|\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428240140 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; F := [-20 y z - 6 x + 17 y - 4 z, 16 y z - 19 y - 9 z - 15, 2 5 x + 9 x z + 13 x - 4 y] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [12 x + 18 y z + 6 z, 10 x y + 6 y - 2 z - y, 2 2 -10 x + 10 x y + 9 y - 9 y] > Problem := [F,G]; Problem := [[-20 y z - 6 x + 17 y - 4 z, 16 y z - 19 y - 9 z - 15, 2 2 2 2 5 x + 9 x z + 13 x - 4 y], [12 x + 18 y z + 6 z, 10 x y + 6 y - 2 z - y, 2 2 -10 x + 10 x y + 9 y - 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=0.18 memory used=26.4MB, alloc=32.3MB, time=0.53 memory used=46.7MB, alloc=32.3MB, time=0.84 memory used=66.4MB, alloc=56.3MB, time=1.16 memory used=107.5MB, alloc=60.3MB, time=1.81 memory used=146.6MB, alloc=84.3MB, time=2.42 memory used=207.9MB, alloc=92.3MB, time=3.44 memory used=269.0MB, alloc=116.3MB, time=4.47 memory used=354.9MB, alloc=116.3MB, time=5.89 memory used=437.9MB, alloc=140.3MB, time=7.34 memory used=519.8MB, alloc=140.3MB, time=8.79 memory used=598.4MB, alloc=396.3MB, time=10.23 memory used=702.5MB, alloc=420.3MB, time=12.13 memory used=829.6MB, alloc=444.3MB, time=14.49 memory used=979.0MB, alloc=468.3MB, time=17.32 memory used=1104.8MB, alloc=492.3MB, time=19.48 memory used=1253.9MB, alloc=516.3MB, time=22.87 memory used=1377.8MB, alloc=516.3MB, time=25.26 memory used=1470.6MB, alloc=516.3MB, time=26.93 memory used=1574.0MB, alloc=516.3MB, time=29.16 memory used=1674.3MB, alloc=516.3MB, time=31.26 memory used=1775.1MB, alloc=540.3MB, time=33.76 memory used=1838.7MB, alloc=540.3MB, time=35.03 memory used=1926.9MB, alloc=540.3MB, time=37.24 memory used=2004.0MB, alloc=540.3MB, time=39.20 memory used=2077.0MB, alloc=540.3MB, time=40.88 memory used=2147.8MB, alloc=540.3MB, time=43.16 memory used=2189.5MB, alloc=540.3MB, time=44.33 memory used=2422.8MB, alloc=564.3MB, time=49.66 memory used=2629.5MB, alloc=588.3MB, time=54.23 memory used=2824.0MB, alloc=612.3MB, time=59.06 memory used=3040.5MB, alloc=636.3MB, time=65.07 memory used=3208.4MB, alloc=660.3MB, time=69.28 memory used=3393.3MB, alloc=684.3MB, time=74.80 memory used=3576.7MB, alloc=684.3MB, time=80.19 memory used=3730.1MB, alloc=684.3MB, time=84.28 memory used=3853.3MB, alloc=684.3MB, time=87.50 memory used=4017.6MB, alloc=708.3MB, time=93.20 memory used=4125.6MB, alloc=708.3MB, time=96.13 memory used=4246.6MB, alloc=708.3MB, time=100.10 |\^/| 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(); 1428240440 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [x z + 14 y + 4 y z + 1, -4 y - 13 z + 17 y + 14 z, 2 2 -x - 7 x z - 12 z - 18 x] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [16 z + 18 y - 18 z + 18, 5 x + 17 y + 9 y z - 11 y, 2 2 -7 x + 5 y + 8 y - 10 z] > Problem := [F,G]; 2 2 2 Problem := [[x z + 14 y + 4 y z + 1, -4 y - 13 z + 17 y + 14 z, 2 2 2 -x - 7 x z - 12 z - 18 x], [16 z + 18 y - 18 z + 18, 2 2 2 2 5 x + 17 y + 9 y z - 11 y, -7 x + 5 y + 8 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=4.3MB, alloc=32.3MB, time=0.18 memory used=26.0MB, alloc=32.3MB, time=0.53 memory used=45.9MB, alloc=56.3MB, time=0.86 memory used=86.2MB, alloc=60.3MB, time=1.49 memory used=129.3MB, alloc=92.3MB, time=2.14 memory used=199.8MB, alloc=92.3MB, time=3.11 memory used=265.8MB, alloc=116.3MB, time=4.14 memory used=349.2MB, alloc=372.3MB, time=5.43 memory used=444.2MB, alloc=372.3MB, time=6.69 memory used=532.2MB, alloc=396.3MB, time=8.02 memory used=646.2MB, alloc=420.3MB, time=9.74 memory used=781.9MB, alloc=420.3MB, time=11.71 memory used=901.9MB, alloc=444.3MB, time=13.53 memory used=1012.0MB, alloc=468.3MB, time=15.38 memory used=1127.5MB, alloc=468.3MB, time=17.04 memory used=1224.2MB, alloc=468.3MB, time=18.52 memory used=1320.5MB, alloc=468.3MB, time=20.26 memory used=1401.8MB, alloc=492.3MB, time=21.53 memory used=1494.3MB, alloc=492.3MB, time=23.17 memory used=1571.3MB, alloc=492.3MB, time=24.46 memory used=1647.3MB, alloc=492.3MB, time=25.61 memory used=1751.1MB, alloc=516.3MB, time=27.77 memory used=1811.5MB, alloc=516.3MB, time=29.06 memory used=1878.5MB, alloc=516.3MB, time=30.56 memory used=1930.4MB, alloc=516.3MB, time=31.58 memory used=1984.8MB, alloc=516.3MB, time=32.58 memory used=2172.1MB, alloc=540.3MB, time=36.12 memory used=2390.1MB, alloc=540.3MB, time=41.56 memory used=2606.6MB, alloc=564.3MB, time=44.97 memory used=2799.4MB, alloc=588.3MB, time=48.09 memory used=2994.2MB, alloc=612.3MB, time=51.18 memory used=3159.0MB, alloc=612.3MB, time=54.22 memory used=3333.6MB, alloc=636.3MB, time=58.20 memory used=3505.7MB, alloc=636.3MB, time=61.41 memory used=3646.0MB, alloc=660.3MB, time=63.67 memory used=3794.9MB, alloc=660.3MB, time=66.61 memory used=3931.9MB, alloc=660.3MB, time=69.47 memory used=4070.2MB, alloc=660.3MB, time=72.35 memory used=4189.6MB, alloc=660.3MB, time=74.90 memory used=4330.0MB, alloc=660.3MB, time=77.61 memory used=4428.4MB, alloc=660.3MB, time=79.77 memory used=4555.8MB, alloc=684.3MB, time=81.97 memory used=4915.6MB, alloc=708.3MB, time=89.08 memory used=5282.1MB, alloc=732.3MB, time=96.23 memory used=5670.7MB, alloc=756.3MB, time=102.37 |\^/| 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(); 1428240740 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [14 y z + 3 z + 9 x + 20 z, 16 x + 18 x y - 11 z - x, 2 -19 x z - 2 y z + 11 z ] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [20 x - 13 y - 12 x, 10 x y - 4 y + 4 x - 5 y, 2 2 -19 x + 17 y z + 4 z + 9 z] > Problem := [F,G]; 2 2 2 Problem := [[14 y z + 3 z + 9 x + 20 z, 16 x + 18 x y - 11 z - x, 2 2 2 2 -19 x z - 2 y z + 11 z ], [20 x - 13 y - 12 x, 10 x y - 4 y + 4 x - 5 y, 2 2 -19 x + 17 y z + 4 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=0.18 memory used=26.0MB, alloc=32.3MB, time=0.49 memory used=47.2MB, alloc=32.3MB, time=0.81 memory used=67.0MB, alloc=56.3MB, time=1.12 memory used=107.0MB, alloc=60.3MB, time=1.73 memory used=145.8MB, alloc=84.3MB, time=2.34 memory used=206.5MB, alloc=92.3MB, time=3.33 memory used=266.6MB, alloc=116.3MB, time=4.29 memory used=349.2MB, alloc=116.3MB, time=5.64 memory used=430.5MB, alloc=140.3MB, time=7.03 memory used=506.2MB, alloc=164.3MB, time=8.27 memory used=577.7MB, alloc=420.3MB, time=9.49 memory used=704.8MB, alloc=444.3MB, time=11.63 memory used=852.4MB, alloc=468.3MB, time=14.29 memory used=1022.6MB, alloc=492.3MB, time=17.54 memory used=1221.3MB, alloc=516.3MB, time=21.15 memory used=1441.6MB, alloc=540.3MB, time=25.39 memory used=1682.1MB, alloc=564.3MB, time=30.48 memory used=1950.4MB, alloc=588.3MB, time=35.84 memory used=2211.6MB, alloc=612.3MB, time=41.08 memory used=2479.9MB, alloc=636.3MB, time=47.09 memory used=2712.2MB, alloc=660.3MB, time=52.89 memory used=2959.2MB, alloc=684.3MB, time=59.15 memory used=3203.3MB, alloc=708.3MB, time=65.87 memory used=3424.8MB, alloc=732.3MB, time=72.24 memory used=3616.8MB, alloc=756.3MB, time=77.49 memory used=3801.9MB, alloc=756.3MB, time=82.83 memory used=3977.5MB, alloc=780.3MB, time=87.81 memory used=4132.1MB, alloc=780.3MB, time=92.20 |\^/| 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(); 1428241040 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [2 x y + 8 y z + 18 x - 14, 12 x z + 10 z + 20 x + 17 y, 2 -14 x - 18 x z + 20 y + 20] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; G := [ 2 2 2 9 z - 12 x - 18 z + 10, 9 x - 2 y - 12 x - 9 y, 19 x y + 7 x + 14 y - 5] > Problem := [F,G]; 2 Problem := [[2 x y + 8 y z + 18 x - 14, 12 x z + 10 z + 20 x + 17 y, 2 -14 x - 18 x z + 20 y + 20], [ 2 2 2 9 z - 12 x - 18 z + 10, 9 x - 2 y - 12 x - 9 y, 19 x y + 7 x + 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=32.0MB, alloc=40.3MB, time=0.63 memory used=59.0MB, alloc=44.3MB, time=1.05 memory used=85.3MB, alloc=68.3MB, time=1.50 memory used=133.3MB, alloc=76.3MB, time=2.26 memory used=179.4MB, alloc=76.3MB, time=2.98 memory used=224.6MB, alloc=100.3MB, time=3.71 memory used=293.0MB, alloc=100.3MB, time=4.81 memory used=361.6MB, alloc=124.3MB, time=5.90 memory used=445.0MB, alloc=380.3MB, time=7.33 memory used=535.5MB, alloc=404.3MB, time=8.85 memory used=650.0MB, alloc=428.3MB, time=10.84 memory used=787.9MB, alloc=452.3MB, time=13.29 memory used=941.2MB, alloc=452.3MB, time=16.09 memory used=1080.9MB, alloc=476.3MB, time=18.78 memory used=1204.1MB, alloc=500.3MB, time=21.20 memory used=1338.8MB, alloc=500.3MB, time=23.99 memory used=1460.3MB, alloc=500.3MB, time=26.31 memory used=1571.1MB, alloc=524.3MB, time=28.53 memory used=1670.1MB, alloc=524.3MB, time=30.63 memory used=1756.4MB, alloc=524.3MB, time=32.53 memory used=1841.0MB, alloc=524.3MB, time=34.33 memory used=1949.0MB, alloc=548.3MB, time=36.64 memory used=2038.0MB, alloc=548.3MB, time=38.64 memory used=2137.8MB, alloc=572.3MB, time=40.93 memory used=2201.4MB, alloc=572.3MB, time=42.54 memory used=2289.1MB, alloc=596.3MB, time=44.60 memory used=2383.1MB, alloc=596.3MB, time=46.78 memory used=2464.9MB, alloc=620.3MB, time=48.79 memory used=2531.1MB, alloc=620.3MB, time=50.49 memory used=2622.2MB, alloc=620.3MB, time=52.66 memory used=2713.1MB, alloc=644.3MB, time=54.77 memory used=2802.4MB, alloc=668.3MB, time=56.79 memory used=2892.0MB, alloc=668.3MB, time=58.84 memory used=2980.3MB, alloc=692.3MB, time=60.94 memory used=3266.4MB, alloc=716.3MB, time=66.51 memory used=3555.7MB, alloc=740.3MB, time=72.17 memory used=3852.3MB, alloc=764.3MB, time=77.96 memory used=4151.3MB, alloc=788.3MB, time=83.93 |\^/| 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(); 1428241340 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 F := [17 x + x z + 4 y - 12 z , -17 x y - 3 x z - 20 y - 14 z , -2 x y + 13 x z - 15 x - 10 y] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [-16 x y + 11 y + 16 z - 18, -4 x + 7 y z + 14 z - 2 z, 2 2 -x - 4 x z + 4 z - 12] > Problem := [F,G]; 2 2 2 2 2 Problem := [[17 x + x z + 4 y - 12 z , -17 x y - 3 x z - 20 y - 14 z , 2 -2 x y + 13 x z - 15 x - 10 y], [-16 x y + 11 y + 16 z - 18, 2 2 2 2 -4 x + 7 y z + 14 z - 2 z, -x - 4 x z + 4 z - 12]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,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=25.2MB, alloc=32.3MB, time=0.48 memory used=44.7MB, alloc=56.3MB, time=0.77 memory used=86.7MB, alloc=60.3MB, time=1.38 memory used=131.3MB, alloc=68.3MB, time=2.00 memory used=174.5MB, alloc=92.3MB, time=2.64 memory used=243.3MB, alloc=92.3MB, time=3.57 memory used=311.5MB, alloc=92.3MB, time=4.50 memory used=378.7MB, alloc=116.3MB, time=5.48 memory used=441.0MB, alloc=372.3MB, time=6.40 memory used=532.3MB, alloc=372.3MB, time=7.53 memory used=622.7MB, alloc=396.3MB, time=8.76 memory used=739.0MB, alloc=396.3MB, time=10.47 memory used=849.1MB, alloc=420.3MB, time=12.02 memory used=985.7MB, alloc=444.3MB, time=14.05 memory used=1103.1MB, alloc=468.3MB, time=15.98 memory used=1222.0MB, alloc=468.3MB, time=17.77 memory used=1331.1MB, alloc=468.3MB, time=19.20 memory used=1456.5MB, alloc=492.3MB, time=20.91 memory used=1562.4MB, alloc=492.3MB, time=22.78 memory used=1658.2MB, alloc=492.3MB, time=24.35 memory used=1736.7MB, alloc=516.3MB, time=25.64 memory used=1824.9MB, alloc=516.3MB, time=27.15 memory used=1915.8MB, alloc=516.3MB, time=28.69 memory used=1995.7MB, alloc=516.3MB, time=29.87 memory used=2081.2MB, alloc=516.3MB, time=31.33 memory used=2151.4MB, alloc=516.3MB, time=32.57 memory used=2223.5MB, alloc=516.3MB, time=33.60 memory used=2305.4MB, alloc=540.3MB, time=34.66 memory used=2380.0MB, alloc=540.3MB, time=36.29 memory used=2434.0MB, alloc=540.3MB, time=37.37 memory used=2487.6MB, alloc=540.3MB, time=38.31 memory used=2540.0MB, alloc=540.3MB, time=39.49 memory used=2592.5MB, alloc=540.3MB, time=40.54 memory used=2829.1MB, alloc=564.3MB, time=43.24 memory used=3057.8MB, alloc=588.3MB, time=46.75 memory used=3255.9MB, alloc=588.3MB, time=50.00 memory used=3468.5MB, alloc=612.3MB, time=52.90 memory used=3663.5MB, alloc=636.3MB, time=56.40 memory used=3846.0MB, alloc=636.3MB, time=59.20 memory used=4014.3MB, alloc=660.3MB, time=62.33 memory used=4203.6MB, alloc=660.3MB, time=65.48 memory used=4351.2MB, alloc=660.3MB, time=68.03 memory used=4503.7MB, alloc=660.3MB, time=71.10 memory used=4636.9MB, alloc=660.3MB, time=73.91 memory used=4750.4MB, alloc=660.3MB, time=76.06 memory used=4907.7MB, alloc=684.3MB, time=79.06 memory used=5054.4MB, alloc=684.3MB, time=81.88 memory used=5187.3MB, alloc=684.3MB, time=84.40 memory used=5290.2MB, alloc=684.3MB, time=86.40 memory used=5423.4MB, alloc=684.3MB, time=89.29 memory used=5775.8MB, alloc=708.3MB, time=96.54 |\^/| 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(); 1428241640 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 F := [-5 x + 15 x z - 2 y - 3 z , 5 x y + 14 y - 4 z - 13, 2 2 -9 x y - 8 x z - 15 y - 2 z ] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-13 x - 3 x y + 11 x + 9 z, -20 x z + 12 y - 17 y - 11, 2 2 8 y + z + 14 y + 14] > Problem := [F,G]; 2 2 2 2 2 Problem := [[-5 x + 15 x z - 2 y - 3 z , 5 x y + 14 y - 4 z - 13, 2 2 2 -9 x y - 8 x z - 15 y - 2 z ], [-13 x - 3 x y + 11 x + 9 z, 2 2 2 -20 x z + 12 y - 17 y - 11, 8 y + z + 14 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=4.4MB, alloc=32.3MB, time=0.18 memory used=25.3MB, alloc=32.3MB, time=0.49 memory used=44.4MB, alloc=56.3MB, time=0.79 memory used=86.1MB, alloc=60.3MB, time=1.39 memory used=128.3MB, alloc=68.3MB, time=2.01 memory used=171.8MB, alloc=92.3MB, time=2.63 memory used=238.2MB, alloc=92.3MB, time=3.57 memory used=307.0MB, alloc=116.3MB, time=4.48 memory used=373.4MB, alloc=116.3MB, time=5.45 memory used=438.3MB, alloc=372.3MB, time=6.44 memory used=526.4MB, alloc=396.3MB, time=7.79 memory used=636.9MB, alloc=396.3MB, time=9.24 memory used=746.8MB, alloc=420.3MB, time=10.92 memory used=879.0MB, alloc=444.3MB, time=12.90 memory used=1003.9MB, alloc=468.3MB, time=14.94 memory used=1117.9MB, alloc=468.3MB, time=16.72 memory used=1207.2MB, alloc=468.3MB, time=17.99 memory used=1305.7MB, alloc=492.3MB, time=19.71 memory used=1379.0MB, alloc=492.3MB, time=20.75 memory used=1479.7MB, alloc=492.3MB, time=22.76 memory used=1552.6MB, alloc=492.3MB, time=24.01 memory used=1630.2MB, alloc=492.3MB, time=25.46 memory used=1691.4MB, alloc=516.3MB, time=26.53 memory used=1750.0MB, alloc=516.3MB, time=27.59 memory used=1822.7MB, alloc=516.3MB, time=28.72 memory used=1875.0MB, alloc=516.3MB, time=29.89 memory used=1924.4MB, alloc=516.3MB, time=30.84 memory used=1970.3MB, alloc=516.3MB, time=32.13 memory used=2011.2MB, alloc=516.3MB, time=33.13 memory used=2228.6MB, alloc=540.3MB, time=36.54 memory used=2407.3MB, alloc=564.3MB, time=39.60 memory used=2550.8MB, alloc=588.3MB, time=42.22 memory used=2721.3MB, alloc=612.3MB, time=45.22 memory used=2873.4MB, alloc=612.3MB, time=47.97 memory used=3028.4MB, alloc=636.3MB, time=50.75 memory used=3182.3MB, alloc=636.3MB, time=53.56 memory used=3265.3MB, alloc=636.3MB, time=55.42 memory used=3394.1MB, alloc=636.3MB, time=57.74 memory used=3482.8MB, alloc=636.3MB, time=59.96 memory used=3596.8MB, alloc=636.3MB, time=62.32 memory used=3694.8MB, alloc=636.3MB, time=64.59 memory used=3777.3MB, alloc=636.3MB, time=66.37 memory used=4083.4MB, alloc=660.3MB, time=72.48 memory used=4411.7MB, alloc=684.3MB, time=79.05 memory used=4749.4MB, alloc=708.3MB, time=86.53 memory used=5126.0MB, alloc=732.3MB, time=94.41 memory used=5489.0MB, alloc=756.3MB, time=102.38 |\^/| 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(); 1428241940 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-12 x + 10 x y - 11 x - 16 y, -15 x - 11 y - 13 x + 10, 2 2 11 y + 11 z + 20 y + 9 z] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [14 x - 15 x z - 10 z + 12 y, -6 x y - 10 x z - 15 z + 15 z, 18 x z - 14 x + 17 y + 8 z] > Problem := [F,G]; 2 2 2 Problem := [[-12 x + 10 x y - 11 x - 16 y, -15 x - 11 y - 13 x + 10, 2 2 2 2 11 y + 11 z + 20 y + 9 z], [14 x - 15 x z - 10 z + 12 y, 2 -6 x y - 10 x z - 15 z + 15 z, 18 x z - 14 x + 17 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=32.3MB, alloc=40.3MB, time=0.59 memory used=59.8MB, alloc=44.3MB, time=1.01 memory used=85.5MB, alloc=68.3MB, time=1.40 memory used=132.4MB, alloc=76.3MB, time=2.16 memory used=180.3MB, alloc=100.3MB, time=2.92 memory used=250.8MB, alloc=100.3MB, time=4.02 memory used=320.0MB, alloc=100.3MB, time=5.14 memory used=383.0MB, alloc=124.3MB, time=6.21 memory used=454.9MB, alloc=380.3MB, time=7.47 memory used=545.6MB, alloc=404.3MB, time=8.95 memory used=660.9MB, alloc=428.3MB, time=10.91 memory used=801.5MB, alloc=452.3MB, time=13.21 memory used=954.7MB, alloc=476.3MB, time=15.79 memory used=1104.8MB, alloc=500.3MB, time=18.55 memory used=1242.1MB, alloc=500.3MB, time=21.17 memory used=1382.1MB, alloc=500.3MB, time=24.02 memory used=1504.5MB, alloc=500.3MB, time=26.46 memory used=1615.3MB, alloc=524.3MB, time=28.70 memory used=1729.1MB, alloc=524.3MB, time=30.78 memory used=1851.2MB, alloc=524.3MB, time=32.77 memory used=1948.7MB, alloc=524.3MB, time=34.64 memory used=2053.6MB, alloc=524.3MB, time=37.09 memory used=2159.5MB, alloc=524.3MB, time=39.56 memory used=2260.1MB, alloc=524.3MB, time=41.90 memory used=2365.0MB, alloc=524.3MB, time=44.62 memory used=2449.4MB, alloc=524.3MB, time=46.32 memory used=2520.8MB, alloc=524.3MB, time=47.54 memory used=2605.5MB, alloc=524.3MB, time=49.54 memory used=2662.7MB, alloc=548.3MB, time=50.89 memory used=2760.6MB, alloc=548.3MB, time=53.65 memory used=2826.9MB, alloc=548.3MB, time=55.30 memory used=2890.6MB, alloc=548.3MB, time=57.09 memory used=2957.9MB, alloc=548.3MB, time=58.96 memory used=3025.7MB, alloc=548.3MB, time=60.84 memory used=3083.0MB, alloc=548.3MB, time=62.56 memory used=3140.9MB, alloc=548.3MB, time=64.29 memory used=3193.5MB, alloc=548.3MB, time=65.82 memory used=3429.0MB, alloc=572.3MB, time=72.11 memory used=3677.9MB, alloc=596.3MB, time=78.24 memory used=3936.0MB, alloc=620.3MB, time=84.81 memory used=4189.9MB, alloc=644.3MB, time=91.78 memory used=4395.7MB, alloc=668.3MB, time=97.15 memory used=4621.7MB, alloc=692.3MB, time=101.84 memory used=4840.9MB, alloc=692.3MB, time=107.86 |\^/| 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(); 1428242240 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-4 x y - 17 x z - 3 y z - 4 z , 8 y + 10 z - 16 x - 8, 2 2 -x + 13 y + 2 y z + 6 x] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [7 x + 6 y + 12 z - 11 z, -15 x y + 7 x z - 7 y z + 4 y, 19 x y - y z - 17 z - 13] > Problem := [F,G]; 2 2 2 Problem := [[-4 x y - 17 x z - 3 y z - 4 z , 8 y + 10 z - 16 x - 8, 2 2 2 2 2 -x + 13 y + 2 y z + 6 x], [7 x + 6 y + 12 z - 11 z, -15 x y + 7 x z - 7 y z + 4 y, 19 x y - y z - 17 z - 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 used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.0MB, alloc=32.3MB, time=0.50 memory used=46.3MB, alloc=32.3MB, time=0.80 memory used=65.0MB, alloc=56.3MB, time=1.09 memory used=104.4MB, alloc=60.3MB, time=1.69 memory used=139.9MB, alloc=84.3MB, time=2.23 memory used=201.3MB, alloc=92.3MB, time=3.19 memory used=267.0MB, alloc=116.3MB, time=4.10 memory used=348.1MB, alloc=116.3MB, time=5.40 memory used=423.6MB, alloc=396.3MB, time=6.60 memory used=531.1MB, alloc=396.3MB, time=8.21 memory used=647.5MB, alloc=420.3MB, time=9.82 memory used=782.8MB, alloc=420.3MB, time=11.74 memory used=911.5MB, alloc=444.3MB, time=13.59 memory used=1034.1MB, alloc=444.3MB, time=15.38 memory used=1153.3MB, alloc=468.3MB, time=17.32 memory used=1273.1MB, alloc=468.3MB, time=19.00 memory used=1372.1MB, alloc=492.3MB, time=20.65 memory used=1480.5MB, alloc=492.3MB, time=22.53 memory used=1569.9MB, alloc=492.3MB, time=24.01 memory used=1642.9MB, alloc=516.3MB, time=25.02 memory used=1748.4MB, alloc=516.3MB, time=27.07 memory used=1822.6MB, alloc=516.3MB, time=28.46 memory used=1913.8MB, alloc=516.3MB, time=30.33 memory used=1982.0MB, alloc=516.3MB, time=31.62 memory used=2048.2MB, alloc=540.3MB, time=32.62 memory used=2103.2MB, alloc=540.3MB, time=33.76 memory used=2170.1MB, alloc=540.3MB, time=35.25 memory used=2234.1MB, alloc=540.3MB, time=36.86 memory used=2280.2MB, alloc=540.3MB, time=37.90 memory used=2332.8MB, alloc=540.3MB, time=38.90 memory used=2537.4MB, alloc=564.3MB, time=42.40 memory used=2750.6MB, alloc=588.3MB, time=46.29 memory used=2943.7MB, alloc=612.3MB, time=49.61 memory used=3130.9MB, alloc=636.3MB, time=52.44 memory used=3301.6MB, alloc=660.3MB, time=54.72 memory used=3454.6MB, alloc=660.3MB, time=57.57 memory used=3618.5MB, alloc=684.3MB, time=60.50 memory used=3725.7MB, alloc=684.3MB, time=62.82 memory used=3873.4MB, alloc=684.3MB, time=65.89 memory used=3997.3MB, alloc=684.3MB, time=68.32 memory used=4119.5MB, alloc=684.3MB, time=70.45 memory used=4249.3MB, alloc=708.3MB, time=72.82 memory used=4353.2MB, alloc=708.3MB, time=75.16 memory used=4445.7MB, alloc=708.3MB, time=77.23 memory used=4809.5MB, alloc=732.3MB, time=83.63 memory used=5158.7MB, alloc=756.3MB, time=89.52 memory used=5515.9MB, alloc=780.3MB, time=95.64 memory used=5892.5MB, alloc=804.3MB, time=104.34 |\^/| 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(); 1428242540 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-8 x - 14 x y - 12 y z + 14 x, 14 x - 4 x y + 8 x z + 12 x, 2 -8 x y - 9 y - 3 z] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [13 x + 11 y z - 4 x + 14 z, -16 x y - 2 y - 12 z - 4 x, 2 13 x + 20 x - 9 z + 4] > Problem := [F,G]; 2 2 Problem := [[-8 x - 14 x y - 12 y z + 14 x, 14 x - 4 x y + 8 x z + 12 x, 2 2 -8 x y - 9 y - 3 z], [13 x + 11 y z - 4 x + 14 z, 2 2 2 -16 x y - 2 y - 12 z - 4 x, 13 x + 20 x - 9 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=0.17 memory used=25.9MB, alloc=32.3MB, time=0.49 memory used=46.3MB, alloc=56.3MB, time=0.80 memory used=88.8MB, alloc=60.3MB, time=1.43 memory used=129.1MB, alloc=84.3MB, time=2.04 memory used=173.9MB, alloc=84.3MB, time=2.72 memory used=233.8MB, alloc=92.3MB, time=3.68 memory used=295.5MB, alloc=116.3MB, time=4.62 memory used=366.1MB, alloc=140.3MB, time=5.75 memory used=433.8MB, alloc=396.3MB, time=6.85 memory used=540.8MB, alloc=420.3MB, time=8.58 memory used=671.1MB, alloc=444.3MB, time=10.79 memory used=815.0MB, alloc=468.3MB, time=13.29 memory used=936.2MB, alloc=468.3MB, time=15.39 memory used=1068.9MB, alloc=492.3MB, time=17.80 memory used=1186.7MB, alloc=492.3MB, time=19.96 memory used=1285.9MB, alloc=492.3MB, time=21.88 memory used=1383.9MB, alloc=492.3MB, time=23.89 memory used=1468.4MB, alloc=516.3MB, time=25.59 memory used=1558.2MB, alloc=516.3MB, time=27.59 memory used=1640.6MB, alloc=516.3MB, time=29.42 memory used=1703.0MB, alloc=516.3MB, time=30.92 memory used=1774.5MB, alloc=516.3MB, time=32.55 memory used=1817.8MB, alloc=516.3MB, time=33.66 memory used=1871.8MB, alloc=516.3MB, time=35.01 memory used=2069.7MB, alloc=540.3MB, time=39.37 memory used=2290.0MB, alloc=564.3MB, time=43.66 memory used=2483.1MB, alloc=588.3MB, time=48.42 memory used=2680.0MB, alloc=612.3MB, time=52.94 memory used=2837.9MB, alloc=636.3MB, time=56.70 memory used=2964.0MB, alloc=660.3MB, time=59.22 memory used=3117.2MB, alloc=684.3MB, time=63.33 memory used=3255.6MB, alloc=684.3MB, time=67.00 memory used=3400.9MB, alloc=684.3MB, time=70.72 memory used=3484.7MB, alloc=708.3MB, time=72.93 memory used=3598.7MB, alloc=708.3MB, time=76.50 memory used=3972.8MB, alloc=732.3MB, time=85.66 memory used=4359.9MB, alloc=756.3MB, time=94.67 memory used=4701.5MB, alloc=780.3MB, time=102.40 |\^/| 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(); 1428242840 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [13 x - 11 y z + 20 x - 15, 9 x - 2 z + 6 y + 10, 2 -19 x z + 18 z - 19 y + 20] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [10 x z - 3 y + 9 x + 15 y, -7 x y + 19 x z - 9 z - 12 y, -18 x y - 11 x z - 17 y - 7] > Problem := [F,G]; 2 2 2 Problem := [[13 x - 11 y z + 20 x - 15, 9 x - 2 z + 6 y + 10, 2 2 -19 x z + 18 z - 19 y + 20], [10 x z - 3 y + 9 x + 15 y, 2 -7 x y + 19 x z - 9 z - 12 y, -18 x y - 11 x z - 17 y - 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=26.2MB, alloc=32.3MB, time=0.51 memory used=46.6MB, alloc=32.3MB, time=0.81 memory used=65.0MB, alloc=56.3MB, time=1.10 memory used=107.1MB, alloc=68.3MB, time=1.73 memory used=147.2MB, alloc=92.3MB, time=2.34 memory used=212.1MB, alloc=92.3MB, time=3.29 memory used=277.6MB, alloc=116.3MB, time=4.26 memory used=345.6MB, alloc=116.3MB, time=5.22 memory used=415.0MB, alloc=372.3MB, time=6.22 memory used=501.1MB, alloc=396.3MB, time=7.54 memory used=611.7MB, alloc=420.3MB, time=9.27 memory used=744.1MB, alloc=444.3MB, time=11.44 memory used=876.8MB, alloc=468.3MB, time=13.52 memory used=977.1MB, alloc=468.3MB, time=14.99 memory used=1084.7MB, alloc=468.3MB, time=16.71 memory used=1209.0MB, alloc=492.3MB, time=18.92 memory used=1308.6MB, alloc=492.3MB, time=20.33 memory used=1394.3MB, alloc=492.3MB, time=21.83 memory used=1484.7MB, alloc=492.3MB, time=23.19 memory used=1562.8MB, alloc=516.3MB, time=24.58 memory used=1638.1MB, alloc=516.3MB, time=25.96 memory used=1700.9MB, alloc=516.3MB, time=27.20 memory used=1777.0MB, alloc=516.3MB, time=28.78 memory used=1838.9MB, alloc=516.3MB, time=29.86 memory used=1902.0MB, alloc=516.3MB, time=30.91 memory used=1963.0MB, alloc=516.3MB, time=32.30 memory used=2008.0MB, alloc=516.3MB, time=33.34 memory used=2216.7MB, alloc=540.3MB, time=36.63 memory used=2409.1MB, alloc=564.3MB, time=39.87 memory used=2590.6MB, alloc=588.3MB, time=42.94 memory used=2772.5MB, alloc=612.3MB, time=46.47 memory used=2973.9MB, alloc=636.3MB, time=51.02 memory used=3115.7MB, alloc=660.3MB, time=53.88 memory used=3280.8MB, alloc=660.3MB, time=56.64 memory used=3429.5MB, alloc=660.3MB, time=59.72 memory used=3566.4MB, alloc=684.3MB, time=62.26 memory used=3707.7MB, alloc=684.3MB, time=65.85 memory used=3838.0MB, alloc=684.3MB, time=68.61 memory used=3946.4MB, alloc=684.3MB, time=71.01 memory used=4044.2MB, alloc=684.3MB, time=73.49 memory used=4404.7MB, alloc=708.3MB, time=81.57 memory used=4787.3MB, alloc=732.3MB, time=89.43 memory used=5172.8MB, alloc=756.3MB, time=97.48 |\^/| 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(); 1428243140 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-8 y + 9 y z + 16 z + 19 y, -10 x y - 3 z + 15 y + 10, 2 -6 x z - 5 y + 19 y + 19 z] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [-4 x - 12 x z - 6 y , -11 x y + 14 z - 9 x + 3 y, 2 2 -16 y + 11 y z - 9 z - 18] > Problem := [F,G]; 2 2 2 Problem := [[-8 y + 9 y z + 16 z + 19 y, -10 x y - 3 z + 15 y + 10, 2 2 2 -6 x z - 5 y + 19 y + 19 z], [-4 x - 12 x z - 6 y , 2 2 2 -11 x y + 14 z - 9 x + 3 y, -16 y + 11 y z - 9 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=0.18 memory used=26.4MB, alloc=32.3MB, time=0.52 memory used=46.9MB, alloc=60.3MB, time=0.82 memory used=86.3MB, alloc=60.3MB, time=1.37 memory used=126.7MB, alloc=60.3MB, time=1.96 memory used=166.4MB, alloc=60.3MB, time=2.50 memory used=212.9MB, alloc=92.3MB, time=3.09 memory used=280.8MB, alloc=92.3MB, time=4.05 memory used=330.1MB, alloc=92.3MB, time=4.48 memory used=400.3MB, alloc=116.3MB, time=5.39 memory used=458.2MB, alloc=116.3MB, time=6.20 memory used=523.9MB, alloc=372.3MB, time=7.20 memory used=613.9MB, alloc=396.3MB, time=8.45 memory used=726.6MB, alloc=396.3MB, time=9.91 memory used=835.3MB, alloc=420.3MB, time=11.23 memory used=965.2MB, alloc=444.3MB, time=13.16 memory used=1074.8MB, alloc=444.3MB, time=14.75 memory used=1180.7MB, alloc=468.3MB, time=16.30 memory used=1301.3MB, alloc=468.3MB, time=18.40 memory used=1406.8MB, alloc=492.3MB, time=20.13 memory used=1496.4MB, alloc=492.3MB, time=21.45 memory used=1601.8MB, alloc=516.3MB, time=22.99 memory used=1683.5MB, alloc=516.3MB, time=24.30 memory used=1762.7MB, alloc=516.3MB, time=25.88 memory used=1827.6MB, alloc=516.3MB, time=26.97 memory used=1905.1MB, alloc=516.3MB, time=28.04 memory used=1969.9MB, alloc=516.3MB, time=29.00 memory used=2028.2MB, alloc=516.3MB, time=30.32 memory used=2086.9MB, alloc=516.3MB, time=31.26 memory used=2134.1MB, alloc=516.3MB, time=32.18 memory used=2172.9MB, alloc=540.3MB, time=33.09 memory used=2236.2MB, alloc=540.3MB, time=34.30 memory used=2281.1MB, alloc=540.3MB, time=35.47 memory used=2483.4MB, alloc=564.3MB, time=38.67 memory used=2695.4MB, alloc=588.3MB, time=42.39 memory used=2878.9MB, alloc=612.3MB, time=44.91 memory used=3068.5MB, alloc=636.3MB, time=48.63 memory used=3231.5MB, alloc=660.3MB, time=51.87 memory used=3445.9MB, alloc=660.3MB, time=54.81 memory used=3624.1MB, alloc=660.3MB, time=57.51 memory used=3774.1MB, alloc=660.3MB, time=59.87 memory used=3892.2MB, alloc=660.3MB, time=62.57 memory used=4102.2MB, alloc=684.3MB, time=65.38 memory used=4219.4MB, alloc=684.3MB, time=67.58 memory used=4338.6MB, alloc=684.3MB, time=70.34 memory used=4435.7MB, alloc=684.3MB, time=72.50 memory used=4785.7MB, alloc=708.3MB, time=79.68 memory used=5158.2MB, alloc=732.3MB, time=86.91 memory used=5549.0MB, alloc=756.3MB, time=93.71 memory used=5868.5MB, alloc=780.3MB, time=100.14 memory used=6175.7MB, alloc=804.3MB, time=106.61 |\^/| 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(); 1428243440 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [8 x y + 5 y + 7 y z + 17 x, -16 x y - 8 y + 12 y z + 20 z, 2 -17 x + 4 x y - 7 x z + 6] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [4 y z - 14 z - 17 x + 18, -16 x z - 4 z + 20 z - 6, 2 14 x y - 20 x z - 20 y ] > Problem := [F,G]; 2 2 Problem := [[8 x y + 5 y + 7 y z + 17 x, -16 x y - 8 y + 12 y z + 20 z, 2 2 -17 x + 4 x y - 7 x z + 6], [4 y z - 14 z - 17 x + 18, 2 2 -16 x z - 4 z + 20 z - 6, 14 x y - 20 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=4.3MB, alloc=32.3MB, time=0.18 memory used=26.3MB, alloc=32.3MB, time=0.51 memory used=46.5MB, alloc=32.3MB, time=0.81 memory used=65.8MB, alloc=56.3MB, time=1.11 memory used=106.3MB, alloc=60.3MB, time=1.74 memory used=144.8MB, alloc=84.3MB, time=2.35 memory used=206.6MB, alloc=92.3MB, time=3.31 memory used=267.4MB, alloc=92.3MB, time=4.23 memory used=326.1MB, alloc=116.3MB, time=5.19 memory used=409.6MB, alloc=116.3MB, time=6.56 memory used=476.7MB, alloc=140.3MB, time=7.61 memory used=554.5MB, alloc=396.3MB, time=9.03 memory used=660.8MB, alloc=420.3MB, time=10.88 memory used=795.2MB, alloc=444.3MB, time=13.16 memory used=925.6MB, alloc=444.3MB, time=15.35 memory used=1042.2MB, alloc=468.3MB, time=17.32 memory used=1171.9MB, alloc=468.3MB, time=19.76 memory used=1291.4MB, alloc=492.3MB, time=22.19 memory used=1409.1MB, alloc=492.3MB, time=24.68 memory used=1528.6MB, alloc=492.3MB, time=27.04 memory used=1628.2MB, alloc=492.3MB, time=29.04 memory used=1736.3MB, alloc=516.3MB, time=31.58 memory used=1818.3MB, alloc=516.3MB, time=33.20 memory used=1897.0MB, alloc=516.3MB, time=34.67 memory used=1980.6MB, alloc=516.3MB, time=36.54 memory used=2060.0MB, alloc=516.3MB, time=38.30 memory used=2129.1MB, alloc=516.3MB, time=39.89 memory used=2193.6MB, alloc=516.3MB, time=41.40 memory used=2267.4MB, alloc=516.3MB, time=43.16 memory used=2334.5MB, alloc=516.3MB, time=44.97 memory used=2400.4MB, alloc=516.3MB, time=46.73 memory used=2457.3MB, alloc=516.3MB, time=48.10 memory used=2504.1MB, alloc=516.3MB, time=49.28 memory used=2704.7MB, alloc=540.3MB, time=53.11 memory used=2885.1MB, alloc=564.3MB, time=56.41 memory used=3066.4MB, alloc=588.3MB, time=59.68 memory used=3259.7MB, alloc=612.3MB, time=63.70 memory used=3435.9MB, alloc=636.3MB, time=67.16 memory used=3644.9MB, alloc=660.3MB, time=71.93 memory used=3875.0MB, alloc=684.3MB, time=77.94 memory used=4009.1MB, alloc=684.3MB, time=80.99 memory used=4125.3MB, alloc=708.3MB, time=83.20 memory used=4278.2MB, alloc=708.3MB, time=87.11 memory used=4420.9MB, alloc=708.3MB, time=91.06 memory used=4539.2MB, alloc=708.3MB, time=94.32 memory used=4638.1MB, alloc=708.3MB, time=96.49 memory used=5005.3MB, alloc=732.3MB, time=104.53 |\^/| 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(); 1428243740 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-5 x y - 20 y + 19 x - 19, -15 x z + 19 y - y z - 11 x, 2 7 x z - 5 z + 6 y + 4 z] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [19 x - 9 y - 6 z - 2, 10 x y - 16 y + 14 y z + 12, 2 -8 x z - 5 y + 8 y z - 8 y] > Problem := [F,G]; 2 2 Problem := [[-5 x y - 20 y + 19 x - 19, -15 x z + 19 y - y z - 11 x, 2 2 2 2 7 x z - 5 z + 6 y + 4 z], [19 x - 9 y - 6 z - 2, 2 2 10 x y - 16 y + 14 y z + 12, -8 x z - 5 y + 8 y z - 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=4.4MB, alloc=32.3MB, time=0.18 memory used=26.6MB, alloc=32.3MB, time=0.51 memory used=47.1MB, alloc=32.3MB, time=0.82 memory used=66.6MB, alloc=56.3MB, time=1.14 memory used=108.5MB, alloc=60.3MB, time=1.82 memory used=149.4MB, alloc=60.3MB, time=2.44 memory used=189.8MB, alloc=92.3MB, time=3.12 memory used=251.4MB, alloc=92.3MB, time=4.08 memory used=316.6MB, alloc=116.3MB, time=5.03 memory used=391.1MB, alloc=372.3MB, time=6.22 memory used=478.6MB, alloc=396.3MB, time=7.55 memory used=589.5MB, alloc=420.3MB, time=9.25 memory used=725.4MB, alloc=444.3MB, time=11.37 memory used=857.3MB, alloc=444.3MB, time=13.53 memory used=985.6MB, alloc=468.3MB, time=15.60 memory used=1100.9MB, alloc=468.3MB, time=17.53 memory used=1218.3MB, alloc=492.3MB, time=19.61 memory used=1316.9MB, alloc=492.3MB, time=21.15 memory used=1409.0MB, alloc=492.3MB, time=22.78 memory used=1515.1MB, alloc=492.3MB, time=24.76 memory used=1594.1MB, alloc=492.3MB, time=26.22 memory used=1676.1MB, alloc=492.3MB, time=27.62 memory used=1746.4MB, alloc=516.3MB, time=28.93 memory used=1809.7MB, alloc=516.3MB, time=30.15 memory used=1872.0MB, alloc=516.3MB, time=31.39 memory used=1935.9MB, alloc=516.3MB, time=32.66 memory used=1998.2MB, alloc=516.3MB, time=34.06 memory used=2059.1MB, alloc=516.3MB, time=35.59 memory used=2109.2MB, alloc=516.3MB, time=36.73 memory used=2159.8MB, alloc=516.3MB, time=37.74 memory used=2210.7MB, alloc=516.3MB, time=38.57 memory used=2254.2MB, alloc=516.3MB, time=39.65 memory used=2457.4MB, alloc=540.3MB, time=43.01 memory used=2673.3MB, alloc=564.3MB, time=47.23 memory used=2841.9MB, alloc=588.3MB, time=50.63 memory used=3016.5MB, alloc=612.3MB, time=54.13 memory used=3177.6MB, alloc=636.3MB, time=57.72 memory used=3290.7MB, alloc=660.3MB, time=59.86 memory used=3453.0MB, alloc=660.3MB, time=63.35 memory used=3579.8MB, alloc=660.3MB, time=65.79 memory used=3718.1MB, alloc=684.3MB, time=68.87 memory used=3815.1MB, alloc=684.3MB, time=71.18 memory used=3943.2MB, alloc=684.3MB, time=73.84 memory used=4073.5MB, alloc=684.3MB, time=77.25 memory used=4427.9MB, alloc=708.3MB, time=84.09 memory used=4798.5MB, alloc=732.3MB, time=92.36 memory used=5190.2MB, alloc=756.3MB, time=99.88 memory used=5583.1MB, alloc=780.3MB, time=108.09 memory used=5888.3MB, alloc=804.3MB, time=114.47 |\^/| 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(); 1428244040 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [-10 x y + 19 x z + 11 y - 17, 8 x y - 19 y + 15 y z - 12 y, 2 -11 x + 14 x + 17 z + 1] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 G := [-4 x - x y - 18 y - 15, 8 x + 3 y + 6 y z + 6 z , 2 10 y z - 13 z - 9 x - 19 z] > Problem := [F,G]; 2 Problem := [[-10 x y + 19 x z + 11 y - 17, 8 x y - 19 y + 15 y z - 12 y, 2 2 2 -11 x + 14 x + 17 z + 1], [-4 x - x y - 18 y - 15, 2 2 2 2 8 x + 3 y + 6 y z + 6 z , 10 y z - 13 z - 9 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=4.3MB, alloc=32.3MB, time=0.18 memory used=26.7MB, alloc=32.3MB, time=0.51 memory used=47.3MB, alloc=32.3MB, time=0.81 memory used=66.7MB, alloc=56.3MB, time=1.11 memory used=105.8MB, alloc=84.3MB, time=1.74 memory used=155.7MB, alloc=84.3MB, time=2.54 memory used=216.9MB, alloc=92.3MB, time=3.56 memory used=275.7MB, alloc=116.3MB, time=4.55 memory used=357.8MB, alloc=116.3MB, time=5.94 memory used=440.3MB, alloc=140.3MB, time=7.33 memory used=538.5MB, alloc=140.3MB, time=9.03 memory used=622.3MB, alloc=420.3MB, time=10.53 memory used=747.4MB, alloc=444.3MB, time=12.76 memory used=897.0MB, alloc=468.3MB, time=15.53 memory used=1043.8MB, alloc=492.3MB, time=18.23 memory used=1192.7MB, alloc=516.3MB, time=21.14 memory used=1321.9MB, alloc=516.3MB, time=23.56 memory used=1432.6MB, alloc=516.3MB, time=25.65 memory used=1544.4MB, alloc=516.3MB, time=27.98 memory used=1639.7MB, alloc=540.3MB, time=30.04 memory used=1736.7MB, alloc=540.3MB, time=32.19 memory used=1839.4MB, alloc=540.3MB, time=34.34 memory used=1935.0MB, alloc=540.3MB, time=36.47 memory used=2016.0MB, alloc=540.3MB, time=38.32 memory used=2098.3MB, alloc=540.3MB, time=40.33 memory used=2160.9MB, alloc=540.3MB, time=41.58 memory used=2243.0MB, alloc=540.3MB, time=43.81 memory used=2323.6MB, alloc=540.3MB, time=45.83 memory used=2378.5MB, alloc=540.3MB, time=47.17 memory used=2597.9MB, alloc=564.3MB, time=52.00 memory used=2831.1MB, alloc=588.3MB, time=57.27 memory used=3074.1MB, alloc=612.3MB, time=63.31 memory used=3295.9MB, alloc=636.3MB, time=68.40 memory used=3495.0MB, alloc=660.3MB, time=73.35 memory used=3668.7MB, alloc=684.3MB, time=77.91 memory used=3870.6MB, alloc=708.3MB, time=83.65 memory used=4049.3MB, alloc=708.3MB, time=88.19 memory used=4199.7MB, alloc=708.3MB, time=92.34 memory used=4338.4MB, alloc=708.3MB, time=96.43 memory used=4491.3MB, alloc=732.3MB, time=100.91 memory used=4631.2MB, alloc=732.3MB, time=105.89 |\^/| 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(); 1428244340 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [-18 x - 2 x y + 12 y - 13 z , -4 x + 18 x z + 12 y z - 17 x, 2 2 16 x + 17 x z + 10 z + 7 z] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-3 x + 17 x y - 12 x + 8, 4 x y - 13 z - 3 y - 7 z, 2 11 x - 12 x + 15 z + 5] > Problem := [F,G]; 2 2 2 2 Problem := [[-18 x - 2 x y + 12 y - 13 z , -4 x + 18 x z + 12 y z - 17 x, 2 2 2 16 x + 17 x z + 10 z + 7 z], [-3 x + 17 x y - 12 x + 8, 2 2 4 x y - 13 z - 3 y - 7 z, 11 x - 12 x + 15 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=4.3MB, alloc=32.3MB, time=0.18 memory used=26.8MB, alloc=32.3MB, time=0.52 memory used=48.2MB, alloc=32.3MB, time=0.85 memory used=68.2MB, alloc=56.3MB, time=1.16 memory used=110.7MB, alloc=60.3MB, time=1.79 memory used=151.3MB, alloc=84.3MB, time=2.39 memory used=217.0MB, alloc=116.3MB, time=3.34 memory used=294.1MB, alloc=372.3MB, time=4.50 memory used=384.0MB, alloc=396.3MB, time=5.81 memory used=497.8MB, alloc=420.3MB, time=7.48 memory used=633.4MB, alloc=444.3MB, time=9.48 memory used=762.4MB, alloc=444.3MB, time=11.41 memory used=889.8MB, alloc=468.3MB, time=13.34 memory used=1008.7MB, alloc=468.3MB, time=15.27 memory used=1110.3MB, alloc=468.3MB, time=16.94 memory used=1198.4MB, alloc=468.3MB, time=18.53 memory used=1288.8MB, alloc=492.3MB, time=20.14 memory used=1366.1MB, alloc=492.3MB, time=21.46 memory used=1440.7MB, alloc=492.3MB, time=22.89 memory used=1504.6MB, alloc=492.3MB, time=24.17 memory used=1574.9MB, alloc=492.3MB, time=25.49 memory used=1643.2MB, alloc=492.3MB, time=26.74 memory used=1712.5MB, alloc=492.3MB, time=28.22 memory used=1776.2MB, alloc=492.3MB, time=29.53 memory used=1832.9MB, alloc=492.3MB, time=30.72 memory used=1881.7MB, alloc=492.3MB, time=31.68 memory used=1932.8MB, alloc=516.3MB, time=32.89 memory used=2142.0MB, alloc=540.3MB, time=36.39 memory used=2360.7MB, alloc=564.3MB, time=40.60 memory used=2543.5MB, alloc=588.3MB, time=43.66 memory used=2723.7MB, alloc=612.3MB, time=47.18 memory used=2898.8MB, alloc=636.3MB, time=50.58 memory used=3052.8MB, alloc=660.3MB, time=53.80 memory used=3225.3MB, alloc=660.3MB, time=56.86 memory used=3370.9MB, alloc=684.3MB, time=59.70 memory used=3515.0MB, alloc=684.3MB, time=63.17 memory used=3644.5MB, alloc=684.3MB, time=65.93 memory used=3767.1MB, alloc=684.3MB, time=68.73 memory used=3865.4MB, alloc=684.3MB, time=71.41 memory used=4218.1MB, alloc=708.3MB, time=78.28 memory used=4586.4MB, alloc=732.3MB, time=86.43 memory used=4982.6MB, alloc=756.3MB, time=94.11 memory used=5396.5MB, alloc=780.3MB, time=102.41 |\^/| 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(); 1428244640 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [14 x - 6 y + 6 x + 17, -3 x y - 12 x z + 12 z - 3 z, 2 -18 x z - 13 y + 6 y + 19 z] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [-19 x y - 4 x z + 14 y + 4 z , -9 x + 16 x y - 8 y + 9 y z, 2 2 2 -15 x + 5 y - 6 z - 17] > Problem := [F,G]; 2 2 2 Problem := [[14 x - 6 y + 6 x + 17, -3 x y - 12 x z + 12 z - 3 z, 2 2 2 -18 x z - 13 y + 6 y + 19 z], [-19 x y - 4 x z + 14 y + 4 z , 2 2 2 2 2 -9 x + 16 x y - 8 y + 9 y z, -15 x + 5 y - 6 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=26.1MB, alloc=32.3MB, time=0.52 memory used=46.1MB, alloc=60.3MB, time=0.85 memory used=86.7MB, alloc=60.3MB, time=1.42 memory used=129.4MB, alloc=68.3MB, time=2.07 memory used=172.8MB, alloc=92.3MB, time=2.67 memory used=238.0MB, alloc=92.3MB, time=3.38 memory used=302.7MB, alloc=92.3MB, time=4.31 memory used=367.5MB, alloc=116.3MB, time=5.33 memory used=436.0MB, alloc=372.3MB, time=6.35 memory used=527.8MB, alloc=396.3MB, time=7.66 memory used=644.6MB, alloc=420.3MB, time=9.34 memory used=781.8MB, alloc=420.3MB, time=11.05 memory used=913.3MB, alloc=444.3MB, time=13.15 memory used=1054.7MB, alloc=444.3MB, time=14.63 memory used=1185.7MB, alloc=444.3MB, time=16.33 memory used=1296.6MB, alloc=468.3MB, time=17.96 memory used=1409.5MB, alloc=468.3MB, time=19.84 memory used=1513.1MB, alloc=468.3MB, time=21.48 memory used=1613.0MB, alloc=492.3MB, time=23.27 memory used=1700.2MB, alloc=492.3MB, time=24.75 memory used=1781.7MB, alloc=492.3MB, time=26.17 memory used=1858.9MB, alloc=492.3MB, time=27.52 memory used=1947.0MB, alloc=492.3MB, time=29.13 memory used=2012.7MB, alloc=492.3MB, time=30.39 memory used=2089.2MB, alloc=492.3MB, time=31.62 memory used=2153.8MB, alloc=492.3MB, time=32.58 memory used=2219.4MB, alloc=492.3MB, time=33.95 memory used=2282.5MB, alloc=492.3MB, time=35.17 memory used=2364.2MB, alloc=516.3MB, time=36.35 memory used=2412.9MB, alloc=516.3MB, time=37.37 memory used=2468.0MB, alloc=516.3MB, time=38.52 memory used=2509.8MB, alloc=516.3MB, time=39.45 memory used=2569.2MB, alloc=516.3MB, time=40.54 memory used=2606.7MB, alloc=516.3MB, time=41.42 memory used=2656.5MB, alloc=516.3MB, time=42.54 memory used=2702.9MB, alloc=516.3MB, time=43.64 memory used=2898.3MB, alloc=540.3MB, time=47.11 memory used=3093.6MB, alloc=564.3MB, time=50.41 memory used=3248.0MB, alloc=588.3MB, time=52.99 memory used=3433.0MB, alloc=612.3MB, time=56.81 memory used=3591.8MB, alloc=636.3MB, time=60.20 memory used=3746.0MB, alloc=660.3MB, time=63.06 memory used=3898.8MB, alloc=660.3MB, time=66.17 memory used=4044.8MB, alloc=684.3MB, time=68.72 memory used=4187.2MB, alloc=684.3MB, time=71.70 memory used=4302.1MB, alloc=684.3MB, time=73.86 memory used=4418.5MB, alloc=684.3MB, time=76.93 memory used=4494.1MB, alloc=684.3MB, time=78.74 memory used=4583.3MB, alloc=708.3MB, time=80.67 memory used=4966.7MB, alloc=732.3MB, time=88.15 memory used=5376.0MB, alloc=756.3MB, time=95.13 memory used=5784.5MB, alloc=780.3MB, time=103.39 memory used=6182.8MB, alloc=804.3MB, time=109.78 |\^/| 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(); 1428244940 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [12 x z - 16 y - 15 y z - 11, -14 x - 3 x - 19 y - 16 z, -2 y z - 12 y + 9 z + 3] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [16 z - 14 x + 16, -9 x - y + 5 y z + 10, -4 y + 2 x + 14 y + 8 z] > Problem := [F,G]; 2 2 Problem := [[12 x z - 16 y - 15 y z - 11, -14 x - 3 x - 19 y - 16 z, -2 y z - 12 y + 9 z + 3], 2 2 2 2 [16 z - 14 x + 16, -9 x - y + 5 y z + 10, -4 y + 2 x + 14 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=4.3MB, alloc=32.3MB, time=0.18 memory used=25.9MB, alloc=32.3MB, time=0.50 memory used=45.4MB, alloc=56.3MB, time=0.81 memory used=88.1MB, alloc=60.3MB, time=1.46 memory used=129.7MB, alloc=68.3MB, time=2.11 memory used=170.8MB, alloc=92.3MB, time=2.74 memory used=233.8MB, alloc=92.3MB, time=3.70 memory used=296.3MB, alloc=116.3MB, time=4.68 memory used=378.1MB, alloc=116.3MB, time=6.00 memory used=455.7MB, alloc=396.3MB, time=7.36 memory used=566.7MB, alloc=420.3MB, time=9.10 memory used=704.2MB, alloc=444.3MB, time=11.16 memory used=832.1MB, alloc=468.3MB, time=13.34 memory used=959.4MB, alloc=468.3MB, time=15.43 memory used=1063.0MB, alloc=468.3MB, time=17.20 memory used=1177.5MB, alloc=468.3MB, time=19.37 memory used=1283.1MB, alloc=492.3MB, time=21.19 memory used=1377.1MB, alloc=492.3MB, time=22.90 memory used=1488.5MB, alloc=492.3MB, time=25.13 memory used=1583.7MB, alloc=492.3MB, time=27.06 memory used=1651.2MB, alloc=492.3MB, time=28.42 memory used=1723.3MB, alloc=492.3MB, time=29.84 memory used=1780.5MB, alloc=492.3MB, time=31.22 memory used=1858.4MB, alloc=492.3MB, time=32.86 memory used=1927.9MB, alloc=516.3MB, time=34.42 memory used=1988.7MB, alloc=516.3MB, time=35.66 memory used=2051.0MB, alloc=516.3MB, time=37.22 memory used=2096.4MB, alloc=516.3MB, time=38.28 memory used=2305.4MB, alloc=540.3MB, time=42.40 memory used=2522.8MB, alloc=564.3MB, time=46.70 memory used=2730.1MB, alloc=588.3MB, time=51.23 memory used=2940.2MB, alloc=612.3MB, time=55.81 memory used=3065.3MB, alloc=636.3MB, time=58.52 memory used=3230.2MB, alloc=660.3MB, time=62.33 memory used=3363.3MB, alloc=660.3MB, time=65.23 memory used=3507.8MB, alloc=660.3MB, time=68.56 memory used=3617.4MB, alloc=684.3MB, time=71.30 memory used=3731.0MB, alloc=684.3MB, time=74.06 memory used=3881.9MB, alloc=684.3MB, time=77.85 memory used=3980.6MB, alloc=684.3MB, time=80.46 memory used=4335.2MB, alloc=708.3MB, time=87.91 memory used=4697.8MB, alloc=732.3MB, time=96.10 |\^/| 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(); 1428245240 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [10 x y - 18 x z + 14 y , 8 x + 3 z + z - 3, 11 y - 15 y z - 12 x + 7] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [7 x y - 15 x z - 8 y z - 15 x, 13 x - 11 z - 7 y + 3, 2 2 -13 y - 10 z + 2 x + 3] > Problem := [F,G]; Problem := [ 2 2 2 2 [10 x y - 18 x z + 14 y , 8 x + 3 z + z - 3, 11 y - 15 y z - 12 x + 7], 2 2 [7 x y - 15 x z - 8 y z - 15 x, 13 x - 11 z - 7 y + 3, 2 2 -13 y - 10 z + 2 x + 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=26.2MB, alloc=32.3MB, time=0.49 memory used=46.9MB, alloc=56.3MB, time=0.82 memory used=87.6MB, alloc=60.3MB, time=1.43 memory used=130.2MB, alloc=92.3MB, time=2.04 memory used=198.3MB, alloc=92.3MB, time=3.00 memory used=264.7MB, alloc=116.3MB, time=3.96 memory used=332.8MB, alloc=372.3MB, time=4.85 memory used=419.6MB, alloc=396.3MB, time=6.19 memory used=532.7MB, alloc=396.3MB, time=7.83 memory used=643.9MB, alloc=420.3MB, time=9.38 memory used=773.5MB, alloc=444.3MB, time=11.27 memory used=903.5MB, alloc=444.3MB, time=13.02 memory used=1020.1MB, alloc=468.3MB, time=14.78 memory used=1130.9MB, alloc=468.3MB, time=16.50 memory used=1274.0MB, alloc=492.3MB, time=18.68 memory used=1363.3MB, alloc=492.3MB, time=19.99 memory used=1480.8MB, alloc=516.3MB, time=21.51 memory used=1588.1MB, alloc=516.3MB, time=23.30 memory used=1680.7MB, alloc=516.3MB, time=24.67 memory used=1760.3MB, alloc=516.3MB, time=26.28 memory used=1827.1MB, alloc=516.3MB, time=27.31 memory used=1909.5MB, alloc=516.3MB, time=28.64 memory used=1966.1MB, alloc=516.3MB, time=29.72 memory used=2014.7MB, alloc=516.3MB, time=30.67 memory used=2074.0MB, alloc=540.3MB, time=31.59 memory used=2155.0MB, alloc=540.3MB, time=32.91 memory used=2208.1MB, alloc=540.3MB, time=34.03 memory used=2249.6MB, alloc=540.3MB, time=34.94 memory used=2466.6MB, alloc=564.3MB, time=38.34 memory used=2685.0MB, alloc=588.3MB, time=42.28 memory used=2855.0MB, alloc=612.3MB, time=44.81 memory used=3043.6MB, alloc=636.3MB, time=47.72 memory used=3203.2MB, alloc=660.3MB, time=50.61 memory used=3360.7MB, alloc=660.3MB, time=53.59 memory used=3504.8MB, alloc=660.3MB, time=56.14 memory used=3640.8MB, alloc=660.3MB, time=58.53 memory used=3776.0MB, alloc=660.3MB, time=61.00 memory used=3904.6MB, alloc=660.3MB, time=63.86 memory used=4045.5MB, alloc=684.3MB, time=67.06 memory used=4122.2MB, alloc=684.3MB, time=68.88 memory used=4234.4MB, alloc=684.3MB, time=71.49 memory used=4338.6MB, alloc=684.3MB, time=74.24 memory used=4676.2MB, alloc=708.3MB, time=79.08 memory used=5055.4MB, alloc=732.3MB, time=84.72 memory used=5454.8MB, alloc=756.3MB, time=91.41 memory used=5850.0MB, alloc=780.3MB, time=98.58 memory used=6195.4MB, alloc=804.3MB, time=105.43 |\^/| 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(); 1428245540 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-16 x + 15 x z - 7 z - 3, -16 x y + 10 y - 14 z - 3 x, 13 x z - y - 13 z + 14] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-10 x z + x - 2 z + 16, 7 x - 20 x z - 9 z - 8 x, 2 -20 x z + 20 y z + 7 z + 2 x] > Problem := [F,G]; 2 2 2 Problem := [[-16 x + 15 x z - 7 z - 3, -16 x y + 10 y - 14 z - 3 x, 13 x z - y - 13 z + 14], [-10 x z + x - 2 z + 16, 2 2 2 7 x - 20 x z - 9 z - 8 x, -20 x z + 20 y z + 7 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=0.17 memory used=26.2MB, alloc=32.3MB, time=0.50 memory used=46.8MB, alloc=56.3MB, time=0.82 memory used=89.5MB, alloc=60.3MB, time=1.47 memory used=130.5MB, alloc=60.3MB, time=2.10 memory used=169.7MB, alloc=84.3MB, time=2.71 memory used=229.9MB, alloc=116.3MB, time=3.67 memory used=311.8MB, alloc=116.3MB, time=4.89 memory used=392.6MB, alloc=116.3MB, time=6.15 memory used=472.3MB, alloc=140.3MB, time=7.46 memory used=547.8MB, alloc=140.3MB, time=8.67 memory used=622.1MB, alloc=396.3MB, time=9.90 memory used=723.6MB, alloc=420.3MB, time=11.56 memory used=846.8MB, alloc=444.3MB, time=13.58 memory used=991.0MB, alloc=468.3MB, time=15.94 memory used=1132.4MB, alloc=468.3MB, time=18.49 memory used=1259.5MB, alloc=492.3MB, time=20.23 memory used=1385.8MB, alloc=516.3MB, time=22.23 memory used=1495.3MB, alloc=516.3MB, time=23.77 memory used=1600.9MB, alloc=540.3MB, time=25.64 memory used=1706.5MB, alloc=540.3MB, time=27.47 memory used=1780.1MB, alloc=540.3MB, time=28.76 memory used=1849.7MB, alloc=540.3MB, time=29.78 memory used=1933.3MB, alloc=540.3MB, time=31.52 memory used=2001.4MB, alloc=540.3MB, time=32.66 memory used=2073.2MB, alloc=540.3MB, time=34.06 memory used=2137.4MB, alloc=540.3MB, time=35.47 memory used=2175.6MB, alloc=540.3MB, time=36.34 memory used=2208.0MB, alloc=540.3MB, time=37.13 memory used=2279.4MB, alloc=540.3MB, time=38.87 memory used=2497.7MB, alloc=564.3MB, time=42.54 memory used=2694.0MB, alloc=588.3MB, time=46.16 memory used=2894.6MB, alloc=612.3MB, time=49.77 memory used=3097.1MB, alloc=636.3MB, time=53.57 memory used=3252.7MB, alloc=660.3MB, time=56.23 memory used=3433.7MB, alloc=684.3MB, time=60.51 memory used=3586.4MB, alloc=684.3MB, time=64.09 memory used=3723.3MB, alloc=684.3MB, time=67.03 memory used=3859.0MB, alloc=684.3MB, time=70.47 memory used=3990.7MB, alloc=708.3MB, time=73.51 memory used=4094.6MB, alloc=708.3MB, time=75.88 memory used=4208.2MB, alloc=708.3MB, time=79.02 memory used=4589.6MB, alloc=732.3MB, time=85.99 |\^/| 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(); 1428245840 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; F := 2 2 2 [9 x z + 20 y + 20 x - 19, -7 y - 18 y z - 7 x + 6 y, 13 z + 14 x - 8 y] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-12 y z + 12 z + 2 x - 2, -16 x z + 18 y z - 4 z - 7 x, 2 -19 x - 4 x y - 20 x + 6 z] > Problem := [F,G]; Problem := [ 2 2 2 [9 x z + 20 y + 20 x - 19, -7 y - 18 y z - 7 x + 6 y, 13 z + 14 x - 8 y] 2 2 , [-12 y z + 12 z + 2 x - 2, -16 x z + 18 y z - 4 z - 7 x, 2 -19 x - 4 x y - 20 x + 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=4.3MB, alloc=32.3MB, time=0.18 memory used=26.0MB, alloc=32.3MB, time=0.51 memory used=46.1MB, alloc=32.3MB, time=0.81 memory used=64.7MB, alloc=56.3MB, time=1.11 memory used=108.2MB, alloc=68.3MB, time=1.74 memory used=148.7MB, alloc=92.3MB, time=2.37 memory used=214.6MB, alloc=92.3MB, time=3.33 memory used=282.3MB, alloc=92.3MB, time=4.31 memory used=346.6MB, alloc=116.3MB, time=5.28 memory used=417.7MB, alloc=372.3MB, time=6.30 memory used=507.3MB, alloc=396.3MB, time=7.67 memory used=617.9MB, alloc=396.3MB, time=9.29 memory used=730.2MB, alloc=420.3MB, time=10.90 memory used=861.4MB, alloc=444.3MB, time=12.92 memory used=978.0MB, alloc=468.3MB, time=14.63 memory used=1098.7MB, alloc=468.3MB, time=16.53 memory used=1203.4MB, alloc=492.3MB, time=18.43 memory used=1299.7MB, alloc=492.3MB, time=20.06 memory used=1386.8MB, alloc=492.3MB, time=21.46 memory used=1466.7MB, alloc=492.3MB, time=22.84 memory used=1553.8MB, alloc=492.3MB, time=24.19 memory used=1631.5MB, alloc=516.3MB, time=25.53 memory used=1706.2MB, alloc=516.3MB, time=26.69 memory used=1781.7MB, alloc=516.3MB, time=28.19 memory used=1856.2MB, alloc=516.3MB, time=29.72 memory used=1909.6MB, alloc=516.3MB, time=30.91 memory used=1961.0MB, alloc=516.3MB, time=31.83 memory used=2008.2MB, alloc=516.3MB, time=32.66 memory used=2074.8MB, alloc=516.3MB, time=34.04 memory used=2117.8MB, alloc=516.3MB, time=35.13 memory used=2313.9MB, alloc=540.3MB, time=38.49 memory used=2514.3MB, alloc=564.3MB, time=42.06 memory used=2718.0MB, alloc=588.3MB, time=45.34 memory used=2920.3MB, alloc=612.3MB, time=49.73 memory used=3131.0MB, alloc=636.3MB, time=54.09 memory used=3269.1MB, alloc=636.3MB, time=56.55 memory used=3435.1MB, alloc=660.3MB, time=59.56 memory used=3588.2MB, alloc=660.3MB, time=62.13 memory used=3724.8MB, alloc=660.3MB, time=65.04 memory used=3884.8MB, alloc=684.3MB, time=68.27 memory used=4019.5MB, alloc=684.3MB, time=71.27 memory used=4158.0MB, alloc=684.3MB, time=74.64 memory used=4266.5MB, alloc=684.3MB, time=76.98 memory used=4364.1MB, alloc=684.3MB, time=79.91 memory used=4730.3MB, alloc=708.3MB, time=87.41 memory used=5114.4MB, alloc=732.3MB, time=95.17 |\^/| 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(); 1428246140 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [-16 x - 12 y - 8 z + 10 x, 16 y - 5 x - 12 y - 20, 2 19 x y - 18 x z + 4 y z - 14 z ] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-11 y z - 2 x + 11, 13 x + 13 x + 20 y - 6 z, -5 x - 16 y + 11 z + 2] > Problem := [F,G]; 2 2 2 2 Problem := [[-16 x - 12 y - 8 z + 10 x, 16 y - 5 x - 12 y - 20, 2 19 x y - 18 x z + 4 y z - 14 z ], 2 2 [-11 y z - 2 x + 11, 13 x + 13 x + 20 y - 6 z, -5 x - 16 y + 11 z + 2]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,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=0.51 memory used=47.4MB, alloc=32.3MB, time=0.81 memory used=66.6MB, alloc=56.3MB, time=1.11 memory used=107.3MB, alloc=60.3MB, time=1.73 memory used=146.9MB, alloc=84.3MB, time=2.35 memory used=210.8MB, alloc=92.3MB, time=3.37 memory used=272.5MB, alloc=116.3MB, time=4.34 memory used=346.8MB, alloc=116.3MB, time=5.49 memory used=414.4MB, alloc=372.3MB, time=6.56 memory used=497.0MB, alloc=396.3MB, time=7.91 memory used=603.1MB, alloc=420.3MB, time=9.61 memory used=733.4MB, alloc=444.3MB, time=11.69 memory used=870.3MB, alloc=468.3MB, time=13.87 memory used=1000.6MB, alloc=468.3MB, time=16.05 memory used=1113.6MB, alloc=492.3MB, time=17.90 memory used=1218.3MB, alloc=492.3MB, time=19.50 memory used=1307.6MB, alloc=492.3MB, time=20.94 memory used=1414.1MB, alloc=516.3MB, time=22.74 memory used=1498.6MB, alloc=516.3MB, time=24.10 memory used=1595.4MB, alloc=516.3MB, time=25.82 memory used=1683.6MB, alloc=516.3MB, time=27.61 memory used=1757.8MB, alloc=540.3MB, time=28.94 memory used=1820.9MB, alloc=540.3MB, time=30.56 memory used=1879.2MB, alloc=540.3MB, time=31.66 memory used=1946.8MB, alloc=540.3MB, time=33.22 memory used=1996.2MB, alloc=540.3MB, time=34.27 memory used=2042.9MB, alloc=540.3MB, time=35.37 memory used=2262.4MB, alloc=564.3MB, time=39.52 memory used=2467.1MB, alloc=588.3MB, time=43.11 memory used=2678.1MB, alloc=612.3MB, time=47.17 memory used=2848.3MB, alloc=636.3MB, time=50.50 memory used=3011.6MB, alloc=660.3MB, time=53.75 memory used=3183.2MB, alloc=660.3MB, time=57.07 memory used=3341.9MB, alloc=660.3MB, time=60.58 memory used=3488.1MB, alloc=660.3MB, time=63.98 memory used=3610.7MB, alloc=660.3MB, time=67.05 memory used=3720.1MB, alloc=684.3MB, time=69.42 memory used=3840.3MB, alloc=684.3MB, time=72.24 memory used=3940.7MB, alloc=684.3MB, time=74.68 memory used=4279.3MB, alloc=708.3MB, time=82.56 memory used=4652.7MB, alloc=732.3MB, time=90.51 memory used=5049.9MB, alloc=756.3MB, time=99.32 memory used=5435.6MB, alloc=780.3MB, time=107.02 |\^/| 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(); 1428246440 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; F := [ 2 2 2 2 2 2 8 x + 3 y - 2 z - 8, 14 y + 7 z - 2 x + 3 y, x - 19 x y + 14 y z + 15 ] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-2 x - 6 x y + 13 y z - 1, -x y + 2 y z + z + 14 z, 2 2 12 x - 13 x y - 9 z - 17] > Problem := [F,G]; Problem := [[ 2 2 2 2 2 2 8 x + 3 y - 2 z - 8, 14 y + 7 z - 2 x + 3 y, x - 19 x y + 14 y z + 15 2 2 ], [-2 x - 6 x y + 13 y z - 1, -x y + 2 y z + z + 14 z, 2 2 12 x - 13 x y - 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=4.3MB, alloc=32.3MB, time=0.17 memory used=27.1MB, alloc=32.3MB, time=0.51 memory used=48.3MB, alloc=32.3MB, time=0.84 memory used=68.4MB, alloc=60.3MB, time=1.15 memory used=109.7MB, alloc=60.3MB, time=1.76 memory used=149.8MB, alloc=84.3MB, time=2.37 memory used=215.4MB, alloc=92.3MB, time=3.33 memory used=281.7MB, alloc=116.3MB, time=4.23 memory used=351.0MB, alloc=116.3MB, time=5.23 memory used=429.7MB, alloc=396.3MB, time=6.44 memory used=540.1MB, alloc=396.3MB, time=8.00 memory used=651.5MB, alloc=420.3MB, time=9.50 memory used=780.4MB, alloc=444.3MB, time=11.29 memory used=894.9MB, alloc=444.3MB, time=13.02 memory used=1013.0MB, alloc=468.3MB, time=14.74 memory used=1150.0MB, alloc=492.3MB, time=17.17 memory used=1264.9MB, alloc=492.3MB, time=19.15 memory used=1353.3MB, alloc=492.3MB, time=20.41 memory used=1465.5MB, alloc=516.3MB, time=22.40 memory used=1540.2MB, alloc=516.3MB, time=23.50 memory used=1623.2MB, alloc=516.3MB, time=24.93 memory used=1693.4MB, alloc=516.3MB, time=26.02 memory used=1770.0MB, alloc=516.3MB, time=27.37 memory used=1844.4MB, alloc=516.3MB, time=28.82 memory used=1902.1MB, alloc=516.3MB, time=29.89 memory used=1963.9MB, alloc=516.3MB, time=31.04 memory used=2023.3MB, alloc=516.3MB, time=32.20 memory used=2085.0MB, alloc=516.3MB, time=33.69 memory used=2287.0MB, alloc=540.3MB, time=37.11 memory used=2491.2MB, alloc=564.3MB, time=40.44 memory used=2682.2MB, alloc=588.3MB, time=43.55 memory used=2854.4MB, alloc=612.3MB, time=46.05 memory used=3019.3MB, alloc=636.3MB, time=48.63 memory used=3189.8MB, alloc=660.3MB, time=51.59 memory used=3359.5MB, alloc=660.3MB, time=54.40 memory used=3513.9MB, alloc=660.3MB, time=56.81 memory used=3646.9MB, alloc=660.3MB, time=59.26 memory used=3783.6MB, alloc=660.3MB, time=62.09 memory used=3891.8MB, alloc=660.3MB, time=64.48 memory used=4009.3MB, alloc=684.3MB, time=67.00 memory used=4104.7MB, alloc=684.3MB, time=69.06 memory used=4459.3MB, alloc=708.3MB, time=75.65 memory used=4832.6MB, alloc=732.3MB, time=82.01 memory used=5211.3MB, alloc=756.3MB, time=89.01 memory used=5590.4MB, alloc=780.3MB, time=96.77 memory used=5909.4MB, alloc=804.3MB, time=103.72 |\^/| 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(); 1428246741 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [10 x - 8 x z + 2 y + 7 z, -9 x - 16 x y - 13 y z - 9 x, 2 -7 x - 10 x z - 16 x + 13 z] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [-17 y - 19 z - 2 x + 6, -10 x + 10 x z + 9 y z + 9, -5 x y - 4 x z - 9 y z + x] > Problem := [F,G]; 2 2 2 Problem := [[10 x - 8 x z + 2 y + 7 z, -9 x - 16 x y - 13 y z - 9 x, 2 2 2 -7 x - 10 x z - 16 x + 13 z], [-17 y - 19 z - 2 x + 6, 2 -10 x + 10 x z + 9 y z + 9, -5 x y - 4 x z - 9 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=4.3MB, alloc=32.3MB, time=0.17 memory used=26.1MB, alloc=32.3MB, time=0.50 memory used=46.3MB, alloc=32.3MB, time=0.80 memory used=64.6MB, alloc=56.3MB, time=1.11 memory used=106.3MB, alloc=60.3MB, time=1.74 memory used=147.1MB, alloc=60.3MB, time=2.35 memory used=187.2MB, alloc=84.3MB, time=2.95 memory used=224.9MB, alloc=84.3MB, time=3.53 memory used=286.5MB, alloc=116.3MB, time=4.50 memory used=365.0MB, alloc=372.3MB, time=5.74 memory used=444.7MB, alloc=396.3MB, time=7.05 memory used=552.1MB, alloc=396.3MB, time=8.70 memory used=663.7MB, alloc=420.3MB, time=10.24 memory used=795.4MB, alloc=444.3MB, time=12.29 memory used=926.4MB, alloc=468.3MB, time=14.41 memory used=1042.6MB, alloc=468.3MB, time=16.38 memory used=1154.1MB, alloc=492.3MB, time=18.23 memory used=1268.3MB, alloc=492.3MB, time=20.31 memory used=1375.7MB, alloc=492.3MB, time=22.25 memory used=1474.6MB, alloc=492.3MB, time=24.45 memory used=1564.4MB, alloc=492.3MB, time=26.18 memory used=1644.4MB, alloc=516.3MB, time=27.82 memory used=1715.8MB, alloc=516.3MB, time=29.38 memory used=1792.3MB, alloc=516.3MB, time=30.98 memory used=1841.7MB, alloc=516.3MB, time=32.09 memory used=1905.4MB, alloc=516.3MB, time=33.61 memory used=1967.3MB, alloc=516.3MB, time=35.18 memory used=2174.8MB, alloc=540.3MB, time=39.28 memory used=2400.6MB, alloc=564.3MB, time=44.05 memory used=2573.3MB, alloc=588.3MB, time=47.81 memory used=2759.3MB, alloc=612.3MB, time=52.43 memory used=2922.3MB, alloc=636.3MB, time=55.99 memory used=3096.3MB, alloc=660.3MB, time=60.22 memory used=3210.4MB, alloc=660.3MB, time=62.92 memory used=3330.9MB, alloc=660.3MB, time=66.24 memory used=3465.1MB, alloc=660.3MB, time=69.46 memory used=3596.1MB, alloc=684.3MB, time=73.08 memory used=3701.4MB, alloc=684.3MB, time=76.45 memory used=4037.8MB, alloc=708.3MB, time=84.35 memory used=4401.3MB, alloc=732.3MB, time=92.53 memory used=4781.2MB, alloc=756.3MB, time=100.64 memory used=5178.2MB, alloc=780.3MB, time=108.32 |\^/| 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(); 1428247041 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-11 x z - 10 y - 15 x, -18 x y + 13 x z + 18 y z + 12 z , 2 -2 x y + 15 z + 14 y + 2] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [-6 x y - 7 z - 12 x + 8 z, 12 y z - 12 x - 13 y - 9, 2 -13 x + 11 y + 13 z + 15] > Problem := [F,G]; 2 2 Problem := [[-11 x z - 10 y - 15 x, -18 x y + 13 x z + 18 y z + 12 z , 2 2 -2 x y + 15 z + 14 y + 2], [-6 x y - 7 z - 12 x + 8 z, 2 12 y z - 12 x - 13 y - 9, -13 x + 11 y + 13 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=26.1MB, alloc=32.3MB, time=0.50 memory used=46.7MB, alloc=32.3MB, time=0.80 memory used=64.6MB, alloc=56.3MB, time=1.08 memory used=107.3MB, alloc=68.3MB, time=1.70 memory used=147.8MB, alloc=92.3MB, time=2.32 memory used=213.2MB, alloc=92.3MB, time=3.26 memory used=278.1MB, alloc=92.3MB, time=4.29 memory used=343.6MB, alloc=116.3MB, time=5.25 memory used=417.0MB, alloc=372.3MB, time=6.34 memory used=504.3MB, alloc=396.3MB, time=7.68 memory used=616.2MB, alloc=420.3MB, time=9.36 memory used=744.7MB, alloc=420.3MB, time=11.48 memory used=877.4MB, alloc=444.3MB, time=13.30 memory used=1004.7MB, alloc=468.3MB, time=15.44 memory used=1138.3MB, alloc=492.3MB, time=17.64 memory used=1239.1MB, alloc=492.3MB, time=19.39 memory used=1337.8MB, alloc=492.3MB, time=21.01 memory used=1411.1MB, alloc=492.3MB, time=22.11 memory used=1509.2MB, alloc=492.3MB, time=23.78 memory used=1599.1MB, alloc=492.3MB, time=25.60 memory used=1673.3MB, alloc=492.3MB, time=26.86 memory used=1762.8MB, alloc=516.3MB, time=28.57 memory used=1830.4MB, alloc=516.3MB, time=29.70 memory used=1917.1MB, alloc=516.3MB, time=31.28 memory used=2002.2MB, alloc=516.3MB, time=33.23 memory used=2061.3MB, alloc=516.3MB, time=34.51 memory used=2125.7MB, alloc=516.3MB, time=35.95 memory used=2178.4MB, alloc=516.3MB, time=37.18 memory used=2228.6MB, alloc=516.3MB, time=38.26 memory used=2283.5MB, alloc=516.3MB, time=39.31 memory used=2484.0MB, alloc=540.3MB, time=43.37 memory used=2699.6MB, alloc=564.3MB, time=47.81 memory used=2884.8MB, alloc=588.3MB, time=51.26 memory used=3063.4MB, alloc=612.3MB, time=54.72 memory used=3240.3MB, alloc=636.3MB, time=58.35 memory used=3401.3MB, alloc=636.3MB, time=61.29 memory used=3567.4MB, alloc=660.3MB, time=64.92 memory used=3706.5MB, alloc=660.3MB, time=68.27 memory used=3873.8MB, alloc=660.3MB, time=72.47 memory used=3977.2MB, alloc=660.3MB, time=74.75 memory used=4103.9MB, alloc=660.3MB, time=77.98 memory used=4229.2MB, alloc=660.3MB, time=80.96 memory used=4325.2MB, alloc=660.3MB, time=83.76 memory used=4437.4MB, alloc=684.3MB, time=86.73 memory used=4805.0MB, alloc=708.3MB, time=94.06 memory used=5183.5MB, alloc=732.3MB, time=102.06 |\^/| 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(); 1428247341 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-19 x z + 15 y z + 19, -10 x + 14 z + 4 y - 2 z, 2 -17 x y - 15 y + 7 x - 11] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [x z - 3 y z - 15 z - 7, 13 x - 8 y z + 11 z - 4 y, 2 2 2 -15 x + 2 y - 3 z + x] > Problem := [F,G]; 2 2 Problem := [[-19 x z + 15 y z + 19, -10 x + 14 z + 4 y - 2 z, 2 2 -17 x y - 15 y + 7 x - 11], [x z - 3 y z - 15 z - 7, 2 2 2 2 2 13 x - 8 y z + 11 z - 4 y, -15 x + 2 y - 3 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=0.18 memory used=27.0MB, alloc=32.3MB, time=0.53 memory used=46.3MB, alloc=56.3MB, time=0.83 memory used=86.2MB, alloc=60.3MB, time=1.42 memory used=130.2MB, alloc=68.3MB, time=2.07 memory used=172.1MB, alloc=92.3MB, time=2.68 memory used=237.8MB, alloc=92.3MB, time=3.61 memory used=301.0MB, alloc=116.3MB, time=4.55 memory used=368.7MB, alloc=116.3MB, time=5.46 memory used=434.9MB, alloc=372.3MB, time=6.50 memory used=521.1MB, alloc=396.3MB, time=7.81 memory used=628.3MB, alloc=420.3MB, time=9.57 memory used=757.8MB, alloc=444.3MB, time=11.45 memory used=890.2MB, alloc=468.3MB, time=13.49 memory used=1003.7MB, alloc=468.3MB, time=15.28 memory used=1110.4MB, alloc=468.3MB, time=16.97 memory used=1217.2MB, alloc=492.3MB, time=18.56 memory used=1304.1MB, alloc=492.3MB, time=20.09 memory used=1406.6MB, alloc=492.3MB, time=21.90 memory used=1507.7MB, alloc=492.3MB, time=23.29 