|\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428240000 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 2 2 F := [-7 x - 12 x y + 19 x z, 2 x y + 10 x z - 6 z , 2 x y + 5 y z + 6 x] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 3 2 2 G := [9 x - 5 y , -10 x + 4 x y z + x, -6 x y z + 5 y - 10 z ] > Problem := [F,G]; Problem := [ 3 2 2 2 2 [-7 x - 12 x y + 19 x z, 2 x y + 10 x z - 6 z , 2 x y + 5 y z + 6 x], 2 2 3 2 2 [9 x - 5 y , -10 x + 4 x y z + x, -6 x y z + 5 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=27.1MB, alloc=32.3MB, time=0.53 memory used=47.7MB, alloc=32.3MB, time=0.84 memory used=67.3MB, alloc=56.3MB, time=1.15 memory used=107.8MB, alloc=60.3MB, time=1.78 memory used=146.9MB, alloc=84.3MB, time=2.41 memory used=209.9MB, alloc=92.3MB, time=3.42 memory used=272.6MB, alloc=92.3MB, time=4.41 memory used=333.2MB, alloc=116.3MB, time=5.41 memory used=416.8MB, alloc=372.3MB, time=6.69 memory used=500.5MB, alloc=396.3MB, time=7.96 memory used=608.6MB, alloc=396.3MB, time=9.71 memory used=722.7MB, alloc=420.3MB, time=11.40 memory used=854.3MB, alloc=444.3MB, time=13.55 memory used=987.6MB, alloc=468.3MB, time=15.82 memory used=1121.9MB, alloc=468.3MB, time=18.22 memory used=1241.5MB, alloc=492.3MB, time=20.26 memory used=1353.9MB, alloc=492.3MB, time=22.34 memory used=1461.4MB, alloc=492.3MB, time=24.19 memory used=1557.1MB, alloc=492.3MB, time=25.93 memory used=1654.4MB, alloc=492.3MB, time=27.53 memory used=1745.6MB, alloc=492.3MB, time=29.02 memory used=1845.4MB, alloc=492.3MB, time=30.81 memory used=1938.9MB, alloc=492.3MB, time=32.59 memory used=2013.8MB, alloc=516.3MB, time=33.88 memory used=2087.0MB, alloc=516.3MB, time=35.46 memory used=2162.2MB, alloc=516.3MB, time=37.17 memory used=2231.6MB, alloc=516.3MB, time=38.54 memory used=2313.0MB, alloc=516.3MB, time=40.22 memory used=2362.2MB, alloc=516.3MB, time=41.25 memory used=2420.0MB, alloc=516.3MB, time=42.44 memory used=2474.5MB, alloc=516.3MB, time=43.63 memory used=2527.7MB, alloc=516.3MB, time=44.77 memory used=2592.3MB, alloc=516.3MB, time=46.24 memory used=2648.4MB, alloc=516.3MB, time=47.04 memory used=2694.2MB, alloc=516.3MB, time=48.08 memory used=2917.8MB, alloc=540.3MB, time=52.04 memory used=3145.1MB, alloc=564.3MB, time=56.67 memory used=3340.6MB, alloc=588.3MB, time=60.76 memory used=3523.4MB, alloc=612.3MB, time=64.72 memory used=3689.5MB, alloc=612.3MB, time=68.41 memory used=3864.7MB, alloc=636.3MB, time=72.24 memory used=4044.0MB, alloc=636.3MB, time=76.50 memory used=4206.2MB, alloc=660.3MB, time=79.97 memory used=4345.8MB, alloc=660.3MB, time=83.18 memory used=4480.0MB, alloc=660.3MB, time=86.21 memory used=4610.3MB, alloc=660.3MB, time=89.13 memory used=4716.0MB, alloc=660.3MB, time=91.54 memory used=4830.0MB, alloc=684.3MB, time=94.12 memory used=4933.9MB, alloc=684.3MB, time=96.41 memory used=5072.5MB, alloc=684.3MB, time=98.99 memory used=5162.4MB, alloc=684.3MB, time=101.24 memory used=5254.0MB, alloc=684.3MB, time=103.71 memory used=5606.6MB, alloc=708.3MB, time=111.55 memory used=5979.4MB, alloc=732.3MB, time=119.19 memory used=6354.6MB, alloc=756.3MB, time=126.73 memory used=6737.4MB, alloc=780.3MB, time=134.58 memory used=7125.6MB, alloc=804.3MB, time=142.68 |\^/| 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(); 1428240300 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; F := [ 2 2 2 3 2 2 2 19 x y + 17 x y - 18 z , -2 x - 4 x z - 6 z, -8 x y + 2 x z - 10 x y] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; G := [ 2 2 3 2 2 -6 x y z - 11 y z - 9 z , 5 x y z + 3 x z + 3 y , -3 x - 10 x z - 6 x y ] > Problem := [F,G]; Problem := [[ 2 2 2 3 2 2 2 19 x y + 17 x y - 18 z , -2 x - 4 x z - 6 z, -8 x y + 2 x z - 10 x y] , [ 2 2 3 2 2 -6 x y z - 11 y z - 9 z , 5 x y z + 3 x z + 3 y , -3 x - 10 x z - 6 x y ] ] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.0MB, alloc=32.3MB, time=0.53 memory used=46.9MB, alloc=32.3MB, time=0.86 memory used=66.0MB, alloc=56.3MB, time=1.18 memory used=105.7MB, alloc=60.3MB, time=1.85 memory used=143.7MB, alloc=84.3MB, time=2.52 memory used=205.1MB, alloc=92.3MB, time=3.56 memory used=264.8MB, alloc=92.3MB, time=4.49 memory used=323.7MB, alloc=116.3MB, time=5.41 memory used=405.6MB, alloc=116.3MB, time=6.70 memory used=485.6MB, alloc=140.3MB, time=8.08 memory used=575.1MB, alloc=396.3MB, time=9.68 memory used=681.6MB, alloc=420.3MB, time=11.53 memory used=812.2MB, alloc=444.3MB, time=13.76 memory used=962.8MB, alloc=468.3MB, time=16.72 memory used=1095.8MB, alloc=492.3MB, time=19.15 memory used=1216.8MB, alloc=492.3MB, time=21.33 memory used=1329.6MB, alloc=492.3MB, time=23.34 memory used=1434.2MB, alloc=516.3MB, time=25.31 memory used=1534.4MB, alloc=516.3MB, time=27.31 memory used=1624.3MB, alloc=516.3MB, time=29.17 memory used=1726.7MB, alloc=516.3MB, time=31.18 memory used=1812.8MB, alloc=516.3MB, time=32.90 memory used=1890.5MB, alloc=516.3MB, time=34.32 memory used=1982.8MB, alloc=516.3MB, time=36.69 memory used=2058.1MB, alloc=516.3MB, time=38.30 memory used=2121.3MB, alloc=516.3MB, time=39.91 memory used=2173.0MB, alloc=516.3MB, time=41.09 memory used=2229.0MB, alloc=516.3MB, time=42.68 memory used=2276.0MB, alloc=516.3MB, time=43.84 memory used=2478.0MB, alloc=540.3MB, time=48.17 memory used=2701.3MB, alloc=564.3MB, time=53.05 memory used=2936.2MB, alloc=588.3MB, time=58.54 memory used=3142.5MB, alloc=612.3MB, time=63.43 memory used=3342.9MB, alloc=636.3MB, time=68.33 memory used=3506.4MB, alloc=660.3MB, time=72.63 memory used=3682.1MB, alloc=684.3MB, time=77.20 memory used=3815.4MB, alloc=684.3MB, time=80.53 memory used=3973.3MB, alloc=684.3MB, time=84.75 memory used=4115.0MB, alloc=708.3MB, time=89.03 memory used=4264.2MB, alloc=708.3MB, time=93.76 memory used=4372.4MB, alloc=708.3MB, time=96.75 memory used=4472.6MB, alloc=708.3MB, time=99.46 memory used=4562.5MB, alloc=708.3MB, time=102.05 |\^/| 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(); 1428240600 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 2 2 F := [-7 x y z - 11 y + y z, 6 x y - 9 x z - 6 x , x y z + 6 y z - 8] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 3 2 G := [19 x z - 16 z - 6 x, -10 x y z + 6 z + 10 y z, x z + 4 y + 7] > Problem := [F,G]; Problem := [ 3 2 2 2 2 [-7 x y z - 11 y + y z, 6 x y - 9 x z - 6 x , x y z + 6 y z - 8], 2 2 3 2 [19 x z - 16 z - 6 x, -10 x y z + 6 z + 10 y z, x z + 4 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=0.17 memory used=26.2MB, alloc=32.3MB, time=0.51 memory used=44.6MB, alloc=56.3MB, time=0.79 memory used=85.4MB, alloc=60.3MB, time=1.42 memory used=125.4MB, alloc=60.3MB, time=2.01 memory used=164.2MB, alloc=84.3MB, time=2.54 memory used=230.2MB, alloc=92.3MB, time=3.52 memory used=293.0MB, alloc=92.3MB, time=4.48 memory used=358.1MB, alloc=116.3MB, time=5.44 memory used=436.1MB, alloc=372.3MB, time=6.68 memory used=520.3MB, alloc=372.3MB, time=7.94 memory used=604.9MB, alloc=396.3MB, time=9.29 memory used=709.0MB, alloc=420.3MB, time=10.95 memory used=837.8MB, alloc=444.3MB, time=12.97 memory used=956.3MB, alloc=444.3MB, time=14.75 memory used=1083.3MB, alloc=468.3MB, time=16.86 memory used=1214.4MB, alloc=492.3MB, time=19.11 memory used=1335.4MB, alloc=492.3MB, time=21.14 memory used=1450.8MB, alloc=492.3MB, time=23.00 memory used=1549.5MB, alloc=492.3MB, time=24.79 memory used=1643.7MB, alloc=492.3MB, time=26.55 memory used=1740.2MB, alloc=492.3MB, time=28.27 memory used=1823.3MB, alloc=492.3MB, time=29.79 memory used=1920.9MB, alloc=492.3MB, time=31.35 memory used=2007.8MB, alloc=516.3MB, time=32.80 memory used=2088.8MB, alloc=516.3MB, time=34.42 memory used=2171.8MB, alloc=516.3MB, time=36.10 memory used=2239.3MB, alloc=516.3MB, time=37.31 memory used=2313.8MB, alloc=516.3MB, time=38.72 memory used=2368.8MB, alloc=516.3MB, time=39.86 memory used=2434.9MB, alloc=516.3MB, time=41.29 memory used=2491.1MB, alloc=516.3MB, time=42.53 memory used=2550.1MB, alloc=516.3MB, time=43.96 memory used=2594.5MB, alloc=516.3MB, time=45.07 memory used=2795.9MB, alloc=540.3MB, time=49.05 memory used=3012.8MB, alloc=564.3MB, time=53.55 memory used=3179.6MB, alloc=588.3MB, time=56.60 memory used=3367.9MB, alloc=612.3MB, time=60.34 memory used=3539.3MB, alloc=636.3MB, time=63.56 memory used=3713.5MB, alloc=636.3MB, time=67.31 memory used=3885.9MB, alloc=660.3MB, time=70.79 memory used=4025.5MB, alloc=660.3MB, time=73.73 memory used=4172.4MB, alloc=660.3MB, time=77.00 memory used=4280.6MB, alloc=660.3MB, time=79.80 memory used=4420.9MB, alloc=660.3MB, time=83.30 memory used=4523.5MB, alloc=684.3MB, time=85.62 memory used=4630.2MB, alloc=684.3MB, time=88.12 memory used=4748.4MB, alloc=684.3MB, time=90.61 memory used=4827.1MB, alloc=684.3MB, time=92.82 memory used=4932.6MB, alloc=684.3MB, time=95.35 |\^/| 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(); 1428240900 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 3 2 2 F := [-9 x y + 15 x z - 12 y , -3 x y z + 8 z - 6, 6 x y - 10 x + 6] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 G := [-5 x y - 14 x z - 18 y, -2 x y + 4 x z - 10 x z , 10 x z + 5 z - 5] > Problem := [F,G]; Problem := [ 2 2 3 2 2 [-9 x y + 15 x z - 12 y , -3 x y z + 8 z - 6, 6 x y - 10 x + 6], 2 2 2 2 [-5 x y - 14 x z - 18 y, -2 x y + 4 x z - 10 x z , 10 x z + 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=0.18 memory used=26.7MB, alloc=32.3MB, time=0.52 memory used=46.7MB, alloc=32.3MB, time=0.83 memory used=66.0MB, alloc=56.3MB, time=1.14 memory used=106.2MB, alloc=60.3MB, time=1.77 memory used=145.2MB, alloc=84.3MB, time=2.38 memory used=209.2MB, alloc=92.3MB, time=3.38 memory used=272.3MB, alloc=116.3MB, time=4.42 memory used=344.8MB, alloc=116.3MB, time=5.48 memory used=426.6MB, alloc=372.3MB, time=6.82 memory used=509.8MB, alloc=396.3MB, time=8.27 memory used=616.6MB, alloc=396.3MB, time=10.13 memory used=722.4MB, alloc=420.3MB, time=11.98 memory used=851.3MB, alloc=444.3MB, time=14.16 memory used=997.8MB, alloc=468.3MB, time=16.89 memory used=1127.7MB, alloc=492.3MB, time=19.21 memory used=1250.8MB, alloc=492.3MB, time=21.45 memory used=1349.7MB, alloc=492.3MB, time=23.02 memory used=1456.4MB, alloc=516.3MB, time=25.14 memory used=1552.0MB, alloc=516.3MB, time=27.01 memory used=1653.5MB, alloc=516.3MB, time=29.37 memory used=1735.5MB, alloc=516.3MB, time=30.77 memory used=1808.5MB, alloc=516.3MB, time=32.37 memory used=1875.9MB, alloc=516.3MB, time=33.84 memory used=1940.1MB, alloc=516.3MB, time=35.19 memory used=2003.8MB, alloc=540.3MB, time=36.34 memory used=2075.5MB, alloc=540.3MB, time=37.92 memory used=2134.1MB, alloc=540.3MB, time=39.44 memory used=2179.6MB, alloc=540.3MB, time=40.41 memory used=2236.5MB, alloc=540.3MB, time=42.06 memory used=2284.6MB, alloc=540.3MB, time=43.31 memory used=2472.2MB, alloc=564.3MB, time=47.20 memory used=2670.1MB, alloc=588.3MB, time=51.86 memory used=2881.6MB, alloc=612.3MB, time=56.71 memory used=3061.6MB, alloc=636.3MB, time=60.92 memory used=3278.0MB, alloc=660.3MB, time=66.77 memory used=3435.3MB, alloc=660.3MB, time=70.68 memory used=3582.1MB, alloc=684.3MB, time=74.26 memory used=3703.2MB, alloc=684.3MB, time=77.33 memory used=3845.6MB, alloc=684.3MB, time=81.46 memory used=3976.0MB, alloc=684.3MB, time=85.19 memory used=4101.4MB, alloc=684.3MB, time=88.87 memory used=4197.9MB, alloc=684.3MB, time=91.65 |\^/| 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(); 1428241200 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 3 2 F := [-10 z + 19 y z + 4 z , 4 x y z - 3 y z + 4, 10 x + 6 x y + 4 z ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 G := [x y z - 12 x y - 16 x z, 9 x y z - z , -7 x y + 10 x y + 10 z] > Problem := [F,G]; Problem := [ 3 2 2 3 2 [-10 z + 19 y z + 4 z , 4 x y z - 3 y z + 4, 10 x + 6 x y + 4 z ], 2 2 [x y z - 12 x y - 16 x z, 9 x y z - z , -7 x y + 10 x 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=0.17 memory used=26.5MB, alloc=32.3MB, time=0.50 memory used=47.3MB, alloc=32.3MB, time=0.81 memory used=67.6MB, alloc=32.3MB, time=1.14 memory used=85.1MB, alloc=56.3MB, time=1.44 memory used=121.7MB, alloc=84.3MB, time=2.05 memory used=180.4MB, alloc=92.3MB, time=3.06 memory used=237.5MB, alloc=116.3MB, time=4.02 memory used=316.6MB, alloc=116.3MB, time=5.32 memory used=394.5MB, alloc=140.3MB, time=6.69 memory used=490.6MB, alloc=164.3MB, time=8.22 memory used=590.2MB, alloc=420.3MB, time=10.03 memory used=713.3MB, alloc=444.3MB, time=12.41 memory used=859.2MB, alloc=468.3MB, time=15.31 memory used=1031.9MB, alloc=492.3MB, time=18.64 memory used=1226.9MB, alloc=516.3MB, time=22.51 memory used=1446.4MB, alloc=540.3MB, time=27.23 memory used=1686.0MB, alloc=564.3MB, time=33.23 memory used=1957.0MB, alloc=588.3MB, time=38.71 memory used=2235.1MB, alloc=612.3MB, time=45.98 memory used=2536.4MB, alloc=636.3MB, time=54.32 memory used=2857.7MB, alloc=660.3MB, time=62.93 memory used=3196.0MB, alloc=684.3MB, time=72.75 memory used=3477.8MB, alloc=708.3MB, time=80.63 memory used=3752.2MB, alloc=732.3MB, time=88.55 |\^/| 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(); 1428241500 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; F := 2 3 2 3 [-13 x y z + 2 x z - 8 x, -7 x y - 2 z + 10 z , -10 x y z + 8 y - 6 x y] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 3 2 G := [4 x + 14 x y - 16 z, 2 x z + 7 z - 7 x, 10 x z + 6 z - 8 z ] > Problem := [F,G]; Problem := [ 2 3 2 3 [-13 x y z + 2 x z - 8 x, -7 x y - 2 z + 10 z , -10 x y z + 8 y - 6 x y] 2 2 2 2 3 2 , [4 x + 14 x y - 16 z, 2 x z + 7 z - 7 x, 10 x z + 6 z - 8 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.3MB, alloc=32.3MB, time=0.48 memory used=47.6MB, alloc=32.3MB, time=0.79 memory used=67.0MB, alloc=56.3MB, time=1.09 memory used=105.2MB, alloc=60.3MB, time=1.65 memory used=142.0MB, alloc=84.3MB, time=2.21 memory used=203.6MB, alloc=92.3MB, time=3.12 memory used=261.5MB, alloc=116.3MB, time=3.99 memory used=342.7MB, alloc=140.3MB, time=5.22 memory used=430.8MB, alloc=396.3MB, time=6.60 memory used=529.9MB, alloc=420.3MB, time=8.12 memory used=644.7MB, alloc=444.3MB, time=10.07 memory used=790.3MB, alloc=468.3MB, time=12.36 memory used=952.2MB, alloc=492.3MB, time=15.15 memory used=1096.8MB, alloc=492.3MB, time=17.63 memory used=1228.0MB, alloc=516.3MB, time=19.90 memory used=1367.0MB, alloc=516.3MB, time=22.44 memory used=1490.0MB, alloc=516.3MB, time=24.85 memory used=1606.7MB, alloc=540.3MB, time=27.16 memory used=1736.8MB, alloc=540.3MB, time=30.07 memory used=1833.9MB, alloc=540.3MB, time=32.28 memory used=1920.4MB, alloc=540.3MB, time=34.23 memory used=2006.9MB, alloc=564.3MB, time=36.13 memory used=2083.6MB, alloc=564.3MB, time=37.86 memory used=2148.9MB, alloc=564.3MB, time=39.34 memory used=2208.3MB, alloc=564.3MB, time=40.69 memory used=2267.4MB, alloc=564.3MB, time=42.14 memory used=2315.5MB, alloc=564.3MB, time=43.42 memory used=2362.8MB, alloc=564.3MB, time=44.72 memory used=2599.3MB, alloc=588.3MB, time=49.18 memory used=2839.9MB, alloc=612.3MB, time=54.53 memory used=3070.2MB, alloc=636.3MB, time=59.73 memory used=3282.1MB, alloc=660.3MB, time=64.32 memory used=3444.4MB, alloc=684.3MB, time=67.78 memory used=3614.0MB, alloc=708.3MB, time=71.54 memory used=3790.0MB, alloc=732.3MB, time=75.97 memory used=3932.1MB, alloc=756.3MB, time=79.16 memory used=4090.2MB, alloc=756.3MB, time=82.63 memory used=4251.7MB, alloc=756.3MB, time=87.29 memory used=4413.7MB, alloc=756.3MB, time=92.33 memory used=4546.4MB, alloc=756.3MB, time=95.60 |\^/| 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(); 1428241800 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 3 2 F := [-20 z - 9 x y - 16 x, -9 x z + 3 x z - 4 z, -4 x - 7 x y - 6 x] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 G := [-4 x y z - 19 z + 11 x y, 7 y z - 10 z - 8 y, -4 x y - 3 x + 3] > Problem := [F,G]; Problem := [ 3 2 2 3 2 [-20 z - 9 x y - 16 x, -9 x z + 3 x z - 4 z, -4 x - 7 x y - 6 x], 3 2 [-4 x y z - 19 z + 11 x y, 7 y z - 10 z - 8 y, -4 x y - 3 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=4.4MB, alloc=32.3MB, time=0.18 memory used=26.6MB, alloc=32.3MB, time=0.51 memory used=47.8MB, alloc=32.3MB, time=0.82 memory used=67.4MB, alloc=56.3MB, time=1.13 memory used=107.2MB, alloc=60.3MB, time=1.75 memory used=146.7MB, alloc=60.3MB, time=2.35 memory used=184.8MB, alloc=84.3MB, time=2.95 memory used=238.3MB, alloc=84.3MB, time=3.80 memory used=296.6MB, alloc=92.3MB, time=4.76 memory used=352.1MB, alloc=116.3MB, time=5.64 memory used=432.6MB, alloc=116.3MB, time=6.90 memory used=509.2MB, alloc=140.3MB, time=8.17 memory used=592.9MB, alloc=140.3MB, time=9.50 memory used=682.4MB, alloc=396.3MB, time=11.08 memory used=782.7MB, alloc=420.3MB, time=12.82 memory used=910.9MB, alloc=444.3MB, time=14.94 memory used=1060.9MB, alloc=444.3MB, time=17.05 memory used=1211.3MB, alloc=444.3MB, time=19.48 memory used=1357.9MB, alloc=468.3MB, time=21.81 memory used=1512.1MB, alloc=468.3MB, time=24.33 memory used=1626.7MB, alloc=468.3MB, time=25.31 memory used=1776.0MB, alloc=492.3MB, time=27.55 memory used=1951.6MB, alloc=492.3MB, time=30.02 memory used=2120.9MB, alloc=516.3MB, time=33.34 memory used=2250.8MB, alloc=516.3MB, time=36.00 memory used=2369.0MB, alloc=516.3MB, time=38.34 memory used=2516.9MB, alloc=540.3MB, time=41.55 memory used=2630.8MB, alloc=540.3MB, time=43.85 memory used=2755.3MB, alloc=540.3MB, time=46.39 memory used=2869.9MB, alloc=540.3MB, time=48.97 memory used=2976.8MB, alloc=564.3MB, time=51.33 memory used=3064.1MB, alloc=564.3MB, time=53.22 memory used=3156.5MB, alloc=564.3MB, time=55.15 memory used=3293.1MB, alloc=564.3MB, time=56.02 memory used=3437.9MB, alloc=564.3MB, time=57.80 memory used=3581.9MB, alloc=564.3MB, time=59.03 memory used=3693.1MB, alloc=564.3MB, time=59.62 memory used=3822.3MB, alloc=564.3MB, time=61.64 memory used=3950.7MB, alloc=564.3MB, time=62.47 memory used=4066.9MB, alloc=564.3MB, time=63.59 memory used=4168.3MB, alloc=564.3MB, time=64.11 memory used=4290.8MB, alloc=564.3MB, time=64.63 memory used=4436.4MB, alloc=564.3MB, time=67.13 memory used=4507.1MB, alloc=564.3MB, time=68.94 memory used=4568.4MB, alloc=564.3MB, time=70.43 memory used=4648.6MB, alloc=588.3MB, time=72.51 memory used=4711.4MB, alloc=588.3MB, time=74.03 memory used=4793.8MB, alloc=588.3MB, time=76.22 memory used=4867.3MB, alloc=588.3MB, time=78.14 memory used=4934.5MB, alloc=588.3MB, time=79.72 memory used=4990.2MB, alloc=588.3MB, time=81.28 memory used=5246.1MB, alloc=612.3MB, time=85.87 memory used=5495.0MB, alloc=636.3MB, time=90.87 memory used=5762.2MB, alloc=660.3MB, time=95.81 memory used=6034.8MB, alloc=684.3MB, time=101.02 memory used=6324.6MB, alloc=708.3MB, time=106.29 |\^/| 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(); 1428242100 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 2 2 F := [-20 x - 12 x y z - 4 z, -4 x y - 8 x z - 4 z , -6 y z - 3 x z + 8 x] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 3 2 2 2 G := [-12 x y + x y z - 6 y z, -8 y - 3 x y + 8 z , 9 x y - 6 y z + 10 x] > Problem := [F,G]; Problem := [ 3 2 2 2 2 [-20 x - 12 x y z - 4 z, -4 x y - 8 x z - 4 z , -6 y z - 3 x z + 8 x], 2 2 3 2 2 2 [-12 x y + x y z - 6 y z, -8 y - 3 x y + 8 z , 9 x y - 6 y 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=4.2MB, alloc=32.3MB, time=0.17 memory used=26.5MB, alloc=32.3MB, time=0.51 memory used=47.2MB, alloc=32.3MB, time=0.82 memory used=66.0MB, alloc=56.3MB, time=1.11 memory used=106.4MB, alloc=60.3MB, time=1.73 memory used=144.6MB, alloc=84.3MB, time=2.34 memory used=210.4MB, alloc=92.3MB, time=3.31 memory used=272.6MB, alloc=116.3MB, time=4.27 memory used=337.8MB, alloc=116.3MB, time=5.21 memory used=408.4MB, alloc=372.3MB, time=6.33 memory used=494.3MB, alloc=396.3MB, time=7.69 memory used=604.3MB, alloc=420.3MB, time=9.42 memory used=734.2MB, alloc=420.3MB, time=11.28 memory used=848.5MB, alloc=444.3MB, time=12.95 memory used=976.4MB, alloc=444.3MB, time=14.78 memory used=1097.8MB, alloc=468.3MB, time=16.75 memory used=1205.0MB, alloc=468.3MB, time=18.16 memory used=1326.7MB, alloc=468.3MB, time=19.44 memory used=1428.7MB, alloc=492.3MB, time=21.03 memory used=1523.9MB, alloc=492.3MB, time=22.42 memory used=1613.0MB, alloc=492.3MB, time=23.52 memory used=1702.4MB, alloc=492.3MB, time=25.08 memory used=1780.2MB, alloc=492.3MB, time=26.39 memory used=1861.4MB, alloc=492.3MB, time=27.79 memory used=1953.0MB, alloc=516.3MB, time=28.89 memory used=2054.6MB, alloc=516.3MB, time=30.73 memory used=2120.6MB, alloc=516.3MB, time=31.86 memory used=2200.8MB, alloc=516.3MB, time=33.00 memory used=2295.0MB, alloc=516.3MB, time=34.12 memory used=2351.6MB, alloc=516.3MB, time=35.09 memory used=2412.0MB, alloc=516.3MB, time=36.01 memory used=2476.2MB, alloc=516.3MB, time=37.12 memory used=2548.3MB, alloc=516.3MB, time=38.75 memory used=2611.9MB, alloc=516.3MB, time=40.20 memory used=2648.7MB, alloc=516.3MB, time=41.11 memory used=2844.3MB, alloc=540.3MB, time=44.94 memory used=3022.0MB, alloc=564.3MB, time=48.04 memory used=3201.2MB, alloc=588.3MB, time=51.33 memory used=3384.1MB, alloc=612.3MB, time=55.21 memory used=3540.5MB, alloc=636.3MB, time=58.72 memory used=3698.0MB, alloc=660.3MB, time=62.39 memory used=3807.2MB, alloc=660.3MB, time=64.82 memory used=3907.4MB, alloc=660.3MB, time=67.35 memory used=4033.0MB, alloc=660.3MB, time=70.14 memory used=4125.8MB, alloc=660.3MB, time=72.27 memory used=4434.9MB, alloc=684.3MB, time=76.50 memory used=4811.3MB, alloc=708.3MB, time=81.75 memory used=5164.8MB, alloc=732.3MB, time=88.80 memory used=5522.5MB, alloc=756.3MB, time=96.21 memory used=5861.3MB, alloc=780.3MB, time=101.91 memory used=6197.8MB, alloc=804.3MB, time=109.01 memory used=6510.1MB, alloc=828.3MB, time=114.45 |\^/| 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(); 1428242400 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 2 F := [-8 y z + 2 y z + 16 z, 4 x + 10 x y - 2 x z, 8 x z - 8 x] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 2 G := [19 y z - 2 z - 18 x, 3 y z - 7 y + 8 y z, -x y z - 8 x y - 3 y z] > Problem := [F,G]; 2 3 2 2 Problem := [[-8 y z + 2 y z + 16 z, 4 x + 10 x y - 2 x z, 8 x z - 8 x], 2 3 2 2 [19 y z - 2 z - 18 x, 3 y z - 7 y + 8 y z, -x y z - 8 x y - 3 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.2MB, alloc=32.3MB, time=0.48 memory used=47.3MB, alloc=32.3MB, time=0.77 memory used=67.4MB, alloc=32.3MB, time=1.06 memory used=86.2MB, alloc=56.3MB, time=1.34 memory used=123.5MB, alloc=60.3MB, time=1.92 memory used=158.6MB, alloc=84.3MB, time=2.49 memory used=215.7MB, alloc=84.3MB, time=3.37 memory used=271.3MB, alloc=108.3MB, time=4.26 memory used=348.4MB, alloc=116.3MB, time=5.54 memory used=423.5MB, alloc=140.3MB, time=6.81 memory used=521.1MB, alloc=164.3MB, time=8.54 memory used=637.5MB, alloc=188.3MB, time=10.61 memory used=745.5MB, alloc=444.3MB, time=12.75 memory used=882.6MB, alloc=468.3MB, time=15.65 memory used=1043.0MB, alloc=492.3MB, time=18.70 memory used=1224.8MB, alloc=516.3MB, time=22.77 memory used=1428.3MB, alloc=540.3MB, time=27.41 memory used=1653.2MB, alloc=564.3MB, time=32.51 memory used=1906.3MB, alloc=588.3MB, time=39.36 memory used=2184.6MB, alloc=612.3MB, time=47.69 memory used=2486.3MB, alloc=636.3MB, time=57.18 memory used=2812.7MB, alloc=660.3MB, time=67.92 memory used=3155.1MB, alloc=684.3MB, time=79.05 memory used=3513.6MB, alloc=708.3MB, time=90.08 |\^/| 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(); 1428242700 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 3 2 3 F := [16 x y + 19 y + 12 x y, -2 y - 2 y, x z - 3 y + 2 x z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 3 G := [19 x y + 14 z + 16 x z, 7 x y z + 3 y z - 2, 4 x y + 2 x y z - 7 y ] > Problem := [F,G]; 2 3 3 2 3 Problem := [[16 x y + 19 y + 12 x y, -2 y - 2 y, x z - 3 y + 2 x z], 2 3 2 3 [19 x y + 14 z + 16 x z, 7 x y z + 3 y z - 2, 4 x y + 2 x y z - 7 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.8MB, alloc=32.3MB, time=0.50 memory used=47.0MB, alloc=32.3MB, time=0.79 memory used=65.2MB, alloc=56.3MB, time=1.08 memory used=105.7MB, alloc=60.3MB, time=1.69 memory used=144.6MB, alloc=60.3MB, time=2.26 memory used=182.5MB, alloc=84.3MB, time=2.85 memory used=219.9MB, alloc=84.3MB, time=3.39 memory used=284.5MB, alloc=92.3MB, time=4.37 memory used=351.8MB, alloc=116.3MB, time=5.31 memory used=419.1MB, alloc=116.3MB, time=6.31 memory used=476.4MB, alloc=372.3MB, time=7.22 memory used=559.0MB, alloc=396.3MB, time=8.50 memory used=676.3MB, alloc=396.3MB, time=10.12 memory used=788.5MB, alloc=420.3MB, time=11.64 memory used=921.9MB, alloc=444.3MB, time=13.53 memory used=1060.7MB, alloc=468.3MB, time=15.31 memory used=1165.0MB, alloc=468.3MB, time=17.14 memory used=1325.9MB, alloc=468.3MB, time=23.73 memory used=1449.4MB, alloc=468.3MB, time=25.93 memory used=1573.6MB, alloc=468.3MB, time=27.48 memory used=1714.8MB, alloc=492.3MB, time=29.06 memory used=1848.5MB, alloc=492.3MB, time=30.54 memory used=1939.5MB, alloc=492.3MB, time=31.90 memory used=2062.4MB, alloc=516.3MB, time=33.34 memory used=2171.3MB, alloc=516.3MB, time=34.06 memory used=2270.9MB, alloc=516.3MB, time=34.53 memory used=2563.9MB, alloc=516.3MB, time=72.21 memory used=2813.0MB, alloc=516.3MB, time=73.15 memory used=2945.9MB, alloc=516.3MB, time=73.70 memory used=3204.4MB, alloc=516.3MB, time=74.30 memory used=3457.6MB, alloc=516.3MB, time=75.21 memory used=3767.5MB, alloc=516.3MB, time=75.80 memory used=3943.9MB, alloc=516.3MB, time=76.22 memory used=4140.4MB, alloc=516.3MB, time=76.65 memory used=4354.1MB, alloc=516.3MB, time=77.09 memory used=4648.8MB, alloc=516.3MB, time=88.66 memory used=4742.3MB, alloc=516.3MB, time=89.07 memory used=4927.2MB, alloc=516.3MB, time=91.88 memory used=5145.6MB, alloc=516.3MB, time=94.28 memory used=5353.4MB, alloc=516.3MB, time=97.88 memory used=5566.4MB, alloc=540.3MB, time=99.71 memory used=5813.1MB, alloc=540.3MB, time=103.47 memory used=5893.1MB, alloc=540.3MB, time=104.86 memory used=5977.5MB, alloc=540.3MB, time=106.16 memory used=6062.5MB, alloc=540.3MB, time=107.24 memory used=6209.4MB, alloc=540.3MB, time=109.34 memory used=6315.7MB, alloc=540.3MB, time=110.47 memory used=6374.1MB, alloc=540.3MB, time=111.63 memory used=6439.6MB, alloc=540.3MB, time=112.82 memory used=6517.0MB, alloc=540.3MB, time=114.00 memory used=6592.3MB, alloc=540.3MB, time=115.16 memory used=6668.0MB, alloc=540.3MB, time=116.20 memory used=6724.7MB, alloc=540.3MB, time=117.35 memory used=6768.5MB, alloc=540.3MB, time=118.00 memory used=6856.2MB, alloc=564.3MB, time=118.98 memory used=6966.8MB, alloc=564.3MB, time=119.53 memory used=7089.7MB, alloc=564.3MB, time=120.07 memory used=7179.9MB, alloc=564.3MB, time=120.50 memory used=7315.1MB, alloc=564.3MB, time=121.24 memory used=7429.4MB, alloc=564.3MB, time=121.75 memory used=7528.2MB, alloc=564.3MB, time=122.17 memory used=7674.9MB, alloc=564.3MB, time=127.65 memory used=7791.0MB, alloc=564.3MB, time=128.15 memory used=7893.4MB, alloc=564.3MB, time=128.60 memory used=8087.7MB, alloc=564.3MB, time=129.69 memory used=8202.5MB, alloc=564.3MB, time=130.69 memory used=8261.1MB, alloc=564.3MB, time=131.60 memory used=8311.9MB, alloc=564.3MB, time=132.49 memory used=8358.8MB, alloc=564.3MB, time=133.57 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428243000 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 3 2 F := [20 x y z - 3 y + 7 y, -9 x y z - 7 y z + z , -4 x z - 5 y - 10 y ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 3 2 G := [-x z - 6 y z - 4 y , -3 y - 2 x - 3 z, -6 x y z + 4 y z + 4 x] > Problem := [F,G]; Problem := [ 2 2 2 2 3 2 [20 x y z - 3 y + 7 y, -9 x y z - 7 y z + z , -4 x z - 5 y - 10 y ], 2 2 2 3 2 [-x z - 6 y z - 4 y , -3 y - 2 x - 3 z, -6 x y z + 4 y 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=0.17 memory used=26.2MB, alloc=32.3MB, time=0.50 memory used=46.4MB, alloc=32.3MB, time=0.80 memory used=65.6MB, alloc=56.3MB, time=1.10 memory used=105.0MB, alloc=60.3MB, time=1.68 memory used=142.4MB, alloc=84.3MB, time=2.24 memory used=204.8MB, alloc=92.3MB, time=3.21 memory used=265.3MB, alloc=116.3MB, time=4.17 memory used=340.9MB, alloc=116.3MB, time=5.36 memory used=414.4MB, alloc=372.3MB, time=6.54 memory used=497.0MB, alloc=396.3MB, time=7.87 memory used=605.5MB, alloc=420.3MB, time=9.49 memory used=740.4MB, alloc=444.3MB, time=11.60 memory used=865.2MB, alloc=444.3MB, time=13.62 memory used=990.5MB, alloc=468.3MB, time=15.45 memory used=1083.2MB, alloc=468.3MB, time=16.83 memory used=1188.8MB, alloc=468.3MB, time=18.50 memory used=1292.7MB, alloc=492.3MB, time=20.46 memory used=1402.8MB, alloc=492.3MB, time=22.69 memory used=1519.7MB, alloc=492.3MB, time=25.10 memory used=1620.2MB, alloc=516.3MB, time=27.20 memory used=1715.7MB, alloc=516.3MB, time=29.07 memory used=1791.1MB, alloc=516.3MB, time=30.48 memory used=1868.7MB, alloc=516.3MB, time=31.98 memory used=1935.6MB, alloc=516.3MB, time=33.37 memory used=1984.5MB, alloc=516.3MB, time=34.27 memory used=2042.3MB, alloc=516.3MB, time=35.41 memory used=2108.0MB, alloc=516.3MB, time=36.97 memory used=2150.3MB, alloc=516.3MB, time=37.93 memory used=2209.5MB, alloc=516.3MB, time=39.55 memory used=2413.8MB, alloc=540.3MB, time=43.28 memory used=2631.4MB, alloc=564.3MB, time=47.16 memory used=2848.0MB, alloc=588.3MB, time=51.76 memory used=3034.1MB, alloc=612.3MB, time=55.26 memory used=3211.5MB, alloc=636.3MB, time=58.68 memory used=3369.3MB, alloc=660.3MB, time=62.45 memory used=3570.1MB, alloc=684.3MB, time=67.77 memory used=3711.1MB, alloc=684.3MB, time=71.28 memory used=3834.3MB, alloc=684.3MB, time=73.89 memory used=3993.6MB, alloc=684.3MB, time=76.96 memory used=4094.5MB, alloc=684.3MB, time=79.19 memory used=4193.9MB, alloc=684.3MB, time=81.45 memory used=4333.8MB, alloc=684.3MB, time=85.50 memory used=4450.2MB, alloc=708.3MB, time=88.19 memory used=4836.0MB, alloc=732.3MB, time=95.07 |\^/| 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(); 1428243300 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 2 3 F := [19 x + 7 x y - 15 y, 4 x z + 10 y + 5 z, 3 x - 4 y] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 G := [-6 y z + 2 x y - 3 y, -8 x z + 10 z - 2 x, -7 x y - 6 x z + 6 y] > Problem := [F,G]; 3 2 2 2 3 Problem := [[19 x + 7 x y - 15 y, 4 x z + 10 y + 5 z, 3 x - 4 y], 2 2 2 2 [-6 y z + 2 x y - 3 y, -8 x z + 10 z - 2 x, -7 x y - 6 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=4.3MB, alloc=32.3MB, time=0.17 memory used=26.7MB, alloc=32.3MB, time=0.52 memory used=47.8MB, alloc=32.3MB, time=0.83 memory used=67.9MB, alloc=56.3MB, time=1.15 memory used=108.8MB, alloc=60.3MB, time=1.77 memory used=148.8MB, alloc=60.3MB, time=2.35 memory used=187.0MB, alloc=84.3MB, time=2.94 memory used=222.3MB, alloc=84.3MB, time=3.47 memory used=287.9MB, alloc=116.3MB, time=4.43 memory used=358.3MB, alloc=372.3MB, time=5.50 memory used=447.4MB, alloc=396.3MB, time=6.90 memory used=559.1MB, alloc=396.3MB, time=8.56 memory used=670.4MB, alloc=420.3MB, time=10.25 memory used=804.6MB, alloc=444.3MB, time=12.36 memory used=928.3MB, alloc=444.3MB, time=14.37 memory used=1035.3MB, alloc=444.3MB, time=16.18 memory used=1158.3MB, alloc=468.3MB, time=18.25 memory used=1270.6MB, alloc=468.3MB, time=20.23 memory used=1362.9MB, alloc=468.3MB, time=21.84 memory used=1444.1MB, alloc=468.3MB, time=23.29 memory used=1529.4MB, alloc=468.3MB, time=24.86 memory used=1600.1MB, alloc=468.3MB, time=26.19 memory used=1679.8MB, alloc=492.3MB, time=27.69 memory used=1746.1MB, alloc=492.3MB, time=29.01 memory used=1822.3MB, alloc=492.3MB, time=30.14 memory used=1903.1MB, alloc=492.3MB, time=31.34 memory used=1973.4MB, alloc=492.3MB, time=32.68 memory used=2037.7MB, alloc=492.3MB, time=33.78 memory used=2097.4MB, alloc=492.3MB, time=35.05 memory used=2153.8MB, alloc=492.3MB, time=36.27 memory used=2209.9MB, alloc=492.3MB, time=37.38 memory used=2259.5MB, alloc=492.3MB, time=38.64 memory used=2447.6MB, alloc=516.3MB, time=41.79 memory used=2617.4MB, alloc=540.3MB, time=44.82 memory used=2830.7MB, alloc=564.3MB, time=49.01 memory used=3049.2MB, alloc=588.3MB, time=53.44 memory used=3271.6MB, alloc=612.3MB, time=57.85 memory used=3502.7MB, alloc=636.3MB, time=62.70 memory used=3744.5MB, alloc=660.3MB, time=67.83 memory used=3996.0MB, alloc=684.3MB, time=73.17 memory used=4255.2MB, alloc=708.3MB, time=78.73 memory used=4523.4MB, alloc=732.3MB, time=84.54 memory used=4805.6MB, alloc=756.3MB, time=90.40 memory used=5078.6MB, alloc=780.3MB, time=98.07 memory used=5325.8MB, alloc=804.3MB, time=107.53 |\^/| 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(); 1428243600 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 2 2 3 F := [-5 x y + 20 z - 9 x , 9 x y z - x z + 7 z , 6 y + 6 x z - 3 x] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 2 3 G := [12 x + 16 x z + 18 x , -3 x y + 9 x y + 3 z, 8 x - 7 y z + 4 z] > Problem := [F,G]; Problem := [ 2 3 2 2 2 3 [-5 x y + 20 z - 9 x , 9 x y z - x z + 7 z , 6 y + 6 x z - 3 x], 3 2 2 2 3 [12 x + 16 x z + 18 x , -3 x y + 9 x y + 3 z, 8 x - 7 y z + 4 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.4MB, alloc=32.3MB, time=0.48 memory used=47.3MB, alloc=32.3MB, time=0.80 memory used=67.2MB, alloc=56.3MB, time=1.12 memory used=108.0MB, alloc=60.3MB, time=1.73 memory used=147.4MB, alloc=60.3MB, time=2.33 memory used=183.1MB, alloc=84.3MB, time=2.88 memory used=222.5MB, alloc=84.3MB, time=3.50 memory used=287.2MB, alloc=116.3MB, time=4.42 memory used=356.6MB, alloc=372.3MB, time=5.46 memory used=445.4MB, alloc=396.3MB, time=6.67 memory used=556.6MB, alloc=420.3MB, time=8.28 memory used=687.1MB, alloc=444.3MB, time=10.24 memory used=827.6MB, alloc=468.3MB, time=12.51 memory used=944.0MB, alloc=468.3MB, time=14.37 memory used=1060.0MB, alloc=492.3MB, time=16.49 memory used=1165.6MB, alloc=492.3MB, time=18.30 memory used=1261.9MB, alloc=492.3MB, time=20.08 memory used=1349.7MB, alloc=516.3MB, time=21.70 memory used=1437.5MB, alloc=516.3MB, time=23.39 memory used=1503.2MB, alloc=516.3MB, time=24.68 memory used=1578.8MB, alloc=516.3MB, time=26.26 memory used=1640.8MB, alloc=516.3MB, time=27.56 memory used=1695.7MB, alloc=516.3MB, time=28.73 memory used=1748.9MB, alloc=516.3MB, time=30.10 memory used=1803.1MB, alloc=516.3MB, time=31.41 memory used=1845.9MB, alloc=516.3MB, time=32.43 memory used=2042.1MB, alloc=540.3MB, time=36.01 memory used=2239.5MB, alloc=564.3MB, time=40.22 memory used=2411.9MB, alloc=588.3MB, time=43.33 memory used=2590.8MB, alloc=612.3MB, time=46.79 memory used=2730.0MB, alloc=636.3MB, time=49.12 memory used=2882.5MB, alloc=660.3MB, time=52.61 memory used=2995.0MB, alloc=684.3MB, time=54.76 memory used=3146.4MB, alloc=684.3MB, time=58.26 memory used=3244.8MB, alloc=684.3MB, time=60.39 memory used=3377.1MB, alloc=684.3MB, time=63.39 memory used=3482.5MB, alloc=684.3MB, time=65.88 memory used=3831.8MB, alloc=708.3MB, time=72.23 memory used=4192.7MB, alloc=732.3MB, time=79.52 memory used=4570.5MB, alloc=756.3MB, time=87.85 memory used=4949.7MB, alloc=780.3MB, time=97.53 memory used=5294.3MB, alloc=804.3MB, time=105.53 memory used=5597.0MB, alloc=828.3MB, time=112.55 |\^/| 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(); 1428243900 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 3 2 3 2 2 F := [-15 x y z - 8 y - 18 z , -8 x z + 4 z + 6, 2 x + 8 x z + 8 y z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 3 3 G := [-4 y + 20 z - 3 x, -2 x y z + 7 y z - 6 x, 5 y + 2 y z] > Problem := [F,G]; Problem := [ 3 3 2 3 2 2 [-15 x y z - 8 y - 18 z , -8 x z + 4 z + 6, 2 x + 8 x z + 8 y z], 3 3 3 [-4 y + 20 z - 3 x, -2 x y z + 7 y z - 6 x, 5 y + 2 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=25.4MB, alloc=32.3MB, time=0.49 memory used=45.0MB, alloc=32.3MB, time=0.77 memory used=63.0MB, alloc=56.3MB, time=1.06 memory used=107.6MB, alloc=68.3MB, time=1.71 memory used=154.7MB, alloc=92.3MB, time=2.30 memory used=223.0MB, alloc=92.3MB, time=3.28 memory used=286.5MB, alloc=116.3MB, time=4.23 memory used=351.8MB, alloc=116.3MB, time=5.16 memory used=420.4MB, alloc=372.3MB, time=6.17 memory used=503.5MB, alloc=396.3MB, time=7.50 memory used=613.7MB, alloc=396.3MB, time=9.16 memory used=720.6MB, alloc=420.3MB, time=10.89 memory used=856.4MB, alloc=444.3MB, time=13.01 memory used=979.7MB, alloc=468.3MB, time=14.88 memory used=1104.5MB, alloc=468.3MB, time=17.03 memory used=1211.9MB, alloc=468.3MB, time=18.81 memory used=1315.6MB, alloc=492.3MB, time=20.29 memory used=1423.9MB, alloc=492.3MB, time=22.21 memory used=1530.9MB, alloc=492.3MB, time=24.11 memory used=1617.7MB, alloc=492.3MB, time=25.66 memory used=1699.1MB, alloc=516.3MB, time=26.84 memory used=1771.7MB, alloc=516.3MB, time=27.96 memory used=1850.1MB, alloc=516.3MB, time=29.11 memory used=1924.3MB, alloc=516.3MB, time=30.66 memory used=1987.3MB, alloc=516.3MB, time=31.88 memory used=2037.3MB, alloc=516.3MB, time=32.74 memory used=2084.6MB, alloc=516.3MB, time=33.74 memory used=2293.5MB, alloc=540.3MB, time=37.28 memory used=2485.1MB, alloc=564.3MB, time=40.66 memory used=2656.5MB, alloc=588.3MB, time=42.99 memory used=2865.8MB, alloc=612.3MB, time=45.13 memory used=3018.8MB, alloc=636.3MB, time=47.77 memory used=3157.7MB, alloc=636.3MB, time=49.80 memory used=3309.0MB, alloc=660.3MB, time=52.95 memory used=3442.8MB, alloc=660.3MB, time=55.90 memory used=3551.7MB, alloc=660.3MB, time=58.27 memory used=3684.4MB, alloc=660.3MB, time=61.35 memory used=3782.7MB, alloc=660.3MB, time=63.56 memory used=3892.8MB, alloc=660.3MB, time=66.60 memory used=4194.3MB, alloc=684.3MB, time=71.11 memory used=4544.8MB, alloc=708.3MB, time=77.45 memory used=4911.1MB, alloc=732.3MB, time=84.75 memory used=5285.7MB, alloc=756.3MB, time=93.10 memory used=5628.4MB, alloc=780.3MB, time=99.09 memory used=5869.6MB, alloc=804.3MB, time=103.47 memory used=6130.9MB, alloc=828.3MB, time=109.11 memory used=6386.0MB, alloc=852.3MB, time=114.68 |\^/| 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(); 1428244200 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 2 2 F := [-18 x + 20 x y - 14 y, 8 x y - 10 x y - y z, 2 x z - x y z + 2 x z ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 3 3 G := [18 y z - 5 x - 17 x, 5 x y - 9 x z - 4 y , -10 x + 2 x y z - 10 x] > Problem := [F,G]; Problem := [ 3 2 2 2 2 [-18 x + 20 x y - 14 y, 8 x y - 10 x y - y z, 2 x z - x y z + 2 x z ], 2 2 2 2 3 3 [18 y z - 5 x - 17 x, 5 x y - 9 x z - 4 y , -10 x + 2 x y 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=26.5MB, alloc=32.3MB, time=0.48 memory used=47.2MB, alloc=32.3MB, time=0.77 memory used=66.6MB, alloc=56.3MB, time=1.07 memory used=105.9MB, alloc=60.3MB, time=1.65 memory used=143.2MB, alloc=84.3MB, time=2.22 memory used=202.6MB, alloc=92.3MB, time=3.17 memory used=261.0MB, alloc=116.3MB, time=4.07 memory used=344.4MB, alloc=116.3MB, time=5.35 memory used=425.4MB, alloc=140.3MB, time=6.63 memory used=511.4MB, alloc=140.3MB, time=8.00 memory used=583.1MB, alloc=396.3MB, time=9.18 memory used=683.5MB, alloc=420.3MB, time=10.82 memory used=808.3MB, alloc=444.3MB, time=12.91 memory used=954.8MB, alloc=468.3MB, time=15.39 memory used=1092.9MB, alloc=492.3MB, time=17.63 memory used=1227.1MB, alloc=492.3MB, time=19.97 memory used=1361.5MB, alloc=516.3MB, time=22.50 memory used=1476.3MB, alloc=516.3MB, time=24.59 memory used=1565.3MB, alloc=516.3MB, time=26.13 memory used=1655.5MB, alloc=516.3MB, time=27.80 memory used=1745.6MB, alloc=540.3MB, time=29.47 memory used=1826.8MB, alloc=540.3MB, time=31.19 memory used=1914.7MB, alloc=540.3MB, time=33.07 memory used=1979.9MB, alloc=540.3MB, time=34.26 memory used=2043.5MB, alloc=540.3MB, time=35.82 memory used=2113.8MB, alloc=540.3MB, time=37.52 memory used=2168.1MB, alloc=540.3MB, time=38.86 memory used=2223.5MB, alloc=540.3MB, time=40.31 memory used=2447.3MB, alloc=564.3MB, time=44.37 memory used=2643.6MB, alloc=588.3MB, time=48.05 memory used=2846.5MB, alloc=612.3MB, time=52.24 memory used=3030.3MB, alloc=636.3MB, time=56.07 memory used=3189.1MB, alloc=660.3MB, time=59.54 memory used=3334.7MB, alloc=684.3MB, time=62.83 memory used=3452.8MB, alloc=684.3MB, time=65.65 memory used=3587.3MB, alloc=684.3MB, time=68.83 memory used=3703.7MB, alloc=684.3MB, time=71.61 memory used=3787.5MB, alloc=684.3MB, time=73.65 memory used=4131.5MB, alloc=708.3MB, time=81.09 memory used=4513.7MB, alloc=732.3MB, time=88.41 memory used=4909.4MB, alloc=756.3MB, time=95.89 memory used=5314.6MB, alloc=780.3MB, time=103.50 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428244500 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 3 2 3 2 F := [-11 y z - 16 x + 18, 3 x + 4 x y + x z, -8 x y z + 4 y + 7 y ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 2 2 G := [-17 x , -4 x y z - 10 y + 8 y z , 3 x y z - 7 y + 6 z ] > Problem := [F,G]; Problem := [ 2 2 3 2 3 2 [-11 y z - 16 x + 18, 3 x + 4 x y + x z, -8 x y z + 4 y + 7 y ], 2 3 2 2 2 [-17 x , -4 x y z - 10 y + 8 y z , 3 x y z - 7 y + 6 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=25.0MB, alloc=32.3MB, time=0.48 memory used=44.1MB, alloc=32.3MB, time=0.76 memory used=62.8MB, alloc=56.3MB, time=1.05 memory used=105.4MB, alloc=68.3MB, time=1.66 memory used=152.0MB, alloc=68.3MB, time=2.23 memory used=194.4MB, alloc=92.3MB, time=2.87 memory used=260.9MB, alloc=92.3MB, time=3.82 memory used=331.4MB, alloc=116.3MB, time=4.74 memory used=392.9MB, alloc=372.3MB, time=5.58 memory used=482.3MB, alloc=372.3MB, time=6.76 memory used=573.0MB, alloc=396.3MB, time=7.99 memory used=685.3MB, alloc=396.3MB, time=9.56 memory used=803.5MB, alloc=420.3MB, time=11.11 memory used=937.0MB, alloc=444.3MB, time=13.05 memory used=1061.2MB, alloc=444.3MB, time=14.93 memory used=1172.9MB, alloc=468.3MB, time=16.52 memory used=1288.2MB, alloc=468.3MB, time=18.39 memory used=1388.6MB, alloc=468.3MB, time=20.10 memory used=1501.8MB, alloc=492.3MB, time=21.69 memory used=1621.4MB, alloc=492.3MB, time=22.99 memory used=1733.5MB, alloc=492.3MB, time=24.39 memory used=1819.0MB, alloc=492.3MB, time=25.45 memory used=1907.0MB, alloc=492.3MB, time=26.95 memory used=1988.5MB, alloc=492.3MB, time=28.38 memory used=2078.4MB, alloc=492.3MB, time=29.65 memory used=2155.9MB, alloc=516.3MB, time=30.80 memory used=2233.1MB, alloc=516.3MB, time=32.29 memory used=2291.9MB, alloc=516.3MB, time=33.37 memory used=2354.6MB, alloc=516.3MB, time=34.65 memory used=2404.7MB, alloc=516.3MB, time=35.69 memory used=2471.8MB, alloc=516.3MB, time=37.04 memory used=2521.3MB, alloc=516.3MB, time=38.11 memory used=2551.4MB, alloc=516.3MB, time=38.93 memory used=2763.5MB, alloc=540.3MB, time=41.89 memory used=2975.9MB, alloc=564.3MB, time=45.87 memory used=3174.2MB, alloc=588.3MB, time=49.10 memory used=3351.1MB, alloc=588.3MB, time=51.49 memory used=3565.0MB, alloc=588.3MB, time=54.11 memory used=3791.6MB, alloc=612.3MB, time=57.96 memory used=3988.4MB, alloc=636.3MB, time=61.33 memory used=4226.1MB, alloc=636.3MB, time=64.45 memory used=4409.7MB, alloc=636.3MB, time=68.00 memory used=4578.2MB, alloc=660.3MB, time=71.88 memory used=4707.9MB, alloc=660.3MB, time=74.84 memory used=4828.1MB, alloc=660.3MB, time=77.03 memory used=4932.2MB, alloc=660.3MB, time=79.64 memory used=5053.8MB, alloc=660.3MB, time=82.65 memory used=5133.9MB, alloc=660.3MB, time=84.47 memory used=5216.3MB, alloc=660.3MB, time=86.73 memory used=5319.7MB, alloc=684.3MB, time=89.47 memory used=5679.1MB, alloc=708.3MB, time=96.51 memory used=6067.1MB, alloc=732.3MB, time=103.91 |\^/| 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(); 1428244800 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 3 3 3 F := [13 x y - 7 x y - 19 y, y - 5 z - 3 x z, -y + 2 x - 2 y] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 G := [17 y z - 12 x y + 18 y, -6 x z - 10 y z - 9, 10 x y + 9] > Problem := [F,G]; 2 2 3 3 3 Problem := [[13 x y - 7 x y - 19 y, y - 5 z - 3 x z, -y + 2 x - 2 y], 2 2 2 [17 y z - 12 x y + 18 y, -6 x z - 10 y z - 9, 10 x y + 9]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.7MB, alloc=32.3MB, time=0.50 memory used=48.3MB, alloc=32.3MB, time=0.83 memory used=68.8MB, alloc=56.3MB, time=1.15 memory used=109.0MB, alloc=60.3MB, time=1.75 memory used=148.6MB, alloc=84.3MB, time=2.37 memory used=215.3MB, alloc=92.3MB, time=3.35 memory used=277.6MB, alloc=116.3MB, time=4.33 memory used=357.3MB, alloc=116.3MB, time=5.55 memory used=434.6MB, alloc=372.3MB, time=6.78 memory used=518.6MB, alloc=396.3MB, time=8.14 memory used=629.2MB, alloc=420.3MB, time=9.88 memory used=770.4MB, alloc=420.3MB, time=11.90 memory used=903.6MB, alloc=444.3MB, time=14.09 memory used=1035.6MB, alloc=468.3MB, time=16.28 memory used=1181.4MB, alloc=492.3MB, time=18.64 memory used=1336.9MB, alloc=492.3MB, time=21.40 memory used=1511.1MB, alloc=516.3MB, time=24.29 memory used=1690.5MB, alloc=540.3MB, time=27.33 memory used=1879.4MB, alloc=564.3MB, time=30.50 memory used=2036.3MB, alloc=588.3MB, time=33.24 memory used=2194.4MB, alloc=612.3MB, time=36.20 memory used=2346.6MB, alloc=636.3MB, time=39.12 memory used=2495.0MB, alloc=660.3MB, time=42.08 memory used=2649.6MB, alloc=660.3MB, time=45.16 memory used=2794.2MB, alloc=684.3MB, time=48.11 memory used=3039.5MB, alloc=708.3MB, time=55.87 memory used=3304.2MB, alloc=732.3MB, time=65.47 memory used=3571.8MB, alloc=756.3MB, time=76.01 memory used=3849.1MB, alloc=780.3MB, time=87.52 memory used=4144.3MB, alloc=804.3MB, time=99.87 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428245100 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 F := [-4 z + 16 x + 2, 4 y z - 2 x z - 4, -7 y - 6 x] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 3 2 G := [-14 y z - 9 x - 13, -3 y z - 7, 2 x - 10 z ] > Problem := [F,G]; 2 2 2 Problem := [[-4 z + 16 x + 2, 4 y z - 2 x z - 4, -7 y - 6 x], 2 2 3 2 [-14 y z - 9 x - 13, -3 y z - 7, 2 x - 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=0.17 memory used=26.7MB, alloc=32.3MB, time=0.50 memory used=48.0MB, alloc=32.3MB, time=0.81 memory used=69.2MB, alloc=56.3MB, time=1.14 memory used=110.1MB, alloc=60.3MB, time=1.75 memory used=150.0MB, alloc=60.3MB, time=2.32 memory used=187.6MB, alloc=84.3MB, time=2.90 memory used=222.2MB, alloc=84.3MB, time=3.38 memory used=281.9MB, alloc=116.3MB, time=4.33 memory used=366.0MB, alloc=116.3MB, time=5.63 memory used=438.8MB, alloc=140.3MB, time=6.73 memory used=513.8MB, alloc=396.3MB, time=7.95 memory used=619.8MB, alloc=420.3MB, time=9.69 memory used=751.8MB, alloc=420.3MB, time=11.87 memory used=882.9MB, alloc=444.3MB, time=14.07 memory used=1029.6MB, alloc=468.3MB, time=16.54 memory used=1185.8MB, alloc=492.3MB, time=19.48 memory used=1314.8MB, alloc=492.3MB, time=21.83 memory used=1416.1MB, alloc=492.3MB, time=23.69 memory used=1541.5MB, alloc=516.3MB, time=26.07 memory used=1636.8MB, alloc=516.3MB, time=27.89 memory used=1743.8MB, alloc=516.3MB, time=29.97 memory used=1852.9MB, alloc=516.3MB, time=32.19 memory used=1936.4MB, alloc=516.3MB, time=33.97 memory used=2022.2MB, alloc=516.3MB, time=35.80 memory used=2094.8MB, alloc=516.3MB, time=37.46 memory used=2160.0MB, alloc=516.3MB, time=38.90 memory used=2220.1MB, alloc=540.3MB, time=40.35 memory used=2304.9MB, alloc=540.3MB, time=42.44 memory used=2372.3MB, alloc=540.3MB, time=44.08 memory used=2427.4MB, alloc=540.3MB, time=45.44 memory used=2477.1MB, alloc=540.3MB, time=46.73 memory used=2696.5MB, alloc=564.3MB, time=51.44 memory used=2937.3MB, alloc=588.3MB, time=56.80 memory used=3149.8MB, alloc=612.3MB, time=60.97 memory used=3383.2MB, alloc=636.3MB, time=65.67 memory used=3633.9MB, alloc=660.3MB, time=70.82 memory used=3943.0MB, alloc=684.3MB, time=75.51 memory used=4274.9MB, alloc=708.3MB, time=80.22 memory used=4628.9MB, alloc=732.3MB, time=85.38 memory used=4964.3MB, alloc=756.3MB, time=91.76 memory used=5273.2MB, alloc=780.3MB, time=98.34 |\^/| 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(); 1428245400 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 2 2 F := [-18 z - 17 y z + 16 z , 4 y z + 5 x - 1, -2 x y + 7 y z - x y] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 2 2 3 G := [10 x z - 3 y z + 14 y, -6 x y + 3 y z - 2 x , 6 y z + 3 z - 2 x y] > Problem := [F,G]; Problem := [ 3 2 2 2 2 [-18 z - 17 y z + 16 z , 4 y z + 5 x - 1, -2 x y + 7 y z - x y], 2 2 2 2 2 2 3 [10 x z - 3 y z + 14 y, -6 x y + 3 y z - 2 x , 6 y z + 3 z - 2 x y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.6MB, alloc=32.3MB, time=0.50 memory used=47.0MB, alloc=32.3MB, time=0.80 memory used=65.7MB, alloc=56.3MB, time=1.09 memory used=103.7MB, alloc=60.3MB, time=1.66 memory used=141.3MB, alloc=60.3MB, time=2.10 memory used=180.6MB, alloc=84.3MB, time=2.64 memory used=220.7MB, alloc=84.3MB, time=3.09 memory used=281.2MB, alloc=92.3MB, time=4.02 memory used=342.2MB, alloc=92.3MB, time=4.95 memory used=399.4MB, alloc=116.3MB, time=5.90 memory used=478.4MB, alloc=116.3MB, time=7.24 memory used=556.8MB, alloc=140.3MB, time=8.25 memory used=641.6MB, alloc=396.3MB, time=9.57 memory used=742.6MB, alloc=420.3MB, time=11.20 memory used=875.8MB, alloc=444.3MB, time=13.09 memory used=1025.1MB, alloc=468.3MB, time=15.27 memory used=1167.2MB, alloc=468.3MB, time=17.63 memory used=1299.3MB, alloc=492.3MB, time=19.76 memory used=1437.4MB, alloc=492.3MB, time=21.96 memory used=1571.8MB, alloc=516.3MB, time=24.40 memory used=1699.1MB, alloc=516.3MB, time=26.91 memory used=1798.7MB, alloc=516.3MB, time=28.81 memory used=1901.7MB, alloc=516.3MB, time=30.76 memory used=1991.1MB, alloc=516.3MB, time=32.55 memory used=2112.6MB, alloc=516.3MB, time=34.07 memory used=2198.7MB, alloc=516.3MB, time=35.37 memory used=2302.7MB, alloc=540.3MB, time=36.89 memory used=2453.7MB, alloc=540.3MB, time=38.46 memory used=2532.2MB, alloc=540.3MB, time=39.79 memory used=2629.2MB, alloc=540.3MB, time=41.70 memory used=2691.1MB, alloc=540.3MB, time=42.86 memory used=2777.8MB, alloc=540.3MB, time=44.96 memory used=2841.6MB, alloc=540.3MB, time=46.44 memory used=2914.3MB, alloc=540.3MB, time=48.26 memory used=2960.8MB, alloc=540.3MB, time=49.28 memory used=3022.5MB, alloc=540.3MB, time=50.94 memory used=3087.2MB, alloc=540.3MB, time=52.55 memory used=3309.5MB, alloc=564.3MB, time=57.10 memory used=3546.1MB, alloc=588.3MB, time=62.52 memory used=3769.9MB, alloc=612.3MB, time=67.34 memory used=3983.7MB, alloc=636.3MB, time=72.08 memory used=4167.4MB, alloc=660.3MB, time=75.93 memory used=4381.1MB, alloc=684.3MB, time=81.21 memory used=4559.8MB, alloc=708.3MB, time=85.31 memory used=4716.8MB, alloc=732.3MB, time=89.52 memory used=4844.1MB, alloc=732.3MB, time=92.49 memory used=4974.4MB, alloc=732.3MB, time=95.42 memory used=5117.7MB, alloc=756.3MB, time=98.47 |\^/| 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(); 1428245700 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 2 3 F := [19 x y + 10 x z + 19 x, -5 x y + 7 x y z + 7 x , -9 x z + 9 z + 5] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 2 3 G := [3 x + 4 x y z - 8 y z, 7 x y - 8 x z + 5 y , -4 y z + 2 z + 2 z] > Problem := [F,G]; Problem := [ 2 2 2 2 2 3 [19 x y + 10 x z + 19 x, -5 x y + 7 x y z + 7 x , -9 x z + 9 z + 5], 3 2 2 2 3 [3 x + 4 x y z - 8 y z, 7 x y - 8 x z + 5 y , -4 y z + 2 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=26.3MB, alloc=32.3MB, time=0.49 memory used=46.6MB, alloc=32.3MB, time=0.78 memory used=65.9MB, alloc=56.3MB, time=1.07 memory used=105.6MB, alloc=60.3MB, time=1.67 memory used=145.8MB, alloc=84.3MB, time=2.28 memory used=208.4MB, alloc=92.3MB, time=3.25 memory used=270.4MB, alloc=348.3MB, time=4.16 memory used=332.1MB, alloc=372.3MB, time=5.11 memory used=419.1MB, alloc=372.3MB, time=6.41 memory used=504.2MB, alloc=396.3MB, time=7.66 memory used=609.5MB, alloc=396.3MB, time=9.33 memory used=719.3MB, alloc=420.3MB, time=11.10 memory used=850.4MB, alloc=444.3MB, time=13.27 memory used=954.6MB, alloc=468.3MB, time=14.78 memory used=1095.3MB, alloc=468.3MB, time=17.39 memory used=1220.0MB, alloc=492.3MB, time=19.50 memory used=1320.0MB, alloc=492.3MB, time=21.21 memory used=1402.5MB, alloc=492.3MB, time=22.66 memory used=1502.8MB, alloc=492.3MB, time=24.46 memory used=1592.4MB, alloc=516.3MB, time=25.89 memory used=1674.0MB, alloc=516.3MB, time=26.99 memory used=1750.1MB, alloc=516.3MB, time=28.60 memory used=1810.8MB, alloc=516.3MB, time=29.75 memory used=1861.4MB, alloc=516.3MB, time=30.67 memory used=1929.3MB, alloc=516.3MB, time=32.22 memory used=1975.2MB, alloc=516.3MB, time=33.29 memory used=2029.8MB, alloc=516.3MB, time=34.52 memory used=2088.2MB, alloc=516.3MB, time=35.95 memory used=2136.5MB, alloc=516.3MB, time=36.97 memory used=2175.8MB, alloc=516.3MB, time=37.82 memory used=2377.9MB, alloc=540.3MB, time=41.26 memory used=2601.8MB, alloc=564.3MB, time=45.46 memory used=2778.1MB, alloc=588.3MB, time=48.85 memory used=2944.3MB, alloc=612.3MB, time=52.09 memory used=3128.2MB, alloc=636.3MB, time=55.26 memory used=3276.5MB, alloc=636.3MB, time=57.95 memory used=3457.2MB, alloc=636.3MB, time=60.79 memory used=3567.6MB, alloc=636.3MB, time=63.05 memory used=3679.4MB, alloc=660.3MB, time=65.20 memory used=3813.6MB, alloc=660.3MB, time=68.32 memory used=3954.3MB, alloc=660.3MB, time=71.29 memory used=4046.3MB, alloc=660.3MB, time=73.51 memory used=4157.1MB, alloc=660.3MB, time=76.04 memory used=4246.8MB, alloc=660.3MB, time=78.22 memory used=4344.0MB, alloc=660.3MB, time=81.04 memory used=4672.2MB, alloc=684.3MB, time=88.22 |\^/| 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(); 1428246000 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 3 F := [12 x - 12 x y - 19 x z, 5 x z - 10 y z + 3 y, -2 x + 3 x y + 4 y] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 3 2 G := [-10 y z - 19 x - 7 y, 4 x y + 2 y z + x, -4 x - 8 y ] > Problem := [F,G]; Problem := [ 2 2 2 3 [12 x - 12 x y - 19 x z, 5 x z - 10 y z + 3 y, -2 x + 3 x y + 4 y], 2 2 2 2 3 2 [-10 y z - 19 x - 7 y, 4 x y + 2 y z + x, -4 x - 8 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=25.9MB, alloc=32.3MB, time=0.49 memory used=45.9MB, alloc=32.3MB, time=0.78 memory used=65.1MB, alloc=56.3MB, time=1.08 memory used=106.8MB, alloc=68.3MB, time=1.72 memory used=146.9MB, alloc=92.3MB, time=2.31 memory used=212.5MB, alloc=92.3MB, time=3.18 memory used=277.9MB, alloc=92.3MB, time=4.13 memory used=338.6MB, alloc=116.3MB, time=5.06 memory used=404.4MB, alloc=372.3MB, time=6.03 memory used=488.9MB, alloc=396.3MB, time=7.34 memory used=601.2MB, alloc=420.3MB, time=9.00 memory used=733.3MB, alloc=444.3MB, time=11.04 memory used=848.0MB, alloc=444.3MB, time=12.83 memory used=965.4MB, alloc=444.3MB, time=14.36 memory used=1086.9MB, alloc=468.3MB, time=16.30 memory used=1213.3MB, alloc=468.3MB, time=17.65 memory used=1323.1MB, alloc=468.3MB, time=19.33 memory used=1420.0MB, alloc=468.3MB, time=20.97 memory used=1508.5MB, alloc=468.3MB, time=22.52 memory used=1605.7MB, alloc=492.3MB, time=24.33 memory used=1687.3MB, alloc=492.3MB, time=25.84 memory used=1760.9MB, alloc=492.3MB, time=27.27 memory used=1840.3MB, alloc=492.3MB, time=28.85 memory used=1905.1MB, alloc=492.3MB, time=30.06 memory used=1969.3MB, alloc=492.3MB, time=31.42 memory used=2031.1MB, alloc=492.3MB, time=32.45 memory used=2078.5MB, alloc=492.3MB, time=33.51 memory used=2134.1MB, alloc=492.3MB, time=34.73 memory used=2189.1MB, alloc=492.3MB, time=35.94 memory used=2245.9MB, alloc=516.3MB, time=36.99 memory used=2304.9MB, alloc=516.3MB, time=38.20 memory used=2505.6MB, alloc=540.3MB, time=41.16 memory used=2716.0MB, alloc=564.3MB, time=44.33 memory used=2909.0MB, alloc=588.3MB, time=47.92 memory used=3075.6MB, alloc=612.3MB, time=50.79 memory used=3249.2MB, alloc=612.3MB, time=54.13 memory used=3468.5MB, alloc=636.3MB, time=58.35 memory used=3676.1MB, alloc=660.3MB, time=62.16 memory used=3891.9MB, alloc=684.3MB, time=66.08 memory used=4152.6MB, alloc=708.3MB, time=70.86 memory used=4395.9MB, alloc=732.3MB, time=75.69 memory used=4610.3MB, alloc=756.3MB, time=80.37 memory used=4831.7MB, alloc=780.3MB, time=85.18 memory used=5052.9MB, alloc=804.3MB, time=89.96 memory used=5272.7MB, alloc=828.3MB, time=94.79 memory used=5477.6MB, alloc=852.3MB, time=99.38 memory used=5666.3MB, alloc=876.3MB, time=103.54 |\^/| 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(); 1428246300 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 2 F := [-19 x z + y + 11 x z, 4 y z - 8 y z - 3 x, 6 x z - 5 x] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 2 3 3 G := [-z - 6 x z, 6 x z - 6 y + 9 z , -2 x - 2 y + 7] > Problem := [F,G]; 2 3 2 2 Problem := [[-19 x z + y + 11 x z, 4 y z - 8 y z - 3 x, 6 x z - 5 x], 3 2 2 2 3 3 [-z - 6 x z, 6 x z - 6 y + 9 z , -2 x - 2 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=4.4MB, alloc=32.3MB, time=0.18 memory used=26.3MB, alloc=32.3MB, time=0.48 memory used=47.5MB, alloc=32.3MB, time=0.78 memory used=67.6MB, alloc=56.3MB, time=1.10 memory used=110.0MB, alloc=68.3MB, time=1.74 memory used=152.0MB, alloc=68.3MB, time=2.33 memory used=196.2MB, alloc=92.3MB, time=2.89 memory used=265.8MB, alloc=92.3MB, time=3.79 memory used=332.8MB, alloc=116.3MB, time=4.71 memory used=404.1MB, alloc=372.3MB, time=5.72 memory used=496.1MB, alloc=396.3MB, time=6.91 memory used=610.6MB, alloc=396.3MB, time=8.43 memory used=719.3MB, alloc=420.3MB, time=9.96 memory used=854.9MB, alloc=444.3MB, time=11.48 memory used=998.7MB, alloc=468.3MB, time=13.64 memory used=1126.0MB, alloc=468.3MB, time=15.57 memory used=1229.6MB, alloc=492.3MB, time=17.12 memory used=1332.0MB, alloc=492.3MB, time=18.57 memory used=1431.3MB, alloc=492.3MB, time=20.09 memory used=1517.4MB, alloc=492.3MB, time=21.39 memory used=1587.4MB, alloc=492.3MB, time=22.29 memory used=1656.3MB, alloc=516.3MB, time=23.28 memory used=1728.0MB, alloc=516.3MB, time=24.55 memory used=1800.0MB, alloc=516.3MB, time=25.76 memory used=1868.4MB, alloc=516.3MB, time=26.85 memory used=1920.9MB, alloc=516.3MB, time=27.70 memory used=1966.1MB, alloc=516.3MB, time=28.60 memory used=2016.2MB, alloc=540.3MB, time=29.43 memory used=2228.2MB, alloc=564.3MB, time=32.41 memory used=2417.5MB, alloc=588.3MB, time=34.96 memory used=2596.9MB, alloc=612.3MB, time=37.81 memory used=2773.2MB, alloc=636.3MB, time=41.11 memory used=2933.4MB, alloc=636.3MB, time=44.03 memory used=3090.9MB, alloc=660.3MB, time=46.70 memory used=3224.6MB, alloc=660.3MB, time=48.80 memory used=3349.5MB, alloc=660.3MB, time=51.42 memory used=3472.9MB, alloc=660.3MB, time=53.88 memory used=3583.3MB, alloc=660.3MB, time=56.29 memory used=3697.5MB, alloc=660.3MB, time=58.95 memory used=3802.9MB, alloc=660.3MB, time=61.10 memory used=3887.6MB, alloc=660.3MB, time=63.00 memory used=4209.7MB, alloc=684.3MB, time=68.30 memory used=4552.3MB, alloc=708.3MB, time=74.08 memory used=4885.4MB, alloc=732.3MB, time=78.83 memory used=5279.4MB, alloc=756.3MB, time=84.49 memory used=5687.7MB, alloc=780.3MB, time=89.79 memory used=6030.0MB, alloc=804.3MB, time=96.80 memory used=6339.2MB, alloc=828.3MB, time=103.76 memory used=6632.4MB, alloc=852.3MB, time=109.77 |\^/| 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(); 1428246600 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 3 2 F := [-10 x - 7 x y - x, -x - 9 x + 10, 4 y + 5 x - 2 z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 3 3 2 G := [14 x z + 7 x y - 7 x z, 6 x + y z, -6 y - 6 y z - 2] > Problem := [F,G]; 3 2 3 2 Problem := [[-10 x - 7 x y - x, -x - 9 x + 10, 4 y + 5 x - 2 z], 2 2 3 3 2 [14 x z + 7 x y - 7 x z, 6 x + y z, -6 y - 6 y 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=0.49 memory used=46.0MB, alloc=56.3MB, time=0.79 memory used=87.2MB, alloc=60.3MB, time=1.40 memory used=126.5MB, alloc=60.3MB, time=1.97 memory used=165.2MB, alloc=84.3MB, time=2.53 memory used=229.8MB, alloc=92.3MB, time=3.52 memory used=293.9MB, alloc=116.3MB, time=4.47 memory used=367.8MB, alloc=116.3MB, time=5.50 memory used=433.9MB, alloc=372.3MB, time=6.37 memory used=526.0MB, alloc=396.3MB, time=7.55 memory used=637.4MB, alloc=420.3MB, time=9.16 memory used=763.6MB, alloc=444.3MB, time=11.54 memory used=894.1MB, alloc=468.3MB, time=13.92 memory used=1041.5MB, alloc=492.3MB, time=16.57 memory used=1199.6MB, alloc=516.3MB, time=19.45 memory used=1366.8MB, alloc=540.3MB, time=23.71 memory used=1528.1MB, alloc=564.3MB, time=29.22 memory used=1701.0MB, alloc=588.3MB, time=35.52 memory used=1881.9MB, alloc=612.3MB, time=43.08 memory used=2082.7MB, alloc=636.3MB, time=51.60 memory used=2307.4MB, alloc=660.3MB, time=60.99 memory used=2556.1MB, alloc=684.3MB, time=71.48 memory used=2828.7MB, alloc=684.3MB, time=82.89 memory used=3101.2MB, alloc=708.3MB, time=94.37 |\^/| 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(); 1428246900 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 3 2 2 2 F := [7 x z - 9 x z + 20 y , -y - x z, 9 x y - 7 x z - 3 y z ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 3 3 3 G := [-16 x z - 9 x y + 19 x z, -8 x z + 2 y - 4 y z, 9 x - 5 z ] > Problem := [F,G]; 2 2 3 2 2 2 Problem := [[7 x z - 9 x z + 20 y , -y - x z, 9 x y - 7 x z - 3 y z ], 2 2 3 3 3 [-16 x z - 9 x y + 19 x z, -8 x z + 2 y - 4 y z, 9 x - 5 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.0MB, alloc=32.3MB, time=0.50 memory used=45.9MB, alloc=56.3MB, time=0.80 memory used=86.0MB, alloc=60.3MB, time=1.37 memory used=124.8MB, alloc=84.3MB, time=1.98 memory used=164.1MB, alloc=84.3MB, time=2.59 memory used=225.3MB, alloc=92.3MB, time=3.58 memory used=285.7MB, alloc=116.3MB, time=4.57 memory used=369.1MB, alloc=116.3MB, time=5.93 memory used=451.5MB, alloc=140.3MB, time=7.32 memory used=539.4MB, alloc=140.3MB, time=8.89 memory used=617.1MB, alloc=420.3MB, time=10.33 memory used=742.6MB, alloc=444.3MB, time=12.52 memory used=886.3MB, alloc=468.3MB, time=14.80 memory used=1032.0MB, alloc=492.3MB, time=17.23 memory used=1167.1MB, alloc=492.3MB, time=19.44 memory used=1299.2MB, alloc=516.3MB, time=21.73 memory used=1395.9MB, alloc=516.3MB, time=23.41 memory used=1513.0MB, alloc=516.3MB, time=25.70 memory used=1615.9MB, alloc=516.3MB, time=27.72 memory used=1697.0MB, alloc=516.3MB, time=29.10 memory used=1798.8MB, alloc=516.3MB, time=31.14 memory used=1890.8MB, alloc=540.3MB, time=33.09 memory used=1954.8MB, alloc=540.3MB, time=34.44 memory used=2034.8MB, alloc=540.3MB, time=36.12 memory used=2099.2MB, alloc=540.3MB, time=37.47 memory used=2163.2MB, alloc=540.3MB, time=38.55 memory used=2240.5MB, alloc=540.3MB, time=40.49 memory used=2293.2MB, alloc=540.3MB, time=41.64 memory used=2346.7MB, alloc=540.3MB, time=42.71 memory used=2414.5MB, alloc=540.3MB, time=44.78 memory used=2641.5MB, alloc=564.3MB, time=49.41 memory used=2892.0MB, alloc=588.3MB, time=53.91 memory used=3088.1MB, alloc=612.3MB, time=57.61 memory used=3283.3MB, alloc=636.3MB, time=62.38 memory used=3480.4MB, alloc=660.3MB, time=67.12 memory used=3704.1MB, alloc=684.3MB, time=73.08 memory used=3882.3MB, alloc=708.3MB, time=77.93 memory used=4051.3MB, alloc=708.3MB, time=82.65 memory used=4198.6MB, alloc=708.3MB, time=86.71 memory used=4352.4MB, alloc=708.3MB, time=91.36 memory used=4488.9MB, alloc=708.3MB, time=94.53 memory used=4636.1MB, alloc=732.3MB, time=99.11 memory used=4778.6MB, alloc=732.3MB, time=103.31 |\^/| 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(); 1428247201 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 3 2 3 F := [16 x z - 11 x , -8 x y + 5 y + 10 z, -7 x y - 8 z - 9] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; G := [ 2 2 2 2 2 2 2 2 3 -4 x y - 15 x z + 20 y z, 4 x z - 7 y z + 3 z , 8 x y - 7 y z - 7 z ] > Problem := [F,G]; 2 2 2 3 2 3 Problem := [[16 x z - 11 x , -8 x y + 5 y + 10 z, -7 x y - 8 z - 9], [ 2 2 2 2 2 2 2 2 3 -4 x y - 15 x z + 20 y z, 4 x z - 7 y z + 3 z , 8 x y - 7 y 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=26.0MB, alloc=32.3MB, time=0.50 memory used=45.8MB, alloc=56.3MB, time=0.80 memory used=87.5MB, alloc=60.3MB, time=1.40 memory used=128.5MB, alloc=60.3MB, time=1.97 memory used=165.2MB, alloc=84.3MB, time=2.50 memory used=234.9MB, alloc=92.3MB, time=3.48 memory used=299.1MB, alloc=92.3MB, time=4.24 memory used=358.5MB, alloc=92.3MB, time=4.85 memory used=417.3MB, alloc=372.3MB, time=5.63 memory used=503.4MB, alloc=372.3MB, time=6.97 memory used=589.7MB, alloc=396.3MB, time=8.27 memory used=699.0MB, alloc=396.3MB, time=9.79 memory used=808.4MB, alloc=396.3MB, time=11.07 memory used=914.7MB, alloc=420.3MB, time=12.48 memory used=1049.0MB, alloc=420.3MB, time=14.18 memory used=1147.3MB, alloc=420.3MB, time=15.17 memory used=1279.5MB, alloc=444.3MB, time=16.80 memory used=1402.3MB, alloc=444.3MB, time=18.54 memory used=1502.0MB, alloc=468.3MB, time=20.01 memory used=1612.7MB, alloc=468.3MB, time=21.51 memory used=1729.5MB, alloc=468.3MB, time=23.06 memory used=1832.6MB, alloc=492.3MB, time=24.89 memory used=1943.1MB, alloc=492.3MB, time=26.83 memory used=2033.5MB, alloc=492.3MB, time=28.21 memory used=2117.2MB, alloc=492.3MB, time=29.52 memory used=2202.3MB, alloc=516.3MB, time=31.10 memory used=2271.3MB, alloc=516.3MB, time=32.24 memory used=2347.9MB, alloc=516.3MB, time=33.24 memory used=2411.5MB, alloc=516.3MB, time=34.27 memory used=2485.6MB, alloc=516.3MB, time=35.94 memory used=2535.3MB, alloc=516.3MB, time=36.94 memory used=2580.7MB, alloc=540.3MB, time=37.90 memory used=2631.9MB, alloc=540.3MB, time=38.78 memory used=2823.5MB, alloc=540.3MB, time=40.76 memory used=3026.4MB, alloc=564.3MB, time=43.68 memory used=3217.5MB, alloc=588.3MB, time=46.43 memory used=3406.4MB, alloc=612.3MB, time=49.81 memory used=3573.8MB, alloc=636.3MB, time=52.96 memory used=3699.0MB, alloc=636.3MB, time=55.10 memory used=3845.8MB, alloc=636.3MB, time=57.94 memory used=3988.5MB, alloc=636.3MB, time=60.53 memory used=4096.1MB, alloc=660.3MB, time=62.96 memory used=4211.9MB, alloc=660.3MB, time=65.20 memory used=4403.4MB, alloc=660.3MB, time=68.02 memory used=4597.0MB, alloc=660.3MB, time=71.01 memory used=4768.3MB, alloc=660.3MB, time=73.43 memory used=4942.5MB, alloc=660.3MB, time=74.93 memory used=5124.0MB, alloc=660.3MB, time=77.25 memory used=5295.5MB, alloc=660.3MB, time=78.62 memory used=5471.8MB, alloc=660.3MB, time=80.79 memory used=5652.3MB, alloc=660.3MB, time=82.12 memory used=5801.5MB, alloc=660.3MB, time=83.08 memory used=5969.7MB, alloc=660.3MB, time=84.45 memory used=6253.4MB, alloc=660.3MB, time=88.33 memory used=6347.0MB, alloc=660.3MB, time=90.13 memory used=6481.7MB, alloc=684.3MB, time=91.91 memory used=6621.3MB, alloc=708.3MB, time=94.11 memory used=6777.4MB, alloc=708.3MB, time=97.11 memory used=7005.8MB, alloc=708.3MB, time=99.43 memory used=7233.5MB, alloc=708.3MB, time=101.61 memory used=7589.4MB, alloc=732.3MB, time=106.88 memory used=7811.8MB, alloc=756.3MB, time=109.44 memory used=8035.3MB, alloc=756.3MB, time=112.65 memory used=8257.0MB, alloc=756.3MB, time=115.10 memory used=8480.0MB, alloc=756.3MB, time=117.69 memory used=8680.2MB, alloc=756.3MB, time=119.36 |\^/| 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(); 1428247501 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 3 2 F := [-13 z + 19 x z - 9 y , -10 x + 3 x, 10 x y - 4 x y - 4 x] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 G := [x y - 4 y z + 6 x y, -6 x y - 2 y z - 4 x, -7 x y z - 7 y z - 3 z ] > Problem := [F,G]; 3 2 3 2 Problem := [[-13 z + 19 x z - 9 y , -10 x + 3 x, 10 x y - 4 x y - 4 x], 2 2 2 2 [x y - 4 y z + 6 x y, -6 x y - 2 y z - 4 x, -7 x y z - 7 y z - 3 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.2MB, alloc=32.3MB, time=0.47 memory used=47.6MB, alloc=32.3MB, time=0.78 memory used=67.2MB, alloc=32.3MB, time=1.06 memory used=86.0MB, alloc=56.3MB, time=1.35 memory used=124.8MB, alloc=60.3MB, time=1.93 memory used=161.3MB, alloc=84.3MB, time=2.52 memory used=210.7MB, alloc=84.3MB, time=3.31 memory used=270.2MB, alloc=116.3MB, time=4.31 memory used=352.2MB, alloc=116.3MB, time=5.60 memory used=434.6MB, alloc=116.3MB, time=6.95 memory used=509.0MB, alloc=396.3MB, time=8.12 memory used=615.3MB, alloc=396.3MB, time=9.85 memory used=716.1MB, alloc=420.3MB, time=11.64 memory used=842.1MB, alloc=444.3MB, time=13.88 memory used=997.0MB, alloc=444.3MB, time=16.02 memory used=1142.9MB, alloc=468.3MB, time=18.79 memory used=1285.2MB, alloc=492.3MB, time=20.74 memory used=1433.7MB, alloc=492.3MB, time=23.65 memory used=1583.5MB, alloc=516.3MB, time=25.25 memory used=1700.9MB, alloc=516.3MB, time=26.95 memory used=1803.4MB, alloc=516.3MB, time=27.46 memory used=1929.1MB, alloc=516.3MB, time=28.59 memory used=2049.2MB, alloc=516.3MB, time=29.62 memory used=2183.1MB, alloc=516.3MB, time=31.43 memory used=2302.4MB, alloc=516.3MB, time=32.22 memory used=2427.5MB, alloc=516.3MB, time=33.27 memory used=2575.9MB, alloc=516.3MB, time=34.78 memory used=2736.8MB, alloc=516.3MB, time=37.08 memory used=2886.5MB, alloc=540.3MB, time=39.39 memory used=3024.2MB, alloc=540.3MB, time=41.41 memory used=3158.8MB, alloc=540.3MB, time=43.73 memory used=3295.9MB, alloc=564.3MB, time=46.04 memory used=3449.3MB, alloc=564.3MB, time=48.31 memory used=3637.2MB, alloc=588.3MB, time=50.68 memory used=3906.8MB, alloc=588.3MB, time=52.71 memory used=4081.0MB, alloc=588.3MB, time=54.94 memory used=4199.3MB, alloc=588.3MB, time=56.82 memory used=4344.1MB, alloc=612.3MB, time=59.60 memory used=4486.2MB, alloc=636.3MB, time=62.51 memory used=4614.5MB, alloc=660.3MB, time=65.09 memory used=4747.6MB, alloc=684.3MB, time=67.82 memory used=4872.0MB, alloc=708.3MB, time=70.36 memory used=5000.2MB, alloc=732.3MB, time=73.01 memory used=5118.8MB, alloc=732.3MB, time=75.47 memory used=5213.5MB, alloc=756.3MB, time=77.62 memory used=5318.7MB, alloc=780.3MB, time=79.96 memory used=5418.8MB, alloc=780.3MB, time=82.20 memory used=5526.4MB, alloc=804.3MB, time=84.69 memory used=5605.6MB, alloc=804.3MB, time=86.52 memory used=5708.8MB, alloc=828.3MB, time=88.79 memory used=5798.2MB, alloc=828.3MB, time=90.96 memory used=5862.3MB, alloc=828.3MB, time=92.75 memory used=5952.1MB, alloc=852.3MB, time=95.19 memory used=6028.4MB, alloc=876.3MB, time=97.31 memory used=6130.1MB, alloc=876.3MB, time=99.53 memory used=6198.2MB, alloc=876.3MB, time=101.33 memory used=6278.8MB, alloc=900.3MB, time=103.42 memory used=6652.2MB, alloc=924.3MB, time=109.90 |\^/| 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(); 1428247801 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 2 3 2 2 F := [9 x z + 2 z - z , -3 x y - 6 z - 2 y, 4 y - 3 y - 2 z ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 2 2 2 2 G := [-13 x y + 3 x z + 7 z , 5 y z + 7 x - 9 x y, 4 x y + x z + 8 y z ] > Problem := [F,G]; 2 3 2 2 3 2 2 Problem := [[9 x z + 2 z - z , -3 x y - 6 z - 2 y, 4 y - 3 y - 2 z ], 2 2 2 2 2 2 2 2 [-13 x y + 3 x z + 7 z , 5 y z + 7 x - 9 x y, 4 x y + x z + 8 y z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.3MB, alloc=32.3MB, time=0.49 memory used=47.1MB, alloc=32.3MB, time=0.79 memory used=65.9MB, alloc=56.3MB, time=1.10 memory used=104.6MB, alloc=60.3MB, time=1.68 memory used=141.7MB, alloc=84.3MB, time=2.24 memory used=200.0MB, alloc=92.3MB, time=3.14 memory used=257.1MB, alloc=92.3MB, time=4.00 memory used=314.9MB, alloc=116.3MB, time=4.91 memory used=392.8MB, alloc=396.3MB, time=6.15 memory used=492.7MB, alloc=396.3MB, time=7.86 memory used=593.3MB, alloc=420.3MB, time=9.59 memory used=718.0MB, alloc=420.3MB, time=11.81 memory used=840.9MB, alloc=444.3MB, time=14.02 memory used=986.8MB, alloc=468.3MB, time=16.79 memory used=1148.1MB, alloc=492.3MB, time=19.67 memory used=1298.3MB, alloc=516.3MB, time=22.55 memory used=1434.1MB, alloc=516.3MB, time=25.08 memory used=1542.8MB, alloc=516.3MB, time=27.21 memory used=1677.6MB, alloc=540.3MB, time=29.98 memory used=1789.5MB, alloc=540.3MB, time=32.06 memory used=1891.6MB, alloc=540.3MB, time=34.36 memory used=1979.1MB, alloc=540.3MB, time=36.18 memory used=2082.4MB, alloc=564.3MB, time=38.88 memory used=2171.0MB, alloc=564.3MB, time=40.91 memory used=2255.4MB, alloc=564.3MB, time=42.91 memory used=2319.2MB, alloc=564.3MB, time=44.60 memory used=2412.8MB, alloc=564.3MB, time=47.38 memory used=2492.6MB, alloc=564.3MB, time=49.72 memory used=2554.0MB, alloc=564.3MB, time=51.31 memory used=2593.2MB, alloc=588.3MB, time=52.32 memory used=2835.7MB, alloc=612.3MB, time=57.66 memory used=3096.0MB, alloc=636.3MB, time=64.20 memory used=3334.0MB, alloc=660.3MB, time=69.70 memory used=3531.9MB, alloc=684.3MB, time=74.46 memory used=3725.6MB, alloc=708.3MB, time=79.30 memory used=3900.5MB, alloc=708.3MB, time=83.65 memory used=4027.4MB, alloc=732.3MB, time=86.25 memory used=4170.2MB, alloc=732.3MB, time=90.61 memory used=4342.9MB, alloc=732.3MB, time=95.52 |\^/| 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(); 1428248101 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 3 3 2 2 F := [9 z + 14 y - 20 y, -x y + 6 z + 6 y, -4 y + 4 y + 3 z ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 2 2 G := [7 x + 3 x z, -x y + 2 y - 2 z , -3 x y - 10 y - 8 y z] > Problem := [F,G]; 3 2 2 3 3 2 2 Problem := [[9 z + 14 y - 20 y, -x y + 6 z + 6 y, -4 y + 4 y + 3 z ], 3 2 2 2 2 [7 x + 3 x z, -x y + 2 y - 2 z , -3 x y - 10 y - 8 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.9MB, alloc=32.3MB, time=0.50 memory used=46.8MB, alloc=32.3MB, time=0.79 memory used=65.6MB, alloc=56.3MB, time=1.08 memory used=104.1MB, alloc=60.3MB, time=1.66 memory used=141.0MB, alloc=84.3MB, time=2.23 memory used=202.6MB, alloc=92.3MB, time=3.18 memory used=261.4MB, alloc=116.3MB, time=4.19 memory used=342.6MB, alloc=116.3MB, time=5.49 memory used=419.4MB, alloc=140.3MB, time=6.77 memory used=499.8MB, alloc=140.3MB, time=8.08 memory used=571.5MB, alloc=420.3MB, time=9.30 memory used=698.8MB, alloc=444.3MB, time=11.41 memory used=853.1MB, alloc=468.3MB, time=14.02 memory used=1013.8MB, alloc=492.3MB, time=16.94 memory used=1164.1MB, alloc=492.3MB, time=19.77 memory used=1321.4MB, alloc=516.3MB, time=22.93 memory used=1469.2MB, alloc=516.3MB, time=26.09 memory used=1608.0MB, alloc=540.3MB, time=29.19 memory used=1712.5MB, alloc=540.3MB, time=31.26 memory used=1833.1MB, alloc=540.3MB, time=33.84 memory used=1934.0MB, alloc=540.3MB, time=35.91 memory used=2027.3MB, alloc=540.3MB, time=37.84 memory used=2132.4MB, alloc=540.3MB, time=40.37 memory used=2221.5MB, alloc=540.3MB, time=42.48 memory used=2296.2MB, alloc=540.3MB, time=44.23 memory used=2382.3MB, alloc=540.3MB, time=46.51 memory used=2465.4MB, alloc=564.3MB, time=48.55 memory used=2535.5MB, alloc=564.3MB, time=50.27 memory used=2601.0MB, alloc=564.3MB, time=51.84 memory used=2661.0MB, alloc=564.3MB, time=53.26 memory used=2727.3MB, alloc=564.3MB, time=54.42 memory used=2784.3MB, alloc=564.3MB, time=55.89 memory used=2853.5MB, alloc=564.3MB, time=57.88 memory used=2898.7MB, alloc=564.3MB, time=59.11 memory used=2942.1MB, alloc=564.3MB, time=60.32 memory used=3179.8MB, alloc=588.3MB, time=65.57 memory used=3438.7MB, alloc=612.3MB, time=71.40 memory used=3660.1MB, alloc=636.3MB, time=76.16 memory used=3890.4MB, alloc=660.3MB, time=81.57 memory used=4149.4MB, alloc=684.3MB, time=88.43 memory used=4325.7MB, alloc=708.3MB, time=92.12 memory used=4535.2MB, alloc=732.3MB, time=97.25 |\^/| 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(); 1428248401 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 3 3 F := [9 y - 10 y z - 17 y z, 6 y + x y - 8 z, 7 x - 10 z - 8] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 3 2 2 G := [18 x y + 17 x, 8 x z - 4 y + y z, 9 x y + 2 y + 4 y z] > Problem := [F,G]; 3 2 3 3 Problem := [[9 y - 10 y z - 17 y z, 6 y + x y - 8 z, 7 x - 10 z - 8], 2 2 3 2 2 [18 x y + 17 x, 8 x z - 4 y + y z, 9 x y + 2 y + 4 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.8MB, alloc=32.3MB, time=0.50 memory used=46.9MB, alloc=32.3MB, time=0.80 memory used=65.8MB, alloc=56.3MB, time=1.09 memory used=106.9MB, alloc=68.3MB, time=1.72 memory used=147.3MB, alloc=92.3MB, time=2.33 memory used=213.0MB, alloc=92.3MB, time=3.33 memory used=277.7MB, alloc=116.3MB, time=4.29 memory used=346.7MB, alloc=116.3MB, time=5.37 memory used=413.9MB, alloc=372.3MB, time=6.37 memory used=498.7MB, alloc=396.3MB, time=7.65 memory used=608.0MB, alloc=420.3MB, time=9.32 memory used=737.6MB, alloc=444.3MB, time=11.30 memory used=857.5MB, alloc=468.3MB, time=13.22 memory used=972.0MB, alloc=468.3MB, time=14.99 memory used=1070.8MB, alloc=468.3MB, time=16.73 memory used=1154.7MB, alloc=468.3MB, time=18.16 memory used=1245.9MB, alloc=492.3MB, time=19.63 memory used=1330.8MB, alloc=492.3MB, time=20.95 memory used=1408.6MB, alloc=492.3MB, time=22.26 memory used=1471.4MB, alloc=492.3MB, time=23.42 memory used=1531.5MB, alloc=492.3MB, time=24.49 memory used=1594.0MB, alloc=516.3MB, time=25.88 memory used=1639.8MB, alloc=516.3MB, time=26.90 memory used=1692.4MB, alloc=516.3MB, time=28.01 memory used=1901.6MB, alloc=540.3MB, time=31.36 memory used=2063.3MB, alloc=564.3MB, time=34.12 memory used=2254.7MB, alloc=588.3MB, time=37.88 memory used=2415.4MB, alloc=612.3MB, time=40.79 memory used=2563.6MB, alloc=612.3MB, time=43.85 memory used=2706.2MB, alloc=636.3MB, time=46.46 memory used=2848.2MB, alloc=636.3MB, time=49.25 memory used=2965.8MB, alloc=636.3MB, time=51.95 memory used=3075.7MB, alloc=636.3MB, time=54.55 memory used=3185.0MB, alloc=636.3MB, time=56.94 memory used=3502.6MB, alloc=660.3MB, time=62.90 memory used=3835.9MB, alloc=684.3MB, time=69.67 memory used=4183.9MB, alloc=708.3MB, time=77.06 memory used=4530.0MB, alloc=732.3MB, time=84.07 memory used=4864.1MB, alloc=756.3MB, time=91.62 memory used=5195.6MB, alloc=780.3MB, time=98.95 memory used=5438.9MB, alloc=804.3MB, time=104.35 memory used=5690.4MB, alloc=828.3MB, time=109.66 |\^/| 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(); 1428248701 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 F := [-6 y + 11 x y - 20 x, -x y z - 5 x z - 1, -4 x y z - 6 y z - 4 x] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 3 2 3 3 G := [-3 y - 11 x , 3 y + y z , -9 y - 6 z + 5] > Problem := [F,G]; Problem := [ 3 2 [-6 y + 11 x y - 20 x, -x y z - 5 x z - 1, -4 x y z - 6 y z - 4 x], 3 2 3 2 3 3 [-3 y - 11 x , 3 y + y z , -9 y - 6 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=26.0MB, alloc=32.3MB, time=0.53 memory used=46.7MB, alloc=32.3MB, time=0.86 memory used=66.1MB, alloc=56.3MB, time=1.17 memory used=105.1MB, alloc=60.3MB, time=1.76 memory used=143.0MB, alloc=84.3MB, time=2.34 memory used=204.6MB, alloc=92.3MB, time=3.29 memory used=267.1MB, alloc=92.3MB, time=4.13 memory used=328.8MB, alloc=92.3MB, time=4.99 memory used=393.8MB, alloc=116.3MB, time=5.89 memory used=463.5MB, alloc=116.3MB, time=6.90 memory used=544.5MB, alloc=140.3MB, time=8.20 memory used=611.5MB, alloc=140.3MB, time=9.24 memory used=675.4MB, alloc=396.3MB, time=10.26 memory used=778.3MB, alloc=396.3MB, time=11.88 memory used=884.5MB, alloc=420.3MB, time=13.31 memory used=1014.4MB, alloc=444.3MB, time=14.97 memory used=1144.4MB, alloc=444.3MB, time=16.57 memory used=1276.0MB, alloc=468.3MB, time=18.29 memory used=1382.5MB, alloc=468.3MB, time=19.67 memory used=1516.8MB, alloc=468.3MB, time=21.44 memory used=1645.6MB, alloc=468.3MB, time=22.72 memory used=1729.2MB, alloc=492.3MB, time=23.79 memory used=1826.7MB, alloc=492.3MB, time=25.40 memory used=1941.6MB, alloc=492.3MB, time=27.10 memory used=2084.5MB, alloc=492.3MB, time=28.14 memory used=2216.2MB, alloc=492.3MB, time=29.28 memory used=2348.8MB, alloc=492.3MB, time=30.47 memory used=2486.9MB, alloc=492.3MB, time=31.70 memory used=2563.6MB, alloc=492.3MB, time=32.84 memory used=2640.4MB, alloc=492.3MB, time=33.87 memory used=2717.5MB, alloc=492.3MB, time=34.85 memory used=2786.5MB, alloc=492.3MB, time=36.24 memory used=2878.8MB, alloc=492.3MB, time=37.98 memory used=3017.7MB, alloc=516.3MB, time=39.95 memory used=3086.2MB, alloc=516.3MB, time=41.04 memory used=3129.9MB, alloc=516.3MB, time=41.90 memory used=3198.6MB, alloc=516.3MB, time=43.29 memory used=3247.2MB, alloc=516.3MB, time=44.16 memory used=3303.8MB, alloc=516.3MB, time=45.35 memory used=3342.1MB, alloc=516.3MB, time=46.33 memory used=3386.1MB, alloc=516.3MB, time=47.27 memory used=3449.4MB, alloc=516.3MB, time=48.29 memory used=3576.9MB, alloc=516.3MB, time=48.96 memory used=3688.0MB, alloc=516.3MB, time=52.29 memory used=3757.2MB, alloc=516.3MB, time=53.50 memory used=3782.7MB, alloc=516.3MB, time=54.25 memory used=3968.0MB, alloc=516.3MB, time=58.19 memory used=4161.3MB, alloc=540.3MB, time=61.00 memory used=4372.1MB, alloc=564.3MB, time=64.63 memory used=4527.0MB, alloc=564.3MB, time=65.65 memory used=4672.3MB, alloc=564.3MB, time=69.19 memory used=4812.2MB, alloc=564.3MB, time=70.65 memory used=4995.4MB, alloc=564.3MB, time=74.14 memory used=5113.5MB, alloc=564.3MB, time=74.87 memory used=5238.8MB, alloc=564.3MB, time=75.80 memory used=5447.4MB, alloc=564.3MB, time=78.51 memory used=5636.4MB, alloc=588.3MB, time=81.88 memory used=5808.0MB, alloc=588.3MB, time=85.76 memory used=5957.9MB, alloc=588.3MB, time=88.50 memory used=6150.2MB, alloc=612.3MB, time=91.81 memory used=6367.7MB, alloc=612.3MB, time=96.78 memory used=6598.0MB, alloc=612.3MB, time=99.02 memory used=6803.5MB, alloc=636.3MB, time=105.93 memory used=6978.3MB, alloc=636.3MB, time=116.56 memory used=7135.1MB, alloc=636.3MB, time=117.38 memory used=7247.6MB, alloc=636.3MB, time=118.12 memory used=7374.2MB, alloc=636.3MB, time=118.90 memory used=7520.1MB, alloc=636.3MB, time=119.71 memory used=7689.6MB, alloc=636.3MB, time=120.52 memory used=7890.0MB, alloc=636.3MB, time=121.48 memory used=8022.2MB, alloc=636.3MB, time=122.23 memory used=8168.8MB, alloc=636.3MB, time=123.00 memory used=8330.4MB, alloc=636.3MB, time=123.75 memory used=8516.0MB, alloc=636.3MB, time=124.53 memory used=8723.0MB, alloc=636.3MB, time=126.97 memory used=8872.9MB, alloc=636.3MB, time=129.31 memory used=8991.2MB, alloc=636.3MB, time=131.45 memory used=9174.5MB, alloc=636.3MB, time=133.07 memory used=9329.3MB, alloc=636.3MB, time=134.15 memory used=9470.9MB, alloc=636.3MB, time=135.12 memory used=9618.0MB, alloc=636.3MB, time=136.24 memory used=9767.3MB, alloc=636.3MB, time=137.23 memory used=9912.1MB, alloc=636.3MB, time=138.17 memory used=10053.7MB, alloc=636.3MB, time=139.03 memory used=10193.9MB, alloc=636.3MB, time=140.05 |\^/| 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(); 1428249001 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 F := [18 x y z - 15 y + 14, 4 x + 6 z - 5, -9 x y + 10 y - y z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 2 G := [20 x y - 15 z + 8 z, x y - x z + 5 x z, -2 x y - 8 x y z - 7 z] > Problem := [F,G]; 3 2 2 Problem := [[18 x y z - 15 y + 14, 4 x + 6 z - 5, -9 x y + 10 y - y z], 2 2 2 2 2 [20 x y - 15 z + 8 z, x y - x z + 5 x z, -2 x y - 8 x y 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=47.7MB, alloc=32.3MB, time=0.82 memory used=66.9MB, alloc=56.3MB, time=1.12 memory used=108.5MB, alloc=60.3MB, time=1.75 memory used=149.6MB, alloc=60.3MB, time=2.36 memory used=188.8MB, alloc=84.3MB, time=2.96 memory used=227.3MB, alloc=84.3MB, time=3.57 memory used=288.4MB, alloc=116.3MB, time=4.55 memory used=368.3MB, alloc=372.3MB, time=5.83 memory used=454.8MB, alloc=396.3MB, time=7.15 memory used=562.3MB, alloc=420.3MB, time=8.86 memory used=695.1MB, alloc=444.3MB, time=11.01 memory used=852.6MB, alloc=468.3MB, time=13.64 memory used=982.7MB, alloc=468.3MB, time=15.87 memory used=1110.4MB, alloc=468.3MB, time=18.01 memory used=1239.6MB, alloc=492.3MB, time=20.65 memory used=1344.0MB, alloc=492.3MB, time=22.67 memory used=1461.2MB, alloc=492.3MB, time=25.07 memory used=1569.9MB, alloc=492.3MB, time=27.39 memory used=1664.5MB, alloc=516.3MB, time=29.33 memory used=1764.6MB, alloc=516.3MB, time=31.53 memory used=1844.2MB, alloc=516.3MB, time=33.28 memory used=1921.5MB, alloc=516.3MB, time=34.96 memory used=1988.6MB, alloc=516.3MB, time=36.60 memory used=2044.2MB, alloc=516.3MB, time=38.03 memory used=2108.4MB, alloc=516.3MB, time=39.63 memory used=2174.4MB, alloc=516.3MB, time=41.27 memory used=2224.6MB, alloc=516.3MB, time=42.38 memory used=2288.2MB, alloc=516.3MB, time=44.11 memory used=2493.1MB, alloc=540.3MB, time=48.66 memory used=2720.7MB, alloc=564.3MB, time=53.75 memory used=2948.1MB, alloc=588.3MB, time=58.65 memory used=3146.5MB, alloc=612.3MB, time=63.21 memory used=3355.6MB, alloc=636.3MB, time=68.29 memory used=3541.0MB, alloc=660.3MB, time=72.62 memory used=3707.6MB, alloc=684.3MB, time=76.74 memory used=3868.6MB, alloc=708.3MB, time=80.72 memory used=4021.5MB, alloc=708.3MB, time=84.77 memory used=4130.9MB, alloc=708.3MB, time=87.76 memory used=4282.7MB, alloc=708.3MB, time=91.94 memory used=4378.5MB, alloc=708.3MB, time=94.59 memory used=4471.5MB, alloc=732.3MB, time=96.83 memory used=4866.0MB, alloc=756.3MB, time=107.04 |\^/| 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(); 1428249301 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 2 2 2 F := [-8 x z + 4 y + 9 x z, -9 y z - 5 y + 5 x, -4 x y + 5 y - 9] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 G := [-15 x z - x y + 10 y z, -7 x y z + 8 x, -4 y z + 8 y z + 6 x ] > Problem := [F,G]; 2 3 2 2 2 2 Problem := [[-8 x z + 4 y + 9 x z, -9 y z - 5 y + 5 x, -4 x y + 5 y - 9], 2 2 2 2 [-15 x z - x y + 10 y z, -7 x y z + 8 x, -4 y z + 8 y z + 6 x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=25.1MB, alloc=32.3MB, time=0.47 memory used=43.9MB, alloc=32.3MB, time=0.75 memory used=63.1MB, alloc=56.3MB, time=1.03 memory used=109.8MB, alloc=68.5MB, time=1.61 memory used=152.9MB, alloc=68.5MB, time=2.25 memory used=195.2MB, alloc=68.5MB, time=2.86 memory used=237.6MB, alloc=92.5MB, time=3.45 memory used=309.9MB, alloc=92.5MB, time=4.36 memory used=373.8MB, alloc=92.5MB, time=5.32 memory used=437.2MB, alloc=116.5MB, time=6.23 memory used=518.9MB, alloc=372.5MB, time=7.37 memory used=605.1MB, alloc=372.5MB, time=8.53 memory used=693.3MB, alloc=396.5MB, time=9.83 memory used=808.5MB, alloc=420.5MB, time=11.34 memory used=927.0MB, alloc=420.5MB, time=13.11 memory used=1059.4MB, alloc=420.5MB, time=14.79 memory used=1145.3MB, alloc=420.5MB, time=15.53 memory used=1258.3MB, alloc=444.5MB, time=17.30 memory used=1386.0MB, alloc=444.5MB, time=18.97 memory used=1510.4MB, alloc=444.5MB, time=20.12 memory used=1597.5MB, alloc=444.5MB, time=21.99 memory used=1693.5MB, alloc=444.5MB, time=23.83 memory used=1793.8MB, alloc=444.5MB, time=25.59 memory used=1909.4MB, alloc=444.5MB, time=28.59 memory used=2028.7MB, alloc=468.5MB, time=30.19 memory used=2165.0MB, alloc=468.5MB, time=32.67 memory used=2263.7MB, alloc=468.5MB, time=33.23 memory used=2366.8MB, alloc=468.5MB, time=35.18 memory used=2520.4MB, alloc=468.5MB, time=39.30 memory used=2653.1MB, alloc=468.5MB, time=41.94 memory used=2761.1MB, alloc=468.5MB, time=43.67 memory used=2884.6MB, alloc=468.5MB, time=45.50 memory used=2994.5MB, alloc=492.5MB, time=47.80 memory used=3091.5MB, alloc=492.5MB, time=49.26 memory used=3176.2MB, alloc=492.5MB, time=50.77 memory used=3305.6MB, alloc=492.5MB, time=52.49 memory used=3450.9MB, alloc=516.5MB, time=56.38 memory used=3532.7MB, alloc=516.5MB, time=57.70 memory used=3620.7MB, alloc=516.5MB, time=59.13 memory used=3699.7MB, alloc=516.5MB, time=61.21 memory used=3762.0MB, alloc=516.5MB, time=62.39 memory used=3879.2MB, alloc=516.5MB, time=64.04 memory used=4021.2MB, alloc=516.5MB, time=66.80 memory used=4093.5MB, alloc=516.5MB, time=68.77 memory used=4161.6MB, alloc=516.5MB, time=69.96 memory used=4232.7MB, alloc=516.5MB, time=71.48 memory used=4284.1MB, alloc=516.5MB, time=72.54 memory used=4338.7MB, alloc=516.5MB, time=73.73 memory used=4474.5MB, alloc=540.5MB, time=75.84 memory used=4665.0MB, alloc=540.5MB, time=77.45 memory used=4881.6MB, alloc=564.5MB, time=81.19 memory used=5123.4MB, alloc=588.5MB, time=85.46 memory used=5375.4MB, alloc=588.5MB, time=89.56 memory used=5608.8MB, alloc=612.5MB, time=92.64 memory used=5792.0MB, alloc=636.5MB, time=96.08 memory used=6042.1MB, alloc=660.5MB, time=100.70 memory used=6220.8MB, alloc=660.5MB, time=104.03 memory used=6382.0MB, alloc=684.5MB, time=106.58 memory used=6599.1MB, alloc=684.5MB, time=109.99 memory used=6773.0MB, alloc=684.5MB, time=112.66 memory used=6957.4MB, alloc=684.5MB, time=115.50 memory used=7173.6MB, alloc=684.5MB, time=118.72 memory used=7438.1MB, alloc=684.5MB, time=122.69 memory used=7714.0MB, alloc=684.5MB, time=130.75 memory used=7878.7MB, alloc=684.5MB, time=131.85 memory used=8248.0MB, alloc=708.5MB, time=134.33 |\^/| 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(); 1428249601 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 2 2 3 F := [15 z - 14 x + 17 z, 10 x z - 8 x - 9 z , 4 x z - 5 y + 10 x] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 G := [-14 x y + 8 y z + 7, -x y - 6 y z - x z, 4 x y z - 10 y + 3 z] > Problem := [F,G]; 3 2 2 2 2 3 Problem := [[15 z - 14 x + 17 z, 10 x z - 8 x - 9 z , 4 x z - 5 y + 10 x], 2 2 2 2 [-14 x y + 8 y z + 7, -x y - 6 y z - x z, 4 x y z - 10 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=4.2MB, alloc=32.3MB, time=0.17 memory used=26.2MB, alloc=32.3MB, time=0.51 memory used=45.2MB, alloc=60.3MB, time=0.80 memory used=89.5MB, alloc=60.3MB, time=1.27 memory used=122.0MB, alloc=61.2MB, time=1.37 memory used=160.4MB, alloc=63.6MB, time=2.35 memory used=187.4MB, alloc=63.6MB, time=2.42 memory used=213.5MB, alloc=63.6MB, time=2.52 memory used=273.7MB, alloc=71.6MB, time=3.04 memory used=336.7MB, alloc=71.6MB, time=3.86 memory used=397.1MB, alloc=71.6MB, time=4.85 memory used=452.9MB, alloc=71.6MB, time=5.97 memory used=509.9MB, alloc=71.6MB, time=6.49 memory used=567.4MB, alloc=71.6MB, time=7.02 memory used=612.1MB, alloc=71.6MB, time=7.54 memory used=644.7MB, alloc=71.6MB, time=7.76 memory used=690.6MB, alloc=71.6MB, time=8.11 memory used=745.5MB, alloc=71.6MB, time=8.56 memory used=792.5MB, alloc=71.6MB, time=9.13 memory used=831.4MB, alloc=95.6MB, time=9.75 memory used=898.0MB, alloc=95.6MB, time=10.71 memory used=951.4MB, alloc=375.6MB, time=11.46 memory used=1041.6MB, alloc=399.6MB, time=12.68 memory used=1121.5MB, alloc=399.6MB, time=13.31 memory used=1197.6MB, alloc=399.6MB, time=13.74 memory used=1262.4MB, alloc=399.6MB, time=14.07 memory used=1334.2MB, alloc=399.6MB, time=14.51 memory used=1397.4MB, alloc=399.6MB, time=14.80 memory used=1475.4MB, alloc=399.6MB, time=15.29 memory used=1550.9MB, alloc=399.6MB, time=16.24 memory used=1600.3MB, alloc=399.6MB, time=16.43 memory used=1679.7MB, alloc=399.6MB, time=17.43 memory used=1732.3MB, alloc=399.6MB, time=17.64 memory used=1793.0MB, alloc=399.6MB, time=17.94 memory used=1929.3MB, alloc=399.6MB, time=20.77 memory used=2067.6MB, alloc=399.6MB, time=23.02 memory used=2174.4MB, alloc=399.6MB, time=25.26 memory used=2300.6MB, alloc=399.6MB, time=26.54 memory used=2425.3MB, alloc=399.6MB, time=28.91 memory used=2513.8MB, alloc=399.6MB, time=30.18 memory used=2628.5MB, alloc=423.6MB, time=31.39 memory used=2796.2MB, alloc=423.6MB, time=35.29 memory used=2957.9MB, alloc=423.6MB, time=37.58 memory used=3081.8MB, alloc=423.6MB, time=39.23 memory used=3159.4MB, alloc=423.6MB, time=39.63 memory used=3241.9MB, alloc=423.6MB, time=40.05 memory used=3330.0MB, alloc=423.6MB, time=40.56 memory used=3422.3MB, alloc=423.6MB, time=41.66 memory used=3482.1MB, alloc=423.6MB, time=41.89 memory used=3572.1MB, alloc=423.6MB, time=42.96 memory used=3632.0MB, alloc=423.6MB, time=43.22 memory used=3740.2MB, alloc=423.6MB, time=44.16 memory used=3874.0MB, alloc=423.6MB, time=45.57 memory used=4010.2MB, alloc=423.6MB, time=46.90 memory used=4141.8MB, alloc=423.6MB, time=48.38 memory used=4272.0MB, alloc=423.6MB, time=50.12 memory used=4374.8MB, alloc=447.6MB, time=51.36 memory used=4478.9MB, alloc=447.6MB, time=52.69 memory used=4613.2MB, alloc=447.6MB, time=53.81 memory used=4709.6MB, alloc=447.6MB, time=54.56 memory used=4796.0MB, alloc=447.6MB, time=55.27 memory used=4877.4MB, alloc=447.6MB, time=55.75 memory used=4968.2MB, alloc=447.6MB, time=56.23 memory used=5051.5MB, alloc=447.6MB, time=56.76 memory used=5138.5MB, alloc=447.6MB, time=57.27 memory used=5221.7MB, alloc=447.6MB, time=57.72 memory used=5311.4MB, alloc=447.6MB, time=58.25 memory used=5404.5MB, alloc=447.6MB, time=59.22 memory used=5462.1MB, alloc=447.6MB, time=59.52 memory used=5562.7MB, alloc=447.6MB, time=60.58 memory used=5627.6MB, alloc=447.6MB, time=60.93 memory used=5690.7MB, alloc=447.6MB, time=61.22 memory used=5794.9MB, alloc=447.6MB, time=62.43 memory used=5893.1MB, alloc=447.6MB, time=63.45 memory used=6013.6MB, alloc=471.6MB, time=64.45 memory used=6130.0MB, alloc=471.6MB, time=65.65 memory used=6240.4MB, alloc=471.6MB, time=66.83 memory used=6344.2MB, alloc=471.6MB, time=67.87 memory used=6424.9MB, alloc=471.6MB, time=69.21 memory used=6502.2MB, alloc=471.6MB, time=70.56 memory used=6572.7MB, alloc=495.6MB, time=71.83 memory used=6633.6MB, alloc=495.6MB, time=72.94 memory used=6699.3MB, alloc=495.6MB, time=74.02 memory used=6767.6MB, alloc=495.6MB, time=75.20 memory used=6832.4MB, alloc=495.6MB, time=76.20 memory used=6896.2MB, alloc=495.6MB, time=77.06 memory used=6945.3MB, alloc=495.6MB, time=78.02 memory used=6994.2MB, alloc=495.6MB, time=79.05 memory used=7045.7MB, alloc=495.6MB, time=80.05 memory used=7094.1MB, alloc=495.6MB, time=80.93 memory used=7296.2MB, alloc=519.6MB, time=83.82 memory used=7494.5MB, alloc=543.6MB, time=86.18 memory used=7715.6MB, alloc=543.6MB, time=89.02 memory used=7860.5MB, alloc=543.6MB, time=90.50 memory used=8078.3MB, alloc=567.6MB, time=93.11 memory used=8306.2MB, alloc=567.6MB, time=95.06 memory used=8422.8MB, alloc=567.6MB, time=95.80 memory used=8539.3MB, alloc=567.6MB, time=96.54 memory used=8658.3MB, alloc=567.6MB, time=97.36 memory used=8761.9MB, alloc=567.6MB, time=97.97 memory used=8881.5MB, alloc=567.6MB, time=98.71 memory used=8986.9MB, alloc=567.6MB, time=99.36 memory used=9104.9MB, alloc=567.6MB, time=100.18 memory used=9212.0MB, alloc=567.6MB, time=100.82 memory used=9333.3MB, alloc=567.6MB, time=101.47 memory used=9532.0MB, alloc=567.6MB, time=102.71 memory used=9629.3MB, alloc=567.6MB, time=103.31 memory used=9749.4MB, alloc=567.6MB, time=104.14 memory used=9854.1MB, alloc=567.6MB, time=104.74 memory used=9976.7MB, alloc=567.6MB, time=105.60 memory used=10080.7MB, alloc=567.6MB, time=106.23 memory used=10292.7MB, alloc=567.6MB, time=107.22 memory used=10415.8MB, alloc=567.6MB, time=108.16 memory used=10515.1MB, alloc=567.6MB, time=108.75 memory used=10638.6MB, alloc=567.6MB, time=109.53 memory used=10760.1MB, alloc=567.6MB, time=110.25 memory used=10896.9MB, alloc=567.6MB, time=113.04 memory used=10996.1MB, alloc=567.6MB, time=113.68 memory used=11106.5MB, alloc=567.6MB, time=114.31 memory used=11343.6MB, alloc=567.6MB, time=115.24 memory used=11498.5MB, alloc=567.6MB, time=115.92 memory used=11686.0MB, alloc=567.6MB, time=116.63 memory used=11917.7MB, alloc=567.6MB, time=117.61 memory used=12053.1MB, alloc=567.6MB, time=120.43 memory used=12160.5MB, alloc=567.6MB, time=121.11 memory used=12256.3MB, alloc=567.6MB, time=121.72 memory used=12380.7MB, alloc=567.6MB, time=122.35 memory used=12553.1MB, alloc=567.6MB, time=123.09 memory used=12708.4MB, alloc=567.6MB, time=123.81 memory used=12896.6MB, alloc=567.6MB, time=124.57 memory used=13112.5MB, alloc=567.6MB, time=125.51 memory used=13252.1MB, alloc=567.6MB, time=126.83 memory used=13373.8MB, alloc=567.6MB, time=127.72 memory used=13515.8MB, alloc=567.6MB, time=128.43 memory used=13638.4MB, alloc=567.6MB, time=129.19 memory used=13761.8MB, alloc=567.6MB, time=130.19 memory used=13867.6MB, alloc=567.6MB, time=130.83 memory used=14117.7MB, alloc=591.6MB, time=133.12 memory used=14347.0MB, alloc=591.6MB, time=135.04 memory used=14492.9MB, alloc=591.6MB, time=136.30 memory used=14682.7MB, alloc=591.6MB, time=138.62 memory used=14824.1MB, alloc=591.6MB, time=139.86 memory used=15004.2MB, alloc=591.6MB, time=141.20 memory used=15246.6MB, alloc=591.6MB, time=145.24 memory used=15491.8MB, alloc=591.6MB, time=148.25 memory used=15632.8MB, alloc=591.6MB, time=149.57 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428249901 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 2 2 2 2 3 F := [11 x y - 20 z + 14 x , -x z - 5 x z + 4 y, x y - 10 x z + 2 y ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 3 G := [-8 y z - 11 y + 20 z, 5 x z + 9 y z + 2 x y, 10 y + 7 x y] > Problem := [F,G]; Problem := [ 2 3 2 2 2 2 2 3 [11 x y - 20 z + 14 x , -x z - 5 x z + 4 y, x y - 10 x z + 2 y ], 2 2 3 [-8 y z - 11 y + 20 z, 5 x z + 9 y z + 2 x y, 10 y + 7 x y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.3MB, alloc=32.3MB, time=0.49 memory used=45.3MB, alloc=56.3MB, time=0.78 memory used=87.3MB, alloc=60.3MB, time=1.39 memory used=129.2MB, alloc=68.3MB, time=1.99 memory used=170.2MB, alloc=92.3MB, time=2.60 memory used=235.4MB, alloc=92.3MB, time=3.52 memory used=300.9MB, alloc=116.3MB, time=4.45 memory used=372.2MB, alloc=116.3MB, time=5.53 memory used=441.1MB, alloc=372.3MB, time=6.57 memory used=530.0MB, alloc=396.3MB, time=7.77 memory used=632.8MB, alloc=396.3MB, time=9.41 memory used=746.3MB, alloc=420.3MB, time=10.98 memory used=871.7MB, alloc=420.3MB, time=12.76 memory used=1003.0MB, alloc=444.3MB, time=14.79 memory used=1128.2MB, alloc=468.3MB, time=17.00 memory used=1279.5MB, alloc=468.3MB, time=19.02 memory used=1400.5MB, alloc=468.3MB, time=20.65 memory used=1531.9MB, alloc=468.3MB, time=22.34 memory used=1679.0MB, alloc=468.3MB, time=24.49 memory used=1780.6MB, alloc=468.3MB, time=26.05 memory used=1884.5MB, alloc=492.3MB, time=27.98 memory used=1997.2MB, alloc=492.3MB, time=30.06 memory used=2088.4MB, alloc=492.3MB, time=31.89 memory used=2202.9MB, alloc=492.3MB, time=33.59 memory used=2293.8MB, alloc=492.3MB, time=35.05 memory used=2380.7MB, alloc=516.3MB, time=36.40 memory used=2468.4MB, alloc=516.3MB, time=38.23 memory used=2539.3MB, alloc=516.3MB, time=39.48 memory used=2596.1MB, alloc=516.3MB, time=40.54 memory used=2671.3MB, alloc=516.3MB, time=42.18 memory used=2752.9MB, alloc=516.3MB, time=44.05 memory used=2822.2MB, alloc=516.3MB, time=45.65 memory used=2870.7MB, alloc=516.3MB, time=46.67 memory used=2939.4MB, alloc=516.3MB, time=48.07 memory used=2990.7MB, alloc=516.3MB, time=49.33 memory used=3191.7MB, alloc=540.3MB, time=53.35 memory used=3413.4MB, alloc=564.3MB, time=57.24 memory used=3625.6MB, alloc=588.3MB, time=60.75 memory used=3828.0MB, alloc=612.3MB, time=63.84 memory used=4018.7MB, alloc=636.3MB, time=67.82 memory used=4198.9MB, alloc=660.3MB, time=71.96 memory used=4381.1MB, alloc=660.3MB, time=75.18 memory used=4535.5MB, alloc=660.3MB, time=78.13 memory used=4731.0MB, alloc=660.3MB, time=81.44 memory used=4937.4MB, alloc=660.3MB, time=84.21 memory used=5083.6MB, alloc=684.3MB, time=86.96 memory used=5207.3MB, alloc=684.3MB, time=89.36 memory used=5376.5MB, alloc=684.3MB, time=92.28 memory used=5524.8MB, alloc=684.3MB, time=94.84 memory used=5634.2MB, alloc=684.3MB, time=97.29 memory used=5759.0MB, alloc=684.3MB, time=100.14 memory used=5883.6MB, alloc=708.3MB, time=103.11 memory used=5988.9MB, alloc=708.3MB, time=105.93 memory used=6102.5MB, alloc=708.3MB, time=108.91 |\^/| 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(); 1428250201 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 2 2 F := [-5 x z - 11 z + 11 z, 4 x z + 2 y z, -3 x - 5 y - z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 2 G := [-5 x y + 2 x z + 18 z , -x z + 2 z - 8 z, 4 y z + 9 x y + 6 x z] > Problem := [F,G]; 2 3 2 2 2 Problem := [[-5 x z - 11 z + 11 z, 4 x z + 2 y z, -3 x - 5 y - z], 2 2 2 2 2 [-5 x y + 2 x z + 18 z , -x z + 2 z - 8 z, 4 y z + 9 x y + 6 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.6MB, alloc=32.3MB, time=0.50 memory used=47.7MB, alloc=32.3MB, time=0.82 memory used=67.7MB, alloc=56.3MB, time=1.14 memory used=107.5MB, alloc=60.3MB, time=1.73 memory used=145.5MB, alloc=84.3MB, time=2.32 memory used=208.6MB, alloc=92.3MB, time=3.25 memory used=269.9MB, alloc=116.3MB, time=4.20 memory used=348.9MB, alloc=116.3MB, time=5.37 memory used=424.0MB, alloc=372.3MB, time=6.55 memory used=505.8MB, alloc=396.3MB, time=7.82 memory used=614.9MB, alloc=396.3MB, time=9.42 memory used=719.2MB, alloc=420.3MB, time=11.09 memory used=846.2MB, alloc=444.3MB, time=13.15 memory used=989.5MB, alloc=468.3MB, time=15.73 memory used=1126.5MB, alloc=492.3MB, time=18.07 memory used=1247.7MB, alloc=492.3MB, time=20.28 memory used=1362.8MB, alloc=492.3MB, time=22.27 memory used=1483.7MB, alloc=516.3MB, time=24.76 memory used=1589.4MB, alloc=516.3MB, time=26.78 memory used=1673.0MB, alloc=516.3MB, time=28.47 memory used=1755.9MB, alloc=516.3MB, time=30.25 memory used=1830.0MB, alloc=516.3MB, time=31.72 memory used=1913.8MB, alloc=516.3MB, time=33.54 memory used=1986.7MB, alloc=516.3MB, time=35.34 memory used=2069.7MB, alloc=516.3MB, time=37.38 memory used=2128.9MB, alloc=516.3MB, time=38.69 memory used=2197.6MB, alloc=516.3MB, time=40.41 memory used=2248.8MB, alloc=516.3MB, time=41.67 memory used=2299.9MB, alloc=516.3MB, time=43.00 memory used=2503.1MB, alloc=540.3MB, time=47.19 memory used=2727.7MB, alloc=564.3MB, time=51.93 memory used=2928.0MB, alloc=588.3MB, time=55.96 memory used=3127.3MB, alloc=612.3MB, time=59.95 memory used=3296.3MB, alloc=636.3MB, time=63.69 memory used=3488.0MB, alloc=660.3MB, time=68.01 memory used=3726.0MB, alloc=684.3MB, time=74.63 memory used=3894.9MB, alloc=684.3MB, time=78.83 memory used=4038.6MB, alloc=684.3MB, time=81.98 memory used=4179.7MB, alloc=684.3MB, time=85.23 memory used=4345.7MB, alloc=684.3MB, time=89.99 memory used=4473.3MB, alloc=684.3MB, time=93.82 |\^/| 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(); 1428250501 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; F := 2 2 2 2 2 2 2 [18 y z - 7 x z + 10 z, 9 x z - 9 y z + 7 z , -7 x y + 4 x z + 4 y z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 3 2 3 2 3 G := [16 y z - 13 x + 5 z , 7 x + 5 x z + 10 y , x + 8 y z + 9 z ] > Problem := [F,G]; Problem := [ 2 2 2 2 2 2 2 [18 y z - 7 x z + 10 z, 9 x z - 9 y z + 7 z , -7 x y + 4 x z + 4 y z] 2 2 2 3 2 3 2 3 , [16 y z - 13 x + 5 z , 7 x + 5 x z + 10 y , x + 8 y z + 9 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.5MB, alloc=32.3MB, time=0.50 memory used=47.0MB, alloc=32.3MB, time=0.80 memory used=66.2MB, alloc=56.3MB, time=1.10 memory used=107.4MB, alloc=60.3MB, time=1.68 memory used=147.4MB, alloc=60.3MB, time=2.25 memory used=187.4MB, alloc=92.3MB, time=2.87 memory used=252.8MB, alloc=92.3MB, time=3.75 memory used=312.4MB, alloc=116.3MB, time=4.68 memory used=385.0MB, alloc=372.3MB, time=5.77 memory used=471.7MB, alloc=372.3MB, time=6.98 memory used=561.8MB, alloc=396.3MB, time=8.12 memory used=681.2MB, alloc=420.3MB, time=9.49 memory used=816.9MB, alloc=444.3MB, time=11.40 memory used=933.6MB, alloc=444.3MB, time=13.07 memory used=1066.7MB, alloc=468.3MB, time=14.73 memory used=1192.2MB, alloc=468.3MB, time=16.37 memory used=1310.2MB, alloc=468.3MB, time=17.90 memory used=1418.4MB, alloc=468.3MB, time=19.34 memory used=1523.7MB, alloc=492.3MB, time=20.95 memory used=1611.1MB, alloc=492.3MB, time=22.24 memory used=1700.7MB, alloc=492.3MB, time=23.82 memory used=1776.9MB, alloc=492.3MB, time=24.94 memory used=1842.5MB, alloc=492.3MB, time=26.20 memory used=1913.9MB, alloc=492.3MB, time=27.21 memory used=1988.1MB, alloc=492.3MB, time=28.60 memory used=2055.4MB, alloc=492.3MB, time=29.66 memory used=2115.8MB, alloc=516.3MB, time=30.95 memory used=2178.2MB, alloc=516.3MB, time=32.25 memory used=2227.9MB, alloc=516.3MB, time=33.19 memory used=2282.4MB, alloc=516.3MB, time=34.11 memory used=2331.7MB, alloc=516.3MB, time=35.35 memory used=2541.4MB, alloc=540.3MB, time=38.48 memory used=2758.7MB, alloc=564.3MB, time=41.39 memory used=2937.6MB, alloc=588.3MB, time=44.44 memory used=3175.2MB, alloc=612.3MB, time=47.44 memory used=3384.0MB, alloc=612.3MB, time=50.19 memory used=3586.8MB, alloc=636.3MB, time=52.95 memory used=3769.4MB, alloc=636.3MB, time=54.82 memory used=3993.2MB, alloc=636.3MB, time=57.33 memory used=4159.1MB, alloc=660.3MB, time=60.20 memory used=4328.3MB, alloc=660.3MB, time=63.03 memory used=4455.7MB, alloc=660.3MB, time=65.33 memory used=4589.8MB, alloc=660.3MB, time=67.67 memory used=4693.7MB, alloc=660.3MB, time=69.74 memory used=4805.1MB, alloc=660.3MB, time=71.97 memory used=4933.9MB, alloc=660.3MB, time=74.34 memory used=5040.6MB, alloc=684.3MB, time=76.68 memory used=5222.2MB, alloc=684.3MB, time=79.18 memory used=5366.6MB, alloc=684.3MB, time=81.34 memory used=5456.6MB, alloc=684.3MB, time=83.27 memory used=5824.8MB, alloc=708.3MB, time=87.86 memory used=6175.5MB, alloc=732.3MB, time=93.74 memory used=6574.7MB, alloc=756.3MB, time=100.37 memory used=6967.1MB, alloc=780.3MB, time=107.22 memory used=7355.4MB, alloc=804.3MB, time=112.71 memory used=7705.8MB, alloc=828.3MB, time=118.12 |\^/| 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(); 1428250801 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 3 2 F := [-4 y z + 19 x - y, 2 x y z - y + 4 z, 10 x - x y + 8 y] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 3 2 2 2 G := [3 y z - 6 z , -2 y - 7 y z - 2 z, 5 x z - 9 y z + 1] > Problem := [F,G]; 2 3 3 2 Problem := [[-4 y z + 19 x - y, 2 x y z - y + 4 z, 10 x - x y + 8 y], 2 2 3 2 2 2 [3 y z - 6 z , -2 y - 7 y z - 2 z, 5 x z - 9 y z + 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=26.3MB, alloc=32.3MB, time=0.48 memory used=47.4MB, alloc=32.3MB, time=0.79 memory used=65.6MB, alloc=56.3MB, time=1.07 memory used=104.5MB, alloc=60.3MB, time=1.66 memory used=142.7MB, alloc=60.3MB, time=2.23 memory used=180.0MB, alloc=84.3MB, time=2.81 memory used=228.3MB, alloc=84.3MB, time=3.53 memory used=286.5MB, alloc=92.3MB, time=4.43 memory used=348.0MB, alloc=116.3MB, time=5.46 memory used=413.1MB, alloc=116.3MB, time=5.84 memory used=468.3MB, alloc=116.3MB, time=6.07 memory used=534.2MB, alloc=116.8MB, time=9.66 memory used=577.1MB, alloc=116.8MB, time=9.79 memory used=661.1MB, alloc=116.8MB, time=11.41 memory used=739.6MB, alloc=116.8MB, time=12.62 memory used=808.8MB, alloc=140.8MB, time=13.68 memory used=879.1MB, alloc=396.8MB, time=14.83 memory used=982.9MB, alloc=420.8MB, time=16.40 memory used=1105.5MB, alloc=444.8MB, time=18.44 memory used=1251.4MB, alloc=468.8MB, time=20.72 memory used=1376.6MB, alloc=468.8MB, time=22.43 memory used=1496.7MB, alloc=492.8MB, time=24.40 memory used=1631.7MB, alloc=492.8MB, time=27.36 memory used=1780.4MB, alloc=492.8MB, time=30.52 memory used=1887.1MB, alloc=492.8MB, time=32.83 memory used=1982.7MB, alloc=492.8MB, time=34.17 memory used=2083.4MB, alloc=492.8MB, time=36.03 memory used=2173.3MB, alloc=516.8MB, time=37.62 memory used=2339.8MB, alloc=516.8MB, time=38.94 memory used=2477.2MB, alloc=516.8MB, time=46.07 memory used=2567.9MB, alloc=516.8MB, time=46.49 memory used=2665.3MB, alloc=516.8MB, time=46.89 memory used=2744.1MB, alloc=516.8MB, time=47.26 memory used=2839.2MB, alloc=516.8MB, time=47.62 memory used=2963.6MB, alloc=516.8MB, time=48.11 memory used=3109.5MB, alloc=516.8MB, time=56.49 memory used=3203.1MB, alloc=516.8MB, time=56.94 memory used=3313.2MB, alloc=516.8MB, time=57.38 memory used=3387.3MB, alloc=516.8MB, time=57.72 memory used=3473.5MB, alloc=516.8MB, time=58.08 memory used=3578.3MB, alloc=516.8MB, time=58.44 memory used=3710.9MB, alloc=516.8MB, time=59.15 memory used=3850.7MB, alloc=516.8MB, time=66.21 memory used=3938.8MB, alloc=516.8MB, time=66.62 memory used=4038.9MB, alloc=516.8MB, time=67.01 memory used=4115.4MB, alloc=516.8MB, time=67.35 memory used=4207.6MB, alloc=516.8MB, time=67.70 memory used=4354.3MB, alloc=516.8MB, time=69.03 memory used=4472.5MB, alloc=516.8MB, time=70.07 memory used=4556.7MB, alloc=516.8MB, time=71.81 memory used=4647.7MB, alloc=516.8MB, time=74.07 memory used=4810.4MB, alloc=540.8MB, time=89.83 memory used=4930.3MB, alloc=540.8MB, time=90.37 memory used=5034.2MB, alloc=540.8MB, time=90.88 memory used=5169.2MB, alloc=540.8MB, time=95.06 memory used=5282.9MB, alloc=540.8MB, time=96.44 memory used=5396.9MB, alloc=540.8MB, time=99.53 memory used=5516.6MB, alloc=540.8MB, time=101.96 memory used=5652.0MB, alloc=540.8MB, time=103.10 memory used=5808.7MB, alloc=540.8MB, time=120.04 memory used=5922.8MB, alloc=540.8MB, time=120.57 memory used=6016.9MB, alloc=540.8MB, time=121.04 memory used=6091.9MB, alloc=540.8MB, time=122.19 memory used=6177.5MB, alloc=540.8MB, time=123.09 memory used=6275.9MB, alloc=540.8MB, time=125.64 memory used=6398.5MB, alloc=540.8MB, time=126.97 memory used=6504.1MB, alloc=540.8MB, time=129.55 memory used=6555.1MB, alloc=540.8MB, time=130.38 memory used=6623.2MB, alloc=564.8MB, time=131.60 memory used=6675.4MB, alloc=564.8MB, time=132.92 memory used=6910.9MB, alloc=588.8MB, time=137.36 |\^/| 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(); 1428251101 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 3 3 2 F := [9 y - 17 z - 2 x, -7 y + 8 x y + 2, 8 y z + 2 x y + 3 x z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 2 G := [15 x z - 8 y z - 10 z, -4 x y - 5 x z - 4 z , -10 z - 5 z - 9] > Problem := [F,G]; 3 3 3 2 Problem := [[9 y - 17 z - 2 x, -7 y + 8 x y + 2, 8 y z + 2 x y + 3 x z], 2 2 2 2 2 [15 x z - 8 y z - 10 z, -4 x y - 5 x z - 4 z , -10 z - 5 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=26.3MB, alloc=32.3MB, time=0.49 memory used=46.8MB, alloc=32.3MB, time=0.79 memory used=64.5MB, alloc=56.3MB, time=1.07 memory used=106.5MB, alloc=60.3MB, time=1.68 memory used=147.0MB, alloc=60.3MB, time=2.23 memory used=187.4MB, alloc=84.3MB, time=2.83 memory used=235.5MB, alloc=84.3MB, time=3.57 memory used=295.4MB, alloc=116.3MB, time=4.55 memory used=379.0MB, alloc=116.3MB, time=5.85 memory used=460.7MB, alloc=116.3MB, time=7.12 memory used=517.4MB, alloc=396.3MB, time=7.94 memory used=622.2MB, alloc=396.3MB, time=9.38 memory used=737.2MB, alloc=420.3MB, time=10.88 memory used=872.5MB, alloc=444.3MB, time=12.83 memory used=1019.2MB, alloc=444.3MB, time=15.43 memory used=1170.8MB, alloc=468.3MB, time=18.16 memory used=1338.5MB, alloc=492.3MB, time=21.49 memory used=1482.2MB, alloc=492.3MB, time=24.25 memory used=1597.3MB, alloc=516.3MB, time=26.28 memory used=1696.7MB, alloc=516.3MB, time=28.06 memory used=1797.8MB, alloc=516.3MB, time=29.96 memory used=1914.7MB, alloc=516.3MB, time=32.35 memory used=2008.8MB, alloc=516.3MB, time=34.35 memory used=2096.6MB, alloc=516.3MB, time=36.05 memory used=2180.2MB, alloc=516.3MB, time=37.73 memory used=2255.0MB, alloc=516.3MB, time=39.35 memory used=2326.7MB, alloc=540.3MB, time=40.86 memory used=2412.9MB, alloc=540.3MB, time=42.71 memory used=2484.1MB, alloc=540.3MB, time=44.12 memory used=2569.3MB, alloc=540.3MB, time=45.15 memory used=2636.7MB, alloc=540.3MB, time=46.54 memory used=2700.4MB, alloc=540.3MB, time=47.82 memory used=2771.3MB, alloc=540.3MB, time=49.27 memory used=2839.5MB, alloc=540.3MB, time=50.82 memory used=2912.1MB, alloc=540.3MB, time=52.49 memory used=3000.2MB, alloc=540.3MB, time=53.47 memory used=3095.4MB, alloc=540.3MB, time=54.53 memory used=3209.8MB, alloc=540.3MB, time=55.65 memory used=3252.3MB, alloc=540.3MB, time=56.38 memory used=3295.8MB, alloc=540.3MB, time=57.37 memory used=3349.5MB, alloc=540.3MB, time=58.44 memory used=3579.2MB, alloc=564.3MB, time=62.42 memory used=3819.5MB, alloc=588.3MB, time=67.38 memory used=4024.2MB, alloc=612.3MB, time=71.27 memory used=4212.1MB, alloc=636.3MB, time=74.66 memory used=4420.7MB, alloc=660.3MB, time=78.79 memory used=4610.6MB, alloc=684.3MB, time=82.92 memory used=4821.6MB, alloc=708.3MB, time=87.71 memory used=4997.1MB, alloc=708.3MB, time=91.92 memory used=5134.8MB, alloc=732.3MB, time=94.36 memory used=5288.7MB, alloc=732.3MB, time=97.30 memory used=5438.5MB, alloc=732.3MB, time=101.51 memory used=5600.0MB, alloc=732.3MB, time=104.79 memory used=5707.6MB, alloc=732.3MB, time=107.32 |\^/| 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(); 1428251401 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 2 F := [-9 y z - 11 z + 12 x y, 2 y z - x z + 6 y , -3 x z - x] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 2 G := [-x z + 12 y z - 8 z, -4 y z - 3 x z + 6 z, 2 x y - 4 x - 4 x] > Problem := [F,G]; 2 3 2 2 Problem := [[-9 y z - 11 z + 12 x y, 2 y z - x z + 6 y , -3 x z - x], 2 2 2 2 2 [-x z + 12 y z - 8 z, -4 y z - 3 x z + 6 z, 2 x y - 4 x - 4 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.4MB, alloc=32.3MB, time=0.49 memory used=47.5MB, alloc=32.3MB, time=0.79 memory used=67.2MB, alloc=56.3MB, time=1.09 memory used=106.2MB, alloc=60.3MB, time=1.67 memory used=142.5MB, alloc=84.3MB, time=2.22 memory used=202.0MB, alloc=92.3MB, time=3.13 memory used=259.5MB, alloc=116.3MB, time=4.01 memory used=337.8MB, alloc=116.3MB, time=5.23 memory used=415.0MB, alloc=140.3MB, time=6.44 memory used=504.3MB, alloc=140.3MB, time=7.83 memory used=582.7MB, alloc=420.3MB, time=9.15 memory used=704.2MB, alloc=444.3MB, time=11.12 memory used=855.0MB, alloc=468.3MB, time=13.55 memory used=1001.1MB, alloc=492.3MB, time=15.96 memory used=1153.3MB, alloc=516.3MB, time=18.67 memory used=1275.7MB, alloc=516.3MB, time=20.89 memory used=1407.9MB, alloc=516.3MB, time=23.17 memory used=1523.2MB, alloc=516.3MB, time=25.24 memory used=1641.4MB, alloc=516.3MB, time=27.61 memory used=1748.5MB, alloc=540.3MB, time=29.81 memory used=1842.3MB, alloc=540.3MB, time=31.81 memory used=1931.0MB, alloc=540.3MB, time=33.70 memory used=1997.8MB, alloc=540.3MB, time=34.97 memory used=2068.1MB, alloc=540.3MB, time=36.45 memory used=2122.3MB, alloc=540.3MB, time=37.78 memory used=2192.0MB, alloc=540.3MB, time=39.57 memory used=2264.0MB, alloc=540.3MB, time=41.44 memory used=2330.4MB, alloc=540.3MB, time=43.29 memory used=2555.0MB, alloc=564.3MB, time=47.52 memory used=2797.5MB, alloc=588.3MB, time=52.79 memory used=3026.6MB, alloc=612.3MB, time=57.57 memory used=3242.9MB, alloc=636.3MB, time=62.15 memory used=3424.6MB, alloc=660.3MB, time=66.40 memory used=3637.2MB, alloc=684.3MB, time=72.13 memory used=3826.3MB, alloc=708.3MB, time=76.88 memory used=3965.7MB, alloc=708.3MB, time=80.50 memory used=4118.5MB, alloc=732.3MB, time=84.59 memory used=4239.0MB, alloc=732.3MB, time=88.03 memory used=4370.3MB, alloc=732.3MB, time=91.38 memory used=4435.7MB, alloc=732.3MB, time=93.16 memory used=4530.9MB, alloc=732.3MB, time=95.28 memory used=4649.0MB, alloc=732.3MB, time=98.55 memory used=5038.0MB, alloc=756.3MB, time=106.71 |\^/| 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(); 1428251701 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 3 2 2 2 3 2 F := [-20 y + 10 x y - 12 z, -9 x - 4 x y + 6 y , 6 x y + 9 y + 9 y ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 G := [-18 x y - 9 y + 11 z, -7 x z + 8 y + 10, 10 y z - 4 x z - 5 y z] > Problem := [F,G]; Problem := [ 3 3 2 2 2 3 2 [-20 y + 10 x y - 12 z, -9 x - 4 x y + 6 y , 6 x y + 9 y + 9 y ], 2 2 [-18 x y - 9 y + 11 z, -7 x z + 8 y + 10, 10 y z - 4 x z - 5 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.19 memory used=26.2MB, alloc=32.3MB, time=0.52 memory used=47.0MB, alloc=32.3MB, time=0.82 memory used=66.9MB, alloc=56.3MB, time=1.13 memory used=106.0MB, alloc=60.3MB, time=1.74 memory used=142.8MB, alloc=84.3MB, time=2.32 memory used=202.5MB, alloc=92.3MB, time=3.31 memory used=261.5MB, alloc=92.3MB, time=4.26 memory used=318.5MB, alloc=116.3MB, time=5.19 memory used=396.6MB, alloc=116.3MB, time=6.50 memory used=475.4MB, alloc=140.3MB, time=7.79 memory used=559.7MB, alloc=396.3MB, time=9.19 memory used=661.5MB, alloc=420.3MB, time=10.96 memory used=784.7MB, alloc=444.3MB, time=13.05 memory used=934.7MB, alloc=468.3MB, time=15.64 memory used=1079.9MB, alloc=492.3MB, time=18.18 memory used=1222.8MB, alloc=492.3MB, time=20.82 memory used=1337.3MB, alloc=492.3MB, time=22.87 memory used=1460.5MB, alloc=516.3MB, time=25.17 memory used=1576.1MB, alloc=516.3MB, time=27.56 memory used=1688.8MB, alloc=516.3MB, time=29.95 memory used=1800.9MB, alloc=540.3MB, time=32.33 memory used=1890.4MB, alloc=540.3MB, time=34.18 memory used=1970.9MB, alloc=540.3MB, time=36.00 memory used=2034.6MB, alloc=540.3MB, time=37.37 memory used=2095.1MB, alloc=540.3MB, time=38.72 memory used=2145.2MB, alloc=540.3MB, time=39.88 memory used=2212.3MB, alloc=540.3MB, time=41.42 memory used=2269.5MB, alloc=564.3MB, time=42.83 memory used=2333.7MB, alloc=564.3MB, time=44.40 memory used=2405.2MB, alloc=588.3MB, time=46.18 memory used=2638.7MB, alloc=612.3MB, time=51.10 memory used=2864.1MB, alloc=636.3MB, time=55.97 memory used=3094.8MB, alloc=660.3MB, time=60.84 memory used=3335.5MB, alloc=684.3MB, time=65.87 memory used=3575.9MB, alloc=708.3MB, time=71.04 memory used=3819.3MB, alloc=732.3MB, time=76.31 memory used=4065.4MB, alloc=756.3MB, time=81.73 memory used=4315.3MB, alloc=780.3MB, time=87.27 memory used=4566.3MB, alloc=804.3MB, time=92.78 memory used=4818.7MB, alloc=828.3MB, time=98.48 memory used=5072.7MB, alloc=852.3MB, time=104.24 |\^/| 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(); 1428252001 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 2 2 F := [2 y z - 2 z + 2 y, -5 y z - 8 x y + 9 z, -8 x z + 10 x z + 4 z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 3 G := [9 x z - 8 x y - 6 z, 2 x z + 10 y z, -7 y - 3 x y + 8 x] > Problem := [F,G]; Problem := [ 2 3 2 2 2 [2 y z - 2 z + 2 y, -5 y z - 8 x y + 9 z, -8 x z + 10 x z + 4 z], 2 2 2 3 [9 x z - 8 x y - 6 z, 2 x z + 10 y z, -7 y - 3 x y + 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=4.2MB, alloc=32.3MB, time=0.17 memory used=26.2MB, alloc=32.3MB, time=0.48 memory used=47.7MB, alloc=32.3MB, time=0.79 memory used=67.2MB, alloc=32.3MB, time=1.07 memory used=84.9MB, alloc=56.3MB, time=1.35 memory used=124.9MB, alloc=60.3MB, time=1.95 memory used=162.5MB, alloc=84.3MB, time=2.52 memory used=203.3MB, alloc=84.3MB, time=3.13 memory used=265.6MB, alloc=92.3MB, time=4.08 memory used=326.0MB, alloc=116.3MB, time=5.02 memory used=408.2MB, alloc=116.3MB, time=6.27 memory used=486.2MB, alloc=396.3MB, time=7.50 memory used=585.7MB, alloc=396.3MB, time=9.11 memory used=692.9MB, alloc=420.3MB, time=10.71 memory used=823.1MB, alloc=444.3MB, time=12.72 memory used=951.2MB, alloc=468.3MB, time=14.76 memory used=1063.7MB, alloc=468.3MB, time=16.61 memory used=1164.3MB, alloc=468.3MB, time=18.30 memory used=1284.6MB, alloc=492.3MB, time=20.17 memory used=1380.5MB, alloc=492.3MB, time=21.84 memory used=1483.1MB, alloc=492.3MB, time=23.79 memory used=1567.5MB, alloc=492.3MB, time=25.30 memory used=1666.4MB, alloc=516.3MB, time=27.45 memory used=1742.0MB, alloc=516.3MB, time=28.90 memory used=1816.9MB, alloc=516.3MB, time=30.47 memory used=1874.4MB, alloc=516.3MB, time=31.63 memory used=1936.5MB, alloc=516.3MB, time=33.06 memory used=1989.8MB, alloc=516.3MB, time=34.15 memory used=2049.3MB, alloc=516.3MB, time=35.57 memory used=2236.8MB, alloc=540.3MB, time=39.19 memory used=2438.4MB, alloc=564.3MB, time=43.45 memory used=2621.1MB, alloc=588.3MB, time=47.49 memory used=2798.1MB, alloc=612.3MB, time=51.47 memory used=2980.9MB, alloc=636.3MB, time=54.95 memory used=3131.1MB, alloc=636.3MB, time=58.18 memory used=3273.6MB, alloc=660.3MB, time=61.42 memory used=3379.5MB, alloc=660.3MB, time=64.07 memory used=3527.9MB, alloc=660.3MB, time=67.96 memory used=3650.5MB, alloc=660.3MB, time=71.04 memory used=3765.6MB, alloc=660.3MB, time=74.12 memory used=3870.6MB, alloc=660.3MB, time=76.91 memory used=4187.9MB, alloc=684.3MB, time=84.41 memory used=4538.4MB, alloc=708.3MB, time=92.17 memory used=4913.7MB, alloc=732.3MB, time=99.57 memory used=5292.6MB, alloc=756.3MB, time=107.81 |\^/| 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(); 1428252301 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 3 F := [-6 x y z + 2 x z - 9 y z, -7 x y - 8 y z - 8 z , 2 3 x y z - 10 x z - 4 z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 2 G := [14 z - 13 x - 19 z, 7 x z - 8 x, 6 x + x z - z] > Problem := [F,G]; 2 2 2 2 3 Problem := [[-6 x y z + 2 x z - 9 y z, -7 x y - 8 y z - 8 z , 2 3 x y z - 10 x z - 4 z], 3 2 2 2 [14 z - 13 x - 19 z, 7 x z - 8 x, 6 x + x z - z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.6MB, alloc=32.3MB, time=0.50 memory used=47.0MB, alloc=32.3MB, time=0.80 memory used=65.8MB, alloc=56.3MB, time=1.09 memory used=106.0MB, alloc=60.3MB, time=1.69 memory used=145.1MB, alloc=60.3MB, time=2.27 memory used=183.2MB, alloc=84.3MB, time=2.84 memory used=230.7MB, alloc=84.3MB, time=3.55 memory used=287.3MB, alloc=116.3MB, time=4.45 memory used=367.9MB, alloc=116.3MB, time=5.71 memory used=447.0MB, alloc=140.3MB, time=6.96 memory used=516.9MB, alloc=396.3MB, time=8.07 memory used=618.7MB, alloc=396.3MB, time=9.63 memory used=725.3MB, alloc=420.3MB, time=11.22 memory used=847.4MB, alloc=444.3MB, time=13.20 memory used=991.2MB, alloc=468.3MB, time=15.54 memory used=1152.3MB, alloc=468.3MB, time=17.41 memory used=1300.1MB, alloc=492.3MB, time=19.86 memory used=1414.0MB, alloc=492.3MB, time=21.91 memory used=1513.7MB, alloc=516.3MB, time=23.34 memory used=1614.3MB, alloc=516.3MB, time=25.01 memory used=1699.7MB, alloc=516.3MB, time=26.54 memory used=1797.2MB, alloc=516.3MB, time=28.41 memory used=1872.8MB, alloc=516.3MB, time=29.83 memory used=1947.2MB, alloc=516.3MB, time=31.20 memory used=2021.8MB, alloc=516.3MB, time=32.67 memory used=2090.4MB, alloc=540.3MB, time=33.80 memory used=2149.8MB, alloc=540.3MB, time=34.81 memory used=2199.0MB, alloc=540.3MB, time=35.88 memory used=2247.4MB, alloc=540.3MB, time=36.71 memory used=2468.7MB, alloc=564.3MB, time=40.83 memory used=2664.9MB, alloc=588.3MB, time=44.00 memory used=2863.7MB, alloc=612.3MB, time=47.72 memory used=3035.8MB, alloc=636.3MB, time=50.43 memory used=3195.9MB, alloc=660.3MB, time=53.63 memory used=3340.5MB, alloc=684.3MB, time=56.02 memory used=3479.1MB, alloc=708.3MB, time=58.73 memory used=3618.2MB, alloc=708.3MB, time=61.81 memory used=3723.5MB, alloc=708.3MB, time=64.24 memory used=3842.9MB, alloc=708.3MB, time=66.95 memory used=3945.2MB, alloc=708.3MB, time=69.56 memory used=4317.1MB, alloc=732.3MB, time=75.96 memory used=4706.3MB, alloc=756.3MB, time=82.88 memory used=5065.1MB, alloc=780.3MB, time=89.11 memory used=5422.5MB, alloc=804.3MB, time=96.19 |\^/| 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(); 1428252601 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 3 2 F := [-19 y - 7 y z - 13 z, -10 z - 4 y - 7, -6 y z + 10 y z - 4 y] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; G := 2 2 2 2 2 3 [-17 x y + 16 y z - 3 x, 10 x y - 10 y z + 9 y, 10 x z + 2 x y - 9 y ] > Problem := [F,G]; 3 2 3 2 Problem := [[-19 y - 7 y z - 13 z, -10 z - 4 y - 7, -6 y z + 10 y z - 4 y], 2 2 2 2 2 3 [-17 x y + 16 y z - 3 x, 10 x y - 10 y z + 9 y, 10 x z + 2 x 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=4.3MB, alloc=32.3MB, time=0.17 memory used=26.7MB, alloc=32.3MB, time=0.51 memory used=47.1MB, alloc=32.3MB, time=0.81 memory used=66.0MB, alloc=56.3MB, time=1.11 memory used=105.9MB, alloc=60.3MB, time=1.71 memory used=142.6MB, alloc=84.3MB, time=2.25 memory used=207.1MB, alloc=92.3MB, time=3.17 memory used=272.6MB, alloc=116.3MB, time=4.10 memory used=354.8MB, alloc=116.3MB, time=5.30 memory used=417.6MB, alloc=372.3MB, time=6.22 memory used=502.1MB, alloc=396.3MB, time=7.46 memory used=610.5MB, alloc=420.3MB, time=9.06 memory used=743.2MB, alloc=444.3MB, time=10.96 memory used=871.4MB, alloc=468.3MB, time=12.93 memory used=982.8MB, alloc=468.3MB, time=14.67 memory used=1096.7MB, alloc=492.3MB, time=16.46 memory used=1196.4MB, alloc=492.3MB, time=18.02 memory used=1294.2MB, alloc=492.3MB, time=19.64 memory used=1378.7MB, alloc=492.3MB, time=20.96 memory used=1460.6MB, alloc=516.3MB, time=22.20 memory used=1532.9MB, alloc=516.3MB, time=23.47 memory used=1608.6MB, alloc=516.3MB, time=24.96 memory used=1679.5MB, alloc=516.3MB, time=26.36 memory used=1735.8MB, alloc=516.3MB, time=27.42 memory used=1786.5MB, alloc=516.3MB, time=28.28 memory used=1855.3MB, alloc=516.3MB, time=29.78 memory used=1908.2MB, alloc=516.3MB, time=30.93 memory used=1951.0MB, alloc=516.3MB, time=31.74 memory used=2010.4MB, alloc=516.3MB, time=33.21 memory used=2208.9MB, alloc=540.3MB, time=36.77 memory used=2415.4MB, alloc=564.3MB, time=40.47 memory used=2607.3MB, alloc=588.3MB, time=44.09 memory used=2771.6MB, alloc=612.3MB, time=47.03 memory used=2916.4MB, alloc=636.3MB, time=49.61 memory used=3066.0MB, alloc=660.3MB, time=52.89 memory used=3226.8MB, alloc=660.3MB, time=55.98 memory used=3331.8MB, alloc=660.3MB, time=58.03 memory used=3442.4MB, alloc=660.3MB, time=60.75 memory used=3529.5MB, alloc=660.3MB, time=62.59 memory used=3650.4MB, alloc=660.3MB, time=65.76 memory used=3744.4MB, alloc=660.3MB, time=68.09 memory used=3836.0MB, alloc=660.3MB, time=70.50 memory used=4152.5MB, alloc=684.3MB, time=76.01 memory used=4492.4MB, alloc=708.3MB, time=83.01 memory used=4850.9MB, alloc=732.3MB, time=90.57 memory used=5221.0MB, alloc=756.3MB, time=99.22 memory used=5568.2MB, alloc=780.3MB, time=107.18 |\^/| 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(); 1428252901 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 3 2 F := [6 x z - 14 y - 3 x, 4 x z - 2 y z + 3 y, 5 x - 8 x y z - 6 z ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 3 3 2 G := [-11 x - 15 x y + 5 z, -8 y z - 2 z - 8 y, -x - 8 x z - 5 y] > Problem := [F,G]; Problem := [ 2 2 2 3 2 [6 x z - 14 y - 3 x, 4 x z - 2 y z + 3 y, 5 x - 8 x y z - 6 z ], 3 2 2 3 3 2 [-11 x - 15 x y + 5 z, -8 y z - 2 z - 8 y, -x - 8 x z - 5 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=25.2MB, alloc=32.3MB, time=0.48 memory used=46.7MB, alloc=36.3MB, time=0.78 memory used=66.8MB, alloc=60.3MB, time=1.05 memory used=109.3MB, alloc=60.3MB, time=1.68 memory used=145.5MB, alloc=60.3MB, time=2.10 memory used=194.7MB, alloc=68.3MB, time=2.68 memory used=243.5MB, alloc=92.3MB, time=3.21 memory used=312.6MB, alloc=92.3MB, time=4.14 memory used=377.9MB, alloc=348.3MB, time=5.00 memory used=447.6MB, alloc=372.3MB, time=5.91 memory used=542.7MB, alloc=372.3MB, time=7.19 memory used=630.9MB, alloc=396.3MB, time=8.25 memory used=760.7MB, alloc=396.3MB, time=9.70 memory used=874.5MB, alloc=396.3MB, time=11.02 memory used=985.9MB, alloc=420.3MB, time=12.35 memory used=1094.8MB, alloc=420.3MB, time=13.74 memory used=1209.9MB, alloc=444.3MB, time=15.44 memory used=1306.7MB, alloc=444.3MB, time=16.91 memory used=1408.5MB, alloc=444.3MB, time=18.14 memory used=1501.5MB, alloc=444.3MB, time=19.37 memory used=1589.8MB, alloc=468.3MB, time=20.70 memory used=1669.3MB, alloc=468.3MB, time=21.83 memory used=1742.6MB, alloc=468.3MB, time=23.02 memory used=1823.4MB, alloc=468.3MB, time=24.50 memory used=1915.2MB, alloc=468.3MB, time=26.13 memory used=1997.9MB, alloc=468.3MB, time=27.53 memory used=2066.8MB, alloc=492.3MB, time=28.60 memory used=2144.9MB, alloc=492.3MB, time=29.59 memory used=2200.4MB, alloc=492.3MB, time=30.51 memory used=2254.2MB, alloc=492.3MB, time=31.40 memory used=2306.0MB, alloc=492.3MB, time=32.19 memory used=2360.4MB, alloc=492.3MB, time=33.38 memory used=2407.9MB, alloc=492.3MB, time=34.32 memory used=2457.3MB, alloc=492.3MB, time=35.28 memory used=2647.2MB, alloc=516.3MB, time=38.19 memory used=2815.1MB, alloc=540.3MB, time=40.72 memory used=2968.6MB, alloc=564.3MB, time=43.02 memory used=3106.8MB, alloc=588.3MB, time=44.82 memory used=3240.3MB, alloc=588.3MB, time=47.19 memory used=3366.7MB, alloc=612.3MB, time=49.16 memory used=3504.6MB, alloc=612.3MB, time=51.47 memory used=3606.8MB, alloc=636.3MB, time=53.62 memory used=3707.8MB, alloc=636.3MB, time=55.53 memory used=3825.5MB, alloc=636.3MB, time=58.00 memory used=3936.7MB, alloc=636.3MB, time=60.04 memory used=4096.4MB, alloc=660.3MB, time=62.16 memory used=4167.1MB, alloc=660.3MB, time=63.85 memory used=4555.7MB, alloc=684.3MB, time=68.68 memory used=4819.2MB, alloc=708.3MB, time=71.75 memory used=5091.6MB, alloc=708.3MB, time=74.91 memory used=5480.0MB, alloc=732.3MB, time=80.22 memory used=5845.7MB, alloc=756.3MB, time=86.03 memory used=6160.4MB, alloc=780.3MB, time=90.85 memory used=6532.7MB, alloc=804.3MB, time=96.03 memory used=6797.4MB, alloc=828.3MB, time=100.05 memory used=7114.0MB, alloc=852.3MB, time=105.48 |\^/| 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(); 1428253201 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 3 3 2 F := [14 x y z + 4 x z + 10, -8 x z + 2 z + 3 x, -6 x + 10 x z + 2 x] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 3 G := [8 x y + 11 x - 7 x z, 3 x y + 2 x z - 2 x z, 10 x - x y - z] > Problem := [F,G]; Problem := [ 2 2 3 3 2 [14 x y z + 4 x z + 10, -8 x z + 2 z + 3 x, -6 x + 10 x z + 2 x], 2 2 2 2 3 [8 x y + 11 x - 7 x z, 3 x y + 2 x z - 2 x z, 10 x - x y - z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.4MB, alloc=32.3MB, time=0.52 memory used=47.5MB, alloc=32.3MB, time=0.85 memory used=67.8MB, alloc=56.3MB, time=1.17 memory used=109.8MB, alloc=60.3MB, time=1.82 memory used=149.3MB, alloc=60.3MB, time=2.40 memory used=190.4MB, alloc=92.3MB, time=3.04 memory used=249.3MB, alloc=92.3MB, time=3.96 memory used=312.1MB, alloc=116.3MB, time=4.91 memory used=388.4MB, alloc=372.3MB, time=6.09 memory used=473.4MB, alloc=396.3MB, time=7.40 memory used=582.7MB, alloc=420.3MB, time=9.08 memory used=716.9MB, alloc=444.3MB, time=11.25 memory used=865.4MB, alloc=468.3MB, time=13.61 memory used=998.0MB, alloc=468.3MB, time=15.74 memory used=1118.5MB, alloc=468.3MB, time=17.91 memory used=1244.8MB, alloc=492.3MB, time=20.13 memory used=1351.2MB, alloc=492.3MB, time=21.99 memory used=1463.7MB, alloc=492.3MB, time=24.15 memory used=1549.2MB, alloc=492.3MB, time=25.82 memory used=1642.6MB, alloc=492.3MB, time=27.71 memory used=1734.0MB, alloc=516.3MB, time=29.58 memory used=1816.8MB, alloc=516.3MB, time=31.22 memory used=1892.0MB, alloc=516.3MB, time=32.85 memory used=1969.2MB, alloc=516.3MB, time=34.38 memory used=2035.8MB, alloc=516.3MB, time=35.88 memory used=2094.2MB, alloc=516.3MB, time=37.26 memory used=2155.4MB, alloc=516.3MB, time=38.78 memory used=2206.8MB, alloc=516.3MB, time=40.07 memory used=2263.9MB, alloc=516.3MB, time=41.50 memory used=2466.0MB, alloc=540.3MB, time=45.82 memory used=2694.3MB, alloc=564.3MB, time=51.04 memory used=2887.6MB, alloc=588.3MB, time=55.39 memory used=3083.6MB, alloc=612.3MB, time=59.75 memory used=3275.0MB, alloc=636.3MB, time=63.73 memory used=3451.8MB, alloc=660.3MB, time=67.88 memory used=3613.1MB, alloc=684.3MB, time=71.46 memory used=3735.3MB, alloc=684.3MB, time=74.50 memory used=3878.1MB, alloc=684.3MB, time=78.19 memory used=4005.0MB, alloc=684.3MB, time=81.05 memory used=4168.2MB, alloc=708.3MB, time=86.03 memory used=4230.4MB, alloc=708.3MB, time=87.81 memory used=4344.4MB, alloc=708.3MB, time=91.05 memory used=4460.0MB, alloc=708.3MB, time=93.99 memory used=4834.7MB, alloc=732.3MB, time=102.11 |\^/| 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(); 1428253501 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 3 2 F := [5 x - 4 y + 13 z, 6 y z + 8 x z + 5 z, 2 x - 7 x y + 5 x z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 3 2 G := [-8 x y - 15 x y z - 19 z, 7 x y + 9 y - 7 y z, 7 x - 2 x z + 3 x z] > Problem := [F,G]; 2 2 3 2 Problem := [[5 x - 4 y + 13 z, 6 y z + 8 x z + 5 z, 2 x - 7 x y + 5 x z], 2 2 2 3 2 [-8 x y - 15 x y z - 19 z, 7 x y + 9 y - 7 y z, 7 x - 2 x z + 3 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.4MB, alloc=32.3MB, time=0.48 memory used=47.0MB, alloc=32.3MB, time=0.78 memory used=67.3MB, alloc=56.3MB, time=1.09 memory used=108.8MB, alloc=60.3MB, time=1.70 memory used=146.8MB, alloc=84.3MB, time=2.28 memory used=204.2MB, alloc=92.3MB, time=3.16 memory used=261.9MB, alloc=116.3MB, time=4.03 memory used=342.1MB, alloc=116.3MB, time=5.28 memory used=418.4MB, alloc=140.3MB, time=6.55 memory used=500.6MB, alloc=140.3MB, time=7.83 memory used=575.4MB, alloc=420.3MB, time=9.08 memory used=693.9MB, alloc=444.3MB, time=11.03 memory used=837.1MB, alloc=468.3MB, time=13.31 memory used=984.8MB, alloc=492.3MB, time=15.83 memory used=1094.9MB, alloc=492.3MB, time=17.73 memory used=1210.3MB, alloc=516.3MB, time=19.81 memory used=1320.3MB, alloc=516.3MB, time=21.84 memory used=1417.1MB, alloc=516.3MB, time=23.84 memory used=1523.7MB, alloc=516.3MB, time=26.17 memory used=1627.3MB, alloc=516.3MB, time=28.49 memory used=1708.0MB, alloc=540.3MB, time=30.42 memory used=1787.0MB, alloc=540.3MB, time=32.25 memory used=1850.2MB, alloc=540.3MB, time=33.61 memory used=1929.0MB, alloc=540.3MB, time=35.50 memory used=1983.8MB, alloc=540.3MB, time=36.68 memory used=2048.7MB, alloc=540.3MB, time=38.36 memory used=2270.3MB, alloc=564.3MB, time=42.85 memory used=2464.6MB, alloc=588.3MB, time=48.73 memory used=2693.9MB, alloc=612.3MB, time=56.86 memory used=2887.5MB, alloc=636.3MB, time=64.11 memory used=3053.6MB, alloc=660.3MB, time=70.54 memory used=3227.4MB, alloc=684.3MB, time=77.94 memory used=3367.4MB, alloc=684.3MB, time=83.84 memory used=3487.3MB, alloc=684.3MB, time=88.72 memory used=3608.8MB, alloc=684.3MB, time=93.96 memory used=3955.3MB, alloc=708.3MB, time=107.88 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428253801 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 3 F := [12 x - 12 z - 13, 8 y z - 7 x, 4 x y z + y + 3 y z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 3 3 2 2 2 G := [x + 6 y + 20 z , 9 x + 4 z - 8, -8 x - 10 y z - 8] > Problem := [F,G]; 2 2 2 3 Problem := [[12 x - 12 z - 13, 8 y z - 7 x, 4 x y z + y + 3 y z], 3 3 3 2 2 2 [x + 6 y + 20 z , 9 x + 4 z - 8, -8 x - 10 y z - 8]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.31 memory used=25.6MB, alloc=32.3MB, time=0.87 memory used=45.2MB, alloc=32.3MB, time=1.39 memory used=64.2MB, alloc=56.3MB, time=1.89 memory used=105.4MB, alloc=60.3MB, time=2.95 memory used=144.9MB, alloc=60.3MB, time=3.95 memory used=188.3MB, alloc=92.3MB, time=4.96 memory used=255.5MB, alloc=92.3MB, time=6.58 memory used=319.8MB, alloc=116.3MB, time=8.20 memory used=386.2MB, alloc=372.3MB, time=9.77 memory used=475.9MB, alloc=396.3MB, time=11.94 memory used=587.3MB, alloc=396.3MB, time=14.65 memory used=703.1MB, alloc=420.3MB, time=17.27 memory used=830.8MB, alloc=444.3MB, time=20.39 memory used=937.5MB, alloc=444.3MB, time=22.79 memory used=1072.4MB, alloc=468.3MB, time=26.38 memory used=1200.7MB, alloc=468.3MB, time=30.04 memory used=1321.2MB, alloc=492.3MB, time=32.30 memory used=1435.7MB, alloc=516.3MB, time=34.50 memory used=1551.5MB, alloc=540.3MB, time=36.36 memory used=1644.2MB, alloc=540.3MB, time=38.76 memory used=1725.6MB, alloc=540.3MB, time=41.14 memory used=1801.5MB, alloc=540.3MB, time=43.75 memory used=1866.5MB, alloc=540.3MB, time=45.73 memory used=1934.8MB, alloc=540.3MB, time=47.37 memory used=1986.7MB, alloc=540.3MB, time=48.83 memory used=2034.9MB, alloc=540.3MB, time=50.21 memory used=2076.9MB, alloc=564.3MB, time=51.74 memory used=2322.8MB, alloc=588.3MB, time=56.70 memory used=2500.2MB, alloc=612.3MB, time=60.85 memory used=2666.3MB, alloc=636.3MB, time=65.60 memory used=2811.2MB, alloc=660.3MB, time=69.13 memory used=2944.0MB, alloc=684.3MB, time=72.64 memory used=3066.8MB, alloc=684.3MB, time=76.87 memory used=3180.2MB, alloc=684.3MB, time=80.04 memory used=3283.4MB, alloc=684.3MB, time=82.88 memory used=3381.5MB, alloc=684.3MB, time=86.83 memory used=3480.1MB, alloc=684.3MB, time=89.86 memory used=3598.5MB, alloc=708.3MB, time=92.89 memory used=3715.0MB, alloc=708.3MB, time=96.31 memory used=4078.1MB, alloc=732.3MB, time=105.64 memory used=4491.1MB, alloc=756.3MB, time=114.15 |\^/| 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(); 1428254101 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 2 F := [14 y - y z - 18 x, 8 y z - 4 x + 7 y z, -2 x z - 6 x + 1] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 3 2 3 2 G := [9 x y + 8 z - 19 x, -x z - 2 z - 9 y, -5 y z + 4 z + 2 y ] > Problem := [F,G]; 3 2 2 2 Problem := [[14 y - y z - 18 x, 8 y z - 4 x + 7 y z, -2 x z - 6 x + 1], 2 3 2 3 2 3 2 [9 x y + 8 z - 19 x, -x z - 2 z - 9 y, -5 y z + 4 z + 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=4.2MB, alloc=32.3MB, time=0.30 memory used=25.2MB, alloc=32.3MB, time=0.85 memory used=45.4MB, alloc=60.3MB, time=1.31 memory used=86.6MB, alloc=60.3MB, time=2.32 memory used=134.5MB, alloc=68.3MB, time=3.19 memory used=179.0MB, alloc=68.3MB, time=4.27 memory used=221.8MB, alloc=68.3MB, time=5.19 memory used=264.3MB, alloc=68.3MB, time=6.07 memory used=312.6MB, alloc=92.3MB, time=7.46 memory used=384.2MB, alloc=92.3MB, time=8.72 memory used=439.6MB, alloc=92.3MB, time=9.84 memory used=503.2MB, alloc=116.3MB, time=11.38 memory used=563.2MB, alloc=116.3MB, time=12.86 memory used=628.7MB, alloc=372.3MB, time=13.94 memory used=698.1MB, alloc=372.3MB, time=14.66 memory used=781.2MB, alloc=372.3MB, time=18.09 memory used=835.3MB, alloc=372.3MB, time=18.51 memory used=918.3MB, alloc=372.3MB, time=21.99 memory used=966.8MB, alloc=372.3MB, time=22.41 memory used=1071.8MB, alloc=372.3MB, time=31.35 memory used=1132.5MB, alloc=372.3MB, time=31.85 memory used=1170.6MB, alloc=372.3MB, time=32.13 memory used=1256.1MB, alloc=396.3MB, time=33.49 memory used=1339.4MB, alloc=396.3MB, time=36.81 memory used=1403.3MB, alloc=396.3MB, time=37.29 memory used=1484.9MB, alloc=396.3MB, time=40.56 memory used=1579.7MB, alloc=396.3MB, time=41.98 memory used=1683.0MB, alloc=396.3MB, time=49.86 memory used=1733.4MB, alloc=396.3MB, time=50.15 memory used=1834.3MB, alloc=396.3MB, time=51.89 memory used=1947.8MB, alloc=420.3MB, time=54.47 memory used=2096.0MB, alloc=420.3MB, time=57.26 memory used=2214.0MB, alloc=444.3MB, time=60.26 memory used=2333.2MB, alloc=444.3MB, time=63.21 memory used=2443.8MB, alloc=468.3MB, time=65.68 memory used=2561.2MB, alloc=468.3MB, time=68.49 memory used=2644.8MB, alloc=468.3MB, time=69.08 memory used=2735.8MB, alloc=468.3MB, time=69.62 memory used=2800.3MB, alloc=468.3MB, time=70.09 memory used=2867.6MB, alloc=468.3MB, time=70.55 memory used=2945.4MB, alloc=468.3MB, time=71.03 memory used=3033.7MB, alloc=468.3MB, time=71.53 memory used=3119.9MB, alloc=468.3MB, time=71.98 memory used=3181.8MB, alloc=468.3MB, time=72.40 memory used=3242.5MB, alloc=468.3MB, time=72.78 memory used=3324.7MB, alloc=468.3MB, time=78.22 memory used=3455.6MB, alloc=468.3MB, time=154.74 memory used=3558.0MB, alloc=468.3MB, time=155.57 memory used=3625.4MB, alloc=468.3MB, time=156.10 memory used=3709.5MB, alloc=468.3MB, time=156.62 memory used=3791.1MB, alloc=468.3MB, time=157.10 memory used=3849.1MB, alloc=468.3MB, time=157.53 memory used=3912.4MB, alloc=468.3MB, time=157.97 memory used=3980.9MB, alloc=468.3MB, time=158.40 memory used=4055.4MB, alloc=468.3MB, time=158.84 memory used=4137.5MB, alloc=468.3MB, time=159.31 memory used=4226.5MB, alloc=468.3MB, time=159.76 memory used=4333.8MB, alloc=468.3MB, time=160.25 memory used=4493.7MB, alloc=468.3MB, time=161.10 memory used=4646.4MB, alloc=468.3MB, time=161.70 |\^/| 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(); 1428254401 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 3 2 3 2 F := [20 x z - 20 x y z + 10 x , 8 x + 5 y z + 10 x, y - 3 z + 2 x] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 3 2 3 G := [17 x + 17 z + 16 z, -7 z - 6 x + 8 y z, -5 z + 3 y z - 8 x] > Problem := [F,G]; Problem := [ 2 2 3 2 3 2 [20 x z - 20 x y z + 10 x , 8 x + 5 y z + 10 x, y - 3 z + 2 x], 3 2 3 2 3 [17 x + 17 z + 16 z, -7 z - 6 x + 8 y z, -5 z + 3 y z - 8 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.30 memory used=25.4MB, alloc=32.3MB, time=0.85 memory used=44.6MB, alloc=56.3MB, time=1.35 memory used=94.2MB, alloc=64.9MB, time=2.48 memory used=143.8MB, alloc=72.9MB, time=3.23 memory used=197.3MB, alloc=72.9MB, time=4.79 memory used=242.9MB, alloc=72.9MB, time=5.82 memory used=294.6MB, alloc=72.9MB, time=6.85 memory used=333.2MB, alloc=96.9MB, time=7.89 memory used=398.7MB, alloc=96.9MB, time=9.50 memory used=451.4MB, alloc=96.9MB, time=10.46 memory used=511.3MB, alloc=96.9MB, time=11.55 memory used=584.8MB, alloc=120.9MB, time=13.79 memory used=665.6MB, alloc=376.9MB, time=15.73 memory used=737.8MB, alloc=376.9MB, time=17.60 memory used=825.2MB, alloc=376.9MB, time=19.68 memory used=909.9MB, alloc=376.9MB, time=21.34 memory used=968.8MB, alloc=376.9MB, time=22.39 memory used=1025.2MB, alloc=376.9MB, time=23.28 memory used=1108.2MB, alloc=400.9MB, time=24.78 memory used=1215.6MB, alloc=400.9MB, time=29.25 memory used=1268.7MB, alloc=400.9MB, time=29.54 memory used=1368.3MB, alloc=400.9MB, time=31.48 memory used=1473.1MB, alloc=424.9MB, time=34.20 memory used=1595.5MB, alloc=424.9MB, time=37.07 memory used=1709.2MB, alloc=448.9MB, time=39.77 memory used=1845.7MB, alloc=448.9MB, time=42.35 memory used=1970.3MB, alloc=448.9MB, time=44.73 memory used=2069.5MB, alloc=448.9MB, time=46.44 memory used=2136.1MB, alloc=448.9MB, time=46.89 memory used=2191.6MB, alloc=448.9MB, time=47.25 memory used=2274.6MB, alloc=448.9MB, time=48.52 memory used=2339.6MB, alloc=448.9MB, time=48.93 memory used=2421.3MB, alloc=448.9MB, time=49.78 memory used=2534.7MB, alloc=448.9MB, time=51.81 memory used=2627.4MB, alloc=448.9MB, time=53.12 memory used=2745.7MB, alloc=472.9MB, time=55.94 memory used=2847.1MB, alloc=472.9MB, time=58.02 memory used=2980.7MB, alloc=472.9MB, time=60.81 memory used=3077.1MB, alloc=472.9MB, time=63.11 memory used=3154.0MB, alloc=472.9MB, time=64.99 memory used=3253.3MB, alloc=472.9MB, time=67.33 memory used=3346.9MB, alloc=472.9MB, time=69.78 memory used=3429.9MB, alloc=472.9MB, time=72.38 memory used=3510.5MB, alloc=496.9MB, time=74.89 memory used=3578.5MB, alloc=496.9MB, time=76.71 memory used=3645.4MB, alloc=496.9MB, time=78.41 memory used=3694.4MB, alloc=496.9MB, time=79.78 memory used=3776.1MB, alloc=520.9MB, time=82.05 memory used=3843.4MB, alloc=520.9MB, time=84.31 memory used=3914.8MB, alloc=520.9MB, time=86.54 memory used=4020.4MB, alloc=520.9MB, time=89.10 memory used=4080.8MB, alloc=520.9MB, time=91.14 memory used=4138.9MB, alloc=520.9MB, time=93.08 memory used=4184.9MB, alloc=520.9MB, time=94.79 memory used=4432.8MB, alloc=544.9MB, time=99.65 memory used=4626.1MB, alloc=544.9MB, time=109.64 memory used=4847.4MB, alloc=568.9MB, time=114.52 memory used=5141.3MB, alloc=592.9MB, time=119.75 memory used=5293.6MB, alloc=616.9MB, time=124.03 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428254701 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 F := [6 z - 16 x z - 18 x, -5 x , x y z - 2 y z - x] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; G := [ 2 2 2 2 2 2 14 x z - 16 y z - 11 x y, -3 x y + 2 y z - 9 x, -x y - 5 x z - 8 y z] > Problem := [F,G]; 3 2 Problem := [[6 z - 16 x z - 18 x, -5 x , x y z - 2 y z - x], [ 2 2 2 2 2 2 14 x z - 16 y z - 11 x y, -3 x y + 2 y z - 9 x, -x y - 5 x z - 8 y z] ] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.30 memory used=25.5MB, alloc=32.3MB, time=0.85 memory used=45.2MB, alloc=56.3MB, time=1.38 memory used=86.6MB, alloc=60.3MB, time=2.36 memory used=129.2MB, alloc=68.3MB, time=3.26 memory used=168.7MB, alloc=68.3MB, time=4.27 memory used=209.1MB, alloc=92.3MB, time=5.32 memory used=276.2MB, alloc=92.3MB, time=6.98 memory used=343.4MB, alloc=92.3MB, time=8.61 memory used=410.9MB, alloc=116.3MB, time=10.28 memory used=474.4MB, alloc=116.3MB, time=11.90 memory used=535.8MB, alloc=372.3MB, time=13.17 memory used=624.1MB, alloc=396.3MB, time=15.58 memory used=733.1MB, alloc=396.3MB, time=18.50 memory used=838.9MB, alloc=420.3MB, time=21.41 memory used=973.5MB, alloc=420.3MB, time=24.98 memory used=1110.2MB, alloc=444.3MB, time=28.38 memory used=1237.3MB, alloc=444.3MB, time=31.52 memory used=1360.1MB, alloc=444.3MB, time=34.73 memory used=1493.1MB, alloc=468.3MB, time=38.64 memory used=1613.1MB, alloc=492.3MB, time=42.35 memory used=1725.2MB, alloc=492.3MB, time=45.52 memory used=1828.6MB, alloc=492.3MB, time=48.31 memory used=1935.6MB, alloc=492.3MB, time=51.59 memory used=2011.1MB, alloc=516.3MB, time=53.81 memory used=2111.0MB, alloc=516.3MB, time=57.02 memory used=2184.2MB, alloc=516.3MB, time=59.08 memory used=2273.1MB, alloc=516.3MB, time=62.18 memory used=2349.7MB, alloc=516.3MB, time=64.57 memory used=2417.6MB, alloc=516.3MB, time=67.00 memory used=2475.7MB, alloc=516.3MB, time=68.90 memory used=2529.7MB, alloc=516.3MB, time=70.65 memory used=2588.0MB, alloc=516.3MB, time=72.36 memory used=2656.8MB, alloc=516.3MB, time=74.95 memory used=2707.5MB, alloc=516.3MB, time=76.89 memory used=2756.2MB, alloc=516.3MB, time=78.75 memory used=2969.8MB, alloc=540.3MB, time=84.45 memory used=3155.6MB, alloc=564.3MB, time=90.10 memory used=3356.3MB, alloc=588.3MB, time=96.01 memory used=3532.1MB, alloc=612.3MB, time=101.72 memory used=3718.0MB, alloc=636.3MB, time=107.75 |\^/| 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(); 1428255002 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 3 2 2 2 F := [18 x + 11 y, 2 x y - 9 z + 6 y , 3 x - 3 y + 3 y] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 2 G := [11 x y - 15 x y z + 8 z , -3 y z - 2 x y, -y z - 5 x z + 4 y] > Problem := [F,G]; 3 2 3 2 2 2 Problem := [[18 x + 11 y, 2 x y - 9 z + 6 y , 3 x - 3 y + 3 y], 2 3 2 2 [11 x y - 15 x y z + 8 z , -3 y z - 2 x y, -y z - 5 x z + 4 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.31 memory used=26.9MB, alloc=32.3MB, time=0.90 memory used=47.6MB, alloc=32.3MB, time=1.44 memory used=67.3MB, alloc=56.3MB, time=1.99 memory used=107.3MB, alloc=60.3MB, time=3.05 memory used=146.6MB, alloc=60.3MB, time=4.07 memory used=184.3MB, alloc=84.3MB, time=5.11 memory used=231.0MB, alloc=84.3MB, time=6.33 memory used=292.3MB, alloc=92.3MB, time=7.96 memory used=352.7MB, alloc=92.3MB, time=9.51 memory used=414.8MB, alloc=116.3MB, time=10.86 memory used=486.7MB, alloc=372.3MB, time=12.61 memory used=566.8MB, alloc=372.3MB, time=14.78 memory used=651.3MB, alloc=396.3MB, time=16.92 memory used=761.4MB, alloc=420.3MB, time=19.72 memory used=892.4MB, alloc=444.3MB, time=23.22 memory used=1017.6MB, alloc=444.3MB, time=26.57 memory used=1137.3MB, alloc=468.3MB, time=29.44 memory used=1268.7MB, alloc=468.3MB, time=33.05 memory used=1365.0MB, alloc=468.3MB, time=35.47 memory used=1454.3MB, alloc=468.3MB, time=36.89 memory used=1551.3MB, alloc=468.3MB, time=38.32 memory used=1649.4MB, alloc=468.3MB, time=39.50 memory used=1769.7MB, alloc=468.3MB, time=41.98 memory used=1872.6MB, alloc=492.3MB, time=44.59 memory used=2006.0MB, alloc=492.3MB, time=46.81 memory used=2135.2MB, alloc=492.3MB, time=48.02 memory used=2272.1MB, alloc=492.3MB, time=49.21 memory used=2371.5MB, alloc=492.3MB, time=52.25 memory used=2513.7MB, alloc=492.3MB, time=53.17 memory used=2673.1MB, alloc=492.3MB, time=54.65 memory used=2817.6MB, alloc=492.3MB, time=55.61 memory used=2936.5MB, alloc=492.3MB, time=57.17 memory used=3068.7MB, alloc=492.3MB, time=58.05 memory used=3145.5MB, alloc=492.3MB, time=58.66 memory used=3240.2MB, alloc=492.3MB, time=59.30 memory used=3364.4MB, alloc=492.3MB, time=64.39 memory used=3481.0MB, alloc=492.3MB, time=65.23 memory used=3695.5MB, alloc=492.3MB, time=66.39 memory used=3985.9MB, alloc=492.3MB, time=67.43 memory used=4166.4MB, alloc=492.3MB, time=68.12 memory used=4324.7MB, alloc=492.3MB, time=70.92 memory used=4429.3MB, alloc=492.3MB, time=73.17 memory used=4554.3MB, alloc=492.3MB, time=74.57 memory used=4695.7MB, alloc=492.3MB, time=75.82 memory used=4816.1MB, alloc=492.3MB, time=77.38 memory used=4942.1MB, alloc=492.3MB, time=78.23 memory used=5084.1MB, alloc=492.3MB, time=79.90 memory used=5190.7MB, alloc=492.3MB, time=80.69 memory used=5269.5MB, alloc=492.3MB, time=81.33 memory used=5411.6MB, alloc=492.3MB, time=83.89 memory used=5503.6MB, alloc=492.3MB, time=86.71 memory used=5601.8MB, alloc=492.3MB, time=89.03 memory used=5712.1MB, alloc=492.3MB, time=90.31 memory used=5802.4MB, alloc=492.3MB, time=91.48 memory used=5930.7MB, alloc=492.3MB, time=92.86 memory used=6029.4MB, alloc=492.3MB, time=93.64 memory used=6116.4MB, alloc=492.3MB, time=96.20 memory used=6200.8MB, alloc=492.3MB, time=98.43 memory used=6311.8MB, alloc=492.3MB, time=100.02 memory used=6412.2MB, alloc=492.3MB, time=101.10 memory used=6520.9MB, alloc=492.3MB, time=104.01 memory used=6635.9MB, alloc=492.3MB, time=105.27 memory used=6718.3MB, alloc=492.3MB, time=105.96 memory used=6804.5MB, alloc=492.3MB, time=106.64 memory used=6920.7MB, alloc=492.3MB, time=107.95 memory used=7003.8MB, alloc=492.3MB, time=108.66 memory used=7089.2MB, alloc=492.3MB, time=109.34 memory used=7185.2MB, alloc=492.3MB, time=114.10 memory used=7311.6MB, alloc=516.3MB, time=115.92 memory used=7415.4MB, alloc=516.3MB, time=116.75 memory used=7515.1MB, alloc=516.3MB, time=117.52 memory used=7639.5MB, alloc=516.3MB, time=118.31 memory used=7719.1MB, alloc=516.3MB, time=119.00 memory used=7863.7MB, alloc=516.3MB, time=121.24 memory used=7957.6MB, alloc=516.3MB, time=122.04 memory used=8064.2MB, alloc=516.3MB, time=122.83 memory used=8188.4MB, alloc=516.3MB, time=123.62 memory used=8263.1MB, alloc=516.3MB, time=124.31 memory used=8346.8MB, alloc=516.3MB, time=125.03 memory used=8438.9MB, alloc=516.3MB, time=125.74 memory used=8543.2MB, alloc=516.3MB, time=126.46 memory used=8663.7MB, alloc=516.3MB, time=127.19 |\^/| 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(); 1428255302 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 3 2 F := [10 x y z + 8 y z - x z, 7 y z + 4 y - 3 y z, 3 x + 8 x z + 4 y z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 2 3 3 G := [12 y z - 11 x y + 16 z, -5 x z + 6 x - 6 y , 3 x y + 4 y - 3 z ] > Problem := [F,G]; Problem := [ 2 2 2 3 2 [10 x y z + 8 y z - x z, 7 y z + 4 y - 3 y z, 3 x + 8 x z + 4 y z], 2 2 2 2 2 3 3 [12 y z - 11 x y + 16 z, -5 x z + 6 x - 6 y , 3 x y + 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=26.9MB, alloc=32.3MB, time=0.88 memory used=46.6MB, alloc=32.3MB, time=1.38 memory used=65.6MB, alloc=56.3MB, time=1.90 memory used=104.2MB, alloc=60.3MB, time=2.90 memory used=140.5MB, alloc=84.3MB, time=3.89 memory used=200.7MB, alloc=92.3MB, time=5.47 memory used=259.5MB, alloc=116.3MB, time=7.10 memory used=341.4MB, alloc=116.3MB, time=9.29 memory used=419.1MB, alloc=396.3MB, time=11.44 memory used=518.0MB, alloc=420.3MB, time=14.30 memory used=642.5MB, alloc=444.3MB, time=17.77 memory used=787.6MB, alloc=468.3MB, time=22.03 memory used=942.2MB, alloc=492.3MB, time=26.52 memory used=1064.8MB, alloc=516.3MB, time=29.95 memory used=1183.4MB, alloc=516.3MB, time=33.45 memory used=1306.7MB, alloc=516.3MB, time=36.99 memory used=1428.0MB, alloc=540.3MB, time=40.85 memory used=1556.9MB, alloc=540.3MB, time=45.42 memory used=1667.8MB, alloc=540.3MB, time=49.29 memory used=1766.5MB, alloc=540.3MB, time=52.39 memory used=1856.2MB, alloc=540.3MB, time=55.55 memory used=1932.8MB, alloc=564.3MB, time=58.33 memory used=2007.7MB, alloc=564.3MB, time=60.91 memory used=2080.1MB, alloc=564.3MB, time=63.72 memory used=2157.0MB, alloc=564.3MB, time=66.88 memory used=2241.6MB, alloc=564.3MB, time=70.25 memory used=2312.6MB, alloc=564.3MB, time=73.26 memory used=2376.6MB, alloc=564.3MB, time=76.08 memory used=2612.8MB, alloc=588.3MB, time=83.87 memory used=2859.0MB, alloc=612.3MB, time=92.68 memory used=3097.1MB, alloc=636.3MB, time=101.77 memory used=3319.6MB, alloc=660.3MB, time=110.75 |\^/| 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(); 1428255602 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 2 2 F := [x y + 5 x y - 2 y z, -5 x y - 9 y z, 4 x z - 4 x - x y] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 2 3 G := [-18 x - 9 x z + 2, 7 x y - 10 x y - 8, -6 z - 7 x z + x] > Problem := [F,G]; 2 2 2 2 2 2 Problem := [[x y + 5 x y - 2 y z, -5 x y - 9 y z, 4 x z - 4 x - x y], 3 2 2 2 3 [-18 x - 9 x z + 2, 7 x y - 10 x y - 8, -6 z - 7 x z + x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.8MB, alloc=32.3MB, time=0.88 memory used=48.0MB, alloc=32.3MB, time=1.42 memory used=68.5MB, alloc=56.3MB, time=1.96 memory used=109.6MB, alloc=60.3MB, time=3.02 memory used=149.0MB, alloc=60.3MB, time=4.06 memory used=187.2MB, alloc=84.3MB, time=5.08 memory used=230.9MB, alloc=84.3MB, time=6.25 memory used=289.2MB, alloc=92.3MB, time=7.89 memory used=346.2MB, alloc=116.3MB, time=9.42 memory used=425.5MB, alloc=116.3MB, time=11.52 memory used=502.1MB, alloc=140.3MB, time=13.64 memory used=584.7MB, alloc=140.3MB, time=15.92 memory used=672.4MB, alloc=396.3MB, time=18.43 memory used=773.1MB, alloc=420.3MB, time=21.32 memory used=897.5MB, alloc=420.3MB, time=24.81 memory used=1020.1MB, alloc=444.3MB, time=28.30 memory used=1162.9MB, alloc=468.3MB, time=32.27 memory used=1314.5MB, alloc=468.3MB, time=36.62 memory used=1466.0MB, alloc=492.3MB, time=41.11 memory used=1611.2MB, alloc=516.3MB, time=45.55 memory used=1769.2MB, alloc=540.3MB, time=50.19 memory used=1992.0MB, alloc=564.3MB, time=56.97 memory used=2225.4MB, alloc=588.3MB, time=64.15 memory used=2449.5MB, alloc=612.3MB, time=71.26 memory used=2670.1MB, alloc=636.3MB, time=78.28 memory used=2892.0MB, alloc=660.3MB, time=85.06 memory used=3182.0MB, alloc=684.3MB, time=92.98 memory used=3395.8MB, alloc=708.3MB, time=99.80 memory used=3647.5MB, alloc=732.3MB, time=106.97 |\^/| 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(); 1428255902 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 3 2 2 F := [5 x y + 18 x y + 10 y , 4 z + 5 x z - 8, -7 x z + 3 x z + 5 z ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 3 2 G := [-6 x y - 5 x y z - 13 z , -8 x y z + 7 y + 7 y z, x y z + 4 y - 3 x] > Problem := [F,G]; Problem := [ 2 2 2 3 2 2 [5 x y + 18 x y + 10 y , 4 z + 5 x z - 8, -7 x z + 3 x z + 5 z ], 2 3 3 2 [-6 x y - 5 x y z - 13 z , -8 x y z + 7 y + 7 y z, x y z + 4 y - 3 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.31 memory used=26.3MB, alloc=32.3MB, time=0.86 memory used=47.7MB, alloc=32.3MB, time=1.42 memory used=67.5MB, alloc=56.3MB, time=1.95 memory used=107.4MB, alloc=60.3MB, time=2.99 