=877.6MB, time=237.37 memory used=12261.0MB, alloc=901.6MB, time=243.41 memory used=12594.2MB, alloc=915.8MB, time=244.95 memory used=12734.6MB, alloc=915.8MB, time=246.10 memory used=13089.7MB, alloc=915.8MB, time=247.70 memory used=13395.3MB, alloc=915.8MB, time=249.37 memory used=13709.4MB, alloc=939.8MB, time=253.41 memory used=13988.8MB, alloc=939.8MB, time=254.91 memory used=14111.8MB, alloc=939.8MB, time=256.16 memory used=14254.1MB, alloc=939.8MB, time=257.48 memory used=14415.1MB, alloc=939.8MB, time=258.77 memory used=14600.2MB, alloc=939.8MB, time=260.07 memory used=14745.8MB, alloc=939.8MB, time=261.31 memory used=14900.1MB, alloc=939.8MB, time=262.56 memory used=15304.4MB, alloc=939.8MB, time=265.39 memory used=15679.1MB, alloc=939.8MB, time=277.44 memory used=15947.2MB, alloc=939.8MB, time=278.92 memory used=16085.8MB, alloc=939.8MB, time=280.22 memory used=16202.5MB, alloc=939.8MB, time=281.48 memory used=16331.0MB, alloc=939.8MB, time=282.76 memory used=16470.4MB, alloc=939.8MB, time=284.04 memory used=16623.4MB, alloc=939.8MB, time=285.32 memory used=16790.7MB, alloc=939.8MB, time=286.63 memory used=16974.0MB, alloc=939.8MB, time=287.92 memory used=17128.1MB, alloc=939.8MB, time=289.23 memory used=17267.3MB, alloc=939.8MB, time=290.49 memory used=17416.9MB, alloc=939.8MB, time=291.75 memory used=17574.0MB, alloc=939.8MB, time=293.04 memory used=17742.7MB, alloc=939.8MB, time=294.31 memory used=17926.2MB, alloc=939.8MB, time=295.61 memory used=18107.8MB, alloc=939.8MB, time=296.89 memory used=18265.7MB, alloc=939.8MB, time=298.13 memory used=18675.6MB, alloc=939.8MB, time=309.78 memory used=18954.8MB, alloc=939.8MB, time=311.38 memory used=19063.9MB, alloc=939.8MB, time=312.78 memory used=19178.9MB, alloc=939.8MB, time=314.18 memory used=19305.8MB, alloc=939.8MB, time=315.61 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428495094 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 3 3 2 F := [16 x y + 9 x z - 3 y , 19 x y - 20 x - 7 y z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 4 3 4 3 2 G := [13 x y - 10 z - 13 x , -15 x + 2 x y + 11 x y z] > Problem := [F,G]; 2 2 3 3 3 2 Problem := [[16 x y + 9 x z - 3 y , 19 x y - 20 x - 7 y z], 3 4 3 4 3 2 [13 x y - 10 z - 13 x , -15 x + 2 x y + 11 x y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.16 memory used=24.3MB, alloc=32.3MB, time=0.43 memory used=45.0MB, alloc=36.3MB, time=0.68 memory used=67.2MB, alloc=60.3MB, time=1.15 memory used=169.9MB, alloc=60.3MB, time=2.22 memory used=195.7MB, alloc=60.3MB, time=2.28 memory used=295.1MB, alloc=68.3MB, time=3.08 memory used=346.6MB, alloc=68.3MB, time=3.27 memory used=401.2MB, alloc=68.3MB, time=3.45 memory used=455.4MB, alloc=68.3MB, time=4.21 memory used=504.3MB, alloc=68.3MB, time=7.46 memory used=563.1MB, alloc=68.3MB, time=7.75 memory used=621.3MB, alloc=68.3MB, time=8.05 memory used=653.2MB, alloc=68.3MB, time=8.17 memory used=676.6MB, alloc=68.3MB, time=8.24 memory used=699.3MB, alloc=68.3MB, time=8.30 memory used=727.0MB, alloc=68.3MB, time=8.38 memory used=753.5MB, alloc=68.3MB, time=8.44 memory used=771.3MB, alloc=68.3MB, time=8.49 memory used=791.0MB, alloc=68.3MB, time=8.55 memory used=811.9MB, alloc=68.3MB, time=8.61 memory used=834.7MB, alloc=68.3MB, time=8.66 memory used=860.3MB, alloc=68.3MB, time=8.73 memory used=892.3MB, alloc=68.3MB, time=8.84 memory used=923.4MB, alloc=68.3MB, time=9.04 memory used=970.0MB, alloc=68.3MB, time=9.56 memory used=1011.6MB, alloc=68.3MB, time=10.01 memory used=1051.0MB, alloc=68.3MB, time=10.42 memory used=1090.7MB, alloc=68.3MB, time=10.93 memory used=1137.7MB, alloc=68.3MB, time=11.48 memory used=1179.5MB, alloc=92.3MB, time=11.99 memory used=1256.2MB, alloc=92.3MB, time=12.59 memory used=1326.5MB, alloc=92.3MB, time=13.29 memory used=1368.0MB, alloc=116.3MB, time=34.01 memory used=1397.2MB, alloc=140.3MB, time=43.05 memory used=1449.5MB, alloc=164.3MB, time=43.28 memory used=1489.3MB, alloc=188.3MB, time=43.43 memory used=1545.5MB, alloc=188.3MB, time=43.63 memory used=1605.4MB, alloc=188.3MB, time=43.82 memory used=1667.5MB, alloc=188.3MB, time=44.03 memory used=1731.5MB, alloc=188.3MB, time=44.22 memory used=1797.5MB, alloc=188.3MB, time=44.42 memory used=1865.3MB, alloc=188.3MB, time=44.62 memory used=1935.1MB, alloc=188.3MB, time=44.81 memory used=2006.7MB, alloc=188.3MB, time=45.00 memory used=2080.1MB, alloc=188.3MB, time=45.18 memory used=2155.2MB, alloc=188.3MB, time=45.38 memory used=2232.0MB, alloc=188.3MB, time=45.57 memory used=2310.6MB, alloc=188.3MB, time=45.76 memory used=2390.7MB, alloc=188.3MB, time=45.97 memory used=2472.8MB, alloc=188.3MB, time=46.16 memory used=2566.7MB, alloc=188.3MB, time=46.38 memory used=2662.5MB, alloc=188.3MB, time=46.60 memory used=2736.8MB, alloc=188.3MB, time=46.77 memory used=2791.0MB, alloc=212.3MB, time=46.93 memory used=2852.3MB, alloc=236.3MB, time=47.09 memory used=2917.6MB, alloc=236.3MB, time=47.26 memory used=2984.1MB, alloc=236.3MB, time=47.41 memory used=3052.5MB, alloc=236.3MB, time=47.57 memory used=3121.7MB, alloc=236.3MB, time=47.73 memory used=3191.5MB, alloc=236.3MB, time=47.88 memory used=3262.1MB, alloc=236.3MB, time=48.05 memory used=3333.3MB, alloc=236.3MB, time=48.20 memory used=3405.2MB, alloc=236.3MB, time=48.37 memory used=3478.0MB, alloc=236.3MB, time=48.53 memory used=3563.4MB, alloc=236.3MB, time=48.71 memory used=3649.7MB, alloc=236.3MB, time=48.88 memory used=3736.7MB, alloc=236.3MB, time=49.07 memory used=3824.5MB, alloc=236.3MB, time=49.24 memory used=3913.1MB, alloc=236.3MB, time=49.42 memory used=4002.3MB, alloc=236.3MB, time=49.59 memory used=4092.3MB, alloc=236.3MB, time=49.76 memory used=4182.9MB, alloc=236.3MB, time=49.93 memory used=4274.2MB, alloc=236.3MB, time=50.11 memory used=4366.1MB, alloc=236.3MB, time=50.28 memory used=4458.5MB, alloc=236.3MB, time=50.44 memory used=4551.5MB, alloc=236.3MB, time=50.61 memory used=4645.4MB, alloc=236.3MB, time=50.79 memory used=4753.0MB, alloc=236.3MB, time=50.99 memory used=4861.2MB, alloc=236.3MB, time=51.18 memory used=4970.0MB, alloc=236.3MB, time=51.37 memory used=5079.3MB, alloc=236.3MB, time=51.56 memory used=5189.1MB, alloc=236.3MB, time=51.74 memory used=5299.5MB, alloc=236.3MB, time=51.93 memory used=5410.2MB, alloc=236.3MB, time=52.11 memory used=5521.3MB, alloc=236.3MB, time=52.29 memory used=5632.9MB, alloc=236.3MB, time=52.48 memory used=5745.4MB, alloc=236.3MB, time=52.66 memory used=5871.1MB, alloc=236.3MB, time=52.85 memory used=5997.5MB, alloc=236.3MB, time=53.05 memory used=6124.2MB, alloc=236.3MB, time=53.23 memory used=6251.0MB, alloc=236.3MB, time=53.43 memory used=6378.0MB, alloc=236.3MB, time=53.62 memory used=6505.2MB, alloc=236.3MB, time=53.82 memory used=6646.4MB, alloc=236.3MB, time=54.03 memory used=6700.3MB, alloc=251.8MB, time=54.16 memory used=6713.9MB, alloc=251.8MB, time=54.24 memory used=6718.3MB, alloc=507.8MB, time=54.31 memory used=6887.0MB, alloc=507.8MB, time=54.75 memory used=7009.5MB, alloc=507.8MB, time=55.00 memory used=7134.8MB, alloc=507.8MB, time=55.24 memory used=7260.8MB, alloc=507.8MB, time=55.47 memory used=7386.5MB, alloc=507.8MB, time=55.71 memory used=7512.0MB, alloc=507.8MB, time=55.98 memory used=7650.8MB, alloc=507.8MB, time=56.23 memory used=7789.0MB, alloc=507.8MB, time=56.49 memory used=7926.5MB, alloc=507.8MB, time=56.73 memory used=8063.3MB, alloc=507.8MB, time=56.99 memory used=8212.8MB, alloc=507.8MB, time=57.27 memory used=8361.1MB, alloc=507.8MB, time=57.53 memory used=8508.2MB, alloc=507.8MB, time=57.78 memory used=8654.2MB, alloc=507.8MB, time=58.04 memory used=8811.7MB, alloc=507.8MB, time=58.29 memory used=8967.3MB, alloc=507.8MB, time=58.56 memory used=9121.8MB, alloc=507.8MB, time=58.83 memory used=9285.3MB, alloc=507.8MB, time=59.11 memory used=9446.9MB, alloc=507.8MB, time=59.38 memory used=9617.9MB, alloc=507.8MB, time=59.66 memory used=9786.2MB, alloc=507.8MB, time=59.93 memory used=9961.0MB, alloc=507.8MB, time=60.22 memory used=10143.3MB, alloc=507.8MB, time=60.52 memory used=10331.3MB, alloc=507.8MB, time=60.81 memory used=10523.2MB, alloc=507.8MB, time=61.11 memory used=10717.7MB, alloc=507.8MB, time=61.41 memory used=10922.1MB, alloc=507.8MB, time=61.73 memory used=11132.7MB, alloc=507.8MB, time=62.04 memory used=11344.6MB, alloc=507.8MB, time=62.36 memory used=11567.0MB, alloc=507.8MB, time=62.68 memory used=11799.6MB, alloc=507.8MB, time=63.00 memory used=12097.8MB, alloc=507.8MB, time=93.37 memory used=12185.6MB, alloc=507.8MB, time=93.61 memory used=12275.7MB, alloc=507.8MB, time=93.84 memory used=12371.2MB, alloc=507.8MB, time=94.07 memory used=12471.6MB, alloc=507.8MB, time=94.35 memory used=12584.8MB, alloc=507.8MB, time=94.63 memory used=12703.0MB, alloc=507.8MB, time=94.91 memory used=12825.8MB, alloc=507.8MB, time=95.21 memory used=12953.2MB, alloc=507.8MB, time=95.49 memory used=13085.3MB, alloc=507.8MB, time=95.74 memory used=13232.0MB, alloc=507.8MB, time=96.03 memory used=13367.2MB, alloc=507.8MB, time=96.29 memory used=13456.1MB, alloc=507.8MB, time=96.48 memory used=13532.6MB, alloc=507.8MB, time=96.66 memory used=13608.4MB, alloc=507.8MB, time=96.83 memory used=13687.9MB, alloc=507.8MB, time=97.00 memory used=13768.6MB, alloc=507.8MB, time=97.18 memory used=13850.3MB, alloc=507.8MB, time=97.35 memory used=13932.9MB, alloc=507.8MB, time=97.53 memory used=14016.4MB, alloc=507.8MB, time=97.72 memory used=14100.9MB, alloc=507.8MB, time=97.90 memory used=14186.1MB, alloc=507.8MB, time=98.07 memory used=14272.2MB, alloc=507.8MB, time=98.24 memory used=14359.1MB, alloc=507.8MB, time=98.42 memory used=14446.8MB, alloc=507.8MB, time=98.61 memory used=14535.2MB, alloc=507.8MB, time=98.79 memory used=14624.3MB, alloc=507.8MB, time=98.99 memory used=14714.1MB, alloc=507.8MB, time=99.16 memory used=14804.9MB, alloc=507.8MB, time=99.36 memory used=14909.2MB, alloc=507.8MB, time=99.54 memory used=15014.3MB, alloc=507.8MB, time=99.74 memory used=15120.1MB, alloc=507.8MB, time=99.93 memory used=15226.7MB, alloc=507.8MB, time=100.11 memory used=15334.0MB, alloc=507.8MB, time=100.29 memory used=15441.9MB, alloc=507.8MB, time=100.48 memory used=15550.4MB, alloc=507.8MB, time=100.67 memory used=15659.4MB, alloc=507.8MB, time=100.85 memory used=15769.1MB, alloc=507.8MB, time=101.03 memory used=15879.4MB, alloc=507.8MB, time=101.24 memory used=16003.9MB, alloc=507.8MB, time=101.45 memory used=16128.9MB, alloc=507.8MB, time=101.64 memory used=16254.3MB, alloc=507.8MB, time=101.85 memory used=16380.2MB, alloc=507.8MB, time=102.04 memory used=16506.4MB, alloc=507.8MB, time=102.24 memory used=16632.8MB, alloc=507.8MB, time=102.44 memory used=16759.8MB, alloc=507.8MB, time=102.64 memory used=16900.9MB, alloc=507.8MB, time=102.86 memory used=17042.1MB, alloc=507.8MB, time=103.08 memory used=17183.4MB, alloc=507.8MB, time=103.32 memory used=17333.5MB, alloc=507.8MB, time=103.54 memory used=17521.6MB, alloc=507.8MB, time=103.87 memory used=17651.8MB, alloc=507.8MB, time=104.11 memory used=17777.1MB, alloc=507.8MB, time=104.34 memory used=17903.1MB, alloc=507.8MB, time=104.59 memory used=18028.8MB, alloc=507.8MB, time=104.82 memory used=18154.3MB, alloc=507.8MB, time=105.08 memory used=18293.1MB, alloc=507.8MB, time=105.33 memory used=18431.3MB, alloc=507.8MB, time=105.60 memory used=18568.8MB, alloc=507.8MB, time=105.86 memory used=18705.6MB, alloc=507.8MB, time=106.11 memory used=18855.1MB, alloc=507.8MB, time=106.36 memory used=19003.4MB, alloc=507.8MB, time=106.61 memory used=19150.5MB, alloc=507.8MB, time=106.86 memory used=19296.5MB, alloc=507.8MB, time=107.12 memory used=19454.0MB, alloc=507.8MB, time=107.38 memory used=19609.6MB, alloc=507.8MB, time=107.64 memory used=19764.1MB, alloc=507.8MB, time=107.89 memory used=19927.6MB, alloc=507.8MB, time=108.17 memory used=20089.2MB, alloc=507.8MB, time=108.43 memory used=20260.2MB, alloc=507.8MB, time=108.71 memory used=20428.6MB, alloc=507.8MB, time=108.97 memory used=20603.3MB, alloc=507.8MB, time=109.25 memory used=20785.6MB, alloc=507.8MB, time=109.54 memory used=20973.6MB, alloc=507.8MB, time=109.83 memory used=21165.5MB, alloc=507.8MB, time=110.12 memory used=21360.0MB, alloc=507.8MB, time=110.42 memory used=21564.4MB, alloc=507.8MB, time=110.73 memory used=21775.0MB, alloc=507.8MB, time=111.05 memory used=21986.9MB, alloc=507.8MB, time=111.36 memory used=22209.3MB, alloc=507.8MB, time=111.68 memory used=22441.9MB, alloc=507.8MB, time=112.00 memory used=22740.1MB, alloc=507.8MB, time=169.32 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428495394 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 3 3 2 4 F := [10 x + 5 y z - 19 z , 15 x y - 18 x y z + 14 z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 2 3 G := [15 x y z - 5 x + 20 x y , 18 x y - 14 x ] > Problem := [F,G]; 4 3 3 3 2 4 Problem := [[10 x + 5 y z - 19 z , 15 x y - 18 x y z + 14 z ], 2 3 2 2 2 3 [15 x y z - 5 x + 20 x y , 18 x y - 14 x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=25.4MB, alloc=32.3MB, time=0.47 memory used=45.6MB, alloc=56.3MB, time=0.77 memory used=89.8MB, alloc=60.8MB, time=1.08 memory used=119.9MB, alloc=60.8MB, time=1.21 memory used=165.3MB, alloc=60.8MB, time=1.72 memory used=211.3MB, alloc=68.8MB, time=2.35 memory used=246.3MB, alloc=71.0MB, time=2.46 memory used=272.0MB, alloc=71.0MB, time=2.54 memory used=289.9MB, alloc=71.0MB, time=2.61 memory used=310.6MB, alloc=71.0MB, time=2.68 memory used=333.0MB, alloc=71.0MB, time=2.76 memory used=358.5MB, alloc=71.0MB, time=2.84 memory used=385.5MB, alloc=71.0MB, time=2.92 memory used=415.8MB, alloc=71.0MB, time=3.01 memory used=434.7MB, alloc=71.0MB, time=3.08 memory used=450.6MB, alloc=71.0MB, time=3.14 memory used=466.2MB, alloc=71.0MB, time=3.21 memory used=482.1MB, alloc=71.0MB, time=3.28 memory used=500.0MB, alloc=71.0MB, time=3.34 memory used=518.2MB, alloc=71.0MB, time=3.41 memory used=536.6MB, alloc=71.0MB, time=3.49 memory used=557.2MB, alloc=71.0MB, time=3.55 memory used=577.8MB, alloc=71.0MB, time=3.62 memory used=598.6MB, alloc=71.0MB, time=3.69 memory used=621.1MB, alloc=71.0MB, time=3.77 memory used=643.9MB, alloc=71.0MB, time=3.83 memory used=667.9MB, alloc=71.0MB, time=3.90 memory used=694.0MB, alloc=71.0MB, time=3.97 memory used=721.4MB, alloc=71.0MB, time=4.05 memory used=749.8MB, alloc=71.0MB, time=4.12 memory used=778.3MB, alloc=71.0MB, time=4.19 memory used=793.6MB, alloc=71.0MB, time=4.24 memory used=809.5MB, alloc=71.0MB, time=4.29 memory used=826.0MB, alloc=71.0MB, time=4.35 memory used=843.0MB, alloc=71.0MB, time=4.40 memory used=861.4MB, alloc=71.0MB, time=4.46 memory used=901.7MB, alloc=71.0MB, time=4.81 memory used=931.9MB, alloc=71.0MB, time=4.91 memory used=950.6MB, alloc=71.0MB, time=5.00 memory used=972.4MB, alloc=71.0MB, time=5.07 memory used=998.1MB, alloc=71.0MB, time=5.15 memory used=1027.1MB, alloc=71.0MB, time=5.23 memory used=1049.3MB, alloc=71.0MB, time=5.30 memory used=1065.9MB, alloc=71.0MB, time=5.37 memory used=1084.0MB, alloc=71.0MB, time=5.44 memory used=1103.3MB, alloc=71.0MB, time=5.51 memory used=1123.7MB, alloc=71.0MB, time=5.58 memory used=1146.3MB, alloc=71.0MB, time=5.65 memory used=1170.4MB, alloc=71.0MB, time=5.72 memory used=1197.0MB, alloc=71.0MB, time=5.78 memory used=1225.4MB, alloc=71.0MB, time=7.08 memory used=1253.8MB, alloc=95.0MB, time=14.64 memory used=1292.1MB, alloc=95.0MB, time=31.55 memory used=1330.9MB, alloc=95.0MB, time=49.35 memory used=1394.6MB, alloc=95.0MB, time=52.09 memory used=1430.7MB, alloc=95.0MB, time=52.16 memory used=1458.5MB, alloc=95.0MB, time=52.22 memory used=1488.8MB, alloc=95.0MB, time=52.29 memory used=1521.4MB, alloc=95.0MB, time=52.37 memory used=1557.9MB, alloc=95.0MB, time=52.44 memory used=1600.7MB, alloc=95.0MB, time=52.52 memory used=1663.1MB, alloc=97.8MB, time=53.16 memory used=1705.2MB, alloc=97.8MB, time=53.28 memory used=1742.3MB, alloc=97.8MB, time=53.39 memory used=1786.5MB, alloc=97.8MB, time=53.52 memory used=1837.2MB, alloc=97.8MB, time=53.64 memory used=1869.3MB, alloc=97.8MB, time=53.74 memory used=1899.5MB, alloc=97.8MB, time=53.83 memory used=1932.0MB, alloc=97.8MB, time=53.93 memory used=1967.2MB, alloc=97.8MB, time=54.02 memory used=2005.0MB, alloc=97.8MB, time=54.13 memory used=2045.1MB, alloc=97.8MB, time=54.22 memory used=2089.3MB, alloc=97.8MB, time=54.33 memory used=2136.8MB, alloc=97.8MB, time=54.42 memory used=2188.4MB, alloc=97.8MB, time=54.54 memory used=2221.4MB, alloc=97.8MB, time=54.61 memory used=2250.1MB, alloc=97.8MB, time=54.68 memory used=2280.8MB, alloc=97.8MB, time=54.75 memory used=2344.7MB, alloc=97.8MB, time=56.52 memory used=2402.3MB, alloc=97.8MB, time=57.32 memory used=2454.6MB, alloc=97.8MB, time=57.49 memory used=2499.4MB, alloc=97.8MB, time=57.63 memory used=2538.9MB, alloc=121.8MB, time=57.77 memory used=2575.8MB, alloc=121.8MB, time=57.90 memory used=2615.7MB, alloc=121.8MB, time=58.04 memory used=2656.7MB, alloc=121.8MB, time=58.17 memory used=2699.8MB, alloc=121.8MB, time=58.31 memory used=2744.8MB, alloc=121.8MB, time=58.44 memory used=2791.8MB, alloc=121.8MB, time=58.58 memory used=2840.6MB, alloc=121.8MB, time=58.71 memory used=2891.3MB, alloc=121.8MB, time=58.86 memory used=2944.2MB, alloc=121.8MB, time=59.01 memory used=3006.2MB, alloc=121.8MB, time=59.18 memory used=3070.3MB, alloc=121.8MB, time=59.33 memory used=3126.7MB, alloc=121.8MB, time=59.47 memory used=3157.6MB, alloc=145.8MB, time=59.59 memory used=3195.0MB, alloc=145.8MB, time=59.71 memory used=3237.7MB, alloc=145.8MB, time=59.84 memory used=3281.6MB, alloc=145.8MB, time=59.96 memory used=3326.2MB, alloc=145.8MB, time=60.11 memory used=3371.4MB, alloc=145.8MB, time=60.24 memory used=3417.4MB, alloc=145.8MB, time=60.37 memory used=3463.9MB, alloc=145.8MB, time=60.49 memory used=3511.1MB, alloc=145.8MB, time=60.62 memory used=3558.9MB, alloc=145.8MB, time=60.75 memory used=3607.2MB, alloc=145.8MB, time=60.88 memory used=3656.1MB, alloc=145.8MB, time=61.02 memory used=3706.6MB, alloc=145.8MB, time=61.17 memory used=3766.0MB, alloc=145.8MB, time=61.32 memory used=3826.7MB, alloc=145.8MB, time=61.47 memory used=3888.1MB, alloc=145.8MB, time=61.61 memory used=3950.2MB, alloc=145.8MB, time=61.75 memory used=4012.8MB, alloc=145.8MB, time=61.89 memory used=4076.0MB, alloc=145.8MB, time=62.03 memory used=4139.8MB, alloc=145.8MB, time=62.17 memory used=4204.1MB, alloc=145.8MB, time=62.31 memory used=4268.8MB, alloc=145.8MB, time=62.46 memory used=4334.4MB, alloc=145.8MB, time=62.63 memory used=4410.9MB, alloc=145.8MB, time=62.79 memory used=4488.0MB, alloc=145.8MB, time=62.95 memory used=4565.5MB, alloc=145.8MB, time=63.12 memory used=4643.4MB, alloc=145.8MB, time=63.27 memory used=4721.6MB, alloc=145.8MB, time=63.42 memory used=4800.1MB, alloc=145.8MB, time=63.57 memory used=4864.2MB, alloc=145.8MB, time=63.70 memory used=4898.0MB, alloc=169.8MB, time=63.81 memory used=4941.7MB, alloc=169.8MB, time=63.91 memory used=4986.4MB, alloc=169.8MB, time=64.02 memory used=5031.2MB, alloc=169.8MB, time=64.12 memory used=5076.0MB, alloc=169.8MB, time=64.23 memory used=5121.7MB, alloc=169.8MB, time=64.33 memory used=5177.0MB, alloc=169.8MB, time=64.46 memory used=5232.9MB, alloc=169.8MB, time=64.59 memory used=5288.8MB, alloc=169.8MB, time=64.71 memory used=5344.6MB, alloc=169.8MB, time=64.83 memory used=5400.3MB, alloc=169.8MB, time=64.94 memory used=5455.9MB, alloc=169.8MB, time=65.06 memory used=5511.3MB, alloc=169.8MB, time=65.18 memory used=5566.7MB, alloc=169.8MB, time=65.30 memory used=5621.8MB, alloc=169.8MB, time=65.41 memory used=5676.8MB, alloc=169.8MB, time=65.53 memory used=5732.6MB, alloc=169.8MB, time=65.65 memory used=5797.2MB, alloc=169.8MB, time=65.78 memory used=5862.2MB, alloc=169.8MB, time=65.90 memory used=5926.9MB, alloc=169.8MB, time=66.02 memory used=5991.1MB, alloc=169.8MB, time=66.14 memory used=6054.8MB, alloc=169.8MB, time=66.26 memory used=6118.1MB, alloc=169.8MB, time=66.39 memory used=6182.2MB, alloc=169.8MB, time=66.50 memory used=6253.4MB, alloc=169.8MB, time=66.64 memory used=6325.0MB, alloc=169.8MB, time=66.78 memory used=6395.8MB, alloc=169.8MB, time=66.91 memory used=6466.6MB, alloc=169.8MB, time=67.04 memory used=6544.3MB, alloc=169.8MB, time=67.17 memory used=6621.5MB, alloc=169.8MB, time=67.30 memory used=6697.4MB, alloc=169.8MB, time=67.45 memory used=6780.7MB, alloc=169.8MB, time=67.58 memory used=6862.2MB, alloc=169.8MB, time=67.72 memory used=6950.0MB, alloc=169.8MB, time=67.85 memory used=7035.1MB, alloc=169.8MB, time=67.99 memory used=7125.2MB, alloc=169.8MB, time=68.14 memory used=7219.1MB, alloc=169.8MB, time=68.28 memory used=7315.4MB, alloc=169.8MB, time=68.43 memory used=7412.5MB, alloc=169.8MB, time=68.57 memory used=7514.3MB, alloc=169.8MB, time=68.71 memory used=7622.0MB, alloc=169.8MB, time=68.86 memory used=7726.5MB, alloc=179.8MB, time=69.00 memory used=7841.5MB, alloc=179.8MB, time=72.01 memory used=7940.8MB, alloc=179.8MB, time=72.29 memory used=8019.1MB, alloc=179.8MB, time=72.53 memory used=8109.5MB, alloc=179.8MB, time=72.77 memory used=8215.7MB, alloc=179.8MB, time=73.00 memory used=8310.7MB, alloc=179.8MB, time=73.22 memory used=8370.3MB, alloc=179.8MB, time=73.40 memory used=8436.4MB, alloc=179.8MB, time=73.57 memory used=8505.3MB, alloc=179.8MB, time=73.77 memory used=8576.6MB, alloc=179.8MB, time=73.96 memory used=8650.4MB, alloc=179.8MB, time=74.15 memory used=8726.5MB, alloc=179.8MB, time=74.36 memory used=8805.2MB, alloc=179.8MB, time=74.53 memory used=8892.5MB, alloc=179.8MB, time=74.75 memory used=8982.5MB, alloc=179.8MB, time=74.96 memory used=9074.7MB, alloc=179.8MB, time=75.16 memory used=9169.2MB, alloc=179.8MB, time=75.38 memory used=9273.4MB, alloc=179.8MB, time=75.59 memory used=9379.7MB, alloc=179.8MB, time=75.82 memory used=9488.1MB, alloc=179.8MB, time=76.05 memory used=9557.9MB, alloc=179.8MB, time=76.19 memory used=9608.8MB, alloc=179.8MB, time=76.30 memory used=9659.5MB, alloc=179.8MB, time=76.41 memory used=9710.5MB, alloc=179.8MB, time=76.53 memory used=9762.5MB, alloc=179.8MB, time=76.65 memory used=9822.0MB, alloc=179.8MB, time=76.78 memory used=9882.5MB, alloc=179.8MB, time=76.92 memory used=9943.2MB, alloc=179.8MB, time=77.04 memory used=10004.2MB, alloc=179.8MB, time=77.17 memory used=10065.4MB, alloc=179.8MB, time=77.29 memory used=10126.8MB, alloc=179.8MB, time=77.42 memory used=10188.4MB, alloc=179.8MB, time=77.54 memory used=10250.2MB, alloc=179.8MB, time=77.67 memory used=10312.8MB, alloc=179.8MB, time=77.79 memory used=10382.9MB, alloc=179.8MB, time=77.93 memory used=10453.9MB, alloc=179.8MB, time=78.07 memory used=10524.9MB, alloc=179.8MB, time=78.21 memory used=10595.9MB, alloc=179.8MB, time=78.34 memory used=10666.9MB, alloc=179.8MB, time=78.47 memory used=10738.4MB, alloc=179.8MB, time=78.60 memory used=10817.6MB, alloc=179.8MB, time=78.75 memory used=10897.1MB, alloc=179.8MB, time=78.89 memory used=10976.3MB, alloc=179.8MB, time=79.03 memory used=11055.1MB, alloc=179.8MB, time=79.17 memory used=11142.3MB, alloc=179.8MB, time=79.32 memory used=11229.0MB, alloc=179.8MB, time=79.46 memory used=11315.1MB, alloc=179.8MB, time=79.61 memory used=11401.1MB, alloc=179.8MB, time=79.75 memory used=11493.6MB, alloc=179.8MB, time=79.90 memory used=11585.5MB, alloc=179.8MB, time=80.05 memory used=11684.5MB, alloc=179.8MB, time=80.20 memory used=11782.2MB, alloc=179.8MB, time=80.36 memory used=11886.0MB, alloc=179.8MB, time=80.52 memory used=11987.9MB, alloc=179.8MB, time=80.67 memory used=12094.8MB, alloc=179.8MB, time=80.82 memory used=12206.4MB, alloc=179.8MB, time=80.98 memory used=12321.6MB, alloc=179.8MB, time=81.15 memory used=12353.2MB, alloc=179.8MB, time=81.23 memory used=12358.7MB, alloc=179.8MB, time=81.28 memory used=12359.5MB, alloc=179.8MB, time=81.32 memory used=12364.4MB, alloc=435.8MB, time=81.37 memory used=12496.0MB, alloc=435.8MB, time=81.76 memory used=12632.4MB, alloc=435.8MB, time=81.99 memory used=12776.2MB, alloc=435.8MB, time=82.23 memory used=12928.7MB, alloc=435.8MB, time=82.47 memory used=13088.5MB, alloc=435.8MB, time=82.71 memory used=13434.7MB, alloc=435.8MB, time=243.74 memory used=13681.0MB, alloc=435.8MB, time=274.33 memory used=13855.2MB, alloc=435.8MB, time=274.58 memory used=14155.1MB, alloc=435.8MB, time=276.43 memory used=14308.0MB, alloc=435.8MB, time=309.22 memory used=14395.7MB, alloc=435.8MB, time=309.44 memory used=14494.7MB, alloc=435.8MB, time=309.65 memory used=14566.8MB, alloc=435.8MB, time=309.79 memory used=14655.8MB, alloc=435.8MB, time=309.94 memory used=14799.1MB, alloc=435.8MB, time=310.94 memory used=14916.3MB, alloc=435.8MB, time=313.86 memory used=14990.4MB, alloc=435.8MB, time=314.09 memory used=15080.2MB, alloc=435.8MB, time=314.33 memory used=15182.7MB, alloc=435.8MB, time=314.58 memory used=15250.1MB, alloc=435.8MB, time=314.78 memory used=15305.8MB, alloc=435.8MB, time=314.96 memory used=15367.3MB, alloc=435.8MB, time=315.15 memory used=15431.5MB, alloc=435.8MB, time=315.34 memory used=15498.3MB, alloc=435.8MB, time=315.54 memory used=15568.0MB, alloc=435.8MB, time=315.74 memory used=15646.0MB, alloc=435.8MB, time=315.95 memory used=15726.8MB, alloc=435.8MB, time=316.15 memory used=15810.4MB, alloc=435.8MB, time=316.36 memory used=15896.6MB, alloc=435.8MB, time=316.56 memory used=15985.7MB, alloc=435.8MB, time=316.78 memory used=16084.0MB, alloc=435.8MB, time=316.99 memory used=16185.0MB, alloc=435.8MB, time=317.22 memory used=16272.7MB, alloc=435.8MB, time=317.42 memory used=16324.4MB, alloc=435.8MB, time=317.57 memory used=16372.4MB, alloc=435.8MB, time=317.70 memory used=16418.2MB, alloc=435.8MB, time=317.84 memory used=16471.9MB, alloc=435.8MB, time=317.98 memory used=16526.1MB, alloc=435.8MB, time=318.12 memory used=16581.0MB, alloc=435.8MB, time=318.26 memory used=16636.3MB, alloc=435.8MB, time=318.40 memory used=16692.1MB, alloc=435.8MB, time=318.54 memory used=16748.4MB, alloc=435.8MB, time=318.67 memory used=16805.2MB, alloc=435.8MB, time=318.81 memory used=16862.4MB, alloc=435.8MB, time=318.94 memory used=16920.1MB, alloc=435.8MB, time=319.08 memory used=16978.1MB, alloc=435.8MB, time=319.22 memory used=17036.7MB, alloc=435.8MB, time=319.36 memory used=17095.6MB, alloc=435.8MB, time=319.50 memory used=17154.9MB, alloc=435.8MB, time=319.63 memory used=17214.7MB, alloc=435.8MB, time=319.77 memory used=17283.3MB, alloc=435.8MB, time=319.92 memory used=17352.3MB, alloc=435.8MB, time=320.07 memory used=17421.7MB, alloc=435.8MB, time=320.22 memory used=17491.6MB, alloc=435.8MB, time=320.37 memory used=17561.7MB, alloc=435.8MB, time=320.52 memory used=17632.3MB, alloc=435.8MB, time=320.67 memory used=17703.1MB, alloc=435.8MB, time=320.81 memory used=17774.3MB, alloc=435.8MB, time=320.95 memory used=17845.7MB, alloc=435.8MB, time=321.10 memory used=17917.6MB, alloc=435.8MB, time=321.25 memory used=17998.6MB, alloc=435.8MB, time=321.41 memory used=18079.6MB, alloc=435.8MB, time=321.57 memory used=18161.1MB, alloc=435.8MB, time=321.73 memory used=18242.6MB, alloc=435.8MB, time=321.89 memory used=18324.4MB, alloc=435.8MB, time=322.04 memory used=18406.2MB, alloc=435.8MB, time=322.19 memory used=18488.4MB, alloc=435.8MB, time=322.35 memory used=18579.6MB, alloc=435.8MB, time=322.52 memory used=18670.8MB, alloc=435.8MB, time=322.68 memory used=18762.0MB, alloc=435.8MB, time=322.83 memory used=18853.1MB, alloc=435.8MB, time=322.99 memory used=18944.1MB, alloc=435.8MB, time=323.16 memory used=19035.2MB, alloc=435.8MB, time=323.32 memory used=19134.7MB, alloc=435.8MB, time=323.49 memory used=19234.3MB, alloc=435.8MB, time=323.65 memory used=19399.4MB, alloc=435.8MB, time=323.94 memory used=19525.7MB, alloc=435.8MB, time=324.19 memory used=19650.6MB, alloc=435.8MB, time=324.43 memory used=19783.3MB, alloc=435.8MB, time=324.67 memory used=19914.9MB, alloc=435.8MB, time=324.92 memory used=20053.8MB, alloc=435.8MB, time=325.17 memory used=20191.0MB, alloc=435.8MB, time=325.42 memory used=20334.2MB, alloc=435.8MB, time=325.67 memory used=20483.5MB, alloc=435.8MB, time=325.93 memory used=20638.1MB, alloc=435.8MB, time=326.19 memory used=20796.7MB, alloc=435.8MB, time=326.46 memory used=20958.4MB, alloc=435.8MB, time=326.74 memory used=21122.6MB, alloc=435.8MB, time=327.01 memory used=21294.5MB, alloc=435.8MB, time=327.29 memory used=21471.8MB, alloc=435.8MB, time=327.58 memory used=21652.2MB, alloc=435.8MB, time=327.86 memory used=21841.2MB, alloc=435.8MB, time=328.15 memory used=22038.3MB, alloc=435.8MB, time=328.44 memory used=22247.3MB, alloc=435.8MB, time=328.73 memory used=22423.5MB, alloc=435.8MB, time=330.36 memory used=22505.9MB, alloc=435.8MB, time=330.62 memory used=22611.1MB, alloc=435.8MB, time=330.91 memory used=22679.9MB, alloc=435.8MB, time=331.13 memory used=22743.6MB, alloc=435.8MB, time=331.33 memory used=22811.8MB, alloc=435.8MB, time=331.53 memory used=22887.7MB, alloc=435.8MB, time=331.73 memory used=22967.6MB, alloc=435.8MB, time=331.92 memory used=23055.6MB, alloc=435.8MB, time=332.14 memory used=23147.2MB, alloc=435.8MB, time=332.32 memory used=23247.2MB, alloc=435.8MB, time=332.52 memory used=23350.6MB, alloc=435.8MB, time=332.74 memory used=23427.9MB, alloc=435.8MB, time=332.92 memory used=23480.4MB, alloc=435.8MB, time=333.06 memory used=23533.9MB, alloc=435.8MB, time=333.20 memory used=23593.3MB, alloc=435.8MB, time=333.35 memory used=23653.2MB, alloc=435.8MB, time=333.49 memory used=23713.8MB, alloc=435.8MB, time=333.62 memory used=23774.7MB, alloc=435.8MB, time=333.75 memory used=23836.2MB, alloc=435.8MB, time=333.89 memory used=23903.5MB, alloc=435.8MB, time=334.04 memory used=23971.2MB, alloc=435.8MB, time=334.18 memory used=24039.3MB, alloc=435.8MB, time=334.32 memory used=24113.0MB, alloc=435.8MB, time=334.47 memory used=24187.0MB, alloc=435.8MB, time=334.62 memory used=24261.0MB, alloc=435.8MB, time=334.78 memory used=24340.6MB, alloc=435.8MB, time=334.94 memory used=24420.1MB, alloc=435.8MB, time=335.11 memory used=24504.8MB, alloc=435.8MB, time=335.27 memory used=24589.0MB, alloc=435.8MB, time=335.43 memory used=24678.1MB, alloc=435.8MB, time=335.59 memory used=24771.8MB, alloc=435.8MB, time=335.75 memory used=24869.4MB, alloc=435.8MB, time=335.91 memory used=24965.6MB, alloc=435.8MB, time=336.07 memory used=25069.8MB, alloc=435.8MB, time=336.24 memory used=25176.3MB, alloc=435.8MB, time=336.40 memory used=25383.6MB, alloc=435.8MB, time=336.72 memory used=25519.1MB, alloc=435.8MB, time=336.96 memory used=25665.3MB, alloc=435.8MB, time=337.20 memory used=25820.9MB, alloc=435.8MB, time=337.44 memory used=26068.2MB, alloc=435.8MB, time=380.05 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428495694 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 2 2 2 2 F := [2 z - 5 x - 15 z, -12 x y + 8 x y + 5 y z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 G := [-12 x y z - 8 x z + x y, 11 x y z - 5 x y z + 9 z ] > Problem := [F,G]; 4 3 2 2 2 2 Problem := [[2 z - 5 x - 15 z, -12 x y + 8 x y + 5 y z ], 2 2 2 2 2 [-12 x y z - 8 x z + x y, 11 x y z - 5 x y z + 9 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.16 memory used=26.4MB, alloc=32.3MB, time=0.49 memory used=46.2MB, alloc=56.3MB, time=0.81 memory used=87.9MB, alloc=60.3MB, time=1.39 memory used=127.6MB, alloc=68.3MB, time=1.98 memory used=162.4MB, alloc=68.3MB, time=2.25 memory used=195.3MB, alloc=68.3MB, time=2.58 memory used=233.5MB, alloc=68.3MB, time=3.00 memory used=274.9MB, alloc=92.3MB, time=3.60 memory used=336.2MB, alloc=92.3MB, time=4.26 memory used=402.2MB, alloc=92.3MB, time=5.19 memory used=465.0MB, alloc=116.3MB, time=6.02 memory used=543.4MB, alloc=116.3MB, time=7.11 memory used=612.2MB, alloc=372.3MB, time=8.07 memory used=698.3MB, alloc=396.3MB, time=9.22 memory used=801.2MB, alloc=396.3MB, time=10.18 memory used=870.9MB, alloc=396.3MB, time=10.54 memory used=949.4MB, alloc=396.3MB, time=11.03 memory used=1006.5MB, alloc=396.3MB, time=11.24 memory used=1065.9MB, alloc=396.3MB, time=11.50 memory used=1124.7MB, alloc=396.3MB, time=11.72 memory used=1181.0MB, alloc=396.3MB, time=12.39 memory used=1262.6MB, alloc=396.3MB, time=14.45 memory used=1309.7MB, alloc=396.3MB, time=14.64 memory used=1378.3MB, alloc=396.3MB, time=15.03 memory used=1445.1MB, alloc=396.3MB, time=15.32 memory used=1498.1MB, alloc=396.3MB, time=15.49 memory used=1566.2MB, alloc=396.3MB, time=15.83 memory used=1619.8MB, alloc=396.3MB, time=16.01 memory used=1703.2MB, alloc=396.3MB, time=18.53 memory used=1753.1MB, alloc=396.3MB, time=18.70 memory used=1822.7MB, alloc=396.3MB, time=19.07 memory used=1880.3MB, alloc=396.3MB, time=19.28 memory used=1932.0MB, alloc=396.3MB, time=19.46 memory used=1998.8MB, alloc=396.3MB, time=19.76 memory used=2054.3MB, alloc=396.3MB, time=19.96 memory used=2100.2MB, alloc=396.3MB, time=20.13 memory used=2170.9MB, alloc=396.3MB, time=21.37 memory used=2220.8MB, alloc=396.3MB, time=21.54 memory used=2289.0MB, alloc=396.3MB, time=21.91 memory used=2345.3MB, alloc=396.3MB, time=22.12 memory used=2395.8MB, alloc=396.3MB, time=22.29 memory used=2462.7MB, alloc=396.3MB, time=22.61 memory used=2518.7MB, alloc=396.3MB, time=22.82 memory used=2564.8MB, alloc=396.3MB, time=23.00 memory used=2635.6MB, alloc=396.3MB, time=24.27 memory used=2684.7MB, alloc=396.3MB, time=24.45 memory used=2752.8MB, alloc=396.3MB, time=24.99 memory used=2810.9MB, alloc=396.3MB, time=25.25 memory used=2864.8MB, alloc=396.3MB, time=25.45 memory used=2925.6MB, alloc=396.3MB, time=25.65 memory used=2966.0MB, alloc=396.3MB, time=25.84 memory used=3009.1MB, alloc=396.3MB, time=26.02 memory used=3056.9MB, alloc=396.3MB, time=26.19 memory used=3109.9MB, alloc=396.3MB, time=26.37 memory used=3168.8MB, alloc=396.3MB, time=26.55 memory used=3228.7MB, alloc=396.3MB, time=26.73 memory used=3271.2MB, alloc=396.3MB, time=26.88 memory used=3310.4MB, alloc=396.3MB, time=27.02 memory used=3372.1MB, alloc=396.3MB, time=27.53 memory used=3429.4MB, alloc=396.3MB, time=27.76 memory used=3482.5MB, alloc=396.3MB, time=27.97 memory used=3543.2MB, alloc=396.3MB, time=28.18 memory used=3583.7MB, alloc=396.3MB, time=28.35 memory used=3626.7MB, alloc=396.3MB, time=28.54 memory used=3674.5MB, alloc=396.3MB, time=28.72 memory used=3727.5MB, alloc=396.3MB, time=28.89 memory used=3786.4MB, alloc=396.3MB, time=29.08 memory used=3846.2MB, alloc=396.3MB, time=29.25 memory used=3888.6MB, alloc=396.3MB, time=29.40 memory used=3928.1MB, alloc=396.3MB, time=29.55 memory used=3981.7MB, alloc=396.3MB, time=30.03 memory used=4041.5MB, alloc=396.3MB, time=30.55 memory used=4097.3MB, alloc=396.3MB, time=30.75 memory used=4147.8MB, alloc=396.3MB, time=30.92 memory used=4214.0MB, alloc=396.3MB, time=31.23 memory used=4268.1MB, alloc=396.3MB, time=31.42 memory used=4313.8MB, alloc=396.3MB, time=31.60 memory used=4383.1MB, alloc=396.3MB, time=32.87 memory used=4432.6MB, alloc=396.3MB, time=33.05 memory used=4510.4MB, alloc=396.3MB, time=33.50 memory used=4647.6MB, alloc=396.3MB, time=35.32 memory used=4755.6MB, alloc=396.3MB, time=36.45 memory used=4859.1MB, alloc=396.3MB, time=37.60 memory used=4931.2MB, alloc=396.3MB, time=38.14 memory used=4996.8MB, alloc=396.3MB, time=38.49 memory used=5073.1MB, alloc=396.3MB, time=39.06 memory used=5125.7MB, alloc=396.3MB, time=39.27 memory used=5165.8MB, alloc=396.3MB, time=39.45 memory used=5228.0MB, alloc=396.3MB, time=39.76 memory used=5281.1MB, alloc=396.3MB, time=39.97 memory used=5321.2MB, alloc=396.3MB, time=40.13 memory used=5387.7MB, alloc=396.3MB, time=41.37 memory used=5432.2MB, alloc=396.3MB, time=41.54 memory used=5494.0MB, alloc=396.3MB, time=41.88 memory used=5545.0MB, alloc=396.3MB, time=42.07 memory used=5592.1MB, alloc=396.3MB, time=42.25 memory used=5652.5MB, alloc=396.3MB, time=42.55 memory used=5701.5MB, alloc=396.3MB, time=42.74 memory used=5747.0MB, alloc=396.3MB, time=42.93 memory used=5811.3MB, alloc=396.3MB, time=44.15 memory used=5858.5MB, alloc=396.3MB, time=44.35 memory used=5907.5MB, alloc=396.3MB, time=44.52 memory used=5962.2MB, alloc=396.3MB, time=44.85 memory used=6032.4MB, alloc=420.3MB, time=45.51 memory used=6095.8MB, alloc=420.3MB, time=45.76 memory used=6168.2MB, alloc=420.3MB, time=46.00 memory used=6218.4MB, alloc=420.3MB, time=46.20 memory used=6275.6MB, alloc=420.3MB, time=46.40 memory used=6341.0MB, alloc=420.3MB, time=46.62 memory used=6417.2MB, alloc=420.3MB, time=46.85 memory used=6482.8MB, alloc=420.3MB, time=47.06 memory used=6531.0MB, alloc=420.3MB, time=47.23 memory used=6604.7MB, alloc=420.3MB, time=47.74 memory used=6674.0MB, alloc=420.3MB, time=48.01 memory used=6751.5MB, alloc=420.3MB, time=48.26 memory used=6806.3MB, alloc=420.3MB, time=48.49 memory used=6861.4MB, alloc=420.3MB, time=48.69 memory used=6924.7MB, alloc=420.3MB, time=48.90 memory used=6998.3MB, alloc=420.3MB, time=49.13 memory used=7075.5MB, alloc=420.3MB, time=49.35 memory used=7123.3MB, alloc=420.3MB, time=49.52 memory used=7176.0MB, alloc=420.3MB, time=49.69 memory used=7236.6MB, alloc=420.3MB, time=50.21 memory used=7320.0MB, alloc=420.3MB, time=50.84 memory used=7380.7MB, alloc=420.3MB, time=51.04 memory used=7460.6MB, alloc=420.3MB, time=51.38 memory used=7523.7MB, alloc=420.3MB, time=51.59 memory used=7609.6MB, alloc=420.3MB, time=52.70 memory used=7671.4MB, alloc=420.3MB, time=52.91 memory used=7782.8MB, alloc=420.3MB, time=53.92 memory used=7907.7MB, alloc=420.3MB, time=55.36 memory used=8018.8MB, alloc=420.3MB, time=56.81 memory used=8138.7MB, alloc=444.3MB, time=58.02 memory used=8229.8MB, alloc=444.3MB, time=58.38 memory used=8327.4MB, alloc=444.3MB, time=59.13 memory used=8418.5MB, alloc=444.3MB, time=59.53 memory used=8543.2MB, alloc=444.3MB, time=61.87 memory used=8670.8MB, alloc=444.3MB, time=63.04 memory used=8766.5MB, alloc=444.3MB, time=63.71 memory used=8859.2MB, alloc=444.3MB, time=64.25 memory used=8955.7MB, alloc=444.3MB, time=64.90 memory used=9023.9MB, alloc=444.3MB, time=65.23 memory used=9102.8MB, alloc=444.3MB, time=65.55 memory used=9168.7MB, alloc=444.3MB, time=65.84 memory used=9224.2MB, alloc=444.3MB, time=66.11 memory used=9286.1MB, alloc=444.3MB, time=66.37 memory used=9355.9MB, alloc=444.3MB, time=66.63 memory used=9436.9MB, alloc=444.3MB, time=66.91 memory used=9507.5MB, alloc=444.3MB, time=67.17 memory used=9560.0MB, alloc=444.3MB, time=67.38 memory used=9660.0MB, alloc=444.3MB, time=68.14 memory used=9726.0MB, alloc=444.3MB, time=68.45 memory used=9808.2MB, alloc=444.3MB, time=68.77 memory used=9862.4MB, alloc=444.3MB, time=69.03 memory used=9920.6MB, alloc=444.3MB, time=69.32 memory used=9984.9MB, alloc=444.3MB, time=69.59 memory used=10058.0MB, alloc=444.3MB, time=69.87 memory used=10140.3MB, alloc=444.3MB, time=70.13 memory used=10198.5MB, alloc=444.3MB, time=70.36 memory used=10281.8MB, alloc=444.3MB, time=79.30 memory used=10373.6MB, alloc=444.3MB, time=81.60 memory used=10441.4MB, alloc=444.3MB, time=81.87 memory used=10504.5MB, alloc=444.3MB, time=82.15 memory used=10581.9MB, alloc=444.3MB, time=82.43 memory used=10653.8MB, alloc=444.3MB, 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used=21989.1MB, alloc=468.3MB, time=157.08 memory used=22120.7MB, alloc=468.3MB, time=158.75 memory used=22238.8MB, alloc=468.3MB, time=159.75 memory used=22390.0MB, alloc=468.3MB, time=161.45 memory used=22519.6MB, alloc=492.3MB, time=162.93 memory used=22607.6MB, alloc=492.3MB, time=164.32 memory used=22739.2MB, alloc=492.3MB, time=165.41 memory used=22866.5MB, alloc=492.3MB, time=166.69 memory used=22979.9MB, alloc=492.3MB, time=167.91 memory used=23062.1MB, alloc=492.3MB, time=168.27 memory used=23172.3MB, alloc=492.3MB, time=169.83 memory used=23301.0MB, alloc=516.3MB, time=171.02 memory used=23448.5MB, alloc=516.3MB, time=172.66 memory used=23534.0MB, alloc=516.3MB, time=173.94 memory used=23629.2MB, alloc=516.3MB, time=175.17 memory used=23726.8MB, alloc=516.3MB, time=176.42 memory used=23793.9MB, alloc=516.3MB, time=177.56 memory used=23876.5MB, alloc=516.3MB, time=178.67 memory used=23942.2MB, alloc=516.3MB, time=179.73 memory used=24003.3MB, alloc=516.3MB, time=180.89 memory 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used=47456.6MB, alloc=588.3MB, time=340.39 memory used=47635.4MB, alloc=588.3MB, time=341.01 memory used=47817.8MB, alloc=588.3MB, time=341.62 memory used=48008.8MB, alloc=588.3MB, time=342.27 memory used=48202.9MB, alloc=588.3MB, time=342.97 memory used=48400.3MB, alloc=588.3MB, time=343.62 memory used=48605.0MB, alloc=588.3MB, time=344.26 memory used=48812.3MB, alloc=588.3MB, time=345.00 memory used=49000.9MB, alloc=588.3MB, time=345.69 memory used=49168.1MB, alloc=588.3MB, time=346.35 memory used=49332.2MB, alloc=588.3MB, time=346.99 memory used=49500.7MB, alloc=588.3MB, time=347.60 memory used=49667.6MB, alloc=588.3MB, time=348.24 memory used=49837.8MB, alloc=588.3MB, time=348.94 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428495994 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 3 2 2 2 2 2 F := [12 x - 4 y z - 16 y , -9 x y + 11 x z - 11 x z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 3 G := [-13 x z - x z + y , -6 y z + x y z - 12 z ] > Problem := [F,G]; 4 3 3 2 2 2 2 2 Problem := [[12 x - 4 y z - 16 y , -9 x y + 11 x z - 11 x z], 3 2 2 2 2 3 [-13 x z - x z + y , -6 y z + x y z - 12 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.19 memory used=26.5MB, alloc=32.3MB, time=0.53 memory used=44.5MB, alloc=56.3MB, time=0.78 memory used=92.8MB, alloc=60.9MB, time=2.02 memory used=138.2MB, alloc=61.5MB, time=4.55 memory used=162.6MB, alloc=61.5MB, time=4.62 memory used=191.6MB, alloc=61.5MB, time=4.70 memory used=211.4MB, alloc=61.5MB, time=4.76 memory used=234.0MB, alloc=61.5MB, time=4.82 memory used=260.1MB, alloc=61.5MB, time=4.88 memory used=289.7MB, alloc=61.5MB, time=4.94 memory used=322.5MB, alloc=61.5MB, time=5.01 memory used=342.0MB, alloc=61.5MB, time=5.06 memory used=360.7MB, alloc=61.5MB, time=5.10 memory used=380.6MB, alloc=61.5MB, time=5.15 memory used=401.7MB, alloc=61.5MB, time=5.20 memory used=423.9MB, alloc=61.5MB, time=5.25 memory used=448.1MB, alloc=61.5MB, time=5.30 memory used=475.3MB, alloc=61.5MB, time=5.35 memory used=520.5MB, alloc=61.5MB, time=6.87 memory used=563.0MB, alloc=61.5MB, time=8.77 memory used=588.9MB, alloc=61.5MB, time=8.84 memory used=616.6MB, alloc=61.5MB, time=8.91 memory used=637.1MB, alloc=61.5MB, time=8.97 memory used=660.6MB, alloc=61.5MB, time=9.03 memory used=687.0MB, alloc=61.5MB, time=9.10 memory used=716.8MB, alloc=61.5MB, time=9.16 memory used=748.8MB, alloc=61.5MB, time=9.23 memory used=766.8MB, alloc=61.5MB, time=9.27 memory used=786.1MB, alloc=61.5MB, time=9.32 memory used=806.6MB, alloc=61.5MB, time=9.38 memory used=828.2MB, alloc=61.5MB, time=9.44 memory used=851.5MB, alloc=61.5MB, time=9.51 memory used=876.4MB, alloc=61.5MB, time=9.57 memory used=904.8MB, alloc=61.5MB, time=9.63 memory used=944.2MB, alloc=61.5MB, time=9.96 memory used=985.3MB, alloc=62.5MB, time=10.45 memory used=1010.1MB, alloc=62.5MB, time=10.51 memory used=1036.0MB, alloc=62.5MB, time=10.58 memory used=1076.9MB, alloc=62.5MB, time=10.95 memory used=1114.8MB, alloc=63.4MB, time=11.21 memory used=1153.4MB, alloc=63.4MB, time=11.53 memory used=1178.1MB, alloc=63.4MB, time=11.60 memory used=1209.9MB, alloc=63.4MB, time=12.03 memory used=1255.5MB, alloc=71.4MB, time=12.57 memory used=1298.4MB, alloc=71.4MB, time=13.08 memory used=1328.0MB, alloc=95.4MB, time=13.32 memory used=1372.2MB, alloc=95.4MB, time=13.46 memory used=1408.8MB, alloc=95.4MB, time=13.59 memory used=1445.2MB, alloc=95.4MB, time=13.71 memory used=1474.5MB, alloc=95.4MB, time=13.82 memory used=1523.1MB, alloc=95.4MB, time=14.05 memory used=1560.7MB, alloc=95.4MB, time=14.17 memory used=1602.1MB, alloc=95.4MB, time=14.28 memory used=1633.8MB, alloc=95.4MB, time=14.39 memory used=1665.8MB, alloc=95.4MB, time=14.49 memory used=1730.4MB, alloc=95.4MB, time=25.89 memory used=1777.4MB, alloc=119.4MB, time=49.46 memory used=1866.3MB, alloc=119.4MB, time=54.50 memory used=1973.3MB, alloc=119.4MB, time=55.19 memory used=2028.9MB, alloc=119.4MB, time=55.35 memory used=2071.1MB, alloc=119.4MB, time=55.49 memory used=2119.5MB, alloc=119.4MB, time=55.64 memory used=2176.9MB, alloc=119.4MB, time=55.78 memory used=2238.6MB, alloc=119.4MB, time=55.91 memory used=2273.4MB, alloc=119.4MB, time=56.01 memory used=2311.2MB, alloc=119.4MB, time=56.12 memory used=2351.9MB, alloc=119.4MB, time=56.23 memory used=2395.4MB, alloc=119.4MB, time=56.34 memory used=2441.8MB, alloc=119.4MB, time=56.44 memory used=2490.9MB, alloc=119.4MB, time=56.54 memory used=2542.6MB, alloc=119.4MB, time=56.65 memory used=2598.4MB, alloc=119.4MB, time=56.77 memory used=2656.4MB, alloc=119.4MB, time=56.87 memory used=2718.0MB, alloc=119.4MB, time=56.98 memory used=2791.8MB, alloc=131.8MB, time=57.11 memory used=2800.1MB, alloc=131.8MB, time=57.17 memory used=2808.5MB, alloc=131.8MB, time=57.22 memory used=2817.0MB, alloc=131.8MB, time=57.28 memory used=2826.8MB, alloc=131.8MB, time=57.33 memory used=2836.8MB, alloc=131.8MB, time=57.39 memory used=2846.7MB, alloc=131.8MB, time=57.45 memory used=2856.5MB, alloc=131.8MB, time=57.50 memory used=2866.2MB, alloc=131.8MB, time=57.56 memory used=2875.9MB, alloc=131.8MB, time=57.61 memory used=2885.5MB, alloc=131.8MB, time=57.67 memory used=2895.0MB, alloc=131.8MB, time=57.72 memory used=2904.6MB, alloc=131.8MB, time=57.78 memory used=2915.4MB, alloc=131.8MB, time=57.83 memory used=2926.2MB, alloc=131.8MB, time=57.89 memory used=2936.9MB, alloc=131.8MB, time=57.95 memory used=2947.4MB, alloc=131.8MB, time=58.00 memory used=2957.9MB, alloc=131.8MB, time=58.06 memory used=2969.6MB, alloc=131.8MB, time=58.13 memory used=2981.2MB, alloc=131.8MB, time=58.20 memory used=2992.7MB, alloc=131.8MB, time=58.26 memory used=3004.0MB, alloc=131.8MB, time=58.32 memory used=3016.4MB, alloc=131.8MB, time=58.38 memory used=3028.6MB, alloc=131.8MB, time=58.45 memory used=3040.5MB, alloc=131.8MB, time=58.52 memory used=3053.3MB, alloc=131.8MB, time=58.62 memory used=3065.8MB, alloc=131.8MB, time=58.70 memory used=3079.1MB, alloc=131.8MB, time=58.78 memory used=3092.2MB, alloc=131.8MB, time=58.86 memory used=3105.6MB, alloc=131.8MB, time=58.93 memory used=3119.5MB, alloc=131.8MB, time=59.00 memory used=3133.8MB, alloc=131.8MB, time=59.06 memory used=3148.3MB, alloc=131.8MB, time=59.12 memory used=3162.5MB, alloc=131.8MB, time=59.18 memory used=3178.4MB, alloc=131.8MB, time=59.24 memory used=3194.2MB, alloc=131.8MB, time=59.32 memory used=3259.3MB, alloc=131.8MB, time=59.62 memory used=3317.4MB, alloc=131.8MB, time=59.94 memory used=3399.6MB, alloc=131.8MB, time=62.26 memory used=3459.4MB, alloc=131.8MB, time=62.44 memory used=3508.4MB, alloc=131.8MB, time=62.56 memory used=3569.0MB, alloc=131.8MB, time=62.69 memory used=3608.3MB, alloc=131.8MB, time=62.78 memory used=3654.3MB, alloc=131.8MB, time=62.88 memory used=3706.8MB, alloc=131.8MB, time=62.98 memory used=3779.6MB, alloc=131.8MB, time=63.25 memory used=3831.8MB, alloc=131.8MB, time=63.39 memory used=3925.0MB, alloc=131.8MB, time=65.02 memory used=3988.4MB, alloc=131.8MB, time=65.36 memory used=4094.3MB, alloc=131.8MB, time=66.08 memory used=4207.7MB, alloc=131.8MB, time=66.78 memory used=4321.5MB, alloc=131.8MB, time=67.97 memory used=4436.7MB, alloc=131.8MB, time=70.01 memory used=4551.4MB, alloc=131.8MB, time=72.75 memory used=4657.0MB, alloc=131.8MB, time=74.87 memory used=4707.4MB, alloc=131.8MB, time=75.01 memory used=4784.0MB, alloc=131.8MB, time=75.71 memory used=4847.8MB, alloc=131.8MB, time=76.10 memory used=4929.6MB, alloc=387.8MB, time=77.07 memory used=5007.7MB, alloc=387.8MB, time=77.77 memory used=5092.7MB, alloc=387.8MB, time=78.80 memory used=5135.8MB, alloc=387.8MB, time=78.99 memory used=5214.7MB, alloc=387.8MB, time=101.26 memory used=5287.3MB, alloc=387.8MB, time=104.83 memory used=5349.4MB, alloc=387.8MB, time=105.22 memory used=5395.4MB, alloc=387.8MB, time=105.39 memory used=5429.0MB, alloc=387.8MB, time=105.53 memory used=5468.4MB, alloc=387.8MB, time=105.70 memory used=5514.0MB, alloc=387.8MB, time=105.85 memory used=5566.0MB, alloc=387.8MB, time=106.01 memory used=5595.1MB, alloc=387.8MB, time=106.13 memory used=5625.9MB, alloc=387.8MB, time=106.25 memory used=5658.3MB, alloc=387.8MB, time=106.38 memory used=5692.4MB, alloc=387.8MB, time=106.49 memory used=5729.1MB, alloc=387.8MB, time=106.62 memory used=5768.3MB, alloc=387.8MB, time=106.73 memory used=5810.7MB, alloc=387.8MB, time=106.85 memory used=5855.8MB, alloc=387.8MB, time=106.98 memory used=5904.6MB, alloc=387.8MB, time=107.11 memory used=5956.7MB, alloc=387.8MB, time=107.23 memory used=6102.7MB, alloc=387.8MB, time=109.41 memory used=6142.9MB, alloc=387.8MB, time=109.56 memory used=6189.3MB, alloc=387.8MB, time=109.72 memory used=6227.2MB, alloc=387.8MB, time=109.84 memory used=6262.9MB, alloc=387.8MB, time=109.96 memory used=6314.0MB, alloc=387.8MB, time=110.22 memory used=6402.5MB, alloc=387.8MB, time=110.96 memory used=6482.9MB, alloc=387.8MB, time=111.81 memory used=6520.3MB, alloc=387.8MB, time=111.95 memory used=6566.1MB, alloc=387.8MB, time=112.10 memory used=6596.8MB, alloc=387.8MB, time=112.20 memory used=6632.1MB, alloc=387.8MB, time=112.32 memory used=6674.8MB, alloc=387.8MB, time=112.44 memory used=6743.5MB, alloc=387.8MB, time=113.17 memory used=6792.1MB, alloc=387.8MB, time=113.45 memory used=6859.7MB, alloc=387.8MB, time=113.89 memory used=6949.3MB, alloc=387.8MB, time=115.03 memory used=7029.1MB, alloc=411.8MB, time=116.05 memory used=7137.3MB, alloc=435.8MB, time=117.45 memory used=7271.2MB, alloc=435.8MB, time=125.26 memory used=7331.7MB, alloc=435.8MB, time=125.50 memory used=7387.8MB, alloc=435.8MB, time=125.73 memory used=7460.0MB, alloc=435.8MB, time=125.95 memory used=7503.9MB, alloc=435.8MB, time=126.14 memory used=7553.3MB, alloc=435.8MB, time=126.35 memory used=7609.1MB, alloc=435.8MB, time=126.54 memory used=7709.8MB, alloc=435.8MB, time=134.17 memory used=7782.5MB, alloc=435.8MB, time=134.46 memory used=7833.1MB, alloc=435.8MB, time=134.69 memory used=7900.5MB, alloc=435.8MB, time=134.93 memory used=7955.1MB, alloc=435.8MB, time=135.12 memory used=8003.0MB, alloc=435.8MB, time=135.30 memory used=8057.8MB, alloc=435.8MB, time=135.50 memory used=8143.6MB, alloc=435.8MB, time=136.29 memory used=8202.5MB, alloc=435.8MB, time=136.53 memory used=8316.0MB, alloc=435.8MB, time=137.61 memory used=8455.6MB, alloc=459.8MB, time=138.85 memory used=8594.0MB, alloc=459.8MB, time=140.14 memory used=8729.9MB, alloc=459.8MB, time=141.70 memory used=8815.4MB, alloc=483.8MB, time=143.11 memory used=8968.3MB, alloc=483.8MB, time=144.78 memory used=9083.5MB, alloc=483.8MB, time=145.69 memory used=9199.5MB, alloc=483.8MB, time=147.15 memory used=9300.0MB, alloc=507.8MB, time=148.35 memory used=9388.4MB, alloc=507.8MB, time=149.65 memory used=9494.6MB, alloc=507.8MB, time=150.88 memory used=9596.7MB, alloc=507.8MB, time=151.51 memory used=9715.3MB, alloc=507.8MB, time=160.80 memory used=9891.2MB, alloc=507.8MB, time=192.10 memory used=9983.2MB, alloc=507.8MB, time=192.62 memory used=10060.9MB, alloc=507.8MB, time=193.06 memory used=10164.1MB, alloc=507.8MB, time=193.53 memory used=10226.2MB, alloc=531.8MB, time=193.92 memory used=10309.0MB, alloc=531.8MB, time=194.36 memory used=10403.3MB, alloc=531.8MB, time=194.76 memory used=10509.2MB, alloc=531.8MB, time=195.17 memory used=10629.2MB, alloc=531.8MB, time=195.64 memory used=10851.5MB, alloc=531.8MB, time=196.34 memory used=11016.1MB, alloc=531.8MB, time=196.82 memory used=11241.0MB, alloc=531.8MB, time=197.59 memory used=11396.5MB, alloc=531.8MB, time=236.91 memory used=11567.7MB, alloc=531.8MB, time=238.53 memory used=11658.1MB, alloc=531.8MB, time=238.99 memory used=11772.8MB, alloc=531.8MB, time=239.47 memory used=11847.2MB, alloc=531.8MB, time=239.86 memory used=11932.6MB, alloc=531.8MB, time=240.35 memory used=12028.1MB, alloc=531.8MB, time=240.73 memory used=12136.6MB, alloc=531.8MB, time=241.12 memory used=12258.7MB, alloc=531.8MB, time=241.53 memory used=12449.4MB, alloc=531.8MB, time=242.04 memory used=12613.8MB, alloc=531.8MB, time=242.57 memory used=12858.4MB, alloc=531.8MB, time=245.90 memory used=12959.6MB, alloc=531.8MB, time=246.34 memory used=13053.0MB, alloc=531.8MB, time=246.71 memory used=13188.3MB, alloc=531.8MB, time=247.43 memory used=13288.4MB, alloc=531.8MB, time=247.90 memory used=13412.1MB, alloc=531.8MB, time=248.57 memory used=13534.8MB, alloc=531.8MB, time=258.16 memory used=13726.5MB, alloc=531.8MB, time=291.33 memory used=13871.7MB, alloc=531.8MB, time=292.26 memory used=13965.7MB, alloc=531.8MB, time=292.74 memory used=14078.4MB, alloc=531.8MB, time=293.21 memory used=14154.6MB, alloc=531.8MB, time=293.61 memory used=14240.6MB, alloc=531.8MB, time=294.03 memory used=14338.5MB, alloc=531.8MB, time=294.46 memory used=14449.3MB, alloc=531.8MB, time=294.89 memory used=14575.5MB, alloc=531.8MB, time=295.38 memory used=14747.8MB, alloc=531.8MB, time=295.92 memory used=14911.9MB, alloc=531.8MB, time=296.45 memory used=15148.2MB, alloc=531.8MB, time=298.01 memory used=15255.8MB, alloc=531.8MB, time=298.58 memory used=15354.9MB, alloc=531.8MB, time=299.10 memory used=15437.0MB, alloc=531.8MB, time=299.60 memory used=15530.9MB, alloc=531.8MB, time=300.11 memory used=15639.2MB, alloc=531.8MB, time=300.62 memory used=15764.0MB, alloc=531.8MB, time=301.18 memory used=15849.2MB, alloc=531.8MB, time=301.57 memory used=15923.2MB, alloc=531.8MB, time=301.96 memory used=16003.3MB, alloc=531.8MB, time=302.37 memory used=16092.5MB, alloc=531.8MB, time=302.77 memory used=16223.6MB, alloc=531.8MB, time=303.87 memory used=16324.7MB, alloc=531.8MB, time=304.43 memory used=16430.7MB, alloc=531.8MB, time=304.94 memory used=16512.3MB, alloc=531.8MB, time=305.39 memory used=16605.5MB, alloc=531.8MB, time=305.87 memory used=16713.2MB, alloc=531.8MB, time=306.33 memory used=16834.3MB, alloc=531.8MB, time=306.82 memory used=16927.6MB, alloc=531.8MB, time=307.28 memory used=16999.7MB, alloc=531.8MB, time=307.71 memory used=17080.2MB, alloc=531.8MB, time=308.12 memory used=17167.9MB, alloc=531.8MB, time=308.50 memory used=17309.0MB, alloc=531.8MB, time=335.45 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428496294 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 F := [18 x y z - 5 x y z + y z, 9 y - 8 y z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 4 3 2 G := [-12 y z + 3 x - 5 z, -7 x + 20 x z + 5 y z] > Problem := [F,G]; 2 2 2 3 Problem := [[18 x y z - 5 x y z + y z, 9 y - 8 y z], 2 2 4 3 2 [-12 y z + 3 x - 5 z, -7 x + 20 x z + 5 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.4MB, alloc=32.3MB, time=0.52 memory used=47.0MB, alloc=32.3MB, time=0.83 memory used=66.4MB, alloc=60.3MB, time=1.14 memory used=108.6MB, alloc=60.3MB, time=1.75 memory used=139.1MB, alloc=84.3MB, time=2.23 memory used=203.0MB, alloc=92.3MB, time=3.20 memory used=265.7MB, alloc=116.3MB, time=4.21 memory used=338.6MB, alloc=116.3MB, time=5.28 memory used=399.2MB, alloc=372.3MB, time=6.26 memory used=484.5MB, alloc=396.3MB, time=7.56 memory used=591.5MB, alloc=420.3MB, time=9.43 memory used=725.4MB, alloc=444.3MB, time=11.75 memory used=863.6MB, alloc=468.3MB, time=14.29 memory used=1014.6MB, alloc=492.3MB, time=17.19 memory used=1184.9MB, alloc=516.3MB, time=20.34 memory used=1369.9MB, alloc=540.3MB, time=23.87 memory used=1567.9MB, alloc=564.3MB, time=27.63 memory used=1759.6MB, alloc=588.3MB, time=31.39 memory used=1946.6MB, alloc=612.3MB, time=35.34 memory used=2124.6MB, alloc=636.3MB, time=39.79 memory used=2326.7MB, alloc=660.3MB, time=47.30 memory used=2534.0MB, alloc=684.3MB, time=55.40 memory used=2752.8MB, alloc=708.3MB, time=64.51 memory used=2985.3MB, alloc=732.3MB, time=73.73 memory used=3232.5MB, alloc=756.3MB, time=84.37 memory used=3493.7MB, alloc=780.3MB, time=94.87 memory used=3766.5MB, alloc=804.3MB, time=106.95 memory used=4056.5MB, alloc=828.3MB, time=120.34 memory used=4370.5MB, alloc=852.3MB, time=134.34 memory used=4708.4MB, alloc=876.3MB, time=149.80 memory used=5070.2MB, alloc=900.3MB, time=165.64 memory used=5456.0MB, alloc=924.3MB, time=183.29 memory used=5865.7MB, alloc=948.3MB, time=202.15 memory used=6299.3MB, alloc=948.3MB, time=221.93 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428496594 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 2 F := [18 x y + 12 y z - 4 x y, -11 x + 13 x + 17 z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 4 3 2 G := [-17 y - 9 x y - 17 z, -8 x - 14 y - 7 y ] > Problem := [F,G]; 3 2 3 2 2 Problem := [[18 x y + 12 y z - 4 x y, -11 x + 13 x + 17 z ], 3 4 3 2 [-17 y - 9 x y - 17 z, -8 x - 14 y - 7 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=25.3MB, alloc=32.3MB, time=0.47 memory used=44.4MB, alloc=32.3MB, time=0.74 memory used=63.8MB, alloc=32.3MB, time=0.95 memory used=78.1MB, alloc=32.3MB, time=1.02 memory used=94.7MB, alloc=56.3MB, time=1.16 memory used=131.8MB, alloc=56.3MB, time=1.32 memory used=166.6MB, alloc=61.1MB, time=1.69 memory used=213.4MB, alloc=69.1MB, time=2.26 memory used=262.5MB, alloc=69.1MB, time=2.80 memory used=301.5MB, alloc=93.1MB, time=3.38 memory used=369.6MB, alloc=93.1MB, time=4.48 memory used=427.5MB, alloc=117.1MB, time=5.53 memory used=506.4MB, alloc=141.1MB, time=6.97 memory used=599.7MB, alloc=165.1MB, time=9.16 memory used=698.0MB, alloc=189.1MB, time=12.49 memory used=813.7MB, alloc=189.1MB, time=16.72 N1 := 2931 > GB := Basis(F, plex(op(vars))); 3 3 2 3 2 2 GB := [66 x y + 153 x y - 78 x y - 34 x y, -11 x + 13 x + 17 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=940.9MB, alloc=189.1MB, time=19.51 N2 := 701 > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 3 2 2 3 H := [18 x y + 12 y z - 4 x y, -11 x + 13 x + 17 z , -17 y - 9 x y - 17 z, 4 3 2 -8 x - 14 y - 7 y ] > J:=[op(GB),op(G)]; 3 3 2 3 2 2 J := [66 x y + 153 x y - 78 x y - 34 x y, -11 x + 13 x + 17 z , 3 4 3 2 -17 y - 9 x y - 17 z, -8 x - 14 y - 7 y ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 10, 14, 4, 4, 3, 2, 1, 3/4, 3/4, 1/2, 7/12, 1/4, 4, 9, 14, 4, 4, 3, 2, 1, 3/4, 1/2, 8/13, 8/13, 2/13, 1, 0, 0] > save(F, G, cat("ranSet/34", convert(F, string),".txt")); > quit memory used=1003.9MB, alloc=189.1MB, time=20.82 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428496617 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 4 3 2 F := [10 y + 13 z - 17 x y, -19 y + 7 x - 5] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 G := [18 x y - 17 x y + 16 y z, 8 x z + 20 x y z + 7 y z] > Problem := [F,G]; 4 4 3 2 Problem := [[10 y + 13 z - 17 x y, -19 y + 7 x - 5], 2 3 2 [18 x y - 17 x y + 16 y z, 8 x z + 20 x y z + 7 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.15 memory used=25.8MB, alloc=32.3MB, time=0.44 memory used=46.5MB, alloc=32.3MB, time=0.75 memory used=66.4MB, alloc=60.3MB, time=1.07 memory used=108.2MB, alloc=60.3MB, time=1.64 memory used=149.9MB, alloc=60.3MB, time=2.21 memory used=191.0MB, alloc=92.3MB, time=2.84 memory used=255.5MB, alloc=92.3MB, time=3.74 memory used=322.0MB, alloc=92.3MB, time=4.52 memory used=388.5MB, alloc=116.3MB, time=5.55 memory used=478.0MB, alloc=116.3MB, time=6.95 memory used=554.0MB, alloc=140.3MB, time=8.28 memory used=652.0MB, alloc=164.3MB, time=9.88 memory used=770.8MB, alloc=188.3MB, time=11.80 memory used=896.4MB, alloc=212.3MB, time=14.51 memory used=1019.7MB, alloc=236.3MB, time=18.33 memory used=1153.3MB, alloc=260.3MB, time=23.11 memory used=1305.4MB, alloc=284.3MB, time=28.84 memory used=1481.4MB, alloc=284.3MB, time=35.31 memory used=1657.5MB, alloc=308.3MB, time=41.98 memory used=1857.6MB, alloc=308.3MB, time=49.93 N1 := 5915 > GB := Basis(F, plex(op(vars))); 3 2 4 2 GB := [19 y - 7 x + 5, 247 z + 70 x y - 323 x y - 50 y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=2068.2MB, alloc=308.3MB, time=56.82 memory used=2145.1MB, alloc=564.3MB, time=58.32 memory used=2394.1MB, alloc=588.3MB, time=63.06 memory used=2653.3MB, alloc=612.3MB, time=68.82 memory used=2883.1MB, alloc=636.3MB, time=77.14 memory used=3116.8MB, alloc=660.3MB, time=86.93 memory used=3374.5MB, alloc=684.3MB, time=97.69 memory used=3656.3MB, alloc=708.3MB, time=109.11 N2 := 5959 > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 4 4 3 2 2 H := [10 y + 13 z - 17 x y, -19 y + 7 x - 5, 18 x y - 17 x y + 16 y z, 3 2 8 x z + 20 x y z + 7 y z] > J:=[op(GB),op(G)]; 3 2 4 2 J := [19 y - 7 x + 5, 247 z + 70 y x - 323 y x - 50 y, 2 3 2 18 x y - 17 x y + 16 y z, 8 x z + 20 x y z + 7 y z] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 11, 14, 4, 2, 4, 4, 1, 1, 3/4, 1/2, 2/3, 5/12, 4, 11, 14, 4, 2, 3, 4, 1, 1, 3/4, 7/13, 9/13, 5/13, 0, 0, 0] > save(F, G, cat("ranSet/34", convert(F, string),".txt")); > quit memory used=3770.7MB, alloc=708.3MB, time=113.16 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428496743 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 3 3 2 F := [-13 x y z - 14 y z - 18 y z , -3 y z - 4 y + 17 y ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 2 G := [12 x y + 3 y z - 15 x, -18 x y z - 7 x z + 12 y z] > Problem := [F,G]; 2 3 2 3 3 2 Problem := [[-13 x y z - 14 y z - 18 y z , -3 y z - 4 y + 17 y ], 3 2 2 2 2 2 [12 x y + 3 y z - 15 x, -18 x y z - 7 x z + 12 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=25.4MB, alloc=32.3MB, time=0.49 memory used=45.1MB, alloc=32.3MB, time=0.76 memory used=64.0MB, alloc=56.3MB, time=1.01 memory used=106.4MB, alloc=60.3MB, time=1.56 memory used=142.3MB, alloc=60.3MB, time=2.06 memory used=184.2MB, alloc=68.3MB, time=2.63 memory used=230.5MB, alloc=68.3MB, time=3.22 memory used=271.8MB, alloc=92.3MB, time=3.78 memory used=337.5MB, alloc=92.3MB, time=4.49 memory used=413.4MB, alloc=92.3MB, time=5.27 memory used=479.6MB, alloc=92.3MB, time=6.05 memory used=525.5MB, alloc=92.3MB, time=6.47 memory used=588.4MB, alloc=92.3MB, time=7.47 memory used=653.3MB, alloc=92.3MB, time=8.43 memory used=717.6MB, alloc=116.3MB, time=9.33 memory used=783.4MB, alloc=116.3MB, time=10.22 memory used=835.7MB, alloc=116.3MB, time=10.51 memory used=878.7MB, alloc=116.3MB, time=11.18 memory used=964.1MB, alloc=128.2MB, time=14.13 memory used=1024.1MB, alloc=128.2MB, time=14.63 memory used=1083.0MB, alloc=384.2MB, time=15.44 memory used=1185.6MB, alloc=408.2MB, time=16.81 memory used=1249.8MB, alloc=408.2MB, time=17.09 memory used=1306.3MB, alloc=408.2MB, time=17.27 memory used=1353.5MB, alloc=408.2MB, time=17.44 memory used=1411.1MB, alloc=408.2MB, time=17.62 memory used=1473.6MB, alloc=408.2MB, time=17.79 memory used=1514.2MB, alloc=408.2MB, time=17.92 memory used=1579.6MB, alloc=408.2MB, time=23.86 memory used=1653.6MB, alloc=408.2MB, time=25.46 memory used=1707.1MB, alloc=408.2MB, time=25.63 memory used=1758.4MB, alloc=408.2MB, time=25.79 memory used=1805.3MB, alloc=408.2MB, time=25.93 memory used=1886.9MB, alloc=408.2MB, time=26.39 memory used=2008.5MB, alloc=408.2MB, time=28.27 memory used=2082.8MB, alloc=408.2MB, time=28.88 memory used=2152.3MB, alloc=408.2MB, time=29.42 memory used=2240.2MB, alloc=408.2MB, time=30.22 memory used=2325.9MB, alloc=408.2MB, time=31.05 memory used=2373.6MB, alloc=408.2MB, time=31.32 memory used=2553.1MB, alloc=408.2MB, time=38.78 memory used=2602.8MB, alloc=408.2MB, time=38.96 memory used=2704.8MB, alloc=408.2MB, time=40.40 memory used=2817.6MB, alloc=432.2MB, time=41.86 memory used=2906.3MB, alloc=432.2MB, time=42.41 memory used=2963.5MB, alloc=432.2MB, time=42.63 memory used=3040.8MB, alloc=432.2MB, time=44.29 memory used=3115.1MB, alloc=432.2MB, time=46.58 memory used=3173.4MB, alloc=432.2MB, time=46.78 memory used=3303.3MB, alloc=432.2MB, time=48.33 memory used=3414.3MB, alloc=456.2MB, time=50.27 memory used=3539.6MB, alloc=456.2MB, time=51.41 memory used=3632.8MB, alloc=456.2MB, time=52.09 memory used=3709.8MB, alloc=456.2MB, time=52.66 memory used=3801.5MB, alloc=456.2MB, time=58.99 memory used=3878.5MB, alloc=456.2MB, time=59.26 memory used=3938.5MB, alloc=456.2MB, time=59.47 memory used=4006.7MB, alloc=456.2MB, time=59.67 memory used=4113.9MB, alloc=456.2MB, time=59.99 memory used=4215.4MB, alloc=456.2MB, time=80.19 memory used=4289.7MB, alloc=456.2MB, time=81.10 memory used=4366.4MB, alloc=456.2MB, time=81.36 memory used=4428.9MB, alloc=456.2MB, time=81.58 memory used=4488.8MB, alloc=456.2MB, time=81.80 memory used=4557.6MB, alloc=456.2MB, time=82.02 memory used=4638.7MB, alloc=456.2MB, time=82.27 memory used=4872.5MB, alloc=456.2MB, time=83.59 memory used=5052.0MB, alloc=456.2MB, time=84.55 memory used=5215.5MB, alloc=456.2MB, time=85.38 memory used=5372.7MB, alloc=456.2MB, time=86.10 memory used=5529.2MB, alloc=456.2MB, time=86.83 memory used=5683.9MB, alloc=456.2MB, time=87.50 memory used=5840.0MB, alloc=456.2MB, time=88.21 memory used=5990.4MB, alloc=456.2MB, time=88.92 memory used=6139.6MB, alloc=456.2MB, time=89.59 memory used=6286.9MB, alloc=456.2MB, time=90.29 memory used=6438.0MB, alloc=456.2MB, time=91.10 memory used=6619.2MB, alloc=456.2MB, time=92.13 memory used=6789.9MB, alloc=456.2MB, time=93.08 memory used=6956.8MB, alloc=456.2MB, time=93.96 memory used=7136.1MB, alloc=456.2MB, time=95.07 memory used=7309.9MB, alloc=456.2MB, time=95.97 memory used=7489.6MB, alloc=456.2MB, time=97.15 memory used=7609.3MB, alloc=456.2MB, time=97.65 memory used=7745.0MB, alloc=456.2MB, time=98.07 memory used=7922.9MB, alloc=456.2MB, time=98.55 memory used=8088.9MB, alloc=456.2MB, time=99.02 memory used=8259.5MB, alloc=456.2MB, time=99.48 memory used=8443.2MB, alloc=456.2MB, time=100.00 memory used=8625.7MB, alloc=456.2MB, time=100.49 memory used=8813.1MB, alloc=456.2MB, time=101.02 memory used=9012.4MB, alloc=456.2MB, time=101.51 memory used=9230.3MB, alloc=456.2MB, time=102.08 memory used=9475.3MB, alloc=456.2MB, time=102.68 memory used=9746.5MB, alloc=456.2MB, time=103.39 memory used=10061.0MB, alloc=456.2MB, time=104.12 memory used=10405.8MB, alloc=456.2MB, time=104.89 memory used=10784.7MB, alloc=456.2MB, time=105.74 memory used=11187.1MB, alloc=456.2MB, time=106.70 memory used=11524.8MB, alloc=456.2MB, time=108.84 memory used=11643.3MB, alloc=456.2MB, time=109.43 memory used=11766.9MB, alloc=456.2MB, time=109.87 memory used=11912.1MB, alloc=456.2MB, time=110.31 memory used=12084.7MB, alloc=456.2MB, time=110.78 memory used=12312.1MB, alloc=456.2MB, time=111.30 memory used=12600.8MB, alloc=456.2MB, time=111.95 memory used=12947.0MB, alloc=456.2MB, time=112.72 memory used=13293.0MB, alloc=456.2MB, time=113.50 memory used=13678.2MB, alloc=456.2MB, time=114.44 memory used=14079.6MB, alloc=456.2MB, time=115.34 memory used=14474.1MB, alloc=456.2MB, time=116.14 memory used=14671.8MB, alloc=456.2MB, time=117.05 memory used=14792.0MB, alloc=456.2MB, time=117.43 memory used=14933.4MB, alloc=456.2MB, time=117.84 memory used=15101.3MB, alloc=456.2MB, time=118.27 memory used=15306.7MB, alloc=456.2MB, time=118.76 memory used=15599.0MB, alloc=456.2MB, time=119.38 memory used=15983.7MB, alloc=456.2MB, time=120.18 memory used=16369.9MB, alloc=456.2MB, time=120.97 memory used=16768.3MB, alloc=456.2MB, time=121.78 memory used=17156.9MB, alloc=456.2MB, time=122.59 memory used=17545.3MB, alloc=456.2MB, time=123.40 memory used=17931.3MB, alloc=456.2MB, time=124.20 memory used=18086.8MB, alloc=456.2MB, time=125.26 memory used=18194.0MB, alloc=480.2MB, time=125.81 memory used=18315.7MB, alloc=480.2MB, time=126.31 memory used=18437.0MB, alloc=480.2MB, time=126.77 memory used=18567.5MB, alloc=480.2MB, time=127.29 memory used=18702.2MB, alloc=480.2MB, time=127.76 memory used=18843.9MB, alloc=480.2MB, time=128.33 memory used=19029.2MB, alloc=480.2MB, time=130.03 memory used=19170.0MB, alloc=480.2MB, time=130.48 memory used=19362.7MB, alloc=480.2MB, time=130.98 memory used=19621.6MB, alloc=480.2MB, time=131.54 memory used=19954.4MB, alloc=480.2MB, time=132.39 memory used=20286.3MB, alloc=480.2MB, time=133.12 memory used=20657.1MB, alloc=480.2MB, time=133.90 memory used=21053.9MB, alloc=480.2MB, time=134.66 memory used=21454.9MB, alloc=480.2MB, time=135.49 memory used=21857.4MB, alloc=480.2MB, time=136.29 memory used=22246.2MB, alloc=480.2MB, time=137.05 memory used=22636.9MB, alloc=480.2MB, time=137.85 memory used=22960.3MB, alloc=480.2MB, time=139.22 memory used=23106.0MB, alloc=480.2MB, time=139.74 memory used=23303.2MB, alloc=480.2MB, time=140.27 memory used=23566.1MB, alloc=480.2MB, time=140.87 memory used=23980.2MB, alloc=480.2MB, time=141.75 memory used=24373.7MB, alloc=480.2MB, time=142.58 memory used=24766.5MB, alloc=480.2MB, time=143.41 memory used=25143.6MB, alloc=480.2MB, time=144.19 memory used=25525.2MB, alloc=480.2MB, time=145.00 memory used=25898.5MB, alloc=480.2MB, time=145.79 memory used=26263.7MB, alloc=480.2MB, time=146.53 memory used=26634.7MB, alloc=480.2MB, time=147.28 memory used=26997.3MB, alloc=480.2MB, time=148.03 memory used=27364.1MB, alloc=480.2MB, time=148.78 memory used=27730.0MB, alloc=480.2MB, time=149.51 memory used=28097.5MB, alloc=480.2MB, time=150.27 memory used=28452.4MB, alloc=480.2MB, time=151.99 memory used=28582.8MB, alloc=480.2MB, time=152.55 memory used=28721.2MB, alloc=480.2MB, time=153.40 memory used=28887.1MB, alloc=480.2MB, time=154.05 memory used=29096.5MB, alloc=480.2MB, time=154.66 memory used=29375.2MB, alloc=480.2MB, time=155.32 memory used=29781.5MB, alloc=480.2MB, time=156.17 memory used=30156.5MB, alloc=480.2MB, time=157.07 memory used=30531.6MB, alloc=480.2MB, time=157.84 memory used=30895.8MB, alloc=480.2MB, time=158.54 memory used=31250.7MB, alloc=480.2MB, time=159.23 memory used=31604.4MB, alloc=480.2MB, time=159.95 memory used=31956.8MB, alloc=480.2MB, time=160.63 memory used=32315.0MB, alloc=480.2MB, time=161.45 memory used=32672.3MB, alloc=480.2MB, time=162.24 memory used=33034.3MB, alloc=480.2MB, time=162.97 memory used=33390.0MB, alloc=480.2MB, time=163.72 memory used=33748.5MB, alloc=480.2MB, time=164.47 memory used=34107.4MB, alloc=480.2MB, time=165.19 memory used=34469.6MB, alloc=480.2MB, time=165.95 memory used=34820.6MB, alloc=480.2MB, time=166.67 memory used=35181.0MB, alloc=480.2MB, time=167.46 memory used=35539.6MB, alloc=480.2MB, time=168.21 memory used=35895.2MB, alloc=480.2MB, time=168.93 memory used=36253.4MB, alloc=480.2MB, time=169.67 memory used=36610.3MB, alloc=480.2MB, time=170.44 memory used=36966.9MB, alloc=480.2MB, time=171.18 memory used=37325.6MB, alloc=480.2MB, time=172.08 memory used=37686.3MB, alloc=480.2MB, time=172.80 memory used=38045.9MB, alloc=480.2MB, time=173.53 memory used=38404.0MB, alloc=480.2MB, time=174.21 memory used=38768.3MB, alloc=480.2MB, time=174.93 memory used=39125.0MB, alloc=480.2MB, time=175.62 memory used=39430.8MB, alloc=480.2MB, time=177.45 memory used=39561.7MB, alloc=480.2MB, time=178.07 memory used=39698.3MB, alloc=480.2MB, time=178.54 memory used=39836.0MB, alloc=480.2MB, time=179.02 memory used=39978.0MB, alloc=480.2MB, time=179.47 memory used=40133.3MB, alloc=480.2MB, time=179.96 memory used=40298.8MB, alloc=480.2MB, time=180.46 memory used=40478.1MB, alloc=480.2MB, time=180.97 memory used=40671.2MB, alloc=480.2MB, time=181.48 memory used=40878.3MB, alloc=480.2MB, time=182.01 memory used=41100.5MB, alloc=480.2MB, time=182.56 memory used=41341.6MB, alloc=480.2MB, time=183.14 memory used=41618.3MB, alloc=480.2MB, time=184.13 memory used=41820.9MB, alloc=480.2MB, time=185.29 memory used=42021.6MB, alloc=480.2MB, time=186.53 memory used=42219.1MB, alloc=480.2MB, time=187.62 memory used=42419.8MB, alloc=480.2MB, time=189.01 memory used=42615.1MB, alloc=480.2MB, time=190.08 memory used=42813.2MB, alloc=480.2MB, time=191.34 memory used=43008.4MB, alloc=480.2MB, time=192.47 memory used=43196.0MB, alloc=480.2MB, time=193.45 memory used=43376.5MB, alloc=480.2MB, time=194.43 memory used=43556.2MB, alloc=480.2MB, time=195.42 memory used=43746.7MB, alloc=480.2MB, time=196.97 memory used=43939.8MB, alloc=480.2MB, time=198.40 memory used=44127.3MB, alloc=480.2MB, time=200.14 memory used=44309.9MB, alloc=480.2MB, time=201.92 memory used=44483.8MB, alloc=480.2MB, time=203.90 memory used=45058.7MB, alloc=504.2MB, time=215.61 memory used=45248.6MB, alloc=528.2MB, time=217.99 memory used=45872.3MB, alloc=528.2MB, time=230.54 memory used=46501.0MB, alloc=528.2MB, time=242.99 memory used=47111.3MB, alloc=552.2MB, time=255.88 memory used=47333.1MB, alloc=576.2MB, time=259.07 memory used=48051.0MB, alloc=576.2MB, time=273.89 memory used=48773.4MB, alloc=600.2MB, time=288.59 memory used=49004.3MB, alloc=624.2MB, time=292.83 memory used=49314.0MB, alloc=624.2MB, time=296.64 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428497043 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 F := [-2 y z - 8 y + 16 y, -5 y z - 13 y z - 9] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 3 3 2 G := [-7 x z - 2 y z + 12 x z , -20 y z + 11 y + 7 y z ] > Problem := [F,G]; 3 3 2 Problem := [[-2 y z - 8 y + 16 y, -5 y z - 13 y z - 9], 3 2 2 2 3 3 2 [-7 x z - 2 y z + 12 x z , -20 y z + 11 y + 7 y z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.7MB, alloc=32.3MB, time=0.51 memory used=46.1MB, alloc=56.3MB, time=0.82 memory used=88.3MB, alloc=60.3MB, time=1.43 memory used=128.3MB, alloc=60.3MB, time=2.03 memory used=165.9MB, alloc=84.3MB, time=2.62 memory used=228.6MB, alloc=92.3MB, time=3.56 memory used=296.4MB, alloc=92.3MB, time=4.39 memory used=359.7MB, alloc=92.3MB, time=5.34 memory used=419.9MB, alloc=92.3MB, time=6.11 memory used=479.0MB, alloc=92.3MB, time=6.87 memory used=540.9MB, alloc=116.3MB, time=7.72 memory used=609.1MB, alloc=116.3MB, time=8.69 memory used=680.6MB, alloc=372.3MB, time=9.52 memory used=765.5MB, alloc=372.3MB, time=10.35 memory used=864.8MB, alloc=372.3MB, time=11.55 memory used=942.3MB, alloc=372.3MB, time=12.26 memory used=1029.7MB, alloc=396.3MB, time=13.38 memory used=1143.7MB, alloc=396.3MB, time=14.86 memory used=1199.3MB, alloc=396.3MB, time=15.17 memory used=1247.9MB, alloc=396.3MB, time=15.46 memory used=1298.6MB, alloc=396.3MB, time=15.73 memory used=1349.6MB, alloc=396.3MB, time=16.03 memory used=1400.8MB, alloc=396.3MB, time=16.33 memory used=1450.7MB, alloc=396.3MB, time=16.61 memory used=1510.7MB, alloc=396.3MB, time=16.99 memory used=1555.6MB, alloc=420.3MB, time=17.31 memory used=1622.8MB, alloc=420.3MB, time=17.63 memory used=1673.1MB, alloc=420.3MB, time=17.91 memory used=1731.8MB, alloc=420.3MB, time=18.15 memory used=1801.1MB, alloc=420.3MB, time=18.40 memory used=1881.2MB, alloc=420.3MB, time=18.65 memory used=1926.4MB, alloc=420.3MB, time=18.82 memory used=1971.8MB, alloc=420.3MB, time=19.00 memory used=2019.6MB, alloc=420.3MB, time=19.19 memory used=2071.9MB, alloc=420.3MB, time=19.37 memory used=2128.0MB, alloc=420.3MB, time=19.61 memory used=2187.3MB, alloc=420.3MB, time=19.82 memory used=2251.0MB, alloc=420.3MB, time=20.02 memory used=2320.1MB, alloc=420.3MB, time=20.24 memory used=2394.9MB, alloc=420.3MB, time=20.43 memory used=2485.7MB, alloc=420.3MB, time=20.81 memory used=2551.0MB, alloc=420.3MB, time=21.10 memory used=2612.6MB, alloc=420.3MB, time=21.36 memory used=2664.7MB, alloc=420.3MB, time=21.62 memory used=2726.9MB, alloc=420.3MB, time=21.89 memory used=2797.6MB, alloc=420.3MB, time=22.14 memory used=2869.8MB, alloc=420.3MB, time=22.40 memory used=2912.0MB, alloc=420.3MB, time=22.59 memory used=2957.6MB, alloc=420.3MB, time=22.81 memory used=3005.7MB, alloc=420.3MB, time=22.99 memory used=3057.7MB, alloc=420.3MB, time=23.19 memory used=3113.7MB, alloc=420.3MB, time=23.39 memory used=3173.0MB, alloc=420.3MB, time=23.59 memory used=3237.9MB, alloc=420.3MB, time=23.80 memory used=3307.7MB, alloc=420.3MB, time=24.01 memory used=3383.3MB, alloc=420.3MB, time=24.22 memory used=3485.1MB, alloc=420.3MB, time=35.86 memory used=3563.1MB, alloc=420.3MB, time=36.60 memory used=3617.3MB, alloc=420.3MB, time=36.85 memory used=3687.6MB, alloc=420.3MB, time=37.12 memory used=3748.9MB, alloc=420.3MB, time=37.35 memory used=3794.6MB, alloc=420.3MB, time=37.54 memory used=3846.0MB, alloc=420.3MB, time=37.73 memory used=3900.5MB, alloc=420.3MB, time=37.93 memory used=3959.7MB, alloc=420.3MB, time=38.13 memory used=4023.8MB, alloc=420.3MB, time=38.34 memory used=4093.0MB, alloc=420.3MB, time=38.55 memory used=4169.0MB, alloc=420.3MB, time=38.77 memory used=4375.8MB, alloc=420.3MB, time=39.38 memory used=4521.5MB, alloc=420.3MB, time=39.72 memory used=4683.1MB, alloc=420.3MB, time=40.07 memory used=4863.2MB, alloc=420.3MB, time=40.45 memory used=5067.4MB, alloc=420.3MB, time=40.85 memory used=5292.2MB, alloc=420.3MB, time=41.24 memory used=5421.3MB, alloc=420.3MB, time=42.63 memory used=5489.2MB, alloc=420.3MB, time=42.87 memory used=5542.2MB, alloc=420.3MB, time=43.10 memory used=5611.6MB, alloc=420.3MB, time=43.32 memory used=5668.2MB, alloc=420.3MB, time=43.50 memory used=5717.2MB, alloc=420.3MB, time=43.66 memory used=5772.9MB, alloc=420.3MB, time=43.82 memory used=5854.3MB, alloc=420.3MB, time=44.95 memory used=5914.6MB, alloc=420.3MB, time=45.23 memory used=5974.6MB, alloc=420.3MB, time=45.47 memory used=6027.4MB, alloc=420.3MB, time=45.66 memory used=6090.4MB, alloc=420.3MB, time=45.86 memory used=6164.7MB, alloc=420.3MB, time=46.07 memory used=6361.8MB, alloc=420.3MB, time=47.09 memory used=6444.5MB, alloc=420.3MB, time=47.63 memory used=6517.5MB, alloc=420.3MB, time=47.94 memory used=6576.5MB, alloc=420.3MB, time=48.16 memory used=6652.6MB, alloc=420.3MB, time=48.47 memory used=6717.6MB, alloc=420.3MB, time=48.72 memory used=6773.9MB, alloc=420.3MB, time=48.94 memory used=6866.2MB, alloc=420.3MB, time=55.28 memory used=6925.5MB, alloc=420.3MB, time=55.51 memory used=6993.0MB, alloc=420.3MB, time=55.76 memory used=7040.7MB, alloc=420.3MB, time=55.94 memory used=7097.2MB, alloc=420.3MB, time=56.14 memory used=7162.7MB, alloc=420.3MB, time=56.34 memory used=7289.0MB, alloc=420.3MB, time=56.96 memory used=7362.8MB, alloc=420.3MB, time=57.32 memory used=7430.4MB, alloc=420.3MB, time=57.79 memory used=7549.2MB, alloc=420.3MB, time=58.84 memory used=7624.0MB, alloc=420.3MB, time=59.18 memory used=7688.6MB, alloc=420.3MB, time=59.49 memory used=7747.1MB, alloc=420.3MB, time=59.70 memory used=7832.1MB, alloc=420.3MB, time=63.25 memory used=7887.5MB, alloc=420.3MB, time=63.47 memory used=7947.1MB, alloc=420.3MB, time=63.66 memory used=7997.4MB, alloc=420.3MB, time=63.83 memory used=8092.8MB, alloc=420.3MB, time=64.54 memory used=8160.1MB, alloc=420.3MB, time=64.94 memory used=8283.8MB, alloc=444.3MB, time=67.12 memory used=8376.5MB, alloc=444.3MB, time=68.17 memory used=8571.6MB, alloc=444.3MB, time=69.59 memory used=8745.7MB, alloc=468.3MB, time=71.80 memory used=8844.1MB, alloc=468.3MB, time=72.85 memory used=8977.7MB, alloc=468.3MB, time=74.32 memory used=9120.0MB, alloc=468.3MB, time=75.65 memory used=9266.8MB, alloc=468.3MB, time=76.85 memory used=9384.0MB, alloc=468.3MB, time=78.51 memory used=9516.1MB, alloc=468.3MB, time=80.22 memory used=9634.1MB, alloc=468.3MB, time=81.49 memory used=9818.6MB, alloc=468.3MB, time=83.55 memory used=9994.2MB, alloc=468.3MB, time=84.94 memory used=10171.2MB, alloc=492.3MB, time=87.07 memory used=10325.0MB, alloc=516.3MB, time=89.51 memory used=10488.7MB, alloc=516.3MB, time=90.31 memory used=10676.7MB, alloc=516.3MB, time=91.85 memory used=10847.8MB, alloc=516.3MB, time=92.73 memory used=11025.8MB, alloc=516.3MB, time=93.99 memory used=11221.5MB, alloc=516.3MB, time=95.66 memory used=11408.5MB, alloc=516.3MB, time=97.03 memory used=11595.5MB, alloc=516.3MB, time=98.32 memory used=11782.7MB, alloc=516.3MB, time=99.64 memory used=11988.2MB, alloc=516.3MB, time=101.56 memory used=12193.9MB, alloc=516.3MB, time=103.35 memory used=12394.4MB, alloc=540.3MB, time=105.49 memory used=12630.3MB, alloc=540.3MB, time=107.54 memory used=12849.9MB, alloc=540.3MB, time=109.71 memory used=13006.2MB, alloc=564.3MB, time=111.90 memory used=13183.3MB, alloc=564.3MB, time=113.89 memory used=13269.0MB, alloc=564.3MB, time=115.52 memory used=13412.1MB, alloc=588.3MB, time=118.13 memory used=13545.2MB, alloc=612.3MB, time=120.71 memory used=13700.1MB, alloc=636.3MB, time=124.20 memory used=13823.0MB, alloc=636.3MB, time=127.16 memory used=13965.8MB, alloc=660.3MB, time=130.84 memory used=14084.8MB, alloc=684.3MB, time=133.51 memory used=14208.0MB, alloc=708.3MB, time=135.89 memory used=14323.2MB, alloc=708.3MB, time=138.12 memory used=14454.3MB, alloc=732.3MB, time=140.71 memory used=14578.5MB, alloc=756.3MB, time=143.44 memory used=14676.4MB, alloc=756.3MB, time=145.50 memory used=14795.0MB, alloc=756.3MB, time=147.93 memory used=14898.2MB, alloc=780.3MB, time=150.07 memory used=15017.5MB, alloc=804.3MB, time=152.83 memory used=15173.7MB, alloc=804.3MB, time=155.67 memory used=15272.8MB, alloc=804.3MB, time=158.12 memory used=15415.3MB, alloc=828.3MB, time=160.65 memory used=15533.8MB, alloc=828.3MB, time=163.30 memory used=15660.0MB, alloc=852.3MB, time=166.14 memory used=15788.3MB, alloc=876.3MB, time=169.08 memory used=15906.4MB, alloc=900.3MB, time=171.84 memory used=16017.5MB, alloc=924.3MB, time=174.55 memory used=16118.9MB, alloc=924.3MB, time=176.97 memory used=16213.2MB, alloc=948.3MB, time=179.35 memory used=16625.0MB, alloc=972.3MB, time=188.08 memory used=17100.6MB, alloc=996.3MB, time=196.83 memory used=17567.2MB, alloc=1020.3MB, time=206.33 memory used=18044.5MB, alloc=1044.3MB, time=215.27 memory used=18525.5MB, alloc=1068.3MB, time=224.69 memory used=18965.4MB, alloc=1092.3MB, time=234.79 memory used=19391.1MB, alloc=1116.3MB, time=243.90 memory used=19856.1MB, alloc=1140.3MB, time=253.26 memory used=20291.1MB, alloc=1164.3MB, time=262.54 memory used=20729.1MB, alloc=1188.3MB, time=271.75 memory used=21189.0MB, alloc=1212.3MB, time=281.18 memory used=21640.3MB, alloc=1236.3MB, time=290.90 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428497343 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [2 x y + 17 x y z - 17 x y, 5 x z - 14 x + 15] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 3 G := [-10 x y + 5 x z - 9 x z, -17 x y + y z - 20 x y z] > Problem := [F,G]; 2 2 2 2 Problem := [[2 x y + 17 x y z - 17 x y, 5 x z - 14 x + 15], 3 3 2 2 3 [-10 x y + 5 x z - 9 x z, -17 x y + y z - 20 x y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.7MB, alloc=32.3MB, time=0.53 memory used=47.1MB, alloc=60.3MB, time=0.85 memory used=88.9MB, alloc=60.3MB, time=1.47 memory used=130.6MB, alloc=68.3MB, time=2.01 memory used=171.1MB, alloc=92.3MB, time=2.63 memory used=232.2MB, alloc=92.3MB, time=3.62 memory used=295.2MB, alloc=92.3MB, time=4.55 memory used=360.9MB, alloc=116.3MB, time=5.49 memory used=426.7MB, alloc=372.3MB, time=6.49 memory used=513.1MB, alloc=372.3MB, time=7.83 memory used=597.7MB, alloc=396.3MB, time=8.88 memory used=708.1MB, alloc=396.3MB, time=10.81 memory used=823.8MB, alloc=420.3MB, time=12.55 memory used=961.4MB, alloc=420.3MB, time=14.28 memory used=1097.0MB, alloc=444.3MB, time=16.25 memory used=1229.7MB, alloc=468.3MB, time=18.47 memory used=1355.2MB, alloc=468.3MB, time=20.32 memory used=1517.4MB, alloc=468.3MB, time=22.32 memory used=1721.5MB, alloc=468.3MB, time=24.23 memory used=1905.9MB, alloc=468.3MB, time=25.82 memory used=2040.0MB, alloc=492.3MB, time=28.26 memory used=2250.6MB, alloc=492.3MB, time=30.13 memory used=2459.8MB, alloc=492.3MB, time=32.11 memory used=2574.1MB, alloc=492.3MB, time=33.83 memory used=2725.5MB, alloc=492.3MB, time=35.45 memory used=2865.5MB, alloc=492.3MB, time=36.97 memory used=3059.8MB, alloc=492.3MB, time=38.69 memory used=3161.0MB, alloc=492.3MB, time=40.17 memory used=3326.3MB, alloc=492.3MB, time=41.64 memory used=3519.5MB, alloc=492.3MB, time=43.33 memory used=3685.3MB, alloc=492.3MB, time=45.10 memory used=3788.6MB, alloc=516.3MB, time=46.89 memory used=3902.5MB, alloc=516.3MB, time=49.44 memory used=4005.0MB, alloc=516.3MB, time=51.06 memory used=4134.2MB, alloc=516.3MB, time=53.15 memory used=4231.0MB, alloc=516.3MB, time=55.27 memory used=4319.0MB, alloc=540.3MB, time=56.74 memory used=4421.0MB, alloc=540.3MB, time=58.20 memory used=4533.0MB, alloc=540.3MB, time=59.56 memory used=4689.3MB, alloc=540.3MB, time=61.21 memory used=4764.7MB, alloc=540.3MB, time=62.62 memory used=4826.8MB, alloc=540.3MB, time=63.84 memory used=4886.7MB, alloc=540.3MB, time=65.12 memory used=5106.5MB, alloc=564.3MB, time=66.84 memory used=5362.6MB, alloc=564.3MB, time=67.79 memory used=5792.3MB, alloc=564.3MB, time=68.93 memory used=6178.3MB, alloc=564.3MB, time=69.87 memory used=6552.3MB, alloc=564.3MB, time=70.83 memory used=6923.0MB, alloc=564.3MB, time=71.83 memory used=7285.5MB, alloc=564.3MB, time=72.77 memory used=7650.8MB, alloc=564.3MB, time=73.69 memory used=8073.0MB, alloc=564.3MB, time=75.69 memory used=8310.2MB, alloc=564.3MB, time=76.45 memory used=8687.7MB, alloc=564.3MB, time=77.67 memory used=9086.8MB, alloc=564.3MB, time=78.62 memory used=9466.0MB, alloc=564.3MB, time=79.50 memory used=9837.7MB, alloc=564.3MB, time=80.62 memory used=10201.8MB, alloc=564.3MB, time=81.76 memory used=10565.0MB, alloc=564.3MB, time=82.65 memory used=10929.8MB, alloc=564.3MB, time=83.58 memory used=11289.3MB, alloc=564.3MB, time=84.50 memory used=11534.9MB, alloc=564.3MB, time=86.52 memory used=11744.3MB, alloc=564.3MB, time=88.32 memory used=11844.1MB, alloc=564.3MB, time=90.20 memory used=11993.5MB, alloc=564.3MB, time=91.84 memory used=12172.2MB, alloc=564.3MB, time=92.67 memory used=12369.5MB, alloc=564.3MB, time=93.47 memory used=12593.6MB, alloc=564.3MB, time=94.47 memory used=12842.6MB, alloc=564.3MB, time=95.28 memory used=13128.4MB, alloc=564.3MB, time=96.20 memory used=13396.1MB, alloc=588.3MB, time=98.21 memory used=13601.7MB, alloc=588.3MB, time=100.25 memory used=13816.6MB, alloc=588.3MB, time=101.87 memory used=14023.8MB, alloc=588.3MB, time=102.67 memory used=14261.3MB, alloc=588.3MB, time=103.51 memory used=14531.7MB, alloc=588.3MB, time=104.40 memory used=14795.1MB, alloc=588.3MB, time=106.29 memory used=15005.6MB, alloc=588.3MB, time=107.33 memory used=15213.5MB, alloc=588.3MB, time=108.18 memory used=15448.9MB, alloc=588.3MB, time=109.03 memory used=15678.1MB, alloc=588.3MB, time=110.74 memory used=15896.3MB, alloc=588.3MB, time=112.55 memory used=16140.1MB, alloc=588.3MB, time=113.47 memory used=16405.9MB, alloc=588.3MB, time=114.36 memory used=16704.5MB, alloc=588.3MB, time=115.25 memory used=17037.7MB, alloc=588.3MB, time=116.31 memory used=17442.4MB, alloc=588.3MB, time=117.41 memory used=17713.9MB, alloc=588.3MB, time=119.04 memory used=17827.7MB, alloc=588.3MB, time=120.10 memory used=18026.6MB, alloc=588.3MB, time=121.82 memory used=18263.6MB, alloc=588.3MB, time=122.79 memory used=18515.7MB, alloc=588.3MB, time=123.70 memory used=18800.4MB, alloc=588.3MB, time=125.30 memory used=19014.7MB, alloc=588.3MB, time=126.21 memory used=19230.2MB, alloc=588.3MB, time=127.01 memory used=19498.0MB, alloc=588.3MB, time=128.65 memory used=19694.5MB, alloc=588.3MB, time=129.46 memory used=19902.4MB, alloc=588.3MB, time=130.28 memory used=20100.6MB, alloc=588.3MB, time=131.76 memory used=20297.9MB, alloc=612.3MB, time=132.86 memory used=20503.4MB, alloc=612.3MB, time=134.62 memory used=20718.9MB, alloc=612.3MB, time=135.87 memory used=20884.0MB, alloc=612.3MB, time=137.39 memory used=21019.1MB, alloc=612.3MB, time=138.65 memory used=21197.8MB, alloc=612.3MB, time=140.43 memory used=21315.6MB, alloc=612.3MB, time=141.98 memory used=21365.4MB, alloc=612.3MB, time=143.23 memory used=21630.2MB, alloc=636.3MB, time=147.39 memory used=21940.6MB, alloc=660.3MB, time=151.34 memory used=22280.9MB, alloc=684.3MB, time=155.38 memory used=22612.8MB, alloc=708.3MB, time=160.78 memory used=22927.5MB, alloc=732.3MB, time=166.98 memory used=23233.3MB, alloc=756.3MB, time=173.46 memory used=23548.9MB, alloc=780.3MB, time=180.15 memory used=23920.8MB, alloc=804.3MB, time=185.62 memory used=24293.0MB, alloc=828.3MB, time=192.21 memory used=24701.4MB, alloc=852.3MB, time=198.46 memory used=25102.4MB, alloc=876.3MB, time=205.07 memory used=25455.5MB, alloc=900.3MB, time=212.07 memory used=25863.0MB, alloc=924.3MB, time=220.55 memory used=26274.3MB, alloc=948.3MB, time=228.82 memory used=26698.0MB, alloc=972.3MB, time=237.04 memory used=27113.9MB, alloc=996.3MB, time=245.37 memory used=27523.4MB, alloc=1020.3MB, time=254.03 memory used=27936.6MB, alloc=1044.3MB, time=262.67 memory used=28348.4MB, alloc=1068.3MB, time=271.94 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428497643 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 3 2 2 F := [8 x y - 16 y z + 7 x z, -10 x z + 7 x y + 16 x y] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 4 3 3 G := [15 x y z + 4 x - 18 y z, 15 x - 6 x y - 8 y z ] > Problem := [F,G]; 3 3 2 3 2 2 Problem := [[8 x y - 16 y z + 7 x z, -10 x z + 7 x y + 16 x y], 2 2 4 3 3 [15 x y z + 4 x - 18 y z, 15 x - 6 x y - 8 y z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.1MB, alloc=32.3MB, time=0.18 memory used=26.6MB, alloc=33.3MB, time=0.41 memory used=44.6MB, alloc=33.3MB, time=0.54 memory used=68.4MB, alloc=33.3MB, time=0.72 memory used=86.2MB, alloc=33.3MB, time=0.79 memory used=108.4MB, alloc=33.3MB, time=0.99 memory used=132.1MB, alloc=37.3MB, time=1.33 memory used=155.4MB, alloc=37.3MB, time=1.66 memory used=176.7MB, alloc=61.3MB, time=1.98 memory used=214.8MB, alloc=61.3MB, time=2.22 memory used=244.5MB, alloc=61.3MB, time=2.39 memory used=275.3MB, alloc=61.3MB, time=2.48 memory used=310.0MB, alloc=61.3MB, time=3.01 memory used=348.6MB, alloc=61.3MB, time=3.25 memory used=394.2MB, alloc=61.3MB, time=3.71 memory used=428.0MB, alloc=61.3MB, time=4.20 memory used=486.9MB, alloc=69.9MB, time=4.67 memory used=546.2MB, alloc=70.4MB, time=5.48 memory used=598.2MB, alloc=70.4MB, time=6.22 memory used=645.2MB, alloc=70.4MB, time=6.82 memory used=688.9MB, alloc=70.4MB, time=7.50 memory used=729.5MB, alloc=94.4MB, time=8.01 memory used=806.4MB, alloc=94.4MB, time=8.80 memory used=873.6MB, alloc=94.4MB, time=9.59 memory used=943.1MB, alloc=94.4MB, time=10.47 memory used=1004.5MB, alloc=94.4MB, time=11.11 memory used=1052.1MB, alloc=94.4MB, time=11.39 memory used=1111.0MB, alloc=94.4MB, time=11.98 memory used=1156.6MB, alloc=94.4MB, time=12.19 memory used=1187.3MB, alloc=94.4MB, time=12.31 memory used=1223.1MB, alloc=94.4MB, time=12.43 memory used=1267.8MB, alloc=94.4MB, time=13.72 memory used=1310.9MB, alloc=94.4MB, time=13.91 memory used=1340.0MB, alloc=94.4MB, time=14.01 memory used=1378.9MB, alloc=94.4MB, time=14.17 memory used=1424.5MB, alloc=94.4MB, time=14.55 memory used=1485.0MB, alloc=94.4MB, time=15.24 memory used=1554.5MB, alloc=350.4MB, time=16.20 memory used=1593.2MB, alloc=350.4MB, time=16.45 memory used=1667.2MB, alloc=374.4MB, time=17.21 memory used=1773.8MB, alloc=374.4MB, time=18.11 memory used=1862.2MB, alloc=374.4MB, time=19.25 memory used=1942.8MB, alloc=398.4MB, time=20.03 memory used=2011.2MB, alloc=398.4MB, time=20.41 memory used=2076.0MB, alloc=398.4MB, time=20.75 memory used=2155.5MB, alloc=398.4MB, time=21.60 memory used=2210.5MB, alloc=398.4MB, time=21.80 memory used=2273.8MB, alloc=398.4MB, time=22.05 memory used=2335.1MB, alloc=398.4MB, time=22.30 memory used=2387.4MB, alloc=398.4MB, time=22.48 memory used=2474.4MB, alloc=398.4MB, time=23.66 memory used=2528.0MB, alloc=398.4MB, time=23.84 memory used=2592.3MB, alloc=398.4MB, time=24.13 memory used=2647.7MB, alloc=398.4MB, time=24.35 memory used=2695.3MB, alloc=398.4MB, time=24.53 memory used=2743.8MB, alloc=398.4MB, time=24.72 memory used=2801.4MB, alloc=398.4MB, time=24.91 memory used=2863.7MB, alloc=398.4MB, time=25.08 memory used=2902.1MB, alloc=398.4MB, time=25.23 memory used=2943.5MB, alloc=398.4MB, time=25.37 memory used=2989.9MB, alloc=398.4MB, time=25.51 memory used=3058.7MB, alloc=398.4MB, time=28.81 memory used=3143.0MB, alloc=398.4MB, time=29.87 memory used=3190.5MB, alloc=398.4MB, time=30.08 memory used=3249.6MB, alloc=398.4MB, time=30.27 memory used=3289.8MB, alloc=398.4MB, time=30.43 memory used=3337.0MB, alloc=398.4MB, time=30.59 memory used=3391.7MB, alloc=398.4MB, time=30.75 memory used=3466.5MB, alloc=398.4MB, time=31.04 memory used=3518.8MB, alloc=398.4MB, time=31.26 memory used=3598.2MB, alloc=398.4MB, time=32.10 memory used=3652.7MB, alloc=398.4MB, time=32.30 memory used=3706.7MB, alloc=398.4MB, time=32.58 memory used=3793.8MB, alloc=398.4MB, time=34.23 memory used=3875.3MB, alloc=398.4MB, time=34.65 memory used=3928.4MB, alloc=398.4MB, time=34.84 memory used=3977.5MB, alloc=398.4MB, time=35.02 memory used=4022.9MB, alloc=398.4MB, time=35.17 memory used=4084.5MB, alloc=398.4MB, time=35.46 memory used=4148.4MB, alloc=398.4MB, time=35.78 memory used=4263.9MB, alloc=398.4MB, time=41.57 memory used=4315.6MB, alloc=398.4MB, time=41.77 memory used=4368.4MB, alloc=398.4MB, time=41.96 memory used=4422.5MB, alloc=398.4MB, time=42.13 memory used=4462.9MB, alloc=398.4MB, time=42.31 memory used=4509.0MB, alloc=398.4MB, time=42.53 memory used=4561.5MB, alloc=398.4MB, time=42.75 memory used=4621.1MB, alloc=398.4MB, time=43.01 memory used=4725.1MB, alloc=398.4MB, time=43.77 memory used=4787.9MB, alloc=398.4MB, time=44.05 memory used=4831.6MB, alloc=398.4MB, time=44.30 memory used=4882.4MB, alloc=398.4MB, time=44.62 memory used=4943.0MB, alloc=398.4MB, time=44.98 memory used=4996.0MB, alloc=422.4MB, time=45.26 memory used=5042.8MB, alloc=422.4MB, time=45.53 memory used=5093.4MB, alloc=422.4MB, time=45.85 memory used=5150.6MB, alloc=422.4MB, time=46.13 memory used=5210.4MB, alloc=422.4MB, time=46.37 memory used=5273.0MB, alloc=422.4MB, time=46.61 memory used=5342.1MB, alloc=422.4MB, time=46.87 memory used=5413.9MB, alloc=422.4MB, time=47.09 memory used=5492.6MB, alloc=422.4MB, time=47.35 memory used=5573.9MB, alloc=422.4MB, time=47.60 memory used=5642.9MB, alloc=422.4MB, time=47.81 memory used=5684.7MB, alloc=422.4MB, time=47.98 memory used=5725.7MB, alloc=422.4MB, time=48.16 memory used=5772.4MB, alloc=422.4MB, time=48.34 memory used=5819.5MB, alloc=422.4MB, time=48.51 memory used=5866.8MB, alloc=422.4MB, time=48.72 memory used=5914.3MB, alloc=422.4MB, time=48.92 memory used=5962.3MB, alloc=422.4MB, time=49.11 memory used=6015.1MB, alloc=422.4MB, time=49.30 memory used=6068.1MB, alloc=422.4MB, time=49.49 memory used=6121.3MB, alloc=422.4MB, time=49.68 memory used=6179.5MB, alloc=422.4MB, time=49.86 memory used=6237.4MB, alloc=422.4MB, time=50.06 memory used=6295.5MB, alloc=422.4MB, time=50.24 memory used=6357.6MB, alloc=422.4MB, time=50.44 memory used=6419.7MB, alloc=422.4MB, time=50.63 memory used=6485.5MB, alloc=422.4MB, time=50.87 memory used=6555.6MB, alloc=422.4MB, time=51.07 memory used=6629.0MB, alloc=422.4MB, time=51.26 memory used=6701.3MB, alloc=422.4MB, time=51.44 memory used=6779.3MB, alloc=422.4MB, time=51.63 memory used=6859.3MB, alloc=422.4MB, time=51.88 memory used=6943.7MB, alloc=422.4MB, time=52.09 memory used=7152.9MB, alloc=422.4MB, time=52.57 memory used=7393.0MB, alloc=422.4MB, time=61.96 memory used=7478.3MB, alloc=422.4MB, time=108.85 memory used=7564.2MB, alloc=422.4MB, time=145.06 memory used=7728.6MB, alloc=422.4MB, time=146.31 memory used=7886.9MB, alloc=422.4MB, time=147.63 memory used=8015.1MB, alloc=422.4MB, time=148.51 memory used=8083.2MB, alloc=422.4MB, time=148.76 memory used=8143.9MB, alloc=422.4MB, time=149.01 memory used=8218.6MB, alloc=422.4MB, time=149.28 memory used=8289.6MB, alloc=422.4MB, time=149.53 memory used=8337.9MB, alloc=422.4MB, time=149.76 memory used=8390.9MB, alloc=422.4MB, time=149.94 memory used=8448.2MB, alloc=422.4MB, time=150.12 memory used=8509.9MB, alloc=422.4MB, time=150.40 memory used=8575.7MB, alloc=422.4MB, time=150.68 memory used=8645.6MB, alloc=422.4MB, time=150.95 memory used=8721.7MB, alloc=422.4MB, time=151.15 memory used=8803.7MB, alloc=422.4MB, time=151.35 memory used=9023.5MB, alloc=422.4MB, time=151.92 memory used=9168.4MB, alloc=422.4MB, time=152.25 memory used=9330.3MB, alloc=422.4MB, time=152.58 memory used=9513.7MB, alloc=422.4MB, time=152.98 memory used=9761.7MB, alloc=422.4MB, time=153.63 memory used=9876.8MB, alloc=422.4MB, time=157.98 memory used=9947.8MB, alloc=422.4MB, time=158.25 memory used=10027.1MB, alloc=422.4MB, time=158.52 memory used=10080.9MB, alloc=422.4MB, time=158.73 memory used=10145.0MB, alloc=422.4MB, time=158.92 memory used=10221.6MB, alloc=422.4MB, time=159.11 memory used=10326.6MB, alloc=422.4MB, time=159.50 memory used=10392.1MB, alloc=422.4MB, time=159.74 memory used=10461.8MB, alloc=422.4MB, time=159.94 memory used=10534.1MB, alloc=422.4MB, time=160.23 memory used=10603.0MB, alloc=422.4MB, time=160.53 memory used=10683.1MB, alloc=422.4MB, time=160.79 memory used=10737.9MB, alloc=422.4MB, time=160.99 memory used=10818.8MB, alloc=422.4MB, time=161.40 memory used=10884.7MB, alloc=422.4MB, time=161.60 memory used=10963.2MB, alloc=422.4MB, time=161.92 memory used=11035.7MB, alloc=422.4MB, time=162.15 memory used=11111.5MB, alloc=422.4MB, time=162.46 memory used=11180.9MB, alloc=422.4MB, time=162.68 memory used=11264.2MB, alloc=422.4MB, time=163.13 memory used=11332.1MB, alloc=422.4MB, time=163.35 memory used=11409.4MB, alloc=422.4MB, time=163.71 memory used=11478.2MB, alloc=422.4MB, time=163.94 memory used=11551.0MB, alloc=422.4MB, time=164.18 memory used=11624.6MB, alloc=422.4MB, time=164.43 memory used=11695.9MB, alloc=422.4MB, time=164.66 memory used=11777.2MB, alloc=422.4MB, time=165.03 memory used=11842.1MB, alloc=422.4MB, time=165.28 memory used=11917.3MB, alloc=422.4MB, time=165.51 memory used=11973.9MB, alloc=422.4MB, time=165.69 memory used=12059.9MB, alloc=422.4MB, time=166.24 memory used=12132.7MB, alloc=422.4MB, time=166.51 memory used=12189.3MB, alloc=422.4MB, time=166.75 memory used=12257.2MB, alloc=422.4MB, time=167.00 memory used=12336.7MB, alloc=422.4MB, time=167.26 memory used=12414.2MB, alloc=422.4MB, time=167.50 memory used=12462.0MB, alloc=422.4MB, time=167.68 memory used=12513.9MB, alloc=422.4MB, time=167.86 memory used=12567.1MB, alloc=422.4MB, time=168.04 memory used=12623.6MB, alloc=422.4MB, time=168.22 memory used=12683.4MB, alloc=422.4MB, time=168.41 memory used=12746.3MB, alloc=422.4MB, time=168.59 memory used=12812.0MB, alloc=422.4MB, time=168.78 memory used=12882.7MB, alloc=422.4MB, time=168.96 memory used=12957.8MB, alloc=422.4MB, time=169.15 memory used=13038.7MB, alloc=422.4MB, time=169.35 memory used=13246.3MB, alloc=422.4MB, time=169.72 memory used=13399.4MB, alloc=422.4MB, time=170.03 memory used=13499.8MB, alloc=422.4MB, time=170.48 memory used=13566.7MB, alloc=422.4MB, time=170.72 memory used=13633.2MB, alloc=422.4MB, time=170.95 memory used=13693.6MB, alloc=422.4MB, time=171.19 memory used=13781.9MB, alloc=422.4MB, time=171.68 memory used=13853.3MB, alloc=422.4MB, time=171.91 memory used=13912.9MB, alloc=422.4MB, time=172.10 memory used=14072.1MB, alloc=422.4MB, time=173.90 memory used=14244.6MB, alloc=422.4MB, time=175.95 memory used=14362.4MB, alloc=422.4MB, time=177.37 memory used=14432.6MB, alloc=422.4MB, time=177.60 memory used=14488.5MB, alloc=422.4MB, time=177.88 memory used=14631.7MB, alloc=422.4MB, time=179.08 memory used=14789.4MB, alloc=422.4MB, time=180.78 memory used=14903.5MB, alloc=422.4MB, time=182.10 memory used=14961.9MB, alloc=422.4MB, time=182.33 memory used=15034.5MB, alloc=422.4MB, time=182.58 memory used=15083.6MB, alloc=422.4MB, time=182.85 memory used=15140.5MB, alloc=422.4MB, time=183.10 memory used=15207.6MB, alloc=422.4MB, time=183.30 memory used=15284.3MB, alloc=422.4MB, time=183.51 memory used=15460.3MB, alloc=422.4MB, time=209.74 memory used=15580.5MB, alloc=422.4MB, time=213.80 memory used=15645.0MB, alloc=422.4MB, time=214.04 memory used=15701.2MB, alloc=422.4MB, time=214.25 memory used=15773.4MB, alloc=422.4MB, time=214.47 memory used=15832.4MB, alloc=422.4MB, time=214.67 memory used=15880.1MB, alloc=422.4MB, time=214.84 memory used=15931.7MB, alloc=422.4MB, time=215.01 memory used=15988.7MB, alloc=422.4MB, time=215.19 memory used=16050.8MB, alloc=422.4MB, time=215.39 memory used=16119.3MB, alloc=422.4MB, time=215.57 memory used=16193.8MB, alloc=422.4MB, time=215.77 memory used=16409.9MB, alloc=422.4MB, time=216.14 memory used=16571.1MB, alloc=422.4MB, time=216.45 memory used=16744.7MB, alloc=422.4MB, time=217.61 memory used=16901.1MB, alloc=422.4MB, time=218.78 memory used=17054.2MB, alloc=422.4MB, time=220.53 memory used=17137.6MB, alloc=422.4MB, time=221.00 memory used=17194.3MB, alloc=422.4MB, time=221.22 memory used=17269.3MB, alloc=422.4MB, time=221.51 memory used=17347.6MB, alloc=422.4MB, time=222.30 memory used=17415.0MB, alloc=422.4MB, time=222.58 memory used=17480.7MB, alloc=422.4MB, time=222.91 memory used=17552.3MB, alloc=422.4MB, time=223.22 memory used=17622.3MB, alloc=422.4MB, time=223.51 memory used=17679.9MB, alloc=422.4MB, time=223.73 memory used=17777.5MB, alloc=422.4MB, time=225.13 memory used=17837.0MB, alloc=422.4MB, time=225.35 memory used=17890.7MB, alloc=422.4MB, time=225.55 memory used=17968.9MB, alloc=422.4MB, time=225.98 memory used=18030.6MB, alloc=422.4MB, time=226.23 memory used=18088.7MB, alloc=422.4MB, time=226.47 memory used=18137.0MB, alloc=422.4MB, time=226.70 memory used=18194.1MB, alloc=422.4MB, time=226.94 memory used=18262.4MB, alloc=422.4MB, time=227.17 memory used=18321.3MB, alloc=446.4MB, time=227.39 memory used=18375.9MB, alloc=446.4MB, time=227.59 memory used=18437.4MB, alloc=446.4MB, time=227.79 memory used=18505.8MB, alloc=446.4MB, time=228.00 memory used=18584.3MB, alloc=446.4MB, time=228.21 memory used=18712.7MB, alloc=446.4MB, time=233.14 memory used=18786.5MB, alloc=446.4MB, time=233.39 memory used=18867.1MB, alloc=446.4MB, time=233.66 memory used=18926.5MB, alloc=446.4MB, time=233.86 memory used=18998.3MB, alloc=446.4MB, time=234.06 memory used=19084.2MB, alloc=446.4MB, time=234.28 memory used=19227.0MB, alloc=446.4MB, time=234.81 memory used=19302.6MB, alloc=446.4MB, time=235.05 memory used=19409.3MB, alloc=446.4MB, time=236.31 memory used=19487.6MB, alloc=446.4MB, time=236.57 memory used=19553.7MB, alloc=446.4MB, time=236.76 memory used=19663.5MB, alloc=446.4MB, time=237.41 memory used=19733.4MB, alloc=446.4MB, time=237.68 memory used=19807.3MB, alloc=446.4MB, time=237.91 memory used=19888.5MB, alloc=446.4MB, time=238.21 memory used=19963.1MB, alloc=446.4MB, time=238.47 memory used=20042.5MB, alloc=446.4MB, time=238.71 memory used=20123.7MB, alloc=446.4MB, time=239.11 memory used=20202.6MB, alloc=446.4MB, time=239.38 memory used=20285.8MB, alloc=446.4MB, time=239.70 memory used=20362.2MB, alloc=446.4MB, time=239.93 memory used=20447.0MB, alloc=446.4MB, time=240.24 memory used=20523.6MB, alloc=446.4MB, time=240.48 memory used=20611.8MB, alloc=446.4MB, time=240.91 memory used=20684.5MB, alloc=446.4MB, time=241.15 memory used=20769.9MB, alloc=446.4MB, time=241.48 memory used=20848.0MB, alloc=446.4MB, time=241.73 memory used=20929.1MB, alloc=446.4MB, time=242.06 memory used=21007.2MB, alloc=446.4MB, time=242.34 memory used=21088.5MB, alloc=446.4MB, time=242.71 memory used=21162.3MB, alloc=446.4MB, time=242.99 memory used=21243.4MB, alloc=446.4MB, time=243.25 memory used=21307.3MB, alloc=446.4MB, time=243.46 memory used=21403.9MB, alloc=446.4MB, time=244.07 memory used=21475.9MB, alloc=446.4MB, time=244.35 memory used=21542.8MB, alloc=446.4MB, time=244.64 memory used=21623.1MB, alloc=446.4MB, time=244.90 memory used=21716.4MB, alloc=446.4MB, time=245.17 memory used=21773.3MB, alloc=446.4MB, time=245.38 memory used=21828.0MB, alloc=446.4MB, time=245.58 memory used=21883.7MB, alloc=446.4MB, time=245.79 memory used=21942.9MB, alloc=446.4MB, time=246.00 memory used=22008.2MB, alloc=446.4MB, time=246.21 memory used=22076.8MB, alloc=446.4MB, time=246.43 memory used=22150.7MB, alloc=446.4MB, time=246.65 memory used=22229.6MB, alloc=446.4MB, time=246.87 memory used=22315.1MB, alloc=446.4MB, time=247.08 memory used=22405.7MB, alloc=446.4MB, time=247.31 memory used=22570.7MB, alloc=446.4MB, time=247.67 memory used=22725.0MB, alloc=446.4MB, time=248.00 memory used=22831.0MB, alloc=446.4MB, time=248.49 memory used=22909.6MB, alloc=446.4MB, time=248.74 memory used=22975.3MB, alloc=446.4MB, time=248.96 memory used=23058.4MB, alloc=446.4MB, time=249.39 memory used=23142.3MB, alloc=446.4MB, time=249.68 memory used=23212.0MB, alloc=446.4MB, time=249.91 memory used=23362.1MB, alloc=446.4MB, time=251.20 memory used=23436.5MB, alloc=446.4MB, time=251.47 memory used=23504.5MB, alloc=446.4MB, time=251.69 memory used=23646.9MB, alloc=446.4MB, time=253.16 memory used=23743.9MB, alloc=446.4MB, time=253.68 memory used=23819.0MB, alloc=446.4MB, time=253.97 memory used=23886.5MB, alloc=446.4MB, time=254.22 memory used=23946.7MB, alloc=446.4MB, time=254.44 memory used=24018.4MB, alloc=446.4MB, time=254.67 memory used=24103.4MB, alloc=446.4MB, time=254.90 memory used=24275.1MB, alloc=446.4MB, time=255.99 memory used=24395.5MB, alloc=446.4MB, time=257.51 memory used=24493.8MB, alloc=446.4MB, time=258.71 memory used=24602.4MB, alloc=470.4MB, time=260.08 memory used=24710.2MB, alloc=470.4MB, time=261.19 memory used=24795.4MB, alloc=470.4MB, time=262.36 memory used=24875.4MB, alloc=470.4MB, time=263.48 memory used=24962.4MB, alloc=494.4MB, time=264.71 memory used=25139.7MB, alloc=494.4MB, time=266.64 memory used=25222.3MB, alloc=494.4MB, time=267.00 memory used=25369.9MB, alloc=494.4MB, time=270.85 memory used=25458.5MB, alloc=494.4MB, time=271.23 memory used=25540.1MB, alloc=494.4MB, time=271.57 memory used=25633.0MB, alloc=494.4MB, time=271.95 memory used=25751.3MB, alloc=494.4MB, time=272.74 memory used=25847.5MB, alloc=494.4MB, time=273.20 memory used=25933.4MB, alloc=518.4MB, time=273.61 memory used=26015.3MB, alloc=518.4MB, time=274.01 memory used=26109.0MB, alloc=518.4MB, time=274.43 memory used=26216.0MB, alloc=518.4MB, time=274.93 memory used=26339.7MB, alloc=518.4MB, time=275.38 memory used=26458.3MB, alloc=518.4MB, time=275.79 memory used=26530.9MB, alloc=518.4MB, time=276.13 memory used=26606.8MB, alloc=518.4MB, time=276.47 memory used=26689.3MB, alloc=518.4MB, time=276.81 memory used=26777.4MB, alloc=518.4MB, time=277.15 memory used=26869.6MB, alloc=518.4MB, time=277.50 memory used=26970.3MB, alloc=518.4MB, time=277.87 memory used=27080.9MB, alloc=518.4MB, time=278.22 memory used=27204.9MB, alloc=518.4MB, time=278.56 memory used=27396.9MB, alloc=518.4MB, time=331.85 memory used=27649.7MB, alloc=518.4MB, time=333.70 memory used=27810.5MB, alloc=518.4MB, time=334.55 memory used=27908.5MB, alloc=518.4MB, time=334.98 memory used=28016.6MB, alloc=518.4MB, time=335.37 memory used=28098.0MB, alloc=518.4MB, time=335.72 memory used=28192.3MB, alloc=518.4MB, time=336.07 memory used=28301.0MB, alloc=518.4MB, time=336.44 memory used=28425.7MB, alloc=518.4MB, time=336.81 memory used=28612.4MB, alloc=518.4MB, time=337.29 memory used=28880.6MB, alloc=518.4MB, time=338.54 memory used=29000.6MB, alloc=518.4MB, time=338.96 memory used=29133.2MB, alloc=518.4MB, time=339.67 memory used=29280.3MB, alloc=518.4MB, time=342.51 memory used=29382.4MB, alloc=518.4MB, time=342.89 memory used=29500.1MB, alloc=518.4MB, time=343.54 memory used=29651.2MB, alloc=518.4MB, time=344.65 memory used=29733.9MB, alloc=518.4MB, time=345.81 memory used=29827.2MB, alloc=518.4MB, time=351.32 memory used=30011.8MB, alloc=518.4MB, time=364.88 memory used=30110.8MB, alloc=518.4MB, time=365.41 memory used=30209.8MB, alloc=518.4MB, time=365.84 memory used=30297.1MB, alloc=518.4MB, time=366.24 memory used=30402.8MB, alloc=518.4MB, time=366.61 memory used=30673.2MB, alloc=518.4MB, time=367.86 memory used=30797.1MB, alloc=518.4MB, time=369.20 memory used=30895.6MB, alloc=518.4MB, time=369.66 memory used=31018.8MB, alloc=518.4MB, time=370.35 memory used=31148.4MB, alloc=518.4MB, time=371.08 memory used=31249.6MB, alloc=518.4MB, time=371.57 memory used=31353.8MB, alloc=518.4MB, time=372.08 memory used=31462.1MB, alloc=518.4MB, time=372.65 memory used=31567.2MB, alloc=518.4MB, time=373.18 memory used=31673.5MB, alloc=518.4MB, time=373.68 memory used=31782.6MB, alloc=518.4MB, time=374.20 memory used=31892.3MB, alloc=518.4MB, time=374.75 memory used=31994.9MB, alloc=518.4MB, time=375.20 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428497943 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 F := [-5 x y + 16 x - 10, 18 x y + 13 y z - 13 y] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 3 G := [12 x y - 11 y z + 2 x y , -x y z - 13 z - 9 x z] > Problem := [F,G]; 3 3 2 Problem := [[-5 x y + 16 x - 10, 18 x y + 13 y z - 13 y], 3 2 2 2 2 3 [12 x y - 11 y z + 2 x y , -x y z - 13 z - 9 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.20 memory used=26.8MB, alloc=32.3MB, time=0.54 memory used=47.6MB, alloc=32.3MB, time=0.88 memory used=66.6MB, alloc=56.3MB, time=1.22 memory used=108.0MB, alloc=60.3MB, time=1.84 memory used=149.1MB, alloc=60.3MB, time=2.46 memory used=188.2MB, alloc=84.3MB, time=3.07 memory used=232.7MB, alloc=84.3MB, time=3.74 memory used=293.3MB, alloc=92.3MB, time=4.60 memory used=358.3MB, alloc=116.3MB, time=5.57 memory used=447.9MB, alloc=116.3MB, time=6.98 memory used=526.7MB, alloc=140.3MB, time=8.62 memory used=622.0MB, alloc=164.3MB, time=10.36 memory used=734.0MB, alloc=444.3MB, time=12.58 memory used=866.1MB, alloc=468.3MB, time=15.04 memory used=998.6MB, alloc=492.3MB, time=19.26 memory used=1139.0MB, alloc=516.3MB, time=24.27 memory used=1290.0MB, alloc=540.3MB, time=30.39 memory used=1465.0MB, alloc=540.3MB, time=37.82 memory used=1640.0MB, alloc=564.3MB, time=44.84 memory used=1839.1MB, alloc=564.3MB, time=53.21 memory used=2038.2MB, alloc=588.3MB, time=61.59 N1 := 6149 > GB := Basis(F, plex(op(vars))); 3 2 2 GB := [5 y x - 16 x + 10, 288 x y - 65 x y - 180 x y + 208 x z - 130 z, 2 65 y z + 288 x - 65 y - 180] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=2278.0MB, alloc=588.3MB, time=67.59 memory used=2550.9MB, alloc=588.3MB, time=72.56 memory used=2711.3MB, alloc=588.3MB, time=74.46 memory used=2925.5MB, alloc=612.3MB, time=77.19 memory used=3218.6MB, alloc=636.3MB, time=82.02 memory used=3518.3MB, alloc=660.3MB, time=86.57 memory used=3761.0MB, alloc=684.3MB, time=89.15 memory used=3929.8MB, alloc=684.3MB, time=90.43 memory used=4122.5MB, alloc=684.3MB, time=91.99 memory used=4341.1MB, alloc=684.3MB, time=93.81 memory used=4632.3MB, alloc=684.3MB, time=97.91 memory used=4974.0MB, alloc=708.3MB, time=102.62 memory used=5339.5MB, alloc=732.3MB, time=108.56 memory used=5773.3MB, alloc=756.3MB, time=114.48 memory used=6202.7MB, alloc=780.3MB, time=123.83 memory used=6561.2MB, alloc=804.3MB, time=130.71 memory used=6970.9MB, alloc=828.3MB, time=139.97 memory used=7338.2MB, alloc=852.3MB, time=148.79 memory used=7697.4MB, alloc=876.3MB, time=156.88 memory used=8070.7MB, alloc=900.3MB, time=164.53 memory used=8457.6MB, alloc=924.3MB, time=179.07 memory used=8810.3MB, alloc=948.3MB, time=195.95 memory used=9164.7MB, alloc=972.3MB, time=213.08 memory used=9528.6MB, alloc=996.3MB, time=231.15 memory used=9903.4MB, alloc=1020.3MB, time=249.03 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428498243 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 2 2 F := [8 x y z - 14 x y + 12 x , -15 x y z - 12 y z - 16 y ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 3 3 3 G := [8 x y z - 16 x z - 20 y z, 16 x y + 13 z + x] > Problem := [F,G]; 2 2 2 2 2 2 2 Problem := [[8 x y z - 14 x y + 12 x , -15 x y z - 12 y z - 16 y ], 2 3 3 3 3 [8 x y z - 16 x z - 20 y z, 16 x y + 13 z + x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.21 memory used=26.8MB, alloc=32.3MB, time=0.62 memory used=46.9MB, alloc=56.3MB, time=0.92 memory used=88.3MB, alloc=60.3MB, time=1.67 memory used=129.9MB, alloc=60.3MB, time=2.24 memory used=173.3MB, alloc=60.3MB, time=2.63 memory used=220.1MB, alloc=68.3MB, time=3.17 memory used=263.6MB, alloc=68.3MB, time=3.65 memory used=303.3MB, alloc=92.3MB, time=4.26 memory used=369.5MB, alloc=92.3MB, time=5.23 memory used=421.7MB, alloc=92.3MB, time=6.05 memory used=468.4MB, alloc=92.3MB, time=6.68 memory used=509.2MB, alloc=92.3MB, time=7.04 memory used=570.9MB, alloc=92.3MB, time=7.66 memory used=631.4MB, alloc=116.3MB, time=8.53 memory used=711.9MB, alloc=372.3MB, time=9.65 memory used=796.7MB, alloc=372.3MB, time=10.99 memory used=882.4MB, alloc=396.3MB, time=12.26 memory used=988.9MB, alloc=396.3MB, time=13.65 memory used=1068.3MB, alloc=396.3MB, time=14.35 memory used=1134.8MB, alloc=396.3MB, time=15.68 memory used=1204.9MB, alloc=396.3MB, time=16.14 memory used=1285.6MB, alloc=396.3MB, time=18.66 memory used=1341.0MB, alloc=396.3MB, time=18.86 memory used=1382.5MB, alloc=396.3MB, time=19.02 memory used=1454.6MB, alloc=396.3MB, time=19.89 memory used=1519.3MB, alloc=420.3MB, time=20.14 memory used=1574.4MB, alloc=420.3MB, time=20.38 memory used=1640.5MB, alloc=420.3MB, time=20.63 memory used=1719.1MB, alloc=420.3MB, time=20.91 memory used=1791.6MB, alloc=420.3MB, time=21.15 memory used=1841.0MB, alloc=420.3MB, time=21.37 memory used=1892.8MB, alloc=420.3MB, time=21.57 memory used=1948.9MB, alloc=420.3MB, time=21.78 memory used=2010.8MB, alloc=420.3MB, time=21.99 memory used=2077.3MB, alloc=420.3MB, time=22.19 memory used=2150.7MB, alloc=420.3MB, time=22.41 memory used=2232.4MB, alloc=420.3MB, time=22.65 memory used=2293.2MB, alloc=420.3MB, time=22.84 memory used=2396.9MB, alloc=420.3MB, time=23.81 memory used=2452.4MB, alloc=420.3MB, time=24.05 memory used=2517.9MB, alloc=420.3MB, time=24.30 memory used=2595.7MB, alloc=420.3MB, time=24.53 memory used=2671.3MB, alloc=420.3MB, time=24.75 memory used=2719.9MB, alloc=420.3MB, time=24.96 memory used=2771.5MB, alloc=420.3MB, time=25.16 memory used=2827.6MB, alloc=420.3MB, time=25.38 memory used=2887.4MB, alloc=420.3MB, time=25.61 memory used=2952.2MB, alloc=420.3MB, time=25.82 memory used=3024.1MB, alloc=420.3MB, time=26.02 memory used=3103.6MB, alloc=420.3MB, time=26.23 memory used=3170.4MB, alloc=420.3MB, time=26.42 memory used=3253.8MB, alloc=420.3MB, time=49.21 memory used=3385.2MB, alloc=420.3MB, time=53.98 memory used=3458.7MB, alloc=420.3MB, time=54.22 memory used=3536.6MB, alloc=420.3MB, time=54.41 memory used=3693.2MB, alloc=420.3MB, time=55.22 memory used=3754.1MB, alloc=420.3MB, time=55.49 memory used=3885.2MB, alloc=420.3MB, time=55.94 memory used=4087.0MB, alloc=420.3MB, time=56.66 memory used=4242.9MB, alloc=420.3MB, time=56.94 memory used=4417.7MB, alloc=420.3MB, time=57.26 memory used=4667.8MB, alloc=420.3MB, time=59.11 memory used=4724.9MB, alloc=420.3MB, time=59.44 memory used=4784.9MB, alloc=420.3MB, time=59.66 memory used=4853.7MB, alloc=420.3MB, time=59.96 memory used=4932.6MB, alloc=420.3MB, time=60.32 memory used=5005.0MB, alloc=420.3MB, time=60.65 memory used=5051.2MB, alloc=420.3MB, time=60.88 memory used=5098.5MB, alloc=420.3MB, time=61.14 memory used=5149.2MB, alloc=420.3MB, time=61.36 memory used=5203.0MB, alloc=420.3MB, time=61.59 memory used=5259.8MB, alloc=420.3MB, time=61.79 memory used=5321.8MB, alloc=420.3MB, time=62.00 memory used=5386.1MB, alloc=420.3MB, time=62.19 memory used=5454.6MB, alloc=420.3MB, time=62.40 memory used=5528.9MB, alloc=420.3MB, time=62.60 memory used=5607.4MB, alloc=420.3MB, time=62.80 memory used=5686.4MB, alloc=420.3MB, time=63.00 memory used=5731.3MB, alloc=420.3MB, time=63.16 memory used=5777.2MB, alloc=420.3MB, time=63.31 memory used=5826.6MB, alloc=420.3MB, time=63.48 memory used=5901.1MB, alloc=420.3MB, time=64.37 memory used=5999.8MB, alloc=420.3MB, time=65.04 memory used=6054.3MB, alloc=420.3MB, time=65.27 memory used=6114.6MB, alloc=420.3MB, time=65.50 memory used=6183.7MB, alloc=420.3MB, time=65.78 memory used=6263.0MB, alloc=420.3MB, time=66.05 memory used=6333.0MB, alloc=420.3MB, time=66.28 memory used=6379.2MB, alloc=420.3MB, time=66.49 memory used=6429.1MB, alloc=420.3MB, time=66.70 memory used=6479.9MB, alloc=420.3MB, time=66.90 memory used=6533.8MB, alloc=420.3MB, time=67.12 memory used=6593.3MB, alloc=420.3MB, time=67.33 memory used=6655.4MB, alloc=420.3MB, time=67.54 memory used=6722.2MB, alloc=420.3MB, time=67.79 memory used=6793.0MB, alloc=420.3MB, time=68.05 memory used=6867.1MB, alloc=420.3MB, time=68.37 memory used=6947.3MB, alloc=420.3MB, time=68.68 memory used=7020.9MB, alloc=420.3MB, time=68.91 memory used=7065.3MB, alloc=420.3MB, time=69.09 memory used=7112.3MB, alloc=420.3MB, time=69.25 memory used=7162.9MB, alloc=420.3MB, time=69.41 memory used=7238.4MB, alloc=420.3MB, time=72.77 memory used=7406.8MB, alloc=420.3MB, time=102.48 memory used=7484.6MB, alloc=420.3MB, time=102.66 memory used=7654.0MB, alloc=420.3MB, time=102.98 memory used=7842.4MB, alloc=420.3MB, time=105.25 memory used=7903.7MB, alloc=420.3MB, time=105.49 memory used=7955.2MB, alloc=420.3MB, time=105.75 memory used=8012.9MB, alloc=420.3MB, time=106.00 memory used=8077.9MB, alloc=420.3MB, time=106.23 memory used=8150.1MB, alloc=420.3MB, time=106.47 memory used=8226.7MB, alloc=420.3MB, time=106.71 memory used=8296.7MB, alloc=420.3MB, time=106.96 memory used=8339.0MB, alloc=420.3MB, time=107.17 memory used=8384.2MB, alloc=444.3MB, time=107.38 memory used=8442.8MB, alloc=444.3MB, time=107.59 memory used=8506.4MB, alloc=444.3MB, time=107.82 memory used=8571.6MB, alloc=444.3MB, time=108.04 memory used=8641.7MB, alloc=444.3MB, time=108.25 memory used=8716.5MB, alloc=444.3MB, time=108.50 memory used=8792.4MB, alloc=444.3MB, time=108.81 memory used=8872.9MB, alloc=444.3MB, time=109.15 memory used=8957.9MB, alloc=444.3MB, time=109.44 memory used=9047.1MB, alloc=444.3MB, time=109.72 memory used=9140.1MB, alloc=444.3MB, time=109.98 memory used=9236.6MB, alloc=444.3MB, time=110.21 memory used=9339.8MB, alloc=444.3MB, time=110.45 memory used=9414.8MB, alloc=444.3MB, time=110.66 memory used=9469.1MB, alloc=444.3MB, time=110.89 memory used=9523.2MB, alloc=444.3MB, time=111.14 memory used=9580.0MB, alloc=444.3MB, time=111.42 memory used=9638.7MB, alloc=444.3MB, time=111.60 memory used=9699.1MB, alloc=444.3MB, time=111.77 memory used=9760.4MB, alloc=444.3MB, time=111.95 memory used=9825.2MB, alloc=444.3MB, time=112.13 memory used=9892.1MB, alloc=444.3MB, time=112.31 memory used=9962.1MB, alloc=444.3MB, time=112.49 memory used=10035.0MB, alloc=444.3MB, time=112.67 memory used=10112.3MB, alloc=444.3MB, time=112.85 memory used=10206.1MB, alloc=444.3MB, time=113.29 memory used=10321.5MB, alloc=444.3MB, time=115.44 memory used=10398.7MB, alloc=444.3MB, time=115.75 memory used=10469.6MB, alloc=444.3MB, time=116.02 memory used=10551.4MB, alloc=444.3MB, time=116.31 memory used=10643.5MB, alloc=444.3MB, time=116.59 memory used=10746.1MB, alloc=444.3MB, time=116.91 memory used=10812.8MB, alloc=444.3MB, time=117.20 memory used=10868.4MB, alloc=444.3MB, time=117.51 memory used=10927.4MB, alloc=444.3MB, time=117.87 memory used=10991.2MB, alloc=444.3MB, time=118.12 memory used=11056.4MB, alloc=444.3MB, time=118.34 memory used=11126.5MB, alloc=444.3MB, time=118.56 memory used=11197.7MB, alloc=444.3MB, time=118.80 memory used=11273.4MB, alloc=444.3MB, time=119.05 memory used=11353.9MB, alloc=444.3MB, time=119.29 memory used=11438.8MB, alloc=444.3MB, time=119.63 memory used=11528.0MB, alloc=444.3MB, time=120.03 memory used=11621.0MB, alloc=444.3MB, time=120.34 memory used=11717.5MB, alloc=444.3MB, time=120.61 memory used=11820.7MB, alloc=444.3MB, time=120.94 memory used=11896.0MB, alloc=444.3MB, time=121.26 memory used=11950.1MB, alloc=444.3MB, time=121.49 memory used=12004.2MB, alloc=444.3MB, time=121.74 memory used=12061.0MB, alloc=444.3MB, time=122.02 memory used=12119.7MB, alloc=444.3MB, time=122.25 memory used=12180.0MB, alloc=444.3MB, time=122.52 memory used=12241.4MB, alloc=444.3MB, time=122.78 memory used=12306.1MB, alloc=444.3MB, time=123.05 memory used=12373.0MB, alloc=444.3MB, time=123.28 memory used=12443.1MB, alloc=444.3MB, time=123.53 memory used=12515.9MB, alloc=444.3MB, time=123.77 memory used=12592.8MB, alloc=444.3MB, time=124.04 memory used=12744.1MB, alloc=444.3MB, time=163.50 memory used=12948.9MB, alloc=444.3MB, time=170.32 memory used=13099.9MB, alloc=444.3MB, time=170.60 memory used=13265.6MB, alloc=444.3MB, time=170.88 memory used=13393.3MB, alloc=444.3MB, time=171.86 memory used=13479.6MB, alloc=444.3MB, time=172.09 memory used=13634.0MB, alloc=444.3MB, time=172.59 memory used=13793.7MB, alloc=444.3MB, time=172.88 memory used=14007.1MB, alloc=444.3MB, time=173.27 memory used=14268.3MB, alloc=444.3MB, time=174.14 memory used=14526.4MB, alloc=444.3MB, time=174.52 memory used=14715.5MB, alloc=444.3MB, time=174.83 memory used=14929.5MB, alloc=444.3MB, time=175.13 memory used=15136.3MB, alloc=444.3MB, time=175.48 memory used=15394.3MB, alloc=444.3MB, time=175.86 memory used=15571.6MB, alloc=444.3MB, time=176.14 memory used=15776.1MB, alloc=444.3MB, time=176.45 memory used=15977.3MB, alloc=444.3MB, time=176.73 memory used=16167.9MB, alloc=444.3MB, time=197.92 memory used=16292.2MB, alloc=444.3MB, time=199.01 memory used=16371.2MB, alloc=444.3MB, time=199.25 memory used=16447.2MB, alloc=444.3MB, time=199.48 memory used=16539.0MB, alloc=444.3MB, time=199.73 memory used=16598.4MB, alloc=444.3MB, time=199.90 memory used=16738.4MB, alloc=444.3MB, time=208.13 memory used=16855.8MB, alloc=444.3MB, time=220.96 memory used=16935.6MB, alloc=444.3MB, time=221.22 memory used=17005.1MB, alloc=444.3MB, time=221.45 memory used=17095.3MB, alloc=444.3MB, time=221.68 memory used=17159.6MB, alloc=444.3MB, time=221.86 memory used=17236.4MB, alloc=444.3MB, time=222.20 memory used=17356.0MB, alloc=444.3MB, time=223.21 memory used=17462.1MB, alloc=444.3MB, time=225.05 memory used=17557.1MB, alloc=444.3MB, time=225.52 memory used=17664.7MB, alloc=444.3MB, time=227.79 memory used=17740.4MB, alloc=444.3MB, time=228.02 memory used=17851.5MB, alloc=444.3MB, time=228.94 memory used=17920.2MB, alloc=444.3MB, time=229.21 memory used=18001.5MB, alloc=444.3MB, time=229.51 memory used=18096.6MB, alloc=444.3MB, time=229.78 memory used=18153.9MB, alloc=444.3MB, time=230.00 memory used=18215.9MB, alloc=444.3MB, time=230.24 memory used=18284.3MB, alloc=444.3MB, time=230.48 memory used=18358.1MB, alloc=444.3MB, time=230.79 memory used=18438.9MB, alloc=444.3MB, time=231.12 memory used=18529.2MB, alloc=444.3MB, time=231.35 memory used=18622.6MB, alloc=444.3MB, time=231.60 memory used=18676.6MB, alloc=444.3MB, time=231.79 memory used=18735.5MB, alloc=444.3MB, time=231.96 memory used=18844.0MB, alloc=444.3MB, time=232.98 memory used=18911.4MB, alloc=444.3MB, time=233.28 memory used=18996.0MB, alloc=444.3MB, time=233.61 memory used=19086.2MB, alloc=444.3MB, time=233.93 memory used=19142.1MB, alloc=444.3MB, time=234.18 memory used=19204.4MB, alloc=444.3MB, time=234.42 memory used=19272.8MB, alloc=444.3MB, time=234.66 memory used=19346.7MB, alloc=444.3MB, time=234.90 memory used=19429.6MB, alloc=444.3MB, time=235.13 memory used=19520.0MB, alloc=444.3MB, time=235.41 memory used=19610.5MB, alloc=444.3MB, time=235.65 memory used=19664.8MB, alloc=444.3MB, time=235.86 memory used=19724.8MB, alloc=444.3MB, time=236.05 memory used=19874.2MB, alloc=444.3MB, time=263.97 memory used=19971.5MB, alloc=444.3MB, time=264.22 memory used=20062.8MB, alloc=444.3MB, time=264.41 memory used=20294.9MB, alloc=444.3MB, time=266.32 memory used=20368.0MB, alloc=444.3MB, time=266.60 memory used=20440.2MB, alloc=444.3MB, time=266.88 memory used=20528.0MB, alloc=444.3MB, time=267.17 memory used=20613.6MB, alloc=444.3MB, time=267.45 memory used=20668.5MB, alloc=444.3MB, time=267.67 memory used=20725.9MB, alloc=444.3MB, time=267.90 memory used=20787.8MB, alloc=444.3MB, time=268.12 memory used=20854.0MB, alloc=444.3MB, time=268.38 memory used=20927.0MB, alloc=444.3MB, time=268.67 memory used=21003.8MB, alloc=444.3MB, time=268.92 memory used=21086.7MB, alloc=444.3MB, time=269.19 memory used=21175.1MB, alloc=444.3MB, time=269.46 memory used=21272.8MB, alloc=444.3MB, time=269.72 memory used=21334.6MB, alloc=444.3MB, time=269.92 memory used=21387.1MB, alloc=444.3MB, time=270.10 memory used=21441.2MB, alloc=444.3MB, time=270.29 memory used=21498.5MB, alloc=444.3MB, time=270.46 memory used=21560.6MB, alloc=444.3MB, time=270.65 memory used=21627.0MB, alloc=444.3MB, time=270.83 memory used=21731.0MB, alloc=444.3MB, time=272.14 memory used=21809.3MB, alloc=444.3MB, time=272.44 memory used=21880.1MB, alloc=444.3MB, time=272.70 memory used=21964.2MB, alloc=444.3MB, time=272.97 memory used=22055.9MB, alloc=444.3MB, time=273.25 memory used=22109.9MB, alloc=444.3MB, time=273.48 memory used=22166.7MB, alloc=444.3MB, time=273.72 memory used=22228.3MB, alloc=444.3MB, time=273.97 memory used=22294.3MB, alloc=444.3MB, time=274.19 memory used=22364.3MB, alloc=444.3MB, time=274.42 memory used=22441.0MB, alloc=444.3MB, time=274.64 memory used=22523.8MB, alloc=444.3MB, time=274.91 memory used=22612.1MB, alloc=444.3MB, time=275.16 memory used=22707.5MB, alloc=444.3MB, time=275.39 memory used=22776.0MB, alloc=444.3MB, time=275.60 memory used=22829.0MB, alloc=444.3MB, time=275.78 memory used=22883.3MB, alloc=444.3MB, time=275.95 memory used=22941.1MB, alloc=444.3MB, time=276.12 memory used=23002.2MB, alloc=444.3MB, time=276.30 memory used=23068.0MB, alloc=444.3MB, time=276.48 memory used=23151.8MB, alloc=444.3MB, time=282.65 memory used=23343.9MB, alloc=444.3MB, time=309.72 memory used=23524.2MB, alloc=444.3MB, time=310.07 memory used=23774.1MB, alloc=444.3MB, time=312.81 memory used=23835.2MB, alloc=444.3MB, time=313.09 memory used=23903.3MB, alloc=444.3MB, time=313.36 memory used=23980.0MB, alloc=444.3MB, time=313.63 memory used=24067.1MB, alloc=444.3MB, time=313.93 memory used=24152.3MB, alloc=444.3MB, time=314.20 memory used=24203.8MB, alloc=444.3MB, time=314.48 memory used=24255.8MB, alloc=444.3MB, time=314.75 memory used=24310.6MB, alloc=444.3MB, time=315.05 memory used=24370.5MB, alloc=444.3MB, time=315.35 memory used=24431.9MB, alloc=444.3MB, time=315.65 memory used=24494.7MB, alloc=444.3MB, time=315.95 memory used=24562.7MB, alloc=444.3MB, time=316.19 memory used=24632.1MB, alloc=444.3MB, time=316.46 memory used=24706.6MB, alloc=444.3MB, time=316.71 memory used=24782.2MB, alloc=444.3MB, time=316.97 memory used=24863.1MB, alloc=444.3MB, time=317.21 memory used=24948.9MB, alloc=444.3MB, time=317.52 memory used=25035.4MB, alloc=444.3MB, time=317.79 memory used=25126.1MB, alloc=444.3MB, time=318.07 memory used=25198.4MB, alloc=444.3MB, time=318.30 memory used=25244.9MB, alloc=444.3MB, time=318.50 memory used=25292.2MB, alloc=444.3MB, time=318.70 memory used=25340.2MB, alloc=444.3MB, time=318.91 memory used=25392.0MB, alloc=444.3MB, time=319.09 memory used=25443.4MB, alloc=444.3MB, time=319.31 memory used=25494.3MB, alloc=444.3MB, time=319.50 memory used=25548.7MB, alloc=444.3MB, time=319.72 memory used=25602.3MB, alloc=444.3MB, time=319.92 memory used=25659.1MB, alloc=444.3MB, time=320.12 memory used=25718.6MB, alloc=444.3MB, time=320.32 memory used=25780.5MB, alloc=444.3MB, time=320.54 memory used=25841.1MB, alloc=444.3MB, time=320.74 memory used=25906.0MB, alloc=444.3MB, time=320.94 memory used=25972.1MB, alloc=444.3MB, time=321.15 memory used=26041.3MB, alloc=444.3MB, time=321.36 memory used=26112.3MB, alloc=444.3MB, time=321.59 memory used=26188.3MB, alloc=444.3MB, time=321.81 memory used=26267.5MB, alloc=444.3MB, time=322.01 memory used=26365.6MB, alloc=444.3MB, time=324.45 memory used=26461.6MB, alloc=444.3MB, time=324.81 memory used=26524.4MB, alloc=444.3MB, time=325.11 memory used=26596.1MB, alloc=444.3MB, time=325.42 memory used=26678.5MB, alloc=444.3MB, time=325.73 memory used=26771.6MB, alloc=444.3MB, time=326.03 memory used=26841.7MB, alloc=444.3MB, time=326.29 memory used=26893.9MB, alloc=444.3MB, time=326.52 memory used=26947.6MB, alloc=444.3MB, time=326.75 memory used=27002.9MB, alloc=444.3MB, time=326.97 memory used=27063.5MB, alloc=444.3MB, time=327.19 memory used=27125.5MB, alloc=444.3MB, time=327.42 memory used=27192.9MB, alloc=444.3MB, time=327.66 memory used=27261.6MB, alloc=444.3MB, time=327.93 memory used=27335.6MB, alloc=444.3MB, time=328.22 memory used=27410.8MB, alloc=444.3MB, time=328.49 memory used=27491.1MB, alloc=444.3MB, time=328.73 memory used=27572.3MB, alloc=444.3MB, time=328.99 memory used=27658.4MB, alloc=444.3MB, time=329.23 memory used=27749.4MB, alloc=444.3MB, time=329.48 memory used=27842.9MB, alloc=444.3MB, time=329.73 memory used=27894.3MB, alloc=444.3MB, time=329.91 memory used=27943.2MB, alloc=444.3MB, time=330.10 memory used=27991.2MB, alloc=468.3MB, time=330.29 memory used=28052.4MB, alloc=468.3MB, time=330.49 memory used=28117.3MB, alloc=468.3MB, time=330.70 memory used=28185.5MB, alloc=468.3MB, time=330.90 memory used=28256.7MB, alloc=468.3MB, time=331.11 memory used=28326.9MB, alloc=468.3MB, time=331.33 memory used=28402.7MB, alloc=468.3MB, time=331.55 memory used=28480.3MB, alloc=468.3MB, time=331.77 memory used=28559.1MB, alloc=468.3MB, time=331.99 memory used=28641.1MB, alloc=468.3MB, time=332.20 memory used=28727.8MB, alloc=468.3MB, time=332.43 memory used=28820.0MB, alloc=468.3MB, time=332.64 memory used=28917.8MB, alloc=468.3MB, time=332.87 memory used=29026.1MB, alloc=468.3MB, time=333.19 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428498543 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 4 3 3 2 2 F := [12 x y z - 11 y - 3 y z, -9 x + x y - 7 x y ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 3 2 G := [-6 x y z - 3 y z + 20 x, -x y + 8 y + 7 z ] > Problem := [F,G]; 2 4 3 3 2 2 Problem := [[12 x y z - 11 y - 3 y z, -9 x + x y - 7 x y ], 2 2 2 3 3 2 [-6 x y z - 3 y z + 20 x, -x y + 8 y + 7 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=25.5MB, alloc=32.3MB, time=0.49 memory used=44.6MB, alloc=32.3MB, time=0.67 memory used=67.1MB, alloc=36.3MB, time=0.96 memory used=89.0MB, alloc=60.3MB, time=1.22 memory used=126.9MB, alloc=60.3MB, time=1.68 memory used=173.1MB, alloc=68.3MB, time=2.30 memory used=209.6MB, alloc=92.3MB, time=4.26 memory used=252.1MB, alloc=92.3MB, time=7.89 memory used=319.3MB, alloc=92.3MB, time=11.57 memory used=366.7MB, alloc=92.3MB, time=11.94 memory used=439.3MB, alloc=92.3MB, time=12.78 memory used=511.8MB, alloc=92.3MB, time=13.49 memory used=576.5MB, alloc=92.3MB, time=14.35 memory used=637.3MB, alloc=116.3MB, time=15.09 memory used=702.6MB, alloc=116.3MB, time=15.47 memory used=743.9MB, alloc=116.3MB, time=15.62 memory used=792.8MB, alloc=116.3MB, time=15.78 memory used=827.3MB, alloc=116.3MB, time=15.94 memory used=868.3MB, alloc=116.3MB, time=16.08 memory used=930.4MB, alloc=116.3MB, time=16.37 memory used=971.3MB, alloc=116.3MB, time=16.53 memory used=1021.1MB, alloc=116.3MB, time=16.68 memory used=1055.4MB, alloc=116.3MB, time=16.81 memory used=1096.1MB, alloc=116.3MB, time=16.94 memory used=1169.0MB, alloc=116.3MB, time=18.52 memory used=1216.2MB, alloc=116.3MB, time=18.67 memory used=1253.8MB, alloc=116.3MB, time=18.81 memory used=1303.1MB, alloc=116.3MB, time=18.95 memory used=1366.8MB, alloc=116.3MB, time=20.21 memory used=1433.6MB, alloc=120.0MB, time=20.45 memory used=1483.5MB, alloc=120.0MB, time=20.64 memory used=1516.6MB, alloc=120.0MB, time=20.78 memory used=1551.3MB, alloc=120.0MB, time=20.94 memory used=1590.3MB, alloc=120.0MB, time=21.12 memory used=1631.7MB, alloc=120.0MB, time=21.28 memory used=1678.2MB, alloc=120.0MB, time=21.44 memory used=1727.0MB, alloc=120.0MB, time=21.60 memory used=1781.2MB, alloc=120.0MB, time=21.78 memory used=1822.3MB, alloc=144.0MB, time=21.96 memory used=1861.5MB, alloc=144.0MB, time=22.13 memory used=1904.3MB, alloc=144.0MB, time=22.28 memory used=1948.4MB, alloc=144.0MB, time=22.45 memory used=1993.8MB, alloc=144.0MB, time=22.61 memory used=2042.4MB, alloc=144.0MB, time=22.79 memory used=2092.2MB, alloc=144.0MB, time=22.95 memory used=2146.2MB, alloc=144.0MB, time=23.13 memory used=2201.1MB, alloc=144.0MB, time=23.32 memory used=2259.0MB, alloc=144.0MB, time=23.50 memory used=2321.3MB, alloc=144.0MB, time=23.69 memory used=2386.9MB, alloc=144.0MB, time=23.88 memory used=2453.4MB, alloc=144.0MB, time=24.07 memory used=2524.4MB, alloc=144.0MB, time=24.26 memory used=2598.8MB, alloc=144.0MB, time=24.45 memory used=2662.8MB, alloc=144.0MB, time=24.61 memory used=2700.9MB, alloc=144.0MB, time=24.74 memory used=2740.3MB, alloc=144.0MB, time=24.87 memory used=2781.5MB, alloc=144.0MB, time=25.00 memory used=2824.3MB, alloc=144.0MB, time=25.11 memory used=2868.5MB, alloc=144.0MB, time=25.25 memory used=2914.9MB, alloc=144.0MB, time=25.37 memory used=2963.6MB, alloc=144.0MB, time=25.49 memory used=3036.4MB, alloc=144.0MB, time=35.22 memory used=3112.1MB, alloc=168.0MB, time=68.30 memory used=3198.6MB, alloc=168.0MB, time=134.00 memory used=3311.6MB, alloc=168.0MB, time=272.62 memory used=3412.6MB, alloc=168.0MB, time=310.26 memory used=3527.1MB, alloc=168.0MB, time=311.03 memory used=3618.5MB, alloc=168.0MB, time=311.47 memory used=3702.3MB, alloc=168.0MB, time=311.71 memory used=3762.6MB, alloc=168.0MB, time=311.92 memory used=3822.1MB, alloc=168.0MB, time=312.11 memory used=3887.8MB, alloc=168.0MB, time=312.29 memory used=3960.8MB, alloc=168.0MB, time=312.50 memory used=4041.3MB, alloc=168.0MB, time=312.72 memory used=4129.3MB, alloc=168.0MB, time=312.92 memory used=4203.0MB, alloc=168.0MB, time=313.10 memory used=4252.4MB, alloc=168.0MB, time=313.25 memory used=4301.3MB, alloc=168.0MB, time=313.40 memory used=4354.1MB, alloc=168.0MB, time=313.54 memory used=4408.1MB, alloc=168.0MB, time=313.68 memory used=4463.1MB, alloc=168.0MB, time=313.84 memory used=4521.8MB, alloc=168.0MB, time=313.99 memory used=4581.5MB, alloc=168.0MB, time=314.15 memory used=4644.9MB, alloc=168.0MB, time=314.30 memory used=4709.2MB, alloc=168.0MB, time=314.46 memory used=4777.2MB, alloc=168.0MB, time=314.62 memory used=4846.0MB, alloc=168.0MB, time=314.78 memory used=4918.3MB, alloc=168.0MB, time=314.95 memory used=4991.5MB, alloc=168.0MB, time=315.10 memory used=5067.8MB, alloc=168.0MB, time=315.25 memory used=5147.7MB, alloc=168.0MB, time=315.41 memory used=5230.9MB, alloc=168.0MB, time=315.57 memory used=5317.3MB, alloc=168.0MB, time=315.73 memory used=5406.7MB, alloc=168.0MB, time=315.90 memory used=5498.8MB, alloc=168.0MB, time=316.06 memory used=5529.7MB, alloc=179.8MB, time=316.19 memory used=5537.8MB, alloc=179.8MB, time=316.28 memory used=5543.6MB, alloc=179.8MB, time=316.38 memory used=5549.5MB, alloc=179.8MB, time=316.45 memory used=5555.4MB, alloc=179.8MB, time=316.54 memory used=5561.2MB, alloc=179.8MB, time=316.62 memory used=5567.1MB, alloc=179.8MB, time=316.70 memory used=5573.0MB, alloc=179.8MB, time=316.79 memory used=5578.8MB, alloc=179.8MB, time=316.87 memory used=5584.7MB, alloc=179.8MB, time=316.95 memory used=5590.7MB, alloc=179.8MB, time=317.03 memory used=5596.7MB, alloc=179.8MB, time=317.11 memory used=5605.1MB, alloc=179.8MB, time=317.20 memory used=5611.2MB, alloc=179.8MB, time=317.29 memory used=5619.7MB, alloc=179.8MB, time=317.38 memory used=5625.8MB, alloc=179.8MB, time=317.46 memory used=5634.2MB, alloc=179.8MB, time=317.55 memory used=5640.4MB, alloc=179.8MB, time=317.63 memory used=5648.8MB, alloc=179.8MB, time=317.72 memory used=5657.4MB, alloc=179.8MB, time=317.81 memory used=5666.1MB, alloc=179.8MB, time=317.90 memory used=5674.8MB, alloc=179.8MB, time=317.99 memory used=5683.4MB, alloc=179.8MB, time=318.07 memory used=5692.1MB, alloc=179.8MB, time=318.16 memory used=5700.7MB, alloc=179.8MB, time=318.25 memory used=5709.3MB, alloc=179.8MB, time=318.33 memory used=5717.9MB, alloc=179.8MB, time=318.42 memory used=5726.5MB, alloc=179.8MB, time=318.51 memory used=5735.1MB, alloc=179.8MB, time=318.60 memory used=5743.7MB, alloc=179.8MB, time=318.69 memory used=5752.2MB, alloc=179.8MB, time=318.78 memory used=5760.7MB, alloc=179.8MB, time=318.87 memory used=5769.3MB, alloc=179.8MB, time=318.96 memory used=5777.8MB, alloc=179.8MB, time=319.06 memory used=5786.3MB, alloc=179.8MB, time=319.15 memory used=5794.7MB, alloc=179.8MB, time=319.25 memory used=5803.2MB, alloc=179.8MB, time=319.33 memory used=5811.6MB, alloc=179.8MB, time=319.42 memory used=5820.1MB, alloc=179.8MB, time=319.51 memory used=5828.5MB, alloc=179.8MB, time=319.59 memory used=5836.9MB, alloc=179.8MB, time=319.67 memory used=5845.3MB, alloc=179.8MB, time=319.76 memory used=5853.6MB, alloc=179.8MB, time=319.85 memory used=5862.0MB, alloc=179.8MB, time=319.93 memory used=5870.3MB, alloc=179.8MB, time=320.02 memory used=5878.6MB, alloc=179.8MB, time=320.11 memory used=5886.9MB, alloc=179.8MB, time=320.19 memory used=5895.2MB, alloc=179.8MB, time=320.28 memory used=5903.5MB, alloc=179.8MB, time=320.37 memory used=5911.7MB, alloc=179.8MB, time=320.45 memory used=5919.9MB, alloc=179.8MB, time=320.54 memory used=5928.2MB, alloc=179.8MB, time=320.62 memory used=5936.3MB, alloc=179.8MB, time=320.71 memory used=5944.5MB, alloc=179.8MB, time=320.80 memory used=5952.7MB, alloc=179.8MB, time=320.89 memory used=5960.8MB, alloc=179.8MB, time=320.98 memory used=5968.9MB, alloc=179.8MB, time=321.06 memory used=5977.0MB, alloc=179.8MB, time=321.14 memory used=5985.1MB, alloc=179.8MB, time=321.23 memory used=5993.2MB, alloc=179.8MB, time=321.32 memory used=6001.4MB, alloc=179.8MB, time=321.40 memory used=6011.9MB, alloc=179.8MB, time=321.49 memory used=6020.2MB, alloc=179.8MB, time=321.58 memory used=6030.5MB, alloc=179.8MB, time=321.66 memory used=6041.1MB, alloc=179.8MB, time=321.75 memory used=6051.6MB, alloc=179.8MB, time=321.85 memory used=6062.1MB, alloc=179.8MB, time=321.94 memory used=6072.5MB, alloc=179.8MB, time=322.03 memory used=6083.0MB, alloc=179.8MB, time=322.13 memory used=6093.3MB, alloc=179.8MB, time=322.22 memory used=6103.7MB, alloc=179.8MB, time=322.30 memory used=6114.0MB, alloc=179.8MB, time=322.39 memory used=6124.2MB, alloc=179.8MB, time=322.47 memory used=6134.4MB, alloc=179.8MB, time=322.56 memory used=6144.6MB, alloc=179.8MB, time=322.65 memory used=6154.7MB, alloc=179.8MB, time=322.74 memory used=6164.8MB, alloc=179.8MB, time=322.83 memory used=6174.8MB, alloc=179.8MB, time=322.92 memory used=6184.8MB, alloc=179.8MB, time=323.00 memory used=6194.8MB, alloc=179.8MB, time=323.08 memory used=6204.7MB, alloc=179.8MB, time=323.17 memory used=6214.5MB, alloc=179.8MB, time=323.25 memory used=6224.3MB, alloc=179.8MB, time=323.34 memory used=6234.1MB, alloc=179.8MB, time=323.43 memory used=6244.0MB, alloc=179.8MB, time=323.52 memory used=6255.8MB, alloc=179.8MB, time=323.61 memory used=6265.8MB, alloc=179.8MB, time=323.70 memory used=6277.3MB, alloc=179.8MB, time=323.79 memory used=6289.2MB, alloc=179.8MB, time=323.88 memory used=6301.0MB, alloc=179.8MB, time=323.98 memory used=6312.6MB, alloc=179.8MB, time=324.06 memory used=6324.2MB, alloc=179.8MB, time=324.15 memory used=6335.7MB, alloc=179.8MB, time=324.24 memory used=6347.2MB, alloc=179.8MB, time=324.33 memory used=6358.5MB, alloc=179.8MB, time=324.42 memory used=6369.8MB, alloc=179.8MB, time=324.51 memory used=6380.9MB, alloc=179.8MB, time=324.60 memory used=6392.0MB, alloc=179.8MB, time=324.69 memory used=6403.3MB, alloc=179.8MB, time=324.76 memory used=6416.1MB, alloc=179.8MB, time=324.86 memory used=6429.0MB, alloc=179.8MB, time=324.95 memory used=6441.8MB, alloc=179.8MB, time=325.04 memory used=6454.5MB, alloc=179.8MB, time=325.14 memory used=6467.0MB, alloc=179.8MB, time=325.23 memory used=6479.4MB, alloc=179.8MB, time=325.32 memory used=6491.7MB, alloc=179.8MB, time=325.41 memory used=6503.8MB, alloc=179.8MB, time=325.50 memory used=6516.0MB, alloc=179.8MB, time=325.59 memory used=6529.5MB, alloc=179.8MB, time=325.69 memory used=6543.1MB, alloc=179.8MB, time=325.78 memory used=6556.5MB, alloc=179.8MB, time=325.88 memory used=6569.7MB, alloc=179.8MB, time=325.97 memory used=6582.6MB, alloc=179.8MB, time=326.07 memory used=6595.9MB, alloc=179.8MB, time=326.16 memory used=6609.7MB, alloc=179.8MB, time=326.26 memory used=6623.7MB, alloc=179.8MB, time=326.35 memory used=6637.4MB, alloc=179.8MB, time=326.44 memory used=6651.3MB, alloc=179.8MB, time=326.54 memory used=6665.6MB, alloc=179.8MB, time=326.63 memory used=6679.9MB, alloc=179.8MB, time=326.72 memory used=6695.4MB, alloc=179.8MB, time=326.81 memory used=6710.4MB, alloc=179.8MB, time=326.91 memory used=6725.3MB, alloc=179.8MB, time=327.00 memory used=6740.6MB, alloc=179.8MB, time=327.09 memory used=6756.3MB, alloc=179.8MB, time=327.18 memory used=6772.0MB, alloc=179.8MB, time=327.27 memory used=6788.4MB, alloc=179.8MB, time=327.36 memory used=6805.3MB, alloc=179.8MB, time=327.46 memory used=6822.3MB, alloc=179.8MB, time=327.54 memory used=6839.7MB, alloc=179.8MB, time=327.63 memory used=6942.9MB, alloc=435.8MB, time=328.43 memory used=7115.7MB, alloc=435.8MB, time=330.87 memory used=7188.2MB, alloc=435.8MB, time=331.08 memory used=7268.9MB, alloc=435.8MB, time=331.28 memory used=7337.3MB, alloc=435.8MB, time=331.45 memory used=7402.0MB, alloc=435.8MB, time=331.60 memory used=7628.4MB, alloc=435.8MB, time=333.84 memory used=7808.0MB, alloc=435.8MB, time=335.01 memory used=7988.5MB, alloc=435.8MB, time=336.16 memory used=8166.8MB, alloc=435.8MB, time=337.71 memory used=8345.6MB, alloc=435.8MB, time=339.62 memory used=8522.1MB, alloc=435.8MB, time=341.98 memory used=8699.1MB, alloc=435.8MB, time=344.61 memory used=8876.5MB, alloc=435.8MB, time=348.07 memory used=9055.3MB, alloc=435.8MB, time=351.87 memory used=9231.3MB, alloc=435.8MB, time=356.20 memory used=9408.8MB, alloc=435.8MB, time=361.27 memory used=9584.6MB, alloc=435.8MB, time=366.94 memory used=9757.6MB, alloc=435.8MB, time=373.27 memory used=9934.9MB, alloc=435.8MB, time=379.54 memory used=10108.4MB, alloc=435.8MB, time=387.11 memory used=10285.2MB, alloc=435.8MB, time=394.36 memory used=10459.5MB, alloc=435.8MB, time=402.65 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428498843 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 3 3 F := [-10 x + 10 y + 2 x z, 9 x y + 13 x y - x z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 4 2 2 G := [12 x z - x y - 7 x z, -11 x - 3 x y z - 20 x y ] > Problem := [F,G]; 3 3 3 3 Problem := [[-10 x + 10 y + 2 x z, 9 x y + 13 x y - x z], 3 2 4 2 2 [12 x z - x y - 7 x z, -11 x - 3 x y z - 20 x y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=26.0MB, alloc=32.3MB, time=0.50 memory used=45.7MB, alloc=32.3MB, time=0.79 memory used=63.5MB, alloc=56.3MB, time=1.06 memory used=106.9MB, alloc=68.3MB, time=1.63 memory used=152.1MB, alloc=68.3MB, time=2.22 memory used=194.0MB, alloc=92.3MB, time=2.81 memory used=260.8MB, alloc=92.3MB, time=3.62 memory used=305.8MB, alloc=92.3MB, time=3.86 memory used=351.4MB, alloc=92.3MB, time=4.36 memory used=399.9MB, alloc=92.3MB, time=6.39 memory used=431.8MB, alloc=92.3MB, time=6.50 memory used=462.3MB, alloc=92.3MB, time=6.60 memory used=499.6MB, alloc=92.3MB, time=6.72 memory used=524.2MB, alloc=92.3MB, time=6.80 memory used=557.9MB, alloc=92.3MB, time=6.97 memory used=596.8MB, alloc=92.3MB, time=7.17 memory used=651.4MB, alloc=92.3MB, time=7.68 memory used=703.8MB, alloc=92.3MB, time=8.08 memory used=782.0MB, alloc=93.6MB, time=8.64 memory used=858.9MB, alloc=95.0MB, time=9.76 memory used=937.2MB, alloc=351.0MB, time=11.16 memory used=1008.6MB, alloc=351.0MB, time=11.85 memory used=1077.8MB, alloc=351.0MB, time=13.09 memory used=1153.0MB, alloc=351.0MB, time=14.56 memory used=1221.6MB, alloc=375.0MB, time=15.47 memory used=1301.6MB, alloc=375.0MB, time=16.21 memory used=1347.4MB, alloc=375.0MB, time=16.43 memory used=1448.6MB, alloc=375.0MB, time=17.42 memory used=1519.5MB, alloc=375.0MB, time=18.09 memory used=1622.3MB, alloc=399.0MB, time=19.23 memory used=1699.7MB, alloc=399.0MB, time=19.75 memory used=1749.1MB, alloc=399.0MB, time=19.96 memory used=1801.3MB, alloc=399.0MB, time=20.12 memory used=1857.7MB, alloc=399.0MB, time=20.37 memory used=1912.8MB, alloc=399.0MB, time=20.57 memory used=1969.1MB, alloc=399.0MB, time=20.88 memory used=2017.9MB, alloc=399.0MB, time=21.07 memory used=2094.6MB, alloc=399.0MB, time=21.59 memory used=2147.5MB, alloc=399.0MB, time=21.81 memory used=2192.0MB, alloc=399.0MB, time=22.00 memory used=2235.0MB, alloc=399.0MB, time=22.19 memory used=2285.8MB, alloc=399.0MB, time=22.37 memory used=2346.6MB, alloc=399.0MB, time=22.56 memory used=2402.1MB, alloc=399.0MB, time=22.93 memory used=2461.3MB, alloc=399.0MB, time=23.18 memory used=2516.2MB, alloc=399.0MB, time=23.38 memory used=2555.2MB, alloc=399.0MB, time=23.56 memory used=2601.9MB, alloc=399.0MB, time=23.74 memory used=2657.0MB, alloc=399.0MB, time=23.94 memory used=2711.3MB, alloc=399.0MB, time=24.11 memory used=2791.7MB, alloc=399.0MB, time=34.16 memory used=2874.7MB, alloc=399.0MB, time=41.04 memory used=2925.2MB, alloc=399.0MB, time=41.25 memory used=2969.5MB, alloc=399.0MB, time=41.43 memory used=3023.7MB, alloc=399.0MB, time=41.63 memory used=3079.8MB, alloc=399.0MB, time=41.83 memory used=3115.0MB, alloc=399.0MB, time=41.99 memory used=3152.7MB, alloc=399.0MB, time=42.15 memory used=3192.7MB, alloc=399.0MB, time=42.30 memory used=3236.4MB, alloc=399.0MB, time=42.46 memory used=3281.9MB, alloc=399.0MB, time=42.64 memory used=3331.2MB, alloc=399.0MB, time=42.81 memory used=3384.3MB, alloc=399.0MB, time=42.98 memory used=3439.0MB, alloc=399.0MB, time=43.16 memory used=3497.1MB, alloc=399.0MB, time=43.34 memory used=3559.0MB, alloc=399.0MB, time=43.52 memory used=3714.7MB, alloc=399.0MB, time=44.02 memory used=3864.0MB, alloc=399.0MB, time=44.38 memory used=4031.3MB, alloc=399.0MB, time=44.72 memory used=4218.6MB, alloc=399.0MB, time=45.10 memory used=4434.4MB, alloc=399.0MB, time=45.48 memory used=4610.2MB, alloc=399.0MB, time=46.12 memory used=4692.5MB, alloc=399.0MB, time=46.92 memory used=4743.2MB, alloc=399.0MB, time=47.12 memory used=4787.5MB, alloc=399.0MB, time=47.27 memory used=4836.1MB, alloc=399.0MB, time=47.43 memory used=4894.3MB, alloc=399.0MB, time=47.66 memory used=5003.7MB, alloc=399.0MB, time=48.51 memory used=5141.0MB, alloc=399.0MB, time=49.89 memory used=5223.7MB, alloc=399.0MB, time=50.45 memory used=5359.5MB, alloc=399.0MB, time=51.95 memory used=5438.1MB, alloc=423.0MB, time=52.58 memory used=5508.4MB, alloc=423.0MB, time=52.91 memory used=5570.1MB, alloc=423.0MB, time=53.14 memory used=5649.4MB, alloc=423.0MB, time=53.53 memory used=5723.2MB, alloc=423.0MB, time=53.87 memory used=5817.0MB, alloc=423.0MB, time=61.91 memory used=5900.3MB, alloc=423.0MB, time=62.28 memory used=5957.4MB, alloc=423.0MB, time=62.51 memory used=6031.2MB, alloc=423.0MB, time=62.74 memory used=6076.8MB, alloc=423.0MB, time=62.93 memory used=6128.1MB, alloc=423.0MB, time=63.12 memory used=6185.0MB, alloc=423.0MB, time=63.32 memory used=6249.4MB, alloc=423.0MB, time=63.52 memory used=6321.9MB, alloc=423.0MB, time=63.72 memory used=6527.5MB, alloc=423.0MB, time=64.10 memory used=6661.2MB, alloc=423.0MB, time=64.55 memory used=6789.3MB, alloc=423.0MB, time=65.74 memory used=6920.5MB, alloc=423.0MB, time=66.99 memory used=6977.1MB, alloc=423.0MB, time=67.24 memory used=7044.9MB, alloc=423.0MB, time=67.46 memory used=7089.7MB, alloc=423.0MB, time=67.64 memory used=7157.3MB, alloc=423.0MB, time=67.95 memory used=7217.1MB, alloc=423.0MB, time=68.19 memory used=7326.8MB, alloc=423.0MB, time=69.23 memory used=7380.2MB, alloc=423.0MB, time=69.47 memory used=7444.1MB, alloc=423.0MB, time=69.70 memory used=7490.2MB, alloc=423.0MB, time=69.89 memory used=7560.5MB, alloc=423.0MB, time=70.21 memory used=7624.8MB, alloc=423.0MB, time=70.55 memory used=7758.2MB, alloc=423.0MB, time=71.79 memory used=7883.9MB, alloc=423.0MB, time=72.72 memory used=7978.1MB, alloc=423.0MB, time=73.78 memory used=8095.7MB, alloc=423.0MB, time=74.92 memory used=8190.9MB, alloc=447.0MB, time=78.76 memory used=8260.8MB, alloc=447.0MB, time=79.04 memory used=8335.8MB, alloc=447.0MB, time=79.30 memory used=8394.7MB, alloc=447.0MB, time=79.52 memory used=8485.3MB, alloc=447.0MB, time=80.02 memory used=8619.7MB, alloc=447.0MB, time=81.33 memory used=8753.1MB, alloc=447.0MB, time=82.80 memory used=8834.9MB, alloc=447.0MB, time=83.95 memory used=8966.1MB, alloc=471.0MB, time=85.07 memory used=9093.4MB, alloc=471.0MB, time=85.65 memory used=9272.4MB, alloc=471.0MB, time=87.51 memory used=9403.6MB, alloc=471.0MB, time=88.00 memory used=9542.0MB, alloc=471.0MB, time=88.47 memory used=9714.4MB, alloc=471.0MB, time=89.47 memory used=9863.3MB, alloc=471.0MB, time=89.95 memory used=10049.7MB, alloc=471.0MB, time=90.47 memory used=10285.8MB, alloc=471.0MB, time=91.05 memory used=10631.9MB, alloc=471.0MB, time=91.76 memory used=11019.7MB, alloc=471.0MB, time=92.52 memory used=11397.8MB, alloc=471.0MB, time=93.27 memory used=11766.3MB, alloc=471.0MB, time=93.99 memory used=12136.4MB, alloc=471.0MB, time=94.73 memory used=12499.1MB, alloc=471.0MB, time=95.47 memory used=12863.1MB, alloc=471.0MB, time=96.19 memory used=13220.9MB, alloc=471.0MB, time=96.92 memory used=13571.2MB, alloc=471.0MB, time=97.65 memory used=13981.9MB, alloc=471.0MB, time=99.08 memory used=14132.7MB, alloc=471.0MB, time=99.67 memory used=14313.9MB, alloc=471.0MB, time=100.21 memory used=14538.8MB, alloc=471.0MB, time=100.78 memory used=14874.0MB, alloc=471.0MB, time=101.52 memory used=15268.8MB, alloc=471.0MB, time=102.33 memory used=15641.9MB, alloc=471.0MB, time=103.10 memory used=16020.1MB, alloc=471.0MB, time=103.87 memory used=16382.9MB, alloc=471.0MB, time=104.61 memory used=16744.9MB, alloc=471.0MB, time=105.33 memory used=17100.8MB, alloc=471.0MB, time=106.08 memory used=17452.1MB, alloc=471.0MB, time=106.84 memory used=17803.0MB, alloc=471.0MB, time=107.62 memory used=18253.1MB, alloc=471.0MB, time=108.77 memory used=18428.0MB, alloc=471.0MB, time=109.83 memory used=18580.6MB, alloc=471.0MB, time=110.32 memory used=18773.1MB, alloc=471.0MB, time=110.85 memory used=19025.8MB, alloc=471.0MB, time=111.47 memory used=19405.3MB, alloc=471.0MB, time=112.27 memory used=19786.1MB, alloc=471.0MB, time=113.02 memory used=20162.9MB, alloc=471.0MB, time=113.78 memory used=20531.3MB, alloc=471.0MB, time=114.52 memory used=20893.4MB, alloc=471.0MB, time=115.27 memory used=21259.1MB, alloc=471.0MB, time=116.06 memory used=21618.9MB, alloc=471.0MB, time=116.81 memory used=21976.0MB, alloc=471.0MB, time=117.58 memory used=22286.4MB, alloc=471.0MB, time=118.89 memory used=22424.7MB, alloc=471.0MB, time=119.41 memory used=22570.7MB, alloc=471.0MB, time=119.93 memory used=22744.8MB, alloc=471.0MB, time=120.78 memory used=22901.0MB, alloc=471.0MB, time=121.69 memory used=23035.1MB, alloc=471.0MB, time=122.21 memory used=23204.1MB, alloc=471.0MB, time=122.73 memory used=23397.4MB, alloc=471.0MB, time=123.28 memory used=23597.3MB, alloc=471.0MB, time=123.85 memory used=23824.6MB, alloc=471.0MB, time=124.62 memory used=23973.3MB, alloc=471.0MB, time=125.48 memory used=24151.1MB, alloc=471.0MB, time=126.90 memory used=24299.0MB, alloc=471.0MB, time=127.81 memory used=24429.7MB, alloc=471.0MB, time=128.35 memory used=24564.1MB, alloc=471.0MB, time=128.84 memory used=24706.2MB, alloc=471.0MB, time=129.32 memory used=24861.5MB, alloc=471.0MB, time=130.09 memory used=25004.3MB, alloc=471.0MB, time=130.57 memory used=25186.2MB, alloc=471.0MB, time=131.09 memory used=25419.8MB, alloc=471.0MB, time=131.67 memory used=25782.1MB, alloc=471.0MB, time=132.38 memory used=26157.4MB, alloc=471.0MB, time=133.15 memory used=26525.2MB, alloc=471.0MB, time=133.93 memory used=26885.9MB, alloc=471.0MB, time=134.68 memory used=27256.2MB, alloc=471.0MB, time=135.52 memory used=27623.4MB, alloc=471.0MB, time=136.32 memory used=27988.6MB, alloc=471.0MB, time=137.09 memory used=28343.6MB, alloc=471.0MB, time=137.85 memory used=28700.6MB, alloc=471.0MB, time=139.19 memory used=28850.7MB, alloc=471.0MB, time=140.25 memory used=28970.4MB, alloc=495.0MB, time=140.85 memory used=29104.7MB, alloc=495.0MB, time=141.41 memory used=29280.5MB, alloc=495.0MB, time=143.01 memory used=29443.3MB, alloc=495.0MB, time=143.82 memory used=29632.3MB, alloc=495.0MB, time=145.04 memory used=29822.5MB, alloc=495.0MB, time=146.11 memory used=30015.6MB, alloc=495.0MB, time=147.56 memory used=30204.2MB, alloc=495.0MB, time=148.73 memory used=30340.8MB, alloc=495.0MB, time=149.40 memory used=30481.0MB, alloc=495.0MB, time=150.08 memory used=30639.3MB, alloc=495.0MB, time=150.82 memory used=30845.6MB, alloc=495.0MB, time=152.40 memory used=30984.4MB, alloc=495.0MB, time=153.11 memory used=31123.6MB, alloc=495.0MB, time=153.79 memory used=31269.0MB, alloc=495.0MB, time=154.49 memory used=31416.1MB, alloc=495.0MB, time=155.11 memory used=31614.8MB, alloc=495.0MB, time=156.29 memory used=31808.3MB, alloc=495.0MB, time=157.57 memory used=31975.9MB, alloc=495.0MB, time=158.13 memory used=32199.9MB, alloc=495.0MB, time=158.74 memory used=32532.9MB, alloc=495.0MB, time=159.49 memory used=32921.3MB, alloc=495.0MB, time=160.32 memory used=33291.2MB, alloc=495.0MB, time=161.11 memory used=33657.7MB, alloc=495.0MB, time=161.88 memory used=34015.1MB, alloc=495.0MB, time=162.62 memory used=34367.7MB, alloc=495.0MB, time=163.34 memory used=34719.8MB, alloc=495.0MB, time=164.11 memory used=35072.6MB, alloc=495.0MB, time=164.86 memory used=35420.8MB, alloc=495.0MB, time=165.61 memory used=35766.8MB, alloc=495.0MB, time=166.39 memory used=36097.9MB, alloc=495.0MB, time=167.79 memory used=36257.7MB, alloc=495.0MB, time=168.35 memory used=36464.2MB, alloc=495.0MB, time=168.97 memory used=36693.9MB, alloc=495.0MB, time=169.60 memory used=36941.5MB, alloc=495.0MB, time=170.32 memory used=37104.2MB, alloc=495.0MB, time=171.19 memory used=37261.2MB, alloc=495.0MB, time=171.77 memory used=37431.6MB, alloc=495.0MB, time=172.66 memory used=37607.8MB, alloc=495.0MB, time=173.26 memory used=37833.5MB, alloc=495.0MB, time=173.86 memory used=38158.5MB, alloc=495.0MB, time=174.59 memory used=38570.5MB, alloc=495.0MB, time=175.44 memory used=38952.0MB, alloc=495.0MB, time=176.22 memory used=39330.6MB, alloc=495.0MB, time=176.99 memory used=39701.2MB, alloc=495.0MB, time=177.74 memory used=40064.6MB, alloc=495.0MB, time=178.57 memory used=40427.0MB, alloc=495.0MB, time=179.34 memory used=40785.1MB, alloc=495.0MB, time=180.11 memory used=40981.3MB, alloc=495.0MB, time=181.55 memory used=41108.8MB, alloc=495.0MB, time=183.76 memory used=41247.4MB, alloc=519.0MB, time=186.44 memory used=41458.9MB, alloc=543.0MB, time=188.94 memory used=41710.3MB, alloc=543.0MB, time=191.33 memory used=41976.7MB, alloc=543.0MB, time=193.43 memory used=42190.1MB, alloc=567.0MB, time=196.04 memory used=42449.9MB, alloc=567.0MB, time=198.16 memory used=42733.9MB, alloc=567.0MB, time=200.65 memory used=42972.4MB, alloc=567.0MB, time=203.07 memory used=43196.8MB, alloc=591.0MB, time=205.56 memory used=43376.2MB, alloc=591.0MB, time=207.86 memory used=43598.4MB, alloc=591.0MB, time=210.14 memory used=43783.2MB, alloc=591.0MB, time=212.44 memory used=43909.6MB, alloc=615.0MB, time=214.97 memory used=44060.1MB, alloc=615.0MB, time=217.29 memory used=44227.9MB, alloc=639.0MB, time=219.76 memory used=44400.6MB, alloc=639.0MB, time=222.21 memory used=44615.5MB, alloc=663.0MB, time=224.50 memory used=44862.5MB, alloc=663.0MB, time=226.74 memory used=45043.9MB, alloc=663.0MB, time=229.30 memory used=45170.4MB, alloc=663.0MB, time=231.71 memory used=45303.1MB, alloc=687.0MB, time=234.19 memory used=45463.0MB, alloc=687.0MB, time=236.25 memory used=45590.0MB, alloc=687.0MB, time=238.52 memory used=45726.0MB, alloc=711.0MB, time=240.67 memory used=45871.1MB, alloc=711.0MB, time=243.00 memory used=46046.4MB, alloc=711.0MB, time=245.35 memory used=46251.1MB, alloc=711.0MB, time=247.60 memory used=46406.3MB, alloc=711.0MB, time=249.63 memory used=46555.7MB, alloc=735.0MB, time=251.97 memory used=46755.1MB, alloc=735.0MB, time=254.07 memory used=46946.4MB, alloc=735.0MB, time=256.06 memory used=47071.7MB, alloc=735.0MB, time=258.02 memory used=47194.8MB, alloc=735.0MB, time=260.02 memory used=47313.7MB, alloc=735.0MB, time=262.10 memory used=47530.8MB, alloc=735.0MB, time=264.10 memory used=47685.2MB, alloc=759.0MB, time=266.26 memory used=47822.4MB, alloc=759.0MB, time=268.15 memory used=48005.2MB, alloc=759.0MB, time=270.16 memory used=48132.5MB, alloc=759.0MB, time=272.13 memory used=48230.1MB, alloc=759.0MB, time=274.02 memory used=48317.0MB, alloc=783.0MB, time=276.04 memory used=48441.5MB, alloc=807.0MB, time=279.95 memory used=48766.2MB, alloc=831.0MB, time=291.80 memory used=49090.6MB, alloc=855.0MB, time=304.31 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428499143 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 F := [-11 x - 2 x y + 5 z , -11 y z + 3 x z + 11 x y] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 3 3 3 G := [5 x + 3 y z + 12 z , 19 x z - 10 z + 9 z] > Problem := [F,G]; 3 2 3 2 Problem := [[-11 x - 2 x y + 5 z , -11 y z + 3 x z + 11 x y], 4 3 3 3 3 [5 x + 3 y z + 12 z , 19 x z - 10 z + 9 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=25.4MB, alloc=32.3MB, time=0.47 memory used=45.6MB, alloc=60.3MB, time=0.77 memory used=86.8MB, alloc=60.3MB, time=1.29 memory used=121.1MB, alloc=60.3MB, time=1.52 memory used=157.3MB, alloc=60.3MB, time=1.93 memory used=205.8MB, alloc=68.3MB, time=2.54 memory used=250.0MB, alloc=68.3MB, time=3.61 memory used=282.2MB, alloc=68.3MB, time=5.31 memory used=303.7MB, alloc=68.3MB, time=5.39 memory used=324.8MB, alloc=68.3MB, time=5.48 memory used=351.2MB, alloc=68.3MB, time=5.56 memory used=369.2MB, alloc=68.3MB, time=5.63 memory used=386.1MB, alloc=68.3MB, time=5.70 memory used=404.4MB, alloc=68.3MB, time=5.76 memory used=424.5MB, alloc=68.3MB, time=5.84 memory used=446.8MB, alloc=68.3MB, time=5.91 memory used=471.5MB, alloc=68.3MB, time=5.98 memory used=507.8MB, alloc=83.8MB, time=6.08 memory used=525.5MB, alloc=83.8MB, time=6.26 memory used=553.0MB, alloc=83.8MB, time=6.38 memory used=573.7MB, alloc=83.8MB, time=6.47 memory used=600.6MB, alloc=83.8MB, time=6.56 memory used=619.6MB, alloc=83.8MB, time=6.65 memory used=636.2MB, alloc=83.8MB, time=6.72 memory used=654.5MB, alloc=83.8MB, time=6.80 memory used=674.8MB, alloc=83.8MB, time=6.89 memory used=697.0MB, alloc=83.8MB, time=6.97 memory used=721.2MB, alloc=83.8MB, time=7.05 memory used=748.9MB, alloc=83.8MB, time=7.13 memory used=767.5MB, alloc=83.8MB, time=7.20 memory used=783.2MB, alloc=83.8MB, time=7.26 memory used=800.0MB, alloc=83.8MB, time=7.32 memory used=818.1MB, alloc=83.8MB, time=7.38 memory used=851.6MB, alloc=83.8MB, time=9.99 memory used=881.2MB, alloc=107.8MB, time=18.32 memory used=932.3MB, alloc=107.8MB, time=29.31 memory used=970.5MB, alloc=107.8MB, time=29.44 memory used=1005.8MB, alloc=107.8MB, time=29.56 memory used=1051.7MB, alloc=107.8MB, time=29.69 memory used=1083.3MB, alloc=107.8MB, time=29.79 memory used=1112.4MB, alloc=107.8MB, time=29.89 memory used=1143.6MB, alloc=107.8MB, time=29.98 memory used=1178.6MB, alloc=107.8MB, time=30.07 memory used=1216.5MB, alloc=107.8MB, time=30.16 memory used=1258.3MB, alloc=107.8MB, time=30.27 memory used=1303.8MB, alloc=107.8MB, time=30.37 memory used=1360.3MB, alloc=107.8MB, time=30.49 memory used=1370.5MB, alloc=107.8MB, time=30.54 memory used=1380.4MB, alloc=107.8MB, time=30.59 memory used=1390.1MB, alloc=107.8MB, time=30.65 memory used=1399.9MB, alloc=107.8MB, time=30.70 memory used=1409.7MB, alloc=107.8MB, time=30.76 memory used=1420.5MB, alloc=107.8MB, time=30.81 memory used=1431.4MB, alloc=107.8MB, time=30.87 memory used=1442.2MB, alloc=107.8MB, time=30.93 memory used=1454.1MB, alloc=107.8MB, time=30.99 memory used=1465.9MB, alloc=107.8MB, time=31.04 memory used=1477.5MB, alloc=107.8MB, time=31.10 memory used=1490.1MB, alloc=107.8MB, time=31.16 memory used=1502.5MB, alloc=107.8MB, time=31.22 memory used=1515.9MB, alloc=107.8MB, time=31.28 memory used=1528.8MB, alloc=107.8MB, time=31.34 memory used=1542.6MB, alloc=107.8MB, time=31.40 memory used=1556.9MB, alloc=107.8MB, time=31.45 memory used=1571.6MB, alloc=107.8MB, time=31.52 memory used=1586.6MB, alloc=107.8MB, time=31.57 memory used=1601.7MB, alloc=107.8MB, time=31.64 memory used=1618.0MB, alloc=107.8MB, time=31.70 memory used=1635.3MB, alloc=107.8MB, time=31.76 memory used=1691.8MB, alloc=107.8MB, time=32.14 memory used=1740.2MB, alloc=107.8MB, time=32.34 memory used=1785.5MB, alloc=107.8MB, time=32.44 memory used=1825.1MB, alloc=107.8MB, time=32.53 memory used=1914.2MB, alloc=107.8MB, time=33.74 memory used=1969.0MB, alloc=107.8MB, time=34.09 memory used=2014.5MB, alloc=107.8MB, time=34.35 memory used=2051.0MB, alloc=107.8MB, time=34.46 memory used=2092.5MB, alloc=107.8MB, time=34.57 memory used=2121.4MB, alloc=107.8MB, time=34.65 memory used=2154.1MB, alloc=107.8MB, time=34.74 memory used=2191.9MB, alloc=107.8MB, time=34.83 memory used=2234.6MB, alloc=107.8MB, time=34.92 memory used=2291.7MB, alloc=107.8MB, time=35.03 memory used=2301.2MB, alloc=107.8MB, time=35.08 memory used=2310.9MB, alloc=107.8MB, time=35.13 memory used=2320.9MB, alloc=107.8MB, time=35.18 memory used=2331.6MB, alloc=107.8MB, time=35.23 memory used=2342.1MB, alloc=107.8MB, time=35.28 memory used=2353.0MB, alloc=107.8MB, time=35.33 memory used=2364.5MB, alloc=107.8MB, time=35.38 memory used=2376.0MB, alloc=107.8MB, time=35.44 memory used=2387.5MB, alloc=107.8MB, time=35.50 memory used=2399.6MB, alloc=107.8MB, time=35.56 memory used=2412.2MB, alloc=107.8MB, time=35.62 memory used=2425.3MB, alloc=107.8MB, time=35.69 memory used=2438.4MB, alloc=107.8MB, time=35.75 memory used=2452.0MB, alloc=107.8MB, time=35.82 memory used=2465.9MB, alloc=107.8MB, time=35.87 memory used=2479.7MB, alloc=107.8MB, time=35.94 memory used=2494.7MB, alloc=107.8MB, time=36.00 memory used=2509.8MB, alloc=107.8MB, time=36.06 memory used=2525.3MB, alloc=107.8MB, time=36.12 memory used=2541.8MB, alloc=107.8MB, time=36.18 memory used=2558.2MB, alloc=107.8MB, time=36.25 memory used=2619.1MB, alloc=107.8MB, time=36.54 memory used=2659.4MB, alloc=107.8MB, time=36.66 memory used=2691.3MB, alloc=107.8MB, time=36.75 memory used=2721.8MB, alloc=107.8MB, time=36.84 memory used=2756.9MB, alloc=107.8MB, time=36.93 memory used=2796.9MB, alloc=107.8MB, time=37.01 memory used=2841.8MB, alloc=107.8MB, time=37.11 memory used=2873.8MB, alloc=107.8MB, time=37.19 memory used=2883.2MB, alloc=107.8MB, time=37.24 memory used=2892.9MB, alloc=107.8MB, time=37.29 memory used=2902.8MB, alloc=107.8MB, time=37.34 memory used=2913.5MB, alloc=107.8MB, time=37.39 memory used=2924.0MB, alloc=107.8MB, time=37.44 memory used=2934.9MB, alloc=107.8MB, time=37.49 memory used=2946.4MB, alloc=107.8MB, time=37.55 memory used=2957.9MB, alloc=107.8MB, time=37.61 memory used=2969.4MB, alloc=107.8MB, time=37.67 memory used=2981.5MB, alloc=107.8MB, time=37.72 memory used=2994.1MB, alloc=107.8MB, time=37.79 memory used=3007.2MB, alloc=107.8MB, time=37.85 memory used=3020.3MB, alloc=107.8MB, time=37.91 memory used=3033.9MB, alloc=107.8MB, time=37.97 memory used=3047.8MB, alloc=107.8MB, time=38.03 memory used=3062.3MB, alloc=107.8MB, time=38.09 memory used=3077.2MB, alloc=107.8MB, time=38.16 memory used=3092.3MB, alloc=107.8MB, time=38.22 memory used=3107.8MB, alloc=107.8MB, time=38.28 memory used=3124.1MB, alloc=107.8MB, time=38.34 memory used=3141.0MB, alloc=107.8MB, time=38.40 memory used=3203.1MB, alloc=107.8MB, time=47.70 memory used=3229.5MB, alloc=131.8MB, time=47.83 memory used=3269.2MB, alloc=131.8MB, time=47.98 memory used=3315.8MB, alloc=131.8MB, time=48.14 memory used=3368.3MB, alloc=131.8MB, time=48.32 memory used=3426.5MB, alloc=131.8MB, time=48.51 memory used=3470.2MB, alloc=131.8MB, time=48.67 memory used=3501.3MB, alloc=155.8MB, time=48.82 memory used=3542.4MB, alloc=155.8MB, time=48.96 memory used=3583.7MB, alloc=155.8MB, time=49.11 memory used=3626.8MB, alloc=155.8MB, time=49.25 memory used=3671.8MB, alloc=155.8MB, time=49.40 memory used=3718.5MB, alloc=155.8MB, time=49.55 memory 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time=55.87 memory used=6348.3MB, alloc=203.8MB, time=56.03 memory used=6425.2MB, alloc=203.8MB, time=56.19 memory used=6502.9MB, alloc=203.8MB, time=56.36 memory used=6581.3MB, alloc=203.8MB, time=56.52 memory used=6660.6MB, alloc=203.8MB, time=56.68 memory used=6740.6MB, alloc=203.8MB, time=56.85 memory used=6821.3MB, alloc=203.8MB, time=57.00 memory used=6902.9MB, alloc=203.8MB, time=57.15 memory used=6985.1MB, alloc=203.8MB, time=57.30 memory used=7068.1MB, alloc=203.8MB, time=57.46 memory used=7151.9MB, alloc=203.8MB, time=57.62 memory used=7236.3MB, alloc=203.8MB, time=57.78 memory used=7321.5MB, alloc=203.8MB, time=57.94 memory used=7407.5MB, alloc=203.8MB, time=58.11 memory used=7494.1MB, alloc=203.8MB, time=58.27 memory used=7581.6MB, alloc=203.8MB, time=58.45 memory used=7643.3MB, alloc=203.8MB, time=58.59 memory used=7643.9MB, alloc=203.8MB, time=58.64 memory used=7644.0MB, alloc=459.8MB, time=58.70 memory used=7810.2MB, alloc=459.8MB, time=59.16 memory used=7908.2MB, alloc=459.8MB, time=59.39 memory used=7998.0MB, alloc=459.8MB, time=59.60 memory used=8089.2MB, alloc=459.8MB, time=59.81 memory used=8181.2MB, alloc=459.8MB, time=60.02 memory used=8274.1MB, alloc=459.8MB, time=60.21 memory used=8367.8MB, alloc=459.8MB, time=60.44 memory used=8463.0MB, alloc=459.8MB, time=60.67 memory used=8585.0MB, alloc=459.8MB, time=60.91 memory used=8683.5MB, alloc=459.8MB, time=61.13 memory used=8781.4MB, alloc=459.8MB, time=61.38 memory used=8906.2MB, alloc=459.8MB, time=61.70 memory used=9007.4MB, alloc=459.8MB, time=61.98 memory used=9135.4MB, alloc=459.8MB, time=62.25 memory used=9239.4MB, alloc=459.8MB, time=62.48 memory used=9368.0MB, alloc=459.8MB, time=62.76 memory used=9473.6MB, alloc=459.8MB, time=62.99 memory used=9604.2MB, alloc=459.8MB, time=63.29 memory used=9740.6MB, alloc=459.8MB, time=63.60 memory used=9878.0MB, alloc=459.8MB, time=63.95 memory used=10016.6MB, alloc=459.8MB, time=64.25 memory used=10156.2MB, alloc=459.8MB, time=64.56 memory 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alloc=459.8MB, time=70.97 memory used=13476.0MB, alloc=459.8MB, time=71.28 memory used=13637.2MB, alloc=459.8MB, time=71.58 memory used=13799.3MB, alloc=459.8MB, time=71.89 memory used=13962.1MB, alloc=459.8MB, time=72.20 memory used=14125.7MB, alloc=459.8MB, time=72.52 memory used=14290.2MB, alloc=459.8MB, time=72.83 memory used=14455.3MB, alloc=459.8MB, time=73.14 memory used=14621.3MB, alloc=459.8MB, time=73.45 memory used=14787.9MB, alloc=459.8MB, time=73.76 memory used=14955.4MB, alloc=459.8MB, time=74.05 memory used=15123.5MB, alloc=459.8MB, time=74.35 memory used=15292.4MB, alloc=459.8MB, time=74.65 memory used=15462.0MB, alloc=459.8MB, time=74.95 memory used=15632.2MB, alloc=459.8MB, time=75.27 memory used=15803.2MB, alloc=459.8MB, time=75.58 memory used=15974.9MB, alloc=459.8MB, time=75.88 memory used=16147.2MB, alloc=459.8MB, time=76.21 memory used=16324.9MB, alloc=459.8MB, time=76.52 memory used=16501.0MB, alloc=459.8MB, time=76.84 memory used=16711.7MB, alloc=459.8MB, 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time=94.06 memory used=26223.6MB, alloc=459.8MB, time=94.36 memory used=26415.8MB, alloc=459.8MB, time=94.67 memory used=26608.0MB, alloc=459.8MB, time=94.98 memory used=26800.3MB, alloc=459.8MB, time=95.29 memory used=26992.7MB, alloc=459.8MB, time=95.60 memory used=27185.0MB, alloc=459.8MB, time=95.91 memory used=27377.4MB, alloc=459.8MB, time=96.23 memory used=27569.9MB, alloc=459.8MB, time=96.54 memory used=27762.3MB, alloc=459.8MB, time=96.85 memory used=27954.7MB, alloc=459.8MB, time=97.17 memory used=28147.1MB, alloc=459.8MB, time=97.47 memory used=28339.5MB, alloc=459.8MB, time=97.78 memory used=28531.8MB, alloc=459.8MB, time=98.09 memory used=28724.1MB, alloc=459.8MB, time=98.40 memory used=28916.3MB, alloc=459.8MB, time=98.72 memory used=29108.5MB, alloc=459.8MB, time=99.02 memory used=29300.5MB, alloc=459.8MB, time=99.33 memory used=29492.5MB, alloc=459.8MB, time=99.64 memory used=29684.4MB, alloc=459.8MB, time=99.95 memory used=29876.2MB, alloc=459.8MB, time=100.24 memory 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used=40280.7MB, alloc=459.8MB, time=117.39 memory used=40488.9MB, alloc=459.8MB, time=117.70 memory used=40695.9MB, alloc=459.8MB, time=118.00 memory used=40901.7MB, alloc=459.8MB, time=118.31 memory used=41106.4MB, alloc=459.8MB, time=118.61 memory used=41309.9MB, alloc=459.8MB, time=118.90 memory used=41512.1MB, alloc=459.8MB, time=119.19 memory used=41713.0MB, alloc=459.8MB, time=119.50 memory used=41922.5MB, alloc=459.8MB, time=119.81 memory used=42125.9MB, alloc=459.8MB, time=120.11 memory used=42347.4MB, alloc=459.8MB, time=120.43 memory used=42557.8MB, alloc=459.8MB, time=120.73 memory used=42775.7MB, alloc=459.8MB, time=121.06 memory used=43006.5MB, alloc=459.8MB, time=121.40 memory used=43235.2MB, alloc=459.8MB, time=121.72 memory used=43461.8MB, alloc=459.8MB, time=122.05 memory used=43682.9MB, alloc=459.8MB, time=122.36 memory used=43878.1MB, alloc=459.8MB, time=122.67 memory used=44069.8MB, alloc=459.8MB, time=122.96 memory used=44268.0MB, alloc=459.8MB, time=123.26 memory used=44445.3MB, alloc=459.8MB, time=123.54 memory used=44623.6MB, alloc=459.8MB, time=123.81 memory used=44801.1MB, alloc=459.8MB, time=124.08 memory used=44978.4MB, alloc=459.8MB, time=124.35 memory used=45154.9MB, alloc=459.8MB, time=124.62 memory used=45345.1MB, alloc=459.8MB, time=124.92 memory used=45528.1MB, alloc=459.8MB, time=125.21 memory used=45716.8MB, alloc=459.8MB, time=125.51 memory used=45916.0MB, alloc=459.8MB, time=125.82 memory used=46112.6MB, alloc=459.8MB, time=126.11 memory used=46306.7MB, alloc=459.8MB, time=126.40 memory used=46498.2MB, alloc=459.8MB, time=126.69 memory used=46698.1MB, alloc=459.8MB, time=126.98 memory used=46904.1MB, alloc=459.8MB, time=127.28 memory used=47103.9MB, alloc=459.8MB, time=127.58 memory used=47309.3MB, alloc=459.8MB, time=127.87 memory used=47516.5MB, alloc=459.8MB, time=128.18 memory used=47723.1MB, alloc=459.8MB, time=128.50 memory used=47932.8MB, alloc=459.8MB, time=128.80 memory used=48154.3MB, alloc=459.8MB, time=129.11 memory used=48370.5MB, alloc=459.8MB, time=129.41 memory used=48593.9MB, alloc=459.8MB, time=129.72 memory used=48823.9MB, alloc=459.8MB, time=130.03 memory used=49053.7MB, alloc=459.8MB, time=130.34 memory used=49282.4MB, alloc=459.8MB, time=252.31 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428499443 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 4 3 3 3 F := [-4 x y - 4 z + 13 z , -19 x y - 19 x z - 13 z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 2 2 G := [-10 y - 4 x + 17 x, -14 x z + 2 x y z - 15] > Problem := [F,G]; 2 2 4 3 3 3 Problem := [[-4 x y - 4 z + 13 z , -19 x y - 19 x z - 13 z], 4 2 2 2 2 [-10 y - 4 x + 17 x, -14 x z + 2 x y z - 15]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.19 memory used=23.9MB, alloc=32.3MB, time=0.47 memory used=42.7MB, alloc=32.3MB, time=0.74 memory used=62.4MB, alloc=56.3MB, time=1.01 memory used=102.5MB, alloc=60.3MB, time=1.35 memory used=139.9MB, alloc=60.8MB, time=1.54 memory used=174.0MB, alloc=60.8MB, time=1.64 memory used=205.8MB, alloc=60.8MB, time=1.72 memory used=229.5MB, alloc=60.8MB, time=1.77 memory used=263.1MB, alloc=60.8MB, time=1.90 memory used=289.2MB, alloc=60.8MB, time=1.96 memory used=324.8MB, alloc=60.8MB, time=2.15 memory used=363.4MB, alloc=60.8MB, time=2.41 memory used=401.9MB, alloc=60.8MB, time=2.84 memory used=432.4MB, alloc=60.8MB, time=2.96 memory used=458.8MB, alloc=60.8MB, time=3.01 memory used=508.5MB, alloc=68.8MB, time=3.66 memory used=554.0MB, alloc=68.8MB, time=4.25 memory used=604.4MB, alloc=68.8MB, time=4.74 memory used=629.6MB, alloc=68.8MB, time=4.85 memory used=651.8MB, alloc=68.8MB, time=4.95 memory used=671.6MB, alloc=68.8MB, time=5.03 memory used=692.9MB, alloc=68.8MB, time=5.10 memory used=718.9MB, alloc=68.8MB, time=5.24 memory used=737.9MB, alloc=68.8MB, time=5.31 memory used=758.6MB, alloc=68.8MB, time=5.38 memory used=784.9MB, alloc=68.8MB, time=5.55 memory used=807.2MB, alloc=68.8MB, time=5.65 memory used=827.0MB, alloc=68.8MB, time=5.73 memory used=850.0MB, alloc=68.8MB, time=5.80 memory used=873.0MB, alloc=68.8MB, time=5.92 memory used=892.2MB, alloc=68.8MB, time=5.99 memory used=914.7MB, alloc=68.8MB, time=6.07 memory used=940.2MB, alloc=68.8MB, time=6.22 memory used=960.2MB, alloc=68.8MB, time=6.30 memory used=983.1MB, alloc=92.8MB, time=6.39 memory used=1013.6MB, alloc=92.8MB, time=6.50 memory used=1052.8MB, alloc=92.8MB, time=6.60 memory used=1090.4MB, alloc=92.8MB, time=6.70 memory used=1128.7MB, alloc=92.8MB, time=6.85 memory used=1167.3MB, alloc=92.8MB, time=6.97 memory used=1200.9MB, alloc=92.8MB, time=7.08 memory used=1243.8MB, alloc=92.8MB, time=7.19 memory used=1279.3MB, alloc=92.8MB, time=7.30 memory used=1307.9MB, alloc=92.8MB, time=7.39 memory used=1339.6MB, alloc=92.8MB, time=7.48 memory used=1374.9MB, alloc=92.8MB, time=7.56 memory used=1414.3MB, alloc=92.8MB, time=7.65 memory used=1459.1MB, alloc=92.8MB, time=7.74 memory used=1499.6MB, alloc=107.8MB, time=7.83 memory used=1510.0MB, alloc=107.8MB, time=7.89 memory used=1541.9MB, alloc=107.8MB, time=8.20 memory used=1586.2MB, alloc=107.8MB, time=8.36 memory used=1623.9MB, alloc=107.8MB, time=8.47 memory used=1661.7MB, alloc=107.8MB, time=8.58 memory used=1691.2MB, alloc=107.8MB, time=8.66 memory used=1724.9MB, alloc=107.8MB, time=8.76 memory used=1763.7MB, alloc=107.8MB, time=8.85 memory used=1807.2MB, alloc=107.8MB, time=8.96 memory used=1846.6MB, alloc=107.8MB, time=9.04 memory used=1857.5MB, alloc=107.8MB, time=9.10 memory used=1868.7MB, alloc=107.8MB, time=9.16 memory used=1880.4MB, alloc=107.8MB, time=9.22 memory used=1892.6MB, alloc=107.8MB, time=9.28 memory used=1905.4MB, alloc=107.8MB, time=9.34 memory used=1965.7MB, alloc=107.8MB, time=9.74 memory used=2022.8MB, alloc=107.8MB, time=10.20 memory used=2096.7MB, alloc=107.8MB, time=10.82 memory used=2161.7MB, alloc=107.8MB, time=11.51 memory used=2252.6MB, alloc=107.8MB, time=12.40 memory used=2286.3MB, alloc=107.8MB, time=12.52 memory used=2323.2MB, alloc=107.8MB, time=12.65 memory used=2358.4MB, alloc=107.8MB, time=12.76 memory used=2384.3MB, alloc=107.8MB, time=12.85 memory used=2413.7MB, alloc=107.8MB, time=12.94 memory used=2446.3MB, alloc=107.8MB, time=13.03 memory used=2482.0MB, alloc=107.8MB, time=13.12 memory used=2521.1MB, alloc=107.8MB, time=13.23 memory used=2564.1MB, alloc=107.8MB, time=13.32 memory used=2589.5MB, alloc=107.8MB, time=13.41 memory used=2599.5MB, alloc=107.8MB, time=13.47 memory used=2609.9MB, alloc=107.8MB, time=13.53 memory used=2620.5MB, alloc=107.8MB, time=13.60 memory used=2631.3MB, alloc=107.8MB, time=13.67 memory used=2642.4MB, alloc=107.8MB, time=13.73 memory used=2654.0MB, alloc=107.8MB, time=13.80 memory used=2665.5MB, alloc=107.8MB, time=13.86 memory used=2677.5MB, alloc=107.8MB, time=13.93 memory used=2690.0MB, alloc=107.8MB, time=14.00 memory used=2702.9MB, alloc=107.8MB, time=14.06 memory used=2716.1MB, alloc=107.8MB, time=14.12 memory used=2822.5MB, alloc=107.8MB, time=14.89 memory used=2904.4MB, alloc=107.8MB, time=15.61 memory used=2968.3MB, alloc=107.8MB, time=16.22 memory used=3053.1MB, alloc=107.8MB, time=17.11 memory used=3091.7MB, alloc=107.8MB, time=17.25 memory used=3118.8MB, alloc=107.8MB, time=17.36 memory used=3154.6MB, alloc=107.8MB, time=17.48 memory used=3181.2MB, alloc=107.8MB, time=17.58 memory used=3248.2MB, alloc=107.8MB, time=18.18 memory used=3328.1MB, alloc=107.8MB, time=18.79 memory used=3405.8MB, alloc=107.8MB, time=19.55 memory used=3437.4MB, alloc=107.8MB, time=19.68 memory used=3463.4MB, alloc=107.8MB, time=19.79 memory used=3496.9MB, alloc=107.8MB, time=19.90 memory used=3522.1MB, alloc=107.8MB, time=19.99 memory used=3584.8MB, alloc=107.8MB, time=20.52 memory used=3664.4MB, alloc=107.8MB, time=21.09 memory used=3722.6MB, alloc=107.8MB, time=21.83 memory used=3787.6MB, alloc=363.8MB, time=22.64 memory used=3849.0MB, alloc=387.8MB, time=23.50 memory used=3931.4MB, alloc=387.8MB, time=24.64 memory used=3972.8MB, alloc=387.8MB, time=24.86 memory used=4018.6MB, alloc=387.8MB, time=25.10 memory used=4095.0MB, alloc=387.8MB, time=26.12 memory used=4203.9MB, alloc=387.8MB, time=27.10 memory used=4239.1MB, alloc=411.8MB, time=27.29 memory used=4296.2MB, alloc=411.8MB, time=27.48 memory used=4337.9MB, alloc=411.8MB, time=27.64 memory used=4387.9MB, alloc=411.8MB, time=27.81 memory used=4444.8MB, alloc=411.8MB, time=28.00 memory used=4511.1MB, alloc=411.8MB, time=28.20 memory used=4687.8MB, alloc=411.8MB, time=28.83 memory used=4867.1MB, alloc=411.8MB, time=29.23 memory used=5080.6MB, alloc=411.8MB, time=29.66 memory used=5310.9MB, alloc=411.8MB, time=30.10 memory used=5504.4MB, alloc=411.8MB, time=30.47 memory used=5801.7MB, alloc=411.8MB, time=31.81 memory used=5934.1MB, alloc=411.8MB, time=33.05 memory used=6033.3MB, alloc=411.8MB, time=34.20 memory used=6086.9MB, alloc=411.8MB, time=34.37 memory used=6128.1MB, alloc=411.8MB, time=34.54 memory used=6197.0MB, alloc=411.8MB, time=34.90 memory used=6245.7MB, alloc=411.8MB, time=35.08 memory used=6324.9MB, alloc=411.8MB, time=35.69 memory used=6448.2MB, alloc=411.8MB, time=37.13 memory used=6560.9MB, alloc=435.8MB, time=38.26 memory used=6688.9MB, alloc=435.8MB, time=40.05 memory used=6818.2MB, alloc=459.8MB, time=41.99 memory used=6969.5MB, alloc=459.8MB, time=44.39 memory used=7097.8MB, alloc=483.8MB, time=47.04 memory used=7216.5MB, alloc=507.8MB, time=52.30 memory used=7349.4MB, alloc=531.8MB, time=57.70 N1 := 2973 > GB := Basis(F, plex(op(vars))); 14 2 12 4 12 3 11 2 GB := [521284 x y + 521284 x y + 1694173 x y + 1426672 x y 9 3 8 2 5 2 2 2 + 1159171 x y + 1464216 x y + 667888 x y + 114244 x y , 3 3 11 2 9 4 9 3 19 z x + 19 y x + 13 z, 27436 x y + 27436 x y + 89167 x y 8 2 6 4 5 2 3 4 2 2 + 56316 x y - 18772 x y + 38532 x y + 12844 x y + 8788 x y 3 11 2 9 4 9 3 8 2 + 8788 y z, 54872 x y + 54872 x y + 178334 x y + 131404 x y 6 4 6 3 5 2 3 3 2 2 - 18772 x y + 61009 x y + 102752 x y - 41743 x y + 26364 x y 2 2 2 11 2 9 4 9 3 + 8788 y z - 28561 y z, 27436 x y + 27436 x y + 89167 x y 8 2 6 3 5 2 2 2 3 + 75088 x y + 61009 x y + 77064 x y + 26364 x y + 8788 y z 2 4 2 2 3 - 28561 y z , 4 z + 4 y x - 13 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=7532.1MB, alloc=531.8MB, time=60.99 memory used=7709.5MB, alloc=531.8MB, time=62.78 memory used=7895.0MB, alloc=531.8MB, time=64.66 memory used=8041.1MB, alloc=531.8MB, time=66.62 memory used=8209.5MB, alloc=531.8MB, time=68.28 memory used=8322.7MB, alloc=531.8MB, time=68.76 memory used=8427.1MB, alloc=531.8MB, time=69.19 memory used=8542.3MB, alloc=531.8MB, time=69.70 memory used=8707.8MB, alloc=531.8MB, time=71.57 memory used=8890.7MB, alloc=531.8MB, time=73.18 memory used=9024.4MB, alloc=531.8MB, time=74.95 memory used=9133.1MB, alloc=531.8MB, time=76.36 memory used=9248.4MB, alloc=531.8MB, time=77.05 memory used=9353.5MB, alloc=531.8MB, time=77.57 memory used=9455.9MB, alloc=531.8MB, time=78.02 memory used=9556.2MB, alloc=531.8MB, time=78.47 memory used=9663.7MB, alloc=531.8MB, time=78.95 memory used=9760.3MB, alloc=531.8MB, time=79.37 memory used=9865.3MB, alloc=531.8MB, time=79.84 memory used=9966.8MB, alloc=531.8MB, time=80.28 memory used=10076.2MB, alloc=531.8MB, time=80.79 memory used=10173.5MB, alloc=531.8MB, time=81.24 memory used=10286.3MB, alloc=531.8MB, time=81.75 memory used=10371.7MB, alloc=531.8MB, time=82.12 memory used=10474.2MB, alloc=531.8MB, time=82.47 memory used=10547.3MB, alloc=531.8MB, time=82.76 memory used=10657.3MB, alloc=531.8MB, time=83.25 memory used=10740.6MB, alloc=531.8MB, time=83.60 memory used=10840.7MB, alloc=531.8MB, time=83.95 memory used=10914.3MB, alloc=531.8MB, time=84.24 memory used=11024.3MB, alloc=531.8MB, time=84.90 memory used=11125.2MB, alloc=531.8MB, time=85.27 memory used=11198.7MB, alloc=531.8MB, time=85.58 memory used=11290.5MB, alloc=531.8MB, time=85.88 memory used=11402.0MB, alloc=531.8MB, time=86.32 memory used=11503.4MB, alloc=531.8MB, time=86.87 memory used=11591.3MB, alloc=531.8MB, time=87.26 memory used=11684.5MB, alloc=531.8MB, time=87.62 memory used=11787.2MB, alloc=555.8MB, time=87.99 memory used=11870.3MB, alloc=555.8MB, time=88.31 memory used=11967.6MB, alloc=555.8MB, time=88.63 memory used=12094.6MB, alloc=555.8MB, time=89.38 memory used=12209.4MB, alloc=555.8MB, time=89.82 memory used=12328.7MB, alloc=555.8MB, time=90.21 memory used=12415.5MB, alloc=555.8MB, time=90.52 memory used=12521.7MB, alloc=555.8MB, time=90.84 memory used=12700.5MB, alloc=555.8MB, time=91.34 memory used=12855.4MB, alloc=555.8MB, time=92.93 memory used=12982.1MB, alloc=555.8MB, time=94.23 memory used=13149.8MB, alloc=555.8MB, time=95.48 memory used=13265.8MB, alloc=555.8MB, time=96.03 memory used=13386.2MB, alloc=555.8MB, time=96.55 memory used=13536.3MB, alloc=555.8MB, time=97.60 memory used=13660.5MB, alloc=555.8MB, time=99.14 memory used=13763.4MB, alloc=555.8MB, time=100.50 memory used=13852.8MB, alloc=555.8MB, time=101.86 memory used=13959.1MB, alloc=555.8MB, time=103.25 memory used=14051.7MB, alloc=555.8MB, time=104.70 memory used=14146.6MB, alloc=555.8MB, time=105.97 memory used=14231.2MB, alloc=555.8MB, time=107.30 memory used=14316.9MB, alloc=555.8MB, time=108.61 memory used=14403.0MB, alloc=555.8MB, time=109.97 memory used=14497.3MB, alloc=555.8MB, time=111.15 memory used=14594.4MB, alloc=555.8MB, time=112.36 memory used=14725.5MB, alloc=579.8MB, time=113.56 memory used=14836.4MB, alloc=579.8MB, time=114.10 memory used=14958.4MB, alloc=579.8MB, time=114.60 memory used=15105.6MB, alloc=579.8MB, time=120.18 memory used=15209.8MB, alloc=579.8MB, time=120.67 memory used=15306.2MB, alloc=579.8MB, time=121.14 memory used=15422.4MB, alloc=579.8MB, time=121.63 memory used=15666.7MB, alloc=579.8MB, time=122.32 memory used=15802.3MB, alloc=579.8MB, time=123.55 memory used=16103.8MB, alloc=579.8MB, time=130.16 memory used=16227.8MB, alloc=579.8MB, time=130.78 memory used=16339.1MB, alloc=579.8MB, time=131.34 memory used=16463.5MB, alloc=579.8MB, time=131.87 memory used=16549.6MB, alloc=579.8MB, time=132.35 memory used=16647.5MB, alloc=579.8MB, time=132.83 memory used=16758.2MB, alloc=579.8MB, time=133.30 memory used=16881.2MB, alloc=579.8MB, time=133.77 memory used=17019.0MB, alloc=579.8MB, time=134.25 memory used=17233.5MB, alloc=579.8MB, time=134.95 memory used=17390.5MB, alloc=579.8MB, time=135.65 memory used=17575.2MB, alloc=579.8MB, time=136.21 memory used=17721.9MB, alloc=579.8MB, time=140.43 memory used=17897.0MB, alloc=579.8MB, time=142.06 memory used=18161.6MB, alloc=579.8MB, time=144.05 memory used=18371.3MB, alloc=579.8MB, time=145.66 memory used=18611.0MB, alloc=579.8MB, time=147.94 memory used=18823.2MB, alloc=579.8MB, time=151.03 memory used=19035.4MB, alloc=579.8MB, time=155.61 memory used=19222.9MB, alloc=579.8MB, time=160.64 memory used=19427.2MB, alloc=579.8MB, time=166.95 memory used=19595.0MB, alloc=579.8MB, time=172.96 memory used=19794.8MB, alloc=579.8MB, time=179.55 memory used=19929.9MB, alloc=579.8MB, time=184.54 memory used=20004.2MB, alloc=579.8MB, time=185.66 memory used=20100.5MB, alloc=579.8MB, time=186.88 memory used=20193.2MB, alloc=603.8MB, time=188.60 memory used=20270.9MB, alloc=603.8MB, time=189.87 memory used=20366.2MB, alloc=603.8MB, time=190.82 memory used=20503.3MB, alloc=603.8MB, time=192.03 memory used=20586.3MB, alloc=603.8MB, time=193.26 memory used=20653.8MB, alloc=603.8MB, time=194.48 memory used=20720.4MB, alloc=603.8MB, time=195.56 memory used=20808.5MB, alloc=603.8MB, time=196.56 memory used=20944.0MB, alloc=603.8MB, time=197.35 memory used=21073.8MB, alloc=603.8MB, time=198.38 memory used=21176.2MB, alloc=603.8MB, time=199.17 memory used=21231.2MB, alloc=603.8MB, time=200.22 memory used=21274.0MB, alloc=603.8MB, time=200.99 memory used=21320.5MB, alloc=603.8MB, time=201.87 memory used=21385.2MB, alloc=603.8MB, time=202.83 memory used=21429.2MB, alloc=603.8MB, time=203.83 memory used=21485.3MB, alloc=603.8MB, time=204.68 memory used=21613.8MB, alloc=603.8MB, time=205.37 memory used=21730.8MB, alloc=603.8MB, time=205.96 memory used=22006.2MB, alloc=603.8MB, time=206.76 memory used=22224.0MB, alloc=603.8MB, time=207.72 memory used=22508.3MB, alloc=603.8MB, time=208.53 memory used=22701.3MB, alloc=603.8MB, time=209.49 memory used=22818.0MB, alloc=603.8MB, time=210.07 memory used=23099.0MB, alloc=603.8MB, time=210.87 memory used=23322.3MB, alloc=603.8MB, time=211.82 memory used=23608.5MB, alloc=603.8MB, time=212.65 memory used=23805.5MB, alloc=603.8MB, time=213.62 memory used=23928.1MB, alloc=603.8MB, time=214.20 memory used=24027.6MB, alloc=603.8MB, time=214.73 memory used=24147.1MB, alloc=603.8MB, time=215.26 memory used=24297.8MB, alloc=603.8MB, time=216.11 memory used=24423.5MB, alloc=603.8MB, time=216.78 memory used=24527.7MB, alloc=603.8MB, time=217.34 memory used=24635.6MB, alloc=603.8MB, time=217.98 memory used=24761.9MB, alloc=603.8MB, time=218.56 memory used=24908.3MB, alloc=603.8MB, time=219.17 memory used=25109.4MB, alloc=603.8MB, time=219.89 memory used=25258.4MB, alloc=603.8MB, time=220.51 memory used=25421.4MB, alloc=603.8MB, time=221.15 memory used=25599.5MB, alloc=603.8MB, time=221.79 memory used=25792.4MB, alloc=603.8MB, time=222.45 memory used=25999.8MB, alloc=603.8MB, time=223.12 memory used=26225.2MB, alloc=603.8MB, time=223.80 memory used=26468.3MB, alloc=603.8MB, time=224.49 memory used=26664.6MB, alloc=603.8MB, time=225.13 memory used=26846.9MB, alloc=603.8MB, time=225.73 memory used=27037.7MB, alloc=603.8MB, time=226.33 memory used=27238.8MB, alloc=603.8MB, time=226.96 memory used=27451.6MB, alloc=603.8MB, time=227.59 memory used=27677.7MB, alloc=603.8MB, time=228.22 memory used=28002.8MB, alloc=603.8MB, time=230.15 memory used=28109.0MB, alloc=603.8MB, time=230.71 memory used=28237.9MB, alloc=603.8MB, time=231.28 memory used=28486.0MB, alloc=603.8MB, time=232.05 memory used=28650.9MB, alloc=603.8MB, time=232.71 memory used=28837.0MB, alloc=603.8MB, time=233.40 memory used=29049.3MB, alloc=603.8MB, time=234.10 memory used=29287.0MB, alloc=603.8MB, time=234.81 memory used=29490.2MB, alloc=603.8MB, time=235.46 memory used=29679.4MB, alloc=603.8MB, time=236.10 memory used=29880.9MB, alloc=603.8MB, time=236.75 memory used=30098.2MB, alloc=603.8MB, time=237.43 memory used=30332.7MB, alloc=603.8MB, time=238.10 memory used=30580.8MB, alloc=603.8MB, time=238.78 memory used=30784.8MB, alloc=603.8MB, time=239.40 memory used=31039.6MB, alloc=603.8MB, time=241.03 memory used=31108.0MB, alloc=603.8MB, time=243.58 memory used=31245.8MB, alloc=627.8MB, time=244.36 memory used=31362.5MB, alloc=627.8MB, time=245.11 memory used=31514.7MB, alloc=627.8MB, time=245.82 memory used=31637.6MB, alloc=627.8MB, time=246.45 memory used=31735.6MB, alloc=651.8MB, time=247.07 memory used=31854.7MB, alloc=651.8MB, time=247.72 memory used=31987.2MB, alloc=651.8MB, time=248.39 memory used=32129.1MB, alloc=651.8MB, time=249.04 memory used=32282.4MB, alloc=651.8MB, time=249.69 memory used=32452.4MB, alloc=651.8MB, time=250.39 memory used=32634.4MB, alloc=651.8MB, time=251.09 memory used=32937.8MB, alloc=651.8MB, time=252.02 memory used=33041.0MB, alloc=651.8MB, time=252.63 memory used=33145.5MB, alloc=651.8MB, time=253.23 memory used=33260.9MB, alloc=651.8MB, time=253.86 memory used=33373.0MB, alloc=651.8MB, time=254.48 memory used=33492.9MB, alloc=651.8MB, time=255.11 memory used=33620.3MB, alloc=651.8MB, time=255.77 memory used=33750.0MB, alloc=651.8MB, time=256.40 memory used=33882.1MB, alloc=651.8MB, time=257.05 memory used=34016.4MB, alloc=651.8MB, time=257.68 memory used=34153.0MB, alloc=651.8MB, time=258.33 memory used=34291.7MB, alloc=651.8MB, time=258.95 memory used=34436.6MB, alloc=651.8MB, time=259.59 memory used=34593.2MB, alloc=651.8MB, time=260.25 memory used=34744.6MB, alloc=651.8MB, time=260.91 memory used=34903.3MB, alloc=651.8MB, time=261.58 memory used=35070.7MB, alloc=651.8MB, time=262.24 memory used=35240.2MB, alloc=651.8MB, time=262.91 memory used=35411.9MB, alloc=651.8MB, time=263.61 memory used=35585.4MB, alloc=651.8MB, time=264.30 memory used=35765.7MB, alloc=651.8MB, time=264.99 memory used=35957.6MB, alloc=651.8MB, time=265.66 memory used=36144.3MB, alloc=651.8MB, time=266.35 memory used=36337.0MB, alloc=651.8MB, time=267.03 memory used=36539.3MB, alloc=651.8MB, time=267.74 memory used=36743.2MB, alloc=651.8MB, time=268.47 memory used=36898.4MB, alloc=651.8MB, time=269.12 memory used=37032.8MB, alloc=651.8MB, time=269.71 memory used=37165.0MB, alloc=651.8MB, time=270.32 memory used=37300.8MB, alloc=651.8MB, time=270.95 memory used=37445.7MB, alloc=651.8MB, time=271.58 memory used=37591.2MB, alloc=651.8MB, time=272.21 memory used=37737.0MB, alloc=651.8MB, time=272.86 memory used=37883.2MB, alloc=651.8MB, time=273.51 memory used=38029.9MB, alloc=651.8MB, time=274.14 memory used=38183.2MB, alloc=651.8MB, time=274.78 memory used=38344.8MB, alloc=651.8MB, time=275.54 memory used=38500.4MB, alloc=651.8MB, time=276.25 memory used=38660.6MB, alloc=651.8MB, time=276.94 memory used=38829.1MB, alloc=651.8MB, time=277.73 memory used=38997.7MB, alloc=651.8MB, time=278.38 memory used=39166.2MB, alloc=651.8MB, time=279.12 memory used=39341.9MB, alloc=651.8MB, time=279.89 memory used=39513.9MB, alloc=651.8MB, time=280.61 memory used=39692.0MB, alloc=651.8MB, time=281.31 memory used=39870.8MB, alloc=651.8MB, time=282.02 memory used=40055.8MB, alloc=651.8MB, time=282.74 memory used=40243.9MB, alloc=651.8MB, time=283.50 memory used=40433.7MB, alloc=651.8MB, time=284.22 memory used=40628.6MB, alloc=651.8MB, time=284.93 memory used=40825.7MB, alloc=651.8MB, time=285.59 memory used=41028.3MB, alloc=651.8MB, time=286.27 memory used=41233.4MB, alloc=651.8MB, time=286.95 memory used=41421.5MB, alloc=651.8MB, time=287.61 memory used=41578.6MB, alloc=651.8MB, time=288.23 memory used=41739.5MB, alloc=651.8MB, time=288.87 memory used=41904.7MB, alloc=651.8MB, time=289.60 memory used=42070.4MB, alloc=651.8MB, time=290.24 memory used=42237.4MB, alloc=651.8MB, time=290.90 memory used=42408.6MB, alloc=651.8MB, time=291.54 memory used=42583.1MB, alloc=651.8MB, time=292.21 memory used=42761.4MB, alloc=651.8MB, time=292.88 memory used=42940.7MB, alloc=651.8MB, time=293.53 memory used=43122.0MB, alloc=651.8MB, time=294.21 memory used=43305.7MB, alloc=651.8MB, time=294.89 memory used=43491.5MB, alloc=651.8MB, time=295.55 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428499743 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 2 F := [6 x y z + 4 y z - 13 z , 3 x + 5 z + 9 z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 G := [4 x z - 2 y - 5 z, 10 x - 8 y z + 19 y ] > Problem := [F,G]; 2 3 2 2 2 Problem := [[6 x y z + 4 y z - 13 z , 3 x + 5 z + 9 z], 3 3 2 2 [4 x z - 2 y - 5 z, 10 x - 8 y z + 19 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=26.1MB, alloc=32.3MB, time=0.52 memory used=45.0MB, alloc=56.3MB, time=0.81 memory used=86.5MB, alloc=60.3MB, time=1.38 memory used=128.5MB, alloc=68.3MB, time=2.14 memory used=171.9MB, alloc=92.3MB, time=2.77 memory used=239.8MB, alloc=92.3MB, time=3.75 memory used=299.1MB, alloc=92.3MB, time=4.31 memory used=371.1MB, alloc=92.3MB, time=5.05 memory used=439.2MB, alloc=116.3MB, time=5.77 memory used=512.5MB, alloc=116.3MB, time=6.19 memory used=579.0MB, alloc=372.3MB, time=6.92 memory used=678.1MB, alloc=372.3MB, time=8.11 memory used=763.8MB, alloc=396.3MB, time=9.40 memory used=876.2MB, alloc=396.3MB, time=10.89 memory used=998.8MB, alloc=396.3MB, time=12.15 memory used=1108.5MB, alloc=420.3MB, time=13.53 memory used=1232.9MB, alloc=420.3MB, time=15.23 memory used=1365.1MB, alloc=420.3MB, time=16.68 memory used=1431.4MB, alloc=420.3MB, time=17.05 memory used=1553.8MB, alloc=444.3MB, time=18.56 memory used=1658.7MB, alloc=444.3MB, time=20.19 memory used=1760.7MB, alloc=444.3MB, time=20.93 memory used=1842.9MB, alloc=444.3MB, time=21.36 memory used=1922.3MB, alloc=444.3MB, time=21.73 memory used=2005.0MB, alloc=444.3MB, time=22.16 memory used=2143.4MB, alloc=444.3MB, time=23.50 memory used=2258.4MB, alloc=444.3MB, time=24.67 memory used=2375.1MB, alloc=444.3MB, time=25.98 memory used=2488.5MB, alloc=444.3MB, time=27.55 memory used=2597.5MB, alloc=468.3MB, time=28.87 memory used=2697.2MB, alloc=468.3MB, time=30.21 memory used=2814.6MB, alloc=468.3MB, time=31.06 memory used=2939.7MB, alloc=468.3MB, time=32.22 memory used=3033.5MB, alloc=468.3MB, time=33.63 memory used=3144.3MB, alloc=468.3MB, time=34.53 memory used=3241.5MB, alloc=468.3MB, time=35.67 memory used=3312.6MB, alloc=468.3MB, time=36.51 memory used=3410.4MB, alloc=492.3MB, time=37.65 memory used=3487.7MB, alloc=492.3MB, time=38.86 memory used=3573.0MB, alloc=492.3MB, time=40.34 memory used=3710.6MB, alloc=492.3MB, time=42.07 memory used=3886.8MB, alloc=492.3MB, time=43.49 memory used=4063.3MB, alloc=516.3MB, time=44.72 memory used=4273.7MB, alloc=516.3MB, time=46.76 memory used=4426.8MB, alloc=516.3MB, time=48.68 memory used=4543.0MB, alloc=516.3MB, time=50.29 memory used=4699.4MB, alloc=516.3MB, time=50.97 memory used=4826.9MB, alloc=516.3MB, time=52.82 memory used=4952.8MB, alloc=540.3MB, time=55.24 memory used=5058.4MB, alloc=564.3MB, time=57.45 memory used=5185.7MB, alloc=588.3MB, time=59.96 memory used=5311.5MB, alloc=588.3MB, time=62.36 memory used=5425.8MB, alloc=612.3MB, time=64.68 memory used=5542.1MB, alloc=636.3MB, time=67.05 memory used=5684.0MB, alloc=636.3MB, time=69.47 memory used=5854.5MB, alloc=660.3MB, time=72.06 memory used=5973.4MB, alloc=660.3MB, time=74.10 memory used=6082.9MB, alloc=684.3MB, time=76.05 memory used=6255.3MB, alloc=684.3MB, time=78.42 memory used=6377.5MB, alloc=684.3MB, time=80.28 memory used=6540.0MB, alloc=684.3MB, time=82.34 memory used=6662.0MB, alloc=708.3MB, time=84.50 memory used=6815.9MB, alloc=708.3MB, time=86.51 memory used=6932.0MB, alloc=708.3MB, time=88.56 memory used=7109.7MB, alloc=708.3MB, time=90.72 memory used=7220.5MB, alloc=732.3MB, time=92.93 memory used=7317.2MB, alloc=732.3MB, time=94.98 memory used=7661.9MB, alloc=756.3MB, time=100.57 memory used=8032.7MB, alloc=780.3MB, time=106.09 memory used=8439.5MB, alloc=804.3MB, time=111.50 memory used=8826.0MB, alloc=828.3MB, time=118.63 memory used=9175.2MB, alloc=852.3MB, time=128.55 memory used=9471.1MB, alloc=876.3MB, time=139.88 memory used=9767.8MB, alloc=900.3MB, time=152.09 memory used=10071.7MB, alloc=924.3MB, time=165.71 memory used=10384.8MB, alloc=948.3MB, time=179.04 memory used=10709.2MB, alloc=972.3MB, time=192.89 memory used=11046.1MB, alloc=996.3MB, time=207.47 memory used=11395.7MB, alloc=1020.3MB, time=222.71 memory used=11759.2MB, alloc=1044.3MB, time=238.55 memory used=12129.3MB, alloc=1068.3MB, time=255.35 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428500043 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 4 3 3 F := [-5 x z - 4 y + 10 x z, -9 x y - 3 x + 20] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 3 G := [2 x z - 18 y - 16 y z, 5 y z + 7 z - 14] > Problem := [F,G]; 3 4 3 3 Problem := [[-5 x z - 4 y + 10 x z, -9 x y - 3 x + 20], 2 3 2 2 3 [2 x z - 18 y - 16 y z, 5 y z + 7 z - 14]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=25.1MB, alloc=32.3MB, time=0.49 memory used=48.5MB, alloc=60.3MB, time=0.81 memory used=83.8MB, alloc=61.5MB, time=0.98 memory used=110.8MB, alloc=61.5MB, time=1.06 memory used=153.2MB, alloc=61.5MB, time=1.60 memory used=188.1MB, alloc=61.5MB, time=1.94 memory used=220.7MB, alloc=61.5MB, time=2.26 memory used=247.1MB, alloc=61.5MB, time=2.37 memory used=278.3MB, alloc=61.5MB, time=2.55 memory used=326.3MB, alloc=61.5MB, time=3.05 memory used=370.1MB, alloc=61.5MB, time=3.62 memory used=413.3MB, alloc=61.5MB, time=4.30 memory used=452.2MB, alloc=61.5MB, time=4.76 memory used=483.6MB, alloc=61.5MB, time=4.95 memory used=513.2MB, alloc=61.5MB, time=5.14 memory used=539.5MB, alloc=61.5MB, time=5.34 memory used=570.4MB, alloc=61.5MB, time=5.49 memory used=595.3MB, alloc=61.5MB, time=5.61 memory used=626.5MB, alloc=61.5MB, time=5.78 memory used=647.9MB, alloc=61.5MB, time=5.84 memory used=666.8MB, alloc=61.5MB, time=5.90 memory used=685.1MB, alloc=61.5MB, time=5.96 memory used=714.3MB, alloc=61.5MB, time=6.16 memory used=733.4MB, alloc=61.5MB, time=6.24 memory used=757.5MB, alloc=61.5MB, time=6.34 memory used=782.4MB, alloc=61.5MB, time=6.46 memory used=816.4MB, alloc=85.5MB, time=9.00 memory used=868.9MB, alloc=87.8MB, time=10.06 memory used=915.1MB, alloc=87.9MB, time=10.23 memory used=952.5MB, alloc=87.9MB, time=10.37 memory used=980.2MB, alloc=87.9MB, time=10.49 memory used=1006.5MB, alloc=111.9MB, time=10.61 memory used=1045.9MB, alloc=111.9MB, time=10.77 memory used=1088.0MB, alloc=111.9MB, time=10.93 memory used=1133.7MB, alloc=111.9MB, time=11.09 memory used=1181.8MB, alloc=111.9MB, time=11.25 memory used=1232.2MB, alloc=111.9MB, time=11.41 memory used=1284.9MB, alloc=111.9MB, time=11.57 memory used=1339.7MB, alloc=111.9MB, time=11.73 memory used=1396.8MB, alloc=111.9MB, time=11.89 memory used=1455.8MB, alloc=111.9MB, time=12.07 memory used=1510.0MB, alloc=111.9MB, time=12.23 memory used=1548.7MB, alloc=111.9MB, time=12.35 memory used=1578.4MB, alloc=135.9MB, time=12.49 memory used=1619.2MB, alloc=135.9MB, time=12.65 memory used=1661.4MB, alloc=135.9MB, time=12.80 memory used=1705.9MB, alloc=135.9MB, time=12.94 memory used=1751.1MB, alloc=135.9MB, time=13.10 memory used=1797.2MB, alloc=135.9MB, time=13.24 memory used=1844.0MB, alloc=135.9MB, time=13.39 memory used=1891.5MB, alloc=135.9MB, time=13.52 memory used=1939.8MB, alloc=135.9MB, time=13.68 memory used=1989.7MB, alloc=135.9MB, time=13.83 memory used=2047.1MB, alloc=135.9MB, time=13.99 memory used=2106.0MB, alloc=135.9MB, time=14.18 memory used=2165.8MB, alloc=135.9MB, time=14.36 memory used=2226.4MB, alloc=135.9MB, time=14.51 memory used=2288.0MB, alloc=135.9MB, time=14.67 memory used=2350.3MB, alloc=135.9MB, time=14.82 memory used=2413.4MB, alloc=135.9MB, time=14.99 memory used=2477.3MB, alloc=135.9MB, time=15.17 memory used=2541.9MB, alloc=135.9MB, time=15.34 memory used=2607.2MB, alloc=135.9MB, time=15.51 memory used=2673.3MB, alloc=135.9MB, time=15.67 memory used=2741.0MB, alloc=135.9MB, time=15.85 memory used=2817.1MB, alloc=135.9MB, time=16.04 memory used=2894.8MB, alloc=135.9MB, time=16.21 memory used=2973.3MB, alloc=135.9MB, time=16.39 memory used=3051.1MB, alloc=135.9MB, time=16.55 memory used=3119.0MB, alloc=135.9MB, time=16.70 memory used=3188.3MB, alloc=135.9MB, time=16.85 memory used=3258.9MB, alloc=135.9MB, time=17.02 memory used=3318.3MB, alloc=135.9MB, time=17.15 memory used=3358.8MB, alloc=135.9MB, time=17.26 memory used=3396.4MB, alloc=135.9MB, time=17.37 memory used=3437.1MB, alloc=135.9MB, time=17.47 memory used=3477.9MB, alloc=135.9MB, time=17.58 memory used=3518.9MB, alloc=135.9MB, time=17.69 memory used=3559.9MB, alloc=135.9MB, time=17.81 memory used=3601.0MB, alloc=135.9MB, time=17.93 memory used=3642.3MB, alloc=135.9MB, time=18.04 memory used=3683.6MB, alloc=135.9MB, time=18.15 memory used=3725.0MB, alloc=135.9MB, time=18.25 memory used=3766.5MB, alloc=135.9MB, time=18.36 memory used=3808.1MB, alloc=135.9MB, time=18.46 memory used=3849.7MB, alloc=135.9MB, time=18.57 memory used=3891.4MB, alloc=135.9MB, time=18.67 memory used=3933.2MB, alloc=135.9MB, time=18.78 memory used=3975.0MB, alloc=135.9MB, time=18.88 memory used=4016.9MB, alloc=135.9MB, time=18.99 memory used=4058.8MB, alloc=135.9MB, time=19.09 memory used=4100.8MB, alloc=135.9MB, time=19.20 memory used=4142.7MB, alloc=135.9MB, time=19.30 memory used=4184.8MB, alloc=135.9MB, time=19.39 memory used=4226.8MB, alloc=135.9MB, time=19.49 memory used=4268.9MB, alloc=135.9MB, time=19.59 memory used=4311.0MB, alloc=135.9MB, time=19.70 memory used=4354.5MB, alloc=135.9MB, time=19.81 memory used=4405.8MB, alloc=135.9MB, time=19.92 memory used=4449.9MB, alloc=135.9MB, time=20.01 memory used=4500.8MB, alloc=135.9MB, time=20.13 memory used=4553.4MB, alloc=135.9MB, time=20.24 memory used=4606.0MB, alloc=135.9MB, time=20.35 memory used=4658.5MB, alloc=135.9MB, time=20.46 memory used=4711.0MB, alloc=135.9MB, time=20.58 memory used=4763.4MB, alloc=135.9MB, time=20.70 memory used=4815.8MB, alloc=135.9MB, time=20.80 memory used=4868.1MB, alloc=135.9MB, time=20.92 memory used=4920.3MB, alloc=135.9MB, time=21.03 memory used=4972.4MB, alloc=135.9MB, time=21.14 memory used=5024.4MB, alloc=135.9MB, time=21.27 memory used=5076.4MB, alloc=135.9MB, time=21.37 memory used=5129.8MB, alloc=135.9MB, time=21.48 memory used=5190.5MB, alloc=135.9MB, time=21.59 memory used=5252.3MB, alloc=135.9MB, time=21.71 memory used=5313.8MB, alloc=135.9MB, time=21.83 memory used=5375.2MB, alloc=135.9MB, time=21.95 memory used=5436.2MB, alloc=135.9MB, time=22.08 memory used=5497.0MB, alloc=135.9MB, time=22.20 memory used=5557.5MB, alloc=135.9MB, time=22.31 memory used=5617.7MB, alloc=135.9MB, time=22.42 memory used=5677.7MB, alloc=135.9MB, time=22.54 memory used=5739.1MB, alloc=135.9MB, time=22.66 memory used=5806.6MB, alloc=135.9MB, time=22.78 memory used=5875.1MB, alloc=135.9MB, time=22.90 memory used=5943.1MB, alloc=135.9MB, time=23.01 memory used=6010.5MB, alloc=135.9MB, time=23.12 memory used=6077.5MB, alloc=135.9MB, time=23.24 memory used=6145.5MB, alloc=135.9MB, time=23.35 memory used=6219.0MB, alloc=135.9MB, time=23.48 memory used=6293.1MB, alloc=135.9MB, time=23.61 memory used=6366.2MB, alloc=135.9MB, time=23.73 memory used=6438.7MB, alloc=135.9MB, time=23.86 memory used=6512.5MB, alloc=135.9MB, time=23.98 memory used=6589.6MB, alloc=135.9MB, time=24.10 memory used=6624.4MB, alloc=155.8MB, time=24.20 memory used=6648.4MB, alloc=155.8MB, time=24.28 memory used=6668.6MB, alloc=155.8MB, time=24.34 memory used=6691.3MB, alloc=155.8MB, time=24.41 memory used=6714.9MB, alloc=155.8MB, time=24.48 memory used=6738.2MB, alloc=155.8MB, time=24.56 memory used=6758.0MB, alloc=155.8MB, time=24.62 memory used=6780.1MB, alloc=155.8MB, time=24.69 memory used=6803.0MB, alloc=155.8MB, time=24.76 memory used=6825.8MB, alloc=155.8MB, time=24.84 memory used=6845.2MB, alloc=155.8MB, time=24.90 memory used=6866.6MB, alloc=155.8MB, time=24.96 memory used=6888.9MB, alloc=155.8MB, time=25.04 memory used=6911.0MB, alloc=155.8MB, time=25.10 memory used=6933.8MB, alloc=155.8MB, time=25.17 memory used=6956.4MB, alloc=155.8MB, time=25.24 memory used=6978.8MB, alloc=155.8MB, time=25.31 memory used=7001.1MB, alloc=155.8MB, time=25.38 memory used=7023.1MB, alloc=155.8MB, time=25.45 memory used=7045.0MB, alloc=155.8MB, time=25.52 memory used=7066.6MB, alloc=155.8MB, time=25.59 memory used=7088.1MB, alloc=155.8MB, time=25.66 memory used=7109.4MB, alloc=155.8MB, time=25.75 memory used=7130.4MB, alloc=155.8MB, time=25.82 memory used=7151.3MB, alloc=155.8MB, time=25.88 memory used=7172.0MB, alloc=155.8MB, time=25.96 memory used=7192.4MB, alloc=155.8MB, time=26.03 memory used=7212.6MB, alloc=155.8MB, time=26.09 memory used=7230.0MB, alloc=155.8MB, time=26.16 memory used=7244.1MB, alloc=155.8MB, time=26.23 memory used=7253.9MB, alloc=155.8MB, time=26.29 memory used=7261.1MB, alloc=155.8MB, time=26.34 memory used=7267.2MB, alloc=155.8MB, time=26.40 memory used=7272.3MB, alloc=155.8MB, time=26.45 memory used=7278.2MB, alloc=155.8MB, time=26.49 memory used=7282.8MB, alloc=155.8MB, time=26.55 memory used=7289.4MB, alloc=155.8MB, time=26.60 memory used=7295.9MB, alloc=155.8MB, time=26.66 memory used=7302.3MB, alloc=155.8MB, time=26.72 memory used=7308.8MB, alloc=155.8MB, time=26.79 memory used=7315.2MB, alloc=155.8MB, time=26.85 memory used=7321.6MB, alloc=155.8MB, time=26.91 memory used=7328.0MB, alloc=155.8MB, time=26.96 memory used=7334.4MB, alloc=155.8MB, time=27.01 memory used=7340.7MB, alloc=155.8MB, time=27.07 memory used=7347.0MB, alloc=155.8MB, time=27.12 memory used=7353.3MB, alloc=155.8MB, time=27.18 memory used=7359.6MB, alloc=155.8MB, time=27.23 memory used=7365.8MB, alloc=155.8MB, time=27.28 memory used=7372.0MB, alloc=155.8MB, time=27.34 memory used=7378.2MB, alloc=155.8MB, time=27.40 memory used=7384.4MB, alloc=155.8MB, time=27.48 memory used=7390.5MB, alloc=155.8MB, time=27.54 memory used=7396.6MB, alloc=155.8MB, time=27.59 memory used=7402.7MB, alloc=155.8MB, time=27.65 memory used=7408.8MB, alloc=155.8MB, time=27.70 memory used=7414.8MB, alloc=155.8MB, time=27.75 memory used=7420.8MB, alloc=155.8MB, time=27.81 memory used=7426.8MB, alloc=155.8MB, time=27.86 memory used=7434.8MB, alloc=155.8MB, time=27.91 memory used=7441.8MB, alloc=155.8MB, time=27.97 memory used=7450.5MB, alloc=155.8MB, time=28.02 memory used=7458.4MB, alloc=155.8MB, time=28.09 memory used=7465.3MB, alloc=155.8MB, time=28.14 memory used=7473.8MB, alloc=155.8MB, time=28.20 memory used=7481.6MB, alloc=155.8MB, time=28.25 memory used=7488.4MB, alloc=155.8MB, time=28.31 memory used=7496.7MB, alloc=155.8MB, time=28.37 memory used=7504.6MB, alloc=155.8MB, time=28.42 memory used=7513.5MB, alloc=155.8MB, time=28.48 memory used=7521.5MB, alloc=155.8MB, time=28.54 memory used=7530.2MB, alloc=155.8MB, time=28.59 memory used=7538.2MB, alloc=155.8MB, time=28.64 memory used=7546.6MB, alloc=155.8MB, time=28.70 memory used=7555.1MB, alloc=155.8MB, time=28.76 memory used=7564.8MB, alloc=155.8MB, time=28.81 memory used=7573.4MB, alloc=155.8MB, time=28.86 memory used=7581.7MB, alloc=155.8MB, time=28.92 memory used=7591.1MB, alloc=155.8MB, time=28.97 memory used=7601.5MB, alloc=155.8MB, time=29.03 memory used=7611.7MB, alloc=155.8MB, time=29.09 memory used=7621.9MB, alloc=155.8MB, time=29.14 memory used=7632.0MB, alloc=155.8MB, time=29.19 memory used=7642.1MB, alloc=155.8MB, time=29.25 memory used=7652.1MB, alloc=155.8MB, time=29.31 memory used=7662.4MB, alloc=155.8MB, time=29.37 memory used=7673.4MB, alloc=155.8MB, time=29.42 memory used=7685.0MB, alloc=155.8MB, time=29.48 memory used=7695.4MB, alloc=155.8MB, time=29.54 memory used=7708.0MB, alloc=155.8MB, time=29.60 memory used=7719.2MB, alloc=155.8MB, time=29.66 memory used=7802.1MB, alloc=155.8MB, time=33.26 memory used=7898.2MB, alloc=155.8MB, time=33.56 memory used=7958.7MB, alloc=155.8MB, time=33.75 memory used=8013.4MB, alloc=155.8MB, time=33.94 memory used=8071.0MB, alloc=155.8MB, time=34.13 memory used=8134.6MB, alloc=155.8MB, time=34.33 memory used=8202.4MB, alloc=155.8MB, time=34.52 memory used=8275.0MB, alloc=155.8MB, time=34.71 memory used=8356.6MB, alloc=155.8MB, time=34.92 memory used=8443.0MB, alloc=155.8MB, time=35.11 memory used=8501.3MB, alloc=155.8MB, time=35.29 memory used=8548.0MB, alloc=155.8MB, time=35.44 memory used=8588.5MB, alloc=155.8MB, time=35.59 memory used=8632.3MB, alloc=155.8MB, time=35.76 memory used=8677.0MB, alloc=155.8MB, time=35.92 memory used=8722.6MB, alloc=155.8MB, time=36.06 memory used=8768.8MB, alloc=155.8MB, time=36.21 memory used=8815.9MB, alloc=155.8MB, time=36.36 memory used=8863.6MB, alloc=155.8MB, time=36.51 memory used=8912.2MB, alloc=155.8MB, time=36.65 memory used=8962.4MB, alloc=155.8MB, time=36.81 memory used=9020.0MB, alloc=155.8MB, time=36.96 memory used=9079.1MB, alloc=155.8MB, time=37.12 memory used=9139.2MB, alloc=155.8MB, time=37.28 memory used=9200.1MB, alloc=155.8MB, time=37.43 memory used=9261.8MB, alloc=155.8MB, time=37.58 memory used=9324.4MB, alloc=155.8MB, time=37.75 memory used=9387.7MB, alloc=155.8MB, time=37.90 memory used=9451.8MB, alloc=155.8MB, time=38.05 memory used=9516.6MB, alloc=155.8MB, time=38.19 memory used=9582.1MB, alloc=155.8MB, time=38.36 memory used=9648.4MB, alloc=155.8MB, time=38.53 memory used=9716.3MB, alloc=155.8MB, time=38.69 memory used=9792.6MB, alloc=155.8MB, time=38.86 memory used=9870.5MB, alloc=155.8MB, time=39.02 memory used=9949.2MB, alloc=155.8MB, time=39.19 memory used=10024.1MB, alloc=155.8MB, time=39.36 memory used=10094.3MB, alloc=155.8MB, time=39.52 memory used=10164.5MB, alloc=155.8MB, time=39.67 memory used=10235.2MB, alloc=155.8MB, time=39.83 memory used=10287.1MB, alloc=155.8MB, time=39.95 memory used=10323.9MB, alloc=155.8MB, time=40.05 memory used=10362.8MB, alloc=155.8MB, time=40.16 memory used=10403.6MB, alloc=155.8MB, time=40.27 memory 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alloc=155.8MB, time=42.49 memory used=11321.4MB, alloc=155.8MB, time=42.60 memory used=11372.7MB, alloc=155.8MB, time=42.73 memory used=11416.7MB, alloc=155.8MB, time=42.84 memory used=11467.6MB, alloc=155.8MB, time=42.96 memory used=11520.2MB, alloc=155.8MB, time=43.08 memory used=11572.8MB, alloc=155.8MB, time=43.19 memory used=11625.3MB, alloc=155.8MB, time=43.30 memory used=11677.8MB, alloc=155.8MB, time=43.40 memory used=11730.2MB, alloc=155.8MB, time=43.51 memory used=11782.6MB, alloc=155.8MB, time=43.62 memory used=11834.9MB, alloc=155.8MB, time=43.75 memory used=11887.1MB, alloc=155.8MB, time=43.86 memory used=11939.2MB, alloc=155.8MB, time=43.97 memory used=11991.2MB, alloc=155.8MB, time=44.07 memory used=12043.1MB, alloc=155.8MB, time=44.18 memory used=12096.5MB, alloc=155.8MB, time=44.30 memory used=12157.1MB, alloc=155.8MB, time=44.42 memory used=12218.9MB, alloc=155.8MB, time=44.55 memory used=12280.4MB, alloc=155.8MB, time=44.68 memory used=12341.7MB, alloc=155.8MB, time=44.80 memory used=12402.7MB, alloc=155.8MB, time=44.92 memory used=12463.4MB, alloc=155.8MB, time=45.03 memory used=12523.9MB, alloc=155.8MB, time=45.15 memory used=12584.0MB, alloc=155.8MB, time=45.27 memory used=12644.0MB, alloc=155.8MB, time=45.38 memory used=12705.4MB, alloc=155.8MB, time=45.49 memory used=12772.7MB, alloc=155.8MB, time=45.61 memory used=12841.2MB, alloc=155.8MB, time=45.73 memory used=12909.1MB, alloc=155.8MB, time=45.86 memory used=12976.4MB, alloc=155.8MB, time=45.97 memory used=13043.3MB, alloc=155.8MB, time=46.09 memory used=13111.4MB, alloc=155.8MB, time=46.21 memory used=13184.7MB, alloc=155.8MB, time=46.34 memory used=13258.6MB, alloc=155.8MB, time=46.47 memory used=13331.7MB, alloc=155.8MB, time=46.60 memory used=13405.8MB, alloc=155.8MB, time=46.73 memory used=13484.2MB, alloc=155.8MB, time=46.85 memory used=13570.9MB, alloc=155.8MB, time=46.99 memory used=13581.1MB, alloc=155.8MB, time=47.04 memory used=13591.4MB, alloc=155.8MB, time=47.10 memory used=13606.0MB, alloc=155.8MB, time=47.17 memory used=13616.3MB, alloc=155.8MB, time=47.23 memory used=13630.7MB, alloc=155.8MB, time=47.28 memory used=13640.9MB, alloc=155.8MB, time=47.34 memory used=13655.3MB, alloc=155.8MB, time=47.40 memory used=13665.5MB, alloc=155.8MB, time=47.47 memory used=13679.7MB, alloc=155.8MB, time=47.54 memory used=13689.8MB, alloc=155.8MB, time=47.60 memory used=13703.9MB, alloc=155.8MB, time=47.66 memory used=13714.0MB, alloc=155.8MB, time=47.72 memory used=13728.0MB, alloc=155.8MB, time=47.78 memory used=13738.0MB, alloc=155.8MB, time=47.84 memory used=13751.9MB, alloc=155.8MB, time=47.90 memory used=13761.8MB, alloc=155.8MB, time=47.96 memory used=13775.6MB, alloc=155.8MB, time=48.03 memory used=13785.5MB, alloc=155.8MB, time=48.09 memory used=13799.1MB, alloc=155.8MB, time=48.15 memory used=13809.0MB, alloc=155.8MB, time=48.21 memory used=13822.5MB, alloc=155.8MB, time=48.28 memory used=13832.3MB, alloc=155.8MB, time=48.35 memory used=13845.7MB, alloc=155.8MB, time=48.41 memory used=13855.4MB, alloc=155.8MB, time=48.47 memory used=13868.7MB, alloc=155.8MB, time=48.54 memory used=13878.4MB, alloc=155.8MB, time=48.60 memory used=13891.5MB, alloc=155.8MB, time=48.67 memory used=13901.1MB, alloc=155.8MB, time=48.73 memory used=13914.1MB, alloc=155.8MB, time=48.79 memory used=13923.7MB, alloc=155.8MB, time=48.85 memory used=13936.5MB, alloc=155.8MB, time=48.91 memory used=13946.1MB, alloc=155.8MB, time=48.97 memory used=13958.8MB, alloc=155.8MB, time=49.04 memory used=13968.3MB, alloc=155.8MB, time=49.10 memory used=13980.9MB, alloc=155.8MB, time=49.16 memory used=13990.3MB, alloc=155.8MB, time=49.22 memory used=14002.7MB, alloc=155.8MB, time=49.28 memory used=14012.1MB, alloc=155.8MB, time=49.34 memory used=14024.4MB, alloc=155.8MB, time=49.40 memory used=14033.7MB, alloc=155.8MB, time=49.46 memory used=14045.9MB, alloc=155.8MB, time=49.52 memory used=14055.1MB, alloc=155.8MB, time=49.58 memory used=14067.1MB, alloc=155.8MB, 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used=14222.2MB, alloc=155.8MB, time=50.86 memory used=14224.1MB, alloc=155.8MB, time=50.91 memory used=14225.2MB, alloc=155.8MB, time=50.96 memory used=14228.3MB, alloc=411.8MB, time=51.01 memory used=14369.4MB, alloc=411.8MB, time=51.41 memory used=14519.5MB, alloc=411.8MB, time=51.65 memory used=14680.2MB, alloc=411.8MB, time=51.91 memory used=14793.8MB, alloc=411.8MB, time=101.04 memory used=14862.1MB, alloc=411.8MB, time=144.74 memory