memory used=1599.5MB, alloc=492.3MB, time=24.54 memory used=1690.1MB, alloc=492.3MB, time=25.88 memory used=1774.0MB, alloc=516.3MB, time=27.10 memory used=1852.7MB, alloc=516.3MB, time=28.57 memory used=1923.2MB, alloc=516.3MB, time=30.02 memory used=1997.3MB, alloc=516.3MB, time=31.42 memory used=2060.1MB, alloc=516.3MB, time=32.65 memory used=2105.5MB, alloc=516.3MB, time=33.75 memory used=2163.0MB, alloc=516.3MB, time=35.10 memory used=2194.3MB, alloc=516.3MB, time=35.89 memory used=2404.5MB, alloc=540.3MB, time=38.84 memory used=2628.8MB, alloc=564.3MB, time=43.05 memory used=2816.7MB, alloc=588.3MB, time=46.73 memory used=2997.2MB, alloc=612.3MB, time=50.40 memory used=3172.9MB, alloc=636.3MB, time=53.92 memory used=3317.5MB, alloc=636.3MB, time=56.95 memory used=3456.7MB, alloc=636.3MB, time=59.29 memory used=3597.2MB, alloc=660.3MB, time=62.06 memory used=3728.7MB, alloc=660.3MB, time=65.06 memory used=3843.8MB, alloc=660.3MB, time=67.66 memory used=3960.1MB, alloc=660.3MB, time=70.67 memory used=4056.7MB, alloc=660.3MB, time=73.15 memory used=4141.0MB, alloc=660.3MB, time=75.69 memory used=4476.6MB, alloc=684.3MB, time=82.03 memory used=4817.9MB, alloc=708.3MB, time=87.37 memory used=5192.8MB, alloc=732.3MB, time=94.81 memory used=5577.2MB, alloc=756.3MB, time=102.62 memory used=5894.8MB, alloc=780.3MB, time=109.29 |\^/| 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(); 1428247641 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-17 x + 6 x + 13 y + 3, 18 x + 8 x y - 15 y - 17 z, 2 2 -16 x - 2 x z + 4 y - 2 y] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [-7 x + 9 x z - 5 y z + 4 z, -11 x + 14 y - 12 y z - 7 z , 2 -x z + 2 y - 14 x - 17 y] > Problem := [F,G]; 2 2 2 Problem := [[-17 x + 6 x + 13 y + 3, 18 x + 8 x y - 15 y - 17 z, 2 2 2 -16 x - 2 x z + 4 y - 2 y], [-7 x + 9 x z - 5 y z + 4 z, 2 2 2 2 -11 x + 14 y - 12 y z - 7 z , -x z + 2 y - 14 x - 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=4.4MB, alloc=32.3MB, time=0.18 memory used=26.3MB, alloc=32.3MB, time=0.51 memory used=45.9MB, alloc=32.3MB, time=0.80 memory used=65.4MB, alloc=56.3MB, time=1.10 memory used=107.0MB, alloc=60.3MB, time=1.72 memory used=146.8MB, alloc=60.3MB, time=2.30 memory used=187.2MB, alloc=84.3MB, time=2.92 memory used=225.8MB, alloc=84.3MB, time=3.53 memory used=289.1MB, alloc=92.3MB, time=4.53 memory used=352.0MB, alloc=116.3MB, time=5.52 memory used=414.7MB, alloc=116.3MB, time=6.48 memory used=479.8MB, alloc=396.3MB, time=7.56 memory used=586.8MB, alloc=420.3MB, time=9.25 memory used=720.9MB, alloc=444.3MB, time=11.21 memory used=838.2MB, alloc=444.3MB, time=12.93 memory used=949.5MB, alloc=468.3MB, time=14.55 memory used=1048.9MB, alloc=468.3MB, time=16.25 memory used=1155.5MB, alloc=492.3MB, time=17.86 memory used=1232.9MB, alloc=492.3MB, time=19.13 memory used=1313.4MB, alloc=492.3MB, time=20.53 memory used=1376.9MB, alloc=492.3MB, time=21.52 memory used=1453.6MB, alloc=492.3MB, time=23.03 memory used=1505.8MB, alloc=492.3MB, time=23.93 memory used=1570.5MB, alloc=492.3MB, time=25.32 memory used=1616.4MB, alloc=492.3MB, time=26.22 memory used=1802.5MB, alloc=516.3MB, time=29.58 memory used=1987.7MB, alloc=540.3MB, time=32.68 memory used=2168.3MB, alloc=564.3MB, time=35.80 memory used=2351.1MB, alloc=588.3MB, time=39.17 memory used=2521.5MB, alloc=612.3MB, time=42.66 memory used=2664.7MB, alloc=636.3MB, time=45.86 memory used=2809.1MB, alloc=636.3MB, time=48.65 memory used=2943.2MB, alloc=636.3MB, time=51.55 memory used=3071.3MB, alloc=636.3MB, time=54.35 memory used=3180.2MB, alloc=636.3MB, time=56.88 memory used=3265.7MB, alloc=636.3MB, time=58.90 memory used=3570.9MB, alloc=660.3MB, time=64.96 memory used=3894.2MB, alloc=684.3MB, time=71.46 memory used=4243.3MB, alloc=708.3MB, time=78.04 memory used=4549.4MB, alloc=732.3MB, time=83.92 memory used=4862.3MB, alloc=756.3MB, time=90.23 memory used=5155.1MB, alloc=780.3MB, time=96.59 memory used=5433.6MB, alloc=804.3MB, time=102.99 |\^/| 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(); 1428247941 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; F := [ 2 2 2 -20 x y + 8 y z + 18 z + 7, 5 x y + 9 y - 1, -10 x + 3 x z + 17 y + 18 z ] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 G := [3 x + 14 x y + 4 y + 14 x, 15 x + 18 x z - 16 y - 14 z , 5 x y + 13 x z + 9 z + 14] > Problem := [F,G]; Problem := [[ 2 2 2 -20 x y + 8 y z + 18 z + 7, 5 x y + 9 y - 1, -10 x + 3 x z + 17 y + 18 z 2 2 2 2 2 ], [3 x + 14 x y + 4 y + 14 x, 15 x + 18 x z - 16 y - 14 z , 5 x y + 13 x z + 9 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=0.20 memory used=27.1MB, alloc=32.3MB, time=0.54 memory used=47.1MB, alloc=56.3MB, time=0.85 memory used=88.6MB, alloc=60.3MB, time=1.49 memory used=129.1MB, alloc=60.3MB, time=2.23 memory used=168.5MB, alloc=84.3MB, time=2.85 memory used=232.7MB, alloc=92.3MB, time=3.85 memory used=294.3MB, alloc=116.3MB, time=4.87 memory used=375.4MB, alloc=140.3MB, time=6.26 memory used=440.5MB, alloc=396.3MB, time=7.27 memory used=547.3MB, alloc=396.3MB, time=9.22 memory used=657.8MB, alloc=420.3MB, time=11.18 memory used=795.3MB, alloc=444.3MB, time=13.44 memory used=937.3MB, alloc=468.3MB, time=15.82 memory used=1063.8MB, alloc=468.3MB, time=17.99 memory used=1192.2MB, alloc=492.3MB, time=20.47 memory used=1300.2MB, alloc=492.3MB, time=22.55 memory used=1417.8MB, alloc=492.3MB, time=24.98 memory used=1522.3MB, alloc=492.3MB, time=27.03 memory used=1620.6MB, alloc=492.3MB, time=29.19 memory used=1702.5MB, alloc=492.3MB, time=31.01 memory used=1785.7MB, alloc=516.3MB, time=32.82 memory used=1873.7MB, alloc=516.3MB, time=34.90 memory used=1957.4MB, alloc=516.3MB, time=36.81 memory used=2019.7MB, alloc=516.3MB, time=38.36 memory used=2088.0MB, alloc=516.3MB, time=39.94 memory used=2154.3MB, alloc=516.3MB, time=41.53 memory used=2219.1MB, alloc=516.3MB, time=43.16 memory used=2272.6MB, alloc=516.3MB, time=44.58 memory used=2324.7MB, alloc=516.3MB, time=45.65 memory used=2536.8MB, alloc=540.3MB, time=49.93 memory used=2746.9MB, alloc=564.3MB, time=54.00 memory used=2915.6MB, alloc=588.3MB, time=57.84 memory used=3103.2MB, alloc=612.3MB, time=61.79 memory used=3279.6MB, alloc=636.3MB, time=65.54 memory used=3436.5MB, alloc=660.3MB, time=68.87 memory used=3592.2MB, alloc=684.3MB, time=72.32 memory used=3771.0MB, alloc=708.3MB, time=76.30 memory used=3920.5MB, alloc=708.3MB, time=79.69 memory used=4105.4MB, alloc=732.3MB, time=83.81 memory used=4312.4MB, alloc=756.3MB, time=88.41 memory used=4500.8MB, alloc=780.3MB, time=92.60 memory used=4707.6MB, alloc=804.3MB, time=97.17 |\^/| 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(); 1428248241 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [20 x - 4 x y - 14 x z - 17, 13 x y + x z - 14 y - 3 x, 2 -15 x y + 3 x z - 11 y - 20 y z] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [-15 x y + 15 x - 2 y + 7 z, -13 x y + 4 x z + 5 y z - 8 z , 2 3 x + 4 x z + 8 x - 4] > Problem := [F,G]; 2 2 Problem := [[20 x - 4 x y - 14 x z - 17, 13 x y + x z - 14 y - 3 x, 2 -15 x y + 3 x z - 11 y - 20 y z], [-15 x y + 15 x - 2 y + 7 z, 2 2 -13 x y + 4 x z + 5 y z - 8 z , 3 x + 4 x z + 8 x - 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=4.4MB, alloc=32.3MB, time=0.18 memory used=26.3MB, alloc=32.3MB, time=0.51 memory used=46.7MB, alloc=32.3MB, time=0.81 memory used=66.0MB, alloc=56.3MB, time=1.11 memory used=106.6MB, alloc=60.3MB, time=1.71 memory used=146.1MB, alloc=84.3MB, time=2.31 memory used=210.3MB, alloc=92.3MB, time=3.23 memory used=273.7MB, alloc=116.3MB, time=4.17 memory used=349.2MB, alloc=116.3MB, time=5.28 memory used=427.3MB, alloc=372.3MB, time=6.50 memory used=513.2MB, alloc=396.3MB, time=7.87 memory used=622.7MB, alloc=420.3MB, time=9.64 memory used=754.4MB, alloc=444.3MB, time=11.79 memory used=906.6MB, alloc=468.3MB, time=14.37 memory used=1036.9MB, alloc=468.3MB, time=16.66 memory used=1155.8MB, alloc=492.3MB, time=18.75 memory used=1273.5MB, alloc=492.3MB, time=20.93 memory used=1380.3MB, alloc=492.3MB, time=22.97 memory used=1477.2MB, alloc=492.3MB, time=24.87 memory used=1568.9MB, alloc=492.3MB, time=26.60 memory used=1658.8MB, alloc=516.3MB, time=28.47 memory used=1744.4MB, alloc=516.3MB, time=30.30 memory used=1813.5MB, alloc=516.3MB, time=31.77 memory used=1902.3MB, alloc=516.3MB, time=33.71 memory used=1962.4MB, alloc=516.3MB, time=34.98 memory used=2023.8MB, alloc=516.3MB, time=36.26 memory used=2061.5MB, alloc=540.3MB, time=37.01 memory used=2136.3MB, alloc=540.3MB, time=38.87 memory used=2189.9MB, alloc=540.3MB, time=40.25 memory used=2237.9MB, alloc=540.3MB, time=41.25 memory used=2444.9MB, alloc=564.3MB, time=44.89 memory used=2606.9MB, alloc=588.3MB, time=47.54 memory used=2800.2MB, alloc=612.3MB, time=51.48 memory used=2975.3MB, alloc=636.3MB, time=55.21 memory used=3113.9MB, alloc=660.3MB, time=57.82 memory used=3254.1MB, alloc=660.3MB, time=61.38 memory used=3360.7MB, alloc=660.3MB, time=63.70 memory used=3508.5MB, alloc=660.3MB, time=67.41 memory used=3597.4MB, alloc=660.3MB, time=69.47 memory used=3727.0MB, alloc=684.3MB, time=72.97 memory used=4084.5MB, alloc=708.3MB, time=80.79 memory used=4449.5MB, alloc=732.3MB, time=90.08 memory used=4838.5MB, alloc=756.3MB, time=97.80 |\^/| 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(); 1428248541 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-19 x y - 9 x z + 12 y + z , 18 x y + 6 x z - 7 z + 10 x, -4 x y + 16 x + 10 z - 12] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [x y - 11 y + 20 y + 16 z, -x + 17 x z + 6 y z + 5 z, 2 -2 x + 9 y z + 6 x + 9 z] > Problem := [F,G]; 2 2 2 Problem := [[-19 x y - 9 x z + 12 y + z , 18 x y + 6 x z - 7 z + 10 x, 2 -4 x y + 16 x + 10 z - 12], [x y - 11 y + 20 y + 16 z, 2 2 -x + 17 x z + 6 y z + 5 z, -2 x + 9 y z + 6 x + 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=0.18 memory used=26.5MB, alloc=32.3MB, time=0.52 memory used=46.0MB, alloc=56.3MB, time=0.82 memory used=87.6MB, alloc=60.3MB, time=1.45 memory used=126.1MB, alloc=84.3MB, time=2.05 memory used=162.7MB, alloc=84.3MB, time=2.60 memory used=224.2MB, alloc=92.3MB, time=3.57 memory used=285.6MB, alloc=116.3MB, time=4.52 memory used=367.9MB, alloc=116.3MB, time=5.86 memory used=439.7MB, alloc=396.3MB, time=7.03 memory used=552.8MB, alloc=420.3MB, time=8.67 memory used=681.6MB, alloc=444.3MB, time=10.82 memory used=812.6MB, alloc=444.3MB, time=12.82 memory used=939.0MB, alloc=468.3MB, time=14.85 memory used=1068.7MB, alloc=468.3MB, time=17.24 memory used=1175.1MB, alloc=492.3MB, time=19.08 memory used=1279.1MB, alloc=492.3MB, time=20.91 memory used=1376.1MB, alloc=492.3MB, time=22.67 memory used=1473.7MB, alloc=492.3MB, time=24.44 memory used=1569.7MB, alloc=492.3MB, time=26.50 memory used=1670.8MB, alloc=492.3MB, time=28.73 memory used=1766.3MB, alloc=516.3MB, time=30.89 memory used=1838.8MB, alloc=516.3MB, time=32.54 memory used=1900.6MB, alloc=516.3MB, time=33.71 memory used=1975.7MB, alloc=516.3MB, time=35.48 memory used=2030.3MB, alloc=516.3MB, time=36.60 memory used=2083.3MB, alloc=516.3MB, time=37.95 memory used=2131.6MB, alloc=516.3MB, time=39.17 memory used=2341.4MB, alloc=540.3MB, time=43.31 memory used=2545.0MB, alloc=564.3MB, time=47.44 memory used=2749.7MB, alloc=588.3MB, time=51.97 memory used=2927.4MB, alloc=612.3MB, time=55.74 memory used=3135.9MB, alloc=636.3MB, time=60.82 memory used=3320.6MB, alloc=660.3MB, time=66.07 memory used=3473.6MB, alloc=660.3MB, time=69.61 memory used=3614.9MB, alloc=684.3MB, time=72.65 memory used=3753.0MB, alloc=684.3MB, time=76.27 memory used=3876.1MB, alloc=684.3MB, time=79.32 memory used=3996.2MB, alloc=684.3MB, time=82.12 memory used=4123.5MB, alloc=684.3MB, time=85.62 memory used=4222.2MB, alloc=684.3MB, time=88.52 memory used=4570.3MB, alloc=708.3MB, time=96.82 memory used=4930.8MB, alloc=732.3MB, time=105.52 |\^/| 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(); 1428248841 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [5 y + 12 x - 2 z + 1, 18 x y - 16 x z + 17 y z + 18 y, 2 6 x y + 3 y z - 13 z - 4 x] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [-16 x - x y - 6 y z - 2, 12 x + 10 x z + 18 y - 9, 2 5 x y + 6 y + 16 y z - 14] > Problem := [F,G]; 2 Problem := [[5 y + 12 x - 2 z + 1, 18 x y - 16 x z + 17 y z + 18 y, 2 2 6 x y + 3 y z - 13 z - 4 x], [-16 x - x y - 6 y z - 2, 2 2 2 12 x + 10 x z + 18 y - 9, 5 x y + 6 y + 16 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=0.18 memory used=26.0MB, alloc=32.3MB, time=0.50 memory used=46.2MB, alloc=32.3MB, time=0.81 memory used=64.8MB, alloc=56.3MB, time=1.11 memory used=107.5MB, alloc=68.3MB, time=1.78 memory used=149.6MB, alloc=68.3MB, time=2.40 memory used=189.7MB, alloc=92.3MB, time=3.00 memory used=254.0MB, alloc=92.3MB, time=3.94 memory used=314.3MB, alloc=116.3MB, time=4.91 memory used=380.5MB, alloc=372.3MB, time=5.94 memory used=470.8MB, alloc=396.3MB, time=7.22 memory used=581.7MB, alloc=420.3MB, time=8.96 memory used=715.8MB, alloc=444.3MB, time=10.90 memory used=837.1MB, alloc=444.3MB, time=12.81 memory used=947.5MB, alloc=468.3MB, time=14.51 memory used=1050.7MB, alloc=468.3MB, time=16.12 memory used=1152.0MB, alloc=468.3MB, time=17.75 memory used=1249.8MB, alloc=468.3MB, time=19.38 memory used=1350.2MB, alloc=468.3MB, time=21.18 memory used=1439.1MB, alloc=492.3MB, time=22.85 memory used=1515.4MB, alloc=492.3MB, time=24.35 memory used=1590.4MB, alloc=492.3MB, time=25.82 memory used=1666.3MB, alloc=492.3MB, time=27.32 memory used=1724.1MB, alloc=492.3MB, time=28.43 memory used=1782.0MB, alloc=492.3MB, time=29.80 memory used=1840.8MB, alloc=492.3MB, time=31.15 memory used=1882.9MB, alloc=492.3MB, time=32.12 memory used=2069.6MB, alloc=516.3MB, time=35.56 memory used=2271.4MB, alloc=540.3MB, time=39.26 memory used=2452.4MB, alloc=564.3MB, time=42.77 memory used=2618.4MB, alloc=588.3MB, time=46.21 memory used=2756.4MB, alloc=612.3MB, time=49.16 memory used=2913.2MB, alloc=636.3MB, time=52.38 memory used=3054.1MB, alloc=636.3MB, time=55.41 memory used=3189.1MB, alloc=636.3MB, time=58.39 memory used=3300.1MB, alloc=636.3MB, time=61.00 memory used=3385.1MB, alloc=636.3MB, time=63.14 memory used=3505.1MB, alloc=636.3MB, time=66.16 memory used=3597.3MB, alloc=660.3MB, time=68.57 memory used=3919.8MB, alloc=684.3MB, time=75.30 memory used=4263.6MB, alloc=708.3MB, time=81.75 memory used=4616.0MB, alloc=732.3MB, time=88.52 memory used=4995.1MB, alloc=756.3MB, time=96.96 memory used=5307.3MB, alloc=780.3MB, time=102.13 memory used=5613.8MB, alloc=804.3MB, time=108.92 |\^/| 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(); 1428249141 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-3 x y + 8 y - 11 y - 1, -6 x + 15 x z + 2 y - 2 z, -18 x y - 7 x + 11 y - 20 z] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [-3 x z - 8 z + 11 x + 13 z, -16 x + 14 y + 3 x + 18 z, -7 x y - 2 x z - 6 y z - 11 y] > Problem := [F,G]; 2 2 Problem := [[-3 x y + 8 y - 11 y - 1, -6 x + 15 x z + 2 y - 2 z, 2 -18 x y - 7 x + 11 y - 20 z], [-3 x z - 8 z + 11 x + 13 z, 2 2 -16 x + 14 y + 3 x + 18 z, -7 x y - 2 x z - 6 y z - 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=4.3MB, alloc=32.3MB, time=0.17 memory used=26.3MB, alloc=32.3MB, time=0.50 memory used=46.4MB, alloc=32.3MB, time=0.80 memory used=65.2MB, alloc=56.3MB, time=1.10 memory used=106.2MB, alloc=60.3MB, time=1.74 memory used=146.1MB, alloc=84.3MB, time=2.38 memory used=208.8MB, alloc=92.3MB, time=3.35 memory used=270.7MB, alloc=116.3MB, time=4.34 memory used=339.5MB, alloc=116.3MB, time=5.42 memory used=405.6MB, alloc=372.3MB, time=6.54 memory used=489.3MB, alloc=396.3MB, time=7.93 memory used=596.7MB, alloc=420.3MB, time=9.71 memory used=726.0MB, alloc=444.3MB, time=11.98 memory used=867.7MB, alloc=468.3MB, time=14.37 memory used=985.5MB, alloc=468.3MB, time=16.29 memory used=1103.3MB, alloc=492.3MB, time=18.42 memory used=1224.9MB, alloc=492.3MB, time=20.72 memory used=1330.7MB, alloc=492.3MB, time=22.68 memory used=1422.8MB, alloc=492.3MB, time=24.43 memory used=1511.8MB, alloc=492.3MB, time=26.16 memory used=1596.9MB, alloc=492.3MB, time=27.98 memory used=1680.7MB, alloc=492.3MB, time=29.67 memory used=1747.5MB, alloc=516.3MB, time=31.06 memory used=1816.2MB, alloc=516.3MB, time=32.59 memory used=1878.5MB, alloc=516.3MB, time=34.00 memory used=1941.6MB, alloc=516.3MB, time=35.39 memory used=1993.6MB, alloc=516.3MB, time=36.77 memory used=2204.1MB, alloc=540.3MB, time=40.73 memory used=2420.9MB, alloc=564.3MB, time=45.13 memory used=2630.5MB, alloc=588.3MB, time=49.52 memory used=2817.0MB, alloc=612.3MB, time=53.51 memory used=3000.2MB, alloc=636.3MB, time=58.09 memory used=3158.0MB, alloc=660.3MB, time=61.66 memory used=3309.4MB, alloc=660.3MB, time=65.17 memory used=3448.5MB, alloc=660.3MB, time=68.62 memory used=3582.8MB, alloc=660.3MB, time=71.95 memory used=3702.0MB, alloc=660.3MB, time=74.79 memory used=3828.1MB, alloc=660.3MB, time=78.00 memory used=3931.0MB, alloc=684.3MB, time=80.47 memory used=4026.4MB, alloc=684.3MB, time=83.08 memory used=4379.1MB, alloc=708.3MB, time=90.13 memory used=4748.2MB, alloc=732.3MB, time=98.65 memory used=5132.0MB, alloc=756.3MB, time=107.47 |\^/| 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(); 1428249441 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-6 x z + 7 y z + 2 x + 5 z, 7 x + 20 y + 18 y z - 13 z, 2 16 x + 9 y z - z + 7] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [8 x - 5 x z + 18 z - 2 z, -11 x y - 18 x z + 20 x - 1, -12 x y + 3 y z - 19 x + 16] > Problem := [F,G]; 2 2 Problem := [[-6 x z + 7 y z + 2 x + 5 z, 7 x + 20 y + 18 y z - 13 z, 2 2 2 16 x + 9 y z - z + 7], [8 x - 5 x z + 18 z - 2 z, -11 x y - 18 x z + 20 x - 1, -12 x y + 3 y z - 19 x + 16]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,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=0.51 memory used=47.3MB, alloc=32.3MB, time=0.82 memory used=66.5MB, alloc=56.3MB, time=1.12 memory used=107.0MB, alloc=60.3MB, time=1.74 memory used=146.4MB, alloc=84.3MB, time=2.36 memory used=209.0MB, alloc=92.3MB, time=3.34 memory used=272.5MB, alloc=92.3MB, time=4.33 memory used=334.4MB, alloc=116.3MB, time=5.33 memory used=404.0MB, alloc=372.3MB, time=6.48 memory used=489.3MB, alloc=396.3MB, time=7.87 memory used=597.0MB, alloc=396.3MB, time=9.71 memory used=703.7MB, alloc=420.3MB, time=11.50 memory used=835.6MB, alloc=444.3MB, time=13.84 memory used=980.8MB, alloc=468.3MB, time=16.47 memory used=1124.5MB, alloc=468.3MB, time=19.11 memory used=1233.0MB, alloc=492.3MB, time=21.09 memory used=1355.2MB, alloc=492.3MB, time=23.57 memory used=1486.4MB, alloc=492.3MB, time=26.31 memory used=1597.4MB, alloc=492.3MB, time=28.54 memory used=1698.1MB, alloc=492.3MB, time=30.68 memory used=1805.0MB, alloc=516.3MB, time=33.03 memory used=1900.5MB, alloc=516.3MB, time=35.00 memory used=1985.6MB, alloc=516.3MB, time=36.92 memory used=2078.0MB, alloc=516.3MB, time=39.10 memory used=2185.0MB, alloc=516.3MB, time=41.90 memory used=2259.8MB, alloc=516.3MB, time=43.90 memory used=2328.6MB, alloc=516.3MB, time=45.76 memory used=2390.2MB, alloc=516.3MB, time=47.34 memory used=2445.5MB, alloc=516.3MB, time=48.84 memory used=2513.6MB, alloc=516.3MB, time=50.73 memory used=2578.7MB, alloc=516.3MB, time=52.54 memory used=2645.7MB, alloc=516.3MB, time=54.39 memory used=2854.7MB, alloc=540.3MB, time=59.47 memory used=3080.1MB, alloc=564.3MB, time=65.56 memory used=3330.7MB, alloc=588.3MB, time=72.09 memory used=3556.1MB, alloc=612.3MB, time=77.88 memory used=3808.4MB, alloc=636.3MB, time=84.95 memory used=4002.3MB, alloc=660.3MB, time=90.13 memory used=4170.7MB, alloc=684.3MB, time=94.77 memory used=4342.0MB, alloc=708.3MB, time=99.42 memory used=4507.3MB, alloc=708.3MB, time=103.93 |\^/| 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(); 1428249741 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [10 x y - 6 z + 18 x, -11 x - 19 x y - 13 y - 10 z , 2 2 -4 x - 18 x y + 18 x z + z ] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [-14 x - 3 x y + 9 y - 7 z , -5 x y - 9 x z + 10 z + 20 z, 2 2 6 x y - 4 y - 4 z + 16 z] > Problem := [F,G]; 2 2 2 2 Problem := [[10 x y - 6 z + 18 x, -11 x - 19 x y - 13 y - 10 z , 2 2 2 2 2 -4 x - 18 x y + 18 x z + z ], [-14 x - 3 x y + 9 y - 7 z , 2 2 2 -5 x y - 9 x z + 10 z + 20 z, 6 x y - 4 y - 4 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=0.17 memory used=27.2MB, alloc=32.3MB, time=0.51 memory used=48.3MB, alloc=56.3MB, time=0.83 memory used=90.4MB, alloc=60.3MB, time=1.46 memory used=131.1MB, alloc=84.3MB, time=2.08 memory used=173.5MB, alloc=84.3MB, time=2.73 memory used=238.8MB, alloc=116.3MB, time=3.72 memory used=310.4MB, alloc=372.3MB, time=4.86 memory used=394.6MB, alloc=396.3MB, time=6.25 memory used=503.2MB, alloc=396.3MB, time=8.02 memory used=613.0MB, alloc=420.3MB, time=9.71 memory used=745.7MB, alloc=444.3MB, time=11.87 memory used=879.2MB, alloc=468.3MB, time=14.08 memory used=1007.0MB, alloc=468.3MB, time=15.95 memory used=1131.5MB, alloc=468.3MB, time=18.05 memory used=1245.4MB, alloc=492.3MB, time=19.90 memory used=1346.5MB, alloc=492.3MB, time=21.52 memory used=1446.5MB, alloc=492.3MB, time=23.13 memory used=1559.4MB, alloc=516.3MB, time=25.30 memory used=1661.1MB, alloc=516.3MB, time=27.13 memory used=1773.1MB, alloc=516.3MB, time=29.31 memory used=1877.8MB, alloc=516.3MB, time=31.44 memory used=1969.4MB, alloc=516.3MB, time=33.07 memory used=2071.0MB, alloc=540.3MB, time=35.23 memory used=2152.5MB, alloc=540.3MB, time=36.59 memory used=2236.0MB, alloc=540.3MB, time=38.71 memory used=2319.1MB, alloc=540.3MB, time=40.28 memory used=2412.9MB, alloc=540.3MB, time=42.42 memory used=2483.4MB, alloc=540.3MB, time=43.70 memory used=2546.1MB, alloc=540.3MB, time=45.02 memory used=2602.8MB, alloc=540.3MB, time=46.34 memory used=2668.3MB, alloc=540.3MB, time=48.16 memory used=2706.5MB, alloc=540.3MB, time=49.22 memory used=2757.1MB, alloc=540.3MB, time=50.37 memory used=2986.5MB, alloc=564.3MB, time=54.56 memory used=3193.7MB, alloc=588.3MB, time=58.67 memory used=3366.1MB, alloc=612.3MB, time=61.51 memory used=3537.0MB, alloc=636.3MB, time=65.06 memory used=3686.6MB, alloc=660.3MB, time=67.59 memory used=3842.3MB, alloc=660.3MB, time=71.11 memory used=3984.6MB, alloc=684.3MB, time=74.02 memory used=4116.1MB, alloc=684.3MB, time=77.02 memory used=4225.2MB, alloc=684.3MB, time=79.32 memory used=4359.7MB, alloc=684.3MB, time=82.52 memory used=4475.6MB, alloc=708.3MB, time=84.96 memory used=4584.1MB, alloc=708.3MB, time=87.05 memory used=4956.8MB, alloc=732.3MB, time=94.67 memory used=5347.7MB, alloc=756.3MB, time=102.44 |\^/| 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(); 1428250041 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [17 x y - 7 y + 8 y z - 4 z, 15 x - 6 y + 4 z + 18 y, 2 20 x z - 13 z - 18 x + 3 y] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [-16 x + 18 x z + 2 y + 5 y z, -9 x - 17 x z + 13 y - 13 y, -15 x y - 13 y z + 9 y + 18 z] > Problem := [F,G]; 2 2 2 2 Problem := [[17 x y - 7 y + 8 y z - 4 z, 15 x - 6 y + 4 z + 18 y, 2 2 2 20 x z - 13 z - 18 x + 3 y], [-16 x + 18 x z + 2 y + 5 y z, 2 2 -9 x - 17 x z + 13 y - 13 y, -15 x y - 13 y z + 9 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=0.17 memory used=26.0MB, alloc=32.3MB, time=0.50 memory used=46.2MB, alloc=56.3MB, time=0.81 memory used=87.6MB, alloc=60.3MB, time=1.43 memory used=128.0MB, alloc=92.3MB, time=2.06 memory used=192.2MB, alloc=92.3MB, time=3.01 memory used=254.1MB, alloc=116.3MB, time=3.99 memory used=327.6MB, alloc=372.3MB, time=5.13 memory used=412.5MB, alloc=372.3MB, time=6.46 memory used=496.7MB, alloc=396.3MB, time=7.81 memory used=604.8MB, alloc=420.3MB, time=9.46 memory used=732.8MB, alloc=444.3MB, time=11.60 memory used=863.6MB, alloc=444.3MB, time=13.57 memory used=998.0MB, alloc=468.3MB, time=15.64 memory used=1112.0MB, alloc=492.3MB, time=17.29 memory used=1244.9MB, alloc=492.3MB, time=19.42 memory used=1356.2MB, alloc=516.3MB, time=21.28 memory used=1451.9MB, alloc=516.3MB, time=23.10 memory used=1543.0MB, alloc=516.3MB, time=24.74 memory used=1625.4MB, alloc=516.3MB, time=26.46 memory used=1706.7MB, alloc=516.3MB, time=27.67 memory used=1791.7MB, alloc=516.3MB, time=29.37 memory used=1849.4MB, alloc=516.3MB, time=30.42 memory used=1920.6MB, alloc=516.3MB, time=31.88 memory used=1988.4MB, alloc=516.3MB, time=33.39 memory used=2046.6MB, alloc=516.3MB, time=34.66 memory used=2114.5MB, alloc=516.3MB, time=36.13 memory used=2180.8MB, alloc=516.3MB, time=37.45 memory used=2239.8MB, alloc=516.3MB, time=38.91 memory used=2286.0MB, alloc=516.3MB, time=39.92 memory used=2329.4MB, alloc=516.3MB, time=40.91 memory used=2529.5MB, alloc=540.3MB, time=44.26 memory used=2732.5MB, alloc=564.3MB, time=48.36 memory used=2921.9MB, alloc=588.3MB, time=51.81 memory used=3124.2MB, alloc=612.3MB, time=56.21 memory used=3329.8MB, alloc=636.3MB, time=60.75 memory used=3507.8MB, alloc=660.3MB, time=64.41 memory used=3655.7MB, alloc=660.3MB, time=67.72 memory used=3795.2MB, alloc=660.3MB, time=70.75 memory used=3890.4MB, alloc=660.3MB, time=72.92 memory used=4020.7MB, alloc=660.3MB, time=75.83 memory used=4129.9MB, alloc=684.3MB, time=78.18 memory used=4242.2MB, alloc=684.3MB, time=81.05 memory used=4335.3MB, alloc=684.3MB, time=83.10 memory used=4417.4MB, alloc=684.3MB, time=85.75 memory used=4504.7MB, alloc=684.3MB, time=88.47 memory used=4854.5MB, alloc=708.3MB, time=96.56 |\^/| 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(); 1428250341 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [17 x + 8 y + 20 y z - 3 z, 6 x y + 20 x z + 18 y - 20 z, 2 -20 x y - 5 x z + 4 y + z] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 G := [15 x + 17 y + 5 z - 15 y, 2 x y + 4 x z + 6 z - y, 4 y - 11 y z + 4] > Problem := [F,G]; 2 2 2 Problem := [[17 x + 8 y + 20 y z - 3 z, 6 x y + 20 x z + 18 y - 20 z, 2 -20 x y - 5 x z + 4 y + z], 2 2 2 2 2 [15 x + 17 y + 5 z - 15 y, 2 x y + 4 x z + 6 z - y, 4 y - 11 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=4.4MB, alloc=32.3MB, time=0.17 memory used=26.5MB, 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=107.7MB, alloc=68.3MB, time=1.71 memory used=149.2MB, alloc=92.3MB, time=2.31 memory used=212.9MB, alloc=92.3MB, time=3.26 memory used=277.1MB, alloc=116.3MB, time=4.22 memory used=343.1MB, alloc=116.3MB, time=5.20 memory used=405.0MB, alloc=372.3MB, time=6.18 memory used=480.4MB, alloc=396.3MB, time=7.37 memory used=595.6MB, alloc=420.3MB, time=8.81 memory used=732.2MB, alloc=444.3MB, time=10.78 memory used=848.2MB, alloc=444.3MB, time=12.43 memory used=962.5MB, alloc=468.3MB, time=14.17 memory used=1065.4MB, alloc=468.3MB, time=15.79 memory used=1169.6MB, alloc=468.3MB, time=17.47 memory used=1262.7MB, alloc=492.3MB, time=18.72 memory used=1354.3MB, alloc=492.3MB, time=20.29 memory used=1440.7MB, alloc=492.3MB, time=21.61 memory used=1514.8MB, alloc=492.3MB, time=22.98 memory used=1586.9MB, alloc=492.3MB, time=24.07 memory used=1656.5MB, alloc=492.3MB, time=25.44 memory used=1715.9MB, alloc=492.3MB, time=26.52 memory used=1796.3MB, alloc=492.3MB, time=27.96 memory used=1854.4MB, alloc=492.3MB, time=29.12 memory used=1905.5MB, alloc=516.3MB, time=30.00 memory used=1972.6MB, alloc=516.3MB, time=31.60 memory used=2171.0MB, alloc=540.3MB, time=34.95 memory used=2373.0MB, alloc=564.3MB, time=38.50 memory used=2562.0MB, alloc=588.3MB, time=42.01 memory used=2727.7MB, alloc=612.3MB, time=45.08 memory used=2866.3MB, alloc=612.3MB, time=47.60 memory used=3003.3MB, alloc=612.3MB, time=49.97 memory used=3143.3MB, alloc=636.3MB, time=52.67 memory used=3287.7MB, alloc=636.3MB, time=55.53 memory used=3396.9MB, alloc=636.3MB, time=57.78 memory used=3508.8MB, alloc=636.3MB, time=59.97 memory used=3618.3MB, alloc=636.3MB, time=62.31 memory used=3730.0MB, alloc=660.3MB, time=64.72 memory used=3831.6MB, alloc=660.3MB, time=66.93 memory used=3934.1MB, alloc=660.3MB, time=69.36 memory used=4005.0MB, alloc=660.3MB, time=71.29 memory used=4344.2MB, alloc=684.3MB, time=76.75 memory used=4694.4MB, alloc=708.3MB, time=82.78 memory used=5069.9MB, alloc=732.3MB, time=89.55 memory used=5453.1MB, alloc=756.3MB, time=95.71 memory used=5813.6MB, alloc=780.3MB, time=103.15 |\^/| 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(); 1428250641 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; F := 2 2 [-19 y z - 4 z + 19 x + 2 z, 16 x + 10 x z + 11 y - 6, 14 x y - 18 y + 7] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [13 x z + 15 y - 20 z + 17 x, -6 x - 16 y + 9 y z - 16, 2 2 x y + 12 x z - 11 y z + 2 z ] > Problem := [F,G]; Problem := [ 2 2 [-19 y z - 4 z + 19 x + 2 z, 16 x + 10 x z + 11 y - 6, 14 x y - 18 y + 7] 2 2 2 2 , [13 x z + 15 y - 20 z + 17 x, -6 x - 16 y + 9 y z - 16, 2 2 x y + 12 x z - 11 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=4.3MB, alloc=32.3MB, time=0.17 memory used=26.7MB, alloc=32.3MB, time=0.51 memory used=47.6MB, alloc=32.3MB, time=0.82 memory used=67.0MB, alloc=56.3MB, time=1.13 memory used=109.6MB, alloc=60.3MB, time=1.76 memory used=149.8MB, alloc=84.3MB, time=2.37 memory used=214.4MB, alloc=92.3MB, time=3.31 memory used=277.4MB, alloc=116.3MB, time=4.30 memory used=348.4MB, alloc=116.3MB, time=5.37 memory used=417.7MB, alloc=372.3MB, time=6.50 memory used=507.7MB, alloc=396.3MB, time=7.76 memory used=618.6MB, alloc=420.3MB, time=9.39 memory used=757.2MB, alloc=444.3MB, time=11.42 memory used=904.7MB, alloc=444.3MB, time=13.70 memory used=1031.8MB, alloc=468.3MB, time=15.51 memory used=1159.1MB, alloc=468.3MB, time=17.25 memory used=1276.7MB, alloc=468.3MB, time=19.18 memory used=1383.0MB, alloc=468.3MB, time=20.94 memory used=1487.4MB, alloc=492.3MB, time=22.83 memory used=1582.5MB, alloc=492.3MB, time=24.39 memory used=1676.5MB, alloc=492.3MB, time=26.08 memory used=1756.9MB, alloc=492.3MB, time=27.62 memory used=1848.9MB, alloc=492.3MB, time=29.40 memory used=1902.1MB, alloc=492.3MB, time=30.61 memory used=1979.5MB, alloc=492.3MB, time=31.92 memory used=2048.0MB, alloc=516.3MB, time=33.25 memory used=2111.1MB, alloc=516.3MB, time=34.64 memory used=2175.2MB, alloc=516.3MB, time=35.75 memory used=2235.4MB, alloc=516.3MB, time=36.83 memory used=2299.1MB, alloc=516.3MB, time=38.12 memory used=2353.0MB, alloc=516.3MB, time=39.12 memory used=2416.9MB, alloc=516.3MB, time=40.40 memory used=2471.2MB, alloc=516.3MB, time=41.56 memory used=2519.9MB, alloc=516.3MB, time=42.75 memory used=2721.3MB, alloc=540.3MB, time=46.40 memory used=2920.3MB, alloc=564.3MB, time=49.96 memory used=3092.3MB, alloc=588.3MB, time=52.93 memory used=3278.3MB, alloc=612.3MB, time=56.35 memory used=3440.1MB, alloc=636.3MB, time=59.18 memory used=3604.6MB, alloc=636.3MB, time=62.53 memory used=3751.2MB, alloc=660.3MB, time=65.21 memory used=3931.6MB, alloc=660.3MB, time=69.76 memory used=4053.0MB, alloc=684.3MB, time=72.18 memory used=4178.9MB, alloc=684.3MB, time=75.18 memory used=4278.3MB, alloc=684.3MB, time=77.35 memory used=4358.1MB, alloc=684.3MB, time=79.05 memory used=4457.9MB, alloc=684.3MB, time=82.12 memory used=4812.2MB, alloc=708.3MB, time=88.46 memory used=5194.0MB, alloc=732.3MB, time=94.65 memory used=5555.2MB, alloc=756.3MB, time=102.85 |\^/| 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(); 1428250941 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 F := [9 x + 4 y + 5 y z + 8, x y - 15 y + 7, -5 x y + 8 y - 20 y z - 11 z ] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [12 z - 9 x + 14 z + 6, -7 x + 13 y + 8 z - 6 y, 2 -10 x - 20 x z + 4 z + 7] > Problem := [F,G]; Problem := [ 2 2 2 2 2 [9 x + 4 y + 5 y z + 8, x y - 15 y + 7, -5 x y + 8 y - 20 y z - 11 z ], 2 2 2 2 [12 z - 9 x + 14 z + 6, -7 x + 13 y + 8 z - 6 y, 2 -10 x - 20 x z + 4 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=4.4MB, alloc=32.3MB, time=0.17 memory used=26.4MB, alloc=32.3MB, time=0.51 memory used=47.8MB, alloc=60.3MB, time=0.85 memory used=90.5MB, alloc=60.3MB, time=1.47 memory used=132.6MB, alloc=60.3MB, time=2.09 memory used=172.6MB, alloc=84.3MB, time=2.70 memory used=235.9MB, alloc=92.3MB, time=3.67 memory used=297.6MB, alloc=116.3MB, time=4.64 memory used=372.6MB, alloc=116.3MB, time=5.76 memory used=448.5MB, alloc=372.3MB, time=6.83 memory used=530.9MB, alloc=372.3MB, time=8.03 memory used=618.9MB, alloc=396.3MB, time=9.22 memory used=725.9MB, alloc=396.3MB, time=10.89 memory used=830.0MB, alloc=420.3MB, time=12.56 memory used=963.2MB, alloc=444.3MB, time=14.44 memory used=1100.0MB, alloc=468.3MB, time=16.79 memory used=1220.4MB, alloc=468.3MB, time=18.79 memory used=1335.5MB, alloc=492.3MB, time=20.54 memory used=1439.8MB, alloc=492.3MB, time=22.05 memory used=1552.0MB, alloc=516.3MB, time=24.33 memory used=1634.2MB, alloc=516.3MB, time=25.60 memory used=1712.2MB, alloc=516.3MB, time=27.07 memory used=1789.0MB, alloc=516.3MB, time=28.36 memory used=1848.9MB, alloc=516.3MB, time=29.34 memory used=1931.4MB, alloc=516.3MB, time=30.86 memory used=1986.6MB, alloc=516.3MB, time=31.99 memory used=2042.7MB, alloc=516.3MB, time=32.94 memory used=2119.5MB, alloc=516.3MB, time=34.59 memory used=2167.1MB, alloc=516.3MB, time=35.51 memory used=2209.4MB, alloc=516.3MB, time=36.52 memory used=2394.2MB, alloc=540.3MB, time=39.57 memory used=2588.7MB, alloc=564.3MB, time=43.00 memory used=2777.1MB, alloc=588.3MB, time=46.73 memory used=2934.9MB, alloc=612.3MB, time=49.38 memory used=3123.7MB, alloc=636.3MB, time=53.04 memory used=3254.6MB, alloc=636.3MB, time=55.38 memory used=3383.2MB, alloc=636.3MB, time=58.10 memory used=3527.1MB, alloc=660.3MB, time=61.00 memory used=3681.9MB, alloc=660.3MB, time=64.80 memory used=3805.4MB, alloc=660.3MB, time=67.86 memory used=3899.3MB, alloc=660.3MB, time=70.11 memory used=3966.9MB, alloc=660.3MB, time=71.75 memory used=4297.0MB, alloc=684.3MB, time=78.04 memory used=4656.7MB, alloc=708.3MB, time=84.60 memory used=5035.6MB, alloc=732.3MB, time=91.28 memory used=5421.1MB, alloc=756.3MB, time=98.74 |\^/| 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(); 1428251241 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; F := [ 2 2 2 2 17 x - y + 12 z - 12, 3 x - 14 x - 5 z + 17, 6 x y + 17 y z - 6 x + 18] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [14 x - 7 x z + x + 4 z, -8 x y + 12 x z - 13 y + z, 2 -9 x - 5 x z - x + 9 z] > Problem := [F,G]; Problem := [[ 2 2 2 2 17 x - y + 12 z - 12, 3 x - 14 x - 5 z + 17, 6 x y + 17 y z - 6 x + 18] 2 2 , [14 x - 7 x z + x + 4 z, -8 x y + 12 x z - 13 y + z, 2 -9 x - 5 x z - x + 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=4.4MB, alloc=32.3MB, time=0.18 memory used=26.1MB, alloc=32.3MB, time=0.50 memory used=46.7MB, alloc=32.3MB, time=0.81 memory used=65.8MB, alloc=56.3MB, time=1.11 memory used=106.7MB, alloc=60.3MB, time=1.72 memory used=145.7MB, alloc=84.3MB, time=2.32 memory used=206.5MB, alloc=92.3MB, time=3.31 memory used=267.0MB, alloc=116.3MB, time=4.27 memory used=349.5MB, alloc=116.3MB, time=5.59 memory used=429.8MB, alloc=140.3MB, time=6.87 memory used=486.5MB, alloc=140.3MB, time=7.76 memory used=556.3MB, alloc=396.3MB, time=8.88 memory used=658.1MB, alloc=420.3MB, time=10.63 memory used=790.4MB, alloc=444.3MB, time=12.70 memory used=937.4MB, alloc=468.3MB, time=15.15 memory used=1050.3MB, alloc=468.3MB, time=17.01 memory used=1161.0MB, alloc=492.3MB, time=19.03 memory used=1262.5MB, alloc=492.3MB, time=20.71 memory used=1380.7MB, alloc=492.3MB, time=23.12 memory used=1472.3MB, alloc=492.3MB, time=24.93 memory used=1542.0MB, alloc=492.3MB, time=26.30 memory used=1638.0MB, alloc=516.3MB, time=28.22 memory used=1727.6MB, alloc=516.3MB, time=30.11 memory used=1788.3MB, alloc=516.3MB, time=31.42 memory used=1861.4MB, alloc=516.3MB, time=33.05 memory used=1919.9MB, alloc=516.3MB, time=34.34 memory used=1990.0MB, alloc=516.3MB, time=36.00 memory used=2031.2MB, alloc=516.3MB, time=37.00 memory used=2094.3MB, alloc=516.3MB, time=38.60 memory used=2143.9MB, alloc=516.3MB, time=39.89 memory used=2195.8MB, alloc=516.3MB, time=41.16 memory used=2402.3MB, alloc=540.3MB, time=45.12 memory used=2605.8MB, alloc=564.3MB, time=49.29 memory used=2783.3MB, alloc=588.3MB, time=52.67 memory used=2969.4MB, alloc=612.3MB, time=56.52 memory used=3121.2MB, alloc=636.3MB, time=59.88 memory used=3273.9MB, alloc=636.3MB, time=63.22 memory used=3397.9MB, alloc=636.3MB, time=65.96 memory used=3554.4MB, alloc=660.3MB, time=69.61 memory used=3694.9MB, alloc=660.3MB, time=72.78 memory used=3819.4MB, alloc=660.3MB, time=75.81 memory used=3919.4MB, alloc=660.3MB, time=78.18 memory used=4030.3MB, alloc=660.3MB, time=81.14 memory used=4135.0MB, alloc=660.3MB, time=84.15 memory used=4462.1MB, alloc=684.3MB, time=91.26 memory used=4800.9MB, alloc=708.3MB, time=98.98 memory used=5163.2MB, alloc=732.3MB, time=107.19 |\^/| 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(); 1428251541 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [-20 x - 12 y - 2 z + 12 y, -12 x y + 7 y - 2 y z + 3 x, 2 -15 x - 20 x y - 4 x - 8] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [-9 x - 10 y z - 9 z, -12 x - 12 y + y - 14, -5 x + 5 x y + 4 x z - 2] > Problem := [F,G]; 2 2 2 2 Problem := [[-20 x - 12 y - 2 z + 12 y, -12 x y + 7 y - 2 y z + 3 x, 2 -15 x - 20 x y - 4 x - 8], 2 2 2 2 [-9 x - 10 y z - 9 z, -12 x - 12 y + y - 14, -5 x + 5 x y + 4 x z - 2]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,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=46.3MB, alloc=32.3MB, time=0.79 memory used=65.1MB, alloc=56.3MB, time=1.08 memory used=106.6MB, alloc=60.3MB, time=1.72 memory used=146.9MB, alloc=60.3MB, time=2.34 memory used=187.0MB, alloc=84.3MB, time=2.97 memory used=226.3MB, alloc=84.3MB, time=3.57 memory used=289.5MB, alloc=92.3MB, time=4.58 memory used=350.5MB, alloc=116.3MB, time=5.57 memory used=426.8MB, alloc=116.3MB, time=6.83 memory used=505.0MB, alloc=396.3MB, time=8.15 memory used=615.7MB, alloc=396.3MB, time=9.96 memory used=724.7MB, alloc=420.3MB, time=11.86 memory used=859.6MB, alloc=444.3MB, time=14.20 memory used=1009.1MB, alloc=468.3MB, time=17.01 memory used=1149.9MB, alloc=468.3MB, time=19.63 memory used=1275.4MB, alloc=492.3MB, time=21.98 memory used=1400.6MB, alloc=492.3MB, time=24.36 memory used=1508.7MB, alloc=492.3MB, time=26.36 memory used=1619.4MB, alloc=492.3MB, time=28.59 memory used=1724.4MB, alloc=516.3MB, time=30.55 memory used=1813.2MB, alloc=516.3MB, time=32.35 memory used=1894.1MB, alloc=516.3MB, time=33.86 memory used=1980.2MB, alloc=516.3MB, time=35.79 memory used=2063.1MB, alloc=516.3MB, time=37.70 memory used=2130.6MB, alloc=516.3MB, time=39.09 memory used=2194.9MB, alloc=516.3MB, time=40.57 memory used=2252.7MB, alloc=516.3MB, time=41.81 memory used=2314.1MB, alloc=540.3MB, time=43.23 memory used=2390.0MB, alloc=540.3MB, time=44.98 memory used=2472.9MB, alloc=540.3MB, time=46.73 memory used=2572.2MB, alloc=564.3MB, time=48.90 memory used=2650.5MB, alloc=564.3MB, time=50.67 memory used=2744.4MB, alloc=564.3MB, time=52.72 memory used=2802.8MB, alloc=588.3MB, time=54.19 memory used=2886.4MB, alloc=588.3MB, time=56.20 memory used=2976.2MB, alloc=588.3MB, time=58.08 memory used=3058.6MB, alloc=612.3MB, time=60.07 memory used=3137.2MB, alloc=612.3MB, time=61.98 memory used=3374.8MB, alloc=636.3MB, time=66.92 memory used=3602.3MB, alloc=660.3MB, time=74.95 memory used=3830.1MB, alloc=684.3MB, time=83.79 memory used=4064.6MB, alloc=708.3MB, time=94.15 |\^/| 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(); 1428251841 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [14 x - 14 y + 15 z + 5, -9 x y + x z - 18 z - 18 z, 8 x z + 9 x - 7 z + 18] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; G := [ -16 x y - 12 y z + 17 y + 7, -11 y z - 5 y + 8 z, -12 x y - 11 y - 20 z - 2 ] > Problem := [F,G]; 2 2 2 2 Problem := [[14 x - 14 y + 15 z + 5, -9 x y + x z - 18 z - 18 z, 8 x z + 9 x - 7 z + 18], [ -16 x y - 12 y z + 17 y + 7, -11 y z - 5 y + 8 z, -12 x y - 11 y - 20 z - 2 ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,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=25.7MB, alloc=32.3MB, time=0.51 memory used=45.3MB, alloc=56.3MB, time=0.82 memory used=86.7MB, alloc=60.3MB, time=1.47 memory used=126.5MB, alloc=60.3MB, time=2.09 memory used=164.8MB, alloc=84.3MB, time=2.71 memory used=224.8MB, alloc=92.3MB, time=3.68 memory used=284.9MB, alloc=116.3MB, time=4.63 memory used=367.3MB, alloc=140.3MB, time=6.04 memory used=439.6MB, alloc=396.3MB, time=7.29 memory used=545.7MB, alloc=420.3MB, time=9.15 memory used=678.3MB, alloc=444.3MB, time=11.48 memory used=831.6MB, alloc=468.3MB, time=14.21 memory used=992.3MB, alloc=492.3MB, time=17.26 memory used=1132.6MB, alloc=492.3MB, time=19.94 memory used=1268.5MB, alloc=516.3MB, time=22.68 memory used=1373.1MB, alloc=516.3MB, time=24.72 memory used=1497.9MB, alloc=516.3MB, time=27.20 memory used=1609.2MB, alloc=516.3MB, time=29.50 memory used=1717.4MB, alloc=516.3MB, time=31.85 memory used=1815.6MB, alloc=540.3MB, time=34.04 memory used=1930.1MB, alloc=540.3MB, time=36.83 memory used=2037.2MB, alloc=540.3MB, time=39.62 memory used=2109.9MB, alloc=540.3MB, time=41.27 memory used=2186.6MB, alloc=540.3MB, time=42.94 memory used=2257.0MB, alloc=540.3MB, time=44.50 memory used=2333.4MB, alloc=540.3MB, time=46.32 memory used=2394.2MB, alloc=540.3MB, time=47.82 memory used=2450.6MB, alloc=540.3MB, time=49.18 memory used=2511.5MB, alloc=564.3MB, time=50.72 memory used=2557.2MB, alloc=564.3MB, time=51.97 memory used=2610.2MB, alloc=564.3MB, time=53.44 memory used=2856.3MB, alloc=588.3MB, time=59.20 memory used=3073.3MB, alloc=612.3MB, time=63.76 memory used=3259.8MB, alloc=636.3MB, time=67.35 memory used=3445.9MB, alloc=660.3MB, time=70.91 memory used=3658.5MB, alloc=684.3MB, time=75.94 memory used=3880.4MB, alloc=708.3MB, time=81.59 memory used=4068.3MB, alloc=732.3MB, time=86.95 memory used=4252.3MB, alloc=732.3MB, time=91.95 memory used=4419.1MB, alloc=732.3MB, time=96.22 memory used=4559.1MB, alloc=756.3MB, time=99.80 memory used=4690.4MB, alloc=756.3MB, time=102.46 memory used=4859.1MB, alloc=756.3MB, time=107.80 |\^/| 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(); 1428252141 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [6 x + 6 x y + 6 z - 8 y, 4 x y - 17 y - 6 z + 17, 13 x y + 16 x z - 20 y z - 8 x] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 G := [17 x + 11 y - 5 z + 4, -20 x - 3 y + 3 z + 5 y, 2 7 x + 6 x y - 12 x z + 10 y] > Problem := [F,G]; 2 2 2 2 Problem := [[6 x + 6 x y + 6 z - 8 y, 4 x y - 17 y - 6 z + 17, 2 2 13 x y + 16 x z - 20 y z - 8 x], [17 x + 11 y - 5 z + 4, 2 2 2 2 -20 x - 3 y + 3 z + 5 y, 7 x + 6 x y - 12 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=26.2MB, alloc=32.3MB, time=0.50 memory used=45.8MB, alloc=56.3MB, time=0.81 memory used=84.7MB, alloc=60.3MB, time=1.37 memory used=128.7MB, alloc=92.3MB, time=1.98 memory used=195.1MB, alloc=92.3MB, time=2.93 memory used=259.3MB, alloc=92.3MB, time=3.90 memory used=325.1MB, alloc=372.3MB, time=4.86 memory used=416.4MB, alloc=372.3MB, time=6.14 memory used=505.3MB, alloc=396.3MB, time=7.47 memory used=616.1MB, alloc=420.3MB, time=9.14 memory used=747.9MB, alloc=420.3MB, time=11.05 memory used=872.9MB, alloc=444.3MB, time=12.95 memory used=993.9MB, alloc=468.3MB, time=14.74 memory used=1104.7MB, alloc=468.3MB, time=16.39 memory used=1202.0MB, alloc=492.3MB, time=17.68 memory used=1307.9MB, alloc=492.3MB, time=19.53 memory used=1385.8MB, alloc=492.3MB, time=20.96 memory used=1466.4MB, alloc=492.3MB, time=22.15 memory used=1541.2MB, alloc=492.3MB, time=23.70 memory used=1613.9MB, alloc=492.3MB, time=25.01 memory used=1679.5MB, alloc=492.3MB, time=26.31 memory used=1738.6MB, alloc=492.3MB, time=27.27 memory used=1807.9MB, alloc=516.3MB, time=28.46 memory used=1872.1MB, alloc=516.3MB, time=29.74 memory used=1917.3MB, alloc=516.3MB, time=30.72 memory used=1949.8MB, alloc=516.3MB, time=31.47 memory used=2003.5MB, alloc=516.3MB, time=32.72 memory used=2197.7MB, alloc=540.3MB, time=35.90 memory used=2402.5MB, alloc=564.3MB, time=38.86 memory used=2589.3MB, alloc=588.3MB, time=42.08 memory used=2754.7MB, alloc=588.3MB, time=45.03 memory used=2926.1MB, alloc=612.3MB, time=47.79 memory used=3065.5MB, alloc=612.3MB, time=50.30 memory used=3212.1MB, alloc=636.3MB, time=53.32 memory used=3337.1MB, alloc=636.3MB, time=55.97 memory used=3462.9MB, alloc=636.3MB, time=58.70 memory used=3592.7MB, alloc=636.3MB, time=61.69 memory used=3683.3MB, alloc=636.3MB, time=63.54 memory used=3777.4MB, alloc=636.3MB, time=65.94 memory used=3877.8MB, alloc=660.3MB, time=68.26 memory used=4213.5MB, alloc=684.3MB, time=73.97 memory used=4571.2MB, alloc=708.3MB, time=80.79 memory used=4943.4MB, alloc=732.3MB, time=87.85 memory used=5314.1MB, alloc=756.3MB, time=95.44 memory used=5620.1MB, alloc=780.3MB, time=102.13 |\^/| 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(); 1428252441 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; F := [-19 x z - 9 y z + 9 z + 17, -10 x y + 2 y z + 20 x + 11 y, 2 2 -17 x - 11 x y + x z - y ] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [8 x y - 15 y - 5 y - 14, x y - 15 y - 7 y z - 17 z, -12 x z - 14 x + 19 y - 10 z] > Problem := [F,G]; Problem := [[-19 x z - 9 y z + 9 z + 17, -10 x y + 2 y z + 20 x + 11 y, 2 2 2 -17 x - 11 x y + x z - y ], [8 x y - 15 y - 5 y - 14, 2 x y - 15 y - 7 y z - 17 z, -12 x z - 14 x + 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=26.7MB, alloc=32.3MB, time=0.52 memory used=47.5MB, alloc=32.3MB, time=0.84 memory used=67.7MB, alloc=56.3MB, time=1.16 memory used=108.3MB, alloc=60.3MB, time=1.79 memory used=147.4MB, alloc=84.3MB, time=2.45 memory used=210.8MB, alloc=92.3MB, time=3.43 memory used=275.2MB, alloc=116.3MB, time=4.44 memory used=349.6MB, alloc=116.3MB, time=5.60 memory used=419.2MB, alloc=372.3MB, time=6.70 memory used=504.7MB, alloc=396.3MB, time=8.02 memory used=612.2MB, alloc=420.3MB, time=9.74 memory used=743.9MB, alloc=444.3MB, time=11.89 memory used=885.9MB, alloc=468.3MB, time=14.29 memory used=1007.3MB, alloc=468.3MB, time=16.35 memory used=1134.3MB, alloc=492.3MB, time=18.65 memory used=1238.5MB, alloc=492.3MB, time=20.48 memory used=1334.7MB, alloc=492.3MB, time=22.24 memory used=1430.7MB, alloc=492.3MB, time=23.96 memory used=1519.2MB, alloc=492.3MB, time=25.64 memory used=1603.9MB, alloc=492.3MB, time=27.32 memory used=1670.9MB, alloc=516.3MB, time=28.58 memory used=1736.6MB, alloc=516.3MB, time=30.12 memory used=1790.7MB, alloc=516.3MB, time=31.15 memory used=1853.0MB, alloc=516.3MB, time=32.63 memory used=1901.6MB, alloc=516.3MB, time=33.64 memory used=1951.6MB, alloc=516.3MB, time=34.95 memory used=1997.5MB, alloc=516.3MB, time=36.13 memory used=2209.3MB, alloc=540.3MB, time=40.03 memory used=2418.1MB, alloc=564.3MB, time=44.07 memory used=2611.0MB, alloc=588.3MB, time=48.25 memory used=2785.2MB, alloc=612.3MB, time=51.80 memory used=2986.5MB, alloc=636.3MB, time=56.35 memory used=3151.9MB, alloc=636.3MB, time=59.91 memory used=3316.8MB, alloc=660.3MB, time=63.79 memory used=3449.0MB, alloc=660.3MB, time=66.93 memory used=3567.8MB, alloc=660.3MB, time=69.95 memory used=3685.0MB, alloc=660.3MB, time=72.98 memory used=3824.6MB, alloc=660.3MB, time=77.06 memory used=3930.0MB, alloc=660.3MB, time=80.07 memory used=4260.6MB, alloc=684.3MB, time=87.60 memory used=4608.3MB, alloc=708.3MB, time=95.89 |\^/| 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(); 1428252741 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 F := [-2 x - 5 x y + 17 y - 5 z , -20 y + 3 z - 3 x + 19 z, 2 -2 x y + 7 y + 9 y z - 15 y] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [5 x + 2 x z - 13 y z - 8 z , 8 x z - 5 y - 8 y z - 7 x, 2 2 7 x y - 4 x z + 9 y + 11 z ] > Problem := [F,G]; 2 2 2 2 2 Problem := [[-2 x - 5 x y + 17 y - 5 z , -20 y + 3 z - 3 x + 19 z, 2 2 2 -2 x y + 7 y + 9 y z - 15 y], [5 x + 2 x z - 13 y z - 8 z , 2 2 2 8 x z - 5 y - 8 y z - 7 x, 7 x y - 4 x z + 9 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=0.17 memory used=26.5MB, alloc=32.3MB, time=0.51 memory used=47.2MB, alloc=56.3MB, time=0.83 memory used=89.3MB, alloc=60.3MB, time=1.46 memory used=128.8MB, alloc=84.3MB, time=2.05 memory used=174.1MB, alloc=84.3MB, time=2.74 memory used=235.7MB, alloc=116.3MB, time=3.74 memory used=311.5MB, alloc=372.3MB, time=4.84 memory used=395.9MB, alloc=396.3MB, time=6.23 memory used=509.1MB, alloc=420.3MB, time=7.91 memory used=645.2MB, alloc=444.3MB, time=10.05 memory used=791.8MB, alloc=468.3MB, time=12.54 memory used=933.0MB, alloc=492.3MB, time=14.98 memory used=1050.3MB, alloc=492.3MB, time=16.97 memory used=1157.6MB, alloc=492.3MB, time=18.77 memory used=1269.7MB, alloc=492.3MB, time=20.65 memory used=1372.4MB, alloc=516.3MB, time=22.40 memory used=1480.9MB, alloc=516.3MB, time=24.46 memory used=1581.5MB, alloc=516.3MB, time=26.35 memory used=1667.7MB, alloc=516.3MB, time=27.98 memory used=1733.3MB, alloc=516.3MB, time=29.23 memory used=1818.4MB, alloc=540.3MB, time=30.79 memory used=1897.7MB, alloc=540.3MB, time=32.40 memory used=1978.1MB, alloc=540.3MB, time=34.17 memory used=2064.2MB, alloc=540.3MB, time=36.18 memory used=2142.4MB, alloc=540.3MB, time=38.04 memory used=2211.7MB, alloc=540.3MB, time=39.59 memory used=2291.7MB, alloc=540.3MB, time=41.60 memory used=2347.7MB, alloc=540.3MB, time=42.65 memory used=2390.5MB, alloc=564.3MB, time=43.65 memory used=2651.1MB, alloc=588.3MB, time=47.87 memory used=2907.5MB, alloc=612.3MB, time=53.71 memory used=3105.7MB, alloc=636.3MB, time=57.05 memory used=3308.0MB, alloc=660.3MB, time=61.72 memory used=3463.3MB, alloc=684.3MB, time=64.71 memory used=3652.8MB, alloc=708.3MB, time=68.61 memory used=3829.7MB, alloc=708.3MB, time=72.78 memory used=3967.5MB, alloc=732.3MB, time=76.43 memory used=4114.8MB, alloc=732.3MB, time=80.38 memory used=4222.3MB, alloc=732.3MB, time=82.62 memory used=4361.9MB, alloc=732.3MB, time=86.07 memory used=4458.7MB, alloc=732.3MB, time=88.46 memory used=4848.0MB, alloc=756.3MB, time=97.04 |\^/| 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(); 1428253041 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [20 x - 6 x y + 18 x + 8 z, -16 x - 18 x z + 13 x + 13 y, 2 2 -15 x + 18 x z + 6 y z + 7 z ] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-2 x + 2 x y + 2 x z - 14 y z, 3 x + 3 x + 19 z, 2 -13 y + 13 y z + 20 x + 15 z] > Problem := [F,G]; 2 2 Problem := [[20 x - 6 x y + 18 x + 8 z, -16 x - 18 x z + 13 x + 13 y, 2 2 2 -15 x + 18 x z + 6 y z + 7 z ], [-2 x + 2 x y + 2 x z - 14 y z, 2 2 3 x + 3 x + 19 z, -13 y + 13 y z + 20 x + 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=26.3MB, alloc=32.3MB, time=0.51 memory used=45.9MB, alloc=56.3MB, time=0.81 memory used=88.1MB, alloc=60.3MB, time=1.45 memory used=129.6MB, alloc=60.3MB, time=2.10 memory used=169.3MB, alloc=84.3MB, time=2.72 memory used=230.4MB, alloc=116.3MB, time=3.73 memory used=311.9MB, alloc=372.3MB, time=5.00 memory used=396.6MB, alloc=396.3MB, time=6.29 memory used=503.2MB, alloc=420.3MB, time=7.96 memory used=636.2MB, alloc=444.3MB, time=10.03 memory used=790.6MB, alloc=468.3MB, time=12.62 memory used=931.1MB, alloc=468.3MB, time=15.09 memory used=1054.8MB, alloc=492.3MB, time=17.33 memory used=1181.5MB, alloc=492.3MB, time=19.61 memory used=1299.3MB, alloc=492.3MB, time=21.94 memory used=1411.0MB, alloc=516.3MB, time=24.20 memory used=1515.4MB, alloc=516.3MB, time=26.48 memory used=1608.6MB, alloc=516.3MB, time=28.53 memory used=1687.3MB, alloc=516.3MB, time=30.31 memory used=1779.1MB, alloc=516.3MB, time=32.27 memory used=1839.1MB, alloc=516.3MB, time=33.71 memory used=1925.3MB, alloc=516.3MB, time=35.74 memory used=1992.8MB, alloc=516.3MB, time=37.36 memory used=2063.9MB, alloc=540.3MB, time=39.18 memory used=2119.9MB, alloc=540.3MB, time=40.76 memory used=2179.3MB, alloc=540.3MB, time=42.53 memory used=2400.7MB, alloc=564.3MB, time=47.13 memory used=2599.1MB, alloc=588.3MB, time=51.76 memory used=2824.4MB, alloc=612.3MB, time=56.95 memory used=3016.2MB, alloc=636.3MB, time=61.17 memory used=3174.1MB, alloc=660.3MB, time=64.00 memory used=3359.1MB, alloc=684.3MB, time=68.59 memory used=3509.0MB, alloc=708.3MB, time=71.92 memory used=3640.1MB, alloc=708.3MB, time=75.03 memory used=3780.5MB, alloc=708.3MB, time=78.43 memory used=3904.2MB, alloc=708.3MB, time=81.25 memory used=4002.9MB, alloc=732.3MB, time=83.91 memory used=4117.9MB, alloc=732.3MB, time=87.14 memory used=4524.8MB, alloc=756.3MB, time=96.42 |\^/| 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(); 1428253341 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [4 x y - 8 y - 5 x - 18 z, 14 x z + 18 z - 11 z + 13, 2 -x - 3 x z - 15 x - 3] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-4 x y - 9 y z + 16 z - 14 z, -6 x y - 2 y - 5 y - 14 z, 2 14 x + 4 x y - 3 y - 6] > Problem := [F,G]; 2 2 Problem := [[4 x y - 8 y - 5 x - 18 z, 14 x z + 18 z - 11 z + 13, 2 2 -x - 3 x z - 15 x - 3], [-4 x y - 9 y z + 16 z - 14 z, 2 2 -6 x y - 2 y - 5 y - 14 z, 14 x + 4 x y - 3 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=0.17 memory used=26.5MB, alloc=32.3MB, time=0.51 memory used=47.2MB, alloc=32.3MB, time=0.83 memory used=66.5MB, alloc=56.3MB, time=1.14 memory used=107.7MB, alloc=60.3MB, time=1.78 memory used=148.3MB, alloc=60.3MB, time=2.40 memory used=188.1MB, alloc=84.3MB, time=3.03 memory used=232.5MB, alloc=84.3MB, time=3.72 memory used=294.7MB, alloc=92.3MB, time=4.72 memory used=353.3MB, alloc=116.3MB, time=5.73 memory used=422.9MB, alloc=116.3MB, time=6.80 memory used=492.9MB, alloc=396.3MB, time=8.01 memory used=607.5MB, alloc=420.3MB, time=9.77 memory used=740.5MB, alloc=444.3MB, time=11.91 memory used=862.8MB, alloc=444.3MB, time=13.90 memory used=987.8MB, alloc=468.3MB, time=16.03 memory used=1087.5MB, alloc=468.3MB, time=17.69 memory used=1187.0MB, alloc=468.3MB, time=19.52 memory used=1275.8MB, alloc=468.3MB, time=21.19 memory used=1373.7MB, alloc=492.3MB, time=22.69 memory used=1463.9MB, alloc=492.3MB, time=24.21 memory used=1538.1MB, alloc=492.3MB, time=25.53 memory used=1626.9MB, alloc=492.3MB, time=27.15 memory used=1698.4MB, alloc=492.3MB, time=28.45 memory used=1778.4MB, alloc=492.3MB, time=30.13 memory used=1838.8MB, alloc=492.3MB, time=31.40 memory used=1900.0MB, alloc=492.3MB, time=32.77 memory used=1956.2MB, alloc=492.3MB, time=33.92 memory used=2016.0MB, alloc=516.3MB, time=35.02 memory used=2078.4MB, alloc=516.3MB, time=36.29 memory used=2132.3MB, alloc=516.3MB, time=37.72 memory used=2342.9MB, alloc=540.3MB, time=42.01 memory used=2574.1MB, alloc=564.3MB, time=46.96 memory used=2768.0MB, alloc=588.3MB, time=51.17 memory used=2974.5MB, alloc=612.3MB, time=56.14 memory used=3170.2MB, alloc=636.3MB, time=60.92 memory used=3339.8MB, alloc=636.3MB, time=64.95 memory used=3496.5MB, alloc=660.3MB, time=68.95 memory used=3634.5MB, alloc=660.3MB, time=72.49 memory used=3789.2MB, alloc=660.3MB, time=76.35 memory used=3945.3MB, alloc=660.3MB, time=80.45 memory used=4061.3MB, alloc=684.3MB, time=83.28 memory used=4158.8MB, alloc=684.3MB, time=85.68 memory used=4259.8MB, alloc=684.3MB, time=88.43 memory used=4610.8MB, alloc=708.3MB, time=96.70 memory used=4989.9MB, alloc=732.3MB, time=105.83 |\^/| 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(); 1428253641 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-2 y z + 8 z - 6 x + 18 z, -11 x z + 12 z - 15 y - 7, 2 15 x - 12 x z + 7 y z + 1] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-x y - 20 x - 16 y + 6 z, -16 x + 9 x y - 15 x z + 15 z , -8 x y - 16 x z - 9 y z - 16] > Problem := [F,G]; 2 2 Problem := [[-2 y z + 8 z - 6 x + 18 z, -11 x z + 12 z - 15 y - 7, 2 15 x - 12 x z + 7 y z + 1], [-x y - 20 x - 16 y + 6 z, 2 2 -16 x + 9 x y - 15 x z + 15 z , -8 x y - 16 x z - 9 y z - 16]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,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=0.90 memory used=47.9MB, alloc=32.3MB, time=1.45 memory used=67.9MB, alloc=56.3MB, time=2.02 memory used=109.8MB, alloc=60.3MB, time=3.12 memory used=150.5MB, alloc=84.3MB, time=4.20 memory used=216.4MB, alloc=92.3MB, time=5.91 memory used=280.3MB, alloc=116.3MB, time=7.57 memory used=358.3MB, alloc=116.3MB, time=9.72 memory used=419.0MB, alloc=372.3MB, time=11.30 memory used=503.2MB, alloc=396.3MB, time=13.65 memory used=615.0MB, alloc=420.3MB, time=16.62 memory used=748.9MB, alloc=420.3MB, time=20.32 memory used=880.2MB, alloc=444.3MB, time=24.09 memory used=996.2MB, alloc=468.3MB, time=27.31 memory used=1125.4MB, alloc=492.3MB, time=31.11 memory used=1230.2MB, alloc=492.3MB, time=34.05 memory used=1337.6MB, alloc=492.3MB, time=37.25 memory used=1435.7MB, alloc=492.3MB, time=39.93 memory used=1524.3MB, alloc=516.3MB, time=42.68 memory used=1612.5MB, alloc=516.3MB, time=45.48 memory used=1680.3MB, alloc=516.3MB, time=47.52 memory used=1765.3MB, alloc=516.3MB, time=50.53 memory used=1837.6MB, alloc=516.3MB, time=52.73 memory used=1901.5MB, alloc=516.3MB, time=55.31 memory used=1964.4MB, alloc=516.3MB, time=57.87 memory used=2020.7MB, alloc=516.3MB, time=59.80 memory used=2083.2MB, alloc=516.3MB, time=62.10 memory used=2139.4MB, alloc=516.3MB, time=64.42 memory used=2343.7MB, alloc=540.3MB, time=70.23 memory used=2548.6MB, alloc=564.3MB, time=76.52 memory used=2746.3MB, alloc=588.3MB, time=83.34 memory used=2947.3MB, alloc=612.3MB, time=90.03 memory used=3107.8MB, alloc=636.3MB, time=95.28 memory used=3279.2MB, alloc=660.3MB, time=100.97 memory used=3432.7MB, alloc=660.3MB, time=106.28 memory used=3575.4MB, alloc=660.3MB, time=111.60 memory used=3699.7MB, alloc=660.3MB, time=116.27 memory used=3805.7MB, alloc=660.3MB, time=119.79 |\^/| 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(); 1428253941 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [20 y - y z + 17 y + 7, -18 z - 19 x + 16 z + 14, 2 2 x y + 16 x z + 5 y - z] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [9 x z + x - 2 y - 20, -12 x y - 12 z + 6 x - 18, 2 2 -19 y + 6 y z + 18 z - 18 x] > Problem := [F,G]; 2 2 Problem := [[20 y - y z + 17 y + 7, -18 z - 19 x + 16 z + 14, 2 2 x y + 16 x z + 5 y - z], [9 x z + x - 2 y - 20, 2 2 2 -12 x y - 12 z + 6 x - 18, -19 y + 6 y z + 18 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=26.3MB, alloc=32.3MB, time=0.89 memory used=46.6MB, alloc=32.3MB, time=1.41 memory used=64.2MB, alloc=56.3MB, time=1.91 memory used=106.1MB, alloc=60.3MB, time=2.98 memory used=145.8MB, alloc=84.3MB, time=4.02 memory used=212.4MB, alloc=92.3MB, time=5.71 memory used=277.2MB, alloc=92.3MB, time=7.39 memory used=343.2MB, alloc=116.3MB, time=8.99 memory used=419.9MB, alloc=372.3MB, time=11.03 memory used=503.1MB, alloc=396.3MB, time=13.14 memory used=618.3MB, alloc=396.3MB, time=15.93 memory used=721.4MB, alloc=420.3MB, time=18.72 memory used=852.0MB, alloc=444.3MB, time=22.00 memory used=990.5MB, alloc=468.3MB, time=25.92 memory used=1113.0MB, alloc=492.3MB, time=29.06 memory used=1211.6MB, alloc=492.3MB, time=31.62 memory used=1332.1MB, alloc=492.3MB, time=35.05 memory used=1432.1MB, alloc=492.3MB, time=37.64 memory used=1526.7MB, alloc=492.3MB, time=40.02 memory used=1633.7MB, alloc=492.3MB, time=43.43 memory used=1724.5MB, alloc=492.3MB, time=46.04 memory used=1803.7MB, alloc=516.3MB, time=48.07 memory used=1887.1MB, alloc=516.3MB, time=50.70 memory used=1986.5MB, alloc=516.3MB, time=54.18 memory used=2068.7MB, alloc=516.3MB, time=56.97 memory used=2131.3MB, alloc=516.3MB, time=58.86 memory used=2178.2MB, alloc=516.3MB, time=60.46 memory used=2251.4MB, alloc=516.3MB, time=62.64 memory used=2303.6MB, alloc=516.3MB, time=64.44 memory used=2365.6MB, alloc=516.3MB, time=66.45 memory used=2438.1MB, alloc=516.3MB, time=69.46 memory used=2637.9MB, alloc=540.3MB, time=74.28 memory used=2844.0MB, alloc=564.3MB, time=80.59 memory used=3074.7MB, alloc=588.3MB, time=88.39 memory used=3279.7MB, alloc=612.3MB, time=95.15 memory used=3469.7MB, alloc=636.3MB, time=101.29 memory used=3648.0MB, alloc=660.3MB, time=107.41 |\^/| 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(); 1428254241 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [15 x - 17 y + 15 y z - 20, -8 x y - 9 z - 2 z, 2 6 x z + 9 z + 16 x + 13 y] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [14 x z - 13 y z + 15 x - 10, -12 x - 11 z + 17 x + 2 y, 2 18 y z - 2 z - 15 z - 12] > Problem := [F,G]; 2 2 2 Problem := [[15 x - 17 y + 15 y z - 20, -8 x y - 9 z - 2 z, 2 6 x z + 9 z + 16 x + 13 y], [14 x z - 13 y z + 15 x - 10, 2 2 2 -12 x - 11 z + 17 x + 2 y, 18 y z - 2 z - 15 z - 12]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,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=0.90 memory used=46.9MB, alloc=56.3MB, time=1.44 memory used=90.8MB, alloc=60.3MB, time=2.43 memory used=132.8MB, alloc=68.3MB, time=3.48 memory used=175.7MB, alloc=92.3MB, time=4.54 memory used=239.2MB, alloc=92.3MB, time=6.17 memory used=306.2MB, alloc=116.3MB, time=7.76 memory used=383.7MB, alloc=116.3MB, time=9.40 memory used=448.4MB, alloc=372.3MB, time=10.89 memory used=537.0MB, alloc=396.3MB, time=13.06 memory used=652.5MB, alloc=396.3MB, time=15.73 memory used=737.2MB, alloc=396.3MB, time=17.11 memory used=848.6MB, alloc=420.3MB, time=19.81 memory used=973.0MB, alloc=444.3MB, time=23.04 memory used=1085.4MB, alloc=444.3MB, time=25.74 memory used=1199.7MB, alloc=468.3MB, time=28.90 memory used=1290.9MB, alloc=468.3MB, time=31.44 memory used=1385.9MB, alloc=468.3MB, time=33.84 memory used=1483.5MB, alloc=492.3MB, time=36.18 memory used=1564.0MB, alloc=492.3MB, time=38.43 memory used=1642.1MB, alloc=492.3MB, time=40.57 memory used=1723.4MB, alloc=492.3MB, time=42.68 memory used=1793.0MB, alloc=492.3MB, time=44.70 memory used=1869.2MB, alloc=492.3MB, time=47.04 memory used=1934.5MB, alloc=492.3MB, time=49.12 memory used=2002.5MB, alloc=492.3MB, time=51.37 memory used=2055.6MB, alloc=492.3MB, time=53.18 memory used=2106.5MB, alloc=492.3MB, time=54.82 memory used=2154.3MB, alloc=492.3MB, time=56.42 memory used=2191.6MB, alloc=492.3MB, time=57.90 memory used=2372.9MB, alloc=516.3MB, time=63.00 memory used=2565.5MB, alloc=540.3MB, time=69.12 memory used=2762.7MB, alloc=564.3MB, time=74.64 memory used=2945.9MB, alloc=588.3MB, time=79.58 memory used=3108.6MB, alloc=612.3MB, time=84.23 memory used=3273.1MB, alloc=636.3MB, time=88.07 memory used=3419.4MB, alloc=660.3MB, time=93.05 memory used=3556.1MB, alloc=660.3MB, time=97.62 memory used=3670.9MB, alloc=684.3MB, time=101.24 |\^/| 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(); 1428254541 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [6 x + 16 x z + 11 y z - 2, 12 x + 2 x z - 19 y z - 14 x, 2 2 2 17 x - 3 x z - 17 y - z ] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [-20 x y - 20 y z - 6 z + 10 z, -11 x - 20 x z + 19 y - 20 y, 2 x y + 3 y - 3 y z + 6] > Problem := [F,G]; 2 2 Problem := [[6 x + 16 x z + 11 y z - 2, 12 x + 2 x z - 19 y z - 14 x, 2 2 2 2 17 x - 3 x z - 17 y - z ], [-20 x y - 20 y z - 6 z + 10 z, 2 2 2 -11 x - 20 x z + 19 y - 20 y, x y + 3 y - 3 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=0.87 memory used=45.9MB, alloc=56.3MB, time=1.41 memory used=86.9MB, alloc=60.3MB, time=2.48 memory used=130.1MB, alloc=92.3MB, time=3.56 memory used=196.8MB, alloc=92.3MB, time=5.23 memory used=261.5MB, alloc=92.3MB, time=6.85 memory used=325.1MB, alloc=372.3MB, time=8.52 memory used=409.5MB, alloc=372.3MB, time=10.77 memory used=493.8MB, alloc=396.3MB, time=13.03 memory used=601.8MB, alloc=420.3MB, time=15.93 memory used=730.7MB, alloc=444.3MB, time=19.43 memory used=848.2MB, alloc=468.3MB, time=21.94 memory used=954.2MB, alloc=468.3MB, time=24.69 memory used=1055.7MB, alloc=468.3MB, time=27.32 memory used=1168.0MB, alloc=492.3MB, time=30.58 memory used=1249.8MB, alloc=492.3MB, time=32.96 memory used=1340.1MB, alloc=492.3MB, time=35.49 memory used=1430.3MB, alloc=492.3MB, time=38.30 memory used=1491.8MB, alloc=492.3MB, time=39.99 memory used=1560.3MB, alloc=492.3MB, time=42.07 memory used=1606.5MB, alloc=492.3MB, time=43.63 memory used=1656.7MB, alloc=492.3MB, time=45.23 memory used=1708.7MB, alloc=492.3MB, time=46.97 memory used=1762.7MB, alloc=492.3MB, time=48.92 memory used=1808.2MB, alloc=492.3MB, time=50.56 memory used=1989.4MB, alloc=516.3MB, time=56.02 memory used=2186.2MB, alloc=540.3MB, time=61.80 memory used=2381.2MB, alloc=564.3MB, time=67.34 memory used=2537.2MB, alloc=588.3MB, time=72.17 memory used=2692.8MB, alloc=612.3MB, time=76.83 memory used=2842.5MB, alloc=612.3MB, time=81.92 memory used=3012.7MB, alloc=636.3MB, time=87.78 memory used=3114.2MB, alloc=636.3MB, time=90.90 memory used=3246.2MB, alloc=636.3MB, time=95.80 memory used=3355.4MB, alloc=660.3MB, time=99.97 memory used=3460.2MB, alloc=660.3MB, time=103.98 memory used=3536.1MB, alloc=660.3MB, time=106.80 |\^/| 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(); 1428254841 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [13 x z + 5 y - 6 y z - 4 z , -x - 9 y z - 14 y - 7, 2 2 9 x + 2 x y - 7 y - 2 y] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; G := 2 2 2 2 2 [-19 x z - 16 y + 12 z + 13, -3 y - 19 z + 7 y - 7, 11 x - 9 y - 14 z] > Problem := [F,G]; 2 2 2 Problem := [[13 x z + 5 y - 6 y z - 4 z , -x - 9 y z - 14 y - 7, 2 2 9 x + 2 x y - 7 y - 2 y], 2 2 2 2 2 [-19 x z - 16 y + 12 z + 13, -3 y - 19 z + 7 y - 7, 11 x - 9 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=4.3MB, alloc=32.3MB, time=0.30 memory used=26.4MB, alloc=32.3MB, time=0.89 memory used=46.8MB, alloc=56.3MB, time=1.46 memory used=89.5MB, alloc=60.3MB, time=2.59 memory used=131.0MB, alloc=60.3MB, time=3.67 memory used=165.0MB, alloc=84.3MB, time=4.59 memory used=227.3MB, alloc=92.3MB, time=6.31 memory used=289.4MB, alloc=116.3MB, time=7.97 memory used=365.6MB, alloc=116.3MB, time=10.07 memory used=429.0MB, alloc=372.3MB, time=11.74 memory used=514.6MB, alloc=396.3MB, time=13.99 memory used=629.0MB, alloc=420.3MB, time=17.00 memory used=766.9MB, alloc=420.3MB, time=20.66 memory used=901.8MB, alloc=444.3MB, time=24.28 memory used=1036.5MB, alloc=468.3MB, time=28.28 memory used=1163.1MB, alloc=468.3MB, time=31.91 memory used=1281.2MB, alloc=468.3MB, time=35.46 