memory used=145.8MB, alloc=84.3MB, time=3.98 memory used=208.9MB, alloc=92.3MB, time=5.55 memory used=272.0MB, alloc=92.3MB, time=7.13 memory used=333.6MB, alloc=116.3MB, time=8.72 memory used=416.5MB, alloc=372.3MB, time=10.83 memory used=498.5MB, alloc=372.3MB, time=12.72 memory used=537.4MB, alloc=372.3MB, time=12.96 memory used=592.4MB, alloc=372.3MB, time=13.54 memory used=675.8MB, alloc=396.3MB, time=15.48 memory used=786.2MB, alloc=396.3MB, time=18.36 memory used=890.7MB, alloc=420.3MB, time=21.05 memory used=1019.9MB, alloc=444.3MB, time=24.09 memory used=1141.5MB, alloc=444.3MB, time=27.06 memory used=1243.1MB, alloc=468.3MB, time=29.41 memory used=1348.9MB, alloc=468.3MB, time=32.13 memory used=1433.7MB, alloc=468.3MB, time=34.08 memory used=1523.6MB, alloc=492.3MB, time=36.51 memory used=1609.9MB, alloc=492.3MB, time=39.07 memory used=1684.2MB, alloc=492.3MB, time=40.91 memory used=1749.1MB, alloc=492.3MB, time=42.47 memory used=1822.7MB, alloc=492.3MB, time=44.76 memory used=1888.2MB, alloc=492.3MB, time=46.73 memory used=1958.1MB, alloc=492.3MB, time=48.70 memory used=2007.9MB, alloc=492.3MB, time=50.37 memory used=2058.5MB, alloc=492.3MB, time=52.01 memory used=2109.2MB, alloc=492.3MB, time=53.85 memory used=2151.5MB, alloc=492.3MB, time=55.48 memory used=2338.5MB, alloc=516.3MB, time=60.18 memory used=2501.5MB, alloc=540.3MB, time=64.69 memory used=2687.8MB, alloc=564.3MB, time=69.56 memory used=2873.3MB, alloc=588.3MB, time=74.31 memory used=3026.2MB, alloc=612.3MB, time=78.09 memory used=3260.1MB, alloc=612.3MB, time=85.15 memory used=3439.1MB, alloc=636.3MB, time=89.06 memory used=3586.0MB, alloc=636.3MB, time=92.90 memory used=3697.0MB, alloc=660.3MB, time=96.54 memory used=3912.4MB, alloc=660.3MB, time=100.22 memory used=4107.4MB, alloc=660.3MB, time=103.25 memory used=4271.6MB, alloc=660.3MB, time=104.79 memory used=4409.8MB, alloc=660.3MB, time=106.18 memory used=4596.2MB, alloc=660.3MB, time=118.57 memory used=4745.5MB, alloc=660.3MB, time=120.04 memory used=4890.2MB, alloc=660.3MB, time=121.39 memory used=5028.0MB, alloc=660.3MB, time=122.64 memory used=5219.3MB, alloc=660.3MB, time=126.66 |\^/| 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(); 1428256202 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 3 2 2 2 F := [12 x z + 17 x y - 15 x, -2 x y + 9 z + 5 z , 5 x y + x y z + 4 x z ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 2 2 2 G := [-5 y + 20 x - 2 x z, x z + 7 x + 4, 7 x z + 10 y - 6 z ] > Problem := [F,G]; Problem := [ 2 2 3 2 2 2 [12 x z + 17 x y - 15 x, -2 x y + 9 z + 5 z , 5 x y + x y z + 4 x z ], 3 2 2 2 2 2 [-5 y + 20 x - 2 x z, x z + 7 x + 4, 7 x z + 10 y - 6 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.30 memory used=26.3MB, alloc=32.3MB, time=0.88 memory used=47.2MB, alloc=60.3MB, time=1.41 memory used=89.2MB, alloc=60.3MB, time=2.38 memory used=133.5MB, alloc=68.3MB, time=3.30 memory used=179.0MB, alloc=68.3MB, time=4.34 memory used=226.1MB, alloc=92.3MB, time=5.34 memory used=292.1MB, alloc=92.3MB, time=6.83 memory used=362.3MB, alloc=116.3MB, time=8.36 memory used=429.8MB, alloc=372.3MB, time=9.87 memory used=527.9MB, alloc=372.3MB, time=11.76 memory used=608.5MB, alloc=372.3MB, time=12.79 memory used=669.8MB, alloc=372.3MB, time=14.84 memory used=709.1MB, alloc=372.3MB, time=15.06 memory used=747.9MB, alloc=372.3MB, time=15.27 memory used=839.2MB, alloc=372.3MB, time=17.23 memory used=925.9MB, alloc=396.3MB, time=19.29 memory used=1034.5MB, alloc=420.3MB, time=21.99 memory used=1166.4MB, alloc=444.3MB, time=24.98 memory used=1281.7MB, alloc=444.3MB, time=27.89 memory used=1391.1MB, alloc=444.3MB, time=30.69 memory used=1516.1MB, alloc=468.3MB, time=33.75 memory used=1639.7MB, alloc=468.3MB, time=36.91 memory used=1758.8MB, alloc=468.3MB, time=39.45 memory used=1873.1MB, alloc=492.3MB, time=41.90 memory used=2022.3MB, alloc=492.3MB, time=44.77 memory used=2139.8MB, alloc=492.3MB, time=47.20 memory used=2274.8MB, alloc=492.3MB, time=49.74 memory used=2373.4MB, alloc=492.3MB, time=50.75 memory used=2514.6MB, alloc=492.3MB, time=53.01 memory used=2659.4MB, alloc=492.3MB, time=55.71 memory used=2754.0MB, alloc=492.3MB, time=57.78 memory used=2881.8MB, alloc=516.3MB, time=60.97 memory used=2971.3MB, alloc=516.3MB, time=63.50 memory used=3050.5MB, alloc=516.3MB, time=65.72 memory used=3125.4MB, alloc=516.3MB, time=68.00 memory used=3195.2MB, alloc=516.3MB, time=70.27 memory used=3264.0MB, alloc=516.3MB, time=72.55 memory used=3329.2MB, alloc=516.3MB, time=74.67 memory used=3430.6MB, alloc=516.3MB, time=77.67 memory used=3534.5MB, alloc=516.3MB, time=80.42 memory used=3589.7MB, alloc=516.3MB, time=82.41 memory used=3715.7MB, alloc=516.3MB, time=86.88 memory used=3820.2MB, alloc=516.3MB, time=88.81 memory used=3870.9MB, alloc=516.3MB, time=90.41 memory used=3925.7MB, alloc=516.3MB, time=92.11 memory used=3983.0MB, alloc=516.3MB, time=93.76 memory used=4028.6MB, alloc=516.3MB, time=95.37 memory used=4237.6MB, alloc=540.3MB, time=101.25 memory used=4447.6MB, alloc=564.3MB, time=106.15 memory used=4593.7MB, alloc=564.3MB, time=108.12 memory used=4807.9MB, alloc=588.3MB, time=112.86 memory used=5041.9MB, alloc=612.3MB, time=120.31 memory used=5250.8MB, alloc=612.3MB, time=124.40 |\^/| 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(); 1428256502 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 3 F := [y z - 10, -5 y + 7 z - z, 6 x y - 9 x z - 2 z ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 2 3 2 G := [-9 z - 12 z + y, 9 x z + x y - 6 z , -7 z + 6 y + 9 x] > Problem := [F,G]; 2 2 2 2 3 Problem := [[y z - 10, -5 y + 7 z - z, 6 x y - 9 x z - 2 z ], 3 2 2 2 3 2 [-9 z - 12 z + y, 9 x z + x y - 6 z , -7 z + 6 y + 9 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=24.9MB, alloc=32.3MB, time=0.83 memory used=44.8MB, alloc=60.3MB, time=1.34 memory used=85.7MB, alloc=60.3MB, time=2.38 memory used=125.0MB, alloc=60.3MB, time=3.38 memory used=163.3MB, alloc=84.3MB, time=4.40 memory used=221.0MB, alloc=92.3MB, time=5.18 memory used=283.6MB, alloc=92.3MB, time=6.15 memory used=352.7MB, alloc=92.3MB, time=7.41 memory used=401.5MB, alloc=92.3MB, time=7.87 memory used=464.5MB, alloc=92.3MB, time=9.02 memory used=530.2MB, alloc=92.3MB, time=10.64 memory used=593.9MB, alloc=116.3MB, time=12.30 memory used=673.0MB, alloc=372.3MB, time=14.51 memory used=752.0MB, alloc=372.3MB, time=15.97 memory used=838.7MB, alloc=396.3MB, time=17.99 memory used=946.7MB, alloc=396.3MB, time=20.88 memory used=1054.1MB, alloc=420.3MB, time=23.77 memory used=1203.1MB, alloc=444.3MB, time=26.93 memory used=1344.3MB, alloc=444.3MB, time=29.94 memory used=1484.6MB, alloc=468.3MB, time=33.98 memory used=1604.7MB, alloc=468.3MB, time=36.79 memory used=1725.1MB, alloc=468.3MB, time=39.39 memory used=1842.9MB, alloc=468.3MB, time=42.14 memory used=1953.9MB, alloc=492.3MB, time=43.80 memory used=2052.7MB, alloc=492.3MB, time=44.63 memory used=2154.0MB, alloc=492.3MB, time=45.53 memory used=2275.8MB, alloc=492.3MB, time=48.54 memory used=2360.9MB, alloc=492.3MB, time=49.10 memory used=2523.9MB, alloc=492.3MB, time=51.71 memory used=2677.7MB, alloc=492.3MB, time=54.48 memory used=2790.9MB, alloc=492.3MB, time=57.78 memory used=2973.2MB, alloc=492.3MB, time=61.08 memory used=3116.7MB, alloc=492.3MB, time=63.70 memory used=3245.5MB, alloc=492.3MB, time=66.35 memory used=3334.1MB, alloc=492.3MB, time=68.80 memory used=3421.8MB, alloc=516.3MB, time=71.46 memory used=3511.7MB, alloc=516.3MB, time=74.27 memory used=3594.3MB, alloc=516.3MB, time=76.70 memory used=3691.6MB, alloc=516.3MB, time=78.93 memory used=3777.6MB, alloc=516.3MB, time=80.96 memory used=3844.9MB, alloc=516.3MB, time=83.22 memory used=3938.3MB, alloc=540.3MB, time=85.65 memory used=4041.7MB, alloc=540.3MB, time=88.00 memory used=4113.9MB, alloc=540.3MB, time=89.69 memory used=4202.2MB, alloc=540.3MB, time=93.02 memory used=4282.8MB, alloc=540.3MB, time=95.28 memory used=4369.4MB, alloc=540.3MB, time=97.38 memory used=4426.5MB, alloc=540.3MB, time=99.28 memory used=4478.9MB, alloc=540.3MB, time=101.06 memory used=4529.3MB, alloc=540.3MB, time=102.60 memory used=4591.2MB, alloc=540.3MB, time=104.48 memory used=4786.8MB, alloc=564.3MB, time=108.52 memory used=4988.8MB, alloc=564.3MB, time=114.45 memory used=5194.6MB, alloc=588.3MB, time=121.04 memory used=5389.1MB, alloc=612.3MB, time=127.84 |\^/| 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(); 1428256802 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 2 2 F := [-14 x y + 3 x y z - 17 y z, 9 x + 8 y - 8, 3 y z + 5 x y + 8 y ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 3 2 G := [15 z + 20 x + 15 y, -4 x y - 8 x y - 7 y, -4 x + 2 x z - 10 z] > Problem := [F,G]; Problem := [ 2 2 2 2 2 2 [-14 x y + 3 x y z - 17 y z, 9 x + 8 y - 8, 3 y z + 5 x y + 8 y ], 3 2 3 2 [15 z + 20 x + 15 y, -4 x y - 8 x y - 7 y, -4 x + 2 x 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=4.4MB, alloc=32.3MB, time=0.30 memory used=26.3MB, alloc=32.3MB, time=0.88 memory used=46.8MB, alloc=32.3MB, time=1.43 memory used=66.1MB, alloc=56.3MB, time=1.95 memory used=106.6MB, alloc=60.3MB, time=3.05 memory used=145.5MB, alloc=60.3MB, time=4.11 memory used=184.6MB, alloc=84.3MB, time=5.20 memory used=226.9MB, alloc=84.3MB, time=6.39 memory used=292.4MB, alloc=116.3MB, time=8.08 memory used=374.1MB, alloc=372.3MB, time=10.32 memory used=463.5MB, alloc=396.3MB, time=12.58 memory used=574.6MB, alloc=420.3MB, time=15.42 memory used=708.1MB, alloc=444.3MB, time=19.08 memory used=834.8MB, alloc=444.3MB, time=22.49 memory used=949.7MB, alloc=468.3MB, time=25.63 memory used=1093.7MB, alloc=468.3MB, time=29.02 memory used=1199.2MB, alloc=468.3MB, time=32.06 memory used=1291.0MB, alloc=492.3MB, time=34.45 memory used=1391.6MB, alloc=492.3MB, time=37.18 memory used=1491.7MB, alloc=492.3MB, time=39.84 memory used=1568.0MB, alloc=492.3MB, time=42.08 memory used=1641.3MB, alloc=492.3MB, time=44.30 memory used=1707.3MB, alloc=492.3MB, time=46.39 memory used=1791.8MB, alloc=492.3MB, time=48.76 memory used=1858.1MB, alloc=492.3MB, time=50.80 memory used=1922.7MB, alloc=516.3MB, time=52.80 memory used=1996.3MB, alloc=516.3MB, time=55.15 memory used=2096.1MB, alloc=516.3MB, time=58.02 memory used=2185.9MB, alloc=516.3MB, time=60.93 memory used=2265.6MB, alloc=540.3MB, time=63.69 memory used=2351.1MB, alloc=540.3MB, time=66.61 memory used=2423.0MB, alloc=540.3MB, time=69.09 memory used=2513.1MB, alloc=564.3MB, time=71.58 memory used=2594.3MB, alloc=564.3MB, time=74.16 memory used=2678.1MB, alloc=564.3MB, time=76.80 memory used=2774.1MB, alloc=564.3MB, time=79.94 memory used=2881.1MB, alloc=588.3MB, time=83.65 memory used=2965.6MB, alloc=588.3MB, time=86.82 memory used=3022.5MB, alloc=588.3MB, time=89.13 memory used=3133.1MB, alloc=612.3MB, time=92.58 memory used=3220.2MB, alloc=612.3MB, time=95.93 memory used=3497.2MB, alloc=636.3MB, time=102.92 memory used=3760.6MB, alloc=660.3MB, time=111.47 memory used=4042.4MB, alloc=684.3MB, time=120.40 |\^/| 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(); 1428257102 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 3 2 3 F := [7 x y z - 14 y - 19 x, 5 z - x - x z, -10 z + 9 y z - 7 x] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 G := [-11 x y - 4 x y + 5, -9 x y z - 7 x z - 7 x, 7 y - 5 x] > Problem := [F,G]; 3 3 2 3 Problem := [[7 x y z - 14 y - 19 x, 5 z - x - x z, -10 z + 9 y z - 7 x], 2 3 [-11 x y - 4 x y + 5, -9 x y z - 7 x z - 7 x, 7 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=0.32 memory used=26.2MB, alloc=32.3MB, time=0.89 memory used=46.9MB, alloc=32.3MB, time=1.41 memory used=65.0MB, alloc=56.3MB, time=1.88 memory used=105.5MB, alloc=60.3MB, time=2.87 memory used=146.5MB, alloc=60.3MB, time=3.78 memory used=186.8MB, alloc=60.3MB, time=4.75 memory used=226.1MB, alloc=84.3MB, time=5.60 memory used=289.4MB, alloc=92.3MB, time=6.90 memory used=364.8MB, alloc=92.3MB, time=8.50 memory used=411.1MB, alloc=92.3MB, time=9.40 memory used=468.4MB, alloc=92.3MB, time=10.59 memory used=533.7MB, alloc=116.3MB, time=12.17 memory used=605.8MB, alloc=372.3MB, time=14.05 memory used=694.9MB, alloc=396.3MB, time=16.17 memory used=806.8MB, alloc=396.3MB, time=18.64 memory used=911.8MB, alloc=396.3MB, time=21.67 memory used=981.4MB, alloc=420.3MB, time=30.50 memory used=1044.5MB, alloc=420.3MB, time=30.86 memory used=1178.5MB, alloc=420.3MB, time=33.89 memory used=1306.5MB, alloc=444.3MB, time=36.79 memory used=1453.2MB, alloc=444.3MB, time=45.05 memory used=1570.7MB, alloc=468.3MB, time=47.77 memory used=1688.1MB, alloc=468.3MB, time=50.16 memory used=1795.4MB, alloc=468.3MB, time=51.51 memory used=1935.9MB, alloc=468.3MB, time=115.73 memory used=2015.1MB, alloc=468.3MB, time=116.23 memory used=2089.3MB, alloc=468.3MB, time=116.66 memory used=2171.8MB, alloc=468.3MB, time=117.08 memory used=2283.1MB, alloc=468.3MB, time=118.12 memory used=2366.6MB, alloc=468.3MB, time=118.81 memory used=2450.3MB, alloc=468.3MB, time=119.32 memory used=2533.3MB, alloc=468.3MB, time=119.83 memory used=2715.2MB, alloc=468.3MB, time=121.02 memory used=2922.2MB, alloc=468.3MB, time=121.83 memory used=3132.4MB, alloc=468.3MB, time=122.69 memory used=3288.8MB, alloc=468.3MB, time=124.06 memory used=3379.2MB, alloc=468.3MB, time=124.90 memory used=3471.6MB, alloc=492.3MB, time=136.86 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428257402 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 3 2 2 2 F := [-19 x - 17 z - 8 x z, x y + 2 x z + 4 x, -7 z - 9 z + 1] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 2 G := [6 x z + 6 x y z + 1, -10 x - 5 x z + 10 y , 8 x y z + 2 y z + 2 x z] > Problem := [F,G]; 3 3 2 2 2 Problem := [[-19 x - 17 z - 8 x z, x y + 2 x z + 4 x, -7 z - 9 z + 1], 2 3 2 2 [6 x z + 6 x y z + 1, -10 x - 5 x z + 10 y , 8 x y z + 2 y z + 2 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.32 memory used=26.8MB, alloc=32.3MB, time=0.89 memory used=48.1MB, alloc=32.3MB, time=1.43 memory used=68.4MB, alloc=56.3MB, time=1.97 memory used=109.2MB, alloc=60.3MB, time=3.04 memory used=147.9MB, alloc=84.3MB, time=4.07 memory used=208.6MB, alloc=92.3MB, time=5.67 memory used=268.1MB, alloc=116.3MB, time=7.25 memory used=350.1MB, alloc=116.3MB, time=9.44 memory used=430.9MB, alloc=140.3MB, time=11.70 memory used=497.8MB, alloc=140.3MB, time=13.56 memory used=569.9MB, alloc=396.3MB, time=15.62 memory used=669.3MB, alloc=420.3MB, time=18.45 memory used=795.4MB, alloc=444.3MB, time=22.02 memory used=933.6MB, alloc=468.3MB, time=26.08 memory used=1081.3MB, alloc=492.3MB, time=30.59 memory used=1212.7MB, alloc=492.3MB, time=34.71 memory used=1329.2MB, alloc=516.3MB, time=38.38 memory used=1440.2MB, alloc=516.3MB, time=41.78 memory used=1540.4MB, alloc=516.3MB, time=44.97 memory used=1663.9MB, alloc=516.3MB, time=49.38 memory used=1753.4MB, alloc=540.3MB, time=52.53 memory used=1843.9MB, alloc=540.3MB, time=55.92 memory used=1927.2MB, alloc=540.3MB, time=58.91 memory used=2005.7MB, alloc=540.3MB, time=61.75 memory used=2075.8MB, alloc=540.3MB, time=64.48 memory used=2131.5MB, alloc=540.3MB, time=66.61 memory used=2206.6MB, alloc=540.3MB, time=69.68 memory used=2253.2MB, alloc=540.3MB, time=71.72 memory used=2315.5MB, alloc=540.3MB, time=74.41 memory used=2538.1MB, alloc=564.3MB, time=81.63 memory used=2779.5MB, alloc=588.3MB, time=90.53 memory used=2987.3MB, alloc=612.3MB, time=97.97 |\^/| 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(); 1428257702 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 3 2 2 2 2 F := [-6 y + 9 y z - 11 y z, 3 z + 7 z - 6 x, -x z + 10 y z - 8 y z ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 3 2 3 3 2 G := [-7 z - 19 x y + 8 y z, -9 x y - 5 y - 6 y z , -6 y + 4 z + 9 z ] > Problem := [F,G]; Problem := [ 3 2 3 2 2 2 2 [-6 y + 9 y z - 11 y z, 3 z + 7 z - 6 x, -x z + 10 y z - 8 y z ], 3 2 3 2 3 3 2 [-7 z - 19 x y + 8 y z, -9 x y - 5 y - 6 y z , -6 y + 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=4.4MB, alloc=32.3MB, time=0.31 memory used=27.3MB, alloc=32.3MB, time=0.91 memory used=48.7MB, alloc=32.3MB, time=1.47 memory used=67.7MB, alloc=56.3MB, time=1.96 memory used=112.3MB, alloc=68.3MB, time=3.04 memory used=153.9MB, alloc=92.3MB, time=4.04 memory used=215.0MB, alloc=92.3MB, time=5.63 memory used=276.6MB, alloc=116.3MB, time=7.25 memory used=361.1MB, alloc=116.3MB, time=9.07 memory used=433.2MB, alloc=116.3MB, time=10.71 memory used=514.4MB, alloc=116.3MB, time=12.42 memory used=590.9MB, alloc=372.3MB, time=14.09 memory used=678.2MB, alloc=396.3MB, time=16.04 memory used=792.7MB, alloc=396.3MB, time=18.34 memory used=897.8MB, alloc=396.3MB, time=20.25 memory used=1016.0MB, alloc=420.3MB, time=22.62 memory used=1146.8MB, alloc=444.3MB, time=25.90 memory used=1294.4MB, alloc=468.3MB, time=29.25 memory used=1417.7MB, alloc=468.3MB, time=32.13 memory used=1561.9MB, alloc=468.3MB, time=35.48 memory used=1694.5MB, alloc=492.3MB, time=38.65 memory used=1812.4MB, alloc=492.3MB, time=41.35 memory used=1958.8MB, alloc=492.3MB, time=44.92 memory used=2070.2MB, alloc=516.3MB, time=65.44 memory used=2168.7MB, alloc=516.3MB, time=66.14 memory used=2260.9MB, alloc=516.3MB, time=66.89 memory used=2379.5MB, alloc=516.3MB, time=74.42 memory used=2534.5MB, alloc=516.3MB, time=75.99 memory used=2672.7MB, alloc=516.3MB, time=97.70 memory used=2772.8MB, alloc=516.3MB, time=98.32 memory used=2866.8MB, alloc=516.3MB, time=104.74 memory used=3016.1MB, alloc=516.3MB, time=113.84 memory used=3121.7MB, alloc=516.3MB, time=116.92 memory used=3294.8MB, alloc=516.3MB, time=119.31 memory used=3481.7MB, alloc=540.3MB, time=122.05 memory used=3725.0MB, alloc=540.3MB, time=126.49 memory used=3970.8MB, alloc=540.3MB, time=135.35 |\^/| 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(); 1428258002 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; F := [ 3 2 2 3 2 3 2 11 x + 14 x z - 20 x y, -4 x z + 10 y - 3 y z , -5 x + 4 x y - 10 x y ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 2 3 G := [2 x y + y z - 18 x, -8 x y + 6 z, -8 x z + 6 y z + 9 z ] > Problem := [F,G]; Problem := [[ 3 2 2 3 2 3 2 11 x + 14 x z - 20 x y, -4 x z + 10 y - 3 y z , -5 x + 4 x y - 10 x y 2 2 2 2 2 3 ], [2 x y + y z - 18 x, -8 x y + 6 z, -8 x z + 6 y z + 9 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=32.5MB, alloc=40.3MB, time=1.01 memory used=61.9MB, alloc=44.3MB, time=1.80 memory used=88.9MB, alloc=68.3MB, time=2.53 memory used=137.1MB, alloc=68.3MB, time=3.78 memory used=181.8MB, alloc=92.3MB, time=4.99 memory used=246.6MB, alloc=100.3MB, time=6.85 memory used=312.8MB, alloc=124.3MB, time=8.62 memory used=392.9MB, alloc=124.3MB, time=10.78 memory used=470.8MB, alloc=404.3MB, time=13.00 memory used=584.4MB, alloc=404.3MB, time=16.14 memory used=698.3MB, alloc=428.3MB, time=19.44 memory used=835.8MB, alloc=452.3MB, time=23.44 memory used=993.6MB, alloc=476.3MB, time=28.19 memory used=1162.9MB, alloc=500.3MB, time=33.43 memory used=1293.0MB, alloc=500.3MB, time=37.32 memory used=1420.4MB, alloc=500.3MB, time=41.40 memory used=1537.5MB, alloc=524.3MB, time=44.95 memory used=1639.6MB, alloc=524.3MB, time=48.06 memory used=1749.1MB, alloc=524.3MB, time=51.68 memory used=1850.8MB, alloc=524.3MB, time=54.94 memory used=1956.5MB, alloc=524.3MB, time=58.56 memory used=2071.1MB, alloc=548.3MB, time=62.67 memory used=2164.5MB, alloc=548.3MB, time=66.02 memory used=2242.6MB, alloc=548.3MB, time=68.34 memory used=2324.8MB, alloc=548.3MB, time=71.22 memory used=2394.4MB, alloc=548.3MB, time=73.56 memory used=2455.7MB, alloc=572.3MB, time=75.83 memory used=2519.8MB, alloc=572.3MB, time=78.73 memory used=2567.0MB, alloc=572.3MB, time=80.30 memory used=2609.2MB, alloc=572.3MB, time=81.98 memory used=2833.2MB, alloc=596.3MB, time=88.03 memory used=3002.2MB, alloc=620.3MB, time=92.51 memory used=3237.0MB, alloc=644.3MB, time=100.34 memory used=3405.1MB, alloc=668.3MB, time=105.88 memory used=3570.0MB, alloc=692.3MB, time=112.07 |\^/| 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(); 1428258302 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 2 2 3 2 3 F := [13 x z + y - 7 y z, -10 x y + 4 x z + 6, -6 x - 7 x z + 4 z ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 3 2 G := [14 x y + 9 y + 4 z, -5 x z - 8 x + 5 y, 8 x + 2 x + x z] > Problem := [F,G]; Problem := [ 2 3 2 2 2 3 2 3 [13 x z + y - 7 y z, -10 x y + 4 x z + 6, -6 x - 7 x z + 4 z ], 2 2 3 2 [14 x y + 9 y + 4 z, -5 x z - 8 x + 5 y, 8 x + 2 x + x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.31 memory used=26.9MB, alloc=32.3MB, time=0.89 memory used=47.6MB, alloc=36.3MB, time=1.45 memory used=67.3MB, alloc=60.3MB, time=1.98 memory used=108.1MB, alloc=60.3MB, time=3.00 memory used=143.9MB, alloc=60.3MB, time=3.89 memory used=184.7MB, alloc=92.3MB, time=4.96 memory used=248.6MB, alloc=92.3MB, time=6.61 memory used=311.6MB, alloc=116.3MB, time=8.20 memory used=379.7MB, alloc=372.3MB, time=9.99 memory used=464.2MB, alloc=396.3MB, time=12.23 memory used=578.1MB, alloc=420.3MB, time=15.13 memory used=712.7MB, alloc=444.3MB, time=18.48 memory used=832.5MB, alloc=444.3MB, time=21.22 memory used=933.2MB, alloc=444.3MB, time=23.68 memory used=1054.0MB, alloc=468.3MB, time=26.88 memory used=1156.4MB, alloc=468.3MB, time=29.61 memory used=1259.0MB, alloc=468.3MB, time=32.49 memory used=1341.9MB, alloc=468.3MB, time=34.73 memory used=1423.0MB, alloc=492.3MB, time=37.18 memory used=1508.4MB, alloc=492.3MB, time=39.77 memory used=1576.0MB, alloc=492.3MB, time=41.73 memory used=1647.3MB, alloc=492.3MB, time=43.91 memory used=1713.9MB, alloc=492.3MB, time=45.90 memory used=1781.1MB, alloc=492.3MB, time=47.51 memory used=1842.3MB, alloc=492.3MB, time=49.77 memory used=1890.5MB, alloc=492.3MB, time=51.41 memory used=1946.8MB, alloc=492.3MB, time=53.55 memory used=2144.0MB, alloc=516.3MB, time=59.10 memory used=2348.9MB, alloc=540.3MB, time=65.30 memory used=2538.4MB, alloc=564.3MB, time=71.09 memory used=2692.9MB, alloc=588.3MB, time=75.80 memory used=2862.3MB, alloc=612.3MB, time=81.27 memory used=3021.4MB, alloc=612.3MB, time=86.43 memory used=3138.7MB, alloc=636.3MB, time=90.42 memory used=3256.9MB, alloc=636.3MB, time=94.55 memory used=3366.5MB, alloc=636.3MB, time=98.52 memory used=3479.9MB, alloc=636.3MB, time=102.55 memory used=3602.7MB, alloc=636.3MB, time=106.84 memory used=3717.1MB, alloc=636.3MB, time=109.83 memory used=3806.4MB, alloc=636.3MB, time=113.55 |\^/| 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(); 1428258602 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; F := 2 2 2 2 2 [-3 x y + 6 x y z + 2 z, -5 y z + 10 y z - 10 z, -6 x z + 4 y z - 2 z ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 3 G := [16 x y z + 11 x z + z, 4 x z - 7 y z - 8 z , 2 y - 8 y z - 3 z] > Problem := [F,G]; Problem := [ 2 2 2 2 2 [-3 x y + 6 x y z + 2 z, -5 y z + 10 y z - 10 z, -6 x z + 4 y z - 2 z ] 2 2 3 , [16 x y z + 11 x z + z, 4 x z - 7 y z - 8 z , 2 y - 8 y z - 3 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.3MB, alloc=32.3MB, time=0.83 memory used=47.0MB, alloc=32.3MB, time=1.35 memory used=66.4MB, alloc=56.3MB, time=1.87 memory used=106.2MB, alloc=60.3MB, time=2.91 memory used=143.4MB, alloc=84.3MB, time=3.91 memory used=200.0MB, alloc=92.3MB, time=5.47 memory used=255.5MB, alloc=116.3MB, time=7.00 memory used=333.4MB, alloc=116.3MB, time=9.27 memory used=409.8MB, alloc=140.3MB, time=11.53 memory used=510.3MB, alloc=140.3MB, time=14.66 memory used=608.3MB, alloc=164.3MB, time=17.78 memory used=712.1MB, alloc=188.3MB, time=21.06 memory used=803.5MB, alloc=468.3MB, time=24.08 memory used=957.6MB, alloc=492.3MB, time=28.85 memory used=1120.6MB, alloc=516.3MB, time=33.91 memory used=1295.5MB, alloc=540.3MB, time=39.42 memory used=1483.2MB, alloc=564.3MB, time=45.42 memory used=1680.1MB, alloc=588.3MB, time=51.78 memory used=1885.8MB, alloc=612.3MB, time=58.61 memory used=2097.7MB, alloc=636.3MB, time=65.53 memory used=2318.9MB, alloc=660.3MB, time=72.87 memory used=2543.6MB, alloc=684.3MB, time=81.48 memory used=2747.7MB, alloc=708.3MB, time=92.53 memory used=2958.5MB, alloc=732.3MB, time=104.66 |\^/| 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(); 1428258902 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 3 F := [5 - 7 z, 2 x - y z, -4 x y - 8 x y z - z ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 3 2 G := [-14 y z + 9 x y, x y - 2 y + 6 z, 7 x z - x y] > Problem := [F,G]; 3 2 3 Problem := [[5 - 7 z, 2 x - y z, -4 x y - 8 x y z - z ], 2 2 3 2 [-14 y z + 9 x y, x y - 2 y + 6 z, 7 x z - x y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=27.2MB, alloc=32.3MB, time=0.89 memory used=48.7MB, alloc=36.3MB, time=1.44 memory used=68.5MB, alloc=60.3MB, time=1.97 memory used=110.6MB, alloc=60.3MB, time=2.98 memory used=147.9MB, alloc=84.3MB, time=3.93 memory used=210.2MB, alloc=92.3MB, time=5.47 memory used=272.6MB, alloc=116.3MB, time=7.02 memory used=335.4MB, alloc=116.3MB, time=8.56 memory used=412.1MB, alloc=372.3MB, time=10.59 memory used=495.8MB, alloc=396.3MB, time=12.67 memory used=602.4MB, alloc=420.3MB, time=15.36 memory used=724.0MB, alloc=444.3MB, time=18.29 memory used=849.4MB, alloc=468.3MB, time=21.15 memory used=966.5MB, alloc=468.3MB, time=24.03 memory used=1066.8MB, alloc=468.3MB, time=26.51 memory used=1178.4MB, alloc=492.3MB, time=29.64 memory used=1258.0MB, alloc=492.3MB, time=31.60 memory used=1349.0MB, alloc=492.3MB, time=34.40 memory used=1414.1MB, alloc=516.3MB, time=35.99 memory used=1468.2MB, alloc=516.3MB, time=37.43 memory used=1523.2MB, alloc=516.3MB, time=38.98 memory used=1601.8MB, alloc=516.3MB, time=41.52 memory used=1675.9MB, alloc=516.3MB, time=44.13 memory used=1722.0MB, alloc=516.3MB, time=45.75 memory used=1765.8MB, alloc=516.3MB, time=47.32 memory used=1957.9MB, alloc=540.3MB, time=52.43 memory used=2121.8MB, alloc=564.3MB, time=56.36 memory used=2277.6MB, alloc=588.3MB, time=60.56 memory used=2424.0MB, alloc=612.3MB, time=64.61 memory used=2578.6MB, alloc=636.3MB, time=69.83 memory used=2706.7MB, alloc=660.3MB, time=74.40 memory used=2808.6MB, alloc=660.3MB, time=77.50 memory used=2923.9MB, alloc=660.3MB, time=81.86 memory used=3036.8MB, alloc=660.3MB, time=86.42 memory used=3362.8MB, alloc=684.3MB, time=95.68 memory used=3699.6MB, alloc=708.3MB, time=106.37 memory used=4053.8MB, alloc=732.3MB, time=117.45 |\^/| 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(); 1428259202 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 2 2 3 F := [-9 x + 8 x z - 7 z , 2 x y - 8 y z - 6, 3 y z + 3 z ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 3 2 G := [-6 x + 19 y - 3 y, 2 y - 8 y + 4, -7 y - 8 z] > Problem := [F,G]; 3 2 2 2 2 3 Problem := [[-9 x + 8 x z - 7 z , 2 x y - 8 y z - 6, 3 y z + 3 z ], 2 2 3 2 [-6 x + 19 y - 3 y, 2 y - 8 y + 4, -7 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=4.4MB, alloc=32.3MB, time=0.31 memory used=26.8MB, alloc=32.3MB, time=0.88 memory used=47.2MB, alloc=32.3MB, time=1.41 memory used=65.9MB, alloc=56.3MB, time=1.93 memory used=107.1MB, alloc=60.3MB, time=2.99 memory used=145.5MB, alloc=60.3MB, time=3.94 memory used=181.6MB, alloc=84.3MB, time=4.92 memory used=222.9MB, alloc=84.3MB, time=6.07 memory used=286.7MB, alloc=92.3MB, time=7.70 memory used=349.8MB, alloc=116.3MB, time=9.31 memory used=426.1MB, alloc=116.3MB, time=11.24 memory used=497.9MB, alloc=372.3MB, time=13.02 memory used=581.6MB, alloc=396.3MB, time=15.17 memory used=684.1MB, alloc=396.3MB, time=18.17 memory used=790.7MB, alloc=420.3MB, time=21.16 memory used=918.3MB, alloc=444.3MB, time=24.80 memory used=1061.4MB, alloc=444.3MB, time=28.85 memory used=1184.1MB, alloc=468.3MB, time=32.11 memory used=1332.8MB, alloc=468.3MB, time=34.81 memory used=1448.9MB, alloc=468.3MB, time=37.58 memory used=1566.3MB, alloc=468.3MB, time=40.71 memory used=1724.2MB, alloc=492.3MB, time=45.30 memory used=1898.7MB, alloc=516.3MB, time=50.53 memory used=2091.9MB, alloc=540.3MB, time=56.14 memory used=2286.0MB, alloc=564.3MB, time=62.59 memory used=2483.1MB, alloc=588.3MB, time=69.29 memory used=2670.7MB, alloc=612.3MB, time=75.69 memory used=2867.6MB, alloc=636.3MB, time=82.45 memory used=3081.6MB, alloc=660.3MB, time=88.97 memory used=3264.4MB, alloc=684.3MB, time=95.57 memory used=3427.4MB, alloc=708.3MB, time=101.36 memory used=3650.3MB, alloc=732.3MB, time=112.58 |\^/| 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(); 1428259502 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 F := [16 y z - 10 x y + 4 x, -2 x y - 9 x y + 9 x, -3 x z + x y - 8] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 2 3 G := [-9 x y + 6, -2 x - 9 x y + 8 y, 3 x y - 10 y ] > Problem := [F,G]; 2 2 2 Problem := [[16 y z - 10 x y + 4 x, -2 x y - 9 x y + 9 x, -3 x z + x y - 8], 2 3 2 2 3 [-9 x y + 6, -2 x - 9 x y + 8 y, 3 x y - 10 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=27.0MB, alloc=32.3MB, time=0.90 memory used=46.8MB, alloc=32.3MB, time=1.40 memory used=66.0MB, alloc=56.3MB, time=1.91 memory used=107.3MB, alloc=60.3MB, time=3.00 memory used=146.5MB, alloc=60.3MB, time=4.00 memory used=184.9MB, alloc=84.3MB, time=5.04 memory used=235.5MB, alloc=84.3MB, time=6.38 memory used=297.0MB, alloc=116.3MB, time=8.28 memory used=376.9MB, alloc=116.3MB, time=10.74 memory used=450.2MB, alloc=140.3MB, time=13.02 memory used=544.7MB, alloc=164.3MB, time=15.93 memory used=656.8MB, alloc=188.3MB, time=19.44 memory used=772.7MB, alloc=468.3MB, time=23.14 memory used=906.7MB, alloc=492.3MB, time=29.86 memory used=1054.0MB, alloc=516.3MB, time=37.73 memory used=1214.2MB, alloc=516.3MB, time=47.22 memory used=1373.4MB, alloc=540.3MB, time=56.74 memory used=1556.7MB, alloc=540.3MB, time=67.66 memory used=1740.1MB, alloc=564.3MB, time=78.62 N1 := 5355 > GB := Basis(F, plex(op(vars))); 4 3 2 3 2 GB := [8 x - 18 x - 243 x - 168 x - 1728, -4 x + 27 x + 108 y + 84, 2 2 4 x + 72 z - 27 x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1958.5MB, alloc=564.3MB, time=87.87 N2 := 813 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 H := [16 y z - 10 x y + 4 x, -2 x y - 9 x y + 9 x, -3 z x + y x - 8, 2 3 2 2 3 -9 x y + 6, -2 x - 9 x y + 8 y, 3 x y - 10 y ] > J:=[op(GB),op(G)]; 4 3 2 3 2 J := [8 x - 18 x - 243 x - 168 x - 1728, -4 x + 27 x + 108 y + 84, 2 2 2 3 2 2 3 72 z + 4 x - 27 x, -9 x y + 6, -2 x - 9 x y + 8 y, 3 x y - 10 y ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; 11 featureList := [6, 14, 18, 3, 3, 3, 2, 1, 1, 1/3, --, 5/8, 1/8, 6, 11, 18, 4, 4, 16 12 3, 2, 1, 2/3, 1/6, --, 6/19, 1/19, 3, 0, -1] 19 > save(F, G, cat("ranSet/33", convert(F, string),".txt")); > quit memory used=2004.9MB, alloc=564.3MB, time=90.00 |\^/| 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(); 1428259747 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 3 2 2 3 F := [20 x y - 16 z + 15 z, 3 x - 10 x z - 9 y z, -6 z - 4 x y - 5 x z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 3 2 2 G := [-16 y z + 8 y + 13 y z, 8 x + 3 x y z - 9 x z, 7 x y + 6 x z - x] > Problem := [F,G]; Problem := [ 2 2 3 2 2 3 [20 x y - 16 z + 15 z, 3 x - 10 x z - 9 y z, -6 z - 4 x y - 5 x z], 2 2 3 2 2 [-16 y z + 8 y + 13 y z, 8 x + 3 x y z - 9 x z, 7 x y + 6 x z - x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.2MB, alloc=32.3MB, time=0.87 memory used=46.6MB, alloc=32.3MB, time=1.39 memory used=65.5MB, alloc=56.3MB, time=1.91 memory used=105.1MB, alloc=60.3MB, time=2.97 memory used=144.1MB, alloc=84.3MB, time=3.97 memory used=206.3MB, alloc=92.3MB, time=5.67 memory used=271.5MB, alloc=116.3MB, time=7.36 memory used=356.4MB, alloc=116.3MB, time=9.69 memory used=428.6MB, alloc=396.3MB, time=11.70 memory used=535.0MB, alloc=396.3MB, time=14.53 memory used=648.6MB, alloc=420.3MB, time=17.46 memory used=778.9MB, alloc=444.3MB, time=20.99 memory used=912.3MB, alloc=444.3MB, time=24.35 memory used=1039.3MB, alloc=468.3MB, time=27.66 memory used=1163.6MB, alloc=468.3MB, time=31.03 memory used=1278.2MB, alloc=492.3MB, time=34.09 memory used=1396.0MB, alloc=492.3MB, time=36.89 memory used=1494.7MB, alloc=492.3MB, time=39.77 memory used=1604.1MB, alloc=492.3MB, time=43.07 memory used=1711.6MB, alloc=516.3MB, time=46.45 memory used=1817.4MB, alloc=516.3MB, time=50.03 memory used=1895.0MB, alloc=516.3MB, time=52.26 memory used=1975.2MB, alloc=516.3MB, time=54.04 memory used=2061.0MB, alloc=516.3MB, time=57.05 memory used=2124.1MB, alloc=516.3MB, time=59.12 memory used=2206.8MB, alloc=516.3MB, time=62.38 memory used=2286.1MB, alloc=540.3MB, time=65.52 memory used=2345.2MB, alloc=540.3MB, time=67.73 memory used=2415.0MB, alloc=540.3MB, time=70.51 memory used=2466.4MB, alloc=540.3MB, time=72.43 memory used=2525.8MB, alloc=540.3MB, time=74.72 memory used=2751.9MB, alloc=564.3MB, time=82.41 memory used=2949.5MB, alloc=588.3MB, time=88.49 memory used=3124.8MB, alloc=612.3MB, time=94.35 memory used=3290.2MB, alloc=636.3MB, time=99.24 memory used=3488.2MB, alloc=636.3MB, time=103.43 memory used=3640.4MB, alloc=660.3MB, time=107.55 memory used=3823.5MB, alloc=660.3MB, time=113.66 |\^/| 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(); 1428260047 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 3 2 F := [15 x y + 2 y z - 3 x y, 3 x y + 8 y , 5 y z + y - 5 z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 2 2 2 2 2 2 G := [7 x y - 9 z - 6 x , 9 y z + 10 y + 10 z , -10 x z - 3 y z - 2 x ] > Problem := [F,G]; 2 2 2 3 2 Problem := [[15 x y + 2 y z - 3 x y, 3 x y + 8 y , 5 y z + y - 5 z], 2 3 2 2 2 2 2 2 2 [7 x y - 9 z - 6 x , 9 y z + 10 y + 10 z , -10 x z - 3 y z - 2 x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.31 memory used=26.6MB, alloc=32.3MB, time=0.88 memory used=47.7MB, alloc=32.3MB, time=1.44 memory used=67.1MB, alloc=56.3MB, time=1.96 memory used=108.5MB, alloc=60.3MB, time=2.96 memory used=148.3MB, alloc=60.3MB, time=3.97 memory used=186.9MB, alloc=84.3MB, time=4.96 memory used=231.3MB, alloc=84.3MB, time=6.15 memory used=290.6MB, alloc=92.3MB, time=7.82 memory used=353.9MB, alloc=116.3MB, time=9.44 memory used=424.8MB, alloc=116.3MB, time=11.23 memory used=500.0MB, alloc=372.3MB, time=13.01 memory used=580.3MB, alloc=372.3MB, time=15.36 memory used=663.0MB, alloc=396.3MB, time=17.42 memory used=769.3MB, alloc=396.3MB, time=19.56 memory used=878.5MB, alloc=396.3MB, time=22.54 memory used=982.2MB, alloc=420.3MB, time=25.57 memory used=1113.9MB, alloc=420.3MB, time=29.34 memory used=1236.6MB, alloc=444.3MB, time=33.25 memory used=1394.2MB, alloc=468.3MB, time=37.47 memory used=1486.2MB, alloc=468.3MB, time=38.58 memory used=1631.2MB, alloc=468.3MB, time=42.36 memory used=1771.3MB, alloc=468.3MB, time=45.85 memory used=1922.8MB, alloc=492.3MB, time=50.28 memory used=2055.2MB, alloc=516.3MB, time=54.37 memory used=2185.1MB, alloc=516.3MB, time=57.70 memory used=2313.9MB, alloc=516.3MB, time=61.71 memory used=2417.3MB, alloc=516.3MB, time=64.66 memory used=2555.9MB, alloc=540.3MB, time=69.87 memory used=2661.7MB, alloc=540.3MB, time=73.58 memory used=2751.7MB, alloc=540.3MB, time=76.05 memory used=2833.1MB, alloc=564.3MB, time=78.06 memory used=2932.0MB, alloc=564.3MB, time=81.74 memory used=3011.9MB, alloc=564.3MB, time=84.10 memory used=3084.1MB, alloc=564.3MB, time=85.97 memory used=3156.5MB, alloc=588.3MB, time=87.42 memory used=3238.7MB, alloc=588.3MB, time=90.90 memory used=3309.8MB, alloc=588.3MB, time=93.46 memory used=3369.0MB, alloc=588.3MB, time=95.60 memory used=3423.9MB, alloc=588.3MB, time=97.33 memory used=3481.2MB, alloc=588.3MB, time=99.19 memory used=3537.1MB, alloc=588.3MB, time=100.90 memory used=3807.0MB, alloc=612.3MB, time=109.93 memory used=3989.9MB, alloc=636.3MB, time=116.69 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428260347 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 3 2 F := [11 y z + 16 x + 11 z , -10 x z + 7 z + 9, -7 y - 6 y z - 4 x] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 3 G := [-8 x y + 4 x y - 9 x z, -2 x y - 2 y + 10 x z, -2 y - 2 z] > Problem := [F,G]; Problem := [ 2 2 2 2 3 2 [11 y z + 16 x + 11 z , -10 x z + 7 z + 9, -7 y - 6 y z - 4 x], 2 2 3 [-8 x y + 4 x y - 9 x z, -2 x y - 2 y + 10 x z, -2 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=4.3MB, alloc=32.3MB, time=0.30 memory used=26.3MB, alloc=32.3MB, time=0.86 memory used=47.0MB, alloc=32.3MB, time=1.39 memory used=65.9MB, alloc=56.3MB, time=1.91 memory used=105.8MB, alloc=60.3MB, time=2.97 memory used=144.2MB, alloc=84.3MB, time=4.02 memory used=208.5MB, alloc=92.3MB, time=5.64 memory used=273.2MB, alloc=116.3MB, time=7.22 memory used=344.1MB, alloc=116.3MB, time=8.91 memory used=416.2MB, alloc=396.3MB, time=10.66 memory used=530.8MB, alloc=420.3MB, time=13.35 memory used=664.3MB, alloc=420.3MB, time=16.74 memory used=791.7MB, alloc=444.3MB, time=19.58 memory used=935.0MB, alloc=468.3MB, time=23.52 memory used=1062.1MB, alloc=468.3MB, time=26.73 memory used=1176.1MB, alloc=492.3MB, time=29.73 memory used=1284.3MB, alloc=492.3MB, time=32.49 memory used=1385.8MB, alloc=492.3MB, time=34.95 memory used=1479.0MB, alloc=492.3MB, time=37.43 memory used=1576.0MB, alloc=516.3MB, time=40.07 memory used=1665.6MB, alloc=516.3MB, time=42.78 memory used=1750.6MB, alloc=516.3MB, time=45.09 memory used=1844.7MB, alloc=516.3MB, time=47.91 memory used=1917.2MB, alloc=516.3MB, time=49.75 memory used=1984.1MB, alloc=516.3MB, time=51.65 memory used=2049.6MB, alloc=516.3MB, time=53.72 memory used=2109.5MB, alloc=516.3MB, time=55.40 memory used=2174.2MB, alloc=516.3MB, time=57.29 memory used=2244.7MB, alloc=540.3MB, time=59.49 memory used=2309.2MB, alloc=540.3MB, time=61.69 memory used=2372.4MB, alloc=540.3MB, time=63.93 memory used=2444.2MB, alloc=540.3MB, time=66.65 memory used=2495.6MB, alloc=540.3MB, time=68.32 memory used=2554.9MB, alloc=540.3MB, time=70.55 memory used=2621.9MB, alloc=540.3MB, time=73.05 memory used=2845.3MB, alloc=564.3MB, time=79.25 memory used=3050.0MB, alloc=588.3MB, time=85.12 memory used=3303.3MB, alloc=612.3MB, time=93.13 memory used=3460.8MB, alloc=636.3MB, time=97.96 memory used=3665.0MB, alloc=660.3MB, time=102.94 memory used=3828.9MB, alloc=660.3MB, time=108.09 memory used=4004.1MB, alloc=684.3MB, time=113.64 memory used=4168.8MB, alloc=684.3MB, time=117.94 |\^/| 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(); 1428260647 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 3 3 3 2 F := [14 z - 11 x y + 13 y z, -10 x - 10 z + 9 x y, -2 y - 7 z ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 3 3 G := [20 z + 18 x - 2 z, -10 x y - 3 y z + 8, 5 y - 5 z ] > Problem := [F,G]; 3 3 3 3 2 Problem := [[14 z - 11 x y + 13 y z, -10 x - 10 z + 9 x y, -2 y - 7 z ], 3 2 2 3 3 [20 z + 18 x - 2 z, -10 x y - 3 y z + 8, 5 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=0.30 memory used=26.3MB, alloc=32.3MB, time=0.87 memory used=45.4MB, alloc=32.3MB, time=1.33 memory used=64.1MB, alloc=56.3MB, time=1.83 memory used=106.0MB, alloc=60.3MB, time=2.81 memory used=143.9MB, alloc=60.3MB, time=3.79 memory used=181.5MB, alloc=84.3MB, time=4.77 memory used=213.7MB, alloc=84.3MB, time=5.49 memory used=278.7MB, alloc=92.3MB, time=7.04 memory used=341.3MB, alloc=92.3MB, time=8.35 memory used=410.2MB, alloc=116.3MB, time=9.66 memory used=490.0MB, alloc=372.3MB, time=11.52 memory used=573.5MB, alloc=396.3MB, time=13.64 memory used=687.3MB, alloc=396.3MB, time=16.29 memory used=804.7MB, alloc=420.3MB, time=18.93 memory used=932.7MB, alloc=444.3MB, time=22.28 memory used=1050.0MB, alloc=444.3MB, time=24.58 memory used=1190.4MB, alloc=444.3MB, time=26.96 memory used=1255.8MB, alloc=444.3MB, time=27.33 memory used=1333.8MB, alloc=444.3MB, time=27.85 memory used=1418.6MB, alloc=444.3MB, time=30.56 memory used=1484.5MB, alloc=444.3MB, time=30.92 memory used=1597.4MB, alloc=444.3MB, time=32.96 memory used=1663.6MB, alloc=444.3MB, time=33.42 memory used=1737.9MB, alloc=444.3MB, time=33.87 memory used=1790.2MB, alloc=444.3MB, time=34.25 memory used=1852.1MB, alloc=444.3MB, time=34.66 memory used=1922.4MB, alloc=444.3MB, time=35.07 memory used=2003.2MB, alloc=444.3MB, time=35.49 memory used=2072.8MB, alloc=444.3MB, time=35.86 memory used=2121.3MB, alloc=444.3MB, time=36.19 memory used=2172.9MB, alloc=444.3MB, time=36.50 memory used=2228.7MB, alloc=444.3MB, time=36.83 memory used=2290.6MB, alloc=444.3MB, time=37.17 memory used=2381.9MB, alloc=444.3MB, time=54.21 memory used=2486.8MB, alloc=444.3MB, time=74.60 memory used=2551.5MB, alloc=444.3MB, time=75.00 memory used=2621.8MB, alloc=444.3MB, time=75.41 memory used=2692.3MB, alloc=444.3MB, time=75.80 memory used=2742.4MB, alloc=444.3MB, time=76.12 memory used=2797.9MB, alloc=444.3MB, time=76.45 memory used=2860.1MB, alloc=444.3MB, time=76.80 memory used=2928.8MB, alloc=444.3MB, time=77.16 memory used=3006.3MB, alloc=444.3MB, time=77.52 memory used=3230.7MB, alloc=444.3MB, time=78.43 memory used=3497.8MB, alloc=444.3MB, time=82.83 memory used=3670.7MB, alloc=468.3MB, time=85.83 memory used=3848.6MB, alloc=468.3MB, time=88.30 memory used=4025.6MB, alloc=468.3MB, time=91.45 memory used=4203.7MB, alloc=468.3MB, time=95.68 memory used=4381.0MB, alloc=468.3MB, time=101.21 memory used=4559.4MB, alloc=468.3MB, time=107.92 memory used=4738.5MB, alloc=468.3MB, time=115.28 memory used=4909.0MB, alloc=468.3MB, time=120.27 memory used=5075.7MB, alloc=468.3MB, time=122.47 memory used=5229.2MB, alloc=468.3MB, time=125.05 memory used=5350.6MB, alloc=468.3MB, time=126.63 memory used=5434.4MB, alloc=468.3MB, time=127.18 memory used=5498.7MB, alloc=468.3MB, time=127.62 memory used=5616.6MB, alloc=468.3MB, time=140.49 memory used=5690.9MB, alloc=468.3MB, time=140.99 memory used=5765.6MB, alloc=468.3MB, time=141.45 memory used=5843.3MB, alloc=468.3MB, time=141.89 memory used=5946.3MB, alloc=468.3MB, time=143.16 memory used=6093.6MB, alloc=468.3MB, time=145.27 memory used=6177.5MB, alloc=468.3MB, time=145.95 memory used=6263.3MB, alloc=468.3MB, time=146.63 memory used=6338.6MB, alloc=468.3MB, time=147.10 memory used=6407.6MB, alloc=468.3MB, time=147.55 memory used=6484.0MB, alloc=468.3MB, time=148.04 memory used=6557.2MB, alloc=468.3MB, time=148.68 memory used=6630.1MB, alloc=468.3MB, time=149.15 memory used=6702.7MB, alloc=468.3MB, time=149.57 memory used=6913.8MB, alloc=468.3MB, time=153.24 |\^/| 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(); 1428260947 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 2 3 F := [20 x - 13 x y + 18 x z, 7 x y - x y - 6 y z, 6 x y - 10 y - 7 y z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 2 2 2 G := [-15 x + 19 x y + x z, -3 x y - 3 x - 10 x y, 8 x z - 2 x + 8 z] > Problem := [F,G]; Problem := [ 3 2 2 2 3 [20 x - 13 x y + 18 x z, 7 x y - x y - 6 y z, 6 x y - 10 y - 7 y z], 3 2 2 2 2 2 [-15 x + 19 x y + x z, -3 x y - 3 x - 10 x y, 8 x z - 2 x + 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=26.4MB, alloc=32.3MB, time=0.87 memory used=46.5MB, alloc=32.3MB, time=1.38 memory used=65.8MB, alloc=56.3MB, time=1.89 memory used=107.0MB, alloc=60.3MB, time=2.97 memory used=146.8MB, alloc=84.3MB, time=4.03 memory used=208.6MB, alloc=116.3MB, time=5.74 memory used=290.5MB, alloc=116.3MB, time=7.96 memory used=361.2MB, alloc=140.3MB, time=9.83 memory used=430.9MB, alloc=396.3MB, time=11.74 memory used=536.9MB, alloc=420.3MB, time=14.61 memory used=667.0MB, alloc=444.3MB, time=18.14 memory used=814.3MB, alloc=468.3MB, time=22.35 memory used=944.6MB, alloc=492.3MB, time=26.38 memory used=1057.3MB, alloc=492.3MB, time=29.90 memory used=1180.3MB, alloc=492.3MB, time=33.77 memory used=1269.9MB, alloc=516.3MB, time=36.63 memory used=1394.6MB, alloc=516.3MB, time=40.61 memory used=1492.5MB, alloc=516.3MB, time=43.85 memory used=1589.1MB, alloc=516.3MB, time=47.12 memory used=1684.1MB, alloc=540.3MB, time=50.31 memory used=1781.7MB, alloc=540.3MB, time=53.83 memory used=1882.9MB, alloc=564.3MB, time=57.46 memory used=1998.7MB, alloc=588.3MB, time=61.39 memory used=2119.9MB, alloc=588.3MB, time=65.42 memory used=2210.7MB, alloc=612.3MB, time=68.90 memory used=2306.1MB, alloc=612.3MB, time=72.55 memory used=2403.2MB, alloc=636.3MB, time=76.23 memory used=2497.9MB, alloc=660.3MB, time=79.94 memory used=2566.7MB, alloc=660.3MB, time=82.84 memory used=2659.3MB, alloc=684.3MB, time=86.53 memory used=2750.4MB, alloc=684.3MB, time=90.19 memory used=3021.1MB, alloc=708.3MB, time=99.28 memory used=3305.6MB, alloc=732.3MB, time=108.62 |\^/| 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(); 1428261247 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 F := [9 x z - 11 x y - 8 y z, 5 z, 3 y z + 3 z - 2 x] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 3 2 2 2 G := [-18 x + x y + 14 z, 6 z - 4 y + 5 z , 5 y z - 10 y - 10 z] > Problem := [F,G]; 2 2 Problem := [[9 x z - 11 x y - 8 y z, 5 z, 3 y z + 3 z - 2 x], 3 2 3 2 2 2 [-18 x + x y + 14 z, 6 z - 4 y + 5 z , 5 y z - 10 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=4.2MB, alloc=32.3MB, time=0.30 memory used=26.9MB, alloc=32.3MB, time=0.90 memory used=47.9MB, alloc=56.3MB, time=1.46 memory used=89.4MB, alloc=60.3MB, time=2.54 memory used=128.4MB, alloc=84.3MB, time=3.58 memory used=169.1MB, alloc=84.3MB, time=4.68 memory used=232.3MB, alloc=116.3MB, time=6.38 memory used=305.5MB, alloc=372.3MB, time=8.19 memory used=392.3MB, alloc=396.3MB, time=10.44 memory used=502.2MB, alloc=396.3MB, time=13.29 memory used=607.7MB, alloc=420.3MB, time=16.30 memory used=737.0MB, alloc=444.3MB, time=19.82 memory used=872.3MB, alloc=444.3MB, time=23.43 memory used=1004.1MB, alloc=468.3MB, time=27.14 memory used=1124.4MB, alloc=468.3MB, time=30.39 memory used=1242.0MB, alloc=492.3MB, time=33.68 memory used=1349.3MB, alloc=492.3MB, time=36.93 memory used=1443.5MB, alloc=492.3MB, time=39.76 memory used=1527.3MB, alloc=516.3MB, time=42.21 memory used=1598.8MB, alloc=516.3MB, time=44.51 memory used=1692.2MB, alloc=516.3MB, time=47.33 memory used=1774.2MB, alloc=516.3MB, time=50.28 memory used=1841.3MB, alloc=516.3MB, time=52.44 memory used=1899.4MB, alloc=516.3MB, time=54.15 memory used=1979.5MB, alloc=516.3MB, time=57.09 memory used=2043.6MB, alloc=540.3MB, time=59.30 memory used=2106.2MB, alloc=540.3MB, time=61.82 memory used=2154.9MB, alloc=540.3MB, time=63.82 memory used=2362.4MB, alloc=564.3MB, time=69.51 memory used=2573.3MB, alloc=588.3MB, time=75.37 memory used=2751.5MB, alloc=612.3MB, time=81.09 memory used=2925.5MB, alloc=636.3MB, time=86.51 memory used=3078.6MB, alloc=660.3MB, time=91.79 memory used=3228.1MB, alloc=660.3MB, time=96.23 memory used=3361.6MB, alloc=660.3MB, time=101.16 memory used=3514.9MB, alloc=660.3MB, time=107.05 |\^/| 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(); 1428261547 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 2 2 F := [-13 x y z + 13 x z + 13 y , 5 x z - 9 x + 8 z , -x z + 6 y ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 2 2 G := [20 x + 14 z + 20 x, 5 x y + 10 y + 8 y z, 4 z + 10 y] > Problem := [F,G]; 2 2 2 2 2 2 Problem := [[-13 x y z + 13 x z + 13 y , 5 x z - 9 x + 8 z , -x z + 6 y ], 3 2 2 2 2 [20 x + 14 z + 20 x, 5 x y + 10 y + 8 y z, 4 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=0.30 memory used=26.5MB, alloc=32.3MB, time=0.87 memory used=46.0MB, alloc=56.3MB, time=1.40 memory used=86.8MB, alloc=60.3MB, time=2.46 memory used=126.8MB, alloc=60.3MB, time=3.49 memory used=166.7MB, alloc=84.3MB, time=4.50 memory used=229.8MB, alloc=92.3MB, time=6.10 memory used=290.0MB, alloc=116.3MB, time=7.70 memory used=373.4MB, alloc=116.3MB, time=9.80 memory used=455.6MB, alloc=396.3MB, time=11.94 memory used=565.5MB, alloc=420.3MB, time=14.63 memory used=693.4MB, alloc=420.3MB, time=18.01 memory used=836.5MB, alloc=444.3MB, time=21.12 memory used=957.5MB, alloc=468.3MB, time=23.94 memory used=1086.1MB, alloc=468.3MB, time=26.74 memory used=1214.3MB, alloc=492.3MB, time=30.31 memory used=1333.6MB, alloc=492.3MB, time=33.78 memory used=1431.3MB, alloc=492.3MB, time=36.52 memory used=1531.3MB, alloc=492.3MB, time=39.10 memory used=1631.3MB, alloc=492.3MB, time=41.80 memory used=1724.6MB, alloc=492.3MB, time=44.37 memory used=1804.5MB, alloc=516.3MB, time=46.98 memory used=1882.8MB, alloc=516.3MB, time=49.48 memory used=1949.3MB, alloc=516.3MB, time=51.60 memory used=2016.0MB, alloc=516.3MB, time=53.72 memory used=2076.7MB, alloc=516.3MB, time=55.89 memory used=2133.6MB, alloc=516.3MB, time=57.92 memory used=2182.9MB, alloc=516.3MB, time=59.59 memory used=2391.4MB, alloc=540.3MB, time=65.70 memory used=2613.6MB, alloc=564.3MB, time=72.77 memory used=2805.9MB, alloc=588.3MB, time=78.24 memory used=2973.0MB, alloc=612.3MB, time=83.12 memory used=3127.5MB, alloc=636.3MB, time=87.66 memory used=3302.5MB, alloc=660.3MB, time=92.99 memory used=3444.0MB, alloc=660.3MB, time=97.39 memory used=3568.1MB, alloc=684.3MB, time=101.07 memory used=3685.3MB, alloc=684.3MB, time=105.51 memory used=3838.4MB, alloc=684.3MB, time=110.30 |\^/| 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(); 1428261847 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 3 3 2 2 F := [x y - 9 x z - 15 y z , -6 x - y - 3, 4 y z - 9 y z - 7 z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 G := [12 x y - 4 y z - 20, -4 x y z + x y - 10 y z, 5 x z + 10 y - 3 y] > Problem := [F,G]; 2 2 2 3 3 2 2 Problem := [[x y - 9 x z - 15 y z , -6 x - y - 3, 4 y z - 9 y z - 7 z], 2 2 2 2 [12 x y - 4 y z - 20, -4 x y z + x y - 10 y z, 5 x z + 10 y - 3 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.31 memory used=26.0MB, alloc=32.3MB, time=0.86 memory used=46.9MB, alloc=32.3MB, time=1.40 memory used=65.2MB, alloc=56.3MB, time=1.90 memory used=105.5MB, alloc=60.3MB, time=2.97 memory used=144.3MB, alloc=60.3MB, time=4.01 memory used=181.8MB, alloc=84.3MB, time=5.02 memory used=224.5MB, alloc=84.3MB, time=6.17 memory used=286.2MB, alloc=92.3MB, time=7.82 memory used=347.2MB, alloc=116.3MB, time=9.48 memory used=430.1MB, alloc=116.3MB, time=11.57 memory used=504.2MB, alloc=372.3MB, time=13.26 memory used=588.1MB, alloc=396.3MB, time=15.48 memory used=694.2MB, alloc=396.3MB, time=18.28 memory used=799.1MB, alloc=420.3MB, time=21.24 memory used=927.5MB, alloc=444.3MB, time=24.91 memory used=1075.9MB, alloc=444.3MB, time=29.26 memory used=1219.1MB, alloc=468.3MB, time=33.51 memory used=1341.6MB, alloc=492.3MB, time=36.91 memory used=1472.6MB, alloc=492.3MB, time=40.89 memory used=1596.8MB, alloc=516.3MB, time=44.79 memory used=1683.1MB, alloc=516.3MB, time=47.08 memory used=1787.6MB, alloc=516.3MB, time=50.40 memory used=1886.1MB, alloc=540.3MB, time=53.42 memory used=1980.8MB, alloc=540.3MB, time=56.53 memory used=2071.7MB, alloc=540.3MB, time=59.71 memory used=2160.1MB, alloc=540.3MB, time=62.85 memory used=2231.5MB, alloc=540.3MB, time=65.36 memory used=2291.4MB, alloc=540.3MB, time=67.23 memory used=2366.3MB, alloc=540.3MB, time=69.59 memory used=2429.0MB, alloc=540.3MB, time=71.86 memory used=2475.7MB, alloc=540.3MB, time=73.40 memory used=2519.7MB, alloc=540.3MB, time=74.96 memory used=2724.6MB, alloc=564.3MB, time=81.02 memory used=2918.4MB, alloc=588.3MB, time=87.44 memory used=3125.2MB, alloc=612.3MB, time=93.72 memory used=3307.2MB, alloc=636.3MB, time=99.69 memory used=3486.0MB, alloc=660.3MB, time=105.62 memory used=3694.3MB, alloc=684.3MB, time=111.79 memory used=3835.1MB, alloc=684.3MB, time=116.78 memory used=3968.1MB, alloc=684.3MB, time=121.97 |\^/| 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(); 1428262147 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 3 2 2 F := [17 x z + 19 y z - 7 x , 7 x y - 8 y - 4 y z , -10 z + 4] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; G := [ 2 2 2 2 2 3 2 2 -19 x z - 10 y z + 13 x , -9 x y + 10 x z - 10 y , -2 y - 3 y z + 6 z ] > Problem := [F,G]; 2 2 2 2 3 2 2 Problem := [[17 x z + 19 y z - 7 x , 7 x y - 8 y - 4 y z , -10 z + 4], [ 2 2 2 2 2 3 2 2 -19 x z - 10 y z + 13 x , -9 x y + 10 x z - 10 y , -2 y - 3 y z + 6 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.30 memory used=25.8MB, alloc=36.3MB, time=0.84 memory used=46.2MB, alloc=36.3MB, time=1.28 memory used=65.6MB, alloc=60.3MB, time=1.80 memory used=110.3MB, alloc=68.3MB, time=2.83 memory used=159.3MB, alloc=68.3MB, time=3.70 memory used=206.5MB, alloc=92.3MB, time=4.66 memory used=282.4MB, alloc=92.3MB, time=6.14 memory used=347.6MB, alloc=116.3MB, time=7.55 memory used=409.6MB, alloc=372.3MB, time=8.80 memory used=508.2MB, alloc=372.3MB, time=10.76 memory used=599.4MB, alloc=396.3MB, time=12.65 memory used=731.0MB, alloc=396.3MB, time=15.05 memory used=843.8MB, alloc=420.3MB, time=17.68 memory used=962.4MB, alloc=444.3MB, time=20.38 memory used=1092.2MB, alloc=444.3MB, time=22.76 memory used=1203.2MB, alloc=468.3MB, time=25.26 memory used=1313.8MB, alloc=468.3MB, time=27.64 memory used=1425.8MB, alloc=468.3MB, time=29.92 memory used=1528.0MB, alloc=468.3MB, time=32.46 memory used=1632.3MB, alloc=492.3MB, time=34.60 memory used=1710.6MB, alloc=492.3MB, time=36.44 memory used=1787.9MB, alloc=492.3MB, time=38.30 memory used=1870.2MB, alloc=492.3MB, time=40.46 memory used=1950.6MB, alloc=492.3MB, time=42.15 memory used=2027.6MB, alloc=516.3MB, time=43.83 memory used=2089.1MB, alloc=516.3MB, time=45.37 memory used=2149.9MB, alloc=516.3MB, time=47.28 memory used=2205.2MB, alloc=516.3MB, time=49.01 memory used=2259.8MB, alloc=516.3MB, time=50.59 memory used=2442.8MB, alloc=540.3MB, time=55.09 memory used=2626.9MB, alloc=564.3MB, time=59.14 memory used=2865.5MB, alloc=588.3MB, time=63.84 memory used=3097.5MB, alloc=612.3MB, time=67.94 memory used=3282.7MB, alloc=636.3MB, time=73.13 memory used=3490.0MB, alloc=660.3MB, time=78.31 memory used=3665.9MB, alloc=660.3MB, time=82.37 memory used=3817.7MB, alloc=660.3MB, time=86.15 memory used=3952.8MB, alloc=684.3MB, time=90.43 memory used=4081.4MB, alloc=684.3MB, time=94.51 memory used=4182.1MB, alloc=684.3MB, time=97.68 memory used=4310.6MB, alloc=684.3MB, time=101.84 memory used=4413.7MB, alloc=684.3MB, time=104.97 memory used=4531.4MB, alloc=684.3MB, time=108.94 memory used=4607.8MB, alloc=684.3MB, time=112.24 memory used=4682.1MB, alloc=684.3MB, time=115.16 memory used=4990.7MB, alloc=708.3MB, time=122.74 |\^/| 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(); 1428262447 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 2 2 2 F := [-9 x y + 15 x y + 9 y z, 10 x z - 10 x + 2 y z, -x y - 6 y z + 3] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 2 G := [18 z - 16 x y - 19 y, 4 x y z - 6 x - z , 6 x y z - 4 z - 5] > Problem := [F,G]; Problem := [ 2 2 2 2 2 2 2 [-9 x y + 15 x y + 9 y z, 10 x z - 10 x + 2 y z, -x y - 6 y z + 3], 3 2 2 2 [18 z - 16 x y - 19 y, 4 x y z - 6 x - z , 6 x y z - 4 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=4.2MB, alloc=32.3MB, time=0.30 memory used=26.2MB, alloc=32.3MB, time=0.89 memory used=45.4MB, alloc=56.3MB, time=1.42 memory used=87.4MB, alloc=60.3MB, time=2.53 memory used=128.8MB, alloc=92.3MB, time=3.63 memory used=193.6MB, alloc=92.3MB, time=5.30 memory used=262.0MB, alloc=92.3MB, time=6.99 memory used=325.1MB, alloc=116.3MB, time=8.70 memory used=397.2MB, alloc=116.3MB, time=10.63 memory used=462.4MB, alloc=372.3MB, time=12.36 memory used=551.2MB, alloc=396.3MB, time=14.63 memory used=662.6MB, alloc=396.3MB, time=17.47 memory used=773.1MB, alloc=420.3MB, time=20.35 memory used=903.1MB, alloc=444.3MB, time=23.93 memory used=1025.3MB, alloc=468.3MB, time=27.30 memory used=1121.2MB, alloc=468.3MB, time=29.95 memory used=1224.3MB, alloc=492.3MB, time=32.79 memory used=1324.2MB, alloc=492.3MB, time=35.89 memory used=1414.1MB, alloc=492.3MB, time=38.51 memory used=1503.1MB, alloc=492.3MB, time=41.27 memory used=1570.0MB, alloc=492.3MB, time=43.41 memory used=1629.2MB, alloc=492.3MB, time=45.05 memory used=1702.8MB, alloc=492.3MB, time=47.26 memory used=1755.6MB, alloc=492.3MB, time=48.87 memory used=1802.9MB, alloc=492.3MB, time=50.52 memory used=1849.2MB, alloc=492.3MB, time=51.98 memory used=1912.0MB, alloc=492.3MB, time=54.17 memory used=1958.5MB, alloc=492.3MB, time=55.99 memory used=2149.6MB, alloc=516.3MB, time=61.52 memory used=2339.8MB, alloc=540.3MB, time=67.03 memory used=2532.0MB, alloc=564.3MB, time=73.09 memory used=2684.2MB, alloc=588.3MB, time=77.32 memory used=2829.5MB, alloc=612.3MB, time=82.35 memory used=3001.6MB, alloc=636.3MB, time=87.91 memory used=3130.1MB, alloc=636.3MB, time=92.50 memory used=3259.7MB, alloc=636.3MB, time=96.84 memory used=3385.7MB, alloc=636.3MB, time=100.37 memory used=3481.5MB, alloc=636.3MB, time=103.54 memory used=3613.1MB, alloc=636.3MB, time=108.21 |\^/| 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(); 1428262747 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 2 F := [-17 x z + 13 y + 5 x y, -4 x z - 9 x z + 9 z, -x z - 6 x z + 1] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 3 2 2 2 2 G := [11 x z + 8 y z + 18 z , -4 x z + 8 y - 8 y z, y z + y - 5 y z] > Problem := [F,G]; Problem := [ 2 3 2 2 [-17 x z + 13 y + 5 x y, -4 x z - 9 x z + 9 z, -x z - 6 x z + 1], 2 2 3 2 2 2 2 [11 x z + 8 y z + 18 z , -4 x z + 8 y - 8 y z, y z + y - 5 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.4MB, alloc=32.3MB, time=0.86 memory used=47.2MB, alloc=32.3MB, time=1.40 memory used=65.4MB, alloc=56.3MB, time=1.87 memory used=105.1MB, alloc=60.3MB, time=2.91 memory used=144.1MB, alloc=60.3MB, time=3.84 memory used=187.6MB, alloc=68.3MB, time=4.97 memory used=227.1MB, alloc=92.3MB, time=5.96 memory used=292.7MB, alloc=92.3MB, time=7.26 memory used=339.6MB, alloc=92.3MB, time=8.01 memory used=396.5MB, alloc=92.3MB, time=9.51 memory used=458.0MB, alloc=116.3MB, time=11.05 memory used=534.3MB, alloc=116.3MB, time=13.13 memory used=614.7MB, alloc=372.3MB, time=14.84 memory used=673.3MB, alloc=396.3MB, time=18.03 memory used=741.7MB, alloc=396.3MB, time=18.55 memory used=813.6MB, alloc=396.3MB, time=21.70 memory used=897.0MB, alloc=396.3MB, time=25.00 memory used=995.8MB, alloc=396.3MB, time=26.36 memory used=1115.5MB, alloc=396.3MB, time=30.82 memory used=1189.9MB, alloc=396.3MB, time=31.77 memory used=1268.9MB, alloc=396.3MB, time=35.04 memory used=1329.1MB, alloc=396.3MB, time=35.58 memory used=1407.5MB, alloc=396.3MB, time=38.78 memory used=1472.1MB, alloc=396.3MB, time=39.42 memory used=1536.4MB, alloc=396.3MB, time=42.27 memory used=1637.5MB, alloc=396.3MB, time=43.91 memory used=1709.8MB, alloc=396.3MB, time=47.14 memory used=1805.3MB, alloc=396.3MB, time=49.20 memory used=1879.8MB, alloc=396.3MB, time=51.72 memory used=1968.8MB, alloc=420.3MB, time=53.85 memory used=2096.3MB, alloc=420.3MB, time=59.11 memory used=2213.0MB, alloc=420.3MB, time=63.42 memory used=2301.6MB, alloc=420.3MB, time=66.80 memory used=2382.0MB, alloc=420.3MB, time=69.88 memory used=2450.8MB, alloc=420.3MB, time=70.75 memory used=2580.8MB, alloc=420.3MB, time=75.31 memory used=2667.4MB, alloc=420.3MB, time=78.97 memory used=2732.9MB, alloc=420.3MB, time=79.54 memory used=2801.7MB, alloc=420.3MB, time=80.08 memory used=2880.0MB, alloc=420.3MB, time=83.42 memory used=2944.8MB, alloc=420.3MB, time=84.17 memory used=3016.9MB, alloc=420.3MB, time=84.74 memory used=3084.8MB, alloc=420.3MB, time=85.41 memory used=3166.9MB, alloc=420.3MB, time=88.61 memory used=3265.8MB, alloc=420.3MB, time=90.19 memory used=3358.6MB, alloc=420.3MB, time=93.78 memory used=3463.8MB, alloc=444.3MB, time=96.66 memory used=3598.3MB, alloc=468.3MB, time=100.37 memory used=3729.0MB, alloc=468.3MB, time=103.67 memory used=3854.2MB, alloc=492.3MB, time=107.38 memory used=3972.0MB, alloc=492.3MB, time=110.81 memory used=4076.4MB, alloc=492.3MB, time=113.33 memory used=4183.9MB, alloc=492.3MB, time=115.58 memory used=4291.3MB, alloc=492.3MB, time=117.88 memory used=4400.9MB, alloc=492.3MB, time=120.44 memory used=4548.4MB, alloc=516.3MB, time=125.94 memory used=4663.5MB, alloc=516.3MB, time=126.80 memory used=4816.0MB, alloc=516.3MB, time=131.38 memory used=4961.9MB, alloc=516.3MB, time=133.43 memory used=5070.8MB, alloc=516.3MB, time=135.76 memory used=5206.8MB, alloc=516.3MB, time=139.81 memory used=5343.6MB, alloc=516.3MB, time=141.64 memory used=5440.0MB, alloc=516.3MB, time=143.88 memory used=5530.9MB, alloc=516.3MB, time=146.62 |\^/| 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(); 1428263047 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 3 2 2 F := [-8 y z - 14 y + 8, 7 z + 4 y - 10 z, -8 x z - 8 x y z - 3 y z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 3 G := [6 x z - 12 z + 14 x, 7 x z - 5 x - 7 y , 3 y - x z + 7 z] > Problem := [F,G]; Problem := [ 2 2 3 2 2 [-8 y z - 14 y + 8, 7 z + 4 y - 10 z, -8 x z - 8 x y z - 3 y z], 2 2 2 2 3 [6 x z - 12 z + 14 x, 7 x z - 5 x - 7 y , 3 y - x z + 7 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.31 memory used=26.4MB, alloc=32.3MB, time=0.87 memory used=47.4MB, alloc=32.3MB, time=1.40 memory used=66.0MB, alloc=56.3MB, time=1.87 memory used=106.9MB, alloc=60.3MB, time=2.89 memory used=146.9MB, alloc=60.3MB, time=3.83 memory used=191.2MB, alloc=68.3MB, time=4.73 memory used=240.9MB, alloc=68.3MB, time=5.60 memory used=279.1MB, alloc=92.3MB, time=6.64 memory used=345.1MB, alloc=92.3MB, time=8.18 memory used=410.7MB, alloc=116.3MB, time=9.71 memory used=477.8MB, alloc=372.3MB, time=11.33 memory used=563.4MB, alloc=396.3MB, time=13.54 memory used=680.4MB, alloc=396.3MB, time=15.98 memory used=761.4MB, alloc=420.3MB, time=17.20 memory used=885.1MB, alloc=420.3MB, time=19.16 memory used=1040.9MB, alloc=420.3MB, time=21.78 memory used=1122.9MB, alloc=420.3MB, time=22.59 memory used=1201.4MB, alloc=420.3MB, time=23.31 memory used=1286.0MB, alloc=420.3MB, time=24.68 memory used=1355.6MB, alloc=420.3MB, time=25.33 memory used=1430.1MB, alloc=420.3MB, time=26.53 memory used=1512.5MB, alloc=420.3MB, time=27.39 memory used=1641.9MB, alloc=420.3MB, time=29.40 memory used=1774.2MB, alloc=444.3MB, time=32.45 memory used=1901.7MB, alloc=468.3MB, time=35.74 memory used=2041.2MB, alloc=468.3MB, time=38.77 memory used=2138.6MB, alloc=468.3MB, time=41.25 memory used=2247.8MB, alloc=468.3MB, time=43.46 memory used=2336.4MB, alloc=468.3MB, time=44.87 memory used=2466.2MB, alloc=492.3MB, time=47.05 memory used=2617.2MB, alloc=492.3MB, time=50.49 memory used=2709.3MB, alloc=492.3MB, time=53.08 memory used=2808.1MB, alloc=492.3MB, time=55.30 memory used=2927.2MB, alloc=492.3MB, time=57.43 memory used=3023.2MB, alloc=516.3MB, time=59.78 memory used=3168.9MB, alloc=516.3MB, time=61.62 memory used=3292.2MB, alloc=516.3MB, time=63.83 memory used=3391.0MB, alloc=516.3MB, time=64.51 memory used=3544.3MB, alloc=516.3MB, time=67.02 memory used=3687.7MB, alloc=516.3MB, time=69.38 memory used=3768.6MB, alloc=516.3MB, time=71.49 memory used=3910.6MB, alloc=516.3MB, time=73.13 memory used=4025.2MB, alloc=516.3MB, time=74.05 memory used=4175.4MB, alloc=516.3MB, time=79.90 memory used=4274.7MB, alloc=516.3MB, time=80.62 memory used=4368.8MB, alloc=516.3MB, time=81.30 memory used=4453.2MB, alloc=516.3MB, time=81.92 memory used=4554.7MB, alloc=516.3MB, time=82.58 memory used=4676.0MB, alloc=516.3MB, time=83.29 memory used=4827.0MB, alloc=516.3MB, time=84.35 memory used=4993.0MB, alloc=516.3MB, time=85.16 memory used=5154.4MB, alloc=516.3MB, time=87.53 memory used=5245.9MB, alloc=516.3MB, time=88.18 memory used=5342.3MB, alloc=516.3MB, time=88.83 memory used=5607.4MB, alloc=516.3MB, time=91.27 memory used=5705.7MB, alloc=516.3MB, time=93.10 memory used=5764.5MB, alloc=516.3MB, time=94.78 memory used=5827.5MB, alloc=516.3MB, time=96.86 memory used=5889.5MB, alloc=516.3MB, time=98.61 memory used=5953.3MB, alloc=516.3MB, time=101.86 memory used=6061.5MB, alloc=516.3MB, time=103.16 memory used=6162.4MB, alloc=516.3MB, time=103.85 memory used=6260.7MB, alloc=516.3MB, time=105.37 memory used=6387.1MB, alloc=516.3MB, time=108.15 memory used=6474.2MB, alloc=516.3MB, time=109.74 memory used=6540.5MB, alloc=516.3MB, time=111.66 memory used=6604.3MB, alloc=516.3MB, time=113.65 memory used=6652.5MB, alloc=516.3MB, time=115.13 memory used=6718.1MB, alloc=516.3MB, time=117.40 memory used=6776.1MB, alloc=516.3MB, time=119.64 memory used=6824.9MB, alloc=516.3MB, time=121.45 memory used=6871.2MB, alloc=516.3MB, time=123.12 memory used=7059.8MB, alloc=540.3MB, time=128.28 |\^/| 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(); 1428263347 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; F := [ 2 2 2 2 2 2 -14 x y z - 3 y z + 2 x y, -10 y z + 10 x - 7 x, -6 x z + 2 x y + 6 x ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 2 2 3 G := [-9 x y z + 18 y - 10 x, 10 x y + 9 x - z , 6 x z + 3 y - 2 x z] > Problem := [F,G]; Problem := [[ 2 2 2 2 2 2 -14 x y z - 3 y z + 2 x y, -10 y z + 10 x - 7 x, -6 x z + 2 x y + 6 x 3 2 2 2 2 3 ], [-9 x y z + 18 y - 10 x, 10 x y + 9 x - z , 6 x z + 3 y - 2 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.2MB, alloc=32.3MB, time=0.88 memory used=44.9MB, alloc=56.3MB, time=1.38 memory used=87.2MB, alloc=60.3MB, time=2.42 memory used=132.3MB, alloc=92.3MB, time=3.43 memory used=198.8MB, alloc=92.3MB, time=5.09 memory used=262.6MB, alloc=116.3MB, time=6.69 memory used=334.7MB, alloc=372.3MB, time=8.35 memory used=423.0MB, alloc=396.3MB, time=10.51 memory used=531.2MB, alloc=396.3MB, time=13.07 memory used=648.1MB, alloc=420.3MB, time=15.76 memory used=773.0MB, alloc=420.3MB, time=18.09 memory used=905.7MB, alloc=444.3MB, time=20.93 memory used=1035.4MB, alloc=444.3MB, time=23.88 memory used=1169.9MB, alloc=468.3MB, time=26.24 memory used=1311.1MB, alloc=468.3MB, time=29.45 memory used=1413.2MB, alloc=468.3MB, time=32.15 memory used=1506.1MB, alloc=492.3MB, time=34.29 memory used=1610.2MB, alloc=492.3MB, time=36.83 memory used=1707.1MB, alloc=492.3MB, time=39.31 memory used=1805.1MB, alloc=492.3MB, time=42.41 memory used=1868.7MB, alloc=516.3MB, time=44.23 memory used=1927.7MB, alloc=516.3MB, time=45.78 memory used=2017.1MB, alloc=516.3MB, time=48.77 memory used=2095.7MB, alloc=516.3MB, time=51.33 memory used=2166.8MB, alloc=516.3MB, time=53.49 memory used=2211.6MB, alloc=516.3MB, time=54.89 memory used=2276.0MB, alloc=516.3MB, time=56.49 memory used=2342.2MB, alloc=516.3MB, time=58.03 memory used=2424.6MB, alloc=540.3MB, time=60.21 memory used=2532.5MB, alloc=540.3MB, time=62.90 memory used=2587.0MB, alloc=540.3MB, time=64.58 memory used=2635.3MB, alloc=540.3MB, time=66.16 memory used=2869.2MB, alloc=564.3MB, time=71.16 memory used=3078.7MB, alloc=588.3MB, time=77.31 memory used=3275.3MB, alloc=612.3MB, time=83.11 memory used=3495.7MB, alloc=636.3MB, time=88.85 memory used=3670.6MB, alloc=636.3MB, time=93.09 memory used=3878.8MB, alloc=660.3MB, time=98.17 memory used=4020.4MB, alloc=660.3MB, time=102.18 memory used=4238.8MB, alloc=684.3MB, time=106.71 memory used=4360.5MB, alloc=684.3MB, time=110.63 memory used=4514.1MB, alloc=684.3MB, time=114.34 memory used=4705.9MB, alloc=684.3MB, time=119.49 memory used=4835.3MB, alloc=684.3MB, time=123.38 |\^/| 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(); 1428263647 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 2 F := [4 x z + x y + 5 z, 2 x z + y z + 4 x z, x - 6 x z + 6 y ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 G := [-11 x y + 14 y z - 5, -8 x z - 3 y z + 9 y, 5 x y - 5 y z] > Problem := [F,G]; 2 2 2 2 2 Problem := [[4 x z + x y + 5 z, 2 x z + y z + 4 x z, x - 6 x z + 6 y ], 2 2 2 [-11 x y + 14 y z - 5, -8 x z - 3 y z + 9 y, 5 x y - 5 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.31 memory used=26.5MB, alloc=32.3MB, time=0.88 memory used=47.3MB, alloc=32.3MB, time=1.43 memory used=66.8MB, alloc=56.3MB, time=1.96 memory used=107.9MB, alloc=60.3MB, time=3.07 memory used=147.4MB, alloc=60.3MB, time=4.09 memory used=185.2MB, alloc=84.3MB, time=5.15 memory used=236.3MB, alloc=84.3MB, time=6.58 memory used=297.8MB, alloc=116.3MB, time=8.27 memory used=381.1MB, alloc=372.3MB, time=10.60 memory used=465.8MB, alloc=396.3MB, time=12.83 memory used=573.9MB, alloc=420.3MB, time=15.72 memory used=708.1MB, alloc=444.3MB, time=19.30 memory used=856.2MB, alloc=468.3MB, time=23.56 memory used=989.6MB, alloc=492.3MB, time=27.47 memory used=1111.3MB, alloc=492.3MB, time=31.15 memory used=1221.1MB, alloc=492.3MB, time=34.50 memory used=1324.8MB, alloc=516.3MB, time=37.81 memory used=1420.9MB, alloc=516.3MB, time=41.03 memory used=1501.7MB, alloc=516.3MB, time=43.64 memory used=1573.3MB, alloc=516.3MB, time=46.20 memory used=1649.6MB, alloc=516.3MB, time=48.84 memory used=1714.7MB, alloc=516.3MB, time=51.24 memory used=1775.6MB, alloc=540.3MB, time=53.48 memory used=1837.3MB, alloc=540.3MB, time=55.91 memory used=1898.9MB, alloc=540.3MB, time=58.28 memory used=1956.6MB, alloc=540.3MB, time=60.84 memory used=2176.4MB, alloc=564.3MB, time=68.52 memory used=2367.6MB, alloc=588.3MB, time=74.80 memory used=2552.3MB, alloc=612.3MB, time=81.30 memory used=2713.2MB, alloc=636.3MB, time=87.40 memory used=2856.5MB, alloc=660.3MB, time=91.83 memory used=3023.5MB, alloc=684.3MB, time=97.78 memory used=3142.3MB, alloc=684.3MB, time=101.54 memory used=3281.9MB, alloc=684.3MB, time=107.24 memory used=3393.1MB, alloc=708.3MB, time=110.97 memory used=3509.9MB, alloc=708.3MB, time=115.88 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428263947 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 3 2 F := [-3 x y - 8 x + 8 y, 4 x z + 3 x z + 8 y z, 7 z - 4 x - 2 x z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 G := [-18 x y + 11 x y z - 4 y z, x y z - x z - 4 y, 10 z - 10 z] > Problem := [F,G]; 2 2 3 2 Problem := [[-3 x y - 8 x + 8 y, 4 x z + 3 x z + 8 y z, 7 z - 4 x - 2 x z], 2 2 2 [-18 x y + 11 x y z - 4 y z, x y z - x z - 4 y, 10 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=4.4MB, alloc=32.3MB, time=0.30 memory used=26.6MB, alloc=32.3MB, time=0.86 memory used=47.7MB, alloc=32.3MB, time=1.39 memory used=67.4MB, alloc=56.3MB, time=1.92 memory used=106.3MB, alloc=60.3MB, time=2.95 memory used=143.3MB, alloc=84.3MB, time=3.98 memory used=202.8MB, alloc=92.3MB, time=5.71 memory used=260.8MB, alloc=116.3MB, time=7.43 memory used=341.2MB, alloc=116.3MB, time=9.80 memory used=422.0MB, alloc=140.3MB, time=12.28 memory used=523.0MB, alloc=164.3MB, time=15.27 memory used=612.7MB, alloc=420.3MB, time=18.08 memory used=732.6MB, alloc=444.3MB, time=21.96 memory used=877.4MB, alloc=468.3MB, time=26.90 memory used=1045.0MB, alloc=492.3MB, time=32.78 memory used=1231.4MB, alloc=516.3MB, time=39.38 memory used=1444.2MB, alloc=540.3MB, time=47.41 memory used=1671.3MB, alloc=564.3MB, time=55.26 memory used=1928.1MB, alloc=588.3MB, time=65.36 memory used=2200.6MB, alloc=612.3MB, time=75.72 memory used=2500.1MB, alloc=636.3MB, time=87.42 memory used=2816.0MB, alloc=660.3MB, time=100.05 |\^/| 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(); 1428264247 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 2 2 2 2 F := [-18 y - 10 y z + 18 x , -2 x z - 4 x y - 8, 8 x z + x y - 7 y] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 3 G := [-5 x y z + 3 y + 6 z, x z - 2 x + 2, -10 x y + 7 y - 8 x z] > Problem := [F,G]; Problem := [ 3 2 2 2 2 2 2 [-18 y - 10 y z + 18 x , -2 x z - 4 x y - 8, 8 x z + x y - 7 y], 3 2 2 3 [-5 x y z + 3 y + 6 z, x z - 2 x + 2, -10 x y + 7 y - 8 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=25.6MB, alloc=32.3MB, time=0.87 memory used=45.2MB, alloc=32.3MB, time=1.37 memory used=64.6MB, alloc=56.3MB, time=1.91 memory used=106.1MB, alloc=60.3MB, time=3.05 memory used=146.3MB, alloc=60.3MB, time=4.09 memory used=185.2MB, alloc=84.3MB, time=5.12 memory used=230.8MB, alloc=84.3MB, time=6.36 memory used=294.5MB, alloc=116.3MB, time=8.02 memory used=369.8MB, alloc=372.3MB, time=10.16 memory used=454.3MB, alloc=396.3MB, time=12.45 memory used=563.5MB, alloc=420.3MB, time=15.43 memory used=694.7MB, alloc=420.3MB, time=19.09 memory used=824.7MB, alloc=444.3MB, time=22.99 memory used=964.1MB, alloc=468.3MB, time=27.18 memory used=1095.1MB, alloc=468.3MB, time=30.93 memory used=1207.2MB, alloc=468.3MB, time=34.49 memory used=1314.2MB, alloc=492.3MB, time=37.63 memory used=1439.9MB, alloc=492.3MB, time=41.90 memory used=1556.5MB, alloc=492.3MB, time=45.84 memory used=1653.0MB, alloc=492.3MB, time=49.37 memory used=1735.3MB, alloc=492.3MB, time=52.17 memory used=1824.3MB, alloc=516.3MB, time=55.34 memory used=1911.0MB, alloc=516.3MB, time=58.56 memory used=1991.6MB, alloc=516.3MB, time=61.60 memory used=2080.4MB, alloc=516.3MB, time=65.07 memory used=2136.8MB, alloc=516.3MB, time=67.37 memory used=2193.9MB, alloc=516.3MB, time=69.82 memory used=2254.5MB, alloc=516.3MB, time=72.12 memory used=2295.0MB, alloc=516.3MB, time=73.96 memory used=2350.8MB, alloc=516.3MB, time=76.59 memory used=2544.0MB, alloc=540.3MB, time=83.36 memory used=2732.2MB, alloc=564.3MB, time=88.83 memory used=2921.5MB, alloc=588.3MB, time=95.89 memory used=3120.5MB, alloc=612.3MB, time=102.60 memory used=3268.5MB, alloc=636.3MB, time=107.54 memory used=3435.4MB, alloc=660.3MB, time=112.45 |\^/| 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(); 1428264547 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 2 3 F := [-20 y z + 5 x z + 6, 4 x y + 10 x z - 10 y , -y z - 5 z - 3] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 3 2 2 2 G := [-4 x y z + 9 z + 8 y , -6 y + 2 x + 3 x, -2 x z - y - 3] > Problem := [F,G]; 2 2 2 2 2 3 Problem := [[-20 y z + 5 x z + 6, 4 x y + 10 x z - 10 y , -y z - 5 z - 3], 3 2 3 2 2 2 [-4 x y z + 9 z + 8 y , -6 y + 2 x + 3 x, -2 x z - y - 3]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.31 memory used=24.6MB, alloc=32.3MB, time=0.83 memory used=43.3MB, alloc=32.3MB, time=1.26 memory used=64.0MB, alloc=60.3MB, time=1.77 memory used=107.0MB, alloc=68.3MB, time=2.79 memory used=149.4MB, alloc=68.3MB, time=3.61 memory used=193.2MB, alloc=92.3MB, time=4.59 memory used=267.6MB, alloc=92.3MB, time=5.88 memory used=333.0MB, alloc=92.3MB, time=7.48 memory used=403.7MB, alloc=348.3MB, time=8.81 memory used=463.4MB, alloc=372.3MB, time=10.33 memory used=555.0MB, alloc=396.3MB, time=12.39 memory used=670.7MB, alloc=396.3MB, time=14.94 memory used=788.8MB, alloc=420.3MB, time=17.51 memory used=915.4MB, alloc=420.3MB, time=20.01 memory used=1037.3MB, alloc=444.3MB, time=22.37 memory used=1164.8MB, alloc=444.3MB, time=25.10 memory used=1270.9MB, alloc=468.3MB, time=27.57 memory used=1366.4MB, alloc=468.3MB, time=29.66 memory used=1480.9MB, alloc=468.3MB, time=31.42 memory used=1626.1MB, alloc=468.3MB, time=34.55 memory used=1715.4MB, alloc=468.3MB, time=36.55 memory used=1809.4MB, alloc=468.3MB, time=38.80 memory used=1925.8MB, alloc=468.3MB, time=41.05 memory used=2008.4MB, alloc=468.3MB, time=43.35 memory used=2089.7MB, alloc=468.3MB, time=45.58 memory used=2169.4MB, alloc=492.3MB, time=47.82 memory used=2238.2MB, alloc=492.3MB, time=49.80 memory used=2303.1MB, alloc=492.3MB, time=51.55 memory used=2381.9MB, alloc=492.3MB, time=52.91 memory used=2485.3MB, alloc=492.3MB, time=53.93 memory used=2603.2MB, alloc=492.3MB, time=56.26 memory used=2673.4MB, alloc=492.3MB, time=57.55 memory used=2752.6MB, alloc=492.3MB, time=58.81 memory used=2850.9MB, alloc=492.3MB, time=59.99 memory used=2971.7MB, alloc=492.3MB, time=65.72 memory used=3068.1MB, alloc=492.3MB, time=66.48 memory used=3180.2MB, alloc=492.3MB, time=67.83 memory used=3298.2MB, alloc=492.3MB, time=73.48 memory used=3392.0MB, alloc=492.3MB, time=74.23 memory used=3473.2MB, alloc=492.3MB, time=76.17 memory used=3522.9MB, alloc=492.3MB, time=77.80 memory used=3582.7MB, alloc=492.3MB, time=79.24 memory used=3690.9MB, alloc=492.3MB, time=82.28 memory used=3746.1MB, alloc=492.3MB, time=83.59 memory used=3804.9MB, alloc=492.3MB, time=85.54 memory used=3856.8MB, alloc=492.3MB, time=87.28 memory used=4031.3MB, alloc=516.3MB, time=91.70 memory used=4183.1MB, alloc=516.3MB, time=94.33 memory used=4376.9MB, alloc=540.3MB, time=98.30 memory used=4594.9MB, alloc=540.3MB, time=103.53 memory used=4791.8MB, alloc=564.3MB, time=108.05 memory used=5013.7MB, alloc=564.3MB, time=112.81 memory used=5202.9MB, alloc=588.3MB, time=120.13 memory used=5343.6MB, alloc=588.3MB, time=121.55 memory used=5542.6MB, alloc=588.3MB, time=124.40 memory used=5723.0MB, alloc=588.3MB, time=128.84 memory used=5905.3MB, alloc=588.3MB, time=133.59 memory used=6068.8MB, alloc=588.3MB, time=137.40 |\^/| 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(); 1428264847 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 3 3 2 F := [-9 y z + 12 x - 10 y, x + 3 x y - 1, 3 x + 2 y - 4 y ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 2 G := [-13 x y + 2 x y z + 8 y , 7 x z - 9 x z, -10 x y - 3 x y z + 9 z ] > Problem := [F,G]; 2 2 2 3 3 2 Problem := [[-9 y z + 12 x - 10 y, x + 3 x y - 1, 3 x + 2 y - 4 y ], 2 2 2 2 2 [-13 x y + 2 x y z + 8 y , 7 x z - 9 x z, -10 x y - 3 x y z + 9 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.32 memory used=26.1MB, alloc=32.3MB, time=0.85 memory used=47.4MB, alloc=32.3MB, time=1.39 memory used=67.3MB, alloc=32.3MB, time=1.90 memory used=85.8MB, alloc=56.3MB, time=2.39 memory used=125.7MB, alloc=60.3MB, time=3.46 memory used=164.4MB, alloc=60.3MB, time=4.45 memory used=202.2MB, alloc=84.3MB, time=5.46 memory used=262.9MB, alloc=92.3MB, time=7.16 memory used=321.8MB, alloc=92.3MB, time=8.70 memory used=380.3MB, alloc=116.3MB, time=10.26 memory used=461.6MB, alloc=116.3MB, time=12.48 memory used=546.0MB, alloc=140.3MB, time=14.75 memory used=661.1MB, alloc=140.3MB, time=17.05 memory used=747.8MB, alloc=164.3MB, time=19.63 memory used=848.7MB, alloc=444.3MB, time=22.80 memory used=989.6MB, alloc=468.3MB, time=26.45 memory used=1158.2MB, alloc=492.3MB, time=30.31 memory used=1335.3MB, alloc=516.3MB, time=35.24 memory used=1521.4MB, alloc=540.3MB, time=40.91 memory used=1731.0MB, alloc=564.3MB, time=46.74 memory used=1942.7MB, alloc=588.3MB, time=53.62 memory used=2155.4MB, alloc=612.3MB, time=61.28 memory used=2349.7MB, alloc=636.3MB, time=71.45 memory used=2549.3MB, alloc=660.3MB, time=82.58 memory used=2761.4MB, alloc=684.3MB, time=95.12 memory used=2987.7MB, alloc=708.3MB, time=108.61 |\^/| 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(); 1428265147 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 3 3 F := [13 x z - x y z - 19 z, 5 x y z - 7 y z - 3 z , -6 z - 2 y] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 3 2 2 G := [-20 x z - 6 z - 18, -4 x - 8 z - 7 z, 8 x z + 4 y z + 10] > Problem := [F,G]; 2 2 3 3 Problem := [[13 x z - x y z - 19 z, 5 x y z - 7 y z - 3 z , -6 z - 2 y], 3 3 2 2 [-20 x z - 6 z - 18, -4 x - 8 z - 7 z, 8 x z + 4 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=0.31 memory used=26.4MB, alloc=32.3MB, time=0.89 memory used=46.1MB, alloc=32.3MB, time=1.40 memory used=65.3MB, alloc=56.3MB, time=1.91 memory used=106.2MB, alloc=60.3MB, time=2.98 memory used=145.4MB, alloc=84.3MB, time=4.02 memory used=209.0MB, alloc=92.3MB, time=5.61 memory used=271.2MB, alloc=116.3MB, time=7.17 memory used=350.4MB, alloc=116.3MB, time=9.25 memory used=418.0MB, alloc=372.3MB, time=11.05 memory used=502.8MB, alloc=396.3MB, time=12.99 memory used=608.5MB, alloc=396.3MB, time=15.66 memory used=705.1MB, alloc=396.3MB, time=17.58 memory used=775.9MB, alloc=396.3MB, time=18.15 memory used=841.2MB, alloc=396.3MB, time=19.81 memory used=930.9MB, alloc=396.3MB, time=21.47 memory used=1034.4MB, alloc=420.3MB, time=24.38 memory used=1159.2MB, alloc=444.3MB, time=27.92 memory used=1306.8MB, alloc=444.3MB, time=31.38 memory used=1437.3MB, alloc=468.3MB, time=34.69 memory used=1566.8MB, alloc=468.3MB, time=38.08 memory used=1703.8MB, alloc=492.3MB, time=41.80 memory used=1808.5MB, alloc=492.3MB, time=44.59 memory used=1908.5MB, alloc=516.3MB, time=47.57 memory used=2013.9MB, alloc=516.3MB, time=50.93 memory used=2104.2MB, alloc=516.3MB, time=53.61 memory used=2176.9MB, alloc=516.3MB, time=55.72 memory used=2263.8MB, alloc=516.3MB, time=58.45 memory used=2335.5MB, alloc=516.3MB, time=60.61 memory used=2418.6MB, alloc=516.3MB, time=63.14 memory used=2501.0MB, alloc=516.3MB, time=65.83 memory used=2563.9MB, alloc=540.3MB, time=67.91 memory used=2636.1MB, alloc=540.3MB, time=70.58 memory used=2703.2MB, alloc=540.3MB, time=72.83 memory used=2756.9MB, alloc=540.3MB, time=74.51 memory used=2806.1MB, alloc=540.3MB, time=76.13 memory used=2875.5MB, alloc=540.3MB, time=78.93 memory used=3043.7MB, alloc=540.3MB, time=82.36 memory used=3251.1MB, alloc=564.3MB, time=86.90 memory used=3444.7MB, alloc=588.3MB, time=92.95 memory used=3635.3MB, alloc=612.3MB, time=99.17 memory used=3859.2MB, alloc=612.3MB, time=107.40 memory used=4029.7MB, alloc=636.3MB, time=112.74 memory used=4203.5MB, alloc=636.3MB, time=118.54 memory used=4362.8MB, alloc=660.3MB, time=124.05 memory used=4607.8MB, alloc=660.3MB, time=130.80 |\^/| 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(); 1428265447 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 2 2 F := [17 x z + 17 x - 16 x, 10 x y - 6 x y z - 10 y , -3 x y + 9 x z - 9] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 G := [7 x y z + 10 x z - 15 z , -9 x z - x z + x, 5 x z + 10 x - x z] > Problem := [F,G]; Problem := [ 2 2 2 2 2 2 [17 x z + 17 x - 16 x, 10 x y - 6 x y z - 10 y , -3 x y + 9 x z - 9], 2 2 2 2 [7 x y z + 10 x z - 15 z , -9 x z - x z + x, 5 x z + 10 x - 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=26.4MB, alloc=32.3MB, time=0.85 memory used=46.9MB, alloc=32.3MB, time=1.38 memory used=65.8MB, alloc=56.3MB, time=1.89 memory used=105.1MB, alloc=60.3MB, time=2.94 memory used=142.1MB, alloc=84.3MB, time=3.96 memory used=198.8MB, alloc=92.3MB, time=5.52 memory used=255.1MB, alloc=116.3MB, time=7.08 memory used=333.6MB, alloc=116.3MB, time=9.33 memory used=411.4MB, alloc=140.3MB, time=11.64 memory used=512.2MB, alloc=140.3MB, time=14.71 memory used=614.1MB, alloc=164.3MB, time=18.00 memory used=716.1MB, alloc=188.3MB, time=21.40 memory used=801.1MB, alloc=444.3MB, time=24.37 memory used=944.7MB, alloc=468.3MB, time=29.53 memory used=1106.6MB, alloc=492.3MB, time=35.39 memory used=1288.4MB, alloc=516.3MB, time=41.95 memory used=1483.7MB, alloc=540.3MB, time=48.58 memory used=1700.1MB, alloc=564.3MB, time=56.29 memory used=1949.1MB, alloc=588.3MB, time=65.25 memory used=2221.7MB, alloc=612.3MB, time=75.49 memory used=2511.6MB, alloc=636.3MB, time=87.20 memory used=2828.5MB, alloc=660.3MB, time=100.39 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428265748 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 3 2 3 2 F := [-14 x y - 4 x z + 9 y , -3 x y, 4 x - 5 y z + 10 x] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 3 2 2 G := [-4 x y - 19 x z + 6, 5 x y z + 7 z - x y, 8 y z + 3 x y - 10 z ] > Problem := [F,G]; 2 2 3 2 3 2 Problem := [[-14 x y - 4 x z + 9 y , -3 x y, 4 x - 5 y z + 10 x], 2 2 3 2 2 [-4 x y - 19 x z + 6, 5 x y z + 7 z - x y, 8 y z + 3 x 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=4.2MB, alloc=32.3MB, time=0.30 memory used=25.1MB, alloc=32.3MB, time=0.80 memory used=47.4MB, alloc=36.3MB, time=1.23 memory used=67.4MB, alloc=36.3MB, time=1.59 memory used=89.0MB, alloc=36.3MB, time=1.99 memory used=115.2MB, alloc=36.3MB, time=2.72 memory used=135.2MB, alloc=60.3MB, time=3.24 memory used=181.2MB, alloc=60.3MB, time=4.02 memory used=224.9MB, alloc=60.3MB, time=4.65 memory used=268.4MB, alloc=60.3MB, time=5.30 memory used=311.3MB, alloc=68.3MB, time=6.33 memory used=357.9MB, alloc=68.3MB, time=7.33 memory used=404.6MB, alloc=92.3MB, time=8.14 memory used=445.1MB, alloc=92.3MB, time=9.07 memory used=493.7MB, alloc=92.3MB, time=9.69 memory used=547.6MB, alloc=92.3MB, time=10.52 memory used=607.0MB, alloc=93.1MB, time=11.29 memory used=660.0MB, alloc=93.1MB, time=12.46 memory used=714.3MB, alloc=93.1MB, time=13.13 memory used=757.6MB, alloc=93.1MB, time=13.53 memory used=798.3MB, alloc=93.1MB, time=13.74 memory used=851.5MB, alloc=93.1MB, time=16.06 memory used=890.2MB, alloc=93.1MB, time=16.41 memory used=957.1MB, alloc=349.1MB, time=18.12 memory used=1037.1MB, alloc=349.1MB, time=20.15 memory used=1098.6MB, alloc=349.1MB, time=21.30 memory used=1170.3MB, alloc=349.1MB, time=23.05 memory used=1239.1MB, alloc=373.1MB, time=24.37 memory used=1303.9MB, alloc=373.1MB, time=25.69 memory used=1395.8MB, alloc=373.1MB, time=27.37 memory used=1487.3MB, alloc=397.1MB, time=28.98 memory used=1567.0MB, alloc=397.1MB, time=29.57 memory used=1645.1MB, alloc=397.1MB, time=32.43 memory used=1697.2MB, alloc=397.1MB, time=32.73 memory used=1786.1MB, alloc=397.1MB, time=34.60 memory used=1856.1MB, alloc=397.1MB, time=35.10 memory used=1935.8MB, alloc=397.1MB, time=38.19 memory used=2006.7MB, alloc=397.1MB, time=38.65 memory used=2074.6MB, alloc=397.1MB, time=39.18 memory used=2147.4MB, alloc=397.1MB, time=41.30 memory used=2223.3MB, alloc=397.1MB, time=42.61 memory used=2290.5MB, alloc=397.1MB, time=43.08 memory used=2362.4MB, alloc=397.1MB, time=44.32 memory used=2441.4MB, alloc=397.1MB, time=45.12 memory used=2492.3MB, alloc=397.1MB, time=45.43 memory used=2549.5MB, alloc=397.1MB, time=45.73 memory used=2628.7MB, alloc=397.1MB, time=46.66 memory used=2677.3MB, alloc=397.1MB, time=46.97 memory used=2738.1MB, alloc=397.1MB, time=47.28 memory used=2825.6MB, alloc=397.1MB, time=55.73 memory used=2882.0MB, alloc=397.1MB, time=56.06 memory used=2930.9MB, alloc=397.1MB, time=56.34 memory used=2983.7MB, alloc=397.1MB, time=56.62 memory used=3105.3MB, alloc=397.1MB, time=58.65 memory used=3172.4MB, alloc=397.1MB, time=60.35 memory used=3289.7MB, alloc=397.1MB, time=62.32 memory used=3399.2MB, alloc=421.1MB, time=64.71 memory used=3508.3MB, alloc=445.1MB, time=67.06 memory used=3616.8MB, alloc=445.1MB, time=69.34 memory used=3741.5MB, alloc=445.1MB, time=72.13 memory used=3864.8MB, alloc=445.1MB, time=74.81 memory used=3992.5MB, alloc=445.1MB, time=78.59 memory used=4134.0MB, alloc=445.1MB, time=82.19 memory used=4228.0MB, alloc=469.1MB, time=84.84 memory used=4354.5MB, alloc=469.1MB, time=87.23 memory used=4443.3MB, alloc=469.1MB, time=89.21 memory used=4560.1MB, alloc=469.1MB, time=90.94 memory used=4680.2MB, alloc=469.1MB, time=93.62 memory used=4788.2MB, alloc=469.1MB, time=96.41 memory used=4904.5MB, alloc=469.1MB, time=98.24 memory used=5022.9MB, alloc=469.1MB, time=104.13 memory used=5145.4MB, alloc=469.1MB, time=107.01 memory used=5268.6MB, alloc=469.1MB, time=112.63 memory used=5365.2MB, alloc=493.1MB, time=113.84 memory used=5464.9MB, alloc=493.1MB, time=114.68 memory used=5555.0MB, alloc=493.1MB, time=115.28 memory used=5676.7MB, alloc=493.1MB, time=119.15 memory used=5763.7MB, alloc=493.1MB, time=119.68 memory used=5901.0MB, alloc=493.1MB, time=121.53 memory used=6011.2MB, alloc=493.1MB, time=123.42 memory used=6095.7MB, alloc=493.1MB, time=123.95 memory used=6169.4MB, alloc=493.1MB, time=125.67 memory used=6255.9MB, alloc=493.1MB, time=127.60 |\^/| 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(); 1428266048 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 F := [-5 x y + 19 x z + 4 z, x z - 3 x y z - 9 y, 3 x y - y z - z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 3 2 3 2 G := [10 x + x z + 11 z , 5 x y + 6, 9 x y z + 7 y - 9 z ] > Problem := [F,G]; 2 2 2 Problem := [[-5 x y + 19 x z + 4 z, x z - 3 x y z - 9 y, 3 x y - y z - z], 3 2 3 2 3 2 [10 x + x z + 11 z , 5 x y + 6, 9 x y z + 7 y - 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=31.8MB, alloc=40.3MB, time=1.01 memory used=59.5MB, alloc=40.3MB, time=1.71 memory used=84.7MB, alloc=64.3MB, time=2.40 memory used=132.1MB, alloc=68.3MB, time=3.64 memory used=176.9MB, alloc=92.3MB, time=4.90 memory used=245.3MB, alloc=100.3MB, time=6.78 memory used=313.3MB, alloc=124.3MB, time=8.75 memory used=404.7MB, alloc=124.3MB, time=11.42 memory used=487.0MB, alloc=404.3MB, time=13.88 memory used=603.3MB, alloc=404.3MB, time=17.42 memory used=716.8MB, alloc=428.3MB, time=20.97 memory used=852.5MB, alloc=452.3MB, time=25.08 memory used=1010.9MB, alloc=476.3MB, time=30.19 memory used=1180.5MB, alloc=500.3MB, time=35.73 memory used=1326.3MB, alloc=524.3MB, time=40.68 memory used=1463.6MB, alloc=524.3MB, time=45.40 memory used=1583.3MB, alloc=524.3MB, time=49.27 memory used=1712.5MB, alloc=524.3MB, time=54.03 memory used=1835.6MB, alloc=548.3MB, time=58.61 memory used=1946.9MB, alloc=548.3MB, time=62.73 memory used=2070.2MB, alloc=548.3MB, time=67.38 memory used=2167.9MB, alloc=548.3MB, time=71.13 memory used=2260.6MB, alloc=548.3MB, time=74.76 memory used=2349.1MB, alloc=548.3MB, time=78.12 memory used=2413.4MB, alloc=548.3MB, time=80.57 memory used=2499.7MB, alloc=548.3MB, time=84.24 memory used=2579.5MB, alloc=548.3MB, time=87.48 memory used=2639.2MB, alloc=548.3MB, time=89.75 memory used=2693.9MB, alloc=548.3MB, time=92.07 memory used=2756.6MB, alloc=548.3MB, time=94.75 memory used=2813.3MB, alloc=548.3MB, time=96.52 memory used=2886.9MB, alloc=548.3MB, time=100.02 memory used=3124.0MB, alloc=572.3MB, time=108.74 memory used=3369.2MB, alloc=596.3MB, time=117.63 |\^/| 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(); 1428266348 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 3 2 2 2 F := [-19 x - 19 x z - 14 x y z, -x - 3 z - z, 3 x z - x z + 4] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 2 G := [7 y - 6 y z , 2 x z + 7 x y - 8 z, -8 x + 8 y z] > Problem := [F,G]; 3 2 3 2 2 2 Problem := [[-19 x - 19 x z - 14 x y z, -x - 3 z - z, 3 x z - x z + 4], 3 2 2 2 [7 y - 6 y z , 2 x z + 7 x y - 8 z, -8 x + 8 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.3MB, alloc=32.3MB, time=0.86 memory used=46.6MB, alloc=56.3MB, time=1.39 memory used=88.7MB, alloc=60.3MB, time=2.46 memory used=129.6MB, alloc=92.3MB, time=3.56 memory used=192.4MB, alloc=92.3MB, time=5.09 memory used=254.9MB, alloc=92.3MB, time=6.60 memory used=314.8MB, alloc=116.3MB, time=8.15 memory used=399.7MB, alloc=140.3MB, time=10.35 memory used=465.9MB, alloc=396.3MB, time=12.14 memory used=576.8MB, alloc=420.3MB, time=14.94 memory used=715.9MB, alloc=444.3MB, time=18.22 memory used=841.5MB, alloc=468.3MB, time=21.48 memory used=963.7MB, alloc=468.3MB, time=24.86 memory used=1068.8MB, alloc=492.3MB, time=27.89 memory used=1158.3MB, alloc=492.3MB, time=30.39 memory used=1247.3MB, alloc=492.3MB, time=33.08 memory used=1341.9MB, alloc=492.3MB, time=35.89 memory used=1438.6MB, alloc=492.3MB, time=38.10 memory used=1520.1MB, alloc=492.3MB, time=40.12 memory used=1618.4MB, alloc=492.3MB, time=42.78 memory used=1683.2MB, alloc=516.3MB, time=44.73 memory used=1739.5MB, alloc=516.3MB, time=46.49 memory used=1812.6MB, alloc=516.3MB, time=48.91 memory used=1866.9MB, alloc=516.3MB, time=50.79 memory used=1939.2MB, alloc=516.3MB, time=53.37 memory used=2006.9MB, alloc=516.3MB, time=56.09 memory used=2057.4MB, alloc=516.3MB, time=58.13 memory used=2272.5MB, alloc=540.3MB, time=64.40 memory used=2473.4MB, alloc=564.3MB, time=70.86 memory used=2662.1MB, alloc=588.3MB, time=77.19 memory used=2840.4MB, alloc=612.3MB, time=83.57 memory used=3007.1MB, alloc=636.3MB, time=89.47 memory used=3134.4MB, alloc=660.3MB, time=94.26 memory used=3275.9MB, alloc=660.3MB, time=99.74 memory used=3383.9MB, alloc=660.3MB, time=103.84 memory used=3510.2MB, alloc=660.3MB, time=108.55 memory used=3616.1MB, alloc=660.3MB, time=112.98 |\^/| 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(); 1428266648 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 3 3 3 2 F := [20 x z - 7 y z + 12, 9 x - 10 z + 9 x z, -10 x - 10 x y + 2 y] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 G := [6 y z + 9 y + 19, 9 x z - 6 x , 6 x] > Problem := [F,G]; Problem := [ 2 2 3 3 3 2 [20 x z - 7 y z + 12, 9 x - 10 z + 9 x z, -10 x - 10 x y + 2 y], 2 2 2 [6 y z + 9 y + 19, 9 x z - 6 x , 6 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.31 memory used=26.8MB, alloc=32.3MB, time=0.90 memory used=48.1MB, alloc=32.3MB, time=1.47 memory used=68.2MB, alloc=56.3MB, time=2.03 memory used=109.1MB, alloc=60.3MB, time=3.13 memory used=147.9MB, alloc=84.3MB, time=4.18 memory used=207.5MB, alloc=92.3MB, time=5.82 memory used=267.5MB, alloc=92.3MB, time=7.40 memory used=328.9MB, alloc=116.3MB, time=9.00 memory used=411.2MB, alloc=116.3MB, time=11.24 memory used=491.4MB, alloc=116.3MB, time=13.50 memory used=562.4MB, alloc=396.3MB, time=15.38 memory used=668.7MB, alloc=396.3MB, time=18.35 memory used=772.4MB, alloc=420.3MB, time=21.26 memory used=900.7MB, alloc=420.3MB, time=24.49 memory used=1027.1MB, alloc=420.3MB, time=27.35 memory used=1155.3MB, alloc=444.3MB, time=30.77 memory used=1306.5MB, alloc=468.3MB, time=35.29 memory used=1465.5MB, alloc=492.3MB, time=40.40 memory used=1638.7MB, alloc=516.3MB, time=45.94 memory used=1836.0MB, alloc=540.3MB, time=51.96 memory used=2058.3MB, alloc=564.3MB, time=58.43 memory used=2299.7MB, alloc=588.3MB, time=65.30 memory used=2540.1MB, alloc=612.3MB, time=72.93 memory used=2766.5MB, alloc=636.3MB, time=80.35 memory used=2985.5MB, alloc=660.3MB, time=87.73 memory used=3210.0MB, alloc=684.3MB, time=98.04 memory used=3441.2MB, alloc=708.3MB, time=110.25 |\^/| 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(); 1428266948 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 3 2 F := [17 x y z - 2 z - z, -2 x - x y - 9 y , y z + 9 x - 7 y] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 2 G := [-9 y + 15 x - 20 z, 9 y z - 6 x + 1, 4 x y + y z + 5 y] > Problem := [F,G]; 3 3 2 Problem := [[17 x y z - 2 z - z, -2 x - x y - 9 y , y z + 9 x - 7 y], 2 2 2 2 2 [-9 y + 15 x - 20 z, 9 y z - 6 x + 1, 4 x y + y z + 5 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.7MB, alloc=32.3MB, time=0.87 memory used=47.7MB, alloc=32.3MB, time=1.41 memory used=66.9MB, alloc=56.3MB, time=1.93 memory used=107.3MB, alloc=60.3MB, time=2.97 memory used=146.9MB, alloc=84.3MB, time=4.03 memory used=208.2MB, alloc=92.3MB, time=5.64 memory used=268.6MB, alloc=116.3MB, time=7.23 memory used=350.5MB, alloc=116.3MB, time=9.37 memory used=423.9MB, alloc=396.3MB, time=11.33 memory used=528.2MB, alloc=420.3MB, time=14.16 memory used=659.0MB, alloc=444.3MB, time=17.47 memory used=807.9MB, alloc=468.3MB, time=21.57 memory used=927.2MB, alloc=468.3MB, time=24.85 memory used=1042.0MB, alloc=492.3MB, time=28.05 memory used=1150.5MB, alloc=492.3MB, time=31.16 memory used=1271.4MB, alloc=492.3MB, time=34.80 memory used=1379.3MB, alloc=492.3MB, time=38.13 memory used=1479.6MB, alloc=516.3MB, time=41.36 memory used=1565.1MB, alloc=516.3MB, time=44.27 memory used=1632.4MB, alloc=516.3MB, time=46.51 memory used=1707.7MB, alloc=516.3MB, time=49.08 memory used=1777.0MB, alloc=516.3MB, time=51.47 memory used=1828.1MB, alloc=516.3MB, time=53.26 memory used=1887.6MB, alloc=540.3MB, time=55.40 memory used=1931.8MB, alloc=540.3MB, time=57.18 memory used=2148.9MB, alloc=564.3MB, time=63.77 memory used=2340.1MB, alloc=588.3MB, time=69.45 memory used=2552.8MB, alloc=612.3MB, time=76.88 memory used=2733.5MB, alloc=636.3MB, time=82.65 memory used=2878.2MB, alloc=660.3MB, time=87.58 memory used=3000.5MB, alloc=660.3MB, time=92.26 memory used=3150.8MB, alloc=684.3MB, time=98.03 memory used=3277.9MB, alloc=684.3MB, time=103.03 memory used=3393.7MB, alloc=684.3MB, time=108.02 memory used=3496.9MB, alloc=684.3MB, time=112.26 memory used=3604.9MB, alloc=684.3MB, time=116.84 |\^/| 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(); 1428267248 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 3 2 2 2 F := [8 z + 6 x y - 6 x z, -8 x - 7 x y - 6 y z, -10 z - 8 x - 10 z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 3 2 G := [11 x + y , -3 x - 5 x - 5 z, 8 x y] > Problem := [F,G]; Problem := [ 3 3 2 2 2 [8 z + 6 x y - 6 x z, -8 x - 7 x y - 6 y z, -10 z - 8 x - 10 z], 3 3 2 [11 x + y , -3 x - 5 x - 5 z, 8 x y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=31.0MB, alloc=40.3MB, time=0.99 memory used=57.7MB, alloc=44.3MB, time=1.66 memory used=84.7MB, alloc=68.3MB, time=2.28 memory used=134.0MB, alloc=76.3MB, time=3.52 memory used=177.9MB, alloc=76.3MB, time=4.34 memory used=208.2MB, alloc=76.3MB, time=4.74 memory used=239.3MB, alloc=76.3MB, time=5.08 memory used=281.5MB, alloc=76.3MB, time=5.79 memory used=313.7MB, alloc=76.3MB, time=7.81 memory used=368.8MB, alloc=76.3MB, time=8.76 memory used=416.3MB, alloc=100.3MB, time=9.96 memory used=485.6MB, alloc=100.3MB, time=11.67 memory used=560.6MB, alloc=100.3MB, time=12.90 memory used=609.9MB, alloc=100.3MB, time=13.40 memory used=663.7MB, alloc=100.3MB, time=14.25 memory used=704.9MB, alloc=100.3MB, time=14.74 memory used=765.3MB, alloc=124.3MB, time=15.30 memory used=863.8MB, alloc=124.3MB, time=16.66 memory used=954.7MB, alloc=124.3MB, time=17.57 memory used=1049.0MB, alloc=124.3MB, time=19.23 memory used=1119.3MB, alloc=380.3MB, time=20.88 memory used=1218.8MB, alloc=404.3MB, time=22.67 memory used=1329.4MB, alloc=404.3MB, time=25.08 memory used=1438.6MB, alloc=404.3MB, time=26.94 memory used=1495.5MB, alloc=404.3MB, time=27.40 memory used=1568.9MB, alloc=404.3MB, time=28.22 memory used=1688.9MB, alloc=428.3MB, time=29.61 memory used=1850.1MB, alloc=428.3MB, time=32.28 memory used=2003.0MB, alloc=428.3MB, time=34.75 memory used=2128.1MB, alloc=452.3MB, time=37.89 memory used=2273.8MB, alloc=476.3MB, time=40.98 memory used=2387.6MB, alloc=500.3MB, time=44.03 memory used=2586.5MB, alloc=500.3MB, time=46.66 memory used=2732.6MB, alloc=500.3MB, time=47.57 memory used=2932.5MB, alloc=500.3MB, time=48.61 memory used=3214.0MB, alloc=500.3MB, time=49.84 memory used=3623.6MB, alloc=500.3MB, time=51.54 memory used=4011.3MB, alloc=500.3MB, time=53.02 memory used=4394.4MB, alloc=500.3MB, time=54.54 memory used=4767.9MB, alloc=500.3MB, time=55.98 memory used=5024.8MB, alloc=524.3MB, time=59.91 memory used=5202.0MB, alloc=524.3MB, time=60.94 memory used=5454.5MB, alloc=524.3MB, time=62.10 memory used=5845.3MB, alloc=524.3MB, time=63.60 memory used=6230.5MB, alloc=524.3MB, time=65.03 memory used=6594.7MB, alloc=524.3MB, time=66.40 memory used=6956.8MB, alloc=524.3MB, time=67.82 memory used=7314.6MB, alloc=524.3MB, time=69.19 memory used=7674.0MB, alloc=524.3MB, time=70.64 memory used=8029.6MB, alloc=524.3MB, time=71.99 memory used=8386.6MB, alloc=524.3MB, time=73.34 memory used=8765.2MB, alloc=524.3MB, time=77.13 memory used=8976.1MB, alloc=524.3MB, time=79.45 memory used=9149.8MB, alloc=524.3MB, time=80.54 memory used=9402.0MB, alloc=524.3MB, time=83.55 memory used=9571.8MB, alloc=524.3MB, time=84.58 memory used=9809.6MB, alloc=524.3MB, time=85.72 memory used=10160.9MB, alloc=524.3MB, time=87.13 memory used=10552.5MB, alloc=524.3MB, time=88.60 memory used=10917.1MB, alloc=524.3MB, time=89.94 memory used=11281.3MB, alloc=524.3MB, time=91.35 memory used=11639.3MB, alloc=524.3MB, time=92.75 memory used=11994.7MB, alloc=524.3MB, time=94.16 memory used=12350.4MB, alloc=524.3MB, time=95.59 memory used=12742.8MB, alloc=524.3MB, time=98.82 memory used=12966.7MB, alloc=548.3MB, time=104.01 memory used=13191.8MB, alloc=572.3MB, time=110.55 memory used=13465.0MB, alloc=596.3MB, time=116.40 memory used=13762.5MB, alloc=596.3MB, time=122.46 |\^/| 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(); 1428267548 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 2 3 2 2 F := [-8 z + 9 y z - 3 z , -x y + 2 x z + z, 2 x - 2 y z + 10 y z ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 3 2 G := [-15 x y z + 19 y z, -9 y + y z + 9 x, -3 z + 9 z - 8] > Problem := [F,G]; Problem := [ 3 2 2 2 3 2 2 [-8 z + 9 y z - 3 z , -x y + 2 x z + z, 2 x - 2 y z + 10 y z ], 2 2 3 2 [-15 x y z + 19 y z, -9 y + y z + 9 x, -3 z + 9 z - 8]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.31 memory used=26.5MB, alloc=32.3MB, time=0.87 memory used=47.7MB, alloc=32.3MB, time=1.43 memory used=67.3MB, alloc=56.3MB, time=1.96 memory used=108.3MB, alloc=60.3MB, time=3.05 memory used=147.4MB, alloc=84.3MB, time=4.08 memory used=207.0MB, alloc=92.3MB, time=5.72 memory used=266.4MB, alloc=116.3MB, time=7.36 memory used=344.0MB, alloc=116.3MB, time=9.33 memory used=410.5MB, alloc=396.3MB, time=11.21 memory used=519.6MB, alloc=396.3MB, time=14.00 memory used=625.2MB, alloc=420.3MB, time=16.82 memory used=757.2MB, alloc=444.3MB, time=20.41 memory used=901.4MB, alloc=468.3MB, time=24.41 memory used=1039.0MB, alloc=492.3MB, time=28.28 memory used=1150.8MB, alloc=492.3MB, time=31.21 memory used=1258.6MB, alloc=492.3MB, time=34.32 memory used=1359.1MB, alloc=492.3MB, time=37.22 memory used=1468.5MB, alloc=516.3MB, time=40.08 memory used=1565.3MB, alloc=516.3MB, time=42.77 memory used=1674.2MB, alloc=516.3MB, time=45.50 memory used=1750.6MB, alloc=516.3MB, time=47.78 memory used=1843.5MB, alloc=516.3MB, time=50.98 memory used=1932.7MB, alloc=516.3MB, time=54.15 memory used=2009.7MB, alloc=540.3MB, time=56.37 memory used=2080.3MB, alloc=540.3MB, time=58.50 memory used=2153.9MB, alloc=540.3MB, time=61.12 memory used=2216.6MB, alloc=540.3MB, time=63.03 memory used=2292.9MB, alloc=540.3MB, time=65.16 memory used=2353.8MB, alloc=540.3MB, time=67.02 memory used=2423.3MB, alloc=540.3MB, time=69.73 memory used=2493.9MB, alloc=540.3MB, time=72.48 memory used=2536.8MB, alloc=540.3MB, time=74.14 memory used=2570.6MB, alloc=540.3MB, time=75.52 memory used=2789.5MB, alloc=564.3MB, time=82.44 memory used=3019.7MB, alloc=588.3MB, time=89.87 memory used=3196.0MB, alloc=612.3MB, time=95.29 memory used=3376.3MB, alloc=636.3MB, time=100.98 memory used=3569.9MB, alloc=660.3MB, time=107.25 memory used=3734.5MB, alloc=684.3MB, time=112.40 memory used=3916.7MB, alloc=684.3MB, time=119.19 memory used=4083.8MB, alloc=708.3MB, time=124.28 memory used=4220.1MB, alloc=708.3MB, time=129.43 |\^/| 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(); 1428267848 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 2 F := [-3 x + 7 y z - 19 z, y - 2 y z - 8 z , 7 y z - 10 y] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 3 2 2 G := [-20 x y + z + 14 z, 5 x + 4 y - 9 z, -9 x y + 5 y z - 10 y] > Problem := [F,G]; 3 2 2 2 Problem := [[-3 x + 7 y z - 19 z, y - 2 y z - 8 z , 7 y z - 10 y], 2 2 3 2 2 [-20 x y + z + 14 z, 5 x + 4 y - 9 z, -9 x y + 5 y 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=0.30 memory used=26.3MB, alloc=32.3MB, time=0.87 memory used=46.5MB, alloc=32.3MB, time=1.40 memory used=65.0MB, alloc=56.3MB, time=1.91 memory used=102.4MB, alloc=60.3MB, time=2.88 memory used=141.0MB, alloc=84.3MB, time=3.86 memory used=203.4MB, alloc=92.3MB, time=5.44 memory used=263.0MB, alloc=116.3MB, time=7.02 memory used=336.5MB, alloc=116.3MB, time=9.02 memory used=414.0MB, alloc=396.3MB, time=11.15 memory used=518.0MB, alloc=396.3MB, time=13.88 memory used=617.0MB, alloc=420.3MB, time=16.67 memory used=737.4MB, alloc=444.3MB, time=20.09 memory used=876.1MB, alloc=468.3MB, time=23.88 memory used=1006.5MB, alloc=492.3MB, time=27.57 memory used=1153.1MB, alloc=492.3MB, time=32.12 memory used=1258.8MB, alloc=516.3MB, time=35.33 memory used=1364.1MB, alloc=516.3MB, time=38.61 memory used=1489.3MB, alloc=516.3MB, time=42.96 memory used=1595.4MB, alloc=516.3MB, time=46.53 memory used=1679.4MB, alloc=540.3MB, time=49.47 memory used=1764.3MB, alloc=540.3MB, time=52.51 memory used=1829.6MB, alloc=540.3MB, time=54.66 memory used=1910.3MB, alloc=540.3MB, time=57.62 memory used=1981.3MB, alloc=540.3MB, time=60.39 memory used=2046.5MB, alloc=540.3MB, time=63.07 memory used=2097.0MB, alloc=540.3MB, time=65.03 memory used=2153.8MB, alloc=540.3MB, time=67.39 memory used=2210.6MB, alloc=540.3MB, time=69.94 memory used=2424.6MB, alloc=564.3MB, time=77.83 memory used=2659.9MB, alloc=588.3MB, time=86.39 memory used=2862.5MB, alloc=612.3MB, time=93.79 memory used=3082.0MB, alloc=636.3MB, time=101.92 memory used=3290.9MB, alloc=660.3MB, time=110.24 memory used=3491.4MB, alloc=684.3MB, time=118.51 |\^/| 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(); 1428268148 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 3 2 2 3 2 F := [12 x - x y z - 14 y , -2 x y + 6 y z + 7 z , 3 x y + x z + 4 z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 2 G := [-12 y z + 16 z - 14, -9 x y + 8 x y z + 8 x z, 8 x y z + 3 y + y] > Problem := [F,G]; Problem := [ 3 3 2 2 3 2 [12 x - x y z - 14 y , -2 x y + 6 y z + 7 z , 3 x y + x z + 4 z], 2 3 2 2 [-12 y z + 16 z - 14, -9 x y + 8 x y z + 8 x z, 8 x y z + 3 y + y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.29 memory used=25.9MB, alloc=32.3MB, time=0.86 memory used=46.3MB, alloc=32.3MB, time=1.39 memory used=64.6MB, alloc=56.3MB, time=1.89 memory used=104.0MB, alloc=60.3MB, time=2.97 memory used=143.5MB, alloc=60.3MB, time=3.97 memory used=183.5MB, alloc=84.3MB, time=5.00 memory used=224.7MB, alloc=84.3MB, time=6.06 memory used=286.2MB, alloc=92.3MB, time=7.73 memory used=345.4MB, alloc=116.3MB, time=9.38 memory used=422.5MB, alloc=116.3MB, time=11.28 memory used=482.0MB, alloc=372.3MB, time=12.69 memory used=570.7MB, alloc=396.3MB, time=14.80 memory used=684.9MB, alloc=420.3MB, time=17.61 memory used=818.5MB, alloc=444.3MB, time=20.86 memory used=931.7MB, alloc=444.3MB, time=23.01 memory used=1063.1MB, alloc=468.3MB, time=25.68 memory used=1179.5MB, alloc=468.3MB, time=27.94 memory used=1289.2MB, alloc=468.3MB, time=30.63 memory used=1386.7MB, alloc=468.3MB, time=32.79 memory used=1492.0MB, alloc=468.3MB, time=35.29 memory used=1567.6MB, alloc=468.3MB, time=37.13 memory used=1655.5MB, alloc=468.3MB, time=39.67 memory used=1736.2MB, alloc=492.3MB, time=41.56 memory used=1809.9MB, alloc=492.3MB, time=43.90 memory used=1881.0MB, alloc=492.3MB, time=45.69 memory used=1943.3MB, alloc=492.3MB, time=47.52 memory used=2022.6MB, alloc=492.3MB, time=50.13 memory used=2088.1MB, alloc=492.3MB, time=52.26 memory used=2149.1MB, alloc=492.3MB, time=54.38 memory used=2196.4MB, alloc=492.3MB, time=55.92 memory used=2246.2MB, alloc=492.3MB, time=57.35 memory used=2309.1MB, alloc=492.3MB, time=59.62 memory used=2498.8MB, alloc=516.3MB, time=64.67 memory used=2705.4MB, alloc=540.3MB, time=70.37 memory used=2900.7MB, alloc=564.3MB, time=76.17 memory used=3131.6MB, alloc=588.3MB, time=81.14 memory used=3326.4MB, alloc=612.3MB, time=86.04 memory used=3552.4MB, alloc=612.3MB, time=90.00 memory used=3671.1MB, alloc=612.3MB, time=91.04 memory used=3821.3MB, alloc=612.3MB, time=92.07 memory used=4073.7MB, alloc=612.3MB, time=96.52 memory used=4222.7MB, alloc=612.3MB, time=101.11 memory used=4386.4MB, alloc=636.3MB, time=105.37 memory used=4552.9MB, alloc=636.3MB, time=109.59 memory used=4722.0MB, alloc=636.3MB, time=112.20 memory used=4896.8MB, alloc=636.3MB, time=113.92 memory used=5073.8MB, alloc=636.3MB, time=120.84 memory used=5263.9MB, alloc=636.3MB, time=124.13 memory used=5395.7MB, alloc=636.3MB, time=128.21 memory used=5593.1MB, alloc=636.3MB, time=131.28 memory used=5762.4MB, alloc=660.3MB, time=134.52 memory used=5877.0MB, alloc=660.3MB, time=138.79 |\^/| 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(); 1428268448 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 3 2 2 F := [-2 x - 10 x y z - 18 y z, -4 x y + 3 x z - 3 x, 8 x + 8 x y + x z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 3 2 2 G := [-16 x + 6 y , 8 x z - 9 y z + 7 z, -6 z + y - 2 z ] > Problem := [F,G]; Problem := [ 3 2 2 3 2 2 [-2 x - 10 x y z - 18 y z, -4 x y + 3 x z - 3 x, 8 x + 8 x y + x z], 3 2 2 3 2 2 [-16 x + 6 y , 8 x z - 9 y z + 7 z, -6 z + 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=4.3MB, alloc=32.3MB, time=0.31 memory used=26.5MB, alloc=32.3MB, time=0.86 memory used=47.5MB, alloc=32.3MB, time=1.41 memory used=67.5MB, alloc=56.3MB, time=1.96 memory used=107.5MB, alloc=60.3MB, time=3.00 memory used=145.7MB, alloc=84.3MB, time=4.03 memory used=205.4MB, alloc=92.3MB, time=5.68 memory used=264.4MB, alloc=116.3MB, time=7.28 memory used=345.1MB, alloc=116.3MB, time=9.55 memory used=425.8MB, alloc=140.3MB, time=11.89 memory used=520.3MB, alloc=140.3MB, time=14.64 memory used=611.7MB, alloc=420.3MB, time=17.38 memory used=736.3MB, alloc=420.3MB, time=21.16 memory used=859.4MB, alloc=444.3MB, time=24.85 memory used=1004.1MB, alloc=468.3MB, time=28.99 memory used=1165.9MB, alloc=492.3MB, time=33.96 memory used=1301.5MB, alloc=516.3MB, time=37.86 memory used=1425.7MB, alloc=516.3MB, time=41.67 memory used=1526.2MB, alloc=516.3MB, time=44.43 memory used=1648.0MB, alloc=540.3MB, time=48.29 memory used=1764.1MB, alloc=540.3MB, time=51.87 memory used=1860.7MB, alloc=540.3MB, time=54.62 memory used=1971.8MB, alloc=564.3MB, time=58.35 memory used=2068.1MB, alloc=564.3MB, time=61.75 memory used=2152.0MB, alloc=564.3MB, time=64.62 memory used=2229.3MB, alloc=564.3MB, time=67.38 memory used=2310.1MB, alloc=564.3MB, time=70.32 memory used=2386.1MB, alloc=564.3MB, time=73.01 memory used=2469.2MB, alloc=564.3MB, time=76.28 memory used=2535.2MB, alloc=564.3MB, time=78.54 memory used=2597.3MB, alloc=564.3MB, time=80.99 memory used=2645.8MB, alloc=564.3MB, time=82.81 memory used=2888.9MB, alloc=588.3MB, time=90.75 memory used=3086.7MB, alloc=612.3MB, time=97.12 |\^/| 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(); 1428268748 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 F := [x y + 3 x y z - 12 z, 10 x y z - 6 z, 6 x + 6 z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 G := [-18 x y + x z + 11 x y, 6 x y - 9 x y + y, 8 + 9 x] > Problem := [F,G]; 2 Problem := [[x y + 3 x y z - 12 z, 10 x y z - 6 z, 6 x + 6 z], 2 2 2 [-18 x y + x z + 11 x y, 6 x y - 9 x y + y, 8 + 9 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.4MB, alloc=32.3MB, time=0.84 memory used=47.6MB, alloc=32.3MB, time=1.37 memory used=67.9MB, alloc=56.3MB, time=1.90 memory used=110.2MB, alloc=60.3MB, time=3.08 memory used=150.6MB, alloc=84.3MB, time=4.29 memory used=214.6MB, alloc=84.3MB, time=6.06 memory used=272.7MB, alloc=108.3MB, time=7.74 memory used=350.0MB, alloc=140.3MB, time=10.02 memory used=446.4MB, alloc=164.3MB, time=12.83 memory used=554.8MB, alloc=188.3MB, time=16.60 memory used=663.9MB, alloc=212.3MB, time=21.73 memory used=783.9MB, alloc=236.3MB, time=28.37 memory used=920.3MB, alloc=260.3MB, time=36.52 memory used=1080.7MB, alloc=260.3MB, time=46.09 memory used=1241.1MB, alloc=260.3MB, time=55.66 memory used=1401.4MB, alloc=284.3MB, time=65.34 memory used=1585.8MB, alloc=284.3MB, time=76.42 N1 := 6195 > GB := Basis(F, plex(op(vars))); 3 2 GB := [85 x + 3 x, 17 x + x y, z + x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1773.7MB, alloc=284.3MB, time=86.78 N2 := 427 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 H := [3 z y x + y x - 12 z, 10 x y z - 6 z, 6 x + 6 z, 2 2 2 -18 x y + x z + 11 x y, 6 x y - 9 x y + y, 9 x + 8] > J:=[op(GB),op(G)]; 3 2 2 2 J := [85 x + 3 x, 17 x + x y, z + x, -18 x y + x z + 11 x y, 2 6 x y - 9 x y + y, 9 x + 8] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 14, 14, 3, 2, 2, 2, 1, 2/3, 2/3, 2/3, 8/15, 2/5, 6, 11, 13, 11 3, 3, 1, 2, 1, 1/2, 1/3, --, 3/7, 1/7, 3, 1, 0] 14 > save(F, G, cat("ranSet/33", convert(F, string),".txt")); > quit memory used=1807.8MB, alloc=284.3MB, time=87.96 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428268990 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 F := [7 y z - 13 x + 11 z, 10 y z + 5 x + 3 y, 4 x y + 9 x - 6 y] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 2 2 G := [-14 x - 2 x y + 17 y , -9 x y + 4 x y, 8 x z - 7 x z + 9 y z] > Problem := [F,G]; 2 2 2 Problem := [[7 y z - 13 x + 11 z, 10 y z + 5 x + 3 y, 4 x y + 9 x - 6 y], 2 2 2 2 2 2 [-14 x - 2 x y + 17 y , -9 x y + 4 x y, 8 x z - 7 x z + 9 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.32 memory used=26.4MB, alloc=32.3MB, time=0.88 memory used=47.4MB, alloc=32.3MB, time=1.41 memory used=67.6MB, alloc=32.3MB, time=1.93 memory used=86.8MB, alloc=56.3MB, time=2.45 memory used=127.3MB, alloc=60.3MB, time=3.52 memory used=163.6MB, alloc=84.3MB, time=4.52 memory used=210.7MB, alloc=84.3MB, time=5.81 memory used=270.1MB, alloc=92.3MB, time=7.47 memory used=329.9MB, alloc=116.3MB, time=9.12 memory used=410.6MB, alloc=116.3MB, time=11.39 memory used=492.2MB, alloc=140.3MB, time=13.61 memory used=574.4MB, alloc=140.3MB, time=15.92 memory used=638.9MB, alloc=420.3MB, time=17.75 memory used=766.7MB, alloc=444.3MB, time=21.72 memory used=899.1MB, alloc=468.3MB, time=25.90 memory used=1043.4MB, alloc=492.3MB, time=30.57 memory used=1201.5MB, alloc=516.3MB, time=35.69 memory used=1373.5MB, alloc=540.3MB, time=41.30 memory used=1557.1MB, alloc=564.3MB, time=47.32 memory used=1749.6MB, alloc=588.3MB, time=54.73 memory used=1929.5MB, alloc=612.3MB, time=64.38 memory used=2118.4MB, alloc=636.3MB, time=75.20 memory used=2322.1MB, alloc=660.3MB, time=87.10 memory used=2540.9MB, alloc=684.3MB, time=100.11 memory used=2770.8MB, alloc=708.3MB, time=114.69 memory used=3016.6MB, alloc=732.3MB, time=130.95 |\^/| 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(); 1428269290 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 3 3 2 2 3 F := [-20 x z - 14 y z + 12 z , x + 8 y z + 9 y, -2 x y - 2 x y z - 6 z ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 G := [16 x y z - 9 x y - 20 y z, 8 x y - 4 y z + z, 2 x + 7 x y + 8 z] > Problem := [F,G]; Problem := [ 2 2 3 3 2 2 3 [-20 x z - 14 y z + 12 z , x + 8 y z + 9 y, -2 x y - 2 x y z - 6 z ], 3 2 [16 x y z - 9 x y - 20 y z, 8 x y - 4 y z + z, 2 x + 7 x 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=54.5MB, alloc=68.3MB, time=1.63 memory used=100.9MB, alloc=68.3MB, time=2.82 memory used=146.5MB, alloc=92.3MB, time=4.03 memory used=216.3MB, alloc=100.3MB, time=5.84 memory used=284.1MB, alloc=124.3MB, time=7.67 memory used=371.9MB, alloc=124.3MB, time=9.97 memory used=444.8MB, alloc=404.3MB, time=12.01 memory used=554.8MB, alloc=428.3MB, time=15.08 memory used=689.0MB, alloc=452.3MB, time=18.80 memory used=839.2MB, alloc=476.3MB, time=23.30 memory used=980.0MB, alloc=500.3MB, time=27.58 memory used=1105.9MB, alloc=500.3MB, time=31.37 memory used=1225.0MB, alloc=500.3MB, time=35.22 memory used=1329.0MB, alloc=524.3MB, time=38.61 memory used=1440.6MB, alloc=524.3MB, time=42.42 memory used=1523.7MB, alloc=524.3MB, time=45.07 memory used=1610.3MB, alloc=524.3MB, time=48.11 memory used=1695.8MB, alloc=524.3MB, time=51.19 memory used=1772.5MB, alloc=524.3MB, time=53.99 memory used=1808.4MB, alloc=524.3MB, time=55.45 memory used=1871.2MB, alloc=524.3MB, time=57.96 memory used=1934.7MB, alloc=524.3MB, time=60.56 memory used=1988.4MB, alloc=524.3MB, time=62.78 memory used=2200.3MB, alloc=548.3MB, time=69.99 memory used=2419.0MB, alloc=572.3MB, time=77.61 memory used=2619.8MB, alloc=596.3MB, time=85.07 memory used=2787.4MB, alloc=620.3MB, time=91.55 memory used=2968.4MB, alloc=644.3MB, time=98.67 memory used=3130.7MB, alloc=668.3MB, time=104.91 memory used=3268.5MB, alloc=668.3MB, time=109.98 memory used=3418.7MB, alloc=692.3MB, time=116.06 memory used=3543.3MB, alloc=692.3MB, time=121.57 memory used=3629.9MB, alloc=692.3MB, time=125.24 memory used=3721.0MB, alloc=692.3MB, time=129.28 |\^/| 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(); 1428269591 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 2 3 F := [-20 y - 16 y z - 20 x z, 5 y z + z, -10 y z + 10 z + 5 y z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 2 2 G := [7 x y - 9 x y z + 6 z , 10 x y - 4 x y - 4 y, -4 y z + 10 y z - 8 y] > Problem := [F,G]; 3 2 2 2 3 Problem := [[-20 y - 16 y z - 20 x z, 5 y z + z, -10 y z + 10 z + 5 y z], 2 3 2 2 2 [7 x y - 9 x y z + 6 z , 10 x y - 4 x y - 4 y, -4 y z + 10 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=0.31 memory used=26.4MB, alloc=32.3MB, time=0.86 memory used=47.3MB, alloc=32.3MB, time=1.38 memory used=66.2MB, alloc=56.3MB, time=1.90 memory used=104.9MB, alloc=60.3MB, time=2.90 memory used=143.0MB, alloc=60.3MB, time=3.90 memory used=180.0MB, alloc=84.3MB, time=4.87 memory used=238.3MB, alloc=84.3MB, time=6.39 memory used=296.3MB, alloc=92.3MB, time=7.91 memory used=352.8MB, alloc=116.3MB, time=9.45 memory used=432.6MB, alloc=116.3MB, time=11.62 memory used=510.3MB, alloc=396.3MB, time=13.81 memory used=613.2MB, alloc=396.3MB, time=16.73 memory used=716.2MB, alloc=420.3MB, time=19.62 memory used=843.4MB, alloc=444.3MB, time=23.35 memory used=996.7MB, alloc=444.3MB, time=27.66 memory used=1147.3MB, alloc=468.3MB, time=31.47 memory used=1287.1MB, alloc=468.3MB, time=35.34 memory used=1427.5MB, alloc=468.3MB, time=37.74 memory used=1571.9MB, alloc=492.3MB, time=41.90 memory used=1721.3MB, alloc=492.3MB, time=46.44 memory used=1876.0MB, alloc=516.3MB, time=51.62 memory used=2004.0MB, alloc=516.3MB, time=55.81 memory used=2147.4MB, alloc=540.3MB, time=60.93 memory used=2286.1MB, alloc=540.3MB, time=65.10 memory used=2377.2MB, alloc=540.3MB, time=67.60 memory used=2479.2MB, alloc=540.3MB, time=70.39 memory used=2582.3MB, alloc=540.3MB, time=73.86 memory used=2676.9MB, alloc=564.3MB, time=76.89 memory used=2782.8MB, alloc=564.3MB, time=80.51 memory used=2888.0MB, alloc=564.3MB, time=84.30 memory used=2965.0MB, alloc=564.3MB, time=86.44 memory used=3086.5MB, alloc=564.3MB, time=88.95 memory used=3152.1MB, alloc=564.3MB, time=90.67 memory used=3237.8MB, alloc=564.3MB, time=93.86 memory used=3302.0MB, alloc=588.3MB, time=95.99 memory used=3445.1MB, alloc=588.3MB, time=97.46 memory used=3586.6MB, alloc=588.3MB, time=98.58 memory used=3735.0MB, alloc=588.3MB, time=102.09 memory used=3861.2MB, alloc=588.3MB, time=103.00 memory used=4012.5MB, alloc=588.3MB, time=106.51 memory used=4165.4MB, alloc=588.3MB, time=108.05 memory used=4300.5MB, alloc=588.3MB, time=109.14 memory used=4439.3MB, alloc=588.3MB, time=112.48 memory used=4537.6MB, alloc=588.3MB, time=114.64 memory used=4614.9MB, alloc=588.3MB, time=116.80 memory used=4668.4MB, alloc=588.3MB, time=118.65 memory used=4727.8MB, alloc=588.3MB, time=120.54 memory used=4785.4MB, alloc=588.3MB, time=122.72 memory used=4853.1MB, alloc=588.3MB, time=125.46 memory used=4914.8MB, alloc=588.3MB, time=127.84 memory used=5107.6MB, alloc=588.3MB, time=131.35 memory used=5309.7MB, alloc=612.3MB, time=134.32 memory used=5542.9MB, alloc=636.3MB, time=141.90 |\^/| 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(); 1428269890 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 3 2 2 2 F := [-9 y - 13 y, 3 x y + 9 y + 10 z, -7 x y - 10 y z - y z ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 3 3 2 2 2 G := [-11 z + 8 x - 6, -10 x - 2 y + 6 x z, 4 x y + 10 x + 7 y ] > Problem := [F,G]; 3 2 3 2 2 2 Problem := [[-9 y - 13 y, 3 x y + 9 y + 10 z, -7 x y - 10 y z - y z ], 3 2 3 3 2 2 2 [-11 z + 8 x - 6, -10 x - 2 y + 6 x z, 4 x y + 10 x + 7 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.7MB, alloc=32.3MB, time=0.88 memory used=46.6MB, alloc=32.3MB, time=1.39 memory used=65.1MB, alloc=56.3MB, time=1.88 memory used=106.5MB, alloc=60.3MB, time=2.89 memory used=147.4MB, alloc=60.3MB, time=3.89 memory used=189.0MB, alloc=92.3MB, time=4.96 memory used=259.0MB, alloc=92.3MB, time=6.41 memory used=325.0MB, alloc=92.3MB, time=7.82 memory used=399.3MB, alloc=348.3MB, time=9.48 memory used=472.5MB, alloc=348.3MB, time=11.01 memory used=536.8MB, alloc=372.3MB, time=12.42 memory used=624.8MB, alloc=372.3MB, time=14.55 memory used=713.1MB, alloc=396.3MB, time=16.63 memory used=828.7MB, alloc=396.3MB, time=19.21 memory used=933.4MB, alloc=420.3MB, time=21.62 memory used=1050.1MB, alloc=420.3MB, time=24.24 memory used=1137.9MB, alloc=420.3MB, time=26.06 memory used=1267.4MB, alloc=444.3MB, time=28.67 memory used=1414.3MB, alloc=444.3MB, time=31.67 memory used=1538.1MB, alloc=444.3MB, time=34.02 memory used=1661.2MB, alloc=444.3MB, time=36.47 memory used=1787.2MB, alloc=444.3MB, time=40.49 memory used=1911.8MB, alloc=444.3MB, time=44.03 memory used=2059.7MB, alloc=444.3MB, time=48.56 memory used=2202.0MB, alloc=444.3MB, time=50.95 memory used=2301.6MB, alloc=444.3MB, time=52.46 memory used=2401.2MB, alloc=444.3MB, time=54.88 memory used=2487.4MB, alloc=444.3MB, time=55.60 memory used=2574.9MB, alloc=444.3MB, time=56.30 memory used=2673.6MB, alloc=444.3MB, time=62.77 memory used=2744.1MB, alloc=444.3MB, time=63.43 memory used=2828.4MB, alloc=444.3MB, time=64.22 memory used=2915.8MB, alloc=444.3MB, time=64.90 memory used=3026.1MB, alloc=444.3MB, time=71.56 memory used=3109.0MB, alloc=444.3MB, time=72.27 memory used=3197.1MB, alloc=444.3MB, time=72.96 memory used=3302.2MB, alloc=444.3MB, time=79.48 memory used=3366.1MB, alloc=444.3MB, time=79.94 memory used=3503.1MB, alloc=468.3MB, time=82.96 memory used=3620.1MB, alloc=468.3MB, time=85.28 memory used=3777.3MB, alloc=468.3MB, time=88.59 memory used=3869.1MB, alloc=468.3MB, time=90.47 memory used=4011.2MB, alloc=468.3MB, time=92.58 memory used=4085.4MB, alloc=468.3MB, time=93.16 memory used=4160.7MB, alloc=468.3MB, time=93.69 memory used=4242.8MB, alloc=468.3MB, time=94.81 memory used=4329.5MB, alloc=468.3MB, time=95.45 memory used=4414.4MB, alloc=468.3MB, time=96.01 memory used=4477.7MB, alloc=468.3MB, time=96.53 memory used=4587.9MB, alloc=468.3MB, time=110.16 memory used=4662.0MB, alloc=468.3MB, time=110.68 memory used=4744.2MB, alloc=468.3MB, time=111.22 memory used=4838.5MB, alloc=468.3MB, time=112.46 memory used=4913.5MB, alloc=468.3MB, time=113.03 memory used=4987.8MB, alloc=468.3MB, time=113.56 memory used=5072.6MB, alloc=468.3MB, time=114.74 memory used=5157.1MB, alloc=468.3MB, time=115.36 memory used=5241.2MB, alloc=468.3MB, time=115.93 memory used=5304.4MB, alloc=468.3MB, time=116.42 memory used=5412.9MB, alloc=468.3MB, time=129.92 memory used=5486.6MB, alloc=468.3MB, time=130.46 memory used=5568.4MB, alloc=468.3MB, time=130.97 memory used=5663.4MB, alloc=468.3MB, time=132.22 memory used=5738.8MB, alloc=468.3MB, time=132.79 memory used=5813.8MB, alloc=468.3MB, time=133.32 memory used=5900.9MB, alloc=468.3MB, time=134.42 memory used=5984.0MB, alloc=468.3MB, time=135.04 memory used=6067.8MB, alloc=468.3MB, time=135.62 memory used=6132.1MB, alloc=468.3MB, time=136.11 memory used=6242.4MB, alloc=468.3MB, time=149.79 memory used=6315.5MB, alloc=468.3MB, time=150.34 memory used=6397.9MB, alloc=468.3MB, time=150.89 memory used=6499.1MB, alloc=468.3MB, time=152.38 memory used=6568.1MB, alloc=468.3MB, time=152.94 memory used=6659.9MB, alloc=468.3MB, time=153.53 memory used=6718.1MB, alloc=468.3MB, time=154.02 memory used=6788.0MB, alloc=468.3MB, time=154.50 memory used=6900.8MB, alloc=468.3MB, time=156.15 memory used=6970.0MB, alloc=468.3MB, time=156.72 memory used=7062.1MB, alloc=468.3MB, time=157.34 memory used=7121.0MB, alloc=468.3MB, time=157.84 memory used=7189.8MB, alloc=468.3MB, time=158.38 |\^/| 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(); 1428270191 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 2 3 F := [-13 y z - x - 9 z, -5 x y + 8 y z - 8 z, 3 x y - 7 z + 2 y z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 3 G := [16 x y + 17 y z + 10 y, 4 y z - 2 x y - 9 y , -5 y - 10 x y + 9 y z] > Problem := [F,G]; Problem := [ 2 2 2 2 2 3 [-13 y z - x - 9 z, -5 x y + 8 y z - 8 z, 3 x y - 7 z + 2 y z], 2 2 2 2 3 [16 x y + 17 y z + 10 y, 4 y z - 2 x y - 9 y , -5 y - 10 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=0.30 memory used=27.1MB, alloc=36.3MB, time=0.92 memory used=47.4MB, alloc=60.3MB, time=1.41 memory used=89.1MB, alloc=60.3MB, time=2.45 memory used=130.9MB, alloc=68.3MB, time=3.47 memory used=175.4MB, alloc=68.3MB, time=4.47 memory used=218.6MB, alloc=92.3MB, time=5.54 memory used=286.3MB, alloc=92.3MB, time=7.22 memory used=350.8MB, alloc=116.3MB, time=8.79 memory used=410.2MB, alloc=372.3MB, time=10.22 memory used=503.4MB, alloc=372.3MB, time=12.40 memory used=593.2MB, alloc=396.3MB, time=14.42 memory used=706.6MB, alloc=396.3MB, time=16.91 memory used=810.8MB, alloc=420.3MB, time=19.71 memory used=940.4MB, alloc=444.3MB, time=22.96 memory used=1064.1MB, alloc=444.3MB, time=25.85 memory used=1201.9MB, alloc=468.3MB, time=28.77 memory used=1313.8MB, alloc=468.3MB, time=31.43 memory used=1423.7MB, alloc=468.3MB, time=34.38 memory used=1513.7MB, alloc=492.3MB, time=36.42 memory used=1615.4MB, alloc=492.3MB, time=38.91 memory used=1707.3MB, alloc=492.3MB, time=41.72 memory used=1784.7MB, alloc=516.3MB, time=43.60 memory used=1874.4MB, alloc=516.3MB, time=46.31 memory used=1943.5MB, alloc=516.3MB, time=48.08 memory used=2033.2MB, alloc=516.3MB, time=50.68 memory used=2107.0MB, alloc=516.3MB, time=52.91 memory used=2160.3MB, alloc=516.3MB, time=54.43 memory used=2225.9MB, alloc=516.3MB, time=56.09 memory used=2306.4MB, alloc=516.3MB, time=58.34 memory used=2400.4MB, alloc=516.3MB, time=60.14 memory used=2462.5MB, alloc=516.3MB, time=61.98 memory used=2510.2MB, alloc=516.3MB, time=63.42 memory used=2559.3MB, alloc=540.3MB, time=64.88 memory used=2780.6MB, alloc=564.3MB, time=70.63 memory used=2998.5MB, alloc=588.3MB, time=75.49 memory used=3230.4MB, alloc=612.3MB, time=80.54 memory used=3414.3MB, alloc=612.3MB, time=85.15 memory used=3627.6MB, alloc=636.3MB, time=91.22 memory used=3776.2MB, alloc=636.3MB, time=95.28 memory used=3925.8MB, alloc=636.3MB, time=99.78 memory used=4070.0MB, alloc=636.3MB, time=103.73 memory used=4197.8MB, alloc=660.3MB, time=108.65 memory used=4387.8MB, alloc=684.3MB, time=116.08 memory used=4468.2MB, alloc=684.3MB, time=119.53 memory used=4604.7MB, alloc=684.3MB, 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(); 1428270491 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 3 2 2 F := [-17 x y + 7 y - 16 y, x - 7 x z + y , 7 x y + 9 y z - 6 y z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 G := [-x z + 11 y + 17 y, 8 x - 6 x y z - 10 x y, 3 y z + 6 x y - 5 y z] > Problem := [F,G]; 2 3 2 3 2 2 Problem := [[-17 x y + 7 y - 16 y, x - 7 x z + y , 7 x y + 9 y z - 6 y z], 2 3 2 [-x z + 11 y + 17 y, 8 x - 6 x y z - 10 x y, 3 y z + 6 x y - 5 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.31 memory used=26.4MB, alloc=32.3MB, time=0.88 memory used=47.7MB, alloc=32.3MB, time=1.44 memory used=66.2MB, alloc=56.3MB, time=1.95 memory used=106.4MB, alloc=60.3MB, time=3.03 memory used=145.7MB, alloc=84.3MB, time=4.05 memory used=208.1MB, alloc=92.3MB, time=5.75 memory used=270.0MB, alloc=116.3MB, time=7.43 memory used=352.1MB, alloc=116.3MB, time=9.69 memory used=429.1MB, alloc=396.3MB, time=11.84 memory used=534.1MB, alloc=396.3MB, time=14.73 memory used=640.0MB, alloc=420.3MB, time=17.58 memory used=768.4MB, alloc=444.3MB, time=21.08 memory used=917.9MB, alloc=468.3MB, time=25.00 memory used=1030.2MB, alloc=468.3MB, time=27.41 memory used=1159.9MB, alloc=492.3MB, time=30.79 memory used=1260.7MB, alloc=492.3MB, time=33.76 memory used=1370.7MB, alloc=492.3MB, time=36.96 memory used=1472.8MB, alloc=516.3MB, time=39.27 memory used=1561.4MB, alloc=516.3MB, time=41.45 memory used=1662.8MB, alloc=516.3MB, time=44.64 memory used=1743.1MB, alloc=516.3MB, time=47.36 memory used=1818.5MB, alloc=516.3MB, time=49.32 memory used=1900.3MB, alloc=516.3MB, time=52.14 memory used=1963.4MB, alloc=516.3MB, time=54.17 memory used=2027.8MB, alloc=540.3MB, time=56.35 memory used=2097.0MB, alloc=540.3MB, time=59.07 memory used=2164.8MB, alloc=540.3MB, time=61.80 memory used=2207.9MB, alloc=540.3MB, time=63.60 memory used=2423.6MB, alloc=564.3MB, time=69.45 memory used=2596.7MB, alloc=588.3MB, time=74.61 memory used=2756.3MB, alloc=612.3MB, time=79.88 memory used=2913.2MB, alloc=636.3MB, time=84.00 memory used=3063.9MB, alloc=660.3MB, time=89.03 memory used=3222.2MB, alloc=660.3MB, time=94.44 memory used=3356.0MB, alloc=660.3MB, time=99.45 memory used=3494.6MB, alloc=660.3MB, time=104.49 memory used=3602.5MB, alloc=660.3MB, time=108.59 memory used=3683.5MB, alloc=660.3MB, time=111.26 memory used=3794.5MB, alloc=660.3MB, time=115.43 memory used=3889.2MB, alloc=660.3MB, time=119.45 memory used=4219.0MB, alloc=684.3MB, time=128.60 |\^/| 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(); 1428270791 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 3 3 F := [-15 x z - 11 y + z, -3 x y + x y - 6 x, 3 y - 3 z + 9 y] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 G := [8 - 14 x + 20 z, -3 x + 7 x y z + 6 x, 6 x z - 9 z ] > Problem := [F,G]; 2 2 3 3 Problem := [[-15 x z - 11 y + z, -3 x y + x y - 6 x, 3 y - 3 z + 9 y], 3 2 [8 - 14 x + 20 z, -3 x + 7 x y z + 6 x, 6 x z - 9 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.31 memory used=26.4MB, alloc=32.3MB, time=0.85 memory used=47.8MB, alloc=32.3MB, time=1.38 memory used=67.2MB, alloc=56.3MB, time=1.92 memory used=106.5MB, alloc=60.3MB, time=2.94 memory used=144.1MB, alloc=60.3MB, time=3.89 memory used=179.9MB, alloc=84.3MB, time=4.84 memory used=217.7MB, alloc=84.3MB, time=5.75 memory used=278.1MB, alloc=92.3MB, time=7.27 memory used=336.7MB, alloc=116.3MB, time=8.81 memory used=415.6MB, alloc=116.3MB, time=10.88 memory used=489.7MB, alloc=396.3MB, time=12.84 memory used=595.1MB, alloc=396.3MB, time=15.73 memory used=702.2MB, alloc=420.3MB, time=18.60 memory used=833.9MB, alloc=444.3MB, time=22.05 memory used=985.1MB, alloc=468.3MB, time=26.39 memory used=1126.7MB, alloc=468.3MB, time=30.44 memory used=1238.1MB, alloc=468.3MB, time=33.83 memory used=1368.1MB, alloc=492.3MB, time=37.62 memory used=1501.0MB, alloc=492.3MB, time=41.65 memory used=1627.0MB, alloc=516.3MB, time=45.59 memory used=1750.0MB, alloc=516.3MB, time=49.53 memory used=1860.5MB, alloc=516.3MB, time=53.08 memory used=1948.4MB, alloc=516.3MB, time=55.92 memory used=2037.5MB, alloc=540.3MB, time=58.77 memory used=2135.1MB, alloc=540.3MB, time=62.05 memory used=2246.7MB, alloc=540.3MB, time=64.94 memory used=2338.1MB, alloc=540.3MB, time=67.62 memory used=2424.7MB, alloc=540.3MB, time=69.96 memory used=2486.7MB, alloc=564.3MB, time=72.05 memory used=2562.9MB, alloc=564.3MB, time=74.26 memory used=2642.3MB, alloc=564.3MB, time=77.30 memory used=2749.4MB, alloc=564.3MB, time=80.58 memory used=2866.0MB, alloc=588.3MB, time=84.82 memory used=2997.0MB, alloc=612.3MB, time=89.57 memory used=3154.5MB, alloc=636.3MB, time=94.25 memory used=3346.7MB, alloc=636.3MB, time=99.06 memory used=3510.2MB, alloc=660.3MB, time=103.94 memory used=3624.2MB, alloc=684.3MB, time=108.15 memory used=3735.0MB, alloc=684.3MB, time=112.33 memory used=3840.6MB, alloc=708.3MB, time=116.47 memory used=3915.1MB, alloc=732.3MB, time=119.93 |\^/| 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(); 1428271091 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 2 F := [13 x y - 7 z + 8, 9 x y + 3 y z , x y + 2 x] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 3 2 2 2 2 G := [-7 x + 17 y + 4 y , -2 x z - 10 x y , -2 x y + 3 x y z - 3 y] > Problem := [F,G]; 2 3 2 2 Problem := [[13 x y - 7 z + 8, 9 x y + 3 y z , x y + 2 x], 3 3 2 2 2 2 [-7 x + 17 y + 4 y , -2 x z - 10 x y , -2 x y + 3 x y z - 3 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.31 memory used=26.2MB, alloc=32.3MB, time=0.87 memory used=47.8MB, alloc=32.3MB, time=1.44 memory used=67.3MB, alloc=56.3MB, time=1.97 memory used=106.8MB, alloc=60.3MB, time=2.98 memory used=145.0MB, alloc=84.3MB, time=4.04 memory used=208.1MB, alloc=92.3MB, time=5.72 memory used=272.1MB, alloc=116.3MB, time=7.41 memory used=354.4MB, alloc=116.3MB, time=9.54 memory used=425.5MB, alloc=372.3MB, time=11.47 memory used=511.4MB, alloc=396.3MB, time=13.84 memory used=620.9MB, alloc=420.3MB, time=16.83 memory used=752.9MB, alloc=444.3MB, time=20.52 memory used=908.3MB, alloc=444.3MB, time=23.83 memory used=1034.3MB, alloc=468.3MB, time=27.10 memory used=1158.9MB, alloc=468.3MB, time=30.28 memory used=1282.9MB, alloc=468.3MB, time=33.73 memory used=1407.7MB, alloc=492.3MB, time=36.54 memory used=1520.6MB, alloc=492.3MB, time=39.28 memory used=1615.4MB, alloc=492.3MB, time=41.86 memory used=1702.5MB, alloc=492.3MB, time=44.47 memory used=1840.1MB, alloc=492.3MB, time=46.95 memory used=1949.7MB, alloc=492.3MB, time=49.18 memory used=2040.5MB, alloc=516.3MB, time=51.79 memory used=2122.9MB, alloc=516.3MB, time=53.84 memory used=2209.3MB, alloc=516.3MB, time=56.48 memory used=2315.3MB, alloc=540.3MB, time=60.08 memory used=2425.0MB, alloc=540.3MB, time=63.65 memory used=2564.7MB, alloc=564.3MB, time=68.07 memory used=2696.4MB, alloc=588.3MB, time=72.13 memory used=2817.1MB, alloc=588.3MB, time=76.28 memory used=2930.0MB, alloc=612.3MB, time=80.33 memory used=3040.1MB, alloc=612.3MB, time=84.32 memory used=3145.5MB, alloc=636.3MB, time=88.25 memory used=3256.7MB, alloc=636.3MB, time=92.28 memory used=3360.2MB, alloc=660.3MB, time=96.14 memory used=3456.1MB, alloc=660.3MB, time=99.71 memory used=3551.3MB, alloc=684.3MB, time=103.14 memory used=3644.1MB, alloc=684.3MB, time=106.58 memory used=3765.2MB, alloc=708.3MB, time=112.86 memory used=4031.2MB, alloc=732.3MB, time=127.84 |\^/| 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(); 1428271391 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 2 F := [y - 13 x - 16 y z, -4 x y - 9 z - 6, -10 x z + 10 y] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 G := [10 x y - 9 x y + 18 y z, -z - 9 y - 3 z, -10 x y + 6 y z + z] > Problem := [F,G]; 3 2 2 2 Problem := [[y - 13 x - 16 y z, -4 x y - 9 z - 6, -10 x z + 10 y], 2 2 2 2 [10 x y - 9 x y + 18 y z, -z - 9 y - 3 z, -10 x y + 6 y 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=0.30 memory used=26.5MB, alloc=32.3MB, time=0.88 memory used=46.9MB, alloc=32.3MB, time=1.43 memory used=65.7MB, alloc=56.3MB, time=1.95 memory used=107.2MB, alloc=60.3MB, time=3.01 memory used=147.1MB, alloc=60.3MB, time=4.00 memory used=186.7MB, alloc=92.3MB, time=5.10 memory used=245.5MB, alloc=92.3MB, time=6.62 memory used=309.7MB, alloc=116.3MB, time=8.19 memory used=385.1MB, alloc=372.3MB, time=10.29 memory used=474.1MB, alloc=396.3MB, time=12.47 memory used=587.7MB, alloc=420.3MB, time=15.27 memory used=717.6MB, alloc=444.3MB, time=18.67 memory used=833.6MB, alloc=444.3MB, time=21.58 memory used=938.7MB, alloc=468.3MB, time=24.33 memory used=1043.5MB, alloc=468.3MB, time=27.02 memory used=1146.6MB, alloc=468.3MB, time=30.06 memory used=1225.6MB, alloc=468.3MB, time=32.36 memory used=1322.1MB, alloc=492.3MB, time=35.37 memory used=1398.3MB, alloc=492.3MB, time=37.77 memory used=1474.3MB, alloc=492.3MB, time=40.21 memory used=1550.5MB, alloc=492.3MB, time=42.58 memory used=1623.5MB, alloc=492.3MB, time=44.96 memory used=1683.7MB, alloc=492.3MB, time=46.89 memory used=1734.4MB, alloc=492.3MB, time=48.75 memory used=1792.1MB, alloc=492.3MB, time=50.88 memory used=1837.7MB, alloc=492.3MB, time=52.78 memory used=1880.1MB, alloc=492.3MB, time=54.56 memory used=2069.5MB, alloc=516.3MB, time=59.99 memory used=2278.1MB, alloc=540.3MB, time=66.14 memory used=2478.0MB, alloc=564.3MB, time=71.69 memory used=2655.5MB, alloc=588.3MB, time=76.69 memory used=2830.8MB, alloc=612.3MB, time=81.81 memory used=2991.2MB, alloc=636.3MB, time=86.98 memory used=3138.1MB, alloc=636.3MB, time=90.89 memory used=3273.0MB, alloc=636.3MB, time=95.69 memory used=3391.9MB, alloc=660.3MB, time=99.44 memory used=3507.4MB, alloc=660.3MB, time=103.59 memory used=3619.1MB, alloc=660.3MB, time=107.49 memory used=3737.5MB, alloc=660.3MB, time=111.50 memory used=3850.4MB, alloc=660.3MB, time=115.48 memory used=3946.5MB, alloc=684.3MB, time=118.92 memory used=4277.9MB, alloc=708.3MB, time=129.09 |\^/| 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(); 1428271691 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 3 2 3 2 F := [-9 x z - 2 x y - 3 z , 7 x z - 10 y + 3 y z , 8 x - x y z - 10 x z ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 2 2 G := [11 x y - 7 x - 17 y z, 5 x y - 3 x y + 5 x , 5 x z - 2 x y - y z] > Problem := [F,G]; Problem := [ 2 2 2 2 3 2 3 2 [-9 x z - 2 x y - 3 z , 7 x z - 10 y + 3 y z , 8 x - x y z - 10 x z ], 2 2 2 2 2 2 [11 x y - 7 x - 17 y z, 5 x y - 3 x y + 5 x , 5 x z - 2 x y - y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.31 memory used=26.4MB, alloc=32.3MB, time=0.88 memory used=46.3MB, alloc=56.3MB, time=1.42 memory used=87.7MB, alloc=60.3MB, time=2.48 memory used=130.6MB, alloc=68.3MB, time=3.54 memory used=171.4MB, alloc=92.3MB, time=4.56 memory used=236.9MB, alloc=92.3MB, time=6.19 memory used=299.3MB, alloc=116.3MB, time=7.78 memory used=369.2MB, alloc=116.3MB, time=9.61 memory used=438.1MB, alloc=396.3MB, time=11.23 memory used=550.4MB, alloc=396.3MB, time=14.05 memory used=666.3MB, alloc=420.3MB, time=16.67 memory used=800.3MB, alloc=444.3MB, time=20.16 memory used=917.4MB, alloc=444.3MB, time=23.09 memory used=1033.8MB, alloc=468.3MB, time=25.89 memory used=1139.7MB, alloc=468.3MB, time=28.69 memory used=1252.7MB, alloc=468.3MB, time=31.69 memory used=1341.0MB, alloc=468.3MB, time=33.96 memory used=1435.8MB, alloc=468.3MB, time=36.66 memory used=1529.1MB, alloc=492.3MB, time=39.47 memory used=1621.0MB, alloc=492.3MB, time=42.12 memory used=1710.9MB, alloc=492.3MB, time=44.79 memory used=1793.9MB, alloc=492.3MB, time=47.57 memory used=1856.2MB, alloc=492.3MB, time=49.77 memory used=1930.9MB, alloc=492.3MB, time=52.14 memory used=1991.5MB, alloc=492.3MB, time=54.24 memory used=2050.8MB, alloc=492.3MB, time=56.42 memory used=2104.5MB, alloc=492.3MB, time=58.06 memory used=2155.5MB, alloc=492.3MB, time=60.05 memory used=2203.3MB, alloc=492.3MB, time=61.79 memory used=2251.9MB, alloc=492.3MB, time=63.76 memory used=2431.2MB, alloc=516.3MB, time=69.43 memory used=2641.6MB, alloc=540.3MB, time=75.15 memory used=2838.8MB, alloc=564.3MB, time=80.48 memory used=3007.3MB, alloc=588.3MB, time=85.72 memory used=3150.3MB, alloc=612.3MB, time=90.50 memory used=3300.6MB, alloc=636.3MB, time=95.58 memory used=3465.7MB, alloc=636.3MB, time=100.94 memory used=3612.2MB, alloc=636.3MB, time=106.01 memory used=3739.9MB, alloc=660.3MB, time=110.36 memory used=3854.1MB, alloc=660.3MB, time=114.94 memory used=3973.6MB, alloc=660.3MB, time=119.38 |\^/| 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(); 1428271991 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 2 F := [18 x y + 11 y - 14 y, -3 x z - 9 x y - 6, x z + 3 z + 7 x] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 3 2 3 G := [14 x + 14 x z + 8 y , -8 x z - 3 z - 3 z , -2 x - 10 y] > Problem := [F,G]; 2 2 2 2 2 Problem := [[18 x y + 11 y - 14 y, -3 x z - 9 x y - 6, x z + 3 z + 7 x], 2 2 2 3 2 3 [14 x + 14 x z + 8 y , -8 x z - 3 z - 3 z , -2 x - 10 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.30 memory used=26.3MB, alloc=32.3MB, time=0.86 memory used=47.5MB, alloc=32.3MB, time=1.41 memory used=67.0MB, alloc=56.3MB, time=1.93 memory used=107.3MB, alloc=60.3MB, time=3.00 memory used=145.9MB, alloc=84.3MB, time=4.03 memory used=204.5MB, alloc=92.3MB, time=5.62 memory used=260.4MB, alloc=116.3MB, time=7.15 memory used=341.4MB, alloc=116.3MB, time=9.32 memory used=420.6MB, alloc=140.3MB, time=11.49 memory used=504.9MB, alloc=140.3MB, time=13.81 memory used=588.6MB, alloc=420.3MB, time=16.28 memory used=712.1MB, alloc=420.3MB, time=19.78 memory used=829.5MB, alloc=444.3MB, time=23.06 memory used=972.0MB, alloc=468.3MB, time=27.66 memory used=1125.1MB, alloc=492.3MB, time=32.61 memory used=1285.2MB, alloc=516.3MB, time=37.80 memory used=1454.6MB, alloc=540.3MB, time=43.36 memory used=1631.2MB, alloc=564.3MB, time=49.20 memory used=1817.6MB, alloc=588.3MB, time=55.37 memory used=2017.0MB, alloc=612.3MB, time=61.87 memory used=2214.9MB, alloc=636.3MB, time=68.71 memory used=2424.2MB, alloc=660.3MB, time=75.87 memory used=2618.4MB, alloc=684.3MB, time=82.61 memory used=2815.5MB, alloc=708.3MB, time=92.55 memory used=3012.1MB, alloc=732.3MB, time=103.53 memory used=3218.5MB, alloc=756.3MB, time=115.57 memory used=3437.3MB, alloc=780.3MB, time=128.82 |\^/| 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(); 1428272291 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 3 3 2 2 2 3 F := [-5 x y + 6 y z - 18 y z, 5 x + 2 y + y z, -x z - 8 x y + 3 z ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 2 2 G := [z + 5 z + 2, -7 x y z - 4 x + 8 x y, x y + 8 y z] > Problem := [F,G]; Problem := [ 2 2 3 3 2 2 2 3 [-5 x y + 6 y z - 18 y z, 5 x + 2 y + y z, -x z - 8 x y + 3 z ], 3 2 2 2 2 [z + 5 z + 2, -7 x y z - 4 x + 8 x y, x y + 8 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.31 memory used=26.5MB, alloc=32.3MB, time=0.86 memory used=46.7MB, alloc=32.3MB, time=1.41 memory used=65.3MB, alloc=56.3MB, time=1.94 memory used=105.7MB, alloc=60.3MB, time=3.02 memory used=145.2MB, alloc=84.3MB, time=4.04 memory used=206.5MB, alloc=92.3MB, time=5.66 memory used=268.9MB, alloc=92.3MB, time=7.26 memory used=332.3MB, alloc=116.3MB, time=8.86 memory used=398.5MB, alloc=372.3MB, time=10.42 memory used=487.7MB, alloc=372.3MB, time=12.63 memory used=576.4MB, alloc=396.3MB, time=14.84 memory used=688.9MB, alloc=420.3MB, time=17.71 memory used=831.1MB, alloc=444.3MB, time=21.10 memory used=972.8MB, alloc=444.3MB, time=24.45 memory used=1088.1MB, alloc=468.3MB, time=26.73 memory used=1191.9MB, alloc=468.3MB, time=28.98 memory used=1289.0MB, alloc=468.3MB, time=31.56 memory used=1405.5MB, alloc=492.3MB, time=33.59 memory used=1509.6MB, alloc=492.3MB, time=36.12 memory used=1586.7MB, alloc=492.3MB, time=38.18 memory used=1673.1MB, alloc=492.3MB, time=40.62 memory used=1751.8MB, alloc=516.3MB, time=42.78 memory used=1823.5MB, alloc=516.3MB, time=45.03 memory used=1892.3MB, alloc=516.3MB, time=47.00 memory used=1965.3MB, alloc=516.3MB, time=48.50 memory used=2024.7MB, alloc=516.3MB, time=49.93 memory used=2103.1MB, alloc=516.3MB, time=52.38 memory used=2161.1MB, alloc=516.3MB, time=54.20 memory used=2217.9MB, alloc=516.3MB, time=56.22 memory used=2272.1MB, alloc=516.3MB, time=58.17 memory used=2477.4MB, alloc=540.3MB, time=64.36 memory used=2677.6MB, alloc=564.3MB, time=69.98 memory used=2872.1MB, alloc=588.3MB, time=75.93 memory used=3060.1MB, alloc=612.3MB, time=81.97 memory used=3226.6MB, alloc=636.3MB, time=87.18 memory used=3378.6MB, alloc=660.3MB, time=91.53 memory used=3527.1MB, alloc=660.3MB, time=96.80 memory used=3722.6MB, alloc=684.3MB, time=102.51 memory used=3980.9MB, alloc=684.3MB, time=108.90 memory used=4150.7MB, alloc=684.3MB, time=116.14 memory used=4312.0MB, alloc=684.3MB, time=119.75 memory used=4451.6MB, alloc=708.3MB, time=123.22 memory used=4656.6MB, alloc=708.3MB, time=129.50 memory used=4777.4MB, alloc=708.3MB, time=132.92 memory used=4881.7MB, alloc=708.3MB, time=135.96 memory used=4986.9MB, alloc=708.3MB, time=140.24 memory used=5137.9MB, alloc=732.3MB, time=143.89 |\^/| 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(); 1428272591 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 3 2 2 2 F := [-13 x - 5 x + 9 y, 2 x + 10 x y - x z , -x z - 7 y z + 6 y] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 G := [-2 x z - 9 z - 7 y, 2 x y + 5 x z - 7 x, 8 x z + 3 y - 9 z] > Problem := [F,G]; 3 2 3 2 2 2 Problem := [[-13 x - 5 x + 9 y, 2 x + 10 x y - x z , -x z - 7 y z + 6 y], 2 2 2 2 [-2 x z - 9 z - 7 y, 2 x y + 5 x z - 7 x, 8 x z + 3 y - 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=0.30 memory used=26.8MB, alloc=32.3MB, time=0.89 memory used=48.1MB, alloc=32.3MB, time=1.45 memory used=67.6MB, alloc=56.3MB, time=1.98 memory used=108.2MB, alloc=60.3MB, time=3.05 memory used=145.6MB, alloc=84.3MB, time=4.07 memory used=211.5MB, alloc=92.3MB, time=5.74 memory used=273.4MB, alloc=92.3MB, time=7.29 memory used=337.4MB, alloc=116.3MB, time=8.92 memory used=411.4MB, alloc=372.3MB, time=10.91 memory used=494.8MB, alloc=396.3MB, time=13.19 memory used=598.1MB, alloc=396.3MB, time=16.13 memory used=708.1MB, alloc=420.3MB, time=19.09 memory used=840.5MB, alloc=444.3MB, time=22.58 memory used=998.3MB, alloc=468.3MB, time=26.91 memory used=1142.7MB, alloc=468.3MB, time=31.03 memory used=1285.1MB, alloc=492.3MB, time=34.86 memory used=1420.3MB, alloc=492.3MB, time=38.73 memory used=1541.0MB, alloc=492.3MB, time=42.39 memory used=1646.1MB, alloc=516.3MB, time=45.66 memory used=1746.8MB, alloc=516.3MB, time=48.52 memory used=1869.9MB, alloc=516.3MB, time=52.58 memory used=1962.3MB, alloc=540.3MB, time=55.25 memory used=2063.4MB, alloc=540.3MB, time=58.44 memory used=2131.1MB, alloc=540.3MB, time=60.59 memory used=2202.7MB, alloc=540.3MB, time=62.53 memory used=2285.0MB, alloc=540.3MB, time=65.71 memory used=2355.2MB, alloc=540.3MB, time=68.23 memory used=2419.3MB, alloc=540.3MB, time=70.71 memory used=2463.0MB, alloc=540.3MB, time=72.10 memory used=2521.4MB, alloc=564.3MB, time=74.08 memory used=2769.7MB, alloc=588.3MB, time=81.81 memory used=2993.1MB, alloc=612.3MB, time=88.63 memory used=3186.7MB, alloc=636.3MB, time=94.69 memory used=3356.9MB, alloc=660.3MB, time=100.54 memory used=3552.1MB, alloc=684.3MB, time=107.98 memory used=3746.6MB, alloc=684.3MB, time=115.99 memory used=3903.9MB, alloc=684.3MB, time=121.66 memory used=4040.7MB, alloc=708.3MB, time=125.89 memory used=4200.5MB, alloc=708.3MB, time=131.89 memory used=4313.5MB, alloc=708.3MB, time=135.53 |\^/| 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(); 1428272891 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 2 3 F := [6 x y + 19 y z, -3 x z - 4 y z + 9 z, -9 x y - 5 z - x z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 2 2 2 G := [12 x - 12 x y + 16 x y z, -5 x z + 8 x z - 8 z, 5 x z + 6 y z ] > Problem := [F,G]; 2 2 2 2 2 3 Problem := [[6 x y + 19 y z, -3 x z - 4 y z + 9 z, -9 x y - 5 z - x z], 3 2 2 2 2 2 [12 x - 12 x y + 16 x y z, -5 x z + 8 x z - 8 z, 5 x z + 6 y z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.30 memory used=26.4MB, alloc=32.3MB, time=0.85 memory used=47.8MB, alloc=32.3MB, time=1.41 memory used=67.4MB, alloc=56.3MB, time=1.95 memory used=107.6MB, alloc=60.3MB, time=3.00 memory used=145.6MB, alloc=84.3MB, time=4.02 memory used=203.9MB, alloc=92.3MB, time=5.57 memory used=261.8MB, alloc=116.3MB, time=7.19 memory used=342.9MB, alloc=116.3MB, time=9.44 memory used=424.6MB, alloc=140.3MB, time=11.73 memory used=506.7MB, alloc=140.3MB, time=14.05 memory used=572.9MB, alloc=420.3MB, time=15.67 memory used=705.8MB, alloc=444.3MB, time=19.20 memory used=860.2MB, alloc=468.3MB, time=23.45 memory used=990.2MB, alloc=492.3MB, time=27.00 memory used=1119.5MB, alloc=492.3MB, time=30.96 memory used=1243.7MB, alloc=516.3MB, time=34.76 memory used=1353.0MB, alloc=516.3MB, time=38.16 memory used=1449.9MB, alloc=516.3MB, time=41.20 memory used=1534.8MB, alloc=516.3MB, time=43.76 memory used=1622.5MB, alloc=516.3MB, time=46.60 memory used=1699.4MB, alloc=516.3MB, time=49.16 memory used=1780.1MB, alloc=516.3MB, time=51.82 memory used=1858.9MB, alloc=540.3MB, time=54.61 memory used=1919.6MB, alloc=540.3MB, time=56.74 memory used=1958.9MB, alloc=540.3MB, time=58.33 memory used=2021.8MB, alloc=540.3MB, time=60.56 memory used=2073.6MB, alloc=540.3MB, time=62.50 memory used=2290.9MB, alloc=564.3MB, time=69.78 memory used=2475.8MB, alloc=588.3MB, time=75.76 memory used=2647.7MB, alloc=612.3MB, time=81.02 memory used=2839.7MB, alloc=636.3MB, time=86.94 memory used=3038.3MB, alloc=660.3MB, time=93.92 memory used=3220.9MB, alloc=684.3MB, time=100.81 memory used=3368.7MB, alloc=684.3MB, time=105.60 memory used=3508.1MB, alloc=708.3MB, time=110.40 memory used=3632.8MB, alloc=708.3MB, time=115.44 memory used=3745.8MB, alloc=708.3MB, time=119.89 memory used=3879.2MB, alloc=708.3MB, time=124.64 memory used=3985.9MB, alloc=732.3MB, time=129.51 |\^/| 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(); 1428273191 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 2 F := [-4 - 14 y + 8 z, 9 x - 2 x + 3 x, 3 x y + 9 x y z - 10 z ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 2 G := [-3 y z + 4 y z - 3 x, 4 x z + 8 x + 6 z , 8 x y + 7 z - 7 x] > Problem := [F,G]; 3 2 2 2 Problem := [[-4 - 14 y + 8 z, 9 x - 2 x + 3 x, 3 x y + 9 x y z - 10 z ], 2 2 2 2 2 [-3 y z + 4 y z - 3 x, 4 x z + 8 x + 6 z , 8 x y + 7 z - 7 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.6MB, alloc=32.3MB, time=0.89 memory used=46.9MB, alloc=32.3MB, time=1.40 memory used=66.4MB, alloc=56.3MB, time=1.92 memory used=105.3MB, alloc=60.3MB, time=2.95 memory used=144.9MB, alloc=84.3MB, time=4.00 memory used=206.7MB, alloc=92.3MB, time=5.67 memory used=271.7MB, alloc=92.3MB, time=7.21 memory used=336.1MB, alloc=116.3MB, time=8.85 memory used=418.2MB, alloc=116.3MB, time=11.13 memory used=496.2MB, alloc=140.3MB, time=13.20 memory used=593.0MB, alloc=396.3MB, time=15.38 memory used=705.0MB, alloc=396.3MB, time=18.09 memory used=808.4MB, alloc=420.3MB, time=20.89 memory used=932.7MB, alloc=444.3MB, time=24.44 memory used=1080.8MB, alloc=468.3MB, time=28.78 memory used=1238.5MB, alloc=492.3MB, time=33.19 memory used=1373.2MB, alloc=492.3MB, time=37.17 memory used=1495.7MB, alloc=492.3MB, time=40.48 memory used=1665.2MB, alloc=516.3MB, time=46.17 memory used=1783.2MB, alloc=516.3MB, time=49.74 memory used=1876.2MB, alloc=516.3MB, time=52.70 memory used=1999.2MB, alloc=540.3MB, time=56.59 memory used=2111.1MB, alloc=540.3MB, time=59.94 memory used=2204.2MB, alloc=540.3MB, time=62.55 memory used=2300.5MB, alloc=540.3MB, time=65.59 memory used=2422.1MB, alloc=540.3MB, time=70.19 memory used=2535.0MB, alloc=540.3MB, time=73.90 memory used=2630.9MB, alloc=540.3MB, time=77.08 memory used=2705.4MB, alloc=540.3MB, time=79.63 memory used=2811.1MB, alloc=564.3MB, time=82.78 memory used=2896.9MB, alloc=564.3MB, time=86.16 memory used=2992.1MB, alloc=564.3MB, time=89.73 memory used=3086.4MB, alloc=564.3MB, time=93.61 memory used=3171.2MB, alloc=564.3MB, time=97.10 memory used=3276.5MB, alloc=564.3MB, time=101.77 memory used=3375.6MB, alloc=564.3MB, time=106.26 memory used=3469.5MB, alloc=588.3MB, time=110.70 memory used=3542.6MB, alloc=588.3MB, time=113.52 memory used=3615.2MB, alloc=588.3MB, time=116.70 memory used=3872.6MB, alloc=612.3MB, time=126.67 |\^/| 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(); 1428273491 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 3 2 F := [5 y - 20 y + 10, 2 x z + 7 y z, 6 z - 8 y + y z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 2 G := [20 x y - 9 y + 12 y z, 5 x y + 6 z + 5, -5 y z - 7 z ] > Problem := [F,G]; 3 2 3 2 Problem := [[5 y - 20 y + 10, 2 x z + 7 y z, 6 z - 8 y + y z], 2 3 2 2 [20 x y - 9 y + 12 y z, 5 x y + 6 z + 5, -5 y 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=0.31 memory used=26.6MB, alloc=32.3MB, time=0.88 memory used=47.9MB, alloc=32.3MB, time=1.42 memory used=67.1MB, alloc=56.3MB, time=1.94 memory used=107.0MB, alloc=60.3MB, time=2.99 memory used=144.4MB, alloc=60.3MB, time=3.95 memory used=180.2MB, alloc=84.3MB, time=4.90 memory used=224.0MB, alloc=84.3MB, time=6.08 memory used=282.3MB, alloc=116.3MB, time=7.71 memory used=363.7MB, alloc=116.3MB, time=9.93 memory used=442.7MB, alloc=140.3MB, time=12.16 memory used=537.7MB, alloc=396.3MB, time=15.04 memory used=640.2MB, alloc=420.3MB, time=18.15 memory used=766.1MB, alloc=444.3MB, time=21.88 memory used=915.2MB, alloc=444.3MB, time=26.04 memory used=1061.6MB, alloc=468.3MB, time=30.34 memory used=1220.8MB, alloc=492.3MB, time=34.97 memory used=1366.0MB, alloc=516.3MB, time=39.30 memory used=1497.5MB, alloc=516.3MB, time=42.46 memory used=1634.3MB, alloc=540.3MB, time=46.54 memory used=1771.0MB, alloc=564.3MB, time=51.02 memory used=1921.9MB, alloc=588.3MB, time=55.95 memory used=2075.2MB, alloc=612.3MB, time=61.12 memory used=2228.5MB, alloc=636.3MB, time=66.37 memory used=2374.1MB, alloc=660.3MB, time=71.38 memory used=2513.3MB, alloc=684.3MB, time=76.32 memory used=2640.7MB, alloc=708.3MB, time=80.79 memory used=2768.1MB, alloc=732.3MB, time=85.27 memory used=2881.1MB, alloc=756.3MB, time=89.54 memory used=2990.5MB, alloc=780.3MB, time=93.70 memory used=3104.8MB, alloc=804.3MB, time=98.05 memory used=3211.4MB, alloc=828.3MB, time=102.14 memory used=3318.2MB, alloc=852.3MB, time=106.27 memory used=3429.6MB, alloc=852.3MB, time=110.16 |\^/| 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(); 1428273791 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 3 2 2 F := [-15 x + 12 x - 6 x z, -6 y + 7 x z + 2 y , 3 x y - 7 x] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 3 3 2 3 3 G := [9 x z + 18 y - 6 y, 5 x - 10 y - 2 z , -4 x - 4 z + 2 x] > Problem := [F,G]; 3 2 3 2 2 Problem := [[-15 x + 12 x - 6 x z, -6 y + 7 x z + 2 y , 3 x y - 7 x], 2 3 3 3 2 3 3 [9 x z + 18 y - 6 y, 5 x - 10 y - 2 z , -4 x - 4 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=0.31 memory used=24.8MB, alloc=32.3MB, time=0.84 memory used=44.0MB, alloc=56.3MB, time=1.36 memory used=85.7MB, alloc=60.3MB, time=2.39 memory used=127.9MB, alloc=68.3MB, time=3.47 memory used=204.8MB, alloc=100.3MB, time=5.21 memory used=280.3MB, alloc=100.3MB, time=6.93 memory used=347.8MB, alloc=380.3MB, time=8.54 memory used=448.3MB, alloc=380.3MB, time=10.88 memory used=546.8MB, alloc=404.3MB, time=13.22 memory used=665.4MB, alloc=428.3MB, time=16.17 memory used=812.8MB, alloc=428.3MB, time=19.21 memory used=950.9MB, alloc=452.3MB, time=22.69 memory used=1074.6MB, alloc=452.3MB, time=25.74 memory used=1187.8MB, alloc=476.3MB, time=28.62 memory used=1302.4MB, alloc=476.3MB, time=31.64 memory used=1396.9MB, alloc=476.3MB, time=33.93 memory used=1532.5MB, alloc=476.3MB, time=36.75 memory used=1620.3MB, alloc=476.3MB, time=37.38 memory used=1747.9MB, alloc=476.3MB, time=39.13 memory used=1891.7MB, alloc=476.3MB, time=41.55 memory used=1972.4MB, alloc=476.3MB, time=43.65 memory used=2065.8MB, alloc=476.3MB, time=45.97 memory used=2147.5MB, alloc=476.3MB, time=48.32 memory used=2224.2MB, alloc=500.3MB, time=50.46 memory used=2304.7MB, alloc=500.3MB, time=52.83 memory used=2377.8MB, alloc=500.3MB, time=54.59 memory used=2451.7MB, alloc=500.3MB, time=56.84 memory used=2520.7MB, alloc=500.3MB, time=59.09 memory used=2572.8MB, alloc=500.3MB, time=60.66 memory used=2630.6MB, alloc=500.3MB, time=62.30 memory used=2688.5MB, alloc=500.3MB, time=64.41 memory used=2741.5MB, alloc=500.3MB, time=65.99 memory used=2807.7MB, alloc=500.3MB, time=68.23 memory used=2854.1MB, alloc=500.3MB, time=69.91 memory used=3042.4MB, alloc=524.3MB, time=74.63 memory used=3226.9MB, alloc=548.3MB, time=79.68 memory used=3426.0MB, alloc=572.3MB, time=84.87 memory used=3607.8MB, alloc=596.3MB, time=89.70 memory used=3879.9MB, alloc=596.3MB, time=97.78 