used=14944.8MB, alloc=435.8MB, time=246.42 memory used=15028.0MB, alloc=435.8MB, time=330.96 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428500343 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 3 4 F := [y - 18 y z + 19 y z , -8 y z + 10 z - 16] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 4 2 G := [9 y z - 15 x y , 13 x + 2 x y z + 4 y ] > Problem := [F,G]; 3 2 2 3 4 Problem := [[y - 18 y z + 19 y z , -8 y z + 10 z - 16], 3 2 4 2 [9 y z - 15 x y , 13 x + 2 x y z + 4 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=25.1MB, alloc=32.3MB, time=0.48 memory used=44.4MB, alloc=56.3MB, time=0.78 memory used=86.0MB, alloc=60.3MB, time=1.37 memory used=131.6MB, alloc=68.3MB, time=1.99 memory used=178.1MB, alloc=92.3MB, time=2.67 memory used=249.3MB, alloc=92.3MB, time=3.63 memory used=319.8MB, alloc=92.3MB, time=4.54 memory used=387.0MB, alloc=92.3MB, time=5.39 memory used=462.7MB, alloc=116.3MB, time=6.35 memory used=542.2MB, alloc=116.3MB, time=7.44 memory used=617.8MB, alloc=372.3MB, time=8.77 memory used=715.0MB, alloc=372.3MB, time=9.72 memory used=818.8MB, alloc=396.3MB, time=10.86 memory used=964.1MB, alloc=396.3MB, time=13.35 memory used=1087.1MB, alloc=396.3MB, time=14.76 memory used=1203.6MB, alloc=420.3MB, time=16.45 memory used=1316.1MB, alloc=420.3MB, time=17.57 memory used=1482.2MB, alloc=420.3MB, time=19.29 memory used=1628.3MB, alloc=444.3MB, time=20.92 memory used=1799.7MB, alloc=444.3MB, time=22.62 memory used=1967.5MB, alloc=444.3MB, time=24.74 memory used=2110.0MB, alloc=468.3MB, time=27.05 memory used=2266.6MB, alloc=492.3MB, time=29.71 memory used=2440.9MB, alloc=516.3MB, time=32.50 memory used=2625.8MB, alloc=540.3MB, time=35.72 memory used=2809.7MB, alloc=564.3MB, time=39.08 memory used=2991.2MB, alloc=588.3MB, time=44.22 memory used=3169.3MB, alloc=612.3MB, time=50.13 memory used=3356.8MB, alloc=636.3MB, time=56.78 memory used=3551.0MB, alloc=660.3MB, time=64.60 memory used=3762.5MB, alloc=684.3MB, time=73.44 memory used=3998.0MB, alloc=708.3MB, time=83.22 memory used=4257.3MB, alloc=732.3MB, time=94.17 memory used=4540.7MB, alloc=756.3MB, time=106.11 memory used=4847.9MB, alloc=780.3MB, time=118.82 memory used=5179.1MB, alloc=780.3MB, time=132.52 memory used=5510.3MB, alloc=780.3MB, time=146.03 memory used=5841.4MB, alloc=804.3MB, time=159.55 memory used=6196.5MB, alloc=804.3MB, time=173.94 memory used=6551.3MB, alloc=828.3MB, time=188.41 memory used=6930.1MB, alloc=828.3MB, time=203.80 memory used=7308.8MB, alloc=852.3MB, time=219.16 N1 := 12465 > GB := Basis(F, plex(op(vars))); 9 5 6 2 GB := [31 y + 320912 y - 8340544 y, -31 y - 344776 y + 389120 y z, 8 4 4 -1891 y - 19630504 y + 35118080 z - 56188928] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=7668.3MB, alloc=852.3MB, time=231.45 memory used=7784.5MB, alloc=852.3MB, time=233.72 memory used=7885.5MB, alloc=852.3MB, time=235.62 memory used=8038.2MB, alloc=852.3MB, time=250.38 memory used=8289.2MB, alloc=852.3MB, time=257.74 memory used=8591.2MB, alloc=852.3MB, time=259.38 memory used=8707.0MB, alloc=852.3MB, time=261.25 memory used=8798.4MB, alloc=852.3MB, time=263.15 memory used=8912.2MB, alloc=852.3MB, time=265.37 memory used=9013.4MB, alloc=852.3MB, time=267.28 memory used=9118.6MB, alloc=852.3MB, time=269.38 memory used=9388.0MB, alloc=852.3MB, time=288.52 memory used=9626.0MB, alloc=852.3MB, time=290.22 memory used=9779.2MB, alloc=852.3MB, time=292.12 memory used=9879.5MB, alloc=852.3MB, time=295.02 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428500643 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 3 2 2 F := [14 y z + 8 z - 8 x y, 14 x y + 7 x y - 14 x y ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 3 G := [-16 x z + 13 x z - 8 x y , 4 x y + 13 y - 10 y z] > Problem := [F,G]; 3 3 3 2 2 Problem := [[14 y z + 8 z - 8 x y, 14 x y + 7 x y - 14 x y ], 3 2 2 2 3 [-16 x z + 13 x z - 8 x y , 4 x y + 13 y - 10 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.4MB, alloc=32.3MB, time=0.49 memory used=44.7MB, alloc=56.3MB, time=0.74 memory used=85.1MB, alloc=60.3MB, time=1.30 memory used=128.3MB, alloc=68.3MB, time=1.84 memory used=172.7MB, alloc=68.3MB, time=2.34 memory used=207.3MB, alloc=68.3MB, time=2.57 memory used=237.0MB, alloc=68.3MB, time=2.98 memory used=278.6MB, alloc=68.3MB, time=3.40 memory used=298.6MB, alloc=68.3MB, time=3.46 memory used=321.8MB, alloc=68.3MB, time=3.56 memory used=354.6MB, alloc=92.3MB, time=4.15 memory used=390.2MB, alloc=92.3MB, time=4.27 memory used=428.1MB, alloc=92.3MB, time=4.38 memory used=473.6MB, alloc=92.3MB, time=4.49 memory used=502.2MB, alloc=92.3MB, time=4.59 memory used=530.0MB, alloc=92.3MB, time=4.70 memory used=560.5MB, alloc=92.3MB, time=4.80 memory used=592.4MB, alloc=92.3MB, time=4.89 memory used=625.9MB, alloc=92.3MB, time=4.99 memory used=663.4MB, alloc=92.3MB, time=5.09 memory used=702.4MB, alloc=92.3MB, time=5.19 memory used=743.0MB, alloc=92.3MB, time=5.28 memory used=787.2MB, alloc=92.3MB, time=5.37 memory used=827.1MB, alloc=92.3MB, time=5.46 memory used=855.1MB, alloc=92.3MB, time=5.54 memory used=878.1MB, alloc=92.3MB, time=5.62 memory used=901.2MB, alloc=92.3MB, time=5.69 memory used=924.5MB, alloc=92.3MB, time=5.76 memory used=948.6MB, alloc=92.3MB, time=5.82 memory used=974.9MB, alloc=92.3MB, time=5.89 memory used=1001.9MB, alloc=92.3MB, time=5.96 memory used=1029.0MB, alloc=92.3MB, time=6.03 memory used=1056.7MB, alloc=92.3MB, time=6.11 memory used=1086.9MB, alloc=92.3MB, time=6.19 memory used=1117.5MB, alloc=92.3MB, time=6.26 memory used=1148.1MB, alloc=92.3MB, time=6.34 memory used=1179.4MB, alloc=92.3MB, time=6.40 memory used=1212.3MB, alloc=92.3MB, time=6.48 memory used=1245.9MB, alloc=92.3MB, time=6.56 memory used=1282.4MB, alloc=92.3MB, time=6.64 memory used=1318.6MB, alloc=92.3MB, time=6.72 memory used=1357.4MB, alloc=92.3MB, time=6.81 memory used=1398.5MB, alloc=92.3MB, time=6.90 memory used=1439.5MB, alloc=92.3MB, time=6.98 memory used=1482.2MB, alloc=92.3MB, time=7.06 memory used=1530.2MB, alloc=92.3MB, time=7.15 memory used=1548.1MB, alloc=107.8MB, time=7.23 memory used=1565.9MB, alloc=107.8MB, time=7.29 memory used=1582.8MB, alloc=107.8MB, time=7.35 memory used=1599.1MB, alloc=107.8MB, time=7.42 memory used=1614.7MB, alloc=107.8MB, time=7.48 memory used=1629.3MB, alloc=107.8MB, time=7.53 memory used=1639.4MB, alloc=107.8MB, time=7.58 memory used=1649.2MB, alloc=107.8MB, time=7.63 memory used=1659.6MB, alloc=107.8MB, time=7.67 memory used=1669.8MB, alloc=107.8MB, time=7.74 memory used=1680.6MB, alloc=107.8MB, time=7.79 memory used=1691.8MB, alloc=107.8MB, time=7.84 memory used=1759.3MB, alloc=107.8MB, time=21.86 memory used=1800.9MB, alloc=107.8MB, time=21.98 memory used=1835.5MB, alloc=107.8MB, time=22.08 memory used=1869.0MB, alloc=107.8MB, time=22.17 memory used=1909.1MB, alloc=107.8MB, time=22.26 memory used=1953.7MB, alloc=107.8MB, time=22.36 memory used=1980.2MB, alloc=107.8MB, time=22.42 memory used=2008.0MB, alloc=107.8MB, time=22.49 memory used=2037.3MB, alloc=107.8MB, time=22.56 memory used=2069.0MB, alloc=107.8MB, time=22.63 memory used=2103.1MB, alloc=107.8MB, time=22.69 memory used=2138.2MB, alloc=107.8MB, time=22.77 memory used=2176.8MB, alloc=107.8MB, time=22.85 memory used=2217.8MB, alloc=107.8MB, time=22.94 memory used=2260.8MB, alloc=107.8MB, time=23.03 memory used=2311.6MB, alloc=107.8MB, time=23.13 memory used=2347.5MB, alloc=107.8MB, time=23.21 memory used=2357.8MB, alloc=107.8MB, time=23.26 memory used=2367.0MB, alloc=107.8MB, time=23.32 memory used=2376.3MB, alloc=107.8MB, time=23.36 memory used=2386.7MB, alloc=107.8MB, time=23.41 memory used=2397.2MB, alloc=107.8MB, time=23.47 memory used=2407.7MB, alloc=107.8MB, time=23.53 memory used=2418.1MB, alloc=107.8MB, time=23.58 memory used=2428.4MB, alloc=107.8MB, time=23.63 memory used=2438.9MB, alloc=107.8MB, time=23.68 memory used=2450.2MB, alloc=107.8MB, time=23.73 memory used=2461.7MB, alloc=107.8MB, time=23.78 memory used=2473.0MB, alloc=107.8MB, time=23.83 memory used=2483.4MB, alloc=107.8MB, time=23.88 memory used=2495.1MB, alloc=107.8MB, time=23.94 memory used=2507.3MB, alloc=107.8MB, time=23.99 memory used=2519.6MB, alloc=107.8MB, time=24.04 memory used=2532.3MB, alloc=107.8MB, time=24.10 memory used=2545.2MB, alloc=107.8MB, time=24.15 memory used=2558.6MB, alloc=107.8MB, time=24.20 memory used=2572.3MB, alloc=107.8MB, time=24.26 memory used=2586.3MB, alloc=107.8MB, time=24.32 memory used=2600.8MB, alloc=107.8MB, time=24.37 memory used=2615.1MB, alloc=107.8MB, time=24.42 memory used=2630.7MB, alloc=107.8MB, time=24.48 memory used=2646.9MB, alloc=107.8MB, time=24.53 memory used=2663.9MB, alloc=107.8MB, time=24.58 memory used=2732.9MB, alloc=107.8MB, time=25.24 memory used=2767.1MB, alloc=107.8MB, time=25.35 memory used=2811.1MB, alloc=107.8MB, time=25.47 memory used=2844.8MB, alloc=107.8MB, time=25.57 memory used=2872.8MB, alloc=107.8MB, time=25.68 memory used=2902.8MB, alloc=107.8MB, time=25.77 memory used=2936.6MB, alloc=107.8MB, time=25.87 memory used=2972.1MB, alloc=107.8MB, time=25.96 memory used=3011.5MB, alloc=107.8MB, time=26.07 memory used=3052.5MB, alloc=107.8MB, time=26.16 memory used=3095.6MB, alloc=107.8MB, time=26.27 memory used=3133.0MB, alloc=107.8MB, time=26.35 memory used=3164.0MB, alloc=107.8MB, time=26.43 memory used=3188.3MB, alloc=107.8MB, time=26.50 memory used=3214.2MB, alloc=107.8MB, time=26.58 memory used=3240.3MB, alloc=107.8MB, time=26.65 memory used=3266.5MB, alloc=107.8MB, time=26.72 memory used=3295.6MB, alloc=107.8MB, time=26.80 memory used=3324.7MB, alloc=107.8MB, time=26.86 memory used=3354.2MB, alloc=107.8MB, time=26.93 memory used=3385.5MB, alloc=107.8MB, time=27.00 memory used=3417.6MB, alloc=107.8MB, time=27.07 memory used=3451.2MB, alloc=107.8MB, time=27.14 memory used=3487.5MB, alloc=107.8MB, time=27.21 memory used=3525.9MB, alloc=107.8MB, time=27.29 memory used=3565.7MB, alloc=107.8MB, time=27.37 memory used=3607.1MB, alloc=107.8MB, time=27.45 memory used=3651.5MB, alloc=107.8MB, time=27.53 memory used=3703.1MB, alloc=107.8MB, time=27.63 memory used=3715.9MB, alloc=107.8MB, time=27.68 memory used=3728.1MB, alloc=107.8MB, time=27.74 memory used=3739.9MB, alloc=107.8MB, time=27.79 memory used=3751.4MB, alloc=107.8MB, time=27.85 memory used=3797.7MB, alloc=107.8MB, time=36.65 memory used=3857.8MB, alloc=107.8MB, time=37.60 memory used=3896.7MB, alloc=107.8MB, time=37.71 memory used=3930.4MB, alloc=107.8MB, time=37.80 memory used=3972.1MB, alloc=107.8MB, time=37.91 memory used=4014.2MB, alloc=107.8MB, time=38.00 memory used=4041.1MB, alloc=107.8MB, time=38.09 memory used=4070.2MB, alloc=107.8MB, time=38.17 memory used=4102.1MB, alloc=107.8MB, time=38.24 memory used=4136.2MB, alloc=107.8MB, time=38.32 memory used=4172.6MB, alloc=107.8MB, time=38.40 memory used=4212.4MB, alloc=107.8MB, time=38.49 memory used=4255.4MB, alloc=107.8MB, time=38.58 memory used=4308.0MB, alloc=107.8MB, time=38.67 memory used=4346.0MB, alloc=107.8MB, time=38.74 memory used=4358.3MB, alloc=107.8MB, time=38.79 memory used=4368.2MB, alloc=107.8MB, time=38.84 memory used=4379.2MB, alloc=107.8MB, time=38.89 memory used=4389.3MB, alloc=107.8MB, time=38.94 memory used=4400.0MB, alloc=107.8MB, time=38.98 memory used=4411.6MB, alloc=107.8MB, time=39.03 memory used=4422.4MB, alloc=107.8MB, time=39.09 memory used=4434.6MB, alloc=107.8MB, time=39.14 memory used=4446.9MB, alloc=107.8MB, time=39.21 memory used=4459.8MB, alloc=107.8MB, time=39.26 memory used=4472.6MB, alloc=107.8MB, time=39.31 memory used=4485.8MB, alloc=107.8MB, time=39.36 memory used=4499.2MB, alloc=107.8MB, time=39.41 memory used=4513.7MB, alloc=107.8MB, time=39.46 memory used=4528.8MB, alloc=107.8MB, time=39.52 memory used=4544.7MB, alloc=107.8MB, time=39.58 memory used=4625.6MB, alloc=107.8MB, time=40.50 memory used=4703.5MB, alloc=107.8MB, time=41.32 memory used=4777.8MB, alloc=107.8MB, time=41.95 memory used=4848.5MB, alloc=107.8MB, time=42.67 memory used=4922.5MB, alloc=107.8MB, time=43.80 memory used=4992.1MB, alloc=131.8MB, time=44.50 memory used=5085.0MB, alloc=131.8MB, time=45.30 memory used=5161.4MB, alloc=131.8MB, time=45.55 memory used=5239.0MB, alloc=131.8MB, time=45.78 memory used=5320.9MB, alloc=131.8MB, time=46.00 memory used=5401.9MB, alloc=131.8MB, time=46.25 memory used=5488.7MB, alloc=131.8MB, time=46.92 memory used=5560.0MB, alloc=131.8MB, time=47.15 memory used=5632.8MB, alloc=131.8MB, time=47.38 memory used=5722.6MB, alloc=131.8MB, time=48.03 memory used=5797.7MB, alloc=131.8MB, time=48.32 memory used=5868.6MB, alloc=131.8MB, time=48.53 memory used=5943.0MB, alloc=131.8MB, time=48.76 memory used=6033.0MB, alloc=131.8MB, time=49.64 memory used=6125.6MB, alloc=131.8MB, time=50.32 memory used=6218.9MB, alloc=131.8MB, time=51.59 memory used=6305.6MB, alloc=155.8MB, time=52.75 memory used=6411.7MB, alloc=155.8MB, time=54.50 memory used=6500.8MB, alloc=435.8MB, time=56.04 memory used=6637.6MB, alloc=459.8MB, time=57.52 memory used=6793.2MB, alloc=459.8MB, time=59.49 memory used=6929.5MB, alloc=483.8MB, time=61.99 memory used=7054.3MB, alloc=507.8MB, time=65.81 memory used=7187.2MB, alloc=531.8MB, time=70.72 memory used=7337.4MB, alloc=555.8MB, time=76.58 memory used=7511.4MB, alloc=555.8MB, time=83.32 memory used=7685.5MB, alloc=579.8MB, time=90.20 memory used=7883.6MB, alloc=603.8MB, time=97.86 N1 := 5615 > GB := Basis(F, plex(op(vars))); 3 2 2 3 3 GB := [-2 x y - x y + 2 x y , 7 y z + 4 z - 4 x y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=8097.9MB, alloc=603.8MB, time=102.51 memory used=8289.2MB, alloc=603.8MB, time=104.60 memory used=8427.8MB, alloc=603.8MB, time=105.18 memory used=8550.1MB, alloc=603.8MB, time=105.71 memory used=8709.2MB, alloc=603.8MB, time=106.27 memory used=8827.6MB, alloc=603.8MB, time=106.70 memory used=8936.4MB, alloc=603.8MB, time=107.13 memory used=9057.4MB, alloc=603.8MB, time=107.55 memory used=9194.2MB, alloc=603.8MB, time=107.98 memory used=9348.0MB, alloc=603.8MB, time=108.44 memory used=9667.6MB, alloc=603.8MB, time=122.22 memory used=9817.0MB, alloc=603.8MB, time=123.70 memory used=9946.1MB, alloc=603.8MB, time=124.15 memory used=10077.5MB, alloc=603.8MB, time=124.59 memory used=10252.9MB, alloc=603.8MB, time=125.04 memory used=10415.0MB, alloc=603.8MB, time=125.56 memory used=10749.5MB, alloc=603.8MB, time=126.84 memory used=10871.1MB, alloc=603.8MB, time=127.35 memory used=11029.2MB, alloc=603.8MB, time=127.85 memory used=11145.8MB, alloc=603.8MB, time=128.27 memory used=11261.0MB, alloc=603.8MB, time=128.68 memory used=11393.1MB, alloc=603.8MB, time=129.09 memory used=11548.5MB, alloc=603.8MB, time=129.52 memory used=11807.0MB, alloc=603.8MB, time=139.70 memory used=11945.9MB, alloc=603.8MB, time=140.19 memory used=12063.5MB, alloc=603.8MB, time=140.61 memory used=12225.3MB, alloc=603.8MB, time=141.05 memory used=12412.9MB, alloc=603.8MB, time=141.56 memory used=12664.2MB, alloc=603.8MB, time=143.97 memory used=12956.8MB, alloc=603.8MB, time=147.11 memory used=13184.8MB, alloc=603.8MB, time=147.93 memory used=13421.2MB, alloc=603.8MB, time=149.15 memory used=13650.2MB, alloc=603.8MB, time=150.34 memory used=13878.0MB, alloc=603.8MB, time=151.40 memory used=14139.1MB, alloc=603.8MB, time=154.74 memory used=14350.1MB, alloc=603.8MB, time=158.63 memory used=14622.4MB, alloc=627.8MB, time=162.34 memory used=14902.6MB, alloc=651.8MB, time=169.78 memory used=15135.8MB, alloc=675.8MB, time=179.64 memory used=15385.5MB, alloc=699.8MB, time=190.80 memory used=15659.3MB, alloc=723.8MB, time=202.14 N2 := 5615 > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 3 3 2 2 H := [14 y z + 8 z - 8 x y, 14 x y + 7 x y - 14 x y , 3 2 2 2 3 -16 x z + 13 x z - 8 x y , 4 x y + 13 y - 10 y z] > J:=[op(GB),op(G)]; 3 2 2 3 3 J := [-2 x y - x y + 2 x y , 7 y z + 4 z - 4 x y, 3 2 2 2 3 -16 x z + 13 x z - 8 x y , 4 x y + 13 y - 10 y z] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 11, 15, 4, 3, 3, 3, 1, 1, 3/4, 2/3, 3/4, 5/12, 4, 11, 15, 4, 3, 3, 3, 1, 1, 3/4, 2/3, 3/4, 5/12, 0, 0, 0] > save(F, G, cat("ranSet/34", convert(F, string),".txt")); > quit memory used=15804.0MB, alloc=723.8MB, time=207.85 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428500839 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 F := [-5 x y z - 16 z , 12 x z - 19 x y + 15 y z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 4 G := [-7 x y - 15 y z - 20 y z, -16 y + 15 x y z - 15] > Problem := [F,G]; 3 3 2 2 Problem := [[-5 x y z - 16 z , 12 x z - 19 x y + 15 y z ], 2 2 3 2 4 [-7 x y - 15 y z - 20 y z, -16 y + 15 x y z - 15]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=25.8MB, alloc=32.3MB, time=0.52 memory used=46.1MB, alloc=32.3MB, time=0.82 memory used=65.4MB, alloc=56.3MB, time=1.07 memory used=113.7MB, alloc=60.3MB, time=1.63 memory used=155.1MB, alloc=60.3MB, time=2.10 memory used=199.3MB, alloc=61.1MB, time=2.66 memory used=237.0MB, alloc=61.1MB, time=3.04 memory used=281.5MB, alloc=69.1MB, time=3.59 memory used=319.9MB, alloc=93.1MB, time=4.10 memory used=387.9MB, alloc=93.1MB, time=4.89 memory used=432.9MB, alloc=93.1MB, time=5.21 memory used=478.1MB, alloc=93.1MB, time=5.68 memory used=508.9MB, alloc=93.1MB, time=5.78 memory used=544.8MB, alloc=93.1MB, time=5.89 memory used=587.3MB, alloc=93.1MB, time=6.29 memory used=620.5MB, alloc=93.1MB, time=6.40 memory used=683.4MB, alloc=93.1MB, time=6.91 memory used=741.1MB, alloc=93.1MB, time=15.57 memory used=785.9MB, alloc=93.1MB, time=21.92 memory used=819.3MB, alloc=93.1MB, time=22.04 memory used=846.7MB, alloc=93.1MB, time=22.16 memory used=874.6MB, alloc=93.1MB, time=22.29 memory used=906.9MB, alloc=93.1MB, time=22.42 memory used=944.8MB, alloc=93.1MB, time=22.55 memory used=972.8MB, alloc=93.1MB, time=22.66 memory used=995.5MB, alloc=93.1MB, time=22.76 memory used=1019.8MB, alloc=93.1MB, time=22.85 memory used=1045.3MB, alloc=93.1MB, time=22.94 memory used=1072.8MB, alloc=93.1MB, time=23.04 memory used=1102.2MB, alloc=93.1MB, time=23.13 memory used=1133.8MB, alloc=93.1MB, time=23.23 memory used=1167.7MB, alloc=93.1MB, time=23.32 memory used=1203.3MB, alloc=93.1MB, time=23.41 memory used=1242.5MB, alloc=107.8MB, time=23.52 memory used=1253.6MB, alloc=107.8MB, time=23.58 memory used=1265.6MB, alloc=107.8MB, time=23.65 memory used=1345.6MB, alloc=107.8MB, time=24.35 memory used=1374.6MB, alloc=107.8MB, time=24.46 memory used=1451.3MB, alloc=131.8MB, time=25.11 memory used=1533.7MB, alloc=131.8MB, time=26.13 memory used=1584.0MB, alloc=131.8MB, time=26.37 memory used=1640.8MB, alloc=131.8MB, time=26.76 memory used=1692.0MB, alloc=131.8MB, time=27.03 memory used=1752.7MB, alloc=131.8MB, time=27.87 memory used=1793.4MB, alloc=131.8MB, time=28.02 memory used=1832.8MB, alloc=131.8MB, time=28.14 memory used=1889.2MB, alloc=131.8MB, time=28.89 memory used=1930.4MB, alloc=131.8MB, time=29.02 memory used=1971.4MB, alloc=131.8MB, time=29.14 memory used=2039.8MB, alloc=131.8MB, time=29.71 memory used=2122.1MB, alloc=131.8MB, time=45.07 memory used=2178.8MB, alloc=155.8MB, time=61.03 memory used=2241.8MB, alloc=155.8MB, time=61.25 memory used=2289.1MB, alloc=155.8MB, time=61.41 memory used=2348.9MB, alloc=155.8MB, time=61.57 memory used=2415.9MB, alloc=155.8MB, time=61.73 memory used=2457.2MB, alloc=155.8MB, time=61.86 memory used=2501.9MB, alloc=155.8MB, time=61.98 memory used=2550.9MB, alloc=155.8MB, time=62.11 memory used=2603.9MB, alloc=155.8MB, time=62.24 memory used=2661.9MB, alloc=155.8MB, time=62.38 memory used=2725.8MB, alloc=155.8MB, time=62.52 memory used=2795.8MB, alloc=155.8MB, time=62.66 memory used=2843.8MB, alloc=155.8MB, time=62.78 memory used=2853.8MB, alloc=155.8MB, time=62.86 memory used=2864.2MB, alloc=155.8MB, time=62.94 memory used=2874.4MB, alloc=155.8MB, time=63.02 memory used=2884.4MB, alloc=155.8MB, time=63.10 memory used=2895.2MB, alloc=155.8MB, time=63.19 memory used=2904.7MB, alloc=155.8MB, time=63.27 memory used=2914.9MB, alloc=155.8MB, time=63.37 memory used=2924.8MB, alloc=155.8MB, time=63.46 memory used=2935.3MB, alloc=155.8MB, time=63.55 memory used=2947.4MB, alloc=155.8MB, time=63.63 memory used=2959.7MB, alloc=155.8MB, time=63.73 memory used=2972.1MB, alloc=155.8MB, time=63.81 memory used=2985.2MB, alloc=155.8MB, time=63.89 memory used=2998.4MB, alloc=155.8MB, time=63.96 memory used=3012.4MB, alloc=155.8MB, time=64.04 memory used=3071.8MB, alloc=155.8MB, time=64.59 memory used=3151.6MB, alloc=155.8MB, time=65.04 memory used=3240.5MB, alloc=155.8MB, time=65.86 memory used=3334.5MB, alloc=411.8MB, time=67.32 memory used=3444.0MB, alloc=411.8MB, time=68.27 memory used=3548.0MB, alloc=411.8MB, time=69.73 memory used=3662.5MB, alloc=411.8MB, time=70.69 memory used=3758.1MB, alloc=435.8MB, time=72.22 memory used=3872.8MB, alloc=435.8MB, time=73.46 memory used=4002.0MB, alloc=435.8MB, time=75.02 memory used=4126.6MB, alloc=459.8MB, time=76.58 memory used=4215.4MB, alloc=459.8MB, time=77.03 memory used=4375.8MB, alloc=459.8MB, time=78.48 memory used=4555.5MB, alloc=459.8MB, time=80.14 memory used=4680.3MB, alloc=459.8MB, time=81.95 memory used=4781.4MB, alloc=483.8MB, time=83.43 memory used=4932.0MB, alloc=483.8MB, time=84.82 memory used=5060.8MB, alloc=483.8MB, time=85.67 memory used=5244.9MB, alloc=483.8MB, time=87.19 memory used=5337.5MB, alloc=483.8MB, time=88.45 memory used=5430.2MB, alloc=483.8MB, time=89.01 memory used=5520.2MB, alloc=483.8MB, time=89.59 memory used=5609.9MB, alloc=507.8MB, time=90.26 memory used=5695.4MB, alloc=507.8MB, time=90.62 memory used=5785.5MB, alloc=507.8MB, time=90.97 memory used=5859.3MB, alloc=507.8MB, time=91.27 memory used=5959.6MB, alloc=507.8MB, time=91.85 memory used=6082.4MB, alloc=531.8MB, time=173.95 memory used=6378.8MB, alloc=531.8MB, time=272.45 memory used=6492.2MB, alloc=531.8MB, time=272.81 memory used=6694.2MB, alloc=531.8MB, time=273.39 memory used=6848.9MB, alloc=531.8MB, time=273.86 memory used=7023.1MB, alloc=531.8MB, time=274.33 memory used=7215.1MB, alloc=531.8MB, time=275.05 memory used=7428.0MB, alloc=531.8MB, time=275.64 memory used=7663.1MB, alloc=531.8MB, time=276.20 memory used=7882.1MB, alloc=531.8MB, time=276.69 memory used=8068.8MB, alloc=531.8MB, time=277.15 memory used=8273.7MB, alloc=531.8MB, time=277.62 memory used=8500.1MB, alloc=531.8MB, time=278.10 memory used=8744.1MB, alloc=531.8MB, time=279.53 memory used=8855.9MB, alloc=531.8MB, time=280.02 memory used=8940.2MB, alloc=531.8MB, time=280.34 memory used=9057.8MB, alloc=531.8MB, time=282.67 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428501139 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 F := [-14 x y - 13 z - 4 y, -4 x z + 5 x z + 2 x z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 G := [-11 x y - 11 x z + 11 y z, -15 z + 10 x + 13 y] > Problem := [F,G]; 3 2 2 2 2 Problem := [[-14 x y - 13 z - 4 y, -4 x z + 5 x z + 2 x z], 2 2 2 2 2 [-11 x y - 11 x z + 11 y z, -15 z + 10 x + 13 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.19 memory used=26.0MB, alloc=32.3MB, time=0.52 memory used=44.7MB, alloc=56.3MB, time=0.81 memory used=85.6MB, alloc=60.3MB, time=1.41 memory used=123.9MB, alloc=60.3MB, time=1.97 memory used=162.7MB, alloc=84.3MB, time=2.55 memory used=225.8MB, alloc=92.3MB, time=3.47 memory used=289.4MB, alloc=92.3MB, time=4.58 memory used=354.2MB, alloc=116.3MB, time=5.60 memory used=435.0MB, alloc=372.3MB, time=6.85 memory used=514.9MB, alloc=396.3MB, time=8.26 memory used=621.9MB, alloc=420.3MB, time=9.89 memory used=756.5MB, alloc=444.3MB, time=12.25 memory used=907.2MB, alloc=468.3MB, time=14.90 memory used=1065.6MB, alloc=492.3MB, time=17.82 memory used=1237.9MB, alloc=516.3MB, time=21.09 memory used=1422.5MB, alloc=540.3MB, time=24.55 memory used=1627.0MB, alloc=564.3MB, time=28.28 memory used=1846.1MB, alloc=588.3MB, time=32.11 memory used=2059.8MB, alloc=612.3MB, time=35.96 memory used=2266.7MB, alloc=636.3MB, time=39.66 memory used=2465.0MB, alloc=660.3MB, time=43.14 memory used=2702.5MB, alloc=684.3MB, time=50.13 memory used=2927.8MB, alloc=708.3MB, time=58.06 memory used=3163.7MB, alloc=732.3MB, time=66.77 memory used=3412.1MB, alloc=756.3MB, time=76.07 memory used=3673.2MB, alloc=780.3MB, time=86.19 memory used=3947.4MB, alloc=804.3MB, time=96.91 memory used=4233.5MB, alloc=828.3MB, time=108.45 memory used=4530.9MB, alloc=852.3MB, time=121.27 memory used=4852.3MB, alloc=876.3MB, time=135.23 memory used=5197.5MB, alloc=900.3MB, time=150.16 memory used=5566.8MB, alloc=924.3MB, time=167.25 memory used=5959.9MB, alloc=948.3MB, time=184.16 memory used=6377.0MB, alloc=972.3MB, time=203.45 memory used=6818.1MB, alloc=996.3MB, time=223.61 memory used=7283.0MB, alloc=996.3MB, time=244.30 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428501439 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 2 2 F := [-x y + 9 x z - 18 z , 20 x y - 7 x y z - 15 z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 3 3 G := [-6 y z + 14 y z - 6 x z, -x y - 16 x y - 4 y z] > Problem := [F,G]; 2 2 2 2 2 2 2 Problem := [[-x y + 9 x z - 18 z , 20 x y - 7 x y z - 15 z ], 3 2 2 2 3 3 [-6 y z + 14 y z - 6 x z, -x y - 16 x y - 4 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.19 memory used=25.3MB, alloc=32.3MB, time=0.53 memory used=44.9MB, alloc=36.3MB, time=0.83 memory used=66.7MB, alloc=60.3MB, time=1.10 memory used=111.8MB, alloc=68.3MB, time=1.74 memory used=155.1MB, alloc=68.3MB, time=2.27 memory used=196.0MB, alloc=68.3MB, time=2.69 memory used=236.8MB, alloc=68.3MB, time=3.12 memory used=288.7MB, alloc=92.3MB, time=3.62 memory used=356.3MB, alloc=92.3MB, time=4.48 memory used=425.9MB, alloc=92.3MB, time=5.16 memory used=490.7MB, alloc=92.3MB, time=5.93 memory used=553.2MB, alloc=116.3MB, time=6.85 memory used=618.6MB, alloc=372.3MB, time=7.67 memory used=708.8MB, alloc=372.3MB, time=8.80 memory used=794.9MB, alloc=396.3MB, time=10.03 memory used=907.6MB, alloc=396.3MB, time=11.55 memory used=988.1MB, alloc=396.3MB, time=12.28 memory used=1062.2MB, alloc=396.3MB, time=13.19 memory used=1135.1MB, alloc=396.3MB, time=14.19 memory used=1186.3MB, alloc=396.3MB, time=14.45 memory used=1325.7MB, alloc=396.3MB, time=16.01 memory used=1451.1MB, alloc=420.3MB, time=17.28 memory used=1586.5MB, alloc=420.3MB, time=19.14 memory used=1670.0MB, alloc=420.3MB, time=19.78 memory used=1738.6MB, alloc=420.3MB, time=20.11 memory used=1806.2MB, alloc=420.3MB, time=20.76 memory used=1894.2MB, alloc=420.3MB, time=21.63 memory used=1962.5MB, alloc=420.3MB, time=21.97 memory used=2034.8MB, alloc=420.3MB, time=22.35 memory used=2134.4MB, alloc=420.3MB, time=26.32 memory used=2191.6MB, alloc=420.3MB, time=26.55 memory used=2244.5MB, alloc=420.3MB, time=26.77 memory used=2301.8MB, alloc=420.3MB, time=26.97 memory used=2368.6MB, alloc=420.3MB, time=27.31 memory used=2452.4MB, alloc=444.3MB, time=30.60 memory used=2560.4MB, alloc=444.3MB, time=31.89 memory used=2628.1MB, alloc=444.3MB, time=32.14 memory used=2700.0MB, alloc=444.3MB, time=32.36 memory used=2844.5MB, alloc=444.3MB, time=33.89 memory used=3006.3MB, alloc=444.3MB, time=35.68 memory used=3101.8MB, alloc=444.3MB, time=38.17 memory used=3243.3MB, alloc=444.3MB, time=41.66 memory used=3360.7MB, alloc=468.3MB, time=42.58 memory used=3487.4MB, alloc=468.3MB, time=44.46 memory used=3593.2MB, alloc=468.3MB, time=46.17 memory used=3690.4MB, alloc=492.3MB, time=47.70 memory used=3784.8MB, alloc=492.3MB, time=48.98 memory used=3872.3MB, alloc=492.3MB, time=50.15 memory used=3983.2MB, alloc=492.3MB, time=51.47 memory used=4064.5MB, alloc=492.3MB, time=52.63 memory used=4155.5MB, alloc=516.3MB, time=53.86 memory used=4250.9MB, alloc=516.3MB, time=55.20 memory used=4355.3MB, alloc=516.3MB, time=56.25 memory used=4442.2MB, alloc=516.3MB, time=57.49 memory used=4578.7MB, alloc=516.3MB, time=58.86 memory used=4700.9MB, alloc=516.3MB, time=59.73 memory used=4793.7MB, alloc=516.3MB, time=60.16 memory used=4910.5MB, alloc=516.3MB, time=60.75 memory used=5001.4MB, alloc=516.3MB, time=61.15 memory used=5138.1MB, alloc=516.3MB, time=66.53 memory used=5233.3MB, alloc=516.3MB, time=66.96 memory used=5324.7MB, alloc=516.3MB, time=67.35 memory used=5404.9MB, alloc=516.3MB, time=67.73 memory used=5499.9MB, alloc=516.3MB, time=68.10 memory used=5610.6MB, alloc=516.3MB, time=68.47 memory used=5812.9MB, alloc=516.3MB, time=69.10 memory used=5952.8MB, alloc=516.3MB, time=70.01 memory used=6054.9MB, alloc=516.3MB, time=70.59 memory used=6172.0MB, alloc=516.3MB, time=71.24 memory used=6266.7MB, alloc=516.3MB, time=71.75 memory used=6405.0MB, alloc=516.3MB, time=77.55 memory used=6496.7MB, alloc=516.3MB, time=77.98 memory used=6593.2MB, alloc=516.3MB, time=78.39 memory used=6671.1MB, alloc=516.3MB, time=78.75 memory used=6762.5MB, alloc=516.3MB, time=79.12 memory used=6869.7MB, alloc=516.3MB, time=79.49 memory used=7099.2MB, alloc=516.3MB, time=80.03 memory used=7264.4MB, alloc=516.3MB, time=81.69 memory used=7381.8MB, alloc=516.3MB, time=82.36 memory used=7513.5MB, alloc=516.3MB, time=83.49 memory used=7609.3MB, alloc=516.3MB, time=84.42 memory used=7725.4MB, alloc=516.3MB, time=85.95 memory used=7779.7MB, alloc=516.3MB, time=86.89 memory used=7855.1MB, alloc=540.3MB, time=88.18 memory used=7905.0MB, alloc=540.3MB, time=89.12 memory used=7977.8MB, alloc=540.3MB, time=90.30 memory used=8033.7MB, alloc=540.3MB, time=91.41 memory used=8083.8MB, alloc=540.3MB, time=92.45 memory used=8141.7MB, alloc=540.3MB, time=93.68 memory used=8208.0MB, alloc=540.3MB, time=94.70 memory used=8449.6MB, alloc=540.3MB, time=97.38 memory used=8679.8MB, alloc=564.3MB, time=99.95 memory used=8868.1MB, alloc=564.3MB, time=101.00 memory used=9080.7MB, alloc=564.3MB, time=102.14 memory used=9301.8MB, alloc=564.3MB, time=102.99 memory used=9543.6MB, alloc=564.3MB, time=104.65 memory used=9783.0MB, alloc=564.3MB, time=106.27 memory used=10032.1MB, alloc=564.3MB, time=108.10 memory used=10253.9MB, alloc=564.3MB, time=108.95 memory used=10534.0MB, alloc=564.3MB, time=109.84 memory used=10819.2MB, alloc=564.3MB, time=111.52 memory used=11019.1MB, alloc=564.3MB, time=112.34 memory used=11286.9MB, alloc=564.3MB, time=113.19 memory used=11677.2MB, alloc=564.3MB, time=114.21 memory used=12052.2MB, alloc=564.3MB, time=115.17 memory used=12405.1MB, alloc=564.3MB, time=116.13 memory used=12804.9MB, alloc=564.3MB, time=117.22 memory used=13116.3MB, alloc=588.3MB, time=119.60 memory used=13345.5MB, alloc=588.3MB, time=120.59 memory used=13661.6MB, alloc=588.3MB, time=121.53 memory used=14099.2MB, alloc=588.3MB, time=122.62 memory used=14518.9MB, alloc=588.3MB, time=123.76 memory used=14789.6MB, alloc=588.3MB, time=125.24 memory used=15055.1MB, alloc=588.3MB, time=126.14 memory used=15393.2MB, alloc=588.3MB, time=127.09 memory used=15663.3MB, alloc=588.3MB, time=128.80 memory used=15900.6MB, alloc=588.3MB, time=130.39 memory used=16126.3MB, alloc=588.3MB, time=131.62 memory used=16348.0MB, alloc=588.3MB, time=132.75 memory used=16581.3MB, alloc=588.3MB, time=133.65 memory used=16840.6MB, alloc=588.3MB, time=135.32 memory used=17111.5MB, alloc=612.3MB, time=139.35 memory used=17424.8MB, alloc=636.3MB, time=142.99 memory used=17748.2MB, alloc=660.3MB, time=147.29 memory used=18101.6MB, alloc=684.3MB, time=151.59 memory used=18464.7MB, alloc=708.3MB, time=156.63 memory used=18837.5MB, alloc=732.3MB, time=162.19 memory used=19267.1MB, alloc=756.3MB, time=167.21 memory used=19700.1MB, alloc=780.3MB, time=172.69 memory used=20199.8MB, alloc=804.3MB, time=176.69 memory used=20684.3MB, alloc=828.3MB, time=182.69 memory used=21128.7MB, alloc=852.3MB, time=188.11 memory used=21670.2MB, alloc=876.3MB, time=193.81 memory used=22147.9MB, alloc=876.3MB, time=199.20 memory used=22571.5MB, alloc=900.3MB, time=205.25 memory used=23016.4MB, alloc=924.3MB, time=210.82 memory used=23365.5MB, alloc=948.3MB, time=216.84 memory used=23661.3MB, alloc=972.3MB, time=222.02 memory used=24047.0MB, alloc=996.3MB, time=234.60 memory used=24467.1MB, alloc=1020.3MB, time=251.85 memory used=24881.0MB, alloc=1044.3MB, time=269.64 memory used=25304.9MB, alloc=1068.3MB, time=288.29 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428501740 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 3 2 2 F := [6 x y - 11 y z + 3 x y , 20 x y - 20 x y - 9 y ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 G := [-19 x y z - 3 x z + 12 y , -14 x z + 7 x + 14 y] > Problem := [F,G]; 2 2 2 2 2 3 2 2 Problem := [[6 x y - 11 y z + 3 x y , 20 x y - 20 x y - 9 y ], 2 2 2 2 2 [-19 x y z - 3 x z + 12 y , -14 x z + 7 x + 14 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.20 memory used=25.4MB, alloc=32.3MB, time=0.54 memory used=46.3MB, alloc=32.3MB, time=0.87 memory used=65.1MB, alloc=56.3MB, time=1.16 memory used=106.5MB, alloc=60.3MB, time=1.73 memory used=145.1MB, alloc=84.3MB, time=2.31 memory used=216.9MB, alloc=92.3MB, time=3.23 memory used=288.6MB, alloc=92.3MB, time=4.07 memory used=358.3MB, alloc=116.3MB, time=4.83 memory used=457.4MB, alloc=116.3MB, time=5.97 memory used=545.7MB, alloc=116.3MB, time=7.32 memory used=621.1MB, alloc=140.3MB, time=8.68 memory used=720.1MB, alloc=164.3MB, time=10.43 memory used=839.3MB, alloc=188.3MB, time=12.57 memory used=965.9MB, alloc=468.3MB, time=14.85 memory used=1120.2MB, alloc=492.3MB, time=17.67 memory used=1309.3MB, alloc=492.3MB, time=20.12 memory used=1468.8MB, alloc=516.3MB, time=23.42 memory used=1616.3MB, alloc=540.3MB, time=28.28 memory used=1774.3MB, alloc=564.3MB, time=33.74 memory used=1945.1MB, alloc=588.3MB, time=40.01 memory used=2127.8MB, alloc=612.3MB, time=47.00 memory used=2326.6MB, alloc=636.3MB, time=54.92 memory used=2549.4MB, alloc=660.3MB, time=64.07 memory used=2796.1MB, alloc=660.3MB, time=74.25 memory used=3042.8MB, alloc=684.3MB, time=84.82 memory used=3313.5MB, alloc=684.3MB, time=96.70 memory used=3584.0MB, alloc=684.3MB, time=108.03 memory used=3854.4MB, alloc=708.3MB, time=119.21 memory used=4148.7MB, alloc=708.3MB, time=131.14 memory used=4443.0MB, alloc=708.3MB, time=143.07 memory used=4737.0MB, alloc=732.3MB, time=154.85 memory used=5055.1MB, alloc=756.3MB, time=167.51 memory used=5397.1MB, alloc=780.3MB, time=180.88 N1 := 11391 > GB := Basis(F, plex(op(vars))); 3 2 2 GB := [-20 x y + 20 x y + 9 y , 5 3 2 4 2 2 3 -6 x y + 11 x y z + 3 x y - 11 x y z + 3 x y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=5638.8MB, alloc=780.3MB, time=187.03 memory used=5807.7MB, alloc=780.3MB, time=189.71 memory used=6079.9MB, alloc=780.3MB, time=193.91 memory used=6306.3MB, alloc=780.3MB, time=198.25 memory used=6532.7MB, alloc=780.3MB, time=202.66 memory used=6835.1MB, alloc=804.3MB, time=207.54 memory used=7166.7MB, alloc=828.3MB, time=217.91 memory used=7544.6MB, alloc=852.3MB, time=232.42 memory used=7916.7MB, alloc=876.3MB, time=248.11 memory used=8312.8MB, alloc=900.3MB, time=264.76 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428502039 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 4 4 3 F := [x z + 20 z - x y, -5 z - 6 z + 8 x y] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 3 2 G := [-x y + 5 y z - 3 y z , 12 y z + 19 x z - 20] > Problem := [F,G]; 2 2 4 4 3 Problem := [[x z + 20 z - x y, -5 z - 6 z + 8 x y], 2 2 2 2 2 3 2 [-x y + 5 y z - 3 y z , 12 y z + 19 x z - 20]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.4MB, alloc=32.3MB, time=0.52 memory used=46.0MB, alloc=56.3MB, time=0.82 memory used=85.4MB, alloc=63.2MB, time=1.05 memory used=118.4MB, alloc=63.2MB, time=1.61 memory used=151.3MB, alloc=63.2MB, time=1.80 memory used=181.0MB, alloc=63.2MB, time=1.89 memory used=214.1MB, alloc=63.2MB, time=2.01 memory used=250.2MB, alloc=63.2MB, time=2.31 memory used=282.9MB, alloc=63.2MB, time=2.40 memory used=305.1MB, alloc=63.2MB, time=2.47 memory used=330.9MB, alloc=63.2MB, time=2.53 memory used=360.4MB, alloc=63.2MB, time=2.61 memory used=393.4MB, alloc=63.2MB, time=2.68 memory used=420.9MB, alloc=63.2MB, time=2.75 memory used=438.4MB, alloc=63.2MB, time=2.80 memory used=457.0MB, alloc=63.2MB, time=2.86 memory used=477.6MB, alloc=63.2MB, time=2.92 memory used=498.6MB, alloc=63.2MB, time=2.98 memory used=521.6MB, alloc=63.2MB, time=3.04 memory used=544.7MB, alloc=63.2MB, time=3.11 memory used=569.8MB, alloc=63.2MB, time=3.17 memory used=596.6MB, alloc=63.2MB, time=3.23 memory used=625.0MB, alloc=63.2MB, time=3.29 memory used=654.9MB, alloc=63.2MB, time=3.36 memory used=686.1MB, alloc=63.2MB, time=3.42 memory used=719.7MB, alloc=63.2MB, time=3.48 memory used=749.3MB, alloc=63.2MB, time=3.54 memory used=767.0MB, alloc=63.2MB, time=3.58 memory used=785.2MB, alloc=63.2MB, time=3.63 memory used=803.7MB, alloc=63.2MB, time=3.68 memory used=823.4MB, alloc=63.2MB, time=3.72 memory used=843.8MB, alloc=63.2MB, time=3.77 memory used=866.0MB, alloc=63.2MB, time=3.82 memory used=895.3MB, alloc=63.2MB, time=4.01 memory used=923.2MB, alloc=63.2MB, time=4.37 memory used=946.6MB, alloc=63.2MB, time=4.45 memory used=971.3MB, alloc=63.2MB, time=4.52 memory used=998.8MB, alloc=63.2MB, time=4.59 memory used=1028.5MB, alloc=63.2MB, time=4.65 memory used=1058.9MB, alloc=63.2MB, time=4.72 memory used=1076.4MB, alloc=63.2MB, time=4.78 memory used=1093.4MB, alloc=63.2MB, time=4.83 memory used=1111.5MB, alloc=63.2MB, time=4.88 memory used=1129.9MB, alloc=63.2MB, time=4.94 memory used=1148.6MB, alloc=63.2MB, time=5.00 memory used=1169.3MB, alloc=63.2MB, time=5.06 memory used=1190.3MB, alloc=63.2MB, time=5.12 memory used=1213.3MB, alloc=63.2MB, time=5.17 memory used=1236.3MB, alloc=63.2MB, time=5.23 memory used=1261.3MB, alloc=63.2MB, time=5.29 memory used=1286.3MB, alloc=63.2MB, time=5.35 memory used=1313.2MB, alloc=63.2MB, time=5.41 memory used=1341.6MB, alloc=63.2MB, time=5.47 memory used=1371.4MB, alloc=63.2MB, time=5.53 memory used=1402.5MB, alloc=63.2MB, time=5.59 memory used=1427.3MB, alloc=63.2MB, time=5.65 memory used=1443.0MB, alloc=63.2MB, time=5.69 memory used=1459.0MB, alloc=63.2MB, time=5.73 memory used=1476.0MB, alloc=63.2MB, time=5.78 memory used=1494.0MB, alloc=63.2MB, time=5.83 memory used=1512.4MB, alloc=63.2MB, time=5.87 memory used=1531.2MB, alloc=63.2MB, time=5.91 memory used=1551.0MB, alloc=63.2MB, time=5.96 memory used=1572.1MB, alloc=63.2MB, time=6.01 memory used=1594.2MB, alloc=63.2MB, time=6.05 memory used=1622.2MB, alloc=63.2MB, time=6.21 memory used=1651.0MB, alloc=63.2MB, time=6.39 memory used=1678.3MB, alloc=63.2MB, time=6.51 memory used=1706.7MB, alloc=63.2MB, time=6.63 memory used=1745.8MB, alloc=63.2MB, time=9.02 memory used=1791.8MB, alloc=63.2MB, time=9.97 memory used=1832.7MB, alloc=63.2MB, time=10.37 memory used=1873.2MB, alloc=63.2MB, time=10.84 memory used=1915.0MB, alloc=63.2MB, time=11.45 memory used=1956.0MB, alloc=63.2MB, time=12.00 memory used=1992.7MB, alloc=63.2MB, time=12.32 memory used=2023.6MB, alloc=63.2MB, time=12.55 memory used=2048.2MB, alloc=63.2MB, time=12.63 memory used=2071.2MB, alloc=63.2MB, time=12.75 memory used=2102.0MB, alloc=63.2MB, time=12.96 memory used=2121.8MB, alloc=63.2MB, time=13.02 memory used=2148.1MB, alloc=63.2MB, time=13.23 memory used=2174.6MB, alloc=63.2MB, time=14.51 memory used=2200.4MB, alloc=63.2MB, time=14.71 memory used=2231.7MB, alloc=75.9MB, time=14.85 memory used=2255.0MB, alloc=75.9MB, time=14.92 memory used=2277.3MB, alloc=75.9MB, time=14.99 memory used=2300.7MB, alloc=99.9MB, time=15.47 memory used=2346.9MB, alloc=99.9MB, time=16.41 memory used=2375.1MB, alloc=99.9MB, time=16.51 memory used=2402.1MB, alloc=99.9MB, time=16.61 memory used=2431.4MB, alloc=99.9MB, time=16.73 memory used=2462.4MB, alloc=99.9MB, time=16.83 memory used=2494.9MB, alloc=99.9MB, time=16.93 memory used=2528.9MB, alloc=99.9MB, time=17.03 memory used=2566.7MB, alloc=99.9MB, time=17.14 memory used=2606.0MB, alloc=99.9MB, time=17.25 memory used=2646.9MB, alloc=99.9MB, time=17.36 memory used=2691.8MB, alloc=99.9MB, time=17.48 memory used=2726.0MB, alloc=123.9MB, time=17.59 memory used=2761.2MB, alloc=123.9MB, time=17.72 memory used=2797.9MB, alloc=123.9MB, time=17.83 memory used=2833.7MB, alloc=123.9MB, time=17.95 memory used=2873.4MB, alloc=123.9MB, time=18.06 memory used=2913.6MB, alloc=123.9MB, time=18.19 memory used=2954.5MB, alloc=123.9MB, time=18.30 memory used=2996.1MB, alloc=123.9MB, time=18.43 memory used=3041.6MB, alloc=123.9MB, time=18.55 memory used=3087.6MB, alloc=123.9MB, time=18.68 memory used=3134.2MB, alloc=123.9MB, time=18.80 memory used=3184.7MB, alloc=123.9MB, time=18.93 memory used=3235.7MB, alloc=123.9MB, time=19.05 memory used=3287.1MB, alloc=123.9MB, time=19.18 memory used=3342.3MB, alloc=123.9MB, time=19.31 memory used=3397.9MB, alloc=123.9MB, time=19.44 memory used=3457.2MB, alloc=123.9MB, time=19.57 memory used=3516.6MB, alloc=123.9MB, time=19.72 memory used=3579.6MB, alloc=123.9MB, time=19.85 memory used=3642.4MB, alloc=123.9MB, time=19.99 memory used=3708.6MB, alloc=123.9MB, time=20.13 memory used=3754.8MB, alloc=123.9MB, time=20.24 memory used=3786.5MB, alloc=123.9MB, time=20.32 memory used=3818.2MB, alloc=123.9MB, time=20.40 memory used=3853.1MB, alloc=123.9MB, time=20.48 memory used=3887.7MB, alloc=123.9MB, time=20.57 memory used=3922.0MB, alloc=123.9MB, time=20.65 memory used=3956.1MB, alloc=123.9MB, time=20.75 memory used=3992.8MB, alloc=123.9MB, time=20.84 memory used=4029.3MB, alloc=123.9MB, time=20.92 memory used=4068.3MB, alloc=123.9MB, time=21.02 memory used=4106.8MB, alloc=123.9MB, time=21.11 memory used=4147.5MB, alloc=123.9MB, time=21.20 memory used=4187.5MB, alloc=123.9MB, time=21.29 memory used=4229.3MB, alloc=123.9MB, time=21.38 memory used=4272.9MB, alloc=123.9MB, time=21.47 memory used=4317.7MB, alloc=123.9MB, time=21.56 memory used=4363.4MB, alloc=123.9MB, time=21.65 memory used=4409.3MB, alloc=123.9MB, time=21.75 memory used=4457.5MB, alloc=123.9MB, time=21.84 memory used=4506.6MB, alloc=123.9MB, time=21.94 memory used=4557.3MB, alloc=123.9MB, time=22.03 memory used=4610.3MB, alloc=123.9MB, time=22.13 memory used=4669.6MB, alloc=123.9MB, time=22.33 memory used=4729.2MB, alloc=123.9MB, time=24.41 memory used=4784.9MB, alloc=123.9MB, time=24.64 memory used=4844.3MB, alloc=123.9MB, time=24.79 memory used=4912.4MB, alloc=123.9MB, time=24.94 memory used=4959.5MB, alloc=123.9MB, time=25.06 memory used=4996.3MB, alloc=123.9MB, time=25.17 memory used=5036.1MB, alloc=123.9MB, time=25.28 memory used=5077.0MB, alloc=123.9MB, time=25.39 memory used=5121.0MB, alloc=123.9MB, time=25.51 memory used=5165.6MB, alloc=123.9MB, time=25.65 memory used=5213.3MB, alloc=123.9MB, time=25.79 memory used=5263.8MB, alloc=123.9MB, time=25.92 memory used=5317.1MB, alloc=123.9MB, time=26.04 memory used=5373.0MB, alloc=123.9MB, time=26.17 memory used=5431.0MB, alloc=123.9MB, time=26.32 memory used=5490.9MB, alloc=123.9MB, time=26.45 memory used=5554.9MB, alloc=123.9MB, time=26.56 memory used=5622.2MB, alloc=123.9MB, time=26.70 memory used=5670.3MB, alloc=123.9MB, time=26.80 memory used=5704.6MB, alloc=123.9MB, time=26.90 memory used=5740.7MB, alloc=123.9MB, time=26.99 memory used=5779.3MB, alloc=123.9MB, time=27.07 memory used=5817.7MB, alloc=123.9MB, time=27.16 memory used=5858.5MB, alloc=123.9MB, time=27.24 memory used=5901.9MB, alloc=123.9MB, time=27.33 memory used=5947.3MB, alloc=123.9MB, time=27.42 memory used=6015.5MB, alloc=131.8MB, time=33.58 memory used=6031.5MB, alloc=131.8MB, time=33.64 memory used=6045.7MB, alloc=131.8MB, time=33.69 memory used=6060.6MB, alloc=131.8MB, time=33.75 memory used=6121.3MB, alloc=387.8MB, time=35.34 memory used=6187.5MB, alloc=387.8MB, time=36.91 memory used=6236.6MB, alloc=387.8MB, time=37.04 memory used=6296.5MB, alloc=387.8MB, time=37.20 memory used=6361.0MB, alloc=387.8MB, time=37.41 memory used=6421.6MB, alloc=387.8MB, time=37.72 memory used=6486.6MB, alloc=387.8MB, time=37.98 memory used=6548.6MB, alloc=387.8MB, time=38.12 memory used=6610.6MB, alloc=387.8MB, time=38.24 memory used=6690.5MB, alloc=387.8MB, time=38.83 memory used=6802.5MB, alloc=387.8MB, time=40.02 memory used=6895.2MB, alloc=387.8MB, time=40.95 memory used=6971.2MB, alloc=387.8MB, time=41.75 memory used=7036.5MB, alloc=387.8MB, time=44.29 memory used=7090.1MB, alloc=387.8MB, time=44.44 memory used=7132.5MB, alloc=387.8MB, time=44.55 memory used=7184.9MB, alloc=387.8MB, 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alloc=435.8MB, time=129.22 memory used=13859.0MB, alloc=435.8MB, time=129.48 memory used=13915.3MB, alloc=435.8MB, time=129.72 memory used=13961.7MB, alloc=435.8MB, time=129.92 memory used=14009.2MB, alloc=435.8MB, time=130.12 memory used=14061.4MB, alloc=435.8MB, time=130.34 memory used=14118.3MB, alloc=435.8MB, time=130.56 memory used=14176.7MB, alloc=435.8MB, time=130.77 memory used=14239.9MB, alloc=435.8MB, time=130.99 memory used=14307.6MB, alloc=435.8MB, time=131.20 memory used=14379.8MB, alloc=435.8MB, time=131.42 memory used=14456.2MB, alloc=435.8MB, time=131.64 memory used=14536.5MB, alloc=435.8MB, time=131.88 memory used=14586.6MB, alloc=459.8MB, time=132.08 memory used=14639.0MB, alloc=459.8MB, time=132.25 memory used=14694.6MB, alloc=459.8MB, time=132.44 memory used=14752.8MB, alloc=459.8MB, time=132.63 memory used=14813.2MB, alloc=459.8MB, time=132.81 memory used=14878.4MB, alloc=459.8MB, time=133.00 memory used=14947.4MB, alloc=459.8MB, time=133.19 memory used=15018.8MB, 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alloc=579.8MB, time=253.49 memory used=32464.5MB, alloc=579.8MB, time=253.81 memory used=32570.7MB, alloc=579.8MB, time=254.13 memory used=32676.9MB, alloc=579.8MB, time=254.47 memory used=32792.2MB, alloc=579.8MB, time=254.80 memory used=32907.3MB, alloc=579.8MB, time=255.15 memory used=33022.1MB, alloc=579.8MB, time=255.50 memory used=33136.5MB, alloc=579.8MB, time=255.84 memory used=33259.9MB, alloc=579.8MB, time=256.17 memory used=33382.4MB, alloc=579.8MB, time=256.50 memory used=33504.5MB, alloc=579.8MB, time=256.83 memory used=33634.8MB, alloc=579.8MB, time=257.18 memory used=33764.2MB, alloc=579.8MB, time=257.52 memory used=33892.5MB, alloc=579.8MB, time=257.88 memory used=34028.5MB, alloc=579.8MB, time=258.28 memory used=34163.1MB, alloc=579.8MB, time=258.64 memory used=34304.8MB, alloc=579.8MB, time=258.98 memory used=34444.5MB, alloc=579.8MB, time=259.39 memory used=34590.5MB, alloc=579.8MB, time=259.77 memory used=34734.3MB, alloc=579.8MB, time=260.14 memory used=34882.8MB, alloc=579.8MB, time=260.56 memory used=35036.4MB, alloc=579.8MB, time=260.94 memory used=35193.6MB, alloc=579.8MB, time=261.33 memory used=35353.7MB, alloc=579.8MB, time=261.73 memory used=35515.8MB, alloc=579.8MB, time=262.12 memory used=35685.2MB, alloc=579.8MB, time=262.52 memory used=35859.5MB, alloc=579.8MB, time=262.92 memory used=36103.9MB, alloc=579.8MB, time=263.45 memory used=36237.4MB, alloc=579.8MB, time=263.83 memory used=36374.0MB, alloc=579.8MB, time=264.22 memory used=36514.1MB, alloc=579.8MB, time=264.60 memory used=36660.7MB, alloc=579.8MB, time=265.00 memory used=36948.0MB, alloc=579.8MB, time=271.41 memory used=37084.8MB, alloc=579.8MB, time=273.16 memory used=37229.8MB, alloc=579.8MB, time=273.72 memory used=37392.1MB, alloc=579.8MB, time=274.29 memory used=37565.1MB, alloc=579.8MB, time=274.83 memory used=37677.1MB, alloc=579.8MB, time=275.30 memory used=37774.4MB, alloc=579.8MB, time=275.72 memory used=37864.7MB, alloc=579.8MB, time=276.14 memory used=37956.7MB, alloc=579.8MB, time=276.55 memory used=38059.4MB, alloc=579.8MB, time=277.00 memory used=38164.9MB, alloc=579.8MB, time=277.41 memory used=38273.0MB, alloc=579.8MB, time=277.83 memory used=38383.8MB, alloc=579.8MB, time=278.29 memory used=38497.1MB, alloc=579.8MB, time=278.73 memory used=38613.0MB, alloc=579.8MB, time=279.17 memory used=38731.3MB, alloc=579.8MB, time=279.61 memory used=38852.1MB, alloc=579.8MB, time=280.04 memory used=38975.2MB, alloc=579.8MB, time=280.48 memory used=39100.7MB, alloc=579.8MB, time=280.94 memory used=39228.8MB, alloc=579.8MB, time=281.36 memory used=39369.7MB, alloc=579.8MB, time=281.82 memory used=39513.2MB, alloc=579.8MB, time=282.26 memory used=39659.2MB, alloc=579.8MB, time=282.69 memory used=39807.7MB, alloc=579.8MB, time=283.12 memory used=39958.6MB, alloc=579.8MB, time=283.55 memory used=40111.8MB, alloc=579.8MB, time=284.02 memory used=40267.3MB, alloc=579.8MB, time=284.49 memory used=40425.3MB, alloc=579.8MB, time=284.93 memory used=40576.0MB, alloc=579.8MB, time=285.33 memory used=40666.7MB, alloc=603.8MB, time=285.67 memory used=40753.6MB, alloc=603.8MB, time=286.00 memory used=40839.3MB, alloc=603.8MB, time=286.33 memory used=40927.6MB, alloc=603.8MB, time=286.66 memory used=41016.4MB, alloc=603.8MB, time=287.00 memory used=41105.9MB, alloc=603.8MB, time=287.35 memory used=41195.8MB, alloc=603.8MB, time=287.73 memory used=41286.3MB, alloc=603.8MB, time=288.05 memory used=41377.3MB, alloc=603.8MB, time=288.39 memory used=41468.9MB, alloc=603.8MB, time=288.74 memory used=41561.4MB, alloc=603.8MB, time=289.10 memory used=41667.0MB, alloc=603.8MB, time=289.46 memory used=41773.4MB, alloc=603.8MB, time=289.83 memory used=41880.5MB, alloc=603.8MB, time=290.20 memory used=41988.2MB, alloc=603.8MB, time=290.58 memory used=42096.4MB, alloc=603.8MB, time=290.92 memory used=42205.3MB, alloc=603.8MB, time=291.28 memory used=42314.7MB, alloc=603.8MB, time=291.64 memory used=42424.7MB, alloc=603.8MB, time=291.99 memory used=42535.3MB, alloc=603.8MB, time=292.35 memory used=42646.3MB, alloc=603.8MB, time=292.70 memory used=42757.9MB, alloc=603.8MB, time=293.04 memory used=42870.0MB, alloc=603.8MB, time=293.39 memory used=42982.6MB, alloc=603.8MB, time=293.74 memory used=43095.6MB, alloc=603.8MB, time=294.07 memory used=43209.1MB, alloc=603.8MB, time=294.42 memory used=43323.0MB, alloc=603.8MB, time=294.76 memory used=43437.4MB, alloc=603.8MB, time=295.10 memory used=43552.5MB, alloc=603.8MB, time=295.45 memory used=43682.2MB, alloc=603.8MB, time=295.82 memory used=43812.3MB, alloc=603.8MB, time=296.18 memory used=43942.9MB, alloc=603.8MB, time=296.55 memory used=44074.0MB, alloc=603.8MB, time=296.90 memory used=44205.5MB, alloc=603.8MB, time=297.26 memory used=44337.4MB, alloc=603.8MB, time=297.62 memory used=44469.8MB, alloc=603.8MB, time=297.97 memory used=44602.5MB, alloc=603.8MB, time=298.33 memory used=44735.5MB, alloc=603.8MB, time=298.69 memory used=44868.9MB, alloc=603.8MB, time=299.04 memory used=45002.7MB, alloc=603.8MB, time=299.40 memory used=45136.7MB, alloc=603.8MB, time=299.77 memory used=45271.3MB, alloc=603.8MB, time=300.15 memory used=45420.8MB, alloc=603.8MB, time=300.53 memory used=45570.6MB, alloc=603.8MB, time=300.90 memory used=45720.7MB, alloc=603.8MB, time=301.27 memory used=45871.1MB, alloc=603.8MB, time=301.63 memory used=46021.7MB, alloc=603.8MB, time=302.00 memory used=46172.4MB, alloc=603.8MB, time=302.37 memory used=46323.4MB, alloc=603.8MB, time=302.77 memory used=46474.4MB, alloc=603.8MB, time=303.17 memory used=46625.6MB, alloc=603.8MB, time=303.56 memory used=46777.1MB, alloc=603.8MB, time=303.97 memory used=46943.6MB, alloc=603.8MB, time=304.38 memory used=47110.1MB, alloc=603.8MB, time=304.79 memory used=47276.6MB, alloc=603.8MB, time=305.21 memory used=47443.1MB, alloc=603.8MB, time=305.61 memory used=47609.5MB, alloc=603.8MB, time=306.00 memory used=47775.8MB, alloc=603.8MB, time=306.40 memory used=47942.2MB, alloc=603.8MB, time=306.81 memory used=48123.2MB, alloc=603.8MB, time=307.23 memory used=48304.0MB, alloc=603.8MB, time=307.64 memory used=48484.5MB, alloc=603.8MB, time=308.06 memory used=48664.7MB, alloc=603.8MB, time=308.47 memory used=48844.4MB, alloc=603.8MB, time=308.88 memory used=49144.0MB, alloc=603.8MB, time=309.50 memory used=49263.4MB, alloc=603.8MB, time=309.88 memory used=49381.4MB, alloc=603.8MB, time=310.27 memory used=49499.3MB, alloc=603.8MB, time=310.65 memory used=49616.9MB, alloc=603.8MB, time=311.03 memory used=49734.3MB, alloc=603.8MB, time=311.41 memory used=49851.3MB, alloc=603.8MB, time=311.79 memory used=49968.1MB, alloc=603.8MB, time=312.15 memory used=50084.4MB, alloc=603.8MB, time=312.51 memory used=50200.6MB, alloc=603.8MB, time=312.87 memory used=50330.8MB, alloc=603.8MB, time=313.25 memory used=50460.4MB, alloc=603.8MB, time=313.62 memory used=50589.6MB, alloc=603.8MB, time=313.99 memory used=50718.2MB, alloc=603.8MB, time=314.36 memory used=50846.4MB, alloc=603.8MB, time=314.72 memory used=50973.9MB, alloc=603.8MB, time=315.08 memory used=51101.0MB, alloc=603.8MB, time=315.45 memory used=51227.4MB, alloc=603.8MB, time=315.81 memory used=51353.3MB, alloc=603.8MB, time=316.19 memory used=51492.3MB, alloc=603.8MB, time=316.56 memory used=51630.6MB, alloc=603.8MB, time=316.94 memory used=51768.0MB, alloc=603.8MB, time=317.32 memory used=51904.5MB, alloc=603.8MB, time=317.70 memory used=52040.3MB, alloc=603.8MB, time=318.06 memory used=52175.1MB, alloc=603.8MB, time=318.45 memory used=52322.3MB, alloc=603.8MB, time=318.83 memory used=52468.3MB, alloc=603.8MB, time=319.21 memory used=52613.1MB, alloc=603.8MB, time=319.59 memory used=52756.6MB, alloc=603.8MB, time=319.96 memory used=52899.1MB, alloc=603.8MB, time=320.34 memory used=53052.8MB, alloc=603.8MB, time=320.73 memory used=53205.0MB, alloc=603.8MB, time=321.12 memory used=53355.5MB, alloc=603.8MB, time=321.50 memory used=53504.3MB, alloc=603.8MB, time=321.89 memory used=53663.7MB, alloc=603.8MB, time=322.29 memory used=53820.8MB, alloc=603.8MB, time=322.70 memory used=53975.9MB, alloc=603.8MB, time=323.09 memory used=54140.3MB, alloc=603.8MB, time=323.49 memory used=54302.1MB, alloc=603.8MB, time=323.88 memory used=54461.4MB, alloc=603.8MB, time=324.28 memory used=54628.8MB, alloc=603.8MB, time=324.69 memory used=54792.9MB, alloc=603.8MB, time=325.11 memory used=54964.2MB, alloc=603.8MB, time=325.53 memory used=55131.8MB, alloc=603.8MB, time=325.97 memory used=55305.2MB, alloc=603.8MB, time=326.40 memory used=55483.7MB, alloc=603.8MB, time=326.82 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428502340 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [20 x y z + 20 z + 12, 12 x y + 2 x + 4 z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 3 2 G := [7 x y z - 12 z - 4 y , 3 x z - 19 y + 8 y] > Problem := [F,G]; 2 2 2 Problem := [[20 x y z + 20 z + 12, 12 x y + 2 x + 4 z ], 2 3 2 3 2 [7 x y z - 12 z - 4 y , 3 x z - 19 y + 8 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=26.0MB, alloc=32.3MB, time=0.55 memory used=45.2MB, alloc=60.3MB, time=0.86 memory used=87.0MB, alloc=60.3MB, time=1.49 memory used=129.6MB, alloc=68.3MB, time=1.97 memory used=176.8MB, alloc=68.3MB, time=2.49 memory used=234.6MB, alloc=68.3MB, time=3.08 memory used=291.8MB, alloc=68.3MB, time=3.66 memory used=334.9MB, alloc=68.3MB, time=4.20 memory used=383.9MB, alloc=68.3MB, time=4.70 memory used=426.0MB, alloc=92.3MB, time=5.33 memory used=492.1MB, alloc=92.3MB, time=6.28 memory used=552.6MB, alloc=92.3MB, time=6.84 memory used=600.2MB, alloc=92.3MB, time=7.30 memory used=629.5MB, alloc=92.3MB, time=7.41 memory used=669.7MB, alloc=92.3MB, time=7.66 memory used=712.0MB, alloc=92.3MB, time=7.95 memory used=787.5MB, alloc=116.3MB, time=8.91 memory used=859.4MB, alloc=116.3MB, time=9.66 memory used=932.5MB, alloc=372.3MB, time=10.52 memory used=1016.4MB, alloc=372.3MB, time=11.77 memory used=1104.9MB, alloc=396.3MB, time=12.93 memory used=1215.1MB, alloc=396.3MB, time=14.48 memory used=1302.5MB, alloc=396.3MB, time=15.35 memory used=1358.3MB, alloc=396.3MB, time=15.71 memory used=1416.1MB, alloc=396.3MB, time=17.09 memory used=1468.5MB, alloc=396.3MB, time=17.59 memory used=1524.6MB, alloc=396.3MB, time=17.89 memory used=1599.4MB, alloc=420.3MB, time=18.86 memory used=1684.4MB, alloc=420.3MB, time=19.33 memory used=1776.3MB, alloc=420.3MB, time=19.70 memory used=1836.4MB, alloc=420.3MB, time=19.94 memory used=1903.5MB, alloc=420.3MB, time=20.18 memory used=2000.0MB, alloc=420.3MB, time=20.67 memory used=2059.8MB, alloc=420.3MB, time=20.93 memory used=2129.3MB, alloc=420.3MB, time=21.18 memory used=2225.8MB, alloc=420.3MB, time=23.76 memory used=2294.4MB, alloc=420.3MB, time=24.01 memory used=2351.3MB, alloc=420.3MB, time=24.22 memory used=2450.8MB, alloc=420.3MB, time=24.74 memory used=2509.1MB, alloc=420.3MB, time=24.99 memory used=2578.2MB, alloc=420.3MB, time=25.23 memory used=2671.9MB, alloc=420.3MB, time=25.72 memory used=2734.3MB, alloc=420.3MB, time=25.97 memory used=2804.8MB, alloc=420.3MB, time=26.22 memory used=2899.6MB, alloc=420.3MB, time=29.13 memory used=2968.5MB, alloc=420.3MB, time=29.44 memory used=3025.2MB, alloc=420.3MB, time=29.67 memory used=3136.0MB, alloc=420.3MB, time=30.93 memory used=3229.0MB, alloc=420.3MB, time=31.33 memory used=3302.9MB, alloc=420.3MB, time=31.68 memory used=3353.8MB, alloc=420.3MB, time=31.96 memory used=3407.3MB, alloc=420.3MB, time=32.25 memory used=3465.5MB, alloc=420.3MB, time=32.55 memory used=3528.1MB, alloc=420.3MB, time=32.85 memory used=3597.3MB, alloc=420.3MB, time=33.15 memory used=3671.6MB, alloc=420.3MB, time=33.43 memory used=3741.0MB, alloc=420.3MB, time=33.72 memory used=3805.7MB, alloc=420.3MB, time=33.98 memory used=3852.6MB, alloc=420.3MB, time=34.22 memory used=3899.6MB, alloc=420.3MB, time=34.46 memory used=3949.0MB, alloc=420.3MB, time=34.70 memory used=4000.8MB, alloc=420.3MB, time=34.95 memory used=4056.5MB, alloc=420.3MB, time=35.20 memory used=4117.1MB, alloc=420.3MB, time=35.43 memory used=4186.5MB, alloc=420.3MB, time=35.66 memory used=4293.8MB, alloc=420.3MB, time=38.87 memory used=4384.4MB, alloc=420.3MB, time=39.27 memory used=4448.2MB, alloc=420.3MB, time=39.59 memory used=4501.6MB, alloc=420.3MB, time=39.87 memory used=4552.3MB, alloc=444.3MB, time=40.17 memory used=4621.6MB, alloc=444.3MB, time=40.48 memory used=4698.1MB, alloc=444.3MB, time=40.80 memory used=4782.0MB, alloc=444.3MB, time=41.14 memory used=4870.4MB, alloc=444.3MB, time=41.44 memory used=4966.4MB, alloc=444.3MB, time=41.75 memory used=5057.9MB, alloc=444.3MB, time=42.05 memory used=5126.7MB, alloc=444.3MB, time=42.32 memory used=5187.6MB, alloc=444.3MB, time=42.58 memory used=5245.7MB, alloc=444.3MB, time=42.82 memory used=5300.9MB, alloc=444.3MB, time=43.07 memory used=5358.1MB, alloc=444.3MB, time=43.33 memory used=5416.9MB, alloc=444.3MB, time=43.60 memory used=5480.5MB, alloc=444.3MB, time=43.84 memory used=5544.8MB, alloc=444.3MB, time=44.10 memory used=5609.7MB, alloc=444.3MB, time=44.35 memory used=5675.5MB, alloc=444.3MB, time=44.61 memory used=5745.8MB, alloc=444.3MB, time=44.85 memory used=5816.8MB, alloc=444.3MB, time=45.12 memory used=5892.6MB, alloc=444.3MB, time=45.41 memory used=5968.7MB, alloc=444.3MB, time=45.70 memory used=6045.4MB, alloc=444.3MB, time=45.97 memory used=6126.5MB, alloc=444.3MB, time=46.25 memory used=6207.9MB, alloc=444.3MB, time=46.55 memory used=6293.8MB, alloc=444.3MB, time=46.85 memory used=6384.0MB, alloc=444.3MB, time=47.14 memory used=6469.6MB, alloc=444.3MB, time=47.44 memory used=6555.4MB, alloc=444.3MB, time=47.72 memory used=6643.6MB, alloc=444.3MB, time=48.01 memory used=6732.1MB, alloc=444.3MB, time=48.28 memory used=6822.3MB, alloc=444.3MB, time=48.54 memory used=6895.2MB, alloc=444.3MB, time=48.80 memory used=6953.6MB, alloc=444.3MB, time=49.01 memory used=7005.6MB, alloc=444.3MB, time=49.23 memory used=7057.1MB, alloc=444.3MB, time=49.43 memory used=7109.6MB, alloc=444.3MB, time=49.64 memory used=7165.1MB, alloc=444.3MB, time=49.86 memory used=7220.0MB, alloc=444.3MB, time=50.07 memory used=7277.6MB, alloc=444.3MB, time=50.29 memory used=7334.3MB, alloc=444.3MB, time=50.50 memory used=7393.4MB, alloc=444.3MB, time=50.71 memory used=7454.7MB, alloc=444.3MB, time=50.92 memory used=7517.8MB, alloc=444.3MB, time=51.14 memory used=7582.2MB, alloc=444.3MB, time=51.35 memory used=7647.4MB, alloc=444.3MB, time=51.56 memory used=7713.1MB, alloc=444.3MB, time=51.79 memory used=7781.4MB, alloc=444.3MB, time=52.00 memory used=7851.6MB, alloc=444.3MB, time=52.22 memory used=7925.9MB, alloc=444.3MB, time=52.43 memory used=8004.5MB, alloc=444.3MB, time=52.65 memory used=8088.0MB, alloc=444.3MB, time=52.86 memory used=8438.1MB, alloc=444.3MB, time=77.88 memory used=8668.7MB, alloc=444.3MB, time=78.26 memory used=8965.5MB, alloc=444.3MB, time=81.02 memory used=9131.0MB, alloc=444.3MB, time=82.70 memory used=9240.0MB, alloc=444.3MB, time=83.65 memory used=9377.6MB, alloc=444.3MB, time=84.70 memory used=9544.9MB, alloc=444.3MB, time=86.37 memory used=9654.0MB, alloc=444.3MB, time=87.39 memory used=9768.3MB, alloc=444.3MB, time=88.10 memory used=9843.0MB, alloc=444.3MB, time=88.51 memory used=9924.0MB, alloc=444.3MB, time=88.84 memory used=10032.5MB, alloc=444.3MB, time=89.39 memory used=10103.8MB, alloc=444.3MB, time=89.69 memory used=10181.4MB, alloc=444.3MB, time=89.97 memory used=10293.0MB, alloc=444.3MB, time=92.86 memory used=10365.2MB, alloc=444.3MB, time=93.25 memory used=10479.2MB, alloc=444.3MB, time=94.00 memory used=10550.7MB, alloc=444.3MB, time=94.37 memory used=10627.4MB, alloc=444.3MB, time=94.67 memory used=10737.2MB, alloc=444.3MB, time=95.25 memory used=10812.9MB, alloc=444.3MB, time=95.57 memory used=10907.8MB, alloc=444.3MB, time=98.21 memory used=11006.5MB, alloc=444.3MB, time=98.64 memory used=11076.9MB, alloc=444.3MB, time=98.94 memory used=11212.7MB, alloc=444.3MB, time=100.19 memory used=11317.3MB, alloc=444.3MB, time=100.62 memory used=11380.9MB, alloc=444.3MB, time=100.93 memory used=11443.5MB, alloc=444.3MB, time=101.28 memory used=11513.6MB, alloc=444.3MB, time=101.63 memory used=11591.2MB, alloc=444.3MB, time=101.95 memory used=11676.5MB, alloc=444.3MB, time=102.28 memory used=11761.4MB, alloc=444.3MB, time=102.62 memory used=11839.4MB, alloc=444.3MB, time=102.93 memory used=11894.5MB, alloc=444.3MB, time=103.19 memory used=11950.8MB, alloc=444.3MB, time=103.46 memory used=12011.5MB, alloc=444.3MB, time=103.75 memory used=12076.2MB, alloc=444.3MB, time=104.02 memory used=12147.0MB, alloc=444.3MB, time=104.29 memory used=12226.1MB, alloc=444.3MB, time=104.58 memory used=12348.0MB, alloc=444.3MB, time=107.32 memory used=12456.7MB, alloc=444.3MB, time=107.77 memory used=12527.1MB, alloc=444.3MB, time=108.12 memory used=12590.3MB, alloc=444.3MB, time=108.45 memory used=12654.1MB, alloc=444.3MB, time=108.77 memory used=12722.9MB, alloc=444.3MB, time=109.09 memory used=12798.9MB, alloc=444.3MB, time=109.43 memory used=12878.9MB, alloc=444.3MB, time=109.78 memory used=12965.9MB, alloc=444.3MB, time=110.13 memory used=13055.4MB, alloc=444.3MB, time=110.49 memory used=13131.4MB, alloc=444.3MB, time=110.81 memory used=13193.6MB, alloc=444.3MB, time=111.12 memory used=13250.2MB, alloc=444.3MB, time=111.41 memory used=13303.2MB, alloc=444.3MB, time=111.70 memory used=13355.4MB, alloc=444.3MB, time=111.97 memory used=13409.6MB, alloc=444.3MB, time=112.26 memory used=13464.6MB, alloc=444.3MB, time=112.54 memory used=13520.5MB, alloc=444.3MB, time=112.81 memory used=13581.1MB, alloc=444.3MB, time=113.10 memory used=13642.2MB, alloc=444.3MB, time=113.37 memory used=13703.8MB, alloc=444.3MB, time=113.66 memory used=13766.2MB, alloc=444.3MB, time=113.95 memory used=13833.3MB, alloc=444.3MB, time=114.25 memory used=13900.9MB, alloc=444.3MB, time=114.53 memory used=13969.0MB, alloc=444.3MB, time=114.80 memory used=14041.8MB, alloc=444.3MB, time=115.08 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memory used=15419.7MB, alloc=444.3MB, time=120.49 memory used=15473.1MB, alloc=444.3MB, time=120.72 memory used=15528.5MB, alloc=444.3MB, time=120.96 memory used=15586.6MB, alloc=444.3MB, time=121.18 memory used=15646.5MB, alloc=444.3MB, time=121.41 memory used=15708.0MB, alloc=444.3MB, time=121.65 memory used=15770.5MB, alloc=444.3MB, time=121.88 memory used=15833.7MB, alloc=444.3MB, time=122.12 memory used=15899.7MB, alloc=444.3MB, time=122.35 memory used=15967.6MB, alloc=444.3MB, time=122.59 memory used=16038.2MB, alloc=444.3MB, time=122.83 memory used=16111.7MB, alloc=444.3MB, time=123.08 memory used=16190.2MB, alloc=444.3MB, time=123.33 memory used=16325.9MB, alloc=444.3MB, time=136.03 memory used=16601.3MB, alloc=444.3MB, time=149.31 memory used=16829.3MB, alloc=444.3MB, time=149.71 memory used=17079.4MB, alloc=444.3MB, time=151.65 memory used=17198.5MB, alloc=444.3MB, time=152.78 memory used=17344.5MB, alloc=444.3MB, time=154.56 memory used=17452.5MB, alloc=444.3MB, time=156.04 memory used=17558.4MB, alloc=444.3MB, time=157.50 memory used=17698.6MB, alloc=468.3MB, time=159.64 memory used=17799.2MB, alloc=468.3MB, time=161.14 memory used=17926.7MB, alloc=468.3MB, time=162.25 memory used=18015.6MB, alloc=468.3MB, time=162.75 memory used=18098.3MB, alloc=468.3MB, time=163.24 memory used=18190.7MB, alloc=468.3MB, time=163.89 memory used=18276.6MB, alloc=468.3MB, time=164.33 memory used=18362.6MB, alloc=468.3MB, time=164.80 memory used=18450.9MB, alloc=468.3MB, time=165.25 memory used=18535.3MB, alloc=468.3MB, time=165.64 memory used=18622.7MB, alloc=468.3MB, time=166.10 memory used=18697.7MB, alloc=468.3MB, time=166.48 memory used=18805.0MB, alloc=468.3MB, time=168.56 memory used=18877.7MB, alloc=468.3MB, time=168.91 memory used=18959.2MB, alloc=468.3MB, time=169.24 memory used=19024.8MB, alloc=468.3MB, time=169.53 memory used=19089.2MB, alloc=468.3MB, time=169.82 memory used=19165.7MB, alloc=468.3MB, time=170.11 memory used=19281.4MB, alloc=468.3MB, time=171.14 memory used=19354.6MB, alloc=468.3MB, time=171.51 memory used=19434.3MB, alloc=468.3MB, time=171.84 memory used=19495.8MB, alloc=468.3MB, time=172.13 memory used=19606.0MB, alloc=468.3MB, time=172.78 memory used=19678.8MB, alloc=492.3MB, time=173.18 memory used=19780.9MB, alloc=492.3MB, time=173.65 memory used=19867.8MB, alloc=492.3MB, time=174.06 memory used=19941.3MB, alloc=492.3MB, time=174.43 memory used=20026.3MB, alloc=492.3MB, time=174.83 memory used=20123.6MB, alloc=492.3MB, time=175.20 memory used=20234.4MB, alloc=492.3MB, time=175.59 memory used=20314.8MB, alloc=492.3MB, time=175.94 memory used=20384.6MB, alloc=492.3MB, time=176.25 memory used=20515.2MB, alloc=492.3MB, time=179.75 memory used=20596.1MB, alloc=492.3MB, time=180.20 memory used=20687.8MB, alloc=492.3MB, time=180.66 memory used=20799.3MB, alloc=492.3MB, time=181.07 memory used=20881.9MB, alloc=492.3MB, time=181.45 memory used=20948.8MB, alloc=516.3MB, time=181.82 memory used=21029.9MB, alloc=516.3MB, time=182.19 memory used=21120.1MB, alloc=516.3MB, time=182.58 memory used=21215.5MB, alloc=516.3MB, time=182.99 memory used=21315.8MB, alloc=516.3MB, time=183.37 memory used=21427.3MB, alloc=516.3MB, time=183.79 memory used=21543.6MB, alloc=516.3MB, time=184.20 memory used=21664.6MB, alloc=516.3MB, time=184.62 memory used=21790.9MB, alloc=516.3MB, time=185.04 memory used=21914.0MB, alloc=516.3MB, time=185.42 memory used=22003.4MB, alloc=516.3MB, time=185.75 memory used=22077.7MB, alloc=516.3MB, time=186.07 memory used=22150.3MB, alloc=516.3MB, time=186.39 memory used=22223.0MB, alloc=516.3MB, time=186.70 memory used=22297.0MB, alloc=516.3MB, time=187.01 memory used=22371.9MB, alloc=516.3MB, time=187.32 memory used=22447.7MB, alloc=516.3MB, time=187.62 memory used=22524.4MB, alloc=516.3MB, time=187.93 memory used=22601.8MB, alloc=516.3MB, time=188.24 memory used=22680.2MB, alloc=516.3MB, time=188.55 memory used=22760.0MB, alloc=516.3MB, time=188.85 memory used=22848.2MB, alloc=516.3MB, time=189.17 memory used=22937.8MB, alloc=516.3MB, time=189.48 memory used=23028.3MB, alloc=516.3MB, time=189.80 memory used=23119.5MB, alloc=516.3MB, time=190.14 memory used=23211.4MB, alloc=516.3MB, time=190.48 memory used=23304.0MB, alloc=516.3MB, time=190.80 memory used=23397.6MB, alloc=516.3MB, time=191.15 memory used=23500.9MB, alloc=516.3MB, time=191.50 memory used=23605.0MB, alloc=516.3MB, time=191.87 memory used=23709.6MB, alloc=516.3MB, time=192.22 memory used=23814.8MB, alloc=516.3MB, time=192.57 memory used=23920.5MB, alloc=516.3MB, time=192.95 memory used=24027.7MB, alloc=516.3MB, time=193.31 memory used=24143.1MB, alloc=516.3MB, time=193.67 memory used=24259.7MB, alloc=516.3MB, time=194.03 memory used=24376.6MB, alloc=516.3MB, time=194.39 memory used=24494.0MB, alloc=516.3MB, time=194.74 memory used=24621.1MB, alloc=516.3MB, time=195.11 memory used=24756.1MB, alloc=516.3MB, time=195.50 memory used=24915.7MB, alloc=516.3MB, time=195.92 memory used=25082.6MB, alloc=516.3MB, time=196.33 memory used=25319.9MB, alloc=516.3MB, time=196.82 memory used=25433.7MB, alloc=516.3MB, time=197.19 memory used=25549.2MB, alloc=516.3MB, time=197.56 memory used=25673.6MB, alloc=516.3MB, time=197.93 memory used=25797.2MB, alloc=516.3MB, time=198.30 memory used=25920.2MB, alloc=516.3MB, time=198.67 memory used=26051.4MB, alloc=516.3MB, time=199.04 memory used=26181.6MB, alloc=516.3MB, time=199.42 memory used=26311.5MB, alloc=516.3MB, time=199.79 memory used=26447.0MB, alloc=516.3MB, time=200.18 memory used=26590.5MB, alloc=516.3MB, time=200.56 memory used=26732.0MB, alloc=516.3MB, time=200.94 memory used=26879.7MB, alloc=516.3MB, time=201.33 memory used=27032.9MB, alloc=516.3MB, time=201.72 memory used=27184.4MB, alloc=516.3MB, time=202.11 memory used=27344.6MB, alloc=516.3MB, time=202.50 memory used=27509.3MB, alloc=516.3MB, time=202.90 memory used=27675.8MB, alloc=516.3MB, time=203.30 memory used=27849.3MB, alloc=516.3MB, time=203.69 memory used=28027.7MB, alloc=516.3MB, time=204.10 memory used=28213.5MB, alloc=516.3MB, time=204.51 memory used=28409.0MB, alloc=516.3MB, time=204.91 memory used=28618.1MB, alloc=516.3MB, time=205.33 memory used=28925.8MB, alloc=516.3MB, time=338.61 memory used=29150.6MB, alloc=516.3MB, time=344.24 memory used=29300.2MB, alloc=516.3MB, time=345.24 memory used=29402.4MB, alloc=516.3MB, time=345.68 memory used=29499.5MB, alloc=516.3MB, time=346.12 memory used=29615.2MB, alloc=516.3MB, time=346.56 memory used=29741.2MB, alloc=516.3MB, time=347.00 memory used=29823.4MB, alloc=516.3MB, time=347.36 memory used=29903.5MB, alloc=516.3MB, time=347.71 memory used=29987.9MB, alloc=516.3MB, time=348.05 memory used=30075.8MB, alloc=516.3MB, time=348.37 memory used=30170.6MB, alloc=516.3MB, time=348.71 memory used=30272.4MB, alloc=516.3MB, time=349.04 memory used=30377.5MB, alloc=516.3MB, time=349.38 memory used=30489.7MB, alloc=516.3MB, time=349.71 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428502640 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 3 4 F := [-5 z - 17 x y - 3 x z, -8 x y + 2 x z - 13 y ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 4 3 2 G := [15 z + 19 y z - 12, -6 x - 7 x z - z ] > Problem := [F,G]; 3 3 3 4 Problem := [[-5 z - 17 x y - 3 x z, -8 x y + 2 x z - 13 y ], 3 4 3 2 [15 z + 19 y z - 12, -6 x - 7 x z - z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=25.3MB, alloc=32.3MB, time=0.49 memory used=42.3MB, alloc=56.3MB, time=1.00 memory used=75.3MB, alloc=56.3MB, time=7.09 memory used=98.0MB, alloc=80.3MB, time=16.36 memory used=169.5MB, alloc=80.3MB, time=21.02 memory used=245.1MB, alloc=80.5MB, time=21.34 memory used=282.2MB, alloc=80.5MB, time=21.42 memory used=332.1MB, alloc=80.5MB, time=21.53 memory used=334.6MB, alloc=81.9MB, time=21.55 memory used=350.3MB, alloc=107.8MB, time=21.63 memory used=403.2MB, alloc=107.8MB, time=22.93 memory used=441.3MB, alloc=107.8MB, time=23.26 memory used=467.6MB, alloc=107.8MB, time=23.36 memory used=497.9MB, alloc=107.8MB, time=23.45 memory used=529.7MB, alloc=107.8MB, time=23.55 memory used=563.0MB, alloc=107.8MB, time=23.64 memory used=597.7MB, alloc=107.8MB, time=23.75 memory used=638.1MB, alloc=107.8MB, time=23.85 memory used=680.0MB, alloc=107.8MB, time=23.96 memory used=723.1MB, alloc=107.8MB, time=24.08 memory used=765.0MB, alloc=107.8MB, time=24.19 memory used=793.7MB, alloc=107.8MB, time=24.27 memory used=816.2MB, alloc=107.8MB, time=24.33 memory used=839.4MB, alloc=131.8MB, time=24.41 memory used=873.5MB, alloc=131.8MB, time=24.50 memory used=910.0MB, alloc=131.8MB, time=24.59 memory used=946.9MB, alloc=131.8MB, time=24.68 memory used=984.4MB, alloc=131.8MB, time=24.78 memory used=1027.4MB, alloc=131.8MB, time=24.88 memory used=1070.8MB, alloc=131.8MB, time=24.98 memory used=1114.5MB, alloc=131.8MB, time=25.08 memory used=1163.8MB, alloc=131.8MB, time=25.20 memory used=1213.1MB, alloc=131.8MB, time=25.30 memory used=1262.5MB, alloc=131.8MB, time=25.41 memory used=1317.0MB, alloc=131.8MB, time=25.53 memory used=1371.4MB, alloc=131.8MB, time=25.64 memory used=1430.5MB, alloc=131.8MB, time=25.76 memory used=1488.8MB, alloc=131.8MB, time=25.87 memory used=1551.3MB, alloc=131.8MB, time=25.99 memory used=1617.2MB, alloc=131.8MB, time=26.11 memory used=1688.7MB, alloc=131.8MB, time=26.25 memory used=1697.2MB, alloc=131.8MB, time=26.28 memory used=1704.4MB, alloc=131.8MB, time=26.34 memory used=1712.7MB, alloc=131.8MB, time=26.39 memory used=1721.3MB, alloc=131.8MB, time=26.43 memory used=1729.8MB, alloc=131.8MB, time=26.49 memory used=1738.2MB, alloc=131.8MB, time=26.54 memory used=1746.5MB, alloc=131.8MB, time=26.60 memory used=1754.7MB, alloc=131.8MB, time=26.66 memory used=1762.9MB, alloc=131.8MB, time=26.72 memory used=1771.0MB, alloc=131.8MB, time=26.77 memory used=1779.0MB, alloc=131.8MB, time=26.83 memory used=1787.1MB, alloc=131.8MB, time=26.88 memory used=1798.7MB, alloc=131.8MB, time=26.95 memory used=1810.2MB, alloc=131.8MB, time=27.00 memory used=1821.6MB, alloc=131.8MB, time=27.06 memory used=1832.7MB, alloc=131.8MB, time=27.12 memory used=1843.7MB, alloc=131.8MB, time=27.18 memory used=1854.4MB, alloc=131.8MB, time=27.24 memory used=1864.9MB, alloc=131.8MB, time=27.29 memory used=1875.2MB, alloc=131.8MB, time=27.34 memory used=1885.6MB, alloc=131.8MB, time=27.39 memory used=1898.4MB, alloc=131.8MB, time=27.45 memory used=1911.1MB, alloc=131.8MB, time=27.51 memory used=1923.3MB, alloc=131.8MB, time=27.56 memory used=1935.2MB, alloc=131.8MB, time=27.61 memory used=1949.3MB, alloc=131.8MB, time=27.67 memory used=1962.8MB, alloc=131.8MB, time=27.72 memory used=1977.9MB, alloc=131.8MB, time=27.77 memory used=1992.0MB, alloc=131.8MB, time=27.82 memory used=2006.9MB, alloc=131.8MB, time=27.87 memory used=2024.0MB, alloc=131.8MB, time=27.92 memory used=2040.3MB, alloc=131.8MB, time=27.98 memory used=2060.4MB, alloc=131.8MB, time=28.03 memory used=2082.9MB, alloc=131.8MB, time=28.09 memory used=2124.9MB, alloc=131.8MB, time=29.49 memory used=2174.6MB, alloc=131.8MB, time=36.40 memory used=2179.7MB, alloc=131.8MB, time=36.45 memory used=2180.5MB, alloc=387.8MB, time=36.48 memory used=2451.6MB, alloc=387.8MB, time=197.14 memory used=2674.3MB, alloc=387.8MB, time=381.93 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428502940 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 F := [17 x y z - 18 y z - 6 x, 3 x y z + 18 y z - 7 x y] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 4 2 G := [15 x y z - 2 y z - 18 x y, -4 x - 7 x z + 17 z ] > Problem := [F,G]; 2 2 2 2 2 Problem := [[17 x y z - 18 y z - 6 x, 3 x y z + 18 y z - 7 x y], 2 2 2 2 4 2 [15 x y z - 2 y z - 18 x y, -4 x - 7 x z + 17 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=27.0MB, alloc=32.3MB, time=0.51 memory used=47.3MB, alloc=60.3MB, time=0.83 memory used=89.6MB, alloc=60.3MB, time=1.44 memory used=132.5MB, alloc=68.3MB, time=2.06 memory used=174.0MB, alloc=68.3MB, time=2.63 memory used=214.5MB, alloc=92.3MB, time=3.25 memory used=276.9MB, alloc=92.3MB, time=4.17 memory used=338.8MB, alloc=116.3MB, time=5.12 memory used=418.9MB, alloc=372.3MB, time=6.38 memory used=504.7MB, alloc=372.3MB, time=7.61 memory used=589.6MB, alloc=396.3MB, time=8.74 memory used=699.2MB, alloc=396.3MB, time=10.36 memory used=807.8MB, alloc=420.3MB, time=12.11 memory used=940.6MB, alloc=420.3MB, time=14.18 memory used=1069.0MB, alloc=444.3MB, time=16.25 memory used=1218.6MB, alloc=444.3MB, time=18.69 memory used=1366.5MB, alloc=468.3MB, time=21.08 memory used=1522.5MB, alloc=492.3MB, time=23.67 memory used=1711.8MB, alloc=516.3MB, time=26.56 memory used=1861.5MB, alloc=540.3MB, time=29.19 memory used=2135.4MB, alloc=540.3MB, time=31.91 memory used=2356.5MB, alloc=564.3MB, time=35.37 memory used=2536.3MB, alloc=588.3MB, time=38.77 memory used=2742.7MB, alloc=612.3MB, time=42.43 memory used=3073.4MB, alloc=612.3MB, time=45.81 memory used=3374.5MB, alloc=636.3MB, time=49.70 memory used=3722.0MB, alloc=636.3MB, time=53.63 memory used=3980.2MB, alloc=660.3MB, time=57.16 memory used=4210.9MB, alloc=684.3MB, time=60.62 memory used=4427.4MB, alloc=684.3MB, time=64.10 memory used=4675.8MB, alloc=708.3MB, time=67.62 memory used=4849.4MB, alloc=708.3MB, time=70.78 memory used=5018.1MB, alloc=732.3MB, time=74.16 memory used=5174.1MB, alloc=732.3MB, time=77.20 memory used=5331.9MB, alloc=756.3MB, time=80.27 memory used=5485.4MB, alloc=780.3MB, time=83.44 memory used=5620.4MB, alloc=780.3MB, time=86.20 memory used=5763.2MB, alloc=804.3MB, time=89.23 memory used=5894.4MB, alloc=804.3MB, time=92.04 memory used=6010.3MB, alloc=828.3MB, time=94.53 memory used=6132.1MB, alloc=852.3MB, time=97.21 memory used=6248.1MB, alloc=852.3MB, time=99.79 memory used=6367.6MB, alloc=876.3MB, time=102.41 memory used=6486.5MB, alloc=876.3MB, time=105.09 memory used=6609.9MB, alloc=900.3MB, time=107.70 memory used=6719.1MB, alloc=900.3MB, time=109.87 memory used=6827.0MB, alloc=900.3MB, time=112.15 memory used=6943.3MB, alloc=924.3MB, time=114.69 memory used=7059.0MB, alloc=924.3MB, time=117.24 memory used=7165.8MB, alloc=948.3MB, time=119.66 memory used=7238.6MB, alloc=948.3MB, time=121.53 memory used=7347.2MB, alloc=948.3MB, time=123.76 memory used=7447.9MB, alloc=972.3MB, time=125.96 memory used=7533.4MB, alloc=972.3MB, time=128.13 memory used=7608.7MB, alloc=972.3MB, time=130.13 memory used=7650.4MB, alloc=996.3MB, time=131.78 memory used=7775.0MB, alloc=996.3MB, time=134.01 memory used=8322.1MB, alloc=1020.3MB, time=142.03 memory used=8769.5MB, alloc=1044.3MB, time=157.95 memory used=9194.0MB, alloc=1068.3MB, time=176.14 memory used=9620.7MB, alloc=1092.3MB, time=193.79 memory used=10052.9MB, alloc=1116.3MB, time=212.31 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428503240 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 4 3 2 F := [-18 y z - 17 y + 5 x z, 6 x - 16 x y + 4 y z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 2 G := [3 x y z - 14 x y + 8 x y, 16 x y z - 10 x y + 6 y z ] > Problem := [F,G]; 3 3 4 3 2 Problem := [[-18 y z - 17 y + 5 x z, 6 x - 16 x y + 4 y z ], 2 2 2 3 2 2 [3 x y z - 14 x y + 8 x y, 16 x y z - 10 x y + 6 y z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=24.3MB, alloc=32.3MB, time=0.48 memory used=43.8MB, alloc=56.3MB, time=0.77 memory used=86.5MB, alloc=60.3MB, time=1.20 memory used=136.9MB, alloc=68.7MB, time=1.74 memory used=182.8MB, alloc=68.7MB, time=2.15 memory used=226.9MB, alloc=68.7MB, time=2.76 memory used=269.3MB, alloc=68.7MB, time=3.19 memory used=311.6MB, alloc=68.7MB, time=3.65 memory used=355.5MB, alloc=92.7MB, time=4.22 memory used=416.4MB, alloc=92.7MB, time=5.05 memory used=478.8MB, alloc=348.7MB, time=5.82 memory used=540.1MB, alloc=348.7MB, time=6.57 memory used=591.7MB, alloc=372.7MB, time=7.06 memory used=660.3MB, alloc=372.7MB, time=7.39 memory used=705.6MB, alloc=372.7MB, time=7.56 memory used=778.2MB, alloc=372.7MB, time=7.89 memory used=822.7MB, alloc=372.7MB, time=8.05 memory used=912.0MB, alloc=372.7MB, time=10.79 memory used=957.9MB, alloc=372.7MB, time=10.95 memory used=1000.5MB, alloc=372.7MB, time=11.09 memory used=1063.0MB, alloc=372.7MB, time=11.46 memory used=1119.2MB, alloc=372.7MB, time=11.66 memory used=1180.4MB, alloc=372.7MB, time=11.99 memory used=1235.0MB, alloc=372.7MB, time=12.17 memory used=1311.0MB, alloc=372.7MB, time=14.82 memory used=1368.6MB, alloc=372.7MB, time=15.05 memory used=1416.8MB, alloc=372.7MB, time=15.21 memory used=1473.7MB, alloc=372.7MB, time=15.72 memory used=1543.0MB, alloc=372.7MB, time=15.98 memory used=1590.8MB, alloc=372.7MB, time=16.17 memory used=1629.2MB, alloc=372.7MB, time=16.35 memory used=1672.6MB, alloc=372.7MB, time=16.55 memory used=1722.0MB, alloc=372.7MB, time=16.74 memory used=1775.5MB, alloc=372.7MB, time=16.92 memory used=1824.0MB, alloc=372.7MB, time=17.09 memory used=1858.4MB, alloc=372.7MB, time=17.22 memory used=1896.2MB, alloc=372.7MB, time=17.35 memory used=1946.1MB, alloc=372.7MB, time=17.60 memory used=1991.9MB, alloc=372.7MB, time=17.83 memory used=2064.1MB, alloc=372.7MB, time=18.41 memory used=2127.8MB, alloc=372.7MB, time=18.63 memory used=2164.8MB, alloc=372.7MB, time=18.81 memory used=2205.3MB, alloc=372.7MB, time=18.99 memory used=2250.5MB, alloc=372.7MB, time=19.17 memory used=2302.6MB, alloc=372.7MB, time=19.34 memory used=2355.3MB, alloc=372.7MB, time=19.52 memory used=2395.7MB, alloc=372.7MB, time=19.68 memory used=2431.3MB, alloc=372.7MB, time=19.83 memory used=2470.6MB, alloc=372.7MB, time=19.96 memory used=2521.0MB, alloc=372.7MB, time=20.21 memory used=2577.2MB, alloc=372.7MB, time=22.80 memory used=2672.5MB, alloc=372.7MB, time=28.35 memory used=2721.8MB, alloc=372.7MB, time=28.55 memory used=2773.2MB, alloc=372.7MB, time=28.71 memory used=2815.0MB, alloc=372.7MB, time=28.85 memory used=2854.3MB, alloc=372.7MB, time=28.97 memory used=2900.8MB, alloc=372.7MB, time=29.12 memory used=2969.8MB, alloc=372.7MB, time=29.47 memory used=3019.1MB, alloc=372.7MB, time=29.65 memory used=3062.3MB, alloc=372.7MB, time=29.84 memory used=3109.6MB, alloc=372.7MB, time=29.98 memory used=3190.1MB, alloc=372.7MB, time=32.79 memory used=3236.4MB, alloc=372.7MB, time=32.95 memory used=3277.4MB, alloc=372.7MB, time=33.10 memory used=3376.2MB, alloc=372.7MB, time=34.02 memory used=3451.5MB, alloc=372.7MB, time=37.26 memory used=3497.4MB, alloc=372.7MB, time=37.47 memory used=3537.0MB, alloc=372.7MB, time=37.62 memory used=3584.0MB, alloc=372.7MB, time=37.85 memory used=3690.2MB, alloc=372.7MB, time=38.90 memory used=3758.2MB, alloc=372.7MB, time=40.10 memory used=3800.2MB, alloc=372.7MB, time=40.26 memory used=3900.0MB, alloc=372.7MB, time=41.05 memory used=3992.8MB, alloc=372.7MB, time=42.08 memory used=4049.0MB, alloc=372.7MB, time=42.40 memory used=4094.3MB, alloc=372.7MB, time=42.58 memory used=4142.4MB, alloc=372.7MB, time=42.84 memory used=4198.6MB, alloc=372.7MB, time=43.07 memory used=4234.6MB, alloc=372.7MB, time=43.30 memory used=4316.2MB, alloc=372.7MB, time=46.28 memory used=4354.0MB, alloc=372.7MB, time=46.49 memory used=4394.1MB, alloc=372.7MB, time=46.67 memory used=4439.3MB, alloc=372.7MB, time=46.96 memory used=4493.2MB, alloc=372.7MB, time=47.17 memory used=4528.8MB, alloc=372.7MB, time=47.33 memory used=4594.7MB, alloc=372.7MB, time=47.71 memory used=4635.8MB, alloc=372.7MB, time=47.89 memory used=4690.6MB, alloc=372.7MB, time=49.45 memory used=4763.6MB, alloc=372.7MB, time=50.81 memory used=4803.0MB, alloc=372.7MB, time=50.97 memory used=4839.6MB, alloc=372.7MB, time=51.11 memory used=4896.6MB, alloc=372.7MB, time=51.62 memory used=4953.4MB, alloc=396.7MB, time=51.85 memory used=5011.0MB, alloc=396.7MB, time=52.07 memory used=5060.0MB, alloc=396.7MB, time=52.25 memory used=5117.6MB, alloc=396.7MB, time=52.45 memory used=5181.9MB, alloc=396.7MB, time=52.71 memory used=5240.6MB, alloc=396.7MB, time=52.93 memory used=5283.3MB, alloc=396.7MB, time=53.16 memory used=5332.5MB, alloc=396.7MB, time=53.35 memory used=5418.4MB, alloc=396.7MB, time=53.92 memory used=5490.2MB, alloc=396.7MB, time=54.19 memory used=5537.0MB, alloc=396.7MB, time=54.41 memory used=5590.9MB, alloc=396.7MB, time=54.63 memory used=5653.5MB, alloc=396.7MB, time=54.85 memory used=5717.7MB, alloc=396.7MB, time=55.06 memory used=5763.2MB, alloc=396.7MB, time=55.25 memory used=5809.8MB, alloc=396.7MB, time=55.44 memory used=5888.5MB, alloc=396.7MB, time=62.62 memory used=5991.9MB, alloc=396.7MB, time=63.68 memory used=6047.0MB, alloc=396.7MB, time=63.88 memory used=6103.4MB, alloc=396.7MB, time=64.06 memory used=6151.8MB, alloc=396.7MB, time=64.24 memory used=6214.7MB, alloc=396.7MB, time=64.51 memory used=6297.7MB, alloc=396.7MB, time=64.97 memory used=6358.6MB, alloc=396.7MB, time=65.20 memory used=6416.5MB, alloc=396.7MB, time=65.41 memory used=6502.0MB, alloc=396.7MB, time=68.01 memory used=6567.2MB, alloc=396.7MB, time=68.23 memory used=6621.1MB, alloc=396.7MB, time=68.41 memory used=6742.1MB, alloc=396.7MB, time=71.47 memory used=6801.0MB, alloc=396.7MB, time=71.69 memory used=6853.8MB, alloc=396.7MB, time=71.87 memory used=6915.4MB, alloc=396.7MB, time=72.27 memory used=7043.3MB, alloc=396.7MB, time=74.17 memory used=7095.8MB, alloc=396.7MB, time=74.34 memory used=7224.2MB, alloc=396.7MB, time=75.37 memory used=7304.9MB, alloc=396.7MB, time=75.82 memory used=7386.2MB, alloc=396.7MB, time=76.41 memory used=7500.7MB, alloc=420.7MB, time=77.72 memory used=7620.5MB, alloc=444.7MB, time=79.27 memory used=7735.3MB, alloc=444.7MB, time=80.81 memory used=7873.2MB, alloc=444.7MB, time=81.94 memory used=7966.0MB, alloc=444.7MB, time=82.40 memory used=8055.1MB, alloc=444.7MB, time=82.90 memory used=8162.1MB, alloc=444.7MB, time=83.57 memory used=8253.5MB, alloc=444.7MB, time=84.04 memory used=8358.7MB, alloc=444.7MB, time=86.41 memory used=8444.8MB, alloc=444.7MB, time=86.84 memory used=8541.2MB, alloc=444.7MB, time=87.35 memory used=8648.5MB, alloc=444.7MB, time=89.67 memory used=8716.4MB, alloc=444.7MB, time=89.97 memory used=8825.8MB, alloc=444.7MB, time=90.69 memory used=8885.4MB, alloc=444.7MB, time=90.98 memory used=8955.0MB, alloc=444.7MB, time=91.31 memory used=9034.2MB, alloc=444.7MB, time=91.60 memory used=9087.8MB, alloc=444.7MB, time=91.85 memory used=9191.7MB, alloc=444.7MB, time=92.51 memory used=9256.4MB, alloc=444.7MB, time=92.82 memory used=9323.5MB, alloc=444.7MB, time=93.11 memory used=9404.4MB, alloc=444.7MB, time=93.40 memory used=9459.4MB, alloc=444.7MB, time=93.68 memory used=9678.8MB, alloc=444.7MB, time=104.77 memory used=9861.4MB, alloc=444.7MB, time=105.79 memory used=9949.5MB, alloc=444.7MB, time=107.99 memory used=10037.4MB, alloc=444.7MB, time=108.38 memory used=10174.2MB, alloc=444.7MB, time=111.70 memory used=10242.6MB, alloc=444.7MB, time=112.01 memory used=10314.7MB, alloc=444.7MB, time=112.44 memory used=10460.1MB, alloc=444.7MB, time=114.41 memory used=10572.4MB, alloc=444.7MB, time=115.22 memory used=10666.5MB, alloc=444.7MB, time=116.50 memory used=10768.6MB, alloc=468.7MB, time=117.90 memory used=10878.8MB, alloc=468.7MB, time=119.34 memory used=10994.9MB, alloc=468.7MB, time=121.05 memory used=11094.9MB, alloc=468.7MB, time=122.19 memory used=11233.0MB, alloc=468.7MB, time=123.68 memory used=11330.5MB, alloc=492.7MB, time=124.83 memory used=11431.7MB, alloc=492.7MB, time=125.95 memory used=11551.6MB, alloc=492.7MB, time=126.97 memory used=11679.5MB, alloc=492.7MB, time=127.80 memory used=11774.0MB, alloc=492.7MB, time=129.25 memory used=11896.0MB, alloc=492.7MB, time=129.93 memory used=11993.6MB, alloc=492.7MB, time=130.37 memory used=12072.2MB, alloc=492.7MB, time=130.75 memory used=12244.8MB, alloc=492.7MB, time=149.34 memory used=12355.3MB, alloc=492.7MB, time=149.94 memory used=12446.1MB, alloc=492.7MB, time=150.35 memory used=12520.3MB, alloc=492.7MB, time=150.75 memory used=12607.2MB, alloc=492.7MB, time=151.15 memory used=12708.4MB, alloc=492.7MB, time=151.55 memory used=12803.7MB, alloc=492.7MB, time=151.96 memory used=12867.2MB, alloc=492.7MB, time=152.28 memory used=12934.5MB, alloc=492.7MB, time=152.59 memory used=13006.6MB, alloc=492.7MB, time=152.91 memory used=13085.2MB, alloc=492.7MB, time=153.24 memory used=13170.5MB, alloc=492.7MB, time=153.57 memory used=13264.3MB, alloc=492.7MB, time=153.90 memory used=13387.1MB, alloc=492.7MB, time=154.25 memory used=13543.3MB, alloc=492.7MB, time=155.05 memory used=13634.5MB, alloc=492.7MB, time=155.46 memory used=13792.3MB, alloc=516.7MB, time=190.99 memory used=14001.9MB, alloc=516.7MB, time=197.31 memory used=14253.6MB, alloc=516.7MB, time=197.89 memory used=14383.9MB, alloc=516.7MB, time=198.29 memory used=14521.2MB, alloc=516.7MB, time=198.71 memory used=14666.4MB, alloc=516.7MB, time=199.13 memory used=14821.1MB, alloc=516.7MB, time=199.55 memory used=14989.6MB, alloc=516.7MB, time=199.99 memory used=15188.5MB, alloc=516.7MB, time=201.68 memory used=15333.3MB, alloc=516.7MB, time=203.12 memory used=15437.8MB, alloc=516.7MB, time=204.18 memory used=15574.5MB, alloc=516.7MB, time=205.24 memory used=15794.1MB, alloc=516.7MB, time=240.06 memory used=15936.0MB, alloc=516.7MB, time=240.95 memory used=16044.9MB, alloc=516.7MB, time=241.41 memory used=16124.2MB, alloc=516.7MB, time=241.84 memory used=16214.9MB, alloc=516.7MB, time=242.25 memory used=16319.8MB, alloc=516.7MB, time=242.71 memory used=16438.8MB, alloc=516.7MB, time=243.15 memory used=16532.0MB, alloc=516.7MB, time=243.54 memory used=16602.7MB, alloc=516.7MB, time=243.90 memory used=16676.7MB, alloc=516.7MB, time=244.27 memory used=16755.4MB, alloc=516.7MB, time=244.63 memory used=16838.6MB, alloc=516.7MB, time=244.99 memory used=16927.7MB, alloc=516.7MB, time=245.36 memory used=17022.2MB, alloc=516.7MB, time=245.74 memory used=17123.0MB, alloc=516.7MB, time=246.11 memory used=17230.9MB, alloc=516.7MB, time=246.49 memory used=17355.7MB, alloc=516.7MB, time=246.88 memory used=17610.7MB, alloc=516.7MB, time=247.43 memory used=17783.8MB, alloc=516.7MB, time=248.71 memory used=17846.0MB, alloc=516.7MB, time=249.81 memory used=17974.7MB, alloc=516.7MB, time=250.59 memory used=18079.3MB, alloc=516.7MB, time=251.05 memory used=18169.2MB, alloc=516.7MB, time=251.46 memory used=18371.4MB, alloc=516.7MB, time=270.25 memory used=18477.5MB, alloc=516.7MB, time=270.75 memory used=18566.1MB, alloc=516.7MB, time=271.20 memory used=18655.2MB, alloc=516.7MB, time=271.63 memory used=18761.4MB, alloc=516.7MB, time=272.07 memory used=18877.4MB, alloc=516.7MB, time=272.51 memory used=18950.2MB, alloc=516.7MB, time=272.87 memory used=19025.6MB, alloc=516.7MB, time=273.23 memory used=19107.4MB, alloc=516.7MB, time=273.59 memory used=19195.5MB, alloc=516.7MB, time=273.95 memory used=19292.7MB, alloc=516.7MB, time=274.32 memory used=19400.9MB, alloc=516.7MB, time=274.70 memory used=19599.5MB, alloc=516.7MB, time=275.40 memory used=19701.9MB, alloc=516.7MB, time=275.86 memory used=19798.0MB, alloc=540.7MB, time=279.01 memory used=20077.9MB, alloc=540.7MB, time=318.40 memory used=20344.8MB, alloc=540.7MB, time=319.00 memory used=20475.4MB, alloc=540.7MB, time=319.44 memory used=20612.7MB, alloc=540.7MB, time=319.90 memory used=20757.8MB, alloc=540.7MB, time=320.36 memory used=20910.5MB, alloc=540.7MB, time=320.82 memory used=21077.5MB, alloc=540.7MB, time=321.29 memory used=21271.1MB, alloc=540.7MB, time=322.43 memory used=21332.7MB, alloc=540.7MB, time=323.33 memory used=21419.5MB, alloc=540.7MB, time=326.11 memory used=21641.9MB, alloc=540.7MB, time=359.02 memory used=21766.4MB, alloc=540.7MB, time=359.61 memory used=21872.6MB, alloc=540.7MB, time=360.11 memory used=21969.1MB, alloc=540.7MB, time=360.59 memory used=22082.8MB, alloc=540.7MB, time=361.07 memory used=22215.0MB, alloc=540.7MB, time=361.55 memory used=22320.8MB, alloc=540.7MB, time=361.99 memory used=22400.3MB, alloc=540.7MB, time=362.38 memory used=22486.8MB, alloc=540.7MB, time=362.78 memory used=22578.3MB, alloc=540.7MB, time=363.18 memory used=22676.2MB, alloc=540.7MB, time=363.60 memory used=22781.8MB, alloc=540.7MB, time=364.01 memory used=22895.9MB, alloc=540.7MB, time=364.43 memory used=23018.8MB, alloc=540.7MB, time=364.86 memory used=23163.5MB, alloc=540.7MB, time=365.32 memory used=23401.0MB, alloc=540.7MB, time=365.88 memory used=23617.4MB, alloc=540.7MB, time=366.91 memory used=23754.5MB, alloc=540.7MB, time=367.84 memory used=23865.1MB, alloc=540.7MB, time=368.35 memory used=23960.5MB, alloc=540.7MB, time=368.76 memory used=24082.4MB, alloc=540.7MB, time=369.40 memory used=24193.4MB, alloc=540.7MB, time=370.58 memory used=24262.7MB, alloc=540.7MB, time=371.68 memory used=24382.4MB, alloc=540.7MB, time=372.42 memory used=24514.9MB, alloc=540.7MB, time=373.37 memory used=24634.3MB, alloc=540.7MB, time=373.96 memory used=24721.5MB, alloc=540.7MB, time=374.49 memory used=24823.1MB, alloc=540.7MB, time=375.00 memory used=24944.4MB, alloc=540.7MB, time=375.52 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428503540 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 4 3 2 F := [-16 x z + 19 x y z + 17 y , 5 x y - 5 y z + 15 x y] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 G := [-9 y z - 9 x y + 8, 14 x y z + 9 y z + 14 x ] > Problem := [F,G]; 3 2 4 3 2 Problem := [[-16 x z + 19 x y z + 17 y , 5 x y - 5 y z + 15 x y], 2 2 2 3 2 [-9 y z - 9 x y + 8, 14 x y z + 9 y z + 14 x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=27.6MB, alloc=33.4MB, time=0.40 memory used=47.2MB, alloc=33.4MB, time=0.55 memory used=68.6MB, alloc=33.4MB, time=0.71 memory used=87.3MB, alloc=33.4MB, time=0.90 memory used=121.6MB, alloc=34.1MB, time=2.28 memory used=140.4MB, alloc=34.5MB, time=2.35 memory used=152.8MB, alloc=34.5MB, time=2.38 memory used=165.8MB, alloc=34.5MB, time=2.42 memory used=176.2MB, alloc=34.5MB, time=2.45 memory used=196.8MB, alloc=34.5MB, time=2.62 memory used=218.9MB, alloc=34.5MB, time=2.77 memory used=243.3MB, alloc=34.5MB, time=3.05 memory used=253.9MB, alloc=34.5MB, time=3.08 memory used=265.5MB, alloc=34.5MB, time=3.11 memory used=282.0MB, alloc=34.5MB, time=3.31 memory used=301.6MB, alloc=35.3MB, time=3.38 memory used=318.3MB, alloc=35.3MB, time=3.42 memory used=331.0MB, alloc=59.3MB, time=3.48 memory used=355.7MB, alloc=59.3MB, time=3.54 memory used=385.5MB, alloc=59.3MB, time=3.61 memory used=421.7MB, alloc=59.3MB, time=3.68 memory used=444.6MB, alloc=59.3MB, time=3.74 memory used=467.6MB, alloc=59.3MB, time=3.79 memory used=492.9MB, alloc=59.3MB, time=3.85 memory used=522.0MB, alloc=59.3MB, time=3.90 memory used=565.2MB, alloc=64.8MB, time=4.13 memory used=597.5MB, alloc=64.8MB, time=4.23 memory used=624.5MB, alloc=64.8MB, time=4.33 memory used=657.4MB, alloc=64.8MB, time=4.41 memory used=689.3MB, alloc=64.8MB, time=4.49 memory used=710.9MB, alloc=64.8MB, time=4.55 memory used=734.9MB, alloc=64.8MB, time=4.62 memory used=762.0MB, alloc=64.8MB, time=4.70 memory used=794.3MB, alloc=64.8MB, time=4.78 memory used=852.2MB, alloc=66.8MB, time=8.23 memory used=882.5MB, alloc=66.8MB, time=8.30 memory used=909.9MB, alloc=66.8MB, time=8.37 memory used=935.8MB, alloc=66.8MB, time=8.44 memory used=966.5MB, alloc=66.8MB, time=8.50 memory used=1000.5MB, alloc=66.8MB, time=8.57 memory used=1021.7MB, alloc=66.8MB, time=8.62 memory used=1052.9MB, alloc=66.8MB, time=8.71 memory used=1092.6MB, alloc=66.8MB, time=9.01 memory used=1139.0MB, alloc=66.8MB, time=10.32 memory used=1201.2MB, alloc=66.8MB, time=12.20 memory used=1241.7MB, alloc=66.8MB, time=12.35 memory used=1272.7MB, alloc=66.8MB, time=12.42 memory used=1297.7MB, alloc=66.8MB, time=12.49 memory used=1321.1MB, alloc=66.8MB, time=12.56 memory used=1348.3MB, alloc=66.8MB, time=12.62 memory used=1379.3MB, alloc=66.8MB, time=12.69 memory used=1413.4MB, alloc=66.8MB, time=12.76 memory used=1432.8MB, alloc=66.8MB, time=12.81 memory used=1453.8MB, alloc=66.8MB, time=12.87 memory used=1476.9MB, alloc=66.8MB, time=12.92 memory used=1519.4MB, alloc=66.8MB, time=13.21 memory used=1580.7MB, alloc=66.8MB, time=13.57 memory used=1641.4MB, alloc=66.8MB, time=13.98 memory used=1703.1MB, alloc=66.8MB, time=14.56 memory used=1765.0MB, alloc=66.8MB, time=15.38 memory used=1814.5MB, alloc=66.8MB, time=16.20 memory used=1856.5MB, alloc=66.8MB, time=16.57 memory used=1893.3MB, alloc=66.8MB, time=17.02 memory used=1935.6MB, alloc=74.8MB, time=17.47 memory used=1966.8MB, alloc=74.8MB, time=17.57 memory used=1987.7MB, alloc=74.8MB, time=17.65 memory used=2025.2MB, alloc=74.8MB, time=17.81 memory used=2045.2MB, alloc=74.8MB, time=17.89 memory used=2088.3MB, alloc=74.8MB, time=18.88 memory used=2110.9MB, alloc=74.8MB, time=18.96 memory used=2139.5MB, alloc=74.8MB, time=19.16 memory used=2182.3MB, alloc=74.8MB, time=19.57 memory used=2217.1MB, alloc=74.8MB, time=19.75 memory used=2236.8MB, alloc=74.8MB, time=19.83 memory used=2262.4MB, alloc=74.8MB, time=20.15 memory used=2301.9MB, alloc=74.8MB, time=21.27 memory used=2324.1MB, alloc=74.8MB, time=21.35 memory used=2344.5MB, alloc=74.8MB, time=21.42 memory used=2361.9MB, alloc=74.8MB, time=21.49 memory used=2382.5MB, alloc=74.8MB, time=21.57 memory used=2405.6MB, alloc=74.8MB, time=21.64 memory used=2429.8MB, alloc=74.8MB, time=21.71 memory used=2444.7MB, alloc=74.8MB, time=21.76 memory used=2461.2MB, alloc=74.8MB, time=21.82 memory used=2480.3MB, alloc=74.8MB, time=21.90 memory used=2537.0MB, alloc=98.8MB, time=26.83 memory used=2600.4MB, alloc=98.8MB, time=34.59 memory used=2683.9MB, alloc=98.8MB, time=35.12 memory used=2746.4MB, alloc=98.8MB, time=35.44 memory used=2783.3MB, alloc=98.8MB, time=35.56 memory used=2825.2MB, alloc=98.8MB, time=35.67 memory used=2852.7MB, alloc=98.8MB, time=35.77 memory used=2882.9MB, alloc=98.8MB, time=35.86 memory used=2916.8MB, alloc=98.8MB, time=35.96 memory used=2954.3MB, alloc=98.8MB, time=36.06 memory used=2994.1MB, alloc=98.8MB, time=36.17 memory used=3037.3MB, alloc=98.8MB, time=36.28 memory used=3082.7MB, alloc=98.8MB, time=36.40 memory used=3108.7MB, alloc=98.8MB, time=36.47 memory used=3133.4MB, alloc=98.8MB, time=36.55 memory used=3158.5MB, alloc=98.8MB, time=36.64 memory used=3185.8MB, alloc=98.8MB, time=36.72 memory used=3213.4MB, alloc=98.8MB, time=36.80 memory used=3241.3MB, alloc=98.8MB, time=36.88 memory used=3271.2MB, alloc=98.8MB, time=36.95 memory used=3301.5MB, alloc=98.8MB, time=37.03 memory used=3333.7MB, alloc=98.8MB, time=37.11 memory used=3366.1MB, alloc=98.8MB, time=37.19 memory used=3400.5MB, alloc=98.8MB, time=37.27 memory used=3436.6MB, alloc=98.8MB, time=37.36 memory used=3472.9MB, alloc=98.8MB, time=37.44 memory used=3510.8MB, alloc=98.8MB, time=37.53 memory used=3550.3MB, alloc=98.8MB, time=37.62 memory used=3591.4MB, alloc=98.8MB, time=37.71 memory used=3633.7MB, alloc=98.8MB, time=37.79 memory used=3677.2MB, alloc=98.8MB, time=37.88 memory used=3723.1MB, alloc=98.8MB, time=37.97 memory used=3764.6MB, alloc=107.8MB, time=38.06 memory used=3775.1MB, alloc=107.8MB, time=38.12 memory used=3784.8MB, alloc=107.8MB, time=38.17 memory used=3793.5MB, alloc=107.8MB, time=38.22 memory used=3802.3MB, alloc=107.8MB, time=38.28 memory used=3811.2MB, alloc=107.8MB, time=38.33 memory used=3821.3MB, alloc=107.8MB, time=38.39 memory used=3831.4MB, alloc=107.8MB, time=38.44 memory used=3841.4MB, alloc=107.8MB, time=38.49 memory used=3851.3MB, alloc=107.8MB, time=38.55 memory used=3861.0MB, alloc=107.8MB, time=38.60 memory used=3870.7MB, alloc=107.8MB, time=38.65 memory used=3881.4MB, alloc=107.8MB, time=38.71 memory used=3892.1MB, alloc=107.8MB, time=38.76 memory used=3902.5MB, alloc=107.8MB, time=38.81 memory used=3913.0MB, alloc=107.8MB, time=38.86 memory used=3924.1MB, alloc=107.8MB, time=38.91 memory used=3935.1MB, alloc=107.8MB, time=38.97 memory used=3947.0MB, alloc=107.8MB, time=39.03 memory used=3958.6MB, alloc=107.8MB, time=39.08 memory used=3970.9MB, alloc=107.8MB, time=39.13 memory used=3982.8MB, alloc=107.8MB, time=39.18 memory used=3995.3MB, alloc=107.8MB, time=39.25 memory used=4008.2MB, alloc=107.8MB, time=39.30 memory used=4021.4MB, alloc=107.8MB, time=39.36 memory used=4034.6MB, alloc=107.8MB, time=39.41 memory used=4048.4MB, alloc=107.8MB, time=39.48 memory used=4062.4MB, alloc=107.8MB, time=39.54 memory used=4077.1MB, alloc=107.8MB, time=39.60 memory used=4172.1MB, alloc=107.8MB, time=40.41 memory used=4231.4MB, alloc=107.8MB, time=41.98 memory used=4265.4MB, alloc=107.8MB, time=42.09 memory used=4295.4MB, alloc=107.8MB, time=42.18 memory used=4340.9MB, alloc=107.8MB, time=43.51 memory used=4374.7MB, alloc=107.8MB, time=43.62 memory used=4404.5MB, alloc=107.8MB, time=43.71 memory used=4470.0MB, alloc=107.8MB, time=44.39 memory used=4511.6MB, alloc=131.8MB, time=44.88 memory used=4598.6MB, alloc=131.8MB, time=45.66 memory used=4667.2MB, alloc=131.8MB, time=46.30 memory used=4738.0MB, alloc=131.8MB, time=47.06 memory used=4825.0MB, alloc=131.8MB, time=49.53 memory used=4868.4MB, alloc=131.8MB, time=49.66 memory used=4923.2MB, alloc=387.8MB, time=50.26 memory used=5009.0MB, alloc=387.8MB, time=50.88 memory used=5061.6MB, alloc=387.8MB, time=51.19 memory used=5122.8MB, alloc=387.8MB, time=51.47 memory used=5167.8MB, alloc=387.8MB, time=51.62 memory used=5229.1MB, alloc=387.8MB, time=52.78 memory used=5274.0MB, alloc=387.8MB, time=52.94 memory used=5310.6MB, alloc=387.8MB, time=53.09 memory used=5371.8MB, alloc=387.8MB, time=53.45 memory used=5425.3MB, alloc=387.8MB, time=53.73 memory used=5491.2MB, alloc=387.8MB, time=54.10 memory used=5526.4MB, alloc=387.8MB, time=54.26 memory used=5570.6MB, alloc=387.8MB, time=54.41 memory used=5617.8MB, alloc=387.8MB, time=54.57 memory used=5646.9MB, alloc=387.8MB, time=54.71 memory used=5679.0MB, alloc=387.8MB, time=54.85 memory used=5714.8MB, alloc=387.8MB, time=54.98 memory used=5755.5MB, alloc=387.8MB, time=55.11 memory used=5801.4MB, alloc=387.8MB, time=55.26 memory used=5867.6MB, alloc=387.8MB, time=55.65 memory used=5909.2MB, alloc=387.8MB, time=55.82 memory used=5949.1MB, alloc=387.8MB, time=55.98 memory used=5997.7MB, alloc=387.8MB, time=56.14 memory used=6032.2MB, alloc=411.8MB, time=56.30 memory used=6078.1MB, alloc=411.8MB, time=56.47 memory used=6131.6MB, alloc=411.8MB, time=56.66 memory used=6195.6MB, alloc=411.8MB, time=56.82 memory used=6298.9MB, alloc=411.8MB, time=62.60 memory used=6357.7MB, alloc=411.8MB, time=62.79 memory used=6408.9MB, alloc=411.8MB, time=62.95 memory used=6476.0MB, alloc=411.8MB, time=63.12 memory used=6518.3MB, alloc=411.8MB, time=63.25 memory used=6589.6MB, alloc=411.8MB, time=63.52 memory used=6649.4MB, alloc=411.8MB, time=63.72 memory used=6702.2MB, alloc=411.8MB, time=63.90 memory used=6777.1MB, alloc=411.8MB, time=64.16 memory used=6849.4MB, alloc=411.8MB, time=64.88 memory used=6925.6MB, alloc=411.8MB, time=65.75 memory used=6980.6MB, alloc=411.8MB, time=65.92 memory used=7041.5MB, alloc=411.8MB, time=66.08 memory used=7114.9MB, alloc=411.8MB, time=66.53 memory used=7174.0MB, alloc=411.8MB, time=66.75 memory used=7230.0MB, alloc=411.8MB, time=66.97 memory used=7299.9MB, alloc=411.8MB, time=67.18 memory used=7350.4MB, alloc=411.8MB, time=67.37 memory used=7395.9MB, alloc=411.8MB, time=67.54 memory used=7447.4MB, alloc=411.8MB, time=67.70 memory used=7518.6MB, alloc=411.8MB, time=68.15 memory used=7589.5MB, alloc=411.8MB, time=68.40 memory used=7640.5MB, alloc=411.8MB, time=68.59 memory used=7703.2MB, alloc=411.8MB, time=68.81 memory used=7764.9MB, alloc=411.8MB, time=69.01 memory used=7807.4MB, alloc=411.8MB, time=69.21 memory used=7855.1MB, alloc=411.8MB, time=69.38 memory used=7909.2MB, alloc=411.8MB, time=69.56 memory used=8001.2MB, alloc=411.8MB, time=89.44 memory used=8069.5MB, alloc=435.8MB, time=123.38 memory used=8163.6MB, alloc=435.8MB, time=202.99 memory used=8253.4MB, alloc=459.8MB, time=285.71 memory used=8351.2MB, alloc=459.8MB, time=289.60 memory used=8475.1MB, alloc=459.8MB, time=290.30 memory used=8599.3MB, alloc=459.8MB, time=291.00 memory used=8716.8MB, alloc=459.8MB, time=291.58 memory used=8810.7MB, alloc=459.8MB, time=291.85 memory used=8880.6MB, alloc=459.8MB, time=292.09 memory used=8963.9MB, alloc=459.8MB, time=292.32 memory used=9060.3MB, alloc=459.8MB, time=292.56 memory used=9168.1MB, alloc=459.8MB, time=292.79 memory used=9229.6MB, alloc=459.8MB, time=292.97 memory used=9293.7MB, alloc=459.8MB, time=293.14 memory used=9360.3MB, alloc=459.8MB, time=293.30 memory used=9430.8MB, alloc=459.8MB, time=293.48 memory used=9506.9MB, alloc=459.8MB, time=293.67 memory used=9586.6MB, alloc=459.8MB, time=293.86 memory used=9671.6MB, alloc=459.8MB, time=294.05 memory used=9761.8MB, alloc=459.8MB, time=294.24 memory used=9856.8MB, alloc=459.8MB, time=294.42 memory used=9958.0MB, alloc=459.8MB, time=294.61 memory used=10064.7MB, alloc=459.8MB, time=294.82 memory used=10280.9MB, alloc=459.8MB, time=295.34 memory used=10430.6MB, alloc=459.8MB, time=295.61 memory used=10596.3MB, alloc=459.8MB, time=295.90 memory used=10823.7MB, alloc=459.8MB, time=296.65 memory used=10918.6MB, alloc=459.8MB, time=296.92 memory used=11009.2MB, alloc=459.8MB, time=297.17 memory used=11086.5MB, alloc=459.8MB, time=297.42 memory used=11203.1MB, alloc=459.8MB, time=298.04 memory used=11293.3MB, alloc=459.8MB, time=298.36 memory used=11402.2MB, alloc=459.8MB, time=298.63 memory used=11472.7MB, alloc=459.8MB, time=298.87 memory used=11556.4MB, alloc=459.8MB, time=299.10 memory used=11687.7MB, alloc=459.8MB, time=335.41 memory used=11801.1MB, alloc=459.8MB, time=400.33 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428503840 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 4 2 F := [x z - 19 x, -11 x y z + y + 2 x y] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 3 2 2 2 G := [17 x y z - 8 x + 4 y, 18 x y + 20 y z + 12 y z ] > Problem := [F,G]; 2 4 2 Problem := [[x z - 19 x, -11 x y z + y + 2 x y], 2 3 3 2 2 2 [17 x y z - 8 x + 4 y, 18 x y + 20 y z + 12 y z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=25.6MB, alloc=32.3MB, time=0.49 memory used=45.9MB, alloc=56.3MB, time=0.80 memory used=87.3MB, alloc=60.3MB, time=1.40 memory used=130.8MB, alloc=92.3MB, time=2.02 memory used=195.8MB, alloc=92.3MB, time=2.96 memory used=260.4MB, alloc=92.3MB, time=3.92 memory used=325.4MB, alloc=116.3MB, time=4.87 memory used=396.8MB, alloc=116.3MB, time=5.95 memory used=458.6MB, alloc=372.3MB, time=6.90 memory used=544.4MB, alloc=396.3MB, time=8.14 memory used=654.9MB, alloc=420.3MB, time=9.70 memory used=784.4MB, alloc=444.3MB, time=11.78 memory used=958.8MB, alloc=444.3MB, time=13.84 memory used=1131.3MB, alloc=468.3MB, time=15.89 memory used=1292.9MB, alloc=492.3MB, time=18.83 memory used=1465.0MB, alloc=516.3MB, time=21.96 memory used=1662.2MB, alloc=540.3MB, time=25.34 memory used=1941.0MB, alloc=540.3MB, time=27.53 memory used=2199.1MB, alloc=564.3MB, time=30.26 memory used=2478.1MB, alloc=564.3MB, time=33.40 memory used=2757.3MB, alloc=588.3MB, time=36.40 memory used=3066.3MB, alloc=588.3MB, time=39.53 memory used=3365.7MB, alloc=588.3MB, time=42.81 memory used=3661.5MB, alloc=612.3MB, time=46.09 memory used=3988.9MB, alloc=612.3MB, time=49.31 memory used=4306.0MB, alloc=636.3MB, time=52.68 memory used=4525.4MB, alloc=660.3MB, time=56.57 memory used=4721.7MB, alloc=684.3MB, time=60.37 memory used=4951.8MB, alloc=708.3MB, time=66.42 memory used=5216.1MB, alloc=732.3MB, time=75.41 memory used=5483.2MB, alloc=756.3MB, time=85.05 memory used=5755.7MB, alloc=780.3MB, time=95.78 memory used=6044.2MB, alloc=804.3MB, time=107.33 memory used=6343.1MB, alloc=828.3MB, time=119.64 memory used=6657.9MB, alloc=852.3MB, time=132.89 memory used=6996.7MB, alloc=876.3MB, time=147.22 memory used=7359.4MB, alloc=900.3MB, time=162.59 memory used=7746.0MB, alloc=924.3MB, time=178.82 memory used=8156.6MB, alloc=924.3MB, time=196.06 memory used=8567.1MB, alloc=948.3MB, time=213.34 memory used=9001.6MB, alloc=948.3MB, time=231.78 memory used=9436.1MB, alloc=948.3MB, time=250.22 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428504140 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 3 2 F := [3 x z - 3 y - 7 z, -7 x y - 20 y z - 10 y] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 4 2 2 2 G := [-14 x - 17 y - 17 y z , -4 x z + 12 y z] > Problem := [F,G]; 2 2 3 3 2 Problem := [[3 x z - 3 y - 7 z, -7 x y - 20 y z - 10 y], 4 4 2 2 2 [-14 x - 17 y - 17 y z , -4 x z + 12 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.6MB, alloc=32.3MB, time=0.51 memory used=47.2MB, alloc=32.3MB, time=0.82 memory used=65.7MB, alloc=56.3MB, time=1.09 memory used=108.7MB, alloc=68.3MB, time=1.70 memory used=152.7MB, alloc=68.3MB, time=2.27 memory used=183.0MB, alloc=68.3MB, time=2.48 memory used=212.6MB, alloc=68.3MB, time=2.70 memory used=231.6MB, alloc=68.3MB, time=2.77 memory used=256.4MB, alloc=68.3MB, time=2.94 memory used=276.4MB, alloc=68.3MB, time=3.07 memory used=303.8MB, alloc=68.3MB, time=3.33 memory used=345.2MB, alloc=92.3MB, time=3.92 memory used=408.9MB, alloc=92.3MB, time=4.88 memory used=470.7MB, alloc=92.3MB, time=5.69 memory used=504.2MB, alloc=92.3MB, time=6.25 memory used=544.0MB, alloc=92.3MB, time=7.30 memory used=603.8MB, alloc=116.3MB, time=7.92 memory used=669.9MB, alloc=116.3MB, time=8.65 memory used=738.6MB, alloc=117.3MB, time=9.71 memory used=797.8MB, alloc=117.3MB, time=10.17 memory used=853.2MB, alloc=117.3MB, time=11.00 memory used=900.7MB, alloc=117.3MB, time=11.19 memory used=949.1MB, alloc=117.3MB, time=12.52 memory used=1005.6MB, alloc=117.3MB, time=13.19 memory used=1070.5MB, alloc=373.3MB, time=14.60 memory used=1131.9MB, alloc=373.3MB, time=15.03 memory used=1220.8MB, alloc=397.3MB, time=16.20 memory used=1313.8MB, alloc=397.3MB, time=18.21 memory used=1387.2MB, alloc=397.3MB, time=20.46 memory used=1435.3MB, alloc=397.3MB, time=20.89 memory used=1556.3MB, alloc=397.3MB, time=22.81 memory used=1631.8MB, alloc=397.3MB, time=26.55 memory used=1680.1MB, alloc=397.3MB, time=26.76 memory used=1758.1MB, alloc=397.3MB, time=27.64 memory used=1804.4MB, alloc=397.3MB, time=27.81 memory used=1860.3MB, alloc=397.3MB, time=28.23 memory used=1921.5MB, alloc=397.3MB, time=28.71 memory used=1966.3MB, alloc=397.3MB, time=28.88 memory used=2036.2MB, alloc=397.3MB, time=29.28 memory used=2119.3MB, alloc=421.3MB, time=37.90 memory used=2203.6MB, alloc=421.3MB, time=38.67 memory used=2258.2MB, alloc=421.3MB, time=38.89 memory used=2328.1MB, alloc=421.3MB, time=39.10 memory used=2392.5MB, alloc=421.3MB, time=39.29 memory used=2441.6MB, alloc=421.3MB, time=39.46 memory used=2497.8MB, alloc=421.3MB, time=39.63 memory used=2561.5MB, alloc=421.3MB, time=39.81 memory used=2644.8MB, alloc=421.3MB, time=40.13 memory used=2734.1MB, alloc=421.3MB, time=40.63 memory used=2801.0MB, alloc=421.3MB, time=40.87 memory used=2879.7MB, alloc=421.3MB, time=41.23 memory used=2947.5MB, alloc=421.3MB, time=41.46 memory used=3036.7MB, alloc=421.3MB, time=51.54 memory used=3122.4MB, alloc=421.3MB, time=52.43 memory used=3178.4MB, alloc=421.3MB, time=52.66 memory used=3246.2MB, alloc=421.3MB, time=52.89 memory used=3315.1MB, alloc=421.3MB, time=53.12 memory used=3363.4MB, alloc=421.3MB, time=53.30 memory used=3418.0MB, alloc=421.3MB, time=53.50 memory used=3479.4MB, alloc=421.3MB, time=53.69 memory used=3548.6MB, alloc=421.3MB, time=53.87 memory used=3692.1MB, alloc=421.3MB, time=55.26 memory used=3755.1MB, alloc=421.3MB, time=55.48 memory used=3900.5MB, alloc=421.3MB, time=78.74 memory used=3984.0MB, alloc=421.3MB, time=90.51 memory used=4050.3MB, alloc=421.3MB, time=90.76 memory used=4098.2MB, alloc=421.3MB, time=90.97 memory used=4155.5MB, alloc=421.3MB, time=91.19 memory used=4223.1MB, alloc=421.3MB, time=91.43 memory used=4292.6MB, alloc=421.3MB, time=91.65 memory used=4334.0MB, alloc=421.3MB, time=91.83 memory used=4379.2MB, alloc=421.3MB, time=92.01 memory used=4427.0MB, alloc=421.3MB, time=92.19 memory used=4478.6MB, alloc=421.3MB, time=92.38 memory used=4533.8MB, alloc=421.3MB, time=92.56 memory used=4592.2MB, alloc=421.3MB, time=92.74 memory used=4654.8MB, alloc=421.3MB, time=92.92 memory used=4722.3MB, alloc=421.3MB, time=93.11 memory used=4794.9MB, alloc=421.3MB, time=93.31 memory used=4984.2MB, alloc=421.3MB, time=93.83 memory used=5088.3MB, alloc=421.3MB, time=94.36 memory used=5156.6MB, alloc=421.3MB, time=94.71 memory used=5225.4MB, alloc=421.3MB, time=94.96 memory used=5377.4MB, alloc=421.3MB, time=95.65 memory used=5555.1MB, alloc=421.3MB, time=96.03 memory used=5667.3MB, alloc=421.3MB, time=96.29 memory used=5803.9MB, alloc=421.3MB, time=97.55 memory used=5905.2MB, alloc=421.3MB, time=100.15 memory used=5964.3MB, alloc=421.3MB, time=100.39 memory used=6058.1MB, alloc=421.3MB, time=101.87 memory used=6130.1MB, alloc=421.3MB, time=111.69 memory used=6172.2MB, alloc=421.3MB, time=111.89 memory used=6217.9MB, alloc=421.3MB, time=112.06 memory used=6279.6MB, alloc=421.3MB, time=112.54 memory used=6345.8MB, alloc=421.3MB, time=112.86 memory used=6468.8MB, alloc=421.3MB, time=113.32 memory used=6571.0MB, alloc=421.3MB, time=113.55 memory used=6717.7MB, alloc=421.3MB, time=115.11 memory used=6832.4MB, alloc=445.3MB, time=116.69 memory used=6940.7MB, alloc=445.3MB, time=118.19 memory used=7040.6MB, alloc=469.3MB, time=119.86 memory used=7137.4MB, alloc=469.3MB, time=121.40 memory used=7232.6MB, alloc=469.3MB, time=122.82 memory used=7317.6MB, alloc=469.3MB, time=124.13 memory used=7391.7MB, alloc=493.3MB, time=125.34 memory used=7466.3MB, alloc=493.3MB, time=126.62 memory used=7537.4MB, alloc=493.3MB, time=127.85 memory used=7611.2MB, alloc=493.3MB, time=128.88 memory used=7712.8MB, alloc=493.3MB, time=129.42 memory used=7816.4MB, alloc=493.3MB, time=130.15 memory used=7898.9MB, alloc=493.3MB, time=130.52 memory used=7999.0MB, alloc=493.3MB, time=130.98 memory used=8092.2MB, alloc=493.3MB, time=131.45 memory used=8233.0MB, alloc=493.3MB, time=143.27 memory used=8313.1MB, alloc=493.3MB, time=143.66 memory used=8414.1MB, alloc=493.3MB, time=144.08 memory used=8487.4MB, alloc=493.3MB, time=144.42 memory used=8557.2MB, alloc=493.3MB, time=144.77 memory used=8636.1MB, alloc=493.3MB, time=145.11 memory used=8722.8MB, alloc=493.3MB, time=145.46 memory used=8818.9MB, alloc=493.3MB, time=145.82 memory used=8925.7MB, alloc=493.3MB, time=146.18 memory used=9121.3MB, alloc=493.3MB, time=146.69 memory used=9269.9MB, alloc=493.3MB, time=147.11 memory used=9442.2MB, alloc=493.3MB, time=147.58 memory used=9636.1MB, alloc=493.3MB, time=148.31 memory used=9734.1MB, alloc=493.3MB, time=148.76 memory used=9807.7MB, alloc=493.3MB, time=149.17 memory used=9900.4MB, alloc=493.3MB, time=149.55 memory used=10010.4MB, alloc=493.3MB, time=150.08 memory used=10105.2MB, alloc=493.3MB, time=150.52 memory used=10177.3MB, alloc=493.3MB, time=150.91 memory used=10271.5MB, alloc=493.3MB, time=151.31 memory used=10398.4MB, alloc=493.3MB, time=164.19 memory used=10543.8MB, alloc=493.3MB, time=165.81 memory used=10621.7MB, alloc=493.3MB, time=166.21 memory used=10724.7MB, alloc=493.3MB, time=166.63 memory used=10796.0MB, alloc=493.3MB, time=167.00 memory used=10865.2MB, alloc=493.3MB, time=167.35 memory used=10944.1MB, alloc=493.3MB, time=167.71 memory used=11031.1MB, alloc=493.3MB, time=168.07 memory used=11127.5MB, alloc=493.3MB, time=168.43 memory used=11234.6MB, alloc=493.3MB, time=168.81 memory used=11428.9MB, alloc=493.3MB, time=169.33 memory used=11577.7MB, alloc=493.3MB, time=169.78 memory used=11749.3MB, alloc=493.3MB, time=170.26 memory used=11965.9MB, alloc=493.3MB, time=171.38 memory used=12078.0MB, alloc=493.3MB, time=171.97 memory used=12160.8MB, alloc=493.3MB, time=172.35 memory used=12242.2MB, alloc=493.3MB, time=172.70 memory used=12338.7MB, alloc=493.3MB, time=173.27 memory used=12421.5MB, alloc=493.3MB, time=173.61 memory used=12549.2MB, alloc=493.3MB, time=174.92 memory used=12686.6MB, alloc=493.3MB, time=176.05 memory used=12779.8MB, alloc=493.3MB, time=176.55 memory used=12872.8MB, alloc=493.3MB, time=177.02 memory used=12978.3MB, alloc=493.3MB, time=177.69 memory used=13057.1MB, alloc=493.3MB, time=178.11 memory used=13162.7MB, alloc=493.3MB, time=178.68 memory used=13243.8MB, alloc=493.3MB, time=179.09 memory used=13381.2MB, alloc=493.3MB, time=204.55 memory used=13489.8MB, alloc=493.3MB, time=206.22 memory used=13566.3MB, alloc=493.3MB, time=206.63 memory used=13649.2MB, alloc=493.3MB, time=207.05 memory used=13751.6MB, alloc=493.3MB, time=207.49 memory used=13826.7MB, alloc=493.3MB, time=207.88 memory used=13889.4MB, alloc=517.3MB, time=208.25 memory used=13971.5MB, alloc=517.3MB, time=208.64 memory used=14060.0MB, alloc=517.3MB, time=209.01 memory used=14156.0MB, alloc=517.3MB, time=209.39 memory used=14259.5MB, alloc=517.3MB, time=209.77 memory used=14370.6MB, alloc=517.3MB, time=210.24 memory used=14491.8MB, alloc=517.3MB, time=210.81 memory used=14620.6MB, alloc=517.3MB, time=211.27 memory used=14797.7MB, alloc=517.3MB, time=211.79 memory used=14933.4MB, alloc=517.3MB, time=212.26 memory used=15076.8MB, alloc=517.3MB, time=212.72 memory used=15228.6MB, alloc=517.3MB, time=213.18 memory used=15391.7MB, alloc=517.3MB, time=213.64 memory used=15565.3MB, alloc=517.3MB, time=214.11 memory used=15747.9MB, alloc=517.3MB, time=214.58 memory used=15945.4MB, alloc=517.3MB, time=215.05 memory used=16155.9MB, alloc=517.3MB, time=215.56 memory used=16384.1MB, alloc=517.3MB, time=216.07 memory used=16592.3MB, alloc=517.3MB, time=216.64 memory used=16773.4MB, alloc=517.3MB, time=217.42 memory used=16902.3MB, alloc=517.3MB, time=218.12 memory used=17010.9MB, alloc=517.3MB, time=218.62 memory used=17109.7MB, alloc=517.3MB, time=219.06 memory used=17198.9MB, alloc=517.3MB, time=219.51 memory used=17305.9MB, alloc=517.3MB, time=219.96 memory used=17430.8MB, alloc=517.3MB, time=220.39 memory used=17517.5MB, alloc=517.3MB, time=220.75 memory used=17593.4MB, alloc=517.3MB, time=221.10 memory used=17676.4MB, alloc=517.3MB, time=221.49 memory used=17767.1MB, alloc=517.3MB, time=221.85 memory used=17892.2MB, alloc=517.3MB, time=222.54 memory used=18009.0MB, alloc=517.3MB, time=223.03 memory used=18089.4MB, alloc=517.3MB, time=223.45 memory used=18185.3MB, alloc=517.3MB, time=223.88 memory used=18298.7MB, alloc=517.3MB, time=224.33 memory used=18418.6MB, alloc=517.3MB, time=224.77 memory used=18490.6MB, alloc=517.3MB, time=225.14 memory used=18569.2MB, alloc=517.3MB, time=225.50 memory used=18654.7MB, alloc=517.3MB, time=225.87 memory used=18758.6MB, alloc=517.3MB, time=226.74 memory used=18971.3MB, alloc=517.3MB, time=258.68 memory used=19073.5MB, alloc=517.3MB, time=259.18 memory used=19167.2MB, alloc=517.3MB, time=259.66 memory used=19285.8MB, alloc=517.3MB, time=260.17 memory used=19376.7MB, alloc=517.3MB, time=260.63 memory used=19453.9MB, alloc=517.3MB, time=261.03 memory used=19536.4MB, alloc=517.3MB, time=261.43 memory used=19626.3MB, alloc=517.3MB, time=261.85 memory used=19723.7MB, alloc=517.3MB, time=262.28 memory used=19828.4MB, alloc=517.3MB, time=262.70 memory used=19940.8MB, alloc=517.3MB, time=263.14 memory used=20063.2MB, alloc=517.3MB, time=263.56 memory used=20192.9MB, alloc=517.3MB, time=264.01 memory used=20339.8MB, alloc=517.3MB, time=264.53 memory used=20475.5MB, alloc=517.3MB, time=265.04 memory used=20619.3MB, alloc=517.3MB, time=265.53 memory used=20771.5MB, alloc=517.3MB, time=266.03 memory used=20932.0MB, alloc=517.3MB, time=266.55 memory used=21105.3MB, alloc=517.3MB, time=267.07 memory used=21287.8MB, alloc=517.3MB, time=267.58 memory used=21483.4MB, alloc=517.3MB, time=268.08 memory used=21692.3MB, alloc=517.3MB, time=268.58 memory used=21920.6MB, alloc=517.3MB, time=269.11 memory used=22132.2MB, alloc=517.3MB, time=269.62 memory used=22286.6MB, alloc=517.3MB, time=270.84 memory used=22410.6MB, alloc=517.3MB, time=271.52 memory used=22535.1MB, alloc=517.3MB, time=272.24 memory used=22648.7MB, alloc=517.3MB, time=272.84 memory used=22748.5MB, alloc=517.3MB, time=273.30 memory used=22853.5MB, alloc=517.3MB, time=273.76 memory used=22954.7MB, alloc=517.3MB, time=274.18 memory used=23036.5MB, alloc=517.3MB, time=274.57 memory used=23131.5MB, alloc=517.3MB, time=274.95 memory used=23242.7MB, alloc=517.3MB, time=275.33 memory used=23359.2MB, alloc=517.3MB, time=276.09 memory used=23465.5MB, alloc=517.3MB, time=276.56 memory used=23551.9MB, alloc=517.3MB, time=276.94 memory used=23659.1MB, alloc=517.3MB, time=277.35 memory used=23816.5MB, alloc=517.3MB, time=278.51 memory used=23893.9MB, alloc=517.3MB, time=279.49 memory used=24000.2MB, alloc=517.3MB, time=280.02 memory used=24110.3MB, alloc=517.3MB, time=280.57 memory used=24232.9MB, alloc=517.3MB, time=281.22 memory used=24340.0MB, alloc=517.3MB, time=281.74 memory used=24423.4MB, alloc=517.3MB, time=282.21 memory used=24528.1MB, alloc=517.3MB, time=282.65 memory used=24642.5MB, alloc=517.3MB, time=283.10 memory used=24716.0MB, alloc=517.3MB, time=283.49 memory used=24797.9MB, alloc=517.3MB, time=283.87 memory used=24916.6MB, alloc=517.3MB, time=284.60 memory used=25023.2MB, alloc=517.3MB, time=285.12 memory used=25103.9MB, alloc=517.3MB, time=285.59 memory used=25205.7MB, alloc=517.3MB, time=286.05 memory used=25324.4MB, alloc=517.3MB, time=286.51 memory used=25395.9MB, alloc=517.3MB, time=286.91 memory used=25476.2MB, alloc=517.3MB, time=287.30 memory used=25605.7MB, alloc=517.3MB, time=301.73 memory used=25781.4MB, alloc=517.3MB, time=315.32 memory used=25878.1MB, alloc=517.3MB, time=315.80 memory used=25985.9MB, alloc=517.3MB, time=316.29 memory used=26083.8MB, alloc=517.3MB, time=316.76 memory used=26159.1MB, alloc=517.3MB, time=317.17 memory used=26242.7MB, alloc=517.3MB, time=317.56 memory used=26337.1MB, alloc=517.3MB, time=317.98 memory used=26439.6MB, alloc=517.3MB, time=318.41 memory used=26552.8MB, alloc=517.3MB, time=318.87 memory used=26676.6MB, alloc=517.3MB, time=319.31 memory used=26873.3MB, alloc=517.3MB, time=319.87 memory used=27012.9MB, alloc=517.3MB, time=320.37 memory used=27162.2MB, alloc=517.3MB, time=320.87 memory used=27323.9MB, alloc=517.3MB, time=321.39 memory used=27500.1MB, alloc=517.3MB, time=321.89 memory used=27690.4MB, alloc=517.3MB, time=322.40 memory used=27899.9MB, alloc=517.3MB, time=322.94 memory used=28135.7MB, alloc=517.3MB, time=323.47 memory used=28278.1MB, alloc=517.3MB, time=324.83 memory used=28397.3MB, alloc=517.3MB, time=325.54 memory used=28509.3MB, alloc=517.3MB, time=326.16 memory used=28620.6MB, alloc=517.3MB, time=326.76 memory used=28721.4MB, alloc=517.3MB, time=327.23 memory used=28813.6MB, alloc=517.3MB, time=327.67 memory used=28899.1MB, alloc=517.3MB, time=328.05 memory used=29002.2MB, alloc=517.3MB, time=328.43 memory used=29116.7MB, alloc=517.3MB, time=329.17 memory used=29214.2MB, alloc=517.3MB, time=329.59 memory used=29306.8MB, alloc=517.3MB, time=329.98 memory used=29478.5MB, alloc=517.3MB, time=331.00 memory used=29565.5MB, alloc=517.3MB, time=336.91 memory used=29677.4MB, alloc=541.3MB, time=349.16 memory used=29820.7MB, alloc=565.3MB, time=349.79 memory used=29869.6MB, alloc=589.3MB, time=356.66 memory used=29883.1MB, alloc=613.3MB, time=357.08 memory used=29992.6MB, alloc=637.3MB, time=358.98 memory used=30270.6MB, alloc=637.3MB, time=368.75 memory used=30512.3MB, alloc=663.3MB, time=376.44 memory used=30780.8MB, alloc=661.3MB, time=386.56 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428504440 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 3 3 2 F := [x y + 8 y z - 10 y z , 2 x z - z - 2 z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 3 2 G := [-2 x y z + 8 x - 2 z , 6 x y + 13 x z] > Problem := [F,G]; 2 2 2 2 3 3 2 Problem := [[x y + 8 y z - 10 y z , 2 x z - z - 2 z ], 2 3 3 2 [-2 x y z + 8 x - 2 z , 6 x y + 13 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=26.1MB, alloc=32.3MB, time=0.53 memory used=46.5MB, alloc=32.3MB, time=0.85 memory used=65.4MB, alloc=56.3MB, time=1.16 memory used=103.9MB, alloc=60.3MB, time=1.78 memory used=142.7MB, alloc=84.3MB, time=2.40 memory used=204.9MB, alloc=92.3MB, time=3.44 memory used=265.7MB, alloc=116.3MB, time=4.49 memory used=347.8MB, alloc=116.3MB, time=5.91 memory used=421.0MB, alloc=372.3MB, time=7.19 memory used=503.4MB, alloc=396.3MB, time=8.65 memory used=610.5MB, alloc=420.3MB, time=10.45 memory used=741.1MB, alloc=420.3MB, time=12.55 memory used=865.2MB, alloc=444.3MB, time=14.72 memory used=1011.0MB, alloc=468.3MB, time=17.36 memory used=1158.9MB, alloc=492.3MB, time=19.91 memory used=1364.9MB, alloc=516.3MB, time=22.55 memory used=1546.6MB, alloc=540.3MB, time=25.63 memory used=1717.5MB, alloc=564.3MB, time=28.88 memory used=1923.7MB, alloc=588.3MB, time=32.80 memory used=2126.8MB, alloc=612.3MB, time=36.67 memory used=2331.8MB, alloc=636.3MB, time=40.59 memory used=2600.4MB, alloc=660.3MB, time=44.35 memory used=2881.3MB, alloc=684.3MB, time=48.08 memory used=3177.6MB, alloc=708.3MB, time=52.14 memory used=3542.9MB, alloc=732.3MB, time=56.48 memory used=3820.3MB, alloc=756.3MB, time=60.14 memory used=4203.8MB, alloc=756.3MB, time=64.09 memory used=4381.0MB, alloc=780.3MB, time=67.34 memory used=4541.2MB, alloc=804.3MB, time=70.69 memory used=4701.4MB, alloc=828.3MB, time=73.93 memory used=4856.6MB, alloc=852.3MB, time=77.16 memory used=5024.3MB, alloc=852.3MB, time=80.38 memory used=5186.4MB, alloc=876.3MB, time=83.56 memory used=5320.9MB, alloc=900.3MB, time=86.19 memory used=5446.6MB, alloc=900.3MB, time=88.95 memory used=5587.7MB, alloc=924.3MB, time=91.90 memory used=5731.2MB, alloc=948.3MB, time=94.92 memory used=5844.5MB, alloc=948.3MB, time=97.55 memory used=6013.5MB, alloc=972.3MB, time=100.47 memory used=6154.3MB, alloc=972.3MB, time=103.21 memory used=6272.8MB, alloc=996.3MB, time=106.89 memory used=6439.5MB, alloc=1020.3MB, time=113.14 memory used=6878.7MB, alloc=1044.3MB, time=130.24 memory used=7309.8MB, alloc=1068.3MB, time=147.87 memory used=7741.5MB, alloc=1092.3MB, time=165.77 memory used=8178.7MB, alloc=1116.3MB, time=184.00 memory used=8623.6MB, alloc=1140.3MB, time=202.68 memory used=9078.0MB, alloc=1164.3MB, time=221.64 memory used=9542.4MB, alloc=1188.3MB, time=241.16 memory used=10017.7MB, alloc=1212.3MB, time=261.74 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428504740 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 4 2 F := [18 y z + 18 x z - 2 y z, -4 x y z - 8 z - 5 x y] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 G := [-9 x y z + 14 x y - 10 x y z, 16 x y - 4 y - 16 z] > Problem := [F,G]; 2 2 2 4 2 Problem := [[18 y z + 18 x z - 2 y z, -4 x y z - 8 z - 5 x y], 2 3 2 2 [-9 x y z + 14 x y - 10 x y z, 16 x y - 4 y - 16 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.19 memory used=26.7MB, alloc=32.3MB, time=0.54 memory used=47.7MB, alloc=32.3MB, time=0.84 memory used=67.7MB, alloc=56.3MB, time=1.15 memory used=107.6MB, alloc=60.3MB, time=1.75 memory used=147.6MB, alloc=84.3MB, time=2.30 memory used=214.7MB, alloc=92.3MB, time=3.24 memory used=277.5MB, alloc=92.3MB, time=4.16 memory used=337.3MB, alloc=116.3MB, time=4.96 memory used=424.8MB, alloc=116.3MB, time=5.88 memory used=506.9MB, alloc=116.3MB, time=6.64 memory used=566.3MB, alloc=372.3MB, time=7.33 memory used=660.1MB, alloc=396.3MB, time=8.39 memory used=773.5MB, alloc=396.3MB, time=9.91 memory used=888.2MB, alloc=420.3MB, time=11.36 memory used=1018.8MB, alloc=444.3MB, time=13.08 memory used=1126.6MB, alloc=444.3MB, time=14.53 memory used=1252.6MB, alloc=444.3MB, time=16.14 memory used=1353.1MB, alloc=468.3MB, time=17.00 memory used=1459.5MB, alloc=468.3MB, time=17.48 memory used=1583.2MB, alloc=468.3MB, time=20.89 memory used=1665.4MB, alloc=468.3MB, time=21.23 memory used=1767.0MB, alloc=468.3MB, time=21.76 memory used=1852.9MB, alloc=468.3MB, time=22.12 memory used=1954.3MB, alloc=468.3MB, time=22.62 memory used=2041.2MB, alloc=468.3MB, time=22.99 memory used=2180.5MB, alloc=468.3MB, time=33.62 memory used=2260.9MB, alloc=468.3MB, time=33.97 memory used=2337.6MB, alloc=468.3MB, time=34.30 memory used=2419.8MB, alloc=468.3MB, time=34.60 memory used=2509.5MB, alloc=468.3MB, time=35.29 memory used=2636.7MB, alloc=468.3MB, time=36.29 memory used=2721.6MB, alloc=468.3MB, time=36.67 memory used=2807.4MB, alloc=468.3MB, time=37.12 memory used=2905.8MB, alloc=468.3MB, time=37.56 memory used=2988.8MB, alloc=468.3MB, time=37.89 memory used=3150.3MB, alloc=468.3MB, time=55.35 memory used=3230.3MB, alloc=468.3MB, time=55.69 memory used=3305.0MB, alloc=468.3MB, time=56.01 memory used=3389.7MB, alloc=468.3MB, time=56.31 memory used=3452.9MB, alloc=468.3MB, time=56.57 memory used=3564.9MB, alloc=468.3MB, time=57.64 memory used=3734.3MB, alloc=468.3MB, time=59.19 memory used=3917.3MB, alloc=468.3MB, time=62.33 memory used=4071.2MB, alloc=468.3MB, time=63.71 memory used=4230.2MB, alloc=468.3MB, time=66.61 memory used=4336.2MB, alloc=468.3MB, time=68.01 memory used=4467.8MB, alloc=468.3MB, time=72.03 memory used=4538.8MB, alloc=468.3MB, time=72.38 memory used=4609.9MB, alloc=492.3MB, time=72.71 memory used=4687.1MB, alloc=492.3MB, time=73.03 memory used=4780.5MB, alloc=492.3MB, time=73.38 memory used=5030.4MB, alloc=492.3MB, time=74.11 memory used=5202.1MB, alloc=492.3MB, time=75.34 memory used=5284.4MB, alloc=492.3MB, time=76.64 memory used=5362.6MB, alloc=492.3MB, time=77.79 memory used=5437.3MB, alloc=492.3MB, time=79.01 memory used=5519.9MB, alloc=492.3MB, time=80.38 memory used=5592.6MB, alloc=492.3MB, time=81.59 memory used=5659.7MB, alloc=492.3MB, time=82.70 memory used=5721.8MB, alloc=492.3MB, time=83.92 memory used=5843.2MB, alloc=492.3MB, time=84.89 memory used=5968.1MB, alloc=492.3MB, time=85.83 memory used=6081.4MB, alloc=492.3MB, time=87.97 memory used=6182.3MB, alloc=492.3MB, time=88.54 memory used=6281.5MB, alloc=492.3MB, time=89.09 memory used=6414.0MB, alloc=516.3MB, time=94.94 memory used=6518.2MB, alloc=516.3MB, time=95.40 memory used=6625.1MB, alloc=516.3MB, time=96.14 memory used=6687.7MB, alloc=516.3MB, time=97.07 memory used=6763.1MB, alloc=516.3MB, time=99.91 memory used=6889.8MB, alloc=516.3MB, time=101.93 memory used=6996.5MB, alloc=516.3MB, time=102.42 memory used=7077.2MB, alloc=516.3MB, time=102.82 memory used=7171.3MB, alloc=516.3MB, time=103.22 memory used=7286.1MB, alloc=516.3MB, time=104.32 memory used=7346.9MB, alloc=516.3MB, time=105.06 memory used=7456.6MB, alloc=516.3MB, time=105.96 memory used=7570.4MB, alloc=516.3MB, time=107.41 memory used=7669.8MB, alloc=516.3MB, time=109.27 memory used=7782.5MB, alloc=516.3MB, time=110.01 memory used=7873.1MB, alloc=516.3MB, time=110.46 memory used=7973.8MB, alloc=516.3MB, time=111.20 memory used=8058.3MB, alloc=540.3MB, time=112.42 memory used=8192.3MB, alloc=540.3MB, time=113.82 memory used=8302.3MB, alloc=540.3MB, time=114.40 memory used=8392.6MB, alloc=540.3MB, time=114.95 memory used=8500.6MB, alloc=540.3MB, time=115.50 memory used=8624.8MB, alloc=540.3MB, time=116.08 memory used=8742.4MB, alloc=564.3MB, time=116.65 memory used=8828.8MB, alloc=564.3MB, time=117.11 memory used=8923.6MB, alloc=564.3MB, time=117.60 memory used=9027.5MB, alloc=564.3MB, time=118.10 memory used=9134.9MB, alloc=564.3MB, time=118.59 memory used=9253.4MB, alloc=564.3MB, time=119.09 memory used=9380.3MB, alloc=564.3MB, time=119.60 memory used=9514.5MB, alloc=564.3MB, time=120.11 memory used=9659.0MB, alloc=564.3MB, time=120.61 memory used=9816.3MB, alloc=564.3MB, time=121.15 memory used=9992.5MB, alloc=564.3MB, time=121.74 memory used=10118.0MB, alloc=564.3MB, time=122.26 memory used=10251.7MB, alloc=564.3MB, time=122.79 memory used=10491.6MB, alloc=564.3MB, time=124.47 memory used=10610.6MB, alloc=564.3MB, time=125.10 memory used=10724.8MB, alloc=564.3MB, time=125.68 memory used=10864.3MB, alloc=564.3MB, time=126.32 memory used=11013.9MB, alloc=564.3MB, time=126.88 memory used=11101.7MB, alloc=564.3MB, time=127.35 memory used=11196.1MB, alloc=564.3MB, time=127.82 memory used=11295.1MB, alloc=564.3MB, time=128.30 memory used=11405.7MB, alloc=564.3MB, time=128.80 memory used=11520.7MB, alloc=564.3MB, time=129.30 memory used=11646.2MB, alloc=564.3MB, time=129.79 memory used=11779.4MB, alloc=564.3MB, time=130.32 memory used=11923.7MB, alloc=564.3MB, time=130.84 memory used=12078.9MB, alloc=564.3MB, time=131.36 memory used=12276.1MB, alloc=564.3MB, time=131.97 memory used=12401.7MB, alloc=564.3MB, time=132.48 memory used=12535.4MB, alloc=564.3MB, time=133.00 memory used=12810.2MB, alloc=564.3MB, time=236.32 memory used=13024.4MB, alloc=564.3MB, time=279.35 memory used=13157.5MB, alloc=564.3MB, time=280.12 memory used=13299.5MB, alloc=564.3MB, time=280.73 memory used=13392.6MB, alloc=564.3MB, time=281.27 memory used=13498.0MB, alloc=564.3MB, time=281.80 memory used=13617.4MB, alloc=564.3MB, time=282.34 memory used=13754.0MB, alloc=564.3MB, time=282.90 memory used=13908.4MB, alloc=564.3MB, time=283.48 memory used=14079.0MB, alloc=564.3MB, time=284.09 memory used=14205.0MB, alloc=564.3MB, time=284.71 memory used=14342.2MB, alloc=564.3MB, time=285.26 memory used=14487.5MB, alloc=564.3MB, time=285.84 memory used=14644.5MB, alloc=564.3MB, time=286.41 memory used=14808.9MB, alloc=564.3MB, time=286.99 memory used=14984.1MB, alloc=564.3MB, time=287.61 memory used=15173.1MB, alloc=564.3MB, time=288.20 memory used=15376.0MB, alloc=564.3MB, time=288.84 memory used=15591.0MB, alloc=564.3MB, time=289.46 memory used=15783.9MB, alloc=564.3MB, time=290.06 memory used=15945.3MB, alloc=564.3MB, time=290.62 memory used=16112.7MB, alloc=564.3MB, time=291.18 memory used=16289.8MB, alloc=564.3MB, time=291.76 memory used=16480.8MB, alloc=564.3MB, time=292.36 memory used=16686.2MB, alloc=564.3MB, time=292.95 memory used=17005.8MB, alloc=564.3MB, time=297.27 memory used=17129.4MB, alloc=564.3MB, time=297.84 memory used=17245.0MB, alloc=564.3MB, time=298.33 memory used=17515.8MB, alloc=564.3MB, time=299.06 memory used=17936.9MB, alloc=564.3MB, time=302.16 memory used=18106.2MB, alloc=564.3MB, time=303.47 memory used=18230.4MB, alloc=564.3MB, time=304.12 memory used=18325.7MB, alloc=564.3MB, time=304.65 memory used=18454.4MB, alloc=564.3MB, time=305.50 memory used=18578.0MB, alloc=564.3MB, time=306.18 memory used=18674.4MB, alloc=564.3MB, time=306.75 memory used=18816.4MB, alloc=564.3MB, time=308.22 memory used=18941.1MB, alloc=564.3MB, time=308.86 memory used=19073.0MB, alloc=564.3MB, time=309.71 memory used=19228.5MB, alloc=564.3MB, time=310.78 memory used=19335.6MB, alloc=564.3MB, time=311.39 memory used=19463.9MB, alloc=564.3MB, time=312.03 memory used=19569.4MB, alloc=564.3MB, time=312.56 memory used=19665.3MB, alloc=564.3MB, time=313.06 memory used=19798.4MB, alloc=564.3MB, time=313.83 memory used=19914.2MB, alloc=564.3MB, time=314.48 memory used=20027.5MB, alloc=564.3MB, time=315.08 memory used=20154.2MB, alloc=564.3MB, time=315.66 memory used=20243.7MB, alloc=564.3MB, time=316.15 memory used=20349.1MB, alloc=564.3MB, time=316.65 memory used=20519.2MB, alloc=564.3MB, time=333.27 memory used=20642.5MB, alloc=564.3MB, time=333.87 memory used=20734.4MB, alloc=564.3MB, time=334.39 memory used=20847.2MB, alloc=564.3MB, time=334.92 memory used=20984.6MB, alloc=564.3MB, time=335.49 memory used=21157.7MB, alloc=564.3MB, time=336.13 memory used=21301.0MB, alloc=564.3MB, time=336.74 memory used=21468.7MB, alloc=564.3MB, time=337.35 memory used=21766.8MB, alloc=564.3MB, time=338.72 memory used=21871.0MB, alloc=564.3MB, time=339.34 memory used=21983.7MB, alloc=564.3MB, time=339.97 memory used=22119.3MB, alloc=564.3MB, time=340.59 memory used=22223.5MB, alloc=564.3MB, time=341.17 memory used=22308.7MB, alloc=564.3MB, time=341.69 memory used=22401.8MB, alloc=564.3MB, time=342.19 memory used=22506.1MB, alloc=564.3MB, time=342.72 memory used=22619.2MB, alloc=564.3MB, time=343.24 memory used=22746.4MB, alloc=564.3MB, time=343.77 memory used=22889.4MB, alloc=564.3MB, time=344.29 memory used=23051.0MB, alloc=564.3MB, time=345.40 memory used=23162.8MB, alloc=564.3MB, time=346.03 memory used=23269.8MB, alloc=564.3MB, time=346.61 memory used=23402.2MB, alloc=564.3MB, time=347.23 memory used=23517.2MB, alloc=564.3MB, time=347.78 memory used=23600.5MB, alloc=564.3MB, time=348.29 memory used=23692.6MB, alloc=564.3MB, time=348.79 memory used=23793.6MB, alloc=564.3MB, time=349.30 memory used=23906.0MB, alloc=564.3MB, time=349.82 memory used=24028.7MB, alloc=564.3MB, time=350.34 memory used=24168.0MB, alloc=564.3MB, time=350.86 memory used=24362.8MB, alloc=564.3MB, time=399.57 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428505040 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 4 2 F := [5 x y + 3 x y z - 2 y z, 17 x + 20 x + 5 y] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 2 G := [-19 x z + 15 z - 5 y, 11 x y z - 17 y z ] > Problem := [F,G]; 2 4 2 Problem := [[5 x y + 3 x y z - 2 y z, 17 x + 20 x + 5 y], 2 2 3 2 2 2 [-19 x z + 15 z - 5 y, 11 x y z - 17 y z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.7MB, alloc=32.3MB, time=0.50 memory used=47.4MB, alloc=32.3MB, time=0.81 memory used=67.0MB, alloc=60.3MB, time=1.13 memory used=108.5MB, alloc=68.3MB, time=1.76 memory used=148.8MB, alloc=92.3MB, time=2.37 memory used=212.9MB, alloc=92.3MB, time=3.41 memory used=270.7MB, alloc=116.3MB, time=4.44 memory used=350.8MB, alloc=140.3MB, time=5.82 memory used=449.1MB, alloc=164.3MB, time=7.51 memory used=560.0MB, alloc=188.3MB, time=9.92 memory used=673.3MB, alloc=212.3MB, time=13.63 memory used=796.2MB, alloc=236.3MB, time=18.41 memory used=943.2MB, alloc=236.3MB, time=24.06 memory used=1090.3MB, alloc=260.3MB, time=29.77 N1 := 4479 > GB := Basis(F, plex(op(vars))); 4 2 GB := [17 x + 20 x + 5 y, 9 7 5 5 4 3 2 -289 x - 680 x + 51 x z - 400 x - 34 x z + 60 x z - 40 x z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1260.1MB, alloc=260.3MB, time=34.42 memory used=1469.0MB, alloc=540.3MB, time=37.97 memory used=1696.8MB, alloc=564.3MB, time=42.16 memory used=1901.9MB, alloc=588.3MB, time=49.91 memory used=2116.2MB, alloc=612.3MB, time=58.79 N2 := 3979 > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 4 2 2 2 3 H := [5 x y + 3 x y z - 2 y z, 17 x + 20 x + 5 y, -19 x z + 15 z - 5 y, 2 2 2 11 x y z - 17 y z ] > J:=[op(GB),op(G)]; 4 2 J := [17 x + 20 x + 5 y, 9 7 5 5 4 3 2 -289 x - 680 x + 51 x z - 400 x - 34 x z + 60 x z - 40 x z, 2 2 3 2 2 2 -19 x z + 15 z - 5 y, 11 x y z - 17 y z ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 11, 15, 4, 4, 2, 3, 1, 1, 3/4, 6/11, 7/11, 6/11, 4, 10, 21, 11 9, 9, 2, 3, 1, 3/4, 3/4, --, 4/15, 8/15, 1, -6, -5] 15 > save(F, G, cat("ranSet/34", convert(F, string),".txt")); > quit memory used=2206.7MB, alloc=612.3MB, time=62.20 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428505110 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 2 3 2 F := [13 x z + 13 y z - 2 x , 8 x y - 18 x y - 14 z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 G := [-14 y z + 18 y + 15 z, 3 x y z - 2 x y z - 11 z ] > Problem := [F,G]; 2 2 3 2 2 2 3 2 Problem := [[13 x z + 13 y z - 2 x , 8 x y - 18 x y - 14 z ], 2 2 2 3 [-14 y z + 18 y + 15 z, 3 x y z - 2 x y z - 11 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=25.6MB, alloc=32.3MB, time=0.48 memory used=45.1MB, alloc=56.3MB, time=0.74 memory used=89.6MB, alloc=60.3MB, time=1.26 memory used=135.6MB, alloc=68.3MB, time=1.87 memory used=181.9MB, alloc=68.3MB, time=2.45 memory used=223.8MB, alloc=68.3MB, time=2.89 memory used=250.8MB, alloc=68.3MB, time=3.08 memory used=279.2MB, alloc=68.3MB, time=3.25 memory used=311.4MB, alloc=68.3MB, time=3.57 memory used=350.9MB, alloc=92.3MB, time=9.17 memory used=390.7MB, alloc=92.3MB, time=34.22 memory used=435.9MB, alloc=92.3MB, time=71.41 memory used=470.0MB, alloc=116.3MB, time=88.78 memory used=539.6MB, alloc=116.3MB, time=91.83 memory used=620.8MB, alloc=116.3MB, time=92.39 memory used=673.5MB, alloc=116.3MB, time=92.53 memory used=714.4MB, alloc=116.3MB, time=92.64 memory used=761.0MB, alloc=116.3MB, time=92.77 memory used=813.9MB, alloc=116.3MB, time=92.91 memory used=874.5MB, alloc=116.3MB, time=93.04 memory used=925.5MB, alloc=116.3MB, time=93.16 memory used=960.7MB, alloc=116.3MB, time=93.25 memory used=996.0MB, alloc=116.3MB, time=93.34 memory used=1033.2MB, alloc=116.3MB, time=93.44 memory used=1073.0MB, alloc=116.3MB, time=93.54 memory used=1115.5MB, alloc=116.3MB, time=93.63 memory used=1158.8MB, alloc=116.3MB, time=93.73 memory used=1204.7MB, alloc=116.3MB, time=93.83 memory used=1253.1MB, alloc=116.3MB, time=93.93 memory used=1303.9MB, alloc=116.3MB, time=94.04 memory used=1357.1MB, alloc=116.3MB, time=94.14 memory used=1412.5MB, alloc=116.3MB, time=94.24 memory used=1470.0MB, alloc=116.3MB, time=94.35 memory used=1531.0MB, alloc=116.3MB, time=94.46 memory used=1601.4MB, alloc=122.3MB, time=94.57 memory used=1617.0MB, alloc=131.8MB, time=94.65 memory used=1627.6MB, alloc=131.8MB, time=94.71 memory used=1637.1MB, alloc=131.8MB, time=94.77 memory used=1646.3MB, alloc=131.8MB, time=94.82 memory used=1655.5MB, alloc=131.8MB, time=94.88 memory used=1664.6MB, alloc=131.8MB, time=94.93 memory used=1673.7MB, alloc=131.8MB, time=94.98 memory used=1682.8MB, alloc=131.8MB, time=95.04 memory used=1691.8MB, alloc=131.8MB, time=95.09 memory used=1700.7MB, alloc=131.8MB, time=95.14 memory used=1709.6MB, alloc=131.8MB, time=95.20 memory used=1718.6MB, alloc=131.8MB, time=95.26 memory used=1729.0MB, alloc=131.8MB, time=95.32 memory used=1739.5MB, alloc=131.8MB, time=95.37 memory used=1749.9MB, alloc=131.8MB, time=95.42 memory used=1760.2MB, alloc=131.8MB, time=95.48 memory used=1770.4MB, alloc=131.8MB, time=95.54 memory used=1780.5MB, alloc=131.8MB, time=95.60 memory used=1790.6MB, alloc=131.8MB, time=95.66 memory used=1800.5MB, alloc=131.8MB, time=95.71 memory used=1810.6MB, alloc=131.8MB, time=95.77 memory used=1821.8MB, alloc=131.8MB, time=95.83 memory used=1833.0MB, alloc=131.8MB, time=95.88 memory used=1844.2MB, alloc=131.8MB, time=95.94 memory used=1855.1MB, alloc=131.8MB, time=95.99 memory used=1866.0MB, alloc=131.8MB, time=96.05 memory used=1878.1MB, alloc=131.8MB, time=96.11 memory used=1890.1MB, alloc=131.8MB, time=96.17 memory used=1901.9MB, alloc=131.8MB, time=96.22 memory used=1913.6MB, alloc=131.8MB, time=96.28 memory used=1926.4MB, alloc=131.8MB, time=96.34 memory used=1938.9MB, alloc=131.8MB, time=96.40 memory used=1951.2MB, alloc=131.8MB, time=96.45 memory used=1964.3MB, alloc=131.8MB, time=96.51 memory used=1977.2MB, alloc=131.8MB, time=96.56 memory used=1990.8MB, alloc=131.8MB, time=96.63 memory used=2004.1MB, alloc=131.8MB, time=96.69 memory used=2017.9MB, alloc=131.8MB, time=96.75 memory used=2032.1MB, alloc=131.8MB, time=96.81 memory used=2046.7MB, alloc=131.8MB, time=96.87 memory used=2061.3MB, alloc=131.8MB, time=96.93 memory used=2076.7MB, alloc=131.8MB, time=96.99 memory used=2092.9MB, alloc=131.8MB, time=97.05 memory used=2109.8MB, alloc=131.8MB, time=97.11 memory used=2195.7MB, alloc=131.8MB, time=107.16 memory used=2264.5MB, alloc=131.8MB, time=107.45 memory used=2315.1MB, alloc=131.8MB, time=107.58 memory used=2375.2MB, alloc=131.8MB, time=107.72 memory used=2420.3MB, alloc=131.8MB, time=107.81 memory used=2463.6MB, alloc=131.8MB, time=107.91 memory used=2512.7MB, alloc=131.8MB, time=108.01 memory used=2567.1MB, alloc=131.8MB, time=108.10 memory used=2628.6MB, alloc=131.8MB, time=108.20 memory used=2668.1MB, alloc=131.8MB, time=108.28 memory used=2678.8MB, alloc=131.8MB, time=108.33 memory used=2690.4MB, alloc=131.8MB, time=108.39 memory used=2702.2MB, alloc=131.8MB, time=108.44 memory used=2714.1MB, alloc=131.8MB, time=108.50 memory used=2726.6MB, alloc=131.8MB, time=108.55 memory used=2739.5MB, alloc=131.8MB, time=108.60 memory used=2753.0MB, alloc=131.8MB, time=108.66 memory used=2767.3MB, alloc=131.8MB, time=108.72 memory used=2836.7MB, alloc=131.8MB, time=109.10 memory used=2897.3MB, alloc=131.8MB, time=109.30 memory used=2958.0MB, alloc=131.8MB, time=109.44 memory used=3002.9MB, alloc=131.8MB, time=109.72 memory used=3024.7MB, alloc=131.8MB, time=109.79 memory used=3053.1MB, alloc=131.8MB, time=109.87 memory used=3084.0MB, alloc=131.8MB, time=109.95 memory used=3117.4MB, alloc=131.8MB, time=110.03 memory used=3153.3MB, alloc=131.8MB, time=110.12 memory used=3191.7MB, alloc=131.8MB, time=110.20 memory used=3214.5MB, alloc=131.8MB, time=110.27 memory used=3226.0MB, alloc=131.8MB, time=110.33 memory used=3242.2MB, alloc=131.8MB, time=110.40 memory used=3264.7MB, alloc=131.8MB, time=110.48 memory used=3293.1MB, alloc=131.8MB, time=110.57 memory used=3324.0MB, alloc=131.8MB, time=110.65 memory used=3357.5MB, alloc=131.8MB, time=110.74 memory used=3393.3MB, alloc=131.8MB, time=110.82 memory used=3431.8MB, alloc=131.8MB, time=110.90 memory used=3453.4MB, alloc=131.8MB, time=110.96 memory used=3464.9MB, alloc=131.8MB, time=111.02 memory used=3558.1MB, alloc=131.8MB, time=112.70 memory used=3630.8MB, alloc=131.8MB, time=116.21 memory used=3724.9MB, alloc=131.8MB, time=124.18 memory used=3789.3MB, alloc=131.8MB, time=124.38 memory used=3833.8MB, alloc=131.8MB, time=124.50 memory used=3891.3MB, alloc=131.8MB, time=124.63 memory used=3942.9MB, alloc=131.8MB, time=124.74 memory used=3983.1MB, alloc=131.8MB, time=124.84 memory used=4028.7MB, alloc=131.8MB, time=124.94 memory used=4079.2MB, alloc=131.8MB, time=125.03 memory used=4142.1MB, alloc=131.8MB, time=125.14 memory used=4204.8MB, alloc=131.8MB, time=125.51 memory used=4261.9MB, alloc=131.8MB, time=125.71 memory used=4317.8MB, alloc=131.8MB, time=125.86 memory used=4342.6MB, alloc=131.8MB, time=126.11 memory used=4368.0MB, alloc=131.8MB, time=126.19 memory used=4395.8MB, alloc=131.8MB, time=126.28 memory used=4426.1MB, alloc=131.8MB, time=126.36 memory used=4458.8MB, alloc=131.8MB, time=126.45 memory used=4494.0MB, alloc=131.8MB, time=126.53 memory used=4531.7MB, alloc=131.8MB, time=126.61 memory used=4549.4MB, alloc=131.8MB, time=126.69 memory used=4569.4MB, alloc=131.8MB, time=126.76 memory used=4595.2MB, alloc=131.8MB, time=126.84 memory used=4623.4MB, alloc=131.8MB, time=126.92 memory used=4654.0MB, alloc=131.8MB, time=127.01 memory used=4687.1MB, alloc=131.8MB, time=127.09 memory used=4722.8MB, alloc=131.8MB, time=127.17 memory used=4760.7MB, alloc=131.8MB, time=127.26 memory used=4792.2MB, alloc=131.8MB, time=127.74 memory used=4892.1MB, alloc=131.8MB, time=128.51 memory used=4992.7MB, alloc=131.8MB, time=129.07 memory used=5091.0MB, alloc=131.8MB, time=129.91 memory used=5193.1MB, alloc=131.8MB, time=131.11 memory used=5292.2MB, alloc=131.8MB, time=132.77 memory used=5388.3MB, alloc=131.8MB, time=134.93 memory used=5487.6MB, alloc=131.8MB, time=137.34 memory used=5585.6MB, alloc=131.8MB, time=140.63 memory used=5685.6MB, alloc=131.8MB, time=144.13 memory used=5785.1MB, alloc=131.8MB, time=148.11 memory used=5884.1MB, alloc=131.8MB, time=152.86 memory used=5984.7MB, alloc=131.8MB, time=158.15 memory used=6084.8MB, alloc=131.8MB, time=163.86 memory used=6186.8MB, alloc=131.8MB, time=168.74 memory used=6253.5MB, alloc=131.8MB, time=169.21 memory used=6333.6MB, alloc=131.8MB, time=194.30 memory used=6396.3MB, alloc=155.8MB, time=245.59 memory used=6471.9MB, alloc=155.8MB, time=257.53 memory used=6573.6MB, alloc=155.8MB, time=258.23 memory used=6634.7MB, alloc=155.8MB, time=258.40 memory used=6690.9MB, alloc=155.8MB, time=258.56 memory used=6757.2MB, alloc=155.8MB, time=258.74 memory used=6835.7MB, alloc=155.8MB, time=258.93 memory used=6889.8MB, alloc=155.8MB, time=259.05 memory used=6934.9MB, alloc=155.8MB, time=259.17 memory used=6983.5MB, alloc=155.8MB, time=259.29 memory used=7035.5MB, alloc=155.8MB, time=259.40 memory used=7090.6MB, alloc=155.8MB, time=259.53 memory used=7148.8MB, alloc=155.8MB, time=259.65 memory used=7212.0MB, alloc=155.8MB, time=259.78 memory used=7278.1MB, alloc=155.8MB, time=259.91 memory used=7348.6MB, alloc=155.8MB, time=260.05 memory used=7423.4MB, alloc=155.8MB, time=260.18 memory used=7504.2MB, alloc=155.8MB, time=260.31 memory used=7554.8MB, alloc=155.8MB, time=260.42 memory used=7566.9MB, alloc=155.8MB, time=260.49 memory used=7576.7MB, alloc=155.8MB, time=260.56 memory used=7585.4MB, alloc=155.8MB, time=260.61 memory used=7594.6MB, alloc=155.8MB, time=260.68 memory used=7603.8MB, alloc=155.8MB, time=260.74 memory used=7612.9MB, alloc=155.8MB, time=260.81 memory used=7622.0MB, alloc=155.8MB, time=260.87 memory used=7631.0MB, alloc=155.8MB, time=260.94 memory used=7640.0MB, alloc=155.8MB, time=261.00 memory used=7648.9MB, alloc=155.8MB, time=261.06 memory used=7657.8MB, alloc=155.8MB, time=261.12 memory used=7666.6MB, alloc=155.8MB, time=261.19 memory used=7675.5MB, alloc=155.8MB, time=261.26 memory used=7685.8MB, alloc=155.8MB, time=261.33 memory used=7696.2MB, alloc=155.8MB, time=261.39 memory used=7706.5MB, alloc=155.8MB, time=261.46 memory used=7716.7MB, alloc=155.8MB, time=261.52 memory used=7726.8MB, alloc=155.8MB, time=261.59 memory used=7736.9MB, alloc=155.8MB, time=261.65 memory used=7746.8MB, alloc=155.8MB, time=261.72 memory used=7756.6MB, alloc=155.8MB, time=261.78 memory used=7768.0MB, alloc=155.8MB, time=261.85 memory used=7779.2MB, alloc=155.8MB, time=261.92 memory used=7790.3MB, alloc=155.8MB, time=261.98 memory used=7801.3MB, alloc=155.8MB, time=262.05 memory used=7812.1MB, alloc=155.8MB, time=262.11 memory used=7822.8MB, alloc=155.8MB, time=262.17 memory used=7834.7MB, alloc=155.8MB, time=262.23 memory used=7846.5MB, alloc=155.8MB, time=262.30 memory used=7858.1MB, alloc=155.8MB, time=262.37 memory used=7869.7MB, alloc=155.8MB, time=262.44 memory used=7882.1MB, alloc=155.8MB, time=262.50 memory used=7894.4MB, alloc=155.8MB, time=262.57 memory used=7907.6MB, alloc=155.8MB, time=262.64 memory used=7920.5MB, alloc=155.8MB, time=262.71 memory used=7934.2MB, alloc=155.8MB, time=262.79 memory used=7946.3MB, alloc=155.8MB, time=262.85 memory used=7959.1MB, alloc=155.8MB, time=262.92 memory used=7973.5MB, alloc=155.8MB, time=262.99 memory used=7988.2MB, alloc=155.8MB, time=263.06 memory used=8003.0MB, alloc=155.8MB, time=263.12 memory used=8017.9MB, alloc=155.8MB, time=263.20 memory used=8033.6MB, alloc=155.8MB, time=263.27 memory used=8049.7MB, alloc=155.8MB, time=263.34 memory used=8072.1MB, alloc=155.8MB, time=263.56 memory used=8170.8MB, alloc=155.8MB, time=273.44 memory used=8244.9MB, alloc=155.8MB, time=273.70 memory used=8316.5MB, alloc=155.8MB, time=273.88 memory used=8374.4MB, alloc=155.8MB, time=274.01 memory used=8432.2MB, alloc=155.8MB, time=274.12 memory used=8498.0MB, alloc=155.8MB, time=274.24 memory used=8575.2MB, alloc=155.8MB, time=274.37 memory used=8614.3MB, alloc=155.8MB, time=274.46 memory used=8624.9MB, alloc=155.8MB, time=274.53 memory used=8635.9MB, alloc=155.8MB, time=274.60 memory used=8647.2MB, alloc=155.8MB, time=274.66 memory used=8659.2MB, alloc=155.8MB, time=274.72 memory used=8671.3MB, alloc=155.8MB, time=274.79 memory used=8684.0MB, alloc=155.8MB, time=274.85 memory used=8697.3MB, alloc=155.8MB, time=274.92 memory used=8711.3MB, alloc=155.8MB, time=274.99 memory used=8797.1MB, alloc=155.8MB, time=275.46 memory used=8869.8MB, alloc=155.8MB, time=275.63 memory used=8942.3MB, alloc=155.8MB, time=275.97 memory used=8959.2MB, alloc=155.8MB, time=276.04 memory used=8985.9MB, alloc=155.8MB, time=276.14 memory used=9015.1MB, alloc=155.8MB, time=276.24 memory used=9046.6MB, alloc=155.8MB, time=276.33 memory used=9080.4MB, alloc=155.8MB, time=276.42 memory used=9116.9MB, alloc=155.8MB, time=276.51 memory used=9155.8MB, alloc=155.8MB, time=276.60 memory used=9167.7MB, alloc=155.8MB, time=276.66 memory used=9180.3MB, alloc=155.8MB, time=276.73 memory used=9196.4MB, alloc=155.8MB, time=276.81 memory used=9221.5MB, alloc=155.8MB, time=276.90 memory used=9250.1MB, alloc=155.8MB, time=276.99 memory used=9281.1MB, alloc=155.8MB, time=277.08 memory used=9314.6MB, alloc=155.8MB, time=277.17 memory used=9350.4MB, alloc=155.8MB, time=277.27 memory used=9388.9MB, alloc=155.8MB, time=277.37 memory used=9404.9MB, alloc=155.8MB, time=277.44 memory used=9417.3MB, alloc=155.8MB, time=277.58 memory used=9516.5MB, alloc=155.8MB, time=278.58 memory used=9606.9MB, alloc=155.8MB, time=279.28 memory used=9689.8MB, alloc=155.8MB, time=279.75 memory used=9804.9MB, alloc=155.8MB, time=291.06 memory used=9879.1MB, alloc=155.8MB, time=291.31 memory used=9941.4MB, alloc=155.8MB, time=291.47 memory used=10004.1MB, alloc=155.8MB, time=291.62 memory used=10054.1MB, alloc=155.8MB, time=291.74 memory used=10111.6MB, alloc=155.8MB, time=291.87 memory used=10179.2MB, alloc=155.8MB, time=292.00 memory used=10253.1MB, alloc=155.8MB, time=292.14 memory used=10263.8MB, alloc=155.8MB, time=292.21 memory used=10275.3MB, alloc=155.8MB, time=292.28 memory used=10286.9MB, alloc=155.8MB, time=292.35 memory used=10299.5MB, alloc=155.8MB, time=292.44 memory used=10378.4MB, alloc=411.8MB, time=293.34 memory used=10495.9MB, alloc=411.8MB, time=294.73 memory used=10581.5MB, alloc=411.8MB, time=296.97 memory used=10633.3MB, alloc=411.8MB, time=297.16 memory used=10691.6MB, alloc=411.8MB, time=297.35 memory used=10732.9MB, alloc=411.8MB, time=297.50 memory used=10781.9MB, alloc=411.8MB, time=297.66 memory used=10840.5MB, alloc=411.8MB, time=297.82 memory used=10947.6MB, alloc=411.8MB, time=298.38 memory used=11008.1MB, alloc=411.8MB, time=298.73 memory used=11067.3MB, alloc=411.8MB, time=298.91 memory used=11161.0MB, alloc=435.8MB, time=331.12 memory used=11233.3MB, alloc=459.8MB, time=395.73 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428505410 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 3 2 F := [9 x y z + 17 x z - 11 x z, -9 x y + 5 x y + 8] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 3 G := [19 x z - 10 y z , 15 x y + 16 x z - y] > Problem := [F,G]; 2 3 3 2 Problem := [[9 x y z + 17 x z - 11 x z, -9 x y + 5 x y + 8], 3 2 3 3 [19 x z - 10 y z , 15 x y + 16 x z - y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=26.4MB, alloc=32.3MB, time=0.49 memory used=48.1MB, alloc=32.3MB, time=0.82 memory used=67.3MB, alloc=56.3MB, time=1.11 memory used=107.5MB, alloc=60.3MB, time=1.53 memory used=152.0MB, alloc=60.3MB, time=2.12 memory used=194.8MB, alloc=60.3MB, time=2.78 memory used=234.9MB, alloc=84.3MB, time=3.50 memory used=296.1MB, alloc=84.3MB, time=4.56 memory used=353.1MB, alloc=108.3MB, time=5.57 memory used=429.6MB, alloc=140.3MB, time=6.94 memory used=519.4MB, alloc=164.3MB, time=9.09 memory used=614.9MB, alloc=188.3MB, time=12.46 memory used=728.1MB, alloc=188.3MB, time=16.78 memory used=841.4MB, alloc=212.3MB, time=21.09 N1 := 3683 > GB := Basis(F, plex(op(vars))); 3 2 2 3 GB := [9 y x - 5 y x - 8, 9 y z + 17 z - 11 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=985.4MB, alloc=212.3MB, time=24.88 memory used=1072.4MB, alloc=468.3MB, time=26.11 memory used=1235.4MB, alloc=492.3MB, time=29.00 memory used=1412.1MB, alloc=516.3MB, time=32.65 memory used=1577.4MB, alloc=540.3MB, time=38.82 memory used=1758.6MB, alloc=564.3MB, time=45.95 N2 := 3683 > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 3 3 2 3 2 H := [9 x y z + 17 x z - 11 x z, -9 x y + 5 x y + 8, 19 x z - 10 y z , 3 3 16 z x + 15 y x - y] > J:=[op(GB),op(G)]; 3 2 2 3 3 2 J := [9 y x - 5 y x - 8, 9 y z + 17 z - 11 z, 19 x z - 10 y z , 3 3 16 z x + 15 y x - y] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 11, 16, 4, 3, 3, 3, 1, 1, 3/4, 8/11, 6/11, 6/11, 4, 10, 15, 4, 3, 3, 3, 3/4, 1, 3/4, 5/11, 6/11, 6/11, 1, 1, 0] > save(F, G, cat("ranSet/34", convert(F, string),".txt")); > quit memory used=1826.3MB, alloc=564.3MB, time=48.26 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428505481 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 4 3 F := [-2 x z + 3 x + 4 x, 4 x + 11 y z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 2 2 2 G := [19 x y - 9 y z - 10 z , 6 x z + 10 y z - 17 x z] > Problem := [F,G]; 2 2 4 3 Problem := [[-2 x z + 3 x + 4 x, 4 x + 11 y z], 2 2 2 2 2 2 2 2 [19 x y - 9 y z - 10 z , 6 x z + 10 y z - 17 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=25.4MB, alloc=32.3MB, time=0.49 memory used=45.7MB, alloc=60.3MB, time=0.81 memory used=86.8MB, alloc=60.3MB, time=1.39 memory used=134.6MB, alloc=92.3MB, time=1.94 memory used=202.2MB, alloc=92.3MB, time=2.88 memory used=269.2MB, alloc=116.3MB, time=3.80 memory used=342.6MB, alloc=372.3MB, time=4.64 memory used=432.1MB, alloc=396.3MB, time=5.86 memory used=533.6MB, alloc=396.3MB, time=6.82 memory used=633.0MB, alloc=396.3MB, time=7.49 memory used=745.9MB, alloc=420.3MB, time=8.87 memory used=848.1MB, alloc=420.3MB, time=9.53 memory used=936.3MB, alloc=420.3MB, time=10.57 memory used=1070.1MB, alloc=420.3MB, time=11.95 memory used=1193.0MB, alloc=420.3MB, time=13.26 memory used=1313.9MB, alloc=444.3MB, time=14.92 memory used=1486.3MB, alloc=444.3MB, time=16.61 memory used=1596.9MB, alloc=444.3MB, time=18.25 memory used=1748.6MB, alloc=468.3MB, time=19.85 memory used=1910.1MB, alloc=468.3MB, time=21.40 memory used=2058.1MB, alloc=468.3MB, time=22.75 memory used=2180.4MB, alloc=492.3MB, time=24.74 memory used=2362.9MB, alloc=492.3MB, time=26.03 memory used=2548.7MB, alloc=492.3MB, time=27.50 memory used=2680.1MB, alloc=516.3MB, time=29.92 memory used=2847.3MB, alloc=540.3MB, time=33.27 memory used=3009.6MB, alloc=564.3MB, time=36.17 memory used=3188.1MB, alloc=588.3MB, time=39.53 memory used=3465.8MB, alloc=588.3MB, time=43.30 memory used=3638.5MB, alloc=588.3MB, time=46.83 memory used=3812.1MB, alloc=612.3MB, time=49.68 memory used=3956.2MB, alloc=636.3MB, time=52.38 memory used=4136.7MB, alloc=660.3MB, time=57.33 memory used=4375.4MB, alloc=684.3MB, time=65.56 memory used=4613.9MB, alloc=708.3MB, time=74.62 memory used=4854.5MB, alloc=732.3MB, time=84.80 memory used=5119.1MB, alloc=756.3MB, time=95.88 memory used=5407.5MB, alloc=780.3MB, time=107.95 memory used=5720.0MB, alloc=804.3MB, time=120.92 memory used=6056.3MB, alloc=804.3MB, time=134.82 memory used=6392.7MB, alloc=804.3MB, time=148.79 memory used=6729.0MB, alloc=828.3MB, time=162.70 memory used=7089.2MB, alloc=828.3MB, time=177.52 memory used=7449.5MB, alloc=852.3MB, time=192.51 memory used=7833.6MB, alloc=876.3MB, time=208.21 memory used=8242.0MB, alloc=900.3MB, time=224.72 N1 := 11795 > GB := Basis(F, plex(op(vars))); 6 2 3 3 2 2 3 4 GB := [8 x + 33 x y + 44 x y , 2 x z - 3 x - 4 x, 11 z y + 4 x ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=8350.6MB, alloc=900.3MB, time=227.99 memory used=8411.6MB, alloc=900.3MB, time=229.43 memory used=8484.1MB, alloc=900.3MB, time=230.93 memory used=8556.2MB, alloc=900.3MB, time=232.59 memory used=8619.6MB, alloc=900.3MB, time=233.90 memory used=8729.3MB, alloc=900.3MB, time=235.20 memory used=8862.2MB, alloc=900.3MB, time=236.99 memory used=8930.4MB, alloc=900.3MB, time=238.38 memory used=8990.5MB, alloc=900.3MB, time=239.71 memory used=9055.9MB, alloc=900.3MB, time=241.48 memory used=9111.2MB, alloc=900.3MB, time=243.11 memory used=9190.8MB, alloc=900.3MB, time=244.83 memory used=9280.4MB, alloc=900.3MB, time=246.37 memory used=9353.7MB, alloc=900.3MB, time=248.00 memory used=9668.0MB, alloc=900.3MB, time=252.14 memory used=9836.1MB, alloc=900.3MB, time=255.26 memory used=10367.6MB, alloc=900.3MB, time=261.58 memory used=10905.2MB, alloc=900.3MB, time=267.99 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428505781 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 4 F := [12 x z - 15 x y - 4, 13 x + 19 x y - 5 x z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [5 x y z + 10 y z + 11 x, -19 x z + 8 y z + 10 x y] > Problem := [F,G]; 2 2 4 Problem := [[12 x z - 15 x y - 4, 13 x + 19 x y - 5 x z], 2 2 2 2 [5 x y z + 10 y z + 11 x, -19 x z + 8 y z + 10 x y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=26.7MB, alloc=32.3MB, time=0.52 memory used=47.4MB, alloc=60.3MB, time=0.82 memory used=84.8MB, alloc=61.7MB, time=1.21 memory used=131.8MB, alloc=69.7MB, time=1.82 memory used=173.7MB, alloc=69.7MB, time=2.43 memory used=216.9MB, alloc=93.7MB, time=3.03 memory used=291.9MB, alloc=93.7MB, time=3.90 memory used=357.6MB, alloc=117.7MB, time=4.82 memory used=426.6MB, alloc=373.7MB, time=5.72 memory used=487.8MB, alloc=373.7MB, time=6.07 memory used=548.1MB, alloc=373.7MB, time=6.36 memory used=636.4MB, alloc=373.7MB, time=7.11 memory used=735.2MB, alloc=373.7MB, time=8.00 memory used=803.2MB, alloc=373.7MB, time=8.50 memory used=857.6MB, alloc=373.7MB, time=8.78 memory used=917.7MB, alloc=373.7MB, time=9.22 memory used=1011.5MB, alloc=373.7MB, time=10.21 memory used=1102.1MB, alloc=397.7MB, time=11.51 memory used=1216.1MB, alloc=421.7MB, time=13.24 memory used=1352.0MB, alloc=421.7MB, time=14.96 memory used=1441.1MB, alloc=421.7MB, time=15.57 memory used=1511.7MB, alloc=421.7MB, time=15.91 memory used=1586.1MB, alloc=421.7MB, time=16.45 memory used=1655.5MB, alloc=421.7MB, time=16.76 memory used=1736.4MB, alloc=421.7MB, time=17.14 memory used=1812.7MB, alloc=421.7MB, time=17.70 memory used=1930.8MB, alloc=421.7MB, time=18.93 memory used=2050.1MB, alloc=421.7MB, time=20.22 memory used=2169.3MB, alloc=421.7MB, time=21.28 memory used=2283.7MB, alloc=445.7MB, time=22.88 memory used=2389.2MB, alloc=445.7MB, time=24.47 memory used=2502.1MB, alloc=445.7MB, time=26.04 memory used=2602.7MB, alloc=469.7MB, time=27.70 memory used=2695.1MB, alloc=469.7MB, time=29.23 memory used=2780.6MB, alloc=469.7MB, time=30.63 memory used=2890.1MB, alloc=469.7MB, time=32.03 memory used=2976.4MB, alloc=469.7MB, time=33.43 memory used=3072.5MB, alloc=469.7MB, time=34.72 memory used=3202.9MB, alloc=493.7MB, time=35.92 memory used=3290.9MB, alloc=493.7MB, time=36.35 memory used=3389.7MB, alloc=493.7MB, time=36.81 memory used=3476.5MB, alloc=493.7MB, time=37.22 memory used=3590.6MB, alloc=493.7MB, time=38.08 memory used=3669.9MB, alloc=493.7MB, time=38.42 memory used=3768.1MB, alloc=493.7MB, time=38.88 memory used=3867.8MB, alloc=493.7MB, time=39.33 memory used=3960.4MB, alloc=493.7MB, time=39.73 memory used=4051.8MB, alloc=493.7MB, time=40.20 memory used=4167.7MB, alloc=493.7MB, time=41.02 memory used=4250.5MB, alloc=493.7MB, time=41.40 memory used=4365.1MB, alloc=493.7MB, time=42.12 memory used=4497.1MB, alloc=493.7MB, time=43.32 memory used=4600.5MB, alloc=493.7MB, time=44.27 memory used=4688.3MB, alloc=493.7MB, time=45.43 memory used=4768.9MB, alloc=493.7MB, time=46.51 memory used=4830.6MB, alloc=493.7MB, time=47.63 memory used=4883.9MB, alloc=493.7MB, time=48.58 memory used=4944.1MB, alloc=493.7MB, time=49.68 memory used=4994.1MB, alloc=493.7MB, time=50.68 memory used=5050.3MB, alloc=493.7MB, time=51.73 memory used=5102.1MB, alloc=493.7MB, time=52.84 memory used=5294.8MB, alloc=517.7MB, time=55.79 memory used=5512.7MB, alloc=541.7MB, time=58.68 memory used=5761.4MB, alloc=565.7MB, time=62.35 memory used=6017.8MB, alloc=565.7MB, time=64.93 memory used=6282.5MB, alloc=589.7MB, time=68.19 memory used=6567.0MB, alloc=613.7MB, time=72.73 memory used=6835.8MB, alloc=637.7MB, time=77.94 memory used=7106.3MB, alloc=661.7MB, time=83.25 memory used=7382.1MB, alloc=685.7MB, time=88.92 memory used=7647.8MB, alloc=709.7MB, time=94.39 memory used=7927.0MB, alloc=733.7MB, time=99.90 memory used=8199.2MB, alloc=757.7MB, time=105.16 memory used=8475.8MB, alloc=781.7MB, time=110.30 memory used=8747.0MB, alloc=805.7MB, time=115.37 memory used=9007.2MB, alloc=829.7MB, time=119.69 memory used=9302.0MB, alloc=853.7MB, time=124.85 memory used=9597.0MB, alloc=877.7MB, time=129.86 memory used=9876.5MB, alloc=901.7MB, time=135.08 memory used=10139.2MB, alloc=925.7MB, time=140.06 memory used=10366.8MB, alloc=949.7MB, time=145.00 memory used=10568.0MB, alloc=973.7MB, time=149.61 memory used=10766.8MB, alloc=997.7MB, time=154.35 memory used=10975.5MB, alloc=1021.7MB, time=159.12 memory used=11478.6MB, alloc=1045.7MB, time=172.18 memory used=11885.1MB, alloc=1069.7MB, time=188.07 memory used=12290.5MB, alloc=1093.7MB, time=204.70 memory used=12700.9MB, alloc=1117.7MB, time=222.00 memory used=13119.9MB, alloc=1141.7MB, time=240.03 memory used=13548.8MB, alloc=1165.7MB, time=258.79 memory used=13988.9MB, alloc=1189.7MB, time=278.18 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428506081 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 F := [12 x y - 8 x y z + 16 x z , -3 x z - 12 y z - 18 x y] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 3 2 G := [-10 x y z + 19 y z - 12 z , 6 x y - 5 x - 12 x] > Problem := [F,G]; 3 2 2 2 Problem := [[12 x y - 8 x y z + 16 x z , -3 x z - 12 y z - 18 x y], 2 2 3 3 2 [-10 x y z + 19 y z - 12 z , 6 x y - 5 x - 12 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.8MB, alloc=32.3MB, time=0.51 memory used=48.2MB, alloc=32.3MB, time=0.83 memory used=67.7MB, alloc=56.3MB, time=1.15 memory used=107.9MB, alloc=60.3MB, time=1.77 memory used=146.7MB, alloc=60.3MB, time=2.35 memory used=185.3MB, alloc=84.3MB, time=2.96 memory used=225.8MB, alloc=84.3MB, time=3.59 memory used=290.1MB, alloc=92.3MB, time=4.42 memory used=355.6MB, alloc=92.3MB, time=5.34 memory used=415.4MB, alloc=116.3MB, time=6.29 memory used=477.2MB, alloc=372.3MB, time=7.15 memory used=562.3MB, alloc=396.3MB, time=8.55 memory used=674.8MB, alloc=420.3MB, time=10.17 memory used=797.4MB, alloc=444.3MB, time=12.31 memory used=938.7MB, alloc=468.3MB, time=14.74 memory used=1093.7MB, alloc=492.3MB, time=17.51 memory used=1275.3MB, alloc=516.3MB, time=20.37 memory used=1470.7MB, alloc=540.3MB, time=23.57 memory used=1697.4MB, alloc=564.3MB, time=26.68 memory used=1907.7MB, alloc=588.3MB, time=30.94 memory used=2101.0MB, alloc=612.3MB, time=36.94 memory used=2296.9MB, alloc=636.3MB, time=43.65 memory used=2501.6MB, alloc=660.3MB, time=51.18 memory used=2714.7MB, alloc=684.3MB, time=59.82 memory used=2943.5MB, alloc=708.3MB, time=69.36 memory used=3196.3MB, alloc=732.3MB, time=79.90 memory used=3473.0MB, alloc=756.3MB, time=91.36 memory used=3773.7MB, alloc=780.3MB, time=103.80 memory used=4098.3MB, alloc=780.3MB, time=117.49 memory used=4422.9MB, alloc=804.3MB, time=131.46 memory used=4771.3MB, alloc=804.3MB, time=145.89 memory used=5119.8MB, alloc=804.3MB, time=160.31 memory used=5468.2MB, alloc=828.3MB, time=174.70 memory used=5840.5MB, alloc=828.3MB, time=190.05 memory used=6212.6MB, alloc=828.3MB, time=205.55 memory used=6584.7MB, alloc=852.3MB, time=220.98 memory used=6980.8MB, alloc=852.3MB, time=238.49 memory used=7376.8MB, alloc=876.3MB, time=255.42 memory used=7796.8MB, alloc=900.3MB, time=272.54 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428506381 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 3 3 3 F := [-5 y z - 4 x + 18, -2 x z + 6 y z - 10 x ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 G := [3 z - 6 x y + 19 y z, -11 x y z + 9 x - 12 z] > Problem := [F,G]; 2 2 3 3 3 3 Problem := [[-5 y z - 4 x + 18, -2 x z + 6 y z - 10 x ], 4 [3 z - 6 x y + 19 y z, -11 x y z + 9 x - 12 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=24.4MB, alloc=32.3MB, time=0.47 memory used=43.6MB, alloc=56.3MB, time=0.77 memory used=95.0MB, alloc=60.3MB, time=1.35 memory used=139.7MB, alloc=68.3MB, time=1.86 memory used=179.4MB, alloc=68.3MB, time=2.17 memory used=212.7MB, alloc=68.3MB, time=2.32 memory used=249.0MB, alloc=68.3MB, time=2.51 memory used=290.5MB, alloc=68.3MB, time=2.77 memory used=314.4MB, alloc=68.3MB, time=2.86 memory used=337.0MB, alloc=68.3MB, time=2.94 memory used=363.9MB, alloc=68.3MB, time=3.02 memory used=394.5MB, alloc=68.3MB, time=3.11 memory used=418.2MB, alloc=68.3MB, time=3.18 memory used=436.0MB, alloc=68.3MB, time=3.25 memory used=455.5MB, alloc=68.3MB, time=3.32 memory used=475.5MB, alloc=68.3MB, time=3.39 memory used=497.2MB, alloc=68.3MB, time=3.45 memory used=520.7MB, alloc=68.3MB, time=3.53 memory used=545.8MB, alloc=68.3MB, time=3.60 memory used=572.4MB, alloc=68.3MB, time=3.66 memory used=600.1MB, alloc=68.3MB, time=3.74 memory used=630.3MB, alloc=68.3MB, time=3.82 memory used=662.1MB, alloc=68.3MB, time=3.89 memory used=679.4MB, alloc=68.3MB, time=3.94 memory used=696.8MB, alloc=68.3MB, time=3.99 memory used=714.9MB, alloc=68.3MB, time=4.05 memory used=734.4MB, alloc=68.3MB, time=4.09 memory used=766.1MB, alloc=68.3MB, time=5.95 memory used=811.6MB, alloc=68.3MB, time=11.82 memory used=836.1MB, alloc=68.3MB, time=11.91 memory used=866.3MB, alloc=68.3MB, time=12.00 memory used=885.3MB, alloc=68.3MB, time=12.06 memory used=906.1MB, alloc=68.3MB, time=12.13 memory used=929.1MB, alloc=68.3MB, time=12.21 memory used=954.6MB, alloc=68.3MB, time=12.28 memory used=983.0MB, alloc=68.3MB, time=12.35 memory used=1014.6MB, alloc=68.3MB, time=12.43 memory used=1033.5MB, alloc=68.3MB, time=12.49 memory used=1050.3MB, alloc=68.3MB, time=12.54 memory used=1068.1MB, alloc=68.3MB, time=12.59 memory used=1087.0MB, alloc=68.3MB, time=12.65 memory used=1106.8MB, alloc=68.3MB, time=12.71 memory used=1127.5MB, alloc=68.3MB, time=12.76 memory used=1149.9MB, alloc=68.3MB, time=12.82 memory used=1172.7MB, alloc=68.3MB, time=12.87 memory used=1195.8MB, alloc=68.3MB, time=12.93 memory used=1220.7MB, alloc=68.3MB, time=12.99 memory used=1246.8MB, alloc=68.3MB, time=13.05 memory used=1274.8MB, alloc=68.3MB, time=13.11 memory used=1315.8MB, alloc=78.0MB, time=13.28 memory used=1354.3MB, alloc=78.0MB, time=13.40 memory used=1374.8MB, alloc=78.0MB, time=13.49 memory used=1399.3MB, alloc=78.0MB, time=13.57 memory used=1428.9MB, alloc=78.0MB, time=13.65 memory used=1452.6MB, alloc=78.0MB, time=13.72 memory used=1470.6MB, alloc=78.0MB, time=13.79 memory used=1490.0MB, alloc=78.0MB, time=13.86 memory used=1510.9MB, alloc=78.0MB, time=13.92 memory used=1533.7MB, alloc=78.0MB, time=13.99 memory used=1558.7MB, alloc=78.0MB, time=14.06 memory used=1586.2MB, alloc=78.0MB, time=14.12 memory used=1616.8MB, alloc=78.0MB, time=14.19 memory used=1636.7MB, alloc=78.0MB, time=14.24 memory used=1684.9MB, alloc=78.0MB, time=19.13 memory used=1711.3MB, alloc=78.0MB, time=19.22 memory used=1740.2MB, alloc=78.0MB, time=19.31 memory used=1759.5MB, alloc=78.0MB, time=19.37 memory used=1781.6MB, alloc=78.0MB, time=19.45 memory used=1806.7MB, alloc=78.0MB, time=19.53 memory used=1835.6MB, alloc=78.0MB, time=19.59 memory used=1866.3MB, alloc=78.0MB, time=19.66 memory used=1883.7MB, alloc=78.0MB, time=19.71 memory used=1902.2MB, alloc=78.0MB, time=19.76 memory used=1921.3MB, alloc=78.0MB, time=19.82 memory used=1941.5MB, alloc=78.0MB, time=19.87 memory used=1963.4MB, alloc=78.0MB, time=19.92 memory used=1986.6MB, alloc=78.0MB, time=19.98 memory used=2011.9MB, alloc=78.0MB, time=20.04 memory used=2040.3MB, alloc=78.0MB, time=20.09 memory used=2112.6MB, alloc=78.0MB, time=21.62 memory used=2146.7MB, alloc=78.0MB, time=28.08 memory used=2171.8MB, alloc=102.0MB, time=30.04 memory used=2222.9MB, alloc=102.0MB, time=31.14 memory used=2259.9MB, alloc=102.0MB, time=31.27 memory used=2304.3MB, alloc=102.0MB, time=31.39 memory used=2341.4MB, alloc=102.0MB, time=31.51 memory used=2368.7MB, alloc=102.0MB, time=31.62 memory used=2397.7MB, alloc=102.0MB, time=31.72 memory used=2427.9MB, alloc=102.0MB, time=31.82 memory used=2459.7MB, alloc=102.0MB, time=31.93 memory used=2493.1MB, alloc=102.0MB, time=32.03 memory used=2527.9MB, alloc=102.0MB, time=32.14 memory used=2564.3MB, alloc=102.0MB, time=32.25 memory used=2604.7MB, alloc=102.0MB, time=32.37 memory used=2646.8MB, alloc=102.0MB, time=32.49 memory used=2690.4MB, alloc=102.0MB, time=32.61 memory used=2735.6MB, alloc=102.0MB, time=32.73 memory used=2778.4MB, alloc=102.0MB, time=32.84 memory used=2805.9MB, alloc=102.0MB, time=32.93 memory used=2829.9MB, alloc=102.0MB, time=33.01 memory used=2851.5MB, alloc=102.0MB, time=33.08 memory used=2874.6MB, alloc=102.0MB, time=33.15 memory used=2898.0MB, alloc=102.0MB, time=33.23 memory used=2921.7MB, alloc=102.0MB, time=33.30 memory used=2945.7MB, alloc=102.0MB, time=33.37 memory used=2970.0MB, alloc=102.0MB, time=33.44 memory used=2994.5MB, alloc=102.0MB, time=33.53 memory used=3019.4MB, alloc=102.0MB, time=33.60 memory used=3044.5MB, alloc=102.0MB, time=33.68 memory used=3069.9MB, alloc=102.0MB, time=33.74 memory used=3095.5MB, alloc=102.0MB, time=33.81 memory used=3121.5MB, alloc=102.0MB, time=33.89 memory used=3147.9MB, alloc=102.0MB, time=33.97 memory used=3178.0MB, alloc=102.0MB, time=34.05 memory used=3208.5MB, alloc=102.0MB, time=34.13 memory used=3239.4MB, alloc=102.0MB, time=34.20 memory used=3270.7MB, alloc=102.0MB, time=34.28 memory used=3302.2MB, alloc=102.0MB, time=34.36 memory used=3334.0MB, alloc=102.0MB, time=34.43 memory used=3366.2MB, alloc=102.0MB, time=34.51 memory used=3398.6MB, alloc=102.0MB, time=34.59 memory used=3431.4MB, alloc=102.0MB, time=34.67 memory used=3464.4MB, alloc=102.0MB, time=34.75 memory used=3497.7MB, alloc=102.0MB, time=34.82 memory used=3531.3MB, alloc=102.0MB, time=34.90 memory used=3565.2MB, alloc=102.0MB, time=34.98 memory used=3599.3MB, alloc=102.0MB, time=35.05 memory used=3633.7MB, alloc=102.0MB, time=35.13 memory used=3668.3MB, alloc=102.0MB, time=35.22 memory used=3703.2MB, alloc=102.0MB, time=35.30 memory used=3738.5MB, alloc=102.0MB, time=35.37 memory used=3778.2MB, alloc=102.0MB, time=35.46 memory used=3818.3MB, alloc=102.0MB, time=35.55 memory used=3858.7MB, alloc=102.0MB, time=35.63 memory used=3899.3MB, alloc=102.0MB, time=35.70 memory used=3940.3MB, alloc=102.0MB, time=35.79 memory used=3981.4MB, alloc=102.0MB, time=35.87 memory used=4022.9MB, alloc=102.0MB, time=35.95 memory used=4064.6MB, alloc=102.0MB, time=36.03 memory used=4106.5MB, alloc=102.0MB, time=36.12 memory used=4148.7MB, alloc=102.0MB, time=36.20 memory used=4191.1MB, alloc=102.0MB, time=36.28 memory used=4233.7MB, alloc=102.0MB, time=36.37 memory used=4266.3MB, alloc=107.8MB, time=36.44 memory used=4273.7MB, alloc=107.8MB, time=36.49 memory used=4280.7MB, alloc=107.8MB, time=36.54 memory used=4284.8MB, alloc=107.8MB, time=36.58 memory used=4288.9MB, alloc=107.8MB, time=36.63 memory used=4293.1MB, alloc=107.8MB, time=36.67 memory used=4297.3MB, alloc=107.8MB, time=36.72 memory used=4301.9MB, alloc=107.8MB, time=36.77 memory used=4306.7MB, alloc=107.8MB, time=36.81 memory used=4311.4MB, alloc=107.8MB, time=36.86 memory used=4316.2MB, alloc=107.8MB, time=36.90 memory used=4320.9MB, alloc=107.8MB, time=36.94 memory used=4325.7MB, alloc=107.8MB, time=36.99 memory used=4330.5MB, alloc=107.8MB, time=37.03 memory used=4335.2MB, alloc=107.8MB, time=37.08 memory used=4340.0MB, alloc=107.8MB, time=37.12 memory used=4344.8MB, alloc=107.8MB, time=37.17 memory used=4349.5MB, alloc=107.8MB, time=37.21 memory used=4354.3MB, alloc=107.8MB, time=37.26 memory used=4359.1MB, alloc=107.8MB, time=37.30 memory used=4363.8MB, alloc=107.8MB, time=37.35 memory used=4368.6MB, alloc=107.8MB, time=37.39 memory used=4373.4MB, alloc=107.8MB, time=37.44 memory used=4378.2MB, alloc=107.8MB, time=37.48 memory used=4383.0MB, alloc=107.8MB, time=37.53 memory used=4387.7MB, alloc=107.8MB, time=37.59 memory used=4392.5MB, alloc=107.8MB, time=37.64 memory used=4397.3MB, alloc=107.8MB, time=37.68 memory used=4402.1MB, alloc=107.8MB, time=37.73 memory used=4406.9MB, alloc=107.8MB, time=37.77 memory used=4411.7MB, alloc=107.8MB, time=37.82 memory used=4416.5MB, alloc=107.8MB, time=37.86 memory used=4421.3MB, alloc=107.8MB, time=37.91 memory used=4426.1MB, alloc=107.8MB, time=37.95 memory used=4430.9MB, alloc=107.8MB, time=38.00 memory used=4435.7MB, alloc=107.8MB, time=38.05 memory used=4440.5MB, alloc=107.8MB, time=38.09 memory used=4445.3MB, alloc=107.8MB, time=38.15 memory used=4450.2MB, alloc=107.8MB, time=38.19 memory used=4455.0MB, alloc=107.8MB, time=38.24 memory used=4459.8MB, alloc=107.8MB, time=38.29 memory used=4464.6MB, alloc=107.8MB, time=38.34 memory used=4469.5MB, alloc=107.8MB, time=38.38 memory used=4474.3MB, alloc=107.8MB, time=38.43 memory used=4479.1MB, alloc=107.8MB, time=38.47 memory used=4483.9MB, alloc=107.8MB, time=38.52 memory used=4488.8MB, alloc=107.8MB, time=38.57 memory used=4493.6MB, alloc=107.8MB, time=38.62 memory used=4498.4MB, alloc=107.8MB, time=38.67 memory used=4503.3MB, alloc=107.8MB, time=38.71 memory used=4508.1MB, alloc=107.8MB, time=38.75 memory used=4512.9MB, alloc=107.8MB, time=38.81 memory used=4517.8MB, alloc=107.8MB, time=38.85 memory used=4522.6MB, alloc=107.8MB, time=38.90 memory used=4522.9MB, alloc=363.8MB, time=38.94 memory used=4664.0MB, alloc=363.8MB, time=39.34 memory used=4815.0MB, alloc=363.8MB, time=39.58 memory used=4972.9MB, alloc=363.8MB, time=39.82 memory used=5136.9MB, alloc=363.8MB, time=40.07 memory used=5306.9MB, alloc=363.8MB, time=40.32 memory used=5482.5MB, alloc=363.8MB, time=40.58 memory used=5663.6MB, alloc=363.8MB, time=40.84 memory used=5854.2MB, alloc=363.8MB, time=41.10 memory used=6054.4MB, alloc=363.8MB, time=41.37 memory used=6258.4MB, alloc=363.8MB, time=41.65 memory used=6474.6MB, alloc=363.8MB, time=41.94 memory used=6696.8MB, alloc=363.8MB, time=42.23 memory used=6928.4MB, alloc=363.8MB, time=42.53 memory used=7171.5MB, alloc=363.8MB, time=42.83 memory used=7427.7MB, alloc=363.8MB, time=43.14 memory used=7678.6MB, alloc=363.8MB, time=43.44 memory used=7864.6MB, alloc=363.8MB, time=43.68 memory used=8058.1MB, alloc=363.8MB, time=43.92 memory used=8261.4MB, alloc=363.8MB, time=44.18 memory used=8479.0MB, alloc=363.8MB, time=44.44 memory used=8584.3MB, alloc=363.8MB, time=44.71 memory used=8622.1MB, alloc=363.8MB, time=44.84 memory used=8655.9MB, alloc=363.8MB, time=44.96 memory used=8696.1MB, alloc=363.8MB, time=45.09 memory used=8741.6MB, alloc=363.8MB, time=45.22 memory used=8785.8MB, alloc=363.8MB, time=45.34 memory used=8812.1MB, alloc=363.8MB, time=45.43 memory used=8840.3MB, alloc=363.8MB, time=45.52 memory used=8870.7MB, alloc=363.8MB, time=45.63 memory used=8903.0MB, alloc=363.8MB, time=45.73 memory used=8937.8MB, alloc=363.8MB, time=45.83 memory used=8976.1MB, alloc=363.8MB, time=45.94 memory used=9017.3MB, alloc=363.8MB, time=46.03 memory used=9062.5MB, alloc=363.8MB, time=46.14 memory used=9124.9MB, alloc=363.8MB, time=51.26 memory used=9184.7MB, alloc=387.8MB, time=79.11 memory used=9246.4MB, alloc=387.8MB, time=126.88 memory used=9311.6MB, alloc=411.8MB, time=241.46 memory used=9384.9MB, alloc=435.8MB, time=274.71 memory used=9427.2MB, alloc=459.8MB, time=395.78 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428506681 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 F := [19 x y + 17 y - 5 y, 18 x y z + 14 y z + 20 z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 G := [-3 x z - 2 x z - 20 x y z, -12 x z - 6 z + 18 x] > Problem := [F,G]; 2 2 3 2 Problem := [[19 x y + 17 y - 5 y, 18 x y z + 14 y z + 20 z], 3 2 2 2 2 [-3 x z - 2 x z - 20 x y z, -12 x z - 6 z + 18 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.21 memory used=26.4MB, alloc=32.3MB, time=0.56 memory used=47.5MB, alloc=32.3MB, time=0.88 memory used=67.9MB, alloc=32.3MB, time=1.18 memory used=89.3MB, alloc=56.3MB, time=1.58 memory used=132.6MB, alloc=60.3MB, time=2.36 memory used=173.1MB, alloc=84.3MB, time=3.10 memory used=231.0MB, alloc=108.3MB, time=4.79 N1 := 1563 > GB := Basis(F, plex(op(vars))); 2 2 3 4 3 2 GB := [19 x y + 17 y - 5 y, 5054 x z - 4617 x z - 1377 x z + 8405 z, 2 38 x z + 9 x z + 41 y z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=304.6MB, alloc=108.3MB, time=6.76 memory used=384.6MB, alloc=116.3MB, time=8.11 N2 := 919 > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 3 2 H := [19 x y + 17 y - 5 y, 18 x y z + 14 y z + 20 z, 3 2 2 2 2 -3 x z - 2 x z - 20 x y z, -12 x z - 6 z + 18 x] > J:=[op(GB),op(G)]; 2 2 3 4 3 2 J := [19 x y + 17 y - 5 y, 5054 x z - 4617 x z - 1377 x z + 8405 z, 2 3 2 38 x z + 9 x z + 41 y z, -3 x z - 2 x z - 20 x y z, 2 2 2 -12 x z - 6 z + 18 x] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 10, 15, 4, 2, 3, 3, 1, 3/4, 3/4, 7/12, 1/2, 2/3, 5, 12, 20, 11 5, 4, 3, 3, 1, 3/5, 4/5, --, 5/16, 3/4, -2, -5, -1] 16 > save(F, G, cat("ranSet/34", convert(F, string),".txt")); > quit memory used=444.6MB, alloc=116.3MB, time=9.63 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428506697 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 3 F := [-16 x y + 18 y - 8 z, 3 x y + 17 z + 3] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 2 2 3 G := [-8 y + 5 z + 11 y , -17 x y z + 20 x + 3 y z] > Problem := [F,G]; 3 2 2 3 Problem := [[-16 x y + 18 y - 8 z, 3 x y + 17 z + 3], 4 3 2 2 3 [-8 y + 5 z + 11 y , -17 x y z + 20 x + 3 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.21 memory used=26.2MB, alloc=33.2MB, time=0.50 memory used=44.1MB, alloc=33.3MB, time=0.58 memory used=61.5MB, alloc=33.3MB, time=0.68 memory used=83.5MB, alloc=35.7MB, time=1.00 memory used=95.4MB, alloc=35.7MB, time=1.05 memory used=107.8MB, alloc=35.7MB, time=1.09 memory used=123.1MB, alloc=35.7MB, time=1.20 memory used=142.6MB, alloc=35.7MB, time=1.32 memory used=160.9MB, alloc=35.7MB, time=1.42 memory used=184.4MB, alloc=35.7MB, time=1.85 memory used=199.2MB, alloc=35.7MB, time=1.91 memory used=212.2MB, alloc=35.7MB, time=1.94 memory used=223.2MB, alloc=35.7MB, time=1.98 memory used=242.2MB, alloc=35.7MB, time=2.18 memory used=271.9MB, alloc=39.9MB, time=2.57 memory used=283.3MB, alloc=39.9MB, time=2.61 memory used=295.3MB, alloc=39.9MB, time=2.65 memory used=318.2MB, alloc=39.9MB, time=2.89 memory used=338.9MB, alloc=63.9MB, time=3.19 memory used=384.6MB, alloc=63.9MB, time=3.60 memory used=410.6MB, alloc=63.9MB, time=3.68 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time=155.58 memory used=17344.6MB, alloc=435.8MB, time=155.91 memory used=17495.6MB, alloc=435.8MB, time=156.24 memory used=17657.6MB, alloc=435.8MB, time=156.59 memory used=17832.0MB, alloc=435.8MB, time=156.99 memory used=18019.2MB, alloc=435.8MB, time=157.40 memory used=18228.2MB, alloc=435.8MB, time=157.77 memory used=18368.8MB, alloc=435.8MB, time=158.94 memory used=18429.3MB, alloc=435.8MB, time=159.23 memory used=18501.4MB, alloc=435.8MB, time=159.51 memory used=18588.4MB, alloc=435.8MB, time=159.80 memory used=18646.4MB, alloc=435.8MB, time=160.04 memory used=18697.7MB, alloc=435.8MB, time=160.29 memory used=18751.7MB, alloc=435.8MB, time=160.51 memory used=18810.9MB, alloc=435.8MB, time=160.76 memory used=18872.3MB, alloc=435.8MB, time=161.01 memory used=18939.0MB, alloc=435.8MB, time=161.25 memory used=19007.6MB, alloc=435.8MB, time=161.48 memory used=19081.4MB, alloc=435.8MB, time=161.73 memory used=19160.3MB, alloc=435.8MB, time=161.96 memory used=19244.4MB, alloc=435.8MB, time=162.20 memory used=19326.8MB, alloc=435.8MB, time=162.45 memory used=19377.7MB, alloc=435.8MB, time=162.64 memory used=19421.6MB, alloc=435.8MB, time=162.84 memory used=19466.9MB, alloc=435.8MB, time=163.01 memory used=19515.9MB, alloc=435.8MB, time=163.20 memory used=19564.9MB, alloc=435.8MB, time=163.37 memory used=19617.2MB, alloc=435.8MB, time=163.55 memory used=19669.2MB, alloc=435.8MB, time=163.80 memory used=19724.2MB, alloc=435.8MB, time=163.99 memory used=19779.0MB, alloc=435.8MB, time=164.17 memory used=19835.8MB, alloc=435.8MB, time=164.35 memory used=19895.4MB, alloc=435.8MB, time=164.53 memory used=19956.9MB, alloc=435.8MB, time=164.72 memory used=20020.4MB, alloc=435.8MB, time=164.90 memory used=20087.1MB, alloc=435.8MB, time=165.08 memory used=20157.2MB, alloc=435.8MB, time=165.26 memory used=20231.5MB, alloc=435.8MB, time=165.44 memory used=20308.2MB, alloc=435.8MB, time=165.61 memory used=20390.8MB, alloc=435.8MB, time=165.80 memory used=20500.3MB, alloc=435.8MB, time=166.85 memory used=20564.8MB, alloc=435.8MB, time=167.21 memory used=20632.3MB, alloc=435.8MB, time=167.48 memory used=20712.9MB, alloc=435.8MB, time=167.75 memory used=20783.7MB, alloc=435.8MB, time=168.00 memory used=20833.2MB, alloc=435.8MB, time=168.23 memory used=20885.0MB, alloc=435.8MB, time=168.46 memory used=20940.2MB, alloc=435.8MB, time=168.67 memory used=21000.5MB, alloc=435.8MB, time=168.90 memory used=21063.0MB, alloc=435.8MB, time=169.12 memory used=21130.7MB, alloc=435.8MB, time=169.35 memory used=21203.6MB, alloc=435.8MB, time=169.59 memory used=21278.2MB, alloc=435.8MB, time=169.83 memory used=21357.8MB, alloc=435.8MB, time=170.07 memory used=21442.3MB, alloc=435.8MB, time=170.33 memory used=21509.0MB, alloc=435.8MB, time=170.54 memory used=21553.7MB, alloc=435.8MB, time=170.72 memory used=21600.0MB, alloc=435.8MB, time=170.90 memory used=21645.4MB, alloc=435.8MB, time=171.12 memory used=21694.4MB, alloc=435.8MB, time=171.40 memory used=21743.2MB, alloc=435.8MB, time=171.58 memory used=21795.3MB, alloc=435.8MB, time=171.75 memory used=21847.1MB, alloc=435.8MB, time=171.93 memory used=21901.9MB, alloc=435.8MB, time=172.12 memory used=21959.5MB, alloc=435.8MB, time=172.31 memory used=22016.6MB, alloc=435.8MB, time=172.49 memory used=22075.7MB, alloc=435.8MB, time=172.67 memory used=22139.4MB, alloc=435.8MB, time=172.85 memory used=22204.8MB, alloc=435.8MB, time=173.04 memory used=22273.7MB, alloc=435.8MB, time=173.23 memory used=22344.9MB, alloc=435.8MB, time=173.42 memory used=22419.5MB, alloc=435.8MB, time=173.61 memory used=22498.1MB, alloc=435.8MB, time=173.80 memory used=22595.3MB, alloc=435.8MB, time=179.13 memory used=22758.1MB, alloc=435.8MB, time=199.27 memory used=22830.2MB, alloc=435.8MB, time=199.66 memory used=22906.6MB, alloc=435.8MB, time=199.91 memory used=22961.8MB, alloc=435.8MB, time=200.16 memory used=23022.3MB, alloc=435.8MB, time=200.48 memory used=23089.4MB, alloc=435.8MB, time=200.86 memory used=23164.0MB, alloc=435.8MB, time=201.14 memory used=23246.3MB, alloc=435.8MB, time=201.49 memory used=23317.6MB, alloc=435.8MB, time=201.72 memory used=23367.5MB, alloc=435.8MB, time=201.90 memory used=23415.5MB, alloc=435.8MB, time=202.07 memory used=23465.9MB, alloc=435.8MB, time=202.25 memory used=23517.4MB, alloc=435.8MB, time=202.44 memory used=23572.5MB, alloc=435.8MB, time=202.61 memory used=23628.7MB, alloc=435.8MB, time=202.79 memory used=23688.6MB, alloc=435.8MB, time=202.97 memory used=23749.5MB, alloc=435.8MB, time=203.16 memory used=23814.0MB, alloc=435.8MB, time=203.35 memory used=23879.4MB, alloc=435.8MB, time=203.54 memory used=23948.4MB, alloc=435.8MB, time=203.74 memory used=24020.9MB, alloc=435.8MB, time=203.94 memory used=24094.1MB, alloc=435.8MB, time=204.15 memory used=24170.6MB, alloc=435.8MB, time=204.36 memory used=24250.4MB, alloc=435.8MB, time=204.56 memory used=24333.3MB, alloc=435.8MB, time=204.76 memory used=24419.1MB, alloc=435.8MB, time=204.99 memory used=24613.1MB, alloc=435.8MB, time=205.39 memory used=24755.0MB, alloc=435.8MB, time=205.71 memory used=24905.7MB, alloc=435.8MB, time=206.10 memory used=25066.2MB, alloc=435.8MB, time=206.52 memory used=25237.6MB, alloc=435.8MB, time=206.99 memory used=25421.9MB, alloc=435.8MB, time=207.35 memory used=25626.1MB, alloc=435.8MB, time=207.71 memory used=25834.2MB, alloc=435.8MB, time=209.44 memory used=25893.7MB, alloc=435.8MB, time=209.75 memory used=25958.7MB, alloc=435.8MB, time=210.09 memory used=26033.5MB, alloc=435.8MB, time=210.44 memory used=26116.6MB, alloc=435.8MB, time=210.75 memory used=26181.1MB, alloc=435.8MB, time=211.02 memory used=26230.9MB, alloc=435.8MB, time=211.30 memory used=26280.4MB, alloc=435.8MB, time=211.53 memory used=26334.3MB, alloc=435.8MB, time=211.77 memory used=26390.0MB, alloc=435.8MB, time=212.01 memory used=26447.3MB, alloc=435.8MB, time=212.25 memory used=26506.3MB, alloc=435.8MB, time=212.49 memory used=26567.0MB, alloc=435.8MB, time=212.73 memory used=26633.9MB, alloc=435.8MB, time=212.97 memory used=26702.3MB, alloc=435.8MB, time=213.25 memory used=26772.4MB, alloc=435.8MB, time=213.49 memory used=26848.9MB, alloc=435.8MB, time=213.77 memory used=26926.8MB, alloc=435.8MB, time=214.02 memory used=27006.3MB, alloc=435.8MB, time=214.30 memory used=27092.3MB, alloc=435.8MB, time=214.61 memory used=27159.1MB, alloc=435.8MB, time=214.83 memory used=27209.1MB, alloc=435.8MB, time=215.03 memory used=27252.0MB, alloc=435.8MB, time=215.20 memory used=27294.7MB, alloc=435.8MB, time=215.37 memory used=27338.8MB, alloc=435.8MB, time=215.53 memory used=27383.0MB, alloc=435.8MB, time=215.69 memory used=27427.5MB, alloc=435.8MB, time=215.86 memory used=27472.0MB, alloc=435.8MB, time=216.03 memory used=27516.8MB, alloc=435.8MB, time=216.21 memory used=27562.0MB, alloc=435.8MB, time=216.38 memory used=27612.3MB, alloc=435.8MB, time=216.57 memory used=27662.9MB, alloc=435.8MB, time=216.75 memory used=27713.6MB, alloc=435.8MB, time=216.93 memory used=27764.4MB, alloc=435.8MB, time=217.11 memory used=27815.1MB, alloc=435.8MB, time=217.29 memory used=27866.4MB, alloc=435.8MB, time=217.50 memory used=27922.4MB, alloc=435.8MB, time=217.68 memory used=27978.7MB, alloc=435.8MB, time=217.87 memory used=28034.8MB, alloc=435.8MB, time=218.05 memory used=28091.0MB, alloc=435.8MB, time=218.24 memory used=28152.4MB, alloc=435.8MB, time=218.58 memory used=28213.5MB, alloc=435.8MB, time=218.91 memory used=28274.3MB, alloc=435.8MB, time=219.22 memory used=28334.9MB, alloc=435.8MB, time=219.41 memory used=28400.3MB, alloc=435.8MB, time=219.60 memory used=28465.2MB, alloc=435.8MB, time=219.78 memory used=28530.1MB, alloc=435.8MB, time=219.96 memory used=28598.4MB, alloc=435.8MB, time=220.15 memory used=28666.5MB, alloc=435.8MB, time=220.37 memory used=28738.7MB, alloc=435.8MB, time=220.57 memory used=28810.2MB, alloc=435.8MB, time=220.76 memory used=28884.3MB, alloc=435.8MB, time=220.94 memory used=28962.1MB, alloc=435.8MB, time=221.13 memory used=29042.5MB, alloc=435.8MB, time=221.33 memory used=29125.1MB, alloc=435.8MB, time=221.52 memory used=29209.0MB, alloc=435.8MB, time=221.72 memory used=29315.1MB, alloc=435.8MB, time=221.95 memory used=29476.9MB, alloc=435.8MB, time=222.27 memory used=29621.1MB, alloc=435.8MB, time=222.57 memory used=29812.4MB, alloc=435.8MB, time=223.06 memory used=29981.1MB, alloc=435.8MB, time=224.67 memory used=30141.7MB, alloc=435.8MB, time=226.91 memory used=30304.6MB, alloc=435.8MB, time=230.58 memory used=30490.1MB, alloc=435.8MB, time=233.07 memory used=30652.2MB, alloc=435.8MB, time=234.93 memory used=30816.4MB, alloc=435.8MB, time=238.27 memory used=30939.3MB, alloc=459.8MB, time=297.48 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428506997 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [-16 x y z - x + 14, 14 x y - 5 y + 2] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 G := [2 x y + 6 z - x, -7 x y + 20 x z + 17 y z] > Problem := [F,G]; 2 2 2 2 Problem := [[-16 x y z - x + 14, 14 x y - 5 y + 2], 2 2 3 2 2 [2 x y + 6 z - x, -7 x y + 20 x z + 17 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.0MB, alloc=32.3MB, time=0.48 memory used=46.9MB, alloc=32.3MB, time=0.79 memory used=65.5MB, alloc=60.3MB, time=1.08 memory used=107.7MB, alloc=68.3MB, time=1.68 memory used=148.2MB, alloc=68.3MB, time=2.26 memory used=189.7MB, alloc=92.3MB, time=2.87 memory used=255.5MB, alloc=92.3MB, time=3.81 memory used=320.5MB, alloc=92.3MB, time=4.71 memory used=386.8MB, alloc=116.3MB, time=5.69 memory used=483.6MB, alloc=116.3MB, time=7.23 memory used=575.2MB, alloc=140.3MB, time=8.57 memory used=686.3MB, alloc=140.3MB, time=10.43 memory used=786.5MB, alloc=164.3MB, time=12.16 memory used=887.9MB, alloc=188.3MB, time=14.22 memory used=996.9MB, alloc=444.3MB, time=16.11 memory used=1136.1MB, alloc=468.3MB, time=18.79 memory used=1299.8MB, alloc=492.3MB, time=21.37 memory used=1458.3MB, alloc=516.3MB, time=25.60 memory used=1613.1MB, alloc=540.3MB, time=30.83 memory used=1775.8MB, alloc=564.3MB, time=37.30 memory used=1954.2MB, alloc=588.3MB, time=44.83 memory used=2156.5MB, alloc=612.3MB, time=53.37 memory used=2382.7MB, alloc=612.3MB, time=62.82 memory used=2609.0MB, alloc=612.3MB, time=71.96 memory used=2835.2MB, alloc=636.3MB, time=81.08 memory used=3085.4MB, alloc=636.3MB, time=91.37 memory used=3336.0MB, alloc=660.3MB, time=102.84 N1 := 7891 > GB := Basis(F, plex(op(vars))); 2 2 4 2 2 2 GB := [14 y x - 5 y + 2, -14 x y + 196 x y + 32 x z + 5 x - 70, 2 7 x y + 40 y z - 98 y - 16 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=3625.2MB, alloc=660.3MB, time=108.60 memory used=3889.3MB, alloc=660.3MB, time=113.19 memory used=4171.6MB, alloc=684.3MB, time=118.19 memory used=4428.3MB, alloc=708.3MB, time=122.66 memory used=4673.2MB, alloc=708.3MB, time=126.65 memory used=4938.0MB, alloc=732.3MB, time=131.63 memory used=5178.1MB, alloc=756.3MB, time=136.42 memory used=5515.6MB, alloc=756.3MB, time=141.32 memory used=5936.4MB, alloc=780.3MB, time=147.20 memory used=6317.7MB, alloc=804.3MB, time=152.91 memory used=6731.3MB, alloc=828.3MB, time=158.44 memory used=7109.3MB, alloc=852.3MB, time=164.97 memory used=7523.6MB, alloc=876.3MB, time=171.43 memory used=7986.5MB, alloc=900.3MB, time=178.09 memory used=8334.3MB, alloc=924.3MB, time=184.17 memory used=8851.6MB, alloc=948.3MB, time=194.09 memory used=9387.2MB, alloc=972.3MB, time=203.60 memory used=9903.3MB, alloc=996.3MB, time=213.51 memory used=10415.2MB, alloc=1020.3MB, time=223.62 memory used=10936.7MB, alloc=1044.3MB, time=233.51 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428507298 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 4 2 F := [6 x y z + 18 x y z - 17 x z, 19 x - 12 x - 20 x z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 3 G := [-10 x + 12 x z + 2 y, -6 x z + 11 y - 12 z] > Problem := [F,G]; 2 2 4 2 Problem := [[6 x y z + 18 x y z - 17 x z, 19 x - 12 x - 20 x z], 3 2 2 3 [-10 x + 12 x z + 2 y, -6 x z + 11 y - 12 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.20 memory used=27.1MB, alloc=32.3MB, time=0.54 memory used=48.1MB, alloc=32.3MB, time=0.86 memory used=67.7MB, alloc=56.3MB, time=1.17 memory used=110.0MB, alloc=68.3MB, time=1.80 memory used=150.7MB, alloc=92.3MB, time=2.41 memory used=215.4MB, alloc=92.3MB, time=3.37 memory used=279.0MB, alloc=92.3MB, time=4.31 memory used=340.0MB, alloc=116.3MB, time=5.24 memory used=416.2MB, alloc=372.3MB, time=6.43 memory used=500.7MB, alloc=372.3MB, time=7.72 memory used=586.4MB, alloc=396.3MB, time=8.94 memory used=697.9MB, alloc=420.3MB, time=10.59 memory used=836.9MB, alloc=444.3MB, time=12.35 memory used=981.5MB, alloc=468.3MB, time=14.70 memory used=1130.8MB, alloc=492.3MB, time=17.25 memory used=1293.9MB, alloc=516.3MB, time=20.12 memory used=1467.4MB, alloc=540.3MB, time=23.25 memory used=1651.3MB, alloc=564.3MB, time=26.76 memory used=1853.9MB, alloc=588.3MB, time=30.52 memory used=2063.2MB, alloc=612.3MB, time=34.57 memory used=2262.5MB, alloc=636.3MB, time=38.54 memory used=2464.2MB, alloc=660.3MB, time=42.41 memory used=2658.4MB, alloc=684.3MB, time=46.09 memory used=2849.2MB, alloc=708.3MB, time=50.26 memory used=3070.2MB, alloc=732.3MB, time=57.63 memory used=3294.0MB, alloc=756.3MB, time=65.66 memory used=3527.7MB, alloc=780.3MB, time=74.50 memory used=3774.2MB, alloc=804.3MB, time=84.23 memory used=4034.5MB, alloc=828.3MB, time=94.57 memory used=4308.8MB, alloc=852.3MB, time=105.50 memory used=4597.7MB, alloc=876.3MB, time=117.28 memory used=4901.3MB, alloc=900.3MB, time=129.90 memory used=5219.9MB, alloc=924.3MB, time=143.08 memory used=5553.8MB, alloc=948.3MB, time=156.65 memory used=5897.2MB, alloc=972.3MB, time=171.46 memory used=6261.5MB, alloc=996.3MB, time=187.27 memory used=6649.8MB, alloc=1020.3MB, time=204.16 memory used=7062.0MB, alloc=1044.3MB, time=222.00 memory used=7498.1MB, alloc=1068.3MB, time=241.03 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428507598 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [-5 y z - 14 x z + z , 16 x y z - y z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 2 2 2 G := [16 x - 19 y + 15 z , -4 y z - 5 x y z + 2 x ] > Problem := [F,G]; 2 2 2 2 Problem := [[-5 y z - 14 x z + z , 16 x y z - y z ], 4 2 2 2 2 2 [16 x - 19 y + 15 z , -4 y z - 5 x y z + 2 x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=26.9MB, alloc=32.3MB, time=0.52 memory used=47.8MB, alloc=32.3MB, time=0.82 memory used=66.5MB, alloc=56.3MB, time=1.12 memory used=106.0MB, alloc=60.3MB, time=1.76 memory used=144.3MB, alloc=60.3MB, time=2.34 memory used=182.6MB, alloc=84.3MB, time=2.91 memory used=230.7MB, alloc=84.3MB, time=3.70 memory used=291.9MB, alloc=92.3MB, time=4.61 memory used=353.4MB, alloc=92.3MB, time=5.48 memory used=412.7MB, alloc=116.3MB, time=6.27 memory used=487.0MB, alloc=372.3MB, time=7.40 memory used=588.4MB, alloc=372.3MB, time=8.58 memory used=668.7MB, alloc=372.3MB, time=9.09 memory used=730.7MB, alloc=372.3MB, time=9.33 memory used=811.4MB, alloc=372.3MB, time=10.02 memory used=900.6MB, alloc=396.3MB, time=11.21 memory used=1021.2MB, alloc=396.3MB, time=12.83 memory used=1139.8MB, alloc=420.3MB, time=14.17 memory used=1279.1MB, alloc=420.3MB, time=15.27 memory used=1420.4MB, alloc=420.3MB, time=16.86 memory used=1550.1MB, alloc=444.3MB, time=18.63 memory used=1688.4MB, alloc=444.3MB, time=19.64 memory used=1815.4MB, alloc=444.3MB, time=20.36 memory used=1952.4MB, alloc=468.3MB, time=22.55 memory used=2118.6MB, alloc=468.3MB, time=24.84 memory used=2294.9MB, alloc=492.3MB, time=26.82 memory used=2492.4MB, alloc=492.3MB, time=29.36 memory used=2676.8MB, alloc=516.3MB, time=32.29 memory used=2858.5MB, alloc=540.3MB, time=35.70 memory used=3048.6MB, alloc=564.3MB, time=39.27 memory used=3257.1MB, alloc=588.3MB, time=43.05 memory used=3476.2MB, alloc=612.3MB, time=47.03 memory used=3714.2MB, alloc=636.3MB, time=51.08 memory used=3948.6MB, alloc=660.3MB, time=54.91 memory used=4214.2MB, alloc=684.3MB, time=59.09 memory used=4487.1MB, alloc=708.3MB, time=63.29 memory used=4715.4MB, alloc=732.3MB, time=67.23 memory used=4954.8MB, alloc=756.3MB, time=71.22 memory used=5170.3MB, alloc=780.3MB, time=75.01 memory used=5377.0MB, alloc=804.3MB, time=78.44 memory used=5646.7MB, alloc=828.3MB, time=82.99 memory used=5857.4MB, alloc=852.3MB, time=86.77 memory used=6112.2MB, alloc=876.3MB, time=90.68 memory used=6379.9MB, alloc=900.3MB, time=95.19 memory used=6627.6MB, alloc=924.3MB, time=100.00 memory used=6848.3MB, alloc=948.3MB, time=104.28 memory used=7074.1MB, alloc=972.3MB, time=108.09 memory used=7261.8MB, alloc=996.3MB, time=111.58 memory used=7450.6MB, alloc=1020.3MB, time=115.42 memory used=8006.3MB, alloc=1044.3MB, time=124.93 memory used=8555.7MB, alloc=1068.3MB, time=134.55 memory used=9086.2MB, alloc=1092.3MB, time=145.24 memory used=9584.5MB, alloc=1116.3MB, time=156.87 memory used=10138.4MB, alloc=1140.3MB, time=166.42 memory used=10646.6MB, alloc=1164.3MB, time=178.92 memory used=11041.8MB, alloc=1188.3MB, time=194.60 memory used=11434.7MB, alloc=1212.3MB, time=210.89 memory used=11832.0MB, alloc=1236.3MB, time=227.51 memory used=12236.7MB, alloc=1260.3MB, time=245.23 memory used=12650.8MB, alloc=1284.3MB, time=263.15 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428507898 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 4 3 4 F := [-18 x - 3 z + 19, 12 x + 11 y z + 4 z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 3 2 G := [-9 x y + 6 x y + 16 x z, 4 x y + 3 y z] > Problem := [F,G]; 4 3 4 3 4 Problem := [[-18 x - 3 z + 19, 12 x + 11 y z + 4 z ], 3 3 3 2 [-9 x y + 6 x y + 16 x z, 4 x y + 3 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=25.0MB, alloc=32.3MB, time=0.47 memory used=48.3MB, alloc=36.5MB, time=0.80 memory used=75.7MB, alloc=37.4MB, time=0.99 memory used=103.0MB, alloc=37.9MB, time=1.22 memory used=124.0MB, alloc=37.9MB, time=1.47 memory used=142.5MB, alloc=61.9MB, time=1.82 memory used=185.1MB, alloc=61.9MB, time=2.31 memory used=226.4MB, alloc=61.9MB, time=3.00 memory used=257.7MB, alloc=61.9MB, time=3.09 memory used=292.3MB, alloc=61.9MB, time=3.26 memory used=325.4MB, alloc=62.1MB, time=3.36 memory used=349.5MB, alloc=62.1MB, time=3.43 memory used=372.5MB, alloc=62.1MB, time=3.49 memory used=401.7MB, alloc=62.1MB, time=4.25 memory used=430.3MB, alloc=62.1MB, time=10.00 memory used=463.9MB, alloc=70.8MB, time=11.88 memory used=483.2MB, alloc=70.8MB, time=11.94 memory used=504.0MB, alloc=70.8MB, time=11.99 memory used=540.7MB, alloc=70.8MB, time=12.35 memory used=587.8MB, alloc=70.8MB, time=12.89 memory used=637.3MB, alloc=94.8MB, time=13.38 memory used=709.1MB, alloc=94.8MB, time=14.05 memory used=767.2MB, alloc=94.8MB, time=14.48 memory used=807.5MB, alloc=94.8MB, time=14.68 memory used=845.0MB, alloc=94.8MB, time=14.86 memory used=892.2MB, alloc=94.8MB, time=15.11 memory used=926.8MB, alloc=94.8MB, time=15.23 memory used=954.2MB, alloc=94.8MB, time=15.33 memory used=989.2MB, alloc=94.8MB, time=15.45 memory used=1027.2MB, alloc=94.8MB, time=15.61 memory used=1060.4MB, alloc=94.8MB, time=15.71 memory used=1089.6MB, alloc=94.8MB, time=15.83 memory used=1122.4MB, alloc=94.8MB, time=15.91 memory used=1166.0MB, alloc=94.8MB, time=16.14 memory used=1193.3MB, alloc=94.8MB, time=16.25 memory used=1227.2MB, alloc=94.8MB, time=16.35 memory used=1263.8MB, alloc=94.8MB, time=16.50 memory used=1302.4MB, alloc=94.8MB, time=16.66 memory used=1343.3MB, alloc=94.8MB, time=16.92 memory used=1387.4MB, alloc=94.8MB, time=17.13 memory used=1419.4MB, alloc=94.8MB, time=17.23 memory used=1448.7MB, alloc=94.8MB, time=17.33 memory used=1484.6MB, alloc=94.8MB, time=17.46 memory used=1523.5MB, alloc=94.8MB, time=17.60 memory used=1552.9MB, alloc=94.8MB, time=17.70 memory used=1586.7MB, alloc=94.8MB, time=17.80 memory used=1626.8MB, alloc=94.8MB, time=18.03 memory used=1659.0MB, alloc=94.8MB, time=18.14 memory used=1692.6MB, alloc=94.8MB, time=18.25 memory used=1730.3MB, alloc=94.8MB, time=18.40 memory used=1766.2MB, alloc=94.8MB, time=18.52 memory used=1795.5MB, alloc=94.8MB, time=18.63 memory used=1838.1MB, alloc=94.8MB, time=18.86 memory used=1880.1MB, alloc=94.8MB, time=19.01 memory used=1910.8MB, alloc=94.8MB, time=19.12 memory used=1949.2MB, alloc=94.8MB, time=19.26 memory used=1975.6MB, alloc=94.8MB, time=19.37 memory used=1999.6MB, alloc=94.8MB, time=19.47 memory used=2026.6MB, alloc=94.8MB, time=19.59 memory used=2055.0MB, alloc=94.8MB, time=19.71 memory used=2086.0MB, alloc=94.8MB, time=19.83 memory used=2119.7MB, alloc=94.8MB, time=19.93 memory used=2156.2MB, alloc=94.8MB, time=20.04 memory used=2195.2MB, alloc=94.8MB, time=20.14 memory used=2224.8MB, alloc=94.8MB, time=20.24 memory used=2245.6MB, alloc=94.8MB, time=20.32 memory used=2267.4MB, alloc=118.8MB, time=20.41 memory used=2303.5MB, alloc=118.8MB, time=20.51 memory used=2342.9MB, alloc=118.8MB, time=20.62 memory used=2383.9MB, alloc=118.8MB, time=20.72 memory used=2428.5MB, alloc=118.8MB, time=20.83 memory used=2475.5MB, alloc=118.8MB, time=20.93 memory used=2527.3MB, alloc=118.8MB, time=21.05 memory used=2582.3MB, alloc=118.8MB, time=21.16 memory used=2651.0MB, alloc=131.8MB, time=21.29 memory used=2662.3MB, alloc=131.8MB, time=21.35 memory used=2673.8MB, alloc=131.8MB, time=21.42 memory used=2685.7MB, alloc=131.8MB, time=21.48 memory used=2697.8MB, alloc=131.8MB, time=21.55 memory used=2710.2MB, alloc=131.8MB, time=21.62 memory used=2787.6MB, alloc=131.8MB, time=22.11 memory used=2833.9MB, alloc=131.8MB, time=22.25 memory used=2890.5MB, alloc=131.8MB, time=22.52 memory used=2943.1MB, alloc=131.8MB, time=22.69 memory used=2992.2MB, alloc=131.8MB, time=22.84 memory used=3035.0MB, alloc=131.8MB, time=22.98 memory used=3087.9MB, alloc=131.8MB, time=23.12 memory used=3137.5MB, alloc=131.8MB, time=23.24 memory used=3176.6MB, alloc=131.8MB, time=23.34 memory used=3222.9MB, alloc=131.8MB, time=23.44 memory used=3286.1MB, alloc=131.8MB, time=23.77 memory used=3339.2MB, alloc=131.8MB, time=23.92 memory used=3380.5MB, alloc=131.8MB, time=24.06 memory used=3430.8MB, alloc=131.8MB, time=24.19 memory used=3485.7MB, alloc=131.8MB, time=24.32 memory used=3523.4MB, alloc=131.8MB, time=24.42 memory used=3568.6MB, alloc=131.8MB, time=24.52 memory used=3650.8MB, alloc=131.8MB, time=48.99 memory used=3717.7MB, alloc=131.8MB, time=54.26 memory used=3764.3MB, alloc=131.8MB, time=54.41 memory used=3816.3MB, alloc=131.8MB, time=54.56 memory used=3852.9MB, alloc=131.8MB, time=54.71 memory used=3894.0MB, alloc=131.8MB, time=54.86 memory used=3940.6MB, alloc=131.8MB, time=55.00 memory used=3992.8MB, alloc=131.8MB, time=55.15 memory used=4050.7MB, alloc=131.8MB, time=55.31 memory used=4103.5MB, alloc=131.8MB, time=55.46 memory used=4134.2MB, alloc=131.8MB, time=55.57 memory used=4166.4MB, alloc=131.8MB, time=55.67 memory used=4201.4MB, alloc=131.8MB, time=55.79 memory used=4237.3MB, alloc=131.8MB, time=55.92 memory used=4273.9MB, alloc=131.8MB, time=56.02 memory used=4313.6MB, alloc=131.8MB, time=56.13 memory used=4354.1MB, alloc=131.8MB, time=56.24 memory used=4395.2MB, alloc=131.8MB, time=56.34 memory used=4439.5MB, alloc=131.8MB, time=56.45 memory used=4484.4MB, alloc=131.8MB, time=56.56 memory used=4529.9MB, alloc=131.8MB, time=56.68 memory used=4578.5MB, alloc=131.8MB, time=56.79 memory used=4627.7MB, alloc=131.8MB, time=56.91 memory used=4679.8MB, alloc=131.8MB, time=57.04 memory used=4732.5MB, alloc=131.8MB, time=57.15 memory used=4787.9MB, alloc=131.8MB, time=57.26 memory used=4846.2MB, alloc=131.8MB, time=57.38 memory used=4905.8MB, alloc=131.8MB, time=57.51 memory used=4946.6MB, alloc=131.8MB, time=57.61 memory used=4955.7MB, alloc=131.8MB, time=57.68 memory used=4962.8MB, alloc=131.8MB, time=57.74 memory used=4970.5MB, alloc=131.8MB, time=57.81 memory used=4978.3MB, alloc=131.8MB, time=57.88 memory used=4986.0MB, alloc=131.8MB, time=57.94 memory used=4993.7MB, alloc=131.8MB, time=58.01 memory used=5001.4MB, alloc=131.8MB, time=58.08 memory used=5009.1MB, alloc=131.8MB, time=58.14 memory used=5016.8MB, alloc=131.8MB, time=58.21 memory used=5024.5MB, alloc=131.8MB, time=58.28 memory used=5032.1MB, alloc=131.8MB, time=58.35 memory used=5039.8MB, alloc=131.8MB, time=58.44 memory used=5047.5MB, alloc=131.8MB, time=58.51 memory used=5055.1MB, alloc=131.8MB, time=58.58 memory used=5062.8MB, alloc=131.8MB, time=58.65 memory used=5070.4MB, alloc=131.8MB, time=58.71 memory used=5078.1MB, alloc=131.8MB, time=58.78 memory used=5085.7MB, alloc=131.8MB, time=58.85 memory used=5093.3MB, alloc=131.8MB, time=58.92 memory used=5100.9MB, alloc=131.8MB, time=58.99 memory used=5108.5MB, alloc=131.8MB, time=59.08 memory used=5116.1MB, alloc=131.8MB, time=59.19 memory used=5123.9MB, alloc=131.8MB, time=59.28 memory used=5133.8MB, alloc=131.8MB, time=59.34 memory used=5141.6MB, alloc=131.8MB, time=59.41 memory used=5151.4MB, alloc=131.8MB, time=59.48 memory used=5161.5MB, alloc=131.8MB, time=59.56 memory used=5171.5MB, alloc=131.8MB, time=59.63 memory used=5181.5MB, alloc=131.8MB, time=59.70 memory used=5191.4MB, alloc=131.8MB, time=59.77 memory used=5201.4MB, alloc=131.8MB, time=59.84 memory used=5211.3MB, alloc=131.8MB, time=59.91 memory used=5221.2MB, alloc=131.8MB, time=59.99 memory used=5231.1MB, alloc=131.8MB, time=60.06 memory used=5240.9MB, alloc=131.8MB, time=60.14 memory used=5250.8MB, alloc=131.8MB, time=60.21 memory used=5260.5MB, alloc=131.8MB, time=60.29 memory used=5270.3MB, alloc=131.8MB, time=60.36 memory used=5280.0MB, alloc=131.8MB, time=60.43 memory used=5289.7MB, alloc=131.8MB, time=60.50 memory used=5299.4MB, alloc=131.8MB, time=60.56 memory used=5309.1MB, alloc=131.8MB, time=60.63 memory used=5318.7MB, alloc=131.8MB, time=60.71 memory used=5328.3MB, alloc=131.8MB, time=60.78 memory used=5337.8MB, alloc=131.8MB, time=60.85 memory used=5347.3MB, alloc=131.8MB, time=60.92 memory used=5357.0MB, alloc=131.8MB, time=60.99 memory used=5368.6MB, alloc=131.8MB, time=61.06 memory used=5380.4MB, alloc=131.8MB, time=61.14 memory used=5392.0MB, alloc=131.8MB, time=61.21 memory used=5403.7MB, alloc=131.8MB, time=61.27 memory used=5415.2MB, alloc=131.8MB, time=61.34 memory used=5426.7MB, alloc=131.8MB, time=61.41 memory used=5438.2MB, alloc=131.8MB, time=61.51 memory used=5449.5MB, alloc=131.8MB, time=61.58 memory used=5460.9MB, alloc=131.8MB, time=61.66 memory used=5472.1MB, alloc=131.8MB, time=61.73 memory used=5483.3MB, alloc=131.8MB, time=61.81 memory used=5494.4MB, alloc=131.8MB, time=61.88 memory used=5505.4MB, alloc=131.8MB, time=61.96 memory used=5516.6MB, alloc=131.8MB, time=62.04 memory used=5529.4MB, alloc=131.8MB, time=62.11 memory used=5542.3MB, alloc=131.8MB, time=62.19 memory used=5555.2MB, alloc=131.8MB, time=62.25 memory used=5567.9MB, alloc=131.8MB, time=62.33 memory used=5580.5MB, alloc=131.8MB, time=62.40 memory used=5593.0MB, alloc=131.8MB, time=62.47 memory used=5605.3MB, alloc=131.8MB, time=62.57 memory used=5617.6MB, alloc=131.8MB, time=62.68 memory used=5629.9MB, alloc=131.8MB, time=62.78 memory used=5643.6MB, alloc=131.8MB, time=62.90 memory used=5657.4MB, alloc=131.8MB, time=62.98 memory used=5671.0MB, alloc=131.8MB, time=63.08 memory used=5684.4MB, alloc=131.8MB, time=63.20 memory used=5697.7MB, alloc=131.8MB, time=63.29 memory used=5711.0MB, alloc=131.8MB, time=63.42 memory used=5725.5MB, alloc=131.8MB, time=63.52 memory used=5739.9MB, alloc=131.8MB, time=63.63 memory used=5754.1MB, alloc=131.8MB, time=63.78 memory used=5769.6MB, alloc=131.8MB, time=63.88 memory used=5784.8MB, alloc=131.8MB, time=64.00 memory used=5799.7MB, alloc=131.8MB, time=64.12 memory used=5815.7MB, alloc=131.8MB, time=64.20 memory used=5831.3MB, alloc=131.8MB, time=64.29 memory used=5847.9MB, alloc=131.8MB, time=64.38 memory used=5863.9MB, alloc=131.8MB, time=64.45 memory used=5880.7MB, alloc=131.8MB, time=64.54 memory used=5898.0MB, alloc=131.8MB, time=64.63 memory used=5915.6MB, alloc=131.8MB, time=64.72 memory used=5933.3MB, alloc=131.8MB, time=64.79 memory used=5951.8MB, alloc=131.8MB, time=64.87 memory used=5970.6MB, alloc=131.8MB, time=64.95 memory used=5990.0MB, alloc=131.8MB, time=65.05 memory used=6059.7MB, alloc=131.8MB, time=65.59 memory used=6111.8MB, alloc=131.8MB, time=65.82 memory used=6151.6MB, alloc=131.8MB, time=66.03 memory used=6201.2MB, alloc=131.8MB, time=66.21 memory used=6255.2MB, alloc=131.8MB, time=66.34 memory used=6292.1MB, alloc=131.8MB, time=66.46 memory used=6336.1MB, alloc=131.8MB, time=66.56 memory used=6406.7MB, alloc=131.8MB, time=69.51 memory used=6469.1MB, alloc=131.8MB, time=71.64 memory used=6526.4MB, alloc=131.8MB, time=71.84 memory used=6560.1MB, alloc=131.8MB, time=71.99 memory used=6592.3MB, alloc=155.8MB, time=72.15 memory used=6641.6MB, alloc=155.8MB, time=72.34 memory used=6697.7MB, alloc=155.8MB, time=72.57 memory used=6758.1MB, alloc=155.8MB, time=72.79 memory used=6822.6MB, alloc=155.8MB, time=72.99 memory used=6891.5MB, alloc=155.8MB, time=73.20 memory used=6964.5MB, alloc=155.8MB, time=73.41 memory used=7026.7MB, alloc=155.8MB, time=73.60 memory used=7063.1MB, alloc=179.8MB, time=73.77 memory used=7111.1MB, alloc=179.8MB, time=73.94 memory used=7164.1MB, alloc=179.8MB, time=74.17 memory used=7218.7MB, alloc=179.8MB, time=74.38 memory used=7274.8MB, alloc=179.8MB, time=74.59 memory used=7332.4MB, alloc=179.8MB, time=74.79 memory used=7391.5MB, alloc=179.8MB, time=75.00 memory used=7452.0MB, alloc=179.8MB, time=75.21 memory used=7514.0MB, alloc=179.8MB, time=75.44 memory used=7577.4MB, alloc=179.8MB, time=75.62 memory used=7642.3MB, alloc=179.8MB, time=75.80 memory used=7708.5MB, alloc=179.8MB, time=76.00 memory used=7776.1MB, alloc=179.8MB, time=76.20 memory used=7845.1MB, alloc=179.8MB, time=76.41 memory used=7915.3MB, alloc=179.8MB, time=76.63 memory used=7986.9MB, alloc=179.8MB, time=76.83 memory used=8059.8MB, alloc=179.8MB, time=77.02 memory used=8134.0MB, alloc=179.8MB, time=77.22 memory used=8209.7MB, alloc=179.8MB, time=77.42 memory used=8297.4MB, alloc=179.8MB, time=77.63 memory used=8386.7MB, alloc=179.8MB, time=77.85 memory used=8477.6MB, alloc=179.8MB, time=78.07 memory used=8570.0MB, alloc=179.8MB, time=78.27 memory used=8663.8MB, alloc=179.8MB, time=78.49 memory used=8722.8MB, alloc=179.8MB, time=78.65 memory used=8764.0MB, alloc=203.8MB, time=78.79 memory used=8811.6MB, alloc=203.8MB, time=78.93 memory used=8860.1MB, alloc=203.8MB, time=79.07 memory used=8908.9MB, alloc=203.8MB, time=79.22 memory used=8958.0MB, alloc=203.8MB, time=79.37 memory used=9007.5MB, alloc=203.8MB, time=79.51 memory used=9057.4MB, alloc=203.8MB, time=79.66 memory used=9107.5MB, alloc=203.8MB, time=79.79 memory used=9158.0MB, alloc=203.8MB, time=79.92 memory used=9208.9MB, alloc=203.8MB, time=80.05 memory used=9260.1MB, alloc=203.8MB, time=80.21 memory used=9312.3MB, alloc=203.8MB, time=80.36 memory used=9376.7MB, alloc=203.8MB, time=80.51 memory used=9441.9MB, alloc=203.8MB, time=80.67 memory used=9507.7MB, alloc=203.8MB, time=80.83 memory used=9574.0MB, alloc=203.8MB, time=80.99 memory used=9640.7MB, alloc=203.8MB, time=81.15 memory used=9707.9MB, alloc=203.8MB, time=81.31 memory used=9775.5MB, alloc=203.8MB, time=81.46 memory used=9843.6MB, alloc=203.8MB, time=81.61 memory used=9912.1MB, alloc=203.8MB, time=81.76 memory used=9981.1MB, alloc=203.8MB, time=81.92 memory used=10050.5MB, alloc=203.8MB, time=82.06 memory used=10120.3MB, alloc=203.8MB, time=82.21 memory used=10190.6MB, alloc=203.8MB, time=82.36 memory used=10261.2MB, alloc=203.8MB, time=82.51 memory used=10332.2MB, alloc=203.8MB, time=82.68 memory used=10403.7MB, alloc=203.8MB, time=82.83 memory used=10475.5MB, alloc=203.8MB, time=82.98 memory used=10547.7MB, alloc=203.8MB, time=83.13 memory used=10620.2MB, alloc=203.8MB, time=83.28 memory used=10693.2MB, alloc=203.8MB, time=83.44 memory used=10766.5MB, alloc=203.8MB, time=83.58 memory used=10840.1MB, alloc=203.8MB, time=83.73 memory used=10914.1MB, alloc=203.8MB, time=83.89 memory used=10988.4MB, alloc=203.8MB, time=84.05 memory used=11063.1MB, alloc=203.8MB, time=84.20 memory