memory used=1401.1MB, alloc=492.3MB, time=39.25 memory used=1502.6MB, alloc=492.3MB, time=42.16 memory used=1596.2MB, alloc=492.3MB, time=44.68 memory used=1699.8MB, alloc=492.3MB, time=47.53 memory used=1806.3MB, alloc=492.3MB, time=50.22 memory used=1904.5MB, alloc=516.3MB, time=53.44 memory used=1996.5MB, alloc=516.3MB, time=56.53 memory used=2072.7MB, alloc=516.3MB, time=58.80 memory used=2141.7MB, alloc=516.3MB, time=60.94 memory used=2214.2MB, alloc=516.3MB, time=63.12 memory used=2292.9MB, alloc=516.3MB, time=65.69 memory used=2385.8MB, alloc=516.3MB, time=69.06 memory used=2463.2MB, alloc=516.3MB, time=72.13 memory used=2522.6MB, alloc=540.3MB, time=74.09 memory used=2579.2MB, alloc=540.3MB, time=75.99 memory used=2651.2MB, alloc=540.3MB, time=79.06 memory used=2694.8MB, alloc=540.3MB, time=80.87 memory used=2920.1MB, alloc=564.3MB, time=88.64 memory used=3130.0MB, alloc=588.3MB, time=95.22 memory used=3318.9MB, alloc=612.3MB, time=101.41 memory used=3507.6MB, alloc=636.3MB, time=107.60 memory used=3699.1MB, alloc=636.3MB, time=113.70 |\^/| 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(); 1428255141 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; F := [15 x y + 6 x z + 4 y z + 20 y, -17 y z - 10 x + 19 y - 2 z, 2 2 2 14 x + 20 y + 19 z + x] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [-4 x + 10 x y - 10 y - 12, 8 x + 18 x z + 8 z - 12, 2 2 3 x - 13 z + 12 x - 1] > Problem := [F,G]; Problem := [[15 x y + 6 x z + 4 y z + 20 y, -17 y z - 10 x + 19 y - 2 z, 2 2 2 2 2 14 x + 20 y + 19 z + x], [-4 x + 10 x y - 10 y - 12, 2 2 2 2 8 x + 18 x z + 8 z - 12, 3 x - 13 z + 12 x - 1]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,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=0.88 memory used=46.4MB, alloc=32.3MB, time=1.41 memory used=65.8MB, alloc=56.3MB, time=1.95 memory used=106.2MB, alloc=60.3MB, time=3.03 memory used=145.7MB, alloc=60.3MB, time=4.07 memory used=184.2MB, alloc=84.3MB, time=5.13 memory used=227.0MB, alloc=84.3MB, time=6.35 memory used=289.4MB, alloc=116.3MB, time=8.03 memory used=372.3MB, alloc=372.3MB, time=10.37 memory used=457.4MB, alloc=396.3MB, time=12.56 memory used=566.8MB, alloc=420.3MB, time=15.52 memory used=702.2MB, alloc=444.3MB, time=19.17 memory used=848.7MB, alloc=468.3MB, time=23.33 memory used=976.1MB, alloc=468.3MB, time=27.00 memory used=1122.0MB, alloc=492.3MB, time=31.52 memory used=1239.5MB, alloc=492.3MB, time=34.69 memory used=1343.0MB, alloc=492.3MB, time=37.97 memory used=1441.4MB, alloc=516.3MB, time=40.72 memory used=1537.2MB, alloc=516.3MB, time=43.45 memory used=1642.2MB, alloc=516.3MB, time=46.07 memory used=1725.1MB, alloc=516.3MB, time=48.45 memory used=1813.9MB, alloc=516.3MB, time=51.06 memory used=1877.7MB, alloc=516.3MB, time=53.03 memory used=1942.5MB, alloc=516.3MB, time=55.00 memory used=2041.6MB, alloc=540.3MB, time=58.82 memory used=2135.6MB, alloc=540.3MB, time=62.32 memory used=2204.2MB, alloc=540.3MB, time=64.77 memory used=2299.6MB, alloc=540.3MB, time=68.34 memory used=2357.4MB, alloc=540.3MB, time=70.54 memory used=2428.0MB, alloc=540.3MB, time=73.43 memory used=2480.5MB, alloc=540.3MB, time=75.26 memory used=2534.1MB, alloc=540.3MB, time=77.57 memory used=2578.5MB, alloc=540.3MB, time=79.35 memory used=2801.3MB, alloc=564.3MB, time=86.88 memory used=3042.7MB, alloc=588.3MB, time=95.27 memory used=3249.0MB, alloc=612.3MB, time=102.58 memory used=3451.7MB, alloc=636.3MB, time=109.64 memory used=3660.9MB, alloc=660.3MB, time=117.65 |\^/| 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(); 1428255442 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [18 y - 4 z + 12 y, 2 x + 2 x y - 17 x z + 11 y , 11 y z - 8 x - 15 z] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-12 y - y z - 7 x - 3 z, 19 x + 17 x y + 15 y z + 19 z, 2 20 x + 20 x z + 20 y z - 19 z] > Problem := [F,G]; Problem := [ 2 2 2 2 [18 y - 4 z + 12 y, 2 x + 2 x y - 17 x z + 11 y , 11 y z - 8 x - 15 z], 2 2 [-12 y - y z - 7 x - 3 z, 19 x + 17 x y + 15 y z + 19 z, 2 20 x + 20 x z + 20 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=25.7MB, alloc=32.3MB, time=0.86 memory used=46.3MB, alloc=32.3MB, time=1.38 memory used=65.4MB, alloc=56.3MB, time=1.90 memory used=107.4MB, alloc=68.3MB, time=3.03 memory used=148.6MB, alloc=92.3MB, time=4.10 memory used=212.4MB, alloc=92.3MB, time=5.80 memory used=276.5MB, alloc=92.3MB, time=7.51 memory used=338.4MB, alloc=116.3MB, time=9.22 memory used=406.9MB, alloc=372.3MB, time=11.07 memory used=491.4MB, alloc=396.3MB, time=13.32 memory used=596.8MB, alloc=420.3MB, time=16.29 memory used=727.5MB, alloc=444.3MB, time=19.87 memory used=866.8MB, alloc=468.3MB, time=23.78 memory used=984.2MB, alloc=468.3MB, time=27.01 memory used=1118.6MB, alloc=468.3MB, time=31.10 memory used=1226.1MB, alloc=492.3MB, time=34.19 memory used=1320.5MB, alloc=492.3MB, time=37.03 memory used=1434.5MB, alloc=492.3MB, time=40.88 memory used=1526.3MB, alloc=492.3MB, time=43.89 memory used=1601.2MB, alloc=492.3MB, time=46.18 memory used=1673.4MB, alloc=492.3MB, time=48.56 memory used=1755.5MB, alloc=492.3MB, time=51.41 memory used=1825.9MB, alloc=492.3MB, time=54.06 memory used=1894.4MB, alloc=516.3MB, time=56.47 memory used=1961.3MB, alloc=516.3MB, time=58.73 memory used=2028.1MB, alloc=516.3MB, time=61.22 memory used=2088.2MB, alloc=516.3MB, time=63.46 memory used=2150.7MB, alloc=516.3MB, time=66.13 memory used=2355.6MB, alloc=540.3MB, time=73.03 memory used=2580.7MB, alloc=564.3MB, time=81.12 memory used=2768.7MB, alloc=588.3MB, time=87.88 memory used=3000.7MB, alloc=612.3MB, time=96.83 memory used=3151.1MB, alloc=636.3MB, time=102.37 memory used=3311.5MB, alloc=660.3MB, time=108.47 |\^/| 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(); 1428255742 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [9 x y - 6 z + 15 x - 13 z, -20 x - 13 y - 6 z - 16, 2 2 17 x - 16 x y + 15 y z - 3 z ] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 G := [-18 x z + 5 y + z - 20 y, 2 x + 7 y + 2 z - 4 x, 2 18 x z - 19 y + 18 x + 15 z] > Problem := [F,G]; 2 2 Problem := [[9 x y - 6 z + 15 x - 13 z, -20 x - 13 y - 6 z - 16, 2 2 2 2 17 x - 16 x y + 15 y z - 3 z ], [-18 x z + 5 y + z - 20 y, 2 2 2 2 2 x + 7 y + 2 z - 4 x, 18 x z - 19 y + 18 x + 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=4.5MB, alloc=32.3MB, time=0.33 memory used=26.1MB, alloc=32.3MB, time=0.91 memory used=46.5MB, alloc=56.3MB, time=1.45 memory used=88.0MB, alloc=60.3MB, time=2.51 memory used=129.6MB, alloc=92.3MB, time=3.62 memory used=197.5MB, alloc=92.3MB, time=5.26 memory used=264.3MB, alloc=116.3MB, time=6.88 memory used=332.7MB, alloc=372.3MB, time=8.34 memory used=420.8MB, alloc=396.3MB, time=10.58 memory used=530.9MB, alloc=396.3MB, time=13.47 memory used=640.3MB, alloc=420.3MB, time=16.40 memory used=779.0MB, alloc=444.3MB, time=19.80 memory used=901.1MB, alloc=444.3MB, time=22.81 memory used=1037.4MB, alloc=468.3MB, time=26.26 memory used=1146.4MB, alloc=468.3MB, time=29.26 memory used=1255.7MB, alloc=492.3MB, time=32.20 memory used=1348.0MB, alloc=492.3MB, time=34.67 memory used=1445.2MB, alloc=492.3MB, time=37.57 memory used=1534.1MB, alloc=492.3MB, time=40.01 memory used=1630.4MB, alloc=492.3MB, time=42.98 memory used=1701.7MB, alloc=516.3MB, time=45.06 memory used=1770.8MB, alloc=516.3MB, time=46.78 memory used=1844.9MB, alloc=516.3MB, time=49.40 memory used=1899.8MB, alloc=516.3MB, time=51.21 memory used=1954.3MB, alloc=516.3MB, time=52.98 memory used=2008.5MB, alloc=516.3MB, time=55.14 memory used=2057.9MB, alloc=516.3MB, time=56.96 memory used=2242.9MB, alloc=540.3MB, time=62.07 memory used=2431.8MB, alloc=564.3MB, time=66.92 memory used=2582.0MB, alloc=588.3MB, time=71.08 memory used=2777.3MB, alloc=612.3MB, time=77.49 memory used=2939.8MB, alloc=636.3MB, time=82.50 memory used=3073.1MB, alloc=636.3MB, time=87.22 memory used=3224.2MB, alloc=636.3MB, time=91.74 memory used=3351.9MB, alloc=636.3MB, time=95.66 memory used=3469.6MB, alloc=636.3MB, time=99.99 memory used=3594.3MB, alloc=660.3MB, time=104.45 memory used=3705.6MB, alloc=660.3MB, time=108.05 memory used=3822.3MB, alloc=660.3MB, time=111.41 memory used=3945.0MB, alloc=660.3MB, time=115.55 memory used=4038.4MB, alloc=660.3MB, time=119.15 |\^/| 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(); 1428256042 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-20 x z - z + 14 y + 15 z, 19 y + y z - 3 y - 17, 2 2 -9 x - 13 x y + 15 z - x] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [-10 x + 19 x y - 6 y z + 7 z , 11 x y + y - 10 z - 18 z, 7 x z + 5 x - 10 y - 8] > Problem := [F,G]; 2 2 Problem := [[-20 x z - z + 14 y + 15 z, 19 y + y z - 3 y - 17, 2 2 2 2 -9 x - 13 x y + 15 z - x], [-10 x + 19 x y - 6 y z + 7 z , 2 2 11 x y + y - 10 z - 18 z, 7 x z + 5 x - 10 y - 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=0.32 memory used=26.7MB, alloc=32.3MB, time=0.91 memory used=45.8MB, alloc=56.3MB, time=1.40 memory used=85.0MB, alloc=60.3MB, time=2.40 memory used=124.4MB, alloc=60.3MB, time=3.42 memory used=163.4MB, alloc=84.3MB, time=4.36 memory used=230.9MB, alloc=92.3MB, time=6.02 memory used=293.7MB, alloc=116.3MB, time=7.71 memory used=363.3MB, alloc=116.3MB, time=9.19 memory used=431.0MB, alloc=372.3MB, time=10.80 memory used=519.8MB, alloc=372.3MB, time=13.08 memory used=608.4MB, alloc=396.3MB, time=15.30 memory used=713.8MB, alloc=420.3MB, time=18.20 memory used=850.5MB, alloc=420.3MB, time=21.43 memory used=962.5MB, alloc=420.3MB, time=23.51 memory used=1066.0MB, alloc=420.3MB, time=25.48 memory used=1200.1MB, alloc=444.3MB, time=28.94 memory used=1329.1MB, alloc=468.3MB, time=32.70 memory used=1459.9MB, alloc=492.3MB, time=36.14 memory used=1557.9MB, alloc=492.3MB, time=38.72 memory used=1676.8MB, alloc=492.3MB, time=42.36 memory used=1779.0MB, alloc=516.3MB, time=45.62 memory used=1863.8MB, alloc=516.3MB, time=47.98 memory used=1967.6MB, alloc=516.3MB, time=51.24 memory used=2056.8MB, alloc=516.3MB, time=54.35 memory used=2136.6MB, alloc=516.3MB, time=56.83 memory used=2222.3MB, alloc=516.3MB, time=59.86 memory used=2280.7MB, alloc=516.3MB, time=61.93 memory used=2351.7MB, alloc=516.3MB, time=63.85 memory used=2424.3MB, alloc=516.3MB, time=66.46 memory used=2470.5MB, alloc=540.3MB, time=67.97 memory used=2519.3MB, alloc=540.3MB, time=69.44 memory used=2582.6MB, alloc=540.3MB, time=71.66 memory used=2646.5MB, alloc=540.3MB, time=74.16 memory used=2696.6MB, alloc=540.3MB, time=76.03 memory used=2910.5MB, alloc=564.3MB, time=83.01 memory used=3105.6MB, alloc=588.3MB, time=88.22 memory used=3302.2MB, alloc=612.3MB, time=93.52 memory used=3483.9MB, alloc=636.3MB, time=99.52 |\^/| 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(); 1428256342 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [-10 x - 9 x y - 10 x z - 13 y, -x z - 8 x + 20 y + 15 z, 2 -17 x + 9 x y + 3 x] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; G := [ 2 2 19 x z + 5 y + 17, 13 x z - 17 y z - 2 z + 17, -16 x - 12 x z - 12 y - 17 ] > Problem := [F,G]; 2 Problem := [[-10 x - 9 x y - 10 x z - 13 y, -x z - 8 x + 20 y + 15 z, 2 -17 x + 9 x y + 3 x], [ 2 2 19 x z + 5 y + 17, 13 x z - 17 y z - 2 z + 17, -16 x - 12 x z - 12 y - 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=4.3MB, alloc=32.3MB, time=0.30 memory used=26.2MB, alloc=32.3MB, time=0.86 memory used=46.8MB, alloc=32.3MB, time=1.39 memory used=65.7MB, alloc=56.3MB, time=1.92 memory used=105.9MB, alloc=60.3MB, time=3.02 memory used=145.5MB, alloc=84.3MB, time=4.09 memory used=206.8MB, alloc=92.3MB, time=5.74 memory used=266.5MB, alloc=116.3MB, time=7.41 memory used=347.0MB, alloc=116.3MB, time=9.61 memory used=419.7MB, alloc=396.3MB, time=11.55 memory used=526.9MB, alloc=420.3MB, time=14.52 memory used=664.0MB, alloc=444.3MB, time=18.12 memory used=809.6MB, alloc=468.3MB, time=22.30 memory used=935.7MB, alloc=468.3MB, time=25.86 memory used=1052.9MB, alloc=492.3MB, time=29.28 memory used=1170.6MB, alloc=492.3MB, time=32.92 memory used=1273.6MB, alloc=492.3MB, time=36.23 memory used=1378.6MB, alloc=492.3MB, time=39.61 memory used=1470.9MB, alloc=516.3MB, time=42.56 memory used=1554.9MB, alloc=516.3MB, time=45.44 memory used=1633.6MB, alloc=516.3MB, time=48.09 memory used=1698.2MB, alloc=516.3MB, time=50.49 memory used=1760.6MB, alloc=516.3MB, time=52.83 memory used=1820.3MB, alloc=516.3MB, time=55.06 memory used=1877.5MB, alloc=516.3MB, time=57.20 memory used=1911.3MB, alloc=516.3MB, time=58.76 memory used=1971.1MB, alloc=516.3MB, time=61.23 memory used=2175.1MB, alloc=540.3MB, time=67.66 memory used=2391.8MB, alloc=564.3MB, time=74.60 memory used=2596.7MB, alloc=588.3MB, time=81.32 memory used=2796.2MB, alloc=612.3MB, time=88.10 memory used=2965.6MB, alloc=636.3MB, time=94.42 memory used=3111.9MB, alloc=660.3MB, time=99.28 memory used=3299.2MB, alloc=684.3MB, time=106.50 memory used=3503.4MB, alloc=708.3MB, time=114.14 |\^/| 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(); 1428256642 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [10 x + 5 x y - 8 x z - 12 z , 4 x - 6 x z - 16 y - 1, 2 2 15 x - 6 x y + 7 y z + 14 z ] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [13 x y + 14 x z - 9 y z - 17, 13 x - 14 x y - 20 x z - 15 y, 2 9 x - 10 x y + 17 x z + 2 x] > Problem := [F,G]; 2 2 2 Problem := [[10 x + 5 x y - 8 x z - 12 z , 4 x - 6 x z - 16 y - 1, 2 2 15 x - 6 x y + 7 y z + 14 z ], [13 x y + 14 x z - 9 y z - 17, 2 2 13 x - 14 x y - 20 x z - 15 y, 9 x - 10 x y + 17 x 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=0.30 memory used=26.0MB, alloc=32.3MB, time=0.87 memory used=47.4MB, alloc=32.3MB, time=1.44 memory used=67.3MB, alloc=56.3MB, time=1.99 memory used=109.0MB, alloc=60.3MB, time=3.10 memory used=148.7MB, alloc=84.3MB, time=4.21 memory used=209.1MB, alloc=92.3MB, time=5.87 memory used=270.7MB, alloc=116.3MB, time=7.49 memory used=340.0MB, alloc=116.3MB, time=9.36 memory used=412.4MB, alloc=396.3MB, time=11.30 memory used=522.1MB, alloc=420.3MB, time=14.26 memory used=655.2MB, alloc=444.3MB, time=17.73 memory used=795.4MB, alloc=468.3MB, time=21.56 memory used=935.8MB, alloc=468.3MB, time=25.73 memory used=1061.9MB, alloc=492.3MB, time=29.43 memory used=1183.4MB, alloc=492.3MB, time=32.99 memory used=1290.7MB, alloc=492.3MB, time=36.22 memory used=1394.8MB, alloc=492.3MB, time=39.64 memory used=1483.6MB, alloc=516.3MB, time=42.51 memory used=1576.0MB, alloc=516.3MB, time=45.56 memory used=1663.9MB, alloc=516.3MB, time=48.53 memory used=1744.6MB, alloc=516.3MB, time=51.34 memory used=1808.4MB, alloc=516.3MB, time=53.75 memory used=1864.7MB, alloc=516.3MB, time=55.94 memory used=1915.4MB, alloc=516.3MB, time=57.97 memory used=1977.4MB, alloc=516.3MB, time=60.26 memory used=2036.3MB, alloc=516.3MB, time=62.72 memory used=2240.0MB, alloc=540.3MB, time=69.38 memory used=2453.3MB, alloc=564.3MB, time=76.72 memory used=2659.7MB, alloc=588.3MB, time=83.59 memory used=2845.3MB, alloc=612.3MB, time=90.60 memory used=3028.8MB, alloc=636.3MB, time=97.37 memory used=3189.6MB, alloc=660.3MB, time=103.50 memory used=3344.9MB, alloc=684.3MB, time=109.23 memory used=3498.3MB, alloc=708.3MB, time=114.90 memory used=3633.9MB, alloc=708.3MB, time=120.34 |\^/| 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(); 1428256942 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [13 y z + 9 z + 16 y - 17, -19 x + 6 x y + 9 z + 4 y, 2 2 x z - 11 y - 19 z + 12] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [-15 x y - 17 x z + 16 x - 13, 16 y - 3 y, 12 x y + 4 y + 13 z + 7 z] > Problem := [F,G]; 2 2 2 Problem := [[13 y z + 9 z + 16 y - 17, -19 x + 6 x y + 9 z + 4 y, 2 2 x z - 11 y - 19 z + 12], 2 2 2 [-15 x y - 17 x z + 16 x - 13, 16 y - 3 y, 12 x y + 4 y + 13 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=0.30 memory used=26.4MB, alloc=32.3MB, time=0.88 memory used=47.0MB, alloc=56.3MB, time=1.44 memory used=89.4MB, alloc=60.3MB, time=2.56 memory used=130.5MB, alloc=60.3MB, time=3.64 memory used=168.6MB, alloc=84.3MB, time=4.63 memory used=230.5MB, alloc=92.3MB, time=6.33 memory used=291.5MB, alloc=116.3MB, time=8.01 memory used=367.1MB, alloc=116.3MB, time=9.98 memory used=439.5MB, alloc=396.3MB, time=11.95 memory used=551.6MB, alloc=396.3MB, time=14.94 memory used=662.9MB, alloc=420.3MB, time=17.86 memory used=802.4MB, alloc=420.3MB, time=21.47 memory used=929.2MB, alloc=444.3MB, time=25.06 memory used=1083.1MB, alloc=468.3MB, time=29.79 memory used=1219.8MB, alloc=468.3MB, time=33.74 memory used=1340.5MB, alloc=492.3MB, time=37.16 memory used=1452.0MB, alloc=492.3MB, time=40.31 memory used=1569.7MB, alloc=492.3MB, time=43.17 memory used=1679.5MB, alloc=492.3MB, time=46.28 memory used=1781.8MB, alloc=516.3MB, time=48.92 memory used=1888.1MB, alloc=516.3MB, time=52.27 memory used=1984.8MB, alloc=516.3MB, time=55.39 memory used=2073.0MB, alloc=516.3MB, time=58.00 memory used=2157.9MB, alloc=516.3MB, time=60.62 memory used=2228.7MB, alloc=516.3MB, time=62.77 memory used=2300.0MB, alloc=540.3MB, time=65.09 memory used=2383.9MB, alloc=540.3MB, time=68.25 memory used=2471.1MB, alloc=540.3MB, time=71.29 memory used=2565.2MB, alloc=540.3MB, time=74.83 memory used=2648.2MB, alloc=540.3MB, time=78.12 memory used=2703.9MB, alloc=540.3MB, time=80.12 memory used=2783.6MB, alloc=540.3MB, time=83.25 memory used=2842.1MB, alloc=540.3MB, time=85.53 memory used=2885.1MB, alloc=540.3MB, time=87.05 memory used=2954.0MB, alloc=540.3MB, time=89.93 memory used=3152.5MB, alloc=564.3MB, time=96.12 memory used=3359.1MB, alloc=588.3MB, time=102.67 memory used=3568.5MB, alloc=612.3MB, time=110.03 memory used=3719.0MB, alloc=636.3MB, time=115.18 |\^/| 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(); 1428257242 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-13 x - 9 x z + 8 z + 12, 6 x - 2 y - z + 17, 2 2 4 x z + 13 y + 9 y z - 12 z ] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [2 x - 18 y + 10 y z - 20 z, 11 z - 13 x - 13 y + 11, 2 2 -9 y - 5 z + 14 x + 6 y] > Problem := [F,G]; 2 2 Problem := [[-13 x - 9 x z + 8 z + 12, 6 x - 2 y - z + 17, 2 2 2 2 4 x z + 13 y + 9 y z - 12 z ], [2 x - 18 y + 10 y z - 20 z, 2 2 2 11 z - 13 x - 13 y + 11, -9 y - 5 z + 14 x + 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=4.3MB, alloc=32.3MB, time=0.30 memory used=26.1MB, alloc=32.3MB, time=0.87 memory used=46.3MB, alloc=32.3MB, time=1.38 memory used=65.7MB, alloc=56.3MB, time=1.90 memory used=106.9MB, alloc=60.3MB, time=2.95 memory used=146.3MB, alloc=84.3MB, time=3.99 memory used=210.2MB, alloc=92.3MB, time=5.65 memory used=273.4MB, alloc=116.3MB, time=7.30 memory used=356.5MB, alloc=116.3MB, time=9.46 memory used=430.1MB, alloc=396.3MB, time=11.53 memory used=536.8MB, alloc=420.3MB, time=14.30 memory used=674.9MB, alloc=444.3MB, time=17.57 memory used=814.0MB, alloc=468.3MB, time=21.11 memory used=938.0MB, alloc=468.3MB, time=24.32 memory used=1043.9MB, alloc=492.3MB, time=27.25 memory used=1126.7MB, alloc=492.3MB, time=29.30 memory used=1237.8MB, alloc=492.3MB, time=32.53 memory used=1335.5MB, alloc=492.3MB, time=34.92 memory used=1426.8MB, alloc=492.3MB, time=37.75 memory used=1506.0MB, alloc=492.3MB, time=40.26 memory used=1590.2MB, alloc=492.3MB, time=42.94 memory used=1666.2MB, alloc=516.3MB, time=45.26 memory used=1720.7MB, alloc=516.3MB, time=47.03 memory used=1788.7MB, alloc=516.3MB, time=49.34 memory used=1857.4MB, alloc=516.3MB, time=51.62 memory used=1909.1MB, alloc=516.3MB, time=53.40 memory used=1973.4MB, alloc=516.3MB, time=55.79 memory used=2177.9MB, alloc=540.3MB, time=61.96 memory used=2377.2MB, alloc=564.3MB, time=67.05 memory used=2542.0MB, alloc=588.3MB, time=72.54 memory used=2726.9MB, alloc=612.3MB, time=78.51 memory used=2913.2MB, alloc=636.3MB, time=84.12 memory used=3054.8MB, alloc=636.3MB, time=88.79 memory used=3227.9MB, alloc=660.3MB, time=94.98 memory used=3369.1MB, alloc=660.3MB, time=99.77 memory used=3513.0MB, alloc=660.3MB, time=105.41 |\^/| 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(); 1428257542 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [7 z - 2 x - 14 y + 5, 7 x + 18 x y + 16 y z + 15 y, 2 2 -13 x - 6 x y + 19 y - 2 x] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [3 x - 4 x y - 15 x z + 8 y z, 10 x z + 20 y - 16 y z - 16, -8 x y - 15 x z - 20 x - 18 y] > Problem := [F,G]; 2 2 Problem := [[7 z - 2 x - 14 y + 5, 7 x + 18 x y + 16 y z + 15 y, 2 2 2 -13 x - 6 x y + 19 y - 2 x], [3 x - 4 x y - 15 x z + 8 y z, 2 10 x z + 20 y - 16 y z - 16, -8 x y - 15 x z - 20 x - 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=0.31 memory used=26.5MB, alloc=32.3MB, time=0.89 memory used=47.7MB, alloc=32.3MB, time=1.44 memory used=66.9MB, alloc=56.3MB, time=1.97 memory used=107.6MB, alloc=60.3MB, time=3.04 memory used=147.0MB, alloc=84.3MB, time=4.11 memory used=208.6MB, alloc=92.3MB, time=5.76 memory used=271.4MB, alloc=116.3MB, time=7.41 memory used=344.5MB, alloc=116.3MB, time=9.36 memory used=419.1MB, alloc=396.3MB, time=11.42 memory used=526.5MB, alloc=420.3MB, time=14.29 memory used=656.3MB, alloc=420.3MB, time=17.75 memory used=784.0MB, alloc=444.3MB, time=21.35 memory used=914.4MB, alloc=468.3MB, time=24.88 memory used=1034.4MB, alloc=492.3MB, time=28.38 memory used=1125.6MB, alloc=492.3MB, time=31.02 memory used=1247.9MB, alloc=492.3MB, time=34.46 memory used=1353.1MB, alloc=492.3MB, time=37.60 memory used=1451.8MB, alloc=516.3MB, time=40.52 memory used=1547.5MB, alloc=516.3MB, time=43.41 memory used=1637.0MB, alloc=516.3MB, time=46.38 memory used=1709.5MB, alloc=516.3MB, time=48.40 memory used=1770.6MB, alloc=516.3MB, time=50.36 memory used=1842.4MB, alloc=516.3MB, time=53.06 memory used=1893.5MB, alloc=540.3MB, time=54.64 memory used=1954.6MB, alloc=540.3MB, time=56.64 memory used=2022.1MB, alloc=540.3MB, time=59.40 memory used=2076.7MB, alloc=540.3MB, time=61.45 memory used=2127.6MB, alloc=540.3MB, time=63.42 memory used=2191.4MB, alloc=540.3MB, time=65.97 memory used=2405.0MB, alloc=564.3MB, time=72.05 memory used=2603.4MB, alloc=588.3MB, time=78.11 memory used=2800.5MB, alloc=612.3MB, time=83.68 memory used=2970.7MB, alloc=636.3MB, time=89.16 memory used=3128.0MB, alloc=660.3MB, time=94.35 memory used=3313.9MB, alloc=684.3MB, time=100.77 |\^/| 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(); 1428257842 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [9 x y - 10 y - 15 z + 6 y, -2 x z + 12 y - 10 y - 19, 15 x z + 7 y z + x - 3] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; G := 2 2 2 [-20 y + 4 y z - y - z, 7 x + 10 x y + 8 z + 12 z, 5 x z - x - 7 y + 14] > Problem := [F,G]; 2 2 2 Problem := [[9 x y - 10 y - 15 z + 6 y, -2 x z + 12 y - 10 y - 19, 15 x z + 7 y z + x - 3], 2 2 2 [-20 y + 4 y z - y - z, 7 x + 10 x y + 8 z + 12 z, 5 x z - x - 7 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=4.3MB, alloc=32.3MB, time=0.30 memory used=26.6MB, alloc=32.3MB, time=0.88 memory used=46.5MB, alloc=32.3MB, time=1.39 memory used=65.7MB, alloc=60.3MB, time=1.91 memory used=105.0MB, alloc=60.3MB, time=2.95 memory used=144.8MB, alloc=84.3MB, time=3.99 memory used=207.4MB, alloc=92.3MB, time=5.67 memory used=270.0MB, alloc=92.3MB, time=7.28 memory used=327.8MB, alloc=116.3MB, time=8.92 memory used=407.0MB, alloc=116.3MB, time=11.12 memory used=467.7MB, alloc=140.3MB, time=12.60 memory used=534.8MB, alloc=396.3MB, time=14.39 memory used=638.0MB, alloc=420.3MB, time=17.41 memory used=769.6MB, alloc=444.3MB, time=20.89 memory used=907.3MB, alloc=468.3MB, time=24.61 memory used=1044.8MB, alloc=492.3MB, time=28.84 memory used=1147.1MB, alloc=492.3MB, time=31.59 memory used=1249.6MB, alloc=492.3MB, time=34.39 memory used=1361.1MB, alloc=492.3MB, time=38.23 memory used=1445.8MB, alloc=492.3MB, time=41.02 memory used=1516.8MB, alloc=492.3MB, time=43.15 memory used=1597.6MB, alloc=492.3MB, time=45.95 memory used=1687.4MB, alloc=516.3MB, time=49.20 memory used=1772.0MB, alloc=516.3MB, time=52.43 memory used=1857.2MB, alloc=516.3MB, time=55.79 memory used=1938.2MB, alloc=516.3MB, time=58.94 memory used=1987.0MB, alloc=516.3MB, time=60.71 memory used=2053.7MB, alloc=516.3MB, time=63.44 memory used=2090.2MB, alloc=516.3MB, time=65.05 memory used=2296.5MB, alloc=540.3MB, time=71.70 memory used=2525.7MB, alloc=564.3MB, time=79.86 memory used=2728.6MB, alloc=588.3MB, time=86.67 memory used=2917.4MB, alloc=612.3MB, time=93.21 memory used=3095.2MB, alloc=636.3MB, time=99.94 |\^/| 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(); 1428258142 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-2 x y - 10 y z + 10 z , 8 x - 8 y - 8 y z - 14 y, -11 x z + 2 z + 14] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [7 x y - 19 y z - 3 z - 13 z, 8 x y + 18 x z + 11 y + 10 y, -6 x y - 17 x z - 12 y z + 13 x] > Problem := [F,G]; Problem := [ 2 2 2 [-2 x y - 10 y z + 10 z , 8 x - 8 y - 8 y z - 14 y, -11 x z + 2 z + 14], 2 2 [7 x y - 19 y z - 3 z - 13 z, 8 x y + 18 x z + 11 y + 10 y, -6 x y - 17 x z - 12 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=4.3MB, alloc=32.3MB, time=0.29 memory used=25.9MB, alloc=32.3MB, time=0.86 memory used=46.2MB, alloc=32.3MB, time=1.38 memory used=65.5MB, alloc=56.3MB, time=1.90 memory used=106.8MB, alloc=60.3MB, time=2.97 memory used=147.1MB, alloc=60.3MB, time=4.00 memory used=187.1MB, alloc=92.3MB, time=5.06 memory used=251.2MB, alloc=92.3MB, time=6.67 memory used=313.4MB, alloc=116.3MB, time=8.30 memory used=388.1MB, alloc=372.3MB, time=10.30 memory used=473.6MB, alloc=396.3MB, time=12.47 memory used=585.1MB, alloc=420.3MB, time=15.22 memory used=716.6MB, alloc=444.3MB, time=18.75 memory used=832.9MB, alloc=444.3MB, time=21.63 memory used=943.1MB, alloc=468.3MB, time=24.56 memory used=1061.7MB, alloc=468.3MB, time=27.86 memory used=1154.8MB, alloc=468.3MB, time=30.49 memory used=1243.1MB, alloc=468.3MB, time=32.85 memory used=1354.9MB, alloc=492.3MB, time=36.40 memory used=1446.0MB, alloc=492.3MB, time=39.16 memory used=1515.0MB, alloc=492.3MB, time=41.13 memory used=1601.9MB, alloc=492.3MB, time=44.10 memory used=1680.4MB, alloc=492.3MB, time=46.78 memory used=1738.2MB, alloc=492.3MB, time=48.76 memory used=1807.7MB, alloc=492.3MB, time=51.14 memory used=1861.5MB, alloc=492.3MB, time=52.99 memory used=1922.6MB, alloc=492.3MB, time=55.29 memory used=1970.8MB, alloc=492.3MB, time=57.39 memory used=2157.3MB, alloc=516.3MB, time=62.83 memory used=2359.2MB, alloc=540.3MB, time=69.42 memory used=2558.0MB, alloc=564.3MB, time=75.28 memory used=2744.4MB, alloc=588.3MB, time=81.50 memory used=2906.5MB, alloc=612.3MB, time=86.43 memory used=3070.3MB, alloc=636.3MB, time=92.09 memory used=3209.9MB, alloc=660.3MB, time=97.01 memory used=3329.2MB, alloc=660.3MB, time=101.42 memory used=3465.9MB, alloc=660.3MB, time=106.68 memory used=3593.3MB, alloc=660.3MB, time=111.12 |\^/| 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(); 1428258442 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [4 x + 13 y - 11 z - 9, -4 x z - 13 y - 14 y z - 3 y, 2 -16 x + 9 y z + 15 x + 16 y] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-3 z - 6 x + 18 y - 2, 3 x y - 5 y + 12 x - 19 z, 2 9 x z + 15 y - 19 x - z] > Problem := [F,G]; 2 2 Problem := [[4 x + 13 y - 11 z - 9, -4 x z - 13 y - 14 y z - 3 y, 2 2 -16 x + 9 y z + 15 x + 16 y], [-3 z - 6 x + 18 y - 2, 2 2 3 x y - 5 y + 12 x - 19 z, 9 x z + 15 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=0.30 memory used=26.0MB, alloc=32.3MB, time=0.87 memory used=46.0MB, alloc=56.3MB, time=1.41 memory used=88.2MB, alloc=60.3MB, time=2.52 memory used=128.9MB, alloc=60.3MB, time=3.61 memory used=166.0MB, alloc=84.3MB, time=4.64 memory used=231.0MB, alloc=92.3MB, time=6.36 memory used=294.4MB, alloc=116.3MB, time=8.08 memory used=369.4MB, alloc=116.3MB, time=10.18 memory used=442.9MB, alloc=396.3MB, time=12.28 memory used=555.3MB, alloc=420.3MB, time=15.12 memory used=686.4MB, alloc=444.3MB, time=18.75 memory used=815.6MB, alloc=444.3MB, time=22.14 memory used=946.0MB, alloc=468.3MB, time=25.96 memory used=1063.2MB, alloc=468.3MB, time=29.27 memory used=1175.4MB, alloc=468.3MB, time=32.57 memory used=1277.0MB, alloc=492.3MB, time=35.54 memory used=1377.0MB, alloc=492.3MB, time=38.51 memory used=1466.6MB, alloc=492.3MB, time=41.41 memory used=1560.3MB, alloc=492.3MB, time=44.28 memory used=1644.5MB, alloc=492.3MB, time=46.98 memory used=1729.4MB, alloc=492.3MB, time=49.83 memory used=1792.7MB, alloc=492.3MB, time=51.94 memory used=1885.4MB, alloc=492.3MB, time=55.14 memory used=1948.7MB, alloc=492.3MB, time=57.27 memory used=2012.2MB, alloc=492.3MB, time=59.42 memory used=2067.5MB, alloc=492.3MB, time=61.57 memory used=2112.2MB, alloc=492.3MB, time=63.25 memory used=2164.4MB, alloc=492.3MB, time=65.19 memory used=2225.8MB, alloc=492.3MB, time=67.54 memory used=2265.4MB, alloc=516.3MB, time=69.35 memory used=2462.9MB, alloc=540.3MB, time=75.52 memory used=2678.4MB, alloc=564.3MB, time=82.52 memory used=2866.2MB, alloc=588.3MB, time=89.02 memory used=3044.9MB, alloc=612.3MB, time=94.99 memory used=3222.6MB, alloc=636.3MB, time=100.99 memory used=3378.0MB, alloc=636.3MB, time=106.42 |\^/| 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(); 1428258742 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [14 x - 16 x z + 20 y - 8 z, -6 x - 11 y + 16 y z - 4 x, 2 -9 x y - 5 y - 20 y z - 8 z] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [-3 x y - 6 x z + 17 y + 4 x, -3 x z + 2 y z - 10 x - 20, 2 2 2 -18 x - 15 x y + 12 y + 6 z ] > Problem := [F,G]; 2 2 2 2 Problem := [[14 x - 16 x z + 20 y - 8 z, -6 x - 11 y + 16 y z - 4 x, 2 2 -9 x y - 5 y - 20 y z - 8 z], [-3 x y - 6 x z + 17 y + 4 x, 2 2 2 -3 x z + 2 y z - 10 x - 20, -18 x - 15 x y + 12 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=4.3MB, alloc=32.3MB, time=0.31 memory used=26.4MB, alloc=32.3MB, time=0.88 memory used=46.6MB, alloc=56.3MB, time=1.43 memory used=87.6MB, alloc=60.3MB, time=2.51 memory used=130.4MB, alloc=68.3MB, time=3.62 memory used=170.6MB, alloc=92.3MB, time=4.71 memory used=234.7MB, alloc=92.3MB, time=6.39 memory used=298.4MB, alloc=92.3MB, time=8.02 memory used=361.6MB, alloc=116.3MB, time=9.68 memory used=430.1MB, alloc=372.3MB, time=11.54 memory used=513.8MB, alloc=396.3MB, time=13.76 memory used=619.4MB, alloc=396.3MB, time=16.61 memory used=732.4MB, alloc=420.3MB, time=19.45 memory used=866.2MB, alloc=444.3MB, time=23.16 memory used=976.5MB, alloc=444.3MB, time=26.24 memory used=1088.3MB, alloc=468.3MB, time=29.26 memory used=1198.9MB, alloc=468.3MB, time=32.28 memory used=1299.1MB, alloc=468.3MB, time=35.17 memory used=1407.3MB, alloc=492.3MB, time=38.20 memory used=1494.0MB, alloc=492.3MB, time=40.73 memory used=1587.3MB, alloc=492.3MB, time=43.50 memory used=1660.0MB, alloc=492.3MB, time=45.91 memory used=1729.9MB, alloc=492.3MB, time=48.00 memory used=1814.5MB, alloc=492.3MB, time=50.61 memory used=1890.7MB, alloc=492.3MB, time=52.95 memory used=1953.9MB, alloc=492.3MB, time=55.01 memory used=2019.7MB, alloc=492.3MB, time=57.46 memory used=2066.3MB, alloc=492.3MB, time=59.05 memory used=2117.9MB, alloc=492.3MB, time=61.25 memory used=2166.1MB, alloc=492.3MB, time=63.02 memory used=2352.1MB, alloc=516.3MB, time=68.65 memory used=2545.5MB, alloc=540.3MB, time=74.64 memory used=2723.1MB, alloc=564.3MB, time=80.53 memory used=2884.3MB, alloc=588.3MB, time=85.60 memory used=3065.9MB, alloc=612.3MB, time=91.85 memory used=3226.1MB, alloc=612.3MB, time=97.61 memory used=3356.4MB, alloc=636.3MB, time=101.94 memory used=3515.6MB, alloc=636.3MB, time=107.74 memory used=3655.3MB, alloc=636.3MB, time=112.75 memory used=3787.0MB, alloc=660.3MB, time=117.64 |\^/| 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(); 1428259042 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [17 x y + 6 x z + 6 y - 2 y, -9 x y - 16 y + 16 z + 15 z, 2 x y - 16 x - 18 y - 12] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [3 x - 9 x z + 19 y z - 10 z, -10 y + 11 y z - 6 x + 2 z, 2 13 x y + 6 z - 20 y - 7 z] > Problem := [F,G]; 2 2 2 Problem := [[17 x y + 6 x z + 6 y - 2 y, -9 x y - 16 y + 16 z + 15 z, 2 2 x y - 16 x - 18 y - 12], [3 x - 9 x z + 19 y z - 10 z, 2 2 -10 y + 11 y z - 6 x + 2 z, 13 x y + 6 z - 20 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=4.4MB, alloc=32.3MB, time=0.30 memory used=26.2MB, alloc=32.3MB, time=0.87 memory used=46.8MB, alloc=32.3MB, time=1.40 memory used=66.7MB, alloc=56.3MB, time=1.94 memory used=108.3MB, alloc=60.3MB, time=2.98 memory used=148.3MB, alloc=84.3MB, time=4.03 memory used=212.8MB, alloc=92.3MB, time=5.63 memory used=276.8MB, alloc=116.3MB, time=7.28 memory used=355.6MB, alloc=116.3MB, time=9.26 memory used=427.4MB, alloc=396.3MB, time=11.18 memory used=540.4MB, alloc=396.3MB, time=13.97 memory used=646.3MB, alloc=420.3MB, time=16.88 memory used=777.0MB, alloc=444.3MB, time=20.38 memory used=927.6MB, alloc=468.3MB, time=24.71 memory used=1054.2MB, alloc=468.3MB, time=28.15 memory used=1171.6MB, alloc=492.3MB, time=31.61 memory used=1273.0MB, alloc=492.3MB, time=34.50 memory used=1383.4MB, alloc=492.3MB, time=37.74 memory used=1465.3MB, alloc=492.3MB, time=39.99 memory used=1571.7MB, alloc=492.3MB, time=43.33 memory used=1672.3MB, alloc=516.3MB, time=46.64 memory used=1766.4MB, alloc=516.3MB, time=49.70 memory used=1854.6MB, alloc=516.3MB, time=52.41 memory used=1929.3MB, alloc=516.3MB, time=54.73 memory used=1990.2MB, alloc=516.3MB, time=56.79 memory used=2058.6MB, alloc=540.3MB, time=59.07 memory used=2122.5MB, alloc=540.3MB, time=61.66 memory used=2178.5MB, alloc=540.3MB, time=63.51 memory used=2221.4MB, alloc=540.3MB, time=65.01 memory used=2266.3MB, alloc=540.3MB, time=66.49 memory used=2328.6MB, alloc=540.3MB, time=69.16 memory used=2378.5MB, alloc=540.3MB, time=71.12 memory used=2602.0MB, alloc=564.3MB, time=77.45 memory used=2803.2MB, alloc=588.3MB, time=83.15 memory used=2998.7MB, alloc=612.3MB, time=89.06 memory used=3176.4MB, alloc=636.3MB, time=95.14 memory used=3348.9MB, alloc=660.3MB, time=100.31 memory used=3531.4MB, alloc=684.3MB, time=107.10 memory used=3701.3MB, alloc=684.3MB, time=113.20 |\^/| 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(); 1428259342 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [15 x z - 8 z + 18 y - 2 z, -19 x - 13 x z - 3 y + 11, 2 -2 x - 13 x z - 9 y - 6] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [20 x z - 14 y + 13 x + 20 z, -13 x y - 11 y z + 3 z + 10, 12 x y + 7 x z - 20 y + 20] > Problem := [F,G]; 2 2 Problem := [[15 x z - 8 z + 18 y - 2 z, -19 x - 13 x z - 3 y + 11, 2 2 -2 x - 13 x z - 9 y - 6], [20 x z - 14 y + 13 x + 20 z, 2 -13 x y - 11 y z + 3 z + 10, 12 x y + 7 x z - 20 y + 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=4.3MB, alloc=32.3MB, time=0.30 memory used=26.5MB, alloc=32.3MB, time=0.88 memory used=48.2MB, alloc=32.3MB, time=1.45 memory used=68.9MB, alloc=56.3MB, time=2.01 memory used=110.7MB, alloc=60.3MB, time=3.10 memory used=150.0MB, alloc=84.3MB, time=4.18 memory used=215.0MB, alloc=92.3MB, time=5.86 memory used=280.7MB, alloc=116.3MB, time=7.50 memory used=360.6MB, alloc=116.3MB, time=9.50 memory used=426.8MB, alloc=372.3MB, time=11.23 memory used=515.6MB, alloc=396.3MB, time=13.46 memory used=628.7MB, alloc=420.3MB, time=16.31 memory used=764.2MB, alloc=444.3MB, time=19.89 memory used=898.3MB, alloc=444.3MB, time=23.48 memory used=1020.5MB, alloc=468.3MB, time=26.92 memory used=1140.0MB, alloc=468.3MB, time=30.32 memory used=1248.5MB, alloc=492.3MB, time=33.48 memory used=1352.2MB, alloc=492.3MB, time=36.50 memory used=1449.5MB, alloc=492.3MB, time=39.36 memory used=1556.2MB, alloc=492.3MB, time=42.78 memory used=1645.2MB, alloc=492.3MB, time=45.38 memory used=1739.0MB, alloc=516.3MB, time=48.46 memory used=1816.0MB, alloc=516.3MB, time=50.90 memory used=1884.3MB, alloc=516.3MB, time=53.18 memory used=1960.5MB, alloc=516.3MB, time=55.55 memory used=2030.3MB, alloc=516.3MB, time=57.93 memory used=2095.0MB, alloc=516.3MB, time=60.18 memory used=2161.6MB, alloc=516.3MB, time=62.47 memory used=2227.5MB, alloc=516.3MB, time=64.70 memory used=2293.5MB, alloc=516.3MB, time=67.14 memory used=2346.2MB, alloc=516.3MB, time=69.35 memory used=2553.9MB, alloc=540.3MB, time=75.66 memory used=2762.1MB, alloc=564.3MB, time=82.00 memory used=2959.4MB, alloc=588.3MB, time=88.32 memory used=3126.7MB, alloc=612.3MB, time=93.18 memory used=3311.0MB, alloc=636.3MB, time=99.81 memory used=3472.1MB, alloc=660.3MB, time=104.15 memory used=3645.1MB, alloc=684.3MB, time=109.77 memory used=3782.8MB, alloc=684.3MB, time=113.64 memory used=3960.9MB, alloc=684.3MB, time=119.76 |\^/| 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(); 1428259642 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [14 y + 9 z + 16, 14 y z + 14 z - 10 x - 18 z, 2 14 x z - 15 y + 10 y + 5 z] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [15 y z + 2 x - y - 8, -14 x - 8 x y - 11 x - 19 y, 17 x y + x z - 14 x + 20] > Problem := [F,G]; 2 2 2 Problem := [[14 y + 9 z + 16, 14 y z + 14 z - 10 x - 18 z, 2 14 x z - 15 y + 10 y + 5 z], [15 y z + 2 x - y - 8, 2 -14 x - 8 x y - 11 x - 19 y, 17 x y + x z - 14 x + 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=4.3MB, alloc=32.3MB, time=0.31 memory used=26.7MB, alloc=32.3MB, time=0.89 memory used=47.9MB, alloc=32.3MB, time=1.42 memory used=67.5MB, alloc=56.3MB, time=1.95 memory used=108.3MB, alloc=60.3MB, time=3.00 memory used=147.5MB, alloc=84.3MB, time=4.03 memory used=211.2MB, alloc=92.3MB, time=5.72 memory used=275.3MB, alloc=92.3MB, time=7.36 memory used=335.3MB, alloc=116.3MB, time=9.02 memory used=410.2MB, alloc=372.3MB, time=11.02 memory used=494.3MB, alloc=396.3MB, time=13.26 memory used=603.5MB, alloc=396.3MB, time=16.11 memory used=710.8MB, alloc=420.3MB, time=18.86 memory used=844.4MB, alloc=444.3MB, time=22.32 memory used=975.3MB, alloc=468.3MB, time=25.76 memory used=1115.4MB, alloc=492.3MB, time=29.53 memory used=1251.0MB, alloc=492.3MB, time=33.44 memory used=1364.7MB, alloc=492.3MB, time=36.69 memory used=1460.6MB, alloc=516.3MB, time=39.39 memory used=1552.3MB, alloc=516.3MB, time=42.45 memory used=1625.1MB, alloc=516.3MB, time=44.44 memory used=1730.6MB, alloc=516.3MB, time=47.93 memory used=1821.6MB, alloc=516.3MB, time=51.05 memory used=1898.9MB, alloc=516.3MB, time=53.40 memory used=1979.0MB, alloc=516.3MB, time=56.22 memory used=2049.6MB, alloc=516.3MB, time=58.57 memory used=2106.5MB, alloc=516.3MB, time=60.64 memory used=2152.6MB, alloc=516.3MB, time=62.05 memory used=2217.1MB, alloc=516.3MB, time=64.67 memory used=2266.5MB, alloc=516.3MB, time=66.49 memory used=2470.4MB, alloc=540.3MB, time=72.76 memory used=2672.9MB, alloc=564.3MB, time=79.04 memory used=2859.0MB, alloc=588.3MB, time=84.76 memory used=3026.8MB, alloc=612.3MB, time=90.13 memory used=3196.2MB, alloc=636.3MB, time=95.68 memory used=3372.4MB, alloc=636.3MB, time=102.02 memory used=3542.6MB, alloc=636.3MB, time=107.97 memory used=3692.3MB, alloc=660.3MB, time=112.54 |\^/| 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(); 1428259942 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-5 x + 10 x z - 10 z + 19, 15 x - x z + 14 y z + 6 z, 2 -x z - 4 y z + 7 z - 2 x] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [-4 x + 7 x z + 15 y - 16 y z, 11 x - 9 y + 6 y z + 10 y, 2 -17 x + 8 x y + 20 y] > Problem := [F,G]; 2 2 2 Problem := [[-5 x + 10 x z - 10 z + 19, 15 x - x z + 14 y z + 6 z, 2 2 2 -x z - 4 y z + 7 z - 2 x], [-4 x + 7 x z + 15 y - 16 y z, 2 2 2 11 x - 9 y + 6 y z + 10 y, -17 x + 8 x y + 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=4.3MB, alloc=32.3MB, time=0.30 memory used=26.3MB, alloc=32.3MB, time=0.87 memory used=46.9MB, alloc=32.3MB, time=1.40 memory used=66.4MB, alloc=56.3MB, time=1.94 memory used=108.3MB, alloc=60.3MB, time=3.03 memory used=148.8MB, alloc=84.3MB, time=4.10 memory used=210.4MB, alloc=92.3MB, time=5.75 memory used=274.1MB, alloc=116.3MB, time=7.36 memory used=348.4MB, alloc=116.3MB, time=9.21 memory used=419.0MB, alloc=396.3MB, time=11.14 memory used=530.1MB, alloc=396.3MB, time=13.96 memory used=638.0MB, alloc=420.3MB, time=16.81 memory used=765.9MB, alloc=444.3MB, time=20.31 memory used=897.5MB, alloc=468.3MB, time=23.88 memory used=1007.3MB, alloc=468.3MB, time=26.88 memory used=1125.1MB, alloc=468.3MB, time=29.70 memory used=1235.4MB, alloc=468.3MB, time=32.81 memory used=1329.7MB, alloc=492.3MB, time=35.32 memory used=1428.6MB, alloc=492.3MB, time=38.12 memory used=1541.0MB, alloc=492.3MB, time=41.43 memory used=1621.7MB, alloc=516.3MB, time=43.33 memory used=1726.9MB, alloc=516.3MB, time=45.87 memory used=1808.8MB, alloc=516.3MB, time=48.44 memory used=1892.0MB, alloc=540.3MB, time=51.37 memory used=1959.9MB, alloc=540.3MB, time=53.23 memory used=2023.9MB, alloc=540.3MB, time=54.84 memory used=2098.5MB, alloc=540.3MB, time=57.18 memory used=2146.0MB, alloc=540.3MB, time=58.91 memory used=2195.8MB, alloc=540.3MB, time=60.56 memory used=2397.7MB, alloc=564.3MB, time=66.11 memory used=2601.6MB, alloc=588.3MB, time=72.28 memory used=2801.9MB, alloc=612.3MB, time=76.68 memory used=3008.1MB, alloc=636.3MB, time=83.82 memory used=3175.4MB, alloc=660.3MB, time=89.31 memory used=3325.9MB, alloc=660.3MB, time=93.56 memory used=3491.4MB, alloc=684.3MB, time=98.60 memory used=3658.2MB, alloc=684.3MB, time=103.08 memory used=3791.2MB, alloc=708.3MB, time=107.50 memory used=3940.1MB, alloc=708.3MB, time=112.30 memory used=4044.6MB, alloc=708.3MB, time=115.87 memory used=4152.1MB, alloc=708.3MB, time=120.36 |\^/| 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(); 1428260242 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-5 x y - 3 x z - 15 x + 11 z, -4 x - 19 x z + 4 y z + 10 z , 2 2 -4 x - 15 y - 19 y z - 18 y] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [4 x y + 14 y - 7 z + 13 x, 7 x - 14 y - 17 x + 7 z, 4 x y - 18 x z - 15 y - 3 z] > Problem := [F,G]; 2 2 Problem := [[-5 x y - 3 x z - 15 x + 11 z, -4 x - 19 x z + 4 y z + 10 z , 2 2 2 2 -4 x - 15 y - 19 y z - 18 y], [4 x y + 14 y - 7 z + 13 x, 2 2 7 x - 14 y - 17 x + 7 z, 4 x y - 18 x z - 15 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=0.31 memory used=26.5MB, alloc=32.3MB, time=0.89 memory used=46.7MB, alloc=32.3MB, time=1.42 memory used=66.5MB, alloc=56.3MB, time=1.96 memory used=107.5MB, alloc=60.3MB, time=3.04 memory used=148.0MB, alloc=84.3MB, time=4.10 memory used=212.6MB, alloc=92.3MB, time=5.79 memory used=275.5MB, alloc=116.3MB, time=7.45 memory used=350.3MB, alloc=116.3MB, time=9.41 memory used=414.2MB, alloc=372.3MB, time=11.14 memory used=500.5MB, alloc=396.3MB, time=13.37 memory used=611.3MB, alloc=420.3MB, time=16.21 memory used=744.4MB, alloc=444.3MB, time=19.93 memory used=862.4MB, alloc=444.3MB, time=22.84 memory used=992.6MB, alloc=468.3MB, time=26.35 memory used=1115.8MB, alloc=468.3MB, time=29.73 memory used=1229.0MB, alloc=492.3MB, time=33.26 memory used=1329.9MB, alloc=492.3MB, time=36.19 memory used=1425.4MB, alloc=492.3MB, time=38.97 memory used=1526.9MB, alloc=492.3MB, time=42.00 memory used=1595.9MB, alloc=492.3MB, time=44.16 memory used=1682.0MB, alloc=492.3MB, time=47.02 memory used=1762.3MB, alloc=492.3MB, time=49.59 memory used=1832.1MB, alloc=492.3MB, time=51.52 memory used=1903.1MB, alloc=492.3MB, time=54.00 memory used=1965.0MB, alloc=492.3MB, time=56.07 memory used=2024.5MB, alloc=492.3MB, time=58.15 memory used=2088.5MB, alloc=516.3MB, time=60.22 memory used=2143.8MB, alloc=516.3MB, time=62.20 memory used=2203.4MB, alloc=516.3MB, time=64.43 memory used=2255.4MB, alloc=516.3MB, time=66.38 memory used=2471.8MB, alloc=540.3MB, time=72.40 memory used=2664.1MB, alloc=564.3MB, time=78.39 memory used=2861.9MB, alloc=588.3MB, time=84.63 memory used=3031.0MB, alloc=612.3MB, time=90.47 memory used=3232.4MB, alloc=636.3MB, time=96.36 memory used=3382.0MB, alloc=636.3MB, time=101.67 memory used=3536.9MB, alloc=636.3MB, time=106.35 memory used=3697.7MB, alloc=660.3MB, time=112.22 memory used=3851.2MB, alloc=660.3MB, time=117.71 |\^/| 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(); 1428260542 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [12 x z - 6 y - 14 y z + 18 y, 19 x - 17 y z + 5 y + 5, 2 6 x z + 15 y - 12 y z + 3 x] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [5 x y + 8 x z + 8 y + 3 y, -18 x + 19 x y + 15 y + 3, 2 2 12 y - z - 9 x + 11 z] > Problem := [F,G]; 2 2 Problem := [[12 x z - 6 y - 14 y z + 18 y, 19 x - 17 y z + 5 y + 5, 2 2 6 x z + 15 y - 12 y z + 3 x], [5 x y + 8 x z + 8 y + 3 y, 2 2 2 2 -18 x + 19 x y + 15 y + 3, 12 y - z - 9 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=4.4MB, alloc=32.3MB, time=0.31 memory used=26.2MB, alloc=32.3MB, time=0.89 memory used=46.5MB, alloc=32.3MB, time=1.42 memory used=65.3MB, alloc=56.3MB, time=1.93 memory used=106.8MB, alloc=60.3MB, time=3.00 memory used=147.9MB, alloc=60.3MB, time=4.05 memory used=187.3MB, alloc=84.3MB, time=5.12 memory used=226.4MB, alloc=84.3MB, time=6.14 memory used=289.7MB, alloc=116.3MB, time=7.86 memory used=359.5MB, alloc=372.3MB, time=9.71 memory used=446.7MB, alloc=396.3MB, time=11.94 memory used=557.3MB, alloc=396.3MB, time=14.88 memory used=664.1MB, alloc=420.3MB, time=17.79 memory used=794.0MB, alloc=444.3MB, time=21.41 memory used=927.5MB, alloc=468.3MB, time=25.25 memory used=1035.4MB, alloc=468.3MB, time=28.27 memory used=1149.1MB, alloc=492.3MB, time=31.61 memory used=1250.3MB, alloc=492.3MB, time=34.67 memory used=1359.3MB, alloc=492.3MB, time=38.00 memory used=1461.3MB, alloc=492.3MB, time=41.23 memory used=1548.1MB, alloc=516.3MB, time=43.39 memory used=1647.6MB, alloc=516.3MB, time=46.59 memory used=1724.1MB, alloc=516.3MB, time=49.40 memory used=1787.2MB, alloc=516.3MB, time=51.26 memory used=1852.0MB, alloc=516.3MB, time=53.25 memory used=1910.9MB, alloc=516.3MB, time=55.52 memory used=1974.6MB, alloc=516.3MB, time=58.12 memory used=2186.6MB, alloc=540.3MB, time=63.94 memory used=2374.0MB, alloc=564.3MB, time=69.14 memory used=2559.6MB, alloc=588.3MB, time=74.75 memory used=2749.1MB, alloc=612.3MB, time=80.56 memory used=2908.2MB, alloc=636.3MB, time=85.74 memory used=3073.2MB, alloc=660.3MB, time=91.27 memory used=3206.6MB, alloc=660.3MB, time=95.97 memory used=3322.8MB, alloc=660.3MB, time=99.92 memory used=3430.5MB, alloc=660.3MB, time=104.39 memory used=3499.2MB, alloc=660.3MB, time=106.98 |\^/| 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(); 1428260842 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-17 x - 14 x z - 2 y z + 10 z, -14 x z + 15 y + 20 y - 16, 2 -15 x + 14 y - 5 z + 19] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [-8 x y + 10 y z - 8 x - 7 y, -14 x y - 10 z + 5 x + 5, 2 2 15 x y + 7 y - 12 z + 7 y] > Problem := [F,G]; 2 2 Problem := [[-17 x - 14 x z - 2 y z + 10 z, -14 x z + 15 y + 20 y - 16, 2 -15 x + 14 y - 5 z + 19], [-8 x y + 10 y z - 8 x - 7 y, 2 2 2 -14 x y - 10 z + 5 x + 5, 15 x y + 7 y - 12 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=26.2MB, alloc=32.3MB, time=0.89 memory used=47.1MB, alloc=32.3MB, time=1.45 memory used=66.4MB, alloc=56.3MB, time=1.96 memory used=108.1MB, alloc=60.3MB, time=3.05 memory used=147.8MB, alloc=60.3MB, time=4.07 memory used=188.2MB, alloc=92.3MB, time=5.18 memory used=251.9MB, alloc=92.3MB, time=6.86 memory used=314.5MB, alloc=116.3MB, time=8.55 memory used=387.5MB, alloc=372.3MB, time=10.55 memory used=469.8MB, alloc=396.3MB, time=12.82 memory used=581.5MB, alloc=420.3MB, time=15.73 memory used=713.3MB, alloc=444.3MB, time=18.95 memory used=829.9MB, alloc=468.3MB, time=22.02 memory used=931.4MB, alloc=468.3MB, time=24.68 memory used=1044.7MB, alloc=468.3MB, time=27.66 memory used=1144.5MB, alloc=468.3MB, time=30.55 memory used=1235.0MB, alloc=492.3MB, time=33.27 memory used=1326.4MB, alloc=492.3MB, time=36.15 memory used=1411.4MB, alloc=492.3MB, time=38.73 memory used=1489.4MB, alloc=492.3MB, time=41.17 memory used=1573.4MB, alloc=492.3MB, time=44.00 memory used=1636.5MB, alloc=492.3MB, time=46.04 memory used=1711.6MB, alloc=492.3MB, time=48.69 memory used=1763.8MB, alloc=492.3MB, time=50.36 memory used=1820.9MB, alloc=492.3MB, time=52.63 memory used=1885.7MB, alloc=492.3MB, time=55.04 memory used=1922.8MB, alloc=492.3MB, time=56.77 memory used=2106.5MB, alloc=516.3MB, time=62.67 memory used=2279.4MB, alloc=540.3MB, time=67.78 memory used=2471.9MB, alloc=564.3MB, time=74.29 memory used=2635.4MB, alloc=588.3MB, time=79.36 memory used=2801.0MB, alloc=612.3MB, time=85.23 memory used=2953.4MB, alloc=612.3MB, time=90.43 memory used=3112.4MB, alloc=636.3MB, time=95.89 memory used=3241.9MB, alloc=636.3MB, time=100.59 memory used=3371.5MB, alloc=636.3MB, time=105.32 memory used=3478.2MB, alloc=636.3MB, time=109.42 memory used=3598.9MB, alloc=636.3MB, time=113.82 memory used=3700.5MB, alloc=636.3MB, time=118.05 |\^/| 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(); 1428261142 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [12 x z - 7 z + 17 y - 15 z, 4 x + 10 x y - 20 x z + 14 z, 12 x z + 8 y z + 3 x + 11 z] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [-4 x - 11 y - 16 y z - 7, -7 y + 3 y z + 20 x - 10, 2 -4 x z - 18 y z - 8 z - 6] > Problem := [F,G]; 2 2 Problem := [[12 x z - 7 z + 17 y - 15 z, 4 x + 10 x y - 20 x z + 14 z, 2 2 12 x z + 8 y z + 3 x + 11 z], [-4 x - 11 y - 16 y z - 7, 2 2 -7 y + 3 y z + 20 x - 10, -4 x z - 18 y z - 8 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=26.4MB, alloc=32.3MB, time=0.87 memory used=46.9MB, alloc=32.3MB, time=1.40 memory used=66.0MB, alloc=56.3MB, time=1.94 memory used=107.0MB, alloc=60.3MB, time=3.02 memory used=145.6MB, alloc=60.3MB, time=4.07 memory used=184.5MB, alloc=84.3MB, time=5.14 memory used=221.9MB, alloc=84.3MB, time=6.13 memory used=283.3MB, alloc=92.3MB, time=7.82 memory used=345.0MB, alloc=116.3MB, time=9.49 memory used=417.6MB, alloc=116.3MB, time=11.48 memory used=485.8MB, alloc=396.3MB, time=13.38 memory used=598.2MB, alloc=420.3MB, time=16.08 memory used=729.1MB, alloc=444.3MB, time=19.66 memory used=864.5MB, alloc=468.3MB, time=23.42 memory used=1004.5MB, alloc=492.3MB, time=27.43 memory used=1104.5MB, alloc=492.3MB, time=30.08 memory used=1208.8MB, alloc=492.3MB, time=32.98 memory used=1314.0MB, alloc=492.3MB, time=36.22 memory used=1408.9MB, alloc=492.3MB, time=39.26 memory used=1479.9MB, alloc=492.3MB, time=41.39 memory used=1565.6MB, alloc=492.3MB, time=44.23 memory used=1644.4MB, alloc=492.3MB, time=46.61 memory used=1721.7MB, alloc=492.3MB, time=49.18 memory used=1793.0MB, alloc=492.3MB, time=51.57 memory used=1864.9MB, alloc=492.3MB, time=54.16 memory used=1906.2MB, alloc=492.3MB, time=55.62 memory used=1967.1MB, alloc=492.3MB, time=57.96 memory used=2032.3MB, alloc=516.3MB, time=60.57 memory used=2079.0MB, alloc=516.3MB, time=62.48 memory used=2277.6MB, alloc=540.3MB, time=68.75 memory used=2468.7MB, alloc=564.3MB, time=74.59 memory used=2631.9MB, alloc=588.3MB, time=79.93 memory used=2813.8MB, alloc=612.3MB, time=86.33 memory used=3009.4MB, alloc=636.3MB, time=93.25 memory used=3148.0MB, alloc=636.3MB, time=98.04 memory used=3296.0MB, alloc=636.3MB, time=102.92 memory used=3456.0MB, alloc=660.3MB, time=108.70 |\^/| 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(); 1428261442 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-13 x z + 16 z - 15 x - 6 y, 13 x y + 11 y + 11 y z + 5, 2 -8 x - 5 y z + 10] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [-5 x y + 13 z + 10 y + 12, 10 x y + 9 x z - 7 y z + 2 x, -5 x y - 20 x z - 19 y z + 11] > Problem := [F,G]; 2 2 Problem := [[-13 x z + 16 z - 15 x - 6 y, 13 x y + 11 y + 11 y z + 5, 2 2 -8 x - 5 y z + 10], [-5 x y + 13 z + 10 y + 12, 10 x y + 9 x z - 7 y z + 2 x, -5 x y - 20 x z - 19 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=4.2MB, alloc=32.3MB, time=0.30 memory used=26.9MB, alloc=32.3MB, time=0.90 memory used=48.5MB, alloc=32.3MB, time=1.46 memory used=68.5MB, alloc=56.3MB, time=2.00 memory used=108.8MB, alloc=60.3MB, time=3.06 memory used=148.7MB, alloc=84.3MB, time=4.11 memory used=214.1MB, alloc=92.3MB, time=5.80 memory used=277.2MB, alloc=116.3MB, time=7.45 memory used=349.9MB, alloc=116.3MB, time=9.35 memory used=423.1MB, alloc=372.3MB, time=11.31 memory used=507.1MB, alloc=396.3MB, time=13.53 memory used=611.6MB, alloc=420.3MB, time=16.41 memory used=741.5MB, alloc=444.3MB, time=20.19 memory used=867.0MB, alloc=468.3MB, time=23.59 memory used=994.2MB, alloc=468.3MB, time=27.20 memory used=1099.1MB, alloc=468.3MB, time=30.07 memory used=1205.2MB, alloc=492.3MB, time=32.99 memory used=1294.8MB, alloc=492.3MB, time=35.29 memory used=1392.4MB, alloc=492.3MB, time=38.38 memory used=1475.8MB, alloc=492.3MB, time=40.98 memory used=1543.2MB, alloc=492.3MB, time=43.14 memory used=1628.7MB, alloc=492.3MB, time=45.89 memory used=1707.5MB, alloc=492.3MB, time=48.70 memory used=1771.8MB, alloc=516.3MB, time=50.69 memory used=1837.7MB, alloc=516.3MB, time=53.16 memory used=1882.3MB, alloc=516.3MB, time=54.76 memory used=1950.7MB, alloc=516.3MB, time=57.25 memory used=2010.0MB, alloc=516.3MB, time=59.53 memory used=2214.4MB, alloc=540.3MB, time=65.70 memory used=2433.9MB, alloc=564.3MB, time=72.89 memory used=2646.6MB, alloc=588.3MB, time=80.41 memory used=2828.6MB, alloc=612.3MB, time=86.89 memory used=2979.3MB, alloc=636.3MB, time=92.61 memory used=3139.8MB, alloc=636.3MB, time=98.41 memory used=3276.4MB, alloc=636.3MB, time=103.49 |\^/| 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(); 1428261742 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [12 x - x z + 18 z - 5 y, x - 13 y z + 5 z + 11 x, 2 12 y + 15 y z + 12 x + 10 z] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [18 x - 6 x z + 18 y z - 19 x, 17 x - 5 x z + 16 z - 4, 2 2 -7 x + 16 y + 8 y z + 20 y] > Problem := [F,G]; 2 2 2 2 Problem := [[12 x - x z + 18 z - 5 y, x - 13 y z + 5 z + 11 x, 2 2 12 y + 15 y z + 12 x + 10 z], [18 x - 6 x z + 18 y z - 19 x, 2 2 2 2 17 x - 5 x z + 16 z - 4, -7 x + 16 y + 8 y 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=4.3MB, alloc=32.3MB, time=0.30 memory used=26.0MB, alloc=32.3MB, time=0.87 memory used=46.1MB, alloc=32.3MB, time=1.39 memory used=64.7MB, alloc=56.3MB, time=1.88 memory used=104.8MB, alloc=60.3MB, time=2.94 memory used=142.6MB, alloc=60.3MB, time=3.88 memory used=181.6MB, alloc=84.3MB, time=4.89 memory used=210.5MB, alloc=84.3MB, time=5.59 memory used=273.6MB, alloc=92.3MB, time=7.30 memory used=335.8MB, alloc=116.3MB, time=8.96 memory used=415.1MB, alloc=116.3MB, time=11.05 memory used=485.2MB, alloc=372.3MB, time=12.74 memory used=568.6MB, alloc=396.3MB, time=14.96 memory used=680.2MB, alloc=396.3MB, time=17.61 memory used=788.0MB, alloc=420.3MB, time=20.45 memory used=915.2MB, alloc=444.3MB, time=23.88 memory used=1041.9MB, alloc=468.3MB, time=26.85 memory used=1177.8MB, alloc=492.3MB, time=30.37 memory used=1301.4MB, alloc=492.3MB, time=33.76 memory used=1406.7MB, alloc=492.3MB, time=36.04 memory used=1530.8MB, alloc=516.3MB, time=39.93 memory used=1620.5MB, alloc=516.3MB, time=42.44 memory used=1718.9MB, alloc=516.3MB, time=45.45 memory used=1787.4MB, alloc=516.3MB, time=47.53 memory used=1876.3MB, alloc=516.3MB, time=49.90 memory used=1945.0MB, alloc=516.3MB, time=52.08 memory used=2026.2MB, alloc=516.3MB, time=54.56 memory used=2083.2MB, alloc=516.3MB, time=56.49 memory used=2148.2MB, alloc=516.3MB, time=58.77 memory used=2198.1MB, alloc=540.3MB, time=60.66 memory used=2242.4MB, alloc=540.3MB, time=62.24 memory used=2468.5MB, alloc=564.3MB, time=67.52 memory used=2692.9MB, alloc=588.3MB, time=72.41 memory used=2916.2MB, alloc=612.3MB, time=79.34 memory used=3111.9MB, alloc=636.3MB, time=85.36 memory used=3285.2MB, alloc=660.3MB, time=90.50 memory used=3452.2MB, alloc=660.3MB, time=95.24 memory used=3610.5MB, alloc=684.3MB, time=99.68 memory used=3752.1MB, alloc=684.3MB, time=104.46 memory used=3883.3MB, alloc=684.3MB, time=108.68 memory used=4005.7MB, alloc=684.3MB, time=113.10 memory used=4135.5MB, alloc=684.3MB, time=117.95 |\^/| 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(); 1428262042 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [12 x + 14 x z - y + 5 x, -5 x y - y + 20 y z - 10, 2 -15 x y - 9 x z - 10 z + 5 z] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [16 x - 8 x y + 17 x + 5 y, 19 x y - 2 y z + 18 z - 16, 2 7 x - 20 x y - 11 x + 16] > Problem := [F,G]; 2 2 2 Problem := [[12 x + 14 x z - y + 5 x, -5 x y - y + 20 y z - 10, 2 2 -15 x y - 9 x z - 10 z + 5 z], [16 x - 8 x y + 17 x + 5 y, 2 19 x y - 2 y z + 18 z - 16, 7 x - 20 x y - 11 x + 16]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,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=46.4MB, alloc=56.3MB, time=1.41 memory used=88.9MB, alloc=60.3MB, time=2.53 memory used=130.4MB, alloc=60.3MB, time=3.62 memory used=170.2MB, alloc=84.3MB, time=4.69 memory used=233.4MB, alloc=92.3MB, time=6.40 memory used=293.3MB, alloc=116.3MB, time=8.03 memory used=368.6MB, alloc=116.3MB, time=10.06 memory used=437.7MB, alloc=396.3MB, time=11.97 memory used=547.1MB, alloc=396.3MB, time=14.89 memory used=653.7MB, alloc=420.3MB, time=17.90 memory used=785.3MB, alloc=444.3MB, time=21.61 memory used=923.5MB, alloc=444.3MB, time=25.44 memory used=1058.0MB, alloc=468.3MB, time=29.46 memory used=1189.7MB, alloc=492.3MB, time=33.58 memory used=1300.1MB, alloc=492.3MB, time=36.95 memory used=1402.2MB, alloc=492.3MB, time=40.05 memory used=1485.5MB, alloc=492.3MB, time=42.51 memory used=1586.1MB, alloc=492.3MB, time=46.04 memory used=1683.9MB, alloc=492.3MB, time=49.39 memory used=1763.4MB, alloc=516.3MB, time=51.77 memory used=1848.6MB, alloc=516.3MB, time=54.34 memory used=1919.1MB, alloc=516.3MB, time=56.69 memory used=1980.5MB, alloc=516.3MB, time=58.78 memory used=2058.4MB, alloc=516.3MB, time=61.56 memory used=2116.1MB, alloc=516.3MB, time=63.50 memory used=2174.4MB, alloc=516.3MB, time=65.38 memory used=2228.3MB, alloc=516.3MB, time=67.42 memory used=2283.8MB, alloc=516.3MB, time=69.37 memory used=2326.8MB, alloc=540.3MB, time=71.06 memory used=2557.3MB, alloc=564.3MB, time=78.06 memory used=2798.3MB, alloc=588.3MB, time=85.69 memory used=3032.6MB, alloc=612.3MB, time=92.86 memory used=3291.8MB, alloc=636.3MB, time=100.92 memory used=3568.4MB, alloc=660.3MB, time=109.30 memory used=3852.1MB, alloc=684.3MB, 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(); 1428262342 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-14 x z - 3 y + 14 y - 11, 15 x z + 13 z + 5 x - 14, 2 x + 8 x y - 17 y - 10 z] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [-11 x - 8 x z + 19 y - 2, -8 y z + 4 x - 20 y, 8 y + 17 z - 3 y - 12] > Problem := [F,G]; 2 2 Problem := [[-14 x z - 3 y + 14 y - 11, 15 x z + 13 z + 5 x - 14, 2 x + 8 x y - 17 y - 10 z], 2 2 2 [-11 x - 8 x z + 19 y - 2, -8 y z + 4 x - 20 y, 8 y + 17 z - 3 y - 12]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,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=26.2MB, alloc=32.3MB, time=0.90 memory used=47.7MB, alloc=32.3MB, time=1.46 memory used=67.7MB, alloc=56.3MB, time=2.01 memory used=110.4MB, alloc=60.3MB, time=3.15 memory used=151.6MB, alloc=60.3MB, time=4.23 memory used=191.1MB, alloc=84.3MB, time=5.31 memory used=225.8MB, alloc=84.3MB, time=6.27 memory used=286.3MB, alloc=116.3MB, time=7.97 memory used=366.8MB, alloc=372.3MB, time=10.22 memory used=457.2MB, alloc=396.3MB, time=12.44 memory used=566.7MB, alloc=420.3MB, time=15.45 memory used=694.5MB, alloc=444.3MB, time=18.97 memory used=825.0MB, alloc=444.3MB, time=22.81 memory used=946.2MB, alloc=468.3MB, time=26.37 memory used=1057.4MB, alloc=468.3MB, time=29.65 memory used=1175.4MB, alloc=468.3MB, time=33.36 memory used=1275.9MB, alloc=492.3MB, time=36.49 memory used=1381.9MB, alloc=492.3MB, time=40.01 memory used=1470.6MB, alloc=492.3MB, time=42.95 memory used=1556.3MB, alloc=492.3MB, time=45.69 memory used=1631.9MB, alloc=492.3MB, time=48.25 memory used=1710.4MB, alloc=492.3MB, time=50.85 memory used=1776.0MB, alloc=492.3MB, time=53.20 memory used=1841.2MB, alloc=492.3MB, time=55.67 memory used=1909.4MB, alloc=492.3MB, time=58.10 memory used=1973.8MB, alloc=492.3MB, time=60.54 memory used=2035.5MB, alloc=492.3MB, time=62.87 memory used=2084.6MB, alloc=492.3MB, time=64.52 memory used=2136.5MB, alloc=516.3MB, time=66.68 memory used=2193.7MB, alloc=516.3MB, time=68.96 memory used=2222.3MB, alloc=516.3MB, time=70.24 memory used=2274.3MB, alloc=516.3MB, time=72.46 memory used=2486.5MB, alloc=540.3MB, time=79.29 memory used=2693.8MB, alloc=564.3MB, time=86.10 memory used=2854.8MB, alloc=588.3MB, time=91.31 memory used=3035.3MB, alloc=612.3MB, time=97.20 memory used=3214.1MB, alloc=636.3MB, time=103.33 memory used=3385.7MB, alloc=660.3MB, time=109.75 |\^/| 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(); 1428262642 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-x y + 10 x z - 11 y - 3 y z, 17 y z - 9 z - 6 y - 18 z, 2 2 9 y + 16 y z - 13 z - 16 y] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [-14 x - 3 x y + 5 y + 12 z, 15 x + 8 z - 5 x - 15 y, 2 -19 x y + 8 x z + 7 z - 17 y] > Problem := [F,G]; 2 2 Problem := [[-x y + 10 x z - 11 y - 3 y z, 17 y z - 9 z - 6 y - 18 z, 2 2 2 9 y + 16 y z - 13 z - 16 y], [-14 x - 3 x y + 5 y + 12 z, 2 2 2 15 x + 8 z - 5 x - 15 y, -19 x y + 8 x z + 7 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=4.3MB, alloc=32.3MB, time=0.32 memory used=26.5MB, alloc=32.3MB, time=0.90 memory used=46.3MB, alloc=56.3MB, time=1.43 memory used=88.6MB, alloc=60.3MB, time=2.51 memory used=128.2MB, alloc=92.3MB, time=3.59 memory used=192.9MB, alloc=92.3MB, time=5.24 memory used=262.3MB, alloc=116.3MB, time=6.90 memory used=336.5MB, alloc=372.3MB, time=8.83 memory used=421.1MB, alloc=396.3MB, time=11.05 memory used=539.3MB, alloc=396.3MB, time=13.89 memory used=649.0MB, alloc=420.3MB, time=16.70 memory used=779.8MB, alloc=444.3MB, time=20.16 memory used=907.1MB, alloc=468.3MB, time=23.65 memory used=1031.4MB, alloc=468.3MB, time=27.16 memory used=1141.1MB, alloc=468.3MB, time=30.33 memory used=1264.4MB, alloc=492.3MB, time=33.49 memory used=1378.8MB, alloc=492.3MB, time=36.77 memory used=1469.3MB, alloc=492.3MB, time=39.46 memory used=1563.1MB, alloc=492.3MB, time=42.50 memory used=1659.5MB, alloc=492.3MB, time=45.64 memory used=1755.1MB, alloc=492.3MB, time=48.69 memory used=1834.1MB, alloc=516.3MB, time=51.39 memory used=1899.5MB, alloc=516.3MB, time=53.49 memory used=1969.5MB, alloc=516.3MB, time=55.93 memory used=2036.6MB, alloc=516.3MB, time=58.24 memory used=2109.4MB, alloc=516.3MB, time=61.23 memory used=2179.3MB, alloc=516.3MB, time=63.95 memory used=2240.8MB, alloc=516.3MB, time=66.48 memory used=2295.0MB, alloc=516.3MB, time=68.11 memory used=2345.4MB, alloc=516.3MB, time=70.12 memory used=2550.4MB, alloc=540.3MB, time=76.70 memory used=2771.7MB, alloc=564.3MB, time=83.34 memory used=2979.0MB, alloc=588.3MB, time=89.78 memory used=3189.5MB, alloc=612.3MB, time=95.53 memory used=3388.6MB, alloc=636.3MB, time=102.62 |\^/| 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(); 1428262942 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-9 x + 9 x z - 15 z , -x y - 5 x z + 10 y - 20 y, 2 2 -10 x + 12 x y + 9 y - 4 z] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [12 x y - 7 z - 9 x - 1, 7 x - 8 y z + 7 x + 2, -5 x y + 6 x - 5 z - 5] > Problem := [F,G]; 2 2 2 Problem := [[-9 x + 9 x z - 15 z , -x y - 5 x z + 10 y - 20 y, 2 2 -10 x + 12 x y + 9 y - 4 z], 2 2 [12 x y - 7 z - 9 x - 1, 7 x - 8 y z + 7 x + 2, -5 x y + 6 x - 5 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=4.3MB, alloc=32.3MB, time=0.31 memory used=25.9MB, alloc=32.3MB, time=0.89 memory used=45.4MB, alloc=56.3MB, time=1.43 memory used=87.4MB, alloc=60.3MB, time=2.51 memory used=128.5MB, alloc=60.3MB, time=3.58 memory used=164.3MB, alloc=84.3MB, time=4.55 memory used=228.7MB, alloc=92.3MB, time=6.25 memory used=292.0MB, alloc=116.3MB, time=7.90 memory used=371.1MB, alloc=116.3MB, time=10.09 memory used=442.8MB, alloc=396.3MB, time=11.98 memory used=557.5MB, alloc=420.3MB, time=14.78 memory used=689.6MB, alloc=444.3MB, time=18.40 memory used=812.6MB, alloc=444.3MB, time=21.48 memory used=942.5MB, alloc=468.3MB, time=25.07 memory used=1058.3MB, alloc=468.3MB, time=28.26 memory used=1161.8MB, alloc=468.3MB, time=31.07 memory used=1260.8MB, alloc=468.3MB, time=33.82 memory used=1362.7MB, alloc=492.3MB, time=36.39 memory used=1460.8MB, alloc=492.3MB, time=39.61 memory used=1542.8MB, alloc=492.3MB, time=42.13 memory used=1638.4MB, alloc=492.3MB, time=45.03 memory used=1718.0MB, alloc=492.3MB, time=47.56 memory used=1784.5MB, alloc=492.3MB, time=49.72 memory used=1849.9MB, alloc=492.3MB, time=51.96 memory used=1917.2MB, alloc=492.3MB, time=54.20 memory used=1974.9MB, alloc=492.3MB, time=55.92 memory used=2042.2MB, alloc=492.3MB, time=58.47 memory used=2102.9MB, alloc=516.3MB, time=60.73 memory used=2152.9MB, alloc=516.3MB, time=62.52 memory used=2211.0MB, alloc=516.3MB, time=64.77 memory used=2420.9MB, alloc=540.3MB, time=70.98 memory used=2619.2MB, alloc=564.3MB, time=76.94 memory used=2829.2MB, alloc=588.3MB, time=82.93 memory used=3012.0MB, alloc=612.3MB, time=88.62 memory used=3192.1MB, alloc=636.3MB, time=94.18 memory used=3343.7MB, alloc=636.3MB, time=99.24 memory used=3489.2MB, alloc=636.3MB, time=103.83 memory used=3636.6MB, alloc=636.3MB, time=108.65 memory used=3777.3MB, alloc=660.3MB, time=112.90 |\^/| 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(); 1428263242 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [20 x y - y - 16 x + 10, -16 x z - 11 x - 8 y - 11 z, 2 -16 x y + 3 x z + 17 y + 7 z] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-7 x y - 14 x z + 3 y z - 20, x z - z - 15 x + 14, -12 y - 14 x - 6] > Problem := [F,G]; 2 Problem := [[20 x y - y - 16 x + 10, -16 x z - 11 x - 8 y - 11 z, 2 -16 x y + 3 x z + 17 y + 7 z], 2 2 [-7 x y - 14 x z + 3 y z - 20, x z - z - 15 x + 14, -12 y - 14 x - 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=27.1MB, alloc=32.3MB, time=0.90 memory used=47.2MB, alloc=56.3MB, time=1.44 memory used=89.6MB, alloc=60.3MB, time=2.58 memory used=131.1MB, alloc=60.3MB, time=3.69 memory used=171.5MB, alloc=84.3MB, time=4.81 