memory used=4085.4MB, alloc=620.3MB, time=105.49 memory used=4269.1MB, alloc=620.3MB, time=110.79 memory used=4482.7MB, alloc=620.3MB, time=118.43 memory used=4673.8MB, alloc=620.3MB, time=124.69 memory used=4865.5MB, alloc=644.3MB, time=130.99 memory used=5003.6MB, alloc=644.3MB, time=135.28 memory used=5165.2MB, alloc=644.3MB, time=140.63 memory used=5275.1MB, alloc=644.3MB, time=143.79 memory used=5436.2MB, alloc=668.3MB, time=147.85 memory used=5546.2MB, alloc=668.3MB, time=151.09 memory used=5646.5MB, alloc=668.3MB, time=154.12 |\^/| 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(); 1428274091 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 F := [z - 5 x z - 20 y z, -4 z - 2 x + 8, 3 z + 8 x + 2 z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 3 3 2 G := [-2 x - 14 x + 11, -6 x z + 5 z - 8 z, 7 y - 9 x ] > Problem := [F,G]; 3 2 2 Problem := [[z - 5 x z - 20 y z, -4 z - 2 x + 8, 3 z + 8 x + 2 z], 3 2 2 3 3 2 [-2 x - 14 x + 11, -6 x z + 5 z - 8 z, 7 y - 9 x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.30 memory used=26.4MB, alloc=32.3MB, time=0.87 memory used=47.9MB, alloc=32.3MB, time=1.41 memory used=67.9MB, alloc=32.3MB, time=1.93 memory used=87.5MB, alloc=56.3MB, time=2.47 memory used=127.9MB, alloc=60.3MB, time=3.57 memory used=169.6MB, alloc=84.3MB, time=4.84 memory used=234.6MB, alloc=84.3MB, time=6.74 memory used=291.0MB, alloc=108.3MB, time=8.46 memory used=365.1MB, alloc=132.3MB, time=10.75 memory used=463.1MB, alloc=156.3MB, time=13.58 memory used=571.3MB, alloc=188.3MB, time=16.91 memory used=678.4MB, alloc=212.3MB, time=21.24 memory used=791.5MB, alloc=236.3MB, time=26.51 memory used=913.6MB, alloc=260.3MB, time=33.28 memory used=1052.1MB, alloc=284.3MB, time=41.61 memory used=1214.6MB, alloc=308.3MB, time=51.27 memory used=1401.0MB, alloc=308.3MB, time=62.30 memory used=1587.4MB, alloc=308.3MB, time=73.33 memory used=1773.8MB, alloc=332.3MB, time=84.34 memory used=1984.1MB, alloc=332.3MB, time=96.73 memory used=2194.4MB, alloc=332.3MB, time=109.11 memory used=2404.7MB, alloc=356.3MB, time=121.49 |\^/| 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(); 1428274391 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 2 3 F := [-2 y - y - 2, 8 x y z - 9 y z + 3 z, x y + 8 y + 4] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 2 2 2 G := [-3 x y z - 2 y + 14 x , -10 x y + 6 y z + x, 2 x z + 10 y - 1] > Problem := [F,G]; 3 2 2 2 3 Problem := [[-2 y - y - 2, 8 x y z - 9 y z + 3 z, x y + 8 y + 4], 3 2 2 2 2 2 [-3 x y z - 2 y + 14 x , -10 x y + 6 y z + x, 2 x z + 10 y - 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=0.30 memory used=25.3MB, alloc=32.3MB, time=0.85 memory used=46.2MB, alloc=32.3MB, time=1.39 memory used=66.0MB, alloc=56.3MB, time=1.91 memory used=106.3MB, alloc=60.3MB, time=2.95 memory used=145.9MB, alloc=60.3MB, time=3.95 memory used=184.1MB, alloc=60.3MB, time=4.94 memory used=221.5MB, alloc=84.3MB, time=5.92 memory used=282.5MB, alloc=92.3MB, time=7.52 memory used=343.0MB, alloc=92.3MB, time=9.07 memory used=403.6MB, alloc=116.3MB, time=10.69 memory used=487.8MB, alloc=116.3MB, time=12.89 memory used=554.9MB, alloc=116.3MB, time=14.38 memory used=621.2MB, alloc=372.3MB, time=16.07 memory used=706.1MB, alloc=396.3MB, time=18.13 memory used=815.2MB, alloc=396.3MB, time=20.49 memory used=927.2MB, alloc=396.3MB, time=23.11 memory used=1021.8MB, alloc=420.3MB, time=24.93 memory used=1149.1MB, alloc=420.3MB, time=26.57 memory used=1290.7MB, alloc=420.3MB, time=29.64 memory used=1434.4MB, alloc=444.3MB, time=32.56 memory used=1601.5MB, alloc=444.3MB, time=36.18 memory used=1747.5MB, alloc=468.3MB, time=40.11 memory used=1896.5MB, alloc=492.3MB, time=44.66 memory used=2056.5MB, alloc=516.3MB, time=49.68 memory used=2232.4MB, alloc=540.3MB, time=55.30 memory used=2425.9MB, alloc=564.3MB, time=61.35 memory used=2616.6MB, alloc=588.3MB, time=66.99 memory used=2810.3MB, alloc=612.3MB, time=72.89 memory used=2997.5MB, alloc=636.3MB, time=78.89 memory used=3176.7MB, alloc=660.3MB, time=84.86 memory used=3361.1MB, alloc=684.3MB, time=91.92 memory used=3595.6MB, alloc=708.3MB, time=104.59 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428274691 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 3 3 3 F := [11 z - 8 y + 4, 6 x - 4 y - 3 y, 4 z + 6 x y - 10 x] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 3 2 2 2 3 G := [y z - 13 y + 8, -7 x z + 4 y - 2 y z , 4 x z + 9 x y + 10 y ] > Problem := [F,G]; 3 3 3 3 Problem := [[11 z - 8 y + 4, 6 x - 4 y - 3 y, 4 z + 6 x y - 10 x], 2 2 2 3 2 2 2 3 [y z - 13 y + 8, -7 x z + 4 y - 2 y z , 4 x z + 9 x y + 10 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.31 memory used=24.9MB, alloc=32.3MB, time=0.81 memory used=47.5MB, alloc=32.3MB, time=1.22 memory used=68.5MB, alloc=32.3MB, time=1.54 memory used=89.3MB, alloc=60.3MB, time=2.02 memory used=130.1MB, alloc=60.3MB, time=2.79 memory used=166.2MB, alloc=60.3MB, time=3.15 memory used=202.8MB, alloc=60.3MB, time=3.49 memory used=253.7MB, alloc=64.5MB, time=4.88 memory used=279.9MB, alloc=64.5MB, time=4.99 memory used=307.8MB, alloc=64.5MB, time=5.22 memory used=356.5MB, alloc=64.5MB, time=6.54 memory used=385.5MB, alloc=64.5MB, time=6.69 memory used=410.6MB, alloc=64.5MB, time=6.88 memory used=448.1MB, alloc=64.5MB, time=7.41 memory used=491.8MB, alloc=64.5MB, time=10.50 memory used=536.4MB, alloc=64.5MB, time=13.38 memory used=560.1MB, alloc=64.5MB, time=13.50 memory used=586.8MB, alloc=64.5MB, time=13.62 memory used=606.5MB, alloc=64.5MB, time=13.72 memory used=628.9MB, alloc=64.5MB, time=13.83 memory used=655.6MB, alloc=64.5MB, time=13.94 memory used=698.7MB, alloc=64.5MB, time=14.57 memory used=732.8MB, alloc=64.5MB, time=15.31 memory used=773.7MB, alloc=64.5MB, time=16.30 memory used=801.5MB, alloc=64.5MB, time=16.57 memory used=839.9MB, alloc=64.5MB, time=17.42 memory used=870.7MB, alloc=64.5MB, time=17.85 memory used=922.1MB, alloc=72.5MB, time=22.60 memory used=950.8MB, alloc=72.5MB, time=22.95 memory used=969.7MB, alloc=72.5MB, time=23.07 memory used=1000.0MB, alloc=72.5MB, time=23.41 memory used=1044.4MB, alloc=72.5MB, time=24.27 memory used=1080.6MB, alloc=96.5MB, time=24.80 memory used=1143.4MB, alloc=96.5MB, time=25.99 memory used=1210.5MB, alloc=96.5MB, time=27.27 memory used=1273.8MB, alloc=96.5MB, time=28.47 memory used=1324.0MB, alloc=96.5MB, time=29.62 memory used=1361.1MB, alloc=96.5MB, time=30.11 memory used=1400.1MB, alloc=96.5MB, time=30.63 memory used=1438.9MB, alloc=96.5MB, time=31.06 memory used=1487.1MB, alloc=96.5MB, time=31.63 memory used=1525.6MB, alloc=96.5MB, time=32.04 memory used=1559.4MB, alloc=96.5MB, time=32.25 memory used=1600.6MB, alloc=96.5MB, time=33.49 memory used=1675.2MB, alloc=96.5MB, time=38.02 memory used=1707.9MB, alloc=96.5MB, time=38.20 memory used=1744.7MB, alloc=96.5MB, time=38.39 memory used=1769.2MB, alloc=96.5MB, time=38.57 memory used=1797.6MB, alloc=96.5MB, time=38.73 memory used=1830.2MB, alloc=96.5MB, time=38.90 memory used=1867.4MB, alloc=96.5MB, time=39.07 memory used=1902.4MB, alloc=96.5MB, time=39.22 memory used=1925.0MB, alloc=96.5MB, time=39.35 memory used=1948.9MB, alloc=96.5MB, time=39.48 memory used=1974.9MB, alloc=96.5MB, time=39.61 memory used=2003.0MB, alloc=96.5MB, time=39.75 memory used=2034.6MB, alloc=96.5MB, time=39.89 memory used=2107.0MB, alloc=96.5MB, time=40.80 memory used=2181.4MB, alloc=96.5MB, time=41.73 memory used=2255.9MB, alloc=96.5MB, time=43.73 memory used=2312.7MB, alloc=96.5MB, time=46.53 memory used=2353.9MB, alloc=96.5MB, time=47.75 memory used=2388.3MB, alloc=96.5MB, time=47.94 memory used=2415.5MB, alloc=96.5MB, time=48.11 memory used=2440.7MB, alloc=96.5MB, time=48.27 memory used=2469.3MB, alloc=96.5MB, time=48.44 memory used=2502.3MB, alloc=96.5MB, time=48.61 memory used=2539.7MB, alloc=96.5MB, time=48.79 memory used=2567.1MB, alloc=96.5MB, time=48.95 memory used=2589.2MB, alloc=96.5MB, time=49.08 memory used=2612.4MB, alloc=120.5MB, time=49.24 memory used=2652.5MB, alloc=120.5MB, time=49.40 memory used=2700.2MB, alloc=120.5MB, time=49.58 memory used=2789.4MB, alloc=120.5MB, time=50.98 memory used=2845.8MB, alloc=376.5MB, time=52.30 memory used=2929.7MB, alloc=376.5MB, time=53.63 memory used=2992.0MB, alloc=376.5MB, time=54.86 memory used=3070.1MB, alloc=376.5MB, time=57.68 memory used=3114.3MB, alloc=376.5MB, time=57.94 memory used=3160.4MB, alloc=376.5MB, time=58.17 memory used=3197.7MB, alloc=376.5MB, time=58.39 memory used=3287.4MB, alloc=376.5MB, time=59.56 memory used=3329.2MB, alloc=376.5MB, time=59.81 memory used=3389.5MB, alloc=376.5MB, time=62.86 memory used=3428.3MB, alloc=376.5MB, time=63.10 memory used=3471.4MB, alloc=376.5MB, time=63.32 memory used=3503.7MB, alloc=376.5MB, time=63.51 memory used=3542.6MB, alloc=376.5MB, time=63.71 memory used=3611.2MB, alloc=376.5MB, time=79.38 memory used=3665.7MB, alloc=376.5MB, time=82.58 memory used=3704.8MB, alloc=376.5MB, time=82.83 memory used=3745.3MB, alloc=376.5MB, time=83.07 memory used=3796.1MB, alloc=376.5MB, time=83.31 memory used=3825.9MB, alloc=376.5MB, time=83.49 memory used=3857.8MB, alloc=376.5MB, time=83.70 memory used=3892.4MB, alloc=376.5MB, time=83.89 memory used=3931.0MB, alloc=376.5MB, time=84.09 memory used=3973.4MB, alloc=376.5MB, time=84.30 memory used=4020.1MB, alloc=376.5MB, time=84.57 memory used=4071.4MB, alloc=376.5MB, time=84.77 memory used=4255.8MB, alloc=376.5MB, time=86.55 memory used=4341.5MB, alloc=400.5MB, time=88.47 memory used=4443.2MB, alloc=400.5MB, time=90.02 memory used=4520.5MB, alloc=400.5MB, time=90.75 memory used=4580.2MB, alloc=400.5MB, time=91.29 memory used=4633.5MB, alloc=400.5MB, time=91.76 memory used=4701.9MB, alloc=400.5MB, time=92.44 memory used=4762.8MB, alloc=400.5MB, time=93.07 memory used=4837.1MB, alloc=400.5MB, time=101.64 memory used=4931.1MB, alloc=400.5MB, time=107.56 memory used=4985.9MB, alloc=400.5MB, time=107.87 memory used=5029.3MB, alloc=400.5MB, time=108.15 memory used=5083.7MB, alloc=400.5MB, time=108.43 memory used=5134.6MB, alloc=400.5MB, time=108.69 memory used=5189.9MB, alloc=400.5MB, time=109.18 memory used=5251.2MB, alloc=400.5MB, time=109.66 memory used=5306.0MB, alloc=400.5MB, time=110.19 memory used=5374.7MB, alloc=400.5MB, time=110.89 memory used=5434.8MB, alloc=400.5MB, time=111.52 memory used=5499.6MB, alloc=400.5MB, time=114.84 memory used=5603.2MB, alloc=400.5MB, time=126.08 memory used=5659.2MB, alloc=400.5MB, time=126.41 memory used=5700.7MB, alloc=400.5MB, time=126.69 memory used=5753.4MB, alloc=400.5MB, time=126.97 memory used=5808.1MB, alloc=400.5MB, time=127.24 memory used=5847.8MB, alloc=400.5MB, time=127.49 memory used=5926.7MB, alloc=400.5MB, time=128.28 memory used=5974.3MB, alloc=400.5MB, time=128.58 memory used=6028.1MB, alloc=400.5MB, time=128.88 memory used=6105.1MB, alloc=400.5MB, time=137.02 memory used=6196.8MB, alloc=400.5MB, time=145.48 memory used=6252.7MB, alloc=400.5MB, time=145.81 memory used=6293.7MB, alloc=400.5MB, time=146.08 memory used=6344.2MB, alloc=400.5MB, time=146.37 memory used=6403.4MB, alloc=400.5MB, time=146.67 memory used=6440.3MB, alloc=400.5MB, time=146.90 memory used=6536.7MB, alloc=400.5MB, time=149.01 memory used=6644.9MB, alloc=400.5MB, time=152.75 memory used=6690.6MB, alloc=400.5MB, time=153.06 memory used=6790.4MB, alloc=400.5MB, time=154.72 memory used=6912.1MB, alloc=424.5MB, time=156.66 memory used=7015.7MB, alloc=448.5MB, time=158.87 memory used=7126.1MB, alloc=448.5MB, time=171.35 memory used=7230.4MB, alloc=448.5MB, time=172.55 memory used=7313.5MB, alloc=448.5MB, time=173.21 |\^/| 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(); 1428274991 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 F := [7 x z + 9 x - 13 z, 2 x y + 6 z, -6 x z + 4 x - y z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 3 2 3 G := [3 x + 7 z - 8 x, 10 x z + 3 z - 3 x, 2 y z - 3 y - 9 z] > Problem := [F,G]; 2 2 Problem := [[7 x z + 9 x - 13 z, 2 x y + 6 z, -6 x z + 4 x - y z], 3 3 2 3 [3 x + 7 z - 8 x, 10 x z + 3 z - 3 x, 2 y z - 3 y - 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=0.30 memory used=26.5MB, alloc=32.3MB, time=0.85 memory used=47.3MB, alloc=32.3MB, time=1.38 memory used=66.9MB, alloc=56.3MB, time=1.91 memory used=106.4MB, alloc=60.3MB, time=2.93 memory used=144.9MB, alloc=84.3MB, time=3.96 memory used=205.7MB, alloc=92.3MB, time=5.61 memory used=263.8MB, alloc=116.3MB, time=7.23 memory used=343.2MB, alloc=116.3MB, time=9.36 memory used=419.1MB, alloc=140.3MB, time=11.48 memory used=496.7MB, alloc=140.3MB, time=13.61 memory used=584.6MB, alloc=420.3MB, time=16.21 memory used=710.7MB, alloc=420.3MB, time=19.79 memory used=837.4MB, alloc=444.3MB, time=23.49 memory used=986.0MB, alloc=468.3MB, time=28.19 memory used=1154.1MB, alloc=492.3MB, time=33.59 memory used=1313.1MB, alloc=492.3MB, time=38.76 memory used=1462.4MB, alloc=516.3MB, time=43.73 memory used=1622.6MB, alloc=540.3MB, time=49.42 memory used=1780.2MB, alloc=540.3MB, time=55.02 memory used=1923.2MB, alloc=540.3MB, time=60.03 memory used=2039.3MB, alloc=540.3MB, time=63.99 memory used=2145.6MB, alloc=564.3MB, time=67.75 memory used=2255.3MB, alloc=564.3MB, time=71.09 memory used=2347.4MB, alloc=564.3MB, time=74.59 memory used=2454.2MB, alloc=564.3MB, time=78.43 memory used=2546.9MB, alloc=564.3MB, time=81.92 memory used=2642.9MB, alloc=588.3MB, time=85.54 memory used=2746.0MB, alloc=588.3MB, time=89.51 memory used=2826.3MB, alloc=588.3MB, time=92.54 memory used=2906.8MB, alloc=588.3MB, time=95.77 memory used=2976.3MB, alloc=588.3MB, time=98.45 memory used=3053.8MB, alloc=588.3MB, time=101.58 memory used=3136.4MB, alloc=588.3MB, time=105.22 memory used=3220.4MB, alloc=588.3MB, time=108.97 memory used=3281.7MB, alloc=588.3MB, time=111.36 memory used=3354.9MB, alloc=588.3MB, time=114.71 |\^/| 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(); 1428275291 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 3 3 2 F := [14 x z + 10 y + 20 x, -5 x z - 3 y - 8 y z, 10 z + 4 x + 2 z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 G := [15 x y - 17 z - 15, 9 x y - 9 x y z - 8 y z, 9 y z ] > Problem := [F,G]; Problem := [ 2 3 2 3 3 2 [14 x z + 10 y + 20 x, -5 x z - 3 y - 8 y z, 10 z + 4 x + 2 z], 2 2 2 2 [15 x y - 17 z - 15, 9 x y - 9 x y z - 8 y z, 9 y z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.30 memory used=26.9MB, alloc=32.3MB, time=0.91 memory used=47.4MB, alloc=32.3MB, time=1.45 memory used=67.2MB, alloc=60.3MB, time=2.01 memory used=109.2MB, alloc=60.3MB, time=2.87 memory used=149.9MB, alloc=60.3MB, time=3.90 memory used=192.4MB, alloc=68.3MB, time=4.81 memory used=231.5MB, alloc=92.3MB, time=5.88 memory used=297.3MB, alloc=92.3MB, time=7.44 memory used=362.9MB, alloc=116.3MB, time=9.03 memory used=421.8MB, alloc=116.3MB, time=10.42 memory used=476.8MB, alloc=372.3MB, time=11.86 memory used=561.6MB, alloc=372.3MB, time=13.43 memory used=652.5MB, alloc=396.3MB, time=15.08 memory used=763.0MB, alloc=396.3MB, time=17.24 memory used=873.3MB, alloc=396.3MB, time=20.03 memory used=985.9MB, alloc=420.3MB, time=22.68 memory used=1079.4MB, alloc=420.3MB, time=23.92 memory used=1164.4MB, alloc=420.3MB, time=24.75 memory used=1300.9MB, alloc=420.3MB, time=28.80 memory used=1354.1MB, alloc=420.3MB, time=29.15 memory used=1487.9MB, alloc=444.3MB, time=31.77 memory used=1605.5MB, alloc=444.3MB, time=34.62 memory used=1708.8MB, alloc=468.3MB, time=37.47 memory used=1799.0MB, alloc=468.3MB, time=39.49 memory used=1888.8MB, alloc=468.3MB, time=41.83 memory used=1975.7MB, alloc=468.3MB, time=44.10 memory used=2060.4MB, alloc=492.3MB, time=46.56 memory used=2134.1MB, alloc=492.3MB, time=48.72 memory used=2194.3MB, alloc=492.3MB, time=50.44 memory used=2265.0MB, alloc=492.3MB, time=52.50 memory used=2331.9MB, alloc=492.3MB, time=54.52 memory used=2380.3MB, alloc=492.3MB, time=55.91 memory used=2433.1MB, alloc=492.3MB, time=57.81 memory used=2481.7MB, alloc=492.3MB, time=59.08 memory used=2541.3MB, alloc=492.3MB, time=60.44 memory used=2606.1MB, alloc=492.3MB, time=62.25 memory used=2652.0MB, alloc=492.3MB, time=63.91 memory used=2698.2MB, alloc=492.3MB, time=65.37 memory used=2750.8MB, alloc=492.3MB, time=67.00 memory used=2884.8MB, alloc=516.3MB, time=69.08 memory used=3003.7MB, alloc=516.3MB, time=70.17 memory used=3125.6MB, alloc=516.3MB, time=71.61 memory used=3234.1MB, alloc=516.3MB, time=72.64 memory used=3401.6MB, alloc=516.3MB, time=75.34 memory used=3616.9MB, alloc=540.3MB, time=80.26 memory used=3796.9MB, alloc=564.3MB, time=84.17 memory used=3984.2MB, alloc=588.3MB, time=88.76 memory used=4160.3MB, alloc=612.3MB, time=93.50 memory used=4329.5MB, alloc=636.3MB, time=98.19 memory used=4479.4MB, alloc=636.3MB, time=102.86 memory used=4616.5MB, alloc=660.3MB, time=106.93 memory used=4721.4MB, alloc=660.3MB, time=110.37 memory used=4838.4MB, alloc=660.3MB, time=114.19 memory used=4939.0MB, alloc=660.3MB, time=117.53 memory used=5030.9MB, alloc=660.3MB, time=120.32 memory used=5132.5MB, alloc=660.3MB, time=124.32 memory used=5442.0MB, alloc=684.3MB, time=131.02 memory used=5641.5MB, alloc=684.3MB, time=136.12 |\^/| 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(); 1428275591 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 2 3 F := [-y z - 14 x + 5, 10 y - 6 x + 6 x y, -8 y z + 6 z ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 2 3 2 G := [2 x z + 2 y + 10 y z , -x z - 8 z + 10 y, 9 x + 5 x y - 10 x y z] > Problem := [F,G]; 2 3 2 2 3 Problem := [[-y z - 14 x + 5, 10 y - 6 x + 6 x y, -8 y z + 6 z ], 2 3 2 2 3 2 [2 x z + 2 y + 10 y z , -x z - 8 z + 10 y, 9 x + 5 x y - 10 x y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.9MB, alloc=32.3MB, time=0.87 memory used=48.0MB, alloc=32.3MB, time=1.41 memory used=66.8MB, alloc=56.3MB, time=1.90 memory used=109.7MB, alloc=68.3MB, time=2.96 memory used=149.9MB, alloc=92.3MB, time=3.96 memory used=216.3MB, alloc=92.3MB, time=5.46 memory used=279.5MB, alloc=116.3MB, time=7.02 memory used=361.3MB, alloc=116.3MB, time=9.12 memory used=431.1MB, alloc=396.3MB, time=10.73 memory used=540.1MB, alloc=396.3MB, time=13.32 memory used=644.1MB, alloc=420.3MB, time=15.99 memory used=777.1MB, alloc=444.3MB, time=18.78 memory used=922.9MB, alloc=468.3MB, time=22.49 memory used=1067.4MB, alloc=468.3MB, time=26.46 memory used=1202.1MB, alloc=492.3MB, time=30.05 memory used=1314.2MB, alloc=492.3MB, time=32.86 memory used=1418.7MB, alloc=492.3MB, time=35.40 memory used=1519.6MB, alloc=492.3MB, time=38.07 memory used=1608.1MB, alloc=516.3MB, time=40.58 memory used=1699.4MB, alloc=516.3MB, time=43.23 memory used=1783.8MB, alloc=516.3MB, time=45.83 memory used=1854.2MB, alloc=516.3MB, time=48.09 memory used=1926.7MB, alloc=516.3MB, time=50.47 memory used=2010.1MB, alloc=516.3MB, time=53.53 memory used=2074.5MB, alloc=516.3MB, time=55.74 memory used=2150.6MB, alloc=516.3MB, time=58.61 memory used=2214.3MB, alloc=540.3MB, time=60.37 memory used=2268.9MB, alloc=540.3MB, time=61.97 memory used=2319.3MB, alloc=540.3MB, time=63.74 memory used=2525.9MB, alloc=564.3MB, time=68.10 memory used=2714.7MB, alloc=588.3MB, time=73.09 memory used=2905.7MB, alloc=612.3MB, time=78.17 memory used=3057.7MB, alloc=636.3MB, time=82.18 memory used=3207.6MB, alloc=660.3MB, time=87.20 memory used=3353.7MB, alloc=660.3MB, time=92.18 memory used=3494.5MB, alloc=684.3MB, time=96.31 memory used=3628.2MB, alloc=684.3MB, time=100.89 memory used=3791.6MB, alloc=684.3MB, time=106.04 memory used=3914.6MB, alloc=684.3MB, time=109.50 memory used=4027.8MB, alloc=708.3MB, time=112.92 memory used=4142.5MB, alloc=708.3MB, time=116.67 |\^/| 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(); 1428275891 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 3 3 F := [-3 x z - 5 z + 20 y, 2 x z + 5 y z + 6 z , -3 z - 6 x y - 8 y] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; G := [ 2 2 2 3 2 2 2 -18 y z + 2 x z - 3 y , -6 x z - 10 x y z - 4 z , 4 x z + 8 y z + 10 y ] > Problem := [F,G]; Problem := [ 2 2 2 3 3 [-3 x z - 5 z + 20 y, 2 x z + 5 y z + 6 z , -3 z - 6 x y - 8 y], [ 2 2 2 3 2 2 2 -18 y z + 2 x z - 3 y , -6 x z - 10 x y z - 4 z , 4 x z + 8 y z + 10 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.30 memory used=26.3MB, alloc=32.3MB, time=0.87 memory used=45.9MB, alloc=56.3MB, time=1.39 memory used=87.6MB, alloc=60.3MB, time=2.45 memory used=129.8MB, alloc=84.3MB, time=3.43 memory used=170.8MB, alloc=84.3MB, time=4.54 memory used=236.7MB, alloc=116.3MB, time=6.21 memory used=326.9MB, alloc=116.3MB, time=8.07 memory used=403.5MB, alloc=116.3MB, time=9.71 memory used=479.2MB, alloc=372.3MB, time=11.62 memory used=569.1MB, alloc=396.3MB, time=13.47 memory used=683.2MB, alloc=420.3MB, time=16.41 memory used=811.1MB, alloc=444.3MB, time=19.88 memory used=958.3MB, alloc=468.3MB, time=24.14 memory used=1088.3MB, alloc=492.3MB, time=27.96 memory used=1193.4MB, alloc=492.3MB, time=30.97 memory used=1298.2MB, alloc=492.3MB, time=33.84 memory used=1377.9MB, alloc=492.3MB, time=35.98 memory used=1464.6MB, alloc=516.3MB, time=38.46 memory used=1560.7MB, alloc=516.3MB, time=41.57 memory used=1637.7MB, alloc=516.3MB, time=44.07 memory used=1712.6MB, alloc=516.3MB, time=46.52 memory used=1777.4MB, alloc=516.3MB, time=48.71 memory used=1850.7MB, alloc=540.3MB, time=51.43 memory used=1911.1MB, alloc=540.3MB, time=53.40 memory used=1981.3MB, alloc=540.3MB, time=55.64 memory used=2053.9MB, alloc=540.3MB, time=58.42 memory used=2099.2MB, alloc=540.3MB, time=60.20 memory used=2157.5MB, alloc=540.3MB, time=62.36 memory used=2381.4MB, alloc=564.3MB, time=68.16 memory used=2640.6MB, alloc=588.3MB, time=74.23 memory used=2895.5MB, alloc=612.3MB, time=82.63 memory used=3098.7MB, alloc=636.3MB, time=87.95 memory used=3292.0MB, alloc=660.3MB, time=93.17 memory used=3445.2MB, alloc=684.3MB, time=97.74 memory used=3633.6MB, alloc=708.3MB, time=103.46 memory used=3809.6MB, alloc=708.3MB, time=109.65 memory used=3979.1MB, alloc=732.3MB, time=116.01 memory used=4105.6MB, alloc=732.3MB, time=120.07 memory used=4242.9MB, alloc=732.3MB, time=125.10 memory used=4346.2MB, alloc=732.3MB, time=129.11 memory used=4464.8MB, alloc=732.3MB, time=133.80 memory used=4550.5MB, alloc=732.3MB, time=137.77 |\^/| 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(); 1428276191 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 2 2 2 F := [2 y - 10 y + 4 y, -8 x y + 9 y - 2 z , -10 x - 5 x y - 9 x z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 3 3 2 G := [-20 x y - 7 y + 17 y, -2 y z - 2 z , 2 y + 3 y z - 7] > Problem := [F,G]; Problem := [ 3 2 2 2 2 2 [2 y - 10 y + 4 y, -8 x y + 9 y - 2 z , -10 x - 5 x y - 9 x z], 2 2 2 3 3 2 [-20 x y - 7 y + 17 y, -2 y z - 2 z , 2 y + 3 y z - 7]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.31 memory used=26.4MB, alloc=32.3MB, time=0.84 memory used=47.1MB, alloc=32.3MB, time=1.37 memory used=66.2MB, alloc=56.3MB, time=1.89 memory used=106.2MB, alloc=60.3MB, time=2.98 memory used=144.1MB, alloc=60.3MB, time=3.97 memory used=180.6MB, alloc=84.3MB, time=4.95 memory used=233.5MB, alloc=84.3MB, time=6.38 memory used=289.0MB, alloc=116.3MB, time=8.02 memory used=366.8MB, alloc=116.3MB, time=10.26 memory used=443.9MB, alloc=140.3MB, time=12.54 memory used=542.8MB, alloc=140.3MB, time=15.38 memory used=642.7MB, alloc=164.3MB, time=18.42 memory used=746.5MB, alloc=420.3MB, time=21.58 memory used=862.9MB, alloc=444.3MB, time=25.03 memory used=1001.5MB, alloc=468.3MB, time=29.02 memory used=1160.3MB, alloc=492.3MB, time=34.06 memory used=1324.9MB, alloc=516.3MB, time=39.50 memory used=1496.2MB, alloc=540.3MB, time=45.11 memory used=1676.8MB, alloc=564.3MB, time=51.13 memory used=1865.5MB, alloc=588.3MB, time=57.47 memory used=2061.5MB, alloc=612.3MB, time=64.07 memory used=2263.7MB, alloc=636.3MB, time=71.00 memory used=2470.8MB, alloc=660.3MB, time=78.06 memory used=2681.6MB, alloc=684.3MB, time=85.36 memory used=2895.0MB, alloc=708.3MB, time=92.82 memory used=3111.7MB, alloc=732.3MB, time=100.52 memory used=3329.4MB, alloc=756.3MB, time=108.56 memory used=3520.9MB, alloc=780.3MB, time=119.25 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428276491 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 3 2 3 F := [x y - 20 x y z + 11 y z, x y + 4 z + 6 y , 10 x + 10 x z - 3 z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 G := [-8 x y z - 19 y z - 16 z, -8 x y + 2 y z - 4 z, -7 x y - 8 x y z - y ] > Problem := [F,G]; Problem := [ 2 2 3 2 3 [x y - 20 x y z + 11 y z, x y + 4 z + 6 y , 10 x + 10 x z - 3 z], 2 2 2 2 [-8 x y z - 19 y z - 16 z, -8 x y + 2 y z - 4 z, -7 x y - 8 x y z - y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.5MB, alloc=32.3MB, time=0.87 memory used=47.5MB, alloc=32.3MB, time=1.41 memory used=67.2MB, alloc=32.3MB, time=1.90 memory used=85.8MB, alloc=56.3MB, time=2.40 memory used=122.9MB, alloc=60.3MB, time=3.40 memory used=160.3MB, alloc=84.3MB, time=4.40 memory used=207.0MB, alloc=84.3MB, time=5.67 memory used=266.7MB, alloc=92.3MB, time=7.35 memory used=326.0MB, alloc=116.3MB, time=9.02 memory used=407.5MB, alloc=140.3MB, time=11.35 memory used=496.4MB, alloc=396.3MB, time=13.90 memory used=600.3MB, alloc=420.3MB, time=16.89 memory used=724.8MB, alloc=444.3MB, time=20.66 memory used=874.3MB, alloc=468.3MB, time=25.16 memory used=1013.9MB, alloc=492.3MB, time=29.45 memory used=1145.1MB, alloc=492.3MB, time=33.29 memory used=1288.0MB, alloc=516.3MB, time=37.99 memory used=1434.5MB, alloc=516.3MB, time=42.81 memory used=1559.6MB, alloc=516.3MB, time=46.96 memory used=1687.9MB, alloc=516.3MB, time=51.72 memory used=1803.7MB, alloc=540.3MB, time=56.19 memory used=1913.3MB, alloc=540.3MB, time=60.20 memory used=1995.4MB, alloc=540.3MB, time=63.40 memory used=2105.1MB, alloc=540.3MB, time=67.60 memory used=2192.3MB, alloc=540.3MB, time=71.04 memory used=2284.1MB, alloc=540.3MB, time=74.59 memory used=2384.9MB, alloc=540.3MB, time=78.70 memory used=2465.4MB, alloc=540.3MB, time=82.05 memory used=2553.7MB, alloc=540.3MB, time=85.83 memory used=2618.6MB, alloc=540.3MB, time=88.78 memory used=2692.2MB, alloc=540.3MB, time=92.39 memory used=2770.7MB, alloc=540.3MB, time=96.30 memory used=2990.7MB, alloc=564.3MB, time=104.21 memory used=3235.0MB, alloc=588.3MB, time=113.50 memory used=3476.7MB, alloc=612.3MB, time=123.05 memory used=3702.0MB, alloc=636.3MB, time=132.15 memory used=3912.2MB, alloc=660.3MB, time=140.78 |\^/| 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(); 1428276791 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 2 3 2 2 F := [19 x y - 16 y + 3 y z, 6 x z - y , 7 x y + x + 6 y z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 G := [-14 x y z - 18 y z - 20, x y z + 8 y z - 9 x , 6 x z - 3 y z + 7] > Problem := [F,G]; 2 3 2 2 3 2 2 Problem := [[19 x y - 16 y + 3 y z, 6 x z - y , 7 x y + x + 6 y z], 2 2 2 2 [-14 x y z - 18 y z - 20, x y z + 8 y z - 9 x , 6 x z - 3 y z + 7]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.30 memory used=26.0MB, alloc=32.3MB, time=0.87 memory used=46.5MB, alloc=56.3MB, time=1.28 memory used=83.1MB, alloc=60.3MB, time=2.06 memory used=126.5MB, alloc=68.3MB, time=3.18 memory used=171.6MB, alloc=92.3MB, time=4.28 memory used=239.2MB, alloc=92.3MB, time=5.93 memory used=304.6MB, alloc=92.3MB, time=7.24 memory used=365.7MB, alloc=116.3MB, time=8.68 memory used=428.5MB, alloc=372.3MB, time=10.30 memory used=514.3MB, alloc=396.3MB, time=12.25 memory used=640.1MB, alloc=396.3MB, time=14.78 memory used=754.1MB, alloc=420.3MB, time=17.36 memory used=860.5MB, alloc=444.3MB, time=20.11 memory used=962.5MB, alloc=444.3MB, time=22.69 memory used=1072.0MB, alloc=468.3MB, time=25.24 memory used=1159.1MB, alloc=468.3MB, time=27.45 memory used=1250.9MB, alloc=468.3MB, time=30.00 memory used=1325.8MB, alloc=492.3MB, time=32.09 memory used=1410.9MB, alloc=492.3MB, time=34.45 memory used=1486.7MB, alloc=492.3MB, time=36.28 memory used=1552.3MB, alloc=492.3MB, time=38.11 memory used=1641.6MB, alloc=492.3MB, time=40.33 memory used=1704.4MB, alloc=492.3MB, time=42.27 memory used=1757.1MB, alloc=492.3MB, time=43.73 memory used=1831.2MB, alloc=492.3MB, time=45.54 memory used=1899.2MB, alloc=492.3MB, time=47.31 memory used=1943.7MB, alloc=492.3MB, time=48.87 memory used=1984.4MB, alloc=492.3MB, time=50.20 memory used=2028.5MB, alloc=492.3MB, time=51.69 memory used=2217.4MB, alloc=516.3MB, time=56.72 memory used=2410.7MB, alloc=540.3MB, time=62.25 memory used=2603.3MB, alloc=564.3MB, time=68.26 memory used=2753.6MB, alloc=588.3MB, time=72.67 memory used=2899.4MB, alloc=612.3MB, time=77.01 memory used=3017.1MB, alloc=636.3MB, time=80.88 memory used=3146.7MB, alloc=636.3MB, time=85.06 memory used=3275.4MB, alloc=636.3MB, time=89.38 memory used=3367.7MB, alloc=636.3MB, time=92.50 memory used=3486.6MB, alloc=636.3MB, time=96.73 memory used=3571.4MB, alloc=660.3MB, time=99.64 memory used=3661.3MB, alloc=660.3MB, time=103.51 memory used=3992.8MB, alloc=684.3MB, time=112.93 memory used=4367.5MB, alloc=708.3MB, time=122.77 memory used=4720.2MB, alloc=732.3MB, time=133.48 memory used=5074.8MB, alloc=756.3MB, time=143.28 memory used=5418.8MB, alloc=780.3MB, time=153.25 |\^/| 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(); 1428277091 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 3 2 3 2 F := [-9 z - 7 x + 7 x, 8 x + 2 x y + 2 y , -x - 5 x z ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 2 2 G := [-8 x z + 7 y + 18, -6 x y + 5 x z + 10 x y, 4 x - 9 z + 4] > Problem := [F,G]; 3 2 3 2 3 2 Problem := [[-9 z - 7 x + 7 x, 8 x + 2 x y + 2 y , -x - 5 x z ], 2 2 2 2 2 2 [-8 x z + 7 y + 18, -6 x y + 5 x z + 10 x y, 4 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=0.31 memory used=26.4MB, alloc=32.3MB, time=0.87 memory used=47.4MB, alloc=32.3MB, time=1.42 memory used=67.3MB, alloc=56.3MB, time=1.98 memory used=110.3MB, alloc=60.3MB, time=3.14 memory used=150.5MB, alloc=60.3MB, time=4.20 memory used=188.8MB, alloc=84.3MB, time=5.24 memory used=236.2MB, alloc=84.3MB, time=6.51 memory used=293.5MB, alloc=92.3MB, time=8.09 memory used=349.8MB, alloc=116.3MB, time=9.65 memory used=428.8MB, alloc=116.3MB, time=11.74 memory used=507.9MB, alloc=116.3MB, time=13.80 memory used=586.9MB, alloc=140.3MB, time=15.90 memory used=676.6MB, alloc=396.3MB, time=18.38 memory used=778.0MB, alloc=396.3MB, time=21.19 memory used=878.3MB, alloc=420.3MB, time=24.01 memory used=998.2MB, alloc=420.3MB, time=27.18 memory used=1119.0MB, alloc=444.3MB, time=30.12 memory used=1273.0MB, alloc=468.3MB, time=34.34 memory used=1431.2MB, alloc=492.3MB, time=39.47 memory used=1606.4MB, alloc=516.3MB, time=45.02 memory used=1799.9MB, alloc=540.3MB, time=50.89 memory used=1979.1MB, alloc=564.3MB, time=59.01 memory used=2155.3MB, alloc=588.3MB, time=68.91 memory used=2339.9MB, alloc=612.3MB, time=80.40 memory used=2548.5MB, alloc=636.3MB, time=93.31 memory used=2781.0MB, alloc=660.3MB, time=107.44 memory used=3037.5MB, alloc=660.3MB, time=122.90 |\^/| 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(); 1428277391 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; F := 2 2 3 2 2 2 [-15 x y + 8 x z + 15 y , -4 y z - y z + 5 z , 3 x y z - 3 x z - 5 y z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 2 G := [-x y z + 10 y z + 16 x , 2 x y, -5 x z + 9 z - 7 y] > Problem := [F,G]; Problem := [ 2 2 3 2 2 2 [-15 x y + 8 x z + 15 y , -4 y z - y z + 5 z , 3 x y z - 3 x z - 5 y z] 2 2 2 2 2 , [-x y z + 10 y z + 16 x , 2 x y, -5 x z + 9 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=26.4MB, alloc=32.3MB, time=0.85 memory used=46.5MB, alloc=32.3MB, time=1.36 memory used=65.4MB, alloc=56.3MB, time=1.87 memory used=103.6MB, alloc=60.3MB, time=2.86 memory used=141.0MB, alloc=84.3MB, time=3.85 memory used=200.4MB, alloc=92.3MB, time=5.42 memory used=258.7MB, alloc=92.3MB, time=6.94 memory used=316.6MB, alloc=116.3MB, time=8.48 memory used=395.8MB, alloc=116.3MB, time=10.58 memory used=469.8MB, alloc=140.3MB, time=12.65 memory used=531.2MB, alloc=396.3MB, time=14.27 memory used=633.4MB, alloc=420.3MB, time=17.13 memory used=758.3MB, alloc=444.3MB, time=20.48 memory used=905.2MB, alloc=468.3MB, time=24.58 memory used=1048.1MB, alloc=468.3MB, time=28.53 memory used=1168.7MB, alloc=492.3MB, time=31.88 memory used=1279.9MB, alloc=492.3MB, time=34.99 memory used=1381.6MB, alloc=492.3MB, time=37.91 memory used=1491.7MB, alloc=492.3MB, time=40.98 memory used=1574.4MB, alloc=516.3MB, time=43.42 memory used=1681.3MB, alloc=516.3MB, time=46.67 memory used=1777.9MB, alloc=516.3MB, time=49.87 memory used=1864.5MB, alloc=516.3MB, time=52.65 memory used=1933.6MB, alloc=516.3MB, time=54.77 memory used=2013.1MB, alloc=516.3MB, time=57.37 memory used=2105.6MB, alloc=516.3MB, time=59.49 memory used=2164.2MB, alloc=516.3MB, time=61.39 memory used=2243.6MB, alloc=516.3MB, time=63.80 memory used=2311.8MB, alloc=516.3MB, time=66.22 memory used=2381.4MB, alloc=540.3MB, time=68.91 memory used=2445.5MB, alloc=540.3MB, time=71.40 memory used=2668.4MB, alloc=564.3MB, time=78.32 memory used=2906.5MB, alloc=588.3MB, time=85.88 memory used=3066.7MB, alloc=612.3MB, time=90.63 memory used=3259.8MB, alloc=636.3MB, time=96.74 memory used=3438.8MB, alloc=660.3MB, time=101.66 memory used=3635.9MB, alloc=684.3MB, time=108.61 memory used=3817.4MB, alloc=684.3MB, time=115.39 memory used=3950.8MB, alloc=684.3MB, time=120.36 memory used=4073.4MB, alloc=708.3MB, time=124.61 memory used=4207.8MB, alloc=708.3MB, time=130.08 |\^/| 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(); 1428277691 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 3 F := [-9 y z + y - 10 z, -10 x y + y z + 5, 6 x z - 9 y - 10 x z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 2 G := [-19 y z + 20 y z - 1, -7 x - 6 x y - 2 y, 5 x y - 6 x z - 8 y z] > Problem := [F,G]; 2 2 2 3 Problem := [[-9 y z + y - 10 z, -10 x y + y z + 5, 6 x z - 9 y - 10 x z], 2 3 2 2 [-19 y z + 20 y z - 1, -7 x - 6 x y - 2 y, 5 x y - 6 x z - 8 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.30 memory used=24.9MB, alloc=32.3MB, time=0.83 memory used=45.0MB, alloc=32.3MB, time=1.13 memory used=65.2MB, alloc=32.3MB, time=1.64 memory used=85.6MB, alloc=60.3MB, time=2.18 memory used=126.8MB, alloc=60.3MB, time=2.81 memory used=162.7MB, alloc=60.3MB, time=3.21 memory used=206.8MB, alloc=61.1MB, time=3.95 memory used=248.9MB, alloc=69.1MB, time=4.89 memory used=290.6MB, alloc=69.1MB, time=5.92 memory used=332.5MB, alloc=69.1MB, time=6.65 memory used=353.3MB, alloc=69.1MB, time=6.77 memory used=388.3MB, alloc=69.1MB, time=7.18 memory used=413.1MB, alloc=69.1MB, time=7.51 memory used=459.4MB, alloc=69.1MB, time=8.72 memory used=499.2MB, alloc=93.1MB, time=9.60 memory used=562.1MB, alloc=93.1MB, time=11.10 memory used=624.0MB, alloc=93.1MB, time=12.66 memory used=685.4MB, alloc=117.1MB, time=14.05 memory used=744.7MB, alloc=373.1MB, time=15.54 memory used=812.7MB, alloc=373.1MB, time=16.53 memory used=901.2MB, alloc=373.1MB, time=19.13 memory used=941.6MB, alloc=373.1MB, time=19.36 memory used=1022.0MB, alloc=373.1MB, time=20.88 memory used=1108.1MB, alloc=397.1MB, time=23.02 memory used=1219.8MB, alloc=421.1MB, time=25.68 memory used=1329.1MB, alloc=445.1MB, time=28.42 memory used=1448.3MB, alloc=445.1MB, time=30.12 memory used=1554.3MB, alloc=445.1MB, time=31.18 memory used=1626.9MB, alloc=445.1MB, time=31.63 memory used=1712.5MB, alloc=445.1MB, time=32.97 memory used=1809.6MB, alloc=445.1MB, time=33.85 memory used=1909.4MB, alloc=445.1MB, time=34.60 memory used=1995.9MB, alloc=445.1MB, time=35.76 memory used=2087.2MB, alloc=445.1MB, time=36.46 memory used=2184.6MB, alloc=445.1MB, time=37.98 memory used=2272.4MB, alloc=445.1MB, time=38.72 memory used=2359.1MB, alloc=445.1MB, time=39.39 memory used=2476.4MB, alloc=445.1MB, time=41.21 memory used=2589.9MB, alloc=445.1MB, time=45.02 memory used=2699.5MB, alloc=445.1MB, time=48.01 memory used=2849.1MB, alloc=445.1MB, time=51.40 memory used=2979.3MB, alloc=445.1MB, time=54.68 memory used=3083.8MB, alloc=445.1MB, time=56.14 memory used=3183.7MB, alloc=445.1MB, time=57.19 memory used=3268.8MB, alloc=445.1MB, time=58.39 memory used=3352.9MB, alloc=445.1MB, time=59.10 memory used=3450.3MB, alloc=445.1MB, time=60.73 memory used=3535.4MB, alloc=445.1MB, time=61.44 memory used=3617.4MB, alloc=445.1MB, time=62.13 memory used=3742.7MB, alloc=445.1MB, time=65.18 memory used=3853.2MB, alloc=445.1MB, time=66.69 memory used=3971.1MB, alloc=445.1MB, time=68.83 memory used=4063.9MB, alloc=469.1MB, time=71.03 memory used=4159.2MB, alloc=469.1MB, time=73.51 memory used=4234.8MB, alloc=469.1MB, time=75.12 memory used=4314.3MB, alloc=469.1MB, time=77.18 memory used=4411.9MB, alloc=469.1MB, time=78.95 memory used=4505.1MB, alloc=469.1MB, time=79.67 memory used=4594.5MB, alloc=469.1MB, time=81.59 memory used=4679.4MB, alloc=469.1MB, time=82.24 memory used=4789.7MB, alloc=469.1MB, time=83.37 memory used=4896.9MB, alloc=469.1MB, time=84.21 memory used=5003.6MB, alloc=469.1MB, time=85.62 memory used=5110.4MB, alloc=469.1MB, time=87.31 memory used=5215.4MB, alloc=469.1MB, time=88.16 memory used=5336.9MB, alloc=469.1MB, time=90.35 memory used=5448.1MB, alloc=469.1MB, time=92.80 memory used=5524.6MB, alloc=469.1MB, time=94.67 memory used=5587.2MB, alloc=469.1MB, time=96.52 memory used=5646.6MB, alloc=469.1MB, time=98.35 memory used=5700.8MB, alloc=469.1MB, time=100.01 memory used=5756.0MB, alloc=469.1MB, time=101.89 memory used=5810.6MB, alloc=469.1MB, time=103.64 memory used=5846.2MB, alloc=469.1MB, time=105.05 memory used=6001.7MB, alloc=493.1MB, time=108.67 memory used=6123.0MB, alloc=493.1MB, time=110.74 memory used=6271.8MB, alloc=517.1MB, time=115.30 memory used=6368.3MB, alloc=517.1MB, time=116.14 memory used=6465.1MB, alloc=517.1MB, time=116.88 memory used=6552.0MB, alloc=517.1MB, time=117.57 memory used=6721.7MB, alloc=517.1MB, time=119.80 memory used=6973.8MB, alloc=517.1MB, time=123.86 memory used=7126.4MB, alloc=541.1MB, time=126.87 memory used=7264.8MB, alloc=541.1MB, time=130.27 memory used=7382.4MB, alloc=541.1MB, time=131.21 memory used=7470.8MB, alloc=541.1MB, time=131.99 memory used=7632.7MB, alloc=541.1MB, time=133.93 memory used=7894.4MB, alloc=541.1MB, time=138.48 memory used=8066.2MB, alloc=541.1MB, time=142.91 memory used=8225.4MB, alloc=565.1MB, time=147.62 memory used=8430.8MB, alloc=589.1MB, time=152.36 |\^/| 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(); 1428277991 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 F := [18 y z + 7 x + 19 y, -4 x + 6 y + 4 z, -6 x y - 10 y z - 2] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 3 G := [-17 x z - 15, 10 y z - 9 z + 6 x z, 8 x z - 10 z - 3 x] > Problem := [F,G]; 2 Problem := [[18 y z + 7 x + 19 y, -4 x + 6 y + 4 z, -6 x y - 10 y z - 2], 2 3 2 3 [-17 x z - 15, 10 y z - 9 z + 6 x z, 8 x z - 10 z - 3 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.30 memory used=27.0MB, alloc=32.3MB, time=0.89 memory used=47.5MB, alloc=32.3MB, time=1.42 memory used=66.3MB, alloc=56.3MB, time=1.93 memory used=105.3MB, alloc=60.3MB, time=2.96 memory used=143.6MB, alloc=84.3MB, time=3.99 memory used=203.7MB, alloc=92.3MB, time=5.59 memory used=262.4MB, alloc=116.3MB, time=7.18 memory used=343.0MB, alloc=116.3MB, time=9.32 memory used=421.4MB, alloc=140.3MB, time=11.46 memory used=521.0MB, alloc=164.3MB, time=14.18 memory used=604.6MB, alloc=420.3MB, time=16.50 memory used=727.7MB, alloc=444.3MB, time=19.86 memory used=873.0MB, alloc=468.3MB, time=24.02 memory used=1039.5MB, alloc=492.3MB, time=28.68 memory used=1230.2MB, alloc=516.3MB, time=34.23 memory used=1445.0MB, alloc=540.3MB, time=40.67 memory used=1680.6MB, alloc=564.3MB, time=48.01 memory used=1936.2MB, alloc=588.3MB, time=56.20 memory used=2191.0MB, alloc=612.3MB, time=64.93 memory used=2399.4MB, alloc=636.3MB, time=71.85 memory used=2615.6MB, alloc=660.3MB, time=79.56 memory used=2819.9MB, alloc=684.3MB, time=87.03 memory used=3009.4MB, alloc=708.3MB, time=94.32 memory used=3189.2MB, alloc=732.3MB, time=101.50 memory used=3346.4MB, alloc=732.3MB, time=107.71 memory used=3483.2MB, alloc=732.3MB, time=113.49 memory used=3615.9MB, alloc=732.3MB, time=119.16 |\^/| 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(); 1428278291 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 2 3 2 2 F := [-3 y z + 8 z + 10 x , -8 x y + 3 y + 2 y , -7 x z - 8 x y - 3] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 2 2 G := [-11 y + 17 x z + 11 x, 5 x y + y , -5 x y - 5 x - 10 x z] > Problem := [F,G]; Problem := [ 2 3 2 2 3 2 2 [-3 y z + 8 z + 10 x , -8 x y + 3 y + 2 y , -7 x z - 8 x y - 3], 3 2 2 2 2 [-11 y + 17 x z + 11 x, 5 x y + y , -5 x y - 5 x - 10 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.30 memory used=26.2MB, alloc=32.3MB, time=0.86 memory used=47.4MB, alloc=32.3MB, time=1.41 memory used=67.0MB, alloc=56.3MB, time=1.94 memory used=107.0MB, alloc=60.3MB, time=3.01 memory used=145.4MB, alloc=84.3MB, time=4.00 memory used=209.0MB, alloc=92.3MB, time=5.65 memory used=272.7MB, alloc=116.3MB, time=7.28 memory used=350.0MB, alloc=116.3MB, time=9.26 memory used=431.0MB, alloc=396.3MB, time=11.52 memory used=541.9MB, alloc=396.3MB, time=14.47 memory used=652.5MB, alloc=420.3MB, time=17.44 memory used=786.8MB, alloc=444.3MB, time=21.19 memory used=930.1MB, alloc=468.3MB, time=25.18 memory used=1062.8MB, alloc=468.3MB, time=29.09 memory used=1202.6MB, alloc=492.3MB, time=33.04 memory used=1317.5MB, alloc=492.3MB, time=35.72 memory used=1426.3MB, alloc=492.3MB, time=38.52 memory used=1535.2MB, alloc=492.3MB, time=41.63 memory used=1628.0MB, alloc=516.3MB, time=44.22 memory used=1724.8MB, alloc=516.3MB, time=46.72 memory used=1884.3MB, alloc=516.3MB, time=49.23 memory used=2001.2MB, alloc=516.3MB, time=51.87 memory used=2082.7MB, alloc=516.3MB, time=54.47 memory used=2174.0MB, alloc=516.3MB, time=56.72 memory used=2264.7MB, alloc=516.3MB, time=57.40 memory used=2365.6MB, alloc=516.3MB, time=58.40 memory used=2470.5MB, alloc=540.3MB, time=60.52 memory used=2541.6MB, alloc=540.3MB, time=62.53 memory used=2606.0MB, alloc=540.3MB, time=64.69 memory used=2687.4MB, alloc=540.3MB, time=66.95 memory used=2775.1MB, alloc=540.3MB, time=68.73 memory used=2861.6MB, alloc=540.3MB, time=71.23 memory used=3012.2MB, alloc=564.3MB, time=75.49 memory used=3128.4MB, alloc=564.3MB, time=76.38 memory used=3232.6MB, alloc=564.3MB, time=77.14 memory used=3331.7MB, alloc=564.3MB, time=77.89 memory used=3446.5MB, alloc=564.3MB, time=78.66 memory used=3579.7MB, alloc=564.3MB, time=79.48 memory used=3824.4MB, alloc=564.3MB, time=80.87 memory used=3966.6MB, alloc=564.3MB, time=81.74 memory used=4121.3MB, alloc=564.3MB, time=82.64 memory used=4287.3MB, alloc=564.3MB, time=83.55 memory used=4467.2MB, alloc=564.3MB, time=84.48 memory used=4665.1MB, alloc=564.3MB, time=85.42 memory used=4877.1MB, alloc=564.3MB, time=86.42 memory used=5106.4MB, alloc=564.3MB, time=87.44 memory used=5300.4MB, alloc=564.3MB, time=88.35 memory used=5474.2MB, alloc=564.3MB, time=89.23 memory used=5658.5MB, alloc=564.3MB, time=90.11 memory used=5852.3MB, alloc=564.3MB, time=91.03 memory used=6059.8MB, alloc=564.3MB, time=91.96 memory used=6283.0MB, alloc=564.3MB, time=92.92 memory used=6515.2MB, alloc=564.3MB, time=93.84 memory used=6668.3MB, alloc=564.3MB, time=98.48 memory used=6791.7MB, alloc=564.3MB, time=99.44 memory used=6887.2MB, alloc=564.3MB, time=101.60 memory used=6948.9MB, alloc=564.3MB, time=103.64 memory used=7002.6MB, alloc=564.3MB, time=105.47 memory used=7269.4MB, alloc=588.3MB, time=112.79 memory used=7537.2MB, alloc=588.3MB, time=116.08 memory used=7813.7MB, alloc=612.3MB, time=123.57 memory used=8072.0MB, alloc=636.3MB, time=131.81 memory used=8332.6MB, alloc=660.3MB, time=140.53 memory used=8586.0MB, alloc=684.3MB, time=148.77 |\^/| 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(); 1428278591 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 2 2 F := [14 x z - 10 x y + 15 y , 4 x - 7 x y + 4 z , 9 x z - 6 x y + x] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 2 2 2 G := [18 y + 13 x z - 3 y , -6 x z - x y + 2, -7 x y - z + 8 x] > Problem := [F,G]; Problem := [ 2 2 2 2 2 2 [14 x z - 10 x y + 15 y , 4 x - 7 x y + 4 z , 9 x z - 6 x y + x], 3 2 2 2 2 2 [18 y + 13 x z - 3 y , -6 x z - x y + 2, -7 x y - z + 8 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.3MB, alloc=32.3MB, time=0.86 memory used=45.9MB, alloc=32.3MB, time=1.39 memory used=64.0MB, alloc=56.3MB, time=1.89 memory used=103.5MB, alloc=60.3MB, time=2.95 memory used=140.5MB, alloc=84.3MB, time=3.97 memory used=201.9MB, alloc=92.3MB, time=5.60 memory used=259.0MB, alloc=116.3MB, time=7.18 memory used=334.6MB, alloc=116.3MB, time=9.20 memory used=412.5MB, alloc=396.3MB, time=11.34 memory used=525.1MB, alloc=396.3MB, time=14.07 memory used=629.6MB, alloc=420.3MB, time=17.02 memory used=754.8MB, alloc=444.3MB, time=20.52 memory used=903.9MB, alloc=468.3MB, time=24.73 memory used=1021.1MB, alloc=468.3MB, time=27.82 memory used=1160.5MB, alloc=492.3MB, time=31.67 memory used=1293.4MB, alloc=492.3MB, time=35.38 memory used=1407.3MB, alloc=516.3MB, time=38.00 memory used=1531.7MB, alloc=516.3MB, time=41.79 memory used=1666.6MB, alloc=516.3MB, time=46.22 memory used=1769.1MB, alloc=516.3MB, time=49.48 memory used=1858.4MB, alloc=540.3MB, time=52.17 memory used=1961.6MB, alloc=540.3MB, time=55.77 memory used=2039.9MB, alloc=540.3MB, time=58.12 memory used=2113.9MB, alloc=540.3MB, time=60.41 memory used=2182.9MB, alloc=540.3MB, time=62.44 memory used=2274.9MB, alloc=540.3MB, time=65.62 memory used=2354.4MB, alloc=540.3MB, time=68.33 memory used=2438.3MB, alloc=540.3MB, time=70.36 memory used=2496.2MB, alloc=540.3MB, time=72.27 memory used=2567.8MB, alloc=540.3MB, time=74.76 memory used=2625.4MB, alloc=564.3MB, time=76.27 memory used=2698.5MB, alloc=564.3MB, time=79.03 memory used=2755.0MB, alloc=564.3MB, time=81.20 memory used=2815.3MB, alloc=564.3MB, time=83.19 memory used=2864.7MB, alloc=564.3MB, time=84.80 memory used=2913.4MB, alloc=564.3MB, time=86.72 memory used=3139.2MB, alloc=588.3MB, time=93.52 memory used=3349.2MB, alloc=612.3MB, time=98.89 memory used=3532.1MB, alloc=612.3MB, time=104.30 memory used=3770.4MB, alloc=636.3MB, time=109.24 memory used=3947.9MB, alloc=636.3MB, time=114.90 memory used=4142.7MB, alloc=660.3MB, time=121.57 memory used=4351.5MB, alloc=684.3MB, time=127.58 memory used=4524.2MB, alloc=684.3MB, time=134.01 memory used=4732.4MB, alloc=708.3MB, time=140.47 |\^/| 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(); 1428278891 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 3 2 F := [-6 x y + 14 y z + 18 y z, y z - 8 x - 9 y z, 4 x + 9 y z - 5 x y] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 2 2 3 G := [13 x - 15 x z - 12 y z, -2 x z + 6 z - 3 x, 2 z + 2 x - 9 z] > Problem := [F,G]; Problem := [ 2 2 2 2 3 2 [-6 x y + 14 y z + 18 y z, y z - 8 x - 9 y z, 4 x + 9 y z - 5 x y], 3 2 2 2 2 3 [13 x - 15 x z - 12 y z, -2 x z + 6 z - 3 x, 2 z + 2 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=0.30 memory used=26.6MB, alloc=32.3MB, time=0.88 memory used=48.3MB, alloc=32.3MB, time=1.45 memory used=67.5MB, alloc=56.3MB, time=1.98 memory used=107.2MB, alloc=60.3MB, time=3.01 memory used=145.3MB, alloc=84.3MB, time=4.00 memory used=207.9MB, alloc=92.3MB, time=5.61 memory used=271.3MB, alloc=92.3MB, time=7.17 memory used=335.5MB, alloc=116.3MB, time=8.69 memory used=409.9MB, alloc=372.3MB, time=10.24 memory used=494.7MB, alloc=396.3MB, time=12.38 memory used=610.8MB, alloc=420.3MB, time=15.03 memory used=746.6MB, alloc=420.3MB, time=18.34 memory used=881.0MB, alloc=444.3MB, time=21.60 memory used=1027.8MB, alloc=468.3MB, time=24.42 memory used=1139.5MB, alloc=468.3MB, time=27.26 memory used=1254.5MB, alloc=468.3MB, time=29.63 memory used=1385.5MB, alloc=492.3MB, time=33.41 memory used=1490.5MB, alloc=492.3MB, time=36.54 memory used=1593.1MB, alloc=492.3MB, time=39.76 memory used=1702.2MB, alloc=492.3MB, time=43.19 memory used=1783.5MB, alloc=516.3MB, time=45.26 memory used=1879.0MB, alloc=516.3MB, time=48.40 memory used=1957.9MB, alloc=516.3MB, time=50.41 memory used=2032.0MB, alloc=516.3MB, time=52.83 memory used=2092.0MB, alloc=516.3MB, time=54.75 memory used=2146.6MB, alloc=516.3MB, time=56.40 memory used=2223.2MB, alloc=516.3MB, time=59.18 memory used=2276.6MB, alloc=516.3MB, time=60.71 memory used=2351.1MB, alloc=540.3MB, time=62.48 memory used=2396.4MB, alloc=540.3MB, time=63.98 memory used=2599.7MB, alloc=564.3MB, time=69.59 memory used=2809.9MB, alloc=588.3MB, time=76.13 memory used=2995.1MB, alloc=612.3MB, time=81.59 memory used=3183.9MB, alloc=636.3MB, time=86.31 memory used=3330.3MB, alloc=636.3MB, time=90.71 memory used=3485.7MB, alloc=636.3MB, time=95.93 memory used=3645.8MB, alloc=660.3MB, time=101.28 memory used=3798.8MB, alloc=660.3MB, time=106.32 memory used=3935.9MB, alloc=660.3MB, time=111.11 memory used=4051.5MB, alloc=660.3MB, time=115.91 memory used=4172.7MB, alloc=660.3MB, time=120.10 memory used=4308.9MB, alloc=684.3MB, time=124.74 memory used=4405.7MB, alloc=684.3MB, time=127.86 memory used=4538.8MB, alloc=684.3MB, time=132.64 memory used=4623.9MB, alloc=684.3MB, time=135.99 |\^/| 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(); 1428279191 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 2 2 3 3 F := [-y z + 9 z + 10 x, 9 x z - 6 z + 3 z, -7 x z + 3 y + 5 z ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 G := [-11 x y + 5 z + 12 z, -8 x y + 8 x z - 5 z, 2 x y + 5 x z + 2 y] > Problem := [F,G]; 2 3 2 2 2 3 3 Problem := [[-y z + 9 z + 10 x, 9 x z - 6 z + 3 z, -7 x z + 3 y + 5 z ], 2 2 2 2 [-11 x y + 5 z + 12 z, -8 x y + 8 x z - 5 z, 2 x y + 5 x z + 2 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.5MB, alloc=32.3MB, time=0.87 memory used=47.1MB, alloc=32.3MB, time=1.39 memory used=65.3MB, alloc=56.3MB, time=1.89 memory used=104.5MB, alloc=60.3MB, time=2.93 memory used=142.7MB, alloc=84.3MB, time=3.97 memory used=203.6MB, alloc=92.3MB, time=5.60 memory used=262.0MB, alloc=116.3MB, time=7.20 memory used=342.5MB, alloc=116.3MB, time=9.42 memory used=422.3MB, alloc=140.3MB, time=11.62 memory used=505.4MB, alloc=164.3MB, time=13.96 memory used=577.8MB, alloc=420.3MB, time=15.89 memory used=711.5MB, alloc=444.3MB, time=19.26 memory used=867.0MB, alloc=468.3MB, time=23.59 memory used=1043.8MB, alloc=492.3MB, time=28.83 memory used=1249.7MB, alloc=516.3MB, time=34.45 memory used=1476.7MB, alloc=540.3MB, time=40.98 memory used=1721.5MB, alloc=564.3MB, time=48.43 memory used=1987.2MB, alloc=588.3MB, time=56.13 memory used=2243.8MB, alloc=612.3MB, time=63.97 memory used=2468.7MB, alloc=636.3MB, time=71.47 memory used=2687.6MB, alloc=660.3MB, time=78.35 memory used=2909.4MB, alloc=684.3MB, time=86.07 memory used=3105.3MB, alloc=684.3MB, time=92.77 memory used=3296.8MB, alloc=708.3MB, time=99.65 memory used=3460.1MB, alloc=708.3MB, time=105.53 memory used=3621.1MB, alloc=708.3MB, time=111.58 memory used=3779.8MB, alloc=708.3MB, time=117.29 memory used=3927.1MB, alloc=708.3MB, time=122.62 memory used=4056.6MB, alloc=708.3MB, time=127.59 memory used=4154.7MB, alloc=732.3MB, time=131.19 memory used=4271.4MB, alloc=732.3MB, time=136.53 memory used=4391.0MB, alloc=732.3MB, time=141.87 memory used=4463.7MB, alloc=732.3MB, time=145.44 |\^/| 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(); 1428279491 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 3 2 2 2 3 F := [-7 x z - 9 y z - 11 y, -3 x + 9 x z - 9 y , -3 x y z - 2 x z + 9 y ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 2 G := [-3 x z - 5 x y z - 4 z , 6 x y z - 5 y z, 8 y z + 3 x - 7] > Problem := [F,G]; Problem := [ 2 2 3 2 2 2 3 [-7 x z - 9 y z - 11 y, -3 x + 9 x z - 9 y , -3 x y z - 2 x z + 9 y ], 2 3 2 2 [-3 x z - 5 x y z - 4 z , 6 x y z - 5 y z, 8 y z + 3 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=0.30 memory used=26.8MB, alloc=32.3MB, time=0.88 memory used=48.0MB, alloc=56.3MB, time=1.45 memory used=90.7MB, alloc=60.3MB, time=2.53 memory used=133.2MB, alloc=92.3MB, time=3.59 memory used=196.7MB, alloc=92.3MB, time=5.17 memory used=261.3MB, alloc=116.3MB, time=6.76 memory used=333.1MB, alloc=372.3MB, time=8.58 memory used=420.3MB, alloc=396.3MB, time=10.72 memory used=537.1MB, alloc=420.3MB, time=13.30 memory used=663.8MB, alloc=420.3MB, time=16.26 memory used=781.3MB, alloc=444.3MB, time=19.14 memory used=893.1MB, alloc=444.3MB, time=22.06 memory used=1007.8MB, alloc=468.3MB, time=25.05 memory used=1117.6MB, alloc=468.3MB, time=27.88 memory used=1219.3MB, alloc=468.3MB, time=30.26 memory used=1316.6MB, alloc=468.3MB, time=32.38 memory used=1400.1MB, alloc=492.3MB, time=34.69 memory used=1495.7MB, alloc=492.3MB, time=37.02 memory used=1578.0MB, alloc=492.3MB, time=39.17 memory used=1712.8MB, alloc=492.3MB, time=41.50 memory used=1811.2MB, alloc=492.3MB, time=43.43 memory used=1888.8MB, alloc=492.3MB, time=45.32 memory used=1964.9MB, alloc=492.3MB, time=47.31 memory used=2030.2MB, alloc=492.3MB, time=49.18 memory used=2095.5MB, alloc=492.3MB, time=51.06 memory used=2164.0MB, alloc=492.3MB, time=53.02 memory used=2213.1MB, alloc=516.3MB, time=54.63 memory used=2285.2MB, alloc=516.3MB, time=56.07 memory used=2344.2MB, alloc=516.3MB, time=57.28 memory used=2432.7MB, alloc=516.3MB, time=58.96 memory used=2486.5MB, alloc=516.3MB, time=60.35 memory used=2529.3MB, alloc=516.3MB, time=61.96 memory used=2734.1MB, alloc=516.3MB, time=66.20 memory used=2917.0MB, alloc=540.3MB, time=71.30 memory used=3106.4MB, alloc=564.3MB, time=75.91 memory used=3268.6MB, alloc=588.3MB, time=80.57 memory used=3442.4MB, alloc=612.3MB, time=85.39 memory used=3621.9MB, alloc=636.3MB, time=89.91 memory used=3769.7MB, alloc=660.3MB, time=94.68 memory used=3914.5MB, alloc=660.3MB, time=98.52 memory used=4051.8MB, alloc=660.3MB, time=102.45 memory used=4183.8MB, alloc=660.3MB, time=106.19 memory used=4313.2MB, alloc=684.3MB, time=109.46 memory used=4441.1MB, alloc=684.3MB, time=112.50 memory used=4552.8MB, alloc=708.3MB, time=115.22 memory used=4927.1MB, alloc=732.3MB, time=125.55 memory used=5341.3MB, alloc=756.3MB, time=135.03 memory used=5752.1MB, alloc=780.3MB, time=145.89 memory used=6028.5MB, alloc=804.3MB, time=153.87 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428279792 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 2 2 F := [5 z - 12 x y, 9 x y - 2 x - 8 x y, 3 x y - 3 y z - 2 y] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 G := [-4 x + 11 y - 10, 4 x y - 4 x z + 9, -6 x z + 3 x + 5 y z] > Problem := [F,G]; 3 2 2 2 2 Problem := [[5 z - 12 x y, 9 x y - 2 x - 8 x y, 3 x y - 3 y z - 2 y], 3 2 2 [-4 x + 11 y - 10, 4 x y - 4 x z + 9, -6 x z + 3 x + 5 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.7MB, alloc=32.3MB, time=0.87 memory used=47.7MB, alloc=32.3MB, time=1.44 memory used=67.2MB, alloc=56.3MB, time=1.99 memory used=109.2MB, alloc=60.3MB, time=3.12 memory used=149.2MB, alloc=60.3MB, time=4.17 memory used=188.8MB, alloc=84.3MB, time=5.27 memory used=231.1MB, alloc=84.3MB, time=6.41 memory used=290.1MB, alloc=116.3MB, time=8.05 memory used=373.2MB, alloc=116.3MB, time=10.32 memory used=449.7MB, alloc=140.3MB, time=12.39 memory used=530.2MB, alloc=396.3MB, time=14.69 memory used=639.4MB, alloc=420.3MB, time=17.65 memory used=771.6MB, alloc=444.3MB, time=21.44 memory used=910.8MB, alloc=444.3MB, time=25.35 memory used=1050.3MB, alloc=468.3MB, time=29.33 memory used=1179.6MB, alloc=468.3MB, time=33.05 memory used=1324.9MB, alloc=492.3MB, time=37.54 memory used=1436.5MB, alloc=492.3MB, time=40.97 memory used=1548.8MB, alloc=492.3MB, time=44.33 memory used=1648.4MB, alloc=492.3MB, time=47.36 memory used=1767.1MB, alloc=492.3MB, time=50.33 memory used=1860.6MB, alloc=516.3MB, time=52.85 memory used=1950.4MB, alloc=516.3MB, time=55.66 memory used=2033.1MB, alloc=516.3MB, time=58.29 memory used=2122.8MB, alloc=516.3MB, time=60.93 memory used=2195.1MB, alloc=516.3MB, time=63.15 memory used=2273.3MB, alloc=516.3MB, time=65.63 memory used=2346.4MB, alloc=540.3MB, time=68.40 memory used=2428.0MB, alloc=540.3MB, time=71.20 memory used=2514.1MB, alloc=540.3MB, time=74.05 memory used=2608.2MB, alloc=540.3MB, time=77.39 memory used=2687.4MB, alloc=564.3MB, time=80.14 memory used=2766.7MB, alloc=564.3MB, time=82.98 memory used=2851.9MB, alloc=564.3MB, time=85.87 memory used=2937.2MB, alloc=588.3MB, time=89.03 memory used=3019.1MB, alloc=588.3MB, time=92.18 memory used=3110.1MB, alloc=588.3MB, time=95.68 memory used=3177.9MB, alloc=612.3MB, time=98.47 memory used=3262.2MB, alloc=612.3MB, time=101.81 memory used=3356.3MB, alloc=636.3MB, time=105.43 memory used=3437.4MB, alloc=636.3MB, time=108.75 memory used=3690.5MB, alloc=660.3MB, time=117.28 memory used=3949.7MB, alloc=684.3MB, time=126.30 memory used=4233.2MB, alloc=708.3MB, time=135.49 memory used=4543.2MB, alloc=732.3MB, time=144.73 memory used=4832.4MB, alloc=756.3MB, time=154.83 |\^/| 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(); 1428280092 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 F := [-x y + 20 y - 9, -9 y z - x + 7, x y z - 3 x + 3 x z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 3 2 G := [15 x y - 9 y z + 7 z , 8 x z + 8 x, -7 x y - 5 y - 2 y ] > Problem := [F,G]; 2 2 2 2 Problem := [[-x y + 20 y - 9, -9 y z - x + 7, x y z - 3 x + 3 x z], 2 2 2 2 3 2 [15 x y - 9 y z + 7 z , 8 x z + 8 x, -7 x y - 5 y - 2 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.6MB, alloc=32.3MB, time=0.86 memory used=47.6MB, alloc=32.3MB, time=1.39 memory used=67.0MB, alloc=56.3MB, time=1.92 memory used=106.7MB, alloc=60.3MB, time=2.96 memory used=144.1MB, alloc=60.3MB, time=3.96 memory used=180.7MB, alloc=84.3MB, time=5.00 memory used=229.4MB, alloc=84.3MB, time=6.35 memory used=287.3MB, alloc=116.3MB, time=8.04 memory used=368.6MB, alloc=116.3MB, time=10.32 memory used=449.2MB, alloc=140.3MB, time=12.72 memory used=539.0MB, alloc=396.3MB, time=15.33 memory used=646.7MB, alloc=420.3MB, time=18.35 memory used=773.0MB, alloc=420.3MB, time=22.23 memory used=894.7MB, alloc=444.3MB, time=26.07 memory used=1040.7MB, alloc=468.3MB, time=30.22 memory used=1205.4MB, alloc=492.3MB, time=35.03 memory used=1393.7MB, alloc=516.3MB, time=40.76 memory used=1568.3MB, alloc=540.3MB, time=46.44 memory used=1753.6MB, alloc=564.3MB, time=52.38 memory used=1915.1MB, alloc=588.3MB, time=57.70 memory used=2079.0MB, alloc=612.3MB, time=62.96 memory used=2251.6MB, alloc=636.3MB, time=68.22 memory used=2398.4MB, alloc=660.3MB, time=73.21 memory used=2564.7MB, alloc=684.3MB, time=79.01 memory used=2707.9MB, alloc=708.3MB, time=84.08 memory used=2961.2MB, alloc=732.3MB, time=97.43 memory used=3211.4MB, alloc=756.3MB, time=111.90 memory used=3470.1MB, alloc=780.3MB, time=127.55 memory used=3739.9MB, alloc=804.3MB, time=144.71 |\^/| 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(); 1428280392 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 3 F := [-20 x y + 11 y + 2, -x z + 7 y z + 3 x, -3 z + 4 y z + 8 y] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 G := [9 x - 7 x y + 2 y, 7 y z + 8 x y - 7 y z, -6 x y - 9 y] > Problem := [F,G]; 2 2 2 3 Problem := [[-20 x y + 11 y + 2, -x z + 7 y z + 3 x, -3 z + 4 y z + 8 y], 3 2 2 [9 x - 7 x y + 2 y, 7 y z + 8 x y - 7 y z, -6 x 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=4.3MB, alloc=32.3MB, time=0.31 memory used=26.7MB, alloc=32.3MB, time=0.88 memory used=48.0MB, alloc=32.3MB, time=1.43 memory used=68.0MB, alloc=56.3MB, time=1.98 memory used=108.0MB, alloc=60.3MB, time=3.07 memory used=145.8MB, alloc=84.3MB, time=4.08 memory used=205.5MB, alloc=92.3MB, time=5.69 memory used=266.4MB, alloc=92.3MB, time=7.23 memory used=326.4MB, alloc=116.3MB, time=8.86 memory used=409.5MB, alloc=116.3MB, time=11.08 memory used=493.3MB, alloc=140.3MB, time=13.32 memory used=563.4MB, alloc=396.3MB, time=15.24 memory used=675.3MB, alloc=420.3MB, time=18.03 memory used=807.5MB, alloc=420.3MB, time=21.15 memory used=929.4MB, alloc=444.3MB, time=24.28 memory used=1090.4MB, alloc=468.3MB, time=28.36 memory used=1259.0MB, alloc=492.3MB, time=33.26 memory used=1460.6MB, alloc=516.3MB, time=38.16 memory used=1663.3MB, alloc=540.3MB, time=44.86 memory used=1849.7MB, alloc=564.3MB, time=50.87 memory used=2030.3MB, alloc=588.3MB, time=56.75 memory used=2215.0MB, alloc=612.3MB, time=62.77 memory used=2392.3MB, alloc=636.3MB, time=69.08 memory used=2554.0MB, alloc=660.3MB, time=74.47 memory used=2731.9MB, alloc=684.3MB, time=79.90 memory used=2883.8MB, alloc=708.3MB, time=84.60 memory used=3164.3MB, alloc=732.3MB, time=99.21 memory used=3438.4MB, alloc=756.3MB, time=115.06 memory used=3720.9MB, alloc=780.3MB, time=132.28 |\^/| 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(); 1428280692 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 2 F := [7 x + 20 z + 9 y, 5 y + 6 z + 10, -7 x y - 8 x z - 7 y] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 3 2 G := [5 x y - 18 x y z - 20 z , -7 y - 2 z, 9 x - 2 x z + 5 x z] > Problem := [F,G]; 2 2 2 2 2 Problem := [[7 x + 20 z + 9 y, 5 y + 6 z + 10, -7 x y - 8 x z - 7 y], 2 3 2 3 2 [5 x y - 18 x y z - 20 z , -7 y - 2 z, 9 x - 2 x z + 5 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.5MB, alloc=32.3MB, time=0.89 memory used=47.5MB, alloc=32.3MB, time=1.44 memory used=67.4MB, alloc=60.3MB, time=1.96 memory used=108.9MB, alloc=60.3MB, time=3.01 memory used=147.7MB, alloc=60.3MB, time=3.98 memory used=187.6MB, alloc=92.3MB, time=5.05 memory used=251.0MB, alloc=92.3MB, time=6.69 memory used=309.6MB, alloc=116.3MB, time=8.27 memory used=390.2MB, alloc=116.3MB, time=10.49 memory used=457.8MB, alloc=140.3MB, time=12.01 memory used=519.1MB, alloc=396.3MB, time=13.62 memory used=626.8MB, alloc=420.3MB, time=16.47 memory used=760.4MB, alloc=444.3MB, time=19.82 memory used=893.2MB, alloc=444.3MB, time=23.12 memory used=995.7MB, alloc=468.3MB, time=25.89 memory used=1106.2MB, alloc=468.3MB, time=28.83 memory used=1232.4MB, alloc=468.3MB, time=32.63 memory used=1326.0MB, alloc=468.3MB, time=35.25 memory used=1420.1MB, alloc=492.3MB, time=37.71 memory used=1529.4MB, alloc=492.3MB, time=41.06 memory used=1621.2MB, alloc=492.3MB, time=44.06 memory used=1705.2MB, alloc=492.3MB, time=46.71 memory used=1786.8MB, alloc=492.3MB, time=49.54 memory used=1867.1MB, alloc=492.3MB, time=52.27 memory used=1916.9MB, alloc=492.3MB, time=54.03 memory used=1989.9MB, alloc=492.3MB, time=56.68 memory used=2050.7MB, alloc=516.3MB, time=58.94 memory used=2105.3MB, alloc=516.3MB, time=61.16 memory used=2152.8MB, alloc=516.3MB, time=63.15 memory used=2362.0MB, alloc=540.3MB, time=69.56 memory used=2576.8MB, alloc=564.3MB, time=76.32 memory used=2783.2MB, alloc=588.3MB, time=83.51 memory used=2962.9MB, alloc=612.3MB, time=89.31 memory used=3131.9MB, alloc=636.3MB, time=94.74 memory used=3309.7MB, alloc=636.3MB, time=100.80 memory used=3463.7MB, alloc=660.3MB, time=105.53 memory used=3591.8MB, alloc=660.3MB, time=109.95 memory used=3735.2MB, alloc=660.3MB, time=114.92 memory used=3872.3MB, alloc=660.3MB, time=119.85 memory used=3981.4MB, alloc=660.3MB, time=123.74 memory used=4060.6MB, alloc=660.3MB, time=127.26 memory used=4165.1MB, alloc=660.3MB, time=131.37 memory used=4273.8MB, alloc=684.3MB, time=135.94 |\^/| 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(); 1428280992 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 2 3 F := [-13 y z - 16 z - 18 x, -7 x y + 2 x z + 6 z , -2 x y z + 3 y z + 7 y] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 2 G := [-1 - 11 y + z, -9 y z + x + x, -10 x y + 9 y z - 6 x ] > Problem := [F,G]; Problem := [ 2 3 2 2 3 [-13 y z - 16 z - 18 x, -7 x y + 2 x z + 6 z , -2 x y z + 3 y z + 7 y], 2 2 2 2 2 [-1 - 11 y + z, -9 y z + x + x, -10 x y + 9 y z - 6 x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.5MB, alloc=32.3MB, time=0.88 memory used=46.6MB, alloc=32.3MB, time=1.39 memory used=93.5MB, alloc=68.3MB, time=2.66 memory used=140.5MB, alloc=68.3MB, time=3.88 memory used=184.8MB, alloc=92.3MB, time=5.06 memory used=253.8MB, alloc=100.3MB, time=6.87 memory used=318.4MB, alloc=124.3MB, time=8.61 memory used=380.4MB, alloc=124.3MB, time=10.21 memory used=453.6MB, alloc=404.3MB, time=12.10 memory used=571.2MB, alloc=404.3MB, time=15.12 memory used=687.0MB, alloc=428.3MB, time=18.23 memory used=821.6MB, alloc=452.3MB, time=21.85 memory used=953.9MB, alloc=476.3MB, time=25.41 memory used=1081.4MB, alloc=476.3MB, time=28.90 memory used=1195.4MB, alloc=476.3MB, time=31.73 memory used=1317.5MB, alloc=500.3MB, time=35.19 memory used=1419.0MB, alloc=500.3MB, time=37.93 memory used=1525.9MB, alloc=500.3MB, time=41.21 memory used=1621.5MB, alloc=500.3MB, time=43.92 memory used=1710.2MB, alloc=500.3MB, time=46.64 memory used=1801.2MB, alloc=500.3MB, time=49.47 memory used=1884.9MB, alloc=500.3MB, time=52.19 memory used=1952.1MB, alloc=500.3MB, time=54.20 memory used=2018.1MB, alloc=500.3MB, time=56.50 memory used=2080.4MB, alloc=500.3MB, time=58.49 memory used=2145.4MB, alloc=500.3MB, time=60.76 memory used=2198.1MB, alloc=524.3MB, time=62.56 memory used=2258.3MB, alloc=524.3MB, time=64.68 memory used=2342.4MB, alloc=524.3MB, time=66.26 memory used=2411.5MB, alloc=524.3MB, time=67.84 memory used=2504.0MB, alloc=524.3MB, time=70.23 memory used=2580.2MB, alloc=524.3MB, time=71.80 memory used=2645.5MB, alloc=524.3MB, time=73.78 memory used=2690.6MB, alloc=524.3MB, time=75.64 memory used=2730.7MB, alloc=524.3MB, time=77.27 memory used=2922.2MB, alloc=548.3MB, time=81.64 memory used=3109.7MB, alloc=548.3MB, time=85.56 memory used=3353.8MB, alloc=572.3MB, time=91.12 memory used=3502.8MB, alloc=572.3MB, time=98.21 memory used=3711.9MB, alloc=572.3MB, time=101.38 memory used=3917.1MB, alloc=596.3MB, time=107.22 memory used=4113.6MB, alloc=620.3MB, time=112.91 memory used=4281.8MB, alloc=644.3MB, time=117.97 memory used=4453.5MB, alloc=644.3MB, time=122.99 memory used=4652.9MB, alloc=644.3MB, time=128.52 memory used=4828.5MB, alloc=668.3MB, time=158.18 memory used=4992.4MB, alloc=668.3MB, time=159.73 memory used=5227.0MB, alloc=668.3MB, time=164.92 |\^/| 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(); 1428281292 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 3 F := [y z + 2 x y - 5 z, -8 x y + 7 x y - 5 z , -9 x - 10 x y z - 8] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 3 3 2 G := [19 x + 17 x z + 19, -6 z + 6 x, -10 y - 5 y z + 2 x] > Problem := [F,G]; 2 2 2 3 Problem := [[y z + 2 x y - 5 z, -8 x y + 7 x y - 5 z , -9 x - 10 x y z - 8], 3 2 3 3 2 [19 x + 17 x z + 19, -6 z + 6 x, -10 y - 5 y z + 2 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.31 memory used=26.1MB, alloc=32.3MB, time=0.85 memory used=44.6MB, alloc=56.3MB, time=1.29 memory used=84.4MB, alloc=60.3MB, time=2.27 memory used=126.8MB, alloc=68.3MB, time=3.17 memory used=173.2MB, alloc=68.3MB, time=4.25 memory used=215.3MB, alloc=68.3MB, time=5.29 memory used=254.6MB, alloc=68.3MB, time=6.07 memory used=299.0MB, alloc=92.3MB, time=7.10 memory used=366.0MB, alloc=92.3MB, time=8.61 memory used=429.5MB, alloc=92.3MB, time=10.13 memory used=493.3MB, alloc=116.3MB, time=11.76 memory used=577.9MB, alloc=116.6MB, time=12.96 memory used=655.9MB, alloc=116.6MB, time=14.12 memory used=739.7MB, alloc=116.6MB, time=15.60 memory used=813.5MB, alloc=372.6MB, time=17.00 memory used=900.2MB, alloc=372.6MB, time=19.14 memory used=977.7MB, alloc=396.6MB, time=21.29 memory used=1097.2MB, alloc=396.6MB, time=23.93 memory used=1211.7MB, alloc=420.6MB, time=26.59 memory used=1322.5MB, alloc=444.6MB, time=29.27 memory used=1427.9MB, alloc=444.6MB, time=31.80 memory used=1534.2MB, alloc=468.6MB, time=34.06 memory used=1641.9MB, alloc=468.6MB, time=36.57 memory used=1732.9MB, alloc=468.6MB, time=38.62 memory used=1840.8MB, alloc=468.6MB, time=40.25 memory used=1939.0MB, alloc=468.6MB, time=41.95 memory used=2039.0MB, alloc=468.6MB, time=44.03 memory used=2120.2MB, alloc=468.6MB, time=45.77 memory used=2212.0MB, alloc=492.6MB, time=48.38 memory used=2304.1MB, alloc=492.6MB, time=50.74 memory used=2377.7MB, alloc=492.6MB, time=52.56 memory used=2447.6MB, alloc=492.6MB, time=54.46 memory used=2547.3MB, alloc=492.6MB, time=56.05 memory used=2627.6MB, alloc=492.6MB, time=59.32 memory used=2713.4MB, alloc=492.6MB, time=60.03 memory used=2800.3MB, alloc=492.6MB, time=61.68 memory used=2866.0MB, alloc=492.6MB, time=63.45 memory used=2929.3MB, alloc=492.6MB, time=65.19 memory used=2988.2MB, alloc=492.6MB, time=66.59 memory used=3088.8MB, alloc=492.6MB, time=68.55 memory used=3139.6MB, alloc=492.6MB, time=70.03 memory used=3189.4MB, alloc=492.6MB, time=71.52 memory used=3232.5MB, alloc=492.6MB, time=72.66 memory used=3305.3MB, alloc=492.6MB, time=74.31 memory used=3351.4MB, alloc=492.6MB, time=75.92 memory used=3391.0MB, alloc=492.6MB, time=77.24 memory used=3570.4MB, alloc=516.6MB, time=81.08 memory used=3813.5MB, alloc=540.6MB, time=85.71 memory used=4023.7MB, alloc=540.6MB, time=90.01 memory used=4240.6MB, alloc=564.6MB, time=94.62 memory used=4426.4MB, alloc=564.6MB, time=98.54 memory used=4663.2MB, alloc=588.6MB, time=104.04 memory used=4836.9MB, alloc=588.6MB, time=108.51 memory used=5013.6MB, alloc=588.6MB, time=112.72 memory used=5179.7MB, alloc=588.6MB, time=116.88 memory used=5334.1MB, alloc=588.6MB, time=121.34 memory used=5465.1MB, alloc=612.6MB, time=125.43 memory used=5581.8MB, alloc=612.6MB, time=129.02 memory used=5719.1MB, alloc=612.6MB, time=133.55 memory used=5842.0MB, alloc=636.6MB, time=137.48 memory used=5950.6MB, alloc=636.6MB, time=141.16 memory used=6046.2MB, alloc=636.6MB, time=144.43 |\^/| 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(); 1428281592 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 3 2 2 2 F := [7 y + 18 z + x, -10 x z - 3 y z , -8 x y] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 G := [5 x y z - 5 y z - y , -x y - 6 x z, 8 x z + 6 y z - 9 y z] > Problem := [F,G]; 3 3 2 2 2 Problem := [[7 y + 18 z + x, -10 x z - 3 y z , -8 x y], 2 2 2 2 [5 x y z - 5 y z - y , -x y - 6 x z, 8 x z + 6 y z - 9 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.31 memory used=26.1MB, alloc=32.3MB, time=0.84 memory used=47.3MB, alloc=32.3MB, time=1.36 memory used=66.6MB, alloc=56.3MB, time=1.86 memory used=105.8MB, alloc=60.3MB, time=2.90 memory used=142.9MB, alloc=84.3MB, time=3.88 memory used=200.5MB, alloc=92.3MB, time=5.45 memory used=259.1MB, alloc=116.3MB, time=6.96 memory used=339.5MB, alloc=116.3MB, time=9.04 memory used=418.5MB, alloc=140.3MB, time=11.15 memory used=513.7MB, alloc=140.3MB, time=13.68 memory used=593.5MB, alloc=420.3MB, time=15.82 memory used=714.1MB, alloc=420.3MB, time=18.81 memory used=828.0MB, alloc=444.3MB, time=21.58 memory used=960.2MB, alloc=444.3MB, time=24.80 memory used=1088.1MB, alloc=444.3MB, time=27.25 memory used=1234.2MB, alloc=468.3MB, time=31.44 memory used=1393.1MB, alloc=492.3MB, time=35.78 memory used=1565.9MB, alloc=516.3MB, time=40.73 memory used=1748.6MB, alloc=540.3MB, time=46.29 memory used=1938.0MB, alloc=564.3MB, time=52.29 memory used=2145.2MB, alloc=588.3MB, time=58.63 memory used=2333.1MB, alloc=612.3MB, time=64.72 memory used=2521.9MB, alloc=636.3MB, time=70.28 memory used=2728.8MB, alloc=660.3MB, time=79.76 memory used=2938.6MB, alloc=684.3MB, time=91.44 memory used=3157.3MB, alloc=708.3MB, time=104.21 memory used=3388.6MB, alloc=732.3MB, time=118.16 memory used=3633.8MB, alloc=756.3MB, time=133.49 |\^/| 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(); 1428281892 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 F := [13 x - 4 x y + 20, 4 x z + 3 y - z, 9 x y - 6 y z - z ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 3 2 2 2 G := [-18 x z - 14 x y - 12 y, 8 x - 3 x z + 1, 5 x y + 10 x z - 3 z ] > Problem := [F,G]; 2 2 Problem := [[13 x - 4 x y + 20, 4 x z + 3 y - z, 9 x y - 6 y z - z ], 2 2 3 2 2 2 [-18 x z - 14 x y - 12 y, 8 x - 3 x z + 1, 5 x y + 10 x z - 3 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.30 memory used=26.6MB, alloc=32.3MB, time=0.88 memory used=46.7MB, alloc=32.3MB, time=1.39 memory used=65.8MB, alloc=56.3MB, time=1.91 memory used=105.6MB, alloc=60.3MB, time=2.93 memory used=145.4MB, alloc=84.3MB, time=3.96 memory used=206.4MB, alloc=92.3MB, time=5.58 memory used=267.0MB, alloc=92.3MB, time=7.19 memory used=327.2MB, alloc=116.3MB, time=8.85 memory used=410.2MB, alloc=116.3MB, time=11.09 memory used=492.3MB, alloc=140.3MB, time=13.47 memory used=573.2MB, alloc=396.3MB, time=15.86 memory used=676.7MB, alloc=420.3MB, time=18.81 memory used=807.9MB, alloc=444.3MB, time=22.50 memory used=966.1MB, alloc=468.3MB, time=27.14 memory used=1124.5MB, alloc=492.3MB, time=31.85 memory used=1270.8MB, alloc=492.3MB, time=36.05 memory used=1418.0MB, alloc=516.3MB, time=40.95 memory used=1554.0MB, alloc=516.3MB, time=45.23 memory used=1680.1MB, alloc=516.3MB, time=49.42 memory used=1811.3MB, alloc=516.3MB, time=54.08 memory used=1927.3MB, alloc=540.3MB, time=57.80 memory used=2052.2MB, alloc=540.3MB, time=62.16 memory used=2163.3MB, alloc=540.3MB, time=65.99 memory used=2273.9MB, alloc=540.3MB, time=70.13 memory used=2386.3MB, alloc=540.3MB, time=74.42 memory used=2489.9MB, alloc=540.3MB, time=78.77 memory used=2582.0MB, alloc=540.3MB, time=82.54 memory used=2663.9MB, alloc=540.3MB, time=85.96 memory used=2738.6MB, alloc=540.3MB, time=88.89 memory used=2823.3MB, alloc=540.3MB, time=92.64 memory used=2904.3MB, alloc=540.3MB, time=95.93 memory used=2964.3MB, alloc=540.3MB, time=98.08 memory used=3194.8MB, alloc=564.3MB, time=106.77 memory used=3451.4MB, alloc=588.3MB, time=116.60 memory used=3732.8MB, alloc=612.3MB, time=128.45 memory used=3959.9MB, alloc=636.3MB, time=137.39 memory used=4190.3MB, alloc=660.3MB, time=146.77 |\^/| 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(); 1428282192 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 F := [19 y z + 13 x + 12 z, 7 x z + 5 x y - 6 y, -6 x y + 7 y z - 9 x] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 3 2 2 G := [12 y z + x y, -8 x y z + 7 x z - 6 y , -5 x z + 4 y z - 9 x z] > Problem := [F,G]; Problem := [ 2 2 2 2 [19 y z + 13 x + 12 z, 7 x z + 5 x y - 6 y, -6 x y + 7 y z - 9 x], 2 2 3 2 2 [12 y z + x y, -8 x y z + 7 x z - 6 y , -5 x z + 4 y z - 9 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.5MB, alloc=32.3MB, time=0.86 memory used=46.7MB, alloc=32.3MB, time=1.37 memory used=66.7MB, alloc=56.3MB, time=1.91 memory used=107.0MB, alloc=60.3MB, time=2.94 memory used=145.6MB, alloc=84.3MB, time=3.96 memory used=207.4MB, alloc=92.3MB, time=5.60 memory used=268.3MB, alloc=116.3MB, time=7.18 memory used=349.4MB, alloc=116.3MB, time=9.35 memory used=411.2MB, alloc=396.3MB, time=10.85 memory used=522.9MB, alloc=420.3MB, time=13.40 memory used=652.8MB, alloc=444.3MB, time=16.70 memory used=764.6MB, alloc=444.3MB, time=19.60 memory used=896.5MB, alloc=468.3MB, time=22.99 memory used=1025.7MB, alloc=492.3MB, time=26.77 memory used=1135.9MB, alloc=492.3MB, time=29.92 memory used=1238.6MB, alloc=492.3MB, time=32.91 memory used=1342.1MB, alloc=492.3MB, time=36.10 memory used=1443.1MB, alloc=492.3MB, time=39.22 memory used=1530.9MB, alloc=516.3MB, time=42.17 memory used=1609.6MB, alloc=516.3MB, time=44.85 memory used=1676.4MB, alloc=516.3MB, time=47.32 memory used=1747.3MB, alloc=516.3MB, time=49.58 memory used=1802.3MB, alloc=516.3MB, time=51.46 memory used=1863.2MB, alloc=516.3MB, time=53.30 memory used=1924.2MB, alloc=516.3MB, time=55.55 memory used=1972.0MB, alloc=516.3MB, time=57.18 memory used=2167.0MB, alloc=540.3MB, time=63.56 memory used=2385.1MB, alloc=564.3MB, time=70.03 memory used=2546.0MB, alloc=588.3MB, time=74.37 memory used=2779.2MB, alloc=612.3MB, time=79.27 memory used=2934.0MB, alloc=636.3MB, time=83.77 memory used=3087.5MB, alloc=660.3MB, time=89.37 memory used=3248.6MB, alloc=660.3MB, time=94.99 memory used=3414.2MB, alloc=660.3MB, time=100.78 memory used=3544.2MB, alloc=660.3MB, time=105.26 memory used=3641.8MB, alloc=660.3MB, time=109.07 memory used=3750.1MB, alloc=684.3MB, time=112.75 memory used=3880.1MB, alloc=684.3MB, time=118.42 memory used=4003.2MB, alloc=684.3MB, time=123.37 memory used=4107.4MB, alloc=684.3MB, time=127.75 memory used=4461.8MB, alloc=708.3MB, time=137.73 |\^/| 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(); 1428282492 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 F := [-4 x y z - 15 x y - x, 10 x + 4 x y - 9 y z, 10 x z + y z - 10 z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 2 2 G := [11 z - 8 x z - 11 y, -5 x y + 9 x z - 7 y , -4 x y + 9 y z] > Problem := [F,G]; Problem := [ 2 2 [-4 x y z - 15 x y - x, 10 x + 4 x y - 9 y z, 10 x z + y z - 10 z], 3 2 2 2 2 [11 z - 8 x z - 11 y, -5 x y + 9 x z - 7 y , -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=0.29 memory used=26.4MB, alloc=32.3MB, time=0.85 memory used=46.9MB, alloc=32.3MB, time=1.37 memory used=65.3MB, alloc=56.3MB, time=1.87 memory used=103.6MB, alloc=60.3MB, time=2.87 memory used=140.5MB, alloc=84.3MB, time=3.85 memory used=198.8MB, alloc=92.3MB, time=5.44 memory used=255.3MB, alloc=92.3MB, time=6.91 memory used=310.1MB, alloc=116.3MB, time=8.38 memory used=385.1MB, alloc=116.3MB, time=10.42 memory used=461.5MB, alloc=140.3MB, time=12.49 memory used=558.1MB, alloc=164.3MB, time=15.28 memory used=650.0MB, alloc=164.3MB, time=17.90 memory used=736.7MB, alloc=420.3MB, time=20.46 memory used=857.0MB, alloc=444.3MB, time=24.10 memory used=999.2MB, alloc=468.3MB, time=28.28 memory used=1160.3MB, alloc=468.3MB, time=32.98 memory used=1320.3MB, alloc=492.3MB, time=37.86 memory used=1504.3MB, alloc=516.3MB, time=43.24 memory used=1709.7MB, alloc=540.3MB, time=49.24 memory used=1936.1MB, alloc=564.3MB, time=56.01 memory used=2182.9MB, alloc=588.3MB, time=64.21 memory used=2447.8MB, alloc=612.3MB, time=72.15 memory used=2737.0MB, alloc=636.3MB, time=81.71 memory used=3042.5MB, alloc=660.3MB, time=93.30 memory used=3269.9MB, alloc=684.3MB, time=101.09 memory used=3510.4MB, alloc=708.3MB, time=108.84 memory used=3712.7MB, alloc=732.3MB, time=115.32 memory used=3939.6MB, alloc=756.3MB, time=123.84 |\^/| 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(); 1428282792 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 2 2 2 F := [-13 x z + 15 x y z + x z, -6 x - y z - x z, -5 x z + 5 y z - 5 y ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 3 G := [3 x y z - 2 x z - 19 x y, -y z - 10 y + 2 z , 10 y + 9 y + 10 z] > Problem := [F,G]; Problem := [ 2 3 2 2 2 2 [-13 x z + 15 x y z + x z, -6 x - y z - x z, -5 x z + 5 y z - 5 y ], 2 2 2 2 3 [3 x y z - 2 x z - 19 x y, -y z - 10 y + 2 z , 10 y + 9 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=0.30 memory used=26.7MB, alloc=32.3MB, time=0.87 memory used=45.7MB, alloc=56.3MB, time=1.36 memory used=86.1MB, alloc=60.3MB, time=2.39 memory used=127.9MB, alloc=60.3MB, time=3.30 memory used=169.0MB, alloc=60.3MB, time=4.24 memory used=209.2MB, alloc=60.3MB, time=5.25 memory used=243.2MB, alloc=84.3MB, time=6.06 memory used=311.2MB, alloc=92.3MB, time=7.67 memory used=378.5MB, alloc=92.3MB, time=9.04 memory used=436.3MB, alloc=116.3MB, time=10.62 memory used=505.9MB, alloc=372.3MB, time=12.48 memory used=588.1MB, alloc=372.3MB, time=14.54 memory used=675.1MB, alloc=396.3MB, time=16.64 memory used=784.8MB, alloc=420.3MB, time=19.34 memory used=915.3MB, alloc=420.3MB, time=22.28 memory used=1041.1MB, alloc=420.3MB, time=24.57 memory used=1173.1MB, alloc=420.3MB, time=27.18 memory used=1301.9MB, alloc=444.3MB, time=30.59 memory used=1429.4MB, alloc=444.3MB, time=32.64 memory used=1517.9MB, alloc=444.3MB, time=33.73 memory used=1598.6MB, alloc=444.3MB, time=34.32 memory used=1693.2MB, alloc=444.3MB, time=37.60 memory used=1767.6MB, alloc=444.3MB, time=38.09 memory used=1850.1MB, alloc=444.3MB, time=38.73 memory used=1937.1MB, alloc=444.3MB, time=39.83 memory used=2023.3MB, alloc=444.3MB, time=40.57 memory used=2109.3MB, alloc=444.3MB, time=41.59 memory used=2188.7MB, alloc=444.3MB, time=42.23 memory used=2272.4MB, alloc=444.3MB, time=42.86 memory used=2363.1MB, alloc=444.3MB, time=45.97 memory used=2426.6MB, alloc=444.3MB, time=46.39 memory used=2511.7MB, alloc=444.3MB, time=47.12 memory used=2584.7MB, alloc=444.3MB, time=47.83 memory used=2663.1MB, alloc=444.3MB, time=48.37 memory used=2740.3MB, alloc=444.3MB, time=52.79 memory used=2827.4MB, alloc=444.3MB, time=54.39 memory used=2885.2MB, alloc=444.3MB, time=54.80 memory used=2956.3MB, alloc=444.3MB, time=55.28 memory used=3074.5MB, alloc=444.3MB, time=59.18 memory used=3206.0MB, alloc=468.3MB, time=61.85 memory used=3336.9MB, alloc=468.3MB, time=64.48 memory used=3453.1MB, alloc=468.3MB, time=67.80 memory used=3571.3MB, alloc=492.3MB, time=71.17 memory used=3681.6MB, alloc=492.3MB, time=74.46 memory used=3778.7MB, alloc=492.3MB, time=77.24 memory used=3896.4MB, alloc=492.3MB, time=79.60 memory used=3979.8MB, alloc=492.3MB, time=81.75 memory used=4065.6MB, alloc=492.3MB, time=83.84 memory used=4144.8MB, alloc=492.3MB, time=86.28 memory used=4230.9MB, alloc=492.3MB, time=88.92 memory used=4302.9MB, alloc=516.3MB, time=91.20 memory used=4373.2MB, alloc=516.3MB, time=93.39 memory used=4439.8MB, alloc=516.3MB, time=95.38 memory used=4572.7MB, alloc=516.3MB, time=96.92 memory used=4656.4MB, alloc=516.3MB, time=97.60 memory used=4772.6MB, alloc=516.3MB, time=98.44 memory used=4875.6MB, alloc=516.3MB, time=99.67 memory used=4970.9MB, alloc=516.3MB, time=100.40 memory used=5040.7MB, alloc=516.3MB, time=102.38 memory used=5152.0MB, alloc=516.3MB, time=103.92 memory used=5214.6MB, alloc=516.3MB, time=105.50 memory used=5272.1MB, alloc=516.3MB, time=106.98 memory used=5329.3MB, alloc=516.3MB, time=108.95 memory used=5382.5MB, alloc=516.3MB, time=110.97 memory used=5475.6MB, alloc=516.3MB, time=112.51 memory used=5563.3MB, alloc=516.3MB, time=113.31 memory used=5666.6MB, alloc=516.3MB, time=114.24 memory used=5773.3MB, alloc=516.3MB, time=117.10 memory used=5863.1MB, alloc=516.3MB, time=117.84 memory used=5961.8MB, alloc=516.3MB, time=118.80 memory used=6058.2MB, alloc=540.3MB, time=119.66 memory used=6164.0MB, alloc=540.3MB, time=120.46 memory used=6291.9MB, alloc=540.3MB, time=121.69 memory used=6395.8MB, alloc=540.3MB, time=122.50 memory used=6534.4MB, alloc=540.3MB, time=127.14 memory used=6646.6MB, alloc=540.3MB, time=128.01 memory used=6741.5MB, alloc=540.3MB, time=128.74 memory used=6860.2MB, alloc=540.3MB, time=129.46 memory used=6998.3MB, alloc=540.3MB, time=131.24 memory used=7123.8MB, alloc=540.3MB, time=132.77 memory used=7234.3MB, alloc=540.3MB, time=133.66 memory used=7481.8MB, alloc=540.3MB, time=139.49 memory used=7726.4MB, alloc=540.3MB, time=144.88 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428283092 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 3 2 2 2 2 F := [-17 x - y - 9 x, -3 x y + x z - 4 x y, -y z + 6 y z + 3 z ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; G := [ 2 2 2 2 2 2 -7 y z - 7 y z + 16 x , -5 y z + 9 x y - 9 y z, -4 x z + 8 y z - 7 x z ] > Problem := [F,G]; 3 3 2 2 2 2 Problem := [[-17 x - y - 9 x, -3 x y + x z - 4 x y, -y z + 6 y z + 3 z ], [ 2 2 2 2 2 2 -7 y z - 7 y z + 16 x , -5 y z + 9 x y - 9 y z, -4 x z + 8 y z - 7 x z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.31 memory used=26.2MB, alloc=32.3MB, time=0.85 memory used=75.1MB, alloc=68.3MB, time=2.17 memory used=121.9MB, alloc=68.3MB, time=3.35 memory used=166.0MB, alloc=92.3MB, time=4.52 memory used=213.8MB, alloc=92.3MB, time=5.81 memory used=281.3MB, alloc=100.3MB, time=7.66 memory used=347.1MB, alloc=124.3MB, time=9.49 memory used=434.6MB, alloc=124.3MB, time=11.95 memory used=520.6MB, alloc=148.3MB, time=14.46 memory used=613.7MB, alloc=148.3MB, time=17.14 memory used=694.5MB, alloc=428.3MB, time=19.57 memory used=820.4MB, alloc=452.3MB, time=23.36 memory used=973.6MB, alloc=476.3MB, time=27.36 memory used=1112.0MB, alloc=500.3MB, time=29.74 memory used=1240.3MB, alloc=500.3MB, time=31.90 memory used=1372.6MB, alloc=524.3MB, time=34.46 memory used=1499.1MB, alloc=524.3MB, time=37.03 memory used=1608.9MB, alloc=524.3MB, time=39.37 memory used=1715.3MB, alloc=524.3MB, time=41.53 memory used=1825.3MB, alloc=524.3MB, time=43.99 memory used=1916.4MB, alloc=548.3MB, time=45.99 memory used=2016.2MB, alloc=548.3MB, time=48.12 memory used=2104.5MB, alloc=548.3MB, time=50.18 memory used=2188.9MB, alloc=548.3MB, time=52.14 memory used=2268.8MB, alloc=548.3MB, time=54.28 memory used=2334.3MB, alloc=548.3MB, time=55.78 memory used=2415.0MB, alloc=548.3MB, time=57.85 memory used=2474.0MB, alloc=548.3MB, time=59.34 memory used=2702.9MB, alloc=572.3MB, time=64.95 memory used=2929.9MB, alloc=596.3MB, time=69.91 memory used=3159.7MB, alloc=620.3MB, time=75.24 memory used=3373.4MB, alloc=644.3MB, time=81.23 memory used=3585.4MB, alloc=668.3MB, time=86.66 memory used=3759.2MB, alloc=692.3MB, time=90.90 memory used=3921.1MB, alloc=716.3MB, time=94.97 memory used=4118.3MB, alloc=716.3MB, time=100.44 memory used=4273.1MB, alloc=716.3MB, time=104.72 memory used=4458.5MB, alloc=740.3MB, time=110.66 memory used=4632.3MB, alloc=740.3MB, time=116.16 memory used=4765.0MB, alloc=740.3MB, time=120.29 memory used=5162.4MB, alloc=764.3MB, time=130.61 memory used=5580.4MB, alloc=788.3MB, time=141.16 |\^/| 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(); 1428283392 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 2 2 2 F := [-16 x y + 10 x + 7 x z, 5 x y - 6 y z - 8 z, -8 x y - 5 x z + 6 x ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 3 2 2 2 2 G := [20 x z + 10 x z - z , -5 x - 8 x y z + 10 y z, -2 x y + 5 x + 3 y ] > Problem := [F,G]; Problem := [ 2 2 2 2 2 2 2 [-16 x y + 10 x + 7 x z, 5 x y - 6 y z - 8 z, -8 x y - 5 x z + 6 x ], 2 2 2 3 2 2 2 2 [20 x z + 10 x z - z , -5 x - 8 x y z + 10 y z, -2 x y + 5 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=4.4MB, alloc=32.3MB, time=0.18 memory used=26.5MB, alloc=32.3MB, time=0.53 memory used=47.0MB, alloc=56.3MB, time=0.87 memory used=89.0MB, alloc=60.3MB, time=1.50 memory used=130.3MB, alloc=68.3MB, time=2.13 memory used=168.9MB, alloc=92.3MB, time=2.74 memory used=231.4MB, alloc=92.3MB, time=3.70 memory used=291.2MB, alloc=116.3MB, time=4.67 memory used=372.1MB, alloc=116.3MB, time=5.97 memory used=440.7MB, alloc=372.3MB, time=7.08 memory used=520.3MB, alloc=396.3MB, time=8.44 memory used=626.7MB, alloc=420.3MB, time=10.25 memory used=756.5MB, alloc=420.3MB, time=12.31 memory used=876.3MB, alloc=444.3MB, time=14.44 memory used=1020.8MB, alloc=444.3MB, time=16.98 memory used=1166.0MB, alloc=468.3MB, time=19.55 memory used=1323.6MB, alloc=492.3MB, time=22.49 memory used=1456.7MB, alloc=516.3MB, time=24.93 memory used=1589.1MB, alloc=516.3MB, time=27.80 memory used=1689.5MB, alloc=516.3MB, time=29.59 memory used=1793.3MB, alloc=540.3MB, time=31.67 memory used=1880.3MB, alloc=540.3MB, time=33.15 memory used=1988.4MB, alloc=540.3MB, time=35.47 memory used=2049.5MB, alloc=540.3MB, time=36.71 memory used=2105.1MB, alloc=540.3MB, time=37.75 memory used=2158.6MB, alloc=540.3MB, time=38.74 memory used=2234.9MB, alloc=540.3MB, time=40.55 memory used=2295.9MB, alloc=540.3MB, time=41.93 memory used=2344.7MB, alloc=540.3MB, time=42.98 memory used=2394.3MB, alloc=564.3MB, time=44.09 memory used=2458.4MB, alloc=564.3MB, time=46.05 memory used=2687.6MB, alloc=588.3MB, time=50.82 memory used=2909.0MB, alloc=612.3MB, time=55.31 memory used=3100.5MB, alloc=636.3MB, time=59.21 memory used=3301.9MB, alloc=660.3MB, time=63.41 memory used=3485.2MB, alloc=684.3MB, time=67.45 memory used=3618.5MB, alloc=684.3MB, time=69.90 memory used=3772.2MB, alloc=684.3MB, time=73.58 memory used=3926.9MB, alloc=708.3MB, time=77.03 memory used=4046.0MB, alloc=708.3MB, time=79.58 memory used=4168.4MB, alloc=708.3MB, time=82.60 memory used=4298.4MB, alloc=708.3MB, time=86.19 memory used=4415.9MB, alloc=708.3MB, time=89.62 memory used=4501.9MB, alloc=708.3MB, time=92.03 memory used=4873.3MB, alloc=732.3MB, time=100.77 memory used=5241.8MB, alloc=756.3MB, time=107.60 memory used=5648.3MB, alloc=780.3MB, time=116.86 memory used=6034.5MB, alloc=804.3MB, time=125.05 memory used=6376.8MB, alloc=828.3MB, time=133.97 |\^/| 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(); 1428283692 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 2 3 3 2 F := [12 x z - 16 y z + 7 x, 3 y - y z - 3 y z , 6 x + 3 y - 6 x ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 3 2 2 2 G := [-10 y + 19 y z - 5 z, 8 x z + 9 z - 6 x , 5 x - 8 y + 9 z] > Problem := [F,G]; 2 3 2 2 3 3 2 Problem := [[12 x z - 16 y z + 7 x, 3 y - y z - 3 y z , 6 x + 3 y - 6 x ], 3 2 2 3 2 2 2 [-10 y + 19 y z - 5 z, 8 x z + 9 z - 6 x , 5 x - 8 y + 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=25.8MB, alloc=32.3MB, time=0.50 memory used=45.7MB, alloc=32.3MB, time=0.80 memory used=64.6MB, alloc=56.3MB, time=1.09 memory used=106.5MB, alloc=68.3MB, time=1.72 memory used=149.0MB, alloc=68.3MB, time=2.30 memory used=194.0MB, alloc=92.3MB, time=2.88 memory used=259.1MB, alloc=92.3MB, time=3.78 memory used=321.9MB, alloc=116.3MB, time=4.70 memory used=387.4MB, alloc=372.3MB, time=5.68 memory used=474.1MB, alloc=372.3MB, time=6.92 memory used=565.4MB, alloc=396.3MB, time=8.11 memory used=677.0MB, alloc=396.3MB, time=9.49 memory used=797.1MB, alloc=420.3MB, time=11.08 memory used=928.1MB, alloc=420.3MB, time=12.99 memory used=1041.8MB, alloc=444.3MB, time=14.62 memory used=1159.7MB, alloc=444.3MB, time=16.25 memory used=1262.3MB, alloc=444.3MB, time=17.72 memory used=1372.3MB, alloc=468.3MB, time=19.45 memory used=1481.4MB, alloc=468.3MB, time=20.77 memory used=1591.6MB, alloc=468.3MB, time=21.91 memory used=1688.8MB, alloc=468.3MB, time=23.38 memory used=1784.6MB, alloc=492.3MB, time=24.77 memory used=1874.3MB, alloc=492.3MB, time=25.95 memory used=1966.6MB, alloc=492.3MB, time=27.40 memory used=2061.8MB, alloc=492.3MB, time=29.17 memory used=2138.1MB, alloc=492.3MB, time=30.47 memory used=2220.1MB, alloc=492.3MB, time=31.97 memory used=2282.9MB, alloc=516.3MB, time=33.01 memory used=2365.8MB, alloc=516.3MB, time=34.77 memory used=2430.1MB, alloc=516.3MB, time=36.14 memory used=2487.6MB, alloc=516.3MB, time=37.40 memory used=2535.8MB, alloc=516.3MB, time=38.44 memory used=2595.6MB, alloc=516.3MB, time=39.50 memory used=2652.0MB, alloc=516.3MB, time=40.76 memory used=2852.5MB, alloc=540.3MB, time=43.63 memory used=3023.4MB, alloc=564.3MB, time=46.20 memory used=3200.7MB, alloc=588.3MB, time=49.25 memory used=3390.5MB, alloc=588.3MB, time=51.89 memory used=3574.3MB, alloc=612.3MB, time=54.52 memory used=3757.2MB, alloc=612.3MB, time=57.41 memory used=3920.9MB, alloc=636.3MB, time=60.44 memory used=4058.2MB, alloc=636.3MB, time=63.21 memory used=4187.6MB, alloc=636.3MB, time=65.95 memory used=4302.1MB, alloc=636.3MB, time=68.18 memory used=4431.7MB, alloc=660.3MB, time=70.63 memory used=4541.6MB, alloc=660.3MB, time=72.89 memory used=4657.4MB, alloc=660.3MB, time=75.09 memory used=4749.2MB, alloc=660.3MB, time=77.05 memory used=4843.5MB, alloc=660.3MB, time=79.03 memory used=5163.8MB, alloc=684.3MB, time=83.72 memory used=5513.2MB, alloc=708.3MB, time=88.77 memory used=5886.0MB, alloc=732.3MB, time=93.85 memory used=6224.3MB, alloc=756.3MB, time=97.90 memory used=6641.8MB, alloc=780.3MB, time=105.15 memory used=6965.9MB, alloc=804.3MB, time=110.76 memory used=7300.9MB, alloc=828.3MB, time=115.14 memory used=7685.3MB, alloc=852.3MB, time=120.30 memory used=7968.4MB, alloc=876.3MB, time=123.25 memory used=8258.5MB, alloc=900.3MB, time=128.15 memory used=8575.5MB, alloc=924.3MB, time=133.31 memory used=8852.4MB, alloc=948.3MB, time=138.78 memory used=9114.9MB, alloc=972.3MB, time=145.00 |\^/| 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(); 1428283992 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 3 2 3 2 F := [6 y - 17 z + 5 y , 4 x + 4 y + 8 z, -7 x + 3 y z + 7] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 2 2 2 G := [x + 12 x y z - 11 y , 9 x y + 5 x y + 5 y z, 10 x y + 8 y + 8 y] > Problem := [F,G]; 3 3 2 3 2 Problem := [[6 y - 17 z + 5 y , 4 x + 4 y + 8 z, -7 x + 3 y z + 7], 3 2 2 2 2 2 [x + 12 x y z - 11 y , 9 x y + 5 x y + 5 y z, 10 x y + 8 y + 8 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.4MB, alloc=32.3MB, time=0.51 memory used=46.8MB, alloc=32.3MB, time=0.81 memory used=65.2MB, alloc=56.3MB, time=1.11 memory used=104.9MB, alloc=60.3MB, time=1.73 memory used=143.9MB, alloc=84.3MB, time=2.32 memory used=204.3MB, alloc=92.3MB, time=3.27 memory used=264.8MB, alloc=116.3MB, time=4.24 memory used=337.8MB, alloc=116.3MB, time=5.34 memory used=405.8MB, alloc=372.3MB, time=6.39 memory used=486.8MB, alloc=396.3MB, time=7.65 memory used=593.4MB, alloc=420.3MB, time=9.25 memory used=728.8MB, alloc=444.3MB, time=11.21 memory used=871.2MB, alloc=468.3MB, time=13.22 memory used=1013.3MB, alloc=468.3MB, time=15.14 memory used=1161.9MB, alloc=492.3MB, time=17.67 memory used=1273.7MB, alloc=492.3MB, time=19.12 memory used=1396.5MB, alloc=516.3MB, time=21.00 memory used=1504.3MB, alloc=516.3MB, time=22.67 memory used=1591.2MB, alloc=516.3MB, time=23.94 memory used=1685.6MB, alloc=516.3MB, time=25.40 memory used=1757.3MB, alloc=516.3MB, time=26.63 memory used=1830.1MB, alloc=540.3MB, time=27.70 memory used=1918.1MB, alloc=540.3MB, time=29.21 memory used=1985.3MB, alloc=540.3MB, time=30.33 memory used=2053.0MB, alloc=540.3MB, time=31.40 memory used=2113.0MB, alloc=540.3MB, time=32.50 memory used=2181.5MB, alloc=540.3MB, time=33.55 memory used=2253.8MB, alloc=540.3MB, time=34.79 memory used=2304.6MB, alloc=540.3MB, time=35.84 memory used=2361.9MB, alloc=540.3MB, time=36.85 memory used=2418.7MB, alloc=564.3MB, time=37.80 memory used=2636.9MB, alloc=588.3MB, time=40.95 memory used=2855.7MB, alloc=612.3MB, time=44.23 memory used=3015.5MB, alloc=636.3MB, time=46.81 memory used=3183.8MB, alloc=636.3MB, time=49.57 memory used=3352.0MB, alloc=660.3MB, time=52.06 memory used=3490.8MB, alloc=660.3MB, time=55.04 memory used=3630.0MB, alloc=660.3MB, time=57.53 memory used=3843.2MB, alloc=660.3MB, time=60.28 memory used=3959.3MB, alloc=660.3MB, time=62.61 memory used=4099.4MB, alloc=660.3MB, time=64.77 memory used=4232.9MB, alloc=684.3MB, time=67.31 memory used=4409.2MB, alloc=684.3MB, time=70.05 memory used=4522.3MB, alloc=684.3MB, time=72.34 memory used=4593.1MB, alloc=684.3MB, time=74.22 memory used=4728.8MB, alloc=684.3MB, time=76.09 memory used=4837.8MB, alloc=684.3MB, time=78.93 memory used=5195.9MB, alloc=708.3MB, time=85.05 memory used=5565.5MB, alloc=732.3MB, time=91.32 memory used=5902.1MB, alloc=756.3MB, time=98.06 memory used=6200.5MB, alloc=780.3MB, time=104.61 memory used=6554.7MB, alloc=804.3MB, time=117.25 |\^/| 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(); 1428284292 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 3 2 3 2 3 2 F := [18 x + 14 x y + 20 z , -10 y z - 9 z + 8 x , -6 y - 9 x ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 G := [-19 y z - 6 x - 3 z, x z + 2 z - 5, -10 x z + 6 x] > Problem := [F,G]; 3 2 3 2 3 2 3 2 Problem := [[18 x + 14 x y + 20 z , -10 y z - 9 z + 8 x , -6 y - 9 x ], 2 2 [-19 y z - 6 x - 3 z, x z + 2 z - 5, -10 x z + 6 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.2MB, alloc=32.3MB, time=0.48 memory used=46.7MB, alloc=32.3MB, time=0.78 memory used=66.4MB, alloc=60.3MB, time=1.08 memory used=107.1MB, alloc=60.3MB, time=1.66 memory used=148.1MB, alloc=60.3MB, time=2.24 memory used=188.5MB, alloc=92.3MB, time=2.86 memory used=255.0MB, alloc=92.3MB, time=3.80 memory used=316.8MB, alloc=116.3MB, time=4.75 memory used=395.3MB, alloc=372.3MB, time=5.97 memory used=479.9MB, alloc=396.3MB, time=7.26 memory used=588.0MB, alloc=396.3MB, time=8.91 memory used=698.0MB, alloc=420.3MB, time=10.52 memory used=822.5MB, alloc=444.3MB, time=12.60 memory used=958.6MB, alloc=444.3MB, time=14.71 memory used=1085.8MB, alloc=468.3MB, time=16.68 memory used=1182.2MB, alloc=468.3MB, time=18.00 memory used=1287.7MB, alloc=468.3MB, time=19.27 memory used=1399.2MB, alloc=492.3MB, time=21.07 memory used=1513.2MB, alloc=492.3MB, time=22.95 memory used=1601.5MB, alloc=492.3MB, time=24.42 memory used=1702.4MB, alloc=492.3MB, time=26.23 memory used=1799.3MB, alloc=492.3MB, time=28.05 memory used=1880.6MB, alloc=492.3MB, time=29.52 memory used=1961.5MB, alloc=492.3MB, time=31.09 memory used=2032.4MB, alloc=492.3MB, time=32.52 memory used=2089.6MB, alloc=492.3MB, time=33.64 memory used=2155.3MB, alloc=492.3MB, time=35.05 memory used=2203.5MB, alloc=492.3MB, time=36.08 memory used=2260.6MB, alloc=492.3MB, time=37.16 memory used=2327.3MB, alloc=516.3MB, time=38.44 memory used=2385.0MB, alloc=516.3MB, time=39.78 memory used=2433.4MB, alloc=516.3MB, time=40.87 memory used=2641.0MB, alloc=540.3MB, time=44.81 memory used=2867.0MB, alloc=564.3MB, time=49.16 memory used=3080.5MB, alloc=588.3MB, time=52.43 memory used=3303.6MB, alloc=588.3MB, time=55.27 memory used=3491.1MB, alloc=612.3MB, time=58.99 memory used=3685.4MB, alloc=636.3MB, time=62.93 memory used=3860.3MB, alloc=636.3MB, time=66.97 memory used=4026.1MB, alloc=636.3MB, time=70.39 memory used=4193.1MB, alloc=660.3MB, time=74.27 memory used=4319.7MB, alloc=660.3MB, time=77.24 memory used=4435.8MB, alloc=660.3MB, time=79.99 memory used=4563.3MB, alloc=660.3MB, time=83.16 memory used=4655.0MB, alloc=660.3MB, time=85.61 memory used=4743.1MB, alloc=660.3MB, time=88.18 memory used=5067.7MB, alloc=684.3MB, time=95.50 memory used=5420.9MB, alloc=708.3MB, time=102.73 memory used=5784.1MB, alloc=732.3MB, time=110.59 memory used=6165.4MB, alloc=756.3MB, time=119.06 memory used=6539.6MB, alloc=780.3MB, time=125.01 |\^/| 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(); 1428284592 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 F := [-5 y z - 14 y + 19 z, -7 x - 7 z + 10 y, x z + x y z + 3 x y] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 G := [-5 x y - 8 y z - x, -5 y z + 8 y + 5 z, -8 x y z - x - 5 y z] > Problem := [F,G]; 2 2 2 2 Problem := [[-5 y z - 14 y + 19 z, -7 x - 7 z + 10 y, x z + x y z + 3 x y], 2 2 2 2 [-5 x y - 8 y z - x, -5 y z + 8 y + 5 z, -8 x y z - x - 5 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.6MB, alloc=32.3MB, time=0.50 memory used=47.2MB, alloc=32.3MB, time=0.80 memory used=66.4MB, alloc=56.3MB, time=1.09 memory used=104.7MB, alloc=60.3MB, time=1.66 memory used=143.3MB, alloc=84.3MB, time=2.25 memory used=202.9MB, alloc=92.3MB, time=3.19 memory used=263.2MB, alloc=92.3MB, time=4.12 memory used=322.1MB, alloc=116.3MB, time=5.06 memory used=402.9MB, alloc=116.3MB, time=6.31 memory used=480.3MB, alloc=140.3MB, time=7.54 memory used=560.7MB, alloc=396.3MB, time=8.79 memory used=670.7MB, alloc=420.3MB, time=10.45 memory used=792.1MB, alloc=444.3MB, time=12.14 memory used=932.4MB, alloc=468.3MB, time=14.57 memory used=1051.8MB, alloc=492.3MB, time=16.54 memory used=1160.0MB, alloc=492.3MB, time=18.26 memory used=1264.4MB, alloc=492.3MB, time=19.99 memory used=1360.2MB, alloc=492.3MB, time=21.59 memory used=1447.0MB, alloc=492.3MB, time=22.91 memory used=1521.4MB, alloc=492.3MB, time=24.31 memory used=1602.2MB, alloc=492.3MB, time=25.89 memory used=1678.2MB, alloc=516.3MB, time=27.29 memory used=1742.0MB, alloc=516.3MB, time=28.54 memory used=1810.5MB, alloc=516.3MB, time=30.00 memory used=1864.6MB, alloc=516.3MB, time=31.04 memory used=1933.3MB, alloc=516.3MB, time=32.53 memory used=1996.8MB, alloc=516.3MB, time=33.83 memory used=2050.0MB, alloc=516.3MB, time=35.09 memory used=2255.1MB, alloc=540.3MB, time=39.05 memory used=2461.1MB, alloc=564.3MB, time=42.94 memory used=2634.2MB, alloc=588.3MB, time=46.31 memory used=2790.0MB, alloc=612.3MB, time=49.37 memory used=2949.0MB, alloc=636.3MB, time=52.33 memory used=3096.0MB, alloc=636.3MB, time=55.40 memory used=3252.9MB, alloc=636.3MB, time=58.83 memory used=3394.2MB, alloc=660.3MB, time=61.72 memory used=3509.3MB, alloc=660.3MB, time=64.29 memory used=3636.8MB, alloc=660.3MB, time=67.18 memory used=3748.8MB, alloc=660.3MB, time=69.81 memory used=3840.9MB, alloc=660.3MB, time=72.17 memory used=4174.1MB, alloc=684.3MB, time=78.78 memory used=4522.2MB, alloc=708.3MB, time=85.94 memory used=4892.5MB, alloc=732.3MB, time=92.83 memory used=5250.5MB, alloc=756.3MB, time=99.54 memory used=5597.6MB, alloc=780.3MB, time=106.70 memory used=5929.3MB, alloc=804.3MB, time=112.86 memory used=6262.7MB, alloc=828.3MB, time=119.52 memory used=6564.9MB, alloc=852.3MB, time=125.74 |\^/| 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(); 1428284892 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 3 2 3 2 3 F := [14 x y - 7 x z - 13 z , 5 y z - 3 x z - 3 z, 3 x + 2 y z + 10 z ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 G := [13 x z - 19 y - 3 y, 9 x + 9 x y - 8 y z, -4 y - 5 z + 7] > Problem := [F,G]; Problem := [ 2 2 3 2 3 2 3 [14 x y - 7 x z - 13 z , 5 y z - 3 x z - 3 z, 3 x + 2 y z + 10 z ], 2 2 2 2 [13 x z - 19 y - 3 y, 9 x + 9 x y - 8 y z, -4 y - 5 z + 7]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.1MB, alloc=32.3MB, time=0.48 memory used=47.3MB, alloc=32.3MB, time=0.79 memory used=66.6MB, alloc=56.3MB, time=1.10 memory used=106.0MB, alloc=60.3MB, time=1.71 memory used=144.6MB, alloc=60.3MB, time=2.30 memory used=181.3MB, alloc=84.3MB, time=2.87 memory used=229.4MB, alloc=84.3MB, time=3.63 memory used=288.9MB, alloc=92.3MB, time=4.53 memory used=350.2MB, alloc=116.3MB, time=5.42 memory used=432.6MB, alloc=140.3MB, time=6.70 memory used=506.4MB, alloc=396.3MB, time=7.82 memory used=613.1MB, alloc=420.3MB, time=9.44 memory used=743.7MB, alloc=444.3MB, time=11.45 memory used=886.7MB, alloc=444.3MB, time=13.56 memory used=1016.9MB, alloc=468.3MB, time=15.65 memory used=1131.8MB, alloc=468.3MB, time=17.33 memory used=1251.1MB, alloc=468.3MB, time=18.98 memory used=1357.7MB, alloc=492.3MB, time=20.60 memory used=1477.5MB, alloc=492.3MB, time=22.66 memory used=1581.0MB, alloc=492.3MB, time=24.32 memory used=1711.8MB, alloc=516.3MB, time=26.73 memory used=1837.8MB, alloc=516.3MB, time=28.51 memory used=1947.2MB, alloc=516.3MB, time=29.84 memory used=2039.7MB, alloc=516.3MB, time=31.18 memory used=2127.1MB, alloc=516.3MB, time=32.83 memory used=2210.2MB, alloc=516.3MB, time=34.39 memory used=2299.6MB, alloc=516.3MB, time=36.11 memory used=2378.8MB, alloc=540.3MB, time=37.42 memory used=2450.3MB, alloc=540.3MB, time=38.64 memory used=2524.3MB, alloc=540.3MB, time=39.86 memory used=2617.6MB, alloc=540.3MB, time=40.98 memory used=2681.9MB, alloc=540.3MB, time=42.27 memory used=2795.2MB, alloc=540.3MB, time=43.46 memory used=2925.2MB, alloc=540.3MB, time=45.05 memory used=3024.5MB, alloc=540.3MB, time=45.56 memory used=3133.4MB, alloc=540.3MB, time=46.25 memory used=3199.1MB, alloc=540.3MB, time=47.27 memory used=3257.8MB, alloc=540.3MB, time=48.20 memory used=3311.8MB, alloc=540.3MB, time=49.37 memory used=3359.7MB, alloc=540.3MB, time=50.23 memory used=3420.9MB, alloc=540.3MB, time=51.22 memory used=3474.9MB, alloc=540.3MB, time=52.51 memory used=3695.1MB, alloc=564.3MB, time=57.31 memory used=3804.2MB, alloc=564.3MB, time=57.95 memory used=3909.5MB, alloc=564.3MB, time=58.53 memory used=4005.6MB, alloc=564.3MB, time=59.11 memory used=4122.8MB, alloc=564.3MB, time=59.73 memory used=4368.0MB, alloc=564.3MB, time=60.64 memory used=4515.0MB, alloc=564.3MB, time=61.26 memory used=4693.4MB, alloc=564.3MB, time=61.89 memory used=4892.9MB, alloc=564.3MB, time=64.18 memory used=5001.1MB, alloc=564.3MB, time=64.79 memory used=5105.7MB, alloc=564.3MB, time=65.37 memory used=5370.6MB, alloc=588.3MB, time=67.59 memory used=5594.6MB, alloc=612.3MB, time=71.01 memory used=5779.1MB, alloc=612.3MB, time=73.91 memory used=5980.2MB, alloc=636.3MB, time=77.18 memory used=6169.2MB, alloc=660.3MB, time=80.80 memory used=6335.2MB, alloc=684.3MB, time=83.31 memory used=6515.8MB, alloc=684.3MB, time=86.53 memory used=6682.5MB, alloc=708.3MB, time=89.87 memory used=6839.8MB, alloc=708.3MB, time=92.79 memory used=7006.6MB, alloc=708.3MB, time=96.62 memory used=7114.5MB, alloc=708.3MB, time=98.82 memory used=7236.5MB, alloc=732.3MB, time=101.09 memory used=7367.3MB, alloc=732.3MB, time=104.11 memory used=7451.3MB, alloc=732.3MB, time=106.12 memory used=7835.9MB, alloc=756.3MB, time=113.06 memory used=8245.5MB, alloc=780.3MB, time=119.30 memory used=8655.8MB, alloc=804.3MB, time=127.79 memory used=9020.3MB, alloc=828.3MB, time=133.21 memory used=9371.7MB, alloc=852.3MB, time=139.42 memory used=9701.4MB, alloc=876.3MB, time=145.98 |\^/| 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(); 1428285192 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 2 F := [-18 x z + 13 y z, -10 x y + 6 x y - 5 z, 2 x z + 10 y z + 4 z ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 3 2 2 G := [-7 x y - 19 y z - 3, -9 x y + 8 y, -4 x + 3 x z - 8 y ] > Problem := [F,G]; Problem := [ 2 2 2 2 2 [-18 x z + 13 y z, -10 x y + 6 x y - 5 z, 2 x z + 10 y z + 4 z ], 2 2 3 2 2 [-7 x y - 19 y z - 3, -9 x y + 8 y, -4 x + 3 x 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=4.3MB, alloc=32.3MB, time=0.17 memory used=25.9MB, alloc=32.3MB, time=0.47 memory used=47.5MB, alloc=32.3MB, time=0.78 memory used=66.5MB, alloc=56.3MB, time=1.09 memory used=106.5MB, alloc=60.3MB, time=1.72 memory used=144.7MB, alloc=84.3MB, time=2.31 memory used=203.6MB, alloc=84.3MB, time=3.21 memory used=259.7MB, alloc=116.3MB, time=4.11 memory used=339.8MB, alloc=116.3MB, time=5.40 memory used=419.8MB, alloc=140.3MB, time=6.74 memory used=502.4MB, alloc=140.3MB, time=8.09 memory used=589.1MB, alloc=420.3MB, time=9.73 memory used=715.8MB, alloc=444.3MB, time=11.98 memory used=863.9MB, alloc=444.3MB, time=14.75 memory used=1008.8MB, alloc=468.3MB, time=17.55 memory used=1173.1MB, alloc=492.3MB, time=20.74 memory used=1322.9MB, alloc=516.3MB, time=23.37 memory used=1460.8MB, alloc=516.3MB, time=25.93 memory used=1596.5MB, alloc=540.3MB, time=28.70 memory used=1728.5MB, alloc=564.3MB, time=31.38 memory used=1881.4MB, alloc=588.3MB, time=34.46 memory used=2032.5MB, alloc=612.3MB, time=37.56 memory used=2164.2MB, alloc=636.3MB, time=40.29 memory used=2298.8MB, alloc=660.3MB, time=43.03 memory used=2427.4MB, alloc=684.3MB, time=45.72 memory used=2564.1MB, alloc=708.3MB, time=48.56 memory used=2693.1MB, alloc=732.3MB, time=51.28 memory used=2812.6MB, alloc=756.3MB, time=53.88 memory used=2928.0MB, alloc=756.3MB, time=56.41 memory used=3027.1MB, alloc=780.3MB, time=58.62 memory used=3129.0MB, alloc=804.3MB, time=60.95 memory used=3223.3MB, alloc=804.3MB, time=63.16 memory used=3326.3MB, alloc=828.3MB, time=65.44 memory used=3432.1MB, alloc=852.3MB, time=67.91 memory used=3522.1MB, alloc=876.3MB, time=70.14 memory used=3690.6MB, alloc=900.3MB, time=76.07 memory used=4065.9MB, alloc=924.3MB, time=90.09 memory used=4440.9MB, alloc=948.3MB, time=105.10 memory used=4822.6MB, alloc=972.3MB, time=120.80 |\^/| 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(); 1428285492 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 2 2 F := [-2 x z - 18 y z - 15 x, -2 x - 4 x + x y, -10 x z - 7 x y - 8 y z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 3 G := [13 y z + 20 x y + 17, -7 x z + 5 x y - 6 y z, y - 3 x y - 6 y] > Problem := [F,G]; Problem := [ 2 3 2 2 2 [-2 x z - 18 y z - 15 x, -2 x - 4 x + x y, -10 x z - 7 x y - 8 y z], 2 2 2 3 [13 y z + 20 x y + 17, -7 x z + 5 x y - 6 y z, y - 3 x y - 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=0.17 memory used=26.7MB, alloc=32.3MB, time=0.49 memory used=47.9MB, alloc=32.3MB, time=0.80 memory used=67.6MB, alloc=56.3MB, time=1.10 memory used=107.7MB, alloc=60.3MB, time=1.69 memory used=146.8MB, alloc=84.3MB, time=2.26 memory used=209.3MB, alloc=92.3MB, time=3.18 memory used=268.3MB, alloc=116.3MB, time=4.06 memory used=350.8MB, alloc=116.3MB, time=5.29 memory used=418.1MB, alloc=396.3MB, time=6.33 memory used=523.1MB, alloc=396.3MB, time=7.91 memory used=627.2MB, alloc=420.3MB, time=9.53 memory used=754.9MB, alloc=444.3MB, time=11.46 memory used=887.6MB, alloc=468.3MB, time=13.58 memory used=1022.0MB, alloc=468.3MB, time=15.80 memory used=1134.4MB, alloc=492.3MB, time=17.75 memory used=1241.0MB, alloc=492.3MB, time=19.46 memory used=1335.0MB, alloc=492.3MB, time=21.03 memory used=1418.1MB, alloc=492.3MB, time=22.48 memory used=1497.6MB, alloc=516.3MB, time=23.81 memory used=1573.6MB, alloc=516.3MB, time=25.20 memory used=1641.9MB, alloc=516.3MB, time=26.51 memory used=1718.2MB, alloc=516.3MB, time=27.99 memory used=1781.9MB, alloc=516.3MB, time=29.52 memory used=1859.9MB, alloc=540.3MB, time=31.15 memory used=1939.2MB, alloc=540.3MB, time=32.81 memory used=2014.2MB, alloc=564.3MB, time=34.41 memory used=2063.6MB, alloc=564.3MB, time=35.70 memory used=2282.2MB, alloc=588.3MB, time=40.00 memory used=2505.6MB, alloc=612.3MB, time=44.46 memory used=2740.4MB, alloc=636.3MB, time=49.17 memory used=2986.2MB, alloc=660.3MB, time=54.21 memory used=3234.0MB, alloc=684.3MB, time=59.27 memory used=3483.5MB, alloc=708.3MB, time=64.38 memory used=3732.3MB, alloc=732.3MB, time=69.32 memory used=4023.1MB, alloc=756.3MB, time=74.53 memory used=4288.5MB, alloc=780.3MB, time=79.62 memory used=4527.1MB, alloc=804.3MB, time=84.67 memory used=4755.3MB, alloc=828.3MB, time=89.60 memory used=4976.3MB, alloc=852.3MB, time=94.42 memory used=5210.9MB, alloc=876.3MB, time=99.55 memory used=5421.1MB, alloc=900.3MB, time=104.14 memory used=5712.1MB, alloc=924.3MB, time=112.53 memory used=6047.2MB, alloc=948.3MB, time=125.99 |\^/| 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(); 1428285792 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 3 F := [-6 x y z + 12 z - 10 z, 8 x y - 5 x z - 6 y z, 9 x z - 7 y - y] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 3 G := [-2 z - 4 x - 3, 3 x y z - 8 x z - 7 x, -6 z - 2 x y] > Problem := [F,G]; Problem := [ 3 2 2 3 [-6 x y z + 12 z - 10 z, 8 x y - 5 x z - 6 y z, 9 x z - 7 y - y], 3 2 3 [-2 z - 4 x - 3, 3 x y z - 8 x z - 7 x, -6 z - 2 x y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.0MB, alloc=32.3MB, time=0.51 memory used=46.0MB, alloc=32.3MB, time=0.74 memory used=66.3MB, alloc=60.3MB, time=1.05 memory used=107.3MB, alloc=60.3MB, time=1.65 memory used=146.6MB, alloc=60.3MB, time=2.13 memory used=190.4MB, alloc=92.3MB, time=2.78 memory used=256.8MB, alloc=92.3MB, time=3.73 memory used=315.5MB, alloc=92.3MB, time=4.61 memory used=380.1MB, alloc=116.3MB, time=5.61 memory used=457.1MB, alloc=116.3MB, time=6.85 memory used=536.6MB, alloc=116.3MB, time=7.91 memory used=593.9MB, alloc=116.3MB, time=8.46 memory used=634.9MB, alloc=116.3MB, time=8.67 memory used=705.5MB, alloc=140.3MB, time=9.52 memory used=771.1MB, alloc=396.3MB, time=10.41 memory used=874.9MB, alloc=396.3MB, time=11.62 memory used=977.3MB, alloc=396.3MB, time=13.19 memory used=1080.9MB, alloc=420.3MB, time=14.62 memory used=1206.0MB, alloc=420.3MB, time=16.15 memory used=1330.9MB, alloc=444.3MB, time=18.13 memory used=1474.3MB, alloc=468.3MB, time=20.48 memory used=1596.7MB, alloc=468.3MB, time=22.54 memory used=1706.1MB, alloc=468.3MB, time=24.01 memory used=1818.8MB, alloc=492.3MB, time=25.61 memory used=1946.7MB, alloc=492.3MB, time=27.34 memory used=2076.6MB, alloc=492.3MB, time=29.06 memory used=2189.5MB, alloc=492.3MB, time=30.77 memory used=2302.2MB, alloc=492.3MB, time=32.38 memory used=2401.2MB, alloc=492.3MB, time=33.92 memory used=2495.8MB, alloc=492.3MB, time=35.44 memory used=2589.3MB, alloc=516.3MB, time=36.93 memory used=2664.9MB, alloc=516.3MB, time=38.19 memory used=2762.5MB, alloc=516.3MB, time=39.71 memory used=2849.7MB, alloc=516.3MB, time=41.32 memory used=2936.6MB, alloc=516.3MB, time=42.69 memory used=3005.9MB, alloc=516.3MB, time=43.83 memory used=3065.2MB, alloc=540.3MB, time=44.79 memory used=3130.0MB, alloc=540.3MB, time=45.99 memory used=3185.9MB, alloc=540.3MB, time=47.25 memory used=3235.7MB, alloc=540.3MB, time=48.26 memory used=3306.5MB, alloc=540.3MB, time=49.88 memory used=3365.9MB, alloc=540.3MB, time=51.14 memory used=3420.8MB, alloc=540.3MB, time=52.41 memory used=3466.1MB, alloc=540.3MB, time=53.44 memory used=3684.6MB, alloc=564.3MB, time=57.01 memory used=3850.5MB, alloc=564.3MB, time=58.53 memory used=4068.8MB, alloc=588.3MB, time=61.97 memory used=4295.4MB, alloc=612.3MB, time=64.98 memory used=4517.5MB, alloc=612.3MB, time=68.09 memory used=4706.9MB, alloc=636.3MB, time=71.63 memory used=4868.9MB, alloc=636.3MB, time=74.58 memory used=5048.2MB, alloc=636.3MB, time=76.20 memory used=5267.7MB, alloc=660.3MB, time=79.25 memory used=5455.9MB, alloc=660.3MB, time=82.13 memory used=5627.4MB, alloc=660.3MB, time=84.92 memory used=5786.0MB, alloc=660.3MB, time=88.03 memory used=5951.1MB, alloc=684.3MB, time=91.57 memory used=6053.9MB, alloc=684.3MB, time=93.65 memory used=6205.3MB, alloc=684.3MB, time=97.22 memory used=6352.0MB, alloc=684.3MB, time=101.20 memory used=6476.8MB, alloc=708.3MB, time=104.54 memory used=6575.5MB, alloc=708.3MB, time=107.09 memory used=6938.4MB, alloc=732.3MB, time=115.84 memory used=7330.3MB, alloc=756.3MB, time=123.22 memory used=7580.5MB, alloc=780.3MB, time=126.49 memory used=8008.1MB, alloc=804.3MB, time=132.05 memory used=8246.4MB, alloc=828.3MB, time=134.64 memory used=8479.1MB, alloc=852.3MB, time=136.85 memory used=8736.9MB, alloc=852.3MB, time=139.33 memory used=8973.1MB, alloc=852.3MB, time=142.22 memory used=9252.7MB, alloc=852.3MB, time=144.86 |\^/| 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(); 1428286092 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 F := [12 x y + 8 y z - 1, -10 x y + 2 x + z, -10 x y + 4 x y z + 7 y z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 2 2 G := [-14 x z + 13 x y - 14 y z, -x z + x - 3 x y, 7 x z - 6 x z] > Problem := [F,G]; Problem := [ 2 2 2 2 [12 x y + 8 y z - 1, -10 x y + 2 x + z, -10 x y + 4 x y z + 7 y z], 2 2 2 2 2 2 [-14 x z + 13 x y - 14 y z, -x z + x - 3 x y, 7 x z - 6 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.4MB, alloc=32.3MB, time=0.48 memory used=47.0MB, alloc=32.3MB, time=0.79 memory used=65.9MB, alloc=56.3MB, time=1.09 memory used=104.3MB, alloc=60.3MB, time=1.68 memory used=142.2MB, alloc=84.3MB, time=2.27 memory used=203.3MB, alloc=92.3MB, time=3.25 memory used=269.0MB, alloc=116.3MB, time=4.19 memory used=352.1MB, alloc=116.3MB, time=5.56 memory used=431.6MB, alloc=396.3MB, time=6.90 memory used=539.4MB, alloc=396.3MB, time=8.68 memory used=643.6MB, alloc=420.3MB, time=10.53 memory used=770.8MB, alloc=444.3MB, time=12.65 memory used=892.9MB, alloc=468.3MB, time=14.65 memory used=1018.2MB, alloc=468.3MB, time=16.60 memory used=1169.1MB, alloc=492.3MB, time=19.11 memory used=1308.2MB, alloc=492.3MB, time=21.66 memory used=1416.8MB, alloc=516.3MB, time=23.56 memory used=1503.2MB, alloc=516.3MB, time=25.11 memory used=1588.7MB, alloc=516.3MB, time=26.50 memory used=1699.4MB, alloc=516.3MB, time=28.70 memory used=1776.0MB, alloc=516.3MB, time=30.15 memory used=1865.4MB, alloc=516.3MB, time=32.19 memory used=1931.3MB, alloc=540.3MB, time=33.49 memory used=2003.9MB, alloc=540.3MB, time=35.09 memory used=2087.1MB, alloc=540.3MB, time=37.08 memory used=2143.9MB, alloc=540.3MB, time=38.53 memory used=2208.7MB, alloc=540.3MB, time=40.20 memory used=2268.8MB, alloc=540.3MB, time=41.89 memory used=2483.1MB, alloc=564.3MB, time=45.55 memory used=2693.5MB, alloc=588.3MB, time=49.53 memory used=2915.3MB, alloc=612.3MB, time=54.08 memory used=3095.5MB, alloc=636.3MB, time=57.72 memory used=3270.5MB, alloc=660.3MB, time=61.80 memory used=3420.4MB, alloc=660.3MB, time=64.31 memory used=3567.1MB, alloc=684.3MB, time=67.98 memory used=3718.0MB, alloc=684.3MB, time=71.67 memory used=3848.4MB, alloc=684.3MB, time=74.85 memory used=3956.1MB, alloc=684.3MB, time=77.58 memory used=4053.0MB, alloc=684.3MB, time=79.80 memory used=4131.3MB, alloc=684.3MB, time=81.66 memory used=4477.8MB, alloc=708.3MB, time=89.89 memory used=4833.1MB, alloc=732.3MB, time=97.45 memory used=5207.6MB, alloc=756.3MB, time=107.23 memory used=5608.0MB, alloc=780.3MB, time=117.04 memory used=6011.5MB, alloc=804.3MB, time=127.07 memory used=6390.6MB, alloc=828.3MB, time=136.97 |\^/| 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(); 1428286392 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 2 2 F := [-13 x y - 5 x y z - 4 y z, 3 x + 2 y z - 10 z, x y - 2 x ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 2 2 G := [2 x y + 13 y + 14 x, -8 x y - 5 x z + 3 z, -x z + 5 y z + 9 y z] > Problem := [F,G]; 2 3 2 2 2 Problem := [[-13 x y - 5 x y z - 4 y z, 3 x + 2 y z - 10 z, x y - 2 x ], 2 3 2 2 2 [2 x y + 13 y + 14 x, -8 x y - 5 x z + 3 z, -x z + 5 y z + 9 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.3MB, alloc=32.3MB, time=0.48 memory used=47.5MB, alloc=32.3MB, time=0.77 memory used=68.4MB, alloc=32.3MB, time=1.08 memory used=87.5MB, alloc=56.3MB, time=1.38 memory used=127.7MB, alloc=60.3MB, time=1.99 memory used=167.0MB, alloc=84.3MB, time=2.57 memory used=211.9MB, alloc=84.3MB, time=3.27 memory used=272.4MB, alloc=92.3MB, time=4.25 memory used=332.6MB, alloc=116.3MB, time=5.15 memory used=405.9MB, alloc=116.3MB, time=6.21 memory used=479.7MB, alloc=372.3MB, time=7.31 memory used=566.0MB, alloc=396.3MB, time=8.69 memory used=682.1MB, alloc=420.3MB, time=10.04 memory used=812.0MB, alloc=420.3MB, time=12.18 memory used=920.5MB, alloc=444.3MB, time=14.25 memory used=1045.4MB, alloc=468.3MB, time=16.54 memory used=1189.9MB, alloc=492.3MB, time=19.07 memory used=1367.9MB, alloc=516.3MB, time=21.68 memory used=1555.7MB, alloc=540.3MB, time=24.78 memory used=1755.8MB, alloc=564.3MB, time=28.19 memory used=1969.4MB, alloc=588.3MB, time=31.87 memory used=2170.5MB, alloc=612.3MB, time=35.66 memory used=2380.3MB, alloc=636.3MB, time=42.05 memory used=2585.8MB, alloc=660.3MB, time=49.24 memory used=2801.8MB, alloc=684.3MB, time=57.16 memory used=3030.7MB, alloc=708.3MB, time=65.81 memory used=3273.5MB, alloc=732.3MB, time=75.34 memory used=3530.7MB, alloc=756.3MB, time=85.55 memory used=3797.9MB, alloc=780.3MB, time=97.06 memory used=4086.7MB, alloc=804.3MB, time=109.59 memory used=4399.5MB, alloc=828.3MB, time=123.18 memory used=4736.1MB, alloc=852.3MB, time=137.80 |\^/| 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(); 1428286692 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; F := 2 2 2 2 2 2 [-16 x z - 19 z + 6 z, -4 x y - 7 x z + 3 y z, 5 x y + 4 y z + 8 x z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 G := [2 z + 2 x z + 12 z , 10 x y + 5 x y z - 7 z, -9 x y z + 2 x y + 2 x] > Problem := [F,G]; Problem := [ 2 2 2 2 2 2 [-16 x z - 19 z + 6 z, -4 x y - 7 x z + 3 y z, 5 x y + 4 y z + 8 x z] 3 2 2 , [2 z + 2 x z + 12 z , 10 x y + 5 x y z - 7 z, -9 x y z + 2 x y + 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=26.3MB, alloc=32.3MB, time=0.48 memory used=47.2MB, alloc=32.3MB, time=0.79 memory used=92.3MB, alloc=68.3MB, time=1.48 memory used=136.7MB, alloc=68.3MB, time=2.15 memory used=180.8MB, alloc=92.3MB, time=2.87 memory used=247.5MB, alloc=100.3MB, time=3.93 memory used=313.0MB, alloc=124.3MB, time=4.97 memory used=400.9MB, alloc=124.3MB, time=6.37 memory used=486.3MB, alloc=148.3MB, time=7.78 memory used=568.6MB, alloc=148.3MB, time=9.15 memory used=640.5MB, alloc=428.3MB, time=10.46 memory used=770.4MB, alloc=452.3MB, time=12.64 memory used=927.1MB, alloc=476.3MB, time=15.49 memory used=1075.1MB, alloc=500.3MB, time=18.21 memory used=1197.4MB, alloc=500.3MB, time=20.37 memory used=1327.6MB, alloc=500.3MB, time=22.91 memory used=1434.7MB, alloc=524.3MB, time=24.98 memory used=1541.1MB, alloc=524.3MB, time=27.02 memory used=1649.4MB, alloc=524.3MB, time=29.11 memory used=1748.3MB, alloc=524.3MB, time=31.18 memory used=1851.4MB, alloc=524.3MB, time=33.52 memory used=1925.1MB, alloc=524.3MB, time=35.20 memory used=2001.1MB, alloc=524.3MB, time=37.03 memory used=2095.4MB, alloc=524.3MB, time=39.23 memory used=2157.5MB, alloc=524.3MB, time=40.68 memory used=2240.3MB, alloc=524.3MB, time=42.80 memory used=2324.5MB, alloc=524.3MB, time=45.10 memory used=2400.2MB, alloc=548.3MB, time=47.23 memory used=2632.7MB, alloc=572.3MB, time=53.07 memory used=2885.5MB, alloc=596.3MB, time=59.17 memory used=3094.5MB, alloc=620.3MB, time=64.28 memory used=3305.2MB, alloc=644.3MB, time=69.32 memory used=3489.2MB, alloc=668.3MB, time=73.84 memory used=3698.1MB, alloc=692.3MB, time=79.30 memory used=3860.1MB, alloc=692.3MB, time=83.57 memory used=4011.7MB, alloc=692.3MB, time=87.91 memory used=4136.4MB, alloc=692.3MB, time=91.36 memory used=4260.9MB, alloc=716.3MB, time=95.02 memory used=4400.1MB, alloc=716.3MB, time=99.21 memory used=4498.7MB, alloc=716.3MB, time=102.12 memory used=4592.7MB, alloc=716.3MB, time=104.91 memory used=4954.5MB, alloc=740.3MB, time=114.15 memory used=5330.7MB, alloc=764.3MB, time=124.40 memory used=5722.6MB, alloc=788.3MB, time=135.23 |\^/| 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(); 1428286992 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 2 F := [16 x z + 12 x y , -6 x z + 5 x z + 8 z , 2 x y z - 3 x z - 6 x] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 3 2 2 2 G := [11 x - 10 x z + 18 y , -6 x y - 6 x y - x z, -8 x y - 9 x y z - 6 x] > Problem := [F,G]; Problem := [ 2 2 2 2 2 [16 x z + 12 x y , -6 x z + 5 x z + 8 z , 2 x y z - 3 x z - 6 x], 3 2 3 2 2 2 [11 x - 10 x z + 18 y , -6 x y - 6 x y - x z, -8 x y - 9 x y z - 6 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.4MB, alloc=32.3MB, time=0.51 memory used=47.3MB, alloc=32.3MB, time=0.80 memory used=66.5MB, alloc=56.3MB, time=1.11 memory used=106.4MB, alloc=60.3MB, time=1.74 memory used=144.0MB, alloc=84.3MB, time=2.35 memory used=203.6MB, alloc=92.3MB, time=3.29 memory used=262.5MB, alloc=116.3MB, time=4.25 memory used=342.2MB, alloc=116.3MB, time=5.53 memory used=417.8MB, alloc=140.3MB, time=6.78 memory used=491.5MB, alloc=140.3MB, time=8.05 memory used=566.5MB, alloc=396.3MB, time=9.30 memory used=668.1MB, alloc=420.3MB, time=11.05 memory used=799.2MB, alloc=444.3MB, time=13.18 memory used=936.8MB, alloc=468.3MB, time=15.52 memory used=1075.3MB, alloc=492.3MB, time=18.03 memory used=1192.6MB, alloc=492.3MB, time=20.27 memory used=1310.3MB, alloc=492.3MB, time=22.58 memory used=1426.8MB, alloc=516.3MB, time=24.93 memory used=1538.5MB, alloc=516.3MB, time=27.29 memory used=1656.7MB, alloc=516.3MB, time=29.94 memory used=1757.3MB, alloc=516.3MB, time=32.28 memory used=1840.1MB, alloc=540.3MB, time=34.29 memory used=1904.5MB, alloc=540.3MB, time=35.70 memory used=1971.3MB, alloc=540.3MB, time=37.30 memory used=2044.8MB, alloc=540.3MB, time=39.03 memory used=2109.9MB, alloc=540.3MB, time=40.81 memory used=2177.6MB, alloc=540.3MB, time=42.69 memory used=2397.6MB, alloc=564.3MB, time=47.74 memory used=2638.6MB, alloc=588.3MB, time=53.56 memory used=2894.4MB, alloc=612.3MB, time=59.77 memory used=3088.7MB, alloc=636.3MB, time=64.24 memory used=3261.2MB, alloc=660.3MB, time=68.17 memory used=3436.7MB, alloc=684.3MB, time=72.47 memory used=3596.0MB, alloc=708.3MB, time=76.22 memory used=3742.7MB, alloc=732.3MB, time=79.86 memory used=3865.0MB, alloc=732.3MB, time=82.90 memory used=3991.7MB, alloc=732.3MB, time=86.09 memory used=4076.4MB, alloc=732.3MB, time=88.36 memory used=4172.5MB, alloc=732.3MB, time=91.07 memory used=4251.9MB, alloc=756.3MB, time=93.33 memory used=4626.7MB, alloc=780.3MB, time=101.95 memory used=5035.5MB, alloc=804.3MB, time=112.15 memory used=5473.9MB, alloc=828.3MB, time=123.44 memory used=5847.8MB, alloc=852.3MB, time=132.50 memory used=6208.8MB, alloc=876.3MB, time=141.34 memory used=6552.0MB, alloc=900.3MB, time=150.50 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428287292 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 3 2 3 F := [-12 x z - 11 x z + 18 z, 5 x z + 9 y + 3 y , -2 x - 6 y z + 8 z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 3 2 G := [18 x z + 18 x z + 16 y z, -5 x z - 4 z + 9 y , -2 x y + 5 x z] > Problem := [F,G]; Problem := [ 2 2 3 2 3 [-12 x z - 11 x z + 18 z, 5 x z + 9 y + 3 y , -2 x - 6 y z + 8 z], 2 2 2 2 3 2 [18 x z + 18 x z + 16 y z, -5 x z - 4 z + 9 y , -2 x y + 5 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.6MB, alloc=32.3MB, time=0.50 memory used=47.0MB, alloc=32.3MB, time=0.80 memory used=65.8MB, alloc=56.3MB, time=1.08 memory used=106.2MB, alloc=60.3MB, time=1.66 memory used=145.2MB, alloc=84.3MB, time=2.25 memory used=207.3MB, alloc=92.3MB, time=3.15 memory used=268.0MB, alloc=116.3MB, time=4.08 memory used=346.6MB, alloc=140.3MB, time=5.30 memory used=432.3MB, alloc=396.3MB, time=6.74 memory used=536.4MB, alloc=420.3MB, time=8.40 memory used=660.1MB, alloc=444.3MB, time=10.58 memory used=810.1MB, alloc=468.3MB, time=13.05 memory used=968.9MB, alloc=492.3MB, time=15.91 memory used=1120.2MB, alloc=492.3MB, time=18.70 memory used=1254.3MB, alloc=492.3MB, time=21.32 memory used=1380.0MB, alloc=516.3MB, time=23.87 memory used=1520.8MB, alloc=516.3MB, time=26.85 memory used=1630.8MB, alloc=516.3MB, time=28.96 memory used=1744.0MB, alloc=516.3MB, time=31.24 memory used=1834.1MB, alloc=516.3MB, time=33.19 memory used=1942.4MB, alloc=540.3MB, time=35.83 memory used=2018.4MB, alloc=540.3MB, time=37.59 memory used=2105.4MB, alloc=540.3MB, time=39.47 memory used=2180.9MB, alloc=540.3MB, time=41.40 memory used=2258.1MB, alloc=540.3MB, time=43.41 memory used=2335.2MB, alloc=540.3MB, time=45.18 memory used=2403.4MB, alloc=540.3MB, time=46.86 memory used=2474.4MB, alloc=540.3MB, time=48.67 memory used=2544.3MB, alloc=540.3MB, time=50.53 memory used=2608.2MB, alloc=540.3MB, time=52.21 memory used=2647.4MB, alloc=564.3MB, time=53.21 memory used=2888.2MB, alloc=588.3MB, time=58.82 memory used=3117.5MB, alloc=612.3MB, time=63.94 memory used=3373.2MB, alloc=636.3MB, time=69.51 memory used=3601.2MB, alloc=660.3MB, time=74.56 memory used=3818.9MB, alloc=684.3MB, time=80.25 memory used=3995.5MB, alloc=708.3MB, time=84.07 memory used=4196.3MB, alloc=732.3MB, time=89.93 memory used=4398.0MB, alloc=756.3MB, time=95.74 memory used=4533.6MB, alloc=756.3MB, time=98.66 memory used=4717.4MB, alloc=780.3MB, time=103.41 memory used=4840.0MB, alloc=780.3MB, time=105.97 memory used=4935.3MB, alloc=804.3MB, time=108.45 memory used=5080.5MB, alloc=804.3MB, time=112.87 memory used=5534.8MB, alloc=828.3MB, time=124.38 memory used=5974.3MB, alloc=852.3MB, time=133.94 |\^/| 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(); 1428287592 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; F := [ 2 2 3 3 2 10 x y + 13 x z - 12 y z, -4 x - 9 y - 9 x z, 7 x y + 4 x y z + 5 x y] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 2 2 2 G := [4 x + 7 x y + 6 y , -5 x y + 9 x z, 3 y z + 8 x - 3 y z] > Problem := [F,G]; Problem := [[ 2 2 3 3 2 10 x y + 13 x z - 12 y z, -4 x - 9 y - 9 x z, 7 x y + 4 x y z + 5 x y] 3 2 2 2 2 2 , [4 x + 7 x y + 6 y , -5 x y + 9 x z, 3 y z + 8 x - 3 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.8MB, alloc=32.3MB, time=0.51 memory used=47.0MB, alloc=32.3MB, time=0.81 memory used=65.6MB, alloc=56.3MB, time=1.10 memory used=105.4MB, alloc=60.3MB, time=1.70 memory used=142.9MB, alloc=60.3MB, time=2.25 memory used=182.2MB, alloc=84.3MB, time=2.84 memory used=213.4MB, alloc=84.3MB, time=3.31 memory used=277.3MB, alloc=92.3MB, time=4.29 memory used=341.1MB, alloc=116.3MB, time=5.29 memory used=416.4MB, alloc=116.3MB, time=6.42 memory used=491.5MB, alloc=396.3MB, time=7.64 memory used=602.4MB, alloc=396.3MB, time=9.39 memory used=712.5MB, alloc=420.3MB, time=11.07 memory used=841.8MB, alloc=444.3MB, time=13.17 memory used=985.7MB, alloc=468.3MB, time=15.56 memory used=1116.7MB, alloc=468.3MB, time=17.65 memory used=1238.2MB, alloc=492.3MB, time=19.56 memory used=1347.1MB, alloc=492.3MB, time=21.24 memory used=1444.6MB, alloc=492.3MB, time=23.00 memory used=1540.4MB, alloc=516.3MB, time=24.37 memory used=1656.3MB, alloc=516.3MB, time=26.49 memory used=1746.8MB, alloc=516.3MB, time=28.25 memory used=1808.0MB, alloc=516.3MB, time=29.28 memory used=1871.1MB, alloc=516.3MB, time=30.33 memory used=1959.6MB, alloc=516.3MB, time=32.15 memory used=2032.8MB, alloc=516.3MB, time=33.34 memory used=2116.9MB, alloc=540.3MB, time=35.15 memory used=2188.9MB, alloc=540.3MB, time=36.78 memory used=2239.5MB, alloc=540.3MB, time=37.86 memory used=2294.0MB, alloc=540.3MB, time=38.98 memory used=2342.8MB, alloc=540.3MB, time=39.92 memory used=2571.1MB, alloc=564.3MB, time=44.21 memory used=2762.9MB, alloc=588.3MB, time=47.41 memory used=2930.8MB, alloc=612.3MB, time=50.31 memory used=3170.5MB, alloc=636.3MB, time=54.41 memory used=3323.7MB, alloc=636.3MB, time=56.91 memory used=3494.0MB, alloc=660.3MB, time=60.25 memory used=3651.4MB, alloc=660.3MB, time=63.46 memory used=3818.2MB, alloc=684.3MB, time=66.60 memory used=3953.4MB, alloc=684.3MB, time=69.27 memory used=4075.2MB, alloc=684.3MB, time=71.40 memory used=4201.0MB, alloc=684.3MB, time=74.42 memory used=4334.2MB, alloc=684.3MB, time=77.31 memory used=4454.0MB, alloc=684.3MB, time=79.30 memory used=4518.9MB, alloc=684.3MB, time=80.95 memory used=4587.3MB, alloc=684.3MB, time=82.63 memory used=4933.0MB, alloc=708.3MB, time=89.48 memory used=5298.9MB, alloc=732.3MB, time=97.72 memory used=5681.8MB, alloc=756.3MB, time=105.65 memory used=6111.8MB, alloc=780.3MB, time=113.61 memory used=6518.5MB, alloc=804.3MB, time=122.83 memory used=6837.4MB, alloc=828.3MB, time=128.54 memory used=7030.2MB, alloc=852.3MB, time=137.14 memory used=7262.7MB, alloc=876.3MB, time=145.79 |\^/| 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(); 1428287892 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 F := [-18 x y - 19 y z, 5 y z - 3 x z - 6 x, 9 x + 3 x y + 2 x y z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 3 2 2 2 G := [-10 y + 5 z + 16 x y, 2 x y + 10 x - 10 y, -8 x y + 5 y + 9 y] > Problem := [F,G]; 2 3 2 Problem := [[-18 x y - 19 y z, 5 y z - 3 x z - 6 x, 9 x + 3 x y + 2 x y z], 3 3 2 2 2 [-10 y + 5 z + 16 x y, 2 x y + 10 x - 10 y, -8 x y + 5 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=4.3MB, alloc=32.3MB, time=0.18 memory used=26.4MB, alloc=32.3MB, time=0.49 memory used=47.8MB, alloc=32.3MB, time=0.81 memory used=67.8MB, alloc=56.3MB, time=1.13 memory used=108.8MB, alloc=60.3MB, time=1.77 memory used=148.2MB, alloc=84.3MB, time=2.38 memory used=209.3MB, alloc=92.3MB, time=3.34 memory used=270.6MB, alloc=116.3MB, time=4.28 memory used=341.5MB, alloc=116.3MB, time=5.32 memory used=415.5MB, alloc=396.3MB, time=6.46 memory used=525.7MB, alloc=396.3MB, time=8.18 memory used=635.8MB, alloc=420.3MB, time=9.84 memory used=771.2MB, alloc=444.3MB, time=11.90 memory used=884.1MB, alloc=444.3MB, time=13.68 memory used=1022.7MB, alloc=468.3MB, time=15.94 memory used=1146.0MB, alloc=468.3MB, time=17.92 memory used=1260.7MB, alloc=492.3MB, time=19.86 memory used=1369.3MB, alloc=492.3MB, time=21.66 memory used=1473.0MB, alloc=492.3MB, time=23.43 memory used=1610.3MB, alloc=516.3MB, time=28.65 memory used=1722.9MB, alloc=516.3MB, time=30.10 memory used=1810.6MB, alloc=516.3MB, time=31.31 memory used=1911.0MB, alloc=516.3MB, time=33.16 memory used=1988.1MB, alloc=516.3MB, time=34.50 memory used=2060.0MB, alloc=516.3MB, time=35.83 memory used=2139.6MB, alloc=540.3MB, time=37.33 memory used=2219.1MB, alloc=540.3MB, time=38.68 memory used=2294.2MB, alloc=540.3MB, time=39.65 memory used=2388.8MB, alloc=540.3MB, time=42.30 memory used=2509.2MB, alloc=540.3MB, time=43.54 memory used=2592.4MB, alloc=540.3MB, time=44.78 memory used=2706.6MB, alloc=540.3MB, time=45.96 memory used=2860.2MB, alloc=540.3MB, time=47.49 memory used=2937.9MB, alloc=540.3MB, time=48.89 memory used=3010.6MB, alloc=540.3MB, time=50.09 memory used=3102.2MB, alloc=540.3MB, time=51.31 memory used=3151.7MB, alloc=540.3MB, time=52.44 memory used=3370.7MB, alloc=564.3MB, time=56.32 memory used=3618.1MB, alloc=588.3MB, time=61.91 memory used=3811.5MB, alloc=612.3MB, time=99.10 memory used=3937.2MB, alloc=612.3MB, time=99.75 memory used=4227.8MB, alloc=612.3MB, time=102.34 memory used=4505.1MB, alloc=636.3MB, time=105.94 memory used=4824.4MB, alloc=636.3MB, time=108.91 memory used=5055.9MB, alloc=636.3MB, time=115.43 memory used=5265.3MB, alloc=636.3MB, time=121.77 memory used=5455.6MB, alloc=636.3MB, time=123.35 memory used=5771.3MB, alloc=660.3MB, time=126.54 memory used=6094.4MB, alloc=660.3MB, time=129.20 memory used=6378.0MB, alloc=660.3MB, time=130.89 memory used=6620.0MB, alloc=660.3MB, time=132.24 memory used=6908.2MB, alloc=660.3MB, time=133.72 memory used=7250.1MB, alloc=660.3MB, time=135.29 memory used=7636.4MB, alloc=660.3MB, time=136.95 memory used=8016.1MB, alloc=660.3MB, time=138.65 memory used=8435.2MB, alloc=660.3MB, time=140.42 memory used=8891.1MB, alloc=660.3MB, time=142.26 memory used=9389.0MB, alloc=660.3MB, time=144.22 memory used=9907.2MB, alloc=660.3MB, time=146.23 memory used=10443.4MB, alloc=660.3MB, time=148.25 memory used=11013.3MB, alloc=660.3MB, time=150.41 memory used=11617.5MB, alloc=660.3MB, time=152.65 memory used=12255.8MB, alloc=660.3MB, time=154.91 memory used=12646.8MB, alloc=660.3MB, time=156.54 memory used=12914.6MB, alloc=660.3MB, time=157.83 memory used=13183.3MB, alloc=660.3MB, time=159.13 memory used=13454.6MB, alloc=660.3MB, time=160.51 memory used=13729.3MB, alloc=660.3MB, time=161.83 memory used=14007.5MB, alloc=660.3MB, time=163.16 memory used=14288.5MB, alloc=660.3MB, time=164.49 memory used=14573.4MB, alloc=660.3MB, time=165.85 memory used=14862.1MB, alloc=660.3MB, time=167.20 memory used=15154.7MB, alloc=660.3MB, time=168.56 memory used=15452.0MB, alloc=660.3MB, time=169.93 memory used=15753.7MB, alloc=660.3MB, time=171.35 memory used=16059.8MB, alloc=660.3MB, time=172.76 memory used=16364.7MB, alloc=660.3MB, time=174.19 memory used=16674.0MB, alloc=660.3MB, time=175.64 memory used=16987.8MB, alloc=660.3MB, time=177.16 memory used=17305.7MB, alloc=660.3MB, time=178.60 memory used=17619.7MB, alloc=660.3MB, time=180.03 memory used=17933.2MB, alloc=660.3MB, time=181.46 memory used=18250.6MB, alloc=660.3MB, time=182.92 memory used=18572.1MB, alloc=660.3MB, time=184.38 memory used=18897.8MB, alloc=660.3MB, time=185.84 |\^/| 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(); 1428288192 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 3 2 3 2 F := [-16 x - 11 y + 11, -4 z + 8 z + x, 4 x - x z + z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 2 G := [4 x z + 11 z + 10, -x y - 4 x y z - 4 x z , -10 x z + 7 y z - 7 y z] > Problem := [F,G]; 3 2 3 2 3 2 Problem := [[-16 x - 11 y + 11, -4 z + 8 z + x, 4 x - x z + z], 2 2 2 2 2 [4 x z + 11 z + 10, -x y - 4 x y z - 4 x z , -10 x z + 7 y z - 7 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.5MB, alloc=32.3MB, time=0.50 memory used=47.1MB, alloc=32.3MB, time=0.79 memory used=67.3MB, alloc=32.3MB, time=1.09 memory used=86.5MB, alloc=56.3MB, time=1.40 memory used=125.4MB, alloc=60.3MB, time=2.00 memory used=164.3MB, alloc=84.3MB, time=2.61 memory used=204.5MB, alloc=84.3MB, time=3.25 memory used=266.7MB, alloc=92.3MB, time=4.23 memory used=327.6MB, alloc=116.3MB, time=5.17 memory used=411.6MB, alloc=116.3MB, time=6.48 memory used=494.2MB, alloc=140.3MB, time=7.84 memory used=569.9MB, alloc=140.3MB, time=9.08 memory used=641.0MB, alloc=396.3MB, time=10.32 memory used=748.2MB, alloc=420.3MB, time=12.05 memory used=874.3MB, alloc=444.3MB, time=14.13 memory used=1015.7MB, alloc=468.3MB, time=16.56 memory used=1166.3MB, alloc=492.3MB, time=19.23 memory used=1319.5MB, alloc=492.3MB, time=22.02 memory used=1460.4MB, alloc=516.3MB, time=24.53 memory used=1605.7MB, alloc=516.3MB, time=27.25 memory used=1735.8MB, alloc=516.3MB, time=29.70 memory used=1855.2MB, alloc=516.3MB, time=31.88 memory used=1977.6MB, alloc=540.3MB, time=34.13 memory used=2080.1MB, alloc=540.3MB, time=36.14 memory used=2190.7MB, alloc=540.3MB, time=38.38 memory used=2301.2MB, alloc=540.3MB, time=40.58 memory used=2379.3MB, alloc=540.3MB, time=42.24 memory used=2479.5MB, alloc=540.3MB, time=44.58 memory used=2569.6MB, alloc=540.3MB, time=46.54 memory used=2648.8MB, alloc=540.3MB, time=48.16 memory used=2722.0MB, alloc=540.3MB, time=49.83 memory used=2807.0MB, alloc=540.3MB, time=51.68 memory used=2885.2MB, alloc=540.3MB, time=53.46 memory used=2945.2MB, alloc=564.3MB, time=54.87 memory used=3000.9MB, alloc=564.3MB, time=56.11 memory used=3056.8MB, alloc=564.3MB, time=57.46 memory used=3110.0MB, alloc=564.3MB, time=58.98 memory used=3346.8MB, alloc=588.3MB, time=63.86 memory used=3605.3MB, alloc=612.3MB, time=68.66 memory used=3853.7MB, alloc=636.3MB, time=73.65 memory used=4117.2MB, alloc=660.3MB, time=78.90 memory used=4397.6MB, alloc=684.3MB, time=84.27 memory used=4673.4MB, alloc=708.3MB, time=90.09 memory used=4978.1MB, alloc=732.3MB, time=95.41 memory used=5291.8MB, alloc=756.3MB, time=100.84 memory used=5607.2MB, alloc=780.3MB, time=106.81 memory used=5931.6MB, alloc=804.3MB, time=112.97 memory used=6266.6MB, alloc=828.3MB, time=119.22 memory used=6577.0MB, alloc=852.3MB, time=125.35 memory used=6912.4MB, alloc=876.3MB, time=132.06 memory used=7259.3MB, alloc=900.3MB, 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(); 1428288492 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 3 2 2 F := [-8 y z + 6 x - 10 x z, -2 x z + 6 x y + 4 z , 10 x y - 7 x z - 4 y] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 3 G := [4 x y - 7 x z - 3 y, -8 x z - 3 x y - 9 y, -7 x y + 3 y - z] > Problem := [F,G]; Problem := [ 2 2 2 2 3 2 2 [-8 y z + 6 x - 10 x z, -2 x z + 6 x y + 4 z , 10 x y - 7 x z - 4 y], 2 2 2 3 [4 x y - 7 x z - 3 y, -8 x z - 3 x y - 9 y, -7 x y + 3 y - z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=25.2MB, alloc=32.3MB, time=0.48 memory used=44.0MB, alloc=32.3MB, time=0.75 memory used=63.2MB, alloc=56.3MB, time=1.04 memory used=106.4MB, alloc=60.3MB, time=1.65 memory used=147.1MB, alloc=60.3MB, time=2.23 memory used=187.5MB, alloc=60.3MB, time=2.80 memory used=227.4MB, alloc=84.3MB, time=3.38 memory used=287.4MB, alloc=92.3MB, time=4.22 memory used=354.7MB, alloc=92.3MB, time=5.09 memory used=426.0MB, alloc=116.3MB, time=5.88 memory used=501.4MB, alloc=372.3MB, time=6.80 memory used=605.6MB, alloc=372.3MB, time=8.02 memory used=699.9MB, alloc=396.3MB, time=9.16 memory used=815.8MB, alloc=420.3MB, time=10.71 memory used=924.6MB, alloc=420.3MB, time=12.16 memory used=1055.0MB, alloc=444.3MB, time=14.00 memory used=1170.1MB, alloc=444.3MB, time=15.74 memory used=1279.8MB, alloc=444.3MB, time=17.24 memory used=1408.8MB, alloc=468.3MB, time=18.77 memory used=1508.4MB, alloc=468.3MB, time=20.18 memory used=1611.6MB, alloc=468.3MB, time=21.61 memory used=1703.1MB, alloc=468.3MB, time=23.01 memory used=1797.8MB, alloc=468.3MB, time=24.36 memory used=1892.5MB, alloc=468.3MB, time=25.56 memory used=1992.1MB, alloc=468.3MB, time=26.85 memory used=2064.3MB, alloc=468.3MB, time=28.13 memory used=2139.6MB, alloc=492.3MB, time=29.16 memory used=2207.7MB, alloc=492.3MB, time=30.47 memory used=2274.9MB, alloc=492.3MB, time=31.39 memory used=2347.0MB, alloc=492.3MB, time=32.65 memory used=2390.6MB, alloc=492.3MB, time=33.50 memory used=2446.1MB, alloc=492.3MB, time=34.41 memory used=2515.9MB, alloc=492.3MB, time=35.31 memory used=2579.7MB, alloc=492.3MB, time=36.25 memory used=2651.6MB, alloc=492.3MB, time=37.25 memory used=2696.2MB, alloc=492.3MB, time=38.14 memory used=2755.1MB, alloc=492.3MB, time=39.33 memory used=2831.9MB, alloc=492.3MB, time=40.34 memory used=3058.2MB, alloc=516.3MB, time=43.39 memory used=3249.5MB, alloc=516.3MB, time=47.00 memory used=3351.1MB, alloc=516.3MB, time=47.58 memory used=3438.1MB, alloc=516.3MB, time=48.09 memory used=3588.6MB, alloc=516.3MB, time=49.63 memory used=3806.3MB, alloc=540.3MB, time=52.48 memory used=3993.6MB, alloc=540.3MB, time=54.78 memory used=4166.6MB, alloc=564.3MB, time=57.68 memory used=4350.4MB, alloc=588.3MB, time=60.29 memory used=4532.2MB, alloc=588.3MB, time=63.00 memory used=4685.6MB, alloc=612.3MB, time=65.44 memory used=4802.6MB, alloc=612.3MB, time=67.57 memory used=4914.5MB, alloc=612.3MB, time=69.70 memory used=5049.1MB, alloc=612.3MB, time=72.22 memory used=5248.6MB, alloc=612.3MB, time=74.61 memory used=5421.8MB, alloc=636.3MB, time=76.46 memory used=5578.2MB, alloc=636.3MB, time=78.65 memory used=5715.8MB, alloc=636.3MB, time=81.36 memory used=5913.3MB, alloc=636.3MB, time=83.89 memory used=6109.1MB, alloc=636.3MB, time=87.65 memory used=6279.1MB, alloc=636.3MB, time=90.00 memory used=6407.9MB, alloc=636.3MB, time=90.84 memory used=6576.4MB, alloc=636.3MB, time=93.03 memory used=6641.0MB, alloc=636.3MB, time=94.41 memory used=6820.1MB, alloc=636.3MB, time=97.95 memory used=6958.4MB, alloc=636.3MB, time=98.87 memory used=7131.5MB, alloc=636.3MB, time=101.01 memory used=7230.7MB, alloc=636.3MB, time=102.65 memory used=7330.7MB, alloc=636.3MB, time=104.78 memory used=7383.1MB, alloc=660.3MB, time=106.44 memory used=7741.2MB, alloc=684.3MB, time=111.65 memory used=8119.6MB, alloc=708.3MB, time=117.60 memory used=8417.1MB, alloc=732.3MB, time=121.82 memory used=8790.6MB, alloc=756.3MB, time=126.53 memory used=8983.7MB, alloc=780.3MB, time=128.35 memory used=9374.2MB, alloc=780.3MB, time=133.05 memory used=9639.6MB, alloc=780.3MB, time=135.98 memory used=10001.4MB, alloc=804.3MB, time=141.54 memory used=10279.2MB, alloc=828.3MB, time=146.84 memory used=10560.7MB, alloc=852.3MB, time=151.76 memory used=10836.7MB, alloc=876.3MB, time=156.80 memory used=11132.1MB, alloc=900.3MB, time=163.04 |\^/| 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(); 1428288792 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 3 2 F := [12 x z - 14 y + 7, -10 x y z + 9 y z + 5 x , -3 x y + 9 y + 6 z ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 3 2 2 2 G := [2 x y - 15 y z - 17 z, -4 x - 9 y - 4 x, -5 x y - x z - 9 y ] > Problem := [F,G]; Problem := [ 2 2 2 2 3 2 [12 x z - 14 y + 7, -10 x y z + 9 y z + 5 x , -3 x y + 9 y + 6 z ], 2 3 3 2 2 2 [2 x y - 15 y z - 17 z, -4 x - 9 y - 4 x, -5 x y - x z - 9 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.18 memory used=26.5MB, alloc=32.3MB, time=0.51 memory used=46.4MB, alloc=32.3MB, time=0.80 memory used=64.3MB, alloc=56.3MB, time=1.07 memory used=106.2MB, alloc=68.3MB, time=1.68 memory used=147.8MB, alloc=68.3MB, time=2.24 memory used=188.2MB, alloc=92.3MB, time=2.74 memory used=253.7MB, alloc=92.3MB, time=3.64 memory used=321.6MB, alloc=92.3MB, time=4.47 memory used=389.2MB, alloc=372.3MB, time=5.36 memory used=477.2MB, alloc=372.3MB, time=6.59 memory used=568.5MB, alloc=396.3MB, time=7.83 memory used=680.4MB, alloc=420.3MB, time=9.51 memory used=795.7MB, alloc=420.3MB, time=11.07 memory used=928.9MB, alloc=444.3MB, time=12.78 memory used=1057.6MB, alloc=444.3MB, time=14.74 memory used=1180.0MB, alloc=468.3MB, time=16.41 memory used=1296.2MB, alloc=468.3MB, time=17.95 memory used=1410.2MB, alloc=468.3MB, time=19.80 memory used=1510.0MB, alloc=492.3MB, time=21.16 memory used=1664.2MB, alloc=492.3MB, time=23.84 memory used=1805.2MB, alloc=492.3MB, time=25.10 memory used=1906.5MB, alloc=492.3MB, time=26.23 memory used=2009.2MB, alloc=492.3MB, time=27.57 memory used=2084.4MB, alloc=492.3MB, time=28.60 memory used=2173.4MB, alloc=492.3MB, time=29.86 memory used=2247.8MB, alloc=492.3MB, time=31.04 memory used=2300.7MB, alloc=492.3MB, time=32.01 memory used=2366.5MB, alloc=492.3MB, time=33.20 memory used=2424.9MB, alloc=516.3MB, time=34.35 memory used=2486.1MB, alloc=516.3MB, time=35.58 memory used=2541.0MB, alloc=516.3MB, time=36.70 memory used=2595.0MB, alloc=516.3MB, time=37.68 memory used=2655.1MB, alloc=516.3MB, time=38.60 memory used=2864.1MB, alloc=540.3MB, time=41.54 memory used=3086.0MB, alloc=564.3MB, time=44.91 memory used=3275.8MB, alloc=588.3MB, time=47.44 memory used=3525.7MB, alloc=588.3MB, time=54.98 memory used=3644.4MB, alloc=588.3MB, time=55.64 memory used=3747.7MB, alloc=612.3MB, time=56.23 memory used=3870.1MB, alloc=612.3MB, time=56.81 memory used=4021.5MB, alloc=612.3MB, time=57.41 memory used=4237.0MB, alloc=612.3MB, time=58.24 memory used=4385.2MB, alloc=612.3MB, time=58.87 memory used=4593.3MB, alloc=612.3MB, time=60.37 memory used=4747.8MB, alloc=612.3MB, time=61.72 memory used=4875.4MB, alloc=612.3MB, time=62.39 memory used=5098.2MB, alloc=612.3MB, time=64.86 memory used=5231.6MB, alloc=612.3MB, time=66.92 memory used=5385.5MB, alloc=636.3MB, time=69.59 memory used=5527.4MB, alloc=636.3MB, time=71.72 memory used=5676.8MB, alloc=636.3MB, time=73.79 memory used=5819.8MB, alloc=636.3MB, time=76.12 memory used=5947.3MB, alloc=660.3MB, time=78.68 memory used=6068.5MB, alloc=660.3MB, time=81.24 memory used=6191.5MB, alloc=660.3MB, time=83.83 memory used=6283.6MB, alloc=660.3MB, time=85.50 memory used=6408.1MB, alloc=684.3MB, time=87.39 memory used=6761.7MB, alloc=708.3MB, time=93.38 memory used=7119.4MB, alloc=732.3MB, time=98.74 memory used=7505.3MB, alloc=756.3MB, time=105.16 memory used=7884.3MB, alloc=780.3MB, time=111.80 memory used=8216.3MB, alloc=804.3MB, time=117.14 memory used=8542.6MB, alloc=828.3MB, time=123.69 memory used=8848.1MB, alloc=852.3MB, time=129.54 memory used=9244.1MB, alloc=876.3MB, time=137.29 memory used=9592.1MB, alloc=900.3MB, time=142.21 |\^/| 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(); 1428289092 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; F := [ 2 2 2 2 2 4 x z + 12 y - 4 z , -8 x y - 4 y z + 10 z, -10 x z - 5 x y z + 10 x z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 2 2 2 G := [13 y z - 10 x + 12 y , 7 x y + 5 x y z + 8 y z, -4 x y - 4 x z - 3] > Problem := [F,G]; Problem := [[ 2 2 2 2 2 4 x z + 12 y - 4 z , -8 x y - 4 y z + 10 z, -10 x z - 5 x y z + 10 x z] , 2 2 2 2 2 2 2 [13 y z - 10 x + 12 y , 7 x y + 5 x y z + 8 y z, -4 x y - 4 x z - 3]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.3MB, alloc=32.3MB, time=0.46 memory used=47.7MB, alloc=32.3MB, time=0.75 memory used=66.7MB, alloc=56.3MB, time=1.03 memory used=106.7MB, alloc=60.3MB, time=1.60 memory used=144.8MB, alloc=84.3MB, time=2.17 memory used=205.0MB, alloc=92.3MB, time=3.03 memory used=262.5MB, alloc=92.3MB, time=3.87 memory used=320.8MB, alloc=116.3MB, time=4.77 memory used=390.6MB, alloc=372.3MB, time=5.85 memory used=471.9MB, alloc=396.3MB, time=7.13 memory used=581.9MB, alloc=396.3MB, time=8.68 memory used=689.5MB, alloc=420.3MB, time=10.31 memory used=815.3MB, alloc=444.3MB, time=12.38 memory used=964.8MB, alloc=468.3MB, time=14.89 memory used=1103.3MB, alloc=468.3MB, time=17.09 memory used=1242.4MB, alloc=492.3MB, time=19.36 memory used=1371.9MB, alloc=492.3MB, time=21.41 memory used=1498.0MB, alloc=516.3MB, time=23.61 memory used=1615.3MB, alloc=516.3MB, time=25.76 memory used=1746.5MB, alloc=516.3MB, time=28.30 memory used=1832.6MB, alloc=540.3MB, time=29.76 memory used=1935.5MB, alloc=540.3MB, time=31.63 memory used=2006.0MB, alloc=540.3MB, time=32.98 memory used=2102.7MB, alloc=540.3MB, time=34.96 memory used=2194.0MB, alloc=540.3MB, time=36.97 memory used=2281.8MB, alloc=540.3MB, time=38.99 memory used=2340.2MB, alloc=540.3MB, time=40.20 memory used=2404.8MB, alloc=540.3MB, time=41.63 memory used=2460.7MB, alloc=540.3MB, time=42.97 memory used=2508.2MB, alloc=540.3MB, time=43.99 memory used=2714.5MB, alloc=564.3MB, time=47.55 memory used=2908.6MB, alloc=588.3MB, time=51.10 memory used=3107.6MB, alloc=612.3MB, time=54.90 memory used=3281.6MB, alloc=636.3MB, time=58.52 memory used=3476.9MB, alloc=660.3MB, time=62.99 memory used=3608.7MB, alloc=684.3MB, time=65.69 memory used=3786.1MB, alloc=684.3MB, time=70.26 memory used=3914.6MB, alloc=684.3MB, time=73.30 memory used=4013.1MB, alloc=684.3MB, time=75.89 memory used=4115.5MB, alloc=684.3MB, time=78.49 memory used=4232.1MB, alloc=708.3MB, time=81.01 memory used=4334.2MB, alloc=708.3MB, time=83.10 memory used=4712.0MB, alloc=732.3MB, time=90.83 memory used=5094.9MB, alloc=756.3MB, time=99.50 memory used=5497.8MB, alloc=780.3MB, time=106.09 memory used=5852.4MB, alloc=804.3MB, time=113.86 memory used=6250.6MB, alloc=828.3MB, time=121.57 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428289392 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 3 2 2 F := [19 x y z + 20 y - 16, -6 x y + 9 y z - 4 x , -7 x - 10 x z + y ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 2 2 2 G := [-20 x y - 7 x + 17 z, 9 x y - 10 x + 5 z , -6 y z + 9 y z - 2 x y] > Problem := [F,G]; Problem := [ 2 2 2 3 2 2 [19 x y z + 20 y - 16, -6 x y + 9 y z - 4 x , -7 x - 10 x z + y ], 2 2 2 2 2 2 2 [-20 x y - 7 x + 17 z, 9 x y - 10 x + 5 z , -6 y z + 9 y z - 2 x y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=25.7MB, alloc=32.3MB, time=0.49 memory used=44.8MB, alloc=32.3MB, time=0.78 memory used=64.3MB, alloc=56.3MB, time=1.09 memory used=106.5MB, alloc=68.3MB, time=1.69 memory used=148.6MB, alloc=68.3MB, time=2.26 memory used=193.4MB, alloc=68.3MB, time=2.86 memory used=236.7MB, alloc=92.3MB, time=3.43 memory used=301.6MB, alloc=92.3MB, time=4.37 memory used=365.9MB, alloc=92.3MB, time=5.38 memory used=430.4MB, alloc=116.3MB, time=6.15 memory used=493.4MB, alloc=372.3MB, time=7.08 memory used=587.9MB, alloc=372.3MB, time=8.37 memory used=677.0MB, alloc=396.3MB, time=9.68 memory used=788.4MB, alloc=396.3MB, time=11.07 memory used=913.1MB, alloc=420.3MB, time=12.61 memory used=1039.8MB, alloc=420.3MB, time=14.16 memory used=1150.7MB, alloc=420.3MB, time=15.82 memory used=1265.3MB, alloc=444.3MB, time=17.25 memory used=1388.3MB, alloc=444.3MB, time=18.67 memory used=1527.2MB, alloc=444.3MB, time=20.40 memory used=1617.2MB, alloc=444.3MB, time=21.55 memory used=1722.7MB, alloc=444.3MB, time=23.15 memory used=1820.8MB, alloc=468.3MB, time=24.71 memory used=1908.8MB, alloc=468.3MB, time=26.14 memory used=2003.1MB, alloc=468.3MB, time=27.86 memory used=2081.8MB, alloc=468.3MB, time=29.25 memory used=2159.6MB, alloc=468.3MB, time=30.42 memory used=2246.9MB, alloc=468.3MB, time=31.56 memory used=2352.3MB, alloc=492.3MB, time=32.73 memory used=2456.8MB, alloc=492.3MB, time=33.44 memory used=2537.0MB, alloc=492.3MB, time=34.47 memory used=2612.2MB, alloc=492.3MB, time=35.89 memory used=2690.6MB, alloc=492.3MB, time=37.00 memory used=2782.6MB, alloc=492.3MB, time=38.18 memory used=2840.4MB, alloc=492.3MB, time=39.42 memory used=2907.8MB, alloc=492.3MB, time=40.70 memory used=2977.7MB, alloc=492.3MB, time=41.82 memory used=3038.5MB, alloc=492.3MB, time=42.69 memory used=3105.9MB, alloc=492.3MB, time=43.97 memory used=3181.8MB, alloc=492.3MB, time=44.87 memory used=3233.0MB, alloc=492.3MB, time=45.82 memory used=3291.8MB, alloc=492.3MB, time=46.94 memory used=3494.1MB, alloc=516.3MB, time=49.67 memory used=3681.8MB, alloc=540.3MB, time=52.60 memory used=3887.2MB, alloc=540.3MB, time=55.05 memory used=4116.8MB, alloc=564.3MB, time=58.06 memory used=4332.7MB, alloc=564.3MB, time=61.42 memory used=4535.3MB, alloc=588.3MB, time=64.43 memory used=4694.3MB, alloc=588.3MB, time=66.98 memory used=4865.6MB, alloc=612.3MB, time=70.03 memory used=5040.7MB, alloc=612.3MB, time=72.76 memory used=5197.2MB, alloc=612.3MB, time=75.52 memory used=5415.9MB, alloc=612.3MB, time=77.89 memory used=5568.4MB, alloc=612.3MB, time=79.26 memory used=5772.3MB, alloc=612.3MB, time=80.99 memory used=5924.5MB, alloc=612.3MB, time=83.95 memory used=6035.3MB, alloc=636.3MB, time=86.22 memory used=6127.3MB, alloc=636.3MB, time=88.20 memory used=6252.5MB, alloc=636.3MB, time=90.15 memory used=6389.7MB, alloc=636.3MB, time=92.22 memory used=6513.4MB, alloc=636.3MB, time=94.98 memory used=6632.2MB, alloc=636.3MB, time=97.78 memory used=6752.5MB, alloc=660.3MB, time=99.95 memory used=6861.0MB, alloc=660.3MB, time=101.93 memory used=6988.3MB, alloc=660.3MB, time=104.07 memory used=7084.2MB, alloc=660.3MB, time=106.25 memory used=7412.5MB, alloc=684.3MB, time=111.37 memory used=7637.1MB, alloc=684.3MB, time=113.50 memory used=7808.3MB, alloc=684.3MB, time=115.25 memory used=8162.7MB, alloc=708.3MB, time=119.98 memory used=8531.6MB, alloc=732.3MB, time=125.50 memory used=8902.6MB, alloc=756.3MB, time=132.64 memory used=9219.0MB, alloc=780.3MB, time=138.02 memory used=9554.9MB, alloc=804.3MB, time=144.27 |\^/| 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(); 1428289692 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 3 2 F := [18 x z + 3 x y z - 18 x z, x z + y z + 7 z , x y z - 6 y + 8 y z ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 2 2 3 2 2 G := [-17 x - 10 x z + 17 y, -4 x y + 6 x - 8 y , -2 y + 4 y z + 4 y ] > Problem := [F,G]; Problem := [ 2 2 2 2 3 2 [18 x z + 3 x y z - 18 x z, x z + y z + 7 z , x y z - 6 y + 8 y z ], 3 2 2 2 2 3 2 2 [-17 x - 10 x z + 17 y, -4 x y + 6 x - 8 y , -2 y + 4 y z + 4 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.5MB, alloc=32.3MB, time=0.49 memory used=47.7MB, alloc=32.3MB, time=0.80 memory used=67.4MB, alloc=56.3MB, time=1.10 memory used=107.0MB, alloc=60.3MB, time=1.70 memory used=144.8MB, alloc=84.3MB, time=2.30 memory used=204.9MB, alloc=92.3MB, time=3.24 memory used=265.0MB, alloc=92.3MB, time=4.19 memory used=323.8MB, alloc=116.3MB, time=5.17 memory used=403.3MB, alloc=116.3MB, time=6.44 memory used=481.4MB, alloc=140.3MB, time=7.71 memory used=559.0MB, alloc=396.3MB, time=8.99 memory used=660.9MB, alloc=420.3MB, time=10.74 memory used=788.6MB, alloc=444.3MB, time=12.85 memory used=937.5MB, alloc=468.3MB, time=15.47 memory used=1080.8MB, alloc=492.3MB, time=18.06 memory used=1225.6MB, alloc=492.3MB, time=20.67 memory used=1349.1MB, alloc=516.3MB, time=22.89 memory used=1466.1MB, alloc=516.3MB, time=25.09 memory used=1572.2MB, alloc=516.3MB, time=27.21 memory used=1668.5MB, alloc=516.3MB, time=29.08 memory used=1779.3MB, alloc=516.3MB, time=31.41 memory used=1876.9MB, alloc=516.3MB, time=33.56 memory used=1961.6MB, alloc=516.3MB, time=34.88 memory used=2036.4MB, alloc=516.3MB, time=36.15 memory used=2118.6MB, alloc=516.3MB, time=37.89 memory used=2199.8MB, alloc=540.3MB, time=39.67 memory used=2268.3MB, alloc=540.3MB, time=41.32 