used=11138.0MB, alloc=203.8MB, time=84.37 memory used=11213.3MB, alloc=203.8MB, time=84.53 memory used=11288.9MB, alloc=203.8MB, time=84.69 memory used=11364.8MB, alloc=203.8MB, time=84.85 memory used=11441.0MB, alloc=203.8MB, time=85.00 memory used=11517.5MB, alloc=203.8MB, time=85.15 memory used=11594.4MB, alloc=203.8MB, time=85.31 memory used=11672.1MB, alloc=203.8MB, time=85.46 memory used=11764.2MB, alloc=203.8MB, time=85.63 memory used=11857.4MB, alloc=203.8MB, time=85.80 memory used=11951.0MB, alloc=203.8MB, time=85.97 memory used=12044.9MB, alloc=203.8MB, time=86.13 memory used=12139.1MB, alloc=203.8MB, time=86.30 memory used=12233.7MB, alloc=203.8MB, time=86.47 memory used=12328.6MB, alloc=203.8MB, time=86.65 memory used=12423.7MB, alloc=203.8MB, time=86.82 memory used=12519.2MB, alloc=203.8MB, time=87.00 memory used=12615.0MB, alloc=203.8MB, time=87.17 memory used=12711.0MB, alloc=203.8MB, time=87.35 memory used=12807.2MB, alloc=203.8MB, time=87.51 memory used=12903.7MB, alloc=203.8MB, time=87.68 memory used=13000.5MB, alloc=203.8MB, time=87.85 memory used=13097.4MB, alloc=203.8MB, time=88.02 memory used=13194.6MB, alloc=203.8MB, time=88.18 memory used=13292.0MB, alloc=203.8MB, time=88.35 memory used=13389.5MB, alloc=203.8MB, time=88.52 memory used=13487.3MB, alloc=203.8MB, time=88.69 memory used=13586.1MB, alloc=203.8MB, time=88.87 memory used=13706.7MB, alloc=203.8MB, time=89.06 memory used=13795.2MB, alloc=203.8MB, time=89.23 memory used=13816.2MB, alloc=203.8MB, time=89.31 memory used=13818.4MB, alloc=459.8MB, time=89.38 memory used=13964.4MB, alloc=459.8MB, time=89.82 memory used=14084.2MB, alloc=459.8MB, time=90.08 memory used=14199.3MB, alloc=459.8MB, time=90.33 memory used=14314.5MB, alloc=459.8MB, time=90.58 memory used=14430.6MB, alloc=459.8MB, time=90.82 memory used=14561.6MB, alloc=459.8MB, time=91.07 memory used=14693.5MB, alloc=459.8MB, time=91.31 memory used=14825.4MB, alloc=459.8MB, time=91.55 memory used=14957.2MB, alloc=459.8MB, time=91.80 memory used=15089.0MB, alloc=459.8MB, time=92.04 memory used=15220.8MB, alloc=459.8MB, time=92.29 memory used=15352.5MB, alloc=459.8MB, time=92.52 memory used=15484.0MB, alloc=459.8MB, time=92.75 memory used=15615.5MB, alloc=459.8MB, time=93.00 memory used=15747.7MB, alloc=459.8MB, time=93.23 memory used=15894.2MB, alloc=459.8MB, time=93.48 memory used=16041.3MB, alloc=459.8MB, time=93.73 memory used=16188.0MB, alloc=459.8MB, time=93.99 memory used=16334.4MB, alloc=459.8MB, time=94.27 memory used=16480.4MB, alloc=459.8MB, time=94.51 memory used=16625.8MB, alloc=459.8MB, time=94.76 memory used=16770.9MB, alloc=459.8MB, time=95.01 memory used=16931.4MB, alloc=459.8MB, time=95.27 memory used=17091.1MB, alloc=459.8MB, time=95.53 memory used=17250.1MB, alloc=459.8MB, time=95.81 memory used=17408.2MB, alloc=459.8MB, time=96.08 memory used=17565.6MB, alloc=459.8MB, time=96.37 memory used=17737.4MB, alloc=459.8MB, time=96.64 memory used=17908.1MB, alloc=459.8MB, time=96.92 memory used=18077.5MB, alloc=459.8MB, time=97.18 memory used=18245.5MB, alloc=459.8MB, time=97.45 memory used=18413.7MB, alloc=459.8MB, time=97.75 memory used=18592.1MB, alloc=459.8MB, time=98.06 memory used=18770.2MB, alloc=459.8MB, time=98.40 memory used=18947.4MB, alloc=459.8MB, time=98.70 memory used=19134.8MB, alloc=459.8MB, time=99.00 memory used=19320.7MB, alloc=459.8MB, time=99.30 memory used=19517.9MB, alloc=459.8MB, time=99.63 memory used=19711.8MB, alloc=459.8MB, time=99.95 memory used=19915.7MB, alloc=459.8MB, time=100.25 memory used=20115.6MB, alloc=459.8MB, time=100.57 memory used=20324.0MB, alloc=459.8MB, time=100.88 memory used=20528.5MB, alloc=459.8MB, time=101.17 memory used=20737.5MB, alloc=459.8MB, time=101.47 memory used=20953.2MB, alloc=459.8MB, time=101.78 memory used=21172.7MB, alloc=459.8MB, time=102.10 memory used=21396.1MB, alloc=459.8MB, time=102.42 memory used=21627.3MB, alloc=459.8MB, time=102.74 memory used=21866.6MB, alloc=459.8MB, time=103.08 memory used=22109.5MB, alloc=459.8MB, time=103.40 memory used=22362.5MB, alloc=459.8MB, time=103.73 memory used=22605.8MB, alloc=459.8MB, time=104.04 memory used=22804.0MB, alloc=459.8MB, time=104.32 memory used=22997.5MB, alloc=459.8MB, time=104.58 memory used=23200.1MB, alloc=459.8MB, time=104.86 memory used=23411.5MB, alloc=459.8MB, time=105.13 memory used=23629.4MB, alloc=459.8MB, time=105.41 memory used=23856.3MB, alloc=459.8MB, time=105.72 memory used=24091.7MB, alloc=459.8MB, time=106.04 memory used=24335.9MB, alloc=459.8MB, time=106.34 memory used=24597.4MB, alloc=459.8MB, time=107.34 memory used=24727.0MB, alloc=459.8MB, time=110.60 memory used=24876.0MB, alloc=459.8MB, time=316.46 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428508198 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 F := [6 y z + 16 y - 14 x z, 16 x y + 19 x + 20] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 4 3 G := [17 x z + 10 y - 5 z , -y + 13 x - 7 x y] > Problem := [F,G]; 3 3 2 2 Problem := [[6 y z + 16 y - 14 x z, 16 x y + 19 x + 20], 3 2 2 4 3 [17 x z + 10 y - 5 z , -y + 13 x - 7 x y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.9MB, alloc=32.3MB, time=0.52 memory used=46.8MB, alloc=60.3MB, time=0.82 memory used=84.8MB, alloc=60.3MB, time=1.33 memory used=130.2MB, alloc=68.3MB, time=1.87 memory used=171.3MB, alloc=68.3MB, time=2.31 memory used=214.9MB, alloc=68.3MB, time=2.81 memory used=248.7MB, alloc=68.3MB, time=3.08 memory used=278.8MB, alloc=68.3MB, time=3.28 memory used=301.5MB, alloc=68.3MB, time=3.35 memory used=319.0MB, alloc=68.3MB, time=3.42 memory used=338.4MB, alloc=68.3MB, time=3.49 memory used=361.7MB, alloc=68.3MB, time=3.56 memory used=384.4MB, alloc=68.3MB, time=3.63 memory used=399.1MB, alloc=68.3MB, time=3.69 memory used=414.7MB, alloc=68.3MB, time=3.75 memory used=431.6MB, alloc=68.3MB, time=3.80 memory used=450.0MB, alloc=68.3MB, time=3.86 memory used=470.5MB, alloc=68.3MB, time=3.91 memory used=504.4MB, alloc=68.3MB, time=4.97 memory used=524.8MB, alloc=68.3MB, time=5.07 memory used=547.9MB, alloc=68.3MB, time=5.17 memory used=565.5MB, alloc=68.3MB, time=5.23 memory used=582.6MB, alloc=68.3MB, time=5.30 memory used=601.6MB, alloc=68.3MB, time=5.36 memory used=623.5MB, alloc=68.3MB, time=5.44 memory used=648.7MB, alloc=68.3MB, time=5.50 memory used=666.6MB, alloc=81.9MB, time=5.57 memory used=678.5MB, alloc=83.8MB, time=5.62 memory used=779.5MB, alloc=83.8MB, time=7.16 memory used=801.9MB, alloc=83.8MB, time=7.25 memory used=821.5MB, alloc=83.8MB, time=7.32 memory used=846.3MB, alloc=83.8MB, time=7.40 memory used=861.9MB, alloc=83.8MB, time=7.45 memory used=878.3MB, alloc=83.8MB, time=7.52 memory used=897.0MB, alloc=83.8MB, time=7.59 memory used=917.3MB, alloc=83.8MB, time=7.65 memory used=939.3MB, alloc=83.8MB, time=7.72 memory used=963.8MB, alloc=83.8MB, time=7.78 memory used=995.1MB, alloc=83.8MB, time=7.87 memory used=1006.1MB, alloc=83.8MB, time=7.93 memory used=1017.4MB, alloc=83.8MB, time=7.98 memory used=1029.8MB, alloc=83.8MB, time=8.04 memory used=1042.3MB, alloc=83.8MB, time=8.10 memory used=1055.6MB, alloc=83.8MB, time=8.16 memory used=1069.8MB, alloc=83.8MB, time=8.21 memory used=1086.9MB, alloc=83.8MB, time=8.31 memory used=1115.8MB, alloc=107.8MB, time=8.54 memory used=1154.7MB, alloc=107.8MB, time=8.68 memory used=1189.6MB, alloc=107.8MB, time=8.81 memory used=1220.6MB, alloc=107.8MB, time=8.93 memory used=1254.3MB, alloc=107.8MB, time=9.05 memory used=1293.5MB, alloc=107.8MB, time=9.17 memory used=1338.2MB, alloc=107.8MB, time=9.29 memory used=1377.2MB, alloc=107.8MB, time=9.39 memory used=1401.1MB, alloc=107.8MB, time=9.48 memory used=1426.1MB, alloc=107.8MB, time=9.56 memory used=1452.4MB, alloc=107.8MB, time=9.64 memory used=1480.6MB, alloc=107.8MB, time=9.72 memory used=1509.9MB, alloc=107.8MB, time=9.80 memory used=1542.4MB, alloc=107.8MB, time=9.89 memory used=1575.7MB, alloc=107.8MB, time=9.98 memory used=1611.2MB, alloc=107.8MB, time=10.06 memory used=1648.5MB, alloc=107.8MB, time=10.15 memory used=1689.0MB, alloc=107.8MB, time=10.25 memory used=1732.2MB, alloc=107.8MB, time=10.35 memory used=1778.3MB, alloc=107.8MB, time=10.44 memory used=1840.2MB, alloc=107.8MB, time=18.42 memory used=1890.7MB, alloc=107.8MB, time=30.32 memory used=1958.9MB, alloc=107.8MB, time=30.65 memory used=1993.2MB, alloc=107.8MB, time=30.77 memory used=2032.3MB, alloc=107.8MB, time=30.88 memory used=2069.3MB, alloc=107.8MB, time=30.99 memory used=2096.8MB, alloc=107.8MB, time=31.08 memory used=2126.0MB, alloc=107.8MB, time=31.17 memory used=2159.0MB, alloc=107.8MB, time=31.26 memory used=2194.0MB, alloc=107.8MB, time=31.36 memory used=2232.9MB, alloc=107.8MB, time=31.46 memory used=2273.7MB, alloc=107.8MB, time=31.57 memory used=2318.2MB, alloc=107.8MB, time=31.67 memory used=2358.6MB, alloc=107.8MB, time=31.77 memory used=2368.1MB, alloc=107.8MB, time=31.82 memory used=2376.0MB, alloc=107.8MB, time=31.87 memory used=2385.1MB, alloc=107.8MB, time=31.92 memory used=2394.4MB, alloc=107.8MB, time=31.98 memory used=2403.7MB, alloc=107.8MB, time=32.04 memory used=2413.0MB, alloc=107.8MB, time=32.10 memory used=2422.4MB, alloc=107.8MB, time=32.16 memory used=2431.8MB, alloc=107.8MB, time=32.22 memory used=2441.2MB, alloc=107.8MB, time=32.28 memory used=2450.7MB, alloc=107.8MB, time=32.34 memory used=2460.2MB, alloc=107.8MB, time=32.40 memory used=2469.7MB, alloc=107.8MB, time=32.46 memory used=2479.3MB, alloc=107.8MB, time=32.52 memory used=2488.9MB, alloc=107.8MB, time=32.58 memory used=2498.6MB, alloc=107.8MB, time=32.63 memory used=2508.2MB, alloc=107.8MB, time=32.69 memory used=2517.9MB, alloc=107.8MB, time=32.75 memory used=2527.6MB, alloc=107.8MB, time=32.81 memory used=2537.6MB, alloc=107.8MB, time=32.87 memory used=2549.5MB, alloc=107.8MB, time=32.93 memory used=2559.7MB, alloc=107.8MB, time=32.98 memory used=2571.6MB, alloc=107.8MB, time=33.04 memory used=2583.8MB, alloc=107.8MB, time=33.11 memory used=2596.1MB, alloc=107.8MB, time=33.17 memory used=2608.4MB, alloc=107.8MB, time=33.23 memory used=2620.7MB, alloc=107.8MB, time=33.29 memory used=2633.0MB, alloc=107.8MB, time=33.35 memory used=2645.4MB, alloc=107.8MB, time=33.40 memory used=2657.7MB, alloc=107.8MB, time=33.46 memory used=2670.0MB, alloc=107.8MB, time=33.52 memory used=2682.3MB, alloc=107.8MB, time=33.58 memory used=2694.6MB, alloc=107.8MB, time=33.64 memory used=2707.0MB, alloc=107.8MB, time=33.70 memory used=2719.6MB, alloc=107.8MB, time=33.76 memory used=2734.0MB, alloc=107.8MB, time=33.82 memory used=2748.7MB, alloc=107.8MB, time=33.88 memory used=2763.3MB, alloc=107.8MB, time=33.95 memory used=2778.0MB, alloc=107.8MB, time=34.01 memory used=2792.6MB, alloc=107.8MB, time=34.07 memory used=2807.1MB, alloc=107.8MB, time=34.13 memory used=2821.6MB, alloc=107.8MB, time=34.20 memory used=2836.0MB, alloc=107.8MB, time=34.26 memory used=2850.7MB, alloc=107.8MB, time=34.33 memory used=2867.0MB, alloc=107.8MB, time=34.40 memory used=2883.5MB, alloc=107.8MB, time=34.46 memory used=2900.0MB, alloc=107.8MB, time=34.53 memory used=2916.4MB, alloc=107.8MB, time=34.60 memory used=2932.6MB, alloc=107.8MB, time=34.66 memory used=2949.2MB, alloc=107.8MB, time=34.73 memory used=2966.8MB, alloc=107.8MB, time=34.81 memory used=2984.8MB, alloc=107.8MB, time=34.87 memory used=3002.5MB, alloc=107.8MB, time=34.94 memory used=3022.2MB, alloc=107.8MB, time=35.00 memory used=3041.5MB, alloc=107.8MB, time=35.07 memory used=3059.9MB, alloc=107.8MB, time=35.14 memory used=3074.6MB, alloc=107.8MB, time=35.20 memory used=3087.8MB, alloc=107.8MB, time=35.26 memory used=3100.1MB, alloc=107.8MB, time=35.31 memory used=3113.3MB, alloc=107.8MB, time=35.37 memory used=3126.7MB, alloc=107.8MB, time=35.43 memory used=3139.9MB, alloc=107.8MB, time=35.48 memory used=3153.3MB, alloc=107.8MB, time=35.54 memory used=3167.3MB, alloc=107.8MB, time=35.59 memory used=3181.3MB, alloc=107.8MB, time=35.65 memory used=3195.7MB, alloc=107.8MB, time=35.70 memory used=3210.4MB, alloc=107.8MB, time=35.77 memory used=3225.9MB, alloc=107.8MB, time=35.82 memory used=3241.2MB, alloc=107.8MB, time=35.88 memory used=3257.2MB, alloc=107.8MB, time=35.94 memory used=3273.7MB, alloc=107.8MB, time=35.99 memory used=3290.8MB, alloc=107.8MB, time=36.05 memory used=3336.5MB, alloc=107.8MB, time=36.39 memory used=3418.7MB, alloc=107.8MB, time=37.39 memory used=3464.5MB, alloc=107.8MB, time=37.58 memory used=3519.1MB, alloc=107.8MB, time=40.86 memory used=3574.4MB, alloc=107.8MB, time=41.10 memory used=3607.8MB, alloc=107.8MB, time=41.21 memory used=3645.0MB, alloc=107.8MB, time=41.31 memory used=3693.1MB, alloc=107.8MB, time=41.64 memory used=3759.6MB, alloc=107.8MB, time=42.22 memory used=3802.1MB, alloc=107.8MB, time=42.37 memory used=3875.5MB, alloc=107.8MB, time=45.87 memory used=3911.2MB, alloc=107.8MB, time=45.98 memory used=3942.9MB, alloc=107.8MB, time=46.08 memory used=3979.0MB, alloc=107.8MB, time=46.18 memory used=4045.2MB, alloc=107.8MB, time=46.87 memory used=4097.3MB, alloc=107.8MB, time=47.17 memory used=4130.2MB, alloc=107.8MB, time=47.28 memory used=4171.5MB, alloc=107.8MB, time=49.14 memory used=4233.5MB, alloc=107.8MB, time=50.52 memory used=4270.4MB, alloc=107.8MB, time=50.65 memory used=4298.3MB, alloc=107.8MB, time=50.76 memory used=4328.7MB, alloc=107.8MB, time=50.86 memory used=4364.7MB, alloc=107.8MB, time=50.97 memory used=4406.0MB, alloc=107.8MB, time=51.08 memory used=4432.9MB, alloc=107.8MB, time=51.17 memory used=4457.7MB, alloc=107.8MB, time=51.25 memory used=4484.2MB, alloc=107.8MB, time=51.33 memory used=4512.6MB, alloc=107.8MB, time=51.42 memory used=4542.7MB, alloc=107.8MB, time=51.51 memory used=4575.7MB, alloc=107.8MB, time=51.60 memory used=4609.7MB, alloc=107.8MB, time=51.68 memory used=4647.3MB, alloc=107.8MB, time=51.79 memory used=4690.6MB, alloc=107.8MB, time=51.89 memory used=4750.0MB, alloc=107.8MB, time=52.24 memory used=4790.3MB, alloc=107.8MB, time=52.42 memory used=4825.2MB, alloc=107.8MB, time=52.53 memory used=4852.0MB, alloc=107.8MB, time=52.62 memory used=4884.4MB, alloc=107.8MB, time=52.72 memory used=4940.9MB, alloc=107.8MB, time=55.63 memory used=4993.4MB, alloc=107.8MB, time=55.88 memory used=5022.4MB, alloc=107.8MB, time=56.01 memory used=5056.7MB, alloc=107.8MB, time=56.12 memory used=5094.6MB, alloc=107.8MB, time=56.24 memory used=5118.3MB, alloc=107.8MB, time=56.34 memory used=5143.1MB, alloc=107.8MB, time=56.44 memory used=5170.1MB, alloc=107.8MB, time=56.53 memory used=5199.9MB, alloc=107.8MB, time=56.61 memory used=5232.3MB, alloc=107.8MB, time=56.72 memory used=5267.4MB, alloc=107.8MB, time=56.82 memory used=5305.0MB, alloc=107.8MB, time=56.92 memory used=5345.2MB, alloc=107.8MB, time=57.03 memory used=5383.3MB, alloc=107.8MB, time=57.15 memory used=5392.9MB, alloc=107.8MB, time=57.23 memory used=5402.5MB, alloc=107.8MB, time=57.29 memory used=5412.2MB, alloc=107.8MB, time=57.37 memory used=5421.9MB, alloc=107.8MB, time=57.44 memory used=5431.5MB, alloc=107.8MB, time=57.51 memory used=5441.2MB, alloc=107.8MB, time=57.60 memory used=5450.8MB, alloc=107.8MB, time=57.66 memory used=5462.0MB, alloc=107.8MB, time=57.73 memory used=5473.1MB, alloc=107.8MB, time=57.80 memory used=5484.2MB, alloc=107.8MB, time=57.87 memory used=5495.2MB, alloc=107.8MB, time=57.95 memory used=5506.1MB, alloc=107.8MB, time=58.02 memory used=5517.2MB, alloc=107.8MB, time=58.10 memory used=5529.3MB, alloc=107.8MB, time=58.18 memory used=5541.7MB, alloc=107.8MB, time=58.25 memory used=5553.8MB, alloc=107.8MB, time=58.32 memory used=5566.0MB, alloc=107.8MB, time=58.38 memory used=5579.1MB, alloc=107.8MB, time=58.45 memory used=5592.2MB, alloc=107.8MB, time=58.52 memory used=5605.3MB, alloc=107.8MB, time=58.59 memory used=5619.1MB, alloc=107.8MB, time=58.67 memory used=5633.0MB, alloc=107.8MB, time=58.74 memory used=5647.6MB, alloc=107.8MB, time=58.84 memory used=5663.1MB, alloc=107.8MB, time=58.91 memory used=5678.4MB, alloc=107.8MB, time=58.99 memory used=5694.1MB, alloc=107.8MB, time=59.07 memory used=5711.1MB, alloc=107.8MB, time=59.15 memory used=5728.3MB, alloc=107.8MB, time=59.24 memory used=5746.3MB, alloc=107.8MB, time=59.31 memory used=5764.5MB, alloc=107.8MB, time=59.41 memory used=5784.3MB, alloc=107.8MB, time=59.48 memory used=5943.7MB, alloc=107.8MB, time=64.19 memory used=6070.3MB, alloc=107.8MB, time=65.09 memory used=6104.5MB, alloc=107.8MB, time=65.21 memory used=6135.9MB, alloc=107.8MB, time=65.33 memory used=6163.5MB, alloc=107.8MB, time=65.45 memory used=6195.9MB, alloc=107.8MB, time=65.56 memory used=6233.8MB, alloc=107.8MB, time=65.67 memory used=6268.6MB, alloc=107.8MB, time=65.78 memory used=6292.0MB, alloc=107.8MB, time=65.86 memory used=6316.3MB, alloc=107.8MB, time=65.95 memory used=6342.2MB, alloc=107.8MB, time=66.04 memory used=6370.0MB, alloc=107.8MB, time=66.13 memory used=6400.3MB, alloc=107.8MB, time=66.22 memory used=6432.6MB, alloc=107.8MB, time=66.31 memory used=6466.8MB, alloc=107.8MB, time=66.41 memory used=6504.6MB, alloc=107.8MB, time=66.50 memory used=6545.0MB, alloc=107.8MB, time=66.62 memory used=6632.7MB, alloc=107.8MB, time=67.75 memory used=6663.9MB, alloc=107.8MB, time=67.87 memory used=6696.1MB, alloc=107.8MB, time=67.98 memory used=6783.1MB, alloc=131.8MB, time=82.96 memory used=6821.9MB, alloc=155.8MB, time=103.42 memory used=6899.9MB, alloc=179.8MB, time=114.99 memory used=6965.6MB, alloc=179.8MB, time=170.61 memory used=7107.6MB, alloc=203.8MB, time=171.39 memory used=8480.7MB, alloc=459.8MB, time=181.84 memory used=8517.9MB, alloc=459.8MB, time=183.98 memory used=8553.2MB, alloc=459.8MB, time=186.04 memory used=9256.1MB, alloc=483.8MB, time=193.60 memory used=9600.8MB, alloc=483.8MB, time=197.78 memory used=10263.7MB, alloc=483.8MB, time=205.62 memory used=10882.0MB, alloc=483.8MB, time=213.66 memory used=11003.0MB, alloc=507.8MB, time=214.30 memory used=12342.9MB, alloc=531.8MB, time=225.65 memory used=12379.4MB, alloc=531.8MB, time=227.73 memory used=12606.2MB, alloc=531.8MB, time=237.21 memory used=12750.5MB, alloc=531.8MB, time=239.45 memory used=12866.3MB, alloc=531.8MB, time=241.15 memory used=13009.8MB, alloc=539.4MB, time=244.12 memory used=13017.4MB, alloc=546.9MB, time=244.21 memory used=13025.0MB, alloc=554.5MB, time=244.30 memory used=13032.5MB, alloc=562.1MB, time=244.40 memory used=13040.1MB, alloc=539.4MB, time=244.80 memory used=13401.0MB, alloc=531.8MB, time=250.46 memory used=13542.9MB, alloc=531.8MB, time=250.82 memory used=13672.9MB, alloc=531.8MB, time=251.11 memory used=13947.6MB, alloc=531.8MB, time=251.78 memory used=14129.0MB, alloc=531.8MB, time=252.13 memory used=14399.4MB, alloc=531.8MB, time=268.59 memory used=14548.7MB, alloc=531.8MB, time=268.90 memory used=14673.8MB, alloc=531.8MB, time=269.16 memory used=14787.1MB, alloc=531.8MB, time=269.41 memory used=14897.2MB, alloc=531.8MB, time=269.65 memory used=15004.0MB, alloc=531.8MB, time=269.90 memory used=15111.7MB, alloc=531.8MB, time=270.13 memory used=15220.8MB, alloc=531.8MB, time=270.34 memory used=15330.0MB, alloc=531.8MB, time=270.58 memory used=15449.2MB, alloc=531.8MB, time=270.81 memory used=15572.0MB, alloc=531.8MB, time=271.08 memory used=15698.4MB, alloc=531.8MB, time=271.32 memory used=15828.3MB, alloc=531.8MB, time=271.56 memory used=15961.7MB, alloc=531.8MB, time=271.80 memory used=16098.5MB, alloc=531.8MB, time=272.04 memory used=16238.9MB, alloc=531.8MB, time=272.29 memory used=16390.5MB, alloc=531.8MB, time=272.54 memory used=16545.6MB, alloc=531.8MB, time=272.80 memory used=16704.3MB, alloc=531.8MB, time=273.06 memory used=16874.8MB, alloc=531.8MB, time=273.33 memory used=17132.7MB, alloc=531.8MB, time=273.72 memory used=17352.6MB, alloc=531.8MB, time=274.09 memory used=17525.1MB, alloc=531.8MB, time=274.40 memory used=17676.0MB, alloc=531.8MB, time=274.68 memory used=17813.6MB, alloc=531.8MB, time=274.95 memory used=17953.9MB, alloc=531.8MB, time=275.22 memory used=18089.3MB, alloc=531.8MB, time=275.48 memory used=18236.0MB, alloc=531.8MB, time=275.78 memory used=18384.4MB, alloc=531.8MB, time=276.05 memory used=18534.5MB, alloc=531.8MB, time=276.33 memory used=18686.1MB, alloc=531.8MB, time=276.62 memory used=18839.4MB, alloc=531.8MB, time=276.90 memory used=18994.2MB, alloc=531.8MB, time=277.20 memory used=19150.4MB, alloc=531.8MB, time=277.49 memory used=19308.0MB, alloc=531.8MB, time=277.76 memory used=19467.2MB, alloc=531.8MB, time=278.05 memory used=19638.5MB, alloc=531.8MB, time=278.37 memory used=19811.4MB, alloc=531.8MB, time=278.66 memory used=19985.6MB, alloc=531.8MB, time=278.96 memory used=20161.3MB, alloc=531.8MB, time=279.25 memory used=20338.4MB, alloc=531.8MB, time=279.55 memory used=20516.7MB, alloc=531.8MB, time=279.84 memory used=20696.5MB, alloc=531.8MB, time=280.15 memory used=20888.9MB, alloc=531.8MB, time=280.47 memory used=21082.6MB, alloc=531.8MB, time=280.78 memory used=21277.6MB, alloc=531.8MB, time=281.09 memory used=21473.7MB, alloc=531.8MB, time=281.41 memory used=21671.2MB, alloc=531.8MB, time=281.73 memory used=21869.9MB, alloc=531.8MB, time=282.05 memory used=22081.3MB, alloc=531.8MB, time=282.38 memory used=22293.9MB, alloc=531.8MB, time=282.72 memory used=22507.4MB, alloc=531.8MB, time=283.05 memory used=22722.0MB, alloc=531.8MB, time=283.38 memory used=22937.6MB, alloc=531.8MB, time=283.71 memory used=23166.1MB, alloc=531.8MB, time=284.04 memory used=23395.5MB, alloc=531.8MB, time=284.38 memory used=23625.6MB, alloc=531.8MB, time=284.72 memory used=23856.6MB, alloc=531.8MB, time=285.06 memory used=24100.4MB, alloc=531.8MB, time=285.41 memory used=24343.9MB, alloc=531.8MB, time=285.74 memory used=24567.8MB, alloc=531.8MB, time=286.07 memory used=24776.5MB, alloc=531.8MB, time=286.41 memory used=24968.1MB, alloc=531.8MB, time=286.72 memory used=25151.3MB, alloc=531.8MB, time=287.01 memory used=25326.2MB, alloc=531.8MB, time=287.29 memory used=25493.1MB, alloc=531.8MB, time=287.57 memory used=25664.4MB, alloc=531.8MB, time=287.85 memory used=25836.0MB, alloc=531.8MB, time=288.14 memory used=26007.6MB, alloc=531.8MB, time=288.42 memory used=26179.2MB, alloc=531.8MB, time=288.71 memory used=26363.0MB, alloc=531.8MB, time=288.99 memory used=26546.7MB, alloc=531.8MB, time=289.28 memory used=26730.1MB, alloc=531.8MB, time=289.57 memory used=26913.4MB, alloc=531.8MB, time=289.85 memory used=27096.4MB, alloc=531.8MB, time=290.13 memory used=27279.2MB, alloc=531.8MB, time=290.42 memory used=27473.8MB, alloc=531.8MB, time=290.71 memory used=27668.0MB, alloc=531.8MB, time=291.01 memory used=27861.9MB, alloc=531.8MB, time=291.30 memory used=28055.2MB, alloc=531.8MB, time=291.60 memory used=28248.1MB, alloc=531.8MB, time=291.89 memory used=28452.1MB, alloc=531.8MB, time=292.20 memory used=28655.5MB, alloc=531.8MB, time=292.50 memory used=28858.1MB, alloc=531.8MB, time=292.81 memory used=29060.1MB, alloc=531.8MB, time=293.11 memory used=29272.6MB, alloc=531.8MB, time=293.42 memory used=29484.3MB, alloc=531.8MB, time=293.72 memory used=29694.8MB, alloc=531.8MB, time=294.03 memory used=29915.8MB, alloc=531.8MB, time=294.33 memory used=30135.3MB, alloc=531.8MB, time=294.65 memory used=30353.4MB, alloc=531.8MB, time=294.96 memory used=30581.2MB, alloc=531.8MB, time=295.29 memory used=30807.5MB, alloc=531.8MB, time=295.61 memory used=31042.9MB, alloc=531.8MB, time=295.93 memory used=31276.0MB, alloc=531.8MB, time=296.25 memory used=31517.8MB, alloc=531.8MB, time=296.59 memory used=31756.8MB, alloc=531.8MB, time=296.92 memory used=32003.8MB, alloc=531.8MB, time=297.25 memory used=32247.7MB, alloc=531.8MB, time=297.58 memory used=32498.6MB, alloc=531.8MB, time=297.92 memory used=32736.2MB, alloc=531.8MB, time=298.24 memory used=32939.6MB, alloc=531.8MB, time=298.52 memory used=33132.7MB, alloc=531.8MB, time=298.80 memory used=33326.1MB, alloc=531.8MB, time=299.08 memory used=33519.3MB, alloc=531.8MB, time=299.38 memory used=33718.5MB, alloc=531.8MB, time=299.67 memory used=33914.3MB, alloc=531.8MB, time=299.96 memory used=34115.5MB, alloc=531.8MB, time=300.25 memory used=34321.4MB, alloc=531.8MB, time=300.55 memory used=34531.4MB, alloc=531.8MB, time=300.85 memory used=34744.7MB, alloc=531.8MB, time=301.14 memory used=34960.3MB, alloc=531.8MB, time=301.44 memory used=35177.4MB, alloc=531.8MB, time=301.78 memory used=35395.0MB, alloc=531.8MB, time=302.09 memory used=35619.6MB, alloc=531.8MB, time=302.40 memory used=35848.5MB, alloc=531.8MB, time=302.71 memory used=36079.4MB, alloc=531.8MB, time=303.02 memory used=36315.9MB, alloc=531.8MB, time=303.33 memory used=36553.7MB, alloc=531.8MB, time=303.65 memory used=36798.0MB, alloc=531.8MB, time=303.97 memory used=37049.7MB, alloc=531.8MB, time=304.30 memory used=37308.8MB, alloc=531.8MB, time=304.62 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428508498 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 3 2 F := [-12 x z + 19 x y - 15 z, -16 y z + 5 y + 8 z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 4 3 3 2 G := [15 y - 15 y z - z , x + 19 z - 8 z ] > Problem := [F,G]; 2 2 2 2 3 2 Problem := [[-12 x z + 19 x y - 15 z, -16 y z + 5 y + 8 z ], 4 2 2 4 3 3 2 [15 y - 15 y z - z , x + 19 z - 8 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=24.5MB, alloc=32.3MB, time=0.48 memory used=44.2MB, alloc=32.3MB, time=0.72 memory used=64.0MB, alloc=60.3MB, time=0.99 memory used=106.4MB, alloc=68.3MB, time=1.56 memory used=142.0MB, alloc=68.3MB, time=1.75 memory used=176.7MB, alloc=68.3MB, time=1.89 memory used=202.7MB, alloc=68.3MB, time=1.97 memory used=236.9MB, alloc=68.3MB, time=2.15 memory used=262.2MB, alloc=68.3MB, time=2.22 memory used=293.6MB, alloc=68.3MB, time=2.35 memory used=320.3MB, alloc=68.3MB, time=2.47 memory used=356.0MB, alloc=68.3MB, time=2.68 memory used=380.6MB, alloc=68.3MB, time=2.75 memory used=412.5MB, alloc=68.3MB, time=2.88 memory used=439.4MB, alloc=68.3MB, time=3.01 memory used=484.4MB, alloc=68.3MB, time=3.66 memory used=507.0MB, alloc=68.3MB, time=3.74 memory used=546.2MB, alloc=68.3MB, time=4.17 memory used=590.0MB, alloc=68.3MB, time=4.75 memory used=631.3MB, alloc=68.3MB, time=5.29 memory used=666.1MB, alloc=68.3MB, time=5.57 memory used=689.0MB, alloc=68.3MB, time=5.67 memory used=714.9MB, alloc=68.3MB, time=5.81 memory used=737.3MB, alloc=68.3MB, time=5.91 memory used=758.3MB, alloc=68.3MB, time=5.99 memory used=782.5MB, alloc=68.3MB, time=6.09 memory used=806.4MB, alloc=68.3MB, time=6.19 memory used=838.1MB, alloc=68.3MB, time=6.52 memory used=862.8MB, alloc=92.3MB, time=6.61 memory used=896.4MB, alloc=92.3MB, time=6.73 memory used=939.3MB, alloc=92.3MB, time=6.85 memory used=978.8MB, alloc=92.3MB, time=6.96 memory used=1007.6MB, alloc=92.3MB, time=7.06 memory used=1038.5MB, alloc=92.3MB, time=7.15 memory used=1073.0MB, alloc=92.3MB, time=7.25 memory used=1111.0MB, alloc=92.3MB, time=7.35 memory used=1152.1MB, alloc=92.3MB, time=7.44 memory used=1197.3MB, alloc=92.3MB, time=7.56 memory used=1239.3MB, alloc=92.3MB, time=7.65 memory used=1265.5MB, alloc=92.3MB, time=7.72 memory used=1293.3MB, alloc=92.3MB, time=7.79 memory used=1323.6MB, alloc=92.3MB, time=7.85 memory used=1362.8MB, alloc=92.3MB, time=8.17 memory used=1410.8MB, alloc=92.3MB, time=8.31 memory used=1446.9MB, alloc=92.3MB, time=8.42 memory used=1492.7MB, alloc=92.3MB, time=8.55 memory used=1527.2MB, alloc=92.3MB, time=8.65 memory used=1556.2MB, alloc=92.3MB, time=8.74 memory used=1588.5MB, alloc=92.3MB, time=8.84 memory used=1623.6MB, alloc=92.3MB, time=8.95 memory used=1662.9MB, alloc=92.3MB, time=9.05 memory used=1705.4MB, alloc=92.3MB, time=9.16 memory used=1753.0MB, alloc=92.3MB, time=9.26 memory used=1788.7MB, alloc=92.3MB, time=9.35 memory used=1815.6MB, alloc=92.3MB, time=9.42 memory used=1844.3MB, alloc=92.3MB, time=9.49 memory used=1875.8MB, alloc=92.3MB, time=9.56 memory used=1928.6MB, alloc=92.3MB, time=13.15 memory used=2093.6MB, alloc=92.9MB, time=14.80 memory used=2134.0MB, alloc=92.9MB, time=14.92 memory used=2173.8MB, alloc=92.9MB, time=15.04 memory used=2204.3MB, alloc=92.9MB, time=15.15 memory used=2240.0MB, alloc=92.9MB, time=15.26 memory used=2281.1MB, alloc=92.9MB, time=15.37 memory used=2328.9MB, alloc=92.9MB, time=15.47 memory used=2357.0MB, alloc=92.9MB, time=15.56 memory used=2384.4MB, alloc=92.9MB, time=15.63 memory used=2413.9MB, alloc=92.9MB, time=15.70 memory used=2445.5MB, alloc=92.9MB, time=15.77 memory used=2478.8MB, alloc=92.9MB, time=15.85 memory used=2514.5MB, alloc=92.9MB, time=15.93 memory used=2554.0MB, alloc=92.9MB, time=16.01 memory used=2607.8MB, alloc=92.9MB, time=16.34 memory used=2645.5MB, alloc=92.9MB, time=16.48 memory used=2684.0MB, alloc=92.9MB, time=16.60 memory used=2730.8MB, alloc=92.9MB, time=16.72 memory used=2758.5MB, alloc=92.9MB, time=16.81 memory used=2787.6MB, alloc=92.9MB, time=16.91 memory used=2820.1MB, alloc=92.9MB, time=17.02 memory used=2854.9MB, alloc=92.9MB, time=17.12 memory used=2893.1MB, alloc=92.9MB, time=17.21 memory used=2935.1MB, alloc=92.9MB, time=17.31 memory used=2982.2MB, alloc=92.9MB, time=17.42 memory used=3014.6MB, alloc=92.9MB, time=17.50 memory used=3040.9MB, alloc=92.9MB, time=17.57 memory used=3069.2MB, alloc=92.9MB, time=17.64 memory used=3100.1MB, alloc=92.9MB, time=17.72 memory used=3150.4MB, alloc=92.9MB, time=18.05 memory used=3184.9MB, alloc=92.9MB, time=18.17 memory used=3224.4MB, alloc=92.9MB, time=18.28 memory used=3268.9MB, alloc=92.9MB, time=18.39 memory used=3295.7MB, alloc=92.9MB, time=18.50 memory used=3324.6MB, alloc=92.9MB, time=18.59 memory used=3357.3MB, alloc=92.9MB, time=18.68 memory used=3392.0MB, alloc=92.9MB, time=18.79 memory used=3430.2MB, alloc=92.9MB, time=18.91 memory used=3472.2MB, alloc=92.9MB, time=19.02 memory used=3519.2MB, alloc=92.9MB, time=19.13 memory used=3550.1MB, alloc=92.9MB, time=19.21 memory used=3576.4MB, alloc=92.9MB, time=19.28 memory used=3604.5MB, alloc=92.9MB, time=19.35 memory used=3635.3MB, alloc=92.9MB, time=19.42 memory used=3776.2MB, alloc=92.9MB, time=24.10 memory used=3818.9MB, alloc=92.9MB, time=24.23 memory used=3860.4MB, alloc=92.9MB, time=24.35 memory used=3890.0MB, alloc=92.9MB, time=24.44 memory used=3924.2MB, alloc=92.9MB, time=24.54 memory used=3963.7MB, alloc=92.9MB, time=24.65 memory used=4009.4MB, alloc=92.9MB, time=24.75 memory used=4042.2MB, alloc=92.9MB, time=24.84 memory used=4069.2MB, alloc=92.9MB, time=24.91 memory used=4097.8MB, alloc=92.9MB, time=24.98 memory used=4128.6MB, alloc=92.9MB, time=25.06 memory used=4160.5MB, alloc=92.9MB, time=25.13 memory used=4195.3MB, alloc=92.9MB, time=25.22 memory used=4233.8MB, alloc=92.9MB, time=25.30 memory used=4286.7MB, alloc=92.9MB, time=25.58 memory used=4331.1MB, alloc=92.9MB, time=25.71 memory used=4372.4MB, alloc=92.9MB, time=25.82 memory used=4418.2MB, alloc=92.9MB, time=26.07 memory used=4453.9MB, alloc=92.9MB, time=26.18 memory used=4495.4MB, alloc=92.9MB, time=26.30 memory used=4525.0MB, alloc=92.9MB, time=26.39 memory used=4559.3MB, alloc=92.9MB, time=26.50 memory used=4599.0MB, alloc=92.9MB, time=26.60 memory used=4645.3MB, alloc=92.9MB, time=26.71 memory used=4675.3MB, alloc=92.9MB, time=26.78 memory used=4721.3MB, alloc=92.9MB, time=27.25 memory used=4763.3MB, alloc=92.9MB, time=27.38 memory used=4797.6MB, alloc=92.9MB, time=27.49 memory used=4833.8MB, alloc=92.9MB, time=27.59 memory used=4877.6MB, alloc=92.9MB, time=27.69 memory used=4907.0MB, alloc=92.9MB, time=27.77 memory used=4937.2MB, alloc=92.9MB, time=27.83 memory used=5044.8MB, alloc=92.9MB, time=29.25 memory used=5095.2MB, alloc=92.9MB, time=30.13 memory used=5134.8MB, alloc=92.9MB, time=30.29 memory used=5190.1MB, alloc=92.9MB, time=30.75 memory used=5227.7MB, alloc=92.9MB, time=30.89 memory used=5258.1MB, alloc=92.9MB, time=31.00 memory used=5293.6MB, alloc=92.9MB, time=31.12 memory used=5333.7MB, alloc=92.9MB, time=31.30 memory used=5376.6MB, alloc=92.9MB, time=31.43 memory used=5401.5MB, alloc=92.9MB, time=31.54 memory used=5426.6MB, alloc=92.9MB, time=31.65 memory used=5454.1MB, alloc=92.9MB, time=31.75 memory used=5483.5MB, alloc=92.9MB, time=31.85 memory used=5514.6MB, alloc=92.9MB, time=31.94 memory used=5547.4MB, alloc=92.9MB, time=32.04 memory used=5581.6MB, alloc=92.9MB, time=32.14 memory used=5618.5MB, alloc=92.9MB, time=32.24 memory used=5657.7MB, alloc=92.9MB, time=32.35 memory used=5699.8MB, alloc=92.9MB, time=32.46 memory used=5743.4MB, alloc=92.9MB, time=32.58 memory used=5767.5MB, alloc=92.9MB, time=32.66 memory used=5792.3MB, alloc=92.9MB, time=32.73 memory used=5818.0MB, alloc=92.9MB, time=32.80 memory used=5858.4MB, alloc=92.9MB, time=33.22 memory used=5907.0MB, alloc=92.9MB, time=33.38 memory used=5935.6MB, alloc=92.9MB, time=33.48 memory used=5968.7MB, alloc=92.9MB, time=33.58 memory used=6006.0MB, alloc=92.9MB, time=33.69 memory used=6048.7MB, alloc=92.9MB, time=33.80 memory used=6081.6MB, alloc=92.9MB, time=33.91 memory used=6106.6MB, alloc=92.9MB, time=34.01 memory used=6132.4MB, alloc=92.9MB, time=34.11 memory used=6160.0MB, alloc=92.9MB, time=34.21 memory used=6189.5MB, alloc=92.9MB, time=34.31 memory used=6220.7MB, alloc=92.9MB, time=34.42 memory used=6253.5MB, alloc=92.9MB, time=34.51 memory used=6289.1MB, alloc=92.9MB, time=34.62 memory used=6327.2MB, alloc=92.9MB, time=34.71 memory used=6367.3MB, alloc=92.9MB, time=34.82 memory used=6410.1MB, alloc=92.9MB, time=34.93 memory used=6445.6MB, alloc=92.9MB, time=35.03 memory used=6469.4MB, alloc=92.9MB, time=35.10 memory used=6493.9MB, alloc=92.9MB, time=35.17 memory used=6520.1MB, alloc=92.9MB, time=35.24 memory used=6657.0MB, alloc=93.4MB, time=41.13 memory used=6701.5MB, alloc=93.4MB, time=41.34 memory used=6737.1MB, alloc=93.4MB, time=41.45 memory used=6776.7MB, alloc=93.4MB, time=41.56 memory used=6802.5MB, alloc=93.4MB, time=41.67 memory used=6831.7MB, alloc=93.4MB, time=41.76 memory used=6864.0MB, alloc=93.4MB, time=41.86 memory used=6899.6MB, alloc=93.4MB, time=41.97 memory used=6939.1MB, alloc=93.4MB, time=42.08 memory used=6982.3MB, alloc=93.4MB, time=42.21 memory used=7014.2MB, alloc=93.4MB, time=42.30 memory used=7038.5MB, alloc=93.4MB, time=42.39 memory used=7063.9MB, alloc=93.4MB, time=42.47 memory used=7090.5MB, alloc=93.4MB, time=42.55 memory used=7118.5MB, alloc=93.4MB, time=42.63 memory used=7147.7MB, alloc=93.4MB, time=42.72 memory used=7179.2MB, alloc=93.4MB, time=42.80 memory used=7213.7MB, alloc=93.4MB, time=42.89 memory used=7270.4MB, alloc=93.4MB, time=43.22 memory used=7305.0MB, alloc=93.4MB, time=43.35 memory used=7355.6MB, alloc=93.4MB, time=43.65 memory used=7388.9MB, alloc=93.4MB, time=43.77 memory used=7428.8MB, alloc=93.4MB, time=43.88 memory used=7461.0MB, alloc=93.4MB, time=43.99 memory used=7489.5MB, alloc=93.4MB, time=44.08 memory used=7522.3MB, alloc=93.4MB, time=44.18 memory used=7560.0MB, alloc=93.4MB, time=44.28 memory used=7617.0MB, alloc=93.4MB, time=44.81 memory used=7655.9MB, alloc=93.4MB, time=44.93 memory used=7685.7MB, alloc=93.4MB, time=45.03 memory used=7718.4MB, alloc=93.4MB, time=45.13 memory used=7758.9MB, alloc=93.4MB, time=45.23 memory used=7812.3MB, alloc=93.4MB, time=45.77 memory used=7915.5MB, alloc=93.4MB, time=47.25 memory used=7973.9MB, alloc=93.4MB, time=47.86 memory used=8026.5MB, alloc=93.4MB, time=48.55 memory used=8132.1MB, alloc=349.4MB, time=50.10 memory used=8208.6MB, alloc=373.4MB, time=52.16 memory used=8276.1MB, alloc=373.4MB, time=52.48 memory used=8325.7MB, alloc=373.4MB, time=52.64 memory used=8365.9MB, alloc=373.4MB, time=52.79 memory used=8415.0MB, alloc=373.4MB, time=52.96 memory used=8471.3MB, alloc=373.4MB, time=53.11 memory used=8505.7MB, alloc=373.4MB, time=53.22 memory used=8543.0MB, alloc=373.4MB, time=53.33 memory used=8608.4MB, alloc=373.4MB, time=53.81 memory used=8662.5MB, alloc=373.4MB, time=53.99 memory used=8702.0MB, alloc=373.4MB, time=54.13 memory used=8753.9MB, alloc=373.4MB, time=54.29 memory used=8813.2MB, alloc=373.4MB, time=54.76 memory used=8897.2MB, alloc=373.4MB, time=55.87 memory used=8983.1MB, alloc=373.4MB, time=56.91 memory used=9066.4MB, alloc=373.4MB, time=58.01 memory used=9127.1MB, alloc=373.4MB, time=58.46 memory used=9169.0MB, alloc=397.4MB, time=58.65 memory used=9228.7MB, alloc=397.4MB, time=58.88 memory used=9301.5MB, alloc=397.4MB, time=59.32 memory used=9363.4MB, alloc=397.4MB, time=59.52 memory used=9420.3MB, alloc=397.4MB, time=59.78 memory used=9483.0MB, alloc=397.4MB, time=60.00 memory used=9533.3MB, alloc=397.4MB, time=60.17 memory used=9596.8MB, alloc=397.4MB, time=60.59 memory used=9665.5MB, alloc=397.4MB, time=60.92 memory used=9718.3MB, alloc=397.4MB, time=61.10 memory used=9789.5MB, alloc=397.4MB, time=61.46 memory used=9843.2MB, alloc=397.4MB, time=61.64 memory used=9912.4MB, alloc=397.4MB, time=62.73 memory used=9996.3MB, alloc=397.4MB, time=63.74 memory used=10076.7MB, alloc=397.4MB, time=67.90 memory used=10183.2MB, alloc=397.4MB, time=69.01 memory used=10288.3MB, alloc=397.4MB, time=71.07 memory used=10393.9MB, alloc=397.4MB, time=72.43 memory used=10471.7MB, alloc=397.4MB, time=73.50 memory used=10529.3MB, alloc=397.4MB, time=73.75 memory used=10592.1MB, alloc=397.4MB, time=74.83 memory used=10667.6MB, alloc=397.4MB, time=78.59 memory used=10768.7MB, alloc=397.4MB, time=79.84 memory used=10870.9MB, alloc=397.4MB, time=82.15 memory used=10965.3MB, alloc=421.4MB, time=83.25 memory used=11035.3MB, alloc=421.4MB, time=83.69 memory used=11110.2MB, alloc=421.4MB, time=84.02 memory used=11178.5MB, alloc=421.4MB, time=84.28 memory used=11257.5MB, alloc=421.4MB, time=84.67 memory used=11322.5MB, alloc=421.4MB, time=84.90 memory used=11379.8MB, alloc=421.4MB, time=85.11 memory used=11461.4MB, alloc=421.4MB, time=85.47 memory used=11526.7MB, alloc=421.4MB, time=85.70 memory used=11588.4MB, alloc=421.4MB, time=85.93 memory used=11648.7MB, alloc=421.4MB, time=86.13 memory used=11717.1MB, alloc=421.4MB, time=86.87 memory used=11789.0MB, alloc=421.4MB, time=87.17 memory used=11852.6MB, alloc=421.4MB, time=87.42 memory used=11927.7MB, alloc=421.4MB, time=87.68 memory used=11973.3MB, alloc=421.4MB, time=87.91 memory used=12023.4MB, alloc=421.4MB, time=88.14 memory used=12077.2MB, alloc=421.4MB, time=88.35 memory used=12135.7MB, alloc=421.4MB, time=88.58 memory used=12199.0MB, alloc=421.4MB, time=88.80 memory used=12269.3MB, alloc=421.4MB, time=89.04 memory used=12344.1MB, alloc=421.4MB, time=89.26 memory used=12415.4MB, alloc=421.4MB, time=89.48 memory used=12456.0MB, alloc=421.4MB, time=89.65 memory used=12499.6MB, alloc=421.4MB, time=89.83 memory used=12543.9MB, alloc=421.4MB, time=90.01 memory used=12590.4MB, alloc=421.4MB, time=90.20 memory used=12638.9MB, alloc=421.4MB, time=90.37 memory used=12689.1MB, alloc=421.4MB, time=90.56 memory used=12743.0MB, alloc=421.4MB, time=90.74 memory used=12798.2MB, alloc=421.4MB, time=90.92 memory used=12856.9MB, alloc=421.4MB, time=91.10 memory used=12919.1MB, alloc=421.4MB, time=91.28 memory used=12985.0MB, alloc=421.4MB, time=91.48 memory used=13056.0MB, alloc=421.4MB, time=91.67 memory used=13147.5MB, alloc=421.4MB, time=92.11 memory used=13209.8MB, alloc=421.4MB, time=92.36 memory used=13278.6MB, alloc=421.4MB, time=92.61 memory used=13328.4MB, alloc=421.4MB, time=92.83 memory used=13386.3MB, alloc=421.4MB, time=93.05 memory used=13453.8MB, alloc=421.4MB, time=93.26 memory used=13531.8MB, alloc=421.4MB, time=93.48 memory used=13578.0MB, alloc=421.4MB, time=93.65 memory used=13627.5MB, alloc=421.4MB, time=93.81 memory used=13707.8MB, alloc=421.4MB, time=96.25 memory used=13770.6MB, alloc=421.4MB, time=96.49 memory used=13830.1MB, alloc=421.4MB, time=96.72 memory used=13902.7MB, alloc=421.4MB, time=96.92 memory used=13949.0MB, alloc=421.4MB, time=97.09 memory used=14001.2MB, alloc=421.4MB, time=97.26 memory used=14071.5MB, alloc=421.4MB, time=97.84 memory used=14147.8MB, alloc=421.4MB, time=98.41 memory used=14209.8MB, alloc=421.4MB, time=98.66 memory used=14286.5MB, alloc=421.4MB, time=98.93 memory used=14332.8MB, alloc=421.4MB, time=99.16 memory used=14381.3MB, alloc=421.4MB, time=99.38 memory used=14434.8MB, alloc=421.4MB, time=99.64 memory used=14493.2MB, alloc=421.4MB, time=99.91 memory used=14556.3MB, alloc=421.4MB, time=100.15 memory used=14626.5MB, alloc=421.4MB, time=100.42 memory used=14701.1MB, alloc=421.4MB, time=100.70 memory used=14775.0MB, alloc=421.4MB, time=100.97 memory used=14815.9MB, alloc=421.4MB, time=101.16 memory used=14859.2MB, alloc=421.4MB, time=101.33 memory used=14903.5MB, alloc=421.4MB, time=101.51 memory used=14950.1MB, alloc=421.4MB, time=101.69 memory used=14998.6MB, alloc=421.4MB, time=101.87 memory used=15048.9MB, alloc=421.4MB, time=102.05 memory used=15102.8MB, alloc=421.4MB, time=102.24 memory used=15158.0MB, alloc=421.4MB, time=102.42 memory used=15216.8MB, alloc=421.4MB, time=102.60 memory used=15279.2MB, alloc=421.4MB, time=102.78 memory used=15345.1MB, alloc=421.4MB, time=102.97 memory used=15416.3MB, alloc=421.4MB, time=103.15 memory used=15506.8MB, alloc=421.4MB, time=103.95 memory used=15574.4MB, alloc=421.4MB, time=104.24 memory used=15639.4MB, alloc=421.4MB, time=104.49 memory used=15713.3MB, alloc=421.4MB, time=104.76 memory used=15759.7MB, alloc=421.4MB, time=104.98 memory used=15809.0MB, alloc=421.4MB, time=105.24 memory used=15863.0MB, alloc=421.4MB, time=105.48 memory used=15921.8MB, alloc=421.4MB, time=105.71 memory used=15987.5MB, alloc=421.4MB, time=105.93 memory used=16058.2MB, alloc=421.4MB, time=106.17 memory used=16135.7MB, alloc=421.4MB, time=106.41 memory used=16203.1MB, alloc=421.4MB, time=106.63 memory used=16244.0MB, alloc=421.4MB, time=106.80 memory used=16288.1MB, alloc=421.4MB, time=107.02 memory used=16332.6MB, alloc=421.4MB, time=107.23 memory used=16379.1MB, alloc=421.4MB, time=107.41 memory used=16427.6MB, alloc=421.4MB, time=107.59 memory used=16479.6MB, alloc=421.4MB, time=107.77 memory used=16533.3MB, alloc=421.4MB, time=107.95 memory used=16589.9MB, alloc=421.4MB, time=108.15 memory used=16649.2MB, alloc=421.4MB, time=108.35 memory used=16711.9MB, alloc=421.4MB, time=108.58 memory used=16779.4MB, alloc=421.4MB, time=108.78 memory used=16853.0MB, alloc=421.4MB, time=108.97 memory used=16927.7MB, alloc=421.4MB, time=109.51 memory used=16999.1MB, alloc=421.4MB, time=109.97 memory used=17069.6MB, alloc=421.4MB, time=110.38 memory used=17152.5MB, alloc=421.4MB, time=111.33 memory used=17211.4MB, alloc=421.4MB, time=111.59 memory used=17287.1MB, alloc=421.4MB, time=111.84 memory used=17338.1MB, alloc=421.4MB, time=112.05 memory used=17385.0MB, alloc=421.4MB, time=112.27 memory used=17438.0MB, alloc=421.4MB, time=112.48 memory used=17495.9MB, alloc=421.4MB, time=112.71 memory used=17558.5MB, alloc=421.4MB, time=112.95 memory used=17625.8MB, alloc=421.4MB, time=113.21 memory used=17697.8MB, alloc=421.4MB, time=113.44 memory used=17775.9MB, alloc=421.4MB, time=113.66 memory used=17820.3MB, alloc=421.4MB, time=113.84 memory used=17861.8MB, alloc=421.4MB, time=114.02 memory used=17906.1MB, alloc=421.4MB, time=114.20 memory used=17950.6MB, alloc=421.4MB, time=114.37 memory used=17998.8MB, alloc=421.4MB, time=114.54 memory used=18049.3MB, alloc=421.4MB, time=114.71 memory used=18101.2MB, alloc=421.4MB, time=114.89 memory used=18156.3MB, alloc=421.4MB, time=115.07 memory used=18214.0MB, alloc=421.4MB, time=115.24 memory used=18273.8MB, alloc=421.4MB, time=115.42 memory used=18338.3MB, alloc=421.4MB, time=115.61 memory used=18406.9MB, alloc=421.4MB, time=115.80 memory used=18482.5MB, alloc=421.4MB, time=115.97 memory used=18572.5MB, alloc=421.4MB, time=116.80 memory used=18632.8MB, alloc=421.4MB, time=117.11 memory used=18699.8MB, alloc=421.4MB, time=117.41 memory used=18767.0MB, alloc=421.4MB, time=117.69 memory used=18812.4MB, alloc=421.4MB, time=117.91 memory used=18863.5MB, alloc=421.4MB, time=118.15 memory used=18917.5MB, alloc=421.4MB, time=118.39 memory used=18978.0MB, alloc=421.4MB, time=118.62 memory used=19043.4MB, alloc=421.4MB, time=118.85 memory used=19113.3MB, alloc=421.4MB, time=119.07 memory used=19189.9MB, alloc=421.4MB, time=119.28 memory used=19248.8MB, alloc=421.4MB, time=119.47 memory used=19290.1MB, alloc=421.4MB, time=119.64 memory used=19333.7MB, alloc=421.4MB, time=119.84 memory used=19379.5MB, alloc=421.4MB, time=120.01 memory used=19427.3MB, alloc=421.4MB, time=120.20 memory used=19476.9MB, alloc=421.4MB, time=120.38 memory used=19527.8MB, alloc=421.4MB, time=120.56 memory used=19582.0MB, alloc=421.4MB, time=120.72 memory used=19638.6MB, alloc=421.4MB, time=120.90 memory used=19698.7MB, alloc=421.4MB, time=121.08 memory used=19762.4MB, alloc=421.4MB, time=121.26 memory used=19831.2MB, alloc=421.4MB, time=121.43 memory used=19916.2MB, alloc=421.4MB, time=122.30 memory used=19997.9MB, alloc=421.4MB, time=132.47 memory used=20066.1MB, alloc=421.4MB, time=132.74 memory used=20115.4MB, alloc=421.4MB, time=133.00 memory used=20174.9MB, alloc=421.4MB, time=133.26 memory used=20245.0MB, alloc=421.4MB, time=133.52 memory used=20315.5MB, alloc=421.4MB, time=133.77 memory used=20358.9MB, alloc=421.4MB, time=133.96 memory used=20404.6MB, alloc=421.4MB, time=134.17 memory used=20454.2MB, alloc=421.4MB, time=134.37 memory used=20507.7MB, alloc=421.4MB, time=134.57 memory used=20564.6MB, alloc=421.4MB, time=134.77 memory used=20624.7MB, alloc=421.4MB, time=134.97 memory used=20689.1MB, alloc=421.4MB, time=135.18 memory used=20759.2MB, alloc=421.4MB, time=135.40 memory used=20834.2MB, alloc=421.4MB, time=135.61 memory used=21021.7MB, alloc=421.4MB, time=136.16 memory used=21108.0MB, alloc=421.4MB, time=136.61 memory used=21163.9MB, alloc=421.4MB, time=136.85 memory used=21230.4MB, alloc=421.4MB, time=137.06 memory used=21305.3MB, alloc=421.4MB, time=137.42 memory used=21369.4MB, alloc=421.4MB, time=137.66 memory used=21427.0MB, alloc=421.4MB, time=137.87 memory used=21494.0MB, alloc=421.4MB, time=138.09 memory used=21576.8MB, alloc=421.4MB, time=138.71 memory used=21641.0MB, alloc=421.4MB, time=138.95 memory used=21694.4MB, alloc=421.4MB, time=139.17 memory used=21764.9MB, alloc=421.4MB, time=139.38 memory used=21834.5MB, alloc=421.4MB, time=139.81 memory used=21896.4MB, alloc=421.4MB, time=140.06 memory used=21956.4MB, alloc=421.4MB, time=140.27 memory used=22022.2MB, alloc=421.4MB, time=140.49 memory used=22100.3MB, alloc=421.4MB, time=140.85 memory used=22158.7MB, alloc=421.4MB, time=141.06 memory used=22223.8MB, alloc=421.4MB, time=141.26 memory used=22298.4MB, alloc=421.4MB, time=141.53 memory used=22387.5MB, alloc=421.4MB, time=142.30 memory used=22450.3MB, alloc=421.4MB, time=142.56 memory used=22514.4MB, alloc=421.4MB, time=142.83 memory used=22586.1MB, alloc=421.4MB, time=143.08 memory used=22630.2MB, alloc=421.4MB, time=143.30 memory used=22679.6MB, alloc=421.4MB, time=143.53 memory used=22733.2MB, alloc=421.4MB, time=143.78 memory used=22792.8MB, alloc=421.4MB, time=144.06 memory used=22858.2MB, alloc=421.4MB, time=144.29 memory used=22930.9MB, alloc=421.4MB, time=144.52 memory used=23006.6MB, alloc=421.4MB, time=144.73 memory used=23048.5MB, alloc=421.4MB, time=144.90 memory used=23092.2MB, alloc=421.4MB, time=145.10 memory used=23139.2MB, alloc=421.4MB, time=145.28 memory used=23188.5MB, alloc=421.4MB, time=145.45 memory used=23242.1MB, alloc=421.4MB, time=145.62 memory used=23328.6MB, alloc=421.4MB, time=146.87 memory used=23387.9MB, alloc=421.4MB, time=147.14 memory used=23462.3MB, alloc=421.4MB, time=147.39 memory used=23508.8MB, alloc=421.4MB, time=147.64 memory used=23557.5MB, alloc=421.4MB, time=147.85 memory used=23611.4MB, alloc=421.4MB, time=148.07 memory used=23670.7MB, alloc=421.4MB, time=148.29 memory used=23735.5MB, alloc=421.4MB, time=148.55 memory used=23805.6MB, alloc=421.4MB, time=148.78 memory used=23881.1MB, alloc=421.4MB, time=149.04 memory used=23940.4MB, alloc=421.4MB, time=149.26 memory used=23981.1MB, alloc=421.4MB, time=149.42 memory used=24023.9MB, alloc=421.4MB, time=149.63 memory used=24067.2MB, alloc=421.4MB, time=149.82 memory used=24113.4MB, alloc=421.4MB, time=150.00 memory used=24159.9MB, alloc=421.4MB, time=150.17 memory used=24209.3MB, alloc=421.4MB, time=150.35 memory used=24259.1MB, alloc=421.4MB, time=150.52 memory used=24311.2MB, alloc=421.4MB, time=150.69 memory used=24365.7MB, alloc=421.4MB, time=150.87 memory used=24422.7MB, alloc=421.4MB, time=151.08 memory used=24481.9MB, alloc=421.4MB, time=151.25 memory used=24542.9MB, alloc=421.4MB, time=151.43 memory used=24608.0MB, alloc=421.4MB, time=151.62 memory used=24676.4MB, alloc=421.4MB, time=151.81 memory used=24747.4MB, alloc=421.4MB, time=152.01 memory used=24820.3MB, alloc=421.4MB, time=152.20 memory used=24897.1MB, alloc=421.4MB, time=152.40 memory used=25049.2MB, alloc=421.4MB, time=152.70 memory used=25173.9MB, alloc=421.4MB, time=167.82 memory used=25250.4MB, alloc=421.4MB, time=169.36 memory used=25314.9MB, alloc=421.4MB, time=169.62 memory used=25377.3MB, alloc=421.4MB, time=169.86 memory used=25421.6MB, alloc=421.4MB, time=170.09 memory used=25469.8MB, alloc=421.4MB, time=170.29 memory used=25522.4MB, alloc=421.4MB, time=170.50 memory used=25580.9MB, alloc=421.4MB, time=170.73 memory used=25643.1MB, alloc=421.4MB, time=170.95 memory used=25711.5MB, alloc=421.4MB, time=171.16 memory used=25783.7MB, alloc=421.4MB, time=171.40 memory used=25848.9MB, alloc=421.4MB, time=171.61 memory used=25889.9MB, alloc=445.4MB, time=171.81 memory used=25943.6MB, alloc=445.4MB, time=172.00 memory used=25999.8MB, alloc=445.4MB, time=172.19 memory used=26057.4MB, alloc=445.4MB, time=172.39 memory used=26116.4MB, alloc=445.4MB, time=172.58 memory used=26176.8MB, alloc=445.4MB, time=172.78 memory used=26241.8MB, alloc=445.4MB, time=172.98 memory used=26308.1MB, alloc=445.4MB, time=173.17 memory used=26375.7MB, alloc=445.4MB, time=173.41 memory used=26444.8MB, alloc=445.4MB, time=173.67 memory used=26518.2MB, alloc=445.4MB, time=173.91 memory used=26593.1MB, alloc=445.4MB, time=174.12 memory used=26672.9MB, alloc=445.4MB, time=174.35 memory used=26753.8MB, alloc=445.4MB, time=174.56 memory used=26835.8MB, alloc=445.4MB, time=174.81 memory used=26922.7MB, alloc=445.4MB, time=175.03 memory used=27010.6MB, alloc=445.4MB, time=175.24 memory used=27103.3MB, alloc=445.4MB, time=175.46 memory used=27196.9MB, alloc=445.4MB, time=175.67 memory used=27295.3MB, alloc=445.4MB, time=175.88 memory used=27456.6MB, alloc=445.4MB, time=176.22 memory used=27584.5MB, alloc=445.4MB, time=176.50 memory used=27718.8MB, alloc=445.4MB, time=176.80 memory used=27857.5MB, alloc=445.4MB, time=177.14 memory used=28000.5MB, alloc=445.4MB, time=177.45 memory used=28151.1MB, alloc=445.4MB, time=177.80 memory used=28309.1MB, alloc=445.4MB, time=178.12 memory used=28473.5MB, alloc=445.4MB, time=178.46 memory used=28643.5MB, alloc=445.4MB, time=178.79 memory used=28818.3MB, alloc=445.4MB, time=179.12 memory used=29003.1MB, alloc=445.4MB, time=179.46 memory used=29197.2MB, alloc=445.4MB, time=179.79 memory used=29399.2MB, alloc=445.4MB, time=180.13 memory used=29611.4MB, alloc=445.4MB, time=180.48 memory used=29838.1MB, alloc=445.4MB, time=180.83 memory used=30065.7MB, alloc=445.4MB, time=181.19 memory used=30228.0MB, alloc=469.4MB, time=209.32 memory used=30296.9MB, alloc=493.4MB, time=276.81 memory used=30365.3MB, alloc=517.4MB, time=330.39 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428508798 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [-3 x y - x y - 2 z, -13 x y - 19 x z - 7 z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 3 G := [3 x y + 5 x y + 17 x , 7 x y z + x - 5] > Problem := [F,G]; 2 2 2 2 Problem := [[-3 x y - x y - 2 z, -13 x y - 19 x z - 7 z ], 2 2 3 2 2 3 [3 x y + 5 x y + 17 x , 7 x y z + x - 5]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.2MB, alloc=32.3MB, time=0.49 memory used=45.8MB, alloc=32.3MB, time=0.74 memory used=64.8MB, alloc=56.3MB, time=1.01 memory used=107.3MB, alloc=60.3MB, time=1.53 memory used=150.3MB, alloc=60.3MB, time=2.09 memory used=192.5MB, alloc=84.3MB, time=2.92 N1 := 509 > GB := Basis(F, plex(op(vars))); GB := [ 3 4 3 3 2 4 3 2 2 3 2 2 2 171 x y + 114 x y + 63 x y + 19 x y + 42 x y + 7 x y + 52 x y , 2 3 y x + y x + 2 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=251.6MB, alloc=84.3MB, time=4.10 N2 := 261 > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 2 2 3 2 H := [-3 x y - x y - 2 z, -13 x y - 19 x z - 7 z , 3 x y + 5 x y + 17 x , 2 3 7 z y x + x - 5] > J:=[op(GB),op(G)]; J := [ 3 4 3 3 2 4 3 2 2 3 2 2 2 171 x y + 114 x y + 63 x y + 19 x y + 42 x y + 7 x y + 52 x y , 2 2 2 3 2 2 3 3 y x + y x + 2 z, 3 x y + 5 x y + 17 x , 7 z y x + x - 5] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 11, 14, 4, 3, 3, 2, 1, 1, 3/4, 3/4, 1/2, 1/3, 4, 10, 18, 7, 3, 4, 1, 1, 1, 1/2, 7/8, 3/4, 1/8, 1, -4, -3] > save(F, G, cat("ranSet/34", convert(F, string),".txt")); > quit memory used=295.0MB, alloc=84.3MB, time=4.98 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428508805 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 3 2 F := [-12 x z - 8 x y z + 3 x , 10 x y + 16 x - 15 y ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 3 2 2 G := [-6 x z - 14 x y z + 6 y z , -8 x y - 5 x - 4 z ] > Problem := [F,G]; 3 2 3 3 2 Problem := [[-12 x z - 8 x y z + 3 x , 10 x y + 16 x - 15 y ], 2 2 2 3 3 2 2 [-6 x z - 14 x y z + 6 y z , -8 x y - 5 x - 4 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.4MB, alloc=32.3MB, time=0.51 memory used=46.5MB, alloc=32.3MB, time=0.81 memory used=64.2MB, alloc=56.3MB, time=1.11 memory used=105.3MB, alloc=60.3MB, time=1.74 memory used=145.6MB, alloc=60.3MB, time=2.34 memory used=186.1MB, alloc=92.3MB, time=3.04 memory used=252.3MB, alloc=92.3MB, time=3.76 memory used=315.7MB, alloc=92.3MB, time=4.77 memory used=378.7MB, alloc=92.3MB, time=5.67 memory used=439.5MB, alloc=116.3MB, time=6.53 memory used=516.7MB, alloc=372.3MB, time=7.58 memory used=613.5MB, alloc=372.3MB, time=8.80 memory used=704.6MB, alloc=372.3MB, time=9.79 memory used=795.8MB, alloc=396.3MB, time=11.06 memory used=906.8MB, alloc=396.3MB, time=12.89 memory used=1000.0MB, alloc=420.3MB, time=14.73 memory used=1118.3MB, alloc=444.3MB, time=16.87 memory used=1247.6MB, alloc=468.3MB, time=19.34 memory used=1395.4MB, alloc=492.3MB, time=22.17 memory used=1565.5MB, alloc=516.3MB, time=25.14 memory used=1755.8MB, alloc=540.3MB, time=28.31 memory used=1955.6MB, alloc=564.3MB, time=32.02 memory used=2131.4MB, alloc=588.3MB, time=37.87 memory used=2316.5MB, alloc=612.3MB, time=44.38 memory used=2514.7MB, alloc=636.3MB, time=51.91 memory used=2726.8MB, alloc=660.3MB, time=59.89 memory used=2946.1MB, alloc=684.3MB, time=69.02 memory used=3189.4MB, alloc=708.3MB, time=79.12 memory used=3456.7MB, alloc=732.3MB, time=90.37 memory used=3747.9MB, alloc=756.3MB, time=102.42 memory used=4063.1MB, alloc=756.3MB, time=116.10 memory used=4378.2MB, alloc=756.3MB, time=129.45 memory used=4693.3MB, alloc=780.3MB, time=142.77 memory used=5032.3MB, alloc=780.3MB, time=157.81 memory used=5371.2MB, alloc=780.3MB, time=171.76 memory used=5709.9MB, alloc=804.3MB, time=185.41 memory used=6072.6MB, alloc=804.3MB, time=200.34 memory used=6435.1MB, alloc=828.3MB, time=215.59 memory used=6821.5MB, alloc=852.3MB, time=232.37 N1 := 12841 > GB := Basis(F, plex(op(vars))); 3 3 2 GB := [-10 x y - 16 x + 15 y , 6 5 5 4 4 2 240 x z + 540 x z - 60 x - 256 x z - 135 x + 90 x y, 3 2 12 x z + 8 x y z - 3 x ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=7249.6MB, alloc=852.3MB, time=247.95 memory used=7375.1MB, alloc=852.3MB, time=251.13 memory used=7467.5MB, alloc=852.3MB, time=253.60 memory used=7570.2MB, alloc=852.3MB, time=255.88 memory used=7662.0MB, alloc=852.3MB, time=258.15 memory used=7744.0MB, alloc=852.3MB, time=260.16 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428509106 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 3 3 F := [-17 x y - 16 x y + 5 x, -x y z + 20 y - 16 z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 4 2 G := [-16 x y z + 5 x y z + 17 y z, -15 x y - 10 y + 8 y z ] > Problem := [F,G]; 3 2 2 3 3 Problem := [[-17 x y - 16 x y + 5 x, -x y z + 20 y - 16 z ], 2 2 3 4 2 [-16 x y z + 5 x y z + 17 y z, -15 x y - 10 y + 8 y z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.19 memory used=26.7MB, alloc=32.3MB, time=0.53 memory used=48.0MB, alloc=32.3MB, time=0.85 memory used=67.1MB, alloc=56.3MB, time=1.18 memory used=107.5MB, alloc=60.3MB, time=1.79 memory used=148.2MB, alloc=84.3MB, time=2.70 memory used=226.0MB, alloc=92.3MB, time=3.61 memory used=294.1MB, alloc=92.3MB, time=4.59 memory used=356.4MB, alloc=116.3MB, time=5.57 memory used=444.9MB, alloc=116.3MB, time=6.96 memory used=530.9MB, alloc=140.3MB, time=8.53 memory used=641.8MB, alloc=164.3MB, time=10.37 memory used=768.9MB, alloc=164.3MB, time=11.38 memory used=880.4MB, alloc=164.3MB, time=12.02 memory used=990.0MB, alloc=164.3MB, time=12.61 memory used=1079.8MB, alloc=179.8MB, time=13.13 memory used=1174.2MB, alloc=179.8MB, time=13.72 memory used=1277.4MB, alloc=179.8MB, time=14.24 memory used=1386.6MB, alloc=179.8MB, time=14.72 memory used=1462.1MB, alloc=179.8MB, time=15.08 memory used=1540.6MB, alloc=179.8MB, time=15.43 memory used=1622.5MB, alloc=179.8MB, time=15.79 memory used=1707.9MB, alloc=179.8MB, time=16.18 memory used=1796.5MB, alloc=179.8MB, time=16.55 memory used=1888.6MB, alloc=179.8MB, time=16.91 memory used=1941.5MB, alloc=179.8MB, time=17.16 memory used=1984.8MB, alloc=179.8MB, time=17.38 memory used=2028.3MB, alloc=179.8MB, time=17.63 memory used=2072.9MB, alloc=179.8MB, time=17.86 memory used=2118.1MB, alloc=179.8MB, time=18.10 memory used=2164.0MB, alloc=179.8MB, time=18.34 memory used=2210.2MB, alloc=179.8MB, time=18.59 memory used=2257.6MB, alloc=179.8MB, time=18.84 memory used=2305.6MB, alloc=179.8MB, time=19.08 memory used=2354.2MB, alloc=179.8MB, time=19.34 memory used=2403.1MB, alloc=179.8MB, time=19.57 memory used=2453.1MB, alloc=179.8MB, time=19.82 memory used=2503.8MB, alloc=179.8MB, time=20.04 memory used=2555.2MB, alloc=179.8MB, time=20.27 memory used=2606.7MB, alloc=179.8MB, time=20.51 memory used=2659.5MB, alloc=179.8MB, time=20.79 memory used=2712.9MB, alloc=179.8MB, time=21.02 memory used=2767.0MB, alloc=179.8MB, time=21.27 memory used=2821.3MB, alloc=179.8MB, time=21.54 memory used=2876.8MB, alloc=179.8MB, time=21.77 memory used=2932.9MB, alloc=179.8MB, time=22.02 memory used=2989.7MB, alloc=179.8MB, time=22.27 memory used=3046.7MB, alloc=179.8MB, time=22.50 memory used=3104.9MB, alloc=179.8MB, time=22.75 memory used=3163.8MB, alloc=179.8MB, time=23.00 memory used=3223.4MB, alloc=179.8MB, time=23.25 memory used=3283.1MB, alloc=179.8MB, time=23.49 memory used=3340.3MB, alloc=179.8MB, time=23.74 memory used=3372.4MB, alloc=179.8MB, time=23.92 memory used=3401.0MB, alloc=179.8MB, time=24.08 memory used=3430.1MB, alloc=179.8MB, time=24.26 memory used=3459.2MB, alloc=179.8MB, time=24.45 memory used=3488.5MB, alloc=179.8MB, time=24.62 memory used=3517.9MB, alloc=179.8MB, time=24.80 memory used=3547.3MB, alloc=179.8MB, time=24.97 memory used=3577.1MB, alloc=179.8MB, time=25.15 memory used=3607.0MB, alloc=179.8MB, time=25.33 memory used=3637.0MB, alloc=179.8MB, time=25.49 memory used=3667.2MB, alloc=179.8MB, time=25.67 memory used=3697.4MB, alloc=179.8MB, time=25.84 memory used=3727.8MB, alloc=179.8MB, time=26.00 memory used=3758.4MB, alloc=179.8MB, time=26.18 memory used=3789.2MB, alloc=179.8MB, time=26.37 memory used=3820.1MB, alloc=179.8MB, time=26.58 memory used=3851.0MB, alloc=179.8MB, time=26.80 memory used=3882.2MB, alloc=179.8MB, time=27.01 memory used=3913.6MB, alloc=179.8MB, time=27.23 memory used=3945.0MB, alloc=179.8MB, time=27.45 memory used=3976.8MB, alloc=179.8MB, time=27.65 memory used=4008.4MB, alloc=179.8MB, time=27.83 memory used=4040.3MB, alloc=179.8MB, time=28.01 memory used=4072.5MB, alloc=179.8MB, time=28.19 memory used=4104.7MB, alloc=179.8MB, time=28.37 memory used=4137.2MB, alloc=179.8MB, time=28.55 memory used=4169.4MB, alloc=179.8MB, time=28.72 memory used=4202.1MB, alloc=179.8MB, time=28.90 memory used=4235.1MB, alloc=179.8MB, time=29.08 memory used=4268.0MB, alloc=179.8MB, time=29.26 memory used=4301.2MB, alloc=179.8MB, time=29.44 memory used=4334.4MB, alloc=179.8MB, time=29.62 memory used=4367.7MB, alloc=179.8MB, time=29.79 memory used=4401.3MB, alloc=179.8MB, time=29.96 memory used=4435.0MB, alloc=179.8MB, time=30.12 memory used=4469.0MB, alloc=179.8MB, time=30.30 memory used=4502.8MB, alloc=179.8MB, time=30.47 memory used=4537.0MB, alloc=179.8MB, time=30.64 memory used=4571.3MB, alloc=179.8MB, time=30.92 memory used=4605.7MB, alloc=179.8MB, time=31.15 memory used=4640.5MB, alloc=179.8MB, time=31.34 memory used=4675.1MB, alloc=179.8MB, time=31.52 memory used=4709.9MB, alloc=179.8MB, time=31.70 memory used=4745.1MB, alloc=179.8MB, time=31.89 memory used=4780.4MB, alloc=179.8MB, time=32.06 memory used=4815.8MB, alloc=179.8MB, time=32.24 memory used=4851.1MB, alloc=179.8MB, time=32.41 memory used=4886.6MB, alloc=179.8MB, time=32.58 memory used=4922.5MB, alloc=179.8MB, time=32.75 memory used=4958.4MB, alloc=179.8MB, time=32.93 memory used=4994.6MB, alloc=179.8MB, time=33.10 memory used=5030.7MB, alloc=179.8MB, time=33.28 memory used=5067.0MB, alloc=179.8MB, time=33.46 memory used=5103.6MB, alloc=179.8MB, time=33.63 memory used=5140.2MB, alloc=179.8MB, time=33.80 memory used=5177.2MB, alloc=179.8MB, time=33.97 memory used=5214.0MB, alloc=179.8MB, time=34.17 memory used=5251.1MB, alloc=179.8MB, time=34.36 memory used=5288.5MB, alloc=179.8MB, time=34.56 memory used=5325.8MB, alloc=179.8MB, time=34.73 memory used=5360.3MB, alloc=179.8MB, time=34.92 memory used=5392.4MB, alloc=179.8MB, time=35.10 memory used=5425.1MB, alloc=179.8MB, time=35.27 memory used=5457.7MB, alloc=179.8MB, time=35.44 memory used=5490.4MB, alloc=179.8MB, time=35.61 memory used=5523.4MB, alloc=179.8MB, time=35.78 memory used=5556.0MB, alloc=179.8MB, time=35.97 memory used=5589.4MB, alloc=179.8MB, time=36.15 memory used=5622.5MB, alloc=179.8MB, time=36.33 memory used=5655.8MB, alloc=179.8MB, time=36.51 memory used=5689.3MB, alloc=179.8MB, time=36.68 memory used=5722.6MB, alloc=179.8MB, time=36.86 memory used=5756.5MB, alloc=179.8MB, time=37.04 memory used=5790.4MB, alloc=179.8MB, time=37.21 memory used=5823.9MB, alloc=179.8MB, time=37.38 memory used=5858.1MB, alloc=179.8MB, time=37.56 memory used=5892.2MB, alloc=179.8MB, time=37.73 memory used=5926.3MB, alloc=179.8MB, time=37.92 memory used=5960.7MB, alloc=179.8MB, time=38.11 memory used=5994.9MB, alloc=179.8MB, time=38.29 memory used=6029.6MB, alloc=179.8MB, time=38.48 memory used=6064.4MB, alloc=179.8MB, time=38.67 memory used=6098.8MB, alloc=179.8MB, time=38.85 memory used=6133.9MB, alloc=179.8MB, time=39.04 memory used=6168.8MB, alloc=179.8MB, time=39.26 memory used=6203.8MB, alloc=179.8MB, time=39.47 memory used=6239.2MB, alloc=179.8MB, time=39.70 memory used=6274.3MB, alloc=179.8MB, time=39.91 memory used=6309.9MB, alloc=179.8MB, time=40.09 memory used=6345.6MB, alloc=179.8MB, time=40.27 memory used=6380.8MB, alloc=179.8MB, time=40.46 memory used=6416.8MB, alloc=179.8MB, time=40.64 memory used=6452.6MB, alloc=179.8MB, time=40.81 memory used=6488.5MB, alloc=179.8MB, time=40.98 memory used=6524.7MB, alloc=179.8MB, time=41.16 memory used=6559.9MB, alloc=179.8MB, time=41.33 memory used=6594.9MB, alloc=179.8MB, time=41.50 memory used=6630.1MB, alloc=179.8MB, time=41.68 memory used=6665.5MB, alloc=179.8MB, time=41.87 memory used=6700.9MB, alloc=179.8MB, time=42.06 memory used=6736.4MB, alloc=179.8MB, time=42.25 memory used=6772.0MB, alloc=179.8MB, time=42.43 memory used=6807.8MB, alloc=179.8MB, time=42.60 memory used=6843.7MB, alloc=179.8MB, time=42.78 memory used=6879.6MB, alloc=179.8MB, time=42.95 memory used=6915.7MB, alloc=179.8MB, time=43.13 memory used=6951.8MB, alloc=179.8MB, time=43.30 memory used=6988.1MB, alloc=179.8MB, time=43.49 memory used=7024.5MB, alloc=179.8MB, time=43.67 memory used=7060.9MB, alloc=179.8MB, time=43.85 memory used=7097.5MB, alloc=179.8MB, time=44.03 memory used=7134.2MB, alloc=179.8MB, time=44.21 memory used=7170.9MB, alloc=179.8MB, time=44.39 memory used=7207.8MB, alloc=179.8MB, time=44.57 memory used=7244.8MB, alloc=179.8MB, time=44.76 memory used=7281.9MB, alloc=179.8MB, time=44.94 memory used=7319.1MB, alloc=179.8MB, time=45.12 memory used=7356.4MB, alloc=179.8MB, time=45.30 memory used=7393.8MB, alloc=179.8MB, time=45.48 memory used=7431.3MB, alloc=179.8MB, time=45.67 memory used=7468.9MB, alloc=179.8MB, time=45.85 memory used=7506.6MB, alloc=179.8MB, time=46.04 memory used=7544.4MB, alloc=179.8MB, time=46.23 memory used=7582.3MB, alloc=179.8MB, time=46.42 memory used=7620.4MB, alloc=179.8MB, time=46.60 memory used=7658.5MB, alloc=179.8MB, time=46.79 memory used=7696.7MB, alloc=179.8MB, time=46.96 memory used=7735.0MB, alloc=179.8MB, time=47.14 memory used=7773.5MB, alloc=179.8MB, time=47.33 memory used=7812.0MB, alloc=179.8MB, time=47.51 memory used=7850.6MB, alloc=179.8MB, time=47.69 memory used=7887.9MB, alloc=179.8MB, time=47.88 memory used=7924.5MB, alloc=179.8MB, time=48.06 memory used=7961.3MB, alloc=179.8MB, time=48.24 memory used=7998.1MB, alloc=179.8MB, time=48.42 memory used=8035.1MB, alloc=179.8MB, time=48.60 memory used=8072.2MB, alloc=179.8MB, time=48.78 memory used=8109.5MB, alloc=179.8MB, time=48.97 memory used=8146.8MB, alloc=179.8MB, time=49.15 memory used=8184.2MB, alloc=179.8MB, time=49.33 memory used=8221.8MB, alloc=179.8MB, time=49.52 memory used=8259.4MB, alloc=179.8MB, time=49.71 memory used=8297.1MB, alloc=179.8MB, time=49.90 memory used=8334.9MB, alloc=179.8MB, time=50.09 memory used=8372.8MB, alloc=179.8MB, time=50.29 memory used=8410.8MB, alloc=179.8MB, time=50.48 memory used=8448.9MB, alloc=179.8MB, time=50.67 memory used=8487.1MB, alloc=179.8MB, time=50.86 memory used=8525.4MB, alloc=179.8MB, time=51.05 memory used=8563.7MB, alloc=179.8MB, time=51.24 memory used=8602.2MB, alloc=179.8MB, time=51.43 memory used=8640.7MB, alloc=179.8MB, time=51.62 memory used=8679.4MB, alloc=179.8MB, time=51.81 memory used=8718.1MB, alloc=179.8MB, time=52.00 memory used=8756.9MB, alloc=179.8MB, time=52.18 memory used=8795.8MB, alloc=179.8MB, time=52.36 memory used=8834.9MB, alloc=179.8MB, time=52.55 memory used=8874.0MB, alloc=179.8MB, time=52.75 memory used=8913.2MB, alloc=179.8MB, time=52.94 memory used=8952.5MB, alloc=179.8MB, time=53.14 memory used=8991.8MB, alloc=179.8MB, time=53.33 memory used=9031.3MB, alloc=179.8MB, time=53.52 memory used=9070.8MB, alloc=179.8MB, time=53.71 memory used=9110.4MB, alloc=179.8MB, time=53.91 memory used=9150.2MB, alloc=179.8MB, time=54.09 memory used=9190.1MB, alloc=179.8MB, time=54.28 memory used=9230.0MB, alloc=179.8MB, time=54.47 memory used=9270.0MB, alloc=179.8MB, time=54.66 memory used=9310.1MB, alloc=179.8MB, time=54.85 memory used=9350.4MB, alloc=179.8MB, time=55.03 memory used=9390.6MB, alloc=179.8MB, time=55.23 memory used=9431.1MB, alloc=179.8MB, time=55.43 memory used=9471.5MB, alloc=179.8MB, time=55.63 memory used=9512.1MB, alloc=179.8MB, time=55.82 memory used=9552.8MB, alloc=179.8MB, time=56.02 memory used=9593.6MB, alloc=179.8MB, time=56.21 memory used=9634.4MB, alloc=179.8MB, time=56.43 memory used=9675.4MB, alloc=179.8MB, time=56.62 memory used=9716.4MB, alloc=179.8MB, time=56.81 memory used=9757.6MB, alloc=179.8MB, time=57.00 memory used=9798.8MB, alloc=179.8MB, time=57.19 memory used=9840.1MB, alloc=179.8MB, time=57.38 memory used=9881.6MB, alloc=179.8MB, time=57.57 memory used=9923.1MB, alloc=179.8MB, time=57.76 memory used=9964.7MB, alloc=179.8MB, time=57.96 memory used=10006.3MB, alloc=179.8MB, time=58.14 memory used=10048.1MB, alloc=179.8MB, time=58.35 memory used=10090.0MB, alloc=179.8MB, time=58.55 memory used=10132.0MB, alloc=179.8MB, time=58.74 memory used=10174.1MB, alloc=179.8MB, time=58.93 memory used=10216.2MB, alloc=179.8MB, time=59.14 memory used=10258.5MB, alloc=179.8MB, time=59.33 memory used=10300.8MB, alloc=179.8MB, time=59.55 memory used=10343.2MB, alloc=179.8MB, time=59.76 memory used=10385.8MB, alloc=179.8MB, time=59.95 memory used=10428.4MB, alloc=179.8MB, time=60.16 memory used=10471.2MB, alloc=179.8MB, time=60.36 memory used=10513.8MB, alloc=179.8MB, time=60.56 memory used=10556.4MB, alloc=179.8MB, time=60.76 memory used=10599.1MB, alloc=179.8MB, time=60.95 memory used=10641.8MB, alloc=179.8MB, time=61.14 memory used=10684.8MB, alloc=179.8MB, time=61.34 memory used=10727.5MB, alloc=179.8MB, time=61.53 memory used=10765.6MB, alloc=179.8MB, time=61.72 memory used=10799.3MB, alloc=179.8MB, time=61.89 memory used=10827.2MB, alloc=179.8MB, time=62.04 memory used=10849.5MB, alloc=179.8MB, time=62.17 memory used=10870.3MB, alloc=179.8MB, time=62.31 memory used=10889.3MB, alloc=179.8MB, time=62.44 memory used=10907.7MB, alloc=179.8MB, time=62.58 memory used=10925.1MB, alloc=179.8MB, time=62.71 memory used=10942.0MB, alloc=179.8MB, time=62.84 memory used=10958.8MB, alloc=179.8MB, time=62.97 memory used=10975.3MB, alloc=179.8MB, time=63.10 memory used=10991.7MB, alloc=179.8MB, time=63.23 memory used=11007.6MB, alloc=179.8MB, time=63.36 memory used=11023.8MB, alloc=179.8MB, time=63.49 memory used=11039.5MB, alloc=179.8MB, time=63.62 memory used=11055.2MB, alloc=179.8MB, time=63.75 memory used=11070.6MB, alloc=179.8MB, time=63.88 memory used=11085.9MB, alloc=179.8MB, time=64.00 memory used=11101.1MB, alloc=179.8MB, time=64.13 memory used=11115.9MB, alloc=179.8MB, time=64.26 memory used=11130.5MB, alloc=179.8MB, time=64.39 memory used=11145.1MB, alloc=179.8MB, time=64.51 memory used=11159.5MB, alloc=179.8MB, time=64.64 memory used=11173.9MB, alloc=179.8MB, time=64.76 memory used=11188.3MB, alloc=179.8MB, time=64.88 memory used=11202.4MB, alloc=179.8MB, time=65.00 memory used=11216.0MB, alloc=179.8MB, time=65.14 memory used=11229.9MB, alloc=179.8MB, time=65.27 memory used=11243.4MB, alloc=179.8MB, time=65.40 memory used=11257.1MB, alloc=179.8MB, time=65.53 memory used=11270.4MB, alloc=179.8MB, time=65.66 memory used=11283.8MB, alloc=179.8MB, time=65.79 memory used=11296.9MB, alloc=179.8MB, time=65.92 memory used=11310.0MB, alloc=179.8MB, time=66.05 memory used=11323.0MB, alloc=179.8MB, time=66.17 memory used=11335.8MB, alloc=179.8MB, time=66.30 memory used=11348.4MB, alloc=179.8MB, time=66.43 memory used=11360.9MB, alloc=179.8MB, time=66.55 memory used=11373.6MB, alloc=179.8MB, time=66.67 memory used=11386.2MB, alloc=179.8MB, time=66.80 memory used=11398.7MB, alloc=179.8MB, time=66.93 memory used=11411.2MB, alloc=179.8MB, time=67.06 memory used=11423.5MB, alloc=179.8MB, time=67.18 memory used=11435.8MB, alloc=179.8MB, time=67.31 memory used=11448.1MB, alloc=179.8MB, time=67.44 memory used=11460.2MB, alloc=179.8MB, time=67.56 memory used=11472.1MB, alloc=179.8MB, time=67.69 memory used=11484.0MB, alloc=179.8MB, time=67.81 memory used=11495.9MB, alloc=179.8MB, time=67.94 memory used=11507.8MB, alloc=179.8MB, time=68.06 memory used=11519.6MB, alloc=179.8MB, time=68.18 memory used=11531.3MB, alloc=179.8MB, time=68.31 memory used=11543.1MB, alloc=179.8MB, time=68.43 memory used=11554.9MB, alloc=179.8MB, time=68.55 memory used=11566.5MB, alloc=179.8MB, time=68.67 memory used=11578.1MB, alloc=179.8MB, time=68.79 memory used=11589.8MB, alloc=179.8MB, time=68.91 memory used=11601.3MB, alloc=179.8MB, time=69.04 memory used=11612.8MB, alloc=179.8MB, time=69.16 memory used=11624.2MB, alloc=179.8MB, time=69.28 memory used=11635.8MB, alloc=179.8MB, time=69.40 memory used=11647.3MB, alloc=179.8MB, time=69.52 memory used=11658.7MB, alloc=179.8MB, time=69.63 memory used=11670.2MB, alloc=179.8MB, time=69.75 memory used=11681.4MB, alloc=179.8MB, time=69.86 memory used=11692.8MB, alloc=179.8MB, time=69.98 memory used=11704.1MB, alloc=179.8MB, time=70.10 memory used=11715.3MB, alloc=179.8MB, time=70.22 memory used=11726.5MB, alloc=179.8MB, time=70.34 memory used=11737.8MB, alloc=179.8MB, time=70.46 memory used=11749.1MB, alloc=179.8MB, time=70.58 memory used=11760.4MB, alloc=179.8MB, time=70.70 memory used=11771.8MB, alloc=179.8MB, time=70.83 memory used=11783.0MB, alloc=179.8MB, time=70.95 memory used=11794.5MB, alloc=179.8MB, time=71.07 memory used=11805.8MB, alloc=179.8MB, time=71.19 memory used=11817.3MB, alloc=179.8MB, time=71.31 memory used=11828.4MB, alloc=179.8MB, time=71.42 memory used=11839.5MB, alloc=179.8MB, time=71.54 memory used=11850.6MB, alloc=179.8MB, time=71.66 memory used=11861.7MB, alloc=179.8MB, time=71.77 memory used=11873.0MB, alloc=179.8MB, time=71.88 memory used=11884.1MB, alloc=179.8MB, time=71.99 memory used=11895.2MB, alloc=179.8MB, time=72.11 memory used=11906.2MB, alloc=179.8MB, time=72.23 memory used=11917.2MB, alloc=179.8MB, time=72.33 memory used=11928.4MB, alloc=179.8MB, time=72.46 memory used=11939.4MB, alloc=179.8MB, time=72.57 memory used=11950.4MB, alloc=179.8MB, time=72.69 memory used=11961.5MB, alloc=179.8MB, time=72.81 memory used=11972.6MB, alloc=179.8MB, time=72.92 memory used=11983.6MB, alloc=179.8MB, time=73.02 memory used=11994.6MB, alloc=179.8MB, time=73.14 memory used=12005.6MB, alloc=179.8MB, time=73.25 memory used=12016.7MB, alloc=179.8MB, time=73.36 memory used=12027.6MB, alloc=179.8MB, time=73.47 memory used=12038.6MB, alloc=179.8MB, time=73.59 memory used=12049.7MB, alloc=179.8MB, time=73.70 memory used=12060.6MB, alloc=179.8MB, time=73.81 memory used=12071.7MB, alloc=179.8MB, time=73.93 memory used=12082.7MB, alloc=179.8MB, time=74.04 memory used=12093.6MB, alloc=179.8MB, time=74.16 memory used=12104.8MB, alloc=179.8MB, time=74.27 memory used=12115.6MB, alloc=179.8MB, time=74.39 memory used=12126.7MB, alloc=179.8MB, time=74.50 memory used=12137.5MB, alloc=179.8MB, time=74.61 memory used=12148.6MB, alloc=179.8MB, time=74.72 memory used=12159.5MB, alloc=179.8MB, time=74.85 memory used=12170.5MB, alloc=179.8MB, time=74.97 memory used=12181.3MB, alloc=179.8MB, time=75.08 memory used=12192.2MB, alloc=179.8MB, time=75.20 memory used=12203.1MB, alloc=179.8MB, time=75.32 memory used=12214.3MB, alloc=179.8MB, time=75.44 memory used=12225.1MB, alloc=179.8MB, time=75.55 memory used=12236.1MB, alloc=179.8MB, time=75.66 memory used=12247.0MB, alloc=179.8MB, time=75.78 memory used=12258.2MB, alloc=179.8MB, time=75.89 memory used=12269.1MB, alloc=179.8MB, time=76.02 memory used=12280.1MB, alloc=179.8MB, time=76.14 memory used=12291.0MB, alloc=179.8MB, time=76.25 memory used=12302.2MB, alloc=179.8MB, time=76.37 memory used=12313.1MB, alloc=179.8MB, time=76.49 memory used=12324.1MB, alloc=179.8MB, time=76.62 memory used=12335.0MB, alloc=179.8MB, time=76.75 memory used=12346.1MB, alloc=179.8MB, time=76.87 memory used=12356.9MB, alloc=179.8MB, time=76.99 memory used=12368.0MB, alloc=179.8MB, time=77.12 memory used=12378.7MB, alloc=179.8MB, time=77.23 memory used=12389.7MB, alloc=179.8MB, time=77.35 memory used=12400.6MB, alloc=179.8MB, time=77.47 memory used=12411.5MB, alloc=179.8MB, time=77.59 memory used=12422.5MB, alloc=179.8MB, time=77.71 memory used=12433.4MB, alloc=179.8MB, time=77.83 memory used=12444.5MB, alloc=179.8MB, time=77.94 memory used=12455.5MB, alloc=179.8MB, time=78.05 memory used=12466.6MB, alloc=179.8MB, time=78.17 memory used=12477.4MB, alloc=179.8MB, time=78.29 memory used=12488.3MB, alloc=179.8MB, time=78.41 memory used=12499.5MB, alloc=179.8MB, time=78.54 memory used=12510.4MB, alloc=179.8MB, time=78.66 memory used=12521.5MB, alloc=179.8MB, time=78.79 memory used=12532.4MB, alloc=179.8MB, time=78.91 memory used=12543.4MB, alloc=179.8MB, time=79.03 memory used=12554.4MB, alloc=179.8MB, time=79.15 memory used=12565.5MB, alloc=179.8MB, time=79.26 memory used=12576.6MB, alloc=179.8MB, time=79.39 memory used=12587.6MB, alloc=179.8MB, time=79.51 memory used=12598.7MB, alloc=179.8MB, time=79.63 memory used=12609.6MB, alloc=179.8MB, time=79.75 memory used=12620.7MB, alloc=179.8MB, time=79.87 memory used=12631.6MB, alloc=179.8MB, time=79.99 memory used=12642.6MB, alloc=179.8MB, time=80.12 memory used=12653.7MB, alloc=179.8MB, time=80.24 memory used=12664.6MB, alloc=179.8MB, time=80.35 memory used=12675.7MB, alloc=179.8MB, time=80.48 memory used=12686.6MB, alloc=179.8MB, time=80.60 memory used=12697.4MB, alloc=179.8MB, time=80.72 memory used=12708.3MB, alloc=179.8MB, time=80.84 memory used=12719.4MB, alloc=179.8MB, time=80.96 memory used=12730.3MB, alloc=179.8MB, time=81.08 memory used=12741.4MB, alloc=179.8MB, time=81.19 memory used=12752.4MB, alloc=179.8MB, time=81.30 memory used=12763.3MB, alloc=179.8MB, time=81.41 memory used=12774.2MB, alloc=179.8MB, time=81.52 memory used=12785.3MB, alloc=179.8MB, time=81.64 memory used=12796.2MB, alloc=179.8MB, time=81.75 memory used=12807.3MB, alloc=179.8MB, time=81.87 memory used=12818.3MB, alloc=179.8MB, time=81.99 memory used=12829.2MB, alloc=179.8MB, time=82.10 memory used=12840.3MB, alloc=179.8MB, time=82.21 memory used=12851.5MB, alloc=179.8MB, time=82.34 memory used=12862.4MB, alloc=179.8MB, time=82.45 memory used=12873.8MB, alloc=179.8MB, time=82.57 memory used=12884.7MB, alloc=179.8MB, time=82.69 memory used=12895.7MB, alloc=179.8MB, time=82.80 memory used=12906.8MB, alloc=179.8MB, time=82.91 memory used=12917.9MB, alloc=179.8MB, time=83.02 memory used=12928.9MB, alloc=179.8MB, time=83.13 memory used=12940.2MB, alloc=179.8MB, time=83.25 memory used=12951.2MB, alloc=179.8MB, time=83.36 memory used=12962.2MB, alloc=179.8MB, time=83.48 memory used=12973.5MB, alloc=179.8MB, time=83.59 memory used=12984.4MB, alloc=179.8MB, time=83.70 memory used=12995.6MB, alloc=179.8MB, time=83.81 memory used=13006.8MB, alloc=179.8MB, time=83.93 memory used=13018.0MB, alloc=179.8MB, time=84.04 memory used=13029.1MB, alloc=179.8MB, time=84.15 memory used=13040.3MB, alloc=179.8MB, time=84.26 memory used=13051.3MB, alloc=179.8MB, time=84.37 memory used=13062.7MB, alloc=179.8MB, time=84.48 memory used=13073.9MB, alloc=179.8MB, time=84.59 memory used=13085.1MB, alloc=179.8MB, time=84.70 memory used=13096.3MB, alloc=179.8MB, time=84.81 memory used=13107.4MB, alloc=179.8MB, time=84.91 memory used=13118.8MB, alloc=179.8MB, time=85.03 memory used=13129.9MB, alloc=179.8MB, time=85.14 memory used=13141.0MB, alloc=179.8MB, time=85.25 memory used=13152.4MB, alloc=179.8MB, time=85.35 memory used=13163.6MB, alloc=179.8MB, time=85.47 memory used=13175.0MB, alloc=179.8MB, time=85.58 memory used=13186.2MB, alloc=179.8MB, time=85.68 memory used=13197.4MB, alloc=179.8MB, time=85.79 memory used=13208.8MB, alloc=179.8MB, time=85.90 memory used=13220.0MB, alloc=179.8MB, time=86.01 memory used=13231.5MB, alloc=179.8MB, time=86.13 memory used=13242.6MB, alloc=179.8MB, time=86.23 memory used=13253.8MB, alloc=179.8MB, time=86.34 memory used=13265.2MB, alloc=179.8MB, time=86.44 memory used=13276.4MB, alloc=179.8MB, time=86.55 memory used=13288.0MB, alloc=179.8MB, time=86.66 memory used=13299.2MB, alloc=179.8MB, time=86.77 memory used=13310.7MB, alloc=179.8MB, time=86.88 memory used=13322.0MB, alloc=179.8MB, time=86.99 memory used=13333.4MB, alloc=179.8MB, time=87.09 memory used=13344.7MB, alloc=179.8MB, time=87.20 memory used=13356.1MB, alloc=179.8MB, time=87.31 memory used=13367.5MB, alloc=179.8MB, time=87.42 memory used=13378.9MB, alloc=179.8MB, time=87.54 memory used=13390.5MB, alloc=179.8MB, time=87.66 memory used=13401.9MB, alloc=179.8MB, time=87.77 memory used=13413.3MB, alloc=179.8MB, time=87.90 memory used=13424.6MB, alloc=179.8MB, time=88.03 memory used=13436.3MB, alloc=179.8MB, time=88.15 memory used=13447.7MB, alloc=179.8MB, time=88.27 memory used=13459.1MB, alloc=179.8MB, time=88.40 memory used=13470.7MB, alloc=179.8MB, time=88.51 memory used=13482.1MB, alloc=179.8MB, time=88.63 memory used=13493.6MB, alloc=179.8MB, time=88.76 memory used=13505.0MB, alloc=179.8MB, time=88.89 memory used=13516.5MB, alloc=179.8MB, time=89.01 memory used=13527.9MB, alloc=179.8MB, time=89.12 memory used=13539.7MB, alloc=179.8MB, time=89.25 memory used=13551.2MB, alloc=179.8MB, time=89.38 memory used=13562.6MB, alloc=179.8MB, time=89.50 memory used=13574.1MB, alloc=179.8MB, time=89.62 memory used=13585.8MB, alloc=179.8MB, time=89.74 memory used=13597.3MB, alloc=179.8MB, time=89.86 memory used=13608.8MB, alloc=179.8MB, time=89.98 memory used=13620.3MB, alloc=179.8MB, time=90.11 memory used=13631.8MB, alloc=179.8MB, time=90.23 memory used=13643.4MB, alloc=179.8MB, time=90.35 memory used=13655.0MB, alloc=179.8MB, time=90.47 memory used=13666.6MB, alloc=179.8MB, time=90.60 memory used=13678.1MB, alloc=179.8MB, time=90.72 memory used=13690.0MB, alloc=179.8MB, time=90.84 memory used=13701.5MB, alloc=179.8MB, time=90.96 memory used=13713.2MB, alloc=179.8MB, time=91.08 memory used=13724.7MB, alloc=179.8MB, time=91.20 memory used=13736.4MB, alloc=179.8MB, time=91.32 memory used=13747.9MB, alloc=179.8MB, time=91.43 memory used=13759.5MB, alloc=179.8MB, time=91.55 memory used=13771.1MB, alloc=179.8MB, time=91.67 memory used=13782.8MB, alloc=179.8MB, time=91.79 memory used=13794.3MB, alloc=179.8MB, time=91.90 memory used=13805.8MB, alloc=179.8MB, time=92.02 memory used=13817.6MB, alloc=179.8MB, time=92.14 memory used=13829.0MB, alloc=179.8MB, time=92.27 memory used=13840.6MB, alloc=179.8MB, time=92.38 memory used=13852.0MB, alloc=179.8MB, time=92.50 memory used=13863.6MB, alloc=179.8MB, time=92.61 memory used=13875.3MB, alloc=179.8MB, time=92.73 memory used=13886.8MB, alloc=179.8MB, time=92.84 memory used=13898.5MB, alloc=179.8MB, time=92.96 memory used=13910.0MB, alloc=179.8MB, time=93.08 memory used=13921.6MB, alloc=179.8MB, time=93.19 memory used=13933.4MB, alloc=179.8MB, time=93.31 memory used=13944.9MB, alloc=179.8MB, time=93.43 memory used=13956.6MB, alloc=179.8MB, time=93.55 memory used=13968.1MB, alloc=179.8MB, time=93.67 memory used=13979.8MB, alloc=179.8MB, time=93.79 memory used=13991.4MB, alloc=179.8MB, time=93.91 memory used=14003.1MB, alloc=179.8MB, time=94.03 memory used=14014.6MB, alloc=179.8MB, time=94.14 memory used=14026.2MB, alloc=179.8MB, time=94.26 memory used=14038.0MB, alloc=179.8MB, time=94.38 memory used=14049.7MB, alloc=179.8MB, time=94.49 memory used=14061.3MB, alloc=179.8MB, time=94.61 memory used=14073.0MB, alloc=179.8MB, time=94.72 memory used=14084.6MB, alloc=179.8MB, time=94.83 memory used=14096.1MB, alloc=179.8MB, time=94.95 memory used=14107.8MB, alloc=179.8MB, time=95.06 memory used=14119.4MB, alloc=179.8MB, time=95.18 memory used=14131.2MB, alloc=179.8MB, time=95.29 memory used=14142.7MB, alloc=179.8MB, time=95.40 memory used=14154.2MB, alloc=179.8MB, time=95.52 memory used=14166.0MB, alloc=179.8MB, time=95.63 memory used=14177.6MB, alloc=179.8MB, time=95.75 memory used=14189.6MB, alloc=179.8MB, time=95.86 memory used=14201.2MB, alloc=179.8MB, time=95.98 memory used=14212.8MB, alloc=179.8MB, time=96.09 memory used=14224.6MB, alloc=179.8MB, time=96.20 memory used=14236.3MB, alloc=179.8MB, time=96.31 memory used=14248.2MB, alloc=179.8MB, time=96.43 memory used=14259.8MB, alloc=179.8MB, time=96.54 memory used=14271.4MB, alloc=179.8MB, time=96.66 memory used=14283.2MB, alloc=179.8MB, time=96.77 memory used=14294.9MB, alloc=179.8MB, time=96.88 memory used=14306.8MB, alloc=179.8MB, time=96.99 memory used=14318.6MB, alloc=179.8MB, time=97.10 memory used=14330.3MB, alloc=179.8MB, time=97.22 memory used=14342.1MB, alloc=179.8MB, time=97.33 memory used=14353.8MB, alloc=179.8MB, time=97.44 memory used=14365.9MB, alloc=179.8MB, time=97.55 memory used=14377.6MB, alloc=179.8MB, time=97.66 memory used=14389.5MB, alloc=179.8MB, time=97.77 memory used=14401.3MB, alloc=179.8MB, time=97.87 memory used=14413.4MB, alloc=179.8MB, time=97.99 memory used=14425.3MB, alloc=179.8MB, time=98.09 memory used=14437.2MB, alloc=179.8MB, time=98.20 memory used=14449.0MB, alloc=179.8MB, time=98.31 memory used=14460.8MB, alloc=179.8MB, time=98.42 memory used=14472.7MB, alloc=179.8MB, time=98.54 memory used=14484.6MB, alloc=179.8MB, time=98.64 memory used=14496.5MB, alloc=179.8MB, time=98.75 memory used=14508.0MB, alloc=179.8MB, time=98.86 memory used=14519.5MB, alloc=179.8MB, time=98.97 memory used=14531.0MB, alloc=179.8MB, time=99.09 memory used=14542.6MB, alloc=179.8MB, time=99.21 memory used=14554.2MB, alloc=179.8MB, time=99.33 memory used=14565.7MB, alloc=179.8MB, time=99.45 memory used=14577.1MB, alloc=179.8MB, time=99.56 memory used=14588.5MB, alloc=179.8MB, time=99.68 memory used=14599.8MB, alloc=179.8MB, time=99.79 memory used=14611.2MB, alloc=179.8MB, time=99.90 memory used=14622.6MB, alloc=179.8MB, time=100.02 memory used=14634.0MB, alloc=179.8MB, time=100.13 memory used=14645.4MB, alloc=179.8MB, time=100.25 memory used=14656.9MB, alloc=179.8MB, time=100.36 memory used=14668.5MB, alloc=179.8MB, time=100.48 memory used=14680.3MB, alloc=179.8MB, time=100.59 memory used=14692.0MB, alloc=179.8MB, time=100.70 memory used=14703.7MB, alloc=179.8MB, time=100.80 memory used=14715.5MB, alloc=179.8MB, time=100.92 memory used=14727.2MB, alloc=179.8MB, time=101.06 memory used=14738.7MB, alloc=179.8MB, time=101.17 memory used=14750.2MB, alloc=179.8MB, time=101.29 memory used=14761.7MB, alloc=179.8MB, time=101.42 memory used=14773.2MB, alloc=179.8MB, time=101.54 memory used=14784.6MB, alloc=179.8MB, time=101.66 memory used=14796.1MB, alloc=179.8MB, time=101.78 memory used=14807.9MB, alloc=179.8MB, time=101.90 memory used=14819.8MB, alloc=179.8MB, time=102.02 memory used=14831.5MB, alloc=179.8MB, time=102.13 memory used=14843.1MB, alloc=179.8MB, time=102.25 memory used=14855.0MB, alloc=179.8MB, time=102.37 memory used=14866.8MB, alloc=179.8MB, time=102.50 memory used=14878.3MB, alloc=179.8MB, time=102.61 memory used=14890.0MB, alloc=179.8MB, time=102.73 memory used=14901.5MB, alloc=179.8MB, time=102.85 memory used=14913.0MB, alloc=179.8MB, time=102.97 memory used=14924.4MB, alloc=179.8MB, time=103.09 memory used=14936.0MB, alloc=179.8MB, time=103.21 memory used=14947.6MB, alloc=179.8MB, time=103.32 memory used=14959.3MB, alloc=179.8MB, time=103.43 memory used=14971.2MB, alloc=179.8MB, time=103.56 memory used=14983.0MB, alloc=179.8MB, time=103.68 memory used=14994.8MB, alloc=179.8MB, time=103.79 memory used=15006.6MB, alloc=179.8MB, time=103.91 memory used=15018.4MB, alloc=179.8MB, time=104.04 memory used=15030.2MB, alloc=179.8MB, time=104.16 memory used=15041.8MB, alloc=179.8MB, time=104.28 memory used=15053.3MB, alloc=179.8MB, time=104.39 memory used=15064.9MB, alloc=179.8MB, time=104.50 memory used=15076.5MB, alloc=179.8MB, time=104.62 memory used=15088.1MB, alloc=179.8MB, time=104.75 memory used=15099.7MB, alloc=179.8MB, time=104.86 memory used=15111.3MB, alloc=179.8MB, time=104.98 memory used=15123.1MB, alloc=179.8MB, time=105.10 memory used=15135.0MB, alloc=179.8MB, time=105.22 memory used=15146.9MB, alloc=179.8MB, time=105.34 memory used=15158.6MB, alloc=179.8MB, time=105.45 memory used=15170.4MB, alloc=179.8MB, time=105.56 memory used=15182.4MB, alloc=179.8MB, time=105.68 memory used=15194.3MB, alloc=179.8MB, time=105.80 memory used=15205.9MB, alloc=179.8MB, time=105.91 memory used=15217.5MB, alloc=179.8MB, time=106.03 memory used=15229.2MB, alloc=179.8MB, time=106.15 memory used=15240.8MB, alloc=179.8MB, time=106.26 memory used=15252.4MB, alloc=179.8MB, time=106.37 memory used=15264.1MB, alloc=179.8MB, time=106.49 memory used=15275.7MB, alloc=179.8MB, time=106.61 memory used=15287.4MB, alloc=179.8MB, time=106.72 memory used=15299.1MB, alloc=179.8MB, time=106.84 memory used=15311.0MB, alloc=179.8MB, time=106.96 memory used=15322.9MB, alloc=179.8MB, time=107.08 memory used=15334.9MB, alloc=179.8MB, time=107.20 memory used=15346.8MB, alloc=179.8MB, time=107.32 memory used=15358.8MB, alloc=179.8MB, time=107.44 memory used=15370.8MB, alloc=179.8MB, time=107.56 memory used=15382.8MB, alloc=179.8MB, time=107.69 memory used=15394.6MB, alloc=179.8MB, time=107.81 memory used=15406.4MB, alloc=179.8MB, time=107.93 memory used=15418.1MB, alloc=179.8MB, time=108.07 memory used=15429.9MB, alloc=179.8MB, time=108.19 memory used=15441.8MB, alloc=179.8MB, time=108.31 memory used=15453.9MB, alloc=179.8MB, time=108.42 memory used=15465.9MB, alloc=179.8MB, time=108.53 memory used=15477.9MB, alloc=179.8MB, time=108.65 memory used=15490.0MB, alloc=179.8MB, time=108.77 memory used=15502.0MB, alloc=179.8MB, time=108.89 memory used=15513.8MB, alloc=179.8MB, time=109.01 memory used=15525.6MB, alloc=179.8MB, time=109.12 memory used=15537.4MB, alloc=179.8MB, time=109.24 memory used=15549.2MB, alloc=179.8MB, time=109.35 memory used=15560.9MB, alloc=179.8MB, time=109.47 memory used=15572.6MB, alloc=179.8MB, time=109.58 memory used=15584.3MB, alloc=179.8MB, time=109.69 memory used=15596.0MB, alloc=179.8MB, time=109.81 memory used=15607.8MB, alloc=179.8MB, time=109.92 memory used=15619.6MB, alloc=179.8MB, time=110.04 memory used=15631.3MB, alloc=179.8MB, time=110.14 memory used=15643.2MB, alloc=179.8MB, time=110.26 memory used=15655.2MB, alloc=179.8MB, time=110.38 memory used=15667.3MB, alloc=179.8MB, time=110.49 memory used=15679.3MB, alloc=179.8MB, time=110.60 memory used=15691.3MB, alloc=179.8MB, time=110.71 memory used=15703.4MB, alloc=179.8MB, time=110.82 memory used=15715.5MB, alloc=179.8MB, time=110.93 memory used=15727.6MB, alloc=179.8MB, time=111.04 memory used=15739.5MB, alloc=179.8MB, time=111.17 memory used=15751.4MB, alloc=179.8MB, time=111.29 memory used=15763.3MB, alloc=179.8MB, time=111.40 memory used=15775.1MB, alloc=179.8MB, time=111.53 memory used=15787.0MB, alloc=179.8MB, time=111.64 memory used=15798.8MB, alloc=179.8MB, time=111.76 memory used=15810.6MB, alloc=179.8MB, time=111.88 memory used=15822.4MB, alloc=179.8MB, time=112.00 memory used=15834.3MB, alloc=179.8MB, time=112.11 memory used=15846.1MB, alloc=179.8MB, time=112.23 memory used=15858.0MB, alloc=179.8MB, time=112.35 memory used=15869.8MB, alloc=179.8MB, time=112.47 memory used=15881.7MB, alloc=179.8MB, time=112.58 memory used=15893.8MB, alloc=179.8MB, time=112.70 memory used=15906.0MB, alloc=179.8MB, time=112.82 memory used=15918.1MB, alloc=179.8MB, time=112.94 memory used=15930.2MB, alloc=179.8MB, time=113.06 memory used=15942.2MB, alloc=179.8MB, time=113.18 memory used=15954.3MB, alloc=179.8MB, time=113.30 memory used=15966.6MB, alloc=179.8MB, time=113.43 memory used=15978.8MB, alloc=179.8MB, time=113.55 memory used=15990.7MB, alloc=179.8MB, time=113.67 memory used=16002.6MB, alloc=179.8MB, time=113.80 memory used=16014.5MB, alloc=179.8MB, time=113.92 memory used=16026.5MB, alloc=179.8MB, time=114.04 memory used=16038.4MB, alloc=179.8MB, time=114.15 memory used=16050.4MB, alloc=179.8MB, time=114.27 memory used=16062.3MB, alloc=179.8MB, time=114.38 memory used=16074.3MB, alloc=179.8MB, time=114.50 memory used=16086.2MB, alloc=179.8MB, time=114.61 memory used=16098.3MB, alloc=179.8MB, time=114.73 memory used=16110.5MB, alloc=179.8MB, time=114.86 memory used=16122.8MB, alloc=179.8MB, time=114.99 memory used=16135.0MB, alloc=179.8MB, time=115.11 memory used=16147.3MB, alloc=179.8MB, time=115.23 memory used=16159.8MB, alloc=179.8MB, time=115.35 memory used=16172.1MB, alloc=179.8MB, time=115.48 memory used=16184.2MB, alloc=179.8MB, time=115.61 memory used=16196.2MB, alloc=179.8MB, time=115.73 memory used=16208.2MB, alloc=179.8MB, time=115.85 memory used=16220.3MB, alloc=179.8MB, time=115.97 memory used=16232.3MB, alloc=179.8MB, time=116.09 memory used=16244.3MB, alloc=179.8MB, time=116.21 memory used=16256.5MB, alloc=179.8MB, time=116.33 memory used=16268.7MB, alloc=179.8MB, time=116.45 memory used=16281.1MB, alloc=179.8MB, time=116.57 memory used=16293.4MB, alloc=179.8MB, time=116.69 memory used=16305.7MB, alloc=179.8MB, time=116.82 memory used=16318.2MB, alloc=179.8MB, time=116.93 memory used=16330.6MB, alloc=179.8MB, time=117.05 memory used=16342.7MB, alloc=179.8MB, time=117.17 memory used=16354.8MB, alloc=179.8MB, time=117.28 memory used=16367.0MB, alloc=179.8MB, time=117.40 memory used=16379.1MB, alloc=179.8MB, time=117.52 memory used=16391.2MB, alloc=179.8MB, time=117.63 memory used=16403.4MB, alloc=179.8MB, time=117.75 memory used=16415.7MB, alloc=179.8MB, time=117.87 memory used=16428.0MB, alloc=179.8MB, time=118.00 memory used=16440.4MB, alloc=179.8MB, time=118.12 memory used=16452.7MB, alloc=179.8MB, time=118.24 memory used=16465.1MB, alloc=179.8MB, time=118.35 memory used=16477.5MB, alloc=179.8MB, time=118.47 memory used=16489.6MB, alloc=179.8MB, time=118.59 memory used=16501.7MB, alloc=179.8MB, time=118.70 memory used=16513.9MB, alloc=179.8MB, time=118.81 memory used=16525.9MB, alloc=179.8MB, time=118.93 memory used=16538.0MB, alloc=179.8MB, time=119.05 memory used=16550.1MB, alloc=179.8MB, time=119.17 memory used=16562.2MB, alloc=179.8MB, time=119.29 memory used=16574.3MB, alloc=179.8MB, time=119.41 memory used=16586.5MB, alloc=179.8MB, time=119.53 memory used=16598.6MB, alloc=179.8MB, time=119.64 memory used=16610.8MB, alloc=179.8MB, time=119.77 memory used=16622.9MB, alloc=179.8MB, time=119.88 memory used=16635.0MB, alloc=179.8MB, time=120.00 memory used=16647.1MB, alloc=179.8MB, time=120.12 memory used=16659.2MB, alloc=179.8MB, time=120.24 memory used=16671.3MB, alloc=179.8MB, time=120.36 memory used=16683.5MB, alloc=179.8MB, time=120.48 memory used=16695.6MB, alloc=179.8MB, time=120.60 memory used=16707.6MB, alloc=179.8MB, time=120.72 memory used=16719.8MB, alloc=179.8MB, time=120.84 memory used=16732.1MB, alloc=179.8MB, time=120.95 memory used=16744.2MB, alloc=179.8MB, time=121.07 memory used=16756.4MB, alloc=179.8MB, time=121.19 memory used=16768.5MB, alloc=179.8MB, time=121.30 memory used=16780.7MB, alloc=179.8MB, time=121.41 memory used=16792.8MB, alloc=179.8MB, time=121.53 memory used=16805.1MB, alloc=179.8MB, time=121.64 memory used=16817.1MB, alloc=179.8MB, time=121.76 memory used=16829.3MB, alloc=179.8MB, time=121.87 memory used=16841.5MB, alloc=179.8MB, time=121.99 memory used=16853.8MB, alloc=179.8MB, time=122.10 memory used=16865.9MB, alloc=179.8MB, time=122.21 memory used=16878.1MB, alloc=179.8MB, time=122.32 memory used=16890.3MB, alloc=179.8MB, time=122.43 memory used=16902.4MB, alloc=179.8MB, time=122.54 memory used=16914.6MB, alloc=179.8MB, time=122.66 memory used=16926.9MB, alloc=179.8MB, time=122.77 memory used=16939.1MB, alloc=179.8MB, time=122.88 memory used=16951.3MB, alloc=179.8MB, time=123.00 memory used=16963.5MB, alloc=179.8MB, time=123.12 memory used=16975.8MB, alloc=179.8MB, time=123.22 memory used=16988.0MB, alloc=179.8MB, time=123.33 memory used=17000.3MB, alloc=179.8MB, time=123.46 memory used=17012.5MB, alloc=179.8MB, time=123.59 memory used=17024.8MB, alloc=179.8MB, time=123.71 memory used=17037.0MB, alloc=179.8MB, time=123.83 memory used=17049.3MB, alloc=179.8MB, time=123.95 memory used=17061.5MB, alloc=179.8MB, time=124.07 memory used=17073.8MB, alloc=179.8MB, time=124.20 memory used=17086.1MB, alloc=179.8MB, time=124.32 memory used=17098.5MB, alloc=179.8MB, time=124.44 memory used=17110.6MB, alloc=179.8MB, time=124.56 memory used=17122.9MB, alloc=179.8MB, time=124.68 memory used=17135.3MB, alloc=179.8MB, time=124.80 memory used=17147.5MB, alloc=179.8MB, time=124.91 memory used=17159.8MB, alloc=179.8MB, time=125.03 memory used=17172.3MB, alloc=179.8MB, time=125.16 memory used=17184.5MB, alloc=179.8MB, time=125.28 memory used=17196.8MB, alloc=179.8MB, time=125.40 memory used=17209.0MB, alloc=179.8MB, time=125.52 memory used=17221.4MB, alloc=179.8MB, time=125.64 memory used=17233.9MB, alloc=179.8MB, time=125.76 memory used=17246.1MB, alloc=179.8MB, time=125.88 memory used=17258.5MB, alloc=179.8MB, time=126.01 memory used=17270.8MB, alloc=179.8MB, time=126.13 memory used=17283.3MB, alloc=179.8MB, time=126.25 memory used=17295.6MB, alloc=179.8MB, time=126.38 memory used=17307.8MB, alloc=179.8MB, time=126.50 memory used=17320.2MB, alloc=179.8MB, time=126.63 memory used=17332.6MB, alloc=179.8MB, time=126.75 memory used=17345.1MB, alloc=179.8MB, time=126.86 memory used=17357.3MB, alloc=179.8MB, time=126.98 memory used=17369.8MB, alloc=179.8MB, time=127.09 memory used=17382.1MB, alloc=179.8MB, time=127.21 memory used=17394.5MB, alloc=179.8MB, time=127.34 memory used=17407.0MB, alloc=179.8MB, time=127.46 memory used=17419.4MB, alloc=179.8MB, time=127.57 memory used=17431.8MB, alloc=179.8MB, time=127.72 memory used=17444.1MB, alloc=179.8MB, time=127.84 memory used=17456.5MB, alloc=179.8MB, time=127.96 memory used=17469.0MB, alloc=179.8MB, time=128.09 memory used=17481.4MB, alloc=179.8MB, time=128.21 memory used=17493.8MB, alloc=179.8MB, time=128.32 memory used=17506.4MB, alloc=179.8MB, time=128.44 memory used=17518.6MB, alloc=179.8MB, time=128.56 memory used=17531.3MB, alloc=179.8MB, time=128.67 memory used=17543.8MB, alloc=179.8MB, time=128.79 memory used=17556.2MB, alloc=179.8MB, time=128.92 memory used=17568.6MB, alloc=179.8MB, time=129.03 memory used=17581.0MB, alloc=179.8MB, time=129.15 memory used=17593.6MB, alloc=179.8MB, time=129.27 memory used=17606.1MB, alloc=179.8MB, time=129.39 memory used=17618.5MB, alloc=179.8MB, time=129.51 memory used=17631.0MB, alloc=179.8MB, time=129.64 memory used=17643.5MB, alloc=179.8MB, time=129.77 memory used=17655.9MB, alloc=179.8MB, time=129.89 memory used=17668.5MB, alloc=179.8MB, 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time=349.34 memory used=41046.2MB, alloc=179.8MB, time=349.44 memory used=41053.2MB, alloc=179.8MB, time=349.55 memory used=41059.6MB, alloc=179.8MB, time=349.65 memory used=41066.7MB, alloc=179.8MB, time=349.75 memory used=41072.9MB, alloc=179.8MB, time=349.87 memory used=41079.3MB, alloc=179.8MB, time=349.98 memory used=41086.5MB, alloc=179.8MB, time=350.09 memory used=41092.1MB, alloc=179.8MB, time=350.19 memory used=41098.5MB, alloc=179.8MB, time=350.30 memory used=41105.6MB, alloc=179.8MB, time=350.41 memory used=41111.1MB, alloc=179.8MB, time=350.51 memory used=41117.4MB, alloc=179.8MB, time=350.62 memory used=41124.5MB, alloc=179.8MB, time=350.72 memory used=41130.5MB, alloc=179.8MB, time=350.83 memory used=41136.7MB, alloc=179.8MB, time=350.93 memory used=41143.7MB, alloc=179.8MB, time=351.03 memory used=41149.5MB, alloc=179.8MB, time=351.13 memory used=41155.9MB, alloc=179.8MB, time=351.24 memory used=41162.9MB, alloc=179.8MB, time=351.33 memory used=41168.8MB, alloc=179.8MB, time=351.44 memory used=41175.1MB, alloc=179.8MB, time=351.54 memory used=41182.1MB, alloc=179.8MB, time=351.64 memory used=41188.1MB, alloc=179.8MB, time=351.75 memory used=41194.4MB, alloc=179.8MB, time=351.85 memory used=41201.4MB, alloc=179.8MB, time=351.95 memory used=41207.6MB, alloc=179.8MB, time=352.06 memory used=41213.8MB, alloc=179.8MB, time=352.16 memory used=41220.7MB, alloc=179.8MB, time=352.26 memory used=41226.8MB, alloc=179.8MB, time=352.37 memory used=41233.1MB, alloc=179.8MB, time=352.47 memory used=41240.0MB, alloc=179.8MB, time=352.57 memory used=41246.1MB, alloc=179.8MB, time=352.67 memory used=41252.3MB, alloc=179.8MB, time=352.79 memory used=41259.2MB, alloc=179.8MB, time=352.89 memory used=41265.4MB, alloc=179.8MB, time=353.00 memory used=41271.5MB, alloc=179.8MB, time=353.09 memory used=41278.4MB, alloc=179.8MB, time=353.19 memory used=41284.7MB, alloc=179.8MB, time=353.29 memory used=41290.7MB, alloc=179.8MB, time=353.39 memory used=41297.7MB, alloc=179.8MB, time=353.49 memory used=41303.8MB, alloc=179.8MB, time=353.60 memory used=41309.8MB, alloc=179.8MB, time=353.70 memory used=41316.5MB, alloc=179.8MB, time=353.80 memory used=41323.0MB, alloc=179.8MB, time=353.90 memory used=41328.3MB, alloc=179.8MB, time=354.00 memory used=41334.3MB, alloc=179.8MB, time=354.11 memory used=41341.0MB, alloc=179.8MB, time=354.20 memory used=41347.1MB, alloc=179.8MB, time=354.30 memory used=41352.4MB, alloc=179.8MB, time=354.40 memory used=41358.4MB, alloc=179.8MB, time=354.51 memory used=41365.1MB, alloc=179.8MB, time=354.60 memory used=41371.3MB, alloc=179.8MB, time=354.70 memory used=41377.2MB, alloc=179.8MB, time=354.80 memory used=41383.8MB, alloc=179.8MB, time=354.90 memory used=41390.2MB, alloc=179.8MB, time=355.01 memory used=41395.4MB, alloc=179.8MB, time=355.10 memory used=41401.0MB, alloc=179.8MB, time=355.19 memory used=41407.0MB, alloc=179.8MB, time=355.30 memory used=41413.7MB, alloc=179.8MB, time=355.39 memory used=41419.6MB, alloc=179.8MB, time=355.49 memory used=41425.5MB, alloc=179.8MB, time=355.59 memory used=41432.0MB, alloc=179.8MB, time=355.69 memory used=41438.5MB, alloc=179.8MB, time=355.80 memory used=41443.5MB, alloc=179.8MB, time=355.89 memory used=41449.0MB, alloc=179.8MB, time=355.98 memory used=41455.0MB, alloc=179.8MB, time=356.08 memory used=41461.6MB, alloc=179.8MB, time=356.18 memory used=41467.8MB, alloc=179.8MB, time=356.28 memory used=41473.5MB, alloc=179.8MB, time=356.38 memory used=41479.6MB, alloc=179.8MB, time=356.48 memory used=41486.1MB, alloc=179.8MB, time=356.57 memory used=41491.9MB, alloc=179.8MB, time=356.68 memory used=41497.2MB, alloc=179.8MB, time=356.77 memory used=41503.1MB, alloc=179.8MB, time=356.87 memory used=41509.8MB, alloc=179.8MB, time=356.96 memory used=41516.1MB, alloc=179.8MB, time=357.07 memory used=41521.2MB, alloc=179.8MB, time=357.16 memory used=41526.6MB, alloc=179.8MB, time=357.25 memory used=41532.6MB, alloc=179.8MB, time=357.37 memory used=41539.3MB, alloc=179.8MB, time=357.47 memory used=41545.1MB, alloc=179.8MB, time=357.57 memory used=41550.4MB, alloc=179.8MB, time=357.66 memory used=41555.9MB, alloc=179.8MB, time=357.76 memory used=41562.0MB, alloc=179.8MB, time=357.85 memory used=41568.5MB, alloc=179.8MB, time=357.94 memory used=41574.3MB, alloc=179.8MB, time=358.05 memory used=41579.7MB, alloc=179.8MB, time=358.14 memory used=41585.6MB, alloc=179.8MB, time=358.24 memory used=41592.3MB, alloc=179.8MB, time=358.34 memory used=41598.4MB, alloc=179.8MB, time=358.45 memory used=41603.5MB, alloc=179.8MB, time=358.55 memory used=41609.0MB, alloc=179.8MB, time=358.66 memory used=41614.9MB, alloc=179.8MB, time=358.76 memory used=41621.5MB, alloc=179.8MB, time=358.87 memory used=41627.3MB, alloc=179.8MB, time=358.98 memory used=41632.4MB, alloc=179.8MB, time=359.08 memory used=41637.7MB, alloc=179.8MB, time=359.18 memory used=41643.6MB, alloc=179.8MB, time=359.28 memory used=41650.2MB, alloc=179.8MB, time=359.38 memory used=41656.5MB, alloc=179.8MB, time=359.48 memory used=41661.5MB, alloc=179.8MB, time=359.59 memory used=41666.8MB, alloc=179.8MB, time=359.68 memory used=41672.7MB, alloc=179.8MB, time=359.78 memory used=41679.3MB, alloc=179.8MB, time=359.88 memory used=41685.6MB, alloc=179.8MB, time=359.99 memory used=41690.7MB, alloc=179.8MB, time=360.09 memory used=41696.1MB, alloc=179.8MB, time=360.20 memory used=41702.0MB, alloc=179.8MB, time=360.30 memory used=41708.5MB, alloc=179.8MB, time=360.41 memory used=41714.6MB, alloc=179.8MB, time=360.52 memory used=41719.9MB, alloc=179.8MB, time=360.62 memory used=41725.3MB, alloc=179.8MB, time=360.72 memory used=41731.1MB, alloc=179.8MB, time=360.82 memory used=41737.7MB, alloc=179.8MB, time=360.94 memory used=41743.6MB, alloc=179.8MB, time=361.04 memory used=41748.9MB, alloc=179.8MB, time=361.14 memory used=41754.6MB, alloc=179.8MB, time=361.24 memory used=41760.6MB, alloc=179.8MB, time=361.34 memory used=41767.0MB, alloc=179.8MB, time=361.45 memory used=41772.7MB, alloc=179.8MB, time=361.56 memory used=41777.9MB, alloc=179.8MB, time=361.67 memory used=41783.2MB, alloc=179.8MB, time=361.76 memory used=41788.8MB, alloc=179.8MB, time=361.87 memory used=41795.3MB, alloc=179.8MB, time=361.97 memory used=41801.7MB, alloc=179.8MB, time=362.08 memory used=41806.7MB, alloc=179.8MB, time=362.19 memory used=41812.0MB, alloc=179.8MB, time=362.29 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428509405 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 F := [3 x z + 2 x z, -19 z + 5 y - 9 x] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 2 3 2 G := [-10 x z - 20 y z + 8 y z , 12 x z - 20 x z + 7 x z ] > Problem := [F,G]; 3 3 2 Problem := [[3 x z + 2 x z, -19 z + 5 y - 9 x], 3 3 2 2 2 3 2 [-10 x z - 20 y z + 8 y z , 12 x z - 20 x z + 7 x z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.4MB, alloc=32.3MB, time=0.48 memory used=46.4MB, alloc=56.3MB, time=0.76 memory used=90.0MB, alloc=60.3MB, time=1.32 memory used=139.6MB, alloc=68.3MB, time=1.91 memory used=194.4MB, alloc=68.3MB, time=2.48 memory used=219.7MB, alloc=68.3MB, time=2.59 memory used=239.6MB, alloc=68.3MB, time=2.67 memory used=260.7MB, alloc=68.3MB, time=2.74 memory used=280.2MB, alloc=68.3MB, time=2.81 memory used=296.2MB, alloc=68.3MB, time=2.87 memory used=314.3MB, alloc=68.3MB, time=2.93 memory used=336.0MB, alloc=68.3MB, time=2.99 memory used=365.7MB, alloc=68.3MB, time=3.12 memory used=386.4MB, alloc=68.3MB, time=3.19 memory used=408.0MB, alloc=68.3MB, time=3.27 memory used=428.6MB, alloc=68.3MB, time=3.33 memory used=444.7MB, alloc=68.3MB, time=3.40 memory used=463.1MB, alloc=68.3MB, time=3.45 memory used=484.4MB, alloc=68.3MB, time=3.52 memory used=514.0MB, alloc=68.3MB, time=3.67 memory used=544.1MB, alloc=68.3MB, time=3.95 memory used=563.7MB, alloc=68.3MB, time=4.03 memory used=582.9MB, alloc=68.3MB, time=4.10 memory used=605.8MB, alloc=68.3MB, time=4.18 memory used=628.7MB, alloc=92.3MB, time=4.28 memory used=657.1MB, alloc=92.3MB, time=4.36 memory used=689.3MB, alloc=92.3MB, time=4.45 memory used=725.7MB, alloc=92.3MB, time=4.54 memory used=767.2MB, alloc=92.3MB, time=4.64 memory used=814.3MB, alloc=92.3MB, time=4.74 memory used=833.0MB, alloc=107.8MB, time=4.82 memory used=843.4MB, alloc=107.8MB, time=4.88 memory used=854.4MB, alloc=107.8MB, time=4.94 memory used=865.5MB, alloc=107.8MB, time=4.99 memory used=876.9MB, alloc=107.8MB, time=5.05 memory used=889.1MB, alloc=107.8MB, time=5.11 memory used=901.7MB, alloc=107.8MB, time=5.16 memory used=914.7MB, alloc=107.8MB, time=5.22 memory used=927.9MB, alloc=107.8MB, time=5.28 memory used=941.8MB, alloc=107.8MB, time=5.34 memory used=957.2MB, alloc=107.8MB, time=5.39 memory used=1012.4MB, alloc=107.8MB, time=5.85 memory used=1049.3MB, alloc=107.8MB, time=5.96 memory used=1088.9MB, alloc=107.8MB, time=6.06 memory used=1117.5MB, alloc=107.8MB, time=6.15 memory used=1150.5MB, alloc=107.8MB, time=6.24 memory used=1188.6MB, alloc=107.8MB, time=6.33 memory used=1231.4MB, alloc=107.8MB, time=6.43 memory used=1287.6MB, alloc=107.8MB, time=6.54 memory used=1298.1MB, alloc=107.8MB, time=6.59 memory used=1309.3MB, alloc=107.8MB, time=6.65 memory used=1320.3MB, alloc=107.8MB, time=6.70 memory used=1332.0MB, alloc=107.8MB, time=6.75 memory used=1344.3MB, alloc=107.8MB, time=6.81 memory used=1357.0MB, alloc=107.8MB, time=6.86 memory used=1370.1MB, alloc=107.8MB, time=6.92 memory used=1384.1MB, alloc=107.8MB, time=6.97 memory used=1398.6MB, alloc=107.8MB, time=7.03 memory used=1413.9MB, alloc=107.8MB, time=7.09 memory used=1493.3MB, alloc=107.8MB, time=7.64 memory used=1553.5MB, alloc=107.8MB, time=7.89 memory used=1611.7MB, alloc=107.8MB, time=8.10 memory used=1669.8MB, alloc=107.8MB, time=8.31 memory used=1722.2MB, alloc=107.8MB, time=8.46 memory used=1779.2MB, alloc=107.8MB, time=8.65 memory used=1833.8MB, alloc=107.8MB, time=8.84 memory used=1890.4MB, alloc=107.8MB, time=9.03 memory used=1947.4MB, alloc=107.8MB, time=9.21 memory used=2005.8MB, alloc=107.8MB, time=9.39 memory used=2065.8MB, alloc=107.8MB, time=9.58 memory used=2131.2MB, alloc=107.8MB, time=9.77 memory used=2194.6MB, alloc=107.8MB, time=9.93 memory used=2257.1MB, alloc=107.8MB, time=10.11 memory used=2325.1MB, alloc=107.8MB, time=10.27 memory used=2393.7MB, alloc=107.8MB, time=10.47 memory used=2461.1MB, alloc=107.8MB, time=10.64 memory used=2533.7MB, alloc=107.8MB, time=10.81 memory used=2594.4MB, alloc=107.8MB, time=10.96 memory used=2667.2MB, alloc=107.8MB, time=11.14 memory used=2732.1MB, alloc=107.8MB, time=11.30 memory used=2783.9MB, alloc=107.8MB, time=11.42 memory used=2854.4MB, alloc=107.8MB, time=11.58 memory used=2918.9MB, alloc=107.8MB, time=11.73 memory used=2971.7MB, alloc=107.8MB, time=11.86 memory used=3030.0MB, alloc=107.8MB, time=11.97 memory used=3098.5MB, alloc=107.8MB, time=12.13 memory used=3156.9MB, alloc=107.8MB, time=12.27 memory used=3208.5MB, alloc=107.8MB, time=12.39 memory used=3261.8MB, alloc=107.8MB, time=12.50 memory used=3347.5MB, alloc=107.8MB, time=13.39 memory used=3413.4MB, alloc=107.8MB, time=13.71 memory used=3469.9MB, alloc=107.8MB, time=13.92 memory used=3531.6MB, alloc=107.8MB, time=14.15 memory used=3610.4MB, alloc=107.8MB, time=14.79 memory used=3667.5MB, alloc=107.8MB, time=14.99 memory used=3724.8MB, alloc=107.8MB, time=15.17 memory used=3787.2MB, alloc=107.8MB, time=15.34 memory used=3854.3MB, alloc=107.8MB, time=15.52 memory used=3928.8MB, alloc=107.8MB, time=15.69 memory used=4007.7MB, alloc=107.8MB, time=15.88 memory used=4081.2MB, alloc=107.8MB, time=16.06 memory used=4155.6MB, alloc=107.8MB, time=16.23 memory used=4218.6MB, alloc=107.8MB, time=16.38 memory used=4271.8MB, alloc=107.8MB, time=16.50 memory used=4319.7MB, alloc=107.8MB, time=16.63 memory used=4364.0MB, alloc=107.8MB, time=16.76 memory used=4408.0MB, alloc=107.8MB, time=16.89 memory used=4448.1MB, alloc=107.8MB, time=17.00 memory used=4487.8MB, alloc=107.8MB, time=17.10 memory used=4527.2MB, alloc=107.8MB, time=17.21 memory used=4567.0MB, alloc=107.8MB, time=17.32 memory used=4602.9MB, alloc=107.8MB, time=17.43 memory used=4639.0MB, alloc=107.8MB, time=17.53 memory used=4675.1MB, alloc=107.8MB, time=17.64 memory used=4711.4MB, alloc=107.8MB, time=17.74 memory used=4747.4MB, alloc=107.8MB, time=17.85 memory used=4783.5MB, alloc=107.8MB, time=17.97 memory used=4819.5MB, alloc=107.8MB, time=18.07 memory used=4855.6MB, alloc=107.8MB, time=18.18 memory used=4891.5MB, alloc=107.8MB, time=18.29 memory used=4925.7MB, alloc=107.8MB, time=18.40 memory used=4957.7MB, alloc=107.8MB, time=18.50 memory used=4993.4MB, alloc=107.8MB, time=18.61 memory used=5027.4MB, alloc=107.8MB, time=18.72 memory used=5060.3MB, alloc=107.8MB, time=18.82 memory used=5097.0MB, alloc=107.8MB, time=18.93 memory used=5128.6MB, alloc=107.8MB, time=19.02 memory used=5163.1MB, alloc=107.8MB, time=19.13 memory used=5196.6MB, alloc=107.8MB, time=19.23 memory used=5228.4MB, alloc=107.8MB, time=19.33 memory used=5264.0MB, alloc=107.8MB, time=19.44 memory used=5294.7MB, alloc=107.8MB, time=19.56 memory used=5328.9MB, alloc=107.8MB, time=19.66 memory used=5358.5MB, alloc=107.8MB, time=19.75 memory used=5393.2MB, alloc=107.8MB, time=19.85 memory used=5426.5MB, alloc=107.8MB, time=19.96 memory used=5458.3MB, alloc=107.8MB, time=20.07 memory used=5489.5MB, alloc=107.8MB, time=20.19 memory used=5522.8MB, alloc=107.8MB, time=20.30 memory used=5557.5MB, alloc=107.8MB, time=20.41 memory used=5586.9MB, alloc=107.8MB, time=20.50 memory used=5622.2MB, alloc=107.8MB, time=20.60 memory used=5651.3MB, alloc=107.8MB, time=20.70 memory used=5684.8MB, alloc=107.8MB, time=20.82 memory used=5715.9MB, alloc=107.8MB, time=20.92 memory used=5750.6MB, alloc=107.8MB, time=21.02 memory used=5780.1MB, alloc=107.8MB, time=21.12 memory used=5815.3MB, alloc=107.8MB, time=21.23 memory used=5844.8MB, alloc=107.8MB, time=21.32 memory used=5876.4MB, alloc=107.8MB, time=21.45 memory used=5909.9MB, alloc=107.8MB, time=21.56 memory used=5939.4MB, alloc=107.8MB, time=21.66 memory used=5974.7MB, alloc=107.8MB, time=21.76 memory used=6003.8MB, alloc=107.8MB, time=21.86 memory used=6034.3MB, alloc=107.8MB, time=21.96 memory used=6065.7MB, alloc=107.8MB, time=22.08 memory used=6099.4MB, alloc=107.8MB, time=22.18 memory used=6129.1MB, alloc=107.8MB, time=22.28 memory used=6162.7MB, alloc=107.8MB, time=22.39 memory used=6192.5MB, alloc=107.8MB, time=22.49 memory used=6227.5MB, alloc=107.8MB, time=22.60 memory used=6256.6MB, alloc=107.8MB, time=22.70 memory used=6285.6MB, alloc=107.8MB, time=22.83 memory used=6319.0MB, alloc=107.8MB, time=22.94 memory used=6349.5MB, alloc=107.8MB, time=23.04 memory used=6379.2MB, alloc=107.8MB, time=23.14 memory used=6413.0MB, alloc=107.8MB, time=23.23 memory used=6442.5MB, alloc=107.8MB, time=23.33 memory used=6475.4MB, alloc=107.8MB, time=23.43 memory used=6504.1MB, alloc=107.8MB, time=23.55 memory used=6533.9MB, alloc=107.8MB, time=23.68 memory used=6565.0MB, alloc=107.8MB, time=23.78 memory used=6597.3MB, alloc=107.8MB, time=23.88 memory used=6626.2MB, alloc=107.8MB, time=23.97 memory used=6660.5MB, alloc=107.8MB, time=24.08 memory used=6688.8MB, alloc=107.8MB, time=24.17 memory used=6718.5MB, alloc=107.8MB, time=24.26 memory used=6748.7MB, alloc=107.8MB, time=24.36 memory used=6779.1MB, alloc=107.8MB, time=24.51 memory used=6809.3MB, alloc=107.8MB, time=24.64 memory used=6843.3MB, alloc=107.8MB, time=24.73 memory used=6871.5MB, alloc=107.8MB, time=24.83 memory used=6900.6MB, alloc=107.8MB, time=24.92 memory used=6934.1MB, alloc=107.8MB, time=25.00 memory used=6962.5MB, alloc=107.8MB, time=25.09 memory used=6992.0MB, alloc=107.8MB, time=25.18 memory used=7021.9MB, alloc=107.8MB, time=25.28 memory used=7052.2MB, alloc=107.8MB, time=25.44 memory used=7082.6MB, alloc=107.8MB, time=25.57 memory used=7116.4MB, alloc=107.8MB, time=25.70 memory used=7143.7MB, alloc=107.8MB, time=25.79 memory used=7172.6MB, alloc=107.8MB, time=25.89 memory used=7205.5MB, alloc=107.8MB, time=26.01 memory used=7234.1MB, alloc=107.8MB, time=26.11 memory used=7263.1MB, alloc=107.8MB, time=26.20 memory used=7295.0MB, alloc=107.8MB, time=26.31 memory used=7323.2MB, alloc=107.8MB, time=26.43 memory used=7353.0MB, alloc=107.8MB, time=26.57 memory used=7383.1MB, alloc=107.8MB, time=26.70 memory used=7413.5MB, alloc=107.8MB, time=26.84 memory used=7443.8MB, alloc=107.8MB, time=26.97 memory used=7476.5MB, alloc=107.8MB, time=27.07 memory used=7504.3MB, alloc=107.8MB, time=27.16 memory used=7533.0MB, alloc=107.8MB, time=27.25 memory used=7566.4MB, alloc=107.8MB, time=27.34 memory used=7594.3MB, alloc=107.8MB, time=27.44 memory used=7623.2MB, alloc=107.8MB, time=27.54 memory used=7652.2MB, alloc=107.8MB, time=27.63 memory used=7682.4MB, alloc=107.8MB, time=27.78 memory used=7712.4MB, alloc=107.8MB, time=27.91 memory used=7742.6MB, alloc=107.8MB, time=28.05 memory used=7773.0MB, alloc=107.8MB, time=28.19 memory used=7803.4MB, alloc=107.8MB, time=28.32 memory used=7835.8MB, alloc=107.8MB, time=28.44 memory used=7863.2MB, alloc=107.8MB, time=28.53 memory used=7891.8MB, alloc=107.8MB, time=28.63 memory used=7924.0MB, alloc=107.8MB, time=28.74 memory used=7952.0MB, alloc=107.8MB, time=28.83 memory used=7980.3MB, alloc=107.8MB, time=28.93 memory used=8009.4MB, alloc=107.8MB, time=29.02 memory used=8038.7MB, alloc=107.8MB, time=29.12 memory used=8069.0MB, alloc=107.8MB, time=29.28 memory used=8099.5MB, alloc=107.8MB, time=29.42 memory used=8129.6MB, alloc=107.8MB, time=29.56 memory used=8160.1MB, alloc=107.8MB, time=29.70 memory used=8190.7MB, alloc=107.8MB, time=29.84 memory used=8221.4MB, alloc=107.8MB, time=29.99 memory used=8254.9MB, alloc=107.8MB, time=30.13 memory used=8282.2MB, alloc=107.8MB, time=30.22 memory used=8309.9MB, alloc=107.8MB, time=30.31 memory 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memory used=8959.4MB, alloc=107.8MB, time=32.81 memory used=8989.8MB, alloc=107.8MB, time=32.95 memory used=9020.4MB, alloc=107.8MB, time=33.09 memory used=9050.9MB, alloc=107.8MB, time=33.23 memory used=9081.1MB, alloc=107.8MB, time=33.36 memory used=9111.8MB, alloc=107.8MB, time=33.50 memory used=9142.5MB, alloc=107.8MB, time=33.65 memory used=9173.5MB, alloc=107.8MB, time=33.79 memory used=9204.7MB, alloc=107.8MB, time=33.92 memory used=9234.8MB, alloc=107.8MB, time=34.04 memory used=9266.5MB, alloc=107.8MB, time=34.13 memory used=9296.7MB, alloc=107.8MB, time=34.23 memory used=9324.7MB, alloc=107.8MB, time=34.32 memory used=9353.4MB, alloc=107.8MB, time=34.42 memory used=9382.7MB, alloc=107.8MB, time=34.52 memory used=9414.5MB, alloc=107.8MB, time=34.64 memory used=9445.4MB, alloc=107.8MB, time=34.74 memory used=9471.3MB, alloc=107.8MB, time=34.83 memory used=9545.3MB, alloc=107.8MB, time=35.16 memory used=9601.5MB, alloc=107.8MB, time=35.35 memory used=9663.1MB, alloc=107.8MB, 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alloc=107.8MB, time=40.20 memory used=11254.5MB, alloc=107.8MB, time=40.30 memory used=11282.0MB, alloc=107.8MB, time=40.39 memory used=11314.1MB, alloc=107.8MB, time=40.50 memory used=11340.8MB, alloc=107.8MB, time=40.59 memory used=11368.8MB, alloc=107.8MB, time=40.71 memory used=11399.8MB, alloc=107.8MB, time=40.81 memory used=11425.7MB, alloc=107.8MB, time=40.90 memory used=11455.4MB, alloc=107.8MB, time=41.00 memory used=11484.4MB, alloc=107.8MB, time=41.10 memory used=11511.2MB, alloc=107.8MB, time=41.19 memory used=11538.3MB, alloc=107.8MB, time=41.28 memory used=11570.1MB, alloc=107.8MB, time=41.42 memory used=11596.7MB, alloc=107.8MB, time=41.52 memory used=11623.5MB, alloc=107.8MB, time=41.61 memory used=11655.4MB, alloc=107.8MB, time=41.72 memory used=11681.9MB, alloc=107.8MB, time=41.81 memory used=11709.5MB, alloc=107.8MB, time=41.91 memory used=11737.2MB, alloc=107.8MB, time=42.01 memory used=11765.5MB, alloc=107.8MB, time=42.12 memory used=11796.2MB, alloc=107.8MB, time=42.22 memory used=11822.8MB, alloc=107.8MB, time=42.31 memory used=11853.0MB, alloc=107.8MB, time=42.42 memory used=11881.7MB, alloc=107.8MB, time=42.51 memory used=11908.6MB, alloc=107.8MB, time=42.60 memory used=11935.8MB, alloc=107.8MB, time=42.70 memory used=11961.6MB, alloc=107.8MB, time=42.82 memory used=11992.0MB, alloc=107.8MB, time=42.91 memory used=12019.3MB, alloc=107.8MB, time=43.00 memory used=12045.9MB, alloc=107.8MB, time=43.09 memory used=12076.1MB, alloc=107.8MB, time=43.20 memory used=12104.3MB, alloc=107.8MB, time=43.29 memory used=12131.0MB, alloc=107.8MB, time=43.38 memory used=12158.0MB, alloc=107.8MB, time=43.47 memory used=12184.3MB, alloc=107.8MB, time=43.60 memory used=12210.3MB, alloc=107.8MB, time=43.69 memory used=12240.9MB, alloc=107.8MB, time=43.79 memory used=12266.9MB, alloc=107.8MB, time=43.88 memory used=12293.5MB, alloc=107.8MB, time=43.96 memory used=12325.3MB, alloc=107.8MB, time=44.07 memory used=12351.1MB, alloc=107.8MB, time=44.16 memory 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alloc=107.8MB, time=46.30 memory used=12942.9MB, alloc=107.8MB, time=46.39 memory used=12970.0MB, alloc=107.8MB, time=46.48 memory used=12997.0MB, alloc=107.8MB, time=46.62 memory used=13024.0MB, alloc=107.8MB, time=46.74 memory used=13051.1MB, alloc=107.8MB, time=46.85 memory used=13080.7MB, alloc=107.8MB, time=46.95 memory used=13106.6MB, alloc=107.8MB, time=47.04 memory used=13131.9MB, alloc=107.8MB, time=47.13 memory used=13157.9MB, alloc=107.8MB, time=47.22 memory used=13184.5MB, alloc=107.8MB, time=47.31 memory used=13213.9MB, alloc=107.8MB, time=47.41 memory used=13241.8MB, alloc=107.8MB, time=47.50 memory used=13267.5MB, alloc=107.8MB, time=47.59 memory used=13291.3MB, alloc=107.8MB, time=47.71 memory used=13318.0MB, alloc=107.8MB, time=47.83 memory used=13345.1MB, alloc=107.8MB, time=47.96 memory used=13372.3MB, alloc=107.8MB, time=48.09 memory used=13399.3MB, alloc=107.8MB, time=48.22 memory used=13425.3MB, alloc=107.8MB, time=48.32 memory used=13454.5MB, alloc=107.8MB, time=48.43 memory used=13480.8MB, alloc=107.8MB, time=48.52 memory used=13506.1MB, alloc=107.8MB, time=48.61 memory used=13532.0MB, alloc=107.8MB, time=48.70 memory used=13558.2MB, alloc=107.8MB, time=48.80 memory used=13584.4MB, alloc=107.8MB, time=48.88 memory used=13610.8MB, alloc=107.8MB, time=48.97 memory used=13637.4MB, alloc=107.8MB, time=49.06 memory used=13664.5MB, alloc=107.8MB, time=49.20 memory used=13691.5MB, alloc=107.8MB, time=49.32 memory used=13718.7MB, alloc=107.8MB, time=49.45 memory used=13745.9MB, alloc=107.8MB, time=49.58 memory used=13773.4MB, alloc=107.8MB, time=49.71 memory used=13800.2MB, alloc=107.8MB, time=49.84 memory used=13830.3MB, alloc=107.8MB, time=49.94 memory used=13855.7MB, alloc=107.8MB, time=50.03 memory used=13880.3MB, alloc=107.8MB, time=50.13 memory used=13905.5MB, alloc=107.8MB, time=50.22 memory used=13931.1MB, alloc=107.8MB, time=50.31 memory used=13957.1MB, alloc=107.8MB, time=50.40 memory used=13982.9MB, alloc=107.8MB, time=50.49 memory 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alloc=107.8MB, time=52.79 memory used=14566.0MB, alloc=107.8MB, time=52.92 memory used=14593.2MB, alloc=107.8MB, time=53.04 memory used=14620.9MB, alloc=107.8MB, time=53.17 memory used=14648.6MB, alloc=107.8MB, time=53.30 memory used=14675.4MB, alloc=107.8MB, time=53.43 memory used=14702.5MB, alloc=107.8MB, time=53.55 memory used=14729.6MB, alloc=107.8MB, time=53.68 memory used=14759.0MB, alloc=107.8MB, time=53.77 memory used=14783.0MB, alloc=107.8MB, time=53.86 memory used=14807.5MB, alloc=107.8MB, time=53.95 memory used=14832.5MB, alloc=107.8MB, time=54.04 memory used=14857.9MB, alloc=107.8MB, time=54.13 memory used=14883.7MB, alloc=107.8MB, time=54.23 memory used=14909.2MB, alloc=107.8MB, time=54.32 memory used=14935.2MB, alloc=107.8MB, time=54.41 memory used=14960.8MB, alloc=107.8MB, time=54.51 memory used=14987.2MB, alloc=107.8MB, time=54.64 memory used=15014.3MB, alloc=107.8MB, time=54.77 memory used=15041.7MB, alloc=107.8MB, time=54.89 memory used=15069.1MB, alloc=107.8MB, time=55.02 memory used=15096.7MB, alloc=107.8MB, time=55.16 memory used=15124.5MB, alloc=107.8MB, time=55.29 memory used=15152.4MB, alloc=107.8MB, time=55.42 memory used=15179.7MB, alloc=107.8MB, time=55.55 memory used=15206.8MB, alloc=107.8MB, time=55.68 memory used=15234.1MB, alloc=107.8MB, time=55.81 memory used=15261.5MB, alloc=107.8MB, time=55.93 memory used=15292.0MB, alloc=107.8MB, time=56.03 memory used=15317.0MB, alloc=107.8MB, time=56.12 memory used=15342.4MB, alloc=107.8MB, time=56.21 memory used=15368.0MB, alloc=107.8MB, time=56.30 memory used=15393.8MB, alloc=107.8MB, time=56.39 memory used=15420.0MB, alloc=107.8MB, time=56.48 memory used=15446.1MB, alloc=107.8MB, time=56.57 memory used=15472.4MB, alloc=107.8MB, time=56.66 memory used=15498.6MB, alloc=107.8MB, time=56.76 memory used=15583.3MB, alloc=107.8MB, time=57.11 memory used=15635.2MB, alloc=107.8MB, time=57.29 memory used=15690.8MB, alloc=107.8MB, time=57.46 memory used=15749.4MB, alloc=107.8MB, time=57.62 memory 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alloc=107.8MB, time=60.70 memory used=16878.9MB, alloc=107.8MB, time=60.82 memory used=16925.2MB, alloc=107.8MB, time=60.95 memory used=16967.3MB, alloc=107.8MB, time=61.06 memory used=17009.4MB, alloc=107.8MB, time=61.19 memory used=17041.7MB, alloc=107.8MB, time=61.31 memory used=17087.4MB, alloc=107.8MB, time=61.44 memory used=17130.5MB, alloc=107.8MB, time=61.56 memory used=17170.5MB, alloc=107.8MB, time=61.68 memory used=17202.0MB, alloc=107.8MB, time=61.78 memory used=17243.5MB, alloc=107.8MB, time=61.92 memory used=17285.3MB, alloc=107.8MB, time=62.05 memory used=17326.1MB, alloc=107.8MB, time=62.17 memory used=17358.7MB, alloc=107.8MB, time=62.27 memory used=17387.2MB, alloc=107.8MB, time=62.37 memory used=17428.9MB, alloc=107.8MB, time=62.51 memory used=17470.2MB, alloc=107.8MB, time=62.63 memory used=17508.4MB, alloc=107.8MB, time=62.75 memory used=17539.4MB, alloc=107.8MB, time=62.85 memory used=17570.3MB, alloc=107.8MB, time=62.95 memory used=17598.1MB, alloc=107.8MB, time=63.05 memory used=17643.4MB, alloc=107.8MB, time=63.19 memory used=17681.5MB, alloc=107.8MB, time=63.30 memory used=17714.2MB, alloc=107.8MB, time=63.40 memory used=17743.3MB, alloc=107.8MB, time=63.50 memory used=17771.1MB, alloc=107.8MB, time=63.60 memory used=17803.1MB, alloc=107.8MB, time=63.73 memory used=17843.6MB, alloc=107.8MB, time=63.84 memory used=17875.2MB, alloc=107.8MB, time=63.95 memory used=17909.1MB, alloc=107.8MB, time=64.06 memory used=17938.0MB, alloc=107.8MB, time=64.16 memory used=17965.6MB, alloc=107.8MB, time=64.27 memory used=17992.1MB, alloc=107.8MB, time=64.38 memory used=18032.0MB, alloc=107.8MB, time=64.50 memory used=18067.8MB, alloc=107.8MB, time=64.62 memory used=18098.9MB, alloc=107.8MB, time=64.73 memory used=18128.0MB, alloc=107.8MB, time=64.83 memory used=18155.4MB, alloc=107.8MB, time=64.93 memory used=18181.5MB, alloc=107.8MB, time=65.02 memory used=18206.0MB, alloc=107.8MB, time=65.13 memory used=18245.0MB, alloc=107.8MB, time=65.24 memory 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used=52276.1MB, alloc=107.8MB, time=267.88 memory used=52283.7MB, alloc=107.8MB, time=267.95 memory used=52291.4MB, alloc=107.8MB, time=268.02 memory used=52299.0MB, alloc=107.8MB, time=268.10 memory used=52306.7MB, alloc=107.8MB, time=268.19 memory used=52314.4MB, alloc=107.8MB, time=268.26 memory used=52322.2MB, alloc=107.8MB, time=268.34 memory used=52329.8MB, alloc=107.8MB, time=268.41 memory used=52337.5MB, alloc=107.8MB, time=268.48 memory used=52345.1MB, alloc=107.8MB, time=268.55 memory used=52352.8MB, alloc=107.8MB, time=268.62 memory used=52360.4MB, alloc=107.8MB, time=268.69 memory used=52368.2MB, alloc=107.8MB, time=268.76 memory used=52375.9MB, alloc=107.8MB, time=268.84 memory used=52383.4MB, alloc=107.8MB, time=268.91 memory used=52390.7MB, alloc=107.8MB, time=268.98 memory used=52398.2MB, alloc=107.8MB, time=269.05 memory used=52405.7MB, alloc=107.8MB, time=269.12 memory used=52413.3MB, alloc=107.8MB, time=269.19 memory used=52420.8MB, alloc=107.8MB, time=269.26 memory used=52428.3MB, alloc=107.8MB, time=269.33 memory used=52435.9MB, alloc=107.8MB, time=269.40 memory used=52443.4MB, alloc=107.8MB, time=269.48 memory used=52450.8MB, alloc=107.8MB, time=269.55 memory used=52458.3MB, alloc=107.8MB, time=269.62 memory used=52465.8MB, alloc=107.8MB, time=269.70 memory used=52473.2MB, alloc=107.8MB, time=269.78 memory used=52480.8MB, alloc=107.8MB, time=269.85 memory used=52488.4MB, alloc=107.8MB, time=269.92 memory used=52496.0MB, alloc=107.8MB, time=270.00 memory used=52503.7MB, alloc=107.8MB, time=270.07 memory used=52511.4MB, alloc=107.8MB, time=270.15 memory used=52519.2MB, alloc=107.8MB, time=270.22 memory used=52526.8MB, alloc=107.8MB, time=270.29 memory used=52534.5MB, alloc=107.8MB, time=270.36 memory used=52542.0MB, alloc=107.8MB, time=270.43 memory used=52549.7MB, alloc=107.8MB, time=270.50 memory used=52557.2MB, alloc=107.8MB, time=270.58 memory used=52564.9MB, alloc=107.8MB, time=270.66 memory used=52572.5MB, alloc=107.8MB, time=270.74 memory used=52580.1MB, alloc=107.8MB, time=270.81 memory used=52587.8MB, alloc=107.8MB, time=270.88 memory used=52595.4MB, alloc=107.8MB, time=270.95 memory used=52603.0MB, alloc=107.8MB, time=271.03 memory used=52610.6MB, alloc=107.8MB, time=271.12 memory used=52618.2MB, alloc=107.8MB, time=271.19 memory used=52625.9MB, alloc=107.8MB, time=271.26 memory used=52633.6MB, alloc=107.8MB, time=271.33 memory used=52641.3MB, alloc=107.8MB, time=271.40 memory used=52648.9MB, alloc=107.8MB, time=271.47 memory used=52656.7MB, alloc=107.8MB, time=271.54 memory used=52664.4MB, alloc=107.8MB, time=271.62 memory used=52672.2MB, alloc=107.8MB, time=271.69 memory used=52680.0MB, alloc=107.8MB, time=271.76 memory used=52687.8MB, alloc=107.8MB, time=271.83 memory used=52695.4MB, alloc=107.8MB, time=271.91 memory used=52703.1MB, alloc=107.8MB, time=271.98 memory used=52710.7MB, alloc=107.8MB, time=272.05 memory used=52718.4MB, alloc=107.8MB, time=272.13 memory used=52726.1MB, alloc=107.8MB, time=272.20 memory used=52733.8MB, alloc=107.8MB, time=272.28 memory used=52741.5MB, alloc=107.8MB, time=272.35 memory used=52749.1MB, alloc=107.8MB, time=272.43 memory used=52756.7MB, alloc=107.8MB, time=272.50 memory used=52764.4MB, alloc=107.8MB, time=272.58 memory used=52772.0MB, alloc=107.8MB, time=272.65 memory used=52779.8MB, alloc=107.8MB, time=272.72 memory used=52787.4MB, alloc=107.8MB, time=272.80 memory used=52795.1MB, alloc=107.8MB, time=272.87 memory used=52802.7MB, alloc=107.8MB, time=272.94 memory used=52810.3MB, alloc=107.8MB, time=273.01 memory used=52818.0MB, alloc=107.8MB, time=273.09 memory used=52825.7MB, alloc=107.8MB, time=273.16 memory used=52833.3MB, alloc=107.8MB, time=273.23 memory used=52841.0MB, alloc=107.8MB, time=273.31 memory used=52848.7MB, alloc=107.8MB, time=273.39 memory used=52856.5MB, alloc=107.8MB, time=273.46 memory used=52864.3MB, alloc=107.8MB, time=273.53 memory used=52872.1MB, alloc=107.8MB, time=273.61 memory used=52879.8MB, alloc=107.8MB, time=273.69 memory used=52887.5MB, alloc=107.8MB, time=273.77 memory used=52895.1MB, alloc=107.8MB, time=273.85 memory used=52902.8MB, alloc=107.8MB, time=273.92 memory used=52910.5MB, alloc=107.8MB, time=274.01 memory used=52917.9MB, alloc=107.8MB, time=274.09 memory used=52925.2MB, alloc=107.8MB, time=274.16 memory used=52932.6MB, alloc=107.8MB, time=274.24 memory used=52940.0MB, alloc=107.8MB, time=274.31 memory used=52947.4MB, alloc=107.8MB, time=274.39 memory used=52954.8MB, alloc=107.8MB, time=274.46 memory used=52962.4MB, alloc=107.8MB, time=274.54 memory used=52970.1MB, alloc=107.8MB, time=274.62 memory used=52977.6MB, alloc=107.8MB, time=274.69 memory used=52985.2MB, alloc=107.8MB, time=274.76 memory used=52992.7MB, alloc=107.8MB, time=274.84 memory used=53000.4MB, alloc=107.8MB, time=274.92 memory used=53007.8MB, alloc=107.8MB, time=274.99 memory used=53015.4MB, alloc=107.8MB, time=275.07 memory used=53022.9MB, alloc=107.8MB, time=275.14 memory used=53030.3MB, alloc=107.8MB, time=275.22 memory used=53037.9MB, alloc=107.8MB, time=275.30 memory used=53045.4MB, alloc=107.8MB, time=275.37 memory used=53052.9MB, alloc=107.8MB, time=275.44 memory used=53060.6MB, alloc=107.8MB, time=275.52 memory used=53068.2MB, alloc=107.8MB, time=275.59 memory used=53075.9MB, alloc=107.8MB, time=275.66 memory used=53083.6MB, alloc=107.8MB, time=275.74 memory used=53091.5MB, alloc=107.8MB, time=275.81 memory used=53099.1MB, alloc=107.8MB, time=275.89 memory used=53106.7MB, alloc=107.8MB, time=275.97 memory used=53114.4MB, alloc=107.8MB, time=276.05 memory used=53122.1MB, alloc=107.8MB, time=276.12 memory used=53129.7MB, alloc=107.8MB, time=276.20 memory used=53137.5MB, alloc=107.8MB, time=276.27 memory used=53145.0MB, alloc=107.8MB, time=276.34 memory used=53152.7MB, alloc=107.8MB, time=276.41 memory used=53160.3MB, alloc=107.8MB, time=276.49 memory used=53167.9MB, alloc=107.8MB, time=276.56 memory used=53175.6MB, alloc=107.8MB, time=276.64 memory used=53183.2MB, alloc=107.8MB, time=276.71 memory used=53190.8MB, alloc=107.8MB, time=276.79 memory used=53198.4MB, alloc=107.8MB, time=276.86 memory used=53206.1MB, alloc=107.8MB, time=276.94 memory used=53213.7MB, alloc=107.8MB, time=277.01 memory used=53221.4MB, alloc=107.8MB, time=277.09 memory used=53229.1MB, alloc=107.8MB, time=277.16 memory used=53236.8MB, alloc=107.8MB, time=277.24 memory used=53244.5MB, alloc=107.8MB, time=277.31 memory used=53252.3MB, alloc=107.8MB, time=277.39 memory used=53260.1MB, alloc=107.8MB, time=277.46 memory used=53267.8MB, alloc=107.8MB, time=277.55 memory used=53275.7MB, alloc=107.8MB, time=277.63 memory used=53283.3MB, alloc=107.8MB, time=277.70 memory used=53291.0MB, alloc=107.8MB, time=277.78 memory used=53298.6MB, alloc=107.8MB, time=277.85 memory used=53306.3MB, alloc=107.8MB, time=277.93 memory used=53314.0MB, alloc=107.8MB, time=278.01 memory used=53321.7MB, alloc=107.8MB, time=278.09 memory used=53329.4MB, alloc=107.8MB, time=278.17 memory used=53337.0MB, alloc=107.8MB, time=278.25 memory used=53344.6MB, alloc=107.8MB, time=278.33 memory used=53352.3MB, alloc=107.8MB, time=278.41 memory used=53359.9MB, alloc=107.8MB, time=278.49 memory used=53367.7MB, alloc=107.8MB, time=278.56 memory used=53375.3MB, alloc=107.8MB, time=278.64 memory used=53383.0MB, alloc=107.8MB, time=278.71 memory used=53390.7MB, alloc=107.8MB, time=278.79 memory used=53398.3MB, alloc=107.8MB, time=278.87 memory used=53405.9MB, alloc=107.8MB, time=278.95 memory used=53413.6MB, alloc=107.8MB, time=279.02 memory used=53421.3MB, alloc=107.8MB, time=279.10 memory used=53428.9MB, alloc=107.8MB, time=279.18 memory used=53436.7MB, alloc=107.8MB, time=279.26 memory used=53444.5MB, alloc=107.8MB, time=279.33 memory used=53452.2MB, alloc=107.8MB, time=279.41 memory used=53460.1MB, alloc=107.8MB, time=279.49 memory used=53467.8MB, alloc=107.8MB, time=279.57 memory used=53475.4MB, alloc=107.8MB, time=279.66 memory used=53483.1MB, alloc=107.8MB, time=279.73 memory used=53490.7MB, alloc=107.8MB, time=279.81 memory used=53498.5MB, alloc=107.8MB, time=279.89 memory used=53506.2MB, alloc=107.8MB, time=279.97 memory used=53513.9MB, alloc=107.8MB, time=280.04 memory used=53521.5MB, alloc=107.8MB, time=280.12 memory used=53529.2MB, alloc=107.8MB, time=280.19 memory used=53536.8MB, alloc=107.8MB, time=280.27 memory used=53544.2MB, alloc=107.8MB, time=280.34 memory used=53559.2MB, alloc=107.8MB, time=280.43 memory used=53568.0MB, alloc=107.8MB, time=280.49 memory used=53578.0MB, alloc=107.8MB, time=280.56 memory used=53586.4MB, alloc=107.8MB, time=280.63 memory used=53599.3MB, alloc=107.8MB, time=280.71 memory used=53608.6MB, alloc=107.8MB, time=280.78 memory used=53618.9MB, alloc=107.8MB, time=280.85 memory used=53626.5MB, alloc=107.8MB, time=280.92 memory used=53639.4MB, alloc=107.8MB, time=281.01 memory used=53648.4MB, alloc=107.8MB, time=281.08 memory used=53658.6MB, alloc=107.8MB, time=281.15 memory used=53666.0MB, alloc=107.8MB, time=281.21 memory used=53674.1MB, alloc=107.8MB, time=281.29 memory used=53686.6MB, alloc=107.8MB, time=281.37 memory used=53696.1MB, alloc=107.8MB, time=281.44 memory used=53706.1MB, alloc=107.8MB, time=281.50 memory used=53713.8MB, alloc=107.8MB, time=281.57 memory used=53721.9MB, alloc=107.8MB, time=281.63 memory used=53734.9MB, alloc=107.8MB, time=281.72 memory used=53744.1MB, alloc=107.8MB, time=281.79 memory used=53754.1MB, alloc=107.8MB, time=281.86 memory used=53761.5MB, alloc=107.8MB, time=281.93 memory used=53769.7MB, alloc=107.8MB, time=282.00 memory used=53783.1MB, alloc=107.8MB, time=282.08 memory used=53792.1MB, alloc=107.8MB, time=282.15 memory used=53801.6MB, alloc=107.8MB, time=282.21 memory used=53810.7MB, alloc=107.8MB, time=282.28 memory used=53818.2MB, alloc=107.8MB, time=282.35 memory used=53826.1MB, alloc=107.8MB, time=282.42 memory used=53834.5MB, alloc=107.8MB, time=282.48 memory used=53846.9MB, alloc=107.8MB, time=282.57 memory used=53856.2MB, alloc=107.8MB, time=282.64 memory used=53866.1MB, alloc=107.8MB, time=282.71 memory used=53873.4MB, alloc=107.8MB, time=282.77 memory used=53881.4MB, alloc=107.8MB, time=282.84 memory used=53889.6MB, alloc=107.8MB, time=282.91 memory used=53898.3MB, alloc=107.8MB, time=282.97 memory used=53910.5MB, alloc=107.8MB, time=283.05 memory used=53919.7MB, alloc=107.8MB, time=283.12 memory used=53929.5MB, alloc=107.8MB, time=283.19 memory used=53936.6MB, alloc=107.8MB, time=283.25 memory used=53944.4MB, alloc=107.8MB, time=283.31 memory used=53952.4MB, alloc=107.8MB, time=283.38 memory used=53961.1MB, alloc=107.8MB, time=283.45 memory used=53974.5MB, alloc=107.8MB, time=283.53 memory used=53982.5MB, alloc=107.8MB, time=283.59 memory used=53991.5MB, alloc=107.8MB, time=283.66 memory used=53999.9MB, alloc=107.8MB, time=283.72 memory used=54006.9MB, alloc=107.8MB, time=283.79 memory used=54014.5MB, alloc=107.8MB, time=283.85 memory used=54022.5MB, alloc=107.8MB, time=283.91 memory used=54031.0MB, alloc=107.8MB, time=283.97 memory used=54037.1MB, alloc=107.8MB, time=284.04 memory used=54040.5MB, alloc=107.8MB, time=284.09 memory used=54040.6MB, alloc=363.8MB, time=284.16 memory used=54413.0MB, alloc=363.8MB, time=285.30 memory used=54786.4MB, alloc=363.8MB, time=286.24 memory used=55160.7MB, alloc=363.8MB, time=287.15 memory used=55533.1MB, alloc=363.8MB, time=288.12 memory used=55908.7MB, alloc=363.8MB, time=289.07 memory used=56280.8MB, alloc=363.8MB, time=289.98 memory used=56658.4MB, alloc=363.8MB, time=290.92 memory used=57013.7MB, alloc=363.8MB, time=291.50 memory used=57386.5MB, alloc=363.8MB, time=292.45 memory used=57765.4MB, alloc=363.8MB, time=293.45 memory used=58140.6MB, alloc=363.8MB, time=294.43 memory used=58518.5MB, alloc=363.8MB, time=295.43 memory used=58894.8MB, alloc=363.8MB, time=296.38 memory used=59270.8MB, alloc=363.8MB, time=297.33 memory used=59649.1MB, alloc=363.8MB, time=298.34 memory used=60018.5MB, alloc=363.8MB, time=299.14 memory used=60375.9MB, alloc=363.8MB, time=299.82 memory used=60757.8MB, alloc=363.8MB, time=300.82 memory used=61140.0MB, alloc=363.8MB, time=301.85 memory used=61522.4MB, alloc=363.8MB, time=302.86 memory used=61904.3MB, alloc=363.8MB, time=303.88 memory used=62287.1MB, alloc=363.8MB, time=304.89 memory used=62667.7MB, alloc=363.8MB, time=305.89 memory used=63051.6MB, alloc=363.8MB, time=306.93 memory used=63423.5MB, alloc=363.8MB, time=307.73 memory used=63781.3MB, alloc=363.8MB, time=308.42 memory used=64167.9MB, alloc=363.8MB, time=309.44 memory used=64555.3MB, alloc=363.8MB, time=310.53 memory used=64941.4MB, alloc=363.8MB, time=311.55 memory used=65329.4MB, alloc=363.8MB, time=312.61 memory used=65715.3MB, alloc=363.8MB, time=313.63 memory used=66101.6MB, alloc=363.8MB, time=314.67 memory used=66488.7MB, alloc=363.8MB, time=315.70 memory used=66878.5MB, alloc=363.8MB, time=316.70 memory used=67231.3MB, alloc=363.8MB, time=317.31 memory used=67609.1MB, alloc=363.8MB, time=318.24 memory used=68002.0MB, alloc=363.8MB, time=319.31 memory used=68391.8MB, alloc=363.8MB, time=320.32 memory used=68784.6MB, alloc=363.8MB, time=321.35 memory used=69174.8MB, alloc=363.8MB, time=322.35 memory used=69567.6MB, alloc=363.8MB, time=323.41 memory used=69957.3MB, alloc=363.8MB, time=324.43 memory used=70350.1MB, alloc=363.8MB, time=325.49 memory used=70736.0MB, alloc=363.8MB, time=326.39 memory used=71090.4MB, alloc=363.8MB, time=326.95 memory used=71477.3MB, alloc=363.8MB, time=327.95 memory used=71875.0MB, alloc=363.8MB, time=329.01 memory used=72269.2MB, alloc=363.8MB, time=330.05 memory used=72666.4MB, alloc=363.8MB, time=331.15 memory used=73061.2MB, alloc=363.8MB, time=332.20 memory used=73457.9MB, alloc=363.8MB, time=333.33 memory used=73852.5MB, alloc=363.8MB, time=334.44 memory used=74249.5MB, alloc=363.8MB, time=335.51 memory used=74649.5MB, alloc=363.8MB, time=336.65 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428509706 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 2 2 3 F := [x y z + 7 y z - 5 x z, -8 x y z - 20 y z + 11 y z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 4 2 G := [19 x y + 15 x z - 16 x , -20 y + 5 x z + 12 y z] > Problem := [F,G]; 2 3 2 2 2 2 3 Problem := [[x y z + 7 y z - 5 x z, -8 x y z - 20 y z + 11 y z ], 3 2 2 2 4 2 [19 x y + 15 x z - 16 x , -20 y + 5 x z + 12 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.7MB, alloc=32.3MB, time=0.46 memory used=50.0MB, alloc=36.4MB, time=0.69 memory used=72.3MB, alloc=36.4MB, time=0.99 memory used=93.5MB, alloc=60.4MB, time=1.18 memory used=120.4MB, alloc=60.4MB, time=1.26 memory used=152.3MB, alloc=60.4MB, time=1.34 memory used=172.1MB, alloc=60.4MB, time=1.41 memory used=194.8MB, alloc=60.4MB, time=1.47 memory used=220.5MB, alloc=60.4MB, time=1.54 memory used=249.0MB, alloc=60.4MB, time=1.61 memory used=280.5MB, alloc=60.4MB, time=1.69 memory used=309.5MB, alloc=60.4MB, time=1.76 memory used=327.5MB, alloc=60.4MB, time=1.81 memory used=346.2MB, alloc=60.4MB, time=1.86 memory used=366.4MB, alloc=60.4MB, time=1.92 memory used=387.9MB, alloc=60.4MB, time=1.97 memory used=410.5MB, alloc=60.4MB, time=2.02 memory used=434.0MB, alloc=60.4MB, time=2.08 memory used=459.4MB, alloc=60.4MB, time=2.14 memory used=486.9MB, alloc=60.4MB, time=2.20 memory used=516.7MB, alloc=60.4MB, time=2.26 memory used=556.7MB, alloc=60.4MB, time=2.45 memory used=584.4MB, alloc=60.4MB, time=2.56 memory used=616.4MB, alloc=60.4MB, time=2.67 memory used=636.3MB, alloc=60.4MB, time=2.75 memory used=659.1MB, alloc=60.4MB, time=2.82 memory used=684.7MB, alloc=60.4MB, time=2.89 memory used=713.6MB, alloc=60.4MB, time=2.97 memory used=746.6MB, alloc=60.4MB, time=3.06 memory used=775.1MB, alloc=60.4MB, time=3.13 memory used=793.2MB, alloc=60.4MB, time=3.19 memory used=813.5MB, alloc=60.4MB, time=3.24 memory used=833.7MB, alloc=60.4MB, time=3.30 memory used=855.2MB, alloc=60.4MB, time=3.35 memory used=879.2MB, alloc=60.4MB, time=3.41 memory used=904.0MB, alloc=60.4MB, time=3.47 memory used=930.5MB, alloc=60.4MB, time=3.52 memory used=959.8MB, alloc=60.4MB, time=3.58 memory used=991.7MB, alloc=60.4MB, time=3.64 memory used=1040.0MB, alloc=60.4MB, time=9.25 memory used=1071.6MB, alloc=84.4MB, time=19.47 memory used=1108.9MB, alloc=108.4MB, time=43.10 memory used=1177.6MB, alloc=109.5MB, time=119.33 memory used=1256.4MB, alloc=109.5MB, time=188.82 memory used=1331.9MB, alloc=109.5MB, time=260.29 memory used=1400.4MB, alloc=109.5MB, time=263.18 memory used=1488.7MB, alloc=109.5MB, time=263.78 memory used=1569.2MB, alloc=109.5MB, time=264.37 memory used=1646.7MB, alloc=109.5MB, time=264.78 memory used=1708.2MB, alloc=110.0MB, time=264.95 memory used=1750.2MB, alloc=110.0MB, time=265.07 memory used=1799.7MB, alloc=110.0MB, time=265.21 memory used=1855.9MB, alloc=110.0MB, time=265.35 memory used=1918.2MB, alloc=110.0MB, time=265.51 memory used=1984.2MB, alloc=110.0MB, time=265.67 memory used=2020.9MB, alloc=110.0MB, time=265.76 memory used=2056.5MB, alloc=110.0MB, time=265.85 memory used=2095.2MB, alloc=110.0MB, time=265.95 memory used=2135.3MB, alloc=110.0MB, time=266.05 memory used=2176.7MB, alloc=110.0MB, time=266.15 memory used=2219.4MB, alloc=110.0MB, time=266.25 memory used=2263.4MB, alloc=110.0MB, time=266.35 memory used=2308.6MB, alloc=110.0MB, time=266.44 memory used=2355.1MB, alloc=110.0MB, time=266.54 memory used=2402.9MB, alloc=110.0MB, time=266.65 memory used=2451.9MB, alloc=110.0MB, time=266.76 memory used=2506.6MB, alloc=110.0MB, time=266.87 memory used=2562.7MB, alloc=110.0MB, time=266.98 memory used=2620.1MB, alloc=110.0MB, time=267.09 memory used=2678.8MB, alloc=110.0MB, time=267.20 memory used=2738.8MB, alloc=110.0MB, time=267.31 memory used=2800.0MB, alloc=110.0MB, time=267.42 memory used=2862.4MB, alloc=110.0MB, time=267.54 memory used=2926.1MB, alloc=110.0MB, time=267.66 memory used=2978.8MB, alloc=131.8MB, time=267.78 memory used=2982.9MB, alloc=131.8MB, time=267.83 memory used=2987.5MB, alloc=131.8MB, time=267.87 memory used=2992.7MB, alloc=131.8MB, time=267.91 memory used=2998.1MB, alloc=131.8MB, time=267.95 memory used=3003.5MB, alloc=131.8MB, time=268.00 memory used=3009.0MB, alloc=131.8MB, time=268.04 memory used=3014.4MB, alloc=131.8MB, time=268.08 memory used=3019.8MB, alloc=131.8MB, time=268.12 memory used=3025.3MB, alloc=131.8MB, time=268.17 memory used=3030.7MB, alloc=131.8MB, time=268.20 memory used=3036.2MB, alloc=131.8MB, time=268.25 memory used=3041.7MB, alloc=131.8MB, time=268.28 memory used=3047.1MB, alloc=131.8MB, time=268.32 memory used=3052.6MB, alloc=131.8MB, time=268.37 memory used=3058.1MB, alloc=131.8MB, time=268.41 memory used=3063.6MB, alloc=131.8MB, time=268.45 memory used=3069.1MB, alloc=131.8MB, time=268.49 memory used=3074.6MB, alloc=131.8MB, time=268.53 memory used=3080.2MB, alloc=131.8MB, time=268.57 memory used=3085.7MB, alloc=131.8MB, time=268.61 memory used=3091.2MB, alloc=131.8MB, time=268.65 memory used=3096.8MB, alloc=131.8MB, time=268.69 memory used=3102.3MB, alloc=131.8MB, time=268.74 memory used=3107.9MB, alloc=131.8MB, time=268.78 memory used=3113.5MB, alloc=131.8MB, time=268.83 memory used=3119.0MB, alloc=131.8MB, time=268.87 memory used=3124.6MB, alloc=131.8MB, time=268.92 memory used=3130.2MB, alloc=131.8MB, time=268.95 memory used=3135.8MB, alloc=131.8MB, time=268.99 memory used=3141.4MB, alloc=131.8MB, time=269.04 memory used=3147.0MB, alloc=131.8MB, time=269.08 memory used=3152.6MB, alloc=131.8MB, time=269.12 memory used=3158.2MB, alloc=131.8MB, time=269.16 memory used=3163.9MB, alloc=131.8MB, time=269.20 memory used=3169.5MB, alloc=131.8MB, time=269.24 memory used=3175.1MB, alloc=131.8MB, time=269.29 memory used=3180.8MB, alloc=131.8MB, time=269.33 memory used=3186.5MB, alloc=131.8MB, time=269.37 memory used=3192.1MB, alloc=131.8MB, time=269.42 memory used=3197.8MB, alloc=131.8MB, time=269.47 memory used=3203.5MB, alloc=131.8MB, time=269.51 memory used=3209.2MB, alloc=131.8MB, time=269.56 memory used=3214.9MB, alloc=131.8MB, time=269.60 memory used=3220.6MB, alloc=131.8MB, time=269.64 memory used=3226.3MB, alloc=131.8MB, time=269.68 memory used=3232.0MB, alloc=131.8MB, time=269.72 memory used=3237.7MB, alloc=131.8MB, time=269.77 memory used=3243.4MB, alloc=131.8MB, time=269.81 memory used=3249.2MB, alloc=131.8MB, time=269.86 memory used=3254.9MB, alloc=131.8MB, time=269.90 memory used=3260.6MB, alloc=131.8MB, time=269.94 memory used=3266.4MB, alloc=131.8MB, time=269.99 memory used=3272.2MB, alloc=131.8MB, time=270.03 memory used=3277.9MB, alloc=131.8MB, time=270.08 memory used=3283.7MB, alloc=131.8MB, time=270.13 memory used=3289.5MB, alloc=131.8MB, time=270.18 memory used=3295.2MB, alloc=131.8MB, time=270.22 memory used=3301.0MB, alloc=131.8MB, time=270.26 memory used=3306.8MB, alloc=131.8MB, time=270.31 memory used=3312.7MB, alloc=131.8MB, time=270.35 memory used=3318.5MB, alloc=131.8MB, time=270.40 memory used=3324.3MB, alloc=131.8MB, time=270.44 memory used=3330.1MB, alloc=131.8MB, time=270.49 memory used=3335.9MB, alloc=131.8MB, time=270.53 memory used=3341.8MB, alloc=131.8MB, time=270.57 memory used=3347.6MB, alloc=131.8MB, time=270.61 memory used=3353.5MB, alloc=131.8MB, time=270.67 memory used=3359.3MB, alloc=131.8MB, time=270.71 memory used=3365.2MB, alloc=131.8MB, time=270.76 memory used=3371.1MB, alloc=131.8MB, time=270.80 memory used=3377.0MB, alloc=131.8MB, time=270.84 memory used=3382.8MB, alloc=131.8MB, time=270.88 memory used=3388.7MB, alloc=131.8MB, time=270.92 memory used=3394.6MB, alloc=131.8MB, time=270.97 memory used=3400.6MB, alloc=131.8MB, time=271.01 memory used=3406.5MB, alloc=131.8MB, time=271.06 memory used=3412.4MB, alloc=131.8MB, time=271.11 memory used=3418.3MB, alloc=131.8MB, time=271.15 memory used=3424.2MB, alloc=131.8MB, time=271.19 memory used=3430.2MB, alloc=131.8MB, time=271.23 memory used=3436.1MB, alloc=131.8MB, time=271.27 memory used=3442.1MB, alloc=131.8MB, time=271.32 memory used=3448.0MB, alloc=131.8MB, time=271.36 memory used=3454.0MB, alloc=131.8MB, time=271.40 memory used=3459.9MB, alloc=131.8MB, time=271.44 memory used=3465.9MB, alloc=131.8MB, time=271.48 memory used=3471.9MB, alloc=131.8MB, time=271.52 memory used=3477.9MB, alloc=131.8MB, time=271.57 memory used=3483.9MB, alloc=131.8MB, time=271.61 memory used=3489.9MB, alloc=131.8MB, time=271.65 memory used=3495.9MB, alloc=131.8MB, time=271.69 memory used=3501.9MB, alloc=131.8MB, time=271.73 memory used=3507.9MB, alloc=131.8MB, time=271.77 memory used=3513.9MB, alloc=131.8MB, time=271.82 memory used=3520.0MB, alloc=131.8MB, time=271.86 memory used=3526.0MB, alloc=131.8MB, time=271.90 memory used=3532.1MB, alloc=131.8MB, time=271.94 memory used=3538.1MB, alloc=131.8MB, time=271.98 memory used=3544.2MB, alloc=131.8MB, time=272.02 memory used=3550.2MB, alloc=131.8MB, time=272.07 memory used=3556.3MB, alloc=131.8MB, time=272.11 memory used=3562.4MB, alloc=131.8MB, time=272.15 memory used=3568.4MB, alloc=131.8MB, time=272.19 memory used=3574.5MB, alloc=131.8MB, time=272.23 memory used=3580.6MB, alloc=131.8MB, time=272.27 memory used=3586.7MB, alloc=131.8MB, time=272.31 memory used=3592.8MB, alloc=131.8MB, time=272.35 memory used=3598.9MB, alloc=131.8MB, time=272.39 memory used=3605.0MB, alloc=131.8MB, time=272.43 memory used=3611.1MB, alloc=131.8MB, time=272.47 memory used=3617.3MB, alloc=131.8MB, time=272.50 memory used=3623.4MB, alloc=131.8MB, time=272.55 memory used=3629.5MB, alloc=131.8MB, time=272.59 memory used=3635.7MB, alloc=131.8MB, time=272.63 memory used=3641.8MB, alloc=131.8MB, time=272.67 memory used=3648.0MB, alloc=131.8MB, time=272.71 memory used=3654.1MB, alloc=131.8MB, time=272.75 memory used=3660.3MB, alloc=131.8MB, time=272.79 memory used=3666.5MB, alloc=131.8MB, time=272.83 memory used=3672.6MB, alloc=131.8MB, time=272.87 memory used=3678.8MB, alloc=131.8MB, time=272.92 memory used=3685.0MB, alloc=131.8MB, time=272.96 memory used=3691.2MB, alloc=131.8MB, time=272.99 memory used=3697.4MB, alloc=131.8MB, time=273.04 memory used=3703.6MB, alloc=131.8MB, time=273.08 memory used=3709.8MB, alloc=131.8MB, time=273.12 memory used=3716.0MB, alloc=131.8MB, time=273.17 memory used=3722.2MB, alloc=131.8MB, time=273.21 memory used=3728.4MB, alloc=131.8MB, time=273.26 memory used=3734.7MB, alloc=131.8MB, time=273.30 memory used=3740.9MB, alloc=131.8MB, time=273.34 memory used=3747.1MB, alloc=131.8MB, time=273.39 memory used=3753.4MB, alloc=131.8MB, time=273.44 memory used=3759.6MB, alloc=131.8MB, time=273.49 memory used=3765.9MB, alloc=131.8MB, time=273.53 memory used=3772.2MB, alloc=131.8MB, time=273.56 memory used=3778.4MB, alloc=131.8MB, time=273.61 memory used=3784.7MB, alloc=131.8MB, time=273.65 memory used=3791.0MB, alloc=131.8MB, time=273.69 memory used=3797.3MB, alloc=131.8MB, time=273.74 memory used=3803.6MB, alloc=131.8MB, time=273.78 memory used=3809.9MB, alloc=131.8MB, time=273.82 memory used=3816.2MB, alloc=131.8MB, time=273.86 memory used=3822.5MB, alloc=131.8MB, time=273.90 memory used=3828.8MB, alloc=131.8MB, time=273.94 memory used=3835.1MB, alloc=131.8MB, time=273.99 memory used=3841.4MB, alloc=131.8MB, time=274.03 memory used=3847.7MB, alloc=131.8MB, time=274.07 memory used=3854.1MB, alloc=131.8MB, time=274.11 memory used=3860.4MB, alloc=131.8MB, time=274.15 memory used=3866.8MB, alloc=131.8MB, time=274.19 memory used=3873.1MB, alloc=131.8MB, time=274.23 memory used=3879.4MB, alloc=131.8MB, time=274.27 memory used=3885.8MB, alloc=131.8MB, time=274.31 memory used=3892.2MB, alloc=131.8MB, time=274.35 memory used=3898.5MB, alloc=131.8MB, time=274.39 memory used=3904.9MB, alloc=131.8MB, time=274.44 memory used=3911.3MB, alloc=131.8MB, time=274.48 memory used=3917.7MB, alloc=131.8MB, time=274.52 memory used=3924.1MB, alloc=131.8MB, time=274.56 memory used=3930.5MB, alloc=131.8MB, time=274.60 memory used=3936.8MB, alloc=131.8MB, time=274.64 memory used=3943.2MB, alloc=131.8MB, time=274.68 memory used=3949.6MB, alloc=131.8MB, time=274.72 memory used=3956.1MB, alloc=131.8MB, time=274.76 memory used=3962.5MB, alloc=131.8MB, time=274.81 memory used=3968.9MB, alloc=131.8MB, time=274.85 memory used=3975.3MB, alloc=131.8MB, time=274.89 memory used=3981.8MB, alloc=131.8MB, time=274.93 memory used=3988.2MB, alloc=131.8MB, time=274.98 memory used=3994.6MB, alloc=131.8MB, time=275.01 memory used=4001.1MB, alloc=131.8MB, time=275.05 memory used=4007.5MB, alloc=131.8MB, time=275.09 memory used=4014.0MB, alloc=131.8MB, time=275.14 memory used=4020.4MB, alloc=131.8MB, time=275.18 memory used=4026.9MB, alloc=131.8MB, time=275.23 memory used=4033.4MB, alloc=131.8MB, time=275.27 memory used=4039.8MB, alloc=131.8MB, time=275.32 memory used=4046.3MB, alloc=131.8MB, time=275.37 memory used=4052.8MB, alloc=131.8MB, time=275.41 memory used=4059.3MB, alloc=131.8MB, time=275.44 memory used=4065.7MB, alloc=131.8MB, time=275.49 memory used=4072.3MB, alloc=131.8MB, time=275.53 memory used=4078.7MB, alloc=131.8MB, time=275.57 memory used=4085.3MB, alloc=131.8MB, time=275.61 memory used=4091.8MB, alloc=131.8MB, time=275.65 memory used=4098.3MB, alloc=131.8MB, time=275.70 memory used=4104.8MB, alloc=131.8MB, time=275.74 memory used=4111.3MB, alloc=131.8MB, time=275.78 memory used=4117.8MB, alloc=131.8MB, time=275.83 memory used=4124.4MB, alloc=131.8MB, time=275.88 memory used=4130.9MB, alloc=131.8MB, time=275.92 memory used=4137.4MB, alloc=131.8MB, time=275.97 memory used=4144.0MB, alloc=131.8MB, time=276.02 memory used=4150.5MB, alloc=131.8MB, time=276.06 memory used=4157.1MB, alloc=131.8MB, time=276.10 memory used=4163.6MB, alloc=131.8MB, time=276.15 memory used=4170.2MB, alloc=131.8MB, time=276.20 memory used=4176.8MB, alloc=131.8MB, time=276.24 memory used=4183.3MB, alloc=131.8MB, time=276.29 memory used=4189.9MB, alloc=131.8MB, time=276.33 memory used=4196.5MB, alloc=131.8MB, time=276.38 memory used=4203.0MB, alloc=131.8MB, time=276.42 memory used=4209.6MB, alloc=131.8MB, time=276.46 memory used=4216.2MB, alloc=131.8MB, time=276.50 memory used=4222.8MB, alloc=131.8MB, time=276.55 memory used=4229.4MB, alloc=131.8MB, time=276.59 memory used=4236.0MB, alloc=131.8MB, time=276.63 memory used=4242.6MB, alloc=131.8MB, time=276.67 memory used=4249.2MB, alloc=131.8MB, time=276.71 memory used=4255.8MB, alloc=131.8MB, time=276.75 memory used=4262.5MB, alloc=131.8MB, time=276.79 memory used=4269.1MB, alloc=131.8MB, time=276.83 memory used=4275.7MB, alloc=131.8MB, time=276.87 memory used=4282.3MB, alloc=131.8MB, time=276.91 memory used=4289.0MB, alloc=131.8MB, time=276.95 memory used=4289.1MB, alloc=131.8MB, time=276.99 memory used=4295.7MB, alloc=131.8MB, time=277.04 memory used=4302.4MB, alloc=131.8MB, time=277.08 memory used=4309.0MB, alloc=131.8MB, time=277.12 memory used=4315.6MB, alloc=131.8MB, time=277.17 memory used=4322.3MB, alloc=131.8MB, time=277.21 memory used=4329.0MB, alloc=131.8MB, time=277.24 memory used=4335.7MB, alloc=131.8MB, time=277.29 memory used=4348.8MB, alloc=131.8MB, time=277.35 memory used=4355.6MB, alloc=131.8MB, time=277.39 memory used=4362.4MB, alloc=131.8MB, time=277.43 memory used=4375.5MB, alloc=131.8MB, time=277.48 memory used=4382.4MB, alloc=131.8MB, time=277.53 memory used=4395.6MB, alloc=131.8MB, time=277.58 memory used=4402.5MB, alloc=131.8MB, time=277.62 memory used=4415.7MB, alloc=131.8MB, time=277.68 memory used=4429.2MB, alloc=131.8MB, time=277.73 memory used=4442.6MB, alloc=131.8MB, time=277.78 memory used=4456.0MB, alloc=131.8MB, time=277.83 memory used=4469.5MB, alloc=131.8MB, time=277.88 memory used=4483.0MB, alloc=131.8MB, time=277.93 memory used=4496.4MB, alloc=131.8MB, time=277.99 memory used=4509.9MB, alloc=131.8MB, time=278.04 memory used=4523.5MB, alloc=131.8MB, time=278.09 memory used=4537.0MB, alloc=131.8MB, time=278.15 memory used=4550.5MB, alloc=131.8MB, time=278.20 memory used=4564.1MB, alloc=131.8MB, time=278.26 memory used=4577.6MB, alloc=131.8MB, time=278.31 memory used=4591.2MB, alloc=131.8MB, time=278.36 memory used=4604.8MB, alloc=131.8MB, time=278.42 memory used=4618.4MB, alloc=131.8MB, time=278.47 memory used=4632.0MB, alloc=131.8MB, time=278.52 memory used=4645.7MB, alloc=131.8MB, time=278.58 memory used=4659.3MB, alloc=131.8MB, time=278.63 memory used=4672.9MB, alloc=131.8MB, time=278.69 memory used=4686.6MB, alloc=131.8MB, time=278.74 memory used=4700.3MB, alloc=131.8MB, time=278.79 memory used=4714.0MB, alloc=131.8MB, time=278.84 memory used=4727.7MB, alloc=131.8MB, time=278.89 memory used=4741.4MB, alloc=131.8MB, time=278.94 memory used=4755.1MB, alloc=131.8MB, time=278.99 memory used=4768.8MB, alloc=131.8MB, time=279.05 memory used=4782.6MB, alloc=131.8MB, time=279.10 memory used=4796.3MB, alloc=131.8MB, time=279.15 memory used=4810.1MB, alloc=131.8MB, time=279.21 memory used=4823.9MB, alloc=131.8MB, time=279.26 memory used=4837.6MB, alloc=131.8MB, time=279.32 memory used=4851.5MB, alloc=131.8MB, time=279.37 memory used=4865.3MB, alloc=131.8MB, time=279.42 memory used=4879.1MB, alloc=131.8MB, time=279.47 memory used=4892.9MB, alloc=131.8MB, time=279.52 memory used=4906.8MB, alloc=131.8MB, time=279.57 memory used=4920.6MB, alloc=131.8MB, time=279.62 memory used=4934.5MB, alloc=131.8MB, time=279.67 memory used=4948.3MB, alloc=131.8MB, time=279.72 memory used=4962.2MB, alloc=131.8MB, time=279.77 memory used=4976.1MB, alloc=131.8MB, time=279.82 memory used=4990.0MB, alloc=131.8MB, time=279.88 memory used=5003.9MB, alloc=131.8MB, time=279.92 memory used=5017.8MB, alloc=131.8MB, time=279.98 memory used=5031.7MB, alloc=131.8MB, time=280.03 memory used=5045.6MB, alloc=131.8MB, time=280.08 memory used=5059.5MB, alloc=131.8MB, time=280.13 memory used=5073.5MB, alloc=131.8MB, time=280.18 memory used=5087.4MB, alloc=131.8MB, time=280.22 memory used=5101.4MB, alloc=131.8MB, time=280.27 memory used=5115.3MB, alloc=131.8MB, time=280.32 memory used=5129.3MB, alloc=131.8MB, time=280.37 memory used=5143.3MB, alloc=131.8MB, time=280.42 memory used=5157.3MB, alloc=131.8MB, time=280.48 memory used=5171.2MB, alloc=131.8MB, time=280.52 memory used=5185.2MB, alloc=131.8MB, time=280.58 memory used=5199.2MB, alloc=131.8MB, time=280.63 memory used=5213.2MB, alloc=131.8MB, time=280.69 memory used=5227.3MB, alloc=131.8MB, time=280.75 memory used=5241.3MB, alloc=131.8MB, time=280.80 memory used=5255.3MB, alloc=131.8MB, time=280.86 memory used=5269.3MB, alloc=131.8MB, time=280.91 memory used=5283.4MB, alloc=131.8MB, time=280.96 memory used=5297.4MB, alloc=131.8MB, time=281.01 memory used=5311.5MB, alloc=131.8MB, time=281.07 memory used=5325.5MB, alloc=131.8MB, time=281.12 memory used=5339.6MB, alloc=131.8MB, time=281.17 memory used=5353.7MB, alloc=131.8MB, time=281.22 memory used=5367.7MB, alloc=131.8MB, time=281.28 memory used=5381.8MB, alloc=131.8MB, time=281.33 memory used=5395.9MB, alloc=131.8MB, time=281.38 memory used=5410.0MB, alloc=131.8MB, time=281.44 memory used=5424.1MB, alloc=131.8MB, time=281.50 memory used=5438.2MB, alloc=131.8MB, time=281.55 memory used=5452.3MB, alloc=131.8MB, time=281.60 memory used=5466.4MB, alloc=131.8MB, time=281.65 memory used=5480.5MB, alloc=131.8MB, time=281.70 memory used=5494.6MB, alloc=131.8MB, time=281.75 memory used=5508.7MB, alloc=131.8MB, time=281.80 memory used=5522.8MB, alloc=131.8MB, time=281.85 memory used=5537.0MB, alloc=131.8MB, time=281.91 memory used=5551.1MB, alloc=131.8MB, time=281.96 memory used=5565.2MB, alloc=131.8MB, time=282.01 memory used=5579.3MB, alloc=131.8MB, time=282.06 memory used=5593.5MB, alloc=131.8MB, time=282.10 memory used=5607.6MB, alloc=131.8MB, time=282.15 memory used=5621.8MB, alloc=131.8MB, time=282.20 memory used=5635.9MB, alloc=131.8MB, time=282.25 memory used=5650.0MB, alloc=131.8MB, time=282.31 memory used=5664.2MB, alloc=131.8MB, time=282.36 memory used=5678.3MB, alloc=131.8MB, time=282.41 memory used=5692.5MB, alloc=131.8MB, time=282.46 memory used=5706.6MB, alloc=131.8MB, time=282.52 memory used=5720.8MB, alloc=131.8MB, time=282.56 memory used=5734.9MB, alloc=131.8MB, time=282.61 memory used=5749.1MB, alloc=131.8MB, time=282.66 memory used=5763.3MB, alloc=131.8MB, time=282.72 memory used=5777.4MB, alloc=131.8MB, time=282.77 memory used=5791.6MB, alloc=131.8MB, time=282.82 memory used=5805.7MB, alloc=131.8MB, time=282.87 memory used=5819.9MB, alloc=131.8MB, time=282.92 memory used=5834.1MB, alloc=131.8MB, time=282.97 memory used=5848.2MB, alloc=131.8MB, time=283.02 memory used=5862.4MB, alloc=131.8MB, time=283.08 memory used=5876.5MB, alloc=131.8MB, time=283.12 memory used=5890.7MB, alloc=131.8MB, time=283.18 memory used=5904.9MB, alloc=131.8MB, time=283.22 memory used=5917.2MB, alloc=131.8MB, time=283.28 memory used=5926.6MB, alloc=131.8MB, time=283.32 memory used=5931.5MB, alloc=131.8MB, time=283.36 memory used=5938.5MB, alloc=131.8MB, time=283.40 memory used=5945.6MB, alloc=131.8MB, time=283.44 memory used=5952.7MB, alloc=131.8MB, time=283.49 memory used=5959.8MB, alloc=131.8MB, time=283.53 memory used=5966.8MB, alloc=131.8MB, time=283.57 memory used=5973.9MB, alloc=131.8MB, time=283.61 memory used=5981.0MB, alloc=131.8MB, time=283.65 memory used=5988.0MB, alloc=131.8MB, time=283.68 memory used=5995.1MB, alloc=131.8MB, time=283.72 memory used=6002.2MB, alloc=131.8MB, time=283.76 memory used=6009.2MB, alloc=131.8MB, time=283.80 memory used=6016.3MB, alloc=131.8MB, time=283.83 memory used=6023.3MB, alloc=131.8MB, time=283.87 memory used=6030.4MB, alloc=131.8MB, time=283.92 memory used=6037.5MB, alloc=131.8MB, time=283.96 memory used=6044.5MB, alloc=131.8MB, time=284.00 memory used=6051.6MB, alloc=131.8MB, time=284.04 memory used=6058.6MB, alloc=131.8MB, time=284.08 memory used=6065.7MB, alloc=131.8MB, time=284.12 memory used=6072.8MB, alloc=131.8MB, time=284.17 memory used=6079.8MB, alloc=131.8MB, time=284.21 memory used=6086.9MB, alloc=131.8MB, time=284.25 memory used=6094.0MB, alloc=131.8MB, time=284.30 memory used=6101.0MB, alloc=131.8MB, time=284.33 memory used=6108.1MB, alloc=131.8MB, time=284.38 memory used=6115.1MB, alloc=131.8MB, time=284.42 memory used=6122.2MB, alloc=131.8MB, time=284.46 memory used=6129.3MB, alloc=131.8MB, time=284.50 memory used=6136.3MB, alloc=131.8MB, time=284.54 memory used=6143.4MB, alloc=131.8MB, time=284.58 memory used=6150.4MB, alloc=131.8MB, time=284.62 memory used=6157.5MB, alloc=131.8MB, time=284.67 memory used=6164.6MB, alloc=131.8MB, time=284.72 memory used=6171.6MB, alloc=131.8MB, time=284.76 memory used=6178.7MB, alloc=131.8MB, time=284.81 memory used=6185.7MB, alloc=131.8MB, time=284.85 memory used=6192.8MB, alloc=131.8MB, time=284.89 memory used=6199.8MB, alloc=131.8MB, time=284.94 memory used=6206.9MB, alloc=131.8MB, time=284.98 memory used=6213.9MB, alloc=131.8MB, time=285.03 memory used=6221.0MB, alloc=131.8MB, time=285.06 memory used=6228.0MB, alloc=131.8MB, time=285.11 memory used=6235.1MB, alloc=131.8MB, time=285.15 memory used=6242.1MB, alloc=131.8MB, time=285.19 memory used=6249.2MB, alloc=131.8MB, time=285.24 memory used=6256.2MB, alloc=131.8MB, time=285.27 memory used=6263.2MB, alloc=131.8MB, time=285.31 memory used=6270.3MB, alloc=131.8MB, time=285.35 memory used=6277.3MB, alloc=131.8MB, time=285.39 memory used=6284.4MB, alloc=131.8MB, time=285.43 memory used=6291.4MB, alloc=131.8MB, time=285.47 memory used=6298.5MB, alloc=131.8MB, time=285.51 memory used=6305.5MB, alloc=131.8MB, time=285.55 memory used=6312.6MB, alloc=131.8MB, time=285.59 memory used=6319.6MB, alloc=131.8MB, time=285.63 memory used=6326.6MB, alloc=131.8MB, time=285.68 memory used=6333.7MB, alloc=131.8MB, time=285.72 memory used=6340.7MB, alloc=131.8MB, time=285.75 memory used=6347.7MB, alloc=131.8MB, time=285.80 memory used=6354.8MB, alloc=131.8MB, time=285.83 memory used=6361.8MB, alloc=131.8MB, time=285.88 memory used=6368.8MB, alloc=131.8MB, time=285.92 memory used=6375.8MB, alloc=131.8MB, time=285.96 memory used=6382.9MB, alloc=131.8MB, time=286.00 memory used=6389.9MB, alloc=131.8MB, time=286.04 memory used=6396.9MB, alloc=131.8MB, time=286.08 memory used=6404.0MB, alloc=131.8MB, time=286.12 memory used=6411.0MB, alloc=131.8MB, time=286.17 memory used=6418.0MB, alloc=131.8MB, time=286.21 memory used=6425.0MB, alloc=131.8MB, time=286.24 memory used=6432.0MB, alloc=131.8MB, time=286.28 memory used=6439.0MB, alloc=131.8MB, time=286.33 memory used=6446.0MB, alloc=131.8MB, time=286.38 memory used=6453.1MB, alloc=131.8MB, time=286.41 memory used=6460.1MB, alloc=131.8MB, time=286.45 memory used=6467.1MB, alloc=131.8MB, time=286.50 memory used=6474.1MB, alloc=131.8MB, time=286.54 memory used=6481.1MB, alloc=131.8MB, time=286.58 memory used=6488.1MB, alloc=131.8MB, time=286.62 memory used=6495.1MB, alloc=131.8MB, time=286.66 memory used=6502.1MB, alloc=131.8MB, time=286.70 memory used=6509.1MB, alloc=131.8MB, time=286.74 memory used=6516.1MB, alloc=131.8MB, time=286.78 memory used=6523.1MB, alloc=131.8MB, time=286.83 memory used=6530.1MB, alloc=131.8MB, time=286.87 memory used=6537.1MB, alloc=131.8MB, time=286.92 memory used=6544.1MB, alloc=131.8MB, time=286.96 memory used=6551.1MB, alloc=131.8MB, time=287.01 memory used=6558.1MB, alloc=131.8MB, time=287.05 memory used=6565.1MB, alloc=131.8MB, time=287.10 memory used=6572.0MB, alloc=131.8MB, time=287.14 memory used=6579.0MB, alloc=131.8MB, time=287.19 memory used=6586.0MB, alloc=131.8MB, time=287.23 memory used=6593.0MB, alloc=131.8MB, time=287.27 memory used=6600.0MB, alloc=131.8MB, time=287.31 memory used=6607.0MB, alloc=131.8MB, time=287.35 memory used=6613.9MB, alloc=131.8MB, time=287.39 memory used=6620.9MB, alloc=131.8MB, time=287.43 memory used=6627.9MB, alloc=131.8MB, time=287.47 memory used=6634.8MB, alloc=131.8MB, time=287.51 memory used=6641.8MB, alloc=131.8MB, time=287.56 memory used=6648.8MB, alloc=131.8MB, time=287.59 memory used=6655.8MB, alloc=131.8MB, time=287.64 memory used=6662.7MB, alloc=131.8MB, time=287.69 memory used=6669.7MB, alloc=131.8MB, time=287.73 memory used=6676.7MB, alloc=131.8MB, time=287.78 memory used=6683.6MB, alloc=131.8MB, time=287.82 memory used=6690.6MB, alloc=131.8MB, time=287.86 memory used=6697.5MB, alloc=131.8MB, time=287.90 memory used=6704.5MB, alloc=131.8MB, time=287.95 memory used=6711.4MB, alloc=131.8MB, time=287.99 memory used=6718.4MB, alloc=131.8MB, time=288.03 memory used=6725.3MB, alloc=131.8MB, time=288.08 memory used=6732.3MB, alloc=131.8MB, time=288.12 memory used=6739.2MB, alloc=131.8MB, time=288.16 memory used=6746.2MB, alloc=131.8MB, time=288.20 memory used=6753.1MB, alloc=131.8MB, time=288.24 memory used=6760.0MB, alloc=131.8MB, time=288.29 memory used=6767.0MB, alloc=131.8MB, time=288.33 memory used=6773.9MB, alloc=131.8MB, time=288.37 memory used=6780.8MB, alloc=131.8MB, time=288.41 memory used=6787.8MB, alloc=131.8MB, time=288.45 memory used=6794.7MB, alloc=131.8MB, time=288.50 memory used=6801.6MB, alloc=131.8MB, time=288.54 memory used=6808.5MB, alloc=131.8MB, time=288.58 memory used=6815.4MB, alloc=131.8MB, time=288.62 memory used=6822.4MB, alloc=131.8MB, time=288.66 memory used=6829.3MB, alloc=131.8MB, time=288.69 memory used=6836.2MB, alloc=131.8MB, time=288.74 memory used=6843.1MB, alloc=131.8MB, time=288.78 memory used=6850.0MB, alloc=131.8MB, time=288.82 memory used=6856.9MB, alloc=131.8MB, time=288.86 memory used=6863.8MB, alloc=131.8MB, time=288.90 memory used=6870.7MB, alloc=131.8MB, time=288.94 memory used=6877.6MB, alloc=131.8MB, time=288.98 memory used=6884.5MB, alloc=131.8MB, time=289.02 memory used=6891.3MB, alloc=131.8MB, time=289.07 memory used=6898.2MB, alloc=131.8MB, time=289.11 memory used=6905.1MB, alloc=131.8MB, time=289.15 memory used=6912.1MB, alloc=131.8MB, time=289.19 memory used=6919.1MB, alloc=131.8MB, time=289.23 memory used=6932.6MB, alloc=131.8MB, time=289.28 memory used=6939.7MB, alloc=131.8MB, time=289.32 memory used=6953.2MB, alloc=131.8MB, time=289.37 memory used=6960.3MB, alloc=131.8MB, time=289.41 memory used=6973.8MB, alloc=131.8MB, time=289.46 memory used=6987.5MB, alloc=131.8MB, time=289.51 memory used=7001.2MB, alloc=131.8MB, time=289.56 memory used=7014.9MB, alloc=131.8MB, time=289.62 memory used=7028.5MB, alloc=131.8MB, time=289.67 memory used=7042.2MB, alloc=131.8MB, time=289.73 memory used=7055.8MB, alloc=131.8MB, time=289.78 memory used=7069.5MB, alloc=131.8MB, time=289.83 memory used=7083.1MB, alloc=131.8MB, time=289.88 memory used=7096.7MB, alloc=131.8MB, time=289.93 memory used=7110.3MB, alloc=131.8MB, time=289.98 memory used=7123.9MB, alloc=131.8MB, time=290.03 memory used=7137.5MB, alloc=131.8MB, time=290.08 memory used=7151.0MB, alloc=131.8MB, time=290.14 memory used=7164.6MB, alloc=131.8MB, time=290.19 memory used=7178.1MB, alloc=131.8MB, time=290.24 memory used=7191.6MB, alloc=131.8MB, time=290.29 memory used=7205.1MB, alloc=131.8MB, time=290.34 memory used=7218.6MB, alloc=131.8MB, time=290.39 memory used=7232.1MB, alloc=131.8MB, time=290.45 memory used=7245.6MB, alloc=131.8MB, time=290.50 memory used=7259.0MB, alloc=131.8MB, time=290.55 memory used=7272.4MB, alloc=131.8MB, time=290.60 memory used=7285.9MB, alloc=131.8MB, time=290.65 memory used=7299.3MB, alloc=131.8MB, time=290.70 memory used=7312.7MB, alloc=131.8MB, time=290.76 memory used=7326.1MB, alloc=131.8MB, time=290.81 memory used=7339.4MB, alloc=131.8MB, time=290.86 memory used=7352.8MB, alloc=131.8MB, time=290.92 memory used=7366.1MB, alloc=131.8MB, time=290.96 memory used=7379.4MB, alloc=131.8MB, time=291.01 memory used=7392.8MB, alloc=131.8MB, time=291.07 memory used=7406.0MB, alloc=131.8MB, time=291.12 memory used=7419.3MB, alloc=131.8MB, time=291.17 memory used=7432.6MB, alloc=131.8MB, time=291.22 memory used=7445.8MB, alloc=131.8MB, time=291.27 memory used=7459.1MB, alloc=131.8MB, time=291.32 memory used=7472.3MB, alloc=131.8MB, time=291.37 memory used=7485.5MB, alloc=131.8MB, time=291.42 memory used=7498.7MB, alloc=131.8MB, time=291.48 memory used=7511.8MB, alloc=131.8MB, time=291.53 memory used=7525.0MB, alloc=131.8MB, time=291.57 memory used=7538.1MB, alloc=131.8MB, time=291.63 memory used=7551.2MB, alloc=131.8MB, time=291.68 memory used=7564.3MB, alloc=131.8MB, time=291.73 memory used=7577.4MB, alloc=131.8MB, time=291.78 memory used=7590.5MB, alloc=131.8MB, time=291.82 memory used=7603.5MB, alloc=131.8MB, time=291.87 memory used=7616.5MB, alloc=131.8MB, time=291.92 memory used=7629.5MB, alloc=131.8MB, time=291.97 memory used=7642.5MB, alloc=131.8MB, time=292.02 memory used=7655.5MB, alloc=131.8MB, time=292.06 memory used=7668.5MB, alloc=131.8MB, time=292.11 memory used=7681.4MB, alloc=131.8MB, time=292.16 memory used=7694.3MB, alloc=131.8MB, time=292.20 memory used=7707.2MB, alloc=131.8MB, time=292.25 memory used=7720.1MB, alloc=131.8MB, time=292.31 memory used=7733.0MB, alloc=131.8MB, time=292.36 memory used=7745.8MB, alloc=131.8MB, time=292.42 memory used=7758.7MB, alloc=131.8MB, time=292.46 memory used=7771.5MB, alloc=131.8MB, time=292.52 memory used=7784.3MB, alloc=131.8MB, time=292.58 memory used=7797.0MB, alloc=131.8MB, time=292.63 memory used=7809.8MB, alloc=131.8MB, time=292.68 memory used=7822.5MB, alloc=131.8MB, time=292.72 memory used=7835.2MB, alloc=131.8MB, time=292.78 memory used=7847.9MB, alloc=131.8MB, time=292.83 memory used=7860.6MB, alloc=131.8MB, time=292.88 memory used=7873.2MB, alloc=131.8MB, time=292.93 memory used=7885.9MB, alloc=131.8MB, time=292.98 memory used=7898.5MB, alloc=131.8MB, time=293.02 memory used=7911.1MB, alloc=131.8MB, time=293.08 memory used=7923.7MB, alloc=131.8MB, time=293.14 memory used=7936.2MB, alloc=131.8MB, time=293.20 memory used=7948.7MB, alloc=131.8MB, time=293.24 memory used=7961.2MB, alloc=131.8MB, time=293.29 memory used=7973.7MB, alloc=131.8MB, time=293.34 memory used=7986.2MB, alloc=131.8MB, time=293.39 memory used=7998.6MB, alloc=131.8MB, time=293.44 memory used=8011.1MB, alloc=131.8MB, time=293.48 memory used=8023.4MB, alloc=131.8MB, time=293.53 memory used=8035.8MB, alloc=131.8MB, time=293.58 memory used=8048.2MB, alloc=131.8MB, time=293.63 memory used=8060.5MB, alloc=131.8MB, time=293.68 memory used=8072.8MB, alloc=131.8MB, time=293.72 memory used=8085.1MB, alloc=131.8MB, time=293.77 memory used=8097.4MB, alloc=131.8MB, time=293.82 memory used=8109.6MB, alloc=131.8MB, time=293.87 memory used=8121.8MB, alloc=131.8MB, time=293.92 memory used=8134.0MB, alloc=131.8MB, time=293.96 memory used=8146.2MB, alloc=131.8MB, time=294.01 memory used=8158.5MB, alloc=131.8MB, time=294.07 memory used=8176.5MB, alloc=131.8MB, time=294.13 memory used=8188.9MB, alloc=131.8MB, time=294.18 memory used=8206.7MB, alloc=131.8MB, time=294.23 memory used=8224.8MB, alloc=131.8MB, time=294.29 memory used=8242.7MB, alloc=131.8MB, time=294.35 memory used=8260.6MB, alloc=131.8MB, time=294.41 memory used=8278.5MB, alloc=131.8MB, time=294.47 memory used=8296.3MB, alloc=131.8MB, time=294.52 memory used=8314.1MB, alloc=131.8MB, time=294.57 memory used=8331.9MB, alloc=131.8MB, time=294.63 memory used=8349.5MB, alloc=131.8MB, time=294.68 memory used=8367.1MB, alloc=131.8MB, time=294.74 memory used=8384.6MB, alloc=131.8MB, time=294.80 memory used=8402.1MB, alloc=131.8MB, time=294.86 memory used=8419.5MB, alloc=131.8MB, time=294.91 memory used=8436.8MB, alloc=131.8MB, time=294.96 memory used=8454.1MB, alloc=131.8MB, time=295.02 memory used=8471.4MB, alloc=131.8MB, time=295.07 memory used=8488.5MB, alloc=131.8MB, time=295.12 memory used=8505.6MB, alloc=131.8MB, time=295.18 memory used=8522.7MB, alloc=131.8MB, time=295.24 memory used=8539.7MB, alloc=131.8MB, time=295.29 memory used=8556.6MB, alloc=131.8MB, time=295.35 memory used=8573.4MB, alloc=131.8MB, time=295.40 memory used=8590.2MB, alloc=131.8MB, time=295.46 memory used=8607.0MB, alloc=131.8MB, time=295.51 memory used=8623.6MB, alloc=131.8MB, time=295.56 memory used=8640.2MB, alloc=131.8MB, time=295.62 memory used=8656.7MB, alloc=131.8MB, time=295.67 memory used=8673.2MB, alloc=131.8MB, time=295.72 memory used=8689.6MB, alloc=131.8MB, time=295.78 memory used=8705.9MB, alloc=131.8MB, time=295.84 memory used=8722.2MB, alloc=131.8MB, time=295.89 memory used=8738.4MB, alloc=131.8MB, time=295.94 memory used=8754.5MB, alloc=131.8MB, time=296.00 memory used=8770.6MB, alloc=131.8MB, time=296.05 memory used=8786.6MB, alloc=131.8MB, time=296.10 memory used=8802.5MB, alloc=131.8MB, time=296.15 memory used=8822.8MB, alloc=131.8MB, time=296.20 memory used=8836.0MB, alloc=131.8MB, time=296.25 memory used=8848.4MB, alloc=131.8MB, time=296.30 memory used=8858.8MB, alloc=131.8MB, time=296.34 memory used=8869.2MB, alloc=131.8MB, time=296.38 memory used=8879.6MB, alloc=131.8MB, time=296.43 memory used=8889.9MB, alloc=131.8MB, time=296.48 memory used=8900.1MB, alloc=131.8MB, time=296.52 memory used=8910.4MB, alloc=131.8MB, time=296.57 memory used=8920.6MB, alloc=131.8MB, time=296.61 memory used=8930.9MB, alloc=131.8MB, time=296.66 memory used=8941.2MB, alloc=131.8MB, time=296.71 memory used=8956.1MB, alloc=131.8MB, time=296.76 memory used=8971.2MB, alloc=131.8MB, time=296.81 memory used=8986.2MB, alloc=131.8MB, time=296.86 memory used=9001.1MB, alloc=131.8MB, time=296.91 memory used=9015.9MB, alloc=131.8MB, time=296.97 memory used=9030.7MB, alloc=131.8MB, time=297.02 memory used=9045.4MB, alloc=131.8MB, time=297.07 memory used=9060.0MB, alloc=131.8MB, time=297.12 memory used=9074.6MB, alloc=131.8MB, time=297.17 memory used=9089.0MB, alloc=131.8MB, time=297.22 memory used=9103.4MB, alloc=131.8MB, time=297.27 memory used=9117.7MB, alloc=131.8MB, time=297.32 memory used=9131.9MB, alloc=131.8MB, time=297.38 memory used=9146.1MB, alloc=131.8MB, time=297.43 memory used=9160.1MB, alloc=131.8MB, time=297.48 memory used=9174.1MB, alloc=131.8MB, time=297.53 memory used=9188.0MB, alloc=131.8MB, time=297.58 memory used=9201.8MB, alloc=131.8MB, time=297.63 memory used=9215.5MB, alloc=131.8MB, time=297.68 memory used=9229.2MB, alloc=131.8MB, time=297.72 memory used=9242.7MB, alloc=131.8MB, time=297.78 memory used=9256.2MB, alloc=131.8MB, time=297.83 memory used=9269.6MB, alloc=131.8MB, time=297.88 memory used=9282.9MB, alloc=131.8MB, time=297.93 memory used=9296.1MB, alloc=131.8MB, time=297.98 memory used=9309.3MB, alloc=131.8MB, time=298.03 memory used=9322.3MB, alloc=131.8MB, time=298.08 memory used=9335.5MB, alloc=131.8MB, time=298.13 memory used=9352.4MB, alloc=131.8MB, time=298.18 memory used=9369.4MB, alloc=131.8MB, time=298.24 memory used=9386.2MB, alloc=131.8MB, time=298.29 memory used=9402.9MB, alloc=131.8MB, time=298.34 memory used=9419.4MB, alloc=131.8MB, time=298.39 memory used=9435.8MB, alloc=131.8MB, time=298.45 memory used=9452.0MB, alloc=131.8MB, time=298.50 memory used=9468.0MB, alloc=131.8MB, time=298.56 memory used=9483.8MB, alloc=131.8MB, time=298.62 memory used=9499.5MB, alloc=131.8MB, time=298.67 memory used=9515.0MB, alloc=131.8MB, time=298.72 memory used=9530.4MB, alloc=131.8MB, time=298.77 memory used=9545.6MB, alloc=131.8MB, time=298.83 memory used=9560.7MB, alloc=131.8MB, time=298.88 memory used=9579.2MB, alloc=131.8MB, time=298.94 memory used=9597.5MB, alloc=131.8MB, time=299.00 memory used=9615.5MB, alloc=131.8MB, time=299.06 memory used=9633.2MB, alloc=131.8MB, time=299.11 memory used=9650.6MB, alloc=131.8MB, time=299.17 memory used=9667.8MB, alloc=131.8MB, time=299.22 memory used=9684.7MB, alloc=131.8MB, time=299.27 memory used=9701.5MB, alloc=131.8MB, time=299.32 memory used=9720.8MB, alloc=131.8MB, time=299.38 memory used=9739.9MB, alloc=131.8MB, time=299.44 memory used=9758.6MB, alloc=131.8MB, time=299.49 memory used=9776.9MB, alloc=131.8MB, time=299.55 memory used=9794.8MB, alloc=131.8MB, time=299.60 memory used=9815.1MB, alloc=131.8MB, time=299.66 memory used=9834.8MB, alloc=131.8MB, time=299.71 memory used=9853.9MB, alloc=131.8MB, time=299.77 memory used=9875.0MB, alloc=131.8MB, time=299.83 memory used=9895.3MB, alloc=131.8MB, time=299.89 memory used=9915.0MB, alloc=131.8MB, time=299.94 memory used=9935.8MB, alloc=131.8MB, time=300.00 memory used=9957.9MB, alloc=131.8MB, time=300.06 memory used=9977.0MB, alloc=131.8MB, time=300.12 memory used=9998.3MB, alloc=131.8MB, time=300.18 memory used=10020.1MB, alloc=131.8MB, time=300.24 memory used=10042.4MB, alloc=131.8MB, time=300.30 memory used=10066.4MB, alloc=131.8MB, time=300.35 memory used=10149.2MB, alloc=131.8MB, time=300.66 memory used=10203.6MB, alloc=131.8MB, time=300.80 memory used=10269.8MB, alloc=131.8MB, time=300.95 memory used=10331.8MB, alloc=131.8MB, time=301.07 memory used=10379.3MB, alloc=131.8MB, time=301.18 memory used=10433.9MB, alloc=131.8MB, time=301.29 memory used=10497.3MB, alloc=131.8MB, time=301.41 memory used=10575.1MB, alloc=131.8MB, time=301.68 memory used=10636.9MB, alloc=131.8MB, time=301.84 memory used=10693.3MB, alloc=131.8MB, time=301.99 memory used=10766.3MB, alloc=131.8MB, time=302.14 memory used=10814.0MB, alloc=131.8MB, time=302.25 memory used=10864.3MB, alloc=131.8MB, time=302.35 memory used=10921.6MB, alloc=131.8MB, time=302.45 memory used=10988.3MB, alloc=131.8MB, time=302.57 memory used=11083.8MB, alloc=131.8MB, time=318.25 memory used=11144.8MB, alloc=131.8MB, time=357.16 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428510006 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 F := [2 x z - 3 x z + 12 x , 3 x + 3 y z + 2 z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 4 2 G := [10 y z + 6 x z - 16 z, 17 x - 13 x z + 16 z ] > Problem := [F,G]; 3 2 2 2 2 Problem := [[2 x z - 3 x z + 12 x , 3 x + 3 y z + 2 z ], 2 2 2 4 2 [10 y z + 6 x z - 16 z, 17 x - 13 x z + 16 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.8MB, alloc=32.3MB, time=0.51 memory used=46.9MB, alloc=60.3MB, time=0.85 memory used=89.3MB, alloc=60.3MB, time=1.36 memory used=132.9MB, alloc=68.3MB, time=1.95 memory used=175.3MB, alloc=68.3MB, time=2.52 memory used=214.5MB, alloc=92.3MB, time=3.11 memory used=277.3MB, alloc=92.3MB, time=4.04 memory used=339.6MB, alloc=92.3MB, time=4.72 memory used=389.7MB, alloc=92.3MB, time=5.06 memory used=454.2MB, alloc=92.3MB, time=5.75 memory used=515.3MB, alloc=92.3MB, time=6.44 memory used=576.9MB, alloc=116.3MB, time=7.26 memory used=645.7MB, alloc=372.3MB, time=7.96 memory used=720.3MB, alloc=372.3MB, time=8.50 memory used=774.5MB, alloc=372.3MB, time=8.73 memory used=836.2MB, alloc=372.3MB, time=9.39 memory used=922.1MB, alloc=372.3MB, time=10.55 memory used=1006.3MB, alloc=396.3MB, time=11.75 memory used=1116.8MB, alloc=396.3MB, time=13.36 memory used=1223.5MB, alloc=420.3MB, time=14.63 memory used=1348.6MB, alloc=420.3MB, time=15.92 memory used=1480.3MB, alloc=420.3MB, time=17.34 memory used=1614.9MB, alloc=444.3MB, time=19.40 memory used=1771.8MB, alloc=468.3MB, time=22.11 memory used=1934.1MB, alloc=492.3MB, time=25.13 memory used=2122.2MB, alloc=516.3MB, time=28.31 memory used=2307.9MB, alloc=540.3MB, time=32.10 memory used=2480.3MB, alloc=564.3MB, time=37.33 memory used=2647.4MB, alloc=588.3MB, time=44.31 memory used=2830.9MB, alloc=612.3MB, time=51.74 memory used=3038.4MB, alloc=636.3MB, time=59.91 memory used=3269.8MB, alloc=660.3MB, time=69.00 memory used=3525.1MB, alloc=660.3MB, time=78.77 memory used=3780.5MB, alloc=684.3MB, time=88.73 N1 := 7455 > GB := Basis(F, plex(op(vars))); 7 6 4 2 5 4 2 3 3 3 GB := [-6 x - 12 x + 9 x y - 6 x - 72 x y + 36 x y - 24 x y - 64 x , 6 5 5 5 3 2 4 2 2 6 x z + 9 x y + 6 x z - 48 x + 36 x y - 24 x - 96 x y - 64 x z, 5 4 4 4 2 2 2 2 x z + 3 x y + 2 x z - 8 x + 12 x y + 8 x y z, 3 3 2 2 2 2 2 3 x y - 2 x z + 3 x y z - 2 x z + 8 x , 2 z + 3 z y + 3 x ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=4071.0MB, alloc=684.3MB, time=98.96 memory used=4181.0MB, alloc=684.3MB, time=101.19 memory used=4288.0MB, alloc=684.3MB, time=103.16 memory used=4377.3MB, alloc=684.3MB, time=104.67 memory used=4479.8MB, alloc=684.3MB, time=106.64 memory used=4575.6MB, alloc=684.3MB, time=108.55 memory used=4665.3MB, alloc=684.3MB, time=110.23 memory used=4744.8MB, alloc=684.3MB, time=111.52 memory used=4822.1MB, alloc=684.3MB, time=112.86 memory used=4893.6MB, alloc=684.3MB, time=114.41 memory used=4955.0MB, alloc=684.3MB, time=115.95 memory used=5015.3MB, alloc=684.3MB, time=117.41 memory used=5070.7MB, alloc=684.3MB, time=118.84 memory used=5132.7MB, alloc=684.3MB, time=120.29 memory used=5186.4MB, alloc=684.3MB, time=121.86 memory used=5404.0MB, alloc=708.3MB, time=125.93 memory used=5606.5MB, alloc=732.3MB, time=129.58 memory used=5800.5MB, alloc=756.3MB, time=133.38 memory used=5974.8MB, alloc=756.3MB, time=137.08 memory used=6155.2MB, alloc=780.3MB, time=140.81 memory used=6304.1MB, alloc=780.3MB, time=144.67 memory used=6429.6MB, alloc=780.3MB, time=147.72 memory used=6570.6MB, alloc=780.3MB, time=150.98 memory used=6679.4MB, alloc=804.3MB, time=154.00 memory used=6786.6MB, alloc=804.3MB, time=156.91 memory used=6904.2MB, alloc=804.3MB, time=160.15 memory used=7032.7MB, alloc=804.3MB, time=162.32 memory used=7139.4MB, alloc=804.3MB, time=164.60 memory used=7343.5MB, alloc=804.3MB, time=167.63 memory used=7482.0MB, alloc=804.3MB, time=173.40 memory used=7574.5MB, alloc=828.3MB, time=175.74 memory used=8015.2MB, alloc=852.3MB, time=182.88 memory used=8465.9MB, alloc=876.3MB, time=189.79 memory used=8810.1MB, alloc=900.3MB, time=196.36 memory used=9160.2MB, alloc=924.3MB, time=202.83 memory used=9486.2MB, alloc=948.3MB, time=209.34 memory used=9772.6MB, alloc=972.3MB, time=216.17 memory used=10063.8MB, alloc=996.3MB, time=222.58 memory used=10339.0MB, alloc=1020.3MB, time=228.38 memory used=10571.4MB, alloc=1044.3MB, time=233.06 memory used=11248.4MB, alloc=1068.3MB, time=244.76 memory used=11933.3MB, alloc=1092.3MB, time=258.83 memory used=12621.3MB, alloc=1116.3MB, time=273.29 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428510306 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 4 3 3 2 F := [5 x z + 11 x y - 10 y , 14 x y + 5 z - 14 x ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 3 3 4 G := [18 x - 5 x y z + 4 y , 5 x z - 2 y - 8 z] > Problem := [F,G]; 3 2 2 4 3 3 2 Problem := [[5 x z + 11 x y - 10 y , 14 x y + 5 z - 14 x ], 4 2 3 3 4 [18 x - 5 x y z + 4 y , 5 x z - 2 y - 8 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=26.9MB, alloc=34.3MB, time=0.39 memory used=45.9MB, alloc=34.3MB, time=0.51 memory used=70.2MB, alloc=34.3MB, time=0.75 memory used=82.7MB, alloc=34.3MB, time=0.79 memory used=95.6MB, alloc=34.3MB, time=0.82 memory used=111.5MB, alloc=34.3MB, time=0.86 memory used=122.8MB, alloc=34.3MB, time=0.89 memory used=133.0MB, alloc=34.3MB, time=0.92 memory used=144.6MB, alloc=34.3MB, time=0.95 memory used=158.3MB, alloc=34.3MB, time=0.98 memory used=176.0MB, alloc=34.3MB, time=1.13 memory used=189.7MB, alloc=34.3MB, time=1.19 memory used=210.1MB, alloc=41.6MB, time=1.28 memory used=225.2MB, alloc=41.6MB, time=1.32 memory used=238.1MB, alloc=41.6MB, time=1.35 memory used=252.3MB, alloc=41.6MB, time=1.38 memory used=267.4MB, alloc=41.6MB, time=1.57 memory used=285.9MB, alloc=41.6MB, time=1.62 memory used=296.5MB, alloc=41.6MB, time=1.65 memory used=309.0MB, alloc=41.6MB, time=1.69 memory used=324.2MB, alloc=41.6MB, time=1.73 memory used=334.1MB, alloc=41.6MB, time=1.76 memory used=343.7MB, alloc=41.6MB, time=1.79 memory used=354.3MB, alloc=41.6MB, time=1.82 memory used=366.6MB, alloc=41.6MB, time=1.85 memory used=387.1MB, alloc=65.6MB, time=3.34 memory used=427.2MB, alloc=65.6MB, time=14.57 memory used=461.6MB, alloc=65.6MB, time=22.25 memory used=492.2MB, alloc=65.6MB, time=38.93 memory used=535.7MB, alloc=65.6MB, time=59.09 memory used=574.4MB, alloc=65.6MB, time=86.20 memory used=610.1MB, alloc=65.6MB, time=88.31 memory used=640.4MB, alloc=65.6MB, time=88.41 memory used=666.0MB, alloc=65.6MB, time=88.48 memory used=688.1MB, alloc=65.6MB, time=88.54 memory used=712.7MB, alloc=65.6MB, time=88.60 memory used=741.0MB, alloc=65.6MB, time=88.67 memory used=772.7MB, alloc=65.6MB, time=88.74 memory used=800.7MB, alloc=65.6MB, time=88.79 memory used=821.1MB, alloc=65.6MB, time=88.85 memory used=839.4MB, alloc=65.6MB, time=88.90 memory used=859.1MB, alloc=65.6MB, time=88.95 memory used=879.1MB, alloc=65.6MB, time=89.00 memory used=900.9MB, alloc=65.6MB, time=89.04 memory used=923.1MB, alloc=65.6MB, time=89.09 memory used=946.9MB, alloc=65.6MB, time=89.15 memory used=970.9MB, alloc=65.6MB, time=89.20 memory used=996.5MB, alloc=65.6MB, time=89.25 memory used=1023.6MB, alloc=65.6MB, time=89.30 memory used=1052.1MB, alloc=65.6MB, time=89.35 memory used=1081.9MB, alloc=65.6MB, time=89.41 memory used=1113.0MB, alloc=65.6MB, time=89.46 memory used=1146.3MB, alloc=65.6MB, time=89.52 memory used=1185.7MB, alloc=81.9MB, time=89.59 memory used=1197.9MB, alloc=81.9MB, time=89.62 memory used=1210.1MB, alloc=81.9MB, time=89.66 memory used=1222.3MB, alloc=81.9MB, time=89.69 memory used=1235.5MB, alloc=81.9MB, time=89.73 memory used=1248.3MB, alloc=81.9MB, time=89.76 memory used=1261.9MB, alloc=81.9MB, time=89.80 memory used=1276.2MB, alloc=81.9MB, time=89.84 memory used=1290.1MB, alloc=81.9MB, time=89.87 memory used=1304.5MB, alloc=81.9MB, time=89.91 memory used=1320.0MB, alloc=81.9MB, time=89.95 memory used=1335.6MB, alloc=81.9MB, time=89.99 memory used=1351.8MB, alloc=81.9MB, time=90.04 memory used=1368.7MB, alloc=81.9MB, time=90.08 memory used=1386.8MB, alloc=81.9MB, time=90.12 memory used=1433.5MB, alloc=81.9MB, time=90.56 memory used=1466.5MB, alloc=81.9MB, time=90.64 memory used=1490.7MB, alloc=81.9MB, time=90.71 memory used=1531.2MB, alloc=81.9MB, time=90.93 memory used=1561.9MB, alloc=81.9MB, time=91.00 memory used=1591.2MB, alloc=81.9MB, time=91.08 memory used=1619.9MB, alloc=81.9MB, time=91.14 memory used=1668.4MB, alloc=81.9MB, time=97.39 memory used=1703.9MB, alloc=81.9MB, time=111.38 memory used=1737.7MB, alloc=105.9MB, time=124.58 memory used=1791.1MB, alloc=105.9MB, time=156.33 memory used=1847.4MB, alloc=105.9MB, time=176.46 memory used=1897.0MB, alloc=105.9MB, time=177.47 memory used=1935.1MB, alloc=105.9MB, time=177.57 memory used=1977.1MB, alloc=105.9MB, time=177.67 memory used=2028.3MB, alloc=105.9MB, time=177.78 memory used=2067.7MB, alloc=105.9MB, time=177.85 memory used=2099.9MB, alloc=105.9MB, time=177.91 memory used=2133.7MB, alloc=105.9MB, time=177.98 memory used=2170.2MB, alloc=105.9MB, time=178.05 memory used=2210.3MB, alloc=105.9MB, time=178.11 memory used=2252.7MB, alloc=105.9MB, time=178.20 memory used=2299.5MB, alloc=105.9MB, time=178.27 memory used=2349.4MB, alloc=105.9MB, time=178.35 memory used=2403.0MB, alloc=105.9MB, time=178.43 memory used=2434.4MB, alloc=107.8MB, time=178.52 memory used=2445.5MB, alloc=107.8MB, time=178.56 memory used=2456.3MB, alloc=107.8MB, time=178.62 memory used=2467.3MB, alloc=107.8MB, time=178.67 memory used=2479.3MB, alloc=107.8MB, time=178.71 memory used=2491.1MB, alloc=107.8MB, time=178.75 memory used=2503.7MB, alloc=107.8MB, time=178.79 memory used=2516.0MB, alloc=107.8MB, time=178.83 memory used=2529.0MB, alloc=107.8MB, time=178.88 memory used=2541.8MB, alloc=107.8MB, time=178.91 memory used=2554.8MB, alloc=107.8MB, time=178.96 memory used=2568.4MB, alloc=107.8MB, time=179.00 memory used=2582.3MB, alloc=107.8MB, time=179.03 memory used=2596.8MB, alloc=107.8MB, time=179.08 memory used=2611.9MB, alloc=107.8MB, time=179.12 memory used=2627.6MB, alloc=107.8MB, time=179.17 memory used=2644.7MB, alloc=107.8MB, time=179.21 memory used=2696.0MB, alloc=107.8MB, time=179.68 memory used=2747.1MB, alloc=107.8MB, time=179.89 memory used=2789.6MB, alloc=107.8MB, time=179.96 memory used=2814.4MB, alloc=107.8MB, time=180.03 memory used=2836.2MB, alloc=107.8MB, time=180.09 memory used=2886.5MB, alloc=107.8MB, time=180.18 memory used=2924.2MB, alloc=107.8MB, time=180.48 memory used=2948.3MB, alloc=107.8MB, time=180.56 memory used=2973.7MB, alloc=107.8MB, time=180.62 memory used=3000.4MB, alloc=107.8MB, time=180.71 memory used=3028.4MB, alloc=107.8MB, time=180.78 memory used=3057.6MB, alloc=107.8MB, time=180.86 memory used=3088.1MB, alloc=107.8MB, time=180.93 memory used=3122.3MB, alloc=107.8MB, time=180.99 memory used=3172.9MB, alloc=107.8MB, time=181.08 memory used=3188.9MB, alloc=107.8MB, time=181.12 memory used=3203.8MB, alloc=107.8MB, time=181.17 memory used=3218.9MB, alloc=107.8MB, time=181.21 memory used=3234.3MB, alloc=107.8MB, time=181.26 memory used=3249.9MB, alloc=107.8MB, time=181.30 memory used=3265.7MB, alloc=107.8MB, time=181.35 memory used=3281.7MB, alloc=107.8MB, time=181.39 memory used=3298.0MB, alloc=107.8MB, time=181.44 memory used=3314.5MB, alloc=107.8MB, time=181.51 memory used=3386.7MB, alloc=107.8MB, time=182.65 memory used=3459.6MB, alloc=107.8MB, time=198.26 memory used=3516.4MB, alloc=107.8MB, time=224.84 memory used=3571.3MB, alloc=107.8MB, time=261.97 memory used=3620.8MB, alloc=107.8MB, time=293.76 memory used=3675.2MB, alloc=107.8MB, time=296.42 memory used=3715.2MB, alloc=107.8MB, time=296.55 memory used=3751.8MB, alloc=107.8MB, time=296.66 memory used=3796.1MB, alloc=107.8MB, time=296.76 memory used=3842.7MB, alloc=107.8MB, time=296.87 memory used=3874.1MB, alloc=107.8MB, time=296.95 memory used=3904.6MB, alloc=107.8MB, time=297.03 memory used=3936.6MB, alloc=107.8MB, time=297.10 memory used=3971.0MB, alloc=107.8MB, time=297.18 memory used=4008.8MB, alloc=107.8MB, time=297.26 memory used=4048.8MB, alloc=107.8MB, time=297.35 memory used=4092.1MB, alloc=107.8MB, time=297.43 memory used=4138.4MB, alloc=107.8MB, time=297.51 memory used=4187.3MB, alloc=107.8MB, time=297.61 memory used=4238.9MB, alloc=107.8MB, time=297.72 memory used=4250.7MB, alloc=107.8MB, time=297.76 memory used=4262.7MB, alloc=107.8MB, time=297.82 memory used=4275.3MB, alloc=107.8MB, time=297.87 memory used=4287.8MB, alloc=107.8MB, time=297.91 memory used=4301.2MB, alloc=107.8MB, time=297.96 memory used=4314.3MB, alloc=107.8MB, time=298.00 memory used=4328.2MB, alloc=107.8MB, time=298.04 memory used=4341.7MB, alloc=107.8MB, time=298.09 memory used=4355.9MB, alloc=107.8MB, time=298.13 memory used=4370.6MB, alloc=107.8MB, time=298.19 memory used=4385.6MB, alloc=107.8MB, time=298.24 memory used=4400.8MB, alloc=107.8MB, time=298.30 memory used=4416.6MB, alloc=107.8MB, time=298.35 memory used=4433.6MB, alloc=107.8MB, time=298.40 memory used=4451.3MB, alloc=107.8MB, time=298.45 memory used=4532.6MB, alloc=107.8MB, time=300.52 memory used=4580.2MB, alloc=363.8MB, time=300.98 memory used=4650.1MB, alloc=363.8MB, time=313.85 memory used=4709.2MB, alloc=363.8MB, time=334.19 memory used=4757.9MB, alloc=363.8MB, time=335.15 memory used=4794.7MB, alloc=363.8MB, time=335.28 memory used=4840.5MB, alloc=363.8MB, time=335.40 memory used=4884.0MB, alloc=363.8MB, time=335.52 memory used=4915.3MB, alloc=363.8MB, time=335.62 memory used=4950.2MB, alloc=363.8MB, time=335.72 memory used=4989.7MB, alloc=363.8MB, time=335.79 memory used=5033.8MB, alloc=363.8MB, time=335.87 memory used=5081.2MB, alloc=363.8MB, time=335.95 memory used=5196.6MB, alloc=363.8MB, time=336.50 memory used=5282.3MB, alloc=363.8MB, time=337.15 memory used=5341.7MB, alloc=363.8MB, time=337.64 memory used=5388.6MB, alloc=363.8MB, time=337.87 memory used=5444.8MB, alloc=363.8MB, time=339.05 memory used=5488.3MB, alloc=363.8MB, time=339.21 memory used=5520.0MB, alloc=363.8MB, time=339.32 memory used=5559.0MB, alloc=363.8MB, time=339.45 memory used=5603.4MB, alloc=363.8MB, time=339.57 memory used=5641.7MB, alloc=363.8MB, time=339.68 memory used=5667.0MB, alloc=363.8MB, time=339.79 memory used=5693.0MB, alloc=363.8MB, time=339.92 memory used=5721.8MB, alloc=363.8MB, time=340.05 memory used=5751.5MB, alloc=363.8MB, time=340.14 memory used=5782.2MB, alloc=363.8MB, time=340.26 memory used=5813.8MB, alloc=363.8MB, time=340.38 memory used=5846.7MB, alloc=363.8MB, time=340.50 memory used=5883.4MB, alloc=363.8MB, time=340.60 memory used=5921.3MB, alloc=363.8MB, time=340.71 memory used=5960.0MB, alloc=363.8MB, time=340.81 memory used=5999.7MB, alloc=363.8MB, time=340.92 memory used=6044.1MB, alloc=363.8MB, time=341.03 memory used=6089.1MB, alloc=363.8MB, time=341.14 memory used=6125.7MB, alloc=363.8MB, time=341.26 memory used=6152.4MB, alloc=363.8MB, time=341.35 memory used=6175.4MB, alloc=387.8MB, time=341.43 memory used=6209.2MB, alloc=387.8MB, time=341.52 memory used=6246.6MB, alloc=387.8MB, time=341.61 memory used=6285.0MB, alloc=387.8MB, time=341.69 memory used=6323.5MB, alloc=387.8MB, time=341.78 memory used=6362.9MB, alloc=387.8MB, time=341.89 memory used=6405.4MB, alloc=387.8MB, time=342.03 memory used=6448.4MB, alloc=387.8MB, time=342.12 memory used=6491.6MB, alloc=387.8MB, time=342.23 memory used=6538.8MB, alloc=387.8MB, time=342.33 memory used=6585.9MB, alloc=387.8MB, time=342.46 memory used=6636.7MB, alloc=387.8MB, time=342.57 memory used=6687.2MB, alloc=387.8MB, time=342.69 memory used=6741.1MB, alloc=387.8MB, time=342.79 memory used=6795.3MB, alloc=387.8MB, time=342.89 memory used=6854.1MB, alloc=387.8MB, time=343.01 memory used=6913.2MB, alloc=387.8MB, time=343.14 memory used=6976.1MB, alloc=387.8MB, time=343.27 memory used=7041.8MB, alloc=387.8MB, time=343.40 memory used=7121.2MB, alloc=387.8MB, time=343.52 memory used=7317.3MB, alloc=387.8MB, time=345.12 memory used=7373.2MB, alloc=387.8MB, time=345.31 memory used=7429.7MB, alloc=387.8MB, time=345.50 memory used=7495.5MB, alloc=387.8MB, time=345.67 memory used=7536.7MB, alloc=387.8MB, time=345.83 memory used=7579.1MB, alloc=387.8MB, time=345.96 memory used=7623.0MB, alloc=387.8MB, time=346.13 memory used=7671.4MB, alloc=387.8MB, time=346.30 memory used=7722.6MB, alloc=387.8MB, time=346.46 memory used=7779.5MB, alloc=387.8MB, time=346.61 memory used=7838.5MB, alloc=387.8MB, time=346.74 memory used=7903.5MB, alloc=387.8MB, time=346.88 memory used=7970.5MB, alloc=387.8MB, time=347.01 memory used=8017.0MB, alloc=387.8MB, time=347.13 memory used=8053.3MB, alloc=387.8MB, time=347.23 memory used=8090.3MB, alloc=387.8MB, time=347.32 memory used=8128.6MB, alloc=387.8MB, time=347.40 memory used=8167.0MB, alloc=387.8MB, time=347.49 memory used=8205.7MB, alloc=387.8MB, time=347.60 memory used=8245.4MB, alloc=387.8MB, time=347.68 memory used=8287.6MB, alloc=387.8MB, time=347.77 memory used=8330.7MB, alloc=387.8MB, time=347.86 memory used=8374.7MB, alloc=387.8MB, time=347.96 memory used=8420.9MB, alloc=387.8MB, time=348.06 memory used=8468.6MB, alloc=387.8MB, time=348.15 memory used=8518.6MB, alloc=387.8MB, time=348.26 memory used=8569.8MB, alloc=387.8MB, time=348.35 memory used=8623.3MB, alloc=387.8MB, time=348.45 memory used=8679.4MB, alloc=387.8MB, time=348.55 memory used=8738.8MB, alloc=387.8MB, time=348.66 memory used=8800.1MB, alloc=387.8MB, time=348.77 memory used=8864.0MB, alloc=387.8MB, time=348.87 memory used=8931.3MB, alloc=387.8MB, time=348.98 memory used=9127.4MB, alloc=387.8MB, time=349.38 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428510606 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 3 3 F := [-8 x y + 8 x z - 13 y , -7 y z - 8 y - 9 x z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 4 3 2 G := [2 y + 10 x y z - 19 x, 8 z + 3 y - 6 z ] > Problem := [F,G]; 2 2 3 3 3 Problem := [[-8 x y + 8 x z - 13 y , -7 y z - 8 y - 9 x z], 4 4 3 2 [2 y + 10 x y z - 19 x, 8 z + 3 y - 6 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.19 memory used=30.1MB, alloc=36.8MB, time=0.53 memory used=52.6MB, alloc=60.8MB, time=1.31 memory used=87.0MB, alloc=61.5MB, time=1.40 memory used=110.9MB, alloc=61.5MB, time=1.48 memory used=138.1MB, alloc=61.5MB, time=1.55 memory used=169.7MB, alloc=61.5MB, time=1.64 memory used=206.7MB, alloc=61.5MB, time=1.74 memory used=228.0MB, alloc=61.5MB, time=1.80 memory used=248.4MB, alloc=61.5MB, time=1.87 memory used=267.9MB, alloc=61.5MB, time=1.95 memory used=290.2MB, alloc=61.5MB, time=2.03 memory used=313.2MB, alloc=61.5MB, time=2.10 memory used=336.8MB, alloc=61.5MB, time=2.16 memory used=360.9MB, alloc=61.5MB, time=2.22 memory used=388.3MB, alloc=61.5MB, time=2.28 memory used=416.2MB, alloc=61.5MB, time=2.34 memory used=444.5MB, alloc=61.5MB, time=2.40 memory used=476.1MB, alloc=61.5MB, time=2.45 memory used=508.0MB, alloc=61.5MB, time=2.51 memory used=543.2MB, alloc=61.5MB, time=2.60 memory used=578.2MB, alloc=61.5MB, time=2.66 memory used=598.4MB, alloc=61.5MB, time=2.71 memory used=616.4MB, alloc=61.5MB, time=2.75 memory used=634.7MB, alloc=61.5MB, time=2.82 memory used=652.9MB, alloc=61.5MB, time=2.87 memory used=671.0MB, alloc=61.5MB, time=2.92 memory used=689.2MB, alloc=61.5MB, time=2.96 memory used=709.4MB, alloc=61.5MB, time=3.02 memory used=729.6MB, alloc=61.5MB, time=3.06 memory used=749.9MB, alloc=61.5MB, time=3.11 memory used=771.6MB, alloc=61.5MB, time=3.15 memory used=793.5MB, alloc=61.5MB, time=3.19 memory used=816.7MB, alloc=61.5MB, time=3.24 memory used=841.9MB, alloc=61.5MB, time=3.28 memory used=868.2MB, alloc=61.5MB, time=3.33 memory used=895.2MB, alloc=61.5MB, time=3.37 memory used=923.7MB, alloc=61.5MB, time=3.42 memory used=953.6MB, alloc=61.5MB, time=3.46 memory used=997.0MB, alloc=61.5MB, time=4.21 memory used=1025.6MB, alloc=61.5MB, time=4.29 memory used=1050.6MB, alloc=61.5MB, time=4.38 memory used=1078.4MB, alloc=61.5MB, time=4.47 memory used=1111.0MB, alloc=61.5MB, time=4.55 memory used=1143.7MB, alloc=61.5MB, time=4.64 memory used=1163.1MB, alloc=61.5MB, time=4.71 memory used=1183.0MB, alloc=61.5MB, time=4.76 memory used=1202.2MB, alloc=61.5MB, time=4.82 memory used=1222.3MB, alloc=61.5MB, time=4.87 memory used=1245.0MB, alloc=61.5MB, time=4.92 memory used=1268.6MB, alloc=61.5MB, time=4.99 memory used=1292.5MB, alloc=61.5MB, time=5.05 memory used=1317.2MB, alloc=61.5MB, time=5.10 memory used=1344.7MB, alloc=61.5MB, time=5.16 memory used=1372.9MB, alloc=61.5MB, time=5.23 memory used=1401.6MB, alloc=61.5MB, time=5.30 memory used=1433.1MB, alloc=61.5MB, time=5.36 memory used=1465.1MB, alloc=61.5MB, time=5.43 memory used=1500.0MB, alloc=61.5MB, time=5.49 memory used=1524.2MB, alloc=61.5MB, time=5.54 memory used=1539.5MB, alloc=61.5MB, time=5.58 memory used=1557.4MB, alloc=61.5MB, time=5.62 memory used=1575.7MB, alloc=61.5MB, time=5.67 memory used=1593.7MB, alloc=61.5MB, time=5.72 memory used=1611.7MB, alloc=61.5MB, time=5.76 memory used=1629.8MB, alloc=61.5MB, time=5.80 memory used=1649.8MB, alloc=61.5MB, time=5.85 memory used=1669.8MB, alloc=61.5MB, time=5.90 memory used=1689.9MB, alloc=61.5MB, time=5.95 memory used=1711.5MB, alloc=61.5MB, time=5.99 memory used=1733.3MB, alloc=61.5MB, time=6.04 memory used=1756.0MB, alloc=61.5MB, time=6.08 memory used=1780.9MB, alloc=61.5MB, time=6.13 memory used=1806.7MB, alloc=61.5MB, time=6.18 memory used=1833.2MB, alloc=61.5MB, time=6.23 memory used=1861.3MB, alloc=61.5MB, time=6.28 memory used=1891.0MB, alloc=61.5MB, time=6.33 memory used=1931.6MB, alloc=85.5MB, time=15.22 memory used=1984.9MB, alloc=85.5MB, time=43.25 memory used=2045.6MB, alloc=85.5MB, time=67.48 memory used=2103.9MB, alloc=85.5MB, time=109.76 memory used=2141.0MB, alloc=109.5MB, time=138.28 memory used=2190.5MB, alloc=109.5MB, time=194.80 memory used=2241.9MB, alloc=109.5MB, time=206.88 memory used=2310.5MB, alloc=109.5MB, time=208.32 memory used=2359.7MB, alloc=109.5MB, time=208.43 memory used=2421.8MB, alloc=109.5MB, time=208.56 memory used=2485.6MB, alloc=109.5MB, time=208.68 memory used=2527.6MB, alloc=109.5MB, time=208.76 memory used=2572.9MB, alloc=109.5MB, time=208.84 memory used=2622.6MB, alloc=109.5MB, time=208.94 memory used=2676.3MB, alloc=109.5MB, time=209.03 memory used=2734.1MB, alloc=109.5MB, time=209.12 memory used=2796.0MB, alloc=109.5MB, time=209.22 memory used=2861.5MB, alloc=109.5MB, time=209.31 memory used=2932.7MB, alloc=109.5MB, time=209.41 memory used=2986.3MB, alloc=131.8MB, time=209.52 memory used=2996.2MB, alloc=131.8MB, time=209.56 memory used=3006.9MB, alloc=131.8MB, time=209.60 memory used=3017.6MB, alloc=131.8MB, time=209.65 memory used=3028.3MB, alloc=131.8MB, time=209.69 memory used=3039.0MB, alloc=131.8MB, time=209.73 memory used=3049.7MB, alloc=131.8MB, time=209.76 memory used=3060.3MB, alloc=131.8MB, time=209.80 memory used=3071.0MB, alloc=131.8MB, time=209.84 memory used=3081.6MB, alloc=131.8MB, time=209.87 memory used=3092.4MB, alloc=131.8MB, time=209.91 memory used=3105.0MB, alloc=131.8MB, time=209.95 memory used=3117.7MB, alloc=131.8MB, time=209.99 memory used=3130.3MB, alloc=131.8MB, time=210.03 memory used=3143.0MB, alloc=131.8MB, time=210.07 memory used=3155.6MB, alloc=131.8MB, time=210.10 memory used=3168.1MB, alloc=131.8MB, time=210.14 memory used=3180.6MB, alloc=131.8MB, time=210.18 memory used=3193.1MB, alloc=131.8MB, time=210.22 memory used=3205.5MB, alloc=131.8MB, time=210.26 memory used=3218.0MB, alloc=131.8MB, time=210.30 memory used=3232.2MB, alloc=131.8MB, time=210.34 memory used=3246.4MB, alloc=131.8MB, time=210.38 memory used=3260.6MB, alloc=131.8MB, time=210.43 memory used=3274.7MB, alloc=131.8MB, time=210.47 memory used=3288.6MB, alloc=131.8MB, time=210.52 memory used=3302.5MB, alloc=131.8MB, time=210.56 memory used=3316.4MB, alloc=131.8MB, time=210.60 memory used=3331.8MB, alloc=131.8MB, time=210.65 memory used=3347.2MB, alloc=131.8MB, time=210.69 memory used=3362.5MB, alloc=131.8MB, time=210.73 memory used=3377.6MB, alloc=131.8MB, time=210.78 memory used=3392.7MB, alloc=131.8MB, time=210.83 memory used=3409.0MB, alloc=131.8MB, time=210.87 memory used=3425.3MB, alloc=131.8MB, time=210.91 memory used=3441.3MB, alloc=131.8MB, time=210.96 memory used=3458.8MB, alloc=131.8MB, time=211.00 memory used=3476.1MB, alloc=131.8MB, time=211.05 memory used=3494.6MB, alloc=131.8MB, time=211.10 memory used=3512.5MB, alloc=131.8MB, time=211.14 memory used=3531.6MB, alloc=131.8MB, time=211.19 memory used=3550.0MB, alloc=131.8MB, time=211.23 memory used=3569.3MB, alloc=131.8MB, time=211.29 memory used=3589.2MB, alloc=131.8MB, time=211.34 memory used=3609.4MB, alloc=131.8MB, time=211.38 memory used=3630.0MB, alloc=131.8MB, time=211.43 memory used=3651.3MB, alloc=131.8MB, time=211.48 memory used=3673.8MB, alloc=131.8MB, time=211.53 memory used=3697.5MB, alloc=131.8MB, time=211.58 memory used=3789.6MB, alloc=131.8MB, time=212.53 memory used=3850.9MB, alloc=131.8MB, time=212.69 memory used=3924.7MB, alloc=131.8MB, time=212.86 memory used=3975.3MB, alloc=131.8MB, time=212.99 memory used=4024.7MB, alloc=131.8MB, time=213.10 memory used=4080.1MB, alloc=131.8MB, time=213.23 memory used=4143.6MB, alloc=131.8MB, time=213.37 memory used=4213.1MB, alloc=131.8MB, time=213.49 memory used=4290.7MB, alloc=131.8MB, time=213.63 memory used=4341.3MB, alloc=131.8MB, time=213.73 memory used=4385.1MB, alloc=131.8MB, time=213.82 memory used=4431.7MB, alloc=131.8MB, time=213.91 memory used=4480.0MB, alloc=131.8MB, time=214.00 memory used=4532.0MB, alloc=131.8MB, time=214.08 memory used=4589.1MB, alloc=131.8MB, time=214.17 memory used=4650.6MB, alloc=131.8MB, time=214.26 memory used=4733.2MB, alloc=131.8MB, time=215.05 memory used=4793.1MB, alloc=131.8MB, time=215.20 memory used=4867.2MB, alloc=131.8MB, time=215.36 memory used=4916.5MB, alloc=131.8MB, time=215.48 memory used=4967.7MB, alloc=131.8MB, time=215.59 memory used=5023.1MB, alloc=131.8MB, time=215.71 memory used=5086.8MB, alloc=131.8MB, time=215.84 memory used=5156.3MB, alloc=131.8MB, time=215.98 memory used=5233.8MB, alloc=131.8MB, time=216.11 memory used=5282.9MB, alloc=131.8MB, time=216.20 memory used=5325.1MB, alloc=131.8MB, time=216.28 memory used=5371.6MB, alloc=131.8MB, time=216.37 memory used=5420.0MB, alloc=131.8MB, time=216.46 memory used=5472.0MB, alloc=131.8MB, time=216.56 memory used=5529.1MB, alloc=131.8MB, time=216.66 memory used=5590.4MB, alloc=131.8MB, time=216.75 memory used=5672.7MB, alloc=131.8MB, time=225.65 memory used=5752.0MB, alloc=131.8MB, time=272.26 memory used=5842.0MB, alloc=131.8MB, time=319.96 memory used=5893.1MB, alloc=131.8MB, time=375.92 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428510906 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 2 3 2 F := [6 x y + 19 x y z + 6 x z , 11 x y - 8 x y - x y ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 4 2 2 G := [6 x y + 7 y z + 19 z , 2 x + x y z + 3 x y ] > Problem := [F,G]; 2 2 2 3 2 2 3 2 Problem := [[6 x y + 19 x y z + 6 x z , 11 x y - 8 x y - x y ], 2 2 3 4 2 2 [6 x y + 7 y z + 19 z , 2 x + x y z + 3 x y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=24.7MB, alloc=32.3MB, time=0.48 memory used=45.2MB, alloc=60.3MB, time=0.79 memory used=92.0MB, alloc=60.3MB, time=1.32 memory used=124.3MB, alloc=60.3MB, time=1.49 memory used=167.9MB, alloc=61.5MB, time=1.94 memory used=191.9MB, alloc=61.5MB, time=2.00 memory used=245.4MB, alloc=61.5MB, time=2.61 memory used=296.0MB, alloc=61.5MB, time=3.20 memory used=335.4MB, alloc=61.5MB, time=3.72 memory used=377.7MB, alloc=69.5MB, time=4.25 memory used=407.1MB, alloc=69.5MB, time=5.30 memory used=433.1MB, alloc=69.5MB, time=5.48 memory used=454.5MB, alloc=69.5MB, time=5.58 memory used=483.2MB, alloc=69.5MB, time=5.82 memory used=528.8MB, alloc=93.5MB, time=6.35 memory used=596.1MB, alloc=93.5MB, time=7.58 memory used=664.9MB, alloc=93.5MB, time=8.46 memory used=720.9MB, alloc=93.5MB, time=9.14 memory used=754.1MB, alloc=117.5MB, time=9.29 memory used=794.0MB, alloc=117.5MB, time=9.46 memory used=840.4MB, alloc=117.5MB, time=9.62 memory used=895.1MB, alloc=117.5MB, time=9.79 memory used=944.6MB, alloc=117.5MB, time=9.95 memory used=978.0MB, alloc=117.5MB, time=10.08 memory used=1013.4MB, alloc=117.5MB, time=10.21 memory used=1052.5MB, alloc=117.5MB, time=10.37 memory used=1095.2MB, alloc=117.5MB, time=10.50 memory used=1142.5MB, alloc=117.5MB, time=10.64 memory used=1194.4MB, alloc=117.5MB, time=10.80 memory used=1252.8MB, alloc=117.5MB, time=10.93 memory used=1316.3MB, alloc=117.5MB, time=11.50 memory used=1364.1MB, alloc=117.5MB, time=11.70 memory used=1412.1MB, alloc=117.5MB, time=11.87 memory used=1470.8MB, alloc=117.5MB, time=12.04 memory used=1506.6MB, alloc=117.5MB, time=12.19 memory used=1547.0MB, alloc=117.5MB, time=12.35 memory used=1594.4MB, alloc=117.5MB, time=12.48 memory used=1655.5MB, alloc=117.5MB, time=12.86 memory used=1716.5MB, alloc=117.5MB, time=15.70 memory used=1785.2MB, alloc=117.5MB, time=36.87 memory used=1850.5MB, alloc=117.5MB, time=55.41 memory used=1942.1MB, alloc=117.5MB, time=55.99 memory used=2009.2MB, alloc=117.5MB, time=56.32 memory used=2058.5MB, alloc=117.5MB, time=56.47 memory used=2096.4MB, alloc=117.5MB, time=56.61 memory used=2142.2MB, alloc=117.5MB, time=56.77 memory used=2196.4MB, alloc=117.5MB, time=56.92 memory used=2239.0MB, alloc=117.5MB, time=57.03 memory used=2272.3MB, alloc=117.5MB, time=57.13 memory used=2308.9MB, alloc=117.5MB, time=57.24 memory used=2348.6MB, alloc=117.5MB, time=57.34 memory used=2391.7MB, alloc=117.5MB, time=57.44 memory used=2440.5MB, alloc=117.5MB, time=57.55 memory used=2513.0MB, alloc=118.1MB, time=58.30 memory used=2557.1MB, alloc=118.1MB, time=58.47 memory used=2600.1MB, alloc=118.1MB, time=58.62 memory used=2650.7MB, alloc=118.1MB, time=58.77 memory used=2709.0MB, alloc=118.1MB, time=58.95 memory used=2743.9MB, alloc=118.1MB, time=59.08 memory used=2779.1MB, alloc=118.1MB, time=59.22 memory used=2816.4MB, alloc=118.1MB, time=59.34 memory used=2857.4MB, alloc=118.1MB, time=59.47 memory used=2901.4MB, alloc=118.1MB, time=59.62 memory used=2949.4MB, alloc=118.1MB, time=59.75 memory used=3002.7MB, alloc=118.1MB, time=59.87 memory used=3051.8MB, alloc=118.1MB, time=59.99 memory used=3111.8MB, alloc=118.1MB, time=60.36 memory used=3167.7MB, alloc=118.1MB, time=60.81 memory used=3227.6MB, alloc=118.1MB, time=61.00 memory used=3270.9MB, alloc=118.1MB, time=61.15 memory used=3325.8MB, alloc=118.1MB, time=61.33 memory used=3369.9MB, alloc=118.1MB, time=61.46 memory used=3407.3MB, alloc=118.1MB, time=61.61 memory used=3451.3MB, alloc=118.1MB, time=61.75 memory used=3506.7MB, alloc=118.1MB, time=62.03 memory used=3559.8MB, alloc=118.1MB, time=62.23 memory used=3618.7MB, alloc=121.5MB, time=62.55 memory used=3635.3MB, alloc=131.8MB, time=62.64 memory used=3684.1MB, alloc=131.8MB, time=62.78 memory used=3759.7MB, alloc=131.8MB, time=78.13 memory used=3823.1MB, alloc=131.8MB, time=103.36 memory used=3911.0MB, alloc=131.8MB, time=105.00 memory used=3993.4MB, alloc=131.8MB, time=105.45 memory used=4043.5MB, alloc=131.8MB, time=105.60 memory used=4080.7MB, alloc=131.8MB, time=105.75 memory used=4122.6MB, alloc=131.8MB, time=105.90 memory used=4172.7MB, alloc=131.8MB, time=106.03 memory used=4224.6MB, alloc=131.8MB, time=106.17 memory used=4257.0MB, alloc=131.8MB, time=106.27 memory used=4292.0MB, alloc=131.8MB, time=106.39 memory used=4330.7MB, alloc=131.8MB, time=106.50 memory used=4372.2MB, alloc=131.8MB, time=106.60 memory used=4417.7MB, alloc=131.8MB, time=106.71 memory used=4476.3MB, alloc=131.8MB, time=107.16 memory used=4522.6MB, alloc=131.8MB, time=107.38 memory used=4572.3MB, alloc=131.8MB, time=107.52 memory used=4604.6MB, alloc=131.8MB, time=107.77 memory used=4630.4MB, alloc=131.8MB, time=107.86 memory used=4658.6MB, alloc=131.8MB, time=107.97 memory used=4689.3MB, alloc=131.8MB, time=108.08 memory used=4722.5MB, alloc=131.8MB, time=108.18 memory used=4758.1MB, alloc=131.8MB, time=108.28 memory used=4796.4MB, alloc=131.8MB, time=108.38 memory used=4818.2MB, alloc=131.8MB, time=108.99 memory used=4892.2MB, alloc=131.8MB, time=114.39 memory used=4940.4MB, alloc=155.8MB, time=114.65 memory used=4990.5MB, alloc=155.8MB, time=114.93 memory used=5036.0MB, alloc=155.8MB, time=115.15 memory used=5080.7MB, alloc=155.8MB, time=115.35 memory used=5124.1MB, alloc=155.8MB, time=115.59 memory used=5171.3MB, alloc=155.8MB, time=115.78 memory used=5220.3MB, alloc=155.8MB, time=115.98 memory used=5270.9MB, alloc=155.8MB, time=116.17 memory used=5323.2MB, alloc=155.8MB, time=116.38 memory used=5377.1MB, alloc=155.8MB, time=116.60 memory used=5432.5MB, alloc=155.8MB, time=116.79 memory used=5489.5MB, alloc=179.8MB, time=117.01 memory used=5571.1MB, alloc=179.8MB, time=117.27 memory used=5658.1MB, alloc=179.8MB, time=117.53 memory used=5728.5MB, alloc=179.8MB, time=117.84 memory used=5782.0MB, alloc=179.8MB, time=118.04 memory used=5830.1MB, alloc=179.8MB, time=118.27 memory used=5879.3MB, alloc=179.8MB, time=118.47 memory used=5923.9MB, alloc=179.8MB, time=118.65 memory used=5971.6MB, alloc=179.8MB, time=118.83 memory used=6019.8MB, alloc=179.8MB, time=119.03 memory used=6068.5MB, alloc=179.8MB, time=119.23 memory used=6117.8MB, alloc=179.8MB, time=119.42 memory used=6167.6MB, alloc=179.8MB, time=119.60 memory used=6217.9MB, alloc=179.8MB, time=119.79 memory used=6268.7MB, alloc=179.8MB, time=119.97 memory used=6320.0MB, alloc=179.8MB, time=120.20 memory used=6371.6MB, alloc=179.8MB, time=120.42 memory used=6423.8MB, alloc=179.8MB, time=120.62 memory used=6476.3MB, alloc=203.8MB, time=120.82 memory used=6546.6MB, alloc=203.8MB, time=121.04 memory used=6621.7MB, alloc=203.8MB, time=121.31 memory used=6697.5MB, alloc=203.8MB, time=121.56 memory used=6774.0MB, alloc=203.8MB, time=121.82 memory used=6851.4MB, alloc=203.8MB, time=122.09 memory used=6940.2MB, alloc=203.8MB, time=122.37 memory used=7029.6MB, alloc=203.8MB, time=122.61 memory used=7119.6MB, alloc=203.8MB, time=122.89 memory used=7210.2MB, alloc=203.8MB, time=123.13 memory used=7301.3MB, alloc=203.8MB, time=123.36 memory used=7393.2MB, alloc=203.8MB, time=123.66 memory used=7496.5MB, alloc=203.8MB, time=123.91 memory used=7600.2MB, alloc=203.8MB, time=124.17 memory used=7704.1MB, alloc=203.8MB, time=124.44 memory used=7808.2MB, alloc=203.8MB, time=124.69 memory used=7912.7MB, alloc=203.8MB, time=124.95 memory used=8014.8MB, alloc=203.8MB, time=125.19 memory used=8078.8MB, alloc=203.8MB, time=125.34 memory used=8125.6MB, alloc=203.8MB, time=125.52 memory used=8180.2MB, alloc=227.8MB, time=125.68 memory used=8239.3MB, alloc=227.8MB, time=125.84 memory used=8306.9MB, alloc=227.8MB, time=126.03 memory used=8374.9MB, alloc=227.8MB, time=126.20 memory used=8442.6MB, alloc=227.8MB, time=126.38 memory used=8510.2MB, alloc=227.8MB, time=126.56 memory used=8577.4MB, alloc=227.8MB, time=126.74 memory used=8644.4MB, alloc=227.8MB, time=126.92 memory used=8711.3MB, alloc=227.8MB, time=127.13 memory used=8788.5MB, alloc=227.8MB, time=127.37 memory used=8865.3MB, alloc=227.8MB, time=127.58 memory used=8941.5MB, alloc=227.8MB, time=127.77 memory used=9017.1MB, alloc=227.8MB, time=127.95 memory used=9092.1MB, alloc=227.8MB, time=128.16 memory used=9167.4MB, alloc=227.8MB, time=128.33 