memory used=234.6MB, alloc=92.3MB, time=6.54 memory used=294.4MB, alloc=116.3MB, time=8.21 memory used=377.9MB, alloc=116.3MB, time=10.44 memory used=454.7MB, alloc=396.3MB, time=12.63 memory used=563.2MB, alloc=396.3MB, time=15.67 memory used=670.6MB, alloc=420.3MB, time=18.75 memory used=802.5MB, alloc=444.3MB, time=22.73 memory used=956.3MB, alloc=468.3MB, time=27.44 memory used=1086.2MB, alloc=468.3MB, time=31.32 memory used=1207.0MB, alloc=492.3MB, time=34.88 memory used=1325.1MB, alloc=492.3MB, time=38.50 memory used=1436.5MB, alloc=516.3MB, time=42.07 memory used=1545.7MB, alloc=516.3MB, time=45.69 memory used=1662.1MB, alloc=540.3MB, time=49.66 memory used=1768.9MB, alloc=540.3MB, time=53.14 memory used=1923.1MB, alloc=564.3MB, time=57.78 memory used=2067.4MB, alloc=588.3MB, time=62.47 memory used=2220.3MB, alloc=612.3MB, time=67.66 memory used=2346.4MB, alloc=636.3MB, time=72.04 memory used=2491.1MB, alloc=660.3MB, time=77.05 memory used=2636.8MB, alloc=684.3MB, time=82.02 memory used=2765.6MB, alloc=684.3MB, time=86.67 memory used=2878.4MB, alloc=708.3MB, time=90.80 memory used=3007.0MB, alloc=732.3MB, time=95.48 memory used=3120.7MB, alloc=732.3MB, time=99.81 memory used=3211.3MB, alloc=756.3MB, time=103.43 memory used=3310.7MB, alloc=756.3MB, time=107.33 |\^/| 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(); 1428263542 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [17 x - 3 x z + 3 y z - 20 z , 2 x z - 7 y + 8 z - 4, 2 2 16 x y + 9 x z - 19 y + z ] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; G := [ 2 2 2 2 2 x + 4 y + 11 y z - 12 x, -5 x y - 3 x z - 5 z + x, x - z + 19 x - 4 y] > Problem := [F,G]; 2 2 2 Problem := [[17 x - 3 x z + 3 y z - 20 z , 2 x z - 7 y + 8 z - 4, 2 2 16 x y + 9 x z - 19 y + z ], [ 2 2 2 2 2 x + 4 y + 11 y z - 12 x, -5 x y - 3 x z - 5 z + x, x - z + 19 x - 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=0.30 memory used=25.4MB, alloc=32.3MB, time=0.86 memory used=45.0MB, alloc=32.3MB, time=1.34 memory used=65.6MB, alloc=60.3MB, time=1.87 memory used=108.6MB, alloc=68.3MB, time=2.96 memory used=148.2MB, alloc=68.3MB, time=3.96 memory used=191.9MB, alloc=92.3MB, time=4.96 memory used=256.6MB, alloc=92.3MB, time=6.42 memory used=329.8MB, alloc=92.3MB, time=7.94 memory used=394.6MB, alloc=116.3MB, time=9.56 memory used=459.5MB, alloc=116.3MB, time=11.17 memory used=531.3MB, alloc=116.3MB, time=12.38 memory used=596.8MB, alloc=116.3MB, time=13.84 memory used=660.8MB, alloc=396.3MB, time=15.55 memory used=773.7MB, alloc=396.3MB, time=18.32 memory used=889.2MB, alloc=420.3MB, time=21.03 memory used=1018.8MB, alloc=444.3MB, time=24.49 memory used=1141.9MB, alloc=468.3MB, time=27.38 memory used=1248.4MB, alloc=468.3MB, time=29.80 memory used=1374.3MB, alloc=468.3MB, time=32.60 memory used=1471.1MB, alloc=468.3MB, time=34.89 memory used=1565.7MB, alloc=468.3MB, time=37.49 memory used=1656.8MB, alloc=492.3MB, time=40.05 memory used=1752.6MB, alloc=492.3MB, time=42.93 memory used=1824.8MB, alloc=492.3MB, time=44.99 memory used=1890.9MB, alloc=492.3MB, time=46.98 memory used=1962.3MB, alloc=492.3MB, time=49.24 memory used=2024.6MB, alloc=492.3MB, time=51.19 memory used=2085.8MB, alloc=492.3MB, time=53.12 memory used=2156.8MB, alloc=492.3MB, time=55.71 memory used=2206.3MB, alloc=516.3MB, time=57.25 memory used=2251.1MB, alloc=516.3MB, time=58.71 memory used=2298.6MB, alloc=516.3MB, time=60.27 memory used=2501.3MB, alloc=540.3MB, time=65.65 memory used=2705.9MB, alloc=564.3MB, time=70.00 memory used=2890.2MB, alloc=588.3MB, time=75.17 memory used=3050.3MB, alloc=612.3MB, time=79.95 memory used=3194.4MB, alloc=636.3MB, time=84.76 memory used=3347.7MB, alloc=636.3MB, time=88.87 memory used=3530.6MB, alloc=636.3MB, time=93.61 memory used=3667.3MB, alloc=660.3MB, time=97.45 memory used=3815.9MB, alloc=660.3MB, time=101.65 memory used=3889.6MB, alloc=660.3MB, time=104.66 memory used=3986.0MB, alloc=660.3MB, time=108.05 memory used=4091.6MB, alloc=660.3MB, time=111.99 memory used=4199.5MB, alloc=660.3MB, time=115.39 memory used=4518.6MB, alloc=684.3MB, time=124.79 |\^/| 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(); 1428263842 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [3 x - 5 y - 20 z - 2 z, 16 x y - 19 y z - 10 z + 8, 2 2 13 x - 5 x z + 19 z - 1] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; G := [ 2 2 2 4 x y + 16 x z + 11 x - 11 y, 18 x + 11 y - 13 z - 11, z + y - 18 z - 14 ] > Problem := [F,G]; 2 2 2 Problem := [[3 x - 5 y - 20 z - 2 z, 16 x y - 19 y z - 10 z + 8, 2 2 13 x - 5 x z + 19 z - 1], [ 2 2 2 4 x y + 16 x z + 11 x - 11 y, 18 x + 11 y - 13 z - 11, z + y - 18 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=26.4MB, alloc=32.3MB, time=0.88 memory used=46.7MB, alloc=32.3MB, time=1.41 memory used=65.7MB, alloc=56.3MB, time=1.92 memory used=108.9MB, alloc=68.3MB, time=3.03 memory used=150.4MB, alloc=92.3MB, time=4.08 memory used=215.2MB, alloc=92.3MB, time=5.77 memory used=282.1MB, alloc=92.3MB, time=7.43 memory used=347.9MB, alloc=116.3MB, time=9.10 memory used=416.6MB, alloc=372.3MB, time=10.89 memory used=503.5MB, alloc=396.3MB, time=13.16 memory used=616.3MB, alloc=396.3MB, time=16.03 memory used=721.0MB, alloc=420.3MB, time=18.88 memory used=853.7MB, alloc=444.3MB, time=22.57 memory used=978.5MB, alloc=468.3MB, time=25.80 memory used=1082.8MB, alloc=468.3MB, time=28.69 memory used=1185.3MB, alloc=468.3MB, time=31.38 memory used=1305.7MB, alloc=468.3MB, time=34.96 memory used=1405.9MB, alloc=492.3MB, time=37.82 memory used=1483.0MB, alloc=492.3MB, time=39.90 memory used=1565.0MB, alloc=492.3MB, time=42.45 memory used=1648.3MB, alloc=492.3MB, time=44.94 memory used=1739.4MB, alloc=492.3MB, time=47.67 memory used=1812.8MB, alloc=492.3MB, time=49.94 memory used=1888.6MB, alloc=492.3MB, time=51.90 memory used=1966.8MB, alloc=492.3MB, time=54.52 memory used=2024.6MB, alloc=516.3MB, time=56.39 memory used=2108.6MB, alloc=516.3MB, time=59.38 memory used=2191.2MB, alloc=516.3MB, time=61.97 memory used=2245.0MB, alloc=516.3MB, time=63.85 memory used=2300.2MB, alloc=516.3MB, time=65.42 memory used=2361.5MB, alloc=516.3MB, time=67.95 memory used=2409.8MB, alloc=516.3MB, time=69.62 memory used=2448.0MB, alloc=516.3MB, time=71.07 memory used=2658.3MB, alloc=540.3MB, time=78.37 memory used=2888.3MB, alloc=564.3MB, time=85.77 memory used=3086.8MB, alloc=588.3MB, time=91.56 memory used=3281.6MB, alloc=612.3MB, time=97.92 memory used=3467.8MB, alloc=612.3MB, time=104.75 memory used=3642.2MB, alloc=636.3MB, time=110.63 memory used=3815.4MB, alloc=636.3MB, time=116.72 |\^/| 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(); 1428264142 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-11 y - 18 y z - 20 y - 11, 4 x + 8 x y - 12 z + 11 y, 2 15 x + 11 x z + 4 x + 10 y] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-12 y z - 9 z + 10 z + 9, 12 x z - 8 y - 8 x - 18, 2 -2 y - 16 y z + 2 x - 11] > Problem := [F,G]; 2 2 2 Problem := [[-11 y - 18 y z - 20 y - 11, 4 x + 8 x y - 12 z + 11 y, 2 2 15 x + 11 x z + 4 x + 10 y], [-12 y z - 9 z + 10 z + 9, 2 2 12 x z - 8 y - 8 x - 18, -2 y - 16 y z + 2 x - 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=26.0MB, alloc=32.3MB, time=0.87 memory used=46.0MB, alloc=32.3MB, time=1.39 memory used=65.1MB, alloc=56.3MB, time=1.92 memory used=105.9MB, alloc=60.3MB, time=3.00 memory used=145.9MB, alloc=60.3MB, time=4.06 memory used=185.4MB, alloc=84.3MB, time=5.10 memory used=226.9MB, alloc=84.3MB, time=6.18 memory used=287.1MB, alloc=92.3MB, time=7.83 memory used=348.3MB, alloc=116.3MB, time=9.51 memory used=409.7MB, alloc=116.3MB, time=10.89 memory used=484.4MB, alloc=396.3MB, time=12.91 memory used=593.5MB, alloc=420.3MB, time=15.80 memory used=719.9MB, alloc=420.3MB, time=19.05 memory used=853.1MB, alloc=444.3MB, time=22.32 memory used=974.2MB, alloc=468.3MB, time=25.68 memory used=1067.8MB, alloc=468.3MB, time=28.02 memory used=1170.9MB, alloc=468.3MB, time=30.82 memory used=1279.7MB, alloc=492.3MB, time=34.06 memory used=1387.5MB, alloc=492.3MB, time=37.60 memory used=1474.8MB, alloc=492.3MB, time=40.29 memory used=1561.5MB, alloc=492.3MB, time=43.25 memory used=1624.9MB, alloc=492.3MB, time=45.01 memory used=1700.5MB, alloc=492.3MB, time=47.55 memory used=1769.5MB, alloc=492.3MB, time=49.86 memory used=1837.5MB, alloc=492.3MB, time=52.13 memory used=1904.4MB, alloc=492.3MB, time=54.42 memory used=1964.7MB, alloc=516.3MB, time=56.56 memory used=2019.2MB, alloc=516.3MB, time=58.19 memory used=2071.1MB, alloc=516.3MB, time=60.15 memory used=2116.7MB, alloc=516.3MB, time=61.77 memory used=2328.9MB, alloc=540.3MB, time=68.04 memory used=2515.8MB, alloc=564.3MB, time=73.32 memory used=2720.1MB, alloc=588.3MB, time=79.86 memory used=2894.5MB, alloc=612.3MB, time=85.76 memory used=3077.4MB, alloc=636.3MB, time=90.98 memory used=3202.1MB, alloc=636.3MB, time=95.16 memory used=3360.7MB, alloc=636.3MB, time=100.39 memory used=3491.0MB, alloc=636.3MB, time=104.72 memory used=3617.9MB, alloc=660.3MB, time=109.18 memory used=3738.1MB, alloc=660.3MB, time=113.51 |\^/| 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(); 1428264442 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-x + 17 x z - 6 z + 12 y, -5 x z + 7 y + 14 y z - 15 y, 2 2 -15 x - 20 z + 13 y + 4] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; G := 2 2 2 [16 x z + 5 z - 9 x - 2 z, 20 x + 19 x - z + 5, 18 x + 8 x z - 6 x + 20] > Problem := [F,G]; 2 2 2 Problem := [[-x + 17 x z - 6 z + 12 y, -5 x z + 7 y + 14 y z - 15 y, 2 2 -15 x - 20 z + 13 y + 4], 2 2 2 [16 x z + 5 z - 9 x - 2 z, 20 x + 19 x - z + 5, 18 x + 8 x z - 6 x + 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=4.3MB, alloc=32.3MB, time=0.31 memory used=26.4MB, alloc=32.3MB, time=0.89 memory used=47.2MB, alloc=56.3MB, time=1.44 memory used=89.9MB, alloc=60.3MB, time=2.53 memory used=131.7MB, alloc=84.3MB, time=3.59 memory used=174.5MB, alloc=84.3MB, time=4.68 memory used=237.6MB, alloc=92.3MB, time=6.34 memory used=300.2MB, alloc=116.3MB, time=7.88 memory used=379.9MB, alloc=116.3MB, time=9.99 memory used=448.6MB, alloc=396.3MB, time=11.67 memory used=553.2MB, alloc=396.3MB, time=14.37 memory used=658.6MB, alloc=420.3MB, time=17.14 memory used=786.5MB, alloc=444.3MB, time=20.62 memory used=936.2MB, alloc=444.3MB, time=24.53 memory used=1083.1MB, alloc=468.3MB, time=28.70 memory used=1222.4MB, alloc=492.3MB, time=32.62 memory used=1355.0MB, alloc=492.3MB, time=36.38 memory used=1460.3MB, alloc=492.3MB, time=39.65 memory used=1555.7MB, alloc=516.3MB, time=42.10 memory used=1668.3MB, alloc=516.3MB, time=45.14 memory used=1745.5MB, alloc=516.3MB, time=47.50 memory used=1816.4MB, alloc=540.3MB, time=49.42 memory used=1900.8MB, alloc=540.3MB, time=52.16 memory used=1970.2MB, alloc=540.3MB, time=54.21 memory used=2023.4MB, alloc=540.3MB, time=55.81 memory used=2081.9MB, alloc=540.3MB, time=57.34 memory used=2154.8MB, alloc=540.3MB, time=59.23 memory used=2211.7MB, alloc=540.3MB, time=61.67 memory used=2436.6MB, alloc=564.3MB, time=67.34 memory used=2654.3MB, alloc=588.3MB, time=73.17 memory used=2842.8MB, alloc=612.3MB, time=78.40 memory used=3027.3MB, alloc=636.3MB, time=83.08 memory used=3209.6MB, alloc=660.3MB, time=88.45 memory used=3371.8MB, alloc=684.3MB, time=93.52 memory used=3515.3MB, alloc=684.3MB, time=98.20 memory used=3647.7MB, alloc=684.3MB, time=102.31 memory used=3783.4MB, alloc=684.3MB, time=107.27 memory used=3894.0MB, alloc=684.3MB, time=111.60 memory used=3970.8MB, alloc=684.3MB, time=114.61 |\^/| 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(); 1428264743 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [16 x z - 17 y + z - 13, -11 x - 8 y z - 2 z - 5 y, 2 2 -3 y + 2 z - 2 x - 6] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-7 y z - 20 z + 2 x - z, -13 x z + 5 y z + 20 z + 5 z, 2 -5 z - 6 y - 18 z + 13] > Problem := [F,G]; 2 2 2 2 Problem := [[16 x z - 17 y + z - 13, -11 x - 8 y z - 2 z - 5 y, 2 2 2 -3 y + 2 z - 2 x - 6], [-7 y z - 20 z + 2 x - z, 2 2 -13 x z + 5 y z + 20 z + 5 z, -5 z - 6 y - 18 z + 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 used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.6MB, alloc=32.3MB, time=0.88 memory used=46.8MB, alloc=56.3MB, time=1.43 memory used=87.3MB, alloc=60.3MB, time=2.48 memory used=127.4MB, alloc=84.3MB, time=3.53 memory used=168.2MB, alloc=84.3MB, time=4.62 memory used=227.3MB, alloc=116.3MB, time=6.24 memory used=307.3MB, alloc=116.3MB, time=8.43 memory used=378.6MB, alloc=140.3MB, time=10.45 memory used=459.6MB, alloc=396.3MB, time=12.78 memory used=562.6MB, alloc=420.3MB, time=15.71 memory used=694.0MB, alloc=444.3MB, time=19.37 memory used=835.7MB, alloc=468.3MB, time=23.36 memory used=985.7MB, alloc=492.3MB, time=27.91 memory used=1157.4MB, alloc=516.3MB, time=33.61 memory used=1306.6MB, alloc=516.3MB, time=38.66 memory used=1439.8MB, alloc=540.3MB, time=43.02 memory used=1552.0MB, alloc=540.3MB, time=46.69 memory used=1680.4MB, alloc=540.3MB, time=51.19 memory used=1812.2MB, alloc=540.3MB, time=55.99 memory used=1913.6MB, alloc=564.3MB, time=59.40 memory used=2018.4MB, alloc=564.3MB, time=63.08 memory used=2115.2MB, alloc=564.3MB, time=66.52 memory used=2192.5MB, alloc=564.3MB, time=69.35 memory used=2261.3MB, alloc=564.3MB, time=71.49 memory used=2344.4MB, alloc=564.3MB, time=74.40 memory used=2424.0MB, alloc=588.3MB, time=77.33 memory used=2515.2MB, alloc=588.3MB, time=81.30 memory used=2598.9MB, alloc=588.3MB, time=84.95 memory used=2695.8MB, alloc=588.3MB, time=89.45 memory used=2753.9MB, alloc=588.3MB, time=92.04 memory used=2814.6MB, alloc=588.3MB, time=94.73 memory used=2869.4MB, alloc=588.3MB, time=96.97 memory used=3128.9MB, alloc=612.3MB, time=106.15 |\^/| 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(); 1428265043 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-4 x y + 4 x z - 3 y z + 9 z , -3 x + 11 y + 13 x + 16, 2 6 z - 7 x + 2 y + 17] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; G := [ 2 2 2 2 18 y - y z + 4 z , 19 x z + 2 y - 4 z + 9, -7 x z - 10 y + 18 y z + 18 y ] > Problem := [F,G]; 2 2 2 Problem := [[-4 x y + 4 x z - 3 y z + 9 z , -3 x + 11 y + 13 x + 16, 2 6 z - 7 x + 2 y + 17], [ 2 2 2 2 18 y - y z + 4 z , 19 x z + 2 y - 4 z + 9, -7 x z - 10 y + 18 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=4.3MB, alloc=32.3MB, time=0.30 memory used=26.3MB, alloc=32.3MB, time=0.86 memory used=45.9MB, alloc=56.3MB, time=1.38 memory used=88.7MB, alloc=60.3MB, time=2.43 memory used=129.7MB, alloc=60.3MB, time=3.48 memory used=167.2MB, alloc=84.3MB, time=4.43 memory used=233.2MB, alloc=92.3MB, time=6.05 memory used=292.4MB, alloc=116.3MB, time=7.58 memory used=358.9MB, alloc=116.3MB, time=9.26 memory used=430.5MB, alloc=396.3MB, time=11.11 memory used=537.6MB, alloc=396.3MB, time=13.88 memory used=646.7MB, alloc=420.3MB, time=16.53 memory used=782.4MB, alloc=444.3MB, time=19.85 memory used=900.6MB, alloc=444.3MB, time=22.84 memory used=1024.9MB, alloc=468.3MB, time=26.05 memory used=1146.1MB, alloc=468.3MB, time=29.25 memory used=1274.1MB, alloc=468.3MB, time=32.85 memory used=1386.1MB, alloc=492.3MB, time=36.15 memory used=1479.0MB, alloc=492.3MB, time=38.61 memory used=1582.6MB, alloc=492.3MB, time=41.71 memory used=1674.7MB, alloc=492.3MB, time=43.79 memory used=1778.0MB, alloc=516.3MB, time=46.75 memory used=1863.7MB, alloc=516.3MB, time=49.45 memory used=1941.4MB, alloc=516.3MB, time=51.86 memory used=2033.3MB, alloc=516.3MB, time=54.88 memory used=2108.0MB, alloc=516.3MB, time=57.68 memory used=2164.6MB, alloc=516.3MB, time=59.54 memory used=2219.6MB, alloc=516.3MB, time=61.21 memory used=2285.3MB, alloc=516.3MB, time=63.66 memory used=2346.1MB, alloc=516.3MB, time=65.90 memory used=2403.9MB, alloc=516.3MB, time=68.41 memory used=2603.4MB, alloc=540.3MB, time=73.72 memory used=2803.9MB, alloc=564.3MB, time=78.97 memory used=2993.9MB, alloc=588.3MB, time=84.31 memory used=3190.4MB, alloc=612.3MB, time=90.06 memory used=3365.1MB, alloc=636.3MB, time=95.57 memory used=3527.4MB, alloc=660.3MB, time=99.33 memory used=3695.3MB, alloc=684.3MB, time=104.87 memory used=3846.1MB, alloc=708.3MB, time=110.53 memory used=3971.0MB, alloc=708.3MB, time=115.37 memory used=4068.9MB, alloc=708.3MB, time=118.68 memory used=4148.0MB, alloc=708.3MB, time=121.55 |\^/| 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(); 1428265343 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-11 x + 10 y + 6 y + 19 z, 7 x y - 20 x z - 18 y z + 7 z, 2 2 x + 18 z - 8 z + 20] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [10 x z - 13 y - 18 x - 18, -16 x y + 7 y z + 13 x - 1, 2 2 9 x y + 4 y + 6 z - 4 y] > Problem := [F,G]; 2 2 Problem := [[-11 x + 10 y + 6 y + 19 z, 7 x y - 20 x z - 18 y z + 7 z, 2 2 2 x + 18 z - 8 z + 20], [10 x z - 13 y - 18 x - 18, 2 2 -16 x y + 7 y z + 13 x - 1, 9 x y + 4 y + 6 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=0.30 memory used=25.6MB, alloc=32.3MB, time=0.86 memory used=45.5MB, alloc=56.3MB, time=1.39 memory used=86.5MB, alloc=60.3MB, time=2.45 memory used=129.8MB, alloc=68.3MB, time=3.53 memory used=170.6MB, alloc=92.3MB, time=4.61 memory used=235.4MB, alloc=92.3MB, time=6.26 memory used=301.2MB, alloc=92.3MB, time=7.92 memory used=366.3MB, alloc=116.3MB, time=9.60 memory used=430.1MB, alloc=372.3MB, time=11.35 memory used=514.7MB, alloc=396.3MB, time=13.61 memory used=622.1MB, alloc=396.3MB, time=16.51 memory used=732.9MB, alloc=420.3MB, time=19.25 memory used=845.9MB, alloc=444.3MB, time=21.75 memory used=969.9MB, alloc=468.3MB, time=25.25 memory used=1061.4MB, alloc=468.3MB, time=27.48 memory used=1168.2MB, alloc=468.3MB, time=30.59 memory used=1258.5MB, alloc=468.3MB, time=32.98 memory used=1332.0MB, alloc=468.3MB, time=35.02 memory used=1412.0MB, alloc=492.3MB, time=36.91 memory used=1493.2MB, alloc=492.3MB, time=39.43 memory used=1572.3MB, alloc=492.3MB, time=41.80 memory used=1642.6MB, alloc=492.3MB, time=43.98 memory used=1701.0MB, alloc=492.3MB, time=46.01 memory used=1757.5MB, alloc=492.3MB, time=47.69 memory used=1812.9MB, alloc=492.3MB, time=49.41 memory used=1870.1MB, alloc=492.3MB, time=51.37 memory used=1918.1MB, alloc=492.3MB, time=53.01 memory used=1967.7MB, alloc=492.3MB, time=54.58 memory used=2154.5MB, alloc=516.3MB, time=60.17 memory used=2343.7MB, alloc=540.3MB, time=65.26 memory used=2539.5MB, alloc=564.3MB, time=71.11 memory used=2720.7MB, alloc=588.3MB, time=76.62 memory used=2892.5MB, alloc=612.3MB, time=81.81 memory used=3031.7MB, alloc=612.3MB, time=86.25 memory used=3196.5MB, alloc=636.3MB, time=90.98 memory used=3326.3MB, alloc=636.3MB, time=94.78 memory used=3450.5MB, alloc=636.3MB, time=99.11 memory used=3571.7MB, alloc=636.3MB, time=103.49 memory used=3687.7MB, alloc=636.3MB, time=107.57 memory used=3785.7MB, alloc=660.3MB, time=110.59 memory used=3886.6MB, alloc=660.3MB, time=114.37 memory used=3973.1MB, alloc=660.3MB, time=117.44 |\^/| 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(); 1428265643 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [-19 x z + 16 x + 9 y, 14 x - 7 x z + 9 y z - 9 x, 2 2 12 x - 17 x y + 13 y + 2] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [-15 x + 16 z + 9, -5 x + 18 z - 12 y - 8 z, 10 x - 9 x y - 16 x + z] > Problem := [F,G]; 2 Problem := [[-19 x z + 16 x + 9 y, 14 x - 7 x z + 9 y z - 9 x, 2 2 12 x - 17 x y + 13 y + 2], 2 2 2 2 [-15 x + 16 z + 9, -5 x + 18 z - 12 y - 8 z, 10 x - 9 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=26.7MB, alloc=32.3MB, time=0.88 memory used=47.0MB, alloc=56.3MB, time=1.41 memory used=87.0MB, alloc=60.3MB, time=2.44 memory used=126.3MB, alloc=60.3MB, time=3.44 memory used=164.4MB, alloc=84.3MB, time=4.47 memory used=225.8MB, alloc=92.3MB, time=6.09 memory used=285.9MB, alloc=116.3MB, time=7.69 memory used=368.7MB, alloc=116.3MB, time=9.90 memory used=450.5MB, alloc=140.3MB, time=12.20 memory used=517.9MB, alloc=140.3MB, time=13.68 memory used=586.8MB, alloc=420.3MB, time=15.65 memory used=721.5MB, alloc=444.3MB, time=19.24 memory used=857.3MB, alloc=468.3MB, time=23.12 memory used=1004.4MB, alloc=468.3MB, time=27.00 memory used=1115.4MB, alloc=492.3MB, time=30.25 memory used=1245.9MB, alloc=492.3MB, time=34.20 memory used=1355.3MB, alloc=516.3MB, time=37.63 memory used=1459.5MB, alloc=516.3MB, time=40.90 memory used=1550.0MB, alloc=516.3MB, time=43.67 memory used=1645.5MB, alloc=516.3MB, time=46.95 memory used=1737.6MB, alloc=516.3MB, time=49.93 memory used=1823.4MB, alloc=516.3MB, time=53.03 memory used=1906.6MB, alloc=516.3MB, time=56.05 memory used=1986.7MB, alloc=516.3MB, time=58.98 memory used=2045.9MB, alloc=516.3MB, time=61.15 memory used=2112.8MB, alloc=516.3MB, time=63.73 memory used=2324.2MB, alloc=540.3MB, time=70.25 memory used=2554.1MB, alloc=564.3MB, time=77.59 memory used=2774.5MB, alloc=588.3MB, time=84.87 memory used=2967.4MB, alloc=612.3MB, time=91.27 |\^/| 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(); 1428265943 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-13 y + 11 z - x - 20, 4 x + 4 x y + 11 y z - 7, 2 4 y + 9 y z + 8 x + 2 z] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [8 x y - 2 x z + 11 z + 19, 8 x y - 3 x z + 18 y + 5 z , 2 13 x - 20 x y + 16 x z + 7 y] > Problem := [F,G]; 2 2 2 Problem := [[-13 y + 11 z - x - 20, 4 x + 4 x y + 11 y z - 7, 2 2 4 y + 9 y z + 8 x + 2 z], [8 x y - 2 x z + 11 z + 19, 2 2 2 8 x y - 3 x z + 18 y + 5 z , 13 x - 20 x y + 16 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=4.3MB, alloc=32.3MB, time=0.30 memory used=26.5MB, alloc=32.3MB, time=0.88 memory used=46.9MB, alloc=56.3MB, time=1.44 memory used=87.6MB, alloc=60.3MB, time=2.49 memory used=127.9MB, alloc=92.3MB, time=3.57 memory used=194.4MB, alloc=92.3MB, time=5.22 memory used=257.8MB, alloc=116.3MB, time=6.89 memory used=331.7MB, alloc=372.3MB, time=8.80 memory used=419.6MB, alloc=372.3MB, time=11.11 memory used=504.0MB, alloc=396.3MB, time=13.37 memory used=608.2MB, alloc=396.3MB, time=15.73 memory used=720.6MB, alloc=420.3MB, time=18.63 memory used=850.9MB, alloc=444.3MB, time=22.13 memory used=984.0MB, alloc=444.3MB, time=25.24 memory used=1113.9MB, alloc=468.3MB, time=28.91 memory used=1233.7MB, alloc=468.3MB, time=32.16 memory used=1353.7MB, alloc=492.3MB, time=35.81 memory used=1440.1MB, alloc=492.3MB, time=37.84 memory used=1549.7MB, alloc=492.3MB, time=41.22 memory used=1655.6MB, alloc=516.3MB, time=44.62 memory used=1742.2MB, alloc=516.3MB, time=47.16 memory used=1823.1MB, alloc=516.3MB, time=49.99 memory used=1893.3MB, alloc=516.3MB, time=51.91 memory used=1972.1MB, alloc=516.3MB, time=54.71 memory used=2030.1MB, alloc=516.3MB, time=56.57 memory used=2097.0MB, alloc=516.3MB, time=58.47 memory used=2170.0MB, alloc=516.3MB, time=60.99 memory used=2221.2MB, alloc=516.3MB, time=62.75 memory used=2268.7MB, alloc=540.3MB, time=64.34 memory used=2321.4MB, alloc=540.3MB, time=66.33 memory used=2371.2MB, alloc=540.3MB, time=68.47 memory used=2600.1MB, alloc=564.3MB, time=76.21 memory used=2792.2MB, alloc=588.3MB, time=82.14 memory used=2980.7MB, alloc=612.3MB, time=87.78 memory used=3148.4MB, alloc=636.3MB, time=93.27 memory used=3307.8MB, alloc=636.3MB, time=98.72 memory used=3469.6MB, alloc=636.3MB, time=103.86 memory used=3590.2MB, alloc=660.3MB, time=107.48 memory used=3726.7MB, alloc=660.3MB, time=112.46 |\^/| 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(); 1428266243 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; F := 2 2 [10 x - 13 x y + 4 x z - 11, 19 x z + 11 y - 7 y + 8, 11 x y + y z - 6 y] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [11 x y - 7 x z - 6 y z + 19 z , -12 x z - 14 y + 19 y - 20 z, -18 x y + 17 x + 5 y + 19 z] > Problem := [F,G]; Problem := [ 2 2 [10 x - 13 x y + 4 x z - 11, 19 x z + 11 y - 7 y + 8, 11 x y + y z - 6 y] 2 2 , [11 x y - 7 x z - 6 y z + 19 z , -12 x z - 14 y + 19 y - 20 z, -18 x y + 17 x + 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=4.3MB, alloc=32.3MB, time=0.31 memory used=26.0MB, alloc=32.3MB, time=0.86 memory used=45.3MB, alloc=56.3MB, time=1.39 memory used=85.4MB, alloc=60.3MB, time=2.45 memory used=124.3MB, alloc=84.3MB, time=3.50 memory used=176.8MB, alloc=84.3MB, time=4.90 memory used=234.8MB, alloc=116.3MB, time=6.57 memory used=316.3MB, alloc=116.3MB, time=8.84 memory used=398.1MB, alloc=140.3MB, time=11.14 memory used=484.9MB, alloc=396.3MB, time=13.65 memory used=591.9MB, alloc=420.3MB, time=16.65 memory used=718.5MB, alloc=444.3MB, time=20.45 memory used=869.3MB, alloc=468.3MB, time=25.01 memory used=1032.7MB, alloc=492.3MB, time=30.00 memory used=1186.0MB, alloc=492.3MB, time=34.68 memory used=1316.0MB, alloc=516.3MB, time=38.75 memory used=1427.6MB, alloc=516.3MB, time=42.44 memory used=1562.0MB, alloc=540.3MB, time=47.14 memory used=1684.5MB, alloc=540.3MB, time=51.43 memory used=1787.4MB, alloc=540.3MB, time=55.12 memory used=1866.4MB, alloc=540.3MB, time=57.75 memory used=1957.7MB, alloc=540.3MB, time=61.40 memory used=2049.5MB, alloc=564.3MB, time=65.08 memory used=2131.4MB, alloc=564.3MB, time=68.35 memory used=2219.7MB, alloc=564.3MB, time=72.07 memory used=2278.9MB, alloc=564.3MB, time=74.30 memory used=2362.1MB, alloc=564.3MB, time=78.05 memory used=2418.2MB, alloc=564.3MB, time=80.21 memory used=2472.9MB, alloc=564.3MB, time=82.25 memory used=2724.7MB, alloc=588.3MB, time=90.95 memory used=2961.2MB, alloc=612.3MB, time=99.36 memory used=3126.5MB, alloc=636.3MB, time=104.98 memory used=3288.0MB, alloc=660.3MB, time=110.68 |\^/| 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(); 1428266543 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [5 x - 6 x y - 19 y , 7 x + 10 x y + 12 y + 11 y, 2 -19 x z + 16 y - 11 y z - 19 z] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [-14 x z - 9 y + 15 y z + 19 x, 4 x - 2 y z + 19 z + 5, 2 13 y - 14 y z - 7 y] > Problem := [F,G]; 2 2 2 2 Problem := [[5 x - 6 x y - 19 y , 7 x + 10 x y + 12 y + 11 y, 2 2 -19 x z + 16 y - 11 y z - 19 z], [-14 x z - 9 y + 15 y z + 19 x, 2 2 2 4 x - 2 y z + 19 z + 5, 13 y - 14 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=0.31 memory used=26.4MB, alloc=32.3MB, time=0.87 memory used=47.2MB, alloc=32.3MB, time=1.41 memory used=65.6MB, alloc=56.3MB, time=1.91 memory used=105.3MB, alloc=60.3MB, time=2.96 memory used=144.3MB, alloc=84.3MB, time=4.02 memory used=207.1MB, alloc=92.3MB, time=5.72 memory used=266.8MB, alloc=116.3MB, time=7.36 memory used=349.5MB, alloc=140.3MB, time=9.65 memory used=425.5MB, alloc=396.3MB, time=11.82 memory used=536.0MB, alloc=420.3MB, time=14.75 memory used=670.1MB, alloc=444.3MB, time=18.52 memory used=818.7MB, alloc=468.3MB, time=22.62 memory used=933.6MB, alloc=468.3MB, time=25.97 memory used=1074.4MB, alloc=492.3MB, time=30.31 memory used=1174.0MB, alloc=492.3MB, time=33.45 memory used=1317.6MB, alloc=516.3MB, time=38.51 memory used=1427.0MB, alloc=516.3MB, time=42.02 memory used=1539.3MB, alloc=516.3MB, time=45.78 memory used=1646.2MB, alloc=516.3MB, time=49.58 memory used=1727.2MB, alloc=516.3MB, time=52.32 memory used=1817.4MB, alloc=540.3MB, time=55.63 memory used=1891.8MB, alloc=540.3MB, time=58.12 memory used=1967.3MB, alloc=540.3MB, time=60.85 memory used=2046.2MB, alloc=540.3MB, time=63.92 memory used=2114.6MB, alloc=540.3MB, time=66.74 memory used=2177.5MB, alloc=540.3MB, time=69.27 memory used=2231.2MB, alloc=540.3MB, time=71.27 memory used=2285.6MB, alloc=540.3MB, time=73.57 memory used=2516.5MB, alloc=564.3MB, time=80.65 memory used=2759.6MB, alloc=588.3MB, time=89.49 memory used=2960.8MB, alloc=612.3MB, time=95.67 memory used=3155.7MB, alloc=636.3MB, time=102.36 |\^/| 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(); 1428266843 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-12 x z + 10 y + 2 y z + 15 y, -8 x - 17 x z + 7 y z + 17, 2 2 -5 x - 10 y + 6 y z - 13 y] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [3 x z - 16 y z - 15 z + x, 5 x - 16 x - 9 y + 5, -4 y z - 7 x + 8 y + 19 z] > Problem := [F,G]; 2 2 Problem := [[-12 x z + 10 y + 2 y z + 15 y, -8 x - 17 x z + 7 y z + 17, 2 2 2 -5 x - 10 y + 6 y z - 13 y], [3 x z - 16 y z - 15 z + x, 2 5 x - 16 x - 9 y + 5, -4 y z - 7 x + 8 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=4.3MB, alloc=32.3MB, time=0.31 memory used=26.2MB, alloc=32.3MB, time=0.89 memory used=46.7MB, alloc=32.3MB, time=1.45 memory used=66.2MB, alloc=56.3MB, time=2.00 memory used=106.7MB, alloc=60.3MB, time=3.08 memory used=146.4MB, alloc=84.3MB, time=4.15 memory used=208.4MB, alloc=92.3MB, time=5.88 memory used=270.3MB, alloc=116.3MB, time=7.56 memory used=347.7MB, alloc=116.3MB, time=9.62 memory used=415.6MB, alloc=396.3MB, time=11.51 memory used=525.4MB, alloc=396.3MB, time=14.45 memory used=631.4MB, alloc=420.3MB, time=17.49 memory used=761.8MB, alloc=444.3MB, time=21.19 memory used=911.4MB, alloc=468.3MB, time=25.82 memory used=1035.3MB, alloc=492.3MB, time=29.38 memory used=1151.2MB, alloc=492.3MB, time=32.79 memory used=1253.6MB, alloc=492.3MB, time=35.86 memory used=1363.4MB, alloc=492.3MB, time=39.28 memory used=1466.3MB, alloc=516.3MB, time=42.77 memory used=1564.4MB, alloc=516.3MB, time=46.08 memory used=1646.8MB, alloc=516.3MB, time=48.72 memory used=1725.4MB, alloc=516.3MB, time=51.31 memory used=1797.1MB, alloc=516.3MB, time=53.95 memory used=1863.2MB, alloc=516.3MB, time=56.57 memory used=1914.7MB, alloc=516.3MB, time=58.10 memory used=1970.0MB, alloc=540.3MB, time=60.00 memory used=2039.6MB, alloc=540.3MB, time=62.92 memory used=2079.7MB, alloc=540.3MB, time=64.42 memory used=2295.7MB, alloc=564.3MB, time=70.89 memory used=2496.3MB, alloc=588.3MB, time=77.68 memory used=2666.3MB, alloc=612.3MB, time=83.41 memory used=2840.7MB, alloc=636.3MB, time=89.13 memory used=3014.2MB, alloc=660.3MB, time=96.02 memory used=3188.6MB, alloc=660.3MB, time=102.15 memory used=3340.8MB, alloc=660.3MB, time=107.83 memory used=3486.3MB, alloc=684.3MB, time=113.20 memory used=3610.0MB, alloc=684.3MB, time=118.26 |\^/| 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(); 1428267143 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; F := [ 2 2 2 2 2 -9 x y - 9 y + z + 8 x, -6 x y + 6 y + 8 y z - 1, 5 x + 7 y - 19 y + 8 ] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [-12 y - 10 y z - 14 x - 2, -20 x - 3 y + 18 x + 14, 2 5 x + 17 x z + 18 x - 6 y] > Problem := [F,G]; Problem := [[ 2 2 2 2 2 -9 x y - 9 y + z + 8 x, -6 x y + 6 y + 8 y z - 1, 5 x + 7 y - 19 y + 8 2 2 2 ], [-12 y - 10 y z - 14 x - 2, -20 x - 3 y + 18 x + 14, 2 5 x + 17 x z + 18 x - 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=4.3MB, alloc=32.3MB, time=0.31 memory used=26.6MB, alloc=32.3MB, time=0.90 memory used=47.3MB, alloc=32.3MB, time=1.43 memory used=66.4MB, alloc=56.3MB, time=1.97 memory used=107.6MB, alloc=60.3MB, time=3.08 memory used=147.5MB, alloc=60.3MB, time=4.15 memory used=186.0MB, alloc=84.3MB, time=5.22 memory used=233.6MB, alloc=84.3MB, time=6.56 memory used=295.1MB, alloc=116.3MB, time=8.31 memory used=366.3MB, alloc=372.3MB, time=10.39 memory used=450.1MB, alloc=396.3MB, time=12.84 memory used=557.9MB, alloc=396.3MB, time=15.94 memory used=667.5MB, alloc=420.3MB, time=19.13 memory used=799.1MB, alloc=444.3MB, time=23.11 memory used=940.7MB, alloc=444.3MB, time=27.35 memory used=1079.4MB, alloc=468.3MB, time=31.61 memory used=1201.3MB, alloc=468.3MB, time=35.25 memory used=1314.1MB, alloc=492.3MB, time=38.62 memory used=1448.8MB, alloc=492.3MB, time=43.19 memory used=1539.3MB, alloc=492.3MB, time=45.79 memory used=1645.8MB, alloc=516.3MB, time=49.31 memory used=1748.6MB, alloc=516.3MB, time=52.70 memory used=1835.7MB, alloc=516.3MB, time=55.17 memory used=1931.2MB, alloc=516.3MB, time=58.13 memory used=2005.2MB, alloc=516.3MB, time=60.48 memory used=2074.4MB, alloc=516.3MB, time=62.77 memory used=2159.2MB, alloc=540.3MB, time=65.67 memory used=2233.9MB, alloc=540.3MB, time=68.43 memory used=2316.7MB, alloc=540.3MB, time=71.51 memory used=2403.6MB, alloc=564.3MB, time=74.74 memory used=2494.5MB, alloc=564.3MB, time=77.92 memory used=2571.0MB, alloc=564.3MB, time=80.82 memory used=2647.7MB, alloc=588.3MB, time=83.71 memory used=2735.7MB, alloc=588.3MB, time=86.59 memory used=2846.9MB, alloc=588.3MB, time=89.91 memory used=2945.4MB, alloc=612.3MB, time=93.19 memory used=3025.5MB, alloc=612.3MB, time=96.23 memory used=3098.5MB, alloc=612.3MB, time=98.94 memory used=3180.8MB, alloc=612.3MB, time=102.01 memory used=3259.3MB, alloc=636.3MB, time=105.24 memory used=3521.6MB, alloc=660.3MB, time=113.74 |\^/| 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(); 1428267443 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [x y + 20 y - 6 x - 16 y, 11 x + 15 x y - 16 y z, 2 4 x z - 10 y z + 19 z + 13 z] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-14 x y + 6 x z + 12 y z + 14 z, -10 x + 12 x z - 19 y - 12, 14 x y + 20 y - 12 z - 20] > Problem := [F,G]; 2 2 Problem := [[x y + 20 y - 6 x - 16 y, 11 x + 15 x y - 16 y z, 2 4 x z - 10 y z + 19 z + 13 z], [-14 x y + 6 x z + 12 y z + 14 z, 2 2 -10 x + 12 x z - 19 y - 12, 14 x y + 20 y - 12 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=4.3MB, alloc=32.3MB, time=0.31 memory used=26.2MB, alloc=32.3MB, time=0.87 memory used=45.8MB, alloc=56.3MB, time=1.42 memory used=86.4MB, alloc=60.3MB, time=2.50 memory used=126.2MB, alloc=60.3MB, time=3.56 memory used=164.6MB, alloc=84.3MB, time=4.61 memory used=223.6MB, alloc=92.3MB, time=6.29 memory used=283.6MB, alloc=116.3MB, time=7.91 memory used=365.0MB, alloc=140.3MB, time=10.15 memory used=452.2MB, alloc=396.3MB, time=12.67 memory used=559.8MB, alloc=420.3MB, time=15.62 memory used=689.7MB, alloc=444.3MB, time=19.39 memory used=828.8MB, alloc=468.3MB, time=23.49 memory used=947.9MB, alloc=468.3MB, time=27.09 memory used=1100.4MB, alloc=492.3MB, time=31.96 memory used=1222.8MB, alloc=492.3MB, time=35.84 memory used=1339.7MB, alloc=516.3MB, time=39.67 memory used=1448.4MB, alloc=516.3MB, time=43.35 memory used=1526.3MB, alloc=516.3MB, time=46.03 memory used=1612.1MB, alloc=516.3MB, time=48.90 memory used=1691.7MB, alloc=516.3MB, time=51.81 memory used=1768.4MB, alloc=516.3MB, time=54.42 memory used=1839.3MB, alloc=516.3MB, time=57.10 memory used=1908.0MB, alloc=540.3MB, time=59.57 memory used=1971.0MB, alloc=540.3MB, time=62.01 memory used=2039.6MB, alloc=540.3MB, time=64.87 memory used=2259.5MB, alloc=564.3MB, time=72.75 memory used=2480.8MB, alloc=588.3MB, time=80.57 memory used=2718.1MB, alloc=612.3MB, time=89.44 memory used=2900.1MB, alloc=636.3MB, time=95.83 memory used=3059.7MB, alloc=660.3MB, time=101.52 memory used=3265.0MB, alloc=684.3MB, time=110.04 memory used=3424.1MB, alloc=708.3MB, time=116.16 memory used=3552.8MB, alloc=708.3MB, time=121.63 |\^/| 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(); 1428267743 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [6 x y + 7 x z - 7 y z - 6 x, 8 x - 16 y - 11 y - 2, -20 x y - 2 y + 18 z + 20] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [6 x y - 4 y z + 3 z + 12 x, 18 y - x - 7 y - 11 z, 2 2 -10 x y + 15 x z + 7 y + 12 z ] > Problem := [F,G]; 2 2 Problem := [[6 x y + 7 x z - 7 y z - 6 x, 8 x - 16 y - 11 y - 2, 2 -20 x y - 2 y + 18 z + 20], [6 x y - 4 y z + 3 z + 12 x, 2 2 2 18 y - x - 7 y - 11 z, -10 x y + 15 x z + 7 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=4.3MB, alloc=32.3MB, time=0.30 memory used=26.8MB, alloc=32.3MB, time=0.90 memory used=47.1MB, alloc=56.3MB, time=1.46 memory used=89.0MB, alloc=60.3MB, time=2.55 memory used=128.9MB, alloc=84.3MB, time=3.62 memory used=166.7MB, alloc=84.3MB, time=4.65 memory used=231.1MB, alloc=92.3MB, time=6.39 memory used=295.8MB, alloc=116.3MB, time=8.09 memory used=370.5MB, alloc=116.3MB, time=10.10 memory used=445.9MB, alloc=396.3MB, time=12.28 memory used=556.0MB, alloc=396.3MB, time=15.32 memory used=666.9MB, alloc=420.3MB, time=18.28 memory used=800.4MB, alloc=444.3MB, time=21.87 memory used=936.0MB, alloc=444.3MB, time=25.35 memory used=1060.8MB, alloc=468.3MB, time=28.76 memory used=1183.4MB, alloc=468.3MB, time=32.29 memory used=1299.1MB, alloc=492.3MB, time=35.35 memory used=1409.3MB, alloc=492.3MB, time=38.63 memory used=1516.8MB, alloc=492.3MB, time=42.17 memory used=1600.2MB, alloc=492.3MB, time=44.68 memory used=1697.7MB, alloc=516.3MB, time=47.79 memory used=1788.4MB, alloc=516.3MB, time=50.96 memory used=1858.7MB, alloc=516.3MB, time=53.19 memory used=1941.8MB, alloc=516.3MB, time=56.19 memory used=2005.4MB, alloc=516.3MB, time=58.12 memory used=2071.5MB, alloc=516.3MB, time=60.66 memory used=2138.2MB, alloc=516.3MB, time=63.38 memory used=2196.8MB, alloc=516.3MB, time=65.80 memory used=2242.1MB, alloc=516.3MB, time=67.53 memory used=2447.5MB, alloc=540.3MB, time=74.10 memory used=2668.2MB, alloc=564.3MB, time=81.42 memory used=2870.0MB, alloc=588.3MB, time=88.08 memory used=3050.2MB, alloc=612.3MB, time=93.86 memory used=3211.2MB, alloc=636.3MB, time=98.43 memory used=3362.8MB, alloc=660.3MB, time=103.34 memory used=3502.1MB, alloc=660.3MB, time=108.81 memory used=3617.0MB, alloc=660.3MB, time=113.42 memory used=3729.9MB, alloc=660.3MB, time=117.33 |\^/| 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(); 1428268043 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-7 x y - 9 y z + 13 z - 19 x, x z + 17 y - 5 y + 15 z, 2 x y + 7 y - 8 y - 6] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [-17 x y + 9 x - 18 z - 16, -15 x - 17 x z - 11 y z - 7, 4 x y + 15 y - 5 z + 20] > Problem := [F,G]; 2 2 Problem := [[-7 x y - 9 y z + 13 z - 19 x, x z + 17 y - 5 y + 15 z, 2 x y + 7 y - 8 y - 6], [-17 x y + 9 x - 18 z - 16, 2 -15 x - 17 x z - 11 y z - 7, 4 x y + 15 y - 5 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=4.3MB, alloc=32.3MB, time=0.30 memory used=26.5MB, alloc=32.3MB, time=0.89 memory used=46.5MB, alloc=32.3MB, time=1.41 memory used=64.2MB, alloc=56.3MB, time=1.91 memory used=104.3MB, alloc=60.3MB, time=3.01 memory used=142.5MB, alloc=84.3MB, time=4.05 memory used=206.0MB, alloc=92.3MB, time=5.79 memory used=268.5MB, alloc=116.3MB, time=7.55 memory used=345.7MB, alloc=116.3MB, time=9.68 memory used=421.4MB, alloc=396.3MB, time=11.86 memory used=529.4MB, alloc=396.3MB, time=14.92 memory used=635.0MB, alloc=420.3MB, time=18.05 memory used=765.9MB, alloc=444.3MB, time=21.91 memory used=901.6MB, alloc=468.3MB, time=25.81 memory used=1031.6MB, alloc=468.3MB, time=29.65 memory used=1147.2MB, alloc=492.3MB, time=33.12 memory used=1242.5MB, alloc=492.3MB, time=36.13 memory used=1338.2MB, alloc=492.3MB, time=39.23 memory used=1415.4MB, alloc=492.3MB, time=41.56 memory used=1501.3MB, alloc=492.3MB, time=44.60 memory used=1583.1MB, alloc=492.3MB, time=47.53 memory used=1656.6MB, alloc=492.3MB, time=50.07 memory used=1743.3MB, alloc=492.3MB, time=53.44 memory used=1807.2MB, alloc=492.3MB, time=55.76 memory used=1866.8MB, alloc=492.3MB, time=58.11 memory used=1909.7MB, alloc=492.3MB, time=59.74 memory used=1976.0MB, alloc=516.3MB, time=62.41 memory used=2042.1MB, alloc=516.3MB, time=65.24 memory used=2230.7MB, alloc=540.3MB, time=71.16 memory used=2459.3MB, alloc=564.3MB, time=79.17 memory used=2653.5MB, alloc=588.3MB, time=86.07 memory used=2860.1MB, alloc=612.3MB, time=93.94 memory used=3053.7MB, alloc=636.3MB, time=101.52 memory used=3210.1MB, alloc=636.3MB, time=107.40 memory used=3343.8MB, alloc=636.3MB, time=112.68 memory used=3486.4MB, alloc=660.3MB, time=118.30 memory used=3617.8MB, alloc=660.3MB, time=123.54 memory used=3769.8MB, alloc=660.3MB, time=130.32 |\^/| 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(); 1428268343 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [10 x + 15 x y + 3 z - 4 x, 20 x z + 3 y - 15 z + 19, 2 18 x y + 17 y z + 5 z + 2 y] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-18 x - 10 y z - 10 x + 13, -17 x - 16 x z + 14 z + 5, 2 15 x + 15 x y + 17 x z] > Problem := [F,G]; 2 2 2 Problem := [[10 x + 15 x y + 3 z - 4 x, 20 x z + 3 y - 15 z + 19, 2 2 18 x y + 17 y z + 5 z + 2 y], [-18 x - 10 y z - 10 x + 13, 2 2 -17 x - 16 x z + 14 z + 5, 15 x + 15 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=4.3MB, alloc=32.3MB, time=0.30 memory used=26.1MB, alloc=32.3MB, time=0.86 memory used=47.3MB, alloc=32.3MB, time=1.39 memory used=66.3MB, alloc=56.3MB, time=1.91 memory used=108.3MB, alloc=60.3MB, time=3.03 memory used=147.7MB, alloc=84.3MB, time=4.05 memory used=210.6MB, alloc=92.3MB, time=5.74 memory used=270.0MB, alloc=116.3MB, time=7.31 memory used=352.0MB, alloc=116.3MB, time=9.27 memory used=423.9MB, alloc=396.3MB, time=11.28 memory used=539.5MB, alloc=420.3MB, time=13.95 memory used=674.5MB, alloc=444.3MB, time=17.45 memory used=811.2MB, alloc=444.3MB, time=21.22 memory used=950.2MB, alloc=468.3MB, time=24.89 memory used=1090.1MB, alloc=492.3MB, time=29.24 memory used=1222.8MB, alloc=492.3MB, time=33.05 memory used=1324.8MB, alloc=492.3MB, time=35.91 memory used=1441.2MB, alloc=516.3MB, time=39.55 memory used=1538.7MB, alloc=516.3MB, time=42.42 memory used=1625.0MB, alloc=516.3MB, time=45.15 memory used=1717.1MB, alloc=516.3MB, time=48.18 memory used=1807.2MB, alloc=516.3MB, time=51.18 memory used=1893.2MB, alloc=516.3MB, time=54.03 memory used=1968.2MB, alloc=516.3MB, time=56.41 memory used=2039.1MB, alloc=516.3MB, time=58.94 memory used=2113.8MB, alloc=516.3MB, time=61.52 memory used=2180.0MB, alloc=516.3MB, time=63.91 memory used=2247.3MB, alloc=540.3MB, time=66.22 memory used=2310.4MB, alloc=540.3MB, time=68.59 memory used=2369.0MB, alloc=540.3MB, time=70.69 memory used=2599.2MB, alloc=564.3MB, time=77.59 memory used=2822.1MB, alloc=588.3MB, time=84.29 memory used=3070.1MB, alloc=612.3MB, time=92.65 memory used=3246.8MB, alloc=636.3MB, time=98.28 memory used=3419.9MB, alloc=660.3MB, time=103.66 memory used=3616.2MB, alloc=684.3MB, time=110.36 |\^/| 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(); 1428268643 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; F := [-9 y z - 6 x - 10 y - 10, -20 x y - 19 y z - 14 x + 2, 2 11 x z - 2 y + 10 y z + 12] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; G := [ 2 2 16 x y - 8 y z + 2 y, 6 x + 19 x z - 16 y z - 2 x, 9 y + 10 x - 15 y + 8] > Problem := [F,G]; Problem := [[-9 y z - 6 x - 10 y - 10, -20 x y - 19 y z - 14 x + 2, 2 11 x z - 2 y + 10 y z + 12], [ 2 2 16 x y - 8 y z + 2 y, 6 x + 19 x z - 16 y z - 2 x, 9 y + 10 x - 15 y + 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=0.84 memory used=46.9MB, alloc=32.3MB, time=1.35 memory used=65.6MB, alloc=56.3MB, time=1.84 memory used=103.2MB, alloc=60.3MB, time=2.82 memory used=139.9MB, alloc=84.3MB, time=3.80 memory used=198.0MB, alloc=92.3MB, time=5.36 memory used=256.8MB, alloc=116.3MB, time=6.93 memory used=337.2MB, alloc=116.3MB, time=9.12 memory used=414.9MB, alloc=140.3MB, time=11.23 memory used=500.9MB, alloc=164.3MB, time=13.57 memory used=577.0MB, alloc=420.3MB, time=15.77 memory used=704.2MB, alloc=444.3MB, time=19.32 memory used=847.8MB, alloc=468.3MB, time=23.43 memory used=1023.0MB, alloc=492.3MB, time=28.60 memory used=1219.8MB, alloc=516.3MB, time=34.41 memory used=1438.5MB, alloc=540.3MB, time=41.16 memory used=1674.9MB, alloc=564.3MB, time=48.71 memory used=1936.1MB, alloc=588.3MB, time=57.83 memory used=2219.7MB, alloc=612.3MB, time=67.58 memory used=2500.0MB, alloc=636.3MB, time=77.50 memory used=2751.4MB, alloc=660.3MB, time=86.36 memory used=2982.5MB, alloc=684.3MB, time=95.27 memory used=3207.2MB, alloc=708.3MB, time=104.08 |\^/| 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(); 1428268943 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [4 z + 12 x + 16 y - 6, 15 x y + 15 x z + 13 y + 6, 2 2 -20 y - 17 z + 6 y - 13 z] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-20 x - 7 y z + 12 z - 2, 20 x + 13 y z + 18 x - 8 y, 2 -9 x y - 13 y z - 20 z + 13 x] > Problem := [F,G]; 2 Problem := [[4 z + 12 x + 16 y - 6, 15 x y + 15 x z + 13 y + 6, 2 2 2 -20 y - 17 z + 6 y - 13 z], [-20 x - 7 y z + 12 z - 2, 2 2 20 x + 13 y z + 18 x - 8 y, -9 x y - 13 y z - 20 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=4.3MB, alloc=32.3MB, time=0.30 memory used=26.3MB, alloc=32.3MB, time=0.88 memory used=46.1MB, alloc=56.3MB, time=1.42 memory used=86.8MB, alloc=60.3MB, time=2.51 memory used=126.2MB, alloc=84.3MB, time=3.58 memory used=164.8MB, alloc=84.3MB, time=4.65 memory used=228.8MB, alloc=92.3MB, time=6.37 memory used=289.4MB, alloc=116.3MB, time=8.08 memory used=362.2MB, alloc=116.3MB, time=10.06 memory used=442.6MB, alloc=396.3MB, time=12.39 memory used=552.6MB, alloc=396.3MB, time=15.34 memory used=659.7MB, alloc=420.3MB, time=18.45 memory used=792.2MB, alloc=444.3MB, time=22.15 memory used=933.1MB, alloc=468.3MB, time=26.08 memory used=1078.6MB, alloc=492.3MB, time=30.42 memory used=1190.8MB, alloc=492.3MB, time=33.44 memory used=1312.6MB, alloc=516.3MB, time=37.03 memory used=1424.3MB, alloc=516.3MB, time=40.50 memory used=1526.2MB, alloc=516.3MB, time=43.61 memory used=1612.6MB, alloc=516.3MB, time=46.36 memory used=1704.7MB, alloc=516.3MB, time=49.29 memory used=1778.2MB, alloc=516.3MB, time=51.46 memory used=1858.6MB, alloc=516.3MB, time=54.04 memory used=1926.7MB, alloc=516.3MB, time=56.20 memory used=1967.6MB, alloc=516.3MB, time=57.52 memory used=2043.7MB, alloc=516.3MB, time=60.51 memory used=2116.7MB, alloc=516.3MB, time=63.25 memory used=2168.4MB, alloc=516.3MB, time=65.17 memory used=2212.0MB, alloc=540.3MB, time=66.74 memory used=2274.3MB, alloc=540.3MB, time=69.46 memory used=2320.5MB, alloc=540.3MB, time=71.32 memory used=2531.2MB, alloc=564.3MB, time=77.36 memory used=2735.0MB, alloc=588.3MB, time=83.63 memory used=2942.3MB, alloc=612.3MB, time=90.69 memory used=3115.4MB, alloc=636.3MB, time=96.33 memory used=3320.5MB, alloc=660.3MB, time=103.83 memory used=3486.5MB, alloc=660.3MB, time=109.86 memory used=3644.7MB, alloc=660.3MB, time=115.75 memory used=3797.4MB, alloc=660.3MB, time=121.17 memory used=3934.3MB, alloc=684.3MB, time=126.13 memory used=4076.7MB, alloc=684.3MB, time=131.48 memory used=4212.0MB, alloc=684.3MB, time=137.46 memory used=4314.2MB, alloc=684.3MB, time=141.78 |\^/| 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(); 1428269243 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-13 x y - 6 y z + 9 x + 2 z, -14 x y + 16 y - 17 z - 16 y, 2 4 y - 20 y z + x - 16 y] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [13 x y - 11 x z - 13 y - 17 y, 7 x - 16 x z - 13 z - 14 z, 10 x y + 15 x z - 5 z - 10] > Problem := [F,G]; 2 2 Problem := [[-13 x y - 6 y z + 9 x + 2 z, -14 x y + 16 y - 17 z - 16 y, 2 2 4 y - 20 y z + x - 16 y], [13 x y - 11 x z - 13 y - 17 y, 2 2 7 x - 16 x z - 13 z - 14 z, 10 x y + 15 x z - 5 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=4.3MB, alloc=32.3MB, time=0.30 memory used=26.1MB, alloc=32.3MB, time=0.88 memory used=47.1MB, alloc=32.3MB, time=1.42 memory used=66.2MB, alloc=56.3MB, time=1.95 memory used=107.7MB, alloc=60.3MB, time=3.01 memory used=148.4MB, alloc=60.3MB, time=4.07 memory used=189.9MB, alloc=92.3MB, time=5.17 memory used=254.9MB, alloc=92.3MB, time=6.80 memory used=318.5MB, alloc=92.3MB, time=8.47 memory used=379.9MB, alloc=116.3MB, time=10.12 memory used=454.0MB, alloc=116.3MB, time=12.17 memory used=510.2MB, alloc=396.3MB, time=13.67 memory used=623.1MB, alloc=420.3MB, time=16.45 memory used=754.3MB, alloc=444.3MB, time=20.26 memory used=876.5MB, alloc=444.3MB, time=23.45 memory used=992.9MB, alloc=468.3MB, time=26.44 memory used=1103.7MB, alloc=468.3MB, time=29.40 memory used=1210.1MB, alloc=468.3MB, time=32.33 memory used=1303.2MB, alloc=468.3MB, time=35.00 memory used=1417.7MB, alloc=468.3MB, time=38.74 memory used=1500.2MB, alloc=492.3MB, time=41.28 memory used=1577.6MB, alloc=492.3MB, time=43.69 memory used=1669.9MB, alloc=492.3MB, time=46.67 memory used=1768.4MB, alloc=492.3MB, time=50.22 memory used=1859.1MB, alloc=492.3MB, time=53.61 memory used=1936.7MB, alloc=492.3MB, time=56.51 memory used=2013.4MB, alloc=492.3MB, time=59.49 memory used=2083.8MB, alloc=492.3MB, time=62.04 memory used=2139.9MB, alloc=492.3MB, time=63.92 memory used=2208.6MB, alloc=492.3MB, time=66.48 memory used=2253.7MB, alloc=516.3MB, time=68.10 memory used=2296.9MB, alloc=516.3MB, time=69.53 memory used=2507.6MB, alloc=540.3MB, time=76.49 memory used=2704.0MB, alloc=564.3MB, time=82.24 memory used=2905.5MB, alloc=588.3MB, time=88.85 memory used=3097.4MB, alloc=612.3MB, time=95.06 memory used=3281.9MB, alloc=636.3MB, time=101.11 memory used=3476.2MB, alloc=660.3MB, time=108.97 memory used=3650.0MB, alloc=660.3MB, time=115.57 memory used=3789.7MB, alloc=684.3MB, time=120.35 memory used=3935.2MB, alloc=684.3MB, time=125.64 memory used=4053.2MB, alloc=684.3MB, time=130.20 memory used=4165.7MB, alloc=684.3MB, time=134.56 |\^/| 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(); 1428269543 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-12 x y + 10 y + 15 z - 18 x, -4 x - 9 x z + 7 x - 15 y, 2 2 20 x - 12 x y + 6 y - 19 y] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [-15 x + 20 y + 11 x - 12 y, 3 x - 14 x y + 20 x + 10, -13 y z - 6 x - y + 3] > Problem := [F,G]; 2 2 2 Problem := [[-12 x y + 10 y + 15 z - 18 x, -4 x - 9 x z + 7 x - 15 y, 2 2 2 2 20 x - 12 x y + 6 y - 19 y], [-15 x + 20 y + 11 x - 12 y, 2 3 x - 14 x y + 20 x + 10, -13 y z - 6 x - 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=0.30 memory used=26.9MB, alloc=32.3MB, time=0.89 memory used=48.2MB, alloc=32.3MB, time=1.43 memory used=68.4MB, alloc=56.3MB, time=1.97 memory used=109.5MB, alloc=60.3MB, time=3.04 memory used=148.2MB, alloc=84.3MB, time=4.09 memory used=211.4MB, alloc=92.3MB, time=5.82 memory used=273.3MB, alloc=92.3MB, time=7.48 memory used=334.0MB, alloc=116.3MB, time=9.18 memory used=418.9MB, alloc=116.3MB, time=11.52 memory used=493.5MB, alloc=140.3MB, time=13.61 memory used=572.2MB, alloc=396.3MB, time=15.97 memory used=681.6MB, alloc=420.3MB, time=19.17 memory used=813.0MB, alloc=444.3MB, time=23.12 memory used=948.6MB, alloc=468.3MB, time=27.35 memory used=1093.4MB, alloc=492.3MB, time=32.00 memory used=1258.6MB, alloc=516.3MB, time=37.18 memory used=1439.2MB, alloc=540.3MB, time=42.90 memory used=1630.9MB, alloc=564.3MB, time=49.06 memory used=1820.1MB, alloc=588.3MB, time=55.30 memory used=2002.3MB, alloc=612.3MB, time=61.32 memory used=2179.4MB, alloc=636.3MB, time=67.25 memory used=2341.3MB, alloc=660.3MB, time=72.72 memory used=2569.5MB, alloc=684.3MB, time=84.73 memory used=2799.5MB, alloc=708.3MB, time=97.88 memory used=3040.4MB, alloc=732.3MB, time=112.22 memory used=3294.9MB, alloc=756.3MB, time=127.79 |\^/| 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(); 1428269843 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [15 x z - 8 y + 5 y z + 1, -x + 2 y z + 8 z - 19 x, 2 2 18 x + 16 x y - 13 z + x] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [-20 x y + 13 x z + 18 y - 3 z , -2 y z - 17 z + 14 y - 3 z, 2 2 19 x z - 11 y + 8 z - 7 z] > Problem := [F,G]; 2 2 2 Problem := [[15 x z - 8 y + 5 y z + 1, -x + 2 y z + 8 z - 19 x, 2 2 2 2 18 x + 16 x y - 13 z + x], [-20 x y + 13 x z + 18 y - 3 z , 2 2 2 -2 y z - 17 z + 14 y - 3 z, 19 x z - 11 y + 8 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=0.30 memory used=25.0MB, alloc=32.3MB, time=0.84 memory used=45.9MB, alloc=60.3MB, time=1.36 memory used=84.9MB, alloc=60.3MB, time=2.19 memory used=127.7MB, alloc=60.3MB, time=3.26 memory used=167.8MB, alloc=60.3MB, time=4.00 memory used=216.8MB, alloc=68.3MB, time=5.12 memory used=259.6MB, alloc=92.3MB, time=6.20 memory used=327.4MB, alloc=92.3MB, time=7.80 memory used=392.1MB, alloc=116.3MB, time=9.47 memory used=462.0MB, alloc=116.3MB, time=10.88 memory used=535.6MB, alloc=372.3MB, time=12.84 memory used=629.5MB, alloc=396.3MB, time=14.76 memory used=738.5MB, alloc=420.3MB, time=17.55 memory used=869.8MB, alloc=420.3MB, time=20.50 memory used=950.2MB, alloc=420.3MB, time=21.77 memory used=1091.4MB, alloc=444.3MB, time=24.57 memory used=1255.2MB, alloc=444.3MB, time=27.56 memory used=1391.1MB, alloc=468.3MB, time=30.16 memory used=1505.3MB, alloc=468.3MB, time=33.02 memory used=1594.9MB, alloc=468.3MB, time=35.45 memory used=1702.5MB, alloc=492.3MB, time=38.60 memory used=1790.4MB, alloc=492.3MB, time=40.92 memory used=1912.6MB, alloc=492.3MB, time=43.39 memory used=2023.4MB, alloc=492.3MB, time=45.72 memory used=2118.2MB, alloc=492.3MB, time=48.05 memory used=2197.7MB, alloc=492.3MB, time=50.46 memory used=2275.3MB, alloc=516.3MB, time=52.90 memory used=2332.5MB, alloc=516.3MB, time=54.69 memory used=2397.2MB, alloc=516.3MB, time=56.82 memory used=2450.3MB, alloc=516.3MB, time=58.57 memory used=2513.8MB, alloc=516.3MB, time=60.77 memory used=2568.3MB, alloc=516.3MB, time=62.79 memory used=2616.9MB, alloc=516.3MB, time=64.60 memory used=2809.8MB, alloc=516.3MB, time=68.89 memory used=3034.0MB, alloc=540.3MB, time=74.29 memory used=3245.3MB, alloc=564.3MB, time=80.37 memory used=3422.9MB, alloc=588.3MB, time=85.71 memory used=3606.5MB, alloc=612.3MB, time=91.59 memory used=3784.9MB, alloc=636.3MB, time=96.41 memory used=3992.2MB, alloc=660.3MB, time=101.31 memory used=4147.2MB, alloc=660.3MB, time=106.55 memory used=4290.8MB, alloc=660.3MB, time=111.14 memory used=4509.2MB, alloc=660.3MB, time=114.80 memory used=4702.9MB, alloc=684.3MB, time=118.87 memory used=4812.2MB, alloc=684.3MB, time=122.45 memory used=4947.4MB, alloc=684.3MB, time=126.63 memory used=5083.0MB, alloc=684.3MB, time=131.40 |\^/| 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(); 1428270143 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [16 x z - 14 y - 16 x - 5 z, 13 x z - 10 x - 12 z - 8, 14 x y + 13 x z - 9 x - 7 z] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [15 x - 7 x y + 20 y - 7 y z, -12 y z - 9 x - 6, -4 x z - 19 y z - 17 z] > Problem := [F,G]; 2 Problem := [[16 x z - 14 y - 16 x - 5 z, 13 x z - 10 x - 12 z - 8, 14 x y + 13 x z - 9 x - 7 z], 2 2 [15 x - 7 x y + 20 y - 7 y z, -12 y z - 9 x - 6, -4 x z - 19 y 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=4.3MB, alloc=32.3MB, time=0.30 memory used=26.6MB, alloc=32.3MB, time=0.86 memory used=46.7MB, alloc=32.3MB, time=1.37 memory used=65.7MB, alloc=56.3MB, time=1.88 memory used=105.2MB, alloc=60.3MB, time=2.92 memory used=142.1MB, alloc=84.3MB, time=3.90 memory used=202.6MB, alloc=92.3MB, time=5.50 memory used=261.0MB, alloc=116.3MB, time=7.07 memory used=343.3MB, alloc=116.3MB, time=9.25 memory used=423.7MB, alloc=140.3MB, time=11.48 memory used=510.3MB, alloc=140.3MB, time=13.98 memory used=585.3MB, alloc=420.3MB, time=16.19 memory used=708.8MB, alloc=444.3MB, time=19.65 memory used=848.9MB, alloc=468.3MB, time=23.62 memory used=993.8MB, alloc=492.3MB, time=28.27 memory used=1127.5MB, alloc=516.3MB, time=32.20 memory used=1264.8MB, alloc=516.3MB, time=36.84 memory used=1383.6MB, alloc=516.3MB, time=40.38 memory used=1505.4MB, alloc=516.3MB, time=44.70 memory used=1594.2MB, alloc=540.3MB, time=47.75 memory used=1706.0MB, alloc=540.3MB, time=52.03 memory used=1807.1MB, alloc=540.3MB, time=55.74 memory used=1877.3MB, alloc=540.3MB, time=58.32 memory used=1987.5MB, alloc=540.3MB, time=63.06 memory used=2066.9MB, alloc=540.3MB, time=66.46 memory used=2136.4MB, alloc=540.3MB, time=69.27 memory used=2187.0MB, alloc=540.3MB, time=71.45 memory used=2225.9MB, alloc=540.3MB, time=72.95 memory used=2294.6MB, alloc=540.3MB, time=76.32 memory used=2518.5MB, alloc=564.3MB, time=84.56 memory used=2734.2MB, alloc=588.3MB, time=92.55 memory used=2946.2MB, alloc=612.3MB, time=100.25 memory used=3186.4MB, alloc=636.3MB, time=110.39 memory used=3415.5MB, alloc=660.3MB, time=121.38 |\^/| 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(); 1428270443 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-2 x + 15 y z + 14 x + 10 y, 8 x z - 5 z + 13 x + 16 y, 2 6 x y - 18 y - 20 y z + 8 x] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [-13 x + 9 x y - y + 16 y, 12 x - 13 y + 4 y z - 4 y, 2 2 -13 y + 7 z + 19 y - 2 z] > Problem := [F,G]; 2 2 Problem := [[-2 x + 15 y z + 14 x + 10 y, 8 x z - 5 z + 13 x + 16 y, 2 2 2 6 x y - 18 y - 20 y z + 8 x], [-13 x + 9 x y - y + 16 y, 2 2 2 2 12 x - 13 y + 4 y z - 4 y, -13 y + 7 z + 19 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=4.4MB, alloc=32.3MB, time=0.32 memory used=26.5MB, alloc=32.3MB, time=0.90 memory used=47.1MB, alloc=32.3MB, time=1.45 memory used=66.8MB, alloc=56.3MB, time=2.01 memory used=107.6MB, alloc=60.3MB, time=3.10 memory used=146.2MB, alloc=84.3MB, time=4.16 memory used=209.2MB, alloc=92.3MB, time=5.94 memory used=273.3MB, alloc=116.3MB, time=7.61 memory used=347.1MB, alloc=116.3MB, time=9.67 memory used=418.7MB, alloc=372.3MB, time=11.73 memory used=506.0MB, alloc=396.3MB, time=14.10 memory used=617.3MB, alloc=396.3MB, time=16.91 memory used=726.4MB, alloc=420.3MB, time=19.76 memory used=857.8MB, alloc=444.3MB, time=23.30 memory used=975.3MB, alloc=444.3MB, time=26.19 memory used=1084.0MB, alloc=468.3MB, time=28.90 memory used=1195.2MB, alloc=468.3MB, time=31.67 memory used=1338.1MB, alloc=492.3MB, time=35.82 memory used=1463.6MB, alloc=492.3MB, time=39.26 memory used=1578.3MB, alloc=492.3MB, time=42.56 memory used=1679.0MB, alloc=516.3MB, time=45.68 memory used=1775.5MB, alloc=516.3MB, time=48.36 memory used=1867.6MB, alloc=516.3MB, time=50.98 memory used=1959.1MB, alloc=516.3MB, time=53.91 memory used=2032.0MB, alloc=516.3MB, time=55.99 memory used=2127.7MB, alloc=516.3MB, time=59.19 memory used=2218.1MB, alloc=516.3MB, time=62.49 memory used=2298.0MB, alloc=540.3MB, time=65.07 memory used=2377.5MB, alloc=540.3MB, time=68.07 memory used=2432.5MB, alloc=540.3MB, time=69.94 memory used=2486.5MB, alloc=540.3MB, time=71.78 memory used=2554.9MB, alloc=540.3MB, time=74.32 memory used=2611.9MB, alloc=540.3MB, time=76.18 memory used=2670.0MB, alloc=540.3MB, time=77.98 memory used=2722.4MB, alloc=540.3MB, time=80.33 memory used=2768.8MB, alloc=540.3MB, time=82.19 memory used=2972.7MB, alloc=564.3MB, time=88.06 memory used=3167.7MB, alloc=588.3MB, time=93.95 memory used=3345.5MB, alloc=612.3MB, time=99.34 memory used=3514.9MB, alloc=636.3MB, time=104.82 memory used=3692.7MB, alloc=636.3MB, time=110.51 memory used=3865.3MB, alloc=636.3MB, time=115.83 memory used=4026.5MB, alloc=660.3MB, time=121.34 memory used=4174.8MB, alloc=660.3MB, time=126.17 |\^/| 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(); 1428270743 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-17 x z - 19 y - 6 y z + 17, -13 x - 20 x y - 8 y - 17 y z, 2 2 -15 x z - 20 y + 3 y z - 10 z ] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [x + 4 x y - 3 x z - 10 y z, 19 y + 14 y z + 11 z - 13, 2 2 17 x - z + 6 z + 2] > Problem := [F,G]; 2 2 2 Problem := [[-17 x z - 19 y - 6 y z + 17, -13 x - 20 x y - 8 y - 17 y z, 2 2 2 -15 x z - 20 y + 3 y z - 10 z ], [x + 4 x y - 3 x z - 10 y z, 2 2 2 19 y + 14 y z + 11 z - 13, 17 x - z + 6 z + 2]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,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=26.4MB, alloc=32.3MB, time=0.91 memory used=45.6MB, alloc=56.3MB, time=1.46 memory used=85.5MB, alloc=60.3MB, time=2.56 memory used=128.3MB, alloc=68.3MB, time=3.64 memory used=168.9MB, alloc=92.3MB, time=4.72 memory used=237.8MB, alloc=92.3MB, time=6.32 memory used=301.7MB, alloc=116.3MB, time=8.01 memory used=375.6MB, alloc=116.3MB, time=9.99 memory used=436.4MB, alloc=372.3MB, time=11.48 memory used=520.5MB, alloc=396.3MB, time=13.71 memory used=629.8MB, alloc=420.3MB, time=16.46 memory used=758.3MB, alloc=444.3MB, time=19.81 memory used=889.4MB, alloc=468.3MB, time=23.21 memory used=995.6MB, alloc=468.3MB, time=25.89 memory used=1114.0MB, alloc=468.3MB, time=29.10 memory used=1213.7MB, alloc=492.3MB, time=31.50 memory used=1327.2MB, alloc=492.3MB, time=34.69 memory used=1415.0MB, alloc=492.3MB, time=37.27 memory used=1501.9MB, alloc=492.3MB, time=39.84 memory used=1586.6MB, alloc=492.3MB, time=42.48 memory used=1660.5MB, alloc=492.3MB, time=44.87 memory used=1731.6MB, alloc=492.3MB, time=46.91 memory used=1792.5MB, alloc=492.3MB, time=48.65 memory used=1858.0MB, alloc=516.3MB, time=50.88 memory used=1912.5MB, alloc=516.3MB, time=52.50 memory used=1977.5MB, alloc=516.3MB, time=54.77 memory used=2041.3MB, alloc=516.3MB, time=56.92 memory used=2108.5MB, alloc=516.3MB, time=59.40 memory used=2159.5MB, alloc=516.3MB, time=61.43 memory used=2357.1MB, alloc=540.3MB, time=66.52 memory used=2570.2MB, alloc=564.3MB, time=72.91 memory used=2752.3MB, alloc=588.3MB, time=78.01 memory used=2926.8MB, alloc=612.3MB, time=84.05 memory used=3095.7MB, alloc=636.3MB, time=89.69 memory used=3369.6MB, alloc=636.3MB, time=98.80 memory used=3514.5MB, alloc=636.3MB, time=103.56 memory used=3629.9MB, alloc=636.3MB, time=107.94 memory used=3792.4MB, alloc=660.3MB, time=114.35 memory used=3930.2MB, alloc=660.3MB, time=120.00 memory used=4037.6MB, alloc=660.3MB, time=123.94 memory used=4149.3MB, alloc=684.3MB, time=127.21 |\^/| 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(); 1428271043 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [-4 x - 19 z - 9 x - 15 y, -11 x + 17 x z + y z + 8, -4 x - 13 y - 19] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-11 x y - x + 3 z - 4, -x - 9 x z - 19 z + 16 y, -11 x z + 19 x - 3 y - 7 z] > Problem := [F,G]; Problem := [ 2 2 2 2 [-4 x - 19 z - 9 x - 15 y, -11 x + 17 x z + y z + 8, -4 x - 13 y - 19], 2 2 [-11 x y - x + 3 z - 4, -x - 9 x z - 19 z + 16 y, -11 x z + 19 x - 3 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=4.3MB, alloc=32.3MB, time=0.30 memory used=26.8MB, alloc=32.3MB, time=0.90 memory used=47.5MB, alloc=32.3MB, time=1.44 memory used=66.4MB, alloc=56.3MB, time=1.97 memory used=108.0MB, alloc=60.3MB, time=3.05 memory used=147.2MB, alloc=84.3MB, time=4.14 memory used=211.6MB, alloc=92.3MB, time=5.84 memory used=273.7MB, alloc=116.3MB, time=7.53 memory used=357.6MB, alloc=116.3MB, time=9.85 memory used=439.7MB, alloc=396.3MB, time=12.26 memory used=548.2MB, alloc=420.3MB, time=15.31 memory used=679.2MB, alloc=444.3MB, time=19.09 memory used=813.7MB, alloc=468.3MB, time=23.08 memory used=953.1MB, alloc=468.3MB, time=27.25 memory used=1084.7MB, alloc=492.3MB, time=31.17 memory used=1198.9MB, alloc=492.3MB, time=34.76 memory used=1304.7MB, alloc=516.3MB, time=38.09 memory used=1411.1MB, alloc=516.3MB, time=41.34 memory used=1503.8MB, alloc=516.3MB, time=44.64 memory used=1595.1MB, alloc=516.3MB, time=47.67 memory used=1678.8MB, alloc=516.3MB, time=50.65 memory used=1755.0MB, alloc=516.3MB, time=53.13 memory used=1829.6MB, alloc=516.3MB, time=55.85 memory used=1911.5MB, alloc=540.3MB, time=59.13 memory used=1970.2MB, alloc=540.3MB, time=61.38 memory used=2030.4MB, alloc=540.3MB, time=63.95 memory used=2068.4MB, alloc=540.3MB, time=65.59 memory used=2292.4MB, alloc=564.3MB, time=73.00 memory used=2509.9MB, alloc=588.3MB, time=80.69 memory used=2687.3MB, alloc=612.3MB, time=86.91 memory used=2869.0MB, alloc=636.3MB, time=93.82 memory used=3040.6MB, alloc=660.3MB, time=99.94 memory used=3203.8MB, alloc=660.3MB, time=106.40 memory used=3361.3MB, alloc=660.3MB, time=112.74 memory used=3499.7MB, alloc=660.3MB, time=118.29 memory used=3627.5MB, alloc=660.3MB, time=123.60 memory used=3753.1MB, alloc=660.3MB, time=128.32 memory used=3879.2MB, alloc=684.3MB, time=134.05 |\^/| 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(); 1428271343 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-19 x - 9 y - 6 y - 8, -18 y + 13 x - 5 y + 16, 2 2 -5 x + 10 y z + 4 z - 18] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [-15 x z - 20 y z - x - 15 y, -18 x - 2 x z - 15 z - 15, 2 15 x y - 18 x z + 19 y - 3] > Problem := [F,G]; 2 2 2 Problem := [[-19 x - 9 y - 6 y - 8, -18 y + 13 x - 5 y + 16, 2 2 -5 x + 10 y z + 4 z - 18], [-15 x z - 20 y z - x - 15 y, 2 2 -18 x - 2 x z - 15 z - 15, 15 x y - 18 x 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=0.30 memory used=27.0MB, alloc=32.3MB, time=0.89 memory used=47.9MB, alloc=32.3MB, time=1.43 memory used=68.2MB, alloc=56.3MB, time=1.99 memory used=110.1MB, alloc=60.3MB, time=3.09 memory used=150.5MB, alloc=60.3MB, time=4.15 memory used=190.1MB, alloc=84.3MB, time=5.20 memory used=227.6MB, alloc=84.3MB, time=6.22 memory used=292.1MB, alloc=116.3MB, time=7.83 memory used=369.6MB, alloc=372.3MB, time=9.91 memory used=457.6MB, alloc=396.3MB, time=12.12 memory used=568.2MB, alloc=420.3MB, time=15.02 memory used=702.7MB, alloc=444.3MB, time=18.71 memory used=853.2MB, alloc=468.3MB, time=23.13 memory used=986.5MB, alloc=468.3MB, time=26.92 memory used=1103.1MB, alloc=492.3MB, time=30.37 memory used=1210.8MB, alloc=492.3MB, time=33.55 memory used=1304.7MB, alloc=492.3MB, time=36.37 memory used=1408.5MB, alloc=492.3MB, time=39.55 memory used=1493.0MB, alloc=492.3MB, time=42.14 memory used=1566.1MB, alloc=492.3MB, time=44.57 memory used=1636.8MB, alloc=516.3MB, time=46.78 memory used=1713.1MB, alloc=516.3MB, time=49.51 memory used=1782.2MB, alloc=516.3MB, time=51.96 memory used=1840.4MB, alloc=516.3MB, time=53.90 memory used=1890.1MB, alloc=516.3MB, time=55.66 memory used=1937.7MB, alloc=516.3MB, time=57.42 memory used=1981.1MB, alloc=516.3MB, time=59.10 memory used=2184.9MB, alloc=540.3MB, time=65.59 memory used=2393.9MB, alloc=564.3MB, time=72.53 memory used=2599.4MB, alloc=588.3MB, time=79.54 memory used=2814.7MB, alloc=612.3MB, time=86.90 memory used=3039.7MB, alloc=636.3MB, time=94.56 memory used=3277.6MB, alloc=660.3MB, time=102.62 memory used=3531.7MB, alloc=684.3MB, time=111.13 memory used=3793.5MB, alloc=708.3MB, time=119.98 |\^/| 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(); 1428271643 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-x y - 2 x z - 16 y - 9 z , -3 x - 3 x + 3 z - 13, 2 2 x + 2 x z - 8 z - 9 z] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [-12 x y - 12 y z - 2 x + 2 z, -3 x z + 3 y - 17 y + 7 z, 13 y z + 9 x + 8 y] > Problem := [F,G]; 2 2 2 Problem := [[-x y - 2 x z - 16 y - 9 z , -3 x - 3 x + 3 z - 13, 2 2 x + 2 x z - 8 z - 9 z], [-12 x y - 12 y z - 2 x + 2 z, 2 -3 x z + 3 y - 17 y + 7 z, 13 y z + 9 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=4.4MB, alloc=32.3MB, time=0.30 memory