memory used=2340.9MB, alloc=540.3MB, time=43.10 memory used=2401.5MB, alloc=540.3MB, time=44.70 memory used=2461.0MB, alloc=540.3MB, time=46.16 memory used=2523.7MB, alloc=540.3MB, time=47.83 memory used=2752.9MB, alloc=564.3MB, time=52.61 memory used=2995.4MB, alloc=588.3MB, time=58.03 memory used=3193.6MB, alloc=612.3MB, time=62.21 memory used=3361.7MB, alloc=636.3MB, time=66.36 memory used=3540.4MB, alloc=660.3MB, time=71.05 memory used=3690.7MB, alloc=684.3MB, time=74.67 memory used=3833.5MB, alloc=684.3MB, time=77.87 memory used=4007.3MB, alloc=684.3MB, time=80.95 memory used=4121.6MB, alloc=684.3MB, time=83.82 memory used=4250.4MB, alloc=708.3MB, time=87.36 memory used=4385.0MB, alloc=708.3MB, time=91.28 memory used=4457.6MB, alloc=708.3MB, time=93.58 memory used=4543.7MB, alloc=708.3MB, time=95.91 memory used=4640.0MB, alloc=708.3MB, time=99.06 memory used=5001.9MB, alloc=732.3MB, time=106.78 memory used=5381.0MB, alloc=756.3MB, time=113.43 memory used=5761.5MB, alloc=780.3MB, time=120.64 memory used=6115.4MB, alloc=804.3MB, time=128.22 memory used=6449.1MB, alloc=828.3MB, time=135.61 memory used=6777.5MB, alloc=852.3MB, time=143.10 |\^/| 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(); 1428289992 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 F := [2 x + 20 x + z, 3 x z + 5 x + 8 y, -6 x y - 7 y + 6 y z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 3 2 3 2 G := [-19 x y - 17 y z + 12 y, 8 x - 2 x z - 7 x, 8 x + 3 x y + 4 y z] > Problem := [F,G]; 2 2 2 Problem := [[2 x + 20 x + z, 3 x z + 5 x + 8 y, -6 x y - 7 y + 6 y z], 2 2 3 2 3 2 [-19 x y - 17 y z + 12 y, 8 x - 2 x z - 7 x, 8 x + 3 x y + 4 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.0MB, alloc=32.3MB, time=0.50 memory used=46.4MB, alloc=32.3MB, time=0.80 memory used=65.6MB, alloc=56.3MB, time=1.10 memory used=103.5MB, alloc=60.3MB, time=1.67 memory used=140.8MB, alloc=84.3MB, time=2.25 memory used=200.9MB, alloc=92.3MB, time=3.23 memory used=259.8MB, alloc=92.3MB, time=4.19 memory used=316.5MB, alloc=116.3MB, time=5.13 memory used=395.9MB, alloc=116.3MB, time=6.48 memory used=472.8MB, alloc=140.3MB, time=7.83 memory used=563.0MB, alloc=420.3MB, time=9.40 memory used=687.0MB, alloc=444.3MB, time=11.64 memory used=838.6MB, alloc=468.3MB, time=14.29 memory used=988.7MB, alloc=492.3MB, time=17.05 memory used=1137.5MB, alloc=516.3MB, time=20.02 memory used=1275.9MB, alloc=516.3MB, time=22.80 memory used=1392.2MB, alloc=516.3MB, time=25.31 memory used=1516.8MB, alloc=516.3MB, time=27.92 memory used=1627.5MB, alloc=540.3MB, time=30.20 memory used=1736.0MB, alloc=540.3MB, time=32.70 memory used=1820.0MB, alloc=540.3MB, time=34.66 memory used=1916.6MB, alloc=540.3MB, time=36.95 memory used=2004.7MB, alloc=540.3MB, time=39.29 memory used=2079.3MB, alloc=540.3MB, time=41.40 memory used=2136.3MB, alloc=540.3MB, time=42.71 memory used=2220.9MB, alloc=540.3MB, time=45.08 memory used=2292.0MB, alloc=540.3MB, time=47.13 memory used=2521.0MB, alloc=564.3MB, time=52.77 memory used=2770.6MB, alloc=588.3MB, time=59.11 memory used=3018.5MB, alloc=612.3MB, time=65.03 memory used=3273.4MB, alloc=636.3MB, time=71.52 memory used=3511.5MB, alloc=660.3MB, time=77.71 memory used=3723.8MB, alloc=684.3MB, time=83.53 memory used=3913.9MB, alloc=708.3MB, time=88.89 memory used=4096.8MB, alloc=708.3MB, time=94.04 memory used=4253.3MB, alloc=732.3MB, time=98.53 memory used=4405.3MB, alloc=732.3MB, time=102.69 memory used=4549.7MB, alloc=732.3MB, time=106.87 memory used=4694.1MB, alloc=732.3MB, time=111.04 memory used=5073.3MB, alloc=756.3MB, time=120.70 memory used=5469.7MB, alloc=780.3MB, time=131.09 |\^/| 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(); 1428290292 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 F := [-7 x y - 3 z + 2 x, -7 y z - 8 x + 7, -4 x y + 8 x y z + 5 z ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 3 3 2 G := [7 y z - 11 z + 2 x z, 7 y + 5 y, -3 z - 4 y - 6] > Problem := [F,G]; 2 2 2 2 Problem := [[-7 x y - 3 z + 2 x, -7 y z - 8 x + 7, -4 x y + 8 x y z + 5 z ], 2 3 3 3 2 [7 y z - 11 z + 2 x z, 7 y + 5 y, -3 z - 4 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=26.7MB, alloc=32.3MB, time=0.50 memory used=47.2MB, alloc=32.3MB, time=0.80 memory used=66.4MB, alloc=56.3MB, time=1.11 memory used=105.6MB, alloc=60.3MB, time=1.70 memory used=145.0MB, alloc=60.3MB, time=2.26 memory used=182.5MB, alloc=84.3MB, time=2.82 memory used=228.6MB, alloc=84.3MB, time=3.53 memory used=287.7MB, alloc=116.3MB, time=4.48 memory used=371.3MB, alloc=116.3MB, time=5.76 memory used=448.8MB, alloc=116.3MB, time=6.87 memory used=512.6MB, alloc=116.3MB, time=7.40 memory used=590.6MB, alloc=116.3MB, time=8.26 memory used=667.9MB, alloc=140.3MB, time=9.58 memory used=757.3MB, alloc=140.3MB, time=11.07 memory used=836.6MB, alloc=420.3MB, time=12.41 memory used=969.6MB, alloc=420.3MB, time=14.16 memory used=1097.9MB, alloc=444.3MB, time=15.80 memory used=1268.2MB, alloc=444.3MB, time=18.06 memory used=1411.0MB, alloc=468.3MB, time=20.41 memory used=1576.3MB, alloc=492.3MB, time=23.07 memory used=1718.7MB, alloc=492.3MB, time=25.36 memory used=1859.9MB, alloc=516.3MB, time=27.80 memory used=1971.2MB, alloc=516.3MB, time=29.76 memory used=2083.2MB, alloc=516.3MB, time=31.52 memory used=2196.0MB, alloc=540.3MB, time=33.35 memory used=2290.6MB, alloc=540.3MB, time=34.71 memory used=2391.7MB, alloc=540.3MB, time=36.64 memory used=2544.8MB, alloc=540.3MB, time=38.21 memory used=2693.5MB, alloc=540.3MB, time=39.61 memory used=2794.7MB, alloc=540.3MB, time=41.22 memory used=2877.0MB, alloc=540.3MB, time=42.54 memory used=2959.9MB, alloc=564.3MB, time=43.89 memory used=3056.8MB, alloc=564.3MB, time=46.10 memory used=3168.4MB, alloc=564.3MB, time=48.49 memory used=3264.2MB, alloc=564.3MB, time=50.54 memory used=3353.6MB, alloc=564.3MB, time=52.54 memory used=3431.3MB, alloc=564.3MB, time=54.19 memory used=3492.6MB, alloc=564.3MB, time=55.32 memory used=3546.3MB, alloc=564.3MB, time=56.34 memory used=3601.4MB, alloc=564.3MB, time=57.62 memory used=3678.5MB, alloc=564.3MB, time=59.61 memory used=3734.6MB, alloc=564.3MB, time=60.99 memory used=3800.6MB, alloc=564.3MB, time=62.74 memory used=4032.1MB, alloc=588.3MB, time=66.97 memory used=4242.9MB, alloc=612.3MB, time=70.93 memory used=4496.9MB, alloc=612.3MB, time=74.63 memory used=4676.7MB, alloc=636.3MB, time=77.48 memory used=4913.6MB, alloc=636.3MB, time=80.64 memory used=5097.9MB, alloc=636.3MB, time=82.14 memory used=5274.0MB, alloc=636.3MB, time=83.65 memory used=5546.4MB, alloc=660.3MB, time=86.66 memory used=5754.5MB, alloc=660.3MB, time=89.35 memory used=5993.0MB, alloc=660.3MB, time=93.22 memory used=6167.3MB, alloc=684.3MB, time=96.47 memory used=6399.7MB, alloc=684.3MB, time=99.02 memory used=6600.7MB, alloc=684.3MB, time=100.68 memory used=6823.9MB, alloc=684.3MB, time=102.57 memory used=6981.6MB, alloc=684.3MB, time=104.96 memory used=7197.1MB, alloc=708.3MB, time=108.25 memory used=7356.4MB, alloc=708.3MB, time=111.48 memory used=7584.0MB, alloc=708.3MB, time=114.77 memory used=7784.5MB, alloc=708.3MB, time=116.16 memory used=7976.4MB, alloc=708.3MB, time=117.43 memory used=8159.4MB, alloc=708.3MB, time=118.61 memory used=8363.0MB, alloc=708.3MB, time=120.03 memory used=8552.6MB, alloc=708.3MB, time=121.81 memory used=8783.1MB, alloc=708.3MB, time=123.51 memory used=8984.1MB, alloc=708.3MB, time=125.06 memory used=9186.5MB, alloc=708.3MB, time=126.25 memory used=9464.8MB, alloc=708.3MB, time=129.40 memory used=9623.1MB, alloc=708.3MB, time=131.98 memory used=9874.8MB, alloc=732.3MB, time=134.97 memory used=10056.0MB, alloc=732.3MB, time=137.48 memory used=10301.4MB, alloc=732.3MB, time=140.89 memory used=10536.6MB, alloc=732.3MB, time=142.66 memory used=10755.6MB, alloc=732.3MB, time=144.51 memory used=10945.0MB, alloc=732.3MB, time=145.59 memory used=11135.7MB, alloc=732.3MB, time=146.93 memory used=11325.5MB, alloc=732.3MB, time=148.04 memory used=11522.3MB, alloc=732.3MB, time=149.27 memory used=11716.0MB, alloc=732.3MB, time=150.54 memory used=11920.4MB, alloc=732.3MB, time=152.56 memory used=12119.0MB, alloc=732.3MB, time=153.83 memory used=12328.1MB, alloc=732.3MB, time=157.24 memory used=12495.8MB, alloc=732.3MB, time=158.15 memory used=12702.0MB, alloc=732.3MB, time=159.48 memory used=12911.1MB, alloc=732.3MB, time=162.94 memory used=13078.2MB, alloc=732.3MB, time=163.86 memory used=13281.1MB, alloc=732.3MB, time=164.98 |\^/| 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(); 1428290592 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 F := [-17 x y z - 8 x, 9 x y - 4 x y - 10 x z, x y - 4 x ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; G := [ 2 2 2 2 2 2 3 2 2 20 x z - 11 x z - 9 y z , -6 x z - 9 y z - 8 x , -3 x - 3 y z - 9 x ] > Problem := [F,G]; 2 2 2 Problem := [[-17 x y z - 8 x, 9 x y - 4 x y - 10 x z, x y - 4 x ], [ 2 2 2 2 2 2 3 2 2 20 x z - 11 x z - 9 y z , -6 x z - 9 y z - 8 x , -3 x - 3 y z - 9 x ] ] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.2MB, alloc=32.3MB, time=0.48 memory used=47.2MB, alloc=32.3MB, time=0.79 memory used=66.6MB, alloc=56.3MB, time=1.09 memory used=105.1MB, alloc=60.3MB, time=1.69 memory used=142.5MB, alloc=84.3MB, time=2.30 memory used=204.1MB, alloc=92.3MB, time=3.27 memory used=264.2MB, alloc=116.3MB, time=4.26 memory used=347.2MB, alloc=140.3MB, time=5.63 memory used=426.7MB, alloc=396.3MB, time=6.93 memory used=531.7MB, alloc=396.3MB, time=8.64 memory used=634.8MB, alloc=420.3MB, time=10.37 memory used=759.5MB, alloc=444.3MB, time=12.55 memory used=903.2MB, alloc=468.3MB, time=15.07 memory used=1065.4MB, alloc=492.3MB, time=18.06 memory used=1203.0MB, alloc=516.3MB, time=20.41 memory used=1332.8MB, alloc=516.3MB, time=22.72 memory used=1466.2MB, alloc=516.3MB, time=25.41 memory used=1597.7MB, alloc=540.3MB, time=28.19 memory used=1718.3MB, alloc=540.3MB, time=30.69 memory used=1833.3MB, alloc=540.3MB, time=33.03 memory used=1942.3MB, alloc=540.3MB, time=35.13 memory used=2022.5MB, alloc=540.3MB, time=36.57 memory used=2104.8MB, alloc=540.3MB, time=38.38 memory used=2190.8MB, alloc=540.3MB, time=40.30 memory used=2271.2MB, alloc=540.3MB, time=42.06 memory used=2340.9MB, alloc=540.3MB, time=43.56 memory used=2424.0MB, alloc=540.3MB, time=45.45 memory used=2478.7MB, alloc=540.3MB, time=46.67 memory used=2543.8MB, alloc=540.3MB, time=48.14 memory used=2606.5MB, alloc=540.3MB, time=49.71 memory used=2825.6MB, alloc=564.3MB, time=54.09 memory used=3048.7MB, alloc=588.3MB, time=59.05 memory used=3269.6MB, alloc=612.3MB, time=63.72 memory used=3484.7MB, alloc=636.3MB, time=68.69 memory used=3662.4MB, alloc=660.3MB, time=72.73 memory used=3847.0MB, alloc=684.3MB, time=76.90 memory used=4022.1MB, alloc=684.3MB, time=81.01 memory used=4209.1MB, alloc=684.3MB, time=85.90 memory used=4393.4MB, alloc=708.3MB, time=90.13 memory used=4556.6MB, alloc=708.3MB, time=94.92 memory used=4709.5MB, alloc=708.3MB, time=99.31 memory used=4821.3MB, alloc=732.3MB, time=102.60 memory used=4937.7MB, alloc=732.3MB, time=105.98 memory used=5049.7MB, alloc=732.3MB, time=109.24 memory used=5430.9MB, alloc=756.3MB, time=118.82 memory used=5831.7MB, alloc=780.3MB, time=129.54 memory used=6250.3MB, alloc=804.3MB, time=140.24 |\^/| 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(); 1428290892 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 3 2 F := [-11 y z - x z - 9 z, 10 x z - 10 y - 9 z, -8 y - 9 y - 3] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 G := [x + 12 x , 8 x z + 9 x z - 8 y z, 7 x y - 9 x z - 2 x] > Problem := [F,G]; 2 2 3 2 Problem := [[-11 y z - x z - 9 z, 10 x z - 10 y - 9 z, -8 y - 9 y - 3], 3 2 2 [x + 12 x , 8 x z + 9 x z - 8 y z, 7 x y - 9 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=0.17 memory used=26.2MB, alloc=32.3MB, time=0.47 memory used=47.0MB, alloc=32.3MB, time=0.76 memory used=67.2MB, alloc=32.3MB, time=1.05 memory used=86.4MB, alloc=56.3MB, time=1.34 memory used=128.4MB, alloc=60.3MB, time=2.04 memory used=166.4MB, alloc=84.3MB, time=2.69 memory used=222.8MB, alloc=108.3MB, time=3.65 memory used=295.2MB, alloc=132.3MB, time=5.60 memory used=378.7MB, alloc=132.3MB, time=8.74 N1 := 2297 > GB := Basis(F, plex(op(vars))); 2 GB := [64 x + 1515 x + 9540, -39 - 8 x + 99 y, -15812670 - 1877120 x + 5502946977 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=464.7MB, alloc=132.3MB, time=10.93 memory used=568.1MB, alloc=164.3MB, time=13.20 N2 := 1219 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 3 2 3 2 H := [-11 y z - x z - 9 z, 10 z x - 10 y - 9 z, -8 y - 9 y - 3, x + 12 x , 2 8 x z + 9 x z - 8 y z, 7 x y - 9 x z - 2 x] > J:=[op(GB),op(G)]; 2 J := [64 x + 1515 x + 9540, -39 - 8 x + 99 y, 3 2 2 -15812670 - 1877120 x + 5502946977 z, x + 12 x , 8 x z + 9 x z - 8 y z, 7 x y - 9 x z - 2 x] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 14, 16, 3, 3, 3, 1, 5/6, 5/6, 2/3, 9/17, 6/17, 9/17, 6, 12, 11 12, 3, 3, 1, 1, 1, 1/2, 1/2, --, 3/17, 5/17, 2, 4, 0] 17 > save(F, G, cat("ranSet/33", convert(F, string),".txt")); > quit memory used=592.4MB, alloc=164.3MB, time=13.99 |\^/| 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(); 1428290929 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 2 2 2 F := [-11 x + 5 y + 8 x, 7 x z + 8 x + 2 x, -4 x z - 2 x y z - 5 x ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 2 2 2 G := [3 y - 3 y + 5, -6 x y + 3 x , -8 x - 9 y - 5 y z] > Problem := [F,G]; Problem := [ 3 2 2 2 2 2 [-11 x + 5 y + 8 x, 7 x z + 8 x + 2 x, -4 x z - 2 x y z - 5 x ], 3 2 2 2 2 2 [3 y - 3 y + 5, -6 x y + 3 x , -8 x - 9 y - 5 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.2MB, alloc=32.3MB, time=0.50 memory used=46.6MB, alloc=32.3MB, time=0.79 memory used=65.7MB, alloc=56.3MB, time=1.08 memory used=105.4MB, alloc=60.3MB, time=1.67 memory used=144.7MB, alloc=84.3MB, time=2.27 memory used=205.8MB, alloc=92.3MB, time=3.22 memory used=266.6MB, alloc=92.3MB, time=4.15 memory used=325.4MB, alloc=116.3MB, time=5.06 memory used=409.2MB, alloc=116.3MB, time=6.31 memory used=490.6MB, alloc=140.3MB, time=7.82 memory used=586.1MB, alloc=164.3MB, time=9.55 memory used=695.1MB, alloc=188.3MB, time=11.61 memory used=820.6MB, alloc=212.3MB, time=15.07 memory used=949.0MB, alloc=236.3MB, time=19.89 memory used=1094.6MB, alloc=260.3MB, time=25.79 memory used=1264.7MB, alloc=284.3MB, time=32.50 N1 := 3805 > GB := Basis(F, plex(op(vars))); 8 7 6 5 4 3 GB := [123904 x - 388608 x + 627840 x + 1688208 x + 841337 x - 58752 x 2 7 6 5 4 + 4096 x , 76696576 x - 232618496 x + 361779584 x + 1091895856 x 3 2 3 2 7 + 622037139 x + 2357696 x + 8960000 x y, -11 x + 5 y + 8 x, 123904 x 6 5 4 3 2 2 - 388608 x + 627840 x + 1710736 x + 806009 x + 89600 x z - 29376 x , 2 2 7 x z + 8 x + 2 x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1341.8MB, alloc=284.3MB, time=33.92 memory used=1569.6MB, alloc=540.3MB, time=37.39 memory used=1801.2MB, alloc=540.3MB, time=41.38 memory used=2015.5MB, alloc=564.3MB, time=45.44 memory used=2218.8MB, alloc=588.3MB, time=52.96 memory used=2423.3MB, alloc=612.3MB, time=61.90 memory used=2651.9MB, alloc=636.3MB, time=71.40 N2 := 4293 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 2 2 2 2 H := [-11 x + 5 y + 8 x, 7 x z + 8 x + 2 x, -4 x z - 2 x y z - 5 x , 3 2 2 2 2 2 3 y - 3 y + 5, -6 x y + 3 x , -8 x - 9 y - 5 y z] > J:=[op(GB),op(G)]; 8 7 6 5 4 3 J := [123904 x - 388608 x + 627840 x + 1688208 x + 841337 x - 58752 x 2 7 6 5 4 + 4096 x , 76696576 x - 232618496 x + 361779584 x + 1091895856 x 3 2 3 2 7 + 622037139 x + 2357696 x + 8960000 x y, -11 x + 5 y + 8 x, 123904 x 6 5 4 3 2 2 - 388608 x + 627840 x + 1710736 x + 806009 x + 89600 x z - 29376 x , 2 2 3 2 2 2 2 2 7 x z + 8 x + 2 x, 3 y - 3 y + 5, -6 x y + 3 x , -8 x - 9 y - 5 y z] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; 11 featureList := [6, 13, 17, 3, 3, 3, 2, 5/6, 5/6, 1/2, --, 7/17, 4/17, 8, 15, 36, 17 29 8, 8, 3, 2, 7/8, 5/8, 3/8, --, 1/5, 3/35, -2, -19, -5] 35 > save(F, G, cat("ranSet/33", convert(F, string),".txt")); > quit memory used=2697.9MB, alloc=636.3MB, time=72.96 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428291110 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 F := [-3 x y + 4 z - 9 y, -6 x y + 9 x z - y , 9 x y z - 5 y z - 7] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 2 3 G := [9 x z + 12 y - 8 y z, 10 x + 7 x z + 8 z, 5 x z - 3 y ] > Problem := [F,G]; 2 2 2 2 Problem := [[-3 x y + 4 z - 9 y, -6 x y + 9 x z - y , 9 x y z - 5 y z - 7], 2 3 2 2 3 [9 x z + 12 y - 8 y z, 10 x + 7 x z + 8 z, 5 x z - 3 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.0MB, alloc=32.3MB, time=0.51 memory used=46.1MB, alloc=32.3MB, time=0.81 memory used=65.1MB, alloc=56.3MB, time=1.10 memory used=106.0MB, alloc=60.3MB, time=1.70 memory used=146.0MB, alloc=84.3MB, time=2.31 memory used=209.5MB, alloc=92.3MB, time=3.25 memory used=271.5MB, alloc=92.3MB, time=4.18 memory used=333.5MB, alloc=116.3MB, time=5.14 memory used=415.2MB, alloc=372.3MB, time=6.41 memory used=503.7MB, alloc=396.3MB, time=7.72 memory used=624.0MB, alloc=420.3MB, time=9.22 memory used=763.1MB, alloc=444.3MB, time=11.15 memory used=881.2MB, alloc=468.3MB, time=13.04 memory used=1023.6MB, alloc=468.3MB, time=14.64 memory used=1128.8MB, alloc=468.3MB, time=16.04 memory used=1252.6MB, alloc=468.3MB, time=17.53 memory used=1350.6MB, alloc=468.3MB, time=18.84 memory used=1452.5MB, alloc=468.3MB, time=20.35 memory used=1534.1MB, alloc=492.3MB, time=21.61 memory used=1626.8MB, alloc=492.3MB, time=23.23 memory used=1720.5MB, alloc=492.3MB, time=24.54 memory used=1791.8MB, alloc=492.3MB, time=25.62 memory used=1852.8MB, alloc=492.3MB, time=26.60 memory used=1932.7MB, alloc=492.3MB, time=27.90 memory used=1995.5MB, alloc=492.3MB, time=29.04 memory used=2062.9MB, alloc=492.3MB, time=30.36 memory used=2113.5MB, alloc=492.3MB, time=31.30 memory used=2169.8MB, alloc=492.3MB, time=32.41 memory used=2210.7MB, alloc=492.3MB, time=33.42 memory used=2405.6MB, alloc=516.3MB, time=36.45 memory used=2588.8MB, alloc=540.3MB, time=39.36 memory used=2767.4MB, alloc=564.3MB, time=42.11 memory used=2912.2MB, alloc=588.3MB, time=44.74 memory used=3070.9MB, alloc=612.3MB, time=47.72 memory used=3226.5MB, alloc=612.3MB, time=50.52 memory used=3358.8MB, alloc=612.3MB, time=53.02 memory used=3492.1MB, alloc=636.3MB, time=55.54 memory used=3618.4MB, alloc=636.3MB, time=58.13 memory used=3732.3MB, alloc=636.3MB, time=60.64 memory used=3844.4MB, alloc=636.3MB, time=63.20 memory used=3941.5MB, alloc=636.3MB, time=65.22 memory used=4042.4MB, alloc=636.3MB, time=67.62 memory used=4358.1MB, alloc=660.3MB, time=73.17 memory used=4678.4MB, alloc=684.3MB, time=79.68 memory used=5030.0MB, alloc=708.3MB, time=86.31 memory used=5386.8MB, alloc=732.3MB, time=93.00 memory used=5716.5MB, alloc=756.3MB, time=98.34 memory used=6066.4MB, alloc=780.3MB, time=103.48 memory used=6412.8MB, alloc=804.3MB, time=108.60 memory used=6728.5MB, alloc=828.3MB, time=113.99 memory used=6997.0MB, alloc=852.3MB, time=119.98 memory used=7217.6MB, alloc=876.3MB, time=124.76 memory used=7430.3MB, alloc=900.3MB, time=129.50 memory used=7629.7MB, alloc=924.3MB, time=134.03 memory used=7827.7MB, alloc=948.3MB, time=138.36 memory used=8002.5MB, alloc=972.3MB, time=142.37 |\^/| 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(); 1428291410 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 F := [18 x y + 3 x y z + 15 x, -7 y - 10 y z - 9 x, 10 x y z - 5 x y - z ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 2 2 3 G := [2 x y + 3 z + 12 z , 10 x y + y + 8 z, -x y - 6 y z + 8 z ] > Problem := [F,G]; Problem := [ 2 2 2 [18 x y + 3 x y z + 15 x, -7 y - 10 y z - 9 x, 10 x y z - 5 x y - z ], 2 3 2 2 2 3 [2 x y + 3 z + 12 z , 10 x y + y + 8 z, -x y - 6 y z + 8 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.4MB, alloc=32.3MB, time=0.50 memory used=46.5MB, alloc=32.3MB, time=0.80 memory used=64.1MB, alloc=56.3MB, time=1.08 memory used=103.6MB, alloc=60.3MB, time=1.70 memory used=142.4MB, alloc=84.3MB, time=2.32 memory used=205.1MB, alloc=92.3MB, time=3.29 memory used=266.7MB, alloc=92.3MB, time=4.25 memory used=327.6MB, alloc=116.3MB, time=5.19 memory used=408.8MB, alloc=372.3MB, time=6.47 memory used=487.5MB, alloc=396.3MB, time=7.74 memory used=597.6MB, alloc=420.3MB, time=9.47 memory used=724.1MB, alloc=444.3MB, time=11.60 memory used=853.4MB, alloc=444.3MB, time=13.60 memory used=981.7MB, alloc=468.3MB, time=15.29 memory used=1123.2MB, alloc=492.3MB, time=17.86 memory used=1239.1MB, alloc=492.3MB, time=19.83 memory used=1343.3MB, alloc=492.3MB, time=21.73 memory used=1461.2MB, alloc=492.3MB, time=24.02 memory used=1566.1MB, alloc=492.3MB, time=25.77 memory used=1662.1MB, alloc=516.3MB, time=27.66 memory used=1768.0MB, alloc=516.3MB, time=30.09 memory used=1856.5MB, alloc=516.3MB, time=32.03 memory used=1931.2MB, alloc=516.3MB, time=33.70 memory used=2019.8MB, alloc=516.3MB, time=35.63 memory used=2105.1MB, alloc=516.3MB, time=37.60 memory used=2159.4MB, alloc=516.3MB, time=38.81 memory used=2245.4MB, alloc=516.3MB, time=39.86 memory used=2310.9MB, alloc=516.3MB, time=41.30 memory used=2360.2MB, alloc=516.3MB, time=42.23 memory used=2433.6MB, alloc=516.3MB, time=43.78 memory used=2493.6MB, alloc=516.3MB, time=45.29 memory used=2543.4MB, alloc=540.3MB, time=46.50 memory used=2775.1MB, alloc=564.3MB, time=51.18 memory used=2981.1MB, alloc=588.3MB, time=54.89 memory used=3192.1MB, alloc=612.3MB, time=59.63 memory used=3386.0MB, alloc=636.3MB, time=63.73 memory used=3569.4MB, alloc=636.3MB, time=67.56 memory used=3765.6MB, alloc=660.3MB, time=72.42 memory used=3917.9MB, alloc=660.3MB, time=75.24 memory used=4062.8MB, alloc=660.3MB, time=78.43 memory used=4235.0MB, alloc=684.3MB, time=82.80 memory used=4377.4MB, alloc=684.3MB, time=86.19 memory used=4512.2MB, alloc=684.3MB, time=89.82 memory used=4664.4MB, alloc=684.3MB, time=94.01 memory used=4791.4MB, alloc=708.3MB, time=97.48 memory used=4899.4MB, alloc=708.3MB, time=100.00 memory used=5044.6MB, alloc=708.3MB, time=102.22 memory used=5173.4MB, alloc=708.3MB, time=104.62 memory used=5286.2MB, alloc=708.3MB, time=107.31 memory used=5640.0MB, alloc=732.3MB, time=114.43 memory used=5817.7MB, alloc=756.3MB, time=116.38 memory used=6020.0MB, alloc=756.3MB, time=118.33 memory used=6251.1MB, alloc=756.3MB, time=121.88 memory used=6513.3MB, alloc=756.3MB, time=124.64 memory used=6944.1MB, alloc=780.3MB, time=132.88 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428291710 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 F := [-7 x y - 15 y z - 3 z , -3 x y - y z - 2, -7 x y - 6 y + 8 y] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 2 3 2 2 G := [20 x z - 9 y + 17 x z, 3 x y + 4 y + 8 y, -8 x + 8 y z - 5 x ] > Problem := [F,G]; 2 2 2 Problem := [[-7 x y - 15 y z - 3 z , -3 x y - y z - 2, -7 x y - 6 y + 8 y], 2 3 2 2 3 2 2 [20 x z - 9 y + 17 x z, 3 x y + 4 y + 8 y, -8 x + 8 y z - 5 x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=26.7MB, alloc=32.3MB, time=0.51 memory used=47.0MB, alloc=32.3MB, time=0.82 memory used=65.6MB, alloc=56.3MB, time=1.12 memory used=106.2MB, alloc=60.3MB, time=1.72 memory used=146.5MB, alloc=60.3MB, time=2.29 memory used=187.0MB, alloc=92.3MB, time=2.92 memory used=250.6MB, alloc=92.3MB, time=3.89 memory used=301.0MB, alloc=92.3MB, time=4.34 memory used=356.0MB, alloc=92.3MB, time=4.84 memory used=424.0MB, alloc=92.3MB, time=5.66 memory used=494.3MB, alloc=92.3MB, time=6.74 memory used=550.1MB, alloc=92.3MB, time=7.34 memory used=603.4MB, alloc=92.3MB, time=7.85 memory used=664.6MB, alloc=116.3MB, time=8.62 memory used=727.8MB, alloc=372.3MB, time=9.53 memory used=807.8MB, alloc=372.3MB, time=10.81 memory used=890.4MB, alloc=396.3MB, time=12.04 memory used=1000.0MB, alloc=420.3MB, time=13.65 memory used=1122.6MB, alloc=420.3MB, time=15.49 memory used=1249.6MB, alloc=444.3MB, time=17.54 memory used=1365.3MB, alloc=468.3MB, time=19.36 memory used=1488.1MB, alloc=468.3MB, time=20.96 memory used=1588.7MB, alloc=468.3MB, time=21.87 memory used=1699.4MB, alloc=468.3MB, time=23.08 memory used=1800.3MB, alloc=468.3MB, time=24.22 memory used=1895.6MB, alloc=468.3MB, time=24.65 memory used=1989.9MB, alloc=468.3MB, time=25.68 memory used=2087.7MB, alloc=468.3MB, time=26.15 memory used=2182.3MB, alloc=468.3MB, time=27.23 memory used=2330.5MB, alloc=468.3MB, time=29.51 memory used=2478.8MB, alloc=468.3MB, time=31.86 memory used=2569.6MB, alloc=468.3MB, time=33.16 memory used=2665.5MB, alloc=468.3MB, time=35.41 memory used=2784.2MB, alloc=468.3MB, time=36.68 memory used=2884.9MB, alloc=468.3MB, time=37.37 memory used=2981.5MB, alloc=468.3MB, time=38.47 memory used=3062.7MB, alloc=468.3MB, time=38.95 memory used=3157.2MB, alloc=468.3MB, time=39.44 memory used=3253.6MB, alloc=468.3MB, time=40.48 memory used=3348.6MB, alloc=468.3MB, time=41.63 memory used=3468.9MB, alloc=468.3MB, time=42.95 memory used=3584.8MB, alloc=492.3MB, time=44.68 memory used=3689.0MB, alloc=492.3MB, time=45.28 memory used=3809.9MB, alloc=492.3MB, time=46.20 memory used=3923.0MB, alloc=492.3MB, time=47.73 memory used=4024.7MB, alloc=492.3MB, time=49.35 memory used=4168.6MB, alloc=492.3MB, time=51.45 memory used=4273.8MB, alloc=492.3MB, time=54.07 memory used=4374.8MB, alloc=492.3MB, time=54.63 memory used=4472.9MB, alloc=492.3MB, time=55.13 memory used=4570.7MB, alloc=492.3MB, time=56.37 memory used=4669.4MB, alloc=492.3MB, time=56.84 memory used=4777.0MB, alloc=492.3MB, time=58.16 memory used=4874.9MB, alloc=492.3MB, time=58.68 memory used=4973.8MB, alloc=492.3MB, time=59.18 memory used=5073.7MB, alloc=492.3MB, time=60.43 memory used=5210.5MB, alloc=492.3MB, time=62.16 memory used=5337.3MB, alloc=492.3MB, time=64.02 memory used=5450.2MB, alloc=492.3MB, time=65.58 memory used=5517.2MB, alloc=492.3MB, time=66.76 memory used=5627.1MB, alloc=492.3MB, time=68.30 memory used=5688.7MB, alloc=492.3MB, time=69.38 memory used=5787.2MB, alloc=492.3MB, time=70.92 memory used=5850.2MB, alloc=492.3MB, time=72.01 memory used=5912.9MB, alloc=492.3MB, time=73.30 memory used=5978.5MB, alloc=492.3MB, time=74.62 memory used=6044.0MB, alloc=516.3MB, time=75.98 memory used=6107.9MB, alloc=516.3MB, time=77.30 memory used=6166.5MB, alloc=516.3MB, time=78.57 memory used=6225.1MB, alloc=516.3MB, time=79.82 memory used=6266.7MB, alloc=516.3MB, time=80.79 memory used=6453.2MB, alloc=516.3MB, time=83.46 memory used=6637.2MB, alloc=516.3MB, time=85.50 memory used=6806.1MB, alloc=516.3MB, time=87.73 memory used=7025.5MB, alloc=540.3MB, time=91.37 memory used=7250.6MB, alloc=540.3MB, time=95.04 memory used=7378.3MB, alloc=540.3MB, time=95.96 memory used=7492.4MB, alloc=540.3MB, time=97.74 memory used=7587.8MB, alloc=540.3MB, time=98.34 memory used=7821.9MB, alloc=564.3MB, time=100.31 memory used=8033.8MB, alloc=564.3MB, time=103.04 memory used=8232.4MB, alloc=564.3MB, time=105.11 memory used=8357.4MB, alloc=564.3MB, time=105.86 memory used=8498.2MB, alloc=564.3MB, time=107.85 memory used=8615.9MB, alloc=564.3MB, time=108.57 memory used=8767.5MB, alloc=564.3MB, time=110.56 memory used=8942.1MB, alloc=564.3MB, time=112.20 memory used=9073.0MB, alloc=564.3MB, time=113.17 memory used=9204.8MB, alloc=564.3MB, time=116.36 memory used=9309.7MB, alloc=564.3MB, time=116.98 memory used=9503.6MB, alloc=564.3MB, time=118.46 memory used=9713.1MB, alloc=588.3MB, time=123.70 memory used=9896.5MB, alloc=588.3MB, time=125.78 memory used=10095.2MB, alloc=588.3MB, time=127.62 memory used=10235.4MB, alloc=588.3MB, time=128.55 memory used=10376.8MB, alloc=588.3MB, time=131.71 memory used=10546.2MB, alloc=588.3MB, time=132.96 memory used=10781.5MB, alloc=588.3MB, time=136.99 memory used=10967.5MB, alloc=612.3MB, time=140.54 memory used=11132.1MB, alloc=636.3MB, time=143.13 memory used=11328.8MB, alloc=660.3MB, time=146.13 memory used=11568.8MB, alloc=660.3MB, time=149.19 memory used=11913.1MB, alloc=660.3MB, time=152.76 |\^/| 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(); 1428292010 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 3 2 3 3 F := [18 x z + 12 x + 9 z , -3 x - 10 z - 8, 9 y + 5 z + 9 x y] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 3 G := [1 - 3 x - 5 z, -6 x y - 3 x y z - 10 z, 4 x z - 5 y z + 2 z ] > Problem := [F,G]; 2 2 2 3 2 3 3 Problem := [[18 x z + 12 x + 9 z , -3 x - 10 z - 8, 9 y + 5 z + 9 x y], 2 2 2 3 [1 - 3 x - 5 z, -6 x y - 3 x y z - 10 z, 4 x z - 5 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=26.5MB, alloc=32.3MB, time=0.49 memory used=47.0MB, alloc=32.3MB, time=0.79 memory used=66.3MB, alloc=56.3MB, time=1.09 memory used=107.0MB, alloc=60.3MB, time=1.69 memory used=147.5MB, alloc=84.3MB, time=2.30 memory used=210.5MB, alloc=92.3MB, time=3.25 memory used=272.3MB, alloc=92.3MB, time=4.13 memory used=333.3MB, alloc=116.3MB, time=5.00 memory used=412.5MB, alloc=116.3MB, time=6.19 memory used=489.4MB, alloc=140.3MB, time=7.40 memory used=563.0MB, alloc=396.3MB, time=8.60 memory used=664.1MB, alloc=420.3MB, time=10.18 memory used=788.6MB, alloc=420.3MB, time=12.10 memory used=917.1MB, alloc=444.3MB, time=13.99 memory used=1055.8MB, alloc=468.3MB, time=16.23 memory used=1216.0MB, alloc=468.3MB, time=18.83 memory used=1338.6MB, alloc=492.3MB, time=20.75 memory used=1477.6MB, alloc=516.3MB, time=23.10 memory used=1590.9MB, alloc=516.3MB, time=25.03 memory used=1698.8MB, alloc=516.3MB, time=26.84 memory used=1789.1MB, alloc=516.3MB, time=28.45 memory used=1875.3MB, alloc=540.3MB, time=30.01 memory used=1962.6MB, alloc=540.3MB, time=31.63 memory used=2048.2MB, alloc=540.3MB, time=33.12 memory used=2146.0MB, alloc=540.3MB, time=35.08 memory used=2222.7MB, alloc=540.3MB, time=36.62 memory used=2294.6MB, alloc=540.3MB, time=38.19 memory used=2343.9MB, alloc=540.3MB, time=39.21 memory used=2389.1MB, alloc=540.3MB, time=40.15 memory used=2431.8MB, alloc=540.3MB, time=41.11 memory used=2485.1MB, alloc=564.3MB, time=42.03 memory used=2682.0MB, alloc=588.3MB, time=45.50 memory used=2876.6MB, alloc=612.3MB, time=48.74 memory used=3052.7MB, alloc=636.3MB, time=51.45 memory used=3230.1MB, alloc=660.3MB, time=54.87 memory used=3372.2MB, alloc=660.3MB, time=57.69 memory used=3502.0MB, alloc=684.3MB, time=60.18 memory used=3632.4MB, alloc=684.3MB, time=63.03 memory used=3734.3MB, alloc=684.3MB, time=65.37 memory used=3837.1MB, alloc=684.3MB, time=67.32 memory used=3955.9MB, alloc=684.3MB, time=70.26 memory used=4048.9MB, alloc=684.3MB, time=72.26 memory used=4131.8MB, alloc=708.3MB, time=74.27 memory used=4511.9MB, alloc=732.3MB, time=80.50 memory used=4894.3MB, alloc=756.3MB, time=86.62 memory used=5239.9MB, alloc=780.3MB, time=92.95 memory used=5606.1MB, alloc=804.3MB, time=99.21 memory used=5905.3MB, alloc=828.3MB, time=104.15 memory used=6249.6MB, alloc=852.3MB, time=112.47 memory used=6527.8MB, alloc=876.3MB, time=117.83 memory used=6844.0MB, alloc=900.3MB, time=126.10 |\^/| 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(); 1428292310 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 2 2 F := [5 y z - 17 z - 17, 4 x z + 5 z - 9 x, -5 x y - 2 x z - 10 z ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 2 2 G := [19 x z - 8 y z - 19 y z , -8 x z + 8 y z - 7 z, -5 x z - 10 x] > Problem := [F,G]; Problem := [ 2 2 2 2 2 2 [5 y z - 17 z - 17, 4 x z + 5 z - 9 x, -5 x y - 2 x z - 10 z ], 2 2 2 2 2 2 [19 x z - 8 y z - 19 y z , -8 x z + 8 y z - 7 z, -5 x 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=26.4MB, alloc=32.3MB, time=0.49 memory used=47.5MB, alloc=32.3MB, time=0.80 memory used=67.1MB, alloc=56.3MB, time=1.09 memory used=107.6MB, alloc=60.3MB, time=1.68 memory used=147.2MB, alloc=60.3MB, time=2.26 memory used=188.1MB, alloc=60.3MB, time=2.74 memory used=229.7MB, alloc=84.3MB, time=3.32 memory used=291.4MB, alloc=92.3MB, time=4.24 memory used=352.2MB, alloc=116.3MB, time=5.13 memory used=439.0MB, alloc=116.3MB, time=6.28 memory used=518.8MB, alloc=116.3MB, time=7.54 memory used=575.3MB, alloc=140.3MB, time=8.20 memory used=641.7MB, alloc=396.3MB, time=9.20 memory used=750.2MB, alloc=420.3MB, time=10.76 memory used=888.3MB, alloc=444.3MB, time=12.40 memory used=1019.8MB, alloc=468.3MB, time=14.34 memory used=1138.6MB, alloc=468.3MB, time=16.03 memory used=1250.1MB, alloc=468.3MB, time=17.69 memory used=1368.5MB, alloc=492.3MB, time=19.67 memory used=1472.5MB, alloc=492.3MB, time=21.15 memory used=1561.2MB, alloc=492.3MB, time=22.24 memory used=1661.7MB, alloc=492.3MB, time=23.95 memory used=1766.5MB, alloc=516.3MB, time=25.27 memory used=1844.4MB, alloc=516.3MB, time=26.30 memory used=1926.7MB, alloc=516.3MB, time=27.83 memory used=2007.8MB, alloc=516.3MB, time=29.24 memory used=2088.3MB, alloc=516.3MB, time=30.36 memory used=2162.8MB, alloc=516.3MB, time=31.41 memory used=2234.1MB, alloc=516.3MB, time=32.74 memory used=2291.1MB, alloc=516.3MB, time=33.74 memory used=2347.0MB, alloc=516.3MB, time=35.03 memory used=2392.8MB, alloc=516.3MB, time=35.93 memory used=2455.7MB, alloc=516.3MB, time=37.31 memory used=2658.7MB, alloc=540.3MB, time=40.77 memory used=2869.8MB, alloc=564.3MB, time=44.47 memory used=3068.7MB, alloc=588.3MB, time=47.26 memory used=3256.2MB, alloc=612.3MB, time=50.79 memory used=3409.4MB, alloc=636.3MB, time=53.31 memory used=3552.0MB, alloc=636.3MB, time=55.76 memory used=3723.0MB, alloc=636.3MB, time=58.21 memory used=3861.9MB, alloc=660.3MB, time=60.59 memory used=4006.9MB, alloc=660.3MB, time=63.40 memory used=4150.5MB, alloc=660.3MB, time=65.89 memory used=4290.0MB, alloc=660.3MB, time=68.19 memory used=4421.1MB, alloc=660.3MB, time=70.91 memory used=4621.0MB, alloc=684.3MB, time=73.14 memory used=4760.3MB, alloc=684.3MB, time=75.33 memory used=4864.0MB, alloc=684.3MB, time=77.55 memory used=4981.0MB, alloc=684.3MB, time=80.10 memory used=5072.5MB, alloc=684.3MB, time=82.11 memory used=5140.9MB, alloc=684.3MB, time=83.93 memory used=5494.5MB, alloc=708.3MB, time=89.97 memory used=5852.8MB, alloc=732.3MB, time=96.22 memory used=6196.1MB, alloc=756.3MB, time=102.14 memory used=6563.8MB, alloc=780.3MB, time=108.73 memory used=6911.9MB, alloc=804.3MB, time=115.00 memory used=7220.6MB, alloc=828.3MB, time=119.49 memory used=7534.6MB, alloc=852.3MB, time=127.23 memory used=7784.3MB, alloc=876.3MB, time=132.65 memory used=8024.0MB, alloc=900.3MB, time=137.53 memory used=8235.2MB, alloc=924.3MB, time=142.64 memory used=8491.0MB, alloc=948.3MB, time=148.81 memory used=8666.8MB, alloc=972.3MB, time=153.23 memory used=9264.6MB, alloc=996.3MB, time=163.43 |\^/| 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(); 1428292611 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 2 2 2 2 F := [-19 y - 18 y z + 13 y z, 5 x y - 9 y z - 4 x , -9 y z - 2 y + 5] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 G := [-4 y z + 17 x + 11 z , 9 x z - 4 x z + 2 x, -4 x y + 7 x - 3 z] > Problem := [F,G]; Problem := [ 3 2 2 2 2 2 2 [-19 y - 18 y z + 13 y z, 5 x y - 9 y z - 4 x , -9 y z - 2 y + 5], 2 2 2 2 [-4 y z + 17 x + 11 z , 9 x z - 4 x z + 2 x, -4 x y + 7 x - 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=0.17 memory used=26.6MB, alloc=32.3MB, time=0.51 memory used=47.5MB, alloc=56.3MB, time=0.84 memory used=86.7MB, alloc=60.3MB, time=1.43 memory used=124.5MB, alloc=84.3MB, time=2.02 memory used=168.8MB, alloc=84.3MB, time=2.70 memory used=228.8MB, alloc=92.3MB, time=3.65 memory used=288.1MB, alloc=116.3MB, time=4.58 memory used=370.5MB, alloc=116.3MB, time=5.89 memory used=455.8MB, alloc=396.3MB, time=7.13 memory used=567.7MB, alloc=396.3MB, time=8.79 memory used=672.8MB, alloc=420.3MB, time=10.48 memory used=794.5MB, alloc=420.3MB, time=12.40 memory used=917.4MB, alloc=444.3MB, time=14.46 memory used=1062.7MB, alloc=468.3MB, time=16.84 memory used=1223.9MB, alloc=492.3MB, time=19.67 memory used=1378.4MB, alloc=492.3MB, time=22.59 memory used=1501.5MB, alloc=516.3MB, time=24.64 memory used=1649.7MB, alloc=516.3MB, time=26.79 memory used=1772.2MB, alloc=516.3MB, time=30.16 memory used=1945.4MB, alloc=516.3MB, time=32.95 memory used=2093.1MB, alloc=540.3MB, time=34.67 memory used=2222.7MB, alloc=540.3MB, time=36.94 memory used=2370.9MB, alloc=540.3MB, time=40.44 memory used=2534.1MB, alloc=540.3MB, time=42.86 memory used=2714.7MB, alloc=540.3MB, time=44.95 memory used=2817.6MB, alloc=540.3MB, time=47.07 memory used=2911.3MB, alloc=540.3MB, time=48.70 memory used=3043.8MB, alloc=540.3MB, time=50.88 memory used=3156.3MB, alloc=540.3MB, time=52.78 memory used=3247.9MB, alloc=540.3MB, time=54.35 memory used=3375.9MB, alloc=540.3MB, time=56.18 memory used=3483.3MB, alloc=564.3MB, time=57.91 memory used=3600.4MB, alloc=564.3MB, time=59.62 memory used=3686.3MB, alloc=564.3MB, time=61.71 memory used=3768.9MB, alloc=564.3MB, time=63.73 memory used=3850.9MB, alloc=564.3MB, time=65.52 memory used=3900.7MB, alloc=564.3MB, time=66.79 memory used=3983.9MB, alloc=564.3MB, time=68.58 memory used=4058.5MB, alloc=564.3MB, time=70.00 memory used=4113.0MB, alloc=564.3MB, time=70.96 memory used=4181.3MB, alloc=564.3MB, time=72.72 memory used=4427.6MB, alloc=588.3MB, time=77.30 memory used=4685.0MB, alloc=612.3MB, time=83.06 memory used=4896.9MB, alloc=636.3MB, time=87.03 memory used=5106.0MB, alloc=660.3MB, time=91.62 memory used=5340.6MB, alloc=684.3MB, time=97.38 memory used=5529.3MB, alloc=708.3MB, time=101.77 memory used=5695.4MB, alloc=708.3MB, time=105.17 memory used=5887.1MB, alloc=708.3MB, time=109.65 memory used=6060.6MB, alloc=732.3MB, time=114.39 memory used=6186.6MB, alloc=732.3MB, time=117.38 memory used=6322.2MB, alloc=732.3MB, time=120.22 memory used=6436.5MB, alloc=732.3MB, time=123.12 memory used=6561.6MB, alloc=756.3MB, time=126.41 memory used=6641.5MB, alloc=756.3MB, time=128.82 memory used=7040.5MB, alloc=780.3MB, time=137.01 memory used=7488.0MB, alloc=804.3MB, time=145.60 memory used=7863.7MB, alloc=828.3MB, time=152.84 |\^/| 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(); 1428292911 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 2 2 F := [3 x y z - 17 y z - 6, -5 y z + 4 y , 6 x z - 2 y z + 2 y ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 3 2 G := [15 x z - 16 x y + 10 y z, x z - 3 z - 10 z , -8 x z - 3 y z - y] > Problem := [F,G]; 2 2 2 2 2 2 Problem := [[3 x y z - 17 y z - 6, -5 y z + 4 y , 6 x z - 2 y z + 2 y ], 2 2 2 2 3 2 [15 x z - 16 x y + 10 y z, x z - 3 z - 10 z , -8 x z - 3 y z - y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.16 memory used=26.3MB, alloc=32.3MB, time=0.49 memory used=46.8MB, alloc=32.3MB, time=0.80 memory used=65.4MB, alloc=56.3MB, time=1.09 memory used=105.1MB, alloc=84.3MB, time=1.68 memory used=146.2MB, alloc=84.3MB, time=2.29 memory used=206.1MB, alloc=116.3MB, time=3.23 memory used=285.4MB, alloc=116.3MB, time=4.48 memory used=363.8MB, alloc=140.3MB, time=5.64 memory used=427.4MB, alloc=396.3MB, time=6.60 memory used=528.8MB, alloc=420.3MB, time=8.14 memory used=652.1MB, alloc=444.3MB, time=10.06 memory used=798.6MB, alloc=468.3MB, time=12.34 memory used=940.9MB, alloc=492.3MB, time=14.73 memory used=1063.7MB, alloc=516.3MB, time=16.62 memory used=1174.1MB, alloc=516.3MB, time=18.47 memory used=1282.1MB, alloc=540.3MB, time=20.41 memory used=1390.8MB, alloc=540.3MB, time=22.21 memory used=1489.3MB, alloc=540.3MB, time=23.97 memory used=1579.4MB, alloc=540.3MB, time=25.71 memory used=1656.9MB, alloc=540.3MB, time=27.13 memory used=1745.4MB, alloc=564.3MB, time=28.74 memory used=1829.3MB, alloc=564.3MB, time=30.40 memory used=1905.7MB, alloc=564.3MB, time=31.96 memory used=1990.2MB, alloc=564.3MB, time=33.66 memory used=2081.5MB, alloc=564.3MB, time=35.59 memory used=2151.5MB, alloc=564.3MB, time=36.90 memory used=2214.9MB, alloc=588.3MB, time=38.09 memory used=2270.0MB, alloc=588.3MB, time=38.99 memory used=2340.4MB, alloc=588.3MB, time=40.76 memory used=2384.6MB, alloc=588.3MB, time=42.01 memory used=2618.0MB, alloc=612.3MB, time=46.06 memory used=2818.6MB, alloc=636.3MB, time=49.78 memory used=3006.6MB, alloc=660.3MB, time=52.94 memory used=3209.5MB, alloc=684.3MB, time=57.24 memory used=3400.5MB, alloc=708.3MB, time=60.82 memory used=3558.3MB, alloc=708.3MB, time=64.67 memory used=3700.6MB, alloc=708.3MB, time=68.29 memory used=3860.3MB, alloc=732.3MB, time=72.28 memory used=3993.2MB, alloc=732.3MB, time=75.24 memory used=4142.7MB, alloc=732.3MB, time=79.27 memory used=4271.9MB, alloc=732.3MB, time=82.27 memory used=4397.6MB, alloc=732.3MB, time=85.97 memory used=4490.5MB, alloc=732.3MB, time=88.56 memory used=4872.0MB, alloc=756.3MB, time=95.92 memory used=5293.4MB, alloc=780.3MB, time=102.65 memory used=5704.2MB, alloc=804.3MB, time=109.30 memory used=6066.3MB, alloc=828.3MB, time=116.69 memory used=6406.0MB, alloc=852.3MB, time=124.36 memory used=6708.4MB, alloc=876.3MB, time=130.75 memory used=6997.8MB, alloc=900.3MB, time=136.94 memory used=7344.3MB, alloc=924.3MB, time=144.53 memory used=7638.9MB, alloc=948.3MB, time=149.54 memory used=7934.2MB, alloc=972.3MB, time=156.05 |\^/| 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(); 1428293211 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 F := [4 y z + 12 x - 16 x, 7 x y - 7 y + 3, -y z + 10 y ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 2 2 G := [5 y z + 4 z + 9 x, 4 y z - 8 x - 5 x z, -5 y z + x z] > Problem := [F,G]; 2 2 2 2 Problem := [[4 y z + 12 x - 16 x, 7 x y - 7 y + 3, -y z + 10 y ], 2 3 2 2 2 [5 y z + 4 z + 9 x, 4 y z - 8 x - 5 x z, -5 y z + x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.3MB, alloc=32.3MB, time=0.48 memory used=47.7MB, alloc=32.3MB, time=0.79 memory used=68.0MB, alloc=32.3MB, time=1.10 memory used=87.3MB, alloc=56.3MB, time=1.41 memory used=128.4MB, alloc=60.3MB, time=2.01 memory used=167.0MB, alloc=84.3MB, time=2.60 memory used=210.3MB, alloc=84.3MB, time=3.25 memory used=268.3MB, alloc=116.3MB, time=4.20 memory used=347.6MB, alloc=372.3MB, time=5.39 memory used=430.4MB, alloc=372.3MB, time=6.65 memory used=516.1MB, alloc=396.3MB, time=7.87 memory used=625.2MB, alloc=420.3MB, time=9.49 memory used=757.1MB, alloc=420.3MB, time=11.44 memory used=888.8MB, alloc=444.3MB, time=13.51 memory used=1033.1MB, alloc=468.3MB, time=15.96 memory used=1182.9MB, alloc=492.3MB, time=18.64 memory used=1309.1MB, alloc=492.3MB, time=20.73 memory used=1437.9MB, alloc=492.3MB, time=22.94 memory used=1543.5MB, alloc=516.3MB, time=24.64 memory used=1645.0MB, alloc=516.3MB, time=26.28 memory used=1743.2MB, alloc=516.3MB, time=27.88 memory used=1835.2MB, alloc=516.3MB, time=29.51 memory used=1933.8MB, alloc=516.3MB, time=31.26 memory used=2026.6MB, alloc=516.3MB, time=32.96 memory used=2130.5MB, alloc=540.3MB, time=35.00 memory used=2228.5MB, alloc=540.3MB, time=36.85 memory used=2319.3MB, alloc=540.3MB, time=38.13 memory used=2422.1MB, alloc=540.3MB, time=40.15 memory used=2489.8MB, alloc=540.3MB, time=41.31 memory used=2617.9MB, alloc=540.3MB, time=42.19 memory used=2729.9MB, alloc=540.3MB, time=42.80 memory used=2861.6MB, alloc=540.3MB, time=44.54 memory used=2987.5MB, alloc=540.3MB, time=46.07 memory used=3102.5MB, alloc=540.3MB, time=47.44 memory used=3177.4MB, alloc=540.3MB, time=48.66 memory used=3255.3MB, alloc=564.3MB, time=50.19 memory used=3342.4MB, alloc=564.3MB, time=51.64 memory used=3406.2MB, alloc=564.3MB, time=53.02 memory used=3463.3MB, alloc=564.3MB, time=54.14 memory used=3522.5MB, alloc=564.3MB, time=55.49 memory used=3576.2MB, alloc=564.3MB, time=56.60 memory used=3642.9MB, alloc=564.3MB, time=57.96 memory used=3701.8MB, alloc=564.3MB, time=59.18 memory used=3747.9MB, alloc=564.3MB, time=60.38 memory used=3802.8MB, alloc=564.3MB, time=61.70 memory used=4043.8MB, alloc=588.3MB, time=66.95 memory used=4205.7MB, alloc=612.3MB, time=69.31 memory used=4394.4MB, alloc=612.3MB, time=71.78 memory used=4653.5MB, alloc=636.3MB, time=75.67 memory used=4856.4MB, alloc=660.3MB, time=79.59 memory used=5124.6MB, alloc=660.3MB, time=82.98 memory used=5303.9MB, alloc=660.3MB, time=89.03 memory used=5445.7MB, alloc=660.3MB, time=89.85 memory used=5746.4MB, alloc=660.3MB, time=91.66 memory used=6028.6MB, alloc=660.3MB, time=96.74 memory used=6336.8MB, alloc=684.3MB, time=106.86 memory used=6460.1MB, alloc=708.3MB, time=107.70 memory used=6604.8MB, alloc=708.3MB, time=108.61 memory used=6766.0MB, alloc=708.3MB, time=109.55 memory used=6944.9MB, alloc=708.3MB, time=110.53 memory used=7145.3MB, alloc=708.3MB, time=111.45 memory used=7365.0MB, alloc=708.3MB, time=112.36 memory used=7498.9MB, alloc=708.3MB, time=113.13 memory used=7880.9MB, alloc=708.3MB, time=180.53 memory used=8022.9MB, alloc=708.3MB, time=181.26 memory used=8167.6MB, alloc=708.3MB, time=182.02 memory used=8314.2MB, alloc=708.3MB, time=182.76 memory used=8466.8MB, alloc=708.3MB, time=183.49 memory used=8623.0MB, alloc=708.3MB, time=184.21 memory used=8784.8MB, alloc=708.3MB, time=184.95 memory used=8955.1MB, alloc=708.3MB, time=185.70 memory used=9327.3MB, alloc=708.3MB, time=189.88 memory used=9581.7MB, alloc=708.3MB, time=194.17 |\^/| 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(); 1428293511 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 2 3 2 F := [-x y z - 20 y z - 19, -6 x - 10 x z + 4 y , 8 x + 3 x z + 5 y z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 3 2 2 2 G := [17 y z - 10 z + 12 x y, 10 y - 8 z - 9 x, -6 x z - 8 z - 10] > Problem := [F,G]; Problem := [ 2 3 2 2 3 2 [-x y z - 20 y z - 19, -6 x - 10 x z + 4 y , 8 x + 3 x z + 5 y z], 2 3 3 2 2 2 [17 y z - 10 z + 12 x y, 10 y - 8 z - 9 x, -6 x z - 8 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=4.2MB, alloc=32.3MB, time=0.18 memory used=26.3MB, alloc=32.3MB, time=0.52 memory used=47.0MB, alloc=60.3MB, time=0.81 memory used=87.0MB, alloc=60.3MB, time=1.39 memory used=129.2MB, alloc=68.3MB, time=2.02 memory used=171.7MB, alloc=92.3MB, time=2.53 memory used=245.1MB, alloc=92.3MB, time=3.38 memory used=317.1MB, alloc=348.3MB, time=4.26 memory used=386.2MB, alloc=372.3MB, time=5.24 memory used=478.2MB, alloc=372.3MB, time=6.53 memory used=570.9MB, alloc=396.3MB, time=7.72 memory used=670.0MB, alloc=396.3MB, time=8.73 memory used=755.9MB, alloc=396.3MB, time=9.56 memory used=879.3MB, alloc=420.3MB, time=11.06 memory used=1005.4MB, alloc=420.3MB, time=12.67 memory used=1107.1MB, alloc=444.3MB, time=14.19 memory used=1214.3MB, alloc=444.3MB, time=15.80 memory used=1322.1MB, alloc=468.3MB, time=16.70 memory used=1434.6MB, alloc=468.3MB, time=17.33 memory used=1533.0MB, alloc=468.3MB, time=18.04 memory used=1634.5MB, alloc=468.3MB, time=19.40 memory used=1793.7MB, alloc=468.3MB, time=21.35 memory used=1921.8MB, alloc=468.3MB, time=22.48 memory used=2016.4MB, alloc=468.3MB, time=23.20 memory used=2091.9MB, alloc=468.3MB, time=23.55 memory used=2195.6MB, alloc=468.3MB, time=25.50 memory used=2268.2MB, alloc=468.3MB, time=25.81 memory used=2376.4MB, alloc=468.3MB, time=27.16 memory used=2459.3MB, alloc=468.3MB, time=28.26 memory used=2566.4MB, alloc=468.3MB, time=28.87 memory used=2668.4MB, alloc=468.3MB, time=29.62 memory used=2747.2MB, alloc=468.3MB, time=30.64 memory used=2868.5MB, alloc=492.3MB, time=31.72 memory used=2978.5MB, alloc=492.3MB, time=32.33 memory used=3093.5MB, alloc=492.3MB, time=34.44 memory used=3183.7MB, alloc=492.3MB, time=34.84 memory used=3294.3MB, alloc=492.3MB, time=36.18 memory used=3425.0MB, alloc=492.3MB, time=37.67 memory used=3539.2MB, alloc=492.3MB, time=39.56 memory used=3637.6MB, alloc=492.3MB, time=41.71 memory used=3707.4MB, alloc=492.3MB, time=42.95 memory used=3773.5MB, alloc=492.3MB, time=44.07 memory used=3835.0MB, alloc=492.3MB, time=45.12 memory used=3914.9MB, alloc=492.3MB, time=46.22 memory used=3975.5MB, alloc=492.3MB, time=47.20 memory used=4090.8MB, alloc=492.3MB, time=47.91 memory used=4190.2MB, alloc=492.3MB, time=48.91 memory used=4277.5MB, alloc=492.3MB, time=49.77 memory used=4366.2MB, alloc=492.3MB, time=50.28 memory used=4470.5MB, alloc=492.3MB, time=50.90 memory used=4574.2MB, alloc=492.3MB, time=53.38 memory used=4685.7MB, alloc=492.3MB, time=54.30 memory used=4720.9MB, alloc=492.3MB, time=55.03 memory used=4881.5MB, alloc=516.3MB, time=57.13 memory used=5136.7MB, alloc=516.3MB, time=59.98 memory used=5280.3MB, alloc=516.3MB, time=61.69 memory used=5474.5MB, alloc=540.3MB, time=63.84 memory used=5726.0MB, alloc=540.3MB, time=66.91 memory used=5868.9MB, alloc=540.3MB, time=69.55 memory used=6073.7MB, alloc=540.3MB, time=72.15 memory used=6256.6MB, alloc=564.3MB, time=75.11 memory used=6396.4MB, alloc=588.3MB, time=77.04 memory used=6594.7MB, alloc=612.3MB, time=79.76 memory used=6747.4MB, alloc=636.3MB, time=82.35 memory used=6891.8MB, alloc=636.3MB, time=84.88 memory used=7004.6MB, alloc=660.3MB, time=86.87 memory used=7118.7MB, alloc=660.3MB, time=88.64 memory used=7234.4MB, alloc=660.3MB, time=90.97 memory used=7317.2MB, alloc=660.3MB, time=92.66 memory used=7668.1MB, alloc=684.3MB, time=97.43 memory used=7990.4MB, alloc=708.3MB, time=101.43 memory used=8139.8MB, alloc=732.3MB, time=102.51 memory used=8340.5MB, alloc=732.3MB, time=104.22 memory used=8708.2MB, alloc=756.3MB, time=108.01 memory used=9132.3MB, alloc=780.3MB, time=111.93 memory used=9501.4MB, alloc=804.3MB, time=117.68 memory used=9821.0MB, alloc=828.3MB, time=122.61 memory used=10153.8MB, alloc=852.3MB, time=127.88 memory used=10581.9MB, alloc=876.3MB, time=133.55 memory used=10940.8MB, alloc=900.3MB, time=138.97 memory used=11257.9MB, alloc=924.3MB, time=143.44 memory used=11672.9MB, alloc=948.3MB, time=148.84 memory used=11923.8MB, alloc=972.3MB, time=153.07 memory used=12189.9MB, alloc=996.3MB, time=157.82 memory used=12428.8MB, alloc=1020.3MB, time=162.30 memory used=12615.3MB, alloc=1020.3MB, time=166.07 memory used=13078.6MB, alloc=1020.3MB, time=171.25 memory used=13854.5MB, alloc=1044.3MB, time=183.42 |\^/| 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(); 1428293811 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 2 2 F := [13 x y + 15 x z - 19 z, 4 x y - 5 y - 3 z , -10 x z - 6 y z - 7 z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 3 2 2 G := [14 x + 7 z - 20, 7 x z - 2 x y z + 8 x, -y - 5 y - 8 z ] > Problem := [F,G]; Problem := [ 2 2 2 2 2 2 [13 x y + 15 x z - 19 z, 4 x y - 5 y - 3 z , -10 x z - 6 y z - 7 z], 2 2 2 3 2 2 [14 x + 7 z - 20, 7 x z - 2 x y z + 8 x, -y - 5 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=0.17 memory used=26.7MB, alloc=32.3MB, time=0.50 memory used=48.1MB, alloc=32.3MB, time=0.81 memory used=68.2MB, alloc=56.3MB, time=1.12 memory used=109.2MB, alloc=60.3MB, time=1.72 memory used=148.5MB, alloc=60.3MB, time=2.30 memory used=185.0MB, alloc=84.3MB, time=2.84 memory used=229.1MB, alloc=84.3MB, time=3.53 memory used=289.3MB, alloc=116.3MB, time=4.46 memory used=363.4MB, alloc=372.3MB, time=5.58 memory used=444.7MB, alloc=396.3MB, time=6.82 memory used=553.1MB, alloc=396.3MB, time=8.44 memory used=659.2MB, alloc=420.3MB, time=9.98 memory used=783.8MB, alloc=444.3MB, time=11.94 memory used=930.9MB, alloc=468.3MB, time=14.39 memory used=1057.8MB, alloc=468.3MB, time=16.40 memory used=1171.4MB, alloc=492.3MB, time=18.16 memory used=1286.5MB, alloc=492.3MB, time=19.92 memory used=1387.5MB, alloc=492.3MB, time=21.64 memory used=1502.0MB, alloc=516.3MB, time=23.72 memory used=1595.2MB, alloc=516.3MB, time=25.49 memory used=1664.0MB, alloc=516.3MB, time=26.72 memory used=1752.7MB, alloc=516.3MB, time=28.54 memory used=1847.5MB, alloc=516.3MB, time=30.57 memory used=1904.5MB, alloc=516.3MB, time=31.62 memory used=1957.3MB, alloc=516.3MB, time=32.67 memory used=2032.3MB, alloc=516.3MB, time=34.16 memory used=2083.0MB, alloc=540.3MB, time=35.23 memory used=2134.7MB, alloc=540.3MB, time=36.42 memory used=2341.0MB, alloc=564.3MB, time=40.05 memory used=2545.4MB, alloc=588.3MB, time=43.70 memory used=2719.3MB, alloc=612.3MB, time=46.78 memory used=2872.1MB, alloc=636.3MB, time=49.85 memory used=3001.3MB, alloc=636.3MB, time=52.24 memory used=3147.7MB, alloc=636.3MB, time=55.13 memory used=3302.2MB, alloc=660.3MB, time=58.16 memory used=3444.2MB, alloc=660.3MB, time=61.08 memory used=3586.7MB, alloc=660.3MB, time=64.52 memory used=3693.8MB, alloc=660.3MB, time=66.57 memory used=3806.9MB, alloc=660.3MB, time=69.38 memory used=3892.9MB, alloc=684.3MB, time=71.55 memory used=4234.1MB, alloc=708.3MB, time=78.55 memory used=4600.6MB, alloc=732.3MB, time=86.00 memory used=4959.5MB, alloc=756.3MB, time=93.02 memory used=5290.9MB, alloc=780.3MB, time=100.02 memory used=5635.8MB, alloc=804.3MB, time=107.61 memory used=5931.6MB, alloc=828.3MB, time=113.97 memory used=6230.0MB, alloc=852.3MB, time=120.28 memory used=6490.2MB, alloc=876.3MB, time=125.94 memory used=6752.2MB, alloc=900.3MB, time=131.84 memory used=6990.3MB, alloc=924.3MB, time=137.97 memory used=7133.8MB, alloc=948.3MB, time=142.78 memory used=7329.2MB, alloc=972.3MB, time=147.41 memory used=7452.7MB, alloc=972.3MB, time=151.28 |\^/| 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(); 1428294111 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 3 3 2 F := [-17 x y z - 4 x , -3 x z - 6 z + y z, z + 10 y + 6 y z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 3 2 2 2 2 G := [17 y + 7 x - 2 y , 6 y + 4 y , x z - 10 x y - 3 x ] > Problem := [F,G]; 2 2 3 3 2 Problem := [[-17 x y z - 4 x , -3 x z - 6 z + y z, z + 10 y + 6 y z], 3 2 2 3 2 2 2 2 [17 y + 7 x - 2 y , 6 y + 4 y , x z - 10 x y - 3 x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.3MB, alloc=32.3MB, time=0.47 memory used=47.2MB, alloc=32.3MB, time=0.77 memory used=67.2MB, alloc=56.3MB, time=1.08 memory used=107.3MB, alloc=60.3MB, time=1.70 memory used=146.9MB, alloc=84.3MB, time=2.30 memory used=207.6MB, alloc=92.3MB, time=3.28 memory used=267.3MB, alloc=116.3MB, time=4.18 memory used=348.1MB, alloc=116.3MB, time=5.42 memory used=427.1MB, alloc=140.3MB, time=6.69 memory used=506.9MB, alloc=140.3MB, time=7.87 memory used=577.8MB, alloc=420.3MB, time=8.91 memory used=703.2MB, alloc=420.3MB, time=10.97 memory used=831.3MB, alloc=444.3MB, time=13.05 memory used=971.8MB, alloc=468.3MB, time=15.07 memory used=1091.9MB, alloc=468.3MB, time=16.92 memory used=1221.6MB, alloc=492.3MB, time=19.11 memory used=1343.1MB, alloc=492.3MB, time=20.92 memory used=1444.3MB, alloc=492.3MB, time=22.62 memory used=1542.0MB, alloc=516.3MB, time=24.08 memory used=1637.1MB, alloc=516.3MB, time=25.76 memory used=1734.1MB, alloc=516.3MB, time=27.50 memory used=1826.5MB, alloc=516.3MB, time=29.43 memory used=1906.1MB, alloc=516.3MB, time=30.98 memory used=1981.6MB, alloc=516.3MB, time=32.25 memory used=2061.7MB, alloc=516.3MB, time=33.74 memory used=2125.6MB, alloc=540.3MB, time=34.83 memory used=2191.0MB, alloc=540.3MB, time=36.24 memory used=2254.6MB, alloc=540.3MB, time=37.52 memory used=2309.5MB, alloc=540.3MB, time=38.72 memory used=2362.7MB, alloc=540.3MB, time=40.12 memory used=2585.7MB, alloc=564.3MB, time=44.56 memory used=2849.1MB, alloc=588.3MB, time=47.92 memory used=3043.8MB, alloc=612.3MB, time=51.48 memory used=3226.1MB, alloc=636.3MB, time=54.69 memory used=3435.0MB, alloc=660.3MB, time=57.83 memory used=3608.7MB, alloc=660.3MB, time=60.99 memory used=3838.0MB, alloc=684.3MB, time=64.04 memory used=3985.0MB, alloc=684.3MB, time=66.51 memory used=4126.2MB, alloc=684.3MB, time=69.16 memory used=4259.0MB, alloc=684.3MB, time=71.74 memory used=4416.7MB, alloc=708.3MB, time=74.60 memory used=4538.8MB, alloc=708.3MB, time=76.73 memory used=4657.9MB, alloc=708.3MB, time=79.15 memory used=4777.7MB, alloc=708.3MB, time=81.50 memory used=4897.0MB, alloc=732.3MB, time=84.05 memory used=5049.0MB, alloc=732.3MB, time=87.27 memory used=5448.2MB, alloc=756.3MB, time=93.61 memory used=5765.5MB, alloc=780.3MB, time=100.28 memory used=6086.2MB, alloc=804.3MB, time=106.99 memory used=6417.1MB, alloc=828.3MB, time=114.01 memory used=6767.5MB, alloc=852.3MB, time=120.77 |\^/| 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(); 1428294411 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 2 2 F := [-16 x y - z + 20 x z, 2 y z + 10 y, 7 x z + 5 z - 10 z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 3 G := [9 x y + 17 x y z + 15 y, 3 x + 10 y z - 5, -6 x y - 7 y + 8] > Problem := [F,G]; 2 3 2 2 2 Problem := [[-16 x y - z + 20 x z, 2 y z + 10 y, 7 x z + 5 z - 10 z], 2 3 2 3 [9 x y + 17 x y z + 15 y, 3 x + 10 y z - 5, -6 x y - 7 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=0.17 memory used=26.2MB, alloc=32.3MB, time=0.48 memory used=46.6MB, alloc=32.3MB, time=0.76 memory used=65.7MB, alloc=56.3MB, time=1.05 memory used=105.1MB, alloc=60.3MB, time=1.62 memory used=143.6MB, alloc=60.3MB, time=2.19 memory used=182.4MB, alloc=84.3MB, time=2.77 memory used=228.4MB, alloc=84.3MB, time=3.48 memory used=287.3MB, alloc=92.3MB, time=4.38 memory used=342.7MB, alloc=116.3MB, time=5.24 memory used=418.0MB, alloc=140.3MB, time=6.37 memory used=492.1MB, alloc=396.3MB, time=7.52 memory used=598.5MB, alloc=420.3MB, time=9.20 memory used=732.6MB, alloc=444.3MB, time=11.11 memory used=871.9MB, alloc=444.3MB, time=13.20 memory used=999.9MB, alloc=468.3MB, time=15.08 memory used=1116.6MB, alloc=468.3MB, time=16.86 memory used=1232.5MB, alloc=492.3MB, time=18.69 memory used=1358.4MB, alloc=492.3MB, time=20.89 memory used=1456.8MB, alloc=492.3MB, time=22.68 memory used=1548.6MB, alloc=516.3MB, time=24.09 memory used=1643.1MB, alloc=516.3MB, time=25.74 memory used=1729.7MB, alloc=516.3MB, time=27.42 memory used=1811.2MB, alloc=516.3MB, time=29.07 memory used=1874.4MB, alloc=516.3MB, time=30.26 memory used=1955.7MB, alloc=516.3MB, time=31.86 memory used=2019.5MB, alloc=516.3MB, time=32.96 memory used=2094.7MB, alloc=516.3MB, time=34.61 memory used=2153.8MB, alloc=516.3MB, time=35.74 memory used=2221.6MB, alloc=516.3MB, time=37.38 memory used=2433.2MB, alloc=540.3MB, time=41.13 memory used=2656.3MB, alloc=564.3MB, time=45.32 memory used=2858.9MB, alloc=588.3MB, time=49.01 memory used=3051.1MB, alloc=612.3MB, time=52.30 memory used=3244.7MB, alloc=636.3MB, time=56.41 memory used=3422.9MB, alloc=660.3MB, time=60.51 memory used=3552.9MB, alloc=660.3MB, time=63.49 memory used=3706.5MB, alloc=684.3MB, time=66.67 memory used=3848.5MB, alloc=684.3MB, time=69.84 memory used=3951.4MB, alloc=684.3MB, time=72.48 memory used=4076.5MB, alloc=684.3MB, time=75.54 memory used=4174.5MB, alloc=684.3MB, time=78.02 memory used=4524.9MB, alloc=708.3MB, time=85.34 memory used=4905.4MB, alloc=732.3MB, time=92.44 memory used=5302.5MB, alloc=756.3MB, time=100.64 memory used=5715.9MB, alloc=780.3MB, time=109.15 memory used=6076.1MB, alloc=804.3MB, time=117.63 memory used=6433.8MB, alloc=828.3MB, time=125.42 memory used=6733.2MB, alloc=852.3MB, time=131.93 |\^/| 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(); 1428294711 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 F := [5 x z + 5 y z + 15 y, 4 x z + 3 y z + 10 z, 9 z - 8 x y] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 2 3 3 G := [5 x y + 10 y - 8 y z , 2 x y - 5 z + 4 y, -6 x + 2 x z + 3 y] > Problem := [F,G]; 2 3 Problem := [[5 x z + 5 y z + 15 y, 4 x z + 3 y z + 10 z, 9 z - 8 x y], 2 3 2 2 3 3 [5 x y + 10 y - 8 y z , 2 x y - 5 z + 4 y, -6 x + 2 x z + 3 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.6MB, alloc=32.3MB, time=0.50 memory used=47.3MB, alloc=32.3MB, time=0.80 memory used=67.2MB, alloc=56.3MB, time=1.10 memory used=107.3MB, alloc=60.3MB, time=1.72 memory used=147.0MB, alloc=60.3MB, time=2.32 memory used=184.9MB, alloc=84.3MB, time=2.94 memory used=229.9MB, alloc=84.3MB, time=3.66 memory used=288.2MB, alloc=116.3MB, time=4.60 memory used=368.2MB, alloc=372.3MB, time=5.88 memory used=447.9MB, alloc=396.3MB, time=7.22 memory used=554.1MB, alloc=420.3MB, time=8.97 memory used=679.9MB, alloc=420.3MB, time=11.00 memory used=805.4MB, alloc=444.3MB, time=13.02 memory used=949.4MB, alloc=468.3MB, time=15.46 memory used=1092.3MB, alloc=468.3MB, time=17.86 memory used=1217.7MB, alloc=492.3MB, time=20.20 memory used=1335.3MB, alloc=492.3MB, time=22.37 memory used=1443.4MB, alloc=492.3MB, time=24.36 memory used=1548.7MB, alloc=516.3MB, time=26.24 memory used=1641.2MB, alloc=516.3MB, time=28.01 memory used=1729.4MB, alloc=516.3MB, time=29.61 memory used=1818.8MB, alloc=516.3MB, time=31.56 memory used=1908.5MB, alloc=516.3MB, time=33.45 memory used=1978.1MB, alloc=540.3MB, time=34.90 memory used=2045.8MB, alloc=540.3MB, time=36.38 memory used=2107.4MB, alloc=540.3MB, time=37.55 memory used=2164.8MB, alloc=540.3MB, time=38.51 memory used=2239.0MB, alloc=540.3MB, time=40.27 memory used=2304.6MB, alloc=540.3MB, time=41.95 memory used=2360.7MB, alloc=540.3MB, time=43.35 memory used=2583.5MB, alloc=564.3MB, time=47.78 memory used=2788.8MB, alloc=588.3MB, time=51.75 memory used=2970.8MB, alloc=612.3MB, time=55.28 memory used=3132.3MB, alloc=636.3MB, time=58.45 memory used=3283.0MB, alloc=660.3MB, time=61.73 memory used=3429.1MB, alloc=660.3MB, time=65.01 memory used=3541.5MB, alloc=660.3MB, time=67.69 memory used=3633.3MB, alloc=684.3MB, time=69.63 memory used=3758.6MB, alloc=684.3MB, time=72.92 memory used=3864.2MB, alloc=684.3MB, time=75.72 memory used=4214.2MB, alloc=708.3MB, time=82.96 memory used=4593.7MB, alloc=732.3MB, time=90.43 memory used=4899.0MB, alloc=756.3MB, time=96.44 memory used=5244.9MB, alloc=780.3MB, time=104.21 memory used=5569.6MB, alloc=804.3MB, time=111.46 memory used=5898.8MB, alloc=828.3MB, time=118.07 memory used=6145.8MB, alloc=852.3MB, time=123.74 memory used=6396.6MB, alloc=876.3MB, time=129.71 memory used=6669.0MB, alloc=900.3MB, time=137.16 |\^/| 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(); 1428295011 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 3 2 3 2 F := [16 x - 11 x z - 4 z, 5 y + 8 y z + 4 x z, 5 x - 5 x z + 5 x z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 3 2 2 G := [-12 y z - 19 z + 7 x z, -9 x z - 3 y + 10 z, 10 y z - 3 x y + 9 y ] > Problem := [F,G]; Problem := [ 3 3 2 3 2 [16 x - 11 x z - 4 z, 5 y + 8 y z + 4 x z, 5 x - 5 x z + 5 x z], 2 3 2 3 2 2 [-12 y z - 19 z + 7 x z, -9 x z - 3 y + 10 z, 10 y z - 3 x 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=4.3MB, alloc=32.3MB, time=0.17 memory used=26.2MB, alloc=32.3MB, time=0.47 memory used=46.8MB, alloc=32.3MB, time=0.77 memory used=66.3MB, alloc=56.3MB, time=1.08 memory used=105.5MB, alloc=60.3MB, time=1.65 memory used=144.2MB, alloc=84.3MB, time=2.22 memory used=206.4MB, alloc=92.3MB, time=3.14 memory used=267.0MB, alloc=116.3MB, time=4.03 memory used=348.2MB, alloc=116.3MB, time=5.25 memory used=424.6MB, alloc=396.3MB, time=6.44 memory used=529.3MB, alloc=396.3MB, time=8.03 memory used=640.2MB, alloc=420.3MB, time=9.56 memory used=764.5MB, alloc=444.3MB, time=11.35 memory used=876.3MB, alloc=468.3MB, time=12.99 memory used=983.7MB, alloc=468.3MB, time=14.53 memory used=1082.6MB, alloc=468.3MB, time=16.17 memory used=1188.7MB, alloc=492.3MB, time=17.84 memory used=1281.4MB, alloc=492.3MB, time=19.34 memory used=1366.8MB, alloc=492.3MB, time=20.66 memory used=1446.6MB, alloc=492.3MB, time=22.11 memory used=1519.3MB, alloc=492.3MB, time=23.50 memory used=1583.9MB, alloc=492.3MB, time=24.80 memory used=1644.5MB, alloc=492.3MB, time=26.03 memory used=1704.4MB, alloc=516.3MB, time=27.03 memory used=1772.2MB, alloc=516.3MB, time=28.44 memory used=1827.0MB, alloc=516.3MB, time=29.56 memory used=1868.5MB, alloc=516.3MB, time=30.60 memory used=2071.5MB, alloc=540.3MB, time=34.00 memory used=2263.0MB, alloc=564.3MB, time=37.38 memory used=2425.3MB, alloc=588.3MB, time=40.46 memory used=2609.5MB, alloc=612.3MB, time=43.71 memory used=2771.2MB, alloc=636.3MB, time=46.60 memory used=2910.8MB, alloc=636.3MB, time=49.26 memory used=3043.5MB, alloc=660.3MB, time=51.90 memory used=3169.8MB, alloc=660.3MB, time=54.60 memory used=3285.2MB, alloc=660.3MB, time=56.98 memory used=3447.1MB, alloc=684.3MB, time=59.59 memory used=3571.6MB, alloc=684.3MB, time=62.45 memory used=3675.1MB, alloc=684.3MB, time=64.96 memory used=3774.5MB, alloc=684.3MB, time=67.47 memory used=4111.0MB, alloc=708.3MB, time=73.86 memory used=4448.9MB, alloc=732.3MB, time=80.30 memory used=4805.2MB, alloc=756.3MB, time=87.47 memory used=5185.8MB, alloc=780.3MB, time=95.75 memory used=5517.5MB, alloc=804.3MB, time=101.93 memory used=5812.6MB, alloc=828.3MB, time=107.15 memory used=6076.8MB, alloc=852.3MB, time=112.84 memory used=6348.7MB, alloc=876.3MB, time=118.28 memory used=6575.5MB, alloc=900.3MB, time=123.61 memory used=6840.0MB, alloc=924.3MB, time=130.25 memory used=7021.0MB, alloc=948.3MB, time=134.44 memory used=7198.3MB, alloc=972.3MB, time=138.23 |\^/| 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(); 1428295311 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 F := [-17 x y - 17 y - 3 z, 5 x z + x y - 2 x, -2 x y + 8] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 3 2 2 2 G := [12 x y + 20 x y + 5 y z, -x y - 9 y + 8 y z, -8 x z + y z + 5 z ] > Problem := [F,G]; 2 2 2 Problem := [[-17 x y - 17 y - 3 z, 5 x z + x y - 2 x, -2 x y + 8], 2 2 3 2 2 2 [12 x y + 20 x y + 5 y z, -x y - 9 y + 8 y z, -8 x z + y z + 5 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.4MB, alloc=32.3MB, time=0.49 memory used=47.3MB, alloc=32.3MB, time=0.81 memory used=66.3MB, alloc=56.3MB, time=1.11 memory used=105.9MB, alloc=60.3MB, time=1.71 memory used=143.0MB, alloc=84.3MB, time=2.29 memory used=201.2MB, alloc=92.3MB, time=3.20 memory used=260.5MB, alloc=116.3MB, time=4.14 memory used=341.2MB, alloc=116.3MB, time=5.46 memory used=422.3MB, alloc=140.3MB, time=6.79 memory used=505.1MB, alloc=140.3MB, time=8.15 memory used=587.0MB, alloc=396.3MB, time=9.56 memory used=687.8MB, alloc=420.3MB, time=11.28 memory used=809.2MB, alloc=444.3MB, time=13.39 memory used=951.7MB, alloc=468.3MB, time=15.87 memory used=1112.8MB, alloc=492.3MB, time=18.84 memory used=1256.1MB, alloc=516.3MB, time=21.58 memory used=1388.6MB, alloc=516.3MB, time=24.23 memory used=1524.9MB, alloc=516.3MB, time=26.92 memory used=1636.4MB, alloc=540.3MB, time=29.23 memory used=1748.4MB, alloc=540.3MB, time=31.60 memory used=1871.5MB, alloc=540.3MB, time=34.21 memory used=1988.2MB, alloc=540.3MB, time=36.85 memory used=2097.0MB, alloc=540.3MB, time=39.41 memory used=2167.9MB, alloc=540.3MB, time=40.96 memory used=2267.7MB, alloc=540.3MB, time=43.23 memory used=2351.5MB, alloc=540.3MB, time=45.35 memory used=2429.1MB, alloc=540.3MB, time=47.40 memory used=2494.4MB, alloc=564.3MB, time=49.16 memory used=2576.7MB, alloc=564.3MB, time=51.44 memory used=2627.1MB, alloc=564.3MB, time=52.81 memory used=2685.1MB, alloc=564.3MB, time=54.54 memory used=2734.0MB, alloc=564.3MB, time=55.89 memory used=2975.0MB, alloc=588.3MB, time=61.74 memory used=3213.1MB, alloc=612.3MB, time=67.72 memory used=3442.9MB, alloc=636.3MB, time=73.52 memory used=3671.4MB, alloc=660.3MB, time=79.74 memory used=3896.2MB, alloc=684.3MB, time=85.83 memory used=4121.1MB, alloc=708.3MB, time=92.19 memory used=4336.9MB, alloc=732.3MB, time=98.84 memory used=4532.8MB, alloc=732.3MB, time=104.93 memory used=4693.7MB, alloc=756.3MB, time=109.54 memory used=4855.2MB, alloc=756.3MB, time=114.38 memory used=4960.2MB, alloc=756.3MB, time=117.92 memory used=5070.7MB, alloc=756.3MB, time=121.39 memory used=5224.0MB, alloc=756.3MB, time=126.50 memory used=5344.1MB, alloc=756.3MB, time=130.48 memory used=5738.4MB, alloc=780.3MB, time=141.03 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428295611 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 F := [12 x - 16 x z - 2, 7 x y z - 4 y z + 7 y, -9 x y z - 7 x y - 8 z ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 3 2 2 2 G := [7 x y + 2 x z - 16 y z , x + 3 y z - 5 y z, 4 x z + 8 y z - 5 x y] > Problem := [F,G]; Problem := [ 3 2 2 [12 x - 16 x z - 2, 7 x y z - 4 y z + 7 y, -9 x y z - 7 x y - 8 z ], 2 2 2 3 2 2 2 [7 x y + 2 x z - 16 y z , x + 3 y z - 5 y z, 4 x z + 8 y z - 5 x y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.4MB, alloc=32.3MB, time=0.50 memory used=46.8MB, alloc=56.3MB, time=0.81 memory used=86.8MB, alloc=60.3MB, time=1.42 memory used=125.6MB, alloc=84.3MB, time=2.01 memory used=171.3MB, alloc=84.3MB, time=2.70 memory used=234.3MB, alloc=92.3MB, time=3.66 memory used=295.3MB, alloc=92.3MB, time=4.60 memory used=354.8MB, alloc=116.3MB, time=5.52 memory used=436.7MB, alloc=140.3MB, time=6.82 memory used=517.7MB, alloc=140.3MB, time=8.04 memory used=605.5MB, alloc=396.3MB, time=9.49 memory used=710.2MB, alloc=420.3MB, time=11.13 memory used=840.8MB, alloc=444.3MB, time=13.16 memory used=976.1MB, alloc=444.3MB, time=15.30 memory used=1102.0MB, alloc=468.3MB, time=17.20 memory used=1246.7MB, alloc=468.3MB, time=19.62 memory used=1366.3MB, alloc=492.3MB, time=21.50 memory used=1479.6MB, alloc=492.3MB, time=23.22 memory used=1593.7MB, alloc=492.3MB, time=25.17 memory used=1707.3MB, alloc=492.3MB, time=27.28 memory used=1817.2MB, alloc=492.3MB, time=29.39 memory used=1931.7MB, alloc=492.3MB, time=31.91 memory used=2035.0MB, alloc=516.3MB, time=34.02 memory used=2129.1MB, alloc=516.3MB, time=35.99 memory used=2205.0MB, alloc=516.3MB, time=37.53 memory used=2297.0MB, alloc=516.3MB, time=39.48 memory used=2378.0MB, alloc=516.3MB, time=41.01 memory used=2460.9MB, alloc=516.3MB, time=42.60 memory used=2539.0MB, alloc=516.3MB, time=44.40 memory used=2611.3MB, alloc=516.3MB, time=45.92 memory used=2679.1MB, alloc=516.3MB, time=47.28 memory used=2732.1MB, alloc=516.3MB, time=48.35 memory used=2810.4MB, alloc=516.3MB, time=50.26 memory used=2879.2MB, alloc=516.3MB, time=51.99 memory used=2923.0MB, alloc=516.3MB, time=53.12 memory used=3126.1MB, alloc=540.3MB, time=57.64 memory used=3350.8MB, alloc=564.3MB, time=62.77 memory used=3591.1MB, alloc=588.3MB, time=68.27 memory used=3808.4MB, alloc=612.3MB, time=73.38 memory used=4015.3MB, alloc=636.3MB, time=78.70 memory used=4199.8MB, alloc=660.3MB, time=83.38 memory used=4366.2MB, alloc=660.3MB, time=87.47 memory used=4560.3MB, alloc=684.3MB, time=92.49 memory used=4708.8MB, alloc=684.3MB, time=96.23 memory used=4844.8MB, alloc=684.3MB, time=99.99 memory used=4972.7MB, alloc=684.3MB, time=103.33 memory used=5122.1MB, alloc=684.3MB, time=107.44 memory used=5239.1MB, alloc=684.3MB, time=110.48 memory used=5374.2MB, alloc=708.3MB, time=113.31 memory used=5480.5MB, alloc=708.3MB, time=115.23 memory used=5618.4MB, alloc=708.3MB, time=117.90 memory used=5720.4MB, alloc=708.3MB, time=120.34 memory used=6090.4MB, alloc=732.3MB, time=128.02 memory used=6490.5MB, alloc=756.3MB, time=138.64 memory used=6905.7MB, alloc=780.3MB, time=149.96 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428295911 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 3 2 2 F := [-3 x y - 6 z - 11 y, -x y z + 5 x z , 8 x - 5 y z - y ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 2 G := [5 y + 13 x - 18, -9 x y z + 8 y + 9 y, 8 x + 10 y - 6] > Problem := [F,G]; 2 2 2 3 2 2 Problem := [[-3 x y - 6 z - 11 y, -x y z + 5 x z , 8 x - 5 y z - y ], 3 2 2 2 [5 y + 13 x - 18, -9 x y z + 8 y + 9 y, 8 x + 10 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=4.4MB, alloc=32.3MB, time=0.18 memory used=26.3MB, alloc=32.3MB, time=0.50 memory used=47.4MB, alloc=32.3MB, time=0.80 memory used=66.6MB, alloc=56.3MB, time=1.11 memory used=107.1MB, alloc=60.3MB, time=1.73 memory used=146.3MB, alloc=60.3MB, time=2.32 memory used=184.5MB, alloc=84.3MB, time=2.92 memory used=234.9MB, alloc=84.3MB, time=3.70 memory used=291.1MB, alloc=116.3MB, time=4.63 memory used=371.1MB, alloc=116.3MB, time=5.85 memory used=451.0MB, alloc=140.3MB, time=7.11 memory used=528.1MB, alloc=396.3MB, time=8.37 memory used=631.6MB, alloc=420.3MB, time=10.05 memory used=756.3MB, alloc=420.3MB, time=12.14 memory used=881.6MB, alloc=444.3MB, time=14.29 memory used=1027.5MB, alloc=468.3MB, time=16.77 memory used=1193.5MB, alloc=492.3MB, time=19.77 memory used=1331.9MB, alloc=492.3MB, time=22.11 memory used=1459.0MB, alloc=516.3MB, time=24.40 memory used=1611.1MB, alloc=540.3MB, time=27.24 memory used=1749.4MB, alloc=564.3MB, time=30.01 memory used=1897.3MB, alloc=588.3MB, time=32.99 memory used=2044.7MB, alloc=612.3MB, time=35.90 memory used=2196.6MB, alloc=636.3MB, time=38.73 memory used=2341.8MB, alloc=660.3MB, time=41.63 memory used=2478.2MB, alloc=684.3MB, time=44.51 memory used=2616.4MB, alloc=708.3MB, time=47.49 memory used=2743.7MB, alloc=732.3MB, time=50.23 memory used=2866.4MB, alloc=756.3MB, time=52.91 memory used=2992.6MB, alloc=780.3MB, time=55.69 memory used=3109.4MB, alloc=804.3MB, time=58.31 memory used=3219.1MB, alloc=804.3MB, time=60.79 memory used=3330.9MB, alloc=828.3MB, time=63.99 memory used=3504.0MB, alloc=852.3MB, time=70.35 memory used=3844.7MB, alloc=876.3MB, time=83.26 memory used=4187.7MB, alloc=900.3MB, time=97.02 memory used=4538.7MB, alloc=924.3MB, time=111.39 memory used=4899.7MB, alloc=948.3MB, time=126.68 memory used=5272.2MB, alloc=972.3MB, time=142.41 |\^/| 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(); 1428296211 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 2 2 F := [20 x + 8 x y z - x z , 5 x z + 2 x y - 6 z, -7 x + 9 x z + 8 y ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 3 2 2 2 2 G := [-2 x - 16 y - 8 y , -x y + 5 z + 9 y, 3 x z - 7 x z - 4 z ] > Problem := [F,G]; Problem := [ 3 2 2 2 2 [20 x + 8 x y z - x z , 5 x z + 2 x y - 6 z, -7 x + 9 x z + 8 y ], 3 3 2 2 2 2 [-2 x - 16 y - 8 y , -x y + 5 z + 9 y, 3 x z - 7 x z - 4 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.18 memory used=26.4MB, alloc=32.3MB, time=0.49 memory used=47.1MB, alloc=32.3MB, time=0.80 memory used=66.6MB, alloc=56.3MB, time=1.10 memory used=105.7MB, alloc=60.3MB, time=1.67 memory used=145.0MB, alloc=60.3MB, time=2.22 memory used=183.2MB, alloc=84.3MB, time=2.81 memory used=223.4MB, alloc=84.3MB, time=3.40 memory used=285.2MB, alloc=92.3MB, time=4.32 memory used=344.0MB, alloc=116.3MB, time=5.22 memory used=426.1MB, alloc=116.3MB, time=6.44 memory used=507.9MB, alloc=140.3MB, time=7.71 memory used=589.0MB, alloc=140.3MB, time=8.97 memory used=653.7MB, alloc=396.3MB, time=10.01 memory used=754.9MB, alloc=420.3MB, time=11.62 memory used=887.4MB, alloc=444.3MB, time=13.68 memory used=1010.1MB, alloc=468.3MB, time=15.61 memory used=1143.4MB, alloc=468.3MB, time=17.65 memory used=1250.5MB, alloc=492.3MB, time=19.24 memory used=1369.5MB, alloc=492.3MB, time=21.04 memory used=1483.2MB, alloc=492.3MB, time=22.92 memory used=1557.5MB, alloc=492.3MB, time=24.14 memory used=1658.0MB, alloc=516.3MB, time=25.74 memory used=1748.2MB, alloc=516.3MB, time=27.28 memory used=1816.7MB, alloc=516.3MB, time=28.43 memory used=1879.7MB, alloc=516.3MB, time=29.58 memory used=1935.3MB, alloc=516.3MB, time=30.88 memory used=1991.4MB, alloc=516.3MB, time=31.89 memory used=2047.1MB, alloc=516.3MB, time=33.19 memory used=2089.1MB, alloc=516.3MB, time=34.07 memory used=2131.6MB, alloc=516.3MB, time=34.94 memory used=2183.0MB, alloc=516.3MB, time=35.90 memory used=2391.2MB, alloc=540.3MB, time=39.14 memory used=2602.1MB, alloc=564.3MB, time=42.50 memory used=2800.2MB, alloc=588.3MB, time=46.05 memory used=3001.3MB, alloc=612.3MB, time=49.81 memory used=3178.2MB, alloc=636.3MB, time=52.92 memory used=3315.8MB, alloc=636.3MB, time=55.70 memory used=3478.5MB, alloc=660.3MB, time=58.47 memory used=3626.9MB, alloc=660.3MB, time=61.19 memory used=3790.9MB, alloc=660.3MB, time=64.69 memory used=3919.4MB, alloc=684.3MB, time=67.13 memory used=4068.2MB, alloc=684.3MB, time=70.43 memory used=4191.1MB, alloc=684.3MB, time=73.38 memory used=4308.2MB, alloc=684.3MB, time=76.29 memory used=4423.0MB, alloc=684.3MB, time=78.47 memory used=4775.2MB, alloc=708.3MB, time=85.39 memory used=5147.3MB, alloc=732.3MB, time=92.86 memory used=5546.4MB, alloc=756.3MB, time=100.70 memory used=5940.4MB, alloc=780.3MB, time=108.28 memory used=6314.0MB, alloc=804.3MB, time=116.14 memory used=6650.0MB, alloc=828.3MB, time=123.06 memory used=6927.9MB, alloc=852.3MB, time=129.09 memory used=7251.0MB, alloc=876.3MB, time=136.55 memory used=7561.1MB, alloc=900.3MB, time=143.43 memory used=7830.3MB, alloc=924.3MB, time=149.49 memory used=8034.1MB, alloc=948.3MB, time=155.15 |\^/| 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(); 1428296511 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 3 2 2 3 F := [-8 z - 8 y z + 15 y, -2 y - 9 x - 7 z , -7 y - 2 x z - 8 y] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 3 2 3 G := [-3 x y + 15 z - 7 x z, -4 x y + y + 5 x , -x + 9 x z + 5 z] > Problem := [F,G]; 3 3 2 2 3 Problem := [[-8 z - 8 y z + 15 y, -2 y - 9 x - 7 z , -7 y - 2 x z - 8 y], 2 3 2 3 2 3 [-3 x y + 15 z - 7 x z, -4 x y + y + 5 x , -x + 9 x z + 5 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=25.8MB, alloc=32.3MB, time=0.50 memory used=45.1MB, alloc=60.3MB, time=0.78 memory used=85.1MB, alloc=60.3MB, time=1.30 memory used=129.4MB, alloc=68.3MB, time=1.92 memory used=172.4MB, alloc=68.3MB, time=2.49 memory used=213.1MB, alloc=68.3MB, time=2.90 memory used=247.4MB, alloc=68.3MB, time=3.16 memory used=289.7MB, alloc=92.3MB, time=3.73 memory used=352.2MB, alloc=92.3MB, time=4.52 memory used=418.8MB, alloc=92.3MB, time=5.34 memory used=481.8MB, alloc=372.3MB, time=6.18 memory used=574.8MB, alloc=372.3MB, time=7.31 memory used=666.0MB, alloc=396.3MB, time=8.49 memory used=760.1MB, alloc=396.3MB, time=9.27 memory used=830.3MB, alloc=396.3MB, time=10.09 memory used=900.4MB, alloc=396.3MB, time=10.99 memory used=1018.9MB, alloc=420.3MB, time=13.37 memory used=1141.1MB, alloc=420.3MB, time=14.69 memory used=1281.3MB, alloc=420.3MB, time=16.28 memory used=1419.4MB, alloc=420.3MB, time=17.96 memory used=1519.2MB, alloc=444.3MB, time=19.24 memory used=1636.0MB, alloc=444.3MB, time=20.71 memory used=1714.9MB, alloc=444.3MB, time=21.06 memory used=1818.3MB, alloc=444.3MB, time=21.68 memory used=1923.1MB, alloc=444.3MB, time=26.23 memory used=1995.1MB, alloc=444.3MB, time=26.57 memory used=2056.7MB, alloc=444.3MB, time=26.88 memory used=2160.9MB, alloc=444.3MB, time=27.55 memory used=2248.6MB, alloc=444.3MB, time=28.10 memory used=2326.2MB, alloc=444.3MB, time=28.45 memory used=2432.9MB, alloc=444.3MB, time=33.01 memory used=2505.4MB, alloc=444.3MB, time=33.34 memory used=2571.7MB, alloc=444.3MB, time=33.73 memory used=2686.4MB, alloc=444.3MB, time=35.06 memory used=2798.8MB, alloc=468.3MB, time=42.29 memory used=2900.5MB, alloc=468.3MB, time=43.26 memory used=2983.0MB, alloc=468.3MB, time=43.59 memory used=3107.6MB, alloc=468.3MB, time=44.43 memory used=3248.9MB, alloc=468.3MB, time=46.70 memory used=3346.5MB, alloc=468.3MB, time=47.25 memory used=3456.0MB, alloc=468.3MB, time=48.93 memory used=3579.1MB, alloc=468.3MB, time=50.17 memory used=3703.3MB, alloc=468.3MB, time=54.41 memory used=3842.0MB, alloc=468.3MB, time=55.38 memory used=3930.1MB, alloc=468.3MB, time=56.76 memory used=4015.2MB, alloc=468.3MB, time=57.98 memory used=4090.7MB, alloc=468.3MB, time=59.14 memory used=4192.9MB, alloc=492.3MB, time=60.37 memory used=4317.5MB, alloc=492.3MB, time=61.34 memory used=4460.6MB, alloc=492.3MB, time=77.06 memory used=4548.3MB, alloc=492.3MB, time=77.50 memory used=4641.1MB, alloc=492.3MB, time=77.89 memory used=4720.1MB, alloc=492.3MB, time=78.24 memory used=4845.3MB, alloc=492.3MB, time=79.82 memory used=4912.1MB, alloc=492.3MB, time=80.69 memory used=4979.7MB, alloc=492.3MB, time=81.86 memory used=5077.1MB, alloc=492.3MB, time=82.99 memory used=5130.1MB, alloc=492.3MB, time=83.77 memory used=5210.4MB, alloc=492.3MB, time=84.77 memory used=5263.5MB, alloc=492.3MB, time=85.74 memory used=5326.6MB, alloc=492.3MB, time=86.70 memory used=5377.8MB, alloc=492.3MB, time=87.59 memory used=5434.5MB, alloc=492.3MB, time=88.34 memory used=5535.5MB, alloc=492.3MB, time=96.05 memory used=5623.9MB, alloc=492.3MB, time=96.59 memory used=5705.1MB, alloc=516.3MB, time=97.09 memory used=5800.1MB, alloc=516.3MB, time=97.59 memory used=5900.4MB, alloc=516.3MB, time=98.41 memory used=5954.6MB, alloc=516.3MB, time=99.35 memory used=6005.9MB, alloc=516.3MB, time=100.21 memory used=6213.2MB, alloc=516.3MB, time=102.92 memory used=6310.2MB, alloc=516.3MB, time=103.49 memory used=6433.0MB, alloc=516.3MB, time=105.85 memory used=6526.2MB, alloc=516.3MB, time=106.41 memory used=6630.1MB, alloc=516.3MB, time=106.93 memory used=6706.1MB, alloc=516.3MB, time=107.39 memory used=6803.9MB, alloc=516.3MB, time=107.87 memory used=7055.0MB, alloc=516.3MB, time=110.60 memory used=7226.6MB, alloc=540.3MB, time=113.27 memory used=7440.3MB, alloc=564.3MB, time=115.52 memory used=7652.5MB, alloc=564.3MB, time=118.33 memory used=7763.9MB, alloc=564.3MB, time=119.06 memory used=7884.9MB, alloc=588.3MB, time=119.74 memory used=7984.6MB, alloc=588.3MB, time=120.41 memory used=8102.6MB, alloc=588.3MB, time=121.11 memory used=8235.7MB, alloc=588.3MB, time=121.79 memory used=8383.7MB, alloc=588.3MB, time=122.48 memory used=8538.0MB, alloc=588.3MB, time=123.17 memory used=8628.0MB, alloc=588.3MB, time=123.74 memory used=8718.1MB, alloc=588.3MB, time=124.31 memory used=8814.0MB, alloc=588.3MB, time=124.87 memory used=8914.5MB, alloc=588.3MB, time=125.45 memory used=9022.8MB, alloc=588.3MB, time=126.02 memory used=9135.8MB, alloc=588.3MB, time=126.60 memory used=9255.3MB, alloc=588.3MB, time=127.15 memory used=9383.7MB, alloc=588.3MB, time=127.76 memory used=9519.8MB, alloc=588.3MB, time=128.35 memory used=9665.5MB, alloc=588.3MB, time=128.97 memory used=9824.8MB, alloc=588.3MB, time=129.59 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428296811 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 3 3 F := [5 y z + 8 z - 5, -10 x z + 9 y - 2, 8 x + 5 x + 3 z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 G := [-17 x y z + 12 z + 10 x z, y z + y z, x z + y z + 9 x] > Problem := [F,G]; 2 2 3 3 Problem := [[5 y z + 8 z - 5, -10 x z + 9 y - 2, 8 x + 5 x + 3 z], 3 2 2 [-17 x y z + 12 z + 10 x z, y z + y z, x z + y z + 9 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.4MB, alloc=32.3MB, time=0.49 memory used=47.7MB, alloc=32.3MB, time=0.81 memory used=66.5MB, alloc=56.3MB, time=1.10 memory used=107.0MB, alloc=68.3MB, time=1.73 memory used=145.3MB, alloc=92.3MB, time=2.31 memory used=206.6MB, alloc=92.3MB, time=3.17 memory used=262.7MB, alloc=92.3MB, time=4.04 memory used=319.7MB, alloc=116.3MB, time=4.93 memory used=400.1MB, alloc=116.3MB, time=6.15 memory used=476.3MB, alloc=140.3MB, time=7.30 memory used=556.4MB, alloc=396.3MB, time=8.51 memory used=661.7MB, alloc=420.3MB, time=10.14 memory used=792.7MB, alloc=420.3MB, time=11.87 memory used=926.3MB, alloc=444.3MB, time=13.92 memory used=1070.6MB, alloc=468.3MB, time=16.27 memory used=1220.6MB, alloc=468.3MB, time=18.75 memory used=1362.0MB, alloc=492.3MB, time=21.11 memory used=1505.3MB, alloc=516.3MB, time=23.58 memory used=1640.5MB, alloc=516.3MB, time=25.81 memory used=1774.3MB, alloc=516.3MB, time=28.18 memory used=1891.2MB, alloc=516.3MB, time=30.22 memory used=2013.3MB, alloc=540.3MB, time=32.34 memory used=2130.8MB, alloc=540.3MB, time=33.04 memory used=2225.1MB, alloc=540.3MB, time=34.79 memory used=2350.9MB, alloc=540.3MB, time=36.98 memory used=2486.5MB, alloc=540.3MB, time=38.69 memory used=2586.0MB, alloc=540.3MB, time=40.46 memory used=2676.0MB, alloc=540.3MB, time=42.29 memory used=2750.9MB, alloc=564.3MB, time=43.71 memory used=2858.0MB, alloc=564.3MB, time=44.90 memory used=2947.3MB, alloc=564.3MB, time=46.29 memory used=3057.0MB, alloc=564.3MB, time=48.49 memory used=3144.6MB, alloc=564.3MB, time=50.64 memory used=3234.3MB, alloc=564.3MB, time=52.95 memory used=3325.6MB, alloc=564.3MB, time=55.34 memory used=3383.8MB, alloc=564.3MB, time=56.67 memory used=3445.2MB, alloc=588.3MB, time=58.12 memory used=3498.5MB, alloc=588.3MB, time=59.74 memory used=3750.8MB, alloc=612.3MB, time=65.61 memory used=3923.7MB, alloc=636.3MB, time=68.56 memory used=4132.6MB, alloc=660.3MB, time=72.83 memory used=4261.3MB, alloc=684.3MB, time=75.29 memory used=4398.0MB, alloc=708.3MB, time=77.99 memory used=4554.0MB, alloc=732.3MB, time=81.83 memory used=4663.6MB, alloc=732.3MB, time=83.93 memory used=4813.6MB, alloc=732.3MB, time=88.21 memory used=4936.3MB, alloc=732.3MB, time=90.84 memory used=5061.4MB, alloc=732.3MB, time=94.52 memory used=5153.5MB, alloc=756.3MB, time=96.99 memory used=5559.5MB, alloc=780.3MB, time=104.87 memory used=5978.3MB, alloc=804.3MB, time=113.26 memory used=6323.7MB, alloc=828.3MB, time=120.53 memory used=6580.7MB, alloc=852.3MB, time=125.33 |\^/| 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(); 1428297111 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 3 3 2 F := [16 x + 10 y - 12 z, -8 x y z + 7 z - 6 y z, 6 x - 9 x y + 2 z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 2 G := [-17 x z - 2 y + 1, -2 x y + y - z, 6 x z + 7 z + 8 y] > Problem := [F,G]; Problem := [ 2 2 3 3 2 [16 x + 10 y - 12 z, -8 x y z + 7 z - 6 y z, 6 x - 9 x y + 2 z], 2 2 2 2 2 [-17 x z - 2 y + 1, -2 x y + y - z, 6 x z + 7 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=0.17 memory used=26.4MB, alloc=32.3MB, time=0.49 memory used=47.2MB, alloc=56.3MB, time=0.81 memory used=87.3MB, alloc=60.3MB, time=1.38 memory used=124.2MB, alloc=84.3MB, time=1.95 memory used=164.6MB, alloc=84.3MB, time=2.55 memory used=225.3MB, alloc=92.3MB, time=3.49 memory used=285.0MB, alloc=116.3MB, time=4.40 memory used=363.2MB, alloc=116.3MB, time=5.57 memory used=430.6MB, alloc=372.3MB, time=6.60 memory used=514.2MB, alloc=396.3MB, time=7.82 memory used=620.4MB, alloc=420.3MB, time=9.35 memory used=747.8MB, alloc=444.3MB, time=11.27 memory used=887.6MB, alloc=468.3MB, time=13.28 memory used=1031.6MB, alloc=492.3MB, time=15.58 memory used=1174.8MB, alloc=492.3MB, time=17.96 memory used=1298.2MB, alloc=516.3MB, time=20.12 memory used=1389.2MB, alloc=516.3MB, time=21.59 memory used=1475.7MB, alloc=516.3MB, time=23.11 memory used=1550.7MB, alloc=516.3MB, time=24.38 memory used=1632.6MB, alloc=540.3MB, time=25.78 memory used=1711.4MB, alloc=540.3MB, time=27.30 memory used=1780.0MB, alloc=540.3MB, time=28.64 memory used=1840.2MB, alloc=540.3MB, time=29.92 memory used=1894.8MB, alloc=540.3MB, time=31.05 memory used=1958.7MB, alloc=540.3MB, time=32.40 memory used=2010.0MB, alloc=540.3MB, time=33.54 memory used=2057.2MB, alloc=540.3MB, time=34.58 memory used=2248.6MB, alloc=564.3MB, time=37.66 memory used=2430.1MB, alloc=588.3MB, time=40.86 memory used=2588.5MB, alloc=612.3MB, time=43.56 memory used=2740.9MB, alloc=636.3MB, time=46.64 memory used=2899.8MB, alloc=636.3MB, time=49.68 memory used=3063.3MB, alloc=660.3MB, time=52.24 memory used=3201.8MB, alloc=660.3MB, time=55.13 memory used=3332.1MB, alloc=660.3MB, time=58.06 memory used=3423.5MB, alloc=660.3MB, time=60.04 memory used=3525.3MB, alloc=660.3MB, time=62.51 memory used=3605.1MB, alloc=660.3MB, time=64.56 memory used=3695.4MB, alloc=660.3MB, time=66.65 memory used=4019.5MB, alloc=684.3MB, time=72.71 memory used=4341.3MB, alloc=708.3MB, time=77.61 memory used=4720.7MB, alloc=732.3MB, time=84.10 memory used=5058.4MB, alloc=756.3MB, time=90.41 memory used=5402.0MB, alloc=780.3MB, time=97.82 memory used=5678.1MB, alloc=804.3MB, time=103.53 memory used=6001.3MB, alloc=828.3MB, time=111.59 memory used=6273.1MB, alloc=852.3MB, time=118.23 memory used=6494.0MB, alloc=876.3MB, time=124.37 memory used=6736.2MB, alloc=900.3MB, time=130.66 memory used=6927.0MB, alloc=924.3MB, time=135.64 memory used=7107.8MB, alloc=948.3MB, time=141.18 |\^/| 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(); 1428297411 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 3 2 3 2 2 F := [5 x + 11 y - 17 x z, -10 x y - 2 x y z + 4 z , x y + 5 y z - 10 x] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 2 2 G := [-4 x y - 18 y z, -4 x + 5 x z + 2 x , 6 x y - 9 x z - 9] > Problem := [F,G]; Problem := [ 3 3 2 3 2 2 [5 x + 11 y - 17 x z, -10 x y - 2 x y z + 4 z , x y + 5 y z - 10 x], 2 3 2 2 2 [-4 x y - 18 y z, -4 x + 5 x z + 2 x , 6 x y - 9 x 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=26.2MB, alloc=32.3MB, time=0.49 memory used=46.5MB, alloc=32.3MB, time=0.79 memory used=66.0MB, alloc=56.3MB, time=1.10 memory used=107.2MB, alloc=60.3MB, time=1.71 memory used=147.4MB, alloc=84.3MB, time=2.30 memory used=208.7MB, alloc=92.3MB, time=3.25 memory used=272.8MB, alloc=116.3MB, time=4.21 memory used=354.1MB, alloc=116.3MB, time=5.49 memory used=427.1MB, alloc=396.3MB, time=6.70 memory used=539.4MB, alloc=420.3MB, time=8.40 memory used=664.7MB, alloc=444.3MB, time=10.12 memory used=796.5MB, alloc=444.3MB, time=12.13 memory used=910.7MB, alloc=468.3MB, time=13.83 memory used=1012.8MB, alloc=468.3MB, time=15.40 memory used=1108.7MB, alloc=468.3MB, time=17.09 memory used=1199.4MB, alloc=468.3MB, time=18.65 memory used=1275.8MB, alloc=468.3MB, time=19.96 memory used=1352.0MB, alloc=492.3MB, time=21.23 memory used=1434.6MB, alloc=492.3MB, time=22.73 memory used=1509.9MB, alloc=492.3MB, time=24.17 memory used=1581.0MB, alloc=492.3MB, time=25.41 memory used=1651.8MB, alloc=492.3MB, time=26.86 memory used=1717.8MB, alloc=492.3MB, time=28.26 memory used=1766.7MB, alloc=492.3MB, time=29.22 memory used=1824.0MB, alloc=492.3MB, time=30.41 memory used=1864.9MB, alloc=492.3MB, time=31.32 memory used=1908.5MB, alloc=516.3MB, time=32.22 memory used=2112.4MB, alloc=540.3MB, time=35.81 memory used=2287.6MB, alloc=540.3MB, time=37.76 memory used=2479.9MB, alloc=564.3MB, time=41.03 memory used=2715.3MB, alloc=588.3MB, time=43.95 memory used=2916.0MB, alloc=588.3MB, time=46.72 memory used=3072.0MB, alloc=588.3MB, time=49.75 memory used=3287.8MB, alloc=612.3MB, time=52.69 memory used=3471.5MB, alloc=612.3MB, time=55.28 memory used=3605.9MB, alloc=612.3MB, time=58.19 memory used=3730.9MB, alloc=636.3MB, time=60.98 memory used=3858.5MB, alloc=636.3MB, time=63.60 memory used=3986.0MB, alloc=636.3MB, time=66.24 memory used=4101.6MB, alloc=636.3MB, time=68.44 memory used=4219.9MB, alloc=636.3MB, time=70.50 memory used=4304.3MB, alloc=660.3MB, time=72.38 memory used=4403.8MB, alloc=660.3MB, time=74.61 memory used=4528.7MB, alloc=660.3MB, time=76.60 memory used=4808.5MB, alloc=684.3MB, time=80.31 memory used=5142.4MB, alloc=708.3MB, time=88.11 memory used=5510.0MB, alloc=732.3MB, time=96.19 memory used=5895.7MB, alloc=756.3MB, time=104.90 memory used=6195.5MB, alloc=780.3MB, time=111.41 memory used=6503.8MB, alloc=804.3MB, time=118.34 memory used=6752.9MB, alloc=828.3MB, time=124.23 memory used=7019.1MB, alloc=852.3MB, time=129.15 memory used=7266.0MB, alloc=876.3MB, time=133.26 memory used=7448.3MB, alloc=900.3MB, time=138.35 memory used=7650.6MB, alloc=924.3MB, time=142.74 memory used=7851.9MB, alloc=948.3MB, time=148.28 memory used=8008.2MB, alloc=972.3MB, time=152.86 memory used=8588.7MB, alloc=996.3MB, time=164.56 |\^/| 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(); 1428297711 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 2 3 F := [10 x z + 3 y + 3, 9 x y + 10 y z - 10, 6 x z + y + 6 y z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 3 2 G := [6 y z + 2 z - 13 z, -2 x y - 2 y z - 9 x, 7 y z - 2 z - 5 y ] > Problem := [F,G]; 2 2 2 2 2 3 Problem := [[10 x z + 3 y + 3, 9 x y + 10 y z - 10, 6 x z + y + 6 y z], 2 2 2 3 2 [6 y z + 2 z - 13 z, -2 x y - 2 y z - 9 x, 7 y z - 2 z - 5 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.0MB, alloc=32.3MB, time=0.48 memory used=46.2MB, alloc=32.3MB, time=0.77 memory used=65.2MB, alloc=56.3MB, time=1.06 memory used=104.2MB, alloc=60.3MB, time=1.64 memory used=141.1MB, alloc=84.3MB, time=2.21 memory used=200.9MB, alloc=92.3MB, time=3.15 memory used=262.4MB, alloc=116.3MB, time=4.09 memory used=341.7MB, alloc=116.3MB, time=5.30 memory used=423.2MB, alloc=140.3MB, time=6.65 memory used=505.1MB, alloc=140.3MB, time=8.00 memory used=578.8MB, alloc=396.3MB, time=9.26 memory used=682.8MB, alloc=420.3MB, time=10.82 memory used=808.9MB, alloc=444.3MB, time=12.91 memory used=954.0MB, alloc=444.3MB, time=14.98 memory used=1092.4MB, alloc=468.3MB, time=16.93 memory used=1221.0MB, alloc=468.3MB, time=18.61 memory used=1364.2MB, alloc=492.3MB, time=21.16 memory used=1497.8MB, alloc=492.3MB, time=23.60 memory used=1611.7MB, alloc=492.3MB, time=25.82 memory used=1728.2MB, alloc=516.3MB, time=27.94 memory used=1831.3MB, alloc=516.3MB, time=29.96 memory used=1931.3MB, alloc=516.3MB, time=32.00 memory used=2015.5MB, alloc=540.3MB, time=33.52 memory used=2094.5MB, alloc=540.3MB, time=34.80 memory used=2178.2MB, alloc=540.3MB, time=36.60 memory used=2256.3MB, alloc=540.3MB, time=38.08 memory used=2333.0MB, alloc=540.3MB, time=39.76 memory used=2396.2MB, alloc=540.3MB, time=41.22 memory used=2450.5MB, alloc=540.3MB, time=42.36 memory used=2518.7MB, alloc=540.3MB, time=44.15 memory used=2569.0MB, alloc=540.3MB, time=45.33 memory used=2636.2MB, alloc=540.3MB, time=47.06 memory used=2862.1MB, alloc=564.3MB, time=51.40 memory used=3047.4MB, alloc=588.3MB, time=54.93 memory used=3232.4MB, alloc=612.3MB, time=59.19 memory used=3404.9MB, alloc=636.3MB, time=62.21 memory used=3596.5MB, alloc=660.3MB, time=65.63 memory used=3765.9MB, alloc=660.3MB, time=68.35 memory used=3910.3MB, alloc=684.3MB, time=70.71 memory used=4072.5MB, alloc=684.3MB, time=74.36 memory used=4212.2MB, alloc=684.3MB, time=77.57 memory used=4347.8MB, alloc=684.3MB, time=80.23 memory used=4483.0MB, alloc=684.3MB, time=83.63 memory used=4642.8MB, alloc=708.3MB, time=87.33 memory used=4732.5MB, alloc=708.3MB, time=89.25 memory used=4841.7MB, alloc=708.3MB, time=91.49 memory used=5197.2MB, alloc=732.3MB, time=96.78 memory used=5589.0MB, alloc=756.3MB, time=104.53 memory used=5984.2MB, alloc=780.3MB, time=110.54 memory used=6405.2MB, alloc=804.3MB, time=117.56 memory used=6831.2MB, alloc=828.3MB, time=124.76 memory used=7249.6MB, alloc=852.3MB, time=131.88 memory used=7548.3MB, alloc=876.3MB, time=136.50 memory used=7926.7MB, alloc=900.3MB, time=140.94 memory used=8267.1MB, alloc=924.3MB, time=144.37 memory used=8599.7MB, alloc=924.3MB, time=148.92 memory used=8930.3MB, alloc=924.3MB, time=153.41 memory used=9270.3MB, alloc=948.3MB, time=158.58 memory used=9668.8MB, alloc=948.3MB, time=165.48 memory used=9958.1MB, alloc=972.3MB, time=172.43 |\^/| 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(); 1428298011 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 3 2 2 2 3 F := [19 x y - 9 y - 8 y z, -5 x - 10 x - 5 y , -y z + z + 8 x y] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 2 3 3 3 G := [-11 x + 3 y z - 9 x z, -8 y z - 10 x + 9 x z, -4 x - 7 y - 4 z ] > Problem := [F,G]; 2 2 3 2 2 2 3 Problem := [[19 x y - 9 y - 8 y z, -5 x - 10 x - 5 y , -y z + z + 8 x y], 3 2 2 2 3 3 3 [-11 x + 3 y z - 9 x z, -8 y z - 10 x + 9 x z, -4 x - 7 y - 4 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=25.8MB, alloc=32.3MB, time=0.49 memory used=45.0MB, alloc=32.3MB, time=0.77 memory used=63.8MB, alloc=60.3MB, time=1.07 memory used=104.2MB, alloc=60.3MB, time=1.65 memory used=143.8MB, alloc=60.3MB, time=2.21 memory used=183.9MB, alloc=92.3MB, time=2.82 memory used=247.8MB, alloc=92.3MB, time=3.72 memory used=308.3MB, alloc=116.3MB, time=4.61 memory used=371.5MB, alloc=372.3MB, time=5.44 memory used=458.4MB, alloc=372.3MB, time=6.69 memory used=549.2MB, alloc=396.3MB, time=7.86 memory used=659.2MB, alloc=396.3MB, time=9.41 memory used=761.2MB, alloc=420.3MB, time=10.57 memory used=881.4MB, alloc=420.3MB, time=12.11 memory used=1012.8MB, alloc=444.3MB, time=13.62 memory used=1129.4MB, alloc=444.3MB, time=15.04 memory used=1257.4MB, alloc=444.3MB, time=16.88 memory used=1365.6MB, alloc=444.3MB, time=18.52 memory used=1489.5MB, alloc=468.3MB, time=19.82 memory used=1592.9MB, alloc=468.3MB, time=20.47 memory used=1689.0MB, alloc=468.3MB, time=20.92 memory used=1817.1MB, alloc=468.3MB, time=22.36 memory used=1955.9MB, alloc=468.3MB, time=23.99 memory used=2058.4MB, alloc=468.3MB, time=25.48 memory used=2158.2MB, alloc=468.3MB, time=26.95 memory used=2268.6MB, alloc=492.3MB, time=28.77 memory used=2360.7MB, alloc=492.3MB, time=30.29 memory used=2433.9MB, alloc=492.3MB, time=31.36 memory used=2519.9MB, alloc=492.3MB, time=33.37 memory used=2663.7MB, alloc=492.3MB, time=38.15 memory used=2756.0MB, alloc=492.3MB, time=39.26 memory used=2867.8MB, alloc=516.3MB, time=40.62 memory used=2936.7MB, alloc=516.3MB, time=41.82 memory used=3020.8MB, alloc=516.3MB, time=43.11 memory used=3090.4MB, alloc=516.3MB, time=44.29 memory used=3174.3MB, alloc=516.3MB, time=46.18 memory used=3334.3MB, alloc=516.3MB, time=49.71 memory used=3398.6MB, alloc=516.3MB, time=50.67 memory used=3467.4MB, alloc=516.3MB, time=51.91 memory used=3532.1MB, alloc=516.3MB, time=53.03 memory used=3597.0MB, alloc=516.3MB, time=54.12 memory used=3697.4MB, alloc=540.3MB, time=55.34 memory used=3746.6MB, alloc=540.3MB, time=56.45 memory used=3790.6MB, alloc=540.3MB, time=57.42 memory used=3987.9MB, alloc=564.3MB, time=60.63 memory used=4224.5MB, alloc=588.3MB, time=63.61 memory used=4415.6MB, alloc=588.3MB, time=66.49 memory used=4694.1MB, alloc=588.3MB, time=68.83 memory used=4823.1MB, alloc=588.3MB, time=69.58 memory used=5008.2MB, alloc=612.3MB, time=71.42 memory used=5127.8MB, alloc=612.3MB, time=72.10 memory used=5269.2MB, alloc=612.3MB, time=72.82 memory used=5368.9MB, alloc=612.3MB, time=73.44 memory used=5488.0MB, alloc=612.3MB, time=74.05 memory used=5627.9MB, alloc=612.3MB, time=74.66 memory used=5825.7MB, alloc=636.3MB, time=139.93 |\^/| 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(); 1428298311 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 2 F := [-13 x z + 13 y z - 10 y , -x y z - 6 y z + 10 y z , 3 2 4 x + 9 x y z + 4 y z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 3 2 G := [3 y + 13 z + 10 x, -4 x z - 2 y z - 9 y, 10 x - 6 x z - 5 y z] > Problem := [F,G]; 2 2 2 2 2 Problem := [[-13 x z + 13 y z - 10 y , -x y z - 6 y z + 10 y z , 3 2 4 x + 9 x y z + 4 y z], 3 3 2 [3 y + 13 z + 10 x, -4 x z - 2 y z - 9 y, 10 x - 6 x z - 5 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.0MB, alloc=32.3MB, time=0.50 memory used=46.6MB, alloc=56.3MB, time=0.82 memory used=87.2MB, alloc=60.3MB, time=1.41 memory used=125.8MB, alloc=84.3MB, time=2.01 memory used=166.2MB, alloc=84.3MB, time=2.60 memory used=228.1MB, alloc=116.3MB, time=3.53 memory used=301.7MB, alloc=372.3MB, time=4.61 memory used=387.5MB, alloc=396.3MB, time=5.84 memory used=492.0MB, alloc=420.3MB, time=7.51 memory used=623.5MB, alloc=444.3MB, time=9.56 memory used=761.7MB, alloc=468.3MB, time=11.69 memory used=896.8MB, alloc=492.3MB, time=13.87 memory used=1029.0MB, alloc=492.3MB, time=15.89 memory used=1148.5MB, alloc=516.3MB, time=17.56 memory used=1273.2MB, alloc=516.3MB, time=19.43 memory used=1393.2MB, alloc=516.3MB, time=21.56 memory used=1485.4MB, alloc=540.3MB, time=23.05 memory used=1592.5MB, alloc=540.3MB, time=24.78 memory used=1679.9MB, alloc=540.3MB, time=26.18 memory used=1760.1MB, alloc=540.3MB, time=27.54 memory used=1836.6MB, alloc=540.3MB, time=29.18 memory used=1904.1MB, alloc=540.3MB, time=30.43 memory used=1953.1MB, alloc=540.3MB, time=31.43 memory used=2000.4MB, alloc=540.3MB, time=32.53 memory used=2043.6MB, alloc=540.3MB, time=33.55 memory used=2093.1MB, alloc=540.3MB, time=34.73 memory used=2155.9MB, alloc=564.3MB, time=36.35 memory used=2365.2MB, alloc=588.3MB, time=39.38 memory used=2592.7MB, alloc=612.3MB, time=43.49 memory used=2872.1MB, alloc=636.3MB, time=47.22 memory used=3070.3MB, alloc=660.3MB, time=50.87 memory used=3260.4MB, alloc=684.3MB, time=54.59 memory used=3436.5MB, alloc=708.3MB, time=57.86 memory used=3604.9MB, alloc=708.3MB, time=61.00 memory used=3743.5MB, alloc=732.3MB, time=63.50 memory used=3878.3MB, alloc=732.3MB, time=66.78 memory used=4019.6MB, alloc=732.3MB, time=70.27 memory used=4146.2MB, alloc=756.3MB, time=73.29 memory used=4257.8MB, alloc=756.3MB, time=75.65 memory used=4379.2MB, alloc=756.3MB, time=78.45 memory used=4481.5MB, alloc=756.3MB, time=80.68 memory used=4871.9MB, alloc=780.3MB, time=88.86 memory used=5270.2MB, alloc=804.3MB, time=94.49 memory used=5714.3MB, alloc=828.3MB, time=101.86 memory used=6136.6MB, alloc=852.3MB, time=111.12 memory used=6587.8MB, alloc=876.3MB, time=118.85 memory used=6989.0MB, alloc=900.3MB, time=128.32 memory used=7387.6MB, alloc=924.3MB, time=135.46 memory used=7755.8MB, alloc=948.3MB, time=142.04 memory used=8112.5MB, alloc=972.3MB, time=150.04 |\^/| 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(); 1428298611 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 F := [-16 x y + 18 x y z + 17 y, 6 x y + y z + 9 x, 3 x z + 6 y z - 6] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 3 2 G := [16 x + 14 y z - 9 x, 3 x y - 8 y z + z , -x z + 9 z - 10 y] > Problem := [F,G]; Problem := [ 2 2 2 2 [-16 x y + 18 x y z + 17 y, 6 x y + y z + 9 x, 3 x z + 6 y z - 6], 2 2 2 3 2 [16 x + 14 y z - 9 x, 3 x y - 8 y z + z , -x z + 9 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=0.17 memory used=26.4MB, alloc=32.3MB, time=0.47 memory used=47.7MB, alloc=32.3MB, time=0.78 memory used=68.0MB, alloc=56.3MB, time=1.09 memory used=110.1MB, alloc=60.3MB, time=1.72 memory used=151.1MB, alloc=84.3MB, time=2.31 memory used=215.0MB, alloc=92.3MB, time=3.29 memory used=277.1MB, alloc=116.3MB, time=4.21 memory used=349.9MB, alloc=116.3MB, time=5.31 memory used=425.6MB, alloc=396.3MB, time=6.56 memory used=538.7MB, alloc=420.3MB, time=8.18 memory used=668.6MB, alloc=444.3MB, time=10.38 memory used=802.2MB, alloc=444.3MB, time=12.33 memory used=936.5MB, alloc=468.3MB, time=14.44 memory used=1049.8MB, alloc=468.3MB, time=16.30 memory used=1167.4MB, alloc=492.3MB, time=18.13 memory used=1278.0MB, alloc=492.3MB, time=20.11 memory used=1378.4MB, alloc=492.3MB, time=21.97 memory used=1478.2MB, alloc=492.3MB, time=23.76 memory used=1573.3MB, alloc=492.3MB, time=25.57 memory used=1652.8MB, alloc=492.3MB, time=26.94 memory used=1736.2MB, alloc=492.3MB, time=28.55 memory used=1811.7MB, alloc=492.3MB, time=29.81 memory used=1897.5MB, alloc=516.3MB, time=31.77 memory used=1959.5MB, alloc=516.3MB, time=32.99 memory used=2030.1MB, alloc=516.3MB, time=34.56 memory used=2072.7MB, alloc=516.3MB, time=35.53 memory used=2125.1MB, alloc=516.3MB, time=36.41 memory used=2185.6MB, alloc=516.3MB, time=37.92 memory used=2402.5MB, alloc=540.3MB, time=41.68 memory used=2638.2MB, alloc=564.3MB, time=46.34 memory used=2838.8MB, alloc=588.3MB, time=50.54 memory used=3021.0MB, alloc=612.3MB, time=54.21 memory used=3180.4MB, alloc=636.3MB, time=57.32 memory used=3347.5MB, alloc=636.3MB, time=60.80 memory used=3509.5MB, alloc=660.3MB, time=64.22 memory used=3644.2MB, alloc=660.3MB, time=67.26 memory used=3779.5MB, alloc=660.3MB, time=70.41 memory used=3897.7MB, alloc=660.3MB, time=73.49 memory used=4031.2MB, alloc=660.3MB, time=76.67 memory used=4141.7MB, alloc=660.3MB, time=79.71 memory used=4252.5MB, alloc=660.3MB, time=82.59 memory used=4363.1MB, alloc=684.3MB, time=85.34 memory used=4721.4MB, alloc=708.3MB, time=92.78 memory used=5098.3MB, alloc=732.3MB, time=100.05 memory used=5483.5MB, alloc=756.3MB, time=106.68 memory used=5879.2MB, alloc=780.3MB, time=114.09 memory used=6243.6MB, alloc=804.3MB, time=120.01 memory used=6616.8MB, alloc=828.3MB, time=126.97 memory used=6949.7MB, alloc=852.3MB, time=134.88 memory used=7299.4MB, alloc=876.3MB, time=142.74 memory used=7606.0MB, alloc=900.3MB, time=149.21 memory used=7872.7MB, alloc=924.3MB, time=155.64 memory used=8178.6MB, alloc=948.3MB, time=161.09 memory used=8440.6MB, alloc=972.3MB, time=166.61 |\^/| 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(); 1428298911 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 3 F := [15 x - 11 z - 6 x, 4 x y - 6 y - 10 y z, 10 y z + 2 z - 6 y] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 2 2 2 G := [5 z - 14 x z - 11 y , -5 x z - 8 y z + 8 x y, 9 x z + 7 y + 7 z] > Problem := [F,G]; 2 2 2 2 3 Problem := [[15 x - 11 z - 6 x, 4 x y - 6 y - 10 y z, 10 y z + 2 z - 6 y], 3 2 2 2 2 2 [5 z - 14 x z - 11 y , -5 x z - 8 y z + 8 x y, 9 x z + 7 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=0.18 memory used=26.7MB, alloc=32.3MB, time=0.51 memory used=46.2MB, alloc=32.3MB, time=0.79 memory used=64.7MB, alloc=56.3MB, time=1.09 memory used=105.0MB, alloc=60.3MB, time=1.70 memory used=139.6MB, alloc=60.3MB, time=2.12 memory used=185.6MB, alloc=68.3MB, time=2.71 memory used=229.5MB, alloc=92.3MB, time=3.29 memory used=296.7MB, alloc=92.3MB, time=4.18 memory used=362.2MB, alloc=116.3MB, time=5.08 memory used=426.6MB, alloc=116.3MB, time=5.96 memory used=497.2MB, alloc=372.3MB, time=6.98 memory used=582.9MB, alloc=396.3MB, time=8.12 memory used=693.2MB, alloc=396.3MB, time=9.72 memory used=801.7MB, alloc=420.3MB, time=11.29 memory used=929.0MB, alloc=444.3MB, time=13.47 memory used=1061.6MB, alloc=468.3MB, time=15.57 memory used=1208.6MB, alloc=468.3MB, time=17.14 memory used=1358.1MB, alloc=492.3MB, time=18.71 memory used=1463.1MB, alloc=492.3MB, time=20.25 memory used=1578.8MB, alloc=516.3MB, time=21.61 memory used=1699.4MB, alloc=516.3MB, time=23.31 memory used=1810.7MB, alloc=516.3MB, time=24.73 memory used=1923.7MB, alloc=516.3MB, time=26.10 memory used=2014.7MB, alloc=516.3MB, time=27.59 memory used=2096.1MB, alloc=540.3MB, time=28.83 memory used=2190.8MB, alloc=540.3MB, time=30.54 memory used=2252.0MB, alloc=540.3MB, time=31.60 memory used=2331.4MB, alloc=540.3MB, time=32.67 memory used=2410.1MB, alloc=540.3MB, time=34.18 memory used=2481.7MB, alloc=540.3MB, time=35.35 memory used=2551.0MB, alloc=540.3MB, time=36.41 memory used=2618.2MB, alloc=540.3MB, time=37.73 memory used=2667.6MB, alloc=540.3MB, time=38.81 memory used=2716.0MB, alloc=540.3MB, time=39.76 memory used=2776.0MB, alloc=540.3MB, time=40.92 memory used=2986.6MB, alloc=564.3MB, time=44.12 memory used=3196.4MB, alloc=588.3MB, time=47.56 memory used=3412.1MB, alloc=612.3MB, time=51.00 memory used=3611.4MB, alloc=636.3MB, time=54.18 memory used=3784.0MB, alloc=636.3MB, time=57.39 memory used=3953.1MB, alloc=660.3MB, time=60.32 memory used=4100.6MB, alloc=660.3MB, time=63.47 memory used=4285.0MB, alloc=660.3MB, time=66.66 memory used=4448.0MB, alloc=684.3MB, time=69.13 memory used=4617.4MB, alloc=684.3MB, time=72.47 memory used=4759.9MB, alloc=684.3MB, time=75.73 memory used=4894.2MB, alloc=684.3MB, time=78.57 memory used=5022.8MB, alloc=684.3MB, time=81.40 memory used=5167.3MB, alloc=684.3MB, time=84.01 memory used=5272.7MB, alloc=684.3MB, time=86.51 memory used=5356.0MB, alloc=684.3MB, time=88.44 memory used=5694.9MB, alloc=708.3MB, time=94.71 memory used=6064.7MB, alloc=732.3MB, time=101.19 memory used=6473.7MB, alloc=756.3MB, time=107.18 memory used=6880.9MB, alloc=780.3MB, time=114.04 memory used=7228.6MB, alloc=804.3MB, time=120.67 memory used=7611.5MB, alloc=828.3MB, time=128.11 memory used=7959.6MB, alloc=852.3MB, time=135.09 memory used=8336.6MB, alloc=876.3MB, time=141.66 memory used=8615.6MB, alloc=900.3MB, time=147.01 memory used=8937.3MB, alloc=924.3MB, time=155.54 memory used=9236.6MB, alloc=948.3MB, time=159.93 memory used=9672.8MB, alloc=972.3MB, time=165.80 |\^/| 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(); 1428299211 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 3 2 3 F := [13 x y + x y + 8, 2 x y z + 8 y - 6 y , z - 5 x y + 3 x z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 G := [9 y z - 19 x - 20 y, 6 y z - 4 x y + 2 y z, -y z + 5 y - 2 z ] > Problem := [F,G]; 2 2 3 2 3 Problem := [[13 x y + x y + 8, 2 x y z + 8 y - 6 y , z - 5 x y + 3 x z], 2 2 2 2 [9 y z - 19 x - 20 y, 6 y z - 4 x y + 2 y z, -y z + 5 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=4.3MB, alloc=32.3MB, time=0.18 memory used=26.1MB, alloc=32.3MB, time=0.51 memory used=46.3MB, alloc=32.3MB, time=0.82 memory used=65.5MB, alloc=56.3MB, time=1.12 memory used=105.4MB, alloc=60.3MB, time=1.75 memory used=145.0MB, alloc=84.3MB, time=2.34 memory used=209.6MB, alloc=92.3MB, time=3.32 memory used=274.2MB, alloc=92.3MB, time=4.24 memory used=336.7MB, alloc=116.3MB, time=5.19 memory used=411.5MB, alloc=372.3MB, time=6.42 memory used=498.5MB, alloc=396.3MB, time=7.76 memory used=608.7MB, alloc=420.3MB, time=9.48 memory used=739.9MB, alloc=420.3MB, time=11.66 memory used=872.3MB, alloc=444.3MB, time=13.72 memory used=1000.9MB, alloc=468.3MB, time=15.77 memory used=1103.8MB, alloc=468.3MB, time=17.38 memory used=1232.1MB, alloc=492.3MB, time=19.49 memory used=1341.5MB, alloc=492.3MB, time=21.32 memory used=1468.0MB, alloc=492.3MB, time=23.58 memory used=1572.5MB, alloc=516.3MB, time=25.48 memory used=1669.9MB, alloc=516.3MB, time=27.27 memory used=1749.3MB, alloc=516.3MB, time=28.60 memory used=1850.1MB, alloc=516.3MB, time=30.58 memory used=1933.3MB, alloc=516.3MB, time=32.13 memory used=2003.5MB, alloc=516.3MB, time=33.57 memory used=2069.1MB, alloc=516.3MB, time=34.75 memory used=2136.1MB, alloc=516.3MB, time=36.26 memory used=2216.2MB, alloc=516.3MB, time=38.04 memory used=2298.3MB, alloc=516.3MB, time=39.99 memory used=2362.6MB, alloc=516.3MB, time=41.33 memory used=2420.6MB, alloc=516.3MB, time=42.86 memory used=2476.1MB, alloc=516.3MB, time=44.21 memory used=2682.4MB, alloc=540.3MB, time=47.75 memory used=2868.3MB, alloc=564.3MB, time=51.04 memory used=3069.3MB, alloc=588.3MB, time=55.14 memory used=3255.1MB, alloc=612.3MB, time=59.16 memory used=3420.4MB, alloc=636.3MB, time=62.79 memory used=3595.6MB, alloc=636.3MB, time=66.76 memory used=3815.4MB, alloc=660.3MB, time=72.51 memory used=3965.6MB, alloc=684.3MB, time=75.67 memory used=4134.0MB, alloc=684.3MB, time=79.35 memory used=4250.0MB, alloc=684.3MB, time=81.86 memory used=4438.9MB, alloc=684.3MB, time=86.72 memory used=4561.9MB, alloc=684.3MB, time=89.72 memory used=4687.7MB, alloc=708.3MB, time=92.92 memory used=4810.5MB, alloc=708.3MB, time=95.34 memory used=5181.5MB, alloc=732.3MB, time=104.33 memory used=5592.1MB, alloc=756.3MB, time=112.32 memory used=6018.1MB, alloc=780.3MB, time=121.20 memory used=6410.2MB, alloc=804.3MB, time=129.09 memory used=6752.7MB, alloc=828.3MB, time=137.66 memory used=7039.5MB, alloc=852.3MB, time=144.46 |\^/| 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(); 1428440509 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 3 2 3 F := [13 x z - 2 y z + 5 x z, 10 x - 5 y z , 5 x y z - y - 4 x] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 3 2 G := [-18 y + 16, 10 x y + 5 z + y z, 2 z + 4 x + 5 y] > Problem := [F,G]; 2 2 3 2 3 Problem := [[13 x z - 2 y z + 5 x z, 10 x - 5 y z , 5 x y z - y - 4 x], 2 2 3 2 [-18 y + 16, 10 x y + 5 z + y z, 2 z + 4 x + 5 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.15 memory used=26.5MB, alloc=32.3MB, time=0.43 memory used=47.7MB, alloc=32.3MB, time=0.69 memory used=66.7MB, alloc=56.3MB, time=0.93 memory used=106.8MB, alloc=60.3MB, time=1.40 memory used=145.7MB, alloc=60.3MB, time=1.86 memory used=187.0MB, alloc=92.3MB, time=2.32 memory used=248.8MB, alloc=92.3MB, time=3.06 memory used=310.3MB, alloc=92.3MB, time=3.86 memory used=372.0MB, alloc=116.3MB, time=4.66 memory used=434.3MB, alloc=116.3MB, time=5.36 memory used=510.0MB, alloc=396.3MB, time=6.30 memory used=618.6MB, alloc=396.3MB, time=7.33 memory used=721.1MB, alloc=396.3MB, time=8.25 memory used=828.9MB, alloc=420.3MB, time=9.40 memory used=954.1MB, alloc=420.3MB, time=11.00 memory used=1075.2MB, alloc=444.3MB, time=12.83 memory used=1201.4MB, alloc=468.3MB, time=14.55 memory used=1331.5MB, alloc=468.3MB, time=16.18 memory used=1455.2MB, alloc=492.3MB, time=17.96 memory used=1553.2MB, alloc=492.3MB, time=19.15 memory used=1632.2MB, alloc=492.3MB, time=20.09 memory used=1737.3MB, alloc=516.3MB, time=21.46 memory used=1826.8MB, alloc=516.3MB, time=22.96 memory used=1919.1MB, alloc=516.3MB, time=24.46 memory used=1988.8MB, alloc=516.3MB, time=25.50 memory used=2043.7MB, alloc=516.3MB, time=26.25 memory used=2106.3MB, alloc=540.3MB, time=27.14 memory used=2168.7MB, alloc=540.3MB, time=27.98 memory used=2235.7MB, alloc=540.3MB, time=29.23 memory used=2284.1MB, alloc=540.3MB, time=30.10 memory used=2474.1MB, alloc=564.3MB, time=32.17 memory used=2677.2MB, alloc=588.3MB, time=34.54 memory used=2864.7MB, alloc=612.3MB, time=37.62 memory used=3003.3MB, alloc=636.3MB, time=39.89 memory used=3188.8MB, alloc=660.3MB, time=43.33 memory used=3326.0MB, alloc=660.3MB, time=45.93 memory used=3444.2MB, alloc=660.3MB, time=47.95 memory used=3575.8MB, alloc=684.3MB, time=49.89 memory used=3733.0MB, alloc=684.3MB, time=53.00 memory used=3858.4MB, alloc=684.3MB, time=55.17 memory used=4098.8MB, alloc=684.3MB, time=58.83 memory used=4320.6MB, alloc=684.3MB, time=63.95 memory used=4430.9MB, alloc=684.3MB, time=66.10 memory used=4535.9MB, alloc=708.3MB, time=68.00 memory used=4636.9MB, alloc=708.3MB, time=69.87 memory used=4968.2MB, alloc=732.3MB, time=75.27 memory used=5364.8MB, alloc=756.3MB, time=81.24 memory used=5738.3MB, alloc=780.3MB, time=87.29 memory used=6153.0MB, alloc=804.3MB, time=94.06 memory used=6528.9MB, alloc=828.3MB, time=101.92 memory used=6817.4MB, alloc=852.3MB, time=108.73 memory used=7122.9MB, alloc=876.3MB, time=115.02 memory used=7385.5MB, alloc=900.3MB, time=121.20 memory used=7682.8MB, alloc=924.3MB, time=128.76 memory used=7877.9MB, alloc=948.3MB, time=133.74 memory used=8094.2MB, alloc=972.3MB, time=139.43 memory used=8485.7MB, alloc=996.3MB, time=144.15 memory used=8827.6MB, alloc=996.3MB, time=149.07 memory used=9179.7MB, alloc=1020.3MB, time=155.43 memory used=9815.8MB, alloc=1044.3MB, time=166.29 memory used=10451.0MB, alloc=1068.3MB, time=179.18 memory used=11173.0MB, alloc=1092.3MB, time=192.06 memory used=11855.6MB, alloc=1116.3MB, time=205.60 memory used=12559.6MB, alloc=1140.3MB, time=217.49 memory used=13214.0MB, alloc=1164.3MB, time=231.44 memory used=13912.9MB, alloc=1188.3MB, time=247.96 memory used=14498.8MB, alloc=1212.3MB, time=259.77 memory used=14980.6MB, alloc=1236.3MB, time=271.70 memory used=15611.2MB, alloc=1260.3MB, time=283.32 memory used=16190.5MB, alloc=1284.3MB, time=294.84 memory used=16650.8MB, alloc=1308.3MB, time=307.80 memory used=17181.1MB, alloc=1332.3MB, time=321.74 memory used=17646.2MB, alloc=1356.3MB, time=334.53 memory used=17981.7MB, alloc=1380.3MB, time=343.72 memory used=18566.0MB, alloc=1404.3MB, time=353.78 memory used=19004.9MB, alloc=1428.3MB, time=378.03 memory used=19312.3MB, alloc=1452.3MB, time=382.94 memory used=19639.1MB, alloc=1491.8MB, time=387.81 memory used=19722.1MB, alloc=1515.8MB, time=392.20 memory used=19811.9MB, alloc=1539.8MB, time=396.68 memory used=19910.2MB, alloc=1563.8MB, time=401.10 memory used=20017.6MB, alloc=1587.8MB, time=405.51 memory used=20136.5MB, alloc=1611.8MB, time=409.94 memory used=20631.3MB, alloc=1635.8MB, time=419.46 memory used=20998.6MB, alloc=1659.8MB, time=429.10 memory used=21314.0MB, alloc=1683.8MB, time=438.35 memory used=21672.9MB, alloc=1707.8MB, time=448.98 memory used=21987.9MB, alloc=1731.8MB, time=459.33 memory used=22581.1MB, alloc=1755.8MB, time=466.68 memory used=23126.5MB, alloc=1779.8MB, time=473.17 memory used=23847.0MB, alloc=1803.8MB, time=499.05 memory used=23931.6MB, alloc=1803.8MB, time=503.91 memory used=24027.0MB, alloc=1803.8MB, time=508.79 memory used=24134.6MB, alloc=1803.8MB, time=513.78 memory used=24334.7MB, alloc=1803.8MB, time=519.26 memory used=24923.8MB, alloc=1803.8MB, time=525.33 memory used=25555.2MB, alloc=1803.8MB, time=550.81 memory used=26023.0MB, alloc=1803.8MB, time=556.50 memory used=26109.5MB, alloc=1803.8MB, time=561.60 memory used=26207.1MB, alloc=1803.8MB, time=566.91 memory used=26317.3MB, alloc=1803.8MB, time=572.37 memory used=26845.6MB, alloc=1803.8MB, time=584.10 memory used=27002.1MB, alloc=1803.8MB, time=589.35 memory used=27693.1MB, alloc=1803.8MB, time=597.77 memory used=28283.6MB, alloc=1803.8MB, time=604.59 memory used=28924.3MB, alloc=1803.8MB, time=617.48 memory used=29137.5MB, alloc=1803.8MB, time=623.75 memory used=29847.2MB, alloc=1803.8MB, time=635.38 memory used=30148.3MB, alloc=1803.8MB, time=646.25 memory used=30598.8MB, alloc=1827.8MB, time=658.71 memory used=31158.8MB, alloc=1827.8MB, time=677.07 memory used=31439.0MB, alloc=1827.8MB, time=688.25 memory used=31812.5MB, alloc=1851.8MB, time=697.32 memory used=32185.0MB, alloc=1875.8MB, time=707.49 memory used=32568.2MB, alloc=1875.8MB, time=718.55 memory used=32844.9MB, alloc=1875.8MB, time=728.21 memory used=33054.4MB, alloc=1875.8MB, time=735.59 memory used=33309.2MB, alloc=1875.8MB, time=744.19 memory used=33469.3MB, alloc=1875.8MB, time=753.45 memory used=33770.9MB, alloc=1875.8MB, time=762.49 memory used=34029.0MB, alloc=1899.8MB, time=771.84 memory used=34145.6MB, alloc=1899.8MB, time=780.04 memory used=34300.1MB, alloc=1899.8MB, time=788.97 memory used=34488.4MB, alloc=1899.8MB, time=797.74 memory used=34582.9MB, alloc=1899.8MB, time=805.45 memory used=34643.0MB, alloc=1899.8MB, time=812.44 memory used=34767.2MB, alloc=1899.8MB, time=820.01 memory used=34885.2MB, alloc=1899.8MB, time=829.06 memory used=34959.9MB, alloc=1899.8MB, time=836.48 memory used=35081.1MB, alloc=1899.8MB, time=845.99 memory used=35187.0MB, alloc=1899.8MB, time=854.81 memory used=35317.0MB, alloc=1899.8MB, time=865.74 memory used=35408.7MB, alloc=1899.8MB, time=874.00 memory used=35509.2MB, alloc=1899.8MB, time=881.01 memory used=36131.3MB, alloc=1923.8MB, time=890.76 memory used=36753.1MB, alloc=1923.8MB, time=916.69 memory used=37228.3MB, alloc=1923.8MB, time=924.51 memory used=37312.8MB, alloc=1923.8MB, time=930.96 memory used=37406.4MB, alloc=1923.8MB, time=937.36 memory used=37511.7MB, alloc=1923.8MB, time=943.57 memory used=37632.6MB, alloc=1923.8MB, time=949.78 memory used=38022.7MB, alloc=2179.8MB, time=964.46 memory used=38661.6MB, alloc=2179.8MB, time=972.50 memory used=39316.2MB, alloc=2179.8MB, time=1000.75 memory used=39596.4MB, alloc=2179.8MB, time=1007.54 memory used=39681.2MB, alloc=2179.8MB, time=1013.75 memory used=39774.8MB, alloc=2179.8MB, time=1020.15 memory used=39881.7MB, alloc=2179.8MB, time=1026.58 memory used=40003.8MB, alloc=2179.8MB, time=1032.87 memory used=40714.8MB, alloc=2179.8MB, time=1042.02 memory used=41346.2MB, alloc=2179.8MB, time=1049.92 memory used=41988.0MB, alloc=2179.8MB, time=1066.48 memory used=42968.7MB, alloc=2203.8MB, time=1083.11 memory used=43840.0MB, alloc=2203.8MB, time=1103.54 memory used=44692.9MB, alloc=2203.8MB, time=1127.51 memory used=45640.1MB, alloc=2227.8MB, time=1140.75 memory used=47056.6MB, alloc=2251.8MB, time=1175.45 memory used=48015.8MB, alloc=2275.8MB, time=1203.39 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428441709 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 3 2 3 2 F := [-6 x y + 17 y z + 8 x y, -3 y - 3 y z + 3 y, 9 x - 9 y ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 3 2 2 2 G := [18 x z + 5 z , 10 y + 2 y z + 3 y z, 4 x y z - x + 8 y ] > Problem := [F,G]; 2 2 3 2 3 2 Problem := [[-6 x y + 17 y z + 8 x y, -3 y - 3 y z + 3 y, 9 x - 9 y ], 2 2 3 2 2 2 [18 x z + 5 z , 10 y + 2 y z + 3 y z, 4 x y z - x + 8 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.22 memory used=26.4MB, alloc=32.3MB, time=0.55 memory used=47.3MB, alloc=32.3MB, time=0.88 memory used=67.1MB, alloc=56.3MB, time=1.21 memory used=107.3MB, alloc=60.3MB, time=1.85 memory used=144.4MB, alloc=84.3MB, time=2.45 memory used=204.5MB, alloc=92.3MB, time=3.40 memory used=263.9MB, alloc=92.3MB, time=4.32 memory used=321.8MB, alloc=116.3MB, time=5.32 memory used=402.4MB, alloc=116.3MB, time=6.65 memory used=481.1MB, alloc=140.3MB, time=7.94 memory used=563.1MB, alloc=396.3MB, time=9.41 memory used=662.6MB, alloc=420.3MB, time=11.14 memory used=784.6MB, alloc=444.3MB, time=13.32 memory used=926.9MB, alloc=468.3MB, time=16.04 memory used=1060.7MB, alloc=492.3MB, time=18.39 memory used=1207.7MB, alloc=492.3MB, time=21.16 memory used=1344.3MB, alloc=516.3MB, time=23.83 memory used=1493.3MB, alloc=516.3MB, time=26.90 memory used=1627.9MB, alloc=540.3MB, time=29.57 memory used=1751.2MB, alloc=540.3MB, time=32.00 memory used=1878.6MB, alloc=540.3MB, time=35.17 memory used=1987.2MB, alloc=540.3MB, time=37.57 memory used=2084.4MB, alloc=540.3MB, time=39.68 memory used=2182.5MB, alloc=564.3MB, time=42.12 memory used=2271.4MB, alloc=564.3MB, time=44.37 memory used=2359.1MB, alloc=564.3MB, time=46.58 memory used=2439.7MB, alloc=564.3MB, time=48.83 memory used=2497.2MB, alloc=564.3MB, time=50.24 memory used=2566.4MB, alloc=564.3MB, time=52.13 memory used=2614.6MB, alloc=564.3MB, time=53.42 memory used=2857.0MB, alloc=588.3MB, time=59.22 memory used=3105.0MB, alloc=612.3MB, time=65.25 memory used=3356.5MB, alloc=636.3MB, time=71.87 memory used=3582.0MB, alloc=660.3MB, time=78.10 memory used=3756.2MB, alloc=684.3MB, time=82.38 memory used=3946.6MB, alloc=708.3MB, time=87.31 memory used=4177.8MB, alloc=732.3MB, time=94.83 memory used=4328.9MB, alloc=732.3MB, time=98.93 memory used=4504.2MB, alloc=732.3MB, time=104.15 memory used=4670.7MB, alloc=756.3MB, time=109.21 memory used=4806.5MB, alloc=756.3MB, time=113.22 memory used=4928.6MB, alloc=756.3MB, time=117.23 memory used=5048.3MB, alloc=756.3MB, time=121.25 memory used=5445.5MB, alloc=780.3MB, time=131.22 memory used=5856.4MB, alloc=804.3MB, time=141.37 memory used=6285.7MB, alloc=828.3MB, time=153.32 memory used=6733.1MB, alloc=852.3MB, time=166.47 memory used=7183.7MB, alloc=876.3MB, time=178.08 memory used=7559.5MB, alloc=900.3MB, time=187.96 memory used=7928.1MB, alloc=924.3MB, time=198.07 memory used=8275.4MB, alloc=948.3MB, time=206.93 memory used=8601.0MB, alloc=972.3MB, time=215.60 memory used=8902.6MB, alloc=996.3MB, time=223.10 memory used=9226.7MB, alloc=1020.3MB, time=230.91 memory used=9521.2MB, alloc=1044.3MB, time=238.43 memory used=9993.9MB, alloc=1068.3MB, time=250.21 memory used=10434.2MB, alloc=1092.3MB, time=260.87 memory used=10860.3MB, alloc=1116.3MB, time=271.63 memory used=11270.6MB, alloc=1140.3MB, time=282.20 memory used=11669.1MB, alloc=1164.3MB, time=292.72 memory used=12067.7MB, alloc=1188.3MB, time=303.91 memory used=12445.4MB, alloc=1212.3MB, time=314.22 memory used=12815.9MB, alloc=1236.3MB, time=324.28 memory used=13175.5MB, alloc=1260.3MB, time=334.19 memory used=13533.0MB, alloc=1284.3MB, time=344.61 memory used=13877.8MB, alloc=1308.3MB, time=355.05 memory used=14207.4MB, alloc=1332.3MB, time=365.17 memory used=14539.5MB, alloc=1356.3MB, time=374.88 memory used=14867.5MB, alloc=1380.3MB, time=384.44 memory used=15218.0MB, alloc=1404.3MB, time=394.38 memory used=15548.0MB, alloc=1428.3MB, time=403.94 memory used=15892.6MB, alloc=1452.3MB, time=413.77 memory used=16210.6MB, alloc=1476.3MB, time=423.51 memory used=16541.9MB, alloc=1500.3MB, time=433.40 memory used=16861.9MB, alloc=1524.3MB, time=443.15 memory used=17181.6MB, alloc=1548.3MB, time=452.97 memory used=17511.4MB, alloc=1572.3MB, time=462.97 memory used=17818.9MB, alloc=1596.3MB, time=472.86 memory used=18131.1MB, alloc=1620.3MB, time=482.82 memory used=18440.2MB, alloc=1644.3MB, time=492.91 memory used=18751.9MB, alloc=1668.3MB, time=503.06 memory used=19050.1MB, alloc=1692.3MB, time=513.07 memory used=19343.7MB, alloc=1716.3MB, time=523.02 memory used=19641.2MB, alloc=1740.3MB, time=533.30 memory used=19940.4MB, alloc=1764.3MB, time=544.47 memory used=20240.6MB, alloc=1788.3MB, time=555.71 memory used=20546.1MB, alloc=1812.3MB, time=566.99 memory used=20844.1MB, alloc=1836.3MB, time=577.66 memory used=21140.1MB, alloc=1860.3MB, time=588.20 memory used=21438.6MB, alloc=1884.3MB, time=598.89 memory used=21728.2MB, alloc=1908.3MB, time=609.34 memory used=22011.4MB, alloc=1932.3MB, time=619.89 memory used=22295.1MB, alloc=1956.3MB, time=630.50 memory used=22579.5MB, alloc=1980.3MB, time=641.27 memory used=22863.9MB, alloc=2004.3MB, time=652.11 memory used=23155.1MB, alloc=2028.3MB, time=663.49 memory used=23456.3MB, alloc=2052.3MB, time=674.90 memory used=23740.1MB, alloc=2076.3MB, time=686.95 memory used=23979.9MB, alloc=2100.3MB, time=699.73 memory used=24192.7MB, alloc=2124.3MB, time=713.48 memory used=24412.3MB, alloc=2148.3MB, time=728.59 memory used=24649.2MB, alloc=2172.3MB, time=744.29 memory used=24903.7MB, alloc=2196.3MB, time=762.04 memory used=25175.0MB, alloc=2220.3MB, time=779.74 memory used=25462.8MB, alloc=2244.3MB, time=798.29 memory used=25767.0MB, alloc=2268.3MB, time=817.71 memory used=26087.4MB, alloc=2292.3MB, time=838.06 memory used=26423.3MB, alloc=2316.3MB, time=859.04 memory used=26775.0MB, alloc=2340.3MB, time=880.89 memory used=27142.9MB, alloc=2364.3MB, time=903.10 |\^/| 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(); 1428442909 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 2 F := [-8 x y + 9 x y - 12 y , -9 x y - 9 x z + 10 z, 5 x y + 4 x z + y z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 2 2 2 2 G := [14 x y + 11 z + 9 z, 6 x z + 9 y z - 7 z , -4 x z - 7 y z + 4 x z] > Problem := [F,G]; Problem := [ 2 2 2 2 2 [-8 x y + 9 x y - 12 y , -9 x y - 9 x z + 10 z, 5 x y + 4 x z + y z], 2 3 2 2 2 2 2 [14 x y + 11 z + 9 z, 6 x z + 9 y z - 7 z , -4 x z - 7 y z + 4 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.19 memory used=26.2MB, alloc=32.3MB, time=0.52 memory used=47.1MB, alloc=32.3MB, time=0.83 memory used=67.4MB, alloc=56.3MB, time=1.17 memory used=108.7MB, alloc=60.3MB, time=1.81 memory used=148.6MB, alloc=84.3MB, time=2.45 memory used=210.6MB, alloc=92.3MB, time=3.46 memory used=272.6MB, alloc=116.3MB, time=4.46 memory used=355.0MB, alloc=140.3MB, time=5.93 memory used=420.9MB, alloc=396.3MB, time=7.08 memory used=529.6MB, alloc=420.3MB, time=8.91 memory used=663.2MB, alloc=444.3MB, time=11.17 memory used=797.4MB, alloc=468.3MB, time=13.46 memory used=931.1MB, alloc=468.3MB, time=15.90 memory used=1040.3MB, alloc=468.3MB, time=18.02 memory used=1165.6MB, alloc=492.3MB, time=20.08 memory used=1268.9MB, alloc=492.3MB, time=22.06 memory used=1360.9MB, alloc=492.3MB, time=23.69 memory used=1443.6MB, alloc=492.3MB, time=25.27 memory used=1533.6MB, alloc=516.3MB, time=27.07 memory used=1615.4MB, alloc=516.3MB, time=28.82 memory used=1706.1MB, alloc=516.3MB, time=30.84 memory used=1780.0MB, alloc=516.3MB, time=32.42 memory used=1842.9MB, alloc=516.3MB, time=33.73 memory used=1910.5MB, alloc=516.3MB, time=35.04 memory used=1981.2MB, alloc=516.3MB, time=36.73 memory used=2035.0MB, alloc=516.3MB, time=38.09 memory used=2087.2MB, alloc=540.3MB, time=39.37 memory used=2136.6MB, alloc=540.3MB, time=40.62 memory used=2358.1MB, alloc=564.3MB, time=45.25 memory used=2564.0MB, alloc=588.3MB, time=49.33 memory used=2809.1MB, alloc=612.3MB, time=54.92 memory used=2976.4MB, alloc=636.3MB, time=58.89 memory used=3147.6MB, alloc=660.3MB, time=61.98 memory used=3300.7MB, alloc=684.3MB, time=65.52 memory used=3438.9MB, alloc=684.3MB, time=68.26 memory used=3614.0MB, alloc=684.3MB, time=72.32 memory used=3744.2MB, alloc=708.3MB, time=74.92 memory used=3886.3MB, alloc=708.3MB, time=78.57 memory used=3999.3MB, alloc=708.3MB, time=81.22 memory used=4086.1MB, alloc=708.3MB, time=83.54 memory used=4187.4MB, alloc=708.3MB, time=85.82 memory used=4566.6MB, alloc=732.3MB, time=93.49 memory used=4949.4MB, alloc=756.3MB, time=102.34 memory used=5328.2MB, alloc=780.3MB, time=110.24 memory used=5680.5MB, alloc=804.3MB, time=117.89 memory used=6094.0MB, alloc=828.3MB, time=128.04 memory used=6429.4MB, alloc=852.3MB, time=135.24 memory used=6752.1MB, alloc=876.3MB, time=141.85 memory used=7116.0MB, alloc=900.3MB, time=149.77 memory used=7445.4MB, alloc=924.3MB, time=157.11 memory used=7682.0MB, alloc=948.3MB, time=162.95 memory used=7921.6MB, alloc=972.3MB, time=169.41 memory used=8131.0MB, alloc=996.3MB, time=174.11 memory used=8338.8MB, alloc=1020.3MB, time=180.18 memory used=8505.1MB, alloc=1044.3MB, time=184.71 memory used=9150.1MB, alloc=1068.3MB, time=199.76 memory used=9806.1MB, alloc=1092.3MB, time=215.51 memory used=10483.8MB, alloc=1116.3MB, time=231.73 memory used=11151.1MB, alloc=1140.3MB, time=250.28 memory used=11846.6MB, alloc=1164.3MB, time=268.08 memory used=12411.9MB, alloc=1188.3MB, time=279.36 memory used=13013.7MB, alloc=1212.3MB, time=293.34 memory used=13694.7MB, alloc=1236.3MB, time=312.42 memory used=14352.6MB, alloc=1260.3MB, time=328.89 memory used=14854.5MB, alloc=1284.3MB, time=345.34 memory used=15450.0MB, alloc=1308.3MB, time=363.46 memory used=15954.9MB, alloc=1332.3MB, time=380.83 memory used=16370.4MB, alloc=1356.3MB, time=394.53 memory used=16722.5MB, alloc=1380.3MB, time=407.94 memory used=17033.6MB, alloc=1404.3MB, time=420.45 memory used=17399.6MB, alloc=1428.3MB, time=433.69 memory used=17732.7MB, alloc=1452.3MB, time=447.26 memory used=18034.8MB, alloc=1476.3MB, time=460.12 memory used=18353.2MB, alloc=1500.3MB, time=472.84 memory used=18665.4MB, alloc=1524.3MB, time=484.23 memory used=18912.7MB, alloc=1548.3MB, time=493.72 memory used=19140.2MB, alloc=1572.3MB, time=505.30 memory used=19396.2MB, alloc=1596.3MB, time=514.56 memory used=19663.5MB, alloc=1620.3MB, time=526.91 memory used=19941.4MB, alloc=1644.3MB, time=535.56 memory used=20191.4MB, alloc=1668.3MB, time=547.48 memory used=20354.9MB, alloc=1692.3MB, time=555.60 memory used=20475.5MB, alloc=1716.3MB, time=565.37 memory used=20596.2MB, alloc=1740.3MB, time=573.58 memory used=20772.7MB, alloc=1764.3MB, time=581.92 memory used=20887.0MB, alloc=1788.3MB, time=589.78 memory used=21047.5MB, alloc=1812.3MB, time=598.06 memory used=21217.5MB, alloc=1836.3MB, time=609.42 memory used=21303.6MB, alloc=1860.3MB, time=617.31 memory used=21369.1MB, alloc=1860.3MB, time=624.36 memory used=21500.8MB, alloc=1860.3MB, time=634.41 memory used=21647.8MB, alloc=1860.3MB, time=642.76 memory used=21775.8MB, alloc=1860.3MB, time=650.07 memory used=21947.2MB, alloc=1860.3MB, time=660.56 memory used=22049.7MB, alloc=1860.3MB, time=668.36 memory used=22113.0MB, alloc=1860.3MB, time=674.91 memory used=22181.1MB, alloc=1860.3MB, time=682.32 memory used=22254.3MB, alloc=1860.3MB, time=690.33 memory used=22316.5MB, alloc=1860.3MB, time=697.46 memory used=22401.8MB, alloc=1860.3MB, time=705.58 memory used=22452.8MB, alloc=1860.3MB, time=712.96 memory used=22522.2MB, alloc=1860.3MB, time=720.77 memory used=22576.9MB, alloc=1860.3MB, time=727.77 memory used=22667.3MB, alloc=1860.3MB, time=736.78 memory used=22722.9MB, alloc=1860.3MB, time=744.26 memory used=22787.2MB, alloc=1860.3MB, time=751.71 memory used=22828.1MB, alloc=1860.3MB, time=758.86 memory used=22876.7MB, alloc=2116.3MB, time=772.91 memory used=24130.4MB, alloc=2140.3MB, time=812.41 memory used=25308.8MB, alloc=2164.3MB, time=845.18 memory used=26237.5MB, alloc=2188.3MB, time=864.84 memory used=27051.3MB, alloc=2212.3MB, time=880.08 memory used=28136.1MB, alloc=2236.3MB, time=905.79 memory used=28821.1MB, alloc=2260.3MB, time=921.12 memory used=29813.6MB, alloc=2284.3MB, time=944.20 memory used=31110.2MB, alloc=2308.3MB, time=976.48 memory used=32455.8MB, alloc=2332.3MB, time=1016.71 memory used=33507.0MB, alloc=2356.3MB, time=1043.94 memory used=34499.0MB, alloc=2380.3MB, time=1064.59 memory used=35770.8MB, alloc=2404.3MB, time=1098.45 |\^/| 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(); 1428444109 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 3 2 3 F := [5 x z - 8 x y z + 9 y , 8 x z + y + 4 x , 2 y - 3 z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 G := [-9 x - 16 x z + 3, 10 x + x y - 2, 5 x y z - 5 y z ] > Problem := [F,G]; 2 3 2 3 2 3 Problem := [[5 x z - 8 x y z + 9 y , 8 x z + y + 4 x , 2 y - 3 z], 2 3 2 [-9 x - 16 x z + 3, 10 x + x y - 2, 5 x y z - 5 y z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.3MB, alloc=32.3MB, time=0.49 memory used=47.2MB, alloc=32.3MB, time=0.79 memory used=66.6MB, alloc=56.3MB, time=1.10 memory used=106.4MB, alloc=60.3MB, time=1.68 memory used=144.2MB, alloc=60.3MB, time=2.22 memory used=181.2MB, alloc=84.3MB, time=2.79 memory used=224.4MB, alloc=84.3MB, time=3.47 memory used=282.6MB, alloc=116.3MB, time=4.42 memory used=353.8MB, alloc=372.3MB, time=5.46 memory used=434.6MB, alloc=396.3MB, time=6.71 memory used=543.9MB, alloc=420.3MB, time=8.30 memory used=674.5MB, alloc=444.3MB, time=10.17 memory used=783.8MB, alloc=444.3MB, time=11.67 memory used=903.8MB, alloc=468.3MB, time=13.33 memory used=1035.8MB, alloc=492.3MB, time=15.62 memory used=1137.0MB, alloc=492.3MB, time=17.24 memory used=1235.3MB, alloc=492.3MB, time=18.93 memory used=1324.6MB, alloc=492.3MB, time=20.40 memory used=1420.3MB, alloc=516.3MB, time=22.23 memory used=1493.5MB, alloc=516.3MB, time=23.47 memory used=1554.5MB, alloc=516.3MB, time=24.60 memory used=1619.0MB, alloc=516.3MB, time=25.88 memory used=1677.9MB, alloc=516.3MB, time=27.12 memory used=1723.5MB, alloc=516.3MB, time=28.08 memory used=1927.4MB, alloc=540.3MB, time=31.53 memory used=2110.7MB, alloc=564.3MB, time=34.57 memory used=2303.4MB, alloc=588.3MB, time=38.27 memory used=2470.8MB, alloc=612.3MB, time=41.45 memory used=2618.1MB, alloc=636.3MB, time=44.30 memory used=2763.5MB, alloc=660.3MB, time=47.06 memory used=2908.4MB, alloc=660.3MB, time=49.89 memory used=3014.9MB, alloc=660.3MB, time=52.10 memory used=3130.8MB, alloc=684.3MB, time=54.74 memory used=3238.9MB, alloc=684.3MB, time=57.01 memory used=3318.5MB, alloc=684.3MB, time=59.00 memory used=3656.3MB, alloc=708.3MB, time=65.48 memory used=3973.5MB, alloc=732.3MB, time=72.09 memory used=4265.4MB, alloc=756.3MB, time=78.38 memory used=4551.8MB, alloc=780.3MB, time=84.71 memory used=4838.2MB, alloc=804.3MB, time=91.05 memory used=5145.4MB, alloc=828.3MB, time=97.53 memory used=5442.5MB, alloc=852.3MB, time=104.10 memory used=5733.0MB, alloc=876.3MB, time=110.74 memory used=6022.4MB, alloc=900.3MB, time=117.55 memory used=6315.9MB, alloc=924.3MB, time=124.36 memory used=6615.5MB, alloc=948.3MB, time=131.50 memory used=6863.2MB, alloc=972.3MB, time=141.37 memory used=7108.5MB, alloc=996.3MB, time=151.76 memory used=7362.0MB, alloc=1020.3MB, time=162.88 memory used=7626.6MB, alloc=1044.3MB, time=174.69 memory used=7903.5MB, alloc=1068.3MB, time=187.22 memory used=8194.1MB, alloc=1092.3MB, time=200.48 memory used=8498.6MB, alloc=1116.3MB, time=214.36 memory used=8817.5MB, alloc=1140.3MB, time=229.03 memory used=9151.2MB, alloc=1164.3MB, time=244.52 memory used=9499.8MB, alloc=1188.3MB, time=260.91 memory used=9863.4MB, alloc=1212.3MB, time=277.52 memory used=10241.8MB, alloc=1236.3MB, time=295.02 memory used=10636.0MB, alloc=1260.3MB, time=313.23 memory used=11045.8MB, alloc=1284.3MB, time=332.23 memory used=11471.4MB, alloc=1308.3MB, time=351.85 memory used=11912.6MB, alloc=1332.3MB, time=372.28 memory used=12369.7MB, alloc=1356.3MB, time=393.43 memory used=12841.7MB, alloc=1380.3MB, time=415.55 memory used=13324.2MB, alloc=1404.3MB, time=439.10 memory used=13830.7MB, alloc=1428.3MB, time=463.72 memory used=14361.2MB, alloc=1452.3MB, time=489.21 memory used=14915.6MB, alloc=1476.3MB, time=515.63 memory used=15493.9MB, alloc=1500.3MB, time=543.25 memory used=16096.2MB, alloc=1524.3MB, time=572.01 memory used=16722.4MB, alloc=1548.3MB, time=601.63 memory used=17372.6MB, alloc=1572.3MB, time=632.30 memory used=18046.8MB, alloc=1596.3MB, time=663.81 memory used=18744.8MB, alloc=1620.3MB, time=696.69 memory used=19466.7MB, alloc=1644.3MB, time=730.58 memory used=20212.6MB, alloc=1668.3MB, time=765.56 memory used=20982.5MB, alloc=1692.3MB, time=801.50 memory used=21776.3MB, alloc=1716.3MB, time=838.84 memory used=22594.0MB, alloc=1740.3MB, time=876.92 memory used=23435.7MB, alloc=1764.3MB, time=916.02 memory used=24301.3MB, alloc=1788.3MB, time=956.23 memory used=25190.8MB, alloc=1812.3MB, time=997.49 memory used=26104.2MB, alloc=1836.3MB, time=1039.50 memory used=27041.6MB, alloc=1860.3MB, time=1082.63 |\^/| 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(); 1428445309 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 F := [x z - 18 y z + 19 y, 8 y z + 8 x y - 10, -7 x z - 5 z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 3 2 G := [18 x z - 9 x z - 20, 8 x z - 3 y + 10, -6 x y + 10 z + 7 x ] > Problem := [F,G]; 2 2 2 Problem := [[x z - 18 y z + 19 y, 8 y z + 8 x y - 10, -7 x z - 5 z], 2 2 2 2 3 2 [18 x z - 9 x z - 20, 8 x z - 3 y + 10, -6 x y + 10 z + 7 x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.19 memory used=26.6MB, alloc=32.3MB, time=0.51 memory used=46.3MB, alloc=56.3MB, time=0.82 memory used=85.9MB, alloc=60.3MB, time=1.42 memory used=123.9MB, alloc=84.3MB, time=1.99 memory used=167.9MB, alloc=84.3MB, time=2.70 memory used=227.0MB, alloc=92.3MB, time=3.65 memory used=285.3MB, alloc=116.3MB, time=4.57 memory used=364.5MB, alloc=116.3MB, time=5.79 memory used=442.6MB, alloc=140.3MB, time=7.05 memory used=533.5MB, alloc=164.3MB, time=8.59 memory used=615.0MB, alloc=420.3MB, time=9.99 memory used=735.8MB, alloc=444.3MB, time=12.02 memory used=884.8MB, alloc=468.3MB, time=14.62 memory used=1055.1MB, alloc=492.3MB, time=17.89 memory used=1255.5MB, alloc=516.3MB, time=21.45 memory used=1470.9MB, alloc=540.3MB, time=25.64 memory used=1707.3MB, alloc=564.3MB, time=30.36 memory used=1967.9MB, alloc=588.3MB, time=36.28 memory used=2242.5MB, alloc=612.3MB, time=42.84 memory used=2540.7MB, alloc=636.3MB, time=49.86 memory used=2844.0MB, alloc=660.3MB, time=56.75 memory used=3163.1MB, alloc=684.3MB, time=64.92 memory used=3449.1MB, alloc=708.3MB, time=71.60 memory used=3753.5MB, alloc=732.3MB, time=78.85 memory used=4077.8MB, alloc=756.3MB, time=87.90 memory used=4340.4MB, alloc=780.3MB, time=95.29 memory used=4596.8MB, alloc=804.3MB, time=102.38 memory used=4827.6MB, alloc=828.3MB, time=109.10 memory used=5057.6MB, alloc=852.3MB, time=115.33 memory used=5227.0MB, alloc=852.3MB, time=119.30 memory used=5368.9MB, alloc=852.3MB, time=122.43 memory used=5540.5MB, alloc=876.3MB, time=127.32 memory used=5728.5MB, alloc=876.3MB, time=132.06 memory used=5921.7MB, alloc=876.3MB, time=137.92 memory used=6096.1MB, alloc=876.3MB, time=142.61 memory used=6245.9MB, alloc=876.3MB, time=146.98 memory used=6354.7MB, alloc=900.3MB, time=149.59 memory used=6467.1MB, alloc=900.3MB, time=152.14 memory used=6620.3MB, alloc=900.3MB, time=157.46 memory used=6742.2MB, alloc=900.3MB, time=161.56 memory used=7255.6MB, alloc=924.3MB, time=176.13 memory used=7715.9MB, alloc=948.3MB, time=187.21 memory used=8100.8MB, alloc=972.3MB, time=194.40 memory used=8494.5MB, alloc=996.3MB, time=204.41 memory used=8921.0MB, alloc=1020.3MB, time=214.73 memory used=9195.3MB, alloc=1044.3MB, time=221.20 memory used=9852.3MB, alloc=1068.3MB, time=237.05 memory used=10535.0MB, alloc=1092.3MB, time=255.95 memory used=11247.9MB, alloc=1116.3MB, time=272.70 memory used=11960.1MB, alloc=1140.3MB, time=294.13 memory used=12679.7MB, alloc=1164.3MB, time=317.37 memory used=13432.5MB, alloc=1188.3MB, time=340.09 memory used=14196.5MB, alloc=1212.3MB, time=363.25 memory used=14996.4MB, alloc=1236.3MB, time=384.62 memory used=15794.4MB, alloc=1260.3MB, time=409.84 memory used=16624.4MB, alloc=1284.3MB, time=433.40 memory used=17397.1MB, alloc=1308.3MB, time=455.34 memory used=17652.8MB, alloc=1332.3MB, time=460.95 memory used=17935.7MB, alloc=1356.3MB, time=466.62 memory used=18591.3MB, alloc=1380.3MB, time=479.39 memory used=19426.5MB, alloc=1404.3MB, time=509.36 memory used=20318.9MB, alloc=1428.3MB, time=536.90 memory used=21127.8MB, alloc=1452.3MB, time=562.67 memory used=21932.4MB, alloc=1476.3MB, time=589.27 memory used=22585.2MB, alloc=1500.3MB, time=603.96 memory used=23240.2MB, alloc=1524.3MB, time=623.43 memory used=23838.4MB, alloc=1548.3MB, time=641.16 memory used=24510.3MB, alloc=1572.3MB, time=660.86 memory used=25020.2MB, alloc=1596.3MB, time=680.96 memory used=25593.2MB, alloc=1620.3MB, time=702.54 memory used=26115.9MB, alloc=1644.3MB, time=721.42 memory used=26687.6MB, alloc=1668.3MB, time=733.91 memory used=27079.5MB, alloc=1692.3MB, time=748.23 memory used=27469.7MB, alloc=1716.3MB, time=764.59 memory used=28030.1MB, alloc=1740.3MB, time=782.48 memory used=28593.0MB, alloc=1764.3MB, time=793.67 memory used=28814.8MB, alloc=1788.3MB, time=803.49 memory used=29239.9MB, alloc=1812.3MB, time=823.00 memory used=29688.3MB, alloc=1836.3MB, time=844.76 memory used=30307.6MB, alloc=1860.3MB, time=875.33 memory used=30539.9MB, alloc=1884.3MB, time=888.49 memory used=30908.1MB, alloc=1908.3MB, time=908.17 memory used=31337.4MB, alloc=1932.3MB, time=930.45 memory used=31575.8MB, alloc=1956.3MB, time=946.62 memory used=31854.6MB, alloc=1980.3MB, time=961.99 memory used=32127.8MB, alloc=2004.3MB, time=976.41 memory used=32403.6MB, alloc=2028.3MB, time=993.13 memory used=32733.3MB, alloc=2052.3MB, time=1011.94 memory used=32932.0MB, alloc=2076.3MB, time=1022.89 memory used=33155.7MB, alloc=2100.3MB, time=1037.91 memory used=33453.1MB, alloc=2100.3MB, time=1050.26 memory used=33797.6MB, alloc=2100.3MB, time=1058.49 memory used=34029.6MB, alloc=2100.3MB, time=1067.65 memory used=34195.8MB, alloc=2100.3MB, time=1077.36 memory used=34376.8MB, alloc=2100.3MB, time=1088.35 memory used=34551.5MB, alloc=2100.3MB, time=1097.37 |\^/| 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(); 1428446509 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 3 2 2 3 F := [x - 18 z - 14 x , -8 x z + 6 x + 9 y, -3 x + 4 x y + 4 x z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 3 2 3 2 2 G := [9 z - 4 x - y , 9 y + 7 x + 1, -7 y - 9 y + 4 z ] > Problem := [F,G]; 3 3 2 2 3 Problem := [[x - 18 z - 14 x , -8 x z + 6 x + 9 y, -3 x + 4 x y + 4 x z], 3 2 2 3 2 3 2 2 [9 z - 4 x - y , 9 y + 7 x + 1, -7 y - 9 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=0.19 memory used=24.4MB, alloc=32.3MB, time=0.49 memory used=43.8MB, alloc=56.3MB, time=0.79 memory used=82.2MB, alloc=60.3MB, time=1.34 memory used=122.2MB, alloc=60.3MB, time=1.94 memory used=159.4MB, alloc=84.3MB, time=2.50 memory used=220.8MB, alloc=92.3MB, time=3.42 memory used=282.7MB, alloc=92.3MB, time=4.33 memory used=345.5MB, alloc=116.3MB, time=5.13 memory used=427.8MB, alloc=372.3MB, time=5.96 memory used=511.0MB, alloc=372.3MB, time=7.06 memory used=594.0MB, alloc=372.3MB, time=8.32 memory used=682.3MB, alloc=396.3MB, time=9.52 memory used=792.1MB, alloc=396.3MB, time=11.02 memory used=897.0MB, alloc=396.3MB, time=12.27 memory used=1002.9MB, alloc=420.3MB, time=13.57 memory used=1132.6MB, alloc=420.3MB, time=15.49 memory used=1285.8MB, alloc=420.3MB, time=17.08 memory used=1422.1MB, alloc=420.3MB, time=18.57 memory used=1531.8MB, alloc=420.3MB, time=19.49 memory used=1593.3MB, alloc=420.3MB, time=19.79 memory used=1702.3MB, alloc=420.3MB, time=20.85 memory used=1858.8MB, alloc=420.3MB, time=22.16 memory used=2008.4MB, alloc=444.3MB, time=23.81 memory used=2192.0MB, alloc=444.3MB, time=25.10 memory used=2332.5MB, alloc=444.3MB, time=27.22 memory used=2462.2MB, alloc=468.3MB, time=28.85 memory used=2605.0MB, alloc=468.3MB, time=30.17 memory used=2731.3MB, alloc=468.3MB, time=31.91 memory used=2928.9MB, alloc=468.3MB, time=33.21 memory used=3120.7MB, alloc=468.3MB, time=34.39 memory used=3300.9MB, alloc=468.3MB, time=36.37 memory used=3429.5MB, alloc=492.3MB, time=38.63 memory used=3542.2MB, alloc=516.3MB, time=39.87 memory used=3660.9MB, alloc=516.3MB, time=41.50 memory used=3754.1MB, alloc=516.3MB, time=43.21 memory used=3828.2MB, alloc=516.3MB, time=44.30 memory used=3913.0MB, alloc=540.3MB, time=45.32 memory used=3966.8MB, alloc=540.3MB, time=46.16 memory used=4053.7MB, alloc=540.3MB, time=47.60 memory used=4118.1MB, alloc=540.3MB, time=48.53 memory used=4196.0MB, alloc=540.3MB, time=49.52 memory used=4257.7MB, alloc=540.3MB, time=50.39 memory used=4296.7MB, alloc=540.3MB, time=51.11 memory used=4357.4MB, alloc=540.3MB, time=51.88 memory used=4581.0MB, alloc=564.3MB, time=55.23 memory used=4803.4MB, alloc=588.3MB, time=57.70 memory used=5000.9MB, alloc=612.3MB, time=61.28 memory used=5188.5MB, alloc=636.3MB, time=64.09 memory used=5377.4MB, alloc=660.3MB, time=66.94 memory used=5552.4MB, alloc=660.3MB, time=69.26 memory used=5728.9MB, alloc=684.3MB, time=71.28 memory used=5897.1MB, alloc=684.3MB, time=74.72 memory used=6030.4MB, alloc=708.3MB, time=76.77 memory used=6136.5MB, alloc=708.3MB, time=78.47 memory used=6272.3MB, alloc=708.3MB, time=81.24 memory used=6368.3MB, alloc=708.3MB, time=83.23 memory used=6471.1MB, alloc=708.3MB, time=85.02 memory used=6864.2MB, alloc=732.3MB, time=90.27 memory used=7147.7MB, alloc=756.3MB, time=93.55 memory used=7349.3MB, alloc=780.3MB, time=95.65 memory used=7577.1MB, alloc=780.3MB, time=97.81 memory used=7849.9MB, alloc=780.3MB, time=103.44 memory used=8222.0MB, alloc=780.3MB, time=108.63 memory used=8674.9MB, alloc=804.3MB, time=114.76 memory used=9097.8MB, alloc=828.3MB, time=120.49 memory used=9444.9MB, alloc=852.3MB, time=125.77 memory used=9675.8MB, alloc=876.3MB, time=127.78 memory used=9938.8MB, alloc=900.3MB, time=129.81 memory used=10220.4MB, alloc=900.3MB, time=131.99 memory used=10483.3MB, alloc=900.3MB, time=134.14 memory used=10751.6MB, alloc=900.3MB, time=136.25 memory used=11055.8MB, alloc=900.3MB, time=151.05 memory used=11292.0MB, alloc=900.3MB, time=152.75 memory used=11509.6MB, alloc=900.3MB, time=154.38 memory used=11711.1MB, alloc=900.3MB, time=155.92 memory used=11953.3MB, alloc=900.3MB, time=157.51 memory used=12325.7MB, alloc=915.8MB, time=159.27 memory used=12678.9MB, alloc=915.8MB, time=161.56 memory used=12948.2MB, alloc=915.8MB, time=163.74 memory used=13239.6MB, alloc=915.8MB, time=178.84 memory used=13493.8MB, alloc=915.8MB, time=180.54 memory used=13692.9MB, alloc=915.8MB, time=182.07 memory used=13902.4MB, alloc=915.8MB, time=183.58 memory used=14153.4MB, alloc=915.8MB, time=185.12 memory used=14476.1MB, alloc=915.8MB, time=186.73 memory used=14855.1MB, alloc=915.8MB, time=189.94 memory used=15074.9MB, alloc=939.8MB, time=191.69 memory used=15331.4MB, alloc=939.8MB, time=193.41 memory used=15601.1MB, alloc=939.8MB, time=195.12 memory used=15800.8MB, alloc=939.8MB, time=196.62 memory used=16033.6MB, alloc=939.8MB, time=199.79 memory used=16552.6MB, alloc=939.8MB, time=205.87 memory used=17062.9MB, alloc=939.8MB, time=234.15 memory used=17321.1MB, alloc=939.8MB, time=235.82 memory used=17527.0MB, alloc=939.8MB, time=237.29 memory used=17782.7MB, alloc=939.8MB, time=238.78 memory used=18389.2MB, alloc=963.8MB, time=245.13 memory used=18870.2MB, alloc=987.8MB, time=250.95 memory used=19142.4MB, alloc=987.8MB, time=255.90 memory used=19458.8MB, alloc=987.8MB, time=258.38 memory used=19771.0MB, alloc=987.8MB, time=260.83 memory used=20078.6MB, alloc=987.8MB, time=263.52 memory used=20377.1MB, alloc=987.8MB, time=265.91 memory used=20691.9MB, alloc=987.8MB, time=281.52 memory used=20955.9MB, alloc=987.8MB, time=283.48 memory used=21214.0MB, alloc=987.8MB, time=285.33 memory used=21436.9MB, alloc=987.8MB, time=287.08 memory used=21709.2MB, alloc=987.8MB, time=288.85 memory used=22049.3MB, alloc=987.8MB, time=290.75 memory used=22442.4MB, alloc=987.8MB, time=293.27 memory used=22749.3MB, alloc=1011.8MB, time=307.92 memory used=23040.6MB, alloc=1011.8MB, time=310.97 memory used=23330.7MB, alloc=1011.8MB, time=313.03 memory used=23562.8MB, alloc=1011.8MB, time=314.90 memory used=23851.2MB, alloc=1011.8MB, time=316.76 memory used=24195.5MB, alloc=1011.8MB, time=318.68 memory used=24628.3MB, alloc=1011.8MB, time=322.29 memory used=24866.8MB, alloc=1011.8MB, time=324.42 memory used=25186.2MB, alloc=1011.8MB, time=326.45 memory used=25418.1MB, alloc=1011.8MB, time=328.19 memory used=25674.6MB, alloc=1011.8MB, time=331.66 memory used=26026.6MB, alloc=1011.8MB, time=334.32 memory used=26318.0MB, alloc=1011.8MB, time=336.23 memory used=26724.4MB, alloc=1011.8MB, time=341.13 memory used=27179.6MB, alloc=1011.8MB, time=370.46 memory used=27471.9MB, alloc=1011.8MB, time=372.39 memory used=27704.4MB, alloc=1011.8MB, time=374.12 memory used=28156.2MB, alloc=1011.8MB, time=377.73 memory used=28822.3MB, alloc=1035.8MB, time=385.09 memory used=29413.7MB, alloc=1059.8MB, time=392.90 memory used=29740.5MB, alloc=1059.8MB, time=395.62 memory used=30056.5MB, alloc=1059.8MB, time=398.25 memory used=30374.3MB, alloc=1059.8MB, time=400.76 memory used=30700.2MB, alloc=1059.8MB, time=403.28 memory used=31042.8MB, alloc=1083.8MB, time=406.28 memory used=31355.4MB, alloc=1083.8MB, time=408.69 memory used=31678.0MB, alloc=1083.8MB, time=411.18 memory used=32056.8MB, alloc=1083.8MB, time=415.14 memory used=32356.7MB, alloc=1083.8MB, time=417.43 memory used=32635.1MB, alloc=1083.8MB, time=419.53 memory used=32974.6MB, alloc=1083.8MB, time=423.04 memory used=33295.9MB, alloc=1083.8MB, time=425.30 memory used=33553.1MB, alloc=1083.8MB, time=427.33 memory used=33959.8MB, alloc=1083.8MB, time=469.92 memory used=34230.4MB, alloc=1083.8MB, time=472.20 memory used=34594.8MB, alloc=1083.8MB, time=474.57 memory used=34822.9MB, alloc=1083.8MB, time=476.61 memory used=35069.4MB, alloc=1083.8MB, time=478.64 memory used=35343.3MB, alloc=1083.8MB, time=480.68 memory used=35649.9MB, alloc=1083.8MB, time=482.80 memory used=35991.2MB, alloc=1083.8MB, time=484.98 memory used=36367.4MB, alloc=1083.8MB, time=487.18 memory used=36562.1MB, alloc=1083.8MB, time=489.19 memory used=36636.0MB, alloc=1083.8MB, time=491.07 memory used=36712.2MB, alloc=1083.8MB, time=492.98 memory used=36787.9MB, alloc=1083.8MB, time=494.89 memory used=36865.6MB, alloc=1083.8MB, time=496.78 memory used=36945.7MB, alloc=1083.8MB, time=498.57 memory used=37027.7MB, alloc=1083.8MB, time=500.36 memory used=37111.3MB, alloc=1083.8MB, time=502.16 memory used=37196.3MB, alloc=1083.8MB, time=503.99 memory used=37285.2MB, alloc=1083.8MB, time=505.80 memory used=37374.8MB, alloc=1083.8MB, time=507.61 memory used=37466.9MB, alloc=1083.8MB, time=509.43 memory used=37563.4MB, alloc=1083.8MB, time=511.27 memory used=37660.9MB, alloc=1083.8MB, time=513.07 memory used=37762.1MB, alloc=1083.8MB, time=514.89 memory used=37867.5MB, alloc=1083.8MB, time=516.71 memory used=37978.6MB, alloc=1083.8MB, time=518.52 memory used=38095.8MB, alloc=1083.8MB, time=520.36 memory used=38489.8MB, alloc=1083.8MB, time=523.93 memory used=38808.9MB, alloc=1083.8MB, time=526.15 memory used=39112.5MB, alloc=1083.8MB, time=529.44 memory used=39416.2MB, alloc=1083.8MB, time=531.82 memory used=39718.7MB, alloc=1083.8MB, time=534.14 memory used=40088.3MB, alloc=1083.8MB, time=576.16 memory used=40387.7MB, alloc=1083.8MB, time=578.51 memory used=40701.9MB, alloc=1083.8MB, time=580.83 memory used=41010.9MB, alloc=1107.8MB, time=583.04 memory used=41254.8MB, alloc=1107.8MB, time=585.09 memory used=41530.5MB, alloc=1107.8MB, time=587.15 memory used=41841.0MB, alloc=1107.8MB, time=589.23 memory used=42188.4MB, alloc=1107.8MB, time=591.34 memory used=42573.1MB, alloc=1107.8MB, time=593.46 memory used=42866.5MB, alloc=1107.8MB, time=595.49 memory used=42941.1MB, alloc=1107.8MB, time=597.26 memory used=43017.4MB, alloc=1107.8MB, time=599.05 memory used=43093.1MB, alloc=1107.8MB, time=600.82 memory used=43170.8MB, alloc=1107.8MB, time=602.62 memory used=43250.9MB, alloc=1107.8MB, time=604.45 memory used=43332.9MB, alloc=1107.8MB, time=606.26 memory used=43416.5MB, alloc=1107.8MB, time=608.04 memory used=43501.4MB, alloc=1107.8MB, time=609.83 memory used=43590.4MB, alloc=1107.8MB, time=611.61 memory used=43679.9MB, alloc=1107.8MB, time=613.43 memory used=43772.0MB, alloc=1107.8MB, time=615.24 memory used=43868.6MB, alloc=1107.8MB, time=617.04 memory used=43966.1MB, alloc=1107.8MB, time=618.84 memory used=44067.2MB, alloc=1107.8MB, time=620.64 memory used=44172.6MB, alloc=1107.8MB, time=622.45 memory used=44283.7MB, alloc=1107.8MB, time=624.25 memory used=44400.9MB, alloc=1107.8MB, time=626.07 memory used=44843.1MB, alloc=1107.8MB, time=632.38 memory used=45197.0MB, alloc=1107.8MB, time=634.88 memory used=45454.8MB, alloc=1107.8MB, time=637.36 memory used=45760.5MB, alloc=1107.8MB, time=639.78 memory used=46117.9MB, alloc=1107.8MB, time=642.23 memory used=46503.1MB, alloc=1107.8MB, time=644.75 memory used=46726.9MB, alloc=1107.8MB, time=646.88 memory used=46965.7MB, alloc=1107.8MB, time=649.02 memory used=47225.7MB, alloc=1107.8MB, time=651.18 memory used=47504.0MB, alloc=1107.8MB, time=653.33 memory used=47805.6MB, alloc=1107.8MB, time=655.54 memory used=48136.6MB, alloc=1107.8MB, time=657.73 memory used=48506.8MB, alloc=1107.8MB, time=659.81 memory used=48714.5MB, alloc=1107.8MB, time=661.69 memory used=49192.2MB, alloc=1107.8MB, time=672.00 memory used=49272.2MB, alloc=1107.8MB, time=673.89 memory used=50162.1MB, alloc=1107.8MB, time=682.71 memory used=50965.5MB, alloc=1107.8MB, time=691.89 memory used=51380.9MB, alloc=1107.8MB, time=778.34 memory used=51663.1MB, alloc=1107.8MB, time=780.70 memory used=51983.4MB, alloc=1131.8MB, time=782.91 memory used=52241.7MB, alloc=1131.8MB, time=784.95 memory used=52547.3MB, alloc=1131.8MB, time=787.04 memory used=52907.7MB, alloc=1131.8MB, time=789.16 memory used=53246.2MB, alloc=1131.8MB, time=791.25 memory used=53323.3MB, alloc=1131.8MB, time=793.03 memory used=53404.7MB, alloc=1131.8MB, time=794.81 memory used=53489.2MB, alloc=1131.8MB, time=796.59 memory used=53579.1MB, alloc=1131.8MB, time=798.39 memory used=53676.7MB, alloc=1131.8MB, time=800.19 memory used=54574.4MB, alloc=1131.8MB, time=809.82 memory used=55387.1MB, alloc=1155.8MB, time=819.34 memory used=55761.4MB, alloc=1155.8MB, time=822.18 memory used=56120.7MB, alloc=1155.8MB, time=825.05 memory used=56499.0MB, alloc=1155.8MB, time=827.95 memory used=56863.5MB, alloc=1155.8MB, time=830.86 memory used=57227.6MB, alloc=1155.8MB, time=833.77 memory used=57584.2MB, alloc=1155.8MB, time=836.44 memory used=57972.6MB, alloc=1155.8MB, time=840.44 memory used=58306.5MB, alloc=1155.8MB, time=842.97 memory used=58616.8MB, alloc=1155.8MB, time=845.30 memory used=58978.9MB, alloc=1155.8MB, time=849.00 memory used=59324.6MB, alloc=1155.8MB, time=851.48 memory used=59687.0MB, alloc=1155.8MB, time=893.71 memory used=60033.3MB, alloc=1155.8MB, time=896.52 memory used=60370.1MB, alloc=1155.8MB, time=899.15 memory used=60704.9MB, alloc=1155.8MB, time=901.61 memory used=60959.8MB, alloc=1155.8MB, time=903.91 