memory used=9250.4MB, alloc=227.8MB, time=128.54 memory used=9333.2MB, alloc=227.8MB, time=128.71 memory used=9415.2MB, alloc=227.8MB, time=128.91 memory used=9505.8MB, alloc=227.8MB, time=129.10 memory used=9594.9MB, alloc=227.8MB, time=129.29 memory used=9682.5MB, alloc=227.8MB, time=129.50 memory used=9777.5MB, alloc=227.8MB, time=129.68 memory used=9870.4MB, alloc=227.8MB, time=129.88 memory used=9969.6MB, alloc=227.8MB, time=130.07 memory used=10065.9MB, alloc=227.8MB, time=130.27 memory used=10167.2MB, alloc=227.8MB, time=130.46 memory used=10272.3MB, alloc=227.8MB, time=130.68 memory used=10379.8MB, alloc=227.8MB, time=130.91 memory used=10489.2MB, alloc=227.8MB, time=131.14 memory used=10602.8MB, alloc=227.8MB, time=131.39 memory used=10722.1MB, alloc=227.8MB, time=131.61 memory used=10851.4MB, alloc=227.8MB, time=131.83 memory used=10995.6MB, alloc=227.8MB, time=139.23 memory used=11106.0MB, alloc=227.8MB, time=146.64 memory used=11225.1MB, alloc=227.8MB, time=147.03 memory used=11343.2MB, alloc=227.8MB, time=147.39 memory used=11463.1MB, alloc=227.8MB, time=147.71 memory used=11554.6MB, alloc=227.8MB, time=148.00 memory used=11636.6MB, alloc=227.8MB, time=148.30 memory used=11716.0MB, alloc=227.8MB, time=148.55 memory used=11792.4MB, alloc=227.8MB, time=148.84 memory used=11869.6MB, alloc=227.8MB, time=149.08 memory used=11945.5MB, alloc=227.8MB, time=149.36 memory used=12023.4MB, alloc=227.8MB, time=149.60 memory used=12103.1MB, alloc=227.8MB, time=149.85 memory used=12184.3MB, alloc=227.8MB, time=150.09 memory used=12267.2MB, alloc=227.8MB, time=150.38 memory used=12351.7MB, alloc=227.8MB, time=150.64 memory used=12437.8MB, alloc=227.8MB, time=150.90 memory used=12525.5MB, alloc=227.8MB, time=151.19 memory used=12615.0MB, alloc=227.8MB, time=151.47 memory used=12716.7MB, alloc=227.8MB, time=151.81 memory used=12820.3MB, alloc=227.8MB, time=152.12 memory used=12925.8MB, alloc=227.8MB, time=152.39 memory used=13032.9MB, alloc=227.8MB, time=152.71 memory used=13141.8MB, alloc=227.8MB, time=153.00 memory used=13252.2MB, alloc=227.8MB, time=153.26 memory used=13364.2MB, alloc=227.8MB, time=153.55 memory used=13477.7MB, alloc=227.8MB, time=153.82 memory used=13592.7MB, alloc=227.8MB, time=154.08 memory used=13709.5MB, alloc=227.8MB, time=154.35 memory used=13813.9MB, alloc=227.8MB, time=154.60 memory used=13898.6MB, alloc=227.8MB, time=154.84 memory used=13968.1MB, alloc=227.8MB, time=155.03 memory used=14029.3MB, alloc=227.8MB, time=155.22 memory used=14091.3MB, alloc=227.8MB, time=155.39 memory used=14153.6MB, alloc=251.8MB, time=155.57 memory used=14218.7MB, alloc=251.8MB, time=155.77 memory used=14286.5MB, alloc=251.8MB, time=156.00 memory used=14354.7MB, alloc=251.8MB, time=156.22 memory used=14423.3MB, alloc=251.8MB, time=156.42 memory used=14492.2MB, alloc=251.8MB, time=156.60 memory used=14561.4MB, alloc=251.8MB, time=156.81 memory used=14631.0MB, alloc=251.8MB, time=157.04 memory used=14700.9MB, alloc=251.8MB, time=157.24 memory used=14771.7MB, alloc=251.8MB, time=157.42 memory used=14855.8MB, alloc=251.8MB, time=157.66 memory used=14940.7MB, alloc=251.8MB, time=157.87 memory used=15026.1MB, alloc=251.8MB, time=158.08 memory used=15111.8MB, alloc=251.8MB, time=158.29 memory used=15197.8MB, alloc=251.8MB, time=158.50 memory used=15284.3MB, alloc=251.8MB, time=158.70 memory used=15371.0MB, alloc=251.8MB, time=158.93 memory used=15458.1MB, alloc=251.8MB, time=159.12 memory used=15545.5MB, alloc=251.8MB, time=159.35 memory used=15633.2MB, alloc=251.8MB, time=159.56 memory used=15721.1MB, alloc=251.8MB, time=159.77 memory used=15809.4MB, alloc=251.8MB, time=159.99 memory used=15897.9MB, alloc=251.8MB, time=160.21 memory used=15986.6MB, alloc=251.8MB, time=160.43 memory used=16075.5MB, alloc=251.8MB, time=160.63 memory used=16164.7MB, alloc=251.8MB, time=160.83 memory used=16254.1MB, alloc=251.8MB, time=161.04 memory used=16344.3MB, alloc=251.8MB, time=161.24 memory used=16448.5MB, alloc=251.8MB, time=161.48 memory used=16553.4MB, alloc=251.8MB, time=161.69 memory used=16658.4MB, alloc=251.8MB, time=161.92 memory used=16763.6MB, alloc=251.8MB, time=162.14 memory used=16869.0MB, alloc=251.8MB, time=162.39 memory used=16974.5MB, alloc=251.8MB, time=162.61 memory used=17080.0MB, alloc=251.8MB, time=162.82 memory used=17185.7MB, alloc=251.8MB, time=163.04 memory used=17291.4MB, alloc=251.8MB, time=163.25 memory used=17397.2MB, alloc=251.8MB, time=163.48 memory used=17503.0MB, alloc=251.8MB, time=163.69 memory used=17609.3MB, alloc=251.8MB, time=163.90 memory used=17729.7MB, alloc=251.8MB, time=164.14 memory used=17850.4MB, alloc=251.8MB, time=164.38 memory used=17971.0MB, alloc=251.8MB, time=164.61 memory used=18091.5MB, alloc=251.8MB, time=164.84 memory used=18211.8MB, alloc=251.8MB, time=165.08 memory used=18331.9MB, alloc=251.8MB, time=165.30 memory used=18451.8MB, alloc=251.8MB, time=165.53 memory used=18571.6MB, alloc=251.8MB, time=165.76 memory used=18705.7MB, alloc=251.8MB, time=166.02 memory used=18839.4MB, alloc=251.8MB, time=166.24 memory used=18972.7MB, alloc=251.8MB, time=166.47 memory used=19105.4MB, alloc=251.8MB, time=166.70 memory used=19237.6MB, alloc=251.8MB, time=166.93 memory used=19369.3MB, alloc=251.8MB, time=167.16 memory used=19514.7MB, alloc=251.8MB, time=167.41 memory used=19659.2MB, alloc=251.8MB, time=167.65 memory used=19802.7MB, alloc=251.8MB, time=167.91 memory used=19945.3MB, alloc=251.8MB, time=168.17 memory used=20056.4MB, alloc=251.8MB, time=168.37 memory used=20065.5MB, alloc=251.8MB, time=168.46 memory used=20069.5MB, alloc=507.8MB, time=168.53 memory used=20221.7MB, alloc=507.8MB, time=169.03 memory used=20338.0MB, alloc=507.8MB, time=169.31 memory used=20461.0MB, alloc=507.8MB, time=169.57 memory used=20583.8MB, alloc=507.8MB, time=169.84 memory used=20705.6MB, alloc=507.8MB, time=170.12 memory used=20839.4MB, alloc=507.8MB, time=170.40 memory used=20971.7MB, alloc=507.8MB, time=170.68 memory used=21102.6MB, alloc=507.8MB, time=170.95 memory used=21231.8MB, alloc=507.8MB, time=171.24 memory used=21371.9MB, alloc=507.8MB, time=171.51 memory used=21509.9MB, alloc=507.8MB, time=171.79 memory used=21645.7MB, alloc=507.8MB, time=172.08 memory used=21791.2MB, alloc=507.8MB, time=172.37 memory used=21934.0MB, alloc=507.8MB, time=172.65 memory used=22085.2MB, alloc=507.8MB, time=172.95 memory used=22232.8MB, alloc=507.8MB, time=173.23 memory used=22387.8MB, alloc=507.8MB, time=173.54 memory used=22548.6MB, alloc=507.8MB, time=173.82 memory used=22704.1MB, alloc=507.8MB, time=174.12 memory used=22863.8MB, alloc=507.8MB, time=174.43 memory used=23026.2MB, alloc=507.8MB, time=174.74 memory used=23198.6MB, alloc=507.8MB, time=175.06 memory used=23370.0MB, alloc=507.8MB, time=175.36 memory used=23550.4MB, alloc=507.8MB, time=175.69 memory used=23735.9MB, alloc=507.8MB, time=176.02 memory used=23928.6MB, alloc=507.8MB, time=176.34 memory used=24268.3MB, alloc=507.8MB, time=177.42 memory used=24515.1MB, alloc=507.8MB, time=177.84 memory used=24852.4MB, alloc=507.8MB, time=178.63 memory used=25045.5MB, alloc=507.8MB, time=178.94 memory used=25268.4MB, alloc=507.8MB, time=181.23 memory used=25563.7MB, alloc=507.8MB, time=276.79 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428511206 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 2 3 F := [-x y + 16 y z - 10 z , 19 y z + 2 y z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 2 2 2 G := [-8 x + 16 x z + 19 z, 4 x y z - y z + 20 x ] > Problem := [F,G]; 2 2 3 2 2 2 3 Problem := [[-x y + 16 y z - 10 z , 19 y z + 2 y z ], 4 2 2 2 2 2 [-8 x + 16 x z + 19 z, 4 x y z - y z + 20 x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.20 memory used=26.4MB, alloc=32.3MB, time=0.60 memory used=46.3MB, alloc=56.3MB, time=0.93 memory used=87.3MB, alloc=60.3MB, time=1.55 memory used=129.9MB, alloc=68.3MB, time=2.18 memory used=172.3MB, alloc=92.3MB, time=2.85 memory used=238.8MB, alloc=92.3MB, time=3.87 memory used=305.4MB, alloc=92.3MB, time=4.82 memory used=370.5MB, alloc=116.3MB, time=5.68 memory used=441.8MB, alloc=117.3MB, time=6.11 memory used=518.9MB, alloc=117.3MB, time=7.04 memory used=585.1MB, alloc=373.3MB, time=7.91 memory used=676.9MB, alloc=373.3MB, time=9.21 memory used=763.0MB, alloc=397.3MB, time=10.53 memory used=882.4MB, alloc=397.3MB, time=12.08 memory used=996.7MB, alloc=421.3MB, time=13.58 memory used=1074.1MB, alloc=421.3MB, time=14.06 memory used=1158.1MB, alloc=421.3MB, time=14.57 memory used=1226.3MB, alloc=421.3MB, time=15.26 memory used=1283.2MB, alloc=421.3MB, time=15.48 memory used=1386.8MB, alloc=421.3MB, time=16.54 memory used=1545.5MB, alloc=421.3MB, time=18.78 memory used=1620.9MB, alloc=445.3MB, time=19.63 memory used=1705.0MB, alloc=445.3MB, time=19.95 memory used=1762.9MB, alloc=445.3MB, time=20.21 memory used=1830.2MB, alloc=445.3MB, time=20.46 memory used=1910.2MB, alloc=445.3MB, time=20.73 memory used=1991.4MB, alloc=445.3MB, time=20.99 memory used=2045.2MB, alloc=445.3MB, time=21.21 memory used=2106.1MB, alloc=445.3MB, time=21.43 memory used=2208.8MB, alloc=445.3MB, time=22.20 memory used=2284.9MB, alloc=445.3MB, time=22.52 memory used=2349.1MB, alloc=445.3MB, time=22.77 memory used=2545.5MB, alloc=445.3MB, time=24.23 memory used=2727.7MB, alloc=445.3MB, time=27.13 memory used=2797.5MB, alloc=445.3MB, time=27.44 memory used=2865.3MB, alloc=445.3MB, time=27.70 memory used=2928.5MB, alloc=445.3MB, time=27.97 memory used=2994.3MB, alloc=445.3MB, time=28.21 memory used=3067.9MB, alloc=445.3MB, time=28.46 memory used=3139.9MB, alloc=445.3MB, time=28.69 memory used=3197.6MB, alloc=445.3MB, time=28.91 memory used=3262.2MB, alloc=445.3MB, time=29.12 memory used=3394.5MB, alloc=445.3MB, time=29.62 memory used=3464.9MB, alloc=445.3MB, time=29.90 memory used=3528.4MB, alloc=445.3MB, time=30.15 memory used=3675.7MB, alloc=445.3MB, time=31.26 memory used=3837.2MB, alloc=445.3MB, time=32.90 memory used=3943.5MB, alloc=469.3MB, time=34.57 memory used=4046.5MB, alloc=469.3MB, time=36.16 memory used=4162.0MB, alloc=469.3MB, time=37.37 memory used=4265.5MB, alloc=493.3MB, time=39.10 memory used=4365.1MB, alloc=493.3MB, time=40.76 memory used=4464.6MB, alloc=493.3MB, time=41.18 memory used=4545.1MB, alloc=493.3MB, time=41.51 memory used=4690.0MB, alloc=493.3MB, time=42.59 memory used=4824.0MB, alloc=493.3MB, time=45.27 memory used=4934.8MB, alloc=493.3MB, time=46.74 memory used=5066.4MB, alloc=517.3MB, time=55.15 memory used=5706.2MB, alloc=541.3MB, time=66.65 memory used=5725.8MB, alloc=541.3MB, time=68.07 memory used=6176.4MB, alloc=541.3MB, time=71.97 memory used=6196.1MB, alloc=541.3MB, time=73.31 memory used=6544.4MB, alloc=541.3MB, time=76.73 memory used=6806.1MB, alloc=541.3MB, time=79.86 memory used=6997.0MB, alloc=541.3MB, time=82.52 memory used=7678.7MB, alloc=565.3MB, time=88.58 memory used=7698.5MB, alloc=589.3MB, time=90.00 memory used=7717.5MB, alloc=589.3MB, time=91.34 memory used=7978.6MB, alloc=589.3MB, time=96.73 memory used=8071.6MB, alloc=589.3MB, time=98.19 memory used=8282.9MB, alloc=589.3MB, time=99.76 memory used=8523.5MB, alloc=589.3MB, time=101.03 memory used=8653.9MB, alloc=589.3MB, time=103.31 memory used=8878.2MB, alloc=589.3MB, time=104.28 memory used=9107.1MB, alloc=589.3MB, time=105.22 memory used=9405.7MB, alloc=589.3MB, time=106.55 memory used=9621.4MB, alloc=589.3MB, time=108.53 memory used=9855.7MB, alloc=589.3MB, time=109.77 memory used=10058.5MB, alloc=589.3MB, time=110.60 memory used=10266.6MB, alloc=589.3MB, time=111.39 memory used=10502.5MB, alloc=589.3MB, time=112.26 memory used=10812.8MB, alloc=589.3MB, time=114.16 memory used=11042.6MB, alloc=589.3MB, time=115.24 memory used=11256.0MB, alloc=589.3MB, time=116.15 memory used=11502.6MB, alloc=589.3MB, time=117.08 memory used=11697.5MB, alloc=589.3MB, time=119.17 memory used=11897.5MB, alloc=589.3MB, time=120.78 memory used=12113.3MB, alloc=589.3MB, time=121.81 memory used=12310.1MB, alloc=589.3MB, time=122.62 memory used=12516.7MB, alloc=589.3MB, time=123.38 memory used=12748.1MB, alloc=589.3MB, time=124.20 memory used=13020.9MB, alloc=589.3MB, time=125.10 memory used=13330.1MB, alloc=589.3MB, time=126.02 memory used=13674.7MB, alloc=589.3MB, time=127.00 memory used=14087.9MB, alloc=589.3MB, time=128.15 memory used=14543.4MB, alloc=589.3MB, time=129.30 memory used=14975.5MB, alloc=589.3MB, time=130.40 memory used=15306.4MB, alloc=589.3MB, time=132.37 memory used=15717.9MB, alloc=589.3MB, time=133.41 memory used=16120.1MB, alloc=589.3MB, time=134.35 memory used=16488.4MB, alloc=589.3MB, time=135.21 memory used=16846.9MB, alloc=589.3MB, time=136.09 memory used=17198.9MB, alloc=589.3MB, time=136.90 memory used=17549.1MB, alloc=589.3MB, time=137.77 memory used=17892.0MB, alloc=589.3MB, time=138.58 memory used=18241.6MB, alloc=589.3MB, time=139.44 memory used=18585.0MB, alloc=589.3MB, time=140.26 memory used=18929.6MB, alloc=589.3MB, time=141.11 memory used=19269.9MB, alloc=589.3MB, time=141.90 memory used=19619.4MB, alloc=589.3MB, time=142.71 memory used=19961.4MB, alloc=589.3MB, time=143.49 memory used=20305.5MB, alloc=589.3MB, time=144.33 memory used=20653.9MB, alloc=589.3MB, time=145.18 memory used=20995.7MB, alloc=589.3MB, time=146.00 memory used=21340.0MB, alloc=589.3MB, time=146.81 memory used=21680.2MB, alloc=589.3MB, time=147.61 memory used=22025.3MB, alloc=589.3MB, time=148.43 memory used=22371.9MB, alloc=589.3MB, time=149.33 memory used=22718.2MB, alloc=589.3MB, time=150.20 memory used=23064.9MB, alloc=589.3MB, time=151.01 memory used=23412.0MB, alloc=589.3MB, time=151.86 memory used=23760.8MB, alloc=589.3MB, time=152.73 memory used=24104.1MB, alloc=589.3MB, time=153.55 memory used=24453.8MB, alloc=589.3MB, time=154.42 memory used=24797.3MB, alloc=589.3MB, time=155.24 memory used=25144.4MB, alloc=589.3MB, time=156.06 memory used=25494.5MB, alloc=589.3MB, time=157.00 memory used=25839.8MB, alloc=589.3MB, time=157.84 memory used=26187.9MB, alloc=589.3MB, time=158.72 memory used=26536.2MB, alloc=589.3MB, time=159.62 memory used=26887.6MB, alloc=589.3MB, time=160.48 memory used=27235.1MB, alloc=589.3MB, time=161.35 memory used=27584.4MB, alloc=589.3MB, time=162.23 memory used=27934.6MB, alloc=589.3MB, time=163.09 memory used=28284.0MB, alloc=589.3MB, time=163.95 memory used=28634.0MB, alloc=589.3MB, time=164.83 memory used=28984.1MB, alloc=589.3MB, time=165.69 memory used=29334.7MB, alloc=589.3MB, time=166.52 memory used=29684.9MB, alloc=589.3MB, time=167.37 memory used=30035.4MB, alloc=589.3MB, time=168.20 memory used=30386.4MB, alloc=589.3MB, time=169.07 memory used=30737.4MB, alloc=589.3MB, time=169.95 memory used=31089.0MB, alloc=589.3MB, time=170.81 memory used=31439.9MB, alloc=589.3MB, time=171.78 memory used=31792.5MB, alloc=589.3MB, time=172.74 memory used=32146.4MB, alloc=589.3MB, time=173.61 memory used=32494.5MB, alloc=589.3MB, time=174.53 memory used=32848.1MB, alloc=589.3MB, time=175.39 memory used=33201.2MB, alloc=589.3MB, time=176.27 memory used=33554.9MB, alloc=589.3MB, time=177.20 memory used=33911.1MB, alloc=589.3MB, time=178.12 memory used=34258.6MB, alloc=589.3MB, time=179.02 memory used=34611.4MB, alloc=589.3MB, time=179.95 memory used=34965.5MB, alloc=589.3MB, time=180.96 memory used=35317.8MB, alloc=589.3MB, time=181.85 memory used=35670.5MB, alloc=589.3MB, time=182.71 memory used=36025.1MB, alloc=589.3MB, time=183.60 memory used=36377.3MB, alloc=589.3MB, time=184.53 memory used=36731.0MB, alloc=589.3MB, time=185.42 memory used=37086.4MB, alloc=589.3MB, time=186.41 memory used=37437.8MB, alloc=589.3MB, time=187.41 memory used=37792.1MB, alloc=589.3MB, time=188.34 memory used=38146.1MB, alloc=589.3MB, time=189.20 memory used=38500.6MB, alloc=589.3MB, time=190.08 memory used=38857.3MB, alloc=589.3MB, time=190.94 memory used=39208.7MB, alloc=589.3MB, time=191.79 memory used=39565.3MB, alloc=589.3MB, time=192.75 memory used=39918.7MB, alloc=589.3MB, time=193.72 memory used=40274.4MB, alloc=589.3MB, time=194.68 memory used=40628.4MB, alloc=589.3MB, time=195.54 memory used=40984.0MB, alloc=589.3MB, time=196.45 memory used=41337.8MB, alloc=589.3MB, time=197.30 memory used=41693.6MB, alloc=589.3MB, time=198.21 memory used=42047.4MB, alloc=589.3MB, time=199.11 memory used=42404.2MB, alloc=589.3MB, time=200.03 memory used=42758.9MB, alloc=589.3MB, time=200.98 memory used=43116.9MB, alloc=589.3MB, time=201.95 memory used=43470.7MB, alloc=589.3MB, time=202.84 memory used=43830.6MB, alloc=589.3MB, time=203.75 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428511506 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 4 2 2 F := [-18 x y + 20 x y z + 11 z , -10 x + 19 x y z - 12 x y z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 3 2 3 G := [20 x z + 2 x z - 5 z , -y z + y z - 13 z ] > Problem := [F,G]; 3 3 4 2 2 Problem := [[-18 x y + 20 x y z + 11 z , -10 x + 19 x y z - 12 x y z], 3 2 2 3 2 3 [20 x z + 2 x z - 5 z , -y z + y z - 13 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.1MB, alloc=32.3MB, time=0.54 memory used=45.4MB, alloc=56.3MB, time=0.85 memory used=85.6MB, alloc=60.3MB, time=1.46 memory used=123.8MB, alloc=60.3MB, time=2.05 memory used=159.4MB, alloc=84.3MB, time=2.60 memory used=226.7MB, alloc=92.3MB, time=3.59 memory used=290.5MB, alloc=92.3MB, time=4.57 memory used=357.6MB, alloc=116.3MB, time=5.51 memory used=424.3MB, alloc=372.3MB, time=6.49 memory used=506.3MB, alloc=372.3MB, time=7.70 memory used=598.3MB, alloc=396.3MB, time=8.80 memory used=709.2MB, alloc=396.3MB, time=10.50 memory used=818.8MB, alloc=420.3MB, time=12.21 memory used=961.4MB, alloc=444.3MB, time=14.07 memory used=1106.5MB, alloc=444.3MB, time=16.22 memory used=1228.4MB, alloc=468.3MB, time=18.34 memory used=1353.8MB, alloc=468.3MB, time=20.42 memory used=1467.0MB, alloc=468.3MB, time=22.15 memory used=1596.2MB, alloc=468.3MB, time=23.75 memory used=1687.1MB, alloc=468.3MB, time=25.35 memory used=1828.3MB, alloc=492.3MB, time=26.80 memory used=1944.4MB, alloc=492.3MB, time=27.58 memory used=2078.1MB, alloc=492.3MB, time=28.86 memory used=2188.3MB, alloc=492.3MB, time=30.26 memory used=2291.0MB, alloc=492.3MB, time=31.81 memory used=2381.5MB, alloc=492.3MB, time=33.37 memory used=2460.4MB, alloc=492.3MB, time=34.92 memory used=2534.0MB, alloc=492.3MB, time=36.38 memory used=2658.6MB, alloc=492.3MB, time=37.73 memory used=2753.4MB, alloc=516.3MB, time=38.93 memory used=2844.6MB, alloc=516.3MB, time=40.08 memory used=2898.8MB, alloc=516.3MB, time=41.10 memory used=2962.7MB, alloc=516.3MB, time=42.56 memory used=3052.8MB, alloc=516.3MB, time=43.94 memory used=3110.5MB, alloc=516.3MB, time=45.00 memory used=3232.2MB, alloc=516.3MB, time=46.25 memory used=3304.1MB, alloc=516.3MB, time=47.87 memory used=3355.4MB, alloc=516.3MB, time=48.91 memory used=3406.3MB, alloc=516.3MB, time=50.10 memory used=3446.7MB, alloc=516.3MB, time=51.16 memory used=3630.6MB, alloc=540.3MB, time=52.78 memory used=3861.8MB, alloc=540.3MB, time=55.87 memory used=4102.4MB, alloc=564.3MB, time=59.08 memory used=4355.3MB, alloc=564.3MB, time=61.08 memory used=4546.0MB, alloc=564.3MB, time=62.23 memory used=4750.7MB, alloc=564.3MB, time=63.45 memory used=4998.3MB, alloc=564.3MB, time=64.98 memory used=5324.1MB, alloc=564.3MB, time=66.98 memory used=5733.5MB, alloc=564.3MB, time=69.66 memory used=6198.9MB, alloc=564.3MB, time=72.82 memory used=6633.9MB, alloc=588.3MB, time=75.70 memory used=7049.4MB, alloc=588.3MB, time=78.51 memory used=7461.3MB, alloc=588.3MB, time=81.40 memory used=7879.6MB, alloc=588.3MB, time=84.37 memory used=8307.8MB, alloc=588.3MB, time=87.47 memory used=8705.9MB, alloc=588.3MB, time=90.43 memory used=9111.1MB, alloc=588.3MB, time=93.49 memory used=9518.6MB, alloc=588.3MB, time=96.60 memory used=9937.3MB, alloc=588.3MB, time=99.84 memory used=10321.2MB, alloc=588.3MB, time=102.90 memory used=10709.9MB, alloc=588.3MB, time=106.10 memory used=11105.7MB, alloc=588.3MB, time=109.36 memory used=11502.5MB, alloc=588.3MB, time=112.66 memory used=11898.2MB, alloc=588.3MB, time=115.96 memory used=12295.5MB, alloc=588.3MB, time=119.28 memory used=12695.8MB, alloc=588.3MB, time=122.63 memory used=13105.3MB, alloc=588.3MB, time=126.09 memory used=13460.3MB, alloc=588.3MB, time=129.15 memory used=13812.3MB, alloc=588.3MB, time=132.24 memory used=14170.5MB, alloc=588.3MB, time=135.43 memory used=14534.4MB, alloc=588.3MB, time=138.66 memory used=14900.1MB, alloc=588.3MB, time=141.92 memory used=15266.5MB, alloc=588.3MB, time=145.26 memory used=15633.0MB, alloc=588.3MB, time=148.57 memory used=16001.8MB, alloc=588.3MB, time=152.02 memory used=16367.8MB, alloc=588.3MB, time=155.42 memory used=16738.1MB, alloc=588.3MB, time=158.96 memory used=17110.0MB, alloc=588.3MB, time=162.45 memory used=17479.2MB, alloc=588.3MB, time=166.11 memory used=17852.4MB, alloc=588.3MB, time=169.81 memory used=18226.5MB, alloc=588.3MB, time=173.43 memory used=18600.4MB, alloc=588.3MB, time=177.14 memory used=18979.0MB, alloc=588.3MB, time=180.84 memory used=19362.9MB, alloc=588.3MB, time=184.61 memory used=19751.4MB, alloc=588.3MB, time=188.43 memory used=20132.8MB, alloc=588.3MB, time=192.11 memory used=20484.9MB, alloc=588.3MB, time=195.49 memory used=20840.3MB, alloc=588.3MB, time=198.94 memory used=21199.0MB, alloc=588.3MB, time=202.66 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428511806 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 3 F := [17 y z - 14 x z + 17 x y, -13 x y z + 5 x z + 12 z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 G := [x y z + 2 x - 19 z, -3 y z - 4 x y z + 5 z ] > Problem := [F,G]; 3 2 2 2 3 Problem := [[17 y z - 14 x z + 17 x y, -13 x y z + 5 x z + 12 z ], 2 3 2 [x y z + 2 x - 19 z, -3 y z - 4 x y z + 5 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=25.4MB, alloc=32.3MB, time=0.49 memory used=44.3MB, alloc=56.3MB, time=0.79 memory used=88.2MB, alloc=60.3MB, time=1.33 memory used=134.1MB, alloc=68.3MB, time=1.97 memory used=179.2MB, alloc=68.3MB, time=2.53 memory used=206.2MB, alloc=68.3MB, time=2.66 memory used=234.0MB, alloc=68.3MB, time=2.87 memory used=267.7MB, alloc=68.3MB, time=4.14 memory used=287.5MB, alloc=68.3MB, time=4.21 memory used=313.3MB, alloc=68.3MB, time=4.34 memory used=351.4MB, alloc=68.3MB, time=4.68 memory used=393.0MB, alloc=68.3MB, time=5.24 memory used=433.8MB, alloc=92.3MB, time=5.83 memory used=505.3MB, alloc=92.3MB, time=6.64 memory used=559.3MB, alloc=92.3MB, time=7.65 memory used=591.7MB, alloc=92.3MB, time=7.75 memory used=625.8MB, alloc=92.3MB, time=7.84 memory used=655.6MB, alloc=92.3MB, time=7.91 memory used=715.4MB, alloc=92.3MB, time=10.68 memory used=749.5MB, alloc=92.3MB, time=10.80 memory used=784.5MB, alloc=92.3MB, time=10.89 memory used=820.5MB, alloc=92.3MB, time=11.00 memory used=847.5MB, alloc=92.3MB, time=11.07 memory used=878.1MB, alloc=92.3MB, time=11.15 memory used=914.2MB, alloc=92.3MB, time=11.23 memory used=975.2MB, alloc=92.3MB, time=11.87 memory used=1041.4MB, alloc=92.3MB, time=12.64 memory used=1103.9MB, alloc=116.3MB, time=13.42 memory used=1164.7MB, alloc=372.3MB, time=14.09 memory used=1254.6MB, alloc=372.3MB, time=15.22 memory used=1337.6MB, alloc=396.3MB, time=16.12 memory used=1452.8MB, alloc=420.3MB, time=17.51 memory used=1576.7MB, alloc=420.3MB, time=18.55 memory used=1666.2MB, alloc=420.3MB, time=19.90 memory used=1742.4MB, alloc=420.3MB, time=20.70 memory used=1831.1MB, alloc=420.3MB, time=21.86 memory used=1911.6MB, alloc=420.3MB, time=22.91 memory used=1998.9MB, alloc=420.3MB, time=24.85 memory used=2067.7MB, alloc=420.3MB, time=25.32 memory used=2141.4MB, alloc=420.3MB, time=26.06 memory used=2221.8MB, alloc=420.3MB, time=27.05 memory used=2368.9MB, alloc=420.3MB, time=28.65 memory used=2524.7MB, alloc=420.3MB, time=30.18 memory used=2650.5MB, alloc=420.3MB, time=31.40 memory used=2773.0MB, alloc=444.3MB, time=32.47 memory used=2926.5MB, alloc=444.3MB, time=34.51 memory used=3037.7MB, alloc=468.3MB, time=35.79 memory used=3173.9MB, alloc=468.3MB, time=37.52 memory used=3322.0MB, alloc=492.3MB, time=38.94 memory used=3423.2MB, alloc=492.3MB, time=40.05 memory used=3543.6MB, alloc=492.3MB, time=55.24 memory used=3633.8MB, alloc=492.3MB, time=55.58 memory used=3712.5MB, alloc=492.3MB, time=55.88 memory used=3793.3MB, alloc=492.3MB, time=56.18 memory used=3893.3MB, alloc=492.3MB, time=56.49 memory used=4043.6MB, alloc=492.3MB, time=57.13 memory used=4153.3MB, alloc=492.3MB, time=63.51 memory used=4248.3MB, alloc=492.3MB, time=65.37 memory used=4338.2MB, alloc=492.3MB, time=65.69 memory used=4417.8MB, alloc=492.3MB, time=65.99 memory used=4531.0MB, alloc=492.3MB, time=66.53 memory used=4629.4MB, alloc=492.3MB, time=67.04 memory used=4735.8MB, alloc=492.3MB, time=70.21 memory used=4848.9MB, alloc=492.3MB, time=83.17 memory used=4940.7MB, alloc=492.3MB, time=83.59 memory used=5016.7MB, alloc=492.3MB, time=83.90 memory used=5097.3MB, alloc=492.3MB, time=84.20 memory used=5197.0MB, alloc=492.3MB, time=84.52 memory used=5352.3MB, alloc=492.3MB, time=85.17 memory used=5449.6MB, alloc=492.3MB, time=85.69 memory used=5537.4MB, alloc=492.3MB, time=86.04 memory used=5660.7MB, alloc=516.3MB, time=123.92 memory used=5765.3MB, alloc=516.3MB, time=125.07 memory used=5884.2MB, alloc=516.3MB, time=125.47 memory used=5964.8MB, alloc=516.3MB, time=125.80 memory used=6060.1MB, alloc=516.3MB, time=126.17 memory used=6172.9MB, alloc=516.3MB, time=126.59 memory used=6425.7MB, alloc=516.3MB, time=127.31 memory used=6632.6MB, alloc=516.3MB, time=142.53 memory used=6739.4MB, alloc=516.3MB, time=142.95 memory used=6836.6MB, alloc=516.3MB, time=143.30 memory used=6932.8MB, alloc=516.3MB, time=143.73 memory used=7056.9MB, alloc=516.3MB, time=144.09 memory used=7260.5MB, alloc=516.3MB, time=158.62 memory used=7366.9MB, alloc=516.3MB, time=159.02 memory used=7465.1MB, alloc=516.3MB, time=159.37 memory used=7559.9MB, alloc=516.3MB, time=159.70 memory used=7681.2MB, alloc=516.3MB, time=160.04 memory used=7853.8MB, alloc=516.3MB, time=161.38 memory used=7969.7MB, alloc=516.3MB, time=162.59 memory used=8124.9MB, alloc=516.3MB, time=164.23 memory used=8218.7MB, alloc=516.3MB, time=164.59 memory used=8341.0MB, alloc=516.3MB, time=165.67 memory used=8509.1MB, alloc=516.3MB, time=173.77 memory used=8609.3MB, alloc=516.3MB, time=174.19 memory used=8692.5MB, alloc=516.3MB, time=174.60 memory used=8792.2MB, alloc=516.3MB, time=174.98 memory used=8951.1MB, alloc=516.3MB, time=178.46 memory used=9086.5MB, alloc=516.3MB, time=180.46 memory used=9215.3MB, alloc=516.3MB, time=182.42 memory used=9313.0MB, alloc=540.3MB, time=183.62 memory used=9406.3MB, alloc=540.3MB, time=184.94 memory used=9485.4MB, alloc=540.3MB, time=186.05 memory used=9551.9MB, alloc=540.3MB, time=187.23 memory used=9603.8MB, alloc=540.3MB, time=188.13 memory used=9656.8MB, alloc=540.3MB, time=189.28 memory used=9713.9MB, alloc=540.3MB, time=190.38 memory used=9787.0MB, alloc=540.3MB, time=191.43 memory used=9878.0MB, alloc=540.3MB, time=194.45 memory used=9983.9MB, alloc=540.3MB, time=195.00 memory used=10089.5MB, alloc=540.3MB, time=195.78 memory used=10206.6MB, alloc=540.3MB, time=196.75 memory used=10285.5MB, alloc=540.3MB, time=197.68 memory used=10361.1MB, alloc=540.3MB, time=199.00 memory used=10420.7MB, alloc=540.3MB, time=199.89 memory used=10497.9MB, alloc=540.3MB, time=200.86 memory used=10780.8MB, alloc=564.3MB, time=204.84 memory used=11009.2MB, alloc=564.3MB, time=208.96 memory used=11232.4MB, alloc=588.3MB, time=212.28 memory used=11417.5MB, alloc=612.3MB, time=214.43 memory used=11588.3MB, alloc=636.3MB, time=216.97 memory used=11765.5MB, alloc=660.3MB, time=219.90 memory used=11986.6MB, alloc=660.3MB, time=222.44 memory used=12174.6MB, alloc=660.3MB, time=225.42 memory used=12382.3MB, alloc=660.3MB, time=228.76 memory used=12556.9MB, alloc=660.3MB, time=230.08 memory used=12730.3MB, alloc=660.3MB, time=232.58 memory used=12956.2MB, alloc=660.3MB, time=238.96 memory used=13151.8MB, alloc=660.3MB, time=242.22 memory used=13345.8MB, alloc=684.3MB, time=246.97 memory used=13584.9MB, alloc=684.3MB, time=248.91 memory used=13769.4MB, alloc=684.3MB, time=251.51 memory used=13939.0MB, alloc=684.3MB, time=255.28 memory used=14152.7MB, alloc=684.3MB, time=257.83 memory used=14324.7MB, alloc=708.3MB, time=259.02 memory used=14506.3MB, alloc=708.3MB, time=260.08 memory used=14734.5MB, alloc=708.3MB, time=295.05 memory used=14899.6MB, alloc=708.3MB, time=296.00 memory used=15042.3MB, alloc=708.3MB, time=296.86 memory used=15221.0MB, alloc=708.3MB, time=297.79 memory used=15505.2MB, alloc=708.3MB, time=298.88 memory used=15635.9MB, alloc=708.3MB, time=299.73 memory used=15775.7MB, alloc=708.3MB, time=300.60 memory used=15927.2MB, alloc=708.3MB, time=301.46 memory used=16094.0MB, alloc=708.3MB, time=302.35 memory used=16272.6MB, alloc=708.3MB, time=303.24 memory used=16466.1MB, alloc=708.3MB, time=304.16 memory used=16678.6MB, alloc=708.3MB, time=305.11 memory used=16871.5MB, alloc=708.3MB, time=306.02 memory used=17034.0MB, alloc=708.3MB, time=306.89 memory used=17204.7MB, alloc=708.3MB, time=307.77 memory used=17390.7MB, alloc=708.3MB, time=308.64 memory used=17591.5MB, alloc=708.3MB, time=309.51 memory used=17889.6MB, alloc=708.3MB, time=310.85 memory used=18103.7MB, alloc=708.3MB, time=344.74 memory used=18288.9MB, alloc=708.3MB, time=346.63 memory used=18434.5MB, alloc=708.3MB, time=347.53 memory used=18593.7MB, alloc=708.3MB, time=348.40 memory used=18790.8MB, alloc=708.3MB, time=349.32 memory used=18977.2MB, alloc=708.3MB, time=350.25 memory used=19106.9MB, alloc=708.3MB, time=351.11 memory used=19246.7MB, alloc=708.3MB, time=351.94 memory used=19401.7MB, alloc=708.3MB, time=352.81 memory used=19569.2MB, alloc=708.3MB, time=353.67 memory used=19747.9MB, alloc=708.3MB, time=354.56 memory used=19941.4MB, alloc=708.3MB, time=355.48 memory used=20153.8MB, alloc=708.3MB, time=356.40 memory used=20345.2MB, alloc=708.3MB, time=357.29 memory used=20505.6MB, alloc=708.3MB, time=358.14 memory used=20676.6MB, alloc=708.3MB, time=359.01 memory used=20861.7MB, alloc=708.3MB, time=359.87 memory used=21062.5MB, alloc=708.3MB, time=360.75 memory used=21407.1MB, alloc=708.3MB, time=363.78 memory used=21588.0MB, alloc=708.3MB, time=364.86 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428520579 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 4 3 2 3 F := [6 x y + 6 y z - 17 z , 18 x z + 10 x y z + 16 y ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 3 3 G := [16 y - 11 x y - 13 y, -18 x y - x z - 5 x] > Problem := [F,G]; 2 2 3 4 3 2 3 Problem := [[6 x y + 6 y z - 17 z , 18 x z + 10 x y z + 16 y ], 4 2 3 3 [16 y - 11 x y - 13 y, -18 x y - x z - 5 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=24.2MB, alloc=32.3MB, time=0.48 memory used=42.9MB, alloc=56.3MB, time=0.75 memory used=84.8MB, alloc=62.3MB, time=1.03 memory used=126.4MB, alloc=62.3MB, time=1.38 memory used=167.7MB, alloc=62.3MB, time=1.77 memory used=216.9MB, alloc=70.3MB, time=2.37 memory used=261.1MB, alloc=70.3MB, time=2.93 memory used=307.4MB, alloc=70.3MB, time=3.46 memory used=342.2MB, alloc=70.3MB, time=3.73 memory used=377.7MB, alloc=70.3MB, time=3.92 memory used=406.1MB, alloc=70.3MB, time=4.02 memory used=428.6MB, alloc=70.3MB, time=4.10 memory used=448.5MB, alloc=70.3MB, time=4.17 memory used=477.2MB, alloc=70.3MB, time=4.31 memory used=509.1MB, alloc=70.3MB, time=4.44 memory used=532.8MB, alloc=70.3MB, time=4.53 memory used=553.6MB, alloc=70.3MB, time=4.61 memory used=587.7MB, alloc=70.3MB, time=4.84 memory used=609.6MB, alloc=70.3MB, time=4.92 memory used=641.5MB, alloc=70.3MB, time=5.29 memory used=664.6MB, alloc=70.3MB, time=5.54 memory used=685.1MB, alloc=70.3MB, time=5.66 memory used=705.6MB, alloc=70.3MB, time=5.76 memory used=726.4MB, alloc=70.3MB, time=5.85 memory used=747.6MB, alloc=81.9MB, time=6.43 memory used=779.5MB, alloc=81.9MB, time=6.52 memory used=802.3MB, alloc=81.9MB, time=6.60 memory used=831.0MB, alloc=83.8MB, time=6.69 memory used=860.5MB, alloc=83.8MB, time=6.77 memory used=883.1MB, alloc=83.8MB, time=6.84 memory used=911.0MB, alloc=83.8MB, time=6.92 memory used=940.2MB, alloc=83.8MB, time=7.01 memory used=962.5MB, alloc=83.8MB, time=7.07 memory used=991.6MB, alloc=83.8MB, time=7.87 memory used=1036.4MB, alloc=83.8MB, time=8.24 memory used=1065.2MB, alloc=83.8MB, time=8.34 memory used=1092.7MB, alloc=83.8MB, time=8.43 memory used=1119.9MB, alloc=83.8MB, time=8.52 memory used=1141.7MB, alloc=83.8MB, time=8.60 memory used=1158.8MB, alloc=83.8MB, time=8.67 memory used=1176.5MB, alloc=83.8MB, time=8.74 memory used=1195.2MB, alloc=83.8MB, time=8.81 memory used=1215.6MB, alloc=83.8MB, time=8.88 memory used=1238.3MB, alloc=83.8MB, time=8.95 memory used=1262.8MB, alloc=83.8MB, time=9.02 memory used=1280.1MB, alloc=83.8MB, time=9.08 memory used=1296.3MB, alloc=83.8MB, time=9.14 memory used=1312.7MB, alloc=83.8MB, time=9.19 memory used=1329.8MB, alloc=83.8MB, time=9.24 memory used=1356.5MB, alloc=83.8MB, time=9.62 memory used=1391.5MB, alloc=83.8MB, time=9.74 memory used=1418.9MB, alloc=83.8MB, time=9.84 memory used=1447.8MB, alloc=83.8MB, time=9.93 memory used=1470.3MB, alloc=83.8MB, time=10.02 memory used=1489.2MB, alloc=83.8MB, time=10.10 memory used=1507.3MB, alloc=83.8MB, time=10.16 memory used=1527.0MB, alloc=83.8MB, time=10.23 memory used=1549.0MB, alloc=83.8MB, time=10.30 memory used=1573.7MB, alloc=83.8MB, time=10.38 memory used=1589.9MB, alloc=83.8MB, time=10.43 memory used=1605.2MB, alloc=83.8MB, time=10.48 memory used=1635.2MB, alloc=83.8MB, time=11.89 memory used=1670.1MB, alloc=83.8MB, time=12.28 memory used=1695.9MB, alloc=83.8MB, time=12.36 memory used=1714.5MB, alloc=83.8MB, time=12.43 memory used=1736.3MB, alloc=83.8MB, time=12.51 memory used=1756.7MB, alloc=83.8MB, time=12.58 memory used=1775.3MB, alloc=83.8MB, time=12.65 memory used=1802.4MB, alloc=83.8MB, time=12.88 memory used=1851.4MB, alloc=107.8MB, time=13.41 memory used=1907.8MB, alloc=107.8MB, time=13.83 memory used=2001.5MB, alloc=107.8MB, time=14.51 memory used=2071.6MB, alloc=107.8MB, time=15.13 memory used=2145.1MB, alloc=107.8MB, time=15.64 memory used=2230.2MB, alloc=107.8MB, time=16.08 memory used=2314.0MB, alloc=107.8MB, time=16.56 memory used=2381.9MB, alloc=107.8MB, time=17.50 memory used=2450.5MB, alloc=107.8MB, time=18.36 memory used=2482.6MB, alloc=107.8MB, time=18.49 memory used=2513.8MB, alloc=107.8MB, time=18.61 memory used=2551.6MB, alloc=107.8MB, time=18.73 memory used=2580.5MB, alloc=107.8MB, time=18.83 memory used=2603.0MB, alloc=107.8MB, time=18.93 memory used=2627.4MB, alloc=107.8MB, time=19.03 memory used=2653.0MB, alloc=131.8MB, time=19.15 memory used=2697.7MB, alloc=131.8MB, time=19.28 memory used=2748.2MB, alloc=131.8MB, time=19.41 memory used=2804.3MB, alloc=131.8MB, time=19.57 memory used=2863.7MB, alloc=131.8MB, time=19.71 memory used=2911.9MB, alloc=131.8MB, time=19.84 memory used=2944.3MB, alloc=131.8MB, time=19.94 memory used=2978.4MB, alloc=131.8MB, time=20.04 memory used=3013.1MB, alloc=131.8MB, time=20.14 memory used=3048.3MB, alloc=131.8MB, time=20.24 memory used=3087.1MB, alloc=131.8MB, time=20.34 memory used=3126.2MB, alloc=131.8MB, time=20.44 memory used=3166.0MB, alloc=131.8MB, time=20.55 memory used=3208.6MB, alloc=131.8MB, time=20.65 memory used=3251.8MB, alloc=131.8MB, time=20.76 memory used=3298.2MB, alloc=131.8MB, time=20.87 memory used=3345.0MB, alloc=131.8MB, time=20.98 memory used=3394.3MB, alloc=131.8MB, time=21.08 memory used=3446.7MB, alloc=131.8MB, time=21.20 memory used=3501.8MB, alloc=131.8MB, time=21.32 memory used=3559.2MB, alloc=131.8MB, time=21.42 memory used=3618.5MB, alloc=131.8MB, time=21.53 memory used=3682.0MB, alloc=131.8MB, time=21.64 memory used=3715.2MB, alloc=131.8MB, time=21.73 memory used=3722.6MB, alloc=131.8MB, time=21.80 memory used=3730.2MB, alloc=131.8MB, time=21.86 memory used=3738.0MB, alloc=131.8MB, time=21.93 memory used=3745.7MB, alloc=131.8MB, time=21.99 memory used=3753.4MB, alloc=131.8MB, time=22.05 memory used=3761.0MB, alloc=131.8MB, time=22.11 memory used=3768.5MB, alloc=131.8MB, time=22.18 memory used=3776.5MB, alloc=131.8MB, time=22.24 memory used=3785.8MB, alloc=131.8MB, time=22.31 memory used=3793.8MB, alloc=131.8MB, time=22.37 memory used=3802.7MB, alloc=131.8MB, time=22.44 memory used=3812.2MB, alloc=131.8MB, time=22.51 memory used=3821.5MB, alloc=131.8MB, time=22.57 memory used=3830.7MB, alloc=131.8MB, time=22.63 memory used=3839.7MB, alloc=131.8MB, time=22.70 memory used=3848.6MB, alloc=131.8MB, time=22.76 memory used=3857.8MB, alloc=131.8MB, time=22.83 memory used=3868.0MB, alloc=131.8MB, time=22.90 memory used=3878.5MB, alloc=131.8MB, time=22.97 memory used=3888.7MB, alloc=131.8MB, time=23.03 memory used=3898.7MB, alloc=131.8MB, time=23.10 memory used=3909.0MB, alloc=131.8MB, time=23.17 memory used=3919.7MB, alloc=131.8MB, time=23.24 memory used=3930.6MB, alloc=131.8MB, time=23.30 memory used=3941.7MB, alloc=131.8MB, time=23.37 memory used=3953.3MB, alloc=131.8MB, time=23.44 memory used=3965.5MB, alloc=131.8MB, time=23.51 memory used=3977.9MB, alloc=131.8MB, time=23.59 memory used=3990.6MB, alloc=131.8MB, time=23.65 memory used=4003.5MB, alloc=131.8MB, time=23.73 memory used=4016.7MB, alloc=131.8MB, time=23.80 memory used=4069.4MB, alloc=131.8MB, time=24.35 memory used=4117.3MB, alloc=131.8MB, time=24.51 memory used=4171.9MB, alloc=131.8MB, time=24.66 memory used=4208.7MB, alloc=131.8MB, time=24.80 memory used=4250.7MB, alloc=131.8MB, time=24.94 memory used=4298.2MB, alloc=131.8MB, time=25.09 memory used=4351.4MB, alloc=131.8MB, time=25.23 memory used=4410.2MB, alloc=131.8MB, time=25.38 memory used=4463.2MB, alloc=131.8MB, time=25.53 memory used=4495.0MB, alloc=131.8MB, time=25.63 memory used=4529.4MB, alloc=131.8MB, time=25.73 memory used=4564.8MB, alloc=131.8MB, time=25.84 memory used=4603.3MB, alloc=131.8MB, time=25.94 memory used=4642.0MB, alloc=131.8MB, time=26.04 memory used=4683.7MB, alloc=131.8MB, time=26.16 memory used=4728.1MB, alloc=131.8MB, time=26.27 memory used=4772.9MB, alloc=131.8MB, time=26.39 memory used=4821.8MB, alloc=131.8MB, time=26.50 memory used=4873.2MB, alloc=131.8MB, time=26.61 memory used=4926.1MB, alloc=131.8MB, time=26.73 memory used=4982.5MB, alloc=131.8MB, time=26.85 memory used=5042.0MB, alloc=131.8MB, time=26.97 memory used=5109.6MB, alloc=131.8MB, time=27.09 memory used=5118.3MB, alloc=131.8MB, time=27.16 memory used=5127.2MB, alloc=131.8MB, time=27.23 memory used=5136.2MB, alloc=131.8MB, time=27.30 memory used=5145.7MB, alloc=131.8MB, time=27.37 memory used=5155.6MB, alloc=131.8MB, time=27.43 memory used=5165.6MB, alloc=131.8MB, time=27.50 memory used=5174.9MB, alloc=131.8MB, time=27.56 memory used=5185.1MB, alloc=131.8MB, time=27.62 memory used=5196.0MB, alloc=131.8MB, time=27.69 memory used=5206.5MB, alloc=131.8MB, time=27.76 memory used=5217.2MB, alloc=131.8MB, time=27.85 memory used=5229.0MB, alloc=131.8MB, time=27.91 memory used=5263.6MB, alloc=131.8MB, time=30.73 memory used=5330.2MB, alloc=131.8MB, time=31.49 memory used=5373.4MB, alloc=131.8MB, time=31.63 memory used=5429.8MB, alloc=131.8MB, time=31.78 memory used=5476.1MB, alloc=131.8MB, time=31.90 memory used=5514.2MB, alloc=131.8MB, time=32.03 memory used=5556.3MB, alloc=131.8MB, time=32.14 memory used=5603.9MB, alloc=131.8MB, time=32.25 memory used=5656.6MB, alloc=131.8MB, time=32.36 memory used=5714.1MB, alloc=131.8MB, time=32.48 memory used=5786.1MB, alloc=131.8MB, time=32.60 memory used=5796.2MB, alloc=131.8MB, time=32.67 memory used=5806.5MB, alloc=131.8MB, time=32.73 memory used=5816.7MB, alloc=131.8MB, time=32.79 memory used=5827.7MB, alloc=131.8MB, time=32.86 memory used=5838.5MB, alloc=131.8MB, time=32.94 memory used=5850.1MB, alloc=131.8MB, time=33.00 memory used=5861.3MB, alloc=131.8MB, time=33.07 memory used=5873.2MB, alloc=131.8MB, time=33.14 memory used=5885.6MB, alloc=131.8MB, time=33.21 memory used=5897.7MB, alloc=131.8MB, time=33.28 memory used=5910.4MB, alloc=131.8MB, time=33.34 memory used=5923.6MB, alloc=131.8MB, time=33.41 memory used=5937.4MB, alloc=131.8MB, time=33.50 memory used=6010.6MB, alloc=131.8MB, time=34.02 memory used=6071.2MB, alloc=131.8MB, time=34.63 memory used=6129.5MB, alloc=131.8MB, time=34.78 memory used=6188.1MB, alloc=131.8MB, time=34.93 memory used=6250.8MB, alloc=131.8MB, time=35.83 memory used=6343.5MB, alloc=387.8MB, time=36.76 memory used=6462.9MB, alloc=387.8MB, time=38.09 memory used=6559.1MB, alloc=387.8MB, time=39.04 memory used=6668.9MB, alloc=387.8MB, time=39.72 memory used=6775.3MB, alloc=387.8MB, time=40.46 memory used=6882.1MB, alloc=387.8MB, time=41.30 memory used=6986.9MB, alloc=387.8MB, time=42.16 memory used=7089.0MB, alloc=387.8MB, time=42.95 memory used=7192.9MB, alloc=387.8MB, time=43.93 memory used=7299.6MB, alloc=387.8MB, time=45.32 memory used=7392.3MB, alloc=387.8MB, time=46.52 memory used=7441.4MB, alloc=387.8MB, time=46.71 memory used=7494.4MB, alloc=387.8MB, time=47.01 memory used=7545.4MB, alloc=387.8MB, time=47.27 memory used=7630.0MB, alloc=387.8MB, time=47.95 memory used=7704.3MB, alloc=387.8MB, time=48.55 memory used=7786.4MB, alloc=387.8MB, time=49.45 memory used=7855.2MB, alloc=387.8MB, time=50.12 memory used=7892.2MB, alloc=387.8MB, time=50.24 memory used=7933.2MB, alloc=387.8MB, time=50.39 memory used=7984.6MB, alloc=387.8MB, time=50.53 memory used=8117.9MB, alloc=387.8MB, time=50.97 memory used=8162.8MB, alloc=387.8MB, time=51.20 memory used=8203.7MB, alloc=387.8MB, time=51.36 memory used=8243.3MB, alloc=387.8MB, time=51.53 memory used=8294.0MB, alloc=387.8MB, time=51.69 memory used=8323.7MB, alloc=387.8MB, time=51.82 memory used=8353.9MB, alloc=387.8MB, time=51.95 memory used=8387.0MB, alloc=387.8MB, time=52.09 memory used=8422.3MB, alloc=387.8MB, time=52.22 memory used=8460.7MB, alloc=387.8MB, time=52.35 memory used=8501.8MB, alloc=387.8MB, time=52.49 memory used=8545.6MB, alloc=387.8MB, time=52.65 memory used=8592.4MB, alloc=387.8MB, time=52.79 memory used=8642.5MB, alloc=387.8MB, time=52.92 memory used=8808.8MB, alloc=387.8MB, time=53.34 memory used=8984.3MB, alloc=387.8MB, time=53.87 memory used=9029.7MB, alloc=387.8MB, time=54.02 memory used=9061.7MB, alloc=387.8MB, time=54.15 memory used=9099.3MB, alloc=387.8MB, time=54.30 memory used=9142.2MB, alloc=387.8MB, time=54.44 memory used=9190.9MB, alloc=387.8MB, time=54.59 memory used=9381.0MB, alloc=387.8MB, time=54.97 memory used=9565.9MB, alloc=387.8MB, time=55.34 memory used=9788.8MB, alloc=387.8MB, time=55.73 memory used=10003.9MB, alloc=387.8MB, time=56.11 memory used=10199.1MB, alloc=387.8MB, time=56.48 memory used=10415.9MB, alloc=387.8MB, time=56.83 memory used=10657.3MB, alloc=387.8MB, time=57.21 memory used=10962.8MB, alloc=411.8MB, time=61.37 memory used=11164.3MB, alloc=411.8MB, time=64.00 memory used=11339.6MB, alloc=411.8MB, time=65.83 memory used=11432.5MB, alloc=411.8MB, time=66.26 memory used=11525.3MB, alloc=411.8MB, time=66.67 memory used=11618.8MB, alloc=411.8MB, time=67.10 memory used=11712.2MB, alloc=411.8MB, time=67.52 memory used=11804.7MB, alloc=411.8MB, time=67.92 memory used=11895.3MB, alloc=411.8MB, time=68.35 memory used=11987.9MB, alloc=411.8MB, time=68.78 memory used=12080.5MB, alloc=411.8MB, time=69.22 memory used=12176.2MB, alloc=411.8MB, time=69.69 memory used=12270.3MB, alloc=411.8MB, time=70.15 memory used=12356.2MB, alloc=411.8MB, time=70.56 memory used=12447.6MB, alloc=411.8MB, time=71.04 memory used=12542.9MB, alloc=411.8MB, time=71.53 memory used=12628.1MB, alloc=411.8MB, time=71.98 memory used=12722.7MB, alloc=411.8MB, time=72.47 memory used=12818.5MB, alloc=411.8MB, time=72.98 memory used=12905.7MB, alloc=411.8MB, time=73.51 memory used=13001.7MB, alloc=411.8MB, time=74.02 memory used=13091.9MB, alloc=411.8MB, time=74.56 memory used=13184.5MB, alloc=411.8MB, time=75.11 memory used=13284.7MB, alloc=411.8MB, time=75.73 memory used=13370.9MB, alloc=411.8MB, time=76.30 memory used=13468.8MB, alloc=411.8MB, time=76.89 memory used=13556.8MB, alloc=411.8MB, time=77.46 memory used=13653.9MB, alloc=411.8MB, time=78.06 memory used=13729.8MB, alloc=411.8MB, time=79.01 memory used=13780.2MB, alloc=411.8MB, time=79.17 memory used=13838.5MB, alloc=411.8MB, time=79.34 memory used=13943.3MB, alloc=411.8MB, time=79.74 memory used=14217.0MB, alloc=411.8MB, time=86.09 memory used=14272.0MB, alloc=411.8MB, time=86.31 memory used=14317.1MB, alloc=411.8MB, time=86.50 memory used=14362.8MB, alloc=411.8MB, time=86.67 memory used=14417.3MB, alloc=411.8MB, time=86.85 memory used=14479.4MB, alloc=411.8MB, time=87.03 memory used=14673.9MB, alloc=411.8MB, time=87.44 memory used=14849.4MB, alloc=411.8MB, time=87.84 memory used=15054.2MB, alloc=411.8MB, time=88.27 memory used=15291.1MB, alloc=411.8MB, time=88.72 memory used=15487.8MB, alloc=411.8MB, time=89.10 memory used=15678.7MB, alloc=411.8MB, time=89.47 memory used=15886.0MB, alloc=411.8MB, time=89.90 memory used=16114.3MB, alloc=411.8MB, time=90.32 memory used=16358.1MB, alloc=411.8MB, time=90.74 memory used=16573.7MB, alloc=411.8MB, time=91.12 memory used=16781.7MB, alloc=411.8MB, time=91.49 memory used=17003.0MB, alloc=411.8MB, time=91.86 memory used=17238.8MB, alloc=411.8MB, time=92.24 memory used=17573.9MB, alloc=411.8MB, time=94.61 memory used=17633.2MB, alloc=411.8MB, time=95.66 memory used=17727.4MB, alloc=411.8MB, time=97.35 memory used=17889.4MB, alloc=411.8MB, time=100.49 memory used=18097.4MB, alloc=411.8MB, time=103.15 memory used=18206.3MB, alloc=411.8MB, time=104.53 memory used=18262.6MB, alloc=411.8MB, time=104.87 memory used=18316.0MB, alloc=411.8MB, time=105.06 memory used=18376.7MB, alloc=411.8MB, time=105.54 memory used=18460.4MB, alloc=435.8MB, time=106.66 memory used=18583.3MB, alloc=435.8MB, time=107.49 memory used=18725.3MB, alloc=459.8MB, time=108.20 memory used=18847.3MB, alloc=459.8MB, time=109.07 memory used=19004.0MB, alloc=459.8MB, time=110.30 memory used=19146.0MB, alloc=459.8MB, time=111.26 memory used=19294.0MB, alloc=459.8MB, time=112.23 memory used=19427.4MB, alloc=459.8MB, time=112.98 memory used=19577.0MB, alloc=459.8MB, time=113.78 memory used=19715.2MB, alloc=459.8MB, time=114.57 memory used=19860.9MB, alloc=459.8MB, time=115.41 memory used=19996.8MB, alloc=459.8MB, time=116.28 memory used=20146.5MB, alloc=459.8MB, time=117.16 memory used=20282.1MB, alloc=459.8MB, time=118.04 memory used=20432.1MB, alloc=459.8MB, time=118.93 memory used=20568.5MB, alloc=459.8MB, time=119.84 memory used=20718.8MB, alloc=459.8MB, time=120.77 memory used=20855.9MB, alloc=459.8MB, time=121.78 memory used=21006.1MB, alloc=459.8MB, time=122.72 memory used=21144.3MB, alloc=459.8MB, time=123.74 memory used=21295.4MB, alloc=459.8MB, time=124.76 memory used=21433.6MB, alloc=459.8MB, time=125.85 memory used=21584.2MB, alloc=459.8MB, time=126.91 memory used=21723.1MB, alloc=459.8MB, time=128.00 memory used=21873.4MB, alloc=459.8MB, time=129.06 memory used=22011.6MB, alloc=459.8MB, time=130.18 memory used=22168.0MB, alloc=459.8MB, time=133.37 memory used=22320.2MB, alloc=459.8MB, time=135.29 memory used=22449.2MB, alloc=459.8MB, time=135.78 memory used=22562.6MB, alloc=459.8MB, time=136.16 memory used=22690.1MB, alloc=459.8MB, time=136.55 memory used=22830.8MB, alloc=459.8MB, time=136.99 memory used=22985.2MB, alloc=459.8MB, time=137.43 memory used=23135.5MB, alloc=459.8MB, time=137.88 memory used=23381.2MB, alloc=459.8MB, time=138.54 memory used=23543.4MB, alloc=459.8MB, time=139.53 memory used=23648.6MB, alloc=459.8MB, time=139.91 memory used=23851.6MB, alloc=459.8MB, time=142.40 memory used=23968.0MB, alloc=459.8MB, time=142.90 memory used=24070.1MB, alloc=459.8MB, time=143.24 memory used=24214.5MB, alloc=459.8MB, time=143.67 memory used=24379.8MB, alloc=459.8MB, time=144.06 memory used=24557.2MB, alloc=459.8MB, time=144.46 memory used=24723.4MB, alloc=459.8MB, time=144.84 memory used=24913.7MB, alloc=483.8MB, time=145.30 memory used=25108.1MB, alloc=483.8MB, time=145.75 memory used=25308.3MB, alloc=483.8MB, time=146.20 memory used=25498.7MB, alloc=483.8MB, time=146.62 memory used=25731.8MB, alloc=483.8MB, time=147.12 memory used=25962.1MB, alloc=483.8MB, time=183.03 memory used=26101.1MB, alloc=483.8MB, time=183.59 memory used=26327.4MB, alloc=483.8MB, time=186.68 memory used=26464.5MB, alloc=483.8MB, time=187.19 memory used=26618.3MB, alloc=483.8MB, time=187.65 memory used=26785.4MB, alloc=483.8MB, time=188.11 memory used=26959.8MB, alloc=483.8MB, time=188.59 memory used=27146.0MB, alloc=507.8MB, time=189.13 memory used=27322.5MB, alloc=507.8MB, time=189.63 memory used=27515.8MB, alloc=507.8MB, time=190.16 memory used=27729.8MB, alloc=507.8MB, time=190.70 memory used=27958.7MB, alloc=507.8MB, time=225.87 memory used=28138.2MB, alloc=507.8MB, time=226.71 memory used=28312.9MB, alloc=507.8MB, time=228.24 memory used=28496.1MB, alloc=507.8MB, time=229.46 memory used=28656.0MB, alloc=507.8MB, time=230.00 memory used=28832.3MB, alloc=507.8MB, time=230.54 memory used=29034.7MB, alloc=507.8MB, time=231.12 memory used=29244.2MB, alloc=507.8MB, time=231.74 memory used=29562.0MB, alloc=507.8MB, time=232.68 memory used=29751.6MB, alloc=507.8MB, time=233.46 memory used=29969.1MB, alloc=507.8MB, time=235.32 memory used=30222.5MB, alloc=507.8MB, time=236.79 memory used=30498.1MB, alloc=507.8MB, time=238.21 memory used=30715.5MB, alloc=507.8MB, time=240.87 memory used=31694.2MB, alloc=507.8MB, time=266.25 memory used=32287.7MB, alloc=507.8MB, time=269.00 memory used=32818.9MB, alloc=507.8MB, time=271.15 memory used=33335.7MB, alloc=507.8MB, time=274.38 memory used=34097.7MB, alloc=507.8MB, time=298.27 memory used=34709.2MB, alloc=507.8MB, time=301.20 memory used=35243.0MB, alloc=507.8MB, time=303.41 memory used=35822.1MB, alloc=507.8MB, time=307.53 memory used=36153.3MB, alloc=507.8MB, time=311.63 memory used=36375.2MB, alloc=507.8MB, time=313.75 memory used=36609.4MB, alloc=507.8MB, time=315.09 memory used=36860.6MB, alloc=507.8MB, time=316.43 memory used=37076.6MB, alloc=507.8MB, time=317.78 memory used=37240.7MB, alloc=531.8MB, time=322.04 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428520879 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 4 F := [2 x z - 14 x y z - 19 z, 16 x z - 17 z - 12 x y z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 3 3 2 G := [-2 x y - 5 y z - 7, -12 y z + 3 y z - 14 x z ] > Problem := [F,G]; 3 2 2 2 4 Problem := [[2 x z - 14 x y z - 19 z, 16 x z - 17 z - 12 x y z], 3 2 2 3 3 2 [-2 x y - 5 y z - 7, -12 y z + 3 y z - 14 x z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=26.9MB, alloc=32.3MB, time=0.53 memory used=46.8MB, alloc=56.3MB, time=0.83 memory used=93.2MB, alloc=60.5MB, time=1.39 memory used=130.0MB, alloc=64.6MB, time=1.90 memory used=155.9MB, alloc=64.6MB, time=1.97 memory used=196.2MB, alloc=64.6MB, time=2.46 memory used=232.3MB, alloc=64.6MB, time=2.97 memory used=279.1MB, alloc=96.6MB, time=3.56 memory used=346.0MB, alloc=96.6MB, time=4.35 memory used=395.2MB, alloc=96.6MB, time=4.73 memory used=452.4MB, alloc=96.6MB, time=5.25 memory used=519.6MB, alloc=96.6MB, time=6.00 memory used=582.8MB, alloc=352.6MB, time=6.85 memory used=629.2MB, alloc=352.6MB, time=7.13 memory used=676.7MB, alloc=352.6MB, time=7.39 memory used=739.7MB, alloc=352.6MB, time=16.56 memory used=787.2MB, alloc=352.6MB, time=17.97 memory used=813.3MB, alloc=352.6MB, time=18.11 memory used=843.7MB, alloc=352.6MB, time=18.24 memory used=883.4MB, alloc=352.6MB, time=18.43 memory used=930.0MB, alloc=352.6MB, time=18.70 memory used=977.0MB, alloc=352.6MB, time=18.98 memory used=1036.6MB, alloc=376.6MB, time=28.44 memory used=1098.6MB, alloc=376.6MB, time=29.68 memory used=1146.9MB, alloc=376.6MB, time=29.88 memory used=1213.3MB, alloc=376.6MB, time=30.18 memory used=1294.9MB, alloc=376.6MB, time=33.12 memory used=1373.3MB, alloc=376.6MB, time=40.98 memory used=1417.8MB, alloc=376.6MB, time=41.13 memory used=1495.7MB, alloc=376.6MB, time=42.63 memory used=1580.2MB, alloc=376.6MB, time=43.62 memory used=1650.5MB, alloc=376.6MB, time=44.57 memory used=1749.8MB, alloc=376.6MB, time=45.79 memory used=1815.6MB, alloc=376.6MB, time=46.01 memory used=1866.3MB, alloc=376.6MB, time=46.21 memory used=1901.0MB, alloc=376.6MB, time=46.38 memory used=1936.7MB, alloc=376.6MB, time=46.54 memory used=1975.6MB, alloc=376.6MB, time=46.71 memory used=2018.4MB, alloc=376.6MB, time=46.87 memory used=2065.0MB, alloc=376.6MB, time=47.05 memory used=2113.7MB, alloc=376.6MB, time=47.21 memory used=2166.0MB, alloc=376.6MB, time=47.38 memory used=2218.3MB, alloc=376.6MB, time=47.57 memory used=2248.9MB, alloc=376.6MB, time=47.72 memory used=2278.6MB, alloc=376.6MB, time=47.86 memory used=2308.3MB, alloc=376.6MB, time=48.00 memory used=2340.4MB, alloc=376.6MB, time=48.16 memory used=2372.7MB, alloc=376.6MB, time=48.30 memory used=2405.3MB, alloc=376.6MB, time=48.45 memory used=2440.2MB, alloc=376.6MB, time=48.60 memory used=2475.2MB, alloc=376.6MB, time=48.74 memory used=2512.5MB, alloc=376.6MB, time=48.89 memory used=2550.0MB, alloc=376.6MB, time=49.04 memory used=2589.3MB, alloc=376.6MB, time=49.18 memory used=2630.8MB, alloc=376.6MB, time=49.33 memory used=2674.2MB, alloc=376.6MB, time=49.47 memory used=2719.3MB, alloc=376.6MB, time=49.62 memory used=2765.9MB, alloc=376.6MB, time=49.78 memory used=2813.6MB, alloc=376.6MB, time=49.94 memory used=2864.3MB, alloc=376.6MB, time=50.11 memory used=2913.5MB, alloc=376.6MB, time=50.27 memory used=2954.9MB, alloc=376.6MB, time=50.40 memory used=2997.1MB, alloc=376.6MB, time=50.54 memory used=3034.9MB, alloc=376.6MB, time=50.66 memory used=3064.9MB, alloc=376.6MB, time=50.77 memory used=3095.7MB, alloc=376.6MB, time=50.88 memory used=3128.7MB, alloc=376.6MB, time=50.99 memory used=3163.7MB, alloc=376.6MB, time=51.12 memory used=3201.7MB, alloc=376.6MB, time=51.23 memory used=3251.1MB, alloc=376.6MB, time=51.86 memory used=3322.1MB, alloc=376.6MB, time=52.11 memory used=3381.4MB, alloc=376.6MB, time=52.34 memory used=3416.7MB, alloc=376.6MB, time=52.52 memory used=3451.4MB, alloc=376.6MB, time=52.69 memory used=3489.7MB, alloc=376.6MB, time=52.87 memory used=3531.9MB, alloc=376.6MB, time=53.04 memory used=3578.0MB, alloc=376.6MB, time=53.22 memory used=3626.0MB, alloc=376.6MB, time=53.38 memory used=3677.9MB, alloc=376.6MB, time=53.57 memory used=3732.9MB, alloc=376.6MB, time=53.75 memory used=3768.0MB, alloc=376.6MB, time=53.91 memory used=3796.7MB, alloc=376.6MB, time=54.07 memory used=3826.4MB, alloc=376.6MB, time=54.22 memory used=3858.4MB, alloc=376.6MB, time=54.37 memory used=3890.7MB, alloc=376.6MB, time=54.51 memory used=3923.2MB, alloc=376.6MB, time=54.68 memory used=3958.1MB, alloc=376.6MB, time=54.82 memory used=3993.1MB, alloc=376.6MB, time=54.97 memory used=4030.4MB, alloc=376.6MB, time=55.11 memory used=4067.9MB, alloc=376.6MB, time=55.28 memory used=4107.3MB, alloc=376.6MB, time=55.42 memory used=4148.9MB, alloc=376.6MB, time=55.56 memory used=4192.4MB, alloc=376.6MB, time=55.71 memory used=4237.7MB, alloc=376.6MB, time=55.85 memory used=4284.4MB, alloc=376.6MB, time=56.00 memory used=4332.4MB, alloc=376.6MB, time=56.16 memory used=4383.3MB, alloc=376.6MB, time=56.30 memory used=4434.7MB, alloc=376.6MB, time=56.48 memory used=4475.9MB, alloc=376.6MB, time=56.63 memory used=4519.0MB, alloc=376.6MB, time=56.77 memory used=4558.7MB, alloc=376.6MB, time=56.89 memory used=4589.2MB, alloc=376.6MB, time=57.00 memory used=4619.8MB, alloc=376.6MB, time=57.13 memory used=4652.3MB, alloc=376.6MB, time=57.24 memory used=4686.9MB, alloc=376.6MB, time=57.35 memory used=4724.7MB, alloc=376.6MB, time=57.46 memory used=4767.9MB, alloc=376.6MB, time=57.66 memory used=4831.4MB, alloc=400.6MB, time=78.13 memory used=4904.9MB, alloc=400.6MB, time=112.43 memory used=4976.8MB, alloc=424.6MB, time=165.16 memory used=5076.2MB, alloc=424.6MB, time=250.57 memory used=5164.2MB, alloc=424.6MB, time=256.85 memory used=5247.7MB, alloc=424.6MB, time=257.10 memory used=5317.3MB, alloc=424.6MB, time=257.33 memory used=5375.9MB, alloc=424.6MB, time=257.51 memory used=5441.2MB, alloc=424.6MB, time=257.73 memory used=5513.7MB, alloc=424.6MB, time=257.92 memory used=5594.6MB, alloc=424.6MB, time=258.11 memory used=5683.5MB, alloc=424.6MB, time=258.33 memory used=5764.6MB, alloc=424.6MB, time=258.52 memory used=5816.2MB, alloc=424.6MB, time=258.68 memory used=5870.0MB, alloc=424.6MB, time=258.84 memory used=5927.6MB, alloc=424.6MB, time=259.00 memory used=5988.8MB, alloc=424.6MB, time=259.16 memory used=6053.9MB, alloc=424.6MB, time=259.33 memory used=6123.7MB, alloc=424.6MB, time=259.50 memory used=6198.9MB, alloc=424.6MB, time=259.66 memory used=6311.2MB, alloc=424.6MB, time=260.34 memory used=6394.4MB, alloc=424.6MB, time=260.94 memory used=6472.6MB, alloc=424.6MB, time=261.17 memory used=6550.0MB, alloc=424.6MB, time=261.37 memory used=6665.5MB, alloc=424.6MB, time=262.49 memory used=6744.2MB, alloc=424.6MB, time=262.79 memory used=6813.1MB, alloc=424.6MB, time=263.04 memory used=6893.5MB, alloc=424.6MB, time=263.30 memory used=6984.9MB, alloc=424.6MB, time=263.56 memory used=7076.9MB, alloc=424.6MB, time=263.82 memory used=7132.1MB, alloc=424.6MB, time=264.03 memory used=7190.4MB, alloc=424.6MB, time=264.23 memory used=7252.2MB, alloc=424.6MB, time=264.44 memory used=7319.2MB, alloc=424.6MB, time=264.64 memory used=7389.0MB, alloc=424.6MB, time=264.86 memory used=7463.5MB, alloc=424.6MB, time=265.11 memory used=7544.3MB, alloc=424.6MB, time=265.32 memory used=7630.4MB, alloc=424.6MB, time=265.57 memory used=7722.8MB, alloc=424.6MB, time=265.79 memory used=7806.8MB, alloc=424.6MB, time=266.00 memory used=7881.9MB, alloc=424.6MB, time=266.20 memory used=7937.7MB, alloc=424.6MB, time=266.35 memory used=7998.0MB, alloc=424.6MB, time=266.50 memory used=8066.5MB, alloc=424.6MB, time=266.64 memory used=8180.2MB, alloc=424.6MB, time=267.50 memory used=8267.2MB, alloc=424.6MB, time=267.79 memory used=8335.0MB, alloc=424.6MB, time=268.03 memory used=8414.4MB, alloc=424.6MB, time=268.26 memory used=8505.0MB, alloc=424.6MB, time=268.56 memory used=8602.7MB, alloc=424.6MB, time=268.82 memory used=8659.1MB, alloc=424.6MB, time=269.06 memory used=8716.5MB, alloc=424.6MB, time=269.25 memory used=8778.2MB, alloc=424.6MB, time=269.47 memory used=8845.2MB, alloc=424.6MB, time=269.72 memory used=8915.0MB, alloc=424.6MB, time=269.91 memory used=8989.6MB, alloc=424.6MB, time=270.12 memory used=9070.5MB, alloc=424.6MB, time=270.33 memory used=9156.9MB, alloc=424.6MB, time=270.54 memory used=9249.5MB, alloc=424.6MB, time=270.78 memory used=9334.1MB, alloc=424.6MB, time=270.97 memory used=9410.9MB, alloc=424.6MB, time=271.15 memory used=9467.5MB, alloc=424.6MB, time=271.30 memory used=9528.2MB, alloc=424.6MB, time=271.46 memory used=9596.4MB, alloc=424.6MB, time=271.60 memory used=9700.4MB, alloc=424.6MB, time=292.31 memory used=9788.6MB, alloc=424.6MB, time=348.77 memory used=9884.2MB, alloc=424.6MB, time=427.48 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428521179 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 F := [-4 x y z + 7 z - 17 x z, -17 y z - 5 y z - x] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 3 2 2 2 G := [-7 x y - 8 y z - 20 x , -15 x y + 6 x z + 14 x y z] > Problem := [F,G]; 2 3 2 Problem := [[-4 x y z + 7 z - 17 x z, -17 y z - 5 y z - x], 2 2 3 3 2 2 2 [-7 x y - 8 y z - 20 x , -15 x y + 6 x z + 14 x y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=25.9MB, alloc=32.3MB, time=0.49 memory used=46.1MB, alloc=56.3MB, time=0.79 memory used=88.6MB, alloc=60.3MB, time=1.34 memory used=131.3MB, alloc=60.3MB, time=1.92 memory used=171.4MB, alloc=84.3MB, time=2.53 memory used=242.9MB, alloc=92.3MB, time=3.50 memory used=308.2MB, alloc=116.3MB, time=4.44 memory used=365.6MB, alloc=116.3MB, time=5.15 memory used=447.8MB, alloc=116.3MB, time=5.96 memory used=518.6MB, alloc=116.3MB, time=6.85 memory used=598.9MB, alloc=116.3MB, time=7.63 memory used=668.3MB, alloc=140.3MB, time=8.68 memory used=733.6MB, alloc=396.3MB, time=9.55 memory used=846.0MB, alloc=420.3MB, time=11.05 memory used=979.0MB, alloc=444.3MB, time=13.01 memory used=1114.7MB, alloc=444.3MB, time=14.55 memory used=1245.2MB, alloc=444.3MB, time=16.17 memory used=1375.3MB, alloc=468.3MB, time=18.11 memory used=1492.4MB, alloc=468.3MB, time=20.08 memory used=1598.8MB, alloc=492.3MB, time=21.77 memory used=1743.4MB, alloc=492.3MB, time=23.35 memory used=1843.3MB, alloc=492.3MB, time=24.73 memory used=1979.3MB, alloc=492.3MB, time=26.20 memory used=2071.6MB, alloc=492.3MB, time=27.58 memory used=2157.7MB, alloc=516.3MB, time=28.76 memory used=2239.1MB, alloc=516.3MB, time=29.93 memory used=2313.4MB, alloc=516.3MB, time=31.06 memory used=2391.0MB, alloc=516.3MB, time=32.34 memory used=2455.7MB, alloc=516.3MB, time=33.44 memory used=2542.8MB, alloc=516.3MB, time=34.59 memory used=2619.3MB, alloc=516.3MB, time=35.72 memory used=2703.8MB, alloc=516.3MB, time=36.97 memory used=2777.3MB, alloc=516.3MB, time=37.96 memory used=2840.9MB, alloc=516.3MB, time=39.16 memory used=2909.1MB, alloc=540.3MB, time=40.27 memory used=2957.8MB, alloc=540.3MB, time=41.05 memory used=3012.8MB, alloc=540.3MB, time=42.05 memory used=3062.1MB, alloc=540.3MB, time=43.13 memory used=3305.3MB, alloc=564.3MB, time=46.98 memory used=3570.2MB, alloc=588.3MB, time=50.25 memory used=3830.5MB, alloc=612.3MB, time=54.36 memory used=4141.3MB, alloc=636.3MB, time=58.29 memory used=4468.3MB, alloc=660.3MB, time=62.80 memory used=4821.6MB, alloc=684.3MB, time=67.44 memory used=5129.3MB, alloc=708.3MB, time=72.18 memory used=5402.5MB, alloc=732.3MB, time=77.12 memory used=5681.3MB, alloc=756.3MB, time=82.44 memory used=5914.7MB, alloc=780.3MB, time=87.01 memory used=6170.4MB, alloc=804.3MB, time=92.02 memory used=6440.8MB, alloc=828.3MB, time=97.54 memory used=6773.6MB, alloc=852.3MB, time=102.87 memory used=7169.2MB, alloc=876.3MB, time=107.89 memory used=7469.9MB, alloc=900.3MB, time=113.00 memory used=7732.5MB, alloc=924.3MB, time=118.20 memory used=7989.9MB, alloc=948.3MB, time=123.34 memory used=8223.8MB, alloc=972.3MB, time=128.14 memory used=8443.2MB, alloc=996.3MB, time=132.71 memory used=8663.7MB, alloc=1020.3MB, time=137.37 memory used=9191.1MB, alloc=1044.3MB, time=148.06 memory used=9685.6MB, alloc=1068.3MB, time=160.55 memory used=10086.3MB, alloc=1092.3MB, time=176.41 memory used=10481.9MB, alloc=1116.3MB, time=193.16 memory used=10883.2MB, alloc=1140.3MB, time=210.37 memory used=11291.5MB, alloc=1164.3MB, time=228.48 memory used=11714.4MB, alloc=1188.3MB, time=247.31 memory used=12151.4MB, alloc=1212.3MB, time=266.60 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428521479 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [15 x y z + 10 y + 4 z, -11 x z + 9 x y - 3 y z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 4 2 G := [-12 x z - 8 z - 10 z, -z + 12 y z + 4 y z] > Problem := [F,G]; 2 2 2 Problem := [[15 x y z + 10 y + 4 z, -11 x z + 9 x y - 3 y z], 3 3 4 2 [-12 x z - 8 z - 10 z, -z + 12 y z + 4 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.9MB, alloc=32.3MB, time=0.52 memory used=46.7MB, alloc=32.3MB, time=0.82 memory used=65.8MB, alloc=56.3MB, time=1.13 memory used=107.0MB, alloc=60.3MB, time=1.75 memory used=147.5MB, alloc=60.3MB, time=2.39 memory used=185.9MB, alloc=84.3MB, time=2.98 memory used=224.4MB, alloc=84.3MB, time=3.61 memory used=290.3MB, alloc=92.3MB, time=4.62 memory used=355.0MB, alloc=116.3MB, time=5.58 memory used=424.4MB, alloc=116.3MB, time=6.48 memory used=494.4MB, alloc=372.3MB, time=7.44 memory used=581.8MB, alloc=372.3MB, time=8.78 memory used=667.5MB, alloc=396.3MB, time=10.16 memory used=779.4MB, alloc=396.3MB, time=11.71 memory used=889.5MB, alloc=420.3MB, time=13.54 memory used=1023.9MB, alloc=444.3MB, time=15.82 memory used=1156.6MB, alloc=444.3MB, time=18.00 memory used=1274.9MB, alloc=468.3MB, time=19.78 memory used=1396.0MB, alloc=468.3MB, time=21.90 memory used=1508.3MB, alloc=468.3MB, time=23.62 memory used=1627.3MB, alloc=468.3MB, time=25.83 memory used=1780.4MB, alloc=492.3MB, time=27.74 memory used=1886.2MB, alloc=492.3MB, time=29.17 memory used=1975.3MB, alloc=492.3MB, time=30.79 memory used=2075.8MB, alloc=492.3MB, time=32.82 memory used=2172.8MB, alloc=492.3MB, time=34.77 memory used=2268.4MB, alloc=492.3MB, time=36.64 memory used=2356.1MB, alloc=492.3MB, time=38.57 memory used=2433.0MB, alloc=492.3MB, time=40.07 memory used=2495.4MB, alloc=492.3MB, time=41.26 memory used=2558.9MB, alloc=516.3MB, time=42.60 memory used=2634.0MB, alloc=516.3MB, time=44.27 memory used=2700.2MB, alloc=516.3MB, time=45.65 memory used=2767.0MB, alloc=516.3MB, time=47.08 memory used=2819.2MB, alloc=516.3MB, time=48.19 memory used=2891.6MB, alloc=516.3MB, time=49.54 memory used=2988.2MB, alloc=540.3MB, time=51.17 memory used=3051.1MB, alloc=540.3MB, time=52.51 memory used=3114.3MB, alloc=540.3MB, time=53.85 memory used=3177.2MB, alloc=540.3MB, time=55.22 memory used=3283.2MB, alloc=540.3MB, time=56.77 memory used=3362.3MB, alloc=564.3MB, time=58.26 memory used=3464.6MB, alloc=564.3MB, time=60.09 memory used=3701.9MB, alloc=588.3MB, time=63.82 memory used=3952.0MB, alloc=612.3MB, time=68.03 memory used=4218.9MB, alloc=636.3MB, time=72.28 memory used=4477.9MB, alloc=660.3MB, time=77.41 memory used=4755.2MB, alloc=684.3MB, time=82.72 memory used=5033.0MB, alloc=708.3MB, time=88.65 memory used=5330.9MB, alloc=732.3MB, time=94.23 memory used=5639.2MB, alloc=756.3MB, time=100.39 memory used=5955.4MB, alloc=780.3MB, time=106.70 memory used=6268.7MB, alloc=804.3MB, time=113.06 memory used=6545.4MB, alloc=828.3MB, time=118.75 memory used=6891.3MB, alloc=852.3MB, time=124.61 memory used=7227.9MB, alloc=876.3MB, time=131.81 memory used=7555.0MB, alloc=900.3MB, time=140.44 memory used=7825.4MB, alloc=924.3MB, time=150.53 memory used=8097.4MB, alloc=948.3MB, time=161.44 memory used=8377.4MB, alloc=972.3MB, time=171.29 memory used=8667.4MB, alloc=996.3MB, time=182.22 memory used=8969.4MB, alloc=1020.3MB, time=193.52 memory used=9284.0MB, alloc=1044.3MB, time=205.59 memory used=9612.3MB, alloc=1068.3MB, time=218.48 memory used=9954.1MB, alloc=1092.3MB, time=231.73 memory used=10308.4MB, alloc=1116.3MB, time=245.95 memory used=10679.1MB, alloc=1140.3MB, time=261.57 memory used=11066.5MB, alloc=1164.3MB, time=277.90 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428521779 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 4 3 3 2 F := [-8 x y z + 6 x y z + 19 y , -8 y z - 11 x + 16 z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 3 G := [-18 x y z + 5 x z - 17, -2 x z + 10 x y - 18 z ] > Problem := [F,G]; 2 2 4 3 3 2 Problem := [[-8 x y z + 6 x y z + 19 y , -8 y z - 11 x + 16 z ], 2 2 2 3 2 3 [-18 x y z + 5 x z - 17, -2 x z + 10 x y - 18 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.2MB, alloc=32.3MB, time=0.50 memory used=45.3MB, alloc=60.3MB, time=0.78 memory used=82.2MB, alloc=63.8MB, time=0.95 memory used=112.4MB, alloc=63.8MB, time=1.02 memory used=134.8MB, alloc=63.8MB, time=1.07 memory used=170.3MB, alloc=63.8MB, time=1.23 memory used=204.4MB, alloc=63.8MB, time=1.83 memory used=248.5MB, alloc=63.8MB, time=3.21 memory used=276.9MB, alloc=63.8MB, time=3.27 memory used=302.6MB, alloc=63.8MB, time=3.33 memory used=331.4MB, alloc=63.8MB, time=3.40 memory used=364.7MB, alloc=63.8MB, time=3.50 memory used=396.4MB, alloc=63.8MB, time=3.57 memory used=419.1MB, alloc=63.8MB, time=3.62 memory used=454.7MB, alloc=63.8MB, time=3.74 memory used=484.2MB, alloc=63.8MB, time=3.81 memory used=509.4MB, alloc=63.8MB, time=3.87 memory used=547.0MB, alloc=63.8MB, time=5.64 memory used=596.5MB, alloc=63.8MB, time=7.86 memory used=627.2MB, alloc=63.8MB, time=7.93 memory used=649.5MB, alloc=63.8MB, time=7.99 memory used=676.7MB, alloc=63.8MB, time=8.04 memory used=708.6MB, alloc=63.8MB, time=8.11 memory used=728.9MB, alloc=63.8MB, time=8.15 memory used=759.9MB, alloc=63.8MB, time=8.31 memory used=801.8MB, alloc=63.8MB, time=8.71 memory used=837.5MB, alloc=63.8MB, time=9.14 memory used=860.9MB, alloc=63.8MB, time=9.20 memory used=899.9MB, alloc=63.8MB, time=9.53 memory used=943.8MB, alloc=71.8MB, time=9.87 memory used=988.1MB, alloc=71.8MB, time=10.33 memory used=1032.8MB, alloc=71.8MB, time=10.77 memory used=1074.1MB, alloc=71.8MB, time=11.33 memory used=1115.9MB, alloc=95.8MB, time=11.92 memory used=1161.3MB, alloc=95.8MB, time=12.21 memory used=1202.2MB, alloc=95.8MB, time=12.57 memory used=1230.9MB, alloc=107.8MB, time=12.92 memory used=1268.6MB, alloc=107.8MB, time=13.03 memory used=1306.6MB, alloc=107.8MB, time=13.38 memory used=1345.6MB, alloc=107.8MB, time=13.61 memory used=1380.5MB, alloc=107.8MB, time=13.92 memory used=1396.3MB, alloc=107.8MB, time=14.15 memory used=1434.2MB, alloc=107.8MB, time=14.25 memory used=1472.9MB, alloc=107.8MB, time=14.62 memory used=1514.7MB, alloc=107.8MB, time=14.92 memory used=1569.2MB, alloc=107.8MB, time=16.31 memory used=1608.8MB, alloc=131.8MB, time=16.45 memory used=1646.9MB, alloc=131.8MB, time=16.59 memory used=1692.3MB, alloc=131.8MB, time=16.74 memory used=1743.3MB, alloc=131.8MB, time=16.90 memory used=1799.2MB, alloc=131.8MB, time=17.05 memory used=1863.1MB, alloc=131.8MB, time=17.21 memory used=1899.4MB, alloc=131.8MB, time=17.34 memory used=1931.7MB, alloc=131.8MB, time=17.46 memory used=1967.2MB, alloc=131.8MB, time=17.59 memory used=2003.7MB, alloc=131.8MB, time=17.71 memory used=2041.2MB, alloc=131.8MB, time=17.84 memory used=2079.6MB, alloc=131.8MB, time=17.98 memory used=2119.0MB, alloc=131.8MB, time=18.10 memory used=2159.7MB, alloc=131.8MB, time=18.24 memory used=2205.1MB, alloc=131.8MB, time=18.38 memory used=2251.8MB, alloc=131.8MB, time=18.51 memory used=2299.5MB, 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used=19245.6MB, alloc=155.8MB, time=180.59 memory used=19271.0MB, alloc=155.8MB, time=180.67 memory used=19303.7MB, alloc=155.8MB, time=180.76 memory used=19344.2MB, alloc=155.8MB, time=180.86 memory used=19356.2MB, alloc=155.8MB, time=180.92 memory used=19368.3MB, alloc=155.8MB, time=180.99 memory used=19380.6MB, alloc=155.8MB, time=181.06 memory used=19393.0MB, alloc=155.8MB, time=181.13 memory used=19405.6MB, alloc=155.8MB, time=181.20 memory used=19418.4MB, alloc=155.8MB, time=181.27 memory used=19431.2MB, alloc=155.8MB, time=181.33 memory used=19444.3MB, alloc=155.8MB, time=181.40 memory used=19457.5MB, alloc=155.8MB, time=181.46 memory used=19470.8MB, alloc=155.8MB, time=181.53 memory used=19484.3MB, alloc=155.8MB, time=181.59 memory used=19500.9MB, alloc=155.8MB, time=182.99 memory used=19595.4MB, alloc=155.8MB, time=186.73 memory used=19670.2MB, alloc=155.8MB, time=187.96 memory used=19746.8MB, alloc=155.8MB, time=188.32 memory used=19838.3MB, alloc=155.8MB, time=190.31 memory used=19915.8MB, alloc=155.8MB, time=190.54 memory used=19971.9MB, alloc=155.8MB, time=190.72 memory used=20045.4MB, alloc=155.8MB, time=190.90 memory used=20109.1MB, alloc=155.8MB, time=191.05 memory used=20160.1MB, alloc=155.8MB, time=191.17 memory used=20217.2MB, alloc=155.8MB, time=191.29 memory used=20281.5MB, alloc=155.8MB, time=191.42 memory used=20354.0MB, alloc=155.8MB, time=191.55 memory used=20422.3MB, alloc=155.8MB, time=191.66 memory used=20444.6MB, alloc=155.8MB, time=191.74 memory used=20465.1MB, alloc=155.8MB, time=191.81 memory used=20476.8MB, alloc=155.8MB, time=191.88 memory used=20488.1MB, alloc=155.8MB, time=191.95 memory used=20500.0MB, alloc=155.8MB, time=192.02 memory used=20517.2MB, alloc=155.8MB, time=192.21 memory used=20631.9MB, alloc=411.8MB, time=193.86 memory used=20766.1MB, alloc=411.8MB, time=194.81 memory used=20898.9MB, alloc=411.8MB, time=196.23 memory used=21031.9MB, alloc=411.8MB, time=198.10 memory used=21167.2MB, alloc=411.8MB, time=200.86 memory used=21299.1MB, alloc=411.8MB, time=204.39 memory used=21431.8MB, alloc=411.8MB, time=208.85 memory used=21564.4MB, alloc=411.8MB, time=213.89 memory used=21695.5MB, alloc=411.8MB, time=219.90 memory used=21828.2MB, alloc=411.8MB, time=226.24 memory used=21963.9MB, alloc=411.8MB, time=234.06 memory used=22098.6MB, alloc=411.8MB, time=242.61 memory used=22234.0MB, alloc=411.8MB, time=251.15 memory used=22371.3MB, alloc=411.8MB, time=260.50 memory used=22495.3MB, alloc=411.8MB, time=265.24 memory used=22557.0MB, alloc=411.8MB, time=265.42 memory used=22619.9MB, alloc=411.8MB, time=265.62 memory used=22686.9MB, alloc=411.8MB, time=265.77 memory used=22734.3MB, alloc=411.8MB, time=265.90 memory used=22788.4MB, alloc=411.8MB, time=266.03 memory used=22849.1MB, alloc=411.8MB, time=266.17 memory used=22918.4MB, alloc=411.8MB, time=266.31 memory used=22995.4MB, alloc=411.8MB, time=266.45 memory used=23172.3MB, alloc=411.8MB, time=266.87 memory used=23307.9MB, alloc=411.8MB, time=268.34 memory used=23369.3MB, alloc=411.8MB, time=268.50 memory used=23434.4MB, alloc=411.8MB, time=268.70 memory used=23507.5MB, alloc=411.8MB, time=270.22 memory used=23589.2MB, alloc=411.8MB, time=270.66 memory used=23644.5MB, alloc=411.8MB, time=270.81 memory used=23719.2MB, alloc=411.8MB, time=270.96 memory used=23769.5MB, alloc=411.8MB, time=271.08 memory used=23820.3MB, alloc=411.8MB, time=271.20 memory used=23876.9MB, alloc=411.8MB, time=271.32 memory used=23939.0MB, alloc=411.8MB, time=271.45 memory used=24008.6MB, alloc=411.8MB, time=271.58 memory used=24085.8MB, alloc=411.8MB, time=271.71 memory used=24266.2MB, alloc=411.8MB, time=271.96 memory used=24511.0MB, alloc=411.8MB, time=273.14 memory used=24598.8MB, alloc=411.8MB, time=274.05 memory used=24658.2MB, alloc=411.8MB, time=274.20 memory used=24708.5MB, alloc=411.8MB, time=274.31 memory used=24786.0MB, alloc=411.8MB, time=274.67 memory used=24891.6MB, alloc=411.8MB, time=275.49 memory used=24998.7MB, alloc=411.8MB, time=277.07 memory used=25073.4MB, alloc=411.8MB, time=278.11 memory used=25211.0MB, alloc=411.8MB, time=279.61 memory used=25269.8MB, alloc=411.8MB, time=279.86 memory used=25318.5MB, alloc=411.8MB, time=280.01 memory used=25377.2MB, alloc=411.8MB, time=280.25 memory used=25432.8MB, alloc=411.8MB, time=281.26 memory used=25509.2MB, alloc=411.8MB, time=294.01 memory used=25563.5MB, alloc=411.8MB, time=294.20 memory used=25602.3MB, alloc=435.8MB, time=294.39 memory used=25663.8MB, alloc=435.8MB, time=294.62 memory used=25737.5MB, alloc=435.8MB, time=294.83 memory used=25805.9MB, alloc=435.8MB, time=295.01 memory used=25851.6MB, alloc=435.8MB, time=295.18 memory used=25897.9MB, alloc=435.8MB, time=295.34 memory used=25950.1MB, alloc=435.8MB, time=295.50 memory used=26005.4MB, alloc=435.8MB, time=295.67 memory used=26063.4MB, alloc=435.8MB, time=295.83 memory used=26124.1MB, alloc=435.8MB, time=296.01 memory used=26187.5MB, alloc=435.8MB, time=296.18 memory used=26253.6MB, alloc=435.8MB, time=296.36 memory used=26322.2MB, alloc=435.8MB, time=296.54 memory used=26393.4MB, alloc=435.8MB, time=296.72 memory used=26472.7MB, alloc=435.8MB, time=296.91 memory used=26554.9MB, alloc=435.8MB, time=297.10 memory used=26730.5MB, alloc=435.8MB, time=297.43 memory used=26872.1MB, alloc=435.8MB, time=297.74 memory used=27022.0MB, alloc=435.8MB, time=298.06 memory used=27178.1MB, alloc=435.8MB, time=298.36 memory used=27339.8MB, alloc=435.8MB, time=298.68 memory used=27514.9MB, alloc=435.8MB, time=299.00 memory used=27695.8MB, alloc=435.8MB, time=299.34 memory used=27890.4MB, alloc=435.8MB, time=299.69 memory used=28090.6MB, alloc=435.8MB, time=300.03 memory used=28297.2MB, alloc=435.8MB, time=300.40 memory used=28515.8MB, alloc=435.8MB, time=300.77 memory used=28741.8MB, alloc=435.8MB, time=301.15 memory used=28979.4MB, alloc=435.8MB, time=301.52 memory used=29213.6MB, alloc=435.8MB, time=301.88 memory used=29402.0MB, alloc=435.8MB, time=302.21 memory used=29579.4MB, alloc=435.8MB, time=302.54 memory used=29754.0MB, alloc=435.8MB, time=302.85 memory used=29938.0MB, alloc=435.8MB, time=303.16 memory used=30124.7MB, alloc=435.8MB, time=303.48 memory used=30314.1MB, alloc=435.8MB, time=303.80 memory used=30512.3MB, alloc=435.8MB, time=304.15 memory used=30713.1MB, alloc=435.8MB, time=304.49 memory used=30925.0MB, alloc=435.8MB, time=304.82 memory used=31138.0MB, alloc=435.8MB, time=305.17 memory used=31361.9MB, alloc=435.8MB, time=305.52 memory used=31586.5MB, alloc=435.8MB, time=305.88 memory used=31821.9MB, alloc=435.8MB, time=306.26 memory used=32058.5MB, alloc=435.8MB, time=306.63 memory used=32286.5MB, alloc=435.8MB, time=306.99 memory used=32516.1MB, alloc=435.8MB, time=307.35 memory used=32727.0MB, alloc=435.8MB, time=307.69 memory used=32924.7MB, alloc=435.8MB, time=308.00 memory used=33125.0MB, alloc=435.8MB, time=308.33 memory used=33325.7MB, alloc=435.8MB, time=308.65 memory used=33532.1MB, alloc=435.8MB, time=308.98 memory used=33748.0MB, alloc=435.8MB, time=309.31 memory used=33961.9MB, alloc=435.8MB, time=309.64 memory used=34183.3MB, alloc=435.8MB, time=309.98 memory used=34411.2MB, alloc=435.8MB, time=310.31 memory used=34645.0MB, alloc=435.8MB, time=310.67 memory used=34883.8MB, alloc=435.8MB, time=311.02 memory used=35123.4MB, alloc=435.8MB, time=311.38 memory used=35348.5MB, alloc=435.8MB, time=311.73 memory used=35577.9MB, alloc=435.8MB, time=312.06 memory used=35802.2MB, alloc=435.8MB, time=312.40 memory used=36016.5MB, alloc=435.8MB, time=312.71 memory used=36238.7MB, alloc=435.8MB, time=313.03 memory used=36464.1MB, alloc=435.8MB, time=313.35 memory used=36696.8MB, alloc=435.8MB, time=313.68 memory used=36939.0MB, alloc=435.8MB, time=314.04 memory used=37190.4MB, alloc=435.8MB, time=314.38 memory used=37527.9MB, alloc=435.8MB, time=319.50 memory used=37599.0MB, alloc=435.8MB, time=319.69 memory used=37652.1MB, alloc=435.8MB, time=319.84 memory used=37717.5MB, alloc=435.8MB, time=320.01 memory used=37797.4MB, alloc=435.8MB, time=320.18 memory used=37976.3MB, alloc=435.8MB, time=320.49 memory used=38165.3MB, alloc=435.8MB, time=320.95 memory used=38224.9MB, alloc=435.8MB, time=321.14 memory used=38304.5MB, alloc=435.8MB, time=321.35 memory used=38354.9MB, alloc=435.8MB, time=321.51 memory used=38409.7MB, alloc=435.8MB, time=321.66 memory used=38496.8MB, alloc=435.8MB, time=325.39 memory used=38567.2MB, alloc=435.8MB, time=325.65 memory used=38631.4MB, alloc=435.8MB, time=325.86 memory used=38707.2MB, alloc=435.8MB, time=326.08 memory used=38755.3MB, alloc=435.8MB, time=326.25 memory used=38808.7MB, alloc=435.8MB, time=326.43 memory used=38866.3MB, alloc=435.8MB, time=326.59 memory used=38931.0MB, alloc=435.8MB, time=326.76 memory used=39000.0MB, alloc=435.8MB, time=326.95 memory used=39073.5MB, alloc=435.8MB, time=327.13 memory used=39153.4MB, alloc=435.8MB, time=327.32 memory used=39354.9MB, alloc=435.8MB, time=327.70 memory used=39505.5MB, alloc=435.8MB, time=327.99 memory used=39669.2MB, alloc=435.8MB, time=328.30 memory used=39848.2MB, alloc=435.8MB, time=328.64 memory used=40044.7MB, alloc=435.8MB, time=328.98 memory used=40257.4MB, alloc=435.8MB, time=329.33 memory used=40490.9MB, alloc=435.8MB, time=329.68 memory used=40723.4MB, alloc=435.8MB, time=330.05 memory used=40914.5MB, alloc=435.8MB, time=330.38 memory used=41104.4MB, alloc=435.8MB, time=330.73 memory used=41303.3MB, alloc=435.8MB, time=331.06 memory used=41514.9MB, alloc=435.8MB, time=331.39 memory used=41740.2MB, alloc=435.8MB, time=331.74 memory used=41984.0MB, alloc=435.8MB, time=332.09 memory used=42206.2MB, alloc=435.8MB, time=332.42 memory used=42559.7MB, alloc=435.8MB, time=334.44 memory used=42698.3MB, alloc=435.8MB, time=336.95 memory used=42786.0MB, alloc=435.8MB, time=340.81 memory used=42857.6MB, alloc=435.8MB, time=341.05 memory used=42907.4MB, alloc=435.8MB, time=341.23 memory used=42967.5MB, alloc=435.8MB, time=341.44 memory used=43061.3MB, alloc=435.8MB, time=352.70 memory used=43145.0MB, alloc=435.8MB, time=353.46 memory used=43212.9MB, alloc=435.8MB, time=353.67 memory used=43270.2MB, alloc=435.8MB, time=353.88 memory used=43322.8MB, alloc=435.8MB, time=354.07 memory used=43384.3MB, alloc=435.8MB, time=354.25 memory used=43456.4MB, alloc=435.8MB, time=354.43 memory used=43530.4MB, alloc=435.8MB, time=354.77 memory used=43624.1MB, alloc=435.8MB, time=359.71 memory used=43686.5MB, alloc=435.8MB, time=359.91 memory used=43743.4MB, alloc=435.8MB, time=360.12 memory used=43816.2MB, alloc=435.8MB, time=360.31 memory used=43867.3MB, alloc=435.8MB, time=360.48 memory used=43917.0MB, alloc=435.8MB, time=360.64 memory used=43972.5MB, alloc=435.8MB, time=360.80 memory used=44035.4MB, alloc=435.8MB, time=360.96 memory used=44137.8MB, alloc=435.8MB, time=373.06 memory used=44217.3MB, alloc=435.8MB, time=373.45 memory used=44273.1MB, alloc=435.8MB, time=373.66 memory used=44331.4MB, alloc=435.8MB, time=373.86 memory used=44402.3MB, alloc=435.8MB, time=374.06 memory used=44461.6MB, alloc=435.8MB, time=374.25 memory used=44507.0MB, alloc=435.8MB, time=374.41 memory used=44556.3MB, alloc=435.8MB, time=374.56 memory used=44610.6MB, alloc=435.8MB, time=374.72 memory used=44670.2MB, alloc=435.8MB, time=374.88 memory used=44735.8MB, alloc=435.8MB, time=375.04 memory used=44806.6MB, alloc=435.8MB, time=375.20 memory used=44990.1MB, alloc=435.8MB, time=377.05 memory used=45064.7MB, alloc=435.8MB, time=377.36 memory used=45147.4MB, alloc=435.8MB, time=378.24 memory used=45215.1MB, alloc=435.8MB, time=378.50 memory used=45271.1MB, alloc=435.8MB, time=378.73 memory used=45337.0MB, alloc=435.8MB, time=378.94 memory used=45415.0MB, alloc=435.8MB, time=379.19 memory used=45469.9MB, alloc=435.8MB, time=379.39 memory used=45516.6MB, alloc=435.8MB, time=379.59 memory used=45568.1MB, alloc=435.8MB, time=379.76 memory used=45624.7MB, alloc=435.8MB, time=379.95 memory used=45687.2MB, alloc=435.8MB, time=380.13 memory used=45766.9MB, alloc=459.8MB, time=389.11 memory used=45854.4MB, alloc=459.8MB, time=391.30 memory used=45936.9MB, alloc=459.8MB, time=391.55 memory used=46026.4MB, alloc=459.8MB, time=391.82 memory used=46088.8MB, alloc=459.8MB, time=392.03 memory used=46151.6MB, alloc=459.8MB, time=392.25 memory used=46219.5MB, alloc=459.8MB, time=392.47 memory used=46293.2MB, alloc=459.8MB, time=392.69 memory used=46372.8MB, alloc=459.8MB, time=392.90 memory used=46459.5MB, alloc=459.8MB, time=393.14 memory used=46553.1MB, alloc=459.8MB, time=393.35 memory used=46652.4MB, alloc=459.8MB, time=393.59 memory used=46713.4MB, alloc=459.8MB, time=393.77 memory used=46768.5MB, alloc=459.8MB, time=393.95 memory used=46824.5MB, alloc=459.8MB, time=394.12 memory used=46883.2MB, alloc=459.8MB, time=394.31 memory used=46944.3MB, alloc=459.8MB, time=394.49 memory used=47008.7MB, alloc=459.8MB, time=394.67 memory used=47076.0MB, alloc=459.8MB, time=394.85 memory used=47145.3MB, alloc=459.8MB, time=395.02 memory used=47218.3MB, alloc=459.8MB, time=395.20 memory used=47295.7MB, alloc=459.8MB, time=395.38 memory used=47377.6MB, alloc=459.8MB, time=395.56 memory used=47464.5MB, alloc=459.8MB, time=395.74 memory used=47596.8MB, alloc=459.8MB, time=396.70 memory used=47699.1MB, alloc=459.8MB, time=397.44 memory used=47777.1MB, alloc=459.8MB, time=397.68 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428522079 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 4 2 3 3 F := [-11 x z - 7 z - 10 y z , -5 x y + 2 x z - 15 y z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 G := [-14 x y z - 11 y z , -20 y z - 15 y - 7 z] > Problem := [F,G]; 3 4 2 3 3 Problem := [[-11 x z - 7 z - 10 y z , -5 x y + 2 x z - 15 y z], 2 2 2 3 [-14 x y z - 11 y z , -20 y z - 15 y - 7 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.3MB, alloc=32.3MB, time=0.49 memory used=46.9MB, alloc=32.3MB, time=0.80 memory used=63.7MB, alloc=56.3MB, time=1.06 memory used=104.4MB, alloc=60.3MB, time=1.57 memory used=144.2MB, alloc=84.3MB, time=2.08 memory used=209.0MB, alloc=92.3MB, time=2.87 memory used=272.4MB, alloc=116.3MB, time=3.68 memory used=332.5MB, alloc=116.3MB, time=4.28 memory used=400.2MB, alloc=372.3MB, time=4.95 memory used=486.9MB, alloc=372.3MB, time=5.76 memory used=571.1MB, alloc=396.3MB, time=6.80 memory used=641.9MB, alloc=396.3MB, time=7.14 memory used=718.4MB, alloc=396.3MB, time=7.57 memory used=777.0MB, alloc=396.3MB, time=7.80 memory used=877.2MB, alloc=396.3MB, time=8.64 memory used=992.7MB, alloc=420.3MB, time=9.90 memory used=1137.9MB, alloc=420.3MB, time=11.26 memory used=1265.1MB, alloc=444.3MB, time=12.99 memory used=1412.3MB, alloc=468.3MB, time=15.01 memory used=1600.8MB, alloc=492.3MB, time=17.95 memory used=1814.0MB, alloc=516.3MB, time=21.10 memory used=2022.7MB, alloc=540.3MB, time=23.83 memory used=2207.1MB, alloc=564.3MB, time=26.51 memory used=2407.6MB, alloc=588.3MB, time=29.48 memory used=2597.2MB, alloc=612.3MB, time=32.35 memory used=2780.8MB, alloc=636.3MB, time=35.61 memory used=3003.0MB, alloc=660.3MB, time=41.69 memory used=3226.1MB, alloc=684.3MB, time=48.47 memory used=3459.2MB, alloc=708.3MB, time=55.82 memory used=3705.7MB, alloc=732.3MB, time=63.88 memory used=3958.1MB, alloc=756.3MB, time=73.09 memory used=4234.1MB, alloc=780.3MB, time=83.04 memory used=4534.0MB, alloc=804.3MB, time=93.91 memory used=4857.9MB, alloc=828.3MB, time=105.50 memory used=5205.7MB, alloc=852.3MB, time=117.97 memory used=5577.5MB, alloc=852.3MB, time=131.30 memory used=5949.2MB, alloc=852.3MB, time=144.58 memory used=6320.8MB, alloc=876.3MB, time=157.82 memory used=6716.4MB, alloc=876.3MB, time=171.87 memory used=7112.0MB, alloc=876.3MB, time=186.43 memory used=7507.5MB, alloc=900.3MB, time=201.91 memory used=7926.7MB, alloc=900.3MB, time=218.15 memory used=8345.8MB, alloc=900.3MB, time=234.48 memory used=8765.1MB, alloc=924.3MB, time=249.77 memory used=9208.2MB, alloc=924.3MB, time=266.65 memory used=9651.2MB, alloc=948.3MB, time=284.28 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428522379 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 F := [3 x y z + 19 z + 4 y, 19 x z - 2 x y + 3 y] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 4 2 2 G := [19 x y + 16 x z + 4 y , 19 x y z - 6 x z + 19 x] > Problem := [F,G]; 2 3 2 2 Problem := [[3 x y z + 19 z + 4 y, 19 x z - 2 x y + 3 y], 3 3 4 2 2 [19 x y + 16 x z + 4 y , 19 x y z - 6 x z + 19 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.1MB, alloc=32.3MB, time=0.17 memory used=25.3MB, alloc=36.3MB, time=0.46 memory used=46.1MB, alloc=36.5MB, time=0.72 memory used=61.9MB, alloc=36.5MB, time=0.77 memory used=76.0MB, alloc=36.5MB, time=0.83 memory used=90.3MB, alloc=36.5MB, time=0.88 memory used=103.8MB, alloc=36.5MB, time=0.95 memory used=118.4MB, alloc=36.5MB, time=1.04 memory used=146.5MB, alloc=36.5MB, time=1.30 memory used=173.6MB, alloc=37.0MB, time=1.56 memory used=193.3MB, alloc=61.0MB, time=1.79 memory used=228.2MB, alloc=61.0MB, time=2.25 memory used=278.8MB, alloc=70.3MB, time=2.66 memory used=324.8MB, alloc=70.3MB, time=3.07 memory used=352.9MB, alloc=70.3MB, time=3.21 memory used=381.7MB, alloc=70.3MB, time=3.34 memory used=429.0MB, alloc=70.3MB, time=3.88 memory used=475.1MB, alloc=94.3MB, time=4.42 memory used=544.7MB, alloc=94.3MB, time=5.27 memory used=597.3MB, alloc=94.3MB, time=5.65 memory used=644.9MB, alloc=94.3MB, time=5.88 memory used=684.4MB, alloc=94.3MB, time=6.05 memory used=722.3MB, alloc=94.3MB, time=6.22 memory used=783.3MB, alloc=94.3MB, time=6.96 memory used=815.4MB, alloc=94.3MB, time=7.08 memory used=845.0MB, alloc=94.3MB, time=7.18 memory used=896.0MB, alloc=94.5MB, time=7.43 memory used=931.6MB, alloc=94.5MB, time=7.56 memory used=960.2MB, alloc=94.5MB, time=7.66 memory used=1015.7MB, alloc=95.8MB, time=7.92 memory used=1047.4MB, alloc=95.8MB, time=8.03 memory used=1090.8MB, alloc=95.8MB, time=10.20 memory used=1163.4MB, alloc=95.8MB, time=16.56 memory used=1211.1MB, alloc=95.8MB, time=16.79 memory used=1238.4MB, alloc=95.8MB, time=16.90 memory used=1273.0MB, alloc=95.8MB, time=17.03 memory used=1305.5MB, alloc=95.8MB, time=17.13 memory used=1328.5MB, alloc=95.8MB, time=17.23 memory used=1354.4MB, alloc=95.8MB, time=17.32 memory used=1383.1MB, alloc=95.8MB, time=17.42 memory used=1414.7MB, alloc=95.8MB, time=17.52 memory used=1449.2MB, alloc=95.8MB, time=17.62 memory used=1482.7MB, alloc=95.8MB, time=17.70 memory used=1505.2MB, alloc=95.8MB, time=17.78 memory used=1555.6MB, alloc=95.8MB, time=18.01 memory used=1590.5MB, alloc=95.8MB, time=18.13 memory used=1623.7MB, alloc=95.8MB, time=18.31 memory used=1675.9MB, alloc=95.8MB, time=18.49 memory used=1706.0MB, alloc=95.8MB, time=18.61 memory used=1751.0MB, alloc=95.8MB, time=20.78 memory used=1824.1MB, alloc=95.8MB, time=27.03 memory used=1869.7MB, alloc=95.8MB, time=27.23 memory used=1896.9MB, alloc=95.8MB, time=27.33 memory used=1931.5MB, alloc=95.8MB, time=27.45 memory used=1963.5MB, alloc=95.8MB, time=27.56 memory used=1986.8MB, alloc=95.8MB, time=27.65 memory used=2012.6MB, alloc=95.8MB, time=27.75 memory used=2041.1MB, alloc=95.8MB, time=27.85 memory used=2072.5MB, alloc=95.8MB, time=27.96 memory used=2107.2MB, alloc=95.8MB, time=28.06 memory used=2140.1MB, alloc=95.8MB, time=28.17 memory used=2162.4MB, alloc=95.8MB, time=28.25 memory used=2236.6MB, alloc=95.8MB, time=29.12 memory used=2305.9MB, alloc=351.8MB, time=29.87 memory used=2387.4MB, alloc=351.8MB, time=30.71 memory used=2418.1MB, alloc=375.8MB, time=30.84 memory used=2529.6MB, alloc=375.8MB, time=31.92 memory used=2616.6MB, alloc=375.8MB, time=32.98 memory used=2705.3MB, alloc=399.8MB, time=33.96 memory used=2777.2MB, alloc=399.8MB, time=34.33 memory used=2841.5MB, alloc=399.8MB, time=34.59 memory used=2909.8MB, alloc=399.8MB, time=34.90 memory used=2983.2MB, alloc=399.8MB, time=35.24 memory used=3058.4MB, alloc=399.8MB, time=35.55 memory used=3127.7MB, alloc=399.8MB, time=36.03 memory used=3187.9MB, alloc=399.8MB, time=36.25 memory used=3271.4MB, alloc=399.8MB, time=36.78 memory used=3328.6MB, alloc=399.8MB, time=37.00 memory used=3375.9MB, alloc=399.8MB, time=37.22 memory used=3432.2MB, alloc=399.8MB, time=37.43 memory used=3493.8MB, alloc=399.8MB, time=37.65 memory used=3542.3MB, alloc=399.8MB, time=37.84 memory used=3582.9MB, alloc=399.8MB, time=38.02 memory used=3627.2MB, alloc=399.8MB, time=38.20 memory used=3676.2MB, alloc=399.8MB, time=38.39 memory used=3731.4MB, alloc=399.8MB, time=38.56 memory used=3811.0MB, alloc=399.8MB, time=39.03 memory used=3883.7MB, alloc=399.8MB, time=39.29 memory used=3927.8MB, alloc=399.8MB, time=39.50 memory used=3980.2MB, alloc=399.8MB, time=39.70 memory used=4041.7MB, alloc=399.8MB, time=39.91 memory used=4098.7MB, alloc=399.8MB, time=40.11 memory used=4137.8MB, alloc=399.8MB, time=40.27 memory used=4180.9MB, alloc=399.8MB, time=40.45 memory used=4227.9MB, alloc=399.8MB, time=40.64 memory used=4280.7MB, alloc=399.8MB, time=40.81 memory used=4342.1MB, alloc=399.8MB, time=40.99 memory used=4424.2MB, alloc=399.8MB, time=41.72 memory used=4473.5MB, alloc=399.8MB, time=41.92 memory used=4535.2MB, alloc=399.8MB, time=42.13 memory used=4579.5MB, alloc=399.8MB, time=42.31 memory used=4623.7MB, alloc=399.8MB, time=42.48 memory used=4674.2MB, alloc=399.8MB, time=42.64 memory used=4731.9MB, alloc=399.8MB, time=42.81 memory used=4789.8MB, alloc=399.8MB, time=43.09 memory used=4851.6MB, alloc=399.8MB, time=43.32 memory used=4925.7MB, alloc=399.8MB, time=43.63 memory used=5004.4MB, alloc=399.8MB, time=44.10 memory used=5060.1MB, alloc=399.8MB, time=44.36 memory used=5176.1MB, alloc=399.8MB, time=50.02 memory used=5236.2MB, alloc=399.8MB, time=50.25 memory used=5283.0MB, alloc=399.8MB, time=50.44 memory used=5338.4MB, alloc=399.8MB, time=50.64 memory used=5402.6MB, alloc=399.8MB, time=50.84 memory used=5452.9MB, alloc=399.8MB, time=51.02 memory used=5491.4MB, alloc=399.8MB, time=51.20 memory used=5532.0MB, alloc=399.8MB, time=51.37 memory used=5575.7MB, alloc=399.8MB, time=51.56 memory used=5622.7MB, alloc=399.8MB, time=51.74 memory used=5671.8MB, alloc=399.8MB, time=51.92 memory used=5725.0MB, alloc=399.8MB, time=52.11 memory used=5781.0MB, alloc=399.8MB, time=52.30 memory used=5840.7MB, alloc=399.8MB, time=52.48 memory used=5899.6MB, alloc=399.8MB, time=52.67 memory used=5957.8MB, alloc=399.8MB, time=52.85 memory used=6005.3MB, alloc=399.8MB, time=53.02 memory used=6041.6MB, alloc=399.8MB, time=53.15 memory used=6079.6MB, alloc=399.8MB, time=53.30 memory used=6119.0MB, alloc=399.8MB, time=53.44 memory used=6160.3MB, alloc=399.8MB, time=53.58 memory used=6203.4MB, alloc=399.8MB, time=53.73 memory used=6248.9MB, alloc=399.8MB, time=53.87 memory used=6312.4MB, alloc=399.8MB, time=54.56 memory used=6401.0MB, alloc=399.8MB, time=54.93 memory used=6477.5MB, alloc=399.8MB, time=55.23 memory used=6549.9MB, alloc=399.8MB, time=55.48 memory used=6607.6MB, alloc=399.8MB, time=55.70 memory used=6646.1MB, alloc=399.8MB, time=55.89 memory used=6685.6MB, alloc=399.8MB, time=56.07 memory used=6727.5MB, alloc=399.8MB, time=56.26 memory used=6772.5MB, alloc=399.8MB, time=56.47 memory used=6821.2MB, alloc=399.8MB, time=56.65 memory used=6871.3MB, alloc=399.8MB, time=56.85 memory used=6924.6MB, alloc=399.8MB, time=57.07 memory used=6981.6MB, alloc=399.8MB, time=57.29 memory used=7042.0MB, alloc=399.8MB, time=57.49 memory used=7100.7MB, alloc=399.8MB, time=57.70 memory used=7155.0MB, alloc=399.8MB, time=57.90 memory used=7208.7MB, alloc=399.8MB, time=58.09 memory used=7246.1MB, alloc=423.8MB, time=58.28 memory used=7294.8MB, alloc=423.8MB, time=58.50 memory used=7345.5MB, alloc=423.8MB, time=58.70 memory used=7398.4MB, alloc=423.8MB, time=58.89 memory used=7454.8MB, alloc=423.8MB, time=59.09 memory used=7512.9MB, alloc=423.8MB, time=59.31 memory used=7573.9MB, alloc=423.8MB, time=59.53 memory used=7638.6MB, alloc=423.8MB, time=59.75 memory used=7708.6MB, alloc=423.8MB, time=59.97 memory used=7783.1MB, alloc=423.8MB, time=60.20 memory used=7873.0MB, alloc=423.8MB, time=60.55 memory used=7944.9MB, alloc=423.8MB, time=60.98 memory used=8068.4MB, alloc=423.8MB, time=62.01 memory used=8170.5MB, alloc=423.8MB, time=62.35 memory used=8256.5MB, alloc=423.8MB, time=62.63 memory used=8309.7MB, alloc=423.8MB, time=62.88 memory used=8366.6MB, alloc=423.8MB, time=63.11 memory used=8427.2MB, alloc=423.8MB, time=63.36 memory used=8492.9MB, alloc=423.8MB, time=63.61 memory used=8565.2MB, alloc=423.8MB, time=63.84 memory used=8642.3MB, alloc=423.8MB, time=64.10 memory used=8726.2MB, alloc=423.8MB, time=64.34 memory used=8801.1MB, alloc=423.8MB, time=64.57 memory used=8871.2MB, alloc=423.8MB, time=64.80 memory used=8919.5MB, alloc=423.8MB, time=64.99 memory used=8969.1MB, alloc=423.8MB, time=65.22 memory used=9022.1MB, alloc=423.8MB, time=65.42 memory used=9076.7MB, alloc=423.8MB, time=65.61 memory used=9132.9MB, alloc=423.8MB, time=65.81 memory used=9192.4MB, alloc=423.8MB, time=66.02 memory used=9254.4MB, alloc=423.8MB, time=66.23 memory used=9320.3MB, alloc=423.8MB, time=66.42 memory used=9390.8MB, alloc=423.8MB, time=66.62 memory used=9468.0MB, alloc=423.8MB, time=66.81 memory used=9555.2MB, alloc=423.8MB, time=67.23 memory used=9658.1MB, alloc=423.8MB, time=89.62 memory used=9786.7MB, alloc=423.8MB, time=185.33 memory used=9904.2MB, alloc=423.8MB, time=234.30 memory used=10050.9MB, alloc=423.8MB, time=237.59 memory used=10166.9MB, alloc=423.8MB, time=238.78 memory used=10236.9MB, alloc=423.8MB, time=239.04 memory used=10292.6MB, alloc=423.8MB, time=239.27 memory used=10355.5MB, alloc=423.8MB, time=239.54 memory used=10424.7MB, alloc=423.8MB, time=239.77 memory used=10501.5MB, alloc=423.8MB, time=240.02 memory used=10586.1MB, alloc=423.8MB, time=240.27 memory used=10647.2MB, alloc=423.8MB, time=240.49 memory used=10695.6MB, alloc=423.8MB, time=240.70 memory used=10743.6MB, alloc=423.8MB, time=240.92 memory used=10793.3MB, alloc=423.8MB, time=241.11 memory used=10844.3MB, alloc=423.8MB, time=241.32 memory used=10896.7MB, alloc=423.8MB, time=241.51 memory used=10952.8MB, alloc=423.8MB, time=241.74 memory used=11010.2MB, alloc=423.8MB, time=241.94 memory used=11068.8MB, alloc=423.8MB, time=242.16 memory used=11128.7MB, alloc=423.8MB, time=242.38 memory used=11192.6MB, alloc=423.8MB, time=242.60 memory used=11257.6MB, alloc=423.8MB, time=242.83 memory used=11323.9MB, alloc=423.8MB, time=243.04 memory used=11394.1MB, alloc=423.8MB, time=243.27 memory used=11465.5MB, alloc=423.8MB, time=243.50 memory used=11538.2MB, alloc=423.8MB, time=243.71 memory used=11614.8MB, alloc=423.8MB, time=243.94 memory used=11692.6MB, alloc=423.8MB, time=244.15 memory used=11768.7MB, alloc=423.8MB, time=244.38 memory used=11846.5MB, alloc=423.8MB, time=244.61 memory used=11924.9MB, alloc=423.8MB, time=244.84 memory used=11981.1MB, alloc=423.8MB, time=245.02 memory used=12027.5MB, alloc=423.8MB, time=245.20 memory used=12072.0MB, alloc=423.8MB, time=245.37 memory used=12113.4MB, alloc=423.8MB, time=245.52 memory used=12156.0MB, alloc=423.8MB, time=245.69 memory used=12198.9MB, alloc=423.8MB, time=245.86 memory used=12241.9MB, alloc=423.8MB, time=246.02 memory used=12285.3MB, alloc=423.8MB, time=246.19 memory used=12331.8MB, alloc=423.8MB, time=246.36 memory used=12378.6MB, alloc=423.8MB, time=246.53 memory used=12425.5MB, alloc=423.8MB, time=246.69 memory used=12472.5MB, alloc=423.8MB, time=246.86 memory used=12519.7MB, alloc=423.8MB, time=247.02 memory used=12567.0MB, alloc=423.8MB, time=247.19 memory used=12617.8MB, alloc=423.8MB, time=247.35 memory used=12668.6MB, alloc=423.8MB, time=247.52 memory used=12719.6MB, alloc=423.8MB, time=247.69 memory used=12770.6MB, alloc=423.8MB, time=247.86 memory used=12821.6MB, alloc=423.8MB, time=248.03 memory used=12872.9MB, alloc=423.8MB, time=248.19 memory used=12927.3MB, alloc=423.8MB, time=248.37 memory used=12981.9MB, alloc=423.8MB, time=248.54 memory used=13036.4MB, alloc=423.8MB, time=248.72 memory used=13091.0MB, alloc=423.8MB, time=248.89 memory used=13148.9MB, alloc=423.8MB, time=249.07 memory used=13206.7MB, alloc=423.8MB, time=249.24 memory used=13264.5MB, alloc=423.8MB, time=249.41 memory used=13322.2MB, alloc=423.8MB, time=249.58 memory used=13383.2MB, alloc=423.8MB, time=249.76 memory used=13443.9MB, alloc=423.8MB, time=249.93 memory used=13504.6MB, alloc=423.8MB, time=250.09 memory used=13568.3MB, alloc=423.8MB, time=250.27 memory used=13631.8MB, alloc=423.8MB, time=250.45 memory used=13695.1MB, alloc=423.8MB, time=250.62 memory used=13761.3MB, alloc=423.8MB, time=250.79 memory used=13827.1MB, alloc=423.8MB, time=250.97 memory used=13892.6MB, alloc=423.8MB, time=251.15 memory used=13960.8MB, alloc=423.8MB, time=251.33 memory used=14028.6MB, alloc=423.8MB, time=251.51 memory used=14099.0MB, alloc=423.8MB, time=251.68 memory used=14168.8MB, alloc=423.8MB, time=251.87 memory used=14240.9MB, alloc=423.8MB, time=252.05 memory used=14315.3MB, alloc=423.8MB, time=252.22 memory used=14388.9MB, alloc=423.8MB, time=252.41 memory used=14472.7MB, alloc=423.8MB, time=252.61 memory used=14561.4MB, alloc=423.8MB, time=252.81 memory used=14652.3MB, alloc=423.8MB, time=253.01 memory used=14744.4MB, alloc=423.8MB, time=253.21 memory used=14839.8MB, alloc=423.8MB, time=253.40 memory used=14938.3MB, alloc=423.8MB, time=253.61 memory used=15152.0MB, alloc=423.8MB, time=254.11 memory used=15286.2MB, alloc=423.8MB, time=254.38 memory used=15427.1MB, alloc=423.8MB, time=254.67 memory used=15573.1MB, alloc=423.8MB, time=254.96 memory used=15730.8MB, alloc=423.8MB, time=255.25 memory used=15924.7MB, alloc=423.8MB, time=256.42 memory used=16025.0MB, alloc=423.8MB, time=256.75 memory used=16113.9MB, alloc=423.8MB, time=257.06 memory used=16166.9MB, alloc=423.8MB, time=257.27 memory used=16222.3MB, alloc=423.8MB, time=257.50 memory used=16282.6MB, alloc=423.8MB, time=257.73 memory used=16347.7MB, alloc=423.8MB, time=257.98 memory used=16417.6MB, alloc=423.8MB, time=258.23 memory used=16494.1MB, alloc=423.8MB, time=258.48 memory used=16575.4MB, alloc=423.8MB, time=258.74 memory used=16650.9MB, alloc=423.8MB, time=258.98 memory used=16724.4MB, alloc=423.8MB, time=259.21 memory used=16774.0MB, alloc=423.8MB, time=259.41 memory used=16824.3MB, alloc=423.8MB, time=259.62 memory used=16875.2MB, alloc=423.8MB, time=259.81 memory used=16929.8MB, alloc=423.8MB, time=260.02 memory used=16986.2MB, alloc=423.8MB, time=260.23 memory used=17046.0MB, alloc=423.8MB, time=260.43 memory used=17108.6MB, alloc=423.8MB, time=260.64 memory used=17175.0MB, alloc=423.8MB, time=260.84 memory used=17245.6MB, alloc=423.8MB, time=261.03 memory used=17321.8MB, alloc=423.8MB, time=261.25 memory used=17408.8MB, alloc=423.8MB, time=261.76 memory used=17483.5MB, alloc=423.8MB, time=262.24 memory used=17605.4MB, alloc=423.8MB, time=263.16 memory used=17706.4MB, alloc=423.8MB, time=263.50 memory used=17792.7MB, alloc=423.8MB, time=263.80 memory used=17846.2MB, alloc=423.8MB, time=264.02 memory used=17902.7MB, alloc=423.8MB, time=264.25 memory used=17963.2MB, alloc=423.8MB, time=264.47 memory used=18028.4MB, alloc=423.8MB, time=264.70 memory used=18098.6MB, alloc=423.8MB, time=264.95 memory used=18175.0MB, alloc=423.8MB, time=265.20 memory used=18256.7MB, alloc=423.8MB, time=265.47 memory used=18333.1MB, alloc=423.8MB, time=265.72 memory used=18405.8MB, alloc=423.8MB, time=265.96 memory used=18455.7MB, alloc=423.8MB, time=266.18 memory used=18505.1MB, alloc=423.8MB, time=266.38 memory used=18556.1MB, alloc=423.8MB, time=266.58 memory used=18610.5MB, alloc=423.8MB, time=266.80 memory used=18666.8MB, alloc=423.8MB, time=267.02 memory used=18726.4MB, alloc=423.8MB, time=267.21 memory used=18788.8MB, alloc=423.8MB, time=267.42 memory used=18854.9MB, alloc=423.8MB, time=267.63 memory used=18925.2MB, alloc=423.8MB, time=267.86 memory used=19001.6MB, alloc=423.8MB, time=268.07 memory used=19088.8MB, alloc=423.8MB, time=268.60 memory used=19183.4MB, alloc=423.8MB, time=279.17 memory used=19307.5MB, alloc=423.8MB, time=359.68 memory used=19408.9MB, alloc=423.8MB, time=431.97 memory used=19547.3MB, alloc=423.8MB, time=435.05 memory used=19679.1MB, alloc=423.8MB, time=436.63 memory used=19761.7MB, alloc=423.8MB, time=436.90 memory used=19816.8MB, alloc=423.8MB, time=437.13 memory used=19877.2MB, alloc=423.8MB, time=437.35 memory used=19944.3MB, alloc=423.8MB, time=437.56 memory used=20019.0MB, alloc=423.8MB, time=437.81 memory used=20099.6MB, alloc=423.8MB, time=438.05 memory used=20172.2MB, alloc=423.8MB, time=438.26 memory used=20222.3MB, alloc=423.8MB, time=438.48 memory used=20270.5MB, alloc=423.8MB, time=438.67 memory used=20319.2MB, alloc=423.8MB, time=438.87 memory used=20369.7MB, alloc=423.8MB, time=439.05 memory used=20421.5MB, alloc=423.8MB, time=439.24 memory used=20474.6MB, alloc=423.8MB, time=439.43 memory used=20531.4MB, alloc=423.8MB, time=439.63 memory used=20589.5MB, alloc=423.8MB, time=439.82 memory used=20648.9MB, alloc=423.8MB, time=440.00 memory used=20712.1MB, alloc=423.8MB, time=440.22 memory used=20776.6MB, alloc=423.8MB, time=440.41 memory used=20842.2MB, alloc=423.8MB, time=440.61 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428522679 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 4 2 2 F := [11 x y z + 2 x y z - 8 y, 19 x - 2 x y z + 4 x y] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 2 2 2 G := [-10 x y - 16 y z - 12 y z, -4 x y - 7 x z + 19] > Problem := [F,G]; 2 2 4 2 2 Problem := [[11 x y z + 2 x y z - 8 y, 19 x - 2 x y z + 4 x y], 2 2 2 2 2 2 2 2 [-10 x y - 16 y z - 12 y z, -4 x y - 7 x z + 19]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=25.9MB, alloc=32.3MB, time=0.46 memory used=45.0MB, alloc=56.3MB, time=0.66 memory used=79.7MB, alloc=60.3MB, time=0.97 memory used=125.3MB, alloc=68.3MB, time=1.49 memory used=171.9MB, alloc=68.3MB, time=1.90 memory used=212.4MB, alloc=68.3MB, time=2.44 memory used=253.7MB, alloc=92.3MB, time=2.94 memory used=330.9MB, alloc=92.3MB, time=3.64 memory used=398.2MB, alloc=92.3MB, time=4.27 memory used=463.5MB, alloc=92.3MB, time=5.00 memory used=527.8MB, alloc=92.3MB, time=5.62 memory used=593.7MB, alloc=116.3MB, time=6.35 memory used=672.8MB, alloc=372.3MB, time=7.38 memory used=760.0MB, alloc=372.3MB, time=8.38 memory used=843.1MB, alloc=396.3MB, time=9.20 memory used=959.7MB, alloc=396.3MB, time=10.56 memory used=1079.2MB, alloc=420.3MB, time=11.91 memory used=1212.5MB, alloc=420.3MB, time=13.66 memory used=1329.9MB, alloc=444.3MB, time=15.36 memory used=1468.0MB, alloc=468.3MB, time=17.20 memory used=1629.8MB, alloc=492.3MB, time=19.39 memory used=1808.1MB, alloc=516.3MB, time=21.74 memory used=2011.7MB, alloc=540.3MB, time=24.27 memory used=2227.5MB, alloc=564.3MB, time=27.23 memory used=2442.3MB, alloc=588.3MB, time=30.54 memory used=2652.1MB, alloc=612.3MB, time=35.11 memory used=2848.5MB, alloc=636.3MB, time=40.41 memory used=3050.1MB, alloc=660.3MB, time=46.35 memory used=3261.8MB, alloc=684.3MB, time=52.86 memory used=3483.6MB, alloc=708.3MB, time=60.39 memory used=3721.3MB, alloc=732.3MB, time=68.77 memory used=3982.9MB, alloc=756.3MB, time=78.03 memory used=4268.4MB, alloc=780.3MB, time=88.06 memory used=4577.9MB, alloc=804.3MB, time=98.85 memory used=4911.4MB, alloc=828.3MB, time=110.44 memory used=5268.7MB, alloc=828.3MB, time=122.78 memory used=5626.0MB, alloc=828.3MB, time=134.89 memory used=5983.3MB, alloc=852.3MB, time=147.37 memory used=6364.6MB, alloc=852.3MB, time=160.26 memory used=6745.8MB, alloc=852.3MB, time=173.24 memory used=7126.8MB, alloc=876.3MB, time=186.82 memory used=7531.6MB, alloc=876.3MB, time=203.15 memory used=7936.5MB, alloc=876.3MB, time=217.40 memory used=8341.2MB, alloc=900.3MB, time=231.17 memory used=8769.8MB, alloc=900.3MB, time=245.56 memory used=9198.3MB, alloc=924.3MB, time=260.15 memory used=9650.8MB, alloc=948.3MB, time=275.26 N1 := 15829 > GB := Basis(F, plex(op(vars))); 4 5 2 2 3 2 2 GB := [209 y x + 361 x + 44 y x + 152 y x + 16 y x - 16 y , 5 4 4 3 2 209 x + 38 x z + 76 x + 44 x y + 16 x y - 16 x y, 4 2 2 2 2 2 -19 x + 2 x y z - 4 x y, -19 x y + 2 y z - 4 y , 4 2 2 209 x + 4 x y z + 44 x y - 16 y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=10136.8MB, alloc=948.3MB, time=290.27 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428522979 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 3 F := [12 y - 18 y z, 19 y z + 7 x z - 14 y ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 4 3 G := [6 x y + 14 x y z + 15 x y z, 13 x - 17 x y + 13 y z] > Problem := [F,G]; 2 2 2 2 3 Problem := [[12 y - 18 y z, 19 y z + 7 x z - 14 y ], 3 2 4 3 [6 x y + 14 x y z + 15 x y z, 13 x - 17 x y + 13 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.16 memory used=26.5MB, alloc=32.3MB, time=0.46 memory used=46.7MB, alloc=32.3MB, time=0.75 memory used=65.1MB, alloc=56.3MB, time=1.02 memory used=109.1MB, alloc=68.3MB, time=1.64 memory used=154.1MB, alloc=68.3MB, time=2.13 memory used=195.9MB, alloc=68.3MB, time=2.63 memory used=237.8MB, alloc=92.3MB, time=3.11 memory used=302.3MB, alloc=92.3MB, time=3.86 memory used=387.4MB, alloc=92.3MB, time=4.61 memory used=416.3MB, alloc=92.3MB, time=4.70 memory used=491.2MB, alloc=116.3MB, time=5.18 memory used=587.5MB, alloc=116.3MB, time=5.98 memory used=654.9MB, alloc=372.3MB, time=6.75 memory used=722.5MB, alloc=372.3MB, time=7.21 memory used=825.2MB, alloc=372.3MB, time=7.95 memory used=914.5MB, alloc=396.3MB, time=8.87 memory used=1013.4MB, alloc=396.3MB, time=9.66 memory used=1123.6MB, alloc=396.3MB, time=10.42 memory used=1181.6MB, alloc=396.3MB, time=10.68 memory used=1241.0MB, alloc=396.3MB, time=10.91 memory used=1284.9MB, alloc=396.3MB, time=11.05 memory used=1350.0MB, alloc=396.3MB, time=11.45 memory used=1398.0MB, alloc=396.3MB, time=11.63 memory used=1451.7MB, alloc=396.3MB, time=11.80 memory used=1490.3MB, alloc=396.3MB, time=11.94 memory used=1536.2MB, alloc=396.3MB, time=12.08 memory used=1590.9MB, alloc=396.3MB, time=12.22 memory used=1814.9MB, alloc=396.3MB, time=13.07 memory used=1866.1MB, alloc=396.3MB, time=13.25 memory used=1919.8MB, alloc=396.3MB, time=13.41 memory used=1958.3MB, alloc=396.3MB, time=13.55 memory used=2004.2MB, alloc=396.3MB, time=13.69 memory used=2059.5MB, alloc=396.3MB, time=13.83 memory used=2266.7MB, alloc=396.3MB, time=15.73 memory used=2337.2MB, alloc=396.3MB, time=16.09 memory used=2383.0MB, alloc=396.3MB, time=16.27 memory used=2437.5MB, alloc=396.3MB, time=16.46 memory used=2473.5MB, alloc=396.3MB, time=16.60 memory used=2513.4MB, alloc=396.3MB, time=16.75 memory used=2559.2MB, alloc=396.3MB, time=16.89 memory used=2609.3MB, alloc=396.3MB, time=17.05 memory used=2665.2MB, alloc=396.3MB, time=17.22 memory used=2726.9MB, alloc=396.3MB, time=17.38 memory used=2873.8MB, alloc=396.3MB, time=17.66 memory used=3041.0MB, alloc=396.3MB, time=17.96 memory used=3315.8MB, alloc=396.3MB, time=18.60 memory used=3360.0MB, alloc=396.3MB, time=18.74 memory used=3438.4MB, alloc=396.3MB, time=19.14 memory used=3557.1MB, alloc=420.3MB, time=20.01 memory used=3688.7MB, alloc=420.3MB, time=20.85 memory used=3822.2MB, alloc=420.3MB, time=21.78 memory used=3922.2MB, alloc=420.3MB, time=22.13 memory used=4046.7MB, alloc=420.3MB, time=22.82 memory used=4176.1MB, alloc=420.3MB, time=23.46 memory used=4275.5MB, alloc=420.3MB, time=23.75 memory used=4399.7MB, alloc=420.3MB, time=24.06 memory used=4547.6MB, alloc=420.3MB, time=24.40 memory used=4712.9MB, alloc=420.3MB, time=24.73 memory used=4885.3MB, alloc=420.3MB, time=25.08 memory used=5071.6MB, alloc=420.3MB, time=25.48 memory used=5275.3MB, alloc=420.3MB, time=25.89 memory used=5503.8MB, alloc=420.3MB, time=26.35 memory used=5777.7MB, alloc=420.3MB, time=26.89 memory used=6143.1MB, alloc=420.3MB, time=27.71 memory used=6317.1MB, alloc=420.3MB, time=28.58 memory used=6410.7MB, alloc=420.3MB, time=28.95 memory used=6508.6MB, alloc=420.3MB, time=29.23 memory used=6609.4MB, alloc=420.3MB, time=29.50 memory used=6711.5MB, alloc=420.3MB, time=29.79 memory used=6823.7MB, alloc=420.3MB, time=30.08 memory used=6936.0MB, alloc=420.3MB, time=30.35 memory used=7058.8MB, alloc=420.3MB, time=30.64 memory used=7187.9MB, alloc=420.3MB, time=30.96 memory used=7321.8MB, alloc=420.3MB, time=31.27 memory used=7465.8MB, alloc=420.3MB, time=31.62 memory used=7617.3MB, alloc=420.3MB, time=31.97 memory used=7779.6MB, alloc=420.3MB, time=32.33 memory used=7965.4MB, alloc=420.3MB, time=32.67 memory used=8181.3MB, alloc=420.3MB, time=33.30 memory used=8294.1MB, alloc=420.3MB, time=33.84 memory used=8391.2MB, alloc=420.3MB, time=34.14 memory used=8502.2MB, alloc=420.3MB, time=34.43 memory used=8628.3MB, alloc=420.3MB, time=34.73 memory used=8775.5MB, alloc=420.3MB, time=35.06 memory used=8962.1MB, alloc=420.3MB, time=35.42 memory used=9206.1MB, alloc=420.3MB, time=35.86 memory used=9457.5MB, alloc=420.3MB, time=36.35 memory used=9742.4MB, alloc=420.3MB, time=36.87 memory used=10030.2MB, alloc=420.3MB, time=37.36 memory used=10362.7MB, alloc=420.3MB, time=37.92 memory used=10700.9MB, alloc=420.3MB, time=38.46 memory used=10977.0MB, alloc=420.3MB, time=39.28 memory used=11065.1MB, alloc=420.3MB, time=39.58 memory used=11158.7MB, alloc=420.3MB, time=39.88 memory used=11249.8MB, alloc=420.3MB, time=40.16 memory used=11344.0MB, alloc=420.3MB, time=40.45 memory used=11444.0MB, alloc=420.3MB, time=40.75 memory used=11547.1MB, alloc=420.3MB, time=41.05 memory used=11658.9MB, alloc=420.3MB, time=41.37 memory used=11774.2MB, alloc=420.3MB, time=41.67 memory used=11919.0MB, alloc=420.3MB, time=42.47 memory used=12017.3MB, alloc=444.3MB, time=42.90 memory used=12136.3MB, alloc=444.3MB, time=43.30 memory used=12284.0MB, alloc=444.3MB, time=44.52 memory used=12415.3MB, alloc=468.3MB, time=46.38 memory used=12583.9MB, alloc=492.3MB, time=48.65 memory used=12783.9MB, alloc=516.3MB, time=51.46 memory used=12972.2MB, alloc=540.3MB, time=54.15 memory used=13198.8MB, alloc=564.3MB, time=56.91 memory used=13484.3MB, alloc=564.3MB, time=59.28 memory used=13769.4MB, alloc=588.3MB, time=62.07 memory used=14017.8MB, alloc=612.3MB, time=64.88 memory used=14264.2MB, alloc=612.3MB, time=67.81 memory used=14469.5MB, alloc=636.3MB, time=70.75 memory used=14690.5MB, alloc=660.3MB, time=75.52 memory used=14930.8MB, alloc=684.3MB, time=82.77 memory used=15178.2MB, alloc=708.3MB, time=90.68 memory used=15438.1MB, alloc=732.3MB, time=99.09 memory used=15705.3MB, alloc=756.3MB, time=108.61 memory used=15990.7MB, alloc=780.3MB, time=118.99 memory used=16300.0MB, alloc=804.3MB, time=130.22 memory used=16633.2MB, alloc=828.3MB, time=142.24 memory used=16990.5MB, alloc=828.3MB, time=155.19 memory used=17347.6MB, alloc=828.3MB, time=168.08 memory used=17704.7MB, alloc=852.3MB, time=181.03 memory used=18085.7MB, alloc=852.3MB, time=195.79 memory used=18466.6MB, alloc=852.3MB, time=209.41 memory used=18847.6MB, alloc=876.3MB, time=223.21 memory used=19252.5MB, alloc=876.3MB, time=238.41 memory used=19657.4MB, alloc=900.3MB, time=253.33 memory used=20086.3MB, alloc=900.3MB, time=268.35 memory used=20515.2MB, alloc=924.3MB, time=283.33 N1 := 14127 > GB := Basis(F, plex(op(vars))); 5 3 4 2 4 2 3 GB := [38 y + 14 x y - 63 y , -2 y + 3 y z, 76 y + 63 x z - 126 y ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428523280 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 4 3 F := [-11 x z - 5 z , 4 y - 20 x - 19] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 4 2 2 4 2 G := [13 x y + 13 y + 13 z, -17 x z + 8 z - 10 y z ] > Problem := [F,G]; 3 3 4 3 Problem := [[-11 x z - 5 z , 4 y - 20 x - 19], 3 4 2 2 4 2 [13 x y + 13 y + 13 z, -17 x z + 8 z - 10 y z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.19 memory used=25.7MB, alloc=32.3MB, time=0.43 memory used=44.8MB, alloc=56.3MB, time=0.64 memory used=88.2MB, alloc=60.3MB, time=1.12 memory used=130.5MB, alloc=60.3MB, time=1.58 memory used=167.3MB, alloc=60.3MB, time=1.78 memory used=195.7MB, alloc=60.3MB, time=1.89 memory used=222.5MB, alloc=60.3MB, time=1.99 memory used=253.7MB, alloc=61.9MB, time=2.13 memory used=277.7MB, alloc=61.9MB, time=2.19 memory used=295.0MB, alloc=61.9MB, time=2.24 memory used=326.9MB, alloc=61.9MB, time=2.43 memory used=379.7MB, alloc=69.9MB, time=2.93 memory used=430.6MB, alloc=93.9MB, time=3.40 memory used=496.6MB, alloc=93.9MB, time=4.09 memory used=564.5MB, alloc=349.9MB, time=4.69 memory used=625.1MB, alloc=373.9MB, time=5.35 memory used=717.4MB, alloc=373.9MB, time=6.29 memory used=778.4MB, alloc=373.9MB, time=6.61 memory used=835.5MB, alloc=373.9MB, time=7.28 memory used=874.6MB, alloc=397.9MB, time=7.43 memory used=925.7MB, alloc=397.9MB, time=7.59 memory used=981.4MB, alloc=397.9MB, time=7.74 memory used=1041.6MB, alloc=397.9MB, time=7.89 memory used=1082.6MB, alloc=397.9MB, time=8.01 memory used=1129.8MB, alloc=397.9MB, time=8.13 memory used=1220.2MB, alloc=397.9MB, time=10.30 memory used=1277.9MB, alloc=397.9MB, time=10.48 memory used=1341.9MB, alloc=397.9MB, time=10.67 memory used=1387.6MB, alloc=397.9MB, time=10.83 memory used=1432.3MB, alloc=397.9MB, time=10.97 memory used=1481.2MB, alloc=397.9MB, time=11.12 memory used=1535.6MB, alloc=397.9MB, time=11.29 memory used=1595.5MB, alloc=397.9MB, time=11.46 memory used=1661.0MB, alloc=397.9MB, time=11.64 memory used=1725.9MB, alloc=397.9MB, time=11.79 memory used=1761.8MB, alloc=397.9MB, time=11.91 memory used=1798.1MB, alloc=397.9MB, time=12.03 memory used=1837.8MB, alloc=397.9MB, time=12.16 memory used=1878.1MB, alloc=397.9MB, time=12.28 memory used=1919.3MB, alloc=397.9MB, time=12.40 memory used=1963.3MB, alloc=397.9MB, time=12.53 memory used=2008.0MB, alloc=397.9MB, time=12.66 memory used=2055.6MB, alloc=397.9MB, time=12.79 memory used=2103.8MB, alloc=397.9MB, time=12.92 memory used=2154.9MB, alloc=397.9MB, time=13.04 memory used=2206.5MB, alloc=397.9MB, time=13.17 memory used=2260.9MB, alloc=397.9MB, time=13.30 memory used=2315.7MB, alloc=397.9MB, time=13.43 memory used=2373.1MB, alloc=397.9MB, time=13.55 memory used=2433.2MB, alloc=397.9MB, time=13.69 memory used=2495.8MB, alloc=397.9MB, time=13.82 memory used=2560.8MB, alloc=397.9MB, time=13.97 memory used=2627.9MB, alloc=397.9MB, time=14.11 memory used=2697.0MB, alloc=397.9MB, time=14.25 memory used=2860.9MB, alloc=397.9MB, time=14.64 memory used=2999.8MB, alloc=397.9MB, time=14.87 memory used=3148.0MB, alloc=397.9MB, time=15.12 memory used=3309.2MB, alloc=397.9MB, time=15.38 memory used=3490.0MB, alloc=397.9MB, time=15.64 memory used=3618.6MB, alloc=397.9MB, time=16.30 memory used=3673.4MB, alloc=397.9MB, time=16.46 memory used=3726.0MB, alloc=397.9MB, time=16.62 memory used=3848.4MB, alloc=397.9MB, time=17.75 memory used=3950.8MB, alloc=397.9MB, time=18.33 memory used=4057.5MB, alloc=397.9MB, time=19.01 memory used=4144.4MB, alloc=397.9MB, time=19.33 memory used=4225.9MB, alloc=397.9MB, time=19.59 memory used=4305.5MB, alloc=397.9MB, time=19.85 memory used=4400.2MB, alloc=397.9MB, time=20.30 memory used=4511.3MB, alloc=397.9MB, time=20.94 memory used=4605.5MB, alloc=397.9MB, time=21.46 memory used=4699.9MB, alloc=397.9MB, time=21.87 memory used=4802.3MB, alloc=397.9MB, time=22.38 memory used=4902.8MB, alloc=397.9MB, time=23.01 memory used=4996.4MB, alloc=397.9MB, time=23.42 memory used=5095.6MB, alloc=397.9MB, time=24.12 memory used=5193.0MB, alloc=421.9MB, time=25.47 memory used=5315.9MB, alloc=445.9MB, time=26.87 memory used=5454.0MB, alloc=469.9MB, time=28.77 memory used=5601.9MB, alloc=493.9MB, time=30.82 memory used=5758.7MB, alloc=517.9MB, time=33.55 memory used=5899.9MB, alloc=541.9MB, time=37.30 memory used=6048.6MB, alloc=565.9MB, time=41.69 memory used=6208.1MB, alloc=589.9MB, time=47.05 memory used=6388.4MB, alloc=613.9MB, time=53.15 memory used=6592.6MB, alloc=637.9MB, time=59.94 memory used=6820.7MB, alloc=661.9MB, time=67.66 memory used=7072.8MB, alloc=661.9MB, time=75.98 memory used=7324.8MB, alloc=661.9MB, time=84.37 memory used=7576.9MB, alloc=685.9MB, time=92.79 memory used=7852.9MB, alloc=685.9MB, time=101.90 memory used=8129.1MB, alloc=709.9MB, time=111.03 N1 := 8871 > GB := Basis(F, plex(op(vars))); 4 3 3 3 GB := [4 y - 20 x - 19, 11 x z + 5 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=8299.5MB, alloc=709.9MB, time=114.19 memory used=8518.7MB, alloc=709.9MB, time=115.66 memory used=8612.1MB, alloc=709.9MB, time=116.91 memory used=8710.8MB, alloc=709.9MB, time=118.43 memory used=8831.9MB, alloc=709.9MB, time=120.00 memory used=8974.3MB, alloc=709.9MB, time=121.43 memory used=9185.9MB, alloc=709.9MB, time=122.59 memory used=9391.5MB, alloc=709.9MB, time=125.24 memory used=9576.8MB, alloc=709.9MB, time=125.99 memory used=9764.4MB, alloc=709.9MB, time=126.67 memory used=9951.1MB, alloc=709.9MB, time=127.31 memory used=10096.5MB, alloc=709.9MB, time=127.86 memory used=10261.2MB, alloc=709.9MB, time=128.45 memory used=10446.7MB, alloc=709.9MB, time=129.09 memory used=10656.8MB, alloc=709.9MB, time=129.70 memory used=11024.2MB, alloc=709.9MB, time=130.47 memory used=11163.0MB, alloc=709.9MB, time=131.02 memory used=11311.4MB, alloc=709.9MB, time=131.56 memory used=11472.7MB, alloc=709.9MB, time=132.10 memory used=11653.8MB, alloc=709.9MB, time=132.67 memory used=11924.2MB, alloc=709.9MB, time=134.20 memory used=12108.3MB, alloc=709.9MB, time=135.77 memory used=12405.1MB, alloc=709.9MB, time=136.88 memory used=12719.1MB, alloc=709.9MB, time=138.58 memory used=13023.5MB, alloc=709.9MB, time=140.38 memory used=13307.1MB, alloc=709.9MB, time=143.19 memory used=13560.6MB, alloc=733.9MB, time=146.68 memory used=13742.9MB, alloc=757.9MB, time=149.85 memory used=13993.3MB, alloc=781.9MB, time=156.09 memory used=14330.1MB, alloc=805.9MB, time=167.29 memory used=14673.5MB, alloc=829.9MB, time=179.35 memory used=15040.9MB, alloc=853.9MB, time=192.02 memory used=15432.1MB, alloc=877.9MB, time=205.33 memory used=15847.4MB, alloc=901.9MB, time=219.84 memory used=16287.2MB, alloc=925.9MB, time=235.54 N2 := 8871 > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 3 4 3 3 4 H := [-11 x z - 5 z , 4 y - 20 x - 19, 13 x y + 13 y + 13 z, 2 2 4 2 -17 x z + 8 z - 10 y z ] > J:=[op(GB),op(G)]; 4 3 3 3 3 4 J := [4 y - 20 x - 19, 11 x z + 5 z , 13 x y + 13 y + 13 z, 2 2 4 2 -17 x z + 8 z - 10 y z ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 10, 16, 4, 3, 4, 4, 1, 3/4, 3/4, 4/11, 4/11, 6/11, 4, 10, 16, 4, 3, 4, 4, 1, 3/4, 3/4, 4/11, 4/11, 6/11, 0, 0, 0] > save(F, G, cat("ranSet/34", convert(F, string),".txt")); > quit memory used=16292.2MB, alloc=925.9MB, time=235.70 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428523516 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 F := [18 y - y z + 16 y z, -y + 9 y z + 9 y] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 3 2 2 2 2 G := [15 x y - 18 z + 6 x , 7 x z - 10 x y - 19 y z ] > Problem := [F,G]; 3 2 3 Problem := [[18 y - y z + 16 y z, -y + 9 y z + 9 y], 2 3 2 3 2 2 2 2 [15 x y - 18 z + 6 x , 7 x z - 10 x y - 19 y z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.16 memory used=24.8MB, alloc=32.3MB, time=0.38 memory used=47.6MB, alloc=36.3MB, time=0.62 memory used=71.6MB, alloc=60.5MB, time=0.89 memory used=113.6MB, alloc=60.5MB, time=1.38 memory used=199.1MB, alloc=60.5MB, time=1.80 memory used=235.2MB, alloc=60.5MB, time=2.19 memory used=276.3MB, alloc=60.5MB, time=2.57 memory used=317.7MB, alloc=60.5MB, time=2.97 memory used=354.5MB, alloc=60.5MB, time=3.28 memory used=390.4MB, alloc=63.7MB, time=3.41 memory used=412.9MB, alloc=63.7MB, time=3.72 memory used=439.7MB, alloc=63.7MB, time=3.87 memory used=461.9MB, alloc=63.7MB, time=3.92 memory used=485.5MB, alloc=63.7MB, time=4.02 memory used=521.7MB, alloc=63.7MB, time=4.22 memory used=553.4MB, alloc=63.7MB, time=4.31 memory used=588.1MB, alloc=63.7MB, time=4.55 memory used=638.6MB, alloc=71.7MB, time=4.98 memory used=683.3MB, alloc=95.7MB, time=5.44 memory used=758.8MB, alloc=95.7MB, time=6.13 memory used=824.6MB, alloc=95.7MB, time=6.82 memory used=890.1MB, alloc=119.7MB, time=7.57 memory used=959.4MB, alloc=375.7MB, time=8.40 memory used=1048.3MB, alloc=375.7MB, time=9.32 memory used=1110.4MB, alloc=375.7MB, time=9.77 memory used=1166.7MB, alloc=399.7MB, time=10.54 memory used=1229.6MB, alloc=399.7MB, time=10.78 memory used=1298.8MB, alloc=399.7MB, time=11.72 memory used=1360.1MB, alloc=399.7MB, time=11.99 memory used=1426.5MB, alloc=399.7MB, time=12.34 memory used=1485.5MB, alloc=399.7MB, time=12.52 memory used=1535.2MB, alloc=399.7MB, time=12.66 memory used=1582.3MB, alloc=399.7MB, time=12.81 memory used=1639.9MB, alloc=399.7MB, time=12.96 memory used=1703.0MB, alloc=399.7MB, time=13.21 memory used=1770.2MB, alloc=399.7MB, time=13.56 memory used=1825.0MB, alloc=399.7MB, time=13.72 memory used=1879.5MB, alloc=399.7MB, time=13.88 memory used=1924.8MB, alloc=399.7MB, time=14.03 memory used=1979.9MB, alloc=399.7MB, time=14.18 memory used=2045.1MB, alloc=399.7MB, time=14.43 memory used=2293.1MB, alloc=399.7MB, time=22.33 memory used=2358.0MB, alloc=399.7MB, time=22.78 memory used=2428.2MB, alloc=399.7MB, time=23.10 memory used=2493.6MB, alloc=399.7MB, time=23.61 memory used=2558.0MB, alloc=399.7MB, time=23.92 memory used=2618.3MB, alloc=399.7MB, time=24.09 memory used=2662.7MB, alloc=399.7MB, time=24.23 memory used=2717.1MB, alloc=399.7MB, time=24.37 memory used=2787.7MB, alloc=399.7MB, time=24.74 memory used=2843.7MB, alloc=399.7MB, time=24.90 memory used=2899.9MB, alloc=399.7MB, time=25.06 memory used=2945.8MB, alloc=399.7MB, time=25.23 memory used=3003.2MB, alloc=399.7MB, time=25.38 memory used=3152.7MB, alloc=399.7MB, time=27.07 memory used=3215.8MB, alloc=399.7MB, time=27.92 memory used=3327.9MB, alloc=399.7MB, time=29.03 memory used=3438.3MB, alloc=423.7MB, time=30.14 memory used=3572.8MB, alloc=423.7MB, time=31.43 memory used=3706.4MB, alloc=447.7MB, time=32.74 memory used=3841.5MB, alloc=447.7MB, time=35.30 memory used=3938.2MB, alloc=447.7MB, time=35.68 memory used=4056.4MB, alloc=447.7MB, time=37.91 memory used=4198.9MB, alloc=447.7MB, time=39.30 memory used=4309.1MB, alloc=447.7MB, time=40.38 memory used=4373.6MB, alloc=447.7MB, time=40.61 memory used=4497.4MB, alloc=447.7MB, time=41.49 memory used=4633.9MB, alloc=471.7MB, time=42.90 memory used=4762.2MB, alloc=471.7MB, time=43.87 memory used=4848.0MB, alloc=471.7MB, time=44.18 memory used=4944.6MB, alloc=471.7MB, time=44.71 memory used=5028.7MB, alloc=471.7MB, time=45.01 memory used=5127.4MB, alloc=471.7MB, time=51.97 memory used=5216.5MB, alloc=471.7MB, time=52.70 memory used=5292.0MB, alloc=471.7MB, time=52.97 memory used=5414.9MB, alloc=471.7MB, time=54.24 memory used=5512.7MB, alloc=471.7MB, time=54.62 memory used=5628.9MB, alloc=471.7MB, time=58.29 memory used=5708.3MB, alloc=471.7MB, time=58.63 memory used=5862.3MB, alloc=471.7MB, time=61.81 memory used=5975.0MB, alloc=471.7MB, time=65.68 memory used=6075.6MB, alloc=471.7MB, time=66.45 memory used=6147.1MB, alloc=471.7MB, time=66.71 memory used=6218.7MB, alloc=471.7MB, time=66.98 memory used=6307.4MB, alloc=471.7MB, time=67.24 memory used=6374.2MB, alloc=471.7MB, time=67.46 memory used=6433.6MB, alloc=471.7MB, time=67.67 memory used=6500.0MB, alloc=471.7MB, time=67.88 memory used=6644.9MB, alloc=471.7MB, time=68.85 memory used=6822.5MB, alloc=495.7MB, time=69.79 memory used=7032.2MB, alloc=495.7MB, time=71.06 memory used=7256.2MB, alloc=495.7MB, time=73.65 memory used=7356.5MB, alloc=495.7MB, time=74.06 memory used=7452.1MB, alloc=495.7MB, time=74.48 memory used=7557.9MB, alloc=495.7MB, time=75.43 memory used=7634.5MB, alloc=495.7MB, time=75.76 memory used=7721.2MB, alloc=495.7MB, time=76.11 memory used=7825.4MB, alloc=495.7MB, time=76.43 memory used=7898.7MB, alloc=495.7MB, time=76.70 memory used=7962.7MB, alloc=495.7MB, time=76.96 memory used=8033.0MB, alloc=495.7MB, time=77.22 memory used=8112.2MB, alloc=495.7MB, time=77.50 memory used=8199.3MB, alloc=495.7MB, time=77.77 memory used=8293.8MB, alloc=495.7MB, time=78.04 memory used=8426.2MB, alloc=495.7MB, time=78.36 memory used=8616.0MB, alloc=495.7MB, time=78.77 memory used=8770.4MB, alloc=495.7MB, time=79.87 memory used=8841.8MB, alloc=495.7MB, time=80.24 memory used=8927.9MB, alloc=495.7MB, time=80.57 memory used=9032.8MB, alloc=495.7MB, time=80.92 memory used=9102.9MB, alloc=519.7MB, time=81.21 memory used=9181.6MB, alloc=519.7MB, time=81.49 memory used=9270.7MB, alloc=519.7MB, time=81.78 memory used=9369.5MB, alloc=519.7MB, time=82.07 memory used=9480.6MB, alloc=519.7MB, time=82.37 memory used=9638.0MB, alloc=519.7MB, time=82.72 memory used=9823.3MB, alloc=519.7MB, time=83.11 memory used=9994.8MB, alloc=519.7MB, time=172.48 memory used=10105.9MB, alloc=519.7MB, time=175.45 memory used=10214.7MB, alloc=519.7MB, time=175.83 memory used=10295.9MB, alloc=519.7MB, time=176.16 memory used=10392.9MB, alloc=519.7MB, time=176.50 memory used=10505.4MB, alloc=519.7MB, time=176.85 memory used=10754.1MB, alloc=519.7MB, time=177.42 memory used=10908.9MB, alloc=519.7MB, time=177.86 memory used=11087.7MB, alloc=519.7MB, time=178.32 memory used=11295.6MB, alloc=519.7MB, time=178.81 memory used=11615.0MB, alloc=519.7MB, time=180.75 memory used=11714.2MB, alloc=519.7MB, time=181.13 memory used=11823.8MB, alloc=519.7MB, time=181.52 memory used=11920.9MB, alloc=519.7MB, time=181.83 memory used=12005.9MB, alloc=519.7MB, time=182.10 memory used=12110.4MB, alloc=519.7MB, time=182.40 memory used=12254.5MB, alloc=519.7MB, time=183.00 memory used=12388.3MB, alloc=519.7MB, time=218.97 memory used=12496.6MB, alloc=519.7MB, time=224.54 memory used=12600.1MB, alloc=519.7MB, time=224.91 memory used=12687.6MB, alloc=519.7MB, time=225.21 memory used=12796.7MB, alloc=519.7MB, time=225.51 memory used=13034.2MB, alloc=519.7MB, time=226.00 memory used=13208.4MB, alloc=519.7MB, time=226.40 memory used=13474.0MB, alloc=519.7MB, time=227.90 memory used=13590.2MB, alloc=519.7MB, time=229.29 memory used=13736.8MB, alloc=519.7MB, time=233.48 memory used=13860.5MB, alloc=519.7MB, time=234.59 memory used=13970.5MB, alloc=519.7MB, time=234.93 memory used=14052.8MB, alloc=519.7MB, time=235.22 memory used=14140.9MB, alloc=519.7MB, time=235.51 memory used=14244.4MB, alloc=519.7MB, time=235.80 memory used=14366.2MB, alloc=519.7MB, time=236.11 memory used=14530.5MB, alloc=519.7MB, time=236.50 memory used=14774.5MB, alloc=519.7MB, time=237.66 memory used=14927.0MB, alloc=519.7MB, time=238.91 memory used=15047.9MB, alloc=519.7MB, time=239.47 memory used=15167.9MB, alloc=519.7MB, time=240.36 memory used=15265.3MB, alloc=519.7MB, time=240.77 memory used=15357.8MB, alloc=519.7MB, time=241.11 memory used=15460.2MB, alloc=519.7MB, time=241.43 memory used=15537.3MB, alloc=519.7MB, time=241.71 memory used=15648.5MB, alloc=519.7MB, time=242.29 memory used=15743.1MB, alloc=519.7MB, time=242.66 memory used=15839.3MB, alloc=519.7MB, time=243.03 memory used=15936.8MB, alloc=519.7MB, time=243.36 memory used=16015.6MB, alloc=519.7MB, time=243.64 memory used=16136.4MB, alloc=519.7MB, time=247.99 memory used=16235.7MB, alloc=519.7MB, time=248.33 memory used=16320.0MB, alloc=519.7MB, time=248.63 memory used=16415.9MB, alloc=519.7MB, time=248.92 memory used=16569.4MB, alloc=519.7MB, time=250.58 memory used=16678.2MB, alloc=519.7MB, time=252.07 memory used=16765.0MB, alloc=519.7MB, time=252.36 memory used=16887.5MB, alloc=519.7MB, time=253.07 memory used=16980.2MB, alloc=519.7MB, time=253.42 memory used=17080.1MB, alloc=519.7MB, time=253.73 memory used=17207.7MB, alloc=519.7MB, time=266.07 memory used=17303.1MB, alloc=519.7MB, time=266.43 memory used=17393.7MB, alloc=519.7MB, time=266.74 memory used=17478.4MB, alloc=519.7MB, time=267.02 memory used=17584.9MB, alloc=519.7MB, time=267.31 memory used=17732.3MB, alloc=519.7MB, time=268.03 memory used=17890.3MB, alloc=519.7MB, time=269.01 memory used=17995.2MB, alloc=519.7MB, time=270.02 memory used=18086.3MB, alloc=519.7MB, time=270.37 memory used=18194.7MB, alloc=519.7MB, time=270.88 memory used=18285.6MB, alloc=519.7MB, time=271.20 memory used=18420.3MB, alloc=519.7MB, time=272.35 memory used=18533.8MB, alloc=519.7MB, time=278.81 memory used=18620.1MB, alloc=519.7MB, time=279.12 memory used=18774.9MB, alloc=519.7MB, time=282.02 memory used=18862.9MB, alloc=519.7MB, time=282.35 memory used=19045.7MB, alloc=543.7MB, time=283.57 memory used=19294.7MB, alloc=543.7MB, time=285.74 memory used=19413.1MB, alloc=543.7MB, time=287.85 memory used=19513.1MB, alloc=543.7MB, time=288.29 memory used=19685.2MB, alloc=543.7MB, time=289.32 memory used=19788.9MB, alloc=543.7MB, time=290.44 memory used=19927.1MB, alloc=543.7MB, time=291.49 memory used=20066.0MB, alloc=543.7MB, time=296.53 memory used=20171.0MB, alloc=543.7MB, time=296.93 memory used=20257.2MB, alloc=543.7MB, time=297.26 memory used=20329.8MB, alloc=543.7MB, time=298.07 memory used=20431.8MB, alloc=543.7MB, time=299.01 memory used=20554.3MB, alloc=567.7MB, time=299.90 memory used=20697.7MB, alloc=567.7MB, time=304.71 memory used=20842.7MB, alloc=567.7MB, time=305.41 memory used=21015.6MB, alloc=567.7MB, time=306.54 memory used=21104.9MB, alloc=567.7MB, time=307.59 memory used=21225.0MB, alloc=591.7MB, time=312.02 memory used=21459.6MB, alloc=615.7MB, time=314.69 memory used=21698.7MB, alloc=615.7MB, time=321.28 memory used=21949.5MB, alloc=615.7MB, time=343.12 memory used=22062.6MB, alloc=615.7MB, time=343.54 memory used=22184.3MB, alloc=615.7MB, time=343.95 memory used=22326.3MB, alloc=615.7MB, time=344.38 memory used=22492.9MB, alloc=615.7MB, time=344.82 memory used=22794.3MB, alloc=615.7MB, time=346.29 memory used=22882.2MB, alloc=615.7MB, time=347.25 memory used=23014.9MB, alloc=615.7MB, time=348.27 memory used=23270.9MB, alloc=615.7MB, time=349.49 memory used=23404.0MB, alloc=615.7MB, time=350.72 memory used=23462.2MB, alloc=615.7MB, time=351.61 memory used=23515.0MB, alloc=615.7MB, time=352.40 memory used=23643.4MB, alloc=615.7MB, time=353.06 memory used=23780.7MB, alloc=615.7MB, time=355.72 memory used=23942.4MB, alloc=615.7MB, time=379.67 memory used=24080.8MB, alloc=615.7MB, time=380.15 memory used=24201.3MB, alloc=615.7MB, time=380.56 memory used=24373.4MB, alloc=615.7MB, time=381.20 memory used=24628.6MB, alloc=615.7MB, time=382.41 memory used=24781.1MB, alloc=615.7MB, time=383.08 memory used=24946.2MB, alloc=615.7MB, time=410.21 memory used=25082.5MB, alloc=615.7MB, time=410.76 memory used=25210.3MB, alloc=615.7MB, time=411.22 memory used=25342.3MB, alloc=615.7MB, time=411.64 memory used=25453.2MB, alloc=615.7MB, time=412.52 memory used=25509.1MB, alloc=615.7MB, time=413.32 memory used=25770.7MB, alloc=639.7MB, time=416.53 memory used=25944.4MB, alloc=639.7MB, time=423.74 memory used=26096.5MB, alloc=639.7MB, time=424.29 memory used=26230.6MB, alloc=639.7MB, time=424.81 memory used=26361.4MB, alloc=639.7MB, time=425.27 memory used=26516.1MB, alloc=639.7MB, time=425.75 memory used=26697.4MB, alloc=639.7MB, time=426.24 memory used=26874.3MB, alloc=639.7MB, time=426.77 memory used=27005.6MB, alloc=639.7MB, time=427.24 memory used=27150.5MB, alloc=639.7MB, time=427.73 memory used=27308.8MB, alloc=639.7MB, time=428.24 memory used=27487.3MB, alloc=639.7MB, time=428.77 memory used=27980.6MB, alloc=639.7MB, time=431.51 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428523816 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 3 F := [12 x - x z - 20 z, 3 x y + 17 x z - 6 y z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 G := [4 y + 9 x z + 4 y z, -6 x y - 20 z ] > Problem := [F,G]; 2 3 2 2 3 Problem := [[12 x - x z - 20 z, 3 x y + 17 x z - 6 y z], 3 3 2 [4 y + 9 x z + 4 y z, -6 x y - 20 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=25.6MB, alloc=32.3MB, time=0.48 memory used=45.4MB, alloc=32.3MB, time=0.75 memory used=64.8MB, alloc=56.3MB, time=1.05 memory used=112.9MB, alloc=77.0MB, time=1.45 memory used=161.3MB, alloc=77.0MB, time=2.00 memory used=208.8MB, alloc=77.0MB, time=2.41 memory used=253.5MB, alloc=77.0MB, time=2.85 memory used=296.1MB, alloc=101.0MB, time=3.35 memory used=363.1MB, alloc=101.0MB, time=4.04 memory used=427.2MB, alloc=101.0MB, time=4.55 memory used=491.2MB, alloc=101.0MB, time=5.05 memory used=551.8MB, alloc=125.0MB, time=5.70 memory used=607.0MB, alloc=381.0MB, time=6.32 memory used=696.0MB, alloc=405.0MB, time=7.27 memory used=807.2MB, alloc=405.0MB, time=8.49 memory used=916.2MB, alloc=429.0MB, time=9.75 memory used=1005.7MB, alloc=429.0MB, time=10.40 memory used=1078.8MB, alloc=429.0MB, time=10.82 memory used=1153.9MB, alloc=429.0MB, time=11.35 memory used=1251.0MB, alloc=429.0MB, time=12.11 memory used=1381.2MB, alloc=429.0MB, time=13.28 memory used=1502.2MB, alloc=453.0MB, time=14.54 memory used=1636.7MB, alloc=453.0MB, time=15.90 memory used=1723.3MB, alloc=453.0MB, time=16.41 memory used=1839.5MB, alloc=453.0MB, time=17.21 memory used=1971.6MB, alloc=453.0MB, time=18.44 memory used=2110.3MB, alloc=477.0MB, time=19.74 memory used=2253.6MB, alloc=477.0MB, time=20.94 memory used=2360.6MB, alloc=477.0MB, time=21.66 memory used=2517.5MB, alloc=477.0MB, time=22.81 memory used=2667.0MB, alloc=477.0MB, time=24.62 memory used=2853.6MB, alloc=477.0MB, time=25.86 memory used=3008.9MB, alloc=501.0MB, time=27.38 memory used=3207.4MB, alloc=501.0MB, time=28.85 memory used=3392.1MB, alloc=501.0MB, time=30.43 memory used=3536.9MB, alloc=501.0MB, time=31.92 memory used=3694.7MB, alloc=525.0MB, time=33.93 memory used=3894.0MB, alloc=549.0MB, time=36.30 memory used=4067.9MB, alloc=549.0MB, time=38.31 memory used=4329.0MB, alloc=573.0MB, time=40.44 memory used=4492.5MB, alloc=573.0MB, time=42.83 memory used=4663.1MB, alloc=597.0MB, time=45.19 memory used=4816.4MB, alloc=621.0MB, time=47.58 memory used=4991.4MB, alloc=645.0MB, time=49.94 memory used=5134.7MB, alloc=645.0MB, time=52.20 memory used=5310.8MB, alloc=669.0MB, time=54.47 memory used=5459.0MB, alloc=669.0MB, time=56.69 memory used=5571.6MB, alloc=693.0MB, time=58.65 memory used=5697.3MB, alloc=693.0MB, time=60.87 memory used=5818.8MB, alloc=717.0MB, time=63.03 memory used=5944.6MB, alloc=717.0MB, time=65.16 memory used=6046.8MB, alloc=741.0MB, time=66.97 memory used=6172.2MB, alloc=741.0MB, time=69.06 memory used=6272.2MB, alloc=765.0MB, time=71.44 memory used=6460.5MB, alloc=789.0MB, time=76.96 memory used=6767.9MB, alloc=813.0MB, time=86.34 memory used=7078.9MB, alloc=837.0MB, time=96.70 memory used=7397.8MB, alloc=861.0MB, time=107.58 memory used=7726.9MB, alloc=885.0MB, time=118.79 memory used=8062.0MB, alloc=909.0MB, time=130.97 memory used=8412.3MB, alloc=933.0MB, time=144.25 memory used=8786.5MB, alloc=957.0MB, time=158.48 memory used=9184.6MB, alloc=981.0MB, time=173.36 memory used=9606.8MB, alloc=1005.0MB, time=188.88 memory used=10052.9MB, alloc=1005.0MB, time=205.42 memory used=10498.9MB, alloc=1029.0MB, time=222.10 memory used=10968.8MB, alloc=1029.0MB, time=239.43 memory used=11438.7MB, alloc=1029.0MB, time=256.57 memory used=11908.6MB, alloc=1029.0MB, time=273.92 memory used=12378.4MB, alloc=1053.0MB, time=291.34 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428524116 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 4 F := [-5 y z + 12 x y z + 5 x , 12 x y - 4 y - 10 x] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 4 2 G := [-8 x - 5 x y + 4 x y , 10 z - 12 x - 10 x z] > Problem := [F,G]; 2 2 2 3 4 Problem := [[-5 y z + 12 x y z + 5 x , 12 x y - 4 y - 10 x], 4 2 2 4 2 [-8 x - 5 x y + 4 x y , 10 z - 12 x - 10 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=25.7MB, alloc=32.3MB, time=0.49 memory used=45.4MB, alloc=36.3MB, time=0.73 memory used=64.5MB, alloc=60.3MB, time=1.02 memory used=107.9MB, alloc=60.3MB, time=1.46 memory used=149.8MB, alloc=61.8MB, time=1.75 memory used=172.3MB, alloc=61.8MB, time=1.80 memory used=201.8MB, alloc=61.8MB, time=1.86 memory used=222.0MB, alloc=61.8MB, time=1.91 memory used=260.4MB, alloc=61.8MB, time=2.27 memory used=310.8MB, alloc=61.8MB, time=2.65 memory used=349.7MB, alloc=61.8MB, time=2.79 memory used=390.2MB, alloc=61.8MB, time=2.93 memory used=427.6MB, alloc=61.8MB, time=3.03 memory used=466.9MB, alloc=61.8MB, time=3.13 memory used=506.8MB, alloc=61.8MB, time=3.25 memory used=547.1MB, alloc=61.8MB, time=3.37 memory used=586.2MB, alloc=61.8MB, time=3.48 memory used=628.6MB, alloc=61.8MB, time=3.60 memory used=669.8MB, alloc=61.8MB, time=3.72 memory used=711.2MB, alloc=61.8MB, time=3.82 memory used=766.6MB, alloc=68.2MB, time=4.40 memory used=815.8MB, alloc=68.2MB, time=4.68 memory used=858.5MB, alloc=68.2MB, time=4.88 memory used=911.3MB, alloc=68.2MB, time=5.52 memory used=958.1MB, alloc=68.2MB, time=5.79 memory used=1000.2MB, alloc=68.2MB, time=5.98 memory used=1038.0MB, alloc=68.2MB, time=6.15 memory used=1077.3MB, alloc=68.2MB, time=6.30 memory used=1117.5MB, alloc=68.2MB, time=6.44 memory used=1169.6MB, alloc=68.2MB, time=6.91 memory used=1218.2MB, alloc=68.2MB, time=7.21 memory used=1263.0MB, alloc=68.2MB, time=7.44 memory used=1301.0MB, alloc=68.2MB, time=7.61 memory used=1337.0MB, alloc=68.2MB, time=7.76 memory used=1374.7MB, alloc=68.2MB, time=7.90 memory used=1414.4MB, alloc=68.2MB, time=8.05 memory used=1446.1MB, alloc=68.2MB, time=8.16 memory used=1482.7MB, alloc=68.2MB, time=8.29 memory used=1513.0MB, alloc=68.2MB, time=8.38 memory used=1549.0MB, alloc=68.2MB, time=8.51 memory used=1582.1MB, alloc=68.2MB, time=8.61 memory used=1625.8MB, alloc=68.2MB, time=8.98 memory used=1673.0MB, alloc=68.2MB, time=9.29 memory used=1711.3MB, alloc=68.2MB, time=9.47 memory used=1759.1MB, alloc=68.2MB, time=9.84 memory used=1804.4MB, alloc=68.2MB, time=10.10 memory used=1846.0MB, alloc=68.2MB, time=10.39 memory used=1889.7MB, alloc=92.2MB, time=10.65 memory used=1954.6MB, alloc=92.2MB, time=10.93 memory used=2023.9MB, alloc=92.2MB, time=11.36 memory used=2082.9MB, alloc=92.2MB, time=11.55 memory used=2141.4MB, alloc=92.2MB, time=11.74 memory used=2199.9MB, alloc=92.2MB, time=11.91 memory used=2260.3MB, alloc=92.2MB, time=12.08 memory used=2322.7MB, alloc=92.2MB, time=12.25 memory used=2385.5MB, alloc=92.2MB, time=12.43 memory used=2450.3MB, alloc=92.2MB, time=12.61 memory used=2518.9MB, alloc=92.2MB, time=12.80 memory used=2591.3MB, alloc=97.7MB, time=12.99 memory used=2670.0MB, alloc=107.8MB, time=13.17 memory used=2737.5MB, alloc=107.8MB, time=13.33 memory used=2808.1MB, alloc=107.8MB, time=14.01 memory used=2975.4MB, alloc=107.8MB, time=17.83 memory used=3027.8MB, alloc=107.8MB, time=18.06 memory used=3131.7MB, alloc=107.8MB, time=18.65 memory used=3310.2MB, alloc=107.8MB, time=21.99 memory used=3359.9MB, alloc=107.8MB, time=22.16 memory used=3461.3MB, alloc=107.8MB, time=23.01 memory used=3661.4MB, alloc=107.8MB, time=26.29 memory used=3779.0MB, alloc=107.8MB, time=27.47 memory used=3852.4MB, alloc=107.8MB, time=28.27 memory used=4029.5MB, alloc=107.8MB, time=31.65 memory used=4080.0MB, alloc=107.8MB, time=31.86 memory used=4168.6MB, alloc=107.8MB, time=32.65 memory used=4241.5MB, alloc=107.8MB, time=33.27 memory used=4325.6MB, alloc=131.8MB, time=34.24 memory used=4438.1MB, alloc=131.8MB, time=35.23 memory used=4663.2MB, alloc=131.8MB, time=38.87 memory used=4798.5MB, alloc=131.8MB, time=39.90 memory used=4894.1MB, alloc=131.8MB, time=40.83 memory used=5004.5MB, alloc=131.8MB, time=41.96 memory used=5111.8MB, alloc=131.8MB, time=43.18 memory used=5217.2MB, alloc=155.8MB, time=44.31 memory used=5442.3MB, alloc=155.8MB, time=47.96 memory used=5600.1MB, alloc=155.8MB, time=49.27 memory used=5760.9MB, alloc=155.8MB, time=52.62 memory used=5886.2MB, alloc=155.8MB, time=53.07 memory used=6048.6MB, alloc=155.8MB, time=54.47 memory used=6173.4MB, alloc=179.8MB, time=56.19 memory used=6274.3MB, alloc=203.8MB, time=58.65 memory used=6383.7MB, alloc=227.8MB, time=61.84 memory used=6510.0MB, alloc=227.8MB, time=65.89 memory used=6636.2MB, alloc=251.8MB, time=69.99 memory used=6786.4MB, alloc=251.8MB, time=74.97 N1 := 4623 > GB := Basis(F, plex(op(vars))); 3 4 GB := [-6 x y + 2 y + 5 x, 7 4 3 4 3 2 2 2 -36 x + 12 x y - 72 x z + 24 x y z + 10 x y + 25 x z , 2 2 2 5 y z - 12 x y z - 5 x ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=6950.1MB, alloc=251.8MB, time=78.58 memory used=7122.6MB, alloc=507.8MB, time=80.69 memory used=7296.5MB, alloc=507.8MB, time=83.65 memory used=7450.3MB, alloc=507.8MB, time=85.26 memory used=7573.8MB, alloc=531.8MB, time=87.51 memory used=7724.9MB, alloc=531.8MB, time=90.81 memory used=7856.7MB, alloc=531.8MB, time=94.50 memory used=8007.4MB, alloc=531.8MB, time=95.99 memory used=8155.9MB, alloc=531.8MB, time=100.32 memory used=8247.8MB, alloc=531.8MB, time=100.67 memory used=8361.1MB, alloc=531.8MB, time=101.03 memory used=8438.4MB, alloc=531.8MB, time=101.31 memory used=8526.7MB, alloc=531.8MB, time=101.56 memory used=8680.7MB, alloc=531.8MB, time=104.57 memory used=8775.6MB, alloc=531.8MB, time=104.90 memory used=8871.3MB, alloc=531.8MB, time=105.21 memory used=9035.6MB, alloc=531.8MB, time=118.11 memory used=9165.4MB, alloc=531.8MB, time=122.05 memory used=9258.3MB, alloc=531.8MB, time=122.39 memory used=9351.6MB, alloc=531.8MB, time=122.68 memory used=9468.9MB, alloc=531.8MB, time=122.98 memory used=9541.1MB, alloc=531.8MB, time=123.22 memory used=9618.0MB, alloc=531.8MB, time=123.46 memory used=9704.4MB, alloc=531.8MB, time=123.71 memory used=9802.3MB, alloc=531.8MB, time=123.95 memory used=9916.3MB, alloc=531.8MB, time=124.20 memory used=10106.9MB, alloc=531.8MB, time=127.23 memory used=10201.3MB, alloc=531.8MB, time=127.56 memory used=10313.7MB, alloc=531.8MB, time=128.05 memory used=10491.5MB, alloc=531.8MB, time=130.56 memory used=10638.3MB, alloc=531.8MB, time=132.51 memory used=10730.9MB, alloc=531.8MB, time=132.82 memory used=10854.1MB, alloc=531.8MB, time=133.97 memory used=10986.1MB, alloc=531.8MB, time=135.68 memory used=11163.0MB, alloc=531.8MB, time=138.31 memory used=11304.6MB, alloc=531.8MB, time=139.40 memory used=11414.0MB, alloc=531.8MB, time=139.96 memory used=11635.1MB, alloc=555.8MB, time=171.86 memory used=11766.4MB, alloc=579.8MB, time=297.32 memory used=11910.1MB, alloc=603.8MB, time=471.95 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428524416 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 3 3 2 F := [-12 x y z + 11 y + 8 z , 18 y + 7 y z + 19 x y] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 2 2 2 G := [-5 x - 17 x z - 7 x z , 10 x y z + 14 x z - 4 y z] > Problem := [F,G]; 2 3 3 3 2 Problem := [[-12 x y z + 11 y + 8 z , 18 y + 7 y z + 19 x y], 4 3 2 2 2 [-5 x - 17 x z - 7 x z , 10 x y z + 14 x z - 4 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.6MB, alloc=32.3MB, time=0.49 memory used=47.1MB, alloc=32.3MB, time=0.78 memory used=66.0MB, alloc=56.3MB, time=1.06 memory used=108.5MB, alloc=68.3MB, time=1.67 memory used=151.4MB, alloc=68.3MB, time=2.22 memory used=192.2MB, alloc=68.3MB, time=2.60 memory used=238.5MB, alloc=92.3MB, time=3.13 memory used=312.0MB, alloc=92.3MB, time=4.08 memory used=359.1MB, alloc=92.3MB, time=4.36 memory used=429.4MB, alloc=92.3MB, time=5.20 memory used=494.5MB, alloc=92.3MB, time=5.73 memory used=561.7MB, alloc=92.3MB, time=6.64 memory used=626.3MB, alloc=372.3MB, time=7.44 memory used=710.7MB, alloc=372.3MB, time=8.20 memory used=766.6MB, alloc=372.3MB, time=8.50 memory used=810.3MB, alloc=372.3MB, time=8.65 memory used=876.7MB, alloc=372.3MB, time=14.39 memory used=918.9MB, alloc=372.3MB, time=14.54 memory used=962.1MB, alloc=372.3MB, time=14.69 memory used=1011.1MB, alloc=372.3MB, time=14.82 memory used=1042.7MB, alloc=372.3MB, time=14.94 memory used=1078.7MB, alloc=372.3MB, time=15.05 memory used=1119.0MB, alloc=372.3MB, time=15.17 memory used=1164.6MB, alloc=372.3MB, time=15.29 memory used=1248.2MB, alloc=372.3MB, time=15.90 memory used=1291.8MB, alloc=372.3MB, time=16.05 memory used=1344.7MB, alloc=372.3MB, time=16.41 memory used=1394.1MB, alloc=372.3MB, time=16.65 memory used=1443.3MB, alloc=372.3MB, time=16.80 memory used=1521.2MB, alloc=372.3MB, time=17.79 memory used=1578.6MB, alloc=372.3MB, time=18.48 memory used=1620.0MB, alloc=372.3MB, time=18.61 memory used=1667.5MB, alloc=372.3MB, time=18.87 memory used=1716.6MB, alloc=372.3MB, time=19.10 memory used=1796.8MB, alloc=372.3MB, time=19.88 memory used=1892.9MB, alloc=372.3MB, time=20.55 memory used=1988.4MB, alloc=372.3MB, time=21.24 memory used=2083.6MB, alloc=372.3MB, time=22.22 memory used=2178.5MB, alloc=372.3MB, time=23.62 memory used=2274.9MB, alloc=372.3MB, time=25.57 memory used=2370.5MB, alloc=372.3MB, time=28.01 memory used=2468.3MB, alloc=372.3MB, time=31.12 memory used=2566.3MB, alloc=372.3MB, time=34.41 memory used=2651.7MB, alloc=372.3MB, time=36.25 memory used=2707.9MB, alloc=372.3MB, time=36.59 memory used=2747.7MB, alloc=372.3MB, time=36.73 memory used=2812.6MB, alloc=372.3MB, time=42.47 memory used=2853.7MB, alloc=372.3MB, time=42.62 memory used=2891.0MB, alloc=372.3MB, time=42.77 memory used=2938.7MB, alloc=372.3MB, time=42.92 memory used=2972.7MB, alloc=372.3MB, time=43.04 memory used=3004.2MB, alloc=372.3MB, time=43.16 memory used=3040.2MB, alloc=372.3MB, time=43.27 memory used=3079.3MB, alloc=372.3MB, time=43.38 memory used=3124.2MB, alloc=372.3MB, time=43.50 memory used=3203.5MB, alloc=372.3MB, time=44.11 memory used=3246.3MB, alloc=372.3MB, time=44.37 memory used=3299.7MB, alloc=372.3MB, time=44.53 memory used=3365.4MB, alloc=372.3MB, time=44.97 memory used=3474.9MB, alloc=372.3MB, time=45.23 memory used=3552.9MB, alloc=372.3MB, time=45.39 memory used=3653.0MB, alloc=372.3MB, time=46.04 memory used=3732.5MB, alloc=372.3MB, time=46.72 memory used=3829.9MB, alloc=372.3MB, time=47.71 memory used=3874.0MB, alloc=372.3MB, time=48.00 memory used=3911.9MB, alloc=372.3MB, time=48.14 memory used=3958.9MB, alloc=372.3MB, time=48.44 memory used=4054.4MB, alloc=396.3MB, time=49.51 memory used=4123.7MB, alloc=396.3MB, time=50.13 memory used=4176.3MB, alloc=396.3MB, time=50.30 memory used=4247.8MB, alloc=396.3MB, time=50.81 memory used=4357.2MB, alloc=396.3MB, time=56.91 memory used=4411.0MB, alloc=396.3MB, time=57.10 memory used=4458.2MB, alloc=396.3MB, time=57.27 memory used=4520.2MB, alloc=396.3MB, time=57.46 memory used=4563.8MB, alloc=396.3MB, time=57.61 memory used=4606.2MB, alloc=396.3MB, time=57.75 memory used=4654.4MB, alloc=396.3MB, time=57.90 memory used=4746.3MB, alloc=396.3MB, time=58.51 memory used=4853.0MB, alloc=396.3MB, time=59.79 memory used=4904.3MB, alloc=396.3MB, time=59.98 memory used=4951.6MB, alloc=396.3MB, time=60.15 memory used=4996.3MB, alloc=396.3MB, time=60.31 memory used=5049.8MB, alloc=396.3MB, time=60.47 memory used=5255.1MB, alloc=396.3MB, time=60.97 memory used=5524.8MB, alloc=396.3MB, time=62.85 memory used=5586.5MB, alloc=396.3MB, time=63.54 memory used=5636.0MB, alloc=396.3MB, time=63.72 memory used=5678.7MB, alloc=396.3MB, time=63.88 memory used=5729.7MB, alloc=396.3MB, time=64.05 memory used=5792.1MB, alloc=396.3MB, time=64.22 memory used=5949.7MB, alloc=396.3MB, time=64.57 memory used=6189.4MB, alloc=396.3MB, time=65.80 memory used=6265.8MB, alloc=396.3MB, time=66.30 memory used=6335.2MB, alloc=396.3MB, time=66.53 memory used=6489.6MB, alloc=396.3MB, time=67.71 memory used=6591.9MB, alloc=396.3MB, time=67.93 memory used=6819.0MB, alloc=396.3MB, time=70.59 memory used=7032.5MB, alloc=396.3MB, time=70.96 memory used=7273.1MB, alloc=396.3MB, time=71.34 memory used=7468.0MB, alloc=396.3MB, time=71.65 memory used=7685.2MB, alloc=396.3MB, time=71.95 memory used=7881.4MB, alloc=396.3MB, time=72.24 memory used=8119.1MB, alloc=396.3MB, time=75.57 memory used=8229.9MB, alloc=420.3MB, time=77.19 memory used=8351.1MB, alloc=420.3MB, time=78.91 memory used=8487.6MB, alloc=420.3MB, time=80.43 memory used=8597.0MB, alloc=420.3MB, time=81.00 memory used=8719.7MB, alloc=420.3MB, time=81.90 memory used=8819.0MB, alloc=420.3MB, time=82.39 memory used=8940.5MB, alloc=420.3MB, time=83.77 memory used=9034.0MB, alloc=420.3MB, time=84.18 memory used=9123.5MB, alloc=420.3MB, time=84.56 memory used=9214.0MB, alloc=420.3MB, time=84.96 memory used=9304.3MB, alloc=420.3MB, time=85.35 memory used=9452.5MB, alloc=420.3MB, time=89.35 memory used=9578.7MB, alloc=420.3MB, time=90.27 memory used=9700.2MB, alloc=444.3MB, time=91.63 memory used=9843.1MB, alloc=444.3MB, time=93.07 memory used=9958.6MB, alloc=444.3MB, time=93.54 memory used=10091.1MB, alloc=444.3MB, time=96.59 memory used=10243.5MB, alloc=444.3MB, time=97.73 memory used=10360.6MB, alloc=444.3MB, time=98.23 memory used=10507.6MB, alloc=444.3MB, time=101.56 memory used=10640.4MB, alloc=444.3MB, time=102.40 memory used=10776.6MB, alloc=444.3MB, time=103.32 memory used=10913.0MB, alloc=444.3MB, time=104.23 memory used=11061.6MB, alloc=444.3MB, time=105.39 memory used=11215.9MB, alloc=444.3MB, time=107.34 memory used=11369.1MB, alloc=444.3MB, time=109.26 memory used=11529.8MB, alloc=468.3MB, time=110.74 memory used=11729.4MB, alloc=468.3MB, time=112.91 memory used=11862.5MB, alloc=468.3MB, time=113.51 memory used=12070.7MB, alloc=468.3MB, time=116.04 memory used=12252.2MB, alloc=492.3MB, time=117.48 memory used=12460.7MB, alloc=492.3MB, time=118.99 memory used=12759.0MB, alloc=492.3MB, time=126.60 memory used=12897.5MB, alloc=492.3MB, time=128.81 memory used=13389.3MB, alloc=492.3MB, time=131.89 memory used=13594.6MB, alloc=492.3MB, time=138.60 memory used=13779.6MB, alloc=492.3MB, time=141.04 memory used=14209.6MB, alloc=492.3MB, time=142.65 memory used=14359.9MB, alloc=492.3MB, time=143.17 memory used=14522.5MB, alloc=492.3MB, time=143.70 memory used=14700.6MB, alloc=492.3MB, time=144.23 memory used=14889.5MB, alloc=492.3MB, time=144.78 memory used=15139.8MB, alloc=492.3MB, time=150.73 memory used=15272.1MB, alloc=492.3MB, time=152.90 memory used=15781.6MB, alloc=492.3MB, time=156.18 memory used=16029.2MB, alloc=492.3MB, time=158.80 memory used=16211.7MB, alloc=516.3MB, time=161.34 memory used=16451.7MB, alloc=540.3MB, time=164.26 memory used=16716.6MB, alloc=540.3MB, time=167.60 memory used=16972.7MB, alloc=540.3MB, time=170.16 memory used=17196.8MB, alloc=564.3MB, time=177.55 memory used=17364.3MB, alloc=588.3MB, time=180.30 memory used=18022.1MB, alloc=588.3MB, time=185.26 memory used=18244.2MB, alloc=612.3MB, time=189.15 memory used=18445.3MB, alloc=612.3MB, time=196.47 memory used=18655.0MB, alloc=612.3MB, time=199.90 memory used=19234.5MB, alloc=612.3MB, time=203.89 memory used=19439.0MB, alloc=636.3MB, time=207.52 memory used=19737.1MB, alloc=660.3MB, time=210.06 memory used=19983.2MB, alloc=660.3MB, time=211.32 memory used=20235.8MB, alloc=660.3MB, time=212.57 memory used=20526.1MB, alloc=660.3MB, time=214.00 memory used=20851.1MB, alloc=660.3MB, time=215.61 memory used=21242.9MB, alloc=660.3MB, time=217.56 memory used=21674.0MB, alloc=660.3MB, time=219.76 memory used=22190.7MB, alloc=660.3MB, time=222.39 memory used=22650.3MB, alloc=660.3MB, time=224.86 memory used=23078.6MB, alloc=660.3MB, time=227.25 memory used=23513.2MB, alloc=660.3MB, time=229.70 memory used=23915.2MB, alloc=660.3MB, time=231.99 memory used=24323.1MB, alloc=660.3MB, time=234.33 memory used=24740.4MB, alloc=660.3MB, time=236.83 memory used=25122.7MB, alloc=660.3MB, time=239.15 memory used=25510.4MB, alloc=660.3MB, time=241.48 memory used=25905.1MB, alloc=660.3MB, time=243.88 memory used=26309.6MB, alloc=660.3MB, time=246.35 memory used=26709.6MB, alloc=660.3MB, time=248.54 memory used=27063.7MB, alloc=660.3MB, time=250.41 memory used=27426.1MB, alloc=660.3MB, time=252.31 memory used=27796.9MB, alloc=660.3MB, time=254.28 memory used=28169.4MB, alloc=660.3MB, time=256.21 memory used=28542.8MB, alloc=660.3MB, time=258.15 memory used=28916.9MB, alloc=660.3MB, time=260.13 memory used=29294.1MB, alloc=660.3MB, time=262.16 memory used=29676.7MB, alloc=660.3MB, time=264.19 memory used=30028.1MB, alloc=660.3MB, time=266.08 memory used=30382.3MB, alloc=660.3MB, time=267.98 memory used=30742.5MB, alloc=660.3MB, time=269.95 memory used=31108.3MB, alloc=660.3MB, time=272.00 memory used=31475.2MB, alloc=660.3MB, time=273.99 memory used=31845.7MB, alloc=660.3MB, time=276.06 memory used=32215.1MB, alloc=660.3MB, time=278.10 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428524716 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 3 2 F := [2 y z - 2 x z - 19 x, x y + 11 x - 20 y z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 2 3 G := [17 x y z + 3 y z - 13 x y , -9 x y z - 17 x y z + 14 y z ] > Problem := [F,G]; 2 3 3 2 Problem := [[2 y z - 2 x z - 19 x, x y + 11 x - 20 y z ], 2 2 2 2 2 2 3 [17 x y z + 3 y z - 13 x y , -9 x y z - 17 x y z + 14 y z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.16 memory used=26.7MB, alloc=32.3MB, time=0.44 memory used=47.0MB, alloc=32.3MB, time=0.67 memory used=66.7MB, alloc=56.3MB, time=0.92 memory used=108.8MB, alloc=60.3MB, time=1.46 memory used=151.1MB, alloc=60.3MB, time=1.89 memory used=192.9MB, alloc=68.3MB, time=2.33 memory used=233.0MB, alloc=92.3MB, time=2.84 memory used=298.6MB, alloc=92.3MB, time=3.54 memory used=360.0MB, alloc=92.3MB, time=4.25 memory used=426.4MB, alloc=116.3MB, time=4.91 memory used=502.9MB, alloc=372.3MB, time=5.81 memory used=588.0MB, alloc=396.3MB, time=6.80 memory used=690.9MB, alloc=396.3MB, time=7.83 memory used=767.6MB, alloc=396.3MB, time=8.38 memory used=840.8MB, alloc=396.3MB, time=8.79 memory used=947.8MB, alloc=396.3MB, time=9.66 memory used=1075.1MB, alloc=420.3MB, time=10.74 memory used=1213.3MB, alloc=420.3MB, time=11.94 memory used=1303.0MB, alloc=420.3MB, time=12.50 memory used=1384.9MB, alloc=420.3MB, time=12.99 memory used=1504.4MB, alloc=420.3MB, time=13.80 memory used=1635.9MB, alloc=444.3MB, time=15.33 memory used=1762.6MB, alloc=444.3MB, time=16.80 memory used=1870.8MB, alloc=444.3MB, time=17.91 memory used=1952.7MB, alloc=444.3MB, time=18.32 memory used=2051.1MB, alloc=468.3MB, time=19.00 memory used=2167.6MB, alloc=468.3MB, time=19.71 memory used=2309.7MB, alloc=468.3MB, time=20.69 memory used=2417.7MB, alloc=468.3MB, time=21.75 memory used=2524.2MB, alloc=468.3MB, time=22.95 memory used=2633.9MB, alloc=492.3MB, time=24.43 memory used=2745.1MB, alloc=492.3MB, time=25.72 memory used=2842.0MB, alloc=492.3MB, time=26.88 memory used=2916.5MB, alloc=492.3MB, time=27.85 memory used=2998.7MB, alloc=492.3MB, time=28.97 memory used=3076.7MB, alloc=492.3MB, time=30.04 memory used=3165.8MB, alloc=492.3MB, time=31.50 memory used=3245.1MB, alloc=516.3MB, time=32.72 memory used=3341.4MB, alloc=516.3MB, time=33.71 memory used=3439.8MB, alloc=516.3MB, time=34.60 memory used=3495.2MB, alloc=516.3MB, time=35.52 memory used=3574.6MB, alloc=516.3MB, time=36.51 memory used=3657.5MB, alloc=516.3MB, time=37.42 memory used=3714.8MB, alloc=516.3MB, time=38.38 memory used=3780.7MB, alloc=516.3MB, time=39.14 memory used=3895.8MB, alloc=516.3MB, time=39.91 memory used=4004.3MB, alloc=516.3MB, time=40.64 memory used=4115.8MB, alloc=516.3MB, time=41.52 memory used=4163.5MB, alloc=516.3MB, time=42.25 memory used=4208.5MB, alloc=516.3MB, time=42.91 memory used=4264.8MB, alloc=516.3MB, time=43.71 memory used=4451.4MB, alloc=540.3MB, time=45.69 memory used=4660.5MB, alloc=564.3MB, time=48.38 memory used=4869.0MB, alloc=588.3MB, time=51.27 memory used=5118.3MB, alloc=612.3MB, time=54.31 memory used=5407.7MB, alloc=636.3MB, time=57.59 memory used=5714.4MB, alloc=660.3MB, time=60.59 memory used=5989.1MB, alloc=684.3MB, time=65.19 memory used=6214.7MB, alloc=708.3MB, time=69.11 memory used=6513.1MB, alloc=732.3MB, time=74.15 memory used=6774.7MB, alloc=756.3MB, time=78.44 memory used=7028.3MB, alloc=780.3MB, time=82.25 memory used=7287.2MB, alloc=804.3MB, time=86.48 memory used=7530.3MB, alloc=828.3MB, time=91.05 memory used=7754.1MB, alloc=852.3MB, time=95.29 memory used=8019.5MB, alloc=876.3MB, time=99.96 memory used=8250.5MB, alloc=900.3MB, time=104.17 memory used=8482.7MB, alloc=924.3MB, time=108.09 memory used=8697.4MB, alloc=948.3MB, time=112.25 memory used=8877.6MB, alloc=972.3MB, time=116.05 memory used=9099.8MB, alloc=996.3MB, time=120.06 memory used=9315.2MB, alloc=1020.3MB, time=124.00 memory used=9831.7MB, alloc=1044.3MB, time=133.09 memory used=10392.6MB, alloc=1068.3MB, time=141.75 memory used=10935.2MB, alloc=1092.3MB, time=150.86 memory used=11519.6MB, alloc=1116.3MB, time=159.75 memory used=12094.4MB, alloc=1140.3MB, time=167.84 memory used=12527.5MB, alloc=1164.3MB, time=181.89 memory used=12943.7MB, alloc=1188.3MB, time=196.33 memory used=13361.2MB, alloc=1212.3MB, time=211.22 memory used=13782.3MB, alloc=1236.3MB, time=226.56 memory used=14212.4MB, alloc=1260.3MB, time=242.33 memory used=14652.5MB, alloc=1284.3MB, time=258.74 memory used=15105.1MB, alloc=1308.3MB, time=275.82 memory used=15569.2MB, alloc=1332.3MB, time=293.08 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428525016 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 4 3 F := [15 x y + 17 x y z + 6 x z , 6 x - 10 y z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 3 3 2 G := [-11 x y + 4 y + 4 x, 5 y z - 5 x - 2 x z ] > Problem := [F,G]; 3 2 4 3 Problem := [[15 x y + 17 x y z + 6 x z , 6 x - 10 y z], 2 2 3 3 3 2 [-11 x y + 4 y + 4 x, 5 y z - 5 x - 2 x z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=25.6MB, alloc=36.3MB, time=0.49 memory used=47.1MB, alloc=36.3MB, time=0.75 memory used=66.3MB, alloc=60.3MB, time=1.00 memory used=110.5MB, alloc=60.3MB, time=1.36 memory used=145.8MB, alloc=60.3MB, time=1.56 memory used=191.0MB, alloc=62.2MB, time=2.47 memory used=241.7MB, alloc=62.6MB, time=2.84 memory used=270.1MB, alloc=62.6MB, time=2.91 memory used=291.3MB, alloc=62.6MB, time=2.97 memory used=315.5MB, alloc=62.6MB, time=3.03 memory used=344.5MB, alloc=62.6MB, time=3.09 memory used=377.9MB, alloc=62.6MB, time=3.30 memory used=415.0MB, alloc=62.6MB, time=3.40 memory used=438.6MB, alloc=62.6MB, time=3.47 memory used=459.4MB, alloc=62.6MB, time=3.54 memory used=483.2MB, alloc=62.6MB, time=3.60 memory used=510.0MB, alloc=62.6MB, time=3.67 memory used=540.7MB, alloc=62.6MB, time=3.74 memory used=567.8MB, alloc=62.6MB, time=3.81 memory used=584.6MB, alloc=62.6MB, time=3.86 memory used=603.0MB, alloc=62.6MB, time=3.91 memory used=622.4MB, alloc=62.6MB, time=3.97 memory used=642.8MB, alloc=62.6MB, time=4.02 memory used=665.1MB, alloc=62.6MB, time=4.08 memory used=688.8MB, alloc=62.6MB, time=4.14 memory used=715.1MB, alloc=62.6MB, time=4.19 memory used=751.0MB, alloc=62.6MB, time=4.45 memory used=792.1MB, alloc=64.6MB, time=4.57 memory used=820.9MB, alloc=64.6MB, time=4.66 memory used=840.7MB, alloc=64.6MB, time=4.73 memory used=864.2MB, alloc=64.6MB, time=4.80 memory used=890.5MB, alloc=64.6MB, time=4.87 memory used=919.2MB, alloc=64.6MB, time=4.95 memory used=950.8MB, alloc=64.6MB, time=5.03 memory used=968.7MB, alloc=64.6MB, time=5.09 memory used=986.4MB, alloc=64.6MB, time=5.15 memory used=1005.9MB, alloc=64.6MB, time=5.22 memory used=1026.5MB, alloc=64.6MB, time=5.29 memory used=1048.0MB, alloc=64.6MB, time=5.35 memory used=1071.8MB, alloc=64.6MB, time=5.41 memory used=1097.6MB, alloc=64.6MB, time=5.47 memory used=1127.7MB, alloc=64.6MB, time=5.57 memory used=1179.3MB, alloc=64.6MB, time=14.69 memory used=1229.4MB, alloc=64.6MB, time=21.62 memory used=1288.5MB, alloc=64.6MB, time=21.99 memory used=1342.9MB, alloc=64.6MB, time=22.31 memory used=1367.8MB, alloc=64.6MB, time=22.38 memory used=1394.4MB, alloc=64.6MB, time=22.45 memory used=1421.1MB, alloc=64.6MB, time=22.52 memory used=1439.7MB, alloc=64.6MB, time=22.58 memory used=1459.9MB, alloc=64.6MB, time=22.63 memory used=1482.0MB, alloc=64.6MB, time=22.68 memory used=1505.9MB, alloc=64.6MB, time=22.74 memory used=1532.5MB, alloc=64.6MB, time=22.80 memory used=1561.9MB, alloc=64.6MB, time=22.86 memory used=1593.7MB, alloc=64.6MB, time=22.93 memory used=1611.9MB, alloc=64.6MB, time=22.97 memory used=1628.4MB, alloc=64.6MB, time=23.02 memory used=1646.1MB, alloc=64.6MB, time=23.06 memory used=1664.6MB, alloc=64.6MB, time=23.11 memory used=1683.7MB, alloc=64.6MB, time=23.15 memory used=1703.5MB, alloc=64.6MB, time=23.20 memory used=1724.7MB, alloc=64.6MB, time=23.26 memory used=1746.6MB, alloc=64.6MB, time=23.31 memory used=1768.5MB, alloc=64.6MB, time=23.35 memory used=1792.2MB, alloc=64.6MB, time=23.41 memory used=1816.8MB, alloc=64.6MB, time=23.46 memory used=1843.6MB, alloc=64.6MB, time=23.51 memory used=1890.1MB, alloc=64.6MB, time=24.40 memory used=1928.7MB, alloc=64.6MB, time=24.57 memory used=1956.1MB, alloc=64.6MB, time=24.65 memory used=1976.4MB, alloc=64.6MB, time=24.71 memory used=2001.1MB, alloc=64.6MB, time=24.76 memory used=2027.3MB, alloc=64.6MB, time=24.81 memory used=2070.4MB, alloc=64.6MB, time=25.43 memory used=2127.7MB, alloc=64.6MB, time=27.41 memory used=2154.8MB, alloc=64.6MB, time=27.49 memory used=2183.0MB, alloc=64.6MB, time=27.56 memory used=2202.0MB, alloc=64.6MB, time=27.62 memory used=2224.6MB, alloc=64.6MB, time=27.68 memory used=2250.6MB, alloc=64.6MB, time=27.73 memory used=2280.3MB, alloc=64.6MB, time=27.80 memory used=2298.2MB, alloc=64.6MB, time=27.85 memory used=2317.3MB, alloc=64.6MB, time=27.89 memory used=2363.8MB, alloc=64.6MB, time=28.24 memory used=2408.5MB, alloc=72.6MB, time=28.71 memory used=2453.0MB, alloc=72.6MB, time=29.15 memory used=2491.7MB, alloc=96.6MB, time=29.45 memory used=2555.1MB, alloc=96.6MB, time=29.87 memory used=2625.6MB, alloc=96.6MB, time=30.42 memory used=2694.2MB, alloc=96.6MB, time=31.60 memory used=2747.7MB, alloc=96.6MB, time=32.01 memory used=2778.9MB, alloc=96.6MB, time=32.11 memory used=2813.2MB, alloc=96.6MB, time=32.22 memory used=2848.1MB, alloc=96.6MB, time=32.37 memory used=2913.6MB, alloc=96.6MB, time=33.00 memory used=2972.4MB, alloc=96.6MB, time=33.33 memory used=3022.3MB, alloc=96.6MB, time=35.03 memory used=3093.0MB, alloc=120.6MB, time=35.80 memory used=3209.9MB, alloc=120.6MB, time=36.92 memory used=3275.8MB, alloc=120.6MB, time=37.29 memory used=3324.0MB, alloc=120.6MB, time=37.42 memory used=3373.0MB, alloc=120.6MB, time=37.56 memory used=3424.7MB, alloc=120.6MB, time=37.77 memory used=3489.4MB, alloc=120.6MB, time=38.09 memory used=3536.2MB, alloc=120.6MB, time=38.23 memory used=3581.8MB, alloc=120.6MB, time=38.36 memory used=3634.6MB, alloc=120.6MB, time=38.57 memory used=3681.0MB, alloc=120.6MB, time=38.72 memory used=3714.7MB, alloc=131.8MB, time=38.87 memory used=3734.2MB, alloc=131.8MB, time=38.95 memory used=3787.2MB, alloc=131.8MB, time=39.06 memory used=3814.0MB, alloc=131.8MB, time=39.17 memory used=3833.5MB, alloc=131.8MB, time=39.27 memory used=3886.2MB, alloc=131.8MB, time=39.41 memory used=3972.4MB, alloc=131.8MB, time=39.96 memory used=4088.4MB, alloc=131.8MB, time=40.73 memory used=4184.4MB, alloc=131.8MB, time=41.79 memory used=4236.4MB, alloc=131.8MB, time=41.94 memory used=4277.0MB, alloc=131.8MB, time=42.06 memory used=4347.9MB, alloc=131.8MB, time=42.65 memory used=4396.9MB, alloc=131.8MB, time=42.80 memory used=4435.5MB, alloc=131.8MB, time=42.91 memory used=4524.3MB, alloc=131.8MB, time=46.24 memory used=4577.1MB, alloc=131.8MB, time=46.39 memory used=4616.3MB, alloc=131.8MB, time=46.51 memory used=4735.1MB, alloc=131.8MB, time=47.36 memory used=4840.2MB, alloc=131.8MB, time=47.94 memory used=4945.1MB, alloc=131.8MB, time=48.64 memory used=5050.9MB, alloc=131.8MB, time=49.48 memory used=5157.7MB, alloc=131.8MB, time=50.49 memory used=5262.2MB, alloc=131.8MB, time=51.67 memory used=5367.6MB, alloc=131.8MB, time=52.73 memory used=5474.1MB, alloc=131.8MB, time=53.98 memory used=5611.3MB, alloc=131.8MB, time=55.90 memory used=5686.7MB, alloc=131.8MB, time=56.65 memory used=5760.5MB, alloc=131.8MB, time=58.98 memory used=5803.1MB, alloc=131.8MB, time=59.11 memory used=5841.8MB, alloc=131.8MB, time=59.23 memory used=5901.2MB, alloc=131.8MB, time=59.75 memory used=5953.4MB, alloc=387.8MB, time=60.38 memory used=6034.2MB, alloc=411.8MB, time=61.27 memory used=6155.0MB, alloc=411.8MB, time=64.15 memory used=6208.9MB, alloc=411.8MB, time=64.33 memory used=6253.9MB, alloc=411.8MB, time=64.48 memory used=6363.2MB, alloc=411.8MB, time=66.20 memory used=6456.2MB, alloc=411.8MB, time=67.87 memory used=6555.6MB, alloc=411.8MB, time=74.45 memory used=6631.2MB, alloc=411.8MB, time=74.71 memory used=6688.8MB, alloc=411.8MB, time=75.04 memory used=6779.0MB, alloc=411.8MB, time=77.75 memory used=6824.8MB, alloc=411.8MB, time=77.91 memory used=6876.6MB, alloc=411.8MB, time=78.08 memory used=6913.3MB, alloc=411.8MB, time=78.21 memory used=6995.1MB, alloc=411.8MB, time=84.73 memory used=7070.8MB, alloc=411.8MB, time=85.06 memory used=7114.0MB, alloc=411.8MB, time=85.22 memory used=7166.9MB, alloc=411.8MB, time=85.39 memory used=7207.0MB, alloc=435.8MB, time=85.55 memory used=7262.0MB, alloc=435.8MB, time=85.70 memory used=7369.9MB, alloc=435.8MB, time=86.38 memory used=7495.2MB, alloc=435.8MB, time=89.29 memory used=7599.3MB, alloc=435.8MB, time=91.85 memory used=7665.8MB, alloc=435.8MB, time=92.07 memory used=7718.3MB, alloc=435.8MB, time=92.22 memory used=7865.0MB, alloc=435.8MB, time=93.36 memory used=8010.8MB, alloc=435.8MB, time=94.54 memory used=8149.7MB, alloc=435.8MB, time=95.83 memory used=8278.7MB, alloc=435.8MB, time=97.37 memory used=8407.2MB, alloc=459.8MB, time=99.07 memory used=8563.4MB, alloc=483.8MB, time=101.19 memory used=8726.5MB, alloc=507.8MB, time=103.57 memory used=8901.9MB, alloc=531.8MB, time=105.97 memory used=9061.7MB, alloc=555.8MB, time=108.06 memory used=9243.9MB, alloc=579.8MB, time=112.78 memory used=9424.6MB, alloc=603.8MB, time=118.55 memory used=9614.7MB, alloc=627.8MB, time=125.13 memory used=9828.8MB, alloc=651.8MB, time=132.39 memory used=10066.8MB, alloc=651.8MB, time=141.35 memory used=10304.9MB, alloc=675.8MB, time=151.08 N1 := 6601 > GB := Basis(F, plex(op(vars))); 3 7 9 5 4 3 4 5 5 GB := [125 x y + 18 x + 85 x y , 25 x y + 17 x y + 6 x z, 4 3 3 2 -3 x + 5 y z, 15 x y + 17 x y z + 6 x z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=10582.1MB, alloc=675.8MB, time=158.86 memory used=10737.9MB, alloc=675.8MB, time=160.51 memory used=10965.1MB, alloc=675.8MB, time=161.72 memory used=11202.9MB, alloc=675.8MB, time=166.25 memory used=11359.3MB, alloc=675.8MB, time=166.81 memory used=11569.2MB, alloc=675.8MB, time=171.47 memory used=11776.4MB, alloc=675.8MB, time=172.52 memory used=11964.5MB, alloc=675.8MB, time=173.99 memory used=12198.0MB, alloc=675.8MB, time=175.89 memory used=12436.5MB, alloc=675.8MB, time=178.99 memory used=12593.0MB, alloc=675.8MB, time=179.57 memory used=12706.0MB, alloc=675.8MB, time=181.03 memory used=12810.7MB, alloc=675.8MB, time=182.40 memory used=12980.3MB, alloc=675.8MB, time=183.68 memory used=13168.2MB, alloc=675.8MB, time=186.41 memory used=13307.4MB, alloc=675.8MB, time=186.91 memory used=13529.4MB, alloc=675.8MB, time=193.46 memory used=13691.0MB, alloc=675.8MB, time=194.00 memory used=13822.5MB, alloc=675.8MB, time=194.49 memory used=14055.1MB, alloc=675.8MB, time=197.00 memory used=14234.4MB, alloc=675.8MB, time=197.80 memory used=14371.3MB, alloc=675.8MB, time=198.29 memory used=14544.5MB, alloc=675.8MB, time=199.61 memory used=14652.8MB, alloc=675.8MB, time=200.79 memory used=14759.1MB, alloc=675.8MB, time=201.89 memory used=14867.5MB, alloc=675.8MB, time=203.05 memory used=15086.6MB, alloc=675.8MB, time=204.89 memory used=15159.7MB, alloc=675.8MB, time=206.02 memory used=15312.2MB, alloc=675.8MB, time=208.12 memory used=15524.7MB, alloc=699.8MB, time=350.09 memory used=15807.9MB, alloc=699.8MB, time=356.21 memory used=15946.3MB, alloc=699.8MB, time=356.90 memory used=16090.8MB, alloc=699.8MB, time=357.60 memory used=16257.6MB, alloc=699.8MB, time=358.30 memory used=16447.5MB, alloc=699.8MB, time=358.99 memory used=16612.1MB, alloc=699.8MB, time=359.68 memory used=16729.7MB, alloc=699.8MB, time=360.33 memory used=16850.0MB, alloc=723.8MB, time=361.00 memory used=16990.6MB, alloc=723.8MB, time=361.59 memory used=17141.0MB, alloc=723.8MB, time=362.27 memory used=17300.2MB, alloc=723.8MB, time=362.94 memory used=17470.9MB, alloc=723.8MB, time=363.55 memory used=17652.4MB, alloc=723.8MB, time=364.17 memory used=17843.9MB, alloc=723.8MB, time=364.89 memory used=18047.0MB, alloc=723.8MB, time=365.60 memory used=18263.0MB, alloc=723.8MB, time=366.34 memory used=18630.5MB, alloc=723.8MB, time=367.28 memory used=18769.2MB, alloc=723.8MB, time=367.90 memory used=18914.3MB, alloc=723.8MB, time=368.54 memory used=19067.6MB, alloc=723.8MB, time=369.18 memory used=19227.8MB, alloc=723.8MB, time=369.81 memory used=19398.9MB, alloc=723.8MB, time=370.43 memory used=19689.5MB, alloc=723.8MB, time=371.80 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428525316 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 4 3 F := [-13 z - 19 y z , x y z - 3 y + 6 y z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 G := [-7 x z + 16 x y z - 8 y z, -2 z + 4 y ] > Problem := [F,G]; 4 2 2 4 3 Problem := [[-13 z - 19 y z , x y z - 3 y + 6 y z], 2 2 3 2 [-7 x z + 16 x y z - 8 y z, -2 z + 4 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.4MB, alloc=32.3MB, time=0.47 memory used=46.0MB, alloc=32.3MB, time=0.75 memory used=64.0MB, alloc=56.3MB, time=1.02 memory used=106.8MB, alloc=68.3MB, time=1.50 memory used=149.4MB, alloc=68.3MB, time=2.05 memory used=190.2MB, alloc=68.3MB, time=2.50 memory used=233.3MB, alloc=92.3MB, time=3.05 memory used=300.0MB, alloc=92.3MB, time=3.91 memory used=361.4MB, alloc=116.3MB, time=4.78 memory used=428.9MB, alloc=116.3MB, time=5.62 memory used=492.9MB, alloc=116.3MB, time=6.01 memory used=568.1MB, alloc=116.3MB, time=7.06 memory used=635.0MB, alloc=396.3MB, time=7.94 memory used=750.8MB, alloc=420.3MB, time=9.53 memory used=874.1MB, alloc=444.3MB, time=11.59 memory used=1013.5MB, alloc=468.3MB, time=13.92 memory used=1149.4MB, alloc=492.3MB, time=17.85 memory used=1283.4MB, alloc=516.3MB, time=23.04 memory used=1441.6MB, alloc=540.3MB, time=28.93 N1 := 4081 > GB := Basis(F, plex(op(vars))); 13 4 8 2 10 12 10 8 4 GB := [117 y + 19 x y + 228 x y + 684 y , 13 x y z - 39 x y 6 6 4 8 2 10 12 2 9 + 234 x y - 1404 x y + 8424 x y - 50544 y - 49248 x y 11 8 2 6 5 4 7 2 9 11 - 295488 y , 13 x y z - 39 x y + 234 x y - 1404 x y + 8424 y 2 8 10 2 4 3 + 8208 x y + 49248 y , x y z - 3 y + 6 y z, 6 2 6 2 4 5 2 7 9 8 39 x y z + 26 x y z - 117 x y + 468 x y - 1404 y - 8208 y , 6 4 4 4 2 2 4 3 2 6 8 -13 x y z + 39 x y + 104 x y z + 104 x y z - 234 x y + 468 y 4 2 2 5 7 4 2 4 2 2 5 + 152 x y z - 456 x y + 2736 y , -13 x y z - 13 x y z + 39 x y 2 2 3 7 4 2 4 6 4 2 + 156 x y z - 117 y - 38 x y z + 114 x y - 684 y , 13 z + 19 y z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1657.6MB, alloc=540.3MB, time=34.90 memory used=1871.1MB, alloc=540.3MB, time=39.78 memory used=1988.1MB, alloc=540.3MB, time=40.19 memory used=2085.4MB, alloc=540.3MB, time=40.53 memory used=2325.4MB, alloc=540.3MB, time=42.78 memory used=2481.9MB, alloc=540.3MB, time=43.92 memory used=2623.6MB, alloc=540.3MB, time=45.44 memory used=2741.8MB, alloc=540.3MB, time=46.66 memory used=2863.5MB, alloc=540.3MB, time=47.11 memory used=2969.1MB, alloc=540.3MB, time=47.50 memory used=3143.6MB, alloc=540.3MB, time=53.25 memory used=3283.6MB, alloc=540.3MB, time=53.62 memory used=3480.3MB, alloc=540.3MB, time=54.21 memory used=3619.9MB, alloc=540.3MB, time=54.59 memory used=3959.6MB, alloc=564.3MB, time=73.41 memory used=4146.8MB, alloc=564.3MB, time=102.77 memory used=4251.9MB, alloc=564.3MB, time=103.32 memory used=4352.5MB, alloc=564.3MB, time=103.77 memory used=4463.0MB, alloc=564.3MB, time=104.20 memory used=4584.4MB, alloc=564.3MB, time=104.64 memory used=4716.2MB, alloc=564.3MB, time=105.09 memory used=4858.6MB, alloc=564.3MB, time=105.56 memory used=5012.5MB, alloc=564.3MB, time=106.04 memory used=5112.0MB, alloc=564.3MB, time=106.40 memory used=5199.4MB, alloc=564.3MB, time=106.75 memory used=5285.4MB, alloc=564.3MB, time=107.09 memory used=5375.7MB, alloc=564.3MB, time=107.44 memory used=5468.5MB, alloc=564.3MB, time=107.78 memory used=5562.9MB, alloc=564.3MB, time=108.15 memory used=5662.1MB, alloc=564.3MB, time=108.50 memory used=5762.8MB, alloc=564.3MB, time=108.86 memory used=5868.3MB, alloc=564.3MB, time=109.22 memory used=5975.0MB, alloc=564.3MB, time=109.58 memory used=6086.6MB, alloc=564.3MB, time=109.93 memory used=6202.9MB, alloc=564.3MB, time=110.29 memory used=6320.2MB, alloc=564.3MB, time=110.66 memory used=6442.1MB, alloc=564.3MB, time=111.03 memory used=6568.5MB, alloc=564.3MB, time=111.40 memory used=6699.3MB, alloc=564.3MB, time=111.78 memory used=6834.2MB, alloc=564.3MB, time=112.16 memory used=6973.1MB, alloc=564.3MB, time=112.54 memory used=7115.7MB, alloc=564.3MB, time=112.93 memory used=7261.8MB, alloc=564.3MB, time=113.33 memory used=7414.8MB, alloc=564.3MB, time=113.72 memory used=7684.6MB, alloc=564.3MB, time=114.28 memory used=7820.3MB, alloc=564.3MB, time=114.69 memory used=7951.5MB, alloc=564.3MB, time=115.10 memory used=8086.6MB, alloc=564.3MB, time=115.52 memory used=8226.5MB, alloc=564.3MB, time=115.93 memory used=8369.7MB, alloc=564.3MB, time=116.34 memory used=8515.5MB, alloc=564.3MB, time=116.75 memory used=8666.1MB, alloc=564.3MB, time=117.18 memory used=8822.9MB, alloc=564.3MB, time=117.61 memory used=8983.6MB, alloc=564.3MB, time=118.04 memory used=9150.2MB, alloc=564.3MB, time=118.46 memory used=9324.5MB, alloc=564.3MB, time=118.90 memory used=9508.8MB, alloc=564.3MB, time=119.34 memory used=9903.5MB, alloc=564.3MB, time=121.07 memory used=10080.5MB, alloc=588.3MB, time=209.31 memory used=10231.6MB, alloc=588.3MB, time=318.68 memory used=10367.9MB, alloc=588.3MB, time=334.24 memory used=10567.5MB, alloc=612.3MB, time=335.90 memory used=10754.1MB, alloc=612.3MB, time=337.62 memory used=10925.2MB, alloc=612.3MB, time=338.73 memory used=11058.2MB, alloc=612.3MB, time=339.15 memory used=11202.7MB, alloc=612.3MB, time=339.60 memory used=11360.0MB, alloc=612.3MB, time=340.07 memory used=11530.2MB, alloc=612.3MB, time=340.50 memory used=11709.2MB, alloc=612.3MB, time=340.94 memory used=11847.0MB, alloc=612.3MB, time=341.33 memory used=11955.0MB, alloc=612.3MB, time=341.68 memory used=12058.5MB, alloc=612.3MB, time=342.05 memory used=12163.8MB, alloc=612.3MB, time=342.44 memory used=12267.8MB, alloc=612.3MB, time=342.77 memory used=12375.1MB, alloc=612.3MB, time=343.11 memory used=12489.2MB, alloc=612.3MB, time=343.45 memory used=12605.3MB, alloc=612.3MB, time=343.80 memory used=12723.2MB, alloc=612.3MB, time=344.14 memory used=12842.9MB, alloc=612.3MB, time=344.50 memory used=12969.6MB, alloc=612.3MB, time=344.87 memory used=13098.0MB, alloc=612.3MB, time=345.23 memory used=13228.1MB, alloc=612.3MB, time=345.60 memory used=13365.3MB, alloc=612.3MB, time=345.97 memory used=13504.1MB, alloc=612.3MB, time=346.35 memory used=13644.6MB, alloc=612.3MB, time=346.73 memory used=13792.1MB, alloc=612.3MB, time=347.10 memory used=13941.2MB, alloc=612.3MB, time=347.48 memory used=14097.3MB, alloc=612.3MB, time=347.87 memory used=14254.8MB, alloc=612.3MB, time=348.24 memory used=14413.7MB, alloc=612.3MB, time=348.63 memory used=14579.5MB, alloc=612.3MB, time=349.03 memory used=14746.4MB, alloc=612.3MB, time=349.44 memory used=14920.3MB, alloc=612.3MB, time=349.82 memory used=15095.1MB, alloc=612.3MB, time=350.19 memory used=15276.7MB, alloc=612.3MB, time=350.57 memory used=15576.5MB, alloc=612.3MB, time=351.09 memory used=15726.5MB, alloc=612.3MB, time=351.47 memory used=15861.7MB, alloc=612.3MB, time=351.83 memory used=15991.4MB, alloc=612.3MB, time=352.21 memory used=16122.0MB, alloc=612.3MB, time=352.57 memory used=16255.1MB, alloc=612.3MB, time=352.94 memory used=16388.0MB, alloc=612.3MB, time=353.33 memory used=16520.7MB, alloc=612.3MB, time=353.71 memory used=16659.1MB, alloc=612.3MB, time=354.08 memory used=16797.3MB, alloc=612.3MB, time=354.49 memory used=16940.9MB, alloc=612.3MB, time=354.91 memory used=17083.9MB, alloc=612.3MB, time=355.32 memory used=17232.2MB, alloc=612.3MB, time=355.71 memory used=17379.7MB, alloc=612.3MB, time=356.10 memory used=17532.2MB, alloc=612.3MB, time=356.51 memory used=17683.6MB, alloc=612.3MB, time=356.91 memory used=17839.6MB, alloc=612.3MB, time=357.31 memory used=18000.0MB, alloc=612.3MB, time=357.72 memory used=18158.8MB, alloc=612.3MB, time=358.14 memory used=18321.8MB, alloc=612.3MB, time=358.55 memory used=18487.9MB, alloc=612.3MB, time=358.97 memory used=18657.3MB, alloc=612.3MB, time=359.39 memory used=18829.4MB, alloc=612.3MB, time=359.81 memory used=19003.7MB, alloc=612.3MB, time=360.23 memory used=19185.0MB, alloc=612.3MB, time=360.65 memory used=19367.3MB, alloc=612.3MB, time=361.08 memory used=19555.1MB, alloc=612.3MB, time=361.52 memory used=19746.9MB, alloc=612.3MB, time=361.95 memory used=19941.4MB, alloc=612.3MB, time=362.39 memory used=20141.7MB, alloc=612.3MB, time=362.83 memory used=20345.4MB, alloc=612.3MB, time=363.27 memory used=20554.2MB, alloc=612.3MB, time=363.70 memory used=20768.2MB, alloc=612.3MB, time=364.15 memory used=20990.5MB, alloc=612.3MB, time=364.61 memory used=21220.4MB, alloc=612.3MB, time=365.07 memory used=21450.3MB, alloc=612.3MB, time=365.53 memory used=21695.9MB, alloc=612.3MB, time=372.86 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428525616 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 F := [5 x z - 2 z + 13, -4 x y + 12 x + 19 y] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 4 3 G := [11 y z + 2 y z + 19 z , 5 x + 15 z + 12 x] > Problem := [F,G]; 2 2 3 2 Problem := [[5 x z - 2 z + 13, -4 x y + 12 x + 19 y], 2 2 2 2 4 3 [11 y z + 2 y z + 19 z , 5 x + 15 z + 12 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.1MB, alloc=32.3MB, time=0.17 memory used=26.0MB, alloc=32.3MB, time=0.46 N1 := 149 > GB := Basis(F, plex(op(vars))); 2 2 2 3 GB := [4 y x - 19 y - 12 x, -5 x z + 2 z - 13] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=47.8MB, alloc=32.3MB, time=0.81 memory used=67.6MB, alloc=32.3MB, time=1.07 N2 := 149 > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 3 2 2 2 2 2 H := [5 z x - 2 z + 13, -4 x y + 12 x + 19 y, 11 y z + 2 y z + 19 z , 4 3 5 x + 15 z + 12 x] > J:=[op(GB),op(G)]; 2 2 2 3 2 2 2 2 J := [4 y x - 19 y - 12 x, -5 x z + 2 z - 13, 11 y z + 2 y z + 19 z , 4 3 5 x + 15 z + 12 x] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 8, 15, 4, 4, 2, 3, 3/4, 1/2, 3/4, 5/12, 1/3, 1/2, 4, 8, 15, 4, 4, 2, 3, 3/4, 1/2, 3/4, 5/12, 1/3, 1/2, 0, 0, 0] > save(F, G, cat("ranSet/34", convert(F, string),".txt")); > quit memory used=76.1MB, alloc=32.3MB, time=1.21 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428525618 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 F := [-16 x y - 7 x y z + 3 y z, -18 x z + 15 y z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 2 G := [19 x z - x y + 2 x, -18 x z - 12 y z - 15 x ] > Problem := [F,G]; 3 2 2 2 Problem := [[-16 x y - 7 x y z + 3 y z, -18 x z + 15 y z], 3 2 3 2 2 [19 x z - x y + 2 x, -18 x z - 12 y z - 15 x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.9MB, alloc=32.3MB, time=0.48 memory used=47.9MB, alloc=32.3MB, time=0.77 memory used=67.0MB, alloc=56.3MB, time=1.05 memory used=107.0MB, alloc=60.3MB, time=1.61 memory used=144.8MB, alloc=84.3MB, time=2.14 memory used=206.9MB, alloc=92.3MB, time=3.05 memory used=269.1MB, alloc=116.3MB, time=3.98 memory used=343.6MB, alloc=116.3MB, time=5.08 memory used=416.0MB, alloc=372.3MB, time=6.13 memory used=499.9MB, alloc=396.3MB, time=7.40 memory used=609.0MB, alloc=396.3MB, time=8.87 memory used=715.0MB, alloc=420.3MB, time=10.59 memory used=837.6MB, alloc=444.3MB, time=12.71 memory used=971.2MB, alloc=468.3MB, time=15.06 memory used=1121.2MB, alloc=492.3MB, time=17.75 memory used=1287.6MB, alloc=516.3MB, time=20.67 memory used=1465.0MB, alloc=540.3MB, time=23.91 memory used=1648.6MB, alloc=564.3MB, time=27.30 memory used=1838.0MB, alloc=588.3MB, time=32.42 memory used=2019.4MB, alloc=612.3MB, time=38.54 memory used=2209.0MB, alloc=636.3MB, time=44.77 memory used=2411.8MB, alloc=660.3MB, time=51.42 memory used=2620.9MB, alloc=684.3MB, time=59.66 memory used=2853.7MB, alloc=708.3MB, time=68.83 memory used=3110.4MB, alloc=732.3MB, time=79.20 memory used=3391.1MB, alloc=756.3MB, time=90.33 memory used=3695.6MB, alloc=780.3MB, time=102.49 memory used=4024.2MB, alloc=780.3MB, time=115.24 memory used=4352.6MB, alloc=804.3MB, time=127.52 memory used=4705.1MB, alloc=804.3MB, time=140.69 memory used=5057.5MB, alloc=804.3MB, time=153.60 memory used=5409.8MB, alloc=828.3MB, time=167.44 memory used=5786.2MB, alloc=828.3MB, time=182.17 memory used=6162.5MB, alloc=852.3MB, time=196.90 memory used=6562.9MB, alloc=852.3MB, time=211.89 memory used=6963.2MB, alloc=876.3MB, time=227.40 N1 := 13437 > GB := Basis(F, plex(op(vars))); 5 3 2 2 4 3 2 3 GB := [-6 x y + 5 x y , -6 x z + 5 y z, -54 x z + 105 x z + 200 x y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=7337.1MB, alloc=876.3MB, time=237.56 memory used=7452.4MB, alloc=876.3MB, time=240.01 memory used=7552.4MB, alloc=876.3MB, time=242.22 memory used=7642.4MB, alloc=876.3MB, time=244.02 memory used=7730.8MB, alloc=876.3MB, time=246.05 memory used=7827.5MB, alloc=876.3MB, time=247.86 memory used=7925.7MB, alloc=876.3MB, time=249.92 memory used=8032.0MB, alloc=876.3MB, time=252.21 memory used=8146.8MB, alloc=876.3MB, time=254.48 memory used=8280.3MB, alloc=876.3MB, time=256.89 memory used=8391.3MB, alloc=876.3MB, time=259.21 memory used=8502.9MB, alloc=876.3MB, time=261.70 memory used=8621.4MB, alloc=876.3MB, time=264.22 memory used=8733.1MB, alloc=900.3MB, time=266.45 memory used=8866.3MB, alloc=900.3MB, time=268.64 memory used=8968.6MB, alloc=900.3MB, time=270.90 memory used=9069.8MB, alloc=924.3MB, time=273.02 memory used=9169.7MB, alloc=924.3MB, time=275.00 memory used=9262.7MB, alloc=948.3MB, time=277.39 memory used=9362.4MB, alloc=948.3MB, time=279.60 memory used=9443.0MB, alloc=972.3MB, time=281.73 memory used=9585.9MB, alloc=996.3MB, time=286.33 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428525918 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 3 F := [2 z - 9 x y z - 14 x z, 2 x y + 17 x y ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 3 2 2 G := [20 z + 6 x z + 14 z , 8 z + 5 y + 19 z ] > Problem := [F,G]; 4 3 3 Problem := [[2 z - 9 x y z - 14 x z, 2 x y + 17 x y ], 4 2 2 3 2 2 [20 z + 6 x z + 14 z , 8 z + 5 y + 19 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=32.4MB, alloc=40.3MB, time=0.59 memory used=59.2MB, alloc=40.3MB, time=0.99 memory used=85.1MB, alloc=68.3MB, time=1.37 memory used=133.5MB, alloc=76.3MB, time=2.08 memory used=183.6MB, alloc=76.3MB, time=2.77 memory used=231.5MB, alloc=100.3MB, time=3.42 memory used=314.2MB, alloc=100.3MB, time=4.28 memory used=386.8MB, alloc=100.3MB, time=5.19 memory used=443.0MB, alloc=100.3MB, time=5.67 memory used=514.3MB, alloc=100.3MB, time=6.46 memory used=594.1MB, alloc=124.3MB, time=7.37 memory used=697.8MB, alloc=124.3MB, time=8.58 memory used=793.9MB, alloc=148.3MB, time=9.84 memory used=915.2MB, alloc=148.3MB, time=11.63 memory used=1025.7MB, alloc=172.3MB, time=13.38 memory used=1142.0MB, alloc=196.3MB, time=15.89 memory used=1250.1MB, alloc=220.3MB, time=19.64 memory used=1378.3MB, alloc=244.3MB, time=24.16 N1 := 3599 > GB := Basis(F, plex(op(vars))); 3 3 4 GB := [2 x y + 17 x y , 2 z - 9 x y z - 14 x z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1533.7MB, alloc=244.3MB, time=28.46 memory used=1616.6MB, alloc=500.3MB, time=29.58 memory used=1771.6MB, alloc=500.3MB, time=31.37 memory used=1935.3MB, alloc=500.3MB, time=33.05 memory used=2139.1MB, alloc=500.3MB, time=35.16 memory used=2354.4MB, alloc=524.3MB, time=37.55 memory used=2576.6MB, alloc=548.3MB, time=40.60 memory used=2765.5MB, alloc=572.3MB, time=46.11 memory used=2963.0MB, alloc=596.3MB, time=52.13 N2 := 3599 > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 4 3 3 4 2 2 H := [2 z - 9 x y z - 14 x z, 2 x y + 17 x y , 20 z + 6 x z + 14 z , 3 2 2 8 z + 19 z + 5 y ] > J:=[op(GB),op(G)]; 3 3 4 4 2 2 J := [2 x y + 17 x y , 2 z - 9 x y z - 14 x z, 20 z + 6 x z + 14 z , 3 2 2 8 z + 19 z + 5 y ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 9, 15, 4, 3, 3, 4, 3/4, 3/4, 3/4, 5/11, 4/11, 8/11, 4, 9, 15, 4, 3, 3, 4, 3/4, 3/4, 3/4, 5/11, 4/11, 8/11, 0, 0, 0] > save(F, G, cat("ranSet/34", convert(F, string),".txt")); > quit memory used=3006.1MB, alloc=596.3MB, time=53.13 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428525973 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 4 2 F := [5 x z - 10 x z + 16 x y z, -12 x + 14 x y z - z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 4 3 2 G := [9 y z + 20 x y - 4 z , -10 z - 4 x + 3 x z] > Problem := [F,G]; 2 2 3 4 2 Problem := [[5 x z - 10 x z + 16 x y z, -12 x + 14 x y z - z ], 3 2 4 3 2 [9 y z + 20 x y - 4 z , -10 z - 4 x + 3 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.13 memory used=26.1MB, alloc=32.3MB, time=0.45 memory used=45.5MB, alloc=56.3MB, time=0.72 memory used=86.8MB, alloc=60.3MB, time=1.28 memory used=127.9MB, alloc=68.3MB, time=1.70 memory used=168.2MB, alloc=68.3MB, time=2.05 memory used=210.7MB, alloc=92.3MB, time=2.47 memory used=278.4MB, alloc=92.3MB, time=3.21 memory used=342.9MB, alloc=92.3MB, time=3.87 memory used=383.2MB, alloc=92.3MB, time=4.09 memory used=424.6MB, alloc=92.3MB, time=4.25 memory used=464.6MB, alloc=92.3MB, time=4.46 memory used=500.8MB, alloc=92.3MB, time=4.61 memory used=530.4MB, alloc=92.3MB, time=4.69 memory used=568.5MB, alloc=92.3MB, time=4.82 memory used=611.7MB, alloc=92.3MB, time=5.08 memory used=646.7MB, alloc=92.3MB, time=5.20 memory used=679.4MB, alloc=92.3MB, time=5.29 memory used=713.0MB, alloc=92.3MB, time=5.42 memory used=764.6MB, alloc=92.3MB, time=5.83 memory used=795.7MB, alloc=92.3MB, time=5.92 memory used=822.4MB, alloc=92.3MB, time=6.00 memory used=855.2MB, alloc=92.3MB, time=6.10 memory used=881.3MB, alloc=92.3MB, time=6.17 memory used=913.4MB, alloc=92.3MB, time=6.32 memory used=953.5MB, alloc=92.3MB, time=6.45 memory used=979.6MB, alloc=92.3MB, time=6.54 memory used=1012.2MB, alloc=92.3MB, time=6.63 memory used=1044.1MB, alloc=116.3MB, time=6.74 memory used=1080.8MB, alloc=116.3MB, time=6.86 memory used=1125.1MB, alloc=116.3MB, time=6.96 memory used=1199.9MB, alloc=116.3MB, time=14.36 memory used=1263.0MB, alloc=116.3MB, time=16.14 memory used=1315.5MB, alloc=116.3MB, time=16.27 memory used=1353.3MB, alloc=116.3MB, time=16.37 memory used=1395.7MB, alloc=116.3MB, time=16.49 memory used=1445.4MB, alloc=116.3MB, time=16.60 memory used=1502.3MB, alloc=116.3MB, time=16.72 memory used=1549.4MB, alloc=116.3MB, time=16.82 memory used=1583.1MB, alloc=116.3MB, time=16.90 memory used=1618.0MB, alloc=116.3MB, time=16.99 memory used=1654.6MB, alloc=116.3MB, time=17.08 memory used=1693.5MB, alloc=116.3MB, time=17.17 memory used=1734.5MB, alloc=116.3MB, time=17.25 memory used=1777.6MB, alloc=116.3MB, time=17.34 memory used=1822.6MB, alloc=116.3MB, time=17.44 memory used=1871.0MB, alloc=116.3MB, time=17.53 memory used=1922.6MB, alloc=116.3MB, time=17.63 memory used=1976.8MB, alloc=116.3MB, time=17.73 memory used=2033.5MB, alloc=116.3MB, time=17.83 memory used=2104.5MB, alloc=131.8MB, time=17.96 memory used=2116.7MB, alloc=131.8MB, time=18.02 memory used=2126.5MB, alloc=131.8MB, time=18.08 memory used=2135.8MB, alloc=131.8MB, time=18.14 memory used=2145.3MB, alloc=131.8MB, time=18.20 memory used=2155.5MB, alloc=131.8MB, time=18.27 memory used=2165.7MB, alloc=131.8MB, time=18.33 memory used=2175.9MB, alloc=131.8MB, time=18.39 memory used=2186.9MB, alloc=131.8MB, time=18.45 memory used=2197.7MB, alloc=131.8MB, time=18.52 memory used=2208.6MB, alloc=131.8MB, time=18.59 memory used=2219.9MB, alloc=131.8MB, time=18.66 memory used=2231.2MB, alloc=131.8MB, time=18.73 memory used=2243.2MB, alloc=131.8MB, time=18.80 memory used=2254.9MB, alloc=131.8MB, time=18.86 memory used=2266.9MB, alloc=131.8MB, time=18.92 memory used=2279.5MB, alloc=131.8MB, time=18.98 memory used=2292.4MB, alloc=131.8MB, time=19.05 memory used=2305.4MB, alloc=131.8MB, time=19.11 memory used=2319.1MB, alloc=131.8MB, time=19.18 memory used=2333.1MB, alloc=131.8MB, time=19.25 memory used=2347.9MB, alloc=131.8MB, time=19.31 memory used=2406.9MB, alloc=131.8MB, time=19.54 memory used=2452.5MB, alloc=131.8MB, time=19.67 memory used=2501.1MB, alloc=131.8MB, time=19.80 memory used=2574.0MB, alloc=131.8MB, time=22.17 memory used=2622.3MB, alloc=131.8MB, time=22.29 memory used=2663.2MB, alloc=131.8MB, time=22.42 memory used=2713.1MB, alloc=131.8MB, time=22.54 memory used=2771.7MB, alloc=131.8MB, time=22.66 memory used=2807.9MB, alloc=131.8MB, time=22.76 memory used=2843.5MB, alloc=131.8MB, time=22.84 memory used=2881.5MB, alloc=131.8MB, time=22.93 memory used=2923.3MB, alloc=131.8MB, time=23.02 memory used=2968.3MB, alloc=131.8MB, time=23.11 memory used=3017.1MB, alloc=131.8MB, time=23.21 memory used=3069.0MB, alloc=131.8MB, time=23.31 memory used=3127.6MB, alloc=131.8MB, time=23.41 memory used=3148.4MB, alloc=131.8MB, time=23.48 memory used=3159.6MB, alloc=131.8MB, time=23.55 memory used=3171.4MB, alloc=131.8MB, time=23.61 memory used=3209.7MB, alloc=131.8MB, time=23.88 memory used=3286.2MB, alloc=131.8MB, time=24.96 memory used=3349.6MB, alloc=131.8MB, time=25.20 memory used=3393.6MB, alloc=131.8MB, time=25.34 memory used=3443.9MB, alloc=131.8MB, time=25.47 memory used=3481.2MB, alloc=131.8MB, time=25.60 memory used=3526.6MB, alloc=131.8MB, time=25.72 memory used=3604.6MB, alloc=131.8MB, time=28.72 memory used=3655.2MB, alloc=131.8MB, time=28.88 memory used=3692.4MB, alloc=131.8MB, time=29.01 memory used=3736.8MB, alloc=131.8MB, time=29.15 memory used=3790.5MB, alloc=131.8MB, time=29.29 memory used=3837.8MB, alloc=131.8MB, time=29.41 memory used=3871.5MB, alloc=131.8MB, time=29.50 memory used=3907.2MB, alloc=131.8MB, time=29.59 memory used=3946.7MB, alloc=131.8MB, time=29.69 memory used=3989.6MB, alloc=131.8MB, time=29.79 memory used=4035.4MB, alloc=131.8MB, time=29.88 memory used=4085.5MB, alloc=131.8MB, time=29.99 memory used=4139.8MB, alloc=131.8MB, time=30.10 memory used=4180.4MB, alloc=131.8MB, time=30.19 memory used=4191.4MB, alloc=131.8MB, time=30.26 memory used=4203.1MB, alloc=131.8MB, time=30.32 memory used=4339.7MB, alloc=131.8MB, time=31.41 memory used=4444.4MB, alloc=131.8MB, time=32.09 memory used=4547.6MB, alloc=131.8MB, time=32.95 memory used=4651.1MB, alloc=131.8MB, time=34.14 memory used=4754.5MB, alloc=131.8MB, time=35.71 memory used=4857.5MB, alloc=131.8MB, time=37.70 memory used=4961.0MB, alloc=131.8MB, time=40.13 memory used=5064.6MB, alloc=131.8MB, time=43.03 memory used=5167.6MB, alloc=131.8MB, time=46.36 memory used=5270.6MB, alloc=131.8MB, time=50.11 memory used=5374.2MB, alloc=131.8MB, time=54.34 memory used=5475.8MB, alloc=131.8MB, time=58.90 memory used=5571.7MB, alloc=131.8MB, time=62.03 memory used=5628.7MB, alloc=131.8MB, time=62.26 memory used=5678.4MB, alloc=131.8MB, time=62.44 memory used=5741.0MB, alloc=131.8MB, time=62.75 memory used=5790.6MB, alloc=131.8MB, time=62.90 memory used=5834.7MB, alloc=131.8MB, time=63.03 memory used=5902.7MB, alloc=131.8MB, time=63.49 memory used=5950.9MB, alloc=131.8MB, time=63.63 memory used=5993.3MB, alloc=131.8MB, time=63.75 memory used=6036.8MB, alloc=131.8MB, time=63.86 memory used=6093.1MB, alloc=131.8MB, time=64.07 memory used=6136.4MB, alloc=131.8MB, time=64.20 memory used=6188.7MB, alloc=131.8MB, time=64.34 memory used=6224.4MB, alloc=131.8MB, time=64.46 memory used=6263.1MB, alloc=131.8MB, time=64.56 memory used=6309.1MB, alloc=131.8MB, time=64.68 memory used=6399.6MB, alloc=131.8MB, time=73.87 memory used=6445.4MB, alloc=131.8MB, time=74.01 memory used=6491.2MB, alloc=131.8MB, time=74.14 memory used=6526.7MB, alloc=131.8MB, time=74.26 memory used=6567.5MB, alloc=131.8MB, time=74.38 memory used=6613.8MB, alloc=131.8MB, time=74.51 memory used=6666.6MB, alloc=131.8MB, time=74.64 memory used=6711.6MB, alloc=131.8MB, time=74.75 memory used=6743.6MB, alloc=131.8MB, time=74.85 memory used=6775.1MB, alloc=131.8MB, time=74.94 memory used=6808.4MB, alloc=131.8MB, time=75.03 memory used=6843.9MB, alloc=131.8MB, time=75.13 memory used=6881.5MB, alloc=131.8MB, time=75.23 memory used=6921.2MB, alloc=131.8MB, time=75.33 memory used=6962.9MB, alloc=131.8MB, time=75.43 memory used=7006.2MB, alloc=131.8MB, time=75.54 memory used=7051.4MB, alloc=131.8MB, time=75.65 memory used=7099.6MB, alloc=131.8MB, time=75.77 memory used=7150.6MB, alloc=131.8MB, time=75.88 memory used=7203.8MB, alloc=131.8MB, time=75.99 memory used=7268.5MB, alloc=131.8MB, time=76.11 memory used=7282.2MB, alloc=131.8MB, time=76.19 memory used=7291.8MB, alloc=131.8MB, time=76.26 memory used=7300.9MB, alloc=131.8MB, time=76.33 memory used=7310.2MB, alloc=131.8MB, time=76.40 memory 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used=30377.5MB, alloc=483.8MB, time=479.92 memory used=30460.2MB, alloc=483.8MB, time=480.11 memory used=30560.7MB, alloc=483.8MB, time=480.30 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428526273 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 4 2 F := [7 z - 9 z + 20 x, -20 x + 20 y z - 19 y] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 G := [-12 x z + 5 x z, 19 x y z + y - 13] > Problem := [F,G]; 4 2 4 2 Problem := [[7 z - 9 z + 20 x, -20 x + 20 y z - 19 y], 3 2 3 [-12 x z + 5 x z, 19 x y z + y - 13]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory 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time=58.19 memory used=7918.0MB, alloc=155.8MB, time=58.27 memory used=7933.1MB, alloc=155.8MB, time=58.35 memory used=7948.6MB, alloc=155.8MB, time=58.43 memory used=8023.5MB, alloc=155.8MB, time=58.82 memory used=8089.7MB, alloc=411.8MB, time=59.39 memory used=8220.3MB, alloc=411.8MB, time=59.84 memory used=8347.8MB, alloc=411.8MB, time=60.28 memory used=8467.7MB, alloc=411.8MB, time=60.87 memory used=8566.9MB, alloc=411.8MB, time=61.61 memory used=8702.9MB, alloc=411.8MB, time=71.86 memory used=8788.4MB, alloc=411.8MB, time=72.38 memory used=8866.5MB, alloc=411.8MB, time=73.61 memory used=8922.9MB, alloc=411.8MB, time=73.82 memory used=8968.3MB, alloc=411.8MB, time=74.00 memory used=9023.6MB, alloc=411.8MB, time=74.18 memory used=9088.7MB, alloc=411.8MB, time=74.36 memory used=9128.0MB, alloc=411.8MB, time=74.50 memory used=9167.0MB, alloc=411.8MB, time=74.64 memory used=9209.9MB, alloc=411.8MB, time=74.79 memory used=9254.8MB, alloc=411.8MB, time=74.92 memory used=9301.7MB, alloc=411.8MB, time=75.06 memory used=9352.9MB, alloc=411.8MB, time=75.22 memory used=9406.0MB, alloc=411.8MB, time=75.36 memory used=9463.6MB, alloc=411.8MB, time=75.52 memory used=9522.9MB, alloc=411.8MB, time=75.68 memory used=9586.7MB, alloc=411.8MB, time=75.85 memory used=9655.4MB, alloc=411.8MB, time=76.01 memory used=9807.8MB, alloc=411.8MB, time=76.46 memory used=9959.7MB, alloc=411.8MB, time=76.77 memory used=10126.3MB, alloc=411.8MB, time=77.11 memory used=10311.4MB, alloc=411.8MB, time=77.46 memory used=10516.4MB, alloc=411.8MB, time=77.80 memory used=10741.6MB, alloc=411.8MB, time=78.17 memory used=10984.6MB, alloc=411.8MB, time=78.54 memory used=11173.6MB, alloc=411.8MB, time=78.87 memory used=11368.0MB, alloc=411.8MB, time=79.29 memory used=11419.8MB, alloc=411.8MB, time=79.45 memory used=11483.0MB, alloc=411.8MB, time=79.65 memory used=11537.6MB, alloc=411.8MB, time=80.17 memory used=11625.0MB, alloc=411.8MB, time=123.60 memory used=11685.9MB, alloc=435.8MB, time=226.52 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memory used=15978.8MB, alloc=459.8MB, time=264.89 memory used=16174.0MB, alloc=459.8MB, time=265.25 memory used=16372.0MB, alloc=459.8MB, time=265.60 memory used=16573.0MB, alloc=459.8MB, time=265.95 memory used=16776.8MB, alloc=459.8MB, time=266.32 memory used=16983.3MB, alloc=459.8MB, time=266.68 memory used=17204.2MB, alloc=459.8MB, time=267.05 memory used=17427.8MB, alloc=459.8MB, time=267.42 memory used=17654.2MB, alloc=459.8MB, time=267.79 memory used=17883.0MB, alloc=459.8MB, time=268.16 memory used=18114.4MB, alloc=459.8MB, time=268.53 memory used=18360.4MB, alloc=459.8MB, time=268.89 memory used=18590.6MB, alloc=459.8MB, time=269.25 memory used=18766.8MB, alloc=459.8MB, time=269.54 memory used=18931.6MB, alloc=459.8MB, time=269.84 memory used=19095.4MB, alloc=459.8MB, time=270.14 memory used=19260.1MB, alloc=459.8MB, time=270.46 memory used=19438.3MB, alloc=459.8MB, time=270.78 memory used=19617.4MB, alloc=459.8MB, time=271.10 memory used=19797.3MB, alloc=459.8MB, time=271.41 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memory used=32912.9MB, alloc=459.8MB, time=292.18 memory used=33172.1MB, alloc=459.8MB, time=292.55 memory used=33405.9MB, alloc=459.8MB, time=292.90 memory used=33728.7MB, alloc=459.8MB, time=355.70 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428526573 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 F := [10 y z + 17 x - 1, 4 x z + 10 y + 4 z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 4 3 2 G := [9 x z + 10 z + 16 z, x z + 14 x z - 12 z] > Problem := [F,G]; 3 2 2 Problem := [[10 y z + 17 x - 1, 4 x z + 10 y + 4 z], 3 4 3 2 [9 x z + 10 z + 16 z, x z + 14 x z - 12 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=25.6MB, alloc=32.3MB, time=0.50 memory used=43.8MB, alloc=56.3MB, time=0.78 memory used=85.1MB, alloc=60.3MB, time=1.33 memory used=126.8MB, alloc=68.3MB, time=1.86 memory used=169.8MB, alloc=68.3MB, time=2.44 memory used=212.4MB, alloc=68.3MB, time=2.95 memory used=255.7MB, alloc=68.3MB, time=3.32 memory used=283.4MB, alloc=68.3MB, time=3.42 memory used=302.7MB, alloc=68.3MB, time=3.48 memory used=331.5MB, alloc=68.3MB, time=3.60 memory used=355.7MB, alloc=68.3MB, time=3.69 memory used=381.5MB, alloc=68.3MB, time=3.82 memory used=409.7MB, alloc=68.3MB, time=3.90 memory used=428.4MB, alloc=68.3MB, time=3.96 memory used=452.3MB, alloc=68.3MB, time=4.03 memory used=474.4MB, alloc=68.3MB, time=4.09 memory used=490.5MB, alloc=68.3MB, time=4.15 memory used=508.8MB, alloc=68.3MB, time=4.21 memory used=537.7MB, alloc=68.3MB, time=4.37 memory used=562.3MB, alloc=68.3MB, time=4.45 memory used=580.8MB, alloc=68.3MB, time=4.50 memory used=603.9MB, alloc=68.3MB, time=4.57 memory used=624.9MB, alloc=68.3MB, time=4.63 memory used=640.6MB, alloc=68.3MB, time=4.69 memory used=658.3MB, alloc=68.3MB, time=4.74 memory used=679.2MB, alloc=92.3MB, time=5.19 memory used=717.2MB, alloc=92.3MB, time=6.10 memory used=757.2MB, alloc=92.3MB, time=6.18 memory used=805.9MB, alloc=92.3MB, time=6.51 memory used=850.9MB, alloc=92.3MB, time=6.63 memory used=883.0MB, alloc=92.3MB, time=6.73 memory used=919.2MB, alloc=92.3MB, time=6.84 memory used=962.3MB, alloc=92.3MB, time=6.96 memory used=1006.1MB, alloc=92.3MB, time=7.06 memory used=1031.7MB, alloc=92.3MB, time=7.13 memory used=1059.5MB, alloc=92.3MB, time=7.23 memory used=1088.2MB, alloc=92.3MB, time=7.32 memory used=1119.3MB, alloc=92.3MB, time=7.43 memory used=1152.4MB, alloc=92.3MB, time=7.52 memory used=1187.4MB, alloc=92.3MB, time=7.61 memory used=1225.8MB, alloc=92.3MB, time=7.70 memory used=1267.0MB, alloc=92.3MB, time=7.78 memory used=1311.8MB, alloc=92.3MB, time=7.86 memory used=1354.1MB, alloc=92.3MB, time=7.95 memory used=1379.8MB, alloc=92.3MB, time=8.01 memory used=1417.5MB, alloc=92.3MB, time=8.93 memory used=1473.9MB, alloc=92.7MB, time=9.06 memory used=1505.7MB, alloc=92.7MB, time=9.18 memory used=1537.2MB, alloc=92.7MB, time=9.28 memory used=1570.8MB, alloc=92.7MB, time=9.39 memory used=1609.3MB, alloc=92.7MB, time=9.48 memory used=1651.1MB, alloc=92.7MB, time=9.59 memory used=1697.9MB, alloc=92.7MB, time=9.69 memory used=1725.5MB, alloc=92.7MB, time=9.77 memory used=1750.0MB, alloc=92.7MB, time=9.85 memory used=1774.2MB, alloc=92.7MB, time=9.93 memory used=1799.0MB, alloc=92.7MB, time=10.01 memory used=1824.4MB, alloc=92.7MB, time=10.09 memory used=1850.5MB, alloc=92.7MB, time=10.17 memory used=1880.1MB, alloc=92.7MB, time=10.26 memory used=1910.4MB, alloc=92.7MB, time=10.35 memory used=1941.2MB, alloc=92.7MB, time=10.44 memory used=1972.6MB, alloc=92.7MB, time=10.52 memory used=2004.5MB, alloc=92.7MB, time=10.61 memory used=2037.1MB, alloc=92.7MB, time=10.70 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memory used=2854.1MB, alloc=116.7MB, time=12.54 memory used=2900.3MB, alloc=116.7MB, time=12.62 memory used=2946.1MB, alloc=116.7MB, time=12.71 memory used=2991.7MB, alloc=116.7MB, time=12.79 memory used=3039.5MB, alloc=116.7MB, time=12.87 memory used=3090.5MB, alloc=116.7MB, time=12.96 memory used=3140.5MB, alloc=116.7MB, time=13.04 memory used=3192.7MB, alloc=116.7MB, time=13.13 memory used=3246.7MB, alloc=116.7MB, time=13.22 memory used=3302.2MB, alloc=116.7MB, time=13.31 memory used=3361.5MB, alloc=116.7MB, time=13.40 memory used=3423.3MB, alloc=116.7MB, time=13.49 memory used=3486.4MB, alloc=116.7MB, time=13.58 memory used=3553.5MB, alloc=116.7MB, time=13.67 memory used=3617.0MB, alloc=131.8MB, time=13.77 memory used=3627.6MB, alloc=131.8MB, time=13.82 memory used=3638.1MB, alloc=131.8MB, time=13.86 memory used=3706.0MB, alloc=131.8MB, time=14.19 memory used=3785.5MB, alloc=131.8MB, time=19.50 memory used=3839.2MB, alloc=131.8MB, time=19.58 memory used=3901.7MB, alloc=131.8MB, time=19.66 memory used=3988.9MB, alloc=131.8MB, time=20.20 memory used=4039.6MB, alloc=131.8MB, time=20.31 memory used=4095.1MB, alloc=131.8MB, time=20.48 memory used=4165.4MB, alloc=131.8MB, time=20.97 memory used=4215.4MB, alloc=131.8MB, time=21.09 memory used=4268.6MB, alloc=131.8MB, time=21.21 memory used=4334.9MB, alloc=131.8MB, time=21.34 memory used=4375.3MB, alloc=131.8MB, time=21.42 memory used=4418.4MB, alloc=131.8MB, time=21.51 memory used=4466.1MB, alloc=131.8MB, time=21.59 memory used=4520.0MB, alloc=131.8MB, time=21.68 memory used=4601.7MB, alloc=131.8MB, time=22.03 memory used=4698.3MB, alloc=131.8MB, time=24.11 memory used=4769.3MB, alloc=131.8MB, time=24.33 memory used=4825.1MB, alloc=131.8MB, time=24.50 memory used=4876.8MB, alloc=131.8MB, time=24.62 memory used=4930.7MB, alloc=131.8MB, time=24.73 memory used=4992.6MB, alloc=131.8MB, time=25.00 memory used=5045.5MB, alloc=131.8MB, time=25.12 memory used=5098.3MB, alloc=131.8MB, time=25.22 memory used=5155.0MB, alloc=131.8MB, time=25.38 memory used=5210.8MB, alloc=131.8MB, time=25.52 memory used=5268.2MB, alloc=131.8MB, time=25.69 memory used=5319.7MB, alloc=131.8MB, time=25.81 memory used=5377.0MB, alloc=131.8MB, time=25.93 memory used=5437.4MB, alloc=131.8MB, time=26.23 memory used=5488.6MB, alloc=131.8MB, time=26.36 memory used=5544.7MB, alloc=131.8MB, time=26.46 memory used=5603.8MB, alloc=131.8MB, time=27.35 memory used=5682.6MB, alloc=131.8MB, time=27.57 memory used=5738.6MB, alloc=131.8MB, time=27.74 memory used=5777.5MB, alloc=131.8MB, time=27.87 memory used=5823.0MB, alloc=131.8MB, time=28.00 memory used=5872.9MB, alloc=131.8MB, time=28.14 memory used=5926.5MB, alloc=131.8MB, time=28.26 memory used=5984.0MB, alloc=131.8MB, time=28.40 memory used=6049.0MB, alloc=131.8MB, time=28.55 memory used=6094.7MB, alloc=131.8MB, time=28.67 memory used=6126.3MB, alloc=131.8MB, time=28.76 memory used=6158.7MB, alloc=131.8MB, time=28.86 memory used=6192.5MB, alloc=131.8MB, time=28.98 memory used=6227.0MB, alloc=131.8MB, time=29.09 memory used=6262.2MB, alloc=131.8MB, time=29.19 memory used=6298.0MB, alloc=131.8MB, time=29.30 memory used=6335.1MB, alloc=131.8MB, time=29.43 memory used=6377.0MB, alloc=131.8MB, time=29.53 memory used=6420.2MB, alloc=131.8MB, time=29.65 memory used=6464.1MB, alloc=131.8MB, time=29.76 memory used=6508.7MB, alloc=131.8MB, time=29.86 memory used=6554.0MB, alloc=131.8MB, time=29.97 memory used=6599.9MB, alloc=131.8MB, time=30.08 memory used=6646.4MB, alloc=131.8MB, time=30.21 memory used=6693.5MB, alloc=131.8MB, time=30.32 memory used=6742.2MB, alloc=131.8MB, time=30.44 memory used=6795.6MB, alloc=131.8MB, time=30.55 memory used=6850.4MB, alloc=131.8MB, time=30.67 memory used=6905.8MB, alloc=131.8MB, time=30.80 memory used=6961.7MB, alloc=131.8MB, time=30.91 memory used=7018.2MB, alloc=131.8MB, time=31.02 memory used=7076.2MB, alloc=131.8MB, time=31.14 memory used=7138.8MB, alloc=131.8MB, time=31.26 memory used=7180.8MB, alloc=131.8MB, time=31.36 memory used=7212.9MB, alloc=131.8MB, time=31.44 memory used=7242.6MB, alloc=155.8MB, time=31.54 memory used=7281.9MB, alloc=155.8MB, time=31.63 memory used=7326.1MB, alloc=155.8MB, time=31.73 memory used=7371.2MB, alloc=155.8MB, time=31.83 memory used=7416.4MB, alloc=155.8MB, time=31.93 memory used=7461.7MB, alloc=155.8MB, time=32.03 memory used=7507.0MB, alloc=155.8MB, time=32.13 memory used=7552.4MB, alloc=155.8MB, time=32.23 memory used=7597.8MB, alloc=155.8MB, time=32.35 memory used=7644.1MB, alloc=155.8MB, time=32.45 memory used=7695.1MB, alloc=155.8MB, time=32.55 memory used=7746.8MB, alloc=155.8MB, time=32.65 memory used=7798.5MB, alloc=155.8MB, time=32.75 memory used=7850.0MB, alloc=155.8MB, time=32.85 memory used=7901.4MB, alloc=155.8MB, time=32.96 memory used=7953.7MB, alloc=155.8MB, time=33.06 memory used=8010.0MB, alloc=155.8MB, time=33.17 memory used=8067.0MB, alloc=155.8MB, time=33.28 memory used=8123.7MB, alloc=155.8MB, time=33.38 memory used=8181.0MB, alloc=155.8MB, time=33.49 memory used=8242.0MB, alloc=155.8MB, time=33.59 memory used=8303.3MB, alloc=155.8MB, time=33.70 memory used=8365.2MB, alloc=155.8MB, time=33.81 memory used=8430.0MB, alloc=155.8MB, time=33.92 memory used=8495.0MB, alloc=155.8MB, time=34.03 memory used=8560.6MB, alloc=155.8MB, time=34.13 memory used=8628.6MB, alloc=155.8MB, time=34.25 memory used=8699.9MB, alloc=155.8MB, time=34.36 memory used=8771.9MB, alloc=155.8MB, time=34.47 memory used=8846.0MB, alloc=155.8MB, time=34.59 memory used=8922.6MB, alloc=155.8MB, time=34.70 memory used=9001.4MB, alloc=155.8MB, time=34.81 memory used=9083.9MB, alloc=155.8MB, time=34.92 memory used=9168.8MB, alloc=155.8MB, time=35.04 memory used=9251.9MB, alloc=155.8MB, time=35.15 memory used=9261.9MB, alloc=155.8MB, time=35.20 memory used=9271.4MB, alloc=155.8MB, time=35.26 memory used=9280.7MB, alloc=155.8MB, time=35.31 memory used=9289.9MB, alloc=155.8MB, time=35.36 memory used=9298.9MB, alloc=155.8MB, time=35.41 memory used=9307.7MB, alloc=155.8MB, time=35.46 memory used=9415.0MB, alloc=155.8MB, time=38.65 memory used=9480.8MB, alloc=155.8MB, time=38.85 memory used=9535.9MB, alloc=155.8MB, time=38.99 memory used=9594.0MB, alloc=155.8MB, time=39.17 memory used=9658.0MB, alloc=155.8MB, time=39.35 memory used=9731.8MB, alloc=155.8MB, time=39.53 memory used=9811.5MB, alloc=155.8MB, time=39.71 memory used=9889.0MB, alloc=155.8MB, time=39.92 memory used=9938.0MB, alloc=155.8MB, time=40.08 memory used=9980.2MB, alloc=155.8MB, time=40.23 memory used=10022.7MB, alloc=155.8MB, time=40.39 memory used=10067.5MB, alloc=155.8MB, time=40.53 memory used=10113.4MB, alloc=155.8MB, time=40.65 memory used=10160.4MB, alloc=155.8MB, time=40.78 memory used=10208.6MB, alloc=155.8MB, time=40.90 memory used=10257.8MB, alloc=155.8MB, time=41.04 memory used=10308.0MB, alloc=155.8MB, time=41.16 memory used=10359.3MB, alloc=155.8MB, time=41.31 memory used=10411.7MB, alloc=155.8MB, time=41.45 memory used=10465.0MB, alloc=155.8MB, time=41.60 memory used=10519.4MB, alloc=155.8MB, time=41.72 memory used=10574.8MB, alloc=155.8MB, time=41.85 memory used=10631.8MB, alloc=155.8MB, time=41.98 memory used=10697.0MB, alloc=155.8MB, time=42.15 memory used=10763.9MB, alloc=155.8MB, time=42.32 memory used=10831.9MB, alloc=155.8MB, time=42.49 memory used=10901.2MB, alloc=155.8MB, time=42.63 memory used=10971.6MB, alloc=155.8MB, time=42.79 memory used=11043.2MB, alloc=155.8MB, time=42.93 memory used=11115.9MB, alloc=155.8MB, time=43.08 memory used=11189.8MB, alloc=155.8MB, time=43.22 memory used=11264.8MB, alloc=155.8MB, time=43.37 memory used=11340.8MB, alloc=155.8MB, time=43.52 memory used=11411.5MB, alloc=155.8MB, time=43.68 memory used=11458.7MB, alloc=179.8MB, time=43.78 memory used=11505.1MB, alloc=179.8MB, time=43.89 memory used=11551.5MB, alloc=179.8MB, time=44.00 memory used=11599.5MB, alloc=179.8MB, time=44.10 memory used=11649.1MB, alloc=179.8MB, time=44.21 memory used=11699.5MB, alloc=179.8MB, time=44.32 memory 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alloc=179.8MB, time=46.69 memory used=12893.0MB, alloc=179.8MB, time=46.80 memory used=12951.5MB, alloc=179.8MB, time=46.92 memory used=13020.2MB, alloc=179.8MB, time=47.04 memory used=13079.6MB, alloc=179.8MB, time=47.15 memory used=13148.8MB, alloc=179.8MB, time=47.28 memory used=13219.3MB, alloc=179.8MB, time=47.40 memory used=13290.2MB, alloc=179.8MB, time=47.52 memory used=13361.4MB, alloc=179.8MB, time=47.65 memory used=13432.9MB, alloc=179.8MB, time=47.77 memory used=13504.7MB, alloc=179.8MB, time=47.91 memory used=13576.8MB, alloc=179.8MB, time=48.03 memory used=13649.2MB, alloc=179.8MB, time=48.16 memory used=13722.0MB, alloc=179.8MB, time=48.28 memory used=13794.9MB, alloc=179.8MB, time=48.40 memory used=13868.2MB, alloc=179.8MB, time=48.53 memory used=13941.7MB, alloc=179.8MB, time=48.65 memory used=14015.4MB, alloc=179.8MB, time=48.77 memory used=14089.4MB, alloc=179.8MB, time=48.90 memory used=14163.7MB, alloc=179.8MB, time=49.03 memory used=14238.1MB, alloc=179.8MB, 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time=60.44 memory used=22155.4MB, alloc=435.8MB, time=60.70 memory used=22397.5MB, alloc=435.8MB, time=60.96 memory used=22660.9MB, alloc=435.8MB, time=61.78 memory used=22789.1MB, alloc=435.8MB, time=171.62 memory used=22893.0MB, alloc=435.8MB, time=257.12 memory used=22979.4MB, alloc=435.8MB, time=258.72 memory used=23075.5MB, alloc=435.8MB, time=258.95 memory used=23141.0MB, alloc=435.8MB, time=259.14 memory used=23210.1MB, alloc=435.8MB, time=259.32 memory used=23288.0MB, alloc=435.8MB, time=259.51 memory used=23375.8MB, alloc=435.8MB, time=259.70 memory used=23470.8MB, alloc=435.8MB, time=259.90 memory used=23575.9MB, alloc=435.8MB, time=260.09 memory used=23645.8MB, alloc=435.8MB, time=260.22 memory used=23701.9MB, alloc=435.8MB, time=260.34 memory used=23759.3MB, alloc=435.8MB, time=260.47 memory used=23819.1MB, alloc=435.8MB, time=260.59 memory used=23880.4MB, alloc=435.8MB, time=260.71 memory used=23943.2MB, alloc=435.8MB, time=260.83 memory used=24011.5MB, alloc=435.8MB, time=260.95 memory used=24081.3MB, alloc=435.8MB, time=261.08 memory used=24152.6MB, alloc=435.8MB, time=261.22 memory used=24225.4MB, alloc=435.8MB, time=261.35 memory used=24299.9MB, alloc=435.8MB, time=261.48 memory used=24379.6MB, alloc=435.8MB, time=261.61 memory used=24461.1MB, alloc=435.8MB, time=261.75 memory used=24544.0MB, alloc=435.8MB, time=261.88 memory used=24628.4MB, alloc=435.8MB, time=262.03 memory used=24718.8MB, alloc=435.8MB, time=262.16 memory used=24810.5MB, alloc=435.8MB, time=262.30 memory used=24903.6MB, alloc=435.8MB, time=262.44 memory used=24998.2MB, alloc=435.8MB, time=262.58 memory used=25098.4MB, alloc=435.8MB, time=262.72 