used=26.1MB, alloc=32.3MB, time=0.86 memory used=46.3MB, alloc=56.3MB, time=1.40 memory used=88.3MB, alloc=60.3MB, time=2.46 memory used=129.6MB, alloc=60.3MB, time=3.52 memory used=170.0MB, alloc=84.3MB, time=4.60 memory used=232.5MB, alloc=92.3MB, time=6.25 memory used=293.1MB, alloc=116.3MB, time=7.91 memory used=373.6MB, alloc=116.3MB, time=10.14 memory used=446.9MB, alloc=396.3MB, time=12.20 memory used=551.0MB, alloc=396.3MB, time=15.00 memory used=656.1MB, alloc=420.3MB, time=17.98 memory used=784.2MB, alloc=444.3MB, time=21.61 memory used=936.8MB, alloc=468.3MB, time=26.09 memory used=1076.3MB, alloc=468.3MB, time=30.18 memory used=1233.7MB, alloc=492.3MB, time=35.13 memory used=1346.4MB, alloc=492.3MB, time=38.50 memory used=1462.0MB, alloc=492.3MB, time=41.97 memory used=1561.8MB, alloc=516.3MB, time=45.01 memory used=1673.5MB, alloc=516.3MB, time=48.92 memory used=1753.0MB, alloc=516.3MB, time=51.52 memory used=1854.7MB, alloc=516.3MB, time=55.35 memory used=1922.1MB, alloc=540.3MB, time=57.72 memory used=2002.0MB, alloc=540.3MB, time=60.60 memory used=2076.8MB, alloc=540.3MB, time=63.28 memory used=2134.6MB, alloc=540.3MB, time=64.95 memory used=2177.8MB, alloc=540.3MB, time=66.39 memory used=2254.1MB, alloc=540.3MB, time=69.83 memory used=2303.0MB, alloc=540.3MB, time=72.00 memory used=2523.0MB, alloc=564.3MB, time=79.85 memory used=2732.8MB, alloc=588.3MB, time=86.10 memory used=2913.8MB, alloc=612.3MB, time=91.49 memory used=3094.4MB, alloc=636.3MB, time=97.79 memory used=3273.9MB, alloc=660.3MB, time=104.29 memory used=3440.0MB, alloc=684.3MB, time=110.33 memory used=3575.2MB, alloc=684.3MB, time=114.92 memory used=3718.4MB, alloc=684.3MB, time=120.75 |\^/| 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(); 1428271943 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [8 z - 8 y - 15 z + 16, -12 x z - 10 y z + 2 x + 2 y, -7 x + 7 z + 13] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [20 x + 19 y z + 10 x + 4, -14 x y + 17 x z + 10 z + 13 z, 2 2 3 x + 6 x z - 12 y + 13 z] > Problem := [F,G]; Problem := [ 2 2 [8 z - 8 y - 15 z + 16, -12 x z - 10 y z + 2 x + 2 y, -7 x + 7 z + 13], [ 2 2 20 x + 19 y z + 10 x + 4, -14 x y + 17 x z + 10 z + 13 z, 2 2 3 x + 6 x z - 12 y + 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=0.32 memory used=26.6MB, alloc=32.3MB, time=0.90 memory used=47.3MB, alloc=36.3MB, time=1.45 memory used=66.5MB, alloc=60.3MB, time=1.98 memory used=108.1MB, alloc=60.3MB, time=3.04 memory used=149.7MB, alloc=60.3MB, time=4.10 memory used=190.5MB, alloc=92.3MB, time=5.20 memory used=253.5MB, alloc=92.3MB, time=6.81 memory used=314.8MB, alloc=116.3MB, time=8.44 memory used=389.0MB, alloc=372.3MB, time=10.46 memory used=474.6MB, alloc=396.3MB, time=12.73 memory used=584.7MB, alloc=420.3MB, time=15.61 memory used=722.7MB, alloc=444.3MB, time=19.11 memory used=842.6MB, alloc=468.3MB, time=22.16 memory used=954.5MB, alloc=468.3MB, time=25.08 memory used=1060.2MB, alloc=468.3MB, time=27.90 memory used=1152.6MB, alloc=468.3MB, time=30.40 memory used=1252.1MB, alloc=492.3MB, time=33.13 memory used=1332.4MB, alloc=492.3MB, time=35.61 memory used=1415.2MB, alloc=492.3MB, time=38.18 memory used=1486.7MB, alloc=492.3MB, time=40.34 memory used=1555.7MB, alloc=492.3MB, time=42.50 memory used=1635.2MB, alloc=492.3MB, time=45.37 memory used=1701.6MB, alloc=492.3MB, time=47.80 memory used=1769.6MB, alloc=492.3MB, time=50.33 memory used=1819.1MB, alloc=492.3MB, time=52.07 memory used=1869.7MB, alloc=492.3MB, time=54.08 memory used=2056.7MB, alloc=516.3MB, time=59.66 memory used=2262.8MB, alloc=540.3MB, time=65.78 memory used=2455.3MB, alloc=564.3MB, time=71.66 memory used=2642.6MB, alloc=588.3MB, time=77.51 memory used=2797.2MB, alloc=612.3MB, time=82.95 memory used=2945.5MB, alloc=636.3MB, time=87.70 memory used=3083.8MB, alloc=636.3MB, time=92.21 memory used=3223.2MB, alloc=660.3MB, time=97.59 memory used=3350.3MB, alloc=660.3MB, time=102.28 memory used=3463.9MB, alloc=660.3MB, time=106.47 memory used=3555.0MB, alloc=660.3MB, time=110.48 memory used=3892.7MB, alloc=684.3MB, time=120.63 memory used=4244.7MB, alloc=708.3MB, time=131.82 |\^/| 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(); 1428272243 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [3 x z + y - 3 y z - 3 x, -6 x - 6 x y - 7 x z - x, 2 2 16 x + x z + 7 y + 19 y] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [17 x y + 2 x + 11 y + 15 z, 6 x y + 7 x z + 4 y + 11 z, 2 8 x + 3 x z + 11 x - 6 z] > Problem := [F,G]; 2 2 Problem := [[3 x z + y - 3 y z - 3 x, -6 x - 6 x y - 7 x z - x, 2 2 16 x + x z + 7 y + 19 y], [17 x y + 2 x + 11 y + 15 z, 2 2 6 x y + 7 x z + 4 y + 11 z, 8 x + 3 x z + 11 x - 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=0.30 memory used=26.2MB, alloc=32.3MB, time=0.87 memory used=47.0MB, alloc=32.3MB, time=1.41 memory used=66.7MB, alloc=56.3MB, time=1.96 memory used=107.4MB, alloc=60.3MB, time=3.04 memory used=146.2MB, alloc=84.3MB, time=4.10 memory used=208.6MB, alloc=92.3MB, time=5.72 memory used=269.3MB, alloc=116.3MB, time=7.33 memory used=347.3MB, alloc=116.3MB, time=9.36 memory used=421.0MB, alloc=396.3MB, time=11.37 memory used=527.9MB, alloc=396.3MB, time=14.32 memory used=633.8MB, alloc=420.3MB, time=17.20 memory used=762.0MB, alloc=444.3MB, time=20.82 memory used=912.1MB, alloc=468.3MB, time=25.05 memory used=1039.9MB, alloc=468.3MB, time=28.75 memory used=1161.2MB, alloc=492.3MB, time=32.34 memory used=1293.8MB, alloc=492.3MB, time=36.50 memory used=1407.3MB, alloc=516.3MB, time=40.09 memory used=1517.8MB, alloc=516.3MB, time=43.64 memory used=1610.6MB, alloc=516.3MB, time=46.07 memory used=1697.9MB, alloc=516.3MB, time=48.90 memory used=1764.3MB, alloc=540.3MB, time=51.06 memory used=1821.5MB, alloc=540.3MB, time=52.70 memory used=1897.5MB, alloc=540.3MB, time=55.62 memory used=1951.9MB, alloc=540.3MB, time=57.37 memory used=2015.7MB, alloc=540.3MB, time=59.28 memory used=2083.2MB, alloc=540.3MB, time=62.02 memory used=2133.9MB, alloc=540.3MB, time=63.75 memory used=2179.1MB, alloc=540.3MB, time=65.34 memory used=2375.7MB, alloc=564.3MB, time=70.99 memory used=2595.3MB, alloc=588.3MB, time=78.11 memory used=2800.7MB, alloc=612.3MB, time=84.97 memory used=2982.4MB, alloc=636.3MB, time=91.01 memory used=3147.4MB, alloc=660.3MB, time=96.81 memory used=3308.5MB, alloc=684.3MB, time=102.48 memory used=3421.9MB, alloc=684.3MB, time=106.50 memory used=3566.7MB, alloc=684.3MB, time=111.94 memory used=3710.1MB, alloc=684.3MB, time=117.61 memory used=3827.0MB, alloc=684.3MB, time=122.23 memory used=3918.3MB, alloc=684.3MB, time=126.29 |\^/| 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(); 1428272543 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-7 x - 2 x z + 8 y z - 7 y, 6 x - 18 x z + 19 y + 12 y, 2 -19 x y - 9 x z + 6 z - 20 y] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [-12 x y - 13 y z - 4 y - 17, -4 y - 4 x - 11 y + 20 z, 2 14 y + 15 x - 6 y - 7 z] > Problem := [F,G]; 2 2 2 Problem := [[-7 x - 2 x z + 8 y z - 7 y, 6 x - 18 x z + 19 y + 12 y, 2 -19 x y - 9 x z + 6 z - 20 y], [-12 x y - 13 y z - 4 y - 17, 2 2 -4 y - 4 x - 11 y + 20 z, 14 y + 15 x - 6 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=4.3MB, alloc=32.3MB, time=0.30 memory used=26.6MB, alloc=32.3MB, time=0.89 memory used=46.9MB, alloc=56.3MB, time=1.44 memory used=88.8MB, alloc=60.3MB, time=2.53 memory used=130.7MB, alloc=92.3MB, time=3.64 memory used=196.7MB, alloc=92.3MB, time=5.24 memory used=261.4MB, alloc=116.3MB, time=6.93 memory used=341.1MB, alloc=372.3MB, time=9.03 memory used=427.7MB, alloc=396.3MB, time=11.22 memory used=536.1MB, alloc=420.3MB, time=14.18 memory used=672.2MB, alloc=444.3MB, time=17.72 memory used=795.3MB, alloc=444.3MB, time=20.91 memory used=902.5MB, alloc=468.3MB, time=23.70 memory used=1006.7MB, alloc=468.3MB, time=26.49 memory used=1119.6MB, alloc=468.3MB, time=29.81 memory used=1208.8MB, alloc=468.3MB, time=32.44 memory used=1316.4MB, alloc=468.3MB, time=35.73 memory used=1407.7MB, alloc=492.3MB, time=38.54 memory used=1493.7MB, alloc=492.3MB, time=41.35 memory used=1570.8MB, alloc=492.3MB, time=43.79 memory used=1636.3MB, alloc=492.3MB, time=46.02 memory used=1715.9MB, alloc=492.3MB, time=48.66 memory used=1781.0MB, alloc=492.3MB, time=50.91 memory used=1848.5MB, alloc=492.3MB, time=53.22 memory used=1906.2MB, alloc=492.3MB, time=55.24 memory used=1956.7MB, alloc=492.3MB, time=57.14 memory used=2016.2MB, alloc=492.3MB, time=59.41 memory used=2055.1MB, alloc=492.3MB, time=61.12 memory used=2234.2MB, alloc=516.3MB, time=66.61 memory used=2431.7MB, alloc=540.3MB, time=72.47 memory used=2592.3MB, alloc=564.3MB, time=77.47 memory used=2752.2MB, alloc=588.3MB, time=82.38 memory used=2910.8MB, alloc=612.3MB, time=87.88 memory used=3101.1MB, alloc=636.3MB, time=94.67 memory used=3249.0MB, alloc=660.3MB, time=99.12 memory used=3386.5MB, alloc=660.3MB, time=103.34 memory used=3527.6MB, alloc=684.3MB, time=108.98 memory used=3634.9MB, alloc=684.3MB, time=112.46 memory used=3780.5MB, alloc=684.3MB, time=118.53 memory used=3897.9MB, alloc=684.3MB, time=122.47 memory used=4001.7MB, alloc=684.3MB, time=127.23 memory used=4360.0MB, alloc=708.3MB, time=138.14 |\^/| 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(); 1428272843 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; F := 2 2 [4 x z + 5 z + 15 x - 5, -7 x z - 19 x - 9 y - 13 z, -7 y - 15 y z + 3 z] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [9 x y + 2 x z - y - 12 y, x - 9 x y + x - 15 z, 2 2 -7 x + 17 x y + 20 z + 8 x] > Problem := [F,G]; Problem := [ 2 2 [4 x z + 5 z + 15 x - 5, -7 x z - 19 x - 9 y - 13 z, -7 y - 15 y z + 3 z] 2 2 , [9 x y + 2 x z - y - 12 y, x - 9 x y + x - 15 z, 2 2 -7 x + 17 x y + 20 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=4.3MB, alloc=32.3MB, time=0.30 memory used=26.4MB, alloc=32.3MB, time=0.87 memory used=46.3MB, alloc=56.3MB, time=1.43 memory used=87.8MB, alloc=60.3MB, time=2.51 memory used=128.8MB, alloc=84.3MB, time=3.59 memory used=170.0MB, alloc=84.3MB, time=4.70 memory used=231.9MB, alloc=92.3MB, time=6.38 memory used=292.6MB, alloc=116.3MB, time=8.03 memory used=375.7MB, alloc=116.3MB, time=10.28 memory used=456.1MB, alloc=140.3MB, time=12.60 memory used=522.4MB, alloc=140.3MB, time=14.44 memory used=592.0MB, alloc=396.3MB, time=16.39 memory used=703.4MB, alloc=420.3MB, time=19.23 memory used=837.1MB, alloc=444.3MB, time=22.76 memory used=971.6MB, alloc=468.3MB, time=26.49 memory used=1098.9MB, alloc=492.3MB, time=30.41 memory used=1209.9MB, alloc=492.3MB, time=33.58 memory used=1321.6MB, alloc=492.3MB, time=36.86 memory used=1420.6MB, alloc=492.3MB, time=40.05 memory used=1519.5MB, alloc=492.3MB, time=43.16 memory used=1615.9MB, alloc=492.3MB, time=46.27 memory used=1698.4MB, alloc=492.3MB, time=49.14 memory used=1785.6MB, alloc=516.3MB, time=52.43 memory used=1868.7MB, alloc=516.3MB, time=55.43 memory used=1937.3MB, alloc=516.3MB, time=58.16 memory used=1994.8MB, alloc=516.3MB, time=60.16 memory used=2056.4MB, alloc=516.3MB, time=62.59 memory used=2120.2MB, alloc=516.3MB, time=65.14 memory used=2168.6MB, alloc=516.3MB, time=66.90 memory used=2374.6MB, alloc=540.3MB, time=73.95 memory used=2605.8MB, alloc=564.3MB, time=81.68 memory used=2803.7MB, alloc=588.3MB, time=88.59 memory used=2989.2MB, alloc=612.3MB, time=94.73 memory used=3173.7MB, alloc=636.3MB, time=101.41 memory used=3343.2MB, alloc=636.3MB, time=107.18 memory used=3496.7MB, alloc=660.3MB, time=113.38 memory used=3631.3MB, alloc=660.3MB, time=118.29 memory used=3789.2MB, alloc=660.3MB, time=124.31 memory used=3927.8MB, alloc=660.3MB, time=130.40 |\^/| 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(); 1428273143 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [9 x z - 14 z + 14 x + 1, -4 x - 14 x z + 17 z - 20 z, 2 14 y + 16 y z - 14 x + 13 y] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [13 x y + 14 y + 7 y z - 9 y, 20 x y - 19 y - 16 z + 1, 2 2 -4 y - 4 y z - z + 14] > Problem := [F,G]; 2 2 2 Problem := [[9 x z - 14 z + 14 x + 1, -4 x - 14 x z + 17 z - 20 z, 2 2 14 y + 16 y z - 14 x + 13 y], [13 x y + 14 y + 7 y z - 9 y, 2 2 20 x y - 19 y - 16 z + 1, -4 y - 4 y z - 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=0.31 memory used=26.5MB, alloc=32.3MB, time=0.88 memory used=46.2MB, alloc=32.3MB, time=1.40 memory used=64.1MB, alloc=56.3MB, time=1.91 memory used=103.2MB, alloc=60.3MB, time=2.96 memory used=141.9MB, alloc=84.3MB, time=4.03 memory used=203.4MB, alloc=92.3MB, time=5.71 memory used=261.5MB, alloc=116.3MB, time=7.26 memory used=342.3MB, alloc=116.3MB, time=9.37 memory used=422.2MB, alloc=140.3MB, time=11.61 memory used=509.9MB, alloc=140.3MB, time=14.07 memory used=581.2MB, alloc=396.3MB, time=15.98 memory used=685.6MB, alloc=420.3MB, time=18.95 memory used=815.9MB, alloc=444.3MB, time=22.42 memory used=971.5MB, alloc=468.3MB, time=26.71 memory used=1133.9MB, alloc=492.3MB, time=31.75 memory used=1268.7MB, alloc=492.3MB, time=35.82 memory used=1406.5MB, alloc=492.3MB, time=39.93 memory used=1541.1MB, alloc=516.3MB, time=43.55 memory used=1675.4MB, alloc=516.3MB, time=47.59 memory used=1793.8MB, alloc=540.3MB, time=51.11 memory used=1905.6MB, alloc=540.3MB, time=54.69 memory used=2023.1MB, alloc=540.3MB, time=58.71 memory used=2127.3MB, alloc=540.3MB, time=62.22 memory used=2239.2MB, alloc=540.3MB, time=66.11 memory used=2325.4MB, alloc=540.3MB, time=68.99 memory used=2413.6MB, alloc=540.3MB, time=72.12 memory used=2495.0MB, alloc=564.3MB, time=74.78 memory used=2559.3MB, alloc=564.3MB, time=77.26 memory used=2617.0MB, alloc=564.3MB, time=79.05 memory used=2693.2MB, alloc=564.3MB, time=82.19 memory used=2740.1MB, alloc=564.3MB, time=83.92 memory used=2808.5MB, alloc=564.3MB, time=86.84 memory used=2858.9MB, alloc=564.3MB, time=88.71 memory used=2919.5MB, alloc=564.3MB, time=91.24 memory used=3116.9MB, alloc=588.3MB, time=97.58 memory used=3331.1MB, alloc=612.3MB, time=104.22 memory used=3535.7MB, alloc=636.3MB, time=110.68 memory used=3746.6MB, alloc=660.3MB, 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(); 1428273443 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [2 x - 19 y - 20 x + 3 z, 11 x z - 6 z + 16 x - 13 y, -7 x y + 9 x z + 3 y z + 14 y] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-9 x + 17 x y - 2 y - 3 z, -6 y + 11 y z + y + 6 z, -x y + 10 y z - 4 y - 3 z] > Problem := [F,G]; 2 2 2 Problem := [[2 x - 19 y - 20 x + 3 z, 11 x z - 6 z + 16 x - 13 y, 2 -7 x y + 9 x z + 3 y z + 14 y], [-9 x + 17 x y - 2 y - 3 z, 2 -6 y + 11 y z + y + 6 z, -x y + 10 y z - 4 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=0.30 memory used=26.1MB, alloc=32.3MB, time=0.88 memory used=46.0MB, alloc=56.3MB, time=1.42 memory used=85.6MB, alloc=60.3MB, time=2.47 memory used=125.7MB, alloc=84.3MB, time=3.53 memory used=170.6MB, alloc=84.3MB, time=4.75 memory used=234.2MB, alloc=92.3MB, time=6.45 memory used=295.0MB, alloc=116.3MB, time=8.12 memory used=370.8MB, alloc=116.3MB, time=10.17 memory used=448.8MB, alloc=396.3MB, time=12.37 memory used=554.3MB, alloc=396.3MB, time=15.32 memory used=656.0MB, alloc=420.3MB, time=18.43 memory used=785.7MB, alloc=444.3MB, time=22.27 memory used=925.2MB, alloc=468.3MB, time=26.35 memory used=1060.8MB, alloc=468.3MB, time=30.46 memory used=1202.2MB, alloc=492.3MB, time=35.04 memory used=1317.6MB, alloc=492.3MB, time=38.70 memory used=1437.5MB, alloc=492.3MB, time=42.68 memory used=1544.6MB, alloc=492.3MB, time=46.32 memory used=1644.9MB, alloc=516.3MB, time=49.95 memory used=1757.3MB, alloc=516.3MB, time=54.33 memory used=1860.2MB, alloc=516.3MB, time=58.28 memory used=1942.2MB, alloc=516.3MB, time=61.43 memory used=2021.6MB, alloc=516.3MB, time=64.56 memory used=2085.8MB, alloc=516.3MB, time=67.07 memory used=2159.7MB, alloc=516.3MB, time=70.19 memory used=2229.9MB, alloc=516.3MB, time=73.19 memory used=2293.3MB, alloc=516.3MB, time=76.05 memory used=2344.3MB, alloc=516.3MB, time=78.17 memory used=2545.8MB, alloc=540.3MB, time=85.76 memory used=2770.3MB, alloc=564.3MB, time=94.40 memory used=3008.5MB, alloc=588.3MB, time=103.90 memory used=3227.9MB, alloc=612.3MB, time=112.62 |\^/| 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(); 1428273743 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-19 x + 15 z - 10 z + 8, -x y - 9 x z + 11 y - 11 z, 2 2 11 x + 2 x y + 17 z - 13] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [-15 x y + 15 x + 15 z - 9, -18 x - 12 x z + 17 z + 18, 2 -13 x - 15 x y + 18 x + 14 y] > Problem := [F,G]; 2 2 2 Problem := [[-19 x + 15 z - 10 z + 8, -x y - 9 x z + 11 y - 11 z, 2 2 11 x + 2 x y + 17 z - 13], [-15 x y + 15 x + 15 z - 9, 2 2 -18 x - 12 x z + 17 z + 18, -13 x - 15 x y + 18 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=4.3MB, alloc=32.3MB, time=0.30 memory used=26.6MB, alloc=32.3MB, time=0.89 memory used=47.0MB, alloc=32.3MB, time=1.41 memory used=66.0MB, alloc=56.3MB, time=1.94 memory used=106.8MB, alloc=60.3MB, time=3.00 memory used=146.9MB, alloc=84.3MB, time=4.06 memory used=210.2MB, alloc=92.3MB, time=5.73 memory used=272.7MB, alloc=92.3MB, time=7.37 memory used=333.9MB, alloc=116.3MB, time=9.02 memory used=414.4MB, alloc=372.3MB, time=11.20 memory used=496.6MB, alloc=396.3MB, time=13.49 memory used=604.9MB, alloc=420.3MB, time=16.45 memory used=732.6MB, alloc=444.3MB, time=19.98 memory used=884.1MB, alloc=444.3MB, time=24.19 memory used=1022.0MB, alloc=468.3MB, time=28.13 memory used=1158.0MB, alloc=492.3MB, time=32.14 memory used=1298.1MB, alloc=492.3MB, time=36.45 memory used=1412.2MB, alloc=492.3MB, time=39.93 memory used=1523.5MB, alloc=492.3MB, time=43.32 memory used=1633.0MB, alloc=492.3MB, time=46.69 memory used=1736.8MB, alloc=492.3MB, time=49.92 memory used=1856.2MB, alloc=516.3MB, time=54.08 memory used=1958.8MB, alloc=516.3MB, time=57.22 memory used=2045.4MB, alloc=516.3MB, time=60.12 memory used=2128.9MB, alloc=516.3MB, time=63.00 memory used=2209.9MB, alloc=516.3MB, time=65.75 memory used=2291.0MB, alloc=516.3MB, time=68.84 memory used=2367.5MB, alloc=516.3MB, time=71.74 memory used=2435.8MB, alloc=516.3MB, time=74.31 memory used=2497.4MB, alloc=516.3MB, time=76.69 memory used=2555.2MB, alloc=516.3MB, time=79.06 memory used=2619.3MB, alloc=516.3MB, time=81.63 memory used=2676.4MB, alloc=516.3MB, time=83.97 memory used=2874.2MB, alloc=540.3MB, time=90.46 memory used=3097.9MB, alloc=564.3MB, time=97.82 memory used=3325.4MB, alloc=588.3MB, time=104.86 memory used=3533.5MB, alloc=612.3MB, time=111.70 memory used=3721.8MB, alloc=636.3MB, time=118.28 memory used=3926.4MB, alloc=660.3MB, time=125.64 |\^/| 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(); 1428274043 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [x y - 5 z + 16 x - 14 y, -14 x + 14 x y + 14 x + 19, 2 2 -17 y - y z - 13 z - 12] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [-4 x z + 10 z - 8 x + 9 z, 10 y + 11 y z - 11 z - 10 x, 2 -17 y + 15 x + 18 z + 16] > Problem := [F,G]; 2 2 Problem := [[x y - 5 z + 16 x - 14 y, -14 x + 14 x y + 14 x + 19, 2 2 2 -17 y - y z - 13 z - 12], [-4 x z + 10 z - 8 x + 9 z, 2 2 2 10 y + 11 y z - 11 z - 10 x, -17 y + 15 x + 18 z + 16]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,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=26.1MB, alloc=32.3MB, time=0.88 memory used=46.4MB, alloc=56.3MB, time=1.43 memory used=88.4MB, alloc=60.3MB, time=2.52 memory used=128.7MB, alloc=60.3MB, time=3.53 memory used=167.5MB, alloc=84.3MB, time=4.56 memory used=233.6MB, alloc=92.3MB, time=6.19 memory used=299.0MB, alloc=116.3MB, time=7.93 memory used=366.9MB, alloc=116.3MB, time=9.62 memory used=431.7MB, alloc=372.3MB, time=11.44 memory used=516.5MB, alloc=396.3MB, time=13.79 memory used=629.5MB, alloc=420.3MB, time=16.58 memory used=765.0MB, alloc=444.3MB, time=20.34 memory used=899.3MB, alloc=468.3MB, time=23.99 memory used=1029.7MB, alloc=468.3MB, time=27.84 memory used=1142.0MB, alloc=468.3MB, time=30.76 memory used=1253.0MB, alloc=492.3MB, time=33.92 memory used=1359.6MB, alloc=492.3MB, time=36.91 memory used=1459.0MB, alloc=492.3MB, time=40.04 memory used=1556.9MB, alloc=492.3MB, time=43.11 memory used=1651.7MB, alloc=516.3MB, time=45.67 memory used=1745.2MB, alloc=516.3MB, time=48.30 memory used=1832.6MB, alloc=516.3MB, time=51.10 memory used=1904.5MB, alloc=516.3MB, time=53.39 memory used=1977.8MB, alloc=516.3MB, time=55.50 memory used=2037.7MB, alloc=516.3MB, time=57.47 memory used=2114.4MB, alloc=516.3MB, time=60.14 memory used=2175.7MB, alloc=516.3MB, time=62.18 memory used=2244.8MB, alloc=516.3MB, time=64.19 memory used=2300.1MB, alloc=516.3MB, time=66.12 memory used=2361.1MB, alloc=540.3MB, time=68.15 memory used=2412.5MB, alloc=540.3MB, time=69.88 memory used=2455.1MB, alloc=540.3MB, time=71.50 memory used=2683.8MB, alloc=564.3MB, time=78.25 memory used=2878.3MB, alloc=588.3MB, time=83.97 memory used=3052.9MB, alloc=612.3MB, time=89.71 memory used=3234.0MB, alloc=636.3MB, time=95.32 memory used=3393.8MB, alloc=636.3MB, time=100.78 memory used=3534.4MB, alloc=660.3MB, time=105.44 memory used=3676.0MB, alloc=660.3MB, time=110.89 memory used=3852.7MB, alloc=660.3MB, time=118.03 memory used=3974.7MB, alloc=660.3MB, time=122.29 memory used=4076.9MB, alloc=684.3MB, time=125.54 memory used=4191.8MB, alloc=684.3MB, time=130.44 memory used=4301.7MB, alloc=684.3MB, time=134.97 memory used=4391.2MB, alloc=684.3MB, time=139.16 |\^/| 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(); 1428274343 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-20 y - 16 y z + 14, -12 x - 3 x z + 5 z, 12 x y + 18 z - 20 x + 9 z] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [-8 x y - 10 x z + 3 z + 11 x, 9 x y + 13 y z - 19 z + 3, 2 2 2 -8 x - 3 x y - 12 y + 8 z ] > Problem := [F,G]; Problem := [ 2 2 2 [-20 y - 16 y z + 14, -12 x - 3 x z + 5 z, 12 x y + 18 z - 20 x + 9 z], 2 [-8 x y - 10 x z + 3 z + 11 x, 9 x y + 13 y z - 19 z + 3, 2 2 2 -8 x - 3 x y - 12 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=4.3MB, alloc=32.3MB, time=0.30 memory used=26.3MB, alloc=32.3MB, time=0.87 memory used=46.8MB, alloc=32.3MB, time=1.40 memory used=65.5MB, alloc=56.3MB, time=1.90 memory used=106.4MB, alloc=60.3MB, time=2.95 memory used=145.7MB, alloc=84.3MB, time=4.01 memory used=210.4MB, alloc=92.3MB, time=5.70 memory used=274.6MB, alloc=92.3MB, time=7.36 memory used=335.7MB, alloc=116.3MB, time=9.04 memory used=410.4MB, alloc=372.3MB, time=10.99 memory used=497.5MB, alloc=396.3MB, time=13.22 memory used=606.1MB, alloc=420.3MB, time=16.05 memory used=741.1MB, alloc=420.3MB, time=19.33 memory used=862.8MB, alloc=444.3MB, time=22.60 memory used=994.8MB, alloc=468.3MB, time=26.03 memory used=1131.6MB, alloc=492.3MB, time=30.21 memory used=1250.5MB, alloc=492.3MB, time=33.49 memory used=1354.7MB, alloc=492.3MB, time=36.21 memory used=1447.5MB, alloc=516.3MB, time=38.81 memory used=1540.6MB, alloc=516.3MB, time=41.66 memory used=1626.8MB, alloc=516.3MB, time=44.29 memory used=1704.7MB, alloc=516.3MB, time=46.57 memory used=1786.4MB, alloc=516.3MB, time=49.37 memory used=1871.8MB, alloc=516.3MB, time=52.35 memory used=1945.6MB, alloc=516.3MB, time=55.00 memory used=2020.4MB, alloc=516.3MB, time=57.66 memory used=2080.2MB, alloc=516.3MB, time=59.66 memory used=2132.2MB, alloc=516.3MB, time=61.33 memory used=2195.8MB, alloc=516.3MB, time=63.65 memory used=2249.9MB, alloc=516.3MB, time=65.66 memory used=2448.5MB, alloc=540.3MB, time=71.38 memory used=2659.9MB, alloc=564.3MB, time=78.05 memory used=2847.6MB, alloc=588.3MB, time=82.90 memory used=3054.1MB, alloc=612.3MB, time=89.68 memory used=3255.1MB, alloc=636.3MB, time=96.86 memory used=3421.3MB, alloc=660.3MB, time=102.26 memory used=3566.2MB, alloc=660.3MB, time=106.97 memory used=3708.2MB, alloc=660.3MB, time=111.46 |\^/| 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(); 1428274644 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; F := [ 2 2 2 2 2 -3 y + 9 z - 8 x - 14 z, -14 z - 5 y + 10 z - 4, 3 x + 6 y + 14 z + 15 ] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [-9 x y - 15 y z - 15 z + 15, -19 x y - 18 x z - z + 17 z, 2 7 x z - 16 y + 14 z] > Problem := [F,G]; Problem := [[ 2 2 2 2 2 -3 y + 9 z - 8 x - 14 z, -14 z - 5 y + 10 z - 4, 3 x + 6 y + 14 z + 15 2 ], [-9 x y - 15 y z - 15 z + 15, -19 x y - 18 x z - z + 17 z, 2 7 x z - 16 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=4.3MB, alloc=32.3MB, time=0.30 memory used=26.2MB, alloc=32.3MB, time=0.87 memory used=46.3MB, alloc=56.3MB, time=1.41 memory used=86.9MB, alloc=60.3MB, time=2.46 memory used=131.3MB, alloc=68.3MB, time=3.57 memory used=172.7MB, alloc=92.3MB, time=4.62 memory used=240.3MB, alloc=92.3MB, time=6.23 memory used=306.6MB, alloc=116.3MB, time=7.84 memory used=374.2MB, alloc=116.3MB, time=9.45 memory used=442.7MB, alloc=372.3MB, time=11.08 memory used=533.9MB, alloc=396.3MB, time=13.26 memory used=647.7MB, alloc=396.3MB, time=15.96 memory used=759.2MB, alloc=420.3MB, time=18.72 memory used=880.9MB, alloc=444.3MB, time=22.29 memory used=1007.8MB, alloc=468.3MB, time=25.29 memory used=1125.7MB, alloc=468.3MB, time=28.51 memory used=1229.9MB, alloc=468.3MB, time=31.00 memory used=1339.2MB, alloc=492.3MB, time=33.99 memory used=1434.1MB, alloc=492.3MB, time=36.65 memory used=1532.0MB, alloc=492.3MB, time=38.80 memory used=1625.7MB, alloc=492.3MB, time=41.48 memory used=1715.3MB, alloc=492.3MB, time=43.79 memory used=1798.0MB, alloc=516.3MB, time=46.30 memory used=1860.9MB, alloc=516.3MB, time=48.42 memory used=1926.3MB, alloc=516.3MB, time=50.15 memory used=1982.7MB, alloc=516.3MB, time=51.83 memory used=2056.8MB, alloc=516.3MB, time=53.82 memory used=2122.1MB, alloc=516.3MB, time=55.89 memory used=2176.8MB, alloc=516.3MB, time=57.40 memory used=2244.1MB, alloc=516.3MB, time=59.59 memory used=2307.4MB, alloc=516.3MB, time=61.69 memory used=2372.0MB, alloc=516.3MB, time=63.93 memory used=2415.5MB, alloc=516.3MB, time=65.60 memory used=2622.8MB, alloc=540.3MB, time=70.65 memory used=2855.0MB, alloc=564.3MB, time=77.32 memory used=3052.4MB, alloc=588.3MB, time=83.99 memory used=3239.3MB, alloc=612.3MB, time=88.53 memory used=3428.0MB, alloc=612.3MB, time=93.21 memory used=3595.8MB, alloc=636.3MB, time=98.10 memory used=3779.5MB, alloc=636.3MB, time=103.82 memory used=3958.5MB, alloc=636.3MB, time=109.45 memory used=4109.5MB, alloc=660.3MB, time=113.92 memory used=4221.9MB, alloc=660.3MB, time=118.46 |\^/| 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(); 1428274944 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [17 x y + 16 x z - 8 x - 15, 8 x z + 16 y z - 12 z + 19 y, 2 16 z + 5 x - 16 z + 3] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [-x + 20 x y - 14 x z + 18 z , x + 14 x y - 14 y z - 3 z , -16 x z - 5 x + 10 z - 16] > Problem := [F,G]; 2 Problem := [[17 x y + 16 x z - 8 x - 15, 8 x z + 16 y z - 12 z + 19 y, 2 2 2 16 z + 5 x - 16 z + 3], [-x + 20 x y - 14 x z + 18 z , 2 2 x + 14 x y - 14 y z - 3 z , -16 x z - 5 x + 10 z - 16]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,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=46.5MB, alloc=56.3MB, time=1.42 memory used=88.8MB, alloc=60.3MB, time=2.49 memory used=129.3MB, alloc=60.3MB, time=3.53 memory used=168.8MB, alloc=84.3MB, time=4.55 memory used=230.5MB, alloc=92.3MB, time=6.16 memory used=290.0MB, alloc=116.3MB, time=7.70 memory used=368.8MB, alloc=140.3MB, time=9.72 memory used=435.1MB, alloc=396.3MB, time=11.49 memory used=545.7MB, alloc=396.3MB, time=14.34 memory used=657.2MB, alloc=420.3MB, time=17.16 memory used=793.9MB, alloc=444.3MB, time=20.67 memory used=944.6MB, alloc=468.3MB, time=24.70 memory used=1082.5MB, alloc=492.3MB, time=28.64 memory used=1202.4MB, alloc=492.3MB, time=32.10 memory used=1340.4MB, alloc=492.3MB, time=36.36 memory used=1454.2MB, alloc=516.3MB, time=39.95 memory used=1563.6MB, alloc=516.3MB, time=43.42 memory used=1661.6MB, alloc=516.3MB, time=46.58 memory used=1760.5MB, alloc=516.3MB, time=49.82 memory used=1839.9MB, alloc=516.3MB, time=52.56 memory used=1919.7MB, alloc=516.3MB, time=55.34 memory used=2012.5MB, alloc=516.3MB, time=58.50 memory used=2085.1MB, alloc=516.3MB, time=61.05 memory used=2153.7MB, alloc=516.3MB, time=63.59 memory used=2221.7MB, alloc=516.3MB, time=66.09 memory used=2295.3MB, alloc=516.3MB, time=68.75 memory used=2350.6MB, alloc=516.3MB, time=70.73 memory used=2407.7MB, alloc=516.3MB, time=73.14 memory used=2464.4MB, alloc=516.3MB, time=75.32 memory used=2501.6MB, alloc=516.3MB, time=77.04 memory used=2707.8MB, alloc=540.3MB, time=83.63 memory used=2937.5MB, alloc=564.3MB, time=91.26 memory used=3176.8MB, alloc=588.3MB, time=99.16 memory used=3415.8MB, alloc=612.3MB, time=107.57 memory used=3611.6MB, alloc=636.3MB, time=114.54 |\^/| 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(); 1428275244 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-11 x - 14 x z - 3 y z + 13 z , -11 x - 17 x y + 18 y z + 4 z, 11 x z + 2 y z - 19 x + 18] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [-16 x y + 2 y + 7 z - 15 z, -6 x y + 10 z - 4 x - 10 z, -9 x y + 4 y z - x + 19 z] > Problem := [F,G]; 2 2 2 Problem := [[-11 x - 14 x z - 3 y z + 13 z , -11 x - 17 x y + 18 y z + 4 z, 2 2 11 x z + 2 y z - 19 x + 18], [-16 x y + 2 y + 7 z - 15 z, 2 -6 x y + 10 z - 4 x - 10 z, -9 x y + 4 y z - 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=0.30 memory used=26.8MB, alloc=32.3MB, time=0.90 memory used=47.6MB, alloc=32.3MB, time=1.45 memory used=66.8MB, alloc=56.3MB, time=1.99 memory used=107.0MB, alloc=60.3MB, time=3.08 memory used=145.4MB, alloc=84.3MB, time=4.11 memory used=207.4MB, alloc=92.3MB, time=5.82 memory used=268.0MB, alloc=116.3MB, time=7.54 memory used=351.2MB, alloc=116.3MB, time=9.95 memory used=424.7MB, alloc=396.3MB, time=12.02 memory used=532.2MB, alloc=396.3MB, time=15.14 memory used=638.4MB, alloc=420.3MB, time=18.21 memory used=768.2MB, alloc=444.3MB, time=21.88 memory used=919.6MB, alloc=468.3MB, time=26.46 memory used=1054.0MB, alloc=492.3MB, time=30.62 memory used=1192.8MB, alloc=492.3MB, time=34.93 memory used=1315.8MB, alloc=516.3MB, time=38.75 memory used=1415.1MB, alloc=516.3MB, time=41.27 memory used=1548.5MB, alloc=540.3MB, time=46.20 memory used=1646.0MB, alloc=540.3MB, time=49.67 memory used=1738.1MB, alloc=540.3MB, time=52.72 memory used=1837.4MB, alloc=540.3MB, time=56.20 memory used=1911.0MB, alloc=540.3MB, time=58.45 memory used=2001.2MB, alloc=540.3MB, time=61.87 memory used=2089.9MB, alloc=540.3MB, time=65.22 memory used=2151.5MB, alloc=540.3MB, time=67.46 memory used=2234.2MB, alloc=540.3MB, time=70.75 memory used=2294.5MB, alloc=540.3MB, time=72.87 memory used=2352.0MB, alloc=564.3MB, time=74.63 memory used=2408.4MB, alloc=564.3MB, time=76.46 memory used=2646.5MB, alloc=588.3MB, time=84.20 memory used=2862.7MB, alloc=612.3MB, time=91.36 memory used=3019.6MB, alloc=636.3MB, time=96.73 memory used=3195.8MB, alloc=660.3MB, time=102.58 memory used=3367.1MB, alloc=660.3MB, time=108.74 memory used=3511.4MB, alloc=660.3MB, time=114.00 memory used=3665.0MB, alloc=684.3MB, time=119.49 memory used=3809.1MB, alloc=684.3MB, time=124.90 memory used=3957.3MB, alloc=684.3MB, time=130.93 |\^/| 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(); 1428275544 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [20 x + 19 x y - 6 x - 16 z, 4 x y + 18 y z - 10 z - 11 y, 2 2 -10 x + 6 x z + 17 z + 16 x] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-9 x + 6 y z + 5 x + 11 y, -4 x y - 3 y + 7 y + 19, 2 -14 x + 13 y z - 7 x + 19] > Problem := [F,G]; 2 2 Problem := [[20 x + 19 x y - 6 x - 16 z, 4 x y + 18 y z - 10 z - 11 y, 2 2 2 -10 x + 6 x z + 17 z + 16 x], [-9 x + 6 y z + 5 x + 11 y, 2 2 -4 x y - 3 y + 7 y + 19, -14 x + 13 y z - 7 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=0.29 memory used=26.6MB, alloc=32.3MB, time=0.87 memory used=46.8MB, alloc=32.3MB, time=1.38 memory used=66.3MB, alloc=56.3MB, time=1.89 memory used=106.5MB, alloc=60.3MB, time=2.92 memory used=145.9MB, alloc=84.3MB, time=3.97 memory used=208.3MB, alloc=92.3MB, time=5.67 memory used=269.2MB, alloc=92.3MB, time=7.30 memory used=329.5MB, alloc=116.3MB, time=8.94 memory used=411.3MB, alloc=116.3MB, time=11.15 memory used=493.0MB, alloc=140.3MB, time=13.36 memory used=576.9MB, alloc=396.3MB, time=15.79 memory used=685.3MB, alloc=420.3MB, time=18.85 memory used=821.8MB, alloc=444.3MB, time=22.34 memory used=964.0MB, alloc=468.3MB, time=26.52 memory used=1085.8MB, alloc=468.3MB, time=29.84 memory used=1209.7MB, alloc=492.3MB, time=33.14 memory used=1332.8MB, alloc=492.3MB, time=36.79 memory used=1442.8MB, alloc=492.3MB, time=40.26 memory used=1542.3MB, alloc=492.3MB, time=43.47 memory used=1643.5MB, alloc=516.3MB, time=46.76 memory used=1733.9MB, alloc=516.3MB, time=49.70 memory used=1813.2MB, alloc=516.3MB, time=52.05 memory used=1903.3MB, alloc=516.3MB, time=55.42 memory used=1973.3MB, alloc=516.3MB, time=57.76 memory used=2043.1MB, alloc=516.3MB, time=60.53 memory used=2098.7MB, alloc=516.3MB, time=62.35 memory used=2160.9MB, alloc=516.3MB, time=65.15 memory used=2214.7MB, alloc=516.3MB, time=67.13 memory used=2277.1MB, alloc=516.3MB, time=69.86 memory used=2329.1MB, alloc=516.3MB, time=71.95 memory used=2539.0MB, alloc=540.3MB, time=79.07 memory used=2753.5MB, alloc=564.3MB, time=86.43 memory used=2952.9MB, alloc=588.3MB, time=92.97 memory used=3145.0MB, alloc=612.3MB, time=99.52 memory used=3329.4MB, alloc=636.3MB, time=106.98 memory used=3500.5MB, alloc=660.3MB, time=113.23 memory used=3651.6MB, alloc=660.3MB, time=118.90 |\^/| 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(); 1428275844 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [4 y z + 12 x - 15 y - 20, 2 x + 9 z + 10 x + 6 z, 2 -6 x z - 5 z - 13 x - 8] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [-15 y z - 11 x + 6 z + 7, 17 x + 4 y z - 9 y - 19, 2 12 x y + 10 y + 16 y - 5] > Problem := [F,G]; 2 2 Problem := [[4 y z + 12 x - 15 y - 20, 2 x + 9 z + 10 x + 6 z, 2 -6 x z - 5 z - 13 x - 8], [-15 y z - 11 x + 6 z + 7, 2 2 17 x + 4 y z - 9 y - 19, 12 x y + 10 y + 16 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=4.4MB, alloc=32.3MB, time=0.30 memory used=26.7MB, alloc=32.3MB, time=0.86 memory used=47.0MB, alloc=32.3MB, time=1.37 memory used=66.3MB, alloc=56.3MB, time=1.89 memory used=105.4MB, alloc=60.3MB, time=2.92 memory used=142.7MB, alloc=84.3MB, time=3.92 memory used=203.0MB, alloc=92.3MB, time=5.55 memory used=262.5MB, alloc=92.3MB, time=7.26 memory used=321.8MB, alloc=116.3MB, time=8.95 memory used=404.8MB, alloc=116.3MB, time=11.32 memory used=487.8MB, alloc=140.3MB, time=13.83 memory used=571.8MB, alloc=396.3MB, time=16.31 memory used=673.5MB, alloc=420.3MB, time=19.38 memory used=797.7MB, alloc=444.3MB, time=23.06 memory used=946.5MB, alloc=468.3MB, time=27.67 memory used=1119.1MB, alloc=492.3MB, time=33.35 memory used=1292.1MB, alloc=492.3MB, time=38.95 memory used=1449.1MB, alloc=516.3MB, time=44.34 memory used=1602.7MB, alloc=516.3MB, time=49.50 memory used=1740.9MB, alloc=540.3MB, time=54.31 memory used=1866.3MB, alloc=540.3MB, time=58.48 memory used=2002.6MB, alloc=540.3MB, time=63.15 memory used=2125.8MB, alloc=540.3MB, time=67.70 memory used=2250.2MB, alloc=540.3MB, time=72.28 memory used=2356.5MB, alloc=540.3MB, time=76.12 memory used=2448.3MB, alloc=540.3MB, time=79.55 memory used=2563.2MB, alloc=540.3MB, time=84.38 memory used=2676.7MB, alloc=564.3MB, time=89.06 memory used=2762.6MB, alloc=564.3MB, time=92.50 memory used=2851.1MB, alloc=564.3MB, time=96.25 memory used=2925.7MB, alloc=564.3MB, time=99.22 memory used=2994.7MB, alloc=564.3MB, time=102.15 memory used=3054.6MB, alloc=564.3MB, time=104.56 memory used=3097.5MB, alloc=564.3MB, time=106.52 memory used=3143.4MB, alloc=564.3MB, time=108.60 memory used=3195.8MB, alloc=564.3MB, time=110.89 memory used=3436.3MB, alloc=588.3MB, time=118.83 memory used=3668.8MB, alloc=612.3MB, time=126.68 |\^/| 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(); 1428276144 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [6 x y + x z - 13 y z - 12 z , -11 x - 14 y - 5 z - 10, 2 2 5 x + 9 y z + 9 z - 1] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [11 x y - 3 y + 17 z - 4 z, -5 y + 14 y z - 17 z - 5 z, -15 x y - 11 y z + 15 x - 13] > Problem := [F,G]; 2 2 2 Problem := [[6 x y + x z - 13 y z - 12 z , -11 x - 14 y - 5 z - 10, 2 2 2 2 5 x + 9 y z + 9 z - 1], [11 x y - 3 y + 17 z - 4 z, 2 2 -5 y + 14 y z - 17 z - 5 z, -15 x y - 11 y z + 15 x - 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 used=4.4MB, alloc=32.3MB, time=0.31 memory used=25.1MB, alloc=32.3MB, time=0.85 memory used=46.3MB, alloc=60.3MB, time=1.34 memory used=90.2MB, alloc=60.3MB, time=2.37 memory used=135.8MB, alloc=68.3MB, time=3.43 memory used=179.3MB, alloc=92.3MB, time=4.53 memory used=246.3MB, alloc=92.3MB, time=5.97 memory used=317.7MB, alloc=348.3MB, time=7.37 memory used=386.5MB, alloc=372.3MB, time=8.96 memory used=475.6MB, alloc=372.3MB, time=11.21 memory used=548.9MB, alloc=372.3MB, time=12.36 memory used=600.3MB, alloc=372.3MB, time=13.03 memory used=654.0MB, alloc=372.3MB, time=13.72 memory used=746.8MB, alloc=396.3MB, time=15.71 memory used=861.6MB, alloc=396.3MB, time=18.38 memory used=972.8MB, alloc=420.3MB, time=21.17 memory used=1101.6MB, alloc=444.3MB, time=24.36 memory used=1226.7MB, alloc=444.3MB, time=27.76 memory used=1347.7MB, alloc=468.3MB, time=31.00 memory used=1474.7MB, alloc=468.3MB, time=33.83 memory used=1590.6MB, alloc=468.3MB, time=36.58 memory used=1709.8MB, alloc=468.3MB, time=39.02 memory used=1817.6MB, alloc=492.3MB, time=41.55 memory used=1916.7MB, alloc=492.3MB, time=44.30 memory used=2003.2MB, alloc=492.3MB, time=46.83 memory used=2086.8MB, alloc=492.3MB, time=49.31 memory used=2162.2MB, alloc=492.3MB, time=51.57 memory used=2242.4MB, alloc=492.3MB, time=53.62 memory used=2320.4MB, alloc=492.3MB, time=55.96 memory used=2380.9MB, alloc=492.3MB, time=57.86 memory used=2455.7MB, alloc=516.3MB, time=60.02 memory used=2521.4MB, alloc=516.3MB, time=61.95 memory used=2591.4MB, alloc=516.3MB, time=64.65 memory used=2650.4MB, alloc=516.3MB, time=66.48 memory used=2699.1MB, alloc=516.3MB, time=68.00 memory used=2750.9MB, alloc=516.3MB, time=69.52 memory used=2806.5MB, alloc=516.3MB, time=71.42 memory used=3007.1MB, alloc=540.3MB, time=76.49 memory used=3207.5MB, alloc=564.3MB, time=80.95 memory used=3407.3MB, alloc=588.3MB, time=86.43 memory used=3639.8MB, alloc=612.3MB, time=93.87 memory used=3800.5MB, alloc=636.3MB, time=98.80 memory used=4004.6MB, alloc=660.3MB, time=103.03 memory used=4191.3MB, alloc=660.3MB, time=107.72 memory used=4336.5MB, alloc=684.3MB, time=111.47 memory used=4502.6MB, alloc=684.3MB, time=116.62 memory used=4625.1MB, alloc=684.3MB, time=120.51 memory used=4754.4MB, alloc=684.3MB, time=124.82 memory used=4859.4MB, alloc=684.3MB, time=128.32 memory used=4956.2MB, alloc=708.3MB, time=131.23 memory used=5075.5MB, alloc=708.3MB, time=135.65 |\^/| 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(); 1428276444 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [-14 x z + 10 y z - 5 x - 20, -4 x y + 17 y + 11 y z - 16 x, 2 8 x z + y - 10 x - 4 z] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [11 x y + 19 z + 14 z + 3, 4 x z - y z - 6 y - 9 z, 2 2 -3 x - 12 y + y z + 12] > Problem := [F,G]; 2 Problem := [[-14 x z + 10 y z - 5 x - 20, -4 x y + 17 y + 11 y z - 16 x, 2 2 8 x z + y - 10 x - 4 z], [11 x y + 19 z + 14 z + 3, 2 2 4 x z - y z - 6 y - 9 z, -3 x - 12 y + y z + 12]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,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=0.85 memory used=45.4MB, alloc=32.3MB, time=1.35 memory used=64.0MB, alloc=56.3MB, time=1.86 memory used=105.1MB, alloc=60.3MB, time=2.93 memory used=146.0MB, alloc=60.3MB, time=3.95 memory used=186.6MB, alloc=92.3MB, time=5.03 memory used=252.0MB, alloc=92.3MB, time=6.68 memory used=315.1MB, alloc=116.3MB, time=8.37 memory used=389.0MB, alloc=372.3MB, time=10.27 memory used=474.5MB, alloc=396.3MB, time=12.53 memory used=581.6MB, alloc=420.3MB, time=15.35 memory used=715.1MB, alloc=444.3MB, time=18.60 memory used=840.7MB, alloc=444.3MB, time=21.79 memory used=955.3MB, alloc=468.3MB, time=24.62 memory used=1083.6MB, alloc=468.3MB, time=28.26 memory used=1182.7MB, alloc=492.3MB, time=30.80 memory used=1270.8MB, alloc=492.3MB, time=33.15 memory used=1366.4MB, alloc=492.3MB, time=35.82 memory used=1456.9MB, alloc=492.3MB, time=38.75 memory used=1529.1MB, alloc=492.3MB, time=40.95 memory used=1603.0MB, alloc=492.3MB, time=43.26 memory used=1653.3MB, alloc=492.3MB, time=44.83 memory used=1706.1MB, alloc=492.3MB, time=46.70 memory used=1777.7MB, alloc=492.3MB, time=49.16 memory used=1823.8MB, alloc=492.3MB, time=50.81 memory used=1870.2MB, alloc=492.3MB, time=52.30 memory used=2058.0MB, alloc=516.3MB, time=57.81 memory used=2256.7MB, alloc=540.3MB, time=63.86 memory used=2432.6MB, alloc=564.3MB, time=69.16 memory used=2600.4MB, alloc=588.3MB, time=74.25 memory used=2743.8MB, alloc=612.3MB, time=78.70 memory used=2910.4MB, alloc=636.3MB, time=84.17 memory used=3049.6MB, alloc=636.3MB, time=88.96 memory used=3172.8MB, alloc=636.3MB, time=93.34 memory used=3299.8MB, alloc=636.3MB, time=97.64 memory used=3414.0MB, alloc=636.3MB, time=101.85 memory used=3512.6MB, alloc=660.3MB, time=106.03 memory used=3844.1MB, alloc=684.3MB, time=116.68 memory used=4191.9MB, alloc=708.3MB, time=127.45 memory used=4542.7MB, alloc=732.3MB, time=138.76 |\^/| 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(); 1428276744 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-18 x z + 12 y z + 13 z - 10 y, 2 x + 4 x y - 17 x z + 8 x, 2 -13 y - 10 y z - 5 x + 11] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [-11 x - 8 y - 20 z + 10 y, 18 x y - x z + 11 y + 4 x, 2 2 y z - 7 z - 15 x - 2 y] > Problem := [F,G]; 2 2 Problem := [[-18 x z + 12 y z + 13 z - 10 y, 2 x + 4 x y - 17 x z + 8 x, 2 2 2 2 -13 y - 10 y z - 5 x + 11], [-11 x - 8 y - 20 z + 10 y, 2 2 18 x y - x z + 11 y + 4 x, 2 y z - 7 z - 15 x - 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=4.4MB, alloc=32.3MB, time=0.30 memory used=26.6MB, alloc=32.3MB, time=0.88 memory used=47.6MB, alloc=32.3MB, time=1.43 memory used=67.0MB, alloc=56.3MB, time=1.97 memory used=109.0MB, alloc=68.3MB, time=3.07 memory used=149.5MB, alloc=92.3MB, time=4.15 memory used=217.0MB, alloc=92.3MB, time=5.76 memory used=280.8MB, alloc=116.3MB, time=7.38 memory used=352.2MB, alloc=116.3MB, time=9.17 memory used=420.8MB, alloc=372.3MB, time=10.90 memory used=505.2MB, alloc=396.3MB, time=13.14 memory used=615.3MB, alloc=420.3MB, time=15.99 memory used=742.8MB, alloc=444.3MB, time=19.45 memory used=886.4MB, alloc=468.3MB, time=23.17 memory used=1017.8MB, alloc=468.3MB, time=26.89 memory used=1143.8MB, alloc=492.3MB, time=30.25 memory used=1243.7MB, alloc=492.3MB, time=32.85 memory used=1333.9MB, alloc=492.3MB, time=35.13 memory used=1428.7MB, alloc=492.3MB, time=37.85 memory used=1527.4MB, alloc=492.3MB, time=40.72 memory used=1612.3MB, alloc=516.3MB, time=42.94 memory used=1704.2MB, alloc=516.3MB, time=45.66 memory used=1776.9MB, alloc=516.3MB, time=47.75 memory used=1860.1MB, alloc=516.3MB, time=50.35 memory used=1925.9MB, alloc=516.3MB, time=52.58 memory used=1992.1MB, alloc=516.3MB, time=54.98 memory used=2051.4MB, alloc=516.3MB, time=57.01 memory used=2113.0MB, alloc=516.3MB, time=59.18 memory used=2158.0MB, alloc=516.3MB, time=60.86 memory used=2208.8MB, alloc=516.3MB, time=62.54 memory used=2424.7MB, alloc=540.3MB, time=68.13 memory used=2645.1MB, alloc=564.3MB, time=75.47 memory used=2844.7MB, alloc=588.3MB, time=81.24 memory used=3021.0MB, alloc=612.3MB, time=86.47 memory used=3203.7MB, alloc=636.3MB, time=92.65 memory used=3374.4MB, alloc=660.3MB, time=97.37 memory used=3524.0MB, alloc=660.3MB, time=101.46 memory used=3682.2MB, alloc=660.3MB, time=106.30 memory used=3825.9MB, alloc=660.3MB, time=111.18 memory used=3966.0MB, alloc=684.3MB, time=116.01 memory used=4100.0MB, alloc=684.3MB, time=121.27 memory used=4224.2MB, alloc=684.3MB, time=126.29 memory used=4329.5MB, alloc=684.3MB, time=130.69 memory used=4415.1MB, alloc=684.3MB, time=134.35 memory used=4765.1MB, alloc=708.3MB, time=146.58 |\^/| 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(); 1428277044 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [19 y + 15 y z - 9 z , 15 x y - 7 x - 12 y + 6, 2 -7 x - 2 x z + 2 y z - 10 z] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [16 x z + y - 18 y z - 15 z, 15 x y - 13 x z + 11 z + 17 x, 11 x y + 15 y z + 5 y + 12] > Problem := [F,G]; 2 2 Problem := [[19 y + 15 y z - 9 z , 15 x y - 7 x - 12 y + 6, 2 2 -7 x - 2 x z + 2 y z - 10 z], [16 x z + y - 18 y z - 15 z, 2 15 x y - 13 x z + 11 z + 17 x, 11 x y + 15 y z + 5 y + 12]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,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=0.90 memory used=47.4MB, alloc=32.3MB, time=1.44 memory used=66.5MB, alloc=56.3MB, time=1.96 memory used=107.6MB, alloc=60.3MB, time=3.05 memory used=147.0MB, alloc=84.3MB, time=4.09 memory used=207.9MB, alloc=92.3MB, time=5.77 memory used=270.4MB, alloc=116.3MB, time=7.45 memory used=352.1MB, alloc=116.3MB, time=9.62 memory used=421.6MB, alloc=396.3MB, time=11.50 memory used=530.9MB, alloc=396.3MB, time=14.44 memory used=637.2MB, alloc=420.3MB, time=17.41 memory used=767.5MB, alloc=444.3MB, time=21.11 memory used=904.7MB, alloc=468.3MB, time=25.07 memory used=1025.0MB, alloc=468.3MB, time=28.60 memory used=1137.3MB, alloc=492.3MB, time=31.81 memory used=1257.3MB, alloc=492.3MB, time=35.38 memory used=1355.1MB, alloc=492.3MB, time=37.97 memory used=1437.3MB, alloc=492.3MB, time=40.49 memory used=1533.1MB, alloc=492.3MB, time=43.30 memory used=1621.2MB, alloc=516.3MB, time=46.19 memory used=1707.4MB, alloc=516.3MB, time=48.84 memory used=1780.1MB, alloc=516.3MB, time=51.11 memory used=1852.9MB, alloc=516.3MB, time=53.68 memory used=1922.3MB, alloc=516.3MB, time=55.90 memory used=1986.4MB, alloc=516.3MB, time=58.08 memory used=2061.5MB, alloc=516.3MB, time=61.00 memory used=2115.6MB, alloc=516.3MB, time=62.81 memory used=2176.5MB, alloc=516.3MB, time=65.17 memory used=2236.9MB, alloc=540.3MB, time=67.58 memory used=2454.8MB, alloc=564.3MB, time=74.45 memory used=2632.0MB, alloc=588.3MB, time=79.64 memory used=2840.4MB, alloc=612.3MB, time=86.74 memory used=3009.6MB, alloc=636.3MB, time=92.02 memory used=3191.4MB, alloc=660.3MB, time=98.51 memory used=3340.7MB, alloc=660.3MB, time=103.46 memory used=3482.3MB, alloc=660.3MB, time=108.56 memory used=3613.8MB, alloc=660.3MB, time=113.40 memory used=3739.0MB, alloc=660.3MB, time=117.99 memory used=3865.6MB, alloc=660.3MB, time=122.96 memory used=3985.3MB, alloc=684.3MB, time=127.64 memory used=4103.3MB, alloc=684.3MB, time=132.79 memory used=4445.4MB, alloc=708.3MB, time=143.16 |\^/| 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(); 1428277344 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [14 x z - y + 8 y + 4, -16 x + 9 x y - 7 x, -19 y z - 9 x + 14 z + 4] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [-6 x + 9 z + 19 x - 3 z, -13 x - 4 y - 17 y z + 13, 2 2 20 y + 5 z + 12 x + 12] > Problem := [F,G]; Problem := [ 2 2 [14 x z - y + 8 y + 4, -16 x + 9 x y - 7 x, -19 y z - 9 x + 14 z + 4], [ 2 2 2 2 -6 x + 9 z + 19 x - 3 z, -13 x - 4 y - 17 y z + 13, 2 2 20 y + 5 z + 12 x + 12]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,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=0.87 memory used=47.5MB, alloc=32.3MB, time=1.41 memory used=67.1MB, alloc=56.3MB, time=1.94 memory used=107.5MB, alloc=60.3MB, time=2.97 memory used=145.8MB, alloc=84.3MB, time=3.98 memory used=210.1MB, alloc=92.3MB, time=5.60 memory used=275.2MB, alloc=116.3MB, time=7.16 memory used=353.1MB, alloc=116.3MB, time=9.13 memory used=426.5MB, alloc=372.3MB, time=10.95 memory used=512.3MB, alloc=396.3MB, time=13.11 memory used=620.3MB, alloc=420.3MB, time=15.94 memory used=751.0MB, alloc=444.3MB, time=19.33 memory used=885.5MB, alloc=444.3MB, time=22.82 memory used=1014.4MB, alloc=468.3MB, time=26.36 memory used=1134.8MB, alloc=468.3MB, time=29.24 memory used=1247.6MB, alloc=468.3MB, time=32.02 memory used=1358.7MB, alloc=492.3MB, time=35.16 memory used=1450.7MB, alloc=492.3MB, time=37.61 memory used=1552.3MB, alloc=492.3MB, time=40.12 memory used=1643.4MB, alloc=492.3MB, time=42.54 memory used=1736.2MB, alloc=516.3MB, time=45.40 memory used=1794.6MB, alloc=516.3MB, time=47.26 memory used=1882.5MB, alloc=516.3MB, time=49.99 memory used=1956.5MB, alloc=516.3MB, time=52.10 memory used=2029.5MB, alloc=516.3MB, time=54.30 memory used=2096.9MB, alloc=516.3MB, time=56.63 memory used=2166.7MB, alloc=516.3MB, time=59.18 memory used=2222.1MB, alloc=516.3MB, time=61.07 memory used=2296.3MB, alloc=516.3MB, time=63.68 memory used=2346.3MB, alloc=516.3MB, time=65.53 memory used=2402.7MB, alloc=516.3MB, time=67.21 memory used=2451.7MB, alloc=516.3MB, time=68.91 memory used=2507.1MB, alloc=516.3MB, time=71.19 memory used=2707.6MB, alloc=540.3MB, time=77.15 memory used=2910.7MB, alloc=564.3MB, time=82.90 memory used=3069.2MB, alloc=588.3MB, time=87.51 memory used=3256.0MB, alloc=612.3MB, time=93.15 memory used=3426.6MB, alloc=636.3MB, time=98.70 memory used=3569.0MB, alloc=636.3MB, time=103.17 memory used=3719.8MB, alloc=660.3MB, time=107.42 memory used=3846.5MB, alloc=660.3MB, time=111.02 memory used=3985.5MB, alloc=660.3MB, time=115.64 memory used=4137.0MB, alloc=684.3MB, time=120.72 memory used=4255.7MB, alloc=684.3MB, time=125.14 memory used=4375.0MB, alloc=684.3MB, time=129.64 memory used=4460.1MB, alloc=684.3MB, time=132.66 |\^/| 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(); 1428277644 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [3 y z - 4 z - 6 y + 15 z, -14 x - 14 x z - 14 y z - 5 z, 2 -8 x + 16 x z + 19 y z] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [-18 x + 2 x y + 10 x z + 10, -x - 5 x z - 11 y z + 3 z , 2 2 x - 17 x z + 14 z + 11 z] > Problem := [F,G]; 2 2 Problem := [[3 y z - 4 z - 6 y + 15 z, -14 x - 14 x z - 14 y z - 5 z, 2 2 -8 x + 16 x z + 19 y z], [-18 x + 2 x y + 10 x z + 10, 2 2 2 2 -x - 5 x z - 11 y z + 3 z , x - 17 x z + 14 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=0.30 memory used=26.2MB, alloc=32.3MB, time=0.86 memory used=46.7MB, alloc=32.3MB, time=1.37 memory used=66.6MB, alloc=56.3MB, time=1.91 memory used=107.7MB, alloc=60.3MB, time=2.96 memory used=146.3MB, alloc=84.3MB, time=4.00 memory used=208.5MB, alloc=92.3MB, time=5.64 memory used=269.5MB, alloc=116.3MB, time=7.28 memory used=347.7MB, alloc=116.3MB, time=9.39 memory used=428.2MB, alloc=140.3MB, time=11.69 memory used=488.1MB, alloc=140.3MB, time=13.20 memory used=554.7MB, alloc=396.3MB, time=15.10 memory used=667.6MB, alloc=420.3MB, time=17.89 memory used=800.9MB, alloc=444.3MB, time=21.41 memory used=942.3MB, alloc=468.3MB, time=25.41 memory used=1066.2MB, alloc=468.3MB, time=28.85 memory used=1167.0MB, alloc=492.3MB, time=31.79 memory used=1284.3MB, alloc=492.3MB, time=35.45 memory used=1387.4MB, alloc=492.3MB, time=38.66 memory used=1486.4MB, alloc=492.3MB, time=41.63 memory used=1570.1MB, alloc=516.3MB, time=44.36 memory used=1658.9MB, alloc=516.3MB, time=47.51 memory used=1738.0MB, alloc=516.3MB, time=50.33 memory used=1820.6MB, alloc=516.3MB, time=53.34 memory used=1893.9MB, alloc=516.3MB, time=55.99 memory used=1956.3MB, alloc=516.3MB, time=58.29 memory used=2023.7MB, alloc=516.3MB, time=61.08 memory used=2069.8MB, alloc=516.3MB, time=62.91 memory used=2284.1MB, alloc=540.3MB, time=70.04 memory used=2492.7MB, alloc=564.3MB, time=77.08 memory used=2684.6MB, alloc=588.3MB, time=83.97 memory used=2872.7MB, alloc=612.3MB, time=90.92 memory used=3021.9MB, alloc=636.3MB, time=96.42 memory used=3200.9MB, alloc=636.3MB, time=103.49 memory used=3352.0MB, alloc=660.3MB, time=109.06 memory used=3505.7MB, alloc=660.3MB, time=115.85 memory used=3665.4MB, alloc=660.3MB, time=122.65 |\^/| 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(); 1428277944 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-12 x y + 20 y + 7 y z + 5 x, 5 x - 4 y z - 5 y + 2 z, 2 3 x + 9 x y + 12 x - 18 y] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-11 x y + 5 y + 7 y - 7, -12 y - 10 x - 17 y + 20, 6 x y - 18 x z - 20 y - 20] > Problem := [F,G]; 2 2 Problem := [[-12 x y + 20 y + 7 y z + 5 x, 5 x - 4 y z - 5 y + 2 z, 2 2 3 x + 9 x y + 12 x - 18 y], [-11 x y + 5 y + 7 y - 7, 2 -12 y - 10 x - 17 y + 20, 6 x y - 18 x z - 20 y - 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=4.3MB, alloc=32.3MB, time=0.31 memory used=26.9MB, alloc=32.3MB, time=0.90 memory used=48.1MB, alloc=32.3MB, time=1.46 memory used=67.8MB, alloc=56.3MB, time=1.99 memory used=108.1MB, alloc=60.3MB, time=3.03 memory used=146.9MB, alloc=84.3MB, time=4.08 memory used=207.9MB, alloc=92.3MB, time=5.73 memory used=267.9MB, alloc=92.3MB, time=7.34 memory used=328.0MB, alloc=116.3MB, time=8.97 memory used=409.7MB, alloc=116.3MB, time=11.17 memory used=483.7MB, alloc=140.3MB, time=13.25 memory used=579.6MB, alloc=420.3MB, time=16.27 memory used=695.2MB, alloc=444.3MB, time=19.81 memory used=823.6MB, alloc=468.3MB, time=23.78 memory used=966.4MB, alloc=492.3MB, time=28.13 memory used=1125.1MB, alloc=516.3MB, time=33.00 memory used=1297.0MB, alloc=540.3MB, time=38.40 memory used=1481.3MB, alloc=564.3MB, time=44.22 memory used=1648.1MB, alloc=588.3MB, time=49.56 memory used=1849.6MB, alloc=612.3MB, time=59.10 memory used=2047.0MB, alloc=636.3MB, time=70.14 memory used=2257.1MB, alloc=660.3MB, time=82.45 memory used=2482.3MB, alloc=684.3MB, time=96.03 memory used=2723.5MB, alloc=708.3MB, time=110.73 |\^/| 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(); 1428278244 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [11 x + 20 y - 2 y z - 4, 17 x y + 5 z - 17 z + 6, 2 2 -20 y - 8 z + 4 y + 1] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [13 x - 17 x z + 9 y + 12 x, 18 x y - 14 y z + 12 z + 13 x, 2 8 y + 5 y z - 10 x + 19 z] > Problem := [F,G]; 2 2 2 Problem := [[11 x + 20 y - 2 y z - 4, 17 x y + 5 z - 17 z + 6, 2 2 2 2 -20 y - 8 z + 4 y + 1], [13 x - 17 x z + 9 y + 12 x, 2 2 18 x y - 14 y z + 12 z + 13 x, 8 y + 5 y z - 10 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=4.3MB, alloc=32.3MB, time=0.29 memory used=26.1MB, alloc=32.3MB, time=0.86 memory used=45.3MB, alloc=56.3MB, time=1.36 memory used=86.6MB, alloc=60.3MB, time=2.42 memory used=130.0MB, alloc=68.3MB, time=3.47 memory used=173.2MB, alloc=92.3MB, time=4.47 memory used=239.7MB, alloc=92.3MB, time=6.14 memory used=305.1MB, alloc=92.3MB, time=7.77 memory used=370.8MB, alloc=116.3MB, time=9.27 memory used=441.1MB, alloc=372.3MB, time=10.87 memory used=529.6MB, alloc=372.3MB, time=13.20 memory used=620.2MB, alloc=396.3MB, time=15.44 memory used=732.4MB, alloc=396.3MB, time=17.96 memory used=847.0MB, alloc=420.3MB, time=20.67 memory used=978.5MB, alloc=420.3MB, time=23.73 memory used=1109.7MB, alloc=444.3MB, time=26.77 memory used=1237.0MB, alloc=468.3MB, time=30.10 memory used=1345.7MB, alloc=468.3MB, time=32.52 memory used=1467.4MB, alloc=492.3MB, time=35.87 memory used=1568.4MB, alloc=492.3MB, time=38.10 memory used=1678.3MB, alloc=492.3MB, time=41.35 memory used=1777.2MB, alloc=492.3MB, time=44.13 memory used=1863.1MB, alloc=492.3MB, time=46.39 memory used=1964.2MB, alloc=516.3MB, time=49.45 memory used=2057.0MB, alloc=516.3MB, time=52.32 memory used=2120.2MB, alloc=516.3MB, time=54.07 memory used=2199.9MB, alloc=516.3MB, time=56.14 memory used=2276.5MB, alloc=516.3MB, time=58.19 memory used=2341.8MB, alloc=516.3MB, time=60.01 memory used=2400.6MB, alloc=516.3MB, time=61.60 memory used=2483.5MB, alloc=540.3MB, time=63.50 memory used=2555.6MB, alloc=540.3MB, time=65.72 memory used=2601.5MB, alloc=540.3MB, time=67.11 memory used=2653.1MB, alloc=540.3MB, time=68.66 memory used=2710.5MB, alloc=540.3MB, time=70.13 memory used=2940.4MB, alloc=564.3MB, time=76.79 memory used=3131.0MB, alloc=588.3MB, time=82.48 memory used=3347.5MB, alloc=612.3MB, time=87.90 memory used=3552.6MB, alloc=636.3MB, time=92.94 memory used=3732.9MB, alloc=636.3MB, time=98.21 memory used=3914.2MB, alloc=636.3MB, time=103.17 memory used=4069.6MB, alloc=660.3MB, time=107.58 memory used=4244.6MB, alloc=660.3MB, time=112.45 memory used=4358.6MB, alloc=660.3MB, time=115.69 memory used=4507.3MB, alloc=660.3MB, time=120.62 memory used=4650.5MB, alloc=684.3MB, time=125.72 memory used=4817.3MB, alloc=684.3MB, time=132.15 memory used=4937.7MB, alloc=684.3MB, time=135.88 memory used=5096.8MB, alloc=684.3MB, time=140.19 memory used=5217.0MB, alloc=684.3MB, time=143.80 memory used=5330.7MB, alloc=684.3MB, time=147.58 |\^/| 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(); 1428278544 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-19 x + 20 x y + 9 y z - 8 y, 20 z + 6 x + 9 z - 15, 2 -13 x - 16 x y - 12 x + 19 z] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 G := [x - 18 y + 15 y z - 19 z , -20 x y - 17 x z - y - 15 z , 2 -8 y z - 19 z - 13 z + 17] > Problem := [F,G]; 2 2 Problem := [[-19 x + 20 x y + 9 y z - 8 y, 20 z + 6 x + 9 z - 15, 2 2 2 2 -13 x - 16 x y - 12 x + 19 z], [x - 18 y + 15 y z - 19 z , 2 2 2 -20 x y - 17 x z - y - 15 z , -8 y z - 19 z - 13 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=4.3MB, alloc=32.3MB, time=0.30 memory used=26.6MB, alloc=32.3MB, time=0.89 memory used=47.4MB, alloc=32.3MB, time=1.43 memory used=66.2MB, alloc=56.3MB, time=1.95 memory used=109.8MB, alloc=68.3MB, time=3.05 memory used=151.4MB, alloc=92.3MB, time=4.16 memory used=218.3MB, alloc=92.3MB, time=5.83 memory used=286.4MB, alloc=116.3MB, time=7.51 memory used=358.1MB, alloc=116.3MB, time=9.36 memory used=433.7MB, alloc=372.3MB, time=11.43 memory used=521.2MB, alloc=396.3MB, time=13.55 memory used=635.1MB, alloc=396.3MB, time=16.34 memory used=750.8MB, alloc=420.3MB, time=18.94 memory used=884.7MB, alloc=444.3MB, time=22.51 memory used=1012.5MB, alloc=444.3MB, time=25.67 memory used=1142.0MB, alloc=468.3MB, time=28.98 memory used=1264.1MB, alloc=468.3MB, time=32.44 memory used=1375.5MB, alloc=492.3MB, time=35.46 memory used=1488.3MB, alloc=492.3MB, time=38.31 memory used=1593.5MB, alloc=492.3MB, time=41.38 memory used=1688.9MB, alloc=492.3MB, time=44.19 memory used=1784.2MB, alloc=516.3MB, time=46.74 memory used=1873.5MB, alloc=516.3MB, time=49.50 memory used=1960.5MB, alloc=516.3MB, time=52.38 memory used=2033.2MB, alloc=516.3MB, time=54.40 memory used=2131.2MB, alloc=516.3MB, time=57.35 memory used=2195.2MB, alloc=516.3MB, time=59.41 memory used=2269.3MB, alloc=516.3MB, time=61.41 memory used=2352.4MB, alloc=516.3MB, time=64.00 memory used=2411.7MB, alloc=516.3MB, time=66.03 memory used=2461.5MB, alloc=516.3MB, time=67.55 memory used=2532.2MB, alloc=516.3MB, time=69.81 memory used=2590.6MB, alloc=516.3MB, time=72.21 memory used=2794.3MB, alloc=540.3MB, time=78.79 memory used=3020.4MB, alloc=564.3MB, time=84.61 memory used=3242.5MB, alloc=588.3MB, time=90.59 memory used=3431.4MB, alloc=612.3MB, time=95.80 memory used=3610.8MB, alloc=612.3MB, time=101.79 memory used=3773.6MB, alloc=636.3MB, time=107.22 memory used=3963.8MB, alloc=636.3MB, time=112.01 memory used=4151.7MB, alloc=660.3MB, time=115.98 memory used=4317.6MB, alloc=660.3MB, time=121.07 memory used=4466.2MB, alloc=660.3MB, time=125.01 memory used=4612.9MB, alloc=660.3MB, time=130.27 memory used=4749.9MB, alloc=660.3MB, time=135.49 |\^/| 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(); 1428278844 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [19 x - 17 x z - 11 y + 7 z , -3 y - 20 x - y + 11 z, 2 2 5 x + 3 x y + 7 y + 5 y z] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [-7 y - 16 z - 16 x + 11 z, -2 x z + 5 z + 3 z - 16, 2 -19 x y - 11 y z + 11 z - 5] > Problem := [F,G]; 2 2 2 2 Problem := [[19 x - 17 x z - 11 y + 7 z , -3 y - 20 x - y + 11 z, 2 2 2 2 5 x + 3 x y + 7 y + 5 y z], [-7 y - 16 z - 16 x + 11 z, 2 2 -2 x z + 5 z + 3 z - 16, -19 x y - 11 y z + 11 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=26.5MB, alloc=32.3MB, time=0.87 memory used=47.5MB, alloc=60.3MB, time=1.38 memory used=85.2MB, alloc=60.3MB, time=2.28 memory used=127.0MB, alloc=68.3MB, time=3.33 memory used=168.7MB, alloc=92.3MB, time=4.30 memory used=238.3MB, alloc=92.3MB, time=5.75 memory used=302.9MB, alloc=92.3MB, time=7.39 memory used=368.2MB, alloc=92.3MB, time=8.64 memory used=417.3MB, alloc=92.3MB, time=9.33 memory used=485.2MB, alloc=116.3MB, time=10.88 memory used=555.7MB, alloc=372.3MB, time=12.52 memory used=646.2MB, alloc=396.3MB, time=14.56 memory used=752.0MB, alloc=396.3MB, time=17.43 memory used=860.6MB, alloc=420.3MB, time=19.91 memory used=990.3MB, alloc=420.3MB, time=22.38 memory used=1104.9MB, alloc=444.3MB, time=24.86 memory used=1244.6MB, alloc=444.3MB, time=28.63 memory used=1368.6MB, alloc=468.3MB, time=31.63 memory used=1500.3MB, alloc=468.3MB, time=35.12 memory used=1613.4MB, alloc=492.3MB, time=37.96 memory used=1711.0MB, alloc=492.3MB, time=40.30 memory used=1815.2MB, alloc=516.3MB, time=42.15 memory used=1917.3MB, alloc=516.3MB, time=44.99 memory used=2009.8MB, alloc=516.3MB, time=47.06 memory used=2109.9MB, alloc=516.3MB, time=49.84 memory used=2198.2MB, alloc=516.3MB, time=52.40 memory used=2282.3MB, alloc=516.3MB, time=54.44 memory used=2373.9MB, alloc=540.3MB, time=56.31 memory used=2468.6MB, alloc=540.3MB, time=58.57 memory used=2530.8MB, alloc=540.3MB, time=60.35 memory used=2590.0MB, alloc=540.3MB, time=61.83 memory used=2649.6MB, alloc=540.3MB, time=63.45 memory used=2729.7MB, alloc=540.3MB, time=65.72 memory used=2789.1MB, alloc=540.3MB, time=67.66 memory used=2857.2MB, alloc=540.3MB, time=69.78 memory used=2907.0MB, alloc=540.3MB, time=71.75 memory used=3099.7MB, alloc=564.3MB, time=76.28 memory used=3314.7MB, alloc=588.3MB, time=82.06 memory used=3493.1MB, alloc=612.3MB, time=86.45 memory used=3687.3MB, alloc=636.3MB, time=91.37 memory used=3833.7MB, alloc=636.3MB, time=95.38 memory used=3974.8MB, alloc=660.3MB, time=99.97 memory used=4151.7MB, alloc=660.3MB, time=106.18 memory used=4292.2MB, alloc=660.3MB, time=110.84 memory used=4407.5MB, alloc=660.3MB, time=114.37 memory used=4532.3MB, alloc=684.3MB, time=117.81 memory used=4650.6MB, alloc=684.3MB, time=120.85 memory used=4801.5MB, alloc=684.3MB, time=126.22 memory used=4936.2MB, alloc=708.3MB, time=129.61 memory used=5297.6MB, alloc=732.3MB, time=137.37 |\^/| 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(); 1428279144 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [9 x z + 17 y z - 19 z - 9, 11 x - 12 y - 12 y z + 13 z, 2 -3 x y - 8 z + 18 x - 8] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [-11 x + 13 z - 16 x - 15, 19 x - 14 y + 6 y z + 4 y, 2 2 15 x + 14 y z + 6 z - 16 z] > Problem := [F,G]; 2 2 Problem := [[9 x z + 17 y z - 19 z - 9, 11 x - 12 y - 12 y z + 13 z, 2 2 2 -3 x y - 8 z + 18 x - 8], [-11 x + 13 z - 16 x - 15, 2 2 2 2 19 x - 14 y + 6 y z + 4 y, 15 x + 14 y z + 6 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=0.30 memory used=26.3MB, alloc=32.3MB, time=0.87 memory used=46.5MB, alloc=32.3MB, time=1.38 memory used=65.3MB, alloc=60.3MB, time=1.90 memory used=105.9MB, alloc=60.3MB, time=2.95 memory used=143.3MB, alloc=84.3MB, time=3.93 memory used=207.2MB, alloc=92.3MB, time=5.51 memory used=274.4MB, alloc=92.3MB, time=7.15 memory used=338.5MB, alloc=116.3MB, time=8.78 memory used=413.5MB, alloc=372.3MB, time=10.75 memory used=501.9MB, alloc=396.3MB, time=12.92 memory used=608.7MB, alloc=396.3MB, time=15.62 memory used=713.7MB, alloc=396.3MB, time=17.90 memory used=821.6MB, alloc=420.3MB, time=20.53 memory used=956.3MB, alloc=444.3MB, time=23.86 memory used=1088.4MB, alloc=468.3MB, time=27.61 memory used=1212.7MB, alloc=468.3MB, time=30.44 memory used=1314.3MB, alloc=492.3MB, time=32.88 memory used=1421.9MB, alloc=492.3MB, time=35.88 memory used=1509.3MB, alloc=492.3MB, time=37.79 memory used=1614.0MB, alloc=492.3MB, time=40.47 memory used=1706.6MB, alloc=516.3MB, time=43.13 memory used=1773.5MB, alloc=516.3MB, time=45.03 memory used=1854.0MB, alloc=516.3MB, time=47.72 memory used=1918.4MB, alloc=516.3MB, time=49.54 memory used=1984.1MB, alloc=516.3MB, time=51.32 memory used=2044.6MB, alloc=516.3MB, time=53.45 memory used=2089.8MB, alloc=516.3MB, time=54.82 memory used=2139.1MB, alloc=516.3MB, time=56.27 memory used=2349.2MB, alloc=540.3MB, time=62.25 memory used=2566.6MB, alloc=564.3MB, time=68.34 memory used=2741.4MB, alloc=588.3MB, time=72.33 memory used=2921.8MB, alloc=612.3MB, time=77.26 memory used=3076.3MB, alloc=636.3MB, time=81.74 memory used=3259.0MB, alloc=636.3MB, time=87.58 memory used=3376.1MB, alloc=636.3MB, time=90.91 memory used=3532.8MB, alloc=660.3MB, time=95.37 memory used=3652.9MB, alloc=660.3MB, time=98.81 memory used=3788.1MB, alloc=660.3MB, time=103.13 memory used=3904.7MB, alloc=660.3MB, time=106.56 memory used=4034.0MB, alloc=684.3MB, time=110.52 memory used=4111.4MB, alloc=684.3MB, time=113.65 memory used=4476.8MB, alloc=708.3MB, time=123.80 memory used=4850.9MB, alloc=732.3MB, time=134.07 memory used=5211.5MB, alloc=756.3MB, time=143.16 |\^/| 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(); 1428279444 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; F := 2 2 [-10 y z - 18 z, 8 x - 9 y z - 15 z + 13, -10 x y + 11 y - 11 y z + 10 y] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [19 y z - 6 z - 6 y + 8 z, -8 x - 8 x z - 19 z + 14, 14 x y + 15 y z + 13 z - 13] > Problem := [F,G]; Problem := [ 2 2 [-10 y z - 18 z, 8 x - 9 y z - 15 z + 13, -10 x y + 11 y - 11 y z + 10 y] 2 2 , [19 y z - 6 z - 6 y + 8 z, -8 x - 8 x z - 19 z + 14, 14 x y + 15 y z + 13 z - 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 used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.3MB, alloc=32.3MB, time=0.85 memory used=47.1MB, alloc=32.3MB, time=1.40 memory used=65.4MB, alloc=56.3MB, time=1.90 memory used=104.3MB, alloc=60.3MB, time=2.95 memory used=139.7MB, alloc=84.3MB, time=3.90 memory used=197.2MB, alloc=92.3MB, time=5.49 memory