memory used=61248.0MB, alloc=1155.8MB, time=906.22 memory used=61572.0MB, alloc=1155.8MB, time=908.53 memory used=61936.9MB, alloc=1155.8MB, time=910.88 memory used=62346.5MB, alloc=1155.8MB, time=913.28 memory used=62546.1MB, alloc=1155.8MB, time=915.40 memory used=62620.7MB, alloc=1155.8MB, time=917.39 memory used=62697.0MB, alloc=1155.8MB, time=919.32 memory used=62772.5MB, alloc=1155.8MB, time=921.28 memory used=62850.4MB, alloc=1155.8MB, time=923.25 memory used=62930.4MB, alloc=1155.8MB, time=925.19 memory used=63012.4MB, alloc=1155.8MB, time=927.07 memory used=63096.0MB, alloc=1155.8MB, time=928.96 memory used=63181.0MB, alloc=1155.8MB, time=930.84 memory used=63267.3MB, alloc=1155.8MB, time=932.74 memory used=63356.6MB, alloc=1155.8MB, time=934.65 memory used=63448.8MB, alloc=1155.8MB, time=936.53 memory used=63542.8MB, alloc=1155.8MB, time=938.42 memory used=63640.3MB, alloc=1155.8MB, time=940.30 memory used=63742.0MB, alloc=1155.8MB, time=942.21 memory used=63845.6MB, alloc=1155.8MB, time=944.14 memory used=63955.3MB, alloc=1155.8MB, time=946.05 memory used=64070.9MB, alloc=1155.8MB, time=947.96 memory used=64501.3MB, alloc=1155.8MB, time=951.70 memory used=64835.5MB, alloc=1155.8MB, time=954.04 memory used=65191.7MB, alloc=1155.8MB, time=957.58 memory used=65523.6MB, alloc=1155.8MB, time=960.12 memory used=65820.2MB, alloc=1155.8MB, time=962.45 memory used=66252.5MB, alloc=1155.8MB, time=1004.42 memory used=66553.0MB, alloc=1155.8MB, time=1007.06 memory used=66931.6MB, alloc=1155.8MB, time=1009.67 memory used=67178.1MB, alloc=1155.8MB, time=1011.96 memory used=67456.6MB, alloc=1155.8MB, time=1014.24 memory used=67768.8MB, alloc=1155.8MB, time=1016.54 memory used=68119.1MB, alloc=1155.8MB, time=1018.88 memory used=68511.9MB, alloc=1155.8MB, time=1021.25 memory used=68851.7MB, alloc=1155.8MB, time=1023.54 memory used=68924.0MB, alloc=1155.8MB, time=1025.54 memory used=69000.3MB, alloc=1155.8MB, time=1027.53 memory used=69075.8MB, alloc=1155.8MB, time=1029.52 memory used=69153.8MB, alloc=1155.8MB, time=1031.53 memory used=69233.9MB, alloc=1155.8MB, time=1033.51 memory used=69315.9MB, alloc=1155.8MB, time=1035.48 memory used=69399.6MB, alloc=1155.8MB, time=1037.49 memory used=69484.6MB, alloc=1155.8MB, time=1039.44 memory used=69570.9MB, alloc=1155.8MB, time=1041.43 memory used=69660.4MB, alloc=1155.8MB, time=1043.42 memory used=69752.6MB, alloc=1155.8MB, time=1045.40 memory used=69846.8MB, alloc=1155.8MB, time=1047.36 memory used=69944.4MB, alloc=1155.8MB, time=1049.36 memory used=70044.2MB, alloc=1155.8MB, time=1051.37 memory used=70147.9MB, alloc=1155.8MB, time=1053.40 memory used=70258.0MB, alloc=1155.8MB, time=1055.45 memory used=70373.7MB, alloc=1155.8MB, time=1057.49 memory used=70838.8MB, alloc=1155.8MB, time=1063.73 memory used=71178.9MB, alloc=1179.8MB, time=1066.43 memory used=71473.4MB, alloc=1179.8MB, time=1068.99 memory used=71826.8MB, alloc=1179.8MB, time=1071.65 memory used=72242.0MB, alloc=1179.8MB, time=1074.36 memory used=72562.3MB, alloc=1179.8MB, time=1076.76 memory used=72816.6MB, alloc=1179.8MB, time=1079.04 memory used=73091.1MB, alloc=1179.8MB, time=1081.30 memory used=73389.1MB, alloc=1179.8MB, time=1083.59 memory used=73716.7MB, alloc=1179.8MB, time=1085.90 memory used=74077.9MB, alloc=1179.8MB, time=1088.24 memory used=74485.1MB, alloc=1179.8MB, time=1090.58 memory used=74644.3MB, alloc=1179.8MB, time=1092.55 memory used=75121.5MB, alloc=1179.8MB, time=1103.00 memory used=75201.3MB, alloc=1179.8MB, time=1104.89 memory used=76079.6MB, alloc=1179.8MB, time=1113.61 memory used=76882.9MB, alloc=1203.8MB, time=1168.23 memory used=77267.8MB, alloc=1203.8MB, time=1207.74 memory used=77669.0MB, alloc=1203.8MB, time=1210.42 memory used=77942.0MB, alloc=1203.8MB, time=1212.72 memory used=78265.9MB, alloc=1203.8MB, time=1215.05 memory used=78653.1MB, alloc=1203.8MB, time=1217.41 memory used=79020.0MB, alloc=1203.8MB, time=1219.73 memory used=79097.5MB, alloc=1203.8MB, time=1221.73 memory used=79177.0MB, alloc=1203.8MB, time=1223.70 memory used=79261.6MB, alloc=1203.8MB, time=1225.68 memory used=79351.4MB, alloc=1203.8MB, time=1227.70 memory used=79448.3MB, alloc=1203.8MB, time=1229.67 memory used=80421.5MB, alloc=1203.8MB, time=1239.96 memory used=81330.9MB, alloc=1227.8MB, time=1253.71 memory used=82115.1MB, alloc=1251.8MB, time=1268.00 memory used=82588.9MB, alloc=1275.8MB, time=1274.26 memory used=82947.3MB, alloc=1299.8MB, time=1278.27 memory used=83302.9MB, alloc=1323.8MB, time=1282.06 memory used=83694.0MB, alloc=1347.8MB, time=1286.12 memory used=84042.7MB, alloc=1371.8MB, time=1289.43 memory used=84453.8MB, alloc=1395.8MB, time=1293.05 memory used=84886.7MB, alloc=1419.8MB, time=1296.87 memory used=85378.2MB, alloc=1443.8MB, time=1300.72 memory used=85850.3MB, alloc=1443.8MB, time=1304.33 memory used=86309.2MB, alloc=1443.8MB, time=1308.04 memory used=86819.2MB, alloc=1443.8MB, time=1311.95 memory used=87229.7MB, alloc=1443.8MB, time=1315.19 memory used=87553.3MB, alloc=1443.8MB, time=1318.22 memory used=87635.5MB, alloc=1443.8MB, time=1320.86 memory used=88028.7MB, alloc=1443.8MB, time=1324.55 memory used=88495.6MB, alloc=1443.8MB, time=1329.42 memory used=88893.9MB, alloc=1443.8MB, time=1332.64 memory used=89363.0MB, alloc=1443.8MB, time=1335.88 memory used=89441.6MB, alloc=1443.8MB, time=1338.52 memory used=89524.6MB, alloc=1443.8MB, time=1341.16 memory used=89612.0MB, alloc=1443.8MB, time=1343.76 memory used=89707.3MB, alloc=1443.8MB, time=1346.40 |\^/| 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(); 1428447710 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 3 2 2 F := [-2 x y z - 6 y - 10 x, 9 x y z + 2 y + 2 x, 4 x y + 2 x y - 7 x z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 3 G := [-17 x y z + 9 y z - 8, 10 x y - 7 x z + 5, 5 x + 4 x y z] > Problem := [F,G]; Problem := [ 3 3 2 2 [-2 x y z - 6 y - 10 x, 9 x y z + 2 y + 2 x, 4 x y + 2 x y - 7 x z], 2 2 2 3 [-17 x y z + 9 y z - 8, 10 x y - 7 x z + 5, 5 x + 4 x y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.4MB, alloc=32.3MB, time=0.50 memory used=46.3MB, alloc=32.3MB, time=0.78 memory used=64.9MB, alloc=56.3MB, time=1.06 memory used=106.0MB, alloc=60.3MB, time=1.67 memory used=143.2MB, alloc=60.3MB, time=2.20 memory used=183.6MB, alloc=68.3MB, time=2.78 memory used=224.2MB, alloc=92.3MB, time=3.36 memory used=287.3MB, alloc=92.3MB, time=4.26 memory used=350.6MB, alloc=116.3MB, time=5.19 memory used=423.2MB, alloc=116.3MB, time=6.23 memory used=491.8MB, alloc=372.3MB, time=7.27 memory used=585.3MB, alloc=396.3MB, time=8.52 memory used=700.1MB, alloc=396.3MB, time=10.14 memory used=812.5MB, alloc=420.3MB, time=11.77 memory used=942.9MB, alloc=444.3MB, time=13.64 memory used=1056.5MB, alloc=444.3MB, time=15.41 memory used=1175.4MB, alloc=444.3MB, time=17.20 memory used=1289.0MB, alloc=468.3MB, time=19.01 memory used=1391.7MB, alloc=468.3MB, time=20.68 memory used=1488.8MB, alloc=468.3MB, time=22.27 memory used=1587.1MB, alloc=468.3MB, time=23.86 memory used=1679.7MB, alloc=468.3MB, time=25.34 memory used=1767.8MB, alloc=468.3MB, time=26.86 memory used=1847.6MB, alloc=492.3MB, time=28.18 memory used=1920.9MB, alloc=492.3MB, time=29.44 memory used=1995.0MB, alloc=492.3MB, time=30.70 memory used=2068.6MB, alloc=492.3MB, time=32.09 memory used=2129.9MB, alloc=492.3MB, time=33.24 memory used=2198.1MB, alloc=492.3MB, time=34.52 memory used=2257.8MB, alloc=492.3MB, time=35.69 memory used=2316.1MB, alloc=492.3MB, time=36.83 memory used=2388.2MB, alloc=492.3MB, time=38.48 memory used=2439.9MB, alloc=492.3MB, time=39.59 memory used=2486.9MB, alloc=516.3MB, time=40.59 memory used=2693.7MB, alloc=540.3MB, time=44.08 memory used=2865.4MB, alloc=564.3MB, time=46.50 memory used=3054.5MB, alloc=588.3MB, time=49.91 memory used=3205.1MB, alloc=612.3MB, time=52.53 memory used=3348.3MB, alloc=636.3MB, time=55.21 memory used=3462.8MB, alloc=636.3MB, time=57.09 memory used=3602.8MB, alloc=636.3MB, time=60.07 memory used=3695.9MB, alloc=636.3MB, time=62.02 memory used=3775.0MB, alloc=636.3MB, time=63.61 memory used=3872.3MB, alloc=660.3MB, time=65.93 memory used=4196.3MB, alloc=684.3MB, time=71.75 memory used=4552.5MB, alloc=708.3MB, time=77.14 memory used=4881.6MB, alloc=732.3MB, time=82.64 memory used=5182.6MB, alloc=756.3MB, time=87.85 memory used=5523.4MB, alloc=780.3MB, time=93.99 memory used=5791.6MB, alloc=804.3MB, time=99.36 memory used=6023.3MB, alloc=828.3MB, time=103.99 memory used=6257.5MB, alloc=852.3MB, time=109.34 memory used=6451.7MB, alloc=876.3MB, time=113.24 memory used=6640.5MB, alloc=900.3MB, time=118.33 memory used=7154.5MB, alloc=924.3MB, time=128.22 memory used=7689.3MB, alloc=948.3MB, time=138.14 memory used=8222.2MB, alloc=972.3MB, time=149.45 memory used=8791.8MB, alloc=996.3MB, time=159.78 memory used=9349.2MB, alloc=1020.3MB, time=172.52 memory used=9891.7MB, alloc=1044.3MB, time=183.58 memory used=10400.5MB, alloc=1068.3MB, time=195.83 memory used=10780.2MB, alloc=1092.3MB, time=205.11 memory used=11268.5MB, alloc=1116.3MB, time=215.99 memory used=11732.3MB, alloc=1140.3MB, time=228.24 memory used=12097.9MB, alloc=1164.3MB, time=237.62 memory used=12481.7MB, alloc=1188.3MB, time=248.48 memory used=12792.6MB, alloc=1212.3MB, time=257.66 memory used=13085.8MB, alloc=1236.3MB, time=267.12 memory used=13359.1MB, alloc=1260.3MB, time=276.67 memory used=13670.1MB, alloc=1284.3MB, time=286.13 memory used=13940.0MB, alloc=1308.3MB, time=296.13 memory used=14224.9MB, alloc=1332.3MB, time=305.43 memory used=14363.3MB, alloc=1356.3MB, time=311.73 memory used=14590.4MB, alloc=1380.3MB, time=321.06 memory used=14740.9MB, alloc=1404.3MB, time=329.03 memory used=14831.1MB, alloc=1428.3MB, time=335.08 memory used=14920.6MB, alloc=1452.3MB, time=340.73 memory used=15030.8MB, alloc=1476.3MB, time=348.41 memory used=15112.5MB, alloc=1500.3MB, time=354.22 memory used=15211.9MB, alloc=1524.3MB, time=360.19 memory used=15320.9MB, alloc=1548.3MB, time=366.32 memory used=15376.5MB, alloc=1572.3MB, time=373.14 memory used=15455.1MB, alloc=1572.3MB, time=379.27 memory used=15482.4MB, alloc=1572.3MB, time=384.67 memory used=15541.6MB, alloc=1572.3MB, time=390.50 memory used=15635.6MB, alloc=1572.3MB, time=396.73 memory used=15706.8MB, alloc=1572.3MB, time=404.13 memory used=15796.8MB, alloc=1572.3MB, time=410.49 memory used=15810.1MB, alloc=1572.3MB, time=415.88 memory used=15892.4MB, alloc=1572.3MB, time=421.88 memory used=15946.4MB, alloc=1572.3MB, time=427.59 memory used=16038.5MB, alloc=1572.3MB, time=434.67 memory used=16102.8MB, alloc=1572.3MB, time=441.76 memory used=16142.7MB, alloc=1572.3MB, time=447.51 memory used=16237.4MB, alloc=1572.3MB, time=453.74 memory used=16294.2MB, alloc=1572.3MB, time=459.50 memory used=16375.6MB, alloc=1572.3MB, time=465.65 memory used=16421.0MB, alloc=1572.3MB, time=471.61 memory used=16492.7MB, alloc=1852.3MB, time=483.71 memory used=17523.2MB, alloc=1876.3MB, time=510.73 memory used=18548.6MB, alloc=1900.3MB, time=538.21 memory used=19587.2MB, alloc=1924.3MB, time=564.27 memory used=20612.0MB, alloc=1948.3MB, time=591.54 memory used=21642.1MB, alloc=1972.3MB, time=618.95 memory used=22667.8MB, alloc=1996.3MB, time=646.52 memory used=23622.4MB, alloc=2020.3MB, time=674.26 memory used=24528.4MB, alloc=2044.3MB, time=701.89 memory used=25231.9MB, alloc=2068.3MB, time=724.72 memory used=25918.0MB, alloc=2092.3MB, time=748.02 memory used=26640.3MB, alloc=2116.3MB, time=772.09 memory used=27260.1MB, alloc=2140.3MB, time=798.45 memory used=27858.0MB, alloc=2164.3MB, time=820.86 memory used=28242.2MB, alloc=2188.3MB, time=839.74 memory used=28603.0MB, alloc=2212.3MB, time=857.20 memory used=29088.2MB, alloc=2236.3MB, time=879.01 memory used=29517.0MB, alloc=2260.3MB, time=901.60 memory used=30010.1MB, alloc=2284.3MB, time=924.27 memory used=30700.2MB, alloc=2308.3MB, time=950.93 memory used=31319.6MB, alloc=2332.3MB, time=976.88 memory used=31781.2MB, alloc=2356.3MB, time=999.94 memory used=32358.2MB, alloc=2380.3MB, time=1025.37 memory used=32983.8MB, alloc=2404.3MB, time=1052.43 memory used=33538.2MB, alloc=2428.3MB, time=1078.19 memory used=33899.3MB, alloc=2452.3MB, time=1100.07 |\^/| 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(); 1428448910 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 3 2 F := [17 y z + 18 z + 15 y z, -3 x + 3 y z, -x y z - 5 y + 9 x ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 3 2 3 2 2 G := [9 x - 5 x y - 9 z , -6 x y + 7 x z - 5 y z, -4 x - 3 y - 4 z ] > Problem := [F,G]; 2 3 2 3 2 Problem := [[17 y z + 18 z + 15 y z, -3 x + 3 y z, -x y z - 5 y + 9 x ], 3 2 3 2 3 2 2 [9 x - 5 x y - 9 z , -6 x y + 7 x z - 5 y z, -4 x - 3 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=0.19 memory used=26.1MB, alloc=32.3MB, time=0.51 memory used=45.8MB, alloc=56.3MB, time=0.81 memory used=84.8MB, alloc=60.3MB, time=1.39 memory used=126.1MB, alloc=92.3MB, time=1.99 memory used=195.1MB, alloc=92.3MB, time=2.89 memory used=259.7MB, alloc=116.3MB, time=3.82 memory used=331.7MB, alloc=372.3MB, time=4.81 memory used=421.9MB, alloc=396.3MB, time=5.99 memory used=530.8MB, alloc=420.3MB, time=7.59 memory used=663.1MB, alloc=444.3MB, time=9.39 memory used=783.1MB, alloc=444.3MB, time=11.11 memory used=910.1MB, alloc=468.3MB, time=12.85 memory used=1041.0MB, alloc=468.3MB, time=14.32 memory used=1174.4MB, alloc=468.3MB, time=16.17 memory used=1290.2MB, alloc=492.3MB, time=17.68 memory used=1404.8MB, alloc=492.3MB, time=19.12 memory used=1527.4MB, alloc=492.3MB, time=20.96 memory used=1620.4MB, alloc=492.3MB, time=22.42 memory used=1706.2MB, alloc=516.3MB, time=23.50 memory used=1780.2MB, alloc=516.3MB, time=24.62 memory used=1882.8MB, alloc=516.3MB, time=25.91 memory used=1964.4MB, alloc=516.3MB, time=27.48 memory used=2024.8MB, alloc=516.3MB, time=28.79 memory used=2090.3MB, alloc=540.3MB, time=29.80 memory used=2141.6MB, alloc=540.3MB, time=30.63 memory used=2190.6MB, alloc=540.3MB, time=31.50 memory used=2246.0MB, alloc=540.3MB, time=32.40 memory used=2290.4MB, alloc=540.3MB, time=33.54 memory used=2320.1MB, alloc=540.3MB, time=34.37 memory used=2521.7MB, alloc=564.3MB, time=37.53 memory used=2726.8MB, alloc=588.3MB, time=40.02 memory used=2925.4MB, alloc=612.3MB, time=42.82 memory used=3083.8MB, alloc=636.3MB, time=45.23 memory used=3236.2MB, alloc=660.3MB, time=48.12 memory used=3374.8MB, alloc=660.3MB, time=50.59 memory used=3500.1MB, alloc=660.3MB, time=52.75 memory used=3628.0MB, alloc=660.3MB, time=55.08 memory used=3723.2MB, alloc=660.3MB, time=56.95 memory used=3827.8MB, alloc=684.3MB, time=58.78 memory used=3933.8MB, alloc=684.3MB, time=61.11 memory used=4019.3MB, alloc=684.3MB, time=63.09 memory used=4365.1MB, alloc=708.3MB, time=68.32 memory used=4734.3MB, alloc=732.3MB, time=74.26 memory used=5049.1MB, alloc=756.3MB, time=79.47 memory used=5352.1MB, alloc=780.3MB, time=84.83 memory used=5687.9MB, alloc=804.3MB, time=89.83 memory used=6006.9MB, alloc=828.3MB, time=94.57 memory used=6361.5MB, alloc=852.3MB, time=100.98 memory used=6657.3MB, alloc=876.3MB, time=105.62 memory used=6951.4MB, alloc=900.3MB, time=110.76 memory used=7213.6MB, alloc=924.3MB, time=115.23 memory used=7455.0MB, alloc=948.3MB, time=119.82 memory used=7650.0MB, alloc=972.3MB, time=124.26 memory used=7995.5MB, alloc=996.3MB, time=128.13 memory used=8333.3MB, alloc=1020.3MB, time=132.39 memory used=8651.8MB, alloc=1044.3MB, time=138.26 memory used=9357.0MB, alloc=1068.3MB, time=148.72 memory used=10043.1MB, alloc=1092.3MB, time=161.64 memory used=10710.6MB, alloc=1116.3MB, time=174.59 memory used=11365.7MB, alloc=1140.3MB, time=189.02 memory used=12028.8MB, alloc=1164.3MB, time=203.60 memory used=12621.7MB, alloc=1188.3MB, time=216.38 memory used=13179.5MB, alloc=1212.3MB, time=226.70 memory used=13677.7MB, alloc=1236.3MB, time=239.00 memory used=14141.0MB, alloc=1260.3MB, time=250.41 memory used=14596.5MB, alloc=1284.3MB, time=261.15 memory used=15000.1MB, alloc=1308.3MB, time=270.53 memory used=15402.5MB, alloc=1332.3MB, time=280.32 memory used=15778.6MB, alloc=1356.3MB, time=289.34 memory used=16285.9MB, alloc=1380.3MB, time=299.04 memory used=16556.8MB, alloc=1404.3MB, time=307.48 memory used=17125.1MB, alloc=1428.3MB, time=317.40 memory used=17514.2MB, alloc=1452.3MB, time=326.22 memory used=17876.6MB, alloc=1476.3MB, time=336.47 memory used=18118.1MB, alloc=1500.3MB, time=344.68 memory used=18392.3MB, alloc=1524.3MB, time=353.09 memory used=18627.0MB, alloc=1548.3MB, time=360.96 memory used=18898.1MB, alloc=1572.3MB, time=369.49 memory used=19181.8MB, alloc=1596.3MB, time=380.26 memory used=19455.8MB, alloc=1620.3MB, time=389.53 memory used=19694.9MB, alloc=1644.3MB, time=398.05 memory used=19936.2MB, alloc=1668.3MB, time=408.15 memory used=20103.3MB, alloc=1692.3MB, time=415.46 memory used=20163.6MB, alloc=1716.3MB, time=421.86 memory used=20314.0MB, alloc=1740.3MB, time=429.24 memory used=20422.4MB, alloc=1764.3MB, time=436.02 memory used=20611.2MB, alloc=1788.3MB, time=444.07 memory used=20719.4MB, alloc=1812.3MB, time=450.63 memory used=20843.5MB, alloc=1812.3MB, time=458.16 memory used=20941.0MB, alloc=1812.3MB, time=465.33 memory used=21070.1MB, alloc=1812.3MB, time=473.15 memory used=21200.8MB, alloc=1812.3MB, time=481.35 memory used=21332.3MB, alloc=1812.3MB, time=490.57 memory used=21435.1MB, alloc=1812.3MB, time=497.48 memory used=21551.2MB, alloc=1812.3MB, time=504.68 memory used=21633.0MB, alloc=1812.3MB, time=511.06 memory used=21734.0MB, alloc=1812.3MB, time=518.42 memory used=21874.8MB, alloc=1836.3MB, time=525.36 memory used=21999.5MB, alloc=1836.3MB, time=533.09 memory used=22076.2MB, alloc=1860.3MB, time=540.04 memory used=22117.7MB, alloc=1860.3MB, time=546.65 memory used=22177.7MB, alloc=1860.3MB, time=553.46 memory used=22242.3MB, alloc=1860.3MB, time=560.59 memory used=22246.1MB, alloc=1860.3MB, time=566.87 memory used=22312.3MB, alloc=1860.3MB, time=573.72 memory used=22315.3MB, alloc=1860.3MB, time=579.96 memory used=22423.4MB, alloc=1884.3MB, time=587.04 memory used=22478.8MB, alloc=1884.3MB, time=593.79 memory used=22548.6MB, alloc=1884.3MB, time=600.68 memory used=22583.5MB, alloc=1884.3MB, time=607.22 memory used=22661.9MB, alloc=1884.3MB, time=615.93 memory used=22728.8MB, alloc=1884.3MB, time=624.36 memory used=22739.5MB, alloc=1884.3MB, time=630.87 memory used=22753.2MB, alloc=1884.3MB, time=637.40 memory used=22807.7MB, alloc=1884.3MB, time=644.69 memory used=22810.8MB, alloc=2140.3MB, time=657.99 memory used=24086.9MB, alloc=2164.3MB, time=685.29 memory used=25333.3MB, alloc=2188.3MB, time=710.78 memory used=26474.4MB, alloc=2212.3MB, time=735.24 memory used=27674.2MB, alloc=2236.3MB, time=764.48 memory used=28749.9MB, alloc=2260.3MB, time=789.71 memory used=29771.6MB, alloc=2284.3MB, time=815.55 memory used=30859.5MB, alloc=2308.3MB, time=841.06 memory used=31786.2MB, alloc=2332.3MB, time=862.99 memory used=32554.6MB, alloc=2356.3MB, time=889.36 memory used=33406.3MB, alloc=2380.3MB, time=916.20 memory used=33938.1MB, alloc=2404.3MB, time=936.62 memory used=34774.8MB, alloc=2428.3MB, time=961.54 memory used=35374.6MB, alloc=2452.3MB, time=982.48 memory used=35788.9MB, alloc=2476.3MB, time=1002.45 memory used=36301.5MB, alloc=2500.3MB, time=1026.19 memory used=36823.3MB, alloc=2524.3MB, time=1047.77 memory used=37349.9MB, alloc=2548.3MB, time=1073.69 memory used=37659.9MB, alloc=2572.3MB, time=1094.07 memory used=38055.1MB, alloc=2596.3MB, time=1114.69 memory used=38322.6MB, alloc=2620.3MB, time=1133.03 memory used=38525.9MB, alloc=2644.3MB, time=1152.06 memory used=38877.8MB, alloc=2668.3MB, time=1171.46 memory used=39204.5MB, alloc=2692.3MB, time=1192.53 memory used=39451.8MB, alloc=2716.3MB, time=1211.39 memory used=39632.0MB, alloc=2740.3MB, time=1229.83 memory used=39958.5MB, alloc=2764.3MB, time=1249.65 memory used=40146.0MB, alloc=2788.3MB, time=1267.95 memory used=40301.3MB, alloc=2812.3MB, time=1285.06 memory used=40514.5MB, alloc=2836.3MB, time=1303.84 memory used=40841.5MB, alloc=2860.3MB, time=1323.60 |\^/| 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(); 1428450110 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 2 F := [15 x + 13 y z + 8 x, 5 y z - 5 x y + 3 y , -2 y z + 4 y z - 10 x z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 3 2 2 2 2 2 2 G := [17 x + 18 y + 18 z , 8 x z + 3 x - 4 y , -8 x z + 4 y + 2 y z] > Problem := [F,G]; Problem := [ 2 2 2 2 2 [15 x + 13 y z + 8 x, 5 y z - 5 x y + 3 y , -2 y z + 4 y z - 10 x z], 3 3 2 2 2 2 2 2 [17 x + 18 y + 18 z , 8 x z + 3 x - 4 y , -8 x z + 4 y + 2 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.17 memory used=26.6MB, alloc=32.3MB, time=0.48 memory used=47.9MB, alloc=32.3MB, time=0.79 memory used=67.6MB, alloc=56.3MB, time=1.08 memory used=107.7MB, alloc=60.3MB, time=1.70 memory used=147.6MB, alloc=84.3MB, time=2.29 memory used=209.3MB, alloc=92.3MB, time=3.23 memory used=270.9MB, alloc=116.3MB, time=4.15 memory used=344.4MB, alloc=116.3MB, time=5.24 memory used=415.5MB, alloc=396.3MB, time=6.34 memory used=524.3MB, alloc=420.3MB, time=7.91 memory used=654.3MB, alloc=444.3MB, time=9.88 memory used=773.4MB, alloc=444.3MB, time=11.49 memory used=917.1MB, alloc=444.3MB, time=13.14 memory used=1051.6MB, alloc=468.3MB, time=14.66 memory used=1185.6MB, alloc=468.3MB, time=16.93 memory used=1295.5MB, alloc=492.3MB, time=18.35 memory used=1404.5MB, alloc=492.3MB, time=20.00 memory used=1526.5MB, alloc=492.3MB, time=21.99 memory used=1609.3MB, alloc=516.3MB, time=23.26 memory used=1703.8MB, alloc=516.3MB, time=24.83 memory used=1777.8MB, alloc=516.3MB, time=25.93 memory used=1848.6MB, alloc=516.3MB, time=27.33 memory used=1916.2MB, alloc=516.3MB, time=28.37 memory used=1984.4MB, alloc=516.3MB, time=29.65 memory used=2028.2MB, alloc=540.3MB, time=30.48 memory used=2089.0MB, alloc=540.3MB, time=31.40 memory used=2137.8MB, alloc=540.3MB, time=32.34 memory used=2329.7MB, alloc=564.3MB, time=35.35 memory used=2520.6MB, alloc=588.3MB, time=38.65 memory used=2687.7MB, alloc=612.3MB, time=40.97 memory used=2863.3MB, alloc=636.3MB, time=43.54 memory used=2993.4MB, alloc=660.3MB, time=45.61 memory used=3116.1MB, alloc=684.3MB, time=47.91 memory used=3266.9MB, alloc=684.3MB, time=50.47 memory used=3391.6MB, alloc=684.3MB, time=52.65 memory used=3484.0MB, alloc=684.3MB, time=54.33 memory used=3607.6MB, alloc=684.3MB, time=56.88 memory used=3711.9MB, alloc=708.3MB, time=58.78 memory used=3820.0MB, alloc=708.3MB, time=61.27 memory used=4195.8MB, alloc=732.3MB, time=67.11 memory used=4596.1MB, alloc=756.3MB, time=73.18 memory used=5000.2MB, alloc=780.3MB, time=78.88 memory used=5372.1MB, alloc=804.3MB, time=84.28 memory used=5755.5MB, alloc=828.3MB, time=89.74 memory used=6109.1MB, alloc=852.3MB, time=95.04 memory used=6471.1MB, alloc=876.3MB, time=100.37 memory used=6729.5MB, alloc=900.3MB, time=105.38 memory used=7001.9MB, alloc=924.3MB, time=111.75 memory used=7256.3MB, alloc=948.3MB, time=117.85 memory used=7441.6MB, alloc=972.3MB, time=122.76 memory used=7602.9MB, alloc=996.3MB, time=127.47 memory used=8171.3MB, alloc=1020.3MB, time=140.02 memory used=8748.2MB, alloc=1044.3MB, time=153.11 memory used=9358.2MB, alloc=1068.3MB, time=165.27 memory used=9981.8MB, alloc=1092.3MB, time=177.60 memory used=10583.1MB, alloc=1116.3MB, time=188.32 memory used=11223.3MB, alloc=1140.3MB, time=200.21 memory used=11733.3MB, alloc=1164.3MB, time=208.44 memory used=12298.0MB, alloc=1188.3MB, time=219.46 memory used=12827.4MB, alloc=1212.3MB, time=229.76 memory used=13314.3MB, alloc=1236.3MB, time=240.93 memory used=13798.5MB, alloc=1260.3MB, time=252.79 memory used=14232.0MB, alloc=1284.3MB, time=263.38 memory used=14673.0MB, alloc=1308.3MB, time=275.01 memory used=15085.2MB, alloc=1332.3MB, time=286.43 memory used=15489.2MB, alloc=1356.3MB, time=296.08 memory used=15894.4MB, alloc=1380.3MB, time=307.59 memory used=16225.4MB, alloc=1404.3MB, time=318.45 memory used=16475.8MB, alloc=1428.3MB, time=326.66 memory used=16823.6MB, alloc=1452.3MB, time=337.70 memory used=17172.3MB, alloc=1476.3MB, time=349.29 memory used=17393.6MB, alloc=1500.3MB, time=357.31 memory used=17606.0MB, alloc=1524.3MB, time=365.27 memory used=17917.5MB, alloc=1548.3MB, time=375.56 memory used=18083.8MB, alloc=1572.3MB, time=382.81 memory used=18191.4MB, alloc=1596.3MB, time=389.47 memory used=18342.5MB, alloc=1620.3MB, time=396.30 memory used=18459.4MB, alloc=1644.3MB, time=403.74 memory used=18549.1MB, alloc=1668.3MB, time=410.38 memory used=18722.6MB, alloc=1692.3MB, time=420.66 memory used=18822.0MB, alloc=1716.3MB, time=427.71 memory used=18928.3MB, alloc=1740.3MB, time=435.35 memory used=19032.9MB, alloc=1764.3MB, time=442.12 memory used=19186.6MB, alloc=1788.3MB, time=452.50 memory used=19287.5MB, alloc=1812.3MB, time=459.51 memory used=19389.4MB, alloc=1836.3MB, time=466.32 memory used=19468.8MB, alloc=1860.3MB, time=473.55 memory used=19557.9MB, alloc=1860.3MB, time=480.33 memory used=19606.6MB, alloc=1860.3MB, time=486.79 memory used=19675.5MB, alloc=1860.3MB, time=494.08 memory used=19762.8MB, alloc=1860.3MB, time=500.88 memory used=19828.6MB, alloc=1860.3MB, time=507.99 memory used=19868.0MB, alloc=1860.3MB, time=514.42 memory used=19901.1MB, alloc=1860.3MB, time=520.69 memory used=19967.0MB, alloc=1860.3MB, time=527.02 memory used=19991.4MB, alloc=1860.3MB, time=532.96 memory used=20042.3MB, alloc=1860.3MB, time=539.22 memory used=20070.4MB, alloc=1860.3MB, time=545.50 memory used=20162.9MB, alloc=1860.3MB, time=554.29 memory used=20213.2MB, alloc=1860.3MB, time=561.15 memory used=20231.7MB, alloc=1860.3MB, time=567.05 memory used=20268.1MB, alloc=1860.3MB, time=573.52 memory used=20298.0MB, alloc=1860.3MB, time=579.53 memory used=20338.4MB, alloc=1860.3MB, time=585.68 memory used=20361.1MB, alloc=1860.3MB, time=591.63 memory used=20397.0MB, alloc=1860.3MB, time=597.86 memory used=20397.7MB, alloc=2116.3MB, time=609.89 memory used=21630.2MB, alloc=2140.3MB, time=634.34 memory used=22821.2MB, alloc=2164.3MB, time=661.16 memory used=24026.7MB, alloc=2188.3MB, time=687.52 memory used=25164.6MB, alloc=2212.3MB, time=717.82 memory used=26165.7MB, alloc=2236.3MB, time=740.29 memory used=27247.7MB, alloc=2260.3MB, time=767.72 memory used=28367.3MB, alloc=2284.3MB, time=793.68 memory used=29339.6MB, alloc=2308.3MB, time=817.49 memory used=30243.0MB, alloc=2332.3MB, time=840.49 memory used=31063.3MB, alloc=2356.3MB, time=864.45 memory used=31853.3MB, alloc=2380.3MB, time=889.36 memory used=32672.6MB, alloc=2404.3MB, time=915.12 memory used=33324.8MB, alloc=2428.3MB, time=941.56 memory used=33932.3MB, alloc=2452.3MB, time=970.93 memory used=34320.7MB, alloc=2476.3MB, time=993.88 memory used=34713.6MB, alloc=2500.3MB, time=1017.33 memory used=35041.1MB, alloc=2524.3MB, time=1037.05 memory used=35416.9MB, alloc=2548.3MB, time=1060.30 memory used=35718.5MB, alloc=2572.3MB, time=1078.25 memory used=36062.2MB, alloc=2596.3MB, time=1101.51 memory used=36319.0MB, alloc=2620.3MB, time=1120.38 memory used=36481.4MB, alloc=2644.3MB, time=1137.40 memory used=36629.7MB, alloc=2668.3MB, time=1153.98 memory used=36892.8MB, alloc=2692.3MB, time=1175.93 |\^/| 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(); 1428451310 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 2 2 2 F := [19 y + 10 y z + 19 y z, 7 x z - 10 z + 3 y, -5 x z - 5 x - 2 y z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 2 3 G := [12 y z - 7 x - 19 x, -10 x z - 4 x z + 8 z , -3 y + 9 x z - 9 y z] > Problem := [F,G]; Problem := [ 3 2 2 2 2 2 [19 y + 10 y z + 19 y z, 7 x z - 10 z + 3 y, -5 x z - 5 x - 2 y z], 2 2 2 2 2 3 [12 y z - 7 x - 19 x, -10 x z - 4 x z + 8 z , -3 y + 9 x z - 9 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.3MB, alloc=32.3MB, time=0.49 memory used=46.9MB, alloc=32.3MB, time=0.79 memory used=64.8MB, alloc=56.3MB, time=1.07 memory used=102.9MB, alloc=60.3MB, time=1.65 memory used=140.2MB, alloc=84.3MB, time=2.19 memory used=204.5MB, alloc=92.3MB, time=3.12 memory used=268.1MB, alloc=116.3MB, time=4.01 memory used=338.6MB, alloc=116.3MB, time=5.03 memory used=408.1MB, alloc=372.3MB, time=6.06 memory used=489.1MB, alloc=396.3MB, time=7.35 memory used=593.3MB, alloc=420.3MB, time=8.94 memory used=716.6MB, alloc=444.3MB, time=10.71 memory used=847.5MB, alloc=468.3MB, time=12.71 memory used=963.4MB, alloc=468.3MB, time=14.42 memory used=1080.4MB, alloc=492.3MB, time=16.23 memory used=1204.5MB, alloc=492.3MB, time=18.44 memory used=1293.5MB, alloc=516.3MB, time=19.72 memory used=1394.2MB, alloc=516.3MB, time=21.42 memory used=1490.5MB, alloc=516.3MB, time=23.08 memory used=1588.3MB, alloc=516.3MB, time=24.88 memory used=1668.2MB, alloc=516.3MB, time=26.16 memory used=1746.6MB, alloc=516.3MB, time=27.49 memory used=1817.5MB, alloc=516.3MB, time=29.03 memory used=1866.8MB, alloc=540.3MB, time=30.09 memory used=1910.4MB, alloc=540.3MB, time=31.00 memory used=1954.9MB, alloc=540.3MB, time=32.02 memory used=2169.2MB, alloc=564.3MB, time=35.09 memory used=2357.7MB, alloc=588.3MB, time=38.23 memory used=2579.2MB, alloc=612.3MB, time=42.32 memory used=2776.4MB, alloc=636.3MB, time=46.38 memory used=2933.2MB, alloc=660.3MB, time=49.68 memory used=3060.0MB, alloc=660.3MB, time=52.18 memory used=3183.0MB, alloc=660.3MB, time=55.00 memory used=3315.0MB, alloc=684.3MB, time=57.94 memory used=3406.3MB, alloc=684.3MB, time=60.05 memory used=3526.8MB, alloc=684.3MB, time=62.47 memory used=3615.1MB, alloc=684.3MB, time=64.46 memory used=3982.7MB, alloc=708.3MB, time=71.11 memory used=4353.6MB, alloc=732.3MB, time=79.02 memory used=4748.7MB, alloc=756.3MB, time=86.59 memory used=5122.6MB, alloc=780.3MB, time=94.60 memory used=5515.9MB, alloc=804.3MB, time=101.17 memory used=5854.0MB, alloc=828.3MB, time=108.91 memory used=6145.5MB, alloc=852.3MB, time=116.18 memory used=6395.0MB, alloc=876.3MB, time=123.14 memory used=6648.0MB, alloc=900.3MB, time=129.15 memory used=6862.9MB, alloc=924.3MB, time=134.95 memory used=7060.0MB, alloc=948.3MB, time=140.21 memory used=7293.6MB, alloc=972.3MB, time=147.95 memory used=7883.5MB, alloc=996.3MB, time=162.89 memory used=8477.0MB, alloc=1020.3MB, time=177.64 memory used=9126.6MB, alloc=1044.3MB, time=192.34 memory used=9751.3MB, alloc=1068.3MB, time=208.49 memory used=10394.0MB, alloc=1092.3MB, time=224.19 memory used=11061.9MB, alloc=1116.3MB, time=237.79 memory used=11712.1MB, alloc=1140.3MB, time=251.15 memory used=12312.8MB, alloc=1164.3MB, time=265.64 memory used=12874.1MB, alloc=1188.3MB, time=280.39 memory used=13431.3MB, alloc=1212.3MB, time=293.19 memory used=13885.4MB, alloc=1236.3MB, time=303.55 memory used=14385.8MB, alloc=1260.3MB, time=317.19 memory used=14899.9MB, alloc=1284.3MB, time=334.30 memory used=15326.3MB, alloc=1308.3MB, time=344.12 memory used=15685.0MB, alloc=1332.3MB, time=356.47 memory used=16172.4MB, alloc=1356.3MB, time=374.29 memory used=16491.2MB, alloc=1380.3MB, time=383.86 memory used=16784.3MB, alloc=1404.3MB, time=392.14 memory used=17199.7MB, alloc=1428.3MB, time=408.50 memory used=17477.2MB, alloc=1452.3MB, time=418.90 memory used=17667.4MB, alloc=1476.3MB, time=426.99 memory used=17962.4MB, alloc=1500.3MB, time=437.68 memory used=18171.1MB, alloc=1524.3MB, time=446.87 memory used=18389.9MB, alloc=1548.3MB, time=454.53 memory used=18580.1MB, alloc=1572.3MB, time=462.28 memory used=18781.8MB, alloc=1596.3MB, time=471.97 memory used=18995.1MB, alloc=1620.3MB, time=482.29 memory used=19134.4MB, alloc=1644.3MB, time=489.74 memory used=19284.6MB, alloc=1668.3MB, time=497.50 memory used=19448.9MB, alloc=1692.3MB, time=504.54 memory used=19607.3MB, alloc=1716.3MB, time=515.29 memory used=19705.6MB, alloc=1740.3MB, time=523.37 memory used=19808.6MB, alloc=1764.3MB, time=531.10 memory used=19945.6MB, alloc=1788.3MB, time=542.28 memory used=19994.8MB, alloc=1812.3MB, time=548.99 memory used=20091.8MB, alloc=1836.3MB, time=556.59 memory used=20156.5MB, alloc=1860.3MB, time=563.14 memory used=20223.6MB, alloc=1860.3MB, time=570.41 memory used=20306.9MB, alloc=1860.3MB, time=578.87 memory used=20382.7MB, alloc=1860.3MB, time=587.94 memory used=20435.5MB, alloc=1860.3MB, time=595.23 memory used=20512.2MB, alloc=1860.3MB, time=603.23 memory used=20584.6MB, alloc=1860.3MB, time=612.28 memory used=20664.6MB, alloc=1860.3MB, time=620.38 memory used=20717.9MB, alloc=1860.3MB, time=627.44 memory used=20766.1MB, alloc=1860.3MB, time=634.31 memory used=20809.5MB, alloc=1860.3MB, time=640.56 memory used=20844.8MB, alloc=1860.3MB, time=647.57 memory used=20869.0MB, alloc=1860.3MB, time=653.96 memory used=20884.4MB, alloc=2116.3MB, time=667.10 memory used=22151.7MB, alloc=2140.3MB, time=699.26 memory used=23379.0MB, alloc=2164.3MB, time=730.65 memory used=24682.6MB, alloc=2188.3MB, time=762.40 memory used=25885.1MB, alloc=2212.3MB, time=798.05 memory used=27083.4MB, alloc=2236.3MB, time=835.07 memory used=28311.1MB, alloc=2260.3MB, time=865.08 memory used=29472.3MB, alloc=2284.3MB, time=900.69 memory used=30567.5MB, alloc=2308.3MB, time=929.48 memory used=31561.1MB, alloc=2332.3MB, time=965.56 memory used=32361.5MB, alloc=2356.3MB, time=993.78 memory used=33418.8MB, alloc=2380.3MB, time=1041.00 memory used=33848.7MB, alloc=2404.3MB, time=1062.95 memory used=34573.4MB, alloc=2428.3MB, time=1091.74 memory used=35280.8MB, alloc=2452.3MB, time=1119.90 memory used=35650.4MB, alloc=2476.3MB, time=1138.27 memory used=36143.6MB, alloc=2500.3MB, time=1164.55 |\^/| 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(); 1428452510 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 3 F := [-2 x y + 13 x z - 17, -8 y z - 8 y z - y, -5 x y - 7 z + 3 x y] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 2 G := [-11 x z - 7 x y - 8 y, -3 x z + 10 z - 2 x, -x z + 6 x z - 9 x y] > Problem := [F,G]; Problem := [ 2 2 2 2 3 [-2 x y + 13 x z - 17, -8 y z - 8 y z - y, -5 x y - 7 z + 3 x y], 2 2 2 2 2 [-11 x z - 7 x y - 8 y, -3 x z + 10 z - 2 x, -x z + 6 x z - 9 x y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.2MB, alloc=32.3MB, time=0.49 memory used=45.6MB, alloc=56.3MB, time=0.78 memory used=86.8MB, alloc=60.3MB, time=1.35 memory used=128.3MB, alloc=60.3MB, time=1.95 memory used=167.6MB, alloc=84.3MB, time=2.53 memory used=236.5MB, alloc=92.3MB, time=3.51 memory used=299.4MB, alloc=116.3MB, time=4.54 memory used=379.2MB, alloc=116.3MB, time=5.75 memory used=449.9MB, alloc=372.3MB, time=6.68 memory used=541.9MB, alloc=396.3MB, time=7.91 memory used=652.2MB, alloc=396.3MB, time=9.49 memory used=761.1MB, alloc=420.3MB, time=10.97 memory used=893.5MB, alloc=444.3MB, time=13.18 memory used=1023.3MB, alloc=444.3MB, time=15.13 memory used=1163.8MB, alloc=468.3MB, time=17.49 memory used=1295.1MB, alloc=468.3MB, time=19.76 memory used=1398.8MB, alloc=492.3MB, time=21.49 memory used=1519.7MB, alloc=492.3MB, time=23.25 memory used=1611.3MB, alloc=492.3MB, time=24.71 memory used=1701.6MB, alloc=492.3MB, time=26.26 memory used=1791.2MB, alloc=492.3MB, time=27.82 memory used=1865.1MB, alloc=492.3MB, time=29.15 memory used=1955.5MB, alloc=492.3MB, time=30.89 memory used=2033.8MB, alloc=516.3MB, time=32.44 memory used=2124.6MB, alloc=516.3MB, time=34.55 memory used=2199.2MB, alloc=516.3MB, time=36.01 memory used=2276.4MB, alloc=516.3MB, time=37.73 memory used=2345.9MB, alloc=516.3MB, time=39.21 memory used=2411.5MB, alloc=516.3MB, time=40.79 memory used=2485.2MB, alloc=516.3MB, time=42.60 memory used=2553.7MB, alloc=516.3MB, time=44.35 memory used=2610.3MB, alloc=516.3MB, time=45.65 memory used=2673.8MB, alloc=516.3MB, time=47.16 memory used=2884.5MB, alloc=540.3MB, time=50.88 memory used=3113.2MB, alloc=564.3MB, time=55.48 memory used=3333.4MB, alloc=588.3MB, time=59.76 memory used=3580.1MB, alloc=612.3MB, time=65.58 memory used=3782.7MB, alloc=636.3MB, time=70.02 memory used=3973.8MB, alloc=660.3MB, time=73.88 memory used=4147.0MB, alloc=660.3MB, time=77.30 memory used=4331.3MB, alloc=684.3MB, time=81.50 memory used=4477.8MB, alloc=684.3MB, time=85.04 memory used=4636.7MB, alloc=684.3MB, time=88.96 memory used=4805.0MB, alloc=684.3MB, time=93.72 memory used=4923.9MB, alloc=684.3MB, time=96.84 memory used=5054.5MB, alloc=684.3MB, time=99.97 memory used=5199.5MB, alloc=684.3MB, time=103.49 memory used=5292.6MB, alloc=684.3MB, time=105.56 memory used=5640.3MB, alloc=708.3MB, time=113.94 memory used=6003.2MB, alloc=732.3MB, time=120.68 memory used=6404.6MB, alloc=756.3MB, time=130.26 memory used=6823.7MB, alloc=780.3MB, time=140.44 memory used=7257.5MB, alloc=804.3MB, time=151.62 memory used=7683.6MB, alloc=828.3MB, time=163.19 memory used=8106.7MB, alloc=852.3MB, time=174.85 memory used=8476.6MB, alloc=876.3MB, time=184.27 memory used=8840.0MB, alloc=900.3MB, time=194.70 memory used=9186.8MB, alloc=924.3MB, time=203.45 memory used=9466.1MB, alloc=948.3MB, time=211.24 memory used=9772.1MB, alloc=972.3MB, time=219.28 memory used=10136.2MB, alloc=996.3MB, time=230.52 memory used=10438.3MB, alloc=1020.3MB, time=238.95 memory used=10767.8MB, alloc=1044.3MB, time=247.63 memory used=11464.5MB, alloc=1068.3MB, time=265.24 memory used=12158.8MB, alloc=1092.3MB, time=285.29 memory used=12870.4MB, alloc=1116.3MB, time=305.05 memory used=13593.7MB, alloc=1140.3MB, time=324.57 memory used=14346.0MB, alloc=1164.3MB, time=341.14 memory used=15081.0MB, alloc=1188.3MB, time=364.04 memory used=15818.5MB, alloc=1212.3MB, time=387.12 memory used=16545.1MB, alloc=1236.3MB, time=403.88 memory used=17281.0MB, alloc=1260.3MB, time=421.65 memory used=18050.6MB, alloc=1284.3MB, time=440.14 memory used=18793.5MB, alloc=1308.3MB, time=461.63 memory used=19463.6MB, alloc=1332.3MB, time=478.98 memory used=20145.5MB, alloc=1356.3MB, time=503.41 memory used=20753.3MB, alloc=1380.3MB, time=524.52 memory used=21297.6MB, alloc=1404.3MB, time=542.11 memory used=21898.7MB, alloc=1428.3MB, time=555.19 memory used=22428.3MB, alloc=1452.3MB, time=571.53 memory used=22853.7MB, alloc=1476.3MB, time=582.59 memory used=23305.8MB, alloc=1500.3MB, time=598.04 memory used=23679.0MB, alloc=1524.3MB, time=610.06 memory used=23999.7MB, alloc=1548.3MB, time=619.18 memory used=24374.6MB, alloc=1572.3MB, time=635.04 memory used=24664.7MB, alloc=1596.3MB, time=646.05 memory used=25030.4MB, alloc=1620.3MB, time=660.02 memory used=25307.4MB, alloc=1644.3MB, time=671.47 memory used=25535.5MB, alloc=1668.3MB, time=680.10 memory used=25909.3MB, alloc=1692.3MB, time=697.52 memory used=26096.3MB, alloc=1716.3MB, time=707.65 memory used=26409.1MB, alloc=1740.3MB, time=723.06 memory used=26596.8MB, alloc=1764.3MB, time=733.28 memory used=26712.4MB, alloc=1788.3MB, time=741.62 memory used=26857.3MB, alloc=1812.3MB, time=749.87 memory used=27087.2MB, alloc=1836.3MB, time=764.36 memory used=27227.7MB, alloc=1860.3MB, time=773.42 memory used=27298.0MB, alloc=1884.3MB, time=780.17 memory used=27385.0MB, alloc=1908.3MB, time=788.70 memory used=27472.1MB, alloc=1932.3MB, time=796.99 memory used=27580.7MB, alloc=1956.3MB, time=806.79 memory used=27759.5MB, alloc=1980.3MB, time=819.09 memory used=27828.9MB, alloc=2004.3MB, time=827.63 memory used=27855.3MB, alloc=2028.3MB, time=834.59 memory used=27932.2MB, alloc=2028.3MB, time=843.03 memory used=28031.7MB, alloc=2028.3MB, time=851.16 memory used=28123.2MB, alloc=2028.3MB, time=858.97 memory used=28168.7MB, alloc=2028.3MB, time=866.63 memory used=28214.6MB, alloc=2028.3MB, time=873.85 memory used=28282.3MB, alloc=2028.3MB, time=881.04 memory used=28296.3MB, alloc=2028.3MB, time=887.81 memory used=28346.2MB, alloc=2284.3MB, time=902.44 memory used=29822.6MB, alloc=2308.3MB, time=942.38 memory used=31290.8MB, alloc=2332.3MB, time=984.39 memory used=32615.9MB, alloc=2356.3MB, time=1013.22 memory used=34118.1MB, alloc=2380.3MB, time=1059.72 memory used=35569.4MB, alloc=2404.3MB, time=1103.70 memory used=36993.3MB, alloc=2428.3MB, time=1146.54 memory used=38178.4MB, alloc=2452.3MB, time=1181.54 |\^/| 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(); 1428453710 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 3 2 2 F := [18 y - 3 x y - 16 x, 5 y + 8 y , -5 x y + 4 y z + z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 G := [-7 x - 6 y z + 11 y, -10 y z, 6 x y z - 4 y z - 7 x z] > Problem := [F,G]; 3 3 2 2 Problem := [[18 y - 3 x y - 16 x, 5 y + 8 y , -5 x y + 4 y z + z], 3 2 2 [-7 x - 6 y z + 11 y, -10 y z, 6 x y z - 4 y z - 7 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=31.8MB, alloc=40.3MB, time=0.56 memory used=59.5MB, alloc=40.3MB, time=0.95 memory used=85.3MB, alloc=40.3MB, time=1.33 memory used=110.1MB, alloc=68.3MB, time=1.73 memory used=155.8MB, alloc=68.3MB, time=2.42 memory used=200.2MB, alloc=68.3MB, time=3.10 memory used=243.7MB, alloc=92.3MB, time=3.79 memory used=308.8MB, alloc=124.3MB, time=4.86 memory used=399.4MB, alloc=148.3MB, time=6.45 memory used=498.2MB, alloc=172.3MB, time=8.20 memory used=608.1MB, alloc=452.3MB, time=10.19 memory used=746.7MB, alloc=476.3MB, time=12.47 memory used=891.9MB, alloc=500.3MB, time=15.14 memory used=1051.3MB, alloc=524.3MB, time=17.94 memory used=1217.3MB, alloc=548.3MB, time=21.40 memory used=1377.4MB, alloc=572.3MB, time=26.50 memory used=1547.0MB, alloc=596.3MB, time=32.33 memory used=1730.8MB, alloc=620.3MB, time=39.11 memory used=1930.0MB, alloc=644.3MB, time=46.54 memory used=2143.1MB, alloc=668.3MB, time=54.77 memory used=2370.6MB, alloc=692.3MB, time=64.11 memory used=2622.0MB, alloc=716.3MB, time=74.33 memory used=2897.4MB, alloc=740.3MB, time=85.47 memory used=3196.8MB, alloc=740.3MB, time=97.62 memory used=3496.2MB, alloc=764.3MB, time=109.82 memory used=3819.4MB, alloc=764.3MB, time=122.78 memory used=4142.6MB, alloc=764.3MB, time=135.71 memory used=4465.8MB, alloc=788.3MB, time=148.61 memory used=4812.8MB, alloc=788.3MB, time=162.37 memory used=5159.7MB, alloc=788.3MB, time=176.16 memory used=5506.6MB, alloc=812.3MB, time=190.04 memory used=5877.1MB, alloc=812.3MB, time=204.66 memory used=6247.7MB, alloc=836.3MB, time=219.38 memory used=6642.3MB, alloc=860.3MB, time=234.88 N1 := 13321 > GB := Basis(F, plex(op(vars))); 2 2 GB := [175 x + 1152 x, 5 x y + 8 x, 18 y + 7 x, 105 z + 1024 x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=7065.3MB, alloc=860.3MB, time=245.84 memory used=7547.4MB, alloc=884.3MB, time=258.27 memory used=7977.3MB, alloc=908.3MB, time=276.12 memory used=8422.8MB, alloc=932.3MB, time=294.87 memory used=8892.6MB, alloc=956.3MB, time=314.46 N2 := 7069 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 3 2 2 H := [18 y - 3 x y - 16 x, 5 y + 8 y , -5 x y + 4 y z + z, 3 2 2 -7 x - 6 y z + 11 y, -10 y z, 6 x y z - 4 y z - 7 x z] > J:=[op(GB),op(G)]; 2 2 J := [175 x + 1152 x, 5 x y + 8 x, 18 y + 7 x, 105 z + 1024 x, 3 2 2 -7 x - 6 y z + 11 y, -10 y z, 6 x y z - 4 y z - 7 x z] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; 11 featureList := [6, 14, 18, 3, 3, 3, 2, 2/3, 1, 2/3, 6/17, --, 7/17, 7, 15, 16, 17 3, 3, 2, 2, 6/7, 5/7, 4/7, 9/17, 7/17, 6/17, -1, 2, 0] > save(F, G, cat("ranSet/33", convert(F, string),".txt")); > quit memory used=8968.9MB, alloc=956.3MB, time=316.98 |\^/| 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(); 1428454052 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 2 2 F := [-9 x y + 19 y + z , -9 y - 9 y + 8 z, -4 x y - 10 x y z + y z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 3 G := [-4 x - 2 x y - 9 z , -6 x y + 3 x + 9, 9 x - 2 x y - 2 z] > Problem := [F,G]; Problem := [ 2 2 2 2 2 2 [-9 x y + 19 y + z , -9 y - 9 y + 8 z, -4 x y - 10 x y z + y z], 2 2 3 [-4 x - 2 x y - 9 z , -6 x y + 3 x + 9, 9 x - 2 x y - 2 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.4MB, alloc=32.3MB, time=0.50 memory used=47.3MB, alloc=32.3MB, time=0.81 memory used=66.7MB, alloc=56.3MB, time=1.11 memory used=107.2MB, alloc=60.3MB, time=1.72 memory used=147.0MB, alloc=84.3MB, time=2.30 memory used=210.0MB, alloc=92.3MB, time=3.27 memory used=273.8MB, alloc=116.3MB, time=4.20 memory used=353.1MB, alloc=116.3MB, time=5.43 memory used=426.4MB, alloc=396.3MB, time=6.64 memory used=534.6MB, alloc=420.3MB, time=8.35 memory used=666.7MB, alloc=420.3MB, time=10.40 memory used=797.7MB, alloc=444.3MB, time=12.43 memory used=918.6MB, alloc=468.3MB, time=14.32 memory used=1040.5MB, alloc=468.3MB, time=16.42 memory used=1150.1MB, alloc=492.3MB, time=18.11 memory used=1268.3MB, alloc=492.3MB, time=20.01 memory used=1361.8MB, alloc=492.3MB, time=21.59 memory used=1470.6MB, alloc=516.3MB, time=23.59 memory used=1556.4MB, alloc=516.3MB, time=25.17 memory used=1641.0MB, alloc=516.3MB, time=26.69 memory used=1715.5MB, alloc=516.3MB, time=28.16 memory used=1798.0MB, alloc=516.3MB, time=29.86 memory used=1860.1MB, alloc=516.3MB, time=31.14 memory used=1934.9MB, alloc=516.3MB, time=32.86 memory used=1991.6MB, alloc=516.3MB, time=34.03 memory used=2060.4MB, alloc=516.3MB, time=35.68 memory used=2264.9MB, alloc=540.3MB, time=39.41 memory used=2477.8MB, alloc=564.3MB, time=43.10 memory used=2675.8MB, alloc=588.3MB, time=46.89 memory used=2873.3MB, alloc=612.3MB, time=50.63 memory used=3058.4MB, alloc=636.3MB, time=54.68 memory used=3210.1MB, alloc=660.3MB, time=57.80 memory used=3358.4MB, alloc=660.3MB, time=61.05 memory used=3503.1MB, alloc=660.3MB, time=64.21 memory used=3641.9MB, alloc=684.3MB, time=67.36 memory used=3788.3MB, alloc=684.3MB, time=71.09 memory used=3927.3MB, alloc=684.3MB, time=74.42 memory used=4013.5MB, alloc=684.3MB, time=76.52 memory used=4364.5MB, alloc=708.3MB, time=83.96 memory used=4735.2MB, alloc=732.3MB, time=92.01 memory used=5111.6MB, alloc=756.3MB, time=100.66 memory used=5514.1MB, alloc=780.3MB, time=109.98 memory used=5843.1MB, alloc=804.3MB, time=117.57 memory used=6178.8MB, alloc=828.3MB, time=126.17 memory used=6418.2MB, alloc=852.3MB, time=131.94 memory used=6678.0MB, alloc=876.3MB, time=137.80 memory used=6878.8MB, alloc=900.3MB, time=142.78 memory used=7140.1MB, alloc=924.3MB, time=149.08 memory used=7425.1MB, alloc=948.3MB, time=157.07 memory used=7602.8MB, alloc=972.3MB, time=161.86 memory used=7792.9MB, alloc=996.3MB, time=166.82 memory used=8357.4MB, alloc=1020.3MB, time=179.14 memory used=8865.9MB, alloc=1044.3MB, time=190.82 memory used=9375.0MB, alloc=1068.3MB, time=202.52 memory used=9885.7MB, alloc=1092.3MB, time=214.24 memory used=10406.6MB, alloc=1116.3MB, time=225.73 memory used=10909.8MB, alloc=1140.3MB, time=237.34 memory used=11386.5MB, alloc=1164.3MB, time=250.17 memory used=11760.2MB, alloc=1188.3MB, time=266.73 memory used=12135.3MB, alloc=1212.3MB, time=283.95 memory used=12517.9MB, alloc=1236.3MB, time=302.04 memory used=12911.3MB, alloc=1260.3MB, time=320.89 memory used=13319.5MB, alloc=1284.3MB, time=340.45 memory used=13744.7MB, alloc=1308.3MB, time=360.74 memory used=14179.8MB, alloc=1332.3MB, time=381.74 memory used=14627.5MB, alloc=1356.3MB, time=403.46 memory used=15088.5MB, alloc=1380.3MB, time=425.82 memory used=15562.6MB, alloc=1404.3MB, time=448.56 memory used=16050.7MB, alloc=1428.3MB, time=472.11 memory used=16553.3MB, alloc=1452.3MB, time=496.58 memory used=17060.5MB, alloc=1476.3MB, time=522.24 memory used=17591.1MB, alloc=1500.3MB, time=549.05 memory used=18145.7MB, alloc=1524.3MB, time=576.82 memory used=18724.3MB, alloc=1548.3MB, time=605.90 memory used=19326.8MB, alloc=1572.3MB, time=636.26 memory used=19953.2MB, alloc=1596.3MB, time=667.46 memory used=20603.6MB, alloc=1620.3MB, time=699.86 memory used=21277.9MB, alloc=1644.3MB, time=733.76 memory used=21976.1MB, alloc=1668.3MB, time=768.12 memory used=22698.2MB, alloc=1692.3MB, time=803.44 memory used=23444.4MB, alloc=1716.3MB, time=839.80 memory used=24214.4MB, alloc=1740.3MB, time=877.38 memory used=25008.3MB, alloc=1764.3MB, time=915.92 memory used=25826.2MB, alloc=1788.3MB, time=955.81 memory used=26668.0MB, alloc=1812.3MB, time=996.68 memory used=27533.8MB, alloc=1836.3MB, time=1038.78 memory used=28423.5MB, alloc=1860.3MB, time=1081.74 memory used=29337.0MB, alloc=1884.3MB, time=1125.98 |\^/| 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(); 1428455252 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 3 2 2 2 F := [-9 x - 6 x y z + 14 z , -2 y z - 8 z + 10 z , -6 y z - 5 y z - 10 y] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; G := [ 2 2 2 2 2 2 2 2 2 20 x y + 4 x - 15 z , -3 x y + 4 x z - 5 x y , -7 x y - 5 x z - 9 y ] > Problem := [F,G]; Problem := [ 3 2 2 3 2 2 2 [-9 x - 6 x y z + 14 z , -2 y z - 8 z + 10 z , -6 y z - 5 y z - 10 y], 2 2 2 2 2 2 2 2 2 [20 x y + 4 x - 15 z , -3 x y + 4 x z - 5 x y , -7 x y - 5 x z - 9 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.17 memory used=26.5MB, alloc=32.3MB, time=0.51 memory used=45.8MB, alloc=56.3MB, time=0.79 memory used=87.1MB, alloc=60.3MB, time=1.41 memory used=127.8MB, alloc=60.3MB, time=2.01 memory used=167.4MB, alloc=84.3MB, time=2.59 memory used=243.1MB, alloc=92.5MB, time=3.44 memory used=304.1MB, alloc=116.5MB, time=4.39 memory used=382.8MB, alloc=116.5MB, time=5.53 memory used=449.1MB, alloc=396.5MB, time=6.52 memory used=553.3MB, alloc=420.5MB, time=8.16 memory used=678.0MB, alloc=420.5MB, time=10.06 memory used=817.6MB, alloc=444.5MB, time=11.78 memory used=964.2MB, alloc=468.5MB, time=13.77 memory used=1098.7MB, alloc=468.5MB, time=15.95 memory used=1216.9MB, alloc=468.5MB, time=17.60 memory used=1349.6MB, alloc=492.5MB, time=19.88 memory used=1476.0MB, alloc=492.5MB, time=22.13 memory used=1577.7MB, alloc=516.5MB, time=23.94 memory used=1669.8MB, alloc=516.5MB, time=25.55 memory used=1750.2MB, alloc=516.5MB, time=26.99 memory used=1830.3MB, alloc=516.5MB, time=28.06 memory used=1905.6MB, alloc=516.5MB, time=29.39 memory used=1978.2MB, alloc=516.5MB, time=30.73 memory used=2053.2MB, alloc=516.5MB, time=31.97 memory used=2116.7MB, alloc=540.5MB, time=33.28 memory used=2175.0MB, alloc=540.5MB, time=34.38 memory used=2235.1MB, alloc=540.5MB, time=35.64 memory used=2293.9MB, alloc=540.5MB, time=36.94 memory used=2350.5MB, alloc=540.5MB, time=38.06 memory used=2405.8MB, alloc=540.5MB, time=39.19 memory used=2464.0MB, alloc=540.5MB, time=40.17 memory used=2504.2MB, alloc=540.5MB, time=41.05 memory used=2736.9MB, alloc=564.5MB, time=44.69 memory used=2959.9MB, alloc=588.5MB, time=48.45 memory used=3151.8MB, alloc=612.5MB, time=51.72 memory used=3343.2MB, alloc=636.5MB, time=55.31 memory used=3532.0MB, alloc=660.5MB, time=58.52 memory used=3726.4MB, alloc=684.5MB, time=63.06 memory used=3885.9MB, alloc=684.5MB, time=66.02 memory used=4059.3MB, alloc=708.5MB, time=70.01 memory used=4231.8MB, alloc=708.5MB, time=73.70 memory used=4367.3MB, alloc=708.5MB, time=76.08 memory used=4490.0MB, alloc=708.5MB, time=78.48 memory used=4657.8MB, alloc=732.5MB, time=81.82 memory used=4774.3MB, alloc=732.5MB, time=84.45 memory used=4891.6MB, alloc=732.5MB, time=86.46 memory used=5017.3MB, alloc=732.5MB, time=89.83 memory used=5406.8MB, alloc=756.5MB, time=98.18 memory used=5823.0MB, alloc=780.5MB, time=106.39 memory used=6225.3MB, alloc=804.5MB, time=115.11 memory used=6658.4MB, alloc=828.5MB, time=125.60 memory used=7034.3MB, alloc=852.5MB, time=134.41 memory used=7416.0MB, alloc=876.5MB, time=144.13 memory used=7752.9MB, alloc=900.5MB, time=151.12 memory used=8072.9MB, alloc=924.5MB, time=157.30 memory used=8387.6MB, alloc=948.5MB, time=164.22 memory used=8616.8MB, alloc=972.5MB, time=169.11 memory used=8947.4MB, alloc=996.5MB, time=175.46 memory used=9170.7MB, alloc=1020.5MB, time=180.20 memory used=9428.4MB, alloc=1044.5MB, time=187.20 memory used=10108.6MB, alloc=1068.5MB, time=200.39 memory used=10804.0MB, alloc=1092.5MB, time=215.14 memory used=11481.7MB, alloc=1116.5MB, time=230.96 memory used=12182.2MB, alloc=1140.5MB, time=245.31 memory used=12919.9MB, alloc=1164.5MB, time=262.99 memory used=13637.1MB, alloc=1188.5MB, time=284.50 memory used=14385.2MB, alloc=1212.5MB, time=301.96 memory used=15150.8MB, alloc=1236.5MB, time=321.97 memory used=15901.4MB, alloc=1260.5MB, time=341.31 memory used=16613.9MB, alloc=1284.5MB, time=365.28 memory used=17303.4MB, alloc=1308.5MB, time=386.88 memory used=18023.9MB, alloc=1332.5MB, time=410.38 memory used=18581.8MB, alloc=1356.5MB, time=426.65 memory used=19106.8MB, alloc=1380.5MB, time=441.19 memory used=19669.5MB, alloc=1404.5MB, time=459.22 memory used=20115.2MB, alloc=1428.5MB, time=473.44 memory used=20632.5MB, alloc=1452.5MB, time=491.38 memory used=21023.7MB, alloc=1476.5MB, time=504.97 memory used=21595.8MB, alloc=1500.5MB, time=522.87 memory used=22033.6MB, alloc=1524.5MB, time=536.55 memory used=22357.7MB, alloc=1548.5MB, time=546.54 memory used=22763.3MB, alloc=1572.5MB, time=559.78 memory used=23103.0MB, alloc=1596.5MB, time=574.47 memory used=23538.3MB, alloc=1620.5MB, time=592.30 memory used=23916.1MB, alloc=1644.5MB, time=609.54 memory used=24276.9MB, alloc=1668.5MB, time=625.61 memory used=24493.8MB, alloc=1692.5MB, time=637.90 memory used=24790.3MB, alloc=1716.5MB, time=652.75 memory used=24913.9MB, alloc=1740.5MB, time=660.37 memory used=25132.2MB, alloc=1764.5MB, time=671.27 memory used=25283.9MB, alloc=1788.5MB, time=679.73 memory used=25463.2MB, alloc=1812.5MB, time=689.59 memory used=25583.0MB, alloc=1836.5MB, time=696.58 memory used=25830.2MB, alloc=1860.5MB, time=708.59 memory used=26064.9MB, alloc=1884.5MB, time=720.60 memory used=26303.6MB, alloc=1908.5MB, time=731.50 memory used=26582.9MB, alloc=1932.5MB, time=741.70 memory used=26714.3MB, alloc=1932.5MB, time=749.69 memory used=26931.2MB, alloc=1956.5MB, time=760.07 memory used=27123.3MB, alloc=1956.5MB, time=772.11 memory used=27285.2MB, alloc=1956.5MB, time=783.26 memory used=27451.2MB, alloc=1956.5MB, time=793.11 memory used=27635.2MB, alloc=1956.5MB, time=801.27 memory used=27809.9MB, alloc=1956.5MB, time=810.60 memory used=27940.9MB, alloc=1956.5MB, time=819.95 memory used=28090.1MB, alloc=1956.5MB, time=830.69 memory used=28226.3MB, alloc=1956.5MB, time=839.72 memory used=28376.0MB, alloc=1956.5MB, time=848.27 memory used=28508.1MB, alloc=1956.5MB, time=857.38 memory used=28592.8MB, alloc=1956.5MB, time=864.77 memory used=28719.2MB, alloc=1980.5MB, time=872.59 memory used=28836.3MB, alloc=1980.5MB, time=881.66 memory used=28933.4MB, alloc=1980.5MB, time=889.28 memory used=29027.7MB, alloc=1980.5MB, time=897.18 memory used=29079.6MB, alloc=1980.5MB, time=904.05 memory used=29180.6MB, alloc=1980.5MB, time=912.96 memory used=29252.7MB, alloc=1980.5MB, time=920.67 memory used=29320.3MB, alloc=1980.5MB, time=927.87 memory used=29385.6MB, alloc=1980.5MB, time=934.95 memory used=29479.3MB, alloc=1980.5MB, time=942.61 memory used=29564.2MB, alloc=1980.5MB, time=950.78 memory used=29657.2MB, alloc=1980.5MB, time=959.36 memory used=29744.4MB, alloc=1980.5MB, time=967.17 memory used=29764.4MB, alloc=1980.5MB, time=973.82 memory used=29807.7MB, alloc=1980.5MB, time=981.25 memory used=29830.5MB, alloc=1980.5MB, time=988.61 memory used=29868.7MB, alloc=1980.5MB, time=996.08 memory used=29983.5MB, alloc=1980.5MB, time=1006.81 memory used=30024.4MB, alloc=1980.5MB, time=1014.21 memory used=30102.7MB, alloc=1980.5MB, time=1021.92 memory used=30192.2MB, alloc=1980.5MB, time=1031.35 memory used=30291.2MB, alloc=1980.5MB, time=1040.97 memory used=30384.1MB, alloc=1980.5MB, time=1049.91 memory used=30456.7MB, alloc=1980.5MB, time=1058.47 memory used=30475.4MB, alloc=1980.5MB, time=1065.93 memory used=30508.7MB, alloc=1980.5MB, time=1073.75 memory used=30530.3MB, alloc=1980.5MB, time=1080.72 memory used=30605.3MB, alloc=1980.5MB, time=1088.97 memory used=30638.6MB, alloc=1980.5MB, time=1095.73 memory used=30690.3MB, alloc=2004.5MB, time=1103.96 memory used=30735.0MB, alloc=2004.5MB, time=1111.56 memory used=30783.1MB, alloc=2004.5MB, time=1119.03 memory used=30826.4MB, alloc=2004.5MB, time=1126.63 memory used=30854.0MB, alloc=2260.5MB, time=1140.94 memory used=32293.6MB, alloc=2284.5MB, time=1182.01 |\^/| 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(); 1428456452 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 F := [15 x z - 8 y z - 13 y, -8 x y - 10 x y - 4 y, 4 x y - 2 y - 10 y z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 3 2 3 2 G := [-14 x z + 4 x z - 7 x, -7 x y + y + y z, -7 x - 8 x y - 2 x z] > Problem := [F,G]; Problem := [ 2 2 2 [15 x z - 8 y z - 13 y, -8 x y - 10 x y - 4 y, 4 x y - 2 y - 10 y z], 2 2 2 3 2 3 2 [-14 x z + 4 x z - 7 x, -7 x y + y + y z, -7 x - 8 x y - 2 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.6MB, alloc=32.3MB, time=0.50 memory used=47.6MB, alloc=32.3MB, time=0.79 memory used=66.0MB, alloc=56.3MB, time=1.07 memory used=105.0MB, alloc=60.3MB, time=1.66 memory used=144.3MB, alloc=84.3MB, time=2.25 memory used=206.1MB, alloc=92.3MB, time=3.21 memory used=265.7MB, alloc=116.3MB, time=4.12 memory used=348.3MB, alloc=116.3MB, time=5.40 memory used=427.8MB, alloc=140.3MB, time=6.71 memory used=503.9MB, alloc=140.3MB, time=7.95 memory used=567.9MB, alloc=396.3MB, time=9.00 memory used=672.9MB, alloc=420.3MB, time=10.69 memory used=800.1MB, alloc=444.3MB, time=12.81 memory used=937.8MB, alloc=468.3MB, time=15.11 memory used=1070.8MB, alloc=492.3MB, time=17.44 memory used=1190.9MB, alloc=492.3MB, time=19.44 memory used=1310.8MB, alloc=492.3MB, time=21.62 memory used=1414.4MB, alloc=516.3MB, time=23.54 memory used=1517.5MB, alloc=516.3MB, time=25.45 memory used=1623.0MB, alloc=516.3MB, time=27.67 memory used=1712.3MB, alloc=516.3MB, time=29.50 memory used=1806.0MB, alloc=516.3MB, time=31.43 memory used=1878.0MB, alloc=516.3MB, time=33.08 memory used=1946.2MB, alloc=516.3MB, time=34.78 memory used=2005.6MB, alloc=516.3MB, time=36.23 memory used=2067.0MB, alloc=516.3MB, time=37.76 memory used=2126.2MB, alloc=540.3MB, time=39.19 memory used=2351.0MB, alloc=564.3MB, time=43.71 memory used=2581.9MB, alloc=588.3MB, time=48.60 memory used=2775.8MB, alloc=612.3MB, time=52.68 memory used=2958.1MB, alloc=636.3MB, time=56.61 memory used=3125.4MB, alloc=660.3MB, time=60.09 memory used=3290.4MB, alloc=684.3MB, time=63.74 memory used=3435.8MB, alloc=684.3MB, time=67.17 memory used=3589.6MB, alloc=684.3MB, time=70.73 memory used=3731.6MB, alloc=708.3MB, time=74.08 memory used=3834.5MB, alloc=708.3MB, time=76.65 memory used=3970.4MB, alloc=732.3MB, time=79.84 memory used=4112.3MB, alloc=732.3MB, time=83.14 memory used=4230.6MB, alloc=756.3MB, time=86.20 memory used=4605.7MB, alloc=780.3MB, time=93.70 memory used=4950.0MB, alloc=804.3MB, time=100.95 memory used=5285.0MB, alloc=828.3MB, time=108.20 memory used=5641.9MB, alloc=852.3MB, time=115.46 memory used=5992.8MB, alloc=876.3MB, time=122.87 memory used=6327.1MB, alloc=900.3MB, time=130.41 memory used=6665.0MB, alloc=924.3MB, time=137.93 memory used=7000.9MB, alloc=948.3MB, time=145.45 memory used=7336.4MB, alloc=972.3MB, time=152.97 memory used=7700.0MB, alloc=996.3MB, time=160.32 memory used=8053.8MB, alloc=1020.3MB, time=168.18 memory used=8412.5MB, alloc=1044.3MB, time=175.94 memory used=8783.0MB, alloc=1068.3MB, time=183.83 memory used=9147.0MB, alloc=1092.3MB, time=191.98 memory used=9511.2MB, alloc=1116.3MB, time=200.14 memory used=9857.7MB, alloc=1140.3MB, time=208.39 memory used=10212.3MB, alloc=1164.3MB, time=216.68 memory used=10567.6MB, alloc=1188.3MB, time=225.09 memory used=10902.5MB, alloc=1212.3MB, time=233.37 memory used=11250.0MB, alloc=1236.3MB, time=241.67 memory used=11596.1MB, alloc=1260.3MB, time=250.20 memory used=11924.8MB, alloc=1284.3MB, time=258.60 memory used=12253.8MB, alloc=1308.3MB, time=267.04 memory used=12582.4MB, alloc=1332.3MB, time=275.63 memory used=12938.0MB, alloc=1356.3MB, time=284.31 memory used=13233.8MB, alloc=1380.3MB, time=294.77 memory used=13486.7MB, alloc=1404.3MB, time=306.90 memory used=13749.6MB, alloc=1428.3MB, time=319.77 memory used=14023.6MB, alloc=1452.3MB, time=333.39 memory used=14310.5MB, alloc=1476.3MB, time=347.90 memory used=14611.1MB, alloc=1500.3MB, time=363.18 memory used=14925.9MB, alloc=1524.3MB, time=378.99 memory used=15255.2MB, alloc=1548.3MB, time=395.22 memory used=15599.0MB, alloc=1572.3MB, time=412.57 memory used=15958.0MB, alloc=1596.3MB, time=430.64 memory used=16331.5MB, alloc=1620.3MB, time=449.26 memory used=16720.4MB, alloc=1644.3MB, time=468.56 memory used=17124.9MB, alloc=1668.3MB, time=488.55 memory used=17545.0MB, alloc=1692.3MB, time=509.54 memory used=17980.9MB, alloc=1716.3MB, time=531.19 memory used=18432.6MB, alloc=1740.3MB, time=553.88 memory used=18899.9MB, alloc=1764.3MB, time=577.34 memory used=19383.2MB, alloc=1788.3MB, time=601.72 memory used=19881.9MB, alloc=1812.3MB, time=626.91 memory used=20396.7MB, alloc=1836.3MB, time=652.85 memory used=20927.4MB, alloc=1860.3MB, time=679.71 memory used=21474.2MB, alloc=1884.3MB, time=707.58 memory used=22037.2MB, alloc=1908.3MB, time=735.84 memory used=22616.0MB, alloc=1932.3MB, time=765.02 memory used=23211.0MB, alloc=1956.3MB, time=795.05 memory used=23821.9MB, alloc=1980.3MB, time=826.23 memory used=24448.9MB, alloc=2004.3MB, time=857.59 memory used=25091.4MB, alloc=2028.3MB, time=889.67 memory used=25750.1MB, alloc=2052.3MB, time=922.43 memory used=26424.5MB, alloc=2076.3MB, time=956.21 memory used=27115.2MB, alloc=2100.3MB, time=990.74 memory used=27821.7MB, alloc=2124.3MB, time=1026.10 memory used=28544.3MB, alloc=2148.3MB, time=1062.64 memory used=29282.8MB, alloc=2172.3MB, time=1099.09 |\^/| 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(); 1428457652 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 3 2 2 2 F := [x y - 15 y + 8 z, -5 x - 5 x y - 2 z, -4 x + 9 x y + 2 z ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 2 G := [-20 z + 17 x z - 3 y z, 10 x y - 8 y z - 5 z, -4 x y + 10 x] > Problem := [F,G]; 2 3 3 2 2 2 Problem := [[x y - 15 y + 8 z, -5 x - 5 x y - 2 z, -4 x + 9 x y + 2 z ], 3 2 2 2 [-20 z + 17 x z - 3 y z, 10 x y - 8 y z - 5 z, -4 x 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=26.7MB, alloc=32.3MB, time=0.50 memory used=47.7MB, alloc=32.3MB, time=0.80 memory used=68.6MB, alloc=60.3MB, time=1.13 memory used=109.6MB, alloc=60.3MB, time=1.71 memory used=149.3MB, alloc=84.3MB, time=2.31 memory used=213.2MB, alloc=92.3MB, time=3.22 memory used=274.9MB, alloc=116.3MB, time=4.12 memory used=353.0MB, alloc=116.3MB, time=5.28 memory used=418.1MB, alloc=372.3MB, time=6.28 memory used=503.3MB, alloc=396.3MB, time=7.55 memory used=610.9MB, alloc=420.3MB, time=9.18 memory used=739.7MB, alloc=444.3MB, time=11.16 memory used=862.6MB, alloc=444.3MB, time=12.83 memory used=990.6MB, alloc=468.3MB, time=14.83 memory used=1110.8MB, alloc=468.3MB, time=16.84 memory used=1214.6MB, alloc=468.3MB, time=18.61 memory used=1315.5MB, alloc=492.3MB, time=20.27 memory used=1416.9MB, alloc=492.3MB, time=22.02 memory used=1500.9MB, alloc=492.3MB, time=23.27 memory used=1581.6MB, alloc=492.3MB, time=24.30 memory used=1679.2MB, alloc=492.3MB, time=25.94 memory used=1790.7MB, alloc=492.3MB, time=27.06 memory used=1860.0MB, alloc=492.3MB, time=28.11 memory used=1982.0MB, alloc=492.3MB, time=29.49 memory used=2066.0MB, alloc=516.3MB, time=30.87 memory used=2187.4MB, alloc=516.3MB, time=31.64 memory used=2319.9MB, alloc=516.3MB, time=32.57 memory used=2435.9MB, alloc=516.3MB, time=33.51 memory used=2498.8MB, alloc=516.3MB, time=34.62 memory used=2577.4MB, alloc=516.3MB, time=35.80 memory used=2644.8MB, alloc=516.3MB, time=37.16 memory used=2701.8MB, alloc=516.3MB, time=38.22 memory used=2756.7MB, alloc=516.3MB, time=39.34 memory used=2860.1MB, alloc=516.3MB, time=40.23 memory used=2917.2MB, alloc=516.3MB, time=41.81 memory used=3018.5MB, alloc=540.3MB, time=42.40 memory used=3160.6MB, alloc=540.3MB, time=43.35 memory used=3201.4MB, alloc=540.3MB, time=44.32 memory used=3435.4MB, alloc=564.3MB, time=47.40 memory used=3646.5MB, alloc=564.3MB, time=50.55 memory used=3854.4MB, alloc=588.3MB, time=54.36 memory used=4022.7MB, alloc=612.3MB, time=57.53 memory used=4169.3MB, alloc=636.3MB, time=59.93 memory used=4307.8MB, alloc=636.3MB, time=62.70 memory used=4433.6MB, alloc=660.3MB, time=64.97 memory used=4577.9MB, alloc=660.3MB, time=68.04 memory used=4677.3MB, alloc=660.3MB, time=70.29 memory used=4782.3MB, alloc=660.3MB, time=72.66 memory used=5103.6MB, alloc=684.3MB, time=78.60 memory used=5469.6MB, alloc=708.3MB, time=83.62 memory used=5816.4MB, alloc=732.3MB, time=90.25 memory used=6133.7MB, alloc=756.3MB, time=95.89 memory used=6451.2MB, alloc=780.3MB, time=102.31 memory used=6665.0MB, alloc=804.3MB, time=106.92 memory used=6891.4MB, alloc=828.3MB, time=112.13 memory used=7111.6MB, alloc=852.3MB, time=117.09 memory used=7313.5MB, alloc=876.3MB, time=121.94 memory used=7477.0MB, alloc=900.3MB, time=125.85 memory used=7963.9MB, alloc=924.3MB, time=136.39 memory used=8486.7MB, alloc=948.3MB, time=145.08 memory used=8981.4MB, alloc=972.3MB, time=153.06 memory used=9522.1MB, alloc=996.3MB, time=161.54 memory used=9978.8MB, alloc=1020.3MB, time=168.71 memory used=10603.6MB, alloc=1044.3MB, time=178.19 memory used=11057.4MB, alloc=1068.3MB, time=184.78 memory used=11638.2MB, alloc=1092.3MB, time=193.27 memory used=12143.2MB, alloc=1116.3MB, time=200.89 memory used=12800.7MB, alloc=1140.3MB, time=211.45 memory used=13422.1MB, alloc=1164.3MB, time=222.80 memory used=13952.7MB, alloc=1188.3MB, time=234.70 memory used=14421.0MB, alloc=1212.3MB, time=242.77 memory used=14945.9MB, alloc=1236.3MB, time=250.57 memory used=15387.4MB, alloc=1260.3MB, time=256.51 memory used=15917.6MB, alloc=1284.3MB, time=264.25 memory used=16307.2MB, alloc=1308.3MB, time=269.93 memory used=16689.7MB, alloc=1332.3MB, time=276.36 memory used=17360.4MB, alloc=1356.3MB, time=286.30 memory used=17837.1MB, alloc=1380.3MB, time=296.19 memory used=18405.1MB, alloc=1404.3MB, time=305.76 memory used=18850.2MB, alloc=1428.3MB, time=313.42 memory used=19325.8MB, alloc=1452.3MB, time=321.84 memory used=19841.7MB, alloc=1476.3MB, time=330.82 memory used=20311.1MB, alloc=1500.3MB, time=340.79 memory used=20645.6MB, alloc=1524.3MB, time=350.03 memory used=20910.2MB, alloc=1548.3MB, time=359.14 memory used=21197.1MB, alloc=1572.3MB, time=369.04 memory used=21428.3MB, alloc=1596.3MB, time=378.50 memory used=21696.6MB, alloc=1620.3MB, time=387.79 memory used=21927.3MB, alloc=1644.3MB, time=396.87 memory used=22113.6MB, alloc=1668.3MB, time=405.97 memory used=22303.9MB, alloc=1668.3MB, time=414.46 memory used=22473.7MB, alloc=1668.3MB, time=423.27 memory used=22609.3MB, alloc=1692.3MB, time=430.46 memory used=22772.0MB, alloc=1692.3MB, time=438.96 memory used=22912.7MB, alloc=1692.3MB, time=447.20 memory used=23002.2MB, alloc=1692.3MB, time=453.86 memory used=23060.2MB, alloc=1692.3MB, time=460.02 memory used=23186.3MB, alloc=1692.3MB, time=467.89 memory used=23251.6MB, alloc=1692.3MB, time=474.08 memory used=23354.3MB, alloc=1692.3MB, time=480.64 memory used=23452.9MB, alloc=1692.3MB, time=487.15 memory used=23552.7MB, alloc=1692.3MB, time=494.99 memory used=23583.2MB, alloc=1692.3MB, time=500.93 memory used=23666.3MB, alloc=1692.3MB, time=507.50 memory used=23756.9MB, alloc=1692.3MB, time=514.11 memory used=23854.0MB, alloc=1692.3MB, time=521.73 memory used=23924.4MB, alloc=1692.3MB, time=528.67 memory used=23962.4MB, alloc=1692.3MB, time=534.74 memory used=23997.6MB, alloc=1692.3MB, time=540.53 memory used=24011.0MB, alloc=1692.3MB, time=546.08 memory used=24086.1MB, alloc=1692.3MB, time=553.21 memory used=24137.2MB, alloc=1692.3MB, time=559.58 memory used=24162.5MB, alloc=1692.3MB, time=565.49 memory used=24214.6MB, alloc=1692.3MB, time=572.55 memory used=24260.9MB, alloc=1692.3MB, time=578.89 memory used=24283.6MB, alloc=1692.3MB, time=584.70 memory used=24299.5MB, alloc=1692.3MB, time=590.69 memory used=24355.3MB, alloc=1692.3MB, time=597.23 memory used=24370.1MB, alloc=1692.3MB, time=603.11 memory used=24404.9MB, alloc=1948.3MB, time=615.39 memory used=25513.9MB, alloc=1972.3MB, time=639.41 memory used=26598.5MB, alloc=1996.3MB, time=664.61 memory used=27664.7MB, alloc=2020.3MB, time=693.79 memory used=28298.3MB, alloc=2044.3MB, time=708.27 memory used=28855.0MB, alloc=2068.3MB, time=721.12 memory used=29776.3MB, alloc=2092.3MB, time=738.33 memory used=30482.4MB, alloc=2116.3MB, time=752.61 memory used=31030.2MB, alloc=2140.3MB, time=764.75 memory used=31895.8MB, alloc=2164.3MB, time=781.95 memory used=32800.1MB, alloc=2188.3MB, time=800.93 memory used=33309.4MB, alloc=2212.3MB, time=812.72 memory used=33897.1MB, alloc=2236.3MB, time=824.57 memory used=34674.3MB, alloc=2260.3MB, time=839.56 memory used=35540.8MB, alloc=2284.3MB, time=857.35 memory used=36559.6MB, alloc=2308.3MB, time=880.65 memory used=37465.7MB, alloc=2332.3MB, time=902.10 memory used=38489.5MB, alloc=2356.3MB, time=927.11 memory used=39756.5MB, alloc=2380.3MB, time=950.01 memory used=40867.8MB, alloc=2404.3MB, time=981.94 memory used=41912.8MB, alloc=2428.3MB, time=1016.64 memory used=42990.2MB, alloc=2452.3MB, time=1054.50 memory used=43959.6MB, alloc=2476.3MB, time=1088.69 memory used=45049.5MB, alloc=2500.3MB, time=1122.12 memory used=45966.2MB, alloc=2524.3MB, time=1153.78 memory used=46958.1MB, alloc=2548.3MB, time=1185.36 memory used=47932.2MB, alloc=2572.3MB, time=1215.54 |\^/| 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(); 1428458852 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 2 3 2 F := [8 x y - 3 y - 9 z, 7 y z, -4 x y + 6 z - 6 z ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 G := [-5 x z + 13 y z + 4 x, -3 - y, -9 x y + 8 y] > Problem := [F,G]; 2 3 2 2 3 2 Problem := [[8 x y - 3 y - 9 z, 7 y z, -4 x y + 6 z - 6 z ], 2 2 [-5 x z + 13 y z + 4 x, -3 - y, -9 x y + 8 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.19 memory used=26.2MB, alloc=32.3MB, time=0.51 memory used=47.2MB, alloc=32.3MB, time=0.81 memory used=65.3MB, alloc=56.3MB, time=1.09 memory used=104.5MB, alloc=60.3MB, time=1.66 memory used=140.9MB, alloc=60.3MB, time=1.98 memory used=171.9MB, alloc=60.3MB, time=2.26 memory used=213.7MB, alloc=60.3MB, time=2.74 memory used=255.5MB, alloc=60.3MB, time=3.22 memory used=290.7MB, alloc=84.3MB, time=3.73 memory used=353.5MB, alloc=92.3MB, time=4.66 memory used=414.2MB, alloc=92.3MB, time=5.33 memory used=487.1MB, alloc=92.3MB, time=6.07 memory used=559.6MB, alloc=92.3MB, time=6.91 memory used=625.0MB, alloc=116.3MB, time=7.71 memory used=689.2MB, alloc=372.3MB, time=8.57 memory used=777.1MB, alloc=396.3MB, time=9.70 memory used=886.2MB, alloc=396.3MB, time=11.06 memory used=991.7MB, alloc=396.3MB, time=12.49 memory used=1105.3MB, alloc=396.3MB, time=13.57 memory used=1221.4MB, alloc=420.3MB, time=15.23 memory used=1348.9MB, alloc=420.3MB, time=16.11 memory used=1456.4MB, alloc=420.3MB, time=16.70 memory used=1561.0MB, alloc=420.3MB, time=17.14 memory used=1691.0MB, alloc=420.3MB, time=18.80 memory used=1823.6MB, alloc=444.3MB, time=20.88 memory used=1964.1MB, alloc=468.3MB, time=23.13 memory used=2124.2MB, alloc=492.3MB, time=25.61 memory used=2302.0MB, alloc=516.3MB, time=28.39 memory used=2494.7MB, alloc=540.3MB, time=31.66 memory used=2703.8MB, alloc=564.3MB, time=35.05 memory used=2942.7MB, alloc=588.3MB, time=38.22 memory used=3180.0MB, alloc=612.3MB, time=42.94 memory used=3376.1MB, alloc=636.3MB, time=49.38 memory used=3578.5MB, alloc=660.3MB, time=56.55 memory used=3790.0MB, alloc=684.3MB, time=64.53 memory used=4007.8MB, alloc=708.3MB, time=73.67 memory used=4247.5MB, alloc=732.3MB, time=83.82 memory used=4511.2MB, alloc=756.3MB, time=95.05 memory used=4798.9MB, alloc=780.3MB, time=107.20 memory used=5110.4MB, alloc=804.3MB, time=120.21 memory used=5446.0MB, alloc=828.3MB, time=134.26 memory used=5805.4MB, alloc=828.3MB, time=149.26 memory used=6164.9MB, alloc=828.3MB, time=164.12 memory used=6524.3MB, alloc=852.3MB, time=179.02 memory used=6907.7MB, alloc=852.3MB, time=194.68 memory used=7291.1MB, alloc=876.3MB, time=210.37 memory used=7698.3MB, alloc=876.3MB, time=227.12 memory used=8105.7MB, alloc=900.3MB, time=243.77 memory used=8537.0MB, alloc=924.3MB, time=261.29 N1 := 13793 > GB := Basis(F, plex(op(vars))); 2 5 3 GB := [y x, y , y + 3 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 717 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 2 2 3 2 H := [-3 y + 8 y x - 9 z, 7 z y , -4 x y + 6 z - 6 z , 2 2 -5 x z + 13 y z + 4 x, -3 - y, -9 x y + 8 y] > J:=[op(GB),op(G)]; 2 5 3 2 2 J := [y x, y , y + 3 z, -5 x z + 13 y z + 4 x, -3 - y, -9 x y + 8 y] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 14, 16, 3, 2, 3, 3, 2/3, 1, 2/3, 5/16, 1/2, 3/8, 6, 11, 18, 5, 2, 5, 2, 1/2, 1, 1/3, 4/13, 7/13, 3/13, 3, -2, -2] > save(F, G, cat("ranSet/33", convert(F, string),".txt")); > quit memory used=9008.3MB, alloc=924.3MB, time=277.63 |\^/| 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(); 1428459162 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; F := [ 2 2 2 2 2 3 15 y z - 11 x y + 18 y , -9 x y z + 6 x z - 6 y z, -x z - 2 y - 4 x z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 G := [6 x y z - x y - 13 y, -9 x z + 3 x z + y z, -9 x y z - 4 z ] > Problem := [F,G]; Problem := [[ 2 2 2 2 2 3 15 y z - 11 x y + 18 y , -9 x y z + 6 x z - 6 y z, -x z - 2 y - 4 x z] 2 2 2 2 , [6 x y z - x y - 13 y, -9 x z + 3 x z + y z, -9 x y z - 4 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.8MB, alloc=32.3MB, time=0.49 memory used=47.5MB, alloc=32.3MB, time=0.78 memory used=65.1MB, alloc=56.3MB, time=1.05 memory used=104.4MB, alloc=60.3MB, time=1.61 memory used=142.0MB, alloc=84.3MB, time=2.17 memory used=201.2MB, alloc=92.3MB, time=3.04 memory used=259.9MB, alloc=116.3MB, time=3.99 memory used=338.9MB, alloc=116.3MB, time=5.20 memory used=416.4MB, alloc=140.3MB, time=6.47 memory used=490.8MB, alloc=140.3MB, time=7.57 memory used=561.3MB, alloc=396.3MB, time=8.61 memory used=663.9MB, alloc=420.3MB, time=10.24 memory used=787.7MB, alloc=444.3MB, time=12.16 memory used=933.2MB, alloc=468.3MB, time=14.70 memory used=1081.8MB, alloc=492.3MB, time=17.34 memory used=1229.3MB, alloc=516.3MB, time=20.06 memory used=1380.9MB, alloc=516.3MB, time=23.02 memory used=1508.0MB, alloc=540.3MB, time=25.33 memory used=1615.7MB, alloc=540.3MB, time=27.52 memory used=1717.7MB, alloc=540.3MB, time=29.51 memory used=1820.5MB, alloc=540.3MB, time=31.66 memory used=1909.4MB, alloc=540.3MB, time=33.68 memory used=1983.9MB, alloc=540.3MB, time=35.28 memory used=2061.5MB, alloc=564.3MB, time=36.99 memory used=2132.8MB, alloc=564.3MB, time=38.80 memory used=2210.9MB, alloc=564.3MB, time=40.61 memory used=2273.9MB, alloc=564.3MB, time=42.17 memory used=2324.1MB, alloc=564.3MB, time=43.50 memory used=2560.2MB, alloc=588.3MB, time=48.42 memory used=2813.1MB, alloc=612.3MB, time=54.38 memory used=2996.2MB, alloc=636.3MB, time=58.10 memory used=3163.8MB, alloc=660.3MB, time=61.44 memory used=3351.1MB, alloc=684.3MB, time=65.71 memory used=3533.2MB, alloc=708.3MB, time=69.93 memory used=3697.3MB, alloc=732.3MB, time=74.32 memory used=3844.4MB, alloc=732.3MB, time=78.27 memory used=3948.5MB, alloc=732.3MB, time=80.88 memory used=4054.8MB, alloc=732.3MB, time=83.11 memory used=4180.4MB, alloc=732.3MB, time=86.76 memory used=4560.6MB, alloc=756.3MB, time=94.67 memory used=4953.2MB, alloc=780.3MB, time=105.40 memory used=5379.3MB, alloc=804.3MB, time=115.41 memory used=5817.0MB, alloc=828.3MB, time=126.48 memory used=6234.5MB, alloc=852.3MB, time=137.36 memory used=6571.4MB, alloc=876.3MB, time=145.92 memory used=6882.1MB, alloc=900.3MB, time=153.54 memory used=7161.8MB, alloc=924.3MB, time=161.11 memory used=7432.8MB, alloc=948.3MB, time=168.85 memory used=7624.3MB, alloc=972.3MB, time=174.28 memory used=7874.9MB, alloc=996.3MB, time=182.19 memory used=8473.3MB, alloc=1020.3MB, time=197.12 memory used=9082.8MB, alloc=1044.3MB, time=213.12 memory used=9695.7MB, alloc=1068.3MB, time=230.09 memory used=10301.4MB, alloc=1092.3MB, time=249.07 memory used=10947.5MB, alloc=1116.3MB, time=268.09 memory used=11608.8MB, alloc=1140.3MB, time=288.46 memory used=12282.5MB, alloc=1164.3MB, time=309.32 memory used=12935.3MB, alloc=1188.3MB, time=331.96 memory used=13611.8MB, alloc=1212.3MB, time=354.25 memory used=14198.1MB, alloc=1236.3MB, time=372.24 memory used=14863.6MB, alloc=1260.3MB, time=397.55 memory used=15344.8MB, alloc=1284.3MB, time=414.21 memory used=15851.0MB, alloc=1308.3MB, time=432.56 memory used=16385.0MB, alloc=1332.3MB, time=450.69 memory used=16729.1MB, alloc=1356.3MB, time=463.86 memory used=17173.9MB, alloc=1380.3MB, time=481.32 memory used=17478.5MB, alloc=1404.3MB, time=494.10 memory used=17783.8MB, alloc=1428.3MB, time=506.42 memory used=18093.9MB, alloc=1452.3MB, time=518.86 memory used=18336.3MB, alloc=1476.3MB, time=530.37 memory used=18704.2MB, alloc=1500.3MB, time=546.33 memory used=18831.6MB, alloc=1524.3MB, time=556.34 memory used=19050.5MB, alloc=1548.3MB, time=567.60 memory used=19300.9MB, alloc=1572.3MB, time=579.55 memory used=19504.6MB, alloc=1596.3MB, time=591.21 memory used=19650.0MB, alloc=1620.3MB, time=600.90 memory used=19851.9MB, alloc=1644.3MB, time=612.56 memory used=19961.3MB, alloc=1668.3MB, time=620.98 memory used=20047.8MB, alloc=1692.3MB, time=629.84 memory used=20183.0MB, alloc=1716.3MB, time=639.52 memory used=20356.2MB, alloc=1740.3MB, time=650.55 memory used=20450.6MB, alloc=1764.3MB, time=658.17 memory used=20560.9MB, alloc=1788.3MB, time=668.59 memory used=20641.7MB, alloc=2092.3MB, time=682.89 memory used=21879.8MB, alloc=2116.3MB, time=723.37 memory used=23100.4MB, alloc=2140.3MB, time=762.45 memory used=24316.6MB, alloc=2164.3MB, time=800.54 memory used=25528.6MB, alloc=2188.3MB, time=838.26 memory used=26758.0MB, alloc=2212.3MB, time=878.52 memory used=27970.9MB, alloc=2236.3MB, time=917.71 memory used=29028.0MB, alloc=2260.3MB, time=949.17 memory used=29986.8MB, alloc=2284.3MB, time=979.47 memory used=30892.9MB, alloc=2308.3MB, time=1006.12 memory used=31583.7MB, alloc=2332.3MB, time=1030.97 memory used=32229.1MB, alloc=2356.3MB, time=1055.58 memory used=32835.6MB, alloc=2380.3MB, time=1080.10 |\^/| 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(); 1428460362 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 2 2 3 F := [-7 x y - 14 z + 8 x z, 7 x - 2 x y + 6 z, -x y + y z - 9 z ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 2 3 2 G := [14 y + 20 y z - 3, -10 x z - 9 y z - 6 z, 5 x - 4 x z - 3 z ] > Problem := [F,G]; 2 3 2 2 2 3 Problem := [[-7 x y - 14 z + 8 x z, 7 x - 2 x y + 6 z, -x y + y z - 9 z ], 3 2 2 2 3 2 [14 y + 20 y z - 3, -10 x z - 9 y z - 6 z, 5 x - 4 x z - 3 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.6MB, alloc=32.3MB, time=0.52 memory used=46.9MB, alloc=32.3MB, time=0.81 memory used=66.4MB, alloc=56.3MB, time=1.12 memory used=107.6MB, alloc=68.3MB, time=1.76 memory used=149.5MB, alloc=92.3MB, time=2.34 memory used=216.1MB, alloc=92.3MB, time=3.31 memory used=280.8MB, alloc=116.3MB, time=4.30 memory used=350.0MB, alloc=116.3MB, time=5.30 memory used=418.3MB, alloc=372.3MB, time=6.33 memory used=506.4MB, alloc=396.3MB, time=7.63 memory used=621.7MB, alloc=420.3MB, time=9.09 memory used=756.7MB, alloc=444.3MB, time=11.14 memory used=880.9MB, alloc=444.3MB, time=13.10 memory used=997.7MB, alloc=468.3MB, time=14.89 memory used=1103.4MB, alloc=468.3MB, time=16.40 memory used=1209.7MB, alloc=468.3MB, time=18.01 memory used=1308.6MB, alloc=492.3MB, time=19.48 memory used=1414.5MB, alloc=492.3MB, time=20.92 memory used=1526.0MB, alloc=492.3MB, time=22.22 memory used=1679.2MB, alloc=492.3MB, time=23.89 memory used=1774.8MB, alloc=492.3MB, time=25.25 memory used=1861.8MB, alloc=492.3MB, time=26.79 memory used=1960.0MB, alloc=492.3MB, time=28.01 memory used=2063.3MB, alloc=492.3MB, time=29.21 memory used=2155.3MB, alloc=492.3MB, time=30.44 memory used=2233.3MB, alloc=516.3MB, time=31.72 memory used=2307.2MB, alloc=516.3MB, time=32.87 memory used=2384.1MB, alloc=516.3MB, time=34.12 memory used=2463.8MB, alloc=516.3MB, time=35.01 memory used=2591.4MB, alloc=516.3MB, time=36.29 memory used=2686.3MB, alloc=516.3MB, time=36.79 memory used=2766.2MB, alloc=516.3MB, time=37.97 memory used=2833.0MB, alloc=516.3MB, time=39.36 memory used=2886.9MB, alloc=516.3MB, time=40.43 memory used=2951.0MB, alloc=516.3MB, time=41.84 memory used=2994.5MB, alloc=516.3MB, time=42.86 memory used=3037.0MB, alloc=516.3MB, time=43.81 memory used=3237.7MB, alloc=540.3MB, time=47.06 memory used=3428.9MB, alloc=564.3MB, time=49.58 memory used=3617.1MB, alloc=588.3MB, time=53.00 memory used=3796.1MB, alloc=612.3MB, time=55.60 memory used=3961.1MB, alloc=636.3MB, time=58.56 memory used=4110.5MB, alloc=660.3MB, time=61.30 memory used=4266.8MB, alloc=660.3MB, time=64.34 memory used=4378.6MB, alloc=660.3MB, time=66.47 memory used=4525.5MB, alloc=684.3MB, time=69.32 memory used=4624.1MB, alloc=684.3MB, time=71.23 memory used=4706.8MB, alloc=684.3MB, time=72.94 memory used=4812.4MB, alloc=684.3MB, time=75.17 memory used=5174.1MB, alloc=708.3MB, time=80.32 memory used=5450.6MB, alloc=732.3MB, time=83.63 memory used=5632.5MB, alloc=756.3MB, time=84.89 memory used=5854.2MB, alloc=756.3MB, time=90.33 memory used=6050.7MB, alloc=756.3MB, time=91.58 memory used=6283.8MB, alloc=756.3MB, time=97.19 memory used=6464.4MB, alloc=756.3MB, time=98.29 memory used=6682.1MB, alloc=756.3MB, time=99.74 memory used=6904.1MB, alloc=756.3MB, time=105.22 memory used=7201.0MB, alloc=756.3MB, time=108.06 memory used=7535.0MB, alloc=756.3MB, time=115.13 memory used=7887.5MB, alloc=780.3MB, time=119.72 memory used=8260.8MB, alloc=804.3MB, time=126.92 memory used=8564.2MB, alloc=828.3MB, time=132.66 memory used=8877.4MB, alloc=852.3MB, time=138.47 memory used=9243.4MB, alloc=876.3MB, time=147.36 memory used=9525.8MB, alloc=900.3MB, time=158.81 memory used=9862.1MB, alloc=924.3MB, time=165.76 memory used=10150.4MB, alloc=924.3MB, time=171.18 memory used=10409.9MB, alloc=948.3MB, time=176.33 memory used=10784.8MB, alloc=948.3MB, time=188.18 memory used=11187.6MB, alloc=948.3MB, time=193.13 memory used=11610.8MB, alloc=948.3MB, time=199.64 memory used=11904.8MB, alloc=972.3MB, time=205.95 memory used=12143.0MB, alloc=972.3MB, time=211.60 memory used=12333.4MB, alloc=996.3MB, time=215.34 memory used=12563.7MB, alloc=996.3MB, time=220.39 memory used=12740.2MB, alloc=1252.3MB, time=224.38 memory used=13159.7MB, alloc=1276.3MB, time=230.09 memory used=13468.0MB, alloc=1276.3MB, time=232.45 memory used=13803.5MB, alloc=1276.3MB, time=235.17 memory used=14088.2MB, alloc=1276.3MB, time=237.41 memory used=14449.1MB, alloc=1276.3MB, time=256.35 memory used=14722.5MB, alloc=1276.3MB, time=258.54 memory used=15068.1MB, alloc=1276.3MB, time=261.14 memory used=15347.0MB, alloc=1276.3MB, time=263.47 memory used=15687.6MB, alloc=1276.3MB, time=266.26 memory used=15975.2MB, alloc=1276.3MB, time=268.54 memory used=16329.6MB, alloc=1276.3MB, time=287.32 memory used=16598.1MB, alloc=1276.3MB, time=289.44 memory used=16944.3MB, alloc=1276.3MB, time=292.11 memory used=17229.1MB, alloc=1276.3MB, time=294.43 memory used=17582.2MB, alloc=1276.3MB, time=297.16 memory used=17861.1MB, alloc=1276.3MB, time=299.39 memory used=18211.4MB, alloc=1276.3MB, time=318.48 memory used=18473.1MB, alloc=1276.3MB, time=320.62 memory used=18982.7MB, alloc=1276.3MB, time=326.18 memory used=19592.5MB, alloc=1300.3MB, time=335.46 memory used=19962.2MB, alloc=1300.3MB, time=354.21 memory used=20221.7MB, alloc=1300.3MB, time=356.31 memory used=20822.7MB, alloc=1300.3MB, time=364.33 memory used=21173.6MB, alloc=1300.3MB, time=367.27 memory used=21466.7MB, alloc=1300.3MB, time=369.65 memory used=21790.6MB, alloc=1300.3MB, time=372.44 memory used=22156.3MB, alloc=1300.3MB, time=391.58 memory used=22457.2MB, alloc=1300.3MB, time=393.94 memory used=22728.3MB, alloc=1300.3MB, time=396.09 memory used=23077.2MB, alloc=1300.3MB, time=398.90 memory used=23414.1MB, alloc=1300.3MB, time=401.59 memory used=23701.3MB, alloc=1300.3MB, time=403.98 memory used=24071.0MB, alloc=1300.3MB, time=422.81 memory used=24349.0MB, alloc=1300.3MB, time=425.04 memory used=24688.5MB, alloc=1300.3MB, time=427.80 memory used=24978.8MB, alloc=1300.3MB, time=430.35 memory used=25325.1MB, alloc=1300.3MB, time=433.19 memory used=25619.7MB, alloc=1300.3MB, time=435.59 memory used=25981.1MB, alloc=1300.3MB, time=454.75 memory used=26253.5MB, alloc=1300.3MB, time=457.07 memory used=26771.6MB, alloc=1300.3MB, time=462.50 memory used=27222.6MB, alloc=1300.3MB, time=482.68 memory used=27494.1MB, alloc=1324.3MB, time=484.90 memory used=28055.8MB, alloc=1324.3MB, time=491.95 memory used=28698.0MB, alloc=1348.3MB, time=505.15 memory used=29307.9MB, alloc=1372.3MB, time=519.22 memory used=29850.1MB, alloc=1396.3MB, time=526.75 memory used=30235.4MB, alloc=1420.3MB, time=530.70 memory used=30635.2MB, alloc=1444.3MB, time=553.36 memory used=31031.0MB, alloc=1468.3MB, time=556.71 memory used=31451.4MB, alloc=1492.3MB, time=565.43 memory used=31923.2MB, alloc=1492.3MB, time=583.47 memory used=32360.2MB, alloc=1492.3MB, time=587.26 memory used=32989.4MB, alloc=1492.3MB, time=612.77 memory used=33565.4MB, alloc=1492.3MB, time=635.41 memory used=34331.0MB, alloc=1516.3MB, time=648.11 memory used=34782.0MB, alloc=1540.3MB, time=653.55 memory used=35257.5MB, alloc=1540.3MB, time=658.89 memory used=35697.1MB, alloc=1540.3MB, time=664.81 memory used=36138.0MB, alloc=1540.3MB, time=669.59 memory used=36497.2MB, alloc=1564.3MB, time=673.11 memory used=36885.3MB, alloc=1564.3MB, time=676.55 memory used=37294.6MB, alloc=1564.3MB, time=680.71 memory used=37686.3MB, alloc=1564.3MB, time=684.55 memory used=38120.3MB, alloc=1564.3MB, time=688.11 memory used=38446.0MB, alloc=1564.3MB, time=691.33 memory used=38918.4MB, alloc=1564.3MB, time=753.70 memory used=39305.0MB, alloc=1564.3MB, time=757.19 memory used=39660.5MB, alloc=1564.3MB, time=760.62 memory used=40265.3MB, alloc=1579.8MB, time=764.48 memory used=40866.3MB, alloc=1579.8MB, time=769.55 memory used=41265.3MB, alloc=1579.8MB, time=773.45 memory used=41626.3MB, alloc=1579.8MB, time=776.73 memory used=42047.9MB, alloc=1579.8MB, time=781.01 memory used=42437.9MB, alloc=1579.8MB, time=784.65 memory used=42878.2MB, alloc=1579.8MB, time=788.30 memory used=43190.2MB, alloc=1579.8MB, time=791.49 memory used=43665.8MB, alloc=1579.8MB, time=853.67 memory used=44047.1MB, alloc=1579.8MB, time=857.21 memory used=44419.0MB, alloc=1579.8MB, time=860.38 memory used=44959.6MB, alloc=1579.8MB, time=863.73 memory used=45568.8MB, alloc=1579.8MB, time=868.71 memory used=45954.2MB, alloc=1579.8MB, time=872.33 memory used=46327.4MB, alloc=1579.8MB, time=875.59 memory used=46742.4MB, alloc=1579.8MB, time=879.89 memory used=47135.1MB, alloc=1579.8MB, time=883.53 memory used=47582.4MB, alloc=1579.8MB, time=887.10 memory used=47891.4MB, alloc=1579.8MB, time=890.34 memory used=48362.6MB, alloc=1579.8MB, time=952.60 memory used=48746.9MB, alloc=1579.8MB, time=955.96 memory used=49113.7MB, alloc=1579.8MB, time=959.12 memory used=49677.0MB, alloc=1579.8MB, time=962.49 memory used=50510.9MB, alloc=1579.8MB, time=971.27 memory used=51111.0MB, alloc=1579.8MB, time=1034.81 memory used=51473.7MB, alloc=1579.8MB, time=1037.87 memory used=51858.5MB, alloc=1579.8MB, time=1040.89 memory used=52332.1MB, alloc=1579.8MB, time=1044.15 memory used=53183.7MB, alloc=1603.8MB, time=1053.32 memory used=53624.1MB, alloc=1603.8MB, time=1057.13 memory used=54049.7MB, alloc=1603.8MB, time=1060.74 memory used=54510.3MB, alloc=1603.8MB, time=1079.88 memory used=55002.9MB, alloc=1603.8MB, time=1083.68 memory used=55430.0MB, alloc=1603.8MB, time=1087.45 memory used=55872.9MB, alloc=1603.8MB, time=1091.16 memory used=56343.4MB, alloc=1603.8MB, time=1110.64 memory used=56825.2MB, alloc=1603.8MB, time=1114.38 memory used=57239.2MB, alloc=1603.8MB, time=1117.90 memory used=57690.7MB, alloc=1603.8MB, time=1121.85 memory used=58172.6MB, alloc=1603.8MB, time=1140.68 memory used=58727.9MB, alloc=1603.8MB, time=1146.00 memory used=59427.3MB, alloc=1603.8MB, time=1168.18 memory used=60130.8MB, alloc=1603.8MB, time=1176.42 memory used=60782.1MB, alloc=1627.8MB, time=1191.49 memory used=61332.4MB, alloc=1651.8MB, time=1204.24 memory used=61898.7MB, alloc=1675.8MB, time=1218.05 memory used=62519.8MB, alloc=1699.8MB, time=1226.70 memory used=63112.9MB, alloc=1723.8MB, time=1242.62 memory used=63607.2MB, alloc=1747.8MB, time=1256.27 memory used=64064.7MB, alloc=1771.8MB, time=1268.72 memory used=64487.4MB, alloc=1795.8MB, time=1279.81 |\^/| 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(); 1428461562 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 3 2 2 2 F := [2 x y z + 6 z - 6 x , 9 x - 4 x z - 5 x, 5 x y z - 4 x + 3 z ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 G := [3 x y + 9 x y z - 2 y , -6 x z + 5 x y - 7, 2 y z + 5 x - 3 z] > Problem := [F,G]; Problem := [ 3 2 3 2 2 2 [2 x y z + 6 z - 6 x , 9 x - 4 x z - 5 x, 5 x y z - 4 x + 3 z ], 2 2 2 2 [3 x y + 9 x y z - 2 y , -6 x z + 5 x y - 7, 2 y z + 5 x - 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=0.18 memory used=26.5MB, alloc=32.3MB, time=0.50 memory used=47.5MB, alloc=32.3MB, time=0.81 memory used=67.7MB, alloc=56.3MB, time=1.12 memory used=109.3MB, alloc=60.3MB, time=1.73 memory used=148.8MB, alloc=84.3MB, time=2.33 memory used=211.0MB, alloc=92.3MB, time=3.30 memory used=270.7MB, alloc=116.3MB, time=4.22 memory used=352.4MB, alloc=116.3MB, time=5.51 memory used=429.3MB, alloc=396.3MB, time=6.72 memory used=537.0MB, alloc=420.3MB, time=8.54 memory used=671.0MB, alloc=444.3MB, time=10.82 memory used=831.4MB, alloc=444.3MB, time=13.48 memory used=985.1MB, alloc=468.3MB, time=16.09 memory used=1112.2MB, alloc=492.3MB, time=18.22 memory used=1263.8MB, alloc=492.3MB, time=21.10 memory used=1402.9MB, alloc=492.3MB, time=23.68 memory used=1531.2MB, alloc=516.3MB, time=26.12 memory used=1644.3MB, alloc=516.3MB, time=28.16 memory used=1753.4MB, alloc=516.3MB, time=30.44 memory used=1869.3MB, alloc=516.3MB, time=32.84 memory used=1959.2MB, alloc=516.3MB, time=34.68 memory used=2056.4MB, alloc=516.3MB, time=36.81 memory used=2141.4MB, alloc=516.3MB, time=38.56 memory used=2216.8MB, alloc=540.3MB, time=40.23 memory used=2302.5MB, alloc=540.3MB, time=42.24 memory used=2366.2MB, alloc=540.3MB, time=43.79 memory used=2429.9MB, alloc=540.3MB, time=45.23 memory used=2499.4MB, alloc=540.3MB, time=46.85 memory used=2546.7MB, alloc=540.3MB, time=48.05 memory used=2604.9MB, alloc=540.3MB, time=49.63 memory used=2823.4MB, alloc=564.3MB, time=53.86 memory used=3071.1MB, alloc=588.3MB, time=58.62 memory used=3308.6MB, alloc=612.3MB, time=63.62 memory used=3513.8MB, alloc=636.3MB, time=67.78 memory used=3680.5MB, alloc=660.3MB, time=71.35 memory used=3865.7MB, alloc=684.3MB, time=75.84 memory used=4070.2MB, alloc=708.3MB, time=81.35 memory used=4242.3MB, alloc=708.3MB, time=85.82 memory used=4369.9MB, alloc=732.3MB, time=88.51 memory used=4543.0MB, alloc=732.3MB, time=92.79 memory used=4651.9MB, alloc=732.3MB, time=95.67 memory used=4784.9MB, alloc=732.3MB, time=99.84 memory used=4931.1MB, alloc=732.3MB, time=104.32 memory used=5017.5MB, alloc=732.3MB, time=107.35 memory used=5414.4MB, alloc=756.3MB, time=117.19 memory used=5843.1MB, alloc=780.3MB, time=126.39 memory used=6275.5MB, alloc=804.3MB, time=137.42 memory used=6699.9MB, alloc=828.3MB, time=147.05 memory used=7137.7MB, alloc=852.3MB, time=160.98 memory used=7507.2MB, alloc=876.3MB, time=170.66 memory used=7886.6MB, alloc=900.3MB, time=179.40 memory used=8331.2MB, alloc=924.3MB, time=194.76 memory used=8597.0MB, alloc=948.3MB, time=200.55 memory used=8976.7MB, alloc=972.3MB, time=212.66 memory used=9254.0MB, alloc=996.3MB, time=220.17 memory used=9515.8MB, alloc=1020.3MB, time=228.73 memory used=9767.1MB, alloc=1044.3MB, time=237.22 memory used=10462.4MB, alloc=1068.3MB, time=253.47 memory used=11151.0MB, alloc=1092.3MB, time=272.65 memory used=11851.7MB, alloc=1116.3MB, time=292.82 memory used=12572.3MB, alloc=1140.3MB, time=314.80 memory used=13317.3MB, alloc=1164.3MB, time=335.57 memory used=14077.9MB, alloc=1188.3MB, time=356.25 memory used=14810.6MB, alloc=1212.3MB, time=379.88 memory used=15586.4MB, alloc=1236.3MB, time=403.44 memory used=16304.6MB, alloc=1260.3MB, time=427.17 memory used=16963.7MB, alloc=1284.3MB, time=446.05 memory used=17520.2MB, alloc=1308.3MB, time=463.15 memory used=18235.2MB, alloc=1332.3MB, time=488.18 memory used=18839.4MB, alloc=1356.3MB, time=506.31 memory used=19385.5MB, alloc=1380.3MB, time=523.46 memory used=19907.9MB, alloc=1404.3MB, time=542.05 memory used=20537.9MB, alloc=1428.3MB, time=567.40 memory used=21014.0MB, alloc=1452.3MB, time=586.03 memory used=21419.1MB, alloc=1476.3MB, time=601.61 memory used=21832.0MB, alloc=1500.3MB, time=617.83 memory used=22107.0MB, alloc=1524.3MB, time=630.55 memory used=22503.8MB, alloc=1548.3MB, time=648.11 memory used=22869.4MB, alloc=1572.3MB, time=664.94 memory used=23201.4MB, alloc=1596.3MB, time=681.77 memory used=23503.6MB, alloc=1620.3MB, time=694.10 memory used=23820.6MB, alloc=1644.3MB, time=708.32 memory used=24059.8MB, alloc=1668.3MB, time=719.92 memory used=24167.8MB, alloc=1692.3MB, time=728.25 memory used=24427.3MB, alloc=1716.3MB, time=743.83 memory used=24634.5MB, alloc=1740.3MB, time=757.17 memory used=24864.7MB, alloc=1764.3MB, time=769.90 memory used=25030.4MB, alloc=1788.3MB, time=778.38 memory used=25276.4MB, alloc=1812.3MB, time=792.48 memory used=25410.2MB, alloc=1836.3MB, time=801.89 memory used=25458.4MB, alloc=1836.3MB, time=808.14 memory used=25585.4MB, alloc=1860.3MB, time=817.64 memory used=25610.9MB, alloc=1860.3MB, time=824.31 memory used=25652.1MB, alloc=1860.3MB, time=830.92 memory used=25876.2MB, alloc=1860.3MB, time=845.19 memory used=25978.0MB, alloc=1860.3MB, time=854.49 memory used=26076.5MB, alloc=1860.3MB, time=862.98 memory used=26184.5MB, alloc=1860.3MB, time=871.29 memory used=26269.5MB, alloc=1860.3MB, time=879.10 memory used=26295.7MB, alloc=1860.3MB, time=885.63 memory used=26365.7MB, alloc=1860.3MB, time=894.31 memory used=26465.0MB, alloc=1860.3MB, time=904.92 memory used=26476.4MB, alloc=2116.3MB, time=918.41 memory used=27745.4MB, alloc=2140.3MB, time=967.41 memory used=29094.9MB, alloc=2164.3MB, time=1016.78 memory used=30461.1MB, alloc=2188.3MB, time=1067.11 memory used=31813.5MB, alloc=2212.3MB, time=1120.76 |\^/| 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(); 1428462763 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 3 2 2 F := [-17 y z + 18 x + 10 z, -5 x z + 4 y - 5 z, 6 y + 6 x - 4 y ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 G := [-18 y + 16 x z + 16 y z, -2 x z + 2 x + 6 x z, -10 x] > Problem := [F,G]; Problem := [ 2 2 2 2 3 2 2 [-17 y z + 18 x + 10 z, -5 x z + 4 y - 5 z, 6 y + 6 x - 4 y ], 3 2 2 [-18 y + 16 x z + 16 y z, -2 x z + 2 x + 6 x 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=4.4MB, alloc=32.3MB, time=0.20 memory used=26.5MB, alloc=32.3MB, time=0.52 memory used=45.7MB, alloc=56.3MB, time=0.82 memory used=87.0MB, alloc=60.3MB, time=1.38 memory used=127.2MB, alloc=60.3MB, time=1.97 memory used=168.2MB, alloc=60.3MB, time=2.50 memory used=207.5MB, alloc=84.3MB, time=3.07 memory used=242.3MB, alloc=84.3MB, time=3.62 memory used=306.6MB, alloc=92.3MB, time=4.53 memory used=367.1MB, alloc=116.3MB, time=5.28 memory used=428.3MB, alloc=116.3MB, time=6.02 memory used=503.7MB, alloc=372.3MB, time=6.94 memory used=600.2MB, alloc=396.3MB, time=8.13 memory used=713.6MB, alloc=420.3MB, time=9.73 memory used=834.2MB, alloc=420.3MB, time=10.92 memory used=931.6MB, alloc=420.3MB, time=11.99 memory used=994.3MB, alloc=420.3MB, time=12.24 memory used=1072.7MB, alloc=420.3MB, time=12.60 memory used=1152.9MB, alloc=420.3MB, time=12.99 memory used=1247.2MB, alloc=420.3MB, time=17.44 memory used=1310.9MB, alloc=420.3MB, time=17.68 memory used=1363.8MB, alloc=420.3MB, time=17.89 memory used=1430.0MB, alloc=420.3MB, time=18.11 memory used=1507.5MB, alloc=420.3MB, time=18.50 memory used=1588.3MB, alloc=420.3MB, time=18.86 memory used=1682.6MB, alloc=420.3MB, time=23.04 memory used=1746.6MB, alloc=420.3MB, time=23.29 memory used=1798.7MB, alloc=420.3MB, time=23.49 memory used=1865.6MB, alloc=420.3MB, time=23.72 memory used=2001.6MB, alloc=420.3MB, time=24.98 memory used=2153.1MB, alloc=444.3MB, time=26.74 memory used=2282.4MB, alloc=444.3MB, time=28.40 memory used=2388.1MB, alloc=444.3MB, time=29.86 memory used=2495.0MB, alloc=468.3MB, time=31.35 memory used=2603.6MB, alloc=468.3MB, time=33.03 memory used=2695.1MB, alloc=468.3MB, time=34.45 memory used=2783.4MB, alloc=492.3MB, time=35.84 memory used=2870.6MB, alloc=492.3MB, time=37.38 memory used=2946.6MB, alloc=492.3MB, time=38.76 memory used=3026.0MB, alloc=492.3MB, time=40.13 memory used=3092.2MB, alloc=492.3MB, time=41.29 memory used=3151.8MB, alloc=492.3MB, time=42.19 memory used=3274.2MB, alloc=492.3MB, time=43.41 memory used=3368.7MB, alloc=492.3MB, time=44.34 memory used=3446.8MB, alloc=492.3MB, time=45.36 memory used=3526.6MB, alloc=492.3MB, time=46.45 memory used=3578.4MB, alloc=492.3MB, time=47.45 memory used=3628.4MB, alloc=492.3MB, time=48.53 memory used=3730.8MB, alloc=516.3MB, time=49.35 memory used=3847.6MB, alloc=516.3MB, time=50.12 memory used=3929.7MB, alloc=516.3MB, time=50.64 memory used=4041.6MB, alloc=516.3MB, time=51.18 memory used=4118.6MB, alloc=516.3MB, time=51.64 memory used=4197.2MB, alloc=516.3MB, time=52.08 memory used=4288.8MB, alloc=516.3MB, time=52.54 memory used=4405.1MB, alloc=516.3MB, time=53.28 memory used=4488.2MB, alloc=516.3MB, time=53.81 memory used=4600.0MB, alloc=516.3MB, time=54.33 memory used=4677.1MB, alloc=516.3MB, time=54.79 memory used=4755.8MB, alloc=516.3MB, time=55.23 memory used=4847.4MB, alloc=516.3MB, time=55.69 memory used=4996.5MB, alloc=516.3MB, time=69.28 memory used=5100.3MB, alloc=516.3MB, time=69.82 memory used=5175.4MB, alloc=516.3MB, time=70.29 memory used=5264.2MB, alloc=516.3MB, time=70.78 memory used=5370.3MB, alloc=516.3MB, time=71.27 memory used=5599.5MB, alloc=516.3MB, time=72.19 memory used=5757.5MB, alloc=516.3MB, time=72.78 memory used=5947.5MB, alloc=516.3MB, time=73.40 memory used=6171.7MB, alloc=516.3MB, time=74.56 memory used=6259.2MB, alloc=516.3MB, time=75.11 memory used=6361.9MB, alloc=516.3MB, time=75.68 memory used=6451.8MB, alloc=516.3MB, time=76.19 memory used=6527.1MB, alloc=516.3MB, time=76.65 memory used=6614.6MB, alloc=516.3MB, time=77.15 memory used=6726.6MB, alloc=516.3MB, time=77.86 memory used=6815.1MB, alloc=516.3MB, time=78.39 memory used=6917.8MB, alloc=516.3MB, time=78.93 memory used=7008.9MB, alloc=516.3MB, time=79.39 memory used=7083.7MB, alloc=516.3MB, time=79.85 memory used=7170.6MB, alloc=516.3MB, time=80.28 memory used=7316.8MB, alloc=516.3MB, time=93.56 memory used=7413.9MB, alloc=516.3MB, time=94.08 memory used=7502.3MB, alloc=516.3MB, time=94.56 memory used=7586.2MB, alloc=516.3MB, time=95.02 memory used=7685.9MB, alloc=516.3MB, time=95.47 memory used=7804.1MB, alloc=516.3MB, time=95.94 memory used=7951.9MB, alloc=516.3MB, time=96.49 memory used=8109.7MB, alloc=516.3MB, time=97.05 memory used=8299.9MB, alloc=516.3MB, time=97.63 memory used=8477.0MB, alloc=516.3MB, time=98.66 memory used=8570.6MB, alloc=516.3MB, time=99.19 memory used=8665.8MB, alloc=516.3MB, time=99.68 memory used=8768.9MB, alloc=516.3MB, time=100.30 memory used=8867.2MB, alloc=516.3MB, time=100.82 memory used=8970.7MB, alloc=516.3MB, time=105.88 memory used=9080.7MB, alloc=516.3MB, time=106.62 memory used=9168.4MB, alloc=516.3MB, time=107.09 memory used=9261.5MB, alloc=516.3MB, time=107.56 memory used=9517.1MB, alloc=516.3MB, time=108.25 memory used=9673.5MB, alloc=516.3MB, time=109.30 memory used=9725.6MB, alloc=516.3MB, time=110.13 memory used=9938.4MB, alloc=516.3MB, time=112.83 memory used=10153.3MB, alloc=540.3MB, time=115.91 memory used=10359.6MB, alloc=564.3MB, time=118.12 memory used=10610.4MB, alloc=564.3MB, time=120.54 memory used=10828.9MB, alloc=588.3MB, time=123.63 memory used=11040.6MB, alloc=588.3MB, time=125.87 memory used=11249.4MB, alloc=612.3MB, time=128.78 memory used=11561.8MB, alloc=636.3MB, time=132.38 memory used=11804.8MB, alloc=636.3MB, time=136.11 memory used=12102.1MB, alloc=660.3MB, time=138.36 memory used=12412.7MB, alloc=660.3MB, time=140.42 memory used=12668.1MB, alloc=660.3MB, time=141.71 memory used=12948.7MB, alloc=660.3MB, time=142.89 memory used=13345.7MB, alloc=660.3MB, time=145.46 memory used=13571.6MB, alloc=684.3MB, time=148.80 memory used=13817.0MB, alloc=708.3MB, time=153.60 memory used=14095.7MB, alloc=732.3MB, time=158.83 memory used=14352.2MB, alloc=756.3MB, time=163.60 memory used=14622.1MB, alloc=780.3MB, time=168.69 memory used=14859.0MB, alloc=804.3MB, time=173.20 memory used=15080.7MB, alloc=828.3MB, time=177.62 memory used=15284.7MB, alloc=852.3MB, time=181.86 memory used=15494.2MB, alloc=876.3MB, time=186.24 memory used=15742.6MB, alloc=900.3MB, time=190.83 memory used=15981.0MB, alloc=924.3MB, time=195.41 memory used=16181.7MB, alloc=948.3MB, time=199.65 memory used=16412.9MB, alloc=972.3MB, time=204.09 memory used=16758.2MB, alloc=996.3MB, time=208.86 memory used=17337.8MB, alloc=1020.3MB, time=217.66 memory used=17937.6MB, alloc=1044.3MB, time=225.90 memory used=18534.6MB, alloc=1068.3MB, time=235.42 memory used=19162.5MB, alloc=1092.3MB, time=244.13 memory used=19757.0MB, alloc=1116.3MB, time=254.47 memory used=20325.6MB, alloc=1140.3MB, time=265.73 memory used=20837.4MB, alloc=1164.3MB, time=280.48 memory used=21258.2MB, alloc=1188.3MB, time=297.66 memory used=21679.2MB, alloc=1212.3MB, time=315.69 memory used=22104.9MB, alloc=1236.3MB, time=333.85 memory used=22538.7MB, alloc=1260.3MB, time=352.72 memory used=22982.2MB, alloc=1284.3MB, time=372.75 memory used=23437.0MB, alloc=1308.3MB, time=393.62 memory used=23904.1MB, alloc=1332.3MB, time=414.76 memory used=24383.3MB, alloc=1356.3MB, time=436.72 memory used=24875.7MB, alloc=1380.3MB, time=459.18 memory used=25381.8MB, alloc=1404.3MB, time=482.20 memory used=25902.2MB, alloc=1428.3MB, time=506.45 memory used=26436.5MB, alloc=1452.3MB, time=531.14 memory used=26985.6MB, alloc=1476.3MB, time=556.68 memory used=27549.7MB, alloc=1500.3MB, time=583.30 memory used=28128.5MB, alloc=1524.3MB, time=610.79 memory used=28723.2MB, alloc=1548.3MB, time=639.25 memory used=29334.1MB, alloc=1572.3MB, time=668.57 memory used=29952.7MB, alloc=1596.3MB, time=699.30 memory used=30595.1MB, alloc=1620.3MB, time=729.92 memory used=31261.5MB, alloc=1644.3MB, time=761.36 memory used=31951.9MB, alloc=1668.3MB, time=793.81 memory used=32666.2MB, alloc=1692.3MB, time=827.30 memory used=33404.4MB, alloc=1716.3MB, time=861.76 memory used=34166.6MB, alloc=1740.3MB, time=897.50 memory used=34952.7MB, alloc=1764.3MB, time=934.16 memory used=35762.8MB, alloc=1788.3MB, time=971.95 memory used=36596.7MB, alloc=1812.3MB, time=1010.72 |\^/| 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(); 1428463963 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 3 F := [8 x y z + 11 y z + 19 x , 7 y z + 3 y , -x - 3 x y z + 7 x y] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 3 3 3 2 G := [-10 x z + 10 y z + 20 x, -3 y + 10 x z + 3, 5 y - 5 z - 10 y ] > Problem := [F,G]; 2 2 2 2 3 Problem := [[8 x y z + 11 y z + 19 x , 7 y z + 3 y , -x - 3 x y z + 7 x y], 2 2 3 3 3 2 [-10 x z + 10 y z + 20 x, -3 y + 10 x z + 3, 5 y - 5 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=4.4MB, alloc=32.3MB, time=0.20 memory used=25.9MB, alloc=36.3MB, time=0.51 memory used=47.1MB, alloc=60.3MB, time=0.80 memory used=84.8MB, alloc=60.3MB, time=1.27 memory used=127.8MB, alloc=68.3MB, time=1.84 memory used=170.5MB, alloc=92.3MB, time=2.38 memory used=242.3MB, alloc=92.3MB, time=3.11 memory used=313.4MB, alloc=92.3MB, time=4.01 memory used=381.4MB, alloc=116.3MB, time=4.93 memory used=445.9MB, alloc=372.3MB, time=5.74 memory used=547.4MB, alloc=372.3MB, time=6.95 memory used=641.4MB, alloc=396.3MB, time=8.16 memory used=758.5MB, alloc=396.3MB, time=9.44 memory used=865.1MB, alloc=420.3MB, time=11.01 memory used=989.4MB, alloc=444.3MB, time=12.65 memory used=1100.9MB, alloc=444.3MB, time=14.09 memory used=1196.8MB, alloc=444.3MB, time=15.46 memory used=1296.8MB, alloc=468.3MB, time=16.62 memory used=1404.7MB, alloc=468.3MB, time=18.05 memory used=1485.9MB, alloc=468.3MB, time=19.21 memory used=1559.2MB, alloc=468.3MB, time=20.23 memory used=1620.1MB, alloc=492.3MB, time=21.12 memory used=1695.3MB, alloc=492.3MB, time=22.14 memory used=1774.9MB, alloc=492.3MB, time=23.49 memory used=1858.7MB, alloc=492.3MB, time=24.85 memory used=1909.4MB, alloc=492.3MB, time=25.85 memory used=1973.8MB, alloc=492.3MB, time=26.86 memory used=2020.5MB, alloc=492.3MB, time=27.91 memory used=2061.5MB, alloc=492.3MB, time=28.69 memory used=2103.0MB, alloc=492.3MB, time=29.54 memory used=2275.9MB, alloc=516.3MB, time=31.56 memory used=2436.5MB, alloc=540.3MB, time=34.15 memory used=2641.2MB, alloc=564.3MB, time=37.06 memory used=2834.6MB, alloc=588.3MB, time=39.51 memory used=2992.0MB, alloc=612.3MB, time=41.53 memory used=3225.1MB, alloc=612.3MB, time=44.13 memory used=3361.7MB, alloc=612.3MB, time=46.15 memory used=3500.6MB, alloc=612.3MB, time=48.11 memory used=3656.6MB, alloc=636.3MB, time=50.35 memory used=3760.4MB, alloc=636.3MB, time=52.19 memory used=3858.2MB, alloc=636.3MB, time=53.98 memory used=3954.5MB, alloc=636.3MB, time=55.74 memory used=4031.7MB, alloc=636.3MB, time=57.13 memory used=4127.6MB, alloc=636.3MB, time=59.22 memory used=4208.2MB, alloc=636.3MB, time=60.96 memory used=4502.2MB, alloc=660.3MB, time=65.18 memory used=4809.9MB, alloc=684.3MB, time=69.56 memory used=5172.0MB, alloc=708.3MB, time=74.72 memory used=5520.6MB, alloc=732.3MB, time=80.06 memory used=5870.1MB, alloc=756.3MB, time=86.73 memory used=6181.1MB, alloc=780.3MB, time=92.68 memory used=6472.5MB, alloc=804.3MB, time=98.03 memory used=6802.7MB, alloc=828.3MB, time=103.62 memory used=7047.4MB, alloc=852.3MB, time=108.23 memory used=7286.9MB, alloc=876.3MB, time=113.29 memory used=7508.8MB, alloc=900.3MB, time=117.17 memory used=7699.3MB, alloc=924.3MB, time=121.45 memory used=7912.2MB, alloc=948.3MB, time=126.07 memory used=8128.4MB, alloc=972.3MB, time=130.54 memory used=8749.7MB, alloc=996.3MB, time=139.89 memory used=9395.3MB, alloc=1020.3MB, time=150.48 memory used=10052.3MB, alloc=1044.3MB, time=161.83 memory used=10703.0MB, alloc=1068.3MB, time=173.02 memory used=11218.8MB, alloc=1092.3MB, time=181.32 memory used=11801.3MB, alloc=1116.3MB, time=192.74 memory used=12433.7MB, alloc=1140.3MB, time=206.29 memory used=13008.3MB, alloc=1164.3MB, time=219.47 memory used=13608.8MB, alloc=1188.3MB, time=230.22 memory used=13981.5MB, alloc=1212.3MB, time=239.10 memory used=14579.3MB, alloc=1236.3MB, time=250.94 memory used=15067.8MB, alloc=1260.3MB, time=260.83 memory used=15574.8MB, alloc=1284.3MB, time=271.18 memory used=16020.9MB, alloc=1308.3MB, time=281.02 memory used=16398.5MB, alloc=1332.3MB, time=289.96 memory used=16786.0MB, alloc=1356.3MB, time=300.81 memory used=17246.0MB, alloc=1380.3MB, time=309.81 memory used=17627.8MB, alloc=1404.3MB, time=318.66 memory used=17927.5MB, alloc=1428.3MB, time=327.23 memory used=18211.3MB, alloc=1452.3MB, time=335.43 memory used=18491.4MB, alloc=1476.3MB, time=343.93 memory used=18930.6MB, alloc=1500.3MB, time=354.84 memory used=19297.4MB, alloc=1524.3MB, time=363.20 memory used=19683.2MB, alloc=1548.3MB, time=372.18 memory used=20003.3MB, alloc=1572.3MB, time=380.74 memory used=20220.0MB, alloc=1596.3MB, time=388.51 memory used=20363.5MB, alloc=1620.3MB, time=395.41 memory used=20577.9MB, alloc=1644.3MB, time=403.39 memory used=20881.3MB, alloc=1668.3MB, time=412.29 memory used=21035.4MB, alloc=1692.3MB, time=420.14 memory used=21242.2MB, alloc=1716.3MB, time=428.87 memory used=21424.5MB, alloc=1740.3MB, time=436.84 memory used=21580.2MB, alloc=1764.3MB, time=444.52 memory used=21722.3MB, alloc=1764.3MB, time=452.51 memory used=21788.7MB, alloc=1764.3MB, time=458.89 memory used=21879.0MB, alloc=1764.3MB, time=466.29 memory used=22019.7MB, alloc=1764.3MB, time=473.69 memory used=22094.7MB, alloc=1764.3MB, time=480.20 memory used=22208.8MB, alloc=1764.3MB, time=487.30 memory used=22270.6MB, alloc=1764.3MB, time=493.79 memory used=22319.4MB, alloc=1764.3MB, time=500.12 memory used=22418.7MB, alloc=1764.3MB, time=507.69 memory used=22534.7MB, alloc=1764.3MB, time=516.45 memory used=22576.0MB, alloc=1764.3MB, time=522.71 memory used=22655.0MB, alloc=1764.3MB, time=529.17 memory used=22694.7MB, alloc=1764.3MB, time=535.47 memory used=22733.9MB, alloc=1764.3MB, time=541.95 memory used=22823.8MB, alloc=1764.3MB, time=548.74 memory used=22879.1MB, alloc=1764.3MB, time=555.51 memory used=22880.0MB, alloc=1764.3MB, time=561.49 memory used=22899.0MB, alloc=1764.3MB, time=567.79 memory used=22948.5MB, alloc=1764.3MB, time=574.20 memory used=23009.8MB, alloc=1764.3MB, time=580.76 memory used=23015.5MB, alloc=1764.3MB, time=587.01 memory used=23066.4MB, alloc=1764.3MB, time=593.89 memory used=23093.5MB, alloc=2020.3MB, time=606.96 memory used=24268.5MB, alloc=2044.3MB, time=628.70 memory used=25411.6MB, alloc=2068.3MB, time=651.71 memory used=26589.5MB, alloc=2092.3MB, time=680.21 memory used=27716.6MB, alloc=2116.3MB, time=703.11 memory used=28790.4MB, alloc=2140.3MB, time=727.14 memory used=29765.1MB, alloc=2164.3MB, time=752.29 memory used=30803.5MB, alloc=2188.3MB, time=773.99 memory used=31637.8MB, alloc=2212.3MB, time=793.64 memory used=32182.0MB, alloc=2236.3MB, time=808.15 memory used=33111.0MB, alloc=2260.3MB, time=830.96 memory used=33761.7MB, alloc=2284.3MB, time=850.69 memory used=34642.0MB, alloc=2308.3MB, time=874.60 memory used=35527.7MB, alloc=2332.3MB, time=895.48 memory used=36144.3MB, alloc=2356.3MB, time=915.00 memory used=36905.8MB, alloc=2380.3MB, time=938.89 memory used=37559.5MB, alloc=2404.3MB, time=959.40 memory used=38351.8MB, alloc=2428.3MB, time=983.32 memory used=39078.9MB, alloc=2452.3MB, time=1010.78 memory used=39630.4MB, alloc=2476.3MB, time=1030.28 memory used=40347.9MB, alloc=2500.3MB, time=1050.94 memory used=40896.0MB, alloc=2524.3MB, time=1070.46 memory used=41470.0MB, alloc=2548.3MB, time=1094.53 memory used=41920.8MB, alloc=2572.3MB, time=1114.20 memory used=42455.6MB, alloc=2596.3MB, time=1134.34 memory used=42898.3MB, alloc=2620.3MB, time=1157.64 memory used=43324.2MB, alloc=2644.3MB, time=1181.17 memory used=43709.3MB, alloc=2668.3MB, time=1204.30 memory used=44020.2MB, alloc=2692.3MB, time=1224.92 memory used=44362.7MB, alloc=2716.3MB, time=1247.37 |\^/| 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(); 1428465163 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 3 2 F := [2 y - 3 y - 8 z, -2 z + 6 x y, 5 y z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 2 G := [18 y z + 9 x - 14 z, 3 x z - 8 z + 5, 10 x y + 7 y z - 7 x ] > Problem := [F,G]; 3 3 2 Problem := [[2 y - 3 y - 8 z, -2 z + 6 x y, 5 y z], 2 2 2 2 2 [18 y z + 9 x - 14 z, 3 x z - 8 z + 5, 10 x y + 7 y z - 7 x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.21 memory used=26.1MB, alloc=32.3MB, time=0.53 memory used=45.9MB, alloc=56.3MB, time=0.81 memory used=87.3MB, alloc=60.3MB, time=1.34 memory used=133.2MB, alloc=68.3MB, time=1.78 memory used=163.7MB, alloc=68.3MB, time=1.92 memory used=204.5MB, alloc=68.3MB, time=2.23 memory used=227.4MB, alloc=68.3MB, time=2.30 memory used=269.2MB, alloc=68.3MB, time=2.71 memory used=292.8MB, alloc=68.3MB, time=2.78 memory used=336.4MB, alloc=68.3MB, time=3.53 memory used=380.7MB, alloc=68.3MB, time=4.17 memory used=419.8MB, alloc=68.3MB, time=4.76 memory used=467.1MB, alloc=68.3MB, time=5.30 memory used=514.0MB, alloc=68.3MB, time=5.94 memory used=552.8MB, alloc=68.3MB, time=6.43 memory used=593.3MB, alloc=92.3MB, time=7.02 memory used=659.5MB, alloc=92.3MB, time=7.88 memory used=723.9MB, alloc=116.3MB, time=8.63 memory used=790.1MB, alloc=372.3MB, time=9.48 memory used=873.8MB, alloc=372.3MB, time=10.32 memory used=928.5MB, alloc=372.3MB, time=10.63 memory used=986.9MB, alloc=372.3MB, time=11.08 memory used=1033.7MB, alloc=372.3MB, time=11.28 memory used=1087.9MB, alloc=372.3MB, time=11.63 memory used=1148.8MB, alloc=372.3MB, time=12.01 memory used=1221.2MB, alloc=372.3MB, time=14.17 memory used=1264.0MB, alloc=372.3MB, time=14.33 memory used=1302.8MB, alloc=372.3MB, time=14.47 memory used=1338.7MB, alloc=372.3MB, time=14.61 memory used=1381.7MB, alloc=372.3MB, time=14.75 memory used=1416.9MB, alloc=372.3MB, time=14.87 memory used=1477.0MB, alloc=372.3MB, time=15.17 memory used=1544.4MB, alloc=372.3MB, time=17.33 memory used=1588.8MB, alloc=372.3MB, time=17.49 memory used=1620.2MB, alloc=372.3MB, time=17.62 memory used=1658.5MB, alloc=372.3MB, time=17.77 memory used=1702.8MB, alloc=372.3MB, time=17.91 memory used=1751.6MB, alloc=372.3MB, time=18.24 memory used=1794.5MB, alloc=372.3MB, time=18.42 memory used=1835.2MB, alloc=372.3MB, time=18.58 memory used=1881.2MB, alloc=372.3MB, time=18.75 memory used=1911.3MB, alloc=372.3MB, time=18.89 memory used=1945.9MB, alloc=372.3MB, time=19.03 memory used=1986.3MB, alloc=372.3MB, time=19.17 memory used=2046.7MB, alloc=372.3MB, time=19.51 memory used=2082.2MB, alloc=372.3MB, time=19.67 memory used=2128.3MB, alloc=372.3MB, time=19.84 memory used=2164.9MB, alloc=372.3MB, time=19.99 memory used=2196.9MB, alloc=372.3MB, time=20.14 memory used=2233.9MB, alloc=372.3MB, time=20.29 memory used=2293.7MB, alloc=372.3MB, time=22.24 memory used=2336.4MB, alloc=372.3MB, time=22.42 memory used=2378.0MB, alloc=372.3MB, time=22.58 memory used=2411.9MB, alloc=372.3MB, time=22.72 memory used=2452.6MB, alloc=372.3MB, time=22.87 memory used=2499.4MB, alloc=372.3MB, time=23.02 memory used=2529.2MB, alloc=372.3MB, time=23.14 memory used=2578.3MB, alloc=372.3MB, time=23.35 memory used=2623.1MB, alloc=372.3MB, time=23.55 memory used=2670.4MB, alloc=372.3MB, time=23.74 memory used=2725.3MB, alloc=372.3MB, time=24.11 memory used=2770.0MB, alloc=372.3MB, time=24.30 memory used=2815.6MB, alloc=372.3MB, time=24.48 memory used=2868.5MB, alloc=372.3MB, time=24.70 memory used=2923.5MB, alloc=372.3MB, time=25.07 memory used=2964.1MB, alloc=372.3MB, time=25.22 memory used=3014.2MB, alloc=372.3MB, time=25.44 memory used=3063.3MB, alloc=372.3MB, time=25.64 memory used=3106.9MB, alloc=372.3MB, time=25.79 memory used=3161.9MB, alloc=372.3MB, time=26.14 memory used=3223.0MB, alloc=372.3MB, time=26.59 memory used=3320.5MB, alloc=372.3MB, time=27.46 memory used=3419.3MB, alloc=372.3MB, time=28.98 memory used=3524.5MB, alloc=372.3MB, time=30.28 memory used=3618.4MB, alloc=372.3MB, time=31.34 memory used=3714.4MB, alloc=372.3MB, time=33.20 memory used=3811.8MB, alloc=396.3MB, time=34.13 memory used=3941.5MB, alloc=396.3MB, time=35.70 memory used=4052.4MB, alloc=396.3MB, time=37.57 memory used=4104.3MB, alloc=396.3MB, time=37.74 memory used=4177.8MB, alloc=396.3MB, time=38.39 memory used=4227.8MB, alloc=396.3MB, time=38.56 memory used=4363.5MB, alloc=396.3MB, time=39.79 memory used=4490.0MB, alloc=396.3MB, time=41.41 memory used=4603.6MB, alloc=396.3MB, time=43.08 memory used=4678.0MB, alloc=396.3MB, time=43.51 memory used=4744.3MB, alloc=396.3MB, time=43.86 memory used=4817.2MB, alloc=396.3MB, time=44.28 memory used=4890.5MB, alloc=396.3MB, time=44.76 memory used=4945.4MB, alloc=396.3MB, time=44.95 memory used=4994.9MB, alloc=396.3MB, time=45.14 memory used=5038.2MB, alloc=396.3MB, time=45.31 memory used=5090.8MB, alloc=396.3MB, time=45.49 memory used=5162.4MB, alloc=396.3MB, time=45.86 memory used=5214.7MB, alloc=396.3MB, time=46.06 memory used=5267.8MB, alloc=396.3MB, time=46.25 memory used=5310.4MB, alloc=396.3MB, time=46.43 memory used=5361.9MB, alloc=396.3MB, time=46.62 memory used=5436.6MB, alloc=396.3MB, time=48.54 memory used=5491.3MB, alloc=396.3MB, time=48.74 memory used=5536.3MB, alloc=396.3MB, time=48.93 memory used=5593.0MB, alloc=396.3MB, time=49.10 memory used=5640.6MB, alloc=396.3MB, time=49.26 memory used=5697.6MB, alloc=396.3MB, time=49.50 memory used=5754.6MB, alloc=396.3MB, time=49.75 memory used=5816.7MB, alloc=396.3MB, time=49.98 memory used=5880.9MB, alloc=396.3MB, time=50.36 memory used=5942.7MB, alloc=396.3MB, time=50.64 memory used=6007.8MB, alloc=396.3MB, time=50.90 memory used=6076.2MB, alloc=396.3MB, time=51.30 memory used=6135.0MB, alloc=396.3MB, time=51.60 memory used=6196.6MB, alloc=396.3MB, time=51.82 memory used=6258.9MB, alloc=396.3MB, time=52.07 memory used=6327.3MB, alloc=396.3MB, time=52.46 memory used=6417.3MB, alloc=396.3MB, time=53.21 memory used=6513.0MB, alloc=396.3MB, time=54.22 memory used=6557.1MB, alloc=396.3MB, time=54.38 memory used=6660.5MB, alloc=396.3MB, time=55.56 memory used=6764.3MB, alloc=420.3MB, time=56.99 memory used=6885.5MB, alloc=420.3MB, time=58.08 memory used=6980.2MB, alloc=420.3MB, time=58.70 memory 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memory used=8369.9MB, alloc=444.3MB, time=99.54 memory used=8432.6MB, alloc=444.3MB, time=99.74 memory used=8497.9MB, alloc=444.3MB, time=99.95 memory used=8567.6MB, alloc=444.3MB, time=100.16 memory used=8639.6MB, alloc=444.3MB, time=100.37 memory used=8715.5MB, alloc=444.3MB, time=100.59 memory used=8795.0MB, alloc=444.3MB, time=100.80 memory used=8879.6MB, alloc=444.3MB, time=101.01 memory used=8968.4MB, alloc=444.3MB, time=101.23 memory used=9060.6MB, alloc=444.3MB, time=101.44 memory used=9163.9MB, alloc=444.3MB, time=101.68 memory used=9314.1MB, alloc=444.3MB, time=102.14 memory used=9460.8MB, alloc=444.3MB, time=102.45 memory used=9599.9MB, alloc=444.3MB, time=103.05 memory used=9688.2MB, alloc=444.3MB, time=103.38 memory used=9766.6MB, alloc=444.3MB, time=103.64 memory used=9867.3MB, alloc=444.3MB, time=104.12 memory used=9944.6MB, alloc=444.3MB, time=104.39 memory used=10015.6MB, alloc=444.3MB, time=104.64 memory used=10136.6MB, alloc=444.3MB, time=138.43 memory 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used=38325.7MB, alloc=828.3MB, time=406.06 memory used=38567.2MB, alloc=828.3MB, time=407.39 memory used=38774.3MB, alloc=828.3MB, time=408.57 memory used=38944.7MB, alloc=828.3MB, time=409.72 memory used=39200.2MB, alloc=828.3MB, time=412.19 memory used=39444.5MB, alloc=828.3MB, time=413.61 memory used=39618.8MB, alloc=828.3MB, time=414.87 memory used=39833.9MB, alloc=828.3MB, time=416.20 memory used=40095.2MB, alloc=828.3MB, time=417.52 memory used=40258.0MB, alloc=828.3MB, time=418.67 memory used=40441.2MB, alloc=828.3MB, time=419.82 memory used=40765.7MB, alloc=828.3MB, time=529.01 memory used=40979.7MB, alloc=828.3MB, time=530.37 memory used=41190.4MB, alloc=828.3MB, time=531.67 memory used=41436.2MB, alloc=828.3MB, time=533.03 memory used=41592.9MB, alloc=828.3MB, time=534.17 memory used=41767.1MB, alloc=828.3MB, time=535.37 memory used=41960.1MB, alloc=828.3MB, time=536.52 memory used=42172.6MB, alloc=828.3MB, time=537.72 memory used=42408.2MB, alloc=828.3MB, time=538.92 memory used=42669.2MB, alloc=828.3MB, time=540.14 memory used=42888.6MB, alloc=843.8MB, time=541.33 memory used=43002.2MB, alloc=843.8MB, time=542.38 memory used=43120.2MB, alloc=843.8MB, time=543.45 memory used=43244.1MB, alloc=843.8MB, time=544.51 memory used=43376.0MB, alloc=843.8MB, time=545.57 memory used=43519.8MB, alloc=843.8MB, time=546.63 memory used=43864.6MB, alloc=843.8MB, time=549.64 memory used=44098.0MB, alloc=843.8MB, time=551.05 memory used=44282.7MB, alloc=843.8MB, time=552.39 memory used=44511.4MB, alloc=843.8MB, time=553.72 memory used=44749.5MB, alloc=843.8MB, time=554.99 memory used=44912.9MB, alloc=843.8MB, time=556.15 memory used=45142.2MB, alloc=843.8MB, time=558.48 memory used=45386.8MB, alloc=843.8MB, time=560.03 memory used=45590.2MB, alloc=843.8MB, time=561.35 memory used=45791.3MB, alloc=843.8MB, time=562.64 memory used=46040.1MB, alloc=843.8MB, time=563.96 memory used=46232.6MB, alloc=843.8MB, time=565.16 memory used=46407.0MB, alloc=843.8MB, time=566.26 memory used=46708.3MB, alloc=843.8MB, time=673.85 memory used=46950.1MB, alloc=843.8MB, time=676.63 memory used=47143.6MB, alloc=843.8MB, time=677.94 memory used=47396.5MB, alloc=843.8MB, time=679.28 memory used=47567.9MB, alloc=843.8MB, time=680.44 memory used=47736.7MB, alloc=843.8MB, time=681.58 memory used=47925.1MB, alloc=843.8MB, time=682.73 memory used=48133.5MB, alloc=843.8MB, time=683.90 memory used=48362.8MB, alloc=843.8MB, time=685.08 memory used=48618.5MB, alloc=843.8MB, time=686.27 memory used=48908.7MB, alloc=843.8MB, time=687.51 memory used=49020.9MB, alloc=843.8MB, time=688.54 memory used=49138.8MB, alloc=843.8MB, time=689.60 memory used=49262.9MB, alloc=843.8MB, time=690.65 memory used=49395.0MB, alloc=843.8MB, time=691.73 memory used=49539.0MB, alloc=843.8MB, time=692.78 memory used=49885.6MB, alloc=843.8MB, time=700.08 memory used=50112.7MB, alloc=843.8MB, time=701.32 memory used=50290.5MB, alloc=843.8MB, time=702.41 memory used=50561.5MB, alloc=843.8MB, time=704.27 memory used=50788.3MB, alloc=843.8MB, time=705.68 memory used=50988.5MB, alloc=843.8MB, time=706.96 memory used=51212.8MB, alloc=843.8MB, time=708.20 memory used=51443.7MB, alloc=843.8MB, time=709.93 memory used=51658.5MB, alloc=843.8MB, time=711.27 memory used=51889.1MB, alloc=843.8MB, time=712.56 memory used=52079.9MB, alloc=843.8MB, time=713.70 memory used=52331.0MB, alloc=843.8MB, time=718.53 memory used=52533.1MB, alloc=843.8MB, time=719.70 memory used=52789.6MB, alloc=843.8MB, time=721.34 memory used=53058.4MB, alloc=843.8MB, time=723.96 memory used=53303.2MB, alloc=843.8MB, time=725.51 memory used=53537.9MB, alloc=843.8MB, time=726.98 memory used=53816.5MB, alloc=843.8MB, time=729.71 memory used=54063.8MB, alloc=843.8MB, time=731.21 memory used=54321.1MB, alloc=843.8MB, time=733.84 memory used=54586.5MB, alloc=843.8MB, time=735.86 memory used=54964.0MB, alloc=843.8MB, time=741.82 memory used=55235.2MB, alloc=843.8MB, time=744.11 memory used=55650.7MB, alloc=867.8MB, time=749.87 memory used=56027.3MB, alloc=891.8MB, time=757.17 memory used=56342.9MB, alloc=915.8MB, time=762.71 memory used=56722.1MB, alloc=939.8MB, time=768.70 memory used=57042.7MB, alloc=963.8MB, time=772.99 memory used=57382.3MB, alloc=987.8MB, time=787.79 memory used=57769.0MB, alloc=1011.8MB, time=792.92 memory used=58103.6MB, alloc=1267.8MB, time=798.01 memory used=58553.8MB, alloc=1267.8MB, time=802.93 memory used=58840.6MB, alloc=1267.8MB, time=805.14 memory used=59120.2MB, alloc=1267.8MB, time=807.39 memory used=59418.1MB, alloc=1267.8MB, time=809.68 memory used=59695.5MB, alloc=1267.8MB, time=812.59 memory used=60002.6MB, alloc=1267.8MB, time=814.68 memory used=60302.0MB, alloc=1267.8MB, time=818.25 memory used=60655.8MB, alloc=1267.8MB, time=821.03 memory used=60990.8MB, alloc=1291.8MB, time=824.42 memory used=61239.6MB, alloc=1291.8MB, time=826.35 memory used=61635.2MB, alloc=1291.8MB, time=828.95 memory used=61900.9MB, alloc=1291.8MB, time=830.89 memory used=62315.0MB, alloc=1291.8MB, time=841.31 memory used=62785.6MB, alloc=1291.8MB, time=843.73 memory used=63105.0MB, alloc=1291.8MB, time=847.81 memory used=63457.1MB, alloc=1291.8MB, time=851.80 memory used=63780.0MB, alloc=1291.8MB, time=854.30 memory used=64045.4MB, alloc=1291.8MB, time=856.25 memory used=64445.7MB, alloc=1291.8MB, time=858.70 memory used=64711.2MB, alloc=1291.8MB, time=860.69 memory used=65006.5MB, alloc=1291.8MB, time=862.60 memory used=65404.4MB, alloc=1291.8MB, time=879.12 memory used=66068.2MB, alloc=1291.8MB, time=886.17 memory used=66500.1MB, alloc=1291.8MB, time=890.27 memory used=67108.7MB, alloc=1315.8MB, time=900.85 memory used=67697.2MB, alloc=1339.8MB, time=914.13 memory used=68058.0MB, alloc=1363.8MB, time=921.21 memory used=68430.9MB, alloc=1387.8MB, time=928.87 memory used=68774.7MB, alloc=1411.8MB, time=946.40 memory used=69157.0MB, alloc=1435.8MB, time=966.64 memory used=69509.6MB, alloc=1435.8MB, time=969.38 memory used=69841.8MB, alloc=1435.8MB, time=972.46 memory used=70212.3MB, alloc=1435.8MB, time=986.77 memory used=70575.2MB, alloc=1435.8MB, time=989.63 memory used=70970.9MB, alloc=1435.8MB, time=995.19 memory used=71349.0MB, alloc=1435.8MB, time=1000.91 memory used=71700.4MB, alloc=1435.8MB, time=1003.98 memory used=72052.0MB, alloc=1435.8MB, time=1006.74 memory used=72542.2MB, alloc=1435.8MB, time=1015.02 memory used=73239.0MB, alloc=1459.8MB, time=1025.12 memory used=73875.6MB, alloc=1483.8MB, time=1033.32 memory used=74238.0MB, alloc=1483.8MB, time=1036.18 memory used=74663.4MB, alloc=1507.8MB, time=1054.81 memory used=75199.4MB, alloc=1507.8MB, time=1057.85 memory used=75581.4MB, alloc=1507.8MB, time=1060.63 memory used=76010.7MB, alloc=1507.8MB, time=1079.13 memory used=76551.9MB, alloc=1507.8MB, time=1082.92 memory used=77185.3MB, alloc=1507.8MB, time=1093.66 memory used=77641.2MB, alloc=1507.8MB, time=1101.52 memory used=78039.6MB, alloc=1507.8MB, time=1104.81 memory used=78383.6MB, alloc=1507.8MB, time=1107.58 memory used=78785.6MB, alloc=1507.8MB, time=1122.01 memory used=79223.0MB, alloc=1507.8MB, time=1127.85 memory used=79632.0MB, alloc=1507.8MB, time=1133.75 memory used=80010.9MB, alloc=1507.8MB, time=1136.99 memory used=80381.1MB, alloc=1507.8MB, time=1139.89 memory used=81006.1MB, alloc=1531.8MB, time=1152.20 memory used=81667.2MB, alloc=1555.8MB, time=1161.74 memory used=82087.2MB, alloc=1555.8MB, time=1165.36 memory used=82484.5MB, alloc=1555.8MB, time=1168.59 memory used=82889.0MB, alloc=1555.8MB, time=1172.39 memory used=83253.4MB, alloc=1555.8MB, time=1175.53 memory used=83603.4MB, alloc=1555.8MB, time=1178.41 memory used=84046.5MB, alloc=1555.8MB, time=1181.43 memory used=84348.6MB, alloc=1555.8MB, time=1184.25 memory used=84575.1MB, alloc=1555.8MB, time=1186.99 memory used=84825.6MB, alloc=1555.8MB, time=1189.74 memory used=85106.6MB, alloc=1555.8MB, time=1192.46 memory used=85672.6MB, alloc=1555.8MB, time=1196.61 memory used=86002.9MB, alloc=1555.8MB, time=1199.59 memory used=86377.5MB, alloc=1555.8MB, time=1202.52 memory used=86998.2MB, alloc=1555.8MB, time=1205.83 memory used=87226.0MB, alloc=1555.8MB, time=1208.54 memory used=87477.8MB, alloc=1555.8MB, time=1211.29 memory used=87758.8MB, alloc=1555.8MB, time=1214.06 memory used=88307.0MB, alloc=1555.8MB, time=1222.43 memory used=88782.2MB, alloc=1555.8MB, time=1225.45 memory used=89062.0MB, alloc=1555.8MB, time=1228.15 memory used=89637.5MB, alloc=1555.8MB, time=1231.67 memory used=90051.0MB, alloc=1555.8MB, time=1234.90 memory used=90416.8MB, alloc=1555.8MB, time=1237.79 memory used=90849.0MB, alloc=1555.8MB, time=1242.50 memory used=91465.8MB, alloc=1555.8MB, time=1246.19 memory used=91868.6MB, alloc=1555.8MB, time=1249.33 memory used=92226.2MB, alloc=1555.8MB, time=1252.31 memory used=92663.3MB, alloc=1555.8MB, time=1257.01 memory used=93300.1MB, alloc=1555.8MB, time=1260.69 memory used=93665.7MB, alloc=1555.8MB, time=1263.54 memory used=94060.6MB, alloc=1555.8MB, time=1266.83 memory used=94497.8MB, alloc=1555.8MB, time=1271.43 memory used=95110.2MB, alloc=1555.8MB, time=1274.89 memory used=95503.6MB, alloc=1555.8MB, time=1278.46 memory used=95987.9MB, alloc=1555.8MB, time=1283.32 memory used=96367.0MB, alloc=1579.8MB, time=1286.54 memory used=96742.9MB, alloc=1579.8MB, time=1289.59 memory used=97058.3MB, alloc=1603.8MB, time=1292.45 memory used=97437.3MB, alloc=1603.8MB, time=1295.36 memory used=97872.2MB, alloc=1603.8MB, time=1298.30 memory used=98374.9MB, alloc=1603.8MB, time=1301.33 memory used=98773.8MB, alloc=1603.8MB, time=1304.26 memory used=98976.6MB, alloc=1603.8MB, time=1306.90 memory used=99188.9MB, alloc=1603.8MB, time=1309.54 memory used=99412.3MB, alloc=1603.8MB, time=1312.25 memory used=99645.8MB, alloc=1603.8MB, time=1314.92 memory used=99892.1MB, alloc=1603.8MB, time=1317.60 memory used=100154.4MB, alloc=1603.8MB, time=1320.33 memory used=100428.2MB, alloc=1603.8MB, time=1323.01 memory used=100718.0MB, alloc=1603.8MB, time=1325.68 memory used=101028.4MB, alloc=1603.8MB, time=1328.38 memory used=101420.0MB, alloc=1603.8MB, time=1332.82 memory used=101829.7MB, alloc=1603.8MB, time=1336.24 memory used=102302.5MB, alloc=1603.8MB, time=1339.45 memory used=102607.7MB, alloc=1603.8MB, time=1342.27 memory used=102961.8MB, alloc=1603.8MB, time=1345.12 memory used=103374.3MB, alloc=1603.8MB, time=1348.01 memory used=103845.0MB, alloc=1603.8MB, time=1350.97 memory used=104485.9MB, alloc=1603.8MB, time=1354.22 memory used=104688.7MB, alloc=1603.8MB, time=1356.84 memory used=104902.7MB, alloc=1603.8MB, time=1359.45 memory used=105126.1MB, alloc=1603.8MB, time=1362.07 memory used=105359.6MB, alloc=1603.8MB, time=1364.75 memory used=105604.9MB, alloc=1603.8MB, time=1367.51 memory used=105867.2MB, alloc=1603.8MB, time=1370.21 memory used=106140.9MB, alloc=1603.8MB, time=1372.91 memory used=106430.5MB, alloc=1603.8MB, time=1375.64 memory used=106741.8MB, alloc=1603.8MB, time=1378.35 memory used=107151.6MB, alloc=1603.8MB, time=1414.43 |\^/| 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(); 1428466363 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 3 2 2 3 2 F := [-x z + 17 y z - 9 z , x y - 8 x z - 2 x y, 5 x + 8 y + 8 z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 G := [-9 y z - y + 4 z, -9 y - 2 y - 1, -2 y z - 10 x y - y z] > Problem := [F,G]; 2 2 3 2 2 3 2 Problem := [[-x z + 17 y z - 9 z , x y - 8 x z - 2 x y, 5 x + 8 y + 8 z], 2 3 2 [-9 y z - y + 4 z, -9 y - 2 y - 1, -2 y z - 10 x y - y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.18 memory used=26.4MB, alloc=32.3MB, time=0.49 memory used=47.6MB, alloc=32.3MB, time=0.78 memory used=66.7MB, alloc=56.3MB, time=1.08 memory used=107.7MB, alloc=60.3MB, time=1.69 memory used=146.5MB, alloc=60.3MB, time=2.26 memory used=184.5MB, alloc=84.3MB, time=2.85 memory used=225.7MB, alloc=84.3MB, time=3.49 memory used=282.4MB, alloc=116.3MB, time=4.42 memory used=364.2MB, alloc=116.3MB, time=5.70 memory used=439.1MB, alloc=140.3MB, time=6.86 memory used=520.1MB, alloc=396.3MB, time=8.21 memory used=622.4MB, alloc=420.3MB, time=9.95 memory used=753.3MB, alloc=444.3MB, time=12.19 memory used=906.7MB, alloc=444.3MB, time=14.83 memory used=1057.9MB, alloc=468.3MB, time=17.52 memory used=1202.9MB, alloc=492.3MB, time=20.28 memory used=1338.8MB, alloc=492.3MB, time=22.77 memory used=1467.8MB, alloc=516.3MB, time=25.12 memory used=1618.8MB, alloc=516.3MB, time=28.46 memory used=1721.4MB, alloc=540.3MB, time=30.36 memory used=1805.6MB, alloc=540.3MB, time=31.95 memory used=1911.9MB, alloc=540.3MB, time=34.17 memory used=2004.6MB, alloc=540.3MB, time=36.04 memory used=2082.2MB, alloc=540.3MB, time=37.79 memory used=2159.4MB, alloc=540.3MB, time=39.44 memory used=2228.2MB, alloc=540.3MB, time=40.92 memory used=2310.1MB, alloc=564.3MB, time=42.86 memory used=2385.1MB, alloc=564.3MB, time=44.71 memory used=2452.3MB, alloc=564.3MB, time=46.36 memory used=2503.9MB, alloc=564.3MB, time=47.60 memory used=2557.8MB, alloc=564.3MB, time=48.92 memory used=2604.7MB, alloc=564.3MB, time=50.16 memory used=2655.3MB, alloc=564.3MB, time=51.40 memory used=2888.7MB, alloc=588.3MB, time=56.06 memory used=3138.0MB, alloc=612.3MB, time=61.90 memory used=3344.3MB, alloc=636.3MB, time=65.51 memory used=3555.5MB, alloc=660.3MB, time=70.61 memory used=3703.2MB, alloc=684.3MB, time=73.33 memory used=3880.2MB, alloc=708.3MB, time=77.17 memory used=4025.7MB, alloc=732.3MB, time=80.75 memory used=4142.2MB, alloc=732.3MB, time=83.68 memory used=4294.4MB, alloc=732.3MB, time=87.79 memory used=4450.1MB, alloc=756.3MB, time=92.08 memory used=4552.4MB, alloc=756.3MB, time=94.69 memory used=4655.7MB, alloc=756.3MB, time=97.36 memory used=5068.6MB, alloc=780.3MB, time=106.48 memory used=5485.7MB, alloc=804.3MB, time=115.95 memory used=5895.9MB, alloc=828.3MB, time=125.43 memory used=6275.2MB, alloc=852.3MB, time=134.64 memory used=6604.3MB, alloc=876.3MB, time=142.83 memory used=6949.5MB, alloc=900.3MB, time=151.62 memory used=7256.3MB, alloc=924.3MB, time=159.63 memory used=7563.0MB, alloc=948.3MB, time=167.06 memory used=7839.7MB, alloc=972.3MB, time=174.62 memory used=8182.8MB, alloc=996.3MB, time=186.22 memory used=8489.4MB, alloc=1020.3MB, time=197.50 memory used=9122.4MB, alloc=1044.3MB, time=213.61 memory used=9776.1MB, alloc=1068.3MB, time=231.34 memory used=10439.2MB, alloc=1092.3MB, time=249.89 memory used=11104.7MB, alloc=1116.3MB, time=270.43 memory used=11804.7MB, alloc=1140.3MB, time=290.31 memory used=12489.9MB, alloc=1164.3MB, time=314.32 memory used=13188.5MB, alloc=1188.3MB, time=334.66 memory used=13827.2MB, alloc=1212.3MB, time=353.91 memory used=14544.8MB, alloc=1236.3MB, time=376.47 memory used=15068.3MB, alloc=1260.3MB, time=392.82 memory used=15761.8MB, alloc=1284.3MB, time=418.94 memory used=16243.5MB, alloc=1308.3MB, time=435.70 memory used=16783.6MB, alloc=1332.3MB, time=454.82 memory used=17223.3MB, alloc=1356.3MB, time=471.69 memory used=17563.9MB, alloc=1380.3MB, time=485.45 memory used=17989.7MB, alloc=1404.3MB, time=503.60 memory used=18337.3MB, alloc=1428.3MB, time=518.29 memory used=18627.5MB, alloc=1452.3MB, time=532.04 memory used=18888.5MB, alloc=1476.3MB, time=545.25 memory used=19168.0MB, alloc=1500.3MB, time=557.14 memory used=19376.1MB, alloc=1524.3MB, time=566.78 memory used=19599.8MB, alloc=1548.3MB, time=578.82 memory used=19784.4MB, alloc=1572.3MB, time=587.38 memory used=19927.1MB, alloc=1596.3MB, time=598.24 memory used=20165.7MB, alloc=1620.3MB, time=610.89 memory used=20305.0MB, alloc=1644.3MB, time=620.22 memory used=20444.5MB, alloc=1668.3MB, time=630.42 memory used=20540.8MB, alloc=1692.3MB, time=638.14 memory used=20683.9MB, alloc=1716.3MB, time=645.51 memory used=20811.9MB, alloc=1740.3MB, time=655.94 memory used=20930.9MB, alloc=1764.3MB, time=664.65 memory used=21077.5MB, alloc=1788.3MB, time=675.24 memory used=21162.9MB, alloc=1812.3MB, time=683.39 memory used=21259.6MB, alloc=1836.3MB, time=691.51 memory used=21356.9MB, alloc=1860.3MB, time=699.02 memory used=21493.8MB, alloc=1860.3MB, time=709.88 memory used=21584.4MB, alloc=1860.3MB, time=718.94 memory used=21706.2MB, alloc=1860.3MB, time=728.82 memory used=21798.4MB, alloc=1860.3MB, time=738.50 memory used=21878.9MB, alloc=1860.3MB, time=747.17 memory used=21937.8MB, alloc=1860.3MB, time=754.62 memory used=22040.6MB, alloc=1860.3MB, time=764.52 memory used=22054.1MB, alloc=1860.3MB, time=770.82 memory used=22127.1MB, alloc=1860.3MB, time=778.25 memory used=22138.2MB, alloc=1860.3MB, time=784.27 memory used=22184.9MB, alloc=1860.3MB, time=791.23 memory used=22189.1MB, alloc=1860.3MB, time=797.09 memory used=22241.4MB, alloc=1860.3MB, time=804.20 memory used=22248.7MB, alloc=2116.3MB, time=816.72 memory used=23562.4MB, alloc=2140.3MB, time=862.37 memory used=24891.4MB, alloc=2164.3MB, time=903.37 memory used=26200.9MB, alloc=2188.3MB, time=944.31 memory used=27434.4MB, alloc=2212.3MB, time=985.13 memory used=28698.6MB, alloc=2236.3MB, time=1025.04 memory used=29835.0MB, alloc=2260.3MB, time=1063.42 memory used=31029.4MB, alloc=2284.3MB, time=1103.94 memory used=31700.5MB, alloc=2308.3MB, time=1129.41 |\^/| 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(); 1428467563 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 2 F := [-14 y z - 13 x z - 3 y z, -6 x y + x y - 6 y z, 6 x y z + 8 x z + 5] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 2 2 3 G := [-7 x y + 9 y z - 7 y z, -x z + 2 y z - 3 x , -x z - 6 z ] > Problem := [F,G]; Problem := [ 2 2 2 2 2 [-14 y z - 13 x z - 3 y z, -6 x y + x y - 6 y z, 6 x y z + 8 x z + 5], 2 2 2 2 2 2 3 [-7 x y + 9 y z - 7 y z, -x z + 2 y z - 3 x , -x z - 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=26.8MB, alloc=32.3MB, time=0.51 memory used=47.9MB, alloc=32.3MB, time=0.82 memory used=67.6MB, alloc=56.3MB, time=1.14 memory used=106.7MB, alloc=60.3MB, time=1.74 memory used=144.1MB, alloc=84.3MB, time=2.33 memory used=203.0MB, alloc=92.3MB, time=3.26 memory used=259.8MB, alloc=116.3MB, time=4.18 memory used=341.3MB, alloc=116.3MB, time=5.46 memory used=419.5MB, alloc=396.3MB, time=6.72 memory used=525.8MB, alloc=420.3MB, time=8.46 memory used=656.3MB, alloc=444.3MB, time=10.48 memory used=809.7MB, alloc=468.3MB, time=13.06 memory used=943.4MB, alloc=492.3MB, time=15.42 memory used=1072.2MB, alloc=492.3MB, time=17.66 memory used=1189.8MB, alloc=492.3MB, time=19.74 memory used=1306.4MB, alloc=516.3MB, time=22.13 memory used=1399.1MB, alloc=516.3MB, time=23.94 memory used=1509.1MB, alloc=516.3MB, time=26.27 memory used=1594.7MB, alloc=516.3MB, time=28.07 memory used=1687.5MB, alloc=516.3MB, time=30.04 memory used=1774.2MB, alloc=516.3MB, time=31.90 memory used=1846.3MB, alloc=516.3MB, time=33.48 memory used=1916.9MB, alloc=540.3MB, time=35.14 memory used=1973.6MB, alloc=540.3MB, time=36.61 memory used=2019.7MB, alloc=540.3MB, time=37.86 memory used=2077.5MB, alloc=540.3MB, time=39.37 memory used=2138.1MB, alloc=540.3MB, time=40.86 memory used=2178.9MB, alloc=540.3MB, time=42.00 memory used=2379.1MB, alloc=564.3MB, time=46.34 memory used=2571.0MB, alloc=588.3MB, time=50.36 memory used=2780.9MB, alloc=612.3MB, time=55.12 memory used=2977.7MB, alloc=636.3MB, time=59.75 memory used=3151.4MB, alloc=660.3MB, time=63.81 memory used=3310.8MB, alloc=660.3MB, time=67.35 memory used=3459.1MB, alloc=684.3MB, time=70.62 memory used=3611.8MB, alloc=684.3MB, time=74.36 memory used=3750.4MB, alloc=684.3MB, time=77.73 memory used=3875.3MB, alloc=684.3MB, time=80.66 memory used=4008.5MB, alloc=684.3MB, time=84.00 memory used=4128.2MB, alloc=708.3MB, time=87.32 memory used=4236.5MB, alloc=708.3MB, time=90.26 memory used=4332.5MB, alloc=708.3MB, time=92.87 memory used=4692.7MB, alloc=732.3MB, time=101.09 memory used=5053.9MB, alloc=756.3MB, time=109.47 memory used=5451.7MB, alloc=780.3MB, time=120.19 memory used=5873.1MB, alloc=804.3MB, time=131.19 memory used=6315.6MB, alloc=828.3MB, time=143.26 memory used=6754.0MB, alloc=852.3MB, time=154.89 memory used=7114.3MB, alloc=876.3MB, time=164.11 memory used=7462.9MB, alloc=900.3MB, time=173.30 memory used=7718.0MB, alloc=924.3MB, time=178.97 memory used=8050.7MB, alloc=948.3MB, time=188.84 memory used=8242.7MB, alloc=972.3MB, time=193.38 memory used=8517.9MB, alloc=996.3MB, time=202.56 memory used=8792.7MB, alloc=1020.3MB, time=211.67 memory used=8976.4MB, alloc=1044.3MB, time=217.00 memory used=9604.0MB, alloc=1068.3MB, time=236.10 memory used=10260.0MB, alloc=1092.3MB, time=255.83 memory used=10927.0MB, alloc=1116.3MB, time=273.21 memory used=11604.9MB, alloc=1140.3MB, time=294.56 memory used=12289.7MB, alloc=1164.3MB, time=315.07 memory used=12993.0MB, alloc=1188.3MB, time=335.88 memory used=13707.0MB, alloc=1212.3MB, time=358.90 memory used=14314.9MB, alloc=1236.3MB, time=377.07 memory used=14851.2MB, alloc=1260.3MB, time=394.01 memory used=15354.0MB, alloc=1284.3MB, time=410.33 memory used=15826.8MB, alloc=1308.3MB, time=426.28 memory used=16318.5MB, alloc=1332.3MB, time=443.14 memory used=16774.9MB, alloc=1356.3MB, time=458.76 memory used=17098.9MB, alloc=1380.3MB, time=471.19 memory used=17425.4MB, alloc=1404.3MB, time=485.32 memory used=17845.9MB, alloc=1428.3MB, time=501.56 memory used=18244.0MB, alloc=1452.3MB, time=514.60 memory used=18677.9MB, alloc=1476.3MB, time=530.53 memory used=18928.9MB, alloc=1500.3MB, time=541.55 memory used=19284.3MB, alloc=1524.3MB, time=557.47 memory used=19412.3MB, alloc=1548.3MB, time=565.04 memory used=19494.7MB, alloc=1572.3MB, time=572.54 memory used=19606.5MB, alloc=1596.3MB, time=580.97 memory used=19828.1MB, alloc=1620.3MB, time=593.86 memory used=19899.5MB, alloc=1644.3MB, time=600.87 memory used=20046.1MB, alloc=1668.3MB, time=610.07 memory used=20131.8MB, alloc=1692.3MB, time=618.96 memory used=20263.8MB, alloc=1716.3MB, time=630.07 memory used=20286.2MB, alloc=1740.3MB, time=636.20 memory used=20326.5MB, alloc=1764.3MB, time=642.62 memory used=20373.2MB, alloc=1788.3MB, time=649.72 memory used=20450.6MB, alloc=2092.3MB, time=663.12 memory used=21735.0MB, alloc=2116.3MB, time=701.02 memory used=23005.9MB, alloc=2140.3MB, time=741.84 memory used=24288.6MB, alloc=2164.3MB, time=783.37 memory used=25558.3MB, alloc=2188.3MB, time=825.43 memory used=26820.0MB, alloc=2212.3MB, time=870.71 memory used=28085.3MB, alloc=2236.3MB, time=916.25 memory used=29333.7MB, alloc=2260.3MB, time=962.99 memory used=30430.7MB, alloc=2284.3MB, time=1006.48 memory used=31305.9MB, alloc=2308.3MB, time=1041.30 memory used=32379.3MB, alloc=2332.3MB, time=1088.44 |\^/| 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(); 1428468763 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 3 2 F := [-19 x y z + 16 y - 6 z, 7 x y + x y + 9 z, -10 x y z - 10 y - 5 y z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 3 G := [-19 y z + 4 y z - 16 x y, 3 x y + 6 x + 3 x y, -x - z] > Problem := [F,G]; Problem := [ 3 2 2 3 2 [-19 x y z + 16 y - 6 z, 7 x y + x y + 9 z, -10 x y z - 10 y - 5 y z], 2 2 2 2 3 [-19 y z + 4 y z - 16 x y, 3 x y + 6 x + 3 x y, -x - z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.2MB, alloc=32.3MB, time=0.52 memory used=47.0MB, alloc=32.3MB, time=0.82 memory used=66.0MB, alloc=56.3MB, time=1.12 memory used=104.5MB, alloc=60.3MB, time=1.71 memory used=143.6MB, alloc=84.3MB, time=2.32 memory used=206.2MB, alloc=92.3MB, time=3.29 memory used=267.8MB, alloc=116.3MB, time=4.27 memory used=352.0MB, alloc=140.3MB, time=5.67 memory used=426.7MB, alloc=396.3MB, time=6.95 memory used=532.9MB, alloc=420.3MB, time=8.69 memory used=662.1MB, alloc=444.3MB, time=10.83 memory used=808.8MB, alloc=468.3MB, time=13.28 memory used=944.5MB, alloc=468.3MB, time=15.64 memory used=1060.6MB, alloc=492.3MB, time=17.47 memory used=1164.8MB, alloc=492.3MB, time=19.17 memory used=1280.1MB, alloc=516.3MB, time=21.49 memory used=1365.8MB, alloc=516.3MB, time=23.29 memory used=1457.5MB, alloc=516.3MB, time=25.14 memory used=1524.6MB, alloc=516.3MB, time=26.43 memory used=1604.6MB, alloc=516.3MB, time=28.04 memory used=1672.7MB, alloc=516.3MB, time=29.55 memory used=1725.8MB, alloc=516.3MB, time=30.69 memory used=1784.6MB, alloc=516.3MB, time=32.12 memory used=1834.8MB, alloc=516.3MB, time=33.32 memory used=2042.0MB, alloc=540.3MB, time=37.36 memory used=2234.6MB, alloc=564.3MB, time=40.80 memory used=2443.2MB, alloc=588.3MB, time=45.06 memory used=2628.3MB, alloc=612.3MB, time=48.67 memory used=2785.0MB, alloc=636.3MB, time=51.88 memory used=2933.2MB, alloc=636.3MB, time=55.13 memory used=3060.3MB, alloc=660.3MB, time=58.08 memory used=3191.1MB, alloc=660.3MB, time=61.40 memory used=3319.9MB, alloc=660.3MB, time=64.82 memory used=3434.4MB, alloc=660.3MB, time=68.06 memory used=3764.1MB, alloc=684.3MB, time=75.71 memory used=4108.3MB, alloc=708.3MB, time=84.00 memory used=4479.1MB, alloc=732.3MB, time=92.84 memory used=4769.2MB, alloc=756.3MB, time=99.78 memory used=5162.7MB, alloc=780.3MB, time=109.21 memory used=5478.3MB, alloc=804.3MB, time=116.24 memory used=5789.2MB, alloc=828.3MB, time=123.62 memory used=6097.2MB, alloc=852.3MB, time=130.67 memory used=6375.7MB, alloc=876.3MB, time=137.43 memory used=6645.5MB, alloc=900.3MB, time=145.20 memory used=6863.6MB, alloc=924.3MB, time=150.91 memory used=7097.4MB, alloc=948.3MB, time=155.87 memory used=7294.0MB, alloc=972.3MB, time=160.79 memory used=7912.6MB, alloc=996.3MB, time=173.60 memory used=8520.5MB, alloc=1020.3MB, time=187.58 memory used=9140.9MB, alloc=1044.3MB, time=203.29 memory used=9756.6MB, alloc=1068.3MB, time=217.03 memory used=10412.0MB, alloc=1092.3MB, time=230.30 memory used=10702.1MB, alloc=1116.3MB, time=235.85 memory used=11371.8MB, alloc=1140.3MB, time=247.22 memory used=12021.2MB, alloc=1164.3MB, time=259.69 memory used=12638.4MB, alloc=1188.3MB, time=269.67 memory used=13241.2MB, alloc=1212.3MB, time=277.79 memory used=13899.8MB, alloc=1236.3MB, time=291.14 memory used=14515.2MB, alloc=1260.3MB, time=304.81 memory used=15136.3MB, alloc=1284.3MB, time=318.66 memory used=15721.1MB, alloc=1308.3MB, time=332.80 memory used=16308.9MB, alloc=1332.3MB, time=346.91 memory used=16919.1MB, alloc=1356.3MB, time=360.80 memory used=17462.8MB, alloc=1380.3MB, time=375.18 memory used=18006.6MB, alloc=1404.3MB, time=389.59 memory used=18559.1MB, alloc=1428.3MB, time=403.65 memory used=19122.0MB, alloc=1452.3MB, time=417.54 memory used=19741.1MB, alloc=1476.3MB, time=431.04 memory used=20366.4MB, alloc=1500.3MB, time=445.44 memory used=20916.0MB, alloc=1524.3MB, time=459.88 memory used=21474.6MB, alloc=1548.3MB, time=474.42 memory used=22060.7MB, alloc=1572.3MB, time=489.20 memory used=22631.3MB, alloc=1596.3MB, time=503.71 memory used=23222.0MB, alloc=1620.3MB, time=517.96 memory used=23815.6MB, alloc=1644.3MB, time=532.48 memory used=24389.0MB, alloc=1668.3MB, time=547.00 memory used=24954.8MB, alloc=1692.3MB, time=561.96 memory used=25522.5MB, alloc=1716.3MB, time=576.71 memory used=26123.7MB, alloc=1740.3MB, time=591.22 memory used=26720.0MB, alloc=1764.3MB, time=606.12 memory used=27321.7MB, alloc=1788.3MB, time=621.03 memory used=27954.2MB, alloc=1812.3MB, time=634.91 memory used=28625.0MB, alloc=1836.3MB, time=650.19 memory used=29075.2MB, alloc=1860.3MB, time=669.50 memory used=29446.3MB, alloc=1884.3MB, time=689.84 memory used=29824.9MB, alloc=1908.3MB, time=710.94 memory used=30212.9MB, alloc=1932.3MB, time=732.75 memory used=30613.0MB, alloc=1956.3MB, time=755.32 memory used=31025.6MB, alloc=1980.3MB, time=778.57 memory used=31451.5MB, alloc=2004.3MB, time=802.78 memory used=31891.4MB, alloc=2028.3MB, time=827.38 memory used=32345.3MB, alloc=2052.3MB, time=852.65 memory used=32814.2MB, alloc=2076.3MB, time=878.58 memory used=33298.0MB, alloc=2100.3MB, time=905.51 memory used=33797.0MB, alloc=2124.3MB, time=933.31 memory used=34311.7MB, alloc=2148.3MB, time=961.91 memory used=34842.0MB, alloc=2172.3MB, time=991.33 memory used=35387.9MB, alloc=2196.3MB, time=1021.61 memory used=35949.3MB, alloc=2220.3MB, time=1052.89 |\^/| 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(); 1428469963 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 2 3 2 F := [4 y z - 5 z + 15 x, -4 x y + 6 y z + 6 x , 10 x y - 10 z + 9 y ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 2 G := [-17 z - 18 x y - 5 y , 4 x z - y - 6 y z, 10 y z - 3 x z - 8 y z] > Problem := [F,G]; Problem := [ 2 2 2 2 2 3 2 [4 y z - 5 z + 15 x, -4 x y + 6 y z + 6 x , 10 x y - 10 z + 9 y ], 3 2 2 2 [-17 z - 18 x y - 5 y , 4 x z - y - 6 y z, 10 y z - 3 x z - 8 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.4MB, alloc=32.3MB, time=0.50 memory used=46.7MB, alloc=56.3MB, time=0.82 memory used=88.7MB, alloc=60.3MB, time=1.39 memory used=128.6MB, alloc=84.3MB, time=1.97 memory used=168.5MB, alloc=84.3MB, time=2.59 memory used=229.8MB, alloc=92.3MB, time=3.51 memory used=297.5MB, alloc=116.3MB, time=4.31 memory used=370.0MB, alloc=116.3MB, time=5.27 memory used=447.5MB, alloc=396.3MB, time=6.52 memory used=562.3MB, alloc=396.3MB, time=7.99 memory used=666.6MB, alloc=420.3MB, time=9.57 memory used=790.5MB, alloc=444.3MB, time=11.59 memory used=941.5MB, alloc=468.3MB, time=13.80 memory used=1084.8MB, alloc=492.3MB, time=16.24 memory used=1204.6MB, alloc=492.3MB, time=18.10 memory used=1318.7MB, alloc=492.3MB, time=19.97 memory used=1460.1MB, alloc=516.3MB, time=22.00 memory used=1589.7MB, alloc=516.3MB, time=24.19 memory used=1767.0MB, alloc=516.3MB, time=27.49 memory used=1901.5MB, alloc=516.3MB, time=29.58 memory used=1999.8MB, alloc=516.3MB, time=31.37 memory used=2116.7MB, alloc=540.3MB, time=33.15 memory used=2204.0MB, alloc=540.3MB, time=34.50 memory used=2340.0MB, alloc=540.3MB, time=36.70 memory used=2432.2MB, alloc=540.3MB, time=38.55 memory used=2496.7MB, alloc=540.3MB, time=39.75 memory used=2573.2MB, alloc=540.3MB, time=41.09 memory used=2659.3MB, alloc=540.3MB, time=42.68 memory used=2740.5MB, alloc=540.3MB, time=44.12 memory used=2816.9MB, alloc=564.3MB, time=45.24 memory used=2894.4MB, alloc=564.3MB, time=46.40 memory used=2975.0MB, alloc=564.3MB, time=47.38 memory used=3045.3MB, alloc=564.3MB, time=48.49 memory used=3127.1MB, alloc=588.3MB, time=49.95 memory used=3375.4MB, alloc=612.3MB, time=54.25 memory used=3630.8MB, alloc=636.3MB, time=58.58 memory used=3855.1MB, alloc=660.3MB, time=62.01 memory used=4092.9MB, alloc=684.3MB, time=65.15 memory used=4271.2MB, alloc=708.3MB, time=68.50 memory used=4442.9MB, alloc=708.3MB, time=71.55 memory used=4619.0MB, alloc=732.3MB, time=75.41 memory used=4798.3MB, alloc=732.3MB, time=78.98 memory used=4958.7MB, alloc=732.3MB, time=82.40 memory used=5125.9MB, alloc=756.3MB, time=85.12 memory used=5241.9MB, alloc=756.3MB, time=87.14 memory used=5384.2MB, alloc=780.3MB, time=89.30 memory used=5556.5MB, alloc=780.3MB, time=93.08 memory used=5755.8MB, alloc=780.3MB, time=95.67 memory used=5853.9MB, alloc=780.3MB, time=97.78 memory used=5962.0MB, alloc=804.3MB, time=99.84 memory used=6399.9MB, alloc=828.3MB, time=108.61 memory used=6853.6MB, alloc=852.3MB, time=117.09 memory used=7089.2MB, alloc=876.3MB, time=121.16 memory used=7543.5MB, alloc=900.3MB, time=127.42 memory used=8011.6MB, alloc=924.3MB, time=136.10 memory used=8478.4MB, alloc=948.3MB, time=143.22 memory used=8895.8MB, alloc=972.3MB, time=148.84 memory used=9381.7MB, alloc=996.3MB, time=159.20 memory used=9771.5MB, alloc=1020.3MB, time=166.60 memory used=10282.5MB, alloc=1044.3MB, time=175.83 memory used=10592.1MB, alloc=1068.3MB, time=180.28 memory used=10921.7MB, alloc=1092.3MB, time=185.56 memory used=11251.1MB, alloc=1116.3MB, time=191.23 memory used=11675.2MB, alloc=1140.3MB, time=196.69 memory used=12231.8MB, alloc=1164.3MB, time=205.05 memory used=12959.2MB, alloc=1188.3MB, time=214.18 memory used=13654.5MB, alloc=1212.3MB, time=234.25 memory used=14118.7MB, alloc=1236.3MB, time=240.69 memory used=14530.5MB, alloc=1236.3MB, time=245.99 memory used=14961.6MB, alloc=1236.3MB, time=251.98 memory used=15653.9MB, alloc=1260.3MB, time=262.80 memory used=16466.2MB, alloc=1284.3MB, time=282.22 memory used=17330.0MB, alloc=1308.3MB, time=299.37 memory used=18122.9MB, alloc=1332.3MB, time=313.10 memory used=18558.8MB, alloc=1356.3MB, time=320.22 memory used=19461.4MB, alloc=1380.3MB, time=337.78 memory used=19953.3MB, alloc=1404.3MB, time=349.63 memory used=20317.6MB, alloc=1428.3MB, time=354.86 memory used=20718.8MB, alloc=1467.8MB, time=364.56 memory used=21118.3MB, alloc=1491.8MB, time=369.56 memory used=21535.0MB, alloc=1515.8MB, time=374.57 memory used=21755.2MB, alloc=1539.8MB, time=385.76 memory used=21845.7MB, alloc=1563.8MB, time=388.73 memory used=22327.7MB, alloc=1587.8MB, time=394.26 memory used=22633.7MB, alloc=1611.8MB, time=404.16 memory used=23626.2MB, alloc=1635.8MB, time=425.86 memory used=24635.3MB, alloc=1659.8MB, time=456.45 memory used=25551.1MB, alloc=1683.8MB, time=476.55 memory used=26494.9MB, alloc=1707.8MB, time=498.77 memory used=27152.5MB, alloc=1731.8MB, time=518.43 memory used=28138.6MB, alloc=1755.8MB, time=538.03 memory used=28822.3MB, alloc=1779.8MB, time=554.88 memory used=29634.7MB, alloc=1803.8MB, time=572.15 memory used=30503.3MB, alloc=1827.8MB, time=590.79 memory used=31535.2MB, alloc=1851.8MB, time=617.45 memory used=32514.6MB, alloc=1875.8MB, time=640.52 memory used=33109.6MB, alloc=1899.8MB, time=655.71 memory used=33674.2MB, alloc=1923.8MB, time=672.09 memory used=34141.4MB, alloc=1947.8MB, time=686.44 memory used=34673.8MB, alloc=1971.8MB, time=703.10 memory used=35100.3MB, alloc=1995.8MB, time=716.94 memory used=35682.8MB, alloc=2019.8MB, time=732.67 memory used=36081.7MB, alloc=2043.8MB, time=744.42 memory used=36587.6MB, alloc=2067.8MB, time=759.75 memory used=37281.7MB, alloc=2091.8MB, time=771.99 memory used=37564.2MB, alloc=2115.8MB, time=781.42 memory used=37870.3MB, alloc=2139.8MB, time=792.30 memory used=38727.7MB, alloc=2163.8MB, time=822.48 memory used=39186.9MB, alloc=2187.8MB, time=835.53 memory used=39531.8MB, alloc=2211.8MB, time=850.11 memory used=40269.3MB, alloc=2235.8MB, time=872.88 memory used=40562.4MB, alloc=2259.8MB, time=885.56 memory used=41418.4MB, alloc=2283.8MB, time=901.33 memory used=41772.3MB, alloc=2307.8MB, time=911.54 memory used=42040.6MB, alloc=2331.8MB, time=920.73 memory used=42799.9MB, alloc=2331.8MB, time=937.41 memory used=43297.7MB, alloc=2331.8MB, time=949.94 memory used=43519.8MB, alloc=2331.8MB, time=959.54 memory used=43913.8MB, alloc=2331.8MB, time=971.98 memory used=44088.4MB, alloc=2331.8MB, time=981.88 memory used=44374.5MB, alloc=2355.8MB, time=997.35 memory used=45180.3MB, alloc=2379.8MB, time=1035.42 memory used=45794.9MB, alloc=2379.8MB, time=1058.43 memory used=46330.4MB, alloc=2379.8MB, time=1075.81 memory used=46724.0MB, alloc=2379.8MB, time=1094.74 memory used=46873.0MB, alloc=2379.8MB, time=1103.73 memory used=46999.5MB, alloc=2379.8MB, time=1113.44 memory used=47745.8MB, alloc=2403.8MB, time=1151.00 memory used=48599.8MB, alloc=2403.8MB, time=1176.45 memory used=48746.9MB, alloc=2403.8MB, time=1185.98 memory used=49025.2MB, alloc=2403.8MB, time=1197.13 memory used=49203.0MB, alloc=2403.8MB, time=1206.24 memory used=49317.2MB, alloc=2403.8MB, time=1214.46 |\^/| 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(); 1428471163 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 2 2 3 2 2 F := [-10 x y - 14 y + 8 z , -5 x y - 7 x y + 8 x y, -4 z + 3 x - 8 z ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 3 2 G := [x + 15 y z - 18 y z, 9 z + 8 x z - 5 z, -7 x y - 10 y - 8 x] > Problem := [F,G]; Problem := [ 2 3 2 2 2 3 2 2 [-10 x y - 14 y + 8 z , -5 x y - 7 x y + 8 x y, -4 z + 3 x - 8 z ], 3 2 3 2 [x + 15 y z - 18 y z, 9 z + 8 x z - 5 z, -7 x y - 10 y - 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=0.18 memory used=26.5MB, alloc=32.3MB, time=0.50 memory used=48.0MB, alloc=32.3MB, time=0.81 memory used=68.4MB, alloc=32.3MB, time=1.11 memory used=86.0MB, alloc=56.3MB, time=1.38 memory used=124.9MB, alloc=60.3MB, time=1.96 memory used=165.0MB, alloc=92.3MB, time=2.56 memory used=228.5MB, alloc=92.3MB, time=3.47 memory used=293.4MB, alloc=116.3MB, time=4.34 memory