memory used=25200.2MB, alloc=435.8MB, time=262.88 memory used=25321.4MB, alloc=435.8MB, time=263.04 memory used=25472.4MB, alloc=435.8MB, time=263.28 memory used=25613.1MB, alloc=435.8MB, time=263.50 memory used=25757.7MB, alloc=435.8MB, time=263.72 memory used=25909.0MB, alloc=435.8MB, time=263.96 memory used=26061.6MB, alloc=435.8MB, time=264.19 memory used=26220.7MB, alloc=435.8MB, time=264.42 memory used=26386.3MB, alloc=435.8MB, time=264.65 memory used=26557.9MB, alloc=435.8MB, time=264.89 memory used=26735.3MB, alloc=435.8MB, time=265.14 memory used=26918.4MB, alloc=435.8MB, time=265.40 memory used=27106.7MB, alloc=435.8MB, time=265.65 memory used=27299.8MB, alloc=435.8MB, time=265.91 memory used=27502.7MB, alloc=435.8MB, time=266.16 memory used=27709.4MB, alloc=435.8MB, time=266.42 memory used=27924.4MB, alloc=435.8MB, time=266.69 memory used=28146.3MB, alloc=435.8MB, time=266.97 memory used=28379.1MB, alloc=435.8MB, time=267.25 memory used=28620.8MB, alloc=435.8MB, time=267.54 memory used=28869.3MB, alloc=435.8MB, time=267.83 memory used=29130.9MB, alloc=435.8MB, time=268.12 memory used=29352.9MB, alloc=435.8MB, time=268.39 memory used=29539.8MB, alloc=435.8MB, time=268.64 memory used=29733.8MB, alloc=435.8MB, time=268.88 memory used=29935.8MB, alloc=435.8MB, time=269.12 memory used=30149.8MB, alloc=435.8MB, time=269.36 memory used=30353.7MB, alloc=435.8MB, time=270.01 memory used=30437.6MB, alloc=435.8MB, time=270.16 memory used=30542.0MB, alloc=435.8MB, time=270.73 memory used=30623.0MB, alloc=435.8MB, time=270.91 memory used=30717.9MB, alloc=435.8MB, time=271.07 memory used=30785.0MB, alloc=435.8MB, time=271.18 memory used=30863.6MB, alloc=435.8MB, time=271.30 memory used=30956.7MB, alloc=435.8MB, time=271.42 memory used=31055.9MB, alloc=435.8MB, time=271.88 memory used=31205.0MB, alloc=435.8MB, time=273.10 memory used=31359.4MB, alloc=435.8MB, time=277.13 memory used=31449.2MB, alloc=435.8MB, time=277.36 memory used=31576.1MB, alloc=435.8MB, time=280.90 memory used=31661.1MB, alloc=435.8MB, time=281.10 memory used=31741.1MB, alloc=435.8MB, time=281.29 memory used=31833.0MB, alloc=435.8MB, time=281.48 memory used=31899.8MB, alloc=435.8MB, time=281.61 memory used=32194.5MB, alloc=435.8MB, time=286.17 memory used=32677.1MB, alloc=435.8MB, time=303.61 memory used=32767.6MB, alloc=435.8MB, time=303.89 memory used=32835.3MB, alloc=435.8MB, time=304.12 memory used=32905.7MB, alloc=435.8MB, time=304.33 memory used=32981.5MB, alloc=435.8MB, time=304.54 memory used=33062.1MB, alloc=435.8MB, time=304.77 memory used=33147.5MB, alloc=435.8MB, time=304.98 memory used=33237.7MB, alloc=435.8MB, time=305.24 memory used=33334.4MB, alloc=435.8MB, time=305.47 memory used=33435.9MB, alloc=435.8MB, time=305.72 memory used=33521.2MB, alloc=435.8MB, time=305.95 memory used=33591.2MB, alloc=435.8MB, time=306.15 memory used=33654.9MB, alloc=435.8MB, time=306.35 memory used=33713.3MB, alloc=435.8MB, time=306.53 memory used=33772.4MB, alloc=435.8MB, time=306.71 memory used=33831.7MB, alloc=435.8MB, time=306.89 memory used=33893.4MB, alloc=435.8MB, time=307.07 memory used=33957.5MB, alloc=435.8MB, time=307.27 memory used=34022.1MB, alloc=435.8MB, time=307.47 memory used=34088.9MB, alloc=435.8MB, time=307.66 memory used=34156.1MB, alloc=435.8MB, time=307.83 memory used=34225.6MB, alloc=435.8MB, time=308.05 memory used=34297.3MB, alloc=435.8MB, time=308.23 memory used=34371.2MB, alloc=435.8MB, time=308.44 memory used=34447.2MB, alloc=435.8MB, time=308.64 memory used=34525.3MB, alloc=435.8MB, time=308.84 memory used=34605.2MB, alloc=435.8MB, time=309.05 memory used=34686.9MB, alloc=435.8MB, time=309.24 memory used=34770.2MB, alloc=435.8MB, time=309.45 memory used=34855.1MB, alloc=435.8MB, time=309.66 memory used=34943.2MB, alloc=435.8MB, time=309.90 memory used=35032.5MB, alloc=435.8MB, time=310.11 memory used=35124.5MB, alloc=435.8MB, time=310.30 memory used=35219.1MB, alloc=435.8MB, time=310.50 memory used=35317.4MB, alloc=435.8MB, time=310.72 memory used=35417.4MB, alloc=435.8MB, time=310.93 memory used=35521.2MB, alloc=435.8MB, time=311.12 memory used=35600.0MB, alloc=435.8MB, time=311.29 memory used=35656.7MB, alloc=435.8MB, time=311.44 memory used=35711.5MB, alloc=435.8MB, time=311.58 memory used=35766.6MB, alloc=435.8MB, time=311.72 memory used=35823.1MB, alloc=435.8MB, time=311.85 memory used=35880.4MB, alloc=435.8MB, time=311.99 memory used=35939.4MB, alloc=435.8MB, time=312.13 memory used=35999.5MB, alloc=435.8MB, time=312.27 memory used=36061.0MB, alloc=435.8MB, time=312.42 memory used=36123.6MB, alloc=435.8MB, time=312.56 memory used=36187.8MB, alloc=435.8MB, time=312.70 memory used=36254.3MB, alloc=435.8MB, time=312.85 memory used=36323.7MB, alloc=435.8MB, time=312.99 memory used=36446.7MB, alloc=435.8MB, time=313.69 memory used=36604.5MB, alloc=435.8MB, time=315.34 memory used=36727.7MB, alloc=435.8MB, time=315.68 memory used=36864.1MB, alloc=435.8MB, time=315.99 memory used=37063.2MB, alloc=435.8MB, time=316.40 memory used=37257.9MB, alloc=435.8MB, time=316.75 memory used=37413.3MB, alloc=435.8MB, time=318.11 memory used=37552.8MB, alloc=435.8MB, time=318.84 memory used=37673.8MB, alloc=435.8MB, time=319.21 memory used=37815.8MB, alloc=435.8MB, time=319.98 memory used=37950.7MB, alloc=435.8MB, time=320.30 memory used=38091.0MB, alloc=435.8MB, time=320.64 memory used=38236.1MB, alloc=435.8MB, time=321.79 memory used=38354.9MB, alloc=435.8MB, time=322.13 memory used=38478.6MB, alloc=435.8MB, time=322.45 memory used=38602.6MB, alloc=435.8MB, time=322.77 memory used=38729.3MB, alloc=435.8MB, time=323.06 memory used=38868.8MB, alloc=435.8MB, time=323.35 memory used=39020.1MB, alloc=435.8MB, time=323.69 memory used=39182.3MB, alloc=435.8MB, time=324.03 memory used=39352.2MB, alloc=435.8MB, time=324.36 memory used=39544.0MB, alloc=435.8MB, time=325.41 memory used=39662.6MB, alloc=435.8MB, time=325.74 memory used=39783.3MB, alloc=435.8MB, time=326.05 memory used=39902.7MB, alloc=435.8MB, time=326.32 memory used=40031.4MB, alloc=435.8MB, time=326.62 memory used=40166.2MB, alloc=435.8MB, time=326.94 memory used=40314.1MB, alloc=435.8MB, time=327.28 memory used=40468.2MB, alloc=435.8MB, time=327.60 memory used=40640.7MB, alloc=435.8MB, time=327.92 memory used=40772.1MB, alloc=435.8MB, time=329.01 memory used=40891.4MB, alloc=435.8MB, time=329.40 memory used=40999.5MB, alloc=435.8MB, time=329.73 memory used=41103.3MB, alloc=435.8MB, time=330.02 memory used=41209.6MB, alloc=435.8MB, time=330.34 memory used=41323.4MB, alloc=435.8MB, time=330.62 memory used=41463.9MB, alloc=435.8MB, time=331.70 memory used=41576.4MB, alloc=435.8MB, time=332.06 memory used=41681.3MB, alloc=435.8MB, time=332.36 memory used=41785.4MB, alloc=435.8MB, time=332.65 memory used=41894.8MB, alloc=435.8MB, time=332.93 memory used=42009.4MB, alloc=435.8MB, time=333.21 memory used=42145.5MB, alloc=435.8MB, time=334.11 memory used=42304.2MB, alloc=435.8MB, time=335.57 memory used=42401.6MB, alloc=435.8MB, time=335.85 memory used=42509.6MB, alloc=435.8MB, time=336.12 memory used=42645.2MB, alloc=435.8MB, time=336.39 memory used=42799.5MB, alloc=435.8MB, time=336.73 memory used=42947.9MB, alloc=435.8MB, time=337.01 memory used=43103.2MB, alloc=435.8MB, time=337.32 memory used=43248.4MB, alloc=435.8MB, time=337.60 memory used=43397.7MB, alloc=435.8MB, time=337.94 memory used=43558.7MB, alloc=435.8MB, time=338.22 memory used=43703.8MB, alloc=435.8MB, time=338.56 memory used=43862.7MB, alloc=435.8MB, time=338.90 memory used=43985.7MB, alloc=435.8MB, time=339.16 memory used=44132.8MB, alloc=435.8MB, time=339.45 memory used=44318.8MB, alloc=435.8MB, time=339.84 memory used=44522.4MB, alloc=435.8MB, time=340.24 memory used=44669.0MB, alloc=435.8MB, time=340.56 memory used=44880.8MB, alloc=435.8MB, time=340.99 memory used=45058.3MB, alloc=435.8MB, time=341.32 memory used=45320.5MB, alloc=435.8MB, time=341.76 memory used=45587.9MB, alloc=435.8MB, time=342.20 memory used=45866.8MB, alloc=435.8MB, time=342.68 memory used=46234.1MB, alloc=435.8MB, time=343.27 memory used=46587.1MB, alloc=435.8MB, time=343.86 memory used=46926.1MB, alloc=435.8MB, time=347.21 memory used=47051.1MB, alloc=435.8MB, time=348.76 memory used=47200.7MB, alloc=435.8MB, time=350.10 memory used=47364.1MB, alloc=435.8MB, time=351.61 memory used=47716.4MB, alloc=435.8MB, time=360.22 memory used=47873.8MB, alloc=435.8MB, time=361.99 memory used=48014.8MB, alloc=435.8MB, time=363.32 memory used=48168.2MB, alloc=459.8MB, time=364.58 memory used=48352.1MB, alloc=459.8MB, time=365.52 memory used=48542.4MB, alloc=459.8MB, time=366.78 memory used=48733.2MB, alloc=459.8MB, time=368.39 memory used=49041.2MB, alloc=459.8MB, time=377.32 memory used=49191.1MB, alloc=459.8MB, time=379.21 memory used=49578.6MB, alloc=459.8MB, time=389.96 memory used=49866.7MB, alloc=459.8MB, time=399.45 memory used=50037.0MB, alloc=483.8MB, time=401.60 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428526873 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 2 2 2 F := [-6 y - 13 x y - 5 y z , -8 x y - x - 10 x] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 4 G := [2 x y - 11 x y z + 6 x z, 15 y + 14 x - 19 z] > Problem := [F,G]; 4 2 2 2 2 2 Problem := [[-6 y - 13 x y - 5 y z , -8 x y - x - 10 x], 3 2 2 4 [2 x y - 11 x y z + 6 x z, 15 y + 14 x - 19 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.16 memory used=23.5MB, alloc=32.3MB, time=0.35 memory used=45.9MB, alloc=36.3MB, time=0.63 memory used=65.0MB, alloc=60.3MB, time=0.89 memory used=108.1MB, alloc=61.1MB, time=1.59 memory used=134.2MB, alloc=61.1MB, time=1.65 memory used=160.3MB, alloc=61.1MB, time=1.71 memory used=193.9MB, alloc=61.1MB, time=1.93 memory used=230.6MB, alloc=61.9MB, time=2.44 memory used=254.7MB, alloc=61.9MB, time=2.50 memory used=284.6MB, alloc=61.9MB, time=2.56 memory used=312.6MB, alloc=61.9MB, time=2.70 memory used=351.2MB, alloc=61.9MB, time=3.04 memory used=394.4MB, alloc=61.9MB, time=3.72 memory used=418.0MB, alloc=61.9MB, time=3.77 memory used=449.8MB, alloc=61.9MB, time=3.91 memory used=477.9MB, alloc=61.9MB, time=4.02 memory used=518.6MB, alloc=61.9MB, time=4.42 memory used=566.3MB, alloc=69.9MB, time=5.96 memory used=598.6MB, alloc=69.9MB, time=8.55 memory used=621.6MB, alloc=69.9MB, time=8.61 memory used=639.3MB, alloc=69.9MB, time=8.67 memory used=662.4MB, alloc=69.9MB, time=8.73 memory used=680.9MB, alloc=69.9MB, time=8.79 memory used=715.6MB, alloc=93.9MB, time=11.83 memory used=762.4MB, alloc=93.9MB, time=12.63 memory used=799.1MB, alloc=93.9MB, time=12.72 memory used=838.8MB, alloc=93.9MB, time=12.84 memory used=916.6MB, alloc=93.9MB, time=16.24 memory used=952.1MB, alloc=93.9MB, time=16.33 memory used=988.1MB, alloc=93.9MB, time=16.41 memory used=1057.9MB, alloc=93.9MB, time=16.97 memory used=1133.2MB, alloc=93.9MB, time=20.52 memory used=1179.3MB, alloc=93.9MB, time=20.85 memory used=1207.2MB, alloc=93.9MB, time=20.94 memory used=1242.5MB, alloc=93.9MB, time=21.04 memory used=1275.6MB, alloc=93.9MB, time=21.20 memory used=1341.0MB, alloc=93.9MB, time=21.71 memory used=1404.7MB, alloc=93.9MB, time=22.22 memory used=1464.5MB, alloc=93.9MB, time=22.72 memory used=1503.3MB, alloc=93.9MB, time=22.94 memory used=1533.7MB, alloc=93.9MB, time=23.08 memory used=1565.2MB, alloc=93.9MB, time=23.20 memory used=1607.5MB, alloc=117.9MB, time=27.07 memory used=1674.6MB, alloc=117.9MB, time=57.23 memory used=1732.0MB, alloc=117.9MB, time=61.94 memory used=1774.1MB, alloc=117.9MB, time=62.07 memory used=1822.7MB, alloc=117.9MB, time=62.22 memory used=1860.1MB, alloc=117.9MB, time=62.33 memory used=1894.3MB, alloc=117.9MB, time=62.45 memory used=1932.8MB, alloc=117.9MB, time=62.55 memory used=1976.2MB, alloc=117.9MB, time=62.66 memory used=2024.5MB, alloc=117.9MB, time=62.78 memory used=2078.8MB, alloc=117.9MB, time=62.89 memory used=2100.9MB, alloc=131.8MB, time=62.98 memory used=2110.1MB, alloc=131.8MB, time=63.05 memory used=2120.1MB, alloc=131.8MB, time=63.12 memory used=2130.1MB, alloc=131.8MB, time=63.19 memory used=2140.1MB, alloc=131.8MB, time=63.27 memory used=2150.0MB, alloc=131.8MB, time=63.34 memory used=2160.0MB, alloc=131.8MB, time=63.41 memory used=2171.1MB, alloc=131.8MB, time=63.47 memory used=2182.2MB, alloc=131.8MB, time=63.54 memory used=2193.3MB, alloc=131.8MB, time=63.61 memory used=2204.4MB, alloc=131.8MB, time=63.69 memory used=2216.4MB, alloc=131.8MB, time=63.75 memory used=2228.4MB, alloc=131.8MB, time=63.83 memory used=2241.5MB, alloc=131.8MB, time=63.90 memory used=2254.3MB, alloc=131.8MB, time=63.98 memory used=2267.1MB, alloc=131.8MB, time=64.05 memory used=2279.3MB, alloc=131.8MB, time=64.12 memory used=2292.4MB, alloc=131.8MB, time=64.19 memory used=2306.4MB, alloc=131.8MB, time=64.27 memory used=2320.9MB, alloc=131.8MB, time=64.34 memory used=2335.9MB, alloc=131.8MB, time=64.42 memory used=2351.8MB, alloc=131.8MB, time=64.49 memory used=2368.5MB, alloc=131.8MB, time=64.56 memory used=2386.1MB, alloc=131.8MB, time=64.63 memory used=2404.9MB, alloc=131.8MB, time=64.71 memory used=2462.0MB, alloc=131.8MB, time=65.22 memory used=2520.4MB, alloc=131.8MB, time=65.51 memory used=2587.2MB, alloc=131.8MB, time=74.95 memory used=2646.2MB, alloc=131.8MB, time=96.68 memory used=2706.4MB, alloc=131.8MB, time=108.17 memory used=2747.4MB, alloc=131.8MB, time=108.31 memory used=2792.6MB, alloc=131.8MB, time=108.45 memory used=2833.1MB, alloc=131.8MB, time=108.56 memory used=2864.8MB, alloc=131.8MB, time=108.66 memory used=2900.3MB, alloc=131.8MB, time=108.77 memory used=2940.7MB, alloc=131.8MB, time=108.87 memory used=2984.5MB, alloc=131.8MB, time=108.99 memory used=3033.3MB, alloc=131.8MB, time=109.10 memory used=3086.7MB, alloc=131.8MB, time=109.21 memory used=3100.5MB, alloc=131.8MB, time=109.29 memory used=3109.5MB, alloc=131.8MB, time=109.36 memory used=3118.9MB, alloc=131.8MB, time=109.44 memory used=3128.3MB, alloc=131.8MB, time=109.51 memory used=3137.7MB, alloc=131.8MB, time=109.58 memory used=3147.0MB, alloc=131.8MB, time=109.65 memory used=3156.5MB, alloc=131.8MB, time=109.72 memory used=3167.2MB, alloc=131.8MB, time=109.79 memory used=3178.0MB, alloc=131.8MB, time=109.87 memory used=3188.8MB, alloc=131.8MB, time=109.95 memory used=3199.5MB, alloc=131.8MB, time=110.02 memory used=3210.1MB, alloc=131.8MB, time=110.10 memory used=3220.8MB, alloc=131.8MB, time=110.17 memory used=3232.6MB, alloc=131.8MB, time=110.24 memory used=3244.5MB, alloc=131.8MB, time=110.32 memory used=3256.3MB, alloc=131.8MB, time=110.40 memory used=3268.1MB, alloc=131.8MB, time=110.47 memory used=3279.5MB, alloc=131.8MB, time=110.54 memory used=3290.7MB, alloc=131.8MB, time=110.61 memory used=3303.3MB, alloc=131.8MB, time=110.68 memory used=3315.6MB, alloc=131.8MB, time=110.76 memory used=3330.1MB, alloc=131.8MB, time=110.83 memory used=3343.3MB, alloc=131.8MB, time=110.90 memory used=3357.1MB, alloc=131.8MB, time=110.98 memory used=3371.9MB, alloc=131.8MB, time=111.06 memory used=3387.2MB, alloc=131.8MB, time=111.14 memory used=3402.9MB, alloc=131.8MB, time=111.21 memory used=3418.8MB, alloc=131.8MB, time=111.28 memory used=3436.2MB, alloc=131.8MB, time=111.36 memory used=3454.1MB, alloc=131.8MB, time=111.44 memory used=3473.2MB, alloc=131.8MB, time=111.51 memory used=3525.3MB, alloc=131.8MB, time=111.84 memory used=3567.7MB, alloc=131.8MB, time=112.01 memory used=3621.6MB, alloc=131.8MB, time=112.13 memory used=3654.8MB, alloc=131.8MB, time=112.38 memory used=3673.8MB, alloc=131.8MB, time=112.46 memory used=3693.9MB, alloc=131.8MB, time=112.54 memory used=3715.0MB, alloc=131.8MB, time=112.62 memory used=3737.2MB, alloc=131.8MB, time=112.70 memory used=3769.8MB, alloc=131.8MB, time=112.79 memory used=3807.3MB, alloc=131.8MB, time=112.89 memory used=3847.1MB, alloc=131.8MB, time=112.98 memory used=3886.4MB, alloc=131.8MB, time=113.06 memory used=3898.6MB, alloc=131.8MB, time=113.13 memory used=3910.9MB, alloc=131.8MB, time=113.20 memory used=3923.4MB, alloc=131.8MB, time=113.26 memory used=3936.0MB, alloc=131.8MB, time=113.33 memory used=3948.9MB, alloc=131.8MB, time=113.39 memory used=3961.9MB, alloc=131.8MB, time=113.46 memory used=4018.3MB, alloc=131.8MB, time=114.22 memory used=4059.2MB, alloc=131.8MB, time=114.33 memory used=4135.7MB, alloc=131.8MB, time=114.79 memory used=4219.8MB, alloc=131.8MB, time=116.83 memory used=4285.3MB, alloc=131.8MB, time=119.57 memory used=4325.6MB, alloc=131.8MB, time=119.71 memory used=4376.1MB, alloc=131.8MB, time=119.86 memory used=4407.6MB, alloc=131.8MB, time=119.97 memory used=4443.2MB, alloc=131.8MB, time=120.08 memory used=4482.6MB, alloc=131.8MB, time=120.19 memory used=4527.8MB, alloc=131.8MB, time=120.31 memory used=4578.8MB, alloc=131.8MB, time=120.42 memory used=4621.4MB, alloc=131.8MB, time=120.54 memory used=4630.9MB, alloc=131.8MB, time=120.60 memory used=4641.2MB, alloc=131.8MB, time=120.68 memory used=4651.5MB, alloc=131.8MB, time=120.75 memory used=4661.8MB, alloc=131.8MB, time=120.82 memory used=4672.0MB, alloc=131.8MB, time=120.90 memory used=4683.1MB, alloc=131.8MB, time=120.97 memory used=4694.2MB, alloc=131.8MB, time=121.03 memory used=4705.3MB, alloc=131.8MB, time=121.11 memory used=4717.1MB, alloc=131.8MB, time=121.18 memory used=4728.8MB, alloc=131.8MB, time=121.25 memory used=4741.4MB, alloc=131.8MB, time=121.32 memory used=4754.8MB, alloc=131.8MB, time=121.39 memory used=4767.8MB, alloc=131.8MB, time=121.46 memory used=4781.3MB, alloc=131.8MB, time=121.53 memory used=4795.3MB, alloc=131.8MB, time=121.61 memory used=4810.2MB, alloc=131.8MB, time=121.68 memory used=4825.2MB, alloc=131.8MB, time=121.75 memory used=4841.6MB, alloc=131.8MB, time=121.82 memory used=4859.2MB, alloc=131.8MB, time=121.90 memory used=4959.6MB, alloc=131.8MB, time=122.83 memory used=5041.5MB, alloc=155.8MB, time=123.33 memory used=5157.5MB, alloc=155.8MB, time=123.88 memory used=5280.0MB, alloc=155.8MB, time=124.61 memory used=5402.1MB, alloc=155.8MB, time=125.64 memory used=5523.1MB, alloc=155.8MB, time=126.90 memory used=5644.7MB, alloc=155.8MB, time=128.81 memory used=5767.7MB, alloc=155.8MB, time=131.01 memory used=5890.3MB, alloc=155.8MB, time=133.48 memory used=6015.3MB, alloc=155.8MB, time=136.61 memory used=6138.4MB, alloc=155.8MB, time=140.32 memory used=6259.4MB, alloc=155.8MB, time=144.06 memory used=6357.7MB, alloc=155.8MB, time=146.05 memory used=6428.4MB, alloc=155.8MB, time=146.45 memory used=6538.9MB, alloc=155.8MB, time=149.54 memory used=6593.2MB, alloc=155.8MB, time=149.74 memory used=6652.1MB, alloc=155.8MB, time=149.92 memory used=6695.9MB, alloc=155.8MB, time=150.06 memory used=6747.5MB, alloc=155.8MB, time=150.20 memory used=6808.3MB, alloc=155.8MB, time=150.34 memory used=6884.9MB, alloc=155.8MB, time=150.50 memory used=6894.8MB, alloc=155.8MB, time=150.58 memory used=6904.0MB, alloc=155.8MB, time=150.65 memory used=6914.1MB, alloc=155.8MB, time=150.72 memory used=6924.4MB, alloc=155.8MB, time=150.80 memory used=6934.5MB, alloc=155.8MB, time=150.88 memory used=6945.8MB, alloc=155.8MB, time=150.95 memory used=6955.8MB, alloc=155.8MB, time=151.03 memory used=6966.7MB, alloc=155.8MB, time=151.11 memory used=6978.6MB, alloc=155.8MB, time=151.18 memory used=6990.4MB, alloc=155.8MB, time=151.26 memory used=7003.0MB, alloc=155.8MB, time=151.34 memory used=7015.4MB, alloc=155.8MB, time=151.41 memory used=7028.4MB, alloc=155.8MB, time=151.50 memory used=7042.1MB, alloc=155.8MB, time=151.57 memory used=7056.1MB, alloc=155.8MB, time=151.65 memory used=7070.4MB, alloc=155.8MB, time=151.74 memory used=7085.5MB, alloc=155.8MB, time=151.82 memory used=7101.7MB, alloc=155.8MB, time=151.91 memory used=7118.6MB, alloc=155.8MB, time=151.99 memory used=7214.4MB, alloc=155.8MB, time=152.64 memory used=7283.6MB, alloc=411.8MB, time=153.28 memory used=7367.9MB, alloc=411.8MB, time=156.61 memory used=7417.2MB, alloc=411.8MB, time=156.75 memory used=7522.0MB, alloc=411.8MB, time=157.67 memory used=7580.8MB, alloc=411.8MB, time=158.00 memory used=7633.6MB, alloc=411.8MB, time=158.28 memory used=7687.3MB, alloc=411.8MB, time=158.56 memory used=7743.9MB, alloc=411.8MB, time=158.77 memory used=7818.9MB, alloc=435.8MB, time=169.57 memory used=7905.6MB, alloc=435.8MB, time=186.67 memory used=7967.5MB, alloc=435.8MB, time=186.87 memory used=8028.2MB, alloc=435.8MB, time=187.05 memory used=8081.1MB, alloc=435.8MB, time=187.21 memory used=8143.5MB, alloc=435.8MB, time=187.37 memory used=8215.9MB, alloc=435.8MB, time=187.56 memory used=8416.8MB, alloc=435.8MB, time=188.09 memory used=8661.2MB, alloc=435.8MB, time=200.86 memory used=8749.4MB, alloc=435.8MB, time=224.99 memory used=8810.0MB, alloc=435.8MB, time=225.20 memory used=8876.7MB, alloc=435.8MB, time=225.39 memory used=8924.3MB, alloc=435.8MB, time=225.55 memory used=8980.9MB, alloc=435.8MB, time=225.73 memory used=9046.2MB, alloc=435.8MB, time=225.90 memory used=9121.2MB, alloc=435.8MB, time=226.07 memory used=9291.9MB, alloc=435.8MB, time=226.41 memory used=9550.1MB, alloc=435.8MB, time=227.32 memory used=9652.5MB, alloc=435.8MB, time=228.06 memory used=9789.2MB, alloc=435.8MB, time=234.73 memory used=9859.7MB, alloc=435.8MB, time=235.71 memory used=9925.2MB, alloc=435.8MB, time=235.94 memory used=9974.3MB, alloc=435.8MB, time=236.10 memory used=10022.7MB, alloc=435.8MB, time=236.27 memory used=10077.6MB, alloc=435.8MB, time=236.45 memory used=10139.4MB, alloc=435.8MB, time=236.62 memory used=10208.1MB, alloc=435.8MB, time=236.81 memory used=10416.8MB, alloc=435.8MB, time=237.21 memory used=10583.0MB, alloc=435.8MB, time=237.54 memory used=10778.6MB, alloc=435.8MB, time=237.90 memory used=11004.8MB, alloc=435.8MB, time=238.28 memory used=11223.2MB, alloc=435.8MB, time=238.63 memory used=11423.6MB, alloc=435.8MB, time=238.97 memory used=11701.3MB, alloc=435.8MB, time=244.71 memory used=11763.2MB, alloc=435.8MB, time=244.97 memory used=11827.9MB, alloc=435.8MB, time=245.16 memory used=11872.3MB, alloc=435.8MB, time=245.32 memory used=11924.3MB, alloc=435.8MB, time=245.48 memory used=11983.9MB, alloc=435.8MB, time=245.68 memory used=12052.6MB, alloc=435.8MB, time=245.90 memory used=12254.1MB, alloc=435.8MB, time=246.31 memory used=12430.9MB, alloc=435.8MB, time=246.63 memory used=12646.2MB, alloc=435.8MB, time=247.00 memory used=12864.9MB, alloc=435.8MB, time=247.36 memory used=13059.0MB, alloc=435.8MB, time=248.36 memory used=13202.4MB, alloc=459.8MB, time=250.53 memory used=13294.9MB, alloc=459.8MB, time=257.75 memory used=13363.2MB, alloc=459.8MB, time=257.95 memory used=13478.9MB, alloc=459.8MB, time=274.75 memory used=13562.5MB, alloc=459.8MB, time=275.68 memory used=13626.0MB, alloc=459.8MB, time=275.87 memory used=13765.1MB, alloc=459.8MB, time=276.57 memory used=13933.6MB, alloc=459.8MB, time=277.90 memory used=14096.3MB, alloc=459.8MB, time=278.94 memory used=14248.4MB, alloc=459.8MB, time=279.89 memory used=14364.1MB, alloc=459.8MB, time=280.31 memory used=14462.8MB, alloc=459.8MB, time=280.61 memory used=14561.9MB, alloc=459.8MB, time=280.92 memory used=14660.4MB, alloc=459.8MB, time=281.22 memory used=14767.4MB, alloc=459.8MB, time=281.55 memory used=14878.6MB, alloc=459.8MB, time=281.87 memory used=14989.6MB, alloc=459.8MB, time=282.20 memory used=15102.9MB, alloc=459.8MB, time=282.55 memory used=15290.7MB, alloc=459.8MB, time=284.55 memory used=15427.4MB, alloc=459.8MB, time=285.20 memory used=15535.9MB, alloc=459.8MB, time=285.57 memory used=15684.0MB, alloc=459.8MB, time=286.76 memory used=15794.7MB, alloc=459.8MB, time=287.19 memory used=15945.0MB, alloc=459.8MB, time=288.19 memory used=16069.4MB, alloc=483.8MB, time=288.75 memory used=16201.1MB, alloc=483.8MB, time=289.45 memory used=16365.4MB, alloc=483.8MB, time=290.20 memory used=16531.2MB, alloc=483.8MB, time=291.24 memory used=16705.2MB, alloc=483.8MB, time=292.07 memory used=16859.8MB, alloc=483.8MB, time=293.01 memory used=16986.1MB, alloc=483.8MB, time=293.43 memory used=17120.8MB, alloc=483.8MB, time=293.81 memory used=17249.8MB, alloc=483.8MB, time=294.21 memory used=17382.2MB, alloc=483.8MB, time=294.57 memory used=17527.3MB, alloc=483.8MB, time=294.98 memory used=17685.5MB, alloc=483.8MB, time=295.44 memory used=17852.3MB, alloc=483.8MB, time=295.87 memory used=18030.0MB, alloc=483.8MB, time=296.33 memory used=18212.2MB, alloc=483.8MB, time=296.75 memory used=18378.5MB, alloc=483.8MB, time=297.19 memory used=18566.5MB, alloc=483.8MB, time=298.44 memory used=18716.7MB, alloc=483.8MB, time=299.16 memory used=18841.3MB, alloc=483.8MB, time=299.61 memory used=19003.2MB, alloc=483.8MB, time=301.57 memory used=19154.2MB, alloc=507.8MB, time=303.54 memory used=19439.0MB, alloc=507.8MB, time=306.42 memory used=19673.4MB, alloc=531.8MB, time=309.00 memory used=19893.0MB, alloc=531.8MB, time=311.24 memory used=20083.6MB, alloc=531.8MB, time=313.57 memory used=20288.1MB, alloc=555.8MB, time=315.81 memory used=20520.6MB, alloc=579.8MB, time=318.41 memory used=20816.3MB, alloc=579.8MB, time=321.34 memory used=21171.6MB, alloc=579.8MB, time=325.07 memory used=21398.0MB, alloc=603.8MB, time=327.78 memory used=21624.8MB, alloc=627.8MB, time=333.37 memory used=21831.6MB, alloc=651.8MB, time=339.56 memory used=22040.8MB, alloc=675.8MB, time=346.86 memory used=22273.9MB, alloc=699.8MB, time=355.08 memory used=22531.1MB, alloc=723.8MB, time=364.44 memory used=22812.2MB, alloc=723.8MB, time=374.56 memory used=23093.3MB, alloc=747.8MB, time=384.54 memory used=23398.5MB, alloc=771.8MB, time=394.99 N1 := 8111 > GB := Basis(F, plex(op(vars))); 2 2 2 GB := [8 x y + x + 10 x, 4 2 2 3 3 2 2 52 x + 20 x z + 240 x y + 520 x - 3 x y + 200 x z - 30 x y, 4 2 2 6 y + 13 x y + 5 y z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=23676.4MB, alloc=771.8MB, time=401.56 memory used=23857.9MB, alloc=771.8MB, time=403.38 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428527173 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 F := [-7 z - 5 x - 7 z , -7 x y + 15 y] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 4 4 G := [-10 x y z - 20 x - 8 z , 18 x - 9 z - 2 x y] > Problem := [F,G]; 3 2 2 2 2 Problem := [[-7 z - 5 x - 7 z , -7 x y + 15 y], 2 2 2 4 4 [-10 x y z - 20 x - 8 z , 18 x - 9 z - 2 x y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=25.7MB, alloc=32.3MB, time=0.50 memory used=45.7MB, alloc=32.3MB, time=0.78 memory used=65.0MB, alloc=60.3MB, time=1.08 memory used=108.3MB, alloc=68.3MB, time=1.72 memory used=150.3MB, alloc=68.3MB, time=2.33 memory used=190.9MB, alloc=92.3MB, time=2.85 memory used=254.9MB, alloc=92.3MB, time=3.58 memory used=320.6MB, alloc=92.3MB, time=4.34 memory used=386.5MB, alloc=116.3MB, time=5.17 memory used=478.3MB, alloc=140.3MB, time=6.36 memory used=586.1MB, alloc=140.3MB, time=7.93 memory used=687.2MB, alloc=164.3MB, time=9.35 memory used=808.9MB, alloc=188.3MB, time=11.09 memory used=923.0MB, alloc=444.3MB, time=12.76 memory used=1048.6MB, alloc=468.3MB, time=15.09 memory used=1169.7MB, alloc=492.3MB, time=18.18 memory used=1300.7MB, alloc=516.3MB, time=22.09 memory used=1449.4MB, alloc=540.3MB, time=26.92 memory used=1622.1MB, alloc=564.3MB, time=32.53 memory used=1818.8MB, alloc=564.3MB, time=38.80 memory used=2015.5MB, alloc=588.3MB, time=45.01 N1 := 5973 > GB := Basis(F, plex(op(vars))); 2 2 3 2 2 GB := [7 x y - 15 y, 7 z + 7 z + 5 x ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=2251.7MB, alloc=588.3MB, time=50.53 memory used=2396.2MB, alloc=588.3MB, time=52.56 memory used=2535.6MB, alloc=588.3MB, time=54.47 memory used=2725.3MB, alloc=588.3MB, time=57.28 memory used=2948.8MB, alloc=612.3MB, time=60.61 memory used=3190.6MB, alloc=636.3MB, time=64.82 memory used=3438.7MB, alloc=660.3MB, time=72.15 memory used=3687.1MB, alloc=684.3MB, time=80.36 memory used=3959.5MB, alloc=708.3MB, time=89.23 memory used=4256.2MB, alloc=732.3MB, time=98.70 N2 := 5973 > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 2 2 2 2 2 2 H := [-7 z - 5 x - 7 z , -7 x y + 15 y, -10 x y z - 20 x - 8 z , 4 4 -9 z + 18 x - 2 y x] > J:=[op(GB),op(G)]; 2 2 3 2 2 2 2 2 J := [7 x y - 15 y, 7 z + 7 z + 5 x , -10 x y z - 20 x - 8 z , 4 4 -9 z + 18 x - 2 y x] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 10, 15, 4, 4, 2, 4, 1, 3/4, 3/4, 6/11, 4/11, 5/11, 4, 10, 15, 4, 4, 2, 4, 1, 3/4, 3/4, 6/11, 4/11, 5/11, 0, 0, 0] > save(F, G, cat("ranSet/34", convert(F, string),".txt")); > quit memory used=4331.0MB, alloc=732.3MB, time=100.43 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428527276 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 3 F := [-4 x y z + 12 y + 9, 20 y z - 3 x z + 5 z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 2 G := [-x y + 2 x z - 5 x y, 2 x y + 18 x y z - 14 x y] > Problem := [F,G]; 2 2 2 2 2 3 Problem := [[-4 x y z + 12 y + 9, 20 y z - 3 x z + 5 z ], 3 2 3 2 2 [-x y + 2 x z - 5 x y, 2 x y + 18 x y z - 14 x y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.16 memory used=26.5MB, alloc=32.3MB, time=0.42 memory used=46.6MB, alloc=32.3MB, time=0.66 memory used=65.3MB, alloc=56.3MB, time=0.89 memory used=105.3MB, alloc=60.3MB, time=1.37 memory used=142.7MB, alloc=60.3MB, time=1.80 memory used=182.0MB, alloc=92.3MB, time=2.26 memory used=243.2MB, alloc=92.3MB, time=3.00 memory used=304.3MB, alloc=116.3MB, time=3.75 memory used=385.8MB, alloc=372.3MB, time=4.75 memory used=470.5MB, alloc=396.3MB, time=5.74 memory used=578.6MB, alloc=396.3MB, time=7.00 memory used=693.5MB, alloc=420.3MB, time=8.28 memory used=810.8MB, alloc=444.3MB, time=9.96 memory used=942.6MB, alloc=468.3MB, time=12.02 memory used=1085.7MB, alloc=492.3MB, time=14.15 memory used=1258.9MB, alloc=516.3MB, time=16.38 memory used=1444.3MB, alloc=540.3MB, time=18.95 memory used=1620.8MB, alloc=564.3MB, time=22.62 memory used=1786.8MB, alloc=588.3MB, time=27.20 memory used=1962.0MB, alloc=612.3MB, time=32.27 memory used=2147.6MB, alloc=636.3MB, time=38.15 memory used=2345.0MB, alloc=660.3MB, time=44.96 memory used=2566.5MB, alloc=684.3MB, time=52.49 memory used=2811.8MB, alloc=708.3MB, time=60.75 memory used=3081.1MB, alloc=732.3MB, time=69.62 memory used=3374.3MB, alloc=732.3MB, time=79.43 memory used=3667.5MB, alloc=756.3MB, time=89.07 memory used=3984.7MB, alloc=756.3MB, time=99.53 memory used=4301.8MB, alloc=756.3MB, time=110.23 memory used=4618.9MB, alloc=780.3MB, time=120.66 memory used=4959.7MB, alloc=780.3MB, time=131.91 memory used=5300.4MB, alloc=804.3MB, time=143.22 memory used=5665.0MB, alloc=828.3MB, time=154.98 memory used=6053.7MB, alloc=852.3MB, time=168.68 N1 := 12261 > GB := Basis(F, plex(op(vars))); 7 2 5 3 3 5 2 3 3 GB := [6400 x y - 1920 x y + 144 x y + 4800 x y - 1440 x y + 108 x y 4 2 4 2 2 2 - 1200 y - 1800 y - 675, 80 y - 12 x y + 20 y z + 60 y - 9 x + 15 z, 6 2 4 3 2 4 2 2 3 2 -1600 x y + 480 x y - 36 x y - 1200 x y + 360 x y - 27 x + 75 x z 3 6 2 4 6 3 2 4 + 300 y + 225 y, -1600 x y + 480 x y + 8000 y - 36 x y - 3600 x y 2 2 4 3 2 3 3 2 + 540 x y + 6000 y - 27 x - 1800 x y + 300 y + 125 z + 135 x 2 - 375 z + 225 y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=6218.7MB, alloc=852.3MB, time=172.72 memory used=6332.6MB, alloc=852.3MB, time=174.64 memory used=6437.9MB, alloc=852.3MB, time=176.37 memory used=6538.4MB, alloc=852.3MB, time=178.08 memory used=6637.1MB, alloc=852.3MB, time=179.70 memory used=6723.0MB, alloc=852.3MB, time=181.30 memory used=6810.6MB, alloc=852.3MB, time=182.99 memory used=6903.5MB, alloc=852.3MB, time=185.07 memory used=6981.2MB, alloc=852.3MB, time=186.65 memory used=7058.5MB, alloc=852.3MB, time=188.08 memory used=7131.9MB, alloc=852.3MB, time=189.56 memory used=7205.0MB, alloc=852.3MB, time=190.96 memory used=7350.4MB, alloc=852.3MB, time=192.32 memory used=7411.3MB, alloc=852.3MB, time=193.60 memory used=7519.0MB, alloc=852.3MB, time=195.14 memory used=7713.2MB, alloc=852.3MB, time=196.64 memory used=7887.9MB, alloc=852.3MB, time=198.04 memory used=7970.4MB, alloc=852.3MB, time=199.27 memory used=8153.7MB, alloc=852.3MB, time=200.74 memory used=8332.5MB, alloc=852.3MB, time=202.31 memory used=8428.1MB, alloc=852.3MB, time=203.55 memory used=8487.2MB, alloc=852.3MB, time=204.85 memory used=8565.5MB, alloc=852.3MB, time=205.93 memory used=8646.7MB, alloc=852.3MB, time=207.23 memory used=8702.6MB, alloc=852.3MB, time=208.35 memory used=8763.0MB, alloc=852.3MB, time=209.40 memory used=8833.7MB, alloc=852.3MB, time=210.90 memory used=8870.4MB, alloc=852.3MB, time=211.78 memory used=8922.9MB, alloc=852.3MB, time=212.74 memory used=9183.1MB, alloc=852.3MB, time=215.28 memory used=9393.7MB, alloc=852.3MB, time=218.26 memory used=9704.2MB, alloc=876.3MB, time=223.69 memory used=10030.6MB, alloc=876.3MB, time=228.94 memory used=10262.8MB, alloc=876.3MB, time=231.64 memory used=10510.3MB, alloc=876.3MB, time=234.74 memory used=10817.4MB, alloc=876.3MB, time=241.35 memory used=11086.8MB, alloc=876.3MB, time=242.84 memory used=11299.2MB, alloc=900.3MB, time=244.06 memory used=11555.0MB, alloc=900.3MB, time=245.31 memory used=11865.3MB, alloc=900.3MB, time=246.67 memory used=12131.9MB, alloc=900.3MB, time=271.10 memory used=12452.4MB, alloc=915.8MB, time=275.14 memory used=12849.8MB, alloc=915.8MB, time=276.71 memory used=13189.0MB, alloc=915.8MB, time=279.99 memory used=13622.7MB, alloc=915.8MB, time=322.66 memory used=13870.2MB, alloc=915.8MB, time=323.97 memory used=14113.4MB, alloc=915.8MB, time=327.04 memory used=14400.5MB, alloc=915.8MB, time=337.69 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428527576 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 4 3 2 F := [-15 x y - x y - 10 x , -6 x + 8 x y - 5 y z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 2 2 G := [20 x z + 19 x + 18 y , -6 y z - 17 x ] > Problem := [F,G]; 2 2 3 2 4 3 2 Problem := [[-15 x y - x y - 10 x , -6 x + 8 x y - 5 y z], 2 2 3 2 2 2 2 [20 x z + 19 x + 18 y , -6 y z - 17 x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.0MB, alloc=32.3MB, time=0.48 memory used=48.4MB, alloc=36.3MB, time=0.74 memory used=69.5MB, alloc=36.3MB, time=0.92 memory used=88.7MB, alloc=60.3MB, time=1.17 memory used=132.6MB, alloc=60.3MB, time=1.57 memory used=173.5MB, alloc=61.2MB, time=1.85 memory used=210.5MB, alloc=61.2MB, time=2.28 memory used=258.3MB, alloc=61.2MB, time=2.72 memory used=300.0MB, alloc=61.2MB, time=3.21 memory used=344.8MB, alloc=69.2MB, time=3.74 memory used=385.8MB, alloc=93.2MB, time=4.35 memory used=462.8MB, alloc=93.2MB, time=5.13 memory used=528.9MB, alloc=93.2MB, time=6.12 N1 := 743 > GB := Basis(F, plex(op(vars))); memory used=587.9MB, alloc=93.2MB, time=7.35 2 2 3 2 6 5 4 2 2 GB := [15 x y + x y + 10 x , -45 x + 57 x y + 4 x y + 25 x z, 3 4 2 -8 y x + 6 x + 5 z y ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=650.5MB, alloc=117.2MB, time=8.08 memory used=708.3MB, alloc=117.2MB, time=8.44 memory used=770.3MB, alloc=117.2MB, time=8.82 memory used=841.9MB, alloc=117.2MB, time=9.65 memory used=925.0MB, alloc=117.2MB, time=10.52 memory used=974.7MB, alloc=117.2MB, time=10.72 memory used=1028.7MB, alloc=117.2MB, time=11.07 memory used=1100.3MB, alloc=117.2MB, time=11.69 memory used=1177.6MB, alloc=117.2MB, time=12.32 memory used=1220.6MB, alloc=117.2MB, time=12.48 memory used=1283.6MB, alloc=117.2MB, time=12.91 memory used=1368.8MB, alloc=117.2MB, time=13.66 memory used=1443.3MB, alloc=373.2MB, time=14.59 memory used=1495.2MB, alloc=373.2MB, time=14.88 memory used=1551.7MB, alloc=373.2MB, time=15.16 memory used=1598.9MB, alloc=373.2MB, time=15.48 memory used=1651.8MB, alloc=373.2MB, time=15.75 memory used=1711.3MB, alloc=373.2MB, time=16.01 memory used=1768.2MB, alloc=373.2MB, time=17.18 memory used=1806.2MB, alloc=373.2MB, time=17.33 memory used=1846.6MB, alloc=373.2MB, time=17.52 memory used=1946.6MB, alloc=373.2MB, time=18.84 memory used=2044.8MB, alloc=397.2MB, time=20.07 memory used=2163.0MB, alloc=397.2MB, time=21.43 memory used=2263.5MB, alloc=397.2MB, time=22.50 memory used=2368.8MB, alloc=397.2MB, time=23.72 memory used=2423.4MB, alloc=397.2MB, time=23.99 memory used=2480.3MB, alloc=397.2MB, time=24.36 memory used=2543.4MB, alloc=397.2MB, time=24.71 memory used=2645.5MB, alloc=421.2MB, time=25.75 memory used=2724.5MB, alloc=421.2MB, time=26.20 memory used=2822.7MB, alloc=421.2MB, time=26.79 memory used=2879.5MB, alloc=421.2MB, time=27.05 memory used=2954.1MB, alloc=421.2MB, time=27.32 memory used=3007.5MB, alloc=421.2MB, time=27.54 memory used=3060.1MB, alloc=421.2MB, time=27.76 memory used=3120.9MB, alloc=421.2MB, time=27.97 memory used=3193.8MB, alloc=421.2MB, time=28.21 memory used=3282.1MB, alloc=421.2MB, time=28.74 memory used=3339.7MB, alloc=421.2MB, time=28.98 memory used=3415.8MB, alloc=421.2MB, time=29.25 memory used=3468.2MB, alloc=421.2MB, time=29.47 memory used=3521.5MB, alloc=421.2MB, time=29.68 memory used=3583.3MB, alloc=421.2MB, time=29.90 memory used=3656.3MB, alloc=421.2MB, time=30.13 memory used=3747.8MB, alloc=421.2MB, time=32.67 memory used=3820.3MB, alloc=421.2MB, time=32.92 memory used=3870.1MB, alloc=421.2MB, time=33.14 memory used=3928.0MB, alloc=421.2MB, time=33.35 memory used=3997.0MB, alloc=421.2MB, time=33.59 memory used=4067.4MB, alloc=421.2MB, time=33.81 memory used=4113.3MB, alloc=421.2MB, time=33.98 memory used=4164.0MB, alloc=421.2MB, time=34.16 memory used=4242.6MB, alloc=421.2MB, time=34.45 memory used=4320.2MB, alloc=421.2MB, time=34.79 memory used=4411.4MB, alloc=421.2MB, time=35.28 memory used=4467.8MB, alloc=421.2MB, time=35.54 memory used=4542.3MB, alloc=421.2MB, time=35.80 memory used=4596.1MB, alloc=421.2MB, time=36.06 memory used=4648.4MB, alloc=421.2MB, time=36.29 memory used=4709.2MB, alloc=421.2MB, time=36.52 memory used=4782.3MB, alloc=421.2MB, time=36.73 memory used=4876.8MB, alloc=421.2MB, time=37.18 memory used=4935.2MB, alloc=421.2MB, time=37.42 memory used=4998.8MB, alloc=421.2MB, time=37.67 memory used=5074.6MB, alloc=421.2MB, time=37.90 memory used=5124.5MB, alloc=421.2MB, time=38.09 memory used=5176.8MB, alloc=421.2MB, time=38.28 memory used=5238.4MB, alloc=421.2MB, time=38.48 memory used=5339.6MB, alloc=421.2MB, time=38.95 memory used=5395.4MB, alloc=421.2MB, time=39.17 memory used=5460.6MB, alloc=421.2MB, time=39.39 memory used=5535.9MB, alloc=421.2MB, time=39.64 memory used=5584.3MB, alloc=421.2MB, time=39.84 memory used=5637.6MB, alloc=421.2MB, time=40.03 memory used=5702.1MB, alloc=421.2MB, time=40.26 memory used=5826.6MB, alloc=421.2MB, time=61.54 memory used=5886.9MB, alloc=421.2MB, time=61.77 memory used=5954.0MB, alloc=421.2MB, time=61.99 memory used=6022.0MB, alloc=421.2MB, time=62.21 memory used=6068.2MB, alloc=421.2MB, time=62.43 memory used=6118.2MB, alloc=421.2MB, time=62.62 memory used=6172.7MB, alloc=421.2MB, time=62.81 memory used=6231.7MB, alloc=421.2MB, time=63.04 memory used=6295.2MB, alloc=421.2MB, time=63.24 memory used=6364.9MB, alloc=421.2MB, time=63.47 memory used=6439.0MB, alloc=421.2MB, time=63.68 memory used=6517.3MB, alloc=421.2MB, time=63.91 memory used=6562.6MB, alloc=421.2MB, time=64.08 memory used=6603.9MB, alloc=421.2MB, time=64.23 memory used=6647.7MB, alloc=421.2MB, time=64.40 memory used=6691.8MB, alloc=421.2MB, time=64.56 memory used=6738.3MB, alloc=421.2MB, time=64.73 memory used=6786.9MB, alloc=421.2MB, time=64.89 memory used=6835.9MB, alloc=421.2MB, time=65.06 memory used=6886.7MB, alloc=421.2MB, time=65.23 memory used=6939.6MB, alloc=421.2MB, time=65.40 memory used=6994.4MB, alloc=421.2MB, time=65.57 memory used=7051.0MB, alloc=421.2MB, time=65.75 memory used=7109.3MB, alloc=421.2MB, time=65.92 memory used=7170.6MB, alloc=421.2MB, time=66.09 memory used=7235.1MB, alloc=421.2MB, time=66.27 memory used=7302.1MB, alloc=421.2MB, time=66.45 memory used=7371.1MB, alloc=421.2MB, time=66.63 memory used=7443.4MB, alloc=421.2MB, time=66.81 memory used=7518.0MB, alloc=421.2MB, time=66.98 memory used=7617.4MB, alloc=421.2MB, time=67.20 memory used=7771.1MB, alloc=421.2MB, time=67.59 memory used=7925.9MB, alloc=421.2MB, time=68.05 memory used=8045.3MB, alloc=421.2MB, time=68.92 memory used=8208.7MB, alloc=421.2MB, time=69.94 memory used=8353.5MB, alloc=421.2MB, time=71.85 memory used=8413.0MB, alloc=421.2MB, time=72.08 memory used=8478.0MB, alloc=421.2MB, time=72.31 memory used=8523.9MB, alloc=421.2MB, time=72.50 memory used=8577.3MB, alloc=421.2MB, time=72.71 memory used=8639.6MB, alloc=421.2MB, time=72.93 memory used=8710.9MB, alloc=421.2MB, time=73.13 memory used=8761.1MB, alloc=421.2MB, time=73.31 memory used=8804.4MB, alloc=421.2MB, time=73.47 memory used=8851.6MB, alloc=421.2MB, time=73.63 memory used=8903.2MB, alloc=421.2MB, time=73.79 memory used=9000.0MB, alloc=421.2MB, time=74.63 memory used=9099.2MB, alloc=421.2MB, time=75.92 memory used=9205.8MB, alloc=421.2MB, time=76.62 memory used=9323.0MB, alloc=445.2MB, time=77.82 memory used=9417.5MB, alloc=445.2MB, time=78.86 memory used=9533.2MB, alloc=445.2MB, time=79.71 memory used=9600.8MB, alloc=445.2MB, time=79.98 memory used=9679.5MB, alloc=445.2MB, time=80.32 memory used=9746.5MB, alloc=445.2MB, time=80.59 memory used=9834.0MB, alloc=445.2MB, time=81.19 memory used=9898.7MB, alloc=445.2MB, time=81.46 memory used=9962.3MB, alloc=445.2MB, time=81.68 memory used=10078.5MB, alloc=445.2MB, time=82.46 memory used=10179.2MB, alloc=445.2MB, time=83.01 memory used=10266.2MB, alloc=445.2MB, time=83.70 memory used=10354.2MB, alloc=445.2MB, time=84.17 memory used=10455.6MB, alloc=445.2MB, time=84.73 memory used=10564.1MB, alloc=445.2MB, time=85.70 memory used=10688.7MB, alloc=469.2MB, time=87.29 memory used=10798.7MB, alloc=469.2MB, time=88.04 memory used=10876.8MB, alloc=469.2MB, time=88.34 memory used=10973.0MB, alloc=469.2MB, time=88.71 memory used=11052.7MB, alloc=469.2MB, time=89.03 memory used=11138.0MB, alloc=469.2MB, time=89.32 memory used=11235.9MB, alloc=469.2MB, time=90.15 memory used=11319.5MB, alloc=469.2MB, time=90.42 memory used=11388.9MB, alloc=469.2MB, time=90.67 memory used=11532.2MB, alloc=469.2MB, time=91.85 memory used=11635.3MB, alloc=469.2MB, time=92.39 memory used=11720.2MB, alloc=469.2MB, time=92.71 memory used=11783.5MB, alloc=469.2MB, time=92.97 memory used=11863.7MB, alloc=469.2MB, time=93.24 memory used=12093.6MB, alloc=469.2MB, time=94.42 memory used=12222.6MB, alloc=469.2MB, time=95.31 memory used=12346.0MB, alloc=469.2MB, time=96.25 memory used=12458.7MB, alloc=469.2MB, time=97.02 memory used=12538.8MB, alloc=469.2MB, time=97.36 memory used=12612.3MB, alloc=469.2MB, time=97.68 memory used=12699.1MB, alloc=469.2MB, time=98.12 memory used=12776.9MB, alloc=469.2MB, time=98.43 memory used=12852.5MB, alloc=469.2MB, time=98.72 memory used=12933.2MB, alloc=469.2MB, time=99.06 memory used=13015.7MB, alloc=469.2MB, time=99.37 memory used=13091.7MB, alloc=469.2MB, time=99.77 memory used=13173.4MB, alloc=469.2MB, time=100.07 memory used=13242.0MB, alloc=469.2MB, time=100.33 memory used=13339.5MB, alloc=469.2MB, time=100.76 memory used=13413.5MB, alloc=469.2MB, time=101.06 memory used=13500.2MB, alloc=469.2MB, time=101.36 memory used=13560.2MB, alloc=469.2MB, time=101.62 memory used=13653.1MB, alloc=469.2MB, time=102.06 memory used=13726.5MB, alloc=469.2MB, time=102.34 memory used=13816.3MB, alloc=469.2MB, time=102.76 memory used=13893.7MB, alloc=469.2MB, time=103.04 memory used=13969.1MB, alloc=469.2MB, time=103.33 memory used=14047.2MB, alloc=469.2MB, time=103.75 memory used=14122.6MB, alloc=469.2MB, time=104.06 memory used=14211.0MB, alloc=469.2MB, time=104.38 memory used=14273.2MB, alloc=469.2MB, time=104.64 memory used=14371.3MB, alloc=469.2MB, time=105.51 memory used=14456.5MB, alloc=469.2MB, time=105.85 memory used=14518.2MB, alloc=469.2MB, time=106.10 memory used=14593.8MB, alloc=469.2MB, time=106.37 memory used=14685.7MB, alloc=469.2MB, time=106.66 memory used=14862.0MB, alloc=469.2MB, time=107.05 memory used=15102.3MB, alloc=469.2MB, time=108.31 memory used=15252.7MB, alloc=469.2MB, time=109.95 memory used=15362.7MB, alloc=469.2MB, time=111.67 memory used=15532.0MB, alloc=469.2MB, time=112.96 memory used=15684.9MB, alloc=469.2MB, time=114.90 memory used=15785.1MB, alloc=469.2MB, time=116.24 memory used=15866.5MB, alloc=469.2MB, time=117.17 memory used=15943.2MB, alloc=469.2MB, time=118.02 memory used=16017.9MB, alloc=469.2MB, time=118.97 memory used=16091.9MB, alloc=493.2MB, time=119.85 memory used=16187.9MB, alloc=493.2MB, time=120.62 memory used=16257.2MB, alloc=493.2MB, time=121.43 memory used=16371.9MB, alloc=493.2MB, time=122.77 memory used=16538.7MB, alloc=517.2MB, time=123.65 memory used=16645.4MB, alloc=517.2MB, time=125.07 memory used=16808.8MB, alloc=517.2MB, time=126.44 memory used=16943.1MB, alloc=517.2MB, time=128.19 memory used=17073.3MB, alloc=517.2MB, time=129.95 memory used=17200.2MB, alloc=517.2MB, time=132.52 memory used=17328.6MB, alloc=517.2MB, time=135.06 memory used=17444.9MB, alloc=541.2MB, time=136.71 memory used=17568.9MB, alloc=565.2MB, time=139.29 memory used=17744.2MB, alloc=589.2MB, time=145.19 N2 := 3193 > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 3 2 4 3 2 H := [-15 x y - x y - 10 x , -6 x + 8 x y - 5 y z, 2 2 3 2 2 2 2 20 z x + 19 x + 18 y , -6 y z - 17 x ] > J:=[op(GB),op(G)]; 2 2 3 2 6 5 4 2 2 J := [15 x y + x y + 10 x , -45 x + 57 x y + 4 x y + 25 x z, 3 4 2 2 2 3 2 2 2 2 -8 y x + 6 x + 5 z y , 20 z x + 19 x + 18 y , -6 y z - 17 x ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 11, 16, 4, 4, 3, 2, 1, 1, 3/4, 8/11, 6/11, 3/11, 5, 14, 22, 6, 6, 3, 2, 1, 1, 4/5, 4/5, 8/15, 4/15, -3, -6, -2] > save(F, G, cat("ranSet/34", convert(F, string),".txt")); > quit memory used=17884.3MB, alloc=589.2MB, time=149.15 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428527706 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 3 3 F := [5 x z - 10 x y + x z , -12 x y + 14 x y - 11 y] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 3 G := [2 x y z + 12 x y - 4 x z, -12 y z + 12 y z] > Problem := [F,G]; 3 2 2 3 3 Problem := [[5 x z - 10 x y + x z , -12 x y + 14 x y - 11 y], 2 3 2 3 [2 x y z + 12 x y - 4 x z, -12 y z + 12 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.2MB, alloc=32.3MB, time=0.46 memory used=47.9MB, alloc=32.3MB, time=0.74 memory used=67.1MB, alloc=56.3MB, time=0.95 memory used=110.4MB, alloc=60.3MB, time=1.35 memory used=154.8MB, alloc=60.3MB, time=1.85 memory used=193.5MB, alloc=84.3MB, time=2.37 N1 := 879 > GB := Basis(F, plex(op(vars))); 3 3 2 2 3 GB := [12 x y - 14 x y + 11 y, 5 x z - 10 x y + x z , 2 3 30 x y z + 6 y z - 70 x y + 55 y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=249.1MB, alloc=84.3MB, time=3.26 memory used=310.7MB, alloc=92.3MB, time=3.96 memory used=371.3MB, alloc=93.2MB, time=4.62 memory used=421.3MB, alloc=101.3MB, time=4.79 memory used=461.6MB, alloc=101.3MB, time=4.99 memory used=495.9MB, alloc=101.3MB, time=5.28 memory used=546.9MB, alloc=102.2MB, time=5.46 memory used=591.5MB, alloc=102.2MB, time=5.67 memory used=628.1MB, alloc=102.2MB, time=5.93 memory used=694.6MB, alloc=126.2MB, time=9.39 memory used=751.8MB, alloc=126.2MB, time=9.55 memory used=833.1MB, alloc=126.2MB, time=10.36 memory used=885.1MB, alloc=126.2MB, time=10.99 memory used=941.4MB, alloc=126.2MB, time=11.21 memory used=990.4MB, alloc=126.2MB, time=12.34 memory used=1038.1MB, alloc=126.2MB, time=12.47 memory used=1120.5MB, alloc=126.2MB, time=13.82 memory used=1167.2MB, alloc=126.2MB, time=13.95 memory used=1237.2MB, alloc=126.2MB, time=14.40 memory used=1322.5MB, alloc=126.4MB, time=15.30 memory used=1369.6MB, alloc=126.4MB, time=15.65 memory used=1439.1MB, alloc=126.9MB, time=15.97 memory used=1494.2MB, alloc=126.9MB, time=16.47 memory used=1543.8MB, alloc=126.9MB, time=16.90 memory used=1630.7MB, alloc=126.9MB, time=23.01 memory used=1671.4MB, alloc=126.9MB, time=23.14 memory used=1718.4MB, alloc=126.9MB, time=23.27 memory used=1784.1MB, alloc=126.9MB, time=23.92 memory used=1876.4MB, alloc=126.9MB, time=27.49 memory used=1920.9MB, alloc=126.9MB, time=27.67 memory used=1984.2MB, alloc=126.9MB, time=28.17 memory used=2066.0MB, alloc=150.9MB, time=29.07 memory used=2158.6MB, alloc=174.9MB, time=30.93 N2 := 1235 > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 2 3 3 H := [5 x z - 10 x y + x z , -12 x y + 14 x y - 11 y, 2 3 2 3 2 x y z + 12 x y - 4 x z, -12 y z + 12 y z] > J:=[op(GB),op(G)]; 3 3 2 2 3 J := [12 x y - 14 x y + 11 y, 5 x z - 10 x y + x z , 2 3 2 3 2 30 x y z + 6 y z - 70 x y + 55 y, 2 x y z + 12 x y - 4 x z, 3 -12 y z + 12 y z] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 10, 16, 4, 3, 3, 3, 3/4, 1, 3/4, 8/11, 8/11, 6/11, 5, 13, 20, 4, 3, 3, 3, 4/5, 1, 4/5, 2/3, 4/5, 8/15, -3, -4, 0] > save(F, G, cat("ranSet/34", convert(F, string),".txt")); > quit memory used=2169.0MB, alloc=174.9MB, time=31.15 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428527731 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 4 2 2 2 F := [14 y + 4 z - 19 x y, -11 x y - 8 x ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 G := [-14 x y - x z - 13 x y, 15 x y z + 5 x y z + 4 x z ] > Problem := [F,G]; 4 4 2 2 2 Problem := [[14 y + 4 z - 19 x y, -11 x y - 8 x ], 2 2 3 2 2 [-14 x y - x z - 13 x y, 15 x y z + 5 x y z + 4 x z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.16 memory used=26.5MB, alloc=32.3MB, time=0.44 memory used=47.3MB, alloc=32.3MB, time=0.72 memory used=65.2MB, alloc=56.3MB, time=0.94 memory used=107.0MB, alloc=60.3MB, time=1.35 memory used=140.5MB, alloc=60.6MB, time=1.53 memory used=183.8MB, alloc=60.6MB, time=2.04 memory used=225.4MB, alloc=60.6MB, time=2.48 memory used=267.0MB, alloc=68.6MB, time=2.95 memory used=306.0MB, alloc=92.6MB, time=3.44 memory used=367.7MB, alloc=92.6MB, time=8.91 memory used=408.6MB, alloc=92.6MB, time=17.51 memory used=455.0MB, alloc=92.6MB, time=17.65 memory used=493.1MB, alloc=92.6MB, time=17.74 memory used=535.3MB, alloc=92.6MB, time=17.83 memory used=566.8MB, alloc=92.6MB, time=17.92 memory used=591.0MB, alloc=92.6MB, time=17.99 memory used=616.8MB, alloc=92.6MB, time=18.07 memory used=644.2MB, alloc=92.6MB, time=18.14 memory used=673.4MB, alloc=92.6MB, time=18.23 memory used=704.6MB, alloc=92.6MB, time=18.31 memory used=737.1MB, alloc=92.6MB, time=18.39 memory used=777.3MB, alloc=116.6MB, time=21.12 memory used=843.4MB, alloc=116.6MB, time=50.83 memory used=891.8MB, alloc=140.6MB, time=82.52 memory used=938.2MB, alloc=140.6MB, time=139.05 memory used=1005.7MB, alloc=140.6MB, time=155.26 memory used=1092.4MB, alloc=140.6MB, time=156.96 memory used=1139.5MB, alloc=140.6MB, time=157.09 memory used=1187.9MB, alloc=140.6MB, time=157.23 memory used=1239.0MB, alloc=140.6MB, time=157.36 memory used=1292.7MB, alloc=140.6MB, time=157.52 memory used=1350.1MB, alloc=140.6MB, time=157.65 memory used=1410.8MB, alloc=140.6MB, time=157.79 memory used=1474.4MB, alloc=140.6MB, time=157.92 memory used=1542.4MB, alloc=140.6MB, time=158.08 memory used=1614.0MB, alloc=140.6MB, time=158.22 memory used=1690.0MB, alloc=140.6MB, time=158.35 memory used=1771.7MB, alloc=140.6MB, time=158.51 memory used=1827.5MB, alloc=140.6MB, time=158.62 memory used=1872.7MB, alloc=140.6MB, time=158.71 memory used=1919.9MB, alloc=140.6MB, time=158.81 memory used=2012.2MB, alloc=140.6MB, time=159.92 memory used=2106.7MB, alloc=140.6MB, time=160.53 memory used=2170.8MB, alloc=140.6MB, time=160.71 memory used=2240.6MB, alloc=140.6MB, time=160.85 memory used=2299.7MB, alloc=140.6MB, time=160.97 memory used=2390.3MB, alloc=143.1MB, time=162.40 memory used=2472.6MB, alloc=143.1MB, time=168.37 memory used=2542.2MB, alloc=143.1MB, time=169.32 memory used=2608.8MB, alloc=143.1MB, time=169.54 memory used=2730.9MB, alloc=399.1MB, time=170.88 memory used=2850.3MB, alloc=399.1MB, time=172.37 memory used=2936.5MB, alloc=399.1MB, time=176.50 memory used=3051.8MB, alloc=399.1MB, time=178.30 memory used=3190.4MB, alloc=399.1MB, time=179.69 memory used=3328.3MB, alloc=399.1MB, time=181.36 memory used=3399.6MB, alloc=399.1MB, time=181.71 memory used=3462.8MB, alloc=399.1MB, time=182.02 memory used=3526.9MB, alloc=399.1MB, time=182.32 memory used=3617.0MB, alloc=399.1MB, time=198.91 memory used=3699.0MB, alloc=399.1MB, time=208.98 memory used=3752.6MB, alloc=399.1MB, time=209.16 memory used=3803.2MB, alloc=399.1MB, time=209.32 memory used=3867.2MB, alloc=399.1MB, time=209.48 memory used=3915.0MB, alloc=399.1MB, time=209.62 memory used=3954.0MB, alloc=399.1MB, time=209.74 memory used=3997.4MB, alloc=399.1MB, time=209.86 memory used=4043.2MB, alloc=399.1MB, time=209.98 memory used=4091.4MB, alloc=399.1MB, time=210.10 memory used=4144.7MB, alloc=399.1MB, time=210.25 memory used=4200.4MB, alloc=399.1MB, time=210.40 memory used=4261.3MB, alloc=399.1MB, time=210.55 memory used=4324.5MB, alloc=399.1MB, time=210.69 memory used=4393.1MB, alloc=399.1MB, time=210.85 memory used=4555.8MB, alloc=399.1MB, time=211.29 memory used=4700.1MB, alloc=399.1MB, time=211.57 memory used=4856.7MB, alloc=399.1MB, time=211.86 memory used=5029.7MB, alloc=399.1MB, time=212.17 memory used=5218.3MB, alloc=399.1MB, time=212.50 memory used=5424.9MB, alloc=399.1MB, time=212.84 memory used=5647.8MB, alloc=399.1MB, time=213.18 memory used=5870.8MB, alloc=399.1MB, time=213.54 memory used=6044.6MB, alloc=399.1MB, time=213.83 memory used=6232.1MB, alloc=399.1MB, time=214.14 memory used=6437.5MB, alloc=399.1MB, time=214.46 memory used=6668.7MB, alloc=399.1MB, time=214.80 memory used=6766.6MB, alloc=423.1MB, time=252.30 memory used=6851.8MB, alloc=447.1MB, time=332.34 memory used=6935.8MB, alloc=447.1MB, time=436.40 memory used=7022.8MB, alloc=447.1MB, time=495.59 memory used=7139.3MB, alloc=447.1MB, time=498.50 memory used=7214.6MB, alloc=447.1MB, time=498.71 memory used=7310.7MB, alloc=447.1MB, time=498.92 memory used=7387.8MB, alloc=447.1MB, time=499.11 memory used=7447.2MB, alloc=447.1MB, time=499.27 memory used=7511.5MB, alloc=447.1MB, time=499.43 memory used=7579.9MB, alloc=447.1MB, time=499.59 memory used=7656.2MB, alloc=447.1MB, time=499.76 memory used=7736.8MB, alloc=447.1MB, time=499.94 memory used=7821.5MB, alloc=447.1MB, time=500.12 memory used=7914.9MB, alloc=447.1MB, time=500.31 memory used=8012.5MB, alloc=447.1MB, time=500.49 memory used=8114.2MB, alloc=447.1MB, time=500.69 memory used=8296.8MB, alloc=447.1MB, time=501.00 memory used=8428.5MB, alloc=447.1MB, time=501.27 memory used=8568.3MB, alloc=447.1MB, time=501.57 memory used=8718.8MB, alloc=447.1MB, time=501.85 memory used=8874.0MB, alloc=447.1MB, time=502.14 memory used=9040.2MB, alloc=447.1MB, time=502.44 memory used=9210.9MB, alloc=447.1MB, time=502.74 memory used=9392.5MB, alloc=447.1MB, time=503.05 memory used=9585.0MB, alloc=447.1MB, time=503.42 memory used=9788.6MB, alloc=447.1MB, time=503.79 memory used=9996.2MB, alloc=447.1MB, time=504.17 memory used=10214.1MB, alloc=447.1MB, time=504.57 memory used=10442.2MB, alloc=447.1MB, time=504.96 memory used=10675.9MB, alloc=447.1MB, time=505.36 memory used=10846.9MB, alloc=447.1MB, time=505.69 memory used=11018.0MB, alloc=447.1MB, time=505.99 memory used=11189.4MB, alloc=447.1MB, time=506.32 memory used=11368.4MB, alloc=447.1MB, time=506.66 memory used=11554.8MB, alloc=447.1MB, time=507.01 memory used=11741.2MB, alloc=447.1MB, time=507.34 memory used=11933.9MB, alloc=447.1MB, time=507.70 memory used=12132.9MB, alloc=447.1MB, time=508.06 memory used=12337.6MB, alloc=447.1MB, time=508.43 memory used=12554.4MB, alloc=447.1MB, time=508.81 memory used=12775.4MB, alloc=447.1MB, time=509.20 memory used=13006.4MB, alloc=447.1MB, time=509.59 memory used=13245.9MB, alloc=447.1MB, time=509.99 memory used=13469.2MB, alloc=447.1MB, time=510.38 memory used=13657.6MB, alloc=447.1MB, time=510.71 memory used=13854.3MB, alloc=447.1MB, time=511.07 memory used=14054.9MB, alloc=447.1MB, time=511.42 memory used=14262.7MB, alloc=447.1MB, time=511.79 memory used=14478.8MB, alloc=447.1MB, time=512.17 memory used=14702.0MB, alloc=447.1MB, time=512.55 memory used=14937.6MB, alloc=447.1MB, time=512.97 memory used=15168.7MB, alloc=447.1MB, time=513.34 memory used=15332.0MB, alloc=447.1MB, time=513.97 memory used=15444.3MB, alloc=447.1MB, time=514.41 memory used=15555.2MB, alloc=447.1MB, time=514.65 memory used=15663.5MB, alloc=447.1MB, time=514.89 memory used=15901.7MB, alloc=447.1MB, time=515.71 memory used=16105.6MB, alloc=447.1MB, time=516.04 memory used=16371.4MB, alloc=447.1MB, time=516.42 memory used=16625.3MB, alloc=447.1MB, time=516.81 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428528031 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 3 2 3 F := [8 x z + 2 y , 13 x y - 11 x y z - 6 y ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 4 2 4 3 2 G := [2 x y + 18 z - 14 x y , -10 x - 7 z - 18 z ] > Problem := [F,G]; 2 3 3 2 3 Problem := [[8 x z + 2 y , 13 x y - 11 x y z - 6 y ], 2 2 4 2 4 3 2 [2 x y + 18 z - 14 x y , -10 x - 7 z - 18 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=26.7MB, alloc=32.3MB, time=0.52 memory used=49.0MB, alloc=32.3MB, time=0.76 memory used=75.6MB, alloc=60.3MB, time=1.15 memory used=139.1MB, alloc=64.6MB, time=1.50 memory used=201.0MB, alloc=64.6MB, time=1.92 memory used=244.2MB, alloc=72.6MB, time=2.50 memory used=282.5MB, alloc=72.6MB, time=2.76 memory used=310.8MB, alloc=72.6MB, time=2.89 memory used=347.2MB, alloc=72.6MB, time=4.53 memory used=365.9MB, alloc=72.6MB, time=4.60 memory used=397.4MB, alloc=72.6MB, time=4.76 memory used=427.9MB, alloc=72.6MB, time=4.87 memory used=448.5MB, alloc=72.6MB, time=4.93 memory used=475.2MB, alloc=72.6MB, time=5.00 memory used=494.3MB, alloc=72.6MB, time=5.07 memory used=524.4MB, alloc=83.8MB, time=9.48 memory used=540.9MB, alloc=83.8MB, time=15.25 memory used=557.1MB, alloc=83.8MB, time=17.38 memory used=586.1MB, alloc=83.8MB, time=20.55 memory used=599.5MB, alloc=83.8MB, time=24.64 memory used=611.1MB, alloc=83.8MB, time=24.69 memory used=620.2MB, alloc=83.8MB, time=24.73 memory used=629.5MB, alloc=83.8MB, time=24.77 memory used=638.4MB, alloc=83.8MB, time=24.82 memory used=647.9MB, alloc=83.8MB, time=24.86 memory used=657.8MB, alloc=83.8MB, time=24.91 memory used=667.9MB, alloc=83.8MB, time=24.95 memory used=678.1MB, alloc=83.8MB, time=24.99 memory used=688.3MB, alloc=83.8MB, time=25.04 memory used=698.3MB, alloc=83.8MB, time=25.08 memory used=709.3MB, alloc=83.8MB, time=25.13 memory used=721.2MB, alloc=83.8MB, time=25.19 memory used=776.3MB, alloc=83.8MB, time=26.17 memory used=827.3MB, alloc=83.8MB, time=27.26 memory used=853.4MB, alloc=83.8MB, time=27.36 memory used=879.6MB, alloc=83.8MB, time=27.51 memory used=928.9MB, alloc=83.8MB, time=28.09 memory used=953.4MB, alloc=83.8MB, time=28.35 memory used=975.2MB, alloc=83.8MB, time=28.52 memory used=999.6MB, alloc=83.8MB, time=28.70 memory used=1030.4MB, alloc=83.8MB, time=28.93 memory used=1048.4MB, alloc=83.8MB, time=29.00 memory used=1066.9MB, alloc=107.8MB, time=29.07 memory used=1105.4MB, alloc=107.8MB, time=29.22 memory used=1144.9MB, alloc=107.8MB, time=29.38 memory used=1192.0MB, alloc=107.8MB, time=29.60 memory used=1231.5MB, alloc=107.8MB, time=29.76 memory used=1271.4MB, alloc=107.8MB, time=29.90 memory used=1306.6MB, alloc=107.8MB, time=29.99 memory used=1347.3MB, alloc=107.8MB, time=30.15 memory used=1386.8MB, alloc=107.8MB, time=30.30 memory used=1433.2MB, alloc=107.8MB, time=30.52 memory used=1471.0MB, alloc=107.8MB, time=30.62 memory used=1502.1MB, alloc=107.8MB, time=30.72 memory used=1540.4MB, alloc=107.8MB, time=30.82 memory used=1584.2MB, alloc=107.8MB, time=30.92 memory used=1610.5MB, alloc=107.8MB, time=30.98 memory used=1637.5MB, alloc=107.8MB, time=31.05 memory used=1667.5MB, alloc=107.8MB, time=31.13 memory used=1699.7MB, alloc=107.8MB, time=31.21 memory used=1735.2MB, alloc=107.8MB, time=31.28 memory used=1773.9MB, alloc=107.8MB, time=31.37 memory used=1816.3MB, alloc=107.8MB, time=31.45 memory used=1873.0MB, alloc=107.8MB, time=31.54 memory used=1883.9MB, alloc=107.8MB, time=31.59 memory used=1893.5MB, alloc=107.8MB, time=31.64 memory used=1903.8MB, alloc=107.8MB, time=31.69 memory used=1914.5MB, alloc=107.8MB, time=31.74 memory used=1925.6MB, alloc=107.8MB, time=31.79 memory used=1977.9MB, alloc=107.8MB, time=32.01 memory used=2009.7MB, alloc=107.8MB, time=32.12 memory used=2046.7MB, alloc=107.8MB, time=32.20 memory used=2090.4MB, alloc=107.8MB, time=32.30 memory used=2117.1MB, alloc=107.8MB, time=32.39 memory used=2146.1MB, alloc=107.8MB, time=32.47 memory used=2177.6MB, alloc=107.8MB, time=32.56 memory used=2212.5MB, alloc=107.8MB, time=32.65 memory used=2252.0MB, alloc=107.8MB, time=32.73 memory used=2296.4MB, alloc=107.8MB, time=32.82 memory used=2315.3MB, alloc=107.8MB, time=32.88 memory used=2325.6MB, alloc=107.8MB, time=32.93 memory used=2383.1MB, alloc=107.8MB, time=33.37 memory used=2421.7MB, alloc=107.8MB, time=33.48 memory used=2454.2MB, alloc=107.8MB, time=33.55 memory used=2486.3MB, alloc=107.8MB, time=33.63 memory used=2525.6MB, alloc=107.8MB, time=33.72 memory used=2581.6MB, alloc=107.8MB, time=34.03 memory used=2623.2MB, alloc=107.8MB, time=34.26 memory used=2660.7MB, alloc=107.8MB, time=34.37 memory used=2699.7MB, alloc=107.8MB, time=34.48 memory used=2729.7MB, alloc=107.8MB, time=34.55 memory used=2781.7MB, alloc=107.8MB, time=34.89 memory used=2821.3MB, alloc=107.8MB, time=35.06 memory used=2865.9MB, alloc=107.8MB, time=35.27 memory used=2900.7MB, alloc=107.8MB, time=35.38 memory used=2939.3MB, alloc=107.8MB, time=35.49 memory used=2975.5MB, alloc=107.8MB, time=35.58 memory used=3004.2MB, alloc=107.8MB, time=35.65 memory used=3037.5MB, alloc=107.8MB, time=35.74 memory used=3082.1MB, alloc=107.8MB, time=35.89 memory used=3117.9MB, alloc=107.8MB, time=36.00 memory used=3155.6MB, alloc=107.8MB, time=36.10 memory used=3190.4MB, alloc=107.8MB, time=36.18 memory used=3220.9MB, alloc=107.8MB, time=36.26 memory used=3274.1MB, alloc=107.8MB, time=36.70 memory used=3310.3MB, alloc=107.8MB, time=36.81 memory used=3348.1MB, alloc=107.8MB, time=36.91 memory used=3378.0MB, alloc=107.8MB, time=36.99 memory used=3414.0MB, alloc=107.8MB, time=37.09 memory used=3472.9MB, alloc=107.8MB, time=37.28 memory used=3514.0MB, alloc=107.8MB, time=37.40 memory used=3545.1MB, alloc=107.8MB, time=37.50 memory used=3586.7MB, alloc=107.8MB, time=37.61 memory used=3616.4MB, alloc=107.8MB, time=37.69 memory used=3662.2MB, alloc=107.8MB, time=38.35 memory used=3699.0MB, alloc=107.8MB, time=38.48 memory used=3740.4MB, alloc=107.8MB, time=38.61 memory used=3766.6MB, alloc=107.8MB, time=38.71 memory used=3795.2MB, alloc=107.8MB, time=38.82 memory used=3828.2MB, alloc=107.8MB, time=38.93 memory used=3863.9MB, alloc=107.8MB, time=39.05 memory used=3902.3MB, alloc=107.8MB, time=39.16 memory used=3946.0MB, alloc=107.8MB, time=39.29 memory used=3982.3MB, alloc=107.8MB, time=39.39 memory used=4005.1MB, alloc=107.8MB, time=39.47 memory used=4028.5MB, alloc=107.8MB, time=39.55 memory used=4053.1MB, alloc=107.8MB, time=39.63 memory used=4078.4MB, alloc=107.8MB, time=39.70 memory used=4104.2MB, alloc=107.8MB, time=39.78 memory used=4130.5MB, alloc=107.8MB, time=39.86 memory used=4157.3MB, alloc=107.8MB, time=39.93 memory used=4184.5MB, alloc=107.8MB, time=40.02 memory used=4212.3MB, alloc=107.8MB, time=40.10 memory used=4240.8MB, alloc=107.8MB, time=40.19 memory used=4272.7MB, alloc=107.8MB, time=40.27 memory used=4305.4MB, alloc=107.8MB, time=40.35 memory used=4338.6MB, alloc=107.8MB, time=40.44 memory used=4372.2MB, alloc=107.8MB, time=40.52 memory used=4406.3MB, alloc=107.8MB, time=40.60 memory used=4440.8MB, alloc=107.8MB, time=40.69 memory used=4479.5MB, alloc=107.8MB, time=40.78 memory used=4518.6MB, alloc=107.8MB, time=40.87 memory used=4558.1MB, alloc=107.8MB, time=40.96 memory used=4598.0MB, alloc=107.8MB, time=41.06 memory used=4638.5MB, alloc=107.8MB, time=41.16 memory used=4685.9MB, alloc=107.8MB, time=41.26 memory used=4706.6MB, alloc=107.8MB, time=41.33 memory used=4714.6MB, alloc=107.8MB, time=41.38 memory used=4721.4MB, alloc=107.8MB, time=41.43 memory used=4728.5MB, alloc=107.8MB, time=41.48 memory used=4732.5MB, alloc=107.8MB, time=41.52 memory used=4736.4MB, alloc=107.8MB, time=41.56 memory used=4740.0MB, alloc=107.8MB, time=41.61 memory used=4743.5MB, alloc=107.8MB, time=41.65 memory used=4747.4MB, alloc=107.8MB, time=41.69 memory used=4751.4MB, alloc=107.8MB, time=41.74 memory used=4755.5MB, alloc=107.8MB, time=41.78 memory used=4759.5MB, alloc=107.8MB, time=41.83 memory used=4763.5MB, alloc=107.8MB, time=41.88 memory used=4767.5MB, alloc=107.8MB, time=41.93 memory used=4771.5MB, alloc=107.8MB, time=41.98 memory used=4775.5MB, alloc=107.8MB, time=42.05 memory used=4779.5MB, alloc=107.8MB, time=42.10 memory used=4783.5MB, alloc=107.8MB, time=42.14 memory used=4787.6MB, alloc=107.8MB, time=42.20 memory used=4791.6MB, alloc=107.8MB, time=42.24 memory used=4795.6MB, alloc=107.8MB, time=42.29 memory used=4799.6MB, alloc=107.8MB, time=42.34 memory used=4803.6MB, alloc=107.8MB, time=42.38 memory used=4807.6MB, alloc=107.8MB, time=42.43 memory used=4811.7MB, alloc=107.8MB, time=42.48 memory used=4815.7MB, alloc=107.8MB, time=42.53 memory used=4819.7MB, alloc=107.8MB, time=42.58 memory used=4823.7MB, alloc=107.8MB, time=42.62 memory used=4827.8MB, alloc=107.8MB, time=42.67 memory used=4831.8MB, alloc=107.8MB, time=42.72 memory used=4835.8MB, alloc=107.8MB, time=42.77 memory used=4839.8MB, alloc=107.8MB, time=42.82 memory used=4843.8MB, alloc=107.8MB, time=42.87 memory used=4847.9MB, alloc=107.8MB, time=42.91 memory used=4852.3MB, alloc=107.8MB, time=42.96 memory used=4856.6MB, alloc=107.8MB, time=43.01 memory used=4864.0MB, alloc=107.8MB, time=43.06 memory used=4868.4MB, alloc=107.8MB, time=43.12 memory used=4872.7MB, alloc=107.8MB, time=43.16 memory used=4880.1MB, alloc=107.8MB, time=43.22 memory used=4884.6MB, alloc=107.8MB, time=43.26 memory used=4892.2MB, alloc=107.8MB, time=43.31 memory used=4896.7MB, alloc=107.8MB, time=43.36 memory used=4904.2MB, alloc=107.8MB, time=43.42 memory used=4908.8MB, alloc=107.8MB, time=43.46 memory used=4916.3MB, alloc=107.8MB, time=43.52 memory used=4921.0MB, alloc=107.8MB, time=43.57 memory used=4928.4MB, alloc=107.8MB, time=43.62 memory used=4933.1MB, alloc=107.8MB, time=43.67 memory used=4940.5MB, alloc=107.8MB, time=43.72 memory used=4945.1MB, alloc=107.8MB, time=43.77 memory used=4952.5MB, alloc=107.8MB, time=43.82 memory used=4960.6MB, alloc=107.8MB, time=43.88 memory used=4968.6MB, alloc=107.8MB, time=43.94 memory used=4976.6MB, alloc=107.8MB, time=43.99 memory used=4984.6MB, alloc=107.8MB, time=44.05 memory used=4992.7MB, alloc=107.8MB, time=44.10 memory used=5000.7MB, alloc=107.8MB, time=44.15 memory used=5008.7MB, alloc=107.8MB, time=44.20 memory used=5016.7MB, alloc=107.8MB, time=44.26 memory used=5024.7MB, alloc=107.8MB, time=44.32 memory used=5032.7MB, alloc=107.8MB, time=44.37 memory used=5040.7MB, alloc=107.8MB, time=44.42 memory used=5048.7MB, alloc=107.8MB, time=44.48 memory used=5056.6MB, alloc=107.8MB, time=44.53 memory used=5064.6MB, alloc=107.8MB, time=44.59 memory used=5072.6MB, alloc=107.8MB, time=44.65 memory used=5080.5MB, alloc=107.8MB, time=44.70 memory used=5088.5MB, alloc=107.8MB, time=44.76 memory used=5096.4MB, alloc=107.8MB, time=44.81 memory used=5104.3MB, alloc=107.8MB, time=44.87 memory used=5112.3MB, alloc=107.8MB, time=44.92 memory used=5120.2MB, alloc=107.8MB, time=44.97 memory used=5128.1MB, alloc=107.8MB, time=45.03 memory used=5136.0MB, alloc=107.8MB, time=45.08 memory used=5143.9MB, alloc=107.8MB, time=45.14 memory used=5151.7MB, alloc=107.8MB, time=45.19 memory used=5159.6MB, alloc=107.8MB, time=45.25 memory used=5167.4MB, alloc=107.8MB, time=45.30 memory used=5175.3MB, alloc=107.8MB, time=45.36 memory used=5183.1MB, alloc=107.8MB, time=45.41 memory used=5190.9MB, alloc=107.8MB, time=45.47 memory used=5198.7MB, alloc=107.8MB, time=45.52 memory 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memory used=5381.7MB, alloc=107.8MB, time=46.71 memory used=5392.9MB, alloc=107.8MB, time=46.76 memory used=5403.9MB, alloc=107.8MB, time=46.83 memory used=5415.0MB, alloc=107.8MB, time=46.89 memory used=5425.9MB, alloc=107.8MB, time=46.94 memory used=5436.8MB, alloc=107.8MB, time=46.99 memory used=5447.7MB, alloc=107.8MB, time=47.05 memory used=5458.5MB, alloc=107.8MB, time=47.11 memory used=5469.3MB, alloc=107.8MB, time=47.16 memory used=5480.0MB, alloc=107.8MB, time=47.22 memory used=5490.7MB, alloc=107.8MB, time=47.28 memory used=5501.3MB, alloc=107.8MB, time=47.33 memory used=5511.9MB, alloc=107.8MB, time=47.39 memory used=5522.4MB, alloc=107.8MB, time=47.45 memory used=5532.8MB, alloc=107.8MB, time=47.50 memory used=5543.2MB, alloc=107.8MB, time=47.56 memory used=5553.5MB, alloc=107.8MB, time=47.61 memory used=5564.4MB, alloc=107.8MB, time=47.66 memory used=5574.9MB, alloc=107.8MB, time=47.72 memory used=5587.5MB, alloc=107.8MB, time=47.77 memory used=5598.5MB, alloc=107.8MB, time=47.82 memory used=5610.9MB, alloc=107.8MB, time=47.88 memory used=5624.1MB, alloc=107.8MB, time=47.94 memory used=5637.2MB, alloc=107.8MB, time=48.01 memory used=5650.1MB, alloc=107.8MB, time=48.06 memory used=5662.9MB, alloc=107.8MB, time=48.12 memory used=5675.6MB, alloc=107.8MB, time=48.18 memory used=5688.2MB, alloc=107.8MB, time=48.24 memory used=5700.6MB, alloc=107.8MB, time=48.29 memory used=5713.0MB, alloc=107.8MB, time=48.35 memory used=5725.8MB, alloc=107.8MB, time=48.41 memory used=5740.2MB, alloc=107.8MB, time=48.47 memory used=5755.0MB, alloc=107.8MB, time=48.54 memory used=5769.5MB, alloc=107.8MB, time=48.60 memory used=5783.9MB, alloc=107.8MB, time=48.66 memory used=5798.0MB, alloc=107.8MB, time=48.71 memory used=5812.0MB, alloc=107.8MB, time=48.78 memory used=5826.4MB, alloc=107.8MB, time=48.84 memory used=5841.7MB, alloc=107.8MB, time=48.91 memory used=5857.3MB, alloc=107.8MB, time=48.97 memory used=5872.6MB, alloc=107.8MB, time=49.03 memory used=5888.3MB, alloc=107.8MB, time=49.09 memory used=5904.5MB, alloc=107.8MB, time=49.15 memory used=5920.8MB, alloc=107.8MB, time=49.22 memory used=5937.7MB, alloc=107.8MB, time=49.28 memory used=5954.9MB, alloc=107.8MB, time=49.34 memory used=5972.7MB, alloc=107.8MB, time=49.40 memory used=5989.1MB, alloc=107.8MB, time=49.47 memory used=6001.6MB, alloc=107.8MB, time=49.52 memory used=6014.2MB, alloc=107.8MB, time=49.58 memory used=6026.8MB, alloc=107.8MB, time=49.63 memory used=6039.7MB, alloc=107.8MB, time=49.69 memory used=6116.3MB, alloc=107.8MB, time=51.93 memory used=6191.5MB, alloc=107.8MB, time=52.51 memory used=6244.9MB, alloc=107.8MB, time=52.81 memory used=6280.6MB, alloc=107.8MB, time=52.93 memory used=6309.8MB, alloc=107.8MB, time=53.03 memory used=6344.6MB, alloc=107.8MB, time=53.15 memory used=6385.6MB, alloc=107.8MB, time=53.26 memory used=6420.1MB, alloc=107.8MB, time=53.36 memory used=6444.8MB, alloc=107.8MB, time=53.45 memory used=6469.4MB, alloc=107.8MB, time=53.53 memory 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memory used=6947.3MB, alloc=107.8MB, time=55.10 memory used=6955.1MB, alloc=107.8MB, time=55.16 memory used=6963.0MB, alloc=107.8MB, time=55.22 memory used=6970.8MB, alloc=107.8MB, time=55.27 memory used=6978.7MB, alloc=107.8MB, time=55.32 memory used=6986.6MB, alloc=107.8MB, time=55.36 memory used=6994.5MB, alloc=107.8MB, time=55.41 memory used=7002.4MB, alloc=107.8MB, time=55.45 memory used=7010.3MB, alloc=107.8MB, time=55.50 memory used=7018.2MB, alloc=107.8MB, time=55.55 memory used=7026.1MB, alloc=107.8MB, time=55.59 memory used=7034.0MB, alloc=107.8MB, time=55.64 memory used=7042.0MB, alloc=107.8MB, time=55.68 memory used=7049.9MB, alloc=107.8MB, time=55.73 memory used=7057.9MB, alloc=107.8MB, time=55.77 memory used=7065.9MB, alloc=107.8MB, time=55.82 memory used=7073.8MB, alloc=107.8MB, time=55.87 memory used=7081.8MB, alloc=107.8MB, time=55.92 memory used=7089.8MB, alloc=107.8MB, time=55.97 memory used=7097.7MB, alloc=107.8MB, time=56.01 memory used=7105.7MB, alloc=107.8MB, time=56.07 memory used=7113.9MB, alloc=107.8MB, time=56.12 memory used=7122.1MB, alloc=107.8MB, time=56.17 memory used=7132.4MB, alloc=107.8MB, time=56.22 memory used=7140.7MB, alloc=107.8MB, time=56.27 memory used=7151.0MB, alloc=107.8MB, time=56.32 memory used=7161.7MB, alloc=107.8MB, time=56.37 memory used=7172.3MB, alloc=107.8MB, time=56.42 memory used=7183.0MB, alloc=107.8MB, time=56.47 memory used=7193.6MB, alloc=107.8MB, time=56.52 memory used=7204.3MB, alloc=107.8MB, time=56.57 memory used=7214.9MB, alloc=107.8MB, time=56.62 memory used=7225.5MB, alloc=107.8MB, time=56.68 memory used=7236.2MB, alloc=107.8MB, time=56.73 memory used=7246.8MB, alloc=107.8MB, time=56.78 memory used=7257.4MB, alloc=107.8MB, time=56.84 memory used=7268.0MB, alloc=107.8MB, time=56.88 memory used=7278.5MB, alloc=107.8MB, time=56.93 memory used=7289.1MB, alloc=107.8MB, time=56.98 memory used=7299.7MB, alloc=107.8MB, time=57.03 memory used=7310.2MB, alloc=107.8MB, time=57.07 memory used=7320.7MB, alloc=107.8MB, time=57.12 memory used=7331.2MB, alloc=107.8MB, time=57.17 memory used=7341.7MB, alloc=107.8MB, time=57.22 memory used=7352.1MB, alloc=107.8MB, time=57.27 memory used=7362.8MB, alloc=107.8MB, time=57.32 memory used=7375.5MB, alloc=107.8MB, time=57.38 memory used=7388.5MB, alloc=107.8MB, time=57.43 memory used=7401.4MB, alloc=107.8MB, time=57.48 memory used=7414.3MB, alloc=107.8MB, time=57.53 memory used=7427.1MB, alloc=107.8MB, time=57.58 memory used=7439.9MB, alloc=107.8MB, time=57.63 memory used=7452.6MB, alloc=107.8MB, time=57.69 memory used=7465.3MB, alloc=107.8MB, time=57.75 memory used=7477.9MB, alloc=107.8MB, time=57.80 memory used=7490.5MB, alloc=107.8MB, time=57.85 memory used=7503.0MB, alloc=107.8MB, time=57.91 memory used=7515.4MB, alloc=107.8MB, time=57.96 memory used=7528.1MB, alloc=107.8MB, time=58.02 memory used=7542.5MB, alloc=107.8MB, time=58.07 memory used=7557.2MB, alloc=107.8MB, time=58.14 memory used=7571.7MB, alloc=107.8MB, time=58.19 memory used=7586.1MB, alloc=107.8MB, time=58.26 memory used=7600.4MB, alloc=107.8MB, time=58.31 memory used=7614.6MB, alloc=107.8MB, time=58.36 memory used=7628.7MB, alloc=107.8MB, time=58.42 memory used=7643.0MB, alloc=107.8MB, time=58.47 memory used=7658.9MB, alloc=107.8MB, time=58.52 memory used=7674.9MB, alloc=107.8MB, time=58.58 memory used=7690.6MB, alloc=107.8MB, time=58.63 memory used=7706.1MB, alloc=107.8MB, time=58.68 memory used=7721.9MB, alloc=107.8MB, time=58.73 memory used=7738.8MB, alloc=107.8MB, time=58.79 memory used=7755.8MB, alloc=107.8MB, time=58.85 memory used=7772.5MB, alloc=107.8MB, time=58.91 memory used=7789.3MB, alloc=107.8MB, time=58.96 memory used=7806.5MB, alloc=107.8MB, time=59.02 memory used=7821.3MB, alloc=107.8MB, time=59.07 memory used=7836.6MB, alloc=107.8MB, time=59.12 memory used=7851.5MB, alloc=107.8MB, time=59.17 memory used=7865.3MB, alloc=107.8MB, time=59.22 memory used=7876.9MB, alloc=107.8MB, time=59.27 memory used=7888.8MB, alloc=107.8MB, time=59.31 memory used=7900.6MB, alloc=107.8MB, time=59.36 memory used=7912.7MB, alloc=107.8MB, time=59.41 memory used=7925.4MB, alloc=107.8MB, time=59.47 memory used=7938.0MB, alloc=107.8MB, time=59.53 memory used=7950.9MB, alloc=107.8MB, time=59.58 memory used=7964.2MB, alloc=107.8MB, time=59.64 memory used=7977.9MB, alloc=107.8MB, time=59.70 memory used=7991.8MB, alloc=107.8MB, time=59.74 memory used=8006.4MB, alloc=107.8MB, time=59.80 memory used=8021.5MB, alloc=107.8MB, time=59.85 memory used=8083.1MB, alloc=107.8MB, time=60.46 memory used=8121.8MB, alloc=107.8MB, time=60.66 memory used=8161.3MB, alloc=107.8MB, time=60.79 memory used=8196.5MB, alloc=107.8MB, time=60.89 memory used=8226.9MB, alloc=107.8MB, time=61.00 memory used=8262.9MB, alloc=107.8MB, time=61.12 memory used=8305.2MB, alloc=107.8MB, time=61.22 memory used=8339.5MB, alloc=107.8MB, time=61.32 memory used=8364.4MB, alloc=107.8MB, time=61.38 memory used=8391.2MB, alloc=107.8MB, time=61.45 memory used=8420.5MB, alloc=107.8MB, time=61.52 memory used=8452.0MB, alloc=107.8MB, time=61.60 memory used=8486.4MB, alloc=107.8MB, time=61.67 memory used=8524.3MB, alloc=107.8MB, time=61.74 memory used=8565.8MB, alloc=107.8MB, time=61.83 memory used=8613.6MB, alloc=107.8MB, time=62.04 memory used=8649.6MB, alloc=107.8MB, time=62.15 memory used=8684.1MB, alloc=107.8MB, time=62.27 memory used=8724.1MB, alloc=107.8MB, time=62.37 memory used=8751.4MB, alloc=107.8MB, time=62.44 memory used=8804.9MB, alloc=131.8MB, time=75.36 memory used=8827.3MB, alloc=131.8MB, time=88.37 memory used=8833.5MB, alloc=131.8MB, time=88.42 memory used=8837.2MB, alloc=131.8MB, time=88.46 memory used=8838.1MB, alloc=387.8MB, time=88.50 memory used=9053.8MB, alloc=387.8MB, time=180.48 memory used=9252.8MB, alloc=387.8MB, time=180.89 memory used=9412.3MB, alloc=387.8MB, time=181.14 memory used=9591.8MB, alloc=387.8MB, time=181.42 memory used=9794.2MB, alloc=387.8MB, time=181.74 memory used=10018.6MB, alloc=387.8MB, time=182.07 memory used=10271.2MB, alloc=387.8MB, time=182.41 memory used=10466.5MB, alloc=387.8MB, time=182.67 memory used=10683.6MB, alloc=387.8MB, time=183.19 memory used=10732.3MB, alloc=387.8MB, time=183.33 memory used=10779.8MB, alloc=387.8MB, time=183.45 memory used=10841.1MB, alloc=387.8MB, time=183.58 memory used=10879.9MB, alloc=387.8MB, time=183.68 memory used=10931.7MB, alloc=387.8MB, time=185.94 memory used=10981.2MB, alloc=387.8MB, time=187.86 memory used=11019.8MB, alloc=411.8MB, time=188.01 memory used=11081.7MB, alloc=411.8MB, time=188.21 memory used=11153.0MB, alloc=411.8MB, time=188.41 memory used=11206.1MB, alloc=411.8MB, time=188.56 memory used=11246.4MB, alloc=411.8MB, time=188.69 memory used=11288.9MB, alloc=411.8MB, time=188.81 memory used=11331.0MB, alloc=411.8MB, time=188.93 memory used=11374.8MB, alloc=411.8MB, time=189.06 memory used=11420.4MB, alloc=411.8MB, time=189.21 memory used=11467.7MB, alloc=411.8MB, time=189.37 memory used=11516.7MB, alloc=411.8MB, time=189.51 memory used=11567.4MB, alloc=411.8MB, time=189.67 memory used=11619.7MB, alloc=411.8MB, time=189.84 memory used=11673.7MB, alloc=411.8MB, time=190.00 memory used=11729.2MB, alloc=411.8MB, time=190.15 memory used=11786.3MB, alloc=411.8MB, time=190.32 memory used=11845.0MB, alloc=411.8MB, time=190.48 memory used=11905.3MB, alloc=411.8MB, time=190.64 memory used=11967.1MB, alloc=411.8MB, time=190.81 memory used=12025.5MB, alloc=435.8MB, time=190.97 memory used=12079.7MB, alloc=435.8MB, time=191.11 memory used=12122.5MB, alloc=435.8MB, time=191.24 memory used=12164.0MB, alloc=435.8MB, time=191.36 memory used=12207.8MB, alloc=435.8MB, time=191.48 memory used=12253.2MB, alloc=435.8MB, time=191.61 memory used=12299.3MB, alloc=435.8MB, time=191.73 memory used=12346.0MB, alloc=435.8MB, time=191.86 memory used=12393.3MB, alloc=435.8MB, time=191.99 memory used=12441.2MB, alloc=435.8MB, time=192.12 memory used=12489.7MB, alloc=435.8MB, time=192.24 memory used=12538.9MB, alloc=435.8MB, time=192.37 memory used=12588.6MB, alloc=435.8MB, time=192.50 memory used=12638.9MB, alloc=435.8MB, time=192.63 memory used=12689.7MB, alloc=435.8MB, time=192.76 memory used=12741.1MB, alloc=435.8MB, time=192.90 memory used=12793.1MB, alloc=435.8MB, time=193.02 memory used=12845.7MB, alloc=435.8MB, time=193.16 memory used=12898.7MB, alloc=435.8MB, time=193.29 memory used=12952.4MB, alloc=435.8MB, time=193.42 memory used=13006.5MB, alloc=435.8MB, time=193.56 memory used=13061.2MB, alloc=435.8MB, time=193.69 memory used=13116.5MB, alloc=435.8MB, time=193.82 memory used=13172.2MB, alloc=435.8MB, time=193.95 memory used=13228.4MB, alloc=435.8MB, time=194.09 memory used=13285.2MB, alloc=435.8MB, time=194.22 memory used=13342.5MB, alloc=435.8MB, time=194.36 memory used=13400.2MB, alloc=435.8MB, time=194.49 memory used=13458.4MB, alloc=459.8MB, time=194.63 memory used=13536.5MB, alloc=459.8MB, time=194.79 memory used=13625.8MB, alloc=459.8MB, time=194.97 memory used=13716.2MB, alloc=459.8MB, time=195.15 memory used=13807.6MB, alloc=459.8MB, time=195.33 memory used=13900.0MB, alloc=459.8MB, time=195.52 memory used=13993.4MB, alloc=459.8MB, time=195.70 memory used=14087.8MB, alloc=459.8MB, time=195.89 memory used=14183.2MB, alloc=459.8MB, time=196.07 memory used=14279.4MB, alloc=459.8MB, time=196.27 memory used=14376.6MB, alloc=459.8MB, time=196.46 memory used=14474.7MB, alloc=459.8MB, time=196.65 memory used=14573.6MB, alloc=459.8MB, time=196.84 memory used=14673.3MB, alloc=459.8MB, time=197.02 memory used=14773.9MB, alloc=459.8MB, time=197.20 memory used=14875.3MB, alloc=459.8MB, time=197.39 memory used=15077.7MB, alloc=459.8MB, time=197.74 memory used=15195.9MB, alloc=459.8MB, time=197.99 memory used=15313.2MB, alloc=459.8MB, time=198.26 memory used=15436.1MB, alloc=459.8MB, time=198.51 memory used=15560.0MB, alloc=459.8MB, time=198.76 memory used=15684.7MB, alloc=459.8MB, time=199.02 memory used=15810.3MB, alloc=459.8MB, time=199.26 memory used=15936.7MB, alloc=459.8MB, time=199.53 memory used=16063.9MB, alloc=459.8MB, time=199.79 memory used=16191.9MB, alloc=459.8MB, time=200.05 memory used=16321.9MB, alloc=459.8MB, time=200.31 memory used=16468.5MB, alloc=459.8MB, time=200.58 memory used=16617.3MB, alloc=459.8MB, time=200.86 memory used=16766.9MB, alloc=459.8MB, time=201.15 memory used=16917.2MB, alloc=459.8MB, time=201.42 memory used=17068.2MB, alloc=459.8MB, time=201.72 memory used=17219.9MB, alloc=459.8MB, time=202.01 memory used=17372.2MB, alloc=459.8MB, time=202.30 memory used=17524.9MB, alloc=459.8MB, time=202.59 memory used=17678.3MB, alloc=459.8MB, time=202.89 memory used=17833.8MB, alloc=459.8MB, time=203.19 memory used=18005.7MB, alloc=459.8MB, time=203.50 memory used=18179.7MB, alloc=459.8MB, time=203.81 memory used=18354.1MB, alloc=459.8MB, time=204.12 memory used=18528.7MB, alloc=459.8MB, time=204.44 memory used=18703.6MB, alloc=459.8MB, time=204.75 memory used=18878.7MB, alloc=459.8MB, time=205.05 memory used=19055.5MB, alloc=459.8MB, time=205.37 memory used=19248.8MB, alloc=459.8MB, time=205.71 memory used=19443.4MB, alloc=459.8MB, time=206.04 memory used=19637.9MB, alloc=459.8MB, time=206.38 memory used=19832.1MB, alloc=459.8MB, time=206.71 memory used=20026.2MB, alloc=459.8MB, time=207.06 memory used=20239.1MB, alloc=459.8MB, time=207.42 memory used=20451.3MB, alloc=459.8MB, time=207.78 memory used=20662.7MB, alloc=459.8MB, time=208.13 memory used=20873.3MB, alloc=459.8MB, time=208.50 memory used=21101.9MB, alloc=459.8MB, time=208.88 memory used=21329.0MB, alloc=459.8MB, time=209.25 memory used=21554.6MB, alloc=459.8MB, time=209.61 memory used=21781.2MB, alloc=459.8MB, time=209.97 memory used=22019.0MB, alloc=459.8MB, time=210.35 memory used=22248.2MB, alloc=459.8MB, time=210.72 memory used=22467.0MB, alloc=459.8MB, time=211.08 memory used=22673.2MB, alloc=459.8MB, time=211.42 memory used=22846.5MB, alloc=459.8MB, time=211.71 memory used=23016.6MB, alloc=459.8MB, time=211.98 memory used=23188.1MB, alloc=459.8MB, time=212.27 memory used=23357.5MB, alloc=459.8MB, time=212.55 memory used=23524.8MB, alloc=459.8MB, time=212.84 memory used=23706.2MB, alloc=459.8MB, time=213.15 memory used=23884.6MB, alloc=459.8MB, time=213.44 memory used=24062.3MB, alloc=459.8MB, time=213.73 memory used=24248.0MB, alloc=459.8MB, time=214.03 memory used=24432.1MB, alloc=459.8MB, time=214.33 memory used=24626.8MB, alloc=459.8MB, time=214.64 memory used=24818.9MB, alloc=459.8MB, time=214.95 memory used=25015.3MB, alloc=459.8MB, time=215.25 memory used=25221.3MB, alloc=459.8MB, time=215.56 memory used=25432.8MB, alloc=459.8MB, time=215.88 memory used=25647.7MB, alloc=459.8MB, time=216.19 memory used=25866.4MB, alloc=459.8MB, time=216.50 memory used=26090.0MB, alloc=459.8MB, time=216.84 memory used=26323.0MB, alloc=459.8MB, time=217.17 memory used=26567.1MB, alloc=459.8MB, time=217.49 memory used=26823.7MB, alloc=459.8MB, time=217.82 memory used=27000.0MB, alloc=459.8MB, time=218.96 memory used=27121.1MB, alloc=459.8MB, time=219.52 memory used=27266.8MB, alloc=459.8MB, time=219.81 memory used=27501.6MB, alloc=459.8MB, time=221.04 memory used=27740.1MB, alloc=459.8MB, time=221.41 memory used=28014.1MB, alloc=459.8MB, time=221.81 memory used=28310.8MB, alloc=459.8MB, time=226.84 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428528331 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 F := [-2 y z - 8 x z + 13 x y , -5 x + 8 y + 11] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 2 2 G := [17 x - y z + 6 x z , -12 y z - 15 x z - 4 x] > Problem := [F,G]; 3 2 2 2 Problem := [[-2 y z - 8 x z + 13 x y , -5 x + 8 y + 11], 4 3 2 2 [17 x - y z + 6 x z , -12 y z - 15 x z - 4 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.2MB, alloc=32.3MB, time=0.51 memory used=46.1MB, alloc=56.3MB, time=0.81 memory used=82.5MB, alloc=60.3MB, time=1.29 memory used=125.9MB, alloc=68.3MB, time=1.85 memory used=168.5MB, alloc=92.3MB, time=2.40 memory used=235.3MB, alloc=92.3MB, time=3.24 memory used=280.5MB, alloc=92.3MB, time=3.89 memory used=344.2MB, alloc=92.3MB, time=5.17 memory used=413.7MB, alloc=92.3MB, time=6.00 memory used=480.1MB, alloc=116.3MB, time=6.85 memory used=549.8MB, alloc=372.3MB, time=7.81 memory used=633.9MB, alloc=372.3MB, time=8.75 memory used=692.2MB, alloc=396.3MB, time=9.69 memory used=749.7MB, alloc=396.3MB, time=9.92 memory used=805.4MB, alloc=396.3MB, time=10.12 memory used=866.0MB, alloc=396.3MB, time=10.33 memory used=908.5MB, alloc=396.3MB, time=10.51 memory used=949.8MB, alloc=396.3MB, time=10.69 memory used=996.6MB, alloc=396.3MB, time=10.85 memory used=1046.2MB, alloc=396.3MB, time=11.04 memory used=1101.2MB, alloc=396.3MB, time=11.25 memory used=1158.5MB, alloc=396.3MB, time=11.43 memory used=1221.2MB, alloc=396.3MB, time=11.63 memory used=1286.3MB, alloc=396.3MB, time=11.81 memory used=1329.7MB, alloc=396.3MB, time=11.97 memory used=1366.9MB, alloc=396.3MB, time=12.11 memory used=1403.3MB, alloc=396.3MB, time=12.25 memory used=1441.4MB, alloc=396.3MB, time=12.39 memory used=1479.7MB, alloc=396.3MB, time=12.53 memory used=1518.1MB, alloc=396.3MB, time=12.67 memory used=1560.2MB, alloc=396.3MB, time=12.82 memory used=1602.3MB, alloc=396.3MB, time=12.97 memory used=1647.7MB, alloc=396.3MB, time=13.12 memory used=1692.8MB, alloc=396.3MB, time=13.27 memory used=1741.1MB, alloc=396.3MB, time=13.43 memory used=1792.1MB, alloc=396.3MB, time=13.57 memory used=1845.6MB, alloc=396.3MB, time=13.73 memory used=1900.9MB, alloc=396.3MB, time=13.88 memory used=1957.6MB, alloc=396.3MB, time=14.03 memory used=2017.8MB, alloc=396.3MB, time=14.17 memory used=2080.5MB, alloc=396.3MB, time=14.32 memory used=2153.4MB, alloc=396.3MB, time=14.51 memory used=2296.0MB, alloc=396.3MB, time=15.68 memory used=2346.6MB, alloc=396.3MB, time=15.90 memory used=2409.8MB, alloc=396.3MB, time=16.14 memory used=2457.1MB, alloc=396.3MB, time=16.34 memory used=2498.7MB, alloc=396.3MB, time=16.52 memory used=2540.6MB, alloc=396.3MB, time=16.69 memory used=2588.7MB, alloc=396.3MB, time=16.89 memory used=2639.2MB, alloc=396.3MB, time=17.07 memory used=2695.1MB, alloc=396.3MB, time=17.24 memory used=2753.2MB, alloc=396.3MB, time=17.43 memory used=2816.6MB, alloc=396.3MB, time=17.62 memory used=2873.9MB, alloc=396.3MB, time=17.80 memory used=2913.3MB, alloc=420.3MB, time=17.95 memory used=2960.4MB, alloc=420.3MB, time=18.10 memory used=3009.3MB, alloc=420.3MB, time=18.26 memory used=3060.0MB, alloc=420.3MB, time=18.43 memory used=3114.1MB, alloc=420.3MB, time=18.59 memory used=3172.2MB, alloc=420.3MB, time=18.76 memory used=3233.6MB, alloc=420.3MB, time=18.92 memory used=3298.1MB, alloc=420.3MB, time=19.09 memory used=3365.1MB, alloc=420.3MB, time=19.26 memory used=3437.5MB, alloc=420.3MB, time=19.44 memory used=3514.0MB, alloc=420.3MB, time=19.62 memory used=3593.3MB, alloc=420.3MB, time=19.80 memory used=3680.6MB, alloc=420.3MB, time=19.98 memory used=3853.0MB, alloc=420.3MB, time=33.55 memory used=3965.9MB, alloc=420.3MB, time=65.59 memory used=4104.0MB, alloc=420.3MB, time=66.37 memory used=4171.3MB, alloc=420.3MB, time=66.58 memory used=4252.0MB, alloc=420.3MB, time=66.80 memory used=4310.6MB, alloc=420.3MB, time=66.98 memory used=4367.4MB, alloc=420.3MB, time=67.15 memory used=4431.5MB, alloc=420.3MB, time=67.33 memory used=4504.2MB, alloc=420.3MB, time=67.51 memory used=4586.5MB, alloc=420.3MB, time=67.72 memory used=4786.7MB, alloc=420.3MB, time=68.15 memory used=5018.0MB, alloc=420.3MB, time=69.00 memory used=5170.9MB, alloc=420.3MB, time=71.09 memory used=5337.8MB, alloc=420.3MB, time=72.45 memory used=5479.5MB, alloc=420.3MB, time=74.24 memory used=5626.2MB, alloc=420.3MB, time=78.11 memory used=5687.6MB, alloc=420.3MB, time=78.37 memory used=5737.5MB, alloc=420.3MB, time=78.57 memory used=5816.9MB, alloc=420.3MB, time=79.03 memory used=5984.8MB, alloc=420.3MB, time=80.75 memory used=6042.9MB, alloc=420.3MB, time=81.01 memory used=6100.2MB, alloc=444.3MB, time=81.26 memory used=6160.8MB, alloc=444.3MB, time=81.49 memory used=6236.0MB, alloc=444.3MB, time=81.74 memory used=6326.5MB, alloc=444.3MB, time=82.00 memory used=6476.3MB, alloc=444.3MB, time=82.38 memory used=6645.1MB, alloc=444.3MB, time=82.77 memory used=6848.0MB, alloc=444.3MB, time=83.19 memory used=7059.9MB, alloc=444.3MB, time=83.61 memory used=7248.3MB, alloc=444.3MB, time=83.99 memory used=7520.0MB, alloc=444.3MB, time=85.93 memory used=7687.0MB, alloc=444.3MB, time=87.92 memory used=7845.2MB, alloc=444.3MB, time=89.04 memory used=8008.5MB, alloc=444.3MB, time=90.29 memory used=8176.6MB, alloc=468.3MB, time=91.82 memory used=8383.4MB, alloc=468.3MB, time=92.68 memory used=8584.8MB, alloc=468.3MB, time=93.26 memory used=8770.5MB, alloc=468.3MB, time=93.76 memory used=9025.1MB, alloc=468.3MB, time=95.01 memory used=9231.3MB, alloc=468.3MB, time=97.26 memory used=9415.8MB, alloc=468.3MB, time=98.72 memory used=9620.6MB, alloc=468.3MB, time=99.57 memory used=9819.7MB, alloc=468.3MB, time=100.13 memory used=9998.6MB, alloc=468.3MB, time=100.63 memory used=10191.7MB, alloc=468.3MB, time=101.16 memory used=10387.5MB, alloc=468.3MB, time=101.67 memory used=10599.3MB, alloc=468.3MB, time=102.21 memory used=10820.3MB, alloc=468.3MB, time=102.75 memory used=11089.2MB, alloc=468.3MB, time=104.52 memory used=11247.0MB, alloc=468.3MB, time=105.45 memory used=11420.6MB, alloc=468.3MB, time=106.54 memory used=11598.4MB, alloc=468.3MB, time=107.72 memory used=11759.3MB, alloc=468.3MB, time=108.21 memory used=11944.1MB, alloc=468.3MB, time=108.76 memory used=12109.6MB, alloc=468.3MB, time=109.26 memory used=12320.1MB, alloc=468.3MB, time=110.47 memory used=12444.2MB, alloc=468.3MB, time=110.95 memory used=12601.3MB, alloc=468.3MB, time=111.43 memory used=12800.9MB, alloc=468.3MB, time=111.96 memory used=13057.9MB, alloc=468.3MB, time=112.60 memory used=13368.5MB, alloc=468.3MB, time=113.37 memory used=13571.7MB, alloc=468.3MB, time=114.17 memory used=13769.8MB, alloc=468.3MB, time=115.11 memory used=13933.6MB, alloc=468.3MB, time=116.09 memory used=14051.7MB, alloc=468.3MB, time=116.58 memory used=14200.5MB, alloc=468.3MB, time=117.06 memory used=14348.9MB, alloc=468.3MB, time=117.55 memory used=14506.3MB, alloc=468.3MB, time=117.98 memory used=14675.0MB, alloc=468.3MB, time=118.47 memory used=14851.3MB, alloc=468.3MB, time=118.91 memory used=15040.1MB, alloc=468.3MB, time=119.38 memory used=15240.0MB, alloc=468.3MB, time=119.89 memory used=15445.9MB, alloc=468.3MB, time=120.36 memory used=15674.5MB, alloc=468.3MB, time=120.89 memory used=15938.9MB, alloc=468.3MB, time=121.49 memory used=16298.1MB, alloc=468.3MB, time=122.25 memory used=16684.2MB, alloc=468.3MB, time=122.97 memory used=17020.5MB, alloc=468.3MB, time=123.66 memory used=17360.9MB, alloc=468.3MB, time=124.39 memory used=17703.8MB, alloc=468.3MB, time=125.13 memory used=18050.7MB, alloc=468.3MB, time=125.86 memory used=18370.7MB, alloc=468.3MB, time=126.63 memory used=18708.3MB, alloc=468.3MB, time=127.49 memory used=19061.3MB, alloc=468.3MB, time=128.37 memory used=19408.3MB, alloc=468.3MB, time=129.13 memory used=19741.5MB, alloc=468.3MB, time=129.96 memory used=20029.5MB, alloc=468.3MB, time=131.26 memory used=20226.0MB, alloc=468.3MB, time=132.28 memory used=20353.1MB, alloc=468.3MB, time=132.78 memory used=20552.9MB, alloc=468.3MB, time=133.65 memory used=20758.0MB, alloc=468.3MB, time=134.55 memory used=20948.6MB, alloc=468.3MB, time=135.31 memory used=21124.3MB, alloc=468.3MB, time=136.00 memory used=21315.0MB, alloc=468.3MB, time=136.92 memory used=21520.5MB, alloc=468.3MB, time=137.75 memory used=21716.4MB, alloc=468.3MB, time=138.53 memory used=21897.4MB, alloc=468.3MB, time=139.25 memory used=22077.7MB, alloc=468.3MB, time=140.18 memory used=22209.0MB, alloc=468.3MB, time=140.63 memory used=22367.5MB, alloc=468.3MB, time=141.11 memory used=22538.8MB, alloc=468.3MB, time=141.57 memory used=22726.3MB, alloc=468.3MB, time=142.06 memory used=23057.1MB, alloc=468.3MB, time=142.69 memory used=23431.3MB, alloc=468.3MB, time=143.39 memory used=23799.1MB, alloc=468.3MB, time=144.09 memory used=24166.4MB, alloc=468.3MB, time=144.76 memory used=24530.7MB, alloc=468.3MB, time=145.43 memory used=24891.9MB, alloc=468.3MB, time=146.07 memory used=25258.0MB, alloc=468.3MB, time=146.82 memory used=25623.4MB, alloc=468.3MB, time=147.58 memory used=25989.9MB, alloc=468.3MB, time=148.29 memory used=26362.4MB, alloc=468.3MB, time=149.04 memory used=26783.3MB, alloc=468.3MB, time=150.36 memory used=26951.2MB, alloc=492.3MB, time=151.88 memory used=27153.2MB, alloc=492.3MB, time=154.22 memory used=27393.7MB, alloc=516.3MB, time=157.30 memory used=27649.9MB, alloc=516.3MB, time=160.47 memory used=27884.6MB, alloc=540.3MB, time=163.55 memory used=28071.5MB, alloc=540.3MB, time=165.79 memory used=28270.4MB, alloc=564.3MB, time=168.06 memory used=28450.0MB, alloc=588.3MB, time=170.19 memory used=28643.3MB, alloc=588.3MB, time=172.54 memory used=28846.8MB, alloc=612.3MB, time=174.96 memory used=29026.6MB, alloc=612.3MB, time=177.28 memory used=30762.9MB, alloc=612.3MB, time=245.87 memory used=31752.7MB, alloc=612.3MB, time=248.52 memory used=32719.0MB, alloc=612.3MB, time=284.30 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428528631 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [13 x z + 4 x - 2 z, 4 y z - 14 z - 4] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 4 2 2 2 2 3 G := [10 x y + 10 y - 8 y z , -5 y z + 3 y z - 20 z ] > Problem := [F,G]; 2 2 Problem := [[13 x z + 4 x - 2 z, 4 y z - 14 z - 4], 3 4 2 2 2 2 3 [10 x y + 10 y - 8 y z , -5 y z + 3 y z - 20 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.5MB, alloc=32.3MB, time=0.49 memory used=47.0MB, alloc=32.3MB, time=0.77 memory used=65.6MB, alloc=56.3MB, time=1.05 memory used=103.0MB, alloc=60.3MB, time=1.61 memory used=141.5MB, alloc=84.3MB, time=2.18 memory used=200.0MB, alloc=92.3MB, time=3.07 memory used=264.5MB, alloc=92.3MB, time=3.98 memory used=323.3MB, alloc=116.3MB, time=4.88 memory used=403.6MB, alloc=116.3MB, time=6.08 memory used=472.9MB, alloc=116.3MB, time=7.02 memory used=551.1MB, alloc=140.3MB, time=8.29 memory used=628.2MB, alloc=140.3MB, time=9.38 memory used=706.2MB, alloc=396.3MB, time=10.49 memory used=800.5MB, alloc=396.3MB, time=11.53 memory used=910.1MB, alloc=420.3MB, time=12.97 memory used=1046.4MB, alloc=420.3MB, time=14.60 memory used=1181.4MB, alloc=444.3MB, time=16.32 memory used=1346.5MB, alloc=444.3MB, time=18.52 memory used=1508.1MB, alloc=468.3MB, time=20.78 memory used=1694.6MB, alloc=468.3MB, time=22.91 memory used=1875.2MB, alloc=492.3MB, time=24.78 memory used=2076.5MB, alloc=492.3MB, time=26.82 memory used=2257.8MB, alloc=516.3MB, time=28.91 memory used=2455.1MB, alloc=540.3MB, time=31.27 memory used=2667.2MB, alloc=564.3MB, time=33.94 memory used=2884.2MB, alloc=588.3MB, time=36.97 memory used=3128.9MB, alloc=612.3MB, time=40.09 memory used=3380.8MB, alloc=636.3MB, time=43.46 memory used=3648.4MB, alloc=660.3MB, time=47.10 memory used=3884.3MB, alloc=684.3MB, time=50.57 memory used=4162.2MB, alloc=708.3MB, time=54.61 memory used=4404.5MB, alloc=732.3MB, time=58.39 memory used=4614.5MB, alloc=756.3MB, time=61.86 memory used=4853.5MB, alloc=780.3MB, time=65.41 memory used=5033.1MB, alloc=804.3MB, time=68.31 memory used=5382.9MB, alloc=828.3MB, time=73.17 memory used=5733.2MB, alloc=852.3MB, time=78.31 memory used=6109.0MB, alloc=876.3MB, time=83.11 memory used=6490.0MB, alloc=900.3MB, time=88.35 memory used=6872.7MB, alloc=924.3MB, time=93.89 memory used=7211.6MB, alloc=948.3MB, time=100.82 memory used=7492.3MB, alloc=972.3MB, time=109.57 memory used=7775.7MB, alloc=996.3MB, time=118.67 memory used=8067.8MB, alloc=1020.3MB, time=128.30 memory used=8370.2MB, alloc=1044.3MB, time=138.69 memory used=8684.1MB, alloc=1068.3MB, time=149.60 memory used=9010.9MB, alloc=1092.3MB, time=160.91 memory used=9351.0MB, alloc=1116.3MB, time=172.86 memory used=9704.8MB, alloc=1140.3MB, time=185.37 memory used=10072.7MB, alloc=1164.3MB, time=198.41 memory used=10454.3MB, alloc=1188.3MB, time=211.81 memory used=10850.5MB, alloc=1212.3MB, time=225.91 memory used=11261.3MB, alloc=1236.3MB, time=240.31 memory used=11686.7MB, alloc=1260.3MB, time=255.52 memory used=12127.4MB, alloc=1284.3MB, time=271.37 memory used=12583.2MB, alloc=1308.3MB, time=287.99 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428528931 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 F := [9 x y + 4 x z - 15 x z, 4 y z - 17 y z - 9 x] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 4 3 2 G := [15 y z - 6 x y - 5 y z, x - 2 x y + 5 y z] > Problem := [F,G]; 3 3 2 2 Problem := [[9 x y + 4 x z - 15 x z, 4 y z - 17 y z - 9 x], 2 2 4 3 2 [15 y z - 6 x y - 5 y z, x - 2 x y + 5 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=30.0MB, alloc=39.1MB, time=0.44 memory used=51.2MB, alloc=39.1MB, time=0.50 memory used=66.4MB, alloc=39.1MB, time=0.53 memory used=77.9MB, alloc=39.1MB, time=0.57 memory used=97.7MB, alloc=39.1MB, time=0.66 memory used=117.7MB, alloc=39.1MB, time=0.71 memory used=131.5MB, alloc=39.1MB, time=0.75 memory used=143.2MB, alloc=39.1MB, time=0.78 memory used=171.9MB, alloc=39.2MB, time=1.49 memory used=191.3MB, alloc=39.2MB, time=1.54 memory used=202.6MB, alloc=39.2MB, time=1.57 memory used=216.3MB, alloc=39.2MB, time=1.61 memory used=233.0MB, alloc=39.2MB, time=1.64 memory used=242.4MB, alloc=39.2MB, time=1.68 memory used=252.5MB, alloc=39.2MB, time=1.70 memory used=263.6MB, alloc=39.2MB, time=1.73 memory used=276.3MB, alloc=39.2MB, time=1.77 memory used=295.4MB, alloc=39.2MB, time=1.89 memory used=316.9MB, alloc=39.2MB, time=1.95 memory used=333.3MB, alloc=39.2MB, time=1.99 memory used=343.8MB, alloc=39.2MB, time=2.02 memory used=360.8MB, alloc=39.2MB, time=2.10 memory used=381.6MB, alloc=39.2MB, time=2.15 memory used=397.1MB, alloc=39.2MB, time=2.19 memory used=408.2MB, alloc=39.2MB, time=2.23 memory used=430.3MB, alloc=39.2MB, time=2.90 memory used=456.4MB, alloc=39.2MB, time=3.03 memory used=469.1MB, alloc=39.2MB, time=3.07 memory used=481.7MB, alloc=39.2MB, time=3.11 memory used=497.0MB, alloc=39.2MB, time=3.15 memory used=509.7MB, alloc=39.2MB, time=3.18 memory used=519.2MB, alloc=39.2MB, time=3.21 memory used=529.6MB, alloc=39.2MB, time=3.24 memory used=541.0MB, alloc=39.2MB, time=3.27 memory used=554.2MB, alloc=39.2MB, time=3.30 memory used=572.4MB, alloc=39.2MB, time=3.39 memory used=591.8MB, alloc=39.2MB, time=3.60 memory used=618.2MB, alloc=39.2MB, time=3.81 memory used=628.9MB, alloc=39.2MB, time=3.84 memory used=642.1MB, alloc=39.2MB, time=3.88 memory used=665.4MB, alloc=39.2MB, time=4.13 memory used=685.5MB, alloc=63.2MB, time=4.41 memory used=733.0MB, alloc=64.0MB, time=4.63 memory used=769.1MB, alloc=64.0MB, time=4.76 memory used=804.5MB, alloc=64.0MB, time=5.20 memory used=846.7MB, alloc=64.0MB, time=5.72 memory used=876.3MB, alloc=64.0MB, time=5.80 memory used=898.6MB, alloc=64.0MB, time=5.87 memory used=936.3MB, alloc=64.0MB, time=6.14 memory used=982.4MB, alloc=72.0MB, time=6.49 memory used=1036.4MB, alloc=72.0MB, time=7.07 memory used=1098.4MB, alloc=72.0MB, time=7.61 memory used=1137.8MB, alloc=72.0MB, time=7.86 memory used=1182.9MB, alloc=72.0MB, time=8.26 memory used=1226.4MB, alloc=72.0MB, time=8.80 memory used=1267.0MB, alloc=96.0MB, time=9.40 memory used=1345.0MB, alloc=96.0MB, time=10.17 memory used=1412.9MB, alloc=96.0MB, time=10.96 memory used=1463.6MB, alloc=96.0MB, time=11.15 memory used=1494.0MB, alloc=96.0MB, time=11.28 memory used=1523.6MB, alloc=96.0MB, time=11.40 memory used=1558.9MB, alloc=96.0MB, time=11.53 memory used=1593.9MB, alloc=96.0MB, time=11.64 memory used=1621.2MB, alloc=96.0MB, time=11.84 memory used=1675.6MB, alloc=96.1MB, time=12.04 memory used=1707.6MB, alloc=96.1MB, time=12.19 memory used=1736.2MB, alloc=96.1MB, time=12.30 memory used=1770.6MB, alloc=96.1MB, time=12.42 memory used=1807.5MB, alloc=96.1MB, time=12.54 memory used=1831.3MB, alloc=96.1MB, time=12.63 memory used=1907.2MB, alloc=96.1MB, time=17.28 memory used=1953.8MB, alloc=96.1MB, time=17.47 memory used=1985.0MB, alloc=96.1MB, time=17.56 memory used=2022.6MB, alloc=96.1MB, time=17.69 memory used=2046.1MB, alloc=96.1MB, time=17.80 memory used=2072.3MB, alloc=96.1MB, time=17.90 memory used=2102.0MB, alloc=96.1MB, time=18.02 memory used=2134.9MB, alloc=96.1MB, time=18.13 memory used=2172.1MB, alloc=96.1MB, time=18.24 memory used=2204.5MB, alloc=96.1MB, time=18.33 memory used=2226.7MB, alloc=96.1MB, time=18.40 memory used=2251.0MB, alloc=96.1MB, time=18.47 memory used=2300.0MB, alloc=96.1MB, time=18.71 memory used=2339.3MB, alloc=96.1MB, time=18.82 memory used=2366.0MB, alloc=96.1MB, time=18.91 memory used=2398.1MB, alloc=96.1MB, time=19.01 memory used=2437.0MB, alloc=96.1MB, time=19.10 memory used=2463.2MB, alloc=96.1MB, time=19.18 memory used=2509.4MB, alloc=96.1MB, time=19.41 memory used=2551.5MB, alloc=96.1MB, time=19.54 memory used=2577.4MB, alloc=96.1MB, time=19.65 memory used=2608.6MB, alloc=96.1MB, time=19.75 memory used=2646.5MB, alloc=96.1MB, time=19.85 memory used=2674.9MB, alloc=96.1MB, time=19.94 memory used=2723.4MB, alloc=96.1MB, time=23.81 memory used=2787.8MB, alloc=96.1MB, time=24.71 memory used=2817.7MB, alloc=96.1MB, time=24.81 memory used=2854.3MB, alloc=96.1MB, time=24.92 memory used=2884.3MB, alloc=96.1MB, time=25.01 memory used=2909.4MB, alloc=96.1MB, time=25.10 memory used=2937.5MB, alloc=96.1MB, time=25.19 memory used=2968.8MB, alloc=96.1MB, time=25.29 memory used=3003.8MB, alloc=96.1MB, time=25.38 memory used=3043.2MB, alloc=96.1MB, time=25.47 memory used=3068.2MB, alloc=96.1MB, time=25.55 memory used=3091.4MB, alloc=96.1MB, time=25.62 memory used=3117.2MB, alloc=96.1MB, time=25.69 memory used=3165.2MB, alloc=96.1MB, time=25.88 memory used=3217.1MB, alloc=96.1MB, time=27.34 memory used=3256.0MB, alloc=96.1MB, time=27.46 memory used=3293.0MB, alloc=96.1MB, time=27.57 memory used=3318.4MB, alloc=96.1MB, time=27.66 memory used=3346.7MB, alloc=96.1MB, time=27.75 memory used=3380.5MB, alloc=96.1MB, time=27.85 memory used=3440.9MB, alloc=96.1MB, time=28.35 memory used=3510.1MB, alloc=96.1MB, time=29.13 memory used=3550.5MB, alloc=96.1MB, time=29.31 memory used=3578.7MB, alloc=96.1MB, time=29.42 memory used=3642.2MB, alloc=120.1MB, time=29.90 memory used=3703.2MB, alloc=120.1MB, time=30.42 memory used=3765.2MB, alloc=376.1MB, time=31.06 memory used=3853.3MB, alloc=400.1MB, time=31.91 memory used=3948.1MB, alloc=400.1MB, time=32.35 memory used=3997.3MB, alloc=400.1MB, time=32.52 memory used=4061.5MB, alloc=400.1MB, time=32.74 memory used=4142.7MB, alloc=400.1MB, time=33.09 memory used=4194.2MB, alloc=400.1MB, time=33.28 memory used=4272.0MB, alloc=400.1MB, time=36.14 memory used=4359.8MB, alloc=400.1MB, time=39.43 memory used=4420.1MB, alloc=400.1MB, time=39.60 memory used=4464.6MB, alloc=400.1MB, time=39.75 memory used=4520.3MB, alloc=400.1MB, time=39.93 memory used=4590.4MB, alloc=400.1MB, time=40.27 memory used=4660.1MB, alloc=400.1MB, time=40.48 memory used=4714.4MB, alloc=400.1MB, time=40.64 memory used=4791.4MB, alloc=400.1MB, time=40.94 memory used=4847.6MB, alloc=400.1MB, time=41.14 memory used=4907.2MB, alloc=400.1MB, time=41.32 memory used=5010.4MB, alloc=400.1MB, time=47.23 memory used=5065.7MB, alloc=400.1MB, time=47.42 memory used=5116.4MB, alloc=400.1MB, time=47.58 memory used=5165.9MB, alloc=400.1MB, time=47.74 memory used=5225.2MB, alloc=400.1MB, time=47.92 memory used=5293.7MB, alloc=400.1MB, time=48.22 memory used=5375.1MB, alloc=400.1MB, time=49.93 memory used=5425.6MB, alloc=400.1MB, time=50.09 memory used=5499.6MB, alloc=400.1MB, time=50.44 memory used=5577.0MB, alloc=400.1MB, time=50.83 memory used=5653.8MB, alloc=400.1MB, time=51.18 memory used=5724.8MB, alloc=400.1MB, time=51.69 memory used=5788.9MB, alloc=400.1MB, time=51.97 memory used=5872.8MB, alloc=400.1MB, time=52.64 memory used=5928.1MB, alloc=400.1MB, time=52.90 memory used=5996.9MB, alloc=400.1MB, time=53.14 memory used=6056.1MB, alloc=400.1MB, time=53.31 memory used=6104.2MB, alloc=400.1MB, time=53.45 memory used=6175.6MB, alloc=400.1MB, time=53.76 memory used=6234.2MB, alloc=400.1MB, time=53.92 memory used=6283.8MB, alloc=400.1MB, time=54.06 memory used=6357.2MB, alloc=400.1MB, time=55.87 memory used=6408.4MB, alloc=400.1MB, time=56.03 memory used=6479.3MB, alloc=400.1MB, time=56.33 memory used=6545.5MB, alloc=400.1MB, time=56.59 memory used=6615.1MB, alloc=400.1MB, time=57.38 memory used=6676.1MB, alloc=400.1MB, time=57.74 memory used=6742.2MB, alloc=400.1MB, time=57.96 memory used=6797.0MB, alloc=400.1MB, time=58.16 memory used=6855.2MB, alloc=400.1MB, time=58.32 memory used=6898.8MB, alloc=400.1MB, time=58.48 memory used=6973.3MB, alloc=400.1MB, 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alloc=568.1MB, time=357.63 memory used=31116.6MB, alloc=568.1MB, time=358.11 memory used=31209.3MB, alloc=568.1MB, time=358.58 memory used=31309.1MB, alloc=568.1MB, time=359.07 memory used=31413.1MB, alloc=568.1MB, time=359.53 memory used=31524.0MB, alloc=568.1MB, time=360.03 memory used=31645.3MB, alloc=568.1MB, time=360.52 memory used=31773.7MB, alloc=568.1MB, time=361.02 memory used=31909.0MB, alloc=568.1MB, time=361.51 memory used=32051.0MB, alloc=568.1MB, time=362.01 memory used=32264.4MB, alloc=568.1MB, time=362.62 memory used=32388.6MB, alloc=568.1MB, time=363.14 memory used=32518.9MB, alloc=568.1MB, time=363.65 memory used=32653.3MB, alloc=568.1MB, time=364.16 memory used=32795.0MB, alloc=568.1MB, time=364.69 memory used=32943.4MB, alloc=568.1MB, time=365.22 memory used=33097.9MB, alloc=568.1MB, time=365.73 memory used=33261.0MB, alloc=568.1MB, time=366.27 memory used=33431.3MB, alloc=568.1MB, time=366.81 memory used=33610.4MB, alloc=568.1MB, time=367.35 memory used=33801.2MB, alloc=568.1MB, time=367.91 memory used=34001.6MB, alloc=568.1MB, time=368.48 memory used=34218.9MB, alloc=568.1MB, time=369.10 memory used=34419.7MB, alloc=568.1MB, time=369.69 memory used=34581.9MB, alloc=568.1MB, time=370.39 memory used=34822.1MB, alloc=568.1MB, time=373.15 memory used=35002.9MB, alloc=568.1MB, time=379.76 memory used=35133.5MB, alloc=568.1MB, time=380.45 memory used=35246.6MB, alloc=568.1MB, time=381.01 memory used=35348.2MB, alloc=568.1MB, time=381.60 memory used=35470.2MB, alloc=568.1MB, time=382.18 memory used=35610.7MB, alloc=568.1MB, time=382.75 memory used=35692.7MB, alloc=568.1MB, time=383.25 memory used=35783.1MB, alloc=568.1MB, time=383.75 memory used=35883.3MB, alloc=568.1MB, time=384.25 memory used=36018.2MB, alloc=568.1MB, time=392.08 memory used=36174.6MB, alloc=568.1MB, time=398.93 memory used=36279.0MB, alloc=568.1MB, time=399.46 memory used=36417.2MB, alloc=568.1MB, time=400.08 memory used=36501.2MB, alloc=568.1MB, time=400.60 memory used=36596.7MB, alloc=568.1MB, time=401.15 memory used=36703.1MB, alloc=568.1MB, time=401.64 memory used=36823.6MB, alloc=568.1MB, time=402.15 memory used=36958.8MB, alloc=568.1MB, time=402.66 memory used=37208.2MB, alloc=568.1MB, time=403.28 memory used=37345.3MB, alloc=568.1MB, time=403.83 memory used=37503.2MB, alloc=568.1MB, time=404.37 memory used=37721.9MB, alloc=568.1MB, time=405.92 memory used=37993.9MB, alloc=568.1MB, time=408.29 memory used=38254.6MB, alloc=568.1MB, time=411.82 memory used=38517.6MB, alloc=568.1MB, time=418.91 memory used=38778.6MB, alloc=568.1MB, time=429.08 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428529231 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 3 3 2 2 2 F := [20 x y z - 19 x z + 9 y , -11 x z - 20 y z + 15 x ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 3 G := [16 x z - 6 y z - 19 x, -18 x z - 10 x + y z] > Problem := [F,G]; 2 3 3 3 2 2 2 Problem := [[20 x y z - 19 x z + 9 y , -11 x z - 20 y z + 15 x ], 3 2 3 3 [16 x z - 6 y z - 19 x, -18 x z - 10 x + y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=27.1MB, alloc=32.3MB, time=0.49 memory used=47.3MB, alloc=56.3MB, time=0.79 memory used=89.6MB, alloc=60.3MB, time=1.39 memory used=131.3MB, alloc=68.3MB, time=1.97 memory used=174.6MB, alloc=92.3MB, time=2.54 memory used=238.4MB, alloc=92.3MB, time=3.41 memory used=299.7MB, alloc=116.3MB, time=4.30 memory used=372.7MB, alloc=116.3MB, time=5.18 memory used=452.7MB, alloc=372.3MB, time=6.11 memory used=541.3MB, alloc=396.3MB, time=6.99 memory used=656.0MB, alloc=396.3MB, time=8.19 memory used=756.2MB, alloc=420.3MB, time=9.50 memory used=897.0MB, alloc=420.3MB, time=10.89 memory used=1025.2MB, alloc=444.3MB, time=11.95 memory used=1153.5MB, alloc=444.3MB, time=12.67 memory used=1302.1MB, alloc=444.3MB, time=14.16 memory used=1458.9MB, alloc=468.3MB, time=15.34 memory used=1591.5MB, alloc=468.3MB, time=16.16 memory used=1694.3MB, alloc=468.3MB, time=16.61 memory used=1861.4MB, alloc=468.3MB, time=19.00 memory used=2011.0MB, alloc=468.3MB, time=20.43 memory used=2185.3MB, alloc=492.3MB, time=21.72 memory used=2322.0MB, alloc=492.3MB, time=23.38 memory used=2449.5MB, alloc=492.3MB, time=24.67 memory used=2545.2MB, alloc=492.3MB, time=25.96 memory used=2636.4MB, alloc=492.3MB, time=27.10 memory used=2735.4MB, alloc=516.3MB, time=28.05 memory used=2831.6MB, alloc=516.3MB, time=29.31 memory used=2906.1MB, alloc=516.3MB, time=30.21 memory used=2987.9MB, alloc=516.3MB, time=31.36 memory used=3064.1MB, alloc=516.3MB, time=32.26 memory used=3140.7MB, alloc=516.3MB, time=33.40 memory used=3210.8MB, alloc=516.3MB, time=34.46 memory used=3284.9MB, alloc=516.3MB, time=35.47 memory used=3341.5MB, alloc=516.3MB, time=36.27 memory used=3431.3MB, alloc=540.3MB, time=37.03 memory used=3515.3MB, alloc=540.3MB, time=37.65 memory used=3657.9MB, alloc=540.3MB, time=38.29 memory used=3739.3MB, alloc=540.3MB, time=39.09 memory used=3797.2MB, alloc=540.3MB, time=39.90 memory used=3871.8MB, alloc=540.3MB, time=40.90 memory used=3947.3MB, alloc=540.3MB, time=41.89 memory used=4031.7MB, alloc=540.3MB, time=42.60 memory used=4104.6MB, alloc=540.3MB, time=43.28 memory used=4166.2MB, alloc=540.3MB, time=44.27 memory used=4225.4MB, alloc=540.3MB, time=45.21 memory used=4449.3MB, alloc=564.3MB, time=48.03 memory used=4697.6MB, alloc=564.3MB, time=50.17 memory used=4913.6MB, alloc=588.3MB, time=52.87 memory used=5143.7MB, alloc=612.3MB, time=55.56 memory used=5343.8MB, alloc=636.3MB, time=58.43 memory used=5518.5MB, alloc=636.3MB, time=60.62 memory used=5780.3MB, alloc=636.3MB, time=62.95 memory used=5957.1MB, alloc=636.3MB, time=64.08 memory used=6115.4MB, alloc=636.3MB, time=67.71 memory used=6269.9MB, alloc=636.3MB, time=68.66 memory used=6434.5MB, alloc=660.3MB, time=69.71 memory used=6590.0MB, alloc=660.3MB, time=70.57 memory used=6732.0MB, alloc=660.3MB, time=71.32 memory used=6915.5MB, alloc=660.3MB, time=72.18 memory used=7033.7MB, alloc=660.3MB, time=72.86 memory used=7153.8MB, alloc=660.3MB, time=73.56 memory used=7291.2MB, alloc=660.3MB, time=74.26 memory used=7446.2MB, alloc=660.3MB, time=74.95 memory used=7627.6MB, alloc=660.3MB, time=75.64 memory used=7772.2MB, alloc=660.3MB, time=76.45 memory used=8014.0MB, alloc=660.3MB, time=114.54 memory used=8177.0MB, alloc=660.3MB, time=115.34 memory used=8298.9MB, alloc=660.3MB, time=115.98 memory used=8436.8MB, alloc=660.3MB, time=116.65 memory used=8601.8MB, alloc=660.3MB, time=117.31 memory used=8903.2MB, alloc=660.3MB, time=118.13 memory used=9036.9MB, alloc=660.3MB, time=118.78 memory used=9181.8MB, alloc=660.3MB, time=119.45 memory used=9341.1MB, alloc=660.3MB, time=120.14 memory used=9519.5MB, alloc=660.3MB, time=120.85 memory used=9725.9MB, alloc=660.3MB, time=121.57 memory used=10026.1MB, alloc=660.3MB, time=124.13 memory used=10222.6MB, alloc=684.3MB, time=127.09 memory used=10377.9MB, alloc=684.3MB, time=127.95 memory used=10573.3MB, alloc=684.3MB, time=128.87 memory used=10724.8MB, alloc=708.3MB, time=129.65 memory used=10861.1MB, alloc=708.3MB, time=130.39 memory used=11010.2MB, alloc=708.3MB, time=131.24 memory used=11172.0MB, alloc=708.3MB, time=132.07 memory used=11344.0MB, alloc=708.3MB, time=132.92 memory used=11526.4MB, alloc=708.3MB, time=133.73 memory used=11731.0MB, alloc=708.3MB, time=134.56 memory used=11945.8MB, alloc=708.3MB, time=135.40 memory used=12147.1MB, alloc=708.3MB, time=136.20 memory used=12288.1MB, alloc=732.3MB, time=136.94 memory used=12419.8MB, alloc=732.3MB, time=137.61 memory used=12550.3MB, alloc=732.3MB, time=138.33 memory used=12687.4MB, alloc=732.3MB, time=139.02 memory used=12827.1MB, alloc=732.3MB, time=139.71 memory used=12969.2MB, alloc=732.3MB, time=140.39 memory used=13113.7MB, alloc=756.3MB, time=141.09 memory used=13276.1MB, alloc=756.3MB, time=141.80 memory used=13442.2MB, alloc=756.3MB, time=142.53 memory used=13611.4MB, alloc=756.3MB, time=143.22 memory used=13800.0MB, alloc=756.3MB, time=143.98 memory used=13991.4MB, alloc=756.3MB, time=144.71 memory used=14185.5MB, alloc=756.3MB, time=145.47 memory used=14382.2MB, alloc=756.3MB, time=146.21 memory used=14581.3MB, alloc=756.3MB, time=146.93 memory used=14783.7MB, alloc=756.3MB, time=147.66 memory used=15005.0MB, alloc=756.3MB, time=148.41 memory used=15229.3MB, alloc=756.3MB, time=149.17 memory used=15455.6MB, alloc=756.3MB, time=149.91 memory used=15684.3MB, alloc=756.3MB, time=150.66 memory used=15933.6MB, alloc=756.3MB, time=151.44 memory used=16184.6MB, alloc=756.3MB, time=152.22 memory used=16437.3MB, alloc=756.3MB, time=152.99 memory used=16718.9MB, alloc=756.3MB, time=153.78 memory used=16981.1MB, alloc=756.3MB, time=154.60 memory used=17092.2MB, alloc=771.8MB, time=155.32 memory used=17197.5MB, alloc=771.8MB, time=156.01 memory used=17294.4MB, alloc=771.8MB, time=156.67 memory used=17391.4MB, alloc=771.8MB, time=157.32 memory used=17489.3MB, alloc=771.8MB, time=157.98 memory used=17604.8MB, alloc=771.8MB, time=158.68 memory used=17721.1MB, alloc=771.8MB, time=159.36 memory used=17837.3MB, alloc=771.8MB, time=160.03 memory used=17953.6MB, alloc=771.8MB, time=160.68 memory used=18069.7MB, alloc=771.8MB, time=161.32 memory used=18185.6MB, alloc=771.8MB, time=161.97 memory used=18301.4MB, alloc=771.8MB, time=162.60 memory used=18417.1MB, alloc=771.8MB, time=163.23 memory used=18532.5MB, alloc=771.8MB, time=163.86 memory used=18647.7MB, alloc=771.8MB, time=164.49 memory used=18762.7MB, alloc=771.8MB, time=165.12 memory used=18877.5MB, alloc=771.8MB, time=165.75 memory used=19011.0MB, alloc=771.8MB, time=166.40 memory used=19144.0MB, alloc=771.8MB, time=167.07 memory used=19276.6MB, alloc=771.8MB, time=167.73 memory used=19408.6MB, alloc=771.8MB, time=168.38 memory used=19540.0MB, alloc=771.8MB, time=169.04 memory used=19670.8MB, alloc=771.8MB, time=169.67 memory used=19801.0MB, alloc=771.8MB, time=170.36 memory used=19930.7MB, alloc=771.8MB, time=171.05 memory used=20077.8MB, alloc=771.8MB, time=171.71 memory used=20224.0MB, alloc=771.8MB, time=172.36 memory used=20369.1MB, alloc=771.8MB, time=173.02 memory used=20513.1MB, alloc=771.8MB, time=173.66 memory used=20655.9MB, alloc=771.8MB, time=174.32 memory used=20798.7MB, alloc=771.8MB, time=174.98 memory used=20955.3MB, alloc=771.8MB, time=175.64 memory used=21111.3MB, alloc=771.8MB, time=176.31 memory used=21265.5MB, alloc=771.8MB, time=176.97 memory used=21419.1MB, alloc=771.8MB, time=177.63 memory used=21584.9MB, alloc=771.8MB, time=178.30 memory used=21749.3MB, alloc=771.8MB, time=178.96 memory used=21911.1MB, alloc=771.8MB, time=179.65 memory used=22085.9MB, alloc=771.8MB, time=180.34 memory used=22257.1MB, alloc=771.8MB, time=181.01 memory used=22439.7MB, alloc=771.8MB, time=181.70 memory used=22617.8MB, alloc=771.8MB, time=182.37 memory used=22805.3MB, alloc=771.8MB, time=183.04 memory used=22989.1MB, alloc=771.8MB, time=183.73 memory used=23177.3MB, alloc=771.8MB, time=184.40 memory used=23370.2MB, alloc=771.8MB, time=185.09 memory used=23569.0MB, alloc=771.8MB, time=185.79 memory used=23777.3MB, alloc=771.8MB, time=186.48 memory used=23993.7MB, alloc=771.8MB, time=187.18 memory used=24213.2MB, alloc=771.8MB, time=187.87 memory used=24446.2MB, alloc=771.8MB, time=188.59 memory used=24636.2MB, alloc=771.8MB, time=189.25 memory used=24807.3MB, alloc=771.8MB, time=189.90 memory used=25025.5MB, alloc=771.8MB, time=190.84 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428529531 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 3 2 F := [15 z + 16 x z - 4 x , 17 x y + 20 x z + 14] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 2 G := [7 x y z + 11 x z + 18, -4 x z - 6 x y - 11 x z ] > Problem := [F,G]; 4 2 2 3 2 Problem := [[15 z + 16 x z - 4 x , 17 x y + 20 x z + 14], 2 2 2 2 2 2 [7 x y z + 11 x z + 18, -4 x z - 6 x y - 11 x z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=33.2MB, alloc=40.3MB, time=1.41 memory used=63.1MB, alloc=44.3MB, time=2.46 memory used=93.6MB, alloc=44.3MB, time=3.42 memory used=123.4MB, alloc=44.9MB, time=5.88 memory used=141.3MB, alloc=44.9MB, time=5.93 memory used=155.6MB, alloc=44.9MB, time=5.97 memory used=173.9MB, alloc=44.9MB, time=6.02 memory used=208.3MB, alloc=44.9MB, time=6.46 memory used=241.5MB, alloc=44.9MB, time=6.85 memory used=267.6MB, alloc=44.9MB, time=7.12 memory used=299.7MB, alloc=68.9MB, time=8.37 memory used=350.1MB, alloc=70.7MB, time=11.06 memory used=383.1MB, alloc=70.7MB, time=11.37 memory used=446.4MB, alloc=78.7MB, time=13.82 memory used=512.7MB, alloc=78.7MB, time=15.88 memory used=563.6MB, alloc=78.7MB, time=17.53 memory used=595.1MB, alloc=78.7MB, time=18.28 memory used=637.1MB, alloc=78.7MB, time=20.04 memory used=680.4MB, alloc=78.7MB, time=21.40 memory used=743.1MB, alloc=78.7MB, time=24.67 memory used=767.5MB, alloc=78.7MB, time=24.77 memory used=802.5MB, alloc=78.7MB, time=25.06 memory used=858.6MB, alloc=78.7MB, time=25.71 memory used=890.3MB, alloc=78.7MB, time=25.92 memory used=948.3MB, alloc=102.7MB, time=26.41 memory used=1011.4MB, alloc=102.7MB, time=27.45 memory used=1049.3MB, alloc=102.7MB, time=27.83 memory used=1092.4MB, alloc=102.7MB, time=28.21 memory used=1122.7MB, alloc=102.7MB, time=28.54 memory used=1158.3MB, alloc=102.7MB, time=28.86 memory used=1201.5MB, alloc=102.7MB, time=29.21 memory used=1252.7MB, alloc=102.7MB, time=30.26 memory used=1293.0MB, alloc=102.7MB, time=30.63 memory used=1330.5MB, alloc=102.7MB, time=30.98 memory used=1362.6MB, alloc=102.7MB, time=31.31 memory used=1402.1MB, alloc=102.7MB, time=31.66 memory used=1446.7MB, alloc=102.7MB, time=34.51 memory used=1487.9MB, alloc=102.7MB, time=39.94 memory used=1534.4MB, alloc=102.7MB, time=41.46 memory used=1578.6MB, alloc=102.7MB, time=42.03 memory used=1631.8MB, alloc=102.7MB, time=46.81 memory used=1673.9MB, alloc=102.7MB, time=47.43 memory used=1714.7MB, alloc=102.7MB, time=48.01 memory used=1765.3MB, alloc=102.7MB, time=49.34 memory used=1806.8MB, alloc=102.7MB, time=49.74 memory used=1840.7MB, alloc=102.7MB, time=50.06 memory used=1873.4MB, alloc=102.7MB, time=50.39 memory used=1913.2MB, alloc=102.7MB, time=50.70 memory used=1966.5MB, alloc=102.7MB, time=51.77 memory used=2003.9MB, alloc=102.7MB, time=52.14 memory used=2042.2MB, alloc=102.7MB, time=52.48 memory used=2073.7MB, alloc=102.7MB, time=52.81 memory used=2111.8MB, alloc=102.7MB, time=53.13 memory used=2157.4MB, alloc=102.7MB, time=61.86 memory used=2203.7MB, alloc=115.8MB, time=93.97 memory used=2258.6MB, alloc=115.8MB, time=98.65 memory used=2296.8MB, alloc=115.8MB, time=98.93 memory used=2338.4MB, alloc=115.8MB, time=99.22 memory used=2359.5MB, alloc=115.8MB, time=99.44 memory used=2370.6MB, alloc=115.8MB, time=99.64 memory used=2422.4MB, alloc=115.8MB, time=101.22 memory used=2456.1MB, alloc=115.8MB, time=101.64 memory used=2493.2MB, alloc=115.8MB, time=102.36 memory used=2520.6MB, alloc=115.8MB, time=102.67 memory used=2566.4MB, alloc=115.8MB, time=103.05 memory used=2599.8MB, alloc=115.8MB, time=103.40 memory used=2645.7MB, alloc=115.8MB, time=103.77 memory used=2683.0MB, alloc=115.8MB, time=105.09 memory used=2701.9MB, alloc=115.8MB, time=105.33 memory used=2721.9MB, alloc=115.8MB, time=105.57 memory used=2742.9MB, alloc=115.8MB, time=105.82 memory used=2768.6MB, alloc=115.8MB, time=106.08 memory used=2804.2MB, alloc=115.8MB, time=106.36 memory used=2842.2MB, alloc=115.8MB, time=106.65 memory used=2882.5MB, alloc=115.8MB, time=106.94 memory used=2913.7MB, alloc=115.8MB, time=107.19 memory used=2925.9MB, alloc=115.8MB, time=107.38 memory used=2938.2MB, alloc=115.8MB, time=107.56 memory used=2950.8MB, alloc=115.8MB, time=107.75 memory used=2963.5MB, alloc=115.8MB, time=107.96 memory used=2976.4MB, alloc=115.8MB, time=108.15 memory used=2993.5MB, alloc=115.8MB, time=108.43 memory used=3012.2MB, alloc=115.8MB, time=108.67 memory used=3031.9MB, alloc=115.8MB, time=108.91 memory used=3052.7MB, alloc=115.8MB, time=109.15 memory used=3076.1MB, alloc=115.8MB, time=109.39 memory used=3111.1MB, alloc=115.8MB, time=109.68 memory used=3148.6MB, alloc=115.8MB, time=109.97 memory used=3188.5MB, alloc=115.8MB, time=110.25 memory used=3224.5MB, alloc=115.8MB, time=110.53 memory used=3236.6MB, alloc=115.8MB, time=110.72 memory used=3248.8MB, alloc=115.8MB, time=110.91 memory used=3261.3MB, alloc=115.8MB, time=111.10 memory used=3274.0MB, alloc=115.8MB, time=111.30 memory used=3286.8MB, alloc=115.8MB, time=111.49 memory used=3340.5MB, alloc=115.8MB, time=113.52 memory used=3387.1MB, alloc=115.8MB, time=114.17 memory used=3430.4MB, alloc=115.8MB, time=115.73 memory used=3488.5MB, alloc=115.8MB, time=125.98 memory used=3523.6MB, alloc=115.8MB, time=126.31 memory used=3563.9MB, alloc=115.8MB, time=126.66 memory used=3598.5MB, alloc=115.8MB, time=127.41 memory used=3642.0MB, alloc=115.8MB, time=127.86 memory used=3685.8MB, alloc=115.8MB, time=128.25 memory used=3715.7MB, alloc=115.8MB, time=128.55 memory used=3749.2MB, alloc=115.8MB, time=128.86 memory used=3789.9MB, alloc=115.8MB, time=129.21 memory used=3840.9MB, alloc=115.8MB, time=130.19 memory used=3880.7MB, alloc=115.8MB, time=130.59 memory used=3915.9MB, alloc=115.8MB, time=130.93 memory used=3947.8MB, alloc=115.8MB, time=131.25 memory used=3986.4MB, alloc=115.8MB, time=131.59 memory used=4032.8MB, alloc=115.8MB, time=143.59 memory used=4072.9MB, alloc=115.8MB, time=171.81 memory used=4127.6MB, alloc=115.8MB, time=176.44 memory used=4165.5MB, alloc=115.8MB, time=176.70 memory used=4208.0MB, alloc=115.8MB, time=176.98 memory used=4228.8MB, alloc=115.8MB, time=177.19 memory used=4240.2MB, alloc=115.8MB, time=177.37 memory used=4298.7MB, alloc=115.8MB, time=178.95 memory used=4343.4MB, alloc=115.8MB, time=179.88 memory used=4382.6MB, alloc=115.8MB, time=180.50 memory used=4428.1MB, alloc=115.8MB, time=181.25 memory used=4471.8MB, alloc=115.8MB, time=181.90 memory used=4543.0MB, alloc=115.8MB, time=183.96 memory used=4588.7MB, alloc=115.8MB, time=185.00 memory used=4636.5MB, alloc=139.8MB, time=215.59 memory used=4710.4MB, alloc=139.8MB, time=251.00 memory used=4762.0MB, alloc=139.8MB, time=251.47 memory used=4810.2MB, alloc=139.8MB, time=251.92 memory used=4870.5MB, alloc=139.8MB, time=252.38 memory used=4908.6MB, alloc=139.8MB, time=252.70 memory used=4951.7MB, alloc=139.8MB, time=253.01 memory used=5000.1MB, alloc=139.8MB, time=253.34 memory used=5065.7MB, alloc=139.8MB, time=254.12 memory used=5144.7MB, alloc=139.8MB, time=256.64 memory used=5219.1MB, alloc=395.8MB, time=259.42 memory used=5322.3MB, alloc=395.8MB, time=261.82 memory used=5407.5MB, alloc=395.8MB, time=273.56 memory used=5448.9MB, alloc=395.8MB, time=274.01 memory used=5490.7MB, alloc=395.8MB, time=274.40 memory used=5560.1MB, alloc=395.8MB, time=276.49 memory used=5610.4MB, alloc=395.8MB, time=280.96 memory used=5674.4MB, alloc=395.8MB, time=282.51 memory used=5730.8MB, alloc=395.8MB, time=287.19 memory used=5780.7MB, alloc=395.8MB, time=288.29 memory used=5823.5MB, alloc=395.8MB, time=288.76 memory used=5912.3MB, alloc=395.8MB, time=292.76 memory used=5953.7MB, alloc=395.8MB, time=293.22 memory used=6047.9MB, alloc=419.8MB, time=296.54 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428529831 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 3 F := [-x z + 12 y z - 19 y z , -16 x y z - 8 x y z + 6 z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 G := [20 y z - 6 x z + y z, -15 x y z - 3 x y z + x y z] > Problem := [F,G]; 3 2 2 2 3 Problem := [[-x z + 12 y z - 19 y z , -16 x y z - 8 x y z + 6 z ], 3 2 2 2 [20 y z - 6 x z + y z, -15 x y z - 3 x y z + x y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.60 memory used=26.4MB, alloc=32.3MB, time=1.73 memory used=47.0MB, alloc=32.3MB, time=2.77 memory used=66.4MB, alloc=56.3MB, time=3.76 memory used=137.0MB, alloc=100.3MB, time=7.36 memory used=209.0MB, alloc=100.3MB, time=10.82 memory used=281.4MB, alloc=100.3MB, time=14.10 memory used=349.0MB, alloc=124.3MB, time=17.62 memory used=424.3MB, alloc=124.3MB, time=21.40 memory used=495.9MB, alloc=380.3MB, time=24.84 memory used=585.6MB, alloc=404.3MB, time=29.55 memory used=699.6MB, alloc=404.3MB, time=35.33 memory used=811.8MB, alloc=428.3MB, time=41.25 memory used=946.3MB, alloc=452.3MB, time=47.73 memory used=1087.3MB, alloc=452.3MB, time=55.05 memory used=1227.8MB, alloc=476.3MB, time=62.71 memory used=1362.2MB, alloc=500.3MB, time=69.21 memory used=1566.8MB, alloc=500.3MB, time=75.46 memory used=1776.2MB, alloc=500.3MB, time=82.01 memory used=1965.2MB, alloc=500.3MB, time=86.29 memory used=2165.0MB, alloc=524.3MB, time=94.71 memory used=2335.8MB, alloc=524.3MB, time=103.06 memory used=2497.8MB, alloc=548.3MB, time=111.74 memory used=2683.1MB, alloc=572.3MB, time=122.61 memory used=2833.8MB, alloc=596.3MB, time=132.25 memory used=3000.3MB, alloc=620.3MB, time=141.90 memory used=3240.9MB, alloc=644.3MB, time=151.08 memory used=3584.3MB, alloc=644.3MB, time=161.11 memory used=3881.0MB, alloc=644.3MB, time=166.69 memory used=4197.0MB, alloc=668.3MB, time=175.81 memory used=4477.4MB, alloc=668.3MB, time=185.16 memory used=4672.1MB, alloc=668.3MB, time=192.97 memory used=4903.3MB, alloc=692.3MB, time=202.03 memory used=5133.4MB, alloc=716.3MB, time=210.78 memory used=5324.1MB, alloc=716.3MB, time=219.72 memory used=5499.2MB, alloc=740.3MB, time=228.25 memory used=5681.7MB, alloc=764.3MB, time=237.69 memory used=5843.2MB, alloc=764.3MB, time=247.03 memory used=5985.3MB, alloc=788.3MB, time=255.94 memory used=6130.9MB, alloc=788.3MB, time=264.24 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428530131 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 4 2 4 F := [18 x y - 7 y z - 20 y z, 16 x + 12 x y z + 17 y ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 G := [8 x + 6 x y + z, -18 x y z - 5 x z - 17 y z] > Problem := [F,G]; 3 2 2 4 2 4 Problem := [[18 x y - 7 y z - 20 y z, 16 x + 12 x y z + 17 y ], 4 2 [8 x + 6 x y + z, -18 x y z - 5 x z - 17 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.61 memory used=26.8MB, alloc=32.3MB, time=1.77 memory used=46.4MB, alloc=56.3MB, time=2.74 memory used=87.7MB, alloc=60.3MB, time=4.43 memory used=130.6MB, alloc=68.3MB, time=6.20 memory used=175.6MB, alloc=92.3MB, time=7.74 memory used=247.1MB, alloc=92.3MB, time=10.12 memory used=315.1MB, alloc=348.3MB, time=12.73 memory used=377.6MB, alloc=348.3MB, time=14.68 memory used=449.5MB, alloc=348.3MB, time=17.46 memory used=524.4MB, alloc=372.3MB, time=19.91 memory used=613.8MB, alloc=372.3MB, time=23.28 memory used=656.2MB, alloc=372.3MB, time=23.82 memory used=688.9MB, alloc=372.3MB, time=24.25 memory used=740.6MB, alloc=372.3MB, time=24.88 memory used=781.8MB, alloc=372.3MB, time=25.39 memory used=817.2MB, alloc=372.3MB, time=25.86 memory used=869.9MB, alloc=372.3MB, time=26.61 memory used=912.4MB, alloc=372.3MB, time=27.25 memory used=1000.8MB, alloc=396.3MB, time=30.25 memory used=1054.3MB, alloc=396.3MB, time=30.83 memory used=1113.1MB, alloc=396.3MB, time=31.50 memory used=1177.0MB, alloc=396.3MB, time=32.16 memory used=1227.4MB, alloc=396.3MB, time=32.71 memory used=1291.9MB, alloc=396.3MB, time=33.62 memory used=1397.7MB, alloc=396.3MB, time=36.89 memory used=1529.9MB, alloc=396.3MB, time=40.50 memory used=1638.8MB, alloc=396.3MB, time=44.95 memory used=1726.7MB, alloc=396.3MB, time=47.70 memory used=1813.1MB, alloc=396.3MB, time=49.84 memory used=1929.8MB, alloc=420.3MB, time=51.79 memory used=2061.9MB, alloc=420.3MB, time=56.29 memory used=2154.7MB, alloc=420.3MB, time=61.21 memory used=2223.8MB, alloc=420.3MB, time=62.15 memory used=2290.1MB, alloc=420.3MB, time=62.89 memory used=2340.7MB, alloc=420.3MB, time=63.47 memory used=2402.0MB, alloc=420.3MB, time=64.11 memory used=2476.1MB, alloc=420.3MB, time=64.79 memory used=2625.4MB, alloc=420.3MB, time=67.11 memory used=2684.8MB, alloc=420.3MB, time=67.79 memory used=2744.7MB, alloc=420.3MB, time=68.42 memory used=2824.9MB, alloc=420.3MB, time=70.16 memory used=2904.3MB, alloc=420.3MB, time=71.76 memory used=2978.1MB, alloc=420.3MB, time=72.50 memory used=3116.4MB, alloc=420.3MB, time=77.93 memory used=3242.6MB, alloc=420.3MB, time=81.51 memory used=3355.6MB, alloc=444.3MB, time=83.60 memory used=3482.7MB, alloc=444.3MB, time=85.23 memory used=3638.5MB, alloc=444.3MB, time=93.96 memory used=3753.6MB, alloc=444.3MB, time=95.42 memory used=3868.5MB, alloc=444.3MB, time=96.78 memory used=3987.3MB, alloc=444.3MB, time=98.10 memory used=4113.1MB, alloc=444.3MB, time=99.40 memory used=4259.5MB, alloc=444.3MB, time=101.21 memory used=4415.3MB, alloc=444.3MB, time=105.64 memory used=4555.3MB, alloc=444.3MB, time=108.70 memory used=4689.3MB, alloc=468.3MB, time=115.53 memory used=4886.7MB, alloc=468.3MB, time=130.11 memory used=5054.4MB, alloc=492.3MB, time=138.25 memory used=5216.8MB, alloc=516.3MB, time=147.53 memory used=5401.7MB, alloc=540.3MB, time=158.66 memory used=5593.4MB, alloc=564.3MB, time=172.65 memory used=5762.6MB, alloc=588.3MB, time=189.13 memory used=5940.2MB, alloc=612.3MB, time=207.62 memory used=6123.2MB, alloc=636.3MB, time=229.14 memory used=6329.6MB, alloc=660.3MB, time=253.31 memory used=6559.9MB, alloc=684.3MB, time=280.41 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428530431 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 4 2 F := [-16 x z - 9 y , -16 z - 17 x y - 10 x z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 2 4 G := [-6 x y + 8 y z + 17 x, 12 x z + 20 x z + 15 y ] > Problem := [F,G]; 2 2 3 4 2 Problem := [[-16 x z - 9 y , -16 z - 17 x y - 10 x z], 2 2 2 3 2 2 4 [-6 x y + 8 y z + 17 x, 12 x z + 20 x z + 15 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.60 memory used=27.0MB, alloc=32.3MB, time=1.31 memory used=51.4MB, alloc=32.3MB, time=2.73 memory used=72.6MB, alloc=35.2MB, time=2.97 memory used=84.7MB, alloc=35.2MB, time=3.09 memory used=99.0MB, alloc=35.2MB, time=3.21 memory used=113.0MB, alloc=35.2MB, time=3.33 memory used=124.5MB, alloc=35.2MB, time=3.43 memory used=149.4MB, alloc=39.2MB, time=4.31 memory used=163.8MB, alloc=39.2MB, time=4.45 memory used=176.6MB, alloc=39.2MB, time=4.58 memory used=198.9MB, alloc=39.2MB, time=5.36 memory used=219.8MB, alloc=39.2MB, time=5.77 memory used=237.9MB, alloc=39.2MB, time=5.95 memory used=248.1MB, alloc=39.2MB, time=6.07 memory used=263.6MB, alloc=39.2MB, time=6.37 memory used=282.7MB, alloc=39.2MB, time=6.57 memory used=294.2MB, alloc=39.2MB, time=6.70 memory used=305.7MB, alloc=39.2MB, time=6.82 memory used=331.3MB, alloc=63.2MB, time=15.24 memory used=386.4MB, alloc=63.2MB, time=43.23 memory used=416.3MB, alloc=63.2MB, time=43.50 memory used=451.1MB, alloc=63.2MB, time=43.76 memory used=473.6MB, alloc=63.2MB, time=43.95 memory used=497.6MB, alloc=63.2MB, time=44.14 memory used=524.8MB, alloc=63.2MB, time=44.34 memory used=555.8MB, alloc=63.2MB, time=44.55 memory used=590.5MB, alloc=63.2MB, time=44.77 memory used=620.4MB, alloc=63.2MB, time=44.96 memory used=640.9MB, alloc=63.2MB, time=45.11 memory used=662.5MB, alloc=63.2MB, time=45.26 memory used=685.4MB, alloc=63.2MB, time=45.41 memory used=709.8MB, alloc=63.2MB, time=45.56 memory used=735.3MB, alloc=63.2MB, time=45.71 memory used=762.7MB, alloc=63.2MB, time=45.87 memory used=792.9MB, alloc=63.2MB, time=46.04 memory used=832.4MB, alloc=63.2MB, time=47.21 memory used=860.3MB, alloc=63.2MB, time=47.43 memory used=904.9MB, alloc=63.2MB, time=48.35 memory used=951.9MB, alloc=63.2MB, time=50.53 memory used=995.2MB, alloc=63.5MB, time=55.32 memory used=1025.4MB, alloc=63.5MB, time=55.55 memory used=1051.2MB, alloc=63.5MB, time=55.74 memory used=1074.8MB, alloc=63.5MB, time=55.92 memory used=1102.4MB, alloc=63.5MB, time=56.11 memory used=1134.2MB, alloc=63.5MB, time=56.31 memory used=1169.1MB, alloc=63.5MB, time=56.51 memory used=1188.6MB, alloc=63.5MB, time=56.65 memory used=1208.9MB, alloc=63.5MB, time=56.79 memory used=1231.4MB, alloc=63.5MB, time=56.93 memory used=1255.9MB, alloc=63.5MB, time=57.09 memory used=1284.1MB, alloc=63.5MB, time=57.25 memory used=1329.6MB, alloc=63.5MB, time=58.99 memory used=1378.2MB, alloc=63.5MB, time=60.39 memory used=1430.2MB, alloc=73.1MB, time=64.19 memory used=1457.9MB, alloc=73.1MB, time=64.43 memory used=1482.5MB, alloc=73.1MB, time=64.66 memory used=1539.1MB, alloc=73.1MB, time=66.20 memory used=1602.6MB, alloc=73.1MB, time=67.76 memory used=1665.9MB, alloc=73.1MB, time=69.24 memory used=1726.9MB, alloc=73.1MB, time=70.77 memory used=1788.2MB, alloc=73.1MB, time=72.86 memory used=1850.0MB, alloc=73.1MB, time=75.25 memory used=1911.0MB, alloc=73.1MB, time=78.25 memory used=1972.5MB, alloc=73.1MB, time=81.60 memory used=2034.1MB, alloc=73.1MB, time=85.67 memory used=2067.9MB, alloc=73.1MB, time=86.46 memory used=2090.4MB, alloc=73.1MB, time=86.68 memory used=2134.4MB, alloc=73.1MB, time=88.36 memory used=2167.9MB, alloc=73.1MB, time=89.03 memory used=2190.8MB, alloc=73.1MB, time=89.25 memory used=2226.2MB, alloc=73.1MB, time=89.91 memory used=2276.5MB, alloc=73.1MB, time=91.96 memory used=2314.8MB, alloc=73.1MB, time=93.35 memory used=2369.7MB, alloc=73.1MB, time=95.15 memory used=2443.7MB, alloc=73.1MB, time=98.33 memory used=2472.0MB, alloc=73.1MB, time=99.04 memory used=2498.3MB, alloc=73.1MB, time=99.63 memory used=2539.9MB, alloc=73.1MB, time=101.31 memory used=2563.9MB, alloc=73.1MB, time=101.54 memory used=2582.7MB, alloc=73.1MB, time=101.75 memory used=2607.4MB, alloc=73.1MB, time=101.98 memory used=2650.8MB, alloc=73.1MB, time=103.02 memory used=2690.4MB, alloc=73.1MB, time=104.81 memory used=2733.2MB, alloc=97.1MB, time=111.00 memory used=2775.5MB, alloc=97.1MB, time=111.37 memory used=2813.9MB, alloc=97.1MB, time=111.69 memory used=2858.6MB, alloc=97.1MB, time=111.99 memory used=2887.2MB, alloc=97.1MB, time=112.24 memory used=2919.4MB, alloc=97.1MB, time=112.52 memory used=2955.3MB, alloc=97.1MB, time=112.81 memory used=2996.5MB, alloc=97.1MB, time=113.13 memory used=3040.0MB, alloc=97.1MB, time=113.42 memory used=3081.2MB, alloc=97.1MB, time=116.67 memory used=3141.2MB, alloc=97.1MB, time=119.01 memory used=3175.5MB, alloc=97.1MB, time=119.32 memory used=3220.2MB, alloc=97.1MB, time=119.68 memory used=3253.7MB, alloc=97.1MB, time=119.98 memory used=3284.3MB, alloc=97.1MB, time=120.23 memory used=3318.5MB, alloc=97.1MB, time=120.50 memory used=3357.5MB, alloc=97.1MB, time=120.80 memory used=3401.2MB, alloc=97.1MB, time=121.08 memory used=3434.5MB, alloc=97.1MB, time=121.33 memory used=3498.4MB, alloc=97.1MB, time=136.92 memory used=3553.0MB, alloc=97.1MB, time=137.44 memory used=3585.4MB, alloc=97.1MB, time=137.73 memory used=3624.3MB, alloc=97.1MB, time=138.02 memory used=3670.6MB, alloc=97.1MB, time=138.36 memory used=3700.5MB, alloc=97.1MB, time=138.67 memory used=3728.0MB, alloc=97.1MB, time=138.94 memory used=3757.9MB, alloc=97.1MB, time=139.24 memory used=3790.3MB, alloc=97.1MB, time=139.49 memory used=3824.9MB, alloc=97.1MB, time=139.77 memory used=3862.5MB, alloc=97.1MB, time=140.04 memory used=3902.8MB, alloc=97.1MB, time=140.33 memory used=3946.3MB, alloc=97.1MB, time=140.60 memory used=3993.6MB, alloc=97.1MB, time=140.88 memory used=4021.3MB, alloc=97.1MB, time=141.10 memory used=4046.9MB, alloc=97.1MB, time=141.30 memory used=4074.0MB, alloc=97.1MB, time=141.50 memory used=4101.7MB, alloc=97.1MB, time=141.71 memory used=4131.5MB, alloc=97.1MB, time=141.93 memory used=4171.7MB, alloc=97.1MB, time=142.34 memory used=4244.9MB, alloc=353.1MB, time=144.88 memory used=4321.5MB, alloc=353.1MB, time=147.62 memory used=4354.4MB, alloc=353.1MB, time=147.92 memory used=4389.9MB, alloc=353.1MB, time=148.22 memory used=4417.4MB, alloc=353.1MB, time=148.50 memory used=4480.9MB, alloc=353.1MB, time=150.16 memory used=4564.0MB, alloc=353.1MB, time=152.28 memory used=4638.8MB, alloc=377.1MB, time=153.96 memory used=4718.1MB, alloc=377.1MB, time=155.46 memory used=4788.9MB, alloc=377.1MB, time=156.70 memory used=4825.6MB, alloc=377.1MB, time=157.12 memory used=4865.7MB, alloc=377.1MB, time=157.54 memory used=4913.8MB, alloc=377.1MB, time=157.98 memory used=4964.0MB, alloc=377.1MB, time=158.39 memory used=4993.8MB, alloc=377.1MB, time=158.73 memory used=5025.9MB, alloc=377.1MB, time=159.08 memory used=5060.0MB, alloc=377.1MB, time=159.42 memory used=5096.0MB, alloc=377.1MB, time=159.78 memory used=5136.5MB, alloc=377.1MB, time=160.12 memory used=5179.4MB, alloc=377.1MB, time=160.52 memory used=5226.7MB, alloc=377.1MB, time=160.88 memory used=5275.9MB, alloc=377.1MB, time=161.24 memory used=5333.6MB, alloc=377.1MB, time=162.66 memory used=5386.3MB, alloc=377.1MB, time=163.17 memory used=5422.4MB, alloc=377.1MB, time=163.62 memory used=5466.5MB, alloc=377.1MB, time=164.08 memory used=5518.1MB, alloc=377.1MB, time=164.55 memory used=5558.9MB, alloc=377.1MB, time=164.94 memory used=5588.5MB, alloc=377.1MB, time=165.30 memory used=5620.8MB, alloc=377.1MB, time=165.65 memory used=5656.7MB, alloc=377.1MB, time=166.05 memory used=5694.2MB, alloc=377.1MB, time=166.47 memory used=5736.3MB, alloc=377.1MB, time=166.87 memory used=5781.7MB, alloc=377.1MB, time=167.29 memory used=5831.9MB, alloc=377.1MB, time=167.73 memory used=5870.7MB, alloc=377.1MB, time=168.07 memory used=5957.6MB, alloc=377.1MB, time=238.92 memory used=6025.2MB, alloc=377.1MB, time=295.53 memory used=6068.5MB, alloc=377.1MB, time=296.00 memory used=6115.5MB, alloc=377.1MB, time=296.43 memory used=6147.9MB, alloc=377.1MB, time=296.82 memory used=6184.5MB, alloc=377.1MB, time=297.23 memory used=6226.2MB, alloc=377.1MB, time=297.64 memory used=6273.0MB, alloc=377.1MB, time=298.04 memory used=6324.9MB, alloc=377.1MB, time=298.42 memory used=6357.3MB, alloc=377.1MB, time=298.72 memory used=6386.5MB, alloc=377.1MB, time=299.04 memory used=6417.5MB, alloc=377.1MB, time=299.35 memory used=6450.0MB, alloc=377.1MB, time=299.65 memory used=6483.8MB, alloc=377.1MB, time=299.96 memory used=6520.2MB, alloc=377.1MB, time=300.30 memory used=6557.6MB, alloc=377.1MB, time=300.64 memory used=6598.0MB, alloc=377.1MB, time=300.96 memory used=6640.1MB, alloc=377.1MB, time=301.29 memory used=6685.3MB, alloc=377.1MB, time=301.62 memory used=6733.3MB, alloc=377.1MB, time=301.97 memory used=6783.4MB, alloc=377.1MB, time=302.31 memory used=6908.8MB, alloc=377.1MB, time=304.07 memory used=6952.2MB, alloc=377.1MB, time=304.54 memory used=6990.5MB, alloc=377.1MB, time=304.95 memory used=7035.9MB, alloc=377.1MB, time=305.42 memory used=7090.5MB, alloc=377.1MB, time=305.94 memory used=7123.6MB, alloc=377.1MB, time=306.34 memory used=7155.0MB, alloc=377.1MB, time=306.76 memory used=7189.1MB, alloc=377.1MB, time=307.13 memory used=7225.0MB, alloc=377.1MB, time=307.49 memory used=7264.1MB, alloc=377.1MB, time=307.87 memory used=7307.4MB, alloc=377.1MB, time=308.25 memory used=7355.1MB, alloc=377.1MB, time=308.64 memory used=7407.3MB, alloc=377.1MB, time=309.02 memory used=7458.9MB, alloc=377.1MB, time=310.31 memory used=7515.4MB, alloc=377.1MB, time=310.88 memory used=7551.5MB, alloc=377.1MB, time=311.31 memory used=7595.2MB, alloc=377.1MB, time=311.73 memory used=7646.5MB, alloc=377.1MB, time=312.22 memory used=7689.3MB, alloc=377.1MB, time=312.63 memory used=7718.9MB, alloc=377.1MB, time=312.99 memory used=7751.0MB, alloc=377.1MB, time=313.35 memory used=7785.2MB, alloc=377.1MB, time=313.74 memory used=7822.6MB, alloc=377.1MB, time=314.14 memory used=7863.0MB, alloc=377.1MB, time=314.50 memory used=7907.3MB, alloc=377.1MB, time=314.88 memory used=7956.4MB, alloc=377.1MB, time=315.30 memory used=7998.7MB, alloc=377.1MB, time=315.66 memory used=8077.0MB, alloc=377.1MB, time=386.51 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428530731 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 3 2 F := [-x z - 3 x z + 15 y, -16 x y - 8 y z + 2 x z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 3 3 3 G := [3 x y z + 7 y z - 7 z , 8 x z + 19 x + 10 y ] > Problem := [F,G]; 3 2 2 3 2 Problem := [[-x z - 3 x z + 15 y, -16 x y - 8 y z + 2 x z], 2 2 3 3 3 3 [3 x y z + 7 y z - 7 z , 8 x z + 19 x + 10 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.60 memory used=26.7MB, alloc=32.3MB, time=1.77 memory used=46.8MB, alloc=32.3MB, time=2.84 memory used=64.8MB, alloc=56.3MB, time=3.85 memory used=106.9MB, alloc=68.3MB, time=5.56 memory used=150.7MB, alloc=68.3MB, time=7.24 memory used=201.7MB, alloc=68.3MB, time=8.93 memory used=246.1MB, alloc=68.3MB, time=10.62 memory used=290.5MB, alloc=68.3MB, time=12.60 memory used=331.9MB, alloc=68.3MB, time=14.62 memory used=370.7MB, alloc=92.3MB, time=16.76 memory used=437.6MB, alloc=92.3MB, time=19.84 memory used=502.1MB, alloc=92.3MB, time=22.38 memory used=562.2MB, alloc=116.3MB, time=25.36 memory used=636.1MB, alloc=116.3MB, time=28.52 memory used=697.6MB, alloc=372.3MB, time=31.05 memory used=786.0MB, alloc=396.3MB, time=34.69 memory used=873.2MB, alloc=396.3MB, time=36.72 memory used=958.3MB, alloc=396.3MB, time=38.12 memory used=1036.4MB, alloc=396.3MB, time=39.13 memory used=1117.9MB, alloc=396.3MB, time=40.26 memory used=1183.1MB, alloc=396.3MB, time=40.95 memory used=1256.8MB, alloc=396.3MB, time=42.31 memory used=1338.0MB, alloc=396.3MB, time=43.40 memory used=1416.2MB, alloc=396.3MB, time=44.41 memory used=1485.6MB, alloc=396.3MB, time=45.26 memory used=1599.1MB, alloc=396.3MB, time=48.27 memory used=1716.8MB, alloc=396.3MB, time=51.16 memory used=1844.8MB, alloc=420.3MB, time=54.39 memory used=1931.5MB, alloc=420.3MB, time=55.33 memory used=2037.4MB, alloc=420.3MB, time=56.01 memory used=2142.8MB, alloc=420.3MB, time=56.52 memory used=2236.6MB, alloc=420.3MB, time=56.93 memory used=2330.7MB, alloc=420.3MB, time=57.32 memory used=2452.8MB, alloc=420.3MB, time=58.16 memory used=2595.8MB, alloc=420.3MB, time=59.32 memory used=2709.7MB, alloc=420.3MB, time=60.16 memory used=2823.0MB, alloc=420.3MB, time=60.92 memory used=2926.5MB, alloc=420.3MB, time=61.42 memory used=3026.0MB, alloc=420.3MB, time=61.85 memory used=3148.3MB, alloc=444.3MB, time=63.07 memory used=3282.7MB, alloc=444.3MB, time=64.12 memory used=3390.3MB, alloc=444.3MB, time=65.35 memory used=3498.6MB, alloc=444.3MB, time=66.74 memory used=3593.8MB, alloc=468.3MB, time=67.85 memory used=3687.2MB, alloc=468.3MB, time=68.97 memory used=3780.8MB, alloc=468.3MB, time=70.27 memory used=3881.4MB, alloc=468.3MB, time=71.66 memory used=3996.8MB, alloc=468.3MB, time=72.70 memory used=4084.4MB, alloc=468.3MB, time=73.13 memory used=4177.0MB, alloc=468.3MB, time=73.60 memory used=4277.2MB, alloc=468.3MB, time=74.21 memory used=4370.5MB, alloc=468.3MB, time=74.67 memory used=4462.6MB, alloc=468.3MB, time=75.12 memory used=4551.8MB, alloc=468.3MB, time=75.57 memory used=4642.7MB, alloc=468.3MB, time=76.02 memory used=4731.8MB, alloc=468.3MB, time=76.45 memory used=4818.7MB, alloc=468.3MB, time=76.81 memory used=4882.8MB, alloc=468.3MB, time=77.13 memory used=4977.4MB, alloc=468.3MB, time=77.54 memory used=5044.8MB, alloc=468.3MB, time=77.87 memory used=5142.7MB, alloc=468.3MB, time=78.38 memory used=5208.3MB, alloc=468.3MB, time=78.70 memory used=5304.4MB, alloc=468.3MB, time=79.12 memory used=5380.3MB, alloc=468.3MB, time=79.45 memory used=5463.5MB, alloc=468.3MB, time=79.87 memory used=5545.1MB, alloc=468.3MB, time=80.28 memory used=5621.7MB, alloc=468.3MB, time=80.75 memory used=5704.1MB, alloc=468.3MB, time=81.12 memory used=5773.0MB, alloc=468.3MB, time=81.45 memory used=5868.6MB, alloc=468.3MB, time=81.92 memory used=5965.2MB, alloc=468.3MB, time=82.42 memory used=6044.2MB, alloc=468.3MB, time=82.78 memory used=6121.9MB, alloc=492.3MB, time=83.13 memory used=6200.7MB, alloc=492.3MB, time=83.49 memory used=6301.3MB, alloc=492.3MB, time=83.83 memory used=6403.2MB, alloc=492.3MB, time=84.27 memory used=6503.8MB, alloc=492.3MB, time=84.69 memory used=6589.4MB, alloc=492.3MB, time=85.05 memory used=6677.0MB, alloc=492.3MB, time=85.41 memory used=6782.1MB, alloc=492.3MB, time=85.76 memory used=6884.1MB, alloc=492.3MB, time=86.45 memory used=6974.8MB, alloc=492.3MB, time=86.81 memory used=7067.1MB, alloc=492.3MB, time=87.16 memory used=7160.5MB, alloc=492.3MB, time=87.48 memory used=7233.8MB, alloc=492.3MB, time=87.76 memory used=7361.1MB, alloc=492.3MB, time=88.49 memory used=7471.3MB, alloc=492.3MB, time=89.00 memory used=7573.5MB, alloc=492.3MB, time=89.44 memory used=7695.0MB, alloc=492.3MB, time=90.03 memory used=7797.3MB, alloc=492.3MB, time=90.47 memory used=7905.3MB, alloc=492.3MB, time=90.94 memory used=8023.6MB, alloc=492.3MB, time=91.69 memory used=8134.2MB, alloc=492.3MB, time=92.14 memory used=8215.6MB, alloc=492.3MB, time=92.50 memory used=8334.6MB, alloc=492.3MB, time=93.01 memory used=8429.4MB, alloc=492.3MB, time=93.41 memory used=8511.3MB, alloc=492.3MB, time=93.77 memory used=8641.9MB, alloc=492.3MB, time=94.53 memory used=8729.9MB, alloc=492.3MB, time=94.89 memory used=8864.8MB, alloc=492.3MB, time=95.92 memory used=9000.7MB, alloc=492.3MB, time=96.91 memory used=9121.8MB, alloc=492.3MB, time=97.85 memory used=9208.2MB, alloc=492.3MB, time=98.22 memory used=9348.3MB, alloc=492.3MB, time=99.43 memory used=9425.4MB, alloc=492.3MB, time=100.56 memory used=9495.7MB, alloc=492.3MB, time=101.61 memory used=9563.1MB, alloc=492.3MB, time=102.56 memory used=9621.4MB, alloc=492.3MB, time=103.37 memory used=9669.2MB, alloc=492.3MB, time=104.07 memory used=9735.5MB, alloc=492.3MB, time=104.88 memory used=9809.4MB, alloc=492.3MB, time=105.43 memory used=9874.9MB, alloc=492.3MB, time=105.91 memory used=9961.8MB, alloc=492.3MB, time=106.72 memory used=10012.1MB, alloc=492.3MB, time=107.52 memory used=10069.9MB, alloc=492.3MB, time=108.36 memory used=10130.4MB, alloc=492.3MB, time=109.25 memory used=10191.7MB, alloc=492.3MB, time=110.08 memory used=10238.5MB, alloc=492.3MB, time=110.76 memory used=10304.9MB, alloc=492.3MB, time=111.59 memory used=10350.6MB, alloc=492.3MB, time=112.29 memory used=10401.1MB, alloc=492.3MB, time=113.12 memory used=10569.6MB, alloc=492.3MB, time=114.87 memory used=10751.3MB, alloc=492.3MB, time=116.27 memory used=10878.2MB, alloc=492.3MB, time=117.10 memory used=10991.3MB, alloc=492.3MB, time=117.72 memory used=11108.7MB, alloc=492.3MB, time=118.66 memory used=11229.9MB, alloc=492.3MB, time=120.97 memory used=11336.4MB, alloc=516.3MB, time=121.55 memory used=11445.8MB, alloc=516.3MB, time=122.05 memory used=11559.2MB, alloc=516.3MB, time=122.73 memory used=11797.3MB, alloc=516.3MB, time=125.56 memory used=11954.6MB, alloc=516.3MB, time=126.23 memory used=12064.1MB, alloc=516.3MB, time=126.79 memory used=12149.1MB, alloc=516.3MB, time=127.30 memory used=12249.1MB, alloc=516.3MB, time=127.80 memory used=12349.6MB, alloc=516.3MB, time=128.31 memory used=12442.3MB, alloc=516.3MB, time=128.76 memory used=12597.0MB, alloc=516.3MB, time=158.76 memory used=12728.4MB, alloc=516.3MB, time=160.05 memory used=12819.9MB, alloc=516.3MB, time=160.58 memory used=12933.2MB, alloc=516.3MB, time=161.12 memory used=13033.4MB, alloc=516.3MB, time=161.61 memory used=13110.9MB, alloc=516.3MB, time=162.09 memory used=13197.1MB, alloc=516.3MB, time=162.56 memory used=13294.5MB, alloc=516.3MB, time=163.04 memory used=13393.7MB, alloc=516.3MB, time=163.50 memory used=13489.1MB, alloc=516.3MB, time=163.95 memory used=13683.7MB, alloc=516.3MB, time=165.70 memory used=13930.6MB, alloc=516.3MB, time=167.68 memory used=14162.0MB, alloc=516.3MB, time=170.45 memory used=14385.9MB, alloc=516.3MB, time=173.30 memory used=14588.6MB, alloc=516.3MB, time=175.42 memory used=14745.5MB, alloc=516.3MB, time=176.35 memory used=14864.6MB, alloc=516.3MB, time=177.09 memory used=15006.4MB, alloc=516.3MB, time=178.20 memory used=15125.8MB, alloc=516.3MB, time=178.86 memory used=15257.5MB, alloc=516.3MB, time=181.18 memory used=15356.8MB, alloc=516.3MB, time=181.71 memory used=15445.4MB, alloc=516.3MB, time=182.21 memory used=15678.4MB, alloc=540.3MB, time=184.36 memory used=15918.2MB, alloc=540.3MB, time=186.56 memory used=16137.7MB, alloc=540.3MB, time=188.86 memory used=16257.6MB, alloc=540.3MB, time=189.53 memory used=16355.3MB, alloc=540.3MB, time=190.13 memory used=16475.3MB, alloc=540.3MB, time=190.74 memory used=16586.6MB, alloc=540.3MB, time=191.30 memory used=16665.5MB, alloc=540.3MB, time=191.83 memory used=16751.4MB, alloc=540.3MB, time=192.35 memory used=16847.3MB, alloc=540.3MB, time=192.90 memory used=16954.3MB, alloc=540.3MB, time=193.44 memory used=17074.8MB, alloc=540.3MB, time=193.96 memory used=17244.8MB, alloc=540.3MB, time=224.33 memory used=17367.3MB, alloc=540.3MB, time=225.43 memory used=17484.7MB, alloc=540.3MB, time=226.03 memory used=17569.2MB, alloc=540.3MB, time=226.58 memory used=17665.9MB, alloc=540.3MB, time=227.11 memory used=17776.3MB, alloc=540.3MB, time=227.68 memory used=17902.8MB, alloc=540.3MB, time=228.23 memory used=18001.9MB, alloc=540.3MB, time=228.74 memory used=18076.7MB, alloc=540.3MB, time=229.22 memory used=18157.5MB, alloc=540.3MB, time=229.70 memory used=18243.8MB, alloc=540.3MB, time=230.18 memory used=18335.9MB, alloc=540.3MB, time=230.67 memory used=18434.9MB, alloc=540.3MB, time=231.16 memory used=18543.0MB, alloc=540.3MB, time=231.64 memory used=18660.6MB, alloc=540.3MB, time=232.13 memory used=18887.9MB, alloc=540.3MB, time=233.88 memory used=19086.6MB, alloc=564.3MB, time=236.55 memory used=19307.1MB, alloc=564.3MB, time=239.90 memory used=19417.9MB, alloc=564.3MB, time=240.49 memory used=19518.3MB, alloc=564.3MB, time=241.03 memory used=19614.0MB, alloc=564.3MB, time=241.57 memory used=19727.0MB, alloc=564.3MB, time=242.11 memory used=19859.5MB, alloc=564.3MB, time=242.66 memory used=20041.5MB, alloc=564.3MB, time=243.39 memory used=20183.9MB, alloc=564.3MB, time=243.96 memory used=20384.6MB, alloc=588.3MB, time=246.60 memory used=20558.2MB, alloc=588.3MB, time=248.97 memory used=20724.1MB, alloc=612.3MB, time=251.42 memory used=20931.3MB, alloc=612.3MB, time=253.70 memory used=21147.5MB, alloc=636.3MB, time=256.26 memory used=21340.5MB, alloc=636.3MB, time=257.50 memory used=21506.2MB, alloc=636.3MB, time=258.43 memory used=21669.2MB, alloc=636.3MB, time=259.37 memory used=21828.7MB, alloc=636.3MB, time=260.19 memory used=21993.8MB, alloc=636.3MB, time=261.14 memory used=22178.1MB, alloc=636.3MB, time=263.11 memory used=22342.3MB, alloc=636.3MB, time=264.09 memory used=22501.5MB, alloc=636.3MB, time=264.95 memory used=22661.6MB, alloc=636.3MB, time=266.03 memory used=22835.3MB, alloc=636.3MB, time=267.46 memory used=22974.5MB, alloc=636.3MB, time=268.23 memory used=23125.9MB, alloc=636.3MB, time=269.05 memory used=23295.7MB, alloc=636.3MB, time=272.78 memory used=23448.7MB, alloc=636.3MB, time=273.51 memory used=23562.5MB, alloc=636.3MB, time=274.16 memory used=23705.1MB, alloc=636.3MB, time=274.83 memory used=24037.1MB, alloc=636.3MB, time=276.75 memory used=24258.2MB, alloc=636.3MB, time=278.85 memory used=24485.4MB, alloc=660.3MB, time=286.20 memory used=24656.0MB, alloc=660.3MB, time=287.17 memory used=24813.0MB, alloc=660.3MB, time=288.10 memory used=25015.5MB, alloc=660.3MB, time=289.40 memory used=25184.2MB, alloc=660.3MB, time=290.30 memory used=25353.1MB, alloc=660.3MB, time=291.30 memory used=25553.6MB, alloc=660.3MB, time=293.20 memory used=25756.8MB, alloc=660.3MB, time=294.44 memory used=25925.7MB, alloc=660.3MB, time=295.36 memory used=26092.4MB, alloc=660.3MB, time=296.39 memory used=26278.7MB, alloc=660.3MB, time=297.84 memory used=26419.5MB, alloc=660.3MB, time=298.56 memory used=26587.8MB, alloc=660.3MB, time=299.47 memory used=26762.6MB, alloc=660.3MB, time=303.22 memory used=26914.7MB, alloc=660.3MB, time=303.98 memory used=27046.5MB, alloc=660.3MB, time=304.68 memory used=27216.4MB, alloc=660.3MB, time=305.38 memory used=27457.8MB, alloc=660.3MB, time=307.30 memory used=27665.8MB, alloc=660.3MB, time=309.36 memory used=27884.2MB, alloc=660.3MB, time=310.98 memory used=28042.4MB, alloc=660.3MB, time=311.88 memory used=28196.1MB, alloc=660.3MB, time=312.81 memory used=28350.2MB, alloc=660.3MB, time=313.81 memory used=28511.2MB, alloc=660.3MB, time=314.84 memory used=28681.7MB, alloc=660.3MB, time=316.09 memory used=28825.7MB, alloc=660.3MB, time=316.95 memory used=28960.4MB, alloc=660.3MB, time=317.74 memory used=29088.9MB, alloc=660.3MB, time=318.51 memory used=29245.6MB, alloc=660.3MB, time=319.31 memory used=29513.9MB, alloc=660.3MB, time=320.22 memory used=29749.4MB, alloc=660.3MB, time=321.48 memory used=29908.5MB, alloc=660.3MB, time=322.31 memory used=30024.5MB, alloc=660.3MB, time=323.06 memory used=30166.2MB, alloc=660.3MB, time=323.85 memory used=30337.2MB, alloc=660.3MB, time=324.64 memory used=30519.1MB, alloc=660.3MB, time=325.45 memory used=30768.2MB, alloc=660.3MB, time=327.03 memory used=30897.8MB, alloc=660.3MB, time=327.80 memory used=31050.8MB, alloc=660.3MB, time=328.57 memory used=31282.6MB, alloc=660.3MB, time=329.47 memory used=31436.9MB, alloc=660.3MB, time=330.24 memory used=31668.5MB, alloc=660.3MB, time=333.02 memory used=31983.2MB, alloc=660.3MB, time=335.03 memory used=32188.3MB, alloc=684.3MB, time=338.42 memory used=32401.6MB, alloc=684.3MB, time=340.56 memory used=32583.7MB, alloc=684.3MB, time=341.64 memory used=32713.3MB, alloc=684.3MB, time=342.49 memory used=32864.2MB, alloc=684.3MB, time=343.41 memory used=33041.5MB, alloc=684.3MB, time=344.29 memory used=33235.9MB, alloc=684.3MB, time=345.21 memory used=33360.6MB, alloc=684.3MB, time=345.98 memory used=33479.1MB, alloc=708.3MB, time=346.75 memory used=33618.5MB, alloc=708.3MB, time=347.52 memory used=33770.5MB, alloc=708.3MB, time=348.32 memory used=33928.3MB, alloc=708.3MB, time=349.20 memory used=34097.1MB, alloc=708.3MB, time=350.09 memory used=34276.8MB, alloc=708.3MB, time=350.97 memory used=34469.2MB, alloc=708.3MB, time=351.87 memory used=34674.4MB, alloc=708.3MB, time=352.77 memory used=34914.9MB, alloc=708.3MB, time=353.70 memory used=35194.4MB, alloc=708.3MB, time=354.73 memory used=35331.3MB, alloc=708.3MB, time=355.56 memory used=35448.3MB, alloc=708.3MB, time=356.37 memory used=35569.7MB, alloc=708.3MB, time=357.18 memory used=35697.6MB, alloc=708.3MB, time=358.00 memory used=35826.7MB, alloc=708.3MB, time=358.83 memory used=35962.8MB, alloc=708.3MB, time=359.64 memory used=36106.2MB, alloc=708.3MB, time=360.47 memory used=36252.9MB, alloc=708.3MB, time=361.31 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428531031 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 4 2 4 3 F := [4 x z + 6 z - 10 y, x y z - 20 z - 13 z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 2 2 2 3 G := [11 x + 4 x z - 15 x y , -3 x z + 12 x z + 7 x y] > Problem := [F,G]; 2 2 4 2 4 3 Problem := [[4 x z + 6 z - 10 y, x y z - 20 z - 13 z ], 4 2 2 2 2 2 3 [11 x + 4 x z - 15 x y , -3 x z + 12 x z + 7 x y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.2MB, alloc=32.3MB, time=0.51 memory used=45.9MB, alloc=56.3MB, time=0.82 memory used=87.1MB, alloc=60.3MB, time=1.44 memory used=129.6MB, alloc=68.3MB, time=1.85 memory used=174.4MB, alloc=68.3MB, time=2.29 memory used=216.1MB, alloc=92.3MB, time=2.77 memory used=281.9MB, alloc=92.3MB, time=3.52 memory used=347.3MB, alloc=92.3MB, time=4.11 memory used=414.7MB, alloc=92.3MB, time=4.68 memory used=480.9MB, alloc=92.3MB, time=5.16 memory used=544.0MB, alloc=116.3MB, time=5.79 memory used=613.6MB, alloc=116.3MB, time=6.52 memory used=681.4MB, alloc=372.3MB, time=7.29 memory used=774.6MB, alloc=372.3MB, time=8.10 memory used=855.3MB, alloc=396.3MB, time=8.98 memory used=964.7MB, alloc=420.3MB, time=10.34 memory used=1092.1MB, alloc=444.3MB, time=11.78 memory used=1240.6MB, alloc=444.3MB, time=13.21 memory used=1374.3MB, alloc=468.3MB, time=14.81 memory used=1498.7MB, alloc=468.3MB, time=16.17 memory used=1604.0MB, alloc=468.3MB, time=17.46 memory used=1704.3MB, alloc=492.3MB, time=18.76 memory used=1800.7MB, alloc=492.3MB, time=20.03 memory used=1953.7MB, alloc=492.3MB, time=21.29 memory used=2093.4MB, alloc=492.3MB, time=22.29 memory used=2188.1MB, alloc=492.3MB, time=22.68 memory used=2283.6MB, alloc=492.3MB, time=23.05 memory used=2412.1MB, alloc=492.3MB, time=23.74 memory used=2492.1MB, alloc=492.3MB, time=24.09 memory used=2589.2MB, alloc=492.3MB, time=29.82 memory used=2716.9MB, alloc=492.3MB, time=44.68 memory used=2793.8MB, alloc=492.3MB, time=44.94 memory used=2875.1MB, alloc=492.3MB, time=45.21 memory used=2961.2MB, alloc=492.3MB, time=45.47 memory used=3090.5MB, alloc=492.3MB, time=46.15 memory used=3168.4MB, alloc=492.3MB, time=46.52 memory used=3279.7MB, alloc=516.3MB, time=49.13 memory used=3434.8MB, alloc=516.3MB, time=49.67 memory used=3554.5MB, alloc=516.3MB, time=50.14 memory used=3645.3MB, alloc=516.3MB, time=50.57 memory used=3731.3MB, alloc=516.3MB, time=50.97 memory used=3816.9MB, alloc=516.3MB, time=51.38 memory used=3906.7MB, alloc=516.3MB, time=51.79 memory used=4002.8MB, alloc=516.3MB, time=52.20 memory used=4105.7MB, alloc=516.3MB, time=52.62 memory used=4215.1MB, alloc=516.3MB, time=53.09 memory used=4334.9MB, alloc=516.3MB, time=53.50 memory used=4460.4MB, alloc=516.3MB, time=53.94 memory used=4584.5MB, alloc=516.3MB, time=54.35 memory used=4659.5MB, alloc=516.3MB, time=54.75 memory used=4728.5MB, alloc=516.3MB, time=55.11 memory used=4798.7MB, alloc=516.3MB, time=55.47 memory used=4872.3MB, alloc=516.3MB, time=55.84 memory used=4948.9MB, alloc=516.3MB, time=56.16 memory used=5028.0MB, alloc=516.3MB, time=56.49 memory used=5109.2MB, alloc=516.3MB, time=56.82 memory used=5195.5MB, alloc=516.3MB, time=57.16 memory used=5285.5MB, alloc=516.3MB, time=57.49 memory used=5377.8MB, alloc=516.3MB, time=57.83 memory used=5476.6MB, alloc=516.3MB, time=58.20 memory used=5580.3MB, alloc=516.3MB, time=58.55 memory used=5693.7MB, alloc=516.3MB, time=58.90 memory used=5829.6MB, alloc=516.3MB, time=62.88 memory used=5926.1MB, alloc=516.3MB, time=63.32 memory used=6018.9MB, alloc=516.3MB, time=63.73 memory used=6112.4MB, alloc=516.3MB, time=64.17 memory used=6211.0MB, alloc=516.3MB, time=64.61 memory used=6317.2MB, alloc=516.3MB, time=65.01 memory used=6431.6MB, alloc=516.3MB, time=65.42 memory used=6554.4MB, alloc=516.3MB, time=65.87 memory used=6674.5MB, alloc=516.3MB, time=66.28 memory used=6760.0MB, alloc=516.3MB, time=66.65 memory used=6839.3MB, alloc=516.3MB, time=67.00 memory used=6913.9MB, alloc=540.3MB, time=67.34 memory used=6997.2MB, alloc=540.3MB, time=67.72 memory used=7085.9MB, alloc=540.3MB, time=68.09 memory used=7179.3MB, alloc=540.3MB, time=68.47 memory used=7273.5MB, alloc=540.3MB, time=68.86 memory used=7372.4MB, alloc=540.3MB, time=69.26 memory used=7475.8MB, alloc=540.3MB, time=69.66 memory used=7583.6MB, alloc=540.3MB, time=70.03 memory used=7695.4MB, alloc=540.3MB, time=70.43 memory used=7810.8MB, alloc=540.3MB, time=70.81 memory used=7929.5MB, alloc=540.3MB, time=71.20 memory used=8055.0MB, alloc=540.3MB, time=71.58 memory used=8182.2MB, alloc=540.3MB, time=71.95 memory used=8314.6MB, alloc=540.3MB, time=72.34 memory used=8454.4MB, alloc=540.3MB, time=72.73 memory used=8599.6MB, alloc=540.3MB, time=73.12 memory used=8737.2MB, alloc=540.3MB, time=73.52 memory used=8819.4MB, alloc=540.3MB, time=73.82 memory used=8899.0MB, alloc=540.3MB, time=74.12 memory used=8981.5MB, alloc=540.3MB, time=74.42 memory used=9068.3MB, alloc=540.3MB, time=74.72 memory used=9158.9MB, alloc=540.3MB, time=75.02 memory used=9272.4MB, alloc=540.3MB, time=75.49 memory used=9432.1MB, alloc=540.3MB, time=76.03 memory used=9809.5MB, alloc=540.3MB, time=158.02 memory used=10005.3MB, alloc=540.3MB, time=158.44 memory used=10206.9MB, alloc=540.3MB, time=158.85 memory used=10418.2MB, alloc=540.3MB, time=159.27 memory used=10600.6MB, alloc=540.3MB, time=161.04 memory used=10742.4MB, alloc=540.3MB, time=162.12 memory used=10863.6MB, alloc=540.3MB, time=163.22 memory used=11045.1MB, alloc=540.3MB, time=164.57 memory used=11162.2MB, alloc=540.3MB, time=165.53 memory used=11232.4MB, alloc=540.3MB, time=166.49 memory used=11350.6MB, alloc=540.3MB, time=167.60 memory used=11479.9MB, alloc=540.3MB, time=168.82 memory used=11625.6MB, alloc=540.3MB, time=169.41 memory used=11753.0MB, alloc=540.3MB, time=169.99 memory used=11900.2MB, alloc=540.3MB, time=170.76 memory used=12025.4MB, alloc=540.3MB, time=171.29 memory used=12188.3MB, alloc=540.3MB, time=191.73 memory used=12291.8MB, alloc=540.3MB, time=192.07 memory used=12402.6MB, alloc=540.3MB, time=192.41 memory used=12528.8MB, alloc=540.3MB, time=193.12 memory used=12735.2MB, alloc=540.3MB, time=193.79 memory used=12950.3MB, alloc=540.3MB, time=194.80 memory used=13058.1MB, alloc=540.3MB, time=195.27 memory used=13217.1MB, alloc=540.3MB, time=198.14 memory used=13377.6MB, alloc=540.3MB, time=198.76 memory used=13485.0MB, alloc=540.3MB, time=199.29 memory used=13580.0MB, alloc=540.3MB, time=199.77 memory used=13671.8MB, alloc=540.3MB, time=200.24 memory used=13768.9MB, alloc=540.3MB, time=200.75 memory used=13874.0MB, alloc=540.3MB, time=201.26 memory used=13986.4MB, alloc=540.3MB, time=201.77 memory used=14109.8MB, alloc=540.3MB, time=202.24 memory used=14239.8MB, alloc=540.3MB, time=202.73 memory used=14379.9MB, alloc=540.3MB, time=203.23 memory used=14496.8MB, alloc=540.3MB, time=203.69 memory used=14573.9MB, alloc=540.3MB, time=204.12 memory used=14650.2MB, alloc=540.3MB, time=204.55 memory used=14728.8MB, alloc=540.3MB, time=204.98 memory used=14810.4MB, alloc=540.3MB, time=205.39 memory used=14894.7MB, alloc=540.3MB, time=205.80 memory used=14984.8MB, alloc=540.3MB, time=206.21 memory used=15079.5MB, alloc=540.3MB, time=206.66 memory used=15177.5MB, alloc=540.3MB, time=207.10 memory used=15280.2MB, alloc=540.3MB, time=207.54 memory used=15387.6MB, alloc=540.3MB, time=207.96 memory used=15503.1MB, alloc=540.3MB, time=208.37 memory used=15652.2MB, alloc=540.3MB, time=211.31 memory used=15768.5MB, alloc=540.3MB, time=212.95 memory used=15870.8MB, alloc=540.3MB, time=213.46 memory used=15973.1MB, alloc=540.3MB, time=213.94 memory used=16079.6MB, alloc=540.3MB, time=214.42 memory used=16193.2MB, alloc=540.3MB, time=214.88 memory used=16316.2MB, alloc=540.3MB, time=215.41 memory used=16452.0MB, alloc=540.3MB, time=215.92 memory used=16576.1MB, alloc=540.3MB, time=216.40 memory used=16666.7MB, alloc=540.3MB, time=216.85 memory used=16751.1MB, alloc=564.3MB, time=217.31 memory used=16844.4MB, alloc=564.3MB, time=217.74 memory used=16939.0MB, alloc=564.3MB, time=218.17 memory used=17037.1MB, alloc=564.3MB, time=218.61 memory used=17140.4MB, alloc=564.3MB, time=219.05 memory used=17248.6MB, alloc=564.3MB, time=219.49 memory used=17361.4MB, alloc=564.3MB, time=219.92 memory used=17478.5MB, alloc=564.3MB, time=220.36 memory used=17599.6MB, alloc=564.3MB, time=220.84 memory used=17724.2MB, alloc=564.3MB, time=221.33 memory used=17856.1MB, alloc=564.3MB, time=221.80 memory used=17994.3MB, alloc=564.3MB, time=222.30 memory used=18137.6MB, alloc=564.3MB, time=222.77 memory used=18288.5MB, alloc=564.3MB, time=223.27 memory used=18444.8MB, alloc=564.3MB, time=223.76 memory used=18600.4MB, alloc=564.3MB, time=224.25 memory used=18694.8MB, alloc=564.3MB, time=224.61 memory used=18781.5MB, alloc=564.3MB, time=224.99 memory used=18872.6MB, alloc=564.3MB, time=225.40 memory used=18966.8MB, alloc=564.3MB, time=225.77 memory used=19067.5MB, alloc=564.3MB, time=226.12 memory used=19204.1MB, alloc=564.3MB, time=226.76 memory used=19557.5MB, alloc=564.3MB, time=309.24 memory used=19750.9MB, alloc=564.3MB, time=309.69 memory used=19948.6MB, alloc=564.3MB, time=310.14 memory used=20156.4MB, alloc=564.3MB, time=310.60 memory used=20322.2MB, alloc=564.3MB, time=311.99 memory used=20431.8MB, alloc=564.3MB, time=312.99 memory used=20516.6MB, alloc=564.3MB, time=313.86 memory used=20598.4MB, alloc=564.3MB, time=315.04 memory used=20655.8MB, alloc=564.3MB, time=315.87 memory used=20726.7MB, alloc=564.3MB, time=317.03 memory used=20801.4MB, alloc=564.3MB, time=318.28 memory used=20875.8MB, alloc=564.3MB, time=319.23 memory used=21007.6MB, alloc=564.3MB, time=320.10 memory used=21122.1MB, alloc=564.3MB, time=320.85 memory used=21271.5MB, alloc=564.3MB, time=322.00 memory used=21394.4MB, alloc=564.3MB, time=322.56 memory used=21537.3MB, alloc=564.3MB, time=323.11 memory used=21637.1MB, alloc=564.3MB, time=323.61 memory used=21749.2MB, alloc=564.3MB, time=324.11 memory used=21879.1MB, alloc=564.3MB, time=324.64 memory used=22028.2MB, alloc=564.3MB, time=325.18 memory used=22154.0MB, alloc=564.3MB, time=325.64 memory used=22247.0MB, alloc=564.3MB, time=326.03 memory used=22360.0MB, alloc=564.3MB, time=326.56 memory used=22482.7MB, alloc=564.3MB, time=327.77 memory used=22608.0MB, alloc=564.3MB, time=328.32 memory used=22741.5MB, alloc=564.3MB, time=328.88 memory used=22840.2MB, alloc=564.3MB, time=329.38 memory used=22954.8MB, alloc=564.3MB, time=329.87 memory used=23085.5MB, alloc=564.3MB, time=330.40 memory used=23236.9MB, alloc=564.3MB, time=330.95 memory used=23351.7MB, alloc=564.3MB, time=331.42 memory used=23445.6MB, alloc=564.3MB, time=331.83 memory used=23584.8MB, alloc=564.3MB, time=350.04 memory used=23753.7MB, alloc=564.3MB, time=392.52 memory used=23871.6MB, alloc=564.3MB, time=393.01 memory used=23995.4MB, alloc=564.3MB, time=393.52 memory used=24137.4MB, alloc=564.3MB, time=394.03 memory used=24230.4MB, alloc=564.3MB, time=394.45 memory used=24330.4MB, alloc=564.3MB, time=394.87 memory used=24441.9MB, alloc=564.3MB, time=395.29 memory used=24565.5MB, alloc=564.3MB, time=395.73 memory used=24704.4MB, alloc=564.3MB, time=396.17 memory used=24859.5MB, alloc=564.3MB, time=396.61 memory used=25008.7MB, alloc=564.3MB, time=397.11 memory used=25160.1MB, alloc=564.3MB, time=398.24 memory used=25281.6MB, alloc=564.3MB, time=398.82 memory used=25423.2MB, alloc=564.3MB, time=399.37 memory used=25520.2MB, alloc=564.3MB, time=399.85 memory used=25631.8MB, alloc=564.3MB, time=400.35 memory used=25758.6MB, alloc=564.3MB, time=400.89 memory used=25904.5MB, alloc=564.3MB, time=401.39 memory used=26032.0MB, alloc=564.3MB, time=401.88 memory used=26123.0MB, alloc=564.3MB, time=402.29 memory used=26242.3MB, alloc=564.3MB, time=404.20 memory used=26357.9MB, alloc=588.3MB, time=409.76 memory used=26489.1MB, alloc=588.3MB, time=410.38 memory used=26615.4MB, alloc=588.3MB, time=411.00 memory used=26741.8MB, alloc=588.3MB, time=411.58 memory used=26870.4MB, alloc=588.3MB, time=412.18 memory used=27015.1MB, alloc=588.3MB, time=412.85 memory used=27165.1MB, alloc=588.3MB, time=413.46 memory used=27291.4MB, alloc=588.3MB, time=414.06 memory used=27410.6MB, alloc=588.3MB, time=414.62 memory used=27520.2MB, alloc=588.3MB, time=415.20 memory used=27625.1MB, alloc=612.3MB, time=415.76 memory used=27738.0MB, alloc=612.3MB, time=416.36 memory used=27843.3MB, alloc=612.3MB, time=416.91 memory used=27955.7MB, alloc=612.3MB, time=417.49 memory used=28071.2MB, alloc=612.3MB, time=418.02 memory used=28189.1MB, alloc=612.3MB, time=418.60 memory used=28310.3MB, alloc=612.3MB, time=419.21 memory used=28444.3MB, alloc=612.3MB, time=419.79 memory used=28581.7MB, alloc=612.3MB, time=420.34 memory used=28721.6MB, alloc=612.3MB, time=420.98 memory used=28864.1MB, alloc=612.3MB, time=421.57 memory used=29008.9MB, alloc=612.3MB, time=422.20 memory used=29156.7MB, alloc=612.3MB, time=422.83 memory used=29318.4MB, alloc=612.3MB, time=423.47 memory used=29483.2MB, alloc=612.3MB, time=424.03 memory used=29650.3MB, alloc=612.3MB, time=424.61 memory used=29819.5MB, alloc=612.3MB, time=425.22 memory used=29991.8MB, alloc=612.3MB, time=425.84 memory used=30158.0MB, alloc=612.3MB, time=426.39 memory used=30292.7MB, alloc=612.3MB, time=426.88 memory used=30405.9MB, alloc=612.3MB, time=427.34 memory used=30509.7MB, alloc=636.3MB, time=427.81 memory used=30614.8MB, alloc=660.3MB, time=428.35 memory used=30724.4MB, alloc=660.3MB, time=428.84 memory used=30841.1MB, alloc=660.3MB, time=429.35 memory used=30959.4MB, alloc=660.3MB, time=429.89 memory used=31078.1MB, alloc=660.3MB, time=430.34 memory used=31197.3MB, alloc=660.3MB, time=430.80 memory used=31317.9MB, alloc=660.3MB, time=431.24 memory used=31451.3MB, alloc=660.3MB, time=431.72 memory used=31586.2MB, alloc=660.3MB, time=432.25 memory used=31721.2MB, alloc=660.3MB, time=432.76 memory used=31856.4MB, alloc=660.3MB, time=433.29 memory used=31991.8MB, alloc=660.3MB, time=433.81 memory used=32127.2MB, alloc=660.3MB, time=434.34 memory used=32264.1MB, alloc=660.3MB, time=434.86 memory used=32412.8MB, alloc=660.3MB, time=435.37 memory used=32562.9MB, alloc=660.3MB, time=435.84 memory used=32712.7MB, alloc=660.3MB, time=436.33 memory used=32862.1MB, alloc=660.3MB, time=436.85 memory used=33013.2MB, alloc=660.3MB, time=437.38 memory used=33174.4MB, alloc=660.3MB, time=437.92 memory used=33336.9MB, alloc=660.3MB, time=438.45 memory used=33498.8MB, alloc=660.3MB, time=438.96 memory used=33674.0MB, alloc=660.3MB, time=439.49 memory used=33847.9MB, alloc=660.3MB, time=440.03 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428531331 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 F := [12 x y - 5 y z + 3 x z, -2 x y z + 15 x z - 13 z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 3 2 2 G := [-19 x y - 10 y z - y z , -14 x y - 14 y z + 20 x] > Problem := [F,G]; 3 2 2 Problem := [[12 x y - 5 y z + 3 x z, -2 x y z + 15 x z - 13 z ], 3 3 2 3 2 2 [-19 x y - 10 y z - y z , -14 x y - 14 y z + 20 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.20 memory used=25.2MB, alloc=32.3MB, time=0.50 memory used=43.9MB, alloc=56.3MB, time=0.77 memory used=86.2MB, alloc=60.3MB, time=1.31 memory used=124.3MB, alloc=60.8MB, time=1.56 memory used=165.2MB, alloc=60.8MB, time=1.96 memory used=207.8MB, alloc=60.8MB, time=2.43 memory used=250.5MB, alloc=60.8MB, time=2.85 memory used=281.8MB, alloc=60.8MB, time=3.10 memory used=311.9MB, alloc=60.9MB, time=3.23 memory used=332.9MB, alloc=60.9MB, time=3.29 memory used=350.8MB, alloc=60.9MB, time=3.33 memory used=372.2MB, alloc=60.9MB, time=3.39 memory used=394.5MB, alloc=60.9MB, time=3.44 memory used=409.3MB, alloc=60.9MB, time=3.48 memory used=426.0MB, alloc=60.9MB, time=3.53 memory used=456.3MB, alloc=60.9MB, time=3.70 memory used=478.6MB, alloc=60.9MB, time=3.75 memory used=497.2MB, alloc=60.9MB, time=3.81 memory used=516.4MB, alloc=60.9MB, time=3.86 memory used=539.3MB, alloc=60.9MB, time=3.91 memory used=559.3MB, alloc=60.9MB, time=3.96 memory used=574.4MB, alloc=60.9MB, time=4.00 memory used=591.6MB, alloc=60.9MB, time=4.04 memory used=622.0MB, alloc=60.9MB, time=4.67 memory used=651.2MB, alloc=61.2MB, time=4.78 memory used=675.4MB, alloc=61.2MB, time=4.84 memory used=692.1MB, alloc=61.2MB, time=4.90 memory used=709.6MB, alloc=61.2MB, time=4.96 memory used=730.0MB, alloc=61.2MB, time=5.02 memory used=752.4MB, alloc=61.2MB, time=5.07 memory used=777.8MB, alloc=61.2MB, time=5.12 memory used=794.7MB, alloc=85.2MB, time=5.19 memory used=823.2MB, alloc=85.2MB, time=5.25 memory used=854.9MB, alloc=85.2MB, time=5.32 memory used=890.2MB, alloc=85.2MB, time=5.39 memory used=929.3MB, alloc=85.2MB, time=5.46 memory used=975.1MB, alloc=85.2MB, time=5.53 memory used=1041.7MB, alloc=94.5MB, time=6.33 memory used=1108.0MB, alloc=94.5MB, time=7.16 memory used=1172.4MB, alloc=94.5MB, time=7.92 memory used=1232.2MB, alloc=94.5MB, time=8.50 memory used=1279.9MB, alloc=94.5MB, time=8.86 memory used=1326.8MB, alloc=94.5MB, time=9.76 memory used=1367.0MB, alloc=118.5MB, time=10.62 memory used=1410.6MB, alloc=118.5MB, time=10.77 memory used=1462.8MB, alloc=118.5MB, time=10.94 memory used=1533.5MB, alloc=118.5MB, time=12.67 memory used=1579.6MB, alloc=118.5MB, time=12.81 memory used=1626.9MB, alloc=118.5MB, time=12.92 memory used=1709.7MB, alloc=118.5MB, time=13.56 memory used=1794.6MB, alloc=374.5MB, time=14.27 memory used=1867.1MB, alloc=374.5MB, time=14.90 memory used=1947.6MB, alloc=374.5MB, time=30.65 memory used=1996.3MB, alloc=374.5MB, time=31.16 memory used=2038.7MB, alloc=374.5MB, time=31.30 memory used=2076.7MB, alloc=374.5MB, time=31.43 memory used=2123.3MB, alloc=374.5MB, time=31.56 memory used=2167.6MB, alloc=374.5MB, time=31.68 memory used=2199.0MB, alloc=374.5MB, time=31.79 memory used=2233.4MB, alloc=374.5MB, time=31.89 memory used=2273.0MB, alloc=374.5MB, time=32.00 memory used=2353.0MB, alloc=374.5MB, time=33.01 memory used=2441.0MB, alloc=374.5MB, time=34.08 memory used=2526.6MB, alloc=398.5MB, time=35.09 memory used=2596.1MB, alloc=398.5MB, time=35.46 memory used=2664.2MB, alloc=398.5MB, time=36.11 memory used=2727.2MB, alloc=398.5MB, time=36.37 memory used=2791.3MB, alloc=398.5MB, time=36.74 memory used=2882.6MB, alloc=398.5MB, time=43.41 memory used=2946.3MB, alloc=398.5MB, time=43.84 memory used=2992.8MB, alloc=398.5MB, time=44.03 memory used=3047.7MB, alloc=398.5MB, time=44.20 memory used=3106.2MB, alloc=398.5MB, time=44.38 memory used=3145.8MB, alloc=398.5MB, time=44.53 memory used=3190.1MB, alloc=398.5MB, time=44.66 memory used=3242.4MB, alloc=398.5MB, time=44.81 memory used=3333.1MB, alloc=398.5MB, time=51.57 memory used=3396.4MB, alloc=398.5MB, time=51.99 memory used=3443.8MB, alloc=398.5MB, time=52.17 memory used=3497.7MB, alloc=398.5MB, time=52.34 memory used=3557.1MB, alloc=398.5MB, time=52.51 memory used=3596.8MB, alloc=398.5MB, time=52.64 memory used=3640.5MB, alloc=398.5MB, time=52.77 memory used=3692.1MB, alloc=398.5MB, time=52.91 memory used=3824.6MB, alloc=398.5MB, time=54.03 memory used=3904.9MB, alloc=398.5MB, time=80.67 memory used=3971.3MB, alloc=422.5MB, time=128.82 memory used=4058.2MB, alloc=422.5MB, time=137.16 memory used=4128.3MB, alloc=422.5MB, time=137.36 memory used=4181.5MB, alloc=422.5MB, time=137.53 memory used=4244.8MB, alloc=422.5MB, time=137.74 memory used=4320.5MB, alloc=422.5MB, time=137.92 memory used=4388.6MB, alloc=422.5MB, time=138.12 memory used=4435.0MB, alloc=422.5MB, time=138.28 memory used=4484.2MB, alloc=422.5MB, time=138.44 memory used=4537.4MB, alloc=422.5MB, time=138.61 memory used=4594.3MB, alloc=422.5MB, time=138.78 memory used=4656.1MB, alloc=422.5MB, time=138.94 memory used=4722.2MB, alloc=422.5MB, time=139.11 memory used=4793.4MB, alloc=422.5MB, time=139.28 memory used=4869.8MB, alloc=422.5MB, time=139.46 memory used=4956.8MB, alloc=422.5MB, time=139.66 memory used=5098.0MB, alloc=422.5MB, time=140.09 memory used=5183.1MB, alloc=422.5MB, time=140.59 memory used=5266.2MB, alloc=422.5MB, time=140.96 memory used=5350.9MB, alloc=422.5MB, time=141.17 memory used=5436.3MB, alloc=422.5MB, time=141.41 memory used=5590.7MB, alloc=422.5MB, time=141.91 memory used=5808.9MB, alloc=422.5MB, time=142.25 memory used=5972.3MB, alloc=422.5MB, time=142.57 memory used=6206.2MB, alloc=422.5MB, time=142.97 memory used=6331.0MB, alloc=422.5MB, time=143.21 memory used=6498.7MB, alloc=422.5MB, time=144.20 memory used=6565.2MB, alloc=422.5MB, time=144.39 memory used=6636.7MB, alloc=422.5MB, time=144.59 memory used=6734.9MB, alloc=422.5MB, time=148.92 memory used=6847.3MB, alloc=422.5MB, time=153.41 memory used=6910.9MB, alloc=422.5MB, time=153.61 memory used=6975.3MB, alloc=422.5MB, time=153.83 memory used=7055.8MB, alloc=422.5MB, time=154.03 memory used=7105.4MB, alloc=422.5MB, time=154.19 memory used=7157.1MB, alloc=422.5MB, time=154.35 memory used=7214.0MB, alloc=422.5MB, time=154.51 memory used=7276.3MB, alloc=422.5MB, time=154.69 memory used=7343.7MB, alloc=422.5MB, time=154.85 memory used=7417.5MB, alloc=422.5MB, time=155.03 memory used=7497.1MB, alloc=422.5MB, time=155.20 memory used=7691.1MB, alloc=422.5MB, time=155.53 memory used=7850.8MB, alloc=422.5MB, time=155.81 memory used=8004.0MB, alloc=422.5MB, time=156.19 memory used=8138.1MB, alloc=422.5MB, time=165.17 memory used=8204.7MB, alloc=422.5MB, time=165.40 memory used=8264.0MB, alloc=422.5MB, time=165.63 memory used=8339.7MB, alloc=422.5MB, time=165.84 memory used=8400.5MB, alloc=422.5MB, time=166.05 memory used=8450.0MB, alloc=422.5MB, time=166.21 memory used=8504.4MB, alloc=422.5MB, time=166.38 memory used=8564.3MB, alloc=422.5MB, time=166.55 memory used=8629.4MB, alloc=422.5MB, time=166.71 memory used=8699.4MB, alloc=422.5MB, time=166.89 memory used=8777.0MB, alloc=422.5MB, time=167.06 memory used=8861.9MB, alloc=422.5MB, time=167.24 memory used=9002.8MB, alloc=422.5MB, time=167.53 memory used=9163.6MB, alloc=422.5MB, time=167.83 memory used=9392.2MB, alloc=422.5MB, time=176.62 memory used=9488.0MB, alloc=446.5MB, time=225.13 memory used=9582.5MB, alloc=446.5MB, time=274.57 memory used=9740.2MB, alloc=446.5MB, time=275.51 memory used=9823.0MB, alloc=446.5MB, time=275.78 memory used=9887.5MB, alloc=446.5MB, time=276.01 memory used=9965.1MB, alloc=446.5MB, time=276.24 memory used=10058.1MB, alloc=446.5MB, time=276.50 memory used=10132.5MB, alloc=446.5MB, time=276.71 memory used=10187.8MB, alloc=446.5MB, time=276.89 memory used=10246.4MB, alloc=446.5MB, time=277.08 memory used=10310.1MB, alloc=446.5MB, time=277.26 memory used=10376.3MB, alloc=446.5MB, time=277.46 memory used=10447.8MB, alloc=446.5MB, time=277.66 memory used=10521.8MB, alloc=446.5MB, time=277.85 memory used=10601.0MB, alloc=446.5MB, time=278.04 memory used=10682.5MB, alloc=446.5MB, time=278.24 memory used=10769.4MB, alloc=446.5MB, time=278.44 memory used=10861.6MB, alloc=446.5MB, time=278.64 memory used=10959.1MB, alloc=446.5MB, time=278.85 memory used=11161.4MB, alloc=446.5MB, time=279.20 memory used=11295.3MB, alloc=446.5MB, time=279.49 memory used=11439.9MB, alloc=446.5MB, time=279.78 memory used=11592.6MB, alloc=446.5MB, time=280.07 memory used=11752.7MB, alloc=446.5MB, time=280.37 memory used=11922.9MB, alloc=446.5MB, time=280.67 memory used=12105.2MB, alloc=446.5MB, time=280.99 memory used=12297.8MB, alloc=446.5MB, time=281.31 memory used=12506.4MB, alloc=446.5MB, time=281.67 memory used=12728.1MB, alloc=446.5MB, time=282.00 memory used=12960.3MB, alloc=446.5MB, time=282.33 memory used=13138.0MB, alloc=446.5MB, time=282.62 memory used=13318.5MB, alloc=446.5MB, time=285.00 memory used=13464.0MB, alloc=446.5MB, time=286.56 memory used=13599.9MB, alloc=446.5MB, time=288.22 memory used=13705.0MB, alloc=446.5MB, time=288.89 memory used=13781.6MB, alloc=470.5MB, time=297.05 memory used=13908.7MB, alloc=470.5MB, time=301.51 memory used=14067.6MB, alloc=470.5MB, time=306.87 memory used=14167.9MB, alloc=470.5MB, time=307.96 memory used=14309.2MB, alloc=470.5MB, time=309.20 memory used=14451.0MB, alloc=470.5MB, time=310.96 memory used=14590.9MB, alloc=470.5MB, time=312.83 memory used=14719.1MB, alloc=470.5MB, time=314.80 memory used=14794.4MB, alloc=470.5MB, time=315.10 memory used=14923.0MB, alloc=470.5MB, time=316.24 memory used=15041.5MB, alloc=470.5MB, time=317.48 memory used=15168.4MB, alloc=470.5MB, time=318.72 memory used=15299.1MB, alloc=470.5MB, time=319.78 memory used=15384.8MB, alloc=494.5MB, time=320.90 memory used=15475.1MB, alloc=494.5MB, time=321.28 memory used=15552.8MB, alloc=494.5MB, time=321.62 memory used=15650.7MB, alloc=494.5MB, time=322.01 memory used=15758.9MB, alloc=494.5MB, time=322.38 memory used=15818.9MB, alloc=518.5MB, time=322.68 memory used=15896.9MB, alloc=518.5MB, time=322.98 memory used=15981.5MB, alloc=518.5MB, time=323.30 memory used=16075.6MB, alloc=518.5MB, time=323.62 memory used=16174.2MB, alloc=518.5MB, time=323.96 memory used=16280.6MB, alloc=518.5MB, time=324.28 memory used=16397.3MB, alloc=518.5MB, time=324.61 memory used=16523.1MB, alloc=518.5MB, time=324.94 memory used=16657.6MB, alloc=518.5MB, time=325.28 memory used=16809.9MB, alloc=518.5MB, time=325.72 memory used=16944.2MB, alloc=518.5MB, time=326.13 memory used=17084.1MB, alloc=518.5MB, time=326.53 memory used=17234.4MB, alloc=518.5MB, time=326.95 memory used=17395.2MB, alloc=518.5MB, time=327.36 memory used=17569.8MB, alloc=518.5MB, time=327.78 memory used=17760.8MB, alloc=518.5MB, time=328.20 memory used=18005.7MB, alloc=518.5MB, time=400.39 memory used=18118.9MB, alloc=518.5MB, time=401.48 memory used=18222.1MB, alloc=518.5MB, time=401.84 memory used=18313.0MB, alloc=518.5MB, time=402.14 memory used=18421.0MB, alloc=518.5MB, time=402.46 memory used=18548.3MB, alloc=518.5MB, time=402.78 memory used=18732.5MB, alloc=518.5MB, time=403.21 memory used=18879.3MB, alloc=518.5MB, time=403.61 memory used=19043.0MB, alloc=518.5MB, time=404.02 memory used=19226.4MB, alloc=518.5MB, time=404.44 memory used=19428.2MB, alloc=518.5MB, time=404.87 memory used=19651.6MB, alloc=518.5MB, time=405.31 memory used=19859.6MB, alloc=518.5MB, time=405.73 memory used=20035.3MB, alloc=518.5MB, time=406.12 memory used=20226.4MB, alloc=518.5MB, time=406.54 memory used=20432.2MB, alloc=518.5MB, time=406.97 memory used=20658.9MB, alloc=518.5MB, time=407.38 memory used=20991.4MB, alloc=518.5MB, time=408.31 memory used=21177.7MB, alloc=518.5MB, time=409.11 memory used=21424.4MB, alloc=518.5MB, time=410.63 memory used=21531.8MB, alloc=518.5MB, time=411.83 memory used=21672.4MB, alloc=518.5MB, time=412.84 memory used=21808.5MB, alloc=518.5MB, time=419.71 memory used=21908.1MB, alloc=518.5MB, time=420.03 memory used=22017.9MB, alloc=518.5MB, time=420.35 memory used=22219.2MB, alloc=518.5MB, time=420.77 memory used=22404.6MB, alloc=518.5MB, time=421.17 memory used=22705.7MB, alloc=518.5MB, time=428.33 memory used=22812.8MB, alloc=518.5MB, time=428.72 memory used=22908.4MB, alloc=518.5MB, time=429.03 memory used=23160.2MB, alloc=518.5MB, time=429.54 memory used=23344.0MB, alloc=518.5MB, time=429.95 memory used=23647.1MB, alloc=518.5MB, time=430.86 memory used=23771.7MB, alloc=518.5MB, time=431.62 memory used=23884.3MB, alloc=518.5MB, time=432.04 memory used=23995.1MB, alloc=518.5MB, time=432.46 memory used=24110.3MB, alloc=518.5MB, time=433.00 memory used=24276.5MB, alloc=518.5MB, time=434.10 memory used=24423.6MB, alloc=518.5MB, time=442.75 memory used=24536.2MB, alloc=518.5MB, time=443.50 memory used=24641.1MB, alloc=518.5MB, time=443.88 memory used=24727.4MB, alloc=518.5MB, time=444.18 memory used=24831.2MB, alloc=518.5MB, time=444.49 memory used=24956.8MB, alloc=518.5MB, time=444.81 memory used=25119.1MB, alloc=518.5MB, time=445.20 memory used=25280.7MB, alloc=518.5MB, time=445.60 memory used=25583.4MB, alloc=518.5MB, time=447.23 memory used=25697.7MB, alloc=518.5MB, time=447.66 memory used=25787.0MB, alloc=518.5MB, time=448.05 memory used=25884.0MB, alloc=518.5MB, time=448.45 memory used=25998.6MB, alloc=518.5MB, time=448.82 memory used=26107.1MB, alloc=518.5MB, time=449.17 memory used=26178.6MB, alloc=518.5MB, time=449.47 memory used=26255.8MB, alloc=518.5MB, time=449.77 memory used=26338.9MB, alloc=518.5MB, time=450.07 memory used=26430.2MB, alloc=518.5MB, time=450.39 memory used=26530.0MB, alloc=518.5MB, time=450.71 memory used=26636.7MB, alloc=518.5MB, time=451.05 memory used=26753.2MB, alloc=518.5MB, time=451.38 memory used=26883.8MB, alloc=518.5MB, time=451.72 memory used=27034.4MB, alloc=518.5MB, time=452.13 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428531631 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 3 3 2 F := [-4 y - 19 y z + 18 z , 2 y z - 10 x y + 13] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 4 G := [6 x y z + 6 x y + 9 y , 19 x y z - 3 y z - 5 z ] > Problem := [F,G]; 4 3 3 3 2 Problem := [[-4 y - 19 y z + 18 z , 2 y z - 10 x y + 13], 2 2 3 4 [6 x y z + 6 x y + 9 y , 19 x y z - 3 y z - 5 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=25.4MB, alloc=32.3MB, time=0.50 memory used=44.8MB, alloc=56.3MB, time=0.79 memory used=86.6MB, alloc=60.3MB, time=1.37 memory used=128.0MB, alloc=68.3MB, time=1.95 memory used=168.6MB, alloc=68.3MB, time=2.35 memory used=204.5MB, alloc=68.3MB, time=2.62 memory used=225.7MB, alloc=68.3MB, time=2.69 memory used=254.7MB, alloc=68.3MB, time=2.98 memory used=284.4MB, alloc=68.3MB, time=3.20 memory used=347.9MB, alloc=92.3MB, time=4.74 memory used=405.1MB, alloc=92.3MB, time=4.97 memory used=446.4MB, alloc=92.3MB, time=5.08 memory used=481.4MB, alloc=92.3MB, time=5.19 memory used=512.3MB, alloc=92.3MB, time=5.28 memory used=546.5MB, alloc=92.3MB, time=5.38 memory used=585.7MB, alloc=92.3MB, time=5.48 memory used=629.7MB, alloc=92.3MB, time=5.58 memory used=674.7MB, alloc=92.3MB, time=5.67 memory used=700.0MB, alloc=92.3MB, time=5.75 memory used=727.3MB, alloc=92.3MB, time=5.83 memory used=756.5MB, alloc=92.3MB, time=5.91 memory used=787.2MB, alloc=92.3MB, time=5.99 memory used=820.0MB, alloc=92.3MB, time=6.07 memory used=854.1MB, alloc=92.3MB, time=6.15 memory used=890.5MB, alloc=92.3MB, time=6.24 memory used=930.0MB, alloc=92.3MB, time=6.31 memory used=983.9MB, alloc=92.3MB, time=6.60 memory used=1080.4MB, alloc=92.8MB, time=8.14 memory used=1119.8MB, alloc=92.8MB, time=8.27 memory used=1148.3MB, alloc=92.8MB, time=8.39 memory used=1182.1MB, alloc=92.8MB, time=8.51 memory used=1223.0MB, alloc=92.8MB, time=8.63 memory used=1258.0MB, alloc=92.8MB, time=8.74 memory used=1282.2MB, alloc=92.8MB, time=8.83 memory used=1308.6MB, alloc=92.8MB, time=8.92 memory used=1336.1MB, alloc=92.8MB, time=9.01 memory used=1366.4MB, alloc=92.8MB, time=9.10 memory used=1397.8MB, alloc=92.8MB, time=9.19 memory used=1432.1MB, alloc=92.8MB, time=9.29 memory used=1467.3MB, alloc=92.8MB, time=9.38 memory used=1505.5MB, alloc=92.8MB, time=9.48 memory used=1544.4MB, alloc=92.8MB, time=9.58 memory used=1586.0MB, alloc=92.8MB, time=9.68 memory used=1630.6MB, alloc=92.8MB, time=9.78 memory used=1647.5MB, alloc=107.8MB, time=9.86 memory used=1656.0MB, alloc=107.8MB, time=9.92 memory used=1664.3MB, alloc=107.8MB, time=9.98 memory used=1672.6MB, alloc=107.8MB, time=10.04 memory used=1680.9MB, alloc=107.8MB, time=10.10 memory used=1689.2MB, alloc=107.8MB, time=10.16 memory used=1697.6MB, alloc=107.8MB, time=10.21 memory used=1706.2MB, alloc=107.8MB, time=10.28 memory used=1714.6MB, alloc=107.8MB, time=10.33 memory used=1724.7MB, alloc=107.8MB, time=10.39 memory used=1733.4MB, alloc=107.8MB, time=10.45 memory used=1743.5MB, alloc=107.8MB, time=10.51 memory used=1753.9MB, alloc=107.8MB, time=10.56 memory used=1764.4MB, alloc=107.8MB, time=10.62 memory used=1774.8MB, alloc=107.8MB, time=10.69 memory used=1785.2MB, alloc=107.8MB, time=10.75 memory used=1795.6MB, alloc=107.8MB, time=10.81 memory used=1806.0MB, alloc=107.8MB, time=10.87 memory used=1816.4MB, alloc=107.8MB, time=10.93 memory used=1826.7MB, alloc=107.8MB, time=10.99 memory used=1837.1MB, alloc=107.8MB, time=11.05 memory used=1847.4MB, alloc=107.8MB, time=11.11 memory used=1857.9MB, alloc=107.8MB, time=11.18 memory used=1870.0MB, alloc=107.8MB, time=11.24 memory used=1882.2MB, alloc=107.8MB, time=11.31 memory used=1894.4MB, alloc=107.8MB, time=11.37 memory used=1906.6MB, alloc=107.8MB, time=11.43 memory used=1918.7MB, alloc=107.8MB, time=11.49 memory used=1930.8MB, alloc=107.8MB, time=11.56 memory used=1942.7MB, alloc=107.8MB, time=11.62 memory used=1954.7MB, alloc=107.8MB, time=11.68 memory used=1966.8MB, alloc=107.8MB, time=11.74 memory used=1980.2MB, alloc=107.8MB, time=11.80 memory used=1993.8MB, alloc=107.8MB, time=11.86 memory used=2007.4MB, alloc=107.8MB, time=11.92 memory used=2020.8MB, alloc=107.8MB, time=11.99 memory used=2034.1MB, alloc=107.8MB, time=12.05 memory used=2047.7MB, alloc=107.8MB, time=12.12 memory used=2062.1MB, alloc=107.8MB, time=12.18 memory used=2076.7MB, alloc=107.8MB, time=12.25 memory used=2091.1MB, alloc=107.8MB, time=12.31 memory used=2105.9MB, alloc=107.8MB, time=12.37 memory used=2121.1MB, alloc=107.8MB, time=12.43 memory used=2136.5MB, alloc=107.8MB, time=12.50 memory used=2152.2MB, alloc=107.8MB, time=12.56 memory used=2168.1MB, alloc=107.8MB, time=12.63 memory used=2184.5MB, alloc=107.8MB, time=12.69 memory used=2201.3MB, alloc=107.8MB, time=12.76 memory used=2218.4MB, alloc=107.8MB, time=12.82 memory used=2236.8MB, alloc=107.8MB, time=12.90 memory used=2254.8MB, alloc=107.8MB, time=12.97 memory used=2273.6MB, alloc=107.8MB, time=13.04 memory used=2293.1MB, alloc=107.8MB, time=13.11 memory used=2312.5MB, alloc=107.8MB, time=13.18 memory used=2393.4MB, alloc=107.8MB, time=14.07 memory used=2452.9MB, alloc=107.8MB, time=14.66 memory used=2500.5MB, alloc=107.8MB, time=15.12 memory used=2589.1MB, alloc=107.8MB, time=16.62 memory used=2619.7MB, alloc=131.8MB, time=16.77 memory used=2662.9MB, alloc=131.8MB, time=16.92 memory used=2707.8MB, alloc=131.8MB, 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alloc=131.8MB, time=19.17 memory used=3313.2MB, alloc=131.8MB, time=19.23 memory used=3323.4MB, alloc=131.8MB, time=19.30 memory used=3332.0MB, alloc=131.8MB, time=19.38 memory used=3342.1MB, alloc=131.8MB, time=19.44 memory used=3352.5MB, alloc=131.8MB, time=19.52 memory used=3362.8MB, alloc=131.8MB, time=19.59 memory used=3373.2MB, alloc=131.8MB, time=19.66 memory used=3383.5MB, alloc=131.8MB, time=19.73 memory used=3393.8MB, alloc=131.8MB, time=19.80 memory used=3404.0MB, alloc=131.8MB, time=19.87 memory used=3414.3MB, alloc=131.8MB, time=19.95 memory used=3424.5MB, alloc=131.8MB, time=20.02 memory used=3434.7MB, alloc=131.8MB, time=20.09 memory used=3444.8MB, alloc=131.8MB, time=20.16 memory used=3455.2MB, alloc=131.8MB, time=20.23 memory used=3467.1MB, alloc=131.8MB, time=20.30 memory used=3479.1MB, alloc=131.8MB, time=20.37 memory used=3491.1MB, alloc=131.8MB, time=20.44 memory used=3503.0MB, alloc=131.8MB, time=20.52 memory used=3514.8MB, alloc=131.8MB, time=20.59 memory 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memory used=35011.6MB, alloc=651.8MB, time=138.89 memory used=35180.8MB, alloc=651.8MB, time=139.20 memory used=35348.0MB, alloc=651.8MB, time=139.52 memory used=35513.1MB, alloc=651.8MB, time=139.83 memory used=35676.2MB, alloc=651.8MB, time=140.17 memory used=35857.2MB, alloc=651.8MB, time=140.51 memory used=36035.5MB, alloc=651.8MB, time=140.84 memory used=36211.0MB, alloc=651.8MB, time=141.16 memory used=36383.8MB, alloc=651.8MB, time=141.50 memory used=36572.4MB, alloc=651.8MB, time=141.83 memory used=36757.4MB, alloc=651.8MB, time=142.17 memory used=36938.9MB, alloc=651.8MB, time=142.51 memory used=37118.7MB, alloc=651.8MB, time=142.83 memory used=37307.7MB, alloc=651.8MB, time=143.17 memory used=37494.3MB, alloc=651.8MB, time=143.53 memory used=37692.3MB, alloc=651.8MB, time=143.89 memory used=37884.6MB, alloc=651.8MB, time=144.26 memory used=38086.3MB, alloc=651.8MB, time=144.62 memory used=38282.5MB, alloc=651.8MB, time=144.95 memory used=38482.7MB, alloc=651.8MB, time=145.30 memory used=38689.2MB, alloc=651.8MB, time=145.64 memory used=38898.7MB, alloc=651.8MB, time=145.99 memory used=39109.8MB, alloc=651.8MB, time=146.35 memory used=39327.0MB, alloc=651.8MB, time=146.69 memory used=39548.4MB, alloc=651.8MB, time=147.06 memory used=39775.0MB, alloc=651.8MB, time=147.42 memory used=40010.1MB, alloc=651.8MB, time=147.79 memory used=40426.9MB, alloc=651.8MB, time=156.65 memory used=40614.6MB, alloc=651.8MB, time=157.22 memory used=40843.6MB, alloc=651.8MB, time=157.85 memory used=41109.1MB, alloc=651.8MB, time=158.43 memory used=41262.1MB, alloc=651.8MB, time=158.87 memory used=41416.7MB, alloc=651.8MB, time=159.30 memory used=41578.0MB, alloc=651.8MB, time=159.71 memory used=41746.3MB, alloc=651.8MB, time=160.18 memory used=41930.8MB, alloc=651.8MB, time=160.66 memory used=42121.9MB, alloc=651.8MB, time=161.15 memory used=42319.7MB, alloc=651.8MB, time=161.59 memory used=42534.2MB, alloc=651.8MB, time=162.03 memory used=42755.2MB, alloc=651.8MB, time=162.54 memory used=42993.4MB, alloc=651.8MB, time=163.05 memory used=43237.6MB, alloc=651.8MB, time=163.49 memory used=43499.1MB, alloc=651.8MB, time=163.99 memory used=43685.1MB, alloc=651.8MB, time=164.37 memory used=43820.0MB, alloc=651.8MB, time=164.68 memory used=43947.3MB, alloc=651.8MB, time=164.99 memory used=44087.9MB, alloc=651.8MB, time=165.31 memory used=44229.3MB, alloc=651.8MB, time=165.63 memory used=44371.5MB, alloc=651.8MB, time=165.94 memory used=44514.5MB, alloc=651.8MB, time=166.26 memory used=44658.4MB, alloc=651.8MB, time=166.58 memory used=44815.7MB, alloc=651.8MB, time=166.91 memory used=44973.5MB, alloc=651.8MB, time=167.23 memory used=45131.8MB, alloc=651.8MB, time=167.59 memory used=45290.6MB, alloc=651.8MB, time=167.97 memory used=45462.6MB, alloc=651.8MB, time=168.31 memory used=45634.6MB, alloc=651.8MB, time=168.64 memory used=45806.8MB, alloc=651.8MB, time=168.98 memory used=45991.8MB, alloc=651.8MB, time=169.32 memory used=46176.3MB, alloc=651.8MB, time=169.66 memory used=46360.4MB, alloc=651.8MB, time=170.01 memory used=46556.5MB, alloc=651.8MB, time=170.35 memory used=46751.8MB, alloc=651.8MB, time=170.72 memory used=46958.2MB, alloc=651.8MB, time=171.08 memory used=47163.1MB, alloc=651.8MB, time=171.44 memory used=47378.3MB, alloc=651.8MB, time=171.80 memory used=47590.9MB, alloc=651.8MB, time=172.16 memory used=47812.8MB, alloc=651.8MB, time=172.53 memory used=48042.8MB, alloc=651.8MB, time=172.90 memory used=48279.9MB, alloc=651.8MB, time=173.29 memory used=48522.7MB, alloc=651.8MB, time=173.67 memory used=48769.8MB, alloc=651.8MB, time=174.06 memory used=49029.8MB, alloc=651.8MB, time=174.43 memory used=49397.1MB, alloc=651.8MB, time=174.93 memory used=49522.5MB, alloc=651.8MB, time=175.22 memory used=49647.7MB, alloc=651.8MB, time=175.51 memory used=49776.5MB, alloc=651.8MB, time=175.80 memory used=49907.9MB, alloc=651.8MB, time=176.10 memory used=50047.6MB, alloc=651.8MB, time=176.40 memory used=50186.7MB, alloc=651.8MB, time=176.71 memory used=50332.6MB, alloc=651.8MB, time=177.02 memory used=50482.2MB, alloc=651.8MB, time=177.34 memory used=50640.5MB, alloc=651.8MB, time=177.65 memory used=50995.6MB, alloc=651.8MB, time=220.14 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428531931 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 3 F := [-x - 10 y - 18, -14 x y - 6 x z + z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 3 3 2 G := [18 x y z + 12 z - 5 y z, 7 x z + 2 x z - 10 x z ] > Problem := [F,G]; 3 2 2 2 3 Problem := [[-x - 10 y - 18, -14 x y - 6 x z + z], 2 3 3 3 2 [18 x y z + 12 z - 5 y z, 7 x z + 2 x z - 10 x z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.1MB, alloc=32.3MB, time=0.50 memory used=46.6MB, alloc=32.3MB, time=0.80 memory used=65.0MB, alloc=56.3MB, time=1.09 memory used=106.5MB, alloc=60.3MB, time=1.63 memory used=143.9MB, alloc=60.3MB, time=2.15 memory used=184.1MB, alloc=68.3MB, time=2.75 memory used=224.4MB, alloc=92.3MB, time=3.36 memory used=289.1MB, alloc=92.3MB, time=4.22 memory used=354.4MB, alloc=92.3MB, time=5.13 memory used=412.8MB, alloc=92.3MB, time=5.68 memory used=473.0MB, alloc=92.3MB, time=6.25 memory used=529.8MB, alloc=116.3MB, time=6.71 memory used=610.8MB, alloc=372.3MB, time=7.44 memory used=702.3MB, alloc=372.3MB, time=8.38 memory used=786.8MB, alloc=372.3MB, time=9.20 memory used=870.1MB, alloc=396.3MB, time=10.44 memory used=972.4MB, alloc=396.3MB, time=11.34 memory used=1035.2MB, alloc=396.3MB, time=11.68 memory used=1138.8MB, alloc=396.3MB, time=12.82 memory used=1259.6MB, alloc=396.3MB, time=14.29 memory used=1353.9MB, alloc=396.3MB, time=14.98 memory used=1472.1MB, alloc=420.3MB, time=16.26 memory used=1616.3MB, alloc=420.3MB, time=17.73 memory used=1749.8MB, alloc=444.3MB, time=19.78 memory used=1900.0MB, alloc=468.3MB, time=22.00 memory used=2102.7MB, alloc=468.3MB, time=24.20 memory used=2306.2MB, alloc=468.3MB, time=25.63 memory used=2507.2MB, alloc=468.3MB, time=27.10 memory used=2688.6MB, alloc=492.3MB, time=29.23 memory used=2899.2MB, alloc=492.3MB, time=31.78 memory used=3102.5MB, alloc=516.3MB, time=34.17 memory used=3329.1MB, alloc=540.3MB, time=36.90 memory used=3579.6MB, alloc=540.3MB, time=39.96 memory used=3817.8MB, alloc=564.3MB, time=42.89 memory used=4079.0MB, alloc=588.3MB, time=45.65 memory used=4349.1MB, alloc=612.3MB, time=49.29 memory used=4610.0MB, alloc=636.3MB, time=53.07 memory used=4830.3MB, alloc=660.3MB, time=56.19 memory used=5070.1MB, alloc=684.3MB, time=62.46 memory used=5303.3MB, alloc=708.3MB, time=69.14 memory used=5543.4MB, alloc=732.3MB, time=76.55 memory used=5793.9MB, alloc=756.3MB, time=84.42 memory used=6055.4MB, alloc=780.3MB, time=93.02 memory used=6324.0MB, alloc=804.3MB, time=102.64 memory used=6616.5MB, alloc=828.3MB, time=112.99 memory used=6932.8MB, alloc=852.3MB, time=124.09 memory used=7273.2MB, alloc=876.3MB, time=135.92 memory used=7637.5MB, alloc=900.3MB, time=148.76 memory used=8025.7MB, alloc=924.3MB, time=162.57 memory used=8437.8MB, alloc=948.3MB, time=177.54 memory used=8873.9MB, alloc=948.3MB, time=193.21 memory used=9310.0MB, alloc=948.3MB, time=208.65 memory used=9746.0MB, alloc=948.3MB, time=224.15 memory used=10181.9MB, alloc=972.3MB, time=239.62 memory used=10641.8MB, alloc=972.3MB, time=256.39 memory used=11101.5MB, alloc=972.3MB, time=272.60 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428532231 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 4 3 2 2 2 F := [-8 y - 8 z + 15 x , -14 x z + 8 x y + 7 x y] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 3 3 2 G := [12 x - 3 x z - 7 x y , -7 x - 19 x z - 18] > Problem := [F,G]; 4 4 3 2 2 2 Problem := [[-8 y - 8 z + 15 x , -14 x z + 8 x y + 7 x y], 4 2 2 3 3 2 [12 x - 3 x z - 7 x y , -7 x - 19 x z - 18]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=24.3MB, alloc=32.3MB, time=0.46 memory used=43.4MB, alloc=56.3MB, time=0.73 memory used=86.1MB, alloc=60.3MB, time=1.32 memory used=132.8MB, alloc=68.3MB, time=1.86 memory used=178.8MB, alloc=68.3MB, time=2.43 memory used=227.1MB, alloc=92.3MB, time=2.97 memory used=291.8MB, alloc=92.3MB, time=3.92 memory used=360.4MB, alloc=116.3MB, time=4.76 memory used=422.6MB, alloc=372.3MB, time=5.47 memory used=515.0MB, alloc=372.3MB, time=6.39 memory used=607.0MB, alloc=396.3MB, time=7.44 memory used=711.7MB, alloc=396.3MB, time=8.30 memory used=808.2MB, alloc=396.3MB, time=8.90 memory used=924.5MB, alloc=396.3MB, time=9.78 memory used=1021.6MB, alloc=396.3MB, time=10.45 memory used=1140.6MB, alloc=420.3MB, time=11.47 memory used=1237.6MB, alloc=420.3MB, time=12.15 memory used=1374.9MB, alloc=420.3MB, time=13.39 memory used=1522.6MB, alloc=420.3MB, time=14.74 memory used=1648.6MB, alloc=444.3MB, time=15.87 memory used=1728.2MB, alloc=444.3MB, time=16.45 memory used=1871.0MB, alloc=444.3MB, time=17.82 memory used=1984.2MB, alloc=444.3MB, time=18.97 memory used=2103.3MB, alloc=444.3MB, time=19.86 memory used=2234.7MB, alloc=444.3MB, time=22.75 memory used=2306.3MB, alloc=468.3MB, time=23.08 memory used=2387.5MB, alloc=468.3MB, time=23.39 memory used=2469.5MB, alloc=468.3MB, time=23.70 memory used=2533.5MB, alloc=468.3MB, time=23.97 memory used=2605.6MB, alloc=468.3MB, time=24.21 memory used=2687.7MB, alloc=468.3MB, time=24.49 memory used=2777.5MB, alloc=468.3MB, time=24.76 memory used=2879.3MB, alloc=468.3MB, time=25.05 memory used=3048.5MB, alloc=468.3MB, time=25.57 memory used=3195.8MB, alloc=468.3MB, time=25.96 memory used=3362.5MB, alloc=468.3MB, time=26.35 memory used=3547.8MB, alloc=468.3MB, time=26.74 memory used=3761.3MB, alloc=468.3MB, time=27.14 memory used=3971.5MB, alloc=468.3MB, time=27.53 memory used=4084.1MB, alloc=468.3MB, time=28.48 memory used=4194.1MB, alloc=468.3MB, time=29.23 memory used=4291.3MB, alloc=468.3MB, time=29.54 memory used=4385.4MB, alloc=468.3MB, time=29.86 memory used=4562.2MB, alloc=468.3MB, time=31.35 memory used=4812.8MB, alloc=468.3MB, time=31.81 memory used=5066.1MB, alloc=468.3MB, time=32.29 memory used=5319.1MB, alloc=468.3MB, time=32.84 memory used=5558.3MB, alloc=468.3MB, time=36.36 memory used=5843.6MB, alloc=468.3MB, time=36.83 memory used=6020.2MB, alloc=468.3MB, time=37.19 memory used=6221.3MB, alloc=468.3MB, time=37.55 memory used=6432.9MB, alloc=468.3MB, time=37.89 memory used=6644.1MB, alloc=468.3MB, time=38.34 memory used=6927.4MB, alloc=468.3MB, time=38.83 memory used=7103.5MB, alloc=468.3MB, time=39.17 memory used=7305.3MB, alloc=468.3MB, time=39.52 memory used=7515.9MB, alloc=468.3MB, time=39.87 memory used=7729.9MB, alloc=468.3MB, time=40.37 memory used=8029.1MB, alloc=468.3MB, time=40.86 memory used=8205.5MB, alloc=468.3MB, time=41.21 memory used=8414.1MB, alloc=468.3MB, time=41.56 memory used=8617.9MB, alloc=468.3MB, time=41.90 memory used=8880.3MB, alloc=468.3MB, time=47.45 memory used=8969.3MB, alloc=468.3MB, time=48.44 memory used=9076.3MB, alloc=468.3MB, time=49.20 memory used=9195.5MB, alloc=468.3MB, time=50.29 memory used=9315.8MB, alloc=468.3MB, time=51.52 memory used=9430.3MB, alloc=492.3MB, time=53.25 memory used=9598.4MB, alloc=516.3MB, time=55.75 memory used=9753.6MB, alloc=540.3MB, time=58.15 memory used=9918.4MB, alloc=564.3MB, time=60.96 memory used=10073.7MB, alloc=588.3MB, time=63.46 memory used=10217.0MB, alloc=612.3MB, time=66.00 memory used=10428.0MB, alloc=636.3MB, time=71.73 memory used=10642.3MB, alloc=660.3MB, time=78.13 memory used=10855.1MB, alloc=684.3MB, time=85.52 memory used=11086.8MB, alloc=708.3MB, time=93.57 memory used=11342.4MB, alloc=732.3MB, time=102.68 memory used=11622.0MB, alloc=756.3MB, time=112.60 memory used=11925.5MB, alloc=780.3MB, time=123.32 memory used=12252.9MB, alloc=780.3MB, time=134.72 memory used=12580.3MB, alloc=780.3MB, time=146.12 memory used=12907.6MB, alloc=804.3MB, time=157.58 memory used=13259.1MB, alloc=828.3MB, time=169.67 memory used=13634.4MB, alloc=852.3MB, time=182.54 N1 := 10685 > GB := Basis(F, plex(op(vars))); 3 4 6 3 2 2 2 2 GB := [392 x y - 735 x + 128 x y + 224 x y + 98 x y , 2 2 2 14 x z - 8 x y - 7 x y, 2 4 5 2 2 2 2 4 4 3 392 x y - 735 x + 128 x y + 196 x y z + 112 x y , 8 y + 8 z - 15 x ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=13798.2MB, alloc=852.3MB, time=187.07 memory used=13882.8MB, alloc=852.3MB, time=188.68 memory used=13969.3MB, alloc=852.3MB, time=190.37 memory used=14030.7MB, alloc=852.3MB, time=191.84 memory used=14136.5MB, alloc=852.3MB, time=193.06 memory used=14220.1MB, alloc=852.3MB, time=194.46 memory used=14325.5MB, alloc=852.3MB, time=195.88 memory used=14397.1MB, alloc=852.3MB, time=197.26 memory used=14458.1MB, alloc=852.3MB, time=198.59 memory used=14525.3MB, alloc=852.3MB, time=199.75 memory used=14588.7MB, alloc=852.3MB, time=200.98 memory used=14643.9MB, alloc=852.3MB, time=202.18 memory used=14695.7MB, alloc=852.3MB, time=203.30 memory used=14747.5MB, alloc=852.3MB, time=204.55 memory used=14795.7MB, alloc=852.3MB, time=205.84 memory used=14822.7MB, alloc=852.3MB, time=206.74 memory used=15125.4MB, alloc=852.3MB, time=209.32 memory used=15418.8MB, alloc=852.3MB, time=212.49 memory used=15686.6MB, alloc=852.3MB, time=215.08 memory used=15945.4MB, alloc=852.3MB, time=217.47 memory used=16223.6MB, alloc=852.3MB, time=220.06 memory used=16398.2MB, alloc=852.3MB, time=222.67 memory used=16647.9MB, alloc=852.3MB, time=225.70 memory used=16834.9MB, alloc=852.3MB, time=228.04 memory used=17113.7MB, alloc=852.3MB, time=229.93 memory used=17308.9MB, alloc=852.3MB, time=231.99 memory used=17543.3MB, alloc=852.3MB, time=234.29 memory used=17810.9MB, alloc=852.3MB, time=236.95 memory used=17947.4MB, alloc=852.3MB, time=239.21 memory used=18158.4MB, alloc=876.3MB, time=241.57 memory used=18329.6MB, alloc=876.3MB, time=243.79 memory used=18518.8MB, alloc=876.3MB, time=246.24 memory used=18680.1MB, alloc=876.3MB, time=248.77 memory used=18930.3MB, alloc=876.3MB, time=250.42 memory used=19164.8MB, alloc=876.3MB, time=252.06 memory used=19424.0MB, alloc=876.3MB, time=254.35 memory used=19815.0MB, alloc=900.3MB, time=257.20 memory used=20059.0MB, alloc=900.3MB, time=260.05 memory used=20380.4MB, alloc=924.3MB, time=262.77 memory used=20979.4MB, alloc=948.3MB, time=269.01 memory used=21397.6MB, alloc=972.3MB, time=275.40 memory used=21779.7MB, alloc=996.3MB, time=281.84 memory used=22192.4MB, alloc=1020.3MB, time=287.92 memory used=22476.6MB, alloc=1044.3MB, time=292.42 memory used=22954.2MB, alloc=1068.3MB, time=296.62 memory used=23280.1MB, alloc=1092.3MB, time=299.18 memory used=23632.8MB, alloc=1092.3MB, time=302.00 memory used=24188.4MB, alloc=1116.3MB, time=307.90 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428532531 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 4 2 2 F := [8 x y + 9 y + 7 x y , -4 x y z + 20 x y - 19 x] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 4 G := [-4 x z - 3 x z - 12 x, 12 y z - 5 z ] > Problem := [F,G]; 2 2 4 2 2 Problem := [[8 x y + 9 y + 7 x y , -4 x y z + 20 x y - 19 x], 2 2 3 4 [-4 x z - 3 x z - 12 x, 12 y z - 5 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=32.2MB, alloc=40.3MB, time=0.56 memory used=59.6MB, alloc=40.3MB, time=0.97 memory used=85.0MB, alloc=64.3MB, time=1.34 memory used=134.1MB, alloc=68.3MB, time=2.16 memory used=177.2MB, alloc=92.3MB, time=2.90 memory used=237.4MB, alloc=116.3MB, time=4.08 memory used=307.3MB, alloc=140.3MB, time=6.14 N1 := 1791 > GB := Basis(F, plex(op(vars))); 3 2 2 4 4 3 2 GB := [8 x + 9 x y + 7 x , -64 x + 81 y - 112 x - 49 x , 3 2 32 x z + 28 x z + 180 x y - 171 x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=401.9MB, alloc=148.3MB, time=7.46 memory used=507.2MB, alloc=148.3MB, time=9.04 memory used=607.9MB, alloc=172.3MB, time=10.72 memory used=722.7MB, alloc=196.3MB, time=13.63 memory used=841.1MB, alloc=220.3MB, time=17.20 N2 := 2515 > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 4 2 2 H := [8 x y + 9 y + 7 x y , -4 x y z + 20 x y - 19 x, 2 2 3 4 -4 x z - 3 x z - 12 x, 12 y z - 5 z ] > J:=[op(GB),op(G)]; 3 2 2 4 4 3 2 J := [8 x + 9 x y + 7 x , -64 x + 81 y - 112 x - 49 x , 3 2 2 2 32 x z + 28 x z + 180 x y - 171 x, -4 x z - 3 x z - 12 x, 3 4 12 y z - 5 z ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 9, 15, 4, 2, 4, 4, 3/4, 3/4, 3/4, 8/11, 6/11, 5/11, 5, 11, 13 18, 4, 4, 4, 4, 4/5, 4/5, 3/5, --, 1/4, 3/8, -2, -3, 0] 16 > save(F, G, cat("ranSet/34", convert(F, string),".txt")); > quit memory used=863.6MB, alloc=220.3MB, time=17.75 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428532550 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 4 2 2 2 2 F := [4 x y z - 16 y z - 6 z , -18 x y z - x z + 9 x y z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 4 4 G := [-11 y z - 11 x y + 19 x y, 8 x z + 8 y - 6 z ] > Problem := [F,G]; 2 2 2 4 2 2 2 2 Problem := [[4 x y z - 16 y z - 6 z , -18 x y z - x z + 9 x y z], 3 2 2 2 4 4 [-11 y z - 11 x y + 19 x y, 8 x z + 8 y - 6 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.1MB, alloc=32.3MB, time=0.15 memory used=25.7MB, alloc=32.3MB, time=0.44 memory used=44.9MB, alloc=56.3MB, time=0.69 memory used=86.1MB, alloc=60.3MB, time=1.27 memory used=131.6MB, alloc=60.3MB, time=1.70 memory used=185.1MB, alloc=60.3MB, time=2.15 memory used=228.9MB, alloc=68.3MB, time=2.53 memory used=262.5MB, alloc=68.3MB, time=2.71 memory used=308.8MB, alloc=92.3MB, time=2.97 memory used=372.0MB, alloc=92.3MB, time=3.53 memory used=439.9MB, alloc=92.3MB, time=4.18 memory used=504.3MB, alloc=92.3MB, time=5.00 memory used=575.9MB, alloc=116.3MB, time=5.83 memory used=648.3MB, alloc=372.3MB, time=6.68 memory used=744.7MB, alloc=396.3MB, time=7.76 memory used=865.5MB, alloc=396.3MB, time=9.15 memory used=964.5MB, alloc=396.3MB, time=10.14 memory used=1034.9MB, alloc=396.3MB, time=10.62 memory used=1097.3MB, alloc=396.3MB, time=10.88 memory used=1152.6MB, alloc=396.3MB, time=11.14 memory used=1240.1MB, alloc=420.3MB, time=14.14 memory used=1314.8MB, alloc=420.3MB, time=14.89 memory used=1393.4MB, alloc=420.3MB, time=15.16 memory used=1447.7MB, alloc=420.3MB, time=15.40 memory used=1512.3MB, alloc=420.3MB, time=15.61 memory used=1580.8MB, alloc=420.3MB, time=15.83 memory used=1650.5MB, alloc=420.3MB, time=16.14 memory used=1743.5MB, alloc=420.3MB, time=16.92 memory used=1796.4MB, alloc=420.3MB, time=17.12 memory used=1858.5MB, alloc=420.3MB, time=17.35 memory used=1926.9MB, alloc=420.3MB, time=17.57 memory used=2001.4MB, alloc=420.3MB, time=18.57 memory used=2094.6MB, alloc=420.3MB, time=59.74 memory used=2176.3MB, alloc=444.3MB, time=110.00 memory used=2253.1MB, alloc=444.3MB, time=151.83 memory used=2349.5MB, alloc=444.3MB, time=153.71 memory used=2418.5MB, alloc=444.3MB, time=153.92 memory used=2487.3MB, alloc=444.3MB, time=154.14 memory used=2568.1MB, alloc=444.3MB, time=154.31 memory used=2651.3MB, alloc=444.3MB, time=154.94 memory used=2742.7MB, alloc=468.3MB, time=157.99 memory used=2820.3MB, alloc=468.3MB, time=158.29 memory used=2900.5MB, alloc=468.3MB, time=158.58 memory used=2979.2MB, alloc=468.3MB, time=158.86 memory used=3060.8MB, alloc=468.3MB, time=159.13 memory used=3146.8MB, alloc=468.3MB, time=159.41 memory used=3234.9MB, alloc=468.3MB, time=159.68 memory used=3329.9MB, alloc=468.3MB, time=159.97 memory used=3432.1MB, alloc=468.3MB, time=160.24 memory used=3535.7MB, alloc=468.3MB, time=160.53 memory used=3646.1MB, alloc=468.3MB, time=160.85 memory used=3756.6MB, alloc=468.3MB, time=161.16 memory used=3834.9MB, alloc=468.3MB, time=161.41 memory used=3894.4MB, alloc=468.3MB, time=161.64 memory used=3950.2MB, alloc=468.3MB, time=161.87 memory used=4009.1MB, alloc=468.3MB, time=162.09 memory used=4068.3MB, alloc=468.3MB, time=162.35 memory used=4132.5MB, alloc=468.3MB, time=162.59 memory used=4196.1MB, alloc=468.3MB, time=162.82 memory used=4259.4MB, alloc=468.3MB, time=163.08 memory used=4327.2MB, alloc=468.3MB, time=163.31 memory used=4394.4MB, alloc=468.3MB, time=163.57 memory used=4465.9MB, alloc=468.3MB, time=163.84 memory used=4541.0MB, alloc=468.3MB, time=164.09 memory used=4614.8MB, alloc=468.3MB, time=164.35 memory used=4691.1MB, alloc=468.3MB, time=164.61 memory used=4770.4MB, alloc=468.3MB, time=164.83 memory used=4855.7MB, alloc=468.3MB, time=165.07 memory used=4942.1MB, alloc=468.3MB, time=165.30 memory used=5027.6MB, alloc=468.3MB, time=165.53 memory used=5105.9MB, alloc=468.3MB, time=165.75 memory used=5186.6MB, alloc=468.3MB, time=165.97 memory used=5266.8MB, alloc=468.3MB, time=166.19 memory used=5362.3MB, alloc=468.3MB, time=169.26 memory used=5451.6MB, alloc=468.3MB, time=174.65 memory used=5532.8MB, alloc=492.3MB, time=179.19 memory used=5617.6MB, alloc=492.3MB, time=179.50 memory used=5689.8MB, alloc=492.3MB, time=179.76 memory used=5762.1MB, alloc=492.3MB, time=180.03 memory used=5836.8MB, alloc=492.3MB, time=180.30 memory used=5912.9MB, alloc=492.3MB, time=180.55 memory used=5989.7MB, alloc=492.3MB, time=180.81 memory used=6067.5MB, alloc=492.3MB, time=181.07 memory used=6138.8MB, alloc=492.3MB, time=181.30 memory used=6210.7MB, alloc=492.3MB, time=181.56 memory used=6283.5MB, alloc=492.3MB, time=181.80 memory used=6356.9MB, alloc=492.3MB, time=182.06 memory used=6430.9MB, alloc=492.3MB, time=182.31 memory used=6504.9MB, alloc=492.3MB, time=182.58 memory used=6581.0MB, alloc=492.3MB, time=182.82 memory used=6657.6MB, alloc=492.3MB, time=183.05 memory used=6735.0MB, alloc=492.3MB, time=183.30 memory used=6821.2MB, alloc=492.3MB, time=183.54 memory used=6907.9MB, alloc=492.3MB, time=183.80 memory used=6995.2MB, alloc=492.3MB, time=184.07 memory used=7082.9MB, alloc=492.3MB, time=184.31 memory used=7171.0MB, alloc=492.3MB, time=184.58 memory used=7259.5MB, alloc=492.3MB, time=184.82 memory used=7348.3MB, alloc=492.3MB, time=185.06 memory