used=254.3MB, alloc=116.3MB, time=7.08 memory used=332.1MB, alloc=116.3MB, time=9.34 memory used=409.9MB, alloc=140.3MB, time=11.58 memory used=509.0MB, alloc=164.3MB, time=14.51 memory used=598.3MB, alloc=420.3MB, time=17.28 memory used=718.9MB, alloc=444.3MB, time=21.05 memory used=860.4MB, alloc=468.3MB, time=25.48 memory used=1017.4MB, alloc=492.3MB, time=30.33 memory used=1195.3MB, alloc=516.3MB, time=36.29 memory used=1399.8MB, alloc=540.3MB, time=43.32 memory used=1625.6MB, alloc=564.3MB, time=51.24 memory used=1874.0MB, alloc=588.3MB, time=60.15 memory used=2140.8MB, alloc=612.3MB, time=69.87 memory used=2435.7MB, alloc=636.3MB, time=80.82 memory used=2748.0MB, alloc=660.3MB, time=93.04 memory used=3050.5MB, alloc=684.3MB, time=105.16 memory used=3332.5MB, alloc=708.3MB, time=117.19 memory used=3618.0MB, alloc=732.3MB, time=129.01 memory used=3905.6MB, alloc=756.3MB, time=141.06 |\^/| 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(); 1428279744 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [-19 x - 17 x z + 15 y + 12 z, -17 x - 5 y z + 16 z + 16 y, 12 x z - 3 x + 15 y - 4 z] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [-19 x z + 9 y - 5 z - 10, 10 x y - 16 x z + 4 y - 10 y z, 2 14 x - 11 y z - 3 x] > Problem := [F,G]; 2 2 2 2 Problem := [[-19 x - 17 x z + 15 y + 12 z, -17 x - 5 y z + 16 z + 16 y, 2 2 12 x z - 3 x + 15 y - 4 z], [-19 x z + 9 y - 5 z - 10, 2 2 10 x y - 16 x z + 4 y - 10 y z, 14 x - 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=4.3MB, alloc=32.3MB, time=0.29 memory used=26.0MB, alloc=32.3MB, time=0.86 memory used=46.5MB, alloc=32.3MB, time=1.41 memory used=66.1MB, alloc=56.3MB, time=1.94 memory used=107.3MB, alloc=68.3MB, time=3.03 memory used=147.7MB, alloc=92.3MB, time=4.09 memory used=211.5MB, alloc=92.3MB, time=5.69 memory used=275.4MB, alloc=116.3MB, time=7.33 memory used=346.2MB, alloc=116.3MB, time=9.20 memory used=416.9MB, alloc=372.3MB, time=11.11 memory used=500.3MB, alloc=396.3MB, time=13.32 memory used=612.8MB, alloc=420.3MB, time=16.08 memory used=743.0MB, alloc=444.3MB, time=19.35 memory used=889.7MB, alloc=468.3MB, time=23.33 memory used=1011.9MB, alloc=468.3MB, time=26.85 memory used=1126.0MB, alloc=492.3MB, time=29.72 memory used=1225.0MB, alloc=492.3MB, time=31.98 memory used=1319.3MB, alloc=492.3MB, time=34.69 memory used=1419.4MB, alloc=492.3MB, time=37.57 memory used=1509.2MB, alloc=492.3MB, time=40.39 memory used=1596.7MB, alloc=516.3MB, time=42.86 memory used=1675.9MB, alloc=516.3MB, time=45.26 memory used=1758.0MB, alloc=516.3MB, time=47.91 memory used=1844.1MB, alloc=516.3MB, time=50.94 memory used=1898.3MB, alloc=516.3MB, time=52.80 memory used=1963.0MB, alloc=516.3MB, time=55.20 memory used=2010.7MB, alloc=516.3MB, time=56.83 memory used=2060.7MB, alloc=516.3MB, time=58.38 memory used=2269.3MB, alloc=540.3MB, time=65.21 memory used=2483.9MB, alloc=564.3MB, time=71.82 memory used=2683.5MB, alloc=588.3MB, time=77.65 memory used=2859.2MB, alloc=612.3MB, time=82.95 memory used=3026.1MB, alloc=636.3MB, time=87.86 memory used=3195.9MB, alloc=660.3MB, time=92.81 memory used=3328.6MB, alloc=660.3MB, time=97.48 memory used=3473.1MB, alloc=660.3MB, time=102.15 memory used=3601.7MB, alloc=660.3MB, time=106.75 memory used=3715.1MB, alloc=660.3MB, time=110.97 memory used=3832.0MB, alloc=684.3MB, time=115.12 memory used=3924.8MB, alloc=684.3MB, time=118.47 memory used=4037.2MB, alloc=684.3MB, time=122.86 memory used=4400.9MB, alloc=708.3MB, time=134.61 memory used=4774.7MB, alloc=732.3MB, time=147.56 |\^/| 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(); 1428280044 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; F := [20 x y - 8 y z - 17 y - z, 12 x y + 2 y z - 4 y - 16 z, 2 2 -10 x + 4 x y - 9 z + 15] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [2 x y - 10 x z - 16 z + 13, -18 x y + 10 y z - 19 x + 8, 14 y z + 8 y + z + 10] > Problem := [F,G]; Problem := [[20 x y - 8 y z - 17 y - z, 12 x y + 2 y z - 4 y - 16 z, 2 2 2 -10 x + 4 x y - 9 z + 15], [2 x y - 10 x z - 16 z + 13, -18 x y + 10 y z - 19 x + 8, 14 y z + 8 y + 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=4.3MB, alloc=32.3MB, time=0.30 memory used=26.7MB, alloc=32.3MB, time=0.88 memory used=47.5MB, alloc=32.3MB, time=1.41 memory used=66.7MB, alloc=56.3MB, time=1.94 memory used=103.1MB, alloc=60.3MB, time=2.92 memory used=138.7MB, alloc=84.3MB, time=3.91 memory used=196.5MB, alloc=92.3MB, time=5.52 memory used=253.3MB, alloc=116.3MB, time=7.10 memory used=331.8MB, alloc=116.3MB, time=9.27 memory used=408.0MB, alloc=140.3MB, time=11.50 memory used=495.8MB, alloc=140.3MB, time=14.08 memory used=580.1MB, alloc=420.3MB, time=16.61 memory used=701.3MB, alloc=444.3MB, time=20.27 memory used=848.0MB, alloc=468.3MB, time=24.59 memory used=1015.2MB, alloc=492.3MB, time=29.89 memory used=1191.3MB, alloc=516.3MB, time=35.53 memory used=1340.6MB, alloc=516.3MB, time=40.38 memory used=1508.5MB, alloc=540.3MB, time=46.49 memory used=1677.7MB, alloc=540.3MB, time=53.19 memory used=1850.9MB, alloc=564.3MB, time=60.53 memory used=1978.2MB, alloc=564.3MB, time=65.45 memory used=2098.1MB, alloc=588.3MB, time=70.23 memory used=2199.1MB, alloc=588.3MB, time=74.25 memory used=2322.2MB, alloc=588.3MB, time=79.88 memory used=2461.1MB, alloc=588.3MB, time=85.85 memory used=2558.6MB, alloc=588.3MB, time=89.81 memory used=2653.0MB, alloc=588.3MB, time=93.58 memory used=2746.1MB, alloc=588.3MB, time=97.43 memory used=2822.6MB, alloc=588.3MB, time=100.74 memory used=2926.9MB, alloc=612.3MB, time=105.90 memory used=3024.5MB, alloc=612.3MB, time=110.63 memory used=3105.0MB, alloc=612.3MB, time=114.40 memory used=3189.0MB, alloc=612.3MB, time=118.23 memory used=3268.9MB, alloc=612.3MB, time=122.16 memory used=3370.5MB, alloc=612.3MB, time=127.42 memory used=3462.8MB, alloc=612.3MB, time=132.55 memory used=3555.8MB, alloc=612.3MB, time=137.64 memory used=3625.1MB, alloc=612.3MB, 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(); 1428280344 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; F := [ 2 2 2 2 2 17 x - 4 z - 15 x - 9 z, -19 x - 17 z + 5 y - z, -10 y + x - 18 y + 15 ] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [-8 x + 12 x y - x z + 10 y, 11 y + 14, -14 y z + 20 z + 10 x - 19 z] > Problem := [F,G]; Problem := [[ 2 2 2 2 2 17 x - 4 z - 15 x - 9 z, -19 x - 17 z + 5 y - z, -10 y + x - 18 y + 15 2 2 2 ], [-8 x + 12 x y - x z + 10 y, 11 y + 14, -14 y z + 20 z + 10 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=4.4MB, alloc=32.3MB, time=0.30 memory used=26.6MB, alloc=32.3MB, time=0.88 memory used=46.7MB, alloc=56.3MB, time=1.44 memory used=88.8MB, alloc=60.3MB, time=2.58 memory used=130.2MB, alloc=60.3MB, time=3.66 memory used=170.5MB, alloc=84.3MB, time=4.79 memory used=232.6MB, alloc=92.3MB, time=6.52 memory used=293.7MB, alloc=116.3MB, time=8.23 memory used=368.3MB, alloc=116.3MB, time=10.28 memory used=450.7MB, alloc=396.3MB, time=12.76 memory used=558.5MB, alloc=396.3MB, time=15.80 memory used=669.0MB, alloc=420.3MB, time=19.03 memory used=802.6MB, alloc=444.3MB, time=23.00 memory used=936.7MB, alloc=444.3MB, time=26.85 memory used=1075.5MB, alloc=468.3MB, time=31.02 memory used=1212.1MB, alloc=468.3MB, time=35.38 memory used=1338.8MB, alloc=492.3MB, time=39.43 memory used=1454.0MB, alloc=492.3MB, time=43.25 memory used=1573.8MB, alloc=492.3MB, time=47.20 memory used=1688.9MB, alloc=492.3MB, time=51.26 memory used=1786.1MB, alloc=492.3MB, time=54.61 memory used=1879.6MB, alloc=516.3MB, time=57.69 memory used=1978.4MB, alloc=516.3MB, time=61.20 memory used=2062.1MB, alloc=516.3MB, time=64.06 memory used=2140.1MB, alloc=516.3MB, time=66.89 memory used=2220.3MB, alloc=516.3MB, time=69.85 memory used=2290.6MB, alloc=516.3MB, time=72.46 memory used=2371.4MB, alloc=516.3MB, time=75.59 memory used=2446.1MB, alloc=516.3MB, time=78.37 memory used=2519.3MB, alloc=516.3MB, time=81.20 memory used=2578.8MB, alloc=516.3MB, time=83.74 memory used=2640.5MB, alloc=540.3MB, time=86.27 memory used=2694.8MB, alloc=540.3MB, time=88.58 memory used=2752.1MB, alloc=540.3MB, time=90.95 memory used=2977.6MB, alloc=564.3MB, time=98.47 memory used=3214.5MB, alloc=588.3MB, time=106.22 memory used=3463.1MB, alloc=612.3MB, time=114.65 memory used=3704.3MB, alloc=636.3MB, time=122.92 memory used=3967.0MB, alloc=660.3MB, time=131.49 memory used=4243.7MB, alloc=684.3MB, time=140.23 |\^/| 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(); 1428280644 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [11 x + 5 x y - 2 x + 11 z, -16 x + 8 y + 17 z + 3, 2 -7 x y + 13 x z - 17 z + 3 z] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [-11 x + 11 x z - 11 y - 15, -17 x + 10 x y + 10 y + 5 x, 2 -5 x y + 13 x z + 13 y z - 17 z ] > Problem := [F,G]; 2 2 2 2 Problem := [[11 x + 5 x y - 2 x + 11 z, -16 x + 8 y + 17 z + 3, 2 2 -7 x y + 13 x z - 17 z + 3 z], [-11 x + 11 x z - 11 y - 15, 2 2 2 -17 x + 10 x y + 10 y + 5 x, -5 x y + 13 x z + 13 y 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=4.3MB, alloc=32.3MB, time=0.30 memory used=26.7MB, alloc=32.3MB, time=0.90 memory used=47.4MB, alloc=32.3MB, time=1.45 memory used=67.7MB, alloc=56.3MB, time=2.01 memory used=109.8MB, alloc=60.3MB, time=3.13 memory used=149.3MB, alloc=84.3MB, time=4.20 memory used=211.3MB, alloc=92.3MB, time=5.88 memory used=274.9MB, alloc=116.3MB, time=7.52 memory used=349.9MB, alloc=116.3MB, time=9.49 memory used=416.2MB, alloc=372.3MB, time=11.27 memory used=501.5MB, alloc=396.3MB, time=13.60 memory used=614.2MB, alloc=420.3MB, time=16.68 memory used=748.2MB, alloc=444.3MB, time=20.55 memory used=888.8MB, alloc=468.3MB, time=24.68 memory used=1031.0MB, alloc=468.3MB, time=28.84 memory used=1149.0MB, alloc=468.3MB, time=32.19 memory used=1260.7MB, alloc=492.3MB, time=35.51 memory used=1363.1MB, alloc=492.3MB, time=38.51 memory used=1473.3MB, alloc=492.3MB, time=41.74 memory used=1570.9MB, alloc=492.3MB, time=44.85 memory used=1669.9MB, alloc=516.3MB, time=48.03 memory used=1759.3MB, alloc=516.3MB, time=50.75 memory used=1828.2MB, alloc=516.3MB, time=52.91 memory used=1919.0MB, alloc=516.3MB, time=56.16 memory used=1978.1MB, alloc=516.3MB, time=58.13 memory used=2043.7MB, alloc=516.3MB, time=59.95 memory used=2129.6MB, alloc=516.3MB, time=63.29 memory used=2207.3MB, alloc=516.3MB, time=66.51 memory used=2259.4MB, alloc=516.3MB, time=68.40 memory used=2313.9MB, alloc=540.3MB, time=69.92 memory used=2363.1MB, alloc=540.3MB, time=71.54 memory used=2593.2MB, alloc=564.3MB, time=78.30 memory used=2802.4MB, alloc=588.3MB, time=85.03 memory used=2998.3MB, alloc=612.3MB, time=91.20 memory used=3183.7MB, alloc=636.3MB, time=97.35 memory used=3354.2MB, alloc=660.3MB, time=103.20 memory used=3503.4MB, alloc=660.3MB, time=109.10 memory used=3667.2MB, alloc=660.3MB, time=114.95 memory used=3798.3MB, alloc=660.3MB, time=119.34 memory used=3934.3MB, alloc=684.3MB, time=124.61 memory used=4084.2MB, alloc=684.3MB, time=130.80 memory used=4226.2MB, alloc=684.3MB, time=137.00 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428280944 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-11 x + 10 x z + 2 z - 3, -20 x - 9 x y - 18 x z + 15 x, 2 2 2 -20 x - 11 y - 19 z + z] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [20 x z + 6 z - 8 x - 13 y, -12 x z + 19 y z - 20 z - 10, 2 -11 x + 19 y z - 18 x + 20] > Problem := [F,G]; 2 2 2 Problem := [[-11 x + 10 x z + 2 z - 3, -20 x - 9 x y - 18 x z + 15 x, 2 2 2 2 -20 x - 11 y - 19 z + z], [20 x z + 6 z - 8 x - 13 y, 2 -12 x z + 19 y z - 20 z - 10, -11 x + 19 y z - 18 x + 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=4.4MB, alloc=32.3MB, time=0.31 memory used=26.3MB, alloc=32.3MB, time=0.87 memory used=46.4MB, alloc=56.3MB, time=1.40 memory used=86.2MB, alloc=60.3MB, time=2.43 memory used=126.1MB, alloc=84.3MB, time=3.49 memory used=170.5MB, alloc=84.3MB, time=4.67 memory used=235.5MB, alloc=92.3MB, time=6.40 memory used=300.0MB, alloc=116.3MB, time=8.05 memory used=377.4MB, alloc=116.3MB, time=10.16 memory used=446.1MB, alloc=396.3MB, time=11.96 memory used=555.9MB, alloc=420.3MB, time=14.89 memory used=688.7MB, alloc=444.3MB, time=18.59 memory used=813.6MB, alloc=468.3MB, time=21.77 memory used=965.2MB, alloc=492.3MB, time=26.11 memory used=1104.9MB, alloc=492.3MB, time=30.24 memory used=1243.5MB, alloc=516.3MB, time=34.63 memory used=1377.0MB, alloc=516.3MB, time=39.05 memory used=1483.7MB, alloc=516.3MB, time=42.34 memory used=1579.0MB, alloc=516.3MB, time=45.22 memory used=1652.4MB, alloc=540.3MB, time=47.47 memory used=1758.8MB, alloc=540.3MB, time=51.29 memory used=1846.1MB, alloc=540.3MB, time=54.22 memory used=1934.6MB, alloc=540.3MB, time=57.27 memory used=2007.9MB, alloc=540.3MB, time=59.19 memory used=2084.4MB, alloc=540.3MB, time=62.09 memory used=2146.7MB, alloc=540.3MB, time=64.01 memory used=2210.1MB, alloc=540.3MB, time=66.45 memory used=2265.1MB, alloc=540.3MB, time=68.12 memory used=2325.8MB, alloc=540.3MB, time=70.77 memory used=2557.2MB, alloc=564.3MB, time=77.30 memory used=2803.4MB, alloc=588.3MB, time=85.60 memory used=3026.3MB, alloc=612.3MB, time=92.92 memory used=3220.2MB, alloc=636.3MB, time=98.77 memory used=3401.3MB, alloc=660.3MB, time=105.49 memory used=3569.2MB, alloc=684.3MB, time=110.73 memory used=3743.0MB, alloc=708.3MB, time=116.19 memory used=3875.4MB, alloc=708.3MB, time=121.00 memory used=4042.5MB, alloc=708.3MB, time=127.68 memory used=4178.9MB, alloc=708.3MB, time=132.98 memory used=4312.4MB, alloc=708.3MB, time=138.05 memory used=4463.4MB, alloc=708.3MB, time=144.95 |\^/| 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(); 1428281244 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [17 x y - 10 y + 14 y z + 2 x, -20 x - 8 y z + 8 z + 14 z, 2 2 8 x - 17 y + 4 y z - 17 x] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; G := 2 2 2 2 [2 x z + z - 9 x - z, 9 x - 9 x y + 5 x + 4 y, 8 x - 17 y z + 16 z - z] > Problem := [F,G]; 2 2 2 Problem := [[17 x y - 10 y + 14 y z + 2 x, -20 x - 8 y z + 8 z + 14 z, 2 2 8 x - 17 y + 4 y z - 17 x], 2 2 2 2 [2 x z + z - 9 x - z, 9 x - 9 x y + 5 x + 4 y, 8 x - 17 y z + 16 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=0.29 memory used=26.6MB, alloc=32.3MB, time=0.83 memory used=47.5MB, alloc=32.3MB, time=1.34 memory used=66.6MB, alloc=56.3MB, time=1.83 memory used=107.3MB, alloc=60.3MB, time=2.81 memory used=145.6MB, alloc=60.3MB, time=3.79 memory used=184.8MB, alloc=92.3MB, time=4.83 memory used=248.1MB, alloc=92.3MB, time=6.42 memory used=313.0MB, alloc=116.3MB, time=7.96 memory used=385.9MB, alloc=372.3MB, time=9.73 memory used=476.2MB, alloc=372.3MB, time=11.76 memory used=557.0MB, alloc=396.3MB, time=13.33 memory used=671.0MB, alloc=396.3MB, time=16.13 memory used=775.1MB, alloc=420.3MB, time=18.91 memory used=905.2MB, alloc=444.3MB, time=22.44 memory used=1030.1MB, alloc=444.3MB, time=25.69 memory used=1158.1MB, alloc=468.3MB, time=28.55 memory used=1266.6MB, alloc=468.3MB, time=31.40 memory used=1385.9MB, alloc=468.3MB, time=34.20 memory used=1486.5MB, alloc=468.3MB, time=36.97 memory used=1578.2MB, alloc=492.3MB, time=39.48 memory used=1678.1MB, alloc=492.3MB, time=42.26 memory used=1772.5MB, alloc=492.3MB, time=45.05 memory used=1875.7MB, alloc=492.3MB, time=48.15 memory used=1970.8MB, alloc=492.3MB, time=51.17 memory used=2049.9MB, alloc=516.3MB, time=53.35 memory used=2145.9MB, alloc=516.3MB, time=56.58 memory used=2207.4MB, alloc=516.3MB, time=58.38 memory used=2269.4MB, alloc=516.3MB, time=60.21 memory used=2338.9MB, alloc=516.3MB, time=62.73 memory used=2396.3MB, alloc=516.3MB, time=64.45 memory used=2461.8MB, alloc=516.3MB, time=66.70 memory used=2512.5MB, alloc=516.3MB, time=68.54 memory used=2561.6MB, alloc=516.3MB, time=70.37 memory used=2771.6MB, alloc=540.3MB, time=75.74 memory used=2978.6MB, alloc=564.3MB, time=81.85 memory used=3165.7MB, alloc=588.3MB, time=86.93 memory used=3355.9MB, alloc=612.3MB, time=92.16 memory used=3518.1MB, alloc=636.3MB, time=97.23 memory used=3669.0MB, alloc=636.3MB, time=102.13 memory used=3825.0MB, alloc=660.3MB, time=107.33 memory used=3962.9MB, alloc=660.3MB, time=111.36 memory used=4109.7MB, alloc=684.3MB, time=116.71 memory used=4232.7MB, alloc=684.3MB, time=121.51 memory used=4364.6MB, alloc=684.3MB, time=126.62 memory used=4474.8MB, alloc=684.3MB, time=131.35 |\^/| 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(); 1428281544 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [3 x y + 2 z - 4 y + 19 z, -18 x y - 5 x + 20 y - 12, 2 2 7 x - 8 y + 10 y z + 6 x] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-2 x y - 7 y + 19 y z + 17 x, -11 x - 17 y z - 14 x + 17 z, 2 -18 y + 5 y - 10] > Problem := [F,G]; 2 Problem := [[3 x y + 2 z - 4 y + 19 z, -18 x y - 5 x + 20 y - 12, 2 2 2 7 x - 8 y + 10 y z + 6 x], [-2 x y - 7 y + 19 y z + 17 x, 2 2 -11 x - 17 y z - 14 x + 17 z, -18 y + 5 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=4.3MB, alloc=32.3MB, time=0.31 memory used=26.7MB, alloc=32.3MB, time=0.87 memory used=46.7MB, alloc=32.3MB, time=1.39 memory used=65.3MB, alloc=56.3MB, time=1.88 memory used=105.4MB, alloc=60.3MB, time=2.95 memory used=144.1MB, alloc=60.3MB, time=3.96 memory used=181.8MB, alloc=84.3MB, time=4.98 memory used=226.6MB, alloc=84.3MB, time=6.16 memory used=286.1MB, alloc=116.3MB, time=7.81 memory used=360.7MB, alloc=372.3MB, time=9.73 memory used=443.5MB, alloc=396.3MB, time=12.05 memory used=553.5MB, alloc=396.3MB, time=14.94 memory used=659.0MB, alloc=420.3MB, time=17.97 memory used=788.7MB, alloc=444.3MB, time=21.62 memory used=919.0MB, alloc=444.3MB, time=25.40 memory used=1059.5MB, alloc=468.3MB, time=29.42 memory used=1203.6MB, alloc=492.3MB, time=33.86 memory used=1320.2MB, alloc=492.3MB, time=37.19 memory used=1443.2MB, alloc=492.3MB, time=40.85 memory used=1553.8MB, alloc=516.3MB, time=44.03 memory used=1652.2MB, alloc=516.3MB, time=47.02 memory used=1753.2MB, alloc=516.3MB, time=50.31 memory used=1836.0MB, alloc=516.3MB, time=52.73 memory used=1927.8MB, alloc=516.3MB, time=55.71 memory used=2007.2MB, alloc=516.3MB, time=58.12 memory used=2080.4MB, alloc=540.3MB, time=60.53 memory used=2164.0MB, alloc=540.3MB, time=63.54 memory used=2268.5MB, alloc=540.3MB, time=66.77 memory used=2363.0MB, alloc=564.3MB, time=69.86 memory used=2447.0MB, alloc=564.3MB, time=72.82 memory used=2533.7MB, alloc=588.3MB, time=75.61 memory used=2614.7MB, alloc=588.3MB, time=78.58 memory used=2679.9MB, alloc=588.3MB, time=81.16 memory used=2782.4MB, alloc=612.3MB, time=84.10 memory used=2881.6MB, alloc=612.3MB, time=87.11 memory used=2971.3MB, alloc=612.3MB, time=90.26 memory used=3052.2MB, alloc=612.3MB, time=93.34 memory used=3127.9MB, alloc=636.3MB, time=96.36 memory used=3205.6MB, alloc=636.3MB, time=99.35 memory used=3271.9MB, alloc=636.3MB, time=102.11 memory used=3527.1MB, alloc=660.3MB, time=110.42 memory used=3792.6MB, alloc=684.3MB, time=119.05 memory used=4087.4MB, alloc=708.3MB, time=127.71 memory used=4380.2MB, alloc=732.3MB, time=137.27 |\^/| 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(); 1428281844 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-17 x + 8 x z + 7 z - 13, -19 y - 3 y z - 2 x - 18 z, 2 2 -15 x y + 4 y + 18 y z + 3 z ] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [-12 x z - 9 y z - 8 z - 4, -15 x y + 12 x z - 15 z + 11, 2 10 x - 10 x - 20 y + 20 z] > Problem := [F,G]; 2 2 2 Problem := [[-17 x + 8 x z + 7 z - 13, -19 y - 3 y z - 2 x - 18 z, 2 2 -15 x y + 4 y + 18 y z + 3 z ], [-12 x z - 9 y z - 8 z - 4, 2 2 -15 x y + 12 x z - 15 z + 11, 10 x - 10 x - 20 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=4.3MB, alloc=32.3MB, time=0.30 memory used=26.4MB, alloc=32.3MB, time=0.89 memory used=46.9MB, alloc=32.3MB, time=1.41 memory used=66.0MB, alloc=56.3MB, time=1.93 memory used=107.1MB, alloc=60.3MB, time=3.00 memory used=143.7MB, alloc=60.3MB, time=3.95 memory used=182.6MB, alloc=84.3MB, time=5.01 memory used=219.6MB, alloc=84.3MB, time=5.98 memory used=283.0MB, alloc=92.3MB, time=7.71 memory used=343.6MB, alloc=116.3MB, time=9.41 memory used=414.9MB, alloc=116.3MB, time=11.25 memory used=482.0MB, alloc=396.3MB, time=13.13 memory used=589.7MB, alloc=396.3MB, time=16.04 memory used=697.7MB, alloc=420.3MB, time=18.79 memory used=827.0MB, alloc=444.3MB, time=21.87 memory used=944.9MB, alloc=468.3MB, time=25.12 memory used=1089.0MB, alloc=492.3MB, time=29.39 memory used=1203.3MB, alloc=492.3MB, time=32.68 memory used=1310.3MB, alloc=492.3MB, time=35.56 memory used=1392.2MB, alloc=492.3MB, time=37.59 memory used=1488.4MB, alloc=492.3MB, time=40.52 memory used=1572.5MB, alloc=516.3MB, time=43.15 memory used=1654.4MB, alloc=516.3MB, time=45.96 memory used=1731.2MB, alloc=516.3MB, time=48.59 memory used=1780.8MB, alloc=516.3MB, time=50.33 memory used=1852.7MB, alloc=516.3MB, time=52.81 memory used=1906.9MB, alloc=516.3MB, time=54.65 memory used=1972.8MB, alloc=516.3MB, time=56.93 memory used=2008.4MB, alloc=516.3MB, time=58.41 memory used=2044.3MB, alloc=516.3MB, time=59.93 memory used=2254.7MB, alloc=540.3MB, time=65.88 memory used=2464.0MB, alloc=564.3MB, time=71.64 memory used=2640.3MB, alloc=588.3MB, time=77.25 memory used=2828.9MB, alloc=612.3MB, time=82.57 memory used=3015.7MB, alloc=636.3MB, time=88.85 memory used=3186.7MB, alloc=636.3MB, time=93.97 memory used=3325.1MB, alloc=636.3MB, time=98.17 memory used=3471.1MB, alloc=636.3MB, time=104.06 memory used=3602.9MB, alloc=636.3MB, time=108.55 memory used=3699.5MB, alloc=636.3MB, time=112.24 memory used=3815.1MB, alloc=660.3MB, time=116.75 memory used=3930.8MB, alloc=660.3MB, time=121.24 memory used=4037.3MB, alloc=660.3MB, time=125.93 memory used=4370.9MB, alloc=684.3MB, time=137.56 |\^/| 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(); 1428282144 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [-11 x - 19 x z - y - 19, 11 y - 17 y z - 6 z - 16 z, 2 4 x z - 6 z - 20 x + 14 y] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [-19 x + 2 x z + 3 y - 2, 4 x y - 15 x z - 15 y z - 8 z, 2 2 2 -6 x + 14 y + 8 z - 3 x] > Problem := [F,G]; 2 2 2 2 Problem := [[-11 x - 19 x z - y - 19, 11 y - 17 y z - 6 z - 16 z, 2 2 4 x z - 6 z - 20 x + 14 y], [-19 x + 2 x z + 3 y - 2, 2 2 2 4 x y - 15 x z - 15 y z - 8 z, -6 x + 14 y + 8 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=4.3MB, alloc=32.3MB, time=0.30 memory used=26.3MB, alloc=32.3MB, time=0.89 memory used=46.7MB, alloc=32.3MB, time=1.42 memory used=64.8MB, alloc=56.3MB, time=1.92 memory used=108.2MB, alloc=68.3MB, time=3.04 memory used=150.2MB, alloc=92.3MB, time=4.11 memory used=217.0MB, alloc=92.3MB, time=5.75 memory used=285.1MB, alloc=116.3MB, time=7.36 memory used=353.1MB, alloc=116.3MB, time=9.01 memory used=412.8MB, alloc=372.3MB, time=10.46 memory used=502.3MB, alloc=396.3MB, time=12.56 memory used=616.4MB, alloc=420.3MB, time=15.35 memory used=746.2MB, alloc=444.3MB, time=18.81 memory used=868.2MB, alloc=468.3MB, time=21.81 memory used=983.8MB, alloc=468.3MB, time=24.76 memory used=1107.2MB, alloc=468.3MB, time=28.31 memory used=1207.6MB, alloc=492.3MB, time=30.66 memory used=1295.8MB, alloc=492.3MB, time=32.87 memory used=1395.2MB, alloc=516.3MB, time=35.88 memory used=1473.4MB, alloc=516.3MB, time=37.99 memory used=1555.6MB, alloc=516.3MB, time=40.50 memory used=1631.9MB, alloc=516.3MB, time=42.74 memory used=1688.6MB, alloc=516.3MB, time=44.22 memory used=1758.2MB, alloc=516.3MB, time=46.51 memory used=1815.1MB, alloc=516.3MB, time=48.20 memory used=1869.4MB, alloc=516.3MB, time=49.64 memory used=1932.1MB, alloc=516.3MB, time=51.25 memory used=2153.5MB, alloc=540.3MB, time=56.68 memory used=2360.2MB, alloc=564.3MB, time=62.31 memory used=2551.6MB, alloc=588.3MB, time=66.88 memory used=2720.4MB, alloc=612.3MB, time=71.68 memory used=2886.6MB, alloc=636.3MB, time=76.41 memory used=3027.6MB, alloc=636.3MB, time=80.40 memory used=3159.4MB, alloc=636.3MB, time=84.54 memory used=3290.0MB, alloc=660.3MB, time=88.63 memory used=3409.2MB, alloc=660.3MB, time=92.15 memory used=3535.4MB, alloc=660.3MB, time=95.49 memory used=3647.2MB, alloc=660.3MB, time=99.49 memory used=3758.0MB, alloc=660.3MB, time=103.61 memory used=4092.7MB, alloc=684.3MB, time=112.91 memory used=4432.0MB, alloc=708.3MB, time=123.84 memory used=4802.7MB, alloc=732.3MB, time=133.69 memory used=5198.1MB, alloc=756.3MB, time=144.37 |\^/| 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(); 1428282444 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [7 x y + 11 x z + 12 z + 9 z, 10 x z + 10 z + 9, -z - 14 x + 11] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [3 x y + 20 y z + 11 z - 2 z, -19 x z - 7 y z + 4 x + 19 z, 2 -4 x z + 12 y z - 17 z - 20 x] > Problem := [F,G]; 2 2 Problem := [[7 x y + 11 x z + 12 z + 9 z, 10 x z + 10 z + 9, -z - 14 x + 11], 2 [3 x y + 20 y z + 11 z - 2 z, -19 x z - 7 y z + 4 x + 19 z, 2 -4 x z + 12 y z - 17 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=26.5MB, alloc=32.3MB, time=0.89 memory used=47.7MB, alloc=32.3MB, time=1.43 memory used=67.5MB, alloc=56.3MB, time=1.97 memory used=110.6MB, alloc=60.3MB, time=3.07 memory used=151.1MB, alloc=84.3MB, time=4.14 memory used=214.6MB, alloc=92.3MB, time=5.84 memory used=276.5MB, alloc=116.3MB, time=7.50 memory used=357.9MB, alloc=140.3MB, time=9.70 memory used=434.5MB, alloc=396.3MB, time=11.75 memory used=543.5MB, alloc=420.3MB, time=14.68 memory used=680.4MB, alloc=444.3MB, time=18.05 memory used=828.9MB, alloc=468.3MB, time=22.13 memory used=969.8MB, alloc=468.3MB, time=26.29 memory used=1092.7MB, alloc=492.3MB, time=29.73 memory used=1209.0MB, alloc=492.3MB, time=33.13 memory used=1309.4MB, alloc=492.3MB, time=36.24 memory used=1424.0MB, alloc=492.3MB, time=39.60 memory used=1538.8MB, alloc=492.3MB, time=43.39 memory used=1637.6MB, alloc=516.3MB, time=46.86 memory used=1728.4MB, alloc=516.3MB, time=49.98 memory used=1812.1MB, alloc=516.3MB, time=52.86 memory used=1900.3MB, alloc=516.3MB, time=56.01 memory used=1974.2MB, alloc=516.3MB, time=58.65 memory used=2038.5MB, alloc=516.3MB, time=61.00 memory used=2122.4MB, alloc=516.3MB, time=64.08 memory used=2194.0MB, alloc=516.3MB, time=66.78 memory used=2251.7MB, alloc=516.3MB, time=68.79 memory used=2460.6MB, alloc=540.3MB, time=76.13 memory used=2689.6MB, alloc=564.3MB, time=84.76 memory used=2941.8MB, alloc=588.3MB, time=93.67 memory used=3172.3MB, alloc=612.3MB, time=102.58 memory used=3386.4MB, alloc=636.3MB, time=110.70 memory used=3558.7MB, alloc=660.3MB, time=117.29 memory used=3737.5MB, alloc=684.3MB, time=124.41 memory used=3917.4MB, alloc=684.3MB, time=131.64 |\^/| 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(); 1428282744 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [7 x y + 8 y + 2 y z - 5 x, 13 y z - 17 z + 7 z + 10, 2 -12 x z + 18 y z - 16 z + 16 y] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; G := [ 2 2 2 9 x + 2 x - 10 y + 14 z, y z + 8 z + 12 y + 2, -5 x + 14 y z - 10 y + 8] > Problem := [F,G]; 2 2 Problem := [[7 x y + 8 y + 2 y z - 5 x, 13 y z - 17 z + 7 z + 10, 2 -12 x z + 18 y z - 16 z + 16 y], [ 2 2 2 9 x + 2 x - 10 y + 14 z, y z + 8 z + 12 y + 2, -5 x + 14 y z - 10 y + 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=26.4MB, alloc=32.3MB, time=0.88 memory used=46.6MB, alloc=32.3MB, time=1.41 memory used=64.6MB, alloc=56.3MB, time=1.89 memory used=105.6MB, alloc=60.3MB, time=2.96 memory used=145.9MB, alloc=84.3MB, time=4.04 memory used=210.2MB, alloc=92.3MB, time=5.73 memory used=274.9MB, alloc=116.3MB, time=7.39 memory used=341.2MB, alloc=116.3MB, time=9.12 memory used=414.5MB, alloc=372.3MB, time=11.06 memory used=499.9MB, alloc=396.3MB, time=13.30 memory used=612.5MB, alloc=420.3MB, time=16.03 memory used=743.2MB, alloc=420.3MB, time=19.67 memory used=872.0MB, alloc=444.3MB, time=23.24 memory used=998.3MB, alloc=468.3MB, time=26.76 memory used=1127.9MB, alloc=468.3MB, time=30.49 memory used=1234.7MB, alloc=492.3MB, time=33.44 memory used=1345.7MB, alloc=492.3MB, time=36.41 memory used=1453.0MB, alloc=492.3MB, time=39.36 memory used=1574.4MB, alloc=492.3MB, time=43.36 memory used=1669.2MB, alloc=492.3MB, time=46.01 memory used=1764.2MB, alloc=492.3MB, time=48.80 memory used=1855.3MB, alloc=516.3MB, time=51.50 memory used=1940.2MB, alloc=516.3MB, time=54.32 memory used=2025.7MB, alloc=516.3MB, time=57.22 memory used=2092.9MB, alloc=516.3MB, time=59.20 memory used=2164.6MB, alloc=516.3MB, time=61.77 memory used=2226.4MB, alloc=516.3MB, time=63.46 memory used=2295.2MB, alloc=516.3MB, time=66.06 memory used=2353.2MB, alloc=516.3MB, time=68.11 memory used=2410.5MB, alloc=516.3MB, time=70.26 memory used=2474.9MB, alloc=516.3MB, time=72.51 memory used=2531.3MB, alloc=516.3MB, time=74.56 memory used=2747.2MB, alloc=540.3MB, time=80.66 memory used=2967.1MB, alloc=564.3MB, time=86.48 memory used=3185.6MB, alloc=588.3MB, time=93.08 memory used=3383.2MB, alloc=612.3MB, time=98.79 memory used=3582.6MB, alloc=636.3MB, time=105.67 memory used=3772.7MB, alloc=660.3MB, time=112.15 memory used=3941.7MB, alloc=660.3MB, time=118.37 |\^/| 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(); 1428283044 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [13 x z + 19 y - 8 z + 15, 18 x - 7 z + 14 y - 13, 2 2 20 x y - 5 y + 14 z - 4] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-2 x y - 11 y z + z + 20, 2 x - 5 x z - 8 z - 16 y, 2 2 17 x - 10 y z + 20 z - 8 x] > Problem := [F,G]; 2 2 Problem := [[13 x z + 19 y - 8 z + 15, 18 x - 7 z + 14 y - 13, 2 2 20 x y - 5 y + 14 z - 4], [-2 x y - 11 y z + z + 20, 2 2 2 2 2 x - 5 x z - 8 z - 16 y, 17 x - 10 y z + 20 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=4.3MB, alloc=32.3MB, time=0.29 memory used=27.0MB, alloc=32.3MB, time=0.90 memory used=47.7MB, alloc=56.3MB, time=1.46 memory used=89.3MB, alloc=60.3MB, time=2.55 memory used=129.5MB, alloc=84.3MB, time=3.61 memory used=164.0MB, alloc=84.3MB, time=4.49 memory used=228.6MB, alloc=92.3MB, time=6.17 memory used=291.1MB, alloc=116.3MB, time=7.80 memory used=364.4MB, alloc=116.3MB, time=9.72 memory used=432.2MB, alloc=372.3MB, time=11.56 memory used=518.7MB, alloc=396.3MB, time=13.93 memory used=627.2MB, alloc=396.3MB, time=16.88 memory used=737.4MB, alloc=420.3MB, time=19.67 memory used=870.4MB, alloc=444.3MB, time=23.41 memory used=990.5MB, alloc=444.3MB, time=26.54 memory used=1117.3MB, alloc=468.3MB, time=30.14 memory used=1235.1MB, alloc=492.3MB, time=33.40 memory used=1334.0MB, alloc=492.3MB, time=35.97 memory used=1441.0MB, alloc=492.3MB, time=39.02 memory used=1541.0MB, alloc=492.3MB, time=42.00 memory used=1632.8MB, alloc=516.3MB, time=44.63 memory used=1742.6MB, alloc=516.3MB, time=48.04 memory used=1831.5MB, alloc=516.3MB, time=49.87 memory used=1901.3MB, alloc=516.3MB, time=51.21 memory used=1991.4MB, alloc=516.3MB, time=52.98 memory used=2073.8MB, alloc=516.3MB, time=54.92 memory used=2124.2MB, alloc=516.3MB, time=56.01 memory used=2174.2MB, alloc=516.3MB, time=56.96 memory used=2236.7MB, alloc=540.3MB, time=58.75 memory used=2279.0MB, alloc=540.3MB, time=59.88 memory used=2483.8MB, alloc=564.3MB, time=63.76 memory used=2673.1MB, alloc=588.3MB, time=67.62 memory used=2873.9MB, alloc=612.3MB, time=71.55 memory used=3074.2MB, alloc=636.3MB, time=75.95 memory used=3247.8MB, alloc=660.3MB, time=79.41 memory used=3374.2MB, alloc=660.3MB, time=81.65 memory used=3534.7MB, alloc=660.3MB, time=85.09 memory used=3669.9MB, alloc=660.3MB, time=88.35 memory used=3807.0MB, alloc=660.3MB, time=91.32 memory used=3914.2MB, alloc=660.3MB, time=93.57 memory used=4038.9MB, alloc=684.3MB, time=96.54 memory used=4160.7MB, alloc=684.3MB, time=100.07 memory used=4248.8MB, alloc=684.3MB, time=102.48 memory used=4599.4MB, alloc=708.3MB, time=110.76 memory used=4979.5MB, alloc=732.3MB, time=118.49 memory used=5373.2MB, alloc=756.3MB, time=126.87 memory used=5765.1MB, alloc=780.3MB, time=136.79 |\^/| 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(); 1428283344 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [13 x y - 20 y - 8 y z - 7, 7 x - 13 x z + 7 z + 17 z, 2 -16 x + 18 x y - 18 y z + 15 z] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 G := [14 x z + 19 y - 3 z + 13 z, -18 y - z - 9 z + 5, -16 x z - 3 z + 9] > Problem := [F,G]; 2 2 2 Problem := [[13 x y - 20 y - 8 y z - 7, 7 x - 13 x z + 7 z + 17 z, 2 -16 x + 18 x y - 18 y z + 15 z], 2 2 2 2 2 [14 x z + 19 y - 3 z + 13 z, -18 y - z - 9 z + 5, -16 x z - 3 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=0.17 memory used=25.1MB, alloc=32.3MB, time=0.48 memory used=45.1MB, alloc=56.3MB, time=0.79 memory used=83.8MB, alloc=60.3MB, time=1.26 memory used=127.7MB, alloc=68.3MB, time=1.85 memory used=170.1MB, alloc=68.3MB, time=2.42 memory used=211.0MB, alloc=92.3MB, time=3.02 memory used=277.7MB, alloc=92.3MB, time=3.92 memory used=349.9MB, alloc=92.3MB, time=4.83 memory used=414.2MB, alloc=92.3MB, time=5.81 memory used=463.6MB, alloc=116.3MB, time=6.32 memory used=539.7MB, alloc=372.3MB, time=7.27 memory used=628.5MB, alloc=372.3MB, time=8.55 memory used=711.6MB, alloc=396.3MB, time=9.95 memory used=822.4MB, alloc=396.3MB, time=11.73 memory used=930.1MB, alloc=420.3MB, time=13.47 memory used=1051.5MB, alloc=420.3MB, time=14.87 memory used=1183.3MB, alloc=420.3MB, time=16.70 memory used=1310.8MB, alloc=444.3MB, time=18.83 memory used=1456.6MB, alloc=468.3MB, time=21.34 memory used=1596.2MB, alloc=468.3MB, time=23.81 memory used=1728.6MB, alloc=468.3MB, time=25.72 memory used=1846.6MB, alloc=492.3MB, time=27.88 memory used=1962.8MB, alloc=492.3MB, time=29.86 memory used=2082.0MB, alloc=492.3MB, time=31.69 memory used=2178.4MB, alloc=492.3MB, time=33.56 memory used=2270.5MB, alloc=516.3MB, time=35.25 memory used=2378.2MB, alloc=516.3MB, time=37.47 memory used=2491.2MB, alloc=516.3MB, time=39.92 memory used=2576.4MB, alloc=516.3MB, time=41.60 memory used=2665.2MB, alloc=516.3MB, time=43.27 memory used=2739.8MB, alloc=516.3MB, time=44.69 memory used=2819.4MB, alloc=516.3MB, time=46.47 memory used=2908.3MB, alloc=516.3MB, time=48.55 memory used=2983.6MB, alloc=540.3MB, time=50.08 memory used=3058.2MB, alloc=540.3MB, time=51.45 memory used=3181.6MB, alloc=540.3MB, time=52.94 memory used=3280.0MB, alloc=540.3MB, time=54.18 memory used=3336.2MB, alloc=540.3MB, time=55.16 memory used=3409.4MB, alloc=540.3MB, time=56.84 memory used=3470.2MB, alloc=540.3MB, time=57.94 memory used=3547.0MB, alloc=540.3MB, time=59.22 memory used=3611.1MB, alloc=540.3MB, time=60.58 memory used=3853.7MB, alloc=564.3MB, time=63.91 memory used=4080.0MB, alloc=588.3MB, time=68.02 memory used=4311.3MB, alloc=612.3MB, time=73.06 memory used=4521.9MB, alloc=636.3MB, time=76.95 memory used=4720.7MB, alloc=636.3MB, time=81.05 memory used=4918.8MB, alloc=660.3MB, time=84.89 memory used=5135.8MB, alloc=684.3MB, time=90.30 memory used=5322.4MB, alloc=684.3MB, time=94.21 memory used=5508.1MB, alloc=684.3MB, time=98.77 memory used=5659.1MB, alloc=708.3MB, time=102.18 memory used=5809.2MB, alloc=708.3MB, time=105.57 memory used=5943.0MB, alloc=708.3MB, time=108.63 memory used=6051.5MB, alloc=708.3MB, time=111.27 memory used=6217.9MB, alloc=708.3MB, time=115.02 memory used=6338.7MB, alloc=708.3MB, time=118.22 memory used=6484.8MB, alloc=708.3MB, time=122.03 memory used=6566.4MB, alloc=708.3MB, time=124.23 memory used=6688.3MB, alloc=732.3MB, time=126.58 memory used=6816.1MB, alloc=732.3MB, time=129.12 memory used=7213.7MB, alloc=756.3MB, time=136.84 |\^/| 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(); 1428283644 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [11 y + 15 y z - 19 z + 11 y, -4 x y + 10 x z + 11 y z + 12, 2 -3 x y - 10 y z - 4 z - 4 x] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [-8 x y - 12 z - 9 x - 15 z, -19 x - 12 y + 16 z + 17, 2 15 x - 18 y z + 4 x - 5] > Problem := [F,G]; 2 2 Problem := [[11 y + 15 y z - 19 z + 11 y, -4 x y + 10 x z + 11 y z + 12, 2 2 -3 x y - 10 y z - 4 z - 4 x], [-8 x y - 12 z - 9 x - 15 z, 2 2 2 -19 x - 12 y + 16 z + 17, 15 x - 18 y z + 4 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=4.3MB, alloc=32.3MB, time=0.18 memory used=26.3MB, alloc=32.3MB, time=0.51 memory used=46.5MB, alloc=56.3MB, time=0.84 memory used=87.1MB, alloc=60.3MB, time=1.46 memory used=129.7MB, alloc=92.3MB, time=2.08 memory used=198.4MB, alloc=92.3MB, time=3.02 memory used=262.8MB, alloc=116.3MB, time=4.02 memory used=328.1MB, alloc=372.3MB, time=4.92 memory used=419.2MB, alloc=372.3MB, time=6.21 memory used=509.5MB, alloc=396.3MB, time=7.47 memory used=617.3MB, alloc=420.3MB, time=9.18 memory used=742.9MB, alloc=420.3MB, time=10.97 memory used=864.7MB, alloc=444.3MB, time=12.74 memory used=988.7MB, alloc=468.3MB, time=14.76 memory used=1089.6MB, alloc=468.3MB, time=16.20 memory used=1186.7MB, alloc=468.3MB, time=17.70 memory used=1293.2MB, alloc=492.3MB, time=19.53 memory used=1385.5MB, alloc=492.3MB, time=20.87 memory used=1493.0MB, alloc=492.3MB, time=22.79 memory used=1576.4MB, alloc=492.3MB, time=24.49 memory used=1654.6MB, alloc=516.3MB, time=25.59 memory used=1739.3MB, alloc=516.3MB, time=27.01 memory used=1800.1MB, alloc=516.3MB, time=28.28 memory used=1873.7MB, alloc=516.3MB, time=29.77 memory used=1926.2MB, alloc=516.3MB, time=30.94 memory used=1993.4MB, alloc=516.3MB, time=32.28 memory used=2039.9MB, alloc=516.3MB, time=33.53 memory used=2089.0MB, alloc=516.3MB, time=34.49 memory used=2307.6MB, alloc=540.3MB, time=37.88 memory used=2525.2MB, alloc=564.3MB, time=41.55 memory used=2703.2MB, alloc=588.3MB, time=44.36 memory used=2890.3MB, alloc=612.3MB, time=47.38 memory used=3062.1MB, alloc=636.3MB, time=49.86 memory used=3220.0MB, alloc=636.3MB, time=53.05 memory used=3369.0MB, alloc=660.3MB, time=56.34 memory used=3500.6MB, alloc=660.3MB, time=59.67 memory used=3626.5MB, alloc=660.3MB, time=62.60 memory used=3759.7MB, alloc=660.3MB, time=65.05 memory used=3861.0MB, alloc=684.3MB, time=66.91 memory used=3963.1MB, alloc=684.3MB, time=69.40 memory used=4061.1MB, alloc=684.3MB, time=71.51 memory used=4167.4MB, alloc=684.3MB, time=74.22 memory used=4536.7MB, alloc=708.3MB, time=80.37 memory used=4919.9MB, alloc=732.3MB, time=87.45 memory used=5308.9MB, alloc=756.3MB, time=95.66 memory used=5681.7MB, alloc=780.3MB, time=103.58 memory used=6046.7MB, alloc=804.3MB, time=110.37 memory used=6372.1MB, alloc=828.3MB, time=116.93 memory used=6663.9MB, alloc=852.3MB, time=123.77 memory used=6924.5MB, alloc=876.3MB, time=129.54 memory used=7201.0MB, alloc=900.3MB, time=136.00 memory used=7459.5MB, alloc=924.3MB, time=143.31 |\^/| 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(); 1428283944 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [16 x + 4 y z + 15 z - 11, 11 x - 11 x y + 20 y + 12, 2 -y - y z - 12 x - 8] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-8 x y - 7 z + 9 x + 15 z, -6 x - 18 x z + 15 x - 18, 19 x y + 17 x z - y - 10 z] > Problem := [F,G]; 2 2 2 Problem := [[16 x + 4 y z + 15 z - 11, 11 x - 11 x y + 20 y + 12, 2 2 -y - y z - 12 x - 8], [-8 x y - 7 z + 9 x + 15 z, 2 -6 x - 18 x z + 15 x - 18, 19 x y + 17 x z - 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=26.7MB, alloc=32.3MB, time=0.51 memory used=47.3MB, alloc=32.3MB, time=0.82 memory used=66.4MB, alloc=56.3MB, time=1.12 memory used=107.2MB, alloc=60.3MB, time=1.74 memory used=146.0MB, alloc=84.3MB, time=2.35 memory used=208.6MB, alloc=92.3MB, time=3.34 memory used=270.3MB, alloc=116.3MB, time=4.33 memory used=354.5MB, alloc=116.3MB, time=5.71 memory used=439.2MB, alloc=140.3MB, time=7.08 memory used=520.2MB, alloc=140.3MB, time=8.41 memory used=595.4MB, alloc=396.3MB, time=9.69 memory used=699.9MB, alloc=420.3MB, time=11.51 memory used=829.6MB, alloc=444.3MB, time=13.69 memory used=983.6MB, alloc=468.3MB, time=16.49 memory used=1131.2MB, alloc=468.3MB, time=19.11 memory used=1255.6MB, alloc=492.3MB, time=21.16 memory used=1405.8MB, alloc=516.3MB, time=24.37 memory used=1526.4MB, alloc=516.3MB, time=26.64 memory used=1636.5MB, alloc=516.3MB, time=28.71 memory used=1735.2MB, alloc=516.3MB, time=30.70 memory used=1845.0MB, alloc=516.3MB, time=33.02 memory used=1934.2MB, alloc=516.3MB, time=34.79 memory used=2030.6MB, alloc=516.3MB, time=36.81 memory used=2116.9MB, alloc=516.3MB, time=38.64 memory used=2202.9MB, alloc=516.3MB, time=40.42 memory used=2291.8MB, alloc=516.3MB, time=42.31 memory used=2369.1MB, alloc=540.3MB, time=44.12 memory used=2437.2MB, alloc=540.3MB, time=45.78 memory used=2510.4MB, alloc=540.3MB, time=47.55 memory used=2559.4MB, alloc=540.3MB, time=48.77 memory used=2624.7MB, alloc=540.3MB, time=50.54 memory used=2856.0MB, alloc=564.3MB, time=55.89 memory used=3081.3MB, alloc=588.3MB, time=60.99 memory used=3301.0MB, alloc=612.3MB, time=66.29 memory used=3513.3MB, alloc=636.3MB, time=71.51 memory used=3755.4MB, alloc=660.3MB, time=77.54 memory used=3962.6MB, alloc=660.3MB, time=82.86 memory used=4150.5MB, alloc=684.3MB, time=87.58 memory used=4337.5MB, alloc=684.3MB, time=92.69 memory used=4500.5MB, alloc=684.3MB, time=97.09 memory used=4636.1MB, alloc=684.3MB, time=100.63 memory used=4797.8MB, alloc=708.3MB, time=105.49 memory used=4946.0MB, alloc=708.3MB, time=109.85 memory used=5062.3MB, alloc=708.3MB, time=113.48 memory used=5174.7MB, alloc=708.3MB, time=116.87 memory used=5286.3MB, alloc=708.3MB, time=120.46 memory used=5663.6MB, alloc=732.3MB, time=129.48 memory used=6062.1MB, alloc=756.3MB, time=138.54 |\^/| 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(); 1428284244 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-14 x - 14 y + 7 z + 3, -19 x - 6 y + 16, 17 y + 17 y z + 12] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [4 x z + 19 z - 16 x - 10 y, 6 x + 19 x z - 13 y z - 2 y, 2 -x y + 10 y + 6 x - 15 z] > Problem := [F,G]; 2 2 2 Problem := [[-14 x - 14 y + 7 z + 3, -19 x - 6 y + 16, 17 y + 17 y z + 12], 2 2 [4 x z + 19 z - 16 x - 10 y, 6 x + 19 x z - 13 y z - 2 y, 2 -x y + 10 y + 6 x - 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=0.18 memory used=27.0MB, alloc=32.3MB, time=0.51 memory used=47.7MB, alloc=32.3MB, time=0.81 memory used=67.0MB, alloc=56.3MB, time=1.11 memory used=108.4MB, alloc=60.3MB, time=1.72 memory used=147.6MB, alloc=84.3MB, time=2.30 memory used=212.2MB, alloc=92.3MB, time=3.28 memory used=275.4MB, alloc=116.3MB, time=4.28 memory used=343.4MB, alloc=116.3MB, time=5.33 memory used=411.4MB, alloc=372.3MB, time=6.45 memory used=496.1MB, alloc=396.3MB, time=7.76 memory used=604.5MB, alloc=420.3MB, time=9.44 memory used=733.3MB, alloc=444.3MB, time=11.47 memory used=839.3MB, alloc=444.3MB, time=13.12 memory used=965.5MB, alloc=468.3MB, time=15.22 memory used=1063.7MB, alloc=468.3MB, time=16.83 memory used=1143.5MB, alloc=468.3MB, time=18.00 memory used=1247.5MB, alloc=492.3MB, time=20.00 memory used=1329.2MB, alloc=492.3MB, time=21.29 memory used=1421.2MB, alloc=492.3MB, time=22.98 memory used=1500.6MB, alloc=492.3MB, time=24.59 memory used=1573.3MB, alloc=492.3MB, time=26.13 memory used=1626.7MB, alloc=492.3MB, time=27.19 memory used=1690.9MB, alloc=492.3MB, time=28.61 memory used=1739.1MB, alloc=492.3MB, time=29.69 memory used=1800.4MB, alloc=492.3MB, time=31.09 memory used=1849.2MB, alloc=492.3MB, time=32.11 memory used=2035.4MB, alloc=516.3MB, time=35.38 memory used=2223.7MB, alloc=540.3MB, time=38.84 memory used=2387.7MB, alloc=564.3MB, time=42.07 memory used=2560.0MB, alloc=588.3MB, time=45.40 memory used=2723.1MB, alloc=612.3MB, time=48.51 memory used=2896.4MB, alloc=636.3MB, time=52.40 memory used=3026.6MB, alloc=636.3MB, time=55.19 memory used=3150.3MB, alloc=636.3MB, time=57.85 memory used=3278.0MB, alloc=636.3MB, time=60.99 memory used=3408.1MB, alloc=636.3MB, time=64.34 memory used=3520.1MB, alloc=636.3MB, time=67.30 memory used=3608.0MB, alloc=660.3MB, time=69.54 memory used=3937.5MB, alloc=684.3MB, time=76.74 memory used=4289.4MB, alloc=708.3MB, time=84.45 memory used=4659.1MB, alloc=732.3MB, time=92.86 memory used=5049.7MB, alloc=756.3MB, time=101.17 memory used=5411.3MB, alloc=780.3MB, time=109.25 memory used=5712.9MB, alloc=804.3MB, time=115.92 memory used=6007.1MB, alloc=828.3MB, time=122.93 memory used=6277.9MB, alloc=852.3MB, time=129.40 |\^/| 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(); 1428284544 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [5 x - 9 x z - 6 y - 9 z, -18 x - 2 y - 13 z + 2 x, 17 x y - 5 x z - 6 y z - 13 z] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-15 y + 12 x - 14 z - 7, -x y + 20 y - 3 y z - 15 y, 2 -19 x y + 11 y + 5 y z - 10 z] > Problem := [F,G]; 2 2 2 2 Problem := [[5 x - 9 x z - 6 y - 9 z, -18 x - 2 y - 13 z + 2 x, 2 17 x y - 5 x z - 6 y z - 13 z], [-15 y + 12 x - 14 z - 7, 2 2 -x y + 20 y - 3 y z - 15 y, -19 x y + 11 y + 5 y z - 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=4.3MB, alloc=32.3MB, time=0.18 memory used=26.0MB, alloc=32.3MB, time=0.49 memory used=45.9MB, alloc=32.3MB, time=0.79 memory used=63.4MB, alloc=56.3MB, time=1.07 memory used=103.5MB, alloc=60.3MB, time=1.67 memory used=141.7MB, alloc=84.3MB, time=2.24 memory used=203.0MB, alloc=92.3MB, time=3.19 memory used=264.1MB, alloc=116.3MB, time=4.14 memory used=344.8MB, alloc=116.3MB, time=5.41 memory used=422.6MB, alloc=140.3MB, time=6.74 memory used=501.3MB, alloc=140.3MB, time=7.98 memory used=570.4MB, alloc=420.3MB, time=9.12 memory used=697.2MB, alloc=444.3MB, time=11.13 memory used=849.3MB, alloc=468.3MB, time=13.56 memory used=990.6MB, alloc=468.3MB, time=15.97 memory used=1106.5MB, alloc=492.3MB, time=17.90 memory used=1243.2MB, alloc=492.3MB, time=20.43 memory used=1359.2MB, alloc=492.3MB, time=22.61 memory used=1479.9MB, alloc=516.3MB, time=24.85 memory used=1579.7MB, alloc=516.3MB, time=26.82 memory used=1685.8MB, alloc=516.3MB, time=29.01 memory used=1779.2MB, alloc=516.3MB, time=31.04 memory used=1854.5MB, alloc=516.3MB, time=32.69 memory used=1937.0MB, alloc=516.3MB, time=34.64 memory used=1993.3MB, alloc=516.3MB, time=36.10 memory used=2057.3MB, alloc=540.3MB, time=37.58 memory used=2121.9MB, alloc=540.3MB, time=39.02 memory used=2184.0MB, alloc=540.3MB, time=40.51 memory used=2409.3MB, alloc=564.3MB, time=45.10 memory used=2629.2MB, alloc=588.3MB, time=49.48 memory used=2856.5MB, alloc=612.3MB, time=54.29 memory used=3089.2MB, alloc=636.3MB, time=59.95 memory used=3290.5MB, alloc=660.3MB, time=64.67 memory used=3490.0MB, alloc=684.3MB, time=69.56 memory used=3681.3MB, alloc=708.3MB, time=74.30 memory used=3847.1MB, alloc=732.3MB, time=78.70 memory used=3949.8MB, alloc=732.3MB, time=81.00 memory used=4085.3MB, alloc=732.3MB, time=84.86 memory used=4203.2MB, alloc=732.3MB, time=87.42 memory used=4299.5MB, alloc=732.3MB, time=89.84 memory used=4440.6MB, alloc=756.3MB, time=94.21 memory used=4867.2MB, alloc=780.3MB, time=102.77 memory used=5298.9MB, alloc=804.3MB, time=112.19 |\^/| 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(); 1428284844 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [4 x - 10 y z + 4 x + 8, -10 y + 19 y z - z , -18 x z - 10 x + 6 z - 3] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [-12 x + 17 x y + 9, 11 x y + 8 y + 4 y z + 10 z , -x - 13 y z + 9] > Problem := [F,G]; Problem := [ 2 2 2 [4 x - 10 y z + 4 x + 8, -10 y + 19 y z - z , -18 x z - 10 x + 6 z - 3], 2 2 2 2 [-12 x + 17 x y + 9, 11 x y + 8 y + 4 y z + 10 z , -x - 13 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=0.17 memory used=26.6MB, alloc=32.3MB, time=0.49 memory used=47.7MB, alloc=32.3MB, time=0.80 memory used=67.0MB, alloc=56.3MB, time=1.11 memory used=107.6MB, alloc=60.3MB, time=1.73 memory used=148.6MB, alloc=60.3MB, time=2.36 memory used=188.7MB, alloc=84.3MB, time=2.97 memory used=232.6MB, alloc=84.3MB, time=3.62 memory used=292.1MB, alloc=92.3MB, time=4.60 memory used=357.3MB, alloc=116.3MB, time=5.52 memory used=436.5MB, alloc=140.3MB, time=6.78 memory used=504.7MB, alloc=396.3MB, time=7.82 memory used=607.3MB, alloc=420.3MB, time=9.51 memory used=747.6MB, alloc=444.3MB, time=11.42 memory used=874.1MB, alloc=444.3MB, time=13.22 memory used=1010.6MB, alloc=468.3MB, time=15.37 memory used=1129.1MB, alloc=468.3MB, time=17.15 memory used=1241.2MB, alloc=468.3MB, time=18.87 memory used=1341.8MB, alloc=492.3MB, time=20.50 memory used=1448.0MB, alloc=492.3MB, time=21.97 memory used=1542.2MB, alloc=492.3MB, time=23.49 memory used=1635.9MB, alloc=492.3MB, time=24.92 memory used=1730.8MB, alloc=492.3MB, time=26.59 memory used=1813.0MB, alloc=492.3MB, time=28.11 memory used=1886.2MB, alloc=516.3MB, time=29.53 memory used=1950.0MB, alloc=516.3MB, time=30.69 memory used=2014.3MB, alloc=516.3MB, time=32.03 memory used=2089.5MB, alloc=516.3MB, time=33.42 memory used=2151.1MB, alloc=516.3MB, time=34.66 memory used=2215.0MB, alloc=516.3MB, time=36.13 memory used=2426.8MB, alloc=540.3MB, time=39.76 memory used=2647.4MB, alloc=564.3MB, time=43.84 memory used=2857.6MB, alloc=588.3MB, time=47.60 memory used=3055.0MB, alloc=612.3MB, time=51.20 memory used=3194.6MB, alloc=636.3MB, time=53.88 memory used=3362.3MB, alloc=660.3MB, time=57.33 memory used=3521.2MB, alloc=660.3MB, time=60.26 memory used=3633.2MB, alloc=660.3MB, time=62.57 memory used=3795.3MB, alloc=684.3MB, time=65.41 memory used=3952.4MB, alloc=684.3MB, time=68.22 memory used=4092.4MB, alloc=684.3MB, time=71.06 memory used=4170.9MB, alloc=684.3MB, time=73.07 memory used=4252.4MB, alloc=684.3MB, time=74.89 memory used=4344.5MB, alloc=684.3MB, time=77.06 memory used=4688.7MB, alloc=708.3MB, time=82.49 memory used=5073.4MB, alloc=732.3MB, time=89.34 memory used=5468.2MB, alloc=756.3MB, time=96.75 memory used=5851.5MB, alloc=780.3MB, time=103.64 memory used=6251.3MB, alloc=804.3MB, time=111.44 memory used=6620.9MB, alloc=828.3MB, time=119.44 memory used=7000.7MB, alloc=852.3MB, time=127.46 memory used=7326.4MB, alloc=876.3MB, time=135.15 |\^/| 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(); 1428285144 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; F := [ 2 2 2 2 -7 x y - 14 z - 12, -7 x y + y + 8 z + 20 z, -4 x y - 13 y - 9 x - 2 z] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-5 x z + z - 7 z + 16, -19 x - 8 x y + 5 y + 15, -9 x y + 9 x z - 12 y z + 16 z] > Problem := [F,G]; Problem := [[ 2 2 2 2 -7 x y - 14 z - 12, -7 x y + y + 8 z + 20 z, -4 x y - 13 y - 9 x - 2 z] 2 2 , [-5 x z + z - 7 z + 16, -19 x - 8 x y + 5 y + 15, -9 x y + 9 x z - 12 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=0.18 memory used=25.9MB, alloc=32.3MB, time=0.50 memory used=46.5MB, alloc=56.3MB, time=0.82 memory used=88.7MB, alloc=60.3MB, time=1.45 memory used=130.6MB, alloc=92.3MB, time=2.07 memory used=196.5MB, alloc=92.3MB, time=3.01 memory used=259.1MB, alloc=116.3MB, time=3.93 memory used=327.6MB, alloc=372.3MB, time=4.94 memory used=415.9MB, alloc=396.3MB, time=6.27 memory used=527.2MB, alloc=420.3MB, time=7.97 memory used=660.1MB, alloc=420.3MB, time=9.88 memory used=786.1MB, alloc=444.3MB, time=11.90 memory used=896.6MB, alloc=444.3MB, time=13.73 memory used=1020.8MB, alloc=468.3MB, time=15.41 memory used=1132.0MB, alloc=468.3MB, time=17.34 memory used=1240.0MB, alloc=468.3MB, time=19.29 memory used=1343.0MB, alloc=468.3MB, time=21.27 memory used=1438.2MB, alloc=492.3MB, time=23.09 memory used=1519.1MB, alloc=492.3MB, time=24.53 memory used=1608.4MB, alloc=492.3MB, time=26.16 memory used=1687.6MB, alloc=492.3MB, time=27.77 memory used=1765.8MB, alloc=492.3MB, time=29.44 memory used=1842.9MB, alloc=492.3MB, time=31.00 memory used=1914.1MB, alloc=492.3MB, time=32.47 memory used=1982.2MB, alloc=516.3MB, time=33.74 memory used=2042.5MB, alloc=516.3MB, time=35.16 memory used=2098.2MB, alloc=516.3MB, time=36.26 memory used=2160.1MB, alloc=516.3MB, time=37.53 memory used=2221.5MB, alloc=516.3MB, time=38.59 memory used=2271.2MB, alloc=516.3MB, time=39.66 memory used=2487.5MB, alloc=540.3MB, time=43.43 memory used=2711.4MB, alloc=564.3MB, time=47.64 memory used=2920.0MB, alloc=588.3MB, time=51.60 memory used=3108.7MB, alloc=612.3MB, time=55.45 memory used=3256.9MB, alloc=636.3MB, time=58.65 memory used=3428.2MB, alloc=660.3MB, time=62.73 memory used=3529.4MB, alloc=660.3MB, time=64.81 memory used=3658.3MB, alloc=660.3MB, time=67.75 memory used=3773.4MB, alloc=660.3MB, time=70.68 memory used=3898.7MB, alloc=660.3MB, time=73.63 memory used=4018.9MB, alloc=660.3MB, time=76.65 memory used=4102.6MB, alloc=684.3MB, time=78.91 memory used=4188.6MB, alloc=684.3MB, time=80.75 memory used=4531.8MB, alloc=708.3MB, time=88.57 memory used=4891.7MB, alloc=732.3MB, time=96.23 memory used=5285.5MB, alloc=756.3MB, time=104.63 memory used=5680.4MB, alloc=780.3MB, time=114.21 memory used=6037.4MB, alloc=804.3MB, time=122.81 memory used=6384.7MB, alloc=828.3MB, time=130.60 memory used=6679.2MB, alloc=852.3MB, time=137.05 |\^/| 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(); 1428285445 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [11 z - 8 x + 19, 2 x y + 16 y + 19 x - 7, 15 x - 10 x y + 15 x z - 18] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [2 x - 15 x y - 14 z - 16, -15 x y - 15 x - 11 y - 15, 2 14 x y + 18 y z + 14 z - 5 z] > Problem := [F,G]; Problem := [ 2 2 2 [11 z - 8 x + 19, 2 x y + 16 y + 19 x - 7, 15 x - 10 x y + 15 x z - 18], 2 2 [2 x - 15 x y - 14 z - 16, -15 x y - 15 x - 11 y - 15, 2 14 x y + 18 y z + 14 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=0.19 memory used=26.8MB, alloc=32.3MB, time=0.52 memory used=48.1MB, alloc=32.3MB, time=0.83 memory used=68.7MB, alloc=56.3MB, time=1.15 memory used=110.7MB, alloc=60.3MB, time=1.78 memory used=151.4MB, alloc=60.3MB, time=2.38 memory used=190.9MB, alloc=92.3MB, time=3.01 memory used=254.0MB, alloc=116.3MB, time=3.93 memory used=329.8MB, alloc=116.3MB, time=5.14 memory used=402.8MB, alloc=396.3MB, time=6.33 memory used=512.9MB, alloc=396.3MB, time=8.05 memory used=622.9MB, alloc=420.3MB, time=9.85 memory used=756.1MB, alloc=444.3MB, time=12.08 memory used=896.9MB, alloc=468.3MB, time=14.52 memory used=1039.6MB, alloc=468.3MB, time=17.06 memory used=1165.7MB, alloc=492.3MB, time=19.31 memory used=1297.0MB, alloc=492.3MB, time=21.70 memory used=1417.1MB, alloc=492.3MB, time=23.92 memory used=1516.1MB, alloc=492.3MB, time=25.83 memory used=1618.7MB, alloc=492.3MB, time=27.80 memory used=1713.0MB, alloc=516.3MB, time=29.64 memory used=1803.3MB, alloc=516.3MB, time=31.44 memory used=1888.6MB, alloc=516.3MB, time=33.19 memory used=1963.7MB, alloc=516.3MB, time=34.93 memory used=2035.1MB, alloc=516.3MB, time=36.52 memory used=2102.6MB, alloc=516.3MB, time=37.98 memory used=2171.6MB, alloc=516.3MB, time=39.73 memory used=2227.4MB, alloc=516.3MB, time=40.94 memory used=2286.1MB, alloc=540.3MB, time=42.31 memory used=2331.7MB, alloc=540.3MB, time=43.50 memory used=2544.2MB, alloc=564.3MB, time=47.67 memory used=2762.6MB, alloc=588.3MB, time=52.10 memory used=2991.4MB, alloc=612.3MB, time=56.78 memory used=3231.5MB, alloc=636.3MB, time=61.71 memory used=3483.5MB, alloc=660.3MB, time=66.89 memory used=3746.5MB, alloc=684.3MB, time=72.27 memory used=4015.8MB, alloc=708.3MB, time=77.79 memory used=4297.5MB, alloc=732.3MB, time=83.54 memory used=4569.1MB, alloc=756.3MB, time=91.36 memory used=4808.3MB, alloc=780.3MB, time=100.62 memory used=5058.1MB, alloc=804.3MB, time=110.71 memory used=5319.4MB, alloc=828.3MB, time=121.60 |\^/| 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(); 1428285745 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [8 x y + 20 z + 4 y + 6 z, 9 x y + 4 x z + 17 z - 2 z, x y + 4 y z - 16 y + 6] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [x y - 15 y z + 17 z - 17 x, 18 x z - 2 y + 20 z - 11, 4 x z - 15 x - 6 y + 18 z] > Problem := [F,G]; 2 2 Problem := [[8 x y + 20 z + 4 y + 6 z, 9 x y + 4 x z + 17 z - 2 z, 2 x y + 4 y z - 16 y + 6], [x y - 15 y z + 17 z - 17 x, 2 18 x z - 2 y + 20 z - 11, 4 x z - 15 x - 6 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=0.17 memory used=25.9MB, alloc=32.3MB, time=0.50 memory used=46.6MB, alloc=32.3MB, time=0.80 memory used=64.9MB, alloc=56.3MB, time=1.08 memory used=107.0MB, alloc=68.3MB, time=1.71 memory used=146.0MB, alloc=92.3MB, time=2.33 memory used=212.5MB, alloc=92.3MB, time=3.30 memory used=276.8MB, alloc=92.3MB, time=4.24 memory used=341.2MB, alloc=116.3MB, time=5.23 memory used=409.3MB, alloc=372.3MB, time=6.24 memory used=491.1MB, alloc=396.3MB, time=7.53 memory used=604.1MB, alloc=420.3MB, time=9.24 memory used=733.1MB, alloc=444.3MB, time=11.22 memory used=865.8MB, alloc=468.3MB, time=13.05 memory used=1011.4MB, alloc=492.3MB, time=15.59 memory used=1132.3MB, alloc=492.3MB, time=17.52 memory used=1245.4MB, alloc=492.3MB, time=19.30 memory used=1353.4MB, alloc=492.3MB, time=21.02 memory used=1444.0MB, alloc=516.3MB, time=22.40 memory used=1536.9MB, alloc=516.3MB, time=24.23 memory used=1629.4MB, alloc=516.3MB, time=26.05 memory used=1715.7MB, alloc=516.3MB, time=27.60 memory used=1786.7MB, alloc=516.3MB, time=28.99 memory used=1857.8MB, alloc=516.3MB, time=30.11 memory used=1934.5MB, alloc=516.3MB, time=31.92 memory used=2000.1MB, alloc=516.3MB, time=33.49 memory used=2053.8MB, alloc=516.3MB, time=34.54 memory used=2110.9MB, alloc=516.3MB, time=35.86 memory used=2163.2MB, alloc=516.3MB, time=37.03 memory used=2211.7MB, alloc=516.3MB, time=38.15 memory used=2412.5MB, alloc=540.3MB, time=41.81 memory used=2628.5MB, alloc=564.3MB, time=45.88 memory used=2818.0MB, alloc=588.3MB, time=49.07 memory used=3024.9MB, alloc=612.3MB, time=53.15 memory used=3217.4MB, alloc=636.3MB, time=56.46 memory used=3397.8MB, alloc=660.3MB, time=59.94 memory used=3572.3MB, alloc=660.3MB, time=63.42 memory used=3737.0MB, alloc=660.3MB, time=66.87 memory used=3872.5MB, alloc=660.3MB, time=69.94 memory used=4042.2MB, alloc=660.3MB, time=74.21 memory used=4161.0MB, alloc=684.3MB, time=77.28 memory used=4293.1MB, alloc=684.3MB, time=80.66 memory used=4400.3MB, alloc=684.3MB, time=83.51 memory used=4510.4MB, alloc=684.3MB, time=86.97 memory used=4866.6MB, alloc=708.3MB, time=94.48 memory used=5219.5MB, alloc=732.3MB, time=103.49 memory used=5616.2MB, alloc=756.3MB, time=112.09 memory used=6014.1MB, alloc=780.3MB, time=120.94 memory used=6409.4MB, alloc=804.3MB, time=129.99 |\^/| 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(); 1428286045 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-19 x z - 4 z - 13 x - 9 z, -7 y + 9 z + 8, -x y + 7 y z + 12 y + 19 z] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [-2 x y - 7 x z + 6 z - 18, -6 x - 14 x y - 15 y - 2, 2 11 x - 9 y z - 19 x + 7] > Problem := [F,G]; Problem := [ 2 2 [-19 x z - 4 z - 13 x - 9 z, -7 y + 9 z + 8, -x y + 7 y z + 12 y + 19 z], 2 [-2 x y - 7 x z + 6 z - 18, -6 x - 14 x y - 15 y - 2, 2 11 x - 9 y z - 19 x + 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=48.2MB, alloc=32.3MB, time=0.83 memory used=67.8MB, alloc=56.3MB, time=1.14 memory used=108.2MB, alloc=60.3MB, time=1.75 memory used=148.2MB, alloc=84.3MB, time=2.33 memory used=211.3MB, alloc=92.3MB, time=3.27 memory used=273.6MB, alloc=116.3MB, time=4.27 memory used=358.2MB, alloc=116.3MB, time=5.63 memory used=439.7MB, alloc=396.3MB, time=7.03 memory used=547.3MB, alloc=420.3MB, time=8.77 memory used=677.7MB, alloc=444.3MB, time=10.90 memory used=816.2MB, alloc=468.3MB, time=13.20 memory used=950.6MB, alloc=468.3MB, time=15.49 memory used=1087.1MB, alloc=492.3MB, time=18.01 memory used=1210.5MB, alloc=492.3MB, time=20.21 memory used=1345.4MB, alloc=492.3MB, time=22.87 memory used=1447.4MB, alloc=516.3MB, time=24.80 memory used=1546.5MB, alloc=516.3MB, time=27.07 memory used=1645.2MB, alloc=516.3MB, time=29.28 memory used=1726.8MB, alloc=516.3MB, time=31.28 memory used=1806.0MB, alloc=516.3MB, time=33.11 memory used=1864.5MB, alloc=516.3MB, time=34.51 memory used=1928.2MB, alloc=516.3MB, time=36.06 memory used=2007.7MB, alloc=516.3MB, time=37.97 memory used=2053.5MB, alloc=516.3MB, time=39.08 memory used=2102.5MB, alloc=516.3MB, time=40.27 memory used=2153.7MB, alloc=516.3MB, time=41.48 memory used=2216.9MB, alloc=516.3MB, time=43.15 memory used=2421.6MB, alloc=540.3MB, time=47.79 memory used=2627.6MB, alloc=564.3MB, time=52.33 memory used=2863.4MB, alloc=588.3MB, time=58.50 memory used=3067.7MB, alloc=612.3MB, time=63.06 memory used=3256.8MB, alloc=636.3MB, time=66.93 memory used=3419.8MB, alloc=660.3MB, time=70.49 memory used=3574.7MB, alloc=660.3MB, time=74.03 memory used=3714.3MB, alloc=684.3MB, time=77.58 memory used=3853.2MB, alloc=684.3MB, time=80.94 memory used=3963.8MB, alloc=684.3MB, time=83.60 memory used=4090.0MB, alloc=684.3MB, time=86.94 memory used=4186.5MB, alloc=684.3MB, time=89.59 memory used=4279.2MB, alloc=684.3MB, time=92.21 memory used=4345.3MB, alloc=708.3MB, time=94.32 memory used=4710.6MB, alloc=732.3MB, time=102.86 memory used=5075.6MB, alloc=756.3MB, time=110.42 memory used=5440.2MB, alloc=780.3MB, time=118.06 memory used=5800.2MB, alloc=804.3MB, time=125.74 memory used=6139.0MB, alloc=828.3MB, time=133.28 |\^/| 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(); 1428286345 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [18 x y + 7 y z - 20 z - 13, -16 x z - 17 y - 11 z + 15, 2 2 -x - 3 x z - 2 z - 19 z] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [x y - 16 x z - 11 y z - 9 x, 5 x z + 3 y + 19 x + 16 y, 18 x y - 6 x z + 16 x - 6] > Problem := [F,G]; 2 2 Problem := [[18 x y + 7 y z - 20 z - 13, -16 x z - 17 y - 11 z + 15, 2 2 -x - 3 x z - 2 z - 19 z], [x y - 16 x z - 11 y z - 9 x, 2 5 x z + 3 y + 19 x + 16 y, 18 x y - 6 x z + 16 x - 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=0.52 memory used=46.7MB, alloc=32.3MB, time=0.82 memory used=64.5MB, alloc=56.3MB, time=1.13 memory used=105.5MB, alloc=60.3MB, time=1.76 memory used=141.0MB, alloc=60.3MB, time=2.28 memory used=180.9MB, alloc=92.3MB, time=2.90 memory used=244.0MB, alloc=92.3MB, time=3.85 memory used=306.1MB, alloc=116.3MB, time=4.81 memory used=381.6MB, alloc=372.3MB, time=6.03 memory used=463.4MB, alloc=396.3MB, time=7.34 memory used=573.2MB, alloc=420.3MB, time=9.09 memory used=703.2MB, alloc=444.3MB, time=11.31 memory used=830.6MB, alloc=444.3MB, time=13.24 memory used=967.0MB, alloc=468.3MB, time=15.72 memory used=1088.8MB, alloc=468.3MB, time=17.86 memory used=1194.9MB, alloc=492.3MB, time=19.76 memory used=1299.5MB, alloc=492.3MB, time=21.66 memory used=1397.4MB, alloc=492.3MB, time=23.42 memory used=1504.7MB, alloc=492.3MB, time=25.66 memory used=1598.9MB, alloc=492.3MB, time=27.61 memory used=1693.6MB, alloc=492.3MB, time=29.55 memory used=1784.5MB, alloc=492.3MB, time=31.41 memory used=1863.5MB, alloc=492.3MB, time=33.19 memory used=1943.6MB, alloc=516.3MB, time=35.02 memory used=2011.0MB, alloc=516.3MB, time=36.72 memory used=2080.8MB, alloc=516.3MB, time=38.45 memory used=2156.0MB, alloc=516.3MB, time=40.39 memory used=2198.9MB, alloc=516.3MB, time=41.46 memory used=2258.5MB, alloc=516.3MB, time=42.95 memory used=2465.2MB, alloc=540.3MB, time=46.95 memory used=2676.0MB, alloc=564.3MB, time=51.24 memory used=2912.9MB, alloc=588.3MB, time=56.84 memory used=3055.3MB, alloc=612.3MB, time=59.98 memory used=3233.9MB, alloc=636.3MB, time=63.93 memory used=3385.1MB, alloc=660.3MB, time=67.15 memory used=3535.1MB, alloc=660.3MB, time=70.56 memory used=3676.4MB, alloc=660.3MB, time=74.31 memory used=3808.9MB, alloc=660.3MB, time=77.46 memory used=3920.6MB, alloc=684.3MB, time=80.49 memory used=4031.0MB, alloc=684.3MB, time=83.21 memory used=4135.6MB, alloc=684.3MB, time=85.80 memory used=4258.3MB, alloc=684.3MB, time=89.65 memory used=4348.6MB, alloc=684.3MB, time=92.31 memory used=4437.3MB, alloc=684.3MB, time=95.33 memory used=4791.3MB, alloc=708.3MB, time=101.04 memory used=5155.9MB, alloc=732.3MB, time=108.54 memory used=5532.0MB, alloc=756.3MB, time=116.18 memory used=5865.7MB, alloc=780.3MB, time=123.33 memory used=6200.6MB, alloc=804.3MB, time=130.61 memory used=6475.0MB, alloc=828.3MB, time=137.42 memory used=6810.6MB, alloc=852.3MB, time=146.12 memory used=7063.6MB, alloc=876.3MB, time=151.45 |\^/| 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(); 1428286645 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-11 x y - 17 z - 15 x, -10 x + 3 x z + 13 z + 16 y, 2 2 15 x + 19 y - 3 x + 12 z] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 G := [-18 x + 9 y - 3, 20 x - 5 x z + 19 z - 9 x, 14 y + 17 z + 16 y - 6] > Problem := [F,G]; 2 2 2 Problem := [[-11 x y - 17 z - 15 x, -10 x + 3 x z + 13 z + 16 y, 2 2 15 x + 19 y - 3 x + 12 z], 2 2 2 2 2 [-18 x + 9 y - 3, 20 x - 5 x z + 19 z - 9 x, 14 y + 17 z + 16 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=32.0MB, alloc=44.3MB, time=0.59 memory used=59.0MB, alloc=44.3MB, time=0.97 memory used=84.8MB, alloc=68.3MB, time=1.36 memory used=134.3MB, alloc=76.3MB, time=2.06 memory used=182.1MB, alloc=100.3MB, time=2.75 memory used=253.2MB, alloc=100.3MB, time=3.79 memory used=323.3MB, alloc=100.3MB, time=4.84 memory used=392.3MB, alloc=124.3MB, time=5.86 memory used=455.9MB, alloc=380.3MB, time=6.75 memory used=548.8MB, alloc=380.3MB, time=8.15 memory used=641.6MB, alloc=404.3MB, time=9.54 memory used=754.2MB, alloc=428.3MB, time=11.32 memory used=885.4MB, alloc=428.3MB, time=13.17 memory used=1019.7MB, alloc=452.3MB, time=15.42 memory used=1146.4MB, alloc=476.3MB, time=17.39 memory used=1261.9MB, alloc=476.3MB, time=19.18 memory used=1377.8MB, alloc=500.3MB, time=21.13 memory used=1500.8MB, alloc=500.3MB, time=23.31 memory used=1586.3MB, alloc=500.3MB, time=24.59 memory used=1701.4MB, alloc=524.3MB, time=26.54 memory used=1779.5MB, alloc=524.3MB, time=28.16 memory used=1845.1MB, alloc=524.3MB, time=29.27 memory used=1927.6MB, alloc=524.3MB, time=30.92 memory used=2003.7MB, alloc=524.3MB, time=32.56 memory used=2067.0MB, alloc=524.3MB, time=33.77 memory used=2120.2MB, alloc=524.3MB, time=34.69 memory used=2189.1MB, alloc=524.3MB, time=36.29 memory used=2243.9MB, alloc=524.3MB, time=37.41 memory used=2451.6MB, alloc=548.3MB, time=40.67 memory used=2646.3MB, alloc=572.3MB, time=44.06 memory used=2834.0MB, alloc=596.3MB, time=47.48 memory used=3007.0MB, alloc=620.3MB, time=50.85 memory used=3160.2MB, alloc=644.3MB, time=53.81 memory used=3316.7MB, alloc=644.3MB, time=56.95 memory used=3452.2MB, alloc=668.3MB, time=59.23 