used=379.8MB, alloc=372.3MB, time=5.49 memory used=479.1MB, alloc=372.3MB, time=6.56 memory used=544.7MB, alloc=372.3MB, time=7.15 memory used=584.7MB, alloc=372.3MB, time=7.39 memory used=637.3MB, alloc=372.3MB, time=7.75 memory used=720.6MB, alloc=396.3MB, time=8.91 memory used=820.7MB, alloc=396.3MB, time=10.34 memory used=925.4MB, alloc=420.3MB, time=11.79 memory used=1051.4MB, alloc=444.3MB, time=13.65 memory used=1202.0MB, alloc=444.3MB, time=15.23 memory used=1278.0MB, alloc=444.3MB, time=24.54 memory used=1374.8MB, alloc=444.3MB, time=38.60 memory used=1432.3MB, alloc=444.3MB, time=38.80 memory used=1521.5MB, alloc=444.3MB, time=39.33 memory used=1602.7MB, alloc=468.3MB, time=50.62 memory used=1705.1MB, alloc=468.3MB, time=62.93 memory used=1796.2MB, alloc=468.3MB, time=63.30 memory used=1897.5MB, alloc=468.3MB, time=66.11 memory used=2010.3MB, alloc=468.3MB, time=87.03 memory used=2082.9MB, alloc=468.3MB, time=87.25 memory used=2176.8MB, alloc=468.3MB, time=87.83 memory used=2267.6MB, alloc=468.3MB, time=88.14 memory used=2441.0MB, alloc=468.3MB, time=88.73 memory used=2645.6MB, alloc=468.3MB, time=89.16 memory used=2831.5MB, alloc=468.3MB, time=94.22 memory used=2990.0MB, alloc=468.3MB, time=96.03 memory used=3137.7MB, alloc=468.3MB, time=97.39 memory used=3233.2MB, alloc=492.3MB, time=120.40 memory used=3361.0MB, alloc=492.3MB, time=146.42 memory used=3439.5MB, alloc=492.3MB, time=146.66 memory used=3526.0MB, alloc=492.3MB, time=146.90 memory used=3619.6MB, alloc=492.3MB, time=147.17 memory used=3737.3MB, alloc=492.3MB, time=147.72 memory used=3851.5MB, alloc=492.3MB, time=183.98 memory used=3974.7MB, alloc=492.3MB, time=197.01 memory used=4052.4MB, alloc=492.3MB, time=197.26 memory used=4137.1MB, alloc=492.3MB, time=197.53 memory used=4228.9MB, alloc=492.3MB, time=197.79 memory used=4344.1MB, alloc=492.3MB, time=198.23 memory used=4452.3MB, alloc=492.3MB, time=221.31 memory used=4587.3MB, alloc=492.3MB, time=247.48 memory used=4662.7MB, alloc=492.3MB, time=247.75 memory used=4745.9MB, alloc=492.3MB, time=248.01 memory used=4836.1MB, alloc=492.3MB, time=248.27 memory used=4984.8MB, alloc=492.3MB, time=251.78 memory used=5075.2MB, alloc=492.3MB, time=252.11 memory used=5250.7MB, alloc=492.3MB, time=253.90 memory used=5397.9MB, alloc=492.3MB, time=256.97 memory used=5482.6MB, alloc=492.3MB, time=257.35 memory used=5561.5MB, alloc=492.3MB, time=257.74 memory used=5655.0MB, alloc=492.3MB, time=258.14 memory used=5761.1MB, alloc=492.3MB, time=258.55 memory used=5846.4MB, alloc=516.3MB, time=258.93 memory used=5922.4MB, alloc=516.3MB, time=259.28 memory used=6003.0MB, alloc=516.3MB, time=259.65 memory used=6089.8MB, alloc=516.3MB, time=260.04 memory used=6182.6MB, alloc=516.3MB, time=260.42 memory used=6285.0MB, alloc=516.3MB, time=260.80 memory used=6392.7MB, alloc=516.3MB, time=261.17 memory used=6509.2MB, alloc=516.3MB, time=261.53 memory used=6633.5MB, alloc=516.3MB, time=261.88 memory used=6758.4MB, alloc=516.3MB, time=262.23 memory used=6848.4MB, alloc=516.3MB, time=262.53 memory used=6922.0MB, alloc=516.3MB, time=262.82 memory used=6996.7MB, alloc=516.3MB, time=263.11 memory used=7077.1MB, alloc=516.3MB, time=263.39 memory used=7160.3MB, alloc=516.3MB, time=263.69 memory used=7250.2MB, alloc=516.3MB, time=263.97 memory used=7347.8MB, alloc=516.3MB, time=264.25 memory used=7458.7MB, alloc=516.3MB, time=264.53 memory used=7657.2MB, alloc=516.3MB, time=307.96 memory used=7924.7MB, alloc=516.3MB, time=752.22 memory used=8158.6MB, alloc=516.3MB, time=1060.53 memory used=8330.8MB, alloc=531.8MB, time=1208.23 memory used=8649.2MB, alloc=531.8MB, time=1226.65 memory used=8845.0MB, alloc=531.8MB, time=1227.04 memory used=9046.7MB, alloc=531.8MB, time=1227.45 memory used=9251.1MB, alloc=531.8MB, time=1227.86 memory used=9463.3MB, alloc=531.8MB, time=1228.27 memory used=9676.1MB, alloc=531.8MB, time=1228.69 memory used=9893.7MB, alloc=531.8MB, time=1229.11 memory used=10116.0MB, alloc=531.8MB, time=1229.53 memory used=10276.5MB, alloc=531.8MB, time=1229.90 memory used=10428.9MB, alloc=531.8MB, time=1230.25 memory used=10586.4MB, alloc=531.8MB, time=1230.61 memory used=10747.2MB, alloc=531.8MB, time=1230.96 memory used=10909.4MB, alloc=531.8MB, time=1231.29 memory used=11075.7MB, alloc=531.8MB, time=1231.65 memory used=11243.4MB, alloc=531.8MB, time=1232.01 memory used=11416.4MB, alloc=531.8MB, time=1232.37 memory used=11596.0MB, alloc=531.8MB, time=1232.74 memory used=11782.3MB, alloc=531.8MB, time=1233.11 memory used=12065.7MB, alloc=531.8MB, time=1238.73 memory used=12159.0MB, alloc=531.8MB, time=1239.13 memory used=12271.9MB, alloc=531.8MB, time=1239.56 memory used=12405.1MB, alloc=531.8MB, time=1239.99 memory used=12487.2MB, alloc=531.8MB, time=1240.34 memory used=12565.5MB, alloc=531.8MB, time=1240.70 memory used=12651.0MB, alloc=531.8MB, time=1241.06 memory used=12742.6MB, alloc=531.8MB, time=1241.41 memory used=12840.1MB, alloc=531.8MB, time=1241.77 memory used=12943.3MB, alloc=531.8MB, time=1242.17 memory used=13055.4MB, alloc=531.8MB, time=1242.54 memory used=13175.9MB, alloc=531.8MB, time=1242.92 memory used=13303.5MB, alloc=531.8MB, time=1243.30 memory used=13417.2MB, alloc=531.8MB, time=1243.67 memory used=13488.8MB, alloc=531.8MB, time=1243.97 memory used=13562.8MB, alloc=531.8MB, time=1244.25 memory used=13639.0MB, alloc=531.8MB, time=1244.54 memory used=13719.0MB, alloc=531.8MB, time=1244.83 memory used=13804.4MB, alloc=531.8MB, time=1245.13 memory used=13896.6MB, alloc=531.8MB, time=1245.42 memory used=13997.4MB, alloc=531.8MB, time=1245.70 memory used=14114.7MB, alloc=531.8MB, time=1245.98 memory used=14518.0MB, alloc=531.8MB, time=1653.98 |\^/| 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(); 1428472363 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 3 2 2 2 2 2 F := [15 x z + 14 y z - 8, -x - 5 x z + 7 x y , -7 y z - y - 2 z ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 3 2 2 G := [12 x z + 3 y z - 17 z, 4 x z + 2 y - 9 y z , -2 x y + 5 y + 6 z] > Problem := [F,G]; Problem := [ 2 2 3 2 2 2 2 2 [15 x z + 14 y z - 8, -x - 5 x z + 7 x y , -7 y z - y - 2 z ], 2 2 2 3 2 2 [12 x z + 3 y z - 17 z, 4 x z + 2 y - 9 y z , -2 x y + 5 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=0.17 memory used=26.3MB, alloc=32.3MB, time=0.49 memory used=47.5MB, alloc=32.3MB, time=0.79 memory used=67.9MB, alloc=56.3MB, time=1.11 memory used=109.5MB, alloc=68.3MB, time=1.73 memory used=148.2MB, alloc=92.3MB, time=2.33 memory used=211.6MB, alloc=116.3MB, time=3.28 memory used=283.2MB, alloc=372.3MB, time=4.34 memory used=371.3MB, alloc=396.3MB, time=5.64 memory used=483.6MB, alloc=420.3MB, time=7.32 memory used=616.1MB, alloc=444.3MB, time=9.38 memory used=750.6MB, alloc=468.3MB, time=11.49 memory used=866.8MB, alloc=468.3MB, time=13.32 memory used=986.5MB, alloc=468.3MB, time=15.25 memory used=1091.4MB, alloc=492.3MB, time=16.87 memory used=1186.5MB, alloc=492.3MB, time=18.33 memory used=1273.7MB, alloc=492.3MB, time=19.75 memory used=1362.0MB, alloc=492.3MB, time=21.19 memory used=1461.8MB, alloc=492.3MB, time=23.01 memory used=1544.7MB, alloc=492.3MB, time=24.46 memory used=1618.0MB, alloc=516.3MB, time=25.68 memory used=1684.4MB, alloc=516.3MB, time=26.73 memory used=1755.8MB, alloc=516.3MB, time=28.05 memory used=1824.0MB, alloc=516.3MB, time=29.34 memory used=1895.9MB, alloc=516.3MB, time=30.77 memory used=1974.0MB, alloc=516.3MB, time=32.50 memory used=2045.1MB, alloc=516.3MB, time=33.95 memory used=2119.9MB, alloc=516.3MB, time=35.56 memory used=2172.2MB, alloc=540.3MB, time=36.69 memory used=2395.8MB, alloc=564.3MB, time=40.87 memory used=2594.1MB, alloc=588.3MB, time=44.05 memory used=2753.1MB, alloc=612.3MB, time=46.37 memory used=2906.1MB, alloc=636.3MB, time=49.48 memory used=3052.0MB, alloc=660.3MB, time=51.91 memory used=3188.0MB, alloc=660.3MB, time=54.81 memory used=3320.5MB, alloc=660.3MB, time=57.62 memory used=3455.5MB, alloc=660.3MB, time=60.48 memory used=3577.5MB, alloc=684.3MB, time=62.98 memory used=3702.6MB, alloc=684.3MB, time=65.93 memory used=3818.9MB, alloc=684.3MB, time=68.61 memory used=4165.1MB, alloc=708.3MB, time=74.96 memory used=4537.7MB, alloc=732.3MB, time=81.81 memory used=4924.7MB, alloc=756.3MB, time=88.75 memory used=5260.4MB, alloc=780.3MB, time=94.57 memory used=5520.6MB, alloc=804.3MB, time=99.84 memory used=5791.1MB, alloc=828.3MB, time=105.14 memory used=6087.1MB, alloc=852.3MB, time=110.31 memory used=6353.0MB, alloc=876.3MB, time=115.53 memory used=6608.6MB, alloc=900.3MB, time=121.26 memory used=6848.7MB, alloc=924.3MB, time=125.76 memory used=7038.1MB, alloc=948.3MB, time=130.32 memory used=7249.8MB, alloc=972.3MB, time=135.79 memory used=7836.7MB, alloc=996.3MB, time=146.67 memory used=8420.7MB, alloc=1020.3MB, time=159.73 memory used=9003.9MB, alloc=1044.3MB, time=171.38 memory used=9612.9MB, alloc=1068.3MB, time=182.34 memory used=10246.6MB, alloc=1092.3MB, time=195.59 memory used=10885.3MB, alloc=1116.3MB, time=210.58 memory used=11474.2MB, alloc=1140.3MB, time=223.89 memory used=12003.8MB, alloc=1164.3MB, time=237.80 memory used=12550.1MB, alloc=1188.3MB, time=252.58 memory used=13036.8MB, alloc=1212.3MB, time=266.65 memory used=13440.9MB, alloc=1236.3MB, time=277.48 memory used=13818.1MB, alloc=1260.3MB, time=287.63 memory used=14227.4MB, alloc=1284.3MB, time=300.19 memory used=14579.6MB, alloc=1308.3MB, time=310.03 memory used=14959.5MB, alloc=1332.3MB, time=320.40 memory used=15316.9MB, alloc=1356.3MB, time=331.03 memory used=15625.2MB, alloc=1380.3MB, time=341.41 memory used=15923.9MB, alloc=1404.3MB, time=351.25 memory used=16119.8MB, alloc=1428.3MB, time=358.33 memory used=16393.0MB, alloc=1452.3MB, time=367.73 memory used=16691.1MB, alloc=1476.3MB, time=377.34 memory used=16821.9MB, alloc=1500.3MB, time=384.39 memory used=17078.3MB, alloc=1524.3MB, time=394.68 memory used=17249.6MB, alloc=1548.3MB, time=403.55 memory used=17414.0MB, alloc=1572.3MB, time=412.43 memory used=17526.8MB, alloc=1596.3MB, time=419.32 memory used=17605.8MB, alloc=1620.3MB, time=425.42 memory used=17740.9MB, alloc=1644.3MB, time=432.59 memory used=17923.5MB, alloc=1668.3MB, time=439.68 memory used=18039.8MB, alloc=1692.3MB, time=446.93 memory used=18156.6MB, alloc=1716.3MB, time=453.14 memory used=18410.1MB, alloc=1740.3MB, time=461.70 memory used=18523.3MB, alloc=1764.3MB, time=468.67 memory used=18713.8MB, alloc=1788.3MB, time=476.85 memory used=18860.3MB, alloc=1788.3MB, time=484.27 memory used=18935.4MB, alloc=1788.3MB, time=490.52 memory used=19022.7MB, alloc=1788.3MB, time=496.75 memory used=19120.8MB, alloc=1788.3MB, time=504.78 memory used=19226.7MB, alloc=1812.3MB, time=511.89 memory used=19353.9MB, alloc=1812.3MB, time=518.80 memory used=19385.5MB, alloc=1812.3MB, time=524.32 memory used=19503.0MB, alloc=1812.3MB, time=532.10 memory used=19549.1MB, alloc=1812.3MB, time=538.60 memory used=19613.6MB, alloc=1812.3MB, time=545.06 memory used=19663.0MB, alloc=1812.3MB, time=551.41 memory used=19777.4MB, alloc=1812.3MB, time=559.38 memory used=19804.6MB, alloc=1812.3MB, time=565.23 memory used=19810.6MB, alloc=1812.3MB, time=570.71 memory used=19843.7MB, alloc=1812.3MB, time=576.51 memory used=19904.6MB, alloc=1812.3MB, time=582.99 memory used=19984.2MB, alloc=1812.3MB, time=590.71 memory used=20014.9MB, alloc=1812.3MB, time=596.74 memory used=20072.7MB, alloc=1812.3MB, time=603.20 memory used=20109.1MB, alloc=2068.3MB, time=615.30 memory used=21382.5MB, alloc=2092.3MB, time=641.14 memory used=22588.7MB, alloc=2116.3MB, time=667.37 memory used=23799.6MB, alloc=2140.3MB, time=695.14 memory used=24943.1MB, alloc=2164.3MB, time=723.34 memory used=26077.0MB, alloc=2188.3MB, time=748.16 memory used=27236.7MB, alloc=2212.3MB, time=772.54 memory used=28315.7MB, alloc=2236.3MB, time=801.22 memory used=29471.7MB, alloc=2260.3MB, time=840.39 memory used=30356.0MB, alloc=2284.3MB, time=866.48 memory used=31174.4MB, alloc=2308.3MB, time=892.14 memory used=32042.3MB, alloc=2332.3MB, time=919.24 memory used=32789.7MB, alloc=2356.3MB, time=945.88 memory used=33499.0MB, alloc=2380.3MB, time=972.33 memory used=34198.3MB, alloc=2404.3MB, time=999.01 |\^/| 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(); 1428473564 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 3 2 F := [-13 x z - 13 y + 15 x y, -5 y z - 5 z - 2, 10 y z + y z + 3 z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 2 G := [-4 x - 2 x y - 5, -8 x y z + 6 x z - 4, 8 x z - 10 x + 9] > Problem := [F,G]; Problem := [ 2 3 2 3 2 [-13 x z - 13 y + 15 x y, -5 y z - 5 z - 2, 10 y z + y z + 3 z], 3 2 2 2 [-4 x - 2 x y - 5, -8 x y z + 6 x z - 4, 8 x z - 10 x + 9]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.7MB, alloc=32.3MB, time=0.50 memory used=47.6MB, alloc=32.3MB, time=0.80 memory used=66.8MB, alloc=56.3MB, time=1.09 memory used=108.3MB, alloc=60.3MB, time=1.67 memory used=147.8MB, alloc=60.3MB, time=2.22 memory used=191.1MB, alloc=84.3MB, time=2.78 memory used=229.0MB, alloc=84.3MB, time=3.21 memory used=292.2MB, alloc=92.3MB, time=4.12 memory used=353.9MB, alloc=116.3MB, time=5.02 memory used=421.2MB, alloc=116.3MB, time=6.00 memory used=484.9MB, alloc=372.3MB, time=6.95 memory used=569.6MB, alloc=396.3MB, time=8.13 memory used=678.4MB, alloc=420.3MB, time=9.71 memory used=801.5MB, alloc=420.3MB, time=11.24 memory used=941.1MB, alloc=444.3MB, time=12.60 memory used=1087.4MB, alloc=444.3MB, time=14.19 memory used=1215.6MB, alloc=468.3MB, time=16.10 memory used=1330.9MB, alloc=468.3MB, time=17.91 memory used=1439.3MB, alloc=492.3MB, time=19.72 memory used=1547.5MB, alloc=492.3MB, time=21.51 memory used=1655.7MB, alloc=492.3MB, time=23.45 memory used=1739.6MB, alloc=516.3MB, time=24.81 memory used=1817.4MB, alloc=516.3MB, time=26.09 memory used=1891.5MB, alloc=516.3MB, time=27.49 memory used=1987.4MB, alloc=516.3MB, time=28.86 memory used=2056.5MB, alloc=516.3MB, time=30.04 memory used=2137.8MB, alloc=516.3MB, time=31.62 memory used=2204.8MB, alloc=540.3MB, time=32.72 memory used=2257.7MB, alloc=540.3MB, time=33.84 memory used=2322.7MB, alloc=540.3MB, time=35.15 memory used=2383.0MB, alloc=540.3MB, time=36.44 memory used=2431.1MB, alloc=540.3MB, time=37.47 memory used=2639.1MB, alloc=564.3MB, time=40.98 memory used=2852.5MB, alloc=588.3MB, time=44.95 memory used=3030.5MB, alloc=612.3MB, time=48.19 memory used=3210.6MB, alloc=636.3MB, time=51.67 memory used=3344.4MB, alloc=660.3MB, time=53.99 memory used=3498.6MB, alloc=660.3MB, time=56.84 memory used=3655.7MB, alloc=684.3MB, time=59.64 memory used=3787.8MB, alloc=684.3MB, time=62.52 memory used=3901.5MB, alloc=684.3MB, time=64.68 memory used=4018.1MB, alloc=684.3MB, time=67.18 memory used=4100.0MB, alloc=684.3MB, time=69.08 memory used=4216.2MB, alloc=684.3MB, time=71.86 memory used=4558.5MB, alloc=708.3MB, time=78.58 memory used=4804.2MB, alloc=732.3MB, time=81.37 memory used=5202.3MB, alloc=756.3MB, time=86.10 memory used=5628.8MB, alloc=780.3MB, time=91.55 memory used=6037.3MB, alloc=804.3MB, time=99.13 memory used=6385.7MB, alloc=828.3MB, time=105.66 memory used=6732.8MB, alloc=852.3MB, time=113.33 memory used=7055.7MB, alloc=876.3MB, time=120.44 memory used=7375.3MB, alloc=900.3MB, time=128.17 memory used=7644.6MB, alloc=924.3MB, time=134.90 memory used=7991.2MB, alloc=948.3MB, time=143.00 memory used=8270.1MB, alloc=972.3MB, time=148.48 memory used=8495.7MB, alloc=996.3MB, time=152.47 memory used=8755.6MB, alloc=1020.3MB, time=158.26 memory used=8974.4MB, alloc=1044.3MB, time=163.98 memory used=9535.8MB, alloc=1068.3MB, time=174.36 memory used=10149.6MB, alloc=1092.3MB, time=185.30 memory used=10820.4MB, alloc=1116.3MB, time=199.87 memory used=11546.8MB, alloc=1140.3MB, time=216.10 memory used=12276.2MB, alloc=1164.3MB, time=233.55 memory used=13006.1MB, alloc=1188.3MB, time=250.78 memory used=13730.2MB, alloc=1212.3MB, time=271.81 memory used=14357.7MB, alloc=1236.3MB, time=287.86 memory used=15036.6MB, alloc=1260.3MB, time=306.92 memory used=15649.2MB, alloc=1284.3MB, time=326.71 memory used=16189.0MB, alloc=1308.3MB, time=342.85 memory used=16703.2MB, alloc=1332.3MB, time=359.48 memory used=17165.4MB, alloc=1356.3MB, time=375.88 memory used=17670.6MB, alloc=1380.3MB, time=388.53 memory used=18193.9MB, alloc=1404.3MB, time=399.46 memory used=18721.1MB, alloc=1428.3MB, time=410.90 memory used=19140.9MB, alloc=1452.3MB, time=422.11 memory used=19576.6MB, alloc=1476.3MB, time=434.23 memory used=20162.7MB, alloc=1500.3MB, time=445.80 memory used=20550.7MB, alloc=1524.3MB, time=452.22 memory used=20980.5MB, alloc=1548.3MB, time=462.16 memory used=21360.4MB, alloc=1572.3MB, time=472.05 memory used=21941.6MB, alloc=1596.3MB, time=480.82 memory used=22523.2MB, alloc=1620.3MB, time=491.82 memory used=22899.0MB, alloc=1644.3MB, time=500.82 memory used=23382.2MB, alloc=1668.3MB, time=511.84 memory used=23998.1MB, alloc=1692.3MB, time=521.49 memory used=24303.2MB, alloc=1716.3MB, time=532.48 memory used=24887.0MB, alloc=1740.3MB, time=545.73 memory used=25361.7MB, alloc=1779.8MB, time=558.78 memory used=25744.1MB, alloc=1803.8MB, time=568.71 memory used=26124.7MB, alloc=1827.8MB, time=579.27 memory used=26370.0MB, alloc=1851.8MB, time=589.11 memory used=26502.5MB, alloc=1875.8MB, time=596.40 memory used=26760.5MB, alloc=1899.8MB, time=606.14 memory used=26927.8MB, alloc=1923.8MB, time=614.46 memory used=27127.9MB, alloc=1947.8MB, time=624.45 memory used=27362.8MB, alloc=1947.8MB, time=634.41 memory used=27482.7MB, alloc=1947.8MB, time=642.86 memory used=27607.8MB, alloc=1947.8MB, time=650.70 memory used=27823.3MB, alloc=1947.8MB, time=659.70 memory used=28225.7MB, alloc=1947.8MB, time=670.54 memory used=28426.1MB, alloc=1947.8MB, time=678.22 memory used=28591.0MB, alloc=1947.8MB, time=686.23 memory used=28907.9MB, alloc=1947.8MB, time=698.03 memory used=29152.2MB, alloc=1947.8MB, time=705.80 memory used=29362.3MB, alloc=1947.8MB, time=714.02 memory used=29934.1MB, alloc=1947.8MB, time=728.34 memory used=30022.8MB, alloc=1947.8MB, time=736.48 memory used=30308.4MB, alloc=1971.8MB, time=744.77 memory used=30528.2MB, alloc=1971.8MB, time=753.28 memory used=30645.0MB, alloc=1971.8MB, time=761.07 memory used=30805.0MB, alloc=1971.8MB, time=769.22 memory used=30889.0MB, alloc=1971.8MB, time=776.11 memory used=31006.0MB, alloc=1971.8MB, time=784.92 memory used=31099.2MB, alloc=1971.8MB, time=792.09 memory used=31203.2MB, alloc=1971.8MB, time=799.49 memory used=31312.6MB, alloc=1971.8MB, time=808.76 memory used=31388.1MB, alloc=1971.8MB, time=816.46 memory used=31590.0MB, alloc=1971.8MB, time=825.02 memory used=31739.5MB, alloc=1971.8MB, time=832.13 memory used=31883.8MB, alloc=1971.8MB, time=839.49 memory used=31909.9MB, alloc=1971.8MB, time=846.16 memory used=32026.8MB, alloc=1971.8MB, time=855.22 memory used=32101.9MB, alloc=1971.8MB, time=862.41 memory used=32275.3MB, alloc=1971.8MB, time=869.82 memory used=32509.6MB, alloc=1995.8MB, time=878.11 memory used=32776.0MB, alloc=1995.8MB, time=890.54 memory used=32999.3MB, alloc=1995.8MB, time=897.10 memory used=33091.2MB, alloc=1995.8MB, time=903.50 memory used=33372.9MB, alloc=1995.8MB, time=911.71 memory used=33568.8MB, alloc=1995.8MB, time=918.05 memory used=33946.1MB, alloc=1995.8MB, time=926.23 memory used=34568.8MB, alloc=1995.8MB, time=951.26 memory used=34647.8MB, alloc=1995.8MB, time=957.56 memory used=34735.4MB, alloc=1995.8MB, time=963.87 memory used=34832.3MB, alloc=1995.8MB, time=970.19 memory used=34942.4MB, alloc=1995.8MB, time=976.46 memory used=35070.3MB, alloc=1995.8MB, time=982.75 memory used=35326.7MB, alloc=1995.8MB, time=989.90 memory used=35489.0MB, alloc=1995.8MB, time=996.91 memory used=35567.7MB, alloc=1995.8MB, time=1004.33 memory used=35609.3MB, alloc=2251.8MB, time=1018.19 memory used=37041.8MB, alloc=2275.8MB, time=1046.94 memory used=38164.8MB, alloc=2299.8MB, time=1070.09 memory used=38368.0MB, alloc=2323.8MB, time=1076.62 memory used=38793.1MB, alloc=2347.8MB, time=1085.19 memory used=39204.6MB, alloc=2371.8MB, time=1093.88 memory used=39811.1MB, alloc=2395.8MB, time=1111.20 memory used=39977.6MB, alloc=2419.8MB, time=1118.74 memory used=40186.9MB, alloc=2443.8MB, time=1126.26 memory used=40413.3MB, alloc=2467.8MB, time=1133.76 memory used=41996.6MB, alloc=2491.8MB, time=1166.47 memory used=43464.8MB, alloc=2515.8MB, time=1201.97 |\^/| 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(); 1428474764 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 3 2 2 F := [-9 y z - 18 z + 13 x, 5 x z - 5 y + 6 y , 8 x y z - 5 y - 8] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 G := [4 x y + 3 y + 18 z, -4 x - 8 x y z + 7 z, -7 y z - 7 x y - 10 y] > Problem := [F,G]; 2 2 2 3 2 2 Problem := [[-9 y z - 18 z + 13 x, 5 x z - 5 y + 6 y , 8 x y z - 5 y - 8], 2 3 2 [4 x y + 3 y + 18 z, -4 x - 8 x y z + 7 z, -7 y z - 7 x y - 10 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.21 memory used=25.7MB, alloc=32.3MB, time=0.51 memory used=47.3MB, alloc=36.3MB, time=0.82 memory used=67.0MB, alloc=60.3MB, time=1.10 memory used=108.6MB, alloc=68.3MB, time=1.66 memory used=156.6MB, alloc=68.3MB, time=2.22 memory used=198.8MB, alloc=68.3MB, time=2.81 memory used=243.1MB, alloc=92.3MB, time=3.38 memory used=306.3MB, alloc=92.3MB, time=4.18 memory used=369.7MB, alloc=348.3MB, time=5.06 memory used=434.9MB, alloc=372.3MB, time=5.83 memory used=523.5MB, alloc=372.3MB, time=7.09 memory used=609.3MB, alloc=396.3MB, time=8.35 memory used=719.6MB, alloc=396.3MB, time=9.58 memory used=838.0MB, alloc=420.3MB, time=10.95 memory used=963.2MB, alloc=420.3MB, time=12.84 memory used=1067.2MB, alloc=444.3MB, time=14.03 memory used=1164.3MB, alloc=444.3MB, time=15.27 memory used=1282.7MB, alloc=444.3MB, time=16.66 memory used=1379.5MB, alloc=468.3MB, time=17.74 memory used=1475.9MB, alloc=468.3MB, time=19.14 memory used=1570.8MB, alloc=468.3MB, time=20.40 memory used=1639.5MB, alloc=468.3MB, time=21.35 memory used=1734.9MB, alloc=468.3MB, time=22.50 memory used=1798.3MB, alloc=468.3MB, time=23.43 memory used=1887.6MB, alloc=468.3MB, time=24.50 memory used=1968.7MB, alloc=468.3MB, time=25.57 memory used=2020.3MB, alloc=468.3MB, time=26.48 memory used=2089.4MB, alloc=468.3MB, time=27.44 memory used=2147.0MB, alloc=468.3MB, time=28.22 memory used=2200.8MB, alloc=468.3MB, time=29.14 memory used=2252.0MB, alloc=468.3MB, time=29.90 memory used=2324.5MB, alloc=492.3MB, time=30.93 memory used=2366.1MB, alloc=492.3MB, time=31.77 memory used=2411.3MB, alloc=492.3MB, time=32.68 memory used=2600.7MB, alloc=516.3MB, time=35.75 memory used=2787.7MB, alloc=540.3MB, time=38.70 memory used=2970.1MB, alloc=564.3MB, time=41.67 memory used=3130.7MB, alloc=588.3MB, time=44.02 memory used=3315.1MB, alloc=612.3MB, time=46.18 memory used=3478.4MB, alloc=612.3MB, time=49.12 memory used=3624.3MB, alloc=612.3MB, time=51.50 memory used=3756.8MB, alloc=636.3MB, time=53.66 memory used=3918.3MB, alloc=636.3MB, time=55.39 memory used=4041.8MB, alloc=636.3MB, time=57.54 memory used=4172.0MB, alloc=636.3MB, time=59.63 memory used=4381.5MB, alloc=636.3MB, time=61.58 memory used=4507.9MB, alloc=636.3MB, time=63.42 memory used=4608.3MB, alloc=636.3MB, time=65.47 memory used=4703.1MB, alloc=636.3MB, time=67.06 memory used=4802.6MB, alloc=636.3MB, time=69.11 memory used=4889.6MB, alloc=660.3MB, time=70.96 memory used=5215.4MB, alloc=684.3MB, time=76.92 memory used=5576.9MB, alloc=708.3MB, time=82.24 memory used=5925.3MB, alloc=732.3MB, time=87.62 memory used=6299.6MB, alloc=756.3MB, time=92.54 memory used=6684.8MB, alloc=780.3MB, time=97.33 memory used=6958.5MB, alloc=804.3MB, time=102.23 memory used=7289.1MB, alloc=828.3MB, time=106.98 memory used=7586.4MB, alloc=852.3MB, time=112.24 memory used=7908.6MB, alloc=876.3MB, time=116.95 memory used=8156.0MB, alloc=900.3MB, time=122.48 memory used=8377.5MB, alloc=924.3MB, time=126.29 memory used=8586.2MB, alloc=948.3MB, time=130.29 memory used=8810.5MB, alloc=972.3MB, time=135.13 memory used=8998.9MB, alloc=972.3MB, time=139.09 memory used=9159.9MB, alloc=972.3MB, time=142.66 memory used=9763.6MB, alloc=996.3MB, time=153.87 memory used=10358.5MB, alloc=1020.3MB, time=163.40 memory used=10966.2MB, alloc=1044.3MB, time=172.85 memory used=11619.8MB, alloc=1068.3MB, time=182.78 memory used=12151.0MB, alloc=1092.3MB, time=192.40 memory used=12712.0MB, alloc=1116.3MB, time=203.09 memory used=13167.5MB, alloc=1140.3MB, time=211.66 memory used=13626.0MB, alloc=1164.3MB, time=221.45 memory used=14124.2MB, alloc=1188.3MB, time=230.63 memory used=14548.6MB, alloc=1212.3MB, time=240.27 memory used=14972.1MB, alloc=1236.3MB, time=249.03 memory used=15358.8MB, alloc=1260.3MB, time=258.32 memory used=15641.7MB, alloc=1284.3MB, time=265.69 memory used=16026.7MB, alloc=1308.3MB, time=276.42 memory used=16336.0MB, alloc=1332.3MB, time=286.21 memory used=16552.9MB, alloc=1356.3MB, time=293.67 memory used=16694.4MB, alloc=1380.3MB, time=299.48 memory used=16934.8MB, alloc=1404.3MB, time=308.83 memory used=17133.1MB, alloc=1428.3MB, time=316.36 memory used=17306.7MB, alloc=1452.3MB, time=323.06 memory used=17501.9MB, alloc=1476.3MB, time=330.94 memory used=17651.0MB, alloc=1500.3MB, time=338.06 memory used=17837.2MB, alloc=1524.3MB, time=345.09 memory used=17892.8MB, alloc=1548.3MB, time=350.88 memory used=18035.7MB, alloc=1572.3MB, time=357.44 memory used=18191.3MB, alloc=1596.3MB, time=366.00 memory used=18287.6MB, alloc=1620.3MB, time=372.31 memory used=18417.0MB, alloc=1644.3MB, time=379.17 memory used=18519.8MB, alloc=1668.3MB, time=385.64 memory used=18568.0MB, alloc=1668.3MB, time=391.66 memory used=18615.1MB, alloc=1668.3MB, time=397.56 memory used=18723.6MB, alloc=1668.3MB, time=405.58 memory used=18844.7MB, alloc=1668.3MB, time=413.82 memory used=18911.6MB, alloc=1668.3MB, time=420.38 memory used=18979.7MB, alloc=1924.3MB, time=432.55 memory used=20068.4MB, alloc=1948.3MB, time=452.40 memory used=21211.5MB, alloc=1972.3MB, time=474.59 memory used=22253.3MB, alloc=1996.3MB, time=499.20 memory used=23134.6MB, alloc=2020.3MB, time=517.53 memory used=23589.4MB, alloc=2044.3MB, time=528.04 memory used=24567.0MB, alloc=2068.3MB, time=547.22 memory used=25641.8MB, alloc=2092.3MB, time=569.84 memory used=26443.6MB, alloc=2116.3MB, time=587.51 memory used=27423.2MB, alloc=2140.3MB, time=608.30 memory used=28373.3MB, alloc=2164.3MB, time=629.95 memory used=29171.6MB, alloc=2188.3MB, time=647.85 memory used=29980.1MB, alloc=2212.3MB, time=667.00 memory used=30782.9MB, alloc=2236.3MB, time=692.98 memory used=31339.1MB, alloc=2260.3MB, time=713.90 memory used=32016.3MB, alloc=2284.3MB, time=737.64 memory used=32558.5MB, alloc=2308.3MB, time=756.91 memory used=33386.0MB, alloc=2332.3MB, time=779.76 memory used=33739.8MB, alloc=2356.3MB, time=797.50 memory used=34197.5MB, alloc=2380.3MB, time=816.49 memory used=34604.6MB, alloc=2404.3MB, time=834.43 memory used=35069.1MB, alloc=2428.3MB, time=854.41 memory used=35311.7MB, alloc=2452.3MB, time=869.69 memory used=35614.9MB, alloc=2476.3MB, time=886.44 memory used=36099.7MB, alloc=2500.3MB, time=906.53 memory used=36425.8MB, alloc=2524.3MB, time=924.74 memory used=36610.1MB, alloc=2548.3MB, time=940.69 memory used=37002.8MB, alloc=2572.3MB, time=958.00 memory used=37305.0MB, alloc=2596.3MB, time=974.26 memory used=37588.8MB, alloc=2620.3MB, time=992.65 memory used=37743.1MB, alloc=2644.3MB, time=1009.24 memory used=37930.9MB, alloc=2668.3MB, time=1025.13 memory used=38085.2MB, alloc=2692.3MB, time=1041.53 memory used=38296.8MB, alloc=2716.3MB, time=1058.96 memory used=38491.4MB, alloc=2740.3MB, time=1075.07 memory used=38603.5MB, alloc=2764.3MB, time=1090.23 memory used=38727.7MB, alloc=2788.3MB, time=1106.13 memory used=38810.3MB, alloc=2812.3MB, time=1121.25 memory used=38864.7MB, alloc=2836.3MB, time=1136.14 memory used=39070.0MB, alloc=2860.3MB, time=1152.40 memory used=39133.8MB, alloc=2884.3MB, time=1167.28 memory used=39362.5MB, alloc=2908.3MB, time=1183.83 memory used=39463.4MB, alloc=2932.3MB, time=1200.18 |\^/| 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(); 1428475964 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 F := [x y - 14 x y - 6 x, -y + 6 z + 9, -10 x y - 9 y z - 5 x z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 G := [13 x y z + 8 x z - 5 x y, -x y z - 7 x z + 7 y z, -6 x z + 4 x + 9 x] > Problem := [F,G]; 2 2 2 2 Problem := [[x y - 14 x y - 6 x, -y + 6 z + 9, -10 x y - 9 y z - 5 x z], 2 2 2 [13 x y z + 8 x z - 5 x y, -x y z - 7 x z + 7 y z, -6 x z + 4 x + 9 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.1MB, alloc=32.3MB, time=0.47 memory used=47.5MB, alloc=32.3MB, time=0.76 memory used=66.4MB, alloc=56.3MB, time=1.05 memory used=106.0MB, alloc=60.3MB, time=1.64 memory used=144.7MB, alloc=60.3MB, time=2.21 memory used=182.5MB, alloc=84.3MB, time=2.79 memory used=233.9MB, alloc=84.3MB, time=3.57 memory used=292.2MB, alloc=116.3MB, time=4.49 memory used=369.4MB, alloc=116.3MB, time=5.67 memory used=446.1MB, alloc=140.3MB, time=6.96 memory used=530.4MB, alloc=396.3MB, time=8.36 memory used=632.4MB, alloc=396.3MB, time=10.11 memory used=732.9MB, alloc=420.3MB, time=11.89 memory used=857.9MB, alloc=420.3MB, time=14.13 memory used=983.4MB, alloc=444.3MB, time=16.36 memory used=1125.9MB, alloc=468.3MB, time=18.98 memory used=1292.0MB, alloc=492.3MB, time=22.05 memory used=1437.5MB, alloc=492.3MB, time=24.38 memory used=1578.1MB, alloc=516.3MB, time=26.69 memory used=1726.6MB, alloc=540.3MB, time=29.49 memory used=1837.0MB, alloc=540.3MB, time=31.40 memory used=1966.6MB, alloc=564.3MB, time=33.67 memory used=2118.7MB, alloc=588.3MB, time=35.96 memory used=2247.1MB, alloc=588.3MB, time=38.28 memory used=2378.5MB, alloc=612.3MB, time=40.74 memory used=2519.1MB, alloc=636.3MB, time=42.95 memory used=2609.9MB, alloc=636.3MB, time=44.69 memory used=2744.0MB, alloc=660.3MB, time=47.30 memory used=2899.6MB, alloc=684.3MB, time=50.32 memory used=3024.3MB, alloc=708.3MB, time=52.87 memory used=3149.0MB, alloc=732.3MB, time=55.37 memory used=3263.8MB, alloc=732.3MB, time=57.75 memory used=3399.3MB, alloc=756.3MB, time=60.58 memory used=3511.2MB, alloc=780.3MB, time=63.03 memory used=3626.7MB, alloc=804.3MB, time=65.57 memory used=3745.8MB, alloc=828.3MB, time=68.19 memory used=3845.3MB, alloc=828.3MB, time=70.48 memory used=3964.1MB, alloc=852.3MB, time=72.92 memory used=4075.9MB, alloc=876.3MB, time=75.51 memory used=4178.7MB, alloc=876.3MB, time=77.92 memory used=4272.8MB, alloc=900.3MB, time=80.20 memory used=4379.2MB, alloc=924.3MB, time=82.77 memory used=4768.7MB, alloc=948.3MB, time=90.35 memory used=5107.9MB, alloc=972.3MB, time=97.11 memory used=5514.7MB, alloc=996.3MB, time=105.52 memory used=5914.7MB, alloc=1020.3MB, time=113.75 memory used=6303.7MB, alloc=1044.3MB, time=121.90 memory used=6687.0MB, alloc=1068.3MB, time=130.07 memory used=7060.7MB, alloc=1092.3MB, time=138.14 memory used=7426.9MB, alloc=1116.3MB, time=146.12 memory used=7786.9MB, alloc=1140.3MB, time=154.13 memory used=8144.9MB, alloc=1164.3MB, time=162.12 memory used=8507.3MB, alloc=1188.3MB, time=170.02 memory used=8849.3MB, alloc=1212.3MB, time=178.00 memory used=9205.1MB, alloc=1236.3MB, time=186.12 memory used=9552.4MB, alloc=1260.3MB, time=194.05 memory used=9887.3MB, alloc=1284.3MB, time=201.94 memory used=10164.8MB, alloc=1308.3MB, time=211.51 memory used=10413.8MB, alloc=1332.3MB, time=222.56 memory used=10673.8MB, alloc=1356.3MB, time=234.21 memory used=10945.8MB, alloc=1380.3MB, time=246.46 memory used=11231.7MB, alloc=1404.3MB, time=259.68 memory used=11531.7MB, alloc=1428.3MB, time=273.55 memory used=11846.4MB, alloc=1452.3MB, time=288.23 memory used=12176.0MB, alloc=1476.3MB, time=303.67 memory used=12520.4MB, alloc=1500.3MB, time=319.53 memory used=12880.5MB, alloc=1524.3MB, time=335.88 memory used=13255.7MB, alloc=1548.3MB, time=352.77 memory used=13646.2MB, alloc=1572.3MB, time=370.65 memory used=14052.3MB, alloc=1596.3MB, time=389.18 memory used=14474.5MB, alloc=1620.3MB, time=408.53 memory used=14912.2MB, alloc=1644.3MB, time=428.59 memory used=15365.8MB, alloc=1668.3MB, time=449.25 memory used=15835.6MB, alloc=1692.3MB, time=470.73 memory used=16321.4MB, alloc=1716.3MB, time=492.99 memory used=16822.7MB, alloc=1740.3MB, time=516.25 memory used=17340.4MB, alloc=1764.3MB, time=540.46 memory used=17874.3MB, alloc=1788.3MB, time=565.28 memory used=18424.6MB, alloc=1812.3MB, time=590.95 memory used=18991.4MB, alloc=1836.3MB, time=617.88 memory used=19574.5MB, alloc=1860.3MB, time=645.23 memory used=20174.2MB, alloc=1884.3MB, time=673.35 memory used=20790.1MB, alloc=1908.3MB, time=702.07 memory used=21422.6MB, alloc=1932.3MB, time=732.76 memory used=22071.1MB, alloc=1956.3MB, time=763.97 memory used=22735.8MB, alloc=1980.3MB, time=795.08 memory used=23417.3MB, alloc=2004.3MB, time=826.00 memory used=24115.1MB, alloc=2028.3MB, time=858.19 memory used=24829.6MB, alloc=2052.3MB, time=891.09 memory used=25560.2MB, alloc=2076.3MB, time=924.77 |\^/| 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(); 1428477164 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 3 3 2 3 2 2 F := [y z - 16 z - 18 y, 5 x - 9 z + 10 x , -6 x - 3 x z - 6 y z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 2 2 2 2 2 G := [-14 x y - 7 z + 17 y , -4 x y - x z - 7 y, -7 x z + 5 x - 4 z ] > Problem := [F,G]; Problem := [ 2 2 3 3 2 3 2 2 [y z - 16 z - 18 y, 5 x - 9 z + 10 x , -6 x - 3 x z - 6 y z], 2 3 2 2 2 2 2 2 [-14 x y - 7 z + 17 y , -4 x y - x z - 7 y, -7 x z + 5 x - 4 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.18 memory used=25.7MB, alloc=32.3MB, time=0.49 memory used=44.9MB, alloc=32.3MB, time=0.76 memory used=63.6MB, alloc=56.3MB, time=1.04 memory used=104.5MB, alloc=60.3MB, time=1.65 memory used=138.2MB, alloc=60.3MB, time=2.08 memory used=179.9MB, alloc=68.3MB, time=2.60 memory used=226.8MB, alloc=92.3MB, time=3.21 memory used=291.6MB, alloc=92.3MB, time=4.17 memory used=352.9MB, alloc=348.3MB, time=4.92 memory used=423.9MB, alloc=372.3MB, time=5.83 memory used=511.6MB, alloc=372.3MB, time=7.03 memory used=603.9MB, alloc=396.3MB, time=8.29 memory used=719.8MB, alloc=396.3MB, time=9.82 memory used=831.5MB, alloc=420.3MB, time=11.43 memory used=950.6MB, alloc=420.3MB, time=13.06 memory used=1068.4MB, alloc=420.3MB, time=14.30 memory used=1180.8MB, alloc=444.3MB, time=15.86 memory used=1297.5MB, alloc=444.3MB, time=17.37 memory used=1411.6MB, alloc=444.3MB, time=18.64 memory used=1517.2MB, alloc=444.3MB, time=19.97 memory used=1631.9MB, alloc=444.3MB, time=21.36 memory used=1731.8MB, alloc=444.3MB, time=22.84 memory used=1835.0MB, alloc=468.3MB, time=24.10 memory used=1925.4MB, alloc=468.3MB, time=25.39 memory used=2000.1MB, alloc=468.3MB, time=26.51 memory used=2079.5MB, alloc=468.3MB, time=27.65 memory used=2182.1MB, alloc=468.3MB, time=28.73 memory used=2264.7MB, alloc=468.3MB, time=29.82 memory used=2339.6MB, alloc=468.3MB, time=30.89 memory used=2424.0MB, alloc=492.3MB, time=32.44 memory used=2486.0MB, alloc=492.3MB, time=33.52 memory used=2566.8MB, alloc=492.3MB, time=34.87 memory used=2635.6MB, alloc=492.3MB, time=35.91 memory used=2715.8MB, alloc=492.3MB, time=37.38 memory used=2775.2MB, alloc=492.3MB, time=38.52 memory used=2828.0MB, alloc=492.3MB, time=39.44 memory used=2890.1MB, alloc=492.3MB, time=40.45 memory used=2947.6MB, alloc=492.3MB, time=41.50 memory used=2997.1MB, alloc=492.3MB, time=42.34 memory used=3054.5MB, alloc=492.3MB, time=43.14 memory used=3111.1MB, alloc=492.3MB, time=44.22 memory used=3169.6MB, alloc=492.3MB, time=45.23 memory used=3221.1MB, alloc=492.3MB, time=45.85 memory used=3273.1MB, alloc=492.3MB, time=46.82 memory used=3468.7MB, alloc=516.3MB, time=49.55 memory used=3635.6MB, alloc=516.3MB, time=51.30 memory used=3770.5MB, alloc=516.3MB, time=52.31 memory used=3888.2MB, alloc=516.3MB, time=53.05 memory used=3994.1MB, alloc=516.3MB, time=53.71 memory used=4099.4MB, alloc=516.3MB, time=54.27 memory used=4210.9MB, alloc=516.3MB, time=56.16 memory used=4323.7MB, alloc=516.3MB, time=57.00 memory used=4533.8MB, alloc=540.3MB, time=59.92 memory used=4713.2MB, alloc=564.3MB, time=62.74 memory used=4886.8MB, alloc=564.3MB, time=65.43 memory used=5075.0MB, alloc=588.3MB, time=68.33 memory used=5289.0MB, alloc=588.3MB, time=71.09 memory used=5462.7MB, alloc=588.3MB, time=72.29 memory used=5629.8MB, alloc=588.3MB, time=73.77 memory used=5760.7MB, alloc=588.3MB, time=75.73 memory used=5968.1MB, alloc=612.3MB, time=77.93 memory used=6159.0MB, alloc=612.3MB, time=79.72 memory used=6300.0MB, alloc=612.3MB, time=80.57 memory used=6438.9MB, alloc=612.3MB, time=81.34 memory used=6551.3MB, alloc=612.3MB, time=82.07 memory used=6689.6MB, alloc=612.3MB, time=82.80 memory used=6825.7MB, alloc=612.3MB, time=83.49 memory used=6995.9MB, alloc=612.3MB, time=84.71 memory used=7144.5MB, alloc=612.3MB, time=85.51 memory used=7251.6MB, alloc=612.3MB, time=86.27 memory used=7383.4MB, alloc=612.3MB, time=87.02 memory used=7531.3MB, alloc=612.3MB, time=87.73 memory used=7722.7MB, alloc=612.3MB, time=95.93 memory used=7850.7MB, alloc=612.3MB, time=96.65 memory used=7978.6MB, alloc=612.3MB, time=97.33 memory used=8178.1MB, alloc=612.3MB, time=99.75 memory used=8398.2MB, alloc=612.3MB, time=102.49 memory used=8611.8MB, alloc=612.3MB, time=104.15 memory used=8778.3MB, alloc=612.3MB, time=105.18 memory used=8943.2MB, alloc=612.3MB, time=107.31 memory used=9107.2MB, alloc=612.3MB, time=109.44 memory used=9254.3MB, alloc=612.3MB, time=111.84 memory used=9379.8MB, alloc=612.3MB, time=113.79 memory used=9495.7MB, alloc=612.3MB, time=115.83 memory used=9625.3MB, alloc=636.3MB, time=118.06 memory used=9767.8MB, alloc=636.3MB, time=120.39 memory used=9970.5MB, alloc=636.3MB, time=122.47 memory used=10174.3MB, alloc=636.3MB, time=124.15 memory used=10343.2MB, alloc=636.3MB, time=125.29 memory used=10486.0MB, alloc=636.3MB, time=126.19 memory used=10651.9MB, alloc=636.3MB, time=128.63 memory used=10781.3MB, alloc=636.3MB, time=130.52 memory used=10927.5MB, alloc=660.3MB, time=132.85 memory used=11125.3MB, alloc=660.3MB, time=135.02 memory used=11337.1MB, alloc=660.3MB, time=136.62 memory used=11539.2MB, alloc=660.3MB, time=138.71 memory used=11672.6MB, alloc=660.3MB, time=140.54 memory used=11788.4MB, alloc=660.3MB, time=142.86 memory used=11889.9MB, alloc=660.3MB, time=144.90 memory used=12209.4MB, alloc=684.3MB, time=149.44 memory used=12461.3MB, alloc=684.3MB, time=152.08 memory used=12609.6MB, alloc=684.3MB, time=153.23 memory used=12789.4MB, alloc=684.3MB, time=154.38 memory used=12922.3MB, alloc=684.3MB, time=155.45 memory used=13137.3MB, alloc=684.3MB, time=157.18 memory used=13301.8MB, alloc=684.3MB, time=158.35 memory used=13461.7MB, alloc=684.3MB, time=159.45 memory used=13668.9MB, alloc=684.3MB, time=175.60 memory used=13868.6MB, alloc=684.3MB, time=177.03 memory used=14012.9MB, alloc=684.3MB, time=178.07 memory used=14359.1MB, alloc=708.3MB, time=182.93 memory used=14734.8MB, alloc=732.3MB, time=189.14 memory used=15030.4MB, alloc=732.3MB, time=194.49 memory used=15403.1MB, alloc=756.3MB, time=199.25 memory used=15665.7MB, alloc=756.3MB, time=203.10 memory used=15912.5MB, alloc=756.3MB, time=205.85 memory used=16089.7MB, alloc=756.3MB, time=207.25 memory used=16318.5MB, alloc=756.3MB, time=208.69 memory used=16471.3MB, alloc=756.3MB, time=209.98 memory used=16632.2MB, alloc=756.3MB, time=211.26 memory used=16826.8MB, alloc=756.3MB, time=212.53 memory used=17074.6MB, alloc=756.3MB, time=215.25 memory used=17250.6MB, alloc=756.3MB, time=216.66 memory used=17476.9MB, alloc=756.3MB, time=218.08 memory used=17634.8MB, alloc=756.3MB, time=219.37 memory used=17795.0MB, alloc=756.3MB, time=220.69 memory used=17986.1MB, alloc=756.3MB, time=222.01 memory used=18294.9MB, alloc=756.3MB, time=269.52 memory used=18506.0MB, alloc=756.3MB, time=270.92 memory used=18665.1MB, alloc=756.3MB, time=272.17 memory used=18869.6MB, alloc=756.3MB, time=273.48 memory used=19108.1MB, alloc=756.3MB, time=275.69 memory used=19365.6MB, alloc=756.3MB, time=277.91 memory used=19629.3MB, alloc=756.3MB, time=280.45 memory used=19829.2MB, alloc=756.3MB, time=281.83 memory used=19998.5MB, alloc=756.3MB, time=283.10 memory used=20227.2MB, alloc=756.3MB, time=285.08 memory used=20433.7MB, alloc=756.3MB, time=286.50 memory used=20626.0MB, alloc=756.3MB, time=294.10 memory used=20841.5MB, alloc=756.3MB, time=295.93 memory used=21189.5MB, alloc=756.3MB, time=299.85 memory used=21573.3MB, alloc=756.3MB, time=304.45 memory used=21942.5MB, alloc=780.3MB, time=310.20 memory used=22241.1MB, alloc=804.3MB, time=314.34 memory used=22597.2MB, alloc=804.3MB, time=320.07 memory used=22996.1MB, alloc=828.3MB, time=325.28 memory used=23321.6MB, alloc=828.3MB, time=331.11 memory used=23626.3MB, alloc=852.3MB, time=336.66 memory used=23942.6MB, alloc=852.3MB, time=342.69 memory used=24303.0MB, alloc=876.3MB, time=347.73 memory used=24597.1MB, alloc=876.3MB, time=352.19 memory used=24896.9MB, alloc=876.3MB, time=357.24 memory used=25149.2MB, alloc=876.3MB, time=361.89 memory used=25352.9MB, alloc=900.3MB, time=366.12 memory used=25683.9MB, alloc=900.3MB, time=371.39 memory used=26040.5MB, alloc=900.3MB, time=375.90 memory used=26361.9MB, alloc=900.3MB, time=380.59 memory used=26658.0MB, alloc=900.3MB, time=384.10 memory used=26948.2MB, alloc=924.3MB, time=386.85 memory used=27214.0MB, alloc=924.3MB, time=389.03 memory used=27444.1MB, alloc=924.3MB, time=391.04 memory used=27674.7MB, alloc=924.3MB, time=392.98 memory used=27943.3MB, alloc=924.3MB, time=394.91 memory used=28198.7MB, alloc=924.3MB, time=396.81 memory used=28414.1MB, alloc=924.3MB, time=398.60 memory used=28621.1MB, alloc=924.3MB, time=400.43 memory used=28857.2MB, alloc=924.3MB, time=402.19 memory used=29184.7MB, alloc=924.3MB, time=404.98 memory used=29459.1MB, alloc=924.3MB, time=407.17 memory used=29698.9MB, alloc=924.3MB, time=409.16 memory used=29924.9MB, alloc=924.3MB, time=411.08 memory used=30196.6MB, alloc=924.3MB, time=413.12 memory used=30450.7MB, alloc=924.3MB, time=415.01 memory used=30671.3MB, alloc=924.3MB, time=416.81 memory used=30878.5MB, alloc=924.3MB, time=418.56 memory used=31113.9MB, alloc=924.3MB, time=420.31 memory used=31432.1MB, alloc=924.3MB, time=437.33 memory used=31790.2MB, alloc=924.3MB, time=453.22 memory used=32052.0MB, alloc=924.3MB, time=455.24 memory used=32265.9MB, alloc=924.3MB, time=457.01 memory used=32507.6MB, alloc=924.3MB, time=458.80 memory used=32810.1MB, alloc=939.8MB, time=460.74 memory used=33146.2MB, alloc=939.8MB, time=463.94 memory used=33420.2MB, alloc=939.8MB, time=466.92 memory used=33585.9MB, alloc=939.8MB, time=468.66 memory used=33812.5MB, alloc=939.8MB, time=470.39 memory used=34123.8MB, alloc=939.8MB, time=475.81 memory used=34506.5MB, alloc=939.8MB, time=482.02 memory used=34810.9MB, alloc=939.8MB, time=486.28 memory used=35107.0MB, alloc=939.8MB, time=493.18 memory used=35329.4MB, alloc=963.8MB, time=498.48 memory used=35687.6MB, alloc=963.8MB, time=502.51 memory used=36001.1MB, alloc=963.8MB, time=505.41 memory used=36310.7MB, alloc=963.8MB, time=508.49 memory used=36647.7MB, alloc=963.8MB, time=511.63 memory used=36993.2MB, alloc=963.8MB, time=514.78 memory used=37246.0MB, alloc=963.8MB, time=516.87 memory used=37477.7MB, alloc=963.8MB, time=518.79 memory used=37774.6MB, alloc=963.8MB, time=521.45 memory used=38033.3MB, alloc=963.8MB, time=523.51 memory used=38280.3MB, alloc=963.8MB, time=525.44 memory used=38572.5MB, alloc=963.8MB, time=531.67 memory used=38828.0MB, alloc=963.8MB, time=533.61 memory used=39169.6MB, alloc=963.8MB, time=536.94 memory used=39570.0MB, alloc=963.8MB, time=541.01 memory used=39859.4MB, alloc=963.8MB, time=543.81 memory used=40170.2MB, alloc=963.8MB, time=546.57 memory used=40458.0MB, alloc=963.8MB, time=549.23 memory used=40745.2MB, alloc=963.8MB, time=552.09 memory used=41038.1MB, alloc=963.8MB, time=555.26 memory used=41313.7MB, alloc=963.8MB, time=557.36 memory used=41517.6MB, alloc=963.8MB, time=559.23 memory used=41770.1MB, alloc=963.8MB, time=561.20 memory used=42111.3MB, alloc=963.8MB, time=563.22 memory used=42194.7MB, alloc=963.8MB, time=564.87 memory used=42275.3MB, alloc=963.8MB, time=566.58 memory used=42363.3MB, alloc=963.8MB, time=568.26 memory used=42720.5MB, alloc=963.8MB, time=571.26 memory used=42981.4MB, alloc=963.8MB, time=573.28 memory used=43196.1MB, alloc=963.8MB, time=575.25 memory used=43460.0MB, alloc=963.8MB, time=577.18 memory used=43789.9MB, alloc=963.8MB, time=579.19 memory used=43869.8MB, alloc=963.8MB, time=580.88 memory used=43954.2MB, alloc=963.8MB, time=582.58 memory used=44047.6MB, alloc=963.8MB, time=584.25 memory used=44359.7MB, alloc=963.8MB, time=595.42 memory used=44606.6MB, alloc=963.8MB, time=597.36 memory used=44817.2MB, alloc=963.8MB, time=599.20 memory used=44901.0MB, alloc=963.8MB, time=600.90 memory used=44994.3MB, alloc=963.8MB, time=602.61 memory used=45099.0MB, alloc=963.8MB, time=604.32 memory used=45576.9MB, alloc=963.8MB, time=610.34 memory used=46099.7MB, alloc=963.8MB, time=615.86 memory used=46650.8MB, alloc=987.8MB, time=625.07 memory used=47086.5MB, alloc=1011.8MB, time=630.10 memory used=47726.0MB, alloc=1035.8MB, time=642.71 memory used=48352.0MB, alloc=1059.8MB, time=655.33 memory used=49023.8MB, alloc=1083.8MB, time=665.68 memory used=49681.3MB, alloc=1107.8MB, time=678.44 memory used=50330.4MB, alloc=1131.8MB, time=688.33 memory used=50910.3MB, alloc=1155.8MB, time=699.97 memory used=51560.5MB, alloc=1179.8MB, time=709.86 memory used=52152.6MB, alloc=1203.8MB, time=720.30 memory used=52679.8MB, alloc=1227.8MB, time=731.52 memory used=53131.5MB, alloc=1251.8MB, time=740.25 memory used=53786.6MB, alloc=1275.8MB, time=750.19 memory used=54141.3MB, alloc=1299.8MB, time=756.07 memory used=54473.0MB, alloc=1323.8MB, time=761.39 memory used=55051.1MB, alloc=1347.8MB, time=772.22 memory used=55468.4MB, alloc=1371.8MB, time=780.63 memory used=55871.6MB, alloc=1395.8MB, time=788.64 memory used=56260.7MB, alloc=1419.8MB, time=798.90 memory used=56560.7MB, alloc=1443.8MB, time=807.29 memory used=56836.4MB, alloc=1467.8MB, time=814.55 memory used=57079.9MB, alloc=1491.8MB, time=821.83 memory used=57302.5MB, alloc=1515.8MB, time=831.21 memory used=57575.7MB, alloc=1539.8MB, time=839.80 memory used=57791.5MB, alloc=1563.8MB, time=847.03 memory used=57968.1MB, alloc=1587.8MB, time=854.02 memory used=58131.2MB, alloc=1611.8MB, time=862.24 memory used=58347.4MB, alloc=1635.8MB, time=870.90 memory used=58525.7MB, alloc=1659.8MB, time=878.08 memory used=58798.6MB, alloc=1683.8MB, time=885.91 memory used=59083.7MB, alloc=1707.8MB, time=893.64 memory used=59275.4MB, alloc=1731.8MB, time=901.27 memory used=59433.4MB, alloc=1755.8MB, time=908.26 memory used=59634.5MB, alloc=1779.8MB, time=915.44 memory used=59783.2MB, alloc=1779.8MB, time=924.79 memory used=59892.2MB, alloc=1803.8MB, time=932.16 memory used=60032.7MB, alloc=1803.8MB, time=939.69 memory used=60125.8MB, alloc=1803.8MB, time=946.69 memory used=60256.5MB, alloc=1803.8MB, time=954.11 memory used=60347.1MB, alloc=1803.8MB, time=960.69 memory used=60408.0MB, alloc=1803.8MB, time=967.09 memory used=60456.4MB, alloc=1803.8MB, time=973.72 memory used=60510.6MB, alloc=1803.8MB, time=980.13 memory used=60557.0MB, alloc=1803.8MB, time=986.27 memory used=60621.0MB, alloc=1803.8MB, time=992.71 memory used=60685.7MB, alloc=1803.8MB, time=1000.38 memory used=60743.3MB, alloc=1803.8MB, time=1007.27 memory used=60803.0MB, alloc=1803.8MB, time=1013.60 memory used=60881.7MB, alloc=1803.8MB, time=1020.33 memory used=60948.0MB, alloc=1803.8MB, time=1026.61 memory used=61162.9MB, alloc=1803.8MB, time=1034.36 memory used=61225.3MB, alloc=1803.8MB, time=1041.13 memory used=61242.5MB, alloc=1803.8MB, time=1047.21 memory used=61299.4MB, alloc=1803.8MB, time=1053.61 memory used=61341.3MB, alloc=1803.8MB, time=1060.23 memory used=61376.6MB, alloc=2059.8MB, time=1072.65 memory used=62589.0MB, alloc=2083.8MB, time=1094.64 memory used=63244.4MB, alloc=2107.8MB, time=1105.81 memory used=63788.8MB, alloc=2131.8MB, time=1114.02 memory used=64380.6MB, alloc=2155.8MB, time=1122.68 memory used=65040.2MB, alloc=2179.8MB, time=1138.00 memory used=66237.9MB, alloc=2203.8MB, time=1161.16 memory used=67276.8MB, alloc=2227.8MB, time=1180.40 memory used=68509.3MB, alloc=2251.8MB, time=1202.54 memory used=69676.4MB, alloc=2275.8MB, time=1228.76 memory used=70811.7MB, alloc=2299.8MB, time=1253.42 memory used=71813.6MB, alloc=2323.8MB, time=1274.98 |\^/| 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(); 1428478364 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; F := 2 2 2 2 2 2 2 [20 x z + 16 y z - 5 x y, -9 x y + 4 y - 6 z, -4 x y + 10 y z - 8 y ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 3 2 2 3 2 G := [-6 x z + 15 y z - 10 x z, 2 y - 5 z - 1, 10 x y + 5 y - 5 x ] > Problem := [F,G]; Problem := [ 2 2 2 2 2 2 2 [20 x z + 16 y z - 5 x y, -9 x y + 4 y - 6 z, -4 x y + 10 y z - 8 y ] 2 2 3 2 2 3 2 , [-6 x z + 15 y z - 10 x z, 2 y - 5 z - 1, 10 x y + 5 y - 5 x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.23 memory used=26.6MB, alloc=32.3MB, time=0.55 memory used=47.7MB, alloc=32.3MB, time=0.85 memory used=66.8MB, alloc=56.3MB, time=1.16 memory used=106.5MB, alloc=60.3MB, time=1.74 memory used=145.2MB, alloc=60.3MB, time=2.29 memory used=183.8MB, alloc=84.3MB, time=2.86 memory used=223.5MB, alloc=84.3MB, time=3.49 memory used=282.4MB, alloc=92.3MB, time=4.43 memory used=342.8MB, alloc=116.3MB, time=5.36 memory used=405.4MB, alloc=116.3MB, time=6.26 memory used=477.2MB, alloc=396.3MB, time=7.37 memory used=584.4MB, alloc=420.3MB, time=8.88 memory used=711.9MB, alloc=444.3MB, time=10.67 memory used=838.7MB, alloc=468.3MB, time=12.52 memory used=956.2MB, alloc=468.3MB, time=14.41 memory used=1049.6MB, alloc=468.3MB, time=15.94 memory used=1146.6MB, alloc=468.3MB, time=17.41 memory used=1246.3MB, alloc=492.3MB, time=19.08 memory used=1333.2MB, alloc=492.3MB, time=20.47 memory used=1411.7MB, alloc=492.3MB, time=21.92 memory used=1479.8MB, alloc=492.3MB, time=23.21 memory used=1551.3MB, alloc=492.3MB, time=24.61 memory used=1612.8MB, alloc=492.3MB, time=25.86 memory used=1674.1MB, alloc=492.3MB, time=27.11 memory used=1717.1MB, alloc=492.3MB, time=28.16 memory used=1772.7MB, alloc=492.3MB, time=29.41 memory used=1955.5MB, alloc=516.3MB, time=32.30 memory used=2151.6MB, alloc=540.3MB, time=35.72 memory used=2323.6MB, alloc=564.3MB, time=38.79 memory used=2468.6MB, alloc=588.3MB, time=41.36 memory used=2632.2MB, alloc=612.3MB, time=44.53 memory used=2784.3MB, alloc=636.3MB, time=47.47 memory used=2923.7MB, alloc=660.3MB, time=50.49 memory used=3075.5MB, alloc=660.3MB, time=53.54 memory used=3182.2MB, alloc=660.3MB, time=55.98 memory used=3288.2MB, alloc=660.3MB, time=58.47 memory used=3385.4MB, alloc=660.3MB, time=60.70 memory used=3698.7MB, alloc=684.3MB, time=66.62 memory used=4037.4MB, alloc=708.3MB, time=72.93 memory used=4366.3MB, alloc=732.3MB, time=78.53 memory used=4695.1MB, alloc=756.3MB, time=84.75 memory used=5034.5MB, alloc=780.3MB, time=91.68 memory used=5332.3MB, alloc=804.3MB, time=98.06 memory used=5595.0MB, alloc=828.3MB, time=103.21 memory used=5834.9MB, alloc=852.3MB, time=108.29 memory used=6045.9MB, alloc=876.3MB, time=113.46 memory used=6259.2MB, alloc=900.3MB, time=118.81 memory used=6459.8MB, alloc=924.3MB, time=124.29 memory used=7003.3MB, alloc=948.3MB, time=134.05 memory used=7527.1MB, alloc=972.3MB, time=146.77 memory used=8066.3MB, alloc=996.3MB, time=159.94 memory used=8643.1MB, alloc=1020.3MB, time=171.37 memory used=9216.4MB, alloc=1044.3MB, time=184.85 memory used=9793.4MB, alloc=1068.3MB, time=199.18 memory used=10377.6MB, alloc=1092.3MB, time=212.22 memory used=10883.8MB, alloc=1116.3MB, time=224.44 memory used=11378.9MB, alloc=1140.3MB, time=235.97 memory used=11935.8MB, alloc=1164.3MB, time=250.85 memory used=12431.1MB, alloc=1188.3MB, time=264.49 memory used=12842.1MB, alloc=1212.3MB, time=277.10 memory used=13272.6MB, alloc=1236.3MB, time=288.88 memory used=13613.6MB, alloc=1260.3MB, time=299.51 memory used=13934.7MB, alloc=1284.3MB, time=310.23 memory used=14237.3MB, alloc=1308.3MB, time=320.51 memory used=14505.3MB, alloc=1332.3MB, time=329.88 memory used=14836.2MB, alloc=1356.3MB, time=340.70 memory used=15133.5MB, alloc=1380.3MB, time=352.86 memory used=15327.8MB, alloc=1404.3MB, time=361.74 memory used=15579.1MB, alloc=1428.3MB, time=371.95 memory used=15784.6MB, alloc=1452.3MB, time=381.84 memory used=15976.0MB, alloc=1476.3MB, time=391.53 memory used=16165.2MB, alloc=1500.3MB, time=401.50 memory used=16264.9MB, alloc=1524.3MB, time=408.43 memory used=16409.1MB, alloc=1548.3MB, time=417.56 memory used=16513.6MB, alloc=1572.3MB, time=423.92 memory used=16608.2MB, alloc=1596.3MB, time=430.10 memory used=16696.6MB, alloc=1620.3MB, time=436.39 memory used=16747.8MB, alloc=1644.3MB, time=442.35 memory used=16824.2MB, alloc=1668.3MB, time=449.73 memory used=16877.1MB, alloc=1692.3MB, time=456.00 memory used=17026.0MB, alloc=1716.3MB, time=462.84 memory used=17096.4MB, alloc=1716.3MB, time=470.25 memory used=17186.6MB, alloc=1716.3MB, time=477.12 memory used=17249.0MB, alloc=1716.3MB, time=483.05 memory used=17313.5MB, alloc=1716.3MB, time=489.09 memory used=17365.0MB, alloc=1716.3MB, time=496.15 memory used=17413.2MB, alloc=1716.3MB, time=502.25 memory used=17446.4MB, alloc=1716.3MB, time=508.05 memory used=17460.5MB, alloc=1716.3MB, time=513.74 memory used=17484.4MB, alloc=1972.3MB, time=525.69 memory used=18614.5MB, alloc=1996.3MB, time=557.61 memory used=19769.8MB, alloc=2020.3MB, time=583.29 memory used=20916.2MB, alloc=2044.3MB, time=610.25 memory used=21987.9MB, alloc=2068.3MB, time=633.22 memory used=22920.3MB, alloc=2092.3MB, time=652.36 memory used=23991.2MB, alloc=2116.3MB, time=678.32 memory used=25101.6MB, alloc=2140.3MB, time=703.62 memory used=26031.9MB, alloc=2164.3MB, time=731.28 memory used=27006.6MB, alloc=2188.3MB, time=752.91 memory used=27974.1MB, alloc=2212.3MB, time=776.03 memory used=28731.8MB, alloc=2236.3MB, time=794.68 memory used=29827.0MB, alloc=2260.3MB, time=819.49 memory used=30734.1MB, alloc=2284.3MB, time=849.40 memory used=31479.0MB, alloc=2308.3MB, time=875.55 memory used=32295.2MB, alloc=2332.3MB, time=903.47 memory used=32969.2MB, alloc=2356.3MB, time=928.48 memory used=33740.4MB, alloc=2380.3MB, time=956.32 memory used=34476.5MB, alloc=2404.3MB, time=983.18 memory used=35053.7MB, alloc=2428.3MB, time=1006.97 memory used=35293.8MB, alloc=2452.3MB, time=1024.01 memory used=35935.6MB, alloc=2476.3MB, time=1054.04 memory used=36447.1MB, alloc=2500.3MB, time=1085.77 memory used=36950.8MB, alloc=2524.3MB, time=1117.57 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428479564 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 3 2 2 3 F := [-19 x z + 3 y z + 14 y z, 6 y z + z - 8 z , -7 x y + 10 y + 9 y z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 G := [17 x y + 13 x y - 10, -9 y z - 8 x - 5 z, -6 x y z - 4 x z - 6 z] > Problem := [F,G]; Problem := [ 2 2 2 3 2 2 3 [-19 x z + 3 y z + 14 y z, 6 y z + z - 8 z , -7 x y + 10 y + 9 y z], 2 2 [17 x y + 13 x y - 10, -9 y z - 8 x - 5 z, -6 x y z - 4 x z - 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=26.3MB, alloc=32.3MB, time=0.49 memory used=46.7MB, alloc=32.3MB, time=0.77 memory used=66.8MB, alloc=56.3MB, time=1.08 memory used=108.0MB, alloc=60.3MB, time=1.70 memory used=147.3MB, alloc=60.3MB, time=2.29 memory used=185.8MB, alloc=84.3MB, time=2.88 memory used=230.0MB, alloc=84.3MB, time=3.54 memory used=287.5MB, alloc=116.3MB, time=4.48 memory used=369.0MB, alloc=116.3MB, time=5.74 memory used=449.8MB, alloc=140.3MB, time=7.03 memory used=534.7MB, alloc=396.3MB, time=8.45 memory used=643.0MB, alloc=420.3MB, time=10.16 memory used=774.2MB, alloc=444.3MB, time=12.32 memory used=922.6MB, alloc=444.3MB, time=14.76 memory used=1061.0MB, alloc=468.3MB, time=16.93 memory used=1185.4MB, alloc=468.3MB, time=18.77 memory used=1318.6MB, alloc=492.3MB, time=20.70 memory used=1471.8MB, alloc=492.3MB, time=22.36 memory used=1599.1MB, alloc=516.3MB, time=24.52 memory used=1718.9MB, alloc=516.3MB, time=26.14 memory used=1836.3MB, alloc=516.3MB, time=27.67 memory used=2049.2MB, alloc=516.3MB, time=29.55 memory used=2261.2MB, alloc=540.3MB, time=31.43 memory used=2391.2MB, alloc=540.3MB, time=33.62 memory used=2534.0MB, alloc=564.3MB, time=35.65 memory used=2661.6MB, alloc=564.3MB, time=37.45 memory used=2864.5MB, alloc=564.3MB, time=39.47 memory used=3078.7MB, alloc=564.3MB, time=40.96 memory used=3183.2MB, alloc=588.3MB, time=42.97 memory used=3303.6MB, alloc=612.3MB, time=45.36 memory used=3435.2MB, alloc=612.3MB, time=47.63 memory used=3596.6MB, alloc=636.3MB, time=50.46 memory used=3736.7MB, alloc=660.3MB, time=53.08 memory used=3854.6MB, alloc=684.3MB, time=55.48 memory used=3971.9MB, alloc=708.3MB, time=57.76 memory used=4083.1MB, alloc=708.3MB, time=60.09 memory used=4201.2MB, alloc=732.3MB, time=62.54 memory used=4309.3MB, alloc=756.3MB, time=64.82 memory used=4413.3MB, alloc=756.3MB, time=67.06 memory used=4524.5MB, alloc=780.3MB, time=69.50 memory used=4614.5MB, alloc=780.3MB, time=71.48 memory used=4717.7MB, alloc=804.3MB, time=73.67 memory used=4810.0MB, alloc=804.3MB, time=75.77 memory used=4902.8MB, alloc=828.3MB, time=77.83 memory used=4984.7MB, alloc=828.3MB, time=79.81 memory used=5355.2MB, alloc=852.3MB, time=86.78 memory used=5680.6MB, alloc=876.3MB, time=93.26 memory used=6053.9MB, alloc=900.3MB, time=99.99 memory used=6385.1MB, alloc=924.3MB, time=106.68 memory used=6747.4MB, alloc=948.3MB, time=113.66 memory used=7131.5MB, alloc=972.3MB, time=120.42 memory used=7485.3MB, alloc=996.3MB, time=127.94 memory used=7774.6MB, alloc=1020.3MB, time=138.52 memory used=8061.4MB, alloc=1044.3MB, time=149.85 memory used=8357.7MB, alloc=1068.3MB, time=161.89 memory used=8666.9MB, alloc=1092.3MB, time=174.71 memory used=8988.5MB, alloc=1116.3MB, time=188.33 memory used=9323.3MB, alloc=1140.3MB, time=202.62 memory used=9672.3MB, alloc=1164.3MB, time=217.62 memory used=10036.7MB, alloc=1188.3MB, time=233.34 memory used=10416.3MB, alloc=1212.3MB, time=249.81 memory used=10811.3MB, alloc=1236.3MB, time=267.03 memory used=11220.7MB, alloc=1260.3MB, time=284.67 memory used=11645.5MB, alloc=1284.3MB, time=303.07 memory used=12085.5MB, alloc=1308.3MB, time=322.29 memory used=12541.2MB, alloc=1332.3MB, time=342.21 memory used=13012.6MB, alloc=1356.3MB, time=362.90 memory used=13500.1MB, alloc=1380.3MB, time=384.34 memory used=14003.9MB, alloc=1404.3MB, time=406.65 memory used=14524.3MB, alloc=1428.3MB, time=429.69 memory used=15060.4MB, alloc=1452.3MB, time=453.79 memory used=15612.5MB, alloc=1476.3MB, time=478.91 memory used=16181.3MB, alloc=1500.3MB, time=504.76 memory used=16766.7MB, alloc=1524.3MB, time=531.59 memory used=17368.9MB, alloc=1548.3MB, time=559.15 memory used=17988.2MB, alloc=1572.3MB, time=587.54 memory used=18624.4MB, alloc=1596.3MB, time=616.80 memory used=19277.7MB, alloc=1620.3MB, time=647.45 memory used=19947.9MB, alloc=1644.3MB, time=678.31 memory used=20633.1MB, alloc=1668.3MB, time=710.31 memory used=21333.6MB, alloc=1692.3MB, time=743.37 memory used=22058.1MB, alloc=1716.3MB, time=777.12 memory used=22806.5MB, alloc=1740.3MB, time=812.41 memory used=23578.9MB, alloc=1764.3MB, time=848.87 memory used=24375.2MB, alloc=1788.3MB, time=886.43 memory used=25195.5MB, alloc=1812.3MB, time=924.94 memory used=26039.7MB, alloc=1836.3MB, time=964.46 |\^/| 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(); 1428480764 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 3 2 2 2 F := [-15 y z + 18 y - 2 y, -z + 5 x z + 2 y z, 2 x z - 2 y z + 8 z ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 2 G := [6 x - 20 x y + 9 y, 2 x y - y + 6, -5 y z - 6 x z - 3 y] > Problem := [F,G]; Problem := [ 2 2 3 2 2 2 [-15 y z + 18 y - 2 y, -z + 5 x z + 2 y z, 2 x z - 2 y z + 8 z ], 3 2 2 2 [6 x - 20 x y + 9 y, 2 x y - y + 6, -5 y z - 6 x z - 3 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=32.4MB, alloc=40.3MB, time=0.58 memory used=59.6MB, alloc=40.3MB, time=0.98 memory used=85.4MB, alloc=40.3MB, time=1.36 memory used=109.7MB, alloc=68.3MB, time=1.74 memory used=155.5MB, alloc=68.3MB, time=2.46 memory used=200.9MB, alloc=92.3MB, time=3.21 memory used=244.7MB, alloc=92.3MB, time=3.96 memory used=311.1MB, alloc=100.3MB, time=5.07 memory used=375.1MB, alloc=124.3MB, time=6.15 memory used=460.2MB, alloc=124.3MB, time=7.59 memory used=546.9MB, alloc=148.3MB, time=9.01 memory used=629.9MB, alloc=148.3MB, time=10.41 memory used=696.2MB, alloc=428.3MB, time=11.61 memory used=829.1MB, alloc=452.3MB, time=13.91 memory used=984.5MB, alloc=476.3MB, time=16.68 memory used=1145.7MB, alloc=476.3MB, time=19.58 memory used=1295.5MB, alloc=500.3MB, time=22.20 memory used=1443.9MB, alloc=500.3MB, time=25.05 memory used=1594.5MB, alloc=524.3MB, time=28.09 memory used=1733.7MB, alloc=524.3MB, time=31.04 memory used=1846.5MB, alloc=548.3MB, time=33.41 memory used=1948.0MB, alloc=548.3MB, time=35.46 memory used=2070.7MB, alloc=548.3MB, time=38.16 memory used=2178.5MB, alloc=548.3MB, time=40.65 memory used=2262.6MB, alloc=548.3MB, time=42.43 memory used=2346.6MB, alloc=572.3MB, time=44.39 memory used=2427.9MB, alloc=572.3MB, time=46.29 memory used=2484.5MB, alloc=572.3MB, time=47.59 memory used=2548.0MB, alloc=572.3MB, time=49.02 memory used=2618.0MB, alloc=572.3MB, time=50.76 memory used=2681.0MB, alloc=572.3MB, time=52.31 memory used=2728.6MB, alloc=572.3MB, time=53.41 memory used=2961.8MB, alloc=596.3MB, time=58.10 memory used=3218.2MB, alloc=620.3MB, time=62.81 memory used=3456.0MB, alloc=644.3MB, time=67.70 memory used=3697.4MB, alloc=668.3MB, time=72.81 memory used=3943.0MB, alloc=692.3MB, time=77.94 memory used=4197.2MB, alloc=716.3MB, time=83.29 memory used=4443.9MB, alloc=740.3MB, time=88.48 memory used=4704.1MB, alloc=764.3MB, time=93.86 memory used=4953.5MB, alloc=788.3MB, time=98.77 memory used=5256.0MB, alloc=812.3MB, time=104.41 memory used=5553.0MB, alloc=836.3MB, time=109.84 memory used=5822.3MB, alloc=860.3MB, time=114.86 memory used=6173.8MB, alloc=884.3MB, time=122.03 memory used=6523.9MB, alloc=908.3MB, time=129.05 memory used=6853.3MB, alloc=932.3MB, time=136.16 memory used=7178.7MB, alloc=956.3MB, time=143.52 memory used=7512.1MB, alloc=980.3MB, time=150.83 memory used=7842.3MB, alloc=1004.3MB, time=158.09 memory used=8123.4MB, alloc=1028.3MB, time=168.13 memory used=8389.1MB, alloc=1052.3MB, time=179.13 memory used=8664.9MB, alloc=1076.3MB, time=191.17 memory used=8953.4MB, alloc=1100.3MB, time=203.91 memory used=9255.7MB, alloc=1124.3MB, time=217.18 memory used=9571.9MB, alloc=1148.3MB, time=231.15 memory used=9903.2MB, alloc=1172.3MB, time=245.79 memory used=10249.3MB, alloc=1196.3MB, time=261.28 memory used=10610.6MB, alloc=1220.3MB, time=277.49 memory used=10987.4MB, alloc=1244.3MB, time=294.58 memory used=11379.5MB, alloc=1268.3MB, time=312.35 memory used=11786.4MB, alloc=1292.3MB, time=330.54 memory used=12208.7MB, alloc=1316.3MB, time=349.66 memory used=12646.3MB, alloc=1340.3MB, time=369.36 memory used=13099.6MB, alloc=1364.3MB, time=389.74 memory used=13567.7MB, alloc=1388.3MB, time=410.91 memory used=14050.4MB, alloc=1412.3MB, time=432.80 memory used=14548.2MB, alloc=1436.3MB, time=455.58 memory used=15061.3MB, alloc=1460.3MB, time=479.21 memory used=15589.1MB, alloc=1484.3MB, time=503.92 memory used=16132.3MB, alloc=1508.3MB, time=529.21 memory used=16691.3MB, alloc=1532.3MB, time=555.35 memory used=17265.9MB, alloc=1556.3MB, time=582.26 memory used=17856.1MB, alloc=1580.3MB, time=609.88 memory used=18461.9MB, alloc=1604.3MB, time=638.41 memory used=19083.5MB, alloc=1628.3MB, time=667.78 memory used=19720.7MB, alloc=1652.3MB, time=697.95 memory used=20370.7MB, alloc=1676.3MB, time=729.02 memory used=21034.9MB, alloc=1700.3MB, time=761.21 memory used=21723.1MB, alloc=1724.3MB, time=793.70 memory used=22435.3MB, alloc=1748.3MB, time=827.33 memory used=23171.4MB, alloc=1772.3MB, time=862.19 memory used=23931.4MB, alloc=1796.3MB, time=897.88 memory used=24715.4MB, alloc=1820.3MB, time=934.54 memory used=25523.3MB, alloc=1844.3MB, time=972.46 memory used=26355.2MB, alloc=1868.3MB, time=1011.54 memory used=27211.0MB, alloc=1892.3MB, time=1051.34 memory used=28090.7MB, alloc=1916.3MB, time=1092.40 |\^/| 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(); 1428481965 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 2 2 F := [-5 x z + 2 y + 8 y, -5 y z + 7 y z + y , 2 x y + 9 x z - 5] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 2 3 2 3 2 G := [7 x y - 12 y - 5 y z , -4 x z - 9 z - 5 z , 3 y + 10 y z - 10 x y] > Problem := [F,G]; 2 2 2 2 2 2 Problem := [[-5 x z + 2 y + 8 y, -5 y z + 7 y z + y , 2 x y + 9 x z - 5], 2 3 2 2 3 2 3 2 [7 x y - 12 y - 5 y z , -4 x z - 9 z - 5 z , 3 y + 10 y z - 10 x y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.19 memory used=26.3MB, alloc=32.3MB, time=0.50 memory used=46.8MB, alloc=32.3MB, time=0.80 memory used=65.7MB, alloc=56.3MB, time=1.10 memory used=105.4MB, alloc=60.3MB, time=1.67 memory used=143.3MB, alloc=60.3MB, time=2.23 memory used=183.2MB, alloc=92.3MB, time=2.83 memory used=243.3MB, alloc=92.3MB, time=3.75 memory used=305.6MB, alloc=92.3MB, time=4.62 memory used=369.9MB, alloc=116.3MB, time=5.50 memory used=441.5MB, alloc=116.3MB, time=6.43 memory used=515.9MB, alloc=396.3MB, time=7.59 memory used=619.7MB, alloc=420.3MB, time=9.23 memory used=747.7MB, alloc=420.3MB, time=11.14 memory used=875.4MB, alloc=444.3MB, time=13.10 memory used=1005.9MB, alloc=468.3MB, time=14.87 memory used=1122.8MB, alloc=468.3MB, time=16.40 memory used=1233.7MB, alloc=468.3MB, time=18.12 memory used=1363.5MB, alloc=492.3MB, time=20.17 memory used=1483.5MB, alloc=492.3MB, time=22.07 memory used=1611.3MB, alloc=516.3MB, time=24.20 memory used=1725.5MB, alloc=516.3MB, time=26.11 memory used=1828.6MB, alloc=516.3MB, time=27.79 memory used=1918.9MB, alloc=540.3MB, time=29.10 memory used=2011.0MB, alloc=540.3MB, time=30.99 memory used=2086.5MB, alloc=540.3MB, time=32.15 memory used=2163.8MB, alloc=540.3MB, time=33.61 memory used=2226.3MB, alloc=540.3MB, time=34.80 memory used=2292.2MB, alloc=540.3MB, time=35.81 memory used=2356.4MB, alloc=540.3MB, time=37.00 memory used=2415.5MB, alloc=540.3MB, time=38.21 memory used=2457.6MB, alloc=540.3MB, time=39.11 memory used=2666.1MB, alloc=564.3MB, time=42.44 memory used=2897.2MB, alloc=588.3MB, time=46.47 memory used=3101.0MB, alloc=612.3MB, time=50.64 memory used=3254.7MB, alloc=636.3MB, time=53.12 memory used=3413.6MB, alloc=660.3MB, time=56.23 memory used=3571.9MB, alloc=684.3MB, time=59.18 memory used=3701.0MB, alloc=684.3MB, time=61.61 memory used=3828.7MB, alloc=708.3MB, time=63.76 memory used=3947.9MB, alloc=708.3MB, time=66.44 memory used=4026.8MB, alloc=708.3MB, time=68.13 memory used=4147.0MB, alloc=708.3MB, time=71.03 memory used=4261.9MB, alloc=708.3MB, time=74.09 memory used=4641.2MB, alloc=732.3MB, time=80.84 memory used=5042.8MB, alloc=756.3MB, time=86.82 memory used=5456.1MB, alloc=780.3MB, time=93.92 memory used=5854.6MB, alloc=804.3MB, time=100.88 memory used=6223.7MB, alloc=828.3MB, time=106.76 memory used=6606.7MB, alloc=852.3MB, time=114.00 memory used=6919.6MB, alloc=876.3MB, time=120.53 memory used=7224.9MB, alloc=900.3MB, time=126.70 memory used=7524.2MB, alloc=924.3MB, time=133.07 memory used=7784.2MB, alloc=948.3MB, time=138.78 memory used=8042.9MB, alloc=972.3MB, time=145.12 memory used=8341.6MB, alloc=996.3MB, time=153.64 memory used=8597.0MB, alloc=1020.3MB, time=160.70 memory used=9216.0MB, alloc=1044.3MB, time=175.65 memory used=9852.9MB, alloc=1068.3MB, time=191.26 memory used=10493.7MB, alloc=1092.3MB, time=208.38 memory used=11154.5MB, alloc=1116.3MB, time=224.78 memory used=11826.7MB, alloc=1140.3MB, time=241.72 memory used=12513.9MB, alloc=1164.3MB, time=259.46 memory used=13215.7MB, alloc=1188.3MB, time=276.25 memory used=13831.5MB, alloc=1212.3MB, time=290.68 memory used=14477.1MB, alloc=1236.3MB, time=307.09 memory used=15029.9MB, alloc=1260.3MB, time=321.62 memory used=15607.5MB, alloc=1284.3MB, time=337.19 memory used=16132.8MB, alloc=1308.3MB, time=352.59 memory used=16689.5MB, alloc=1332.3MB, time=367.41 memory used=17193.6MB, alloc=1356.3MB, time=383.22 memory used=17708.4MB, alloc=1380.3MB, time=400.60 memory used=18135.5MB, alloc=1404.3MB, time=415.40 memory used=18548.7MB, alloc=1428.3MB, time=430.16 memory used=18884.5MB, alloc=1452.3MB, time=440.61 memory used=19257.2MB, alloc=1476.3MB, time=454.28 memory used=19471.2MB, alloc=1500.3MB, time=463.40 memory used=19812.5MB, alloc=1524.3MB, time=477.22 memory used=20055.4MB, alloc=1548.3MB, time=486.83 memory used=20206.3MB, alloc=1572.3MB, time=494.76 memory used=20413.8MB, alloc=1596.3MB, time=503.62 memory used=20736.8MB, alloc=1620.3MB, time=517.43 memory used=20917.8MB, alloc=1644.3MB, time=527.19 memory used=21189.2MB, alloc=1668.3MB, time=541.07 memory used=21498.3MB, alloc=1692.3MB, time=555.97 memory used=21622.7MB, alloc=1716.3MB, time=564.69 memory used=21739.3MB, alloc=1740.3MB, time=571.88 memory used=21830.5MB, alloc=1764.3MB, time=579.36 memory used=22085.8MB, alloc=1788.3MB, time=593.27 memory used=22177.3MB, alloc=1812.3MB, time=600.27 memory used=22222.6MB, alloc=1836.3MB, time=606.44 memory used=22288.4MB, alloc=1860.3MB, time=613.68 memory used=22384.1MB, alloc=1884.3MB, time=620.79 memory used=22443.9MB, alloc=1908.3MB, time=628.09 memory used=22476.2MB, alloc=1932.3MB, time=634.32 memory used=22637.9MB, alloc=1932.3MB, time=644.38 memory used=22786.8MB, alloc=1932.3MB, time=653.87 memory used=22866.6MB, alloc=1932.3MB, time=661.31 memory used=22913.5MB, alloc=1932.3MB, time=667.68 memory used=22978.9MB, alloc=1932.3MB, time=674.23 memory used=23027.2MB, alloc=1932.3MB, time=681.04 memory used=23068.4MB, alloc=1932.3MB, time=687.41 memory used=23099.9MB, alloc=2188.3MB, time=700.12 memory used=24408.6MB, alloc=2212.3MB, time=736.14 memory used=25725.0MB, alloc=2236.3MB, time=776.78 memory used=27019.0MB, alloc=2260.3MB, time=813.05 memory used=28288.8MB, alloc=2284.3MB, time=848.49 memory used=29556.6MB, alloc=2308.3MB, time=883.81 memory used=30588.5MB, alloc=2332.3MB, time=910.63 memory used=31831.7MB, alloc=2356.3MB, time=951.08 memory used=32785.0MB, alloc=2380.3MB, time=983.14 memory used=33757.6MB, alloc=2404.3MB, time=1014.55 memory used=34839.5MB, alloc=2428.3MB, time=1055.01 memory used=35837.4MB, alloc=2452.3MB, time=1088.12 memory used=36828.5MB, alloc=2476.3MB, time=1131.36 |\^/| 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(); 1428483165 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 2 F := [-18 x - 2 y - 7, 9 y z + x y - 2, -4 y z - 4 x y - 9 x z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 3 2 3 G := [-14 x y + 10 y - 4 y z, 5 x - 8 y z - 5, -8 y - 8 x + 4 z] > Problem := [F,G]; 3 2 2 2 Problem := [[-18 x - 2 y - 7, 9 y z + x y - 2, -4 y z - 4 x y - 9 x z], 2 3 3 2 3 [-14 x y + 10 y - 4 y z, 5 x - 8 y z - 5, -8 y - 8 x + 4 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.23 memory used=25.8MB, alloc=32.3MB, time=0.55 memory used=45.0MB, alloc=56.3MB, time=0.84 memory used=87.1MB, alloc=60.3MB, time=1.45 memory used=127.4MB, alloc=60.3MB, time=2.04 memory used=167.1MB, alloc=84.3MB, time=2.63 memory used=234.2MB, alloc=92.3MB, time=3.56 memory used=297.8MB, alloc=92.3MB, time=4.42 memory used=365.6MB, alloc=116.3MB, time=5.17 memory used=442.2MB, alloc=372.3MB, time=6.24 memory used=529.4MB, alloc=396.3MB, time=7.51 memory used=640.2MB, alloc=396.3MB, time=9.13 memory used=750.8MB, alloc=420.3MB, time=10.41 memory used=879.6MB, alloc=420.3MB, time=11.84 memory used=1025.4MB, alloc=420.3MB, time=13.77 memory used=1157.3MB, alloc=420.3MB, time=15.46 memory used=1287.4MB, alloc=444.3MB, time=16.98 memory used=1378.9MB, alloc=444.3MB, time=17.86 memory used=1461.6MB, alloc=444.3MB, time=18.58 memory used=1558.4MB, alloc=444.3MB, time=19.55 memory used=1688.8MB, alloc=444.3MB, time=20.85 memory used=1795.5MB, alloc=444.3MB, time=22.32 memory used=1904.0MB, alloc=444.3MB, time=23.86 memory used=2012.5MB, alloc=468.3MB, time=25.16 memory used=2144.9MB, alloc=468.3MB, time=26.26 memory used=2232.6MB, alloc=468.3MB, time=27.57 memory used=2334.2MB, alloc=468.3MB, time=29.16 memory used=2419.9MB, alloc=468.3MB, time=30.62 memory used=2500.5MB, alloc=468.3MB, time=31.85 memory used=2573.0MB, alloc=492.3MB, time=32.82 memory used=2647.8MB, alloc=492.3MB, time=34.14 memory used=2727.4MB, alloc=492.3MB, time=35.38 memory used=2789.1MB, alloc=492.3MB, time=36.52 memory used=2842.6MB, alloc=492.3MB, time=37.47 memory used=2880.7MB, alloc=492.3MB, time=38.19 memory used=2929.0MB, alloc=492.3MB, time=39.11 memory used=3123.6MB, alloc=516.3MB, time=41.59 memory used=3299.5MB, alloc=540.3MB, time=43.81 memory used=3474.9MB, alloc=564.3MB, time=46.69 memory used=3641.8MB, alloc=588.3MB, time=49.02 memory used=3819.0MB, alloc=612.3MB, time=51.94 memory used=3981.8MB, alloc=612.3MB, time=54.89 memory used=4107.0MB, alloc=636.3MB, time=56.99 memory used=4226.6MB, alloc=636.3MB, time=58.75 memory used=4363.7MB, alloc=636.3MB, time=61.49 memory used=4482.3MB, alloc=660.3MB, time=63.44 memory used=4572.6MB, alloc=660.3MB, time=65.13 memory used=4661.5MB, alloc=660.3MB, time=66.74 memory used=4925.8MB, alloc=660.3MB, time=69.67 memory used=5288.5MB, alloc=684.3MB, time=74.20 memory used=5633.9MB, alloc=708.3MB, time=78.76 memory used=5982.4MB, alloc=732.3MB, time=83.35 memory used=6366.5MB, alloc=756.3MB, time=88.28 memory used=6752.5MB, alloc=780.3MB, time=93.47 memory used=7085.5MB, alloc=804.3MB, time=98.50 memory used=7465.4MB, alloc=828.3MB, time=103.65 memory used=7791.1MB, alloc=852.3MB, time=108.13 memory used=8136.0MB, alloc=876.3MB, time=112.58 memory used=8530.5MB, alloc=900.3MB, time=117.43 memory used=8781.3MB, alloc=924.3MB, time=121.52 memory used=9129.5MB, alloc=948.3MB, time=125.53 memory used=9515.9MB, alloc=972.3MB, time=129.94 memory used=9805.9MB, alloc=972.3MB, time=134.46 memory used=10099.9MB, alloc=996.3MB, time=138.91 memory used=10307.1MB, alloc=996.3MB, time=143.46 memory used=10929.6MB, alloc=1020.3MB, time=153.96 memory used=11371.6MB, alloc=1044.3MB, time=160.71 memory used=11694.9MB, alloc=1068.3MB, time=165.40 memory used=12024.3MB, alloc=1092.3MB, time=169.08 memory used=12421.3MB, alloc=1116.3MB, time=172.06 memory used=13094.4MB, alloc=1140.3MB, time=180.70 memory used=13699.1MB, alloc=1164.3MB, time=188.40 memory used=14443.1MB, alloc=1188.3MB, time=199.27 memory used=14899.5MB, alloc=1212.3MB, time=206.20 memory used=15250.0MB, alloc=1236.3MB, time=210.11 memory used=15637.5MB, alloc=1260.3MB, time=215.30 memory used=15963.6MB, alloc=1284.3MB, time=218.37 memory used=16307.1MB, alloc=1308.3MB, time=221.39 memory used=16740.4MB, alloc=1332.3MB, time=227.17 memory used=17156.5MB, alloc=1371.8MB, time=231.08 memory used=17350.8MB, alloc=1371.8MB, time=233.87 memory used=17899.6MB, alloc=1371.8MB, time=238.90 memory used=18410.6MB, alloc=1371.8MB, time=244.01 memory used=19097.7MB, alloc=1395.8MB, time=254.62 memory used=19776.4MB, alloc=1419.8MB, time=266.21 memory used=20428.9MB, alloc=1443.8MB, time=278.08 memory used=21023.9MB, alloc=1467.8MB, time=289.53 memory used=21510.5MB, alloc=1491.8MB, time=298.90 memory used=21944.7MB, alloc=1515.8MB, time=309.90 memory used=22454.2MB, alloc=1539.8MB, time=319.81 memory used=22864.6MB, alloc=1563.8MB, time=328.81 memory used=23516.2MB, alloc=1587.8MB, time=340.00 memory used=23793.6MB, alloc=1611.8MB, time=347.16 memory used=24081.0MB, alloc=1635.8MB, time=355.17 memory used=24294.6MB, alloc=1659.8MB, time=361.41 memory used=24716.2MB, alloc=1659.8MB, time=371.65 memory used=25050.0MB, alloc=1683.8MB, time=380.60 memory used=25242.7MB, alloc=1683.8MB, time=386.94 memory used=25483.8MB, alloc=1683.8MB, time=394.99 memory used=25721.1MB, alloc=1683.8MB, time=402.88 memory used=26173.2MB, alloc=1683.8MB, time=410.23 memory used=26593.5MB, alloc=1683.8MB, time=418.64 memory used=26908.9MB, alloc=1707.8MB, time=426.22 memory used=27217.2MB, alloc=1707.8MB, time=433.34 memory used=27436.4MB, alloc=1707.8MB, time=440.79 memory used=27677.4MB, alloc=1707.8MB, time=448.55 memory used=28310.6MB, alloc=1731.8MB, time=456.91 memory used=28443.6MB, alloc=1731.8MB, time=461.61 memory used=28530.6MB, alloc=1731.8MB, time=466.27 memory used=28629.0MB, alloc=1731.8MB, time=470.94 memory used=28744.1MB, alloc=1731.8MB, time=475.63 memory used=29319.1MB, alloc=1731.8MB, time=484.47 memory used=29921.6MB, alloc=1731.8MB, time=493.88 memory used=30472.1MB, alloc=1731.8MB, time=501.69 memory used=30672.4MB, alloc=1731.8MB, time=508.61 memory used=30866.9MB, alloc=1731.8MB, time=515.38 memory used=30959.0MB, alloc=1731.8MB, time=521.52 memory used=31123.1MB, alloc=1731.8MB, time=528.54 memory used=31674.4MB, alloc=1731.8MB, time=535.77 memory used=31788.0MB, alloc=1731.8MB, time=542.33 memory used=31885.1MB, alloc=1731.8MB, time=548.32 memory used=32051.4MB, alloc=1755.8MB, time=555.28 memory used=32098.4MB, alloc=1755.8MB, time=561.09 memory used=32406.5MB, alloc=1755.8MB, time=567.76 memory used=32968.7MB, alloc=1755.8MB, time=574.67 memory used=33247.2MB, alloc=1755.8MB, time=580.72 memory used=33368.1MB, alloc=1755.8MB, time=586.89 memory used=33936.6MB, alloc=1755.8MB, time=593.31 memory used=34554.4MB, alloc=1755.8MB, time=602.64 memory used=34845.1MB, alloc=1755.8MB, time=609.25 memory used=34994.6MB, alloc=1755.8MB, time=615.92 memory used=35077.8MB, alloc=1755.8MB, time=622.08 memory used=35175.2MB, alloc=1755.8MB, time=628.33 memory used=35230.6MB, alloc=1755.8MB, time=634.08 memory used=35446.3MB, alloc=1755.8MB, time=640.79 memory used=35921.6MB, alloc=1755.8MB, time=648.46 memory used=35951.3MB, alloc=1755.8MB, time=654.31 memory used=36286.7MB, alloc=1755.8MB, time=663.92 memory used=36640.9MB, alloc=1755.8MB, time=669.86 memory used=36722.5MB, alloc=1755.8MB, time=675.48 memory used=36814.3MB, alloc=1755.8MB, time=681.07 memory used=36915.8MB, alloc=1755.8MB, time=686.65 memory used=37105.5MB, alloc=1755.8MB, time=692.79 memory used=37201.8MB, alloc=1755.8MB, time=699.39 memory used=37346.9MB, alloc=1755.8MB, time=706.08 memory used=37411.3MB, alloc=1755.8MB, time=712.02 memory used=37587.5MB, alloc=2011.8MB, time=724.48 memory used=38744.9MB, alloc=2035.8MB, time=745.46 memory used=39866.6MB, alloc=2059.8MB, time=763.13 memory used=41015.2MB, alloc=2083.8MB, time=784.09 memory used=42162.2MB, alloc=2107.8MB, time=803.54 memory used=43336.0MB, alloc=2131.8MB, time=826.18 memory used=44410.4MB, alloc=2155.8MB, time=839.96 memory used=45522.5MB, alloc=2179.8MB, time=857.10 memory used=46651.0MB, alloc=2203.8MB, time=882.05 memory used=47756.0MB, alloc=2227.8MB, time=909.09 memory used=48865.9MB, alloc=2251.8MB, time=935.82 memory used=49785.4MB, alloc=2275.8MB, time=963.23 memory used=50713.2MB, alloc=2299.8MB, time=990.80 memory used=51559.5MB, alloc=2323.8MB, time=1017.46 memory used=52379.2MB, alloc=2347.8MB, time=1044.13 memory used=53225.8MB, alloc=2371.8MB, time=1069.49 memory used=54107.3MB, alloc=2395.8MB, time=1093.83 memory used=54938.7MB, alloc=2419.8MB, time=1119.54 memory used=55759.8MB, alloc=2443.8MB, time=1144.87 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428484365 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 3 2 2 2 F := [14 x y z - 6 z - 16 y z, -x - 8 x z - 6 z , 2 x y - 2 x y z - 10 y] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 G := [17 x y z - 10 y - 15, 4 x y - 9 x z - 9 z, 3 z + 10 x y + 5 z] > Problem := [F,G]; Problem := [ 3 3 2 2 2 [14 x y z - 6 z - 16 y z, -x - 8 x z - 6 z , 2 x y - 2 x y z - 10 y], 2 3 [17 x y z - 10 y - 15, 4 x y - 9 x z - 9 z, 3 z + 10 x 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=0.18 memory used=26.5MB, alloc=32.3MB, time=0.49 memory used=46.8MB, alloc=32.3MB, time=0.79 memory used=65.8MB, alloc=56.3MB, time=1.09 memory used=104.1MB, alloc=60.3MB, time=1.67 memory used=141.7MB, alloc=84.3MB, time=2.24 memory used=201.4MB, alloc=92.3MB, time=3.16 memory used=260.4MB, alloc=92.3MB, time=4.07 memory used=317.5MB, alloc=116.3MB, time=4.99 memory used=398.7MB, alloc=116.3MB, time=6.21 memory used=477.1MB, alloc=140.3MB, time=7.43 memory used=557.3MB, alloc=396.3MB, time=8.72 memory used=661.8MB, alloc=420.3MB, time=10.43 memory used=788.6MB, alloc=444.3MB, time=12.50 memory used=936.2MB, alloc=468.3MB, time=15.03 memory used=1062.3MB, alloc=468.3MB, time=17.01 memory used=1198.5MB, alloc=492.3MB, time=19.42 memory used=1311.2MB, alloc=492.3MB, time=21.31 memory used=1431.3MB, alloc=492.3MB, time=23.30 memory used=1543.9MB, alloc=516.3MB, time=25.16 memory used=1654.0MB, alloc=516.3MB, time=27.13 memory used=1756.7MB, alloc=516.3MB, time=28.98 memory used=1855.1MB, alloc=516.3MB, time=30.85 memory used=1939.2MB, alloc=516.3MB, time=32.46 memory used=2015.2MB, alloc=516.3MB, time=33.93 memory used=2094.1MB, alloc=516.3MB, time=35.55 memory used=2173.5MB, alloc=516.3MB, time=37.24 memory used=2249.5MB, alloc=516.3MB, time=38.84 memory used=2313.6MB, alloc=516.3MB, time=40.34 memory used=2387.9MB, alloc=516.3MB, time=42.03 memory used=2441.9MB, alloc=540.3MB, time=43.35 memory used=2488.2MB, alloc=540.3MB, time=44.31 memory used=2544.4MB, alloc=540.3MB, time=45.72 memory used=2580.4MB, alloc=540.3MB, time=46.50 memory used=2801.8MB, alloc=564.3MB, time=51.08 memory used=3026.9MB, alloc=588.3MB, time=55.46 memory used=3226.3MB, alloc=612.3MB, time=59.29 memory used=3393.6MB, alloc=636.3MB, time=62.42 memory used=3564.5MB, alloc=660.3MB, time=65.74 memory used=3728.3MB, alloc=684.3MB, time=68.90 memory used=3890.1MB, alloc=684.3MB, time=71.86 memory used=4042.9MB, alloc=684.3MB, time=74.74 memory used=4174.4MB, alloc=708.3MB, time=77.32 memory used=4294.8MB, alloc=708.3MB, time=79.74 memory used=4432.5MB, alloc=708.3MB, time=82.60 memory used=4557.5MB, alloc=708.3MB, time=86.17 memory used=4676.2MB, alloc=708.3MB, time=88.99 memory used=4829.0MB, alloc=732.3MB, time=93.41 memory used=4975.9MB, alloc=732.3MB, time=97.59 memory used=5074.3MB, alloc=732.3MB, time=100.21 memory used=5460.1MB, alloc=756.3MB, time=108.62 memory used=5862.8MB, alloc=780.3MB, time=117.98 memory used=6292.8MB, alloc=804.3MB, time=127.83 memory used=6693.7MB, alloc=828.3MB, time=136.09 memory used=7090.6MB, alloc=852.3MB, time=144.31 memory used=7432.9MB, alloc=876.3MB, time=151.74 memory used=7780.2MB, alloc=900.3MB, time=161.80 memory used=8089.8MB, alloc=924.3MB, time=170.11 memory used=8387.6MB, alloc=948.3MB, time=176.54 memory used=8712.1MB, alloc=972.3MB, time=184.63 memory used=8960.4MB, alloc=996.3MB, time=190.08 memory used=9200.8MB, alloc=1020.3MB, time=197.36 memory used=9412.6MB, alloc=1044.3MB, time=202.39 memory used=10080.9MB, alloc=1068.3MB, time=216.40 memory used=10740.5MB, alloc=1092.3MB, time=235.14 memory used=11431.8MB, alloc=1116.3MB, time=250.67 memory used=12134.0MB, alloc=1140.3MB, time=267.67 memory used=12826.0MB, alloc=1164.3MB, time=287.27 memory used=13510.0MB, alloc=1188.3MB, time=307.27 memory used=14212.8MB, alloc=1212.3MB, time=328.70 memory used=14914.1MB, alloc=1236.3MB, time=348.18 memory used=15562.6MB, alloc=1260.3MB, time=364.85 memory used=16266.3MB, alloc=1284.3MB, time=387.93 memory used=16917.4MB, alloc=1308.3MB, time=411.49 memory used=17338.2MB, alloc=1332.3MB, time=423.53 memory used=17846.5MB, alloc=1356.3MB, time=438.96 memory used=18281.5MB, alloc=1380.3MB, time=454.03 memory used=18719.2MB, alloc=1404.3MB, time=469.45 memory used=19082.3MB, alloc=1428.3MB, time=481.44 memory used=19421.7MB, alloc=1452.3MB, time=493.69 memory used=19734.4MB, alloc=1476.3MB, time=502.90 memory used=20094.9MB, alloc=1500.3MB, time=517.80 memory used=20444.3MB, alloc=1524.3MB, time=532.76 memory used=20827.3MB, alloc=1548.3MB, time=547.91 memory used=21037.3MB, alloc=1572.3MB, time=556.40 memory used=21306.3MB, alloc=1596.3MB, time=565.83 memory used=21568.3MB, alloc=1620.3MB, time=579.18 memory used=21787.7MB, alloc=1644.3MB, time=588.45 memory used=22044.9MB, alloc=1668.3MB, time=601.24 memory used=22203.4MB, alloc=1692.3MB, time=610.61 memory used=22285.9MB, alloc=1716.3MB, time=617.80 memory used=22498.3MB, alloc=1740.3MB, time=628.99 memory used=22645.3MB, alloc=1764.3MB, time=639.81 memory used=22788.3MB, alloc=1788.3MB, time=647.95 memory used=22895.3MB, alloc=1812.3MB, time=655.21 memory used=23149.7MB, alloc=1836.3MB, time=668.45 memory used=23227.9MB, alloc=1860.3MB, time=676.22 memory used=23342.9MB, alloc=1884.3MB, time=683.77 memory used=23442.7MB, alloc=1908.3MB, time=691.00 memory used=23526.3MB, alloc=1908.3MB, time=697.84 memory used=23713.2MB, alloc=1908.3MB, time=710.15 memory used=23862.0MB, alloc=1908.3MB, time=719.91 memory used=23895.9MB, alloc=1908.3MB, time=726.69 memory used=24001.1MB, alloc=1908.3MB, time=734.09 memory used=24090.6MB, alloc=1908.3MB, time=741.49 memory used=24285.5MB, alloc=1908.3MB, time=754.12 memory used=24390.1MB, alloc=1908.3MB, time=762.91 memory used=24468.2MB, alloc=1908.3MB, time=770.65 memory used=24562.8MB, alloc=1908.3MB, time=778.45 memory used=24645.0MB, alloc=1908.3MB, time=785.80 memory used=24727.0MB, alloc=1932.3MB, time=792.50 memory used=24806.9MB, alloc=1932.3MB, time=800.47 memory used=24878.1MB, alloc=1932.3MB, time=807.55 memory used=24924.4MB, alloc=1932.3MB, time=815.85 memory used=25034.7MB, alloc=1932.3MB, time=826.81 memory used=25041.0MB, alloc=2188.3MB, time=841.09 memory used=26414.9MB, alloc=2212.3MB, time=882.42 memory used=27768.6MB, alloc=2236.3MB, time=922.15 memory used=29090.0MB, alloc=2260.3MB, time=974.67 |\^/| 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(); 1428485565 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 F := [-6 x y z - 5 y z - 12 x z, 7 x y z + 10 x - 3 y z, -3 x + 4 x z - 7 z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 G := [16 x y z - 5 x + 13 y z, -7 x z - 3 y - 8 z , -6 y z + 5 y + 3 z] > Problem := [F,G]; Problem := [ 2 2 2 [-6 x y z - 5 y z - 12 x z, 7 x y z + 10 x - 3 y z, -3 x + 4 x z - 7 z], 2 2 2 2 [16 x y z - 5 x + 13 y z, -7 x z - 3 y - 8 z , -6 y z + 5 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=0.19 memory used=26.4MB, alloc=32.3MB, time=0.51 memory used=47.6MB, alloc=32.3MB, time=0.85 memory used=67.0MB, alloc=56.3MB, time=1.18 memory used=106.2MB, alloc=60.3MB, time=1.76 memory used=143.1MB, alloc=84.3MB, time=2.32 memory used=200.7MB, alloc=92.3MB, time=3.19 memory used=255.8MB, alloc=92.3MB, time=4.05 memory used=312.1MB, alloc=116.3MB, time=4.96 memory used=393.8MB, alloc=140.3MB, time=6.29 memory used=460.9MB, alloc=140.3MB, time=7.33 memory used=528.7MB, alloc=396.3MB, time=8.43 memory used=633.9MB, alloc=420.3MB, time=10.07 memory used=759.1MB, alloc=444.3MB, time=12.23 memory used=897.1MB, alloc=468.3MB, time=14.97 memory used=1044.8MB, alloc=492.3MB, time=17.96 memory used=1182.3MB, alloc=492.3MB, time=20.69 memory used=1310.1MB, alloc=516.3MB, time=23.09 memory used=1444.3MB, alloc=516.3MB, time=26.02 memory used=1554.0MB, alloc=516.3MB, time=28.06 memory used=1664.1MB, alloc=516.3MB, time=30.36 memory used=1779.1MB, alloc=516.3MB, time=32.96 memory used=1874.2MB, alloc=540.3MB, time=35.03 memory used=1978.9MB, alloc=540.3MB, time=37.39 memory used=2061.2MB, alloc=540.3MB, time=39.32 memory used=2138.4MB, alloc=540.3MB, time=41.10 memory used=2218.3MB, alloc=540.3MB, time=43.04 memory used=2292.2MB, alloc=540.3MB, time=44.86 memory used=2354.8MB, alloc=540.3MB, time=46.36 memory used=2415.3MB, alloc=540.3MB, time=47.79 memory used=2481.5MB, alloc=540.3MB, time=49.49 memory used=2546.0MB, alloc=540.3MB, time=51.24 memory used=2603.0MB, alloc=540.3MB, time=52.85 memory used=2653.2MB, alloc=564.3MB, time=54.22 memory used=2861.8MB, alloc=588.3MB, time=59.09 memory used=3078.9MB, alloc=612.3MB, time=64.11 memory used=3284.4MB, alloc=636.3MB, time=69.09 memory used=3468.2MB, alloc=660.3MB, time=73.58 memory used=3665.5MB, alloc=684.3MB, time=77.92 memory used=3831.0MB, alloc=684.3MB, time=81.83 memory used=3993.6MB, alloc=684.3MB, time=85.40 memory used=4129.1MB, alloc=708.3MB, time=88.91 memory used=4276.8MB, alloc=708.3MB, time=92.43 memory used=4455.4MB, alloc=732.3MB, time=96.58 memory used=4645.1MB, alloc=756.3MB, time=100.57 memory used=4880.8MB, alloc=780.3MB, time=105.33 memory used=5103.5MB, alloc=804.3MB, time=110.04 memory used=5317.4MB, alloc=828.3MB, time=115.42 memory used=5510.1MB, alloc=852.3MB, time=120.97 memory used=5685.4MB, alloc=876.3MB, time=125.65 memory used=5881.6MB, alloc=900.3MB, time=131.06 memory used=6047.9MB, alloc=924.3MB, time=136.25 memory used=6171.5MB, alloc=948.3MB, time=140.10 memory used=6615.3MB, alloc=972.3MB, time=152.23 memory used=7050.5MB, alloc=996.3MB, time=161.73 memory used=7476.9MB, alloc=1020.3MB, time=171.07 memory used=7896.9MB, alloc=1044.3MB, time=180.44 memory used=8321.4MB, alloc=1068.3MB, time=189.84 memory used=8745.3MB, alloc=1092.3MB, time=199.79 memory used=9088.8MB, alloc=1116.3MB, time=213.42 memory used=9424.7MB, alloc=1140.3MB, time=227.80 memory used=9763.7MB, alloc=1164.3MB, time=242.51 memory used=10110.6MB, alloc=1188.3MB, time=257.85 memory used=10467.5MB, alloc=1212.3MB, time=273.79 memory used=10836.2MB, alloc=1236.3MB, time=290.69 memory used=11217.3MB, alloc=1260.3MB, time=309.73 memory used=11611.8MB, alloc=1284.3MB, time=328.72 memory used=12018.8MB, alloc=1308.3MB, time=349.91 memory used=12440.0MB, alloc=1332.3MB, time=370.65 memory used=12875.5MB, alloc=1356.3MB, time=393.12 memory used=13326.5MB, alloc=1380.3MB, time=415.04 memory used=13793.4MB, alloc=1404.3MB, time=437.68 memory used=14275.8MB, alloc=1428.3MB, time=460.72 memory used=14773.4MB, alloc=1452.3MB, time=480.94 |\^/| 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(); 1428486459 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 2 F := [-3 x - 8 x y z - 20 y z, -6 x z - 7 x y + 9 z ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 G := [6 y z - 3 x z - 15 y, 4 x y - 3 x z + 9 y] > Problem := [F,G]; 3 2 2 2 Problem := [[-3 x - 8 x y z - 20 y z, -6 x z - 7 x y + 9 z ], 2 2 2 [6 y z - 3 x z - 15 y, 4 x y - 3 x z + 9 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=25.3MB, alloc=32.3MB, time=0.49 memory used=43.7MB, alloc=56.3MB, time=0.76 memory used=85.4MB, alloc=60.3MB, time=1.36 memory used=127.4MB, alloc=68.3MB, time=1.91 memory used=173.0MB, alloc=92.3MB, time=2.51 memory used=240.7MB, alloc=92.3MB, time=3.39 memory used=303.8MB, alloc=348.3MB, time=4.22 memory used=370.2MB, alloc=372.3MB, time=5.13 memory used=463.4MB, alloc=372.3MB, time=6.37 memory used=552.7MB, alloc=396.3MB, time=7.60 memory used=669.8MB, alloc=396.3MB, time=9.15 memory used=779.2MB, alloc=420.3MB, time=10.58 memory used=909.9MB, alloc=420.3MB, time=12.22 memory used=1041.2MB, alloc=444.3MB, time=14.06 memory used=1156.1MB, alloc=444.3MB, time=15.78 memory used=1272.1MB, alloc=468.3MB, time=17.44 memory used=1370.8MB, alloc=468.3MB, time=18.91 memory used=1511.3MB, alloc=492.3MB, time=21.17 memory used=1666.6MB, alloc=516.3MB, time=23.60 memory used=1827.8MB, alloc=540.3MB, time=26.60 memory used=1987.6MB, alloc=564.3MB, time=29.59 memory used=2141.8MB, alloc=564.3MB, time=32.54 memory used=2297.1MB, alloc=588.3MB, time=35.34 memory used=2439.1MB, alloc=612.3MB, time=37.93 memory used=2569.7MB, alloc=612.3MB, time=40.54 memory used=2699.6MB, alloc=636.3MB, time=43.02 memory used=2846.7MB, alloc=636.3MB, time=45.70 memory used=2981.3MB, alloc=660.3MB, time=48.18 memory used=3112.6MB, alloc=684.3MB, time=50.81 memory used=3241.9MB, alloc=684.3MB, time=53.46 memory used=3371.4MB, alloc=708.3MB, time=56.72 memory used=3632.1MB, alloc=732.3MB, time=66.28 memory used=3894.5MB, alloc=756.3MB, time=76.59 memory used=4176.5MB, alloc=780.3MB, time=88.15 memory used=4469.5MB, alloc=804.3MB, time=100.91 memory used=4766.2MB, alloc=828.3MB, time=115.21 memory used=5080.3MB, alloc=852.3MB, time=129.72 memory used=5418.4MB, alloc=876.3MB, time=145.80 memory used=5780.4MB, alloc=900.3MB, time=162.86 memory used=6166.3MB, alloc=924.3MB, time=180.93 memory used=6576.2MB, alloc=924.3MB, time=199.84 memory used=6986.0MB, alloc=924.3MB, time=219.57 memory used=7395.8MB, alloc=948.3MB, time=238.91 |\^/| 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(); 1428486759 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 3 3 2 F := [14 x z + 5 x + 19 y z, 6 x + z - 9 x ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 G := [-17 x z - 15 y z + 9, 9 x z - 3 x - x] > Problem := [F,G]; 2 2 3 3 2 Problem := [[14 x z + 5 x + 19 y z, 6 x + z - 9 x ], 2 2 2 [-17 x z - 15 y z + 9, 9 x z - 3 x - x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.7MB, alloc=32.3MB, time=0.52 memory used=47.8MB, alloc=32.3MB, time=0.84 memory used=67.4MB, alloc=56.3MB, time=1.17 memory used=108.7MB, alloc=60.3MB, time=1.83 memory used=150.0MB, alloc=60.3MB, time=2.52 memory used=192.2MB, alloc=92.3MB, time=3.16 memory used=255.0MB, alloc=92.3MB, time=4.13 memory used=317.7MB, alloc=92.3MB, time=5.08 memory used=383.1MB, alloc=116.3MB, time=6.17 memory used=466.3MB, alloc=116.3MB, time=7.70 memory used=546.3MB, alloc=140.3MB, time=9.12 memory used=645.9MB, alloc=164.3MB, time=11.52 memory used=766.7MB, alloc=188.3MB, time=13.77 memory used=893.1MB, alloc=468.3MB, time=16.12 memory used=1037.9MB, alloc=492.3MB, time=19.84 memory used=1177.1MB, alloc=516.3MB, time=24.39 memory used=1323.4MB, alloc=540.3MB, time=30.17 memory used=1488.0MB, alloc=564.3MB, time=36.87 memory used=1676.5MB, alloc=564.3MB, time=44.91 memory used=1865.0MB, alloc=588.3MB, time=52.52 memory used=2077.5MB, alloc=588.3MB, time=61.02 memory used=2290.0MB, alloc=612.3MB, time=70.34 memory used=2526.8MB, alloc=636.3MB, time=80.31 N1 := 7073 > GB := Basis(F, plex(op(vars))); 9 8 7 6 5 2 6 GB := [16464 x - 24696 x + 67032 x y - 100548 x y + 90972 x y - 125 x 4 2 3 3 2 3 7 6 5 - 136458 x y + 41154 x y - 61731 x y , 1176 x - 1764 x + 3192 x y 4 4 3 2 2 2 2 2 - 4788 x y + 25 x z + 2166 x y - 3249 x y , 14 z x + 19 z y + 5 x , 5 4 3 2 2 2 3 3 2 -84 x + 126 x - 114 x y + 5 x z + 171 x y, z + 6 x - 9 x ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=2700.7MB, alloc=636.3MB, time=84.29 memory used=2838.2MB, alloc=636.3MB, time=86.57 memory used=2961.2MB, alloc=636.3MB, time=88.79 memory used=3066.4MB, alloc=636.3MB, time=90.71 memory used=3171.2MB, alloc=636.3MB, time=93.00 memory used=3290.1MB, alloc=636.3MB, time=95.22 memory used=3412.8MB, alloc=636.3MB, time=96.99 memory used=3617.2MB, alloc=636.3MB, time=98.33 memory used=3753.7MB, alloc=636.3MB, time=100.14 memory used=3858.7MB, alloc=636.3MB, time=101.92 memory used=3952.1MB, alloc=636.3MB, time=103.51 memory used=4056.1MB, alloc=636.3MB, time=105.31 memory used=4147.5MB, alloc=636.3MB, time=107.25 memory used=4237.5MB, alloc=636.3MB, time=109.42 memory used=4315.1MB, alloc=636.3MB, time=111.04 memory used=4392.1MB, alloc=636.3MB, time=112.63 memory used=4477.7MB, alloc=636.3MB, time=114.59 memory used=4533.8MB, alloc=636.3MB, time=115.84 memory used=4605.4MB, alloc=636.3MB, time=117.37 memory used=4684.9MB, alloc=660.3MB, time=118.65 memory used=4753.2MB, alloc=660.3MB, time=119.95 memory used=4806.4MB, alloc=660.3MB, time=121.05 memory used=4859.9MB, alloc=660.3MB, time=122.74 memory used=4900.5MB, alloc=660.3MB, time=124.06 memory used=4962.5MB, alloc=660.3MB, time=125.63 memory used=5005.5MB, alloc=660.3MB, time=126.69 memory used=5053.6MB, alloc=660.3MB, time=127.87 memory used=5285.2MB, alloc=684.3MB, time=131.64 memory used=5490.6MB, alloc=708.3MB, time=135.44 memory used=5738.2MB, alloc=708.3MB, time=138.08 memory used=5932.3MB, alloc=708.3MB, time=139.55 memory used=6139.0MB, alloc=708.3MB, time=140.88 memory used=6339.4MB, alloc=708.3MB, time=142.50 memory used=6604.3MB, alloc=732.3MB, time=179.28 memory used=6751.4MB, alloc=756.3MB, time=245.02 |\^/| 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(); 1428487059 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 3 2 F := [15 x z + 16 x y + 19 x, -8 y z + 7 z + 4 z ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 G := [19 z - 12 y z - 6, 4 y z - 2 x ] > Problem := [F,G]; 2 2 3 2 Problem := [[15 x z + 16 x y + 19 x, -8 y z + 7 z + 4 z ], 3 2 2 [19 z - 12 y z - 6, 4 y z - 2 x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.16 memory used=26.5MB, alloc=32.3MB, time=0.47 memory used=47.9MB, alloc=32.3MB, time=0.78 memory used=66.6MB, alloc=56.3MB, time=1.07 memory used=104.7MB, alloc=60.3MB, time=1.66 memory used=141.0MB, alloc=84.3MB, time=2.22 memory used=201.6MB, alloc=92.3MB, time=3.18 memory used=262.3MB, alloc=92.3MB, time=4.15 memory used=320.5MB, alloc=116.3MB, time=5.09 memory used=404.5MB, alloc=372.3MB, time=6.37 memory used=488.0MB, alloc=396.3MB, time=7.75 memory used=587.0MB, alloc=420.3MB, time=9.79 memory used=701.2MB, alloc=444.3MB, time=11.91 memory used=830.4MB, alloc=468.3MB, time=14.34 memory used=973.4MB, alloc=492.3MB, time=16.95 memory used=1115.0MB, alloc=516.3MB, time=21.62 memory used=1262.3MB, alloc=540.3MB, time=26.56 memory used=1416.7MB, alloc=564.3MB, time=32.63 memory used=1592.7MB, alloc=588.3MB, time=39.43 memory used=1792.6MB, alloc=588.3MB, time=47.38 memory used=1992.5MB, alloc=612.3MB, time=55.37 memory used=2216.4MB, alloc=612.3MB, time=64.44 memory used=2440.2MB, alloc=612.3MB, time=73.66 memory used=2663.9MB, alloc=636.3MB, time=83.04 memory used=2911.4MB, alloc=660.3MB, time=93.00 N1 := 8217 > GB := Basis(F, plex(op(vars))); 3 2 GB := [15360 x y + 15424 x y + 15392 x y + 22249 x, 2 2 -128 x y + 112 x y z - 88 x y + 133 x z + 76 x, 15 x z + 16 x y + 19 x, 2 3 2 -8 y z + 7 z + 4 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=3191.0MB, alloc=660.3MB, time=101.91 memory used=3367.0MB, alloc=660.3MB, time=105.18 memory used=3521.9MB, alloc=660.3MB, time=107.97 memory used=3775.2MB, alloc=660.3MB, time=113.32 memory used=4035.8MB, alloc=684.3MB, time=118.72 memory used=4327.8MB, alloc=708.3MB, time=128.05 memory used=4602.0MB, alloc=732.3MB, time=138.95 memory used=4897.0MB, alloc=756.3MB, time=151.56 memory used=5216.0MB, alloc=780.3MB, time=164.56 memory used=5558.9MB, alloc=804.3MB, time=179.08 memory used=5925.7MB, alloc=828.3MB, time=193.96 N2 := 8217 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 3 2 3 H := [15 x z + 16 x y + 19 x, -8 y z + 7 z + 4 z , 19 z - 12 y z - 6, 2 2 4 y z - 2 x ] > J:=[op(GB),op(G)]; 3 2 J := [15360 x y + 15424 x y + 15392 x y + 22249 x, 2 2 -128 x y + 112 x y z - 88 x y + 133 x z + 76 x, 15 x z + 16 x y + 19 x, 2 3 2 3 2 2 -8 y z + 7 z + 4 z , 19 z - 12 y z - 6, 4 y z - 2 x ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 10, 12, 3, 2, 1, 3, 1/2, 1, 1, 4/11, 4/11, 7/11, 6, 15, 19, 13 4, 2, 3, 3, 2/3, 1, 5/6, --, 1/2, 9/20, -5, -7, -1] 20 > save(F, G, cat("ranSet/33", convert(F, string),".txt")); > quit memory used=6166.3MB, alloc=828.3MB, time=203.20 |\^/| 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(); 1428487314 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 2 3 F := [-3 z + 18 z + 9 x, 2 x y + 7 y z - 8 z ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 2 G := [20 x y z + 5 y - 6 z, 6 x y + 2 x z + 4 y ] > Problem := [F,G]; 3 2 2 2 3 Problem := [[-3 z + 18 z + 9 x, 2 x y + 7 y z - 8 z ], 3 2 2 2 [20 x y z + 5 y - 6 z, 6 x y + 2 x z + 4 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=24.9MB, alloc=32.3MB, time=0.49 memory used=44.2MB, alloc=60.3MB, time=0.76 memory used=90.0MB, alloc=64.9MB, time=1.06 memory used=125.7MB, alloc=64.9MB, time=1.16 memory used=149.9MB, alloc=64.9MB, time=1.24 memory used=178.8MB, alloc=64.9MB, time=1.32 memory used=213.8MB, alloc=64.9MB, time=1.40 memory used=236.3MB, alloc=64.9MB, time=1.46 memory used=276.7MB, alloc=64.9MB, time=1.67 memory used=316.5MB, alloc=64.9MB, time=1.77 memory used=339.7MB, alloc=64.9MB, time=1.84 memory used=367.3MB, alloc=64.9MB, time=1.92 memory used=400.6MB, alloc=64.9MB, time=2.00 memory used=426.6MB, alloc=64.9MB, time=2.07 memory used=464.0MB, alloc=64.9MB, time=3.27 memory used=505.1MB, alloc=64.9MB, time=3.42 memory used=536.2MB, alloc=64.9MB, time=3.50 memory used=560.2MB, alloc=64.9MB, time=3.55 memory used=585.6MB, alloc=64.9MB, time=3.61 memory used=628.1MB, alloc=64.9MB, time=3.83 memory used=686.2MB, alloc=64.9MB, time=4.79 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time=30.49 memory used=4727.7MB, alloc=107.8MB, time=30.59 memory used=4776.9MB, alloc=107.8MB, time=30.71 memory used=4788.0MB, alloc=107.8MB, time=30.78 memory used=4795.5MB, alloc=107.8MB, time=30.84 memory used=4803.1MB, alloc=107.8MB, time=30.91 memory used=4808.9MB, alloc=107.8MB, time=30.96 memory used=4815.1MB, alloc=107.8MB, time=31.02 memory used=4821.4MB, alloc=107.8MB, time=31.08 memory used=4827.7MB, alloc=107.8MB, time=31.14 memory used=4834.0MB, alloc=107.8MB, time=31.20 memory used=4840.3MB, alloc=107.8MB, time=31.26 memory used=4846.7MB, alloc=107.8MB, time=31.32 memory used=4853.0MB, alloc=107.8MB, time=31.38 memory used=4859.3MB, alloc=107.8MB, time=31.43 memory used=4865.7MB, alloc=107.8MB, time=31.48 memory used=4872.0MB, alloc=107.8MB, time=31.54 memory used=4878.4MB, alloc=107.8MB, time=31.59 memory used=4884.7MB, alloc=107.8MB, time=31.64 memory used=4891.1MB, alloc=107.8MB, time=31.69 memory used=4897.4MB, alloc=107.8MB, time=31.75 memory used=4903.8MB, 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alloc=107.8MB, time=49.05 memory used=7543.3MB, alloc=107.8MB, time=49.11 memory used=7555.6MB, alloc=107.8MB, time=49.17 memory used=7613.9MB, alloc=107.8MB, time=49.76 memory used=7646.2MB, alloc=107.8MB, time=49.87 memory used=7726.7MB, alloc=107.8MB, time=50.67 memory used=7784.7MB, alloc=107.8MB, time=51.52 memory used=7837.6MB, alloc=387.8MB, time=52.31 memory used=7910.0MB, alloc=387.8MB, time=52.76 memory used=7985.0MB, alloc=387.8MB, time=53.42 memory used=8038.0MB, alloc=387.8MB, time=53.68 memory used=8097.7MB, alloc=387.8MB, time=53.89 memory used=8138.0MB, alloc=387.8MB, time=54.04 memory used=8189.5MB, alloc=387.8MB, time=54.20 memory used=8237.2MB, alloc=387.8MB, time=54.52 memory used=8297.0MB, alloc=387.8MB, time=54.75 memory used=8337.5MB, alloc=387.8MB, time=54.91 memory used=8389.0MB, alloc=387.8MB, time=55.10 memory used=8438.4MB, alloc=387.8MB, time=56.74 memory used=8499.2MB, alloc=387.8MB, time=57.31 memory used=8545.3MB, alloc=387.8MB, time=57.46 memory 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time=211.46 memory used=27911.6MB, alloc=531.8MB, time=211.67 memory used=28012.8MB, alloc=531.8MB, time=211.88 memory used=28114.0MB, alloc=531.8MB, time=212.11 memory used=28215.3MB, alloc=531.8MB, time=212.33 memory used=28316.7MB, alloc=531.8MB, time=212.55 memory used=28419.3MB, alloc=531.8MB, time=212.77 memory used=28540.0MB, alloc=531.8MB, time=213.00 memory used=28661.7MB, alloc=531.8MB, time=213.24 memory used=28783.3MB, alloc=531.8MB, time=213.48 memory used=28905.0MB, alloc=531.8MB, time=213.72 memory used=29026.6MB, alloc=531.8MB, time=213.95 memory used=29148.3MB, alloc=531.8MB, time=214.19 memory used=29269.9MB, alloc=531.8MB, time=214.44 memory used=29391.4MB, alloc=531.8MB, time=214.67 memory used=29512.9MB, alloc=531.8MB, time=214.91 memory used=29634.4MB, alloc=531.8MB, time=215.14 memory used=29755.7MB, alloc=531.8MB, time=215.37 memory used=29877.1MB, alloc=531.8MB, time=215.60 memory used=29998.3MB, alloc=531.8MB, time=215.84 memory used=30119.4MB, alloc=531.8MB, time=216.09 memory used=30240.5MB, alloc=531.8MB, time=216.32 memory used=30361.4MB, alloc=531.8MB, time=216.55 memory used=30482.2MB, alloc=531.8MB, time=216.77 memory used=30602.9MB, alloc=531.8MB, time=216.99 memory used=30723.4MB, alloc=531.8MB, time=217.21 memory used=30844.0MB, alloc=531.8MB, time=217.45 memory used=30965.6MB, alloc=531.8MB, time=217.69 memory used=31104.7MB, alloc=531.8MB, time=217.93 memory used=31244.6MB, alloc=531.8MB, time=218.17 memory used=31384.2MB, alloc=531.8MB, time=218.42 memory used=31523.6MB, alloc=531.8MB, time=218.67 memory used=31662.7MB, alloc=531.8MB, time=218.93 memory used=31801.5MB, alloc=531.8MB, time=219.19 memory used=31939.9MB, alloc=531.8MB, time=219.44 memory used=32078.1MB, alloc=531.8MB, time=219.70 memory used=32215.9MB, alloc=531.8MB, time=219.94 memory used=32353.4MB, alloc=531.8MB, time=220.17 memory used=32490.5MB, alloc=531.8MB, time=220.40 memory used=32627.3MB, alloc=531.8MB, time=220.67 memory used=32763.7MB, alloc=531.8MB, time=220.92 memory used=32901.1MB, alloc=531.8MB, time=221.18 memory used=33054.9MB, alloc=531.8MB, time=221.43 memory used=33209.2MB, alloc=531.8MB, time=221.69 memory used=33363.0MB, alloc=531.8MB, time=221.95 memory used=33516.1MB, alloc=531.8MB, time=222.22 memory used=33668.5MB, alloc=531.8MB, time=222.49 memory used=33820.4MB, alloc=531.8MB, time=222.75 memory used=33971.5MB, alloc=531.8MB, time=223.00 memory used=34121.9MB, alloc=531.8MB, time=223.26 memory used=34283.0MB, alloc=531.8MB, time=223.54 memory used=34458.3MB, alloc=531.8MB, time=223.85 memory used=34643.5MB, alloc=531.8MB, time=224.17 memory used=34827.5MB, alloc=531.8MB, time=224.48 memory used=35010.2MB, alloc=531.8MB, time=224.77 memory used=35191.6MB, alloc=531.8MB, time=225.08 memory used=35385.9MB, alloc=531.8MB, time=225.43 memory used=35639.5MB, alloc=531.8MB, time=226.02 memory used=35788.8MB, alloc=531.8MB, time=226.34 memory used=35899.8MB, alloc=531.8MB, time=226.59 memory used=36014.7MB, alloc=531.8MB, time=226.87 memory used=36135.3MB, alloc=531.8MB, time=227.14 memory used=36255.1MB, alloc=531.8MB, time=227.40 memory used=36374.0MB, alloc=531.8MB, time=227.68 memory used=36492.2MB, alloc=531.8MB, time=227.93 memory used=36609.5MB, alloc=531.8MB, time=228.19 memory used=36726.0MB, alloc=531.8MB, time=228.45 memory used=36841.6MB, alloc=531.8MB, time=228.71 memory used=36956.5MB, alloc=531.8MB, time=228.96 memory used=37071.5MB, alloc=531.8MB, time=229.21 memory used=37199.6MB, alloc=531.8MB, time=229.48 memory used=37327.5MB, alloc=531.8MB, time=229.74 memory used=37454.2MB, alloc=531.8MB, time=230.00 memory used=37579.7MB, alloc=531.8MB, time=230.28 memory used=37703.9MB, alloc=531.8MB, time=230.53 memory used=37826.9MB, alloc=531.8MB, time=230.79 memory used=37949.8MB, alloc=531.8MB, time=231.05 memory used=38084.0MB, alloc=531.8MB, time=231.29 memory used=38217.5MB, alloc=531.8MB, time=231.55 memory used=38349.4MB, alloc=531.8MB, time=231.81 memory used=38479.6MB, alloc=531.8MB, time=232.07 memory used=38609.2MB, alloc=531.8MB, time=232.33 memory used=38748.5MB, alloc=531.8MB, time=232.59 memory used=38886.6MB, alloc=531.8MB, time=232.86 memory used=39022.7MB, alloc=531.8MB, time=233.14 memory used=39169.4MB, alloc=531.8MB, time=233.43 memory used=39313.2MB, alloc=531.8MB, time=233.71 memory used=39454.2MB, alloc=531.8MB, time=233.99 memory used=39604.4MB, alloc=531.8MB, time=234.27 memory used=39751.1MB, alloc=531.8MB, time=234.56 memory used=39905.6MB, alloc=531.8MB, time=234.83 memory used=40055.8MB, alloc=531.8MB, time=235.11 memory used=40212.3MB, alloc=531.8MB, time=235.38 memory used=40364.6MB, alloc=531.8MB, time=235.65 memory used=40519.4MB, alloc=531.8MB, time=235.93 memory used=40678.5MB, alloc=531.8MB, time=236.20 memory used=40839.5MB, alloc=531.8MB, time=236.48 memory used=41008.9MB, alloc=531.8MB, time=236.75 memory used=41176.6MB, alloc=531.8MB, time=237.02 memory used=41351.2MB, alloc=531.8MB, time=237.31 memory used=41529.3MB, alloc=531.8MB, time=237.60 memory used=41714.5MB, alloc=531.8MB, time=237.87 memory used=42002.9MB, alloc=531.8MB, time=250.19 |\^/| 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(); 1428487614 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 3 2 F := [-13 x y z + 5 y - 2 x z, 9 x - 2 x y + 2 y] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 3 2 3 G := [x y + 11 y - 12 y, 6 y - 9 y z + 3 z ] > Problem := [F,G]; 3 3 2 Problem := [[-13 x y z + 5 y - 2 x z, 9 x - 2 x y + 2 y], 2 3 3 2 3 [x y + 11 y - 12 y, 6 y - 9 y z + 3 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.1MB, alloc=32.3MB, time=0.17 memory used=26.2MB, alloc=32.3MB, time=0.49 memory used=46.4MB, alloc=32.3MB, time=0.78 memory used=65.9MB, alloc=32.3MB, time=1.07 memory used=84.7MB, alloc=56.3MB, time=1.36 memory used=124.2MB, alloc=60.3MB, time=1.95 memory used=168.6MB, alloc=84.3MB, time=2.65 memory used=219.9MB, alloc=84.3MB, time=3.38 memory used=279.0MB, alloc=116.3MB, time=4.44 memory used=356.7MB, alloc=140.3MB, time=5.85 memory used=452.8MB, alloc=164.3MB, time=7.54 memory used=565.1MB, alloc=188.3MB, time=9.52 memory used=664.9MB, alloc=468.3MB, time=11.35 memory used=810.9MB, alloc=492.3MB, time=13.90 memory used=964.5MB, alloc=516.3MB, time=16.84 memory used=1113.6MB, alloc=540.3MB, time=21.61 memory used=1271.7MB, alloc=564.3MB, time=27.11 memory used=1443.8MB, alloc=588.3MB, time=33.23 memory used=1631.5MB, alloc=612.3MB, time=40.23 memory used=1831.4MB, alloc=636.3MB, time=48.21 memory used=2051.5MB, alloc=660.3MB, time=57.39 memory used=2295.6MB, alloc=684.3MB, time=67.30 memory used=2563.5MB, alloc=684.3MB, time=78.33 memory used=2831.4MB, alloc=684.3MB, time=88.96 memory used=3099.3MB, alloc=708.3MB, time=99.48 memory used=3391.1MB, alloc=708.3MB, time=110.94 memory used=3682.8MB, alloc=708.3MB, time=122.64 memory used=3974.3MB, alloc=732.3MB, time=134.06 memory used=4289.8MB, alloc=732.3MB, time=146.38 memory used=4605.4MB, alloc=732.3MB, time=158.70 memory used=4920.8MB, alloc=756.3MB, time=170.99 memory used=5260.1MB, alloc=780.3MB, time=184.31 |\^/| 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(); 1428487914 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 2 2 F := [-18 x y + 2 x z + 3 y z , -6 x y + 10 y z + 8 x ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 G := [13 x y + 6 x + 14 y, -z + 6 x ] > Problem := [F,G]; 2 2 2 2 2 2 Problem := [[-18 x y + 2 x z + 3 y z , -6 x y + 10 y z + 8 x ], 3 2 [13 x y + 6 x + 14 y, -z + 6 x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.6MB, alloc=32.3MB, time=0.49 memory used=48.0MB, alloc=32.3MB, time=0.81 memory used=68.6MB, alloc=56.3MB, time=1.14 memory used=108.8MB, alloc=60.3MB, time=1.75 memory used=147.3MB, alloc=84.3MB, time=2.34 memory used=212.6MB, alloc=92.3MB, time=3.48 memory used=271.7MB, alloc=116.3MB, time=4.53 memory used=353.2MB, alloc=116.3MB, time=5.93 memory used=428.1MB, alloc=140.3MB, time=7.29 memory used=530.8MB, alloc=164.3MB, time=8.85 memory used=652.3MB, alloc=188.3MB, time=10.80 memory used=779.7MB, alloc=212.3MB, time=13.91 memory used=908.3MB, alloc=236.3MB, time=17.93 memory used=1043.6MB, alloc=260.3MB, time=23.33 memory used=1202.7MB, alloc=260.3MB, time=29.62 memory used=1361.6MB, alloc=284.3MB, time=35.85 memory used=1544.6MB, alloc=284.3MB, time=42.92 memory used=1727.8MB, alloc=308.3MB, time=50.08 N1 := 5587 > GB := Basis(F, plex(op(vars))); 3 2 2 3 2 2 2 2 GB := [-6 x y + 81 x y + 8 x + 12 x y, -81 x y + 10 x z - 12 x , 2 2 2 -3 x y + 5 y z + 4 x ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1832.4MB, alloc=308.3MB, time=52.21 memory used=2078.0MB, alloc=564.3MB, time=56.70 memory used=2319.7MB, alloc=588.3MB, time=61.81 memory used=2531.4MB, alloc=612.3MB, time=69.89 memory used=2751.9MB, alloc=636.3MB, time=79.34 memory used=2996.8MB, alloc=660.3MB, time=90.16 N2 := 4781 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 2 2 H := [-18 x y + 2 x z + 3 y z , -6 x y + 10 y z + 8 x , 13 y x + 14 y + 6 x, 3 2 -z + 6 x ] > J:=[op(GB),op(G)]; 3 2 2 3 2 2 2 2 J := [-6 x y + 81 x y + 8 x + 12 x y, -81 x y + 10 x z - 12 x , 2 2 2 3 2 -3 x y + 5 y z + 4 x , 13 y x + 14 y + 6 x, -z + 6 x ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 10, 11, 3, 2, 1, 3, 1, 3/4, 3/4, 7/11, 6/11, 4/11, 5, 12, 15, 4, 3, 2, 3, 1, 4/5, 3/5, 4/5, 8/15, 1/5, -2, -4, -1] > save(F, G, cat("ranSet/33", convert(F, string),".txt")); > quit memory used=3030.4MB, alloc=660.3MB, time=91.47 |\^/| 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(); 1428488062 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 F := [6 y z + 2, -3 x y + 4 y z - 7] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 G := [13 x y z - 6 z - 15 z, -10 x - 8 x y + 9] > Problem := [F,G]; 2 2 2 Problem := [[6 y z + 2, -3 x y + 4 y z - 7], 2 3 2 [13 x y z - 6 z - 15 z, -10 x - 8 x y + 9]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=26.4MB, alloc=32.3MB, time=0.52 memory used=46.8MB, alloc=32.3MB, time=0.82 memory used=66.4MB, alloc=56.3MB, time=1.12 memory used=106.7MB, alloc=60.3MB, time=1.72 memory used=145.2MB, alloc=60.3MB, time=2.32 memory used=184.0MB, alloc=84.3MB, time=3.04 memory used=233.4MB, alloc=84.3MB, time=3.96 memory used=288.5MB, alloc=108.3MB, time=4.98 memory used=363.1MB, alloc=140.3MB, time=6.36 memory used=454.6MB, alloc=164.3MB, time=8.04 memory used=557.2MB, alloc=188.3MB, time=10.76 memory used=666.4MB, alloc=212.3MB, time=14.64 memory used=792.5MB, alloc=236.3MB, time=19.55 memory used=942.5MB, alloc=236.3MB, time=25.40 memory used=1092.6MB, alloc=260.3MB, time=31.19 N1 := 4639 > GB := Basis(F, plex(op(vars))); 2 2 2 GB := [9 y x + 25, -3 x + 25 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1273.1MB, alloc=260.3MB, time=35.93 N2 := 755 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 H := [6 y z + 2, -3 x y + 4 y z - 7, 13 x y z - 6 z - 15 z, 3 2 -10 x - 8 x y + 9] > J:=[op(GB),op(G)]; 2 2 2 2 3 2 J := [9 y x + 25, -3 x + 25 z , 13 x y z - 6 z - 15 z, -10 x - 8 x y + 9] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 10, 12, 3, 3, 2, 2, 3/4, 1, 3/4, 4/11, 5/11, 5/11, 4, 9, 11, 3, 3, 2, 2, 1, 3/4, 1/2, 1/2, 3/10, 2/5, 1, 1, 0] > save(F, G, cat("ranSet/33", convert(F, string),".txt")); > quit memory used=1288.5MB, alloc=260.3MB, time=36.41 |\^/| 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(); 1428488118 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 3 F := [-19 x y z + 7 x z - 4 z , -3 x y z + 6 z - 3 x] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 2 3 G := [-20 y z - 3 z - 5 x , 3 x y - 2 y + 9] > Problem := [F,G]; 2 2 3 Problem := [[-19 x y z + 7 x z - 4 z , -3 x y z + 6 z - 3 x], 2 3 2 2 3 [-20 y z - 3 z - 5 x , 3 x y - 2 y + 9]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=25.5MB, alloc=32.3MB, time=0.48 memory used=45.2MB, alloc=36.3MB, time=0.75 memory used=63.3MB, alloc=60.3MB, time=1.02 memory used=106.6MB, alloc=68.3MB, time=1.62 memory used=145.9MB, alloc=68.3MB, time=1.95 memory used=189.7MB, alloc=68.3MB, time=2.43 memory used=232.5MB, alloc=68.3MB, time=3.03 memory used=274.8MB, alloc=92.3MB, time=3.62 memory used=342.2MB, alloc=92.3MB, time=4.49 memory used=405.1MB, alloc=92.3MB, time=5.20 memory used=470.2MB, alloc=93.4MB, time=6.29 memory used=501.5MB, alloc=93.4MB, time=6.40 memory used=548.0MB, alloc=93.4MB, time=6.74 memory used=610.6MB, alloc=117.4MB, time=7.63 memory used=691.6MB, alloc=117.8MB, time=11.06 memory used=745.2MB, alloc=117.8MB, time=11.25 memory used=786.5MB, alloc=117.8MB, time=11.40 memory used=831.6MB, alloc=117.8MB, time=11.53 memory used=907.2MB, alloc=117.8MB, time=12.22 memory used=975.3MB, alloc=117.8MB, time=12.68 memory used=1032.6MB, alloc=117.8MB, time=15.82 memory used=1081.4MB, alloc=117.8MB, time=16.13 memory used=1126.6MB, alloc=117.8MB, time=16.27 memory used=1168.0MB, alloc=117.8MB, time=16.40 memory used=1204.4MB, alloc=117.8MB, time=16.52 memory used=1246.6MB, alloc=117.8MB, time=16.64 memory used=1299.4MB, alloc=117.8MB, time=16.77 memory used=1319.4MB, alloc=131.8MB, time=16.88 memory used=1332.6MB, alloc=131.8MB, time=16.96 memory used=1402.7MB, alloc=131.8MB, time=18.12 memory used=1469.4MB, alloc=387.8MB, time=19.24 memory used=1556.3MB, alloc=387.8MB, time=20.44 memory used=1633.6MB, alloc=387.8MB, time=21.25 memory used=1693.8MB, alloc=387.8MB, time=22.31 memory used=1730.5MB, alloc=387.8MB, time=22.46 memory used=1810.5MB, alloc=387.8MB, time=23.38 memory used=1893.0MB, alloc=411.8MB, time=24.40 memory used=2014.9MB, alloc=411.8MB, time=25.69 memory used=2132.1MB, alloc=411.8MB, time=26.93 memory used=2241.4MB, alloc=435.8MB, time=28.02 memory used=2379.9MB, alloc=435.8MB, time=29.30 memory used=2508.6MB, alloc=435.8MB, time=31.32 memory used=2625.3MB, alloc=459.8MB, time=33.44 memory used=2766.9MB, alloc=483.8MB, time=35.86 memory used=2935.9MB, alloc=507.8MB, time=38.40 memory used=3114.2MB, alloc=531.8MB, time=41.44 memory used=3296.9MB, alloc=555.8MB, time=45.87 memory used=3460.0MB, alloc=579.8MB, time=51.35 memory used=3628.1MB, alloc=603.8MB, time=58.01 memory used=3813.5MB, alloc=627.8MB, time=65.57 memory used=4022.9MB, alloc=651.8MB, time=74.20 memory used=4256.3MB, alloc=651.8MB, time=83.80 memory used=4489.6MB, alloc=675.8MB, time=93.49 memory used=4747.0MB, alloc=675.8MB, time=104.33 memory used=5004.5MB, alloc=699.8MB, time=115.02 N1 := 7749 > GB := Basis(F, plex(op(vars))); 4 2 3 3 3 2 4 2 2 3 GB := [-931 x y + 13718 x y + 1064 x y - 343 x - 304 x y + 588 x 2 2 2 3 2 2 3 - 336 x + 64 x, -19 x y + 7 x z - 4 x z, -931 x y + 13718 x y 2 2 2 3 2 + 532 x y + 2888 x y z - 343 x + 392 x - 112 x, 2 2 -19 x y z + 7 x z - 4 z , 3 2 2 3 2 2 3 2 2 931 x y - 13718 x y - 1064 x y + 343 x + 608 y z - 588 x + 224 x, 3 -x y z + 2 z - x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=5241.6MB, alloc=699.8MB, time=121.22 memory used=5377.6MB, alloc=699.8MB, time=123.32 memory used=5497.2MB, alloc=699.8MB, time=125.37 memory used=5617.3MB, alloc=699.8MB, time=127.03 memory used=5739.1MB, alloc=699.8MB, time=128.62 memory used=5979.3MB, alloc=699.8MB, time=133.35 memory used=6143.5MB, alloc=699.8MB, time=133.98 memory used=6333.9MB, alloc=699.8MB, time=138.05 memory used=6492.8MB, alloc=699.8MB, time=138.67 memory used=7048.4MB, alloc=699.8MB, time=142.06 memory used=7258.4MB, alloc=699.8MB, time=145.52 memory used=7425.1MB, alloc=699.8MB, time=147.21 memory used=7590.4MB, alloc=699.8MB, time=147.91 memory used=7758.9MB, alloc=699.8MB, time=149.80 memory used=7911.1MB, alloc=699.8MB, time=150.45 memory used=8251.3MB, alloc=723.8MB, time=172.16 memory used=8401.4MB, alloc=747.8MB, time=172.86 memory used=8566.9MB, alloc=747.8MB, time=173.59 memory used=8734.4MB, alloc=747.8MB, time=174.34 memory used=8907.5MB, alloc=747.8MB, time=175.06 memory used=9080.3MB, alloc=747.8MB, time=175.81 memory used=9256.8MB, alloc=747.8MB, time=176.51 memory used=9436.9MB, alloc=747.8MB, time=177.22 memory used=9620.4MB, alloc=747.8MB, time=177.97 memory used=9807.7MB, alloc=747.8MB, time=178.76 memory used=9999.9MB, alloc=747.8MB, time=179.51 memory used=10197.2MB, alloc=747.8MB, time=180.29 memory used=10399.1MB, alloc=747.8MB, time=181.03 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428488418 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 3 2 F := [-12 x z + 17 y , -9 x z + z - 6 z ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 3 G := [13 y + 9 x + 17 y, 2 x z - 4 z + 5 x z] > Problem := [F,G]; 2 2 3 2 Problem := [[-12 x z + 17 y , -9 x z + z - 6 z ], 3 2 3 [13 y + 9 x + 17 y, 2 x z - 4 z + 5 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=4.1MB, alloc=32.3MB, time=0.17 memory used=26.5MB, alloc=32.3MB, time=0.50 memory used=46.3MB, alloc=32.3MB, time=0.78 memory used=66.4MB, alloc=56.3MB, time=1.12 memory used=107.3MB, alloc=84.3MB, time=1.84 N1 := 795 > GB := Basis(F, plex(op(vars))); 2 4 6 4 2 4 4 4 GB := [-108 x y + 17 y - 72 x y , 12 z x - 17 y , -9 x y + y z - 6 y , 4 2 2 2 2 3 2 -51 y + 4 y z - 24 y z, -51 y z + 4 z - 24 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=163.2MB, alloc=84.3MB, time=2.87 memory used=222.1MB, alloc=92.3MB, time=3.76 memory used=280.6MB, alloc=116.3MB, time=4.66 memory used=365.4MB, alloc=140.3MB, time=5.99 memory used=468.6MB, alloc=164.3MB, time=7.82 memory used=584.8MB, alloc=188.3MB, time=10.08 memory used=712.4MB, alloc=212.3MB, time=12.59 memory used=840.0MB, alloc=236.3MB, time=16.14 memory used=971.7MB, alloc=260.3MB, time=20.54 memory used=1114.0MB, alloc=284.3MB, time=26.09 memory used=1280.1MB, alloc=308.3MB, time=32.49 memory used=1470.2MB, alloc=308.3MB, time=39.70 memory used=1660.4MB, alloc=332.3MB, time=46.95 memory used=1874.4MB, alloc=332.3MB, time=55.15 memory used=2088.4MB, alloc=356.3MB, time=63.36 memory used=2326.9MB, alloc=380.3MB, time=72.18 N2 := 7215 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 3 2 3 H := [-12 x z + 17 y , -9 x z + z - 6 z , 13 y + 17 y + 9 x, 2 3 2 x z - 4 z + 5 x z] > J:=[op(GB),op(G)]; 2 4 6 4 2 4 4 4 J := [-108 x y + 17 y - 72 x y , 12 z x - 17 y , -9 x y + y z - 6 y , 4 2 2 2 2 3 2 3 -51 y + 4 y z - 24 y z, -51 y z + 4 z - 24 z , 13 y + 17 y + 9 x, 2 3 2 x z - 4 z + 5 x z] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 9, 11, 3, 2, 3, 3, 1, 1/2, 3/4, 5/11, 3/11, 7/11, 7, 16, 26, 13 6, 2, 6, 3, 5/7, 6/7, 5/7, 7/20, --, 1/2, -7, -15, -3] 20 > save(F, G, cat("ranSet/33", convert(F, string),".txt")); > quit memory used=2328.6MB, alloc=380.3MB, time=72.26 |\^/| 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(); 1428488547 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 F := [-4 x y z - 4 x z - 7 y z, 6 x + 8 y + 8 y] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 3 G := [12 x z + 16 y + 17 y z, 7 x z + 5 y - 3 z] > Problem := [F,G]; 2 2 Problem := [[-4 x y z - 4 x z - 7 y z, 6 x + 8 y + 8 y], 2 2 3 [12 x z + 16 y + 17 y z, 7 x z + 5 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=32.0MB, alloc=40.3MB, time=0.56 memory used=60.1MB, alloc=40.3MB, time=0.97 memory used=87.7MB, alloc=64.3MB, time=1.48 memory used=135.6MB, alloc=68.3MB, time=2.32 memory used=179.0MB, alloc=92.3MB, time=3.10 memory used=240.4MB, alloc=116.3MB, time=4.94 N1 := 1797 > GB := Basis(F, plex(op(vars))); 2 2 4 3 2 GB := [4 y + 3 x + 4 y, 48 x z + 168 x z + 147 x z - 112 x z, 3 2 12 x z + 21 x z + 28 y z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=318.7MB, alloc=116.3MB, time=7.65 memory used=402.5MB, alloc=148.3MB, time=9.10 memory used=509.9MB, alloc=172.3MB, time=11.24 memory used=623.6MB, alloc=196.3MB, time=15.22 N2 := 1909 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 H := [-4 x y z - 4 x z - 7 y z, 6 x + 8 y + 8 y, 17 z y + 12 z x + 16 y , 2 3 7 z x + 5 y - 3 z] > J:=[op(GB),op(G)]; 2 2 4 3 2 J := [4 y + 3 x + 4 y, 48 x z + 168 x z + 147 x z - 112 x z, 3 2 2 2 3 12 x z + 21 x z + 28 y z, 17 z y + 12 z x + 16 y , 7 z x + 5 y - 3 z] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 11, 10, 3, 2, 3, 1, 1, 1, 3/4, 5/12, 7/12, 7/12, 5, 13, 16, 11 5, 4, 3, 1, 1, 4/5, 4/5, 9/16, 3/8, --, -2, -6, -2] 16 > save(F, G, cat("ranSet/33", convert(F, string),".txt")); > quit memory used=636.5MB, alloc=196.3MB, time=15.57 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428488573 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 F := [-18 x y + 6 y z - 2 y, 8 x z + 5 y z - 5 z ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 3 G := [-6 z - 13 x z + 11 y, -2 x + 9 x y + 9 x] > Problem := [F,G]; 2 2 Problem := [[-18 x y + 6 y z - 2 y, 8 x z + 5 y z - 5 z ], 3 3 [-6 z - 13 x z + 11 y, -2 x + 9 x y + 9 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.3MB, alloc=32.3MB, time=0.47 memory used=47.1MB, alloc=32.3MB, time=0.77 memory used=67.3MB, alloc=56.3MB, time=1.08 memory used=108.3MB, alloc=60.3MB, time=1.68 memory used=147.9MB, alloc=84.3MB, time=2.27 memory used=208.4MB, alloc=92.3MB, time=3.19 memory used=268.4MB, alloc=116.3MB, time=4.12 memory used=351.2MB, alloc=140.3MB, time=5.61 memory used=449.3MB, alloc=420.3MB, time=7.33 memory used=567.1MB, alloc=444.3MB, time=9.55 memory used=697.6MB, alloc=468.3MB, time=12.10 memory used=839.2MB, alloc=492.3MB, time=14.84 memory used=992.1MB, alloc=516.3MB, time=17.79 memory used=1154.1MB, alloc=540.3MB, time=21.01 memory used=1334.8MB, alloc=564.3MB, time=24.29 memory used=1517.5MB, alloc=588.3MB, time=27.87 memory used=1705.7MB, alloc=612.3MB, time=31.59 memory used=1891.8MB, alloc=636.3MB, time=36.72 memory used=2067.6MB, alloc=660.3MB, time=42.91 memory used=2253.2MB, alloc=684.3MB, time=50.30 memory used=2451.3MB, alloc=708.3MB, time=58.44 memory used=2663.6MB, alloc=732.3MB, time=67.09 memory used=2890.4MB, alloc=756.3MB, time=76.40 memory used=3132.3MB, alloc=780.3MB, time=86.59 memory used=3390.3MB, alloc=804.3MB, time=97.81 memory used=3664.6MB, alloc=828.3MB, time=110.03 memory used=3956.8MB, alloc=852.3MB, time=123.26 memory used=4264.2MB, alloc=876.3MB, time=137.06 memory used=4589.4MB, alloc=900.3MB, time=152.23 memory used=4938.5MB, alloc=924.3MB, time=168.36 memory used=5311.6MB, alloc=948.3MB, time=185.45 memory used=5708.6MB, alloc=972.3MB, time=204.42 |\^/| 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(); 1428488873 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 F := [-14 x z - 12 x z - 19 x z, -9 y z - 8 y - 2 z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 3 3 2 G := [17 x + 12 y + 6 z, -2 x - 4 x z + 3 x y z] > Problem := [F,G]; 2 2 2 Problem := [[-14 x z - 12 x z - 19 x z, -9 y z - 8 y - 2 z], 3 3 3 2 [17 x + 12 y + 6 z, -2 x - 4 x z + 3 x y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.2MB, alloc=32.3MB, time=0.51 memory used=45.9MB, alloc=56.3MB, time=0.82 memory used=86.4MB, alloc=60.3MB, time=1.45 memory used=128.5MB, alloc=92.3MB, time=2.06 memory used=194.4MB, alloc=92.3MB, time=3.06 memory used=262.5MB, alloc=116.3MB, time=4.05 memory used=336.0MB, alloc=372.3MB, time=5.16 memory used=423.5MB, alloc=396.3MB, time=6.55 memory used=536.6MB, alloc=420.3MB, time=8.24 memory used=668.4MB, alloc=444.3MB, time=10.25 memory used=791.7MB, alloc=444.3MB, time=12.09 memory used=900.0MB, alloc=468.3MB, time=13.54 memory used=1009.2MB, alloc=468.3MB, time=15.24 memory used=1116.9MB, alloc=468.3MB, time=16.96 memory used=1211.9MB, alloc=492.3MB, time=18.38 memory used=1349.1MB, alloc=492.3MB, time=19.46 memory used=1444.4MB, alloc=492.3MB, time=20.68 memory used=1539.1MB, alloc=516.3MB, time=22.24 memory used=1663.9MB, alloc=516.3MB, time=24.04 memory used=1762.3MB, alloc=516.3MB, time=26.03 memory used=1875.8MB, alloc=540.3MB, time=28.21 memory used=2017.2MB, alloc=564.3MB, time=31.24 memory used=2155.2MB, alloc=588.3MB, time=34.26 memory used=2271.2MB, alloc=612.3MB, time=36.88 memory used=2388.2MB, alloc=636.3MB, time=39.58 memory used=2496.7MB, alloc=660.3MB, time=42.04 memory used=2615.2MB, alloc=660.3MB, time=44.82 memory used=2730.9MB, alloc=684.3MB, time=47.37 memory used=2840.3MB, alloc=708.3MB, time=49.88 memory used=2950.6MB, alloc=708.3MB, time=52.52 memory used=3039.3MB, alloc=732.3MB, time=54.78 memory used=3115.3MB, alloc=732.3MB, time=56.68 memory used=3202.9MB, alloc=756.3MB, time=58.79 memory used=3282.9MB, alloc=756.3MB, time=60.83 memory used=3580.1MB, alloc=780.3MB, time=69.28 memory used=3846.8MB, alloc=804.3MB, time=79.77 memory used=4120.3MB, alloc=828.3MB, time=91.09 memory used=4404.4MB, alloc=852.3MB, time=103.46 memory used=4699.0MB, alloc=876.3MB, time=116.63 memory used=5005.3MB, alloc=900.3MB, time=129.76 memory used=5325.8MB, alloc=924.3MB, time=144.30 memory used=5661.4MB, alloc=948.3MB, time=159.69 memory used=6007.1MB, alloc=972.3MB, time=176.29 memory used=6372.3MB, alloc=996.3MB, time=193.18 memory used=6761.4MB, alloc=1020.3MB, time=211.10 memory used=7174.4MB, alloc=1044.3MB, time=230.01 |\^/| 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(); 1428489173 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 3 2 F := [-10 x y + 10 y z, 9 y + 9 x - z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 3 2 G := [6 y - 4 z - 8, y z - 8 y z + 5] > Problem := [F,G]; Problem := [ 2 2 3 2 3 3 2 [-10 x y + 10 y z, 9 y + 9 x - z], [6 y - 4 z - 8, y z - 8 y z + 5]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.0MB, alloc=32.3MB, time=0.52 memory used=46.3MB, alloc=60.3MB, time=0.82 memory used=87.4MB, alloc=60.3MB, time=1.37 memory used=131.7MB, alloc=68.3MB, time=1.97 memory used=174.5MB, alloc=68.3MB, time=2.62 memory used=221.6MB, alloc=68.3MB, time=3.39 memory used=264.4MB, alloc=92.3MB, time=4.04 memory used=333.3MB, alloc=92.3MB, time=5.02 memory used=400.4MB, alloc=116.3MB, time=5.90 memory used=462.8MB, alloc=116.3MB, time=6.67 memory used=540.6MB, alloc=119.0MB, time=7.14 memory used=597.6MB, alloc=119.0MB, time=7.39 memory used=650.9MB, alloc=119.0MB, time=7.59 memory used=726.9MB, alloc=119.0MB, time=13.91 memory used=773.1MB, alloc=119.0MB, time=14.07 memory used=808.4MB, alloc=119.0MB, time=14.21 memory used=887.3MB, alloc=119.0MB, time=14.86 memory used=950.2MB, alloc=119.0MB, time=15.62 memory used=1004.9MB, alloc=375.0MB, time=16.40 memory used=1094.5MB, alloc=375.0MB, time=17.16 memory used=1146.4MB, alloc=375.0MB, time=17.44 memory used=1214.2MB, alloc=375.0MB, time=24.79 memory used=1252.6MB, alloc=375.0MB, time=24.96 memory used=1339.5MB, alloc=375.0MB, time=25.71 memory used=1450.3MB, alloc=399.0MB, time=27.49 memory used=1581.6MB, alloc=399.0MB, time=28.57 memory used=1706.6MB, alloc=399.0MB, time=30.36 memory used=1830.9MB, alloc=399.0MB, time=32.01 memory used=1963.1MB, alloc=399.0MB, time=34.65 memory used=2068.7MB, alloc=399.0MB, time=36.26 memory used=2220.5MB, alloc=423.0MB, time=37.70 memory used=2408.1MB, alloc=423.0MB, time=39.04 memory used=2547.7MB, alloc=447.0MB, time=41.31 memory used=2762.3MB, alloc=447.0MB, time=44.08 memory used=2932.4MB, alloc=447.0MB, time=45.02 memory used=3096.8MB, alloc=447.0MB, time=46.87 memory used=3251.5MB, alloc=447.0MB, time=47.97 memory used=3397.4MB, alloc=471.0MB, time=50.23 memory used=3544.3MB, alloc=495.0MB, time=52.89 memory used=3713.5MB, alloc=519.0MB, time=55.78 memory used=3890.5MB, alloc=543.0MB, time=59.16 memory used=4053.7MB, alloc=567.0MB, time=64.54 memory used=4223.5MB, alloc=591.0MB, time=70.70 memory used=4397.3MB, alloc=615.0MB, time=78.12 memory used=4595.0MB, alloc=639.0MB, time=86.58 memory used=4816.6MB, alloc=663.0MB, time=96.10 memory used=5062.3MB, alloc=687.0MB, time=106.53 memory used=5331.9MB, alloc=687.0MB, time=117.71 memory used=5601.6MB, alloc=711.0MB, time=128.92 N1 := 7695 > GB := Basis(F, plex(op(vars))); 5 2 2 2 3 2 GB := [9 y + 9 x y - x y , -9 y - 9 x + z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=5910.4MB, alloc=711.0MB, time=138.85 memory used=6032.8MB, alloc=711.0MB, time=141.09 memory used=6298.0MB, alloc=711.0MB, time=148.80 memory used=6412.6MB, alloc=711.0MB, time=150.61 memory used=6629.3MB, alloc=711.0MB, time=152.58 memory used=6811.1MB, alloc=711.0MB, time=154.94 memory used=6989.2MB, alloc=711.0MB, time=157.02 memory used=7178.4MB, alloc=711.0MB, time=159.18 memory used=7406.2MB, alloc=711.0MB, time=162.25 memory used=7636.0MB, alloc=711.0MB, time=164.25 memory used=7847.8MB, alloc=711.0MB, time=167.35 N2 := 1775 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 3 2 3 3 2 H := [-10 x y + 10 y z, 9 y + 9 x - z, 6 y - 4 z - 8, z y - 8 z y + 5] > J:=[op(GB),op(G)]; J := [ 5 2 2 2 3 2 3 3 2 9 y + 9 x y - x y , -9 y - 9 x + z, 6 y - 4 z - 8, z y - 8 z y + 5] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 10, 12, 3, 2, 3, 3, 1/2, 1, 1, 2/11, 6/11, 5/11, 4, 9, 14, 5, 2, 5, 3, 1/2, 1, 3/4, 1/4, 7/12, 1/3, 1, -2, -2] > save(F, G, cat("ranSet/33", convert(F, string),".txt")); > quit memory used=7977.0MB, alloc=711.0MB, time=172.27 |\^/| 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(); 1428489392 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 3 F := [-19 x y - 14 x + 17 x z, 6 x - 6 x + 6 z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 G := [9 y z + 11 z, 4 x + 7 x y - 2 x y] > Problem := [F,G]; 2 2 3 Problem := [[-19 x y - 14 x + 17 x z, 6 x - 6 x + 6 z], 3 2 [9 y z + 11 z, 4 x + 7 x y - 2 x y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=25.7MB, alloc=32.3MB, time=0.47 memory used=47.9MB, alloc=32.3MB, time=0.84 memory used=68.7MB, alloc=56.3MB, time=1.21 memory used=109.9MB, alloc=80.3MB, time=2.28 N1 := 927 > GB := Basis(F, plex(op(vars))); 4 2 2 3 GB := [17 x + 19 x y - 3 x , x + z - x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=146.9MB, alloc=80.3MB, time=3.02 N2 := 557 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 3 H := [-19 x y - 14 x + 17 x z, 6 x - 6 x + 6 z, 9 y z + 11 z, 3 2 4 x + 7 x y - 2 x y] > J:=[op(GB),op(G)]; 4 2 2 3 3 2 J := [17 x + 19 x y - 3 x , x + z - x, 9 y z + 11 z, 4 x + 7 x y - 2 x y] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 9, 11, 3, 3, 2, 1, 3/4, 3/4, 3/4, 8/11, 4/11, 4/11, 4, 8, 12, 4, 4, 2, 1, 3/4, 3/4, 1/2, 8/11, 4/11, 3/11, 1, -1, -1] > save(F, G, cat("ranSet/33", convert(F, string),".txt")); > quit memory used=192.4MB, alloc=84.3MB, time=3.91 |\^/| 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(); 1428489398 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 F := [5 x z - 2 y z + 8 x, 3 y z - x y + 9 y ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 2 3 G := [-19 y z + 7 z + 14 x , 2 x z - 2 y + y] > Problem := [F,G]; 2 2 2 2 Problem := [[5 x z - 2 y z + 8 x, 3 y z - x y + 9 y ], 2 3 2 2 3 [-19 y z + 7 z + 14 x , 2 x z - 2 y + y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=24.0MB, alloc=32.3MB, time=0.45 memory used=43.9MB, alloc=60.3MB, time=0.74 memory used=87.4MB, alloc=60.3MB, time=1.27 memory used=131.9MB, alloc=68.3MB, time=1.86 memory used=181.9MB, alloc=92.3MB, time=2.42 memory used=246.3MB, alloc=92.3MB, time=3.09 memory used=309.2MB, alloc=348.3MB, time=3.89 memory used=385.5MB, alloc=348.3MB, time=4.69 memory used=453.1MB, alloc=372.3MB, time=5.41 memory used=528.5MB, alloc=372.3MB, time=6.09 memory used=626.9MB, alloc=372.3MB, time=7.15 memory used=722.0MB, alloc=372.3MB, time=8.32 memory used=808.7MB, alloc=396.3MB, time=9.48 memory used=881.0MB, alloc=396.3MB, time=10.83 memory used=967.9MB, alloc=396.3MB, time=11.60 memory used=1101.1MB, alloc=396.3MB, time=12.83 memory used=1224.1MB, alloc=420.3MB, time=14.16 memory used=1363.8MB, alloc=420.3MB, time=15.38 memory used=1493.9MB, alloc=420.3MB, time=16.74 memory used=1578.0MB, alloc=420.3MB, time=17.55 memory used=1666.0MB, alloc=420.3MB, time=21.09 memory used=1728.8MB, alloc=420.3MB, time=21.35 memory used=1777.0MB, alloc=420.3MB, time=21.58 memory used=1838.3MB, alloc=420.3MB, time=21.82 memory used=1893.0MB, alloc=420.3MB, time=22.02 memory used=1962.3MB, alloc=420.3MB, time=22.48 memory used=2090.4MB, alloc=420.3MB, time=24.26 memory used=2251.6MB, alloc=444.3MB, time=25.81 memory used=2404.8MB, alloc=444.3MB, time=28.52 memory used=2522.8MB, alloc=444.3MB, time=29.64 memory used=2632.7MB, alloc=444.3MB, time=30.98 memory used=2751.4MB, alloc=444.3MB, time=32.33 memory used=2842.1MB, alloc=444.3MB, time=33.33 memory used=2903.9MB, alloc=444.3MB, time=33.60 memory used=3006.1MB, alloc=444.3MB, time=41.43 memory used=3075.3MB, alloc=444.3MB, time=41.76 memory used=3134.5MB, alloc=444.3MB, time=42.05 memory used=3201.6MB, alloc=444.3MB, time=42.32 memory used=3271.5MB, alloc=444.3MB, time=42.59 memory used=3328.5MB, alloc=444.3MB, time=42.84 memory used=3453.7MB, alloc=444.3MB, time=43.65 memory used=3562.7MB, alloc=444.3MB, time=44.58 memory used=3687.6MB, alloc=444.3MB, time=45.79 memory used=3778.7MB, alloc=468.3MB, time=46.99 memory used=3874.7MB, alloc=468.3MB, time=48.19 memory used=3961.9MB, alloc=468.3MB, time=49.43 memory used=4048.5MB, alloc=468.3MB, time=50.49 memory used=4127.7MB, alloc=468.3MB, time=51.78 memory used=4250.6MB, alloc=468.3MB, time=53.10 memory used=4317.2MB, alloc=468.3MB, time=53.57 memory used=4411.2MB, alloc=492.3MB, time=54.73 memory used=4501.3MB, alloc=492.3MB, time=55.16 memory used=4581.2MB, alloc=492.3MB, time=55.52 memory used=4759.5MB, alloc=492.3MB, time=59.15 memory used=4849.8MB, alloc=492.3MB, time=59.66 memory used=4938.1MB, alloc=492.3MB, time=60.24 memory used=5015.0MB, alloc=492.3MB, time=60.67 memory used=5110.1MB, alloc=492.3MB, time=61.13 memory used=5340.1MB, alloc=492.3MB, time=61.84 memory used=5528.3MB, alloc=492.3MB, time=63.56 memory used=5609.9MB, alloc=492.3MB, time=64.04 memory used=5701.5MB, alloc=492.3MB, time=64.42 memory used=5892.9MB, alloc=492.3MB, time=73.61 memory used=5979.6MB, alloc=492.3MB, time=74.05 memory used=6071.1MB, alloc=492.3MB, time=74.63 memory used=6141.9MB, alloc=492.3MB, time=75.08 memory used=6224.0MB, alloc=492.3MB, time=75.46 memory used=6319.5MB, alloc=492.3MB, time=75.85 memory used=6430.0MB, alloc=492.3MB, time=76.25 memory used=6582.7MB, alloc=492.3MB, time=76.84 memory used=6738.9MB, alloc=492.3MB, time=77.49 memory used=6929.2MB, alloc=492.3MB, time=78.01 memory used=7064.6MB, alloc=492.3MB, time=79.13 memory used=7145.7MB, alloc=492.3MB, time=80.09 memory used=7243.8MB, alloc=492.3MB, time=81.13 memory used=7375.3MB, alloc=516.3MB, time=115.42 memory used=7516.2MB, alloc=516.3MB, time=148.28 memory used=7610.8MB, alloc=516.3MB, time=148.76 memory used=7718.5MB, alloc=516.3MB, time=149.42 memory used=7816.2MB, alloc=516.3MB, time=150.04 memory used=7890.9MB, alloc=516.3MB, time=150.58 memory used=7974.0MB, alloc=516.3MB, time=150.98 memory used=8065.5MB, alloc=516.3MB, time=151.41 memory used=8165.6MB, alloc=516.3MB, time=151.85 memory used=8274.3MB, alloc=516.3MB, time=152.28 memory used=8391.5MB, alloc=516.3MB, time=152.74 memory used=8517.2MB, alloc=516.3MB, time=153.19 memory used=8670.2MB, alloc=516.3MB, time=153.72 memory used=8806.2MB, alloc=516.3MB, time=154.23 memory used=8950.6MB, alloc=516.3MB, time=154.77 memory used=9105.2MB, alloc=516.3MB, time=155.38 memory used=9269.5MB, alloc=516.3MB, time=155.97 memory used=9446.7MB, alloc=516.3MB, time=156.52 memory used=9635.7MB, alloc=516.3MB, time=157.08 memory used=9835.5MB, alloc=516.3MB, time=157.68 memory used=10053.4MB, alloc=516.3MB, time=158.28 memory used=10282.0MB, alloc=516.3MB, time=158.90 memory used=10475.9MB, alloc=516.3MB, time=159.44 memory used=10655.7MB, alloc=516.3MB, time=160.00 memory used=10850.4MB, alloc=516.3MB, time=160.54 memory used=11080.2MB, alloc=516.3MB, time=161.92 memory used=11178.2MB, alloc=516.3MB, time=162.34 memory used=11273.6MB, alloc=516.3MB, time=162.74 memory used=11513.7MB, alloc=516.3MB, time=163.89 memory used=11637.8MB, alloc=516.3MB, time=164.84 memory used=11738.3MB, alloc=516.3MB, time=165.29 memory used=11847.2MB, alloc=516.3MB, time=165.94 memory used=11948.3MB, alloc=516.3MB, time=166.40 memory used=12071.2MB, alloc=516.3MB, time=168.21 memory used=12162.6MB, alloc=516.3MB, time=168.63 memory used=12297.1MB, alloc=516.3MB, time=169.61 memory used=12351.8MB, alloc=516.3MB, time=170.46 memory used=12428.1MB, alloc=516.3MB, time=171.56 memory used=12569.3MB, alloc=516.3MB, time=173.13 memory used=12659.5MB, alloc=516.3MB, time=173.60 memory used=12777.1MB, alloc=516.3MB, time=174.10 memory used=12850.4MB, alloc=516.3MB, time=174.50 memory used=12933.4MB, alloc=516.3MB, time=174.90 memory used=13028.0MB, alloc=516.3MB, time=175.29 memory used=13133.5MB, alloc=516.3MB, time=175.73 memory used=13253.0MB, alloc=516.3MB, time=176.15 memory used=13458.4MB, alloc=516.3MB, time=176.72 memory used=13614.3MB, alloc=516.3MB, time=177.19 memory used=13706.0MB, alloc=516.3MB, time=179.04 memory used=13849.8MB, alloc=516.3MB, time=181.23 memory used=13955.0MB, alloc=516.3MB, time=181.70 memory used=14038.0MB, alloc=516.3MB, time=182.14 memory used=14133.3MB, alloc=516.3MB, time=182.91 memory used=14227.7MB, alloc=516.3MB, time=183.82 memory used=14280.8MB, alloc=516.3MB, time=184.80 memory used=14497.5MB, alloc=540.3MB, time=187.24 memory used=14673.8MB, alloc=540.3MB, time=189.18 memory used=14926.1MB, alloc=540.3MB, time=191.86 memory used=15066.3MB, alloc=564.3MB, time=195.27 memory used=15317.3MB, alloc=588.3MB, time=197.88 memory used=15561.3MB, alloc=588.3MB, time=199.02 memory used=15811.7MB, alloc=588.3MB, time=200.03 memory used=16099.6MB, alloc=588.3MB, time=201.02 memory used=16411.2MB, alloc=588.3MB, time=202.05 memory used=16753.3MB, alloc=588.3MB, time=203.10 memory used=17127.3MB, alloc=588.3MB, time=205.91 memory used=17418.7MB, alloc=588.3MB, time=208.68 memory used=17649.4MB, alloc=588.3MB, time=210.22 memory used=17839.4MB, alloc=588.3MB, time=211.20 memory used=18080.5MB, alloc=588.3MB, time=213.78 memory used=18293.7MB, alloc=588.3MB, time=214.96 memory used=18478.3MB, alloc=588.3MB, time=215.90 memory used=18675.1MB, alloc=588.3MB, time=216.91 memory used=18929.4MB, alloc=588.3MB, time=220.09 memory used=19123.0MB, alloc=588.3MB, time=221.08 memory used=19326.1MB, alloc=588.3MB, time=221.98 memory used=19594.8MB, alloc=588.3MB, time=223.53 memory used=19796.8MB, alloc=588.3MB, time=224.58 memory used=19991.6MB, alloc=588.3MB, time=225.48 memory used=20259.1MB, alloc=588.3MB, time=227.15 memory used=20519.5MB, alloc=588.3MB, time=229.64 memory used=20739.3MB, alloc=612.3MB, time=231.08 memory used=20954.8MB, alloc=612.3MB, time=231.96 memory used=21191.9MB, alloc=612.3MB, time=232.89 memory used=21436.5MB, alloc=612.3MB, time=233.83 memory used=21717.2MB, alloc=612.3MB, time=234.85 memory used=22035.9MB, alloc=612.3MB, time=235.89 memory used=22394.3MB, alloc=612.3MB, time=236.98 memory used=22709.0MB, alloc=612.3MB, time=239.40 memory used=23014.8MB, alloc=612.3MB, time=242.10 memory used=23292.5MB, alloc=612.3MB, time=244.24 memory used=23522.0MB, alloc=612.3MB, time=245.25 memory used=23769.5MB, alloc=612.3MB, time=246.24 memory used=24132.9MB, alloc=612.3MB, time=248.06 memory used=24385.0MB, alloc=612.3MB, time=249.55 memory used=24622.8MB, alloc=612.3MB, time=250.50 memory used=24887.6MB, alloc=612.3MB, time=251.51 memory used=25254.6MB, alloc=612.3MB, time=253.43 memory used=25520.8MB, alloc=612.3MB, time=255.41 memory used=25763.3MB, alloc=612.3MB, time=256.51 memory used=26033.8MB, alloc=612.3MB, time=257.53 memory used=26335.4MB, alloc=612.3MB, time=258.61 memory used=26709.8MB, alloc=612.3MB, time=259.82 memory used=26989.7MB, alloc=612.3MB, time=261.30 memory used=27278.2MB, alloc=612.3MB, time=262.36 memory used=27589.3MB, alloc=612.3MB, time=263.42 memory used=27935.5MB, alloc=612.3MB, time=264.67 memory used=28411.3MB, alloc=612.3MB, time=267.08 memory used=28721.4MB, alloc=612.3MB, time=270.25 memory used=28935.9MB, alloc=612.3MB, time=271.45 memory used=29124.2MB, alloc=612.3MB, time=272.41 memory used=29315.4MB, alloc=636.3MB, time=273.38 memory used=29545.7MB, alloc=636.3MB, time=274.35 memory used=29825.6MB, alloc=636.3MB, time=275.36 memory used=30126.2MB, alloc=636.3MB, time=278.15 memory used=30370.7MB, alloc=636.3MB, time=279.45 memory used=30584.8MB, alloc=636.3MB, time=280.49 memory used=30803.4MB, alloc=636.3MB, time=281.44 memory used=31049.6MB, alloc=636.3MB, time=282.49 memory used=31334.3MB, alloc=636.3MB, time=283.47 memory used=31631.7MB, alloc=636.3MB, time=286.14 memory used=31929.9MB, alloc=636.3MB, time=288.26 memory used=32226.8MB, alloc=636.3MB, time=290.25 memory used=32544.2MB, alloc=636.3MB, time=292.74 memory used=32825.5MB, alloc=636.3MB, time=294.90 |\^/| 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(); 1428489698 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 2 2 F := [15 x y + 17 y + 8 x , -4 y z - 5 x + 2 x y] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 G := [-19 x y z - 8 y z - 7 x z, 7 x z + 10 y z + 4 x z] > Problem := [F,G]; 2 3 2 2 2 Problem := [[15 x y + 17 y + 8 x , -4 y z - 5 x + 2 x y], 2 2 2 [-19 x y z - 8 y z - 7 x z, 7 x z + 10 y z + 4 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.5MB, alloc=32.3MB, time=0.51 memory used=47.6MB, alloc=32.3MB, time=0.83 memory used=67.5MB, alloc=56.3MB, time=1.13 memory used=110.1MB, alloc=84.3MB, time=1.86 memory used=165.5MB, alloc=84.3MB, time=2.86 memory used=223.3MB, alloc=116.3MB, time=3.92 memory used=298.4MB, alloc=140.3MB, time=5.37 memory used=384.8MB, alloc=164.3MB, time=8.07 memory used=485.0MB, alloc=164.3MB, time=11.83 N1 := 2815 > GB := Basis(F, plex(op(vars))); 3 2 2 3 2 2 2 GB := [17 y + 15 y x + 8 x , -75 x - 55 x y + 32 x z + 34 x y , 2 2 4 z y - 2 y x + 5 x ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=588.2MB, alloc=164.3MB, time=15.17 memory used=679.2MB, alloc=444.3MB, time=16.63 memory used=815.6MB, alloc=468.3MB, time=18.75 memory used=978.2MB, alloc=492.3MB, time=21.75 memory used=1153.1MB, alloc=516.3MB, time=24.93 memory used=1336.6MB, alloc=540.3MB, time=28.94 memory used=1514.1MB, alloc=564.3MB, time=35.08 memory used=1693.4MB, alloc=588.3MB, time=42.38 memory used=1890.3MB, alloc=612.3MB, time=50.51 memory used=2111.2MB, alloc=636.3MB, time=59.68 memory used=2356.1MB, alloc=660.3MB, time=70.01 memory used=2625.2MB, alloc=684.3MB, time=81.25 N2 := 6695 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 2 2 2 H := [17 y + 15 y x + 8 x , -4 y z - 5 x + 2 x y, 2 2 2 -19 x y z - 8 y z - 7 x z, 7 x z + 10 y z + 4 x z] > J:=[op(GB),op(G)]; 3 2 2 3 2 2 2 J := [17 y + 15 y x + 8 x , -75 x - 55 x y + 32 x z + 34 x y , 2 2 2 2 2 4 z y - 2 y x + 5 x , -19 x y z - 8 y z - 7 x z, 7 x z + 10 y z + 4 x z ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 11, 12, 3, 2, 3, 2, 1, 1, 3/4, 2/3, 7/12, 7/12, 5, 14, 15, 3, 3, 3, 2, 1, 1, 4/5, 3/4, 9/16, 1/2, -3, -3, 0] > save(F, G, cat("ranSet/33", convert(F, string),".txt")); > quit memory used=2773.6MB, alloc=684.3MB, time=86.94 |\^/| 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(); 1428489794 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 3 2 F := [-17 x + 8 y + 16, -5 x + 4 x y + 2 y ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 3 G := [20 x - 17 z + 17 y, -2 x z - 10 z ] > Problem := [F,G]; 3 3 2 Problem := [[-17 x + 8 y + 16, -5 x + 4 x y + 2 y ], 2 2 2 3 [20 x - 17 z + 17 y, -2 x 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=4.2MB, alloc=32.3MB, time=0.19 memory used=26.5MB, alloc=32.3MB, time=0.57 memory used=48.3MB, alloc=32.3MB, time=0.92 memory used=69.1MB, alloc=56.3MB, time=1.35 memory used=111.3MB, alloc=60.3MB, time=2.27 N1 := 741 > GB := Basis(F, plex(op(vars))); 6 4 3 3 GB := [289 x + 272 x - 704 x - 256 x + 256, -17 x + 8 y + 16] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=147.8MB, alloc=60.3MB, time=3.04 N2 := 281 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 3 2 2 2 H := [-17 x + 8 y + 16, -5 x + 4 x y + 2 y , -17 z + 20 x + 17 y, 2 3 -2 x z - 10 z ] > J:=[op(GB),op(G)]; 6 4 3 3 J := [289 x + 272 x - 704 x - 256 x + 256, -17 x + 8 y + 16, 2 2 2 3 -17 z + 20 x + 17 y, -2 x z - 10 z ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 9, 11, 3, 3, 2, 3, 1, 3/4, 1/2, 5/11, 4/11, 3/11, 4, 8, 14, 6, 6, 1, 3, 1, 1/2, 1/2, 7/13, 2/13, 3/13, 1, -3, -3] > save(F, G, cat("ranSet/33", convert(F, string),".txt")); > quit memory used=167.2MB, alloc=60.3MB, time=3.40 |\^/| 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(); 1428489799 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 2 2 F := [-14 x + 17 x z - x y , 4 x z - 7 z ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 3 G := [11 y z - 2 y z - 18 y , -4 x y - 5 y - 10 x z] > Problem := [F,G]; 3 2 2 2 2 Problem := [[-14 x + 17 x z - x y , 4 x z - 7 z ], 2 2 2 2 3 [11 y z - 2 y z - 18 y , -4 x y - 5 y - 10 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.2MB, alloc=32.3MB, time=0.53 memory used=46.8MB, alloc=32.3MB, time=0.83 memory used=66.3MB, alloc=56.3MB, time=1.16 memory used=112.6MB, alloc=68.3MB, time=1.78 memory used=156.1MB, alloc=92.3MB, time=2.45 memory used=221.5MB, alloc=92.3MB, time=3.34 memory used=286.1MB, alloc=116.3MB, time=4.25 memory used=348.9MB, alloc=116.3MB, time=5.11 memory used=415.3MB, alloc=372.3MB, time=6.13 memory used=502.9MB, alloc=396.3MB, time=7.28 memory used=606.9MB, alloc=396.3MB, time=8.56 memory used=716.1MB, alloc=420.3MB, time=10.09 memory used=847.1MB, alloc=444.3MB, time=11.91 memory used=962.6MB, alloc=468.3MB, time=13.58 memory used=1083.3MB, alloc=468.3MB, time=15.37 memory used=1233.2MB, alloc=492.3MB, time=17.80 memory used=1399.2MB, alloc=516.3MB, time=20.95 memory used=1580.8MB, alloc=540.3MB, time=24.45 memory used=1775.0MB, alloc=564.3MB, time=27.80 memory used=1957.6MB, alloc=588.3MB, time=31.33 memory used=2120.9MB, alloc=612.3MB, time=34.59 memory used=2268.1MB, alloc=636.3MB, time=37.49 memory used=2388.6MB, alloc=660.3MB, time=39.94 memory used=2570.9MB, alloc=684.3MB, time=45.49 memory used=2800.7MB, alloc=708.3MB, time=54.25 memory used=3036.0MB, alloc=732.3MB, time=63.24 memory used=3239.0MB, alloc=756.3MB, time=71.29 memory used=3498.7MB, alloc=780.3MB, time=82.39 memory used=3765.3MB, alloc=804.3MB, time=94.06 memory used=4046.4MB, alloc=828.3MB, time=106.73 memory used=4351.5MB, alloc=852.3MB, time=120.33 memory used=4680.5MB, alloc=876.3MB, time=135.13 memory used=5033.4MB, alloc=900.3MB, time=150.55 memory used=5410.2MB, alloc=924.3MB, time=167.46 memory used=5811.1MB, alloc=948.3MB, time=185.41 memory used=6235.8MB, alloc=948.3MB, time=204.24 memory used=6660.5MB, alloc=972.3MB, time=223.10 memory used=7109.1MB, alloc=972.3MB, time=242.83 |\^/| 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(); 1428490099 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 F := [18 x z - 13 x - 4, 10 y z - 9 z - 9] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 2 2 G := [-13 x + 20 x y - 12 x, -7 x y - 5 y z + 7 x ] > Problem := [F,G]; 2 2 2 Problem := [[18 x z - 13 x - 4, 10 y z - 9 z - 9], 3 2 2 2 2 [-13 x + 20 x y - 12 x, -7 x y - 5 y z + 7 x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.4MB, alloc=32.3MB, time=0.51 memory used=47.8MB, alloc=32.3MB, time=0.84 memory used=67.9MB, alloc=56.3MB, time=1.15 memory used=110.2MB, alloc=68.3MB, time=1.84 memory used=150.9MB, alloc=68.3MB, time=2.50 memory used=191.5MB, alloc=68.3MB, time=3.01 memory used=242.1MB, alloc=68.3MB, time=3.58 memory used=279.1MB, alloc=92.3MB, time=3.99 memory used=348.7MB, alloc=92.3MB, time=4.97 memory used=421.9MB, alloc=116.3MB, time=5.96 memory used=518.1MB, alloc=116.3MB, time=7.27 memory used=601.0MB, alloc=116.3MB, time=8.83 memory used=675.8MB, alloc=140.3MB, time=10.23 memory used=776.9MB, alloc=164.3MB, time=12.08 memory used=892.8MB, alloc=188.3MB, time=14.30 memory used=1046.6MB, alloc=188.3MB, time=16.75 memory used=1162.9MB, alloc=212.3MB, time=19.87 memory used=1284.4MB, alloc=236.3MB, time=23.82 memory used=1416.9MB, alloc=260.3MB, time=28.80 memory used=1566.7MB, alloc=284.3MB, time=34.82 memory used=1740.6MB, alloc=284.3MB, time=41.96 memory used=1914.4MB, alloc=308.3MB, time=48.99 memory used=2112.2MB, alloc=308.3MB, time=56.85 memory used=2310.1MB, alloc=332.3MB, time=64.55 N1 := 6623 > GB := Basis(F, plex(op(vars))); 4 2 4 2 2 2 2 GB := [1300 y x + 400 y - 2340 y x - 720 y + 1053 x - 1458 x + 324, 2 2 2 2 2 -130 x y + 117 x + 162 x z - 40 y + 36, 10 z y - 9 z - 9] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=2535.9MB, alloc=332.3MB, time=72.29 memory used=2596.5MB, alloc=588.3MB, time=73.49 memory used=2770.8MB, alloc=588.3MB, time=75.82 memory used=2910.5MB, alloc=588.3MB, time=77.81 memory used=3070.8MB, alloc=588.3MB, time=79.17 memory used=3248.5MB, alloc=588.3MB, time=80.62 memory used=3426.7MB, alloc=588.3MB, time=82.30 memory used=3672.9MB, alloc=588.3MB, time=84.29 memory used=3880.3MB, alloc=588.3MB, time=87.18 memory used=4104.9MB, alloc=612.3MB, time=91.71 memory used=4303.7MB, alloc=636.3MB, time=95.67 memory used=4547.3MB, alloc=660.3MB, time=101.37 memory used=4815.8MB, alloc=684.3MB, time=112.28 memory used=5088.4MB, alloc=708.3MB, time=124.23 memory used=5384.9MB, alloc=732.3MB, time=137.14 N2 := 5719 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 3 2 H := [18 x z - 13 x - 4, 10 z y - 9 z - 9, -13 x + 20 x y - 12 x, 2 2 2 -5 z y - 7 y x + 7 x ] > J:=[op(GB),op(G)]; 4 2 4 2 2 2 2 J := [1300 y x + 400 y - 2340 y x - 720 y + 1053 x - 1458 x + 324, 2 2 2 2 2 -130 x y + 117 x + 162 x z - 40 y + 36, 10 z y - 9 z - 9, 3 2 2 2 2 -13 x + 20 x y - 12 x, -5 z y - 7 y x + 7 x ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 9, 12, 3, 3, 2, 2, 3/4, 3/4, 3/4, 7/12, 1/3, 1/3, 5, 12, 19, 10 6, 3, 4, 2, 4/5, 1, 3/5, 4/7, --, 4/21, -3, -7, -3] 21 > save(F, G, cat("ranSet/33", convert(F, string),".txt")); > quit memory used=5591.5MB, alloc=732.3MB, time=145.35 |\^/| 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(); 1428490274 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 2 F := [5 x y - 6 x y z - 18 y , -6 x z + 7 y z - 10] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 G := [-8 x - 4 z - 18, -x y z - 9 x y - 3 z ] > Problem := [F,G]; 2 3 2 2 Problem := [[5 x y - 6 x y z - 18 y , -6 x z + 7 y z - 10], 3 2 2 [-8 x - 4 z - 18, -x y z - 9 x y - 3 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=24.9MB, alloc=32.3MB, time=0.48 memory used=43.6MB, alloc=32.3MB, time=0.74 memory used=62.7MB, alloc=60.3MB, time=0.98 memory used=107.0MB, alloc=68.3MB, time=1.57 memory used=150.9MB, alloc=68.3MB, time=2.17 memory used=197.1MB, alloc=92.3MB, time=2.72 memory used=263.0MB, alloc=92.3MB, time=3.58 memory used=330.7MB, alloc=92.3MB, time=4.30 memory used=407.1MB, alloc=372.3MB, time=5.07 memory used=508.9MB, alloc=372.3MB, time=6.13 memory used=601.4MB, alloc=396.3MB, time=7.34 memory used=691.1MB, alloc=396.3MB, time=8.04 memory used=797.2MB, alloc=396.3MB, time=8.96 memory used=924.7MB, alloc=420.3MB, time=10.47 memory used=1050.1MB, alloc=420.3MB, time=12.05 memory used=1163.5MB, alloc=444.3MB, time=13.73 memory used=1270.9MB, alloc=444.3MB, time=15.38 memory used=1379.2MB, alloc=468.3MB, time=16.86 memory used=1493.9MB, alloc=468.3MB, time=18.20 memory used=1579.1MB, alloc=468.3MB, time=19.43 memory used=1695.4MB, alloc=468.3MB, time=20.93 memory used=1788.0MB, alloc=468.3MB, time=22.36 memory used=1874.9MB, alloc=468.3MB, time=23.59 memory used=1959.1MB, alloc=468.3MB, time=24.95 memory used=2037.3MB, alloc=492.3MB, time=26.29 memory used=2114.7MB, alloc=492.3MB, time=27.47 memory used=2185.7MB, alloc=492.3MB, time=28.85 