used=7437.8MB, alloc=492.3MB, time=185.33 memory used=7536.1MB, alloc=492.3MB, time=185.59 memory used=7634.8MB, alloc=492.3MB, time=185.87 memory used=7733.7MB, alloc=492.3MB, time=186.13 memory used=7832.8MB, alloc=492.3MB, time=186.37 memory used=7932.1MB, alloc=492.3MB, time=186.63 memory used=8031.8MB, alloc=492.3MB, time=186.91 memory used=8140.0MB, alloc=492.3MB, time=187.17 memory used=8248.4MB, alloc=492.3MB, time=187.46 memory used=8356.7MB, alloc=492.3MB, time=187.73 memory used=8465.2MB, alloc=492.3MB, time=188.01 memory used=8582.2MB, alloc=492.3MB, time=188.31 memory used=8696.9MB, alloc=492.3MB, time=188.59 memory used=8809.7MB, alloc=492.3MB, time=188.84 memory used=8925.6MB, alloc=492.3MB, time=189.12 memory used=9040.9MB, alloc=492.3MB, time=189.37 memory used=9155.6MB, alloc=492.3MB, time=189.65 memory used=9278.4MB, alloc=492.3MB, time=189.94 memory used=9366.3MB, alloc=492.3MB, time=190.19 memory used=9435.5MB, alloc=516.3MB, time=190.40 memory used=9511.4MB, alloc=516.3MB, time=190.62 memory used=9583.6MB, alloc=516.3MB, time=190.82 memory used=9657.5MB, alloc=516.3MB, time=191.03 memory used=9732.1MB, alloc=516.3MB, time=191.23 memory used=9807.4MB, alloc=516.3MB, time=191.44 memory used=9882.2MB, alloc=516.3MB, time=191.64 memory used=9956.5MB, alloc=516.3MB, time=191.84 memory used=10030.7MB, alloc=516.3MB, time=192.05 memory used=10111.6MB, alloc=516.3MB, time=192.25 memory used=10192.1MB, alloc=516.3MB, time=192.45 memory used=10271.8MB, alloc=516.3MB, time=192.66 memory used=10351.0MB, alloc=516.3MB, time=192.88 memory used=10436.8MB, alloc=516.3MB, time=193.10 memory used=10521.6MB, alloc=516.3MB, time=193.32 memory used=10605.6MB, alloc=516.3MB, time=193.54 memory used=10695.7MB, alloc=516.3MB, time=193.75 memory used=10784.3MB, alloc=516.3MB, time=193.96 memory used=10871.8MB, alloc=516.3MB, time=194.20 memory used=10964.6MB, alloc=516.3MB, time=194.41 memory used=11055.9MB, alloc=516.3MB, time=194.63 memory used=11151.8MB, alloc=516.3MB, time=194.84 memory used=11245.8MB, alloc=516.3MB, time=195.06 memory used=11343.8MB, alloc=516.3MB, time=195.28 memory used=11445.1MB, alloc=516.3MB, time=195.52 memory used=11543.8MB, alloc=516.3MB, time=195.74 memory used=11644.7MB, alloc=516.3MB, time=195.97 memory used=11752.0MB, alloc=516.3MB, time=196.20 memory used=11860.1MB, alloc=516.3MB, time=196.43 memory used=11972.1MB, alloc=516.3MB, time=196.66 memory used=12086.2MB, alloc=516.3MB, time=196.89 memory used=12215.6MB, alloc=516.3MB, time=197.14 memory used=12390.2MB, alloc=516.3MB, time=197.50 memory used=12590.1MB, alloc=516.3MB, time=198.05 memory used=12903.7MB, alloc=516.3MB, time=399.45 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428532850 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 F := [-15 x y z - 5 y, -18 x z + 13 y - 1] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 2 2 G := [-2 x y z + 5 x z - 20 y , 13 x y z + 8 y z + x ] > Problem := [F,G]; 2 3 Problem := [[-15 x y z - 5 y, -18 x z + 13 y - 1], 2 2 2 2 2 2 2 [-2 x y z + 5 x z - 20 y , 13 x y z + 8 y z + x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=24.5MB, alloc=32.3MB, time=0.46 memory used=43.4MB, alloc=56.3MB, time=0.75 memory used=84.9MB, alloc=60.3MB, time=1.35 memory used=126.7MB, alloc=68.3MB, time=1.87 memory used=175.5MB, alloc=68.3MB, time=2.44 memory used=218.1MB, alloc=68.3MB, time=2.95 memory used=264.3MB, alloc=68.3MB, time=3.54 memory used=306.5MB, alloc=92.3MB, time=4.15 memory used=367.9MB, alloc=92.3MB, time=4.70 memory used=436.8MB, alloc=92.3MB, time=5.39 memory used=507.3MB, alloc=92.3MB, time=6.25 memory used=571.1MB, alloc=92.3MB, time=7.06 memory used=635.9MB, alloc=348.3MB, time=7.97 memory used=707.4MB, alloc=372.3MB, time=8.79 memory used=789.6MB, alloc=372.3MB, time=9.54 memory used=853.7MB, alloc=372.3MB, time=9.90 memory used=897.0MB, alloc=372.3MB, time=10.04 memory used=948.2MB, alloc=372.3MB, time=10.29 memory used=1036.5MB, alloc=372.3MB, time=11.70 memory used=1149.1MB, alloc=372.3MB, time=12.49 memory used=1249.8MB, alloc=372.3MB, time=13.81 memory used=1302.0MB, alloc=372.3MB, time=14.11 memory used=1379.0MB, alloc=372.3MB, time=14.78 memory used=1456.2MB, alloc=372.3MB, time=15.42 memory used=1567.6MB, alloc=372.3MB, time=17.08 memory used=1664.3MB, alloc=372.3MB, time=17.60 memory used=1759.7MB, alloc=372.3MB, time=18.47 memory used=1809.7MB, alloc=372.3MB, time=18.77 memory used=1870.5MB, alloc=372.3MB, time=19.25 memory used=1927.8MB, alloc=372.3MB, time=19.67 memory used=1997.0MB, alloc=372.3MB, time=20.24 memory used=2048.1MB, alloc=372.3MB, time=20.56 memory used=2099.3MB, alloc=372.3MB, time=20.84 memory used=2138.2MB, alloc=372.3MB, time=20.99 memory used=2181.1MB, alloc=372.3MB, time=21.14 memory used=2227.2MB, alloc=372.3MB, time=21.39 memory used=2268.1MB, alloc=372.3MB, time=21.55 memory used=2325.3MB, alloc=372.3MB, time=22.01 memory used=2411.9MB, alloc=396.3MB, time=23.21 memory used=2519.1MB, alloc=396.3MB, time=24.76 memory used=2588.1MB, alloc=396.3MB, time=25.19 memory used=2680.1MB, alloc=396.3MB, time=26.09 memory used=2809.2MB, alloc=420.3MB, time=27.86 memory used=2963.7MB, alloc=420.3MB, time=28.77 memory used=3078.2MB, alloc=420.3MB, time=30.04 memory used=3235.3MB, alloc=420.3MB, time=31.34 memory used=3398.0MB, alloc=420.3MB, time=32.14 memory used=3557.1MB, alloc=420.3MB, time=32.87 memory used=3705.7MB, alloc=420.3MB, time=33.55 memory used=3851.9MB, alloc=420.3MB, time=34.22 memory used=3976.8MB, alloc=420.3MB, time=35.01 memory used=4095.6MB, alloc=420.3MB, time=35.83 memory used=4189.8MB, alloc=420.3MB, time=36.25 memory used=4274.8MB, alloc=420.3MB, time=36.61 memory used=4359.4MB, alloc=420.3MB, time=36.93 memory used=4448.5MB, alloc=420.3MB, time=37.24 memory used=4545.4MB, alloc=420.3MB, time=37.58 memory used=4658.5MB, alloc=420.3MB, time=37.96 memory used=4778.7MB, alloc=420.3MB, time=38.34 memory used=4941.6MB, alloc=420.3MB, time=41.11 memory used=5040.4MB, alloc=420.3MB, time=41.57 memory used=5129.5MB, alloc=420.3MB, time=41.94 memory used=5214.8MB, alloc=420.3MB, time=42.28 memory used=5300.1MB, alloc=420.3MB, time=42.62 memory used=5389.5MB, alloc=420.3MB, time=42.96 memory used=5491.2MB, alloc=420.3MB, time=43.32 memory used=5601.8MB, alloc=420.3MB, time=43.70 memory used=5752.8MB, alloc=420.3MB, time=45.66 memory used=5893.4MB, alloc=444.3MB, time=47.42 memory used=6015.8MB, alloc=444.3MB, time=47.94 memory used=6123.4MB, alloc=444.3MB, time=48.34 memory used=6229.5MB, alloc=444.3MB, time=48.72 memory used=6337.3MB, alloc=444.3MB, time=49.09 memory used=6485.0MB, alloc=444.3MB, time=50.42 memory used=6595.7MB, alloc=444.3MB, time=50.84 memory used=6725.7MB, alloc=444.3MB, time=51.24 memory used=6880.9MB, alloc=444.3MB, time=51.67 memory used=7036.8MB, alloc=444.3MB, time=52.11 memory used=7203.5MB, alloc=444.3MB, time=52.56 memory used=7382.9MB, alloc=444.3MB, time=53.01 memory used=7570.4MB, alloc=444.3MB, time=53.48 memory used=7772.9MB, alloc=444.3MB, time=53.96 memory used=7982.5MB, alloc=444.3MB, time=54.45 memory used=8249.6MB, alloc=444.3MB, time=55.76 memory used=8359.5MB, alloc=444.3MB, time=56.17 memory used=8494.9MB, alloc=444.3MB, time=56.57 memory used=8668.8MB, alloc=444.3MB, time=57.00 memory used=8850.7MB, alloc=444.3MB, time=57.48 memory used=9038.3MB, alloc=444.3MB, time=57.95 memory used=9237.7MB, alloc=444.3MB, time=58.43 memory used=9446.5MB, alloc=444.3MB, time=58.91 memory used=9685.5MB, alloc=444.3MB, time=59.44 memory used=9943.3MB, alloc=444.3MB, time=60.01 memory used=10244.4MB, alloc=444.3MB, time=60.64 memory used=10654.7MB, alloc=444.3MB, time=62.12 memory used=10768.0MB, alloc=444.3MB, time=62.56 memory used=10873.1MB, alloc=444.3MB, time=62.94 memory used=10982.2MB, alloc=444.3MB, time=63.31 memory used=11099.8MB, alloc=444.3MB, time=63.69 memory used=11231.6MB, alloc=444.3MB, time=64.10 memory used=11371.4MB, alloc=444.3MB, time=64.52 memory used=11531.0MB, alloc=444.3MB, time=66.43 memory used=11701.1MB, alloc=444.3MB, time=68.09 memory 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alloc=612.3MB, time=118.44 memory used=16395.1MB, alloc=636.3MB, time=122.09 memory used=16652.9MB, alloc=636.3MB, time=127.97 memory used=16919.6MB, alloc=636.3MB, time=132.86 memory used=17165.1MB, alloc=636.3MB, time=137.54 memory used=17445.7MB, alloc=636.3MB, time=141.77 memory used=17685.9MB, alloc=660.3MB, time=145.76 memory used=17905.2MB, alloc=684.3MB, time=149.26 memory used=18154.4MB, alloc=708.3MB, time=156.18 memory used=18408.9MB, alloc=732.3MB, time=164.09 memory used=18671.7MB, alloc=756.3MB, time=172.68 memory used=18944.9MB, alloc=780.3MB, time=182.25 memory used=19231.1MB, alloc=804.3MB, time=192.93 memory used=19541.4MB, alloc=828.3MB, time=204.23 memory used=19875.5MB, alloc=852.3MB, time=216.32 memory used=20233.6MB, alloc=876.3MB, time=231.73 memory used=20615.6MB, alloc=876.3MB, time=246.55 memory used=20997.6MB, alloc=876.3MB, time=260.44 memory used=21379.6MB, alloc=900.3MB, time=274.49 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428533150 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 3 2 F := [-17 x - 18 y z - 13 z , 19 x y z + 10 y z + 1] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 3 2 G := [16 x y - x + y z, 5 x y - 3 x y z + 20] > Problem := [F,G]; 4 3 3 2 Problem := [[-17 x - 18 y z - 13 z , 19 x y z + 10 y z + 1], 3 3 3 2 [16 x y - x + y z, 5 x y - 3 x y z + 20]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=24.7MB, alloc=32.3MB, time=0.47 memory used=44.3MB, alloc=60.3MB, time=0.78 memory used=83.0MB, alloc=60.3MB, time=1.27 memory used=127.8MB, alloc=68.3MB, time=1.91 memory used=177.5MB, alloc=92.3MB, time=2.47 memory used=237.0MB, alloc=92.3MB, time=2.94 memory used=293.1MB, alloc=92.3MB, time=3.30 memory used=350.9MB, alloc=92.3MB, time=3.67 memory used=404.1MB, alloc=93.6MB, time=3.91 memory used=458.3MB, alloc=93.6MB, time=4.12 memory used=509.0MB, alloc=93.6MB, time=4.63 memory used=566.3MB, alloc=95.1MB, time=5.03 memory used=632.6MB, alloc=95.1MB, time=5.70 memory used=700.9MB, alloc=95.1MB, time=6.38 memory used=770.2MB, alloc=351.1MB, time=7.20 memory used=838.6MB, alloc=375.1MB, time=8.09 memory used=932.0MB, alloc=375.1MB, time=9.30 memory used=1026.6MB, alloc=375.1MB, time=10.39 memory used=1106.8MB, alloc=399.1MB, time=11.21 memory used=1176.1MB, alloc=399.1MB, time=11.59 memory used=1244.9MB, alloc=399.1MB, time=11.86 memory used=1306.5MB, alloc=399.1MB, time=12.11 memory used=1359.6MB, alloc=399.1MB, time=12.30 memory used=1423.2MB, alloc=399.1MB, time=12.59 memory used=1490.5MB, alloc=399.1MB, time=12.91 memory used=1548.2MB, alloc=399.1MB, time=13.11 memory used=1595.5MB, alloc=399.1MB, time=13.28 memory used=1654.7MB, alloc=399.1MB, time=13.44 memory used=1722.7MB, alloc=399.1MB, time=13.81 memory used=1778.3MB, alloc=399.1MB, time=14.00 memory used=1871.9MB, alloc=399.1MB, time=15.23 memory used=1946.7MB, alloc=399.1MB, time=15.50 memory used=1990.4MB, alloc=399.1MB, time=15.71 memory used=2038.3MB, alloc=399.1MB, time=15.91 memory used=2091.6MB, alloc=399.1MB, time=16.10 memory used=2152.2MB, alloc=399.1MB, time=16.31 memory used=2215.4MB, alloc=399.1MB, time=16.51 memory used=2265.9MB, alloc=399.1MB, time=16.72 memory used=2303.4MB, alloc=399.1MB, time=16.91 memory used=2341.8MB, alloc=399.1MB, time=17.09 memory used=2382.4MB, alloc=399.1MB, time=17.27 memory used=2424.0MB, alloc=399.1MB, time=17.44 memory used=2466.4MB, alloc=399.1MB, time=17.61 memory used=2510.0MB, alloc=399.1MB, time=17.79 memory used=2558.2MB, alloc=399.1MB, time=17.95 memory used=2607.3MB, alloc=399.1MB, time=18.11 memory used=2657.2MB, alloc=399.1MB, time=18.25 memory used=2708.6MB, alloc=399.1MB, time=18.42 memory used=2763.5MB, alloc=399.1MB, time=18.58 memory used=2819.8MB, alloc=399.1MB, time=18.75 memory used=2881.0MB, alloc=399.1MB, time=18.90 memory used=2941.8MB, alloc=399.1MB, time=19.05 memory used=2991.3MB, alloc=399.1MB, time=19.19 memory used=3043.8MB, alloc=399.1MB, time=19.34 memory used=3096.6MB, alloc=399.1MB, time=19.48 memory used=3143.9MB, alloc=423.1MB, time=19.64 memory used=3190.9MB, alloc=423.1MB, time=19.78 memory used=3237.1MB, alloc=423.1MB, time=19.91 memory used=3284.9MB, alloc=423.1MB, time=20.05 memory used=3333.7MB, alloc=423.1MB, time=20.20 memory used=3385.3MB, alloc=423.1MB, time=20.33 memory used=3437.3MB, alloc=423.1MB, time=20.47 memory used=3492.9MB, alloc=423.1MB, time=20.61 memory used=3548.1MB, alloc=423.1MB, time=20.75 memory used=3606.7MB, alloc=423.1MB, time=20.91 memory used=3668.3MB, alloc=423.1MB, time=21.05 memory used=3729.7MB, alloc=423.1MB, time=21.19 memory used=3795.6MB, alloc=423.1MB, time=21.35 memory used=3864.2MB, alloc=423.1MB, time=21.50 memory used=3934.0MB, alloc=423.1MB, time=21.66 memory used=4007.6MB, alloc=423.1MB, time=21.80 memory used=4084.7MB, alloc=423.1MB, time=21.94 memory used=4167.2MB, alloc=423.1MB, time=22.09 memory used=4256.2MB, alloc=423.1MB, time=22.58 memory used=4365.9MB, alloc=423.1MB, time=23.66 memory used=4434.9MB, alloc=423.1MB, time=23.89 memory used=4501.1MB, alloc=423.1MB, time=24.11 memory used=4577.6MB, alloc=423.1MB, time=24.34 memory used=4661.2MB, alloc=423.1MB, time=24.55 memory used=4725.1MB, alloc=423.1MB, time=24.77 memory used=4774.9MB, alloc=423.1MB, time=24.97 memory used=4829.7MB, alloc=423.1MB, time=25.18 memory used=4887.0MB, alloc=423.1MB, time=25.37 memory used=4946.2MB, alloc=423.1MB, time=25.58 memory used=5010.8MB, alloc=423.1MB, time=25.75 memory used=5077.3MB, alloc=423.1MB, time=25.93 memory used=5149.2MB, alloc=423.1MB, time=26.12 memory used=5223.1MB, alloc=423.1MB, time=26.32 memory used=5301.7MB, alloc=423.1MB, time=26.50 memory used=5385.6MB, alloc=423.1MB, time=26.69 memory used=5454.2MB, alloc=423.1MB, time=26.88 memory used=5525.0MB, alloc=423.1MB, time=27.07 memory used=5592.3MB, alloc=423.1MB, time=27.27 memory used=5641.5MB, alloc=423.1MB, time=27.42 memory used=5688.2MB, alloc=423.1MB, time=27.57 memory used=5736.6MB, alloc=423.1MB, time=27.71 memory used=5785.5MB, alloc=423.1MB, time=27.85 memory used=5836.9MB, alloc=423.1MB, time=27.99 memory used=5888.9MB, alloc=423.1MB, time=28.14 memory used=5944.5MB, alloc=423.1MB, time=28.28 memory used=6000.2MB, alloc=423.1MB, time=28.42 memory used=6058.1MB, alloc=423.1MB, time=28.57 memory used=6119.6MB, alloc=423.1MB, time=28.71 memory used=6181.2MB, alloc=423.1MB, 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alloc=423.1MB, time=87.27 memory used=7742.3MB, alloc=423.1MB, time=87.43 memory used=7809.5MB, alloc=423.1MB, time=87.58 memory used=7879.9MB, alloc=423.1MB, time=87.74 memory used=7953.4MB, alloc=423.1MB, time=87.91 memory used=8029.8MB, alloc=423.1MB, time=88.07 memory used=8111.1MB, alloc=423.1MB, time=88.24 memory used=8201.4MB, alloc=423.1MB, time=88.42 memory used=8311.6MB, alloc=423.1MB, time=88.64 memory used=8499.3MB, alloc=423.1MB, time=89.06 memory used=8642.1MB, alloc=423.1MB, time=89.32 memory used=8797.9MB, alloc=423.1MB, time=89.57 memory used=8971.8MB, alloc=423.1MB, time=89.84 memory used=9177.6MB, alloc=423.1MB, time=90.34 memory used=9255.9MB, alloc=423.1MB, time=90.59 memory used=9319.6MB, alloc=423.1MB, time=90.80 memory used=9381.3MB, alloc=423.1MB, time=90.99 memory used=9456.3MB, alloc=423.1MB, time=91.16 memory used=9557.8MB, alloc=423.1MB, time=91.57 memory used=9629.8MB, alloc=423.1MB, time=91.82 memory used=9701.4MB, alloc=423.1MB, time=92.01 memory used=9760.9MB, alloc=423.1MB, time=92.20 memory used=9832.7MB, alloc=423.1MB, time=92.37 memory used=9953.6MB, alloc=423.1MB, time=100.72 memory used=10030.3MB, alloc=423.1MB, time=100.92 memory used=10089.9MB, alloc=423.1MB, time=101.11 memory used=10161.3MB, alloc=423.1MB, time=101.30 memory used=10244.4MB, alloc=423.1MB, time=101.50 memory used=10306.5MB, alloc=423.1MB, time=101.65 memory used=10360.8MB, alloc=423.1MB, time=101.80 memory used=10420.2MB, alloc=423.1MB, time=101.95 memory used=10485.4MB, alloc=423.1MB, time=102.11 memory used=10557.0MB, alloc=423.1MB, time=102.27 memory used=10636.5MB, alloc=423.1MB, time=102.43 memory used=10802.2MB, alloc=423.1MB, time=102.79 memory used=10892.5MB, alloc=423.1MB, time=103.29 memory used=10999.9MB, alloc=423.1MB, time=104.10 memory used=11064.3MB, alloc=423.1MB, time=104.31 memory used=11135.8MB, alloc=423.1MB, time=104.55 memory used=11219.2MB, alloc=423.1MB, time=104.78 memory used=11284.6MB, alloc=423.1MB, time=104.99 memory 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used=15977.4MB, alloc=447.1MB, time=304.54 memory used=16053.0MB, alloc=447.1MB, time=304.72 memory used=16134.1MB, alloc=447.1MB, time=304.90 memory used=16216.5MB, alloc=447.1MB, time=305.09 memory used=16300.0MB, alloc=447.1MB, time=305.27 memory used=16384.6MB, alloc=447.1MB, time=305.45 memory used=16475.1MB, alloc=447.1MB, time=305.65 memory used=16566.6MB, alloc=447.1MB, time=305.84 memory used=16659.2MB, alloc=447.1MB, time=306.03 memory used=16752.8MB, alloc=447.1MB, time=306.22 memory used=16852.3MB, alloc=447.1MB, time=306.41 memory used=16961.2MB, alloc=447.1MB, time=306.62 memory used=17074.9MB, alloc=447.1MB, time=306.82 memory used=17274.3MB, alloc=447.1MB, time=307.15 memory used=17400.7MB, alloc=447.1MB, time=307.40 memory used=17531.5MB, alloc=447.1MB, time=307.66 memory used=17668.4MB, alloc=447.1MB, time=307.92 memory used=17806.0MB, alloc=447.1MB, time=308.18 memory used=17949.5MB, alloc=447.1MB, time=308.45 memory used=18098.9MB, alloc=447.1MB, time=308.71 memory used=18248.4MB, alloc=447.1MB, time=308.99 memory used=18403.2MB, alloc=447.1MB, time=309.27 memory used=18563.2MB, alloc=447.1MB, time=309.55 memory used=18728.1MB, alloc=447.1MB, time=309.84 memory used=18897.5MB, alloc=447.1MB, time=310.13 memory used=19071.1MB, alloc=447.1MB, time=310.42 memory used=19253.6MB, alloc=447.1MB, time=310.70 memory used=19439.6MB, alloc=447.1MB, time=311.00 memory used=19633.0MB, alloc=447.1MB, time=311.31 memory used=19832.9MB, alloc=447.1MB, time=311.60 memory used=20038.3MB, alloc=447.1MB, time=311.91 memory used=20252.4MB, alloc=447.1MB, time=312.22 memory used=20473.3MB, alloc=447.1MB, time=312.52 memory used=20699.7MB, alloc=447.1MB, time=312.84 memory used=20913.1MB, alloc=447.1MB, time=313.15 memory used=21132.3MB, alloc=447.1MB, time=313.45 memory used=21331.5MB, alloc=447.1MB, time=313.73 memory used=21512.7MB, alloc=447.1MB, time=314.00 memory used=21706.3MB, alloc=447.1MB, time=314.27 memory used=21911.0MB, alloc=447.1MB, time=314.82 memory used=21999.7MB, alloc=447.1MB, time=315.08 memory used=22080.7MB, alloc=447.1MB, time=315.30 memory used=22197.7MB, alloc=447.1MB, time=340.24 memory used=22314.7MB, alloc=471.1MB, time=403.40 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428533450 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 3 2 F := [17 x y z + 13 x y + 11 z, 9 x y - 5 z + 12 z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 2 G := [-5 x y z + 3 x z + 12 z , -10 x y z + 16 y z ] > Problem := [F,G]; 2 2 3 3 2 Problem := [[17 x y z + 13 x y + 11 z, 9 x y - 5 z + 12 z ], 2 2 3 2 2 2 [-5 x y z + 3 x z + 12 z , -10 x y z + 16 y z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=24.9MB, alloc=32.3MB, time=0.48 memory used=44.6MB, alloc=56.3MB, time=0.77 memory used=85.6MB, alloc=60.3MB, time=1.39 memory used=126.8MB, alloc=68.3MB, time=1.98 memory used=168.1MB, alloc=92.3MB, time=2.57 memory used=231.7MB, alloc=92.3MB, time=3.33 memory used=299.4MB, alloc=92.3MB, time=4.13 memory used=365.6MB, alloc=92.3MB, time=4.96 memory used=428.6MB, alloc=116.3MB, time=5.86 memory used=495.0MB, alloc=116.3MB, time=6.83 memory used=566.4MB, alloc=372.3MB, time=7.78 memory used=653.0MB, alloc=396.3MB, time=9.05 memory used=762.3MB, alloc=396.3MB, time=10.62 memory used=832.9MB, alloc=396.3MB, time=11.15 memory used=899.6MB, alloc=396.3MB, time=11.57 memory used=957.6MB, alloc=396.3MB, time=11.85 memory used=1010.5MB, alloc=396.3MB, time=12.15 memory used=1121.9MB, alloc=420.3MB, time=13.61 memory used=1252.5MB, alloc=420.3MB, time=15.29 memory used=1379.7MB, alloc=420.3MB, time=16.52 memory used=1461.5MB, alloc=444.3MB, time=17.00 memory used=1551.1MB, alloc=444.3MB, time=17.43 memory used=1638.7MB, alloc=444.3MB, time=17.81 memory used=1771.9MB, alloc=444.3MB, time=19.44 memory used=1920.8MB, alloc=468.3MB, time=21.24 memory used=2051.1MB, alloc=468.3MB, time=22.82 memory used=2174.5MB, alloc=492.3MB, time=24.47 memory used=2312.2MB, alloc=492.3MB, time=26.19 memory used=2408.8MB, alloc=492.3MB, time=27.40 memory used=2501.5MB, alloc=492.3MB, time=28.66 memory used=2618.6MB, alloc=516.3MB, time=30.03 memory used=2759.2MB, alloc=516.3MB, time=31.34 memory used=2844.4MB, alloc=516.3MB, time=32.48 memory used=2939.7MB, alloc=516.3MB, time=33.59 memory used=3045.2MB, alloc=516.3MB, time=35.07 memory used=3176.5MB, alloc=516.3MB, time=35.89 memory used=3291.9MB, alloc=516.3MB, time=36.66 memory used=3384.8MB, alloc=516.3MB, time=37.10 memory used=3470.9MB, alloc=516.3MB, time=37.49 memory used=3578.4MB, alloc=516.3MB, time=37.88 memory used=3660.1MB, alloc=516.3MB, time=38.22 memory used=3756.5MB, alloc=516.3MB, time=38.87 memory used=3858.9MB, alloc=516.3MB, time=39.34 memory used=3944.6MB, alloc=516.3MB, time=39.78 memory used=4032.8MB, alloc=516.3MB, time=40.20 memory used=4140.8MB, alloc=516.3MB, time=40.62 memory used=4216.5MB, alloc=516.3MB, time=40.97 memory used=4369.7MB, alloc=516.3MB, time=45.70 memory used=4528.0MB, alloc=516.3MB, time=46.50 memory used=4625.8MB, alloc=516.3MB, time=46.92 memory used=4706.3MB, alloc=516.3MB, time=47.26 memory used=4790.8MB, alloc=516.3MB, time=47.58 memory used=4916.1MB, alloc=516.3MB, time=48.87 memory used=5009.2MB, alloc=516.3MB, time=49.33 memory used=5116.1MB, alloc=540.3MB, time=49.77 memory used=5203.2MB, alloc=540.3MB, time=50.21 memory used=5305.1MB, alloc=540.3MB, time=50.62 memory used=5422.7MB, alloc=540.3MB, time=51.07 memory used=5557.0MB, alloc=540.3MB, time=51.49 memory used=5653.0MB, alloc=540.3MB, time=51.86 memory used=5734.1MB, alloc=540.3MB, time=52.21 memory used=5821.2MB, alloc=540.3MB, time=52.54 memory used=5914.7MB, alloc=540.3MB, time=52.88 memory used=6015.4MB, alloc=540.3MB, time=53.23 memory used=6125.4MB, alloc=540.3MB, time=53.57 memory used=6248.8MB, alloc=540.3MB, time=53.94 memory used=6411.2MB, alloc=540.3MB, time=55.22 memory used=6536.7MB, alloc=540.3MB, time=55.70 memory used=6628.6MB, alloc=540.3MB, time=56.12 memory used=6725.3MB, alloc=540.3MB, time=56.53 memory used=6838.3MB, alloc=540.3MB, time=56.99 memory used=6969.3MB, alloc=540.3MB, time=57.44 memory used=7081.3MB, alloc=540.3MB, time=57.84 memory used=7160.6MB, alloc=540.3MB, time=58.18 memory used=7245.3MB, alloc=540.3MB, time=58.53 memory used=7336.7MB, alloc=540.3MB, time=58.87 memory used=7435.9MB, alloc=540.3MB, time=59.22 memory used=7542.9MB, alloc=540.3MB, time=59.59 memory used=7663.3MB, alloc=540.3MB, time=59.98 memory used=7815.9MB, alloc=540.3MB, time=60.75 memory used=7968.9MB, alloc=540.3MB, time=61.72 memory used=8096.7MB, alloc=540.3MB, time=62.93 memory used=8221.7MB, alloc=540.3MB, time=64.91 memory used=8363.1MB, alloc=540.3MB, time=65.89 memory used=8535.7MB, alloc=540.3MB, time=67.23 memory used=8745.1MB, alloc=540.3MB, time=70.23 memory used=8880.6MB, alloc=540.3MB, time=71.23 memory used=9012.7MB, alloc=540.3MB, time=73.04 memory used=9119.1MB, alloc=540.3MB, time=73.50 memory used=9209.8MB, alloc=540.3MB, time=73.92 memory used=9320.6MB, alloc=540.3MB, time=74.34 memory used=9450.9MB, alloc=540.3MB, time=74.80 memory used=9541.6MB, alloc=540.3MB, time=75.19 memory used=9618.8MB, alloc=540.3MB, time=75.56 memory used=9701.2MB, alloc=540.3MB, time=75.92 memory used=9789.7MB, alloc=540.3MB, time=76.29 memory used=9884.2MB, alloc=540.3MB, time=76.65 memory used=9984.3MB, alloc=540.3MB, time=77.02 memory used=10089.8MB, alloc=540.3MB, time=77.42 memory used=10204.1MB, alloc=540.3MB, time=77.85 memory used=10326.6MB, alloc=540.3MB, time=78.24 memory used=10456.0MB, alloc=540.3MB, time=78.61 memory used=10684.9MB, alloc=540.3MB, time=79.26 memory used=10819.6MB, alloc=540.3MB, time=79.69 memory used=10967.6MB, alloc=540.3MB, time=80.12 memory used=11129.5MB, alloc=540.3MB, time=80.55 memory used=11322.9MB, alloc=540.3MB, time=82.33 memory used=11421.9MB, alloc=540.3MB, time=82.79 memory used=11516.2MB, alloc=540.3MB, time=83.23 memory used=11629.7MB, alloc=540.3MB, time=83.68 memory used=11762.4MB, alloc=540.3MB, time=84.16 memory used=11842.1MB, alloc=540.3MB, time=84.52 memory used=11919.7MB, alloc=540.3MB, time=84.88 memory used=12002.5MB, alloc=540.3MB, time=85.24 memory used=12091.4MB, alloc=540.3MB, time=85.60 memory used=12186.1MB, alloc=540.3MB, time=85.97 memory used=12286.5MB, alloc=540.3MB, time=86.35 memory used=12392.1MB, alloc=540.3MB, time=86.74 memory used=12506.4MB, alloc=540.3MB, time=87.12 memory used=12628.8MB, alloc=540.3MB, time=87.52 memory used=12758.3MB, alloc=540.3MB, time=87.90 memory used=12970.5MB, alloc=540.3MB, time=88.39 memory used=13108.0MB, alloc=540.3MB, time=88.82 memory used=13256.3MB, alloc=540.3MB, time=89.26 memory used=13420.0MB, alloc=540.3MB, time=89.71 memory used=13670.8MB, alloc=540.3MB, time=91.32 memory used=13777.8MB, alloc=540.3MB, time=91.75 memory used=13903.5MB, alloc=540.3MB, time=92.92 memory used=14010.9MB, alloc=540.3MB, time=93.87 memory used=14105.9MB, alloc=540.3MB, time=95.07 memory used=14235.6MB, alloc=540.3MB, time=96.12 memory used=14337.0MB, alloc=540.3MB, time=97.18 memory used=14401.0MB, alloc=540.3MB, time=98.24 memory used=14475.6MB, alloc=540.3MB, time=99.31 memory used=14608.8MB, alloc=540.3MB, time=100.22 memory used=14692.7MB, alloc=540.3MB, time=101.11 memory used=14755.4MB, alloc=540.3MB, time=102.13 memory used=14811.9MB, alloc=540.3MB, time=102.94 memory used=14861.7MB, alloc=540.3MB, time=103.86 memory used=14905.3MB, alloc=540.3MB, time=104.63 memory used=14959.7MB, alloc=540.3MB, time=105.60 memory used=15009.4MB, alloc=564.3MB, time=106.58 memory used=15221.5MB, alloc=564.3MB, time=108.42 memory used=15331.9MB, alloc=564.3MB, time=108.96 memory used=15444.5MB, alloc=564.3MB, time=109.48 memory used=15711.9MB, alloc=564.3MB, time=111.23 memory used=15884.4MB, alloc=564.3MB, time=113.43 memory used=16090.6MB, alloc=564.3MB, time=114.13 memory used=16328.5MB, alloc=564.3MB, time=115.96 memory used=16503.0MB, alloc=564.3MB, time=117.80 memory used=16604.1MB, alloc=564.3MB, time=118.32 memory used=16844.2MB, alloc=564.3MB, time=119.85 memory used=17026.2MB, alloc=588.3MB, time=121.36 memory used=17182.6MB, alloc=588.3MB, time=124.14 memory used=17305.1MB, alloc=588.3MB, time=124.66 memory used=17462.4MB, alloc=588.3MB, time=125.81 memory used=17624.3MB, alloc=588.3MB, time=126.86 memory used=17779.0MB, alloc=588.3MB, time=129.57 memory used=17903.9MB, alloc=588.3MB, time=130.15 memory used=18009.5MB, alloc=588.3MB, time=130.66 memory used=18173.9MB, alloc=588.3MB, time=131.82 memory used=18290.7MB, alloc=588.3MB, time=132.36 memory used=18693.2MB, alloc=588.3MB, time=139.68 memory used=18825.1MB, alloc=588.3MB, time=140.32 memory used=18983.3MB, alloc=588.3MB, time=141.13 memory used=19108.5MB, alloc=588.3MB, time=141.71 memory used=19330.2MB, alloc=588.3MB, time=143.67 memory used=19594.5MB, alloc=612.3MB, time=145.83 memory used=19877.4MB, alloc=612.3MB, time=148.06 memory used=20198.0MB, alloc=612.3MB, time=150.87 memory used=20432.3MB, alloc=612.3MB, time=152.12 memory used=20658.7MB, alloc=612.3MB, time=152.98 memory used=20943.2MB, alloc=612.3MB, time=154.64 memory used=21254.8MB, alloc=612.3MB, time=173.02 memory used=21501.9MB, alloc=612.3MB, time=174.39 memory used=21776.4MB, alloc=612.3MB, time=176.63 memory used=22016.9MB, alloc=612.3MB, time=178.44 memory used=22317.6MB, alloc=636.3MB, time=181.43 memory used=22600.5MB, alloc=636.3MB, time=182.33 memory used=23009.5MB, alloc=636.3MB, time=183.34 memory used=23373.7MB, alloc=636.3MB, time=184.24 memory used=23693.6MB, alloc=636.3MB, time=185.09 memory used=24056.3MB, alloc=636.3MB, time=186.04 memory used=24411.2MB, alloc=636.3MB, time=186.96 memory used=24728.9MB, alloc=636.3MB, time=187.84 memory used=25072.9MB, alloc=636.3MB, time=188.75 memory used=25403.7MB, alloc=636.3MB, time=189.61 memory used=25731.2MB, alloc=636.3MB, time=190.44 memory used=26060.7MB, alloc=636.3MB, time=191.32 memory used=26389.2MB, alloc=636.3MB, time=192.16 memory used=26756.2MB, alloc=636.3MB, time=209.76 memory used=27034.2MB, alloc=636.3MB, time=212.47 memory used=27330.8MB, alloc=636.3MB, time=216.34 memory used=27584.7MB, alloc=636.3MB, time=217.25 memory used=27873.3MB, alloc=636.3MB, time=218.18 memory used=28192.7MB, alloc=636.3MB, time=221.12 memory used=28421.4MB, alloc=636.3MB, time=222.06 memory used=28724.8MB, alloc=636.3MB, time=225.23 memory used=29045.4MB, alloc=636.3MB, time=226.14 memory used=29447.7MB, alloc=636.3MB, time=227.18 memory used=29762.4MB, alloc=636.3MB, time=228.00 memory used=30092.4MB, alloc=636.3MB, time=228.89 memory used=30406.1MB, alloc=636.3MB, time=229.71 memory used=30727.0MB, alloc=636.3MB, time=230.53 memory used=31053.2MB, alloc=636.3MB, time=231.38 memory used=31368.9MB, alloc=636.3MB, time=232.22 memory used=31689.8MB, alloc=636.3MB, time=233.09 memory used=32008.5MB, alloc=636.3MB, time=233.93 memory used=32343.9MB, alloc=636.3MB, time=234.81 memory used=32658.9MB, alloc=636.3MB, time=235.64 memory used=32979.4MB, alloc=636.3MB, time=236.47 memory used=33298.1MB, alloc=636.3MB, time=237.30 memory used=33619.3MB, alloc=636.3MB, time=238.14 memory used=33941.0MB, alloc=636.3MB, time=238.96 memory used=34262.6MB, alloc=636.3MB, time=239.78 memory used=34584.2MB, alloc=636.3MB, time=240.60 memory used=34906.3MB, alloc=636.3MB, time=241.40 memory used=35228.2MB, alloc=636.3MB, time=242.24 memory used=35551.9MB, alloc=636.3MB, time=243.06 memory used=35875.1MB, alloc=636.3MB, time=243.88 memory used=36192.4MB, alloc=636.3MB, time=244.65 memory used=36515.0MB, alloc=636.3MB, time=245.46 memory used=36838.9MB, alloc=636.3MB, time=246.28 memory 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used=43646.2MB, alloc=636.3MB, time=263.76 memory used=43971.8MB, alloc=636.3MB, time=264.58 memory used=44297.3MB, alloc=636.3MB, time=265.37 memory used=44622.5MB, alloc=636.3MB, time=266.19 memory used=44948.3MB, alloc=636.3MB, time=267.04 memory used=45272.9MB, alloc=636.3MB, time=267.82 memory used=45598.9MB, alloc=636.3MB, time=268.63 memory used=45926.3MB, alloc=636.3MB, time=269.50 memory used=46251.6MB, alloc=636.3MB, time=270.29 memory used=46577.1MB, alloc=636.3MB, time=271.10 memory used=46907.6MB, alloc=636.3MB, time=271.93 memory used=47229.2MB, alloc=636.3MB, time=272.71 memory used=47556.2MB, alloc=636.3MB, time=273.54 memory used=47883.5MB, alloc=636.3MB, time=274.34 memory used=48209.3MB, alloc=636.3MB, time=275.14 memory used=48540.2MB, alloc=636.3MB, time=275.99 memory used=48862.4MB, alloc=636.3MB, time=276.77 memory used=49189.5MB, alloc=636.3MB, time=277.62 memory used=49518.9MB, alloc=636.3MB, time=278.39 memory used=49844.0MB, alloc=636.3MB, time=279.23 memory used=50174.5MB, alloc=636.3MB, time=280.07 memory used=50497.3MB, alloc=636.3MB, time=280.86 memory used=50825.6MB, alloc=636.3MB, time=281.71 memory used=51152.5MB, alloc=636.3MB, time=282.60 memory used=51479.1MB, alloc=636.3MB, time=283.45 memory used=51808.5MB, alloc=636.3MB, time=284.25 memory used=52134.8MB, alloc=636.3MB, time=285.10 memory used=52466.3MB, alloc=636.3MB, time=285.95 memory used=52787.9MB, alloc=636.3MB, time=286.78 memory used=53117.0MB, alloc=636.3MB, time=287.61 memory used=53442.4MB, alloc=636.3MB, time=288.43 memory used=53770.2MB, alloc=636.3MB, time=289.28 memory used=54098.8MB, alloc=636.3MB, time=290.10 memory used=54426.4MB, alloc=636.3MB, time=290.98 memory used=54756.0MB, alloc=636.3MB, time=291.79 memory used=55083.4MB, alloc=636.3MB, time=292.64 memory used=55422.0MB, alloc=636.3MB, time=293.51 memory used=55735.2MB, alloc=636.3MB, time=294.39 memory used=56071.3MB, alloc=636.3MB, time=295.34 memory used=56389.6MB, alloc=636.3MB, time=296.24 memory used=56722.9MB, alloc=636.3MB, time=297.21 memory used=57042.2MB, alloc=636.3MB, time=298.13 memory used=57374.5MB, alloc=636.3MB, time=299.09 memory used=57695.3MB, alloc=636.3MB, time=300.03 memory used=58027.3MB, alloc=636.3MB, time=301.00 memory used=58348.0MB, alloc=636.3MB, time=301.95 memory used=58682.0MB, alloc=636.3MB, time=302.92 memory used=59013.8MB, alloc=636.3MB, time=303.90 memory used=59360.0MB, alloc=636.3MB, time=304.94 memory used=59672.0MB, alloc=636.3MB, time=305.83 memory used=60007.3MB, alloc=636.3MB, time=306.80 memory used=60326.5MB, alloc=636.3MB, time=307.69 memory used=60659.6MB, alloc=636.3MB, time=308.66 memory used=60978.2MB, alloc=636.3MB, time=309.57 memory used=61310.1MB, alloc=636.3MB, time=310.48 memory used=61634.1MB, alloc=636.3MB, time=311.33 memory used=61969.8MB, alloc=636.3MB, time=312.23 memory used=62294.6MB, alloc=636.3MB, time=313.12 memory used=62639.1MB, alloc=636.3MB, time=314.05 memory used=62946.0MB, alloc=636.3MB, time=314.87 memory used=63279.6MB, alloc=636.3MB, time=316.06 memory used=63592.6MB, alloc=636.3MB, time=316.96 memory used=63927.5MB, alloc=636.3MB, time=317.88 memory used=64245.3MB, alloc=636.3MB, time=318.80 memory used=64577.2MB, alloc=636.3MB, time=319.70 memory used=64912.4MB, alloc=636.3MB, time=320.71 memory used=65251.1MB, alloc=636.3MB, time=321.69 memory used=65575.7MB, alloc=636.3MB, time=322.67 memory used=65901.1MB, alloc=636.3MB, time=323.58 memory used=66228.2MB, alloc=636.3MB, time=324.96 memory used=66556.5MB, alloc=636.3MB, time=325.85 memory used=66885.9MB, alloc=636.3MB, time=326.83 memory used=67217.6MB, alloc=636.3MB, time=327.65 memory used=67550.8MB, alloc=636.3MB, time=328.60 memory used=67884.8MB, alloc=636.3MB, time=329.52 memory used=68214.5MB, alloc=636.3MB, time=330.38 memory used=68532.9MB, alloc=636.3MB, time=331.17 memory used=68992.8MB, alloc=636.3MB, time=349.76 memory used=69228.5MB, alloc=636.3MB, time=350.66 memory used=69538.9MB, alloc=636.3MB, time=353.71 memory used=69869.1MB, alloc=636.3MB, time=354.67 memory used=70310.4MB, alloc=636.3MB, time=355.83 memory used=70629.6MB, alloc=636.3MB, time=356.73 memory used=70959.5MB, alloc=636.3MB, time=357.69 memory used=71274.8MB, alloc=636.3MB, time=358.59 memory used=71593.2MB, alloc=636.3MB, time=359.43 memory used=71914.0MB, alloc=636.3MB, time=360.29 memory used=72239.7MB, alloc=636.3MB, time=361.09 memory used=72569.7MB, alloc=636.3MB, time=361.97 memory used=72889.0MB, alloc=636.3MB, time=362.83 memory used=73207.9MB, alloc=636.3MB, time=363.69 memory used=73528.0MB, alloc=636.3MB, time=364.55 memory used=73849.8MB, alloc=636.3MB, time=365.43 memory used=74171.9MB, alloc=636.3MB, time=366.31 memory used=74494.1MB, alloc=636.3MB, time=367.15 memory used=74816.5MB, alloc=636.3MB, time=368.03 memory used=75139.3MB, alloc=636.3MB, time=368.97 memory used=75462.9MB, alloc=636.3MB, time=369.89 memory used=75787.0MB, alloc=636.3MB, time=370.83 memory used=76114.8MB, alloc=636.3MB, time=371.78 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428533750 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 4 2 2 F := [8 x z - 5 x y z + 14 z , 2 x - 14 x y + 14 y] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 3 G := [-14 y z + 15 y - 5 z , 8 x - 19 y - 15] > Problem := [F,G]; 2 2 2 3 4 2 2 Problem := [[8 x z - 5 x y z + 14 z , 2 x - 14 x y + 14 y], 2 2 3 2 3 [-14 y z + 15 y - 5 z , 8 x - 19 y - 15]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=26.5MB, alloc=32.3MB, time=0.51 memory used=46.6MB, alloc=32.3MB, time=0.80 memory used=66.3MB, alloc=56.3MB, time=1.06 memory used=107.6MB, alloc=60.3MB, time=1.56 memory used=147.3MB, alloc=60.3MB, time=2.04 memory used=228.4MB, alloc=100.3MB, time=2.97 memory used=310.5MB, alloc=100.3MB, time=3.39 memory used=387.3MB, alloc=100.3MB, time=3.77 memory used=466.6MB, alloc=100.3MB, time=4.70 memory used=537.3MB, alloc=124.3MB, time=5.70 memory used=640.6MB, alloc=124.3MB, time=6.27 memory used=748.2MB, alloc=124.3MB, time=7.33 memory used=844.9MB, alloc=148.3MB, time=8.66 memory used=945.9MB, alloc=172.3MB, time=10.63 memory used=1047.6MB, alloc=196.3MB, time=13.70 memory used=1165.1MB, alloc=196.3MB, time=17.54 memory used=1282.5MB, alloc=220.3MB, time=21.25 N1 := 3559 > GB := Basis(F, plex(op(vars))); 4 2 2 2 2 2 3 GB := [-x + 7 x y - 7 y, 8 x z - 5 x y z + 14 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1414.1MB, alloc=220.3MB, time=23.56 memory used=1597.8MB, alloc=476.3MB, time=25.40 memory used=1777.0MB, alloc=476.3MB, time=26.80 memory used=1959.0MB, alloc=476.3MB, time=28.33 memory used=2143.1MB, alloc=500.3MB, time=30.57 memory used=2319.1MB, alloc=524.3MB, time=34.81 memory used=2485.0MB, alloc=548.3MB, time=40.19 N2 := 3559 > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 3 4 2 2 H := [8 x z - 5 x y z + 14 z , 2 x - 14 x y + 14 y, 2 2 3 2 3 -14 z y + 15 y - 5 z , 8 x - 19 y - 15] > J:=[op(GB),op(G)]; 4 2 2 2 2 2 3 2 2 3 2 J := [-x + 7 x y - 7 y, 8 x z - 5 x y z + 14 z , -14 z y + 15 y - 5 z , 3 8 x - 19 y - 15] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 9, 15, 4, 4, 3, 3, 3/4, 1, 1/2, 5/12, 1/2, 5/12, 4, 9, 15, 4, 4, 3, 3, 3/4, 1, 1/2, 5/12, 1/2, 5/12, 0, 0, 0] > save(F, G, cat("ranSet/34", convert(F, string),".txt")); > quit memory used=2626.3MB, alloc=548.3MB, time=44.18 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428533796 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 2 F := [-18 x y - 3 x y + 6 x , 16 y z - 16 x y z + 8 x z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 4 2 2 G := [11 x y z + z - 13 y z, -11 x y + 4 x y z] > Problem := [F,G]; 2 2 2 2 2 2 Problem := [[-18 x y - 3 x y + 6 x , 16 y z - 16 x y z + 8 x z], 2 4 2 2 [11 x y z + z - 13 y z, -11 x y + 4 x y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.15 memory used=26.3MB, alloc=32.3MB, time=0.41 memory used=46.5MB, alloc=32.3MB, time=0.64 memory used=66.1MB, alloc=56.3MB, time=0.86 memory used=118.2MB, alloc=60.3MB, time=1.32 memory used=167.7MB, alloc=60.3MB, time=1.67 memory used=212.2MB, alloc=60.3MB, time=2.28 memory used=255.1MB, alloc=84.3MB, time=2.77 memory used=318.2MB, alloc=92.3MB, time=3.64 memory used=380.6MB, alloc=116.3MB, time=4.39 memory used=452.8MB, alloc=140.3MB, time=5.96 memory used=535.5MB, alloc=140.3MB, time=8.29 N1 := 2277 > GB := Basis(F, plex(op(vars))); 2 2 2 2 3 3 2 2 GB := [6 x y + x y - 2 x , -18 x y z + 9 x z + 8 x z , 2 2 2 y z - 2 x y z + x z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=621.1MB, alloc=140.3MB, time=9.76 memory used=708.8MB, alloc=164.3MB, time=10.66 memory used=784.4MB, alloc=164.3MB, time=11.54 memory used=887.0MB, alloc=420.3MB, time=12.64 memory used=1008.1MB, alloc=444.3MB, time=14.01 memory used=1157.3MB, alloc=468.3MB, time=15.82 memory used=1307.6MB, alloc=492.3MB, time=18.07 memory used=1489.6MB, alloc=516.3MB, time=20.32 memory used=1661.6MB, alloc=540.3MB, time=23.86 memory used=1825.2MB, alloc=564.3MB, time=28.50 memory used=1995.5MB, alloc=588.3MB, time=34.10 memory used=2182.5MB, alloc=612.3MB, time=40.59 memory used=2393.4MB, alloc=636.3MB, time=47.89 memory used=2628.3MB, alloc=660.3MB, time=55.70 memory used=2887.1MB, alloc=660.3MB, time=64.39 memory used=3146.0MB, alloc=684.3MB, time=73.13 memory used=3428.9MB, alloc=708.3MB, time=82.75 N2 := 8089 > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 2 2 H := [-18 x y - 3 x y + 6 x , 16 y z - 16 x y z + 8 x z, 2 4 2 2 11 x y z + z - 13 y z, -11 x y + 4 x y z] > J:=[op(GB),op(G)]; 2 2 2 2 3 3 2 2 J := [6 x y + x y - 2 x , -18 x y z + 9 x z + 8 x z , 2 2 2 4 2 2 2 y z - 2 x y z + x z, 11 x y z + z - 13 y z, -11 x y + 4 x y z] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 11, 16, 4, 2, 2, 4, 1, 1, 3/4, 8/11, 8/11, 7/11, 5, 14, 21, 11 5, 3, 2, 4, 1, 1, 4/5, --, 9/14, 5/7, -3, -5, -1] 14 > save(F, G, cat("ranSet/34", convert(F, string),".txt")); > quit memory used=3645.9MB, alloc=708.3MB, time=89.18 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428533888 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 F := [14 x z + 17 x y - 14 y z, -8 x z + 2 x z - 13] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 4 2 2 2 3 2 G := [-3 x z - 17 y + 16 x z, -11 x y - 19 x + 18 x y ] > Problem := [F,G]; 3 3 2 Problem := [[14 x z + 17 x y - 14 y z, -8 x z + 2 x z - 13], 2 2 4 2 2 2 3 2 [-3 x z - 17 y + 16 x z, -11 x y - 19 x + 18 x y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.15 memory used=27.2MB, alloc=32.3MB, time=0.43 memory used=48.4MB, alloc=60.3MB, time=0.71 memory used=92.4MB, alloc=60.3MB, time=1.24 memory used=136.6MB, alloc=60.3MB, time=1.78 memory used=175.8MB, alloc=60.3MB, time=2.14 memory used=209.9MB, alloc=60.3MB, time=3.06 memory used=242.8MB, alloc=60.3MB, time=3.35 memory used=275.9MB, alloc=60.3MB, time=5.46 memory used=297.5MB, alloc=60.3MB, time=8.42 memory used=328.3MB, alloc=60.3MB, time=9.60 memory used=365.3MB, alloc=60.3MB, time=9.94 memory used=412.2MB, alloc=68.3MB, time=10.54 memory used=449.7MB, alloc=68.3MB, time=11.09 memory used=497.0MB, alloc=68.3MB, time=12.07 memory used=542.0MB, alloc=92.3MB, time=12.53 memory used=609.4MB, alloc=92.3MB, time=13.24 memory used=679.7MB, alloc=92.3MB, time=14.27 memory used=751.0MB, alloc=92.3MB, time=15.13 memory used=791.5MB, alloc=116.3MB, time=18.64 memory used=843.3MB, alloc=116.3MB, time=27.13 memory used=894.5MB, alloc=116.3MB, time=30.42 memory used=964.0MB, alloc=116.3MB, time=30.91 memory used=1019.1MB, alloc=116.3MB, time=31.19 memory used=1106.5MB, alloc=116.3MB, time=31.88 memory used=1185.6MB, alloc=372.3MB, time=32.70 memory used=1284.5MB, alloc=372.3MB, time=34.05 memory used=1370.4MB, alloc=372.3MB, time=35.63 memory used=1437.8MB, alloc=372.3MB, time=37.74 memory used=1503.0MB, alloc=396.3MB, time=38.93 memory used=1653.6MB, alloc=396.3MB, time=49.54 memory used=1730.1MB, alloc=396.3MB, time=54.26 memory used=1780.1MB, alloc=396.3MB, time=54.41 memory used=1837.3MB, alloc=396.3MB, time=54.58 memory used=1899.1MB, alloc=396.3MB, time=54.75 memory used=1940.0MB, alloc=396.3MB, time=54.87 memory used=1977.4MB, alloc=396.3MB, time=55.00 memory used=2017.3MB, alloc=396.3MB, time=55.12 memory used=2060.7MB, alloc=396.3MB, time=55.26 memory used=2106.1MB, alloc=396.3MB, time=55.39 memory used=2155.2MB, alloc=396.3MB, time=55.52 memory used=2208.0MB, alloc=396.3MB, time=55.66 memory used=2264.4MB, alloc=396.3MB, time=55.81 memory used=2325.0MB, alloc=396.3MB, time=55.94 memory used=2414.1MB, alloc=396.3MB, time=58.33 memory used=2470.5MB, alloc=396.3MB, time=58.52 memory used=2525.4MB, alloc=396.3MB, time=58.68 memory used=2588.4MB, alloc=396.3MB, time=58.86 memory used=2627.9MB, alloc=396.3MB, time=58.98 memory used=2670.2MB, alloc=396.3MB, time=59.09 memory used=2716.3MB, alloc=396.3MB, time=59.22 memory used=2776.5MB, alloc=396.3MB, time=59.41 memory used=2940.3MB, alloc=396.3MB, time=60.37 memory used=3005.8MB, alloc=396.3MB, time=60.89 memory used=3095.5MB, alloc=396.3MB, time=61.33 memory used=3208.1MB, alloc=396.3MB, time=61.68 memory used=3393.2MB, alloc=396.3MB, time=62.89 memory used=3457.3MB, alloc=396.3MB, time=63.31 memory used=3527.4MB, alloc=396.3MB, time=63.84 memory used=3624.5MB, alloc=420.3MB, time=64.25 memory used=3756.1MB, alloc=420.3MB, time=64.71 memory used=3901.7MB, alloc=420.3MB, time=66.13 memory used=4044.5MB, alloc=420.3MB, time=69.00 memory used=4191.3MB, alloc=420.3MB, time=70.30 memory used=4336.9MB, alloc=420.3MB, time=71.08 memory used=4424.4MB, alloc=420.3MB, time=71.53 memory used=4498.5MB, alloc=420.3MB, time=71.91 memory used=4565.7MB, alloc=420.3MB, time=72.17 memory used=4633.8MB, alloc=420.3MB, time=72.47 memory used=4714.8MB, alloc=420.3MB, time=72.94 memory used=4774.1MB, alloc=420.3MB, time=73.15 memory used=4834.0MB, alloc=420.3MB, time=73.33 memory used=4894.6MB, alloc=420.3MB, time=73.50 memory used=4942.4MB, alloc=420.3MB, time=73.65 memory used=5018.2MB, alloc=420.3MB, time=74.10 memory used=5076.4MB, alloc=420.3MB, time=74.29 memory used=5143.9MB, alloc=420.3MB, time=74.48 memory used=5193.3MB, alloc=420.3MB, time=74.63 memory used=5243.6MB, alloc=420.3MB, time=74.77 memory used=5301.7MB, alloc=420.3MB, time=74.92 memory used=5368.3MB, alloc=420.3MB, time=75.08 memory used=5496.8MB, alloc=420.3MB, time=75.46 memory used=5564.2MB, alloc=420.3MB, time=75.69 memory used=5633.0MB, alloc=420.3MB, time=75.93 memory used=5706.7MB, alloc=420.3MB, time=76.25 memory used=5766.1MB, alloc=420.3MB, time=76.44 memory used=5822.7MB, alloc=420.3MB, time=76.63 memory used=5886.4MB, alloc=420.3MB, time=76.81 memory used=5933.0MB, alloc=420.3MB, time=76.95 memory used=6008.3MB, alloc=420.3MB, time=77.42 memory used=6066.3MB, alloc=420.3MB, time=77.60 memory used=6130.7MB, alloc=420.3MB, time=77.80 memory used=6184.4MB, alloc=420.3MB, time=77.96 memory used=6234.1MB, alloc=420.3MB, time=78.11 memory used=6291.0MB, alloc=420.3MB, time=78.25 memory used=6356.6MB, alloc=420.3MB, time=78.40 memory used=6490.4MB, alloc=420.3MB, time=78.86 memory used=6553.6MB, alloc=420.3MB, time=79.06 memory used=6604.1MB, alloc=420.3MB, time=79.24 memory used=6666.2MB, alloc=420.3MB, time=79.44 memory used=6738.9MB, alloc=420.3MB, time=79.64 memory used=6780.4MB, alloc=420.3MB, time=79.79 memory used=6825.6MB, alloc=420.3MB, time=79.96 memory used=6875.2MB, alloc=420.3MB, time=80.11 memory used=6930.0MB, alloc=420.3MB, time=80.27 memory used=6990.9MB, alloc=420.3MB, time=80.43 memory used=7057.8MB, alloc=420.3MB, time=80.58 memory used=7170.3MB, alloc=420.3MB, time=80.95 memory used=7238.4MB, alloc=420.3MB, time=81.19 memory used=7287.6MB, alloc=420.3MB, time=81.39 memory used=7347.3MB, alloc=420.3MB, time=81.58 memory used=7420.0MB, alloc=420.3MB, time=81.79 memory used=7468.8MB, alloc=420.3MB, time=81.95 memory used=7514.0MB, alloc=420.3MB, time=82.10 memory used=7563.6MB, alloc=420.3MB, time=82.26 memory used=7618.5MB, alloc=420.3MB, time=82.41 memory used=7678.3MB, alloc=420.3MB, time=82.57 memory used=7745.6MB, alloc=420.3MB, time=82.73 memory used=7831.6MB, alloc=420.3MB, time=82.91 memory used=7924.8MB, alloc=420.3MB, time=83.66 memory used=7983.4MB, alloc=420.3MB, time=83.84 memory used=8044.1MB, alloc=420.3MB, time=84.02 memory used=8091.5MB, alloc=420.3MB, time=84.17 memory used=8146.7MB, alloc=420.3MB, time=84.32 memory used=8209.9MB, alloc=420.3MB, time=84.47 memory used=8338.1MB, alloc=420.3MB, time=84.86 memory used=8424.9MB, alloc=420.3MB, time=85.90 memory used=8479.3MB, alloc=420.3MB, time=86.11 memory used=8545.8MB, alloc=420.3MB, time=86.32 memory used=8604.2MB, alloc=444.3MB, time=86.53 memory used=8659.7MB, alloc=444.3MB, time=86.74 memory used=8721.3MB, alloc=444.3MB, time=86.95 memory used=8791.5MB, alloc=444.3MB, time=87.18 memory used=8866.3MB, alloc=444.3MB, time=87.40 memory used=8949.8MB, alloc=444.3MB, time=87.65 memory used=9037.7MB, alloc=444.3MB, time=87.90 memory used=9134.5MB, alloc=444.3MB, time=88.14 memory used=9188.5MB, alloc=444.3MB, time=88.34 memory used=9238.5MB, alloc=444.3MB, time=88.50 memory used=9289.1MB, alloc=444.3MB, time=88.66 memory used=9340.5MB, alloc=444.3MB, time=88.83 memory used=9393.3MB, alloc=444.3MB, time=88.99 memory used=9450.6MB, alloc=444.3MB, time=89.16 memory used=9509.3MB, alloc=444.3MB, time=89.33 memory used=9568.6MB, alloc=444.3MB, time=89.50 memory used=9629.2MB, alloc=444.3MB, time=89.66 memory used=9694.3MB, alloc=444.3MB, time=89.84 memory used=9760.5MB, alloc=444.3MB, time=90.01 memory used=9828.0MB, alloc=444.3MB, time=90.19 memory used=9899.7MB, alloc=444.3MB, time=90.35 memory used=9972.4MB, alloc=444.3MB, time=90.52 memory used=10050.7MB, alloc=444.3MB, time=90.70 memory used=10129.0MB, alloc=444.3MB, time=90.88 memory used=10212.6MB, alloc=444.3MB, time=91.07 memory used=10296.4MB, alloc=444.3MB, time=91.24 memory used=10383.8MB, alloc=444.3MB, time=91.43 memory used=10476.4MB, alloc=444.3MB, time=91.62 memory used=10581.6MB, alloc=444.3MB, time=91.83 memory used=10731.0MB, alloc=444.3MB, time=92.20 memory used=10860.8MB, alloc=444.3MB, time=92.46 memory used=10998.0MB, alloc=444.3MB, time=92.72 memory used=11144.3MB, alloc=444.3MB, time=92.99 memory used=11302.6MB, alloc=444.3MB, time=93.25 memory used=11524.2MB, alloc=444.3MB, time=95.51 memory used=11609.8MB, alloc=444.3MB, time=95.76 memory used=11669.5MB, alloc=444.3MB, time=95.98 memory used=11728.4MB, alloc=444.3MB, time=96.17 memory used=11795.9MB, alloc=444.3MB, time=96.38 memory used=11869.6MB, alloc=444.3MB, time=96.62 memory used=11952.6MB, alloc=444.3MB, time=96.86 memory used=12041.7MB, alloc=444.3MB, time=97.08 memory used=12113.6MB, alloc=444.3MB, time=97.27 memory used=12162.9MB, alloc=444.3MB, time=97.44 memory used=12211.1MB, alloc=444.3MB, time=97.60 memory used=12261.7MB, alloc=444.3MB, time=97.76 memory used=12313.5MB, alloc=468.3MB, time=97.93 memory used=12381.7MB, alloc=468.3MB, time=98.13 memory used=12456.3MB, alloc=468.3MB, time=98.32 memory used=12532.9MB, alloc=468.3MB, time=98.50 memory used=12611.4MB, alloc=468.3MB, time=98.69 memory used=12691.8MB, alloc=468.3MB, time=98.88 memory used=12779.2MB, alloc=468.3MB, time=99.08 memory used=12868.5MB, alloc=468.3MB, time=99.28 memory used=12959.5MB, alloc=468.3MB, time=99.48 memory used=13057.8MB, alloc=468.3MB, time=99.67 memory used=13157.8MB, alloc=468.3MB, time=99.87 memory used=13259.3MB, alloc=468.3MB, time=100.07 memory used=13368.2MB, alloc=468.3MB, time=100.27 memory used=13478.5MB, alloc=468.3MB, time=100.49 memory used=13707.5MB, alloc=468.3MB, time=100.85 memory used=13831.2MB, alloc=468.3MB, time=101.10 memory used=13964.2MB, alloc=468.3MB, time=101.36 memory used=14098.3MB, alloc=468.3MB, time=101.63 memory used=14239.2MB, alloc=468.3MB, time=101.90 memory used=14386.7MB, alloc=468.3MB, time=102.17 memory used=14540.4MB, alloc=468.3MB, time=102.44 memory used=14700.0MB, alloc=468.3MB, time=102.72 memory used=14865.0MB, alloc=468.3MB, time=102.99 memory used=15034.6MB, alloc=468.3MB, time=103.28 memory used=15208.9MB, alloc=468.3MB, time=103.56 memory used=15390.5MB, alloc=468.3MB, time=103.86 memory used=15580.8MB, alloc=468.3MB, time=104.17 memory used=15782.3MB, alloc=468.3MB, time=104.47 memory used=15991.8MB, alloc=468.3MB, time=104.77 memory used=16211.0MB, alloc=468.3MB, time=105.09 memory used=16443.6MB, alloc=468.3MB, time=105.41 memory used=16644.9MB, alloc=468.3MB, time=105.72 memory used=16822.4MB, alloc=468.3MB, time=105.99 memory used=16967.7MB, alloc=468.3MB, time=107.84 memory used=17070.7MB, alloc=468.3MB, time=108.16 memory used=17154.6MB, alloc=468.3MB, time=108.41 memory used=17229.9MB, alloc=468.3MB, time=108.67 memory used=17315.6MB, alloc=468.3MB, time=108.90 memory used=17412.4MB, alloc=468.3MB, time=109.20 memory used=17516.4MB, alloc=468.3MB, time=109.47 memory used=17631.0MB, alloc=468.3MB, time=109.72 memory used=17705.0MB, alloc=468.3MB, time=109.94 memory used=17767.1MB, alloc=468.3MB, time=110.12 memory used=17833.0MB, alloc=468.3MB, time=110.31 memory used=17900.3MB, alloc=468.3MB, time=110.50 memory used=17969.2MB, alloc=468.3MB, time=110.69 memory used=18043.4MB, alloc=468.3MB, time=110.87 memory used=18119.1MB, alloc=468.3MB, time=111.06 memory used=18201.0MB, alloc=468.3MB, time=111.25 memory used=18283.8MB, alloc=468.3MB, time=111.45 memory used=18372.6MB, alloc=468.3MB, time=111.65 memory used=18461.9MB, alloc=468.3MB, time=111.85 memory used=18557.0MB, alloc=468.3MB, time=112.06 memory used=18657.5MB, alloc=468.3MB, time=112.27 memory used=18763.2MB, alloc=468.3MB, time=112.47 memory used=18873.3MB, alloc=468.3MB, time=112.69 memory used=18987.7MB, alloc=468.3MB, time=112.90 memory used=19226.7MB, alloc=468.3MB, time=113.26 memory used=19356.6MB, alloc=468.3MB, time=113.53 memory used=19495.6MB, alloc=468.3MB, time=113.78 memory used=19644.4MB, alloc=468.3MB, time=114.06 memory used=19804.1MB, alloc=468.3MB, time=114.33 memory used=20021.3MB, alloc=468.3MB, time=116.31 memory used=20114.2MB, alloc=468.3MB, time=116.63 memory used=20212.3MB, alloc=468.3MB, time=116.92 memory used=20285.6MB, alloc=468.3MB, time=117.15 memory used=20368.9MB, alloc=468.3MB, time=117.40 memory used=20459.3MB, alloc=468.3MB, time=117.64 memory used=20560.7MB, alloc=468.3MB, time=117.88 memory used=20673.3MB, alloc=468.3MB, time=118.17 memory used=20766.1MB, alloc=468.3MB, time=118.41 memory used=20828.3MB, alloc=468.3MB, time=118.60 memory used=20893.9MB, alloc=468.3MB, time=118.78 memory used=20960.9MB, alloc=468.3MB, time=118.97 memory used=21029.4MB, alloc=468.3MB, time=119.16 memory used=21103.3MB, alloc=468.3MB, time=119.36 memory used=21178.8MB, alloc=468.3MB, time=119.55 memory used=21260.5MB, alloc=468.3MB, time=119.74 memory used=21343.1MB, alloc=468.3MB, time=119.94 memory used=21431.8MB, alloc=468.3MB, time=120.14 memory used=21521.0MB, alloc=468.3MB, time=120.34 memory used=21616.1MB, alloc=468.3MB, time=120.55 memory used=21716.7MB, alloc=468.3MB, time=120.76 memory used=21822.2MB, alloc=468.3MB, time=120.97 memory used=21928.4MB, alloc=468.3MB, time=121.18 memory used=22042.2MB, alloc=468.3MB, time=121.39 memory used=22170.5MB, alloc=468.3MB, time=121.62 memory used=22317.1MB, alloc=468.3MB, time=121.89 memory used=22447.6MB, alloc=468.3MB, time=122.14 memory used=22586.0MB, alloc=468.3MB, time=122.40 memory used=22734.1MB, alloc=468.3MB, time=122.67 memory used=22892.9MB, alloc=468.3MB, time=122.93 memory used=23092.8MB, alloc=468.3MB, time=123.76 memory used=23237.0MB, alloc=468.3MB, time=315.28 memory used=23337.6MB, alloc=492.3MB, time=496.84 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428534188 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 4 2 2 F := [-6 z + 8 y - 18 x y, 19 z + 15 y z + 6 x ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 4 G := [14 x z - 14 x y z - 19 x z , 16 z - 5 x y + 10] > Problem := [F,G]; 4 3 4 2 2 Problem := [[-6 z + 8 y - 18 x y, 19 z + 15 y z + 6 x ], 3 2 2 4 [14 x z - 14 x y z - 19 x z , 16 z - 5 x y + 10]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.8MB, alloc=32.3MB, time=0.51 memory used=47.2MB, alloc=60.3MB, time=0.82 memory used=88.5MB, alloc=60.3MB, time=1.39 memory used=129.5MB, alloc=60.3MB, time=1.94 memory used=170.3MB, alloc=60.3MB, time=2.36 memory used=195.1MB, alloc=60.3MB, time=2.49 memory used=228.8MB, alloc=60.3MB, time=2.76 memory used=271.7MB, alloc=68.3MB, time=3.22 memory used=311.1MB, alloc=92.3MB, time=3.65 memory used=376.8MB, alloc=92.3MB, time=4.52 memory used=444.8MB, alloc=92.3MB, time=5.39 memory used=510.9MB, alloc=116.3MB, time=6.14 memory used=580.3MB, alloc=372.3MB, time=7.09 memory used=674.8MB, alloc=396.3MB, time=8.19 memory used=788.5MB, alloc=396.3MB, time=9.67 memory used=901.6MB, alloc=420.3MB, time=11.06 memory used=1014.9MB, alloc=420.3MB, time=12.56 memory used=1137.9MB, alloc=420.3MB, time=13.75 memory used=1213.7MB, alloc=420.3MB, time=14.40 memory used=1311.7MB, alloc=420.3MB, time=15.29 memory used=1415.9MB, alloc=444.3MB, time=16.51 memory used=1528.7MB, alloc=444.3MB, time=17.37 memory used=1610.0MB, alloc=444.3MB, time=17.76 memory used=1696.1MB, alloc=444.3MB, time=18.61 memory used=1762.3MB, alloc=444.3MB, time=18.87 memory used=1846.2MB, alloc=444.3MB, time=19.36 memory used=1908.5MB, alloc=444.3MB, time=19.64 memory used=1977.2MB, alloc=444.3MB, time=19.90 memory used=2045.7MB, alloc=444.3MB, time=20.15 memory used=2096.9MB, alloc=444.3MB, time=20.38 memory used=2157.7MB, alloc=444.3MB, time=20.60 memory used=2247.9MB, alloc=444.3MB, time=23.22 memory used=2319.2MB, alloc=444.3MB, time=23.48 memory used=2372.8MB, alloc=444.3MB, time=23.70 memory used=2442.2MB, alloc=444.3MB, time=23.91 memory used=2522.8MB, alloc=444.3MB, time=24.27 memory used=2603.7MB, alloc=444.3MB, time=25.00 memory used=2678.2MB, alloc=444.3MB, time=25.34 memory used=2765.7MB, alloc=444.3MB, time=25.81 memory used=2826.2MB, alloc=444.3MB, time=26.08 memory used=2900.1MB, alloc=444.3MB, time=27.10 memory used=2978.8MB, alloc=444.3MB, time=27.50 memory used=3039.3MB, alloc=444.3MB, time=27.73 memory used=3127.4MB, alloc=444.3MB, time=28.23 memory used=3193.4MB, alloc=444.3MB, time=28.50 memory used=3286.8MB, alloc=444.3MB, time=29.38 memory used=3350.3MB, alloc=444.3MB, time=29.63 memory used=3427.9MB, alloc=444.3MB, time=30.00 memory used=3510.6MB, alloc=444.3MB, time=30.80 memory used=3579.3MB, alloc=444.3MB, time=31.07 memory used=3656.3MB, alloc=444.3MB, time=31.46 memory used=3735.0MB, alloc=444.3MB, time=31.86 memory used=3855.3MB, alloc=444.3MB, time=32.80 memory used=3991.1MB, alloc=444.3MB, time=34.04 memory used=4075.2MB, alloc=444.3MB, time=34.58 memory used=4162.0MB, alloc=468.3MB, time=37.53 memory used=4247.6MB, alloc=468.3MB, time=37.84 memory used=4318.2MB, alloc=468.3MB, time=38.10 memory used=4397.7MB, alloc=468.3MB, time=38.35 memory used=4583.8MB, alloc=468.3MB, time=39.56 memory used=4724.2MB, alloc=468.3MB, time=40.56 memory used=4814.2MB, alloc=468.3MB, time=41.47 memory used=4911.5MB, alloc=468.3MB, time=41.96 memory used=5008.0MB, alloc=468.3MB, time=42.72 memory used=5096.7MB, alloc=468.3MB, time=43.10 memory used=5224.5MB, alloc=468.3MB, time=44.27 memory used=5386.7MB, alloc=468.3MB, time=47.07 memory used=5460.5MB, alloc=468.3MB, time=47.36 memory used=5588.0MB, alloc=468.3MB, time=48.46 memory used=5680.3MB, alloc=468.3MB, time=49.80 memory used=5768.6MB, alloc=468.3MB, time=51.12 memory used=5847.3MB, alloc=492.3MB, time=52.29 memory used=5940.5MB, alloc=492.3MB, time=53.64 memory used=6050.3MB, alloc=492.3MB, time=55.49 memory used=6134.4MB, alloc=492.3MB, time=56.58 memory used=6197.5MB, alloc=492.3MB, time=57.58 memory used=6268.8MB, alloc=492.3MB, time=58.57 memory used=6328.3MB, alloc=492.3MB, time=59.53 memory used=6374.8MB, alloc=492.3MB, time=60.45 memory used=6424.7MB, alloc=492.3MB, time=61.34 memory used=6473.0MB, alloc=516.3MB, time=62.20 memory used=6684.7MB, alloc=540.3MB, time=65.19 memory used=6866.2MB, alloc=540.3MB, 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alloc=900.3MB, time=174.78 memory used=13424.2MB, alloc=900.3MB, time=175.46 memory used=13627.4MB, alloc=900.3MB, time=176.11 memory used=13833.6MB, alloc=900.3MB, time=176.75 memory used=14042.8MB, alloc=900.3MB, time=177.39 memory used=14254.9MB, alloc=900.3MB, time=178.06 memory used=14469.9MB, alloc=900.3MB, time=178.70 memory used=14687.9MB, alloc=900.3MB, time=179.35 memory used=14908.7MB, alloc=900.3MB, time=180.00 memory used=15132.4MB, alloc=900.3MB, time=180.66 memory used=15358.9MB, alloc=900.3MB, time=181.31 memory used=15588.3MB, alloc=900.3MB, time=181.98 memory used=15820.4MB, alloc=900.3MB, time=182.64 memory used=16055.2MB, alloc=900.3MB, time=183.29 memory used=16292.8MB, alloc=900.3MB, time=183.94 memory used=16533.1MB, alloc=900.3MB, time=184.64 memory used=16776.1MB, alloc=900.3MB, time=185.31 memory used=17021.7MB, alloc=900.3MB, time=186.00 memory used=17270.0MB, alloc=900.3MB, time=186.69 memory used=17520.8MB, alloc=900.3MB, time=187.36 memory used=17774.3MB, alloc=900.3MB, time=188.04 memory used=18030.3MB, alloc=900.3MB, time=188.70 memory used=18288.8MB, alloc=900.3MB, time=189.38 memory used=18549.9MB, alloc=924.3MB, time=190.08 memory used=18834.2MB, alloc=924.3MB, time=190.80 memory used=19145.1MB, alloc=924.3MB, time=191.55 memory used=19459.3MB, alloc=924.3MB, time=192.25 memory used=19776.7MB, alloc=924.3MB, time=192.98 memory used=20097.4MB, alloc=924.3MB, time=193.71 memory used=20421.3MB, alloc=924.3MB, time=194.44 memory used=20748.4MB, alloc=924.3MB, time=195.16 memory used=21078.5MB, alloc=924.3MB, time=195.91 memory used=21411.8MB, alloc=924.3MB, time=196.63 memory used=21748.0MB, alloc=924.3MB, time=197.37 memory used=22087.3MB, alloc=924.3MB, time=198.11 memory used=22429.5MB, alloc=924.3MB, time=198.85 memory used=22774.7MB, alloc=924.3MB, time=199.57 memory used=23122.7MB, alloc=924.3MB, time=200.31 memory used=23328.3MB, alloc=939.8MB, time=201.10 memory used=23417.7MB, alloc=939.8MB, time=201.56 memory used=23464.1MB, 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alloc=939.8MB, time=211.23 memory used=24518.7MB, alloc=939.8MB, time=211.70 memory used=24570.0MB, alloc=939.8MB, time=212.15 memory used=24621.4MB, alloc=939.8MB, time=212.61 memory used=24672.8MB, alloc=939.8MB, time=213.05 memory used=24724.3MB, alloc=939.8MB, time=213.54 memory used=24775.8MB, alloc=939.8MB, time=214.01 memory used=24827.3MB, alloc=939.8MB, time=214.48 memory used=24878.9MB, alloc=939.8MB, time=214.94 memory used=24930.6MB, alloc=939.8MB, time=215.39 memory used=24982.3MB, alloc=939.8MB, time=215.85 memory used=25034.1MB, alloc=939.8MB, time=216.31 memory used=25085.9MB, alloc=939.8MB, time=216.78 memory used=25137.8MB, alloc=939.8MB, time=217.26 memory used=25189.8MB, alloc=939.8MB, time=217.70 memory used=25241.7MB, alloc=939.8MB, time=218.15 memory used=25293.8MB, alloc=939.8MB, time=218.61 memory used=25345.9MB, alloc=939.8MB, time=219.07 memory used=25398.0MB, alloc=939.8MB, time=219.53 memory used=25450.2MB, alloc=939.8MB, time=220.01 memory used=25502.5MB, 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alloc=939.8MB, time=257.17 memory used=29897.5MB, alloc=939.8MB, time=257.63 memory used=29953.6MB, alloc=939.8MB, time=258.09 memory used=30009.8MB, alloc=939.8MB, time=258.54 memory used=30066.0MB, alloc=939.8MB, time=258.98 memory used=30122.3MB, alloc=939.8MB, time=259.45 memory used=30178.6MB, alloc=939.8MB, time=259.90 memory used=30234.9MB, alloc=939.8MB, time=260.34 memory used=30291.3MB, alloc=939.8MB, time=260.78 memory used=30347.8MB, alloc=939.8MB, time=261.24 memory used=30404.3MB, alloc=939.8MB, time=261.70 memory used=30460.8MB, alloc=939.8MB, time=262.17 memory used=30517.3MB, alloc=939.8MB, time=262.62 memory used=30574.0MB, alloc=939.8MB, time=263.07 memory used=30630.6MB, alloc=939.8MB, time=263.52 memory used=30687.3MB, alloc=939.8MB, time=263.98 memory used=30744.0MB, alloc=939.8MB, time=264.44 memory used=30800.8MB, alloc=939.8MB, time=264.90 memory used=30857.6MB, alloc=939.8MB, time=265.35 memory used=30914.4MB, alloc=939.8MB, time=265.79 memory used=30971.3MB, 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alloc=939.8MB, time=294.05 memory used=34514.2MB, alloc=939.8MB, time=294.51 memory used=34573.4MB, alloc=939.8MB, time=294.96 memory used=34632.6MB, alloc=939.8MB, time=295.43 memory used=34691.9MB, alloc=939.8MB, time=295.88 memory used=34751.2MB, alloc=939.8MB, time=296.34 memory used=34810.5MB, alloc=939.8MB, time=296.80 memory used=34869.9MB, alloc=939.8MB, time=297.25 memory used=34929.3MB, alloc=939.8MB, time=297.71 memory used=34988.7MB, alloc=939.8MB, time=298.16 memory used=35048.2MB, alloc=939.8MB, time=298.61 memory used=35107.7MB, alloc=939.8MB, time=299.06 memory used=35167.2MB, alloc=939.8MB, time=299.52 memory used=35226.8MB, alloc=939.8MB, time=299.98 memory used=35286.3MB, alloc=939.8MB, time=300.44 memory used=35346.1MB, alloc=939.8MB, time=300.92 memory used=35406.6MB, alloc=939.8MB, time=301.37 memory used=35467.0MB, alloc=939.8MB, time=301.86 memory used=35584.8MB, alloc=939.8MB, time=302.37 memory used=35645.7MB, alloc=939.8MB, time=302.85 memory used=35764.3MB, alloc=939.8MB, time=303.36 memory used=35825.8MB, alloc=939.8MB, time=303.83 memory used=35944.1MB, alloc=939.8MB, time=304.34 memory used=36005.6MB, alloc=939.8MB, time=304.82 memory used=36124.1MB, alloc=939.8MB, time=305.35 memory used=36244.3MB, alloc=939.8MB, time=305.93 memory used=36364.6MB, alloc=939.8MB, time=306.44 memory used=36485.0MB, alloc=939.8MB, time=306.99 memory used=36605.5MB, alloc=939.8MB, time=307.51 memory used=36726.2MB, alloc=939.8MB, time=308.04 memory used=36846.9MB, alloc=939.8MB, time=308.56 memory used=36967.8MB, alloc=939.8MB, time=309.08 memory used=37088.8MB, alloc=939.8MB, time=309.59 memory used=37209.9MB, alloc=939.8MB, time=310.10 memory used=37331.1MB, alloc=939.8MB, time=310.61 memory used=37452.4MB, alloc=939.8MB, time=311.14 memory used=37573.9MB, alloc=939.8MB, time=311.66 memory used=37695.4MB, alloc=939.8MB, time=312.18 memory used=37817.1MB, alloc=939.8MB, time=312.70 memory used=37938.9MB, alloc=939.8MB, time=313.22 memory used=38060.8MB, alloc=939.8MB, time=313.74 memory used=38182.8MB, alloc=939.8MB, time=314.26 memory used=38304.9MB, alloc=939.8MB, time=314.79 memory used=38427.1MB, alloc=939.8MB, time=315.31 memory used=38549.4MB, alloc=939.8MB, time=315.82 memory used=38671.8MB, alloc=939.8MB, time=316.33 memory used=38794.4MB, alloc=939.8MB, time=316.89 memory used=38917.0MB, alloc=939.8MB, time=317.42 memory used=39039.7MB, alloc=939.8MB, time=317.94 memory used=39162.6MB, alloc=939.8MB, time=318.47 memory used=39285.5MB, alloc=939.8MB, time=318.97 memory used=39408.5MB, alloc=939.8MB, time=319.48 memory used=39531.6MB, alloc=939.8MB, time=320.00 memory used=39654.9MB, alloc=939.8MB, time=320.52 memory used=39778.2MB, alloc=939.8MB, time=321.06 memory used=39901.6MB, alloc=939.8MB, time=321.58 memory used=40025.1MB, alloc=939.8MB, time=322.10 memory used=40148.7MB, alloc=939.8MB, time=322.64 memory used=40272.4MB, alloc=939.8MB, time=323.18 memory used=40396.2MB, alloc=939.8MB, time=323.69 memory used=40520.1MB, alloc=939.8MB, time=324.21 memory used=40644.1MB, alloc=939.8MB, time=324.74 memory used=40768.1MB, alloc=939.8MB, time=325.24 memory used=40892.3MB, alloc=939.8MB, time=325.76 memory used=41016.5MB, alloc=939.8MB, time=326.27 memory used=41140.8MB, alloc=939.8MB, time=326.79 memory used=41265.2MB, alloc=939.8MB, time=327.30 memory used=41389.7MB, alloc=939.8MB, time=327.82 memory used=41514.3MB, alloc=939.8MB, time=328.33 memory used=41639.0MB, alloc=939.8MB, time=328.84 memory used=41763.8MB, alloc=939.8MB, time=329.37 memory used=41888.6MB, alloc=939.8MB, time=329.90 memory used=42013.5MB, alloc=939.8MB, time=330.42 memory used=42138.5MB, alloc=939.8MB, time=330.93 memory used=42263.5MB, alloc=939.8MB, time=331.44 memory used=42388.7MB, alloc=939.8MB, time=331.96 memory used=42513.9MB, alloc=939.8MB, time=332.49 memory used=42639.2MB, alloc=939.8MB, time=333.00 memory used=42764.5MB, alloc=939.8MB, time=333.53 memory used=42890.0MB, alloc=939.8MB, time=334.05 memory used=43015.5MB, alloc=939.8MB, time=334.57 memory used=43141.1MB, alloc=939.8MB, time=335.09 memory used=43266.7MB, alloc=939.8MB, time=335.60 memory used=43392.5MB, alloc=939.8MB, time=336.11 memory used=43518.2MB, alloc=939.8MB, time=336.64 memory used=43644.1MB, alloc=939.8MB, time=337.16 memory used=43770.0MB, alloc=939.8MB, time=337.68 memory used=43896.1MB, alloc=939.8MB, time=338.20 memory used=44022.1MB, alloc=939.8MB, time=338.74 memory used=44148.3MB, alloc=939.8MB, time=339.25 memory used=44274.5MB, alloc=939.8MB, time=339.78 memory used=44400.7MB, alloc=939.8MB, time=340.30 memory used=44527.0MB, alloc=939.8MB, time=340.82 memory used=44653.4MB, alloc=939.8MB, time=341.36 memory used=44779.8MB, alloc=939.8MB, time=341.89 memory used=44906.3MB, alloc=939.8MB, time=342.46 memory used=45032.9MB, alloc=939.8MB, time=342.98 memory used=45159.5MB, alloc=939.8MB, time=343.51 memory used=45286.2MB, alloc=939.8MB, time=344.03 memory used=45412.9MB, alloc=939.8MB, time=344.55 memory used=45539.7MB, alloc=939.8MB, time=345.06 memory used=45666.5MB, alloc=939.8MB, time=345.60 memory used=45793.4MB, alloc=939.8MB, time=346.12 memory used=45920.4MB, alloc=939.8MB, time=346.65 memory used=46047.4MB, alloc=939.8MB, time=347.17 memory used=46174.4MB, alloc=939.8MB, time=347.69 memory used=46301.5MB, alloc=939.8MB, time=348.21 memory used=46428.6MB, alloc=939.8MB, time=348.73 memory used=46555.8MB, alloc=939.8MB, time=349.26 memory used=46683.1MB, alloc=939.8MB, time=349.78 memory used=46810.3MB, alloc=939.8MB, time=350.32 memory used=46937.6MB, alloc=939.8MB, time=350.84 memory used=47065.0MB, alloc=939.8MB, time=351.34 memory used=47192.4MB, alloc=939.8MB, time=351.87 memory used=47319.9MB, alloc=939.8MB, time=352.39 memory used=47447.4MB, alloc=939.8MB, time=352.92 memory used=47574.9MB, alloc=939.8MB, time=353.45 memory used=47702.5MB, alloc=939.8MB, time=353.97 memory used=47830.1MB, alloc=939.8MB, time=354.48 memory used=47957.8MB, alloc=939.8MB, time=354.98 memory used=48085.5MB, alloc=939.8MB, time=355.51 memory used=48213.2MB, alloc=939.8MB, time=356.03 memory used=48341.0MB, alloc=939.8MB, time=356.56 memory used=48468.7MB, alloc=939.8MB, time=357.08 memory used=48596.6MB, alloc=939.8MB, time=357.58 memory used=48724.4MB, alloc=939.8MB, time=358.11 memory used=48852.3MB, alloc=939.8MB, time=358.62 memory used=48980.2MB, alloc=939.8MB, time=359.14 memory used=49108.2MB, alloc=939.8MB, time=359.65 memory used=49236.1MB, alloc=939.8MB, time=360.16 memory used=49364.2MB, alloc=939.8MB, time=360.68 memory used=49492.2MB, alloc=939.8MB, time=361.19 memory used=49620.2MB, alloc=939.8MB, time=361.72 memory used=49748.3MB, alloc=939.8MB, time=362.24 memory used=49876.4MB, alloc=939.8MB, time=362.77 memory used=50004.6MB, alloc=939.8MB, time=363.28 memory used=50132.7MB, alloc=939.8MB, time=363.81 memory used=50260.9MB, alloc=939.8MB, time=364.31 memory used=50389.1MB, alloc=939.8MB, time=364.83 memory used=50517.3MB, alloc=939.8MB, time=365.34 memory used=50645.5MB, alloc=939.8MB, time=365.86 memory used=50773.8MB, alloc=939.8MB, time=366.37 memory used=50902.1MB, alloc=939.8MB, time=366.89 memory used=51030.4MB, alloc=939.8MB, time=367.39 memory used=51158.6MB, alloc=939.8MB, time=367.90 memory used=51286.9MB, alloc=939.8MB, time=368.43 memory used=51415.3MB, alloc=939.8MB, time=368.99 memory used=51543.6MB, alloc=939.8MB, time=369.51 memory used=51672.0MB, alloc=939.8MB, time=370.03 memory used=51800.3MB, alloc=939.8MB, time=370.54 memory used=51928.7MB, alloc=939.8MB, time=371.04 memory used=52057.1MB, alloc=939.8MB, time=371.55 memory used=52185.4MB, alloc=939.8MB, time=372.07 memory used=52313.8MB, alloc=939.8MB, time=372.59 memory used=52442.2MB, alloc=939.8MB, time=373.10 memory used=52570.7MB, alloc=939.8MB, time=373.62 memory used=52699.1MB, alloc=939.8MB, time=374.12 memory used=52827.5MB, alloc=939.8MB, time=374.64 memory used=52955.9MB, alloc=939.8MB, time=375.13 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428534488 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 4 3 2 F := [-9 x z - 4 y - 6 y z , -15 x + 13 x - 20 x z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 4 G := [-11 x y + 7 x z - 20 z, 15 y + 11 x z - 7 y z] > Problem := [F,G]; 2 3 2 4 3 2 Problem := [[-9 x z - 4 y - 6 y z , -15 x + 13 x - 20 x z ], 3 2 4 [-11 x y + 7 x z - 20 z, 15 y + 11 x z - 7 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.3MB, alloc=32.6MB, time=0.38 memory used=46.5MB, alloc=32.6MB, time=0.57 memory used=70.0MB, alloc=32.6MB, time=0.78 memory used=88.2MB, alloc=32.6MB, time=0.91 memory used=113.3MB, alloc=36.6MB, time=1.46 memory used=128.2MB, alloc=36.6MB, time=1.73 memory used=139.1MB, alloc=36.6MB, time=1.76 memory used=161.0MB, alloc=36.6MB, time=1.92 memory used=181.7MB, alloc=60.6MB, time=2.18 memory used=229.0MB, alloc=68.6MB, time=2.65 memory used=268.2MB, alloc=68.6MB, time=2.95 memory used=294.4MB, alloc=68.6MB, time=3.03 memory used=315.7MB, alloc=68.6MB, time=3.09 memory used=342.0MB, alloc=68.6MB, time=3.16 memory used=366.8MB, alloc=68.6MB, time=3.23 memory used=383.4MB, alloc=68.6MB, time=3.28 memory used=401.8MB, alloc=68.6MB, time=3.35 memory used=422.0MB, alloc=68.6MB, time=3.41 memory used=444.7MB, alloc=68.6MB, time=3.47 memory used=469.7MB, alloc=68.6MB, time=3.53 memory used=502.1MB, alloc=68.6MB, time=3.69 memory used=542.3MB, alloc=68.6MB, time=7.97 memory used=579.8MB, alloc=68.6MB, time=8.11 memory used=606.9MB, alloc=68.6MB, time=8.18 memory used=624.9MB, alloc=68.6MB, time=8.24 memory used=646.5MB, alloc=68.6MB, time=8.30 memory used=671.2MB, alloc=68.6MB, time=8.36 memory used=698.9MB, alloc=68.6MB, time=8.42 memory used=724.9MB, alloc=68.6MB, time=8.48 memory used=740.5MB, alloc=68.6MB, time=8.53 memory used=758.0MB, alloc=68.6MB, time=8.58 memory used=775.8MB, alloc=68.6MB, time=8.62 memory used=795.0MB, alloc=68.6MB, time=8.67 memory used=815.3MB, alloc=68.6MB, time=8.72 memory used=836.9MB, alloc=68.6MB, time=8.77 memory used=859.6MB, alloc=68.6MB, time=8.82 memory used=883.1MB, alloc=68.6MB, time=8.87 memory used=907.4MB, alloc=68.6MB, time=8.92 memory used=933.1MB, alloc=68.6MB, time=8.97 memory used=961.2MB, alloc=68.6MB, time=9.05 memory used=997.0MB, alloc=81.9MB, time=9.14 memory used=1008.2MB, alloc=83.8MB, time=9.21 memory used=1019.4MB, alloc=83.8MB, time=9.27 memory used=1031.4MB, alloc=83.8MB, time=9.32 memory used=1043.6MB, alloc=83.8MB, time=9.36 memory used=1065.8MB, alloc=83.8MB, time=9.61 memory used=1094.3MB, alloc=83.8MB, time=9.69 memory used=1114.8MB, alloc=83.8MB, time=9.75 memory used=1141.1MB, alloc=83.8MB, time=9.82 memory used=1163.3MB, alloc=83.8MB, time=9.88 memory used=1182.5MB, alloc=83.8MB, time=9.92 memory used=1209.7MB, alloc=83.8MB, time=10.04 memory used=1247.1MB, alloc=83.8MB, time=10.29 memory used=1270.3MB, alloc=83.8MB, time=10.35 memory used=1297.5MB, alloc=83.8MB, time=10.74 memory used=1336.2MB, alloc=83.8MB, time=12.90 memory used=1362.0MB, alloc=83.8MB, time=12.97 memory used=1381.8MB, alloc=83.8MB, time=13.03 memory used=1405.9MB, alloc=83.8MB, time=13.08 memory used=1434.4MB, alloc=83.8MB, time=13.14 memory used=1455.4MB, alloc=83.8MB, time=13.19 memory used=1473.1MB, alloc=83.8MB, time=13.23 memory used=1492.3MB, alloc=83.8MB, time=13.28 memory used=1512.9MB, alloc=83.8MB, time=13.32 memory used=1535.8MB, alloc=83.8MB, time=13.37 memory used=1560.9MB, alloc=83.8MB, time=13.42 memory used=1591.4MB, alloc=83.8MB, time=13.55 memory used=1618.7MB, alloc=83.8MB, time=13.66 memory used=1653.0MB, alloc=83.8MB, time=13.82 memory used=1710.4MB, alloc=83.8MB, time=14.40 memory used=1763.9MB, alloc=83.8MB, time=14.65 memory used=1812.6MB, alloc=83.8MB, time=15.20 memory used=1867.4MB, alloc=83.8MB, time=15.70 memory used=1919.0MB, alloc=83.8MB, time=15.97 memory used=1966.8MB, alloc=83.8MB, time=16.27 memory used=2016.4MB, alloc=83.8MB, time=16.62 memory used=2063.7MB, alloc=83.8MB, time=17.04 memory used=2113.6MB, alloc=83.8MB, time=17.55 memory used=2162.5MB, alloc=83.8MB, time=18.19 memory used=2211.7MB, alloc=83.8MB, time=18.91 memory used=2261.0MB, alloc=83.8MB, time=19.68 memory used=2309.7MB, alloc=83.8MB, time=20.67 memory used=2358.8MB, alloc=83.8MB, time=21.43 memory used=2410.4MB, alloc=83.8MB, time=22.18 memory used=2448.9MB, alloc=83.8MB, time=22.52 memory used=2469.8MB, alloc=83.8MB, time=22.58 memory used=2489.4MB, alloc=83.8MB, time=22.64 memory used=2513.5MB, alloc=83.8MB, time=22.70 memory used=2531.1MB, alloc=83.8MB, time=22.75 memory used=2547.7MB, alloc=83.8MB, time=22.79 memory used=2569.6MB, alloc=83.8MB, time=22.88 memory used=2622.3MB, alloc=83.8MB, time=23.34 memory used=2672.9MB, alloc=83.8MB, time=23.59 memory used=2715.8MB, alloc=83.8MB, time=23.85 memory used=2767.2MB, alloc=107.8MB, time=24.27 memory used=2855.0MB, alloc=107.8MB, time=24.75 memory used=2933.3MB, alloc=107.8MB, time=25.69 memory used=2974.1MB, alloc=107.8MB, time=26.15 memory used=3023.2MB, alloc=107.8MB, time=26.52 memory used=3095.6MB, alloc=107.8MB, time=27.13 memory used=3126.9MB, alloc=107.8MB, time=27.23 memory used=3161.6MB, alloc=107.8MB, time=27.34 memory used=3243.6MB, alloc=107.8MB, time=27.84 memory used=3325.0MB, alloc=107.8MB, time=28.34 memory used=3404.1MB, alloc=107.8MB, time=28.92 memory used=3467.7MB, alloc=107.8MB, time=29.77 memory used=3508.8MB, alloc=107.8MB, time=30.15 memory used=3573.3MB, alloc=131.8MB, time=30.83 memory used=3646.7MB, alloc=387.8MB, time=31.39 memory used=3743.6MB, alloc=411.8MB, time=32.11 memory used=3847.8MB, alloc=435.8MB, time=33.30 memory used=3956.6MB, alloc=435.8MB, time=34.06 memory used=4041.6MB, alloc=435.8MB, time=34.75 memory used=4095.8MB, alloc=435.8MB, time=34.97 memory used=4163.1MB, alloc=435.8MB, time=35.18 memory used=4206.6MB, alloc=435.8MB, time=35.37 memory used=4256.9MB, alloc=435.8MB, time=35.59 memory used=4312.2MB, alloc=435.8MB, time=35.80 memory used=4374.6MB, alloc=435.8MB, time=35.98 memory used=4446.0MB, alloc=435.8MB, time=36.20 memory used=4497.3MB, alloc=435.8MB, time=36.36 memory used=4538.6MB, alloc=435.8MB, time=36.50 memory used=4582.9MB, alloc=435.8MB, time=36.66 memory used=4631.0MB, alloc=435.8MB, time=36.82 memory used=4697.6MB, alloc=435.8MB, time=37.07 memory used=4784.7MB, alloc=435.8MB, time=52.18 memory used=4864.8MB, alloc=435.8MB, time=52.89 memory used=4915.5MB, alloc=435.8MB, time=53.09 memory used=4980.9MB, alloc=435.8MB, time=53.29 memory used=5035.2MB, alloc=435.8MB, time=53.46 memory used=5079.6MB, alloc=435.8MB, time=53.62 memory used=5130.0MB, alloc=435.8MB, time=53.78 memory used=5185.3MB, alloc=435.8MB, time=53.95 memory used=5246.5MB, alloc=435.8MB, time=54.11 memory used=5314.5MB, alloc=435.8MB, time=54.28 memory used=5534.1MB, alloc=435.8MB, time=54.76 memory used=5693.1MB, alloc=435.8MB, time=55.61 memory used=5749.2MB, alloc=435.8MB, time=55.82 memory used=5819.0MB, alloc=435.8MB, time=56.02 memory used=5862.6MB, alloc=459.8MB, time=56.22 memory used=5927.5MB, alloc=459.8MB, time=56.44 memory used=6005.3MB, alloc=459.8MB, time=56.64 memory used=6095.1MB, alloc=459.8MB, time=56.86 memory used=6164.6MB, alloc=459.8MB, time=57.05 memory used=6220.1MB, alloc=459.8MB, time=57.22 memory used=6282.0MB, alloc=459.8MB, time=57.39 memory used=6381.9MB, alloc=459.8MB, time=62.25 memory used=6456.4MB, alloc=459.8MB, time=62.49 memory used=6542.0MB, alloc=459.8MB, time=62.71 memory used=6599.9MB, alloc=459.8MB, time=62.88 memory used=6669.2MB, alloc=459.8MB, time=63.06 memory used=6751.5MB, alloc=459.8MB, time=63.24 memory used=6939.0MB, alloc=459.8MB, time=63.95 memory used=7017.2MB, alloc=459.8MB, time=64.20 memory used=7088.6MB, alloc=459.8MB, time=64.43 memory used=7153.9MB, alloc=459.8MB, time=64.65 memory used=7229.9MB, alloc=459.8MB, time=64.87 memory used=7319.0MB, alloc=459.8MB, time=65.12 memory used=7394.8MB, alloc=459.8MB, time=65.34 memory used=7447.8MB, alloc=459.8MB, time=65.51 memory used=7505.1MB, alloc=459.8MB, time=65.69 memory used=7566.8MB, alloc=459.8MB, time=65.87 memory used=7633.7MB, alloc=459.8MB, time=66.04 memory used=7707.5MB, alloc=459.8MB, time=66.23 memory used=7789.0MB, alloc=459.8MB, time=66.41 memory used=7889.1MB, alloc=459.8MB, time=66.77 memory used=7970.9MB, alloc=459.8MB, time=67.04 memory used=8035.9MB, alloc=459.8MB, time=67.27 memory used=8123.9MB, alloc=459.8MB, time=67.47 memory used=8185.1MB, alloc=459.8MB, time=67.64 memory used=8282.4MB, alloc=459.8MB, time=70.24 memory used=8360.7MB, alloc=459.8MB, time=70.46 memory used=8424.2MB, alloc=459.8MB, time=70.63 memory used=8515.7MB, alloc=459.8MB, time=70.91 memory used=8608.3MB, alloc=459.8MB, time=71.65 memory used=8695.0MB, alloc=459.8MB, time=71.90 memory used=8753.0MB, alloc=459.8MB, time=72.13 memory used=8822.0MB, alloc=459.8MB, time=72.35 memory used=8902.4MB, alloc=459.8MB, time=72.58 memory used=8996.3MB, alloc=459.8MB, time=72.81 memory used=9056.7MB, alloc=459.8MB, time=72.98 memory used=9112.7MB, alloc=459.8MB, time=73.16 memory used=9172.5MB, alloc=459.8MB, time=73.34 memory used=9236.9MB, alloc=459.8MB, time=73.53 memory used=9307.5MB, alloc=459.8MB, time=73.71 memory used=9383.0MB, alloc=459.8MB, time=73.88 memory used=9466.9MB, alloc=459.8MB, time=74.07 memory used=9564.5MB, alloc=459.8MB, time=74.78 memory used=9649.3MB, alloc=459.8MB, time=75.04 memory used=9711.4MB, alloc=459.8MB, time=75.29 memory used=9779.2MB, alloc=459.8MB, time=75.54 memory used=9859.0MB, alloc=459.8MB, time=75.77 memory used=9952.4MB, alloc=459.8MB, time=76.01 memory used=10015.6MB, alloc=459.8MB, time=76.20 memory used=10069.2MB, alloc=459.8MB, time=76.38 memory used=10127.0MB, alloc=459.8MB, time=76.56 memory used=10190.9MB, alloc=459.8MB, time=76.75 memory used=10259.1MB, alloc=459.8MB, time=76.94 memory used=10334.7MB, alloc=459.8MB, time=77.12 memory used=10416.8MB, alloc=459.8MB, time=77.32 memory used=10517.7MB, alloc=459.8MB, time=89.99 memory used=10632.0MB, alloc=459.8MB, time=98.72 memory used=10703.0MB, alloc=459.8MB, time=98.97 memory used=10791.2MB, alloc=459.8MB, time=99.19 memory used=10847.0MB, alloc=459.8MB, time=99.38 memory used=10911.0MB, alloc=459.8MB, time=99.56 memory used=10984.5MB, alloc=459.8MB, time=99.74 memory used=11068.0MB, alloc=459.8MB, time=99.92 memory used=11191.4MB, alloc=459.8MB, time=100.16 memory used=11347.4MB, alloc=459.8MB, time=100.45 memory used=11479.5MB, alloc=459.8MB, time=100.88 memory used=11557.5MB, alloc=459.8MB, time=101.12 memory used=11626.6MB, alloc=459.8MB, time=101.30 memory used=11694.2MB, alloc=459.8MB, time=101.48 memory used=11783.9MB, alloc=459.8MB, time=101.77 memory used=11860.5MB, alloc=459.8MB, time=101.96 memory used=11937.9MB, alloc=459.8MB, time=102.29 memory used=12019.5MB, alloc=459.8MB, time=102.58 memory used=12094.3MB, alloc=459.8MB, time=102.83 memory used=12175.7MB, alloc=459.8MB, time=103.11 memory used=12251.0MB, alloc=459.8MB, time=103.36 memory used=12336.7MB, alloc=459.8MB, time=103.77 memory used=12416.5MB, alloc=459.8MB, time=104.01 memory used=12482.8MB, alloc=459.8MB, time=104.19 memory used=12567.0MB, alloc=459.8MB, time=104.49 memory used=12641.6MB, alloc=459.8MB, time=104.68 memory used=12723.3MB, alloc=459.8MB, time=104.98 memory used=12797.2MB, alloc=459.8MB, time=105.18 memory used=12879.2MB, alloc=459.8MB, time=105.48 memory used=12953.5MB, alloc=459.8MB, time=105.70 memory used=13042.9MB, alloc=459.8MB, time=106.12 memory used=13113.6MB, alloc=459.8MB, time=106.31 memory used=13201.0MB, alloc=459.8MB, time=106.70 memory used=13276.5MB, alloc=459.8MB, time=106.95 memory used=13346.6MB, alloc=459.8MB, time=107.18 memory used=13435.8MB, alloc=459.8MB, time=107.41 memory used=13499.4MB, alloc=459.8MB, time=107.60 memory used=13560.3MB, alloc=459.8MB, time=107.78 memory used=13628.6MB, alloc=459.8MB, time=107.97 memory used=13708.5MB, alloc=459.8MB, time=108.16 memory used=13805.5MB, alloc=459.8MB, time=108.45 memory used=13879.1MB, alloc=459.8MB, time=108.68 memory used=13956.0MB, alloc=459.8MB, time=108.90 memory used=14043.5MB, alloc=459.8MB, time=109.97 memory used=14124.1MB, alloc=459.8MB, time=110.19 memory used=14186.0MB, alloc=459.8MB, time=110.36 memory used=14258.7MB, alloc=459.8MB, time=110.54 memory used=14362.5MB, alloc=459.8MB, time=110.83 memory used=14440.4MB, alloc=459.8MB, time=111.05 memory used=14518.3MB, alloc=459.8MB, time=111.32 memory used=14595.1MB, alloc=459.8MB, time=111.54 memory used=14688.4MB, alloc=459.8MB, time=112.98 memory used=14762.9MB, alloc=459.8MB, time=113.21 memory used=14844.1MB, alloc=459.8MB, time=113.45 memory used=14904.6MB, alloc=459.8MB, time=113.62 memory used=14977.1MB, alloc=459.8MB, time=113.80 memory used=15063.4MB, alloc=459.8MB, time=113.99 memory used=15230.1MB, alloc=459.8MB, time=114.42 memory used=15305.9MB, alloc=459.8MB, time=114.65 memory used=15384.4MB, alloc=459.8MB, time=114.92 memory used=15460.4MB, alloc=459.8MB, time=115.10 memory used=15539.2MB, alloc=459.8MB, time=115.36 memory used=15615.5MB, alloc=459.8MB, time=115.58 memory used=15714.6MB, alloc=459.8MB, time=117.11 memory used=15789.1MB, alloc=459.8MB, time=117.34 memory used=15869.9MB, alloc=459.8MB, time=117.55 memory used=15930.4MB, alloc=459.8MB, time=117.72 memory used=16002.9MB, alloc=459.8MB, time=117.91 memory used=16089.4MB, alloc=459.8MB, time=118.09 memory used=16329.8MB, alloc=459.8MB, time=119.24 memory used=16505.6MB, alloc=459.8MB, time=120.51 memory used=16682.3MB, alloc=459.8MB, time=122.46 memory used=16872.4MB, alloc=459.8MB, time=124.72 memory used=17041.3MB, alloc=459.8MB, time=125.88 memory used=17212.6MB, alloc=459.8MB, time=127.05 memory used=17386.1MB, alloc=459.8MB, time=128.75 memory used=17569.3MB, alloc=459.8MB, time=130.84 memory used=17665.0MB, alloc=459.8MB, time=131.68 memory used=17817.7MB, alloc=459.8MB, time=132.94 memory used=17979.5MB, alloc=459.8MB, time=134.04 memory used=18141.9MB, alloc=459.8MB, time=135.15 memory used=18304.7MB, alloc=459.8MB, time=136.70 memory used=18473.0MB, alloc=459.8MB, time=138.72 memory used=18608.2MB, alloc=459.8MB, time=140.13 memory used=18699.1MB, alloc=459.8MB, time=141.32 memory used=18766.6MB, alloc=459.8MB, time=141.54 memory used=18823.9MB, alloc=459.8MB, time=141.73 memory used=18908.6MB, alloc=459.8MB, time=142.40 memory used=18975.6MB, alloc=459.8MB, time=142.62 memory used=19036.6MB, alloc=459.8MB, time=142.81 memory used=19173.2MB, alloc=459.8MB, time=144.15 memory used=19322.7MB, alloc=483.8MB, time=145.12 memory used=19517.1MB, alloc=483.8MB, time=146.48 memory used=19716.7MB, alloc=483.8MB, time=148.35 memory used=19918.5MB, alloc=483.8MB, time=151.53 memory used=20079.4MB, alloc=483.8MB, time=153.17 memory used=20179.1MB, alloc=483.8MB, time=153.99 memory used=20266.0MB, alloc=483.8MB, time=154.28 memory used=20330.6MB, alloc=483.8MB, time=154.56 memory used=20399.1MB, alloc=483.8MB, time=154.80 memory used=20478.8MB, alloc=483.8MB, time=155.08 memory used=20574.2MB, alloc=483.8MB, time=155.36 memory used=20636.7MB, alloc=483.8MB, time=155.57 memory used=20694.6MB, alloc=483.8MB, time=155.77 memory used=20759.3MB, alloc=483.8MB, time=155.98 memory used=20864.0MB, alloc=483.8MB, time=157.30 memory used=20978.3MB, alloc=483.8MB, time=172.25 memory used=21052.8MB, alloc=483.8MB, time=172.55 memory used=21143.3MB, alloc=483.8MB, time=172.81 memory used=21200.8MB, alloc=483.8MB, time=173.04 memory used=21266.8MB, alloc=483.8MB, time=173.26 memory used=21342.2MB, alloc=483.8MB, time=173.47 memory used=21428.0MB, alloc=483.8MB, time=173.69 memory used=21669.7MB, alloc=483.8MB, time=174.09 memory used=21845.6MB, alloc=483.8MB, time=174.89 memory used=21929.5MB, alloc=483.8MB, time=175.19 memory used=21989.9MB, alloc=483.8MB, time=175.45 memory used=22061.1MB, alloc=483.8MB, time=175.71 memory used=22144.7MB, alloc=483.8MB, time=175.98 memory used=22235.0MB, alloc=483.8MB, time=176.24 memory used=22289.6MB, alloc=483.8MB, time=176.44 memory used=22348.8MB, alloc=483.8MB, time=176.66 memory used=22414.9MB, alloc=483.8MB, time=176.86 memory used=22525.4MB, alloc=483.8MB, time=182.11 memory used=22601.8MB, alloc=483.8MB, time=182.37 memory used=22673.9MB, alloc=483.8MB, time=182.60 memory used=22739.8MB, alloc=483.8MB, time=182.82 memory used=22819.5MB, alloc=483.8MB, time=183.05 memory used=22998.1MB, alloc=483.8MB, time=183.46 memory used=23097.6MB, alloc=483.8MB, time=184.14 memory used=23172.9MB, alloc=483.8MB, time=184.41 memory used=23260.9MB, alloc=483.8MB, time=184.71 memory used=23322.6MB, alloc=483.8MB, time=184.91 memory used=23397.8MB, alloc=483.8MB, time=185.12 memory used=23485.6MB, alloc=483.8MB, time=185.45 memory used=23561.3MB, alloc=483.8MB, time=185.69 memory used=23651.0MB, alloc=483.8MB, time=186.06 memory used=23734.8MB, alloc=483.8MB, time=186.42 memory used=23812.3MB, alloc=483.8MB, time=186.70 memory used=23895.9MB, alloc=483.8MB, time=187.05 memory used=23973.3MB, alloc=483.8MB, time=187.29 memory used=24063.2MB, alloc=483.8MB, time=187.73 memory used=24136.9MB, alloc=483.8MB, time=187.97 memory used=24225.4MB, alloc=483.8MB, time=188.33 memory used=24302.8MB, alloc=483.8MB, time=188.58 memory used=24386.5MB, alloc=483.8MB, time=188.91 memory used=24463.8MB, alloc=483.8MB, time=189.19 memory used=24548.3MB, alloc=483.8MB, time=189.53 memory used=24625.2MB, alloc=483.8MB, time=189.78 memory used=24718.5MB, alloc=483.8MB, time=190.25 memory used=24791.1MB, alloc=483.8MB, time=190.49 memory used=24890.7MB, alloc=483.8MB, time=191.02 memory used=24970.5MB, alloc=483.8MB, time=191.30 memory used=25041.0MB, alloc=483.8MB, time=191.57 memory used=25131.8MB, alloc=483.8MB, time=191.84 memory used=25199.8MB, alloc=483.8MB, time=192.06 memory used=25261.4MB, alloc=483.8MB, time=192.30 memory used=25332.9MB, alloc=483.8MB, time=192.52 memory used=25416.5MB, alloc=483.8MB, time=192.75 memory used=25518.1MB, alloc=483.8MB, time=193.08 memory used=25592.6MB, alloc=483.8MB, time=193.34 memory used=25668.3MB, alloc=483.8MB, time=193.58 memory used=25760.0MB, alloc=483.8MB, time=194.67 memory used=25842.4MB, alloc=483.8MB, time=194.92 memory used=25906.3MB, alloc=483.8MB, time=195.14 memory used=25987.5MB, alloc=483.8MB, time=195.36 memory used=26089.3MB, alloc=483.8MB, time=195.72 memory used=26166.3MB, alloc=483.8MB, time=195.96 memory used=26250.2MB, alloc=483.8MB, time=196.27 memory used=26326.8MB, alloc=483.8MB, time=196.51 memory used=26430.2MB, alloc=483.8MB, time=198.02 memory used=26512.7MB, alloc=483.8MB, time=198.31 memory used=26579.8MB, alloc=483.8MB, time=198.54 memory used=26649.8MB, alloc=483.8MB, time=198.77 memory used=26733.2MB, alloc=483.8MB, time=199.00 memory used=26905.7MB, alloc=483.8MB, time=199.41 memory used=26986.4MB, alloc=483.8MB, time=199.69 memory used=27070.4MB, alloc=483.8MB, time=200.01 memory used=27150.2MB, alloc=483.8MB, time=200.29 memory used=27231.8MB, alloc=483.8MB, time=200.58 memory used=27309.5MB, alloc=483.8MB, time=200.87 memory used=27414.7MB, alloc=483.8MB, time=202.43 memory used=27492.0MB, alloc=483.8MB, time=202.71 memory used=27571.3MB, alloc=483.8MB, time=202.95 memory used=27635.9MB, alloc=483.8MB, time=203.17 memory used=27714.1MB, alloc=483.8MB, time=203.41 memory used=27806.8MB, alloc=483.8MB, time=203.64 memory used=28077.2MB, alloc=483.8MB, time=205.21 memory used=28260.1MB, alloc=483.8MB, time=206.53 memory used=28385.9MB, alloc=483.8MB, time=207.39 memory used=28587.6MB, alloc=483.8MB, time=208.81 memory used=28684.8MB, alloc=483.8MB, time=209.66 memory used=28760.6MB, alloc=507.8MB, time=209.96 memory used=28842.7MB, alloc=507.8MB, time=210.21 memory used=29028.7MB, alloc=507.8MB, time=211.34 memory used=29204.6MB, alloc=507.8MB, time=212.60 memory used=29309.2MB, alloc=507.8MB, time=213.11 memory used=29397.5MB, alloc=507.8MB, time=213.43 memory used=29467.4MB, alloc=507.8MB, time=213.69 memory used=29549.4MB, alloc=507.8MB, time=213.97 memory used=29647.8MB, alloc=507.8MB, time=214.26 memory used=29779.7MB, alloc=507.8MB, time=218.32 memory used=29864.1MB, alloc=507.8MB, time=218.68 memory used=29947.0MB, alloc=507.8MB, time=218.99 memory used=30017.3MB, alloc=507.8MB, time=219.27 memory used=30100.7MB, alloc=507.8MB, time=219.55 memory used=30199.3MB, alloc=507.8MB, time=219.85 memory used=30399.0MB, alloc=507.8MB, time=220.30 memory used=30572.9MB, alloc=507.8MB, time=220.73 memory used=30786.2MB, alloc=507.8MB, time=221.18 memory used=30964.9MB, alloc=507.8MB, time=221.74 memory used=31054.6MB, alloc=507.8MB, time=222.04 memory used=31123.2MB, alloc=507.8MB, time=222.30 memory used=31208.5MB, alloc=507.8MB, time=222.58 memory used=31338.4MB, alloc=507.8MB, time=224.37 memory used=31444.4MB, alloc=507.8MB, time=224.85 memory used=31525.4MB, alloc=507.8MB, time=225.16 memory used=31601.7MB, alloc=507.8MB, time=225.44 memory used=31697.6MB, alloc=507.8MB, time=225.74 memory used=31898.4MB, alloc=507.8MB, time=226.17 memory used=32127.9MB, alloc=507.8MB, time=226.94 memory used=32221.0MB, alloc=507.8MB, time=227.30 memory used=32330.2MB, alloc=507.8MB, time=228.33 memory used=32435.9MB, alloc=531.8MB, time=229.20 memory used=32575.8MB, alloc=531.8MB, time=230.18 memory used=32701.4MB, alloc=531.8MB, time=231.78 memory used=32832.6MB, alloc=531.8MB, time=232.77 memory used=32914.9MB, alloc=531.8MB, time=233.68 memory used=33001.6MB, alloc=531.8MB, time=234.72 memory used=33128.2MB, alloc=531.8MB, time=235.50 memory used=33238.3MB, alloc=555.8MB, time=236.43 memory used=33346.4MB, alloc=555.8MB, time=236.86 memory used=33442.3MB, alloc=555.8MB, time=237.27 memory used=33560.8MB, alloc=555.8MB, time=237.72 memory used=33668.9MB, alloc=555.8MB, time=238.09 memory used=33747.9MB, alloc=555.8MB, time=238.42 memory used=33836.1MB, alloc=555.8MB, time=238.75 memory used=33933.9MB, alloc=555.8MB, time=239.10 memory used=34043.3MB, alloc=555.8MB, time=239.45 memory used=34171.0MB, alloc=555.8MB, time=239.80 memory used=34329.0MB, alloc=555.8MB, time=240.46 memory used=34435.0MB, alloc=555.8MB, time=240.86 memory used=34531.5MB, alloc=555.8MB, time=241.20 memory used=34662.3MB, alloc=555.8MB, time=244.50 memory used=34768.8MB, alloc=555.8MB, time=244.87 memory used=34865.6MB, alloc=555.8MB, time=245.24 memory used=35042.8MB, alloc=555.8MB, time=245.76 memory used=35167.3MB, alloc=555.8MB, time=246.79 memory used=35275.4MB, alloc=555.8MB, time=247.26 memory used=35371.0MB, alloc=555.8MB, time=247.68 memory used=35489.2MB, alloc=555.8MB, time=248.12 memory used=35597.4MB, alloc=555.8MB, time=248.52 memory used=35676.1MB, alloc=555.8MB, time=248.86 memory used=35761.9MB, alloc=555.8MB, time=249.22 memory used=35859.5MB, alloc=555.8MB, time=249.58 memory used=35969.2MB, alloc=555.8MB, time=249.94 memory used=36095.2MB, alloc=555.8MB, time=250.29 memory used=36262.8MB, alloc=555.8MB, time=251.31 memory used=36361.4MB, alloc=555.8MB, time=251.73 memory used=36462.8MB, alloc=555.8MB, time=252.18 memory used=36590.4MB, alloc=555.8MB, time=252.63 memory used=36680.9MB, alloc=555.8MB, time=253.07 memory used=36762.1MB, alloc=555.8MB, time=253.42 memory used=36852.9MB, alloc=555.8MB, time=253.76 memory used=36952.9MB, alloc=555.8MB, time=254.11 memory used=37067.3MB, alloc=555.8MB, time=254.48 memory used=37244.7MB, alloc=555.8MB, time=267.79 memory used=37408.3MB, alloc=555.8MB, time=281.07 memory used=37506.3MB, alloc=555.8MB, time=281.46 memory used=37615.4MB, alloc=555.8MB, time=281.83 memory used=37699.0MB, alloc=555.8MB, time=282.18 memory used=37794.4MB, alloc=555.8MB, time=282.53 memory used=37904.0MB, alloc=555.8MB, time=282.89 memory used=38029.5MB, alloc=555.8MB, time=283.27 memory used=38241.1MB, alloc=555.8MB, time=283.75 memory used=38401.0MB, alloc=555.8MB, time=284.18 memory used=38589.0MB, alloc=555.8MB, time=284.62 memory used=38813.3MB, alloc=555.8MB, time=285.26 memory used=38923.8MB, alloc=555.8MB, time=285.69 memory used=39039.8MB, alloc=555.8MB, time=286.17 memory used=39158.8MB, alloc=555.8MB, time=286.65 memory used=39288.3MB, alloc=555.8MB, time=287.26 memory used=39403.4MB, alloc=555.8MB, time=287.71 memory used=39517.0MB, alloc=555.8MB, time=288.19 memory used=39635.8MB, alloc=555.8MB, time=288.63 memory used=39756.4MB, alloc=555.8MB, time=289.16 memory used=39876.9MB, alloc=555.8MB, time=289.73 memory used=39992.1MB, alloc=555.8MB, time=290.12 memory used=40081.0MB, alloc=555.8MB, time=290.47 memory used=40200.2MB, alloc=555.8MB, time=290.90 memory used=40321.3MB, alloc=555.8MB, time=291.95 memory used=40425.2MB, alloc=555.8MB, time=292.35 memory used=40538.8MB, alloc=555.8MB, time=292.83 memory used=40654.9MB, alloc=555.8MB, time=293.26 memory used=40786.6MB, alloc=555.8MB, time=294.62 memory used=40886.4MB, alloc=555.8MB, time=294.98 memory used=41019.0MB, alloc=555.8MB, time=295.44 memory used=41138.1MB, alloc=555.8MB, time=295.93 memory used=41251.0MB, alloc=555.8MB, time=296.37 memory used=41389.1MB, alloc=555.8MB, time=297.76 memory used=41492.7MB, alloc=555.8MB, time=298.14 memory used=41597.6MB, alloc=555.8MB, time=298.49 memory used=41737.8MB, alloc=555.8MB, time=299.49 memory used=41818.5MB, alloc=555.8MB, time=300.39 memory used=41931.2MB, alloc=555.8MB, time=301.30 memory used=42014.3MB, alloc=555.8MB, time=302.03 memory used=42130.5MB, alloc=555.8MB, time=302.84 memory used=42287.0MB, alloc=555.8MB, time=303.96 memory used=42409.2MB, alloc=555.8MB, time=304.76 memory used=42541.5MB, alloc=555.8MB, time=305.62 memory used=42636.3MB, alloc=555.8MB, time=306.52 memory used=42711.7MB, alloc=555.8MB, time=307.38 memory used=42749.2MB, alloc=555.8MB, time=307.98 memory used=42801.9MB, alloc=555.8MB, time=308.78 memory used=42990.6MB, alloc=579.8MB, time=311.33 memory used=43121.8MB, alloc=603.8MB, time=312.17 memory used=43229.4MB, alloc=603.8MB, time=312.71 memory used=43404.4MB, alloc=603.8MB, time=316.17 memory used=43526.0MB, alloc=627.8MB, time=316.78 memory used=43648.0MB, alloc=627.8MB, time=317.28 memory used=43850.5MB, alloc=627.8MB, time=318.89 memory used=43979.6MB, alloc=627.8MB, time=319.40 memory used=44184.7MB, alloc=627.8MB, time=320.79 memory used=44336.7MB, alloc=627.8MB, time=322.21 memory used=44618.4MB, alloc=627.8MB, time=324.50 memory used=44940.0MB, alloc=627.8MB, time=326.81 memory used=45166.6MB, alloc=651.8MB, time=330.46 memory used=45325.5MB, alloc=651.8MB, time=333.38 memory used=45558.2MB, alloc=651.8MB, time=335.45 memory used=45791.8MB, alloc=651.8MB, time=337.13 memory used=45917.0MB, alloc=651.8MB, time=337.80 memory used=46049.1MB, alloc=651.8MB, time=338.39 memory used=46208.6MB, alloc=651.8MB, time=339.41 memory used=46346.5MB, alloc=651.8MB, time=340.07 memory used=46491.4MB, alloc=675.8MB, time=346.72 memory used=46683.3MB, alloc=675.8MB, time=351.63 memory used=46822.7MB, alloc=675.8MB, time=352.23 memory used=47046.4MB, alloc=675.8MB, time=353.97 memory used=47316.5MB, alloc=675.8MB, time=357.99 memory used=47634.2MB, alloc=675.8MB, time=360.82 memory used=47845.1MB, alloc=675.8MB, time=362.36 memory used=48020.3MB, alloc=675.8MB, time=363.23 memory used=48169.4MB, alloc=675.8MB, time=363.96 memory used=48357.3MB, alloc=675.8MB, time=367.17 memory used=48585.7MB, alloc=675.8MB, time=368.91 memory used=48759.1MB, alloc=699.8MB, time=371.06 memory used=48933.4MB, alloc=699.8MB, time=373.31 memory used=49219.7MB, alloc=699.8MB, time=375.10 memory used=49380.8MB, alloc=699.8MB, time=375.94 memory used=49554.9MB, alloc=699.8MB, time=376.97 memory used=49704.7MB, alloc=699.8MB, time=377.77 memory used=49978.3MB, alloc=699.8MB, time=378.65 memory used=50141.2MB, alloc=699.8MB, time=379.55 memory used=50453.8MB, alloc=699.8MB, time=380.48 memory used=50664.5MB, alloc=699.8MB, time=381.86 memory used=50867.4MB, alloc=699.8MB, time=382.66 memory used=51034.6MB, alloc=699.8MB, time=383.58 memory used=51347.7MB, alloc=699.8MB, time=384.48 memory used=51512.3MB, alloc=699.8MB, time=385.42 memory used=51821.2MB, alloc=699.8MB, time=386.32 memory used=52003.2MB, alloc=699.8MB, time=387.26 memory used=52272.9MB, alloc=699.8MB, time=388.12 memory used=52537.7MB, alloc=699.8MB, time=389.55 memory used=52831.1MB, alloc=699.8MB, time=390.85 memory used=52980.7MB, alloc=699.8MB, time=391.61 memory used=53254.3MB, alloc=699.8MB, time=392.48 memory used=53417.4MB, alloc=699.8MB, time=393.35 memory used=53730.6MB, alloc=699.8MB, time=394.27 memory used=54019.4MB, alloc=699.8MB, time=398.42 memory used=54193.1MB, alloc=699.8MB, time=399.17 memory used=54340.6MB, alloc=699.8MB, time=399.91 memory used=54511.2MB, alloc=699.8MB, time=400.72 memory used=54723.9MB, alloc=699.8MB, time=401.57 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428534788 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 3 3 F := [-14 x z + 15 x y z + 4 y z, -3 y z - 4 x y z - 11 y ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 3 2 2 G := [8 x - 18 x y z - 20 y , 18 y - 9 z + 13 z] > Problem := [F,G]; 3 2 3 3 3 Problem := [[-14 x z + 15 x y z + 4 y z, -3 y z - 4 x y z - 11 y ], 4 2 3 2 2 [8 x - 18 x y z - 20 y , 18 y - 9 z + 13 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.1MB, alloc=32.3MB, time=0.18 memory used=25.1MB, alloc=32.3MB, time=0.48 memory used=47.7MB, alloc=32.3MB, time=0.71 memory used=71.7MB, alloc=36.3MB, time=0.89 memory used=92.9MB, alloc=60.3MB, time=1.16 memory used=139.3MB, alloc=60.3MB, time=1.44 memory used=185.2MB, alloc=68.3MB, time=1.95 memory used=231.0MB, alloc=68.3MB, time=2.57 memory used=252.1MB, alloc=68.3MB, time=2.65 memory used=270.7MB, alloc=68.3MB, time=2.72 memory used=292.6MB, alloc=68.3MB, time=2.79 memory used=318.2MB, alloc=68.3MB, time=2.86 memory used=339.6MB, alloc=68.3MB, time=2.92 memory used=354.8MB, alloc=68.3MB, time=2.98 memory used=372.1MB, alloc=68.3MB, time=3.04 memory used=391.4MB, alloc=68.3MB, time=3.09 memory used=414.0MB, alloc=68.3MB, time=3.20 memory used=440.4MB, alloc=68.3MB, time=3.54 memory used=459.1MB, alloc=68.3MB, time=3.60 memory used=480.9MB, alloc=68.3MB, time=3.67 memory used=506.5MB, alloc=68.3MB, time=3.75 memory used=529.8MB, alloc=68.3MB, time=3.82 memory used=545.2MB, alloc=68.3MB, time=3.88 memory used=562.6MB, alloc=68.3MB, time=3.93 memory used=581.9MB, alloc=68.3MB, time=4.00 memory used=603.7MB, alloc=68.3MB, time=4.05 memory used=631.7MB, alloc=68.3MB, time=4.26 memory used=659.8MB, alloc=68.3MB, time=4.35 memory used=680.9MB, alloc=68.3MB, time=4.41 memory used=704.9MB, alloc=68.3MB, time=4.69 memory used=732.5MB, alloc=83.8MB, time=12.98 memory used=757.5MB, alloc=83.8MB, time=27.17 memory used=776.5MB, alloc=83.8MB, time=27.24 memory used=786.8MB, alloc=83.8MB, time=32.45 memory used=807.2MB, alloc=83.8MB, time=32.98 memory used=813.7MB, alloc=83.8MB, time=34.42 memory used=824.0MB, alloc=83.8MB, time=35.11 memory used=826.5MB, alloc=339.8MB, time=35.14 memory used=1072.1MB, alloc=339.8MB, time=38.07 memory used=1162.2MB, alloc=339.8MB, time=39.52 memory used=1180.6MB, alloc=339.8MB, time=39.60 memory used=1202.3MB, alloc=339.8MB, time=39.67 memory used=1228.0MB, alloc=339.8MB, time=39.73 memory used=1252.0MB, alloc=339.8MB, time=39.81 memory used=1267.4MB, alloc=339.8MB, time=39.86 memory used=1284.8MB, alloc=339.8MB, time=39.92 memory used=1304.2MB, alloc=339.8MB, time=39.97 memory used=1326.2MB, alloc=339.8MB, time=40.04 memory used=1352.8MB, alloc=339.8MB, time=40.24 memory used=1373.3MB, alloc=339.8MB, time=40.30 memory used=1400.1MB, alloc=339.8MB, time=40.65 memory used=1417.9MB, alloc=339.8MB, time=40.72 memory used=1438.3MB, alloc=339.8MB, time=40.78 memory used=1462.7MB, alloc=339.8MB, time=40.85 memory used=1488.1MB, alloc=339.8MB, time=40.92 memory used=1503.1MB, alloc=339.8MB, time=40.98 memory used=1519.6MB, alloc=339.8MB, time=41.04 memory used=1537.9MB, alloc=339.8MB, time=41.10 memory used=1558.4MB, alloc=339.8MB, time=41.16 memory used=1584.7MB, alloc=339.8MB, time=41.38 memory used=1606.3MB, alloc=339.8MB, time=41.45 memory used=1645.6MB, alloc=339.8MB, time=44.54 memory used=1923.2MB, alloc=339.8MB, time=74.67 memory used=2080.0MB, alloc=339.8MB, time=75.99 memory used=2099.5MB, alloc=339.8MB, time=76.06 memory used=2136.1MB, alloc=339.8MB, time=76.20 memory used=2160.4MB, alloc=339.8MB, time=76.27 memory used=2181.6MB, alloc=339.8MB, time=76.33 memory used=2215.8MB, alloc=339.8MB, time=76.42 memory used=2241.0MB, alloc=339.8MB, time=76.49 memory used=2262.5MB, alloc=339.8MB, time=76.54 memory used=2286.3MB, alloc=339.8MB, time=76.70 memory used=2326.3MB, alloc=339.8MB, time=76.77 memory used=2368.7MB, alloc=339.8MB, time=76.84 memory used=2533.7MB, alloc=339.8MB, time=77.10 memory used=2579.2MB, alloc=339.8MB, time=77.18 memory used=2617.9MB, alloc=339.8MB, time=77.25 memory used=2659.2MB, alloc=339.8MB, time=77.32 memory used=2861.6MB, alloc=339.8MB, time=77.85 memory used=2970.4MB, alloc=339.8MB, time=78.00 memory used=3034.0MB, alloc=339.8MB, time=78.10 memory used=3100.1MB, alloc=339.8MB, time=78.20 memory used=3168.8MB, alloc=339.8MB, time=78.30 memory used=3375.7MB, alloc=339.8MB, time=78.53 memory used=3592.2MB, alloc=339.8MB, time=78.76 memory used=3819.5MB, alloc=339.8MB, time=78.98 memory used=4035.8MB, alloc=339.8MB, time=79.93 memory used=4078.0MB, alloc=339.8MB, time=80.33 memory used=4114.6MB, alloc=363.8MB, time=84.69 memory used=4150.7MB, alloc=387.8MB, time=98.77 memory used=4205.9MB, alloc=387.8MB, time=122.41 memory used=4264.9MB, alloc=387.8MB, time=123.25 memory used=4316.4MB, alloc=387.8MB, time=123.39 memory used=4379.6MB, alloc=387.8MB, time=123.52 memory used=4419.0MB, alloc=387.8MB, time=123.61 memory used=4464.7MB, alloc=387.8MB, time=123.70 memory used=4548.7MB, alloc=387.8MB, time=124.59 memory used=4645.1MB, alloc=387.8MB, time=125.32 memory used=4721.7MB, alloc=387.8MB, time=126.23 memory used=4788.6MB, alloc=387.8MB, time=127.16 memory used=4842.6MB, alloc=387.8MB, time=127.37 memory used=4890.9MB, alloc=387.8MB, time=127.52 memory used=4926.1MB, alloc=387.8MB, time=127.65 memory used=4984.3MB, alloc=387.8MB, time=127.91 memory used=5028.2MB, alloc=387.8MB, time=128.05 memory used=5072.8MB, alloc=387.8MB, time=128.21 memory used=5111.7MB, alloc=387.8MB, time=128.35 memory used=5198.4MB, alloc=387.8MB, time=134.11 memory used=5300.4MB, alloc=387.8MB, time=134.56 memory used=5343.3MB, alloc=387.8MB, time=134.70 memory used=5386.5MB, alloc=387.8MB, time=134.84 memory used=5428.8MB, alloc=387.8MB, time=134.96 memory used=5464.4MB, alloc=387.8MB, time=135.05 memory used=5522.8MB, alloc=387.8MB, time=135.30 memory used=5568.2MB, alloc=387.8MB, time=135.44 memory used=5607.7MB, alloc=387.8MB, time=135.56 memory used=5649.0MB, alloc=387.8MB, time=135.69 memory used=5706.5MB, alloc=387.8MB, time=135.94 memory used=5755.4MB, alloc=387.8MB, time=136.07 memory used=5790.8MB, alloc=387.8MB, time=136.18 memory used=5855.5MB, alloc=387.8MB, time=141.12 memory used=5961.1MB, alloc=387.8MB, time=142.34 memory used=6022.1MB, alloc=387.8MB, time=142.55 memory used=6060.5MB, alloc=387.8MB, time=142.67 memory used=6109.0MB, alloc=387.8MB, time=142.80 memory used=6142.2MB, alloc=387.8MB, time=142.90 memory used=6193.8MB, alloc=387.8MB, time=143.12 memory used=6273.6MB, alloc=387.8MB, time=143.67 memory used=6359.2MB, alloc=387.8MB, time=144.26 memory used=6423.2MB, alloc=387.8MB, time=144.61 memory used=6479.0MB, alloc=387.8MB, time=145.15 memory used=6546.6MB, alloc=387.8MB, time=145.92 memory used=6634.9MB, alloc=411.8MB, time=149.22 memory used=6691.3MB, alloc=411.8MB, time=149.82 memory used=6743.0MB, alloc=411.8MB, time=149.97 memory used=6801.4MB, alloc=411.8MB, time=150.11 memory used=6875.4MB, alloc=411.8MB, time=153.34 memory used=6957.6MB, alloc=411.8MB, time=153.61 memory used=7006.8MB, alloc=411.8MB, time=153.76 memory used=7066.0MB, alloc=411.8MB, time=153.90 memory used=7170.2MB, alloc=411.8MB, time=154.54 memory used=7292.8MB, alloc=411.8MB, time=155.31 memory used=7407.8MB, alloc=411.8MB, time=156.05 memory used=7523.1MB, alloc=435.8MB, time=157.21 memory used=7657.2MB, alloc=435.8MB, time=158.57 memory used=7744.4MB, alloc=459.8MB, time=159.19 memory used=7818.4MB, alloc=459.8MB, time=159.46 memory used=7888.5MB, alloc=459.8MB, time=159.70 memory used=7951.7MB, alloc=459.8MB, time=159.91 memory used=8027.0MB, alloc=459.8MB, time=160.16 memory used=8116.5MB, alloc=459.8MB, time=160.38 memory used=8172.8MB, alloc=459.8MB, time=160.56 memory used=8246.0MB, alloc=459.8MB, time=161.01 memory used=8326.3MB, alloc=459.8MB, time=161.29 memory used=8406.0MB, alloc=459.8MB, time=161.55 memory used=8465.8MB, alloc=459.8MB, time=161.78 memory used=8536.1MB, alloc=459.8MB, time=162.03 memory used=8620.8MB, alloc=459.8MB, time=162.25 memory used=8691.4MB, alloc=459.8MB, time=162.45 memory used=8748.1MB, alloc=459.8MB, time=162.63 memory used=8855.6MB, alloc=459.8MB, time=185.72 memory used=9020.9MB, alloc=459.8MB, time=187.06 memory used=9142.8MB, alloc=459.8MB, time=187.57 memory used=9208.7MB, alloc=459.8MB, time=187.81 memory used=9295.4MB, alloc=459.8MB, time=188.03 memory used=9349.9MB, alloc=459.8MB, time=188.22 memory used=9411.2MB, alloc=459.8MB, time=188.40 memory used=9481.5MB, alloc=459.8MB, time=188.60 memory used=9562.6MB, alloc=459.8MB, time=188.80 memory used=9717.8MB, alloc=459.8MB, time=189.23 memory used=9807.9MB, alloc=459.8MB, time=189.81 memory used=9925.0MB, alloc=459.8MB, time=191.14 memory used=9995.5MB, alloc=459.8MB, time=191.36 memory used=10061.2MB, alloc=459.8MB, time=191.55 memory used=10128.9MB, alloc=459.8MB, time=191.75 memory used=10256.3MB, alloc=459.8MB, time=193.09 memory used=10328.5MB, alloc=459.8MB, time=193.31 memory used=10392.5MB, alloc=459.8MB, time=193.50 memory used=10504.5MB, alloc=459.8MB, time=193.98 memory used=10689.9MB, alloc=459.8MB, time=196.69 memory used=10866.1MB, alloc=459.8MB, time=197.67 memory used=11037.0MB, alloc=459.8MB, time=199.03 memory used=11139.7MB, alloc=459.8MB, time=199.73 memory used=11276.7MB, alloc=459.8MB, time=201.02 memory used=11384.3MB, alloc=459.8MB, time=201.87 memory used=11442.6MB, alloc=459.8MB, time=202.08 memory used=11547.5MB, alloc=459.8MB, time=202.68 memory used=11608.5MB, alloc=459.8MB, time=202.91 memory used=11765.9MB, alloc=483.8MB, time=204.28 memory used=11892.7MB, alloc=483.8MB, time=205.01 memory used=12020.7MB, alloc=483.8MB, time=210.75 memory used=12183.4MB, alloc=483.8MB, time=211.57 memory used=12262.7MB, alloc=483.8MB, time=211.86 memory used=12330.7MB, alloc=483.8MB, time=212.09 memory used=12405.0MB, alloc=483.8MB, time=212.33 memory used=12515.8MB, alloc=483.8MB, time=213.10 memory used=12589.9MB, alloc=483.8MB, time=213.36 memory used=12704.8MB, alloc=483.8MB, time=214.16 memory used=12865.9MB, alloc=483.8MB, time=215.33 memory used=13001.9MB, alloc=483.8MB, time=222.91 memory used=13109.9MB, alloc=507.8MB, time=223.66 memory used=13225.2MB, alloc=507.8MB, time=224.27 memory used=13318.1MB, alloc=507.8MB, time=224.60 memory used=13398.4MB, alloc=507.8MB, time=224.90 memory used=13474.9MB, alloc=507.8MB, time=225.17 memory used=13561.2MB, alloc=507.8MB, time=225.44 memory used=13659.4MB, alloc=507.8MB, time=225.72 memory used=13771.7MB, alloc=507.8MB, time=226.02 memory used=13944.1MB, alloc=507.8MB, time=226.42 memory used=14096.1MB, alloc=507.8MB, time=226.81 memory used=14263.4MB, alloc=507.8MB, time=227.21 memory used=14450.6MB, alloc=507.8MB, time=227.60 memory used=14657.2MB, alloc=507.8MB, time=228.04 memory used=14882.3MB, alloc=507.8MB, time=228.48 memory used=15122.5MB, alloc=507.8MB, time=228.94 memory used=15299.1MB, alloc=507.8MB, time=229.33 memory used=15490.9MB, alloc=507.8MB, time=229.75 memory used=15694.6MB, alloc=507.8MB, time=230.16 memory used=15915.6MB, alloc=507.8MB, time=230.58 memory used=16158.7MB, alloc=507.8MB, time=231.00 memory used=16505.7MB, alloc=507.8MB, time=233.20 memory used=16697.0MB, alloc=507.8MB, time=234.77 memory used=16851.1MB, alloc=507.8MB, time=236.04 memory used=16991.0MB, alloc=507.8MB, time=236.66 memory used=17123.4MB, alloc=507.8MB, time=237.17 memory used=17258.6MB, alloc=507.8MB, time=237.68 memory used=17405.5MB, alloc=507.8MB, time=238.18 memory used=17547.7MB, alloc=507.8MB, time=238.67 memory used=17727.2MB, alloc=507.8MB, time=239.19 memory used=17913.6MB, alloc=507.8MB, time=239.75 memory used=18148.8MB, alloc=507.8MB, time=240.38 memory used=18368.1MB, alloc=507.8MB, time=240.96 memory used=18593.6MB, alloc=507.8MB, time=241.57 memory used=18871.4MB, alloc=507.8MB, time=242.25 memory used=19167.0MB, alloc=507.8MB, time=242.96 memory used=19441.1MB, alloc=507.8MB, time=243.65 memory used=19731.5MB, alloc=507.8MB, time=244.34 memory used=20036.0MB, alloc=507.8MB, time=245.07 memory used=20352.9MB, alloc=507.8MB, time=245.82 memory used=20701.0MB, alloc=507.8MB, time=246.62 memory used=21065.8MB, alloc=507.8MB, time=247.49 memory used=21471.6MB, alloc=507.8MB, time=248.45 memory used=21952.5MB, alloc=507.8MB, time=249.57 memory used=22370.9MB, alloc=507.8MB, time=250.54 memory used=22763.5MB, alloc=507.8MB, time=251.48 memory used=23146.0MB, alloc=507.8MB, time=252.40 memory used=23504.9MB, alloc=507.8MB, time=253.30 memory used=23801.2MB, alloc=507.8MB, time=254.11 memory used=24152.5MB, alloc=507.8MB, time=254.95 memory used=24500.8MB, alloc=507.8MB, time=255.80 memory used=24802.0MB, alloc=507.8MB, time=256.66 memory used=25153.8MB, alloc=507.8MB, time=257.56 memory used=25463.3MB, alloc=507.8MB, time=258.43 memory used=25817.3MB, alloc=507.8MB, time=259.29 memory used=26134.0MB, alloc=507.8MB, time=260.21 memory used=26492.1MB, alloc=507.8MB, time=261.13 memory used=26815.4MB, alloc=507.8MB, time=262.11 memory used=27176.5MB, alloc=507.8MB, time=263.00 memory used=27506.9MB, alloc=507.8MB, time=263.95 memory used=27869.7MB, alloc=507.8MB, time=264.84 memory used=28207.8MB, alloc=507.8MB, time=265.77 memory used=28571.3MB, alloc=507.8MB, time=266.66 memory used=28914.9MB, alloc=507.8MB, time=267.63 memory used=29282.7MB, alloc=507.8MB, time=268.54 memory used=29629.6MB, alloc=507.8MB, time=269.54 memory used=29981.4MB, alloc=507.8MB, time=270.51 memory used=30352.3MB, alloc=507.8MB, time=271.45 memory used=30710.7MB, alloc=507.8MB, time=272.46 memory used=31081.8MB, alloc=507.8MB, time=273.37 memory used=31443.6MB, alloc=507.8MB, time=274.37 memory used=31805.8MB, alloc=507.8MB, time=275.38 memory used=32184.0MB, alloc=507.8MB, time=276.35 memory used=32555.2MB, alloc=507.8MB, time=277.41 memory used=32930.3MB, alloc=507.8MB, time=278.38 memory used=33305.1MB, alloc=507.8MB, time=279.40 memory used=33682.8MB, alloc=507.8MB, time=280.47 memory used=34063.6MB, alloc=507.8MB, time=281.36 memory used=34445.6MB, alloc=507.8MB, time=282.47 memory used=34829.0MB, alloc=507.8MB, time=283.54 memory used=35203.6MB, alloc=507.8MB, time=284.49 memory used=35545.4MB, alloc=507.8MB, time=285.47 memory used=35881.8MB, alloc=507.8MB, time=286.49 memory used=36247.5MB, alloc=507.8MB, time=287.40 memory used=36580.7MB, alloc=507.8MB, time=288.44 memory used=36915.0MB, alloc=507.8MB, time=289.48 memory used=37249.1MB, alloc=507.8MB, time=290.46 memory used=37606.5MB, alloc=507.8MB, time=291.38 memory used=37944.3MB, alloc=507.8MB, time=292.41 memory used=38283.2MB, alloc=507.8MB, time=293.41 memory used=38636.4MB, alloc=507.8MB, time=294.30 memory used=38979.4MB, alloc=507.8MB, time=295.33 memory used=39323.4MB, alloc=507.8MB, time=296.37 memory used=39665.5MB, alloc=507.8MB, time=297.38 memory used=40023.7MB, alloc=507.8MB, time=298.30 memory used=40369.9MB, alloc=507.8MB, time=299.36 memory used=40720.6MB, alloc=507.8MB, time=300.50 memory used=41067.5MB, alloc=507.8MB, time=301.56 memory used=41428.6MB, alloc=507.8MB, time=302.50 memory used=41781.6MB, alloc=507.8MB, time=303.57 memory used=42138.7MB, alloc=507.8MB, time=304.66 memory used=42491.0MB, alloc=507.8MB, time=305.67 memory used=42785.3MB, alloc=531.8MB, time=307.36 memory used=42961.7MB, alloc=531.8MB, time=307.97 memory used=43210.4MB, alloc=531.8MB, time=308.61 memory used=43642.8MB, alloc=531.8MB, time=309.55 memory used=44041.1MB, alloc=531.8MB, time=310.44 memory used=44435.7MB, alloc=531.8MB, time=311.26 memory used=44815.1MB, alloc=531.8MB, time=312.08 memory used=45190.7MB, alloc=531.8MB, time=312.91 memory used=45561.7MB, alloc=531.8MB, time=313.73 memory used=45920.8MB, alloc=531.8MB, time=314.55 memory used=46284.5MB, alloc=531.8MB, time=315.38 memory used=46648.1MB, alloc=531.8MB, time=316.26 memory used=47008.3MB, alloc=531.8MB, time=317.15 memory used=47374.7MB, alloc=531.8MB, time=317.99 memory used=47741.9MB, alloc=531.8MB, time=318.91 memory used=48110.9MB, alloc=531.8MB, time=319.88 memory used=48485.5MB, alloc=531.8MB, time=320.89 memory used=48861.3MB, alloc=531.8MB, time=321.88 memory used=49236.1MB, alloc=531.8MB, time=322.85 memory used=49609.9MB, alloc=531.8MB, time=323.78 memory used=49995.7MB, alloc=531.8MB, time=324.80 memory used=50385.9MB, alloc=531.8MB, time=326.02 memory used=50758.4MB, alloc=531.8MB, time=326.96 memory used=51148.7MB, alloc=531.8MB, time=328.05 memory used=51516.8MB, alloc=531.8MB, time=329.06 memory used=51885.7MB, alloc=531.8MB, time=330.05 memory used=52236.0MB, alloc=531.8MB, time=331.11 memory used=52588.8MB, alloc=531.8MB, time=332.12 memory used=52936.4MB, alloc=531.8MB, time=333.17 memory used=53282.1MB, alloc=531.8MB, time=334.23 memory used=53626.4MB, alloc=531.8MB, time=335.07 memory used=53962.1MB, alloc=531.8MB, time=336.19 memory used=54310.7MB, alloc=531.8MB, time=337.01 memory used=54644.2MB, alloc=531.8MB, time=338.07 memory used=54979.9MB, alloc=531.8MB, time=339.20 memory used=55324.0MB, alloc=531.8MB, time=340.15 memory used=55660.8MB, alloc=531.8MB, time=341.29 memory used=56153.0MB, alloc=531.8MB, time=343.42 memory used=56423.5MB, alloc=531.8MB, time=344.89 memory used=56625.8MB, alloc=531.8MB, time=345.91 memory used=56833.5MB, alloc=531.8MB, time=346.53 memory used=57144.4MB, alloc=531.8MB, time=347.27 memory used=57559.0MB, alloc=531.8MB, time=348.12 memory used=57939.3MB, alloc=531.8MB, time=348.91 memory used=58315.8MB, alloc=531.8MB, time=349.70 memory used=58689.4MB, alloc=531.8MB, time=350.51 memory used=59057.0MB, alloc=531.8MB, time=351.32 memory used=59428.5MB, alloc=531.8MB, time=352.13 memory used=59804.3MB, alloc=531.8MB, time=352.98 memory used=60175.1MB, alloc=531.8MB, time=353.80 memory used=60543.8MB, alloc=531.8MB, time=354.64 memory used=60901.2MB, alloc=531.8MB, time=355.46 memory used=61252.5MB, alloc=531.8MB, time=356.36 memory used=61603.4MB, alloc=531.8MB, time=357.22 memory used=61949.2MB, alloc=531.8MB, time=358.15 memory used=62298.1MB, alloc=531.8MB, time=359.06 memory used=62648.0MB, alloc=531.8MB, time=359.87 memory used=62991.9MB, alloc=531.8MB, time=360.86 memory used=63338.8MB, alloc=531.8MB, time=361.85 memory used=63686.4MB, alloc=531.8MB, time=362.69 memory used=64031.7MB, alloc=531.8MB, time=363.80 memory used=64381.1MB, alloc=531.8MB, time=364.67 memory used=64728.5MB, alloc=531.8MB, time=365.82 memory used=64979.3MB, alloc=531.8MB, time=367.18 memory used=65154.4MB, alloc=531.8MB, time=367.94 memory used=65308.9MB, alloc=531.8MB, time=368.50 memory used=65467.4MB, alloc=531.8MB, time=369.05 memory used=65635.4MB, alloc=531.8MB, time=369.62 memory used=65860.8MB, alloc=531.8MB, time=371.05 memory used=66030.2MB, alloc=531.8MB, time=371.69 memory used=66185.0MB, alloc=531.8MB, time=372.23 memory used=66343.3MB, alloc=531.8MB, time=372.77 memory used=66517.9MB, alloc=531.8MB, time=373.32 memory used=66765.4MB, alloc=531.8MB, time=374.89 memory used=67003.3MB, alloc=531.8MB, time=376.43 memory used=67161.8MB, alloc=531.8MB, time=377.01 memory used=67397.7MB, alloc=531.8MB, time=377.59 memory used=67677.6MB, alloc=531.8MB, time=378.27 memory used=67971.9MB, alloc=531.8MB, time=378.94 memory used=68318.1MB, alloc=531.8MB, time=379.69 memory used=68626.6MB, alloc=531.8MB, time=381.22 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428535088 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 4 3 2 F := [-5 x y - 11 x y + 16 x, 16 x + 3 x z + 3 x z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 2 2 G := [15 y z + 7 x z - 13 y z, -x z - 3 y ] > Problem := [F,G]; 3 2 2 4 3 2 Problem := [[-5 x y - 11 x y + 16 x, 16 x + 3 x z + 3 x z ], 2 2 2 2 2 2 2 [15 y z + 7 x z - 13 y z, -x z - 3 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.8MB, alloc=32.3MB, time=0.51 memory used=47.8MB, alloc=32.3MB, time=0.81 memory used=68.2MB, alloc=60.3MB, time=1.13 memory used=114.7MB, alloc=68.3MB, time=1.73 memory used=157.4MB, alloc=68.3MB, time=2.17 memory used=204.5MB, alloc=68.3MB, time=2.69 memory used=246.8MB, alloc=68.3MB, time=3.23 memory used=288.3MB, alloc=92.3MB, time=3.79 memory used=357.8MB, alloc=92.3MB, time=4.65 memory used=425.4MB, alloc=92.3MB, time=5.62 memory used=485.0MB, alloc=116.3MB, time=6.60 memory used=565.1MB, alloc=140.3MB, time=7.99 memory used=648.6MB, alloc=164.3MB, time=9.99 N1 := 1761 > GB := Basis(F, plex(op(vars))); 3 2 2 4 3 2 GB := [5 x y + 11 x y - 16 x, 16 x + 3 x z + 3 x z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=754.8MB, alloc=164.3MB, time=11.38 memory used=835.1MB, alloc=420.3MB, time=12.17 memory used=968.9MB, alloc=420.3MB, time=13.68 memory used=1105.0MB, alloc=420.3MB, time=15.42 memory used=1225.0MB, alloc=444.3MB, time=17.44 N2 := 1761 > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 2 4 3 2 H := [-5 x y - 11 x y + 16 x, 16 x + 3 x z + 3 x z , 2 2 2 2 2 2 2 15 y z + 7 x z - 13 y z, -x z - 3 y ] > J:=[op(GB),op(G)]; 3 2 2 4 3 2 J := [5 x y + 11 x y - 16 x, 16 x + 3 x z + 3 x z , 2 2 2 2 2 2 2 15 y z + 7 x z - 13 y z, -x z - 3 y ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 10, 16, 4, 4, 2, 3, 1, 3/4, 3/4, 8/11, 5/11, 6/11, 4, 10, 16, 4, 4, 2, 3, 1, 3/4, 3/4, 8/11, 5/11, 6/11, 0, 0, 0] > save(F, G, cat("ranSet/34", convert(F, string),".txt")); > quit memory used=1304.3MB, alloc=444.3MB, time=19.38 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428535108 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 3 2 F := [7 x z - 7 x y z - 14 y z, 3 x z + x y + 8 x] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 2 G := [-19 x y - 9 x + 9 z, -4 x z - 3 y z + 12 x ] > Problem := [F,G]; 3 2 3 3 2 Problem := [[7 x z - 7 x y z - 14 y z, 3 x z + x y + 8 x], 2 2 2 3 2 2 [-19 x y - 9 x + 9 z, -4 x z - 3 y z + 12 x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.14 memory used=26.4MB, alloc=32.3MB, time=0.42 memory used=46.7MB, alloc=32.3MB, time=0.69 memory used=65.9MB, alloc=56.3MB, time=0.95 memory used=106.8MB, alloc=68.3MB, time=1.48 memory used=148.2MB, alloc=68.3MB, time=2.00 memory used=186.8MB, alloc=92.3MB, time=2.49 memory used=250.0MB, alloc=92.3MB, time=3.20 memory used=315.8MB, alloc=116.3MB, time=3.98 memory used=382.2MB, alloc=372.3MB, time=4.72 memory used=472.1MB, alloc=396.3MB, time=5.75 memory used=584.5MB, alloc=396.3MB, time=7.12 memory used=695.1MB, alloc=420.3MB, time=8.37 memory used=826.2MB, alloc=420.3MB, time=9.62 memory used=931.8MB, alloc=420.3MB, time=10.72 memory used=1058.9MB, alloc=444.3MB, time=12.50 memory used=1167.0MB, alloc=444.3MB, time=14.03 memory used=1278.7MB, alloc=468.3MB, time=15.31 memory used=1375.3MB, alloc=468.3MB, time=16.54 memory used=1493.6MB, alloc=468.3MB, time=17.55 memory used=1595.4MB, alloc=468.3MB, time=18.66 memory used=1684.0MB, alloc=468.3MB, time=19.97 memory used=1769.8MB, alloc=468.3MB, time=21.19 memory used=1856.1MB, alloc=468.3MB, time=22.40 memory used=1955.9MB, alloc=468.3MB, time=23.48 memory used=2059.4MB, alloc=468.3MB, time=24.36 memory used=2177.2MB, alloc=468.3MB, time=25.20 memory used=2256.3MB, alloc=468.3MB, time=26.06 memory used=2395.6MB, alloc=492.3MB, time=27.01 memory used=2482.1MB, alloc=492.3MB, time=28.20 memory used=2567.3MB, alloc=492.3MB, time=35.45 memory used=2700.3MB, alloc=492.3MB, time=47.92 memory used=2798.8MB, alloc=492.3MB, time=48.36 memory used=2867.3MB, alloc=492.3MB, time=48.73 memory used=2944.8MB, alloc=492.3MB, time=49.14 memory used=3033.4MB, alloc=492.3MB, time=49.55 memory used=3133.6MB, alloc=492.3MB, time=49.97 memory used=3240.7MB, alloc=492.3MB, time=50.38 memory used=3303.6MB, alloc=492.3MB, time=50.71 memory used=3365.0MB, alloc=516.3MB, time=51.05 memory used=3443.1MB, alloc=516.3MB, time=51.40 memory used=3526.3MB, alloc=516.3MB, time=51.75 memory used=3612.5MB, alloc=516.3MB, time=52.11 memory used=3704.8MB, alloc=516.3MB, time=52.47 memory used=3800.2MB, alloc=516.3MB, time=52.82 memory used=3901.5MB, alloc=516.3MB, time=53.18 memory used=4009.4MB, alloc=516.3MB, time=53.54 memory used=4119.8MB, alloc=516.3MB, time=53.91 memory used=4236.7MB, alloc=516.3MB, time=54.27 memory used=4359.9MB, alloc=516.3MB, time=54.63 memory used=4489.4MB, alloc=516.3MB, time=55.01 memory used=4625.1MB, alloc=516.3MB, time=55.39 memory used=4786.0MB, alloc=516.3MB, time=55.97 memory used=4914.1MB, alloc=516.3MB, time=56.40 memory used=5049.2MB, alloc=516.3MB, time=56.82 memory used=5189.3MB, alloc=516.3MB, time=57.24 memory used=5334.3MB, alloc=516.3MB, time=57.68 memory used=5483.7MB, alloc=516.3MB, time=58.11 memory used=5641.4MB, alloc=516.3MB, time=58.59 memory used=5803.0MB, alloc=516.3MB, time=59.05 memory used=5970.7MB, alloc=516.3MB, time=59.48 memory used=6145.8MB, alloc=516.3MB, time=59.92 memory used=6329.2MB, alloc=516.3MB, time=60.38 memory used=6521.0MB, alloc=516.3MB, time=60.83 memory used=6721.9MB, alloc=516.3MB, time=61.29 memory used=6932.6MB, alloc=516.3MB, time=61.77 memory used=7155.3MB, alloc=516.3MB, time=62.23 memory used=7393.8MB, alloc=516.3MB, time=62.72 memory used=7586.6MB, alloc=516.3MB, time=63.18 memory used=7683.3MB, alloc=516.3MB, time=64.05 memory used=7779.2MB, alloc=516.3MB, time=64.73 memory used=7859.5MB, alloc=516.3MB, time=66.05 memory used=7908.0MB, alloc=516.3MB, time=66.86 memory used=7961.7MB, alloc=516.3MB, time=67.94 memory used=8096.4MB, alloc=516.3MB, time=68.65 memory used=8221.3MB, alloc=516.3MB, time=70.17 memory used=8327.7MB, alloc=516.3MB, time=70.63 memory used=8433.4MB, alloc=516.3MB, time=71.72 memory used=8487.9MB, alloc=516.3MB, time=72.55 memory used=8542.1MB, alloc=516.3MB, time=73.60 memory used=8607.4MB, alloc=516.3MB, time=74.42 memory used=8655.9MB, alloc=516.3MB, time=75.37 memory used=8720.9MB, alloc=516.3MB, time=76.17 memory used=8846.6MB, alloc=516.3MB, time=77.06 memory used=8954.5MB, alloc=516.3MB, time=77.93 memory used=9050.3MB, alloc=516.3MB, time=78.60 memory used=9154.7MB, alloc=516.3MB, time=79.19 memory used=9244.2MB, alloc=516.3MB, time=79.70 memory used=9334.8MB, alloc=516.3MB, time=80.21 memory used=9447.9MB, alloc=516.3MB, time=80.74 memory used=9537.2MB, alloc=516.3MB, time=81.22 memory used=9615.7MB, alloc=516.3MB, time=81.64 memory used=9736.0MB, alloc=516.3MB, time=82.37 memory used=9835.4MB, alloc=516.3MB, time=82.90 memory used=9920.8MB, alloc=516.3MB, time=83.40 memory used=10026.1MB, alloc=516.3MB, time=83.91 memory used=10130.1MB, alloc=516.3MB, time=84.39 memory used=10204.1MB, alloc=516.3MB, time=84.84 memory used=10337.1MB, alloc=516.3MB, time=93.19 memory used=10431.9MB, alloc=516.3MB, time=93.74 memory used=10536.6MB, alloc=516.3MB, time=94.28 memory used=10633.5MB, alloc=516.3MB, time=94.73 memory used=10710.2MB, alloc=516.3MB, time=95.21 memory used=10796.5MB, alloc=516.3MB, time=95.62 memory used=10893.5MB, alloc=516.3MB, time=96.03 memory used=11004.4MB, alloc=516.3MB, time=96.45 memory used=11240.3MB, alloc=516.3MB, time=97.01 memory used=11497.4MB, alloc=516.3MB, time=98.84 memory used=11703.1MB, alloc=516.3MB, time=110.90 memory used=11798.1MB, alloc=516.3MB, time=111.38 memory used=11883.6MB, alloc=516.3MB, time=111.84 memory used=11991.1MB, alloc=516.3MB, time=112.33 memory used=12087.1MB, alloc=540.3MB, time=112.80 memory used=12169.6MB, alloc=540.3MB, time=113.23 memory used=12260.6MB, alloc=540.3MB, time=113.65 memory used=12360.4MB, alloc=540.3MB, time=114.07 memory used=12471.1MB, alloc=540.3MB, time=114.51 memory used=12592.4MB, alloc=540.3MB, time=114.95 memory used=12723.7MB, alloc=540.3MB, time=115.42 memory used=12869.1MB, alloc=540.3MB, time=115.87 memory used=13003.2MB, alloc=540.3MB, time=116.35 memory used=13133.4MB, alloc=540.3MB, time=116.83 memory used=13271.9MB, alloc=540.3MB, time=117.31 memory used=13424.2MB, alloc=540.3MB, time=117.80 memory used=13592.7MB, alloc=540.3MB, time=118.27 memory used=13971.7MB, alloc=540.3MB, time=120.77 memory used=14237.4MB, alloc=540.3MB, time=122.86 memory used=14499.4MB, alloc=540.3MB, time=126.12 memory used=14739.8MB, alloc=540.3MB, time=129.26 memory used=14864.4MB, alloc=540.3MB, time=129.93 memory used=15056.4MB, alloc=540.3MB, time=131.98 memory used=15191.8MB, alloc=540.3MB, time=132.91 memory used=15348.1MB, alloc=540.3MB, time=133.99 memory used=15474.1MB, alloc=540.3MB, time=134.77 memory used=15579.9MB, alloc=540.3MB, time=135.31 memory used=15667.4MB, alloc=540.3MB, time=135.82 memory used=15773.5MB, alloc=540.3MB, time=136.33 memory used=15891.0MB, alloc=540.3MB, time=136.85 memory used=15965.9MB, alloc=540.3MB, time=137.34 memory used=16089.2MB, alloc=540.3MB, time=138.16 memory used=16200.2MB, alloc=540.3MB, time=138.75 memory used=16283.2MB, alloc=540.3MB, time=139.29 memory used=16384.1MB, alloc=540.3MB, time=139.83 memory used=16507.4MB, alloc=540.3MB, time=140.38 memory used=16584.7MB, alloc=540.3MB, time=140.84 memory used=16720.8MB, alloc=540.3MB, time=149.55 memory used=16820.3MB, alloc=540.3MB, time=150.13 memory used=16928.8MB, alloc=540.3MB, time=150.69 memory used=17026.0MB, alloc=540.3MB, time=151.18 memory used=17107.5MB, alloc=540.3MB, time=151.63 memory used=17200.9MB, alloc=540.3MB, time=152.09 memory used=17307.4MB, alloc=540.3MB, time=152.56 memory used=17429.6MB, alloc=540.3MB, time=153.04 memory used=17688.2MB, alloc=540.3MB, time=154.58 memory used=17903.3MB, alloc=564.3MB, time=156.69 memory used=18156.4MB, alloc=564.3MB, time=163.37 memory used=18272.9MB, alloc=564.3MB, time=163.97 memory used=18377.0MB, alloc=564.3MB, time=164.57 memory used=18514.4MB, alloc=564.3MB, time=165.16 memory used=18599.3MB, alloc=564.3MB, time=165.64 memory used=18697.9MB, alloc=564.3MB, time=166.13 memory used=18822.9MB, alloc=564.3MB, time=166.91 memory used=18997.9MB, alloc=564.3MB, time=168.85 memory used=19155.3MB, alloc=588.3MB, time=171.23 memory used=19323.2MB, alloc=588.3MB, time=173.31 memory used=19458.8MB, alloc=588.3MB, time=174.13 memory used=19594.9MB, alloc=588.3MB, time=174.88 memory used=19729.5MB, alloc=588.3MB, time=175.92 memory used=19875.2MB, alloc=588.3MB, time=176.72 memory used=19982.9MB, alloc=588.3MB, time=177.43 memory used=20095.2MB, alloc=612.3MB, time=178.12 memory used=20251.6MB, alloc=612.3MB, time=178.81 memory used=20383.2MB, alloc=612.3MB, time=179.45 memory used=20483.2MB, alloc=612.3MB, time=180.05 memory used=20594.4MB, alloc=612.3MB, time=180.67 memory used=20716.1MB, alloc=612.3MB, time=181.29 memory used=20847.9MB, alloc=612.3MB, time=181.91 memory used=20994.3MB, alloc=612.3MB, time=182.54 memory used=21154.2MB, alloc=612.3MB, time=183.15 memory used=21425.3MB, alloc=612.3MB, time=183.89 memory used=21678.7MB, alloc=612.3MB, time=185.16 memory used=21794.9MB, alloc=612.3MB, time=185.83 memory used=21931.9MB, alloc=612.3MB, time=186.59 memory used=22100.6MB, alloc=612.3MB, time=187.30 memory used=22203.8MB, alloc=612.3MB, time=187.91 memory used=22307.2MB, alloc=612.3MB, time=188.53 memory used=22422.7MB, alloc=612.3MB, time=189.15 memory used=22549.1MB, alloc=612.3MB, time=189.77 memory used=22685.5MB, alloc=612.3MB, time=190.38 memory used=22835.4MB, alloc=612.3MB, time=191.02 memory used=23001.6MB, alloc=612.3MB, time=191.64 memory used=23208.1MB, alloc=612.3MB, time=192.32 memory used=23476.1MB, alloc=612.3MB, time=224.56 memory used=23609.4MB, alloc=612.3MB, time=225.29 memory used=23741.7MB, alloc=612.3MB, time=225.97 memory used=23851.4MB, alloc=612.3MB, time=226.60 memory used=23978.6MB, alloc=612.3MB, time=227.21 memory used=24124.7MB, alloc=612.3MB, time=227.84 memory used=24289.2MB, alloc=612.3MB, time=228.46 memory used=24504.5MB, alloc=612.3MB, time=229.16 memory used=24631.2MB, alloc=612.3MB, time=229.78 memory used=24767.5MB, alloc=612.3MB, time=230.42 memory used=24914.2MB, alloc=612.3MB, time=231.06 memory used=25073.1MB, alloc=612.3MB, time=231.71 memory used=25242.3MB, alloc=612.3MB, time=232.36 memory used=25426.2MB, alloc=612.3MB, time=233.00 memory used=25627.2MB, alloc=612.3MB, time=233.70 memory used=25837.9MB, alloc=612.3MB, time=234.34 memory used=26116.0MB, alloc=612.3MB, time=236.61 memory used=26289.3MB, alloc=612.3MB, time=237.86 memory used=26428.9MB, alloc=612.3MB, time=238.52 memory used=26549.6MB, alloc=612.3MB, time=239.14 memory used=26683.3MB, alloc=612.3MB, time=239.76 memory used=26839.9MB, alloc=612.3MB, time=240.57 memory used=26985.7MB, alloc=612.3MB, time=241.19 memory used=27097.7MB, alloc=612.3MB, time=241.78 memory used=27258.6MB, alloc=612.3MB, time=242.65 memory used=27401.2MB, alloc=612.3MB, time=243.32 memory used=27523.5MB, alloc=612.3MB, time=243.90 memory used=27704.1MB, alloc=612.3MB, time=244.72 memory used=27850.9MB, alloc=612.3MB, time=245.49 memory used=28102.8MB, alloc=612.3MB, time=247.88 memory used=28416.7MB, alloc=612.3MB, time=249.98 memory used=28544.1MB, alloc=612.3MB, time=250.67 memory used=28691.9MB, alloc=612.3MB, time=251.31 memory used=28916.9MB, alloc=612.3MB, time=252.18 memory used=29053.3MB, alloc=612.3MB, time=252.81 memory used=29283.4MB, alloc=612.3MB, time=253.67 memory used=29410.2MB, alloc=612.3MB, time=254.29 memory used=29659.8MB, alloc=612.3MB, time=255.35 memory used=29796.7MB, alloc=612.3MB, time=256.09 memory used=29915.5MB, alloc=612.3MB, time=256.75 memory used=30031.4MB, alloc=612.3MB, time=257.38 memory used=30165.1MB, alloc=612.3MB, time=258.03 memory used=30320.3MB, alloc=612.3MB, time=258.71 memory used=30561.6MB, alloc=612.3MB, time=259.50 memory used=30689.9MB, alloc=612.3MB, time=260.17 memory used=30831.0MB, alloc=612.3MB, time=260.82 memory used=30983.3MB, alloc=612.3MB, time=261.48 memory used=31151.3MB, alloc=612.3MB, time=262.15 memory used=31736.4MB, alloc=612.3MB, time=278.17 memory used=31870.1MB, alloc=612.3MB, time=278.89 memory used=31982.7MB, alloc=612.3MB, time=279.50 memory used=32120.2MB, alloc=612.3MB, time=280.13 memory used=32285.1MB, alloc=612.3MB, time=280.80 memory used=32436.7MB, alloc=612.3MB, time=281.48 memory used=32568.5MB, alloc=612.3MB, time=282.11 memory used=32712.6MB, alloc=612.3MB, time=282.77 memory used=32869.7MB, alloc=612.3MB, time=283.44 memory used=33042.5MB, alloc=612.3MB, time=284.13 memory used=33230.4MB, alloc=612.3MB, time=284.83 memory used=33435.7MB, alloc=612.3MB, time=285.51 memory used=33647.7MB, alloc=612.3MB, time=286.22 memory used=33806.2MB, alloc=612.3MB, time=286.88 memory used=33977.0MB, alloc=612.3MB, time=287.52 memory used=34159.6MB, alloc=612.3MB, time=288.20 memory used=34516.9MB, alloc=636.3MB, time=296.93 memory used=34758.5MB, alloc=636.3MB, time=400.69 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428535408 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 2 F := [-19 x y - x y + 20 z , 12 x z + 9 x + 2 z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 3 2 2 G := [2 y - 10 x z - 9, 3 x y - 18 x y z + 11 x y ] > Problem := [F,G]; 3 2 3 2 2 Problem := [[-19 x y - x y + 20 z , 12 x z + 9 x + 2 z], 4 2 3 2 2 [2 y - 10 x z - 9, 3 x y - 18 x y z + 11 x y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=25.9MB, alloc=32.3MB, time=0.50 memory used=45.1MB, alloc=56.3MB, time=0.77 memory used=94.6MB, alloc=65.4MB, time=1.29 memory used=120.2MB, alloc=65.4MB, time=1.37 memory used=146.0MB, alloc=65.4MB, time=1.44 memory used=194.9MB, alloc=65.4MB, time=1.92 memory used=221.2MB, alloc=65.4MB, time=2.01 memory used=256.4MB, alloc=65.4MB, time=2.26 memory used=298.6MB, alloc=65.4MB, time=2.73 memory used=341.0MB, alloc=65.4MB, time=3.29 memory used=371.6MB, alloc=65.4MB, time=3.70 memory used=414.2MB, alloc=73.4MB, time=4.23 memory used=461.0MB, alloc=97.4MB, time=4.82 memory used=532.6MB, alloc=97.4MB, time=5.64 memory used=592.1MB, alloc=353.4MB, time=6.38 memory used=654.9MB, alloc=353.4MB, time=6.99 memory used=702.6MB, alloc=353.4MB, time=7.20 memory used=747.6MB, alloc=353.4MB, time=7.38 memory used=804.3MB, alloc=353.4MB, time=9.20 memory used=843.4MB, alloc=353.4MB, time=9.35 memory used=872.5MB, alloc=353.4MB, time=9.48 memory used=909.8MB, alloc=353.4MB, time=9.60 memory used=935.7MB, alloc=353.4MB, time=9.72 memory used=960.3MB, alloc=353.4MB, time=9.82 memory used=987.4MB, alloc=353.4MB, time=9.92 memory used=1017.8MB, alloc=353.4MB, time=10.03 memory used=1064.2MB, alloc=353.4MB, time=10.21 memory used=1109.1MB, alloc=353.4MB, time=10.41 memory used=1161.0MB, alloc=353.4MB, time=12.26 memory used=1210.8MB, alloc=353.4MB, time=12.51 memory used=1238.3MB, alloc=353.4MB, time=12.63 memory used=1273.0MB, alloc=353.4MB, time=12.75 memory used=1302.8MB, alloc=353.4MB, time=12.86 memory used=1326.3MB, alloc=353.4MB, time=12.96 memory used=1352.8MB, alloc=353.4MB, time=13.06 memory used=1381.4MB, alloc=353.4MB, time=13.16 memory used=1418.8MB, alloc=353.4MB, time=13.31 memory used=1499.9MB, alloc=377.4MB, time=14.21 memory used=1607.8MB, alloc=377.4MB, time=35.42 memory used=1675.3MB, alloc=377.4MB, time=59.11 memory used=1739.7MB, alloc=377.4MB, time=59.38 memory used=1778.6MB, alloc=377.4MB, time=59.54 memory used=1821.7MB, alloc=377.4MB, time=59.71 memory used=1871.1MB, alloc=377.4MB, time=59.87 memory used=1927.2MB, alloc=377.4MB, time=60.04 memory used=1964.1MB, alloc=377.4MB, time=60.19 memory used=1998.0MB, alloc=377.4MB, time=60.32 memory used=2031.2MB, alloc=377.4MB, time=60.47 memory used=2066.8MB, alloc=377.4MB, time=60.61 memory used=2104.9MB, alloc=377.4MB, time=60.75 memory used=2144.0MB, alloc=377.4MB, time=60.90 memory used=2185.5MB, alloc=377.4MB, time=61.04 memory used=2229.4MB, alloc=377.4MB, time=61.17 memory used=2274.1MB, alloc=377.4MB, time=61.33 memory used=2321.2MB, alloc=377.4MB, time=61.47 memory used=2370.6MB, alloc=377.4MB, time=61.61 memory used=2422.2MB, alloc=377.4MB, time=61.76 memory used=2476.0MB, alloc=377.4MB, time=61.91 memory used=2529.4MB, alloc=377.4MB, time=62.06 memory used=2565.6MB, alloc=377.4MB, time=62.18 memory used=2596.3MB, alloc=377.4MB, time=62.30 memory used=2625.8MB, alloc=377.4MB, time=62.42 memory used=2657.0MB, alloc=377.4MB, time=62.54 memory used=2688.1MB, alloc=377.4MB, time=62.65 memory used=2719.3MB, alloc=377.4MB, time=62.77 memory used=2751.7MB, alloc=377.4MB, time=62.89 memory used=2785.5MB, alloc=377.4MB, time=63.01 memory used=2819.1MB, alloc=377.4MB, time=63.12 memory used=2853.8MB, alloc=377.4MB, time=63.24 memory used=2889.7MB, alloc=377.4MB, time=63.36 memory used=2926.5MB, alloc=377.4MB, time=63.48 memory used=2964.2MB, alloc=377.4MB, time=63.60 memory used=3002.6MB, alloc=377.4MB, time=63.73 memory used=3042.8MB, alloc=377.4MB, time=63.85 memory used=3084.6MB, alloc=377.4MB, time=63.97 memory used=3127.6MB, alloc=377.4MB, time=64.09 memory used=3171.2MB, alloc=377.4MB, time=64.22 memory used=3217.2MB, alloc=377.4MB, time=64.34 memory used=3264.2MB, alloc=377.4MB, time=64.47 memory used=3311.8MB, alloc=377.4MB, time=64.59 memory used=3362.1MB, alloc=377.4MB, time=64.71 memory used=3452.7MB, alloc=377.4MB, time=65.28 memory used=3540.2MB, alloc=377.4MB, time=65.91 memory used=3613.1MB, alloc=377.4MB, time=67.61 memory used=3655.1MB, alloc=377.4MB, time=67.76 memory used=3708.3MB, alloc=377.4MB, time=68.03 memory used=3775.6MB, alloc=377.4MB, time=69.56 memory used=3834.0MB, alloc=377.4MB, time=69.97 memory used=3873.5MB, alloc=377.4MB, time=70.11 memory used=3973.1MB, alloc=377.4MB, time=71.22 memory used=4030.9MB, alloc=401.4MB, time=95.77 memory used=4109.7MB, alloc=401.4MB, time=120.22 memory used=4203.8MB, alloc=401.4MB, time=120.71 memory used=4264.8MB, alloc=401.4MB, time=120.91 memory used=4312.3MB, alloc=401.4MB, time=121.09 memory used=4370.5MB, alloc=401.4MB, time=121.28 memory used=4439.4MB, alloc=401.4MB, time=121.48 memory used=4489.4MB, alloc=401.4MB, time=121.63 memory used=4532.1MB, alloc=401.4MB, time=121.77 memory used=4578.3MB, alloc=401.4MB, time=121.91 memory used=4629.0MB, alloc=401.4MB, time=122.06 memory used=4684.8MB, alloc=401.4MB, time=122.20 memory used=4745.4MB, alloc=401.4MB, time=122.35 memory used=4822.0MB, alloc=401.4MB, time=122.64 memory used=4902.5MB, alloc=401.4MB, time=123.30 memory used=5025.2MB, alloc=401.4MB, time=124.64 memory used=5138.3MB, alloc=401.4MB, time=125.98 memory used=5255.5MB, alloc=401.4MB, time=127.58 memory used=5367.3MB, alloc=425.4MB, time=128.94 memory used=5463.6MB, alloc=425.4MB, time=129.70 memory used=5539.9MB, alloc=425.4MB, time=130.05 memory used=5610.2MB, alloc=425.4MB, time=130.38 memory used=5728.0MB, alloc=425.4MB, time=131.61 memory used=5813.7MB, alloc=425.4MB, time=132.35 memory used=5984.8MB, alloc=449.4MB, time=133.59 memory used=6168.8MB, alloc=449.4MB, time=134.73 memory used=6358.4MB, alloc=449.4MB, time=136.38 memory used=6503.3MB, alloc=449.4MB, time=140.94 memory used=6595.2MB, alloc=449.4MB, time=141.31 memory used=6654.5MB, alloc=473.4MB, time=141.61 memory used=6740.4MB, alloc=473.4MB, time=141.94 memory used=6841.5MB, alloc=473.4MB, time=142.30 memory used=6929.7MB, alloc=473.4MB, time=142.62 memory used=6992.6MB, alloc=473.4MB, time=142.89 memory used=7055.6MB, alloc=473.4MB, time=143.18 memory used=7118.8MB, alloc=473.4MB, time=143.48 memory used=7191.0MB, alloc=473.4MB, time=143.75 memory used=7267.0MB, alloc=473.4MB, time=144.05 memory used=7346.2MB, alloc=473.4MB, time=144.33 memory used=7428.5MB, alloc=473.4MB, time=144.61 memory used=7513.8MB, alloc=473.4MB, time=144.91 memory used=7602.1MB, alloc=473.4MB, time=145.20 memory used=7693.2MB, alloc=473.4MB, time=145.48 memory used=7787.1MB, alloc=473.4MB, time=145.78 memory used=7883.9MB, alloc=473.4MB, time=146.10 memory used=7984.3MB, alloc=473.4MB, time=146.43 memory used=8062.2MB, alloc=497.4MB, time=146.71 memory used=8128.6MB, alloc=497.4MB, time=146.96 memory used=8194.2MB, alloc=497.4MB, time=147.20 memory used=8255.4MB, alloc=497.4MB, time=147.45 memory used=8319.2MB, alloc=497.4MB, time=147.69 memory used=8384.5MB, alloc=497.4MB, time=147.93 memory used=8450.7MB, alloc=497.4MB, time=148.16 memory used=8517.7MB, alloc=497.4MB, time=148.40 memory used=8585.4MB, alloc=497.4MB, time=148.65 memory used=8653.9MB, alloc=497.4MB, time=148.89 memory used=8723.3MB, alloc=497.4MB, time=149.14 memory used=8793.3MB, alloc=497.4MB, time=149.38 memory used=8864.1MB, alloc=521.4MB, time=149.64 memory used=8951.7MB, alloc=521.4MB, time=149.92 memory used=9048.5MB, alloc=521.4MB, time=150.19 memory used=9146.6MB, alloc=521.4MB, time=150.47 memory used=9245.8MB, alloc=521.4MB, time=150.74 memory used=9346.2MB, alloc=521.4MB, time=151.02 memory used=9447.7MB, alloc=521.4MB, time=151.31 memory used=9550.3MB, alloc=521.4MB, time=151.58 memory used=9653.9MB, alloc=521.4MB, time=151.86 memory used=9758.6MB, alloc=521.4MB, time=152.15 memory used=9865.9MB, alloc=521.4MB, time=152.43 memory used=9984.5MB, alloc=521.4MB, time=152.72 memory used=10105.6MB, alloc=521.4MB, time=153.01 memory used=10227.8MB, alloc=521.4MB, time=153.30 memory used=10351.1MB, alloc=521.4MB, time=153.60 memory used=10475.3MB, alloc=521.4MB, time=153.90 memory used=10600.5MB, alloc=521.4MB, time=154.19 memory used=10726.5MB, alloc=521.4MB, time=154.48 memory used=10853.5MB, alloc=521.4MB, time=154.78 memory used=10983.4MB, alloc=521.4MB, time=155.08 memory used=11124.2MB, alloc=521.4MB, time=155.39 memory used=11267.8MB, alloc=521.4MB, time=155.69 memory used=11424.0MB, alloc=521.4MB, time=156.02 memory used=11638.5MB, alloc=521.4MB, time=156.50 memory used=11805.9MB, alloc=521.4MB, time=156.95 memory used=11921.1MB, alloc=521.4MB, time=157.26 memory used=12031.5MB, alloc=521.4MB, time=157.56 memory used=12146.0MB, alloc=521.4MB, time=157.87 memory used=12263.6MB, alloc=521.4MB, time=158.19 memory used=12381.4MB, alloc=521.4MB, time=158.50 memory used=12499.4MB, alloc=521.4MB, time=158.81 memory used=12619.5MB, alloc=521.4MB, time=159.13 memory used=12750.5MB, alloc=521.4MB, time=159.46 memory used=12883.6MB, alloc=521.4MB, time=159.78 memory used=13016.5MB, alloc=521.4MB, time=160.11 memory used=13149.4MB, alloc=521.4MB, time=160.44 memory used=13282.2MB, alloc=521.4MB, time=160.76 memory used=13415.0MB, alloc=521.4MB, time=161.09 memory used=13550.0MB, alloc=521.4MB, time=161.42 memory used=13694.6MB, alloc=521.4MB, time=161.76 memory used=13841.2MB, alloc=521.4MB, time=162.08 memory used=13987.3MB, alloc=521.4MB, time=162.42 memory used=14132.9MB, alloc=521.4MB, time=162.76 memory used=14280.5MB, alloc=521.4MB, time=163.10 memory used=14437.0MB, alloc=521.4MB, time=163.45 memory used=14594.9MB, alloc=521.4MB, time=163.79 memory used=14751.9MB, alloc=521.4MB, time=164.14 memory used=14910.7MB, alloc=521.4MB, time=164.48 memory used=15076.9MB, alloc=521.4MB, time=164.83 memory used=15244.3MB, alloc=521.4MB, time=165.19 memory used=15412.8MB, alloc=521.4MB, time=165.54 memory used=15587.8MB, alloc=521.4MB, time=165.90 memory used=15763.5MB, alloc=521.4MB, time=166.26 memory used=15950.0MB, alloc=521.4MB, time=166.63 memory used=16133.7MB, alloc=521.4MB, time=167.01 memory used=16327.0MB, alloc=521.4MB, time=167.38 memory used=16519.7MB, alloc=521.4MB, time=167.76 memory used=16717.8MB, alloc=521.4MB, time=168.13 memory used=16920.3MB, alloc=521.4MB, time=168.52 memory used=17131.5MB, alloc=521.4MB, time=168.90 memory used=17346.9MB, alloc=521.4MB, time=169.30 memory used=17565.4MB, alloc=521.4MB, time=169.69 memory used=17794.8MB, alloc=521.4MB, time=170.09 memory used=18031.4MB, alloc=521.4MB, time=170.48 memory used=18253.9MB, alloc=521.4MB, time=170.86 memory used=18547.2MB, alloc=521.4MB, time=272.77 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428535708 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 2 2 F := [-17 x - 18 x y z + 18 x z , -x y z + 10 x + 13 x y] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 2 2 G := [20 x y + 16 x z + 10 x z , 13 x y + 17 x y z - 9 z] > Problem := [F,G]; 4 2 2 2 2 Problem := [[-17 x - 18 x y z + 18 x z , -x y z + 10 x + 13 x y], 3 3 2 2 2 2 [20 x y + 16 x z + 10 x z , 13 x y + 17 x y z - 9 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=24.6MB, alloc=32.3MB, time=0.40 memory used=46.0MB, alloc=36.4MB, time=0.68 memory used=65.8MB, alloc=60.4MB, time=0.97 memory used=110.4MB, alloc=61.1MB, time=1.39 memory used=134.9MB, alloc=61.1MB, time=1.45 memory used=194.1MB, alloc=69.7MB, time=2.08 memory used=253.3MB, alloc=70.3MB, time=2.92 memory used=293.4MB, alloc=70.3MB, time=3.25 memory used=334.5MB, alloc=70.3MB, time=3.61 memory used=386.0MB, alloc=70.3MB, time=4.19 memory used=428.6MB, alloc=70.3MB, time=4.62 memory used=458.5MB, alloc=70.3MB, time=4.86 memory used=501.3MB, alloc=70.3MB, time=5.37 memory used=541.6MB, alloc=94.3MB, time=5.83 memory used=604.7MB, alloc=94.3MB, time=6.47 memory used=663.7MB, alloc=94.3MB, time=7.24 memory used=720.9MB, alloc=374.3MB, time=7.97 memory used=804.6MB, alloc=374.3MB, time=8.67 memory used=854.8MB, alloc=374.3MB, time=8.83 memory used=906.6MB, alloc=374.3MB, time=9.47 memory used=965.1MB, alloc=374.3MB, time=9.76 memory used=1013.6MB, alloc=374.3MB, time=9.97 memory used=1079.3MB, alloc=374.3MB, time=10.52 memory used=1122.1MB, alloc=374.3MB, time=10.70 memory used=1166.4MB, alloc=374.3MB, time=10.87 memory used=1219.4MB, alloc=374.3MB, time=11.03 memory used=1250.9MB, alloc=374.3MB, time=11.17 memory used=1285.9MB, alloc=374.3MB, time=11.30 memory used=1325.1MB, alloc=374.3MB, time=11.44 memory used=1368.6MB, alloc=374.3MB, time=11.58 memory used=1418.3MB, alloc=374.3MB, time=11.73 memory used=1476.9MB, alloc=374.3MB, time=12.21 memory used=1527.3MB, alloc=374.3MB, time=12.41 memory used=1568.2MB, alloc=374.3MB, time=12.56 memory used=1619.3MB, alloc=374.3MB, time=12.74 memory used=1656.8MB, alloc=374.3MB, time=12.88 memory used=1689.6MB, alloc=374.3MB, time=13.03 memory used=1726.2MB, alloc=374.3MB, time=13.17 memory used=1767.4MB, alloc=374.3MB, time=13.31 memory used=1814.5MB, alloc=374.3MB, time=13.46 memory used=1864.7MB, alloc=374.3MB, time=13.59 memory used=1945.0MB, alloc=374.3MB, time=22.68 memory used=1989.2MB, alloc=374.3MB, time=22.85 memory used=2027.0MB, alloc=374.3MB, time=22.99 memory used=2065.8MB, alloc=374.3MB, time=23.14 memory used=2112.7MB, alloc=374.3MB, time=23.28 memory used=2158.2MB, alloc=374.3MB, time=23.41 memory used=2188.8MB, alloc=374.3MB, time=23.52 memory used=2221.7MB, alloc=374.3MB, time=23.63 memory used=2260.1MB, alloc=374.3MB, time=23.74 memory used=2314.1MB, alloc=374.3MB, time=23.95 memory used=2367.6MB, alloc=374.3MB, time=24.21 memory used=2425.8MB, alloc=374.3MB, time=24.50 memory used=2488.4MB, alloc=374.3MB, time=24.85 memory used=2531.8MB, alloc=374.3MB, time=25.01 memory used=2577.5MB, alloc=374.3MB, time=25.17 memory used=2613.3MB, alloc=374.3MB, time=25.31 memory used=2668.6MB, alloc=374.3MB, time=25.61 memory used=2713.9MB, alloc=374.3MB, time=25.77 memory used=2760.9MB, alloc=374.3MB, time=25.93 memory used=2796.6MB, alloc=374.3MB, time=26.07 memory used=2852.8MB, alloc=374.3MB, time=27.61 memory used=2906.7MB, alloc=374.3MB, time=27.82 memory used=2944.2MB, alloc=374.3MB, time=27.95 memory used=3000.6MB, alloc=374.3MB, time=28.24 memory used=3044.3MB, alloc=374.3MB, time=28.41 memory used=3090.4MB, alloc=374.3MB, time=28.56 memory used=3126.3MB, alloc=374.3MB, time=28.69 memory used=3180.3MB, alloc=374.3MB, time=28.94 memory used=3225.6MB, alloc=374.3MB, time=29.12 memory used=3272.5MB, alloc=374.3MB, time=29.29 memory used=3307.4MB, alloc=374.3MB, time=29.42 memory used=3359.3MB, alloc=374.3MB, time=30.82 memory used=3418.2MB, alloc=374.3MB, time=31.16 memory used=3454.8MB, alloc=374.3MB, time=31.28 memory used=3506.0MB, alloc=374.3MB, time=31.48 memory used=3622.8MB, alloc=374.3MB, time=32.82 memory used=3741.1MB, alloc=374.3MB, time=34.23 memory used=3850.5MB, alloc=374.3MB, time=35.60 memory used=3914.3MB, alloc=374.3MB, time=37.19 memory used=3952.2MB, alloc=374.3MB, time=37.33 memory used=3996.1MB, alloc=374.3MB, time=37.46 memory used=4066.5MB, alloc=374.3MB, time=46.53 memory used=4120.2MB, alloc=374.3MB, time=46.79 memory used=4162.6MB, alloc=374.3MB, time=46.94 memory used=4196.4MB, alloc=374.3MB, time=47.07 memory used=4236.9MB, alloc=374.3MB, time=47.22 memory used=4285.2MB, alloc=374.3MB, time=47.37 memory used=4319.3MB, alloc=374.3MB, time=47.48 memory used=4348.7MB, alloc=374.3MB, time=47.60 memory used=4381.1MB, alloc=374.3MB, time=47.71 memory used=4419.4MB, alloc=374.3MB, time=47.83 memory used=4508.9MB, alloc=398.3MB, time=48.65 memory used=4638.3MB, alloc=398.3MB, time=50.17 memory used=4739.5MB, alloc=398.3MB, time=51.09 memory used=4800.7MB, alloc=398.3MB, time=51.33 memory used=4859.6MB, alloc=398.3MB, time=51.54 memory used=4903.3MB, alloc=398.3MB, time=51.72 memory used=4973.5MB, alloc=398.3MB, time=52.08 memory used=5028.7MB, alloc=398.3MB, time=52.29 memory used=5077.3MB, alloc=398.3MB, time=52.48 memory used=5146.4MB, alloc=398.3MB, time=56.98 memory used=5210.5MB, alloc=398.3MB, time=57.21 memory used=5258.2MB, alloc=398.3MB, time=57.40 memory used=5310.1MB, alloc=398.3MB, time=57.58 memory used=5380.7MB, alloc=398.3MB, time=57.97 memory used=5511.2MB, alloc=398.3MB, time=63.40 memory used=5574.4MB, alloc=398.3MB, time=63.80 memory used=5617.1MB, alloc=398.3MB, time=63.99 memory used=5669.7MB, alloc=398.3MB, time=64.17 memory used=5767.4MB, alloc=398.3MB, time=65.02 memory used=5839.6MB, alloc=398.3MB, time=65.48 memory used=5886.3MB, alloc=398.3MB, time=65.69 memory used=5953.5MB, alloc=422.3MB, time=66.51 memory used=6027.8MB, alloc=422.3MB, time=66.81 memory used=6098.6MB, alloc=422.3MB, time=67.07 memory used=6158.7MB, alloc=422.3MB, time=67.31 memory used=6210.8MB, alloc=422.3MB, time=67.54 memory used=6270.8MB, alloc=422.3MB, time=67.76 memory used=6340.9MB, alloc=422.3MB, time=68.01 memory used=6410.7MB, alloc=422.3MB, time=68.22 memory used=6479.0MB, alloc=422.3MB, time=68.82 memory used=6543.6MB, alloc=422.3MB, time=69.08 memory used=6619.3MB, alloc=422.3MB, time=69.35 memory used=6672.3MB, alloc=422.3MB, time=69.56 memory used=6726.8MB, alloc=422.3MB, time=69.78 memory used=6790.0MB, alloc=422.3MB, time=70.01 memory used=6862.7MB, alloc=422.3MB, time=70.24 memory used=6924.5MB, alloc=422.3MB, time=70.44 memory used=7002.8MB, alloc=422.3MB, time=85.54 memory used=7078.7MB, alloc=422.3MB, time=86.27 memory used=7134.6MB, alloc=422.3MB, time=86.50 memory used=7198.4MB, alloc=422.3MB, time=86.70 memory used=7273.3MB, alloc=422.3MB, time=86.91 memory used=7319.7MB, alloc=422.3MB, time=87.08 memory used=7372.0MB, alloc=422.3MB, time=87.27 memory used=7430.3MB, alloc=422.3MB, time=87.45 memory used=7497.8MB, alloc=422.3MB, time=87.63 memory used=7576.4MB, alloc=422.3MB, time=87.95 memory used=7659.6MB, alloc=422.3MB, time=88.44 memory used=7736.4MB, alloc=422.3MB, time=88.77 memory used=7820.1MB, alloc=422.3MB, time=89.32 memory used=7888.5MB, alloc=422.3MB, time=89.56 memory used=7941.6MB, alloc=422.3MB, time=89.77 memory used=8010.1MB, alloc=422.3MB, time=89.99 memory used=8087.9MB, alloc=422.3MB, time=90.40 memory used=8159.1MB, alloc=422.3MB, time=90.65 memory used=8211.2MB, alloc=422.3MB, time=90.88 memory used=8278.1MB, alloc=422.3MB, time=91.10 memory used=8361.8MB, alloc=422.3MB, time=94.07 memory used=8423.8MB, alloc=422.3MB, time=94.29 memory used=8494.8MB, alloc=422.3MB, time=94.51 memory used=8545.1MB, alloc=422.3MB, time=94.69 memory used=8622.8MB, alloc=422.3MB, time=95.13 memory used=8688.8MB, alloc=422.3MB, time=95.38 memory used=8744.4MB, alloc=422.3MB, time=95.60 memory used=8816.0MB, alloc=422.3MB, time=95.81 memory used=8890.3MB, alloc=422.3MB, time=96.25 memory used=8958.1MB, alloc=422.3MB, time=96.49 memory used=9011.7MB, alloc=422.3MB, time=96.73 memory used=9079.9MB, alloc=422.3MB, time=96.94 memory used=9162.4MB, alloc=422.3MB, time=99.91 memory used=9222.6MB, alloc=422.3MB, time=100.14 memory used=9292.4MB, alloc=422.3MB, time=100.36 memory used=9349.8MB, alloc=422.3MB, time=100.58 memory used=9493.5MB, alloc=422.3MB, time=104.70 memory used=9557.6MB, alloc=422.3MB, time=104.94 memory used=9614.7MB, alloc=422.3MB, time=105.17 memory used=9676.1MB, alloc=422.3MB, time=105.39 memory used=9767.1MB, alloc=422.3MB, time=105.99 memory used=9889.7MB, alloc=422.3MB, time=106.85 memory used=9972.0MB, alloc=422.3MB, time=107.37 memory used=10081.4MB, alloc=422.3MB, time=108.59 memory used=10204.8MB, alloc=446.3MB, time=110.01 memory used=10314.3MB, alloc=446.3MB, time=111.27 memory used=10412.5MB, alloc=446.3MB, time=112.53 memory used=10499.5MB, alloc=470.3MB, time=113.71 memory used=10608.2MB, alloc=470.3MB, time=114.38 memory used=10706.9MB, alloc=470.3MB, time=114.83 memory used=10797.1MB, alloc=470.3MB, time=115.51 memory used=10883.5MB, alloc=470.3MB, time=115.89 memory used=10956.2MB, alloc=470.3MB, time=116.25 memory used=11027.8MB, alloc=470.3MB, time=116.56 memory used=11113.2MB, alloc=470.3MB, time=116.88 memory used=11209.9MB, alloc=470.3MB, time=117.20 memory used=11266.5MB, alloc=470.3MB, time=117.47 memory used=11325.4MB, alloc=470.3MB, time=117.74 memory used=11389.6MB, alloc=470.3MB, time=118.03 memory used=11460.2MB, alloc=470.3MB, time=118.30 memory used=11537.8MB, alloc=470.3MB, time=118.59 memory used=11622.6MB, alloc=470.3MB, time=118.86 memory used=11718.8MB, alloc=470.3MB, time=119.14 memory used=11837.3MB, alloc=470.3MB, time=124.49 memory used=11908.5MB, alloc=470.3MB, time=124.78 memory used=11995.4MB, alloc=470.3MB, time=125.09 memory used=12055.9MB, alloc=470.3MB, time=125.35 memory used=12124.7MB, alloc=470.3MB, time=125.62 memory used=12204.3MB, alloc=470.3MB, time=125.89 memory used=12296.1MB, alloc=470.3MB, time=126.16 memory used=12542.3MB, alloc=470.3MB, time=126.88 memory used=12647.4MB, alloc=470.3MB, time=127.61 memory used=12741.4MB, alloc=470.3MB, time=128.09 memory used=12836.4MB, alloc=470.3MB, time=128.48 memory used=12921.1MB, alloc=470.3MB, time=128.90 memory used=13044.3MB, alloc=470.3MB, time=130.51 memory used=13125.6MB, alloc=470.3MB, time=130.87 memory used=13211.0MB, alloc=470.3MB, time=131.23 memory used=13282.5MB, alloc=494.3MB, time=131.58 memory used=13357.0MB, alloc=494.3MB, time=131.95 memory used=13444.6MB, alloc=494.3MB, time=132.26 memory used=13545.5MB, alloc=494.3MB, time=132.60 memory used=13661.5MB, alloc=494.3MB, time=132.95 memory used=13733.2MB, alloc=494.3MB, time=133.23 memory used=13803.2MB, alloc=494.3MB, time=133.48 memory used=13881.5MB, alloc=494.3MB, time=133.74 memory used=14029.4MB, alloc=494.3MB, time=190.56 memory used=14142.6MB, alloc=518.3MB, time=297.86 memory used=14268.0MB, alloc=542.3MB, time=448.16 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428536008 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 3 3 2 F := [-2 x y - 3 y + 12, -15 x y + 20 x z + 4 x z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 G := [-12 x z - 19 x z - 15 y, -2 x y + 14 x y z - 8 x z ] > Problem := [F,G]; 3 3 3 3 2 Problem := [[-2 x y - 3 y + 12, -15 x y + 20 x z + 4 x z], 3 2 2 2 2 [-12 x z - 19 x z - 15 y, -2 x y + 14 x y z - 8 x z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=24.9MB, alloc=32.3MB, time=0.47 memory used=44.1MB, alloc=32.3MB, time=0.75 memory used=62.9MB, alloc=56.3MB, time=1.00 memory used=104.3MB, alloc=60.3MB, time=1.33 memory used=142.6MB, alloc=60.3MB, time=1.86 memory used=183.6MB, alloc=60.3MB, time=2.46 memory used=224.4MB, alloc=60.3MB, time=3.04 memory used=266.8MB, alloc=92.3MB, time=3.63 memory used=334.5MB, alloc=92.3MB, time=4.59 memory used=399.2MB, alloc=92.3MB, time=5.35 memory used=467.3MB, alloc=92.3MB, time=6.16 memory used=530.8MB, alloc=116.3MB, time=6.87 memory used=603.2MB, alloc=372.3MB, time=7.91 memory used=688.9MB, alloc=396.3MB, time=9.21 memory used=800.0MB, alloc=420.3MB, time=10.83 memory used=938.8MB, alloc=444.3MB, time=12.95 memory used=1087.2MB, alloc=468.3MB, time=15.49 memory used=1257.3MB, alloc=492.3MB, time=18.26 memory used=1444.9MB, alloc=516.3MB, time=21.32 memory used=1651.4MB, alloc=540.3MB, time=24.66 memory used=1873.0MB, alloc=564.3MB, time=28.34 memory used=2137.0MB, alloc=588.3MB, time=31.51 memory used=2437.1MB, alloc=588.3MB, time=34.50 memory used=2654.8MB, alloc=612.3MB, time=38.16 memory used=2845.8MB, alloc=636.3MB, time=41.66 memory used=3086.7MB, alloc=660.3MB, time=48.95 memory used=3319.8MB, alloc=684.3MB, time=57.04 memory used=3561.5MB, alloc=708.3MB, time=65.89 memory used=3814.6MB, alloc=732.3MB, time=75.54 memory used=4074.9MB, alloc=756.3MB, time=86.43 memory used=4355.8MB, alloc=780.3MB, time=97.95 memory used=4660.8MB, alloc=804.3MB, time=109.03 memory used=4989.6MB, alloc=828.3MB, time=120.84 memory used=5342.4MB, alloc=852.3MB, time=133.40 memory used=5719.2MB, alloc=852.3MB, time=146.91 memory used=6095.8MB, alloc=852.3MB, time=160.62 memory used=6472.5MB, alloc=876.3MB, time=175.13 memory used=6873.1MB, alloc=876.3MB, time=189.46 memory used=7273.6MB, alloc=876.3MB, time=203.69 memory used=7674.2MB, alloc=900.3MB, time=217.88 memory used=8098.7MB, alloc=900.3MB, time=232.87 memory used=8523.1MB, alloc=924.3MB, time=247.88 memory used=8971.3MB, alloc=924.3MB, time=263.93 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428536308 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 4 2 2 2 F := [6 x y - 13 x y z - 9 x y , -14 x + 6 x y - 13 y z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 2 2 2 G := [12 x - 5 x z - 15 x y z, -5 x y z + 15 y z - 6 x z] > Problem := [F,G]; 3 2 2 4 2 2 2 Problem := [[6 x y - 13 x y z - 9 x y , -14 x + 6 x y - 13 y z ], 4 3 2 2 2 [12 x - 5 x z - 15 x y z, -5 x y z + 15 y z - 6 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.6MB, alloc=32.3MB, time=0.47 memory used=47.5MB, alloc=32.3MB, time=0.77 memory used=66.9MB, alloc=56.3MB, time=1.04 memory used=107.7MB, alloc=60.3MB, time=1.64 memory used=147.7MB, alloc=60.3MB, time=2.21 memory used=188.0MB, alloc=84.3MB, time=2.78 memory used=227.7MB, alloc=84.3MB, time=3.36 memory used=291.5MB, alloc=92.3MB, time=4.31 memory used=356.6MB, alloc=116.3MB, time=5.20 memory used=423.9MB, alloc=116.3MB, time=6.20 memory used=492.9MB, alloc=372.3MB, time=7.18 memory used=576.5MB, alloc=372.3MB, time=8.19 memory used=669.1MB, alloc=396.3MB, time=9.17 memory used=777.4MB, alloc=396.3MB, time=10.32 memory used=848.8MB, alloc=396.3MB, time=11.64 memory used=935.6MB, alloc=396.3MB, time=13.04 memory used=1027.3MB, alloc=396.3MB, time=14.19 memory used=1140.3MB, alloc=420.3MB, time=15.33 memory used=1271.8MB, alloc=420.3MB, time=16.78 memory used=1397.9MB, alloc=444.3MB, time=18.39 memory used=1523.2MB, alloc=468.3MB, time=19.96 memory used=1640.6MB, alloc=468.3MB, time=21.78 memory used=1764.0MB, alloc=468.3MB, time=23.25 memory used=1886.9MB, alloc=468.3MB, time=24.56 memory used=1988.9MB, alloc=492.3MB, time=26.03 memory used=2091.0MB, alloc=492.3MB, time=27.37 memory used=2173.9MB, alloc=492.3MB, time=28.43 memory used=2319.7MB, alloc=492.3MB, time=29.97 memory used=2484.1MB, alloc=492.3MB, time=31.15 memory used=2582.4MB, alloc=492.3MB, time=32.21 memory used=2695.3MB, alloc=516.3MB, time=63.28 memory used=2808.9MB, alloc=516.3MB, time=65.77 memory used=2891.0MB, alloc=516.3MB, time=66.09 memory used=2995.8MB, alloc=516.3MB, time=66.42 memory used=3199.2MB, alloc=516.3MB, time=67.05 memory used=3458.4MB, alloc=516.3MB, time=71.10 memory used=3560.3MB, alloc=516.3MB, time=71.51 memory used=3648.1MB, alloc=516.3MB, time=71.85 memory used=3852.2MB, alloc=516.3MB, time=73.18 memory used=4029.6MB, alloc=516.3MB, time=75.15 memory used=4181.4MB, alloc=516.3MB, time=76.40 memory used=4272.4MB, alloc=516.3MB, time=77.46 memory used=4380.4MB, alloc=516.3MB, time=80.41 memory used=4495.5MB, alloc=516.3MB, time=83.57 memory used=4585.0MB, alloc=516.3MB, time=84.63 memory used=4711.3MB, alloc=516.3MB, time=86.33 memory used=4827.6MB, alloc=516.3MB, time=92.22 memory used=4930.2MB, alloc=516.3MB, time=92.82 memory used=5026.5MB, alloc=516.3MB, time=93.21 memory used=5104.6MB, alloc=516.3MB, time=94.98 memory used=5208.1MB, alloc=516.3MB, time=95.78 memory used=5327.0MB, alloc=516.3MB, time=97.44 memory used=5448.0MB, alloc=540.3MB, time=98.42 memory used=5630.4MB, alloc=540.3MB, time=100.34 memory used=5698.8MB, alloc=540.3MB, time=101.38 memory used=5815.5MB, alloc=540.3MB, time=102.48 memory used=5906.6MB, alloc=540.3MB, time=103.32 memory used=5960.8MB, alloc=540.3MB, time=104.24 memory used=6026.6MB, alloc=540.3MB, time=105.08 memory used=6168.3MB, alloc=540.3MB, time=120.21 memory used=6258.8MB, alloc=540.3MB, time=120.60 memory used=6385.4MB, alloc=540.3MB, time=121.38 memory used=6523.0MB, alloc=540.3MB, time=124.26 memory used=6637.1MB, alloc=540.3MB, time=125.02 memory used=6683.3MB, alloc=540.3MB, time=125.89 memory used=6738.8MB, alloc=540.3MB, time=126.69 memory used=6809.3MB, alloc=540.3MB, time=127.70 memory used=6901.7MB, alloc=540.3MB, time=129.79 memory used=6974.4MB, alloc=540.3MB, time=131.01 memory used=7021.6MB, alloc=564.3MB, time=131.83 memory used=7197.6MB, alloc=564.3MB, time=133.20 memory used=7309.0MB, alloc=564.3MB, time=133.66 memory used=7608.6MB, alloc=564.3MB, time=135.98 memory used=7744.8MB, alloc=564.3MB, time=136.84 memory used=7897.2MB, alloc=564.3MB, time=137.67 memory used=8079.9MB, alloc=564.3MB, time=139.34 memory used=8332.3MB, alloc=588.3MB, time=142.42 memory used=8627.5MB, alloc=612.3MB, time=145.12 memory used=8872.2MB, alloc=612.3MB, time=146.43 memory used=9122.9MB, alloc=612.3MB, time=147.78 memory used=9391.3MB, alloc=612.3MB, time=149.69 memory used=9696.9MB, alloc=612.3MB, time=152.06 memory used=9946.8MB, alloc=612.3MB, time=153.59 memory used=10219.3MB, alloc=636.3MB, time=157.48 memory used=10453.8MB, alloc=636.3MB, time=158.43 memory used=10750.8MB, alloc=636.3MB, time=162.30 memory used=11011.4MB, alloc=636.3MB, time=165.55 memory used=11269.5MB, alloc=636.3MB, time=166.86 memory used=11580.6MB, alloc=636.3MB, time=171.25 memory used=11858.9MB, alloc=636.3MB, time=172.82 memory used=12143.1MB, alloc=636.3MB, time=174.81 memory used=12408.1MB, alloc=636.3MB, time=176.28 memory used=12737.6MB, alloc=660.3MB, time=179.83 memory used=13052.7MB, alloc=684.3MB, time=183.82 memory used=13374.3MB, alloc=708.3MB, time=188.25 memory used=13664.8MB, alloc=732.3MB, time=192.73 memory used=14045.5MB, alloc=756.3MB, time=200.54 memory used=14425.5MB, alloc=780.3MB, time=206.86 memory used=14662.6MB, alloc=804.3MB, time=210.53 memory used=14981.6MB, alloc=828.3MB, time=216.15 memory used=15263.9MB, alloc=852.3MB, time=220.87 memory used=15525.8MB, alloc=876.3MB, time=226.13 memory used=16016.6MB, alloc=900.3MB, time=243.61 memory used=16318.3MB, alloc=924.3MB, time=248.28 memory used=16803.1MB, alloc=948.3MB, time=263.69 memory used=17153.6MB, alloc=972.3MB, time=269.11 memory used=17619.6MB, alloc=996.3MB, time=284.76 memory used=18252.0MB, alloc=1020.3MB, time=294.24 memory used=18796.4MB, alloc=1044.3MB, time=302.92 memory used=19388.7MB, alloc=1068.3MB, time=312.75 memory used=19994.7MB, alloc=1092.3MB, time=324.13 memory used=20558.6MB, alloc=1116.3MB, time=333.12 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428536608 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 2 2 F := [10 y z + 11 y z + 5 y , 15 x y - 17 x y z + 15 y z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 2 2 G := [-8 x y + 7 x - 12 x y , -18 x z - 11 y z + 3 x ] > Problem := [F,G]; 3 2 2 2 2 2 2 Problem := [[10 y z + 11 y z + 5 y , 15 x y - 17 x y z + 15 y z], 3 3 2 2 2 2 [-8 x y + 7 x - 12 x y , -18 x z - 11 y z + 3 x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=25.9MB, alloc=32.3MB, time=0.50 memory used=45.9MB, alloc=56.3MB, time=0.80 memory used=87.4MB, alloc=60.3MB, time=1.39 memory used=130.7MB, alloc=68.3MB, time=1.99 memory used=172.1MB, alloc=92.3MB, time=2.59 memory used=240.4MB, alloc=92.3MB, time=3.48 memory used=296.1MB, alloc=92.3MB, time=3.96 memory used=359.7MB, alloc=92.3MB, time=4.64 memory used=413.7MB, alloc=92.3MB, time=5.20 memory used=480.9MB, alloc=92.3MB, time=6.04 memory used=539.2MB, alloc=116.3MB, time=7.30 memory used=608.2MB, alloc=116.3MB, time=7.67 memory used=689.9MB, alloc=372.3MB, time=8.40 memory used=782.7MB, alloc=372.3MB, time=9.12 memory used=855.6MB, alloc=372.3MB, time=10.69 memory used=1059.1MB, alloc=396.3MB, time=14.58 memory used=1469.0MB, alloc=420.3MB, time=17.47 memory used=1515.2MB, alloc=421.3MB, time=18.21 memory used=1516.2MB, alloc=422.3MB, time=18.28 memory used=1517.2MB, alloc=423.3MB, time=18.36 memory used=1518.2MB, alloc=424.3MB, time=18.43 memory used=1519.2MB, alloc=421.3MB, time=18.53 memory used=1614.5MB, alloc=420.3MB, time=19.06 memory used=1694.5MB, alloc=420.3MB, time=19.27 memory used=1758.3MB, alloc=420.3MB, time=19.46 memory used=1892.8MB, alloc=420.3MB, time=20.19 memory used=2005.7MB, alloc=420.3MB, time=20.53 memory used=2267.2MB, alloc=420.3MB, time=22.31 memory used=2403.3MB, alloc=420.3MB, time=22.64 memory used=2562.6MB, alloc=420.3MB, time=22.98 memory used=2840.8MB, alloc=420.3MB, time=23.57 memory used=3219.3MB, alloc=420.3MB, time=24.33 memory used=3574.0MB, alloc=420.3MB, time=24.95 memory used=3928.5MB, alloc=420.3MB, time=25.58 memory used=4282.8MB, alloc=420.3MB, time=26.20 memory used=4625.1MB, alloc=420.3MB, time=26.76 memory used=4975.8MB, alloc=420.3MB, time=27.34 memory used=5315.9MB, alloc=420.3MB, time=27.90 memory used=5659.6MB, alloc=420.3MB, time=28.46 memory used=6004.0MB, alloc=420.3MB, time=29.04 memory used=6353.9MB, alloc=420.3MB, time=29.59 memory used=6707.3MB, alloc=420.3MB, time=30.23 memory used=7052.8MB, alloc=420.3MB, time=30.81 memory used=7423.0MB, alloc=420.3MB, time=31.43 memory used=7769.1MB, alloc=420.3MB, time=32.00 memory used=8106.1MB, alloc=420.3MB, time=32.47 memory used=8450.0MB, alloc=420.3MB, time=33.01 memory used=8797.1MB, alloc=420.3MB, time=33.59 memory used=9132.7MB, alloc=420.3MB, time=34.10 memory used=9473.4MB, alloc=420.3MB, time=34.68 memory used=9823.7MB, alloc=420.3MB, time=35.25 memory used=10153.6MB, alloc=420.3MB, time=35.81 memory used=10497.0MB, alloc=420.3MB, time=36.36 memory used=10830.6MB, alloc=420.3MB, time=36.87 memory used=11175.6MB, alloc=420.3MB, time=37.44 memory used=11511.7MB, alloc=420.3MB, time=38.01 memory used=11853.4MB, alloc=420.3MB, time=38.57 memory used=12189.0MB, alloc=420.3MB, time=39.12 memory used=12534.9MB, alloc=420.3MB, time=39.68 memory used=12869.4MB, alloc=420.3MB, time=40.28 memory used=13217.1MB, alloc=420.3MB, time=40.84 memory used=13546.6MB, alloc=420.3MB, time=41.37 memory used=13886.6MB, alloc=420.3MB, time=41.89 memory used=14229.8MB, alloc=420.3MB, time=42.50 memory used=14565.6MB, alloc=420.3MB, time=43.03 memory used=14912.0MB, alloc=420.3MB, time=43.58 memory used=15241.2MB, alloc=420.3MB, time=44.10 memory used=15581.6MB, alloc=420.3MB, time=44.63 memory used=15929.2MB, alloc=420.3MB, time=45.27 memory used=16260.9MB, alloc=420.3MB, time=45.81 memory used=16598.6MB, alloc=420.3MB, time=46.34 memory used=16949.2MB, alloc=420.3MB, time=46.88 memory used=17284.6MB, alloc=420.3MB, time=47.50 memory used=17623.0MB, alloc=420.3MB, time=48.05 memory used=17965.2MB, alloc=420.3MB, time=48.55 memory used=18308.1MB, alloc=420.3MB, time=49.12 memory used=18650.1MB, alloc=420.3MB, time=49.75 memory used=18990.4MB, alloc=420.3MB, time=50.32 memory used=19339.0MB, alloc=420.3MB, time=50.87 memory used=19670.7MB, alloc=420.3MB, time=51.39 memory used=20011.4MB, alloc=420.3MB, time=51.92 memory used=20350.1MB, alloc=420.3MB, time=52.45 memory used=20691.2MB, alloc=420.3MB, time=53.06 memory used=21032.4MB, alloc=420.3MB, time=53.61 memory used=21367.4MB, alloc=420.3MB, time=54.14 memory used=21707.4MB, alloc=420.3MB, time=54.68 memory used=22046.7MB, alloc=420.3MB, time=55.23 memory used=22388.2MB, alloc=420.3MB, time=55.85 memory used=22730.9MB, alloc=420.3MB, time=56.42 memory used=23063.8MB, alloc=420.3MB, time=56.95 memory used=23400.7MB, alloc=420.3MB, time=57.49 memory used=23740.0MB, alloc=420.3MB, time=58.04 memory used=24327.0MB, alloc=420.3MB, time=61.31 memory used=24464.8MB, alloc=420.3MB, time=74.15 memory used=24593.0MB, alloc=420.3MB, time=74.77 memory used=24729.4MB, alloc=420.3MB, time=75.74 memory used=24861.4MB, alloc=420.3MB, time=76.54 memory used=24987.9MB, alloc=444.3MB, time=77.96 memory used=25035.7MB, alloc=445.3MB, time=78.57 memory used=25036.7MB, alloc=446.3MB, time=78.68 memory used=25037.7MB, alloc=447.3MB, time=78.78 memory used=25038.7MB, alloc=448.3MB, time=78.89 memory used=25039.7MB, alloc=445.3MB, time=79.02 memory used=25444.8MB, alloc=444.3MB, time=102.01 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428536908 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 3 2 F := [10 x y z + 18 y z + 9 x y z, -6 x z - y z + 8 x y ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 4 2 2 G := [x y + 3 z + 11 x , 19 z - 6 x - y ] > Problem := [F,G]; 2 2 2 3 3 2 Problem := [[10 x y z + 18 y z + 9 x y z, -6 x z - y z + 8 x y ], 2 2 3 2 4 2 2 [x y + 3 z + 11 x , 19 z - 6 x - y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.5MB, alloc=32.3MB, time=0.49 memory used=47.7MB, alloc=32.3MB, time=0.80 memory used=68.2MB, alloc=60.3MB, time=1.08 memory used=111.7MB, alloc=68.3MB, time=1.69 memory used=154.2MB, alloc=68.3MB, time=2.19 memory used=198.2MB, alloc=68.3MB, time=2.75 memory used=238.9MB, alloc=92.3MB, time=3.34 memory used=305.5MB, alloc=92.3MB, time=4.14 memory used=347.4MB, alloc=92.3MB, time=4.48 memory used=409.8MB, alloc=92.3MB, time=5.16 memory used=479.0MB, alloc=116.3MB, time=5.95 memory used=548.8MB, alloc=116.3MB, time=7.01 memory used=621.3MB, alloc=372.3MB, time=7.97 memory used=713.3MB, alloc=372.3MB, time=9.23 memory used=787.5MB, alloc=372.3MB, time=9.98 memory used=834.9MB, alloc=372.3MB, time=10.88 memory used=879.8MB, alloc=372.3MB, time=11.53 memory used=930.2MB, alloc=372.3MB, time=11.78 memory used=967.0MB, alloc=372.3MB, time=11.90 memory used=1086.6MB, alloc=372.3MB, time=12.35 memory used=1153.5MB, alloc=372.3MB, time=12.51 memory used=1270.8MB, alloc=372.3MB, time=13.05 memory used=1323.0MB, alloc=396.3MB, time=13.73 memory used=1384.1MB, alloc=396.3MB, time=13.96 memory used=1449.4MB, alloc=396.3MB, time=14.76 memory used=1547.0MB, alloc=396.3MB, time=15.88 memory used=1662.5MB, alloc=396.3MB, time=17.07 memory used=1772.0MB, alloc=396.3MB, time=18.57 memory used=1880.3MB, alloc=420.3MB, time=19.72 memory used=2009.8MB, alloc=444.3MB, time=21.22 memory used=2142.2MB, alloc=444.3MB, time=22.70 memory used=2254.2MB, alloc=468.3MB, time=23.92 memory used=2382.3MB, alloc=468.3MB, time=25.38 memory used=2523.1MB, alloc=468.3MB, time=26.98 memory used=2621.8MB, alloc=468.3MB, time=28.16 memory used=2726.2MB, alloc=492.3MB, time=29.34 memory used=2846.1MB, alloc=492.3MB, time=30.40 memory used=2929.6MB, alloc=492.3MB, time=30.75 memory used=3022.8MB, alloc=492.3MB, time=31.07 memory used=3110.1MB, alloc=492.3MB, time=31.54 memory used=3224.2MB, alloc=492.3MB, time=34.58 memory used=3330.4MB, alloc=492.3MB, time=35.05 memory used=3439.8MB, alloc=492.3MB, time=36.65 memory used=3562.4MB, alloc=492.3MB, time=37.47 memory used=3685.0MB, alloc=492.3MB, time=39.26 memory used=3787.3MB, alloc=492.3MB, time=39.88 memory used=3882.8MB, alloc=492.3MB, time=40.23 memory used=3976.9MB, alloc=492.3MB, time=40.62 memory used=4115.1MB, alloc=492.3MB, time=44.54 memory used=4258.2MB, alloc=516.3MB, time=46.68 memory used=4456.3MB, alloc=516.3MB, time=47.66 memory used=4574.4MB, alloc=516.3MB, time=51.75 memory used=4679.8MB, alloc=516.3MB, time=52.17 memory used=4787.2MB, alloc=540.3MB, time=52.58 memory used=4879.3MB, alloc=540.3MB, time=52.99 memory used=4969.5MB, alloc=540.3MB, time=53.37 memory used=5066.9MB, alloc=540.3MB, time=53.75 memory used=5172.0MB, alloc=540.3MB, time=54.18 memory used=5283.1MB, alloc=540.3MB, time=54.59 memory used=5400.3MB, alloc=540.3MB, time=54.99 memory used=5529.5MB, alloc=540.3MB, time=55.40 memory used=5664.6MB, alloc=540.3MB, time=55.78 memory used=5797.7MB, alloc=540.3MB, time=56.16 memory used=5888.5MB, alloc=564.3MB, time=56.51 memory used=5977.4MB, alloc=564.3MB, time=56.83 memory used=6069.7MB, alloc=564.3MB, time=57.14 memory used=6159.2MB, alloc=564.3MB, time=57.47 memory used=6252.7MB, alloc=564.3MB, time=57.78 memory used=6347.8MB, alloc=564.3MB, time=58.12 memory used=6444.5MB, alloc=564.3MB, time=58.44 memory used=6542.8MB, alloc=564.3MB, time=58.78 memory used=6650.9MB, alloc=564.3MB, time=59.11 memory used=6760.6MB, alloc=564.3MB, time=59.45 memory used=6871.9MB, alloc=564.3MB, time=59.77 memory used=6984.7MB, alloc=564.3MB, time=60.11 memory used=7098.9MB, alloc=564.3MB, time=60.45 memory used=7214.7MB, alloc=564.3MB, time=60.79 memory used=7340.6MB, alloc=564.3MB, time=61.14 memory used=7467.9MB, alloc=564.3MB, time=61.50 memory used=7596.5MB, alloc=564.3MB, time=61.83 memory used=7726.5MB, alloc=564.3MB, time=62.18 memory used=7867.0MB, alloc=564.3MB, time=62.54 memory used=8008.6MB, alloc=564.3MB, time=62.90 memory used=8151.2MB, alloc=564.3MB, time=63.25 memory used=8295.1MB, alloc=564.3MB, time=63.60 memory used=8449.3MB, alloc=564.3MB, time=63.96 memory used=8604.4MB, alloc=564.3MB, time=64.30 memory used=8760.3MB, alloc=564.3MB, time=64.67 memory used=8927.0MB, alloc=564.3MB, time=65.05 memory used=9155.9MB, alloc=564.3MB, time=65.60 memory used=9295.5MB, alloc=564.3MB, time=66.00 memory used=9413.3MB, alloc=564.3MB, time=66.36 memory used=9537.3MB, alloc=564.3MB, time=66.73 memory used=9664.3MB, alloc=564.3MB, time=67.09 memory used=9791.1MB, alloc=564.3MB, time=67.44 memory used=9917.7MB, alloc=564.3MB, time=67.80 memory used=10044.2MB, alloc=564.3MB, time=68.17 memory used=10179.9MB, alloc=564.3MB, time=68.53 memory used=10315.1MB, alloc=564.3MB, time=68.90 memory used=10449.8MB, alloc=564.3MB, time=69.27 memory used=10593.3MB, alloc=564.3MB, time=69.64 memory used=10735.8MB, alloc=564.3MB, time=70.02 memory used=10877.6MB, alloc=564.3MB, time=70.40 memory used=11027.6MB, alloc=564.3MB, time=70.79 memory used=11176.1MB, alloc=564.3MB, time=71.18 memory used=11332.3MB, alloc=564.3MB, time=71.59 memory used=11486.7MB, alloc=564.3MB, time=72.01 memory used=11648.1MB, alloc=564.3MB, time=72.40 memory used=11815.7MB, alloc=564.3MB, time=72.78 memory used=11980.5MB, alloc=564.3MB, time=73.17 memory used=12150.4MB, alloc=564.3MB, time=73.56 memory used=12325.0MB, alloc=564.3MB, time=73.95 memory used=12503.3MB, alloc=564.3MB, time=74.34 memory used=12684.4MB, alloc=564.3MB, time=74.73 memory used=12873.6MB, alloc=564.3MB, time=75.15 memory used=13070.2MB, alloc=564.3MB, time=75.55 memory used=13270.6MB, alloc=564.3MB, time=75.96 memory used=13478.3MB, alloc=564.3MB, time=76.38 memory used=13694.1MB, alloc=564.3MB, time=76.81 memory used=13915.3MB, alloc=564.3MB, time=77.24 memory used=14140.0MB, alloc=564.3MB, time=77.67 memory used=14437.1MB, alloc=564.3MB, time=78.46 memory used=14620.8MB, alloc=588.3MB, time=130.67 memory used=14773.9MB, alloc=612.3MB, time=310.26 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428537208 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 3 2 2 2 F := [19 x y - 15 y z + 12 y z , 16 x z - 12 x y + 5 y z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [18 x y - 4 x z + 7 x, 3 x z + 9 x y z - 8 z] > Problem := [F,G]; 2 2 2 2 3 2 2 2 Problem := [[19 x y - 15 y z + 12 y z , 16 x z - 12 x y + 5 y z], 2 2 [18 x y - 4 x z + 7 x, 3 x z + 9 x y z - 8 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.4MB, alloc=32.3MB, time=0.49 memory used=47.6MB, alloc=32.3MB, time=0.80 memory used=67.2MB, alloc=56.3MB, time=1.11 memory used=108.6MB, alloc=60.3MB, time=1.72 memory used=148.4MB, alloc=60.3MB, time=2.32 memory used=189.0MB, alloc=92.3MB, time=2.96 memory used=251.8MB, alloc=92.3MB, time=3.90 memory used=312.7MB, alloc=92.3MB, time=4.84 memory used=375.2MB, alloc=116.3MB, time=5.79 memory used=457.9MB, alloc=116.3MB, time=7.05 memory used=533.0MB, alloc=396.3MB, time=8.22 memory used=640.5MB, alloc=420.3MB, time=9.96 memory used=774.3MB, alloc=444.3MB, time=12.14 memory used=927.8MB, alloc=468.3MB, time=14.55 memory used=1089.2MB, alloc=492.3MB, time=17.33 memory used=1262.3MB, alloc=516.3MB, time=20.41 memory used=1451.0MB, alloc=540.3MB, time=23.75 memory used=1642.8MB, alloc=564.3MB, time=26.97 memory used=1861.5MB, alloc=588.3MB, time=30.45 memory used=2024.6MB, alloc=612.3MB, time=33.41 memory used=2208.7MB, alloc=636.3MB, time=36.59 memory used=2381.9MB, alloc=660.3MB, time=39.71 memory used=2546.7MB, alloc=684.3MB, time=42.76 memory used=2717.3MB, alloc=708.3MB, time=45.71 memory used=2872.9MB, alloc=732.3MB, time=48.74 memory used=3152.5MB, alloc=756.3MB, time=57.36 memory used=3424.5MB, alloc=780.3MB, time=67.00 memory used=3703.3MB, alloc=804.3MB, time=77.44 memory used=3990.8MB, alloc=828.3MB, time=88.54 memory used=4288.8MB, alloc=852.3MB, time=100.23 memory used=4599.1MB, alloc=876.3MB, time=110.88 memory used=4923.2MB, alloc=900.3MB, time=122.27 memory used=5262.0MB, alloc=924.3MB, time=134.10 memory used=5610.2MB, alloc=948.3MB, time=147.07 memory used=5980.5MB, alloc=972.3MB, time=160.79 memory used=6374.7MB, alloc=996.3MB, time=178.37 memory used=6792.8MB, alloc=1020.3MB, time=195.72 memory used=7234.8MB, alloc=1044.3MB, time=213.94 memory used=7700.8MB, alloc=1068.3MB, time=233.01 memory used=8190.7MB, alloc=1092.3MB, time=253.02 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428537508 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [15 y z - 8 y + 12 z, -3 x y z + 15 x z + 5 x z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 4 2 2 G := [-4 x + 4 x z - 8 x, -9 z + 16 x y + 15 x z ] > Problem := [F,G]; 2 2 2 2 Problem := [[15 y z - 8 y + 12 z, -3 x y z + 15 x z + 5 x z], 4 2 2 4 2 2 [-4 x + 4 x z - 8 x, -9 z + 16 x y + 15 x z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=25.4MB, alloc=32.3MB, time=0.49 memory used=44.6MB, alloc=56.3MB, time=0.78 memory used=84.7MB, alloc=60.3MB, time=1.30 memory used=126.5MB, alloc=68.3MB, time=1.82 memory used=165.0MB, alloc=68.3MB, time=2.39 memory used=204.0MB, alloc=68.3MB, time=2.90 memory used=243.7MB, alloc=92.3MB, time=3.45 memory used=306.6MB, alloc=92.3MB, time=4.09 memory used=362.2MB, alloc=92.3MB, time=4.35 memory used=409.8MB, alloc=92.5MB, time=4.51 memory used=466.3MB, alloc=92.5MB, time=4.94 memory used=536.9MB, alloc=92.5MB, time=5.51 memory used=593.9MB, alloc=92.5MB, time=5.93 memory used=641.4MB, alloc=92.5MB, time=6.13 memory used=683.4MB, alloc=92.5MB, time=6.31 memory used=742.6MB, alloc=92.5MB, time=6.92 memory used=805.2MB, alloc=92.5MB, time=7.59 memory used=868.4MB, alloc=116.5MB, time=8.40 memory used=939.1MB, alloc=116.5MB, time=8.83 memory used=997.4MB, alloc=116.7MB, time=9.08 memory used=1046.9MB, alloc=116.7MB, time=9.31 memory used=1106.7MB, alloc=116.7MB, time=9.65 memory used=1169.8MB, alloc=116.7MB, time=9.98 memory used=1237.8MB, alloc=119.8MB, time=10.32 memory used=1279.8MB, alloc=119.8MB, time=10.46 memory used=1323.1MB, alloc=119.8MB, time=10.60 memory used=1382.2MB, alloc=119.8MB, time=10.84 memory used=1430.4MB, alloc=119.8MB, time=11.01 memory used=1500.5MB, alloc=119.8MB, time=11.68 memory used=1572.8MB, alloc=119.8MB, time=12.38 memory used=1640.5MB, alloc=375.8MB, time=13.36 memory used=1711.5MB, alloc=375.8MB, time=13.83 memory used=1794.6MB, alloc=375.8MB, time=14.59 memory used=1877.8MB, alloc=399.8MB, time=15.65 memory used=1979.3MB, alloc=399.8MB, time=16.96 memory used=2083.8MB, alloc=399.8MB, time=18.23 memory used=2172.2MB, alloc=399.8MB, time=18.83 memory used=2277.4MB, alloc=399.8MB, time=19.96 memory used=2388.2MB, alloc=399.8MB, time=22.13 memory used=2433.4MB, alloc=423.8MB, time=22.34 memory used=2500.1MB, alloc=423.8MB, time=22.55 memory used=2549.0MB, alloc=423.8MB, time=22.74 memory used=2608.6MB, alloc=423.8MB, time=22.93 memory used=2678.1MB, alloc=423.8MB, time=23.12 memory used=2880.1MB, alloc=423.8MB, time=23.66 memory used=3061.8MB, alloc=423.8MB, time=24.01 memory used=3255.9MB, alloc=423.8MB, time=24.65 memory used=3316.7MB, alloc=423.8MB, time=24.81 memory used=3401.1MB, alloc=423.8MB, time=25.65 memory used=3465.4MB, alloc=423.8MB, time=25.87 memory used=3611.9MB, alloc=423.8MB, time=27.40 memory used=3730.1MB, alloc=423.8MB, time=28.82 memory used=3850.4MB, alloc=423.8MB, time=30.42 memory used=3973.9MB, alloc=447.8MB, time=31.59 memory used=4116.0MB, alloc=447.8MB, time=33.31 memory used=4244.9MB, alloc=447.8MB, time=34.72 memory used=4311.3MB, alloc=447.8MB, time=34.97 memory used=4379.0MB, alloc=447.8MB, time=35.26 memory used=4451.3MB, alloc=447.8MB, time=35.62 memory used=4523.7MB, alloc=447.8MB, time=36.03 memory used=4592.1MB, alloc=447.8MB, time=36.32 memory used=4652.8MB, alloc=447.8MB, time=36.56 memory used=4714.5MB, alloc=447.8MB, time=36.80 memory used=4791.6MB, alloc=447.8MB, time=37.05 memory used=4971.5MB, alloc=447.8MB, time=37.45 memory used=5074.3MB, alloc=447.8MB, time=38.26 memory used=5150.1MB, alloc=447.8MB, time=38.97 memory used=5219.0MB, alloc=447.8MB, time=39.25 memory used=5273.1MB, alloc=447.8MB, time=39.47 memory used=5341.0MB, alloc=447.8MB, time=39.70 memory used=5564.6MB, alloc=447.8MB, time=40.14 memory used=5667.6MB, alloc=447.8MB, time=40.93 memory used=5745.8MB, alloc=447.8MB, time=41.65 memory used=5814.6MB, alloc=447.8MB, time=41.92 memory used=5869.1MB, alloc=447.8MB, time=42.14 memory used=5937.3MB, alloc=447.8MB, time=42.38 memory used=6160.7MB, alloc=447.8MB, time=42.82 memory used=6263.6MB, alloc=447.8MB, time=43.61 memory used=6336.6MB, alloc=447.8MB, time=44.26 memory used=6398.9MB, alloc=447.8MB, time=44.48 memory used=6480.0MB, alloc=447.8MB, time=44.97 memory used=6552.8MB, alloc=447.8MB, time=45.36 memory used=6623.1MB, alloc=447.8MB, time=45.68 memory used=6705.8MB, alloc=447.8MB, time=46.27 memory used=6773.9MB, alloc=447.8MB, time=46.55 memory used=6832.1MB, alloc=447.8MB, time=46.78 memory used=6891.6MB, alloc=447.8MB, time=47.01 memory used=6964.3MB, alloc=447.8MB, time=47.23 memory used=7168.7MB, alloc=447.8MB, time=47.66 memory used=7363.0MB, alloc=447.8MB, time=48.28 memory used=7427.4MB, alloc=447.8MB, time=48.53 memory used=7484.9MB, alloc=447.8MB, time=48.77 memory used=7554.5MB, alloc=447.8MB, time=49.02 memory used=7777.4MB, alloc=447.8MB, time=49.50 memory used=7990.4MB, alloc=447.8MB, time=50.51 memory used=8054.0MB, alloc=447.8MB, time=50.76 memory used=8111.4MB, alloc=447.8MB, time=50.98 memory used=8181.2MB, alloc=447.8MB, time=51.21 memory used=8397.2MB, alloc=447.8MB, time=51.63 memory used=8563.9MB, alloc=447.8MB, time=52.16 memory used=8627.5MB, alloc=447.8MB, time=52.41 memory used=8695.7MB, alloc=471.8MB, time=52.69 memory used=8760.3MB, alloc=471.8MB, time=52.92 memory used=8836.4MB, alloc=471.8MB, time=53.16 memory used=8925.5MB, alloc=471.8MB, time=53.39 memory used=9039.5MB, alloc=471.8MB, time=53.67 memory used=9182.6MB, alloc=471.8MB, time=54.04 memory used=9338.3MB, alloc=471.8MB, time=54.57 memory used=9424.7MB, alloc=471.8MB, time=54.87 memory used=9492.6MB, alloc=471.8MB, time=55.12 memory used=9574.5MB, alloc=471.8MB, time=55.38 memory used=9674.0MB, alloc=471.8MB, time=55.64 memory used=9851.7MB, alloc=471.8MB, time=56.38 memory used=9924.0MB, alloc=471.8MB, time=56.64 memory used=10060.0MB, alloc=471.8MB, time=57.10 memory used=10141.0MB, alloc=471.8MB, time=57.40 memory used=10227.7MB, alloc=471.8MB, time=57.68 memory used=10292.5MB, alloc=471.8MB, time=57.92 memory used=10369.2MB, alloc=471.8MB, time=58.18 memory used=10459.9MB, alloc=471.8MB, time=58.47 memory used=10701.9MB, alloc=471.8MB, time=58.96 memory used=10888.3MB, alloc=471.8MB, time=60.38 memory used=10957.9MB, alloc=471.8MB, time=60.68 memory used=11036.6MB, alloc=471.8MB, time=60.98 memory used=11131.4MB, alloc=471.8MB, time=61.32 memory used=11207.0MB, alloc=471.8MB, time=61.61 memory used=11264.2MB, alloc=471.8MB, time=61.86 memory used=11323.7MB, alloc=471.8MB, time=62.10 memory used=11386.8MB, alloc=471.8MB, time=62.33 memory used=11456.6MB, alloc=471.8MB, time=62.56 memory used=11530.1MB, alloc=471.8MB, time=62.80 memory used=11606.7MB, alloc=471.8MB, time=63.07 memory used=11686.7MB, alloc=471.8MB, time=63.34 memory used=11774.4MB, alloc=471.8MB, time=63.63 memory used=11865.7MB, alloc=471.8MB, time=63.92 memory used=11960.0MB, alloc=471.8MB, time=64.19 memory used=12063.4MB, alloc=471.8MB, time=64.45 memory used=12239.7MB, alloc=471.8MB, time=64.86 memory used=12372.3MB, alloc=471.8MB, time=65.21 memory used=12508.1MB, alloc=471.8MB, time=65.58 memory used=12654.5MB, alloc=471.8MB, time=65.96 memory used=12804.0MB, alloc=471.8MB, time=66.34 memory used=12964.0MB, alloc=471.8MB, time=66.73 memory used=13134.3MB, alloc=471.8MB, time=67.12 memory used=13308.1MB, alloc=471.8MB, time=67.52 memory used=13490.0MB, alloc=471.8MB, time=67.94 memory used=13682.6MB, alloc=471.8MB, time=68.36 memory used=13884.2MB, alloc=471.8MB, time=68.80 memory used=14094.5MB, alloc=471.8MB, time=69.23 memory used=14320.7MB, alloc=471.8MB, time=69.69 memory used=14553.9MB, alloc=471.8MB, time=70.15 memory used=14760.2MB, alloc=471.8MB, time=70.58 memory used=14929.2MB, alloc=471.8MB, time=70.96 memory used=15103.1MB, alloc=471.8MB, time=71.36 memory used=15280.9MB, alloc=471.8MB, time=71.73 memory used=15468.9MB, alloc=471.8MB, time=72.12 memory used=15664.6MB, alloc=471.8MB, time=72.52 memory used=15867.4MB, alloc=471.8MB, time=72.92 memory used=16081.3MB, alloc=471.8MB, time=73.31 memory used=16305.8MB, alloc=471.8MB, time=73.73 memory used=16640.8MB, alloc=471.8MB, time=75.54 memory used=16711.1MB, alloc=471.8MB, time=75.87 memory used=16790.7MB, alloc=471.8MB, time=76.21 memory used=16885.9MB, alloc=471.8MB, time=76.53 memory used=16961.4MB, alloc=471.8MB, time=76.82 memory used=17018.7MB, alloc=471.8MB, time=77.07 memory used=17078.2MB, alloc=471.8MB, time=77.31 memory used=17141.3MB, alloc=471.8MB, time=77.56 memory used=17211.0MB, alloc=471.8MB, time=77.81 memory used=17284.5MB, alloc=471.8MB, time=78.06 memory used=17361.1MB, alloc=471.8MB, time=78.34 memory used=17441.1MB, alloc=471.8MB, time=78.60 memory used=17528.9MB, alloc=471.8MB, time=78.86 memory used=17620.1MB, alloc=471.8MB, time=79.15 memory used=17714.3MB, alloc=471.8MB, time=79.43 memory used=17812.2MB, alloc=471.8MB, time=79.70 memory used=17994.1MB, alloc=471.8MB, time=80.13 memory used=18126.7MB, alloc=471.8MB, time=80.49 memory used=18262.5MB, alloc=471.8MB, time=80.86 memory used=18409.0MB, alloc=471.8MB, time=81.25 memory used=18558.5MB, alloc=471.8MB, time=81.63 memory used=18718.4MB, alloc=471.8MB, time=82.03 memory used=18888.8MB, alloc=471.8MB, time=82.45 memory used=19062.6MB, alloc=471.8MB, time=82.84 memory used=19244.4MB, alloc=471.8MB, time=83.25 memory used=19437.0MB, alloc=471.8MB, time=83.68 memory used=19638.7MB, alloc=471.8MB, time=84.11 memory used=19849.0MB, alloc=471.8MB, time=84.57 memory used=20075.1MB, alloc=471.8MB, time=85.00 memory used=20308.3MB, alloc=471.8MB, time=85.39 memory used=20514.7MB, alloc=471.8MB, time=85.79 memory used=20683.7MB, alloc=471.8MB, time=86.13 memory used=20857.5MB, alloc=471.8MB, time=86.48 memory used=21035.4MB, alloc=471.8MB, time=86.87 memory used=21223.4MB, alloc=471.8MB, time=87.28 memory used=21419.1MB, alloc=471.8MB, time=87.68 memory used=21621.8MB, alloc=471.8MB, time=88.08 memory used=21835.8MB, alloc=471.8MB, time=88.48 memory used=22060.3MB, alloc=471.8MB, time=88.90 memory used=22499.1MB, alloc=471.8MB, time=93.36 memory used=22576.9MB, alloc=471.8MB, time=93.67 memory used=22661.8MB, alloc=471.8MB, time=93.93 memory used=22724.0MB, alloc=471.8MB, time=94.16 memory used=22793.6MB, alloc=471.8MB, time=94.41 memory used=22872.4MB, alloc=471.8MB, time=94.68 memory used=22960.6MB, alloc=471.8MB, time=94.95 memory used=23058.4MB, alloc=471.8MB, time=95.22 memory used=23277.4MB, alloc=471.8MB, time=95.66 memory used=23420.8MB, alloc=471.8MB, time=96.01 memory used=23579.7MB, alloc=471.8MB, time=96.39 memory used=23753.7MB, alloc=471.8MB, time=96.77 memory used=23942.2MB, alloc=471.8MB, time=97.16 memory used=24149.1MB, alloc=471.8MB, time=97.56 memory used=24373.7MB, alloc=471.8MB, time=98.00 memory used=24601.4MB, alloc=471.8MB, time=98.39 memory used=24773.0MB, alloc=471.8MB, time=98.76 memory used=24958.2MB, alloc=471.8MB, time=99.13 memory used=25153.1MB, alloc=471.8MB, time=99.53 memory used=25363.8MB, alloc=471.8MB, time=99.92 memory used=25592.7MB, alloc=471.8MB, time=100.33 memory used=25819.2MB, alloc=471.8MB, time=100.74 memory used=25963.9MB, alloc=471.8MB, time=101.73 memory used=26040.5MB, alloc=471.8MB, time=101.98 memory used=26160.0MB, alloc=471.8MB, time=103.27 memory used=26233.5MB, alloc=471.8MB, time=103.61 memory used=26325.5MB, alloc=471.8MB, time=103.98 memory used=26398.6MB, alloc=495.8MB, time=104.29 memory used=26468.6MB, alloc=495.8MB, time=104.59 memory used=26546.8MB, alloc=495.8MB, time=104.88 memory used=26638.1MB, alloc=495.8MB, time=105.21 memory used=26737.3MB, alloc=495.8MB, time=105.58 memory used=26843.2MB, alloc=495.8MB, time=105.89 memory used=26955.6MB, alloc=495.8MB, time=106.26 memory used=27059.1MB, alloc=519.8MB, time=106.59 memory used=27128.6MB, alloc=519.8MB, time=106.84 memory used=27199.4MB, alloc=519.8MB, time=107.09 memory used=27273.7MB, alloc=519.8MB, time=107.35 memory used=27349.9MB, alloc=519.8MB, time=107.62 memory used=27427.8MB, alloc=519.8MB, time=107.90 memory used=27509.1MB, alloc=519.8MB, time=108.16 memory used=27600.3MB, alloc=519.8MB, time=108.43 memory used=27695.0MB, alloc=519.8MB, time=108.71 memory used=27791.6MB, alloc=519.8MB, time=109.00 memory used=27890.0MB, alloc=519.8MB, time=109.28 memory used=27990.2MB, alloc=519.8MB, time=109.59 memory used=28091.9MB, alloc=519.8MB, time=109.88 memory used=28197.3MB, alloc=519.8MB, time=110.18 memory used=28313.2MB, alloc=519.8MB, time=110.48 memory used=28432.7MB, alloc=519.8MB, time=110.80 memory used=28553.8MB, alloc=519.8MB, time=111.10 memory used=28676.3MB, alloc=519.8MB, time=111.42 memory used=28800.1MB, alloc=519.8MB, time=111.74 memory used=28928.7MB, alloc=519.8MB, time=112.02 memory used=29065.1MB, alloc=519.8MB, time=112.35 memory used=29295.3MB, alloc=519.8MB, time=112.85 memory used=29414.1MB, alloc=519.8MB, time=113.18 memory used=29527.9MB, alloc=519.8MB, time=113.51 memory used=29645.4MB, alloc=519.8MB, time=113.85 memory used=29770.5MB, alloc=519.8MB, time=114.20 memory used=29899.1MB, alloc=519.8MB, time=114.54 memory used=30027.8MB, alloc=519.8MB, time=114.88 memory used=30159.8MB, alloc=519.8MB, time=115.20 memory used=30298.9MB, alloc=519.8MB, time=115.53 memory used=30440.9MB, alloc=519.8MB, time=115.89 memory used=30585.6MB, alloc=519.8MB, time=116.27 memory 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used=35747.6MB, alloc=543.8MB, time=134.92 memory used=35889.1MB, alloc=543.8MB, time=135.27 memory used=36032.9MB, alloc=543.8MB, time=135.62 memory used=36179.0MB, alloc=543.8MB, time=135.97 memory used=36423.4MB, alloc=543.8MB, time=136.50 memory used=36537.6MB, alloc=543.8MB, time=136.84 memory used=36651.9MB, alloc=543.8MB, time=137.19 memory used=36767.4MB, alloc=543.8MB, time=137.52 memory used=36883.9MB, alloc=543.8MB, time=137.86 memory used=37001.5MB, alloc=543.8MB, time=138.20 memory used=37120.1MB, alloc=543.8MB, time=138.53 memory used=37239.7MB, alloc=543.8MB, time=138.88 memory used=37360.4MB, alloc=543.8MB, time=139.22 memory used=37481.9MB, alloc=543.8MB, time=139.55 memory used=37604.4MB, alloc=543.8MB, time=139.90 memory used=37727.9MB, alloc=543.8MB, time=140.23 memory used=37852.2MB, alloc=543.8MB, time=140.57 memory used=37977.4MB, alloc=543.8MB, time=140.92 memory used=38103.4MB, alloc=543.8MB, time=141.27 memory used=38230.2MB, alloc=543.8MB, time=141.62 memory 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used=48763.6MB, alloc=543.8MB, time=165.18 memory used=48969.3MB, alloc=543.8MB, time=165.54 memory used=49175.7MB, alloc=543.8MB, time=165.91 memory used=49386.7MB, alloc=543.8MB, time=166.29 memory used=49601.6MB, alloc=543.8MB, time=166.64 memory used=49819.2MB, alloc=543.8MB, time=167.06 memory used=50041.9MB, alloc=543.8MB, time=167.48 memory used=50275.8MB, alloc=543.8MB, time=167.91 memory used=50483.0MB, alloc=543.8MB, time=168.31 memory used=50675.1MB, alloc=543.8MB, time=168.68 memory used=50861.7MB, alloc=543.8MB, time=169.04 memory used=51044.7MB, alloc=543.8MB, time=169.43 memory used=51234.7MB, alloc=543.8MB, time=169.81 memory used=51428.6MB, alloc=543.8MB, time=170.18 memory used=51707.0MB, alloc=543.8MB, time=375.73 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428537808 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 4 2 2 3 F := [13 x y + 15 x y , -12 x + 11 x z - 5 y ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [10 x z - 2 y + 2 x, -13 x z - 19 x z + 5 y] > Problem := [F,G]; 3 3 4 2 2 3 Problem := [[13 x y + 15 x y , -12 x + 11 x z - 5 y ], 2 2 2 [10 x z - 2 y + 2 x, -13 x z - 19 x z + 5 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.0MB, alloc=32.3MB, time=0.49 memory used=45.2MB, alloc=56.3MB, time=0.76 memory used=85.4MB, alloc=60.3MB, time=1.20 memory used=128.1MB, alloc=68.3MB, time=1.79 memory used=171.2MB, alloc=92.3MB, time=2.36 memory used=240.6MB, alloc=92.3MB, time=3.22 memory used=307.4MB, alloc=92.3MB, time=4.02 memory used=364.1MB, alloc=92.3MB, time=4.60 memory used=436.7MB, alloc=92.3MB, time=5.33 memory used=490.2MB, alloc=92.3MB, time=5.85 memory used=557.4MB, alloc=116.3MB, time=6.70 memory used=617.0MB, alloc=116.3MB, time=7.49 memory used=691.8MB, alloc=116.3MB, time=8.19 memory used=764.7MB, alloc=116.3MB, time=8.88 memory used=835.6MB, alloc=116.3MB, time=9.47 memory used=930.2MB, alloc=116.3MB, time=10.53 memory used=1026.1MB, alloc=140.3MB, time=11.69 memory used=1124.0MB, alloc=140.3MB, time=12.92 memory used=1218.4MB, alloc=396.3MB, time=14.08 memory used=1313.0MB, alloc=420.3MB, time=15.64 memory used=1428.6MB, alloc=444.3MB, time=17.52 memory used=1574.1MB, alloc=444.3MB, time=19.58 memory used=1704.7MB, alloc=468.3MB, time=21.72 memory used=1853.4MB, alloc=492.3MB, time=24.12 memory used=2011.1MB, alloc=516.3MB, time=26.87 memory used=2181.9MB, alloc=540.3MB, time=30.86 memory used=2342.2MB, alloc=564.3MB, time=36.05 memory used=2512.9MB, alloc=588.3MB, time=41.77 memory used=2693.5MB, alloc=612.3MB, time=48.58 memory used=2890.4MB, alloc=636.3MB, time=56.29 memory used=3111.2MB, alloc=660.3MB, time=65.02 memory used=3356.0MB, alloc=684.3MB, time=74.68 memory used=3624.8MB, alloc=684.3MB, time=84.92 memory used=3893.5MB, alloc=684.3MB, time=94.70 memory used=4162.2MB, alloc=708.3MB, time=104.23 memory used=4454.8MB, alloc=708.3MB, time=114.64 memory used=4747.5MB, alloc=732.3MB, time=125.01 memory used=5064.1MB, alloc=756.3MB, time=135.92 N1 := 9869 > GB := Basis(F, plex(op(vars))); 3 3 4 2 6 4 2 2 3 GB := [13 x y + 15 x y , -169 x y + 225 y , -12 x + 11 x z - 5 y ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=5294.7MB, alloc=756.3MB, time=141.33 memory used=5417.0MB, alloc=756.3MB, time=143.15 memory used=5528.9MB, alloc=756.3MB, time=144.91 memory used=5629.4MB, alloc=756.3MB, time=146.56 memory used=5741.9MB, alloc=756.3MB, time=148.23 memory used=5850.9MB, alloc=756.3MB, time=149.59 memory used=5962.4MB, alloc=756.3MB, time=150.97 memory used=6053.7MB, alloc=756.3MB, time=152.66 memory used=6144.9MB, alloc=756.3MB, time=153.96 memory used=6257.6MB, alloc=756.3MB, time=155.20 memory used=6363.2MB, alloc=756.3MB, time=156.48 memory used=6482.8MB, alloc=756.3MB, time=158.18 memory used=6628.5MB, alloc=756.3MB, time=160.03 memory used=6754.3MB, alloc=756.3MB, time=161.91 memory used=6887.8MB, alloc=756.3MB, time=164.51 memory used=7021.0MB, alloc=756.3MB, time=166.90 memory used=7150.5MB, alloc=780.3MB, time=169.23 memory used=7278.4MB, alloc=804.3MB, time=171.72 memory used=7418.9MB, alloc=804.3MB, time=173.97 memory used=7553.6MB, alloc=828.3MB, time=176.48 memory used=7667.5MB, alloc=828.3MB, time=178.59 memory used=7789.3MB, alloc=828.3MB, time=180.93 memory used=7904.9MB, alloc=852.3MB, time=183.19 memory used=8012.5MB, alloc=852.3MB, time=185.34 memory used=8129.2MB, alloc=876.3MB, time=187.79 memory used=8232.3MB, alloc=900.3MB, time=189.96 memory used=8331.4MB, alloc=924.3MB, time=192.37 memory used=8555.5MB, alloc=948.3MB, time=199.45 memory used=9016.9MB, alloc=972.3MB, time=215.00 memory used=9477.9MB, alloc=996.3MB, time=230.91 memory used=9936.3MB, alloc=1020.3MB, time=247.93 memory used=10410.2MB, alloc=1044.3MB, time=265.81 memory used=10908.0MB, alloc=1068.3MB, time=284.58 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428538108 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 3 4 2 F := [-10 x + 5 x y z + 15 y z, 5 x y + 13 z - 2 x z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 3 3 2 G := [17 x y z - 8 z + 2 x y, -7 x z - 2 y z + 11 x z] > Problem := [F,G]; 4 2 3 4 2 Problem := [[-10 x + 5 x y z + 15 y z, 5 x y + 13 z - 2 x z ], 2 3 3 3 2 [17 x y z - 8 z + 2 x y, -7 x z - 2 y z + 11 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=25.5MB, alloc=32.3MB, time=0.47 memory used=48.1MB, alloc=37.0MB, time=0.74 memory used=59.8MB, alloc=37.0MB, time=0.78 memory used=75.3MB, alloc=37.0MB, time=0.87 memory used=95.2MB, alloc=61.0MB, time=1.15 memory used=141.2MB, alloc=61.2MB, time=1.46 memory used=165.8MB, alloc=61.2MB, time=1.52 memory used=207.6MB, alloc=61.6MB, time=1.91 memory used=234.4MB, alloc=61.6MB, time=1.98 memory used=258.6MB, alloc=61.6MB, time=2.04 memory used=289.3MB, alloc=61.6MB, time=2.10 memory used=309.4MB, alloc=61.6MB, time=2.15 memory used=352.4MB, alloc=61.6MB, time=2.54 memory used=397.4MB, alloc=69.6MB, time=3.09 memory used=438.5MB, alloc=69.6MB, time=3.44 memory used=471.4MB, alloc=69.6MB, time=3.61 memory used=502.8MB, alloc=69.6MB, time=3.76 memory used=536.3MB, alloc=69.6MB, time=3.94 memory used=579.0MB, alloc=69.6MB, time=4.15 memory used=608.3MB, alloc=69.6MB, time=4.24 memory used=628.8MB, alloc=69.6MB, time=4.30 memory used=652.1MB, alloc=69.6MB, time=4.37 memory used=689.8MB, alloc=69.6MB, time=4.57 memory used=725.6MB, alloc=69.6MB, time=4.68 memory used=749.7MB, alloc=69.6MB, time=4.76 memory used=771.1MB, alloc=69.6MB, time=4.84 memory used=805.9MB, alloc=69.6MB, time=5.84 memory used=861.8MB, alloc=69.6MB, time=10.65 memory used=900.7MB, alloc=69.6MB, time=10.88 memory used=920.2MB, alloc=69.6MB, time=10.96 memory used=945.1MB, alloc=69.6MB, time=11.03 memory used=968.5MB, alloc=69.6MB, time=11.10 memory used=985.6MB, alloc=69.6MB, time=11.16 memory used=1004.7MB, alloc=69.6MB, time=11.22 memory used=1026.8MB, alloc=69.6MB, time=11.28 memory used=1056.3MB, alloc=69.6MB, time=11.72 memory used=1091.4MB, alloc=93.6MB, time=12.63 memory used=1150.6MB, alloc=98.2MB, time=12.84 memory used=1203.4MB, alloc=98.2MB, time=13.02 memory used=1254.1MB, alloc=98.2MB, time=13.19 memory used=1304.4MB, alloc=98.2MB, time=13.35 memory used=1354.8MB, alloc=98.2MB, time=13.51 memory used=1403.1MB, alloc=98.2MB, time=13.66 memory used=1444.2MB, alloc=98.2MB, time=13.78 memory used=1469.0MB, alloc=98.2MB, time=13.88 memory used=1492.6MB, alloc=122.2MB, time=14.00 memory used=1529.6MB, alloc=122.2MB, time=14.16 memory used=1567.9MB, alloc=122.2MB, time=14.29 memory used=1610.7MB, alloc=122.2MB, time=14.43 memory used=1655.0MB, alloc=122.2MB, time=14.57 memory used=1700.2MB, alloc=122.2MB, time=14.72 memory used=1746.4MB, alloc=122.2MB, time=14.86 memory used=1793.5MB, alloc=122.2MB, time=15.02 memory used=1842.1MB, alloc=122.2MB, time=15.17 memory used=1896.0MB, alloc=122.2MB, time=15.32 memory used=1951.1MB, alloc=122.2MB, time=15.49 memory used=2007.1MB, alloc=122.2MB, time=15.64 memory used=2063.9MB, alloc=122.2MB, time=15.79 memory used=2122.2MB, alloc=122.2MB, time=15.97 memory used=2185.5MB, alloc=122.2MB, time=16.13 memory used=2243.2MB, alloc=122.2MB, time=16.28 memory used=2300.2MB, alloc=122.2MB, time=16.44 memory used=2359.9MB, alloc=122.2MB, time=16.59 memory used=2417.8MB, alloc=122.2MB, time=16.75 memory used=2458.3MB, alloc=122.2MB, time=16.87 memory used=2493.3MB, alloc=122.2MB, time=17.01 memory used=2528.8MB, alloc=122.2MB, time=17.14 memory used=2564.9MB, alloc=122.2MB, time=17.26 memory used=2601.1MB, alloc=122.2MB, time=17.39 memory used=2637.3MB, alloc=122.2MB, time=17.51 memory used=2673.6MB, alloc=122.2MB, time=17.63 memory used=2709.9MB, alloc=122.2MB, time=17.75 memory used=2746.2MB, alloc=122.2MB, time=17.87 memory used=2782.4MB, alloc=122.2MB, time=17.99 memory used=2818.8MB, alloc=122.2MB, time=18.11 memory used=2855.8MB, alloc=122.2MB, time=18.23 memory used=2897.4MB, alloc=122.2MB, time=18.35 memory used=2939.5MB, alloc=122.2MB, time=18.47 memory used=2981.5MB, alloc=122.2MB, time=18.58 memory used=3023.4MB, alloc=122.2MB, time=18.71 memory used=3065.1MB, alloc=122.2MB, time=18.83 memory used=3106.8MB, alloc=122.2MB, time=18.95 memory used=3149.4MB, alloc=122.2MB, time=19.07 memory used=3195.5MB, alloc=122.2MB, time=19.18 memory used=3242.2MB, alloc=122.2MB, time=19.30 memory used=3288.6MB, alloc=122.2MB, time=19.44 memory used=3335.5MB, alloc=122.2MB, time=19.55 memory used=3386.1MB, alloc=122.2MB, time=19.69 memory used=3436.7MB, alloc=122.2MB, time=19.82 memory used=3487.2MB, alloc=122.2MB, time=19.94 memory used=3542.0MB, alloc=122.2MB, time=20.05 memory used=3596.1MB, alloc=122.2MB, time=20.18 memory used=3650.2MB, alloc=122.2MB, time=20.30 memory used=3706.8MB, alloc=122.2MB, time=20.44 memory used=3764.1MB, alloc=122.2MB, time=20.56 memory used=3822.5MB, alloc=122.2MB, time=20.70 memory used=3869.5MB, alloc=122.2MB, time=20.81 memory used=3913.3MB, alloc=122.2MB, time=20.92 memory used=3957.3MB, alloc=122.2MB, time=21.02 memory used=4002.0MB, alloc=122.2MB, time=21.12 memory used=4047.7MB, alloc=122.2MB, time=21.22 memory used=4094.0MB, alloc=122.2MB, time=21.32 memory used=4141.5MB, alloc=122.2MB, time=21.42 memory used=4187.9MB, alloc=122.2MB, time=21.51 memory used=4233.9MB, alloc=122.2MB, time=21.61 memory used=4279.8MB, alloc=122.2MB, time=21.70 memory used=4323.6MB, alloc=122.2MB, time=21.78 memory used=4402.0MB, alloc=122.2MB, time=24.11 memory used=4483.5MB, alloc=122.2MB, time=25.67 memory used=4560.5MB, alloc=122.2MB, time=25.90 memory used=4631.3MB, alloc=122.2MB, time=26.10 memory used=4676.5MB, alloc=122.2MB, time=26.25 memory used=4717.0MB, alloc=122.2MB, time=26.40 memory used=4758.8MB, alloc=122.2MB, time=26.54 memory used=4799.6MB, alloc=122.2MB, time=26.68 memory used=4841.6MB, alloc=122.2MB, time=26.84 memory used=4884.9MB, alloc=122.2MB, time=27.00 memory used=4929.8MB, alloc=122.2MB, time=27.15 memory used=4980.3MB, alloc=122.2MB, time=27.31 memory used=5032.4MB, alloc=122.2MB, time=27.47 memory used=5085.9MB, alloc=122.2MB, time=27.61 memory used=5140.7MB, alloc=122.2MB, time=27.76 memory used=5196.8MB, alloc=122.2MB, time=27.90 memory used=5254.1MB, alloc=122.2MB, time=28.06 memory used=5312.7MB, alloc=122.2MB, time=28.21 memory used=5372.2MB, alloc=122.2MB, time=28.35 memory used=5433.3MB, alloc=122.2MB, time=28.52 memory used=5496.0MB, alloc=122.2MB, time=28.69 memory used=5563.0MB, alloc=122.2MB, time=28.85 memory used=5614.9MB, alloc=122.2MB, time=29.00 memory used=5653.9MB, alloc=122.2MB, time=29.12 memory used=5689.0MB, alloc=122.2MB, time=29.23 memory used=5720.7MB, alloc=122.2MB, time=29.34 memory used=5753.3MB, alloc=122.2MB, time=29.45 memory used=5786.5MB, alloc=122.2MB, time=29.56 memory used=5820.1MB, alloc=122.2MB, time=29.68 memory used=5853.9MB, alloc=122.2MB, time=29.80 memory used=5887.9MB, alloc=122.2MB, time=29.91 memory used=5922.2MB, alloc=122.2MB, time=30.03 memory used=5956.7MB, alloc=122.2MB, time=30.15 memory used=5991.4MB, alloc=122.2MB, time=30.27 memory used=6026.3MB, alloc=122.2MB, time=30.38 memory used=6061.4MB, alloc=122.2MB, time=30.49 memory used=6096.8MB, alloc=122.2MB, time=30.60 memory used=6132.3MB, alloc=122.2MB, time=30.71 memory used=6168.1MB, alloc=122.2MB, time=30.83 memory used=6204.0MB, alloc=122.2MB, time=30.95 memory used=6240.1MB, alloc=122.2MB, time=31.07 memory used=6276.4MB, alloc=122.2MB, time=31.19 memory used=6312.9MB, alloc=122.2MB, time=31.30 memory used=6349.6MB, alloc=122.2MB, time=31.41 memory used=6386.5MB, alloc=122.2MB, time=31.54 memory used=6424.1MB, alloc=122.2MB, time=31.68 memory used=6468.4MB, alloc=122.2MB, time=31.82 memory used=6513.3MB, alloc=122.2MB, time=31.96 memory used=6558.4MB, alloc=122.2MB, time=32.07 memory used=6603.7MB, alloc=122.2MB, time=32.19 memory used=6649.2MB, alloc=122.2MB, time=32.30 memory used=6695.0MB, alloc=122.2MB, time=32.40 memory used=6740.9MB, alloc=122.2MB, time=32.51 memory used=6787.0MB, alloc=122.2MB, time=32.65 memory used=6833.4MB, alloc=122.2MB, time=32.76 memory used=6879.8MB, alloc=122.2MB, time=32.87 memory used=6926.5MB, alloc=122.2MB, time=32.99 memory used=6973.3MB, alloc=122.2MB, time=33.11 memory used=7020.3MB, alloc=122.2MB, time=33.21 memory used=7067.4MB, alloc=122.2MB, time=33.32 memory used=7114.7MB, alloc=122.2MB, time=33.43 memory used=7162.1MB, alloc=122.2MB, time=33.54 memory used=7209.7MB, alloc=122.2MB, time=33.67 memory used=7257.4MB, alloc=122.2MB, time=33.80 memory used=7305.9MB, alloc=122.2MB, time=33.91 memory used=7361.4MB, alloc=122.2MB, time=34.03 memory used=7417.4MB, alloc=122.2MB, time=34.16 memory used=7473.6MB, alloc=122.2MB, time=34.28 memory used=7529.9MB, alloc=122.2MB, time=34.41 memory used=7586.3MB, alloc=122.2MB, time=34.53 memory used=7642.8MB, alloc=122.2MB, time=34.67 memory used=7696.7MB, alloc=122.2MB, time=34.80 memory used=7750.0MB, alloc=122.2MB, time=34.91 memory used=7798.5MB, alloc=122.2MB, time=35.03 memory used=7847.4MB, alloc=122.2MB, time=35.15 memory used=7903.3MB, alloc=122.2MB, time=35.29 memory used=7953.3MB, alloc=122.2MB, time=35.39 memory used=8008.9MB, alloc=122.2MB, time=35.50 memory used=8065.7MB, alloc=122.2MB, time=35.62 memory used=8122.5MB, alloc=122.2MB, time=35.73 memory used=8179.3MB, alloc=122.2MB, time=35.85 memory used=8236.0MB, alloc=122.2MB, time=35.97 memory used=8292.8MB, alloc=122.2MB, time=36.08 memory used=8349.5MB, alloc=122.2MB, time=36.20 memory used=8405.9MB, alloc=122.2MB, time=36.32 memory used=8449.5MB, alloc=122.2MB, time=36.43 memory used=8485.6MB, alloc=122.2MB, time=36.53 memory used=8514.7MB, alloc=122.2MB, time=36.61 memory used=8545.0MB, alloc=122.2MB, time=36.69 memory used=8576.3MB, alloc=122.2MB, time=36.77 memory used=8608.0MB, alloc=122.2MB, time=36.86 memory used=8640.0MB, alloc=122.2MB, time=36.94 memory used=8672.0MB, alloc=122.2MB, time=37.03 memory used=8703.9MB, alloc=122.2MB, time=37.11 memory used=8735.7MB, alloc=122.2MB, time=37.19 memory used=8767.6MB, alloc=122.2MB, time=37.27 memory used=8799.4MB, alloc=122.2MB, time=37.35 memory used=8831.1MB, alloc=122.2MB, time=37.43 memory used=8862.8MB, alloc=122.2MB, time=37.50 memory used=8894.4MB, alloc=122.2MB, time=37.58 memory used=8926.0MB, alloc=122.2MB, time=37.65 memory used=8957.6MB, alloc=122.2MB, time=37.73 memory used=8989.1MB, alloc=122.2MB, time=37.81 memory used=9020.5MB, alloc=122.2MB, time=37.88 memory used=9051.8MB, alloc=122.2MB, time=37.96 memory used=9083.1MB, alloc=122.2MB, time=38.04 memory used=9114.4MB, alloc=122.2MB, time=38.12 memory used=9145.5MB, alloc=122.2MB, time=38.19 memory used=9176.6MB, alloc=122.2MB, time=38.26 memory used=9207.7MB, alloc=122.2MB, time=38.34 memory used=9238.6MB, alloc=122.2MB, time=38.41 memory used=9269.5MB, alloc=122.2MB, time=38.49 memory used=9300.3MB, alloc=122.2MB, time=38.56 memory used=9331.1MB, alloc=122.2MB, time=38.64 memory used=9362.6MB, alloc=122.2MB, time=38.72 memory used=9400.2MB, alloc=122.2MB, time=38.80 memory used=9438.3MB, alloc=122.2MB, time=38.90 memory used=9476.2MB, alloc=122.2MB, time=38.98 memory used=9514.0MB, alloc=122.2MB, time=39.06 memory used=9551.7MB, alloc=122.2MB, time=39.14 memory used=9589.2MB, alloc=122.2MB, time=39.23 memory used=9626.5MB, alloc=122.2MB, time=39.31 memory used=9663.7MB, alloc=122.2MB, time=39.39 memory used=9700.7MB, alloc=122.2MB, time=39.47 memory used=9737.6MB, alloc=122.2MB, time=39.56 memory used=9774.3MB, alloc=122.2MB, time=39.63 memory used=9810.8MB, alloc=122.2MB, time=39.71 memory used=9847.1MB, alloc=122.2MB, time=39.80 memory used=9883.3MB, alloc=122.2MB, time=39.88 memory used=9919.4MB, alloc=122.2MB, time=39.96 memory used=9956.1MB, alloc=122.2MB, time=40.05 memory used=9998.2MB, alloc=122.2MB, time=40.14 memory used=10040.6MB, alloc=122.2MB, time=40.22 memory used=10082.7MB, alloc=122.2MB, time=40.31 memory used=10124.6MB, alloc=122.2MB, time=40.38 memory used=10166.1MB, alloc=122.2MB, time=40.47 memory used=10207.3MB, alloc=122.2MB, time=40.55 memory used=10248.2MB, alloc=122.2MB, time=40.63 memory used=10288.8MB, alloc=122.2MB, time=40.71 memory used=10330.0MB, alloc=122.2MB, time=40.79 memory used=10376.0MB, alloc=122.2MB, time=40.88 memory used=10422.1MB, alloc=122.2MB, time=40.97 memory used=10467.7MB, alloc=122.2MB, time=41.06 memory used=10512.8MB, alloc=122.2MB, time=41.14 memory used=10557.4MB, alloc=122.2MB, time=41.23 memory used=10601.6MB, alloc=122.2MB, time=41.31 memory used=10646.2MB, alloc=122.2MB, time=41.40 memory used=10694.6MB, alloc=122.2MB, time=41.49 memory used=10743.1MB, alloc=122.2MB, time=41.57 memory used=10790.8MB, alloc=122.2MB, time=41.66 memory used=10838.1MB, alloc=122.2MB, time=41.75 memory used=10889.9MB, alloc=122.2MB, time=41.84 memory used=10940.9MB, alloc=122.2MB, time=41.92 memory used=10991.0MB, alloc=122.2MB, time=42.01 memory used=11041.1MB, alloc=122.2MB, time=42.10 memory used=11093.3MB, alloc=122.2MB, time=42.21 memory used=11145.5MB, alloc=122.2MB, time=42.30 memory used=11200.9MB, alloc=122.2MB, time=42.40 memory used=11255.7MB, alloc=122.2MB, time=42.49 memory used=11312.1MB, alloc=122.2MB, time=42.58 memory used=11371.4MB, alloc=122.2MB, time=42.67 memory used=11432.3MB, alloc=122.2MB, time=42.76 memory used=11494.4MB, alloc=122.2MB, time=42.85 memory used=11548.9MB, alloc=131.8MB, time=42.95 memory used=11565.9MB, alloc=131.8MB, time=43.00 memory used=11584.1MB, alloc=131.8MB, time=43.06 memory used=11600.8MB, alloc=131.8MB, time=43.11 memory used=11616.5MB, alloc=131.8MB, time=43.17 memory used=11631.8MB, alloc=131.8MB, time=43.23 memory used=11647.7MB, alloc=131.8MB, time=43.29 memory used=11662.6MB, alloc=131.8MB, time=43.34 memory used=11676.7MB, alloc=131.8MB, time=43.39 memory used=11690.9MB, alloc=131.8MB, time=43.45 memory used=11704.3MB, alloc=131.8MB, time=43.49 memory used=11716.9MB, alloc=131.8MB, time=43.54 memory used=11729.4MB, alloc=131.8MB, time=43.59 memory used=11741.4MB, alloc=131.8MB, time=43.64 memory used=11752.4MB, alloc=131.8MB, time=43.69 memory used=11763.0MB, alloc=131.8MB, time=43.73 memory used=11773.6MB, alloc=131.8MB, time=43.78 memory used=11783.6MB, alloc=131.8MB, time=43.83 memory used=11793.6MB, alloc=131.8MB, time=43.87 memory used=11866.4MB, alloc=131.8MB, time=44.28 memory used=11906.4MB, alloc=131.8MB, time=44.54 memory used=11970.9MB, alloc=131.8MB, time=44.66 memory used=11986.5MB, alloc=131.8MB, time=44.73 memory used=12050.7MB, alloc=131.8MB, time=44.84 memory used=12071.3MB, alloc=131.8MB, time=46.07 memory used=12077.0MB, alloc=131.8MB, time=46.91 memory used=12091.8MB, alloc=131.8MB, time=47.98 memory used=12094.7MB, alloc=131.8MB, time=48.02 memory used=12094.7MB, alloc=387.8MB, time=48.05 memory used=12343.0MB, alloc=387.8MB, time=200.04 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428538408 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 3 2 F := [7 x z - 11 x z - 18 x, -5 x y - 14 z + 8 y ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 3 2 G := [-13 x z + 6 y z + 15 z, -9 y z + 15 x + y z] > Problem := [F,G]; 3 2 2 3 2 Problem := [[7 x