memory used=3600.0MB, alloc=668.3MB, time=62.47 memory used=3709.2MB, alloc=668.3MB, time=65.33 memory used=3825.9MB, alloc=668.3MB, time=68.20 memory used=3931.5MB, alloc=668.3MB, time=70.38 memory used=4031.8MB, alloc=668.3MB, time=73.32 memory used=4370.7MB, alloc=692.3MB, time=79.19 memory used=4743.8MB, alloc=716.3MB, time=84.92 memory used=5077.1MB, alloc=740.3MB, time=90.01 memory used=5460.4MB, alloc=764.3MB, time=96.80 memory used=5858.9MB, alloc=788.3MB, time=105.29 memory used=6218.5MB, alloc=812.3MB, time=110.64 memory used=6584.3MB, alloc=836.3MB, time=118.39 memory used=6876.1MB, alloc=860.3MB, time=124.26 memory used=7163.2MB, alloc=884.3MB, time=131.71 memory used=7460.9MB, alloc=908.3MB, time=138.51 |\^/| 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(); 1428286945 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 2 F := [x - 8 x y - 9 x + 12 y, 7 x - 2 y + 20 z - 13 z, x - 9 z - 5 z + 5] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [3 x - 3 y z + 2 z + 13 x, 5 x y + 6 y z - 20 x + 3 y, 2 2 -18 y + 19 z + 20 x + 6] > Problem := [F,G]; Problem := [ 2 2 2 2 2 2 [x - 8 x y - 9 x + 12 y, 7 x - 2 y + 20 z - 13 z, x - 9 z - 5 z + 5], 2 2 [3 x - 3 y z + 2 z + 13 x, 5 x y + 6 y z - 20 x + 3 y, 2 2 -18 y + 19 z + 20 x + 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=26.1MB, alloc=32.3MB, time=0.50 memory used=45.7MB, alloc=56.3MB, time=0.79 memory used=86.8MB, alloc=60.3MB, time=1.41 memory used=128.0MB, alloc=60.3MB, time=2.01 memory used=167.9MB, alloc=84.3MB, time=2.62 memory used=230.4MB, alloc=92.3MB, time=3.58 memory used=291.5MB, alloc=116.3MB, time=4.56 memory used=362.1MB, alloc=116.3MB, time=5.55 memory used=433.2MB, alloc=372.3MB, time=6.55 memory used=525.2MB, alloc=396.3MB, time=7.82 memory used=636.1MB, alloc=420.3MB, time=9.47 memory used=765.4MB, alloc=420.3MB, time=11.39 memory used=894.6MB, alloc=444.3MB, time=12.95 memory used=1014.3MB, alloc=444.3MB, time=14.58 memory used=1146.4MB, alloc=468.3MB, time=16.63 memory used=1271.3MB, alloc=468.3MB, time=18.59 memory used=1382.7MB, alloc=492.3MB, time=20.23 memory used=1472.6MB, alloc=492.3MB, time=21.85 memory used=1570.4MB, alloc=492.3MB, time=23.61 memory used=1676.6MB, alloc=492.3MB, time=25.76 memory used=1757.3MB, alloc=516.3MB, time=27.18 memory used=1848.9MB, alloc=516.3MB, time=28.49 memory used=1950.8MB, alloc=516.3MB, time=29.99 memory used=2032.1MB, alloc=516.3MB, time=31.31 memory used=2102.7MB, alloc=516.3MB, time=32.62 memory used=2172.5MB, alloc=516.3MB, time=34.07 memory used=2237.1MB, alloc=516.3MB, time=35.37 memory used=2305.4MB, alloc=516.3MB, time=36.93 memory used=2368.5MB, alloc=516.3MB, time=38.38 memory used=2421.4MB, alloc=540.3MB, time=39.56 memory used=2471.4MB, alloc=540.3MB, time=40.56 memory used=2705.8MB, alloc=564.3MB, time=44.37 memory used=2934.2MB, alloc=588.3MB, time=48.00 memory used=3123.3MB, alloc=612.3MB, time=51.46 memory used=3326.7MB, alloc=636.3MB, time=54.59 memory used=3518.7MB, alloc=660.3MB, time=58.39 memory used=3692.4MB, alloc=684.3MB, time=62.22 memory used=3833.6MB, alloc=684.3MB, time=64.43 memory used=3956.3MB, alloc=684.3MB, time=67.52 memory used=4076.4MB, alloc=708.3MB, time=69.84 memory used=4227.9MB, alloc=708.3MB, time=73.40 memory used=4329.8MB, alloc=708.3MB, time=75.46 memory used=4439.5MB, alloc=708.3MB, time=77.31 memory used=4558.5MB, alloc=708.3MB, time=80.35 memory used=4655.5MB, alloc=708.3MB, time=82.65 memory used=4747.0MB, alloc=708.3MB, time=85.28 memory used=5121.2MB, alloc=732.3MB, time=92.06 memory used=5505.0MB, alloc=756.3MB, time=100.00 memory used=5914.1MB, alloc=780.3MB, time=106.59 memory used=6291.6MB, alloc=804.3MB, time=112.74 memory used=6671.2MB, alloc=828.3MB, time=119.21 memory used=7031.0MB, alloc=852.3MB, time=127.70 memory used=7369.5MB, alloc=876.3MB, time=135.39 memory used=7699.1MB, alloc=900.3MB, time=141.20 memory used=7985.2MB, alloc=924.3MB, time=147.40 memory used=8188.7MB, alloc=948.3MB, time=152.37 memory used=8383.4MB, alloc=972.3MB, time=157.78 |\^/| 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(); 1428287245 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [20 x z + 20 z - 11 x - 17 z, -16 y - 18 z + 3 y, 2 2 -5 y - 19 z + 16 x - 13 z] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 G := [20 x + 3 x y - 4 y - 18 z , -13 y + 10 y z + z + 13, 2 10 y z + 17 z + 16 x - 14 z] > Problem := [F,G]; 2 2 2 Problem := [[20 x z + 20 z - 11 x - 17 z, -16 y - 18 z + 3 y, 2 2 2 2 2 -5 y - 19 z + 16 x - 13 z], [20 x + 3 x y - 4 y - 18 z , 2 2 2 -13 y + 10 y z + z + 13, 10 y z + 17 z + 16 x - 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=0.50 memory used=46.9MB, alloc=56.3MB, time=0.82 memory used=88.4MB, alloc=60.3MB, time=1.44 memory used=130.7MB, alloc=68.3MB, time=2.06 memory used=171.8MB, alloc=92.3MB, time=2.65 memory used=238.7MB, alloc=92.3MB, time=3.53 memory used=298.6MB, alloc=116.3MB, time=4.47 memory used=380.2MB, alloc=116.3MB, time=5.71 memory used=459.6MB, alloc=396.3MB, time=6.96 memory used=573.8MB, alloc=396.3MB, time=8.50 memory used=682.5MB, alloc=420.3MB, time=10.06 memory used=817.8MB, alloc=444.3MB, time=12.03 memory used=916.7MB, alloc=444.3MB, time=12.82 memory used=1062.4MB, alloc=444.3MB, time=14.47 memory used=1206.1MB, alloc=468.3MB, time=16.64 memory used=1357.8MB, alloc=492.3MB, time=19.41 memory used=1484.7MB, alloc=492.3MB, time=21.62 memory used=1600.4MB, alloc=492.3MB, time=23.54 memory used=1712.5MB, alloc=492.3MB, time=25.43 memory used=1828.8MB, alloc=516.3MB, time=27.23 memory used=1958.2MB, alloc=516.3MB, time=28.81 memory used=2129.9MB, alloc=516.3MB, time=30.81 memory used=2240.0MB, alloc=516.3MB, time=32.07 memory used=2364.4MB, alloc=516.3MB, time=34.04 memory used=2465.4MB, alloc=540.3MB, time=35.81 memory used=2558.0MB, alloc=540.3MB, time=37.60 memory used=2650.0MB, alloc=540.3MB, time=39.27 memory used=2745.4MB, alloc=540.3MB, time=40.98 memory used=2848.9MB, alloc=540.3MB, time=43.01 memory used=2935.5MB, alloc=540.3MB, time=44.81 memory used=3021.2MB, alloc=540.3MB, time=46.79 memory used=3097.7MB, alloc=540.3MB, time=48.63 memory used=3183.4MB, alloc=540.3MB, time=50.42 memory used=3249.1MB, alloc=540.3MB, time=51.69 memory used=3332.1MB, alloc=540.3MB, time=53.65 memory used=3404.5MB, alloc=564.3MB, time=55.18 memory used=3456.6MB, alloc=564.3MB, time=56.29 memory used=3524.5MB, alloc=564.3MB, time=57.48 memory used=3577.3MB, alloc=564.3MB, time=58.88 memory used=3635.7MB, alloc=564.3MB, time=60.36 memory used=3695.3MB, alloc=564.3MB, time=61.68 memory used=3938.6MB, alloc=588.3MB, time=65.42 memory used=4141.6MB, alloc=612.3MB, time=69.49 memory used=4330.7MB, alloc=636.3MB, time=72.47 memory used=4551.0MB, alloc=660.3MB, time=76.41 memory used=4751.0MB, alloc=684.3MB, time=80.41 memory used=4926.6MB, alloc=708.3MB, time=84.07 memory used=5092.9MB, alloc=708.3MB, time=86.86 memory used=5326.8MB, alloc=708.3MB, time=90.04 memory used=5465.6MB, alloc=708.3MB, time=92.84 memory used=5606.7MB, alloc=732.3MB, time=94.88 memory used=5749.3MB, alloc=732.3MB, time=97.37 memory used=5898.8MB, alloc=756.3MB, time=100.83 memory used=6029.7MB, alloc=756.3MB, time=104.15 memory used=6128.9MB, alloc=756.3MB, time=106.43 memory used=6542.6MB, alloc=780.3MB, time=114.77 memory used=6968.4MB, alloc=804.3MB, time=125.15 memory used=7418.0MB, alloc=828.3MB, time=135.36 |\^/| 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(); 1428287545 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-16 x z - 6 y - 9 z - 11, -15 x y - 4 x z - 7 z + 16 x, 2 -10 x - 20 x y - 20 x z - 10 z] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [x z + 5 y - 3 y z - x, -20 y + 19 y z + 2 x - 14 y, 2 -10 y z + 15 z + 16 x - 11] > Problem := [F,G]; 2 2 Problem := [[-16 x z - 6 y - 9 z - 11, -15 x y - 4 x z - 7 z + 16 x, 2 2 -10 x - 20 x y - 20 x z - 10 z], [x z + 5 y - 3 y z - x, 2 2 -20 y + 19 y z + 2 x - 14 y, -10 y z + 15 z + 16 x - 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=26.0MB, alloc=32.3MB, time=0.49 memory used=46.7MB, alloc=32.3MB, time=0.79 memory used=66.0MB, alloc=56.3MB, time=1.09 memory used=106.7MB, alloc=68.3MB, time=1.71 memory used=146.4MB, alloc=92.3MB, time=2.30 memory used=210.0MB, alloc=92.3MB, time=3.25 memory used=273.1MB, alloc=92.3MB, time=4.20 memory used=334.6MB, alloc=116.3MB, time=5.15 memory used=411.0MB, alloc=372.3MB, time=6.33 memory used=491.8MB, alloc=396.3MB, time=7.63 memory used=599.0MB, alloc=420.3MB, time=9.27 memory used=736.4MB, alloc=444.3MB, time=11.25 memory used=861.6MB, alloc=468.3MB, time=13.21 memory used=998.0MB, alloc=468.3MB, time=15.39 memory used=1096.7MB, alloc=468.3MB, time=16.88 memory used=1192.8MB, alloc=468.3MB, time=18.52 memory used=1287.7MB, alloc=492.3MB, time=20.17 memory used=1375.3MB, alloc=492.3MB, time=21.67 memory used=1484.9MB, alloc=492.3MB, time=23.84 memory used=1558.2MB, alloc=492.3MB, time=25.06 memory used=1636.6MB, alloc=492.3MB, time=26.60 memory used=1695.5MB, alloc=492.3MB, time=27.63 memory used=1772.4MB, alloc=492.3MB, time=29.24 memory used=1843.1MB, alloc=492.3MB, time=30.79 memory used=1906.1MB, alloc=492.3MB, time=32.04 memory used=1971.6MB, alloc=492.3MB, time=33.47 memory used=2014.8MB, alloc=516.3MB, time=34.36 memory used=2065.5MB, alloc=516.3MB, time=35.48 memory used=2119.8MB, alloc=516.3MB, time=36.97 memory used=2317.6MB, alloc=540.3MB, time=40.83 memory used=2520.1MB, alloc=564.3MB, time=44.66 memory used=2726.2MB, alloc=588.3MB, time=48.70 memory used=2908.7MB, alloc=612.3MB, time=52.02 memory used=3059.3MB, alloc=612.3MB, time=55.19 memory used=3203.4MB, alloc=636.3MB, time=58.05 memory used=3350.7MB, alloc=636.3MB, time=60.89 memory used=3511.1MB, alloc=636.3MB, time=64.41 memory used=3650.4MB, alloc=660.3MB, time=67.69 memory used=3774.5MB, alloc=660.3MB, time=70.64 memory used=3872.0MB, alloc=660.3MB, time=72.66 memory used=3986.7MB, alloc=660.3MB, time=75.34 memory used=4106.8MB, alloc=660.3MB, time=78.33 memory used=4212.6MB, alloc=660.3MB, time=81.21 memory used=4528.7MB, alloc=684.3MB, time=88.09 memory used=4878.3MB, alloc=708.3MB, time=94.87 memory used=5250.9MB, alloc=732.3MB, time=102.16 memory used=5631.9MB, alloc=756.3MB, time=110.39 memory used=5993.8MB, alloc=780.3MB, time=118.70 memory used=6333.1MB, alloc=804.3MB, time=127.06 memory used=6624.3MB, alloc=828.3MB, time=133.44 |\^/| 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(); 1428287845 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [x y + 8 y + 9, 19 y z - 5 x - 8 y - 16, -13 x y + 8 x z + 20 y z - 10 z] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [-6 x y + 4 z - 16 y + 8 z, 11 x z - 8 y z + 9 y + 13, 2 2 2 -9 x - 7 x y + 19 y - 3 z ] > Problem := [F,G]; Problem := [ 2 [x y + 8 y + 9, 19 y z - 5 x - 8 y - 16, -13 x y + 8 x z + 20 y z - 10 z], 2 [-6 x y + 4 z - 16 y + 8 z, 11 x z - 8 y z + 9 y + 13, 2 2 2 -9 x - 7 x y + 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=26.6MB, alloc=32.3MB, time=0.50 memory used=46.3MB, alloc=56.3MB, time=0.80 memory used=87.2MB, alloc=60.3MB, time=1.43 memory used=127.2MB, alloc=60.3MB, time=2.02 memory used=166.5MB, alloc=84.3MB, time=2.64 memory used=227.3MB, alloc=116.3MB, time=3.60 memory used=306.9MB, alloc=372.3MB, time=4.89 memory used=389.6MB, alloc=396.3MB, time=6.24 memory used=500.7MB, alloc=420.3MB, time=7.98 memory used=634.2MB, alloc=444.3MB, time=10.19 memory used=783.9MB, alloc=468.3MB, time=12.81 memory used=930.1MB, alloc=468.3MB, time=15.32 memory used=1063.7MB, alloc=492.3MB, time=17.61 memory used=1168.4MB, alloc=492.3MB, time=19.22 memory used=1294.0MB, alloc=492.3MB, time=21.57 memory used=1411.2MB, alloc=516.3MB, time=23.46 memory used=1512.8MB, alloc=516.3MB, time=25.19 memory used=1604.3MB, alloc=516.3MB, time=26.76 memory used=1692.3MB, alloc=516.3MB, time=28.30 memory used=1775.2MB, alloc=516.3MB, time=30.08 memory used=1846.0MB, alloc=516.3MB, time=31.56 memory used=1929.9MB, alloc=540.3MB, time=32.84 memory used=1999.8MB, alloc=540.3MB, time=34.23 memory used=2072.1MB, alloc=540.3MB, time=35.76 memory used=2130.2MB, alloc=540.3MB, time=36.96 memory used=2193.2MB, alloc=540.3MB, time=38.41 memory used=2254.8MB, alloc=540.3MB, time=39.77 memory used=2326.1MB, alloc=540.3MB, time=41.50 memory used=2380.0MB, alloc=540.3MB, time=42.76 memory used=2440.2MB, alloc=540.3MB, time=44.46 memory used=2666.2MB, alloc=564.3MB, time=48.78 memory used=2906.9MB, alloc=588.3MB, time=53.82 memory used=3088.3MB, alloc=612.3MB, time=57.23 memory used=3249.6MB, alloc=636.3MB, time=60.47 memory used=3470.2MB, alloc=660.3MB, time=65.81 memory used=3595.2MB, alloc=684.3MB, time=68.48 memory used=3761.9MB, alloc=684.3MB, time=72.36 memory used=3916.9MB, alloc=684.3MB, time=76.22 memory used=4014.6MB, alloc=684.3MB, time=78.46 memory used=4147.7MB, alloc=684.3MB, time=82.19 memory used=4272.2MB, alloc=684.3MB, time=85.59 memory used=4380.9MB, alloc=708.3MB, time=88.30 memory used=4760.2MB, alloc=732.3MB, time=96.18 memory used=5150.7MB, alloc=756.3MB, time=104.49 memory used=5552.4MB, alloc=780.3MB, time=114.59 memory used=5871.0MB, alloc=804.3MB, time=121.22 memory used=6214.8MB, alloc=828.3MB, time=129.22 memory used=6549.6MB, alloc=852.3MB, time=138.32 memory used=6868.9MB, alloc=876.3MB, time=146.07 |\^/| 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(); 1428288145 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-13 x - 3 z - 3 x - 16 z, -4 x y - 17 x z - 4 y z - 13, 2 2 10 x - 14 x z + 13 z + 6 x] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [4 x z + 12 y + 6 x - 2, 9 x + 7 y - 17 y - 2 z, 2 2 -8 x + 20 x z + 13 y - 5 x] > Problem := [F,G]; 2 2 Problem := [[-13 x - 3 z - 3 x - 16 z, -4 x y - 17 x z - 4 y z - 13, 2 2 2 10 x - 14 x z + 13 z + 6 x], [4 x z + 12 y + 6 x - 2, 2 2 2 2 9 x + 7 y - 17 y - 2 z, -8 x + 20 x z + 13 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=4.3MB, alloc=32.3MB, time=0.18 memory used=26.1MB, alloc=32.3MB, time=0.50 memory used=46.7MB, alloc=32.3MB, time=0.81 memory used=67.5MB, alloc=60.3MB, time=1.14 memory used=109.3MB, alloc=68.3MB, time=1.77 memory used=149.7MB, alloc=92.3MB, time=2.40 memory used=215.5MB, alloc=92.3MB, time=3.37 memory used=280.8MB, alloc=116.3MB, time=4.34 memory used=348.5MB, alloc=116.3MB, time=5.38 memory used=412.3MB, alloc=372.3MB, time=6.37 memory used=498.2MB, alloc=396.3MB, time=7.67 memory used=610.1MB, alloc=420.3MB, time=9.29 memory used=740.7MB, alloc=444.3MB, time=11.43 memory used=853.0MB, alloc=468.3MB, time=13.01 memory used=969.6MB, alloc=468.3MB, time=14.84 memory used=1073.0MB, alloc=468.3MB, time=16.47 memory used=1166.4MB, alloc=468.3MB, time=17.89 memory used=1265.5MB, alloc=492.3MB, time=19.46 memory used=1352.6MB, alloc=492.3MB, time=21.00 memory used=1432.2MB, alloc=492.3MB, time=22.40 memory used=1519.5MB, alloc=492.3MB, time=23.89 memory used=1591.9MB, alloc=492.3MB, time=25.35 memory used=1656.4MB, alloc=492.3MB, time=26.54 memory used=1709.6MB, alloc=492.3MB, time=27.60 memory used=1773.4MB, alloc=492.3MB, time=28.87 memory used=1823.5MB, alloc=492.3MB, time=29.82 memory used=1885.4MB, alloc=492.3MB, time=31.21 memory used=1933.8MB, alloc=492.3MB, time=32.21 memory used=1981.9MB, alloc=492.3MB, time=33.43 memory used=2180.0MB, alloc=516.3MB, time=36.32 memory used=2384.1MB, alloc=540.3MB, time=40.23 memory used=2547.0MB, alloc=564.3MB, time=43.04 memory used=2726.8MB, alloc=588.3MB, time=46.29 memory used=2853.5MB, alloc=612.3MB, time=48.90 memory used=3003.8MB, alloc=612.3MB, time=52.07 memory used=3107.3MB, alloc=612.3MB, time=54.16 memory used=3221.7MB, alloc=636.3MB, time=56.37 memory used=3353.9MB, alloc=636.3MB, time=58.85 memory used=3479.1MB, alloc=636.3MB, time=61.19 memory used=3582.3MB, alloc=636.3MB, time=63.36 memory used=3663.8MB, alloc=636.3MB, time=65.19 memory used=3766.3MB, alloc=660.3MB, time=67.27 memory used=3872.6MB, alloc=660.3MB, time=69.61 memory used=4204.3MB, alloc=684.3MB, time=76.07 memory used=4557.8MB, alloc=708.3MB, time=82.58 memory used=4904.7MB, alloc=732.3MB, time=90.16 memory used=5257.8MB, alloc=756.3MB, time=96.82 memory used=5620.2MB, alloc=780.3MB, time=104.58 memory used=5945.3MB, alloc=804.3MB, time=110.96 memory used=6240.9MB, alloc=828.3MB, time=116.96 memory used=6503.0MB, alloc=852.3MB, time=122.69 memory used=6730.3MB, alloc=876.3MB, time=127.63 memory used=6979.6MB, alloc=900.3MB, time=133.03 memory used=7206.1MB, alloc=924.3MB, time=138.12 memory used=7449.3MB, alloc=948.3MB, time=144.24 memory used=7680.6MB, alloc=972.3MB, time=149.79 |\^/| 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(); 1428288445 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-12 y + 4 y z - 17 x - 4 z, 9 x - 16 y z - 8 z + 7, 2 2 19 x - y + 20 y - 8 z] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 2 G := [-5 x + 15 y - 12 z + 9 z, 8 x - 11 y + 3 z + 12 y, 2 2 x + 12 x y + 8 x z - 6 y] > Problem := [F,G]; 2 2 2 Problem := [[-12 y + 4 y z - 17 x - 4 z, 9 x - 16 y z - 8 z + 7, 2 2 2 2 2 19 x - y + 20 y - 8 z], [-5 x + 15 y - 12 z + 9 z, 2 2 2 2 8 x - 11 y + 3 z + 12 y, 2 x + 12 x y + 8 x 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=0.19 memory used=25.9MB, alloc=32.3MB, time=0.51 memory used=46.0MB, alloc=32.3MB, time=0.82 memory used=64.5MB, alloc=56.3MB, time=1.11 memory used=106.8MB, alloc=68.3MB, time=1.75 memory used=148.4MB, alloc=68.3MB, time=2.37 memory used=188.7MB, alloc=92.3MB, time=3.01 memory used=253.3MB, alloc=92.3MB, time=4.00 memory used=319.6MB, alloc=116.3MB, time=5.01 memory used=380.9MB, alloc=372.3MB, time=5.89 memory used=467.7MB, alloc=372.3MB, time=7.23 memory used=553.7MB, alloc=396.3MB, time=8.56 memory used=661.8MB, alloc=396.3MB, time=10.22 memory used=771.2MB, alloc=420.3MB, time=12.01 memory used=900.2MB, alloc=444.3MB, time=14.10 memory used=1018.9MB, alloc=468.3MB, time=16.05 memory used=1125.7MB, alloc=468.3MB, time=17.75 memory used=1238.1MB, alloc=468.3MB, time=19.83 memory used=1329.1MB, alloc=492.3MB, time=21.22 memory used=1439.8MB, alloc=492.3MB, time=23.43 memory used=1525.2MB, alloc=492.3MB, time=24.78 memory used=1615.7MB, alloc=492.3MB, time=26.44 memory used=1703.8MB, alloc=492.3MB, time=27.89 memory used=1778.0MB, alloc=516.3MB, time=29.31 memory used=1836.7MB, alloc=516.3MB, time=30.36 memory used=1911.8MB, alloc=516.3MB, time=31.92 memory used=1964.7MB, alloc=516.3MB, time=32.99 memory used=2022.6MB, alloc=516.3MB, time=34.05 memory used=2091.1MB, alloc=516.3MB, time=35.43 memory used=2139.4MB, alloc=516.3MB, time=36.49 memory used=2190.0MB, alloc=516.3MB, time=37.51 memory used=2376.7MB, alloc=540.3MB, time=40.92 memory used=2593.9MB, alloc=564.3MB, time=45.13 memory used=2770.8MB, alloc=588.3MB, time=48.43 memory used=2933.1MB, alloc=612.3MB, time=51.55 memory used=3108.1MB, alloc=612.3MB, time=55.04 memory used=3251.6MB, alloc=636.3MB, time=58.15 memory used=3419.2MB, alloc=636.3MB, time=62.19 memory used=3551.6MB, alloc=636.3MB, time=64.90 memory used=3674.4MB, alloc=636.3MB, time=67.68 memory used=3836.4MB, alloc=636.3MB, time=70.74 memory used=3949.8MB, alloc=660.3MB, time=72.90 memory used=4098.0MB, alloc=660.3MB, time=76.82 memory used=4213.7MB, alloc=660.3MB, time=79.80 memory used=4320.4MB, alloc=660.3MB, time=82.41 memory used=4656.4MB, alloc=684.3MB, time=89.19 memory used=5016.6MB, alloc=708.3MB, time=96.63 memory used=5385.1MB, alloc=732.3MB, time=105.38 memory used=5773.6MB, alloc=756.3MB, time=114.49 memory used=6092.0MB, alloc=780.3MB, time=121.40 memory used=6430.3MB, alloc=804.3MB, time=129.90 memory used=6734.7MB, alloc=828.3MB, time=137.34 memory used=7016.5MB, alloc=852.3MB, time=145.11 |\^/| 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(); 1428288745 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; F := [ 2 2 2 -19 x z + y + x + 1, 11 x z + 14 y + 5 y - z, 2 x z - 18 z - 2 y + 19 z] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [-13 x y + 19 x z + 10 y + 19 z, 7 x y - 3 z - 20 y - 2, 2 13 z - 13 x - 19 y - 3] > Problem := [F,G]; Problem := [[ 2 2 2 -19 x z + y + x + 1, 11 x z + 14 y + 5 y - z, 2 x z - 18 z - 2 y + 19 z] 2 , [-13 x y + 19 x z + 10 y + 19 z, 7 x y - 3 z - 20 y - 2, 2 13 z - 13 x - 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=0.18 memory used=26.3MB, alloc=32.3MB, time=0.51 memory used=46.5MB, alloc=32.3MB, time=0.82 memory used=65.6MB, alloc=60.3MB, time=1.13 memory used=137.3MB, alloc=100.3MB, time=2.30 memory used=212.5MB, alloc=100.3MB, time=3.40 memory used=282.6MB, alloc=100.3MB, time=4.49 memory used=352.3MB, alloc=124.3MB, time=5.58 memory used=426.4MB, alloc=124.3MB, time=6.70 memory used=494.1MB, alloc=404.3MB, time=7.77 memory used=611.4MB, alloc=404.3MB, time=9.59 memory used=726.6MB, alloc=428.3MB, time=11.35 memory used=864.1MB, alloc=452.3MB, time=13.53 memory used=998.1MB, alloc=476.3MB, time=15.79 memory used=1118.5MB, alloc=476.3MB, time=17.47 memory used=1209.3MB, alloc=476.3MB, time=18.78 memory used=1301.6MB, alloc=476.3MB, time=20.37 memory used=1407.6MB, alloc=500.3MB, time=22.33 memory used=1492.7MB, alloc=500.3MB, time=23.84 memory used=1578.2MB, alloc=500.3MB, time=25.28 memory used=1647.0MB, alloc=500.3MB, time=26.42 memory used=1734.5MB, alloc=500.3MB, time=28.28 memory used=1800.6MB, alloc=500.3MB, time=29.52 memory used=1868.7MB, alloc=500.3MB, time=30.89 memory used=1920.1MB, alloc=500.3MB, time=31.98 memory used=1972.9MB, alloc=524.3MB, time=32.96 memory used=2024.5MB, alloc=524.3MB, time=34.19 memory used=2075.0MB, alloc=524.3MB, time=35.36 memory used=2288.5MB, alloc=548.3MB, time=39.30 memory used=2497.3MB, alloc=572.3MB, time=42.56 memory used=2695.2MB, alloc=596.3MB, time=45.67 memory used=2888.7MB, alloc=620.3MB, time=48.80 memory used=3071.5MB, alloc=644.3MB, time=52.59 memory used=3235.2MB, alloc=644.3MB, time=55.79 memory used=3374.2MB, alloc=644.3MB, time=58.51 memory used=3543.5MB, alloc=668.3MB, time=62.29 memory used=3682.6MB, alloc=668.3MB, time=65.28 memory used=3806.1MB, alloc=668.3MB, time=67.93 memory used=3888.5MB, alloc=668.3MB, time=70.01 memory used=3986.5MB, alloc=668.3MB, time=72.55 memory used=4327.0MB, alloc=692.3MB, time=79.13 memory used=4678.6MB, alloc=716.3MB, time=86.05 memory used=5056.8MB, alloc=740.3MB, time=92.42 memory used=5438.0MB, alloc=764.3MB, time=98.85 memory used=5813.8MB, alloc=788.3MB, time=104.47 memory used=6168.6MB, alloc=812.3MB, time=112.08 memory used=6463.4MB, alloc=836.3MB, time=118.11 memory used=6712.7MB, alloc=860.3MB, time=122.87 memory used=6972.1MB, alloc=884.3MB, time=128.15 |\^/| 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(); 1428289045 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [11 x - 12 x y - 13 y - 13 y z, 6 x - 19 z - 12 z + 11, 2 -4 y - 9 y z + 8 z - 16] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [-8 x y - 16 y z - 5 y + 11, 11 y z + 18 z - 15 y + 5 z, 2 17 y + 16 y z + x - 3 y] > Problem := [F,G]; 2 2 2 2 Problem := [[11 x - 12 x y - 13 y - 13 y z, 6 x - 19 z - 12 z + 11, 2 -4 y - 9 y z + 8 z - 16], [-8 x y - 16 y z - 5 y + 11, 2 2 11 y z + 18 z - 15 y + 5 z, 17 y + 16 y z + x - 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=0.16 memory used=25.9MB, alloc=32.3MB, time=0.47 memory used=45.8MB, alloc=32.3MB, time=0.75 memory used=64.6MB, alloc=56.3MB, time=1.03 memory used=105.5MB, alloc=60.3MB, time=1.59 memory used=144.9MB, alloc=60.3MB, time=2.14 memory used=183.4MB, alloc=84.3MB, time=2.70 memory used=226.6MB, alloc=84.3MB, time=3.33 memory used=287.5MB, alloc=116.3MB, time=4.27 memory used=365.7MB, alloc=372.3MB, time=5.42 memory used=453.2MB, alloc=396.3MB, time=6.61 memory used=556.3MB, alloc=396.3MB, time=8.21 memory used=665.6MB, alloc=420.3MB, time=9.75 memory used=795.9MB, alloc=444.3MB, time=11.78 memory used=936.2MB, alloc=468.3MB, time=13.94 memory used=1068.2MB, alloc=468.3MB, time=15.93 memory used=1209.7MB, alloc=492.3MB, time=18.31 memory used=1362.0MB, alloc=492.3MB, time=21.03 memory used=1469.8MB, alloc=516.3MB, time=22.91 memory used=1569.6MB, alloc=516.3MB, time=24.52 memory used=1690.1MB, alloc=516.3MB, time=26.77 memory used=1809.3MB, alloc=516.3MB, time=29.16 memory used=1893.9MB, alloc=516.3MB, time=30.71 memory used=1974.7MB, alloc=516.3MB, time=32.25 memory used=2053.4MB, alloc=516.3MB, time=33.67 memory used=2138.9MB, alloc=540.3MB, time=35.19 memory used=2224.2MB, alloc=540.3MB, time=36.86 memory used=2288.3MB, alloc=540.3MB, time=38.23 memory used=2371.6MB, alloc=540.3MB, time=39.93 memory used=2440.3MB, alloc=540.3MB, time=41.25 memory used=2505.9MB, alloc=540.3MB, time=42.61 memory used=2554.3MB, alloc=540.3MB, time=43.53 memory used=2614.6MB, alloc=540.3MB, time=44.84 memory used=2667.5MB, alloc=540.3MB, time=46.01 memory used=2721.1MB, alloc=540.3MB, time=47.24 memory used=2765.3MB, alloc=540.3MB, time=48.20 memory used=2980.4MB, alloc=564.3MB, time=51.93 memory used=3179.8MB, alloc=588.3MB, time=55.21 memory used=3410.7MB, alloc=612.3MB, time=59.85 memory used=3604.0MB, alloc=636.3MB, time=63.04 memory used=3829.3MB, alloc=660.3MB, time=67.46 memory used=4004.7MB, alloc=684.3MB, time=70.31 memory used=4159.6MB, alloc=708.3MB, time=73.06 memory used=4337.4MB, alloc=708.3MB, time=77.13 memory used=4482.9MB, alloc=708.3MB, time=80.87 memory used=4600.7MB, alloc=708.3MB, time=83.28 memory used=4754.5MB, alloc=708.3MB, time=86.92 memory used=4867.4MB, alloc=732.3MB, time=89.08 memory used=4967.6MB, alloc=732.3MB, time=91.15 memory used=5102.0MB, alloc=756.3MB, time=94.02 memory used=5525.4MB, alloc=780.3MB, time=102.59 memory used=5960.1MB, alloc=804.3MB, time=112.70 memory used=6408.2MB, alloc=828.3MB, time=122.66 |\^/| 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(); 1428289345 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; F := [ 2 2 2 -11 x + 17 y - 4 y - 15 z, x y - 13 y + 5 x + z, -13 - 19 x - 14 y + 8 z ] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [7 x z - 6 y - 10 y - 7, 15 x y - 6 x z - 15 y z + 19 x, -6 x z - 20 y z + 12 y - 16] > Problem := [F,G]; Problem := [[ 2 2 2 -11 x + 17 y - 4 y - 15 z, x y - 13 y + 5 x + z, -13 - 19 x - 14 y + 8 z 2 ], [7 x z - 6 y - 10 y - 7, 15 x y - 6 x z - 15 y z + 19 x, -6 x z - 20 y z + 12 y - 16]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,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=0.50 memory used=46.1MB, alloc=56.3MB, time=0.82 memory used=88.2MB, alloc=60.3MB, time=1.46 memory used=128.2MB, alloc=60.3MB, time=2.06 memory used=168.0MB, alloc=84.3MB, time=2.66 memory used=229.3MB, alloc=92.3MB, time=3.66 memory used=293.3MB, alloc=116.3MB, time=4.59 memory used=371.7MB, alloc=140.3MB, time=5.79 memory used=441.7MB, alloc=396.3MB, time=6.90 memory used=552.9MB, alloc=420.3MB, time=8.66 memory used=681.2MB, alloc=444.3MB, time=10.76 memory used=806.2MB, alloc=468.3MB, time=12.88 memory used=924.5MB, alloc=468.3MB, time=14.97 memory used=1037.4MB, alloc=468.3MB, time=17.00 memory used=1127.7MB, alloc=492.3MB, time=18.61 memory used=1226.8MB, alloc=492.3MB, time=20.50 memory used=1316.0MB, alloc=492.3MB, time=22.15 memory used=1393.7MB, alloc=492.3MB, time=23.73 memory used=1473.3MB, alloc=492.3MB, time=25.45 memory used=1539.9MB, alloc=492.3MB, time=26.90 memory used=1604.8MB, alloc=492.3MB, time=28.30 memory used=1671.6MB, alloc=492.3MB, time=29.78 memory used=1722.6MB, alloc=492.3MB, time=30.97 memory used=1770.3MB, alloc=492.3MB, time=32.20 memory used=1822.1MB, alloc=492.3MB, time=33.47 memory used=1858.7MB, alloc=516.3MB, time=34.42 memory used=2067.0MB, alloc=540.3MB, time=38.30 memory used=2250.8MB, alloc=564.3MB, time=41.81 memory used=2423.2MB, alloc=588.3MB, time=45.10 memory used=2591.6MB, alloc=612.3MB, time=48.48 memory used=2773.5MB, alloc=636.3MB, time=52.39 memory used=2949.8MB, alloc=660.3MB, time=56.10 memory used=3094.9MB, alloc=660.3MB, time=59.28 memory used=3264.1MB, alloc=684.3MB, time=63.21 memory used=3424.5MB, alloc=684.3MB, time=67.08 memory used=3536.6MB, alloc=684.3MB, time=69.59 memory used=3639.4MB, alloc=684.3MB, time=72.38 memory used=3991.6MB, alloc=708.3MB, time=79.48 memory used=4367.3MB, alloc=732.3MB, time=86.80 memory used=4749.6MB, alloc=756.3MB, time=95.51 memory used=5077.9MB, alloc=780.3MB, time=102.59 memory used=5422.4MB, alloc=804.3MB, time=111.59 memory used=5725.1MB, alloc=828.3MB, time=118.66 memory used=5983.1MB, alloc=852.3MB, time=125.34 memory used=6161.7MB, alloc=876.3MB, time=129.57 memory used=6387.9MB, alloc=900.3MB, time=136.25 |\^/| 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(); 1428289645 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-20 x z - 15 y z + 3 z - 7 z, -4 x z + 10 z + 17 z - 1, 2 -4 x z - 15 y - 3 x + 20 z] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [15 x y - 15 y + 2 y z - 12 y, -17 y + 16 y z - 9 z - 5 x, 2 9 x - 17 x y + 15 x z - 13 y] > Problem := [F,G]; 2 2 Problem := [[-20 x z - 15 y z + 3 z - 7 z, -4 x z + 10 z + 17 z - 1, 2 2 -4 x z - 15 y - 3 x + 20 z], [15 x y - 15 y + 2 y z - 12 y, 2 2 2 -17 y + 16 y z - 9 z - 5 x, 9 x - 17 x y + 15 x z - 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=0.17 memory used=26.0MB, alloc=32.3MB, time=0.47 memory used=46.5MB, alloc=32.3MB, time=0.76 memory used=65.0MB, alloc=56.3MB, time=1.06 memory used=103.4MB, alloc=60.3MB, time=1.62 memory used=139.6MB, alloc=84.3MB, time=2.17 memory used=197.1MB, alloc=92.3MB, time=3.09 memory used=254.8MB, alloc=116.3MB, time=4.03 memory used=333.4MB, alloc=140.3MB, time=5.33 memory used=433.4MB, alloc=164.3MB, time=7.11 memory used=522.1MB, alloc=164.3MB, time=8.76 memory used=618.4MB, alloc=444.3MB, time=10.52 memory used=759.7MB, alloc=468.3MB, time=13.07 memory used=913.7MB, alloc=492.3MB, time=15.76 memory used=1100.6MB, alloc=516.3MB, time=19.60 memory used=1306.3MB, alloc=540.3MB, time=23.72 memory used=1531.8MB, alloc=564.3MB, time=28.08 memory used=1788.4MB, alloc=588.3MB, time=33.46 memory used=2066.4MB, alloc=612.3MB, time=39.65 memory used=2366.5MB, alloc=636.3MB, time=46.15 memory used=2637.9MB, alloc=660.3MB, time=52.35 memory used=2930.1MB, alloc=684.3MB, time=59.61 memory used=3195.2MB, alloc=708.3MB, time=66.73 memory used=3443.1MB, alloc=732.3MB, time=73.83 memory used=3673.8MB, alloc=756.3MB, time=80.28 memory used=3866.5MB, alloc=780.3MB, time=85.78 memory used=4078.4MB, alloc=804.3MB, time=91.94 memory used=4264.2MB, alloc=828.3MB, time=97.21 memory used=4387.0MB, alloc=828.3MB, time=100.74 memory used=4534.3MB, alloc=828.3MB, time=105.14 memory used=4665.2MB, alloc=828.3MB, time=109.39 memory used=4789.8MB, alloc=828.3MB, time=113.46 memory used=5258.2MB, alloc=852.3MB, time=125.08 memory used=5739.5MB, alloc=876.3MB, time=137.35 |\^/| 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(); 1428289945 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; F := 2 2 2 [x - 5 z - 13 y, -6 x y + 4 z - 5 y - 19, 15 x y + 14 x z - 2 y z - 8 x] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [8 x z + 10 y z + 8 x + 15, 16 x y - 11 x z - 11 z + 18 y, 2 2 2 -15 x - y + 13 z - 19 y] > Problem := [F,G]; Problem := [ 2 2 2 [x - 5 z - 13 y, -6 x y + 4 z - 5 y - 19, 15 x y + 14 x z - 2 y z - 8 x] 2 , [8 x z + 10 y z + 8 x + 15, 16 x y - 11 x z - 11 z + 18 y, 2 2 2 -15 x - y + 13 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=4.3MB, alloc=32.3MB, time=0.18 memory used=26.7MB, alloc=32.3MB, time=0.52 memory used=47.6MB, alloc=56.3MB, time=0.84 memory used=89.3MB, alloc=60.3MB, time=1.44 memory used=130.2MB, alloc=92.3MB, time=2.08 memory used=193.4MB, alloc=92.3MB, time=3.00 memory used=256.1MB, alloc=116.3MB, time=3.96 memory used=312.6MB, alloc=372.3MB, time=4.74 memory used=399.7MB, alloc=396.3MB, time=6.06 memory used=511.9MB, alloc=420.3MB, time=7.73 memory used=645.8MB, alloc=444.3MB, time=9.84 memory used=767.2MB, alloc=444.3MB, time=11.82 memory used=900.3MB, alloc=468.3MB, time=14.11 memory used=1011.3MB, alloc=468.3MB, time=16.00 memory used=1111.0MB, alloc=492.3MB, time=17.61 memory used=1220.8MB, alloc=492.3MB, time=19.55 memory used=1299.5MB, alloc=492.3MB, time=21.02 memory used=1363.0MB, alloc=492.3MB, time=22.22 memory used=1453.2MB, alloc=492.3MB, time=23.98 memory used=1518.8MB, alloc=516.3MB, time=25.19 memory used=1574.8MB, alloc=516.3MB, time=26.21 memory used=1645.4MB, alloc=516.3MB, time=27.74 memory used=1707.2MB, alloc=516.3MB, time=28.92 memory used=1770.9MB, alloc=516.3MB, time=30.48 memory used=1814.7MB, alloc=516.3MB, time=31.45 memory used=1843.1MB, alloc=516.3MB, time=32.23 memory used=2047.3MB, alloc=540.3MB, time=35.42 memory used=2241.6MB, alloc=564.3MB, time=38.88 memory used=2405.9MB, alloc=588.3MB, time=41.77 memory used=2546.8MB, alloc=612.3MB, time=44.42 memory used=2697.2MB, alloc=636.3MB, time=47.37 memory used=2840.8MB, alloc=636.3MB, time=50.27 memory used=2979.8MB, alloc=660.3MB, time=53.17 memory used=3086.9MB, alloc=660.3MB, time=55.62 memory used=3190.2MB, alloc=660.3MB, time=58.09 memory used=3293.9MB, alloc=660.3MB, time=60.64 memory used=3379.9MB, alloc=660.3MB, time=62.69 memory used=3709.8MB, alloc=684.3MB, time=69.10 memory used=4053.0MB, alloc=708.3MB, time=76.16 memory used=4388.5MB, alloc=732.3MB, time=82.76 memory used=4710.5MB, alloc=756.3MB, time=89.30 memory used=5031.7MB, alloc=780.3MB, time=96.21 memory used=5316.5MB, alloc=804.3MB, time=102.88 memory used=5571.2MB, alloc=828.3MB, time=108.62 memory used=5810.1MB, alloc=852.3MB, time=114.59 memory used=6042.9MB, alloc=876.3MB, time=120.09 memory used=6246.7MB, alloc=900.3MB, time=125.69 memory used=6767.6MB, alloc=924.3MB, time=136.65 |\^/| 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(); 1428290245 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [16 x z - 5 y + 18 y - 13, -3 x - 2 y z + 2 y - 5, 2 2 -x z + y + 18 z - 15 z] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [-19 x + 2 z - 8 y - 20 z, 14 x - 18 x z + 16 z - 15 y, -19 x y - 14 x - 6 y + 14 z] > Problem := [F,G]; 2 2 Problem := [[16 x z - 5 y + 18 y - 13, -3 x - 2 y z + 2 y - 5, 2 2 2 2 -x z + y + 18 z - 15 z], [-19 x + 2 z - 8 y - 20 z, 2 2 14 x - 18 x z + 16 z - 15 y, -19 x y - 14 x - 6 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=4.4MB, alloc=32.3MB, time=0.17 memory used=26.3MB, alloc=32.3MB, time=0.51 memory used=46.8MB, alloc=32.3MB, time=0.81 memory used=65.5MB, alloc=56.3MB, time=1.11 memory used=108.0MB, alloc=68.3MB, time=1.73 memory used=148.9MB, alloc=68.3MB, time=2.34 memory used=188.2MB, alloc=92.3MB, time=2.95 memory used=255.0MB, alloc=92.3MB, time=3.91 memory used=317.6MB, alloc=116.3MB, time=4.87 memory used=380.5MB, alloc=372.3MB, time=5.80 memory used=468.4MB, alloc=372.3MB, time=7.06 memory used=550.8MB, alloc=396.3MB, time=8.38 memory used=664.0MB, alloc=420.3MB, time=10.01 memory used=797.7MB, alloc=444.3MB, time=12.04 memory used=927.9MB, alloc=468.3MB, time=13.96 memory used=1072.7MB, alloc=468.3MB, time=16.42 memory used=1207.0MB, alloc=492.3MB, time=18.74 memory used=1315.3MB, alloc=492.3MB, time=20.51 memory used=1421.9MB, alloc=492.3MB, time=22.03 memory used=1518.6MB, alloc=492.3MB, time=23.77 memory used=1612.4MB, alloc=516.3MB, time=25.49 memory used=1681.5MB, alloc=516.3MB, time=26.80 memory used=1756.3MB, alloc=516.3MB, time=28.09 memory used=1841.8MB, alloc=516.3MB, time=29.67 memory used=1908.6MB, alloc=516.3MB, time=30.88 memory used=1979.2MB, alloc=516.3MB, time=32.24 memory used=2035.2MB, alloc=516.3MB, time=33.43 memory used=2109.0MB, alloc=516.3MB, time=35.02 memory used=2160.8MB, alloc=516.3MB, time=36.04 memory used=2226.7MB, alloc=516.3MB, time=37.40 memory used=2278.6MB, alloc=516.3MB, time=38.57 memory used=2491.5MB, alloc=540.3MB, time=42.38 memory used=2708.4MB, alloc=564.3MB, time=46.77 memory used=2920.5MB, alloc=588.3MB, time=50.37 memory used=3091.4MB, alloc=612.3MB, time=53.50 memory used=3280.5MB, alloc=636.3MB, time=57.59 memory used=3442.2MB, alloc=636.3MB, time=60.85 memory used=3605.9MB, alloc=636.3MB, time=64.63 memory used=3754.0MB, alloc=636.3MB, time=68.12 memory used=3915.5MB, alloc=660.3MB, time=72.15 memory used=4043.0MB, alloc=660.3MB, time=74.92 memory used=4171.0MB, alloc=660.3MB, time=77.89 memory used=4271.3MB, alloc=660.3MB, time=80.46 memory used=4365.8MB, alloc=660.3MB, time=83.21 memory used=4480.3MB, alloc=660.3MB, time=86.36 memory used=4819.3MB, alloc=684.3MB, time=94.02 memory used=5177.5MB, alloc=708.3MB, time=102.01 memory used=5548.4MB, alloc=732.3MB, time=110.94 memory used=5949.6MB, alloc=756.3MB, time=119.51 memory used=6348.3MB, alloc=780.3MB, time=128.50 memory used=6648.8MB, alloc=804.3MB, time=135.19 memory used=6994.0MB, alloc=828.3MB, time=142.91 |\^/| 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(); 1428290545 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [10 x z - 7 y + 14 z - 4, 15 x z - 18 y z + 9 z , 15 x y + 3 x z - 11 y z + 1] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; G := [ 2 2 2 -11 x z + 13 z - 4 z + 19, 20 x y + 11 x z + 3 y + 6 z , 7 x y + 7 x + 16 ] > Problem := [F,G]; 2 Problem := [[10 x z - 7 y + 14 z - 4, 15 x z - 18 y z + 9 z , 15 x y + 3 x z - 11 y z + 1], [ 2 2 2 -11 x z + 13 z - 4 z + 19, 20 x y + 11 x z + 3 y + 6 z , 7 x y + 7 x + 16 ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,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=0.48 memory used=46.8MB, alloc=32.3MB, time=0.79 memory used=65.6MB, alloc=56.3MB, time=1.07 memory used=105.8MB, alloc=60.3MB, time=1.68 memory used=144.4MB, alloc=84.3MB, time=2.26 memory used=204.2MB, alloc=92.3MB, time=3.18 memory used=260.7MB, alloc=116.3MB, time=4.06 memory used=338.9MB, alloc=116.3MB, time=5.28 memory used=418.5MB, alloc=140.3MB, time=6.59 memory used=512.8MB, alloc=140.3MB, time=8.16 memory used=605.8MB, alloc=420.3MB, time=9.81 memory used=730.2MB, alloc=444.3MB, time=12.02 memory used=874.9MB, alloc=468.3MB, time=14.64 memory used=1040.9MB, alloc=492.3MB, time=17.70 memory used=1195.7MB, alloc=516.3MB, time=20.65 memory used=1336.8MB, alloc=540.3MB, time=23.38 memory used=1465.6MB, alloc=540.3MB, time=25.60 memory used=1592.0MB, alloc=540.3MB, time=28.11 memory used=1705.5MB, alloc=540.3MB, time=30.42 memory used=1790.6MB, alloc=564.3MB, time=32.00 memory used=1900.9MB, alloc=564.3MB, time=34.54 memory used=2018.5MB, alloc=564.3MB, time=37.38 memory used=2100.0MB, alloc=564.3MB, time=39.37 memory used=2175.1MB, alloc=564.3MB, time=40.88 memory used=2264.1MB, alloc=564.3MB, time=43.32 memory used=2341.3MB, alloc=564.3MB, time=45.06 memory used=2435.0MB, alloc=564.3MB, time=47.54 memory used=2484.5MB, alloc=564.3MB, time=48.77 memory used=2556.5MB, alloc=564.3MB, time=50.79 memory used=2608.2MB, alloc=564.3MB, time=52.25 memory used=2851.5MB, alloc=588.3MB, time=57.70 memory used=3107.8MB, alloc=612.3MB, time=63.82 memory used=3318.3MB, alloc=636.3MB, time=68.83 memory used=3523.3MB, alloc=660.3MB, time=73.61 memory used=3699.5MB, alloc=684.3MB, time=77.98 memory used=3909.1MB, alloc=708.3MB, time=84.03 memory used=4074.1MB, alloc=732.3MB, time=88.53 memory used=4210.8MB, alloc=732.3MB, time=92.23 memory used=4362.5MB, alloc=732.3MB, time=97.01 memory used=4511.4MB, alloc=732.3MB, time=101.67 memory used=4664.0MB, alloc=732.3MB, time=106.36 memory used=5057.1MB, alloc=756.3MB, time=116.81 memory used=5468.6MB, alloc=780.3MB, time=128.11 |\^/| 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(); 1428290845 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-19 x + 12 z + 2 y - 9 z, 7 x y - 16 y z - 15 y + 14, 2 2 18 x - 9 x y + 6 z - 13 y] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-10 x z - 15 y z - 12 x - 5, -14 x y + 6 y - z - 14, 2 2 -9 x + 7 y + 6 y - 20] > Problem := [F,G]; 2 2 Problem := [[-19 x + 12 z + 2 y - 9 z, 7 x y - 16 y z - 15 y + 14, 2 2 18 x - 9 x y + 6 z - 13 y], [-10 x z - 15 y z - 12 x - 5, 2 2 2 2 -14 x y + 6 y - z - 14, -9 x + 7 y + 6 y - 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=4.3MB, alloc=32.3MB, time=0.17 memory used=26.6MB, alloc=32.3MB, time=0.51 memory used=46.8MB, alloc=56.3MB, time=0.83 memory used=88.5MB, alloc=60.3MB, time=1.48 memory used=128.6MB, alloc=60.3MB, time=2.08 memory used=168.9MB, alloc=84.3MB, time=2.68 memory used=232.3MB, alloc=92.3MB, time=3.64 memory used=294.6MB, alloc=116.3MB, time=4.56 memory used=379.2MB, alloc=116.3MB, time=5.88 memory used=451.3MB, alloc=396.3MB, time=6.94 memory used=558.4MB, alloc=396.3MB, time=8.62 memory used=670.9MB, alloc=420.3MB, time=10.27 memory used=802.3MB, alloc=444.3MB, time=12.30 memory used=929.7MB, alloc=468.3MB, time=14.22 memory used=1046.1MB, alloc=468.3MB, time=16.04 memory used=1141.4MB, alloc=468.3MB, time=17.54 memory used=1249.5MB, alloc=468.3MB, time=19.30 memory used=1345.2MB, alloc=468.3MB, time=20.80 memory used=1457.7MB, alloc=492.3MB, time=22.83 memory used=1559.7MB, alloc=492.3MB, time=24.70 memory used=1642.1MB, alloc=492.3MB, time=26.02 memory used=1714.7MB, alloc=492.3MB, time=27.41 memory used=1789.0MB, alloc=492.3MB, time=28.89 memory used=1855.1MB, alloc=516.3MB, time=30.23 memory used=1918.3MB, alloc=516.3MB, time=31.47 memory used=1974.7MB, alloc=516.3MB, time=32.55 memory used=2024.0MB, alloc=516.3MB, time=33.52 memory used=2072.7MB, alloc=516.3MB, time=34.55 memory used=2132.8MB, alloc=516.3MB, time=35.51 memory used=2165.5MB, alloc=516.3MB, time=36.28 memory used=2210.3MB, alloc=516.3MB, time=37.28 memory used=2405.9MB, alloc=540.3MB, time=40.57 memory used=2599.3MB, alloc=564.3MB, time=43.74 memory used=2816.0MB, alloc=588.3MB, time=48.25 memory used=2986.6MB, alloc=612.3MB, time=52.03 memory used=3158.0MB, alloc=636.3MB, time=55.27 memory used=3335.4MB, alloc=660.3MB, time=59.31 memory used=3446.1MB, alloc=660.3MB, time=61.66 memory used=3603.4MB, alloc=684.3MB, time=65.20 memory used=3718.4MB, alloc=684.3MB, time=67.40 memory used=3849.3MB, alloc=684.3MB, time=70.40 memory used=3943.4MB, alloc=708.3MB, time=72.41 memory used=4064.4MB, alloc=708.3MB, time=75.58 memory used=4440.0MB, alloc=732.3MB, time=83.47 memory used=4819.3MB, alloc=756.3MB, time=90.43 memory used=5218.6MB, alloc=780.3MB, time=99.58 memory used=5539.0MB, alloc=804.3MB, time=106.04 memory used=5907.8MB, alloc=828.3MB, time=114.70 memory used=6226.0MB, alloc=852.3MB, time=121.39 memory used=6515.6MB, alloc=876.3MB, time=127.70 |\^/| 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(); 1428291145 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [-17 x z + 8 y z - 16 y + 11 z, 8 x y - 9 z + 3 z + 18, 2 10 x z + 13 y - 11 y z - 16 z] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [16 y z - 6 z + 14 x - 2 z, -19 x - 9 x z + 14 y z + 2 y, 2 2 9 x + 7 z + 5 x - 13 z] > Problem := [F,G]; 2 Problem := [[-17 x z + 8 y z - 16 y + 11 z, 8 x y - 9 z + 3 z + 18, 2 2 10 x z + 13 y - 11 y z - 16 z], [16 y z - 6 z + 14 x - 2 z, 2 2 2 -19 x - 9 x z + 14 y z + 2 y, 9 x + 7 z + 5 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=4.3MB, alloc=32.3MB, time=0.18 memory used=26.8MB, alloc=32.3MB, time=0.52 memory used=47.6MB, alloc=32.3MB, time=0.83 memory used=66.7MB, alloc=56.3MB, time=1.14 memory used=107.8MB, alloc=60.3MB, time=1.74 memory used=146.5MB, alloc=84.3MB, time=2.33 memory used=209.0MB, alloc=92.3MB, time=3.24 memory used=270.9MB, alloc=116.3MB, time=4.16 memory used=351.6MB, alloc=116.3MB, time=5.45 memory used=424.3MB, alloc=396.3MB, time=6.61 memory used=530.0MB, alloc=396.3MB, time=8.25 memory used=634.7MB, alloc=420.3MB, time=9.86 memory used=762.5MB, alloc=444.3MB, time=11.84 memory used=912.1MB, alloc=468.3MB, time=14.29 memory used=1051.0MB, alloc=468.3MB, time=16.53 memory used=1190.4MB, alloc=492.3MB, time=18.56 memory used=1299.7MB, alloc=516.3MB, time=20.19 memory used=1416.1MB, alloc=516.3MB, time=22.13 memory used=1517.3MB, alloc=516.3MB, time=23.36 memory used=1626.3MB, alloc=540.3MB, time=25.25 memory used=1724.7MB, alloc=540.3MB, time=27.01 memory used=1818.8MB, alloc=540.3MB, time=28.76 memory used=1895.4MB, alloc=540.3MB, time=30.18 memory used=1981.8MB, alloc=540.3MB, time=32.00 memory used=2053.8MB, alloc=540.3MB, time=33.11 memory used=2138.7MB, alloc=540.3MB, time=34.72 memory used=2201.9MB, alloc=540.3MB, time=35.96 memory used=2257.0MB, alloc=540.3MB, time=36.88 memory used=2327.9MB, alloc=540.3MB, time=38.45 memory used=2383.9MB, alloc=540.3MB, time=39.59 memory used=2424.5MB, alloc=540.3MB, time=40.49 memory used=2652.3MB, alloc=564.3MB, time=44.65 memory used=2881.5MB, alloc=588.3MB, time=48.03 memory used=3100.5MB, alloc=612.3MB, time=51.57 memory used=3270.3MB, alloc=636.3MB, time=54.90 memory used=3464.1MB, alloc=660.3MB, time=58.81 memory used=3638.3MB, alloc=684.3MB, time=61.86 memory used=3790.0MB, alloc=684.3MB, time=64.66 memory used=3934.8MB, alloc=684.3MB, time=67.84 memory used=4088.3MB, alloc=684.3MB, time=71.02 memory used=4209.1MB, alloc=684.3MB, time=73.35 memory used=4346.0MB, alloc=684.3MB, time=76.32 memory used=4477.3MB, alloc=708.3MB, time=78.99 memory used=4589.0MB, alloc=708.3MB, time=81.66 memory used=4964.4MB, alloc=732.3MB, time=88.85 memory used=5350.7MB, alloc=756.3MB, time=94.50 memory used=5771.6MB, alloc=780.3MB, time=101.88 memory used=6200.2MB, alloc=804.3MB, time=110.79 memory used=6603.3MB, alloc=828.3MB, time=120.27 memory used=6942.4MB, alloc=852.3MB, time=127.03 memory used=7283.7MB, alloc=876.3MB, time=134.91 |\^/| 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(); 1428291445 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [18 x + 6 y - 20 z - 6, -19 x + 12 x z - 10 x + 16 z, 2 -12 x y - 8 x z - 3 y - 13] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 G := [8 x - 8 x z + 7 y + 16 y z, -13 x - 2 y + 6 z + 3 x, 2 2 10 x - 2 x y + 6 y + 20 y z] > Problem := [F,G]; 2 2 Problem := [[18 x + 6 y - 20 z - 6, -19 x + 12 x z - 10 x + 16 z, 2 2 2 -12 x y - 8 x z - 3 y - 13], [8 x - 8 x z + 7 y + 16 y z, 2 2 2 2 2 -13 x - 2 y + 6 z + 3 x, 10 x - 2 x y + 6 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=26.4MB, alloc=32.3MB, time=0.50 memory used=47.0MB, alloc=56.3MB, time=0.81 memory used=88.9MB, alloc=60.3MB, time=1.44 memory used=129.8MB, alloc=84.3MB, time=2.05 memory used=171.2MB, alloc=84.3MB, time=2.69 memory used=234.5MB, alloc=92.3MB, time=3.67 memory used=294.9MB, alloc=116.3MB, time=4.62 memory used=372.6MB, alloc=116.3MB, time=5.76 memory used=440.5MB, alloc=396.3MB, time=6.85 memory used=552.0MB, alloc=396.3MB, time=8.45 memory used=666.0MB, alloc=420.3MB, time=10.08 memory used=801.0MB, alloc=444.3MB, time=12.29 memory used=921.3MB, alloc=444.3MB, time=14.44 memory used=1041.1MB, alloc=468.3MB, time=16.55 memory used=1153.7MB, alloc=468.3MB, time=18.62 memory used=1254.3MB, alloc=492.3MB, time=20.41 memory used=1343.2MB, alloc=492.3MB, time=21.89 memory used=1450.2MB, alloc=492.3MB, time=23.80 memory used=1535.4MB, alloc=492.3MB, time=25.32 memory used=1609.2MB, alloc=492.3MB, time=26.73 memory used=1684.7MB, alloc=492.3MB, time=28.16 memory used=1754.5MB, alloc=492.3MB, time=29.51 memory used=1821.3MB, alloc=492.3MB, time=30.91 memory used=1883.6MB, alloc=492.3MB, time=32.24 memory used=1943.2MB, alloc=492.3MB, time=33.52 memory used=1989.1MB, alloc=492.3MB, time=34.55 memory used=2171.4MB, alloc=516.3MB, time=37.98 memory used=2379.4MB, alloc=540.3MB, time=41.72 memory used=2560.6MB, alloc=564.3MB, time=45.32 memory used=2716.5MB, alloc=588.3MB, time=48.27 memory used=2867.0MB, alloc=612.3MB, time=51.23 memory used=3047.4MB, alloc=636.3MB, time=54.95 memory used=3182.4MB, alloc=660.3MB, time=57.70 memory used=3334.8MB, alloc=660.3MB, time=60.99 memory used=3452.6MB, alloc=684.3MB, time=63.24 memory used=3576.2MB, alloc=684.3MB, time=66.01 memory used=3666.7MB, alloc=684.3MB, time=68.51 memory used=4028.6MB, alloc=708.3MB, time=75.26 memory used=4408.3MB, alloc=732.3MB, time=81.63 memory used=4783.6MB, alloc=756.3MB, time=87.93 memory used=5160.8MB, alloc=780.3MB, time=95.92 memory used=5507.8MB, alloc=804.3MB, time=102.97 memory used=5755.9MB, alloc=828.3MB, time=107.74 memory used=6036.6MB, alloc=852.3MB, time=114.47 memory used=6309.4MB, alloc=876.3MB, time=121.13 memory used=6551.2MB, alloc=900.3MB, time=127.25 |\^/| 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(); 1428291745 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [4 x - 5 x y + 16 x z + 18 y, -10 x z - 11 z + 7 y + 10, -16 x z + 7 y z - 6 z + 2] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [13 x - 15 x + 20 z - 8, 20 y + 11 y z - 13 z + 8 x, 2 2 13 x - x z + 3 y - 7 y z] > Problem := [F,G]; 2 2 Problem := [[4 x - 5 x y + 16 x z + 18 y, -10 x z - 11 z + 7 y + 10, 2 -16 x z + 7 y z - 6 z + 2], [13 x - 15 x + 20 z - 8, 2 2 2 2 20 y + 11 y z - 13 z + 8 x, 13 x - x z + 3 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=0.18 memory used=25.9MB, alloc=32.3MB, time=0.50 memory used=46.2MB, alloc=32.3MB, time=0.81 memory used=65.8MB, alloc=60.3MB, time=1.13 memory used=107.0MB, alloc=60.3MB, time=1.74 memory used=145.6MB, alloc=84.3MB, time=2.31 memory used=210.0MB, alloc=92.3MB, time=3.30 memory used=273.3MB, alloc=116.3MB, time=4.30 memory used=353.4MB, alloc=116.3MB, time=5.58 memory used=430.0MB, alloc=396.3MB, time=6.79 memory used=542.4MB, alloc=420.3MB, time=8.35 memory used=676.0MB, alloc=444.3MB, time=10.38 memory used=807.5MB, alloc=468.3MB, time=12.14 memory used=934.8MB, alloc=468.3MB, time=14.01 memory used=1048.7MB, alloc=492.3MB, time=15.80 memory used=1149.6MB, alloc=492.3MB, time=17.37 memory used=1236.8MB, alloc=492.3MB, time=18.79 memory used=1333.8MB, alloc=492.3MB, time=20.42 memory used=1416.1MB, alloc=492.3MB, time=21.87 memory used=1485.9MB, alloc=492.3MB, time=23.06 memory used=1575.3MB, alloc=492.3MB, time=24.92 memory used=1632.8MB, alloc=492.3MB, time=26.03 memory used=1697.1MB, alloc=492.3MB, time=27.34 memory used=1755.7MB, alloc=516.3MB, time=28.52 memory used=1810.9MB, alloc=516.3MB, time=29.86 memory used=1861.1MB, alloc=516.3MB, time=30.86 memory used=2073.4MB, alloc=540.3MB, time=34.50 memory used=2300.8MB, alloc=564.3MB, time=38.70 memory used=2497.7MB, alloc=588.3MB, time=42.40 memory used=2678.6MB, alloc=612.3MB, time=45.98 memory used=2858.7MB, alloc=636.3MB, time=49.65 memory used=3018.0MB, alloc=636.3MB, time=52.97 memory used=3138.6MB, alloc=660.3MB, time=55.52 memory used=3273.0MB, alloc=660.3MB, time=58.52 memory used=3418.4MB, alloc=660.3MB, time=62.02 memory used=3529.1MB, alloc=660.3MB, time=64.66 memory used=3641.7MB, alloc=660.3MB, time=67.66 memory used=3972.3MB, alloc=684.3MB, time=74.23 memory used=4317.1MB, alloc=708.3MB, time=81.45 memory used=4687.5MB, alloc=732.3MB, time=88.74 memory used=5067.2MB, alloc=756.3MB, time=97.01 memory used=5437.4MB, alloc=780.3MB, time=104.72 memory used=5779.1MB, alloc=804.3MB, time=111.80 memory used=6136.5MB, alloc=828.3MB, time=118.55 |\^/| 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(); 1428292045 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-19 x y - 20 y + 2 z - 18, -19 x + 8 y z + 14 z - 20 x, 2 -14 x y + 6 y + 19 x - 6 z] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; G := [ 2 2 2 2 20 y - 11 z + 4 x + 4, -7 x z + 16 y z - 15 z + 5 z, -20 x z + 8 z - 20 ] > Problem := [F,G]; 2 2 2 Problem := [[-19 x y - 20 y + 2 z - 18, -19 x + 8 y z + 14 z - 20 x, 2 -14 x y + 6 y + 19 x - 6 z], [ 2 2 2 2 20 y - 11 z + 4 x + 4, -7 x z + 16 y z - 15 z + 5 z, -20 x z + 8 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=4.3MB, alloc=32.3MB, time=0.17 memory used=26.4MB, alloc=32.3MB, time=0.50 memory used=46.2MB, alloc=56.3MB, time=0.80 memory used=87.3MB, alloc=60.3MB, time=1.39 memory used=125.8MB, alloc=84.3MB, time=1.98 memory used=171.8MB, alloc=84.3MB, time=2.70 memory used=232.7MB, alloc=116.3MB, time=3.70 memory used=317.7MB, alloc=116.3MB, time=5.02 memory used=399.0MB, alloc=140.3MB, time=6.33 memory used=480.8MB, alloc=396.3MB, time=7.71 memory used=584.9MB, alloc=420.3MB, time=9.44 memory used=712.6MB, alloc=444.3MB, time=11.58 memory used=863.0MB, alloc=468.3MB, time=14.03 memory used=1015.7MB, alloc=492.3MB, time=16.57 memory used=1147.4MB, alloc=492.3MB, time=18.71 memory used=1278.3MB, alloc=516.3MB, time=21.05 memory used=1400.9MB, alloc=516.3MB, time=23.34 memory used=1505.4MB, alloc=516.3MB, time=25.20 memory used=1613.1MB, alloc=540.3MB, time=27.32 memory used=1709.9MB, alloc=540.3MB, time=29.32 memory used=1789.8MB, alloc=540.3MB, time=30.82 memory used=1880.0MB, alloc=540.3MB, time=32.71 memory used=1965.2MB, alloc=540.3MB, time=34.51 memory used=2039.1MB, alloc=540.3MB, time=36.18 memory used=2097.2MB, alloc=540.3MB, time=37.67 memory used=2166.3MB, alloc=540.3MB, time=39.25 memory used=2218.0MB, alloc=540.3MB, time=40.38 memory used=2281.6MB, alloc=540.3MB, time=42.03 memory used=2503.2MB, alloc=564.3MB, time=46.22 memory used=2719.6MB, alloc=588.3MB, time=50.49 memory used=2901.5MB, alloc=612.3MB, time=53.78 memory used=3067.6MB, alloc=636.3MB, time=57.55 memory used=3222.9MB, alloc=660.3MB, time=60.87 memory used=3393.0MB, alloc=660.3MB, time=64.99 memory used=3532.6MB, alloc=660.3MB, time=68.10 memory used=3625.7MB, alloc=660.3MB, time=70.13 memory used=3783.1MB, alloc=684.3MB, time=74.55 memory used=3896.8MB, alloc=684.3MB, time=77.57 memory used=3977.2MB, alloc=684.3MB, time=79.42 memory used=4317.7MB, alloc=708.3MB, time=87.11 memory used=4678.1MB, alloc=732.3MB, time=93.90 memory used=5062.2MB, alloc=756.3MB, time=101.83 memory used=5442.0MB, alloc=780.3MB, time=112.77 memory used=5854.3MB, alloc=804.3MB, time=123.49 |\^/| 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(); 1428292345 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; F := [ 2 7 y z - 5 y - 4 z - 9, -20 x y - 19 x z + 15 y z + 18 x, -4 y z + 5 z - 19 ] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [19 x y - 6 y + 19 y z - 6, -2 x y + 5 y + 4 z + 18 x, 2 -19 x y - 3 x z - 16 z - 14 x] > Problem := [F,G]; Problem := [[ 2 7 y z - 5 y - 4 z - 9, -20 x y - 19 x z + 15 y z + 18 x, -4 y z + 5 z - 19 2 2 2 ], [19 x y - 6 y + 19 y z - 6, -2 x y + 5 y + 4 z + 18 x, 2 -19 x y - 3 x z - 16 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=4.3MB, alloc=32.3MB, time=0.17 memory used=26.3MB, alloc=32.3MB, time=0.50 memory used=46.2MB, alloc=32.3MB, time=0.80 memory used=64.3MB, alloc=56.3MB, time=1.08 memory used=106.4MB, alloc=68.3MB, time=1.73 memory used=145.9MB, alloc=92.3MB, time=2.34 memory used=212.2MB, alloc=92.3MB, time=3.27 memory used=274.4MB, alloc=92.3MB, time=4.24 memory used=337.5MB, alloc=116.3MB, time=5.24 memory used=420.6MB, alloc=372.3MB, time=6.53 memory used=511.1MB, alloc=396.3MB, time=7.78 memory used=620.0MB, alloc=396.3MB, time=9.47 memory used=727.7MB, alloc=420.3MB, time=11.00 memory used=865.1MB, alloc=444.3MB, time=13.02 memory used=998.4MB, alloc=444.3MB, time=15.03 memory used=1126.2MB, alloc=468.3MB, time=16.91 memory used=1239.7MB, alloc=468.3MB, time=18.84 memory used=1359.6MB, alloc=492.3MB, time=20.73 memory used=1488.0MB, alloc=492.3MB, time=23.08 memory used=1581.9MB, alloc=492.3MB, time=24.62 memory used=1669.7MB, alloc=516.3MB, time=26.00 memory used=1764.5MB, alloc=516.3MB, time=27.75 memory used=1864.3MB, alloc=516.3MB, time=29.81 memory used=1956.1MB, alloc=516.3MB, time=31.76 memory used=2018.3MB, alloc=516.3MB, time=32.93 memory used=2085.9MB, alloc=516.3MB, time=34.33 memory used=2154.6MB, alloc=516.3MB, time=35.80 memory used=2232.2MB, alloc=516.3MB, time=37.61 memory used=2298.4MB, alloc=516.3MB, time=38.99 memory used=2362.7MB, alloc=516.3MB, time=40.52 memory used=2413.9MB, alloc=516.3MB, time=41.69 memory used=2464.3MB, alloc=540.3MB, time=42.68 memory used=2678.8MB, alloc=564.3MB, time=46.10 memory used=2892.5MB, alloc=588.3MB, time=49.91 memory used=3091.5MB, alloc=612.3MB, time=53.87 memory used=3275.0MB, alloc=636.3MB, time=56.57 memory used=3455.2MB, alloc=636.3MB, time=59.91 memory used=3628.4MB, alloc=660.3MB, time=63.39 memory used=3785.8MB, alloc=660.3MB, time=66.78 memory used=3946.3MB, alloc=660.3MB, time=69.80 memory used=4067.5MB, alloc=660.3MB, time=72.18 memory used=4173.6MB, alloc=684.3MB, time=74.29 memory used=4322.8MB, alloc=684.3MB, time=77.90 memory used=4457.8MB, alloc=684.3MB, time=81.34 memory used=4579.1MB, alloc=684.3MB, time=84.63 memory used=4694.1MB, alloc=684.3MB, time=87.77 memory used=4776.8MB, alloc=684.3MB, time=89.82 memory used=5125.0MB, alloc=708.3MB, time=96.26 memory used=5479.8MB, alloc=732.3MB, time=102.96 memory used=5856.9MB, alloc=756.3MB, time=109.77 memory used=6259.1MB, alloc=780.3MB, time=118.57 memory used=6646.5MB, alloc=804.3MB, time=129.23 memory used=6981.1MB, alloc=828.3MB, time=136.55 memory used=7357.8MB, alloc=852.3MB, time=146.08 memory used=7657.1MB, alloc=876.3MB, time=153.30 memory used=7916.5MB, alloc=900.3MB, time=159.93 |\^/| 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(); 1428292645 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [-12 y - 11 y z - 15 z + 19 y, -x + 2 x y - 4 z + 3 x, 2 2 -10 x - 11 x z + 14 y - 11] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [19 x - 9 x z - 6 y z - 6 z, -20 x - 3 y z - 12 z , -12 y z - 5 z - 20] > Problem := [F,G]; 2 2 2 2 Problem := [[-12 y - 11 y z - 15 z + 19 y, -x + 2 x y - 4 z + 3 x, 2 2 -10 x - 11 x z + 14 y - 11], 2 2 2 2 [19 x - 9 x z - 6 y z - 6 z, -20 x - 3 y z - 12 z , -12 y z - 5 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=4.3MB, alloc=32.3MB, time=0.17 memory used=24.8MB, alloc=32.3MB, time=0.47 memory used=44.6MB, alloc=60.3MB, time=0.76 memory used=85.6MB, alloc=60.3MB, time=1.34 memory used=126.3MB, alloc=60.3MB, time=1.93 memory used=156.8MB, alloc=84.3MB, time=2.32 memory used=222.9MB, alloc=92.3MB, time=3.22 memory used=291.5MB, alloc=348.3MB, time=4.10 memory used=357.6MB, alloc=372.3MB, time=5.06 memory used=448.8MB, alloc=396.3MB, time=6.32 memory used=564.8MB, alloc=396.3MB, time=7.75 memory used=673.8MB, alloc=420.3MB, time=9.41 memory used=787.5MB, alloc=420.3MB, time=11.06 memory used=909.7MB, alloc=444.3MB, time=12.98 memory used=1016.1MB, alloc=468.3MB, time=14.70 memory used=1124.2MB, alloc=468.3MB, time=16.44 memory used=1238.2MB, alloc=468.3MB, time=17.83 memory used=1331.7MB, alloc=468.3MB, time=19.38 memory used=1424.3MB, alloc=492.3MB, time=20.92 memory used=1507.8MB, alloc=492.3MB, time=22.37 memory used=1589.1MB, alloc=492.3MB, time=23.70 memory used=1664.8MB, alloc=492.3MB, time=25.08 memory used=1736.5MB, alloc=492.3MB, time=26.37 memory used=1791.4MB, alloc=492.3MB, time=27.50 memory used=1844.3MB, alloc=492.3MB, time=28.65 memory used=1901.1MB, alloc=492.3MB, time=29.81 memory used=1965.3MB, alloc=492.3MB, time=31.17 memory used=2012.8MB, alloc=492.3MB, time=32.17 memory used=2198.6MB, alloc=516.3MB, time=35.16 memory used=2394.2MB, alloc=540.3MB, time=38.65 memory used=2576.1MB, alloc=564.3MB, time=42.04 memory used=2735.1MB, alloc=588.3MB, time=44.66 memory used=2887.3MB, alloc=612.3MB, time=47.58 memory used=3049.8MB, alloc=636.3MB, time=50.72 memory used=3194.9MB, alloc=660.3MB, time=54.04 memory used=3336.0MB, alloc=660.3MB, time=56.58 memory used=3451.3MB, alloc=660.3MB, time=59.36 memory used=3569.1MB, alloc=660.3MB, time=61.44 memory used=3690.5MB, alloc=660.3MB, time=64.32 memory used=3756.6MB, alloc=660.3MB, time=65.88 memory used=3877.5MB, alloc=684.3MB, time=68.94 memory used=4004.0MB, alloc=684.3MB, time=72.69 memory used=4368.8MB, alloc=708.3MB, time=78.97 memory used=4742.6MB, alloc=732.3MB, time=86.07 memory used=5130.0MB, alloc=756.3MB, time=94.25 memory used=5520.5MB, alloc=780.3MB, time=102.53 memory used=5901.1MB, alloc=804.3MB, time=109.17 memory used=6226.7MB, alloc=828.3MB, time=115.79 memory used=6588.5MB, alloc=852.3MB, time=123.64 memory used=6896.3MB, alloc=876.3MB, time=129.58 memory used=7180.3MB, alloc=900.3MB, time=136.00 memory used=7459.4MB, alloc=924.3MB, time=142.63 memory used=7740.2MB, alloc=948.3MB, time=149.03 memory used=7944.4MB, alloc=972.3MB, time=155.23 |\^/| 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(); 1428292945 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [16 x + 17 z + 7 x - 1, -9 x + 12 y + 14 y z - 7 z, 8 x y - 10 x - 5 y + 2 z] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; G := [ 2 2 2 -6 x - 8 x y - 18 x + 5 z, -4 x + 13 y z + 4 x - 8 z, 9 y + 10 y z + 2 z ] > Problem := [F,G]; 2 2 2 2 Problem := [[16 x + 17 z + 7 x - 1, -9 x + 12 y + 14 y z - 7 z, 8 x y - 10 x - 5 y + 2 z], [ 2 2 2 -6 x - 8 x y - 18 x + 5 z, -4 x + 13 y z + 4 x - 8 z, 9 y + 10 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=4.3MB, alloc=32.3MB, time=0.18 memory used=26.0MB, alloc=32.3MB, time=0.50 memory used=45.4MB, alloc=32.3MB, time=0.77 memory used=63.6MB, alloc=56.3MB, time=1.06 memory used=104.2MB, alloc=60.3MB, time=1.68 memory used=143.2MB, alloc=84.3MB, time=2.28 memory used=205.1MB, alloc=92.3MB, time=3.25 memory used=265.7MB, alloc=116.3MB, time=4.21 memory used=348.3MB, alloc=116.3MB, time=5.50 memory used=422.7MB, alloc=396.3MB, time=6.67 memory used=528.2MB, alloc=420.3MB, time=8.40 memory used=659.1MB, alloc=444.3MB, time=10.53 memory used=806.8MB, alloc=468.3MB, time=12.92 memory used=946.9MB, alloc=468.3MB, time=15.32 memory used=1081.2MB, alloc=492.3MB, time=17.77 memory used=1190.5MB, alloc=492.3MB, time=19.67 memory used=1323.5MB, alloc=492.3MB, time=22.29 memory used=1441.5MB, alloc=516.3MB, time=24.63 memory used=1547.4MB, alloc=516.3MB, time=26.81 memory used=1643.6MB, alloc=516.3MB, time=28.80 memory used=1745.3MB, alloc=516.3MB, time=31.06 memory used=1833.0MB, alloc=516.3MB, time=33.08 memory used=1910.9MB, alloc=516.3MB, time=34.86 memory used=1984.0MB, alloc=516.3MB, time=36.59 memory used=2036.8MB, alloc=516.3MB, time=37.74 memory used=2099.0MB, alloc=516.3MB, time=39.32 memory used=2167.8MB, alloc=540.3MB, time=41.16 memory used=2217.5MB, alloc=540.3MB, time=42.62 memory used=2445.0MB, alloc=564.3MB, time=47.85 memory used=2682.0MB, alloc=588.3MB, time=53.49 memory used=2859.9MB, alloc=612.3MB, time=57.55 memory used=3071.5MB, alloc=636.3MB, time=62.77 memory used=3253.5MB, alloc=660.3MB, time=67.21 memory used=3462.1MB, alloc=684.3MB, time=73.06 memory used=3667.8MB, alloc=708.3MB, time=78.65 memory used=3807.1MB, alloc=708.3MB, time=82.24 memory used=3940.3MB, alloc=708.3MB, time=86.02 memory used=4055.5MB, alloc=732.3MB, time=88.87 memory used=4212.6MB, alloc=732.3MB, time=93.80 memory used=4360.9MB, alloc=732.3MB, time=98.54 memory used=4752.7MB, alloc=756.3MB, time=108.82 memory used=5172.8MB, alloc=780.3MB, time=119.22 memory used=5610.4MB, alloc=804.3MB, time=130.77 memory used=6060.2MB, alloc=828.3MB, time=143.18 memory used=6450.2MB, alloc=852.3MB, time=153.10 |\^/| 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(); 1428293245 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [19 x - 4 y - 19 y z - x, -11 x + 12 z + 13 y + 16 z, 2 4 x z - 12 y z - 8 z + 11] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [6 x + 5 x y + 2 z - 5, -14 x + 18 x y + x + 19 z, 2 -19 x y + 15 x z - 10 y z + 18 z ] > Problem := [F,G]; 2 2 2 2 Problem := [[19 x - 4 y - 19 y z - x, -11 x + 12 z + 13 y + 16 z, 2 2 4 x z - 12 y z - 8 z + 11], [6 x + 5 x y + 2 z - 5, 2 2 -14 x + 18 x y + x + 19 z, -19 x y + 15 x z - 10 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=26.3MB, alloc=32.3MB, time=0.51 memory used=46.2MB, alloc=32.3MB, time=0.81 memory used=65.2MB, alloc=60.3MB, time=1.13 memory used=105.3MB, alloc=60.3MB, time=1.73 memory used=144.2MB, alloc=84.3MB, time=2.34 memory used=207.4MB, alloc=92.3MB, time=3.33 memory used=271.5MB, alloc=92.3MB, time=4.32 memory used=333.8MB, alloc=116.3MB, time=5.28 memory used=414.8MB, alloc=372.3MB, time=6.59 memory used=498.6MB, alloc=396.3MB, time=7.97 memory used=605.5MB, alloc=420.3MB, time=9.69 memory used=741.5MB, alloc=444.3MB, time=11.88 memory used=878.4MB, alloc=468.3MB, time=14.12 memory used=1013.7MB, alloc=468.3MB, time=16.48 memory used=1149.0MB, alloc=492.3MB, time=18.89 memory used=1249.3MB, alloc=492.3MB, time=20.70 memory used=1349.5MB, alloc=492.3MB, time=22.62 memory used=1450.8MB, alloc=492.3MB, time=24.25 memory used=1556.7MB, alloc=492.3MB, time=26.14 memory used=1657.4MB, alloc=492.3MB, time=28.05 memory used=1754.5MB, alloc=516.3MB, time=29.98 memory used=1838.4MB, alloc=516.3MB, time=31.62 memory used=1911.3MB, alloc=516.3MB, time=33.03 memory used=1996.8MB, alloc=516.3MB, time=34.78 memory used=2083.2MB, alloc=516.3MB, time=36.69 memory used=2159.8MB, alloc=516.3MB, time=38.38 memory used=2231.3MB, alloc=516.3MB, time=40.14 memory used=2300.6MB, alloc=516.3MB, time=41.90 memory used=2384.4MB, alloc=516.3MB, time=43.98 memory used=2433.8MB, alloc=516.3MB, time=45.14 memory used=2490.4MB, alloc=516.3MB, time=46.78 memory used=2533.0MB, alloc=516.3MB, time=47.97 memory used=2745.8MB, alloc=540.3MB, time=51.52 memory used=2970.2MB, alloc=564.3MB, time=56.58 memory used=3169.8MB, alloc=588.3MB, time=60.19 memory used=3380.2MB, alloc=612.3MB, time=65.00 memory used=3577.4MB, alloc=636.3MB, time=69.72 memory used=3764.0MB, alloc=636.3MB, time=74.25 memory used=3908.3MB, alloc=636.3MB, time=77.88 memory used=4085.9MB, alloc=660.3MB, time=82.51 memory used=4238.2MB, alloc=660.3MB, time=85.99 memory used=4392.9MB, alloc=660.3MB, time=89.75 memory used=4519.2MB, alloc=660.3MB, time=92.98 memory used=4646.8MB, alloc=660.3MB, time=96.38 memory used=4774.7MB, alloc=684.3MB, time=99.84 memory used=4889.1MB, alloc=684.3MB, time=103.08 memory used=5002.4MB, alloc=684.3MB, time=106.13 memory used=5105.9MB, alloc=684.3MB, time=109.45 memory used=5460.2MB, alloc=708.3MB, time=118.52 memory used=5842.2MB, alloc=732.3MB, time=127.60 memory used=6238.3MB, alloc=756.3MB, time=138.38 |\^/| 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(); 1428293545 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-8 x - 12 x z + 7 x - 17, 10 x y - 16 y - 3 z + 8, 2 2 17 x - 16 y + 19 y + 2] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [11 x z - 18 x + 15 y + 7 z, -20 y - 12 y z + 18 z - 5 x, 2 16 x - 4 x y + 9 y z] > Problem := [F,G]; 2 2 2 Problem := [[-8 x - 12 x z + 7 x - 17, 10 x y - 16 y - 3 z + 8, 2 2 17 x - 16 y + 19 y + 2], [11 x z - 18 x + 15 y + 7 z, 2 2 2 -20 y - 12 y z + 18 z - 5 x, 16 x - 4 x 