memory used=2245.5MB, alloc=492.3MB, time=29.81 memory used=2305.2MB, alloc=492.3MB, time=30.76 memory used=2361.3MB, alloc=492.3MB, time=31.82 memory used=2420.8MB, alloc=492.3MB, time=32.95 memory used=2500.3MB, alloc=492.3MB, time=34.18 memory used=2644.5MB, alloc=492.3MB, time=35.72 memory used=2716.6MB, alloc=516.3MB, time=37.00 memory used=2866.8MB, alloc=516.3MB, time=38.48 memory used=2944.6MB, alloc=516.3MB, time=39.83 memory used=3007.4MB, alloc=516.3MB, time=41.04 memory used=3094.0MB, alloc=516.3MB, time=42.44 memory used=3161.4MB, alloc=516.3MB, time=43.76 memory used=3236.8MB, alloc=540.3MB, time=44.98 memory used=3294.6MB, alloc=540.3MB, time=46.12 memory used=3367.6MB, alloc=540.3MB, time=47.36 memory used=3455.3MB, alloc=540.3MB, time=48.67 memory used=3510.1MB, alloc=540.3MB, time=49.92 memory used=3738.7MB, alloc=564.3MB, time=53.63 memory used=3984.9MB, alloc=588.3MB, time=57.35 memory used=4250.9MB, alloc=612.3MB, time=61.24 memory used=4538.8MB, alloc=636.3MB, time=65.28 memory used=4842.6MB, alloc=660.3MB, time=70.01 memory used=5165.5MB, alloc=684.3MB, time=75.14 memory used=5506.0MB, alloc=708.3MB, time=80.30 memory used=5861.4MB, alloc=732.3MB, time=85.95 memory used=6226.4MB, alloc=756.3MB, time=91.97 memory used=6587.3MB, alloc=780.3MB, time=98.65 memory used=6933.7MB, alloc=804.3MB, time=105.08 memory used=7262.9MB, alloc=828.3MB, time=111.46 memory used=7560.0MB, alloc=852.3MB, time=117.42 memory used=7855.9MB, alloc=876.3MB, time=123.50 memory used=8127.0MB, alloc=900.3MB, time=129.12 memory used=8416.7MB, alloc=924.3MB, time=135.30 memory used=8832.6MB, alloc=948.3MB, time=144.25 memory used=9258.5MB, alloc=972.3MB, time=152.68 memory used=9688.5MB, alloc=996.3MB, time=160.82 memory used=10126.3MB, alloc=1020.3MB, time=169.49 memory used=10515.1MB, alloc=1044.3MB, time=181.50 memory used=10845.9MB, alloc=1068.3MB, time=195.06 memory used=11178.7MB, alloc=1092.3MB, time=209.68 memory used=11519.4MB, alloc=1116.3MB, time=224.91 memory used=11870.2MB, alloc=1140.3MB, time=240.76 memory used=12232.6MB, alloc=1164.3MB, time=257.63 |\^/| 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(); 1428490574 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 2 F := [-3 x z + 4 y z - x, -5 x z - 2 y z + x ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 G := [10 x y z + 11 z + 14 x, 9 x y - 9 x - 9 y z] > Problem := [F,G]; 2 2 2 2 2 Problem := [[-3 x z + 4 y z - x, -5 x z - 2 y z + x ], 3 2 2 [10 x y z + 11 z + 14 x, 9 x y - 9 x - 9 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=24.7MB, alloc=32.3MB, time=0.46 memory used=44.6MB, alloc=36.3MB, time=0.77 memory used=63.2MB, alloc=60.3MB, time=1.06 memory used=107.8MB, alloc=68.3MB, time=1.62 memory used=149.1MB, alloc=68.3MB, time=2.23 memory used=192.4MB, alloc=68.3MB, time=2.83 memory used=232.5MB, alloc=92.3MB, time=3.41 memory used=301.7MB, alloc=92.3MB, time=4.33 memory used=369.6MB, alloc=372.3MB, time=5.31 memory used=459.7MB, alloc=372.3MB, time=6.56 memory used=535.1MB, alloc=372.3MB, time=7.30 memory used=624.4MB, alloc=372.3MB, time=8.36 memory used=717.5MB, alloc=396.3MB, time=9.37 memory used=828.2MB, alloc=396.3MB, time=10.78 memory used=935.0MB, alloc=420.3MB, time=12.47 memory used=1049.3MB, alloc=420.3MB, time=14.22 memory used=1174.1MB, alloc=444.3MB, time=15.94 memory used=1291.8MB, alloc=444.3MB, time=17.53 memory used=1427.6MB, alloc=444.3MB, time=18.99 memory used=1549.3MB, alloc=444.3MB, time=20.45 memory used=1676.0MB, alloc=468.3MB, time=22.67 memory used=1786.9MB, alloc=468.3MB, time=23.96 memory used=1915.4MB, alloc=468.3MB, time=25.47 memory used=2034.3MB, alloc=468.3MB, time=26.84 memory used=2147.7MB, alloc=468.3MB, time=28.36 memory used=2265.6MB, alloc=468.3MB, time=29.82 memory used=2365.6MB, alloc=468.3MB, time=31.28 memory used=2464.3MB, alloc=468.3MB, time=32.85 memory used=2558.1MB, alloc=492.3MB, time=34.03 memory used=2655.5MB, alloc=492.3MB, time=35.77 memory used=2728.8MB, alloc=492.3MB, time=37.22 memory used=2792.4MB, alloc=492.3MB, time=38.57 memory used=2854.9MB, alloc=492.3MB, time=39.80 memory used=2923.2MB, alloc=492.3MB, time=41.21 memory used=3004.1MB, alloc=492.3MB, time=42.32 memory used=3104.2MB, alloc=492.3MB, time=43.65 memory used=3182.2MB, alloc=492.3MB, time=44.84 memory used=3240.8MB, alloc=492.3MB, time=46.18 memory used=3326.4MB, alloc=492.3MB, time=47.40 memory used=3447.4MB, alloc=492.3MB, time=48.49 memory used=3542.5MB, alloc=492.3MB, time=49.13 memory used=3621.9MB, alloc=492.3MB, time=49.59 memory used=3728.7MB, alloc=492.3MB, time=51.61 memory used=3810.0MB, alloc=492.3MB, time=52.12 memory used=3886.2MB, alloc=492.3MB, time=52.56 memory used=3999.0MB, alloc=492.3MB, time=53.54 memory used=4085.3MB, alloc=492.3MB, time=54.58 memory used=4155.7MB, alloc=492.3MB, time=55.60 memory used=4212.9MB, alloc=492.3MB, time=56.53 memory used=4258.1MB, alloc=492.3MB, time=57.60 memory used=4309.3MB, alloc=492.3MB, time=58.49 memory used=4363.2MB, alloc=492.3MB, time=59.69 memory used=4410.8MB, alloc=492.3MB, time=60.56 memory used=4505.0MB, alloc=516.3MB, time=61.50 memory used=4560.9MB, alloc=516.3MB, time=62.48 memory used=4673.5MB, alloc=516.3MB, time=63.19 memory used=4788.4MB, alloc=516.3MB, time=64.02 memory used=4937.4MB, alloc=516.3MB, time=65.34 memory used=5127.3MB, alloc=516.3MB, time=68.10 memory used=5305.8MB, alloc=516.3MB, time=71.04 memory used=5486.1MB, alloc=540.3MB, time=74.53 memory used=5669.0MB, alloc=564.3MB, time=77.92 memory used=5829.2MB, alloc=588.3MB, time=79.82 memory used=6039.9MB, alloc=588.3MB, time=82.90 memory used=6158.7MB, alloc=588.3MB, time=83.57 memory used=6281.4MB, alloc=588.3MB, time=84.41 memory used=6443.8MB, alloc=588.3MB, time=86.09 memory used=6660.0MB, alloc=588.3MB, time=88.37 memory used=6888.0MB, alloc=612.3MB, time=91.24 memory used=7104.3MB, alloc=612.3MB, time=94.23 memory used=7259.5MB, alloc=612.3MB, time=96.94 memory used=7434.1MB, alloc=636.3MB, time=99.86 memory used=7564.6MB, alloc=636.3MB, time=102.25 memory used=7875.0MB, alloc=636.3MB, time=105.37 memory used=8160.2MB, alloc=636.3MB, time=107.11 memory used=8385.0MB, alloc=636.3MB, time=110.51 memory used=8674.4MB, alloc=660.3MB, time=113.85 memory used=8853.1MB, alloc=660.3MB, time=117.32 memory used=9122.2MB, alloc=684.3MB, time=121.12 memory used=9329.8MB, alloc=684.3MB, time=124.61 memory used=9547.3MB, alloc=684.3MB, time=127.73 memory used=9826.3MB, alloc=708.3MB, time=130.92 memory used=10058.9MB, alloc=708.3MB, time=134.47 memory used=10249.5MB, alloc=732.3MB, time=138.37 memory used=10452.8MB, alloc=756.3MB, time=142.65 memory used=10614.2MB, alloc=756.3MB, time=146.32 memory used=10826.3MB, alloc=780.3MB, time=150.76 memory used=11096.8MB, alloc=780.3MB, time=155.04 memory used=11351.9MB, alloc=804.3MB, time=159.10 memory used=11589.1MB, alloc=804.3MB, time=163.87 memory used=11767.1MB, alloc=828.3MB, time=167.83 memory used=11968.1MB, alloc=828.3MB, time=172.00 memory used=12152.8MB, alloc=852.3MB, time=175.84 memory used=12306.1MB, alloc=852.3MB, time=179.18 memory used=12454.8MB, alloc=876.3MB, time=182.66 memory used=12627.9MB, alloc=876.3MB, time=186.34 memory used=12823.7MB, alloc=900.3MB, time=190.22 memory used=12972.9MB, alloc=900.3MB, time=193.82 memory used=13449.8MB, alloc=924.3MB, time=202.79 memory used=13906.7MB, alloc=948.3MB, time=212.02 memory used=14370.1MB, alloc=972.3MB, time=221.25 memory used=14840.5MB, alloc=996.3MB, time=230.62 memory used=15337.3MB, alloc=1020.3MB, time=240.49 memory used=15862.6MB, alloc=1044.3MB, time=250.52 memory used=16394.9MB, alloc=1068.3MB, time=261.07 memory used=16905.2MB, alloc=1092.3MB, time=270.90 |\^/| 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(); 1428490874 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 F := [10 x - 10 x y - 11 z , -4 x y - 3 x z - 4 z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 3 G := [2 x + 6 z, 3 x z + 6 z - 10 y] > Problem := [F,G]; 2 2 2 2 Problem := [[10 x - 10 x y - 11 z , -4 x y - 3 x z - 4 z], 2 2 3 [2 x + 6 z, 3 x z + 6 z - 10 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=26.4MB, alloc=32.3MB, time=0.52 memory used=46.6MB, alloc=56.3MB, time=0.84 memory used=87.8MB, alloc=60.3MB, time=1.48 memory used=128.9MB, alloc=92.3MB, time=2.11 memory used=191.8MB, alloc=92.3MB, time=3.05 memory used=253.9MB, alloc=116.3MB, time=4.01 memory used=337.9MB, alloc=372.3MB, time=5.30 memory used=421.1MB, alloc=396.3MB, time=6.59 memory used=527.3MB, alloc=420.3MB, time=8.26 memory used=656.4MB, alloc=444.3MB, time=10.26 memory used=808.6MB, alloc=468.3MB, time=12.76 memory used=976.6MB, alloc=492.3MB, time=15.65 memory used=1162.0MB, alloc=516.3MB, time=18.83 memory used=1350.1MB, alloc=540.3MB, time=22.31 memory used=1561.6MB, alloc=564.3MB, time=25.93 memory used=1764.6MB, alloc=588.3MB, time=29.79 memory used=1961.7MB, alloc=612.3MB, time=33.57 memory used=2151.7MB, alloc=636.3MB, time=37.12 memory used=2336.7MB, alloc=660.3MB, time=41.32 memory used=2552.6MB, alloc=684.3MB, time=48.44 memory used=2773.3MB, alloc=708.3MB, time=56.38 memory used=3005.1MB, alloc=732.3MB, time=65.47 memory used=3249.9MB, alloc=756.3MB, time=74.98 memory used=3509.3MB, alloc=780.3MB, time=86.45 memory used=3781.4MB, alloc=804.3MB, time=99.07 memory used=4062.1MB, alloc=828.3MB, time=113.50 memory used=4366.6MB, alloc=852.3MB, time=128.78 memory used=4695.1MB, alloc=876.3MB, time=144.88 memory used=5047.6MB, alloc=900.3MB, time=161.98 memory used=5424.0MB, alloc=924.3MB, time=179.54 memory used=5824.3MB, alloc=948.3MB, time=197.00 memory used=6248.6MB, alloc=972.3MB, time=217.44 memory used=6696.7MB, alloc=972.3MB, time=239.83 |\^/| 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(); 1428491174 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 F := [10 x + 19 y z, x y - 5 y + 4] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 G := [20 y z - 19 x - 18 y, x y - 7 z + 9 x] > Problem := [F,G]; 2 2 2 Problem := [[10 x + 19 y z, x y - 5 y + 4], 2 3 [20 y z - 19 x - 18 y, x y - 7 z + 9 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=27.1MB, alloc=32.3MB, time=0.54 memory used=47.6MB, alloc=32.3MB, time=0.87 memory used=68.5MB, alloc=60.3MB, time=1.21 memory used=111.3MB, alloc=68.3MB, time=1.86 memory used=153.7MB, alloc=92.3MB, time=2.51 memory used=222.1MB, alloc=92.3MB, time=3.63 memory used=282.5MB, alloc=116.3MB, time=4.79 memory used=362.3MB, alloc=116.3MB, time=6.35 memory used=439.2MB, alloc=140.3MB, time=7.79 memory used=535.2MB, alloc=164.3MB, time=9.62 memory used=642.1MB, alloc=188.3MB, time=12.80 memory used=755.6MB, alloc=212.3MB, time=17.00 memory used=882.1MB, alloc=236.3MB, time=22.21 memory used=1032.7MB, alloc=236.3MB, time=28.64 memory used=1183.4MB, alloc=260.3MB, time=34.62 N1 := 4317 > GB := Basis(F, plex(op(vars))); 2 2 3 2 GB := [y x - 5 y + 4, -5 x y + 25 x y + 38 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1288.9MB, alloc=260.3MB, time=37.21 memory used=1436.4MB, alloc=516.3MB, time=39.51 memory used=1637.1MB, alloc=516.3MB, time=42.89 memory used=1839.6MB, alloc=540.3MB, time=46.53 memory used=2054.8MB, alloc=564.3MB, time=52.18 memory used=2244.4MB, alloc=588.3MB, time=59.95 memory used=2442.5MB, alloc=612.3MB, time=68.59 memory used=2664.6MB, alloc=636.3MB, time=78.11 N2 := 5175 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; H := 2 2 2 3 2 [19 z y + 10 x , y x - 5 y + 4, 20 y z - 19 x - 18 y, -7 z + y x + 9 x] > J:=[op(GB),op(G)]; 2 2 3 2 J := [y x - 5 y + 4, -5 x y + 25 x y + 38 z, 20 y z - 19 x - 18 y, 3 2 -7 z + y x + 9 x] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 11, 10, 3, 2, 2, 3, 1, 1, 3/4, 5/11, 6/11, 3/11, 4, 11, 12, 4, 3, 2, 3, 1, 1, 3/4, 1/2, 7/12, 1/4, 0, -2, -1] > save(F, G, cat("ranSet/33", convert(F, string),".txt")); > quit memory used=2897.0MB, alloc=636.3MB, time=88.01 |\^/| 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(); 1428491279 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 F := [-17 x z - 2 y z - 11 y, 5 x y - 3 y z - x] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 3 2 G := [12 x y + 13 y z + 20, 6 x y z + 4 z - 4 y ] > Problem := [F,G]; 2 2 2 2 Problem := [[-17 x z - 2 y z - 11 y, 5 x y - 3 y z - x], 2 2 3 2 [12 x y + 13 y z + 20, 6 x y z + 4 z - 4 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=23.3MB, alloc=32.3MB, time=0.41 memory used=43.4MB, alloc=60.3MB, time=0.70 memory used=87.3MB, alloc=60.3MB, time=1.11 memory used=133.5MB, alloc=68.3MB, time=1.67 memory used=175.2MB, alloc=68.3MB, time=2.23 memory used=210.9MB, alloc=68.3MB, time=2.52 memory used=244.3MB, alloc=68.3MB, time=2.75 memory used=277.6MB, alloc=68.3MB, time=2.97 memory used=321.9MB, alloc=68.3MB, time=3.44 memory used=367.9MB, alloc=92.3MB, time=3.95 memory used=429.8MB, alloc=92.3MB, time=4.71 memory used=495.7MB, alloc=92.3MB, time=5.69 memory used=531.7MB, alloc=92.3MB, time=5.83 memory used=568.6MB, alloc=92.3MB, time=6.00 memory used=603.9MB, alloc=92.3MB, time=6.34 memory used=641.5MB, alloc=92.3MB, time=6.51 memory used=678.0MB, alloc=92.3MB, time=6.67 memory used=716.2MB, alloc=92.3MB, time=7.03 memory used=752.9MB, alloc=92.3MB, time=7.20 memory used=789.9MB, alloc=92.3MB, time=7.35 memory used=827.0MB, alloc=92.3MB, time=7.71 memory used=891.6MB, alloc=116.3MB, time=8.48 memory used=953.5MB, alloc=372.3MB, time=9.16 memory used=1017.8MB, alloc=372.3MB, time=9.54 memory used=1063.5MB, alloc=372.3MB, time=9.71 memory used=1108.1MB, alloc=372.3MB, time=9.92 memory used=1154.0MB, alloc=372.3MB, time=10.10 memory used=1193.3MB, alloc=372.3MB, time=10.25 memory used=1251.5MB, alloc=372.3MB, time=11.18 memory used=1289.5MB, alloc=372.3MB, time=11.33 memory used=1344.2MB, alloc=372.3MB, time=11.60 memory used=1387.0MB, alloc=372.3MB, time=11.74 memory used=1438.1MB, alloc=372.3MB, time=11.99 memory used=1482.6MB, alloc=372.3MB, time=12.14 memory used=1533.9MB, alloc=372.3MB, time=13.05 memory used=1574.7MB, alloc=372.3MB, time=13.20 memory used=1627.3MB, alloc=372.3MB, time=13.47 memory used=1673.3MB, alloc=372.3MB, time=13.65 memory used=1712.9MB, alloc=372.3MB, time=13.79 memory used=1766.5MB, alloc=372.3MB, time=14.05 memory used=1808.3MB, alloc=372.3MB, time=14.20 memory used=1864.3MB, alloc=372.3MB, time=15.21 memory used=1903.3MB, alloc=372.3MB, time=15.34 memory used=1954.8MB, alloc=372.3MB, time=15.63 memory used=2011.7MB, alloc=372.3MB, time=15.96 memory used=2056.4MB, alloc=372.3MB, time=16.12 memory used=2100.2MB, alloc=372.3MB, time=16.39 memory used=2148.0MB, alloc=372.3MB, time=16.58 memory used=2188.3MB, alloc=372.3MB, time=16.72 memory used=2246.8MB, alloc=372.3MB, time=17.62 memory used=2284.6MB, alloc=372.3MB, time=17.75 memory used=2333.9MB, alloc=372.3MB, time=18.01 memory used=2385.9MB, alloc=372.3MB, time=18.29 memory used=2429.1MB, alloc=372.3MB, time=18.44 memory used=2480.3MB, alloc=372.3MB, time=18.68 memory used=2525.6MB, alloc=372.3MB, time=18.85 memory used=2576.3MB, alloc=372.3MB, time=19.81 memory used=2617.0MB, alloc=372.3MB, time=19.99 memory used=2664.5MB, alloc=372.3MB, time=20.25 memory used=2717.9MB, alloc=372.3MB, time=20.55 memory used=2762.5MB, alloc=372.3MB, time=20.72 memory used=2806.6MB, alloc=372.3MB, time=20.94 memory used=2854.3MB, alloc=372.3MB, time=21.11 memory used=2894.4MB, alloc=372.3MB, time=21.26 memory used=2952.7MB, alloc=372.3MB, time=22.19 memory used=2989.8MB, alloc=372.3MB, time=22.33 memory used=3082.2MB, alloc=372.3MB, time=23.41 memory used=3157.4MB, alloc=372.3MB, time=24.09 memory used=3221.9MB, alloc=372.3MB, time=24.55 memory used=3281.9MB, alloc=372.3MB, time=25.01 memory used=3365.0MB, alloc=396.3MB, time=26.07 memory used=3466.2MB, alloc=396.3MB, time=27.17 memory used=3536.0MB, alloc=396.3MB, time=27.60 memory used=3617.1MB, alloc=396.3MB, time=28.22 memory used=3733.1MB, alloc=396.3MB, time=29.49 memory used=3843.1MB, alloc=420.3MB, time=30.81 memory used=3951.4MB, alloc=420.3MB, time=32.76 memory used=4028.4MB, alloc=420.3MB, time=33.28 memory used=4156.4MB, alloc=420.3MB, time=34.58 memory used=4283.8MB, alloc=420.3MB, time=36.19 memory used=4399.6MB, alloc=420.3MB, time=38.00 memory used=4496.1MB, alloc=444.3MB, time=39.63 memory used=4608.8MB, alloc=444.3MB, time=40.55 memory used=4677.5MB, alloc=444.3MB, time=40.86 memory used=4747.3MB, alloc=444.3MB, time=41.15 memory used=4827.3MB, alloc=444.3MB, time=41.54 memory used=4896.2MB, alloc=444.3MB, time=41.85 memory used=4969.5MB, alloc=444.3MB, time=42.16 memory used=5055.0MB, alloc=444.3MB, time=43.64 memory used=5126.5MB, alloc=444.3MB, time=43.92 memory used=5184.4MB, alloc=444.3MB, time=44.15 memory used=5270.9MB, alloc=444.3MB, time=44.58 memory used=5332.9MB, alloc=444.3MB, time=44.85 memory used=5416.1MB, alloc=444.3MB, time=45.23 memory used=5489.8MB, alloc=444.3MB, time=45.52 memory used=5555.7MB, alloc=444.3MB, time=45.78 memory used=5642.6MB, alloc=444.3MB, time=47.25 memory used=5712.9MB, alloc=444.3MB, time=47.55 memory used=5776.5MB, alloc=444.3MB, time=47.79 memory used=5884.9MB, alloc=444.3MB, time=48.58 memory used=5960.5MB, alloc=444.3MB, time=48.88 memory used=6017.1MB, alloc=444.3MB, time=49.15 memory used=6106.5MB, alloc=444.3MB, time=49.60 memory used=6182.8MB, alloc=444.3MB, time=49.91 memory used=6240.0MB, alloc=444.3MB, time=50.19 memory used=6339.4MB, alloc=444.3MB, time=64.55 memory used=6427.7MB, alloc=444.3MB, time=116.27 memory used=6512.4MB, alloc=444.3MB, time=118.38 memory used=6573.3MB, alloc=444.3MB, time=118.65 memory used=6638.5MB, alloc=444.3MB, time=118.93 memory used=6717.9MB, alloc=444.3MB, time=119.22 memory used=6782.2MB, alloc=444.3MB, time=119.47 memory used=6831.3MB, alloc=444.3MB, time=119.71 memory used=6884.4MB, alloc=444.3MB, time=119.95 memory used=6941.5MB, alloc=444.3MB, time=120.19 memory used=7002.6MB, alloc=444.3MB, time=120.43 memory used=7067.7MB, alloc=444.3MB, time=120.67 memory used=7138.7MB, alloc=444.3MB, time=120.91 memory used=7213.3MB, alloc=444.3MB, time=121.15 memory used=7293.4MB, alloc=444.3MB, time=121.40 memory used=7378.8MB, alloc=444.3MB, time=121.66 memory used=7537.1MB, alloc=444.3MB, time=122.17 memory used=7682.2MB, alloc=444.3MB, time=122.51 memory used=7842.3MB, alloc=444.3MB, time=122.87 memory used=8024.6MB, alloc=444.3MB, time=123.23 memory used=8217.6MB, alloc=444.3MB, time=127.12 memory used=8281.4MB, alloc=444.3MB, time=127.40 memory used=8355.9MB, alloc=444.3MB, time=127.67 memory used=8409.2MB, alloc=444.3MB, time=127.90 memory used=8472.1MB, alloc=444.3MB, time=128.14 memory used=8545.2MB, alloc=444.3MB, time=128.39 memory used=8664.9MB, alloc=444.3MB, time=128.81 memory used=8806.8MB, alloc=444.3MB, time=130.31 memory used=8918.8MB, alloc=444.3MB, time=134.27 memory used=9068.4MB, alloc=468.3MB, time=135.85 memory used=9249.4MB, alloc=468.3MB, time=137.85 memory used=9435.0MB, alloc=468.3MB, time=142.37 memory used=9581.6MB, alloc=468.3MB, time=145.94 memory used=9666.6MB, alloc=468.3MB, time=146.36 memory used=9763.1MB, alloc=468.3MB, time=147.22 memory used=9830.4MB, alloc=468.3MB, time=147.57 memory used=9918.9MB, alloc=468.3MB, time=147.94 memory used=9987.9MB, alloc=468.3MB, time=148.25 memory used=10047.0MB, alloc=468.3MB, time=148.54 memory used=10112.9MB, alloc=468.3MB, time=148.83 memory used=10185.2MB, alloc=468.3MB, time=149.14 memory used=10266.7MB, alloc=468.3MB, time=149.43 memory used=10354.7MB, alloc=468.3MB, time=149.73 memory used=10452.3MB, alloc=468.3MB, time=150.04 memory used=10606.0MB, alloc=468.3MB, time=150.51 memory used=10756.7MB, alloc=468.3MB, time=150.93 memory used=10967.8MB, alloc=468.3MB, time=151.97 memory used=11039.0MB, alloc=468.3MB, time=152.31 memory used=11132.8MB, alloc=468.3MB, time=152.66 memory used=11195.0MB, alloc=468.3MB, time=152.99 memory used=11256.1MB, alloc=468.3MB, time=153.31 memory used=11323.3MB, alloc=468.3MB, time=153.61 memory used=11398.8MB, alloc=468.3MB, time=153.92 memory used=11480.9MB, alloc=468.3MB, time=154.23 memory used=11571.8MB, alloc=468.3MB, time=154.55 memory used=11801.7MB, alloc=468.3MB, time=155.07 memory used=11951.1MB, alloc=468.3MB, time=155.47 memory used=12169.4MB, alloc=468.3MB, time=160.76 memory used=12250.1MB, alloc=468.3MB, time=161.10 memory used=12316.1MB, alloc=468.3MB, time=161.39 memory used=12395.5MB, alloc=468.3MB, time=161.70 memory used=12490.8MB, alloc=468.3MB, time=162.01 memory used=12649.8MB, alloc=468.3MB, time=162.45 memory used=12820.1MB, alloc=468.3MB, time=162.91 memory used=13035.3MB, alloc=468.3MB, time=163.40 memory used=13216.7MB, alloc=468.3MB, time=177.80 memory used=13290.3MB, alloc=468.3MB, time=178.15 memory used=13378.8MB, alloc=468.3MB, time=178.50 memory used=13435.2MB, alloc=468.3MB, time=178.79 memory used=13497.9MB, alloc=468.3MB, time=179.10 memory used=13569.4MB, alloc=468.3MB, time=179.41 memory used=13649.6MB, alloc=468.3MB, time=179.72 memory used=13738.6MB, alloc=468.3MB, time=180.03 memory used=13960.6MB, alloc=468.3MB, time=180.56 memory used=14105.6MB, alloc=468.3MB, time=180.99 memory used=14265.9MB, alloc=468.3MB, time=181.43 memory used=14443.1MB, alloc=468.3MB, time=181.88 memory used=14640.1MB, alloc=468.3MB, time=182.36 memory used=14859.2MB, alloc=468.3MB, time=182.84 memory used=15076.2MB, alloc=468.3MB, time=183.32 memory used=15250.0MB, alloc=468.3MB, time=183.74 memory used=15438.6MB, alloc=468.3MB, time=184.19 memory used=15647.1MB, alloc=468.3MB, time=184.63 memory used=15979.6MB, alloc=468.3MB, time=186.10 memory used=16176.9MB, alloc=492.3MB, time=187.54 memory used=16271.8MB, alloc=492.3MB, time=188.90 memory used=16407.5MB, alloc=492.3MB, time=190.61 memory used=16507.0MB, alloc=492.3MB, time=191.93 memory used=16621.1MB, alloc=492.3MB, time=192.69 memory used=16715.2MB, alloc=492.3MB, time=193.23 memory used=16825.4MB, alloc=492.3MB, time=194.10 memory used=16906.9MB, alloc=492.3MB, time=194.53 memory used=16996.3MB, alloc=492.3MB, time=194.96 memory used=17083.5MB, alloc=492.3MB, time=195.35 memory used=17147.0MB, alloc=492.3MB, time=195.70 memory used=17219.0MB, alloc=492.3MB, time=196.07 memory used=17299.9MB, alloc=492.3MB, time=196.42 memory used=17391.1MB, alloc=492.3MB, time=196.78 memory used=17492.3MB, alloc=492.3MB, time=197.14 memory used=17691.8MB, alloc=492.3MB, time=197.65 memory used=17860.6MB, alloc=492.3MB, time=198.58 memory used=17937.4MB, alloc=492.3MB, time=199.02 memory used=18039.9MB, alloc=492.3MB, time=199.51 memory used=18105.9MB, alloc=492.3MB, time=199.85 memory used=18174.9MB, alloc=492.3MB, time=200.19 memory used=18251.8MB, alloc=492.3MB, time=200.53 memory used=18337.1MB, alloc=492.3MB, time=200.93 memory used=18434.1MB, alloc=492.3MB, time=201.28 memory used=18551.6MB, alloc=492.3MB, time=201.66 memory used=18693.6MB, alloc=492.3MB, time=202.10 memory used=18855.2MB, alloc=492.3MB, time=206.55 memory used=18941.5MB, alloc=492.3MB, time=206.96 memory used=19014.8MB, alloc=492.3MB, time=207.30 memory used=19106.0MB, alloc=492.3MB, time=207.65 memory used=19340.6MB, alloc=492.3MB, time=208.23 memory used=19516.5MB, alloc=492.3MB, time=208.71 memory used=19656.5MB, alloc=492.3MB, time=209.62 memory used=19764.5MB, alloc=492.3MB, time=210.47 memory used=19892.3MB, alloc=492.3MB, time=210.91 memory used=19995.9MB, alloc=492.3MB, time=212.18 memory used=20075.6MB, alloc=492.3MB, time=212.58 memory used=20165.4MB, alloc=492.3MB, time=212.99 memory used=20250.4MB, alloc=516.3MB, time=213.36 memory used=20328.5MB, alloc=516.3MB, time=213.73 memory used=20419.7MB, alloc=516.3MB, time=214.20 memory used=20523.7MB, alloc=516.3MB, time=214.57 memory used=20641.9MB, alloc=516.3MB, time=214.96 memory used=20854.8MB, alloc=516.3MB, time=215.50 memory used=21035.3MB, alloc=516.3MB, time=216.50 memory used=21136.6MB, alloc=516.3MB, time=216.95 memory used=21241.2MB, alloc=516.3MB, time=217.37 memory used=21322.0MB, alloc=516.3MB, time=217.75 memory used=21413.9MB, alloc=516.3MB, time=218.12 memory used=21518.3MB, alloc=516.3MB, time=218.50 memory used=21638.8MB, alloc=516.3MB, time=218.90 memory used=21842.8MB, alloc=516.3MB, time=219.42 memory used=22029.2MB, alloc=516.3MB, time=223.84 memory used=22125.0MB, alloc=516.3MB, time=224.23 memory used=22222.3MB, alloc=516.3MB, time=224.61 memory used=22344.5MB, alloc=516.3MB, time=225.01 memory used=22506.4MB, alloc=516.3MB, time=225.48 memory used=22679.7MB, alloc=516.3MB, time=225.94 memory used=22898.0MB, alloc=516.3MB, time=227.38 memory used=22992.6MB, alloc=516.3MB, time=227.82 memory used=23087.3MB, alloc=516.3MB, time=228.32 memory used=23201.6MB, alloc=516.3MB, time=228.76 memory used=23302.7MB, alloc=516.3MB, time=229.15 memory used=23376.0MB, alloc=516.3MB, time=229.49 memory used=23456.5MB, alloc=516.3MB, time=229.85 memory used=23543.4MB, alloc=516.3MB, time=230.25 memory used=23640.2MB, alloc=516.3MB, time=230.73 memory used=23747.6MB, alloc=516.3MB, time=231.19 memory used=23868.5MB, alloc=516.3MB, time=231.68 memory used=23996.7MB, alloc=516.3MB, time=232.72 memory used=24093.4MB, alloc=516.3MB, time=233.34 memory used=24184.4MB, alloc=516.3MB, time=233.94 memory used=24296.8MB, alloc=516.3MB, time=234.49 memory used=24403.9MB, alloc=516.3MB, time=234.98 memory used=24475.2MB, alloc=516.3MB, time=235.56 memory used=24555.6MB, alloc=516.3MB, time=235.97 memory used=24642.0MB, alloc=516.3MB, time=236.32 memory used=24738.2MB, alloc=516.3MB, time=236.69 memory used=24845.6MB, alloc=516.3MB, time=237.05 memory used=24965.1MB, alloc=516.3MB, time=237.42 memory used=25115.4MB, alloc=540.3MB, time=295.07 |\^/| 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(); 1428491579 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 3 2 F := [-3 y - 10 z + 6, y + 3 y z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 G := [y z - 10 z - 10 y, 5 z - 9 x y - x z] > Problem := [F,G]; Problem := [ 2 2 3 2 2 3 [-3 y - 10 z + 6, y + 3 y z], [y z - 10 z - 10 y, 5 z - 9 x y - x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.6MB, alloc=32.3MB, time=0.50 memory used=47.2MB, alloc=32.3MB, time=0.80 memory used=65.9MB, alloc=56.3MB, time=1.10 memory used=104.5MB, alloc=60.3MB, time=1.68 memory used=140.1MB, alloc=84.3MB, time=2.23 memory used=197.8MB, alloc=92.3MB, time=3.16 memory used=263.4MB, alloc=92.3MB, time=3.99 memory used=325.9MB, alloc=92.3MB, time=4.83 memory used=382.8MB, alloc=116.3MB, time=5.73 memory used=460.0MB, alloc=140.3MB, time=7.00 memory used=543.6MB, alloc=396.3MB, time=8.25 memory used=648.5MB, alloc=420.3MB, time=9.98 memory used=767.5MB, alloc=444.3MB, time=12.05 memory used=896.9MB, alloc=468.3MB, time=14.36 memory used=1045.1MB, alloc=492.3MB, time=17.04 memory used=1209.1MB, alloc=516.3MB, time=19.80 memory used=1387.5MB, alloc=540.3MB, time=22.95 memory used=1581.0MB, alloc=564.3MB, time=26.30 memory used=1784.0MB, alloc=588.3MB, time=29.99 memory used=1997.0MB, alloc=612.3MB, time=33.86 memory used=2197.0MB, alloc=636.3MB, time=37.63 memory used=2384.8MB, alloc=660.3MB, time=43.55 memory used=2577.5MB, alloc=684.3MB, time=50.64 memory used=2782.4MB, alloc=708.3MB, time=58.15 memory used=3000.7MB, alloc=732.3MB, time=66.34 memory used=3233.0MB, alloc=756.3MB, time=75.52 memory used=3480.0MB, alloc=780.3MB, time=85.17 memory used=3742.0MB, alloc=804.3MB, time=95.87 memory used=4019.0MB, alloc=828.3MB, time=107.08 memory used=4303.1MB, alloc=852.3MB, time=119.84 memory used=4610.3MB, alloc=876.3MB, time=133.64 memory used=4941.5MB, alloc=900.3MB, time=148.10 memory used=5296.6MB, alloc=924.3MB, time=164.20 memory used=5675.6MB, alloc=948.3MB, time=180.86 memory used=6078.6MB, alloc=972.3MB, time=198.54 |\^/| 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(); 1428491879 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 F := [6 x y + 6 y - 20 y, -2 y z - 2 y ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 3 2 G := [11 x z + 14 y - 13 x, -2 x + 6 x + 6 z] > Problem := [F,G]; 2 2 2 2 Problem := [[6 x y + 6 y - 20 y, -2 y z - 2 y ], 2 3 3 2 [11 x z + 14 y - 13 x, -2 x + 6 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=4.2MB, alloc=32.3MB, time=0.17 memory used=26.4MB, alloc=32.3MB, time=0.50 memory used=48.0MB, alloc=32.3MB, time=0.82 memory used=68.6MB, alloc=56.3MB, time=1.15 memory used=109.9MB, alloc=60.3MB, time=1.83 memory used=148.8MB, alloc=84.3MB, time=2.54 memory used=207.1MB, alloc=84.3MB, time=3.60 memory used=260.3MB, alloc=108.3MB, time=4.59 memory used=332.0MB, alloc=140.3MB, time=6.23 memory used=411.8MB, alloc=164.3MB, time=8.94 memory used=508.1MB, alloc=164.3MB, time=12.47 memory used=604.6MB, alloc=188.3MB, time=15.83 N1 := 3047 > GB := Basis(F, plex(op(vars))); 2 2 2 2 GB := [3 x y + 3 y - 10 y, y z + y ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=719.7MB, alloc=188.3MB, time=17.84 memory used=859.0MB, alloc=444.3MB, time=20.39 memory used=987.8MB, alloc=468.3MB, time=23.42 memory used=1110.2MB, alloc=492.3MB, time=27.97 N2 := 3047 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 2 3 H := [6 x y + 6 y - 20 y, -2 y z - 2 y , 11 z x + 14 y - 13 x, 3 2 -2 x + 6 x + 6 z] > J:=[op(GB),op(G)]; J := [ 2 2 2 2 2 3 3 2 3 x y + 3 y - 10 y, y z + y , 11 z x + 14 y - 13 x, -2 x + 6 x + 6 z ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 9, 12, 3, 3, 3, 2, 3/4, 3/4, 3/4, 5/11, 6/11, 3/11, 4, 9, 12, 3, 3, 3, 2, 3/4, 3/4, 3/4, 5/11, 6/11, 3/11, 0, 0, 0] > save(F, G, cat("ranSet/33", convert(F, string),".txt")); > quit memory used=1247.7MB, alloc=492.3MB, time=32.75 |\^/| 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(); 1428491916 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 F := [3 x - x z - y z, 10 y z - 3 x y + x z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 G := [-4 y z - 4 z - 15, x z - 10 x] > Problem := [F,G]; 2 2 Problem := [[3 x - x z - y z, 10 y z - 3 x y + x z], 2 2 [-4 y z - 4 z - 15, x 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=4.2MB, alloc=32.3MB, time=0.17 memory used=27.0MB, alloc=32.3MB, time=0.51 memory used=46.9MB, alloc=56.3MB, time=0.83 memory used=87.3MB, alloc=60.3MB, time=1.43 memory used=125.1MB, alloc=84.3MB, time=2.02 memory used=165.8MB, alloc=84.3MB, time=2.63 memory used=232.2MB, alloc=92.3MB, time=3.56 memory used=296.1MB, alloc=116.3MB, time=4.51 memory used=369.1MB, alloc=116.3MB, time=5.62 memory used=434.0MB, alloc=396.3MB, time=6.66 memory used=540.7MB, alloc=420.3MB, time=8.38 memory used=668.1MB, alloc=444.3MB, time=10.46 memory used=793.8MB, alloc=444.3MB, time=12.60 memory used=911.5MB, alloc=468.3MB, time=14.46 memory used=1036.0MB, alloc=492.3MB, time=16.55 memory used=1139.1MB, alloc=492.3MB, time=18.37 memory used=1237.6MB, alloc=492.3MB, time=20.10 memory used=1357.3MB, alloc=516.3MB, time=22.34 memory used=1495.8MB, alloc=540.3MB, time=24.87 memory used=1605.1MB, alloc=564.3MB, time=27.07 memory used=1729.1MB, alloc=588.3MB, time=29.62 memory used=1839.0MB, alloc=588.3MB, time=31.94 memory used=1962.2MB, alloc=612.3MB, time=34.44 memory used=2087.8MB, alloc=636.3MB, time=37.06 memory used=2209.5MB, alloc=660.3MB, time=39.70 memory used=2317.9MB, alloc=684.3MB, time=41.99 memory used=2419.9MB, alloc=684.3MB, time=44.16 memory used=2523.8MB, alloc=708.3MB, time=46.46 memory used=2608.9MB, alloc=708.3MB, time=48.43 memory used=2712.6MB, alloc=732.3MB, time=50.86 memory used=2811.0MB, alloc=732.3MB, time=53.18 memory used=2909.9MB, alloc=756.3MB, time=55.55 memory used=3006.7MB, alloc=756.3MB, time=57.78 memory used=3087.9MB, alloc=780.3MB, time=59.74 memory used=3172.1MB, alloc=780.3MB, time=61.79 memory used=3265.0MB, alloc=804.3MB, time=63.97 memory used=3348.8MB, alloc=828.3MB, time=66.05 memory used=3424.0MB, alloc=828.3MB, time=68.08 memory used=3764.8MB, alloc=852.3MB, time=75.09 memory used=4117.1MB, alloc=876.3MB, time=81.88 memory used=4437.5MB, alloc=900.3MB, time=88.63 memory used=4786.8MB, alloc=924.3MB, time=96.48 memory used=5083.5MB, alloc=948.3MB, time=107.38 memory used=5380.3MB, alloc=972.3MB, time=118.94 memory used=5685.5MB, alloc=996.3MB, time=131.30 memory used=6000.8MB, alloc=1020.3MB, time=144.31 memory used=6327.9MB, alloc=1044.3MB, time=157.98 memory used=6669.1MB, alloc=1068.3MB, time=172.35 memory used=7024.4MB, alloc=1092.3MB, time=187.57 memory used=7394.4MB, alloc=1116.3MB, time=203.27 memory used=7779.6MB, alloc=1140.3MB, time=219.61 memory used=8180.0MB, alloc=1164.3MB, time=237.12 memory used=8595.6MB, alloc=1188.3MB, time=255.27 |\^/| 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(); 1428492216 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 F := [16 z + 17 x - 6 z, 4 x + 10 y + 2 z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 2 G := [x z - 5 x y z - 12 x z , 5 x y + 5 x y + x ] > Problem := [F,G]; 3 2 Problem := [[16 z + 17 x - 6 z, 4 x + 10 y + 2 z], 2 2 2 2 2 [x z - 5 x y z - 12 x z , 5 x y + 5 x y + x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.1MB, alloc=32.3MB, time=0.49 memory used=47.9MB, alloc=32.3MB, time=0.82 memory used=67.1MB, alloc=56.3MB, time=1.12 memory used=107.0MB, alloc=60.3MB, time=1.77 memory used=148.3MB, alloc=84.3MB, time=2.48 memory used=207.7MB, alloc=108.3MB, time=3.57 memory used=288.8MB, alloc=140.3MB, time=4.97 memory used=391.9MB, alloc=164.3MB, time=6.62 memory used=505.0MB, alloc=188.3MB, time=8.59 memory used=622.4MB, alloc=212.3MB, time=11.74 memory used=742.2MB, alloc=236.3MB, time=15.35 memory used=871.2MB, alloc=260.3MB, time=20.04 memory used=1016.1MB, alloc=284.3MB, time=25.75 memory used=1185.0MB, alloc=308.3MB, time=32.37 memory used=1377.8MB, alloc=308.3MB, time=40.01 memory used=1570.6MB, alloc=308.3MB, time=47.96 memory used=1763.3MB, alloc=332.3MB, time=55.78 memory used=1980.1MB, alloc=332.3MB, time=64.46 memory used=2196.8MB, alloc=356.3MB, time=72.93 N1 := 7635 > GB := Basis(F, plex(op(vars))); 3 2 2 3 2 GB := [2000 y + 2400 y x + 960 y x + 128 x - 17 x - 30 y - 12 x, z + 5 y + 2 x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=2428.8MB, alloc=356.3MB, time=80.53 memory used=2716.1MB, alloc=636.3MB, time=88.32 N2 := 2439 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 2 2 H := [16 z + 17 x - 6 z, 4 x + 10 y + 2 z, x z - 5 x y z - 12 x z , 2 2 2 5 x y + 5 x y + x ] > J:=[op(GB),op(G)]; 3 2 2 3 2 J := [2000 y + 2400 y x + 960 y x + 128 x - 17 x - 30 y - 12 x, 2 2 2 2 2 z + 5 y + 2 x, x z - 5 x y z - 12 x z , 5 x y + 5 x y + x ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 10, 10, 3, 2, 2, 3, 1, 3/4, 3/4, 2/3, 1/3, 1/2, 4, 10, 10, 3, 3, 3, 2, 1, 1, 1/2, 3/4, 1/2, 1/4, 0, 0, 0] > save(F, G, cat("ranSet/33", convert(F, string),".txt")); > quit memory used=2804.5MB, alloc=636.3MB, time=91.63 |\^/| 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(); 1428492327 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 2 F := [7 x z + 10 x y + 15 y z, 5 x z - 4 y - 3] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 2 G := [16 x z - 4 y z - 18 x , 10 x y - 8 x + 5 x] > Problem := [F,G]; 2 2 2 2 2 Problem := [[7 x z + 10 x y + 15 y z, 5 x z - 4 y - 3], 2 2 2 2 2 [16 x z - 4 y z - 18 x , 10 x y - 8 x + 5 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=26.7MB, alloc=32.3MB, time=0.52 memory used=46.4MB, alloc=56.3MB, time=0.82 memory used=84.6MB, alloc=60.3MB, time=1.36 memory used=129.4MB, alloc=68.3MB, time=1.95 memory used=173.1MB, alloc=92.3MB, time=2.54 memory used=238.0MB, alloc=92.3MB, time=3.26 memory used=315.1MB, alloc=348.3MB, time=4.09 memory used=390.6MB, alloc=348.3MB, time=5.03 memory used=456.5MB, alloc=348.3MB, time=5.82 memory used=523.9MB, alloc=348.3MB, time=6.68 memory used=594.0MB, alloc=372.3MB, time=7.49 memory used=685.3MB, alloc=372.3MB, time=8.78 memory used=773.2MB, alloc=396.3MB, time=9.56 memory used=889.6MB, alloc=396.3MB, time=10.68 memory used=1015.1MB, alloc=396.3MB, time=12.60 memory used=1133.4MB, alloc=420.3MB, time=14.32 memory used=1303.5MB, alloc=420.3MB, time=17.25 memory used=1429.5MB, alloc=444.3MB, time=19.34 memory used=1567.0MB, alloc=468.3MB, time=21.82 memory used=1717.9MB, alloc=492.3MB, time=24.89 memory used=1865.4MB, alloc=516.3MB, time=30.61 memory used=2015.3MB, alloc=540.3MB, time=36.47 memory used=2184.1MB, alloc=564.3MB, time=43.37 memory used=2376.9MB, alloc=564.3MB, time=51.36 memory used=2569.7MB, alloc=588.3MB, time=59.34 N1 := 5593 > GB := Basis(F, plex(op(vars))); 2 3 4 2 2 2 2 2 2 GB := [50 y x + 60 y + 28 y x + 45 y + 21 x , 5 z x - 4 y - 3, 2 2 2 50 x y + 75 y z + 28 y + 21] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=2802.7MB, alloc=588.3MB, time=67.25 memory used=2922.3MB, alloc=588.3MB, time=69.09 memory used=3054.8MB, alloc=588.3MB, time=70.87 memory used=3281.6MB, alloc=588.3MB, time=73.05 memory used=3493.0MB, alloc=588.3MB, time=75.52 memory used=3781.3MB, alloc=588.3MB, time=78.61 memory used=3999.3MB, alloc=612.3MB, time=81.85 memory used=4176.7MB, alloc=636.3MB, time=85.07 memory used=4343.7MB, alloc=636.3MB, time=88.08 memory used=4596.3MB, alloc=660.3MB, time=95.61 memory used=4850.5MB, alloc=684.3MB, time=106.16 memory used=5111.3MB, alloc=708.3MB, time=117.93 memory used=5396.1MB, alloc=732.3MB, time=130.60 memory used=5704.9MB, alloc=756.3MB, time=144.78 N2 := 6719 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 2 2 2 2 H := [15 z y + 7 z x + 10 y x, 5 z x - 4 y - 3, 16 x z - 4 y z - 18 x , 2 2 10 x y - 8 x + 5 x] > J:=[op(GB),op(G)]; 2 3 4 2 2 2 2 2 2 J := [50 y x + 60 y + 28 y x + 45 y + 21 x , 5 z x - 4 y - 3, 2 2 2 2 2 2 75 z y + 50 y x + 28 y + 21, 16 x z - 4 y z - 18 x , 2 2 10 x y - 8 x + 5 x] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 11, 12, 3, 2, 2, 2, 1, 1, 3/4, 2/3, 5/12, 5/12, 5, 13, 17, 5, 3, 4, 2, 1, 1, 3/5, 5/9, 5/9, 2/9, -2, -5, -2] > save(F, G, cat("ranSet/33", convert(F, string),".txt")); > quit memory used=5941.3MB, alloc=756.3MB, time=155.39 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428492577 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 2 F := [20 x z + 10 x y - 6 x z , -6 x y + x z - 4] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 2 G := [12 y + y z - 6, 8 y z - 7 x + z] > Problem := [F,G]; 2 2 2 2 2 Problem := [[20 x z + 10 x y - 6 x z , -6 x y + x z - 4], 3 2 2 2 [12 y + y z - 6, 8 y z - 7 x + z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=27.4MB, alloc=32.3MB, time=0.53 memory used=49.1MB, alloc=36.3MB, time=0.88 memory used=70.1MB, alloc=60.3MB, time=1.18 memory used=120.0MB, alloc=68.3MB, time=1.79 memory used=161.5MB, alloc=68.3MB, time=2.51 memory used=202.4MB, alloc=92.3MB, time=3.12 memory used=272.7MB, alloc=92.3MB, time=4.17 memory used=337.3MB, alloc=116.3MB, time=5.15 memory used=405.5MB, alloc=372.3MB, time=6.14 memory used=493.2MB, alloc=372.3MB, time=7.05 memory used=546.8MB, alloc=372.3MB, time=7.28 memory used=610.2MB, alloc=372.3MB, time=9.21 memory used=654.1MB, alloc=372.3MB, time=9.36 memory used=690.3MB, alloc=372.3MB, time=9.50 memory used=750.9MB, alloc=372.3MB, time=9.79 memory used=816.8MB, alloc=372.3MB, time=11.89 memory used=861.7MB, alloc=372.3MB, time=12.06 memory used=899.0MB, alloc=372.3MB, time=12.21 memory used=949.5MB, alloc=372.3MB, time=12.41 memory used=1014.0MB, alloc=372.3MB, time=14.35 memory used=1063.8MB, alloc=372.3MB, time=14.54 memory used=1103.5MB, alloc=372.3MB, time=14.70 memory used=1173.6MB, alloc=372.3MB, time=15.38 memory used=1243.2MB, alloc=372.3MB, time=17.56 memory used=1286.1MB, alloc=372.3MB, time=17.70 memory used=1322.5MB, alloc=372.3MB, time=17.85 memory used=1426.6MB, alloc=372.3MB, time=22.63 memory used=1471.8MB, alloc=372.3MB, time=22.80 memory used=1515.6MB, alloc=372.3MB, time=22.95 memory used=1547.4MB, alloc=372.3MB, time=23.08 memory used=1584.7MB, alloc=372.3MB, time=23.22 memory used=1673.1MB, alloc=372.3MB, time=24.03 memory used=1731.5MB, alloc=372.3MB, time=24.39 memory used=1781.0MB, alloc=372.3MB, time=24.65 memory used=1842.3MB, alloc=396.3MB, time=26.54 memory used=1897.1MB, alloc=396.3MB, time=26.73 memory used=1952.4MB, alloc=396.3MB, time=26.92 memory used=2027.6MB, alloc=396.3MB, time=27.25 memory used=2104.5MB, alloc=396.3MB, time=29.32 memory used=2158.6MB, alloc=396.3MB, time=29.50 memory used=2225.7MB, alloc=396.3MB, time=29.72 memory used=2300.4MB, alloc=396.3MB, time=31.20 memory used=2372.0MB, alloc=396.3MB, time=31.83 memory used=2419.6MB, alloc=396.3MB, time=32.01 memory used=2532.6MB, alloc=396.3MB, time=34.59 memory used=2589.3MB, alloc=396.3MB, time=34.77 memory used=2639.6MB, alloc=396.3MB, time=34.94 memory used=2757.1MB, alloc=396.3MB, time=39.57 memory used=2813.7MB, alloc=396.3MB, time=39.76 memory used=2858.9MB, alloc=396.3MB, time=39.93 memory used=2918.3MB, alloc=396.3MB, time=40.10 memory used=3015.1MB, alloc=396.3MB, time=41.06 memory used=3124.6MB, alloc=420.3MB, time=42.57 memory used=3253.4MB, alloc=420.3MB, time=44.36 memory used=3372.0MB, alloc=444.3MB, time=46.08 memory used=3499.2MB, alloc=444.3MB, time=48.13 memory used=3595.2MB, alloc=444.3MB, time=48.83 memory used=3678.8MB, alloc=444.3MB, time=49.23 memory used=3776.2MB, alloc=444.3MB, time=51.17 memory used=3846.2MB, alloc=468.3MB, time=51.50 memory used=3920.7MB, alloc=468.3MB, time=51.83 memory used=4011.1MB, alloc=468.3MB, time=52.18 memory used=4106.5MB, alloc=468.3MB, time=52.76 memory used=4203.7MB, alloc=468.3MB, time=53.20 memory used=4317.6MB, alloc=468.3MB, time=55.29 memory used=4395.8MB, alloc=468.3MB, time=55.64 memory used=4483.5MB, alloc=468.3MB, time=55.97 memory used=4576.2MB, alloc=468.3MB, time=56.40 memory used=4698.4MB, alloc=468.3MB, time=58.07 memory used=4783.5MB, alloc=468.3MB, time=58.48 memory used=4857.5MB, alloc=468.3MB, time=58.83 memory used=4976.0MB, alloc=468.3MB, time=59.78 memory used=5108.2MB, alloc=468.3MB, time=62.63 memory used=5184.8MB, alloc=468.3MB, time=62.99 memory used=5273.8MB, alloc=468.3MB, time=63.29 memory used=5410.0MB, alloc=468.3MB, time=65.77 memory used=5488.2MB, alloc=468.3MB, time=66.12 memory used=5569.7MB, alloc=468.3MB, time=66.40 memory used=5718.1MB, alloc=468.3MB, time=67.92 memory used=5837.5MB, alloc=468.3MB, time=69.49 memory used=5965.1MB, alloc=468.3MB, time=71.04 memory used=6083.6MB, alloc=468.3MB, time=72.56 memory used=6180.3MB, alloc=468.3MB, time=73.78 memory used=6290.1MB, alloc=468.3MB, time=78.51 memory used=6359.2MB, alloc=468.3MB, time=78.82 memory used=6436.4MB, alloc=468.3MB, time=79.12 memory used=6520.7MB, alloc=468.3MB, time=79.78 memory used=6622.2MB, alloc=468.3MB, time=80.35 memory used=6716.9MB, alloc=468.3MB, time=80.69 memory used=6842.5MB, alloc=468.3MB, time=81.69 memory used=6955.5MB, alloc=468.3MB, time=83.09 memory used=7081.8MB, alloc=468.3MB, time=88.60 memory used=7164.3MB, alloc=492.3MB, time=89.16 memory used=7248.5MB, alloc=492.3MB, time=89.50 memory used=7382.4MB, alloc=492.3MB, time=90.78 memory used=7477.1MB, alloc=492.3MB, time=92.33 memory used=7601.6MB, alloc=492.3MB, time=93.64 memory used=7678.1MB, alloc=492.3MB, time=95.02 memory used=7743.2MB, alloc=492.3MB, time=96.15 memory used=7822.5MB, alloc=492.3MB, time=97.62 memory used=7913.9MB, alloc=492.3MB, time=98.88 memory used=7970.6MB, alloc=492.3MB, time=99.95 memory used=8025.3MB, alloc=492.3MB, time=101.08 memory used=8082.5MB, alloc=492.3MB, time=102.17 memory used=8132.8MB, alloc=516.3MB, time=103.11 memory used=8185.8MB, alloc=516.3MB, time=103.99 memory used=8265.1MB, alloc=516.3MB, time=105.02 memory used=8339.9MB, alloc=516.3MB, time=106.12 memory used=8401.0MB, alloc=516.3MB, time=106.93 memory used=8508.2MB, alloc=516.3MB, time=107.45 memory used=8592.1MB, alloc=516.3MB, time=107.91 memory used=8691.0MB, alloc=516.3MB, time=114.92 memory used=8791.5MB, alloc=516.3MB, time=115.45 memory used=8882.0MB, alloc=516.3MB, time=115.94 memory used=8997.5MB, alloc=516.3MB, time=116.44 memory used=9068.7MB, alloc=516.3MB, time=116.86 memory used=9147.3MB, alloc=516.3MB, time=117.26 memory used=9235.8MB, alloc=516.3MB, time=117.66 memory used=9333.5MB, alloc=516.3MB, time=118.08 memory used=9441.5MB, alloc=516.3MB, time=118.50 memory used=9562.5MB, alloc=516.3MB, time=118.93 memory used=9735.1MB, alloc=516.3MB, time=119.63 memory used=9884.0MB, alloc=516.3MB, time=120.11 memory used=10090.0MB, alloc=516.3MB, time=121.31 memory used=10126.4MB, alloc=516.3MB, time=122.11 memory used=10183.4MB, alloc=516.3MB, time=123.22 memory used=10224.1MB, alloc=516.3MB, time=124.18 memory used=10443.4MB, alloc=516.3MB, time=126.88 memory used=10554.5MB, alloc=516.3MB, time=127.94 memory used=10673.4MB, alloc=516.3MB, time=128.94 memory used=10760.9MB, alloc=516.3MB, time=129.48 memory used=10856.5MB, alloc=516.3MB, time=130.00 memory used=10946.9MB, alloc=540.3MB, time=130.48 memory used=11036.4MB, alloc=540.3MB, time=130.92 memory used=11166.1MB, alloc=540.3MB, time=131.72 memory used=11267.5MB, alloc=540.3MB, time=132.24 memory used=11392.2MB, alloc=540.3MB, time=132.76 memory used=11475.8MB, alloc=540.3MB, time=133.18 memory used=11617.1MB, alloc=540.3MB, time=138.87 memory used=11723.5MB, alloc=540.3MB, time=139.43 memory used=11841.2MB, alloc=540.3MB, time=140.01 memory used=11926.5MB, alloc=540.3MB, time=140.50 memory used=12028.3MB, alloc=540.3MB, time=141.02 memory used=12147.5MB, alloc=540.3MB, time=141.50 memory used=12382.7MB, alloc=540.3MB, time=142.12 memory used=12530.5MB, alloc=540.3MB, time=142.66 memory used=12730.5MB, alloc=540.3MB, time=144.02 memory used=12921.9MB, alloc=540.3MB, time=145.63 memory used=13132.1MB, alloc=540.3MB, time=147.53 memory used=13255.5MB, alloc=540.3MB, time=148.12 memory used=13352.6MB, alloc=540.3MB, time=148.62 memory used=13480.1MB, alloc=540.3MB, time=149.14 memory used=13563.0MB, alloc=540.3MB, time=149.59 memory used=13661.0MB, alloc=540.3MB, time=150.03 memory used=13799.8MB, alloc=540.3MB, time=150.94 memory used=13893.7MB, alloc=540.3MB, time=151.46 memory used=14021.7MB, alloc=540.3MB, time=151.96 memory used=14106.4MB, alloc=540.3MB, time=152.40 memory used=14202.8MB, alloc=540.3MB, time=152.83 memory used=14353.6MB, alloc=540.3MB, time=159.32 memory used=14467.5MB, alloc=540.3MB, time=159.86 memory used=14558.7MB, alloc=540.3MB, time=160.33 memory used=14653.2MB, alloc=540.3MB, time=160.80 memory used=14764.7MB, alloc=540.3MB, time=161.25 memory used=14896.2MB, alloc=540.3MB, time=161.72 memory used=15050.2MB, alloc=540.3MB, time=162.24 memory used=15198.0MB, alloc=540.3MB, time=162.75 memory used=15401.1MB, alloc=540.3MB, time=164.08 memory used=15550.8MB, alloc=540.3MB, time=165.27 memory used=15748.4MB, alloc=540.3MB, time=167.68 memory used=15998.8MB, alloc=540.3MB, time=168.32 memory used=16270.5MB, alloc=540.3MB, time=168.99 memory used=16521.9MB, alloc=540.3MB, time=169.69 memory used=16758.3MB, alloc=540.3MB, time=172.97 memory used=16855.5MB, alloc=540.3MB, time=173.59 memory used=16974.3MB, alloc=540.3MB, time=174.14 memory used=17060.6MB, alloc=540.3MB, time=174.64 memory used=17184.3MB, alloc=540.3MB, time=175.47 memory used=17289.4MB, alloc=540.3MB, time=176.08 memory used=17408.7MB, alloc=540.3MB, time=176.66 memory used=17501.3MB, alloc=540.3MB, time=177.17 memory used=17598.7MB, alloc=540.3MB, time=177.71 memory used=17744.6MB, alloc=540.3MB, time=183.58 memory used=17866.3MB, alloc=540.3MB, time=184.10 memory used=17949.8MB, alloc=540.3MB, time=184.57 memory used=18045.7MB, alloc=540.3MB, time=185.07 memory used=18159.7MB, alloc=540.3MB, time=185.58 memory used=18295.1MB, alloc=540.3MB, time=186.10 memory used=18429.9MB, alloc=540.3MB, time=186.67 memory used=18578.4MB, alloc=540.3MB, time=187.24 memory used=18775.3MB, alloc=540.3MB, time=188.60 memory used=18966.7MB, alloc=540.3MB, time=190.22 memory used=19184.3MB, alloc=540.3MB, time=192.40 memory used=19316.5MB, alloc=540.3MB, time=193.13 memory used=19432.7MB, alloc=540.3MB, time=193.80 memory used=19559.0MB, alloc=540.3MB, time=194.80 memory used=19682.9MB, alloc=540.3MB, time=195.80 memory used=19802.1MB, alloc=540.3MB, time=196.31 memory used=20002.9MB, alloc=540.3MB, time=198.84 memory used=20115.7MB, alloc=540.3MB, time=199.45 memory used=20246.1MB, alloc=540.3MB, time=201.42 memory used=20365.4MB, alloc=540.3MB, time=202.22 memory used=20482.2MB, alloc=540.3MB, time=202.84 memory used=20606.5MB, alloc=540.3MB, time=204.79 memory used=20754.1MB, alloc=540.3MB, time=206.19 memory used=20871.0MB, alloc=540.3MB, time=206.86 memory used=21022.2MB, alloc=540.3MB, time=232.69 memory used=21123.6MB, alloc=540.3MB, time=233.24 memory used=21236.3MB, alloc=540.3MB, time=233.78 memory used=21318.8MB, alloc=540.3MB, time=234.24 memory used=21417.4MB, alloc=540.3MB, time=234.70 memory used=21534.4MB, alloc=540.3MB, time=235.17 memory used=21745.6MB, alloc=540.3MB, time=235.78 memory used=22116.8MB, alloc=540.3MB, time=240.47 memory used=22357.9MB, alloc=564.3MB, time=243.20 memory used=22623.6MB, alloc=564.3MB, time=249.16 memory used=22891.2MB, alloc=564.3MB, time=260.88 memory used=23083.0MB, alloc=564.3MB, time=265.91 memory used=23209.4MB, alloc=564.3MB, time=266.67 memory used=23352.5MB, alloc=564.3MB, time=269.46 memory used=23478.5MB, alloc=564.3MB, time=270.19 memory used=23604.8MB, alloc=564.3MB, time=270.91 memory used=23818.4MB, alloc=564.3MB, time=271.85 memory used=24096.7MB, alloc=564.3MB, time=272.66 memory used=24294.6MB, alloc=564.3MB, time=274.61 memory used=24426.6MB, alloc=564.3MB, time=275.53 memory used=24590.0MB, alloc=564.3MB, time=301.93 memory used=24710.6MB, alloc=564.3MB, time=302.54 memory used=24812.0MB, alloc=564.3MB, time=303.08 memory used=24918.9MB, alloc=564.3MB, time=303.61 memory used=25049.7MB, alloc=564.3MB, time=304.18 memory used=25245.2MB, alloc=564.3MB, time=304.87 memory used=25392.5MB, alloc=564.3MB, time=305.47 memory used=25800.2MB, alloc=564.3MB, time=308.88 memory used=26082.5MB, alloc=588.3MB, time=312.13 memory used=26252.8MB, alloc=612.3MB, time=315.46 memory used=26448.2MB, alloc=612.3MB, time=318.40 memory used=26637.1MB, alloc=612.3MB, time=320.05 memory used=26765.1MB, alloc=612.3MB, time=320.76 memory used=26926.6MB, alloc=612.3MB, time=321.98 memory used=27117.1MB, alloc=612.3MB, time=323.54 |\^/| 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(); 1428492877 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 2 2 F := [16 x z + 16 y + 10 y , 3 y z - 9 x - 7 x y] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 2 G := [-18 x z + z + x y, 7 y z - 8 x y + 5 z ] > Problem := [F,G]; 2 3 2 2 2 Problem := [[16 x z + 16 y + 10 y , 3 y z - 9 x - 7 x y], 2 3 2 2 [-18 x z + z + x y, 7 y z - 8 x 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=4.2MB, alloc=32.3MB, time=0.17 memory used=23.9MB, alloc=32.3MB, time=0.42 memory used=42.3MB, alloc=33.7MB, time=0.50 memory used=61.4MB, alloc=33.7MB, time=0.85 memory used=73.8MB, alloc=33.7MB, time=0.89 memory used=91.0MB, alloc=33.7MB, time=0.98 memory used=109.9MB, alloc=33.7MB, time=1.23 memory used=125.8MB, alloc=33.7MB, time=1.34 memory used=145.7MB, alloc=33.7MB, time=1.54 memory used=163.2MB, alloc=33.7MB, time=1.76 memory used=185.2MB, alloc=37.7MB, time=1.99 memory used=204.1MB, alloc=37.7MB, time=2.22 memory used=224.7MB, alloc=61.7MB, time=2.47 memory used=267.4MB, alloc=61.7MB, time=2.77 memory used=300.8MB, alloc=61.7MB, time=2.92 memory used=340.2MB, alloc=61.7MB, time=3.55 memory used=371.2MB, alloc=61.7MB, time=3.72 memory used=398.0MB, alloc=61.7MB, time=3.83 memory used=425.5MB, alloc=61.7MB, time=3.92 memory used=477.7MB, alloc=61.7MB, time=5.29 memory used=503.6MB, alloc=61.7MB, time=5.36 memory used=529.1MB, alloc=61.7MB, time=5.42 memory used=559.2MB, alloc=61.7MB, time=5.60 memory used=606.6MB, alloc=61.7MB, time=6.32 memory used=666.1MB, alloc=69.7MB, time=6.82 memory used=722.1MB, alloc=69.7MB, time=7.19 memory used=778.5MB, alloc=69.7MB, time=7.77 memory used=836.0MB, alloc=70.2MB, time=8.70 memory used=887.8MB, alloc=70.2MB, time=9.52 memory used=940.1MB, alloc=70.2MB, time=10.01 memory used=985.9MB, alloc=70.2MB, time=10.90 memory used=1005.1MB, alloc=70.2MB, time=10.98 memory used=1043.4MB, alloc=70.2MB, time=11.27 memory used=1090.8MB, alloc=94.2MB, time=11.81 memory used=1158.6MB, alloc=94.2MB, time=12.68 memory used=1223.6MB, alloc=94.2MB, time=13.28 memory used=1293.6MB, alloc=94.2MB, time=13.95 memory used=1361.2MB, alloc=94.2MB, time=14.68 memory used=1414.2MB, alloc=94.2MB, time=16.52 memory used=1444.7MB, alloc=94.2MB, time=16.62 memory used=1506.8MB, alloc=94.2MB, time=17.15 memory used=1548.9MB, alloc=94.2MB, time=17.36 memory used=1592.9MB, alloc=94.2MB, time=17.91 memory used=1629.6MB, alloc=94.2MB, time=18.08 memory used=1669.7MB, alloc=94.2MB, time=18.24 memory used=1713.3MB, alloc=94.2MB, time=18.75 memory used=1775.0MB, alloc=94.2MB, time=19.49 memory used=1838.9MB, alloc=118.2MB, time=20.22 memory used=1894.9MB, alloc=118.2MB, time=20.82 memory used=1950.5MB, alloc=374.2MB, time=21.29 memory used=2034.2MB, alloc=398.2MB, time=22.25 memory used=2150.5MB, alloc=422.2MB, time=23.47 memory used=2226.3MB, alloc=422.2MB, time=23.82 memory used=2300.7MB, alloc=422.2MB, time=24.16 memory used=2391.0MB, alloc=422.2MB, time=25.40 memory used=2459.9MB, alloc=422.2MB, time=25.69 memory used=2537.1MB, alloc=422.2MB, time=26.04 memory used=2625.0MB, alloc=422.2MB, time=27.26 memory used=2705.4MB, alloc=422.2MB, time=27.75 memory used=2797.7MB, alloc=422.2MB, time=29.47 memory used=2873.7MB, alloc=422.2MB, time=29.86 memory used=2941.5MB, alloc=422.2MB, time=30.16 memory used=3072.5MB, alloc=422.2MB, time=30.67 memory used=3173.0MB, alloc=422.2MB, time=31.12 memory used=3258.4MB, alloc=422.2MB, time=32.32 memory used=3345.0MB, alloc=422.2MB, time=33.90 memory used=3432.7MB, alloc=422.2MB, time=34.88 memory used=3490.9MB, alloc=422.2MB, time=35.13 memory used=3565.8MB, alloc=422.2MB, time=35.41 memory used=3612.7MB, alloc=422.2MB, time=35.62 memory used=3661.3MB, alloc=422.2MB, time=35.83 memory used=3716.9MB, alloc=422.2MB, time=36.03 memory used=3779.6MB, alloc=422.2MB, time=36.25 memory used=3849.0MB, alloc=422.2MB, time=36.48 memory used=3922.4MB, alloc=422.2MB, time=36.70 memory used=3963.8MB, alloc=422.2MB, time=36.86 memory used=4006.2MB, alloc=422.2MB, time=37.03 memory used=4051.6MB, alloc=422.2MB, time=37.21 memory used=4100.6MB, alloc=422.2MB, time=37.37 memory used=4155.1MB, alloc=422.2MB, time=37.55 memory used=4224.1MB, alloc=422.2MB, time=37.88 memory used=4294.6MB, alloc=422.2MB, time=38.57 memory used=4368.0MB, alloc=422.2MB, time=39.09 memory used=4436.5MB, alloc=422.2MB, time=39.34 memory used=4494.8MB, alloc=422.2MB, time=39.57 memory used=4542.9MB, alloc=422.2MB, time=39.77 memory used=4597.9MB, alloc=422.2MB, time=39.99 memory used=4660.1MB, alloc=422.2MB, time=40.21 memory used=4729.4MB, alloc=422.2MB, time=40.42 memory used=4806.5MB, alloc=422.2MB, time=40.65 memory used=4853.4MB, alloc=422.2MB, time=40.83 memory used=4897.1MB, alloc=422.2MB, time=41.00 memory used=4944.6MB, alloc=422.2MB, time=41.17 memory used=4994.3MB, alloc=422.2MB, time=41.34 memory used=5049.0MB, alloc=422.2MB, time=41.51 memory used=5118.4MB, alloc=422.2MB, time=41.81 memory used=5188.5MB, alloc=422.2MB, time=42.21 memory used=5262.2MB, alloc=422.2MB, time=42.52 memory used=5347.9MB, alloc=422.2MB, time=66.03 memory used=5459.3MB, alloc=422.2MB, time=73.09 memory used=5520.2MB, alloc=422.2MB, time=73.32 memory used=5580.5MB, alloc=422.2MB, time=73.55 memory used=5650.5MB, alloc=422.2MB, time=73.75 memory used=5695.8MB, alloc=422.2MB, time=73.92 memory used=5746.0MB, alloc=422.2MB, time=74.11 memory used=5802.7MB, alloc=422.2MB, time=74.29 memory used=5865.2MB, alloc=422.2MB, time=74.48 memory used=5935.5MB, alloc=422.2MB, time=74.67 memory used=6129.2MB, alloc=422.2MB, time=76.29 memory used=6189.7MB, alloc=422.2MB, time=76.55 memory used=6257.5MB, alloc=422.2MB, time=76.85 memory used=6323.0MB, alloc=422.2MB, time=77.10 memory used=6366.5MB, alloc=422.2MB, time=77.31 memory used=6415.4MB, alloc=422.2MB, time=77.55 memory used=6469.5MB, alloc=422.2MB, time=77.79 memory used=6526.0MB, alloc=422.2MB, time=78.02 memory used=6587.8MB, alloc=422.2MB, time=78.25 memory used=6654.8MB, alloc=422.2MB, time=78.52 memory used=6729.9MB, alloc=422.2MB, time=78.75 memory used=6791.2MB, alloc=446.2MB, time=78.98 memory used=6843.2MB, alloc=446.2MB, time=79.18 memory used=6897.2MB, alloc=446.2MB, time=79.39 memory used=6954.3MB, alloc=446.2MB, time=79.59 memory used=7016.8MB, alloc=446.2MB, time=79.79 memory used=7081.6MB, alloc=446.2MB, time=80.00 memory used=7150.7MB, alloc=446.2MB, time=80.21 memory used=7225.5MB, alloc=446.2MB, time=80.42 memory used=7306.2MB, alloc=446.2MB, time=80.62 memory used=7393.7MB, alloc=446.2MB, time=80.84 memory used=7500.4MB, alloc=446.2MB, time=82.19 memory used=7576.2MB, alloc=446.2MB, time=82.50 memory used=7664.5MB, alloc=446.2MB, time=82.80 memory used=7723.1MB, alloc=446.2MB, time=83.06 memory used=7788.3MB, alloc=446.2MB, time=83.33 memory used=7863.7MB, alloc=446.2MB, time=83.57 memory used=7946.3MB, alloc=446.2MB, time=83.82 memory used=8039.0MB, alloc=446.2MB, time=84.12 memory used=8129.0MB, alloc=446.2MB, time=84.40 memory used=8181.5MB, alloc=446.2MB, time=84.59 memory used=8235.1MB, alloc=446.2MB, time=84.78 memory used=8291.9MB, alloc=446.2MB, time=84.99 memory used=8351.9MB, alloc=446.2MB, time=85.19 memory used=8416.7MB, alloc=446.2MB, time=85.38 memory used=8486.0MB, alloc=446.2MB, time=85.58 memory used=8558.7MB, alloc=446.2MB, time=85.80 memory used=8637.4MB, alloc=446.2MB, time=86.00 memory used=8723.9MB, alloc=446.2MB, time=86.21 memory used=8834.3MB, alloc=446.2MB, time=98.42 memory used=8945.4MB, alloc=446.2MB, time=180.52 memory used=9074.8MB, alloc=446.2MB, time=183.31 memory used=9154.7MB, alloc=446.2MB, time=183.63 memory used=9224.1MB, alloc=446.2MB, time=183.89 memory used=9314.8MB, alloc=446.2MB, time=184.14 memory used=9375.3MB, alloc=446.2MB, time=184.34 memory used=9433.3MB, alloc=446.2MB, time=184.54 memory used=9497.6MB, alloc=446.2MB, time=184.74 memory used=9568.0MB, alloc=446.2MB, time=184.94 memory used=9645.5MB, alloc=446.2MB, time=185.15 memory used=9731.9MB, alloc=446.2MB, time=185.36 memory used=9825.9MB, alloc=446.2MB, time=185.57 memory used=9986.7MB, alloc=446.2MB, time=185.92 memory used=10143.1MB, alloc=446.2MB, time=186.22 memory used=10341.2MB, alloc=446.2MB, time=186.97 memory used=10500.4MB, alloc=446.2MB, time=187.45 memory used=10636.3MB, alloc=446.2MB, time=192.30 memory used=10705.2MB, alloc=446.2MB, time=195.19 memory used=10781.0MB, alloc=446.2MB, time=195.46 memory used=10868.0MB, alloc=446.2MB, time=195.77 memory used=10945.8MB, alloc=446.2MB, time=196.06 memory used=10996.3MB, alloc=470.2MB, time=196.31 memory used=11058.5MB, alloc=470.2MB, time=196.59 memory used=11128.9MB, alloc=470.2MB, time=196.85 memory used=11202.7MB, alloc=470.2MB, time=197.14 memory used=11279.8MB, alloc=470.2MB, time=197.43 memory used=11360.0MB, alloc=470.2MB, time=197.71 memory used=11443.6MB, alloc=470.2MB, time=197.99 memory used=11537.1MB, alloc=470.2MB, time=198.28 memory used=11634.1MB, alloc=470.2MB, time=198.58 memory used=11734.2MB, alloc=470.2MB, time=198.85 memory used=11837.4MB, alloc=470.2MB, time=199.14 memory used=11943.7MB, alloc=470.2MB, time=199.44 memory used=12026.2MB, alloc=470.2MB, time=199.66 memory used=12083.4MB, alloc=470.2MB, time=199.86 memory used=12140.5MB, alloc=494.2MB, time=200.07 memory used=12205.2MB, alloc=494.2MB, time=200.29 memory used=12275.2MB, alloc=494.2MB, time=200.50 memory used=12346.0MB, alloc=494.2MB, time=200.72 memory used=12417.6MB, alloc=494.2MB, time=200.93 memory used=12490.0MB, alloc=494.2MB, time=201.14 memory used=12563.2MB, alloc=494.2MB, time=201.38 memory used=12637.4MB, alloc=494.2MB, time=201.61 memory used=12721.5MB, alloc=494.2MB, time=201.83 memory used=12806.5MB, alloc=494.2MB, time=202.05 memory used=12892.2MB, alloc=494.2MB, time=202.27 memory used=12978.8MB, alloc=494.2MB, time=202.50 memory used=13066.0MB, alloc=494.2MB, time=202.73 memory used=13154.0MB, alloc=494.2MB, time=202.95 memory used=13242.5MB, alloc=494.2MB, time=203.17 memory used=13331.9MB, alloc=494.2MB, time=203.40 memory used=13431.6MB, alloc=494.2MB, time=203.64 memory used=13532.0MB, alloc=494.2MB, time=203.88 memory used=13632.8MB, alloc=494.2MB, time=204.13 memory used=13734.2MB, alloc=494.2MB, time=204.37 memory used=13836.0MB, alloc=494.2MB, time=204.61 memory used=13938.9MB, alloc=494.2MB, time=204.87 memory used=14051.0MB, alloc=494.2MB, time=205.13 memory used=14164.0MB, alloc=494.2MB, time=205.40 memory used=14277.2MB, alloc=494.2MB, time=205.66 memory used=14390.7MB, alloc=494.2MB, time=205.92 memory used=14514.4MB, alloc=494.2MB, time=206.21 memory used=14638.0MB, alloc=494.2MB, time=206.45 memory used=14761.5MB, alloc=494.2MB, time=206.70 memory used=14894.9MB, alloc=494.2MB, time=206.96 memory used=15153.0MB, alloc=494.2MB, time=207.39 memory used=15271.8MB, alloc=494.2MB, time=207.68 memory used=15392.0MB, alloc=494.2MB, time=207.96 memory used=15511.6MB, alloc=494.2MB, time=208.24 memory used=15640.0MB, alloc=494.2MB, time=208.52 memory used=15767.2MB, alloc=494.2MB, time=208.80 memory used=15902.5MB, alloc=494.2MB, time=209.10 memory used=16036.1MB, alloc=494.2MB, time=209.40 memory used=16177.0MB, alloc=494.2MB, time=209.70 memory used=16315.6MB, alloc=494.2MB, time=209.99 memory used=16460.3MB, alloc=494.2MB, time=210.29 memory used=16610.6MB, alloc=494.2MB, time=210.61 memory used=16765.4MB, alloc=494.2MB, time=210.92 memory used=16923.4MB, alloc=494.2MB, time=211.21 memory used=17083.7MB, alloc=494.2MB, time=211.52 memory used=17251.7MB, alloc=494.2MB, time=211.85 memory used=17425.0MB, alloc=494.2MB, time=212.18 memory used=17605.9MB, alloc=494.2MB, time=212.51 memory used=17794.3MB, alloc=494.2MB, time=212.85 memory used=17994.5MB, alloc=494.2MB, time=213.18 memory used=18247.1MB, alloc=494.2MB, time=214.15 memory used=18491.1MB, alloc=494.2MB, time=214.66 memory used=18660.3MB, alloc=494.2MB, time=222.29 memory used=18778.6MB, alloc=494.2MB, time=222.70 memory used=18894.9MB, alloc=494.2MB, time=223.09 memory used=18970.5MB, alloc=494.2MB, time=223.40 memory used=19049.5MB, alloc=494.2MB, time=223.68 memory used=19135.2MB, alloc=494.2MB, time=223.97 memory used=19231.8MB, alloc=494.2MB, time=224.26 memory used=19333.4MB, alloc=494.2MB, time=224.55 memory used=19439.8MB, alloc=494.2MB, time=224.87 memory used=19551.0MB, alloc=494.2MB, time=225.20 memory used=19674.1MB, alloc=494.2MB, time=225.52 memory used=19801.9MB, alloc=494.2MB, time=225.82 memory used=19928.6MB, alloc=494.2MB, time=226.16 memory used=20002.3MB, alloc=494.2MB, time=226.40 memory used=20069.7MB, alloc=494.2MB, time=226.63 memory used=20137.8MB, alloc=494.2MB, time=226.85 memory used=20207.6MB, alloc=494.2MB, time=227.10 memory used=20278.3MB, alloc=494.2MB, time=227.33 memory used=20349.8MB, alloc=494.2MB, time=227.55 memory used=20422.2MB, alloc=494.2MB, time=227.77 memory used=20495.3MB, alloc=494.2MB, time=228.01 memory used=20569.4MB, alloc=494.2MB, time=228.24 memory used=20653.4MB, alloc=494.2MB, time=228.50 memory used=20738.2MB, alloc=494.2MB, time=228.72 memory used=20823.9MB, alloc=494.2MB, time=228.96 memory used=20910.4MB, alloc=494.2MB, time=229.21 memory used=20997.5MB, alloc=494.2MB, time=229.45 memory used=21085.4MB, alloc=494.2MB, time=229.69 memory used=21173.9MB, alloc=494.2MB, time=229.95 memory used=21263.2MB, alloc=494.2MB, time=230.20 memory used=21362.9MB, alloc=494.2MB, time=230.45 memory used=21463.1MB, alloc=494.2MB, time=230.71 memory used=21564.0MB, alloc=494.2MB, time=230.96 memory used=21665.3MB, alloc=494.2MB, time=231.20 memory used=21767.1MB, alloc=494.2MB, time=231.44 memory used=21869.8MB, alloc=494.2MB, time=231.70 memory used=21982.0MB, alloc=494.2MB, time=231.96 memory used=22095.0MB, alloc=494.2MB, time=232.21 memory used=22208.2MB, alloc=494.2MB, time=232.45 memory used=22321.7MB, alloc=494.2MB, time=232.71 memory used=22445.3MB, alloc=494.2MB, time=232.99 memory used=22568.9MB, alloc=494.2MB, time=233.25 memory used=22692.5MB, alloc=494.2MB, time=233.54 memory used=22825.9MB, alloc=494.2MB, time=233.81 memory used=23009.2MB, alloc=494.2MB, time=234.16 memory used=23131.1MB, alloc=494.2MB, time=234.48 memory used=23253.1MB, alloc=494.2MB, time=234.77 memory used=23373.2MB, alloc=494.2MB, time=235.08 memory used=23493.1MB, alloc=494.2MB, time=235.37 memory used=23620.4MB, alloc=494.2MB, time=235.69 memory used=23747.2MB, alloc=494.2MB, time=235.99 memory used=23882.0MB, alloc=494.2MB, time=236.29 memory used=24015.0MB, alloc=494.2MB, time=236.61 memory used=24155.4MB, alloc=494.2MB, time=236.91 memory used=24302.3MB, alloc=494.2MB, time=237.22 memory used=24446.1MB, alloc=494.2MB, time=237.54 memory used=24595.3MB, alloc=494.2MB, time=237.86 memory used=24748.7MB, alloc=494.2MB, time=238.18 memory used=24905.3MB, alloc=494.2MB, time=238.49 memory used=25071.5MB, alloc=494.2MB, time=238.81 memory used=25237.9MB, alloc=494.2MB, time=239.12 memory used=25414.5MB, alloc=494.2MB, time=239.45 memory used=25597.7MB, alloc=494.2MB, time=239.78 memory used=25786.6MB, alloc=494.2MB, time=240.12 memory used=25988.0MB, alloc=494.2MB, time=240.46 memory used=26188.3MB, alloc=494.2MB, time=241.26 memory used=26434.8MB, alloc=494.2MB, time=241.78 memory used=26673.8MB, alloc=494.2MB, time=349.03 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428493177 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 F := [-14 x z + 12 y z + 16 y z , -4 x y z - y z + 2 y z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 2 2 G := [-11 x + 7 x z - 9 x , -7 x z + 10 z ] > Problem := [F,G]; 2 2 2 2 Problem := [[-14 x z + 12 y z + 16 y z , -4 x y z - y z + 2 y z], 3 2 2 2 2 [-11 x + 7 x z - 9 x , -7 x 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=4.2MB, alloc=32.3MB, time=0.17 memory used=26.1MB, alloc=32.3MB, time=0.47 memory used=78.2MB, alloc=68.3MB, time=1.34 memory used=125.9MB, alloc=68.3MB, time=2.17 memory used=168.6MB, alloc=92.3MB, time=2.93 memory used=228.1MB, alloc=116.3MB, time=4.29 memory used=299.0MB, alloc=140.3MB, time=6.69 memory used=390.6MB, alloc=140.3MB, time=9.92 N1 := 2651 > GB := Basis(F, plex(op(vars))); 2 2 2 2 2 GB := [4 x y z + y z - 2 y z, 24 x y z + 39 x z - 12 x y z - 16 x z , 2 2 -24 x y z - 7 x z + 8 y z + 12 y z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=484.3MB, alloc=148.3MB, time=12.11 memory used=583.3MB, alloc=172.3MB, time=13.75 memory used=703.0MB, alloc=196.3MB, time=15.87 memory used=837.2MB, alloc=220.3MB, time=18.27 memory used=945.6MB, alloc=500.3MB, time=20.51 memory used=1096.3MB, alloc=524.3MB, time=25.15 memory used=1251.2MB, alloc=548.3MB, time=30.89 memory used=1423.2MB, alloc=572.3MB, time=37.58 memory used=1619.3MB, alloc=596.3MB, time=45.16 memory used=1839.4MB, alloc=596.3MB, time=53.59 memory used=2059.4MB, alloc=620.3MB, time=62.07 memory used=2303.8MB, alloc=644.3MB, time=70.82 N2 := 6617 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 H := [-14 x z + 12 y z + 16 y z , -4 x y z - y z + 2 y z, 3 2 2 2 2 -11 x + 7 x z - 9 x , -7 x z + 10 z ] > J:=[op(GB),op(G)]; 2 2 2 2 2 J := [4 x y z + y z - 2 y z, 24 x y z + 39 x z - 12 x y z - 16 x z , 2 2 3 2 2 -24 x y z - 7 x z + 8 y z + 12 y z, -11 x + 7 x z - 9 x , 2 2 -7 x z + 10 z ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 10, 12, 3, 3, 2, 2, 1, 1/2, 1, 6/11, 5/11, 9/11, 5, 13, 16, 11 4, 3, 2, 2, 1, 3/5, 1, --, 1/2, 7/8, -3, -4, -1] 16 > save(F, G, cat("ranSet/33", convert(F, string),".txt")); > quit memory used=2327.1MB, alloc=644.3MB, time=71.49 |\^/| 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(); 1428493278 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 3 F := [-16 x y - 20 y z + 2, 9 z - 7 y - 2] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 3 2 G := [20 y - 18 y z + 16 z , -5 y z - 10 x z + z] > Problem := [F,G]; 2 2 3 Problem := [[-16 x y - 20 y z + 2, 9 z - 7 y - 2], 3 2 3 2 [20 y - 18 y z + 16 z , -5 y z - 10 x z + z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.1MB, alloc=32.3MB, time=0.17 memory used=26.1MB, alloc=32.3MB, time=0.48 memory used=46.2MB, alloc=56.3MB, time=0.77 memory used=89.2MB, alloc=60.3MB, time=1.29 memory used=132.2MB, alloc=68.3MB, time=1.83 memory used=170.5MB, alloc=68.3MB, time=2.05 memory used=202.6MB, alloc=68.3MB, time=2.16 memory used=231.9MB, alloc=68.3MB, time=2.28 memory used=273.8MB, alloc=68.3MB, time=3.04 memory used=298.5MB, alloc=68.3MB, time=3.12 memory used=333.1MB, alloc=68.3MB, time=3.47 memory used=365.6MB, alloc=68.3MB, time=3.92 memory used=388.9MB, alloc=68.3MB, time=4.01 memory used=431.5MB, alloc=68.3MB, time=4.41 memory used=471.3MB, alloc=68.3MB, time=4.62 memory used=499.9MB, alloc=68.3MB, time=4.71 memory used=530.2MB, alloc=68.3MB, time=4.83 memory used=565.3MB, alloc=68.3MB, time=5.24 memory used=602.2MB, alloc=68.3MB, time=7.36 memory used=626.4MB, alloc=68.3MB, time=7.43 memory used=644.9MB, alloc=68.3MB, time=7.49 memory used=692.3MB, alloc=68.3MB, time=9.81 memory used=721.1MB, alloc=68.3MB, time=10.05 memory used=743.2MB, alloc=68.3MB, time=10.12 memory used=768.7MB, alloc=68.3MB, time=10.27 memory used=810.6MB, alloc=68.3MB, time=10.68 memory used=843.1MB, alloc=68.3MB, time=10.81 memory used=890.4MB, alloc=92.3MB, time=14.87 memory used=944.8MB, alloc=92.3MB, time=17.65 memory used=984.6MB, alloc=92.3MB, time=17.75 memory used=1018.2MB, alloc=92.3MB, time=17.86 memory used=1059.8MB, alloc=92.3MB, time=17.96 memory used=1095.7MB, alloc=92.3MB, time=18.05 memory used=1140.5MB, alloc=92.3MB, time=18.29 memory used=1209.8MB, alloc=92.3MB, time=19.14 memory used=1271.7MB, alloc=92.3MB, time=19.69 memory used=1314.9MB, alloc=92.3MB, time=19.98 memory used=1358.4MB, alloc=92.3MB, time=20.13 memory used=1394.6MB, alloc=92.3MB, time=20.24 memory used=1427.1MB, alloc=92.3MB, time=20.35 memory used=1456.4MB, alloc=92.3MB, time=20.44 memory used=1496.4MB, alloc=92.3MB, time=20.60 memory used=1530.7MB, alloc=92.3MB, time=20.71 memory used=1570.2MB, alloc=92.3MB, time=21.93 memory used=1618.2MB, alloc=92.3MB, time=22.25 memory used=1683.0MB, alloc=92.3MB, time=23.06 memory used=1714.0MB, alloc=92.3MB, time=23.16 memory used=1750.8MB, alloc=92.3MB, time=23.28 memory used=1781.8MB, alloc=92.3MB, time=23.36 memory used=1807.6MB, alloc=92.3MB, time=23.44 memory used=1837.2MB, alloc=92.3MB, time=23.53 memory used=1875.8MB, alloc=92.3MB, time=23.64 memory used=1927.5MB, alloc=92.3MB, time=24.14 memory used=1955.2MB, alloc=92.3MB, time=24.25 memory used=1986.1MB, alloc=92.3MB, time=24.36 memory used=2022.4MB, alloc=92.3MB, time=24.48 memory used=2059.9MB, alloc=116.3MB, time=24.60 memory used=2095.6MB, alloc=116.3MB, time=24.71 memory used=2135.0MB, alloc=116.3MB, time=24.85 memory used=2180.5MB, alloc=116.3MB, time=24.98 memory used=2231.3MB, alloc=116.3MB, time=25.11 memory used=2288.6MB, alloc=116.3MB, time=25.24 memory used=2348.6MB, alloc=116.3MB, time=25.37 memory used=2382.8MB, alloc=116.3MB, time=25.47 memory used=2420.4MB, alloc=116.3MB, time=25.55 memory used=2492.5MB, alloc=116.3MB, time=35.85 memory used=2554.9MB, alloc=140.3MB, time=61.35 memory used=2616.9MB, alloc=164.3MB, time=121.67 memory used=2689.7MB, alloc=188.3MB, time=176.91 memory used=2775.2MB, alloc=212.3MB, time=251.70 |\^/| 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(); 1428493578 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 F := [12 y z - 17 z, 10 x y + 10 y z + 3] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 3 3 2 G := [18 x y + y + z , -5 z - 7 x - 8 x] > Problem := [F,G]; 2 2 2 Problem := [[12 y z - 17 z, 10 x y + 10 y z + 3], 2 3 3 3 2 [18 x y + y + z , -5 z - 7 x - 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=4.2MB, alloc=32.3MB, time=0.17 memory used=26.6MB, alloc=32.3MB, time=0.50 memory used=46.2MB, alloc=56.3MB, time=0.77 memory used=86.9MB, alloc=60.3MB, time=1.35 memory used=129.7MB, alloc=60.3MB, time=1.87 memory used=181.6MB, alloc=60.3MB, time=2.18 memory used=209.0MB, alloc=60.3MB, time=2.76 memory used=233.0MB, alloc=60.3MB, time=2.84 memory used=283.4MB, alloc=68.3MB, time=3.39 memory used=322.1MB, alloc=92.3MB, time=4.97 memory used=386.8MB, alloc=92.3MB, time=5.49 memory used=447.2MB, alloc=92.3MB, time=6.00 memory used=485.8MB, alloc=92.3MB, time=6.41 memory used=549.6MB, alloc=92.3MB, time=7.50 memory used=613.3MB, alloc=116.3MB, time=8.22 memory used=681.6MB, alloc=372.3MB, time=9.19 memory used=765.4MB, alloc=396.3MB, time=10.33 memory used=864.5MB, alloc=396.3MB, time=11.71 memory used=982.1MB, alloc=396.3MB, time=12.67 memory used=1087.6MB, alloc=420.3MB, time=14.03 memory used=1200.1MB, alloc=420.3MB, time=15.00 memory used=1295.6MB, alloc=420.3MB, time=15.81 memory used=1417.5MB, alloc=420.3MB, time=16.91 memory used=1531.1MB, alloc=444.3MB, time=18.15 memory used=1653.4MB, alloc=444.3MB, time=18.98 memory used=1727.7MB, alloc=444.3MB, time=19.29 memory used=1805.3MB, alloc=444.3MB, time=19.59 memory used=1881.9MB, alloc=444.3MB, time=19.88 memory used=1938.8MB, alloc=444.3MB, time=20.13 memory used=2000.6MB, alloc=444.3MB, time=20.40 memory used=2070.6MB, alloc=444.3MB, time=20.65 memory used=2150.2MB, alloc=444.3MB, time=20.90 memory used=2222.6MB, alloc=444.3MB, time=21.13 memory used=2288.7MB, alloc=444.3MB, time=21.35 memory used=2369.9MB, alloc=444.3MB, time=21.78 memory used=2446.7MB, alloc=444.3MB, time=22.07 memory used=2524.0MB, alloc=444.3MB, time=22.35 memory used=2585.8MB, alloc=444.3MB, time=22.58 memory used=2696.4MB, alloc=444.3MB, time=28.47 memory used=2773.6MB, alloc=444.3MB, time=28.75 memory used=2837.7MB, alloc=444.3MB, time=29.01 memory used=2917.1MB, alloc=444.3MB, time=29.26 memory used=2979.1MB, alloc=444.3MB, time=29.47 memory used=3043.5MB, alloc=444.3MB, time=29.67 memory used=3168.4MB, alloc=444.3MB, time=30.72 memory used=3263.9MB, alloc=444.3MB, time=31.36 memory used=3396.0MB, alloc=444.3MB, time=33.49 memory used=3531.4MB, alloc=444.3MB, time=34.67 memory used=3595.7MB, alloc=444.3MB, time=34.93 memory used=3701.0MB, alloc=444.3MB, time=35.30 memory used=3789.7MB, alloc=444.3MB, time=35.83 memory used=3919.2MB, alloc=444.3MB, time=36.20 memory used=4056.2MB, alloc=468.3MB, time=37.44 memory used=4187.4MB, alloc=468.3MB, time=38.40 memory used=4269.7MB, alloc=468.3MB, time=38.69 memory used=4368.1MB, alloc=468.3MB, time=40.44 memory used=4501.4MB, alloc=468.3MB, time=48.60 memory used=4582.3MB, alloc=468.3MB, time=48.93 memory used=4662.1MB, alloc=468.3MB, time=49.23 memory used=4754.5MB, alloc=468.3MB, time=49.55 memory used=4815.5MB, alloc=468.3MB, time=49.80 memory used=4882.5MB, alloc=468.3MB, time=50.05 memory used=4958.2MB, alloc=468.3MB, time=50.28 memory used=5042.2MB, alloc=468.3MB, time=50.53 memory used=5136.6MB, alloc=468.3MB, time=50.80 memory used=5360.9MB, alloc=468.3MB, time=51.32 memory used=5573.2MB, alloc=468.3MB, time=52.05 memory used=5734.3MB, alloc=468.3MB, time=53.43 memory used=5954.6MB, alloc=468.3MB, time=55.06 memory used=6141.1MB, alloc=468.3MB, time=56.28 memory used=6273.7MB, alloc=468.3MB, time=56.81 memory used=6388.6MB, alloc=468.3MB, time=57.22 memory used=6540.2MB, alloc=468.3MB, time=58.16 memory used=6671.2MB, alloc=468.3MB, time=58.74 memory used=6788.8MB, alloc=468.3MB, time=59.24 memory used=6910.0MB, alloc=468.3MB, time=59.76 memory used=7032.5MB, alloc=468.3MB, time=60.23 memory used=7162.8MB, alloc=468.3MB, time=60.68 memory used=7307.5MB, alloc=468.3MB, time=61.16 memory used=7463.7MB, alloc=468.3MB, time=61.62 memory used=7637.2MB, alloc=468.3MB, time=62.12 memory used=7827.8MB, alloc=468.3MB, time=62.63 memory used=8035.1MB, alloc=468.3MB, time=63.19 memory used=8270.6MB, alloc=468.3MB, time=64.53 memory used=8409.8MB, alloc=468.3MB, time=65.18 memory used=8522.4MB, alloc=468.3MB, time=65.65 memory used=8653.8MB, alloc=492.3MB, time=66.37 memory used=8800.6MB, alloc=492.3MB, time=66.94 memory used=8946.0MB, alloc=492.3MB, time=67.48 memory used=9098.4MB, alloc=492.3MB, time=67.99 memory used=9267.1MB, alloc=492.3MB, time=68.53 memory used=9473.1MB, alloc=492.3MB, time=69.11 memory used=9691.8MB, alloc=492.3MB, time=69.70 memory used=9920.9MB, alloc=492.3MB, time=72.11 memory used=10128.0MB, alloc=492.3MB, time=74.21 memory used=10326.1MB, alloc=516.3MB, time=76.43 memory used=10558.9MB, alloc=516.3MB, time=79.48 memory used=10789.1MB, alloc=540.3MB, time=82.52 memory used=11019.8MB, alloc=540.3MB, time=85.60 memory used=11222.6MB, alloc=564.3MB, time=89.03 memory used=11430.1MB, alloc=588.3MB, time=92.68 memory used=11618.9MB, alloc=612.3MB, time=98.69 memory used=11810.1MB, alloc=636.3MB, time=105.31 memory used=12002.3MB, alloc=660.3MB, time=113.25 memory used=12218.3MB, alloc=684.3MB, time=122.14 memory used=12458.3MB, alloc=708.3MB, time=131.95 memory used=12722.2MB, alloc=732.3MB, time=142.76 memory used=13010.1MB, alloc=756.3MB, time=154.21 memory used=13322.0MB, alloc=780.3MB, time=166.85 memory used=13657.8MB, alloc=780.3MB, time=180.49 memory used=13993.6MB, alloc=804.3MB, time=193.82 N1 := 9207 > GB := Basis(F, plex(op(vars))); 2 4 3 2 GB := [600 x y + 850 x y + 360 x y + 255 y + 54, 2 3 2 2 2 10200 x y - 2160 x y + 14450 x y + 3060 x y - 648 x + 648 z + 4335] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=14191.0MB, alloc=804.3MB, time=198.51 memory used=14434.2MB, alloc=804.3MB, time=200.71 memory used=14723.8MB, alloc=804.3MB, time=232.64 memory used=15218.7MB, alloc=804.3MB, time=307.55 |\^/| 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(); 1428493878 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 3 F := [-13 z + x + 12 y, 7 x + 9 x y - 2 z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 G := [-13 x y z - 4 x , 6 y - 4 y] > Problem := [F,G]; Problem := 3 2 3 2 2 [[-13 z + x + 12 y, 7 x + 9 x y - 2 z], [-13 x y z - 4 x , 6 y - 4 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.5MB, alloc=32.3MB, time=0.49 memory used=47.7MB, alloc=32.3MB, time=0.80 memory used=93.0MB, alloc=68.3MB, time=1.46 memory used=143.9MB, alloc=76.3MB, time=2.24 memory used=189.6MB, alloc=100.3MB, time=3.01 memory used=256.1MB, alloc=124.3MB, time=4.12 memory used=339.8MB, alloc=148.3MB, time=6.14 N1 := 1921 > GB := Basis(F, plex(op(vars))); memory used=429.1MB, alloc=148.3MB, time=9.11 9 7 2 5 3 3 2 GB := [4459 x + 17199 y x + 22113 y x + 9477 y x - 8 x - 96 y, 3 -7 x - 9 x y + 2 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 637 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 3 2 2 H := [-13 z + x + 12 y, 7 x + 9 y x - 2 z, -13 x y z - 4 x , 6 y - 4 y] > J:=[op(GB),op(G)]; 9 7 2 5 3 3 2 J := [4459 x + 17199 y x + 22113 y x + 9477 y x - 8 x - 96 y, 3 2 2 -7 x - 9 x y + 2 z, -13 x y z - 4 x , 6 y - 4 y] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 10, 11, 3, 3, 2, 3, 3/4, 1, 3/4, 1/2, 1/2, 3/10, 4, 9, 17, 9, 9, 3, 1, 3/4, 1, 1/2, 9/13, 8/13, 2/13, 1, -6, -6] > save(F, G, cat("ranSet/33", convert(F, string),".txt")); > quit memory used=525.0MB, alloc=148.3MB, time=10.76 |\^/| 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(); 1428493896 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 2 F := [9 y - 20 y z - 16 x, 7 y z - 4 x + 4 y z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 G := [-8 x z - 13 y z - 12 x z, -y z - 8 z - 2 z] > Problem := [F,G]; 3 2 2 2 Problem := [[9 y - 20 y z - 16 x, 7 y z - 4 x + 4 y z], 2 2 2 2 [-8 x z - 13 y z - 12 x z, -y z - 8 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=4.2MB, alloc=32.3MB, time=0.17 memory used=26.4MB, alloc=32.3MB, time=0.49 memory used=46.3MB, alloc=56.3MB, time=0.79 memory used=87.5MB, alloc=60.3MB, time=1.39 memory used=128.1MB, alloc=60.3MB, time=1.96 memory used=166.5MB, alloc=84.3MB, time=2.52 memory used=228.2MB, alloc=92.3MB, time=3.45 memory used=290.0MB, alloc=116.3MB, time=4.34 memory used=358.9MB, alloc=116.3MB, time=5.21 memory used=436.7MB, alloc=396.3MB, time=6.38 memory used=544.9MB, alloc=420.3MB, time=7.95 memory used=677.3MB, alloc=444.3MB, time=9.82 memory used=820.8MB, alloc=468.3MB, time=12.02 memory used=936.8MB, alloc=468.3MB, time=13.74 memory used=1050.7MB, alloc=492.3MB, time=15.56 memory used=1155.3MB, alloc=492.3MB, time=17.27 memory used=1262.2MB, alloc=516.3MB, time=19.17 memory used=1390.1MB, alloc=516.3MB, time=21.44 memory used=1512.5MB, alloc=540.3MB, time=23.64 memory used=1659.1MB, alloc=564.3MB, time=26.40 memory used=1801.9MB, alloc=588.3MB, time=29.13 memory used=1933.4MB, alloc=612.3MB, time=31.75 memory used=2042.9MB, alloc=636.3MB, time=34.05 memory used=2169.0MB, alloc=660.3MB, time=36.59 memory used=2272.6MB, alloc=660.3MB, time=38.79 memory used=2393.8MB, alloc=684.3MB, time=41.34 memory used=2480.0MB, alloc=684.3MB, time=43.25 memory used=2591.4MB, alloc=708.3MB, time=45.67 memory used=2703.6MB, alloc=732.3MB, time=48.07 memory used=2808.7MB, alloc=732.3MB, time=50.36 memory used=2910.0MB, alloc=756.3MB, time=52.66 memory used=3003.3MB, alloc=780.3MB, time=54.84 memory used=3104.8MB, alloc=780.3MB, time=57.12 memory used=3211.7MB, alloc=780.3MB, time=59.05 memory used=3310.9MB, alloc=804.3MB, time=61.07 memory used=3408.1MB, alloc=804.3MB, time=63.18 memory used=3482.5MB, alloc=828.3MB, time=65.01 memory used=3565.1MB, alloc=828.3MB, time=67.03 memory used=3642.8MB, alloc=852.3MB, time=69.00 memory used=3715.2MB, alloc=876.3MB, time=71.07 memory used=4077.5MB, alloc=900.3MB, time=84.07 memory used=4430.2MB, alloc=924.3MB, time=97.72 memory used=4788.5MB, alloc=948.3MB, time=112.32 memory used=5155.7MB, alloc=972.3MB, time=127.62 memory used=5533.7MB, alloc=996.3MB, time=143.51 memory used=5924.1MB, alloc=1020.3MB, time=159.97 memory used=6327.8MB, alloc=1044.3MB, time=177.27 memory used=6745.8MB, alloc=1068.3MB, time=195.17 memory used=7178.5MB, alloc=1092.3MB, time=213.90 memory used=7625.2MB, alloc=1116.3MB, time=232.94 memory used=8078.6MB, alloc=1140.3MB, time=253.29 |\^/| 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(); 1428494196 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 2 F := [-18 x y z - 20 x z + 16 y z, -2 x y + 6 x z + y z ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 3 2 G := [-2 x y + 2 y , 4 x y + 2 z - 3 y ] > Problem := [F,G]; 2 2 2 2 2 Problem := [[-18 x y z - 20 x z + 16 y z, -2 x y + 6 x z + y z ], 2 2 2 3 2 [-2 x y + 2 y , 4 x y + 2 z - 3 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.4MB, alloc=32.3MB, time=0.50 memory used=46.2MB, alloc=56.3MB, time=0.79 memory used=91.5MB, alloc=60.3MB, time=1.35 memory used=118.4MB, alloc=60.3MB, time=1.92 memory used=159.1MB, alloc=60.3MB, time=2.69 memory used=201.3MB, alloc=60.3MB, time=3.41 memory used=248.2MB, alloc=60.3MB, time=4.03 memory used=289.0MB, alloc=60.3MB, time=4.56 memory used=328.6MB, alloc=84.3MB, time=5.14 memory used=394.0MB, alloc=84.3MB, time=5.51 memory used=448.7MB, alloc=84.3MB, time=5.69 memory used=509.8MB, alloc=86.4MB, time=5.87 memory used=579.7MB, alloc=98.7MB, time=6.07 memory used=659.3MB, alloc=107.1MB, time=6.28 memory used=735.8MB, alloc=107.8MB, time=6.49 memory used=809.1MB, alloc=107.8MB, time=6.69 memory used=880.4MB, alloc=107.8MB, time=6.89 memory used=952.3MB, alloc=107.8MB, time=7.09 memory used=1042.0MB, alloc=107.8MB, time=7.53 memory used=1100.8MB, alloc=107.8MB, time=7.75 memory used=1156.2MB, alloc=107.8MB, time=7.96 memory used=1214.0MB, alloc=107.8MB, time=8.14 memory used=1282.3MB, alloc=107.8MB, time=8.33 memory used=1358.9MB, alloc=107.8MB, time=8.53 memory used=1435.9MB, alloc=107.8MB, time=8.74 memory used=1508.7MB, alloc=107.8MB, time=8.94 memory used=1579.6MB, alloc=107.8MB, time=9.14 memory used=1650.9MB, alloc=107.8MB, time=9.34 memory used=1721.5MB, alloc=107.8MB, time=9.54 memory used=1793.1MB, alloc=107.8MB, time=9.73 memory used=1903.8MB, alloc=107.8MB, time=10.62 memory used=1968.5MB, alloc=107.8MB, time=11.25 memory used=2035.3MB, alloc=107.8MB, time=11.87 memory used=2092.7MB, alloc=131.8MB, time=12.86 memory used=2194.0MB, alloc=131.8MB, time=13.66 memory used=2295.8MB, alloc=131.8MB, time=14.36 memory used=2390.2MB, alloc=131.8MB, time=15.29 memory used=2490.4MB, alloc=131.8MB, time=15.95 memory used=2592.9MB, alloc=131.8MB, time=16.61 memory used=2695.1MB, alloc=131.8MB, time=17.27 memory used=2795.0MB, alloc=131.8MB, time=17.95 memory used=2890.0MB, alloc=155.8MB, time=18.80 memory used=2991.7MB, alloc=155.8MB, time=20.48 memory used=3091.3MB, alloc=179.8MB, time=22.06 memory used=3205.9MB, alloc=459.8MB, time=23.90 memory used=3337.8MB, alloc=483.8MB, time=26.77 memory used=3462.0MB, alloc=507.8MB, time=30.64 memory used=3592.3MB, alloc=531.8MB, time=35.71 memory used=3746.1MB, alloc=555.8MB, time=41.61 memory used=3923.9MB, alloc=555.8MB, time=48.57 memory used=4101.6MB, alloc=579.8MB, time=55.94 memory used=4303.5MB, alloc=579.8MB, time=63.63 N1 := 5769 > GB := Basis(F, plex(op(vars))); 6 5 2 4 3 3 4 2 5 GB := [-200 x y + 486 x y - 783 x y + 240 x y + 64 x y , 3 2 3 2 3 3 2 2 3 9 x y + 10 x y z - 8 x y , -20 x y - 54 x y z + 39 x y z + 8 y z, 2 2 2 2 2 9 x y z + 10 x z - 8 y z, -10 x y - 27 x y z + 24 y z + 5 y z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=4514.3MB, alloc=579.8MB, time=67.45 memory used=4656.0MB, alloc=579.8MB, time=69.98 memory used=4816.5MB, alloc=579.8MB, time=77.94 memory used=5062.6MB, alloc=579.8MB, time=107.31 memory used=5198.6MB, alloc=603.8MB, time=195.26 memory used=5347.8MB, alloc=603.8MB, time=199.48 memory used=5445.2MB, alloc=603.8MB, time=199.87 memory used=5551.2MB, alloc=603.8MB, time=200.27 memory used=5665.9MB, alloc=603.8MB, time=200.69 memory used=5791.4MB, alloc=603.8MB, time=201.11 memory used=5928.3MB, alloc=603.8MB, time=201.52 memory used=6079.4MB, alloc=603.8MB, time=201.94 memory used=6254.0MB, alloc=603.8MB, time=202.41 memory used=6404.6MB, alloc=603.8MB, time=203.02 memory used=6794.4MB, alloc=603.8MB, time=205.80 memory used=6991.0MB, alloc=603.8MB, time=207.08 memory used=7208.3MB, alloc=603.8MB, time=208.31 memory used=7425.9MB, alloc=603.8MB, time=210.05 memory used=7644.1MB, alloc=603.8MB, time=212.35 memory used=7823.5MB, alloc=603.8MB, time=216.22 memory used=7978.0MB, alloc=603.8MB, time=235.35 memory used=8225.7MB, alloc=603.8MB, time=239.18 memory used=8446.6MB, alloc=627.8MB, time=243.28 memory used=8660.3MB, alloc=627.8MB, time=261.55 memory used=8844.0MB, alloc=627.8MB, time=262.49 memory used=9035.6MB, alloc=651.8MB, time=264.24 memory used=9291.1MB, alloc=651.8MB, time=267.66 |\^/| 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(); 1428494496 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 F := [-19 x + 9 x z + 7 x , -6 x y z - 5 x z + 10 y] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 G := [2 y z - 13 x + 13 z, 4 x z + 5 y z + 5 x y] > Problem := [F,G]; 3 2 2 Problem := [[-19 x + 9 x z + 7 x , -6 x y z - 5 x z + 10 y], 2 2 2 [2 y z - 13 x + 13 z, 4 x z + 5 y z + 5 x y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.3MB, alloc=32.3MB, time=0.49 memory used=46.6MB, alloc=32.3MB, time=0.79 memory used=64.1MB, alloc=56.3MB, time=1.07 memory used=104.9MB, alloc=68.3MB, time=1.68 memory used=144.7MB, alloc=92.3MB, time=2.26 memory used=207.1MB, alloc=92.3MB, time=3.20 memory used=269.5MB, alloc=92.3MB, time=4.13 memory used=329.9MB, alloc=116.3MB, time=5.09 memory used=405.6MB, alloc=372.3MB, time=6.27 memory used=487.6MB, alloc=372.3MB, time=7.54 memory used=570.1MB, alloc=396.3MB, time=8.81 memory used=675.0MB, alloc=420.3MB, time=10.54 memory used=806.6MB, alloc=444.3MB, time=12.60 memory used=963.3MB, alloc=468.3MB, time=15.18 memory used=1122.7MB, alloc=492.3MB, time=17.96 memory used=1292.9MB, alloc=516.3MB, time=21.00 memory used=1473.8MB, alloc=540.3MB, time=24.32 memory used=1668.9MB, alloc=564.3MB, time=27.91 memory used=1845.8MB, alloc=588.3MB, time=31.23 memory used=2041.8MB, alloc=612.3MB, time=34.82 memory used=2269.9MB, alloc=636.3MB, time=40.87 memory used=2478.0MB, alloc=660.3MB, time=48.12 memory used=2697.0MB, alloc=684.3MB, time=56.19 memory used=2929.5MB, alloc=708.3MB, time=64.93 memory used=3176.7MB, alloc=732.3MB, time=74.46 memory used=3429.7MB, alloc=756.3MB, time=85.05 memory used=3706.7MB, alloc=780.3MB, time=96.71 memory used=4007.5MB, alloc=804.3MB, time=109.53 memory used=4332.4MB, alloc=828.3MB, time=123.14 memory used=4681.1MB, alloc=852.3MB, time=137.83 memory used=5053.8MB, alloc=876.3MB, time=153.75 memory used=5450.5MB, alloc=876.3MB, time=170.50 memory used=5847.1MB, alloc=876.3MB, time=187.15 memory used=6243.6MB, alloc=876.3MB, time=203.64 memory used=6640.1MB, alloc=900.3MB, time=220.33 memory used=7060.4MB, alloc=900.3MB, time=237.80 memory used=7480.5MB, alloc=924.3MB, time=255.17 |\^/| 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(); 1428494796 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 3 F := [-4 y z + 5 y + 14 z, 10 x y z + 2 y - 3] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 2 2 G := [5 x + 10 x y + 19 y z, 7 y z + 10 y z - y z] > Problem := [F,G]; 2 2 3 Problem := [[-4 y z + 5 y + 14 z, 10 x y z + 2 y - 3], 3 2 2 2 2 [5 x + 10 x y + 19 y z, 7 y z + 10 y z - y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=25.5MB, alloc=32.3MB, time=0.49 memory used=45.4MB, alloc=32.3MB, time=0.79 memory used=63.0MB, alloc=56.3MB, time=1.07 memory used=102.5MB, alloc=60.3MB, time=1.65 memory used=142.7MB, alloc=84.3MB, time=2.25 memory used=204.5MB, alloc=92.3MB, time=3.21 memory used=268.3MB, alloc=92.3MB, time=4.15 memory used=333.9MB, alloc=116.3MB, time=5.09 memory used=408.5MB, alloc=372.3MB, time=6.27 memory used=496.1MB, alloc=396.3MB, time=7.62 memory used=604.7MB, alloc=396.3MB, time=9.31 memory used=713.9MB, alloc=420.3MB, time=10.86 memory used=841.5MB, alloc=444.3MB, time=12.58 memory used=967.7MB, alloc=444.3MB, time=14.25 memory used=1105.3MB, alloc=468.3MB, time=16.35 memory used=1271.1MB, alloc=492.3MB, time=18.94 memory used=1424.5MB, alloc=516.3MB, time=21.49 memory used=1620.6MB, alloc=540.3MB, time=24.52 memory used=1801.9MB, alloc=564.3MB, time=27.62 memory used=1971.1MB, alloc=588.3MB, time=30.74 memory used=2121.9MB, alloc=612.3MB, time=33.51 memory used=2286.8MB, alloc=636.3MB, time=36.75 memory used=2445.9MB, alloc=660.3MB, time=39.80 memory used=2603.2MB, alloc=684.3MB, time=42.83 memory used=2761.1MB, alloc=708.3MB, time=45.93 memory used=2910.3MB, alloc=732.3MB, time=48.99 memory used=3025.2MB, alloc=756.3MB, time=51.43 memory used=3154.1MB, alloc=780.3MB, time=53.97 memory used=3283.4MB, alloc=804.3MB, time=56.53 memory used=3405.3MB, alloc=828.3MB, time=59.16 memory used=3538.1MB, alloc=852.3MB, time=62.01 memory used=3650.1MB, alloc=876.3MB, time=64.48 memory used=3769.9MB, alloc=900.3MB, time=67.17 memory used=3869.6MB, alloc=900.3MB, time=69.39 memory used=3965.8MB, alloc=924.3MB, time=71.78 memory used=4180.4MB, alloc=948.3MB, time=79.38 memory used=4569.5MB, alloc=972.3MB, time=94.04 memory used=4960.6MB, alloc=996.3MB, time=109.28 memory used=5359.1MB, alloc=1020.3MB, time=125.37 memory used=5767.3MB, alloc=1044.3MB, time=141.97 memory used=6187.3MB, alloc=1068.3MB, time=159.64 memory used=6620.2MB, alloc=1092.3MB, time=178.21 memory used=7066.4MB, alloc=1116.3MB, time=197.45 memory used=7527.1MB, alloc=1140.3MB, time=217.41 memory used=8001.3MB, alloc=1164.3MB, time=237.89 memory used=8490.2MB, alloc=1188.3MB, time=259.14 |\^/| 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(); 1428495096 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 F := [-5 x + 7 z + 8 x, 8 x y z + x z - 5 y z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 3 2 G := [17 x + 13 x y - 13 x z, 9 y + 2 y - 8 z] > Problem := [F,G]; 3 2 Problem := [[-5 x + 7 z + 8 x, 8 x y z + x z - 5 y z], 3 2 3 2 [17 x + 13 x y - 13 x z, 9 y + 2 y - 8 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.3MB, alloc=32.3MB, time=0.48 memory used=47.4MB, alloc=32.3MB, time=0.79 memory used=67.4MB, alloc=56.3MB, time=1.10 memory used=107.1MB, alloc=60.3MB, time=1.69 memory used=146.2MB, alloc=60.3MB, time=2.24 memory used=185.5MB, alloc=84.3MB, time=2.75 memory used=230.1MB, alloc=84.3MB, time=3.27 memory used=292.7MB, alloc=92.3MB, time=4.36 memory used=348.6MB, alloc=116.3MB, time=5.34 memory used=424.9MB, alloc=140.3MB, time=6.62 memory used=511.2MB, alloc=164.3MB, time=8.56 memory used=602.6MB, alloc=188.3MB, time=11.49 memory used=709.8MB, alloc=212.3MB, time=15.38 memory used=841.0MB, alloc=212.3MB, time=20.11 memory used=972.4MB, alloc=236.3MB, time=24.74 N1 := 3961 > GB := Basis(F, plex(op(vars))); 4 4 3 2 2 GB := [40 x y + 5 x - 25 x y - 64 x y - 8 x + 40 x y, 3 2 8 x y z + x z - 5 y z, -5 x + 7 z + 8 x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1073.3MB, alloc=236.3MB, time=26.59 memory used=1261.6MB, alloc=492.3MB, time=29.61 memory used=1442.7MB, alloc=516.3MB, time=33.12 memory used=1611.9MB, alloc=540.3MB, time=39.55 memory used=1788.6MB, alloc=564.3MB, time=46.49 N2 := 3961 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 3 2 H := [-5 x + 7 z + 8 x, 8 x y z + x z - 5 y z, 17 x + 13 x y - 13 x z, 3 2 9 y + 2 y - 8 z] > J:=[op(GB),op(G)]; 4 4 3 2 2 J := [40 x y + 5 x - 25 x y - 64 x y - 8 x + 40 x y, 8 x y z + x z - 5 y z, 3 2 3 2 3 2 -5 x + 7 z + 8 x, 17 x + 13 x y - 13 x z, 9 y + 2 y - 8 z] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 10, 12, 3, 3, 3, 2, 3/4, 3/4, 1, 7/12, 5/12, 1/2, 5, 12, 17, 13 5, 4, 3, 2, 4/5, 4/5, 4/5, --, 1/2, 1/3, -2, -5, -2] 18 > save(F, G, cat("ranSet/33", convert(F, string),".txt")); > quit memory used=1959.3MB, alloc=564.3MB, time=52.47 |\^/| 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(); 1428495158 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 3 3 2 2 F := [16 x + 15 y - 9 x z, -6 x - 9 y z + 4 y z ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 3 3 G := [-7 x z + 15 y z - 20 y, 2 x + 10 z + 10 x z] > Problem := [F,G]; 3 3 3 2 2 Problem := [[16 x + 15 y - 9 x z, -6 x - 9 y z + 4 y z ], 2 2 3 3 [-7 x z + 15 y z - 20 y, 2 x + 10 z + 10 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=25.1MB, alloc=32.3MB, time=0.33 memory used=49.7MB, alloc=38.4MB, time=0.56 memory used=66.9MB, alloc=38.4MB, time=0.61 memory used=78.0MB, alloc=38.4MB, time=0.64 memory used=94.2MB, alloc=38.4MB, time=0.71 memory used=114.8MB, alloc=38.5MB, time=0.77 memory used=127.3MB, alloc=38.5MB, time=0.81 memory used=140.0MB, alloc=38.5MB, time=0.84 memory used=166.9MB, alloc=38.5MB, time=2.26 memory used=189.3MB, alloc=38.5MB, time=2.35 memory used=201.9MB, alloc=38.5MB, time=2.38 memory used=218.4MB, alloc=38.5MB, time=2.42 memory used=228.6MB, alloc=38.5MB, time=2.45 memory used=239.5MB, alloc=38.5MB, time=2.49 memory used=251.7MB, alloc=38.5MB, time=2.52 memory used=265.9MB, alloc=38.5MB, time=2.55 memory used=282.2MB, alloc=38.5MB, time=2.61 memory used=304.1MB, alloc=38.5MB, time=2.68 memory used=317.1MB, alloc=38.5MB, time=2.72 memory used=329.4MB, alloc=38.5MB, time=2.75 memory used=350.2MB, alloc=38.5MB, time=2.84 memory used=366.5MB, alloc=38.5MB, time=2.88 memory used=377.9MB, alloc=38.5MB, time=2.92 memory used=397.4MB, alloc=38.5MB, time=3.46 memory used=425.4MB, alloc=38.5MB, time=4.39 memory used=439.4MB, alloc=38.5MB, time=4.43 memory used=453.4MB, alloc=38.5MB, time=4.47 memory used=467.6MB, alloc=38.5MB, time=4.51 memory used=477.5MB, alloc=38.5MB, time=4.54 memory used=488.7MB, alloc=38.5MB, time=4.57 memory used=501.4MB, alloc=38.5MB, time=4.60 memory used=516.1MB, alloc=38.5MB, time=4.64 memory used=533.6MB, alloc=38.5MB, time=4.71 memory used=551.8MB, alloc=38.5MB, time=4.91 memory used=582.9MB, alloc=38.5MB, time=5.74 memory used=597.9MB, alloc=38.5MB, time=5.78 memory used=610.4MB, alloc=38.5MB, time=5.82 memory used=623.2MB, alloc=38.5MB, time=5.86 memory used=632.1MB, alloc=38.5MB, time=5.89 memory used=642.6MB, alloc=38.5MB, time=5.92 memory used=655.2MB, alloc=38.5MB, time=5.95 memory used=681.3MB, alloc=38.5MB, time=6.18 memory used=705.1MB, alloc=38.6MB, time=6.46 memory used=725.3MB, alloc=38.6MB, time=6.75 memory used=744.5MB, alloc=38.6MB, time=6.84 memory used=767.8MB, alloc=38.6MB, time=7.26 memory used=783.4MB, alloc=38.6MB, time=7.35 memory used=804.2MB, alloc=62.6MB, time=7.59 memory used=844.2MB, alloc=62.6MB, time=7.98 memory used=878.6MB, alloc=62.6MB, time=8.08 memory used=904.5MB, alloc=62.6MB, time=8.15 memory used=933.6MB, alloc=62.6MB, time=8.23 memory used=954.4MB, alloc=62.6MB, time=8.29 memory used=985.7MB, alloc=62.6MB, time=8.47 memory used=1011.1MB, alloc=62.6MB, time=8.60 memory used=1042.8MB, alloc=62.6MB, time=8.83 memory used=1074.2MB, alloc=62.6MB, time=8.92 memory used=1101.4MB, alloc=62.6MB, time=9.00 memory used=1129.3MB, alloc=62.6MB, time=9.06 memory used=1150.7MB, alloc=62.6MB, time=9.12 memory used=1182.4MB, alloc=62.6MB, time=9.37 memory used=1208.2MB, alloc=62.6MB, time=9.45 memory used=1248.4MB, alloc=62.6MB, time=12.07 memory used=1289.4MB, alloc=62.6MB, time=12.72 memory used=1319.1MB, alloc=62.6MB, time=12.81 memory used=1340.0MB, alloc=62.6MB, time=12.87 memory used=1365.2MB, alloc=62.6MB, time=12.95 memory used=1395.0MB, alloc=62.6MB, time=13.01 memory used=1423.2MB, alloc=62.6MB, time=13.08 memory used=1442.1MB, alloc=62.6MB, time=13.13 memory used=1462.9MB, alloc=62.6MB, time=13.18 memory used=1485.9MB, alloc=62.6MB, time=13.23 memory used=1511.8MB, alloc=62.6MB, time=13.29 memory used=1545.2MB, alloc=62.6MB, time=13.56 memory used=1571.6MB, alloc=62.6MB, time=13.69 memory used=1598.0MB, alloc=62.6MB, time=13.77 memory used=1639.0MB, alloc=79.5MB, time=14.03 memory used=1665.1MB, alloc=79.5MB, time=14.09 memory used=1703.6MB, alloc=79.5MB, time=14.21 memory used=1730.7MB, alloc=79.5MB, time=14.26 memory used=1760.4MB, alloc=79.5MB, time=14.58 memory used=1800.1MB, alloc=79.5MB, time=14.86 memory used=1846.1MB, alloc=79.5MB, time=17.53 memory used=1896.0MB, alloc=79.5MB, time=17.83 memory used=1923.7MB, alloc=79.5MB, time=17.92 memory used=1945.9MB, alloc=79.5MB, time=17.99 memory used=1968.7MB, alloc=79.5MB, time=18.05 memory used=1995.7MB, alloc=79.5MB, time=18.13 memory used=2027.7MB, alloc=79.5MB, time=18.22 memory used=2047.5MB, alloc=79.5MB, time=18.28 memory used=2066.6MB, alloc=79.5MB, time=18.33 memory used=2087.3MB, alloc=79.5MB, time=18.39 memory used=2110.2MB, alloc=79.5MB, time=18.46 memory used=2135.7MB, alloc=79.5MB, time=18.52 memory used=2171.2MB, alloc=79.5MB, time=18.72 memory used=2205.1MB, alloc=79.5MB, time=18.96 memory used=2248.8MB, alloc=79.5MB, time=20.29 memory used=2290.7MB, alloc=79.5MB, time=20.65 memory used=2317.8MB, alloc=79.5MB, time=20.74 memory used=2340.1MB, alloc=79.5MB, time=20.82 memory used=2363.9MB, alloc=79.5MB, time=20.89 memory used=2392.5MB, alloc=79.5MB, time=20.98 memory used=2416.3MB, alloc=79.5MB, time=21.04 memory used=2435.5MB, alloc=79.5MB, time=21.10 memory used=2457.4MB, alloc=79.5MB, time=21.16 memory used=2507.7MB, alloc=79.5MB, time=21.71 memory used=2561.8MB, alloc=79.5MB, time=22.13 memory used=2616.8MB, alloc=79.5MB, time=22.51 memory used=2673.1MB, alloc=79.5MB, time=22.97 memory used=2728.6MB, alloc=79.5MB, time=23.53 memory used=2784.8MB, alloc=79.5MB, time=24.20 memory used=2839.5MB, alloc=79.5MB, time=25.08 memory used=2895.4MB, alloc=79.5MB, time=26.00 memory used=2950.9MB, alloc=79.5MB, time=27.10 memory used=3006.1MB, alloc=79.5MB, time=28.47 memory used=3061.5MB, alloc=79.5MB, time=29.86 memory used=3107.9MB, alloc=79.5MB, time=30.87 memory used=3139.9MB, alloc=79.5MB, time=31.14 memory used=3181.7MB, alloc=79.5MB, time=31.69 memory used=3219.4MB, alloc=79.5MB, time=32.00 memory used=3244.3MB, alloc=79.5MB, time=32.07 memory used=3262.9MB, alloc=79.5MB, time=32.15 memory used=3285.5MB, alloc=79.5MB, time=32.22 memory used=3312.2MB, alloc=79.5MB, time=32.30 memory used=3331.3MB, alloc=79.5MB, time=32.35 memory used=3348.4MB, alloc=79.5MB, time=32.41 memory used=3367.6MB, alloc=79.5MB, time=32.47 memory used=3389.5MB, alloc=79.5MB, time=32.53 memory 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memory used=5151.6MB, alloc=127.5MB, time=55.86 memory used=5186.5MB, alloc=127.5MB, time=55.96 memory used=5224.4MB, alloc=127.5MB, time=56.07 memory used=5266.5MB, alloc=127.5MB, time=56.17 memory used=5312.0MB, alloc=127.5MB, time=56.28 memory used=5365.0MB, alloc=127.5MB, time=56.40 memory used=5420.8MB, alloc=127.5MB, time=56.74 memory used=5502.0MB, alloc=127.5MB, time=57.45 memory used=5573.7MB, alloc=127.5MB, time=57.84 memory used=5618.3MB, alloc=127.5MB, time=58.00 memory used=5666.0MB, alloc=127.5MB, time=58.15 memory used=5703.6MB, alloc=127.5MB, time=58.29 memory used=5768.3MB, alloc=127.5MB, time=58.59 memory used=5811.4MB, alloc=127.5MB, time=58.75 memory used=5860.6MB, alloc=127.5MB, time=58.90 memory used=5897.3MB, alloc=127.5MB, time=59.03 memory used=5983.6MB, alloc=127.5MB, time=64.32 memory used=6030.7MB, alloc=127.5MB, time=64.46 memory used=6069.0MB, alloc=127.5MB, time=64.59 memory used=6118.2MB, alloc=127.5MB, time=64.72 memory used=6157.3MB, alloc=127.5MB, time=64.84 memory used=6215.7MB, alloc=127.5MB, time=65.10 memory used=6260.5MB, alloc=127.5MB, time=65.28 memory used=6313.5MB, alloc=127.5MB, time=65.45 memory used=6350.8MB, alloc=127.5MB, time=65.57 memory used=6410.3MB, alloc=127.5MB, time=65.85 memory used=6455.4MB, alloc=127.5MB, time=66.01 memory used=6507.5MB, alloc=127.5MB, time=66.16 memory used=6545.1MB, alloc=127.5MB, time=66.30 memory used=6613.6MB, alloc=127.5MB, time=71.54 memory used=6676.1MB, alloc=127.5MB, time=71.80 memory used=6717.7MB, alloc=127.5MB, time=71.94 memory used=6762.4MB, alloc=127.5MB, time=72.09 memory used=6808.7MB, alloc=127.5MB, time=72.23 memory used=6848.5MB, alloc=127.5MB, time=72.37 memory used=6919.9MB, alloc=127.5MB, time=73.25 memory used=6973.4MB, alloc=127.5MB, time=73.62 memory used=7029.1MB, alloc=127.5MB, time=74.29 memory used=7082.1MB, alloc=383.5MB, time=74.87 memory used=7154.9MB, alloc=383.5MB, time=75.87 memory used=7192.7MB, alloc=383.5MB, time=76.00 memory used=7285.9MB, 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time=219.26 memory used=24359.7MB, alloc=455.5MB, time=219.56 memory used=24505.7MB, alloc=455.5MB, time=219.85 memory used=24675.2MB, alloc=455.5MB, time=220.66 memory used=24835.5MB, alloc=455.5MB, time=221.11 memory used=25004.9MB, alloc=455.5MB, time=225.22 memory used=25107.3MB, alloc=479.5MB, time=305.25 |\^/| 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(); 1428495458 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 F := [-18 x y + 4 x z + 4 y z, -2 x - 2 x z + 5 z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 3 2 2 G := [-15 x - z - 4 x z, -7 x z - 8 y + x] > Problem := [F,G]; 2 3 2 Problem := [[-18 x y + 4 x z + 4 y z, -2 x - 2 x z + 5 z], 3 3 2 2 [-15 x - z - 4 x z, -7 x z - 8 y + x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=25.7MB, alloc=32.3MB, time=0.51 memory used=47.3MB, alloc=36.3MB, time=0.80 memory used=65.9MB, alloc=60.3MB, time=1.07 memory used=109.4MB, alloc=60.3MB, time=1.69 memory used=150.9MB, alloc=60.3MB, time=2.32 memory used=192.3MB, alloc=60.3MB, time=2.96 memory used=229.6MB, alloc=84.3MB, time=3.50 memory used=293.6MB, alloc=92.3MB, time=4.38 memory used=356.8MB, alloc=92.3MB, time=5.24 memory used=416.1MB, alloc=92.3MB, time=5.78 memory used=489.9MB, alloc=92.3MB, time=6.58 memory used=547.1MB, alloc=92.3MB, time=7.11 memory used=615.0MB, alloc=348.3MB, time=7.95 memory used=677.4MB, alloc=372.3MB, time=8.95 memory used=767.2MB, alloc=372.3MB, time=9.91 memory used=851.0MB, alloc=372.3MB, time=11.28 memory used=939.1MB, alloc=396.3MB, time=12.64 memory used=1052.7MB, alloc=396.3MB, time=14.14 memory used=1165.7MB, alloc=396.3MB, time=15.65 memory used=1257.0MB, alloc=396.3MB, time=16.47 memory used=1319.6MB, alloc=396.3MB, time=16.84 memory used=1399.4MB, alloc=396.3MB, time=17.54 memory used=1451.9MB, alloc=396.3MB, time=17.80 memory used=1538.1MB, alloc=396.3MB, time=18.65 memory used=1691.3MB, alloc=428.3MB, time=20.80 memory used=1849.0MB, alloc=428.3MB, time=22.56 memory used=2000.3MB, alloc=428.3MB, time=24.28 memory used=2149.0MB, alloc=428.3MB, time=25.90 memory used=2266.1MB, alloc=452.3MB, time=26.65 memory used=2428.0MB, alloc=452.3MB, time=27.81 memory used=2593.4MB, alloc=452.3MB, time=29.03 memory used=2739.3MB, alloc=452.3MB, time=29.88 memory used=2883.1MB, alloc=452.3MB, time=30.74 memory used=3040.1MB, alloc=452.3MB, time=31.92 memory used=3206.9MB, alloc=452.3MB, time=33.10 memory used=3374.6MB, alloc=476.3MB, time=35.49 memory used=3536.2MB, alloc=500.3MB, time=38.35 memory used=3723.2MB, alloc=524.3MB, time=41.46 memory used=3940.6MB, alloc=524.3MB, time=44.60 memory used=4139.1MB, alloc=548.3MB, time=47.88 memory used=4364.9MB, alloc=572.3MB, time=51.66 memory used=4618.4MB, alloc=596.3MB, time=55.30 memory used=4860.9MB, alloc=620.3MB, time=59.37 memory used=5087.7MB, alloc=644.3MB, time=63.00 memory used=5405.5MB, alloc=668.3MB, time=66.92 memory used=5747.8MB, alloc=692.3MB, time=70.79 memory used=6024.5MB, alloc=692.3MB, time=74.33 memory used=6329.8MB, alloc=716.3MB, time=78.17 memory used=6721.2MB, alloc=716.3MB, time=82.44 memory used=7062.5MB, alloc=740.3MB, time=86.68 memory used=7355.6MB, alloc=764.3MB, time=90.61 memory used=7731.0MB, alloc=764.3MB, time=94.79 memory used=8053.3MB, alloc=788.3MB, time=98.46 memory used=8406.7MB, alloc=788.3MB, time=102.50 memory used=8675.7MB, alloc=788.3MB, time=106.12 memory used=8933.8MB, alloc=812.3MB, time=110.10 memory used=9192.3MB, alloc=836.3MB, time=114.14 memory used=9552.9MB, alloc=860.3MB, time=118.61 memory used=9760.7MB, alloc=860.3MB, time=122.35 memory used=9960.1MB, alloc=884.3MB, time=126.11 memory used=10134.0MB, alloc=908.3MB, time=129.57 memory used=10290.4MB, alloc=932.3MB, time=132.92 memory used=10498.5MB, alloc=956.3MB, time=139.28 memory used=10739.8MB, alloc=980.3MB, time=148.25 memory used=10990.9MB, alloc=1004.3MB, time=158.58 memory used=11417.3MB, alloc=1028.3MB, time=175.25 memory used=11842.9MB, alloc=1052.3MB, time=191.58 memory used=12272.9MB, alloc=1076.3MB, time=208.91 memory used=12710.0MB, alloc=1100.3MB, time=227.26 |\^/| 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(); 1428495758 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 F := [11 x z - 2 y z - 1, 8 x z - 8 x - 7] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 G := [-10 x z + 7 x y + 5, -7 x y - 4 z - y] > Problem := [F,G]; 2 2 Problem := [[11 x z - 2 y z - 1, 8 x z - 8 x - 7], 2 2 2 [-10 x z + 7 x y + 5, -7 x y - 4 z - y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.6MB, alloc=32.3MB, time=0.52 memory used=46.4MB, alloc=56.3MB, time=0.83 memory used=86.6MB, alloc=60.3MB, time=1.44 memory used=127.4MB, alloc=84.3MB, time=2.07 memory used=167.3MB, alloc=84.3MB, time=2.71 memory used=232.7MB, alloc=92.3MB, time=3.74 memory used=295.7MB, alloc=116.3MB, time=4.76 memory used=373.6MB, alloc=116.3MB, time=5.99 memory used=448.7MB, alloc=372.3MB, time=6.96 memory used=531.8MB, alloc=396.3MB, time=8.11 memory used=642.6MB, alloc=396.3MB, time=9.73 memory used=724.3MB, alloc=396.3MB, time=10.57 memory used=835.2MB, alloc=420.3MB, time=11.84 memory used=961.4MB, alloc=420.3MB, time=13.43 memory used=1089.0MB, alloc=444.3MB, time=15.64 memory used=1234.3MB, alloc=468.3MB, time=17.78 memory used=1371.6MB, alloc=468.3MB, time=19.06 memory used=1535.3MB, alloc=468.3MB, time=20.60 memory used=1720.1MB, alloc=468.3MB, time=22.23 memory used=1860.1MB, alloc=468.3MB, time=23.05 memory used=2036.7MB, alloc=492.3MB, time=25.07 memory used=2208.3MB, alloc=492.3MB, time=27.26 memory used=2399.3MB, alloc=516.3MB, time=30.12 memory used=2590.5MB, alloc=540.3MB, time=33.53 memory used=2821.5MB, alloc=564.3MB, time=36.52 memory used=3059.7MB, alloc=588.3MB, time=39.98 memory used=3258.9MB, alloc=612.3MB, time=43.07 memory used=3438.2MB, alloc=636.3MB, time=46.56 memory used=3609.3MB, alloc=660.3MB, time=49.94 memory used=3788.2MB, alloc=684.3MB, time=53.17 memory used=3924.7MB, alloc=684.3MB, time=55.89 memory used=4096.3MB, alloc=708.3MB, time=58.98 memory used=4231.3MB, alloc=732.3MB, time=61.71 memory used=4349.2MB, alloc=732.3MB, time=64.15 memory used=4476.5MB, alloc=756.3MB, time=66.67 memory used=4625.7MB, alloc=780.3MB, time=69.71 memory used=4771.5MB, alloc=804.3MB, time=72.40 memory used=5018.2MB, alloc=828.3MB, time=80.55 memory used=5343.0MB, alloc=852.3MB, time=92.60 memory used=5612.8MB, alloc=876.3MB, time=103.66 memory used=5964.3MB, alloc=900.3MB, time=118.52 memory used=6324.3MB, alloc=924.3MB, time=133.82 memory used=6694.0MB, alloc=948.3MB, time=149.59 memory used=7075.8MB, alloc=972.3MB, time=166.17 memory used=7465.5MB, alloc=996.3MB, time=184.21 memory used=7875.5MB, alloc=1020.3MB, time=203.56 memory used=8309.4MB, alloc=1044.3MB, time=223.42 memory used=8767.1MB, alloc=1068.3MB, time=243.97 |\^/| 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(); 1428496058 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 3 F := [16 x y + y z - 13 x , 10 x z + 5 y - 5 y] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 3 G := [-17 x z - 10 y + 7, -7 x z + 10 y - 4 x z] > Problem := [F,G]; 2 2 2 2 3 Problem := [[16 x y + y z - 13 x , 10 x z + 5 y - 5 y], 2 2 2 3 [-17 x z - 10 y + 7, -7 x z + 10 y - 4 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.19 memory used=24.8MB, alloc=32.3MB, time=0.48 memory used=44.8MB, alloc=36.3MB, time=0.76 memory used=67.3MB, alloc=36.3MB, time=1.01 memory used=86.0MB, alloc=36.3MB, time=1.13 memory used=96.7MB, alloc=36.3MB, time=1.16 memory used=107.9MB, alloc=36.3MB, time=1.20 memory used=128.1MB, alloc=36.3MB, time=1.42 memory used=139.4MB, alloc=60.3MB, time=1.48 memory used=178.2MB, alloc=60.3MB, time=1.72 memory used=238.4MB, alloc=69.6MB, time=2.37 memory used=286.3MB, alloc=69.6MB, time=2.92 memory used=330.1MB, alloc=69.6MB, time=4.23 memory used=355.5MB, alloc=69.6MB, time=4.30 memory used=376.5MB, alloc=69.6MB, time=4.37 memory used=403.3MB, alloc=69.6MB, time=4.44 memory used=424.0MB, alloc=69.6MB, time=4.49 memory used=451.0MB, alloc=69.6MB, time=4.64 memory used=494.3MB, alloc=69.6MB, time=5.03 memory used=537.2MB, alloc=69.6MB, time=5.54 memory used=578.8MB, alloc=69.6MB, time=6.12 memory used=623.1MB, alloc=93.6MB, time=6.74 memory used=676.3MB, alloc=93.6MB, time=7.09 memory used=720.5MB, alloc=93.6MB, time=7.24 memory used=769.0MB, alloc=93.6MB, time=8.70 memory used=806.2MB, alloc=93.6MB, time=8.81 memory used=842.1MB, alloc=93.6MB, time=8.92 memory used=880.3MB, alloc=93.6MB, time=9.06 memory used=925.1MB, alloc=93.6MB, time=9.23 memory used=974.3MB, alloc=93.6MB, time=10.65 memory used=1009.3MB, alloc=93.6MB, time=10.77 memory used=1047.0MB, alloc=93.6MB, time=10.87 memory used=1083.2MB, alloc=93.6MB, time=11.00 memory used=1124.6MB, alloc=93.6MB, time=11.38 memory used=1175.4MB, alloc=93.6MB, time=11.73 memory used=1220.5MB, alloc=93.6MB, time=11.90 memory used=1272.0MB, alloc=93.6MB, time=16.49 memory used=1317.6MB, alloc=93.6MB, time=18.14 memory used=1351.1MB, alloc=93.6MB, time=18.25 memory used=1383.8MB, alloc=93.6MB, time=18.34 memory used=1424.3MB, alloc=93.6MB, time=18.45 memory used=1455.2MB, alloc=93.6MB, time=18.54 memory used=1482.0MB, alloc=93.6MB, time=18.62 memory used=1510.9MB, alloc=93.6MB, time=18.70 memory used=1543.7MB, alloc=93.6MB, time=18.79 memory used=1582.8MB, alloc=93.6MB, time=18.87 memory used=1625.3MB, alloc=93.6MB, time=19.18 memory used=1684.8MB, alloc=93.6MB, time=22.08 memory used=1723.1MB, alloc=93.6MB, time=22.20 memory used=1754.2MB, alloc=93.6MB, time=22.30 memory used=1794.2MB, alloc=93.6MB, time=22.39 memory used=1822.2MB, alloc=93.6MB, time=22.47 memory used=1851.8MB, alloc=93.6MB, time=22.55 memory used=1893.3MB, alloc=93.6MB, time=22.78 memory used=1927.9MB, alloc=93.6MB, time=22.95 memory used=1969.7MB, alloc=93.6MB, time=23.17 memory used=2013.7MB, alloc=93.6MB, time=23.36 memory used=2075.4MB, alloc=93.6MB, time=29.08 memory used=2111.6MB, alloc=93.6MB, time=29.19 memory used=2141.1MB, alloc=93.6MB, time=29.29 memory used=2177.8MB, alloc=93.6MB, time=29.40 memory used=2216.4MB, alloc=93.6MB, time=29.49 memory used=2242.0MB, alloc=93.6MB, time=29.57 memory used=2269.2MB, alloc=93.6MB, time=29.64 memory used=2299.7MB, alloc=93.6MB, time=29.72 memory used=2335.0MB, alloc=93.6MB, time=29.81 memory used=2382.3MB, alloc=93.6MB, time=30.08 memory used=2420.2MB, alloc=93.6MB, time=30.30 memory used=2453.2MB, alloc=93.6MB, time=30.40 memory used=2486.8MB, alloc=93.6MB, time=30.50 memory used=2522.4MB, alloc=93.6MB, time=30.60 memory used=2562.5MB, alloc=93.6MB, time=30.91 memory used=2606.9MB, alloc=93.6MB, time=31.16 memory used=2686.4MB, alloc=93.6MB, time=31.98 memory used=2770.0MB, alloc=93.6MB, time=32.75 memory used=2824.0MB, alloc=93.6MB, time=33.73 memory used=2852.5MB, alloc=93.6MB, time=33.83 memory used=2886.4MB, alloc=93.6MB, time=33.93 memory used=2912.0MB, alloc=93.6MB, time=34.01 memory used=2991.5MB, alloc=349.6MB, time=34.77 memory used=3053.4MB, alloc=373.6MB, time=35.69 memory used=3135.8MB, alloc=373.6MB, time=36.46 memory used=3223.1MB, alloc=373.6MB, time=37.34 memory used=3287.7MB, alloc=373.6MB, time=39.66 memory used=3327.8MB, alloc=373.6MB, time=39.81 memory used=3373.5MB, alloc=373.6MB, time=39.97 memory used=3408.2MB, alloc=373.6MB, time=40.10 memory used=3445.6MB, alloc=373.6MB, time=40.22 memory used=3510.6MB, alloc=373.6MB, time=41.56 memory used=3549.1MB, alloc=373.6MB, time=41.71 memory used=3588.1MB, alloc=373.6MB, time=41.84 memory used=3648.3MB, alloc=373.6MB, time=43.83 memory used=3701.8MB, alloc=373.6MB, time=44.54 memory used=3739.8MB, alloc=373.6MB, time=44.68 memory used=3784.8MB, alloc=373.6MB, time=44.82 memory used=3816.9MB, alloc=373.6MB, time=44.94 memory used=3862.3MB, alloc=373.6MB, time=45.13 memory used=3958.1MB, alloc=373.6MB, time=46.56 memory used=3996.4MB, alloc=373.6MB, time=46.71 memory used=4075.3MB, alloc=373.6MB, time=47.42 memory used=4153.5MB, alloc=397.6MB, time=48.33 memory used=4234.8MB, alloc=397.6MB, time=48.89 memory used=4296.2MB, alloc=397.6MB, time=49.13 memory used=4364.6MB, alloc=397.6MB, time=50.50 memory used=4420.6MB, alloc=397.6MB, time=50.70 memory used=4465.6MB, alloc=397.6MB, time=50.85 memory used=4536.9MB, alloc=397.6MB, time=51.40 memory used=4592.8MB, alloc=397.6MB, time=51.61 memory used=4696.3MB, alloc=397.6MB, time=54.96 memory used=4751.4MB, alloc=397.6MB, time=55.24 memory used=4811.7MB, alloc=397.6MB, time=55.43 memory used=4854.0MB, alloc=397.6MB, time=55.58 memory used=4902.1MB, alloc=397.6MB, time=55.75 memory used=4961.8MB, alloc=397.6MB, time=55.94 memory used=5056.6MB, alloc=397.6MB, time=57.25 memory used=5110.2MB, alloc=397.6MB, time=57.47 memory used=5156.8MB, alloc=397.6MB, time=57.65 memory used=5209.3MB, alloc=397.6MB, time=57.82 memory used=5288.5MB, alloc=397.6MB, time=58.32 memory used=5406.5MB, alloc=397.6MB, time=60.93 memory used=5465.0MB, alloc=397.6MB, time=61.18 memory used=5509.3MB, alloc=397.6MB, time=61.36 memory used=5590.8MB, alloc=397.6MB, time=64.39 memory used=5642.9MB, alloc=397.6MB, time=64.62 memory used=5700.8MB, alloc=397.6MB, time=64.82 memory used=5745.8MB, alloc=397.6MB, time=64.99 memory used=5790.9MB, alloc=397.6MB, time=65.17 memory used=5843.3MB, alloc=397.6MB, time=65.34 memory used=5905.9MB, alloc=397.6MB, time=65.53 memory used=6006.1MB, alloc=397.6MB, time=65.98 memory used=6085.1MB, alloc=397.6MB, time=66.50 memory used=6224.1MB, alloc=397.6MB, time=67.40 memory used=6345.5MB, alloc=397.6MB, time=68.56 memory used=6468.7MB, alloc=397.6MB, time=70.69 memory used=6591.1MB, alloc=397.6MB, time=73.72 memory used=6735.9MB, alloc=397.6MB, time=77.47 memory used=6828.0MB, alloc=421.6MB, time=78.40 memory used=6982.4MB, alloc=421.6MB, time=79.38 memory used=7132.0MB, alloc=421.6MB, time=81.57 memory used=7280.5MB, alloc=421.6MB, time=85.41 memory used=7431.6MB, alloc=421.6MB, time=91.37 memory used=7550.1MB, alloc=421.6MB, time=93.11 memory used=7621.2MB, alloc=421.6MB, time=93.47 memory used=7754.2MB, alloc=421.6MB, time=95.14 memory used=7818.3MB, alloc=421.6MB, time=95.37 memory used=7900.3MB, alloc=421.6MB, time=97.68 memory used=7976.6MB, alloc=421.6MB, time=98.76 memory used=8049.3MB, alloc=421.6MB, time=99.01 memory used=8101.0MB, alloc=421.6MB, time=99.19 memory used=8163.7MB, alloc=421.6MB, time=99.39 memory used=8242.1MB, alloc=421.6MB, time=99.60 memory used=8374.9MB, alloc=421.6MB, time=100.23 memory used=8447.5MB, alloc=421.6MB, time=100.69 memory used=8539.7MB, alloc=421.6MB, time=101.22 memory used=8705.6MB, alloc=421.6MB, time=102.47 memory used=8772.3MB, alloc=421.6MB, time=102.78 memory used=8862.8MB, alloc=421.6MB, time=103.65 memory used=8981.5MB, alloc=421.6MB, time=105.12 memory used=9100.7MB, alloc=421.6MB, time=106.61 memory used=9212.1MB, alloc=421.6MB, time=107.98 memory used=9331.1MB, alloc=445.6MB, time=109.77 memory used=9432.5MB, alloc=445.6MB, time=112.10 memory used=9496.5MB, alloc=445.6MB, time=112.35 memory used=9587.9MB, alloc=445.6MB, time=113.30 memory used=9690.7MB, alloc=445.6MB, time=117.33 memory used=9760.0MB, alloc=445.6MB, time=117.61 memory used=9818.0MB, alloc=445.6MB, time=117.85 memory used=9935.7MB, alloc=445.6MB, time=120.55 memory used=10001.7MB, alloc=445.6MB, time=120.84 memory used=10084.6MB, alloc=445.6MB, time=121.81 memory used=10155.6MB, alloc=445.6MB, time=122.16 memory used=10299.5MB, alloc=445.6MB, time=124.77 memory used=10403.2MB, alloc=445.6MB, time=125.65 memory used=10583.2MB, alloc=445.6MB, time=127.38 memory used=10737.3MB, alloc=445.6MB, time=129.87 memory used=10801.3MB, alloc=445.6MB, time=130.17 memory used=10872.7MB, alloc=469.6MB, time=130.66 memory used=10956.6MB, alloc=469.6MB, time=131.00 memory used=11019.9MB, alloc=469.6MB, time=131.25 memory used=11097.7MB, alloc=469.6MB, time=131.53 memory used=11194.6MB, alloc=469.6MB, time=131.83 memory used=11381.6MB, alloc=469.6MB, time=132.75 memory used=11463.5MB, alloc=469.6MB, time=133.09 memory used=11530.8MB, alloc=469.6MB, time=133.37 memory used=11613.0MB, alloc=469.6MB, time=133.71 memory used=11826.6MB, alloc=469.6MB, time=138.21 memory used=11936.9MB, alloc=493.6MB, time=191.13 memory used=12042.9MB, alloc=493.6MB, time=192.71 memory used=12127.4MB, alloc=493.6MB, time=193.07 memory used=12217.0MB, alloc=493.6MB, time=193.45 memory used=12327.2MB, alloc=493.6MB, time=193.84 memory used=12502.2MB, alloc=493.6MB, time=194.44 memory used=12658.8MB, alloc=493.6MB, time=194.93 memory used=12836.6MB, alloc=493.6MB, time=195.43 memory used=13038.3MB, alloc=493.6MB, time=196.01 memory used=13263.6MB, alloc=493.6MB, time=196.58 memory used=13450.8MB, alloc=493.6MB, time=197.11 memory used=13630.2MB, alloc=493.6MB, time=197.61 memory used=13820.1MB, alloc=493.6MB, time=198.14 memory used=14023.9MB, alloc=493.6MB, time=198.70 memory used=14246.2MB, alloc=493.6MB, time=199.27 memory used=14479.9MB, alloc=493.6MB, time=199.83 memory used=14673.1MB, alloc=493.6MB, time=200.41 memory used=14874.2MB, alloc=493.6MB, time=200.95 memory used=15087.1MB, alloc=493.6MB, time=201.49 memory used=15315.7MB, alloc=493.6MB, time=202.04 memory used=15539.1MB, alloc=493.6MB, time=202.57 memory used=15752.0MB, alloc=493.6MB, time=203.11 memory used=15898.6MB, alloc=493.6MB, time=204.04 memory used=16135.3MB, alloc=493.6MB, time=204.64 memory used=16351.7MB, alloc=493.6MB, time=206.84 memory used=16447.7MB, alloc=493.6MB, time=207.21 memory used=16528.0MB, alloc=493.6MB, time=207.53 memory used=16631.1MB, alloc=493.6MB, time=207.88 memory used=16762.8MB, alloc=493.6MB, time=212.16 memory used=16851.4MB, alloc=493.6MB, time=212.50 memory used=17089.6MB, alloc=493.6MB, time=213.11 memory used=17282.4MB, alloc=493.6MB, time=213.61 memory used=17486.2MB, alloc=493.6MB, time=214.11 memory used=17732.3MB, alloc=493.6MB, time=214.91 memory used=18021.4MB, alloc=493.6MB, time=216.75 memory used=18171.8MB, alloc=493.6MB, time=218.56 memory used=18331.2MB, alloc=493.6MB, time=220.12 memory used=18430.4MB, alloc=493.6MB, time=221.56 memory used=18541.6MB, alloc=493.6MB, time=223.29 memory used=18704.8MB, alloc=493.6MB, time=225.22 memory used=18808.0MB, alloc=493.6MB, time=226.69 memory used=18904.6MB, alloc=493.6MB, time=228.29 memory used=18998.2MB, alloc=493.6MB, time=230.03 memory used=19096.4MB, alloc=517.6MB, time=232.14 memory used=19217.3MB, alloc=517.6MB, time=233.11 memory used=19354.1MB, alloc=517.6MB, time=236.75 memory used=19476.8MB, alloc=517.6MB, time=238.61 memory used=19628.0MB, alloc=517.6MB, time=240.38 memory used=19778.0MB, alloc=517.6MB, time=246.52 memory used=19879.1MB, alloc=517.6MB, time=247.38 memory used=19968.9MB, alloc=517.6MB, time=247.78 memory used=20055.1MB, alloc=517.6MB, time=248.14 memory used=20161.3MB, alloc=517.6MB, time=248.53 memory used=20356.5MB, alloc=517.6MB, time=249.07 memory used=20596.8MB, alloc=517.6MB, time=249.99 memory used=20735.0MB, alloc=517.6MB, time=251.44 memory used=20843.7MB, alloc=517.6MB, time=252.09 memory used=20967.2MB, alloc=517.6MB, time=256.04 memory used=21068.7MB, alloc=517.6MB, time=256.48 memory used=21147.7MB, alloc=517.6MB, time=256.85 memory used=21252.3MB, alloc=517.6MB, time=257.27 memory used=21461.5MB, alloc=517.6MB, time=258.03 memory used=21595.5MB, alloc=517.6MB, time=259.29 memory used=21756.7MB, alloc=517.6MB, time=260.47 memory used=21862.1MB, alloc=541.6MB, time=262.11 memory used=21944.5MB, alloc=541.6MB, time=263.03 memory used=22020.3MB, alloc=541.6MB, time=264.10 memory used=22114.9MB, alloc=541.6MB, time=265.87 memory used=22196.9MB, alloc=541.6MB, time=266.96 memory used=22260.0MB, alloc=541.6MB, time=267.94 memory used=22319.5MB, alloc=541.6MB, time=269.03 memory used=22398.4MB, alloc=541.6MB, time=270.39 memory used=22512.8MB, alloc=541.6MB, time=271.85 memory used=22704.2MB, alloc=541.6MB, time=273.32 memory used=22879.0MB, alloc=541.6MB, time=274.79 memory used=23062.4MB, alloc=541.6MB, time=276.31 memory used=23222.6MB, alloc=541.6MB, time=277.61 memory used=23416.5MB, alloc=541.6MB, time=278.83 memory used=23556.7MB, alloc=565.6MB, time=280.13 memory used=23702.8MB, alloc=565.6MB, time=281.67 memory used=23779.6MB, alloc=565.6MB, time=282.91 memory used=23934.1MB, alloc=565.6MB, time=284.30 memory used=24130.9MB, alloc=565.6MB, time=285.49 memory used=24247.4MB, alloc=565.6MB, time=286.92 memory used=24456.4MB, alloc=565.6MB, time=288.47 memory used=24581.4MB, alloc=565.6MB, time=290.03 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428496358 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 3 3 2 F := [13 x - 15 y z + 9 x, -7 x - 2 y + 9 z ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 G := [-9 x + 11 y - 3 y z, -3 y z - 3 x + 7 y] > Problem := [F,G]; 3 3 3 2 Problem := [[13 x - 15 y z + 9 x, -7 x - 2 y + 9 z ], 2 2 2 2 [-9 x + 11 y - 3 y z, -3 y z - 3 x + 7 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=26.0MB, alloc=32.3MB, time=0.51 memory used=48.5MB, alloc=60.3MB, time=0.83 memory used=87.3MB, alloc=60.3MB, time=1.33 memory used=133.9MB, alloc=68.3MB, time=1.93 memory used=176.3MB, alloc=68.3MB, time=2.57 memory used=227.8MB, alloc=68.3MB, time=3.18 memory used=276.5MB, alloc=92.3MB, time=3.80 memory used=342.8MB, alloc=92.3MB, time=4.73 memory used=408.7MB, alloc=348.3MB, time=5.54 memory used=469.9MB, alloc=348.3MB, time=6.09 memory used=542.7MB, alloc=372.3MB, time=6.88 memory used=644.1MB, alloc=372.3MB, time=8.11 memory used=730.1MB, alloc=396.3MB, time=9.53 memory used=840.4MB, alloc=396.3MB, time=10.95 memory used=951.7MB, alloc=396.3MB, time=12.39 memory used=1062.4MB, alloc=420.3MB, time=13.75 memory used=1182.2MB, alloc=420.3MB, time=15.20 memory used=1291.9MB, alloc=420.3MB, time=16.76 memory used=1398.0MB, alloc=444.3MB, time=18.31 memory used=1493.4MB, alloc=468.3MB, time=19.77 memory used=1586.2MB, alloc=468.3MB, time=21.25 memory used=1682.9MB, alloc=468.3MB, time=22.96 memory used=1837.6MB, alloc=492.3MB, time=25.21 memory used=1991.6MB, alloc=492.3MB, time=27.28 memory used=2143.0MB, alloc=516.3MB, time=29.27 memory used=2240.0MB, alloc=516.3MB, time=31.18 memory used=2371.8MB, alloc=540.3MB, time=33.80 memory used=2509.4MB, alloc=564.3MB, time=36.54 memory used=2640.0MB, alloc=588.3MB, time=39.44 memory used=2750.8MB, alloc=588.3MB, time=41.94 memory used=2883.8MB, alloc=612.3MB, time=44.69 memory used=3012.2MB, alloc=636.3MB, time=47.26 memory used=3147.3MB, alloc=636.3MB, time=49.83 memory used=3286.0MB, alloc=660.3MB, time=52.22 memory used=3410.2MB, alloc=660.3MB, time=54.45 memory used=3530.9MB, alloc=684.3MB, time=56.75 memory used=3646.2MB, alloc=684.3MB, time=58.96 memory used=3752.1MB, alloc=684.3MB, time=60.92 memory used=3865.1MB, alloc=708.3MB, time=63.02 memory used=3972.6MB, alloc=708.3MB, time=65.05 memory used=4071.3MB, alloc=732.3MB, time=67.21 memory used=4155.0MB, alloc=732.3MB, time=69.19 memory used=4271.6MB, alloc=732.3MB, time=71.55 memory used=4359.9MB, alloc=756.3MB, time=73.46 memory used=4458.7MB, alloc=756.3MB, time=75.61 memory used=4533.3MB, alloc=756.3MB, time=77.43 memory used=4616.8MB, alloc=780.3MB, time=79.48 memory used=4692.2MB, alloc=780.3MB, time=81.33 memory used=5051.1MB, alloc=804.3MB, time=88.06 memory used=5389.5MB, alloc=828.3MB, time=94.66 memory used=5715.3MB, alloc=852.3MB, time=102.35 memory used=6010.6MB, alloc=876.3MB, time=114.15 memory used=6309.5MB, alloc=900.3MB, time=126.15 memory used=6620.4MB, alloc=924.3MB, time=138.59 memory used=6940.6MB, alloc=948.3MB, time=152.74 memory used=7271.2MB, alloc=972.3MB, time=167.61 memory used=7614.2MB, alloc=996.3MB, time=183.17 memory used=7970.3MB, alloc=1020.3MB, time=199.08 memory used=8340.1MB, alloc=1044.3MB, time=215.27 memory used=8724.3MB, alloc=1068.3MB, time=232.12 memory used=9123.4MB, alloc=1092.3MB, time=249.45 memory used=9537.0MB, alloc=1116.3MB, time=266.98 |\^/| 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(); 1428496658 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 F := [-2 x + 6 x - 11 y, 7 x y z - 5 y - 8 y z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 G := [-5 x z + y z + 11 x, x y + 8 x z - 7 y z] > Problem := [F,G]; 3 2 2 Problem := [[-2 x + 6 x - 11 y, 7 x y z - 5 y - 8 y z], 2 2 2 2 [-5 x z + y z + 11 x, x y + 8 x z - 7 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.1MB, alloc=32.3MB, time=0.17 memory used=26.4MB, alloc=32.3MB, time=0.51 memory used=47.4MB, alloc=32.3MB, time=0.84 memory used=66.1MB, alloc=56.3MB, time=1.15 memory used=137.0MB, alloc=100.3MB, time=2.29 memory used=208.3MB, alloc=100.3MB, time=3.34 memory used=280.4MB, alloc=100.3MB, time=4.44 memory used=348.6MB, alloc=380.3MB, time=5.42 memory used=451.7MB, alloc=380.3MB, time=7.08 memory used=548.9MB, alloc=404.3MB, time=8.74 memory used=677.9MB, alloc=404.3MB, time=10.31 memory used=791.2MB, alloc=428.3MB, time=12.31 memory used=913.7MB, alloc=452.3MB, time=14.49 memory used=1056.1MB, alloc=476.3MB, time=17.06 memory used=1214.3MB, alloc=500.3MB, time=20.09 memory used=1393.3MB, alloc=524.3MB, time=23.28 memory used=1591.9MB, alloc=548.3MB, time=26.92 memory used=1770.6MB, alloc=572.3MB, time=32.62 memory used=1954.3MB, alloc=596.3MB, time=39.22 memory used=2149.0MB, alloc=620.3MB, time=46.40 memory used=2352.6MB, alloc=644.3MB, time=54.96 memory used=2580.2MB, alloc=668.3MB, time=64.39 memory used=2831.7MB, alloc=692.3MB, time=74.51 memory used=3107.1MB, alloc=692.3MB, time=86.08 memory used=3382.5MB, alloc=716.3MB, time=97.82 memory used=3681.9MB, alloc=716.3MB, time=110.34 memory used=3981.3MB, alloc=716.3MB, time=122.50 memory used=4280.6MB, alloc=740.3MB, time=135.44 memory used=4603.9MB, alloc=740.3MB, time=148.85 memory used=4927.0MB, alloc=764.3MB, time=163.32 N1 := 10751 > GB := Basis(F, plex(op(vars))); GB := 3 2 6 5 4 4 3 2 [2 x - 6 x + 11 y, 10 x - 60 x + 77 x z + 90 x - 319 x z + 264 x z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=5295.9MB, alloc=764.3MB, time=176.84 memory used=5422.1MB, alloc=764.3MB, time=179.45 memory used=5549.4MB, alloc=764.3MB, time=182.06 memory used=5647.0MB, alloc=764.3MB, time=184.09 memory used=5802.0MB, alloc=764.3MB, time=186.94 memory used=5982.7MB, alloc=764.3MB, time=190.17 memory used=6245.3MB, alloc=764.3MB, time=194.04 memory used=6415.6MB, alloc=764.3MB, time=197.73 memory used=6583.1MB, alloc=788.3MB, time=201.67 memory used=6743.9MB, alloc=812.3MB, time=205.25 memory used=6908.1MB, alloc=812.3MB, time=209.21 memory used=7061.7MB, alloc=836.3MB, time=212.60 memory used=7206.9MB, alloc=860.3MB, time=215.98 memory used=7415.3MB, alloc=884.3MB, time=223.12 memory used=7723.8MB, alloc=908.3MB, time=235.59 memory used=8161.2MB, alloc=932.3MB, time=253.65 |\^/| 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(); 1428496958 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 F := [-9 y z - 18 y z + 2, -10 x z + 8 y z ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; G := [7 x - 18 y + 20 z, 4 - 5 y - 4 z] > Problem := [F,G]; 2 2 2 2 Problem := [[-9 y z - 18 y z + 2, -10 x z + 8 y z ], [7 x - 18 y + 20 z, 4 - 5 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=31.6MB, alloc=40.3MB, time=0.55 memory used=58.5MB, alloc=40.3MB, time=0.94 memory used=84.0MB, alloc=64.3MB, time=1.34 memory used=128.2MB, alloc=68.3MB, time=2.01 memory used=171.3MB, alloc=92.3MB, time=2.67 memory used=237.1MB, alloc=100.3MB, time=3.71 memory used=301.3MB, alloc=124.3MB, time=4.73 memory used=388.0MB, alloc=148.3MB, time=6.12 memory used=479.0MB, alloc=404.3MB, time=7.64 memory used=583.6MB, alloc=428.3MB, time=9.47 memory used=708.7MB, alloc=452.3MB, time=11.64 memory used=838.0MB, alloc=476.3MB, time=14.02 memory used=978.9MB, alloc=500.3MB, time=16.60 memory used=1131.5MB, alloc=524.3MB, time=19.37 memory used=1296.9MB, alloc=548.3MB, time=22.39 memory used=1473.9MB, alloc=572.3MB, time=25.54 memory used=1655.6MB, alloc=596.3MB, time=28.92 memory used=1845.1MB, alloc=620.3MB, time=32.46 memory used=2042.6MB, alloc=644.3MB, time=36.31 memory used=2219.9MB, alloc=668.3MB, time=39.57 memory used=2413.7MB, alloc=692.3MB, time=45.52 memory used=2605.7MB, alloc=716.3MB, time=52.28 memory used=2808.2MB, alloc=740.3MB, time=59.82 memory used=3023.6MB, alloc=764.3MB, time=68.18 memory used=3252.8MB, alloc=788.3MB, time=77.72 memory used=3495.6MB, alloc=812.3MB, time=87.65 memory used=3753.4MB, alloc=836.3MB, time=99.23 memory used=4025.9MB, alloc=860.3MB, time=111.08 memory used=4313.7MB, alloc=884.3MB, time=123.87 memory used=4617.1MB, alloc=908.3MB, time=136.84 memory used=4936.1MB, alloc=932.3MB, time=151.37 memory used=5266.5MB, alloc=956.3MB, time=166.19 memory used=5615.9MB, alloc=980.3MB, time=183.69 memory used=5989.2MB, alloc=1004.3MB, time=200.66 memory used=6386.4MB, alloc=1028.3MB, time=219.00 memory used=6807.6MB, alloc=1052.3MB, time=237.96 memory used=7252.7MB, alloc=1076.3MB, time=258.42 |\^/| 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(); 1428497258 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 F := [17 x z + 2 y z + 14 z, -x y z + 3 x y] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 2 2 G := [8 y z + 6 z + 16 x, -4 x y + x z - 3 x ] > Problem := [F,G]; 2 2 Problem := [[17 x z + 2 y z + 14 z, -x y z + 3 x y], 2 3 2 2 2 [8 y z + 6 z + 16 x, -4 x y + x z - 3 x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.5MB, alloc=32.3MB, time=0.51 memory used=47.7MB, alloc=32.3MB, time=0.82 memory used=67.3MB, alloc=56.3MB, time=1.14 memory used=105.1MB, alloc=60.3MB, time=1.74 memory used=141.5MB, alloc=84.3MB, time=2.33 memory used=201.0MB, alloc=92.3MB, time=3.30 memory used=258.4MB, alloc=116.3MB, time=4.25 memory used=339.6MB, alloc=116.3MB, time=5.57 memory used=417.5MB, alloc=140.3MB, time=6.87 memory used=507.7MB, alloc=164.3MB, time=8.62 memory used=592.3MB, alloc=420.3MB, time=10.21 memory used=713.0MB, alloc=444.3MB, time=12.24 memory used=854.9MB, alloc=468.3MB, time=15.22 memory used=1007.2MB, alloc=492.3MB, time=18.03 memory used=1172.0MB, alloc=516.3MB, time=21.00 memory used=1345.7MB, alloc=540.3MB, time=24.24 memory used=1529.6MB, alloc=564.3MB, time=27.75 memory used=1728.7MB, alloc=588.3MB, time=31.31 memory used=1909.1MB, alloc=612.3MB, time=36.69 memory used=2088.4MB, alloc=636.3MB, time=42.63 memory used=2278.4MB, alloc=660.3MB, time=49.22 memory used=2481.0MB, alloc=684.3MB, time=56.57 memory used=2695.9MB, alloc=708.3MB, time=65.33 memory used=2920.4MB, alloc=732.3MB, time=74.75 memory used=3168.8MB, alloc=756.3MB, time=85.68 memory used=3441.1MB, alloc=780.3MB, time=97.25 memory used=3737.4MB, alloc=804.3MB, time=110.18 memory used=4057.6MB, alloc=828.3MB, time=124.45 memory used=4401.8MB, alloc=852.3MB, time=139.58 memory used=4769.8MB, alloc=876.3MB, time=156.62 memory used=5161.8MB, alloc=876.3MB, time=174.57 memory used=5553.9MB, alloc=876.3MB, time=192.20 memory used=5945.8MB, alloc=876.3MB, time=209.02 memory used=6337.7MB, alloc=900.3MB, time=225.87 memory used=6753.4MB, alloc=900.3MB, time=243.89 |\^/| 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(); 1428497558 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 F := [-14 y z - 19 x y + y, -6 x z + 2 y ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 2 G := [-18 x y - 5 x z - 20, 5 y - 10 x + 3 y ] > Problem := [F,G]; 2 2 2 Problem := [[-14 y z - 19 x y + y, -6 x z + 2 y ], 2 3 2 2 [-18 x y - 5 x z - 20, 5 y - 10 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=4.1MB, alloc=32.3MB, time=0.18 memory used=25.6MB, alloc=32.3MB, time=0.52 memory used=44.9MB, alloc=32.3MB, time=0.85 memory used=64.6MB, alloc=60.3MB, time=1.13 memory used=107.0MB, alloc=60.3MB, time=1.80 memory used=147.6MB, alloc=84.3MB, time=2.60 memory used=208.7MB, alloc=84.3MB, time=3.83 memory used=262.2MB, alloc=108.3MB, time=5.39 N1 := 1593 > GB := Basis(F, plex(op(vars))); 2 3 2 2 2 GB := [57 x y + 14 y - 3 x y, 3 z x - y , 14 y z + 19 x y - y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=328.2MB, alloc=108.3MB, time=8.08 memory used=403.0MB, alloc=116.3MB, time=9.20 memory used=482.2MB, alloc=140.3MB, time=10.72 memory used=581.1MB, alloc=164.3MB, time=12.82 N2 := 1593 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 H := [-14 y z - 19 x y + y, -6 x z + 2 y , -18 x y - 5 x z - 20, 3 2 2 5 y - 10 x + 3 y ] > J:=[op(GB),op(G)]; 2 3 2 2 2 J := [57 x y + 14 y - 3 x y, 3 z x - y , 14 y z + 19 x y - y, 2 3 2 2 -18 x y - 5 x z - 20, 5 y - 10 x + 3 y ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 11, 12, 3, 2, 3, 2, 1, 1, 3/4, 5/11, 7/11, 3/11, 5, 13, 15, 3, 2, 3, 2, 1, 1, 3/5, 1/2, 5/7, 3/14, -2, -3, 0] > save(F, G, cat("ranSet/33", convert(F, string),".txt")); > quit memory used=648.3MB, alloc=164.3MB, time=15.26 |\^/| 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(); 1428497579 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 F := [13 x z - 10 y z + 2 x , 10 x y z + 6 x + 3] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 2 G := [7 y - 6 y z + 15 z, -9 y - 5 y z - 7 y ] > Problem := [F,G]; 2 2 2 2 Problem := [[13 x z - 10 y z + 2 x , 10 x y z + 6 x + 3], 2 3 2 2 [7 y - 6 y z + 15 z, -9 y - 5 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=4.2MB, alloc=32.3MB, time=0.18 memory used=26.4MB, alloc=32.3MB, time=0.53 memory used=45.5MB, alloc=56.3MB, time=0.85 memory used=86.7MB, alloc=60.3MB, time=1.51 memory used=125.5MB, alloc=84.3MB, time=2.24 memory used=166.1MB, alloc=84.3MB, time=2.87 memory used=229.1MB, alloc=92.3MB, time=3.92 memory used=290.2MB, alloc=116.3MB, time=4.95 memory used=372.6MB, alloc=116.3MB, time=6.19 memory used=447.4MB, alloc=372.3MB, time=7.44 memory used=536.1MB, alloc=396.3MB, time=8.79 memory used=654.0MB, alloc=420.3MB, time=10.70 memory used=786.5MB, alloc=444.3MB, time=13.17 memory used=935.4MB, alloc=444.3MB, time=15.90 memory used=1073.1MB, alloc=468.3MB, time=18.30 memory used=1226.2MB, alloc=492.3MB, time=21.10 memory used=1387.4MB, alloc=516.3MB, time=24.21 memory used=1582.4MB, alloc=540.3MB, time=27.37 memory used=1772.1MB, alloc=564.3MB, time=31.18 memory used=1970.7MB, alloc=588.3MB, time=35.34 memory used=2170.2MB, alloc=612.3MB, time=41.72 memory used=2365.9MB, alloc=636.3MB, time=49.45 memory used=2571.5MB, alloc=660.3MB, time=57.58 memory used=2790.9MB, alloc=684.3MB, time=67.11 memory used=3025.6MB, alloc=708.3MB, time=76.85 memory used=3271.9MB, alloc=732.3MB, time=88.48 memory used=3539.2MB, alloc=756.3MB, time=101.63 memory used=3830.3MB, alloc=780.3MB, time=114.95 memory used=4145.4MB, alloc=804.3MB, time=129.53 memory used=4484.5MB, alloc=828.3MB, time=145.19 memory used=4847.5MB, alloc=828.3MB, time=163.70 memory used=5210.4MB, alloc=828.3MB, time=181.02 memory used=5573.4MB, alloc=852.3MB, time=196.94 memory used=5960.2MB, alloc=852.3MB, time=214.23 memory used=6347.1MB, alloc=852.3MB, time=230.96 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428497879 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 3 F := [2 x z + 6 x y, -10 x z + 8 x y - 2 y ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 G := [4 y z + 6 x y + 16 x z, -4 x y + 3 x - 10 y ] > Problem := [F,G]; 2 2 2 3 Problem := [[2 x z + 6 x y, -10 x z + 8 x y - 2 y ], 2 2 2 2 [4 y z + 6 x y + 16 x z, -4 x y + 3 x - 10 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=25.9MB, alloc=32.3MB, time=0.49 memory used=47.2MB, alloc=32.3MB, time=0.81 memory used=67.3MB, alloc=56.3MB, time=1.12 memory used=108.1MB, alloc=60.3MB, time=1.74 memory used=151.4MB, alloc=84.3MB, time=2.47 memory used=212.8MB, alloc=92.3MB, time=3.48 memory used=267.9MB, alloc=116.3MB, time=4.44 memory used=343.5MB, alloc=140.3MB, time=5.73 memory used=437.3MB, alloc=164.3MB, time=7.36 memory used=547.7MB, alloc=188.3MB, time=10.05 memory used=663.7MB, alloc=212.3MB, time=13.84 memory used=790.1MB, alloc=236.3MB, time=18.73 memory used=940.5MB, alloc=236.3MB, time=24.57 memory used=1091.1MB, alloc=260.3MB, time=30.38 N1 := 4435 > GB := Basis(F, plex(op(vars))); 2 3 2 GB := [-4 x y + y - 15 x y, x z + 3 x y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1260.0MB, alloc=260.3MB, time=34.80 memory used=1464.3MB, alloc=540.3MB, time=40.55 N2 := 1639 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 3 2 H := [2 x z + 6 x y, -10 x z + 8 x y - 2 y , 4 y z + 6 x y + 16 x z, 2 2 2 -4 x y + 3 x - 10 y ] > J:=[op(GB),op(G)]; 2 3 2 2 J := [-4 x y + y - 15 x y, x z + 3 x y, 4 y z + 6 x y + 16 x z, 2 2 2 -4 x y + 3 x - 10 y ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 11, 12, 3, 2, 3, 1, 1, 1, 3/4, 8/11, 7/11, 4/11, 4, 10, 12, 3, 2, 3, 1, 1, 1, 1/2, 8/11, 8/11, 3/11, 1, 0, 0] > save(F, G, cat("ranSet/33", convert(F, string),".txt")); > quit memory used=1478.4MB, alloc=540.3MB, time=41.08 |\^/| 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(); 1428497931 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 3 3 2 F := [11 x y - 18 x y - 17 y , -y - 5 y z - 6 x] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 2 G := [-19 x - 8 x y - 4 x , -8 x y - 2 x y - 10 x] > Problem := [F,G]; 2 2 3 3 2 Problem := [[11 x y - 18 x y - 17 y , -y - 5 y z - 6 x], 3 2 2 2 [-19 x - 8 x y - 4 x , -8 x y - 2 x 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=32.2MB, alloc=40.3MB, time=0.72 memory used=62.4MB, alloc=44.3MB, time=1.34 memory used=88.9MB, alloc=68.3MB, time=1.85 memory used=136.7MB, alloc=92.3MB, time=2.87 N1 := 969 > GB := Basis(F, plex(op(vars))); 3 2 2 3 2 3 GB := [-11 x + 18 x y + 17 x y , 198 x - 511 x y + 289 y , 5 4 3 2 3 2 121 x - 198 x y + 935 x z + 1836 x + 1734 x y, 3 2 2 -198 x + 511 x y + 1445 y z + 1734 x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=203.5MB, alloc=92.3MB, time=4.69 memory used=268.1MB, alloc=100.3MB, time=5.80 memory used=329.8MB, alloc=124.3MB, time=6.91 memory used=420.4MB, alloc=124.3MB, time=8.71 memory used=504.9MB, alloc=148.3MB, time=10.38 memory used=609.0MB, alloc=172.3MB, time=12.32 memory used=727.5MB, alloc=196.3MB, time=15.24 memory used=849.9MB, alloc=220.3MB, time=20.13 memory used=989.4MB, alloc=244.3MB, time=25.90 N2 := 2961 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 3 3 2 3 2 2 H := [11 x y - 18 x y - 17 y , -y - 5 y z - 6 x, -19 x - 8 x y - 4 x , 2 -8 x y - 2 x y - 10 x] > J:=[op(GB),op(G)]; 3 2 2 3 2 3 J := [-11 x + 18 x y + 17 x y , 198 x - 511 x y + 289 y , 5 4 3 2 3 2 121 x - 198 x y + 935 x z + 1836 x + 1734 x y, 3 2 2 3 2 2 -198 x + 511 x y + 1445 y z + 1734 x, -19 x - 8 x y - 4 x , 2 -8 x y - 2 x y - 10 x] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 9, 12, 3, 3, 3, 2, 1, 1, 1/4, 3/4, 2/3, 1/12, 6, 14, 20, 5, 19 11 5, 3, 2, 1, 1, 1/3, --, --, 2/21, -5, -8, -2] 21 21 > save(F, G, cat("ranSet/33", convert(F, string),".txt")); > quit memory used=1037.6MB, alloc=244.3MB, time=27.37 |\^/| 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(); 1428497965 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 3 2 F := [5 x z + z - 10 z , -10 z - 9 z - 2] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 3 2 G := [-15 x y + 18 y - 2 x, 7 y z + 5 z - 10 x ] > Problem := [F,G]; 2 3 2 3 2 Problem := [[5 x z + z - 10 z , -10 z - 9 z - 2], 2 2 3 2 [-15 x y + 18 y - 2 x, 7 y z + 5 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=4.2MB, alloc=32.3MB, time=0.17 memory used=26.1MB, alloc=32.3MB, time=0.51 memory used=47.8MB, alloc=36.3MB, time=0.91 memory used=66.8MB, alloc=60.3MB, time=1.21 memory used=107.2MB, alloc=60.3MB, time=1.82 memory used=149.2MB, alloc=84.3MB, time=2.58 memory used=215.0MB, alloc=84.3MB, time=3.60 memory used=272.8MB, alloc=108.3MB, time=4.67 memory used=344.0MB, alloc=140.3MB, time=6.33 memory used=420.6MB, alloc=164.3MB, time=9.25 memory used=520.6MB, alloc=188.3MB, time=12.82 N1 := 2591 > GB := Basis(F, plex(op(vars))); 3 2 GB := [1250 x - 7725 x + 15900 x - 10902, z + 5 x - 10] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=634.9MB, alloc=188.3MB, time=15.05 N2 := 985 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 3 2 3 2 2 H := [5 x z + z - 10 z , -10 z - 9 z - 2, -15 x y + 18 y - 2 x, 2 3 2 7 y z + 5 z - 10 x ] > J:=[op(GB),op(G)]; 3 2 2 J := [1250 x - 7725 x + 15900 x - 10902, z + 5 x - 10, -15 x y + 18 y - 2 x, 2 3 2 7 y z + 5 z - 10 x ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 8, 11, 3, 2, 2, 3, 3/4, 1/2, 3/4, 1/3, 1/4, 7/12, 4, 8, 9, 3, 3, 2, 3, 1, 1/2, 1/2, 7/13, 3/13, 3/13, 0, 2, 0] > save(F, G, cat("ranSet/33", convert(F, string),".txt")); > quit memory used=688.5MB, alloc=444.3MB, time=16.75 |\^/| 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(); 1428497986 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 F := [16 x y + y + 3 z , -10 x y + 10 y + 3 z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 G := [-11 z - 2 z - 15, 3 x z - 9 z + 6 z] > Problem := [F,G]; 2 2 2 2 Problem := [[16 x y + y + 3 z , -10 x y + 10 y + 3 z], 3 2 2 [-11 z - 2 z - 15, 3 x z - 9 z + 6 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=26.6MB, alloc=32.3MB, time=0.51 memory used=47.5MB, alloc=32.3MB, time=0.82 memory used=67.2MB, alloc=56.3MB, time=1.14 memory used=106.1MB, alloc=60.3MB, time=1.75 memory used=145.4MB, alloc=84.3MB, time=2.34 memory used=208.3MB, alloc=92.3MB, time=3.23 memory used=271.9MB, alloc=92.3MB, time=4.11 memory used=334.9MB, alloc=116.3MB, time=5.05 memory used=406.0MB, alloc=116.3MB, time=5.66 memory used=482.9MB, alloc=116.3MB, time=6.48 memory used=568.5MB, alloc=372.3MB, time=7.52 memory used=674.3MB, alloc=372.3MB, time=8.71 memory used=772.8MB, alloc=396.3MB, time=9.72 memory used=895.0MB, alloc=396.3MB, time=10.89 memory used=1011.4MB, alloc=396.3MB, time=11.74 memory used=1099.9MB, alloc=396.3MB, time=12.04 memory used=1204.1MB, alloc=396.3MB, time=12.37 memory used=1320.8MB, alloc=396.3MB, time=12.69 memory used=1444.5MB, alloc=396.3MB, time=13.04 memory used=1572.5MB, alloc=396.3MB, time=13.85 memory used=1660.6MB, alloc=396.3MB, time=14.17 memory used=1764.3MB, alloc=396.3MB, time=14.48 memory used=1880.7MB, alloc=396.3MB, time=14.80 memory used=2003.8MB, alloc=396.3MB, time=15.16 memory used=2141.4MB, alloc=396.3MB, time=16.64 memory used=2254.6MB, alloc=396.3MB, time=18.32 memory used=2366.1MB, alloc=420.3MB, time=19.94 memory used=2501.9MB, alloc=420.3MB, time=21.73 memory used=2624.0MB, alloc=444.3MB, time=23.61 memory used=2786.7MB, alloc=444.3MB, time=25.28 memory used=2943.0MB, alloc=468.3MB, time=27.13 memory used=3131.4MB, alloc=468.3MB, time=29.12 memory used=3304.8MB, alloc=492.3MB, time=31.65 memory used=3493.2MB, alloc=492.3MB, time=34.46 memory used=3670.3MB, alloc=516.3MB, time=38.03 memory used=3854.6MB, alloc=540.3MB, time=42.52 memory used=4045.3MB, alloc=564.3MB, time=46.44 memory used=4257.9MB, alloc=588.3MB, time=50.55 memory used=4445.9MB, alloc=612.3MB, time=56.14 memory used=4626.4MB, alloc=636.3MB, time=63.45 memory used=4816.4MB, alloc=660.3MB, time=71.50 memory used=5019.1MB, alloc=684.3MB, time=79.77 memory used=5236.3MB, alloc=708.3MB, time=90.01 memory used=5468.8MB, alloc=732.3MB, time=100.45 memory used=5710.9MB, alloc=756.3MB, time=113.55 memory used=5975.2MB, alloc=780.3MB, time=126.67 memory used=6263.5MB, alloc=804.3MB, time=140.49 memory used=6575.7MB, alloc=828.3MB, time=155.95 memory used=6911.8MB, alloc=852.3MB, time=171.68 memory used=7271.9MB, alloc=876.3MB, time=189.28 memory used=7656.0MB, alloc=876.3MB, time=207.52 memory used=8040.0MB, alloc=876.3MB, time=225.12 |\^/| 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(); 1428498286 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 F := [-10 x y - 8 x y, -9 x y + 3 y - 7 z ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 G := [9 x z + 14 z + 11, -3 z + 7 z + 7 y] > Problem := [F,G]; 2 2 2 Problem := [[-10 x y - 8 x y, -9 x y + 3 y - 7 z ], 3 2 [9 x z + 14 z + 11, -3 z + 7 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=4.1MB, alloc=32.3MB, time=0.17 memory used=26.5MB, alloc=32.3MB, time=0.51 memory used=47.6MB, alloc=32.3MB, time=0.84 memory used=67.4MB, alloc=56.3MB, time=1.15 memory used=107.6MB, alloc=60.3MB, time=1.76 memory used=149.0MB, alloc=84.3MB, time=2.38 memory used=213.4MB, alloc=92.3MB, time=3.53 memory used=274.6MB, alloc=116.3MB, time=4.57 memory used=354.0MB, alloc=140.3MB, time=6.18 memory used=451.7MB, alloc=164.3MB, time=7.96 memory used=558.6MB, alloc=188.3MB, time=11.11 memory used=669.3MB, alloc=212.3MB, time=15.14 memory used=789.3MB, alloc=236.3MB, time=20.50 memory used=933.4MB, alloc=236.3MB, time=26.69 memory used=1077.4MB, alloc=260.3MB, time=32.38 memory used=1245.5MB, alloc=260.3MB, time=38.99 N1 := 4955 > GB := Basis(F, plex(op(vars))); 2 2 2 GB := [5 x y + 4 x y, 7 z - 3 y + 9 y x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1392.8MB, alloc=260.3MB, time=42.90 memory used=1603.2MB, alloc=540.3MB, time=46.86 memory used=1825.4MB, alloc=564.3MB, time=52.02 memory used=2028.4MB, alloc=588.3MB, time=59.97 memory used=2236.2MB, alloc=612.3MB, time=69.89 memory used=2468.2MB, alloc=636.3MB, time=79.27 N2 := 4955 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 H := [-10 x y - 8 x y, -9 x y + 3 y - 7 z , 9 z x + 14 z + 11, 3 2 -3 z + 7 z + 7 y] > J:=[op(GB),op(G)]; J := [ 2 2 2 3 2 5 x y + 4 x y, 7 z - 3 y + 9 y x, 9 z x + 14 z + 11, -3 z + 7 z + 7 y] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 9, 10, 3, 2, 2, 3, 3/4, 3/4, 3/4, 4/11, 5/11, 5/11, 4, 9, 10, 3, 2, 2, 3, 3/4, 3/4, 3/4, 4/11, 5/11, 5/11, 0, 0, 0] > save(F, G, cat("ranSet/33", convert(F, string),".txt")); > quit memory used=2610.8MB, alloc=636.3MB, time=84.33 |\^/| 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(); 1428498396 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 3 F := [-3 x z - 10 x y + 10 y z , -8 y + 5 x y + 3 x] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 3 G := [10 x y - 6 x z + 7 x y , -3 z + 3 x y + 8 y] > Problem := [F,G]; 2 2 2 3 Problem := [[-3 x z - 10 x y + 10 y z , -8 y + 5 x y + 3 x], 2 2 2 3 [10 x y - 6 x z + 7 x y , -3 z + 3 x y + 8 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=24.6MB, alloc=32.3MB, time=0.51 memory used=44.3MB, alloc=32.3MB, time=0.82 memory used=61.4MB, alloc=56.3MB, time=1.00 memory used=104.7MB, alloc=60.3MB, time=1.46 memory used=143.9MB, alloc=60.3MB, time=2.01 memory used=187.5MB, alloc=60.3MB, time=2.57 memory used=230.6MB, alloc=60.3MB, time=3.05 memory used=257.3MB, alloc=60.3MB, time=3.25 memory used=294.9MB, alloc=60.3MB, time=3.61 memory used=338.6MB, alloc=60.3MB, time=4.09 memory used=377.7MB, alloc=60.3MB, time=4.61 memory used=418.7MB, alloc=92.3MB, time=5.17 memory used=486.3MB, alloc=92.3MB, time=5.89 memory used=525.8MB, alloc=92.3MB, time=6.11 memory used=595.3MB, alloc=92.3MB, time=6.85 memory used=672.9MB, alloc=92.3MB, time=7.83 memory used=744.8MB, alloc=92.3MB, time=8.69 memory used=813.7MB, alloc=92.3MB, time=9.26 memory used=887.3MB, alloc=92.3MB, time=9.92 memory used=959.9MB, alloc=92.3MB, time=10.63 memory used=1023.8MB, alloc=116.3MB, time=11.61 memory used=1104.5MB, alloc=116.3MB, time=12.96 memory used=1193.9MB, alloc=140.3MB, time=14.43 memory used=1310.7MB, alloc=140.3MB, time=16.45 memory used=1429.5MB, alloc=140.3MB, time=18.19 memory used=1543.0MB, alloc=140.3MB, time=19.91 memory used=1655.9MB, alloc=420.3MB, time=21.80 memory used=1793.8MB, alloc=420.3MB, time=23.93 memory used=1909.1MB, alloc=444.3MB, time=25.87 memory used=2038.1MB, alloc=468.3MB, time=28.53 memory used=2165.3MB, alloc=492.3MB, time=32.54 memory used=2301.6MB, alloc=516.3MB, time=38.06 memory used=2452.5MB, alloc=540.3MB, time=43.99 memory used=2627.4MB, alloc=540.3MB, time=50.85 memory used=2802.4MB, alloc=564.3MB, time=57.88 memory used=3001.4MB, alloc=564.3MB, time=66.09 N1 := 5949 > GB := Basis(F, plex(op(vars))); 3 2 2 3 2 2 GB := [8 y - 5 x y - 3 x, -8 x y z + 5 x z - 10 x y + 10 x z , 2 2 2 -3 x z - 10 x y + 10 y z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=3205.8MB, alloc=564.3MB, time=73.30 memory used=3358.2MB, alloc=564.3MB, time=75.67 memory used=3522.7MB, alloc=564.3MB, time=77.39 memory used=3681.1MB, alloc=564.3MB, time=79.26 memory used=3805.0MB, alloc=564.3MB, time=81.02 memory used=3932.6MB, alloc=588.3MB, time=83.00 memory used=4049.7MB, alloc=588.3MB, time=84.68 memory used=4188.3MB, alloc=588.3MB, time=86.33 memory used=4297.1MB, alloc=588.3MB, time=88.19 memory used=4402.0MB, alloc=588.3MB, time=90.03 memory used=4571.0MB, alloc=588.3MB, time=91.68 memory used=4706.5MB, alloc=588.3MB, time=92.62 memory used=4848.9MB, alloc=588.3MB, time=93.65 memory used=4993.5MB, alloc=588.3MB, time=94.60 memory used=5133.3MB, alloc=588.3MB, time=95.45 memory used=5256.7MB, alloc=588.3MB, time=96.09 memory used=5436.1MB, alloc=612.3MB, time=98.37 memory used=5547.0MB, alloc=612.3MB, time=99.72 memory used=5629.2MB, alloc=612.3MB, time=101.11 memory used=5740.3MB, alloc=612.3MB, time=103.01 memory used=5834.5MB, alloc=612.3MB, time=104.63 memory used=5957.1MB, alloc=612.3MB, time=105.99 memory used=6056.7MB, alloc=612.3MB, time=107.58 memory used=6162.1MB, alloc=612.3MB, time=108.85 memory used=6266.2MB, alloc=612.3MB, time=110.19 memory used=6426.4MB, alloc=612.3MB, time=111.71 memory used=6595.9MB, alloc=612.3MB, time=114.68 memory used=6726.5MB, alloc=612.3MB, time=115.39 memory used=6897.3MB, alloc=636.3MB, time=116.78 memory used=7018.4MB, alloc=636.3MB, time=118.27 memory used=7103.5MB, alloc=636.3MB, time=120.02 memory used=7273.5MB, alloc=636.3MB, time=120.89 memory used=7447.5MB, alloc=636.3MB, time=123.46 memory used=7583.9MB, alloc=636.3MB, time=124.04 memory used=7679.8MB, alloc=636.3MB, time=125.22 memory used=7756.7MB, alloc=636.3MB, time=126.67 memory used=7869.6MB, alloc=636.3MB, time=127.90 memory used=8031.8MB, alloc=636.3MB, time=129.00 memory used=8178.8MB, alloc=636.3MB, time=129.78 memory used=8307.1MB, alloc=636.3MB, time=130.99 memory used=8456.1MB, alloc=636.3MB, time=131.91 memory used=8608.3MB, alloc=636.3MB, time=133.65 memory used=8784.4MB, alloc=636.3MB, time=135.23 memory used=8852.9MB, alloc=636.3MB, time=136.50 memory used=8913.9MB, alloc=636.3MB, time=137.68 memory used=9000.6MB, alloc=636.3MB, time=138.80 memory used=9097.8MB, alloc=636.3MB, time=140.46 memory used=9172.4MB, alloc=636.3MB, time=141.89 memory used=9278.4MB, alloc=636.3MB, time=143.33 memory used=9375.6MB, alloc=636.3MB, time=144.89 memory used=9422.2MB, alloc=636.3MB, time=145.89 memory used=9500.7MB, alloc=636.3MB, time=147.19 memory used=9642.4MB, alloc=636.3MB, time=148.00 memory used=9796.4MB, alloc=660.3MB, time=149.44 memory used=9942.5MB, alloc=660.3MB, time=150.24 memory used=10092.0MB, alloc=660.3MB, time=150.99 memory used=10211.0MB, alloc=660.3MB, time=151.73 memory used=10350.3MB, alloc=660.3MB, time=152.40 memory used=10509.0MB, alloc=660.3MB, time=153.06 memory used=10693.1MB, alloc=660.3MB, time=153.76 memory used=10880.7MB, alloc=660.3MB, time=154.62 memory used=11022.9MB, alloc=660.3MB, time=155.27 memory used=11182.5MB, alloc=660.3MB, time=155.98 memory used=11373.0MB, alloc=660.3MB, time=157.37 memory used=11535.6MB, alloc=660.3MB, time=158.16 memory used=11666.5MB, alloc=660.3MB, time=158.82 memory used=11790.8MB, alloc=660.3MB, time=159.45 memory used=11933.1MB, alloc=660.3MB, time=160.20 memory used=12097.4MB, alloc=660.3MB, time=161.01 memory used=12303.8MB, alloc=660.3MB, time=161.89 memory used=12441.4MB, alloc=660.3MB, time=162.68 memory used=12586.9MB, alloc=660.3MB, time=163.36 memory used=12749.5MB, alloc=660.3MB, time=164.00 memory used=12955.7MB, alloc=660.3MB, time=172.33 memory used=13092.4MB, alloc=660.3MB, time=172.98 memory used=13250.7MB, alloc=660.3MB, time=173.67 memory used=13480.9MB, alloc=660.3MB, time=174.46 memory used=13643.5MB, alloc=660.3MB, time=175.15 memory used=13842.6MB, alloc=660.3MB, time=175.86 memory used=13919.5MB, alloc=660.3MB, time=177.57 memory used=14096.1MB, alloc=660.3MB, time=179.32 memory used=14238.5MB, alloc=660.3MB, time=180.00 memory used=14464.9MB, alloc=660.3MB, time=180.85 memory used=14646.3MB, alloc=660.3MB, time=182.46 