z - 11 x z - 18 x, -5 x y - 14 z + 8 y ], 2 2 3 3 2 [-13 x z + 6 y z + 15 z, -9 y z + 15 x + y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.3MB, alloc=32.3MB, time=0.47 memory used=49.7MB, alloc=37.4MB, time=0.74 memory used=66.8MB, alloc=37.4MB, time=0.79 memory used=76.5MB, alloc=37.4MB, time=0.82 memory used=87.7MB, alloc=37.4MB, time=0.86 memory used=100.2MB, alloc=37.4MB, time=0.89 memory used=114.8MB, alloc=37.4MB, time=0.93 memory used=126.3MB, alloc=37.4MB, time=0.96 memory used=134.3MB, alloc=37.4MB, time=0.99 memory used=142.8MB, alloc=37.4MB, time=1.02 memory used=152.1MB, alloc=37.4MB, time=1.06 memory used=161.9MB, alloc=37.4MB, time=1.09 memory used=172.4MB, alloc=37.4MB, time=1.12 memory used=183.8MB, alloc=37.4MB, time=1.15 memory used=195.9MB, alloc=37.4MB, time=1.18 memory used=209.0MB, alloc=37.4MB, time=1.22 memory used=223.0MB, alloc=37.4MB, time=1.25 memory used=242.9MB, alloc=37.6MB, time=1.38 memory used=259.2MB, alloc=37.6MB, time=1.43 memory used=268.1MB, alloc=61.6MB, time=1.47 memory used=297.9MB, alloc=61.6MB, time=1.54 memory used=326.2MB, alloc=61.6MB, time=1.60 memory used=349.6MB, alloc=61.6MB, time=1.66 memory used=376.8MB, alloc=61.6MB, time=1.71 memory used=408.6MB, alloc=61.6MB, time=1.77 memory used=467.1MB, alloc=63.2MB, time=3.91 memory used=496.5MB, alloc=63.2MB, time=3.98 memory used=520.9MB, alloc=63.2MB, time=4.04 memory used=552.3MB, alloc=63.2MB, time=4.09 memory used=575.9MB, alloc=63.2MB, time=4.14 memory used=598.3MB, alloc=63.2MB, time=4.19 memory used=624.6MB, alloc=63.2MB, time=4.23 memory used=663.7MB, alloc=63.2MB, time=4.81 memory used=753.7MB, alloc=71.2MB, time=6.02 memory used=798.2MB, alloc=71.2MB, time=6.67 memory used=840.2MB, alloc=71.2MB, time=7.33 memory used=882.0MB, alloc=71.2MB, time=7.83 memory used=910.8MB, alloc=71.2MB, time=7.97 memory used=930.1MB, alloc=71.2MB, time=8.05 memory used=951.7MB, alloc=71.2MB, time=8.13 memory used=967.7MB, alloc=71.2MB, time=8.19 memory used=992.4MB, alloc=71.2MB, time=8.38 memory used=1020.6MB, alloc=71.2MB, time=8.57 memory used=1040.3MB, alloc=71.2MB, time=8.65 memory used=1064.2MB, alloc=71.2MB, time=8.74 memory used=1079.6MB, alloc=71.2MB, time=8.80 memory used=1100.0MB, alloc=71.2MB, time=8.92 memory used=1126.3MB, alloc=71.2MB, time=9.31 memory used=1156.0MB, alloc=71.2MB, time=10.01 memory used=1174.6MB, alloc=71.2MB, time=10.08 memory used=1193.6MB, alloc=71.2MB, time=10.15 memory used=1215.4MB, alloc=71.2MB, time=10.22 memory used=1230.4MB, alloc=71.2MB, time=10.28 memory used=1259.2MB, alloc=71.2MB, time=10.55 memory used=1281.9MB, alloc=71.2MB, time=10.68 memory used=1308.0MB, alloc=71.2MB, time=10.86 memory used=1327.3MB, alloc=71.2MB, time=10.94 memory used=1346.2MB, alloc=71.2MB, time=11.01 memory used=1379.7MB, alloc=95.2MB, time=12.51 memory used=1453.4MB, alloc=95.2MB, time=30.56 memory used=1501.9MB, alloc=95.2MB, time=42.62 memory used=1543.2MB, alloc=95.2MB, time=42.78 memory used=1578.9MB, alloc=95.2MB, time=42.89 memory used=1607.7MB, alloc=95.2MB, time=42.97 memory used=1641.4MB, alloc=95.2MB, time=43.06 memory used=1680.0MB, alloc=95.2MB, time=43.16 memory used=1723.5MB, alloc=95.2MB, time=43.26 memory used=1755.1MB, alloc=95.2MB, time=43.34 memory used=1778.5MB, alloc=95.2MB, time=43.41 memory used=1804.2MB, alloc=95.2MB, time=43.49 memory used=1830.7MB, alloc=95.2MB, time=43.56 memory used=1859.4MB, alloc=95.2MB, time=43.64 memory used=1888.9MB, alloc=95.2MB, time=43.72 memory used=1920.5MB, alloc=95.2MB, time=43.79 memory used=1952.8MB, alloc=95.2MB, time=43.87 memory used=1987.4MB, alloc=95.2MB, time=43.95 memory used=2022.5MB, alloc=95.2MB, time=44.04 memory used=2059.8MB, alloc=95.2MB, time=44.12 memory used=2099.2MB, alloc=95.2MB, time=44.19 memory used=2140.7MB, alloc=95.2MB, time=44.27 memory used=2184.1MB, alloc=95.2MB, time=44.34 memory used=2236.4MB, alloc=101.0MB, time=44.42 memory used=2244.9MB, alloc=107.8MB, time=44.47 memory used=2253.4MB, alloc=107.8MB, time=44.52 memory used=2262.3MB, alloc=107.8MB, time=44.57 memory used=2271.2MB, alloc=107.8MB, time=44.62 memory used=2280.0MB, alloc=107.8MB, time=44.66 memory used=2288.8MB, alloc=107.8MB, time=44.71 memory used=2297.6MB, alloc=107.8MB, time=44.76 memory used=2306.3MB, alloc=107.8MB, time=44.81 memory used=2315.3MB, alloc=107.8MB, time=44.85 memory used=2325.5MB, alloc=107.8MB, time=44.91 memory used=2335.8MB, alloc=107.8MB, time=44.95 memory used=2346.1MB, alloc=107.8MB, time=45.00 memory used=2356.3MB, alloc=107.8MB, time=45.05 memory used=2366.4MB, alloc=107.8MB, time=45.10 memory used=2376.5MB, alloc=107.8MB, time=45.15 memory used=2386.5MB, alloc=107.8MB, time=45.20 memory used=2396.7MB, alloc=107.8MB, time=45.26 memory used=2408.0MB, alloc=107.8MB, time=45.31 memory used=2419.3MB, alloc=107.8MB, time=45.38 memory used=2430.6MB, alloc=107.8MB, time=45.44 memory used=2441.7MB, alloc=107.8MB, time=45.50 memory used=2452.8MB, alloc=107.8MB, time=45.55 memory used=2464.0MB, alloc=107.8MB, time=45.61 memory used=2476.1MB, alloc=107.8MB, time=45.66 memory used=2488.2MB, alloc=107.8MB, time=45.72 memory used=2500.1MB, alloc=107.8MB, time=45.77 memory used=2512.1MB, alloc=107.8MB, time=45.83 memory used=2524.8MB, alloc=107.8MB, time=45.89 memory used=2537.4MB, alloc=107.8MB, time=45.94 memory used=2550.2MB, alloc=107.8MB, time=46.00 memory used=2563.3MB, alloc=107.8MB, time=46.05 memory used=2576.6MB, alloc=107.8MB, time=46.10 memory used=2590.3MB, alloc=107.8MB, time=46.15 memory used=2604.9MB, alloc=107.8MB, time=46.20 memory used=2619.2MB, alloc=107.8MB, time=46.26 memory used=2633.8MB, alloc=107.8MB, time=46.31 memory used=2649.3MB, alloc=107.8MB, time=46.36 memory used=2665.0MB, alloc=107.8MB, time=46.41 memory used=2681.2MB, alloc=107.8MB, time=46.46 memory used=2698.0MB, alloc=107.8MB, time=46.51 memory used=2753.4MB, alloc=107.8MB, time=46.90 memory used=2789.8MB, alloc=107.8MB, time=47.00 memory used=2829.5MB, alloc=107.8MB, time=47.10 memory used=2857.8MB, alloc=107.8MB, time=47.19 memory used=2890.3MB, alloc=107.8MB, time=47.30 memory used=2928.6MB, alloc=107.8MB, time=47.40 memory used=2968.8MB, alloc=107.8MB, time=47.68 memory used=2996.6MB, alloc=107.8MB, time=47.78 memory used=3024.2MB, alloc=107.8MB, time=47.85 memory used=3055.0MB, alloc=107.8MB, time=47.93 memory used=3086.6MB, alloc=107.8MB, time=48.03 memory used=3120.8MB, alloc=107.8MB, time=48.13 memory used=3157.6MB, alloc=107.8MB, time=48.23 memory used=3198.0MB, alloc=107.8MB, time=48.33 memory used=3232.4MB, alloc=107.8MB, time=48.51 memory used=3271.2MB, alloc=107.8MB, time=53.46 memory used=3271.6MB, alloc=363.8MB, time=53.50 memory used=3536.5MB, alloc=363.8MB, time=178.64 memory used=3665.9MB, alloc=363.8MB, time=386.38 memory used=3788.0MB, alloc=363.8MB, time=386.70 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428538708 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 3 F := [15 x y + 13 x y + 7 y , -13 z - 10 x z + 18 y z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 3 3 G := [-6 x y + 12 x + 6 x z, -4 x y + 13 x z - 3 x] > Problem := [F,G]; 2 2 2 3 3 Problem := [[15 x y + 13 x y + 7 y , -13 z - 10 x z + 18 y z], 2 2 3 2 3 3 [-6 x y + 12 x + 6 x z, -4 x y + 13 x z - 3 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=26.5MB, alloc=32.3MB, time=0.50 memory used=47.7MB, alloc=32.3MB, time=0.80 memory used=66.8MB, alloc=56.3MB, time=1.10 memory used=105.8MB, alloc=60.3MB, time=1.69 memory used=145.5MB, alloc=60.3MB, time=2.10 memory used=187.4MB, alloc=92.3MB, time=2.72 memory used=249.6MB, alloc=92.3MB, time=3.64 memory used=313.5MB, alloc=92.3MB, time=4.46 memory used=372.8MB, alloc=116.3MB, time=5.36 memory used=448.7MB, alloc=116.3MB, time=6.25 memory used=518.3MB, alloc=372.3MB, time=7.25 memory used=609.9MB, alloc=396.3MB, time=8.52 memory used=716.1MB, alloc=420.3MB, time=10.22 memory used=833.9MB, alloc=444.3MB, time=12.24 memory used=969.6MB, alloc=468.3MB, time=14.51 memory used=1116.7MB, alloc=492.3MB, time=17.09 memory used=1260.7MB, alloc=516.3MB, time=21.32 memory used=1410.4MB, alloc=540.3MB, time=26.30 memory used=1568.4MB, alloc=564.3MB, time=32.40 memory used=1747.4MB, alloc=588.3MB, time=39.40 memory used=1950.3MB, alloc=612.3MB, time=47.31 memory used=2177.1MB, alloc=612.3MB, time=56.15 memory used=2403.9MB, alloc=636.3MB, time=65.02 memory used=2654.8MB, alloc=636.3MB, time=74.75 memory used=2905.9MB, alloc=660.3MB, time=84.45 N1 := 7471 > GB := Basis(F, plex(op(vars))); 2 2 2 3 3 GB := [15 x y + 13 x y + 7 y , 13 z + 10 x z - 18 y z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=3094.7MB, alloc=660.3MB, time=87.92 memory used=3262.0MB, alloc=660.3MB, time=90.62 memory used=3396.4MB, alloc=660.3MB, time=92.60 memory used=3551.7MB, alloc=660.3MB, time=95.06 memory used=3761.2MB, alloc=660.3MB, time=98.97 memory used=3960.2MB, alloc=684.3MB, time=102.63 memory used=4253.6MB, alloc=708.3MB, time=111.49 memory used=4535.1MB, alloc=732.3MB, time=122.66 memory used=4831.7MB, alloc=756.3MB, time=133.34 memory used=5152.2MB, alloc=780.3MB, time=144.63 memory used=5496.8MB, alloc=804.3MB, time=156.29 N2 := 7471 > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 3 3 H := [15 x y + 13 x y + 7 y , -13 z - 10 x z + 18 y z, 2 2 3 2 3 3 -6 x y + 12 x + 6 x z, -4 x y + 13 x z - 3 x] > J:=[op(GB),op(G)]; 2 2 2 3 3 J := [15 x y + 13 x y + 7 y , 13 z + 10 x z - 18 y z, 2 2 3 2 3 3 -6 x y + 12 x + 6 x z, -4 x y + 13 x z - 3 x] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 11, 15, 4, 3, 3, 3, 1, 1, 3/4, 3/4, 1/2, 5/12, 4, 11, 15, 4, 3, 3, 3, 1, 1, 3/4, 3/4, 1/2, 5/12, 0, 0, 0] > save(F, G, cat("ranSet/34", convert(F, string),".txt")); > quit memory used=5841.5MB, alloc=804.3MB, time=166.90 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428538905 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 4 2 2 F := [-7 x y z - 11 y - 12 z , 19 x + x y z + 7 x y z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 G := [19 x y - 17 x y z - 6 x y, 16 x y z + 11 y z + 16 y] > Problem := [F,G]; 2 2 4 2 2 Problem := [[-7 x y z - 11 y - 12 z , 19 x + x y z + 7 x y z ], 3 2 3 [19 x y - 17 x y z - 6 x y, 16 x y z + 11 y z + 16 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=30.8MB, alloc=40.3MB, time=0.48 memory used=62.2MB, alloc=44.3MB, time=0.81 memory used=91.7MB, alloc=44.3MB, time=1.11 memory used=119.2MB, alloc=68.3MB, time=1.42 memory used=160.3MB, alloc=68.3MB, time=1.85 memory used=211.3MB, alloc=76.3MB, time=2.49 memory used=251.5MB, alloc=76.3MB, time=2.74 memory used=278.5MB, alloc=100.3MB, time=2.84 memory used=314.7MB, alloc=100.3MB, time=2.95 memory used=360.6MB, alloc=100.3MB, time=3.05 memory used=405.8MB, alloc=100.3MB, time=3.16 memory used=436.8MB, alloc=100.3MB, time=3.26 memory used=472.0MB, alloc=100.3MB, time=3.35 memory used=512.5MB, alloc=100.3MB, time=3.46 memory used=570.9MB, alloc=100.3MB, time=3.80 memory used=616.9MB, alloc=100.3MB, time=3.94 memory used=657.0MB, alloc=100.3MB, time=4.06 memory used=706.8MB, alloc=100.3MB, time=4.18 memory used=744.4MB, alloc=100.3MB, time=4.28 memory used=777.6MB, alloc=100.3MB, time=4.37 memory used=815.6MB, alloc=100.3MB, time=4.46 memory used=859.0MB, alloc=100.3MB, time=4.57 memory used=933.7MB, alloc=100.3MB, time=18.35 memory used=980.7MB, alloc=100.3MB, time=18.73 memory used=1027.4MB, alloc=100.3MB, time=18.83 memory used=1059.6MB, alloc=100.3MB, time=18.93 memory used=1096.7MB, alloc=100.3MB, time=19.02 memory used=1139.5MB, alloc=100.3MB, time=19.11 memory used=1189.3MB, alloc=100.3MB, time=19.21 memory used=1224.1MB, alloc=100.3MB, time=19.30 memory used=1253.8MB, alloc=100.3MB, time=19.38 memory used=1286.2MB, alloc=100.3MB, time=19.46 memory used=1320.6MB, alloc=100.3MB, time=19.53 memory used=1359.5MB, alloc=100.3MB, time=19.61 memory used=1415.4MB, alloc=100.3MB, time=19.93 memory used=1461.6MB, alloc=100.3MB, time=20.05 memory used=1500.9MB, alloc=100.3MB, time=20.17 memory used=1550.0MB, alloc=100.3MB, time=20.28 memory used=1589.7MB, alloc=100.3MB, time=20.38 memory used=1622.2MB, alloc=100.3MB, time=20.48 memory used=1659.1MB, alloc=100.3MB, time=20.57 memory used=1701.0MB, alloc=100.3MB, time=20.67 memory used=1762.2MB, alloc=100.3MB, time=21.00 memory used=1805.2MB, alloc=100.3MB, time=21.12 memory used=1845.0MB, alloc=100.3MB, time=21.24 memory used=1894.4MB, alloc=100.3MB, time=21.37 memory used=1931.9MB, alloc=100.3MB, time=21.48 memory used=1964.9MB, alloc=100.3MB, time=21.58 memory used=2001.7MB, alloc=100.3MB, time=21.69 memory used=2043.8MB, alloc=100.3MB, time=21.79 memory used=2093.8MB, alloc=100.3MB, time=30.50 memory used=2137.9MB, alloc=100.3MB, time=34.41 memory used=2178.1MB, alloc=100.3MB, time=34.53 memory used=2206.3MB, alloc=100.3MB, time=34.60 memory used=2236.4MB, alloc=100.3MB, time=34.67 memory used=2268.9MB, alloc=100.3MB, time=34.75 memory used=2302.6MB, alloc=100.3MB, time=34.83 memory used=2339.8MB, alloc=100.3MB, time=34.90 memory used=2386.0MB, alloc=100.3MB, time=35.17 memory used=2444.9MB, alloc=102.4MB, time=35.32 memory used=2479.4MB, alloc=102.4MB, time=35.43 memory used=2523.1MB, alloc=102.4MB, time=35.55 memory used=2570.0MB, alloc=102.4MB, time=35.66 memory used=2599.5MB, alloc=102.4MB, time=35.77 memory used=2632.5MB, alloc=102.4MB, time=35.88 memory used=2670.3MB, alloc=102.4MB, time=35.96 memory used=2722.5MB, alloc=102.4MB, time=36.30 memory used=2775.2MB, alloc=102.4MB, time=36.46 memory used=2810.7MB, alloc=102.4MB, time=36.56 memory used=2855.0MB, alloc=102.4MB, time=36.69 memory used=2899.7MB, alloc=102.4MB, time=36.81 memory used=2929.9MB, alloc=102.4MB, time=36.90 memory used=2963.7MB, alloc=102.4MB, time=37.00 memory used=3003.0MB, alloc=102.4MB, time=37.12 memory used=3061.1MB, alloc=102.4MB, time=40.40 memory used=3131.0MB, alloc=102.4MB, time=52.89 memory used=3171.1MB, alloc=102.4MB, time=53.01 memory used=3212.5MB, alloc=102.4MB, time=53.12 memory used=3245.1MB, alloc=102.4MB, time=53.22 memory used=3282.8MB, alloc=102.4MB, time=53.33 memory used=3326.2MB, alloc=102.4MB, time=53.44 memory used=3375.8MB, alloc=102.4MB, time=53.55 memory used=3404.8MB, alloc=102.4MB, time=53.63 memory used=3434.0MB, alloc=102.4MB, time=53.71 memory used=3465.4MB, alloc=102.4MB, time=53.78 memory used=3499.0MB, alloc=102.4MB, time=53.86 memory used=3536.7MB, alloc=102.4MB, time=53.94 memory used=3585.3MB, alloc=102.4MB, time=54.13 memory used=3667.5MB, alloc=102.4MB, time=56.30 memory used=3709.1MB, alloc=102.4MB, time=56.42 memory used=3744.2MB, alloc=102.4MB, time=56.53 memory used=3786.8MB, alloc=102.4MB, time=56.64 memory used=3854.6MB, alloc=102.4MB, time=57.25 memory used=3905.2MB, alloc=102.4MB, time=57.57 memory used=3988.6MB, alloc=102.4MB, time=58.32 memory used=4029.8MB, alloc=102.4MB, time=58.45 memory used=4066.1MB, alloc=102.4MB, time=58.57 memory used=4111.4MB, alloc=102.4MB, time=58.68 memory used=4142.7MB, alloc=102.4MB, time=58.77 memory used=4172.1MB, alloc=102.4MB, time=58.88 memory used=4204.7MB, alloc=102.4MB, time=58.99 memory used=4240.6MB, alloc=102.4MB, time=59.08 memory used=4280.5MB, alloc=102.4MB, time=59.18 memory used=4325.9MB, alloc=102.4MB, time=59.28 memory used=4358.6MB, alloc=102.4MB, time=59.36 memory used=4397.8MB, alloc=102.4MB, time=59.70 memory used=4444.9MB, alloc=102.4MB, time=59.84 memory used=4479.1MB, alloc=102.4MB, time=59.95 memory used=4523.1MB, alloc=102.4MB, time=60.06 memory used=4558.3MB, alloc=102.4MB, time=60.17 memory used=4586.9MB, alloc=102.4MB, time=60.27 memory used=4617.9MB, alloc=102.4MB, time=60.38 memory used=4652.3MB, alloc=102.4MB, time=60.48 memory used=4690.8MB, alloc=102.4MB, time=60.58 memory used=4734.2MB, alloc=102.4MB, time=60.68 memory used=4772.5MB, alloc=102.4MB, time=60.78 memory used=4800.2MB, alloc=102.4MB, time=60.86 memory used=4871.3MB, alloc=102.4MB, time=75.14 memory used=4914.4MB, alloc=102.4MB, time=75.77 memory used=4954.8MB, alloc=102.4MB, time=75.87 memory used=4984.5MB, alloc=102.4MB, time=75.97 memory used=5019.9MB, alloc=102.4MB, time=76.07 memory used=5060.6MB, alloc=102.4MB, time=76.15 memory used=5104.6MB, alloc=102.4MB, time=76.26 memory used=5130.4MB, alloc=102.4MB, time=76.33 memory used=5157.2MB, alloc=102.4MB, time=76.41 memory used=5186.1MB, alloc=102.4MB, time=76.49 memory used=5217.3MB, alloc=102.4MB, time=76.56 memory used=5250.5MB, alloc=102.4MB, time=76.64 memory used=5287.2MB, alloc=102.4MB, time=76.71 memory used=5326.2MB, alloc=102.4MB, time=76.78 memory used=5367.2MB, alloc=102.4MB, time=76.85 memory used=5419.8MB, alloc=115.8MB, time=76.96 memory used=5431.1MB, alloc=115.8MB, time=77.01 memory used=5485.2MB, alloc=115.8MB, time=77.30 memory used=5521.3MB, alloc=115.8MB, time=77.41 memory used=5547.0MB, alloc=115.8MB, time=77.58 memory used=5565.3MB, alloc=115.8MB, time=77.65 memory used=5606.5MB, alloc=115.8MB, time=77.75 memory used=5639.1MB, alloc=115.8MB, time=77.84 memory used=5657.4MB, alloc=115.8MB, time=77.91 memory used=5697.9MB, alloc=115.8MB, time=78.00 memory used=5747.9MB, alloc=115.8MB, time=78.46 memory used=5787.2MB, alloc=115.8MB, time=78.61 memory used=5824.9MB, alloc=115.8MB, time=78.73 memory used=5871.4MB, alloc=115.8MB, time=78.86 memory used=5901.0MB, alloc=115.8MB, time=78.95 memory used=5930.4MB, alloc=115.8MB, time=79.04 memory used=5962.5MB, alloc=115.8MB, time=79.16 memory used=5998.9MB, alloc=115.8MB, time=79.28 memory used=6038.6MB, alloc=115.8MB, time=79.37 memory used=6083.5MB, alloc=115.8MB, time=79.49 memory used=6118.9MB, alloc=115.8MB, time=79.58 memory used=6146.8MB, alloc=115.8MB, time=79.64 memory used=6204.4MB, alloc=115.8MB, time=80.07 memory used=6236.6MB, alloc=115.8MB, time=80.17 memory used=6276.5MB, alloc=115.8MB, time=80.29 memory used=6318.6MB, alloc=115.8MB, time=80.43 memory used=6345.8MB, alloc=115.8MB, time=80.53 memory used=6375.7MB, alloc=115.8MB, time=80.64 memory used=6409.1MB, alloc=115.8MB, time=80.76 memory used=6445.6MB, alloc=115.8MB, time=80.86 memory used=6486.1MB, alloc=115.8MB, time=80.96 memory used=6532.0MB, alloc=115.8MB, time=81.08 memory used=6561.4MB, alloc=115.8MB, time=81.16 memory used=6600.4MB, alloc=115.8MB, time=82.30 memory used=6664.2MB, alloc=115.8MB, time=97.64 memory used=6706.6MB, alloc=115.8MB, time=98.11 memory used=6746.3MB, alloc=115.8MB, time=98.22 memory used=6776.3MB, alloc=115.8MB, time=98.31 memory used=6812.0MB, alloc=115.8MB, time=98.42 memory used=6853.0MB, alloc=115.8MB, time=98.52 memory used=6898.0MB, alloc=115.8MB, time=98.63 memory used=6924.7MB, alloc=115.8MB, time=98.71 memory used=6951.4MB, alloc=115.8MB, time=98.79 memory used=6980.6MB, alloc=115.8MB, time=98.86 memory used=7011.1MB, alloc=115.8MB, time=98.95 memory used=7043.8MB, alloc=115.8MB, time=99.04 memory used=7079.6MB, alloc=115.8MB, time=99.13 memory used=7117.8MB, alloc=115.8MB, time=99.23 memory used=7157.4MB, alloc=115.8MB, time=99.31 memory used=7200.6MB, alloc=115.8MB, time=99.40 memory used=7240.0MB, alloc=115.8MB, time=99.48 memory used=7251.2MB, alloc=115.8MB, time=99.54 memory used=7262.9MB, alloc=115.8MB, time=99.59 memory used=7275.2MB, alloc=115.8MB, time=99.65 memory used=7330.7MB, alloc=115.8MB, time=100.03 memory used=7363.6MB, alloc=115.8MB, time=100.14 memory used=7405.1MB, alloc=115.8MB, time=100.26 memory used=7443.9MB, alloc=115.8MB, time=100.36 memory used=7471.6MB, alloc=115.8MB, time=100.47 memory used=7502.4MB, alloc=115.8MB, time=100.56 memory used=7536.5MB, alloc=115.8MB, time=100.66 memory used=7573.7MB, alloc=115.8MB, time=100.76 memory used=7615.5MB, alloc=115.8MB, time=100.87 memory used=7656.9MB, alloc=115.8MB, time=100.96 memory used=7684.0MB, alloc=115.8MB, time=101.03 memory used=7739.0MB, alloc=115.8MB, time=101.42 memory used=7773.0MB, alloc=115.8MB, time=101.53 memory used=7812.7MB, alloc=115.8MB, time=101.65 memory used=7856.4MB, alloc=115.8MB, time=101.76 memory used=7883.1MB, alloc=115.8MB, time=101.85 memory used=7913.4MB, alloc=115.8MB, time=101.95 memory used=7946.0MB, alloc=115.8MB, time=102.04 memory used=7983.1MB, alloc=115.8MB, time=102.15 memory used=8024.1MB, alloc=115.8MB, time=102.26 memory used=8068.4MB, alloc=115.8MB, time=102.36 memory used=8096.1MB, alloc=115.8MB, time=102.43 memory used=8151.7MB, alloc=115.8MB, time=109.34 memory used=8208.2MB, alloc=115.8MB, time=118.17 memory used=8247.3MB, alloc=115.8MB, time=118.29 memory used=8280.3MB, alloc=115.8MB, time=118.39 memory used=8313.2MB, alloc=115.8MB, time=118.49 memory used=8352.5MB, alloc=115.8MB, time=118.59 memory used=8398.2MB, alloc=115.8MB, time=118.69 memory used=8430.7MB, alloc=115.8MB, time=118.78 memory used=8457.1MB, alloc=115.8MB, time=118.86 memory used=8486.1MB, alloc=115.8MB, time=118.95 memory used=8517.5MB, alloc=115.8MB, time=119.03 memory used=8550.9MB, alloc=115.8MB, time=119.12 memory used=8587.0MB, alloc=115.8MB, time=119.20 memory used=8625.9MB, alloc=115.8MB, time=119.28 memory used=8666.9MB, alloc=115.8MB, time=119.37 memory used=8713.3MB, alloc=115.8MB, time=119.46 memory used=8732.5MB, alloc=115.8MB, time=119.53 memory used=8743.9MB, alloc=115.8MB, time=119.58 memory used=8814.1MB, alloc=115.8MB, time=120.08 memory used=8882.6MB, alloc=115.8MB, time=122.01 memory used=8918.1MB, alloc=115.8MB, time=122.11 memory used=8956.4MB, alloc=115.8MB, time=122.22 memory used=8992.6MB, alloc=115.8MB, time=122.31 memory used=9022.4MB, alloc=115.8MB, time=122.39 memory used=9095.2MB, alloc=115.8MB, time=123.12 memory used=9129.4MB, alloc=115.8MB, time=123.23 memory used=9190.1MB, alloc=115.8MB, time=123.63 memory used=9257.9MB, alloc=115.8MB, time=124.44 memory used=9327.0MB, alloc=139.8MB, time=125.23 memory used=9402.1MB, alloc=139.8MB, time=125.91 memory used=9464.5MB, alloc=139.8MB, time=126.62 memory used=9541.8MB, alloc=139.8MB, time=127.31 memory used=9607.1MB, alloc=395.8MB, time=128.11 memory used=9703.3MB, alloc=395.8MB, time=129.05 memory used=9768.9MB, alloc=395.8MB, time=129.62 memory used=9836.9MB, alloc=395.8MB, time=129.92 memory used=9898.5MB, alloc=395.8MB, time=130.59 memory used=9974.3MB, alloc=395.8MB, time=131.24 memory used=10066.2MB, alloc=395.8MB, time=132.28 memory used=10130.3MB, alloc=395.8MB, 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time=168.93 memory used=16121.0MB, alloc=515.8MB, time=169.23 memory used=16222.1MB, alloc=515.8MB, time=169.54 memory used=16334.8MB, alloc=515.8MB, time=169.87 memory used=16459.3MB, alloc=515.8MB, time=170.21 memory used=16567.6MB, alloc=515.8MB, time=170.52 memory used=16637.3MB, alloc=515.8MB, time=170.78 memory used=16705.1MB, alloc=515.8MB, time=171.02 memory used=16775.5MB, alloc=515.8MB, time=171.27 memory used=16852.8MB, alloc=515.8MB, time=171.52 memory used=16931.0MB, alloc=515.8MB, time=171.79 memory used=17010.1MB, alloc=515.8MB, time=172.06 memory used=17095.9MB, alloc=515.8MB, time=172.33 memory used=17182.5MB, alloc=515.8MB, time=172.59 memory used=17275.5MB, alloc=515.8MB, time=172.86 memory used=17368.9MB, alloc=515.8MB, time=173.11 memory used=17468.4MB, alloc=515.8MB, time=173.38 memory used=17573.8MB, alloc=515.8MB, time=173.69 memory used=17684.7MB, alloc=515.8MB, time=173.97 memory used=17800.6MB, alloc=515.8MB, time=174.25 memory used=17920.6MB, alloc=515.8MB, 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._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428539205 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 2 F := [10 x y + 20 z + 18 x , 10 y z + 11 x ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 3 2 G := [5 x z - 6 y z - 20, -14 x y - 13 x y z - 7 x] > Problem := [F,G]; 3 3 2 2 2 Problem := [[10 x y + 20 z + 18 x , 10 y z + 11 x ], 3 3 3 2 [5 x z - 6 y z - 20, -14 x y - 13 x y z - 7 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.19 memory used=25.2MB, alloc=36.3MB, time=0.50 memory used=47.6MB, alloc=61.8MB, time=0.71 memory used=80.4MB, alloc=61.8MB, time=0.79 memory used=112.9MB, alloc=61.8MB, time=0.87 memory used=139.4MB, alloc=61.8MB, time=0.93 memory used=164.5MB, alloc=61.8MB, time=0.99 memory used=194.7MB, alloc=61.8MB, time=1.05 memory used=240.2MB, alloc=61.8MB, time=1.30 memory used=269.7MB, alloc=61.8MB, time=1.38 memory used=303.7MB, alloc=61.8MB, time=1.45 memory used=327.7MB, alloc=61.8MB, time=1.50 memory used=353.1MB, alloc=61.8MB, time=1.56 memory used=383.0MB, alloc=61.8MB, time=1.61 memory used=436.5MB, alloc=61.8MB, time=5.92 memory used=478.5MB, alloc=62.3MB, time=7.88 memory used=508.9MB, alloc=62.3MB, time=7.95 memory used=533.8MB, alloc=62.3MB, time=8.00 memory used=563.9MB, alloc=62.3MB, time=8.05 memory used=599.7MB, alloc=62.3MB, time=8.13 memory used=622.7MB, alloc=62.3MB, time=8.18 memory used=644.6MB, alloc=62.3MB, time=8.22 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alloc=459.8MB, time=349.74 memory used=42701.3MB, alloc=483.8MB, time=349.97 memory used=42765.0MB, alloc=483.8MB, time=350.19 memory used=42838.5MB, alloc=483.8MB, time=350.42 memory used=42918.2MB, alloc=483.8MB, time=350.65 memory used=43003.8MB, alloc=483.8MB, time=350.89 memory used=43095.2MB, alloc=483.8MB, time=351.13 memory used=43192.3MB, alloc=483.8MB, time=351.39 memory used=43295.4MB, alloc=483.8MB, time=351.65 memory used=43526.7MB, alloc=483.8MB, time=352.13 memory used=43667.8MB, alloc=483.8MB, time=352.47 memory used=43815.1MB, alloc=483.8MB, time=352.82 memory used=43969.2MB, alloc=483.8MB, time=353.19 memory used=44137.8MB, alloc=483.8MB, time=353.59 memory used=44313.4MB, alloc=483.8MB, time=353.98 memory used=44495.5MB, alloc=483.8MB, time=354.38 memory used=44684.7MB, alloc=483.8MB, time=354.77 memory used=44888.0MB, alloc=483.8MB, time=355.19 memory used=45098.4MB, alloc=483.8MB, time=355.62 memory used=45325.0MB, alloc=483.8MB, time=356.06 memory used=45558.1MB, alloc=483.8MB, time=356.49 memory used=45797.2MB, alloc=483.8MB, time=356.91 memory used=45992.7MB, alloc=483.8MB, time=357.31 memory used=46165.5MB, alloc=483.8MB, time=357.67 memory used=46339.6MB, alloc=483.8MB, time=358.03 memory used=46516.0MB, alloc=483.8MB, time=358.39 memory used=46694.7MB, alloc=483.8MB, time=358.76 memory used=46886.9MB, alloc=483.8MB, time=359.14 memory used=47081.3MB, alloc=483.8MB, time=359.51 memory used=47277.9MB, alloc=483.8MB, time=359.90 memory used=47476.6MB, alloc=483.8MB, time=360.28 memory used=47688.9MB, alloc=483.8MB, time=360.68 memory used=47903.2MB, alloc=483.8MB, time=361.10 memory used=48119.4MB, alloc=483.8MB, time=361.51 memory used=48349.4MB, alloc=483.8MB, time=361.93 memory used=48580.9MB, alloc=483.8MB, time=362.35 memory used=48814.0MB, alloc=483.8MB, time=362.77 memory used=49060.6MB, alloc=483.8MB, time=363.21 memory used=49279.0MB, alloc=483.8MB, time=363.60 memory used=49463.6MB, alloc=483.8MB, time=363.96 memory used=49649.5MB, alloc=483.8MB, time=364.33 memory used=49837.1MB, alloc=483.8MB, time=364.70 memory used=50034.8MB, alloc=483.8MB, time=365.07 memory used=50233.9MB, alloc=483.8MB, time=365.46 memory used=50433.1MB, alloc=483.8MB, time=365.84 memory used=50644.8MB, alloc=483.8MB, time=366.24 memory used=50856.2MB, alloc=483.8MB, time=366.63 memory used=51067.4MB, alloc=483.8MB, time=367.02 memory used=51291.0MB, alloc=483.8MB, time=367.44 memory used=51513.7MB, alloc=483.8MB, time=367.83 memory used=51747.8MB, alloc=483.8MB, time=368.23 memory used=51980.7MB, alloc=483.8MB, time=368.65 memory used=52224.4MB, alloc=483.8MB, time=369.06 memory used=52466.6MB, alloc=483.8MB, time=369.47 memory used=52710.5MB, alloc=483.8MB, time=369.87 memory used=52916.5MB, alloc=483.8MB, time=370.22 memory used=53114.3MB, alloc=483.8MB, time=370.58 memory used=53323.9MB, alloc=483.8MB, time=370.95 memory used=53531.4MB, alloc=483.8MB, time=371.32 memory used=53747.9MB, alloc=483.8MB, time=371.69 memory used=53961.6MB, alloc=483.8MB, time=372.06 memory used=54183.5MB, alloc=483.8MB, time=372.45 memory used=54412.7MB, alloc=483.8MB, time=372.84 memory used=54639.0MB, alloc=483.8MB, time=373.23 memory used=54870.2MB, alloc=483.8MB, time=373.62 memory used=55106.5MB, alloc=483.8MB, time=374.01 memory used=55347.1MB, alloc=483.8MB, time=374.40 memory used=55597.9MB, alloc=483.8MB, time=374.82 memory used=55823.9MB, alloc=483.8MB, time=375.21 memory used=56041.1MB, alloc=483.8MB, time=375.59 memory used=56257.7MB, alloc=483.8MB, time=375.96 memory used=56481.5MB, alloc=483.8MB, time=376.34 memory used=56709.6MB, alloc=483.8MB, time=376.72 memory used=56945.7MB, alloc=483.8MB, time=377.11 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428539505 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 3 F := [15 x z + 7 x y + 12 x y, -4 x y z + 2 y z - 20 z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 2 3 3 G := [-11 x z + 16 y z - 17 x y, -3 x z - 3 y z - 11 x ] > Problem := [F,G]; 2 2 3 2 2 3 Problem := [[15 x z + 7 x y + 12 x y, -4 x y z + 2 y z - 20 z ], 2 2 3 2 2 2 3 3 [-11 x z + 16 y z - 17 x y, -3 x z - 3 y z - 11 x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=25.9MB, alloc=32.3MB, time=0.50 memory used=45.1MB, alloc=60.3MB, time=0.79 memory used=86.1MB, alloc=60.3MB, time=1.10 memory used=130.8MB, alloc=68.3MB, time=1.64 memory used=168.9MB, alloc=68.3MB, time=1.82 memory used=210.3MB, alloc=68.3MB, time=2.99 memory used=237.1MB, alloc=68.3MB, time=3.07 memory used=258.7MB, alloc=68.3MB, time=3.13 memory used=282.9MB, alloc=68.3MB, time=3.19 memory used=320.5MB, alloc=68.3MB, time=3.45 memory used=346.8MB, alloc=68.3MB, time=3.52 memory used=389.4MB, alloc=68.3MB, time=4.09 memory used=416.8MB, alloc=68.3MB, time=4.17 memory used=438.0MB, alloc=68.3MB, time=4.23 memory used=486.2MB, alloc=68.3MB, time=4.61 memory used=539.7MB, alloc=68.3MB, time=5.34 memory used=590.1MB, alloc=68.3MB, time=6.13 memory used=630.0MB, alloc=68.3MB, time=6.63 memory used=668.0MB, alloc=68.3MB, time=8.08 memory used=692.8MB, alloc=68.3MB, time=8.16 memory used=714.7MB, alloc=68.3MB, time=8.25 memory used=762.2MB, alloc=68.3MB, time=8.74 memory used=797.6MB, alloc=68.3MB, time=9.02 memory used=821.4MB, alloc=68.3MB, time=9.11 memory used=848.0MB, alloc=68.3MB, time=9.28 memory used=870.5MB, alloc=68.3MB, time=9.35 memory used=887.1MB, alloc=68.3MB, time=9.42 memory used=907.0MB, alloc=68.3MB, time=9.50 memory used=930.2MB, alloc=68.3MB, time=9.58 memory used=952.8MB, alloc=68.3MB, time=9.65 memory used=967.6MB, alloc=68.3MB, time=9.71 memory used=983.6MB, alloc=68.3MB, time=9.77 memory used=1002.1MB, alloc=68.3MB, time=9.82 memory used=1040.0MB, alloc=68.3MB, time=13.00 memory used=1090.9MB, alloc=68.3MB, time=13.33 memory used=1117.9MB, alloc=68.3MB, time=13.43 memory used=1139.4MB, alloc=68.3MB, time=13.50 memory used=1157.1MB, alloc=68.3MB, time=13.57 memory used=1178.4MB, alloc=68.3MB, time=13.65 memory used=1203.2MB, alloc=68.3MB, time=13.73 memory used=1227.3MB, alloc=68.3MB, time=13.79 memory used=1241.5MB, alloc=68.3MB, time=13.85 memory used=1256.5MB, alloc=92.3MB, time=13.92 memory used=1287.3MB, alloc=92.3MB, time=14.00 memory used=1321.4MB, alloc=92.3MB, time=14.08 memory used=1358.5MB, alloc=92.3MB, time=14.18 memory used=1400.2MB, alloc=92.3MB, time=14.28 memory used=1444.8MB, alloc=92.3MB, time=14.38 memory used=1494.8MB, alloc=92.3MB, time=14.47 memory used=1507.8MB, alloc=107.8MB, time=14.54 memory used=1517.3MB, alloc=107.8MB, time=14.59 memory used=1526.4MB, alloc=107.8MB, time=14.64 memory used=1535.7MB, alloc=107.8MB, time=14.70 memory used=1546.1MB, alloc=107.8MB, time=14.75 memory used=1556.6MB, alloc=107.8MB, time=14.81 memory used=1567.1MB, alloc=107.8MB, time=14.86 memory used=1577.6MB, alloc=107.8MB, time=14.91 memory used=1587.9MB, alloc=107.8MB, time=14.96 memory used=1598.4MB, alloc=107.8MB, time=15.02 memory used=1610.1MB, alloc=107.8MB, time=15.07 memory used=1621.7MB, alloc=107.8MB, time=15.12 memory used=1633.2MB, alloc=107.8MB, time=15.17 memory used=1644.9MB, alloc=107.8MB, time=15.22 memory used=1657.3MB, alloc=107.8MB, time=15.28 memory used=1669.7MB, alloc=107.8MB, time=15.33 memory used=1683.4MB, alloc=107.8MB, time=15.39 memory used=1696.7MB, alloc=107.8MB, time=15.44 memory used=1710.1MB, alloc=107.8MB, time=15.49 memory used=1723.8MB, alloc=107.8MB, time=15.55 memory used=1738.7MB, alloc=107.8MB, time=15.61 memory used=1753.3MB, alloc=107.8MB, time=15.67 memory used=1769.1MB, alloc=107.8MB, time=15.73 memory used=1785.5MB, alloc=107.8MB, time=15.79 memory used=1801.9MB, alloc=107.8MB, time=15.85 memory used=1819.1MB, alloc=107.8MB, time=15.91 memory used=1837.2MB, alloc=107.8MB, time=15.96 memory used=1893.1MB, alloc=107.8MB, time=16.27 memory used=1930.4MB, alloc=107.8MB, time=16.39 memory used=1993.7MB, alloc=107.8MB, time=16.90 memory used=2030.6MB, alloc=107.8MB, time=17.00 memory used=2079.2MB, alloc=107.8MB, time=18.66 memory used=2147.2MB, alloc=107.8MB, time=26.31 memory used=2208.6MB, alloc=107.8MB, time=26.61 memory used=2244.8MB, alloc=107.8MB, time=26.72 memory used=2280.5MB, alloc=107.8MB, time=26.83 memory used=2324.3MB, alloc=107.8MB, time=26.94 memory used=2358.4MB, alloc=107.8MB, time=27.04 memory used=2385.2MB, alloc=107.8MB, time=27.12 memory used=2413.9MB, alloc=107.8MB, time=27.20 memory used=2445.7MB, alloc=107.8MB, time=27.29 memory used=2479.0MB, alloc=107.8MB, time=27.38 memory used=2515.4MB, alloc=107.8MB, time=27.47 memory used=2555.2MB, alloc=107.8MB, time=27.56 memory used=2596.2MB, alloc=107.8MB, time=27.66 memory used=2640.4MB, alloc=107.8MB, time=27.76 memory used=2687.8MB, alloc=107.8MB, time=27.86 memory used=2714.0MB, alloc=107.8MB, time=27.94 memory used=2721.7MB, alloc=107.8MB, time=27.99 memory used=2730.2MB, alloc=107.8MB, time=28.03 memory used=2738.7MB, alloc=107.8MB, time=28.08 memory used=2747.3MB, alloc=107.8MB, time=28.13 memory used=2755.8MB, alloc=107.8MB, time=28.18 memory used=2764.4MB, alloc=107.8MB, time=28.23 memory used=2773.0MB, alloc=107.8MB, time=28.28 memory used=2781.6MB, alloc=107.8MB, time=28.33 memory used=2790.2MB, alloc=107.8MB, time=28.38 memory used=2798.8MB, alloc=107.8MB, time=28.44 memory used=2807.5MB, alloc=107.8MB, time=28.48 memory used=2816.1MB, alloc=107.8MB, time=28.53 memory used=2824.9MB, alloc=107.8MB, time=28.59 memory used=2835.5MB, alloc=107.8MB, time=28.64 memory used=2846.3MB, alloc=107.8MB, time=28.69 memory used=2857.1MB, alloc=107.8MB, time=28.75 memory used=2867.9MB, alloc=107.8MB, time=28.80 memory used=2878.7MB, alloc=107.8MB, time=28.85 memory used=2889.5MB, alloc=107.8MB, time=28.91 memory used=2900.3MB, alloc=107.8MB, time=28.96 memory used=2911.1MB, alloc=107.8MB, time=29.01 memory used=2921.8MB, alloc=107.8MB, time=29.07 memory used=2932.6MB, alloc=107.8MB, time=29.12 memory used=2943.3MB, alloc=107.8MB, time=29.18 memory used=2954.0MB, alloc=107.8MB, time=29.23 memory used=2964.7MB, alloc=107.8MB, time=29.28 memory used=2975.5MB, alloc=107.8MB, time=29.34 memory used=2988.1MB, alloc=107.8MB, time=29.40 memory used=3000.8MB, alloc=107.8MB, time=29.46 memory used=3013.4MB, alloc=107.8MB, time=29.52 memory used=3026.0MB, alloc=107.8MB, time=29.57 memory used=3038.5MB, alloc=107.8MB, time=29.62 memory used=3051.0MB, alloc=107.8MB, time=29.67 memory used=3063.4MB, alloc=107.8MB, time=29.73 memory used=3075.7MB, alloc=107.8MB, time=29.79 memory used=3088.3MB, alloc=107.8MB, time=29.85 memory used=3102.2MB, alloc=107.8MB, time=29.90 memory used=3116.2MB, alloc=107.8MB, time=29.96 memory used=3130.2MB, alloc=107.8MB, time=30.01 memory used=3144.0MB, alloc=107.8MB, time=30.07 memory used=3157.7MB, alloc=107.8MB, time=30.13 memory used=3173.3MB, alloc=107.8MB, time=30.18 memory used=3188.6MB, alloc=107.8MB, time=30.23 memory used=3203.7MB, alloc=107.8MB, time=30.29 memory used=3218.8MB, alloc=107.8MB, time=30.34 memory used=3235.0MB, alloc=107.8MB, time=30.40 memory used=3251.1MB, alloc=107.8MB, time=30.46 memory used=3267.2MB, alloc=107.8MB, time=30.52 memory used=3284.1MB, alloc=107.8MB, time=30.58 memory used=3300.9MB, alloc=107.8MB, time=30.64 memory used=3318.8MB, alloc=107.8MB, time=30.70 memory used=3336.5MB, alloc=107.8MB, time=30.76 memory used=3354.7MB, alloc=107.8MB, time=30.82 memory used=3373.6MB, alloc=107.8MB, time=30.88 memory used=3393.0MB, alloc=107.8MB, time=30.94 memory used=3413.5MB, alloc=107.8MB, time=31.01 memory used=3429.9MB, alloc=107.8MB, time=31.06 memory used=3443.8MB, alloc=107.8MB, time=31.11 memory used=3458.0MB, alloc=107.8MB, time=31.16 memory used=3472.8MB, alloc=107.8MB, time=31.22 memory used=3520.2MB, alloc=107.8MB, time=31.52 memory used=3559.5MB, alloc=107.8MB, time=31.74 memory used=3643.3MB, alloc=107.8MB, time=32.45 memory used=3706.9MB, alloc=107.8MB, time=33.83 memory used=3753.9MB, alloc=107.8MB, time=35.92 memory used=3786.3MB, alloc=107.8MB, time=36.00 memory used=3828.0MB, alloc=107.8MB, time=36.12 memory used=3854.7MB, alloc=107.8MB, time=36.19 memory used=3884.6MB, alloc=107.8MB, time=36.26 memory used=3921.0MB, alloc=107.8MB, time=36.33 memory used=3964.9MB, alloc=107.8MB, time=36.57 memory used=4014.7MB, alloc=107.8MB, time=36.95 memory used=4067.8MB, alloc=107.8MB, time=37.98 memory used=4100.1MB, alloc=107.8MB, time=38.08 memory used=4133.3MB, alloc=107.8MB, time=38.16 memory used=4168.8MB, alloc=107.8MB, time=38.32 memory used=4230.9MB, alloc=107.8MB, time=38.87 memory used=4291.2MB, alloc=107.8MB, time=39.69 memory used=4345.5MB, alloc=107.8MB, time=40.33 memory used=4400.3MB, alloc=363.8MB, time=40.98 memory used=4445.7MB, alloc=363.8MB, time=41.27 memory used=4488.9MB, alloc=387.8MB, time=41.99 memory used=4540.7MB, alloc=387.8MB, time=42.19 memory used=4595.1MB, alloc=387.8MB, time=42.42 memory used=4651.3MB, alloc=387.8MB, time=44.41 memory used=4733.2MB, alloc=387.8MB, time=45.25 memory used=4816.4MB, alloc=387.8MB, time=45.98 memory used=4907.9MB, alloc=387.8MB, time=46.99 memory used=4985.2MB, alloc=411.8MB, time=47.63 memory used=5102.0MB, alloc=411.8MB, time=48.90 memory used=5222.9MB, alloc=411.8MB, time=50.10 memory used=5331.6MB, alloc=435.8MB, time=51.02 memory used=5434.4MB, alloc=435.8MB, time=51.79 memory used=5521.0MB, alloc=435.8MB, time=52.35 memory used=5603.9MB, alloc=435.8MB, time=52.77 memory used=5666.4MB, alloc=435.8MB, time=53.00 memory used=5741.5MB, alloc=435.8MB, time=53.25 memory used=5790.0MB, alloc=435.8MB, time=53.45 memory used=5844.4MB, alloc=435.8MB, time=53.66 memory used=5909.8MB, alloc=435.8MB, time=53.85 memory used=6015.3MB, alloc=435.8MB, time=64.50 memory used=6076.9MB, alloc=435.8MB, time=64.72 memory used=6135.4MB, alloc=435.8MB, time=64.93 memory used=6204.8MB, alloc=435.8MB, time=65.13 memory used=6249.8MB, alloc=435.8MB, time=65.29 memory used=6301.6MB, alloc=435.8MB, time=65.45 memory used=6370.1MB, alloc=435.8MB, time=65.81 memory used=6460.5MB, alloc=435.8MB, time=66.53 memory used=6519.1MB, alloc=435.8MB, time=66.79 memory used=6580.1MB, alloc=435.8MB, time=67.02 memory used=6653.7MB, alloc=435.8MB, time=67.26 memory used=6707.1MB, alloc=435.8MB, time=67.47 memory used=6752.3MB, alloc=435.8MB, time=67.69 memory used=6800.6MB, alloc=435.8MB, time=67.88 memory used=6852.5MB, alloc=435.8MB, time=68.08 memory used=6909.0MB, alloc=435.8MB, time=68.28 memory used=6970.4MB, alloc=435.8MB, time=68.51 memory used=7037.9MB, alloc=435.8MB, time=68.73 memory used=7112.0MB, alloc=435.8MB, time=68.95 memory used=7162.6MB, alloc=435.8MB, time=69.12 memory used=7204.5MB, alloc=435.8MB, time=69.28 memory used=7249.5MB, alloc=435.8MB, time=69.43 memory used=7299.0MB, alloc=435.8MB, time=69.59 memory used=7396.5MB, alloc=435.8MB, time=70.33 memory used=7448.9MB, alloc=435.8MB, time=70.56 memory used=7514.6MB, alloc=435.8MB, time=70.80 memory used=7591.6MB, alloc=435.8MB, time=71.04 memory used=7635.2MB, alloc=435.8MB, time=71.25 memory used=7682.2MB, alloc=435.8MB, time=71.46 memory used=7733.3MB, alloc=435.8MB, time=71.66 memory used=7787.5MB, alloc=435.8MB, time=71.88 memory used=7846.8MB, alloc=435.8MB, time=72.10 memory used=7912.7MB, alloc=435.8MB, time=72.30 memory used=7984.1MB, alloc=435.8MB, time=72.52 memory used=8055.5MB, alloc=435.8MB, time=72.73 memory used=8096.1MB, alloc=435.8MB, time=72.90 memory used=8139.7MB, alloc=435.8MB, time=73.05 memory used=8187.1MB, alloc=435.8MB, time=73.21 memory used=8270.5MB, alloc=435.8MB, time=86.54 memory used=8361.6MB, alloc=435.8MB, time=113.99 memory used=8429.1MB, alloc=435.8MB, time=114.24 memory used=8484.8MB, alloc=435.8MB, time=114.47 memory used=8539.8MB, alloc=435.8MB, time=114.69 memory used=8605.2MB, alloc=435.8MB, time=114.90 memory used=8678.5MB, alloc=435.8MB, time=115.12 memory used=8720.8MB, alloc=435.8MB, time=115.28 memory used=8766.1MB, alloc=435.8MB, time=115.45 memory used=8815.3MB, alloc=435.8MB, time=115.62 memory used=8868.1MB, alloc=435.8MB, time=115.79 memory used=8926.0MB, alloc=435.8MB, time=115.97 memory used=8988.6MB, alloc=435.8MB, time=116.14 memory used=9056.3MB, alloc=435.8MB, time=116.32 memory used=9171.5MB, alloc=435.8MB, time=116.71 memory used=9261.7MB, alloc=435.8MB, time=121.56 memory used=9351.5MB, alloc=435.8MB, time=122.36 memory used=9407.7MB, alloc=435.8MB, time=122.55 memory used=9468.2MB, alloc=435.8MB, time=122.73 memory used=9538.9MB, alloc=435.8MB, time=123.02 memory used=9627.9MB, alloc=435.8MB, time=124.23 memory used=9693.7MB, alloc=435.8MB, time=124.50 memory used=9789.2MB, alloc=435.8MB, time=125.80 memory used=9848.9MB, alloc=435.8MB, time=126.01 memory used=9944.7MB, alloc=435.8MB, time=127.19 memory used=10016.5MB, alloc=435.8MB, time=127.46 memory used=10066.2MB, alloc=435.8MB, time=127.69 memory used=10122.9MB, alloc=459.8MB, time=127.93 memory used=10206.8MB, alloc=459.8MB, time=128.22 memory used=10305.4MB, alloc=459.8MB, time=128.53 memory used=10369.0MB, alloc=459.8MB, time=128.77 memory used=10423.5MB, alloc=459.8MB, time=128.99 memory used=10482.4MB, alloc=459.8MB, time=129.22 memory used=10543.0MB, alloc=459.8MB, time=129.44 memory used=10605.6MB, alloc=459.8MB, time=129.66 memory used=10673.0MB, alloc=459.8MB, time=129.89 memory used=10746.3MB, alloc=459.8MB, time=130.13 memory used=10820.8MB, alloc=459.8MB, time=130.38 memory used=10900.8MB, alloc=459.8MB, time=130.63 memory used=10985.9MB, alloc=459.8MB, time=130.86 memory used=11075.9MB, alloc=459.8MB, time=131.10 memory used=11170.5MB, alloc=459.8MB, time=131.35 memory used=11249.1MB, alloc=459.8MB, time=131.57 memory used=11297.8MB, alloc=459.8MB, time=131.75 memory used=11348.9MB, alloc=459.8MB, time=131.94 memory used=11399.7MB, alloc=459.8MB, time=132.13 memory used=11453.8MB, alloc=459.8MB, time=132.31 memory used=11507.2MB, alloc=459.8MB, time=132.50 memory used=11563.6MB, alloc=459.8MB, time=132.68 memory used=11622.5MB, alloc=459.8MB, time=132.86 memory used=11683.6MB, alloc=459.8MB, time=133.05 memory used=11746.2MB, alloc=459.8MB, time=133.24 memory used=11810.2MB, alloc=459.8MB, time=133.42 memory used=11877.1MB, alloc=459.8MB, time=133.62 memory used=11947.5MB, alloc=459.8MB, time=133.80 memory used=12022.8MB, alloc=459.8MB, time=133.99 memory used=12102.4MB, alloc=459.8MB, time=134.17 memory used=12212.5MB, alloc=459.8MB, time=135.42 memory used=12314.8MB, alloc=459.8MB, time=135.76 memory used=12380.8MB, alloc=459.8MB, time=136.04 memory used=12458.8MB, alloc=459.8MB, time=136.30 memory used=12549.3MB, alloc=459.8MB, time=136.57 memory used=12636.8MB, alloc=459.8MB, time=136.85 memory used=12690.8MB, alloc=459.8MB, time=137.08 memory used=12744.9MB, alloc=459.8MB, time=137.31 memory used=12804.3MB, alloc=459.8MB, time=137.55 memory used=12865.7MB, alloc=459.8MB, time=137.77 memory used=12932.5MB, alloc=459.8MB, time=137.99 memory used=13000.9MB, alloc=459.8MB, time=138.23 memory used=13074.8MB, alloc=459.8MB, time=138.48 memory used=13154.2MB, alloc=459.8MB, time=138.71 memory used=13234.7MB, alloc=459.8MB, time=138.94 memory used=13319.8MB, alloc=459.8MB, time=139.20 memory used=13409.9MB, alloc=459.8MB, time=139.43 memory used=13504.9MB, alloc=459.8MB, time=139.69 memory used=13566.7MB, alloc=459.8MB, time=139.88 memory used=13616.9MB, alloc=459.8MB, time=140.06 memory used=13667.9MB, alloc=459.8MB, time=140.24 memory used=13718.4MB, alloc=459.8MB, time=140.42 memory used=13772.4MB, alloc=459.8MB, time=140.60 memory used=13829.3MB, alloc=459.8MB, time=140.78 memory used=13885.2MB, alloc=459.8MB, time=140.96 memory used=13943.5MB, alloc=459.8MB, time=141.15 memory used=14003.8MB, alloc=459.8MB, time=141.34 memory used=14066.3MB, alloc=459.8MB, time=141.53 memory used=14131.8MB, alloc=459.8MB, time=141.72 memory used=14200.2MB, alloc=459.8MB, time=141.91 memory used=14272.2MB, alloc=459.8MB, time=142.10 memory used=14348.8MB, alloc=459.8MB, time=142.29 memory used=14432.1MB, alloc=459.8MB, time=142.48 memory used=14551.2MB, alloc=459.8MB, time=166.23 memory used=14638.6MB, alloc=459.8MB, time=224.59 memory used=14744.4MB, alloc=459.8MB, time=246.31 memory used=14829.1MB, alloc=459.8MB, time=246.52 memory used=14890.5MB, alloc=459.8MB, time=246.73 memory used=14963.7MB, alloc=459.8MB, time=246.93 memory used=15051.6MB, alloc=459.8MB, time=247.14 memory used=15132.6MB, alloc=459.8MB, time=247.33 memory used=15186.0MB, alloc=459.8MB, time=247.49 memory used=15244.7MB, alloc=459.8MB, time=247.64 memory used=15306.4MB, alloc=459.8MB, time=247.80 memory used=15374.1MB, alloc=459.8MB, time=247.95 memory used=15445.7MB, alloc=459.8MB, time=248.11 memory used=15522.3MB, alloc=459.8MB, time=248.27 memory used=15604.8MB, alloc=459.8MB, time=248.44 memory used=15695.0MB, alloc=459.8MB, time=248.60 memory used=15792.8MB, alloc=459.8MB, time=248.77 memory used=15940.9MB, alloc=459.8MB, time=249.11 memory used=16171.6MB, alloc=459.8MB, time=251.31 memory used=16276.1MB, alloc=459.8MB, time=252.60 memory used=16400.1MB, alloc=459.8MB, time=253.15 memory used=16549.8MB, alloc=459.8MB, time=257.27 memory used=16666.1MB, alloc=459.8MB, time=272.15 memory used=16740.7MB, alloc=459.8MB, time=272.34 memory used=16813.2MB, alloc=459.8MB, time=272.52 memory used=16901.0MB, alloc=459.8MB, time=272.73 memory used=16956.3MB, alloc=459.8MB, time=272.87 memory used=17019.3MB, alloc=459.8MB, time=273.02 memory used=17089.9MB, alloc=459.8MB, time=273.17 memory used=17217.6MB, alloc=459.8MB, time=273.70 memory used=17404.2MB, alloc=459.8MB, time=274.94 memory used=17545.4MB, alloc=459.8MB, time=280.11 memory used=17612.1MB, alloc=459.8MB, time=280.30 memory used=17688.3MB, alloc=459.8MB, time=280.48 memory used=17758.6MB, alloc=459.8MB, time=281.35 memory used=17880.7MB, alloc=459.8MB, time=291.66 memory used=17951.8MB, alloc=459.8MB, time=291.88 memory used=18029.6MB, alloc=459.8MB, time=292.07 memory used=18101.1MB, alloc=459.8MB, time=292.25 memory used=18159.3MB, alloc=459.8MB, time=292.41 memory used=18227.3MB, alloc=459.8MB, time=292.58 memory used=18366.7MB, alloc=459.8MB, time=293.39 memory used=18499.5MB, alloc=459.8MB, time=294.50 memory used=18636.5MB, alloc=459.8MB, time=295.78 memory used=18748.4MB, alloc=459.8MB, time=296.77 memory used=18865.0MB, alloc=459.8MB, time=297.37 memory used=18966.3MB, alloc=459.8MB, time=298.15 memory used=19095.4MB, alloc=483.8MB, time=299.18 memory used=19210.8MB, alloc=483.8MB, time=299.90 memory used=19299.2MB, alloc=483.8MB, time=300.17 memory used=19386.9MB, alloc=483.8MB, time=300.42 memory used=19488.3MB, alloc=507.8MB, time=311.87 memory used=19600.0MB, alloc=507.8MB, time=313.51 memory used=19692.2MB, alloc=507.8MB, time=313.75 memory used=19822.4MB, alloc=507.8MB, time=314.42 memory used=19911.8MB, alloc=507.8MB, time=314.75 memory used=20027.9MB, alloc=507.8MB, time=315.05 memory used=20109.8MB, alloc=507.8MB, time=315.32 memory used=20188.5MB, alloc=507.8MB, time=315.60 memory used=20279.7MB, alloc=507.8MB, time=315.85 memory used=20405.0MB, alloc=507.8MB, time=316.47 memory used=20513.6MB, alloc=507.8MB, time=316.81 memory used=20615.9MB, alloc=507.8MB, time=317.10 memory used=20719.4MB, alloc=507.8MB, time=317.39 memory used=20792.7MB, alloc=507.8MB, time=317.67 memory used=20877.1MB, alloc=507.8MB, time=317.95 memory used=20976.6MB, alloc=507.8MB, time=318.20 memory used=21175.2MB, alloc=507.8MB, time=321.61 memory used=21328.2MB, alloc=507.8MB, time=322.48 memory used=21466.0MB, alloc=507.8MB, time=335.47 memory used=21556.6MB, alloc=507.8MB, time=335.76 memory used=21713.9MB, alloc=507.8MB, time=336.51 memory used=21860.4MB, alloc=507.8MB, time=344.68 memory used=21947.5MB, alloc=507.8MB, time=344.97 memory used=22068.7MB, alloc=507.8MB, time=345.68 memory used=22206.5MB, alloc=507.8MB, time=346.29 memory used=22309.6MB, alloc=507.8MB, time=346.69 memory used=22423.1MB, alloc=507.8MB, time=347.17 memory used=22509.1MB, alloc=507.8MB, time=347.48 memory used=22601.7MB, alloc=507.8MB, time=347.79 memory used=22673.2MB, alloc=507.8MB, time=348.03 memory used=22787.4MB, alloc=507.8MB, time=348.55 memory used=22867.7MB, alloc=507.8MB, time=348.84 memory used=22952.3MB, alloc=507.8MB, time=349.10 memory used=23053.3MB, alloc=507.8MB, time=351.03 memory used=23181.2MB, alloc=507.8MB, time=353.58 memory used=23271.0MB, alloc=507.8MB, time=353.86 memory used=23344.0MB, alloc=507.8MB, time=354.12 memory used=23434.9MB, alloc=507.8MB, time=354.38 memory used=23683.4MB, alloc=507.8MB, time=354.83 memory used=23874.6MB, alloc=507.8MB, time=355.19 memory used=24022.7MB, alloc=507.8MB, time=355.68 memory used=24115.9MB, alloc=507.8MB, time=355.99 memory used=24189.4MB, alloc=507.8MB, time=356.25 memory used=24292.2MB, alloc=507.8MB, time=356.65 memory used=24375.9MB, alloc=507.8MB, time=356.97 memory used=24464.1MB, alloc=507.8MB, time=357.25 memory used=24549.4MB, alloc=507.8MB, time=357.57 memory used=24694.7MB, alloc=507.8MB, time=361.62 memory used=24786.0MB, alloc=507.8MB, time=361.91 memory used=24855.5MB, alloc=507.8MB, time=362.16 memory used=24941.0MB, alloc=507.8MB, time=362.41 memory used=25045.2MB, alloc=507.8MB, time=362.69 memory used=25212.1MB, alloc=507.8MB, time=363.05 memory used=25404.2MB, alloc=507.8MB, time=363.43 memory used=25551.7MB, alloc=531.8MB, time=367.47 memory used=25669.1MB, alloc=531.8MB, time=367.85 memory used=25748.4MB, alloc=531.8MB, time=368.20 memory used=25829.3MB, alloc=531.8MB, time=368.50 memory used=25918.2MB, alloc=531.8MB, time=368.84 memory used=26014.6MB, alloc=555.8MB, time=369.18 memory used=26139.8MB, alloc=555.8MB, time=369.57 memory used=26277.3MB, alloc=555.8MB, time=369.95 memory used=26383.8MB, alloc=579.8MB, time=370.28 memory used=26466.9MB, alloc=579.8MB, time=370.57 memory used=26557.6MB, alloc=579.8MB, time=370.87 memory used=26652.1MB, alloc=579.8MB, time=371.17 memory used=26749.4MB, alloc=579.8MB, time=371.46 memory used=26849.8MB, alloc=579.8MB, time=371.77 memory used=26963.0MB, alloc=579.8MB, time=372.08 memory used=27079.4MB, alloc=579.8MB, time=372.39 memory used=27198.8MB, alloc=579.8MB, time=372.70 memory used=27321.1MB, alloc=579.8MB, time=373.02 memory used=27446.1MB, alloc=579.8MB, time=373.33 memory used=27573.9MB, alloc=579.8MB, time=373.65 memory used=27715.9MB, alloc=579.8MB, time=373.98 memory used=27860.7MB, alloc=579.8MB, time=374.31 memory used=28008.1MB, alloc=579.8MB, time=374.64 memory used=28158.1MB, alloc=579.8MB, time=374.97 memory used=28323.0MB, alloc=579.8MB, time=375.31 memory used=28608.0MB, alloc=579.8MB, time=375.80 memory used=28723.9MB, alloc=579.8MB, time=376.12 memory used=28843.0MB, alloc=579.8MB, time=376.46 memory used=28974.5MB, alloc=579.8MB, time=376.80 memory used=29107.7MB, alloc=579.8MB, time=377.14 memory used=29241.7MB, alloc=579.8MB, time=377.48 memory used=29376.4MB, alloc=579.8MB, time=377.81 memory used=29511.8MB, alloc=579.8MB, time=378.17 memory used=29661.2MB, alloc=579.8MB, time=378.52 memory used=29811.1MB, alloc=579.8MB, time=378.88 memory used=29961.2MB, alloc=579.8MB, time=379.23 memory used=30111.7MB, alloc=579.8MB, time=379.59 memory used=30275.9MB, alloc=579.8MB, time=379.95 memory used=30440.0MB, alloc=579.8MB, time=380.32 memory used=30603.9MB, alloc=579.8MB, time=380.69 memory used=30780.9MB, alloc=579.8MB, time=381.05 memory used=30957.3MB, alloc=579.8MB, time=381.42 memory used=31134.3MB, alloc=579.8MB, time=381.79 memory used=31320.3MB, alloc=579.8MB, time=382.16 memory used=31507.5MB, alloc=579.8MB, time=382.54 memory used=31703.6MB, alloc=579.8MB, time=382.93 memory used=31911.2MB, alloc=579.8MB, time=383.32 memory used=32115.5MB, alloc=579.8MB, time=383.71 memory used=32328.8MB, alloc=579.8MB, time=384.10 memory used=32549.5MB, alloc=579.8MB, time=384.51 memory used=32776.2MB, alloc=579.8MB, time=384.92 memory used=33009.4MB, alloc=579.8MB, time=385.32 memory used=33251.6MB, alloc=579.8MB, time=385.73 memory used=33457.2MB, alloc=579.8MB, time=386.11 memory used=33631.1MB, alloc=579.8MB, time=386.47 memory used=33807.2MB, alloc=579.8MB, time=386.82 memory used=33989.3MB, alloc=579.8MB, time=387.18 memory used=34180.2MB, alloc=579.8MB, time=387.54 memory used=34378.2MB, alloc=579.8MB, time=387.91 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428539805 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 F := [18 x y + 5 z , 11 y z - 15 x - 8] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 4 3 2 G := [9 x y - 10 x z + 7 y , 7 y z + 9 x y + 7 x y] > Problem := [F,G]; 3 2 2 2 2 Problem := [[18 x y + 5 z , 11 y z - 15 x - 8], 3 3 4 3 2 [9 x y - 10 x z + 7 y , 7 y z + 9 x y + 7 x y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=31.7MB, alloc=40.3MB, time=0.54 memory used=59.0MB, alloc=44.3MB, time=0.92 memory used=88.5MB, alloc=44.3MB, time=1.29 memory used=117.0MB, alloc=68.3MB, time=1.64 memory used=153.6MB, alloc=68.3MB, time=2.03 memory used=207.6MB, alloc=76.3MB, time=2.58 memory used=251.7MB, alloc=76.3MB, time=2.99 memory used=282.3MB, alloc=76.3MB, time=3.11 memory used=306.4MB, alloc=76.3MB, time=3.19 memory used=334.4MB, alloc=76.3MB, time=3.27 memory used=355.5MB, alloc=76.3MB, time=3.33 memory used=380.5MB, alloc=76.3MB, time=3.40 memory used=409.3MB, alloc=76.3MB, time=3.48 memory used=441.8MB, alloc=76.3MB, time=3.54 memory used=456.3MB, alloc=81.9MB, time=3.60 memory used=466.6MB, alloc=91.8MB, time=3.65 memory used=477.7MB, alloc=91.8MB, time=3.71 memory used=488.7MB, alloc=91.8MB, time=3.76 memory used=500.4MB, alloc=91.8MB, time=3.81 memory used=512.0MB, alloc=91.8MB, time=3.87 memory used=524.4MB, alloc=91.8MB, time=3.92 memory used=537.1MB, alloc=91.8MB, time=3.97 memory used=550.2MB, alloc=91.8MB, time=4.02 memory used=563.6MB, alloc=91.8MB, time=4.08 memory used=577.3MB, alloc=91.8MB, time=4.13 memory used=591.3MB, alloc=91.8MB, time=4.19 memory used=605.8MB, alloc=91.8MB, time=4.24 memory used=619.9MB, alloc=91.8MB, time=4.29 memory used=634.9MB, alloc=91.8MB, time=4.35 memory used=651.5MB, alloc=91.8MB, time=4.41 memory used=701.5MB, alloc=91.8MB, time=7.81 memory used=735.7MB, alloc=91.8MB, time=8.31 memory used=759.1MB, alloc=91.8MB, time=8.40 memory used=782.5MB, alloc=91.8MB, time=8.47 memory used=810.8MB, alloc=91.8MB, time=8.55 memory used=838.9MB, alloc=91.8MB, time=8.65 memory used=856.4MB, alloc=91.8MB, time=8.71 memory used=875.4MB, alloc=91.8MB, time=8.78 memory used=895.2MB, alloc=91.8MB, time=8.84 memory used=917.0MB, alloc=91.8MB, time=8.91 memory used=939.6MB, alloc=91.8MB, time=8.98 memory used=964.2MB, alloc=91.8MB, time=9.06 memory used=990.9MB, alloc=91.8MB, time=9.14 memory used=1018.2MB, alloc=91.8MB, time=9.21 memory used=1047.3MB, alloc=91.8MB, time=9.29 memory used=1078.3MB, alloc=91.8MB, time=9.36 memory used=1107.6MB, alloc=91.8MB, time=9.44 memory used=1116.8MB, alloc=91.8MB, time=9.49 memory used=1126.0MB, alloc=91.8MB, time=9.54 memory used=1136.2MB, alloc=91.8MB, time=9.59 memory used=1146.6MB, alloc=91.8MB, time=9.64 memory used=1157.0MB, alloc=91.8MB, time=9.70 memory used=1167.4MB, alloc=91.8MB, time=9.75 memory used=1177.7MB, alloc=91.8MB, time=9.80 memory used=1188.3MB, alloc=91.8MB, time=9.84 memory used=1199.7MB, alloc=91.8MB, time=9.89 memory used=1211.2MB, alloc=91.8MB, time=9.94 memory used=1222.7MB, alloc=91.8MB, time=9.99 memory used=1234.3MB, alloc=91.8MB, time=10.05 memory used=1246.6MB, alloc=91.8MB, time=10.10 memory used=1259.1MB, alloc=91.8MB, time=10.15 memory used=1272.6MB, alloc=91.8MB, time=10.21 memory used=1285.9MB, alloc=91.8MB, time=10.27 memory used=1300.3MB, alloc=91.8MB, time=10.32 memory used=1314.3MB, alloc=91.8MB, time=10.38 memory used=1329.1MB, alloc=91.8MB, time=10.44 memory used=1344.6MB, alloc=91.8MB, time=10.49 memory used=1360.6MB, alloc=91.8MB, time=10.55 memory used=1376.8MB, alloc=91.8MB, time=10.60 memory used=1393.5MB, alloc=91.8MB, time=10.66 memory used=1411.0MB, alloc=91.8MB, time=10.71 memory used=1429.4MB, alloc=91.8MB, time=10.77 memory used=1464.0MB, alloc=91.8MB, time=10.95 memory used=1492.5MB, alloc=91.8MB, time=11.04 memory used=1513.2MB, alloc=91.8MB, time=11.11 memory used=1537.7MB, alloc=91.8MB, time=11.17 memory used=1568.2MB, alloc=91.8MB, time=11.29 memory used=1629.5MB, alloc=91.8MB, time=11.81 memory used=1688.9MB, alloc=91.8MB, time=12.16 memory used=1747.4MB, alloc=91.8MB, time=12.52 memory used=1806.9MB, alloc=91.8MB, time=12.95 memory used=1865.9MB, alloc=91.8MB, time=13.46 memory used=1925.2MB, alloc=91.8MB, time=14.00 memory used=1972.7MB, alloc=91.8MB, time=14.47 memory used=1996.6MB, alloc=91.8MB, time=14.55 memory used=2024.4MB, alloc=91.8MB, time=14.63 memory used=2043.5MB, alloc=91.8MB, time=14.70 memory used=2066.1MB, alloc=91.8MB, time=14.76 memory used=2093.4MB, alloc=91.8MB, time=14.84 memory used=2131.9MB, alloc=91.8MB, time=15.08 memory used=2169.4MB, alloc=91.8MB, time=15.31 memory used=2193.0MB, alloc=91.8MB, time=15.39 memory used=2221.6MB, alloc=91.8MB, time=15.48 memory used=2240.2MB, alloc=91.8MB, time=15.55 memory used=2261.7MB, alloc=91.8MB, time=15.62 memory used=2286.1MB, alloc=91.8MB, time=15.69 memory used=2314.5MB, alloc=91.8MB, time=15.76 memory used=2350.2MB, alloc=91.8MB, time=15.85 memory used=2361.8MB, alloc=91.8MB, time=15.91 memory used=2374.1MB, alloc=91.8MB, time=15.97 memory used=2440.1MB, alloc=91.8MB, time=16.53 memory used=2497.7MB, alloc=115.8MB, time=16.84 memory used=2590.3MB, alloc=115.8MB, time=17.31 memory used=2675.1MB, alloc=115.8MB, time=17.96 memory used=2758.5MB, alloc=115.8MB, time=18.94 memory used=2840.1MB, alloc=115.8MB, time=20.21 memory used=2924.0MB, alloc=115.8MB, time=22.03 memory used=3006.9MB, alloc=115.8MB, time=23.90 memory used=3089.0MB, alloc=115.8MB, time=26.31 memory used=3172.3MB, alloc=115.8MB, time=28.76 memory used=3253.8MB, alloc=115.8MB, time=31.22 memory used=3335.1MB, alloc=115.8MB, time=33.52 memory used=3429.2MB, alloc=115.8MB, time=34.83 memory used=3504.5MB, alloc=115.8MB, time=35.37 memory used=3596.5MB, alloc=115.8MB, time=35.71 memory used=3677.7MB, alloc=115.8MB, time=36.11 memory used=3761.4MB, alloc=115.8MB, time=36.62 memory used=3841.0MB, alloc=115.8MB, time=37.33 memory used=3917.8MB, alloc=115.8MB, time=38.21 memory used=3996.2MB, alloc=115.8MB, time=39.61 memory used=4074.1MB, alloc=115.8MB, time=40.95 memory used=4150.7MB, alloc=115.8MB, time=42.78 memory used=4227.0MB, alloc=115.8MB, time=44.63 memory used=4303.8MB, alloc=115.8MB, time=46.58 memory used=4382.0MB, alloc=115.8MB, time=48.74 memory used=4459.5MB, alloc=115.8MB, time=50.39 memory used=4536.7MB, alloc=115.8MB, time=51.94 memory used=4618.4MB, alloc=115.8MB, time=52.98 memory used=4684.2MB, alloc=115.8MB, time=53.40 memory used=4734.2MB, alloc=115.8MB, time=53.73 memory used=4791.8MB, alloc=371.8MB, time=54.20 memory used=4854.1MB, alloc=395.8MB, time=54.54 memory used=4914.4MB, alloc=395.8MB, time=54.72 memory used=4979.6MB, alloc=395.8MB, time=54.98 memory used=5031.8MB, alloc=395.8MB, time=55.12 memory used=5096.7MB, alloc=395.8MB, time=55.30 memory used=5149.6MB, alloc=395.8MB, time=55.42 memory used=5187.8MB, alloc=395.8MB, time=55.55 memory used=5236.4MB, alloc=395.8MB, time=55.67 memory used=5289.0MB, alloc=395.8MB, time=55.79 memory used=5324.9MB, alloc=395.8MB, time=55.88 memory used=5366.5MB, alloc=395.8MB, time=55.96 memory used=5413.9MB, alloc=395.8MB, time=56.06 memory used=5466.9MB, alloc=395.8MB, time=56.15 memory used=5525.9MB, alloc=395.8MB, time=56.24 memory used=5704.3MB, alloc=395.8MB, time=56.56 memory used=5878.0MB, alloc=395.8MB, time=56.76 memory used=6076.8MB, alloc=395.8MB, time=56.97 memory used=6236.5MB, alloc=395.8MB, time=79.29 memory used=6303.4MB, alloc=395.8MB, time=82.42 memory used=6364.2MB, alloc=395.8MB, time=82.62 memory used=6414.7MB, alloc=395.8MB, time=82.76 memory used=6458.3MB, alloc=395.8MB, time=82.88 memory used=6493.1MB, alloc=395.8MB, time=83.00 memory used=6531.3MB, alloc=395.8MB, time=83.12 memory used=6572.7MB, alloc=395.8MB, time=83.24 memory used=6617.3MB, alloc=395.8MB, time=83.37 memory used=6664.9MB, alloc=395.8MB, time=83.48 memory used=6715.6MB, alloc=395.8MB, time=83.62 memory used=6772.5MB, alloc=395.8MB, time=83.75 memory used=6817.1MB, alloc=395.8MB, time=83.88 memory used=6848.3MB, alloc=419.8MB, time=83.99 memory used=6889.4MB, alloc=419.8MB, time=84.09 memory used=6931.7MB, alloc=419.8MB, time=84.19 memory used=6975.3MB, alloc=419.8MB, time=84.30 memory used=7024.2MB, alloc=419.8MB, time=84.41 memory used=7074.6MB, alloc=419.8MB, time=84.53 memory used=7126.4MB, alloc=419.8MB, time=84.64 memory used=7179.6MB, alloc=419.8MB, time=84.75 memory used=7234.1MB, alloc=419.8MB, time=84.87 memory used=7290.0MB, alloc=419.8MB, time=84.98 memory used=7347.3MB, alloc=419.8MB, time=85.09 memory used=7405.8MB, alloc=419.8MB, time=85.20 memory used=7465.6MB, alloc=419.8MB, time=85.32 memory used=7526.8MB, alloc=419.8MB, time=85.44 memory used=7594.3MB, alloc=419.8MB, time=85.56 memory used=7663.3MB, alloc=419.8MB, time=85.68 memory used=7733.6MB, alloc=419.8MB, time=85.80 memory used=7805.3MB, alloc=419.8MB, time=85.92 memory used=7878.2MB, alloc=419.8MB, time=86.05 memory used=7952.5MB, alloc=419.8MB, time=86.17 memory used=8027.9MB, alloc=419.8MB, time=86.29 memory used=8211.5MB, alloc=419.8MB, time=86.53 memory used=8344.4MB, alloc=419.8MB, time=86.73 memory used=8483.2MB, alloc=419.8MB, time=86.94 memory used=8631.6MB, alloc=419.8MB, time=87.15 memory used=8783.2MB, alloc=419.8MB, time=87.36 memory used=8938.0MB, alloc=419.8MB, time=87.57 memory used=9102.0MB, alloc=419.8MB, time=87.79 memory used=9269.0MB, alloc=419.8MB, time=88.01 memory used=9445.6MB, alloc=419.8MB, time=88.23 memory used=9624.8MB, alloc=419.8MB, time=88.46 memory used=9813.6MB, alloc=419.8MB, time=88.69 memory used=10012.1MB, alloc=419.8MB, time=88.93 memory used=10212.8MB, alloc=419.8MB, time=89.17 memory used=10422.9MB, alloc=419.8MB, time=89.41 memory used=10642.3MB, alloc=419.8MB, time=89.65 memory used=10863.2MB, alloc=419.8MB, time=89.90 memory used=11093.1MB, alloc=419.8MB, time=90.15 memory used=11331.2MB, alloc=419.8MB, time=90.40 memory used=11577.4MB, alloc=419.8MB, time=90.67 memory used=11816.0MB, alloc=419.8MB, time=90.92 memory used=11986.1MB, alloc=419.8MB, time=91.12 memory used=12158.5MB, alloc=419.8MB, time=91.34 memory used=12339.3MB, alloc=419.8MB, time=91.55 memory used=12526.5MB, alloc=419.8MB, time=91.77 memory used=12712.5MB, alloc=419.8MB, time=91.99 memory used=12904.6MB, alloc=419.8MB, time=92.22 memory used=13101.8MB, alloc=419.8MB, time=92.45 memory used=13303.8MB, alloc=419.8MB, time=92.67 memory used=13510.0MB, alloc=419.8MB, time=92.90 memory used=13726.6MB, alloc=419.8MB, time=93.13 memory used=13945.8MB, alloc=419.8MB, time=93.37 memory used=14173.0MB, alloc=419.8MB, time=93.61 memory used=14406.8MB, alloc=419.8MB, time=93.85 memory used=14645.5MB, alloc=419.8MB, time=94.10 memory used=14892.1MB, alloc=419.8MB, time=94.34 memory used=15148.8MB, alloc=419.8MB, time=94.60 memory used=15367.4MB, alloc=419.8MB, time=94.83 memory used=15571.4MB, alloc=419.8MB, time=95.05 memory used=15781.3MB, alloc=419.8MB, time=95.28 memory used=15999.4MB, alloc=419.8MB, time=95.50 memory used=16230.6MB, alloc=419.8MB, time=95.73 memory used=16313.0MB, alloc=419.8MB, time=96.00 memory used=16381.3MB, alloc=419.8MB, time=96.13 memory used=16435.4MB, alloc=419.8MB, time=96.24 memory used=16504.3MB, alloc=419.8MB, time=96.35 memory used=16582.2MB, alloc=419.8MB, time=96.53 memory used=16643.9MB, alloc=419.8MB, time=96.65 memory used=16781.5MB, alloc=419.8MB, time=97.35 memory used=16939.6MB, alloc=419.8MB, time=98.20 memory used=17050.2MB, alloc=419.8MB, time=98.67 memory used=17125.6MB, alloc=419.8MB, time=98.91 memory used=17197.7MB, alloc=419.8MB, time=99.18 memory used=17274.6MB, alloc=419.8MB, time=99.39 memory used=17334.0MB, alloc=419.8MB, time=99.54 memory used=17390.4MB, alloc=419.8MB, time=99.70 memory used=17454.4MB, alloc=419.8MB, time=99.83 memory used=17500.2MB, alloc=419.8MB, time=99.93 memory used=17555.0MB, alloc=419.8MB, time=100.05 memory used=17618.9MB, alloc=419.8MB, time=100.16 memory used=17691.6MB, alloc=419.8MB, time=100.28 memory used=17866.8MB, alloc=419.8MB, time=100.50 memory used=18040.5MB, alloc=419.8MB, time=100.71 memory used=18239.5MB, alloc=419.8MB, time=100.93 memory used=18419.3MB, alloc=419.8MB, time=123.39 memory used=18514.1MB, alloc=419.8MB, time=126.65 memory used=18572.5MB, alloc=419.8MB, time=126.81 memory used=18635.5MB, alloc=419.8MB, time=126.97 memory used=18679.8MB, alloc=419.8MB, time=127.13 memory used=18730.6MB, alloc=419.8MB, time=127.28 memory used=18787.5MB, alloc=419.8MB, time=127.42 memory used=18849.7MB, alloc=419.8MB, time=127.58 memory used=18917.0MB, alloc=419.8MB, time=127.74 memory used=18983.3MB, alloc=419.8MB, time=127.88 memory used=19026.0MB, alloc=419.8MB, time=128.01 memory used=19064.2MB, alloc=419.8MB, time=128.12 memory used=19102.2MB, alloc=419.8MB, time=128.23 memory used=19141.4MB, alloc=419.8MB, time=128.34 memory used=19181.6MB, alloc=419.8MB, time=128.45 memory used=19222.9MB, alloc=443.8MB, time=128.58 memory used=19280.9MB, alloc=443.8MB, time=128.71 memory used=19342.2MB, alloc=443.8MB, time=128.85 memory used=19405.6MB, alloc=443.8MB, time=128.99 memory used=19475.5MB, alloc=443.8MB, time=129.13 memory used=19547.5MB, alloc=443.8MB, time=129.31 memory used=19621.4MB, alloc=443.8MB, time=129.48 memory used=19697.4MB, alloc=443.8MB, time=129.65 memory used=19775.3MB, alloc=443.8MB, time=129.80 memory used=19855.1MB, alloc=443.8MB, time=129.94 memory used=19936.8MB, alloc=443.8MB, time=130.09 memory used=20025.8MB, alloc=443.8MB, time=130.23 memory used=20116.8MB, alloc=443.8MB, time=130.38 memory used=20209.7MB, alloc=443.8MB, time=130.53 memory used=20393.9MB, alloc=443.8MB, time=130.78 memory used=20526.9MB, alloc=443.8MB, time=131.00 memory used=20665.9MB, alloc=443.8MB, time=131.22 memory used=20814.4MB, alloc=443.8MB, time=131.44 memory used=20965.9MB, alloc=443.8MB, time=131.67 memory used=21120.6MB, alloc=443.8MB, time=131.89 memory used=21284.7MB, alloc=443.8MB, time=132.12 memory used=21451.8MB, alloc=443.8MB, time=132.36 memory used=21628.4MB, alloc=443.8MB, time=132.60 memory used=21807.6MB, alloc=443.8MB, time=132.84 memory used=21996.5MB, alloc=443.8MB, time=133.09 memory used=22195.0MB, alloc=443.8MB, time=133.34 memory used=22395.7MB, alloc=443.8MB, time=133.59 memory used=22605.8MB, alloc=443.8MB, time=133.86 memory used=22825.2MB, alloc=443.8MB, time=134.12 memory used=23046.1MB, alloc=443.8MB, time=134.38 memory used=23276.1MB, alloc=443.8MB, time=134.65 memory used=23514.3MB, alloc=443.8MB, time=134.91 memory used=23760.5MB, alloc=443.8MB, time=135.19 memory used=23998.3MB, alloc=443.8MB, time=135.45 memory used=24169.3MB, alloc=443.8MB, time=135.67 memory used=24341.7MB, alloc=443.8MB, time=135.90 memory used=24522.5MB, alloc=443.8MB, time=136.12 memory used=24709.8MB, alloc=443.8MB, time=136.35 memory used=24895.8MB, alloc=443.8MB, time=136.59 memory used=25087.9MB, alloc=443.8MB, time=136.82 memory used=25285.2MB, alloc=443.8MB, time=137.06 memory used=25487.2MB, alloc=443.8MB, time=137.31 memory used=25693.4MB, alloc=443.8MB, time=137.56 memory used=25903.8MB, alloc=443.8MB, time=137.80 memory used=26122.5MB, alloc=443.8MB, time=138.06 memory used=26350.0MB, alloc=443.8MB, time=138.31 memory used=26584.0MB, alloc=443.8MB, time=138.57 memory used=26823.2MB, alloc=443.8MB, time=138.85 memory used=27070.0MB, alloc=443.8MB, time=139.12 memory used=27327.2MB, alloc=443.8MB, time=139.39 memory used=27543.0MB, alloc=443.8MB, time=139.63 memory used=27746.2MB, alloc=443.8MB, time=139.86 memory used=27957.1MB, alloc=443.8MB, time=140.10 memory used=28176.5MB, alloc=443.8MB, time=140.34 memory used=28406.8MB, alloc=443.8MB, time=140.58 memory used=28510.6MB, alloc=443.8MB, time=140.86 memory used=28585.1MB, alloc=443.8MB, time=141.00 memory used=28656.8MB, alloc=443.8MB, time=141.13 memory used=28752.1MB, alloc=443.8MB, time=141.33 memory used=28825.6MB, alloc=443.8MB, time=141.47 memory used=28986.6MB, alloc=443.8MB, time=142.30 memory used=29121.0MB, alloc=443.8MB, time=142.90 memory used=29374.6MB, alloc=443.8MB, time=143.30 memory used=29498.8MB, alloc=443.8MB, time=143.59 memory used=29691.4MB, alloc=443.8MB, time=144.05 memory used=29854.6MB, alloc=443.8MB, time=144.45 memory used=29929.3MB, alloc=443.8MB, time=144.68 memory used=30002.8MB, alloc=443.8MB, time=144.86 memory used=30223.7MB, alloc=443.8MB, time=145.24 memory used=30416.6MB, alloc=443.8MB, time=145.58 memory used=30654.7MB, alloc=443.8MB, time=145.94 memory used=30840.6MB, alloc=443.8MB, time=146.26 memory used=31048.3MB, alloc=443.8MB, time=146.58 memory used=31312.5MB, alloc=443.8MB, time=147.03 memory used=31386.2MB, alloc=443.8MB, time=147.20 memory used=31590.1MB, alloc=443.8MB, time=147.54 memory used=31797.5MB, alloc=443.8MB, time=147.88 memory used=31988.2MB, alloc=443.8MB, time=148.57 memory used=32059.0MB, alloc=443.8MB, time=148.75 memory used=32269.7MB, alloc=443.8MB, time=149.15 memory used=32480.9MB, alloc=443.8MB, time=149.53 memory used=32690.5MB, alloc=443.8MB, time=149.90 memory used=32893.7MB, alloc=443.8MB, time=150.26 memory used=33126.3MB, alloc=443.8MB, time=150.64 memory used=33349.1MB, alloc=443.8MB, time=151.00 memory used=33565.5MB, alloc=443.8MB, time=151.34 memory used=33804.1MB, alloc=443.8MB, time=151.70 memory used=34149.3MB, alloc=443.8MB, time=153.27 memory used=34287.0MB, alloc=443.8MB, time=153.70 memory used=34421.1MB, alloc=443.8MB, time=154.12 memory used=34558.3MB, alloc=443.8MB, time=154.56 memory used=34690.6MB, alloc=443.8MB, time=154.98 memory used=34826.5MB, alloc=443.8MB, time=155.42 memory used=34965.4MB, alloc=443.8MB, time=155.89 memory used=35100.9MB, alloc=443.8MB, time=156.36 memory used=35241.8MB, alloc=443.8MB, time=156.92 memory used=35380.5MB, alloc=443.8MB, time=157.53 memory used=35520.4MB, alloc=443.8MB, time=158.16 memory used=35664.5MB, alloc=443.8MB, time=158.80 memory used=35805.8MB, alloc=443.8MB, time=159.53 memory used=35951.0MB, alloc=443.8MB, time=160.24 memory used=36093.0MB, alloc=443.8MB, time=161.01 memory used=36239.7MB, alloc=443.8MB, time=161.87 memory used=36386.9MB, alloc=443.8MB, time=162.74 memory used=36532.4MB, alloc=443.8MB, time=163.65 memory used=36680.1MB, alloc=443.8MB, time=164.57 memory used=36829.1MB, alloc=443.8MB, time=165.59 memory used=36975.1MB, alloc=443.8MB, time=166.67 memory used=37122.9MB, alloc=443.8MB, time=167.70 memory used=37274.1MB, alloc=443.8MB, time=168.97 memory used=37421.7MB, alloc=443.8MB, time=170.15 memory used=37571.2MB, alloc=443.8MB, time=171.51 memory used=37719.3MB, alloc=443.8MB, time=172.79 memory used=37868.1MB, alloc=443.8MB, time=174.17 memory used=38015.4MB, alloc=443.8MB, time=175.58 memory used=38166.7MB, alloc=443.8MB, time=177.13 memory used=38314.3MB, alloc=443.8MB, time=178.66 memory used=38462.7MB, alloc=443.8MB, time=180.35 memory used=38613.3MB, alloc=443.8MB, time=182.07 memory used=38765.0MB, alloc=443.8MB, time=183.91 memory used=38912.0MB, alloc=443.8MB, time=185.84 memory used=39059.6MB, alloc=443.8MB, time=187.78 memory used=39206.0MB, alloc=443.8MB, time=189.54 memory used=39355.1MB, alloc=443.8MB, time=191.57 memory used=39507.0MB, alloc=443.8MB, time=194.00 memory used=39659.9MB, alloc=443.8MB, time=196.27 memory used=39815.3MB, alloc=443.8MB, time=198.75 memory used=39978.6MB, alloc=443.8MB, time=201.19 memory used=40143.3MB, alloc=443.8MB, time=203.99 memory used=40303.8MB, alloc=443.8MB, time=206.36 memory used=40366.5MB, alloc=443.8MB, time=206.55 memory used=40428.4MB, alloc=443.8MB, time=206.74 memory used=40503.5MB, alloc=443.8MB, time=206.93 memory used=40697.5MB, alloc=443.8MB, time=207.34 memory used=40871.6MB, alloc=443.8MB, time=207.72 memory used=41075.8MB, alloc=443.8MB, time=208.12 memory used=41313.7MB, alloc=443.8MB, time=208.56 memory used=41499.4MB, alloc=443.8MB, time=208.93 memory used=41686.2MB, alloc=443.8MB, time=209.34 memory used=41887.4MB, alloc=443.8MB, time=209.78 memory used=42106.1MB, alloc=443.8MB, time=210.18 memory used=42336.9MB, alloc=443.8MB, time=210.61 memory used=42569.1MB, alloc=443.8MB, time=211.02 memory used=42759.3MB, alloc=443.8MB, time=211.39 memory used=42961.7MB, alloc=443.8MB, time=211.77 memory used=43172.7MB, alloc=443.8MB, time=212.16 memory used=43391.3MB, alloc=443.8MB, time=212.56 memory used=43622.6MB, alloc=443.8MB, time=212.97 memory used=43861.5MB, alloc=443.8MB, time=213.39 memory used=44087.0MB, alloc=443.8MB, time=213.79 memory used=44295.5MB, alloc=443.8MB, time=214.17 memory used=44502.9MB, alloc=443.8MB, time=214.54 memory used=44717.2MB, alloc=443.8MB, time=214.93 memory used=44938.9MB, alloc=443.8MB, time=215.32 memory used=45170.7MB, alloc=443.8MB, time=215.73 memory used=45412.2MB, alloc=443.8MB, time=216.14 memory used=45646.4MB, alloc=443.8MB, time=216.55 memory used=45860.5MB, alloc=443.8MB, time=216.92 memory used=46079.3MB, alloc=443.8MB, time=217.30 memory used=46298.7MB, alloc=443.8MB, time=217.67 memory used=46523.1MB, alloc=443.8MB, time=218.07 memory used=46753.5MB, alloc=443.8MB, time=218.47 memory used=46992.4MB, alloc=443.8MB, time=218.85 memory used=47237.7MB, alloc=443.8MB, time=219.25 memory used=47458.5MB, alloc=443.8MB, time=219.62 memory used=47679.6MB, alloc=443.8MB, time=219.99 memory used=47901.6MB, alloc=443.8MB, time=220.36 memory used=48130.8MB, alloc=443.8MB, time=220.73 memory used=48368.9MB, alloc=443.8MB, time=221.11 memory used=48609.4MB, alloc=443.8MB, time=221.49 memory used=48854.5MB, alloc=443.8MB, time=221.86 memory used=49084.0MB, alloc=443.8MB, time=222.23 memory used=49306.6MB, alloc=443.8MB, time=222.58 memory used=49539.0MB, alloc=443.8MB, time=222.93 memory used=49775.7MB, alloc=443.8MB, time=223.29 memory used=50020.5MB, alloc=443.8MB, time=223.65 memory used=50481.6MB, alloc=443.8MB, time=226.27 memory used=50546.3MB, alloc=443.8MB, time=226.48 memory used=50603.0MB, alloc=443.8MB, time=226.66 memory used=50672.5MB, alloc=443.8MB, time=226.86 memory used=50753.8MB, alloc=443.8MB, time=227.07 memory used=50913.7MB, alloc=443.8MB, time=227.44 memory used=51079.5MB, alloc=443.8MB, time=227.80 memory used=51271.6MB, alloc=443.8MB, time=228.20 memory used=51495.2MB, alloc=443.8MB, time=228.63 memory used=51719.2MB, alloc=443.8MB, time=229.06 memory used=51890.8MB, alloc=443.8MB, time=229.43 memory used=52075.3MB, alloc=443.8MB, time=229.80 memory used=52271.3MB, alloc=443.8MB, time=230.19 memory used=52479.1MB, alloc=443.8MB, time=230.59 memory used=52703.0MB, alloc=443.8MB, time=231.01 memory used=52938.9MB, alloc=443.8MB, time=231.44 memory used=53152.3MB, alloc=443.8MB, time=231.84 memory used=53339.3MB, alloc=443.8MB, time=232.21 memory used=53536.6MB, alloc=443.8MB, time=232.59 memory used=53740.8MB, alloc=443.8MB, time=232.97 memory used=53949.7MB, alloc=443.8MB, time=233.37 memory used=54166.0MB, alloc=443.8MB, time=233.77 memory used=54396.2MB, alloc=443.8MB, time=234.19 memory used=54634.1MB, alloc=443.8MB, time=234.62 memory used=54859.1MB, alloc=443.8MB, time=235.03 memory used=55053.7MB, alloc=443.8MB, time=235.40 memory used=55252.4MB, alloc=443.8MB, time=235.77 memory used=55454.9MB, alloc=443.8MB, time=236.15 memory used=55670.8MB, alloc=443.8MB, time=236.56 memory used=55893.8MB, alloc=443.8MB, time=236.96 memory used=56119.2MB, alloc=443.8MB, time=237.36 memory used=56346.9MB, alloc=443.8MB, time=237.77 memory used=56580.0MB, alloc=443.8MB, time=238.18 memory used=56818.0MB, alloc=443.8MB, time=238.60 memory used=57018.0MB, alloc=443.8MB, time=238.97 memory used=57230.9MB, alloc=443.8MB, time=239.35 memory used=57448.7MB, alloc=443.8MB, time=239.75 memory used=57667.8MB, alloc=443.8MB, time=240.14 memory used=57887.9MB, alloc=443.8MB, time=240.54 memory used=58109.1MB, alloc=443.8MB, time=240.93 memory used=58335.0MB, alloc=443.8MB, time=241.33 memory used=58572.5MB, alloc=443.8MB, time=241.74 memory used=58814.7MB, alloc=443.8MB, time=242.15 memory used=59035.2MB, alloc=443.8MB, time=242.54 memory used=59242.7MB, alloc=443.8MB, time=242.91 memory used=59452.7MB, alloc=443.8MB, time=243.28 memory used=59660.2MB, alloc=443.8MB, time=243.66 memory used=59878.2MB, alloc=443.8MB, time=244.04 memory used=60102.5MB, alloc=443.8MB, time=244.42 memory used=60326.6MB, alloc=443.8MB, time=244.81 memory used=60556.0MB, alloc=443.8MB, time=245.21 memory used=60792.6MB, alloc=443.8MB, time=245.60 memory used=61034.2MB, alloc=443.8MB, time=246.01 memory used=61252.3MB, alloc=443.8MB, time=246.38 memory used=61466.6MB, alloc=443.8MB, time=246.75 memory used=61681.9MB, alloc=443.8MB, time=247.11 memory used=61901.1MB, alloc=443.8MB, time=247.48 memory used=62125.0MB, alloc=443.8MB, time=247.86 memory used=62353.9MB, alloc=443.8MB, time=248.24 memory used=62587.1MB, alloc=443.8MB, time=248.62 memory used=62824.2MB, alloc=443.8MB, time=249.01 memory used=63065.8MB, alloc=443.8MB, time=249.39 memory used=63292.2MB, alloc=443.8MB, time=249.76 memory used=63511.3MB, alloc=443.8MB, time=250.12 memory used=63734.1MB, alloc=443.8MB, time=250.48 memory used=63964.3MB, alloc=443.8MB, time=250.84 memory used=64198.0MB, alloc=443.8MB, time=251.20 memory used=64434.3MB, alloc=443.8MB, time=251.58 memory used=64677.6MB, alloc=443.8MB, time=251.96 memory used=64926.5MB, alloc=443.8MB, time=252.33 memory used=65163.0MB, alloc=443.8MB, time=252.69 memory used=65393.4MB, alloc=443.8MB, time=253.03 memory used=65624.8MB, alloc=443.8MB, time=253.37 memory used=65916.5MB, alloc=443.8MB, time=254.74 memory used=66009.5MB, alloc=443.8MB, time=255.28 memory used=66086.8MB, alloc=443.8MB, time=255.60 memory used=66217.6MB, alloc=443.8MB, time=256.18 memory used=66360.2MB, alloc=443.8MB, time=256.60 memory used=66492.5MB, alloc=443.8MB, time=257.00 memory used=66629.7MB, alloc=443.8MB, time=257.39 memory used=66754.1MB, alloc=443.8MB, time=257.80 memory used=66905.8MB, alloc=443.8MB, time=258.28 memory used=67052.1MB, alloc=443.8MB, time=258.91 memory used=67195.3MB, alloc=443.8MB, time=259.74 memory used=67339.1MB, alloc=443.8MB, time=260.66 memory used=67484.6MB, alloc=443.8MB, time=261.87 memory used=67625.2MB, alloc=443.8MB, time=263.02 memory used=67765.6MB, alloc=443.8MB, time=264.38 memory used=67900.8MB, alloc=443.8MB, time=265.88 memory used=68037.8MB, alloc=443.8MB, time=267.43 memory used=68172.6MB, alloc=443.8MB, time=269.17 memory used=68304.0MB, alloc=443.8MB, time=271.17 memory used=68439.7MB, alloc=443.8MB, time=273.04 memory used=68574.4MB, alloc=443.8MB, time=275.38 memory used=68706.7MB, alloc=443.8MB, time=277.61 memory used=68839.6MB, alloc=443.8MB, time=280.32 memory used=68969.8MB, alloc=443.8MB, time=283.00 memory used=69099.3MB, alloc=443.8MB, time=285.88 memory used=69229.3MB, alloc=443.8MB, time=288.71 memory used=69361.9MB, alloc=443.8MB, time=291.80 memory used=69494.7MB, alloc=443.8MB, time=295.15 memory used=69629.4MB, alloc=443.8MB, time=298.67 memory used=69763.5MB, alloc=443.8MB, time=301.78 memory used=69899.7MB, alloc=443.8MB, time=305.58 memory used=70034.7MB, alloc=443.8MB, time=309.57 memory used=70170.3MB, alloc=443.8MB, time=313.75 memory used=70300.5MB, alloc=443.8MB, time=318.07 memory used=70434.7MB, alloc=443.8MB, time=321.99 memory used=70573.5MB, alloc=443.8MB, time=326.57 memory used=70707.9MB, alloc=443.8MB, time=331.39 memory used=70839.6MB, alloc=443.8MB, time=336.17 memory used=70975.4MB, alloc=443.8MB, time=340.25 memory used=71115.7MB, alloc=443.8MB, time=344.91 memory used=71256.7MB, alloc=443.8MB, time=349.53 memory used=71395.2MB, alloc=443.8MB, time=353.34 memory used=71540.8MB, alloc=443.8MB, time=357.11 memory used=71683.4MB, alloc=443.8MB, time=360.56 memory used=71823.8MB, alloc=443.8MB, time=363.79 memory used=71971.5MB, alloc=443.8MB, time=364.54 memory used=72043.4MB, alloc=443.8MB, time=364.81 memory used=72139.4MB, alloc=467.8MB, time=365.57 memory used=72258.2MB, alloc=467.8MB, time=366.07 memory used=72425.6MB, alloc=491.8MB, time=366.52 memory used=72607.5MB, alloc=491.8MB, time=367.06 memory used=72784.5MB, alloc=491.8MB, time=367.61 memory used=72963.7MB, alloc=491.8MB, time=368.17 memory used=73139.3MB, alloc=491.8MB, time=368.72 memory used=73312.0MB, alloc=491.8MB, time=369.37 memory used=73480.4MB, alloc=491.8MB, time=370.25 memory used=73651.9MB, alloc=491.8MB, time=371.24 memory used=73816.6MB, alloc=491.8MB, time=372.44 memory used=73985.3MB, alloc=491.8MB, time=373.89 memory used=74146.2MB, alloc=491.8MB, time=375.65 memory used=74311.1MB, alloc=491.8MB, time=377.48 memory used=74472.1MB, alloc=491.8MB, time=379.55 memory used=74638.3MB, alloc=491.8MB, time=381.69 memory used=74798.9MB, alloc=491.8MB, time=384.38 memory used=74963.2MB, alloc=491.8MB, time=387.07 memory used=75127.4MB, alloc=491.8MB, time=389.95 memory used=75290.8MB, alloc=491.8MB, time=393.10 memory used=75455.0MB, alloc=491.8MB, time=396.48 memory used=75621.6MB, alloc=491.8MB, time=400.26 memory used=75787.2MB, alloc=491.8MB, time=404.34 memory used=75947.9MB, alloc=491.8MB, time=408.47 memory used=76113.7MB, alloc=491.8MB, time=412.48 memory used=76282.0MB, alloc=491.8MB, time=417.35 memory used=76444.3MB, alloc=491.8MB, time=422.50 memory used=76610.8MB, alloc=491.8MB, time=427.16 memory used=76770.5MB, alloc=491.8MB, time=432.02 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428540105 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 F := [12 x y z - 19 y z - 5 z , 13 y z + 15 y z - 6 x] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 G := [-7 x y - 20 z + 19 z, -14 x y - 17 z - 17 x] > Problem := [F,G]; 2 2 3 2 2 Problem := [[12 x y z - 19 y z - 5 z , 13 y z + 15 y z - 6 x], 2 3 2 [-7 x y - 20 z + 19 z, -14 x y - 17 z - 17 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.16 memory used=26.1MB, alloc=32.3MB, time=0.46 memory used=46.0MB, alloc=56.3MB, time=0.73 memory used=91.8MB, alloc=60.3MB, time=1.25 memory used=135.3MB, alloc=68.3MB, time=1.61 memory used=175.2MB, alloc=92.3MB, time=1.97 memory used=241.4MB, alloc=92.3MB, time=2.54 memory used=306.8MB, alloc=92.3MB, time=3.00 memory used=344.3MB, alloc=92.3MB, time=3.13 memory used=378.5MB, alloc=92.3MB, time=3.46 memory used=415.9MB, alloc=92.3MB, time=3.58 memory used=453.9MB, alloc=92.3MB, time=3.76 memory used=495.9MB, alloc=92.3MB, time=4.08 memory used=526.3MB, alloc=92.3MB, time=4.17 memory used=565.6MB, alloc=92.3MB, time=4.32 memory used=602.3MB, alloc=92.3MB, time=4.71 memory used=661.8MB, alloc=92.3MB, time=5.11 memory used=724.9MB, alloc=116.3MB, time=6.43 memory used=804.4MB, alloc=116.3MB, time=6.90 memory used=859.6MB, alloc=116.7MB, time=7.07 memory used=915.4MB, alloc=116.7MB, time=7.49 memory used=969.5MB, alloc=116.7MB, time=7.84 memory used=1024.6MB, alloc=116.7MB, time=8.09 memory used=1078.9MB, alloc=116.7MB, time=8.25 memory used=1136.0MB, alloc=116.7MB, time=8.73 memory used=1218.0MB, alloc=372.7MB, time=10.27 memory used=1264.1MB, alloc=372.7MB, time=10.42 memory used=1354.2MB, alloc=372.7MB, time=11.16 memory used=1438.9MB, alloc=396.7MB, time=11.79 memory used=1502.5MB, alloc=396.7MB, time=12.14 memory used=1570.4MB, alloc=396.7MB, time=12.49 memory used=1633.8MB, alloc=396.7MB, time=12.73 memory used=1706.7MB, alloc=396.7MB, time=13.22 memory used=1817.4MB, alloc=396.7MB, time=14.41 memory used=1908.4MB, alloc=396.7MB, time=15.02 memory used=2021.5MB, alloc=396.7MB, time=16.01 memory used=2123.7MB, alloc=420.7MB, time=16.90 memory used=2249.9MB, alloc=444.7MB, time=18.14 memory used=2392.2MB, alloc=444.7MB, time=19.29 memory used=2532.2MB, alloc=444.7MB, time=20.39 memory used=2678.4MB, alloc=468.7MB, time=21.57 memory used=2755.3MB, alloc=468.7MB, time=21.77 memory used=2868.6MB, alloc=468.7MB, time=22.75 memory used=2939.6MB, alloc=468.7MB, time=22.95 memory used=3218.6MB, alloc=468.7MB, time=24.01 memory used=3352.2MB, alloc=468.7MB, time=25.23 memory used=3448.7MB, alloc=468.7MB, time=25.79 memory used=3592.9MB, alloc=468.7MB, time=26.79 memory used=3679.4MB, alloc=468.7MB, time=27.27 memory used=3808.9MB, alloc=492.7MB, time=28.28 memory used=3945.0MB, alloc=492.7MB, time=29.15 memory used=4091.6MB, alloc=492.7MB, time=30.15 memory used=4214.0MB, alloc=492.7MB, time=30.76 memory used=4298.2MB, alloc=492.7MB, time=31.03 memory used=4381.1MB, alloc=492.7MB, time=31.27 memory used=4467.8MB, alloc=492.7MB, time=31.59 memory used=4551.8MB, alloc=492.7MB, time=31.86 memory used=4636.1MB, alloc=492.7MB, time=32.12 memory used=4728.2MB, alloc=492.7MB, time=35.68 memory used=4825.2MB, alloc=492.7MB, time=36.19 memory used=4903.5MB, alloc=492.7MB, time=36.42 memory used=5041.5MB, alloc=492.7MB, time=36.85 memory used=5129.0MB, alloc=492.7MB, time=37.11 memory used=5200.2MB, alloc=492.7MB, time=37.33 memory used=5295.8MB, alloc=492.7MB, time=37.68 memory used=5382.7MB, alloc=492.7MB, time=37.93 memory used=5456.2MB, alloc=492.7MB, time=38.15 memory used=5564.0MB, alloc=492.7MB, time=41.77 memory used=5644.0MB, alloc=492.7MB, time=42.03 memory used=5776.5MB, alloc=492.7MB, time=42.34 memory used=5871.4MB, alloc=492.7MB, time=42.75 memory used=5959.4MB, alloc=492.7MB, time=43.04 memory used=6034.2MB, alloc=492.7MB, time=43.28 memory used=6107.9MB, alloc=492.7MB, time=43.49 memory used=6203.0MB, alloc=492.7MB, time=43.85 memory used=6293.1MB, alloc=492.7MB, time=44.14 memory used=6383.8MB, alloc=492.7MB, time=44.43 memory used=6455.8MB, alloc=492.7MB, time=44.65 memory used=6530.4MB, alloc=492.7MB, time=44.87 memory used=6629.5MB, alloc=492.7MB, time=46.47 memory used=6736.4MB, alloc=492.7MB, time=51.45 memory used=6815.0MB, alloc=492.7MB, time=51.67 memory used=6907.4MB, alloc=492.7MB, time=51.90 memory used=7100.5MB, alloc=492.7MB, time=52.55 memory used=7252.1MB, alloc=492.7MB, time=54.12 memory used=7345.4MB, alloc=492.7MB, time=54.52 memory used=7472.2MB, alloc=492.7MB, time=56.14 memory used=7570.0MB, alloc=492.7MB, time=56.77 memory used=7671.8MB, alloc=492.7MB, time=57.09 memory used=7779.4MB, alloc=492.7MB, time=57.37 memory used=7974.1MB, alloc=492.7MB, time=57.78 memory used=8210.6MB, alloc=492.7MB, time=58.15 memory used=8476.4MB, alloc=492.7MB, time=58.69 memory used=8608.1MB, alloc=492.7MB, time=60.17 memory used=8710.2MB, alloc=492.7MB, time=60.59 memory used=8808.1MB, alloc=492.7MB, time=60.86 memory used=8899.4MB, alloc=492.7MB, time=61.85 memory used=8983.9MB, alloc=492.7MB, time=62.19 memory used=9126.5MB, alloc=492.7MB, time=62.82 memory used=9295.6MB, alloc=516.7MB, time=63.77 memory used=9424.5MB, alloc=516.7MB, time=64.43 memory used=9564.0MB, alloc=516.7MB, time=66.16 memory used=9680.2MB, alloc=516.7MB, time=66.78 memory used=9813.0MB, alloc=516.7MB, time=68.12 memory used=9957.7MB, alloc=516.7MB, time=69.17 memory used=10061.2MB, alloc=516.7MB, time=70.20 memory used=10170.7MB, alloc=516.7MB, time=70.59 memory used=10300.4MB, alloc=516.7MB, time=70.96 memory used=10485.2MB, alloc=516.7MB, time=71.94 memory used=10587.6MB, alloc=516.7MB, time=72.88 memory used=10700.8MB, alloc=516.7MB, time=73.87 memory used=10795.3MB, alloc=516.7MB, time=74.80 memory used=10896.8MB, alloc=540.7MB, time=75.92 memory used=11043.7MB, alloc=540.7MB, time=77.03 memory used=11162.9MB, alloc=540.7MB, time=77.79 memory used=11334.7MB, alloc=540.7MB, time=79.02 memory used=11424.3MB, alloc=540.7MB, time=79.33 memory used=11628.8MB, alloc=540.7MB, time=81.48 memory used=11754.6MB, alloc=540.7MB, time=81.92 memory used=11845.9MB, alloc=564.7MB, time=82.25 memory used=11965.1MB, alloc=564.7MB, time=82.58 memory used=12187.8MB, alloc=564.7MB, time=83.04 memory used=12434.3MB, alloc=564.7MB, time=83.89 memory used=12553.3MB, alloc=564.7MB, time=84.98 memory used=12649.8MB, alloc=564.7MB, time=85.97 memory used=12795.0MB, alloc=564.7MB, time=86.75 memory used=12957.0MB, alloc=564.7MB, time=88.02 memory used=13069.8MB, alloc=564.7MB, time=88.38 memory used=13368.3MB, alloc=564.7MB, time=89.24 memory used=13517.7MB, alloc=564.7MB, time=91.63 memory used=13625.7MB, alloc=564.7MB, time=91.99 memory used=13827.2MB, alloc=564.7MB, time=92.47 memory used=14031.7MB, alloc=564.7MB, time=92.92 memory used=14161.8MB, alloc=564.7MB, time=93.78 memory used=14256.9MB, alloc=564.7MB, time=94.66 memory used=14384.3MB, alloc=588.7MB, time=95.45 memory used=14524.7MB, alloc=588.7MB, time=97.41 memory used=14679.0MB, alloc=588.7MB, time=105.52 memory used=14803.6MB, alloc=588.7MB, time=105.92 memory used=14912.5MB, alloc=588.7MB, time=106.24 memory used=15068.2MB, alloc=588.7MB, time=107.11 memory used=15200.9MB, alloc=588.7MB, time=107.65 memory used=15329.3MB, alloc=588.7MB, time=108.29 memory used=15481.6MB, alloc=588.7MB, time=110.31 memory used=15603.5MB, alloc=588.7MB, time=110.67 memory used=15829.4MB, alloc=588.7MB, time=117.54 memory used=15966.8MB, alloc=588.7MB, time=119.74 memory used=16079.6MB, alloc=588.7MB, time=120.10 memory used=16308.9MB, alloc=588.7MB, time=120.58 memory used=16619.1MB, alloc=612.7MB, time=146.52 memory used=17787.8MB, alloc=612.7MB, time=149.45 memory used=17804.0MB, alloc=612.7MB, time=150.66 memory used=17819.7MB, alloc=612.7MB, time=151.85 memory used=18718.4MB, alloc=612.7MB, time=154.87 memory used=18733.8MB, alloc=612.7MB, time=155.93 memory used=19382.5MB, alloc=612.7MB, time=158.51 memory used=19833.3MB, alloc=612.7MB, time=160.72 memory used=21306.3MB, alloc=636.7MB, time=166.34 memory used=21321.7MB, alloc=636.7MB, time=167.46 memory used=21338.9MB, alloc=636.7MB, time=168.67 memory used=21432.5MB, alloc=665.4MB, time=171.40 memory used=21437.1MB, alloc=670.0MB, time=171.64 memory used=21441.8MB, alloc=674.7MB, time=171.88 memory used=21446.5MB, alloc=679.4MB, time=172.11 memory used=21451.2MB, alloc=665.4MB, time=172.44 memory used=21642.4MB, alloc=660.7MB, time=174.10 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428540405 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 3 3 F := [-13 y + 13 x - 16 x z, -15 x + 2 y - 11 z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 2 G := [-18 x y z - 6 x z - 14 x z , 20 y z - y z + 9 x y] > Problem := [F,G]; 3 2 3 3 3 Problem := [[-13 y + 13 x - 16 x z, -15 x + 2 y - 11 z ], 2 3 2 2 2 [-18 x y z - 6 x z - 14 x z , 20 y z - y z + 9 x y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.4MB, alloc=32.3MB, time=0.45 memory used=47.0MB, alloc=32.3MB, time=0.74 memory used=65.9MB, alloc=56.3MB, time=1.02 memory used=106.2MB, alloc=60.3MB, time=1.58 memory used=147.8MB, alloc=84.3MB, time=2.13 memory used=209.9MB, alloc=92.3MB, time=2.94 memory used=271.0MB, alloc=116.3MB, time=3.75 memory used=352.4MB, alloc=116.3MB, time=4.89 memory used=430.7MB, alloc=396.3MB, time=6.01 memory used=542.8MB, alloc=396.3MB, time=7.20 memory used=614.2MB, alloc=396.3MB, time=8.95 memory used=720.9MB, alloc=396.3MB, time=12.14 memory used=817.3MB, alloc=396.3MB, time=13.20 memory used=922.0MB, alloc=420.3MB, time=14.03 memory used=1007.8MB, alloc=420.3MB, time=16.14 memory used=1146.9MB, alloc=420.3MB, time=17.82 memory used=1267.8MB, alloc=420.3MB, time=19.28 memory used=1401.0MB, alloc=444.3MB, time=20.60 memory used=1541.2MB, alloc=468.3MB, time=22.03 memory used=1657.8MB, alloc=468.3MB, time=23.20 memory used=1783.8MB, alloc=492.3MB, time=24.39 memory used=1893.1MB, alloc=492.3MB, time=25.48 memory used=2008.4MB, alloc=492.3MB, time=26.48 memory used=2124.4MB, alloc=516.3MB, time=27.61 memory used=2220.9MB, alloc=516.3MB, time=28.61 memory used=2390.8MB, alloc=516.3MB, time=30.28 memory used=2518.4MB, alloc=516.3MB, time=31.21 memory used=2630.2MB, alloc=540.3MB, time=32.26 memory used=2758.8MB, alloc=540.3MB, time=33.24 memory used=2862.4MB, alloc=540.3MB, time=33.60 memory used=2987.6MB, alloc=540.3MB, time=34.16 memory used=3091.0MB, alloc=540.3MB, time=34.51 memory used=3231.4MB, alloc=540.3MB, time=42.64 memory used=3334.9MB, alloc=540.3MB, time=42.99 memory used=3449.9MB, alloc=540.3MB, time=43.37 memory used=3561.8MB, alloc=540.3MB, time=43.81 memory used=3685.2MB, alloc=540.3MB, time=44.34 memory used=3791.2MB, alloc=540.3MB, time=44.72 memory used=3918.5MB, alloc=540.3MB, time=46.70 memory used=4043.0MB, alloc=540.3MB, time=53.07 memory used=4137.6MB, alloc=540.3MB, time=53.39 memory used=4281.9MB, alloc=540.3MB, time=54.08 memory used=4418.0MB, alloc=540.3MB, time=54.83 memory used=4580.2MB, alloc=540.3MB, time=57.76 memory used=4769.8MB, alloc=540.3MB, time=59.36 memory used=4884.1MB, alloc=540.3MB, time=60.17 memory used=5024.4MB, alloc=540.3MB, time=62.07 memory used=5160.7MB, alloc=540.3MB, time=63.30 memory used=5237.7MB, alloc=540.3MB, time=64.24 memory used=5400.4MB, alloc=564.3MB, time=66.20 memory used=5502.8MB, alloc=564.3MB, time=66.87 memory used=5666.7MB, alloc=564.3MB, time=69.93 memory used=5725.8MB, alloc=564.3MB, time=70.75 memory used=5834.7MB, alloc=588.3MB, time=71.53 memory used=5957.5MB, alloc=588.3MB, time=72.26 memory used=6116.9MB, alloc=588.3MB, time=78.83 memory used=6236.1MB, alloc=588.3MB, time=79.25 memory used=6360.5MB, alloc=588.3MB, time=79.66 memory used=6554.3MB, alloc=588.3MB, time=80.50 memory used=6700.9MB, alloc=588.3MB, time=81.33 memory used=6761.0MB, alloc=588.3MB, time=82.10 memory used=6831.5MB, alloc=588.3MB, time=82.88 memory used=6904.0MB, alloc=588.3MB, time=83.68 memory used=7156.1MB, alloc=612.3MB, time=85.22 memory used=7369.0MB, alloc=612.3MB, time=86.81 memory used=7572.5MB, alloc=612.3MB, time=98.81 memory used=7721.4MB, alloc=612.3MB, time=99.38 memory used=7924.8MB, alloc=612.3MB, time=101.25 memory used=8118.9MB, alloc=612.3MB, time=112.40 memory used=8250.3MB, alloc=612.3MB, time=112.86 memory used=8543.5MB, alloc=612.3MB, time=114.58 memory used=8825.1MB, alloc=612.3MB, time=116.10 memory used=9137.3MB, alloc=636.3MB, time=119.12 memory used=9484.5MB, alloc=660.3MB, time=121.66 memory used=9865.4MB, alloc=684.3MB, time=124.92 memory used=10197.9MB, alloc=708.3MB, time=128.59 memory used=10526.7MB, alloc=732.3MB, time=132.97 memory used=10763.1MB, alloc=756.3MB, time=135.34 memory used=10994.4MB, alloc=756.3MB, time=137.80 memory used=11243.9MB, alloc=756.3MB, time=141.70 memory used=11463.4MB, alloc=756.3MB, time=144.50 memory used=11676.2MB, alloc=756.3MB, time=147.90 memory used=12017.7MB, alloc=756.3MB, time=152.00 memory used=12262.7MB, alloc=756.3MB, time=154.57 memory used=12496.1MB, alloc=756.3MB, time=157.72 memory used=12752.9MB, alloc=756.3MB, time=161.45 memory used=12959.0MB, alloc=756.3MB, time=163.94 memory used=13268.4MB, alloc=756.3MB, time=168.47 memory used=13632.2MB, alloc=780.3MB, time=172.48 memory used=13936.2MB, alloc=804.3MB, time=176.68 memory used=14248.4MB, alloc=828.3MB, time=180.79 memory used=14509.3MB, alloc=852.3MB, time=184.35 memory used=14856.0MB, alloc=876.3MB, time=188.32 memory used=15157.4MB, alloc=900.3MB, time=191.94 memory used=15495.7MB, alloc=924.3MB, time=195.72 memory used=15750.0MB, alloc=948.3MB, time=199.22 memory used=16033.8MB, alloc=972.3MB, time=202.94 memory used=16503.4MB, alloc=996.3MB, time=209.21 memory used=16902.5MB, alloc=1020.3MB, time=217.58 memory used=17253.2MB, alloc=1044.3MB, time=226.65 memory used=17605.9MB, alloc=1068.3MB, time=236.18 memory used=17965.9MB, alloc=1092.3MB, time=246.18 memory used=18336.3MB, alloc=1116.3MB, time=256.43 memory used=18718.4MB, alloc=1140.3MB, time=267.12 memory used=19112.9MB, alloc=1164.3MB, time=278.36 memory used=19520.9MB, alloc=1188.3MB, time=290.02 memory used=19943.0MB, alloc=1212.3MB, time=301.97 memory used=20378.8MB, alloc=1236.3MB, time=314.43 memory used=20828.5MB, alloc=1260.3MB, time=327.31 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428540705 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 4 2 2 F := [17 x y z - 2 y z + 19 y z , -x - 15 x + 3 z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 G := [17 x y + 5 y , 15 x y - 20 y z - 12 z ] > Problem := [F,G]; 2 3 2 2 4 2 2 Problem := [[17 x y z - 2 y z + 19 y z , -x - 15 x + 3 z ], 2 2 2 3 [17 x y + 5 y , 15 x y - 20 y z - 12 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.14 memory used=26.7MB, alloc=32.3MB, time=0.40 memory used=48.3MB, alloc=32.3MB, time=0.66 memory used=68.9MB, alloc=56.3MB, time=0.92 memory used=110.8MB, alloc=60.3MB, time=1.41 memory used=150.7MB, alloc=84.3MB, time=1.91 memory used=215.0MB, alloc=92.3MB, time=2.87 memory used=274.8MB, alloc=116.3MB, time=3.55 memory used=353.8MB, alloc=140.3MB, time=4.38 memory used=444.4MB, alloc=164.3MB, time=5.49 memory used=535.8MB, alloc=188.3MB, time=7.32 memory used=641.9MB, alloc=212.3MB, time=9.61 memory used=772.0MB, alloc=212.3MB, time=12.21 N1 := 3827 > GB := Basis(F, plex(op(vars))); 8 2 6 2 5 3 4 4 4 2 GB := [-361 x y - 9963 x y - 204 x y + 12 x y - 68220 x y 3 3 2 4 - 3060 x y + 180 x y , 5 2 4 3 4 2 3 2 2 3 2 2 17 x y - 2 x y + 19 x y z + 255 x y - 30 x y + 285 x y z, 4 2 2 2 2 3 4 2 2 -19 x y - 285 x y - 51 x y z + 6 y z, -x - 15 x + 3 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=906.2MB, alloc=212.3MB, time=14.21 memory used=984.1MB, alloc=468.3MB, time=15.04 memory used=1140.8MB, alloc=492.3MB, time=16.45 memory used=1284.5MB, alloc=516.3MB, time=17.74 memory used=1458.5MB, alloc=540.3MB, time=19.44 memory used=1671.6MB, alloc=564.3MB, time=21.80 memory used=1891.8MB, alloc=588.3MB, time=25.77 memory used=2085.5MB, alloc=612.3MB, time=30.48 memory used=2303.4MB, alloc=636.3MB, time=35.57 N2 := 4583 > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 3 2 2 4 2 2 2 H := [17 x y z - 2 y z + 19 y z , -x - 15 x + 3 z , 17 x y + 5 y , 3 2 2 -12 z - 20 z y + 15 y x ] > J:=[op(GB),op(G)]; 8 2 6 2 5 3 4 4 4 2 3 3 J := [-361 x y - 9963 x y - 204 x y + 12 x y - 68220 x y - 3060 x y 2 4 + 180 x y , 5 2 4 3 4 2 3 2 2 3 2 2 17 x y - 2 x y + 19 x y z + 255 x y - 30 x y + 285 x y z, 4 2 2 2 2 3 4 2 2 -19 x y - 285 x y - 51 x y z + 6 y z, -x - 15 x + 3 z , 2 3 2 2 17 x y + 5 y , -12 z - 20 z y + 15 y x ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 10, 13, 4, 4, 3, 3, 1, 3/4, 3/4, 5/11, 7/11, 6/11, 6, 15, 32, 21 10, 8, 4, 3, 1, 5/6, 2/3, 4/5, --, 7/25, -5, -19, -6] 25 > save(F, G, cat("ranSet/34", convert(F, string),".txt")); > quit memory used=2406.1MB, alloc=636.3MB, time=37.34 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428540742 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 4 2 2 F := [13 y z + 15 y z + 18 x z , -8 z + 3 y z + 17 y ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 G := [19 x y - 10 x y z - 16 y, 16 x + 17 x - 16 y] > Problem := [F,G]; 3 3 2 4 2 2 Problem := [[13 y z + 15 y z + 18 x z , -8 z + 3 y z + 17 y ], 3 2 3 [19 x y - 10 x y z - 16 y, 16 x + 17 x - 16 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.12 memory used=26.5MB, alloc=32.3MB, time=0.34 memory used=47.3MB, alloc=32.3MB, time=0.55 memory used=65.5MB, alloc=56.3MB, time=0.73 memory used=108.4MB, alloc=68.3MB, time=1.15 memory used=151.8MB, alloc=68.3MB, time=1.49 memory used=194.4MB, alloc=68.3MB, time=1.85 memory used=236.2MB, alloc=92.3MB, time=2.20 memory used=304.6MB, alloc=92.3MB, time=2.75 memory used=354.1MB, alloc=92.3MB, time=3.05 memory used=438.8MB, alloc=124.3MB, time=3.70 memory used=507.9MB, alloc=124.3MB, time=4.04 memory used=568.7MB, alloc=124.3MB, time=4.26 memory used=638.5MB, alloc=124.3MB, time=4.55 memory used=697.4MB, alloc=124.3MB, time=4.70 memory used=758.5MB, alloc=124.3MB, time=4.89 memory used=832.5MB, alloc=124.3MB, time=5.16 memory used=899.6MB, alloc=124.3MB, time=5.87 memory used=945.1MB, alloc=124.3MB, time=6.02 memory used=1006.6MB, alloc=124.3MB, time=6.16 memory used=1045.8MB, alloc=124.3MB, time=6.27 memory used=1083.7MB, alloc=124.3MB, time=6.40 memory used=1127.3MB, alloc=124.3MB, time=6.51 memory used=1173.8MB, alloc=124.3MB, time=6.63 memory used=1226.3MB, alloc=124.3MB, time=6.76 memory used=1284.9MB, alloc=124.3MB, time=6.89 memory used=1346.1MB, alloc=124.3MB, time=7.03 memory used=1386.1MB, alloc=124.3MB, time=7.12 memory used=1419.3MB, alloc=124.3MB, time=7.21 memory used=1452.0MB, alloc=124.3MB, time=7.30 memory used=1485.6MB, alloc=124.3MB, time=7.38 memory used=1522.0MB, alloc=124.3MB, time=7.47 memory used=1559.1MB, alloc=124.3MB, time=7.55 memory used=1600.2MB, alloc=124.3MB, time=7.64 memory used=1641.1MB, alloc=124.3MB, time=7.73 memory used=1685.6MB, alloc=124.3MB, time=7.83 memory used=1730.3MB, alloc=124.3MB, time=7.92 memory used=1777.3MB, alloc=124.3MB, time=8.01 memory used=1827.0MB, alloc=124.3MB, time=8.11 memory used=1881.2MB, alloc=124.3MB, time=8.20 memory used=1937.2MB, alloc=124.3MB, time=8.30 memory used=1997.1MB, alloc=124.3MB, time=8.40 memory used=2061.3MB, alloc=139.8MB, time=8.50 memory used=2071.4MB, alloc=139.8MB, time=8.57 memory used=2081.4MB, alloc=139.8MB, time=8.62 memory used=2091.5MB, alloc=139.8MB, time=8.68 memory used=2101.7MB, alloc=139.8MB, time=8.74 memory used=2168.3MB, alloc=139.8MB, time=8.95 memory used=2240.8MB, alloc=139.8MB, time=21.70 memory used=2318.2MB, alloc=139.8MB, time=45.55 memory used=2368.4MB, alloc=163.8MB, time=80.19 memory used=2423.1MB, alloc=163.8MB, time=117.90 memory used=2490.4MB, alloc=163.8MB, time=138.15 memory used=2569.3MB, alloc=163.8MB, time=139.20 memory used=2626.3MB, alloc=163.8MB, time=139.35 memory used=2698.8MB, alloc=163.8MB, time=139.51 memory used=2752.9MB, alloc=163.8MB, time=139.63 memory used=2799.2MB, alloc=163.8MB, time=139.74 memory used=2851.4MB, alloc=163.8MB, time=139.85 memory used=2906.9MB, alloc=163.8MB, time=139.97 memory used=2968.0MB, alloc=163.8MB, time=140.08 memory used=3032.2MB, alloc=163.8MB, time=140.21 memory used=3102.2MB, alloc=163.8MB, time=140.33 memory used=3178.2MB, alloc=163.8MB, time=140.45 memory used=3261.2MB, alloc=163.8MB, time=140.59 memory used=3268.9MB, alloc=163.8MB, time=140.65 memory used=3274.7MB, alloc=163.8MB, time=140.71 memory used=3280.5MB, alloc=163.8MB, time=140.77 memory used=3286.7MB, alloc=163.8MB, time=140.83 memory used=3293.0MB, alloc=163.8MB, time=140.88 memory used=3299.3MB, alloc=163.8MB, time=140.94 memory used=3305.6MB, alloc=163.8MB, time=141.00 memory used=3311.9MB, alloc=163.8MB, time=141.06 memory used=3318.3MB, alloc=163.8MB, time=141.12 memory used=3324.6MB, alloc=163.8MB, time=141.19 memory used=3330.9MB, alloc=163.8MB, time=141.26 memory used=3337.3MB, alloc=163.8MB, time=141.32 memory used=3343.7MB, alloc=163.8MB, time=141.39 memory used=3350.1MB, alloc=163.8MB, time=141.45 memory used=3356.5MB, alloc=163.8MB, time=141.52 memory used=3362.9MB, alloc=163.8MB, time=141.57 memory used=3369.3MB, alloc=163.8MB, time=141.63 memory used=3375.7MB, alloc=163.8MB, time=141.68 memory used=3382.2MB, alloc=163.8MB, time=141.74 memory used=3388.6MB, alloc=163.8MB, time=141.80 memory used=3395.1MB, alloc=163.8MB, time=141.86 memory used=3401.5MB, alloc=163.8MB, time=141.92 memory used=3408.0MB, alloc=163.8MB, time=141.98 memory used=3414.5MB, alloc=163.8MB, time=142.05 memory used=3421.0MB, alloc=163.8MB, time=142.11 memory used=3427.5MB, alloc=163.8MB, time=142.17 memory used=3434.1MB, alloc=163.8MB, time=142.23 memory used=3440.8MB, alloc=163.8MB, time=142.29 memory used=3447.4MB, alloc=163.8MB, time=142.35 memory used=3457.0MB, alloc=163.8MB, time=142.42 memory used=3463.8MB, alloc=163.8MB, time=142.48 memory used=3473.4MB, alloc=163.8MB, time=142.54 memory used=3480.3MB, alloc=163.8MB, time=142.60 memory used=3489.9MB, alloc=163.8MB, time=142.67 memory used=3499.8MB, alloc=163.8MB, time=142.73 memory used=3509.7MB, alloc=163.8MB, time=142.79 memory used=3519.7MB, alloc=163.8MB, time=142.85 memory used=3529.6MB, alloc=163.8MB, time=142.91 memory used=3539.6MB, 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alloc=419.8MB, time=182.28 memory used=9487.6MB, alloc=419.8MB, time=182.39 memory used=9561.4MB, alloc=419.8MB, time=182.51 memory used=9650.3MB, alloc=419.8MB, time=182.65 memory used=9805.9MB, alloc=419.8MB, time=182.97 memory used=9958.0MB, alloc=419.8MB, time=183.18 memory used=10126.9MB, alloc=419.8MB, time=183.40 memory used=10317.4MB, alloc=419.8MB, time=183.62 memory used=10538.5MB, alloc=419.8MB, time=183.86 memory used=10745.7MB, alloc=419.8MB, time=184.49 memory used=10817.7MB, alloc=419.8MB, time=184.69 memory used=10886.3MB, alloc=419.8MB, time=184.88 memory used=10983.0MB, alloc=419.8MB, time=185.29 memory used=11044.8MB, alloc=419.8MB, time=185.45 memory used=11104.6MB, alloc=419.8MB, time=185.58 memory used=11187.8MB, alloc=419.8MB, time=187.46 memory used=11245.6MB, alloc=419.8MB, time=187.62 memory used=11318.7MB, alloc=419.8MB, time=187.80 memory used=11361.8MB, alloc=419.8MB, time=187.96 memory used=11404.3MB, alloc=419.8MB, time=188.14 memory used=11449.0MB, alloc=419.8MB, time=188.30 memory used=11496.6MB, alloc=419.8MB, time=188.44 memory used=11547.0MB, alloc=419.8MB, time=188.58 memory used=11599.9MB, alloc=443.8MB, time=188.72 memory used=11676.7MB, alloc=443.8MB, time=188.91 memory used=11762.1MB, alloc=443.8MB, time=189.10 memory used=11852.6MB, alloc=443.8MB, time=189.29 memory used=11905.3MB, alloc=443.8MB, time=189.42 memory used=11947.8MB, alloc=443.8MB, time=189.54 memory used=11996.7MB, alloc=443.8MB, time=189.67 memory used=12046.7MB, alloc=443.8MB, time=189.79 memory used=12097.8MB, alloc=443.8MB, time=189.92 memory used=12150.0MB, alloc=443.8MB, time=190.04 memory used=12203.2MB, alloc=443.8MB, time=190.17 memory used=12257.4MB, alloc=443.8MB, time=190.29 memory used=12312.6MB, alloc=443.8MB, time=190.42 memory used=12368.8MB, alloc=443.8MB, time=190.54 memory used=12425.9MB, alloc=443.8MB, time=190.67 memory used=12484.0MB, alloc=443.8MB, time=190.80 memory used=12542.9MB, alloc=443.8MB, time=190.92 memory used=12602.7MB, alloc=443.8MB, time=191.05 memory used=12663.4MB, alloc=443.8MB, time=191.18 memory used=12724.9MB, alloc=443.8MB, time=191.31 memory used=12787.3MB, alloc=467.8MB, time=191.45 memory used=12870.1MB, alloc=467.8MB, time=191.60 memory used=12960.3MB, alloc=467.8MB, time=191.76 memory used=13051.9MB, alloc=467.8MB, time=191.92 memory used=13144.9MB, alloc=467.8MB, time=192.08 memory used=13239.3MB, alloc=467.8MB, time=192.24 memory used=13336.1MB, alloc=467.8MB, time=192.40 memory used=13445.6MB, alloc=467.8MB, time=192.56 memory used=13557.7MB, alloc=467.8MB, time=192.73 memory used=13772.9MB, alloc=467.8MB, time=193.04 memory used=13890.4MB, alloc=467.8MB, time=193.25 memory used=14022.0MB, alloc=467.8MB, time=193.48 memory used=14154.8MB, alloc=467.8MB, time=193.70 memory used=14288.7MB, alloc=467.8MB, time=193.92 memory used=14423.6MB, alloc=467.8MB, time=194.14 memory used=14559.3MB, alloc=467.8MB, time=194.37 memory used=14710.9MB, alloc=467.8MB, time=194.60 memory used=14863.2MB, alloc=467.8MB, time=194.83 memory used=15016.0MB, alloc=467.8MB, time=195.07 memory used=15170.7MB, alloc=467.8MB, time=195.31 memory used=15337.7MB, alloc=467.8MB, time=195.55 memory used=15506.2MB, alloc=467.8MB, time=195.80 memory used=15676.0MB, alloc=467.8MB, time=196.05 memory used=15857.1MB, alloc=467.8MB, time=196.30 memory used=16038.9MB, alloc=467.8MB, time=196.57 memory used=16234.3MB, alloc=467.8MB, time=196.83 memory used=16427.8MB, alloc=467.8MB, time=197.10 memory used=16633.5MB, alloc=467.8MB, time=197.38 memory used=16850.3MB, alloc=467.8MB, time=197.67 memory used=17066.1MB, alloc=467.8MB, time=197.94 memory used=17297.7MB, alloc=467.8MB, time=198.23 memory used=17538.5MB, alloc=467.8MB, time=198.52 memory used=17778.2MB, alloc=467.8MB, time=198.81 memory used=17953.4MB, alloc=467.8MB, time=199.04 memory used=18129.0MB, alloc=467.8MB, time=199.27 memory used=18305.4MB, alloc=467.8MB, time=199.51 memory used=18492.6MB, alloc=467.8MB, time=199.75 memory used=18687.8MB, alloc=467.8MB, time=200.00 memory used=18893.9MB, alloc=467.8MB, time=200.23 memory used=19085.9MB, alloc=467.8MB, time=207.61 memory used=19211.9MB, alloc=467.8MB, time=259.97 memory used=19361.2MB, alloc=467.8MB, time=380.06 memory used=19433.9MB, alloc=467.8MB, time=472.35 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428541042 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 3 F := [3 y z + 7 x y - 16 x z , -16 x + 19 y + 18 z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 2 4 2 G := [19 x + 10 z + 10 z , -2 x - 16 x y z + 12 x y z] > Problem := [F,G]; 3 2 2 3 Problem := [[3 y z + 7 x y - 16 x z , -16 x + 19 y + 18 z], 4 3 2 4 2 [19 x + 10 z + 10 z , -2 x - 16 x y z + 12 x y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.1MB, alloc=32.3MB, time=0.47 memory used=44.6MB, alloc=56.3MB, time=0.72 memory used=86.2MB, alloc=60.3MB, time=1.27 memory used=132.7MB, alloc=68.3MB, time=1.86 memory used=171.5MB, alloc=68.3MB, time=2.18 memory used=219.6MB, alloc=68.3MB, time=2.70 memory used=269.3MB, alloc=92.3MB, time=3.21 memory used=337.4MB, alloc=92.3MB, time=4.03 memory used=397.9MB, alloc=348.3MB, time=4.85 memory used=459.5MB, alloc=348.3MB, time=5.40 memory used=499.6MB, alloc=348.3MB, time=5.62 memory used=543.6MB, alloc=348.3MB, time=5.87 memory used=573.8MB, alloc=372.3MB, time=6.00 memory used=628.6MB, alloc=372.3MB, time=6.24 memory used=690.4MB, alloc=372.3MB, time=6.51 memory used=744.5MB, alloc=372.3MB, time=6.71 memory used=793.3MB, alloc=372.3MB, time=6.87 memory used=881.7MB, alloc=372.3MB, time=7.65 memory used=976.2MB, alloc=372.3MB, time=8.66 memory used=1078.0MB, alloc=372.3MB, time=9.55 memory used=1170.8MB, alloc=372.3MB, time=10.69 memory used=1211.2MB, alloc=372.3MB, time=10.85 memory used=1289.0MB, alloc=372.3MB, time=11.36 memory used=1382.2MB, alloc=396.3MB, time=12.51 memory used=1491.2MB, alloc=396.3MB, time=13.59 memory used=1590.6MB, alloc=396.3MB, time=14.85 memory used=1664.2MB, alloc=396.3MB, time=17.26 memory used=1716.6MB, alloc=396.3MB, time=17.43 memory used=1761.0MB, alloc=396.3MB, time=17.56 memory used=1805.7MB, alloc=396.3MB, time=17.69 memory used=1860.0MB, alloc=396.3MB, time=17.84 memory used=1912.6MB, alloc=396.3MB, time=17.97 memory used=1949.2MB, alloc=396.3MB, time=18.08 memory used=2033.3MB, alloc=396.3MB, time=18.54 memory used=2157.0MB, alloc=396.3MB, time=19.03 memory used=2269.2MB, alloc=396.3MB, time=19.66 memory used=2330.1MB, alloc=396.3MB, time=19.90 memory used=2383.3MB, alloc=396.3MB, time=20.07 memory used=2440.9MB, alloc=396.3MB, time=20.26 memory used=2491.1MB, alloc=396.3MB, time=20.46 memory used=2536.9MB, alloc=396.3MB, time=20.61 memory used=2589.4MB, alloc=396.3MB, time=20.76 memory used=2629.1MB, alloc=396.3MB, time=20.89 memory used=2668.5MB, alloc=396.3MB, time=21.01 memory used=2713.4MB, alloc=396.3MB, time=21.14 memory used=2766.0MB, alloc=396.3MB, time=21.27 memory used=2838.0MB, alloc=396.3MB, time=21.57 memory used=2888.6MB, alloc=396.3MB, time=21.74 memory used=2927.5MB, alloc=396.3MB, time=21.87 memory used=2974.2MB, alloc=396.3MB, time=22.00 memory used=3072.8MB, alloc=396.3MB, time=22.22 memory used=3119.8MB, alloc=396.3MB, time=22.37 memory used=3172.0MB, alloc=396.3MB, time=22.54 memory used=3262.2MB, alloc=396.3MB, time=23.07 memory used=3314.3MB, alloc=396.3MB, time=23.24 memory used=3396.2MB, alloc=396.3MB, time=23.69 memory used=3494.2MB, alloc=396.3MB, time=24.21 memory used=3599.2MB, alloc=420.3MB, time=24.99 memory used=3686.3MB, alloc=420.3MB, time=25.70 memory used=3747.1MB, alloc=420.3MB, time=25.86 memory used=3808.5MB, alloc=420.3MB, time=26.01 memory used=3861.4MB, alloc=420.3MB, time=26.15 memory used=3928.6MB, alloc=420.3MB, time=26.30 memory used=4062.6MB, alloc=420.3MB, time=27.11 memory used=4191.0MB, alloc=420.3MB, time=27.98 memory used=4268.8MB, alloc=420.3MB, time=28.31 memory used=4336.7MB, alloc=420.3MB, time=28.56 memory used=4409.9MB, alloc=420.3MB, time=28.79 memory used=4462.2MB, alloc=420.3MB, time=28.98 memory used=4533.9MB, alloc=420.3MB, time=29.22 memory used=4590.8MB, alloc=420.3MB, time=29.42 memory used=4647.5MB, alloc=420.3MB, time=29.58 memory used=4710.8MB, alloc=420.3MB, time=29.88 memory used=4787.4MB, alloc=420.3MB, time=30.15 memory used=4846.6MB, alloc=420.3MB, time=30.33 memory used=4922.1MB, alloc=420.3MB, time=30.64 memory used=4984.9MB, alloc=420.3MB, time=30.84 memory used=5045.1MB, alloc=420.3MB, time=31.03 memory used=5121.2MB, alloc=420.3MB, time=31.37 memory used=5192.3MB, alloc=420.3MB, time=31.60 memory used=5246.6MB, alloc=420.3MB, time=31.79 memory used=5308.1MB, alloc=420.3MB, time=31.96 memory used=5384.5MB, alloc=420.3MB, time=32.50 memory used=5442.5MB, alloc=420.3MB, time=32.67 memory used=5496.4MB, alloc=420.3MB, time=32.82 memory used=5565.0MB, alloc=420.3MB, time=33.03 memory used=5630.5MB, alloc=420.3MB, time=33.28 memory used=5758.6MB, alloc=420.3MB, time=34.00 memory used=5885.5MB, alloc=420.3MB, time=34.78 memory used=6001.4MB, alloc=420.3MB, time=35.85 memory used=6057.6MB, alloc=420.3MB, time=36.05 memory used=6111.7MB, alloc=420.3MB, time=36.24 memory used=6262.4MB, alloc=444.3MB, time=36.95 memory used=6363.9MB, alloc=444.3MB, time=37.43 memory used=6493.4MB, alloc=444.3MB, time=38.21 memory used=6600.9MB, alloc=444.3MB, time=38.99 memory used=6672.2MB, alloc=444.3MB, time=39.20 memory used=6734.8MB, alloc=444.3MB, time=39.38 memory used=6803.0MB, alloc=444.3MB, time=39.55 memory used=6965.7MB, alloc=444.3MB, time=40.43 memory used=7071.6MB, alloc=444.3MB, time=41.22 memory used=7205.2MB, alloc=444.3MB, time=42.05 memory used=7297.2MB, alloc=444.3MB, time=42.52 memory used=7369.5MB, alloc=444.3MB, time=42.78 memory used=7423.3MB, alloc=444.3MB, time=43.01 memory used=7488.6MB, alloc=444.3MB, time=43.24 memory used=7568.3MB, alloc=444.3MB, time=43.46 memory used=7620.7MB, alloc=444.3MB, time=43.65 memory used=7672.8MB, alloc=444.3MB, time=43.84 memory used=7730.7MB, alloc=444.3MB, time=44.02 memory used=7834.4MB, alloc=444.3MB, time=45.84 memory used=7898.0MB, alloc=444.3MB, time=46.07 memory used=7967.2MB, alloc=444.3MB, time=46.30 memory used=8028.6MB, alloc=444.3MB, time=46.50 memory used=8081.6MB, alloc=444.3MB, time=46.68 memory used=8142.4MB, alloc=444.3MB, time=46.87 memory used=8212.8MB, alloc=444.3MB, time=47.06 memory used=8368.7MB, alloc=444.3MB, time=47.44 memory used=8442.0MB, alloc=444.3MB, time=47.69 memory used=8500.6MB, alloc=444.3MB, time=47.90 memory used=8573.4MB, alloc=444.3MB, time=48.11 memory used=8650.8MB, alloc=444.3MB, time=48.59 memory used=8719.4MB, alloc=444.3MB, time=48.80 memory used=8773.1MB, alloc=444.3MB, time=48.98 memory used=8877.7MB, alloc=444.3MB, time=49.46 memory used=8951.5MB, alloc=444.3MB, time=49.73 memory used=9078.0MB, alloc=444.3MB, time=50.41 memory used=9214.9MB, alloc=468.3MB, time=51.16 memory used=9295.9MB, alloc=468.3MB, time=51.41 memory used=9374.6MB, alloc=468.3MB, time=51.66 memory used=9476.2MB, alloc=468.3MB, time=52.21 memory used=9556.4MB, alloc=468.3MB, time=52.43 memory used=9698.6MB, alloc=468.3MB, time=53.36 memory used=9814.6MB, alloc=468.3MB, time=54.87 memory used=9894.8MB, alloc=468.3MB, time=55.12 memory used=9975.9MB, alloc=468.3MB, time=55.35 memory used=10061.8MB, alloc=468.3MB, time=55.58 memory used=10124.1MB, alloc=468.3MB, time=55.78 memory used=10195.8MB, alloc=468.3MB, time=55.99 memory used=10278.9MB, alloc=468.3MB, time=56.21 memory used=10374.7MB, alloc=468.3MB, time=56.42 memory used=10586.6MB, alloc=468.3MB, time=57.43 memory used=10675.2MB, alloc=468.3MB, time=58.18 memory used=10761.8MB, alloc=468.3MB, time=58.91 memory used=10892.3MB, alloc=468.3MB, time=59.85 memory used=10992.0MB, alloc=468.3MB, time=60.31 memory used=11093.3MB, alloc=468.3MB, time=61.41 memory used=11173.8MB, alloc=468.3MB, time=61.69 memory used=11237.0MB, alloc=468.3MB, time=61.93 memory used=11304.9MB, alloc=468.3MB, time=62.16 memory used=11386.7MB, alloc=468.3MB, time=62.44 memory used=11636.2MB, alloc=468.3MB, time=63.23 memory used=11761.7MB, alloc=468.3MB, time=64.16 memory used=11880.8MB, alloc=468.3MB, time=65.11 memory used=12006.8MB, alloc=468.3MB, time=65.82 memory used=12139.5MB, alloc=468.3MB, time=66.79 memory used=12229.8MB, alloc=492.3MB, time=67.13 memory used=12368.9MB, alloc=492.3MB, time=68.01 memory used=12485.1MB, alloc=492.3MB, time=68.63 memory used=12628.5MB, alloc=492.3MB, time=69.84 memory used=12705.6MB, alloc=492.3MB, time=70.16 memory used=12793.5MB, alloc=492.3MB, time=70.46 memory used=12895.8MB, alloc=492.3MB, time=70.79 memory used=13011.3MB, alloc=492.3MB, time=71.11 memory used=13082.0MB, alloc=492.3MB, time=71.40 memory used=13226.7MB, alloc=492.3MB, time=72.02 memory used=13343.9MB, alloc=492.3MB, time=72.92 memory used=13416.2MB, alloc=492.3MB, time=73.51 memory used=13522.4MB, alloc=492.3MB, time=74.45 memory used=13718.4MB, alloc=492.3MB, time=75.12 memory used=13922.8MB, alloc=492.3MB, time=75.99 memory used=14057.2MB, alloc=492.3MB, time=76.44 memory used=14193.5MB, alloc=492.3MB, time=76.83 memory used=14366.2MB, alloc=492.3MB, time=77.67 memory used=14513.6MB, alloc=492.3MB, time=78.08 memory used=14669.4MB, alloc=492.3MB, time=78.50 memory used=14846.0MB, alloc=492.3MB, time=78.91 memory used=15041.2MB, alloc=492.3MB, time=79.34 memory used=15265.0MB, alloc=492.3MB, time=80.19 memory used=15425.3MB, alloc=492.3MB, time=80.87 memory used=15587.7MB, alloc=492.3MB, time=82.17 memory used=15677.4MB, alloc=492.3MB, time=83.00 memory used=15780.1MB, alloc=516.3MB, time=83.95 memory used=15929.7MB, alloc=516.3MB, time=85.45 memory used=16113.0MB, alloc=516.3MB, time=86.33 memory used=16314.2MB, alloc=516.3MB, time=86.79 memory used=16596.4MB, alloc=516.3MB, time=87.32 memory used=17014.9MB, alloc=516.3MB, time=88.01 memory used=17396.4MB, alloc=516.3MB, time=88.63 memory used=17771.8MB, alloc=516.3MB, time=89.26 memory used=18134.8MB, alloc=516.3MB, time=89.85 memory used=18501.1MB, alloc=516.3MB, time=90.46 memory used=18848.7MB, alloc=516.3MB, time=91.61 memory used=19025.9MB, alloc=516.3MB, time=92.25 memory used=19189.7MB, alloc=516.3MB, time=92.68 memory used=19373.8MB, alloc=516.3MB, time=93.13 memory used=19577.3MB, alloc=516.3MB, time=93.60 memory used=19782.9MB, alloc=516.3MB, time=95.26 memory used=19964.1MB, alloc=516.3MB, time=95.86 memory used=20185.5MB, alloc=516.3MB, time=96.32 memory used=20468.1MB, alloc=516.3MB, time=96.87 memory used=20820.8MB, alloc=516.3MB, time=97.83 memory used=21034.7MB, alloc=516.3MB, time=98.38 memory used=21313.0MB, alloc=516.3MB, time=98.88 memory used=21734.8MB, alloc=516.3MB, time=99.54 memory used=22116.1MB, alloc=516.3MB, time=100.13 memory used=22480.5MB, alloc=516.3MB, time=100.73 memory used=22841.4MB, alloc=516.3MB, time=101.32 memory used=23210.4MB, alloc=516.3MB, time=102.58 memory used=23397.5MB, alloc=516.3MB, time=103.04 memory used=23599.1MB, alloc=516.3MB, time=103.77 memory used=23774.5MB, alloc=516.3MB, time=104.22 memory used=23991.6MB, alloc=516.3MB, time=105.06 memory used=24172.4MB, alloc=516.3MB, time=105.72 memory used=24372.5MB, alloc=516.3MB, time=106.18 memory used=24637.3MB, alloc=516.3MB, time=106.70 memory used=24944.9MB, alloc=516.3MB, time=107.25 memory used=25128.6MB, alloc=516.3MB, time=108.35 memory used=25293.3MB, alloc=516.3MB, time=109.27 memory used=25476.8MB, alloc=516.3MB, time=109.77 memory used=25716.5MB, alloc=516.3MB, time=110.25 memory used=26071.2MB, alloc=516.3MB, time=110.85 memory used=26469.5MB, alloc=516.3MB, time=111.51 memory used=26902.1MB, alloc=516.3MB, time=113.03 memory used=27076.9MB, alloc=516.3MB, time=114.00 memory used=27209.6MB, alloc=540.3MB, time=114.83 memory used=27400.0MB, alloc=540.3MB, time=115.34 memory used=27649.9MB, alloc=540.3MB, time=115.89 memory used=27925.4MB, alloc=540.3MB, time=116.43 memory used=28227.4MB, alloc=540.3MB, time=117.50 memory used=28421.5MB, alloc=540.3MB, time=118.64 memory used=28654.0MB, alloc=540.3MB, time=119.65 memory used=28901.4MB, alloc=540.3MB, time=120.74 memory used=29135.8MB, alloc=540.3MB, time=121.99 memory used=29388.7MB, alloc=540.3MB, time=123.14 memory used=29640.0MB, alloc=540.3MB, time=124.14 memory used=29839.4MB, alloc=540.3MB, time=125.55 memory used=29975.8MB, alloc=540.3MB, time=126.79 memory used=30121.3MB, alloc=564.3MB, time=128.15 memory used=30290.0MB, alloc=564.3MB, time=129.54 memory used=30457.8MB, alloc=564.3MB, time=130.83 memory used=30625.2MB, alloc=564.3MB, time=132.18 memory used=30817.3MB, alloc=564.3MB, time=133.99 memory used=30961.1MB, alloc=564.3MB, time=135.18 memory used=31135.3MB, alloc=588.3MB, time=136.63 memory used=31272.3MB, alloc=588.3MB, time=137.93 memory used=31382.6MB, alloc=588.3MB, time=139.16 memory used=31490.0MB, alloc=588.3MB, time=140.44 memory used=31600.1MB, alloc=612.3MB, time=141.75 memory used=31694.9MB, alloc=612.3MB, time=142.91 memory used=31784.7MB, alloc=612.3MB, time=144.07 memory used=31882.1MB, alloc=636.3MB, time=145.37 memory used=32224.7MB, alloc=660.3MB, time=148.72 memory used=32538.5MB, alloc=684.3MB, time=151.83 memory used=32911.4MB, alloc=708.3MB, time=154.84 memory used=33313.0MB, alloc=708.3MB, time=156.78 memory used=33704.1MB, alloc=708.3MB, time=159.04 memory used=34127.8MB, alloc=732.3MB, time=162.88 memory used=34533.6MB, alloc=756.3MB, time=165.16 memory used=34958.6MB, alloc=780.3MB, time=168.63 memory used=35419.6MB, alloc=804.3MB, time=172.10 memory used=35919.6MB, alloc=804.3MB, time=174.52 memory used=36444.0MB, alloc=804.3MB, time=177.65 memory used=36936.5MB, alloc=804.3MB, time=180.87 memory used=37415.7MB, alloc=828.3MB, time=184.57 memory used=37893.5MB, alloc=852.3MB, time=188.53 memory used=38373.4MB, alloc=876.3MB, time=192.88 memory used=38915.7MB, alloc=900.3MB, time=196.24 memory used=39408.7MB, alloc=924.3MB, time=200.70 memory used=39797.5MB, alloc=948.3MB, time=205.02 memory used=40404.4MB, alloc=972.3MB, time=210.15 memory used=41039.1MB, alloc=996.3MB, time=215.23 memory used=41678.9MB, alloc=1020.3MB, time=218.24 memory used=42306.5MB, alloc=1044.3MB, time=222.97 memory used=42780.1MB, alloc=1068.3MB, time=234.50 memory used=43241.9MB, alloc=1092.3MB, time=246.61 memory used=43704.2MB, alloc=1116.3MB, time=258.98 memory used=44171.6MB, alloc=1140.3MB, time=271.75 memory used=44649.9MB, alloc=1164.3MB, time=284.93 memory used=45140.5MB, alloc=1188.3MB, time=298.57 memory used=45642.2MB, alloc=1212.3MB, time=312.65 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428541342 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 F := [-7 x - 8 x y + 4 x z, 20 x z - 16 x y - 10 x z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 3 2 3 G := [-16 x - 19 x y z + 18 x z , 15 x - 19 x z - 17 y ] > Problem := [F,G]; 3 2 2 2 Problem := [[-7 x - 8 x y + 4 x z, 20 x z - 16 x y - 10 x z], 4 2 2 3 2 3 [-16 x - 19 x y z + 18 x z , 15 x - 19 x z - 17 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.14 memory used=26.3MB, alloc=32.3MB, time=0.45 memory used=49.1MB, alloc=60.3MB, time=0.69 memory used=94.2MB, alloc=60.3MB, time=1.02 memory used=137.5MB, alloc=68.3MB, time=1.40 memory used=179.2MB, alloc=68.3MB, time=1.65 memory used=224.8MB, alloc=68.3MB, time=1.92 memory used=265.7MB, alloc=92.3MB, time=2.30 memory used=313.5MB, alloc=92.3MB, time=3.35 memory used=358.3MB, alloc=92.3MB, time=3.53 memory used=401.7MB, alloc=92.3MB, time=4.49 memory used=470.8MB, alloc=92.3MB, time=4.89 memory used=541.3MB, alloc=92.3MB, time=5.30 memory used=610.9MB, alloc=92.3MB, time=5.68 memory used=666.3MB, alloc=92.3MB, time=6.80 memory used=707.4MB, alloc=92.3MB, time=7.26 memory used=743.4MB, alloc=92.3MB, time=7.94 memory used=809.9MB, alloc=92.3MB, time=8.39 memory used=878.0MB, alloc=116.3MB, time=8.82 memory used=952.7MB, alloc=372.3MB, time=9.37 memory used=1040.4MB, alloc=396.3MB, time=10.11 memory used=1128.0MB, alloc=396.3MB, time=10.73 memory used=1185.9MB, alloc=396.3MB, time=10.97 memory used=1301.3MB, alloc=396.3MB, time=19.76 memory used=1360.3MB, alloc=396.3MB, time=19.86 memory used=1440.5MB, alloc=396.3MB, time=20.13 memory used=1497.7MB, alloc=396.3MB, time=20.38 memory used=1611.7MB, alloc=396.3MB, time=29.13 memory used=1669.1MB, alloc=396.3MB, time=29.24 memory used=1749.2MB, alloc=396.3MB, time=29.51 memory used=1857.8MB, alloc=396.3MB, time=30.41 memory used=1942.1MB, alloc=396.3MB, time=30.93 memory used=2027.6MB, alloc=396.3MB, time=31.75 memory used=2126.0MB, alloc=420.3MB, time=32.29 memory used=2223.2MB, alloc=420.3MB, time=33.58 memory used=2346.8MB, alloc=420.3MB, time=34.27 memory used=2480.8MB, alloc=444.3MB, time=35.33 memory used=2618.3MB, alloc=468.3MB, time=36.45 memory used=2745.0MB, alloc=468.3MB, time=37.66 memory used=2876.3MB, alloc=492.3MB, time=38.67 memory used=2993.5MB, alloc=492.3MB, time=39.66 memory used=3138.5MB, alloc=492.3MB, time=40.48 memory used=3240.6MB, alloc=492.3MB, time=42.45 memory used=3332.7MB, alloc=492.3MB, time=42.84 memory used=3443.2MB, alloc=492.3MB, time=44.79 memory used=3552.0MB, alloc=492.3MB, time=45.38 memory used=3711.2MB, alloc=492.3MB, time=46.79 memory used=3816.3MB, alloc=492.3MB, time=47.73 memory used=3937.2MB, alloc=492.3MB, time=48.44 memory used=4071.5MB, alloc=516.3MB, time=49.35 memory used=4208.1MB, alloc=516.3MB, time=50.85 memory used=4340.5MB, alloc=516.3MB, time=51.53 memory used=4463.7MB, alloc=516.3MB, time=52.38 memory used=4549.4MB, alloc=516.3MB, time=53.22 memory used=4627.3MB, alloc=516.3MB, time=54.03 memory used=4706.7MB, alloc=516.3MB, time=54.91 memory used=4781.5MB, alloc=516.3MB, time=55.61 memory used=4853.0MB, alloc=516.3MB, time=56.38 memory used=4933.0MB, alloc=540.3MB, time=57.23 memory used=5050.8MB, alloc=540.3MB, time=58.32 memory used=5157.2MB, alloc=540.3MB, time=59.40 memory used=5272.5MB, alloc=564.3MB, time=60.54 memory used=5375.9MB, alloc=564.3MB, time=61.68 memory used=5467.7MB, alloc=564.3MB, time=63.01 memory used=5572.7MB, alloc=588.3MB, time=64.47 memory used=5660.8MB, alloc=588.3MB, time=65.85 memory used=5747.7MB, alloc=612.3MB, time=67.11 memory used=5822.6MB, alloc=612.3MB, time=68.23 memory used=5910.9MB, alloc=636.3MB, time=69.50 memory used=5999.3MB, alloc=636.3MB, time=70.75 memory used=6095.1MB, alloc=660.3MB, time=72.00 memory used=6392.6MB, alloc=684.3MB, time=75.10 memory used=6692.0MB, alloc=708.3MB, time=78.49 memory used=6984.8MB, alloc=732.3MB, time=82.06 memory used=7291.8MB, alloc=756.3MB, time=85.90 memory used=7615.2MB, alloc=780.3MB, time=89.79 memory used=7899.9MB, alloc=804.3MB, time=93.53 memory used=8178.8MB, alloc=828.3MB, time=99.69 memory used=8446.0MB, alloc=852.3MB, time=106.39 memory used=8720.1MB, alloc=876.3MB, time=113.54 memory used=9003.7MB, alloc=900.3MB, time=121.17 memory used=9298.9MB, alloc=924.3MB, time=129.30 memory used=9606.6MB, alloc=948.3MB, time=137.77 memory used=9928.6MB, alloc=972.3MB, time=146.70 memory used=10265.2MB, alloc=996.3MB, time=156.12 memory used=10616.3MB, alloc=1020.3MB, time=166.11 memory used=10980.0MB, alloc=1044.3MB, time=176.69 memory used=11357.0MB, alloc=1068.3MB, time=187.94 memory used=11758.0MB, alloc=1092.3MB, time=199.98 memory used=12183.0MB, alloc=1116.3MB, time=212.53 memory used=12631.9MB, alloc=1140.3MB, time=225.82 memory used=13104.7MB, alloc=1164.3MB, time=239.77 memory used=13601.5MB, alloc=1188.3MB, time=254.45 memory used=14122.2MB, alloc=1212.3MB, time=269.67 memory used=14666.8MB, alloc=1236.3MB, time=285.55 memory used=15235.3MB, alloc=1260.3MB, time=302.12 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428541642 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 F := [-16 y - 10 x z + 15 z , x y z - 6 x y z - 17 x] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 4 3 4 2 G := [-y z - 10 z + 2 x z, -8 x z - 14 y - 20 y z] > Problem := [F,G]; 3 2 2 Problem := [[-16 y - 10 x z + 15 z , x y z - 6 x y z - 17 x], 3 4 3 4 2 [-y z - 10 z + 2 x z, -8 x z - 14 y - 20 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.16 memory used=26.3MB, alloc=32.3MB, time=0.44 memory used=49.2MB, alloc=37.7MB, time=0.64 memory used=68.4MB, alloc=37.7MB, time=0.80 memory used=83.4MB, alloc=37.7MB, time=0.86 memory used=109.7MB, alloc=37.7MB, time=1.17 memory used=122.1MB, alloc=61.7MB, time=1.21 memory used=164.3MB, alloc=61.7MB, time=1.46 memory used=212.3MB, alloc=69.7MB, time=1.83 memory used=242.2MB, alloc=69.7MB, time=1.95 memory used=263.1MB, alloc=69.7MB, time=2.00 memory used=303.0MB, alloc=69.7MB, time=2.22 memory used=330.2MB, alloc=69.7MB, time=2.28 memory used=350.3MB, alloc=69.7MB, time=2.33 memory used=375.6MB, alloc=69.7MB, time=2.39 memory used=400.6MB, alloc=69.7MB, time=2.44 memory used=417.6MB, alloc=69.7MB, time=2.50 memory used=436.5MB, alloc=69.7MB, time=2.55 memory used=465.3MB, alloc=69.7MB, time=2.68 memory used=494.7MB, alloc=69.7MB, time=2.75 memory used=514.8MB, alloc=69.7MB, time=2.81 memory used=540.1MB, alloc=69.7MB, time=2.86 memory used=566.2MB, alloc=69.7MB, time=2.91 memory used=583.7MB, alloc=69.7MB, time=2.96 memory used=602.9MB, alloc=69.7MB, time=3.01 memory used=634.9MB, alloc=69.7MB, time=4.43 memory used=667.5MB, alloc=69.7MB, time=4.86 memory used=693.9MB, alloc=69.7MB, time=4.92 memory used=714.3MB, alloc=69.7MB, time=4.97 memory used=734.5MB, alloc=69.7MB, time=5.02 memory used=757.8MB, alloc=69.7MB, time=5.07 memory used=784.5MB, alloc=69.7MB, time=5.12 memory used=806.9MB, alloc=69.7MB, time=5.16 memory used=824.0MB, alloc=69.7MB, time=5.22 memory used=843.4MB, alloc=69.7MB, time=5.25 memory used=879.8MB, alloc=69.7MB, time=5.41 memory used=916.5MB, alloc=69.7MB, time=5.71 memory used=946.7MB, alloc=69.7MB, time=5.83 memory used=1004.4MB, alloc=69.7MB, time=6.08 memory used=1057.1MB, alloc=69.7MB, time=6.40 memory used=1109.8MB, alloc=69.7MB, time=6.87 memory used=1164.0MB, alloc=69.7MB, time=7.53 memory used=1218.2MB, alloc=69.7MB, time=8.21 memory used=1260.1MB, alloc=93.7MB, time=8.60 memory used=1312.9MB, alloc=93.7MB, time=8.91 memory used=1384.1MB, alloc=93.7MB, time=9.34 memory used=1419.7MB, alloc=93.7MB, time=9.42 memory used=1475.8MB, alloc=93.7MB, time=9.72 memory used=1522.9MB, alloc=93.7MB, time=9.99 memory used=1557.3MB, alloc=93.7MB, time=10.08 memory used=1589.1MB, alloc=93.7MB, time=10.15 memory used=1628.2MB, alloc=93.7MB, time=10.24 memory used=1659.3MB, alloc=93.7MB, time=10.30 memory used=1687.6MB, alloc=93.7MB, time=10.36 memory used=1772.7MB, alloc=93.7MB, time=10.75 memory used=1828.8MB, alloc=93.7MB, time=11.31 memory used=1889.5MB, alloc=93.7MB, time=11.76 memory used=1955.3MB, alloc=117.7MB, time=12.22 memory used=2006.9MB, alloc=117.7MB, time=12.36 memory used=2070.3MB, alloc=119.9MB, time=12.54 memory used=2156.1MB, alloc=119.9MB, time=16.77 memory used=2206.6MB, alloc=119.9MB, time=16.89 memory used=2250.9MB, alloc=119.9MB, time=17.00 memory used=2302.3MB, alloc=119.9MB, time=17.17 memory used=2376.5MB, alloc=120.9MB, time=18.54 memory used=2424.7MB, alloc=120.9MB, time=18.66 memory used=2491.7MB, alloc=120.9MB, time=19.16 memory used=2560.0MB, alloc=376.9MB, time=19.69 memory used=2654.3MB, alloc=400.9MB, time=20.29 memory used=2776.0MB, alloc=400.9MB, time=20.92 memory used=2846.5MB, alloc=400.9MB, time=21.10 memory used=2907.2MB, alloc=400.9MB, time=21.37 memory used=2997.1MB, alloc=400.9MB, time=21.61 memory used=3049.5MB, alloc=400.9MB, time=21.77 memory used=3147.9MB, alloc=400.9MB, time=27.88 memory used=3211.6MB, alloc=400.9MB, time=28.05 memory used=3273.0MB, alloc=400.9MB, time=28.21 memory used=3314.5MB, alloc=400.9MB, time=28.35 memory used=3411.7MB, alloc=400.9MB, time=29.34 memory used=3512.9MB, alloc=400.9MB, time=29.92 memory used=3644.3MB, alloc=424.9MB, time=32.10 memory used=3739.4MB, alloc=424.9MB, time=32.50 memory used=3858.1MB, alloc=424.9MB, time=33.31 memory used=3968.9MB, alloc=424.9MB, time=33.95 memory used=4034.7MB, alloc=424.9MB, time=34.19 memory used=4101.3MB, alloc=424.9MB, time=34.44 memory used=4192.7MB, alloc=448.9MB, time=35.76 memory used=4263.2MB, alloc=448.9MB, time=36.01 memory used=4330.9MB, alloc=448.9MB, time=36.24 memory used=4408.7MB, alloc=448.9MB, time=36.50 memory used=4498.7MB, alloc=448.9MB, time=36.75 memory used=4568.0MB, alloc=448.9MB, time=36.98 memory used=4619.2MB, alloc=448.9MB, time=37.19 memory used=4671.1MB, alloc=448.9MB, time=37.41 memory used=4726.8MB, alloc=448.9MB, time=37.63 memory used=4784.2MB, alloc=472.9MB, time=37.84 memory used=4860.2MB, alloc=472.9MB, time=38.07 memory used=4940.7MB, alloc=472.9MB, time=38.32 memory used=5028.4MB, alloc=472.9MB, time=38.56 memory used=5118.6MB, alloc=472.9MB, time=38.79 memory used=5216.0MB, alloc=472.9MB, time=39.03 memory used=5320.6MB, alloc=472.9MB, time=39.29 memory used=5427.5MB, alloc=472.9MB, time=39.55 memory used=5533.2MB, alloc=472.9MB, time=39.78 memory used=5593.2MB, alloc=472.9MB, time=39.97 memory used=5648.9MB, alloc=472.9MB, time=40.16 memory used=5707.8MB, alloc=472.9MB, time=40.34 memory used=5766.9MB, alloc=472.9MB, time=40.53 memory used=5831.3MB, alloc=472.9MB, time=40.73 memory used=5895.7MB, alloc=472.9MB, time=40.92 memory used=5960.0MB, alloc=472.9MB, time=41.12 memory used=6029.4MB, alloc=472.9MB, time=41.31 memory used=6098.6MB, alloc=472.9MB, time=41.50 memory used=6172.4MB, alloc=472.9MB, time=41.69 memory used=6245.8MB, alloc=472.9MB, time=41.89 memory used=6323.4MB, alloc=472.9MB, time=42.08 memory used=6400.1MB, alloc=472.9MB, time=42.28 memory used=6480.6MB, alloc=472.9MB, time=42.47 memory used=6564.5MB, alloc=472.9MB, time=42.67 memory used=6651.2MB, alloc=472.9MB, time=42.89 memory used=6740.2MB, alloc=472.9MB, time=43.09 memory used=6834.8MB, alloc=472.9MB, time=43.32 memory used=6930.4MB, alloc=472.9MB, time=43.52 memory used=7031.4MB, alloc=472.9MB, time=43.72 memory used=7136.6MB, alloc=472.9MB, time=43.94 memory used=7248.4MB, alloc=472.9MB, time=44.14 memory used=7483.9MB, alloc=472.9MB, time=45.67 memory used=7564.2MB, alloc=472.9MB, time=45.93 memory used=7653.6MB, alloc=472.9MB, time=46.20 memory used=7760.1MB, alloc=472.9MB, time=46.48 memory used=7850.2MB, alloc=472.9MB, time=46.74 memory used=7914.7MB, alloc=472.9MB, time=47.00 memory used=7981.8MB, alloc=472.9MB, time=47.22 memory used=8052.4MB, alloc=472.9MB, time=47.45 memory used=8130.1MB, alloc=472.9MB, time=47.69 memory used=8210.5MB, alloc=472.9MB, time=47.94 memory used=8298.0MB, alloc=472.9MB, time=48.20 memory used=8388.1MB, alloc=472.9MB, time=48.43 memory used=8485.4MB, alloc=472.9MB, time=48.69 memory used=8589.8MB, alloc=472.9MB, time=48.95 memory used=8696.3MB, alloc=472.9MB, time=49.21 memory used=8804.2MB, alloc=472.9MB, time=49.45 memory used=8863.8MB, alloc=472.9MB, time=49.64 memory used=8923.3MB, alloc=472.9MB, time=49.84 memory used=8982.2MB, alloc=472.9MB, time=50.03 memory used=9041.4MB, alloc=472.9MB, time=50.22 memory used=9105.7MB, alloc=472.9MB, time=50.41 memory used=9170.1MB, alloc=472.9MB, time=50.60 memory used=9234.5MB, alloc=472.9MB, time=50.80 memory used=9303.8MB, alloc=472.9MB, time=50.99 memory used=9373.0MB, alloc=472.9MB, time=51.19 memory used=9446.8MB, alloc=472.9MB, time=51.38 memory used=9520.2MB, alloc=472.9MB, time=51.58 memory used=9597.8MB, alloc=472.9MB, time=51.77 memory used=9674.5MB, alloc=472.9MB, time=51.97 memory used=9755.1MB, alloc=472.9MB, time=52.17 memory used=9838.9MB, alloc=472.9MB, time=52.37 memory used=9925.6MB, alloc=472.9MB, time=52.57 memory used=10014.6MB, alloc=472.9MB, time=52.77 memory used=10109.2MB, alloc=472.9MB, time=52.97 memory used=10204.7MB, alloc=472.9MB, time=53.18 memory used=10305.8MB, alloc=472.9MB, time=53.39 memory used=10411.2MB, alloc=472.9MB, time=53.60 memory used=10522.7MB, alloc=472.9MB, time=53.81 memory used=10755.2MB, alloc=472.9MB, time=87.72 memory used=10869.7MB, alloc=472.9MB, time=162.30 memory used=10979.7MB, alloc=472.9MB, time=163.56 memory used=11066.3MB, alloc=472.9MB, time=163.81 memory used=11141.7MB, alloc=472.9MB, time=164.03 memory used=11231.0MB, alloc=472.9MB, time=164.29 memory used=11334.3MB, alloc=472.9MB, time=164.54 memory used=11422.2MB, alloc=472.9MB, time=164.76 memory used=11483.5MB, alloc=472.9MB, time=164.95 memory used=11548.0MB, alloc=472.9MB, time=165.14 memory used=11616.9MB, alloc=472.9MB, time=165.34 memory used=11690.0MB, alloc=472.9MB, time=165.53 memory used=11767.3MB, alloc=472.9MB, time=165.73 memory used=11848.7MB, alloc=472.9MB, time=165.93 memory used=11936.6MB, alloc=472.9MB, time=166.13 memory used=12028.3MB, alloc=472.9MB, time=166.33 memory used=12126.0MB, alloc=472.9MB, time=166.54 memory used=12229.4MB, alloc=472.9MB, time=166.75 memory used=12338.1MB, alloc=472.9MB, time=166.97 memory used=12547.4MB, alloc=472.9MB, time=167.32 memory used=12686.4MB, alloc=472.9MB, time=167.59 memory used=12834.8MB, alloc=472.9MB, time=167.86 memory used=12995.2MB, alloc=472.9MB, time=168.14 memory used=13172.6MB, alloc=472.9MB, time=168.41 memory used=13437.2MB, alloc=472.9MB, time=169.19 memory used=13534.3MB, alloc=472.9MB, time=169.44 memory used=13625.1MB, alloc=472.9MB, time=169.69 memory used=13695.4MB, alloc=472.9MB, time=169.94 memory used=13776.6MB, alloc=472.9MB, time=170.17 memory used=13867.8MB, alloc=472.9MB, time=170.42 memory used=13973.4MB, alloc=472.9MB, time=170.68 memory used=14065.2MB, alloc=472.9MB, time=170.90 memory used=14130.9MB, alloc=472.9MB, time=171.08 memory used=14203.6MB, alloc=472.9MB, time=171.26 memory used=14351.4MB, alloc=472.9MB, time=196.59 memory used=14445.0MB, alloc=472.9MB, time=196.85 memory used=14521.1MB, alloc=472.9MB, time=197.10 memory used=14618.4MB, alloc=472.9MB, time=197.33 memory used=14709.3MB, alloc=472.9MB, time=197.55 memory used=14774.8MB, alloc=472.9MB, time=197.74 memory used=14847.1MB, alloc=472.9MB, time=197.94 memory used=14927.0MB, alloc=472.9MB, time=198.13 memory used=15016.0MB, alloc=472.9MB, time=198.33 memory used=15115.7MB, alloc=472.9MB, time=198.54 memory used=15228.1MB, alloc=472.9MB, time=198.75 memory used=15467.9MB, alloc=472.9MB, time=199.75 memory used=15555.9MB, alloc=472.9MB, time=200.01 memory used=15659.4MB, alloc=472.9MB, time=200.32 memory used=15740.8MB, alloc=472.9MB, time=200.57 memory used=15809.9MB, alloc=472.9MB, time=200.80 memory used=15888.0MB, alloc=472.9MB, time=201.04 memory used=15973.4MB, alloc=472.9MB, time=201.27 memory used=16070.0MB, alloc=472.9MB, time=201.53 memory used=16175.6MB, alloc=472.9MB, time=201.78 memory used=16277.6MB, alloc=472.9MB, time=202.04 memory used=16337.0MB, alloc=472.9MB, time=202.22 memory used=16401.4MB, alloc=472.9MB, time=202.42 memory used=16467.6MB, alloc=472.9MB, time=202.61 memory used=16537.9MB, alloc=472.9MB, time=202.80 memory used=16613.1MB, alloc=472.9MB, time=202.99 memory used=16693.4MB, alloc=472.9MB, time=203.19 memory used=16781.2MB, alloc=472.9MB, time=203.38 memory used=16900.6MB, alloc=472.9MB, time=204.16 memory used=16991.1MB, alloc=472.9MB, time=204.44 memory used=17095.4MB, alloc=472.9MB, time=204.70 memory used=17177.5MB, alloc=472.9MB, time=204.96 memory used=17247.7MB, alloc=472.9MB, time=205.22 memory used=17326.2MB, alloc=472.9MB, time=205.45 memory used=17414.2MB, alloc=472.9MB, time=205.68 memory used=17511.3MB, alloc=472.9MB, time=205.94 memory used=17617.1MB, alloc=472.9MB, time=206.21 memory used=17718.6MB, alloc=472.9MB, time=206.44 memory used=17778.3MB, alloc=472.9MB, time=206.62 memory used=17842.3MB, alloc=472.9MB, time=206.81 memory used=17911.2MB, alloc=472.9MB, time=207.00 memory used=17983.7MB, alloc=472.9MB, time=207.18 memory used=18061.1MB, alloc=472.9MB, time=207.38 memory used=18143.7MB, alloc=472.9MB, time=207.58 memory used=18232.8MB, alloc=472.9MB, time=207.77 memory used=18349.9MB, alloc=472.9MB, time=227.24 memory used=18527.9MB, alloc=472.9MB, time=231.08 memory used=18619.1MB, alloc=472.9MB, time=231.33 memory used=18700.4MB, alloc=472.9MB, time=231.59 memory used=18807.1MB, alloc=472.9MB, time=231.82 memory used=18878.2MB, alloc=472.9MB, time=232.01 memory used=18949.2MB, alloc=472.9MB, time=232.21 memory used=19029.8MB, alloc=472.9MB, time=232.41 memory used=19120.5MB, alloc=472.9MB, time=232.61 memory used=19224.1MB, alloc=472.9MB, time=232.81 memory used=19389.7MB, alloc=472.9MB, time=233.17 memory used=19509.5MB, alloc=472.9MB, time=234.31 memory used=19600.1MB, alloc=472.9MB, time=234.55 memory used=19718.0MB, alloc=472.9MB, time=235.39 memory used=19803.3MB, alloc=472.9MB, time=235.65 memory used=19910.9MB, alloc=472.9MB, time=235.94 memory used=19978.0MB, alloc=472.9MB, time=236.18 memory used=20050.4MB, alloc=472.9MB, time=236.41 memory used=20132.6MB, alloc=472.9MB, time=236.66 memory used=20221.4MB, alloc=472.9MB, time=236.89 memory used=20322.0MB, alloc=472.9MB, time=237.16 memory used=20431.0MB, alloc=472.9MB, time=237.43 memory used=20514.4MB, alloc=472.9MB, time=237.64 memory used=20576.8MB, alloc=472.9MB, time=237.83 memory used=20641.0MB, alloc=472.9MB, time=238.02 memory used=20708.9MB, alloc=472.9MB, time=238.21 memory used=20782.2MB, alloc=472.9MB, time=238.40 memory used=20860.3MB, alloc=472.9MB, time=238.59 memory used=20944.7MB, alloc=472.9MB, time=238.79 memory used=21036.8MB, alloc=472.9MB, time=238.98 memory used=21156.1MB, alloc=472.9MB, time=239.84 memory used=21245.4MB, alloc=472.9MB, time=240.10 memory used=21349.4MB, alloc=472.9MB, time=240.38 memory used=21415.5MB, alloc=472.9MB, time=240.62 memory used=21488.8MB, alloc=472.9MB, time=240.85 memory used=21571.5MB, alloc=472.9MB, time=241.08 memory used=21661.1MB, alloc=472.9MB, time=241.30 memory used=21761.7MB, alloc=472.9MB, time=241.57 memory used=21873.8MB, alloc=472.9MB, time=241.83 memory used=21949.3MB, alloc=472.9MB, time=242.04 memory used=22010.1MB, alloc=472.9MB, time=242.23 memory used=22076.5MB, alloc=472.9MB, time=242.42 memory used=22144.7MB, alloc=472.9MB, time=242.61 memory used=22217.6MB, alloc=472.9MB, time=242.80 memory used=22295.2MB, alloc=472.9MB, time=243.00 memory used=22378.9MB, alloc=472.9MB, time=243.19 memory used=22470.8MB, alloc=472.9MB, time=243.37 memory used=22625.8MB, alloc=472.9MB, time=266.09 memory used=22772.3MB, alloc=472.9MB, time=266.56 memory used=22855.0MB, alloc=472.9MB, time=266.80 memory used=22947.0MB, alloc=472.9MB, time=267.03 memory used=23041.4MB, alloc=472.9MB, time=267.25 memory used=23107.3MB, alloc=472.9MB, time=267.44 memory used=23182.2MB, alloc=472.9MB, time=267.63 memory used=23266.8MB, alloc=472.9MB, time=267.83 memory used=23362.5MB, alloc=472.9MB, time=268.04 memory used=23529.3MB, alloc=472.9MB, time=268.36 memory used=23661.0MB, alloc=472.9MB, time=269.31 memory used=23739.4MB, alloc=472.9MB, time=269.59 memory used=23834.5MB, alloc=472.9MB, time=269.85 memory used=23943.8MB, alloc=472.9MB, time=270.12 memory used=24010.4MB, alloc=472.9MB, time=270.37 memory used=24077.7MB, alloc=472.9MB, time=270.59 memory used=24150.7MB, alloc=472.9MB, time=270.82 memory used=24226.7MB, alloc=472.9MB, time=271.07 memory used=24308.4MB, alloc=472.9MB, time=271.32 memory used=24396.2MB, alloc=472.9MB, time=271.58 memory used=24493.3MB, alloc=472.9MB, time=271.85 memory used=24596.4MB, alloc=472.9MB, time=272.12 memory used=24708.6MB, alloc=472.9MB, time=272.36 memory used=24790.7MB, alloc=472.9MB, time=272.57 memory used=24851.0MB, alloc=472.9MB, time=272.75 memory used=24911.5MB, alloc=472.9MB, time=272.94 memory used=24974.9MB, alloc=472.9MB, time=273.14 memory used=25040.8MB, alloc=472.9MB, time=273.33 memory used=25108.7MB, alloc=472.9MB, time=273.52 memory used=25181.5MB, alloc=472.9MB, time=273.72 memory used=25257.8MB, alloc=472.9MB, time=273.92 memory used=25339.0MB, alloc=472.9MB, time=274.11 memory used=25424.8MB, alloc=472.9MB, time=274.30 memory used=25532.5MB, alloc=472.9MB, time=275.11 memory used=25654.2MB, alloc=472.9MB, time=275.56 memory used=25733.8MB, alloc=472.9MB, time=275.82 memory used=25834.0MB, alloc=472.9MB, time=276.11 memory used=25937.2MB, alloc=472.9MB, time=276.38 memory used=26001.5MB, alloc=472.9MB, time=276.61 memory used=26069.2MB, alloc=472.9MB, time=276.85 memory used=26142.7MB, alloc=472.9MB, time=277.10 memory used=26222.7MB, alloc=472.9MB, time=277.36 memory used=26308.9MB, alloc=472.9MB, time=277.62 memory used=26401.1MB, alloc=472.9MB, time=277.87 memory used=26499.2MB, alloc=472.9MB, time=278.12 memory used=26602.9MB, alloc=472.9MB, time=278.38 memory used=26714.6MB, alloc=472.9MB, time=278.64 memory used=26783.2MB, alloc=472.9MB, time=278.85 memory used=26843.2MB, alloc=472.9MB, time=279.04 memory used=26903.5MB, alloc=472.9MB, time=279.23 memory used=26966.7MB, alloc=472.9MB, time=279.41 memory used=27032.4MB, alloc=472.9MB, time=279.60 memory used=27103.5MB, alloc=472.9MB, time=279.79 memory used=27175.7MB, alloc=472.9MB, time=279.99 memory used=27251.9MB, alloc=472.9MB, time=280.21 memory used=27332.4MB, alloc=472.9MB, time=280.46 memory used=27418.9MB, alloc=472.9MB, time=280.69 memory used=27534.8MB, alloc=472.9MB, time=288.96 memory used=27651.6MB, alloc=472.9MB, time=341.81 memory used=27772.5MB, alloc=472.9MB, time=379.65 memory used=27867.7MB, alloc=472.9MB, time=379.90 memory used=27941.2MB, alloc=472.9MB, time=380.13 memory used=28027.0MB, alloc=472.9MB, time=380.36 memory used=28130.2MB, alloc=472.9MB, time=380.59 memory used=28213.0MB, alloc=472.9MB, time=380.80 memory used=28277.1MB, alloc=472.9MB, time=380.99 memory used=28345.4MB, alloc=472.9MB, time=381.19 memory used=28419.7MB, alloc=472.9MB, time=381.38 memory used=28499.6MB, alloc=472.9MB, time=381.58 memory used=28584.8MB, alloc=472.9MB, time=381.78 memory used=28675.2MB, alloc=472.9MB, time=381.98 memory used=28773.6MB, alloc=472.9MB, time=382.18 memory used=28879.5MB, alloc=472.9MB, time=382.39 memory used=29107.9MB, alloc=472.9MB, time=382.72 memory used=29255.8MB, alloc=472.9MB, time=382.99 memory used=29543.8MB, alloc=472.9MB, time=385.38 memory used=29631.9MB, alloc=472.9MB, time=385.62 memory used=29710.5MB, alloc=472.9MB, time=385.83 memory used=29828.5MB, alloc=472.9MB, time=386.18 memory used=29961.7MB, alloc=472.9MB, time=391.38 memory used=30046.5MB, alloc=472.9MB, time=391.61 memory used=30139.0MB, alloc=472.9MB, time=391.83 memory used=30209.9MB, alloc=472.9MB, time=392.02 memory used=30315.6MB, alloc=472.9MB, time=392.41 memory used=30502.4MB, alloc=472.9MB, time=393.60 memory used=30653.9MB, alloc=472.9MB, time=395.37 memory used=30875.1MB, alloc=472.9MB, time=396.71 memory used=31013.5MB, alloc=472.9MB, time=398.23 memory used=31182.2MB, alloc=472.9MB, time=398.96 memory used=31367.8MB, alloc=472.9MB, time=400.59 memory used=31534.2MB, alloc=472.9MB, time=407.62 memory used=31611.3MB, alloc=472.9MB, time=407.87 memory used=31699.4MB, alloc=472.9MB, time=408.09 memory used=31765.7MB, alloc=472.9MB, time=408.30 memory used=31833.0MB, alloc=472.9MB, time=408.49 memory used=31959.0MB, alloc=472.9MB, time=423.14 memory used=32062.8MB, alloc=472.9MB, time=429.60 memory used=32136.9MB, alloc=472.9MB, time=429.85 memory used=32217.2MB, alloc=472.9MB, time=430.08 memory used=32305.0MB, alloc=472.9MB, time=430.31 memory used=32363.0MB, alloc=472.9MB, time=430.51 memory used=32428.1MB, alloc=472.9MB, time=430.71 memory used=32501.5MB, alloc=472.9MB, time=430.91 memory used=32584.6MB, alloc=472.9MB, time=431.12 memory used=32734.1MB, alloc=472.9MB, time=431.63 memory used=32853.1MB, alloc=496.9MB, time=432.32 memory used=33000.1MB, alloc=496.9MB, time=433.09 memory used=33145.5MB, alloc=496.9MB, time=435.19 memory used=33250.3MB, alloc=496.9MB, time=436.20 memory used=33333.0MB, alloc=496.9MB, time=436.89 memory used=33412.0MB, alloc=496.9MB, time=437.72 memory used=33501.6MB, alloc=496.9MB, time=438.60 memory used=33630.1MB, alloc=496.9MB, time=439.20 memory used=33733.3MB, alloc=496.9MB, time=439.92 memory used=33847.8MB, alloc=496.9MB, time=440.44 memory used=33948.3MB, alloc=496.9MB, time=441.15 memory used=34041.9MB, alloc=496.9MB, time=441.51 memory used=34181.2MB, alloc=496.9MB, time=443.76 memory used=34278.0MB, alloc=496.9MB, time=444.41 memory used=34368.3MB, alloc=520.9MB, time=445.44 memory used=34431.4MB, alloc=520.9MB, time=446.04 memory used=34563.5MB, alloc=520.9MB, time=446.65 memory used=34671.7MB, alloc=520.9MB, time=447.07 memory used=34808.8MB, alloc=544.9MB, time=449.78 memory used=34914.0MB, alloc=544.9MB, time=450.19 memory used=35041.9MB, alloc=544.9MB, time=450.61 memory used=35162.5MB, alloc=544.9MB, time=451.02 memory used=35245.7MB, alloc=544.9MB, time=451.39 memory used=35332.8MB, alloc=544.9MB, time=451.75 memory used=35428.6MB, alloc=544.9MB, time=452.11 memory used=35529.3MB, alloc=544.9MB, time=452.47 memory used=35634.7MB, alloc=544.9MB, time=452.87 memory used=35749.3MB, alloc=544.9MB, time=453.27 memory used=35873.9MB, alloc=544.9MB, time=453.67 memory used=36003.0MB, alloc=544.9MB, time=454.08 memory used=36142.0MB, alloc=544.9MB, time=454.45 memory used=36254.6MB, alloc=568.9MB, time=454.83 memory used=36336.7MB, alloc=568.9MB, time=455.15 memory used=36423.4MB, alloc=568.9MB, time=455.47 memory used=36512.2MB, alloc=568.9MB, time=455.79 memory used=36602.0MB, alloc=568.9MB, time=456.11 memory used=36698.8MB, alloc=568.9MB, time=456.43 memory used=36796.6MB, alloc=568.9MB, time=456.75 memory used=36895.4MB, alloc=568.9MB, time=457.08 memory used=37000.4MB, alloc=568.9MB, time=457.41 memory used=37106.4MB, alloc=568.9MB, time=457.76 memory used=37219.2MB, alloc=568.9MB, time=458.08 memory used=37332.3MB, alloc=568.9MB, time=458.42 memory used=37452.0MB, alloc=568.9MB, time=458.76 memory used=37577.9MB, alloc=568.9MB, time=459.10 memory used=37703.4MB, alloc=568.9MB, time=459.45 memory used=37834.6MB, alloc=568.9MB, time=459.80 memory used=37971.2MB, alloc=568.9MB, time=460.15 memory used=38112.5MB, alloc=568.9MB, time=460.51 memory used=38257.9MB, alloc=568.9MB, time=460.86 memory used=38407.2MB, alloc=568.9MB, time=461.22 memory used=38563.9MB, alloc=568.9MB, time=461.56 memory used=38731.5MB, alloc=568.9MB, time=461.92 memory used=38931.3MB, alloc=568.9MB, time=462.34 memory used=39061.5MB, alloc=568.9MB, time=462.69 memory used=39193.8MB, alloc=568.9MB, time=463.06 memory used=39333.2MB, alloc=568.9MB, time=463.42 memory used=39480.9MB, alloc=568.9MB, time=463.79 memory used=39637.4MB, alloc=568.9MB, time=464.15 memory used=39831.0MB, alloc=568.9MB, time=466.84 memory used=39969.3MB, alloc=568.9MB, time=467.32 memory used=40117.2MB, alloc=568.9MB, time=467.79 memory used=40217.6MB, alloc=568.9MB, time=468.22 memory used=40323.4MB, alloc=568.9MB, time=468.60 memory used=40436.4MB, alloc=568.9MB, time=468.98 memory used=40560.7MB, alloc=568.9MB, time=469.41 memory used=40691.3MB, alloc=568.9MB, time=469.83 memory used=40833.3MB, alloc=568.9MB, time=470.23 memory used=40986.9MB, alloc=568.9MB, time=470.66 memory used=41152.0MB, alloc=568.9MB, time=471.05 memory used=41253.3MB, alloc=568.9MB, time=471.39 memory used=41340.3MB, alloc=568.9MB, time=471.72 memory used=41428.6MB, alloc=568.9MB, time=472.04 memory used=41518.0MB, alloc=568.9MB, time=472.36 memory used=41614.5MB, alloc=568.9MB, time=472.69 memory used=41711.8MB, alloc=568.9MB, time=473.01 memory used=41810.0MB, alloc=568.9MB, time=473.33 memory used=41915.2MB, alloc=568.9MB, time=473.66 memory used=42021.0MB, alloc=568.9MB, time=474.01 memory used=42133.7MB, alloc=568.9MB, time=474.35 memory used=42246.8MB, alloc=568.9MB, time=474.68 memory used=42366.4MB, alloc=568.9MB, time=475.02 memory used=42485.9MB, alloc=568.9MB, time=475.36 memory used=42611.7MB, alloc=568.9MB, time=475.70 memory used=42743.4MB, alloc=568.9MB, time=476.05 memory used=42880.5MB, alloc=568.9MB, time=476.49 memory used=43022.5MB, alloc=568.9MB, time=476.85 memory used=43168.7MB, alloc=568.9MB, time=477.20 memory used=43318.6MB, alloc=568.9MB, time=477.55 memory used=43471.9MB, alloc=568.9MB, time=477.90 memory used=43631.7MB, alloc=568.9MB, time=478.26 memory used=43889.2MB, alloc=568.9MB, time=478.72 memory used=44017.2MB, alloc=568.9MB, time=479.07 memory used=44149.5MB, alloc=568.9MB, time=479.44 memory used=44289.6MB, alloc=568.9MB, time=479.81 memory used=44434.9MB, alloc=568.9MB, time=480.17 memory used=44591.5MB, alloc=568.9MB, time=480.53 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428541942 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 3 3 2 F := [-x z - 2 y z - 7 y , -15 x z - 11 y z + 2 x y ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 3 2 3 G := [15 x z - 15 y , -19 x y - 12 x y z - 20 x ] > Problem := [F,G]; 3 2 2 2 3 3 2 Problem := [[-x z - 2 y z - 7 y , -15 x z - 11 y z + 2 x y ], 3 3 3 2 3 [15 x z - 15 y , -19 x y - 12 x y z - 20 x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.1MB, alloc=32.3MB, time=0.17 memory used=25.6MB, alloc=32.3MB, time=0.46 memory used=48.0MB, alloc=34.0MB, time=0.62 memory used=61.0MB, alloc=34.0MB, time=0.68 memory used=78.0MB, alloc=34.0MB, time=0.73 memory used=91.2MB, alloc=34.0MB, time=0.89 memory used=106.3MB, alloc=34.0MB, time=0.97 memory used=135.1MB, alloc=34.0MB, time=1.67 memory used=146.5MB, alloc=34.0MB, time=1.71 memory used=158.5MB, alloc=34.0MB, time=1.75 memory used=184.9MB, alloc=34.0MB, time=2.22 memory used=211.0MB, alloc=34.0MB, time=2.40 memory used=222.1MB, alloc=34.0MB, time=2.44 memory used=232.9MB, alloc=34.0MB, time=2.48 memory used=244.0MB, alloc=34.0MB, time=2.51 memory used=270.2MB, alloc=34.0MB, time=2.70 memory used=295.8MB, alloc=58.0MB, time=2.92 memory used=358.7MB, alloc=58.3MB, time=3.21 memory used=421.7MB, alloc=62.4MB, time=3.61 memory used=484.7MB, alloc=62.7MB, time=4.13 memory used=534.6MB, alloc=62.7MB, time=4.79 memory used=580.4MB, alloc=62.7MB, time=5.19 memory used=627.0MB, alloc=70.7MB, time=5.75 memory used=675.8MB, alloc=70.7MB, time=6.23 memory used=726.3MB, alloc=94.7MB, time=6.66 memory used=785.9MB, alloc=94.7MB, time=7.06 memory used=836.9MB, alloc=94.7MB, time=7.51 memory used=870.5MB, alloc=94.7MB, time=7.61 memory used=909.0MB, alloc=94.7MB, time=7.71 memory used=951.5MB, alloc=94.7MB, time=7.91 memory used=985.9MB, alloc=94.7MB, time=8.03 memory used=1029.0MB, alloc=94.7MB, time=8.47 memory used=1071.6MB, alloc=94.7MB, time=8.73 memory used=1105.2MB, alloc=94.7MB, time=8.84 memory used=1146.8MB, alloc=94.7MB, time=8.96 memory used=1175.9MB, alloc=94.7MB, time=9.06 memory used=1209.0MB, alloc=94.7MB, time=9.25 memory used=1250.8MB, alloc=94.7MB, time=9.50 memory used=1284.1MB, alloc=94.7MB, time=9.61 memory used=1325.7MB, alloc=94.7MB, time=9.72 memory used=1354.7MB, alloc=94.7MB, time=9.82 memory used=1386.3MB, alloc=94.7MB, time=9.94 memory used=1427.6MB, alloc=94.7MB, time=10.57 memory used=1463.9MB, alloc=118.7MB, time=12.35 memory used=1507.8MB, alloc=118.7MB, time=12.49 memory used=1557.8MB, alloc=118.7MB, time=12.63 memory used=1612.9MB, alloc=118.7MB, time=12.79 memory used=1674.4MB, alloc=118.7MB, time=12.94 memory used=1721.4MB, alloc=118.7MB, time=13.08 memory used=1755.1MB, alloc=118.7MB, time=13.20 memory used=1791.1MB, alloc=118.7MB, time=13.30 memory used=1829.2MB, alloc=118.7MB, time=13.42 memory used=1869.1MB, alloc=118.7MB, time=13.53 memory used=1910.6MB, alloc=118.7MB, time=13.65 memory used=1953.5MB, alloc=118.7MB, time=13.78 memory used=1999.2MB, alloc=118.7MB, time=13.90 memory used=2048.7MB, alloc=118.7MB, time=14.04 memory used=2100.8MB, alloc=118.7MB, time=14.18 memory used=2155.8MB, alloc=118.7MB, time=14.32 memory used=2209.5MB, alloc=118.7MB, time=14.44 memory used=2263.7MB, alloc=118.7MB, time=15.46 memory used=2307.1MB, alloc=118.7MB, time=15.60 memory used=2357.5MB, alloc=118.7MB, time=15.74 memory used=2416.6MB, alloc=118.7MB, time=15.91 memory used=2475.1MB, alloc=118.7MB, time=16.05 memory used=2512.2MB, alloc=118.7MB, time=16.19 memory used=2553.5MB, alloc=118.7MB, time=16.32 memory used=2598.8MB, alloc=118.7MB, time=16.45 memory used=2650.2MB, alloc=118.7MB, time=16.57 memory used=2721.0MB, alloc=131.8MB, time=30.13 memory used=2728.9MB, alloc=131.8MB, time=44.45 memory used=2738.7MB, alloc=131.8MB, time=54.32 memory used=2738.7MB, alloc=387.8MB, time=54.36 memory used=2977.3MB, alloc=387.8MB, time=70.81 memory used=3127.8MB, alloc=387.8MB, time=71.06 memory used=3288.4MB, alloc=387.8MB, time=71.31 memory used=3480.9MB, alloc=387.8MB, time=75.30 memory used=3530.7MB, alloc=387.8MB, time=75.45 memory used=3584.7MB, alloc=387.8MB, time=75.60 memory used=3643.8MB, alloc=387.8MB, time=75.75 memory used=3705.6MB, alloc=387.8MB, time=75.90 memory used=3745.4MB, alloc=387.8MB, time=76.04 memory used=3780.1MB, alloc=387.8MB, time=76.17 memory used=3813.5MB, alloc=387.8MB, time=76.28 memory used=3848.1MB, alloc=387.8MB, time=76.40 memory used=3885.8MB, alloc=387.8MB, time=76.51 memory used=3923.7MB, alloc=387.8MB, time=76.64 memory used=3961.9MB, alloc=387.8MB, time=76.77 memory used=4002.9MB, alloc=387.8MB, time=76.90 memory used=4044.1MB, alloc=387.8MB, time=77.01 memory used=4088.2MB, alloc=387.8MB, time=77.13 memory used=4134.9MB, alloc=387.8MB, time=77.25 memory used=4181.3MB, alloc=387.8MB, time=77.39 memory used=4230.2MB, alloc=387.8MB, time=77.51 memory used=4281.1MB, alloc=387.8MB, time=77.63 memory used=4333.9MB, alloc=387.8MB, time=77.75 memory used=4388.2MB, alloc=387.8MB, time=77.89 memory used=4445.9MB, alloc=387.8MB, time=78.02 memory used=4502.7MB, alloc=387.8MB, time=78.14 memory used=4561.5MB, alloc=387.8MB, time=78.27 memory used=4599.8MB, alloc=387.8MB, time=78.36 memory used=4632.7MB, alloc=387.8MB, time=78.45 memory used=4666.1MB, alloc=387.8MB, time=78.54 memory used=4701.8MB, alloc=387.8MB, time=78.64 memory used=4739.4MB, alloc=387.8MB, time=78.73 memory used=4779.6MB, alloc=387.8MB, time=78.82 memory used=4835.1MB, alloc=387.8MB, time=82.46 memory used=4883.7MB, alloc=387.8MB, time=82.61 memory used=4937.6MB, alloc=387.8MB, time=82.76 memory used=4996.5MB, alloc=387.8MB, time=82.92 memory used=5058.7MB, alloc=387.8MB, time=83.07 memory used=5099.0MB, alloc=387.8MB, time=83.21 memory used=5133.0MB, alloc=387.8MB, time=83.33 memory used=5166.1MB, alloc=387.8MB, time=83.45 memory used=5200.6MB, alloc=387.8MB, time=83.57 memory used=5235.4MB, alloc=387.8MB, time=83.69 memory used=5273.3MB, alloc=387.8MB, time=83.84 memory used=5311.4MB, alloc=387.8MB, time=83.97 memory used=5352.5MB, alloc=387.8MB, time=84.08 memory used=5393.7MB, alloc=387.8MB, time=84.22 memory used=5437.6MB, alloc=387.8MB, time=84.33 memory used=5481.5MB, alloc=387.8MB, time=84.46 memory used=5528.0MB, alloc=387.8MB, time=84.58 memory used=5577.0MB, alloc=387.8MB, time=84.72 memory used=5628.1MB, alloc=387.8MB, time=84.84 memory used=5681.0MB, alloc=387.8MB, time=84.97 memory used=5735.5MB, alloc=387.8MB, time=85.10 memory used=5793.5MB, alloc=387.8MB, time=85.24 memory used=5851.1MB, alloc=387.8MB, time=85.36 memory used=5909.9MB, alloc=387.8MB, time=85.48 memory used=5950.9MB, alloc=387.8MB, time=85.57 memory used=5982.5MB, alloc=387.8MB, time=85.66 memory used=6016.2MB, alloc=387.8MB, time=85.75 memory used=6050.8MB, alloc=387.8MB, time=85.84 memory used=6087.8MB, alloc=387.8MB, time=85.93 memory used=6126.9MB, alloc=387.8MB, time=86.02 memory used=6496.5MB, alloc=387.8MB, time=166.53 memory used=6696.9MB, alloc=387.8MB, time=166.75 memory used=6905.9MB, alloc=387.8MB, time=166.96 memory used=7129.0MB, alloc=387.8MB, time=167.18 memory used=7289.1MB, alloc=387.8MB, time=168.50 memory used=7339.7MB, alloc=387.8MB, time=168.60 memory used=7436.3MB, alloc=387.8MB, time=168.99 memory used=7562.0MB, alloc=387.8MB, time=169.68 memory used=7649.6MB, alloc=387.8MB, time=170.94 memory used=7715.8MB, alloc=387.8MB, time=180.30 memory used=7777.0MB, alloc=411.8MB, time=210.46 memory used=7857.5MB, alloc=411.8MB, time=212.18 memory used=7915.4MB, alloc=411.8MB, time=212.29 memory used=7972.7MB, alloc=411.8MB, time=212.42 memory used=8040.4MB, alloc=411.8MB, time=212.55 memory used=8119.0MB, alloc=411.8MB, time=212.66 memory used=8179.2MB, alloc=411.8MB, time=212.76 memory used=8227.5MB, alloc=411.8MB, time=212.85 memory used=8280.4MB, alloc=411.8MB, time=212.94 memory used=8338.7MB, alloc=411.8MB, time=213.03 memory used=8466.5MB, alloc=411.8MB, time=213.61 memory used=8614.5MB, alloc=411.8MB, time=214.19 memory used=8754.0MB, alloc=411.8MB, time=218.26 memory used=8829.5MB, alloc=411.8MB, time=218.66 memory used=8889.7MB, alloc=411.8MB, time=218.76 memory used=8963.4MB, alloc=435.8MB, time=252.36 memory used=9043.7MB, alloc=435.8MB, time=298.26 memory used=9125.6MB, alloc=435.8MB, time=391.91 memory used=9236.2MB, alloc=435.8MB, time=497.31 memory used=9331.0MB, alloc=435.8MB, time=501.22 memory used=9400.2MB, alloc=435.8MB, time=501.42 memory used=9467.7MB, alloc=435.8MB, time=501.54 memory used=9542.8MB, alloc=435.8MB, time=501.67 memory used=9625.3MB, alloc=435.8MB, time=501.81 memory used=9716.6MB, alloc=435.8MB, time=501.97 memory used=9789.2MB, alloc=435.8MB, time=502.09 memory used=9840.9MB, alloc=435.8MB, time=502.19 memory used=9894.0MB, alloc=435.8MB, time=502.29 memory used=9949.7MB, alloc=435.8MB, time=502.39 memory used=10007.3MB, alloc=435.8MB, time=502.50 memory used=10068.3MB, alloc=435.8MB, time=502.60 memory used=10130.8MB, alloc=435.8MB, time=502.70 memory used=10196.2MB, alloc=435.8MB, time=502.81 memory used=10265.6MB, alloc=435.8MB, time=502.92 memory used=10338.5MB, alloc=435.8MB, time=503.03 memory used=10415.4MB, alloc=435.8MB, time=503.14 memory used=10496.4MB, alloc=435.8MB, time=503.25 memory used=10582.5MB, alloc=435.8MB, time=503.37 memory used=10680.3MB, alloc=435.8MB, time=503.50 memory used=10887.9MB, alloc=435.8MB, time=504.33 memory used=11066.5MB, alloc=435.8MB, time=504.94 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428542242 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 3 F := [15 x z + 4 x y , 11 y z + 3 z + 2 y z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 3 2 2 G := [-15 x z + 18 x y z + 17 z , -9 x z + 8 x z - 10 y ] > Problem := [F,G]; 3 2 3 3 Problem := [[15 x z + 4 x y , 11 y z + 3 z + 2 y z], 2 3 3 2 2 [-15 x z + 18 x y z + 17 z , -9 x z + 8 x z - 10 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.14 memory used=26.7MB, alloc=32.3MB, time=0.43 memory used=46.8MB, alloc=56.3MB, time=0.71 memory used=89.5MB, alloc=60.3MB, time=1.03 memory used=131.4MB, alloc=60.3MB, time=1.41 memory used=166.1MB, alloc=60.3MB, time=1.71 memory used=208.7MB, alloc=92.3MB, time=2.10 memory used=277.7MB, alloc=92.3MB, time=2.58 memory used=332.0MB, alloc=92.3MB, time=2.84 memory used=380.4MB, alloc=92.3MB, time=2.99 memory used=427.9MB, alloc=92.3MB, time=3.20 memory used=495.9MB, alloc=92.3MB, time=3.62 memory used=561.9MB, alloc=92.3MB, time=4.07 memory used=629.9MB, alloc=372.3MB, time=4.62 memory used=722.3MB, alloc=372.3MB, time=5.36 memory used=777.9MB, alloc=372.3MB, time=5.61 memory used=832.4MB, alloc=372.3MB, time=5.82 memory used=872.8MB, alloc=372.3MB, time=5.94 memory used=919.4MB, alloc=372.3MB, time=6.12 memory used=968.9MB, alloc=372.3MB, time=6.28 memory used=1010.2MB, alloc=372.3MB, time=6.41 memory used=1057.9MB, alloc=372.3MB, time=6.62 memory used=1104.2MB, alloc=372.3MB, time=6.73 memory used=1138.5MB, alloc=372.3MB, time=6.84 memory used=1191.4MB, alloc=372.3MB, time=7.21 memory used=1230.8MB, alloc=372.3MB, time=7.30 memory used=1279.3MB, alloc=372.3MB, time=7.49 memory used=1320.5MB, alloc=372.3MB, time=7.59 memory used=1356.1MB, alloc=372.3MB, time=7.70 memory used=1390.2MB, alloc=372.3MB, time=7.81 memory used=1431.0MB, alloc=372.3MB, time=7.92 memory used=1484.6MB, alloc=372.3MB, time=8.13 memory used=1528.0MB, alloc=372.3MB, time=8.24 memory used=1559.5MB, alloc=372.3MB, time=8.34 memory used=1597.5MB, alloc=372.3MB, time=8.45 memory used=1644.2MB, alloc=372.3MB, time=8.56 memory used=1676.8MB, alloc=372.3MB, time=8.64 memory used=1708.1MB, alloc=372.3MB, time=8.73 memory used=1760.7MB, alloc=372.3MB, time=9.63 memory used=1799.4MB, alloc=372.3MB, time=9.74 memory used=1838.6MB, alloc=372.3MB, time=9.83 memory used=1872.3MB, alloc=372.3MB, time=9.91 memory used=1919.0MB, alloc=372.3MB, time=10.09 memory used=1966.9MB, alloc=372.3MB, time=10.29 memory used=2022.7MB, alloc=372.3MB, time=10.58 memory used=2062.7MB, alloc=372.3MB, time=10.71 memory used=2100.0MB, alloc=396.3MB, time=10.83 memory used=2150.8MB, alloc=396.3MB, time=10.96 memory used=2216.5MB, alloc=396.3MB, time=11.09 memory used=2264.2MB, alloc=396.3MB, time=11.19 memory used=2309.4MB, alloc=396.3MB, time=11.29 memory used=2372.7MB, alloc=396.3MB, time=12.99 memory used=2434.5MB, alloc=396.3MB, time=13.39 memory used=2495.0MB, alloc=396.3MB, time=13.52 memory used=2539.5MB, alloc=396.3MB, time=13.62 memory used=2595.0MB, alloc=396.3MB, time=13.72 memory used=2666.7MB, alloc=396.3MB, time=13.98 memory used=2761.5MB, alloc=396.3MB, time=14.62 memory used=2857.9MB, alloc=396.3MB, time=15.12 memory used=2975.3MB, alloc=396.3MB, time=16.00 memory used=3080.3MB, alloc=420.3MB, time=16.97 memory used=3184.1MB, alloc=420.3MB, time=17.59 memory used=3282.8MB, alloc=420.3MB, time=18.15 memory used=3387.0MB, alloc=420.3MB, time=18.71 memory used=3543.9MB, alloc=420.3MB, time=19.92 memory used=3679.4MB, alloc=444.3MB, time=21.16 memory used=3799.0MB, alloc=444.3MB, time=22.34 memory used=3938.1MB, alloc=468.3MB, time=23.32 memory used=4042.2MB, alloc=468.3MB, time=24.02 memory used=4111.5MB, alloc=468.3MB, time=24.22 memory used=4199.3MB, alloc=468.3MB, time=24.75 memory used=4319.5MB, alloc=468.3MB, time=25.49 memory used=4409.3MB, alloc=468.3MB, time=28.25 memory used=4534.7MB, alloc=468.3MB, time=29.11 memory used=4628.4MB, alloc=492.3MB, time=31.13 memory used=4807.4MB, alloc=492.3MB, time=32.11 memory used=4981.6MB, alloc=492.3MB, time=33.28 memory used=5114.3MB, alloc=492.3MB, time=34.17 memory used=5199.7MB, alloc=492.3MB, time=34.44 memory used=5304.4MB, alloc=492.3MB, time=34.98 memory used=5440.3MB, alloc=492.3MB, time=37.85 memory used=5570.0MB, alloc=492.3MB, time=38.70 memory used=5720.2MB, alloc=492.3MB, time=39.70 memory used=5819.1MB, alloc=492.3MB, time=40.14 memory used=5919.9MB, alloc=492.3MB, time=40.58 memory used=6022.5MB, alloc=492.3MB, time=41.11 memory used=6110.9MB, alloc=492.3MB, time=41.38 memory used=6184.3MB, alloc=492.3MB, time=41.62 memory used=6256.0MB, alloc=492.3MB, time=41.85 memory used=6341.7MB, alloc=492.3MB, time=42.09 memory used=6440.6MB, alloc=492.3MB, time=42.34 memory used=6628.7MB, alloc=492.3MB, time=42.83 memory used=6864.1MB, alloc=492.3MB, time=43.56 memory used=6943.7MB, alloc=492.3MB, time=43.80 memory used=7020.1MB, alloc=492.3MB, time=44.04 memory used=7113.3MB, alloc=492.3MB, time=44.29 memory used=7322.4MB, alloc=492.3MB, time=44.70 memory used=7488.5MB, alloc=492.3MB, time=45.05 memory used=7693.4MB, alloc=492.3MB, time=45.41 memory used=7922.5MB, alloc=492.3MB, time=48.85 memory used=8006.4MB, alloc=492.3MB, time=49.11 memory used=8209.9MB, alloc=492.3MB, time=49.52 memory used=8456.9MB, alloc=492.3MB, time=50.15 memory used=8604.1MB, alloc=492.3MB, time=50.97 memory used=8710.4MB, alloc=492.3MB, time=51.77 memory used=8966.5MB, alloc=492.3MB, time=52.72 memory used=9055.5MB, alloc=492.3MB, time=52.97 memory used=9338.3MB, alloc=492.3MB, time=54.07 memory used=9469.7MB, alloc=492.3MB, time=55.09 memory used=9559.1MB, alloc=492.3MB, time=55.94 memory used=9673.9MB, alloc=516.3MB, time=56.50 memory used=9775.7MB, alloc=516.3MB, time=56.83 memory used=9884.0MB, alloc=516.3MB, time=57.24 memory used=10002.7MB, alloc=516.3MB, time=57.80 memory used=10090.5MB, alloc=516.3MB, time=58.11 memory used=10198.6MB, alloc=516.3MB, time=58.42 memory used=10270.3MB, alloc=516.3MB, time=58.68 memory used=10351.6MB, alloc=516.3MB, time=58.94 memory used=10441.8MB, alloc=516.3MB, time=59.21 memory used=10545.3MB, alloc=516.3MB, time=59.48 memory used=10660.1MB, alloc=516.3MB, time=59.76 memory used=10863.3MB, alloc=516.3MB, time=60.15 memory used=11011.4MB, alloc=516.3MB, time=60.49 memory used=11181.0MB, alloc=516.3MB, time=60.83 memory used=11316.4MB, alloc=516.3MB, time=64.54 memory used=11405.2MB, alloc=516.3MB, time=64.81 memory used=11499.5MB, alloc=516.3MB, time=65.08 memory used=11750.7MB, alloc=516.3MB, time=65.51 memory used=11925.8MB, alloc=516.3MB, time=65.91 memory used=12196.2MB, alloc=516.3MB, time=66.81 memory used=12316.9MB, alloc=516.3MB, time=67.35 memory used=12413.3MB, alloc=516.3MB, time=67.68 memory used=12506.6MB, alloc=516.3MB, time=67.97 memory used=12591.5MB, alloc=516.3MB, time=68.22 memory used=12699.2MB, alloc=516.3MB, time=68.49 memory used=12813.1MB, alloc=516.3MB, time=69.25 memory used=12910.3MB, alloc=516.3MB, time=69.51 memory used=13063.1MB, alloc=516.3MB, time=69.89 memory used=13160.8MB, alloc=516.3MB, time=70.27 memory used=13269.4MB, alloc=516.3MB, time=70.68 memory used=13398.5MB, alloc=516.3MB, time=71.56 memory used=13518.8MB, alloc=516.3MB, time=72.48 memory used=13640.1MB, alloc=516.3MB, time=73.49 memory used=13746.7MB, alloc=516.3MB, time=74.34 memory used=13853.8MB, alloc=516.3MB, time=75.23 memory used=13926.2MB, alloc=516.3MB, time=75.98 memory used=14014.2MB, alloc=516.3MB, time=76.76 memory used=14143.0MB, alloc=516.3MB, time=77.64 memory used=14260.4MB, alloc=540.3MB, time=78.42 memory used=14379.8MB, alloc=540.3MB, time=78.92 memory used=14475.5MB, alloc=540.3MB, time=79.23 memory used=14617.8MB, alloc=540.3MB, time=79.95 memory used=14720.8MB, alloc=540.3MB, time=80.29 memory used=14894.7MB, alloc=540.3MB, time=80.84 memory used=15045.4MB, alloc=540.3MB, time=81.34 memory used=15156.4MB, alloc=540.3MB, time=81.88 memory used=15280.4MB, alloc=540.3MB, time=82.60 memory used=15486.0MB, alloc=540.3MB, time=83.52 memory used=15627.3MB, alloc=540.3MB, time=84.92 memory used=15726.3MB, alloc=540.3MB, time=85.26 memory used=15840.0MB, alloc=540.3MB, time=85.58 memory used=16015.7MB, alloc=540.3MB, time=85.98 memory used=16309.7MB, alloc=540.3MB, time=87.58 memory used=16408.2MB, alloc=540.3MB, time=87.90 memory used=16675.6MB, alloc=540.3MB, time=88.40 memory used=16945.2MB, alloc=540.3MB, time=89.37 memory used=17049.5MB, alloc=540.3MB, time=90.05 memory used=17192.5MB, alloc=540.3MB, time=91.02 memory used=17264.2MB, alloc=540.3MB, time=91.80 memory used=17325.1MB, alloc=540.3MB, time=92.57 memory used=17397.2MB, alloc=540.3MB, time=93.38 memory used=17522.5MB, alloc=540.3MB, time=94.10 memory used=17651.6MB, alloc=540.3MB, time=94.93 memory used=17734.2MB, alloc=540.3MB, time=95.63 memory used=17861.9MB, alloc=564.3MB, time=96.54 memory used=17957.1MB, alloc=564.3MB, time=97.25 memory used=18011.2MB, alloc=564.3MB, time=97.83 memory used=18058.1MB, alloc=564.3MB, time=98.53 memory used=18310.3MB, alloc=588.3MB, time=100.44 memory used=18567.4MB, alloc=588.3MB, time=101.70 memory used=18844.6MB, alloc=588.3MB, time=103.25 memory used=19121.1MB, alloc=588.3MB, time=104.99 memory used=19318.9MB, alloc=588.3MB, time=105.63 memory used=19588.0MB, alloc=588.3MB, time=107.23 memory used=19831.7MB, alloc=588.3MB, time=107.91 memory used=20141.3MB, alloc=588.3MB, time=109.29 memory used=20414.6MB, alloc=612.3MB, time=110.91 memory used=20712.3MB, alloc=612.3MB, time=113.13 memory used=20976.4MB, alloc=636.3MB, time=116.11 memory used=21295.1MB, alloc=660.3MB, time=119.05 memory used=21625.7MB, alloc=684.3MB, time=122.24 memory used=21978.0MB, alloc=708.3MB, time=125.81 memory used=22308.9MB, alloc=732.3MB, time=129.48 memory used=22695.2MB, alloc=756.3MB, time=132.79 memory used=23083.8MB, alloc=780.3MB, time=135.81 memory used=23437.5MB, alloc=804.3MB, time=139.66 memory used=23840.5MB, alloc=828.3MB, time=143.56 memory used=24325.0MB, alloc=852.3MB, time=146.18 memory used=24826.9MB, alloc=876.3MB, time=149.63 memory used=25221.7MB, alloc=900.3MB, time=153.52 memory used=25631.1MB, alloc=924.3MB, time=157.41 memory used=26004.7MB, alloc=948.3MB, time=160.95 memory used=26441.6MB, alloc=972.3MB, time=164.68 memory used=26882.0MB, alloc=996.3MB, time=173.14 memory used=27279.9MB, alloc=1020.3MB, time=183.29 memory used=27675.2MB, alloc=1044.3MB, time=193.79 memory used=28075.1MB, alloc=1068.3MB, time=204.75 memory used=28483.0MB, alloc=1092.3MB, time=215.99 memory used=28901.6MB, alloc=1116.3MB, time=227.67 memory used=29325.0MB, alloc=1140.3MB, time=239.89 memory used=29759.0MB, alloc=1164.3MB, time=252.80 memory used=30217.0MB, alloc=1188.3MB, time=266.48 memory used=30698.9MB, alloc=1212.3MB, time=280.68 memory used=31204.8MB, alloc=1236.3MB, time=295.57 memory used=31734.6MB, alloc=1260.3MB, time=311.10 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428542542 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 4 4 2 3 3 F := [-11 x y + 20 y + 13 z , -2 x y z - 11 x y - 8 x ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 4 2 2 G := [-8 y z + 5 x y z + 7 x , 14 x + 7 y z + 3 x z] > Problem := [F,G]; 2 2 4 4 2 3 3 Problem := [[-11 x y + 20 y + 13 z , -2 x y z - 11 x y - 8 x ], 3 2 4 2 2 [-8 y z + 5 x y z + 7 x , 14 x + 7 y z + 3 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.15 memory used=25.8MB, alloc=32.3MB, time=0.36 memory used=48.0MB, alloc=36.3MB, time=0.57 memory used=70.3MB, alloc=36.3MB, time=0.75 memory used=89.8MB, alloc=36.7MB, time=1.07 memory used=99.5MB, alloc=36.7MB, time=1.10 memory used=111.2MB, alloc=60.7MB, time=1.15 memory used=139.4MB, alloc=60.7MB, time=1.24 memory used=201.8MB, alloc=70.2MB, time=1.78 memory used=266.8MB, alloc=71.7MB, time=2.42 memory used=311.5MB, alloc=71.7MB, time=2.78 memory used=357.4MB, alloc=71.7MB, time=3.10 memory used=404.1MB, alloc=71.7MB, time=3.59 memory used=427.0MB, alloc=71.7MB, time=3.66 memory used=448.6MB, alloc=71.7MB, time=3.71 memory used=469.9MB, alloc=71.7MB, time=3.77 memory used=516.9MB, alloc=71.7MB, time=4.23 memory used=539.9MB, alloc=71.7MB, time=4.28 memory used=561.7MB, alloc=71.7MB, time=4.34 memory used=582.0MB, alloc=71.7MB, time=4.38 memory used=626.9MB, alloc=71.7MB, time=4.65 memory used=671.9MB, alloc=71.7MB, time=4.87 memory used=692.8MB, alloc=71.7MB, time=4.93 memory used=714.4MB, alloc=71.7MB, time=5.01 memory used=750.0MB, alloc=71.7MB, time=5.21 memory used=800.2MB, alloc=71.7MB, time=5.51 memory used=843.2MB, alloc=71.7MB, time=5.87 memory used=876.3MB, alloc=95.7MB, time=6.07 memory used=939.9MB, alloc=95.7MB, time=6.43 memory used=995.2MB, alloc=95.7MB, time=6.95 memory used=1061.1MB, alloc=95.7MB, time=7.63 memory used=1123.7MB, alloc=95.7MB, time=8.40 memory used=1200.4MB, alloc=95.7MB, time=9.05 memory used=1252.1MB, alloc=95.7MB, time=9.74 memory used=1334.2MB, alloc=95.7MB, time=10.18 memory used=1377.5MB, alloc=95.7MB, time=10.34 memory used=1428.0MB, alloc=95.7MB, time=10.55 memory used=1456.2MB, alloc=95.7MB, time=10.64 memory used=1492.1MB, alloc=95.7MB, time=10.73 memory used=1525.0MB, alloc=95.7MB, time=10.82 memory used=1549.7MB, alloc=95.7MB, time=10.89 memory used=1577.1MB, alloc=95.7MB, time=10.97 memory used=1608.5MB, alloc=95.7MB, time=11.05 memory used=1655.5MB, alloc=95.7MB, time=11.24 memory used=1690.2MB, alloc=95.7MB, time=11.34 memory used=1721.7MB, alloc=95.7MB, time=11.43 memory used=1761.0MB, alloc=95.7MB, time=11.51 memory used=1787.2MB, alloc=95.7MB, time=11.60 memory used=1813.5MB, alloc=95.7MB, time=11.68 memory used=1843.2MB, alloc=95.7MB, time=11.77 memory used=1877.5MB, alloc=95.7MB, time=11.84 memory used=1944.0MB, alloc=95.7MB, time=16.61 memory used=2003.5MB, alloc=95.7MB, time=16.80 memory used=2039.5MB, alloc=95.7MB, time=16.88 memory used=2065.0MB, alloc=95.7MB, time=16.96 memory used=2096.3MB, alloc=95.7MB, time=17.04 memory used=2133.5MB, alloc=95.7MB, time=17.12 memory used=2159.5MB, alloc=95.7MB, time=17.18 memory used=2185.5MB, alloc=95.7MB, time=17.25 memory used=2236.6MB, alloc=95.7MB, time=17.46 memory used=2267.4MB, alloc=95.7MB, time=17.55 memory used=2298.0MB, alloc=95.7MB, time=17.63 memory used=2336.3MB, alloc=95.7MB, time=17.72 memory used=2362.2MB, alloc=95.7MB, time=17.80 memory used=2388.0MB, alloc=95.7MB, time=17.87 memory used=2435.5MB, alloc=95.7MB, time=18.22 memory used=2470.4MB, alloc=95.7MB, time=18.32 memory used=2496.9MB, alloc=95.7MB, time=18.40 memory used=2526.8MB, alloc=95.7MB, time=18.48 memory used=2560.9MB, alloc=95.7MB, time=18.58 memory used=2600.7MB, alloc=95.7MB, time=18.67 memory used=2627.5MB, alloc=95.7MB, time=18.75 memory used=2649.8MB, alloc=119.7MB, time=18.85 memory used=2687.7MB, alloc=119.7MB, time=18.96 memory used=2730.2MB, alloc=119.7MB, time=19.07 memory used=2775.2MB, alloc=119.7MB, time=19.18 memory used=2824.3MB, alloc=119.7MB, time=19.28 memory used=2878.5MB, alloc=119.7MB, time=19.40 memory used=2938.6MB, alloc=119.7MB, time=19.52 memory used=2986.5MB, alloc=119.7MB, time=19.62 memory used=3020.8MB, alloc=119.7MB, time=19.70 memory used=3058.0MB, alloc=119.7MB, time=19.78 memory used=3104.7MB, alloc=119.7MB, time=19.90 memory used=3157.1MB, alloc=119.7MB, time=21.53 memory used=3198.1MB, alloc=119.7MB, time=21.61 memory used=3277.7MB, alloc=119.7MB, time=21.98 memory used=3319.9MB, alloc=119.7MB, time=22.10 memory used=3370.7MB, alloc=119.7MB, time=22.20 memory used=3428.9MB, alloc=119.7MB, time=22.32 memory used=3463.8MB, alloc=119.7MB, time=22.43 memory used=3503.1MB, alloc=119.7MB, time=22.52 memory used=3547.7MB, alloc=119.7MB, time=22.61 memory used=3598.2MB, alloc=119.7MB, time=22.71 memory used=3669.5MB, alloc=119.7MB, time=23.03 memory used=3724.6MB, alloc=119.7MB, time=23.15 memory used=3770.6MB, alloc=119.7MB, time=23.25 memory used=3828.4MB, alloc=119.7MB, time=23.37 memory used=3873.0MB, alloc=119.7MB, time=23.47 memory used=3910.7MB, alloc=119.7MB, time=23.58 memory used=3952.7MB, alloc=119.7MB, time=23.67 memory used=4000.4MB, alloc=119.7MB, time=23.78 memory used=4059.4MB, alloc=119.7MB, time=23.92 memory used=4146.2MB, alloc=119.7MB, time=43.56 memory used=4201.4MB, alloc=119.7MB, time=58.64 memory used=4258.2MB, alloc=119.7MB, time=59.01 memory used=4308.4MB, alloc=119.7MB, time=59.12 memory used=4347.6MB, alloc=119.7MB, time=59.22 memory used=4394.1MB, alloc=119.7MB, time=59.32 memory used=4449.4MB, alloc=119.7MB, time=59.41 memory used=4499.6MB, alloc=119.7MB, time=59.50 memory used=4533.2MB, alloc=119.7MB, time=59.58 memory used=4570.1MB, alloc=119.7MB, time=59.65 memory used=4609.6MB, alloc=119.7MB, time=59.73 memory used=4652.9MB, alloc=119.7MB, time=59.81 memory used=4699.1MB, alloc=119.7MB, time=59.89 memory used=4750.0MB, alloc=119.7MB, time=59.97 memory used=4819.2MB, alloc=119.7MB, time=60.75 memory used=4885.8MB, alloc=119.7MB, time=60.91 memory used=4922.8MB, alloc=119.7MB, time=61.02 memory used=4961.3MB, alloc=119.7MB, time=61.12 memory used=5003.8MB, alloc=119.7MB, time=61.23 memory used=5052.1MB, alloc=119.7MB, time=61.35 memory used=5103.4MB, alloc=119.7MB, time=61.48 memory used=5158.1MB, alloc=119.7MB, time=61.60 memory used=5212.5MB, alloc=119.7MB, time=61.73 memory used=5243.7MB, alloc=119.7MB, time=61.82 memory used=5272.5MB, alloc=119.7MB, time=61.92 memory used=5302.7MB, alloc=119.7MB, time=62.01 memory used=5333.7MB, alloc=119.7MB, time=62.10 memory used=5368.6MB, alloc=119.7MB, time=62.21 memory used=5404.2MB, alloc=119.7MB, time=62.30 memory used=5440.4MB, alloc=119.7MB, time=62.41 memory used=5477.0MB, alloc=119.7MB, time=62.49 memory used=5514.3MB, alloc=119.7MB, time=62.60 memory used=5556.0MB, alloc=119.7MB, time=62.70 memory used=5598.2MB, alloc=119.7MB, time=62.79 memory used=5640.7MB, alloc=119.7MB, time=62.90 memory used=5683.8MB, alloc=119.7MB, time=63.01 memory used=5731.3MB, alloc=119.7MB, time=63.11 memory used=5779.2MB, alloc=119.7MB, time=63.21 memory used=5827.3MB, alloc=119.7MB, time=63.31 memory used=5879.9MB, alloc=119.7MB, time=63.41 memory used=5932.5MB, alloc=119.7MB, time=63.51 memory used=5985.3MB, alloc=119.7MB, time=63.62 memory used=6042.2MB, alloc=119.7MB, time=63.73 memory used=6094.9MB, alloc=119.7MB, time=63.84 memory used=6125.1MB, alloc=143.7MB, time=63.93 memory used=6164.3MB, alloc=143.7MB, time=64.01 memory used=6206.6MB, alloc=143.7MB, time=64.11 memory used=6248.5MB, alloc=143.7MB, time=64.19 memory used=6290.4MB, alloc=143.7MB, time=64.28 memory used=6335.2MB, alloc=143.7MB, time=64.37 memory used=6379.6MB, alloc=143.7MB, time=64.47 memory used=6427.3MB, alloc=143.7MB, time=64.56 memory used=6474.5MB, alloc=143.7MB, time=64.65 memory used=6523.7MB, alloc=143.7MB, time=64.75 memory used=6575.5MB, alloc=143.7MB, time=64.84 memory used=6629.1MB, alloc=143.7MB, time=64.94 memory used=6684.0MB, alloc=143.7MB, time=65.03 memory used=6742.7MB, alloc=143.7MB, time=65.13 memory used=6803.3MB, alloc=143.7MB, time=65.23 memory used=6865.3MB, alloc=143.7MB, time=65.33 memory used=6931.5MB, alloc=143.7MB, time=65.43 memory used=7020.9MB, alloc=143.7MB, time=66.22 memory used=7098.2MB, alloc=143.7MB, time=66.40 memory used=7151.2MB, alloc=143.7MB, time=66.56 memory used=7214.7MB, alloc=143.7MB, time=66.73 memory used=7284.8MB, alloc=143.7MB, time=66.90 memory used=7364.4MB, alloc=143.7MB, time=67.05 memory used=7425.1MB, alloc=143.7MB, time=67.19 memory used=7470.9MB, alloc=143.7MB, time=67.32 memory used=7517.0MB, alloc=143.7MB, time=67.47 memory used=7568.0MB, alloc=143.7MB, time=67.60 memory used=7620.2MB, alloc=143.7MB, time=67.75 memory used=7673.7MB, alloc=143.7MB, time=67.88 memory used=7732.2MB, alloc=143.7MB, time=68.02 memory used=7791.8MB, alloc=143.7MB, time=68.17 memory used=7856.4MB, alloc=143.7MB, time=68.31 memory used=7921.9MB, alloc=143.7MB, time=68.43 memory used=7992.3MB, alloc=143.7MB, time=68.57 memory used=8063.3MB, alloc=143.7MB, time=68.70 memory used=8139.0MB, alloc=143.7MB, time=68.84 memory used=8219.1MB, alloc=143.7MB, time=68.99 memory used=8294.0MB, alloc=143.7MB, time=69.12 memory used=8336.1MB, alloc=143.7MB, time=69.21 memory used=8377.4MB, alloc=143.7MB, time=69.30 memory used=8419.6MB, alloc=143.7MB, time=69.40 memory used=8461.7MB, alloc=143.7MB, time=69.49 memory used=8506.8MB, alloc=143.7MB, time=69.59 memory used=8551.7MB, alloc=143.7MB, time=69.69 memory used=8599.7MB, alloc=143.7MB, time=69.78 memory used=8647.3MB, alloc=143.7MB, time=69.87 memory used=8696.8MB, alloc=143.7MB, time=69.97 memory used=8749.3MB, alloc=143.7MB, time=70.07 memory used=8803.6MB, alloc=143.7MB, time=70.17 memory used=8859.3MB, alloc=143.7MB, time=70.27 memory used=8916.0MB, alloc=143.7MB, time=70.36 memory used=8975.4MB, alloc=143.7MB, time=70.46 memory used=9038.1MB, alloc=143.7MB, time=70.56 memory used=9104.8MB, alloc=143.7MB, time=70.65 memory used=9180.9MB, alloc=143.7MB, time=70.82 memory used=9276.3MB, alloc=143.7MB, time=104.66 memory used=9358.0MB, alloc=143.7MB, time=145.70 memory used=9440.6MB, alloc=143.7MB, time=206.45 memory used=9528.2MB, alloc=143.7MB, time=215.16 memory used=9598.8MB, alloc=143.7MB, time=215.32 memory used=9649.5MB, alloc=143.7MB, time=215.44 memory used=9705.8MB, alloc=143.7MB, time=215.55 memory used=9770.9MB, alloc=143.7MB, time=215.67 memory used=9844.6MB, alloc=143.7MB, time=215.81 memory used=9909.2MB, alloc=143.7MB, time=215.94 memory used=9953.3MB, alloc=143.7MB, time=216.04 memory used=9999.9MB, alloc=143.7MB, time=216.14 memory used=10049.1MB, alloc=143.7MB, time=216.23 memory used=10100.7MB, alloc=143.7MB, time=216.33 memory used=10156.1MB, alloc=143.7MB, time=216.43 memory used=10215.3MB, alloc=143.7MB, time=216.53 memory used=10277.8MB, alloc=143.7MB, time=216.63 memory used=10343.3MB, alloc=143.7MB, time=216.73 memory used=10412.8MB, alloc=143.7MB, time=216.83 memory used=10488.4MB, alloc=143.7MB, time=216.94 memory used=10571.0MB, alloc=143.7MB, time=217.05 memory used=10585.0MB, alloc=155.8MB, time=217.11 memory used=10594.2MB, alloc=155.8MB, time=217.17 memory used=10603.1MB, alloc=155.8MB, time=217.23 memory used=10612.9MB, alloc=155.8MB, time=217.28 memory used=10622.8MB, alloc=155.8MB, time=217.34 memory used=10632.4MB, alloc=155.8MB, time=217.40 memory used=10643.0MB, alloc=155.8MB, time=217.45 memory used=10653.3MB, alloc=155.8MB, time=217.51 memory used=10663.4MB, alloc=155.8MB, time=217.56 memory used=10674.2MB, alloc=155.8MB, time=217.62 memory used=10684.8MB, alloc=155.8MB, time=217.68 memory used=10696.1MB, alloc=155.8MB, time=217.73 memory used=10707.0MB, alloc=155.8MB, time=217.79 memory used=10718.2MB, alloc=155.8MB, time=217.84 memory used=10729.9MB, alloc=155.8MB, time=217.90 memory used=10741.8MB, alloc=155.8MB, time=217.96 memory used=10753.9MB, alloc=155.8MB, time=218.02 memory used=10766.4MB, alloc=155.8MB, time=218.07 memory used=10779.3MB, alloc=155.8MB, time=218.13 memory used=10792.9MB, alloc=155.8MB, time=218.19 memory used=10896.9MB, alloc=155.8MB, time=218.97 memory used=10951.0MB, alloc=155.8MB, time=219.11 memory used=11011.4MB, alloc=155.8MB, time=219.25 memory used=11082.2MB, alloc=155.8MB, time=219.39 memory used=11162.8MB, alloc=155.8MB, time=219.55 memory used=11218.1MB, alloc=155.8MB, time=219.68 memory used=11265.3MB, alloc=155.8MB, time=219.81 memory used=11313.1MB, alloc=155.8MB, time=219.93 memory used=11365.3MB, alloc=155.8MB, time=220.04 memory used=11418.8MB, alloc=155.8MB, time=220.16 memory used=11476.8MB, alloc=155.8MB, time=220.30 memory used=11539.2MB, alloc=155.8MB, time=220.42 memory used=11602.5MB, alloc=155.8MB, time=220.56 memory used=11669.6MB, alloc=155.8MB, time=220.68 memory used=11740.8MB, alloc=155.8MB, time=220.83 memory used=11815.9MB, alloc=155.8MB, time=220.99 memory used=11896.9MB, alloc=155.8MB, time=221.11 memory used=11957.4MB, alloc=155.8MB, time=221.23 memory used=11999.8MB, alloc=155.8MB, time=221.32 memory used=12043.6MB, alloc=155.8MB, time=221.41 memory used=12089.7MB, alloc=155.8MB, time=221.51 memory used=12137.6MB, alloc=155.8MB, time=221.60 memory used=12186.9MB, alloc=155.8MB, time=221.69 memory used=12237.0MB, alloc=155.8MB, time=221.79 memory used=12290.0MB, alloc=155.8MB, time=221.88 memory used=12345.0MB, alloc=155.8MB, time=221.97 memory used=12404.8MB, alloc=155.8MB, time=222.07 memory used=12474.7MB, alloc=155.8MB, time=222.35 memory used=12571.7MB, alloc=155.8MB, time=222.93 memory used=12623.8MB, alloc=155.8MB, time=223.07 memory used=12683.9MB, alloc=155.8MB, time=223.22 memory used=12754.7MB, alloc=155.8MB, time=223.39 memory used=12835.4MB, alloc=155.8MB, time=223.54 memory used=12888.0MB, alloc=155.8MB, time=223.66 memory used=12932.0MB, alloc=155.8MB, time=223.80 memory used=12979.5MB, alloc=155.8MB, time=223.94 memory used=13031.6MB, alloc=155.8MB, time=224.07 memory used=13084.9MB, alloc=155.8MB, time=224.20 memory used=13142.8MB, alloc=155.8MB, time=224.33 memory used=13201.7MB, alloc=155.8MB, time=224.44 memory used=13264.5MB, alloc=155.8MB, time=224.56 memory used=13331.7MB, alloc=155.8MB, time=224.68 memory used=13402.9MB, alloc=155.8MB, time=224.81 memory used=13477.6MB, alloc=155.8MB, time=224.93 memory used=13559.0MB, alloc=155.8MB, time=225.06 memory used=13621.9MB, alloc=155.8MB, time=225.18 memory used=13662.8MB, alloc=155.8MB, time=225.27 memory used=13706.6MB, alloc=155.8MB, time=225.36 memory used=13749.6MB, alloc=155.8MB, time=225.45 memory used=13794.7MB, alloc=155.8MB, time=225.55 memory used=13841.5MB, alloc=155.8MB, time=225.64 memory used=13890.0MB, alloc=155.8MB, time=225.73 memory used=13940.7MB, alloc=155.8MB, time=225.82 memory used=13993.9MB, alloc=155.8MB, time=225.92 memory used=14050.4MB, alloc=155.8MB, time=226.01 memory used=14111.6MB, alloc=155.8MB, time=226.11 memory used=14195.5MB, alloc=155.8MB, time=240.07 memory used=14263.6MB, alloc=155.8MB, time=279.62 memory used=14338.3MB, alloc=155.8MB, time=321.60 memory used=14420.5MB, alloc=155.8MB, time=368.09 memory used=14504.8MB, alloc=155.8MB, time=369.57 memory used=14572.4MB, alloc=155.8MB, time=369.70 memory used=14620.5MB, alloc=155.8MB, time=369.83 memory used=14676.7MB, alloc=155.8MB, time=369.97 memory used=14741.4MB, alloc=155.8MB, time=370.11 memory used=14815.8MB, alloc=155.8MB, time=370.25 memory used=14874.2MB, alloc=155.8MB, time=370.35 memory used=14917.2MB, alloc=155.8MB, time=370.44 memory used=14962.3MB, alloc=155.8MB, time=370.54 memory used=15011.3MB, alloc=155.8MB, time=370.63 memory used=15062.8MB, alloc=155.8MB, time=370.73 memory used=15116.4MB, alloc=155.8MB, time=370.83 memory used=15173.7MB, alloc=155.8MB, time=370.93 memory used=15234.4MB, alloc=155.8MB, time=371.03 memory used=15299.6MB, alloc=155.8MB, time=371.13 memory used=15368.9MB, alloc=155.8MB, time=371.24 memory used=15442.7MB, alloc=155.8MB, time=371.35 memory used=15522.7MB, alloc=155.8MB, time=371.46 memory used=15540.8MB, alloc=155.8MB, time=371.52 memory used=15549.9MB, alloc=155.8MB, time=371.58 memory used=15559.9MB, alloc=155.8MB, time=371.64 memory used=15569.9MB, alloc=155.8MB, time=371.70 memory used=15579.7MB, alloc=155.8MB, time=371.75 memory used=15589.2MB, alloc=155.8MB, time=371.81 memory used=15599.8MB, alloc=155.8MB, time=371.86 memory used=15610.1MB, alloc=155.8MB, time=371.92 memory used=15620.2MB, alloc=155.8MB, time=371.98 memory used=15630.9MB, alloc=155.8MB, time=372.03 memory used=15641.5MB, alloc=155.8MB, time=372.09 memory used=15652.7MB, alloc=155.8MB, time=372.15 memory used=15663.7MB, alloc=155.8MB, time=372.21 memory used=15674.9MB, alloc=155.8MB, time=372.26 memory used=15686.4MB, alloc=155.8MB, time=372.32 memory used=15698.3MB, alloc=155.8MB, time=372.38 memory used=15710.9MB, alloc=155.8MB, time=372.44 memory used=15723.4MB, alloc=155.8MB, time=372.50 memory used=15736.3MB, alloc=155.8MB, time=372.56 memory used=15750.0MB, alloc=155.8MB, time=372.62 memory used=15834.6MB, alloc=155.8MB, time=372.93 memory used=15906.7MB, alloc=155.8MB, time=373.07 memory used=15963.9MB, alloc=155.8MB, time=373.18 memory used=16023.0MB, alloc=155.8MB, time=373.30 memory used=16096.3MB, alloc=155.8MB, time=373.41 memory used=16182.1MB, alloc=155.8MB, time=373.70 memory used=16249.9MB, alloc=155.8MB, time=373.85 memory used=16311.7MB, alloc=155.8MB, time=373.99 memory used=16368.9MB, alloc=155.8MB, time=374.12 memory used=16438.8MB, alloc=155.8MB, time=374.26 memory used=16539.1MB, alloc=155.8MB, time=379.14 memory used=16602.7MB, alloc=155.8MB, time=379.27 memory used=16671.8MB, alloc=155.8MB, time=379.40 memory used=16728.0MB, alloc=155.8MB, time=379.49 memory used=16819.9MB, alloc=155.8MB, time=379.93 memory used=16878.2MB, alloc=155.8MB, time=380.07 memory used=16950.7MB, alloc=155.8MB, time=380.23 memory used=17019.3MB, alloc=155.8MB, time=380.38 memory used=17067.4MB, alloc=155.8MB, time=380.49 memory used=17121.8MB, alloc=155.8MB, time=380.61 memory used=17180.2MB, alloc=155.8MB, time=380.74 memory used=17244.6MB, alloc=155.8MB, time=380.86 memory used=17316.6MB, alloc=155.8MB, time=380.98 memory used=17395.4MB, alloc=155.8MB, time=381.11 memory used=17464.9MB, alloc=155.8MB, time=381.24 memory used=17509.3MB, alloc=155.8MB, time=381.33 memory used=17557.3MB, alloc=155.8MB, time=381.42 memory used=17608.2MB, alloc=155.8MB, time=381.52 memory used=17664.5MB, alloc=155.8MB, time=381.62 memory used=17746.7MB, alloc=155.8MB, time=382.05 memory used=17815.0MB, alloc=155.8MB, time=382.22 memory used=17881.9MB, alloc=155.8MB, time=382.36 memory used=17960.5MB, alloc=155.8MB, time=382.50 memory used=18008.8MB, alloc=155.8MB, time=382.64 memory used=18060.2MB, alloc=155.8MB, time=382.78 memory used=18118.1MB, alloc=155.8MB, time=382.92 memory used=18182.1MB, alloc=155.8MB, time=383.05 memory used=18251.7MB, alloc=155.8MB, time=383.19 memory used=18328.4MB, alloc=155.8MB, time=383.33 memory used=18407.1MB, alloc=155.8MB, time=383.45 memory used=18452.4MB, alloc=155.8MB, time=383.54 memory used=18500.0MB, alloc=155.8MB, time=383.63 memory used=18549.7MB, alloc=155.8MB, time=383.73 memory used=18603.7MB, alloc=155.8MB, time=383.82 memory used=18665.2MB, alloc=155.8MB, time=384.03 memory used=18732.0MB, alloc=155.8MB, time=385.81 memory used=18822.7MB, alloc=155.8MB, time=386.77 memory used=18893.4MB, alloc=155.8MB, time=386.94 memory used=18950.1MB, alloc=155.8MB, time=387.09 memory used=19019.0MB, alloc=155.8MB, time=387.23 memory used=19099.2MB, alloc=155.8MB, time=387.40 memory used=19150.6MB, alloc=155.8MB, time=387.53 memory used=19195.6MB, alloc=155.8MB, time=387.65 memory used=19244.4MB, alloc=155.8MB, time=387.76 memory used=19298.0MB, alloc=155.8MB, time=387.88 memory used=19353.2MB, alloc=155.8MB, time=387.99 memory used=19413.3MB, alloc=155.8MB, time=388.11 memory used=19474.9MB, alloc=155.8MB, time=388.23 memory used=19541.2MB, alloc=155.8MB, time=388.35 memory used=19612.3MB, alloc=155.8MB, time=388.50 memory used=19688.1MB, alloc=155.8MB, time=388.64 memory used=19768.2MB, alloc=155.8MB, time=388.77 memory used=19835.8MB, alloc=155.8MB, time=388.88 memory used=19876.0MB, alloc=155.8MB, time=388.97 memory used=19918.0MB, alloc=155.8MB, time=389.07 memory used=19960.6MB, alloc=155.8MB, time=389.16 memory used=20003.3MB, alloc=155.8MB, time=389.25 memory used=20048.6MB, alloc=155.8MB, time=389.34 memory used=20094.1MB, alloc=155.8MB, time=389.44 memory used=20142.0MB, alloc=155.8MB, time=389.53 memory used=20193.0MB, alloc=155.8MB, time=389.63 memory used=20243.1MB, alloc=155.8MB, time=389.72 memory used=20295.5MB, alloc=155.8MB, time=389.82 memory used=20349.9MB, alloc=155.8MB, time=389.92 memory used=20406.0MB, alloc=155.8MB, time=390.02 memory used=20465.5MB, alloc=155.8MB, time=390.12 memory used=20528.1MB, alloc=155.8MB, time=390.22 memory used=20592.3MB, alloc=155.8MB, time=390.31 memory used=20661.2MB, alloc=155.8MB, time=390.42 memory used=20733.5MB, alloc=155.8MB, time=390.52 memory used=20813.7MB, alloc=155.8MB, time=390.70 memory used=20911.7MB, alloc=155.8MB, time=391.61 memory used=20971.3MB, alloc=155.8MB, time=391.78 memory used=21032.0MB, alloc=155.8MB, time=391.91 memory used=21103.6MB, alloc=155.8MB, time=392.06 memory used=21178.7MB, alloc=155.8MB, time=392.21 memory used=21223.3MB, alloc=155.8MB, time=392.32 memory used=21269.5MB, alloc=155.8MB, time=392.46 memory used=21318.7MB, alloc=155.8MB, time=392.59 memory used=21372.6MB, alloc=155.8MB, time=392.72 memory used=21428.3MB, alloc=155.8MB, time=392.84 memory used=21488.6MB, alloc=155.8MB, time=392.99 memory used=21550.5MB, alloc=155.8MB, time=393.14 memory used=21617.1MB, alloc=155.8MB, time=393.28 memory used=21688.4MB, alloc=155.8MB, time=393.41 memory used=21764.3MB, alloc=155.8MB, time=393.54 memory used=21844.6MB, alloc=155.8MB, time=393.67 memory used=21905.4MB, alloc=155.8MB, time=393.79 memory used=21944.7MB, alloc=155.8MB, time=393.88 memory used=21986.9MB, alloc=155.8MB, time=393.98 memory used=22029.5MB, alloc=155.8MB, time=394.07 memory used=22072.2MB, alloc=155.8MB, time=394.16 memory used=22117.4MB, alloc=155.8MB, time=394.26 memory used=22162.9MB, alloc=155.8MB, time=394.35 memory used=22210.7MB, alloc=155.8MB, time=394.46 memory used=22261.5MB, alloc=155.8MB, time=394.55 memory used=22311.8MB, alloc=155.8MB, time=394.65 memory used=22363.8MB, alloc=155.8MB, time=394.75 memory used=22418.0MB, alloc=155.8MB, time=394.84 memory used=22474.1MB, alloc=155.8MB, time=394.94 memory used=22533.3MB, alloc=155.8MB, time=395.04 memory used=22595.4MB, alloc=155.8MB, time=395.14 memory used=22659.2MB, alloc=155.8MB, time=395.24 memory used=22727.6MB, alloc=155.8MB, time=395.35 memory used=22800.7MB, alloc=155.8MB, time=395.45 memory used=22879.8MB, alloc=155.8MB, time=395.65 memory used=22966.6MB, alloc=155.8MB, time=398.44 memory used=23074.7MB, alloc=155.8MB, time=398.84 memory used=23171.0MB, alloc=155.8MB, time=399.72 memory used=23250.6MB, alloc=411.8MB, time=400.43 memory used=23393.4MB, alloc=411.8MB, time=405.32 memory used=23474.9MB, alloc=411.8MB, time=417.03 memory used=23538.6MB, alloc=411.8MB, time=417.18 memory used=23588.1MB, alloc=411.8MB, time=417.31 memory used=23651.0MB, alloc=411.8MB, time=417.43 memory used=23718.5MB, alloc=411.8MB, time=417.57 memory used=23762.5MB, alloc=411.8MB, time=417.66 memory used=23812.1MB, alloc=411.8MB, time=417.76 memory used=23867.0MB, alloc=411.8MB, time=417.86 memory used=23930.6MB, alloc=411.8MB, time=417.96 memory used=23996.5MB, alloc=411.8MB, time=418.18 memory used=24119.2MB, alloc=411.8MB, time=419.31 memory used=24263.4MB, alloc=411.8MB, time=420.27 memory used=24358.1MB, alloc=411.8MB, time=436.99 memory used=24425.9MB, alloc=411.8MB, time=437.63 memory used=24481.0MB, alloc=411.8MB, time=437.77 memory used=24530.1MB, alloc=411.8MB, time=437.91 memory used=24590.1MB, alloc=411.8MB, time=438.03 memory used=24650.9MB, alloc=411.8MB, time=438.16 memory used=24690.5MB, alloc=411.8MB, time=438.25 memory used=24734.3MB, alloc=411.8MB, time=438.35 memory used=24782.6MB, alloc=411.8MB, time=438.46 memory used=24835.7MB, alloc=411.8MB, time=438.56 memory used=24902.1MB, alloc=411.8MB, time=438.84 memory used=24985.2MB, alloc=411.8MB, time=466.15 memory used=25061.1MB, alloc=411.8MB, time=508.28 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428542842 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 3 F := [16 x z + 5 y z + 15 x z, 2 y z + 13 y z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 4 2 2 G := [-20 x y z + 2 x y - 5 x y, 10 x + y z - 20 x y] > Problem := [F,G]; 2 2 3 2 3 Problem := [[16 x z + 5 y z + 15 x z, 2 y z + 13 y z], 2 2 4 2 2 [-20 x y z + 2 x y - 5 x y, 10 x + y z - 20 x y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.1MB, alloc=32.3MB, time=0.46 memory used=47.1MB, alloc=32.3MB, time=0.75 memory used=64.6MB, alloc=56.3MB, time=1.00 memory used=106.8MB, alloc=60.3MB, time=1.55 memory used=147.0MB, alloc=60.3MB, time=2.03 memory used=186.7MB, alloc=84.3MB, time=2.57 memory used=229.8MB, alloc=84.3MB, time=3.18 memory used=291.6MB, alloc=92.3MB, time=3.80 memory used=332.2MB, alloc=92.3MB, time=4.04 memory used=404.2MB, alloc=92.3MB, time=4.90 memory used=461.8MB, alloc=92.3MB, time=5.39 memory used=497.5MB, alloc=92.3MB, time=5.57 memory used=541.1MB, alloc=92.3MB, time=5.92 memory used=570.6MB, alloc=92.3MB, time=6.03 memory used=620.2MB, alloc=92.3MB, time=6.42 memory used=692.5MB, alloc=116.3MB, time=7.22 memory used=790.3MB, alloc=116.3MB, time=8.00 memory used=866.1MB, alloc=116.3MB, time=8.35 memory used=956.9MB, alloc=116.3MB, time=9.06 memory used=1033.9MB, alloc=116.3MB, time=9.37 memory used=1104.8MB, alloc=116.3MB, time=9.63 memory used=1171.9MB, alloc=116.3MB, time=9.85 memory used=1244.1MB, alloc=116.3MB, time=10.10 memory used=1317.0MB, alloc=116.3MB, time=10.34 memory used=1392.0MB, alloc=116.3MB, time=10.58 memory used=1467.8MB, alloc=116.3MB, time=10.84 memory used=1548.4MB, alloc=116.3MB, time=11.11 memory used=1634.2MB, alloc=116.3MB, time=11.39 memory used=1710.3MB, alloc=116.3MB, time=11.63 memory used=1781.8MB, alloc=116.3MB, time=11.85 memory used=1876.7MB, alloc=116.3MB, time=12.62 memory used=1963.8MB, alloc=116.3MB, time=13.74 memory used=2034.3MB, alloc=140.3MB, time=14.90 memory used=2135.6MB, alloc=164.3MB, time=16.44 memory used=2269.4MB, alloc=164.3MB, time=17.97 memory used=2377.6MB, alloc=444.3MB, time=19.67 memory used=2503.4MB, alloc=468.3MB, time=22.16 memory used=2627.4MB, alloc=492.3MB, time=25.76 memory used=2759.2MB, alloc=516.3MB, time=28.83 memory used=2908.9MB, alloc=540.3MB, time=32.48 memory used=3082.6MB, alloc=540.3MB, time=36.62 memory used=3256.3MB, alloc=564.3MB, time=40.70 memory used=3454.0MB, alloc=564.3MB, time=45.12 N1 := 5969 > GB := Basis(F, plex(op(vars))); 3 2 2 2 GB := [2 y z + 13 y z, 32 x z + 30 x z - 65 y z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=3655.2MB, alloc=564.3MB, time=48.65 memory used=3846.7MB, alloc=564.3MB, time=50.59 memory used=4067.5MB, alloc=564.3MB, time=51.54 memory used=4276.2MB, alloc=564.3MB, time=52.30 memory used=4536.3MB, alloc=588.3MB, time=54.66 memory used=4827.5MB, alloc=612.3MB, time=56.70 memory used=5058.6MB, alloc=636.3MB, time=59.44 memory used=5317.3MB, alloc=660.3MB, time=65.25 memory used=5571.7MB, alloc=684.3MB, time=71.75 memory used=5850.2MB, alloc=708.3MB, time=78.68 N2 := 5777 > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 3 2 3 2 2 H := [16 x z + 5 y z + 15 x z, 2 y z + 13 y z, -20 x y z + 2 x y - 5 x y, 2 2 4 z y + 10 x - 20 y x] > J:=[op(GB),op(G)]; 3 2 2 2 2 2 J := [2 y z + 13 y z, 32 x z + 30 x z - 65 y z, -20 x y z + 2 x y - 5 x y, 2 2 4 z y + 10 x - 20 y x] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 11, 16, 4, 4, 3, 2, 3/4, 1, 1, 7/11, 8/11, 7/11, 4, 11, 16, 4, 4, 3, 2, 3/4, 1, 1, 7/11, 8/11, 7/11, 0, 0, 0] > save(F, G, cat("ranSet/34", convert(F, string),".txt")); > quit memory used=6146.7MB, alloc=708.3MB, time=84.89 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428542926 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 2 F := [7 y - 4 x y + 9, -x y z - 10 y z - 11 x z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 4 3 G := [-18 x y z + 3 x y + 2 x y, -20 x - 10 y z - 9 x] > Problem := [F,G]; 4 2 2 2 Problem := [[7 y - 4 x y + 9, -x y z - 10 y z - 11 x z], 2 2 4 3 [-18 x y z + 3 x y + 2 x y, -20 x - 10 y z - 9 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.14 memory used=26.5MB, alloc=32.3MB, time=0.34 memory used=47.1MB, alloc=32.3MB, time=0.52 memory used=68.2MB, alloc=56.3MB, time=0.79 memory used=112.6MB, alloc=60.3MB, time=1.28 N1 := 807 > GB := Basis(F, plex(op(vars))); 4 2 3 2 GB := [7 y - 4 x y + 9, 11 x z + 324 x z + 45 x z + 225 z, 2 2 22 x z + 385 y z + 428 x z + 45 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=150.3MB, alloc=60.3MB, time=1.74 memory used=186.8MB, alloc=84.3MB, time=2.06 memory used=250.8MB, alloc=84.3MB, time=2.70 N2 := 771 > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 4 2 2 2 H := [7 y - 4 x y + 9, -x y z - 10 y z - 11 x z, 2 2 4 3 -18 x y z + 3 x y + 2 x y, -20 x - 10 y z - 9 x] > J:=[op(GB),op(G)]; 4 2 3 2 J := [7 y - 4 x y + 9, 11 x z + 324 x z + 45 x z + 225 z, 2 2 2 2 22 x z + 385 y z + 428 x z + 45 z, -18 x y z + 3 x y + 2 x y, 4 3 -20 x - 10 y z - 9 x] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 11, 16, 4, 4, 4, 3, 1, 1, 3/4, 2/3, 2/3, 5/12, 5, 13, 19, 4, 11 10 4, 4, 3, 1, 4/5, 4/5, --, 7/17, --, -2, -3, 0] 17 17 > save(F, G, cat("ranSet/34", convert(F, string),".txt")); > quit memory used=294.9MB, alloc=84.3MB, time=3.20 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428542929 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 F := [7 y z - 8 x y - 14 x y z, -9 y z - 17 y z - 6 y] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 4 2 G := [-15 x z - 14 x y + 3, 10 z - 16 z + 11 x] > Problem := [F,G]; 3 2 3 Problem := [[7 y z - 8 x y - 14 x y z, -9 y z - 17 y z - 6 y], 3 2 4 2 [-15 x z - 14 x y + 3, 10 z - 16 z + 11 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.11 memory used=26.0MB, alloc=32.3MB, time=0.30 memory used=45.0MB, alloc=60.3MB, time=0.48 memory used=87.5MB, alloc=60.3MB, time=0.82 memory used=132.0MB, alloc=60.3MB, time=1.14 memory used=165.8MB, alloc=60.3MB, time=1.35 memory used=211.9MB, alloc=92.3MB, time=1.72 memory used=277.2MB, alloc=92.3MB, time=2.35 memory used=337.6MB, alloc=92.3MB, time=2.79 memory used=397.1MB, alloc=92.3MB, time=3.12 memory used=450.4MB, alloc=92.3MB, time=3.50 memory used=485.6MB, alloc=92.3MB, time=3.65 memory used=525.7MB, alloc=92.3MB, time=3.82 memory used=601.7MB, alloc=116.3MB, time=4.34 memory used=674.6MB, alloc=116.3MB, time=4.84 memory used=748.4MB, alloc=372.3MB, time=5.37 memory used=823.9MB, alloc=372.3MB, time=5.74 memory used=870.6MB, alloc=372.3MB, time=5.91 memory used=920.6MB, alloc=372.3MB, time=6.08 memory used=977.5MB, alloc=372.3MB, time=6.63 memory used=1016.4MB, alloc=372.3MB, time=6.73 memory used=1057.4MB, alloc=372.3MB, time=6.83 memory used=1089.1MB, alloc=372.3MB, time=6.92 memory used=1127.1MB, alloc=372.3MB, time=7.01 memory used=1202.5MB, alloc=372.3MB, time=7.64 memory used=1262.3MB, alloc=372.3MB, time=7.82 memory used=1299.6MB, alloc=372.3MB, time=7.92 memory used=1341.1MB, alloc=372.3MB, time=8.02 memory used=1372.3MB, alloc=372.3MB, time=8.11 memory used=1410.2MB, alloc=372.3MB, time=8.20 memory used=1472.1MB, alloc=372.3MB, time=8.46 memory used=1550.0MB, alloc=372.3MB, time=8.87 memory used=1629.4MB, alloc=372.3MB, time=9.27 memory used=1706.4MB, alloc=396.3MB, time=9.72 memory used=1812.5MB, alloc=396.3MB, time=10.61 memory used=1914.3MB, alloc=420.3MB, time=11.78 memory used=1988.4MB, alloc=420.3MB, time=29.21 memory used=2062.9MB, alloc=420.3MB, time=30.35 memory used=2129.8MB, alloc=420.3MB, time=30.50 memory used=2229.9MB, alloc=420.3MB, time=31.05 memory used=2318.6MB, alloc=420.3MB, time=31.29 memory used=2373.1MB, alloc=420.3MB, time=31.47 memory used=2427.2MB, alloc=420.3MB, time=31.65 memory used=2492.2MB, alloc=420.3MB, time=31.83 memory used=2587.3MB, alloc=420.3MB, time=32.73 memory used=2656.2MB, alloc=420.3MB, time=32.95 memory used=2708.9MB, alloc=420.3MB, time=33.15 memory used=2763.5MB, alloc=420.3MB, time=33.33 memory used=2823.2MB, alloc=420.3MB, time=33.52 memory used=2888.0MB, alloc=420.3MB, time=33.73 memory used=2959.1MB, alloc=420.3MB, time=33.93 memory used=3037.0MB, alloc=420.3MB, time=34.13 memory used=3095.4MB, alloc=420.3MB, time=34.32 memory used=3140.7MB, alloc=420.3MB, time=34.51 memory used=3189.6MB, alloc=420.3MB, time=34.67 memory used=3242.8MB, alloc=420.3MB, time=34.84 memory used=3307.2MB, alloc=420.3MB, time=35.07 memory used=3605.6MB, alloc=420.3MB, time=187.75 memory used=3847.7MB, alloc=420.3MB, time=215.08 memory used=4039.6MB, alloc=420.3MB, time=215.34 memory used=4341.5MB, alloc=420.3MB, time=221.22 memory used=4436.5MB, alloc=420.3MB, time=221.63 memory used=4545.9MB, alloc=420.3MB, time=228.12 memory used=4627.8MB, alloc=420.3MB, time=228.52 memory used=4756.9MB, alloc=420.3MB, time=229.60 memory used=4882.7MB, alloc=444.3MB, time=230.76 memory used=5023.1MB, alloc=444.3MB, time=231.96 memory used=5160.4MB, alloc=444.3MB, time=232.87 memory used=5260.5MB, alloc=444.3MB, time=233.56 memory used=5377.1MB, alloc=444.3MB, time=238.67 memory used=5442.0MB, alloc=444.3MB, time=238.87 memory used=5531.0MB, alloc=468.3MB, time=239.49 memory used=5649.8MB, alloc=468.3MB, time=239.82 memory used=5720.3MB, alloc=468.3MB, time=240.09 memory used=5801.6MB, alloc=468.3MB, time=240.34 memory used=5899.2MB, alloc=468.3MB, time=240.63 memory used=5988.7MB, alloc=468.3MB, time=240.88 memory used=6051.5MB, alloc=468.3MB, time=241.14 memory used=6120.9MB, alloc=468.3MB, time=241.38 memory used=6200.0MB, alloc=468.3MB, time=241.62 memory used=6325.0MB, alloc=468.3MB, time=242.70 memory used=6398.1MB, alloc=468.3MB, time=242.95 memory used=6478.0MB, alloc=468.3MB, time=243.25 memory used=6573.3MB, alloc=468.3MB, time=243.59 memory used=6668.1MB, alloc=468.3MB, time=243.88 memory used=6732.1MB, alloc=468.3MB, time=244.09 memory used=6794.0MB, alloc=468.3MB, time=244.32 memory used=6859.8MB, alloc=468.3MB, time=244.53 memory used=6930.2MB, alloc=468.3MB, time=244.75 memory used=7004.8MB, alloc=468.3MB, time=244.97 memory used=7086.3MB, alloc=468.3MB, time=245.20 memory used=7174.1MB, alloc=468.3MB, time=245.44 memory used=7267.1MB, alloc=468.3MB, time=245.67 memory used=7367.0MB, alloc=468.3MB, time=245.89 memory used=7462.7MB, alloc=468.3MB, time=246.13 memory used=7522.4MB, alloc=468.3MB, time=246.31 memory used=7580.8MB, alloc=468.3MB, time=246.49 memory used=7643.9MB, alloc=468.3MB, time=246.68 memory used=7725.7MB, alloc=468.3MB, time=246.95 memory used=8052.9MB, alloc=468.3MB, time=395.34 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428543229 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 3 3 F := [9 x y - 20 x y + 14 z , -5 x z - 20 y - 10 z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 3 G := [-2 x y z + 3 x y z, x y z + 15 y z - 9 y z ] > Problem := [F,G]; 2 2 2 2 2 3 3 Problem := [[9 x y - 20 x y + 14 z , -5 x z - 20 y - 10 z ], 2 2 2 2 3 [-2 x y z + 3 x y z, x y z + 15 y z - 9 y z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.15 memory used=26.5MB, alloc=32.3MB, time=0.44 memory used=46.2MB, alloc=32.3MB, time=0.70 memory used=64.6MB, alloc=56.3MB, time=0.99 memory used=104.8MB, alloc=60.3MB, time=1.56 memory used=143.4MB, alloc=84.3MB, time=2.10 memory used=212.6MB, alloc=92.3MB, time=2.82 memory used=279.7MB, alloc=92.3MB, time=3.50 memory used=345.6MB, alloc=92.3MB, time=4.34 memory used=406.9MB, alloc=116.3MB, time=5.17 memory used=483.4MB, alloc=116.3MB, time=6.03 memory used=564.4MB, alloc=116.3MB, time=6.67 memory used=634.1MB, alloc=140.3MB, time=7.65 memory used=753.7MB, alloc=140.3MB, time=8.86 memory used=868.6MB, alloc=140.3MB, time=9.68 memory used=981.2MB, alloc=396.3MB, time=10.88 memory used=1103.1MB, alloc=396.3MB, time=12.15 memory used=1186.5MB, alloc=420.3MB, time=12.52 memory used=1320.1MB, alloc=420.3MB, time=13.66 memory used=1442.3MB, alloc=444.3MB, time=15.62 memory used=1593.7MB, alloc=468.3MB, time=17.70 memory used=1762.2MB, alloc=492.3MB, time=20.07 memory used=1953.8MB, alloc=516.3MB, time=22.72 memory used=2169.3MB, alloc=540.3MB, time=25.28 memory used=2407.4MB, alloc=540.3MB, time=27.31 memory used=2628.6MB, alloc=564.3MB, time=29.29 memory used=2864.6MB, alloc=588.3MB, time=31.61 memory used=3072.9MB, alloc=612.3MB, time=33.91 memory used=3284.3MB, alloc=636.3MB, time=36.07 memory used=3539.5MB, alloc=660.3MB, time=38.01 memory used=3764.6MB, alloc=684.3MB, time=40.23 memory used=3971.2MB, alloc=708.3MB, time=42.51 memory used=4146.5MB, alloc=732.3MB, time=45.23 memory used=4420.0MB, alloc=756.3MB, time=51.12 memory used=4689.9MB, alloc=780.3MB, time=57.50 memory used=4965.0MB, alloc=804.3MB, time=64.39 memory used=5251.1MB, alloc=828.3MB, time=71.58 memory used=5548.7MB, alloc=852.3MB, time=79.25 memory used=5858.3MB, alloc=876.3MB, time=87.44 memory used=6179.4MB, alloc=900.3MB, time=96.42 memory used=6516.2MB, alloc=924.3MB, time=105.96 memory used=6877.1MB, alloc=948.3MB, time=116.17 memory used=7261.8MB, alloc=972.3MB, time=127.01 memory used=7670.5MB, alloc=996.3MB, time=138.55 memory used=8103.1MB, alloc=1020.3MB, time=150.81 memory used=8559.6MB, alloc=1044.3MB, time=163.61 memory used=9040.2MB, alloc=1068.3MB, time=177.05 memory used=9544.6MB, alloc=1068.3MB, time=191.13 memory used=10048.9MB, alloc=1068.3MB, time=205.18 memory used=10553.4MB, alloc=1068.3MB, time=219.37 memory used=11057.7MB, alloc=1092.3MB, time=233.44 memory used=11585.9MB, alloc=1092.3MB, time=248.15 memory used=12114.1MB, alloc=1092.3MB, time=262.82 memory used=12642.3MB, alloc=1092.3MB, time=277.60 memory used=13170.5MB, alloc=1116.3MB, time=292.32 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428543529 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 3 3 F := [-20 y - 3 x y, -11 x y - 17 x + 3 z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 4 2 2 3 2 G := [-8 x + 7 x y + 4 y , 5 x z + 15 y z + 11 x z ] > Problem := [F,G]; 4 3 3 3 Problem := [[-20 y - 3 x y, -11 x y - 17 x + 3 z ], 4 2 2 4 2 2 3 2 [-8 x + 7 x y + 4 y , 5 x z + 15 y z + 11 x z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.14 memory used=23.9MB, alloc=32.3MB, time=0.36 memory used=43.5MB, alloc=32.3MB, time=0.59 memory used=61.8MB, alloc=56.3MB, time=0.80 memory used=107.4MB, alloc=60.3MB, time=1.36 memory used=147.6MB, alloc=84.3MB, time=1.94 memory used=208.2MB, alloc=84.3MB, time=2.87 memory used=261.9MB, alloc=108.3MB, time=3.60 memory used=329.0MB, alloc=132.3MB, time=4.74 memory used=412.6MB, alloc=156.3MB, time=6.16 N1 := 2215 > GB := Basis(F, plex(op(vars))); 4 3 3 3 GB := [20 y + 3 x y, -11 x y - 17 x + 3 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=472.8MB, alloc=156.3MB, time=6.84 memory used=578.1MB, alloc=420.3MB, time=7.89 memory used=696.9MB, alloc=444.3MB, time=9.24 memory used=816.8MB, alloc=468.3MB, time=11.44 N2 := 2215 > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 4 3 3 3 4 2 2 4 H := [-20 y - 3 x y, -11 x y - 17 x + 3 z , -8 x + 7 x y + 4 y , 2 2 3 2 5 x z + 15 y z + 11 x z ] > J:=[op(GB),op(G)]; 4 3 3 3 4 2 2 4 J := [20 y + 3 x y, -11 x y - 17 x + 3 z , -8 x + 7 x y + 4 y , 2 2 3 2 5 x z + 15 y z + 11 x z ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 10, 16, 4, 4, 4, 3, 1, 1, 1/2, 7/11, 6/11, 4/11, 4, 10, 16, 4, 4, 4, 3, 1, 1, 1/2, 7/11, 6/11, 4/11, 0, 0, 0] > save(F, G, cat("ranSet/34", convert(F, string),".txt")); > quit memory used=856.8MB, alloc=468.3MB, time=12.03 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428543541 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 