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=26.7MB, alloc=32.3MB, time=0.50 memory used=48.0MB, alloc=32.3MB, time=0.81 memory used=67.4MB, alloc=56.3MB, time=1.12 memory used=108.4MB, alloc=60.3MB, time=1.75 memory used=148.7MB, alloc=84.3MB, time=2.39 memory used=214.2MB, alloc=92.3MB, time=3.37 memory used=277.8MB, alloc=116.3MB, time=4.35 memory used=361.1MB, alloc=116.3MB, time=5.71 memory used=436.8MB, alloc=372.3MB, time=6.90 memory used=522.9MB, alloc=396.3MB, time=8.27 memory used=632.8MB, alloc=420.3MB, time=10.02 memory used=765.7MB, alloc=444.3MB, time=12.24 memory used=894.3MB, alloc=444.3MB, time=14.28 memory used=1028.9MB, alloc=468.3MB, time=16.40 memory used=1161.3MB, alloc=492.3MB, time=18.84 memory used=1272.2MB, alloc=492.3MB, time=20.66 memory used=1371.7MB, alloc=492.3MB, time=22.27 memory used=1480.9MB, alloc=516.3MB, time=24.33 memory used=1571.6MB, alloc=516.3MB, time=25.63 memory used=1676.7MB, alloc=516.3MB, time=28.12 memory used=1751.9MB, alloc=516.3MB, time=29.61 memory used=1820.8MB, alloc=540.3MB, time=31.05 memory used=1886.7MB, alloc=540.3MB, time=32.54 memory used=1935.8MB, alloc=540.3MB, time=33.66 memory used=2005.2MB, alloc=540.3MB, time=35.54 memory used=2084.0MB, alloc=540.3MB, time=37.72 memory used=2142.8MB, alloc=540.3MB, time=39.46 memory used=2197.4MB, alloc=540.3MB, time=41.04 memory used=2422.3MB, alloc=564.3MB, time=44.98 memory used=2621.3MB, alloc=588.3MB, time=48.62 memory used=2827.6MB, alloc=612.3MB, time=52.62 memory used=3004.9MB, alloc=636.3MB, time=56.07 memory used=3172.6MB, alloc=636.3MB, time=59.48 memory used=3326.2MB, alloc=660.3MB, time=62.67 memory used=3470.4MB, alloc=660.3MB, time=65.91 memory used=3613.2MB, alloc=660.3MB, time=69.14 memory used=3709.4MB, alloc=660.3MB, time=71.21 memory used=3815.6MB, alloc=660.3MB, time=74.11 memory used=3933.7MB, alloc=660.3MB, time=77.07 memory used=4016.3MB, alloc=660.3MB, time=79.31 memory used=4356.8MB, alloc=684.3MB, time=85.76 memory used=4708.1MB, alloc=708.3MB, time=93.66 memory used=5077.2MB, alloc=732.3MB, time=101.99 memory used=5472.5MB, alloc=756.3MB, time=109.87 memory used=5862.2MB, alloc=780.3MB, time=119.56 memory used=6205.3MB, alloc=804.3MB, time=126.93 memory used=6507.5MB, alloc=828.3MB, time=134.02 memory used=6806.0MB, alloc=852.3MB, time=142.39 memory used=7123.8MB, alloc=876.3MB, time=151.09 |\^/| 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(); 1428293845 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [4 y - 13 y z - 20 x + 7 z, 8 x - 4 x y + 8 y - 11 z, 8 x y + 6 x z - 15 y z - 12] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-13 x + 18 y z - 19 y - 11 z, -12 x - 17 x z - 13 x - 7 y, 2 18 x - 7 x y - 9 x - 6 z] > Problem := [F,G]; 2 2 Problem := [[4 y - 13 y z - 20 x + 7 z, 8 x - 4 x y + 8 y - 11 z, 2 8 x y + 6 x z - 15 y z - 12], [-13 x + 18 y z - 19 y - 11 z, 2 2 -12 x - 17 x z - 13 x - 7 y, 18 x - 7 x y - 9 x - 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=4.3MB, alloc=32.3MB, time=0.17 memory used=26.6MB, alloc=32.3MB, time=0.50 memory used=47.1MB, alloc=56.3MB, time=0.82 memory used=89.7MB, alloc=60.3MB, time=1.45 memory used=131.9MB, alloc=60.3MB, time=2.07 memory used=172.8MB, alloc=84.3MB, time=2.73 memory used=235.0MB, alloc=92.3MB, time=3.71 memory used=293.5MB, alloc=116.3MB, time=4.65 memory used=378.3MB, alloc=116.3MB, time=6.04 memory used=456.4MB, alloc=396.3MB, time=7.35 memory used=568.2MB, alloc=420.3MB, time=9.20 memory used=706.2MB, alloc=444.3MB, time=11.51 memory used=855.6MB, alloc=444.3MB, time=14.09 memory used=1009.7MB, alloc=468.3MB, time=16.89 memory used=1155.0MB, alloc=492.3MB, time=19.44 memory used=1300.4MB, alloc=492.3MB, time=22.28 memory used=1419.2MB, alloc=516.3MB, time=24.65 memory used=1539.3MB, alloc=516.3MB, time=27.17 memory used=1655.6MB, alloc=516.3MB, time=29.79 memory used=1738.3MB, alloc=516.3MB, time=31.53 memory used=1848.1MB, alloc=516.3MB, time=34.11 memory used=1938.2MB, alloc=516.3MB, time=36.04 memory used=2033.4MB, alloc=516.3MB, time=38.31 memory used=2114.4MB, alloc=516.3MB, time=40.19 memory used=2189.2MB, alloc=516.3MB, time=42.09 memory used=2261.9MB, alloc=516.3MB, time=43.93 memory used=2314.6MB, alloc=540.3MB, time=45.39 memory used=2377.1MB, alloc=540.3MB, time=46.96 memory used=2434.6MB, alloc=540.3MB, time=48.46 memory used=2483.9MB, alloc=540.3MB, time=49.79 memory used=2533.2MB, alloc=540.3MB, time=51.02 memory used=2579.7MB, alloc=540.3MB, time=52.45 memory used=2806.9MB, alloc=564.3MB, time=57.70 memory used=3026.3MB, alloc=588.3MB, time=62.23 memory used=3284.2MB, alloc=612.3MB, time=68.85 memory used=3498.4MB, alloc=636.3MB, time=74.60 memory used=3687.6MB, alloc=660.3MB, time=78.84 memory used=3874.6MB, alloc=684.3MB, time=83.24 memory used=4055.7MB, alloc=708.3MB, time=88.21 memory used=4213.3MB, alloc=708.3MB, time=92.59 memory used=4380.5MB, alloc=708.3MB, time=96.91 memory used=4482.3MB, alloc=708.3MB, time=99.21 memory used=4639.5MB, alloc=708.3MB, time=104.08 memory used=4778.7MB, alloc=708.3MB, time=108.10 memory used=4856.0MB, alloc=708.3MB, time=110.42 memory used=4988.1MB, alloc=732.3MB, time=114.02 memory used=5396.6MB, alloc=756.3MB, time=124.04 memory used=5818.0MB, alloc=780.3MB, time=136.35 memory used=6268.2MB, alloc=804.3MB, time=148.16 |\^/| 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(); 1428294146 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-8 x y - 16 z + 9 y - 12, -17 x z - 7 z + 16 x - 18 y, 2 2 15 x y - 8 y - 14 z + 8 z] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-19 x - 5 x + 3 y + 19, -18 x z + 16 y z + 3 z + 7, 2 -16 x y - 2 y + 15 y z + 19 y] > Problem := [F,G]; 2 2 Problem := [[-8 x y - 16 z + 9 y - 12, -17 x z - 7 z + 16 x - 18 y, 2 2 2 15 x y - 8 y - 14 z + 8 z], [-19 x - 5 x + 3 y + 19, 2 2 -18 x z + 16 y z + 3 z + 7, -16 x y - 2 y + 15 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=4.3MB, alloc=32.3MB, time=0.17 memory used=26.8MB, alloc=32.3MB, time=0.49 memory used=46.4MB, alloc=56.3MB, time=0.81 memory used=87.9MB, alloc=60.3MB, time=1.45 memory used=127.6MB, alloc=60.3MB, time=2.04 memory used=167.1MB, alloc=84.3MB, time=2.66 memory used=228.0MB, alloc=116.3MB, time=3.65 memory used=311.2MB, alloc=116.3MB, time=4.95 memory used=382.7MB, alloc=140.3MB, time=6.10 memory used=457.4MB, alloc=396.3MB, time=7.30 memory used=560.5MB, alloc=420.3MB, time=8.99 memory used=692.8MB, alloc=444.3MB, time=11.20 memory used=847.3MB, alloc=468.3MB, time=13.68 memory used=995.3MB, alloc=492.3MB, time=16.28 memory used=1149.5MB, alloc=492.3MB, time=19.18 memory used=1267.6MB, alloc=492.3MB, time=21.34 memory used=1370.6MB, alloc=492.3MB, time=23.26 memory used=1500.7MB, alloc=516.3MB, time=26.07 memory used=1613.4MB, alloc=516.3MB, time=28.32 memory used=1727.4MB, alloc=516.3MB, time=30.74 memory used=1822.9MB, alloc=516.3MB, time=32.89 memory used=1914.6MB, alloc=516.3MB, time=34.90 memory used=2000.0MB, alloc=540.3MB, time=36.92 memory used=2094.0MB, alloc=540.3MB, time=39.21 memory used=2163.2MB, alloc=540.3MB, time=40.90 memory used=2243.3MB, alloc=540.3MB, time=42.89 memory used=2306.8MB, alloc=540.3MB, time=44.52 memory used=2364.0MB, alloc=540.3MB, time=45.94 memory used=2420.4MB, alloc=540.3MB, time=47.32 memory used=2468.9MB, alloc=540.3MB, time=48.53 memory used=2516.6MB, alloc=540.3MB, time=49.78 memory used=2745.1MB, alloc=564.3MB, time=54.27 memory used=2986.1MB, alloc=588.3MB, time=59.72 memory used=3177.8MB, alloc=612.3MB, time=63.79 memory used=3395.4MB, alloc=636.3MB, time=68.75 memory used=3614.3MB, alloc=660.3MB, time=74.70 memory used=3736.7MB, alloc=684.3MB, time=77.21 memory used=3893.7MB, alloc=708.3MB, time=81.24 memory used=4048.9MB, alloc=708.3MB, time=85.42 memory used=4231.2MB, alloc=708.3MB, time=90.51 memory used=4381.2MB, alloc=708.3MB, time=94.66 memory used=4498.5MB, alloc=732.3MB, time=97.42 memory used=4643.5MB, alloc=732.3MB, time=101.35 memory used=4743.3MB, alloc=732.3MB, time=103.43 memory used=4892.4MB, alloc=756.3MB, time=107.84 memory used=5316.5MB, alloc=780.3MB, time=116.72 |\^/| 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(); 1428294446 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-6 x - 16 y + 14 z + 19, -11 x y + x z + 18 y - 16 z, 2 -20 x y + 20 x z - 3 y + 6 y z] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [4 x z + 10 y z + 17 x + 8, -2 x + 20 x z - 19 y + y, 2 2 -10 x y + 2 y - 8 z - 4 x] > Problem := [F,G]; 2 2 2 Problem := [[-6 x - 16 y + 14 z + 19, -11 x y + x z + 18 y - 16 z, 2 -20 x y + 20 x z - 3 y + 6 y z], [4 x z + 10 y z + 17 x + 8, 2 2 2 2 -2 x + 20 x z - 19 y + y, -10 x y + 2 y - 8 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=26.0MB, alloc=32.3MB, time=0.51 memory used=46.7MB, alloc=32.3MB, time=0.82 memory used=66.5MB, alloc=60.3MB, time=1.12 memory used=106.8MB, alloc=60.3MB, time=1.70 memory used=146.5MB, alloc=84.3MB, time=2.30 memory used=212.2MB, alloc=92.3MB, time=3.25 memory used=277.2MB, alloc=92.3MB, time=4.19 memory used=341.9MB, alloc=116.3MB, time=5.12 memory used=407.2MB, alloc=372.3MB, time=6.12 memory used=490.9MB, alloc=396.3MB, time=7.39 memory used=602.5MB, alloc=420.3MB, time=8.95 memory used=732.3MB, alloc=444.3MB, time=10.72 memory used=848.6MB, alloc=444.3MB, time=12.38 memory used=967.0MB, alloc=468.3MB, time=14.12 memory used=1067.6MB, alloc=468.3MB, time=15.76 memory used=1158.2MB, alloc=468.3MB, time=17.15 memory used=1247.3MB, alloc=492.3MB, time=18.41 memory used=1352.2MB, alloc=492.3MB, time=20.27 memory used=1421.1MB, alloc=492.3MB, time=21.46 memory used=1499.7MB, alloc=492.3MB, time=22.75 memory used=1557.4MB, alloc=492.3MB, time=23.78 memory used=1635.7MB, alloc=492.3MB, time=25.10 memory used=1696.4MB, alloc=492.3MB, time=26.21 memory used=1765.3MB, alloc=492.3MB, time=27.55 memory used=1807.8MB, alloc=492.3MB, time=28.39 memory used=1852.1MB, alloc=492.3MB, time=29.36 memory used=1901.4MB, alloc=492.3MB, time=30.52 memory used=2094.0MB, alloc=516.3MB, time=33.81 memory used=2287.2MB, alloc=540.3MB, time=37.20 memory used=2451.2MB, alloc=564.3MB, time=40.08 memory used=2631.8MB, alloc=588.3MB, time=43.27 memory used=2781.9MB, alloc=612.3MB, time=46.35 memory used=2921.2MB, alloc=636.3MB, time=49.03 memory used=3042.5MB, alloc=636.3MB, time=51.72 memory used=3178.9MB, alloc=636.3MB, time=54.92 memory used=3305.8MB, alloc=636.3MB, time=57.64 memory used=3405.5MB, alloc=636.3MB, time=59.83 memory used=3486.3MB, alloc=636.3MB, time=61.81 memory used=3575.2MB, alloc=636.3MB, time=64.13 memory used=3884.0MB, alloc=660.3MB, time=69.91 memory used=4206.8MB, alloc=684.3MB, time=76.46 memory used=4550.2MB, alloc=708.3MB, time=83.33 memory used=4888.4MB, alloc=732.3MB, time=90.33 memory used=5220.3MB, alloc=756.3MB, time=97.94 memory used=5499.1MB, alloc=780.3MB, time=103.74 memory used=5794.0MB, alloc=804.3MB, time=110.70 memory used=6045.3MB, alloc=828.3MB, time=116.75 memory used=6290.7MB, alloc=852.3MB, time=123.00 memory used=6497.5MB, alloc=876.3MB, time=128.00 memory used=6723.9MB, alloc=900.3MB, time=134.08 memory used=6878.5MB, alloc=924.3MB, time=138.53 |\^/| 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(); 1428294746 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [19 x - 2 y + 19 y z - 20, 10 y + 14 y z - 6 x - 10 y, 2 20 x + y + 12 z + 1] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [-5 x + 2 x z + 18 y z + 12 y, 15 x - 3 x y + 20 z - 11 z, 2 2 9 x z + 16 y - 2 z + 10 x] > Problem := [F,G]; 2 2 2 Problem := [[19 x - 2 y + 19 y z - 20, 10 y + 14 y z - 6 x - 10 y, 2 2 20 x + y + 12 z + 1], [-5 x + 2 x z + 18 y z + 12 y, 2 2 2 2 15 x - 3 x y + 20 z - 11 z, 9 x z + 16 y - 2 z + 10 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=26.1MB, alloc=32.3MB, time=0.49 memory used=45.9MB, alloc=56.3MB, time=0.82 memory used=87.8MB, alloc=60.3MB, time=1.46 memory used=126.9MB, alloc=84.3MB, time=2.09 memory used=166.7MB, alloc=84.3MB, time=2.72 memory used=231.2MB, alloc=92.3MB, time=3.74 memory used=293.7MB, alloc=116.3MB, time=4.75 memory used=367.4MB, alloc=116.3MB, time=5.95 memory used=442.9MB, alloc=396.3MB, time=7.30 memory used=557.0MB, alloc=420.3MB, time=9.02 memory used=676.6MB, alloc=444.3MB, time=10.76 memory used=817.7MB, alloc=468.3MB, time=13.12 memory used=954.6MB, alloc=468.3MB, time=15.40 memory used=1065.8MB, alloc=468.3MB, time=17.09 memory used=1157.5MB, alloc=492.3MB, time=18.53 memory used=1274.6MB, alloc=492.3MB, time=20.66 memory used=1380.0MB, alloc=492.3MB, time=22.55 memory used=1466.0MB, alloc=492.3MB, time=24.03 memory used=1544.6MB, alloc=492.3MB, time=25.41 memory used=1640.2MB, alloc=492.3MB, time=27.32 memory used=1712.2MB, alloc=492.3MB, time=28.79 memory used=1774.4MB, alloc=516.3MB, time=30.15 memory used=1824.8MB, alloc=516.3MB, time=31.16 memory used=1891.3MB, alloc=516.3MB, time=32.63 memory used=1957.7MB, alloc=516.3MB, time=34.20 memory used=2005.2MB, alloc=516.3MB, time=35.31 memory used=2052.6MB, alloc=516.3MB, time=36.43 memory used=2266.1MB, alloc=540.3MB, time=40.43 memory used=2473.3MB, alloc=564.3MB, time=44.38 memory used=2660.8MB, alloc=588.3MB, time=47.77 memory used=2845.2MB, alloc=612.3MB, time=51.54 memory used=3009.3MB, alloc=636.3MB, time=55.35 memory used=3139.6MB, alloc=636.3MB, time=58.06 memory used=3274.1MB, alloc=660.3MB, time=60.90 memory used=3392.0MB, alloc=660.3MB, time=63.65 memory used=3509.2MB, alloc=660.3MB, time=66.34 memory used=3620.6MB, alloc=660.3MB, time=68.93 memory used=3732.3MB, alloc=660.3MB, time=71.59 memory used=3837.4MB, alloc=660.3MB, time=74.31 memory used=3942.9MB, alloc=660.3MB, time=77.03 memory used=4273.7MB, alloc=684.3MB, time=83.26 memory used=4626.1MB, alloc=708.3MB, time=89.97 memory used=4941.5MB, alloc=732.3MB, time=96.05 memory used=5308.5MB, alloc=756.3MB, time=103.69 memory used=5687.4MB, alloc=780.3MB, time=112.25 memory used=5979.1MB, alloc=804.3MB, time=118.15 memory used=6292.1MB, alloc=828.3MB, time=124.08 memory used=6570.1MB, alloc=852.3MB, time=129.61 memory used=6849.1MB, alloc=876.3MB, time=136.67 |\^/| 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(); 1428295046 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; F := [6 x y + 20 y z - 18 x + 14 y, -9 x y - 16 y z + 12 x - 20 z, 12 x z - 2 y z - 13 x - 7 z] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; G := 2 2 [-5 x z - 3 z + 7 y - 14 z, 11 x z + 4 y z - y + 19 z, 7 z - 6 x - z + 4] > Problem := [F,G]; Problem := [[6 x y + 20 y z - 18 x + 14 y, -9 x y - 16 y z + 12 x - 20 z, 12 x z - 2 y z - 13 x - 7 z], 2 2 [-5 x z - 3 z + 7 y - 14 z, 11 x z + 4 y z - y + 19 z, 7 z - 6 x - 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=4.2MB, alloc=32.3MB, time=0.17 memory used=26.6MB, alloc=32.3MB, time=0.50 memory used=46.5MB, alloc=32.3MB, time=0.80 memory used=65.2MB, alloc=56.3MB, time=1.09 memory used=104.4MB, alloc=60.3MB, time=1.67 memory used=141.6MB, alloc=84.3MB, time=2.25 memory used=202.4MB, alloc=92.3MB, time=3.19 memory used=262.3MB, alloc=116.3MB, time=4.13 memory used=345.3MB, alloc=116.3MB, time=5.45 memory used=426.9MB, alloc=140.3MB, time=6.81 memory used=502.7MB, alloc=140.3MB, time=8.04 memory used=586.4MB, alloc=420.3MB, time=9.52 memory used=710.5MB, alloc=444.3MB, time=11.63 memory used=858.5MB, alloc=468.3MB, time=14.18 memory used=1020.2MB, alloc=492.3MB, time=17.18 memory used=1155.7MB, alloc=492.3MB, time=19.70 memory used=1267.0MB, alloc=492.3MB, time=21.71 memory used=1411.3MB, alloc=516.3MB, time=24.59 memory used=1557.9MB, alloc=516.3MB, time=27.68 memory used=1675.8MB, alloc=540.3MB, time=30.22 memory used=1773.2MB, alloc=540.3MB, time=32.41 memory used=1872.1MB, alloc=540.3MB, time=34.55 memory used=1989.0MB, alloc=540.3MB, time=37.47 memory used=2098.5MB, alloc=540.3MB, time=40.12 memory used=2194.4MB, alloc=540.3MB, time=42.38 memory used=2287.2MB, alloc=540.3MB, time=44.64 memory used=2370.5MB, alloc=540.3MB, time=46.93 memory used=2431.5MB, alloc=540.3MB, time=48.39 memory used=2511.4MB, alloc=540.3MB, time=50.54 memory used=2579.3MB, alloc=564.3MB, time=52.28 memory used=2626.6MB, alloc=564.3MB, time=53.46 memory used=2872.0MB, alloc=588.3MB, time=59.13 memory used=3141.2MB, alloc=612.3MB, time=66.01 memory used=3353.1MB, alloc=636.3MB, time=71.03 memory used=3569.7MB, alloc=660.3MB, time=76.18 memory used=3798.1MB, alloc=684.3MB, time=82.47 memory used=3994.5MB, alloc=708.3MB, time=87.41 memory used=4175.1MB, alloc=732.3MB, time=91.66 memory used=4335.7MB, alloc=732.3MB, time=95.50 memory used=4499.8MB, alloc=732.3MB, time=100.31 memory used=4629.7MB, alloc=732.3MB, time=104.08 memory used=4739.0MB, alloc=732.3MB, time=107.44 memory used=4897.9MB, alloc=756.3MB, time=111.75 memory used=5022.7MB, alloc=756.3MB, time=115.92 memory used=5152.4MB, alloc=756.3MB, time=119.25 memory used=5293.3MB, alloc=756.3MB, time=123.98 memory used=5395.7MB, alloc=756.3MB, 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(); 1428295346 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [-5 x - 3 x z + 2 z + 20, -4 x y + 4 y z - 12 z + 4, -5 y z + 9 x - 14 y + 12] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [7 y - 6 z + 20 x - 3, 19 x y - 11 y z - 6 z + 5, 2 2 -8 x + 6 y z - 3 z - 7 z] > Problem := [F,G]; 2 Problem := [[-5 x - 3 x z + 2 z + 20, -4 x y + 4 y z - 12 z + 4, 2 2 -5 y z + 9 x - 14 y + 12], [7 y - 6 z + 20 x - 3, 2 2 2 19 x y - 11 y z - 6 z + 5, -8 x + 6 y z - 3 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=26.7MB, alloc=32.3MB, time=0.50 memory used=47.3MB, alloc=32.3MB, time=0.80 memory used=64.9MB, alloc=56.3MB, time=1.09 memory used=104.4MB, alloc=60.3MB, time=1.70 memory used=142.5MB, alloc=84.3MB, time=2.30 memory used=204.6MB, alloc=92.3MB, time=3.29 memory used=265.8MB, alloc=92.3MB, time=4.29 memory used=324.9MB, alloc=116.3MB, time=5.23 memory used=406.6MB, alloc=372.3MB, time=6.53 memory used=488.3MB, alloc=396.3MB, time=7.88 memory used=596.1MB, alloc=420.3MB, time=9.51 memory used=723.5MB, alloc=444.3MB, time=11.63 memory used=871.5MB, alloc=468.3MB, time=14.16 memory used=1039.2MB, alloc=492.3MB, time=17.27 memory used=1191.7MB, alloc=516.3MB, time=20.11 memory used=1309.1MB, alloc=516.3MB, time=22.10 memory used=1413.3MB, alloc=516.3MB, time=23.90 memory used=1520.1MB, alloc=516.3MB, time=25.81 memory used=1617.8MB, alloc=516.3MB, time=27.81 memory used=1704.6MB, alloc=540.3MB, time=29.39 memory used=1798.2MB, alloc=540.3MB, time=31.26 memory used=1888.7MB, alloc=540.3MB, time=33.06 memory used=1955.8MB, alloc=540.3MB, time=34.31 memory used=2032.9MB, alloc=540.3MB, time=36.14 memory used=2086.9MB, alloc=540.3MB, time=37.30 memory used=2158.2MB, alloc=540.3MB, time=38.86 memory used=2215.0MB, alloc=540.3MB, time=39.95 memory used=2268.6MB, alloc=540.3MB, time=41.03 memory used=2332.1MB, alloc=540.3MB, time=42.79 memory used=2558.1MB, alloc=564.3MB, time=47.73 memory used=2783.7MB, alloc=588.3MB, time=52.02 memory used=2965.3MB, alloc=612.3MB, time=55.28 memory used=3176.0MB, alloc=636.3MB, time=59.86 memory used=3345.1MB, alloc=660.3MB, time=63.41 memory used=3526.6MB, alloc=660.3MB, time=67.75 memory used=3691.3MB, alloc=684.3MB, time=71.72 memory used=3859.6MB, alloc=684.3MB, time=76.03 memory used=4008.1MB, alloc=684.3MB, time=79.75 memory used=4151.0MB, alloc=684.3MB, time=83.39 memory used=4284.7MB, alloc=684.3MB, time=87.36 memory used=4419.8MB, alloc=684.3MB, time=91.36 memory used=4548.1MB, alloc=708.3MB, time=95.28 memory used=4924.2MB, alloc=732.3MB, time=104.72 memory used=5321.0MB, alloc=756.3MB, time=114.64 memory used=5733.0MB, alloc=780.3MB, time=126.31 memory used=6167.3MB, alloc=804.3MB, time=137.42 |\^/| 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(); 1428295646 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; F := [ 2 2 2 -13 x y + y z + 10 z - 4, 6 x y - 17 x - 7 y, -3 x - 13 x z - 8 y - 16 z ] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [-10 x - 10 x y + y + 14 y z, -16 x - 4 x z + 14 x + 13 y, 2 2 -13 x + 19 y z + 11 z + 10] > Problem := [F,G]; Problem := [[ 2 2 2 -13 x y + y z + 10 z - 4, 6 x y - 17 x - 7 y, -3 x - 13 x z - 8 y - 16 z 2 2 2 ], [-10 x - 10 x y + y + 14 y z, -16 x - 4 x z + 14 x + 13 y, 2 2 -13 x + 19 y z + 11 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=32.2MB, alloc=40.3MB, time=0.58 memory used=59.6MB, alloc=44.3MB, time=1.00 memory used=85.4MB, alloc=68.3MB, time=1.40 memory used=134.2MB, alloc=76.3MB, time=2.15 memory used=184.6MB, alloc=100.3MB, time=2.86 memory used=258.6MB, alloc=100.3MB, time=3.92 memory used=329.7MB, alloc=380.3MB, time=5.01 memory used=425.8MB, alloc=380.3MB, time=6.49 memory used=518.8MB, alloc=404.3MB, time=7.98 memory used=640.5MB, alloc=428.3MB, time=9.82 memory used=779.7MB, alloc=428.3MB, time=12.00 memory used=904.9MB, alloc=452.3MB, time=13.97 memory used=1022.4MB, alloc=452.3MB, time=15.99 memory used=1146.0MB, alloc=476.3MB, time=18.05 memory used=1252.3MB, alloc=476.3MB, time=19.68 memory used=1355.6MB, alloc=476.3MB, time=21.17 memory used=1464.2MB, alloc=500.3MB, time=23.01 memory used=1565.8MB, alloc=500.3MB, time=24.65 memory used=1675.2MB, alloc=524.3MB, time=25.87 memory used=1776.1MB, alloc=524.3MB, time=27.83 memory used=1852.5MB, alloc=524.3MB, time=29.09 memory used=1945.7MB, alloc=524.3MB, time=31.03 memory used=2022.8MB, alloc=524.3MB, time=32.47 memory used=2088.8MB, alloc=524.3MB, time=33.89 memory used=2151.4MB, alloc=548.3MB, time=34.96 memory used=2219.3MB, alloc=548.3MB, time=36.12 memory used=2283.3MB, alloc=548.3MB, time=37.65 memory used=2335.2MB, alloc=548.3MB, time=38.64 memory used=2558.0MB, alloc=572.3MB, time=42.44 memory used=2788.5MB, alloc=596.3MB, time=47.33 memory used=2979.6MB, alloc=620.3MB, time=50.79 memory used=3156.2MB, alloc=644.3MB, time=54.18 memory used=3295.0MB, alloc=668.3MB, time=56.64 memory used=3429.9MB, alloc=668.3MB, time=59.69 memory used=3565.3MB, alloc=668.3MB, time=62.83 memory used=3708.6MB, alloc=692.3MB, time=65.79 memory used=3833.3MB, alloc=692.3MB, time=68.46 memory used=3946.3MB, alloc=692.3MB, time=70.67 memory used=4061.5MB, alloc=692.3MB, time=73.23 memory used=4157.8MB, alloc=692.3MB, time=75.33 memory used=4248.5MB, alloc=692.3MB, time=77.67 memory used=4620.6MB, alloc=716.3MB, time=84.53 memory used=5003.4MB, alloc=740.3MB, time=90.75 memory used=5363.0MB, alloc=764.3MB, time=98.45 memory used=5724.7MB, alloc=788.3MB, time=105.01 memory used=6117.0MB, alloc=812.3MB, time=114.69 memory used=6479.0MB, alloc=836.3MB, time=123.63 memory used=6818.0MB, alloc=860.3MB, time=130.59 memory used=7096.2MB, alloc=884.3MB, time=136.03 memory used=7362.7MB, alloc=908.3MB, time=141.18 memory used=7682.6MB, alloc=932.3MB, time=149.68 memory used=7947.9MB, alloc=956.3MB, time=155.30 memory used=8210.7MB, alloc=980.3MB, time=160.82 |\^/| 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(); 1428295946 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-18 x + 8 y z - 4 y - 20, -2 x y - 20 x z - 7 y + 20, -14 x y + 4 x + 4 y - 16 z] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [-5 x z - 19 y + 4 x - 6 z, 19 x - 10 y - 10 y - 11 z, 2 7 x - 13 y z - 18 x - 1] > Problem := [F,G]; 2 2 Problem := [[-18 x + 8 y z - 4 y - 20, -2 x y - 20 x z - 7 y + 20, 2 -14 x y + 4 x + 4 y - 16 z], [-5 x z - 19 y + 4 x - 6 z, 2 2 2 19 x - 10 y - 10 y - 11 z, 7 x - 13 y z - 18 x - 1]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,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=46.6MB, alloc=56.3MB, time=0.83 memory used=88.5MB, alloc=60.3MB, time=1.47 memory used=129.0MB, alloc=60.3MB, time=2.09 memory used=168.2MB, alloc=84.3MB, time=2.70 memory used=229.6MB, alloc=92.3MB, time=3.68 memory used=290.9MB, alloc=116.3MB, time=4.65 memory used=357.8MB, alloc=116.3MB, time=5.62 memory used=427.6MB, alloc=396.3MB, time=6.71 memory used=538.2MB, alloc=396.3MB, time=8.50 memory used=648.6MB, alloc=420.3MB, time=10.27 memory used=784.4MB, alloc=444.3MB, time=12.52 memory used=920.1MB, alloc=468.3MB, time=14.77 memory used=1041.8MB, alloc=468.3MB, time=16.89 memory used=1155.2MB, alloc=468.3MB, time=18.79 memory used=1262.7MB, alloc=468.3MB, time=20.69 memory used=1358.8MB, alloc=492.3MB, time=22.42 memory used=1449.7MB, alloc=492.3MB, time=24.16 memory used=1528.8MB, alloc=492.3MB, time=25.65 memory used=1618.9MB, alloc=492.3MB, time=27.28 memory used=1710.5MB, alloc=492.3MB, time=29.21 memory used=1778.4MB, alloc=492.3MB, time=30.56 memory used=1853.6MB, alloc=492.3MB, time=32.11 memory used=1927.9MB, alloc=492.3MB, time=33.70 memory used=1992.4MB, alloc=492.3MB, time=35.08 memory used=2055.3MB, alloc=492.3MB, time=36.42 memory used=2115.3MB, alloc=516.3MB, time=37.67 memory used=2175.5MB, alloc=516.3MB, time=39.04 memory used=2227.5MB, alloc=516.3MB, time=40.31 memory used=2272.0MB, alloc=516.3MB, time=41.38 memory used=2317.8MB, alloc=516.3MB, time=42.38 memory used=2365.5MB, alloc=516.3MB, time=43.65 memory used=2412.5MB, alloc=516.3MB, time=44.95 memory used=2611.8MB, alloc=540.3MB, time=48.49 memory used=2813.1MB, alloc=564.3MB, time=52.45 memory used=3036.5MB, alloc=588.3MB, time=57.44 memory used=3220.2MB, alloc=612.3MB, time=61.15 memory used=3360.1MB, alloc=636.3MB, time=63.83 memory used=3509.9MB, alloc=660.3MB, time=67.19 memory used=3670.4MB, alloc=660.3MB, time=70.75 memory used=3824.3MB, alloc=660.3MB, time=74.18 memory used=3983.3MB, alloc=684.3MB, time=77.97 memory used=4079.5MB, alloc=684.3MB, time=80.10 memory used=4201.1MB, alloc=684.3MB, time=83.25 memory used=4271.7MB, alloc=684.3MB, time=85.00 memory used=4387.9MB, alloc=684.3MB, time=88.32 memory used=4483.8MB, alloc=684.3MB, time=91.22 memory used=4830.0MB, alloc=708.3MB, time=98.45 memory used=5194.2MB, alloc=732.3MB, time=106.31 memory used=5585.2MB, alloc=756.3MB, time=115.14 memory used=5986.5MB, alloc=780.3MB, time=123.76 memory used=6348.1MB, alloc=804.3MB, time=132.04 memory used=6699.2MB, alloc=828.3MB, time=140.66 memory used=7000.4MB, alloc=852.3MB, time=147.34 |\^/| 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(); 1428296246 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-3 x z - 11 y z + 10 z + 9 x, 18 x - 3 y z + 4 x - 18 z, 2 2 11 x + 8 x y + 4 x z - 16 z ] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [-15 x y - 15 y + 2 y + 4, -11 x - 2 z - 11 x + 17, 2 2 2 -5 x + 8 x y + 15 y + 4 z ] > Problem := [F,G]; 2 2 Problem := [[-3 x z - 11 y z + 10 z + 9 x, 18 x - 3 y z + 4 x - 18 z, 2 2 2 11 x + 8 x y + 4 x z - 16 z ], [-15 x y - 15 y + 2 y + 4, 2 2 2 2 2 -11 x - 2 z - 11 x + 17, -5 x + 8 x y + 15 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=4.4MB, alloc=32.3MB, time=0.17 memory used=26.7MB, alloc=32.3MB, time=0.51 memory used=48.0MB, alloc=32.3MB, time=0.83 memory used=68.3MB, alloc=56.3MB, time=1.16 memory used=110.2MB, alloc=60.3MB, time=1.79 memory used=150.4MB, alloc=84.3MB, time=2.43 memory used=213.9MB, alloc=92.3MB, time=3.45 memory used=274.7MB, alloc=116.3MB, time=4.44 memory used=351.3MB, alloc=116.3MB, time=5.61 memory used=418.1MB, alloc=372.3MB, time=6.63 memory used=505.7MB, alloc=396.3MB, time=7.94 memory used=614.2MB, alloc=420.3MB, time=9.71 memory used=749.1MB, alloc=444.3MB, time=11.74 memory used=877.1MB, alloc=444.3MB, time=13.72 memory used=1011.3MB, alloc=468.3MB, time=15.92 memory used=1121.0MB, alloc=468.3MB, time=17.79 memory used=1219.2MB, alloc=468.3MB, time=19.43 memory used=1316.6MB, alloc=492.3MB, time=21.16 memory used=1413.8MB, alloc=492.3MB, time=22.85 memory used=1493.2MB, alloc=492.3MB, time=24.16 memory used=1591.6MB, alloc=492.3MB, time=25.59 memory used=1675.9MB, alloc=492.3MB, time=27.07 memory used=1763.2MB, alloc=516.3MB, time=28.73 memory used=1815.2MB, alloc=516.3MB, time=29.84 memory used=1880.3MB, alloc=516.3MB, time=31.20 memory used=1947.4MB, alloc=516.3MB, time=32.59 memory used=2003.6MB, alloc=516.3MB, time=33.91 memory used=2055.7MB, alloc=516.3MB, time=35.11 memory used=2106.2MB, alloc=516.3MB, time=36.21 memory used=2153.8MB, alloc=516.3MB, time=37.26 memory used=2358.7MB, alloc=540.3MB, time=41.26 memory used=2567.9MB, alloc=564.3MB, time=45.41 memory used=2784.4MB, alloc=588.3MB, time=49.95 memory used=2976.5MB, alloc=612.3MB, time=53.31 memory used=3141.7MB, alloc=636.3MB, time=56.42 memory used=3336.8MB, alloc=660.3MB, time=60.01 memory used=3470.6MB, alloc=684.3MB, time=62.36 memory used=3657.2MB, alloc=708.3MB, time=67.28 memory used=3808.4MB, alloc=708.3MB, time=71.32 memory used=3916.7MB, alloc=708.3MB, time=73.76 memory used=4033.9MB, alloc=708.3MB, time=76.34 memory used=4144.4MB, alloc=708.3MB, time=79.41 memory used=4529.9MB, alloc=732.3MB, time=86.59 memory used=4920.4MB, alloc=756.3MB, time=95.28 memory used=5271.5MB, alloc=780.3MB, time=103.30 memory used=5649.9MB, alloc=804.3MB, time=112.71 memory used=6005.1MB, alloc=828.3MB, time=120.30 memory used=6325.2MB, alloc=852.3MB, time=128.76 memory used=6599.3MB, alloc=876.3MB, time=135.44 memory used=6861.0MB, alloc=900.3MB, time=140.57 memory used=7080.5MB, alloc=924.3MB, time=146.77 memory used=7394.9MB, alloc=948.3MB, time=153.70 |\^/| 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(); 1428296546 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [20 x y - 10 y z + 11 x + 5 z, -8 y + 17 y - 3 z - 15, 2 2 -7 x z + 16 y - 12 y z - 4 z ] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; G := 2 2 2 2 2 2 [-6 y + 11 y z - 14 z + 2 x, 6 x - 10 x z + 7 z, 6 x - y - 7 z + 8 x] > Problem := [F,G]; 2 Problem := [[20 x y - 10 y z + 11 x + 5 z, -8 y + 17 y - 3 z - 15, 2 2 -7 x z + 16 y - 12 y z - 4 z ], 2 2 2 2 2 2 [-6 y + 11 y z - 14 z + 2 x, 6 x - 10 x z + 7 z, 6 x - y - 7 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=25.9MB, alloc=32.3MB, time=0.49 memory used=46.7MB, alloc=32.3MB, time=0.80 memory used=66.2MB, alloc=56.3MB, time=1.12 memory used=107.1MB, alloc=60.3MB, time=1.74 memory used=146.2MB, alloc=84.3MB, time=2.32 memory used=213.1MB, alloc=92.3MB, time=3.28 memory used=279.9MB, alloc=92.3MB, time=4.23 memory used=342.3MB, alloc=116.3MB, time=5.19 memory used=424.6MB, alloc=372.3MB, time=6.50 memory used=510.5MB, alloc=396.3MB, time=7.77 memory used=615.8MB, alloc=420.3MB, time=9.44 memory used=748.2MB, alloc=444.3MB, time=11.53 memory used=898.7MB, alloc=468.3MB, time=13.93 memory used=1034.0MB, alloc=468.3MB, time=16.07 memory used=1159.2MB, alloc=492.3MB, time=17.95 memory used=1255.3MB, alloc=492.3MB, time=19.38 memory used=1360.5MB, alloc=492.3MB, time=21.11 memory used=1464.0MB, alloc=492.3MB, time=22.77 memory used=1550.3MB, alloc=492.3MB, time=24.13 memory used=1630.7MB, alloc=516.3MB, time=25.38 memory used=1721.4MB, alloc=516.3MB, time=27.07 memory used=1815.4MB, alloc=516.3MB, time=28.81 memory used=1894.1MB, alloc=516.3MB, time=30.20 memory used=1962.5MB, alloc=516.3MB, time=31.60 memory used=2034.1MB, alloc=516.3MB, time=33.03 memory used=2091.7MB, alloc=516.3MB, time=34.17 memory used=2155.3MB, alloc=516.3MB, time=35.56 memory used=2204.5MB, alloc=516.3MB, time=36.78 memory used=2410.9MB, alloc=540.3MB, time=41.01 memory used=2639.6MB, alloc=564.3MB, time=45.25 memory used=2850.4MB, alloc=588.3MB, time=48.90 memory used=3034.5MB, alloc=612.3MB, time=52.13 memory used=3228.0MB, alloc=636.3MB, time=56.36 memory used=3380.3MB, alloc=636.3MB, time=59.77 memory used=3538.7MB, alloc=636.3MB, time=63.11 memory used=3696.1MB, alloc=660.3MB, time=66.50 memory used=3844.6MB, alloc=660.3MB, time=70.13 memory used=3989.2MB, alloc=660.3MB, time=73.55 memory used=4104.1MB, alloc=660.3MB, time=76.26 memory used=4217.9MB, alloc=660.3MB, time=78.75 memory used=4325.5MB, alloc=660.3MB, time=81.70 memory used=4426.6MB, alloc=660.3MB, time=84.48 memory used=4761.6MB, alloc=684.3MB, time=91.36 memory used=5118.7MB, alloc=708.3MB, time=98.64 memory used=5486.2MB, alloc=732.3MB, time=106.41 memory used=5859.2MB, alloc=756.3MB, time=114.86 memory used=6244.6MB, alloc=780.3MB, time=121.99 memory used=6600.7MB, alloc=804.3MB, time=129.19 |\^/| 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(); 1428296846 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; F := 2 2 2 2 2 2 [3 y - 4 y z - 6 z + y, 2 y - 9 y z + 8 z + 8 y, 10 x + 4 x z - 20 y ] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [-3 x z - 7 y - 18 y + 8, 13 y z + 16 x + 13 y - 13, 2 10 x z - 7 z + 14 x - 12] > Problem := [F,G]; Problem := [ 2 2 2 2 2 2 [3 y - 4 y z - 6 z + y, 2 y - 9 y z + 8 z + 8 y, 10 x + 4 x z - 20 y ] 2 , [-3 x z - 7 y - 18 y + 8, 13 y z + 16 x + 13 y - 13, 2 10 x z - 7 z + 14 x - 12]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,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=0.49 memory used=45.1MB, alloc=32.3MB, time=0.78 memory used=63.8MB, alloc=56.3MB, time=1.06 memory used=106.0MB, alloc=60.3MB, time=1.67 memory used=145.9MB, alloc=60.3MB, time=2.26 memory used=188.6MB, alloc=92.3MB, time=2.87 memory used=252.7MB, alloc=92.3MB, time=3.81 memory used=318.5MB, alloc=92.3MB, time=4.67 memory used=380.2MB, alloc=116.3MB, time=5.61 memory used=458.2MB, alloc=116.3MB, time=6.71 memory used=538.4MB, alloc=396.3MB, time=7.94 memory used=654.7MB, alloc=420.3MB, time=9.49 memory used=790.4MB, alloc=444.3MB, time=11.51 memory used=917.2MB, alloc=444.3MB, time=13.37 memory used=1040.3MB, alloc=444.3MB, time=15.19 memory used=1153.9MB, alloc=468.3MB, time=16.59 memory used=1264.6MB, alloc=468.3MB, time=18.31 memory used=1377.9MB, alloc=492.3MB, time=20.18 memory used=1471.2MB, alloc=492.3MB, time=21.73 memory used=1552.2MB, alloc=492.3MB, time=22.97 memory used=1649.1MB, alloc=492.3MB, time=24.47 memory used=1736.9MB, alloc=492.3MB, time=25.66 memory used=1809.4MB, alloc=516.3MB, time=26.91 memory used=1882.2MB, alloc=516.3MB, time=28.09 memory used=1969.5MB, alloc=516.3MB, time=29.57 memory used=2041.7MB, alloc=516.3MB, time=30.77 memory used=2107.5MB, alloc=516.3MB, time=32.12 memory used=2183.3MB, alloc=516.3MB, time=33.79 memory used=2243.8MB, alloc=516.3MB, time=35.05 memory used=2303.4MB, alloc=516.3MB, time=36.08 memory used=2358.2MB, alloc=516.3MB, time=37.07 memory used=2414.2MB, alloc=516.3MB, time=38.11 memory used=2458.9MB, alloc=516.3MB, time=38.90 memory used=2508.5MB, alloc=516.3MB, time=39.81 memory used=2717.7MB, alloc=540.3MB, time=43.39 memory used=2930.4MB, alloc=564.3MB, time=46.95 memory used=3130.3MB, alloc=588.3MB, time=50.45 memory used=3327.0MB, alloc=612.3MB, time=54.00 memory used=3473.0MB, alloc=636.3MB, time=56.98 memory used=3625.8MB, alloc=636.3MB, time=60.08 memory used=3767.6MB, alloc=636.3MB, time=62.72 memory used=3916.8MB, alloc=660.3MB, time=65.63 memory used=4056.3MB, alloc=660.3MB, time=68.59 memory used=4192.0MB, alloc=660.3MB, time=71.29 memory used=4312.2MB, alloc=660.3MB, time=73.86 memory used=4416.4MB, alloc=660.3MB, time=76.00 memory used=4522.1MB, alloc=660.3MB, time=78.58 memory used=4634.6MB, alloc=660.3MB, time=81.18 memory used=4733.7MB, alloc=684.3MB, time=83.67 memory used=5095.2MB, alloc=708.3MB, time=89.46 memory used=5480.8MB, alloc=732.3MB, time=96.01 memory used=5816.3MB, alloc=756.3MB, time=100.72 memory used=6219.2MB, alloc=780.3MB, time=107.41 memory used=6615.0MB, alloc=804.3MB, time=114.69 memory used=6910.4MB, alloc=828.3MB, time=120.20 |\^/| 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(); 1428297146 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [-20 x - 17 x y + 13 x z + 3 x, -x z - 2 x + 17 y - 7, 2 -12 x - 4 y z + 6 y + 19 z] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-7 x z + 3 y - 5 x - 3 z, -8 y - y z + 11 x - 12 y, 2 7 z + 17 y + 9 z - 17] > Problem := [F,G]; 2 Problem := [[-20 x - 17 x y + 13 x z + 3 x, -x z - 2 x + 17 y - 7, 2 2 -12 x - 4 y z + 6 y + 19 z], [-7 x z + 3 y - 5 x - 3 z, 2 2 -8 y - y z + 11 x - 12 y, 7 z + 17 y + 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=4.3MB, alloc=32.3MB, time=0.17 memory used=26.3MB, alloc=32.3MB, time=0.48 memory used=47.2MB, alloc=56.3MB, time=0.80 memory used=88.6MB, alloc=60.3MB, time=1.43 memory used=129.1MB, alloc=92.3MB, time=2.08 memory used=192.9MB, alloc=92.3MB, time=3.06 memory used=255.0MB, alloc=116.3MB, time=4.02 memory used=333.4MB, alloc=372.3MB, time=5.28 memory used=419.8MB, alloc=396.3MB, time=6.57 memory used=528.6MB, alloc=420.3MB, time=8.28 memory used=661.2MB, alloc=444.3MB, time=10.46 memory used=776.6MB, alloc=468.3MB, time=12.21 memory used=915.8MB, alloc=468.3MB, time=14.64 memory used=1035.0MB, alloc=492.3MB, time=16.71 memory used=1150.2MB, alloc=492.3MB, time=19.01 memory used=1248.1MB, alloc=492.3MB, time=20.81 memory used=1343.3MB, alloc=492.3MB, time=22.76 memory used=1432.4MB, alloc=492.3MB, time=24.52 memory used=1519.6MB, alloc=492.3MB, time=26.32 memory used=1597.4MB, alloc=492.3MB, time=28.06 memory used=1669.5MB, alloc=516.3MB, time=29.60 memory used=1730.8MB, alloc=516.3MB, time=30.97 memory used=1795.3MB, alloc=516.3MB, time=32.55 memory used=1848.3MB, alloc=516.3MB, time=33.87 memory used=1891.3MB, alloc=516.3MB, time=35.06 memory used=2102.5MB, alloc=540.3MB, time=39.23 memory used=2288.6MB, alloc=564.3MB, time=43.08 memory used=2505.7MB, alloc=588.3MB, time=47.51 memory used=2685.0MB, alloc=612.3MB, time=51.28 memory used=2845.6MB, alloc=636.3MB, time=54.86 memory used=2996.2MB, alloc=660.3MB, time=58.54 memory used=3120.7MB, alloc=660.3MB, time=61.42 memory used=3281.0MB, alloc=684.3MB, time=65.32 memory used=3398.9MB, alloc=684.3MB, time=67.90 memory used=3487.9MB, alloc=684.3MB, time=69.84 memory used=3646.7MB, alloc=708.3MB, time=74.59 memory used=4022.1MB, alloc=732.3MB, time=83.52 memory used=4424.9MB, alloc=756.3MB, time=91.62 memory used=4837.4MB, alloc=780.3MB, time=101.94 memory used=5207.9MB, alloc=804.3MB, time=110.33 memory used=5624.3MB, alloc=828.3MB, time=121.36 memory used=5952.7MB, alloc=852.3MB, time=129.40 memory used=6265.5MB, alloc=876.3MB, time=137.60 memory used=6643.9MB, alloc=900.3MB, time=149.53 |\^/| 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(); 1428297446 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [7 x y - 7 x z + 4 y z + 8 z , x + 17 z - 18 y, -10 x y - 7 z + 15] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [11 x z - y z - 3 z + 2 z, -4 x - 2 x z - 12 y - 14 x, 2 2 6 y - y z - 2 z + 10 x] > Problem := [F,G]; Problem := [ 2 2 2 [7 x y - 7 x z + 4 y z + 8 z , x + 17 z - 18 y, -10 x y - 7 z + 15], [ 2 2 2 11 x z - y z - 3 z + 2 z, -4 x - 2 x z - 12 y - 14 x, 2 2 6 y - y z - 2 z + 10 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=26.2MB, alloc=32.3MB, time=0.49 memory used=46.7MB, alloc=32.3MB, time=0.79 memory used=65.5MB, alloc=56.3MB, time=1.10 memory used=104.6MB, alloc=60.3MB, time=1.70 memory used=142.2MB, alloc=84.3MB, time=2.29 memory used=202.7MB, alloc=92.3MB, time=3.23 memory used=263.0MB, alloc=116.3MB, time=4.18 memory used=345.6MB, alloc=116.3MB, time=5.47 memory used=425.8MB, alloc=140.3MB, time=6.79 memory used=507.7MB, alloc=140.3MB, time=8.16 memory used=573.7MB, alloc=396.3MB, time=9.29 memory used=674.4MB, alloc=420.3MB, time=10.99 memory used=795.2MB, alloc=444.3MB, time=13.12 memory used=939.7MB, alloc=468.3MB, time=15.74 memory used=1086.1MB, alloc=492.3MB, time=18.42 memory used=1216.4MB, alloc=516.3MB, time=20.85 memory used=1327.6MB, alloc=516.3MB, time=22.69 memory used=1442.1MB, alloc=516.3MB, time=24.84 memory used=1551.4MB, alloc=540.3MB, time=26.97 memory used=1625.3MB, alloc=540.3MB, time=28.26 memory used=1713.3MB, alloc=540.3MB, time=30.28 memory used=1782.7MB, alloc=540.3MB, time=31.67 memory used=1865.2MB, alloc=540.3MB, time=33.52 memory used=1923.5MB, alloc=540.3MB, time=34.72 memory used=1988.4MB, alloc=540.3MB, time=36.01 memory used=2064.7MB, alloc=540.3MB, time=37.98 memory used=2118.0MB, alloc=540.3MB, time=39.31 memory used=2340.4MB, alloc=564.3MB, time=44.22 memory used=2555.6MB, alloc=588.3MB, time=48.41 memory used=2731.7MB, alloc=612.3MB, time=52.35 memory used=2917.8MB, alloc=636.3MB, time=56.65 memory used=3083.6MB, alloc=660.3MB, time=60.49 memory used=3238.9MB, alloc=684.3MB, time=64.18 memory used=3393.7MB, alloc=684.3MB, time=68.35 memory used=3526.2MB, alloc=684.3MB, time=71.78 memory used=3639.1MB, alloc=684.3MB, time=74.23 memory used=3778.7MB, alloc=684.3MB, time=78.17 memory used=4125.5MB, alloc=708.3MB, time=86.38 memory used=4492.3MB, alloc=732.3MB, time=95.35 memory used=4885.5MB, alloc=756.3MB, time=103.73 memory used=5279.5MB, alloc=780.3MB, time=114.07 memory used=5665.1MB, alloc=804.3MB, time=124.23 memory used=6029.4MB, alloc=828.3MB, time=133.81 memory used=6330.4MB, alloc=852.3MB, time=141.30 memory used=6598.4MB, alloc=876.3MB, time=148.18 memory used=6861.5MB, alloc=900.3MB, time=155.56 |\^/| 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(); 1428297746 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [18 x + 5 y - 6 y z - 6 z, 20 y + 3 y z - x - 6 y, 2 2 -19 x - 12 y z - 15 z - 9 x] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-20 x y - 5 x z - 20 y - 18 x, -13 x + x y + 20 y z + 10 x, 2 -2 y + 7 y z + 11 y + 5 z] > Problem := [F,G]; 2 2 2 Problem := [[18 x + 5 y - 6 y z - 6 z, 20 y + 3 y z - x - 6 y, 2 2 2 -19 x - 12 y z - 15 z - 9 x], [-20 x y - 5 x z - 20 y - 18 x, 2 2 -13 x + x y + 20 y z + 10 x, -2 y + 7 y z + 11 y + 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=0.17 memory used=26.3MB, alloc=32.3MB, time=0.52 memory used=46.7MB, alloc=60.3MB, time=0.85 memory used=87.5MB, alloc=60.3MB, time=1.47 memory used=128.3MB, alloc=68.3MB, time=2.10 memory used=170.1MB, alloc=92.3MB, time=2.73 memory used=234.1MB, alloc=92.3MB, time=3.73 memory used=298.5MB, alloc=116.3MB, time=4.75 memory used=373.5MB, alloc=116.3MB, time=5.95 memory used=437.7MB, alloc=372.3MB, time=6.96 memory used=523.4MB, alloc=396.3MB, time=8.33 memory used=629.6MB, alloc=420.3MB, time=10.05 memory used=759.6MB, alloc=420.3MB, time=12.22 memory used=889.0MB, alloc=444.3MB, time=14.39 memory used=995.5MB, alloc=468.3MB, time=16.27 memory used=1127.5MB, alloc=468.3MB, time=18.45 memory used=1231.1MB, alloc=492.3MB, time=20.07 memory used=1338.9MB, alloc=492.3MB, time=22.04 memory used=1438.6MB, alloc=492.3MB, time=23.81 memory used=1539.8MB, alloc=492.3MB, time=25.78 memory used=1634.7MB, alloc=492.3MB, time=27.55 memory used=1707.8MB, alloc=492.3MB, time=28.85 memory used=1814.6MB, alloc=492.3MB, time=31.12 memory used=1889.4MB, alloc=492.3MB, time=32.76 memory used=1953.8MB, alloc=492.3MB, time=34.16 memory used=2023.6MB, alloc=492.3MB, time=35.65 memory used=2082.9MB, alloc=492.3MB, time=37.07 memory used=2131.7MB, alloc=516.3MB, time=38.21 memory used=2195.5MB, alloc=516.3MB, time=39.84 memory used=2246.2MB, alloc=516.3MB, time=41.13 memory used=2296.3MB, alloc=516.3MB, time=42.40 memory used=2345.3MB, alloc=516.3MB, time=43.71 memory used=2551.0MB, alloc=540.3MB, time=47.83 memory used=2777.0MB, alloc=564.3MB, time=52.46 memory used=2979.4MB, alloc=588.3MB, time=56.58 memory used=3172.5MB, alloc=612.3MB, time=60.44 memory used=3359.1MB, alloc=636.3MB, time=64.31 memory used=3559.1MB, alloc=660.3MB, time=68.94 memory used=3746.2MB, alloc=684.3MB, time=73.59 memory used=3910.7MB, alloc=684.3MB, time=77.04 memory used=4030.7MB, alloc=708.3MB, time=79.23 memory used=4181.8MB, alloc=708.3MB, time=83.27 memory used=4290.4MB, alloc=708.3MB, time=85.53 memory used=4378.3MB, alloc=708.3MB, time=87.27 memory used=4486.9MB, alloc=732.3MB, time=89.53 memory used=4890.3MB, alloc=756.3MB, time=98.40 memory used=5281.3MB, alloc=780.3MB, time=105.68 memory used=5718.5MB, alloc=804.3MB, time=115.83 memory used=6100.3MB, alloc=828.3MB, time=123.42 memory used=6454.8MB, alloc=852.3MB, time=130.36 memory used=6794.7MB, alloc=876.3MB, time=137.68 memory used=7098.7MB, alloc=900.3MB, time=145.28 memory used=7313.3MB, alloc=924.3MB, time=149.81 memory used=7575.4MB, alloc=948.3MB, time=155.21 memory used=7792.4MB, alloc=972.3MB, time=160.97 |\^/| 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(); 1428298046 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-2 x + 7 y - 2 y z - 11, -19 x z + 19 z + 5 z - 16, 2 2 -10 y + 19 y z - 2 z + 16 z] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [-16 x + 9 y - 19 y z + 18 x, 5 x z + z - 8 y - 8, 3 x z - 2 y z - 14 x + 20] > Problem := [F,G]; 2 2 2 Problem := [[-2 x + 7 y - 2 y z - 11, -19 x z + 19 z + 5 z - 16, 2 2 2 2 -10 y + 19 y z - 2 z + 16 z], [-16 x + 9 y - 19 y z + 18 x, 2 5 x z + z - 8 y - 8, 3 x z - 2 y z - 14 x + 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=4.3MB, alloc=32.3MB, time=0.17 memory used=26.4MB, alloc=32.3MB, time=0.50 memory used=45.8MB, alloc=56.3MB, time=0.82 memory used=85.0MB, alloc=60.3MB, time=1.41 memory used=125.3MB, alloc=60.3MB, time=2.00 memory used=165.9MB, alloc=84.3MB, time=2.60 memory used=230.6MB, alloc=92.3MB, time=3.57 memory used=295.5MB, alloc=116.3MB, time=4.53 memory used=367.2MB, alloc=116.3MB, time=5.49 memory used=436.5MB, alloc=372.3MB, time=6.34 memory used=524.2MB, alloc=396.3MB, time=7.61 memory used=637.6MB, alloc=396.3MB, time=9.18 memory used=738.2MB, alloc=420.3MB, time=10.81 memory used=867.9MB, alloc=444.3MB, time=12.85 memory used=982.6MB, alloc=468.3MB, time=14.36 memory used=1095.9MB, alloc=468.3MB, time=16.17 memory used=1209.3MB, alloc=492.3MB, time=17.60 memory used=1307.0MB, alloc=492.3MB, time=19.19 memory used=1392.4MB, alloc=492.3MB, time=20.46 memory used=1467.6MB, alloc=492.3MB, time=21.70 memory used=1533.3MB, alloc=492.3MB, time=22.93 memory used=1612.1MB, alloc=492.3MB, time=24.21 memory used=1681.0MB, alloc=492.3MB, time=25.38 memory used=1737.5MB, alloc=516.3MB, time=26.41 memory used=1811.5MB, alloc=516.3MB, time=27.38 memory used=1880.4MB, alloc=516.3MB, time=28.77 memory used=1934.9MB, alloc=516.3MB, time=29.78 memory used=1985.2MB, alloc=516.3MB, time=30.70 memory used=2205.7MB, alloc=540.3MB, time=33.81 memory used=2399.0MB, alloc=564.3MB, time=36.63 memory used=2610.4MB, alloc=588.3MB, time=39.61 memory used=2790.4MB, alloc=612.3MB, time=42.34 memory used=2946.5MB, alloc=612.3MB, time=44.82 memory used=3118.1MB, alloc=636.3MB, time=47.98 memory used=3266.8MB, alloc=636.3MB, time=50.97 memory used=3391.6MB, alloc=660.3MB, time=53.11 memory used=3549.7MB, alloc=660.3MB, time=55.73 memory used=3663.0MB, alloc=660.3MB, time=57.68 memory used=3795.2MB, alloc=660.3MB, time=60.23 memory used=3893.6MB, alloc=660.3MB, time=62.33 memory used=4227.7MB, alloc=684.3MB, time=68.30 memory used=4572.1MB, alloc=708.3MB, time=75.16 memory used=4945.3MB, alloc=732.3MB, time=82.16 memory used=5307.9MB, alloc=756.3MB, time=89.58 memory used=5578.6MB, alloc=780.3MB, time=94.69 memory used=5918.7MB, alloc=804.3MB, time=101.54 memory used=6201.8MB, alloc=828.3MB, time=106.95 memory used=6464.9MB, alloc=852.3MB, time=112.81 memory used=6708.8MB, alloc=876.3MB, time=118.66 memory used=6937.5MB, alloc=900.3MB, time=124.17 memory used=7139.7MB, alloc=924.3MB, time=129.29 memory used=7332.6MB, alloc=948.3MB, time=133.84 memory used=7892.4MB, alloc=972.3MB, time=144.01 |\^/| 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(); 1428298346 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [9 x z - 20 x + 9 y - 13, 6 x y + 7 y z + 12 z + 4 y, 2 19 x y - y + 14 z - 20] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [9 y - 19 y z + 7 y + 4, -x z + 14 y - 19 z + 13 z, 2 -19 x + 19 x y - 5 y z + 14 x] > Problem := [F,G]; 2 Problem := [[9 x z - 20 x + 9 y - 13, 6 x y + 7 y z + 12 z + 4 y, 2 2 19 x y - y + 14 z - 20], [9 y - 19 y z + 7 y + 4, 2 2 2 -x z + 14 y - 19 z + 13 z, -19 x + 19 x y - 5 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=4.3MB, alloc=32.3MB, time=0.18 memory used=26.0MB, alloc=32.3MB, time=0.50 memory used=46.3MB, alloc=32.3MB, time=0.80 memory used=65.5MB, alloc=56.3MB, time=1.10 memory used=108.0MB, alloc=68.3MB, time=1.74 memory used=148.1MB, alloc=68.3MB, time=2.32 memory used=187.8MB, alloc=92.3MB, time=2.90 memory used=250.1MB, alloc=92.3MB, time=3.80 memory used=310.5MB, alloc=116.3MB, time=4.75 memory used=378.6MB, alloc=372.3MB, time=5.76 memory used=470.8MB, alloc=396.3MB, time=6.97 memory used=581.4MB, alloc=420.3MB, time=8.64 memory used=714.4MB, alloc=444.3MB, time=10.72 memory used=830.5MB, alloc=444.3MB, time=12.43 memory used=938.0MB, alloc=468.3MB, time=14.05 memory used=1047.7MB, alloc=468.3MB, time=15.74 memory used=1141.5MB, alloc=468.3MB, time=17.24 memory used=1241.4MB, alloc=468.3MB, time=18.82 memory used=1322.6MB, alloc=468.3MB, time=20.20 memory used=1412.6MB, alloc=492.3MB, time=21.86 memory used=1503.1MB, alloc=492.3MB, time=23.58 memory used=1595.7MB, alloc=492.3MB, time=25.31 memory used=1658.5MB, alloc=492.3MB, time=26.55 memory used=1733.9MB, alloc=492.3MB, time=27.75 memory used=1798.5MB, alloc=492.3MB, time=29.02 memory used=1856.8MB, alloc=492.3MB, time=29.98 memory used=1916.4MB, alloc=516.3MB, time=31.34 memory used=1966.2MB, alloc=516.3MB, time=32.40 memory used=2017.6MB, alloc=516.3MB, time=33.61 memory used=2074.1MB, alloc=516.3MB, time=34.95 memory used=2283.8MB, alloc=540.3MB, time=38.14 memory used=2496.0MB, alloc=564.3MB, time=42.11 memory used=2686.5MB, alloc=588.3MB, time=45.53 memory used=2887.6MB, alloc=612.3MB, time=49.74 memory used=3058.3MB, alloc=636.3MB, time=53.05 memory used=3213.4MB, alloc=636.3MB, time=56.32 memory used=3366.0MB, alloc=636.3MB, time=59.26 memory used=3495.2MB, alloc=660.3MB, time=61.81 memory used=3629.7MB, alloc=660.3MB, time=64.57 memory used=3762.0MB, alloc=660.3MB, time=67.39 memory used=3889.6MB, alloc=660.3MB, time=70.24 memory used=3991.7MB, alloc=660.3MB, time=72.73 memory used=4097.1MB, alloc=660.3MB, time=75.14 memory used=4197.9MB, alloc=684.3MB, time=77.50 memory used=4305.5MB, alloc=684.3MB, time=79.93 memory used=4653.2MB, alloc=708.3MB, time=86.13 memory used=5028.6MB, alloc=732.3MB, time=92.75 memory used=5410.9MB, alloc=756.3MB, time=100.50 memory used=5772.7MB, alloc=780.3MB, time=107.95 memory used=6128.9MB, alloc=804.3MB, time=114.21 memory used=6428.3MB, alloc=828.3MB, time=120.09 memory used=6746.0MB, alloc=852.3MB, time=127.77 memory used=7015.9MB, alloc=876.3MB, time=133.82 memory used=7225.9MB, alloc=900.3MB, time=138.03 memory used=7457.1MB, alloc=924.3MB, time=144.11 memory used=7661.6MB, alloc=948.3MB, time=148.56 memory used=7850.9MB, alloc=972.3MB, time=154.40 |\^/| 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(); 1428298646 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-5 x y + x z + 12 y + 5 z, x z - 14 y + 11 z + 20 z, 2 -19 y - 9 x + 2 y + 10 z] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; G := 2 2 [-x y - 14 x - 10 z, -14 x y + 8 x z - 15 y - 8, -12 x + 17 x y + 14 x z] > Problem := [F,G]; 2 2 Problem := [[-5 x y + x z + 12 y + 5 z, x z - 14 y + 11 z + 20 z, 2 -19 y - 9 x + 2 y + 10 z], 2 2 [-x y - 14 x - 10 z, -14 x y + 8 x z - 15 y - 8, -12 x + 17 x y + 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=0.17 memory used=25.8MB, alloc=32.3MB, time=0.49 memory used=45.8MB, alloc=56.3MB, time=0.80 memory used=86.6MB, alloc=60.3MB, time=1.43 memory used=124.7MB, alloc=84.3MB, time=2.02 memory used=168.3MB, alloc=84.3MB, time=2.69 memory used=229.2MB, alloc=116.3MB, time=3.72 memory used=311.6MB, alloc=116.3MB, time=5.08 memory used=393.0MB, alloc=140.3MB, time=6.46 memory used=475.0MB, alloc=396.3MB, time=7.88 memory used=580.7MB, alloc=420.3MB, time=9.66 memory used=708.0MB, alloc=444.3MB, time=11.91 memory used=856.7MB, alloc=468.3MB, time=14.49 memory used=1004.8MB, alloc=492.3MB, time=17.17 memory used=1147.7MB, alloc=492.3MB, time=19.81 memory used=1285.1MB, alloc=516.3MB, time=22.32 memory used=1417.2MB, alloc=516.3MB, time=24.99 memory used=1533.3MB, alloc=516.3MB, time=27.50 memory used=1633.2MB, alloc=540.3MB, time=29.44 memory used=1739.3MB, alloc=540.3MB, time=31.54 memory used=1811.8MB, alloc=540.3MB, time=33.04 memory used=1895.1MB, alloc=540.3MB, time=34.68 memory used=1981.8MB, alloc=540.3MB, time=36.68 memory used=2044.3MB, alloc=564.3MB, time=38.06 memory used=2110.3MB, alloc=564.3MB, time=39.69 memory used=2169.6MB, alloc=564.3MB, time=41.08 memory used=2219.8MB, alloc=564.3MB, time=42.28 memory used=2458.7MB, alloc=588.3MB, time=46.97 memory used=2711.5MB, alloc=612.3MB, time=53.15 memory used=2908.4MB, alloc=636.3MB, time=57.69 memory used=3104.9MB, alloc=660.3MB, time=62.21 memory used=3279.4MB, alloc=684.3MB, time=66.60 memory used=3418.1MB, alloc=708.3MB, time=69.61 memory used=3559.7MB, alloc=708.3MB, time=73.63 memory used=3709.5MB, alloc=708.3MB, time=77.77 memory used=3825.6MB, alloc=708.3MB, time=80.80 memory used=3941.0MB, alloc=708.3MB, time=84.59 memory used=4327.2MB, alloc=732.3MB, time=93.18 memory used=4724.8MB, alloc=756.3MB, time=103.01 memory used=5140.4MB, alloc=780.3MB, time=113.48 memory used=5453.8MB, alloc=804.3MB, time=121.35 memory used=5821.4MB, alloc=828.3MB, time=131.29 memory used=6088.6MB, alloc=852.3MB, time=138.38 memory used=6376.8MB, alloc=876.3MB, time=146.54 memory used=6649.6MB, alloc=900.3MB, time=153.91 memory used=6881.1MB, alloc=924.3MB, time=161.30 |\^/| 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(); 1428298946 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [4 x + 9 x z + 3 y + 6, -14 x - 11 y - 17 z - 11, 2 2 2 14 x - 5 y + 15 z + 17 z] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [10 x y + 5 y z - 12 z + 14 y, -10 x + x z + 5 y - 1, 2 2 -8 x z - 13 y - 3 z + 17 y] > Problem := [F,G]; 2 2 2 2 Problem := [[4 x + 9 x z + 3 y + 6, -14 x - 11 y - 17 z - 11, 2 2 2 2 14 x - 5 y + 15 z + 17 z], [10 x y + 5 y z - 12 z + 14 y, 2 2 2 2 -10 x + x z + 5 y - 1, -8 x z - 13 y - 3 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=4.4MB, alloc=32.3MB, time=0.17 memory used=27.3MB, alloc=32.3MB, time=0.53 memory used=48.1MB, alloc=32.3MB, time=0.84 memory used=68.0MB, alloc=56.3MB, time=1.15 memory used=107.6MB, alloc=60.3MB, time=1.76 memory used=139.5MB, alloc=84.3MB, time=2.17 memory used=206.9MB, alloc=92.3MB, time=3.14 memory used=272.9MB, alloc=92.3MB, time=4.10 memory used=342.3MB, alloc=116.3MB, time=4.99 memory used=406.7MB, alloc=372.3MB, time=6.00 memory used=492.3MB, alloc=396.3MB, time=7.32 memory used=605.8MB, alloc=396.3MB, time=9.03 memory used=724.9MB, alloc=420.3MB, time=10.59 memory used=863.3MB, alloc=444.3MB, time=12.60 memory used=1002.3MB, alloc=468.3MB, time=14.83 memory used=1114.0MB, alloc=468.3MB, time=16.69 memory used=1218.3MB, alloc=468.3MB, time=18.33 memory used=1327.3MB, alloc=492.3MB, time=20.16 memory used=1430.2MB, alloc=492.3MB, time=21.94 memory used=1544.4MB, alloc=492.3MB, time=24.19 memory used=1644.1MB, alloc=516.3MB, time=25.60 memory used=1740.1MB, alloc=516.3MB, time=27.18 memory used=1810.2MB, alloc=516.3MB, time=28.49 memory used=1892.4MB, alloc=516.3MB, time=29.90 memory used=1969.8MB, alloc=516.3MB, time=31.72 memory used=2033.2MB, alloc=540.3MB, time=32.97 memory used=2097.9MB, alloc=540.3MB, time=34.27 memory used=2167.5MB, alloc=540.3MB, time=35.80 memory used=2222.1MB, alloc=540.3MB, time=36.75 memory used=2288.0MB, alloc=540.3MB, time=37.80 memory used=2332.2MB, alloc=540.3MB, time=38.71 memory used=2416.2MB, alloc=540.3MB, time=39.78 memory used=2645.8MB, alloc=564.3MB, time=44.13 memory used=2869.9MB, alloc=588.3MB, time=48.68 memory used=3050.2MB, alloc=612.3MB, time=52.16 memory used=3255.0MB, alloc=636.3MB, time=55.78 memory used=3440.7MB, alloc=660.3MB, time=59.00 memory used=3605.0MB, alloc=684.3MB, time=62.34 memory used=3760.9MB, alloc=684.3MB, time=64.93 memory used=3925.2MB, alloc=684.3MB, time=67.84 memory used=4084.4MB, alloc=684.3MB, time=70.68 memory used=4238.2MB, alloc=708.3MB, time=72.78 memory used=4376.0MB, alloc=708.3MB, time=75.93 memory used=4515.8MB, alloc=708.3MB, time=78.23 memory used=4669.1MB, alloc=708.3MB, time=81.45 memory used=4761.3MB, alloc=708.3MB, time=83.66 memory used=5146.5MB, alloc=732.3MB, time=91.05 memory used=5555.8MB, alloc=756.3MB, time=99.10 memory used=5914.9MB, alloc=780.3MB, time=106.94 memory used=6328.4MB, alloc=804.3MB, time=116.64 memory used=6703.8MB, alloc=828.3MB, time=123.96 memory used=7126.2MB, alloc=852.3MB, time=132.34 memory used=7431.6MB, alloc=876.3MB, time=139.49 memory used=7781.7MB, alloc=900.3MB, time=148.70 memory used=8097.9MB, alloc=924.3MB, time=156.21 memory used=8390.8MB, alloc=948.3MB, time=164.47 |\^/| 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(); 1428299246 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [15 x + 17 x z + 7 y - 7 y z, 18 x y + 14 y z - 7 z + y, 2 2 4 x + 7 y + 11 y - 9 z] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [-18 x - 10 y - 11 x + 1, 20 y z + 17 z + 6 x + 19 z, 2 2 9 x - 4 x z - 19 y + 10 x] > Problem := [F,G]; 2 2 2 Problem := [[15 x + 17 x z + 7 y - 7 y z, 18 x y + 14 y z - 7 z + y, 2 2 2 2 4 x + 7 y + 11 y - 9 z], [-18 x - 10 y - 11 x + 1, 2 2 2 20 y z + 17 z + 6 x + 19 z, 9 x - 4 x z - 19 y + 10 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=26.9MB, alloc=32.3MB, time=0.51 memory used=48.4MB, alloc=32.3MB, time=0.82 memory used=68.7MB, alloc=60.3MB, time=1.14 memory used=110.8MB, alloc=60.3MB, time=1.75 memory used=146.9MB, alloc=60.3MB, time=2.29 memory used=188.5MB, alloc=92.3MB, time=2.93 memory used=253.2MB, alloc=92.3MB, time=3.85 memory used=318.6MB, alloc=116.3MB, time=4.77 memory used=389.3MB, alloc=372.3MB, time=5.82 memory used=479.4MB, alloc=396.3MB, time=7.05 memory used=592.0MB, alloc=420.3MB, time=8.72 memory used=722.4MB, alloc=444.3MB, time=10.52 memory used=844.6MB, alloc=444.3MB, time=12.30 memory used=959.4MB, alloc=468.3MB, time=13.86 memory used=1067.8MB, alloc=468.3MB, time=15.46 memory used=1168.9MB, alloc=468.3MB, time=16.94 memory used=1272.5MB, alloc=468.3MB, time=18.38 memory used=1362.3MB, alloc=468.3MB, time=19.77 memory used=1442.7MB, alloc=468.3MB, time=21.14 memory used=1518.6MB, alloc=492.3MB, time=22.43 memory used=1588.3MB, alloc=492.3MB, time=23.66 memory used=1663.0MB, alloc=492.3MB, time=24.74 memory used=1734.4MB, alloc=492.3MB, time=25.74 memory used=1797.2MB, alloc=492.3MB, time=26.82 memory used=1842.4MB, alloc=492.3MB, time=27.68 memory used=1903.7MB, alloc=492.3MB, time=28.71 memory used=1961.0MB, alloc=492.3MB, time=29.76 memory used=2004.1MB, alloc=492.3MB, time=30.59 memory used=2060.6MB, alloc=492.3MB, time=31.82 memory used=2108.6MB, alloc=492.3MB, time=32.90 memory used=2290.2MB, alloc=516.3MB, time=36.05 memory used=2467.7MB, alloc=540.3MB, time=38.43 memory used=2651.2MB, alloc=564.3MB, time=41.98 memory used=2813.5MB, alloc=588.3MB, time=45.24 memory used=2967.8MB, alloc=612.3MB, time=47.54 memory used=3129.4MB, alloc=636.3MB, time=50.44 memory used=3259.5MB, alloc=660.3MB, time=52.66 memory used=3361.2MB, alloc=684.3MB, time=54.69 memory used=3500.0MB, alloc=684.3MB, time=57.70 memory used=3595.5MB, alloc=684.3MB, time=60.01 memory used=3667.2MB, alloc=684.3MB, time=61.73 memory used=4031.2MB, alloc=708.3MB, time=67.50 memory used=4400.7MB, alloc=732.3MB, time=73.46 memory used=4794.7MB, alloc=756.3MB, time=79.80 memory used=5152.5MB, alloc=780.3MB, time=85.37 memory used=5468.2MB, alloc=804.3MB, time=90.61 memory used=5760.9MB, alloc=828.3MB, time=95.41 memory used=6032.9MB, alloc=852.3MB, time=100.95 memory used=6244.6MB, alloc=876.3MB, time=105.85 memory used=6463.1MB, alloc=900.3MB, time=109.74 memory used=6682.6MB, alloc=924.3MB, time=114.95 memory used=6905.9MB, alloc=948.3MB, time=119.23 memory used=7112.3MB, alloc=972.3MB, time=124.63 memory used=7704.0MB, alloc=996.3MB, time=134.53 memory used=8298.0MB, alloc=1020.3MB, time=145.58 memory used=8873.9MB, alloc=1044.3MB, time=155.81 |\^/| 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(); 1428299546 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [-11 x z - 4 y - 5 z + 3, 19 x - 10 y - 3 y z - 13 z, 2 -6 y - 17 y z + 13 y] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; G := 2 2 2 [4 y - 14 z + 4 y + 5 z, 4 x y - 9 y z + 3, 10 y z - 17 z - 12 y - 11 z] > Problem := [F,G]; 2 2 2 2 Problem := [[-11 x z - 4 y - 5 z + 3, 19 x - 10 y - 3 y z - 13 z, 2 -6 y - 17 y z + 13 y], 2 2 2 [4 y - 14 z + 4 y + 5 z, 4 x y - 9 y z + 3, 10 y z - 17 z - 12 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=0.19 memory used=26.6MB, alloc=32.3MB, time=0.52 memory used=46.6MB, alloc=56.3MB, time=0.83 memory used=87.1MB, alloc=60.3MB, time=1.43 memory used=127.3MB, alloc=84.3MB, time=2.03 memory used=167.0MB, alloc=84.3MB, time=2.63 memory used=230.2MB, alloc=92.3MB, time=3.59 memory used=294.3MB, alloc=116.3MB, time=4.55 memory used=378.1MB, alloc=116.3MB, time=5.80 memory used=448.0MB, alloc=396.3MB, time=6.82 memory used=559.3MB, alloc=396.3MB, time=8.40 memory used=663.2MB, alloc=420.3MB, time=10.04 memory used=795.8MB, alloc=444.3MB, time=12.10 memory used=941.8MB, alloc=468.3MB, time=14.66 memory used=1082.2MB, alloc=468.3MB, time=16.97 memory used=1213.9MB, alloc=492.3MB, time=18.95 memory used=1339.3MB, alloc=492.3MB, time=20.84 memory used=1463.4MB, alloc=516.3MB, time=22.82 memory used=1580.5MB, alloc=516.3MB, time=24.72 memory used=1685.5MB, alloc=516.3MB, time=26.48 memory used=1797.7MB, alloc=516.3MB, time=28.48 memory used=1904.2MB, alloc=516.3MB, time=30.58 memory used=1997.7MB, alloc=540.3MB, time=32.21 memory used=2078.2MB, alloc=540.3MB, time=33.56 memory used=2142.9MB, alloc=540.3MB, time=34.57 memory used=2222.7MB, alloc=540.3MB, time=36.12 memory used=2292.4MB, alloc=540.3MB, time=37.44 memory used=2391.0MB, alloc=540.3MB, time=39.58 memory used=2457.3MB, alloc=540.3MB, time=41.03 memory used=2536.6MB, alloc=540.3MB, time=42.78 memory used=2588.7MB, alloc=540.3MB, time=43.88 memory used=2657.9MB, alloc=540.3MB, time=45.43 memory used=2715.0MB, alloc=540.3MB, time=46.59 memory used=2767.3MB, alloc=540.3MB, time=47.82 memory used=2989.3MB, alloc=564.3MB, time=50.92 memory used=3205.0MB, alloc=588.3MB, time=55.09 memory used=3408.5MB, alloc=612.3MB, time=58.98 memory used=3642.9MB, alloc=636.3MB, time=64.34 memory used=3822.8MB, alloc=660.3MB, time=67.98 memory used=4009.0MB, alloc=660.3MB, time=72.29 memory used=4200.6MB, alloc=684.3MB, time=76.53 memory used=4366.2MB, alloc=684.3MB, time=80.08 memory used=4510.2MB, alloc=684.3MB, time=83.76 memory used=4655.9MB, alloc=684.3MB, time=87.20 memory used=4803.4MB, alloc=684.3MB, time=90.26 memory used=4928.3MB, alloc=684.3MB, time=93.26 memory used=5057.0MB, alloc=708.3MB, time=96.65 memory used=5207.8MB, alloc=708.3MB, time=101.04 memory used=5334.6MB, alloc=708.3MB, time=104.67 memory used=5458.2MB, alloc=708.3MB, time=107.77 memory used=5562.5MB, alloc=708.3MB, time=110.61 memory used=5930.4MB, alloc=732.3MB, time=118.70 memory used=6324.7MB, alloc=756.3MB, time=125.54 memory used=6719.6MB, alloc=780.3MB, time=133.53 memory used=7146.7MB, alloc=804.3MB, time=140.61 memory used=7593.4MB, alloc=828.3MB, time=151.22 memory used=8019.2MB, alloc=852.3MB, time=161.49 memory used=8409.8MB, alloc=876.3MB, time=170.04 memory used=8743.5MB, alloc=900.3MB, time=176.77 memory used=9087.4MB, alloc=924.3MB, time=185.23 |\^/| 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(); 1428299846 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [2 x - 13 y - 10 z + 9, 3 x - 12 x z + 6 y z - 19, 2 4 x z - 13 z - 8 y - 13 z] > G := [ randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [12 x y - 18 y + 2 z - 16 y, -9 x z - 20 y + 13 y, 2 -10 x + 2 x y - 19 z - 19] > Problem := [F,G]; 2 2 2 Problem := [[2 x - 13 y - 10 z + 9, 3 x - 12 x z + 6 y z - 19, 2 2 2 4 x z - 13 z - 8 y - 13 z], [12 x y - 18 y + 2 z - 16 y, 2 2 -9 x z - 20 y + 13 y, -10 x + 2 x y - 19 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=4.3MB, alloc=32.3MB, time=0.18 memory used=26.3MB, alloc=32.3MB, time=0.49 memory used=46.3MB, alloc=56.3MB, time=0.78 memory used=92.0MB, alloc=92.3MB, time=1.43 memory used=167.1MB, alloc=100.3MB, time=2.49 memory used=240.5MB, alloc=100.3MB, time=3.53 memory used=312.4MB, alloc=124.3MB, time=4.56 memory used=376.1MB, alloc=380.3MB, time=5.52 memory used=468.6MB, alloc=404.3MB, time=6.94 memory used=594.3MB, alloc=428.3MB, time=8.53 memory used=717.1MB, alloc=452.3MB, time=10.21 memory used=828.5MB, alloc=452.3MB, time=11.93 memory used=927.4MB, alloc=452.3MB, time=13.42 memory used=1019.2MB, alloc=476.3MB, time=14.80 memory used=1108.6MB, alloc=476.3MB, time=16.09 memory used=1203.8MB, alloc=476.3MB, time=17.59 memory used=1289.7MB, alloc=476.3MB, time=19.10 memory used=1358.8MB, alloc=476.3MB, time=20.16 memory used=1434.2MB, alloc=476.3MB, time=21.54 memory used=1495.1MB, alloc=476.3MB, time=22.52 memory used=1553.1MB, alloc=476.3MB, time=23.64 memory used=1629.5MB, alloc=476.3MB, time=25.14 memory used=1689.9MB, alloc=476.3MB, time=26.42 memory used=1726.8MB, alloc=500.3MB, time=27.21 memory used=1931.2MB, alloc=524.3MB, time=30.50 memory used=2140.0MB, alloc=548.3MB, time=34.32 memory used=2319.4MB, alloc=572.3MB, time=37.58 memory used=2476.4MB, alloc=596.3MB, time=40.67 memory used=2630.6MB, alloc=620.3MB, time=43.60 memory used=2783.9MB, alloc=620.3MB, time=46.76 memory used=2910.9MB, alloc=620.3MB, time=49.28 memory used=3035.9MB, alloc=644.3MB, time=51.77 memory used=3165.6MB, alloc=644.3MB, time=54.69 memory used=3281.7MB, alloc=644.3MB, time=57.48 memory used=3377.9MB, alloc=644.3MB, time=59.50 memory used=3705.5MB, alloc=668.3MB, time=65.33 memory used=4044.5MB, alloc=692.3MB, time=72.23 memory used=4412.4MB, alloc=716.3MB, time=79.22 memory used=4772.9MB, alloc=740.3MB, time=86.40 memory used=5136.9MB, alloc=764.3MB, time=94.16 memory used=5408.4MB, alloc=788.3MB, time=100.32 memory used=5707.9MB, alloc=812.3MB, time=106.98 memory used=5995.6MB, alloc=836.3MB, time=113.67 memory used=6276.4MB, alloc=860.3MB, time=120.19 memory used=6549.1MB, alloc=884.3MB, time=127.11 memory used=6789.6MB, alloc=908.3MB, time=133.64 memory used=7011.2MB, alloc=932.3MB, time=139.68 memory used=7585.0MB, alloc=956.3MB, time=150.93 memory used=8167.3MB, alloc=980.3MB, time=163.09 memory used=8741.0MB, alloc=1004.3MB, time=177.95 memory used=9337.3MB, alloc=1028.3MB, time=190.66 memory used=9924.0MB, alloc=1052.3MB, time=204.59 memory used=10541.9MB, alloc=1076.3MB, time=218.18 memory used=11165.7MB, alloc=1100.3MB, time=231.94