3 2 F := [12 x y + 5 x y z + 9 y , -4 y z - 2 x y + 19 x y] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 G := [-20 x + 19 x y + 6 x z, 10 y z + 7 x y z + 7 x z] > Problem := [F,G]; 2 3 3 2 Problem := [[12 x y + 5 x y z + 9 y , -4 y z - 2 x y + 19 x y], 3 2 3 [-20 x + 19 x y + 6 x z, 10 y z + 7 x y z + 7 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.13 memory used=26.9MB, alloc=32.3MB, time=0.38 memory used=47.0MB, alloc=56.3MB, time=0.59 memory used=87.0MB, alloc=60.3MB, time=0.93 memory used=129.0MB, alloc=60.3MB, time=1.25 memory used=171.0MB, alloc=60.3MB, time=1.55 memory used=211.0MB, alloc=92.3MB, time=1.94 memory used=275.7MB, alloc=92.3MB, time=2.50 memory used=345.4MB, alloc=116.3MB, time=3.00 memory used=420.7MB, alloc=372.3MB, time=3.64 memory used=504.2MB, alloc=372.3MB, time=4.23 memory used=563.2MB, alloc=372.3MB, time=4.61 memory used=643.5MB, alloc=372.3MB, time=5.09 memory used=743.1MB, alloc=396.3MB, time=5.71 memory used=847.4MB, alloc=396.3MB, time=6.37 memory used=949.1MB, alloc=396.3MB, time=6.92 memory used=1018.2MB, alloc=396.3MB, time=7.67 memory used=1078.1MB, alloc=396.3MB, time=7.85 memory used=1142.4MB, alloc=396.3MB, time=8.61 memory used=1204.7MB, alloc=396.3MB, time=8.85 memory used=1273.4MB, alloc=396.3MB, time=9.60 memory used=1333.1MB, alloc=396.3MB, time=9.80 memory used=1398.9MB, alloc=396.3MB, time=10.56 memory used=1457.6MB, alloc=396.3MB, time=10.75 memory used=1517.8MB, alloc=396.3MB, time=11.30 memory used=1587.8MB, alloc=396.3MB, time=11.92 memory used=1662.2MB, alloc=396.3MB, time=12.26 memory used=1781.3MB, alloc=420.3MB, time=13.00 memory used=1912.1MB, alloc=420.3MB, time=14.12 memory used=2046.9MB, alloc=444.3MB, time=15.12 memory used=2163.0MB, alloc=468.3MB, time=16.33 memory used=2294.9MB, alloc=468.3MB, time=17.30 memory used=2425.2MB, alloc=468.3MB, time=18.23 memory used=2524.3MB, alloc=492.3MB, time=19.22 memory used=2643.4MB, alloc=492.3MB, time=20.23 memory used=2757.8MB, alloc=492.3MB, time=21.21 memory used=2866.1MB, alloc=492.3MB, time=21.80 memory used=2950.0MB, alloc=492.3MB, time=22.09 memory used=3034.4MB, alloc=492.3MB, time=22.44 memory used=3115.8MB, alloc=492.3MB, time=22.72 memory used=3217.9MB, alloc=492.3MB, time=24.39 memory used=3297.7MB, alloc=492.3MB, time=24.66 memory used=3484.6MB, alloc=492.3MB, time=25.25 memory used=3589.4MB, alloc=492.3MB, time=25.67 memory used=3736.6MB, alloc=492.3MB, time=26.66 memory used=3881.7MB, alloc=492.3MB, time=27.53 memory used=3996.5MB, alloc=492.3MB, time=28.41 memory used=4089.2MB, alloc=516.3MB, time=28.81 memory used=4191.8MB, alloc=516.3MB, time=29.19 memory used=4308.4MB, alloc=516.3MB, time=30.19 memory used=4448.5MB, alloc=516.3MB, time=30.56 memory used=4553.0MB, alloc=516.3MB, time=30.92 memory used=4672.2MB, alloc=516.3MB, time=31.98 memory used=4763.2MB, alloc=516.3MB, time=32.30 memory used=4941.6MB, alloc=516.3MB, time=33.00 memory used=5042.2MB, alloc=516.3MB, time=33.37 memory used=5141.2MB, alloc=516.3MB, time=33.70 memory used=5258.9MB, alloc=516.3MB, time=35.06 memory used=5398.5MB, alloc=516.3MB, time=35.46 memory used=5508.3MB, alloc=516.3MB, time=36.15 memory used=5591.9MB, alloc=516.3MB, time=36.95 memory used=5669.9MB, alloc=516.3MB, time=37.79 memory used=5756.4MB, alloc=516.3MB, time=38.58 memory used=5902.9MB, alloc=516.3MB, time=39.46 memory used=6043.8MB, alloc=516.3MB, time=40.29 memory used=6132.8MB, alloc=516.3MB, time=41.03 memory used=6223.6MB, alloc=516.3MB, time=42.01 memory used=6294.0MB, alloc=540.3MB, time=42.75 memory used=6359.8MB, alloc=540.3MB, time=43.59 memory used=6473.5MB, alloc=540.3MB, time=44.64 memory used=6559.3MB, alloc=540.3MB, time=45.66 memory used=6619.9MB, alloc=540.3MB, time=46.52 memory used=6705.2MB, alloc=540.3MB, time=47.55 memory used=6777.2MB, alloc=540.3MB, time=48.52 memory used=6864.7MB, alloc=564.3MB, time=49.46 memory used=6955.8MB, alloc=564.3MB, time=50.40 memory used=7039.0MB, alloc=564.3MB, time=51.42 memory used=7123.4MB, alloc=588.3MB, time=52.53 memory used=7356.6MB, alloc=612.3MB, time=55.18 memory used=7600.4MB, alloc=636.3MB, time=58.03 memory used=7852.5MB, alloc=660.3MB, time=61.05 memory used=8107.6MB, alloc=684.3MB, time=64.23 memory used=8370.5MB, alloc=708.3MB, time=67.50 memory used=8637.7MB, alloc=732.3MB, time=70.94 memory used=8919.1MB, alloc=756.3MB, time=74.46 memory used=9205.3MB, alloc=780.3MB, time=78.14 memory used=9519.4MB, alloc=804.3MB, time=81.76 memory used=9801.7MB, alloc=828.3MB, time=87.13 memory used=10044.8MB, alloc=852.3MB, time=93.16 memory used=10294.0MB, alloc=876.3MB, time=99.69 memory used=10552.5MB, alloc=900.3MB, time=106.72 memory used=10823.2MB, alloc=924.3MB, time=114.14 memory used=11107.6MB, alloc=948.3MB, time=121.94 memory used=11406.9MB, alloc=972.3MB, time=130.20 memory used=11721.2MB, alloc=996.3MB, time=138.96 memory used=12051.0MB, alloc=1020.3MB, time=148.38 memory used=12395.7MB, alloc=1044.3MB, time=158.20 memory used=12755.6MB, alloc=1068.3MB, time=168.48 memory used=13131.4MB, alloc=1092.3MB, time=179.20 memory used=13523.6MB, alloc=1116.3MB, time=190.41 memory used=13928.1MB, alloc=1140.3MB, time=202.21 memory used=14353.6MB, alloc=1164.3MB, time=214.81 memory used=14803.0MB, alloc=1188.3MB, time=227.99 memory used=15276.4MB, alloc=1212.3MB, time=241.78 memory used=15773.8MB, alloc=1236.3MB, time=256.24 memory used=16295.0MB, alloc=1260.3MB, time=271.52 memory used=16840.2MB, alloc=1284.3MB, time=287.30 memory used=17409.3MB, alloc=1308.3MB, time=303.78 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428543841 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 3 4 F := [-20 x - 11 y z + 14 y, 15 x y - 10 z - 9 y z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 3 2 G := [6 x - 20 x y + 6 y, -14 y z - 8 x y + y ] > Problem := [F,G]; 4 2 3 4 Problem := [[-20 x - 11 y z + 14 y, 15 x y - 10 z - 9 y z], 4 2 2 3 2 [6 x - 20 x y + 6 y, -14 y z - 8 x y + y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.15 memory used=28.1MB, alloc=36.5MB, time=0.44 memory used=50.3MB, alloc=36.5MB, time=0.63 memory used=72.6MB, alloc=36.5MB, time=0.79 memory used=93.0MB, alloc=37.0MB, time=0.87 memory used=105.5MB, alloc=37.0MB, time=0.91 memory used=115.8MB, alloc=37.0MB, time=0.94 memory used=125.7MB, alloc=37.0MB, time=0.97 memory used=137.9MB, alloc=37.0MB, time=1.00 memory used=150.0MB, alloc=37.0MB, time=1.03 memory used=167.1MB, alloc=37.0MB, time=1.13 memory used=192.8MB, alloc=37.0MB, time=1.37 memory used=213.3MB, alloc=61.0MB, time=1.61 memory used=250.3MB, alloc=61.0MB, time=1.83 memory used=280.2MB, alloc=61.0MB, time=1.93 memory used=311.3MB, alloc=61.0MB, time=2.05 memory used=344.4MB, alloc=62.4MB, time=2.16 memory used=368.7MB, alloc=62.4MB, time=2.21 memory used=397.8MB, alloc=62.4MB, time=2.26 memory used=418.8MB, alloc=62.4MB, time=2.30 memory used=447.4MB, alloc=62.4MB, time=2.40 memory used=475.7MB, alloc=62.4MB, time=2.47 memory used=503.6MB, alloc=62.4MB, time=2.55 memory used=545.0MB, alloc=62.9MB, time=2.93 memory used=582.8MB, alloc=62.9MB, time=3.02 memory used=604.7MB, alloc=62.9MB, time=3.09 memory used=626.6MB, alloc=62.9MB, time=3.16 memory used=650.0MB, alloc=62.9MB, time=3.22 memory used=677.4MB, alloc=62.9MB, time=3.29 memory used=706.6MB, alloc=62.9MB, time=3.36 memory used=737.8MB, alloc=62.9MB, time=3.43 memory used=757.9MB, alloc=62.9MB, time=3.48 memory used=773.2MB, alloc=62.9MB, time=3.53 memory used=790.1MB, alloc=62.9MB, time=3.59 memory used=807.3MB, alloc=62.9MB, time=3.64 memory used=824.8MB, alloc=62.9MB, time=3.69 memory used=842.6MB, alloc=62.9MB, time=3.74 memory used=860.8MB, alloc=62.9MB, time=3.79 memory used=879.7MB, alloc=62.9MB, time=3.84 memory used=901.3MB, alloc=62.9MB, time=3.90 memory used=923.4MB, alloc=62.9MB, time=3.95 memory used=945.9MB, alloc=62.9MB, time=4.00 memory used=968.7MB, alloc=62.9MB, time=4.06 memory used=991.8MB, alloc=62.9MB, time=4.12 memory used=1015.5MB, alloc=62.9MB, time=4.17 memory used=1042.0MB, alloc=62.9MB, time=4.22 memory used=1069.0MB, alloc=62.9MB, time=4.28 memory used=1096.3MB, alloc=62.9MB, time=4.34 memory used=1124.0MB, alloc=62.9MB, time=4.40 memory used=1154.6MB, alloc=62.9MB, time=4.45 memory used=1184.9MB, alloc=62.9MB, time=4.51 memory used=1204.2MB, alloc=62.9MB, time=4.55 memory used=1218.2MB, alloc=86.9MB, time=4.60 memory used=1244.4MB, alloc=86.9MB, time=4.66 memory used=1271.6MB, alloc=86.9MB, time=4.72 memory used=1299.2MB, alloc=86.9MB, time=4.78 memory used=1328.9MB, alloc=86.9MB, time=4.84 memory used=1358.9MB, alloc=86.9MB, time=4.90 memory used=1391.6MB, alloc=86.9MB, time=4.96 memory used=1424.0MB, alloc=86.9MB, time=5.03 memory used=1459.0MB, alloc=86.9MB, time=5.10 memory used=1493.7MB, alloc=86.9MB, time=5.16 memory used=1530.0MB, alloc=86.9MB, time=5.22 memory used=1569.8MB, alloc=86.9MB, time=5.30 memory used=1611.2MB, alloc=86.9MB, time=5.37 memory used=1653.5MB, alloc=86.9MB, time=5.45 memory used=1698.4MB, alloc=86.9MB, time=5.52 memory used=1746.6MB, alloc=86.9MB, time=5.59 memory used=1815.2MB, alloc=98.4MB, time=6.05 memory used=1858.4MB, alloc=98.4MB, time=6.20 memory used=1898.4MB, alloc=98.4MB, time=6.31 memory used=1946.5MB, alloc=98.4MB, time=6.41 memory used=1996.1MB, alloc=98.4MB, time=6.52 memory used=2026.6MB, alloc=98.4MB, time=6.58 memory used=2057.6MB, alloc=98.4MB, time=6.65 memory used=2090.7MB, alloc=98.4MB, time=6.73 memory used=2127.8MB, alloc=98.4MB, time=6.81 memory used=2166.0MB, alloc=98.4MB, time=6.90 memory used=2205.4MB, alloc=98.4MB, time=6.97 memory used=2248.8MB, alloc=98.4MB, time=7.05 memory used=2293.5MB, alloc=98.4MB, time=7.14 memory used=2341.7MB, alloc=98.4MB, time=7.23 memory used=2394.2MB, alloc=98.4MB, time=7.30 memory used=2444.4MB, alloc=98.4MB, time=7.37 memory used=2472.6MB, alloc=98.4MB, time=7.43 memory used=2498.5MB, alloc=98.4MB, time=7.48 memory used=2525.7MB, alloc=98.4MB, time=7.53 memory used=2556.1MB, alloc=98.4MB, time=7.59 memory used=2586.2MB, alloc=98.4MB, time=7.64 memory used=2616.1MB, alloc=98.4MB, time=7.69 memory used=2648.8MB, alloc=98.4MB, time=7.75 memory used=2680.9MB, alloc=98.4MB, time=7.80 memory used=2715.7MB, alloc=98.4MB, time=7.86 memory used=2752.5MB, alloc=98.4MB, time=7.91 memory used=2789.0MB, alloc=98.4MB, time=7.97 memory used=2828.5MB, alloc=98.4MB, time=8.03 memory used=2869.1MB, alloc=98.4MB, time=8.09 memory used=2912.4MB, alloc=98.4MB, time=8.15 memory used=2958.4MB, alloc=98.4MB, time=8.20 memory used=3016.8MB, alloc=98.4MB, time=8.64 memory used=3104.4MB, alloc=98.4MB, time=29.27 memory used=3196.4MB, alloc=98.4MB, time=37.07 memory used=3298.6MB, alloc=98.4MB, time=37.64 memory used=3344.1MB, alloc=98.4MB, time=37.74 memory used=3391.6MB, alloc=98.4MB, time=37.83 memory used=3423.9MB, alloc=98.4MB, time=37.91 memory used=3459.2MB, alloc=98.4MB, time=37.98 memory used=3498.3MB, alloc=98.4MB, time=38.05 memory used=3542.7MB, alloc=98.4MB, time=38.14 memory used=3590.8MB, alloc=98.4MB, time=38.23 memory used=3640.2MB, alloc=98.4MB, time=38.32 memory used=3670.8MB, alloc=98.4MB, time=38.38 memory used=3699.6MB, alloc=98.4MB, time=38.44 memory used=3727.7MB, alloc=98.4MB, time=38.49 memory used=3758.9MB, alloc=98.4MB, time=38.55 memory used=3791.0MB, alloc=98.4MB, time=38.61 memory used=3823.7MB, alloc=98.4MB, time=38.67 memory used=3857.2MB, alloc=98.4MB, time=38.73 memory used=3891.4MB, alloc=98.4MB, time=38.79 memory used=3926.4MB, alloc=98.4MB, time=38.86 memory used=3964.5MB, alloc=98.4MB, time=38.92 memory used=4003.5MB, alloc=98.4MB, time=38.98 memory used=4043.1MB, alloc=98.4MB, time=39.04 memory used=4083.4MB, alloc=98.4MB, time=39.11 memory used=4127.2MB, alloc=98.4MB, time=39.17 memory used=4171.6MB, alloc=98.4MB, time=39.24 memory used=4216.6MB, alloc=98.4MB, time=39.30 memory used=4265.2MB, alloc=98.4MB, time=39.37 memory used=4314.3MB, alloc=98.4MB, time=39.44 memory used=4364.0MB, alloc=98.4MB, time=39.50 memory used=4420.4MB, alloc=98.4MB, time=39.58 memory used=4434.3MB, alloc=107.8MB, time=39.62 memory used=4441.4MB, alloc=107.8MB, time=39.66 memory used=4448.4MB, alloc=107.8MB, time=39.69 memory used=4453.9MB, alloc=107.8MB, time=39.73 memory used=4459.4MB, alloc=107.8MB, time=39.76 memory used=4465.4MB, alloc=107.8MB, time=39.80 memory used=4471.6MB, alloc=107.8MB, time=39.83 memory used=4477.8MB, alloc=107.8MB, time=39.86 memory used=4484.0MB, alloc=107.8MB, time=39.90 memory used=4490.3MB, alloc=107.8MB, time=39.93 memory used=4496.5MB, alloc=107.8MB, time=39.96 memory used=4502.7MB, alloc=107.8MB, time=40.00 memory used=4509.0MB, alloc=107.8MB, time=40.03 memory used=4515.2MB, alloc=107.8MB, time=40.06 memory used=4521.4MB, alloc=107.8MB, time=40.10 memory used=4527.7MB, alloc=107.8MB, time=40.13 memory used=4533.9MB, alloc=107.8MB, time=40.17 memory used=4540.2MB, alloc=107.8MB, time=40.20 memory used=4546.5MB, alloc=107.8MB, time=40.24 memory used=4552.7MB, alloc=107.8MB, time=40.27 memory used=4559.0MB, alloc=107.8MB, time=40.30 memory used=4565.3MB, alloc=107.8MB, time=40.34 memory used=4571.5MB, alloc=107.8MB, time=40.37 memory used=4577.8MB, alloc=107.8MB, time=40.41 memory used=4584.1MB, alloc=107.8MB, time=40.44 memory used=4590.4MB, alloc=107.8MB, time=40.47 memory used=4596.6MB, alloc=107.8MB, time=40.51 memory used=4602.9MB, alloc=107.8MB, time=40.54 memory used=4609.2MB, alloc=107.8MB, time=40.58 memory used=4615.5MB, alloc=107.8MB, time=40.61 memory used=4621.8MB, alloc=107.8MB, time=40.64 memory used=4628.1MB, alloc=107.8MB, time=40.67 memory used=4634.4MB, alloc=107.8MB, time=40.71 memory used=4640.6MB, alloc=107.8MB, time=40.75 memory used=4646.9MB, alloc=107.8MB, time=40.78 memory used=4653.2MB, alloc=107.8MB, time=40.81 memory used=4659.5MB, alloc=107.8MB, time=40.85 memory used=4665.8MB, alloc=107.8MB, time=40.88 memory used=4672.1MB, alloc=107.8MB, time=40.92 memory used=4678.4MB, alloc=107.8MB, time=40.95 memory used=4684.7MB, alloc=107.8MB, time=40.98 memory used=4691.0MB, alloc=107.8MB, time=41.02 memory used=4697.3MB, alloc=107.8MB, time=41.05 memory used=4703.6MB, alloc=107.8MB, time=41.08 memory used=4709.9MB, alloc=107.8MB, time=41.12 memory used=4716.3MB, alloc=107.8MB, time=41.15 memory used=4722.6MB, alloc=107.8MB, time=41.18 memory used=4728.9MB, alloc=107.8MB, time=41.22 memory used=4735.2MB, alloc=107.8MB, time=41.25 memory used=4741.5MB, alloc=107.8MB, time=41.28 memory used=4747.8MB, alloc=107.8MB, time=41.32 memory used=4754.1MB, alloc=107.8MB, time=41.35 memory used=4760.4MB, alloc=107.8MB, time=41.38 memory used=4766.7MB, alloc=107.8MB, time=41.41 memory used=4773.0MB, alloc=107.8MB, time=41.45 memory used=4779.3MB, alloc=107.8MB, time=41.48 memory used=4785.6MB, alloc=107.8MB, time=41.51 memory used=4791.9MB, alloc=107.8MB, time=41.55 memory used=4798.2MB, alloc=107.8MB, time=41.58 memory used=4804.5MB, alloc=107.8MB, time=41.61 memory used=4810.8MB, alloc=107.8MB, time=41.65 memory used=4817.1MB, alloc=107.8MB, time=41.68 memory used=4823.3MB, alloc=107.8MB, time=41.71 memory used=4829.6MB, alloc=107.8MB, time=41.74 memory used=4835.9MB, alloc=107.8MB, time=41.78 memory used=4842.2MB, alloc=107.8MB, time=41.81 memory used=4848.5MB, alloc=107.8MB, time=41.84 memory used=4854.8MB, alloc=107.8MB, time=41.88 memory used=4861.1MB, alloc=107.8MB, time=41.91 memory used=4867.3MB, alloc=107.8MB, time=41.94 memory used=4873.6MB, alloc=107.8MB, time=41.98 memory used=4879.9MB, alloc=107.8MB, time=42.01 memory used=4886.1MB, alloc=107.8MB, time=42.04 memory used=4892.4MB, alloc=107.8MB, time=42.07 memory used=4898.7MB, alloc=107.8MB, time=42.11 memory used=4904.9MB, alloc=107.8MB, time=42.14 memory used=4911.2MB, alloc=107.8MB, time=42.17 memory used=4917.4MB, alloc=107.8MB, time=42.20 memory used=4923.7MB, alloc=107.8MB, time=42.24 memory used=4929.9MB, alloc=107.8MB, time=42.27 memory used=4936.2MB, alloc=107.8MB, time=42.30 memory used=4942.4MB, alloc=107.8MB, time=42.34 memory 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time=43.79 memory used=5291.6MB, alloc=107.8MB, time=43.83 memory used=5300.3MB, alloc=107.8MB, time=43.86 memory used=5309.1MB, alloc=107.8MB, time=43.90 memory used=5317.8MB, alloc=107.8MB, time=43.93 memory used=5326.5MB, alloc=107.8MB, time=43.97 memory used=5335.1MB, alloc=107.8MB, time=44.00 memory used=5343.8MB, alloc=107.8MB, time=44.04 memory used=5352.4MB, alloc=107.8MB, time=44.07 memory used=5361.0MB, alloc=107.8MB, time=44.11 memory used=5369.7MB, alloc=107.8MB, time=44.14 memory used=5380.9MB, alloc=107.8MB, time=44.18 memory used=5389.7MB, alloc=107.8MB, time=44.22 memory used=5400.7MB, alloc=107.8MB, time=44.25 memory used=5412.0MB, alloc=107.8MB, time=44.29 memory used=5423.2MB, alloc=107.8MB, time=44.33 memory used=5434.3MB, alloc=107.8MB, time=44.37 memory used=5445.4MB, alloc=107.8MB, time=44.40 memory used=5456.5MB, alloc=107.8MB, time=44.44 memory used=5467.5MB, alloc=107.8MB, time=44.48 memory used=5478.4MB, alloc=107.8MB, time=44.51 memory used=5489.3MB, alloc=107.8MB, time=44.55 memory used=5500.1MB, alloc=107.8MB, time=44.59 memory used=5510.9MB, alloc=107.8MB, time=44.62 memory used=5521.7MB, alloc=107.8MB, time=44.66 memory used=5532.3MB, alloc=107.8MB, time=44.70 memory used=5542.9MB, alloc=107.8MB, time=44.73 memory used=5553.5MB, alloc=107.8MB, time=44.77 memory used=5564.0MB, alloc=107.8MB, time=44.81 memory used=5574.4MB, alloc=107.8MB, time=44.85 memory used=5584.8MB, alloc=107.8MB, time=44.88 memory used=5595.3MB, alloc=107.8MB, time=44.92 memory used=5607.9MB, alloc=107.8MB, time=44.96 memory used=5620.5MB, alloc=107.8MB, time=44.99 memory used=5633.1MB, alloc=107.8MB, time=45.03 memory used=5645.6MB, alloc=107.8MB, time=45.07 memory used=5658.0MB, alloc=107.8MB, time=45.11 memory used=5670.3MB, alloc=107.8MB, time=45.14 memory used=5682.4MB, alloc=107.8MB, time=45.18 memory used=5694.5MB, alloc=107.8MB, time=45.22 memory used=5706.4MB, alloc=107.8MB, time=45.26 memory used=5718.2MB, alloc=107.8MB, time=45.29 memory 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memory used=6017.8MB, alloc=107.8MB, time=46.12 memory used=6027.7MB, alloc=107.8MB, time=46.16 memory used=6038.5MB, alloc=107.8MB, time=46.20 memory used=6049.1MB, alloc=107.8MB, time=46.23 memory used=6060.5MB, alloc=107.8MB, time=46.27 memory used=6071.5MB, alloc=107.8MB, time=46.31 memory used=6082.8MB, alloc=107.8MB, time=46.34 memory used=6094.4MB, alloc=107.8MB, time=46.38 memory used=6106.5MB, alloc=107.8MB, time=46.42 memory used=6118.9MB, alloc=107.8MB, time=46.45 memory used=6162.9MB, alloc=107.8MB, time=46.90 memory used=6224.0MB, alloc=107.8MB, time=47.03 memory used=6270.2MB, alloc=107.8MB, time=47.13 memory used=6299.9MB, alloc=107.8MB, time=47.23 memory used=6333.4MB, alloc=107.8MB, time=47.33 memory used=6370.2MB, alloc=107.8MB, time=47.42 memory used=6409.4MB, alloc=107.8MB, time=47.52 memory used=6451.2MB, alloc=107.8MB, time=47.61 memory used=6499.9MB, alloc=107.8MB, time=47.70 memory used=6551.1MB, alloc=107.8MB, time=47.81 memory used=6586.2MB, alloc=107.8MB, time=47.89 memory used=6611.5MB, alloc=107.8MB, time=47.96 memory used=6638.2MB, alloc=107.8MB, time=48.04 memory used=6666.0MB, alloc=107.8MB, time=48.11 memory used=6694.3MB, alloc=107.8MB, time=48.18 memory used=6723.1MB, alloc=107.8MB, time=48.26 memory used=6752.3MB, alloc=107.8MB, time=48.32 memory used=6781.9MB, alloc=107.8MB, time=48.40 memory used=6811.9MB, alloc=107.8MB, time=48.48 memory used=6842.3MB, alloc=107.8MB, time=48.56 memory used=6873.0MB, alloc=107.8MB, time=48.63 memory used=6904.1MB, alloc=107.8MB, time=48.69 memory used=6935.5MB, alloc=107.8MB, time=48.78 memory used=6967.9MB, alloc=107.8MB, time=48.85 memory used=7005.8MB, alloc=107.8MB, time=48.92 memory used=7044.5MB, alloc=107.8MB, time=49.00 memory used=7083.6MB, alloc=107.8MB, time=49.07 memory used=7122.9MB, alloc=107.8MB, time=49.14 memory used=7162.6MB, alloc=107.8MB, time=49.23 memory used=7202.4MB, alloc=107.8MB, time=49.30 memory used=7242.6MB, alloc=107.8MB, time=49.39 memory used=7289.5MB, 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memory used=9305.5MB, alloc=131.8MB, time=58.18 memory used=9346.4MB, alloc=131.8MB, time=58.28 memory used=9382.1MB, alloc=155.8MB, time=58.37 memory used=9426.2MB, alloc=155.8MB, time=58.50 memory used=9475.0MB, alloc=155.8MB, time=58.61 memory used=9516.5MB, alloc=155.8MB, time=58.72 memory used=9560.1MB, alloc=155.8MB, time=58.82 memory used=9605.0MB, alloc=155.8MB, time=58.92 memory used=9650.7MB, alloc=155.8MB, time=59.03 memory used=9697.3MB, alloc=155.8MB, time=59.13 memory used=9744.8MB, alloc=155.8MB, time=59.22 memory used=9793.2MB, alloc=155.8MB, time=59.34 memory used=9842.4MB, alloc=155.8MB, time=59.44 memory used=9892.5MB, alloc=155.8MB, time=59.53 memory used=9943.4MB, alloc=155.8MB, time=59.63 memory used=9995.2MB, alloc=155.8MB, time=59.73 memory used=10047.8MB, alloc=155.8MB, time=59.82 memory used=10101.3MB, alloc=155.8MB, time=59.94 memory used=10155.6MB, alloc=155.8MB, time=60.06 memory used=10210.7MB, alloc=155.8MB, time=60.16 memory used=10266.6MB, alloc=155.8MB, time=60.26 memory used=10323.4MB, alloc=155.8MB, time=60.38 memory used=10380.9MB, alloc=155.8MB, time=60.49 memory used=10439.3MB, alloc=155.8MB, time=60.61 memory used=10498.4MB, alloc=155.8MB, time=60.72 memory used=10558.4MB, alloc=155.8MB, time=60.83 memory used=10619.1MB, alloc=155.8MB, time=60.94 memory used=10680.6MB, alloc=155.8MB, time=61.04 memory used=10742.9MB, alloc=155.8MB, time=61.15 memory used=10806.0MB, alloc=155.8MB, time=61.27 memory used=10869.8MB, alloc=155.8MB, time=61.39 memory used=10934.4MB, alloc=155.8MB, time=61.50 memory used=10999.9MB, alloc=155.8MB, time=61.61 memory used=11066.8MB, alloc=155.8MB, time=61.72 memory used=11149.7MB, alloc=155.8MB, time=61.83 memory used=11218.0MB, alloc=155.8MB, time=61.96 memory used=11271.3MB, alloc=155.8MB, time=62.04 memory used=11317.0MB, alloc=179.8MB, time=62.14 memory used=11362.7MB, alloc=179.8MB, time=62.22 memory used=11411.7MB, alloc=179.8MB, time=62.31 memory used=11461.4MB, alloc=179.8MB, time=62.40 memory used=11511.7MB, alloc=203.8MB, time=62.50 memory used=11559.4MB, alloc=203.8MB, time=62.59 memory used=11611.2MB, alloc=203.8MB, time=62.68 memory used=11665.0MB, alloc=203.8MB, time=62.78 memory used=11719.7MB, alloc=203.8MB, time=62.87 memory used=11774.8MB, alloc=203.8MB, time=62.97 memory used=11830.3MB, alloc=203.8MB, time=63.06 memory used=11886.1MB, alloc=203.8MB, time=63.15 memory used=11942.3MB, alloc=203.8MB, time=63.25 memory used=11999.0MB, alloc=203.8MB, time=63.34 memory used=12056.0MB, alloc=203.8MB, time=63.44 memory used=12113.3MB, alloc=203.8MB, time=63.54 memory used=12171.1MB, alloc=203.8MB, time=63.63 memory used=12229.2MB, alloc=203.8MB, time=63.73 memory used=12287.7MB, alloc=203.8MB, time=63.82 memory used=12346.6MB, alloc=203.8MB, time=63.92 memory used=12405.8MB, alloc=203.8MB, time=64.01 memory used=12465.4MB, alloc=203.8MB, time=64.11 memory used=12525.4MB, alloc=203.8MB, time=64.20 memory used=12585.7MB, alloc=203.8MB, time=64.30 memory 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alloc=203.8MB, time=66.33 memory used=13999.8MB, alloc=203.8MB, time=66.43 memory used=14067.8MB, alloc=203.8MB, time=66.53 memory used=14136.2MB, alloc=203.8MB, time=66.63 memory used=14204.9MB, alloc=203.8MB, time=66.74 memory used=14274.7MB, alloc=203.8MB, time=66.84 memory used=14366.6MB, alloc=203.8MB, time=66.96 memory used=14459.6MB, alloc=203.8MB, time=67.08 memory used=14553.0MB, alloc=203.8MB, time=67.20 memory used=14647.0MB, alloc=203.8MB, time=67.32 memory used=14741.5MB, alloc=203.8MB, time=67.44 memory used=14836.6MB, alloc=203.8MB, time=67.56 memory used=14932.1MB, alloc=203.8MB, time=67.67 memory used=15028.1MB, alloc=203.8MB, time=67.79 memory used=15124.6MB, alloc=203.8MB, time=67.91 memory used=15221.6MB, alloc=203.8MB, time=68.03 memory used=15319.1MB, alloc=203.8MB, time=68.15 memory used=15417.1MB, alloc=203.8MB, time=68.27 memory used=15515.6MB, alloc=203.8MB, time=68.39 memory used=15614.5MB, alloc=203.8MB, time=68.51 memory used=15713.9MB, alloc=203.8MB, time=68.63 memory used=15813.7MB, alloc=203.8MB, time=68.75 memory used=15914.0MB, alloc=203.8MB, time=68.87 memory used=16014.8MB, alloc=203.8MB, time=68.99 memory used=16115.9MB, alloc=203.8MB, time=69.11 memory used=16217.6MB, alloc=203.8MB, time=69.23 memory used=16319.6MB, alloc=203.8MB, time=69.35 memory used=16422.1MB, alloc=203.8MB, time=69.47 memory used=16525.0MB, alloc=203.8MB, time=69.59 memory used=16628.4MB, alloc=203.8MB, time=69.71 memory used=16732.1MB, alloc=203.8MB, time=69.83 memory used=16836.3MB, alloc=203.8MB, time=69.95 memory used=16940.8MB, alloc=203.8MB, time=70.07 memory used=17045.8MB, alloc=203.8MB, time=70.19 memory used=17151.1MB, alloc=203.8MB, time=70.31 memory used=17256.8MB, alloc=203.8MB, time=70.43 memory used=17362.7MB, alloc=203.8MB, time=70.55 memory used=17469.2MB, alloc=203.8MB, time=70.67 memory used=17576.1MB, alloc=203.8MB, time=70.78 memory used=17671.9MB, alloc=203.8MB, time=70.90 memory used=17695.6MB, alloc=203.8MB, time=70.96 memory 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time=77.49 memory used=22671.6MB, alloc=459.8MB, time=77.67 memory used=22819.5MB, alloc=459.8MB, time=77.85 memory used=22967.6MB, alloc=459.8MB, time=78.03 memory used=23115.8MB, alloc=459.8MB, time=78.21 memory used=23264.3MB, alloc=459.8MB, time=78.39 memory used=23412.9MB, alloc=459.8MB, time=78.57 memory used=23561.7MB, alloc=459.8MB, time=78.75 memory used=23710.6MB, alloc=459.8MB, time=78.92 memory used=23859.7MB, alloc=459.8MB, time=79.10 memory used=24008.8MB, alloc=459.8MB, time=79.28 memory used=24158.1MB, alloc=459.8MB, time=79.45 memory used=24307.5MB, alloc=459.8MB, time=79.63 memory used=24457.0MB, alloc=459.8MB, time=79.81 memory used=24606.6MB, alloc=459.8MB, time=80.01 memory used=24756.3MB, alloc=459.8MB, time=80.18 memory used=24906.1MB, alloc=459.8MB, time=80.36 memory used=25055.8MB, alloc=459.8MB, time=80.53 memory used=25205.7MB, alloc=459.8MB, time=80.71 memory used=25355.5MB, alloc=459.8MB, time=80.88 memory used=25505.4MB, alloc=459.8MB, time=81.06 memory used=25655.4MB, alloc=459.8MB, time=81.23 memory used=25805.3MB, alloc=459.8MB, time=81.40 memory used=25955.2MB, alloc=459.8MB, time=81.58 memory used=26105.1MB, alloc=459.8MB, time=81.77 memory used=26256.3MB, alloc=459.8MB, time=81.94 memory used=26434.9MB, alloc=459.8MB, time=82.14 memory used=26614.7MB, alloc=459.8MB, time=82.34 memory used=26794.4MB, alloc=459.8MB, time=82.53 memory used=26974.0MB, alloc=459.8MB, time=82.73 memory used=27153.4MB, alloc=459.8MB, time=82.92 memory used=27332.8MB, alloc=459.8MB, time=83.12 memory used=27512.0MB, alloc=459.8MB, time=83.31 memory used=27691.0MB, alloc=459.8MB, time=83.51 memory used=27869.8MB, alloc=459.8MB, time=83.72 memory used=28048.4MB, alloc=459.8MB, time=83.91 memory used=28226.7MB, alloc=459.8MB, time=84.10 memory used=28404.9MB, alloc=459.8MB, time=84.29 memory used=28582.8MB, alloc=459.8MB, time=84.49 memory used=28760.4MB, alloc=459.8MB, time=84.68 memory used=28937.7MB, alloc=459.8MB, time=84.87 memory used=29114.7MB, alloc=459.8MB, time=85.06 memory used=29291.4MB, alloc=459.8MB, time=85.26 memory used=29469.5MB, alloc=459.8MB, time=85.45 memory used=29673.1MB, alloc=459.8MB, time=85.66 memory used=29877.9MB, alloc=459.8MB, time=85.87 memory used=30082.1MB, alloc=459.8MB, time=86.08 memory used=30285.7MB, alloc=459.8MB, time=86.29 memory used=30488.8MB, alloc=459.8MB, time=86.49 memory used=30691.1MB, alloc=459.8MB, time=86.70 memory used=30892.9MB, alloc=459.8MB, time=86.91 memory used=31094.0MB, alloc=459.8MB, time=87.11 memory used=31294.3MB, alloc=459.8MB, time=87.31 memory used=31493.9MB, alloc=459.8MB, time=87.52 memory used=31692.7MB, alloc=459.8MB, time=87.73 memory used=31919.0MB, alloc=459.8MB, time=87.95 memory used=32144.2MB, alloc=459.8MB, time=88.17 memory used=32368.3MB, alloc=459.8MB, time=88.39 memory used=32591.2MB, alloc=459.8MB, time=88.61 memory used=32812.9MB, alloc=459.8MB, time=88.82 memory used=33033.3MB, alloc=459.8MB, time=89.03 memory used=33252.5MB, alloc=459.8MB, time=89.24 memory used=33470.4MB, alloc=459.8MB, time=89.46 memory used=33713.8MB, alloc=459.8MB, time=89.70 memory used=33955.5MB, alloc=459.8MB, time=89.92 memory used=34192.5MB, alloc=459.8MB, time=90.14 memory used=34415.6MB, alloc=459.8MB, time=90.36 memory used=34592.0MB, alloc=459.8MB, time=90.54 memory used=34741.3MB, alloc=459.8MB, time=90.71 memory used=34886.8MB, alloc=459.8MB, time=90.90 memory used=35040.5MB, alloc=459.8MB, time=91.08 memory used=35193.3MB, alloc=459.8MB, time=91.27 memory used=35345.2MB, alloc=459.8MB, time=91.45 memory used=35496.1MB, alloc=459.8MB, time=91.63 memory used=35646.0MB, alloc=459.8MB, time=91.81 memory used=35794.9MB, alloc=459.8MB, time=91.99 memory used=35944.1MB, alloc=459.8MB, time=92.17 memory used=36113.9MB, alloc=459.8MB, time=92.38 memory used=36283.6MB, alloc=459.8MB, time=92.60 memory used=36451.8MB, alloc=459.8MB, time=92.79 memory used=36618.5MB, alloc=459.8MB, time=92.97 memory used=36783.6MB, alloc=459.8MB, time=93.15 memory used=36947.1MB, alloc=459.8MB, time=93.32 memory used=37109.0MB, alloc=459.8MB, time=93.50 memory used=37270.8MB, alloc=459.8MB, time=93.68 memory used=37450.6MB, alloc=459.8MB, time=93.87 memory used=37629.6MB, alloc=459.8MB, time=94.07 memory used=37806.3MB, alloc=459.8MB, time=94.26 memory used=37980.7MB, alloc=459.8MB, time=94.45 memory used=38152.8MB, alloc=459.8MB, time=94.64 memory used=38324.7MB, alloc=459.8MB, time=94.82 memory used=38510.6MB, alloc=459.8MB, time=95.02 memory used=38695.5MB, alloc=459.8MB, time=95.20 memory used=38877.3MB, alloc=459.8MB, time=95.40 memory used=39058.1MB, alloc=459.8MB, time=95.58 memory used=39250.3MB, alloc=459.8MB, time=95.78 memory used=39440.8MB, alloc=459.8MB, time=95.97 memory used=39629.3MB, alloc=459.8MB, time=96.17 memory used=39826.7MB, alloc=459.8MB, time=96.40 memory used=40021.3MB, alloc=459.8MB, time=96.64 memory used=40227.3MB, alloc=459.8MB, time=96.84 memory used=40428.3MB, alloc=459.8MB, time=97.04 memory used=40635.2MB, alloc=459.8MB, time=97.25 memory used=40850.8MB, alloc=459.8MB, time=97.46 memory used=41071.0MB, alloc=459.8MB, time=97.67 memory used=41293.5MB, alloc=459.8MB, time=97.90 memory used=41515.7MB, alloc=459.8MB, time=98.14 memory used=41745.8MB, alloc=459.8MB, time=98.35 memory used=41977.7MB, alloc=459.8MB, time=98.57 memory used=42221.7MB, alloc=459.8MB, time=98.78 memory used=42474.9MB, alloc=459.8MB, time=99.00 memory used=42823.6MB, alloc=459.8MB, time=309.42 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428544141 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 2 F := [x y - 2 y z - 16 z , 17 x y + 12 x y z - 8 x z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 G := [-15 y z - 18 x y - 9 x, 13 x z + 9 x y - 2 z] > Problem := [F,G]; 2 2 2 3 2 2 Problem := [[x y - 2 y z - 16 z , 17 x y + 12 x y z - 8 x z ], 3 3 2 [-15 y z - 18 x y - 9 x, 13 x z + 9 x y - 2 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=25.9MB, alloc=32.3MB, time=0.48 memory used=45.1MB, alloc=56.3MB, time=0.76 memory used=85.9MB, alloc=60.3MB, time=1.35 memory used=126.6MB, alloc=60.3MB, time=1.91 memory used=166.4MB, alloc=84.3MB, time=2.46 memory used=231.9MB, alloc=92.3MB, time=3.32 memory used=297.3MB, alloc=92.3MB, time=3.97 memory used=362.9MB, alloc=92.3MB, time=4.68 memory used=424.0MB, alloc=92.3MB, time=5.33 memory used=484.4MB, alloc=116.3MB, time=5.95 memory used=540.5MB, alloc=372.3MB, time=6.73 memory used=626.7MB, alloc=372.3MB, time=7.83 memory used=713.6MB, alloc=396.3MB, time=8.93 memory used=824.6MB, alloc=396.3MB, time=10.09 memory used=938.4MB, alloc=396.3MB, time=11.38 memory used=1047.2MB, alloc=396.3MB, time=12.69 memory used=1154.3MB, alloc=420.3MB, time=13.82 memory used=1259.1MB, alloc=420.3MB, time=15.99 memory used=1317.6MB, alloc=420.3MB, time=16.20 memory used=1421.8MB, alloc=420.3MB, time=16.81 memory used=1557.5MB, alloc=420.3MB, time=18.05 memory used=1650.8MB, alloc=420.3MB, time=20.03 memory used=1705.0MB, alloc=420.3MB, time=20.27 memory used=1816.1MB, alloc=420.3MB, time=21.77 memory used=1922.6MB, alloc=444.3MB, time=23.29 memory used=2056.0MB, alloc=444.3MB, time=24.43 memory used=2173.5MB, alloc=444.3MB, time=25.48 memory used=2280.2MB, alloc=444.3MB, time=26.83 memory used=2388.4MB, alloc=444.3MB, time=28.72 memory used=2490.4MB, alloc=444.3MB, time=30.07 memory used=2609.5MB, alloc=468.3MB, time=31.29 memory used=2737.1MB, alloc=468.3MB, time=32.39 memory used=2844.7MB, alloc=468.3MB, time=33.45 memory used=2968.6MB, alloc=468.3MB, time=34.40 memory used=3037.0MB, alloc=468.3MB, time=34.75 memory used=3112.8MB, alloc=468.3MB, time=35.09 memory used=3201.8MB, alloc=468.3MB, time=35.43 memory used=3322.0MB, alloc=468.3MB, time=40.19 memory used=3394.8MB, alloc=468.3MB, time=40.51 memory used=3467.0MB, alloc=468.3MB, time=40.79 memory used=3696.7MB, alloc=468.3MB, time=41.85 memory used=3773.6MB, alloc=468.3MB, time=42.94 memory used=3848.8MB, alloc=468.3MB, time=43.95 memory used=3943.7MB, alloc=468.3MB, time=45.08 memory used=4029.7MB, alloc=468.3MB, time=45.91 memory used=4110.3MB, alloc=468.3MB, time=46.59 memory used=4196.6MB, alloc=468.3MB, time=47.42 memory used=4277.4MB, alloc=468.3MB, time=48.10 memory used=4363.6MB, alloc=468.3MB, time=48.89 memory used=4451.9MB, alloc=468.3MB, time=49.66 memory used=4534.1MB, alloc=468.3MB, time=50.08 memory used=4618.3MB, alloc=468.3MB, time=50.59 memory used=4707.6MB, alloc=492.3MB, time=51.39 memory used=4806.7MB, alloc=492.3MB, time=51.81 memory used=4881.1MB, alloc=492.3MB, time=52.19 memory used=4966.9MB, alloc=492.3MB, time=52.57 memory used=5068.3MB, alloc=492.3MB, time=52.97 memory used=5168.2MB, alloc=492.3MB, time=53.34 memory used=5233.9MB, alloc=492.3MB, time=53.66 memory used=5301.6MB, alloc=492.3MB, time=53.98 memory used=5374.3MB, alloc=492.3MB, time=54.30 memory used=5452.4MB, alloc=492.3MB, time=54.63 memory used=5535.7MB, alloc=492.3MB, time=54.95 memory used=5623.9MB, alloc=492.3MB, time=55.29 memory used=5717.4MB, alloc=492.3MB, time=55.64 memory used=5817.3MB, alloc=492.3MB, time=55.98 memory used=5924.9MB, alloc=492.3MB, time=56.32 memory used=6093.3MB, alloc=492.3MB, time=56.76 memory used=6233.2MB, alloc=492.3MB, time=57.17 memory used=6380.2MB, alloc=492.3MB, time=57.59 memory used=6527.7MB, alloc=492.3MB, time=58.69 memory used=6614.8MB, alloc=492.3MB, time=59.07 memory used=6694.2MB, alloc=492.3MB, time=59.44 memory used=6788.2MB, alloc=492.3MB, time=59.82 memory used=6897.9MB, alloc=492.3MB, time=60.22 memory used=6972.6MB, alloc=492.3MB, time=60.56 memory used=7037.0MB, alloc=492.3MB, time=60.88 memory used=7105.2MB, alloc=492.3MB, time=61.19 memory used=7178.8MB, alloc=492.3MB, time=61.52 memory used=7257.6MB, alloc=492.3MB, time=61.84 memory used=7341.4MB, alloc=492.3MB, time=62.17 memory used=7430.7MB, alloc=492.3MB, time=62.51 memory used=7526.7MB, alloc=492.3MB, time=62.83 memory used=7630.9MB, alloc=492.3MB, time=63.17 memory used=7741.7MB, alloc=492.3MB, time=63.52 memory used=7947.3MB, alloc=492.3MB, time=63.99 memory used=8088.1MB, alloc=492.3MB, time=64.39 memory used=8298.7MB, alloc=492.3MB, time=69.76 memory used=8391.5MB, alloc=492.3MB, time=70.16 memory used=8475.1MB, alloc=492.3MB, time=70.50 memory used=8548.3MB, alloc=492.3MB, time=70.82 memory used=8632.7MB, alloc=492.3MB, time=71.14 memory used=8729.9MB, alloc=492.3MB, time=71.48 memory used=8839.4MB, alloc=492.3MB, time=71.82 memory used=9013.5MB, alloc=492.3MB, time=72.27 memory used=9169.4MB, alloc=492.3MB, time=72.69 memory used=9431.5MB, alloc=492.3MB, time=74.05 memory used=9544.1MB, alloc=492.3MB, time=74.85 memory used=9649.3MB, alloc=492.3MB, time=75.45 memory used=9766.0MB, alloc=492.3MB, time=76.09 memory used=9859.8MB, alloc=492.3MB, time=76.51 memory used=9937.3MB, alloc=492.3MB, time=76.89 memory used=10056.2MB, alloc=492.3MB, time=77.51 memory used=10156.0MB, alloc=492.3MB, time=77.93 memory used=10232.1MB, alloc=492.3MB, time=78.31 memory used=10327.4MB, alloc=492.3MB, time=78.71 memory used=10426.8MB, alloc=492.3MB, time=79.07 memory used=10492.9MB, alloc=492.3MB, time=79.39 memory used=10565.9MB, alloc=492.3MB, time=79.70 memory used=10646.8MB, alloc=492.3MB, time=80.02 memory used=10736.6MB, alloc=492.3MB, time=80.34 memory used=10838.1MB, alloc=492.3MB, time=80.68 memory used=10987.0MB, alloc=492.3MB, time=83.31 memory used=11074.0MB, alloc=492.3MB, time=83.70 memory used=11171.9MB, alloc=492.3MB, time=84.06 memory used=11242.3MB, alloc=492.3MB, time=84.38 memory used=11326.7MB, alloc=492.3MB, time=84.70 memory used=11425.4MB, alloc=492.3MB, time=85.04 memory used=11654.2MB, alloc=492.3MB, time=85.52 memory used=11849.5MB, alloc=492.3MB, time=86.75 memory used=12016.2MB, alloc=492.3MB, time=88.16 memory used=12190.9MB, alloc=492.3MB, time=88.65 memory used=12307.0MB, alloc=492.3MB, time=90.21 memory used=12402.7MB, alloc=492.3MB, time=90.77 memory used=12523.5MB, alloc=492.3MB, time=94.03 memory used=12728.8MB, alloc=492.3MB, time=94.49 memory used=12842.7MB, alloc=492.3MB, time=97.99 memory used=12955.7MB, alloc=492.3MB, time=103.06 memory used=13037.4MB, alloc=492.3MB, time=103.41 memory used=13137.1MB, alloc=492.3MB, time=103.77 memory used=13203.6MB, alloc=492.3MB, time=104.08 memory used=13276.2MB, alloc=492.3MB, time=104.39 memory used=13356.3MB, alloc=492.3MB, time=104.70 memory used=13445.6MB, alloc=492.3MB, time=105.03 memory used=13544.0MB, alloc=492.3MB, time=105.36 memory used=13654.8MB, alloc=492.3MB, time=105.70 memory used=13834.5MB, alloc=492.3MB, time=106.15 memory used=13979.3MB, alloc=492.3MB, time=106.56 memory used=14140.2MB, alloc=492.3MB, time=106.98 memory used=14318.7MB, alloc=492.3MB, time=107.41 memory used=14522.9MB, alloc=492.3MB, time=107.87 memory used=14721.5MB, alloc=492.3MB, time=109.27 memory used=14849.7MB, alloc=492.3MB, time=110.26 memory used=14946.0MB, alloc=492.3MB, time=111.49 memory used=15058.6MB, alloc=516.3MB, time=114.71 memory used=15161.7MB, alloc=516.3MB, time=115.24 memory used=15258.1MB, alloc=516.3MB, time=115.71 memory used=15349.1MB, alloc=516.3MB, time=116.19 memory used=15444.4MB, alloc=516.3MB, time=116.64 memory used=15546.1MB, alloc=516.3MB, time=117.14 memory used=15654.8MB, alloc=516.3MB, time=117.60 memory used=15765.1MB, alloc=516.3MB, time=118.08 memory used=15884.5MB, alloc=516.3MB, time=118.57 memory used=16012.4MB, alloc=516.3MB, time=119.03 memory used=16111.3MB, alloc=516.3MB, time=119.45 memory used=16193.4MB, alloc=516.3MB, time=119.85 memory used=16281.1MB, alloc=516.3MB, time=120.26 memory used=16359.4MB, alloc=516.3MB, time=120.61 memory used=16497.6MB, alloc=540.3MB, time=194.44 memory used=16628.7MB, alloc=540.3MB, time=303.44 memory used=16757.7MB, alloc=540.3MB, time=425.21 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428544441 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 2 F := [9 x y z - 17 y z - 9 x z, 5 x y z + 14 y z - 13 x] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 G := [-10 y z - 20 x y + x y, 8 y z - 18 x z] > Problem := [F,G]; 2 2 2 2 2 2 Problem := [[9 x y z - 17 y z - 9 x z, 5 x y z + 14 y z - 13 x], 3 2 2 [-10 y z - 20 x y + x y, 8 y z - 18 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.16 memory used=25.7MB, alloc=32.3MB, time=0.46 memory used=46.3MB, alloc=32.3MB, time=0.74 memory used=64.1MB, alloc=56.3MB, time=0.99 memory used=103.6MB, alloc=60.3MB, time=1.54 memory used=141.7MB, alloc=60.3MB, time=2.08 memory used=182.1MB, alloc=92.3MB, time=2.63 memory used=244.0MB, alloc=92.3MB, time=3.48 memory used=306.7MB, alloc=92.3MB, time=4.17 memory used=357.9MB, alloc=92.3MB, time=4.64 memory used=420.3MB, alloc=92.3MB, time=5.46 memory used=480.2MB, alloc=92.3MB, time=6.30 memory used=539.4MB, alloc=116.3MB, time=7.14 memory used=617.4MB, alloc=372.3MB, time=8.23 memory used=701.6MB, alloc=372.3MB, time=9.36 memory used=776.6MB, alloc=396.3MB, time=10.15 memory used=847.3MB, alloc=396.3MB, time=10.74 memory used=944.2MB, alloc=396.3MB, time=11.59 memory used=1016.7MB, alloc=396.3MB, time=12.46 memory used=1097.8MB, alloc=396.3MB, time=13.09 memory used=1162.7MB, alloc=396.3MB, time=13.90 memory used=1273.6MB, alloc=396.3MB, time=15.30 memory used=1385.2MB, alloc=396.3MB, time=16.75 memory used=1490.4MB, alloc=420.3MB, time=18.03 memory used=1651.1MB, alloc=444.3MB, time=19.86 memory used=1806.4MB, alloc=444.3MB, time=21.23 memory used=1977.1MB, alloc=444.3MB, time=23.63 memory used=2133.9MB, alloc=444.3MB, time=24.77 memory used=2253.4MB, alloc=444.3MB, time=25.28 memory used=2387.1MB, alloc=444.3MB, time=26.25 memory used=2505.6MB, alloc=444.3MB, time=26.72 memory used=2671.8MB, alloc=444.3MB, time=28.08 memory used=2800.1MB, alloc=444.3MB, time=28.72 memory used=2948.2MB, alloc=444.3MB, time=29.52 memory used=3061.9MB, alloc=444.3MB, time=30.00 memory used=3218.9MB, alloc=444.3MB, time=30.98 memory used=3373.5MB, alloc=468.3MB, time=33.38 memory used=3543.6MB, alloc=468.3MB, time=34.95 memory used=3704.3MB, alloc=492.3MB, time=37.15 memory used=3891.3MB, alloc=516.3MB, time=39.67 memory used=4095.8MB, alloc=540.3MB, time=42.48 memory used=4315.4MB, alloc=564.3MB, time=45.80 memory used=4537.9MB, alloc=588.3MB, time=49.55 memory used=4803.6MB, alloc=612.3MB, time=52.92 memory used=5085.0MB, alloc=636.3MB, time=56.55 memory used=5324.6MB, alloc=660.3MB, time=60.13 memory used=5671.4MB, alloc=684.3MB, time=63.73 memory used=6056.3MB, alloc=684.3MB, time=67.28 memory used=6430.2MB, alloc=708.3MB, time=71.01 memory used=6731.5MB, alloc=732.3MB, time=74.83 memory used=6993.7MB, alloc=732.3MB, time=78.38 memory used=7423.7MB, alloc=756.3MB, time=82.22 memory used=7837.8MB, alloc=756.3MB, time=86.14 memory used=8140.8MB, alloc=780.3MB, time=89.78 memory used=8338.9MB, alloc=804.3MB, time=92.74 memory used=8595.7MB, alloc=804.3MB, time=95.38 memory used=8800.8MB, alloc=828.3MB, time=97.66 memory used=8981.1MB, alloc=852.3MB, time=99.93 memory used=9143.7MB, alloc=876.3MB, time=102.12 memory used=9310.6MB, alloc=876.3MB, time=104.36 memory used=9463.1MB, alloc=900.3MB, time=106.48 memory used=9635.6MB, alloc=924.3MB, time=108.79 memory used=9810.2MB, alloc=948.3MB, time=110.99 memory used=10023.3MB, alloc=972.3MB, time=113.25 memory used=10240.5MB, alloc=996.3MB, time=117.80 memory used=10551.4MB, alloc=1020.3MB, time=125.41 memory used=10990.7MB, alloc=1044.3MB, time=136.69 memory used=11433.0MB, alloc=1068.3MB, time=148.03 memory used=11880.6MB, alloc=1092.3MB, time=159.57 memory used=12337.1MB, alloc=1116.3MB, time=171.60 memory used=12803.9MB, alloc=1140.3MB, time=184.08 memory used=13282.3MB, alloc=1164.3MB, time=196.97 memory used=13772.2MB, alloc=1188.3MB, time=210.29 memory used=14274.7MB, alloc=1212.3MB, time=223.95 memory used=14790.7MB, alloc=1236.3MB, time=238.11 memory used=15317.1MB, alloc=1260.3MB, time=252.89 memory used=15858.7MB, alloc=1284.3MB, time=268.50 memory used=16424.4MB, alloc=1308.3MB, time=284.58 memory used=17013.9MB, alloc=1332.3MB, time=301.34 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428544741 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [12 x z - 19 x z + 6 x, -20 y z + 5 x - 18 y z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 G := [-12 y - 10 y z - 16 y, 12 y - 20 x + 8 y] > Problem := [F,G]; 2 2 2 Problem := [[12 x z - 19 x z + 6 x, -20 y z + 5 x - 18 y z], 4 3 [-12 y - 10 y z - 16 y, 12 y - 20 x + 8 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.14 memory used=26.1MB, alloc=32.3MB, time=0.40 memory used=46.5MB, alloc=32.3MB, time=0.64 memory used=66.2MB, alloc=60.3MB, time=0.89 memory used=108.0MB, alloc=60.3MB, time=1.32 memory used=146.5MB, alloc=84.3MB, time=1.79 memory used=211.1MB, alloc=92.3MB, time=2.69 memory used=267.7MB, alloc=116.3MB, time=3.50 memory used=342.5MB, alloc=140.3MB, time=4.64 memory used=429.1MB, alloc=164.3MB, time=6.96 memory used=529.6MB, alloc=164.3MB, time=9.96 N1 := 2551 > GB := Basis(F, plex(op(vars))); 4 3 2 2 GB := [60 x - 95 x + 120 x y + 108 x y, 12 x z - 19 x z + 6 x, 2 2 20 y z - 5 x + 18 y z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=634.9MB, alloc=164.3MB, time=11.73 memory used=713.4MB, alloc=420.3MB, time=12.67 memory used=832.4MB, alloc=444.3MB, time=14.44 memory used=965.7MB, alloc=468.3MB, time=16.68 memory used=1096.3MB, alloc=492.3MB, time=19.32 N2 := 2551 > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 4 H := [12 x z - 19 x z + 6 x, -20 z y - 18 z y + 5 x , -12 y - 10 y z - 16 y, 3 12 y - 20 x + 8 y] > J:=[op(GB),op(G)]; 4 3 2 2 J := [60 x - 95 x + 120 x y + 108 x y, 12 x z - 19 x z + 6 x, 2 2 4 3 20 y z - 5 x + 18 y z, -12 y - 10 y z - 16 y, 12 y - 20 x + 8 y] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 9, 13, 4, 2, 4, 1, 3/4, 3/4, 3/4, 5/12, 7/12, 5/12, 5, 11, 17, 4, 4, 4, 1, 4/5, 4/5, 3/5, 9/16, 9/16, 5/16, -2, -4, 0] > save(F, G, cat("ranSet/34", convert(F, string),".txt")); > quit memory used=1161.5MB, alloc=492.3MB, time=20.32 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428544762 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 4 2 F := [-8 x y + 6 y + 14 y z, 2 x + 11 x y - 3 z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 2 2 3 G := [17 x y - 17 y + 2 y z , -2 x y + 7 x y z - 4 y z] > Problem := [F,G]; 2 4 2 Problem := [[-8 x y + 6 y + 14 y z, 2 x + 11 x y - 3 z], 2 2 3 2 2 2 2 3 [17 x y - 17 y + 2 y z , -2 x y + 7 x y z - 4 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.13 memory used=25.6MB, alloc=32.3MB, time=0.33 memory used=45.5MB, alloc=32.3MB, time=0.51 memory used=64.7MB, alloc=56.3MB, time=0.70 memory used=106.1MB, alloc=60.3MB, time=1.12 memory used=142.8MB, alloc=60.3MB, time=1.47 memory used=185.9MB, alloc=92.3MB, time=1.87 memory used=250.1MB, alloc=92.3MB, time=2.42 memory used=314.9MB, alloc=116.3MB, time=2.99 memory used=397.0MB, alloc=372.3MB, time=3.58 memory used=485.3MB, alloc=396.3MB, time=4.36 memory used=598.8MB, alloc=420.3MB, time=5.36 memory used=724.1MB, alloc=444.3MB, time=6.53 memory used=864.1MB, alloc=444.3MB, time=7.68 memory used=1009.1MB, alloc=468.3MB, time=8.92 memory used=1200.2MB, alloc=492.3MB, time=10.46 memory used=1368.6MB, alloc=492.3MB, time=12.01 memory used=1555.4MB, alloc=516.3MB, time=13.51 memory used=1743.5MB, alloc=540.3MB, time=15.05 memory used=1873.0MB, alloc=540.3MB, time=16.53 memory used=2024.7MB, alloc=564.3MB, time=18.27 memory used=2170.2MB, alloc=588.3MB, time=20.15 memory used=2308.9MB, alloc=588.3MB, time=21.71 memory used=2466.2MB, alloc=612.3MB, time=23.68 memory used=2609.8MB, alloc=636.3MB, time=25.43 memory used=2749.6MB, alloc=660.3MB, time=27.22 memory used=2887.2MB, alloc=660.3MB, time=28.89 memory used=2994.5MB, alloc=684.3MB, time=30.36 memory used=3118.4MB, alloc=708.3MB, time=32.00 memory used=3252.6MB, alloc=708.3MB, time=33.78 memory used=3366.5MB, alloc=732.3MB, time=35.34 memory used=3482.7MB, alloc=732.3MB, time=36.87 memory used=3587.7MB, alloc=756.3MB, time=38.35 memory used=3701.7MB, alloc=756.3MB, time=39.97 memory used=3820.3MB, alloc=756.3MB, time=41.68 memory used=3920.9MB, alloc=780.3MB, time=43.16 memory used=4033.9MB, alloc=780.3MB, time=44.77 memory used=4141.3MB, alloc=804.3MB, time=46.36 memory used=4247.5MB, alloc=804.3MB, time=47.86 memory used=4364.7MB, alloc=828.3MB, time=49.38 memory used=4468.8MB, alloc=828.3MB, time=50.77 memory used=4572.5MB, alloc=852.3MB, time=52.31 memory used=4660.9MB, alloc=852.3MB, time=53.73 memory used=4746.7MB, alloc=852.3MB, time=55.12 memory used=4835.7MB, alloc=876.3MB, time=56.56 memory used=4918.4MB, alloc=876.3MB, time=58.10 memory used=4994.6MB, alloc=900.3MB, time=59.46 memory used=5364.1MB, alloc=924.3MB, time=63.97 memory used=5683.2MB, alloc=948.3MB, time=68.18 memory used=6130.0MB, alloc=972.3MB, time=74.00 memory used=6585.2MB, alloc=996.3MB, time=79.67 memory used=7038.1MB, alloc=1020.3MB, time=85.51 memory used=7440.3MB, alloc=1044.3MB, time=93.24 memory used=7784.6MB, alloc=1068.3MB, time=102.23 memory used=8135.1MB, alloc=1092.3MB, time=111.71 memory used=8495.2MB, alloc=1116.3MB, time=121.63 memory used=8867.2MB, alloc=1140.3MB, time=131.74 memory used=9251.8MB, alloc=1164.3MB, time=142.38 memory used=9650.0MB, alloc=1188.3MB, time=153.47 memory used=10062.1MB, alloc=1212.3MB, time=165.03 memory used=10488.9MB, alloc=1236.3MB, time=177.02 memory used=10930.7MB, alloc=1260.3MB, time=189.58 memory used=11387.4MB, alloc=1284.3MB, time=202.48 memory used=11859.9MB, alloc=1308.3MB, time=215.85 memory used=12348.0MB, alloc=1332.3MB, time=229.63 memory used=12851.8MB, alloc=1356.3MB, time=244.03 memory used=13371.1MB, alloc=1380.3MB, time=258.84 memory used=13906.2MB, alloc=1404.3MB, time=274.14 memory used=14457.4MB, alloc=1428.3MB, time=289.99 memory used=15025.5MB, alloc=1452.3MB, time=306.51 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428545062 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 F := [-4 x z + 20 x y - y z, -18 x y + 18 z + 17 y] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 4 2 2 G := [6 x z - z - 3 y z, 15 x y z - 7 y z - 4 y ] > Problem := [F,G]; 2 2 3 Problem := [[-4 x z + 20 x y - y z, -18 x y + 18 z + 17 y], 3 4 2 2 [6 x z - z - 3 y z, 15 x y z - 7 y z - 4 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.15 memory used=26.9MB, alloc=32.3MB, time=0.42 memory used=47.0MB, alloc=56.3MB, time=0.67 memory used=89.0MB, alloc=60.3MB, time=1.19 memory used=130.6MB, alloc=60.3MB, time=1.66 memory used=169.5MB, alloc=84.3MB, time=2.13 memory used=232.3MB, alloc=92.3MB, time=2.90 memory used=293.4MB, alloc=92.3MB, time=3.65 memory used=355.1MB, alloc=116.3MB, time=4.37 memory used=426.3MB, alloc=372.3MB, time=5.21 memory used=512.7MB, alloc=396.3MB, time=6.22 memory used=616.2MB, alloc=396.3MB, time=7.13 memory used=734.4MB, alloc=396.3MB, time=8.35 memory used=844.2MB, alloc=420.3MB, time=9.41 memory used=978.7MB, alloc=444.3MB, time=10.96 memory used=1127.1MB, alloc=444.3MB, time=12.96 memory used=1261.4MB, alloc=468.3MB, time=14.87 memory used=1398.2MB, alloc=468.3MB, time=15.98 memory used=1509.2MB, alloc=468.3MB, time=16.50 memory used=1605.7MB, alloc=468.3MB, time=16.88 memory used=1693.2MB, alloc=468.3MB, time=17.18 memory used=1777.1MB, alloc=468.3MB, time=17.50 memory used=1882.2MB, alloc=468.3MB, time=17.95 memory used=2026.8MB, alloc=468.3MB, time=18.92 memory used=2151.6MB, alloc=468.3MB, time=20.07 memory used=2279.2MB, alloc=492.3MB, time=21.08 memory used=2401.6MB, alloc=492.3MB, time=22.42 memory used=2504.0MB, alloc=492.3MB, time=23.54 memory used=2617.0MB, alloc=492.3MB, time=24.80 memory used=2721.6MB, alloc=516.3MB, time=25.97 memory used=2814.1MB, alloc=516.3MB, time=27.06 memory used=2906.3MB, alloc=516.3MB, time=28.15 memory used=2983.3MB, alloc=516.3MB, time=29.17 memory used=3071.8MB, alloc=516.3MB, time=30.27 memory used=3152.9MB, alloc=516.3MB, time=31.34 memory used=3230.0MB, alloc=516.3MB, time=32.37 memory used=3292.5MB, alloc=516.3MB, time=33.30 memory used=3363.0MB, alloc=540.3MB, time=34.03 memory used=3455.0MB, alloc=540.3MB, time=34.64 memory used=3563.7MB, alloc=540.3MB, time=35.36 memory used=3618.3MB, alloc=540.3MB, time=36.16 memory used=3706.9MB, alloc=540.3MB, time=36.81 memory used=3823.5MB, alloc=540.3MB, time=37.32 memory used=3877.0MB, alloc=540.3MB, time=38.14 memory used=3944.8MB, alloc=540.3MB, time=38.89 memory used=4140.2MB, alloc=540.3MB, time=40.48 memory used=4350.4MB, alloc=564.3MB, time=42.50 memory used=4589.6MB, alloc=588.3MB, time=44.44 memory used=4817.4MB, alloc=588.3MB, time=46.46 memory used=5021.2MB, alloc=612.3MB, time=49.01 memory used=5228.6MB, alloc=636.3MB, time=51.44 memory used=5407.7MB, alloc=660.3MB, time=53.54 memory used=5620.9MB, alloc=684.3MB, time=55.86 memory used=5851.1MB, alloc=708.3MB, time=58.37 memory used=6139.4MB, alloc=732.3MB, time=61.01 memory used=6322.2MB, alloc=756.3MB, time=63.34 memory used=6561.3MB, alloc=756.3MB, time=65.51 memory used=6819.7MB, alloc=780.3MB, time=68.33 memory used=7049.4MB, alloc=804.3MB, time=71.23 memory used=7287.2MB, alloc=828.3MB, time=74.12 memory used=7490.2MB, alloc=852.3MB, time=76.75 memory used=7714.6MB, alloc=876.3MB, time=79.68 memory used=7910.7MB, alloc=876.3MB, time=82.51 memory used=8101.8MB, alloc=900.3MB, time=85.21 memory used=8265.1MB, alloc=924.3MB, time=87.76 memory used=8455.7MB, alloc=924.3MB, time=90.47 memory used=8635.7MB, alloc=948.3MB, time=93.25 memory used=8801.4MB, alloc=972.3MB, time=95.96 memory used=8963.6MB, alloc=996.3MB, time=98.67 memory used=9146.1MB, alloc=1020.3MB, time=101.65 memory used=9682.1MB, alloc=1044.3MB, time=108.64 memory used=10242.9MB, alloc=1068.3MB, time=115.27 memory used=10800.6MB, alloc=1092.3MB, time=122.23 memory used=11392.9MB, alloc=1116.3MB, time=128.61 memory used=11981.7MB, alloc=1140.3MB, time=135.55 memory used=12589.5MB, alloc=1164.3MB, time=142.34 memory used=13164.4MB, alloc=1188.3MB, time=149.93 memory used=13734.0MB, alloc=1212.3MB, time=157.79 memory used=14295.2MB, alloc=1236.3MB, time=165.70 memory used=14839.9MB, alloc=1260.3MB, time=173.81 memory used=15380.6MB, alloc=1284.3MB, time=181.96 memory used=15916.8MB, alloc=1308.3MB, time=190.27 memory used=16437.2MB, alloc=1332.3MB, time=198.31 memory used=16996.1MB, alloc=1356.3MB, time=206.32 memory used=17558.7MB, alloc=1380.3MB, time=214.16 memory used=18183.3MB, alloc=1404.3MB, time=220.35 memory used=18709.4MB, alloc=1428.3MB, time=230.66 memory used=19115.2MB, alloc=1452.3MB, time=242.64 memory used=19518.9MB, alloc=1476.3MB, time=254.88 memory used=19927.4MB, alloc=1500.3MB, time=267.16 memory used=20344.4MB, alloc=1524.3MB, time=280.04 memory used=20772.0MB, alloc=1548.3MB, time=293.36 memory used=21211.1MB, alloc=1572.3MB, time=307.11 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428545362 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 2 2 F := [x y + 13 y z - 3 x y, 4 x y z - 4 x y z + 3 y z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 2 2 2 4 3 G := [5 x - 19 x z + 13 x y, 12 x y + 20 y - y ] > Problem := [F,G]; 3 3 2 2 2 2 Problem := [[x y + 13 y z - 3 x y, 4 x y z - 4 x y z + 3 y z ], 4 3 2 2 2 4 3 [5 x - 19 x z + 13 x y, 12 x y + 20 y - y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.5MB, alloc=32.3MB, time=0.47 memory used=47.3MB, alloc=32.3MB, time=0.76 memory used=66.6MB, alloc=56.3MB, time=0.99 memory used=105.7MB, alloc=60.3MB, time=1.53 memory used=143.5MB, alloc=84.3MB, time=1.94 memory used=205.8MB, alloc=92.3MB, time=2.50 memory used=266.7MB, alloc=92.3MB, time=3.03 memory used=328.3MB, alloc=116.3MB, time=3.61 memory used=421.2MB, alloc=116.3MB, time=4.41 memory used=513.1MB, alloc=140.3MB, time=5.19 memory used=609.2MB, alloc=420.3MB, time=6.21 memory used=727.5MB, alloc=444.3MB, time=7.47 memory used=869.4MB, alloc=468.3MB, time=8.86 memory used=1025.2MB, alloc=492.3MB, time=10.48 memory used=1199.8MB, alloc=516.3MB, time=12.28 memory used=1389.8MB, alloc=540.3MB, time=14.28 memory used=1591.6MB, alloc=564.3MB, time=16.55 memory used=1782.4MB, alloc=588.3MB, time=20.20 memory used=1972.7MB, alloc=612.3MB, time=24.44 memory used=2175.0MB, alloc=636.3MB, time=29.18 memory used=2391.4MB, alloc=660.3MB, time=34.53 memory used=2619.9MB, alloc=684.3MB, time=40.48 memory used=2864.7MB, alloc=708.3MB, time=47.07 memory used=3133.4MB, alloc=732.3MB, time=54.39 memory used=3426.1MB, alloc=756.3MB, time=62.21 memory used=3742.6MB, alloc=756.3MB, time=70.58 memory used=4059.2MB, alloc=756.3MB, time=78.96 memory used=4375.6MB, alloc=780.3MB, time=87.46 memory used=4716.1MB, alloc=780.3MB, time=96.36 memory used=5056.4MB, alloc=780.3MB, time=105.17 memory used=5396.7MB, alloc=804.3MB, time=114.03 memory used=5761.1MB, alloc=804.3MB, time=123.51 memory used=6125.3MB, alloc=828.3MB, time=132.78 memory used=6513.4MB, alloc=828.3MB, time=142.56 memory used=6901.4MB, alloc=852.3MB, time=152.09 N1 := 13365 > GB := Basis(F, plex(op(vars))); 4 5 3 6 2 7 8 4 3 3 4 GB := [-64 x y - 688 x y - 108 x y + 27 x y + 384 x y + 1632 x y 2 5 6 4 3 2 2 3 4 + 648 x y - 162 x y - 576 x y + 1296 x y - 972 x y + 243 x y , 5 3 4 4 3 5 2 6 7 5 256 x y + 2944 x y + 2496 x y + 216 x y - 81 x y - 768 x y 4 2 4 3 3 2 4 5 - 8832 x y + 9984 x y z - 7056 x y - 1296 x y + 486 x y 3 2 2 3 4 3 3 4 2 5 - 1296 x y + 1944 x y - 729 x y , -64 x y - 688 x y - 108 x y 6 4 3 2 3 2 3 2 2 + 27 x y + 192 x y + 2064 x y - 2496 x y z + 324 x y + 1872 x y z 4 3 3 2 4 5 4 3 - 81 x y , 16 x y + 184 x y + 9 x y + 156 x y z - 48 x y 2 2 2 3 2 4 3 3 4 - 552 x y + 624 x y z - 27 x y - 468 x y z, -64 x y - 688 x y 2 5 6 4 3 2 3 2 3 - 108 x y + 27 x y + 192 x y + 2064 x y - 2496 x y z + 432 x y 2 2 4 2 2 + 1872 x y z - 162 x y - 324 x y + 243 x y , 2 2 2 2 3 3 4 x y z - 4 x y z + 3 y z , x y + 13 y z - 3 x y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=7320.4MB, alloc=852.3MB, time=160.82 memory used=7457.4MB, alloc=852.3MB, time=162.63 memory used=7591.0MB, alloc=852.3MB, time=164.55 memory used=7858.4MB, alloc=852.3MB, time=166.66 memory used=8132.9MB, alloc=852.3MB, time=168.49 memory used=8255.5MB, alloc=852.3MB, time=170.34 memory used=8334.8MB, alloc=852.3MB, time=171.79 memory used=8433.2MB, alloc=852.3MB, time=173.49 memory used=8518.9MB, alloc=852.3MB, time=174.94 memory used=8617.9MB, alloc=852.3MB, time=176.40 memory used=8693.8MB, alloc=852.3MB, time=177.66 memory used=8758.6MB, alloc=852.3MB, time=178.89 memory used=8850.6MB, alloc=852.3MB, time=180.26 memory used=8945.1MB, alloc=852.3MB, time=181.41 memory used=9021.6MB, alloc=852.3MB, time=182.57 memory used=9087.3MB, alloc=852.3MB, time=183.66 memory used=9142.8MB, alloc=852.3MB, time=185.24 memory used=9203.9MB, alloc=852.3MB, time=186.86 memory used=9250.8MB, alloc=852.3MB, time=188.29 memory used=9292.8MB, alloc=852.3MB, time=189.75 memory used=9501.5MB, alloc=876.3MB, time=192.73 memory used=9702.8MB, alloc=876.3MB, time=195.42 memory used=9882.0MB, alloc=900.3MB, time=197.87 memory used=10070.7MB, alloc=900.3MB, time=200.45 memory used=10278.2MB, alloc=924.3MB, time=203.29 memory used=10782.5MB, alloc=948.3MB, time=208.48 memory used=11076.1MB, alloc=972.3MB, time=210.85 memory used=11581.9MB, alloc=996.3MB, time=215.23 memory used=12048.6MB, alloc=1020.3MB, time=220.77 memory used=12464.4MB, alloc=1044.3MB, time=226.06 memory used=13112.8MB, alloc=1068.3MB, time=233.45 memory used=13493.5MB, alloc=1092.3MB, time=236.98 memory used=14125.8MB, alloc=1116.3MB, time=243.47 memory used=14872.8MB, alloc=1140.3MB, time=252.20 memory used=15621.7MB, alloc=1164.3MB, time=261.62 memory used=16270.5MB, alloc=1188.3MB, time=268.85 memory used=16783.3MB, alloc=1212.3MB, time=273.69 memory used=17645.5MB, alloc=1236.3MB, time=282.84 memory used=18234.3MB, alloc=1260.3MB, time=289.71 memory used=18498.6MB, alloc=1284.3MB, time=292.44 memory used=18803.5MB, alloc=1308.3MB, time=295.44 memory used=19095.8MB, alloc=1332.3MB, time=298.21 memory used=19826.8MB, alloc=1356.3MB, time=304.68 memory used=20611.8MB, alloc=1380.3MB, time=316.29 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428545662 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 3 2 F := [-2 x y z - 5 y z + 20 y z , -11 x y - 9 z - 11 y ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 3 G := [14 x + 19 x y - 3 z, -9 x z - 7 y z - 3 x y] > Problem := [F,G]; 2 2 2 2 2 3 2 Problem := [[-2 x y z - 5 y z + 20 y z , -11 x y - 9 z - 11 y ], 3 2 2 2 3 [14 x + 19 x y - 3 z, -9 x z - 7 y z - 3 x y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.5MB, alloc=32.3MB, time=0.43 memory used=45.4MB, alloc=56.3MB, time=0.70 memory used=87.5MB, alloc=60.3MB, time=1.30 memory used=129.5MB, alloc=68.3MB, time=1.79 memory used=172.3MB, alloc=92.3MB, time=2.22 memory used=239.5MB, alloc=92.3MB, time=2.92 memory used=302.2MB, alloc=348.3MB, time=3.61 memory used=367.2MB, alloc=372.3MB, time=4.16 memory used=462.7MB, alloc=372.3MB, time=4.92 memory used=553.1MB, alloc=396.3MB, time=5.61 memory used=665.0MB, alloc=396.3MB, time=6.52 memory used=779.3MB, alloc=396.3MB, time=7.40 memory used=891.4MB, alloc=420.3MB, time=8.33 memory used=1021.3MB, alloc=420.3MB, time=9.31 memory used=1156.2MB, alloc=444.3MB, time=10.44 memory used=1264.2MB, alloc=444.3MB, time=10.93 memory used=1354.7MB, alloc=444.3MB, time=11.21 memory used=1422.1MB, alloc=444.3MB, time=11.39 memory used=1506.2MB, alloc=444.3MB, time=11.72 memory used=1599.5MB, alloc=444.3MB, time=12.09 memory used=1680.6MB, alloc=444.3MB, time=12.36 memory used=1816.3MB, alloc=444.3MB, time=13.15 memory used=1908.2MB, alloc=444.3MB, time=13.48 memory used=1975.9MB, alloc=444.3MB, time=13.68 memory used=2062.4MB, alloc=444.3MB, time=14.04 memory used=2174.3MB, alloc=444.3MB, time=14.62 memory used=2247.8MB, alloc=444.3MB, time=14.84 memory used=2308.6MB, alloc=444.3MB, time=15.03 memory used=2402.3MB, alloc=444.3MB, time=15.53 memory used=2471.3MB, alloc=444.3MB, time=15.73 memory used=2546.0MB, alloc=444.3MB, time=16.09 memory used=2645.5MB, alloc=444.3MB, time=16.50 memory used=2744.5MB, alloc=444.3MB, time=16.72 memory used=2824.3MB, alloc=444.3MB, time=17.17 memory used=2964.5MB, alloc=444.3MB, time=18.63 memory used=3031.3MB, alloc=444.3MB, time=18.83 memory used=3096.2MB, alloc=444.3MB, time=19.00 memory used=3186.1MB, alloc=444.3MB, time=19.46 memory used=3246.8MB, alloc=444.3MB, time=19.67 memory used=3323.9MB, alloc=444.3MB, time=19.89 memory used=3385.4MB, alloc=444.3MB, time=20.07 memory used=3440.7MB, alloc=444.3MB, time=20.24 memory used=3503.8MB, alloc=444.3MB, time=20.41 memory used=3577.9MB, alloc=444.3MB, time=20.58 memory used=3754.2MB, alloc=444.3MB, time=21.82 memory used=3914.1MB, alloc=444.3MB, time=22.85 memory used=4074.5MB, alloc=444.3MB, time=24.38 memory used=4171.1MB, alloc=444.3MB, time=25.14 memory used=4237.9MB, alloc=444.3MB, time=25.33 memory used=4300.7MB, alloc=444.3MB, time=25.57 memory used=4363.9MB, alloc=444.3MB, time=25.76 memory used=4493.6MB, alloc=444.3MB, time=26.91 memory used=4561.5MB, alloc=444.3MB, time=27.12 memory used=4615.3MB, alloc=444.3MB, time=27.29 memory used=4683.3MB, alloc=444.3MB, time=27.47 memory used=4847.6MB, alloc=444.3MB, time=28.11 memory used=4911.3MB, alloc=444.3MB, time=28.33 memory used=4984.4MB, alloc=468.3MB, time=28.56 memory used=5048.4MB, alloc=468.3MB, time=28.75 memory used=5125.5MB, alloc=468.3MB, time=28.95 memory used=5215.1MB, alloc=468.3MB, time=29.16 memory used=5452.5MB, alloc=468.3MB, time=29.59 memory used=5614.1MB, alloc=468.3MB, time=29.88 memory used=5809.5MB, alloc=468.3MB, time=30.19 memory used=6037.5MB, alloc=468.3MB, time=31.42 memory used=6128.4MB, alloc=468.3MB, time=32.30 memory used=6235.2MB, alloc=468.3MB, time=32.78 memory used=6346.0MB, alloc=468.3MB, time=33.31 memory used=6433.2MB, alloc=468.3MB, time=33.57 memory used=6502.0MB, alloc=468.3MB, time=33.82 memory used=6602.0MB, alloc=468.3MB, time=34.44 memory used=6676.0MB, alloc=468.3MB, time=34.67 memory used=6807.5MB, alloc=468.3MB, time=35.47 memory used=6911.1MB, alloc=468.3MB, time=35.95 memory used=7037.7MB, alloc=468.3MB, time=36.75 memory used=7114.2MB, alloc=468.3MB, time=37.00 memory used=7232.9MB, alloc=468.3MB, time=37.63 memory used=7315.1MB, alloc=468.3MB, time=38.46 memory used=7430.1MB, alloc=492.3MB, time=39.22 memory used=7537.5MB, alloc=492.3MB, time=40.04 memory used=7630.5MB, alloc=492.3MB, time=40.40 memory used=7735.5MB, alloc=492.3MB, time=40.82 memory used=7813.0MB, alloc=492.3MB, time=41.09 memory used=7912.5MB, alloc=492.3MB, time=41.41 memory used=7978.1MB, alloc=492.3MB, time=41.66 memory used=8051.6MB, alloc=492.3MB, time=41.91 memory used=8135.8MB, alloc=492.3MB, time=42.17 memory used=8232.1MB, alloc=492.3MB, time=42.43 memory used=8391.9MB, alloc=492.3MB, time=42.92 memory used=8493.4MB, alloc=492.3MB, time=43.42 memory used=8573.4MB, alloc=492.3MB, time=43.69 memory used=8655.9MB, alloc=492.3MB, time=43.95 memory used=8758.4MB, alloc=492.3MB, time=44.22 memory used=8934.1MB, alloc=492.3MB, time=44.58 memory used=9109.0MB, alloc=492.3MB, time=44.92 memory used=9253.6MB, alloc=492.3MB, time=45.84 memory used=9390.3MB, alloc=492.3MB, time=46.70 memory used=9545.8MB, alloc=492.3MB, time=48.76 memory used=9645.5MB, alloc=492.3MB, time=49.13 memory used=9721.7MB, alloc=492.3MB, time=49.39 memory used=9808.6MB, alloc=492.3MB, time=49.65 memory used=10044.3MB, alloc=492.3MB, time=50.05 memory used=10248.6MB, alloc=492.3MB, time=51.07 memory used=10344.8MB, alloc=492.3MB, time=51.37 memory used=10410.8MB, alloc=492.3MB, time=51.62 memory used=10487.6MB, alloc=492.3MB, time=51.87 memory used=10577.5MB, alloc=492.3MB, time=52.14 memory used=10680.9MB, alloc=492.3MB, time=52.41 memory used=10872.6MB, alloc=492.3MB, time=52.80 memory used=11022.3MB, alloc=492.3MB, time=53.14 memory used=11192.0MB, alloc=492.3MB, time=53.49 memory used=11385.1MB, alloc=492.3MB, time=53.87 memory used=11605.8MB, alloc=492.3MB, time=54.26 memory used=11804.2MB, alloc=492.3MB, time=54.62 memory used=12032.7MB, alloc=492.3MB, time=55.78 memory used=12100.4MB, alloc=492.3MB, time=56.51 memory used=12169.0MB, alloc=492.3MB, time=57.19 memory used=12230.7MB, alloc=492.3MB, time=57.86 memory used=12337.1MB, alloc=492.3MB, time=58.81 memory used=12523.0MB, alloc=516.3MB, time=60.02 memory used=12666.2MB, alloc=516.3MB, time=60.94 memory used=12845.9MB, alloc=516.3MB, time=61.84 memory used=12976.2MB, alloc=516.3MB, time=63.11 memory used=13132.3MB, alloc=516.3MB, time=63.67 memory used=13293.2MB, alloc=516.3MB, time=64.14 memory used=13475.6MB, alloc=516.3MB, time=64.64 memory used=13573.2MB, alloc=516.3MB, time=67.25 memory used=13743.4MB, alloc=516.3MB, time=68.01 memory used=13900.0MB, alloc=516.3MB, time=68.45 memory used=14080.2MB, alloc=516.3MB, time=68.92 memory used=14245.6MB, alloc=516.3MB, time=71.61 memory used=14435.9MB, alloc=516.3MB, time=72.41 memory used=14584.8MB, alloc=516.3MB, time=73.46 memory used=14756.3MB, alloc=516.3MB, time=74.18 memory used=14874.2MB, alloc=516.3MB, time=76.75 memory used=14989.9MB, alloc=516.3MB, time=77.51 memory used=15168.9MB, alloc=516.3MB, time=78.90 memory used=15251.6MB, alloc=516.3MB, time=79.73 memory used=15422.6MB, alloc=540.3MB, time=80.52 memory used=15555.2MB, alloc=540.3MB, time=83.09 memory used=15662.5MB, alloc=540.3MB, time=84.00 memory used=15779.2MB, alloc=540.3MB, time=85.18 memory used=15922.7MB, alloc=540.3MB, time=86.26 memory used=16105.6MB, alloc=564.3MB, time=87.57 memory used=16273.0MB, alloc=564.3MB, time=88.78 memory used=16414.2MB, alloc=564.3MB, time=89.89 memory used=16596.2MB, alloc=564.3MB, time=91.15 memory used=16753.9MB, alloc=564.3MB, time=92.16 memory used=16884.5MB, alloc=588.3MB, time=93.31 memory used=17066.0MB, alloc=588.3MB, time=94.50 memory used=17180.7MB, alloc=588.3MB, time=95.43 memory used=17291.5MB, alloc=588.3MB, time=96.41 memory used=17454.3MB, alloc=588.3MB, time=97.55 memory used=17579.6MB, alloc=588.3MB, time=98.67 memory used=17734.1MB, alloc=588.3MB, time=99.72 memory used=17876.7MB, alloc=588.3MB, time=100.85 memory used=18010.1MB, alloc=612.3MB, time=101.90 memory used=18157.6MB, alloc=612.3MB, time=102.94 memory used=18295.7MB, alloc=612.3MB, time=104.16 memory used=18458.8MB, alloc=612.3MB, time=105.26 memory used=18605.8MB, alloc=612.3MB, time=106.48 memory used=18900.7MB, alloc=612.3MB, time=107.79 memory used=19199.8MB, alloc=636.3MB, time=109.45 memory used=19519.7MB, alloc=636.3MB, time=111.50 memory used=19837.1MB, alloc=636.3MB, time=112.71 memory used=20159.5MB, alloc=660.3MB, time=114.80 memory used=20559.2MB, alloc=684.3MB, time=120.89 memory used=21036.0MB, alloc=684.3MB, time=122.75 memory used=21509.8MB, alloc=684.3MB, time=123.67 memory used=21887.2MB, alloc=684.3MB, time=125.96 memory used=22748.9MB, alloc=708.3MB, time=138.02 memory used=23252.0MB, alloc=708.3MB, time=139.04 memory used=23766.6MB, alloc=708.3MB, time=140.45 memory used=24281.8MB, alloc=708.3MB, time=142.71 memory used=25219.2MB, alloc=708.3MB, time=155.32 memory used=25696.7MB, alloc=708.3MB, time=156.32 memory used=26197.9MB, alloc=708.3MB, time=157.73 memory used=26712.5MB, alloc=732.3MB, time=159.78 memory used=27104.8MB, alloc=756.3MB, time=162.91 memory used=27515.4MB, alloc=780.3MB, time=166.30 memory used=27985.1MB, alloc=780.3MB, time=169.51 memory used=28348.8MB, alloc=804.3MB, time=172.91 memory used=29314.3MB, alloc=828.3MB, time=185.50 memory used=29712.1MB, alloc=852.3MB, time=189.81 memory used=30175.8MB, alloc=876.3MB, time=197.45 memory used=30519.7MB, alloc=900.3MB, time=200.99 memory used=30835.0MB, alloc=924.3MB, time=204.98 memory used=31781.4MB, alloc=948.3MB, time=218.84 memory used=32279.6MB, alloc=972.3MB, time=224.81 memory used=32824.9MB, alloc=996.3MB, time=230.06 memory used=33336.5MB, alloc=1020.3MB, time=237.21 memory used=33722.0MB, alloc=1044.3MB, time=246.74 memory used=34101.8MB, alloc=1068.3MB, time=256.93 memory used=34485.6MB, alloc=1092.3MB, time=267.17 memory used=34876.6MB, alloc=1116.3MB, time=277.82 memory used=35276.6MB, alloc=1140.3MB, time=288.92 memory used=35687.7MB, alloc=1164.3MB, time=300.48 memory used=36112.0MB, alloc=1188.3MB, time=312.59 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428545962 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 2 2 F := [-17 x z + 15 y z + 17 y , 18 x y z + 9 x z - 17 x z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 3 3 G := [11 x y z + 19 z , 10 y z - 19 y + 19 x z] > Problem := [F,G]; 3 3 2 2 2 2 Problem := [[-17 x z + 15 y z + 17 y , 18 x y z + 9 x z - 17 x z], 2 3 3 3 [11 x y z + 19 z , 10 y z - 19 y + 19 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.15 memory used=26.7MB, alloc=32.3MB, time=0.43 memory used=46.8MB, alloc=32.3MB, time=0.67 memory used=65.9MB, alloc=60.3MB, time=0.90 memory used=106.2MB, alloc=68.3MB, time=1.45 memory used=147.8MB, alloc=92.3MB, time=1.97 memory used=214.9MB, alloc=92.3MB, time=2.59 memory used=277.8MB, alloc=372.3MB, time=3.14 memory used=369.8MB, alloc=372.3MB, time=3.88 memory used=455.6MB, alloc=396.3MB, time=4.64 memory used=564.8MB, alloc=420.3MB, time=5.61 memory used=701.2MB, alloc=420.3MB, time=6.66 memory used=824.3MB, alloc=420.3MB, time=7.48 memory used=941.7MB, alloc=444.3MB, time=8.31 memory used=1064.3MB, alloc=444.3MB, time=9.36 memory used=1151.5MB, alloc=444.3MB, time=10.21 memory used=1242.1MB, alloc=468.3MB, time=11.01 memory used=1381.5MB, alloc=492.3MB, time=12.48 memory used=1513.4MB, alloc=492.3MB, time=14.01 memory used=1662.4MB, alloc=516.3MB, time=15.77 memory used=1796.6MB, alloc=540.3MB, time=17.42 memory used=1944.5MB, alloc=564.3MB, time=19.03 memory used=2067.5MB, alloc=564.3MB, time=20.57 memory used=2196.2MB, alloc=588.3MB, time=22.17 memory used=2321.8MB, alloc=612.3MB, time=23.83 memory used=2443.2MB, alloc=612.3MB, time=25.41 memory used=2559.1MB, alloc=636.3MB, time=26.98 memory used=2683.7MB, alloc=660.3MB, time=28.84 memory used=2925.7MB, alloc=684.3MB, time=34.06 memory used=3167.5MB, alloc=708.3MB, time=39.93 memory used=3417.8MB, alloc=732.3MB, time=46.33 memory used=3677.6MB, alloc=756.3MB, time=53.35 memory used=3945.7MB, alloc=780.3MB, time=61.13 memory used=4237.7MB, alloc=804.3MB, time=69.40 memory used=4553.6MB, alloc=828.3MB, time=78.30 memory used=4893.5MB, alloc=852.3MB, time=87.82 memory used=5257.3MB, alloc=852.3MB, time=97.95 memory used=5621.1MB, alloc=876.3MB, time=108.07 memory used=6008.8MB, alloc=876.3MB, time=119.01 memory used=6396.4MB, alloc=876.3MB, time=129.76 memory used=6784.1MB, alloc=876.3MB, time=140.49 memory used=7171.7MB, alloc=900.3MB, time=151.24 memory used=7583.0MB, alloc=900.3MB, time=162.44 memory used=7994.2MB, alloc=924.3MB, time=173.69 memory used=8429.5MB, alloc=924.3MB, time=185.68 memory used=8864.6MB, alloc=948.3MB, time=197.34 memory used=9323.8MB, alloc=972.3MB, time=209.46 memory used=9806.9MB, alloc=996.3MB, time=221.30 N1 := 15259 > GB := Basis(F, plex(op(vars))); 5 3 2 6 4 2 2 4 5 GB := [-306 x y + 270 x y + 289 x y - 153 x y - 255 x y , 5 2 4 2 2 3 2 3 2 2 2 51 x z + 90 x y - 51 x y - 85 x y , 18 x y + 9 x y z - 17 x y , 3 3 2 2 2 2 -17 x z + 15 y z + 17 y , 18 x y z + 9 x z - 17 x z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=9871.0MB, alloc=996.3MB, time=223.26 memory used=10113.8MB, alloc=996.3MB, time=226.43 memory used=10664.8MB, alloc=996.3MB, time=231.68 memory used=11258.0MB, alloc=996.3MB, time=237.67 memory used=11863.3MB, alloc=1020.3MB, time=243.98 memory used=12421.9MB, alloc=1044.3MB, time=248.89 memory used=13112.5MB, alloc=1068.3MB, time=256.20 memory used=13797.3MB, alloc=1092.3MB, time=263.66 memory used=14431.7MB, alloc=1116.3MB, time=269.85 memory used=15125.4MB, alloc=1140.3MB, time=277.71 memory used=15769.1MB, alloc=1164.3MB, time=284.30 memory used=16499.9MB, alloc=1188.3MB, time=293.04 memory used=17191.2MB, alloc=1212.3MB, time=302.89 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428546262 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 2 2 3 F := [-9 x y z - 20 x z - 5 y , -16 x y z - 20 y z + 13 y z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 2 3 2 G := [-13 x + 14 x y z + 16 y z , 8 x z + 14 x z + 3 x y] > Problem := [F,G]; 2 2 2 2 2 2 2 3 Problem := [[-9 x y z - 20 x z - 5 y , -16 x y z - 20 y z + 13 y z ], 4 2 2 2 3 2 [-13 x + 14 x y z + 16 y z , 8 x z + 14 x z + 3 x y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.15 memory used=26.7MB, alloc=32.3MB, time=0.48 memory used=46.7MB, alloc=32.3MB, time=0.74 memory used=65.1MB, alloc=56.3MB, time=0.95 memory used=105.9MB, alloc=60.3MB, time=1.33 memory used=145.0MB, alloc=84.3MB, time=1.69 memory used=208.4MB, alloc=92.3MB, time=2.28 memory used=271.3MB, alloc=92.3MB, time=2.83 memory used=330.4MB, alloc=116.3MB, time=3.39 memory used=408.0MB, alloc=372.3MB, time=4.11 memory used=495.8MB, alloc=396.3MB, time=4.88 memory used=607.3MB, alloc=396.3MB, time=5.88 memory used=709.3MB, alloc=420.3MB, time=6.72 memory used=861.0MB, alloc=420.3MB, time=7.89 memory used=996.4MB, alloc=444.3MB, time=8.92 memory used=1144.2MB, alloc=444.3MB, time=10.22 memory used=1270.7MB, alloc=444.3MB, time=11.31 memory used=1414.3MB, alloc=468.3MB, time=12.59 memory used=1534.9MB, alloc=468.3MB, time=13.76 memory used=1649.2MB, alloc=492.3MB, time=14.84 memory used=1757.5MB, alloc=492.3MB, time=15.70 memory used=1880.7MB, alloc=492.3MB, time=28.46 memory used=2000.5MB, alloc=492.3MB, time=28.75 memory used=2200.6MB, alloc=492.3MB, time=29.97 memory used=2327.8MB, alloc=492.3MB, time=50.00 memory used=2412.4MB, alloc=492.3MB, time=50.24 memory used=2483.4MB, alloc=492.3MB, time=50.44 memory used=2639.0MB, alloc=492.3MB, time=51.57 memory used=2740.6MB, alloc=492.3MB, time=51.98 memory used=2844.7MB, alloc=492.3MB, time=55.21 memory used=2942.4MB, alloc=492.3MB, time=55.54 memory used=3084.4MB, alloc=492.3MB, time=56.22 memory used=3205.2MB, alloc=492.3MB, time=59.68 memory used=3305.9MB, alloc=492.3MB, time=60.12 memory used=3409.1MB, alloc=492.3MB, time=60.53 memory used=3530.9MB, alloc=516.3MB, time=61.70 memory used=3668.4MB, alloc=516.3MB, time=62.86 memory used=3823.0MB, alloc=516.3MB, time=65.27 memory used=3940.9MB, alloc=516.3MB, time=66.30 memory used=4088.5MB, alloc=516.3MB, time=69.14 memory used=4252.5MB, alloc=516.3MB, time=71.25 memory used=4363.0MB, alloc=516.3MB, time=71.92 memory used=4473.4MB, alloc=540.3MB, time=74.62 memory used=4679.1MB, alloc=540.3MB, time=91.34 memory used=4829.1MB, alloc=540.3MB, time=91.83 memory used=5057.5MB, alloc=540.3MB, time=92.35 memory used=5396.3MB, alloc=540.3MB, time=93.48 memory used=5531.9MB, alloc=540.3MB, time=103.60 memory used=5688.1MB, alloc=540.3MB, time=104.62 memory used=5763.9MB, alloc=540.3MB, time=105.49 memory used=5875.6MB, alloc=540.3MB, time=106.38 memory used=5989.5MB, alloc=540.3MB, time=107.22 memory used=6101.3MB, alloc=540.3MB, time=108.06 memory used=6223.1MB, alloc=540.3MB, time=108.81 memory used=6320.1MB, alloc=540.3MB, time=109.15 memory used=6454.9MB, alloc=540.3MB, time=118.48 memory used=6609.3MB, alloc=540.3MB, time=119.77 memory used=6719.1MB, alloc=540.3MB, time=120.16 memory used=6959.8MB, alloc=540.3MB, time=121.07 memory used=7086.0MB, alloc=540.3MB, time=122.28 memory used=7170.5MB, alloc=540.3MB, time=123.22 memory used=7256.1MB, alloc=540.3MB, time=124.16 memory used=7324.8MB, alloc=540.3MB, time=124.86 memory used=7429.9MB, alloc=540.3MB, time=127.05 memory used=7506.0MB, alloc=540.3MB, time=128.00 memory used=7670.8MB, alloc=564.3MB, time=133.41 memory used=7749.2MB, alloc=564.3MB, time=134.19 memory used=7806.8MB, alloc=564.3MB, time=134.96 memory used=7968.3MB, alloc=588.3MB, time=137.18 memory used=8186.9MB, alloc=612.3MB, time=139.35 memory used=8514.2MB, alloc=612.3MB, time=140.86 memory used=8598.1MB, alloc=612.3MB, time=141.93 memory used=8660.3MB, alloc=612.3MB, time=142.73 memory used=8793.1MB, alloc=612.3MB, time=143.73 memory used=8870.2MB, alloc=612.3MB, time=144.51 memory used=8967.3MB, alloc=612.3MB, time=145.45 memory used=9041.3MB, alloc=612.3MB, time=146.27 memory used=9131.1MB, alloc=612.3MB, time=147.24 memory used=9411.7MB, alloc=612.3MB, time=148.11 memory used=9724.0MB, alloc=612.3MB, time=149.19 memory used=10036.0MB, alloc=612.3MB, time=149.96 memory used=10137.7MB, alloc=612.3MB, time=150.82 memory used=10217.5MB, alloc=612.3MB, time=151.68 memory used=10316.8MB, alloc=612.3MB, time=152.62 memory used=10453.0MB, alloc=612.3MB, time=153.65 memory used=10734.7MB, alloc=636.3MB, time=156.74 memory used=11028.3MB, alloc=660.3MB, time=159.99 memory used=11363.4MB, alloc=684.3MB, time=163.05 memory used=11706.5MB, alloc=708.3MB, time=167.10 memory used=12033.9MB, alloc=732.3MB, time=170.97 memory used=12392.4MB, alloc=756.3MB, time=174.72 memory used=12612.3MB, alloc=780.3MB, time=177.53 memory used=12924.2MB, alloc=804.3MB, time=181.43 memory used=13194.8MB, alloc=828.3MB, time=184.98 memory used=13629.0MB, alloc=852.3MB, time=188.70 memory used=14085.5MB, alloc=876.3MB, time=192.64 memory used=14444.7MB, alloc=900.3MB, time=196.67 memory used=14711.6MB, alloc=924.3MB, time=200.23 memory used=15142.2MB, alloc=948.3MB, time=205.90 memory used=15621.7MB, alloc=972.3MB, time=211.41 memory used=16097.7MB, alloc=996.3MB, time=217.34 memory used=16591.7MB, alloc=1020.3MB, time=222.92 memory used=17071.4MB, alloc=1044.3MB, time=229.09 memory used=17442.7MB, alloc=1068.3MB, time=237.78 memory used=17797.1MB, alloc=1092.3MB, time=246.88 memory used=18150.5MB, alloc=1116.3MB, time=256.19 memory used=18506.7MB, alloc=1140.3MB, time=266.03 memory used=18873.3MB, alloc=1164.3MB, time=276.33 memory used=19251.5MB, alloc=1188.3MB, time=287.14 memory used=19643.0MB, alloc=1212.3MB, time=298.21 memory used=20048.1MB, alloc=1236.3MB, time=309.63 memory used=20468.5MB, alloc=1260.3MB, time=321.37 memory used=20900.9MB, alloc=1284.3MB, time=333.53 memory used=21344.8MB, alloc=1308.3MB, time=346.21 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428546562 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 2 F := [-13 x y + 12 x y z - 19, -13 y z + 15 x y - 18 z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 3 2 3 G := [-10 y z + 20 y z + 19 y , 9 x z - 14 x y + 18 z ] > Problem := [F,G]; 2 2 2 2 2 2 Problem := [[-13 x y + 12 x y z - 19, -13 y z + 15 x y - 18 z ], 3 2 2 3 2 3 [-10 y z + 20 y z + 19 y , 9 x z - 14 x y + 18 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.15 memory used=28.3MB, alloc=32.3MB, time=0.40 memory used=49.5MB, alloc=33.1MB, time=0.53 memory used=62.9MB, alloc=33.1MB, time=0.56 memory used=74.4MB, alloc=33.1MB, time=0.59 memory used=90.6MB, alloc=33.1MB, time=0.65 memory used=115.9MB, alloc=33.1MB, time=0.84 memory used=138.6MB, alloc=38.4MB, time=1.09 memory used=154.4MB, alloc=38.4MB, time=1.22 memory used=176.9MB, alloc=40.2MB, time=1.35 memory used=195.4MB, alloc=40.2MB, time=1.40 memory used=212.6MB, alloc=40.2MB, time=1.45 memory used=224.9MB, alloc=40.2MB, time=1.48 memory used=234.2MB, alloc=40.2MB, time=1.52 memory used=244.7MB, alloc=40.2MB, time=1.55 memory used=256.6MB, alloc=40.2MB, time=1.58 memory used=278.3MB, alloc=40.2MB, time=1.71 memory used=296.5MB, alloc=40.2MB, time=1.75 memory used=313.5MB, alloc=40.2MB, time=1.79 memory used=326.9MB, alloc=40.2MB, time=1.83 memory used=336.3MB, alloc=40.2MB, time=1.86 memory used=346.7MB, alloc=40.2MB, time=1.89 memory used=358.4MB, alloc=40.2MB, time=1.92 memory used=377.4MB, alloc=40.2MB, time=2.19 memory used=395.6MB, alloc=40.2MB, time=2.30 memory used=415.0MB, alloc=40.2MB, time=2.51 memory used=438.2MB, alloc=64.2MB, time=2.73 memory used=472.4MB, alloc=64.2MB, time=3.09 memory used=502.9MB, alloc=64.2MB, time=3.17 memory used=531.0MB, alloc=64.2MB, time=3.23 memory used=561.1MB, alloc=64.2MB, time=3.37 memory used=587.9MB, alloc=64.2MB, time=3.44 memory used=614.2MB, alloc=64.2MB, time=3.51 memory used=655.0MB, alloc=64.2MB, time=7.06 memory used=687.7MB, alloc=64.2MB, time=12.83 memory used=744.4MB, alloc=64.2MB, time=13.35 memory used=779.7MB, alloc=64.2MB, time=13.47 memory used=808.4MB, alloc=64.2MB, time=13.53 memory used=827.9MB, alloc=64.2MB, time=13.59 memory used=850.6MB, alloc=64.2MB, time=13.65 memory used=876.5MB, alloc=64.2MB, time=13.71 memory used=906.1MB, alloc=64.2MB, time=13.77 memory used=933.5MB, alloc=64.2MB, time=13.83 memory used=950.5MB, alloc=64.2MB, time=13.88 memory used=968.9MB, alloc=64.2MB, time=13.92 memory used=988.6MB, alloc=64.2MB, time=13.97 memory used=1009.6MB, alloc=64.2MB, time=14.02 memory used=1031.7MB, alloc=64.2MB, time=14.06 memory used=1054.9MB, alloc=64.2MB, time=14.11 memory used=1079.0MB, alloc=64.2MB, time=14.16 memory used=1104.8MB, alloc=64.2MB, time=14.21 memory used=1131.8MB, alloc=64.2MB, time=14.26 memory used=1159.8MB, alloc=64.2MB, time=14.31 memory used=1189.8MB, alloc=64.2MB, time=14.37 memory used=1214.3MB, alloc=83.8MB, time=14.44 memory used=1227.7MB, alloc=83.8MB, time=14.48 memory used=1241.5MB, alloc=83.8MB, time=14.52 memory used=1256.4MB, alloc=83.8MB, time=14.56 memory used=1301.5MB, alloc=83.8MB, time=15.65 memory used=1326.6MB, alloc=83.8MB, time=15.74 memory used=1344.6MB, alloc=83.8MB, time=15.81 memory used=1364.0MB, alloc=83.8MB, time=15.90 memory used=1385.3MB, alloc=83.8MB, time=16.00 memory used=1410.4MB, alloc=83.8MB, time=16.08 memory used=1437.0MB, alloc=83.8MB, time=16.17 memory used=1464.9MB, alloc=83.8MB, time=16.26 memory used=1492.6MB, alloc=83.8MB, time=16.33 memory used=1510.3MB, alloc=83.8MB, time=16.40 memory used=1526.0MB, alloc=83.8MB, time=16.46 memory used=1541.2MB, alloc=83.8MB, time=16.51 memory used=1557.2MB, alloc=83.8MB, time=16.57 memory used=1573.5MB, alloc=83.8MB, time=16.62 memory used=1590.1MB, alloc=83.8MB, time=16.68 memory used=1606.9MB, alloc=107.8MB, time=16.76 memory used=1640.3MB, alloc=107.8MB, time=16.84 memory used=1676.0MB, alloc=107.8MB, time=16.93 memory used=1712.6MB, alloc=107.8MB, time=17.00 memory used=1750.2MB, alloc=107.8MB, time=17.09 memory used=1792.3MB, alloc=107.8MB, time=17.18 memory used=1835.1MB, alloc=107.8MB, time=17.27 memory used=1879.0MB, alloc=107.8MB, time=17.35 memory used=1926.9MB, alloc=107.8MB, time=17.44 memory used=1975.7MB, alloc=107.8MB, time=17.52 memory used=2026.2MB, alloc=107.8MB, time=17.60 memory used=2056.5MB, alloc=107.8MB, time=17.65 memory used=2080.3MB, alloc=107.8MB, time=17.70 memory used=2104.2MB, alloc=107.8MB, time=17.75 memory used=2128.8MB, alloc=107.8MB, time=17.80 memory used=2156.7MB, alloc=107.8MB, time=17.85 memory used=2184.8MB, alloc=107.8MB, time=17.91 memory used=2212.9MB, alloc=107.8MB, time=17.96 memory used=2240.8MB, alloc=107.8MB, time=18.01 memory used=2269.1MB, alloc=107.8MB, time=18.06 memory used=2300.3MB, alloc=107.8MB, time=18.12 memory used=2331.6MB, alloc=107.8MB, time=18.17 memory used=2362.7MB, alloc=107.8MB, time=18.23 memory used=2397.0MB, alloc=107.8MB, time=18.28 memory used=2431.0MB, alloc=107.8MB, time=18.34 memory used=2464.9MB, alloc=107.8MB, time=18.39 memory used=2500.9MB, alloc=107.8MB, time=18.45 memory used=2537.1MB, alloc=107.8MB, time=18.51 memory used=2574.9MB, alloc=107.8MB, time=18.56 memory used=2615.0MB, alloc=107.8MB, time=18.62 memory used=2657.0MB, alloc=107.8MB, time=18.68 memory used=2700.0MB, alloc=107.8MB, time=18.75 memory used=2746.0MB, alloc=107.8MB, time=18.80 memory used=2793.4MB, alloc=107.8MB, time=18.87 memory used=2843.4MB, alloc=107.8MB, time=18.93 memory used=2898.0MB, alloc=107.8MB, time=18.99 memory used=2910.3MB, alloc=107.8MB, time=19.03 memory used=2923.1MB, alloc=107.8MB, time=19.06 memory used=2936.2MB, alloc=107.8MB, time=19.10 memory used=2949.1MB, alloc=107.8MB, time=19.14 memory used=3013.5MB, alloc=107.8MB, time=20.08 memory used=3047.0MB, alloc=107.8MB, time=20.17 memory used=3086.1MB, alloc=107.8MB, time=20.25 memory used=3131.4MB, alloc=107.8MB, time=20.34 memory used=3183.0MB, alloc=107.8MB, time=20.43 memory used=3214.2MB, alloc=107.8MB, time=20.51 memory used=3241.0MB, alloc=107.8MB, time=20.58 memory used=3270.2MB, alloc=107.8MB, time=20.66 memory used=3300.7MB, alloc=107.8MB, time=20.73 memory used=3332.3MB, alloc=107.8MB, time=20.81 memory used=3367.8MB, alloc=107.8MB, time=20.88 memory used=3404.4MB, alloc=107.8MB, time=20.95 memory used=3441.9MB, alloc=107.8MB, time=21.03 memory used=3480.5MB, alloc=107.8MB, time=21.12 memory used=3522.9MB, alloc=107.8MB, time=21.20 memory used=3566.4MB, alloc=107.8MB, time=21.29 memory used=3614.5MB, alloc=107.8MB, time=21.38 memory used=3663.1MB, alloc=107.8MB, time=21.46 memory used=3712.2MB, alloc=107.8MB, time=21.54 memory used=3743.9MB, alloc=107.8MB, time=21.60 memory used=3768.6MB, alloc=107.8MB, time=21.65 memory used=3792.2MB, alloc=107.8MB, time=21.70 memory used=3816.4MB, alloc=107.8MB, time=21.75 memory used=3841.0MB, alloc=107.8MB, time=21.80 memory used=3868.7MB, alloc=107.8MB, time=21.85 memory used=3896.8MB, alloc=107.8MB, time=21.90 memory used=3924.7MB, alloc=107.8MB, time=21.96 memory used=3952.6MB, alloc=107.8MB, time=22.01 memory used=3980.7MB, alloc=107.8MB, time=22.06 memory used=4011.7MB, alloc=107.8MB, time=22.12 memory used=4042.8MB, alloc=107.8MB, time=22.17 memory used=4073.7MB, alloc=107.8MB, time=22.23 memory used=4107.9MB, alloc=107.8MB, time=22.28 memory used=4141.6MB, alloc=107.8MB, time=22.34 memory used=4175.3MB, alloc=107.8MB, time=22.39 memory used=4210.7MB, alloc=107.8MB, time=22.45 memory used=4249.3MB, alloc=107.8MB, time=22.50 memory used=4286.9MB, alloc=107.8MB, time=22.56 memory used=4326.5MB, alloc=107.8MB, time=22.62 memory used=4367.5MB, alloc=107.8MB, time=22.68 memory used=4409.8MB, alloc=107.8MB, time=22.74 memory used=4454.5MB, alloc=107.8MB, time=22.80 memory used=4502.3MB, alloc=107.8MB, time=22.86 memory used=4552.8MB, alloc=107.8MB, time=22.91 memory used=4590.5MB, alloc=107.8MB, time=22.97 memory used=4602.8MB, alloc=107.8MB, time=23.00 memory used=4615.6MB, alloc=107.8MB, time=23.04 memory used=4628.7MB, alloc=107.8MB, time=23.08 memory used=4641.7MB, alloc=107.8MB, time=23.11 memory used=4709.2MB, alloc=131.8MB, time=38.84 memory used=4778.3MB, alloc=131.8MB, time=69.43 memory used=4854.8MB, alloc=131.8MB, time=117.22 memory used=4903.7MB, alloc=155.8MB, time=169.00 memory used=4967.3MB, alloc=155.8MB, time=180.55 memory used=5073.6MB, alloc=155.8MB, time=181.76 memory used=5167.2MB, alloc=155.8MB, time=182.00 memory used=5226.7MB, alloc=155.8MB, time=182.11 memory used=5299.4MB, alloc=155.8MB, time=182.22 memory used=5385.8MB, alloc=155.8MB, time=182.36 memory used=5445.7MB, alloc=155.8MB, time=182.46 memory used=5498.1MB, alloc=155.8MB, time=182.55 memory used=5555.4MB, alloc=155.8MB, time=182.63 memory used=5615.2MB, alloc=155.8MB, time=182.72 memory used=5679.8MB, alloc=155.8MB, time=182.81 memory used=5749.2MB, alloc=155.8MB, time=182.90 memory used=5823.4MB, alloc=155.8MB, time=182.99 memory used=5902.3MB, alloc=155.8MB, time=183.09 memory used=5985.8MB, alloc=155.8MB, time=183.18 memory used=6073.8MB, alloc=155.8MB, time=183.28 memory used=6151.9MB, alloc=155.8MB, time=183.37 memory used=6163.3MB, alloc=155.8MB, time=183.41 memory used=6172.4MB, alloc=155.8MB, time=183.45 memory used=6183.2MB, alloc=155.8MB, time=183.49 memory used=6191.5MB, alloc=155.8MB, time=183.53 memory used=6200.0MB, alloc=155.8MB, time=183.57 memory used=6211.0MB, alloc=155.8MB, time=183.61 memory used=6219.5MB, alloc=155.8MB, time=183.66 memory used=6230.5MB, alloc=155.8MB, time=183.70 memory used=6241.6MB, alloc=155.8MB, time=183.74 memory used=6252.7MB, alloc=155.8MB, time=183.78 memory used=6263.9MB, alloc=155.8MB, time=183.82 memory used=6275.0MB, alloc=155.8MB, time=183.86 memory used=6286.1MB, alloc=155.8MB, time=183.90 memory used=6297.3MB, alloc=155.8MB, time=183.95 memory used=6308.4MB, alloc=155.8MB, time=183.99 memory used=6319.5MB, alloc=155.8MB, time=184.03 memory used=6330.6MB, alloc=155.8MB, time=184.07 memory used=6341.8MB, alloc=155.8MB, time=184.11 memory used=6352.9MB, alloc=155.8MB, time=184.15 memory used=6364.0MB, alloc=155.8MB, time=184.19 memory used=6375.1MB, alloc=155.8MB, time=184.23 memory used=6386.2MB, alloc=155.8MB, time=184.27 memory used=6397.3MB, alloc=155.8MB, time=184.31 memory used=6408.3MB, alloc=155.8MB, time=184.35 memory used=6419.4MB, alloc=155.8MB, time=184.39 memory used=6430.5MB, alloc=155.8MB, time=184.43 memory used=6441.5MB, alloc=155.8MB, time=184.47 memory used=6452.5MB, alloc=155.8MB, time=184.50 memory used=6463.5MB, alloc=155.8MB, time=184.55 memory used=6474.5MB, alloc=155.8MB, time=184.59 memory used=6485.5MB, alloc=155.8MB, time=184.62 memory used=6496.5MB, alloc=155.8MB, time=184.66 memory used=6507.5MB, alloc=155.8MB, time=184.70 memory used=6518.5MB, alloc=155.8MB, time=184.75 memory used=6532.0MB, alloc=155.8MB, time=184.79 memory used=6545.7MB, alloc=155.8MB, time=184.83 memory used=6559.3MB, alloc=155.8MB, time=184.87 memory used=6572.8MB, alloc=155.8MB, time=184.91 memory used=6586.3MB, alloc=155.8MB, time=184.95 memory used=6599.8MB, alloc=155.8MB, time=184.99 memory used=6613.2MB, alloc=155.8MB, time=185.04 memory used=6626.6MB, alloc=155.8MB, time=185.08 memory used=6640.0MB, alloc=155.8MB, time=185.12 memory used=6653.3MB, alloc=155.8MB, time=185.16 memory used=6666.6MB, alloc=155.8MB, time=185.20 memory used=6679.8MB, alloc=155.8MB, time=185.25 memory used=6692.9MB, alloc=155.8MB, time=185.29 memory used=6706.1MB, alloc=155.8MB, time=185.33 memory used=6719.1MB, alloc=155.8MB, time=185.37 memory used=6732.3MB, alloc=155.8MB, time=185.42 memory used=6747.7MB, alloc=155.8MB, time=185.46 memory used=6763.1MB, alloc=155.8MB, time=185.50 memory used=6778.5MB, alloc=155.8MB, time=185.54 memory used=6793.8MB, alloc=155.8MB, time=185.59 memory used=6809.0MB, alloc=155.8MB, time=185.63 memory used=6824.1MB, alloc=155.8MB, time=185.67 memory used=6839.1MB, alloc=155.8MB, time=185.71 memory used=6854.0MB, alloc=155.8MB, time=185.76 memory used=6868.8MB, alloc=155.8MB, time=185.80 memory used=6883.4MB, alloc=155.8MB, time=185.84 memory used=6900.5MB, alloc=155.8MB, time=185.88 memory used=6917.3MB, alloc=155.8MB, time=185.93 memory used=6934.0MB, alloc=155.8MB, time=185.97 memory used=6950.5MB, alloc=155.8MB, time=186.01 memory used=6966.9MB, alloc=155.8MB, time=186.06 memory used=6983.1MB, alloc=155.8MB, time=186.10 memory used=6999.3MB, alloc=155.8MB, time=186.14 memory used=7017.2MB, alloc=155.8MB, time=186.19 memory used=7035.1MB, alloc=155.8MB, time=186.23 memory used=7052.7MB, alloc=155.8MB, time=186.27 memory used=7070.0MB, alloc=155.8MB, time=186.32 memory used=7087.3MB, alloc=155.8MB, time=186.36 memory used=7106.1MB, alloc=155.8MB, time=186.41 memory used=7124.6MB, alloc=155.8MB, time=186.45 memory used=7142.8MB, alloc=155.8MB, time=186.49 memory used=7162.8MB, alloc=155.8MB, time=186.54 memory used=7182.3MB, alloc=155.8MB, time=186.58 memory used=7203.0MB, alloc=155.8MB, time=186.63 memory used=7223.2MB, alloc=155.8MB, time=186.68 memory used=7244.5MB, alloc=155.8MB, time=186.72 memory used=7265.0MB, alloc=155.8MB, time=186.77 memory used=7286.4MB, alloc=155.8MB, time=186.82 memory used=7308.3MB, alloc=155.8MB, time=186.86 memory used=7330.6MB, alloc=155.8MB, time=186.91 memory used=7353.3MB, alloc=155.8MB, time=186.95 memory used=7376.5MB, alloc=155.8MB, time=187.00 memory used=7400.8MB, alloc=155.8MB, time=187.05 memory used=7422.2MB, alloc=155.8MB, time=187.09 memory used=7439.5MB, alloc=155.8MB, time=187.13 memory used=7523.4MB, alloc=155.8MB, time=187.32 memory used=7635.9MB, alloc=155.8MB, time=188.59 memory used=7713.8MB, alloc=155.8MB, time=188.72 memory used=7781.5MB, alloc=155.8MB, time=188.80 memory used=7891.0MB, alloc=155.8MB, time=189.37 memory used=7988.1MB, alloc=155.8MB, time=189.72 memory used=8080.3MB, alloc=155.8MB, time=190.30 memory used=8155.2MB, alloc=155.8MB, time=192.09 memory used=8223.8MB, alloc=155.8MB, time=192.24 memory used=8298.8MB, alloc=155.8MB, time=192.40 memory used=8346.2MB, alloc=155.8MB, time=192.52 memory used=8395.9MB, alloc=155.8MB, time=192.64 memory used=8449.7MB, alloc=155.8MB, time=192.77 memory used=8511.0MB, alloc=155.8MB, time=192.92 memory used=8575.8MB, alloc=155.8MB, time=193.06 memory used=8643.9MB, alloc=155.8MB, time=193.19 memory used=8719.8MB, alloc=155.8MB, time=193.36 memory used=8799.1MB, alloc=155.8MB, time=193.51 memory used=8857.2MB, 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time=195.75 memory used=10032.3MB, alloc=155.8MB, time=195.89 memory used=10112.8MB, alloc=155.8MB, time=196.04 memory used=10192.3MB, alloc=155.8MB, time=196.19 memory used=10231.6MB, alloc=155.8MB, time=196.28 memory used=10237.2MB, alloc=155.8MB, time=196.34 memory used=10241.6MB, alloc=155.8MB, time=196.39 memory used=10246.2MB, alloc=155.8MB, time=196.44 memory used=10251.2MB, alloc=155.8MB, time=196.48 memory used=10256.6MB, alloc=155.8MB, time=196.53 memory used=10262.2MB, alloc=155.8MB, time=196.57 memory used=10267.8MB, alloc=155.8MB, time=196.62 memory used=10273.4MB, alloc=155.8MB, time=196.67 memory used=10278.9MB, alloc=155.8MB, time=196.71 memory used=10284.5MB, alloc=155.8MB, time=196.76 memory used=10290.0MB, alloc=155.8MB, time=196.81 memory used=10295.5MB, alloc=155.8MB, time=196.85 memory used=10301.0MB, alloc=155.8MB, time=196.90 memory used=10306.5MB, alloc=155.8MB, time=196.94 memory used=10312.0MB, alloc=155.8MB, time=196.99 memory used=10317.4MB, alloc=155.8MB, time=197.04 memory used=10322.9MB, alloc=155.8MB, time=197.09 memory used=10328.3MB, alloc=155.8MB, time=197.13 memory used=10333.7MB, alloc=155.8MB, time=197.18 memory used=10339.1MB, alloc=155.8MB, time=197.22 memory used=10344.5MB, alloc=155.8MB, time=197.27 memory used=10349.9MB, alloc=155.8MB, time=197.32 memory used=10355.3MB, alloc=155.8MB, time=197.37 memory used=10360.6MB, alloc=155.8MB, time=197.41 memory used=10366.0MB, alloc=155.8MB, time=197.46 memory used=10371.3MB, alloc=155.8MB, time=197.51 memory used=10376.6MB, alloc=155.8MB, time=197.56 memory used=10381.9MB, alloc=155.8MB, time=197.60 memory used=10387.2MB, alloc=155.8MB, time=197.65 memory used=10392.5MB, alloc=155.8MB, time=197.70 memory used=10397.7MB, alloc=155.8MB, time=197.75 memory used=10402.9MB, alloc=155.8MB, time=197.79 memory used=10408.2MB, alloc=155.8MB, time=197.84 memory used=10413.4MB, alloc=155.8MB, time=197.88 memory used=10418.6MB, alloc=155.8MB, time=197.93 memory used=10423.7MB, alloc=155.8MB, 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time=508.59 memory used=15848.5MB, alloc=203.8MB, time=508.64 memory used=15858.2MB, alloc=203.8MB, time=508.70 memory used=15867.9MB, alloc=203.8MB, time=508.76 memory used=15877.6MB, alloc=203.8MB, time=508.81 memory used=15887.3MB, alloc=203.8MB, time=508.86 memory used=15897.0MB, alloc=203.8MB, time=508.92 memory used=15906.6MB, alloc=203.8MB, time=508.97 memory used=15916.3MB, alloc=203.8MB, time=509.03 memory used=15926.0MB, alloc=203.8MB, time=509.08 memory used=15935.7MB, alloc=203.8MB, time=509.13 memory used=15945.3MB, alloc=203.8MB, time=509.19 memory used=15955.0MB, alloc=203.8MB, time=509.25 memory used=15964.6MB, alloc=203.8MB, time=509.30 memory used=15974.4MB, alloc=203.8MB, time=509.36 memory used=15987.1MB, alloc=203.8MB, time=509.41 memory used=15999.9MB, alloc=203.8MB, time=509.47 memory used=16012.7MB, alloc=203.8MB, time=509.53 memory used=16025.6MB, alloc=203.8MB, time=509.58 memory used=16038.4MB, alloc=203.8MB, time=509.64 memory used=16051.1MB, alloc=203.8MB, time=509.70 memory used=16063.9MB, alloc=203.8MB, time=509.75 memory used=16076.6MB, alloc=203.8MB, time=509.81 memory used=16089.3MB, alloc=203.8MB, time=509.87 memory used=16102.0MB, alloc=203.8MB, time=509.93 memory used=16114.6MB, alloc=203.8MB, time=509.98 memory used=16127.3MB, alloc=203.8MB, time=510.04 memory used=16139.9MB, alloc=203.8MB, time=510.09 memory used=16152.4MB, alloc=203.8MB, time=510.15 memory used=16165.0MB, alloc=203.8MB, time=510.20 memory used=16177.5MB, alloc=203.8MB, time=510.26 memory used=16190.0MB, alloc=203.8MB, time=510.32 memory used=16202.4MB, alloc=203.8MB, time=510.38 memory used=16214.8MB, alloc=203.8MB, time=510.43 memory used=16227.2MB, alloc=203.8MB, time=510.49 memory used=16239.6MB, alloc=203.8MB, time=510.55 memory used=16251.9MB, alloc=203.8MB, time=510.61 memory used=16264.1MB, alloc=203.8MB, time=510.67 memory used=16276.6MB, alloc=203.8MB, time=510.72 memory used=16291.6MB, alloc=203.8MB, time=510.78 memory used=16306.8MB, alloc=203.8MB, time=510.85 memory used=16321.9MB, alloc=203.8MB, time=510.90 memory used=16337.0MB, alloc=203.8MB, time=510.97 memory used=16351.9MB, alloc=203.8MB, time=511.03 memory used=16366.8MB, alloc=203.8MB, time=511.08 memory used=16381.6MB, alloc=203.8MB, time=511.14 memory used=16396.4MB, alloc=203.8MB, time=511.20 memory used=16411.1MB, alloc=203.8MB, time=511.26 memory used=16425.6MB, alloc=203.8MB, time=511.31 memory used=16440.1MB, alloc=203.8MB, time=511.37 memory used=16454.6MB, alloc=203.8MB, time=511.43 memory used=16468.9MB, alloc=203.8MB, time=511.49 memory used=16483.4MB, alloc=203.8MB, time=511.54 memory used=16500.1MB, alloc=203.8MB, time=511.60 memory used=16516.9MB, alloc=203.8MB, time=511.67 memory used=16533.6MB, alloc=203.8MB, time=511.73 memory used=16550.2MB, alloc=203.8MB, time=511.78 memory used=16566.6MB, alloc=203.8MB, time=511.84 memory used=16582.8MB, alloc=203.8MB, time=511.90 memory used=16598.9MB, alloc=203.8MB, time=511.96 memory used=16615.1MB, alloc=203.8MB, time=512.02 memory used=16633.3MB, alloc=203.8MB, time=512.08 memory used=16651.4MB, alloc=203.8MB, time=512.14 memory used=16669.4MB, alloc=203.8MB, time=512.19 memory used=16687.1MB, alloc=203.8MB, time=512.25 memory used=16704.5MB, alloc=203.8MB, time=512.31 memory used=16720.5MB, alloc=203.8MB, time=512.37 memory used=16732.8MB, alloc=203.8MB, time=512.43 memory used=16743.4MB, alloc=203.8MB, time=512.48 memory used=16755.2MB, alloc=203.8MB, time=512.53 memory used=16766.8MB, alloc=203.8MB, time=512.59 memory used=16778.3MB, alloc=203.8MB, time=512.64 memory used=16789.7MB, alloc=203.8MB, time=512.70 memory used=16801.1MB, alloc=203.8MB, time=512.76 memory used=16814.2MB, alloc=203.8MB, time=512.81 memory used=16825.4MB, alloc=203.8MB, time=512.87 memory used=16836.2MB, alloc=203.8MB, time=512.92 memory used=16848.6MB, alloc=203.8MB, time=512.98 memory used=16859.2MB, alloc=203.8MB, time=513.03 memory used=16869.7MB, alloc=203.8MB, time=513.09 memory used=16881.5MB, alloc=203.8MB, time=513.14 memory used=16893.5MB, alloc=203.8MB, time=513.20 memory used=16905.1MB, alloc=203.8MB, time=513.25 memory used=16916.5MB, alloc=203.8MB, time=513.30 memory used=16929.5MB, alloc=203.8MB, time=513.36 memory used=16942.1MB, alloc=203.8MB, time=513.41 memory used=16954.3MB, alloc=203.8MB, time=513.47 memory used=16968.1MB, alloc=203.8MB, time=513.52 memory used=16982.5MB, alloc=203.8MB, time=513.58 memory used=16997.0MB, alloc=203.8MB, time=513.63 memory used=17010.6MB, alloc=203.8MB, time=513.69 memory used=17025.0MB, alloc=203.8MB, time=513.74 memory used=17040.8MB, alloc=203.8MB, time=513.80 memory used=17057.0MB, alloc=203.8MB, time=513.86 memory used=17074.0MB, alloc=203.8MB, time=513.91 memory used=17090.9MB, alloc=203.8MB, time=513.97 memory used=17143.6MB, alloc=203.8MB, time=514.16 memory used=17257.7MB, alloc=203.8MB, time=514.45 memory used=17382.3MB, alloc=203.8MB, time=525.71 memory used=17521.4MB, alloc=203.8MB, time=529.43 memory used=17625.6MB, alloc=203.8MB, time=529.62 memory used=17713.6MB, alloc=203.8MB, time=529.77 memory used=17828.6MB, alloc=203.8MB, time=529.92 memory used=17877.9MB, alloc=203.8MB, time=530.01 memory used=17888.4MB, alloc=203.8MB, time=530.07 memory used=17899.0MB, alloc=203.8MB, time=530.12 memory used=17909.4MB, alloc=203.8MB, time=530.17 memory used=17920.6MB, alloc=203.8MB, time=530.23 memory used=17931.7MB, alloc=203.8MB, time=530.28 memory used=17943.1MB, alloc=203.8MB, time=530.34 memory used=17955.2MB, alloc=203.8MB, time=530.39 memory used=17967.7MB, alloc=203.8MB, time=530.44 memory used=17980.4MB, alloc=203.8MB, time=530.50 memory used=17993.7MB, alloc=203.8MB, time=530.55 memory used=18008.0MB, alloc=203.8MB, time=530.61 memory used=18023.1MB, alloc=203.8MB, time=530.66 memory used=18167.7MB, alloc=203.8MB, time=531.42 memory used=18313.8MB, alloc=459.8MB, time=532.10 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428546862 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 2 2 2 F := [10 x y z + 18 x z + 8 x y , -18 x z - 13 y z + 11 x z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 G := [-20 x + 7 y - 14 y, 13 x y + 7 y z + 12 y] > Problem := [F,G]; 2 2 2 2 2 2 2 2 Problem := [[10 x y z + 18 x z + 8 x y , -18 x z - 13 y z + 11 x z], 3 2 3 [-20 x + 7 y - 14 y, 13 x y + 7 y z + 12 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.15 memory used=26.4MB, alloc=32.3MB, time=0.41 memory used=46.2MB, alloc=32.3MB, time=0.58 memory used=65.1MB, alloc=56.3MB, time=0.76 memory used=107.2MB, alloc=68.3MB, time=1.14 memory used=151.0MB, alloc=68.3MB, time=1.48 memory used=194.2MB, alloc=92.3MB, time=1.85 memory used=260.6MB, alloc=92.3MB, time=2.37 memory used=315.2MB, alloc=92.3MB, time=2.66 memory used=386.3MB, alloc=92.3MB, time=3.19 memory used=451.4MB, alloc=116.3MB, time=3.75 memory used=527.4MB, alloc=116.3MB, time=4.11 memory used=583.8MB, alloc=116.3MB, time=4.47 memory used=631.0MB, alloc=116.3MB, time=4.60 memory used=707.9MB, alloc=116.3MB, time=5.11 memory used=782.2MB, alloc=372.3MB, time=5.86 memory used=870.5MB, alloc=396.3MB, time=6.61 memory used=959.0MB, alloc=396.3MB, time=7.16 memory used=1059.6MB, alloc=396.3MB, time=7.68 memory used=1132.8MB, alloc=396.3MB, time=8.12 memory used=1198.6MB, alloc=396.3MB, time=8.38 memory used=1250.3MB, alloc=396.3MB, time=8.52 memory used=1370.5MB, alloc=396.3MB, time=9.29 memory used=1481.3MB, alloc=420.3MB, time=9.90 memory used=1631.8MB, alloc=420.3MB, time=11.00 memory used=1772.0MB, alloc=420.3MB, time=11.91 memory used=1958.6MB, alloc=420.3MB, time=14.11 memory used=2109.1MB, alloc=420.3MB, time=15.68 memory used=2238.9MB, alloc=444.3MB, time=17.24 memory used=2365.3MB, alloc=468.3MB, time=18.86 memory used=2550.9MB, alloc=492.3MB, time=21.51 memory used=2764.7MB, alloc=516.3MB, time=24.04 memory used=2934.9MB, alloc=540.3MB, time=26.74 memory used=3093.8MB, alloc=564.3MB, time=30.04 memory used=3261.7MB, alloc=588.3MB, time=33.98 memory used=3440.1MB, alloc=612.3MB, time=38.83 memory used=3642.5MB, alloc=636.3MB, time=45.06 memory used=3868.8MB, alloc=660.3MB, time=50.93 memory used=4119.2MB, alloc=660.3MB, time=57.33 memory used=4369.4MB, alloc=684.3MB, time=64.48 memory used=4643.7MB, alloc=684.3MB, time=71.18 memory used=4918.1MB, alloc=708.3MB, time=77.59 N1 := 8387 > GB := Basis(F, plex(op(vars))); GB := [ 5 4 3 6 8 6 2 5 3 4 4 1296 x y + 1872 x y + 676 x y + 1782 x y + 605 x y + 1287 x y , 7 6 2 5 3 4 4 25981560 x z + 11547360 x y - 3920400 x y + 16679520 x y 3 5 2 6 7 5 2 + 12078144 x y + 6023160 x y + 10768004 x y + 21104215 x y 4 3 6 5 2 5 + 20500623 x y , -490050 x z - 217800 x y + 876095 x y z 4 3 3 4 2 5 6 + 463320 x y - 1142908 x y + 334620 x y - 711828 x y 4 2 4 3 2 3 2 2 4 - 1355211 x y , 162 x z + 72 x y + 55 x y z + 117 x y z + 52 x y , 5 4 2 4 2 4 4 3 2 -324 x z - 144 x y - 110 x y z - 104 x y + 169 x y z - 143 x y , 3 2 3 2 3 2 2 2 90 x z - 55 x z - 117 x y z - 52 x y , 5 x y z + 9 x z + 4 x y , 2 2 2 2 2 18 x z + 13 y z - 11 x z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=5219.5MB, alloc=708.3MB, time=82.04 memory used=5412.9MB, alloc=708.3MB, time=84.03 memory used=5556.3MB, alloc=708.3MB, time=85.48 memory used=5701.0MB, alloc=708.3MB, time=86.86 memory used=6035.1MB, alloc=708.3MB, time=88.70 memory used=6428.7MB, alloc=708.3MB, time=93.39 memory used=6691.4MB, alloc=708.3MB, time=94.29 memory used=6906.2MB, alloc=708.3MB, time=95.03 memory used=7089.4MB, alloc=708.3MB, time=95.73 memory used=7312.7MB, alloc=708.3MB, time=96.51 memory used=7517.7MB, alloc=708.3MB, time=97.20 memory used=7746.5MB, alloc=708.3MB, time=97.92 memory used=8176.8MB, alloc=708.3MB, time=135.55 memory used=8398.2MB, alloc=708.3MB, time=136.52 memory used=8629.1MB, alloc=708.3MB, time=137.30 memory used=8828.1MB, alloc=708.3MB, time=138.03 memory used=9028.8MB, alloc=708.3MB, time=138.74 memory used=9219.8MB, alloc=708.3MB, time=139.44 memory used=9440.8MB, alloc=708.3MB, time=140.20 memory used=9649.5MB, alloc=708.3MB, time=140.91 memory used=9856.6MB, alloc=708.3MB, time=141.63 memory used=10088.1MB, alloc=708.3MB, time=142.34 memory used=10301.4MB, alloc=708.3MB, time=143.06 memory used=10526.6MB, alloc=708.3MB, time=143.79 memory used=10753.4MB, alloc=708.3MB, time=144.50 memory used=11047.3MB, alloc=708.3MB, time=145.84 memory used=11388.0MB, alloc=708.3MB, time=147.00 memory used=11674.2MB, alloc=708.3MB, time=147.70 memory used=11869.1MB, alloc=708.3MB, time=149.46 memory used=11989.0MB, alloc=708.3MB, time=150.63 memory used=12081.4MB, alloc=708.3MB, time=151.77 memory used=12215.7MB, alloc=708.3MB, time=152.96 memory used=12459.3MB, alloc=708.3MB, time=162.05 memory used=12644.9MB, alloc=708.3MB, time=166.27 memory used=12947.0MB, alloc=732.3MB, time=178.18 memory used=13236.2MB, alloc=732.3MB, time=230.72 memory used=13549.1MB, alloc=732.3MB, time=231.45 memory used=13705.1MB, alloc=732.3MB, time=232.10 memory used=14081.6MB, alloc=732.3MB, time=401.96 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428547162 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 F := [17 x y z - 9 x z - 19 x z, -18 y z + 4 x z - 10] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 G := [-y z - 10 x y + 19 x z, -12 x y z - 2 x - 10 x y z] > Problem := [F,G]; 2 2 3 2 Problem := [[17 x y z - 9 x z - 19 x z, -18 y z + 4 x z - 10], 2 2 2 3 [-y z - 10 x y + 19 x z, -12 x y z - 2 x - 10 x y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.14 memory used=26.5MB, alloc=32.3MB, time=0.42 memory used=46.2MB, alloc=56.3MB, time=0.70 memory used=87.1MB, alloc=60.3MB, time=1.27 memory used=125.7MB, alloc=84.3MB, time=1.63 memory used=165.1MB, alloc=84.3MB, time=2.00 memory used=229.5MB, alloc=92.3MB, time=2.61 memory used=295.3MB, alloc=116.3MB, time=3.24 memory used=361.8MB, alloc=116.3MB, time=3.83 memory used=430.1MB, alloc=372.3MB, time=4.43 memory used=516.5MB, alloc=396.3MB, time=5.24 memory used=625.8MB, alloc=420.3MB, time=6.34 memory used=758.1MB, alloc=420.3MB, time=7.68 memory used=884.9MB, alloc=444.3MB, time=8.92 memory used=1035.9MB, alloc=444.3MB, time=10.04 memory used=1181.0MB, alloc=468.3MB, time=11.43 memory used=1305.2MB, alloc=468.3MB, time=12.59 memory used=1416.1MB, alloc=468.3MB, time=13.58 memory used=1541.3MB, alloc=492.3MB, time=14.89 memory used=1659.6MB, alloc=492.3MB, time=16.17 memory used=1772.5MB, alloc=516.3MB, time=17.30 memory used=1885.6MB, alloc=516.3MB, time=18.47 memory used=1988.8MB, alloc=516.3MB, time=19.53 memory used=2119.0MB, alloc=516.3MB, time=20.32 memory used=2283.6MB, alloc=516.3MB, time=21.56 memory used=2405.0MB, alloc=516.3MB, time=22.02 memory used=2492.9MB, alloc=516.3MB, time=22.34 memory used=2631.5MB, alloc=540.3MB, time=23.42 memory used=2820.8MB, alloc=540.3MB, time=24.04 memory used=2981.5MB, alloc=540.3MB, time=24.49 memory used=3176.0MB, alloc=540.3MB, time=25.13 memory used=3349.8MB, alloc=540.3MB, time=25.67 memory used=3542.4MB, alloc=540.3MB, time=26.15 memory used=3800.8MB, alloc=540.3MB, time=26.71 memory used=4107.9MB, alloc=540.3MB, time=27.31 memory used=4379.1MB, alloc=540.3MB, time=28.87 memory used=4583.1MB, alloc=540.3MB, time=29.57 memory used=4766.6MB, alloc=540.3MB, time=30.09 memory used=5005.2MB, alloc=564.3MB, time=31.38 memory used=5237.1MB, alloc=564.3MB, time=33.77 memory used=5435.1MB, alloc=564.3MB, time=35.71 memory used=5703.3MB, alloc=564.3MB, time=37.17 memory used=5933.8MB, alloc=564.3MB, time=38.08 memory used=6203.2MB, alloc=564.3MB, time=39.50 memory used=6430.9MB, alloc=564.3MB, time=40.43 memory used=6708.6MB, alloc=564.3MB, time=41.95 memory used=6989.0MB, alloc=564.3MB, time=43.47 memory used=7209.0MB, alloc=564.3MB, time=44.33 memory used=7495.9MB, alloc=564.3MB, time=45.57 memory used=7792.7MB, alloc=564.3MB, time=46.88 memory used=8091.1MB, alloc=564.3MB, time=48.07 memory used=8373.2MB, alloc=588.3MB, time=49.64 memory used=8653.7MB, alloc=588.3MB, time=51.30 memory used=8885.7MB, alloc=588.3MB, time=52.83 memory used=9115.8MB, alloc=588.3MB, time=54.57 memory used=9326.9MB, alloc=588.3MB, time=56.41 memory used=9549.7MB, alloc=588.3MB, time=57.83 memory used=9681.3MB, alloc=588.3MB, time=59.24 memory used=9809.9MB, alloc=612.3MB, time=60.45 memory used=9940.2MB, alloc=612.3MB, time=61.86 memory used=10053.4MB, alloc=612.3MB, time=63.21 memory used=10180.9MB, alloc=636.3MB, time=64.63 memory used=10301.3MB, alloc=636.3MB, time=66.02 memory used=10409.0MB, alloc=660.3MB, time=67.35 memory used=10671.8MB, alloc=660.3MB, time=68.86 memory used=10834.3MB, alloc=660.3MB, time=70.29 memory used=11001.8MB, alloc=660.3MB, time=71.72 memory used=11259.4MB, alloc=684.3MB, time=73.26 memory used=11377.5MB, alloc=684.3MB, time=74.67 memory used=11490.8MB, alloc=684.3MB, time=76.06 memory used=11598.5MB, alloc=684.3MB, time=77.42 memory used=11700.8MB, alloc=708.3MB, time=78.76 memory used=11801.5MB, alloc=708.3MB, time=80.08 memory used=11899.2MB, alloc=708.3MB, time=81.41 memory used=11987.3MB, alloc=732.3MB, time=82.81 memory used=12126.9MB, alloc=756.3MB, time=90.02 memory used=12514.7MB, alloc=756.3MB, time=120.48 memory used=12694.4MB, alloc=756.3MB, time=121.12 memory used=12894.8MB, alloc=756.3MB, time=121.73 memory used=13244.8MB, alloc=756.3MB, time=152.79 memory used=13334.4MB, alloc=756.3MB, time=154.01 memory used=13414.6MB, alloc=756.3MB, time=155.05 memory used=13525.7MB, alloc=756.3MB, time=156.38 memory used=13677.5MB, alloc=756.3MB, time=157.66 memory used=13803.3MB, alloc=756.3MB, time=158.91 memory used=13899.9MB, alloc=756.3MB, time=160.10 memory used=14398.3MB, alloc=780.3MB, time=197.69 memory used=14582.3MB, alloc=780.3MB, time=198.41 memory used=14804.4MB, alloc=780.3MB, time=199.14 memory used=15255.6MB, alloc=780.3MB, time=230.59 memory used=15613.9MB, alloc=804.3MB, time=234.52 memory used=16004.8MB, alloc=828.3MB, time=238.68 memory used=16400.2MB, alloc=852.3MB, time=242.59 memory used=16881.3MB, alloc=876.3MB, time=246.86 memory used=17370.5MB, alloc=900.3MB, time=251.45 memory used=17827.3MB, alloc=924.3MB, time=255.59 memory used=18348.7MB, alloc=948.3MB, time=260.31 memory used=18910.5MB, alloc=972.3MB, time=265.33 memory used=19507.4MB, alloc=996.3MB, time=270.24 memory used=20113.4MB, alloc=1020.3MB, time=275.62 memory used=20730.5MB, alloc=1044.3MB, time=281.22 memory used=21347.2MB, alloc=1068.3MB, time=287.27 memory used=22020.2MB, alloc=1092.3MB, time=292.24 memory used=22714.4MB, alloc=1116.3MB, time=297.19 memory used=23462.0MB, alloc=1140.3MB, time=301.69 memory used=24220.3MB, alloc=1164.3MB, time=306.46 memory used=25030.6MB, alloc=1188.3MB, time=311.11 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428547462 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 4 2 2 F := [-2 y z - 18 x y + 17 z , 17 y + 8 y z + 3 x ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 G := [-x y z - 13 x y, -11 x z - 3 x z - 18 y] > Problem := [F,G]; 3 2 3 4 2 2 Problem := [[-2 y z - 18 x y + 17 z , 17 y + 8 y z + 3 x ], 3 [-x y z - 13 x y, -11 x z - 3 x z - 18 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.14 memory used=26.0MB, alloc=32.3MB, time=0.40 memory used=46.1MB, alloc=60.3MB, time=0.62 memory used=107.4MB, alloc=60.7MB, time=2.14 memory used=154.5MB, alloc=60.7MB, time=2.41 memory used=193.3MB, alloc=60.7MB, time=2.53 memory used=221.0MB, alloc=60.7MB, time=2.59 memory used=243.3MB, alloc=60.7MB, time=2.64 memory used=271.4MB, alloc=60.7MB, time=2.70 memory used=310.2MB, alloc=84.7MB, time=10.67 memory used=357.3MB, alloc=84.7MB, time=26.46 memory used=404.3MB, alloc=84.7MB, time=50.72 memory used=448.3MB, alloc=84.7MB, time=64.52 memory used=520.8MB, alloc=84.7MB, time=64.72 memory used=583.4MB, alloc=84.7MB, time=64.89 memory used=646.0MB, alloc=84.7MB, time=65.08 memory used=708.0MB, alloc=84.7MB, time=65.25 memory used=770.5MB, alloc=84.7MB, time=65.44 memory used=826.8MB, alloc=84.7MB, time=65.62 memory used=864.6MB, alloc=84.7MB, time=65.69 memory used=902.5MB, alloc=84.7MB, time=65.76 memory used=942.4MB, alloc=84.7MB, time=65.83 memory used=987.6MB, alloc=84.7MB, time=65.91 memory used=1030.8MB, alloc=84.7MB, time=65.97 memory used=1067.1MB, alloc=84.7MB, time=66.03 memory used=1098.7MB, alloc=84.7MB, time=66.08 memory used=1129.7MB, alloc=84.7MB, time=66.14 memory used=1162.7MB, alloc=84.7MB, time=66.19 memory used=1197.8MB, alloc=84.7MB, time=66.24 memory used=1235.1MB, alloc=84.7MB, time=66.30 memory used=1277.1MB, alloc=84.7MB, time=66.35 memory used=1321.5MB, alloc=84.7MB, time=66.50 memory used=1393.3MB, alloc=92.7MB, time=66.85 memory used=1478.9MB, alloc=92.7MB, time=67.30 memory used=1553.4MB, alloc=92.7MB, time=68.57 memory used=1602.7MB, alloc=92.7MB, time=68.68 memory used=1638.3MB, alloc=92.7MB, time=68.75 memory used=1693.8MB, alloc=92.7MB, time=75.18 memory used=1737.7MB, alloc=116.7MB, time=90.27 memory used=1799.9MB, alloc=116.7MB, time=119.85 memory used=1888.1MB, alloc=116.7MB, time=128.72 memory used=1973.4MB, alloc=116.7MB, time=128.97 memory used=2058.4MB, alloc=116.7MB, time=129.21 memory used=2144.9MB, alloc=116.7MB, time=129.46 memory used=2220.5MB, alloc=116.7MB, time=129.65 memory used=2272.4MB, alloc=116.7MB, time=129.76 memory used=2327.1MB, alloc=116.7MB, time=129.86 memory used=2390.1MB, alloc=116.7MB, time=129.97 memory used=2443.6MB, alloc=116.7MB, time=130.05 memory used=2487.3MB, alloc=116.7MB, time=130.13 memory used=2531.0MB, alloc=116.7MB, time=130.20 memory used=2579.1MB, alloc=116.7MB, time=130.27 memory used=2632.0MB, alloc=116.7MB, time=130.34 memory used=2724.8MB, alloc=116.7MB, time=130.68 memory used=2819.6MB, alloc=116.7MB, time=131.40 memory used=2888.7MB, alloc=116.7MB, time=131.77 memory used=2998.1MB, alloc=116.7MB, time=133.94 memory used=3051.1MB, alloc=116.7MB, time=134.05 memory used=3091.9MB, alloc=116.7MB, time=134.14 memory used=3137.8MB, alloc=116.7MB, time=134.23 memory used=3196.5MB, alloc=116.7MB, time=134.32 memory used=3208.5MB, alloc=131.8MB, time=134.37 memory used=3220.7MB, alloc=131.8MB, time=134.42 memory used=3277.6MB, alloc=131.8MB, time=134.65 memory used=3345.4MB, alloc=131.8MB, time=147.13 memory used=3389.2MB, alloc=155.8MB, time=174.40 memory used=3454.3MB, alloc=155.8MB, time=220.24 memory used=3513.2MB, alloc=155.8MB, time=234.10 memory used=3591.3MB, alloc=155.8MB, time=237.38 memory used=3656.4MB, alloc=155.8MB, time=237.50 memory used=3710.5MB, alloc=155.8MB, time=237.60 memory used=3759.9MB, alloc=155.8MB, time=237.70 memory used=3813.5MB, alloc=155.8MB, time=237.79 memory used=3873.2MB, alloc=155.8MB, time=237.90 memory used=3937.8MB, alloc=155.8MB, time=238.02 memory used=4009.2MB, alloc=155.8MB, time=238.13 memory used=4076.7MB, alloc=155.8MB, time=238.24 memory used=4094.7MB, alloc=155.8MB, time=238.30 memory used=4108.4MB, alloc=155.8MB, time=238.35 memory used=4119.5MB, alloc=155.8MB, time=238.40 memory used=4128.2MB, alloc=155.8MB, time=238.45 memory used=4136.2MB, alloc=155.8MB, time=238.50 memory used=4144.4MB, alloc=155.8MB, time=238.55 memory used=4152.6MB, alloc=155.8MB, time=238.60 memory used=4160.9MB, alloc=155.8MB, time=238.65 memory used=4171.1MB, alloc=155.8MB, time=238.70 memory used=4181.3MB, alloc=155.8MB, time=238.75 memory used=4191.6MB, alloc=155.8MB, time=238.80 memory used=4201.8MB, alloc=155.8MB, time=238.85 memory used=4212.0MB, alloc=155.8MB, time=238.90 memory used=4222.2MB, alloc=155.8MB, time=238.95 memory used=4232.4MB, alloc=155.8MB, time=239.00 memory used=4242.6MB, alloc=155.8MB, time=239.05 memory used=4252.8MB, alloc=155.8MB, time=239.10 memory used=4262.9MB, alloc=155.8MB, time=239.15 memory used=4273.0MB, alloc=155.8MB, time=239.20 memory used=4283.1MB, alloc=155.8MB, time=239.25 memory used=4293.2MB, alloc=155.8MB, time=239.30 memory used=4303.3MB, alloc=155.8MB, time=239.35 memory used=4315.2MB, alloc=155.8MB, time=239.41 memory used=4327.1MB, alloc=155.8MB, time=239.46 memory used=4339.0MB, alloc=155.8MB, time=239.51 memory used=4350.8MB, alloc=155.8MB, time=239.57 memory used=4362.5MB, alloc=155.8MB, time=239.63 memory used=4374.2MB, alloc=155.8MB, time=239.68 memory used=4385.8MB, alloc=155.8MB, time=239.73 memory used=4397.4MB, alloc=155.8MB, time=239.78 memory used=4410.7MB, alloc=155.8MB, time=239.84 memory used=4424.0MB, alloc=155.8MB, time=239.89 memory used=4437.1MB, alloc=155.8MB, time=239.94 memory used=4450.1MB, alloc=155.8MB, time=240.00 memory used=4463.0MB, alloc=155.8MB, time=240.05 memory used=4475.7MB, alloc=155.8MB, time=240.10 memory used=4490.1MB, alloc=155.8MB, time=240.16 memory used=4504.3MB, alloc=155.8MB, time=240.21 memory used=4518.3MB, alloc=155.8MB, time=240.26 memory used=4532.3MB, alloc=155.8MB, time=240.31 memory used=4547.5MB, alloc=155.8MB, time=240.37 memory used=4562.5MB, alloc=155.8MB, time=240.42 memory used=4578.7MB, alloc=155.8MB, time=240.47 memory used=4594.6MB, alloc=155.8MB, time=240.53 memory used=4610.2MB, alloc=155.8MB, time=240.58 memory used=4626.5MB, alloc=155.8MB, time=240.64 memory used=4643.9MB, alloc=155.8MB, time=240.70 memory used=4660.7MB, alloc=155.8MB, time=240.75 memory used=4678.0MB, alloc=155.8MB, time=240.81 memory used=4696.7MB, alloc=155.8MB, time=240.86 memory used=4715.5MB, alloc=155.8MB, time=240.92 memory used=4734.9MB, alloc=155.8MB, time=240.97 memory used=4755.1MB, alloc=155.8MB, time=241.03 memory used=4773.0MB, alloc=155.8MB, time=241.08 memory used=4896.0MB, alloc=411.8MB, time=241.77 memory used=5014.0MB, alloc=411.8MB, time=243.69 memory used=5130.7MB, alloc=411.8MB, time=244.82 memory used=5235.7MB, alloc=411.8MB, time=245.44 memory used=5288.0MB, alloc=411.8MB, time=245.57 memory used=5350.0MB, alloc=411.8MB, time=245.71 memory used=5393.2MB, alloc=411.8MB, time=245.84 memory used=5442.9MB, alloc=411.8MB, time=245.95 memory used=5515.7MB, alloc=435.8MB, time=256.28 memory used=5564.9MB, alloc=459.8MB, time=282.22 memory used=5618.4MB, alloc=483.8MB, time=327.89 memory used=5677.2MB, alloc=507.8MB, time=359.54 memory used=5749.4MB, alloc=507.8MB, time=441.07 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428547762 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 4 3 2 F := [7 x z + 13 y z - 4 y, -20 x + 8 y z + 18 x z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 4 2 3 G := [10 z + 20 z , -13 x + 10 x y z - 15 x ] > Problem := [F,G]; 3 2 2 4 3 2 Problem := [[7 x z + 13 y z - 4 y, -20 x + 8 y z + 18 x z], 3 2 4 2 3 [10 z + 20 z , -13 x + 10 x y z - 15 x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.7MB, alloc=32.3MB, time=0.47 memory used=46.7MB, alloc=32.3MB, time=0.75 memory used=64.8MB, alloc=56.3MB, time=1.02 memory used=112.8MB, alloc=68.3MB, time=1.69 memory used=157.2MB, alloc=68.3MB, time=2.22 memory used=201.3MB, alloc=92.3MB, time=2.77 memory used=272.4MB, alloc=92.3MB, time=3.72 memory used=343.7MB, alloc=92.3MB, time=4.39 memory used=387.2MB, alloc=92.3MB, time=6.33 memory used=419.9MB, alloc=92.3MB, time=6.45 memory used=463.4MB, alloc=92.3MB, time=6.82 memory used=526.6MB, alloc=116.3MB, time=13.64 memory used=585.3MB, alloc=116.3MB, time=15.07 memory used=635.7MB, alloc=116.3MB, time=15.21 memory used=679.5MB, alloc=116.3MB, time=15.34 memory used=769.6MB, alloc=116.3MB, time=16.14 memory used=864.5MB, alloc=117.6MB, time=17.34 memory used=905.6MB, alloc=117.6MB, time=17.47 memory used=947.3MB, alloc=117.6MB, time=17.58 memory used=1032.0MB, alloc=117.6MB, time=18.36 memory used=1094.6MB, alloc=373.6MB, time=19.13 memory used=1185.6MB, alloc=397.6MB, time=20.21 memory used=1295.6MB, alloc=397.6MB, time=40.57 memory used=1363.1MB, alloc=397.6MB, time=42.75 memory used=1411.3MB, alloc=397.6MB, time=42.95 memory used=1468.1MB, alloc=397.6MB, time=43.15 memory used=1530.1MB, alloc=397.6MB, time=43.36 memory used=1569.0MB, alloc=397.6MB, time=43.54 memory used=1608.2MB, alloc=397.6MB, time=43.72 memory used=1648.8MB, alloc=397.6MB, time=43.88 memory used=1692.8MB, alloc=397.6MB, time=44.05 memory used=1739.3MB, alloc=397.6MB, time=44.21 memory used=1789.0MB, alloc=397.6MB, time=44.40 memory used=1842.5MB, alloc=397.6MB, time=44.57 memory used=1899.1MB, alloc=397.6MB, time=44.74 memory used=1959.9MB, alloc=397.6MB, time=44.91 memory used=2020.4MB, alloc=397.6MB, time=45.08 memory used=2058.9MB, alloc=397.6MB, time=45.23 memory used=2095.2MB, alloc=397.6MB, time=45.36 memory used=2132.0MB, alloc=397.6MB, time=45.49 memory used=2171.8MB, alloc=397.6MB, time=45.63 memory used=2309.0MB, alloc=397.6MB, time=46.57 memory used=2425.6MB, alloc=397.6MB, time=47.17 memory used=2514.4MB, alloc=397.6MB, time=47.89 memory used=2575.5MB, alloc=397.6MB, time=48.14 memory used=2673.4MB, alloc=397.6MB, time=51.25 memory used=2717.9MB, alloc=397.6MB, time=51.42 memory used=2762.1MB, alloc=397.6MB, time=51.56 memory used=2864.3MB, alloc=421.6MB, time=52.46 memory used=2994.5MB, alloc=445.6MB, time=54.17 memory used=3128.0MB, alloc=445.6MB, time=55.26 memory used=3203.6MB, alloc=445.6MB, time=55.54 memory used=3263.6MB, alloc=445.6MB, time=55.80 memory used=3327.3MB, alloc=445.6MB, time=56.03 memory used=3405.6MB, alloc=445.6MB, time=56.26 memory used=3470.2MB, alloc=445.6MB, time=56.45 memory used=3557.1MB, alloc=445.6MB, time=56.96 memory used=3635.3MB, alloc=445.6MB, time=57.22 memory used=3691.2MB, alloc=445.6MB, time=57.46 memory used=3760.8MB, alloc=445.6MB, time=57.71 memory used=3845.4MB, alloc=445.6MB, time=57.94 memory used=3926.9MB, alloc=445.6MB, time=64.90 memory used=4025.6MB, alloc=445.6MB, time=102.37 memory used=4169.6MB, alloc=445.6MB, time=104.02 memory used=4238.1MB, alloc=445.6MB, time=104.27 memory used=4304.3MB, alloc=445.6MB, time=104.53 memory used=4385.3MB, alloc=445.6MB, time=104.79 memory used=4436.0MB, alloc=445.6MB, time=104.99 memory used=4492.9MB, alloc=445.6MB, time=105.19 memory used=4555.7MB, alloc=445.6MB, time=105.38 memory used=4625.3MB, alloc=445.6MB, time=105.59 memory used=4702.5MB, alloc=445.6MB, time=105.80 memory used=4789.5MB, alloc=445.6MB, time=106.02 memory used=4948.4MB, alloc=445.6MB, time=106.49 memory used=5171.8MB, alloc=445.6MB, time=107.87 memory used=5239.0MB, alloc=445.6MB, time=108.10 memory used=5396.1MB, alloc=445.6MB, time=112.20 memory used=5462.3MB, alloc=445.6MB, time=112.45 memory used=5540.7MB, alloc=445.6MB, time=112.71 memory used=5594.4MB, alloc=445.6MB, time=112.90 memory used=5656.2MB, alloc=445.6MB, time=113.10 memory used=5728.7MB, alloc=445.6MB, time=113.30 memory used=5841.1MB, alloc=445.6MB, time=113.90 memory used=5937.9MB, alloc=445.6MB, time=114.42 memory used=6038.5MB, alloc=445.6MB, time=114.71 memory used=6174.8MB, alloc=445.6MB, time=115.90 memory used=6342.8MB, alloc=445.6MB, time=116.99 memory used=6507.8MB, alloc=445.6MB, time=118.64 memory used=6674.5MB, alloc=445.6MB, time=121.47 memory used=6839.9MB, alloc=445.6MB, time=124.44 memory used=6978.1MB, alloc=469.6MB, time=125.74 memory used=7148.0MB, alloc=469.6MB, time=127.53 memory used=7286.6MB, alloc=469.6MB, time=128.32 memory used=7386.8MB, alloc=469.6MB, time=129.23 memory used=7489.2MB, alloc=469.6MB, time=129.61 memory used=7578.8MB, alloc=469.6MB, time=132.78 memory used=7720.0MB, alloc=469.6MB, time=138.34 memory used=7813.3MB, alloc=469.6MB, time=140.94 memory used=7886.4MB, alloc=469.6MB, time=141.18 memory used=8013.5MB, alloc=469.6MB, time=141.99 memory used=8140.5MB, alloc=493.6MB, time=143.62 memory used=8229.7MB, alloc=493.6MB, time=143.90 memory used=8386.5MB, alloc=493.6MB, time=144.69 memory used=8492.5MB, alloc=493.6MB, time=145.69 memory used=8598.9MB, alloc=493.6MB, time=146.78 memory used=8698.8MB, alloc=493.6MB, time=147.23 memory used=8819.5MB, alloc=493.6MB, time=147.60 memory used=8898.2MB, alloc=493.6MB, time=147.88 memory used=9004.1MB, alloc=493.6MB, time=148.27 memory used=9075.0MB, alloc=517.6MB, time=148.58 memory used=9181.8MB, alloc=517.6MB, time=148.91 memory used=9277.3MB, alloc=517.6MB, time=149.21 memory used=9350.9MB, alloc=517.6MB, time=149.47 memory used=9432.7MB, alloc=517.6MB, time=149.74 memory used=9525.0MB, alloc=517.6MB, time=150.02 memory used=9626.0MB, alloc=517.6MB, time=150.31 memory used=9738.2MB, alloc=517.6MB, time=150.60 memory used=9864.8MB, alloc=517.6MB, time=150.90 memory used=10008.4MB, alloc=517.6MB, time=151.25 memory used=10180.2MB, alloc=517.6MB, time=194.21 memory used=10324.7MB, alloc=517.6MB, time=195.06 memory used=10416.8MB, alloc=517.6MB, time=195.40 memory used=10527.9MB, alloc=517.6MB, time=195.73 memory used=10601.0MB, alloc=517.6MB, time=196.01 memory used=10677.6MB, alloc=517.6MB, time=196.28 memory used=10763.4MB, alloc=517.6MB, time=196.57 memory used=10857.1MB, alloc=541.6MB, time=196.87 memory used=10979.4MB, alloc=541.6MB, time=197.18 memory used=11113.9MB, alloc=541.6MB, time=197.51 memory used=11319.1MB, alloc=541.6MB, time=197.93 memory used=11450.3MB, alloc=541.6MB, time=198.28 memory used=11594.6MB, alloc=541.6MB, time=198.64 memory used=11745.9MB, alloc=541.6MB, time=199.00 memory used=11904.0MB, alloc=541.6MB, time=199.36 memory used=12069.3MB, alloc=541.6MB, time=199.74 memory used=12248.5MB, alloc=541.6MB, time=200.12 memory used=12435.1MB, alloc=541.6MB, time=200.50 memory used=12628.1MB, alloc=541.6MB, time=200.90 memory used=12836.9MB, alloc=541.6MB, time=201.30 memory used=13052.1MB, alloc=541.6MB, time=201.72 memory used=13283.7MB, alloc=541.6MB, time=202.14 memory used=13495.4MB, alloc=541.6MB, time=202.53 memory used=13656.6MB, alloc=541.6MB, time=202.90 memory used=13816.1MB, alloc=541.6MB, time=203.26 memory used=13988.1MB, alloc=541.6MB, time=203.62 memory used=14163.3MB, alloc=541.6MB, time=203.99 memory used=14341.0MB, alloc=541.6MB, time=204.36 memory used=14520.9MB, alloc=541.6MB, time=204.73 memory used=14704.0MB, alloc=541.6MB, time=205.10 memory used=14898.8MB, alloc=541.6MB, time=205.50 memory used=15096.9MB, alloc=541.6MB, time=205.88 memory used=15296.9MB, alloc=541.6MB, time=206.27 memory used=15510.7MB, alloc=541.6MB, time=206.67 memory used=15726.5MB, alloc=541.6MB, time=207.06 memory used=15944.0MB, alloc=541.6MB, time=207.46 memory used=16164.7MB, alloc=541.6MB, time=207.85 memory used=16396.0MB, alloc=541.6MB, time=208.26 memory used=16596.6MB, alloc=541.6MB, time=208.65 memory used=16775.5MB, alloc=541.6MB, time=209.01 memory used=16960.8MB, alloc=541.6MB, time=209.37 memory used=17146.7MB, alloc=541.6MB, time=209.75 memory used=17333.1MB, alloc=541.6MB, time=210.11 memory used=17519.8MB, alloc=541.6MB, time=210.49 memory used=17719.3MB, alloc=541.6MB, time=210.87 memory used=17918.9MB, alloc=541.6MB, time=211.25 memory used=18118.7MB, alloc=541.6MB, time=211.63 memory used=18320.3MB, alloc=541.6MB, time=212.02 memory used=18530.2MB, alloc=541.6MB, time=212.41 memory used=18741.8MB, alloc=541.6MB, time=212.80 memory used=18965.2MB, alloc=541.6MB, time=213.22 memory used=19187.9MB, alloc=541.6MB, time=213.63 memory used=19411.3MB, alloc=541.6MB, time=214.03 memory used=19642.7MB, alloc=541.6MB, time=214.43 memory used=19854.6MB, alloc=541.6MB, time=214.81 memory used=20040.4MB, alloc=541.6MB, time=215.17 memory used=20232.1MB, alloc=541.6MB, time=215.55 memory used=20424.1MB, alloc=541.6MB, time=215.92 memory used=20623.1MB, alloc=541.6MB, time=216.28 memory used=20821.8MB, alloc=541.6MB, time=216.64 memory used=21030.3MB, alloc=541.6MB, time=217.03 memory used=21236.5MB, alloc=541.6MB, time=217.41 memory used=21451.2MB, alloc=541.6MB, time=217.80 memory used=21665.5MB, alloc=541.6MB, time=218.19 memory used=21884.3MB, alloc=541.6MB, time=218.57 memory used=22108.5MB, alloc=541.6MB, time=218.97 memory used=22340.7MB, alloc=541.6MB, time=219.35 memory used=22578.0MB, alloc=541.6MB, time=219.75 memory used=22797.2MB, alloc=541.6MB, time=220.13 memory used=23000.2MB, alloc=541.6MB, time=220.51 memory used=23208.0MB, alloc=541.6MB, time=220.88 memory used=23418.3MB, alloc=541.6MB, time=221.25 memory used=23632.1MB, alloc=541.6MB, time=221.63 memory used=23851.7MB, alloc=541.6MB, time=222.01 memory used=24076.6MB, alloc=541.6MB, time=222.39 memory used=24308.6MB, alloc=541.6MB, time=222.77 memory used=24546.4MB, alloc=541.6MB, time=223.15 memory used=24777.1MB, alloc=541.6MB, time=223.53 memory used=25054.4MB, alloc=565.6MB, time=226.80 memory used=25132.5MB, alloc=565.6MB, time=227.57 memory used=25320.6MB, alloc=589.6MB, time=383.89 memory used=25480.1MB, alloc=589.6MB, time=417.59 memory used=25797.0MB, alloc=589.6MB, time=419.35 memory used=25999.5MB, alloc=589.6MB, time=420.32 memory used=26146.9MB, alloc=589.6MB, time=420.78 memory used=26275.6MB, alloc=589.6MB, time=421.16 memory used=26381.2MB, alloc=589.6MB, time=421.49 memory used=26498.6MB, alloc=589.6MB, time=421.83 memory used=26627.0MB, alloc=589.6MB, time=422.17 memory used=26766.3MB, alloc=589.6MB, time=422.52 memory used=26916.7MB, alloc=589.6MB, time=422.88 memory used=27086.2MB, alloc=589.6MB, time=423.26 memory used=27330.3MB, alloc=589.6MB, time=423.73 memory used=27449.0MB, alloc=589.6MB, time=424.08 memory used=27575.6MB, alloc=589.6MB, time=424.44 memory used=27706.6MB, alloc=589.6MB, time=424.79 memory used=27841.9MB, alloc=589.6MB, time=425.14 memory used=27981.4MB, alloc=589.6MB, time=425.51 memory used=28125.1MB, alloc=589.6MB, time=425.87 memory used=28273.1MB, alloc=589.6MB, time=426.25 memory used=28425.7MB, alloc=589.6MB, time=426.62 memory used=28594.4MB, alloc=589.6MB, time=427.01 memory used=28768.3MB, alloc=589.6MB, time=427.39 memory used=28947.0MB, alloc=589.6MB, time=427.79 memory used=29130.1MB, alloc=589.6MB, time=428.20 memory used=29317.8MB, alloc=589.6MB, time=428.60 memory used=29509.9MB, alloc=589.6MB, time=429.00 memory used=29706.4MB, alloc=589.6MB, time=429.41 memory used=29907.1MB, alloc=589.6MB, time=429.82 memory used=30112.2MB, alloc=589.6MB, time=430.22 memory used=30321.5MB, alloc=589.6MB, time=430.63 memory used=30534.8MB, alloc=589.6MB, time=431.05 memory used=30750.7MB, alloc=589.6MB, time=431.46 memory used=30912.8MB, alloc=589.6MB, time=431.82 memory used=31061.2MB, alloc=589.6MB, time=432.18 memory used=31215.6MB, alloc=589.6MB, time=432.54 memory used=31373.7MB, alloc=589.6MB, time=432.91 memory used=31533.5MB, alloc=589.6MB, time=433.27 memory used=31695.2MB, alloc=589.6MB, time=433.64 memory used=31858.6MB, alloc=589.6MB, time=434.01 memory used=32023.8MB, alloc=589.6MB, time=434.38 memory used=32190.7MB, alloc=589.6MB, time=434.76 memory used=32359.4MB, alloc=589.6MB, time=435.13 memory used=32529.7MB, alloc=589.6MB, time=435.50 memory used=32701.6MB, alloc=589.6MB, time=435.88 memory used=32875.2MB, alloc=589.6MB, time=436.25 memory used=33050.5MB, alloc=589.6MB, time=436.63 memory used=33227.3MB, alloc=589.6MB, time=437.01 memory used=33405.7MB, alloc=589.6MB, time=437.39 memory used=33585.7MB, alloc=589.6MB, time=437.76 memory used=33767.3MB, alloc=589.6MB, time=438.14 memory used=33950.3MB, alloc=589.6MB, time=438.54 memory used=34135.8MB, alloc=589.6MB, time=438.93 memory used=34341.6MB, alloc=589.6MB, time=439.33 memory used=34550.2MB, alloc=589.6MB, time=439.74 memory used=34760.6MB, alloc=589.6MB, time=440.13 memory used=34972.7MB, alloc=589.6MB, time=440.54 memory used=35186.5MB, alloc=589.6MB, time=440.96 memory used=35401.9MB, alloc=589.6MB, time=441.36 memory used=35619.0MB, alloc=589.6MB, time=441.76 memory used=35837.8MB, alloc=589.6MB, time=442.16 memory used=36049.1MB, alloc=589.6MB, time=442.56 memory used=36229.6MB, alloc=589.6MB, time=442.94 memory used=36395.3MB, alloc=589.6MB, 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time=458.62 memory used=43963.2MB, alloc=589.6MB, time=459.00 memory used=44142.3MB, alloc=589.6MB, time=459.37 memory used=44321.7MB, alloc=589.6MB, time=459.75 memory used=44501.4MB, alloc=589.6MB, time=460.13 memory used=44681.2MB, alloc=589.6MB, time=460.51 memory used=44861.4MB, alloc=589.6MB, time=460.89 memory used=45041.8MB, alloc=589.6MB, time=461.26 memory used=45222.5MB, alloc=589.6MB, time=461.63 memory used=45403.3MB, alloc=589.6MB, time=462.01 memory used=45584.4MB, alloc=589.6MB, time=462.39 memory used=45765.6MB, alloc=589.6MB, time=462.76 memory used=45947.1MB, alloc=589.6MB, time=463.14 memory used=46128.7MB, alloc=589.6MB, time=463.53 memory used=46310.6MB, alloc=589.6MB, time=463.91 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428548062 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 4 F := [-15 x y - 6 x - 8 z , -16 x y z + 7 y - 6 y z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 3 G := [6 x z + 14 x y - 19, 7 y z - 7 z - 9] > Problem := [F,G]; 3 3 2 2 4 Problem := [[-15 x y - 6 x - 8 z , -16 x y z + 7 y - 6 y z], 3 2 2 3 [6 x z + 14 x y - 19, 7 y z - 7 z - 9]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.15 memory used=26.0MB, alloc=32.5MB, time=0.30 memory used=54.0MB, alloc=36.7MB, time=0.50 memory used=77.9MB, alloc=36.7MB, time=0.67 memory used=100.2MB, alloc=36.7MB, time=0.84 memory used=124.3MB, alloc=60.7MB, time=1.40 memory used=164.5MB, alloc=63.6MB, time=1.47 memory used=188.3MB, alloc=63.6MB, time=1.52 memory used=209.1MB, alloc=63.6MB, time=1.57 memory used=232.7MB, alloc=63.6MB, time=1.62 memory used=258.4MB, alloc=63.6MB, time=1.67 memory used=288.5MB, alloc=63.6MB, time=1.73 memory used=320.9MB, alloc=63.6MB, time=1.78 memory used=342.1MB, alloc=63.6MB, time=1.83 memory used=358.5MB, alloc=63.6MB, time=1.87 memory used=376.3MB, alloc=63.6MB, time=1.91 memory used=394.5MB, alloc=63.6MB, time=1.95 memory used=413.3MB, alloc=63.6MB, time=1.99 memory used=432.4MB, alloc=63.6MB, time=2.03 memory used=452.0MB, alloc=63.6MB, time=2.07 memory used=471.9MB, alloc=63.6MB, time=2.11 memory used=492.3MB, alloc=63.6MB, time=2.16 memory used=513.0MB, alloc=63.6MB, time=2.20 memory used=534.1MB, alloc=63.6MB, time=2.24 memory used=555.8MB, alloc=63.6MB, time=2.28 memory used=580.9MB, alloc=63.6MB, time=2.32 memory used=606.7MB, alloc=63.6MB, time=2.37 memory used=632.8MB, alloc=63.6MB, time=2.42 memory used=659.4MB, alloc=63.6MB, time=2.46 memory used=686.2MB, alloc=63.6MB, time=2.50 memory used=713.4MB, alloc=63.6MB, time=2.55 memory used=740.9MB, alloc=63.6MB, time=2.60 memory used=769.1MB, alloc=63.6MB, time=2.64 memory used=800.7MB, alloc=63.6MB, time=2.69 memory used=823.2MB, alloc=63.6MB, time=2.73 memory used=838.6MB, alloc=87.6MB, time=2.77 memory used=863.4MB, alloc=87.6MB, time=2.82 memory used=891.4MB, alloc=87.6MB, time=2.87 memory used=920.0MB, alloc=87.6MB, time=2.92 memory used=948.8MB, alloc=87.6MB, time=2.97 memory used=977.6MB, alloc=87.6MB, time=3.02 memory used=1006.5MB, alloc=87.6MB, time=3.07 memory used=1035.6MB, alloc=87.6MB, time=3.12 memory used=1068.7MB, alloc=87.6MB, time=3.17 memory used=1101.7MB, alloc=87.6MB, time=3.23 memory used=1134.8MB, alloc=87.6MB, time=3.28 memory used=1167.8MB, alloc=87.6MB, time=3.33 memory used=1204.7MB, alloc=87.6MB, time=3.38 memory used=1241.4MB, alloc=87.6MB, time=3.44 memory used=1277.9MB, alloc=87.6MB, time=3.49 memory used=1317.9MB, alloc=87.6MB, time=3.55 memory used=1357.6MB, alloc=87.6MB, time=3.60 memory used=1397.2MB, alloc=87.6MB, time=3.66 memory used=1439.2MB, alloc=87.6MB, time=3.72 memory used=1481.5MB, alloc=87.6MB, time=3.78 memory used=1525.3MB, alloc=87.6MB, time=3.84 memory used=1572.0MB, alloc=87.6MB, time=3.90 memory used=1620.5MB, alloc=87.6MB, time=3.96 memory used=1670.4MB, alloc=87.6MB, time=4.02 memory used=1723.9MB, alloc=87.6MB, time=4.08 memory used=1779.3MB, alloc=87.6MB, time=4.14 memory used=1813.2MB, alloc=107.8MB, time=4.20 memory used=1823.6MB, alloc=107.8MB, time=4.23 memory used=1834.1MB, alloc=107.8MB, time=4.26 memory used=1845.2MB, alloc=107.8MB, time=4.29 memory used=1856.7MB, alloc=107.8MB, time=4.33 memory used=1868.8MB, alloc=107.8MB, time=4.36 memory used=1881.3MB, alloc=107.8MB, time=4.39 memory used=1893.5MB, alloc=107.8MB, time=4.42 memory used=1906.8MB, alloc=107.8MB, time=4.45 memory used=1950.9MB, alloc=107.8MB, time=5.02 memory used=2000.0MB, alloc=107.8MB, time=5.12 memory used=2041.4MB, alloc=107.8MB, time=5.20 memory used=2090.4MB, alloc=107.8MB, time=5.30 memory used=2142.3MB, alloc=107.8MB, time=5.38 memory used=2172.0MB, alloc=107.8MB, time=5.45 memory used=2204.6MB, alloc=107.8MB, time=5.53 memory used=2239.8MB, alloc=107.8MB, time=5.59 memory used=2276.3MB, alloc=107.8MB, time=5.66 memory used=2314.3MB, alloc=107.8MB, time=5.74 memory used=2357.0MB, alloc=107.8MB, time=5.83 memory used=2401.0MB, alloc=107.8MB, time=5.91 memory used=2446.5MB, alloc=107.8MB, time=5.99 memory used=2496.8MB, alloc=107.8MB, time=6.09 memory used=2548.3MB, alloc=107.8MB, time=6.18 memory used=2604.9MB, alloc=107.8MB, time=6.25 memory used=2641.5MB, alloc=107.8MB, time=6.31 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used=3436.0MB, alloc=107.8MB, time=7.54 memory used=3488.1MB, alloc=107.8MB, time=7.60 memory used=3541.1MB, alloc=107.8MB, time=7.66 memory used=3596.7MB, alloc=107.8MB, time=7.73 memory used=3620.5MB, alloc=107.8MB, time=7.77 memory used=3630.8MB, alloc=107.8MB, time=7.80 memory used=3641.4MB, alloc=107.8MB, time=7.83 memory used=3652.5MB, alloc=107.8MB, time=7.87 memory used=3663.9MB, alloc=107.8MB, time=7.90 memory used=3676.0MB, alloc=107.8MB, time=7.93 memory used=3688.6MB, alloc=107.8MB, time=7.97 memory used=3700.8MB, alloc=107.8MB, time=8.00 memory used=3714.4MB, alloc=107.8MB, time=8.04 memory used=3795.9MB, alloc=107.8MB, time=27.87 memory used=3842.8MB, alloc=107.8MB, time=50.55 memory used=3897.9MB, alloc=107.8MB, time=51.70 memory used=3941.8MB, alloc=107.8MB, time=51.79 memory used=3981.1MB, alloc=107.8MB, time=51.88 memory used=4017.0MB, alloc=107.8MB, time=51.95 memory used=4058.3MB, alloc=107.8MB, time=52.02 memory used=4105.6MB, alloc=107.8MB, time=52.10 memory 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memory used=4884.7MB, alloc=107.8MB, time=53.36 memory used=4895.3MB, alloc=107.8MB, time=53.39 memory used=4905.8MB, alloc=107.8MB, time=53.43 memory used=4916.4MB, alloc=107.8MB, time=53.46 memory used=4927.0MB, alloc=107.8MB, time=53.50 memory used=4937.7MB, alloc=107.8MB, time=53.53 memory used=4948.3MB, alloc=107.8MB, time=53.57 memory used=4958.9MB, alloc=107.8MB, time=53.60 memory used=4969.5MB, alloc=107.8MB, time=53.63 memory used=4980.1MB, alloc=107.8MB, time=53.67 memory used=4990.7MB, alloc=107.8MB, time=53.71 memory used=5001.3MB, alloc=107.8MB, time=53.74 memory used=5011.9MB, alloc=107.8MB, time=53.78 memory used=5022.5MB, alloc=107.8MB, time=53.81 memory used=5033.1MB, alloc=107.8MB, time=53.84 memory used=5043.6MB, alloc=107.8MB, time=53.88 memory used=5054.2MB, alloc=107.8MB, time=53.91 memory used=5064.8MB, alloc=107.8MB, time=53.95 memory used=5075.3MB, alloc=107.8MB, time=53.98 memory used=5085.9MB, alloc=107.8MB, time=54.02 memory used=5096.6MB, alloc=107.8MB, time=54.05 memory used=5109.6MB, alloc=107.8MB, time=54.09 memory used=5122.8MB, alloc=107.8MB, time=54.13 memory used=5135.9MB, alloc=107.8MB, time=54.16 memory used=5149.0MB, alloc=107.8MB, time=54.20 memory used=5162.0MB, alloc=107.8MB, time=54.23 memory used=5175.1MB, alloc=107.8MB, time=54.27 memory used=5188.1MB, alloc=107.8MB, time=54.31 memory used=5201.1MB, alloc=107.8MB, time=54.34 memory used=5214.0MB, alloc=107.8MB, time=54.38 memory used=5226.9MB, alloc=107.8MB, time=54.42 memory used=5239.8MB, alloc=107.8MB, time=54.45 memory used=5252.6MB, alloc=107.8MB, time=54.49 memory used=5265.4MB, alloc=107.8MB, time=54.52 memory used=5278.2MB, alloc=107.8MB, time=54.56 memory used=5290.9MB, alloc=107.8MB, time=54.59 memory used=5303.8MB, alloc=107.8MB, time=54.63 memory used=5318.7MB, alloc=107.8MB, time=54.67 memory used=5333.8MB, alloc=107.8MB, time=54.70 memory used=5348.8MB, alloc=107.8MB, time=54.74 memory used=5363.7MB, alloc=107.8MB, time=54.78 memory used=5378.6MB, alloc=107.8MB, time=54.82 memory used=5393.4MB, alloc=107.8MB, time=54.86 memory used=5408.1MB, alloc=107.8MB, time=54.89 memory used=5422.6MB, alloc=107.8MB, time=54.93 memory used=5437.2MB, alloc=107.8MB, time=54.97 memory used=5451.7MB, alloc=107.8MB, time=55.00 memory used=5468.3MB, alloc=107.8MB, time=55.04 memory used=5484.8MB, alloc=107.8MB, time=55.08 memory used=5501.3MB, alloc=107.8MB, time=55.12 memory used=5517.5MB, alloc=107.8MB, time=55.16 memory used=5533.6MB, alloc=107.8MB, time=55.19 memory used=5549.6MB, alloc=107.8MB, time=55.23 memory used=5565.6MB, alloc=107.8MB, time=55.27 memory used=5583.3MB, alloc=107.8MB, time=55.31 memory used=5600.9MB, alloc=107.8MB, time=55.35 memory used=5618.3MB, alloc=107.8MB, time=55.38 memory used=5635.5MB, alloc=107.8MB, time=55.42 memory used=5652.7MB, alloc=107.8MB, time=55.46 memory used=5671.2MB, alloc=107.8MB, time=55.50 memory used=5689.6MB, alloc=107.8MB, time=55.54 memory used=5707.8MB, alloc=107.8MB, time=55.58 memory used=5727.6MB, alloc=107.8MB, time=55.62 memory used=5746.9MB, alloc=107.8MB, time=55.66 memory used=5767.6MB, alloc=107.8MB, time=55.70 memory used=5787.7MB, alloc=107.8MB, time=55.74 memory used=5808.9MB, alloc=107.8MB, time=55.78 memory used=5829.5MB, alloc=107.8MB, time=55.82 memory used=5850.9MB, alloc=107.8MB, time=55.86 memory used=5872.9MB, alloc=107.8MB, time=55.91 memory used=5895.2MB, alloc=107.8MB, time=55.95 memory used=5917.9MB, alloc=107.8MB, time=55.99 memory used=5941.3MB, alloc=107.8MB, time=56.03 memory used=5965.8MB, alloc=107.8MB, time=56.07 memory used=5987.9MB, alloc=107.8MB, time=56.11 memory used=6005.3MB, alloc=107.8MB, time=56.15 memory used=6071.7MB, alloc=107.8MB, time=56.75 memory used=6108.3MB, alloc=107.8MB, time=56.84 memory used=6153.1MB, alloc=107.8MB, time=56.93 memory used=6205.3MB, alloc=107.8MB, time=57.02 memory used=6245.4MB, alloc=107.8MB, time=57.10 memory used=6277.2MB, alloc=107.8MB, time=57.18 memory used=6311.7MB, alloc=107.8MB, time=57.27 memory used=6347.5MB, alloc=107.8MB, time=57.34 memory used=6384.8MB, alloc=107.8MB, time=57.40 memory used=6423.5MB, alloc=107.8MB, time=57.48 memory used=6466.9MB, alloc=107.8MB, time=57.55 memory used=6511.5MB, alloc=107.8MB, time=57.62 memory used=6557.5MB, alloc=107.8MB, time=57.69 memory used=6608.3MB, alloc=107.8MB, time=57.76 memory used=6660.4MB, alloc=107.8MB, time=57.84 memory used=6712.1MB, alloc=107.8MB, time=57.92 memory used=6740.5MB, alloc=107.8MB, time=57.98 memory used=6766.8MB, alloc=107.8MB, time=58.03 memory used=6795.3MB, alloc=107.8MB, time=58.08 memory used=6824.0MB, alloc=107.8MB, time=58.13 memory used=6852.8MB, alloc=107.8MB, time=58.18 memory used=6881.7MB, alloc=107.8MB, time=58.24 memory used=6910.7MB, alloc=107.8MB, time=58.29 memory used=6943.8MB, alloc=107.8MB, time=58.34 memory used=6976.9MB, alloc=107.8MB, time=58.40 memory used=7010.0MB, alloc=107.8MB, time=58.45 memory used=7043.0MB, alloc=107.8MB, time=58.51 memory used=7076.4MB, alloc=107.8MB, time=58.56 memory used=7112.7MB, alloc=107.8MB, time=58.61 memory used=7149.3MB, alloc=107.8MB, time=58.67 memory used=7186.1MB, alloc=107.8MB, time=58.73 memory used=7225.7MB, alloc=107.8MB, time=58.78 memory used=7265.4MB, alloc=107.8MB, time=58.84 memory used=7308.2MB, alloc=107.8MB, time=58.90 memory used=7350.4MB, alloc=107.8MB, time=58.96 memory used=7395.3MB, alloc=107.8MB, time=59.02 memory used=7442.8MB, alloc=107.8MB, time=59.08 memory used=7489.7MB, alloc=107.8MB, time=59.14 memory used=7540.1MB, alloc=107.8MB, time=59.20 memory used=7591.8MB, alloc=107.8MB, time=59.27 memory used=7646.7MB, alloc=107.8MB, time=59.33 memory used=7708.3MB, alloc=107.8MB, time=59.40 memory used=7718.9MB, alloc=107.8MB, time=59.43 memory used=7729.4MB, alloc=107.8MB, time=59.47 memory used=7740.5MB, alloc=107.8MB, time=59.50 memory used=7752.0MB, alloc=107.8MB, time=59.53 memory used=7764.1MB, alloc=107.8MB, time=59.57 memory used=7776.6MB, alloc=107.8MB, time=59.60 memory used=7789.5MB, alloc=107.8MB, time=59.63 memory used=7803.1MB, alloc=107.8MB, time=59.67 memory used=7858.4MB, alloc=107.8MB, time=60.25 memory used=7901.5MB, alloc=107.8MB, time=60.34 memory used=7943.4MB, alloc=107.8MB, time=60.42 memory used=7993.5MB, alloc=107.8MB, time=60.51 memory used=8042.0MB, alloc=107.8MB, time=60.59 memory used=8072.3MB, alloc=107.8MB, time=60.68 memory used=8103.1MB, alloc=107.8MB, time=60.74 memory used=8138.1MB, alloc=107.8MB, time=60.83 memory used=8174.7MB, alloc=107.8MB, time=60.91 memory used=8212.7MB, alloc=107.8MB, time=60.99 memory used=8252.3MB, alloc=107.8MB, time=61.06 memory used=8296.0MB, alloc=107.8MB, time=61.14 memory used=8341.4MB, alloc=107.8MB, time=61.22 memory used=8391.7MB, alloc=107.8MB, time=61.30 memory used=8443.2MB, alloc=107.8MB, time=61.39 memory used=8496.0MB, alloc=107.8MB, time=61.47 memory used=8534.6MB, alloc=107.8MB, time=61.54 memory used=8561.7MB, alloc=107.8MB, time=61.59 memory used=8590.1MB, alloc=107.8MB, time=61.64 memory used=8618.7MB, alloc=107.8MB, time=61.69 memory used=8647.5MB, alloc=107.8MB, time=61.75 memory used=8676.3MB, alloc=107.8MB, time=61.80 memory used=8705.2MB, alloc=107.8MB, time=61.85 memory used=8734.6MB, alloc=107.8MB, time=61.90 memory used=8767.4MB, alloc=107.8MB, time=61.96 memory used=8800.4MB, alloc=107.8MB, time=62.01 memory used=8833.5MB, alloc=107.8MB, time=62.07 memory used=8866.5MB, alloc=107.8MB, time=62.12 memory used=8903.5MB, alloc=107.8MB, time=62.18 memory used=8940.2MB, alloc=107.8MB, time=62.23 memory used=8976.6MB, alloc=107.8MB, time=62.29 memory used=9016.8MB, alloc=107.8MB, time=62.35 memory used=9056.5MB, alloc=107.8MB, time=62.40 memory used=9096.2MB, alloc=107.8MB, time=62.46 memory used=9138.3MB, alloc=107.8MB, time=62.52 memory used=9180.7MB, alloc=107.8MB, time=62.58 memory used=9225.0MB, alloc=107.8MB, time=62.63 memory used=9271.2MB, alloc=107.8MB, time=62.70 memory used=9320.0MB, alloc=107.8MB, time=62.75 memory used=9370.1MB, alloc=107.8MB, time=62.82 memory used=9423.8MB, alloc=107.8MB, time=62.88 memory used=9479.5MB, alloc=107.8MB, time=62.94 memory used=9515.7MB, alloc=107.8MB, time=63.00 memory used=9526.1MB, alloc=107.8MB, time=63.03 memory used=9536.7MB, alloc=107.8MB, time=63.06 memory used=9547.7MB, alloc=107.8MB, time=63.09 memory used=9559.2MB, alloc=107.8MB, time=63.13 memory used=9570.3MB, alloc=107.8MB, time=63.16 memory used=9581.7MB, alloc=107.8MB, time=63.19 memory used=9593.5MB, alloc=107.8MB, time=63.23 memory used=9606.7MB, alloc=107.8MB, time=63.26 memory used=9623.2MB, alloc=107.8MB, time=63.36 memory used=9695.4MB, alloc=107.8MB, time=83.15 memory used=9741.6MB, alloc=107.8MB, time=106.04 memory used=9804.4MB, alloc=107.8MB, time=107.11 memory used=9853.3MB, alloc=107.8MB, time=107.19 memory used=9887.4MB, alloc=107.8MB, time=107.26 memory used=9925.0MB, alloc=107.8MB, time=107.33 memory used=9967.6MB, alloc=107.8MB, time=107.42 memory used=10016.3MB, alloc=107.8MB, time=107.51 memory used=10068.3MB, alloc=107.8MB, time=107.58 memory used=10098.0MB, alloc=107.8MB, time=107.64 memory used=10127.7MB, alloc=107.8MB, time=107.69 memory used=10159.1MB, alloc=107.8MB, time=107.74 memory used=10191.4MB, alloc=107.8MB, time=107.80 memory used=10224.6MB, alloc=107.8MB, time=107.86 memory used=10260.9MB, alloc=107.8MB, time=107.92 memory used=10298.1MB, alloc=107.8MB, time=107.97 memory used=10336.1MB, alloc=107.8MB, time=108.03 memory used=10377.4MB, alloc=107.8MB, time=108.09 memory used=10419.5MB, alloc=107.8MB, time=108.15 memory used=10462.4MB, alloc=107.8MB, time=108.21 memory used=10508.5MB, alloc=107.8MB, time=108.28 memory used=10555.3MB, alloc=107.8MB, time=108.34 memory used=10605.2MB, alloc=107.8MB, time=108.40 memory used=10655.7MB, alloc=107.8MB, time=108.47 memory used=10709.4MB, alloc=107.8MB, time=108.54 memory used=10738.7MB, alloc=107.8MB, time=108.59 memory used=10749.8MB, alloc=107.8MB, time=108.62 memory used=10759.5MB, alloc=107.8MB, time=108.66 memory used=10770.0MB, alloc=107.8MB, time=108.69 memory used=10780.6MB, alloc=107.8MB, time=108.73 memory used=10791.2MB, alloc=107.8MB, time=108.77 memory used=10801.8MB, alloc=107.8MB, time=108.80 memory used=10812.4MB, alloc=107.8MB, time=108.84 memory used=10823.0MB, alloc=107.8MB, time=108.88 memory used=10833.6MB, alloc=107.8MB, time=108.91 memory used=10844.2MB, alloc=107.8MB, time=108.95 memory used=10854.8MB, alloc=107.8MB, time=108.98 memory used=10865.4MB, alloc=107.8MB, time=109.02 memory used=10876.0MB, alloc=107.8MB, time=109.05 memory used=10886.6MB, alloc=107.8MB, time=109.09 memory used=10897.2MB, alloc=107.8MB, time=109.12 memory used=10907.8MB, alloc=107.8MB, time=109.15 memory used=10918.4MB, alloc=107.8MB, time=109.19 memory used=10929.0MB, alloc=107.8MB, time=109.22 memory used=10939.6MB, alloc=107.8MB, time=109.26 memory used=10950.1MB, alloc=107.8MB, time=109.29 memory used=10960.7MB, alloc=107.8MB, time=109.33 memory used=10971.3MB, alloc=107.8MB, time=109.36 memory used=10981.8MB, alloc=107.8MB, time=109.40 memory used=10992.5MB, alloc=107.8MB, time=109.43 memory used=11005.5MB, alloc=107.8MB, time=109.47 memory used=11018.7MB, alloc=107.8MB, time=109.50 memory used=11031.8MB, alloc=107.8MB, time=109.54 memory used=11044.9MB, alloc=107.8MB, time=109.58 memory used=11058.0MB, alloc=107.8MB, time=109.61 memory used=11071.0MB, alloc=107.8MB, time=109.65 memory used=11084.0MB, alloc=107.8MB, time=109.69 memory used=11097.0MB, alloc=107.8MB, time=109.72 memory used=11109.9MB, alloc=107.8MB, time=109.76 memory used=11122.9MB, alloc=107.8MB, time=109.80 memory used=11135.7MB, alloc=107.8MB, time=109.83 memory used=11148.6MB, alloc=107.8MB, time=109.87 memory used=11161.4MB, alloc=107.8MB, time=109.91 memory used=11174.1MB, alloc=107.8MB, time=109.94 memory used=11186.8MB, alloc=107.8MB, time=109.98 memory used=11199.7MB, alloc=107.8MB, time=110.01 memory used=11214.7MB, alloc=107.8MB, time=110.05 memory used=11229.7MB, alloc=107.8MB, time=110.09 memory used=11244.7MB, alloc=107.8MB, time=110.12 memory used=11259.7MB, alloc=107.8MB, time=110.16 memory used=11274.5MB, alloc=107.8MB, time=110.20 memory used=11289.3MB, alloc=107.8MB, time=110.24 memory used=11304.0MB, alloc=107.8MB, time=110.28 memory used=11318.6MB, alloc=107.8MB, time=110.31 memory used=11333.1MB, alloc=107.8MB, time=110.35 memory used=11347.7MB, alloc=107.8MB, time=110.39 memory used=11364.2MB, alloc=107.8MB, time=110.43 memory used=11380.8MB, alloc=107.8MB, time=110.46 memory used=11397.2MB, alloc=107.8MB, time=110.50 memory used=11413.4MB, alloc=107.8MB, time=110.54 memory used=11429.6MB, alloc=107.8MB, time=110.58 memory used=11445.5MB, alloc=107.8MB, time=110.62 memory used=11461.5MB, alloc=107.8MB, time=110.66 memory used=11479.2MB, alloc=107.8MB, time=110.70 memory used=11496.9MB, alloc=107.8MB, time=110.74 memory used=11514.3MB, alloc=107.8MB, time=110.78 memory used=11531.5MB, alloc=107.8MB, time=110.81 memory used=11548.6MB, alloc=107.8MB, time=110.85 memory used=11567.1MB, alloc=107.8MB, time=110.89 memory used=11585.6MB, alloc=107.8MB, time=110.93 memory used=11603.7MB, alloc=107.8MB, time=110.97 memory used=11623.5MB, alloc=107.8MB, time=111.01 memory used=11642.9MB, alloc=107.8MB, time=111.05 memory used=11663.5MB, alloc=107.8MB, time=111.09 memory used=11683.6MB, alloc=107.8MB, time=111.13 memory used=11704.9MB, alloc=107.8MB, time=111.17 memory used=11725.4MB, alloc=107.8MB, time=111.21 memory used=11746.8MB, alloc=107.8MB, time=111.25 memory used=11768.8MB, alloc=107.8MB, time=111.29 memory used=11791.2MB, alloc=107.8MB, time=111.34 memory used=11813.8MB, alloc=107.8MB, time=111.38 memory used=11837.2MB, alloc=107.8MB, time=111.42 memory used=11861.0MB, alloc=107.8MB, time=111.46 memory used=11883.6MB, alloc=107.8MB, time=111.50 memory used=11900.7MB, alloc=107.8MB, time=111.54 memory used=11953.4MB, alloc=107.8MB, time=111.68 memory used=11997.9MB, alloc=107.8MB, time=111.76 memory used=12038.5MB, alloc=107.8MB, time=111.83 memory used=12116.6MB, alloc=107.8MB, time=115.73 memory used=12162.7MB, alloc=107.8MB, time=115.81 memory used=12199.3MB, alloc=107.8MB, time=115.89 memory used=12245.6MB, alloc=107.8MB, time=115.98 memory used=12295.5MB, alloc=107.8MB, time=116.05 memory used=12327.0MB, alloc=107.8MB, time=116.10 memory used=12360.6MB, alloc=107.8MB, time=116.16 memory used=12397.8MB, alloc=107.8MB, time=116.21 memory used=12438.5MB, alloc=107.8MB, time=116.27 memory used=12482.4MB, alloc=107.8MB, time=116.33 memory used=12530.3MB, alloc=107.8MB, time=116.39 memory used=12582.9MB, alloc=107.8MB, time=116.45 memory used=12632.6MB, alloc=107.8MB, time=116.52 memory used=12644.6MB, alloc=107.8MB, time=116.55 memory used=12657.2MB, alloc=107.8MB, time=116.59 memory used=12670.5MB, alloc=107.8MB, time=116.62 memory used=12684.3MB, alloc=107.8MB, time=116.66 memory used=12698.4MB, alloc=107.8MB, time=116.70 memory used=12712.8MB, alloc=107.8MB, time=116.73 memory used=12727.9MB, alloc=107.8MB, time=116.77 memory used=12743.5MB, alloc=107.8MB, time=116.81 memory used=12760.1MB, alloc=107.8MB, time=116.85 memory used=12811.8MB, alloc=107.8MB, time=117.14 memory used=12884.0MB, alloc=107.8MB, time=126.47 memory used=12922.0MB, alloc=107.8MB, time=153.36 memory used=12964.8MB, alloc=107.8MB, time=168.24 memory used=13009.6MB, alloc=107.8MB, time=190.71 memory used=13087.8MB, alloc=107.8MB, time=192.12 memory used=13151.2MB, alloc=107.8MB, time=192.30 memory used=13195.4MB, alloc=107.8MB, time=192.37 memory used=13229.4MB, alloc=107.8MB, time=192.47 memory used=13262.2MB, alloc=107.8MB, time=192.55 memory used=13298.5MB, alloc=107.8MB, time=192.64 memory used=13338.3MB, alloc=107.8MB, time=192.73 memory used=13383.0MB, alloc=107.8MB, time=192.80 memory used=13431.2MB, alloc=107.8MB, time=192.88 memory used=13465.3MB, alloc=107.8MB, time=192.95 memory used=13491.7MB, alloc=107.8MB, time=193.00 memory used=13519.3MB, alloc=107.8MB, time=193.06 memory used=13547.9MB, alloc=107.8MB, time=193.12 memory used=13577.2MB, alloc=107.8MB, time=193.18 memory used=13607.1MB, alloc=107.8MB, time=193.23 memory used=13637.7MB, alloc=107.8MB, time=193.29 memory used=13669.1MB, alloc=107.8MB, time=193.34 memory used=13703.7MB, alloc=107.8MB, time=193.40 memory used=13738.9MB, alloc=107.8MB, time=193.46 memory used=13774.9MB, alloc=107.8MB, time=193.52 memory used=13811.4MB, alloc=107.8MB, time=193.58 memory used=13848.7MB, alloc=107.8MB, time=193.64 memory used=13889.4MB, alloc=107.8MB, time=193.70 memory used=13930.7MB, alloc=107.8MB, time=193.76 memory used=13972.6MB, alloc=107.8MB, time=193.83 memory used=14015.1MB, alloc=107.8MB, time=193.89 memory used=14061.2MB, alloc=107.8MB, time=193.95 memory used=14107.8MB, alloc=107.8MB, time=194.02 memory used=14154.9MB, alloc=107.8MB, time=194.08 memory used=14210.4MB, alloc=107.8MB, time=194.16 memory used=14219.0MB, alloc=107.8MB, time=194.19 memory used=14225.5MB, alloc=107.8MB, time=194.22 memory used=14230.9MB, alloc=107.8MB, time=194.26 memory used=14236.4MB, alloc=107.8MB, time=194.29 memory used=14242.3MB, alloc=107.8MB, time=194.32 memory used=14248.3MB, alloc=107.8MB, time=194.35 memory used=14254.6MB, alloc=107.8MB, time=194.39 memory used=14260.9MB, alloc=107.8MB, time=194.42 memory used=14267.2MB, alloc=107.8MB, time=194.46 memory used=14273.6MB, alloc=107.8MB, time=194.49 memory used=14279.9MB, alloc=107.8MB, time=194.53 memory used=14286.2MB, alloc=107.8MB, time=194.57 memory used=14292.6MB, alloc=107.8MB, time=194.61 memory used=14298.9MB, alloc=107.8MB, time=194.65 memory used=14305.2MB, alloc=107.8MB, time=194.69 memory used=14311.6MB, alloc=107.8MB, time=194.73 memory used=14317.9MB, alloc=107.8MB, time=194.77 memory used=14324.3MB, alloc=107.8MB, time=194.81 memory used=14330.7MB, alloc=107.8MB, time=194.84 memory used=14337.0MB, alloc=107.8MB, time=194.88 memory used=14343.4MB, alloc=107.8MB, time=194.92 memory used=14349.8MB, alloc=107.8MB, time=194.96 memory used=14356.1MB, alloc=107.8MB, time=195.00 memory used=14362.5MB, alloc=107.8MB, time=195.04 memory used=14368.9MB, alloc=107.8MB, time=195.08 memory used=14375.3MB, alloc=107.8MB, time=195.12 memory used=14381.7MB, alloc=107.8MB, time=195.15 memory used=14388.1MB, alloc=107.8MB, time=195.19 memory used=14394.5MB, alloc=107.8MB, time=195.22 memory used=14400.9MB, alloc=107.8MB, time=195.25 memory used=14407.3MB, alloc=107.8MB, time=195.28 memory used=14413.7MB, alloc=107.8MB, time=195.32 memory used=14420.1MB, alloc=107.8MB, time=195.35 memory used=14426.5MB, alloc=107.8MB, time=195.39 memory used=14432.9MB, alloc=107.8MB, time=195.42 memory used=14439.3MB, alloc=107.8MB, time=195.45 memory used=14445.8MB, alloc=107.8MB, time=195.49 memory used=14452.2MB, alloc=107.8MB, time=195.52 memory used=14458.6MB, alloc=107.8MB, time=195.55 memory used=14465.0MB, alloc=107.8MB, time=195.58 memory used=14471.4MB, alloc=107.8MB, time=195.62 memory used=14477.9MB, alloc=107.8MB, time=195.65 memory used=14484.3MB, alloc=107.8MB, time=195.69 memory used=14490.7MB, alloc=107.8MB, time=195.72 memory used=14497.2MB, alloc=107.8MB, time=195.75 memory used=14503.6MB, alloc=107.8MB, time=195.78 memory used=14510.0MB, alloc=107.8MB, time=195.81 memory used=14516.5MB, alloc=107.8MB, time=195.85 memory used=14522.9MB, alloc=107.8MB, time=195.88 memory used=14529.3MB, alloc=107.8MB, time=195.91 memory used=14535.8MB, alloc=107.8MB, time=195.94 memory used=14542.2MB, alloc=107.8MB, time=195.98 memory used=14548.6MB, alloc=107.8MB, time=196.01 memory used=14555.1MB, alloc=107.8MB, time=196.04 memory used=14561.5MB, alloc=107.8MB, time=196.07 memory used=14567.9MB, alloc=107.8MB, time=196.11 memory used=14574.4MB, alloc=107.8MB, time=196.14 memory used=14580.8MB, alloc=107.8MB, time=196.17 memory used=14587.3MB, alloc=107.8MB, time=196.20 memory used=14593.7MB, alloc=107.8MB, time=196.24 memory used=14600.1MB, alloc=107.8MB, time=196.27 memory used=14606.6MB, alloc=107.8MB, time=196.30 memory used=14613.0MB, alloc=107.8MB, time=196.34 memory used=14619.4MB, alloc=107.8MB, time=196.37 memory used=14625.9MB, alloc=107.8MB, time=196.40 memory used=14632.3MB, alloc=107.8MB, time=196.43 memory used=14638.7MB, alloc=107.8MB, time=196.47 memory used=14645.2MB, alloc=107.8MB, time=196.50 memory used=14651.6MB, alloc=107.8MB, time=196.53 memory used=14658.0MB, alloc=107.8MB, time=196.56 memory used=14664.4MB, alloc=107.8MB, time=196.60 memory used=14670.9MB, alloc=107.8MB, time=196.63 memory used=14677.3MB, alloc=107.8MB, time=196.66 memory used=14683.7MB, alloc=107.8MB, time=196.69 memory used=14690.1MB, alloc=107.8MB, time=196.73 memory used=14696.5MB, alloc=107.8MB, time=196.76 memory used=14702.9MB, alloc=107.8MB, time=196.79 memory used=14709.4MB, alloc=107.8MB, time=196.83 memory used=14715.8MB, alloc=107.8MB, time=196.86 memory used=14722.2MB, alloc=107.8MB, time=196.89 memory used=14728.6MB, alloc=107.8MB, time=196.92 memory used=14735.0MB, alloc=107.8MB, time=196.96 memory used=14741.4MB, alloc=107.8MB, time=196.99 memory used=14747.7MB, alloc=107.8MB, time=197.02 memory used=14754.1MB, alloc=107.8MB, time=197.05 memory used=14760.5MB, alloc=107.8MB, time=197.08 memory used=14766.9MB, alloc=107.8MB, time=197.11 memory used=14773.3MB, alloc=107.8MB, time=197.15 memory used=14779.7MB, alloc=107.8MB, time=197.18 memory used=14786.0MB, alloc=107.8MB, time=197.21 memory used=14792.4MB, alloc=107.8MB, time=197.24 memory used=14798.8MB, alloc=107.8MB, time=197.28 memory used=14805.1MB, alloc=107.8MB, time=197.31 memory used=14811.5MB, alloc=107.8MB, time=197.34 memory used=14817.8MB, alloc=107.8MB, time=197.37 memory used=14824.2MB, alloc=107.8MB, time=197.41 memory used=14830.5MB, alloc=107.8MB, time=197.44 memory used=14836.8MB, alloc=107.8MB, time=197.47 memory used=14843.4MB, alloc=107.8MB, time=197.50 memory used=14849.8MB, alloc=107.8MB, time=197.54 memory used=14859.0MB, alloc=107.8MB, time=197.57 memory used=14865.6MB, alloc=107.8MB, time=197.60 memory used=14874.8MB, alloc=107.8MB, time=197.64 memory used=14884.2MB, alloc=107.8MB, time=197.67 memory used=14893.7MB, alloc=107.8MB, time=197.71 memory used=14903.1MB, alloc=107.8MB, time=197.74 memory used=14912.5MB, alloc=107.8MB, time=197.77 memory used=14921.9MB, alloc=107.8MB, time=197.81 memory used=14931.3MB, alloc=107.8MB, time=197.84 memory used=14940.6MB, alloc=107.8MB, time=197.88 memory used=14950.0MB, alloc=107.8MB, time=197.91 memory used=14959.4MB, alloc=107.8MB, time=197.95 memory used=14968.7MB, alloc=107.8MB, time=197.98 memory used=14978.0MB, alloc=107.8MB, time=198.01 memory used=14987.3MB, alloc=107.8MB, time=198.05 memory used=14996.6MB, alloc=107.8MB, time=198.09 memory used=15005.8MB, alloc=107.8MB, time=198.12 memory used=15015.1MB, alloc=107.8MB, time=198.15 memory used=15024.3MB, alloc=107.8MB, time=198.19 memory used=15033.5MB, alloc=107.8MB, time=198.22 memory used=15042.7MB, alloc=107.8MB, time=198.26 memory used=15051.8MB, alloc=107.8MB, time=198.29 memory used=15061.0MB, alloc=107.8MB, time=198.33 memory used=15070.1MB, alloc=107.8MB, time=198.36 memory used=15079.2MB, alloc=107.8MB, time=198.40 memory used=15088.3MB, alloc=107.8MB, time=198.43 memory used=15097.3MB, alloc=107.8MB, time=198.46 memory used=15106.4MB, alloc=107.8MB, time=198.50 memory used=15115.4MB, alloc=107.8MB, time=198.53 memory used=15124.4MB, alloc=107.8MB, time=198.57 memory used=15133.4MB, alloc=107.8MB, time=198.60 memory used=15142.3MB, alloc=107.8MB, time=198.64 memory used=15151.3MB, alloc=107.8MB, time=198.67 memory used=15160.2MB, alloc=107.8MB, time=198.71 memory used=15169.0MB, alloc=107.8MB, time=198.74 memory used=15177.9MB, alloc=107.8MB, time=198.77 memory used=15186.7MB, alloc=107.8MB, time=198.81 memory used=15195.5MB, alloc=107.8MB, time=198.84 memory used=15204.5MB, alloc=107.8MB, time=198.88 memory used=15216.0MB, alloc=107.8MB, time=198.91 memory used=15225.0MB, alloc=107.8MB, time=198.95 memory used=15236.3MB, alloc=107.8MB, time=198.98 memory used=15247.8MB, alloc=107.8MB, time=199.02 memory used=15259.3MB, alloc=107.8MB, time=199.06 memory used=15270.8MB, alloc=107.8MB, time=199.09 memory used=15282.2MB, alloc=107.8MB, time=199.13 memory used=15293.5MB, alloc=107.8MB, time=199.16 memory used=15304.8MB, alloc=107.8MB, time=199.20 memory used=15316.0MB, alloc=107.8MB, time=199.24 memory used=15327.2MB, alloc=107.8MB, time=199.27 memory used=15338.3MB, alloc=107.8MB, time=199.31 memory used=15349.4MB, alloc=107.8MB, time=199.34 memory used=15360.4MB, alloc=107.8MB, time=199.38 memory used=15371.3MB, alloc=107.8MB, time=199.41 memory used=15382.2MB, alloc=107.8MB, time=199.45 memory used=15393.0MB, alloc=107.8MB, time=199.48 memory used=15403.8MB, alloc=107.8MB, time=199.52 memory used=15414.5MB, alloc=107.8MB, time=199.55 memory used=15425.4MB, alloc=107.8MB, time=199.59 memory used=15438.4MB, alloc=107.8MB, time=199.63 memory used=15451.5MB, alloc=107.8MB, time=199.66 memory used=15464.5MB, alloc=107.8MB, time=199.70 memory used=15477.4MB, alloc=107.8MB, time=199.74 memory used=15490.2MB, alloc=107.8MB, time=199.77 memory used=15502.9MB, alloc=107.8MB, time=199.81 memory used=15515.5MB, alloc=107.8MB, time=199.85 memory used=15528.0MB, alloc=107.8MB, time=199.89 memory used=15540.3MB, alloc=107.8MB, time=199.92 memory used=15552.6MB, alloc=107.8MB, time=199.96 memory used=15564.7MB, alloc=107.8MB, time=200.00 memory used=15576.9MB, alloc=107.8MB, time=200.04 memory used=15591.0MB, alloc=107.8MB, time=200.07 memory used=15605.0MB, alloc=107.8MB, time=200.11 memory used=15618.9MB, alloc=107.8MB, time=200.15 memory used=15632.7MB, alloc=107.8MB, time=200.19 memory used=15646.2MB, alloc=107.8MB, time=200.22 memory used=15659.7MB, alloc=107.8MB, time=200.26 memory used=15673.2MB, alloc=107.8MB, time=200.30 memory used=15688.0MB, alloc=107.8MB, time=200.34 memory used=15702.9MB, alloc=107.8MB, time=200.37 memory used=15717.4MB, alloc=107.8MB, time=200.41 memory used=15731.7MB, alloc=107.8MB, time=200.45 memory used=15747.7MB, alloc=107.8MB, time=200.49 memory used=15763.3MB, alloc=107.8MB, time=200.53 memory used=15778.4MB, alloc=107.8MB, time=200.56 memory used=15791.4MB, alloc=107.8MB, time=200.60 memory used=15802.2MB, alloc=107.8MB, time=200.64 memory used=15812.1MB, alloc=107.8MB, time=200.67 memory used=15822.4MB, alloc=107.8MB, time=200.71 memory used=15832.5MB, alloc=107.8MB, time=200.75 memory used=15842.3MB, alloc=107.8MB, time=200.78 memory used=15852.2MB, alloc=107.8MB, time=200.82 memory used=15862.8MB, alloc=107.8MB, time=200.85 memory used=15873.3MB, alloc=107.8MB, time=200.89 memory used=15883.8MB, alloc=107.8MB, time=200.93 memory used=15894.8MB, alloc=107.8MB, time=200.96 memory used=15905.8MB, alloc=107.8MB, time=201.00 memory used=15917.1MB, alloc=107.8MB, time=201.03 memory used=15928.5MB, alloc=107.8MB, time=201.07 memory used=15940.7MB, alloc=107.8MB, time=201.11 memory used=15952.8MB, alloc=107.8MB, time=201.14 memory used=15965.2MB, alloc=107.8MB, time=201.18 memory used=15978.1MB, alloc=107.8MB, time=201.22 memory used=16065.8MB, alloc=107.8MB, time=201.69 memory used=16133.6MB, alloc=363.8MB, time=202.22 memory used=16204.5MB, alloc=363.8MB, time=202.77 memory used=16234.7MB, alloc=363.8MB, time=202.84 memory used=16273.3MB, alloc=363.8MB, time=202.97 memory used=16304.0MB, alloc=363.8MB, time=203.05 memory used=16344.4MB, alloc=363.8MB, time=203.17 memory used=16375.6MB, alloc=363.8MB, time=203.25 memory used=16413.8MB, alloc=363.8MB, time=203.36 memory used=16458.0MB, alloc=363.8MB, time=204.71 memory used=16506.5MB, alloc=363.8MB, time=205.19 memory used=16545.5MB, alloc=387.8MB, time=205.31 memory used=16583.9MB, alloc=387.8MB, time=205.42 memory used=16624.1MB, alloc=387.8MB, time=205.56 memory used=16669.5MB, alloc=387.8MB, time=205.68 memory used=16718.7MB, alloc=387.8MB, time=205.79 memory used=16771.7MB, alloc=387.8MB, time=205.91 memory used=16828.9MB, alloc=387.8MB, time=206.04 memory used=16875.4MB, alloc=387.8MB, time=206.15 memory used=16907.9MB, alloc=387.8MB, time=206.25 memory used=16939.1MB, alloc=387.8MB, time=206.34 memory used=16968.7MB, alloc=387.8MB, time=206.43 memory used=16999.2MB, alloc=387.8MB, time=206.52 memory used=17030.7MB, alloc=387.8MB, time=206.62 memory used=17067.4MB, alloc=387.8MB, time=206.72 memory used=17105.5MB, alloc=387.8MB, time=206.83 memory used=17144.4MB, alloc=387.8MB, time=206.95 memory used=17184.1MB, alloc=387.8MB, time=207.04 memory used=17224.6MB, alloc=387.8MB, time=207.15 memory used=17265.9MB, alloc=387.8MB, time=207.25 memory used=17307.9MB, alloc=387.8MB, time=207.35 memory used=17350.7MB, alloc=387.8MB, time=207.44 memory used=17394.2MB, alloc=387.8MB, time=207.56 memory used=17438.4MB, alloc=387.8MB, time=207.67 memory used=17483.3MB, alloc=387.8MB, time=207.77 memory used=17528.8MB, alloc=387.8MB, time=207.88 memory used=17575.0MB, alloc=387.8MB, time=207.98 memory used=17622.6MB, alloc=387.8MB, time=208.09 memory used=17676.3MB, alloc=387.8MB, time=208.21 memory used=17731.3MB, alloc=387.8MB, time=208.32 memory used=17787.1MB, alloc=387.8MB, time=208.43 memory used=17843.5MB, alloc=387.8MB, time=208.53 memory used=17895.3MB, alloc=411.8MB, time=208.65 memory used=17941.7MB, alloc=411.8MB, time=208.76 memory used=17983.6MB, alloc=411.8MB, time=208.85 memory used=18023.8MB, alloc=411.8MB, time=208.94 memory used=18060.0MB, alloc=411.8MB, time=209.02 memory used=18096.9MB, alloc=411.8MB, time=209.11 memory used=18134.0MB, alloc=411.8MB, time=209.20 memory used=18171.3MB, alloc=411.8MB, time=209.28 memory used=18208.8MB, alloc=411.8MB, time=209.37 memory used=18247.3MB, alloc=411.8MB, time=209.46 memory used=18292.2MB, alloc=411.8MB, time=209.55 memory used=18337.9MB, alloc=411.8MB, time=209.64 memory used=18383.9MB, alloc=411.8MB, time=209.73 memory used=18430.1MB, alloc=411.8MB, time=209.82 memory used=18476.6MB, alloc=411.8MB, time=209.91 memory used=18523.2MB, alloc=411.8MB, time=210.00 memory used=18570.0MB, alloc=411.8MB, time=210.09 memory used=18617.0MB, alloc=411.8MB, time=210.19 memory used=18664.2MB, alloc=411.8MB, time=210.28 memory used=18711.5MB, alloc=411.8MB, time=210.37 memory used=18759.0MB, alloc=411.8MB, time=210.46 memory used=18806.6MB, alloc=411.8MB, time=210.55 memory used=18854.4MB, alloc=411.8MB, time=210.64 memory used=18903.1MB, alloc=411.8MB, time=210.73 memory used=18958.3MB, alloc=411.8MB, time=210.84 memory used=19014.3MB, alloc=411.8MB, time=210.93 memory used=19070.5MB, alloc=411.8MB, time=211.03 memory used=19126.7MB, alloc=411.8MB, time=211.12 memory used=19182.9MB, alloc=411.8MB, time=211.22 memory used=19239.2MB, alloc=411.8MB, time=211.32 memory used=19295.6MB, alloc=411.8MB, time=211.41 memory used=19351.9MB, alloc=411.8MB, time=211.51 memory used=19409.2MB, alloc=411.8MB, time=211.61 memory used=19472.6MB, alloc=411.8MB, time=211.71 memory used=19536.8MB, alloc=411.8MB, time=211.81 memory used=19600.9MB, alloc=411.8MB, time=211.91 memory used=19664.9MB, alloc=411.8MB, time=212.01 memory used=19728.7MB, alloc=411.8MB, time=212.11 memory used=19792.3MB, alloc=411.8MB, time=212.21 memory used=19856.9MB, alloc=411.8MB, time=212.31 memory used=19926.8MB, alloc=411.8MB, time=212.41 memory used=19997.4MB, alloc=411.8MB, time=212.51 memory used=20067.6MB, alloc=411.8MB, time=212.61 memory used=20137.5MB, alloc=411.8MB, time=212.72 memory used=20208.5MB, alloc=411.8MB, time=212.82 memory used=20283.3MB, alloc=411.8MB, time=212.92 memory used=20359.0MB, alloc=411.8MB, time=213.03 memory used=20434.1MB, alloc=411.8MB, time=213.13 memory used=20515.6MB, alloc=411.8MB, time=213.24 memory used=20730.0MB, alloc=411.8MB, time=213.60 memory used=20863.8MB, alloc=411.8MB, time=213.78 memory used=21002.0MB, alloc=411.8MB, time=213.96 memory used=21142.1MB, alloc=411.8MB, time=214.14 memory used=21288.7MB, alloc=411.8MB, time=214.33 memory used=21439.5MB, alloc=411.8MB, time=214.51 memory used=21598.2MB, alloc=411.8MB, time=214.71 memory used=21764.8MB, alloc=411.8MB, time=214.89 memory used=21966.7MB, alloc=411.8MB, time=216.76 memory used=22020.3MB, alloc=411.8MB, time=216.90 memory used=22079.9MB, alloc=411.8MB, time=217.04 memory used=22148.2MB, alloc=411.8MB, time=217.20 memory used=22224.1MB, alloc=411.8MB, time=217.37 memory used=22295.0MB, alloc=411.8MB, time=217.51 memory used=22342.6MB, alloc=411.8MB, time=217.64 memory used=22388.3MB, alloc=411.8MB, time=217.76 memory used=22434.4MB, alloc=411.8MB, time=217.88 memory used=22482.0MB, alloc=411.8MB, time=218.00 memory used=22531.1MB, alloc=411.8MB, time=218.12 memory used=22582.1MB, alloc=411.8MB, time=218.24 memory used=22639.3MB, alloc=411.8MB, time=218.37 memory used=22698.6MB, alloc=411.8MB, time=218.49 memory used=22759.4MB, alloc=411.8MB, time=218.61 memory used=22821.6MB, alloc=411.8MB, time=218.74 memory used=22885.4MB, alloc=411.8MB, time=218.87 memory used=22950.5MB, alloc=411.8MB, time=218.99 memory used=23017.7MB, alloc=411.8MB, time=219.12 memory used=23091.7MB, alloc=411.8MB, time=219.25 memory used=23167.8MB, alloc=411.8MB, time=219.38 memory used=23245.2MB, alloc=411.8MB, time=219.50 memory used=23317.9MB, alloc=411.8MB, time=219.62 memory used=23363.3MB, alloc=411.8MB, time=219.71 memory used=23404.3MB, alloc=411.8MB, time=219.81 memory used=23444.6MB, alloc=411.8MB, time=219.89 memory used=23480.9MB, alloc=411.8MB, time=219.98 memory used=23517.7MB, alloc=411.8MB, time=220.07 memory used=23554.8MB, alloc=411.8MB, time=220.15 memory used=23592.2MB, alloc=411.8MB, time=220.24 memory used=23629.7MB, alloc=411.8MB, time=220.32 memory used=23667.4MB, alloc=411.8MB, time=220.41 memory used=23706.1MB, alloc=411.8MB, time=220.50 memory used=23751.1MB, alloc=411.8MB, time=220.59 memory used=23797.1MB, alloc=411.8MB, time=220.69 memory used=23843.2MB, alloc=411.8MB, time=220.78 memory used=23889.6MB, alloc=411.8MB, time=220.86 memory used=23936.2MB, alloc=411.8MB, time=220.95 memory used=23983.0MB, alloc=411.8MB, time=221.05 memory used=24030.0MB, alloc=411.8MB, time=221.14 memory used=24077.1MB, alloc=411.8MB, time=221.23 memory used=24124.4MB, alloc=411.8MB, time=221.31 memory used=24171.9MB, alloc=411.8MB, time=221.41 memory used=24219.5MB, alloc=411.8MB, time=221.50 memory used=24267.1MB, alloc=411.8MB, time=221.58 memory used=24315.0MB, alloc=411.8MB, time=221.68 memory used=24363.9MB, alloc=411.8MB, time=221.77 memory used=24419.1MB, alloc=411.8MB, time=221.86 memory used=24475.2MB, alloc=411.8MB, time=221.97 memory used=24531.4MB, alloc=411.8MB, time=222.06 memory used=24587.6MB, alloc=411.8MB, time=222.16 memory used=24643.9MB, alloc=411.8MB, time=222.25 memory used=24700.2MB, alloc=411.8MB, time=222.35 memory used=24756.5MB, alloc=411.8MB, time=222.44 memory used=24812.8MB, alloc=411.8MB, time=222.54 memory used=24870.1MB, alloc=411.8MB, time=222.63 memory used=24933.5MB, alloc=411.8MB, time=222.73 memory used=24997.6MB, alloc=411.8MB, time=222.84 memory used=25061.6MB, alloc=411.8MB, time=222.93 memory used=25125.4MB, alloc=411.8MB, time=223.03 memory used=25189.1MB, alloc=411.8MB, time=223.13 memory used=25252.6MB, alloc=411.8MB, time=223.23 memory used=25317.4MB, alloc=411.8MB, time=223.33 memory used=25386.7MB, alloc=411.8MB, time=223.44 memory used=25457.1MB, alloc=411.8MB, time=223.55 memory used=25527.1MB, alloc=411.8MB, time=223.65 memory used=25596.7MB, alloc=411.8MB, time=223.75 memory used=25667.4MB, alloc=411.8MB, time=223.85 memory used=25741.9MB, alloc=411.8MB, time=223.95 memory used=25817.2MB, alloc=411.8MB, time=224.05 memory used=25893.0MB, alloc=411.8MB, time=224.16 memory used=25981.6MB, alloc=411.8MB, time=224.27 memory used=26157.4MB, alloc=411.8MB, time=224.48 memory used=26292.0MB, alloc=411.8MB, time=224.66 memory used=26430.0MB, alloc=411.8MB, time=224.84 memory used=26569.8MB, alloc=411.8MB, time=225.02 memory used=26716.1MB, alloc=411.8MB, time=225.20 memory used=26868.0MB, alloc=411.8MB, time=225.39 memory used=27028.7MB, alloc=411.8MB, time=225.58 memory used=27195.6MB, alloc=411.8MB, time=225.77 memory used=27383.8MB, alloc=411.8MB, time=269.47 memory used=27456.5MB, alloc=411.8MB, time=333.92 memory used=27532.8MB, alloc=411.8MB, time=387.22 memory used=27603.7MB, alloc=411.8MB, time=388.42 memory used=27674.9MB, alloc=411.8MB, time=388.55 memory used=27727.2MB, alloc=411.8MB, time=388.69 memory used=27776.4MB, alloc=411.8MB, time=388.82 memory used=27832.3MB, alloc=411.8MB, time=388.94 memory used=27893.2MB, alloc=411.8MB, time=389.06 memory used=27961.5MB, alloc=411.8MB, time=389.20 memory used=28034.7MB, alloc=411.8MB, time=389.32 memory used=28105.6MB, alloc=411.8MB, time=389.46 memory used=28151.4MB, alloc=411.8MB, time=389.56 memory used=28193.7MB, alloc=411.8MB, time=389.65 memory used=28235.2MB, alloc=411.8MB, time=389.74 memory used=28278.5MB, alloc=411.8MB, time=389.83 memory used=28322.8MB, alloc=411.8MB, time=389.93 memory used=28371.6MB, alloc=411.8MB, time=390.02 memory used=28421.5MB, alloc=411.8MB, time=390.12 memory used=28472.5MB, alloc=411.8MB, time=390.22 memory used=28524.4MB, alloc=411.8MB, time=390.32 memory used=28577.4MB, alloc=411.8MB, time=390.42 memory used=28631.3MB, alloc=411.8MB, time=390.52 memory used=28686.3MB, alloc=411.8MB, time=390.62 memory used=28745.8MB, alloc=411.8MB, time=390.72 memory used=28806.6MB, alloc=411.8MB, time=390.82 memory used=28868.3MB, alloc=411.8MB, time=390.92 memory used=28931.0MB, alloc=411.8MB, time=391.03 memory used=28994.6MB, alloc=411.8MB, time=391.14 memory used=29063.4MB, alloc=411.8MB, time=391.26 memory used=29133.0MB, alloc=411.8MB, time=391.36 memory used=29203.5MB, alloc=411.8MB, time=391.47 memory used=29275.0MB, alloc=411.8MB, time=391.58 memory used=29351.7MB, alloc=411.8MB, time=391.69 memory used=29429.0MB, alloc=411.8MB, time=391.81 memory used=29612.5MB, alloc=411.8MB, time=392.03 memory used=29748.6MB, alloc=411.8MB, time=392.22 memory used=29893.2MB, alloc=411.8MB, time=392.42 memory used=30044.2MB, alloc=411.8MB, time=392.62 memory used=30201.4MB, alloc=411.8MB, time=392.83 memory used=30364.6MB, alloc=411.8MB, time=393.04 memory used=30533.5MB, alloc=411.8MB, time=393.25 memory used=30707.7MB, alloc=411.8MB, time=393.48 memory used=30891.7MB, alloc=411.8MB, time=393.69 memory used=31080.2MB, alloc=411.8MB, time=393.91 memory used=31276.8MB, alloc=411.8MB, time=394.13 memory used=31481.3MB, alloc=411.8MB, time=394.36 memory used=31695.8MB, alloc=411.8MB, time=394.59 memory used=31919.8MB, alloc=411.8MB, time=394.83 memory used=32155.4MB, alloc=411.8MB, time=395.07 memory used=32402.9MB, alloc=411.8MB, time=395.33 memory used=32644.6MB, alloc=411.8MB, time=395.56 memory used=32824.7MB, alloc=411.8MB, time=395.76 memory used=33012.9MB, alloc=411.8MB, time=395.97 memory used=33212.7MB, alloc=411.8MB, time=396.18 memory used=33451.9MB, alloc=411.8MB, time=396.57 memory used=33524.4MB, alloc=411.8MB, time=396.71 memory used=33583.6MB, alloc=411.8MB, time=396.84 memory used=33639.0MB, alloc=411.8MB, time=396.95 memory used=33704.0MB, alloc=411.8MB, time=397.08 memory used=33780.2MB, alloc=411.8MB, time=397.23 memory used=33863.9MB, alloc=411.8MB, time=401.75 memory used=33952.5MB, alloc=411.8MB, time=411.56 memory used=34022.8MB, alloc=411.8MB, time=411.69 memory used=34076.8MB, alloc=411.8MB, time=411.83 memory used=34140.9MB, alloc=411.8MB, time=411.96 memory used=34216.8MB, alloc=411.8MB, time=412.09 memory used=34289.0MB, alloc=411.8MB, time=412.20 memory used=34335.3MB, alloc=411.8MB, time=412.30 memory used=34384.8MB, alloc=411.8MB, time=412.40 memory used=34436.9MB, alloc=411.8MB, time=412.50 memory used=34492.7MB, alloc=411.8MB, time=412.60 memory used=34552.1MB, alloc=411.8MB, time=412.70 memory used=34613.2MB, alloc=411.8MB, time=412.80 memory used=34679.5MB, alloc=411.8MB, time=412.90 memory used=34749.2MB, alloc=411.8MB, time=413.01 memory used=34822.3MB, alloc=411.8MB, time=413.11 memory used=34900.6MB, alloc=411.8MB, time=413.22 memory used=34983.9MB, alloc=411.8MB, time=413.33 memory used=35169.2MB, alloc=411.8MB, time=413.55 memory used=35320.5MB, alloc=411.8MB, time=413.74 memory used=35488.5MB, alloc=411.8MB, time=413.94 memory used=35678.7MB, alloc=411.8MB, time=414.14 memory used=35892.3MB, alloc=411.8MB, time=417.01 memory used=35965.2MB, alloc=411.8MB, time=417.19 memory used=36013.5MB, alloc=411.8MB, time=417.32 memory used=36064.4MB, alloc=411.8MB, time=417.48 memory used=36121.8MB, alloc=411.8MB, time=417.62 memory used=36183.6MB, alloc=411.8MB, time=417.76 memory used=36249.4MB, alloc=411.8MB, time=417.90 memory used=36319.1MB, alloc=411.8MB, time=418.04 memory used=36392.7MB, alloc=411.8MB, time=418.20 memory used=36448.2MB, alloc=411.8MB, time=418.34 memory used=36487.2MB, alloc=411.8MB, time=418.46 memory used=36526.1MB, alloc=435.8MB, time=418.58 memory used=36576.0MB, alloc=435.8MB, time=418.72 memory used=36629.6MB, alloc=435.8MB, time=418.87 memory used=36684.7MB, alloc=435.8MB, time=419.03 memory used=36741.0MB, alloc=435.8MB, time=419.18 memory used=36798.6MB, alloc=435.8MB, time=419.33 memory used=36857.6MB, alloc=435.8MB, time=419.48 memory used=36918.6MB, alloc=435.8MB, time=419.64 memory used=36988.1MB, alloc=435.8MB, time=419.78 memory used=37059.8MB, alloc=435.8MB, time=419.92 memory used=37132.9MB, alloc=435.8MB, time=420.08 memory used=37207.4MB, alloc=435.8MB, time=420.22 memory used=37283.2MB, alloc=435.8MB, time=420.40 memory used=37360.4MB, alloc=435.8MB, time=420.54 memory used=37438.9MB, alloc=435.8MB, time=420.68 memory used=37518.5MB, alloc=435.8MB, time=420.82 memory used=37599.5MB, alloc=435.8MB, time=420.98 memory used=37682.6MB, alloc=435.8MB, time=421.12 memory used=37775.3MB, alloc=435.8MB, time=421.29 memory used=37870.2MB, alloc=435.8MB, time=421.47 memory used=37966.3MB, alloc=435.8MB, time=421.62 memory used=38032.9MB, alloc=435.8MB, time=421.75 memory used=38080.9MB, alloc=435.8MB, time=421.86 memory used=38128.9MB, alloc=435.8MB, time=421.96 memory used=38170.0MB, alloc=435.8MB, time=422.07 memory used=38213.2MB, alloc=435.8MB, time=422.17 memory used=38257.1MB, alloc=435.8MB, time=422.27 memory used=38301.3MB, alloc=435.8MB, time=422.38 memory used=38345.6MB, alloc=435.8MB, time=422.48 memory used=38390.2MB, alloc=435.8MB, time=422.58 memory used=38434.8MB, alloc=435.8MB, time=422.68 memory used=38479.7MB, alloc=435.8MB, time=422.78 memory used=38524.7MB, alloc=435.8MB, time=422.88 memory used=38569.9MB, alloc=435.8MB, time=422.99 memory used=38615.2MB, alloc=435.8MB, time=423.09 memory used=38660.6MB, alloc=435.8MB, time=423.20 memory used=38706.2MB, alloc=435.8MB, time=423.30 memory used=38752.0MB, alloc=435.8MB, time=423.40 memory used=38797.9MB, alloc=435.8MB, time=423.51 memory used=38845.2MB, alloc=435.8MB, time=423.61 memory used=38901.5MB, alloc=435.8MB, time=423.72 memory used=38949.7MB, alloc=435.8MB, time=423.83 memory used=39005.9MB, alloc=435.8MB, time=423.94 memory used=39063.9MB, alloc=435.8MB, time=424.04 memory used=39122.1MB, alloc=435.8MB, time=424.16 memory used=39180.5MB, alloc=435.8MB, time=424.27 memory used=39238.9MB, alloc=435.8MB, time=424.38 memory used=39297.5MB, alloc=435.8MB, time=424.49 memory used=39356.1MB, alloc=435.8MB, time=424.60 memory used=39414.9MB, alloc=435.8MB, time=424.71 memory used=39473.6MB, alloc=435.8MB, time=424.81 memory used=39532.5MB, alloc=435.8MB, time=424.92 memory used=39591.4MB, alloc=435.8MB, time=425.03 memory used=39650.3MB, alloc=435.8MB, time=425.13 memory used=39709.3MB, alloc=435.8MB, time=425.24 memory used=39768.3MB, alloc=435.8MB, time=425.36 memory used=39828.8MB, alloc=435.8MB, time=425.47 memory used=39898.2MB, alloc=435.8MB, time=425.58 memory used=39969.0MB, alloc=435.8MB, time=425.69 memory used=40039.6MB, alloc=435.8MB, time=425.82 memory used=40110.3MB, alloc=435.8MB, time=425.93 memory used=40180.8MB, alloc=435.8MB, time=426.04 memory used=40251.2MB, alloc=435.8MB, time=426.16 memory used=40321.5MB, alloc=435.8MB, time=426.27 memory used=40391.6MB, alloc=435.8MB, time=426.38 memory used=40461.6MB, alloc=435.8MB, time=426.50 memory used=40531.4MB, alloc=435.8MB, time=426.62 memory used=40602.7MB, alloc=435.8MB, time=426.73 memory used=40682.1MB, alloc=435.8MB, time=426.85 memory used=40762.7MB, alloc=435.8MB, time=426.97 memory used=40842.9MB, alloc=435.8MB, time=427.09 memory used=40922.7MB, alloc=435.8MB, time=427.21 memory used=41002.1MB, alloc=435.8MB, time=427.32 memory used=41081.1MB, alloc=435.8MB, time=427.45 memory used=41161.3MB, alloc=435.8MB, time=427.56 memory used=41248.8MB, alloc=435.8MB, time=427.69 memory used=41337.1MB, alloc=435.8MB, time=427.81 memory used=41424.6MB, alloc=435.8MB, time=427.93 memory used=41511.4MB, alloc=435.8MB, time=428.05 memory used=41599.2MB, alloc=435.8MB, time=428.18 memory used=41693.0MB, alloc=435.8MB, time=428.31 memory used=41787.4MB, alloc=435.8MB, time=428.43 memory used=41896.3MB, alloc=435.8MB, time=428.57 memory used=42081.4MB, alloc=435.8MB, time=428.80 memory used=42207.2MB, alloc=435.8MB, time=428.98 memory used=42335.0MB, alloc=435.8MB, time=429.16 memory used=42466.3MB, alloc=435.8MB, time=429.34 memory used=42600.5MB, alloc=435.8MB, time=429.53 memory used=42739.1MB, alloc=435.8MB, time=429.71 memory used=42880.8MB, alloc=435.8MB, time=429.90 memory used=43030.3MB, alloc=435.8MB, time=430.09 memory used=43184.3MB, alloc=435.8MB, time=430.29 memory used=43344.7MB, alloc=435.8MB, time=430.49 memory used=43528.9MB, alloc=435.8MB, time=489.03 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428548362 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 3 F := [7 x z + 3 x y - 7 x y , 9 x y - 12] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 2 G := [11 x y - 14 x z, 5 x y - 4 x z - 3 x ] > Problem := [F,G]; 3 2 2 2 3 Problem := [[7 x z + 3 x y - 7 x y , 9 x y - 12], 3 2 3 2 2 [11 x y - 14 x z, 5 x y - 4 x z - 3 x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.16 memory used=26.3MB, alloc=32.3MB, time=0.48 memory used=46.5MB, alloc=32.3MB, time=0.75 memory used=67.5MB, alloc=56.3MB, time=1.10 memory used=108.7MB, alloc=60.3MB, time=1.78 memory used=146.6MB, alloc=84.3MB, time=2.42 memory used=204.5MB, alloc=108.3MB, time=3.58 memory used=273.4MB, alloc=132.3MB, time=5.65 N1 := 1637 > GB := Basis(F, plex(op(vars))); 3 2 3 3 GB := [3 y x - 4, 9 x y - 21 x y + 28 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=368.3MB, alloc=140.3MB, time=7.20 memory used=465.8MB, alloc=164.3MB, time=8.75 memory used=578.3MB, alloc=188.3MB, time=12.15 N2 := 2087 > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 2 2 3 3 2 H := [7 x z + 3 x y - 7 x y , 9 x y - 12, 11 x y - 14 x z, 3 2 2 5 x y - 4 x z - 3 x ] > J:=[op(GB),op(G)]; 3 3 2 3 3 2 J := [3 y x - 4, 9 y x - 21 y x + 28 z, 11 x y - 14 x z, 3 2 2 5 x y - 4 x z - 3 x ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 11, 16, 4, 3, 3, 1, 1, 1, 3/4, 9/10, 1/2, 3/10, 4, 11, 17, 5, 3, 3, 1, 1, 1, 3/4, 4/5, 1/2, 3/10, 0, -1, -1] > save(F, G, cat("ranSet/34", convert(F, string),".txt")); > quit memory used=646.6MB, alloc=188.3MB, time=14.12 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428548377 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 3 F := [-17 x y z + 10 x - 11 z, 10 x y - 3 x - 8 x] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 3 4 2 G := [9 x y z + 9 x + z , 19 y + 10 y z + x z] > Problem := [F,G]; 2 2 3 3 Problem := [[-17 x y z + 10 x - 11 z, 10 x y - 3 x - 8 x], 2 3 3 4 2 [9 x y z + 9 x + z , 19 y + 10 y z + x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=25.7MB, alloc=32.3MB, time=0.48 memory used=80.1MB, alloc=70.8MB, time=0.96 memory used=126.3MB, alloc=70.8MB, time=1.64 memory used=158.6MB, alloc=70.8MB, time=1.72 memory used=193.6MB, alloc=70.8MB, time=1.80 memory used=233.6MB, alloc=70.8MB, time=2.03 memory used=273.6MB, alloc=70.8MB, time=2.55 memory used=326.0MB, alloc=78.8MB, time=3.23 memory used=380.1MB, alloc=78.8MB, time=3.88 memory used=434.0MB, alloc=102.8MB, time=4.55 memory used=501.8MB, alloc=102.8MB, time=5.40 memory used=552.6MB, alloc=102.8MB, time=5.77 memory used=599.7MB, alloc=102.8MB, time=5.97 memory used=634.8MB, alloc=102.8MB, time=6.11 memory used=669.0MB, alloc=102.8MB, time=6.22 memory used=712.0MB, alloc=102.8MB, time=6.41 memory used=747.4MB, alloc=102.8MB, time=6.54 memory used=782.0MB, alloc=102.8MB, time=6.67 memory used=826.0MB, alloc=102.8MB, time=8.47 memory used=904.5MB, alloc=102.8MB, time=11.34 memory used=940.6MB, alloc=102.8MB, time=11.46 memory used=971.9MB, alloc=102.8MB, time=11.57 memory used=1012.1MB, alloc=102.8MB, time=11.68 memory used=1044.4MB, alloc=102.8MB, time=11.78 memory used=1071.0MB, alloc=102.8MB, time=11.86 memory used=1101.1MB, alloc=102.8MB, time=11.96 memory used=1136.3MB, alloc=102.8MB, time=12.05 memory used=1181.4MB, alloc=102.8MB, time=12.22 memory used=1237.0MB, alloc=102.8MB, time=13.95 memory used=1271.1MB, alloc=102.8MB, time=14.07 memory used=1306.7MB, alloc=102.8MB, time=14.18 memory used=1341.1MB, alloc=102.8MB, time=14.28 memory used=1369.1MB, alloc=102.8MB, time=14.37 memory used=1430.7MB, alloc=102.8MB, time=14.85 memory used=1494.4MB, alloc=126.8MB, time=23.79 memory used=1548.5MB, alloc=126.8MB, time=58.04 memory used=1628.1MB, alloc=126.8MB, time=77.40 memory used=1681.4MB, alloc=126.8MB, time=77.52 memory used=1724.9MB, alloc=126.8MB, time=77.62 memory used=1770.4MB, alloc=126.8MB, time=77.74 memory used=1823.5MB, alloc=126.8MB, time=77.85 memory used=1885.2MB, alloc=126.8MB, time=77.97 memory used=1924.6MB, alloc=126.8MB, time=78.05 memory used=1961.0MB, alloc=126.8MB, time=78.14 memory used=1999.4MB, alloc=126.8MB, time=78.22 memory used=2040.7MB, alloc=126.8MB, time=78.31 memory used=2084.6MB, alloc=126.8MB, time=78.40 memory used=2131.2MB, alloc=126.8MB, time=78.49 memory used=2180.3MB, alloc=126.8MB, time=78.58 memory used=2231.8MB, alloc=126.8MB, time=78.67 memory used=2287.2MB, alloc=126.8MB, time=78.76 memory used=2344.7MB, alloc=126.8MB, time=78.86 memory used=2407.1MB, alloc=126.8MB, time=78.96 memory used=2451.4MB, alloc=139.8MB, time=79.04 memory used=2460.3MB, alloc=139.8MB, time=79.10 memory used=2468.7MB, alloc=139.8MB, time=79.15 memory used=2478.5MB, alloc=139.8MB, time=79.21 memory used=2488.4MB, alloc=139.8MB, time=79.26 memory used=2498.2MB, alloc=139.8MB, time=79.32 memory used=2507.9MB, alloc=139.8MB, time=79.37 memory used=2517.6MB, alloc=139.8MB, time=79.42 memory used=2527.2MB, alloc=139.8MB, time=79.47 memory used=2536.7MB, alloc=139.8MB, time=79.53 memory used=2546.2MB, alloc=139.8MB, time=79.58 memory used=2555.7MB, alloc=139.8MB, time=79.63 memory used=2566.4MB, alloc=139.8MB, time=79.69 memory used=2577.1MB, alloc=139.8MB, time=79.74 memory used=2587.7MB, alloc=139.8MB, time=79.80 memory used=2598.2MB, alloc=139.8MB, time=79.85 memory used=2608.5MB, alloc=139.8MB, time=79.91 memory used=2620.2MB, alloc=139.8MB, time=79.96 memory used=2631.7MB, alloc=139.8MB, time=80.02 memory used=2643.1MB, alloc=139.8MB, time=80.08 memory used=2654.4MB, alloc=139.8MB, time=80.13 memory used=2666.6MB, alloc=139.8MB, time=80.19 memory used=2678.7MB, alloc=139.8MB, time=80.25 memory used=2690.6MB, alloc=139.8MB, time=80.30 memory used=2703.2MB, alloc=139.8MB, time=80.36 memory used=2715.7MB, alloc=139.8MB, time=80.42 memory used=2728.9MB, alloc=139.8MB, time=80.48 memory used=2742.0MB, alloc=139.8MB, time=80.53 memory used=2755.3MB, alloc=139.8MB, time=80.59 memory used=2769.1MB, alloc=139.8MB, time=80.65 memory used=2783.3MB, alloc=139.8MB, time=80.71 memory used=2797.8MB, alloc=139.8MB, time=80.76 memory used=2812.9MB, alloc=139.8MB, time=80.82 memory used=2828.5MB, alloc=139.8MB, time=80.88 memory used=2845.1MB, alloc=139.8MB, time=80.93 memory used=2918.0MB, alloc=395.8MB, time=81.43 memory used=2992.9MB, alloc=395.8MB, time=81.74 memory used=3080.0MB, alloc=395.8MB, time=83.95 memory used=3151.8MB, alloc=395.8MB, time=84.17 memory used=3199.6MB, alloc=395.8MB, time=84.29 memory used=3273.4MB, alloc=395.8MB, time=85.29 memory used=3333.6MB, alloc=395.8MB, time=85.50 memory used=3443.2MB, alloc=395.8MB, time=93.36 memory used=3500.2MB, alloc=395.8MB, time=93.66 memory used=3556.1MB, alloc=395.8MB, time=93.79 memory used=3594.7MB, alloc=395.8MB, time=93.91 memory used=3638.0MB, alloc=395.8MB, time=94.03 memory used=3714.9MB, alloc=395.8MB, time=94.34 memory used=3804.4MB, alloc=395.8MB, time=94.91 memory used=3899.0MB, alloc=395.8MB, time=95.58 memory used=3991.8MB, alloc=395.8MB, time=96.23 memory used=4089.5MB, alloc=419.8MB, time=97.03 memory used=4192.8MB, alloc=419.8MB, time=97.60 memory used=4261.0MB, alloc=419.8MB, time=97.92 memory used=4318.2MB, alloc=419.8MB, time=98.09 memory used=4362.7MB, alloc=419.8MB, time=98.25 memory used=4416.2MB, alloc=419.8MB, time=98.40 memory used=4480.4MB, alloc=419.8MB, time=98.58 memory used=4528.8MB, alloc=419.8MB, time=98.72 memory used=4569.8MB, alloc=419.8MB, time=98.85 memory used=4615.4MB, alloc=419.8MB, time=98.97 memory used=4682.8MB, alloc=419.8MB, time=99.25 memory used=4738.2MB, alloc=419.8MB, time=99.43 memory used=4788.7MB, alloc=419.8MB, time=99.59 memory used=4835.5MB, alloc=419.8MB, time=99.75 memory used=4891.8MB, alloc=419.8MB, time=99.93 memory used=4956.5MB, alloc=419.8MB, time=100.10 memory used=4995.9MB, alloc=419.8MB, time=100.24 memory used=5037.1MB, alloc=419.8MB, time=100.37 memory used=5083.5MB, alloc=419.8MB, time=100.50 memory used=5166.2MB, alloc=419.8MB, time=105.75 memory used=5277.6MB, alloc=419.8MB, time=109.94 memory used=5330.6MB, alloc=419.8MB, time=110.11 memory used=5384.7MB, alloc=419.8MB, time=110.28 memory used=5445.9MB, alloc=419.8MB, time=110.44 memory used=5485.3MB, alloc=419.8MB, time=110.57 memory used=5529.3MB, alloc=419.8MB, time=110.71 memory used=5577.4MB, alloc=419.8MB, time=110.85 memory used=5629.5MB, alloc=419.8MB, time=110.99 memory used=5686.8MB, alloc=419.8MB, time=111.14 memory used=5749.6MB, alloc=419.8MB, time=111.29 memory used=5962.8MB, alloc=419.8MB, time=111.73 memory used=6138.8MB, alloc=419.8MB, time=112.01 memory used=6333.3MB, alloc=419.8MB, time=112.39 memory used=6380.2MB, alloc=419.8MB, time=112.53 memory used=6456.6MB, alloc=419.8MB, time=114.17 memory used=6531.3MB, alloc=419.8MB, time=116.17 memory used=6582.0MB, alloc=419.8MB, time=116.34 memory used=6641.8MB, alloc=419.8MB, time=116.51 memory used=6682.8MB, alloc=419.8MB, time=116.63 memory used=6729.5MB, alloc=419.8MB, time=116.77 memory used=6781.6MB, alloc=419.8MB, time=116.90 memory used=6841.0MB, alloc=419.8MB, time=117.04 memory used=6907.6MB, alloc=419.8MB, time=117.18 memory used=7083.0MB, alloc=419.8MB, time=117.45 memory used=7218.3MB, alloc=419.8MB, time=117.85 memory used=7267.3MB, alloc=419.8MB, time=118.00 memory used=7337.5MB, alloc=419.8MB, time=118.49 memory used=7391.2MB, alloc=419.8MB, time=118.69 memory used=7449.9MB, alloc=419.8MB, time=118.87 memory used=7490.1MB, alloc=419.8MB, time=119.05 memory used=7536.9MB, alloc=419.8MB, time=119.21 memory used=7588.1MB, alloc=419.8MB, time=119.39 memory used=7645.7MB, alloc=419.8MB, time=119.55 memory used=7710.6MB, alloc=419.8MB, time=119.74 memory used=7764.4MB, alloc=443.8MB, time=119.91 memory used=7812.3MB, alloc=443.8MB, time=120.06 memory used=7863.6MB, alloc=443.8MB, time=120.21 memory used=7916.8MB, alloc=443.8MB, time=120.37 memory used=7973.7MB, alloc=443.8MB, time=120.53 memory used=8035.9MB, alloc=443.8MB, time=120.70 memory used=8099.7MB, alloc=443.8MB, time=120.85 memory used=8167.1MB, alloc=443.8MB, time=121.01 memory used=8239.5MB, alloc=443.8MB, time=121.18 memory used=8316.0MB, alloc=443.8MB, time=121.35 memory used=8396.9MB, alloc=443.8MB, time=121.51 memory used=8483.5MB, alloc=443.8MB, time=121.68 memory used=8701.3MB, alloc=443.8MB, time=122.00 memory used=8852.7MB, alloc=443.8MB, time=122.26 memory used=9023.3MB, alloc=443.8MB, time=122.51 memory used=9215.2MB, alloc=443.8MB, time=129.04 memory used=9280.6MB, alloc=443.8MB, time=129.25 memory used=9363.9MB, alloc=443.8MB, time=129.43 memory used=9416.4MB, alloc=443.8MB, time=129.58 memory used=9476.4MB, alloc=443.8MB, time=129.74 memory used=9544.4MB, alloc=443.8MB, time=129.90 memory used=9620.0MB, alloc=443.8MB, time=130.06 memory used=9705.0MB, alloc=443.8MB, time=130.24 memory used=9915.1MB, alloc=443.8MB, time=130.56 memory used=10083.5MB, alloc=443.8MB, time=130.84 memory used=10288.5MB, alloc=443.8MB, time=131.12 memory used=10409.9MB, alloc=443.8MB, time=131.54 memory used=10489.7MB, alloc=443.8MB, time=131.89 memory used=10564.1MB, alloc=443.8MB, time=132.07 memory used=10643.4MB, alloc=443.8MB, time=132.60 memory used=10711.3MB, alloc=443.8MB, time=132.76 memory used=10821.4MB, alloc=443.8MB, time=133.85 memory used=11041.2MB, alloc=443.8MB, time=136.93 memory used=11071.7MB, alloc=445.3MB, time=137.38 memory used=11073.2MB, alloc=446.8MB, time=137.48 memory used=11074.7MB, alloc=448.3MB, time=137.58 memory used=11076.3MB, alloc=449.8MB, time=137.68 memory used=11077.8MB, alloc=445.3MB, time=137.79 memory used=11175.8MB, alloc=467.8MB, time=166.47 memory used=11241.8MB, alloc=491.8MB, time=234.42 memory used=11316.1MB, alloc=515.8MB, time=347.21 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428548677 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 2 2 2 F := [y + 4 x y z - 14 y z, 8 x z - 12 y z + 14 y z] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 3 2 G := [-10 x y z + 8 x z + 13 y , -13 y z + 18 x + 20 y ] > Problem := [F,G]; 4 2 2 2 2 2 Problem := [[y + 4 x y z - 14 y z, 8 x z - 12 y z + 14 y z], 2 2 2 3 3 2 [-10 x y z + 8 x z + 13 y , -13 y z + 18 x + 20 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=25.5MB, alloc=32.3MB, time=0.45 memory used=44.9MB, alloc=56.3MB, time=0.70 memory used=90.2MB, alloc=61.6MB, time=1.11 memory used=134.6MB, alloc=69.6MB, time=1.73 memory used=174.6MB, alloc=69.6MB, time=2.22 memory used=219.7MB, alloc=93.6MB, time=2.76 memory used=288.5MB, alloc=93.6MB, time=3.61 memory used=354.4MB, alloc=93.6MB, time=4.15 memory used=406.0MB, alloc=93.6MB, time=4.54 memory used=459.6MB, alloc=117.6MB, time=4.97 memory used=529.7MB, alloc=373.6MB, time=5.55 memory used=641.0MB, alloc=373.6MB, time=6.66 memory used=740.9MB, alloc=373.6MB, time=7.87 memory used=832.1MB, alloc=373.6MB, time=8.58 memory used=920.4MB, alloc=397.6MB, time=9.78 memory used=1031.3MB, alloc=397.6MB, time=11.10 memory used=1143.8MB, alloc=421.6MB, time=12.47 memory used=1254.7MB, alloc=421.6MB, time=13.31 memory used=1376.0MB, alloc=421.6MB, time=14.48 memory used=1502.6MB, alloc=445.6MB, time=15.78 memory used=1634.7MB, alloc=445.6MB, time=17.20 memory used=1749.4MB, alloc=445.6MB, time=18.50 memory used=1839.7MB, alloc=445.6MB, time=19.66 memory used=1940.4MB, alloc=469.6MB, time=20.96 memory used=2051.5MB, alloc=469.6MB, time=22.14 memory used=2135.0MB, alloc=469.6MB, time=23.11 memory used=2210.6MB, alloc=469.6MB, time=24.07 memory used=2301.5MB, alloc=493.6MB, time=24.95 memory used=2371.7MB, alloc=493.6MB, time=25.64 memory used=2494.2MB, alloc=493.6MB, time=26.25 memory used=2620.6MB, alloc=493.6MB, time=26.82 memory used=2741.3MB, alloc=493.6MB, time=27.73 memory used=2831.2MB, alloc=493.6MB, time=28.36 memory used=2968.7MB, alloc=493.6MB, time=29.31 memory used=3068.0MB, alloc=493.6MB, time=30.07 memory used=3178.4MB, alloc=493.6MB, time=30.86 memory used=3264.6MB, alloc=493.6MB, time=31.74 memory used=3354.7MB, alloc=493.6MB, time=32.40 memory used=3457.4MB, alloc=493.6MB, time=33.15 memory used=3529.7MB, alloc=493.6MB, time=33.80 memory used=3582.3MB, alloc=493.6MB, time=34.44 memory used=3665.7MB, alloc=517.6MB, time=34.97 memory used=3762.7MB, alloc=517.6MB, time=35.33 memory used=3893.2MB, alloc=517.6MB, time=35.97 memory used=4011.7MB, alloc=517.6MB, time=36.44 memory used=4097.3MB, alloc=517.6MB, time=36.99 memory used=4220.6MB, alloc=517.6MB, time=37.53 memory used=4343.0MB, alloc=517.6MB, time=38.08 memory used=4436.6MB, alloc=517.6MB, time=38.45 memory used=4560.6MB, alloc=517.6MB, time=38.98 memory used=4652.5MB, alloc=517.6MB, time=39.35 memory used=4748.8MB, alloc=517.6MB, time=41.33 memory used=4845.7MB, alloc=517.6MB, time=41.67 memory used=4939.0MB, alloc=517.6MB, time=42.02 memory used=5009.8MB, alloc=517.6MB, time=42.60 memory used=5058.4MB, alloc=517.6MB, time=43.12 memory used=5109.9MB, alloc=517.6MB, time=43.85 memory used=5235.3MB, alloc=517.6MB, time=44.68 memory used=5356.8MB, alloc=517.6MB, time=45.61 memory used=5473.8MB, alloc=517.6MB, time=47.44 memory used=5563.8MB, alloc=541.6MB, time=50.42 memory used=5750.5MB, alloc=565.6MB, time=57.78 memory used=5918.1MB, alloc=565.6MB, time=59.34 memory used=6058.5MB, alloc=565.6MB, time=60.40 memory used=6210.7MB, alloc=565.6MB, time=61.04 memory used=6454.3MB, alloc=565.6MB, time=62.57 memory used=6605.7MB, alloc=589.6MB, time=63.25 memory used=6775.3MB, alloc=613.6MB, time=63.89 memory used=6935.0MB, alloc=613.6MB, time=64.58 memory used=7115.9MB, alloc=613.6MB, time=65.30 memory used=7300.7MB, alloc=613.6MB, time=66.27 memory used=7487.9MB, alloc=613.6MB, time=67.71 memory used=7729.3MB, alloc=613.6MB, time=70.01 memory used=7991.7MB, alloc=613.6MB, time=71.67 memory used=8209.5MB, alloc=613.6MB, time=74.70 memory used=8451.1MB, alloc=613.6MB, time=76.13 memory used=8716.3MB, alloc=613.6MB, time=78.07 memory used=8867.6MB, alloc=613.6MB, time=78.59 memory used=9119.0MB, alloc=613.6MB, time=80.13 memory used=9325.0MB, alloc=637.6MB, time=83.97 memory used=9484.4MB, alloc=637.6MB, time=85.41 memory used=9721.5MB, alloc=637.6MB, time=86.90 memory used=9992.9MB, alloc=637.6MB, time=87.98 memory used=10221.1MB, alloc=637.6MB, time=89.30 memory used=10411.3MB, alloc=637.6MB, time=91.17 memory used=10586.5MB, alloc=637.6MB, time=93.35 memory used=10758.6MB, alloc=637.6MB, time=94.14 memory used=11033.4MB, alloc=661.6MB, time=96.06 memory used=11356.8MB, alloc=661.6MB, time=98.19 memory used=11683.0MB, alloc=661.6MB, time=99.95 memory used=11954.6MB, alloc=685.6MB, time=101.21 memory used=12294.5MB, alloc=685.6MB, time=102.80 memory used=12595.9MB, alloc=685.6MB, time=103.67 memory used=12938.5MB, alloc=685.6MB, time=104.56 memory used=13463.7MB, alloc=685.6MB, time=107.48 memory used=13716.0MB, alloc=685.6MB, time=108.32 memory used=14042.5MB, alloc=685.6MB, time=110.28 memory used=14325.8MB, alloc=709.6MB, time=112.67 memory used=14517.2MB, alloc=733.6MB, time=115.39 memory used=14744.3MB, alloc=757.6MB, time=118.32 memory used=14998.4MB, alloc=781.6MB, time=121.28 memory used=15319.1MB, alloc=805.6MB, time=124.60 memory used=15570.5MB, alloc=829.6MB, time=127.28 memory used=15804.9MB, alloc=853.6MB, time=130.29 memory used=16166.5MB, alloc=877.6MB, time=134.12 memory used=16460.4MB, alloc=877.6MB, time=137.19 memory used=16854.5MB, alloc=901.6MB, time=141.40 memory used=17265.6MB, alloc=901.6MB, time=145.33 memory used=17476.8MB, alloc=925.6MB, time=148.17 memory used=17681.8MB, alloc=949.6MB, time=150.91 memory used=17896.5MB, alloc=973.6MB, time=153.78 memory used=18079.5MB, alloc=973.6MB, time=156.31 memory used=18583.3MB, alloc=997.6MB, time=162.69 memory used=19111.2MB, alloc=1021.6MB, time=169.87 memory used=19509.0MB, alloc=1045.6MB, time=179.87 memory used=19899.5MB, alloc=1069.6MB, time=190.36 memory used=20295.5MB, alloc=1093.6MB, time=201.23 memory used=20698.9MB, alloc=1117.6MB, time=212.51 memory used=21112.5MB, alloc=1141.6MB, time=224.16 memory used=21538.5MB, alloc=1165.6MB, time=236.30 memory used=21977.5MB, alloc=1189.6MB, time=249.20 memory used=22428.2MB, alloc=1213.6MB, time=262.48 memory used=22886.0MB, alloc=1237.6MB, time=276.25 memory used=23367.8MB, alloc=1261.6MB, time=290.69 memory used=23873.6MB, alloc=1285.6MB, time=305.97 memory used=24403.2MB, alloc=1309.6MB, time=321.77 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428548977 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 3 2 3 3 F := [-7 x + 17 x z + 14 z , 7 x y + 3 y + 6 z ] > G := [ randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 G := [4 x y z + 8 x y z - 7 x z , -19 x y + 20 y + 15 z] > Problem := [F,G]; 4 3 3 2 3 3 Problem := [[-7 x + 17 x z + 14 z , 7 x y + 3 y + 6 z ], 2 2 2 2 2 [4 x y z + 8 x y z - 7 x z , -19 x y + 20 y + 15 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.15 memory used=26.4MB, alloc=32.3MB, time=0.42 memory used=46.1MB, alloc=56.3MB, time=0.64 memory used=87.9MB, alloc=60.3MB, time=1.07 memory used=129.0MB, alloc=60.3MB, time=1.52 memory used=172.6MB, alloc=60.3MB, time=2.00 memory used=213.5MB, alloc=92.3MB, time=2.49 memory used=280.2MB, alloc=92.3MB, time=3.22 memory used=347.7MB, alloc=92.3MB, time=3.95 memory used=407.4MB, alloc=92.3MB, time=4.44 memory used=462.3MB, alloc=116.3MB, time=4.79 memory used=536.1MB, alloc=372.3MB, time=5.43 memory used=626.5MB, alloc=372.3MB, time=6.42 memory used=710.4MB, alloc=396.3MB, time=7.22 memory used=774.4MB, alloc=396.3MB, time=7.47 memory used=833.2MB, alloc=396.3MB, time=7.67 memory used=892.4MB, alloc=396.3MB, time=7.86 memory used=959.2MB, alloc=396.3MB, time=8.09 memory used=1008.7MB, alloc=396.3MB, time=8.24 memory used=1075.7MB, alloc=396.3MB, time=8.47 memory used=1126.9MB, alloc=396.3MB, time=8.62 memory used=1223.2MB, alloc=396.3MB, time=10.14 memory used=1277.0MB, alloc=396.3MB, time=10.30 memory used=1336.2MB, alloc=396.3MB, time=10.45 memory used=1381.7MB, alloc=396.3MB, time=10.57 memory used=1427.7MB, alloc=396.3MB, time=10.69 memory used=1484.6MB, alloc=396.3MB, time=10.82 memory used=1550.8MB, alloc=396.3MB, time=11.10 memory used=1603.7MB, alloc=396.3MB, time=11.26 memory used=1654.5MB, alloc=396.3MB, time=11.41 memory used=1717.2MB, alloc=396.3MB, time=11.57 memory used=1757.4MB, alloc=396.3MB, time=11.70 memory used=1820.0MB, alloc=396.3MB, time=11.96 memory used=1872.9MB, alloc=396.3MB, time=12.13 memory used=1925.4MB, alloc=396.3MB, time=12.28 memory used=1987.1MB, alloc=396.3MB, time=12.42 memory used=2028.4MB, alloc=396.3MB, time=12.53 memory used=2100.9MB, alloc=396.3MB, time=14.00 memory used=2151.2MB, alloc=396.3MB, time=14.16 memory used=2206.6MB, alloc=396.3MB, time=14.30 memory used=2250.0MB, alloc=396.3MB, time=14.43 memory used=2301.4MB, alloc=396.3MB, time=14.56 memory used=2373.6MB, alloc=396.3MB, time=14.80 memory used=2427.7MB, alloc=396.3MB, time=14.96 memory used=2482.4MB, alloc=396.3MB, time=15.13 memory used=2548.6MB, alloc=396.3MB, time=15.37 memory used=2598.2MB, alloc=396.3MB, time=15.52 memory used=2666.2MB, alloc=396.3MB, time=15.77 memory used=2715.4MB, alloc=396.3MB, time=15.91 memory used=2784.8MB, alloc=396.3MB, time=16.64 memory used=2839.8MB, alloc=396.3MB, time=16.79 memory used=2895.7MB, alloc=396.3MB, time=16.97 memory used=2948.5MB, alloc=396.3MB, time=17.13 memory used=3012.2MB, alloc=396.3MB, time=17.34 memory used=3065.3MB, alloc=396.3MB, time=17.50 memory used=3132.1MB, alloc=396.3MB, time=18.17 memory used=3185.6MB, alloc=396.3MB, time=18.34 memory used=3235.7MB, alloc=396.3MB, time=18.46 memory used=3301.3MB, alloc=396.3MB, time=18.73 memory used=3350.2MB, alloc=396.3MB, time=18.89 memory used=3407.7MB, alloc=396.3MB, time=19.03 memory used=3488.9MB, alloc=396.3MB, time=19.50 memory used=3601.9MB, alloc=396.3MB, time=20.35 memory used=3713.7MB, alloc=420.3MB, time=21.64 memory used=3841.0MB, alloc=420.3MB, time=22.83 memory used=3918.8MB, alloc=420.3MB, time=23.42 memory used=4026.0MB, alloc=420.3MB, time=24.05 memory used=4185.5MB, alloc=420.3MB, time=25.27 memory used=4296.8MB, alloc=444.3MB, time=26.27 memory used=4414.6MB, alloc=444.3MB, time=27.32 memory used=4501.7MB, alloc=444.3MB, time=27.68 memory used=4562.1MB, alloc=444.3MB, time=27.88 memory used=4640.5MB, alloc=444.3MB, time=28.15 memory used=4702.0MB, alloc=444.3MB, time=28.38 memory used=4778.9MB, alloc=444.3MB, time=28.84 memory used=4839.1MB, alloc=444.3MB, time=29.05 memory used=4910.0MB, alloc=444.3MB, time=29.29 memory used=4979.3MB, alloc=444.3MB, time=29.54 memory used=5064.4MB, alloc=444.3MB, time=30.06 memory used=5126.7MB, alloc=444.3MB, time=30.27 memory used=5236.3MB, alloc=444.3MB, time=30.81 memory used=5307.4MB, alloc=468.3MB, time=31.04 memory used=5391.0MB, alloc=468.3MB, time=31.30 memory used=5478.5MB, alloc=468.3MB, time=31.55 memory used=5585.8MB, alloc=468.3MB, time=32.73 memory used=5668.3MB, alloc=468.3MB, time=32.95 memory used=5743.3MB, alloc=468.3MB, time=33.15 memory used=5822.6MB, alloc=468.3MB, time=33.34 memory used=5980.2MB, alloc=468.3MB, time=34.13 memory used=6106.5MB, alloc=468.3MB, time=35.16 memory used=6185.6MB, alloc=468.3MB, time=35.40 memory used=6267.8MB, alloc=468.3MB, time=35.65 memory used=6350.9MB, alloc=468.3MB, time=35.96 memory used=6425.2MB, alloc=468.3MB, time=36.20 memory used=6514.6MB, alloc=468.3MB, time=36.43 memory used=6572.2MB, alloc=468.3MB, time=36.62 memory used=6637.4MB, alloc=468.3MB, time=36.82 memory used=6712.7MB, alloc=468.3MB, time=37.03 memory used=6797.9MB, alloc=468.3MB, time=37.24 memory used=6893.8MB, alloc=468.3MB, time=37.45 memory used=7053.1MB, alloc=468.3MB, time=37.85 memory used=7197.2MB, alloc=468.3MB, time=38.25 memory used=7278.7MB, alloc=468.3MB, time=38.48 memory used=7351.3MB, alloc=468.3MB, time=38.71 memory used=7413.5MB, alloc=468.3MB, time=38.90 memory used=7484.1MB, alloc=468.3MB, time=39.10 memory used=7564.6MB, alloc=468.3MB, time=39.30 memory used=7655.7MB, alloc=468.3MB, time=39.51 memory used=7857.8MB, alloc=468.3MB, time=39.82 memory used=8049.3MB, alloc=468.3MB, time=42.28 memory used=8133.9MB, alloc=468.3MB, time=42.51 memory used=8193.4MB, alloc=468.3MB, time=42.72 memory used=8266.3MB, alloc=468.3MB, time=42.92 memory used=8350.6MB, alloc=468.3MB, time=43.15 memory used=8450.9MB, alloc=468.3MB, time=43.38 memory used=8588.0MB, alloc=468.3MB, time=43.68 memory used=8745.6MB, alloc=468.3MB, time=43.98 memory used=8925.9MB, alloc=468.3MB, time=44.30 memory used=9134.5MB, alloc=468.3MB, time=44.64 memory used=9353.6MB, alloc=468.3MB, time=44.97 memory used=9533.6MB, alloc=468.3MB, time=45.27 memory used=9781.1MB, alloc=468.3MB, time=46.25 memory used=9957.4MB, alloc=468.3MB, time=47.65 memory used=10034.5MB, alloc=468.3MB, time=47.89 memory used=10102.3MB, alloc=468.3MB, time=48.09 memory used=10186.0MB, alloc=468.3MB, time=48.31 memory used=10401.6MB, alloc=468.3MB, time=48.68 memory used=10573.2MB, alloc=468.3MB, time=48.99 memory used=10786.3MB, alloc=468.3MB, time=49.32 memory used=11003.3MB, alloc=468.3MB, time=50.21 memory used=11088.1MB, alloc=468.3MB, time=50.51 memory used=11169.8MB, alloc=468.3MB, time=50.85 memory used=11249.5MB, alloc=468.3MB, time=51.09 memory used=11310.4MB, alloc=468.3MB, time=51.30 memory used=11385.8MB, alloc=468.3MB, time=51.52 memory used=11477.6MB, alloc=468.3MB, time=51.73 memory used=11599.0MB, alloc=468.3MB, time=52.14 memory used=11675.7MB, alloc=468.3MB, time=52.39 memory used=11738.1MB, alloc=468.3MB, time=52.59 memory used=11815.0MB, alloc=468.3MB, time=52.81 memory used=11960.8MB, alloc=468.3MB, time=53.95 memory used=12036.4MB, alloc=468.3MB, time=54.19 memory used=12106.9MB, alloc=468.3MB, time=54.40 memory used=12325.8MB, alloc=468.3MB, time=54.77 memory used=12461.1MB, alloc=468.3MB, time=55.25 memory used=12546.6MB, alloc=468.3MB, time=55.51 memory used=12603.1MB, alloc=468.3MB, time=55.73 memory used=12667.8MB, alloc=468.3MB, time=55.95 memory used=12742.9MB, alloc=468.3MB, time=56.17 memory used=12830.0MB, alloc=468.3MB, time=56.40 memory used=13022.4MB, alloc=468.3MB, time=56.74 memory used=13252.8MB, alloc=468.3MB, time=57.50 memory used=13343.3MB, alloc=468.3MB, time=57.88 memory used=13411.4MB, alloc=468.3MB, time=58.12 memory used=13488.2MB, alloc=492.3MB, time=58.37 memory used=13561.9MB, alloc=492.3MB, time=58.60 memory used=13650.8MB, alloc=492.3MB, time=58.83 memory used=13757.1MB, alloc=492.3MB, time=59.07 memory used=13948.1MB, alloc=492.3MB, time=59.58 memory used=14044.3MB, alloc=492.3MB, time=59.86 memory used=14121.3MB, alloc=492.3MB, time=60.10 memory used=14203.3MB, alloc=492.3MB, time=60.34 memory used=14301.0MB, alloc=492.3MB, time=60.59 memory used=14512.7MB, alloc=492.3MB, time=64.94 memory used=14628.2MB, alloc=492.3MB, time=65.29 memory used=14705.0MB, 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used=21083.9MB, alloc=588.3MB, time=97.82 memory used=21267.4MB, alloc=612.3MB, time=99.63 memory used=21393.4MB, alloc=636.3MB, time=101.17 memory used=21537.2MB, alloc=636.3MB, time=102.90 memory used=21662.6MB, alloc=660.3MB, time=104.33 memory used=21805.3MB, alloc=660.3MB, time=106.01 memory used=21993.5MB, alloc=684.3MB, time=107.75 memory used=22112.4MB, alloc=684.3MB, time=109.24 memory used=22249.7MB, alloc=708.3MB, time=110.87 memory used=22423.1MB, alloc=708.3MB, time=113.09 memory used=22583.8MB, alloc=708.3MB, time=114.72 memory used=22706.1MB, alloc=732.3MB, time=116.40 memory used=22825.5MB, alloc=732.3MB, time=117.92 memory used=22916.0MB, alloc=732.3MB, time=119.31 memory used=23009.4MB, alloc=756.3MB, time=120.89 memory used=23300.6MB, alloc=780.3MB, time=127.27 memory used=23588.1MB, alloc=804.3MB, time=134.28 memory used=23883.1MB, alloc=828.3MB, time=141.80 memory used=24188.9MB, alloc=852.3MB, time=149.75 memory used=24506.2MB, alloc=876.3MB, time=158.07 memory 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