memory used=14812.9MB, alloc=660.3MB, time=184.03 memory used=14973.3MB, alloc=660.3MB, time=184.84 memory used=15118.5MB, alloc=660.3MB, time=188.99 memory used=15300.1MB, alloc=660.3MB, time=190.43 memory used=15425.8MB, alloc=660.3MB, time=191.09 memory used=15594.7MB, alloc=660.3MB, time=191.79 memory used=15778.7MB, alloc=660.3MB, time=192.54 memory used=15941.6MB, alloc=660.3MB, time=193.24 memory used=16282.4MB, alloc=660.3MB, time=195.27 memory used=16342.3MB, alloc=660.3MB, time=196.44 memory used=16396.8MB, alloc=660.3MB, time=197.61 memory used=16448.8MB, alloc=660.3MB, time=198.78 memory used=16538.9MB, alloc=660.3MB, time=199.94 memory used=16672.0MB, alloc=660.3MB, time=201.34 memory used=16728.4MB, alloc=660.3MB, time=202.37 memory used=16772.9MB, alloc=660.3MB, time=203.38 memory used=17015.7MB, alloc=660.3MB, time=206.03 memory used=17256.7MB, alloc=684.3MB, time=208.34 memory used=17498.3MB, alloc=684.3MB, time=210.78 memory used=17652.9MB, alloc=684.3MB, time=211.62 memory used=17800.1MB, alloc=684.3MB, time=212.38 memory used=17945.7MB, alloc=684.3MB, time=213.11 memory used=18137.0MB, alloc=684.3MB, time=214.51 memory used=18344.1MB, alloc=684.3MB, time=219.35 memory used=18494.7MB, alloc=684.3MB, time=220.13 memory used=18659.6MB, alloc=684.3MB, time=220.90 memory used=18847.5MB, alloc=684.3MB, time=221.70 memory used=19218.0MB, alloc=684.3MB, time=225.61 memory used=19359.7MB, alloc=684.3MB, time=226.40 memory used=19656.9MB, alloc=684.3MB, time=227.41 memory used=19974.4MB, alloc=684.3MB, time=229.24 memory used=20165.2MB, alloc=684.3MB, time=230.82 memory used=20318.8MB, alloc=684.3MB, time=231.70 memory used=20474.2MB, alloc=684.3MB, time=232.53 memory used=20638.4MB, alloc=684.3MB, time=239.21 memory used=20823.9MB, alloc=684.3MB, time=240.92 memory used=20964.4MB, alloc=684.3MB, time=241.71 memory used=21123.1MB, alloc=684.3MB, time=242.51 memory used=21403.4MB, alloc=684.3MB, time=243.49 memory used=21533.4MB, alloc=684.3MB, time=244.23 memory used=21680.0MB, alloc=684.3MB, time=245.00 memory used=21848.9MB, alloc=684.3MB, time=245.79 memory used=22239.3MB, alloc=708.3MB, time=249.58 memory used=22531.2MB, alloc=708.3MB, time=252.96 memory used=22764.7MB, alloc=708.3MB, time=254.86 memory used=23137.0MB, alloc=708.3MB, time=261.69 memory used=23426.8MB, alloc=708.3MB, time=265.04 memory used=23619.3MB, alloc=708.3MB, time=266.32 memory used=23804.6MB, alloc=708.3MB, time=267.18 |\^/| 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(); 1428498696 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 3 2 F := [-3 x y + 17 y - 14 y, -10 x + 10 y - 9 y] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 G := [8 x z - 10 z - 2, 10 x y - 7 x z + 5 z ] > Problem := [F,G]; 2 3 3 2 Problem := [[-3 x y + 17 y - 14 y, -10 x + 10 y - 9 y], 2 2 [8 x z - 10 z - 2, 10 x y - 7 x z + 5 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.5MB, alloc=32.3MB, time=0.48 memory used=47.6MB, alloc=32.3MB, time=0.78 memory used=67.3MB, alloc=56.3MB, time=1.08 memory used=112.6MB, alloc=60.3MB, time=1.83 memory used=153.6MB, alloc=84.3MB, time=2.50 memory used=215.9MB, alloc=84.3MB, time=3.49 memory used=271.0MB, alloc=108.3MB, time=4.43 memory used=344.1MB, alloc=132.3MB, time=6.16 memory used=427.4MB, alloc=156.3MB, time=8.94 memory used=529.9MB, alloc=156.3MB, time=12.65 N1 := 2799 > GB := Basis(F, plex(op(vars))); 9 8 7 6 4 3 GB := [14450 x - 450 x + 2295 x - 23800 x + 1890 x + 161 x , 8 7 6 910579726100000 x - 105902917260000 x + 153755067177000 x 5 4 3 - 1512300179600000 x + 128807338380000 x + 108125474832630 x + 81801186567 y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=640.3MB, alloc=164.3MB, time=15.48 N2 := 1009 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 3 3 2 H := [-3 x y + 17 y - 14 y, -10 x + 10 y - 9 y, 8 x z - 10 z - 2, 2 2 10 y x + 5 z - 7 z x] > J:=[op(GB),op(G)]; 9 8 7 6 4 3 J := [14450 x - 450 x + 2295 x - 23800 x + 1890 x + 161 x , 8 7 6 910579726100000 x - 105902917260000 x + 153755067177000 x 5 4 3 - 1512300179600000 x + 128807338380000 x + 108125474832630 x 2 2 + 81801186567 y, 8 x z - 10 z - 2, 10 y x + 5 z - 7 z x] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 9, 11, 3, 3, 3, 2, 1, 3/4, 1/2, 5/12, 1/2, 1/3, 4, 8, 22, 9, 15 9, 2, 2, 1, 1/2, 1/2, --, 2/19, 4/19, 1, -11, -6] 19 > save(F, G, cat("ranSet/33", convert(F, string),".txt")); > quit memory used=751.4MB, alloc=164.3MB, time=17.88 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428498722 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 F := [-10 x y - 19 y + 4 z, -7 x z + y - 3 z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 3 2 2 G := [15 x + 11 x y - 6 y z, 3 x + x y + 9 y z] > Problem := [F,G]; 2 3 2 Problem := [[-10 x y - 19 y + 4 z, -7 x z + y - 3 z], 3 2 3 2 2 [15 x + 11 x y - 6 y z, 3 x + 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=4.2MB, alloc=32.3MB, time=0.17 memory used=24.5MB, alloc=32.3MB, time=0.48 memory used=43.3MB, alloc=32.3MB, time=0.75 memory used=62.2MB, alloc=56.3MB, time=1.01 memory used=107.4MB, alloc=68.3MB, time=1.57 memory used=151.6MB, alloc=68.3MB, time=2.16 memory used=196.9MB, alloc=68.3MB, time=2.70 memory used=241.2MB, alloc=92.3MB, time=3.29 memory used=309.4MB, alloc=92.3MB, time=4.13 memory used=376.2MB, alloc=92.3MB, time=5.03 memory used=444.0MB, alloc=116.3MB, time=6.11 memory used=531.1MB, alloc=140.3MB, time=7.44 memory used=632.4MB, alloc=140.3MB, time=9.11 memory used=724.3MB, alloc=164.3MB, time=10.93 memory used=822.4MB, alloc=188.3MB, time=14.17 memory used=932.5MB, alloc=212.3MB, time=18.44 N1 := 3151 > GB := Basis(F, plex(op(vars))); 3 2 2 3 2 3 2 3 GB := [70 x y + 133 x y + 30 x y + 57 y - 4 y, -10 x y - 19 y + 4 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1070.7MB, alloc=212.3MB, time=23.07 memory used=1140.7MB, alloc=468.3MB, time=24.16 memory used=1310.9MB, alloc=492.3MB, time=26.88 N2 := 1293 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 3 2 2 3 H := [-10 x y - 19 y + 4 z, -7 x z + y - 3 z, 11 y x + 15 x - 6 z y, 2 2 3 9 z y + y x + 3 x ] > J:=[op(GB),op(G)]; 3 2 2 3 2 3 2 3 J := [70 x y + 133 x y + 30 x y + 57 y - 4 y, -10 x y - 19 y + 4 z, 2 3 2 2 3 11 y x + 15 x - 6 z y, 9 z y + y x + 3 x ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 12, 12, 3, 3, 3, 1, 1, 1, 1, 1/2, 7/12, 5/12, 4, 11, 14, 5, 11 3, 3, 1, 1, 1, 3/4, 4/7, --, 3/14, 1, -2, -2] 14 > save(F, G, cat("ranSet/33", convert(F, string),".txt")); > quit memory used=1387.3MB, alloc=492.3MB, time=29.22 |\^/| 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(); 1428498758 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 3 3 2 F := [-15 x y - 7 x y z - 19 z , -2 x + 7 z - 6 z ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 G := [7 x y + 14 x z - 17 z, 3 y z + 7 z ] > Problem := [F,G]; 2 2 3 3 2 Problem := [[-15 x y - 7 x y z - 19 z , -2 x + 7 z - 6 z ], 2 2 [7 x y + 14 x z - 17 z, 3 y 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=4.2MB, alloc=32.3MB, time=0.18 memory used=26.3MB, alloc=32.3MB, time=0.49 memory used=47.4MB, alloc=32.3MB, time=0.80 memory used=65.0MB, alloc=56.3MB, time=1.06 memory used=105.6MB, alloc=60.3MB, time=1.64 memory used=147.1MB, alloc=60.3MB, time=2.17 memory used=190.9MB, alloc=68.3MB, time=2.72 memory used=219.0MB, alloc=68.3MB, time=2.88 memory used=250.4MB, alloc=68.3MB, time=3.33 memory used=269.3MB, alloc=68.3MB, time=3.39 memory used=299.1MB, alloc=68.3MB, time=3.60 memory used=346.0MB, alloc=92.3MB, time=4.15 memory used=417.0MB, alloc=92.3MB, time=5.07 memory used=471.5MB, alloc=92.3MB, time=6.47 memory used=529.6MB, alloc=92.3MB, time=7.03 memory used=599.6MB, alloc=92.3MB, time=7.49 memory used=675.9MB, alloc=92.3MB, time=8.38 memory used=750.5MB, alloc=92.3MB, time=9.30 memory used=824.5MB, alloc=92.3MB, time=10.02 memory used=888.6MB, alloc=116.3MB, time=10.89 memory used=978.0MB, alloc=116.3MB, time=12.19 memory used=1073.8MB, alloc=140.3MB, time=13.41 memory used=1192.9MB, alloc=140.3MB, time=15.05 memory used=1294.8MB, alloc=164.3MB, time=16.80 memory used=1417.5MB, alloc=188.3MB, time=18.82 memory used=1571.4MB, alloc=444.3MB, time=20.86 memory used=1717.0MB, alloc=468.3MB, time=22.89 memory used=1863.5MB, alloc=492.3MB, time=25.64 memory used=2004.1MB, alloc=516.3MB, time=29.46 memory used=2149.0MB, alloc=540.3MB, time=34.06 memory used=2299.0MB, alloc=564.3MB, time=39.82 memory used=2469.6MB, alloc=588.3MB, time=46.52 memory used=2664.2MB, alloc=612.3MB, time=54.12 memory used=2882.7MB, alloc=612.3MB, time=62.74 memory used=3101.2MB, alloc=636.3MB, time=71.44 memory used=3343.5MB, alloc=636.3MB, time=80.93 memory used=3585.9MB, alloc=636.3MB, time=90.56 memory used=3828.3MB, alloc=660.3MB, time=100.09 memory used=4094.7MB, alloc=660.3MB, time=110.61 memory used=4360.9MB, alloc=684.3MB, time=121.17 memory used=4651.2MB, alloc=708.3MB, time=132.29 N1 := 9623 > GB := Basis(F, plex(op(vars))); 5 3 2 6 4 3 2 5 4 2 GB := [4802 x y + 165375 x y - 83790 x y + 66150 x y + 11172 x y 5 3 2 4 9 6 4 + 27436 x - 129960 x y + 153900 x y , 11529602 x y + 397065375 x y 8 8 6 3 5 4 - 268239720 x y + 31294634 x z + 158826150 x y - 4618923750 x y 7 7 5 3 4 4 + 1950212250 x y - 546059430 x z - 2771354250 x y + 13432584375 x y 6 6 5 2 4 3 - 4537228500 x y + 3176059950 x z + 369513900 x y + 10746067500 x y 2 5 6 5 4 2 + 12725606250 x y + 907445700 x - 6157667250 x z - 6447640500 x y 2 4 5 4 3 2 + 5090242500 x y - 5278000500 x + 859685400 x y + 12500527500 x y 3 3 3 6 - 5000211000 x y + 2333431800 x z + 11842605000 x y , -235298 x y 3 4 5 5 3 3 - 8103375 x y + 4105710 x y - 638666 x z - 3241350 x y 2 4 4 4 2 3 + 47131875 x y - 15920100 x y + 7429380 x z + 37705500 x y 3 3 2 6 - 21605850 x z - 18519300 x + 43861500 x y + 20468700 x y z, 235298 x y 3 4 5 5 3 3 + 8103375 x y - 4105710 x y + 638666 x z + 3241350 x y 2 4 4 4 2 3 - 47131875 x y + 15920100 x y - 7429380 x z - 37705500 x y 3 3 2 + 21605850 x z + 18519300 x + 55557900 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=4991.1MB, alloc=708.3MB, time=137.48 memory used=5348.6MB, alloc=708.3MB, time=143.00 memory used=5580.0MB, alloc=708.3MB, time=144.34 memory used=5814.9MB, alloc=708.3MB, time=167.48 memory used=6006.6MB, alloc=708.3MB, time=168.11 memory used=6209.4MB, alloc=708.3MB, time=169.14 memory used=6667.9MB, alloc=708.3MB, time=189.34 memory used=6988.5MB, alloc=723.8MB, time=190.39 memory used=7170.0MB, alloc=723.8MB, time=191.04 memory used=7518.3MB, alloc=723.8MB, time=192.13 memory used=7736.9MB, alloc=723.8MB, time=192.96 memory used=8036.6MB, alloc=723.8MB, time=196.19 memory used=8221.2MB, alloc=723.8MB, time=196.87 memory used=8413.1MB, alloc=723.8MB, time=197.56 memory used=8568.6MB, alloc=723.8MB, time=198.18 memory used=8753.9MB, alloc=723.8MB, time=198.84 memory used=8962.5MB, alloc=723.8MB, time=199.49 memory used=9128.9MB, alloc=723.8MB, time=200.09 memory used=9317.2MB, alloc=723.8MB, time=200.72 memory used=9532.7MB, alloc=723.8MB, time=201.35 memory used=9863.8MB, alloc=723.8MB, time=205.44 memory used=10041.2MB, alloc=723.8MB, time=206.09 memory used=10277.8MB, alloc=723.8MB, time=206.83 memory used=10434.6MB, alloc=723.8MB, time=207.44 memory used=10622.8MB, alloc=723.8MB, time=208.08 memory used=10828.4MB, alloc=723.8MB, time=208.71 memory used=10996.4MB, alloc=723.8MB, time=209.28 memory used=11188.0MB, alloc=723.8MB, time=209.87 memory used=11649.6MB, alloc=723.8MB, time=228.62 memory used=11823.8MB, alloc=723.8MB, time=229.27 memory used=12114.1MB, alloc=723.8MB, time=230.12 memory used=12261.1MB, alloc=723.8MB, time=230.68 memory used=12431.1MB, alloc=723.8MB, time=231.28 memory used=12626.2MB, alloc=723.8MB, time=231.90 memory used=12832.5MB, alloc=723.8MB, time=232.54 memory used=12996.3MB, alloc=723.8MB, time=233.10 memory used=13174.6MB, alloc=723.8MB, time=233.70 memory used=13364.8MB, alloc=723.8MB, time=234.31 memory used=13574.8MB, alloc=723.8MB, time=234.94 memory used=13785.1MB, alloc=723.8MB, time=235.56 memory used=13968.0MB, alloc=723.8MB, time=236.13 memory used=14166.8MB, alloc=723.8MB, time=236.71 memory used=14382.6MB, alloc=723.8MB, time=237.31 memory used=14769.6MB, alloc=723.8MB, time=241.47 memory used=15021.5MB, alloc=723.8MB, time=242.07 memory used=15333.0MB, alloc=723.8MB, time=246.66 memory used=15610.7MB, alloc=723.8MB, time=247.43 memory used=15767.5MB, alloc=723.8MB, time=247.99 memory used=15954.9MB, alloc=723.8MB, time=248.58 memory used=16159.9MB, alloc=723.8MB, time=249.19 memory used=16326.8MB, alloc=723.8MB, time=249.75 memory used=16515.2MB, alloc=723.8MB, time=250.34 memory used=16729.9MB, alloc=723.8MB, time=250.95 memory used=17099.4MB, alloc=723.8MB, time=252.19 memory used=17413.5MB, alloc=723.8MB, time=255.28 memory used=17568.1MB, alloc=723.8MB, time=255.84 memory used=17759.0MB, alloc=723.8MB, time=256.45 memory used=18157.9MB, alloc=723.8MB, time=262.57 memory used=18462.2MB, alloc=723.8MB, time=263.49 memory used=18619.7MB, alloc=723.8MB, time=264.13 memory used=18806.1MB, alloc=723.8MB, time=264.81 memory used=19010.7MB, alloc=723.8MB, time=265.53 memory used=19176.5MB, alloc=723.8MB, time=266.16 memory used=19362.9MB, alloc=723.8MB, time=266.78 memory used=19573.9MB, alloc=723.8MB, time=267.45 memory used=19769.2MB, alloc=723.8MB, time=268.05 memory used=20015.4MB, alloc=723.8MB, time=270.52 memory used=20272.0MB, alloc=723.8MB, time=272.58 memory used=20528.1MB, alloc=723.8MB, time=294.92 memory used=20697.4MB, alloc=723.8MB, time=295.62 memory used=21000.2MB, alloc=723.8MB, time=296.57 memory used=21144.3MB, alloc=723.8MB, time=297.23 memory used=21311.9MB, alloc=723.8MB, time=297.92 memory used=21499.5MB, alloc=723.8MB, time=298.59 memory used=21710.6MB, alloc=723.8MB, time=299.32 memory used=21880.7MB, alloc=723.8MB, time=299.96 memory used=22045.0MB, alloc=723.8MB, time=300.58 memory used=22221.5MB, alloc=723.8MB, time=301.25 memory used=22412.2MB, alloc=723.8MB, time=301.89 memory used=22615.2MB, alloc=723.8MB, time=302.61 memory used=22835.8MB, alloc=723.8MB, time=303.33 memory used=23017.7MB, alloc=723.8MB, time=303.96 memory used=23201.3MB, alloc=723.8MB, time=304.60 memory used=23393.6MB, alloc=723.8MB, time=305.28 memory used=23598.2MB, alloc=723.8MB, time=305.93 memory used=23815.2MB, alloc=723.8MB, time=306.59 memory used=24018.3MB, alloc=723.8MB, time=307.28 memory used=24214.9MB, alloc=723.8MB, time=307.90 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428499058 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 2 F := [-10 x y + 17 y + 2 z, x z - 3 y z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 G := [16 x y + 16 y - 8 z , 9 x y + x y z - 9 y z] > Problem := [F,G]; 2 3 2 2 Problem := [[-10 x y + 17 y + 2 z, x z - 3 y z], 2 2 2 2 [16 x y + 16 y - 8 z , 9 x y + x y z - 9 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.6MB, alloc=32.3MB, time=0.51 memory used=47.8MB, alloc=32.3MB, time=0.83 memory used=67.6MB, alloc=56.3MB, time=1.15 memory used=109.0MB, alloc=60.3MB, time=1.79 memory used=148.3MB, alloc=84.3MB, time=2.40 memory used=210.3MB, alloc=92.3MB, time=3.36 memory used=272.4MB, alloc=116.3MB, time=4.30 memory used=350.9MB, alloc=116.3MB, time=5.47 memory used=429.7MB, alloc=396.3MB, time=6.76 memory used=536.9MB, alloc=420.3MB, time=8.56 memory used=652.8MB, alloc=444.3MB, time=10.62 memory used=785.0MB, alloc=468.3MB, time=12.94 memory used=928.0MB, alloc=492.3MB, time=15.54 memory used=1084.0MB, alloc=516.3MB, time=18.39 memory used=1252.9MB, alloc=540.3MB, time=21.48 memory used=1430.8MB, alloc=564.3MB, time=24.77 memory used=1616.5MB, alloc=588.3MB, time=28.23 memory used=1795.6MB, alloc=612.3MB, time=31.58 memory used=1998.0MB, alloc=636.3MB, time=37.00 memory used=2184.1MB, alloc=660.3MB, time=43.55 memory used=2379.4MB, alloc=684.3MB, time=50.63 memory used=2587.8MB, alloc=708.3MB, time=58.41 memory used=2809.5MB, alloc=732.3MB, time=67.03 memory used=3045.7MB, alloc=756.3MB, time=76.34 memory used=3296.2MB, alloc=780.3MB, time=86.53 memory used=3561.8MB, alloc=804.3MB, time=97.24 memory used=3837.0MB, alloc=828.3MB, time=109.49 memory used=4133.4MB, alloc=852.3MB, time=124.00 memory used=4453.7MB, alloc=876.3MB, time=140.07 memory used=4798.0MB, alloc=900.3MB, time=157.46 memory used=5166.2MB, alloc=924.3MB, time=175.50 memory used=5558.4MB, alloc=948.3MB, time=192.84 memory used=5974.5MB, alloc=972.3MB, time=211.11 memory used=6414.5MB, alloc=996.3MB, time=230.80 memory used=6878.5MB, alloc=996.3MB, time=251.38 |\^/| 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(); 1428499358 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 3 F := [-3 x + 20 z , -9 y z - z + 7 z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 2 2 G := [6 x y - 13 x z - 8 x z , -7 x z - 8 x y + 5 y ] > Problem := [F,G]; 2 2 2 3 Problem := [[-3 x + 20 z , -9 y z - z + 7 z], 2 2 2 2 2 2 [6 x y - 13 x z - 8 x z , -7 x z - 8 x y + 5 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=25.9MB, alloc=32.3MB, time=0.50 memory used=48.2MB, alloc=56.3MB, time=0.77 memory used=91.3MB, alloc=60.3MB, time=1.37 memory used=135.5MB, alloc=60.3MB, time=1.89 memory used=179.4MB, alloc=60.3MB, time=2.32 memory used=223.1MB, alloc=84.3MB, time=2.81 memory used=262.8MB, alloc=84.3MB, time=3.31 memory used=328.7MB, alloc=92.3MB, time=4.25 memory used=394.1MB, alloc=116.3MB, time=5.20 memory used=464.1MB, alloc=116.3MB, time=6.25 memory used=525.1MB, alloc=372.3MB, time=7.18 memory used=611.6MB, alloc=396.3MB, time=8.42 memory used=725.4MB, alloc=420.3MB, time=10.04 memory used=861.4MB, alloc=444.3MB, time=11.93 memory used=992.3MB, alloc=468.3MB, time=14.01 memory used=1114.8MB, alloc=468.3MB, time=16.07 memory used=1219.9MB, alloc=492.3MB, time=17.88 memory used=1327.9MB, alloc=492.3MB, time=19.52 memory used=1427.1MB, alloc=516.3MB, time=21.23 memory used=1519.6MB, alloc=516.3MB, time=22.90 memory used=1648.3MB, alloc=540.3MB, time=25.07 memory used=1751.1MB, alloc=540.3MB, time=27.05 memory used=1897.2MB, alloc=564.3MB, time=29.86 memory used=2040.9MB, alloc=588.3MB, time=32.73 memory used=2178.4MB, alloc=612.3MB, time=35.76 memory used=2311.6MB, alloc=636.3MB, time=39.01 memory used=2440.8MB, alloc=660.3MB, time=41.75 memory used=2574.3MB, alloc=684.3MB, time=44.56 memory used=2706.1MB, alloc=708.3MB, time=47.23 memory used=2825.7MB, alloc=732.3MB, time=49.79 memory used=2945.3MB, alloc=756.3MB, time=52.43 memory used=3052.9MB, alloc=780.3MB, time=54.85 memory used=3150.0MB, alloc=804.3MB, time=57.12 memory used=3237.6MB, alloc=828.3MB, time=59.26 memory used=3331.4MB, alloc=828.3MB, time=61.56 memory used=3426.8MB, alloc=852.3MB, time=64.16 memory used=3838.1MB, alloc=876.3MB, time=71.56 memory used=4226.9MB, alloc=900.3MB, time=79.21 memory used=4610.4MB, alloc=924.3MB, time=87.25 memory used=4988.0MB, alloc=948.3MB, time=95.18 memory used=5339.9MB, alloc=972.3MB, time=103.90 memory used=5629.2MB, alloc=996.3MB, time=115.70 memory used=5917.3MB, alloc=1020.3MB, time=127.66 memory used=6210.5MB, alloc=1044.3MB, time=139.97 memory used=6512.1MB, alloc=1068.3MB, time=152.65 memory used=6824.4MB, alloc=1092.3MB, time=165.99 memory used=7148.4MB, alloc=1116.3MB, time=180.67 memory used=7484.6MB, alloc=1140.3MB, time=195.24 memory used=7833.3MB, alloc=1164.3MB, time=210.74 |\^/| 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(); 1428499658 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 2 F := [13 x z + 15 x - 19 y, 9 x y - 6 y z - 10 y ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 3 2 2 G := [16 x y + 2 x y z - 11 z , -6 x - 4 x y - 5 x ] > Problem := [F,G]; 2 2 2 2 2 Problem := [[13 x z + 15 x - 19 y, 9 x y - 6 y z - 10 y ], 2 2 3 2 2 [16 x y + 2 x y z - 11 z , -6 x - 4 x 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=4.2MB, alloc=32.3MB, time=0.17 memory used=26.6MB, alloc=32.3MB, time=0.51 memory used=48.4MB, alloc=32.3MB, time=0.84 memory used=67.9MB, alloc=56.3MB, time=1.15 memory used=108.3MB, alloc=60.3MB, time=1.78 memory used=148.8MB, alloc=84.3MB, time=2.49 memory used=208.4MB, alloc=84.3MB, time=3.57 memory used=263.7MB, alloc=108.3MB, time=4.62 memory used=338.1MB, alloc=140.3MB, time=6.10 memory used=423.2MB, alloc=164.3MB, time=8.80 memory used=519.0MB, alloc=188.3MB, time=12.71 memory used=638.9MB, alloc=188.3MB, time=17.48 N1 := 3059 > GB := Basis(F, plex(op(vars))); 3 2 2 2 3 2 2 GB := [-117 x y + 40 x y + 114 y , 13 z x + 15 x - 19 y, 2 2 2 -9 x y + 6 y z + 10 y ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=753.9MB, alloc=188.3MB, time=19.68 memory used=893.1MB, alloc=468.3MB, time=22.21 memory used=1048.2MB, alloc=492.3MB, time=25.77 memory used=1193.1MB, alloc=516.3MB, time=31.42 N2 := 3059 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 2 H := [13 z x + 15 x - 19 y, 9 x y - 6 y z - 10 y , 2 2 3 2 2 2 z y x + 16 y x - 11 z , -6 x - 4 x y - 5 x ] > J:=[op(GB),op(G)]; 3 2 2 2 3 2 2 J := [-117 x y + 40 x y + 114 y , 13 z x + 15 x - 19 y, 2 2 2 2 2 3 2 2 -9 x y + 6 y z + 10 y , 2 z y x + 16 y x - 11 z , -6 x - 4 x y - 5 x ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 11, 12, 3, 3, 2, 2, 1, 1, 3/4, 2/3, 7/12, 1/3, 5, 13, 17, 5, 3, 3, 2, 1, 1, 3/5, 2/3, 2/3, 4/15, -2, -5, -2] > save(F, G, cat("ranSet/33", convert(F, string),".txt")); > quit memory used=1317.3MB, alloc=516.3MB, time=36.20 |\^/| 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(); 1428499703 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 F := [17 x - y - 12 y, 7 x z + 5 x y + x] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 G := [-4 y z - 4 x y + 19 y , -2 y z + 10 x - 2 y z] > Problem := [F,G]; 3 2 2 Problem := [[17 x - y - 12 y, 7 x z + 5 x y + x], 2 2 2 2 [-4 y z - 4 x y + 19 y , -2 y z + 10 x - 2 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.19 memory used=26.5MB, alloc=32.3MB, time=0.52 memory used=46.7MB, alloc=32.3MB, time=0.83 memory used=65.2MB, alloc=56.3MB, time=1.12 memory used=106.0MB, alloc=60.3MB, time=1.75 memory used=146.5MB, alloc=84.3MB, time=2.39 memory used=209.8MB, alloc=92.3MB, time=3.37 memory used=272.1MB, alloc=116.3MB, time=4.36 memory used=355.3MB, alloc=140.3MB, time=5.89 memory used=455.6MB, alloc=164.3MB, time=7.70 memory used=566.7MB, alloc=188.3MB, time=9.63 memory used=668.1MB, alloc=444.3MB, time=11.48 memory used=819.2MB, alloc=500.3MB, time=15.92 memory used=971.1MB, alloc=524.3MB, time=22.05 memory used=1137.5MB, alloc=524.3MB, time=29.00 memory used=1303.7MB, alloc=548.3MB, time=35.84 memory used=1494.1MB, alloc=548.3MB, time=43.41 N1 := 5357 > GB := Basis(F, plex(op(vars))); 3 2 2 GB := [-17 x + y + 12 y, 7 x z + 5 x y + x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1687.2MB, alloc=548.3MB, time=50.61 memory used=1911.7MB, alloc=548.3MB, time=54.66 memory used=2136.0MB, alloc=572.3MB, time=58.84 memory used=2373.2MB, alloc=596.3MB, time=63.68 memory used=2595.5MB, alloc=620.3MB, time=71.72 memory used=2817.7MB, alloc=644.3MB, time=81.43 memory used=3063.8MB, alloc=668.3MB, time=91.72 N2 := 5357 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 2 2 2 H := [17 x - y - 12 y, 7 x z + 5 x y + x, -4 y z - 4 x y + 19 y , 2 2 -2 y z + 10 x - 2 y z] > J:=[op(GB),op(G)]; 3 2 2 2 2 J := [-17 x + y + 12 y, 7 x z + 5 x y + x, -4 y z - 4 x y + 19 y , 2 2 -2 y z + 10 x - 2 y z] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 11, 12, 3, 3, 2, 2, 1, 1, 3/4, 1/2, 2/3, 1/3, 4, 11, 12, 3, 3, 2, 2, 1, 1, 3/4, 1/2, 2/3, 1/3, 0, 0, 0] > save(F, G, cat("ranSet/33", convert(F, string),".txt")); > quit memory used=3324.3MB, alloc=668.3MB, time=102.29 |\^/| 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(); 1428499831 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 F := [-14 x z + 2 y - 10 y, 9 x y - 4 z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 G := [-14 z + 3 y z + 9 x, 10 y z + 9 x - 2 x] > Problem := [F,G]; 2 3 2 Problem := [[-14 x z + 2 y - 10 y, 9 x y - 4 z], 3 2 2 [-14 z + 3 y z + 9 x, 10 y z + 9 x - 2 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=26.3MB, alloc=32.3MB, time=0.49 memory used=46.0MB, alloc=32.3MB, time=0.65 memory used=62.4MB, alloc=32.3MB, time=0.76 memory used=82.6MB, alloc=56.3MB, time=1.08 memory used=122.5MB, alloc=60.3MB, time=1.65 memory used=169.1MB, alloc=68.3MB, time=2.18 memory used=197.9MB, alloc=68.3MB, time=2.34 memory used=235.8MB, alloc=68.3MB, time=2.67 memory used=260.8MB, alloc=68.3MB, time=2.78 memory used=287.3MB, alloc=68.3MB, time=2.87 memory used=310.2MB, alloc=68.3MB, time=2.95 memory used=330.0MB, alloc=68.3MB, time=3.01 memory used=355.7MB, alloc=68.3MB, time=3.69 memory used=385.4MB, alloc=68.3MB, time=4.00 memory used=404.8MB, alloc=68.3MB, time=4.07 memory used=424.9MB, alloc=68.3MB, time=4.15 memory used=446.0MB, alloc=68.3MB, time=4.21 memory used=476.9MB, alloc=68.3MB, time=4.49 memory used=505.7MB, alloc=68.3MB, time=4.66 memory used=536.7MB, alloc=68.3MB, time=4.84 memory used=587.7MB, alloc=68.3MB, time=5.36 memory used=640.8MB, alloc=92.3MB, time=5.92 memory used=715.1MB, alloc=92.3MB, time=6.62 memory used=784.3MB, alloc=92.3MB, time=7.54 memory used=841.6MB, alloc=92.3MB, time=8.08 memory used=895.4MB, alloc=92.3MB, time=8.52 memory used=935.6MB, alloc=92.3MB, time=8.74 memory used=973.7MB, alloc=92.3MB, time=9.10 memory used=1007.2MB, alloc=92.3MB, time=9.27 memory used=1087.1MB, alloc=116.5MB, time=10.27 memory used=1166.7MB, alloc=116.5MB, time=12.34 memory used=1213.6MB, alloc=116.5MB, time=12.48 memory used=1252.4MB, alloc=116.5MB, time=12.62 memory used=1299.8MB, alloc=116.5MB, time=12.78 memory used=1355.5MB, alloc=116.5MB, time=12.93 memory used=1391.6MB, alloc=116.5MB, time=13.05 memory used=1425.8MB, alloc=116.5MB, time=13.16 memory used=1462.8MB, alloc=116.5MB, time=13.26 memory used=1503.2MB, alloc=116.5MB, time=13.38 memory used=1546.6MB, alloc=116.5MB, time=13.49 memory used=1594.7MB, alloc=116.5MB, time=13.60 memory used=1646.0MB, alloc=116.5MB, time=13.72 memory used=1701.5MB, alloc=131.8MB, time=13.86 memory used=1712.9MB, alloc=131.8MB, time=13.94 memory used=1724.8MB, alloc=131.8MB, time=14.01 memory used=1786.8MB, alloc=131.8MB, time=14.44 memory used=1826.0MB, alloc=131.8MB, time=14.59 memory used=1878.3MB, alloc=131.8MB, time=14.75 memory used=1915.1MB, alloc=131.8MB, time=14.86 memory used=1952.3MB, alloc=131.8MB, time=14.96 memory used=2028.1MB, alloc=131.8MB, time=15.40 memory used=2134.1MB, alloc=131.8MB, time=16.20 memory used=2245.7MB, alloc=131.8MB, time=16.89 memory used=2324.7MB, alloc=131.8MB, time=17.82 memory used=2418.4MB, alloc=131.8MB, time=18.62 memory used=2527.3MB, alloc=131.8MB, time=19.34 memory used=2631.0MB, alloc=387.8MB, time=20.36 memory used=2741.9MB, alloc=387.8MB, time=22.98 memory used=2783.8MB, alloc=387.8MB, time=23.12 memory used=2820.8MB, alloc=387.8MB, time=23.27 memory used=2854.8MB, alloc=387.8MB, time=23.42 memory used=2894.7MB, alloc=387.8MB, time=23.57 memory used=2941.2MB, alloc=387.8MB, time=23.73 memory used=2978.9MB, alloc=411.8MB, time=23.90 memory used=3020.6MB, alloc=411.8MB, time=24.05 memory used=3067.3MB, alloc=411.8MB, time=24.20 memory used=3118.8MB, alloc=411.8MB, time=24.34 memory used=3176.3MB, alloc=411.8MB, time=24.47 memory used=3239.9MB, alloc=411.8MB, time=24.62 memory used=3358.0MB, alloc=411.8MB, time=25.17 memory used=3413.4MB, alloc=411.8MB, time=25.36 memory used=3473.6MB, alloc=411.8MB, time=25.55 memory used=3524.0MB, alloc=411.8MB, time=25.69 memory used=3573.4MB, alloc=411.8MB, time=25.83 memory used=3696.4MB, alloc=411.8MB, time=26.87 memory used=3832.6MB, alloc=411.8MB, time=28.05 memory used=3939.1MB, alloc=411.8MB, time=29.13 memory used=4048.5MB, alloc=411.8MB, time=30.64 memory used=4152.2MB, alloc=435.8MB, time=32.10 memory used=4257.7MB, alloc=435.8MB, time=33.05 memory used=4336.2MB, alloc=435.8MB, time=34.07 memory used=4439.1MB, alloc=435.8MB, time=34.92 memory used=4539.6MB, alloc=435.8MB, time=35.88 memory used=4668.8MB, alloc=459.8MB, time=37.37 memory used=4779.9MB, alloc=459.8MB, time=38.12 memory used=4851.5MB, alloc=459.8MB, time=38.38 memory used=4922.7MB, alloc=459.8MB, time=38.71 memory used=5013.1MB, alloc=459.8MB, time=41.26 memory used=5082.8MB, alloc=459.8MB, time=41.54 memory used=5142.7MB, alloc=459.8MB, time=41.80 memory used=5220.0MB, alloc=459.8MB, time=42.10 memory used=5416.0MB, alloc=459.8MB, time=42.69 memory used=5629.0MB, alloc=459.8MB, time=43.13 memory used=5768.9MB, alloc=459.8MB, time=43.74 memory used=5915.3MB, alloc=459.8MB, time=45.31 memory used=6154.5MB, alloc=459.8MB, time=49.39 memory used=6226.2MB, alloc=459.8MB, time=49.68 memory used=6283.2MB, alloc=459.8MB, time=49.92 memory used=6352.0MB, alloc=459.8MB, time=50.16 memory used=6432.2MB, alloc=459.8MB, time=50.43 memory used=6620.1MB, alloc=459.8MB, time=50.86 memory used=6798.1MB, alloc=459.8MB, time=51.27 memory used=7013.4MB, alloc=459.8MB, time=51.72 memory used=7237.1MB, alloc=459.8MB, time=52.16 memory used=7438.1MB, alloc=459.8MB, time=52.54 memory used=7653.4MB, alloc=459.8MB, time=53.56 memory used=7719.3MB, alloc=459.8MB, time=53.82 memory used=7785.3MB, alloc=459.8MB, time=54.06 memory used=8026.6MB, alloc=459.8MB, time=54.57 memory used=8244.9MB, alloc=459.8MB, time=55.00 memory used=8403.3MB, alloc=459.8MB, time=56.50 memory used=8557.1MB, alloc=459.8MB, time=57.96 memory used=8673.0MB, alloc=459.8MB, time=59.50 memory used=8762.1MB, alloc=459.8MB, time=60.10 memory used=8832.7MB, alloc=459.8MB, time=60.50 memory used=8931.1MB, alloc=483.8MB, time=61.14 memory used=9012.5MB, alloc=483.8MB, time=61.46 memory used=9097.9MB, alloc=483.8MB, time=61.87 memory used=9197.1MB, alloc=483.8MB, time=62.36 memory used=9276.7MB, alloc=483.8MB, time=62.70 memory used=9363.9MB, alloc=483.8MB, time=63.67 memory used=9451.1MB, alloc=483.8MB, time=64.01 memory used=9517.9MB, alloc=483.8MB, time=64.26 memory used=9605.9MB, alloc=483.8MB, time=64.54 memory used=9781.8MB, alloc=483.8MB, time=65.79 memory used=9884.8MB, alloc=483.8MB, time=66.89 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alloc=531.8MB, time=100.09 memory used=16383.2MB, alloc=531.8MB, time=101.55 memory used=16487.3MB, alloc=531.8MB, time=101.96 memory used=16574.3MB, alloc=531.8MB, time=102.34 memory used=16679.0MB, alloc=531.8MB, time=102.74 memory used=16800.7MB, alloc=531.8MB, time=103.16 memory used=17010.3MB, alloc=531.8MB, time=103.73 memory used=17169.9MB, alloc=531.8MB, time=104.21 memory used=17349.7MB, alloc=531.8MB, time=104.74 memory used=17553.3MB, alloc=531.8MB, time=105.26 memory used=17783.9MB, alloc=531.8MB, time=105.82 memory used=18002.0MB, alloc=531.8MB, time=106.36 memory used=18198.0MB, alloc=531.8MB, time=106.84 memory used=18453.6MB, alloc=531.8MB, time=108.30 memory used=18588.9MB, alloc=531.8MB, time=109.85 memory used=18765.6MB, alloc=531.8MB, time=111.23 memory used=18869.4MB, alloc=531.8MB, time=112.62 memory used=19017.3MB, alloc=531.8MB, time=114.05 memory used=19113.5MB, alloc=531.8MB, time=115.47 memory used=19230.1MB, alloc=531.8MB, time=116.33 memory used=19343.0MB, 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alloc=579.8MB, time=238.86 memory used=49319.5MB, alloc=579.8MB, time=239.77 memory used=49647.3MB, alloc=579.8MB, time=240.65 memory used=49984.6MB, alloc=579.8MB, time=241.57 memory used=50314.9MB, alloc=579.8MB, time=242.46 memory used=50647.0MB, alloc=579.8MB, time=243.35 memory used=50988.8MB, alloc=579.8MB, time=244.22 memory used=51303.1MB, alloc=579.8MB, time=245.09 memory used=51607.5MB, alloc=579.8MB, time=245.86 memory used=51933.0MB, alloc=579.8MB, time=246.72 memory used=52228.1MB, alloc=579.8MB, time=247.43 memory used=52602.6MB, alloc=579.8MB, time=250.80 memory used=52787.9MB, alloc=579.8MB, time=251.82 memory used=52953.2MB, alloc=579.8MB, time=252.61 memory used=53130.3MB, alloc=579.8MB, time=253.36 memory used=53356.2MB, alloc=603.8MB, time=254.65 memory used=53569.7MB, alloc=603.8MB, time=255.69 memory used=53760.6MB, alloc=603.8MB, time=256.49 memory used=53969.5MB, alloc=603.8MB, time=257.34 memory used=54217.9MB, alloc=603.8MB, time=258.67 memory used=54413.6MB, alloc=603.8MB, time=259.50 memory used=54605.0MB, alloc=603.8MB, time=260.31 memory used=54807.0MB, alloc=603.8MB, time=261.09 memory used=55028.0MB, alloc=603.8MB, time=261.90 memory used=55286.1MB, alloc=603.8MB, time=262.82 memory used=55569.9MB, alloc=603.8MB, time=263.74 memory used=55885.4MB, alloc=603.8MB, time=264.74 memory used=56237.1MB, alloc=603.8MB, time=265.72 memory used=56637.1MB, alloc=603.8MB, time=266.76 memory used=57023.8MB, alloc=603.8MB, time=267.74 memory used=57408.5MB, alloc=603.8MB, time=268.75 memory used=57744.8MB, alloc=603.8MB, time=270.65 memory used=57933.8MB, alloc=603.8MB, time=271.51 memory used=58120.6MB, alloc=603.8MB, time=272.30 memory used=58310.7MB, alloc=603.8MB, time=273.07 memory used=58514.5MB, alloc=603.8MB, time=273.83 memory used=58754.5MB, alloc=603.8MB, time=274.66 memory used=59025.7MB, alloc=603.8MB, time=275.56 memory used=59324.4MB, alloc=603.8MB, time=276.49 memory used=59643.5MB, alloc=603.8MB, time=277.38 memory used=59997.9MB, alloc=603.8MB, time=278.32 memory used=60413.0MB, alloc=603.8MB, time=279.34 memory used=60797.6MB, alloc=603.8MB, time=280.28 memory used=61130.2MB, alloc=603.8MB, time=281.09 memory used=61516.8MB, alloc=603.8MB, time=282.05 memory used=61830.5MB, alloc=603.8MB, time=282.82 memory used=62303.4MB, alloc=603.8MB, time=285.96 memory used=62579.3MB, alloc=603.8MB, time=288.07 memory used=62824.5MB, alloc=603.8MB, time=289.17 memory used=63163.4MB, alloc=603.8MB, time=290.10 memory used=63589.2MB, alloc=603.8MB, time=291.20 memory used=64022.2MB, alloc=603.8MB, time=292.32 memory used=64415.4MB, alloc=603.8MB, time=293.37 memory used=64788.2MB, alloc=603.8MB, time=294.33 memory used=65204.4MB, alloc=603.8MB, time=297.33 memory used=65405.4MB, alloc=603.8MB, time=298.36 memory used=65585.2MB, alloc=603.8MB, time=299.17 memory used=65839.6MB, alloc=603.8MB, time=300.94 memory used=66059.2MB, alloc=603.8MB, time=302.30 memory used=66320.9MB, alloc=627.8MB, time=305.53 memory used=66599.6MB, alloc=651.8MB, time=310.33 |\^/| 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(); 1428500131 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 3 2 F := [11 y z - 12 z + 2 x y, -5 x z - 8 y + 2 y ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 G := [-5 x y - 14 x z - 8 y, -7 x y - 9 z - 4] > Problem := [F,G]; 2 3 2 3 2 Problem := [[11 y z - 12 z + 2 x y, -5 x z - 8 y + 2 y ], 2 2 2 [-5 x y - 14 x z - 8 y, -7 x y - 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=31.8MB, alloc=40.3MB, time=0.58 memory used=59.5MB, alloc=44.3MB, time=0.99 memory used=85.7MB, alloc=68.3MB, time=1.38 memory used=135.7MB, alloc=76.3MB, time=2.09 memory used=186.4MB, alloc=76.3MB, time=2.80 memory used=237.0MB, alloc=100.3MB, time=3.48 memory used=308.8MB, alloc=100.3MB, time=4.48 memory used=380.0MB, alloc=100.3MB, time=5.51 memory used=444.9MB, alloc=380.3MB, time=6.41 memory used=545.5MB, alloc=380.3MB, time=7.71 memory used=630.8MB, alloc=380.3MB, time=8.70 memory used=672.1MB, alloc=380.3MB, time=8.86 memory used=751.6MB, alloc=380.3MB, time=9.71 memory used=845.8MB, alloc=404.3MB, time=11.11 memory used=964.0MB, alloc=428.3MB, time=12.67 memory used=1102.5MB, alloc=428.3MB, time=14.45 memory used=1223.4MB, alloc=452.3MB, time=16.17 memory used=1369.3MB, alloc=452.3MB, time=17.53 memory used=1454.5MB, alloc=452.3MB, time=18.70 memory used=1591.2MB, alloc=452.3MB, time=19.98 memory used=1749.7MB, alloc=452.3MB, time=21.20 memory used=1885.0MB, alloc=452.3MB, time=23.03 memory used=1997.6MB, alloc=476.3MB, time=24.90 memory used=2095.7MB, alloc=476.3MB, time=26.45 memory used=2190.9MB, alloc=476.3MB, time=27.91 memory used=2276.3MB, alloc=476.3MB, time=28.33 memory used=2372.4MB, alloc=476.3MB, time=28.92 memory used=2489.2MB, alloc=500.3MB, time=30.35 memory used=2573.2MB, alloc=500.3MB, time=31.74 memory used=2679.9MB, alloc=500.3MB, time=32.88 memory used=2787.9MB, alloc=500.3MB, time=33.51 memory used=2999.4MB, alloc=500.3MB, time=35.60 memory used=3146.1MB, alloc=500.3MB, time=41.83 memory used=3244.4MB, alloc=500.3MB, time=43.31 memory used=3345.3MB, alloc=500.3MB, time=43.74 memory used=3412.0MB, alloc=500.3MB, time=44.09 memory used=3489.1MB, alloc=500.3MB, time=44.45 memory used=3575.6MB, alloc=500.3MB, time=44.81 memory used=3674.9MB, alloc=500.3MB, time=45.20 memory used=3785.3MB, alloc=500.3MB, time=45.58 memory used=3929.4MB, alloc=500.3MB, time=46.23 memory used=4076.0MB, alloc=500.3MB, time=46.70 memory used=4238.4MB, alloc=500.3MB, time=47.20 memory used=4417.4MB, alloc=500.3MB, time=47.70 memory used=4615.5MB, alloc=500.3MB, time=48.22 memory used=4835.5MB, alloc=500.3MB, time=48.76 memory used=5047.3MB, alloc=500.3MB, time=49.28 memory used=5225.4MB, alloc=500.3MB, time=49.76 memory used=5419.6MB, alloc=500.3MB, time=50.25 memory used=5714.0MB, alloc=500.3MB, time=51.48 memory used=5836.2MB, alloc=500.3MB, time=52.75 memory used=5946.9MB, alloc=500.3MB, time=54.01 memory used=6040.6MB, alloc=500.3MB, time=55.66 memory used=6154.1MB, alloc=500.3MB, time=56.63 memory used=6242.6MB, alloc=524.3MB, time=57.89 memory used=6359.0MB, alloc=524.3MB, time=59.64 memory used=6532.0MB, alloc=524.3MB, time=60.59 memory used=6733.6MB, alloc=524.3MB, time=61.93 memory used=6920.6MB, alloc=524.3MB, time=63.12 memory used=7093.3MB, alloc=524.3MB, time=64.81 memory used=7224.2MB, alloc=524.3MB, time=66.42 memory used=7405.8MB, alloc=548.3MB, time=67.64 memory used=7606.0MB, alloc=548.3MB, time=68.36 memory used=7870.4MB, alloc=548.3MB, time=69.16 memory used=8139.8MB, alloc=548.3MB, time=69.93 memory used=8438.0MB, alloc=548.3MB, time=70.77 memory used=8621.1MB, alloc=548.3MB, time=72.61 memory used=8823.8MB, alloc=548.3MB, time=74.02 memory used=8990.3MB, alloc=548.3MB, time=74.77 memory used=9192.0MB, alloc=548.3MB, time=76.68 memory used=9320.1MB, alloc=548.3MB, time=78.29 memory used=9460.2MB, alloc=548.3MB, time=79.82 memory used=9537.4MB, alloc=548.3MB, time=81.30 memory used=9625.7MB, alloc=548.3MB, time=82.91 memory used=9737.7MB, alloc=572.3MB, time=84.89 memory used=9842.7MB, alloc=572.3MB, time=86.84 memory used=9938.1MB, alloc=596.3MB, time=88.73 memory used=10039.9MB, alloc=596.3MB, time=90.64 memory used=10128.2MB, alloc=620.3MB, time=92.35 memory used=10249.8MB, alloc=620.3MB, time=94.32 memory used=10379.4MB, alloc=620.3MB, time=95.99 memory used=10507.7MB, alloc=620.3MB, time=97.80 memory used=10640.3MB, alloc=620.3MB, time=99.54 memory used=10748.4MB, alloc=620.3MB, time=101.22 memory used=11034.6MB, alloc=644.3MB, time=104.94 memory used=11306.2MB, alloc=668.3MB, time=109.64 memory used=11592.0MB, alloc=692.3MB, time=114.61 memory used=11899.4MB, alloc=716.3MB, time=119.66 memory used=12214.9MB, alloc=740.3MB, time=125.18 memory used=12612.3MB, alloc=764.3MB, time=130.34 memory used=13040.4MB, alloc=788.3MB, time=134.96 memory used=13371.0MB, alloc=812.3MB, time=140.89 memory used=13711.3MB, alloc=836.3MB, time=146.84 memory used=14045.3MB, alloc=860.3MB, time=152.87 memory used=14401.9MB, alloc=884.3MB, time=158.84 memory used=14775.3MB, alloc=908.3MB, time=164.93 memory used=15077.1MB, alloc=932.3MB, time=171.00 memory used=15497.1MB, alloc=956.3MB, time=180.14 memory used=15838.2MB, alloc=980.3MB, time=192.71 memory used=16174.9MB, alloc=1004.3MB, time=206.09 memory used=16518.4MB, alloc=1028.3MB, time=220.17 memory used=16870.4MB, alloc=1052.3MB, time=234.73 memory used=17233.6MB, alloc=1076.3MB, time=249.96 memory used=17607.6MB, alloc=1100.3MB, time=265.90 |\^/| 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(); 1428500431 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 F := [18 x z + 12 x - 8 z, 6 y z + 7 x + 9] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 2 3 G := [7 x z + 19 y - 16 x , -5 x y + 2 y - x z] > Problem := [F,G]; 2 2 2 Problem := [[18 x z + 12 x - 8 z, 6 y z + 7 x + 9], 2 3 2 2 3 [7 x z + 19 y - 16 x , -5 x y + 2 y - x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=25.5MB, alloc=32.3MB, time=0.49 memory used=45.3MB, alloc=32.3MB, time=0.78 memory used=63.3MB, alloc=56.3MB, time=1.04 memory used=108.6MB, alloc=68.3MB, time=1.63 memory used=154.1MB, alloc=68.3MB, time=2.20 memory used=198.7MB, alloc=92.3MB, time=2.80 memory used=263.9MB, alloc=92.3MB, time=3.45 memory used=333.8MB, alloc=92.3MB, time=4.33 memory used=408.1MB, alloc=92.3MB, time=5.14 memory used=456.3MB, alloc=92.3MB, time=6.99 memory used=492.3MB, alloc=92.3MB, time=7.20 memory used=518.5MB, alloc=92.3MB, time=7.30 memory used=547.8MB, alloc=92.3MB, time=7.41 memory used=587.1MB, alloc=92.3MB, time=7.71 memory used=652.8MB, alloc=348.3MB, time=8.47 memory used=725.4MB, alloc=372.3MB, time=9.04 memory used=838.3MB, alloc=372.3MB, time=10.67 memory used=906.4MB, alloc=372.3MB, time=11.09 memory used=972.8MB, alloc=372.3MB, time=13.36 memory used=1014.7MB, alloc=372.3MB, time=13.52 memory used=1061.2MB, alloc=372.3MB, time=13.68 memory used=1094.3MB, alloc=372.3MB, time=13.79 memory used=1134.2MB, alloc=372.3MB, time=13.92 memory used=1182.9MB, alloc=372.3MB, time=14.05 memory used=1290.6MB, alloc=372.3MB, time=15.06 memory used=1381.9MB, alloc=372.3MB, time=16.01 memory used=1471.5MB, alloc=372.3MB, time=16.99 memory used=1576.9MB, alloc=396.3MB, time=18.20 memory used=1703.9MB, alloc=420.3MB, time=19.56 memory used=1855.1MB, alloc=420.3MB, time=21.45 memory used=1978.6MB, alloc=420.3MB, time=22.16 memory used=2097.9MB, alloc=420.3MB, time=22.80 memory used=2236.9MB, alloc=420.3MB, time=23.99 memory used=2369.8MB, alloc=420.3MB, time=25.03 memory used=2539.9MB, alloc=452.3MB, time=27.01 memory used=2683.8MB, alloc=476.3MB, time=29.29 memory used=2845.9MB, alloc=500.3MB, time=31.93 memory used=3022.6MB, alloc=524.3MB, time=34.84 memory used=3218.8MB, alloc=548.3MB, time=38.11 memory used=3452.2MB, alloc=572.3MB, time=41.41 memory used=3692.2MB, alloc=596.3MB, time=45.13 memory used=3923.3MB, alloc=620.3MB, time=48.91 memory used=4115.3MB, alloc=644.3MB, time=52.37 memory used=4347.2MB, alloc=668.3MB, time=58.35 memory used=4579.9MB, alloc=692.3MB, time=66.52 memory used=4820.4MB, alloc=716.3MB, time=75.29 memory used=5072.9MB, alloc=740.3MB, time=84.87 memory used=5339.9MB, alloc=764.3MB, time=95.31 memory used=5615.6MB, alloc=788.3MB, time=106.83 memory used=5908.9MB, alloc=812.3MB, time=119.38 memory used=6226.2MB, alloc=836.3MB, time=132.99 memory used=6567.4MB, alloc=860.3MB, time=147.52 memory used=6932.5MB, alloc=884.3MB, time=163.14 memory used=7321.6MB, alloc=884.3MB, time=179.96 memory used=7710.6MB, alloc=908.3MB, time=196.43 memory used=8123.6MB, alloc=908.3MB, time=214.43 memory used=8536.5MB, alloc=908.3MB, time=232.47 memory used=8949.4MB, alloc=932.3MB, time=250.10 memory used=9386.3MB, alloc=932.3MB, time=268.38 |\^/| 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(); 1428500731 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 F := [-x + 11 y - 7 z, x z - 4 x - 2 y] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 G := [x z + 16 x y + 13 x z, 7 y z - 10 x y] > Problem := [F,G]; 2 Problem := [[-x + 11 y - 7 z, x z - 4 x - 2 y], 2 2 [x z + 16 x y + 13 x z, 7 y z - 10 x y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.3MB, alloc=32.3MB, time=0.49 memory used=46.3MB, alloc=32.3MB, time=0.78 memory used=65.1MB, alloc=56.3MB, time=1.07 memory used=104.9MB, alloc=60.3MB, time=1.67 memory used=145.2MB, alloc=84.3MB, time=2.34 memory used=205.9MB, alloc=92.3MB, time=3.42 memory used=260.8MB, alloc=116.3MB, time=4.40 memory used=334.2MB, alloc=140.3MB, time=5.71 memory used=425.7MB, alloc=164.3MB, time=7.38 memory used=531.6MB, alloc=188.3MB, time=10.38 memory used=644.1MB, alloc=212.3MB, time=14.41 memory used=773.3MB, alloc=212.3MB, time=19.65 memory used=902.5MB, alloc=236.3MB, time=24.85 memory used=1055.8MB, alloc=260.3MB, time=31.02 N1 := 4451 > GB := Basis(F, plex(op(vars))); 3 2 GB := [-x + 11 x y - 28 x - 14 y, x + 7 z - 11 y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1183.9MB, alloc=260.3MB, time=34.36 N2 := 1379 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; H := [ 2 2 2 -x + 11 y - 7 z, z x - 2 y - 4 x, x z + 16 x y + 13 x z, 7 y z - 10 x y] > J:=[op(GB),op(G)]; 3 2 2 J := [-x + 11 x y - 28 x - 14 y, x + 7 z - 11 y, x z + 16 x y + 13 x z, 2 7 y z - 10 x y] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 12, 10, 3, 2, 2, 1, 1, 1, 1, 7/11, 5/11, 5/11, 4, 11, 11, 3, 3, 2, 1, 1, 1, 3/4, 2/3, 1/2, 1/3, 1, -1, 0] > save(F, G, cat("ranSet/33", convert(F, string),".txt")); > quit memory used=1337.4MB, alloc=516.3MB, time=38.59 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428500778 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 F := [y z + 3 y z - 13, 10 x y + 10 x z - x z ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 G := [-7 x y - 11 x z + 5 y , -2 x y z + z + 6] > Problem := [F,G]; 2 2 2 2 Problem := [[y z + 3 y z - 13, 10 x y + 10 x z - x z ], 2 2 2 [-7 x y - 11 x z + 5 y , -2 x y z + 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=4.1MB, alloc=32.3MB, time=0.17 memory used=24.5MB, alloc=32.3MB, time=0.48 memory used=43.8MB, alloc=56.3MB, time=0.78 memory used=85.5MB, alloc=60.3MB, time=1.39 memory used=125.1MB, alloc=60.3MB, time=1.96 memory used=160.9MB, alloc=84.3MB, time=2.46 memory used=227.5MB, alloc=92.3MB, time=3.28 memory used=287.6MB, alloc=348.3MB, time=4.19 memory used=354.3MB, alloc=372.3MB, time=5.22 memory used=439.6MB, alloc=372.3MB, time=6.53 memory used=517.9MB, alloc=396.3MB, time=7.40 memory used=629.1MB, alloc=396.3MB, time=9.09 memory used=743.0MB, alloc=420.3MB, time=10.82 memory used=864.0MB, alloc=444.3MB, time=12.61 memory used=993.7MB, alloc=444.3MB, time=14.65 memory used=1106.3MB, alloc=444.3MB, time=16.15 memory used=1212.2MB, alloc=468.3MB, time=17.84 memory used=1351.9MB, alloc=468.3MB, time=19.22 memory used=1440.6MB, alloc=468.3MB, time=20.66 memory used=1541.2MB, alloc=468.3MB, time=22.23 memory used=1635.6MB, alloc=492.3MB, time=24.00 memory used=1718.4MB, alloc=492.3MB, time=25.53 memory used=1790.6MB, alloc=492.3MB, time=26.70 memory used=1865.4MB, alloc=492.3MB, time=28.21 memory used=1942.0MB, alloc=492.3MB, time=29.74 memory used=2006.5MB, alloc=492.3MB, time=31.05 memory used=2078.0MB, alloc=492.3MB, time=32.44 memory used=2179.9MB, alloc=516.3MB, time=33.81 memory used=2260.3MB, alloc=516.3MB, time=35.53 memory used=2327.0MB, alloc=516.3MB, time=36.90 memory used=2407.5MB, alloc=516.3MB, time=38.22 memory used=2479.3MB, alloc=516.3MB, time=39.64 memory used=2565.0MB, alloc=540.3MB, time=41.38 memory used=2644.2MB, alloc=540.3MB, time=43.00 memory used=2731.3MB, alloc=564.3MB, time=44.71 memory used=2801.6MB, alloc=564.3MB, time=46.24 memory used=2878.6MB, alloc=564.3MB, time=47.87 memory used=2954.4MB, alloc=588.3MB, time=49.67 memory used=3176.9MB, alloc=612.3MB, time=53.91 memory used=3413.0MB, alloc=636.3MB, time=58.48 memory used=3656.3MB, alloc=660.3MB, time=63.44 memory used=3904.5MB, alloc=684.3MB, time=68.56 memory used=4175.5MB, alloc=708.3MB, time=74.16 memory used=4468.8MB, alloc=732.3MB, time=79.89 memory used=4729.5MB, alloc=756.3MB, time=88.25 memory used=4970.1MB, alloc=780.3MB, time=97.79 memory used=5218.5MB, alloc=804.3MB, time=108.23 memory used=5479.1MB, alloc=828.3MB, time=119.40 memory used=5752.6MB, alloc=852.3MB, time=131.00 memory used=6039.4MB, alloc=876.3MB, time=144.55 memory used=6340.9MB, alloc=900.3MB, time=159.98 memory used=6656.9MB, alloc=924.3MB, time=175.62 memory used=6986.0MB, alloc=948.3MB, time=190.54 memory used=7324.2MB, alloc=972.3MB, time=205.89 memory used=7686.3MB, alloc=996.3MB, time=223.41 memory used=8072.4MB, alloc=1020.3MB, time=243.23 |\^/| 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(); 1428501078 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 3 F := [20 x y - 4 x y z + 12 y, 2 x y + 7 y - 5 y] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 3 2 2 G := [7 y + 4 z - 13 z, -5 x - 5 x - 4 y ] > Problem := [F,G]; 2 2 3 Problem := [[20 x y - 4 x y z + 12 y, 2 x y + 7 y - 5 y], 3 2 3 2 2 [7 y + 4 z - 13 z, -5 x - 5 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=4.1MB, alloc=32.3MB, time=0.17 memory used=26.5MB, alloc=32.3MB, time=0.51 memory used=46.1MB, alloc=56.3MB, time=0.82 memory used=87.7MB, alloc=60.3MB, time=1.57 memory used=128.0MB, alloc=84.3MB, time=2.41 memory used=183.6MB, alloc=108.3MB, time=3.51 memory used=260.8MB, alloc=140.3MB, time=4.90 memory used=354.1MB, alloc=164.3MB, time=6.87 memory used=455.1MB, alloc=188.3MB, time=10.02 memory used=567.1MB, alloc=188.3MB, time=14.32 memory used=679.0MB, alloc=212.3MB, time=18.75 memory used=815.4MB, alloc=236.3MB, time=23.65 N1 := 3703 > GB := Basis(F, plex(op(vars))); 2 3 2 GB := [2 x y + 7 y - 5 y, -5 x y + x y z - 3 y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=900.5MB, alloc=236.3MB, time=25.17 memory used=1080.0MB, alloc=516.3MB, time=28.65 memory used=1271.5MB, alloc=540.3MB, time=34.12 memory used=1454.5MB, alloc=564.3MB, time=42.37 N2 := 3703 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 3 3 2 H := [20 x y - 4 x y z + 12 y, 2 x y + 7 y - 5 y, 7 y + 4 z - 13 z, 3 2 2 -5 x - 5 x - 4 y ] > J:=[op(GB),op(G)]; 2 3 2 3 2 J := [2 x y + 7 y - 5 y, -5 x y + x y z - 3 y, 7 y + 4 z - 13 z, 3 2 2 -5 x - 5 x - 4 y ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 9, 12, 3, 3, 3, 2, 3/4, 1, 1/2, 5/12, 2/3, 1/4, 4, 9, 12, 3, 3, 3, 2, 3/4, 1, 1/2, 5/12, 2/3, 1/4, 0, 0, 0] > save(F, G, cat("ranSet/33", convert(F, string),".txt")); > quit memory used=1621.7MB, alloc=564.3MB, time=49.00 |\^/| 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(); 1428501151 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 F := [3 x y + 15 y - 2, -3 y z - x y + 10 x z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 3 G := [-18 x y + 10 x z - 8 y, 8 y z + 7 z + z] > Problem := [F,G]; 2 Problem := [[3 x y + 15 y - 2, -3 y z - x y + 10 x z], 2 2 3 [-18 x y + 10 x z - 8 y, 8 y z + 7 z + z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.23 memory used=26.4MB, alloc=32.3MB, time=0.62 memory used=45.6MB, alloc=56.3MB, time=0.96 memory used=85.3MB, alloc=60.3MB, time=1.59 memory used=125.2MB, alloc=60.3MB, time=2.17 memory used=163.9MB, alloc=60.3MB, time=2.64 memory used=205.2MB, alloc=60.3MB, time=3.30 memory used=245.1MB, alloc=84.3MB, time=3.94 memory used=307.1MB, alloc=92.3MB, time=4.92 memory used=374.9MB, alloc=92.3MB, time=5.88 memory used=433.7MB, alloc=116.3MB, time=6.80 memory used=504.0MB, alloc=372.3MB, time=7.91 memory used=587.6MB, alloc=396.3MB, time=9.39 memory used=690.3MB, alloc=420.3MB, time=11.30 memory used=804.2MB, alloc=444.3MB, time=13.49 memory used=932.8MB, alloc=468.3MB, time=15.80 memory used=1080.3MB, alloc=492.3MB, time=18.63 memory used=1242.4MB, alloc=516.3MB, time=21.48 memory used=1413.6MB, alloc=540.3MB, time=24.64 memory used=1599.1MB, alloc=564.3MB, time=28.06 memory used=1788.4MB, alloc=588.3MB, time=31.91 memory used=1965.5MB, alloc=612.3MB, time=37.52 memory used=2147.4MB, alloc=636.3MB, time=43.75 memory used=2339.5MB, alloc=660.3MB, time=50.71 memory used=2547.3MB, alloc=684.3MB, time=58.51 memory used=2770.5MB, alloc=708.3MB, time=67.04 memory used=3007.5MB, alloc=732.3MB, time=76.35 memory used=3255.2MB, alloc=756.3MB, time=86.76 memory used=3526.9MB, alloc=780.3MB, time=98.09 memory used=3822.5MB, alloc=804.3MB, time=110.44 memory used=4142.0MB, alloc=828.3MB, time=123.89 memory used=4485.4MB, alloc=852.3MB, time=138.30 memory used=4852.9MB, alloc=876.3MB, time=154.78 memory used=5244.2MB, alloc=876.3MB, time=171.29 memory used=5635.5MB, alloc=876.3MB, time=188.27 memory used=6026.8MB, alloc=876.3MB, time=206.18 memory used=6418.0MB, alloc=900.3MB, time=223.30 memory used=6833.1MB, alloc=900.3MB, time=241.14 |\^/| 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(); 1428501451 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 3 3 2 F := [12 x - 12 y - 13 y, 3 x + 7 x z + 6 x z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 G := [13 x + 9 y z - 2 y z, -10 y z + 7 z + 3] > Problem := [F,G]; 3 3 3 2 Problem := [[12 x - 12 y - 13 y, 3 x + 7 x z + 6 x z], 3 2 2 [13 x + 9 y z - 2 y z, -10 y z + 7 z + 3]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=26.7MB, alloc=32.3MB, time=0.53 memory used=47.8MB, alloc=32.3MB, time=0.86 memory used=67.1MB, alloc=56.3MB, time=1.17 memory used=108.1MB, alloc=60.3MB, time=1.79 memory used=149.0MB, alloc=60.3MB, time=2.36 memory used=189.5MB, alloc=60.3MB, time=2.94 memory used=229.3MB, alloc=84.3MB, time=3.51 memory used=297.7MB, alloc=92.3MB, time=4.62 memory used=361.4MB, alloc=116.3MB, time=5.76 memory used=440.9MB, alloc=140.3MB, time=7.20 memory used=545.9MB, alloc=140.3MB, time=8.93 memory used=645.0MB, alloc=164.3MB, time=10.66 memory used=756.8MB, alloc=188.3MB, time=12.62 memory used=874.0MB, alloc=468.3MB, time=14.78 memory used=1007.6MB, alloc=492.3MB, time=18.53 memory used=1146.3MB, alloc=516.3MB, time=23.04 memory used=1297.6MB, alloc=540.3MB, time=28.41 memory used=1459.9MB, alloc=564.3MB, time=34.74 memory used=1646.1MB, alloc=588.3MB, time=42.03 memory used=1856.3MB, alloc=588.3MB, time=50.23 memory used=2066.5MB, alloc=588.3MB, time=58.40 memory used=2276.7MB, alloc=612.3MB, time=66.51 memory used=2510.8MB, alloc=612.3MB, time=75.58 memory used=2744.9MB, alloc=636.3MB, time=84.74 memory used=3003.3MB, alloc=660.3MB, time=94.68 N1 := 8055 > GB := Basis(F, plex(op(vars))); 3 3 3 2 GB := [-12 x + 12 y + 13 y, 3 x + 7 x z + 6 x z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=3186.9MB, alloc=660.3MB, time=98.20 memory used=3362.2MB, alloc=660.3MB, time=101.06 memory used=3616.3MB, alloc=660.3MB, time=105.49 memory used=3847.7MB, alloc=684.3MB, time=109.83 memory used=4159.6MB, alloc=708.3MB, time=119.42 memory used=4450.3MB, alloc=732.3MB, time=130.92 memory used=4752.5MB, alloc=756.3MB, time=143.22 memory used=5078.7MB, alloc=780.3MB, time=156.31 memory used=5428.8MB, alloc=804.3MB, time=171.22 memory used=5803.0MB, alloc=828.3MB, time=187.01 N2 := 8055 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 3 3 2 2 3 H := [-12 y + 12 x - 13 y, 3 x + 7 x z + 6 x z, 9 z y + 13 x - 2 z y, 2 -10 y z + 7 z + 3] > J:=[op(GB),op(G)]; 3 3 3 2 2 3 J := [-12 x + 12 y + 13 y, 3 x + 7 x z + 6 x z, 9 z y + 13 x - 2 z y, 2 -10 y z + 7 z + 3] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 9, 12, 3, 3, 3, 2, 3/4, 3/4, 3/4, 5/12, 5/12, 1/2, 4, 9, 12, 3, 3, 3, 2, 3/4, 3/4, 3/4, 5/12, 5/12, 1/2, 0, 0, 0] > save(F, G, cat("ranSet/33", convert(F, string),".txt")); > quit memory used=6045.2MB, alloc=828.3MB, time=196.82 |\^/| 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(); 1428501678 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 F := [-20 x y - 12 x y z - 5 y , 6 x z + 7 x y + 9 x z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 3 2 G := [6 x y - 2 y z, -9 z - 4 y - 9 y] > Problem := [F,G]; 2 3 2 Problem := [[-20 x y - 12 x y z - 5 y , 6 x z + 7 x y + 9 x z], 2 2 3 2 [6 x y - 2 y z, -9 z - 4 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=4.2MB, alloc=32.3MB, time=0.18 memory used=26.2MB, alloc=32.3MB, time=0.56 memory used=46.2MB, alloc=32.3MB, time=0.86 memory used=64.3MB, alloc=56.3MB, time=1.14 memory used=103.6MB, alloc=60.3MB, time=1.77 memory used=142.2MB, alloc=84.3MB, time=2.34 memory used=203.0MB, alloc=92.3MB, time=3.29 memory used=264.0MB, alloc=116.3MB, time=4.28 memory used=340.9MB, alloc=116.3MB, time=5.46 memory used=415.1MB, alloc=372.3MB, time=6.44 memory used=495.6MB, alloc=396.3MB, time=7.77 memory used=603.2MB, alloc=420.3MB, time=9.44 memory used=741.4MB, alloc=444.3MB, time=11.53 memory used=903.5MB, alloc=444.3MB, time=13.20 memory used=1037.2MB, alloc=468.3MB, time=15.80 memory used=1184.2MB, alloc=492.3MB, time=18.51 memory used=1345.5MB, alloc=516.3MB, time=21.47 memory used=1524.1MB, alloc=540.3MB, time=24.67 memory used=1721.1MB, alloc=564.3MB, time=28.07 memory used=1945.3MB, alloc=588.3MB, time=31.52 memory used=2142.3MB, alloc=612.3MB, time=37.23 memory used=2328.5MB, alloc=636.3MB, time=43.71 memory used=2525.0MB, alloc=660.3MB, time=51.03 memory used=2734.7MB, alloc=684.3MB, time=59.15 memory used=2958.6MB, alloc=708.3MB, time=68.11 memory used=3194.2MB, alloc=732.3MB, time=78.34 memory used=3445.6MB, alloc=756.3MB, time=89.61 memory used=3720.9MB, alloc=780.3MB, time=101.57 memory used=4020.2MB, alloc=804.3MB, time=114.18 memory used=4343.4MB, alloc=828.3MB, time=128.57 memory used=4690.6MB, alloc=852.3MB, time=144.57 memory used=5061.6MB, alloc=852.3MB, time=161.45 memory used=5432.6MB, alloc=876.3MB, time=177.52 memory used=5827.6MB, alloc=876.3MB, time=194.65 memory used=6222.5MB, alloc=876.3MB, time=211.60 memory used=6617.3MB, alloc=876.3MB, time=228.21 memory used=7012.2MB, alloc=900.3MB, time=244.62 memory used=7430.7MB, alloc=900.3MB, time=262.33 |\^/| 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(); 1428501979 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 3 F := [-20 x y - 9 y - 2, 2 x z - 3 y + 3 y z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 G := [-8 x y - x y + 10 y z, x y z - 2 x z + 9 y] > Problem := [F,G]; 2 2 2 3 Problem := [[-20 x y - 9 y - 2, 2 x z - 3 y + 3 y z], 2 [-8 x y - x y + 10 y z, x y z - 2 x z + 9 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.1MB, alloc=32.3MB, time=0.17 memory used=26.0MB, alloc=32.3MB, time=0.51 memory used=45.1MB, alloc=32.3MB, time=0.79 memory used=64.1MB, alloc=56.3MB, time=1.10 memory used=105.5MB, alloc=60.3MB, time=1.72 memory used=145.7MB, alloc=60.3MB, time=2.32 memory used=183.9MB, alloc=84.3MB, time=2.92 memory used=233.7MB, alloc=84.3MB, time=3.83 memory used=291.8MB, alloc=116.3MB, time=4.93 memory used=369.5MB, alloc=116.3MB, time=6.37 memory used=442.6MB, alloc=140.3MB, time=7.68 memory used=534.6MB, alloc=164.3MB, time=9.35 memory used=642.5MB, alloc=188.3MB, time=11.68 memory used=757.2MB, alloc=212.3MB, time=15.39 memory used=883.7MB, alloc=236.3MB, time=20.05 memory used=1026.4MB, alloc=260.3MB, time=25.63 memory used=1193.1MB, alloc=260.3MB, time=32.19 memory used=1359.8MB, alloc=284.3MB, time=38.78 N1 := 5061 > GB := Basis(F, plex(op(vars))); 2 2 6 4 4 2 GB := [20 y x + 9 y + 2, 400 x y + 126 x z + 40 x - 78 x y - 27 z - 6, 4 2 2 -400 x y + 54 x z - 40 x + 81 y z + 18 y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1559.3MB, alloc=284.3MB, time=45.20 memory used=1632.2MB, alloc=540.3MB, time=46.54 memory used=1853.3MB, alloc=540.3MB, time=50.15 memory used=2077.2MB, alloc=564.3MB, time=53.92 memory used=2327.3MB, alloc=588.3MB, time=58.63 memory used=2583.6MB, alloc=612.3MB, time=63.49 memory used=2841.5MB, alloc=636.3MB, time=68.57 memory used=3108.9MB, alloc=660.3MB, time=73.84 memory used=3387.7MB, alloc=684.3MB, time=79.10 memory used=3685.3MB, alloc=708.3MB, time=84.65 memory used=3984.7MB, alloc=732.3MB, time=90.50 memory used=4287.4MB, alloc=756.3MB, time=96.45 memory used=4598.6MB, alloc=780.3MB, time=102.91 memory used=4868.2MB, alloc=804.3MB, time=112.75 memory used=5138.9MB, alloc=828.3MB, time=123.67 memory used=5420.1MB, alloc=852.3MB, time=135.16 memory used=5714.2MB, alloc=876.3MB, time=147.56 memory used=6022.4MB, alloc=900.3MB, time=161.53 memory used=6345.1MB, alloc=924.3MB, time=176.72 memory used=6683.5MB, alloc=948.3MB, time=192.07 memory used=7038.1MB, alloc=972.3MB, time=208.31 memory used=7409.3MB, alloc=996.3MB, time=225.90 memory used=7793.6MB, alloc=1020.3MB, time=244.72 |\^/| 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(); 1428502279 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 2 F := [-14 x - 9 x y z - 3 y z , -x z - 3 y z - 8 x] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 G := [-3 y z + 14 z + 5, -9 x y - 5 x y z - 3 x y] > Problem := [F,G]; 3 2 2 2 Problem := [[-14 x - 9 x y z - 3 y z , -x z - 3 y z - 8 x], 2 3 2 [-3 y z + 14 z + 5, -9 x y - 5 x y z - 3 x y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.20 memory used=26.5MB, alloc=32.3MB, time=0.61 memory used=46.3MB, alloc=56.3MB, time=0.98 memory used=85.6MB, alloc=60.3MB, time=1.60 memory used=127.3MB, alloc=60.3MB, time=2.29 memory used=167.9MB, alloc=84.3MB, time=2.91 memory used=239.2MB, alloc=92.3MB, time=3.75 memory used=305.5MB, alloc=92.3MB, time=4.72 memory used=369.5MB, alloc=116.3MB, time=5.65 memory used=436.1MB, alloc=116.3MB, time=6.44 memory used=497.4MB, alloc=118.5MB, time=6.79 memory used=550.4MB, alloc=118.5MB, time=7.19 memory used=606.8MB, alloc=118.5MB, time=7.38 memory used=662.5MB, alloc=118.5MB, time=8.48 memory used=722.3MB, alloc=118.5MB, time=8.85 memory used=782.7MB, alloc=118.5MB, time=9.65 memory used=871.2MB, alloc=118.5MB, time=10.85 memory used=956.1MB, alloc=374.5MB, time=11.93 memory used=1025.3MB, alloc=374.5MB, time=12.43 memory used=1077.1MB, alloc=374.5MB, time=12.72 memory used=1129.1MB, alloc=374.5MB, time=12.94 memory used=1181.9MB, alloc=374.5MB, time=13.46 memory used=1225.8MB, alloc=374.5MB, time=13.70 memory used=1285.3MB, alloc=374.5MB, time=14.11 memory used=1373.3MB, alloc=374.5MB, time=15.29 memory used=1464.0MB, alloc=398.5MB, time=16.60 memory used=1575.9MB, alloc=398.5MB, time=18.36 memory used=1660.6MB, alloc=398.5MB, time=18.78 memory used=1745.8MB, alloc=422.5MB, time=19.44 memory used=1840.6MB, alloc=422.5MB, time=19.83 memory used=1895.4MB, alloc=422.5MB, time=20.11 memory used=1981.6MB, alloc=422.5MB, time=20.58 memory used=2083.5MB, alloc=422.5MB, time=20.99 memory used=2146.8MB, alloc=422.5MB, time=21.29 memory used=2212.0MB, alloc=422.5MB, time=21.56 memory used=2308.7MB, alloc=422.5MB, time=22.34 memory used=2412.1MB, alloc=422.5MB, time=22.81 memory used=2525.6MB, alloc=422.5MB, time=24.11 memory used=2670.8MB, alloc=422.5MB, time=25.99 memory used=2784.6MB, alloc=422.5MB, time=27.41 memory used=2901.7MB, alloc=422.5MB, time=28.89 memory used=3025.1MB, alloc=446.5MB, time=32.45 memory used=3133.4MB, alloc=446.5MB, time=32.91 memory used=3236.9MB, alloc=446.5MB, time=33.35 memory used=3338.1MB, alloc=446.5MB, time=33.78 memory used=3435.6MB, alloc=446.5MB, time=34.20 memory used=3533.4MB, alloc=446.5MB, time=34.62 memory used=3634.5MB, alloc=446.5MB, time=35.04 memory used=3707.3MB, alloc=446.5MB, time=35.42 memory used=3767.7MB, alloc=446.5MB, time=35.77 memory used=3824.4MB, alloc=446.5MB, time=36.10 memory used=3879.9MB, alloc=446.5MB, time=36.42 memory used=3935.5MB, alloc=446.5MB, time=36.76 memory used=3991.6MB, alloc=446.5MB, time=37.09 memory used=4049.0MB, alloc=446.5MB, time=37.42 memory used=4107.4MB, alloc=446.5MB, time=37.77 memory used=4166.8MB, alloc=446.5MB, time=38.10 memory used=4228.5MB, alloc=446.5MB, time=38.44 memory used=4290.7MB, alloc=446.5MB, time=38.78 memory used=4354.7MB, alloc=446.5MB, time=39.11 memory used=4420.2MB, alloc=446.5MB, time=39.44 memory used=4486.8MB, alloc=446.5MB, time=39.79 memory used=4555.5MB, alloc=446.5MB, time=40.14 memory used=4625.4MB, alloc=446.5MB, time=40.47 memory used=4697.1MB, alloc=446.5MB, time=40.80 memory used=4770.5MB, alloc=446.5MB, time=41.14 memory used=4846.0MB, alloc=446.5MB, time=41.49 memory used=4924.7MB, alloc=446.5MB, time=41.81 memory used=5006.4MB, alloc=446.5MB, time=42.14 memory used=5114.9MB, alloc=470.5MB, time=49.08 memory used=5185.2MB, alloc=494.5MB, time=58.04 memory used=5278.9MB, alloc=494.5MB, time=58.46 memory used=5370.3MB, alloc=494.5MB, time=58.86 memory used=5460.5MB, alloc=494.5MB, time=59.29 memory used=5550.9MB, alloc=494.5MB, time=59.72 memory used=5641.4MB, alloc=494.5MB, time=60.13 memory used=5732.1MB, alloc=494.5MB, time=60.56 memory used=5823.0MB, alloc=494.5MB, time=60.94 memory used=5914.4MB, alloc=494.5MB, time=61.35 memory used=6011.6MB, alloc=494.5MB, time=61.75 memory used=6108.9MB, alloc=494.5MB, time=62.11 memory used=6206.4MB, alloc=494.5MB, time=62.51 memory used=6304.0MB, alloc=494.5MB, time=62.92 memory used=6401.7MB, alloc=494.5MB, time=63.28 memory used=6499.5MB, alloc=494.5MB, time=63.65 memory used=6597.5MB, alloc=494.5MB, time=64.01 memory used=6695.4MB, alloc=494.5MB, time=64.38 memory used=6793.5MB, alloc=494.5MB, time=64.74 memory used=6892.0MB, alloc=494.5MB, time=65.15 memory used=6996.3MB, alloc=494.5MB, time=65.53 memory used=7100.7MB, alloc=494.5MB, time=65.91 memory used=7205.1MB, alloc=494.5MB, time=66.29 memory used=7309.6MB, alloc=494.5MB, time=66.69 memory used=7414.0MB, alloc=494.5MB, time=67.05 memory used=7518.5MB, alloc=494.5MB, time=67.42 memory used=7623.3MB, alloc=494.5MB, time=67.80 memory used=7733.9MB, alloc=494.5MB, time=68.16 memory used=7844.4MB, alloc=494.5MB, time=68.59 memory used=7954.9MB, alloc=494.5MB, time=68.98 memory used=8065.4MB, alloc=494.5MB, time=69.43 memory used=8175.7MB, alloc=494.5MB, time=69.84 memory used=8286.0MB, alloc=494.5MB, time=70.25 memory used=8396.6MB, alloc=494.5MB, time=70.68 memory used=8512.7MB, alloc=494.5MB, time=71.04 memory used=8628.8MB, alloc=494.5MB, time=71.44 memory used=8744.7MB, alloc=494.5MB, time=71.84 memory used=8860.4MB, alloc=494.5MB, time=72.21 memory used=8975.8MB, alloc=494.5MB, time=72.57 memory used=9091.5MB, alloc=494.5MB, time=72.96 memory used=9212.7MB, alloc=494.5MB, time=73.36 memory used=9333.6MB, alloc=494.5MB, time=73.74 memory used=9454.2MB, alloc=494.5MB, time=74.13 memory used=9574.8MB, alloc=494.5MB, time=74.52 memory used=9700.8MB, alloc=494.5MB, time=74.90 memory used=9826.5MB, alloc=494.5MB, time=75.27 memory used=9951.7MB, alloc=494.5MB, time=75.63 memory used=10076.5MB, alloc=494.5MB, time=76.02 memory used=10201.3MB, alloc=494.5MB, time=76.41 memory used=10331.2MB, alloc=494.5MB, time=76.78 memory used=10444.8MB, alloc=494.5MB, time=77.15 memory used=10540.9MB, alloc=494.5MB, time=77.49 memory used=10626.2MB, alloc=494.5MB, time=77.83 memory used=10707.5MB, alloc=494.5MB, time=78.27 memory used=10785.0MB, alloc=494.5MB, time=78.63 memory used=10861.8MB, alloc=494.5MB, time=78.96 memory used=10935.2MB, alloc=494.5MB, time=79.47 memory used=11008.6MB, alloc=494.5MB, time=79.78 memory used=11081.7MB, alloc=494.5MB, time=80.07 memory used=11154.8MB, alloc=494.5MB, time=80.37 memory used=11227.3MB, alloc=518.5MB, time=80.67 memory used=11308.6MB, alloc=518.5MB, time=81.00 memory used=11392.2MB, alloc=518.5MB, time=81.32 memory used=11475.4MB, alloc=518.5MB, time=81.65 memory used=11558.4MB, alloc=518.5MB, time=82.00 memory used=11640.5MB, alloc=518.5MB, time=82.35 memory used=11722.3MB, alloc=518.5MB, time=82.67 memory used=11803.4MB, alloc=518.5MB, time=83.00 memory used=11879.3MB, alloc=518.5MB, time=83.33 memory used=11955.3MB, alloc=518.5MB, time=83.66 memory used=12031.4MB, alloc=518.5MB, time=84.00 memory used=12107.7MB, alloc=518.5MB, time=84.31 memory used=12188.7MB, alloc=518.5MB, time=84.67 memory used=12269.2MB, alloc=518.5MB, time=85.03 memory used=12349.4MB, alloc=518.5MB, time=85.37 memory used=12429.1MB, alloc=518.5MB, time=85.70 memory used=12508.4MB, alloc=518.5MB, time=86.02 memory used=12587.5MB, alloc=518.5MB, time=86.35 memory used=12671.2MB, alloc=518.5MB, time=86.66 memory used=12754.3MB, alloc=518.5MB, time=86.99 memory used=12836.9MB, alloc=518.5MB, time=87.31 memory used=12919.0MB, alloc=518.5MB, time=87.68 memory used=13000.7MB, alloc=518.5MB, time=88.00 memory used=13086.8MB, alloc=518.5MB, time=88.39 memory used=13172.2MB, alloc=518.5MB, time=88.73 memory used=13256.9MB, alloc=518.5MB, time=89.06 memory used=13341.0MB, alloc=518.5MB, time=89.43 memory used=13424.6MB, alloc=518.5MB, time=89.78 memory used=13512.3MB, alloc=518.5MB, time=90.12 memory used=13599.1MB, alloc=518.5MB, time=90.50 memory used=13685.4MB, alloc=518.5MB, time=90.89 memory used=13775.4MB, alloc=518.5MB, time=91.23 memory used=13864.5MB, alloc=518.5MB, time=91.59 memory used=13952.7MB, alloc=518.5MB, time=91.96 memory used=14040.2MB, alloc=518.5MB, time=92.35 memory used=14131.1MB, alloc=518.5MB, time=92.71 memory used=14221.1MB, alloc=518.5MB, time=93.08 memory used=14314.3MB, alloc=518.5MB, time=93.43 memory used=14406.2MB, alloc=518.5MB, time=93.82 memory used=14497.2MB, alloc=518.5MB, time=94.22 memory used=14590.9MB, alloc=518.5MB, time=94.60 memory used=14683.5MB, alloc=518.5MB, time=95.01 memory used=14778.5MB, alloc=518.5MB, time=95.37 memory used=14872.3MB, alloc=518.5MB, time=95.73 memory used=14968.3MB, alloc=518.5MB, time=96.12 memory used=15066.4MB, alloc=518.5MB, time=96.50 memory used=15162.8MB, alloc=518.5MB, time=96.87 memory used=15260.9MB, alloc=518.5MB, time=97.23 memory used=15360.5MB, alloc=518.5MB, time=97.60 memory used=15461.3MB, alloc=518.5MB, time=98.00 memory used=15562.9MB, alloc=518.5MB, time=98.40 memory used=15665.2MB, alloc=518.5MB, time=98.76 memory used=15767.6MB, alloc=518.5MB, time=99.13 memory used=15870.0MB, alloc=518.5MB, time=99.52 memory used=15974.8MB, alloc=518.5MB, time=99.87 memory used=16078.4MB, alloc=518.5MB, time=100.26 memory used=16183.2MB, alloc=518.5MB, time=100.63 memory used=16290.8MB, alloc=518.5MB, time=101.03 memory used=16399.6MB, alloc=518.5MB, time=101.43 memory used=16508.3MB, alloc=518.5MB, time=101.80 memory used=16619.2MB, alloc=518.5MB, time=102.20 memory used=16732.5MB, alloc=518.5MB, time=102.60 memory used=16847.9MB, alloc=518.5MB, time=102.96 memory used=16966.0MB, alloc=518.5MB, time=103.36 memory used=17131.5MB, alloc=518.5MB, time=108.99 memory used=17261.1MB, alloc=518.5MB, time=109.53 memory used=17374.2MB, alloc=518.5MB, time=110.04 memory used=17478.5MB, alloc=518.5MB, time=110.53 memory used=17576.8MB, alloc=518.5MB, time=110.98 memory used=17672.3MB, alloc=518.5MB, time=111.43 memory used=17768.6MB, alloc=518.5MB, time=111.87 memory used=17866.1MB, alloc=518.5MB, time=112.31 memory used=17966.7MB, alloc=518.5MB, time=112.81 memory used=18070.0MB, alloc=518.5MB, time=113.29 memory used=18173.4MB, alloc=518.5MB, time=113.75 memory used=18279.6MB, alloc=518.5MB, time=114.25 memory used=18388.5MB, alloc=518.5MB, time=114.71 memory used=18499.9MB, alloc=518.5MB, time=115.21 memory used=18613.8MB, alloc=518.5MB, time=115.68 memory used=18729.9MB, alloc=518.5MB, time=116.11 memory used=18848.0MB, alloc=518.5MB, time=116.52 memory used=18968.0MB, alloc=518.5MB, time=116.97 memory used=19089.7MB, alloc=518.5MB, time=117.42 memory used=19215.4MB, alloc=518.5MB, time=117.87 memory used=19342.2MB, alloc=518.5MB, time=118.29 memory used=19472.5MB, alloc=518.5MB, time=118.71 memory used=19605.6MB, alloc=518.5MB, time=119.16 memory used=19741.0MB, alloc=518.5MB, time=119.62 memory used=19880.6MB, alloc=518.5MB, time=120.09 memory used=20023.2MB, alloc=518.5MB, time=120.52 memory used=20167.9MB, alloc=518.5MB, time=120.98 memory used=20317.7MB, alloc=518.5MB, time=121.41 memory used=20470.5MB, alloc=518.5MB, time=121.84 memory used=20627.4MB, alloc=518.5MB, time=122.31 memory used=20789.6MB, alloc=518.5MB, time=122.73 memory used=20952.2MB, alloc=518.5MB, time=123.18 memory used=21059.1MB, alloc=518.5MB, 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time=263.91 memory used=46350.6MB, alloc=518.5MB, time=264.35 memory used=46488.5MB, alloc=518.5MB, time=264.77 memory used=46646.4MB, alloc=518.5MB, time=265.59 memory used=46776.8MB, alloc=518.5MB, time=266.06 memory used=46889.7MB, alloc=518.5MB, time=266.49 memory used=46996.2MB, alloc=518.5MB, time=266.90 memory used=47126.9MB, alloc=518.5MB, time=267.33 memory used=47390.1MB, alloc=518.5MB, time=279.49 memory used=47508.9MB, alloc=518.5MB, time=279.90 memory used=47633.9MB, alloc=518.5MB, time=280.26 memory used=47743.7MB, alloc=518.5MB, time=280.57 memory used=47889.8MB, alloc=518.5MB, time=281.62 memory used=48064.4MB, alloc=518.5MB, time=283.37 memory used=48248.2MB, alloc=518.5MB, time=285.31 memory used=48365.7MB, alloc=518.5MB, time=287.15 memory used=48473.8MB, alloc=518.5MB, time=288.85 memory used=48563.3MB, alloc=518.5MB, time=290.23 memory used=48661.6MB, alloc=518.5MB, time=291.60 memory used=48784.0MB, alloc=518.5MB, time=292.58 memory used=48889.5MB, alloc=518.5MB, 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time=317.12 memory used=50739.0MB, alloc=518.5MB, time=317.98 memory used=50829.7MB, alloc=518.5MB, time=318.56 memory used=50930.8MB, alloc=518.5MB, time=319.09 memory used=51006.8MB, alloc=518.5MB, time=319.55 memory used=51123.8MB, alloc=518.5MB, time=320.51 memory used=51212.0MB, alloc=518.5MB, time=321.12 memory used=51308.5MB, alloc=518.5MB, time=321.71 memory used=51388.9MB, alloc=518.5MB, time=322.21 |\^/| 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(); 1428502579 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 F := [-5 z - 6 x y + 18, -4 x y + x z + 7 y z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 3 2 G := [9 x z + x y + 9 z , x + 5 y z - 6 x] > Problem := [F,G]; 3 2 2 Problem := [[-5 z - 6 x y + 18, -4 x y + x z + 7 y z], 2 2 2 3 2 [9 x z + x y + 9 z , x + 5 y z - 6 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=24.6MB, alloc=32.3MB, time=0.49 memory used=43.2MB, alloc=56.3MB, time=0.80 memory used=82.2MB, alloc=61.2MB, time=1.19 memory used=123.0MB, alloc=61.2MB, time=1.56 memory used=157.4MB, alloc=61.2MB, time=1.97 memory used=201.2MB, alloc=69.2MB, time=2.56 memory used=250.4MB, alloc=69.2MB, time=3.09 memory used=294.8MB, alloc=69.2MB, time=3.65 memory used=336.8MB, alloc=93.2MB, time=4.27 memory used=397.2MB, alloc=93.2MB, time=5.10 memory used=465.8MB, alloc=93.2MB, time=5.91 memory used=514.8MB, alloc=93.2MB, time=6.33 memory used=557.9MB, alloc=93.2MB, time=6.54 memory used=602.3MB, alloc=93.2MB, time=7.00 memory used=647.2MB, alloc=93.2MB, time=7.35 memory used=692.6MB, alloc=93.2MB, time=7.63 memory used=734.3MB, alloc=93.2MB, time=7.94 memory used=773.7MB, alloc=93.2MB, time=8.21 memory used=814.2MB, alloc=93.2MB, time=8.46 memory used=873.0MB, alloc=93.2MB, time=8.89 memory used=944.3MB, alloc=373.2MB, time=9.67 memory used=1047.0MB, alloc=373.2MB, time=10.62 memory used=1147.0MB, alloc=373.2MB, time=11.43 memory used=1224.1MB, alloc=373.2MB, time=12.07 memory used=1286.3MB, alloc=373.2MB, time=12.37 memory used=1349.1MB, alloc=373.2MB, time=12.93 memory used=1415.9MB, alloc=373.2MB, time=13.51 memory used=1501.8MB, alloc=373.2MB, time=14.31 memory used=1601.3MB, alloc=397.2MB, time=15.35 memory used=1705.1MB, alloc=397.2MB, time=16.49 memory used=1837.1MB, alloc=397.2MB, time=17.76 memory used=1947.0MB, alloc=421.2MB, time=19.13 memory used=2031.3MB, alloc=421.2MB, time=19.64 memory used=2112.1MB, alloc=421.2MB, time=20.10 memory used=2180.8MB, alloc=421.2MB, time=20.42 memory used=2250.0MB, alloc=421.2MB, time=20.80 memory used=2327.0MB, alloc=421.2MB, time=21.47 memory used=2392.5MB, alloc=421.2MB, time=21.75 memory used=2473.8MB, alloc=421.2MB, time=22.46 memory used=2544.1MB, alloc=421.2MB, time=22.76 memory used=2614.3MB, alloc=421.2MB, time=23.05 memory used=2692.3MB, alloc=421.2MB, time=24.14 memory used=2745.0MB, alloc=421.2MB, time=24.35 memory used=2820.8MB, alloc=421.2MB, time=24.73 memory used=2952.4MB, alloc=421.2MB, time=26.11 memory used=3064.6MB, alloc=445.2MB, time=27.68 memory used=3158.3MB, alloc=445.2MB, time=29.10 memory used=3277.9MB, alloc=469.2MB, time=30.55 memory used=3413.7MB, alloc=469.2MB, time=32.88 memory used=3566.4MB, alloc=469.2MB, time=35.24 memory used=3703.9MB, alloc=469.2MB, time=37.83 memory used=3837.8MB, alloc=469.2MB, time=38.53 memory used=4004.8MB, alloc=469.2MB, time=51.67 memory used=4121.9MB, alloc=469.2MB, time=52.14 memory used=4191.3MB, alloc=469.2MB, time=52.50 memory used=4266.2MB, alloc=469.2MB, time=52.85 memory used=4348.9MB, alloc=469.2MB, time=53.19 memory used=4538.3MB, alloc=469.2MB, time=54.79 memory used=4724.4MB, alloc=469.2MB, time=56.56 memory used=4909.3MB, alloc=469.2MB, time=59.53 memory used=5097.3MB, alloc=469.2MB, time=64.20 memory used=5302.1MB, alloc=493.2MB, time=66.18 memory used=5490.1MB, alloc=493.2MB, time=67.68 memory used=5652.1MB, alloc=493.2MB, time=70.14 memory used=5837.7MB, alloc=493.2MB, time=74.42 memory used=6005.2MB, alloc=493.2MB, time=76.65 memory used=6101.7MB, alloc=493.2MB, time=77.04 memory used=6201.3MB, alloc=493.2MB, time=77.41 memory used=6275.6MB, alloc=493.2MB, time=77.69 memory used=6388.3MB, alloc=493.2MB, time=79.70 memory used=6509.3MB, alloc=493.2MB, time=80.31 memory used=6602.9MB, alloc=493.2MB, time=80.75 memory used=6685.3MB, alloc=493.2MB, time=81.11 memory used=6814.3MB, alloc=493.2MB, time=93.22 memory used=6954.0MB, alloc=493.2MB, time=94.55 memory used=7042.3MB, alloc=493.2MB, time=94.95 memory used=7127.7MB, alloc=493.2MB, time=95.34 memory used=7231.4MB, alloc=493.2MB, time=95.71 memory used=7324.2MB, alloc=493.2MB, time=96.06 memory used=7391.5MB, alloc=493.2MB, time=96.36 memory used=7465.0MB, alloc=493.2MB, time=96.66 memory used=7545.1MB, alloc=493.2MB, time=96.96 memory used=7631.2MB, alloc=493.2MB, time=97.26 memory used=7725.9MB, alloc=493.2MB, time=97.57 memory used=7829.2MB, alloc=493.2MB, time=97.89 memory used=7943.3MB, alloc=493.2MB, time=98.20 memory used=8110.2MB, alloc=493.2MB, time=98.73 memory used=8266.4MB, alloc=493.2MB, time=99.92 memory used=8409.9MB, alloc=493.2MB, time=101.28 memory used=8562.7MB, alloc=493.2MB, time=102.56 memory used=8651.6MB, alloc=493.2MB, time=103.93 memory used=8766.6MB, alloc=493.2MB, time=105.90 memory used=8855.8MB, alloc=493.2MB, time=106.91 memory used=8937.5MB, alloc=493.2MB, time=108.08 memory used=9010.1MB, alloc=493.2MB, time=109.36 memory used=9108.5MB, alloc=493.2MB, time=110.47 memory used=9201.9MB, alloc=517.2MB, time=111.43 memory used=9247.2MB, alloc=517.2MB, time=112.30 memory used=9317.5MB, alloc=517.2MB, time=113.24 memory used=9372.3MB, alloc=517.2MB, time=114.04 memory used=9429.6MB, alloc=517.2MB, time=115.08 memory used=9479.4MB, alloc=517.2MB, time=115.89 memory used=9524.9MB, alloc=517.2MB, time=116.78 memory used=9577.4MB, alloc=517.2MB, time=117.71 memory used=9631.6MB, alloc=517.2MB, time=118.38 memory used=9705.9MB, alloc=517.2MB, time=119.14 memory used=9771.8MB, alloc=517.2MB, time=120.01 memory used=9935.5MB, alloc=517.2MB, time=122.15 memory used=10148.8MB, alloc=541.2MB, time=125.85 memory used=10402.2MB, alloc=541.2MB, time=128.64 memory used=10668.7MB, alloc=541.2MB, time=133.05 memory used=10836.5MB, alloc=541.2MB, time=134.29 memory used=10965.4MB, alloc=541.2MB, time=134.90 memory used=11060.9MB, alloc=541.2MB, time=135.40 memory used=11209.1MB, alloc=541.2MB, time=136.24 memory used=11308.3MB, alloc=541.2MB, time=136.76 memory used=11446.7MB, alloc=541.2MB, time=137.80 memory used=11550.0MB, alloc=541.2MB, time=138.30 memory used=11701.3MB, alloc=541.2MB, time=139.33 memory used=11802.6MB, alloc=541.2MB, time=140.03 memory used=11942.4MB, alloc=541.2MB, time=140.90 memory used=12044.8MB, alloc=541.2MB, time=141.42 memory used=12193.9MB, alloc=541.2MB, time=147.25 memory used=12294.6MB, alloc=541.2MB, time=147.81 memory used=12410.5MB, alloc=541.2MB, time=148.36 memory used=12523.5MB, alloc=541.2MB, time=148.86 memory used=12608.2MB, alloc=541.2MB, time=149.31 memory used=12721.6MB, alloc=541.2MB, time=150.36 memory used=12909.3MB, alloc=565.2MB, time=154.03 memory used=13090.7MB, alloc=565.2MB, time=155.56 memory used=13229.4MB, alloc=565.2MB, time=156.23 memory used=13454.3MB, alloc=565.2MB, time=172.34 memory used=13571.8MB, alloc=565.2MB, time=172.94 memory used=13706.8MB, alloc=565.2MB, time=173.53 memory used=13835.3MB, alloc=565.2MB, time=174.07 memory used=13932.7MB, alloc=565.2MB, time=174.57 memory used=14043.9MB, alloc=565.2MB, time=175.09 memory used=14299.1MB, alloc=565.2MB, time=176.96 memory used=14605.3MB, alloc=565.2MB, time=179.87 memory used=14827.9MB, alloc=565.2MB, time=182.98 memory used=15044.8MB, alloc=565.2MB, time=185.43 memory used=15255.2MB, alloc=565.2MB, time=193.41 memory used=15365.6MB, alloc=565.2MB, time=193.94 memory used=15559.9MB, alloc=565.2MB, time=202.52 memory used=15712.9MB, alloc=565.2MB, time=203.86 memory used=16014.3MB, alloc=589.2MB, time=206.44 memory used=16290.5MB, alloc=589.2MB, time=208.78 memory used=16466.5MB, alloc=589.2MB, time=213.77 memory used=16581.8MB, alloc=589.2MB, time=214.39 memory used=16698.4MB, alloc=589.2MB, time=214.97 memory used=16929.5MB, alloc=589.2MB, time=218.55 memory used=17256.7MB, alloc=613.2MB, time=221.52 memory used=17597.4MB, alloc=613.2MB, time=229.14 memory used=17763.4MB, alloc=613.2MB, time=232.14 memory used=18006.2MB, alloc=613.2MB, time=237.61 memory used=18227.0MB, alloc=613.2MB, time=240.25 memory used=18452.0MB, alloc=613.2MB, time=242.82 memory used=18593.0MB, alloc=637.2MB, time=245.12 memory used=18772.1MB, alloc=661.2MB, time=246.85 memory used=19009.8MB, alloc=661.2MB, time=310.98 memory used=19257.0MB, alloc=661.2MB, time=313.30 memory used=19404.8MB, alloc=661.2MB, time=314.22 memory used=19577.6MB, alloc=661.2MB, time=315.17 memory used=19757.1MB, alloc=661.2MB, time=316.08 memory used=19872.9MB, alloc=661.2MB, time=316.89 memory used=19996.5MB, alloc=661.2MB, time=317.67 memory used=20130.2MB, alloc=661.2MB, time=318.49 memory used=20275.6MB, alloc=661.2MB, time=319.29 memory used=20426.3MB, alloc=661.2MB, time=320.09 memory used=20571.2MB, alloc=661.2MB, time=320.89 memory used=20725.8MB, alloc=661.2MB, time=321.67 memory used=20889.2MB, alloc=661.2MB, time=322.46 memory used=21063.3MB, alloc=661.2MB, time=323.23 memory used=21202.4MB, alloc=661.2MB, time=323.95 memory used=21336.8MB, alloc=661.2MB, time=324.65 memory used=21492.6MB, alloc=661.2MB, time=325.35 memory used=21744.9MB, alloc=661.2MB, time=329.26 memory used=21966.4MB, alloc=661.2MB, time=330.41 |\^/| 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(); 1428502879 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 3 F := [-13 x y - 4 x y z + 13 z, 6 x z + 2 x y z + 7 y ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 3 3 G := [-17 x y + 14 y - 19 y, -4 x + 7 y + 10 y] > Problem := [F,G]; 2 2 3 Problem := [[-13 x y - 4 x y z + 13 z, 6 x z + 2 x y z + 7 y ], 2 3 3 3 [-17 x y + 14 y - 19 y, -4 x + 7 y + 10 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.7MB, alloc=32.3MB, time=0.51 memory used=47.4MB, alloc=32.3MB, time=0.81 memory used=67.0MB, alloc=56.3MB, time=1.11 memory used=109.6MB, alloc=60.3MB, time=1.78 memory used=150.3MB, alloc=84.3MB, time=2.47 memory used=212.6MB, alloc=92.3MB, time=3.53 memory used=268.5MB, alloc=116.3MB, time=5.01 N1 := 1291 > GB := Basis(F, plex(op(vars))); 3 2 2 3 4 3 2 2 3 GB := [-78 x y - 26 x y + 28 x y - 91 y , 12 x z - 13 x y + 14 y + 13 z, 2 2 3 4 -39 x y - 13 x y + 14 y + 39 x z + 13 y z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=342.6MB, alloc=116.3MB, time=6.58 memory used=422.6MB, alloc=140.3MB, time=7.90 N2 := 651 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 3 H := [-13 x y - 4 x y z + 13 z, 2 z y x + 6 z x + 7 y , 2 3 3 3 -17 x y + 14 y - 19 y, -4 x + 7 y + 10 y] > J:=[op(GB),op(G)]; 3 2 2 3 4 3 2 3 2 J := [-78 x y - 26 x y + 28 x y - 91 y , 12 z x + 14 y - 13 y x + 13 z, 2 2 3 4 2 3 -39 x y - 13 x y + 14 y + 39 x z + 13 y z, -17 x y + 14 y - 19 y, 3 3 -4 x + 7 y + 10 y] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 10, 12, 3, 3, 3, 1, 1, 1, 1/2, 1/2, 3/4, 1/3, 5, 12, 18, 5, 10 15 3, 4, 1, 1, 1, 2/5, --, --, 4/19, -2, -6, -2] 19 19 > save(F, G, cat("ranSet/33", convert(F, string),".txt")); > quit memory used=460.1MB, alloc=140.3MB, time=8.70 |\^/| 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(); 1428502893 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 2 F := [x + 17 y + 15, -6 y z + 2 x y - 7 z ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 G := [8 y z + 17 y - 2 z, -8 x y + 9 x z - 3 x] > Problem := [F,G]; 3 2 2 2 Problem := [[x + 17 y + 15, -6 y z + 2 x y - 7 z ], 2 2 2 [8 y z + 17 y - 2 z, -8 x y + 9 x z - 3 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=25.7MB, alloc=32.3MB, time=0.49 memory used=45.9MB, alloc=32.3MB, time=0.78 memory used=64.5MB, alloc=56.3MB, time=1.07 memory used=106.6MB, alloc=60.3MB, time=1.69 memory used=148.2MB, alloc=60.3MB, time=2.30 memory used=189.6MB, alloc=92.3MB, time=2.91 memory used=254.5MB, alloc=92.3MB, time=3.84 memory used=318.7MB, alloc=116.3MB, time=4.89 memory used=402.4MB, alloc=116.3MB, time=6.30 memory used=478.4MB, alloc=140.3MB, time=7.62 memory used=574.1MB, alloc=164.3MB, time=9.26 memory used=688.2MB, alloc=188.3MB, time=11.23 memory used=811.4MB, alloc=212.3MB, time=14.70 memory used=939.4MB, alloc=236.3MB, time=19.41 memory used=1086.5MB, alloc=236.3MB, time=25.10 memory used=1233.7MB, alloc=260.3MB, time=30.75 N1 := 4389 > GB := Basis(F, plex(op(vars))); 3 2 3 2 4 2 GB := [x + 17 y + 15, 36 x z - 12 x - 238 x y + 1373 z - 180 x, 2 2 6 y z - 2 x y + 7 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1416.0MB, alloc=260.3MB, time=36.07 memory used=1491.7MB, alloc=516.3MB, time=37.40 memory used=1636.9MB, alloc=516.3MB, time=39.59 memory used=1775.3MB, alloc=516.3MB, time=41.76 memory used=1911.9MB, alloc=540.3MB, time=43.93 memory used=2024.9MB, alloc=540.3MB, time=45.73 memory used=2141.3MB, alloc=540.3MB, time=47.50 memory used=2265.9MB, alloc=564.3MB, time=48.91 memory used=2380.0MB, alloc=564.3MB, time=50.36 memory used=2481.5MB, alloc=564.3MB, time=51.88 memory used=2597.6MB, alloc=564.3MB, time=53.89 memory used=2695.4MB, alloc=564.3MB, time=55.67 memory used=2812.8MB, alloc=588.3MB, time=57.20 memory used=2951.7MB, alloc=588.3MB, time=58.48 memory used=3028.5MB, alloc=588.3MB, time=59.90 memory used=3111.7MB, alloc=588.3MB, time=61.45 memory used=3189.9MB, alloc=588.3MB, time=62.95 memory used=3293.0MB, alloc=588.3MB, time=64.07 memory used=3374.2MB, alloc=588.3MB, time=65.42 memory used=3441.5MB, alloc=588.3MB, time=66.69 memory used=3514.6MB, alloc=588.3MB, time=67.72 memory used=3590.6MB, alloc=612.3MB, time=68.79 memory used=3656.2MB, alloc=612.3MB, time=69.98 memory used=3716.2MB, alloc=612.3MB, time=71.18 memory used=3811.8MB, alloc=612.3MB, time=72.70 memory used=4003.8MB, alloc=612.3MB, time=74.46 memory used=4086.3MB, alloc=612.3MB, time=75.90 memory used=4162.3MB, alloc=612.3MB, time=77.44 memory used=4235.1MB, alloc=612.3MB, time=78.88 memory used=4306.3MB, alloc=636.3MB, time=80.33 memory used=4396.3MB, alloc=636.3MB, time=81.63 memory used=4459.3MB, alloc=636.3MB, time=83.13 memory used=4553.6MB, alloc=636.3MB, time=85.22 memory used=4665.6MB, alloc=636.3MB, time=87.35 memory used=4768.3MB, alloc=660.3MB, time=89.24 memory used=4847.6MB, alloc=660.3MB, time=91.03 memory used=5151.5MB, alloc=684.3MB, time=96.46 memory used=5478.2MB, alloc=708.3MB, time=102.43 memory used=5812.6MB, alloc=732.3MB, time=108.51 memory used=6147.9MB, alloc=756.3MB, time=114.99 memory used=6499.4MB, alloc=780.3MB, time=121.48 memory used=6794.1MB, alloc=804.3MB, time=127.17 memory used=7099.6MB, alloc=828.3MB, time=133.09 memory used=7446.9MB, alloc=852.3MB, time=139.25 memory used=7813.8MB, alloc=876.3MB, time=150.54 memory used=8136.8MB, alloc=900.3MB, time=163.23 memory used=8464.3MB, alloc=924.3MB, time=177.17 memory used=8797.5MB, alloc=948.3MB, time=191.78 memory used=9144.8MB, alloc=972.3MB, time=208.02 |\^/| 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(); 1428503193 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 F := [5 x y + 4 z + 12 x, -9 x y z + 7 y z + 9 y] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 G := [-3 y z - 8 y + 3 y z, -8 x z + 10 y - 3 z] > Problem := [F,G]; 2 3 2 Problem := [[5 x y + 4 z + 12 x, -9 x y z + 7 y z + 9 y], 2 2 2 2 [-3 y z - 8 y + 3 y z, -8 x z + 10 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=4.2MB, alloc=32.3MB, time=0.17 memory used=26.0MB, alloc=32.3MB, time=0.50 memory used=45.5MB, alloc=56.3MB, time=0.80 memory used=87.5MB, alloc=60.3MB, time=1.44 memory used=126.6MB, alloc=84.3MB, time=2.08 memory used=161.2MB, alloc=84.3MB, time=2.57 memory used=226.3MB, alloc=92.3MB, time=3.46 memory used=291.7MB, alloc=372.3MB, time=4.36 memory used=380.0MB, alloc=372.3MB, time=5.66 memory used=468.4MB, alloc=396.3MB, time=6.85 memory used=582.6MB, alloc=396.3MB, time=8.53 memory used=688.2MB, alloc=420.3MB, time=10.12 memory used=831.6MB, alloc=420.3MB, time=11.56 memory used=958.4MB, alloc=444.3MB, time=13.40 memory used=1087.3MB, alloc=468.3MB, time=15.42 memory used=1206.0MB, alloc=468.3MB, time=17.02 memory used=1375.3MB, alloc=468.3MB, time=18.72 memory used=1511.5MB, alloc=468.3MB, time=20.18 memory used=1595.1MB, alloc=492.3MB, time=21.40 memory used=1705.5MB, alloc=492.3MB, time=22.04 memory used=1833.5MB, alloc=492.3MB, time=22.91 memory used=1932.9MB, alloc=492.3MB, time=23.72 memory used=2025.9MB, alloc=492.3MB, time=24.25 memory used=2177.5MB, alloc=492.3MB, time=25.59 memory used=2273.1MB, alloc=492.3MB, time=26.94 memory used=2368.7MB, alloc=492.3MB, time=28.47 memory used=2459.4MB, alloc=492.3MB, time=29.91 memory used=2548.3MB, alloc=492.3MB, time=31.64 memory used=2657.8MB, alloc=516.3MB, time=33.01 memory used=2781.4MB, alloc=516.3MB, time=34.04 memory used=2875.0MB, alloc=516.3MB, time=34.44 memory used=2969.1MB, alloc=516.3MB, time=34.81 memory used=3120.5MB, alloc=516.3MB, time=36.36 memory used=3215.7MB, alloc=516.3MB, time=36.77 memory used=3303.7MB, alloc=516.3MB, time=37.13 memory used=3430.8MB, alloc=516.3MB, time=38.28 memory used=3521.5MB, alloc=516.3MB, time=39.37 memory used=3608.9MB, alloc=516.3MB, time=40.66 memory used=3690.1MB, alloc=516.3MB, time=41.72 memory used=3757.9MB, alloc=516.3MB, time=43.00 memory used=3831.2MB, alloc=516.3MB, time=44.18 memory used=3891.6MB, alloc=516.3MB, time=45.29 memory used=3965.5MB, alloc=516.3MB, time=46.71 memory used=4037.0MB, alloc=540.3MB, time=48.15 memory used=4135.8MB, alloc=540.3MB, time=49.80 memory used=4225.8MB, alloc=540.3MB, time=51.73 memory used=4321.9MB, alloc=564.3MB, time=53.82 memory used=4401.7MB, alloc=564.3MB, time=55.65 memory used=4478.1MB, alloc=564.3MB, time=57.43 memory used=4542.5MB, alloc=588.3MB, time=59.05 memory used=4623.8MB, alloc=588.3MB, time=61.15 memory used=4876.7MB, alloc=612.3MB, time=65.26 memory used=5123.6MB, alloc=636.3MB, time=70.13 memory used=5350.9MB, alloc=660.3MB, time=78.33 memory used=5568.9MB, alloc=684.3MB, time=87.24 memory used=5792.1MB, alloc=708.3MB, time=96.46 memory used=6023.4MB, alloc=732.3MB, time=106.56 memory used=6278.7MB, alloc=756.3MB, time=117.79 memory used=6557.8MB, alloc=780.3MB, time=129.94 memory used=6861.0MB, alloc=804.3MB, time=143.11 memory used=7187.9MB, alloc=828.3MB, time=157.25 memory used=7539.0MB, alloc=852.3MB, time=172.01 memory used=7913.8MB, alloc=852.3MB, time=187.90 memory used=8288.8MB, alloc=876.3MB, time=203.77 memory used=8687.8MB, alloc=900.3MB, time=220.91 N1 := 11059 > GB := Basis(F, plex(op(vars))); 4 3 3 4 2 5 6 4 GB := [-3645 x y + 8505 x y - 6615 x y + 1715 x y - 8748 x y 3 2 2 3 4 3 3 2 4 + 20412 x y - 15876 x y + 4116 x y - 2916 y, 405 x y - 630 x y 5 3 2 2 3 + 245 x y + 972 x y - 1512 x y + 588 x y + 324 y z, 3 2 4 z + 5 y x + 12 x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=9140.0MB, alloc=900.3MB, time=235.76 memory used=9546.2MB, alloc=900.3MB, time=239.71 memory used=9834.7MB, alloc=900.3MB, time=243.06 memory used=10242.5MB, alloc=900.3MB, time=249.26 memory used=10625.1MB, alloc=900.3MB, time=251.53 memory used=10905.4MB, alloc=900.3MB, time=253.15 memory used=11170.5MB, alloc=900.3MB, time=256.40 memory used=11350.4MB, alloc=900.3MB, time=259.36 memory used=11627.1MB, alloc=900.3MB, time=262.08 memory used=11872.7MB, alloc=900.3MB, time=266.04 |\^/| 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(); 1428503493 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 3 2 F := [6 x + 15 y + 11 y z, 4 x z + 6 x - 2] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 G := [-14 x y + 5 y z - 14 z, -2 x y - x y z + 9 y z] > Problem := [F,G]; 3 3 2 Problem := [[6 x + 15 y + 11 y z, 4 x z + 6 x - 2], 2 2 2 2 [-14 x y + 5 y z - 14 z, -2 x y - x y z + 9 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=25.9MB, alloc=32.3MB, time=0.49 memory used=46.5MB, alloc=32.3MB, time=0.80 memory used=65.5MB, alloc=56.3MB, time=1.10 memory used=106.0MB, alloc=60.3MB, time=1.71 memory used=146.1MB, alloc=84.3MB, time=2.31 memory used=209.4MB, alloc=92.3MB, time=3.27 memory used=271.2MB, alloc=116.3MB, time=4.27 memory used=349.0MB, alloc=116.3MB, time=5.33 memory used=421.5MB, alloc=372.3MB, time=6.39 memory used=508.0MB, alloc=396.3MB, time=7.70 memory used=622.3MB, alloc=420.3MB, time=9.44 memory used=749.2MB, alloc=420.3MB, time=11.49 memory used=868.2MB, alloc=444.3MB, time=13.44 memory used=1005.8MB, alloc=468.3MB, time=15.70 memory used=1156.3MB, alloc=492.3MB, time=18.29 memory used=1322.2MB, alloc=516.3MB, time=21.17 memory used=1514.8MB, alloc=540.3MB, time=24.22 memory used=1726.9MB, alloc=564.3MB, time=27.65 memory used=1933.7MB, alloc=588.3MB, time=31.34 memory used=2118.3MB, alloc=612.3MB, time=34.75 memory used=2308.9MB, alloc=636.3MB, time=38.62 memory used=2527.9MB, alloc=660.3MB, time=46.05 memory used=2752.1MB, alloc=684.3MB, time=54.16 memory used=2987.8MB, alloc=708.3MB, time=62.87 memory used=3237.7MB, alloc=732.3MB, time=72.59 memory used=3503.0MB, alloc=756.3MB, time=83.18 memory used=3784.0MB, alloc=780.3MB, time=94.49 memory used=4073.0MB, alloc=804.3MB, time=107.22 memory used=4385.4MB, alloc=828.3MB, time=120.72 memory used=4721.7MB, alloc=852.3MB, time=135.11 memory used=5082.0MB, alloc=876.3MB, time=150.26 memory used=5466.2MB, alloc=900.3MB, time=166.60 memory used=5874.3MB, alloc=900.3MB, time=183.89 memory used=6282.4MB, alloc=900.3MB, time=201.02 memory used=6690.5MB, alloc=900.3MB, time=218.75 memory used=7098.6MB, alloc=924.3MB, time=235.94 |\^/| 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(); 1428503793 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 F := [-2 x y + 2 x y - 12 x, 7 x z + 4 y z - 3 z ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 G := [2 x - 18 z + 5 y, 9 x y - 3 y z + 9 y] > Problem := [F,G]; 2 2 Problem := [[-2 x y + 2 x y - 12 x, 7 x z + 4 y z - 3 z ], 2 2 2 [2 x - 18 z + 5 y, 9 x y - 3 y z + 9 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.2MB, alloc=32.3MB, time=0.48 memory used=47.3MB, alloc=32.3MB, time=0.79 memory used=66.7MB, alloc=56.3MB, time=1.09 memory used=106.9MB, alloc=60.3MB, time=1.70 memory used=145.4MB, alloc=84.3MB, time=2.30 memory used=203.7MB, alloc=84.3MB, time=3.20 memory used=261.8MB, alloc=116.3MB, time=4.27 memory used=338.2MB, alloc=140.3MB, time=5.61 memory used=429.7MB, alloc=164.3MB, time=7.21 memory used=536.8MB, alloc=188.3MB, time=9.08 memory used=649.7MB, alloc=468.3MB, time=11.05 memory used=783.3MB, alloc=492.3MB, time=13.50 memory used=922.8MB, alloc=516.3MB, time=16.94 memory used=1059.8MB, alloc=540.3MB, time=21.34 memory used=1208.3MB, alloc=564.3MB, time=26.44 memory used=1371.3MB, alloc=588.3MB, time=32.31 memory used=1548.8MB, alloc=612.3MB, time=39.21 memory used=1742.3MB, alloc=636.3MB, time=47.22 memory used=1959.7MB, alloc=660.3MB, time=56.19 memory used=2201.1MB, alloc=684.3MB, time=66.07 memory used=2466.3MB, alloc=684.3MB, time=76.83 memory used=2731.6MB, alloc=684.3MB, time=87.50 memory used=2996.7MB, alloc=708.3MB, time=98.07 memory used=3285.9MB, alloc=708.3MB, time=109.53 memory used=3575.0MB, alloc=708.3MB, time=121.01 memory used=3864.1MB, alloc=732.3MB, time=132.92 memory used=4177.2MB, alloc=732.3MB, time=145.43 memory used=4490.2MB, alloc=756.3MB, time=157.81 memory used=4827.2MB, alloc=780.3MB, time=171.19 N1 := 11771 > GB := Basis(F, plex(op(vars))); 2 2 GB := [x y - x y + 6 x, -7 x z - 4 y z + 3 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=5190.0MB, alloc=780.3MB, time=184.79 memory used=5595.7MB, alloc=780.3MB, time=192.27 memory used=5979.3MB, alloc=804.3MB, time=199.75 memory used=6361.1MB, alloc=828.3MB, time=212.80 memory used=6723.8MB, alloc=852.3MB, time=227.06 memory used=7090.5MB, alloc=876.3MB, time=242.59 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428504093 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 3 F := [-2 x y + 13 x y + 7 z , -3 x z - y ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 3 G := [-5 x z - 14 x z - 6 y, -9 x + x z + 4 y ] > Problem := [F,G]; 2 2 2 3 Problem := [[-2 x y + 13 x y + 7 z , -3 x z - y ], 2 3 2 3 [-5 x z - 14 x z - 6 y, -9 x + x z + 4 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.3MB, alloc=32.3MB, time=0.50 memory used=48.2MB, alloc=32.3MB, time=0.74 memory used=76.9MB, alloc=60.6MB, time=0.97 memory used=131.0MB, alloc=68.6MB, time=1.42 memory used=197.0MB, alloc=68.6MB, time=1.97 memory used=257.0MB, alloc=68.6MB, time=2.47 memory used=299.2MB, alloc=68.6MB, time=3.06 memory used=343.2MB, alloc=68.6MB, time=3.65 memory used=387.2MB, alloc=92.6MB, time=4.11 memory used=443.4MB, alloc=92.6MB, time=4.44 memory used=493.7MB, alloc=92.6MB, time=4.80 memory used=581.0MB, alloc=92.6MB, time=5.65 memory used=652.3MB, alloc=92.6MB, time=6.22 memory used=734.7MB, alloc=92.6MB, time=6.90 memory used=821.8MB, alloc=348.6MB, time=7.61 memory used=880.6MB, alloc=348.6MB, time=8.40 memory used=933.4MB, alloc=348.6MB, time=8.79 memory used=1017.5MB, alloc=348.6MB, time=9.36 memory used=1087.6MB, alloc=372.6MB, time=10.16 memory used=1181.9MB, alloc=372.6MB, time=11.28 memory used=1263.4MB, alloc=396.6MB, time=12.46 memory used=1372.4MB, alloc=420.6MB, time=13.88 memory used=1488.0MB, alloc=420.6MB, time=15.12 memory used=1599.1MB, alloc=420.6MB, time=16.07 memory used=1725.1MB, alloc=420.6MB, time=17.08 memory used=1855.7MB, alloc=420.6MB, time=18.54 memory used=1967.4MB, alloc=420.6MB, time=19.61 memory used=2073.5MB, alloc=420.6MB, time=20.53 memory used=2193.7MB, alloc=444.6MB, time=21.92 memory used=2315.7MB, alloc=444.6MB, time=23.36 memory used=2414.7MB, alloc=444.6MB, time=24.76 memory used=2533.2MB, alloc=468.6MB, time=26.25 memory used=2640.8MB, alloc=468.6MB, time=27.44 memory used=2788.7MB, alloc=468.6MB, time=28.70 memory used=2894.0MB, alloc=468.6MB, time=29.27 memory used=2974.1MB, alloc=468.6MB, time=29.63 memory used=3068.5MB, alloc=468.6MB, time=30.15 memory used=3168.0MB, alloc=468.6MB, time=30.80 memory used=3249.1MB, alloc=468.6MB, time=31.11 memory used=3313.5MB, alloc=468.6MB, time=31.36 memory used=3441.0MB, alloc=468.6MB, time=32.52 memory used=3516.7MB, alloc=468.6MB, time=32.83 memory used=3602.6MB, alloc=468.6MB, time=33.24 memory used=3675.9MB, alloc=468.6MB, time=33.53 memory used=3777.1MB, alloc=468.6MB, time=34.69 memory used=3875.9MB, alloc=468.6MB, time=35.84 memory used=3977.1MB, alloc=468.6MB, time=37.08 memory used=4055.8MB, alloc=468.6MB, time=38.21 memory used=4145.0MB, alloc=492.6MB, time=39.33 memory used=4244.1MB, alloc=492.6MB, time=40.59 memory used=4311.4MB, alloc=492.6MB, time=41.64 memory used=4383.2MB, alloc=492.6MB, time=42.60 memory used=4474.6MB, alloc=492.6MB, time=43.58 memory used=4590.4MB, alloc=492.6MB, time=45.32 memory used=4710.1MB, alloc=492.6MB, time=46.13 memory used=4794.0MB, alloc=492.6MB, time=47.05 memory used=4861.2MB, alloc=492.6MB, time=48.13 memory used=4933.8MB, alloc=492.6MB, time=49.15 memory used=4998.0MB, alloc=492.6MB, time=50.26 memory used=5068.7MB, alloc=516.6MB, time=51.63 memory used=5120.9MB, alloc=516.6MB, time=52.46 memory used=5189.1MB, alloc=516.6MB, time=53.40 memory used=5263.9MB, alloc=516.6MB, time=54.44 memory used=5339.5MB, alloc=516.6MB, time=55.39 memory used=5387.8MB, alloc=516.6MB, time=56.20 memory used=5454.5MB, alloc=516.6MB, time=57.32 memory used=5526.7MB, alloc=516.6MB, time=58.52 memory used=5613.9MB, alloc=516.6MB, time=59.73 memory used=5824.9MB, alloc=540.6MB, time=61.65 memory used=6042.5MB, alloc=540.6MB, time=63.33 memory used=6290.9MB, alloc=540.6MB, time=65.90 memory used=6519.5MB, alloc=540.6MB, time=67.77 memory used=6725.5MB, alloc=540.6MB, time=69.19 memory used=6959.3MB, alloc=540.6MB, time=71.43 memory used=7202.0MB, alloc=564.6MB, time=74.25 memory used=7449.4MB, alloc=564.6MB, time=76.63 memory used=7685.7MB, alloc=564.6MB, time=78.57 memory used=7944.2MB, alloc=564.6MB, time=81.16 memory used=8207.4MB, alloc=588.6MB, time=84.28 memory used=8426.0MB, alloc=612.6MB, time=88.65 memory used=8660.0MB, alloc=636.6MB, time=93.21 memory used=8907.5MB, alloc=660.6MB, time=97.91 memory used=9184.9MB, alloc=684.6MB, time=102.74 memory used=9476.1MB, alloc=708.6MB, time=107.84 memory used=9798.6MB, alloc=732.6MB, time=113.18 memory used=10128.0MB, alloc=756.6MB, time=118.59 memory used=10423.3MB, alloc=780.6MB, time=124.41 memory used=10723.0MB, alloc=804.6MB, time=130.29 memory used=11057.3MB, alloc=828.6MB, time=136.00 memory used=11331.5MB, alloc=852.6MB, time=142.13 memory used=11572.1MB, alloc=876.6MB, time=147.10 memory used=11825.7MB, alloc=900.6MB, time=152.76 memory used=12214.3MB, alloc=924.6MB, time=160.43 memory used=12635.2MB, alloc=948.6MB, time=166.21 memory used=13034.3MB, alloc=972.6MB, time=174.74 memory used=13455.1MB, alloc=996.6MB, time=182.98 memory used=13850.7MB, alloc=1020.6MB, time=195.35 memory used=14176.1MB, alloc=1044.6MB, time=209.43 memory used=14505.2MB, alloc=1068.6MB, time=223.95 memory used=14842.4MB, alloc=1092.6MB, time=239.48 memory used=15189.0MB, alloc=1116.6MB, time=254.93 |\^/| 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(); 1428504393 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 F := [-5 z + 15 y - z, -9 x + 6 y z - 9] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 2 G := [-4 x z + 4 y z + 19 y, 8 x y - y + 3 z ] > Problem := [F,G]; 2 3 Problem := [[-5 z + 15 y - z, -9 x + 6 y z - 9], 2 2 2 2 2 [-4 x z + 4 y z + 19 y, 8 x y - 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=4.2MB, alloc=32.3MB, time=0.20 memory used=24.6MB, alloc=32.3MB, time=0.53 memory used=43.5MB, alloc=56.3MB, time=0.83 memory used=84.5MB, alloc=60.3MB, time=1.47 memory used=123.6MB, alloc=60.3MB, time=2.07 memory used=160.8MB, alloc=60.3MB, time=2.59 memory used=205.4MB, alloc=92.3MB, time=3.22 memory used=271.8MB, alloc=92.3MB, time=4.20 memory used=337.2MB, alloc=116.3MB, time=5.16 memory used=400.9MB, alloc=372.3MB, time=6.08 memory used=485.2MB, alloc=372.3MB, time=7.39 memory used=573.4MB, alloc=396.3MB, time=8.55 memory used=687.9MB, alloc=396.3MB, time=10.02 memory used=799.8MB, alloc=420.3MB, time=11.51 memory used=935.9MB, alloc=420.3MB, time=13.17 memory used=1066.8MB, alloc=420.3MB, time=14.78 memory used=1199.3MB, alloc=444.3MB, time=16.87 memory used=1336.4MB, alloc=444.3MB, time=18.64 memory used=1468.6MB, alloc=468.3MB, time=20.77 memory used=1595.3MB, alloc=468.3MB, time=22.75 memory used=1697.9MB, alloc=468.3MB, time=24.18 memory used=1797.2MB, alloc=492.3MB, time=25.69 memory used=1910.3MB, alloc=492.3MB, time=27.17 memory used=2031.9MB, alloc=492.3MB, time=29.02 memory used=2180.9MB, alloc=516.3MB, time=31.09 memory used=2328.9MB, alloc=516.3MB, time=33.34 memory used=2462.6MB, alloc=516.3MB, time=35.45 memory used=2589.9MB, alloc=540.3MB, time=37.73 memory used=2761.0MB, alloc=564.3MB, time=40.21 memory used=2943.0MB, alloc=564.3MB, time=42.60 memory used=3123.0MB, alloc=588.3MB, time=45.27 memory used=3265.2MB, alloc=588.3MB, time=47.81 memory used=3412.8MB, alloc=612.3MB, time=50.32 memory used=3546.5MB, alloc=612.3MB, time=52.87 memory used=3676.3MB, alloc=636.3MB, time=55.44 memory used=3804.2MB, alloc=636.3MB, time=57.73 memory used=3936.7MB, alloc=660.3MB, time=60.49 memory used=4055.8MB, alloc=684.3MB, time=62.92 memory used=4173.3MB, alloc=684.3MB, time=65.29 memory used=4284.8MB, alloc=708.3MB, time=67.76 memory used=4400.2MB, alloc=708.3MB, time=70.19 memory used=4529.8MB, alloc=732.3MB, time=72.78 memory used=4641.7MB, alloc=732.3MB, time=75.18 memory used=4761.2MB, alloc=732.3MB, time=77.68 memory used=4863.9MB, alloc=756.3MB, time=79.93 memory used=4974.9MB, alloc=756.3MB, time=82.38 memory used=5074.5MB, alloc=780.3MB, time=84.57 memory used=5157.1MB, alloc=780.3MB, time=86.56 memory used=5234.1MB, alloc=780.3MB, time=88.44 memory used=5304.7MB, alloc=804.3MB, time=90.29 memory used=5384.3MB, alloc=804.3MB, time=92.31 memory used=5459.3MB, alloc=828.3MB, time=94.28 memory used=5553.8MB, alloc=828.3MB, time=96.31 memory used=5943.8MB, alloc=852.3MB, time=103.12 memory used=6288.2MB, alloc=876.3MB, time=114.78 memory used=6609.8MB, alloc=900.3MB, time=127.54 memory used=6935.5MB, alloc=924.3MB, time=141.13 memory used=7270.2MB, alloc=948.3MB, time=155.36 memory used=7615.1MB, alloc=972.3MB, time=170.41 memory used=7971.3MB, alloc=996.3MB, time=186.30 memory used=8340.1MB, alloc=1020.3MB, time=202.57 memory used=8723.2MB, alloc=1044.3MB, time=219.42 memory used=9120.4MB, alloc=1068.3MB, time=236.62 memory used=9527.5MB, alloc=1092.3MB, time=254.54 memory used=9944.8MB, alloc=1116.3MB, time=273.62 |\^/| 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(); 1428504693 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 F := [17 y z - 8 x z - 9 y , -9 x y + 4 x z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 G := [-13 x z - 14 z + 13 x, -7 x y + 7 z + 3] > Problem := [F,G]; 2 2 2 Problem := [[17 y z - 8 x z - 9 y , -9 x y + 4 x z], 2 2 [-13 x z - 14 z + 13 x, -7 x y + 7 z + 3]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=26.3MB, alloc=32.3MB, time=0.53 memory used=46.7MB, alloc=32.3MB, time=0.83 memory used=65.3MB, alloc=56.3MB, time=1.13 memory used=107.5MB, alloc=68.3MB, time=1.79 memory used=146.5MB, alloc=92.3MB, time=2.41 memory used=210.5MB, alloc=92.3MB, time=3.39 memory used=276.7MB, alloc=92.3MB, time=4.29 memory used=342.8MB, alloc=116.3MB, time=5.27 memory used=423.7MB, alloc=372.3MB, time=6.61 memory used=506.9MB, alloc=396.3MB, time=8.02 memory used=619.0MB, alloc=396.3MB, time=9.71 memory used=725.7MB, alloc=420.3MB, time=11.54 memory used=861.6MB, alloc=420.3MB, time=13.41 memory used=990.9MB, alloc=444.3MB, time=15.43 memory used=1127.3MB, alloc=468.3MB, time=17.49 memory used=1279.0MB, alloc=492.3MB, time=19.68 memory used=1454.0MB, alloc=492.3MB, time=22.24 memory used=1637.7MB, alloc=516.3MB, time=25.42 memory used=1835.4MB, alloc=540.3MB, time=28.90 memory used=2041.4MB, alloc=564.3MB, time=32.57 memory used=2233.9MB, alloc=588.3MB, time=36.18 memory used=2456.2MB, alloc=612.3MB, time=39.74 memory used=2656.9MB, alloc=636.3MB, time=43.29 memory used=2843.2MB, alloc=660.3MB, time=46.77 memory used=3021.0MB, alloc=684.3MB, time=50.86 memory used=3262.7MB, alloc=708.3MB, time=59.46 memory used=3508.5MB, alloc=732.3MB, time=68.90 memory used=3764.1MB, alloc=756.3MB, time=78.80 memory used=4031.8MB, alloc=780.3MB, time=89.61 memory used=4304.1MB, alloc=804.3MB, time=101.38 memory used=4592.8MB, alloc=828.3MB, time=114.34 memory used=4905.5MB, alloc=852.3MB, time=128.42 memory used=5242.0MB, alloc=876.3MB, time=143.37 memory used=5602.5MB, alloc=900.3MB, time=158.87 memory used=5987.0MB, alloc=924.3MB, time=175.39 memory used=6395.4MB, alloc=948.3MB, time=192.88 memory used=6827.7MB, alloc=948.3MB, time=212.20 memory used=7260.0MB, alloc=948.3MB, time=231.92 |\^/| 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(); 1428504993 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 F := [-7 x - 11 x y + 9 z, 2 x y z - 6 y + 10 z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 3 3 G := [-17 x + 20 y - 7 y, 2 x + 9 y - 6 z] > Problem := [F,G]; 2 3 Problem := [[-7 x - 11 x y + 9 z, 2 x y z - 6 y + 10 z], 3 2 3 3 [-17 x + 20 y - 7 y, 2 x + 9 y - 6 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=25.8MB, alloc=32.3MB, time=0.52 memory used=45.3MB, alloc=60.3MB, time=0.84 memory used=84.2MB, alloc=60.3MB, time=1.41 memory used=125.8MB, alloc=68.3MB, time=2.05 memory used=169.8MB, alloc=92.3MB, time=2.78 memory used=234.6MB, alloc=92.3MB, time=3.94 memory used=293.0MB, alloc=116.3MB, time=5.02 memory used=375.6MB, alloc=140.3MB, time=6.40 memory used=471.6MB, alloc=164.3MB, time=8.15 memory used=583.1MB, alloc=188.3MB, time=10.56 memory used=700.3MB, alloc=212.3MB, time=14.26 memory used=827.1MB, alloc=236.3MB, time=19.03 memory used=972.5MB, alloc=236.3MB, time=24.77 memory used=1117.9MB, alloc=260.3MB, time=30.50 memory used=1287.4MB, alloc=260.3MB, time=37.20 N1 := 4789 > GB := Basis(F, plex(op(vars))); 3 2 2 3 2 2 GB := [-7 x y - 11 x y + 27 y - 35 x - 55 x y, -7 x - 11 x y + 9 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1426.8MB, alloc=260.3MB, time=41.06 memory used=1632.4MB, alloc=540.3MB, time=47.08 N2 := 1615 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 3 3 2 H := [-7 x - 11 x y + 9 z, 2 x y z - 6 y + 10 z, -17 x + 20 y - 7 y, 3 3 9 y + 2 x - 6 z] > J:=[op(GB),op(G)]; 3 2 2 3 2 2 J := [-7 x y - 11 x y + 27 y - 35 x - 55 x y, -7 x - 11 x y + 9 z, 3 2 3 3 -17 x + 20 y - 7 y, 9 y + 2 x - 6 z] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 11, 11, 3, 3, 3, 1, 1, 1, 3/4, 5/12, 1/2, 1/3, 4, 10, 12, 4, 3, 3, 1, 1, 1, 1/2, 4/7, 4/7, 1/7, 1, -1, -1] > save(F, G, cat("ranSet/33", convert(F, string),".txt")); > quit memory used=1633.7MB, alloc=540.3MB, time=47.13 |\^/| 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(); 1428505055 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 3 F := [-20 x z - y z + 20 y , -7 x y + 3 y + 6 x] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 G := [6 y z - 14 x y - x, 7 x y - 9 x z - 2 y z] > Problem := [F,G]; 2 2 2 2 3 Problem := [[-20 x z - y z + 20 y , -7 x y + 3 y + 6 x], 2 2 2 [6 y z - 14 x y - x, 7 x y - 9 x z - 2 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.7MB, alloc=32.3MB, time=0.53 memory used=49.2MB, alloc=60.3MB, time=0.86 memory used=90.8MB, alloc=60.3MB, time=1.47 memory used=132.7MB, alloc=60.3MB, time=2.02 memory used=169.6MB, alloc=60.3MB, time=2.31 memory used=200.3MB, alloc=60.3MB, time=2.51 memory used=239.0MB, alloc=60.3MB, time=2.94 memory used=283.5MB, alloc=92.3MB, time=3.48 memory used=349.1MB, alloc=92.3MB, time=4.40 memory used=416.4MB, alloc=92.3MB, time=5.26 memory used=482.6MB, alloc=116.3MB, time=6.09 memory used=551.4MB, alloc=116.3MB, time=7.08 memory used=620.9MB, alloc=372.3MB, time=7.91 memory used=687.3MB, alloc=372.3MB, time=8.53 memory used=792.1MB, alloc=372.3MB, time=9.75 memory used=887.8MB, alloc=396.3MB, time=11.04 memory used=997.7MB, alloc=420.3MB, time=12.55 memory used=1125.4MB, alloc=420.3MB, time=14.12 memory used=1270.7MB, alloc=444.3MB, time=16.02 memory used=1445.3MB, alloc=444.3MB, time=17.44 memory used=1609.0MB, alloc=444.3MB, time=19.00 memory used=1769.9MB, alloc=468.3MB, time=20.42 memory used=1911.4MB, alloc=468.3MB, time=21.03 memory used=2109.1MB, alloc=468.3MB, time=23.13 memory used=2252.4MB, alloc=468.3MB, time=23.90 memory used=2411.4MB, alloc=468.3MB, time=24.94 memory used=2576.9MB, alloc=492.3MB, time=27.67 memory used=2768.3MB, alloc=492.3MB, time=30.89 memory used=2950.7MB, alloc=516.3MB, time=33.94 memory used=3164.5MB, alloc=540.3MB, time=37.03 memory used=3397.4MB, alloc=540.3MB, time=40.16 memory used=3575.8MB, alloc=564.3MB, time=43.17 memory used=3740.4MB, alloc=588.3MB, time=45.99 memory used=3936.5MB, alloc=588.3MB, time=48.99 memory used=4118.4MB, alloc=612.3MB, time=51.99 memory used=4270.7MB, alloc=636.3MB, time=54.70 memory used=4425.3MB, alloc=636.3MB, time=57.34 memory used=4587.9MB, alloc=636.3MB, time=59.93 memory used=4771.2MB, alloc=660.3MB, time=63.14 memory used=4914.1MB, alloc=660.3MB, time=65.61 memory used=5089.4MB, alloc=684.3MB, time=68.25 memory used=5415.9MB, alloc=684.3MB, time=71.24 memory used=5716.6MB, alloc=708.3MB, time=74.13 memory used=5992.8MB, alloc=732.3MB, time=83.42 memory used=6275.8MB, alloc=756.3MB, time=93.83 memory used=6565.6MB, alloc=780.3MB, time=105.02 memory used=6868.0MB, alloc=804.3MB, time=117.53 memory used=7183.4MB, alloc=828.3MB, time=130.55 memory used=7503.2MB, alloc=852.3MB, time=144.60 memory used=7847.0MB, alloc=876.3MB, time=159.79 memory used=8214.7MB, alloc=900.3MB, time=175.84 memory used=8606.3MB, alloc=924.3MB, time=192.83 memory used=9021.9MB, alloc=924.3MB, time=211.34 memory used=9437.3MB, alloc=924.3MB, time=229.63 memory used=9852.8MB, alloc=924.3MB, time=247.65 |\^/| 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(); 1428505355 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 F := [5 y z + 11 z - 18 y , -7 x y z + 3 y z - 3 y] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 G := [-12 y z + 6 x z, 7 y - 6 z] > Problem := [F,G]; 2 3 2 Problem := [[5 y z + 11 z - 18 y , -7 x y z + 3 y z - 3 y], 2 [-12 y z + 6 x z, 7 y - 6 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.1MB, alloc=32.3MB, time=0.17 memory used=26.1MB, alloc=32.3MB, time=0.48 memory used=46.9MB, alloc=32.3MB, time=0.79 memory used=65.9MB, alloc=56.3MB, time=1.08 memory used=108.4MB, alloc=60.3MB, time=1.82 memory used=146.6MB, alloc=84.3MB, time=2.50 memory used=205.9MB, alloc=108.3MB, time=3.56 memory used=278.8MB, alloc=140.3MB, time=5.33 memory used=358.9MB, alloc=140.3MB, time=8.26 memory used=439.2MB, alloc=164.3MB, time=11.08 N1 := 2579 > GB := Basis(F, plex(op(vars))); 3 3 2 3 3 2 3 2 GB := [686 x y - 882 x y + 378 x y - 35 x y - 54 y + 15 y + 33 y, 2 3 3 3 2 -98 x y + 84 x y - 18 y + 5 y + 11 y z, 2 4 4 3 4 3 3 2 -2450 x y + 2100 x y - 2310 x y - 450 y + 1115 y + 1331 z - 2178 y ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=545.1MB, alloc=164.3MB, time=12.97 memory used=625.9MB, alloc=420.3MB, time=14.28 memory used=743.2MB, alloc=444.3MB, time=16.15 memory used=888.7MB, alloc=468.3MB, time=18.62 memory used=1050.2MB, alloc=492.3MB, time=21.50 memory used=1216.4MB, alloc=516.3MB, time=25.39 memory used=1369.0MB, alloc=540.3MB, time=31.10 memory used=1534.0MB, alloc=564.3MB, time=37.75 memory used=1723.1MB, alloc=588.3MB, time=45.35 N2 := 4639 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 3 2 2 H := [5 y z + 11 z - 18 y , -7 x y z + 3 y z - 3 y, -12 y z + 6 x z, -6 z + 7 y] > J:=[op(GB),op(G)]; 3 3 2 3 3 2 3 2 J := [686 x y - 882 x y + 378 x y - 35 x y - 54 y + 15 y + 33 y, 2 3 3 3 2 -98 x y + 84 x y - 18 y + 5 y + 11 y z, 2 4 4 3 4 3 3 2 -2450 x y + 2100 x y - 2310 x y - 450 y + 1115 y + 1331 z - 2178 y , 2 -12 y z + 6 x z, -6 z + 7 y] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 10, 10, 3, 1, 2, 3, 1/2, 1, 1, 1/5, 7/10, 7/10, 5, 13, 21, 6, 10 20 3, 4, 3, 4/5, 1, 4/5, --, --, 5/23, -3, -11, -3] 23 23 > save(F, G, cat("ranSet/33", convert(F, string),".txt")); > quit memory used=1869.8MB, alloc=588.3MB, time=50.79 |\^/| 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(); 1428505424 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 F := [9 x z - 4 x y z, -6 x y - 7 x z - 8 x y] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 3 G := [10 x y z + 10 z + 17, y + 3 z + 10 z] > Problem := [F,G]; 2 2 2 Problem := [[9 x z - 4 x y z, -6 x y - 7 x z - 8 x y], 3 3 [10 x y z + 10 z + 17, y + 3 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=4.1MB, alloc=32.3MB, time=0.17 memory used=26.3MB, alloc=32.3MB, time=0.50 memory used=46.2MB, alloc=56.3MB, time=0.80 memory used=87.3MB, alloc=60.3MB, time=1.43 memory used=128.4MB, alloc=60.3MB, time=2.00 memory used=169.2MB, alloc=84.3MB, time=2.55 memory used=230.1MB, alloc=92.3MB, time=3.16 memory used=281.7MB, alloc=92.3MB, time=4.33 memory used=314.2MB, alloc=92.3MB, time=4.44 memory used=346.8MB, alloc=92.3MB, time=4.52 memory used=405.1MB, alloc=92.3MB, time=5.13 memory used=475.5MB, alloc=92.3MB, time=6.11 memory used=530.9MB, alloc=116.3MB, time=7.11 memory used=605.9MB, alloc=140.3MB, time=8.52 memory used=688.8MB, alloc=164.3MB, time=11.37 N1 := 1839 > GB := Basis(F, plex(op(vars))); 3 2 2 2 2 2 2 GB := [-27 x y + 12 x y - 36 x y + 16 x y , 6 x y + 7 x z + 8 x y, 2 27 x y + 14 x y z + 36 x y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=798.5MB, alloc=164.3MB, time=13.56 memory used=877.1MB, alloc=420.3MB, time=14.84 memory used=1001.0MB, alloc=420.3MB, time=16.75 memory used=1124.4MB, alloc=444.3MB, time=18.61 memory used=1256.3MB, alloc=444.3MB, time=20.13 memory used=1334.3MB, alloc=444.3MB, time=22.24 memory used=1393.0MB, alloc=468.3MB, time=22.50 memory used=1535.7MB, alloc=468.3MB, time=23.83 memory used=1641.6MB, alloc=468.3MB, time=25.34 memory used=1769.1MB, alloc=468.3MB, time=26.53 memory used=1941.5MB, alloc=492.3MB, time=29.33 memory used=2114.4MB, alloc=516.3MB, time=32.51 memory used=2286.7MB, alloc=540.3MB, time=37.71 memory used=2449.1MB, alloc=564.3MB, time=44.59 memory used=2635.6MB, alloc=588.3MB, time=52.33 N2 := 4045 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 H := [9 x z - 4 x y z, -6 x y - 7 x z - 8 x y, 10 z y x + 10 z + 17, 3 3 3 z + y + 10 z] > J:=[op(GB),op(G)]; 3 2 2 2 2 2 2 J := [-27 x y + 12 x y - 36 x y + 16 x y , 6 x y + 7 x z + 8 x y, 2 3 3 27 x y + 14 x y z + 36 x y, 10 z y x + 10 z + 17, 3 z + y + 10 z] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 11, 12, 3, 2, 3, 3, 3/4, 1, 1, 6/11, 5/11, 7/11, 5, 13, 16, 11 11 4, 3, 3, 3, 4/5, 1, 4/5, --, --, 3/8, -2, -4, -1] 16 16 > save(F, G, cat("ranSet/33", convert(F, string),".txt")); > quit memory used=2713.2MB, alloc=588.3MB, time=55.18 |\^/| 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(); 1428505495 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 2 F := [-4 x z - 18 x - y , -2 x z + 7 y z + 5 x y] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 G := [-8 z + 20 x - 6, -10 x y + 2] > Problem := [F,G]; 2 2 2 2 2 Problem := [[-4 x z - 18 x - y , -2 x z + 7 y z + 5 x y], 2 2 [-8 z + 20 x - 6, -10 x y + 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=4.1MB, alloc=32.3MB, time=0.18 memory used=27.1MB, alloc=32.3MB, time=0.53 memory used=48.2MB, alloc=32.3MB, time=0.84 memory used=68.7MB, alloc=56.3MB, time=1.18 memory used=110.7MB, alloc=60.3MB, time=1.82 memory used=151.3MB, alloc=60.3MB, time=2.42 memory used=193.8MB, alloc=84.3MB, time=3.17 memory used=255.7MB, alloc=84.3MB, time=4.29 memory used=314.2MB, alloc=108.3MB, time=5.35 memory used=392.9MB, alloc=140.3MB, time=6.96 memory used=481.5MB, alloc=164.3MB, time=9.97 N1 := 1769 > GB := Basis(F, plex(op(vars))); 6 4 2 2 4 6 2 3 GB := [49 y + 854 y x - 500 y x + 72 x + 100 y x , 4 4 2 3 5 3 252 x y + 40 x z - 868 x y - 49 y - 100 x y, 4 2 2 2 4 2 2 36 x - 124 x y + 20 x y z - 7 y , -2 x z + 7 y z + 5 x y, 2 2 2 4 z x + y + 18 x ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=585.1MB, alloc=164.3MB, time=11.89 memory used=719.0MB, alloc=420.3MB, time=13.76 memory used=840.4MB, alloc=444.3MB, time=20.77 memory used=1599.3MB, alloc=444.3MB, time=27.89 memory used=2043.7MB, alloc=444.3MB, time=44.55 memory used=2185.1MB, alloc=444.3MB, time=46.53 memory used=2359.4MB, alloc=444.3MB, time=48.84 memory used=2527.2MB, alloc=444.3MB, time=51.40 memory used=2709.9MB, alloc=444.3MB, time=53.66 memory used=2879.8MB, alloc=468.3MB, time=55.75 memory used=3222.8MB, alloc=468.3MB, time=59.62 memory used=3796.8MB, alloc=468.3MB, time=73.33 memory used=3914.7MB, alloc=492.3MB, time=103.93 memory used=5011.1MB, alloc=492.3MB, time=110.33 memory used=5463.3MB, alloc=492.3MB, time=118.31 memory used=5671.7MB, alloc=492.3MB, time=120.31 memory used=5857.7MB, alloc=516.3MB, time=122.99 memory used=6339.7MB, alloc=540.3MB, time=133.30 memory used=7332.8MB, alloc=540.3MB, time=141.37 memory used=7598.8MB, alloc=540.3MB, time=144.76 memory used=7867.3MB, alloc=564.3MB, time=181.61 memory used=8665.5MB, alloc=564.3MB, time=216.50 memory used=8904.6MB, alloc=564.3MB, time=218.33 memory used=9204.4MB, alloc=564.3MB, time=234.98 memory used=9774.8MB, alloc=564.3MB, time=241.26 memory used=10130.5MB, alloc=564.3MB, time=245.03 memory used=10463.2MB, alloc=564.3MB, time=249.42 memory used=12214.7MB, alloc=564.3MB, time=260.86 memory used=12768.5MB, alloc=564.3MB, time=265.26 memory used=12943.9MB, alloc=588.3MB, time=321.96 memory used=13889.5MB, alloc=588.3MB, time=330.54 memory used=14532.1MB, alloc=588.3MB, time=351.08 memory used=14858.2MB, alloc=588.3MB, time=354.21 memory used=15227.3MB, alloc=612.3MB, time=358.85 memory used=15496.2MB, alloc=636.3MB, time=362.48 |\^/| 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(); 1428505795 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 F := [8 x y - 9 y z + 12 z , y z + 4 z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 G := [10 x y z - 20 y - 5 x , -7 x y + 6 x z + 2 x] > Problem := [F,G]; 2 2 2 Problem := [[8 x y - 9 y z + 12 z , y z + 4 z], 3 2 [10 x y z - 20 y - 5 x , -7 x y + 6 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=4.2MB, alloc=32.3MB, time=0.18 memory used=26.3MB, alloc=32.3MB, time=0.53 memory used=46.9MB, alloc=32.3MB, time=0.85 memory used=64.2MB, alloc=56.3MB, time=1.14 memory used=104.2MB, alloc=60.3MB, time=1.78 memory used=143.0MB, alloc=60.3MB, time=2.39 memory used=181.6MB, alloc=84.3MB, time=3.01 memory used=224.5MB, alloc=84.3MB, time=3.69 memory used=289.2MB, alloc=92.3MB, time=4.64 memory used=354.6MB, alloc=116.3MB, time=5.52 memory used=450.7MB, alloc=116.3MB, time=6.50 memory used=532.5MB, alloc=140.3MB, time=7.90 memory used=629.4MB, alloc=164.3MB, time=9.61 memory used=738.7MB, alloc=444.3MB, time=11.59 memory used=867.1MB, alloc=468.3MB, time=14.24 memory used=990.4MB, alloc=492.3MB, time=18.07 memory used=1120.3MB, alloc=516.3MB, time=23.06 memory used=1271.2MB, alloc=540.3MB, time=29.09 memory used=1446.1MB, alloc=540.3MB, time=35.91 memory used=1621.0MB, alloc=564.3MB, time=42.72 memory used=1820.0MB, alloc=588.3MB, time=50.51 N1 := 5717 > GB := Basis(F, plex(op(vars))); 2 3 2 2 2 2 GB := [x y + 4 x y, y z + 4 z, 8 y x + 12 z - 9 z y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=2054.7MB, alloc=588.3MB, time=55.70 memory used=2339.2MB, alloc=588.3MB, time=59.63 memory used=2598.3MB, alloc=612.3MB, time=64.34 memory used=2862.5MB, alloc=636.3MB, time=71.73 memory used=3091.0MB, alloc=660.3MB, time=81.14 memory used=3343.1MB, alloc=684.3MB, time=91.58 memory used=3619.3MB, alloc=708.3MB, time=103.08 N2 := 5717 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 3 2 H := [8 y x + 12 z - 9 z y, y z + 4 z, 10 x y z - 20 y - 5 x , -7 x y + 6 x z + 2 x] > J:=[op(GB),op(G)]; 2 3 2 2 2 2 J := [x y + 4 x y, y z + 4 z, 8 y x + 12 z - 9 z y, 3 2 10 x y z - 20 y - 5 x , -7 x y + 6 x z + 2 x] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 11, 11, 3, 2, 3, 2, 3/4, 1, 1, 6/11, 6/11, 6/11, 5, 13, 16, 5, 2, 3, 2, 4/5, 1, 4/5, 8/13, 8/13, 6/13, -2, -5, -2] > save(F, G, cat("ranSet/33", convert(F, string),".txt")); > quit memory used=3747.8MB, alloc=708.3MB, time=108.04 |\^/| 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(); 1428505910 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 2 F := [16 y z - 9 y z - 16 y , -x y - 7 x - 8 x y] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 3 G := [-18 x - 7 x z + 4 x, -5 z - 5 x] > Problem := [F,G]; 2 2 2 2 2 Problem := [[16 y z - 9 y z - 16 y , -x y - 7 x - 8 x y], 3 2 3 [-18 x - 7 x z + 4 x, -5 z - 5 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=26.7MB, alloc=32.3MB, time=0.53 memory used=46.1MB, alloc=32.3MB, time=0.82 memory used=64.7MB, alloc=56.3MB, time=1.10 memory used=104.5MB, alloc=60.3MB, time=1.75 memory used=145.4MB, alloc=84.3MB, time=2.49 memory used=207.7MB, alloc=84.3MB, time=3.62 memory used=264.4MB, alloc=108.3MB, time=4.65 memory used=335.7MB, alloc=140.3MB, time=6.30 memory used=414.1MB, alloc=164.3MB, time=9.11 memory used=513.9MB, alloc=164.3MB, time=12.80 N1 := 2687 > GB := Basis(F, plex(op(vars))); 2 2 2 2 2 2 GB := [x y + 7 x + 8 x y, 9 x z + 112 x z + 128 x y z - 112 x - 128 x y, 2 2 2 -16 y z + 9 y z + 16 y ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=618.4MB, alloc=164.3MB, time=15.01 memory used=707.2MB, alloc=420.3MB, time=16.50 memory used=821.0MB, alloc=444.3MB, time=18.38 memory used=958.3MB, alloc=444.3MB, time=20.58 memory used=1095.9MB, alloc=468.3MB, time=22.89 memory used=1259.8MB, alloc=492.3MB, time=25.65 memory used=1448.5MB, alloc=516.3MB, time=29.10 memory used=1659.1MB, alloc=540.3MB, time=32.58 memory used=1899.9MB, alloc=564.3MB, time=36.06 memory used=2150.7MB, alloc=588.3MB, time=40.03 memory used=2414.1MB, alloc=612.3MB, time=44.20 memory used=2695.0MB, alloc=636.3MB, time=48.57 memory used=2950.0MB, alloc=660.3MB, time=54.93 memory used=3177.0MB, alloc=684.3MB, time=62.55 memory used=3406.9MB, alloc=708.3MB, time=70.80 memory used=3643.3MB, alloc=732.3MB, time=80.10 memory used=3888.4MB, alloc=756.3MB, time=90.52 memory used=4157.4MB, alloc=780.3MB, time=101.89 memory used=4450.2MB, alloc=804.3MB, time=114.21 memory used=4767.1MB, alloc=828.3MB, time=127.49 memory used=5107.9MB, alloc=852.3MB, time=141.72 memory used=5472.6MB, alloc=876.3MB, time=156.98 memory used=5861.2MB, alloc=900.3MB, time=173.16 memory used=6273.9MB, alloc=900.3MB, time=190.34 memory used=6686.4MB, alloc=900.3MB, time=207.28 memory used=7098.9MB, alloc=924.3MB, time=224.26 memory used=7535.4MB, alloc=924.3MB, time=241.91 memory used=7971.7MB, alloc=948.3MB, time=259.58 memory used=8432.1MB, alloc=948.3MB, time=278.34 |\^/| 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(); 1428506210 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 2 F := [-20 x + 18 x y z - 10 z , -10 x y + 7 x ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 G := [8 z - 10 x - 17, 8 y z - 9 y z + z] > Problem := [F,G]; 3 2 2 2 Problem := [[-20 x + 18 x y z - 10 z , -10 x y + 7 x ], 3 2 2 [8 z - 10 x - 17, 8 y z - 9 y z + z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=26.1MB, alloc=32.3MB, time=0.50 memory used=45.0MB, alloc=56.3MB, time=0.80 memory used=87.0MB, alloc=60.3MB, time=1.40 memory used=127.8MB, alloc=60.3MB, time=2.01 memory used=167.4MB, alloc=84.3MB, time=2.61 memory used=231.1MB, alloc=92.3MB, time=3.45 memory used=295.8MB, alloc=92.3MB, time=4.43 memory used=363.6MB, alloc=116.3MB, time=5.49 memory used=446.8MB, alloc=140.3MB, time=6.95 memory used=554.5MB, alloc=140.3MB, time=8.62 memory used=651.3MB, alloc=164.3MB, time=10.32 memory used=754.2MB, alloc=188.3MB, time=13.09 memory used=862.1MB, alloc=212.3MB, time=16.89 memory used=986.9MB, alloc=236.3MB, time=21.57 memory used=1135.6MB, alloc=236.3MB, time=27.16 memory used=1284.5MB, alloc=260.3MB, time=32.72 N1 := 4333 > GB := Basis(F, plex(op(vars))); 2 2 3 2 GB := [10 x y - 7 x , -9 z y x + 10 x + 5 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1378.1MB, alloc=260.3MB, time=34.52 memory used=1583.2MB, alloc=516.3MB, time=37.62 memory used=1804.7MB, alloc=516.3MB, time=41.23 memory used=2001.1MB, alloc=540.3MB, time=45.12 memory used=2177.0MB, alloc=564.3MB, time=51.58 memory used=2364.1MB, alloc=588.3MB, time=59.06 memory used=2575.5MB, alloc=612.3MB, time=67.39 N2 := 4333 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 2 2 3 2 H := [-20 x + 18 x y z - 10 z , -10 x y + 7 x , 8 z - 10 x - 17, 2 8 y z - 9 y z + z] > J:=[op(GB),op(G)]; 2 2 3 2 3 2 J := [10 x y - 7 x , -9 z y x + 10 x + 5 z , 8 z - 10 x - 17, 2 8 y z - 9 y z + z] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 9, 12, 3, 3, 2, 3, 3/4, 3/4, 3/4, 5/11, 4/11, 6/11, 4, 9, 12, 3, 3, 2, 3, 3/4, 3/4, 3/4, 5/11, 4/11, 6/11, 0, 0, 0] > save(F, G, cat("ranSet/33", convert(F, string),".txt")); > quit memory used=2591.2MB, alloc=612.3MB, time=67.86 |\^/| 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(); 1428506284 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 3 2 2 F := [-7 x y - 10 y z - 16 z, -9 x - 3 x z + 5 y z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 2 2 G := [-x - 19 x z + 14 y z , -5 x y + 4 x y + 6 z] > Problem := [F,G]; 2 2 3 2 2 Problem := [[-7 x y - 10 y z - 16 z, -9 x - 3 x z + 5 y z], 3 2 2 2 2 [-x - 19 x z + 14 y z , -5 x y + 4 x y + 6 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.6MB, alloc=32.3MB, time=0.52 memory used=46.8MB, alloc=36.3MB, time=0.82 memory used=65.6MB, alloc=60.3MB, time=1.12 memory used=106.3MB, alloc=60.3MB, time=1.72 memory used=138.1MB, alloc=60.3MB, time=2.13 memory used=181.2MB, alloc=92.3MB, time=2.76 memory used=250.2MB, alloc=92.3MB, time=3.69 memory used=315.4MB, alloc=116.3MB, time=4.63 memory used=380.4MB, alloc=372.3MB, time=5.57 memory used=468.5MB, alloc=372.3MB, time=6.86 memory used=558.8MB, alloc=396.3MB, time=8.06 memory used=667.0MB, alloc=420.3MB, time=9.66 memory used=797.5MB, alloc=420.3MB, time=11.50 memory used=911.6MB, alloc=444.3MB, time=13.06 memory used=1029.5MB, alloc=444.3MB, time=14.78 memory used=1129.2MB, alloc=468.3MB, time=16.30 memory used=1227.1MB, alloc=468.3MB, time=17.67 memory used=1320.5MB, alloc=468.3MB, time=19.03 memory used=1451.9MB, alloc=492.3MB, time=21.32 memory used=1584.2MB, alloc=516.3MB, time=23.84 memory used=1707.1MB, alloc=540.3MB, time=26.19 memory used=1833.8MB, alloc=540.3MB, time=28.71 memory used=1944.8MB, alloc=564.3MB, time=30.87 memory used=2059.2MB, alloc=564.3MB, time=33.13 memory used=2190.8MB, alloc=588.3MB, time=35.66 memory used=2407.6MB, alloc=612.3MB, time=42.91 memory used=2614.1MB, alloc=636.3MB, time=51.99 memory used=2828.2MB, alloc=660.3MB, time=61.68 memory used=3066.2MB, alloc=684.3MB, time=71.80 memory used=3328.2MB, alloc=708.3MB, time=82.79 memory used=3614.3MB, alloc=708.3MB, time=94.95 memory used=3900.5MB, alloc=732.3MB, time=107.29 N1 := 7299 > GB := Basis(F, plex(op(vars))); 4 3 2 2 3 3 3 2 2 GB := [-21 x y + 90 x y + 35 x y + 144 x , 18 x + 7 x y + 6 x z + 16 z, 2 2 10 z y + 7 y x + 16 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=4036.2MB, alloc=732.3MB, time=111.47 memory used=4111.1MB, alloc=732.3MB, time=113.29 memory used=4186.6MB, alloc=732.3MB, time=115.04 memory used=4252.3MB, alloc=732.3MB, time=116.63 memory used=4323.6MB, alloc=732.3MB, time=118.30 memory used=4379.4MB, alloc=732.3MB, time=119.66 memory used=4434.3MB, alloc=732.3MB, time=121.07 memory used=4482.0MB, alloc=732.3MB, time=122.35 memory used=4540.5MB, alloc=732.3MB, time=123.84 memory used=4583.0MB, alloc=732.3MB, time=124.83 memory used=4636.6MB, alloc=732.3MB, time=126.24 memory used=4680.9MB, alloc=732.3MB, time=127.51 memory used=4891.0MB, alloc=732.3MB, time=130.89 memory used=5149.1MB, alloc=732.3MB, time=135.67 memory used=5457.1MB, alloc=756.3MB, time=141.72 memory used=5818.4MB, alloc=780.3MB, time=154.59 memory used=6139.2MB, alloc=804.3MB, time=169.08 N2 := 5291 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 3 2 2 H := [-7 x y - 10 y z - 16 z, -9 x - 3 x z + 5 y z, 3 2 2 2 2 -x - 19 x z + 14 y z , -5 x y + 4 x y + 6 z] > J:=[op(GB),op(G)]; 4 3 2 2 3 3 2 2 3 J := [-21 x y + 90 x y + 35 x y + 144 x , 6 z x + 7 y x + 18 x + 16 z, 2 2 3 2 2 2 2 10 z y + 7 y x + 16 z, -x - 19 x z + 14 y z , -5 x y + 4 x y + 6 z] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 12, 12, 3, 3, 2, 2, 1, 1, 1, 7/12, 1/2, 7/12, 5, 14, 17, 5, 12 4, 3, 2, 1, 1, 4/5, --, 9/17, 7/17, -2, -5, -2] 17 > save(F, G, cat("ranSet/33", convert(F, string),".txt")); > quit memory used=6473.3MB, alloc=804.3MB, time=183.13 |\^/| 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(); 1428506495 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 F := [16 x z - 4 z + 9 x, 7 x y + 4 z ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 2 G := [-13 y z - 17 y, 8 z + 9 y + 8 z ] > Problem := [F,G]; Problem := [ 2 2 2 2 3 2 2 [16 x z - 4 z + 9 x, 7 x y + 4 z ], [-13 y z - 17 y, 8 z + 9 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=0.17 memory used=26.6MB, alloc=32.3MB, time=0.51 memory used=48.4MB, alloc=60.3MB, time=0.85 memory used=89.7MB, alloc=60.3MB, time=1.48 memory used=130.5MB, alloc=92.3MB, time=2.13 memory used=198.0MB, alloc=92.3MB, time=3.06 memory used=262.0MB, alloc=92.3MB, time=4.01 memory used=322.7MB, alloc=116.3MB, time=4.93 memory used=406.0MB, alloc=140.3MB, time=6.32 memory used=505.7MB, alloc=164.3MB, time=8.24 N1 := 1479 > GB := Basis(F, plex(op(vars))); 4 2 2 GB := [448 x y + 49 x y + 126 x y + 81 x, 16 x z + 7 x y + 9 x, 3 2 -28 x y + 7 x y z + 9 x z, 4 z + 7 y x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=611.9MB, alloc=164.3MB, time=11.08 memory used=711.6MB, alloc=420.3MB, time=12.71 memory used=837.4MB, alloc=420.3MB, time=14.72 memory used=963.5MB, alloc=444.3MB, time=16.67 memory used=1121.9MB, alloc=468.3MB, time=19.08 memory used=1298.3MB, alloc=492.3MB, time=21.94 memory used=1496.7MB, alloc=516.3MB, time=25.14 memory used=1735.3MB, alloc=540.3MB, time=28.45 memory used=1973.2MB, alloc=564.3MB, time=32.66 memory used=2233.6MB, alloc=588.3MB, time=36.86 memory used=2504.3MB, alloc=612.3MB, time=41.43 memory used=2779.1MB, alloc=636.3MB, time=46.67 N2 := 2099 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 3 2 2 H := [16 z x - 4 z + 9 x, 4 z + 7 y x, -13 y z - 17 y, 8 z + 8 z + 9 y ] > J:=[op(GB),op(G)]; 4 2 2 J := [448 x y + 49 x y + 126 x y + 81 x, 16 x z + 7 x y + 9 x, 3 2 2 -28 x y + 7 x y z + 9 x z, 4 z + 7 y x, -13 y z - 17 y, 3 2 2 8 z + 8 z + 9 y ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 9, 11, 3, 2, 2, 3, 1/2, 3/4, 1, 3/10, 2/5, 3/5, 6, 15, 20, 5, 11 10 4, 2, 3, 2/3, 1, 5/6, --, --, 7/17, -6, -9, -2] 17 17 > save(F, G, cat("ranSet/33", convert(F, string),".txt")); > quit memory used=2938.1MB, alloc=636.3MB, time=52.81 |\^/| 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(); 1428506565 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 F := [-12 x y - 12 x y + 5 y z, 4 y z - 10 x + 9 y] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 3 2 G := [2 y + 18 x z + 13 y , 10 x - 6 z - 5 z] > Problem := [F,G]; 2 2 2 2 Problem := [[-12 x y - 12 x y + 5 y z, 4 y z - 10 x + 9 y], 3 2 3 2 [2 y + 18 x z + 13 y , 10 x - 6 z - 5 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=24.8MB, alloc=32.3MB, time=0.53 memory used=43.7MB, alloc=56.3MB, time=0.81 memory used=85.9MB, alloc=60.4MB, time=1.35 memory used=130.1MB, alloc=68.4MB, time=2.02 memory used=172.4MB, alloc=92.4MB, time=2.68 memory used=246.3MB, alloc=92.4MB, time=3.53 memory used=310.4MB, alloc=92.4MB, time=4.05 memory used=360.1MB, alloc=92.4MB, time=4.47 memory used=431.5MB, alloc=92.4MB, time=5.17 memory used=504.1MB, alloc=92.4MB, time=5.88 memory used=571.0MB, alloc=372.4MB, time=6.78 memory used=662.4MB, alloc=372.4MB, time=7.79 memory used=770.5MB, alloc=372.4MB, time=9.00 memory used=860.4MB, alloc=396.4MB, time=10.25 memory used=973.4MB, alloc=396.4MB, time=11.41 memory used=1097.1MB, alloc=420.4MB, time=13.04 memory used=1212.1MB, alloc=420.4MB, time=13.89 memory used=1279.5MB, alloc=420.4MB, time=14.16 memory used=1348.2MB, alloc=420.4MB, time=14.48 memory used=1418.8MB, alloc=420.4MB, time=14.75 memory used=1487.5MB, alloc=420.4MB, time=15.08 memory used=1557.5MB, alloc=420.4MB, time=15.37 memory used=1636.8MB, alloc=420.4MB, time=16.05 memory used=1699.1MB, alloc=420.4MB, time=16.26 memory used=1753.5MB, alloc=420.4MB, time=16.43 memory used=1823.9MB, alloc=420.4MB, time=16.71 memory used=1899.3MB, alloc=420.4MB, time=17.40 memory used=1959.3MB, alloc=420.4MB, time=17.59 memory used=2032.5MB, alloc=420.4MB, time=17.98 memory used=2095.2MB, alloc=420.4MB, time=18.21 memory used=2164.4MB, alloc=420.4MB, time=18.49 memory used=2235.9MB, alloc=420.4MB, time=18.80 memory used=2363.7MB, alloc=420.4MB, time=19.91 memory used=2467.3MB, alloc=420.4MB, time=20.74 memory used=2613.7MB, alloc=420.4MB, time=22.59 memory used=2734.1MB, alloc=420.4MB, time=24.17 memory used=2846.4MB, alloc=444.4MB, time=25.68 memory used=2986.5MB, alloc=444.4MB, time=26.97 memory used=3130.4MB, alloc=444.4MB, time=29.16 memory used=3271.6MB, alloc=444.4MB, time=30.44 memory used=3385.0MB, alloc=444.4MB, time=32.10 memory used=3537.3MB, alloc=468.4MB, time=34.18 memory used=3686.4MB, alloc=492.4MB, time=36.93 memory used=3883.9MB, alloc=516.4MB, time=39.70 memory used=4072.1MB, alloc=540.4MB, time=43.52 memory used=4260.5MB, alloc=564.4MB, time=48.60 memory used=4437.6MB, alloc=588.4MB, time=55.69 memory used=4614.5MB, alloc=612.4MB, time=63.01 memory used=4815.4MB, alloc=636.4MB, time=71.51 memory used=5040.5MB, alloc=660.4MB, time=81.19 memory used=5289.7MB, alloc=684.4MB, time=91.77 N1 := 6073 > GB := Basis(F, plex(op(vars))); 3 2 2 3 4 2 GB := [576 y x + 1152 y x + 576 y x - 250 x + 225 y, 4 3 2 2 2 -12 x - 12 x y + 5 x z, -12 x y - 12 x y + 5 y z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=5472.2MB, alloc=684.4MB, time=97.02 memory used=5582.9MB, alloc=684.4MB, time=98.99 memory used=5765.8MB, alloc=684.4MB, time=101.97 memory used=6101.6MB, alloc=708.4MB, time=112.85 N2 := 2375 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 3 2 H := [-12 x y - 12 x y + 5 y z, 4 y z - 10 x + 9 y, 2 y + 18 z x + 13 y , 3 2 10 x - 6 z - 5 z] > J:=[op(GB),op(G)]; 3 2 2 3 4 2 J := [576 y x + 1152 y x + 576 y x - 250 x + 225 y, 4 3 2 2 2 -12 x - 12 x y + 5 x z, -12 x y - 12 x y + 5 y z, 3 2 3 2 2 y + 18 z x + 13 y , 10 x - 6 z - 5 z] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 11, 12, 3, 3, 3, 2, 1, 3/4, 1, 5/12, 7/12, 5/12, 5, 13, 18, 11 10 5, 4, 3, 2, 1, 4/5, 4/5, --, --, 5/17, -2, -6, -2] 17 17 > save(F, G, cat("ranSet/33", convert(F, string),".txt")); > quit memory used=6101.8MB, alloc=708.4MB, 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(); 1428506725 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 3 3 2 F := [20 z - 20 x z - 3 z, 6 x - 7 y + 6 y z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 3 2 G := [-5 y z + 8 x - 12, 9 x z + 2 z - 9 z ] > Problem := [F,G]; 3 3 3 2 Problem := [[20 z - 20 x z - 3 z, 6 x - 7 y + 6 y z], 2 2 3 2 [-5 y z + 8 x - 12, 9 x z + 2 z - 9 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=26.2MB, alloc=32.3MB, time=0.53 memory used=45.4MB, alloc=56.3MB, time=0.82 memory used=87.9MB, alloc=60.3MB, time=1.41 memory used=127.7MB, alloc=60.3MB, time=2.01 memory used=168.1MB, alloc=60.3MB, time=2.51 memory used=210.8MB, alloc=68.3MB, time=3.01 memory used=251.1MB, alloc=68.3MB, time=3.34 memory used=283.7MB, alloc=68.3MB, time=3.56 memory used=310.6MB, alloc=68.3MB, time=3.71 memory used=347.9MB, alloc=68.3MB, time=4.20 memory used=386.7MB, alloc=68.3MB, time=4.42 memory used=409.0MB, alloc=68.3MB, time=4.50 memory used=426.2MB, alloc=68.3MB, time=4.57 memory used=459.7MB, alloc=68.3MB, time=4.71 memory used=482.0MB, alloc=68.3MB, time=4.81 memory used=510.5MB, alloc=68.3MB, time=4.91 memory used=541.6MB, alloc=68.3MB, time=7.10 memory used=574.4MB, alloc=68.3MB, time=7.51 memory used=592.8MB, alloc=68.3MB, time=7.60 memory used=616.7MB, alloc=68.3MB, time=7.68 memory used=636.0MB, alloc=68.3MB, time=7.76 memory used=652.1MB, alloc=92.3MB, time=7.85 memory used=687.3MB, alloc=92.3MB, time=7.97 memory used=729.4MB, alloc=92.3MB, time=8.07 memory used=770.2MB, alloc=92.3MB, time=8.22 memory used=819.9MB, alloc=92.3MB, time=8.47 memory used=874.8MB, alloc=92.3MB, time=10.89 memory used=922.7MB, alloc=92.3MB, time=11.30 memory used=964.6MB, alloc=92.3MB, time=11.42 memory used=996.3MB, alloc=92.3MB, time=11.51 memory used=1034.9MB, alloc=92.3MB, time=11.61 memory used=1076.7MB, alloc=92.3MB, time=11.70 memory used=1142.6MB, alloc=92.3MB, time=12.30 memory used=1209.8MB, alloc=92.3MB, time=13.25 memory used=1272.6MB, alloc=92.3MB, time=13.99 memory used=1336.8MB, alloc=92.3MB, time=14.68 memory used=1404.7MB, alloc=116.3MB, time=15.54 memory used=1465.6MB, alloc=116.3MB, time=15.99 memory used=1522.9MB, alloc=116.3MB, time=16.27 memory used=1570.5MB, alloc=116.3MB, time=16.44 memory used=1607.3MB, alloc=116.3MB, time=16.64 memory used=1647.8MB, alloc=116.3MB, time=16.77 memory used=1707.7MB, alloc=116.3MB, time=17.00 memory used=1750.6MB, alloc=116.3MB, time=17.14 memory used=1792.2MB, alloc=116.3MB, time=17.27 memory used=1830.9MB, alloc=116.3MB, time=17.39 memory used=1892.0MB, alloc=116.3MB, time=20.31 memory used=1953.0MB, alloc=116.3MB, time=21.67 memory used=1994.1MB, alloc=116.3MB, time=21.82 memory used=2036.5MB, alloc=116.3MB, time=21.96 memory used=2088.1MB, alloc=116.3MB, time=22.10 memory used=2130.8MB, alloc=116.3MB, time=22.22 memory used=2162.3MB, alloc=116.3MB, time=22.34 memory used=2196.8MB, alloc=116.3MB, time=22.45 memory used=2234.0MB, alloc=116.3MB, time=22.56 memory used=2273.8MB, alloc=116.3MB, time=22.67 memory used=2317.5MB, alloc=116.3MB, time=22.80 memory used=2363.7MB, alloc=116.3MB, time=22.92 memory used=2413.4MB, alloc=116.3MB, time=23.04 memory used=2467.4MB, alloc=116.3MB, time=23.17 memory used=2516.1MB, alloc=131.8MB, time=23.30 memory used=2525.5MB, alloc=131.8MB, time=23.38 memory used=2535.5MB, alloc=131.8MB, time=23.45 memory used=2545.3MB, alloc=131.8MB, time=23.56 memory used=2555.1MB, alloc=131.8MB, time=23.67 memory used=2565.1MB, alloc=131.8MB, time=23.77 memory used=2575.8MB, alloc=131.8MB, time=23.86 memory used=2586.7MB, alloc=131.8MB, time=23.94 memory used=2597.4MB, alloc=131.8MB, time=24.01 memory used=2608.2MB, alloc=131.8MB, time=24.09 memory used=2619.6MB, alloc=131.8MB, time=24.18 memory used=2631.1MB, alloc=131.8MB, time=24.26 memory used=2642.7MB, alloc=131.8MB, time=24.35 memory used=2654.7MB, alloc=131.8MB, time=24.43 memory used=2666.7MB, alloc=131.8MB, time=24.51 memory used=2678.9MB, alloc=131.8MB, time=24.59 memory used=2691.4MB, alloc=131.8MB, time=24.66 memory used=2704.4MB, alloc=131.8MB, time=24.73 memory used=2717.7MB, alloc=131.8MB, time=24.81 memory used=2731.3MB, alloc=131.8MB, time=24.90 memory used=2745.5MB, alloc=131.8MB, time=24.99 memory used=2760.2MB, alloc=131.8MB, time=25.08 memory used=2816.9MB, alloc=131.8MB, time=25.32 memory used=2864.5MB, alloc=131.8MB, time=25.50 memory used=2900.9MB, alloc=131.8MB, time=25.67 memory used=2945.7MB, alloc=131.8MB, time=25.79 memory used=3002.2MB, alloc=131.8MB, time=26.03 memory used=3051.6MB, alloc=131.8MB, time=26.18 memory used=3085.9MB, alloc=131.8MB, time=26.30 memory used=3128.4MB, alloc=131.8MB, time=26.44 memory used=3204.1MB, alloc=131.8MB, time=30.61 memory used=3249.7MB, alloc=131.8MB, time=30.77 memory used=3285.3MB, alloc=131.8MB, time=30.91 memory used=3328.9MB, alloc=131.8MB, time=31.06 memory used=3382.4MB, alloc=131.8MB, time=31.19 memory used=3417.4MB, alloc=131.8MB, time=31.31 memory used=3449.8MB, alloc=131.8MB, time=31.43 memory used=3484.6MB, alloc=131.8MB, time=31.54 memory used=3522.1MB, alloc=131.8MB, time=31.65 memory used=3562.0MB, alloc=131.8MB, time=31.76 memory used=3605.9MB, alloc=131.8MB, time=31.88 memory used=3651.9MB, alloc=131.8MB, time=31.99 memory used=3701.5MB, alloc=131.8MB, time=32.11 memory used=3755.7MB, alloc=131.8MB, time=32.23 memory used=3794.3MB, alloc=131.8MB, time=32.34 memory used=3803.6MB, alloc=131.8MB, time=32.42 memory used=3813.6MB, alloc=131.8MB, time=32.49 memory used=3823.4MB, alloc=131.8MB, time=32.58 memory used=3833.2MB, alloc=131.8MB, time=32.65 memory used=3843.2MB, alloc=131.8MB, time=32.73 memory used=3853.9MB, alloc=131.8MB, time=32.81 memory used=3864.8MB, alloc=131.8MB, time=32.89 memory used=3875.5MB, alloc=131.8MB, time=32.97 memory used=3886.3MB, alloc=131.8MB, time=33.05 memory used=3897.7MB, alloc=131.8MB, time=33.14 memory used=3909.2MB, alloc=131.8MB, time=33.22 memory used=3920.8MB, alloc=131.8MB, time=33.30 memory used=3932.0MB, alloc=131.8MB, time=33.38 memory used=3943.9MB, alloc=131.8MB, time=33.46 memory used=3956.5MB, alloc=131.8MB, time=33.54 memory used=3969.0MB, alloc=131.8MB, time=33.62 memory used=3982.1MB, alloc=131.8MB, time=33.71 memory used=3995.3MB, alloc=131.8MB, time=33.78 memory used=4008.9MB, alloc=131.8MB, time=33.87 memory used=4023.2MB, alloc=131.8MB, time=33.95 memory used=4037.8MB, alloc=131.8MB, time=34.04 memory used=4110.7MB, alloc=131.8MB, time=34.54 memory used=4152.2MB, alloc=131.8MB, time=34.67 memory used=4202.2MB, alloc=131.8MB, time=34.87 memory used=4243.7MB, alloc=131.8MB, time=35.02 memory used=4292.8MB, alloc=131.8MB, time=35.22 memory used=4365.0MB, alloc=131.8MB, time=35.79 memory used=4429.3MB, alloc=387.8MB, time=36.63 memory used=4521.5MB, alloc=387.8MB, time=37.74 memory used=4610.9MB, alloc=387.8MB, time=38.68 memory used=4681.8MB, alloc=387.8MB, time=39.12 memory used=4751.3MB, alloc=387.8MB, time=39.46 memory used=4833.7MB, alloc=387.8MB, time=40.09 memory used=4913.9MB, alloc=387.8MB, time=40.99 memory used=4993.4MB, alloc=411.8MB, time=42.28 memory used=5107.0MB, alloc=435.8MB, time=44.02 memory used=5233.2MB, alloc=459.8MB, time=45.99 memory used=5392.0MB, alloc=459.8MB, time=48.18 memory used=5526.4MB, alloc=483.8MB, time=50.75 memory used=5659.1MB, alloc=507.8MB, time=54.12 memory used=5788.3MB, alloc=531.8MB, time=58.25 memory used=5922.6MB, alloc=555.8MB, time=63.92 memory used=6079.2MB, alloc=579.8MB, time=70.49 memory used=6259.8MB, alloc=603.8MB, time=77.76 memory used=6464.3MB, alloc=603.8MB, time=85.81 memory used=6668.8MB, alloc=627.8MB, time=94.91 memory used=6897.4MB, alloc=627.8MB, time=104.28 memory used=7125.9MB, alloc=651.8MB, time=113.95 N1 := 7389 > GB := Basis(F, plex(op(vars))); 9 6 3 3 6 9 4 4 7 GB := [-1080 x + 3780 x y - 4410 x y + 1715 y + 1080 x y - 1260 x y 3 4 7 6 6 3 4 7 + 162 x y - 189 y , 2520 x y + 1080 x z - 4410 x y + 1715 y 4 2 5 3 2 5 2 3 3 + 1080 x y - 1260 x y + 162 x y - 189 y , 6 z y - 7 y + 6 x , 3 2 3 3 2 5 4 3 1470 x y + 1260 x y z + 1080 x z - 1715 y - 1080 x + 1260 x y 3 3 3 - 162 x + 189 y , 20 z - 20 x z - 3 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=7385.2MB, alloc=651.8MB, time=122.50 memory used=7679.4MB, alloc=651.8MB, time=148.16 memory used=7830.1MB, alloc=651.8MB, time=148.84 memory used=7973.1MB, alloc=651.8MB, time=149.45 memory used=8099.1MB, alloc=651.8MB, time=150.01 memory used=8246.4MB, alloc=651.8MB, time=150.59 memory used=8417.4MB, alloc=651.8MB, time=151.19 memory used=8722.1MB, alloc=651.8MB, time=152.22 memory used=8867.6MB, alloc=651.8MB, time=152.84 memory used=9026.5MB, alloc=651.8MB, time=153.61 memory used=9195.6MB, alloc=651.8MB, time=154.24 memory used=9375.0MB, alloc=651.8MB, time=154.86 memory used=9568.6MB, alloc=651.8MB, time=155.51 memory used=9776.4MB, alloc=651.8MB, time=156.16 memory used=9997.5MB, alloc=651.8MB, time=156.82 memory used=10236.2MB, alloc=651.8MB, time=157.49 memory used=10486.9MB, alloc=651.8MB, time=158.19 memory used=10676.5MB, alloc=651.8MB, time=158.80 memory used=10863.9MB, alloc=651.8MB, time=159.42 memory used=11058.0MB, alloc=651.8MB, time=160.04 memory used=11261.5MB, alloc=651.8MB, time=160.65 memory used=11476.6MB, alloc=651.8MB, time=161.27 memory used=11705.9MB, alloc=651.8MB, time=162.01 memory used=11953.1MB, alloc=651.8MB, time=162.68 memory used=12188.0MB, alloc=651.8MB, time=163.30 memory used=12524.3MB, alloc=651.8MB, time=167.31 memory used=12678.9MB, alloc=651.8MB, time=167.93 memory used=12821.5MB, alloc=651.8MB, time=168.49 memory used=12992.9MB, alloc=651.8MB, time=169.05 memory used=13112.6MB, alloc=651.8MB, time=169.51 memory used=13431.2MB, alloc=651.8MB, time=175.29 |\^/| 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(); 1428507025 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 3 F := [17 x z + 20 x y + 13 z, -2 x - 10 y + 2 z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 G := [-8 x z - 8 y + y, -7 x y z + 9 x z + 8 x z] > Problem := [F,G]; 2 2 3 Problem := [[17 x z + 20 x y + 13 z, -2 x - 10 y + 2 z], 2 3 2 [-8 x z - 8 y + y, -7 x y z + 9 x z + 8 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=26.3MB, alloc=32.3MB, time=0.51 memory used=47.3MB, alloc=32.3MB, time=0.85 memory used=66.1MB, alloc=56.3MB, time=1.19 memory used=105.1MB, alloc=60.3MB, time=1.83 memory used=143.5MB, alloc=84.3MB, time=2.52 memory used=206.0MB, alloc=92.3MB, time=3.60 memory used=265.5MB, alloc=116.3MB, time=4.74 memory used=348.5MB, alloc=116.3MB, time=6.06 memory used=430.4MB, alloc=116.3MB, time=7.41 memory used=503.5MB, alloc=140.3MB, time=8.55 memory used=579.9MB, alloc=396.3MB, time=9.72 memory used=684.7MB, alloc=420.3MB, time=11.54 memory used=808.7MB, alloc=444.3MB, time=13.72 memory used=936.2MB, alloc=468.3MB, time=16.05 memory used=1076.5MB, alloc=492.3MB, time=18.71 memory used=1237.6MB, alloc=516.3MB, time=21.55 memory used=1416.8MB, alloc=540.3MB, time=24.80 memory used=1598.9MB, alloc=564.3MB, time=28.29 memory used=1784.9MB, alloc=588.3MB, time=31.92 memory used=1972.3MB, alloc=612.3MB, time=37.27 memory used=2150.6MB, alloc=636.3MB, time=43.62 memory used=2339.1MB, alloc=660.3MB, time=50.93 memory used=2540.8MB, alloc=684.3MB, time=58.54 memory used=2757.0MB, alloc=708.3MB, time=67.03 memory used=2988.1MB, alloc=732.3MB, time=76.57 memory used=3233.6MB, alloc=756.3MB, time=87.94 memory used=3490.4MB, alloc=780.3MB, time=100.58 memory used=3771.1MB, alloc=804.3MB, time=112.80 memory used=4075.7MB, alloc=828.3MB, time=126.59 memory used=4404.3MB, alloc=852.3MB, time=140.92 memory used=4756.9MB, alloc=876.3MB, time=156.34 memory used=5133.4MB, alloc=900.3MB, time=172.70 memory used=5533.8MB, alloc=900.3MB, time=189.85 memory used=5934.1MB, alloc=924.3MB, time=207.15 memory used=6358.4MB, alloc=924.3MB, time=225.38 |\^/| 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(); 1428507325 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 3 2 3 F := [-12 x z - 8 y z + 12 z , -8 x y + 7 z + 2 x y] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 G := [-4 x y + 9 x - 12 y, 2 y z - 6 x ] > Problem := [F,G]; 2 2 3 2 3 Problem := [[-12 x z - 8 y z + 12 z , -8 x y + 7 z + 2 x y], 2 2 [-4 x y + 9 x - 12 y, 2 y z - 6 x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.4MB, alloc=32.3MB, time=0.52 memory used=44.8MB, alloc=56.3MB, time=0.80 memory used=86.5MB, alloc=60.3MB, time=1.42 memory used=126.3MB, alloc=60.3MB, time=2.00 memory used=166.6MB, alloc=60.3MB, time=2.53 memory used=210.4MB, alloc=68.3MB, time=3.16 memory used=252.5MB, alloc=92.3MB, time=3.64 memory used=320.8MB, alloc=92.3MB, time=4.52 memory used=389.7MB, alloc=92.3MB, time=5.57 memory used=462.9MB, alloc=92.3MB, time=6.35 memory used=523.4MB, alloc=116.3MB, time=7.44 memory used=604.6MB, alloc=140.3MB, time=8.90 memory used=714.8MB, alloc=140.3MB, time=10.69 memory used=818.3MB, alloc=164.3MB, time=12.40 memory used=925.5MB, alloc=188.3MB, time=14.73 memory used=1033.8MB, alloc=212.3MB, time=18.02 memory used=1148.3MB, alloc=236.3MB, time=22.48 memory used=1286.7MB, alloc=260.3MB, time=27.75 memory used=1449.0MB, alloc=260.3MB, time=33.83 memory used=1611.4MB, alloc=284.3MB, time=39.71 N1 := 5117 > GB := Basis(F, plex(op(vars))); 7 6 2 5 3 2 6 6 5 2 GB := [3024 x y - 3456 x y + 6048 x y + 784 x y - 1512 x y + 2592 x y 4 3 6 5 4 2 3 3 3 2 - 3024 x y - 196 x y + 189 x y - 648 x y + 378 x y + 54 x y , 6 5 2 5 4 3 3 4 2 5 -3456 x y - 4032 x y + 5220 x y z + 1176 x y - 1344 x y - 784 x y 5 4 2 4 3 3 2 4 5 + 2592 x y + 2016 x y - 3033 x y z - 294 x y + 672 x y + 196 x y 4 3 2 3 4 3 2 - 648 x y - 252 x y + 648 x y z - 84 x y + 54 x y - 54 x y z, 5 4 3 2 2 4 4 3 144 x y - 144 x y z + 84 x y z + 56 x y - 72 x y + 72 x y z 2 2 4 3 2 3 2 3 - 21 x y z - 14 x y + 9 x y - 9 x y z, -96 x y + 84 x y z 2 3 3 2 2 2 3 3 2 + 56 x y + 56 x y z + 48 x y - 21 x y z - 14 x y - 14 y z - 6 x y 4 3 2 3 4 3 2 3 , -36 x y + 36 x y z - 24 x y + 14 y z + 9 x y - 9 x y z + 6 x y , 2 2 2 -24 x y + 21 x z + 14 y z + 6 x y, 3 2 2 2 2 2 3 12 x y - 12 x y z + 7 y z - 3 x y + 3 x y z, -8 x y + 7 z + 2 x y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1818.6MB, alloc=284.3MB, time=44.90 memory used=2066.0MB, alloc=540.3MB, time=48.38 memory used=2198.6MB, alloc=540.3MB, time=49.43 memory used=2341.2MB, alloc=540.3MB, time=50.54 memory used=2531.3MB, alloc=540.3MB, time=52.11 memory used=2716.0MB, alloc=540.3MB, time=55.60 memory used=2835.6MB, alloc=540.3MB, time=58.60 memory used=2964.2MB, alloc=540.3MB, time=59.03 memory used=3159.2MB, alloc=540.3MB, time=63.92 memory used=3262.5MB, alloc=540.3MB, time=64.39 memory used=3456.4MB, alloc=540.3MB, time=67.47 memory used=3686.6MB, alloc=540.3MB, time=69.90 memory used=3905.8MB, alloc=540.3MB, time=72.59 memory used=4122.4MB, alloc=540.3MB, time=77.01 memory used=4340.3MB, alloc=540.3MB, time=83.82 memory used=4528.3MB, alloc=540.3MB, time=90.73 memory used=4771.1MB, alloc=540.3MB, time=98.20 memory used=5021.8MB, alloc=564.3MB, time=101.11 memory used=5290.7MB, alloc=588.3MB, time=104.19 memory used=5478.1MB, alloc=588.3MB, time=105.47 memory used=5639.2MB, alloc=588.3MB, time=106.23 memory used=5878.4MB, alloc=612.3MB, time=109.03 memory used=6144.6MB, alloc=636.3MB, time=112.98 memory used=6390.1MB, alloc=636.3MB, time=114.83 memory used=6533.9MB, alloc=636.3MB, time=115.87 memory used=6725.5MB, alloc=636.3MB, time=117.11 memory used=7074.2MB, alloc=660.3MB, time=121.26 memory used=7413.4MB, alloc=660.3MB, time=125.59 memory used=7737.9MB, alloc=660.3MB, time=133.09 memory used=8031.8MB, alloc=660.3MB, time=144.78 memory used=8189.5MB, alloc=660.3MB, time=145.46 memory used=8428.8MB, alloc=660.3MB, time=155.84 memory used=8720.2MB, alloc=684.3MB, time=160.69 memory used=8960.8MB, alloc=684.3MB, time=169.05 memory used=9206.2MB, alloc=684.3MB, time=177.90 memory used=9449.1MB, alloc=684.3MB, time=188.63 memory used=9695.4MB, alloc=684.3MB, time=203.09 memory used=9940.6MB, alloc=684.3MB, time=222.16 memory used=10184.4MB, alloc=684.3MB, time=245.95 memory used=10429.5MB, alloc=684.3MB, time=272.77 memory used=10676.8MB, alloc=684.3MB, time=290.58 memory used=10863.8MB, alloc=684.3MB, time=296.76 memory used=11053.8MB, alloc=684.3MB, time=297.84 memory used=11356.2MB, alloc=684.3MB, time=310.81 memory used=11647.8MB, alloc=684.3MB, time=315.26 memory used=11963.4MB, alloc=684.3MB, time=320.29 memory used=12277.3MB, alloc=684.3MB, time=326.52 memory used=12567.1MB, alloc=684.3MB, time=332.98 memory used=12844.8MB, alloc=684.3MB, time=340.52 memory used=13117.5MB, alloc=684.3MB, time=350.82 memory used=13392.6MB, alloc=684.3MB, time=363.86 memory used=13662.6MB, alloc=684.3MB, time=380.16 memory used=13932.1MB, alloc=684.3MB, time=398.17 |\^/| 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(); 1428507625 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 F := [-14 x - 2, 5 x y z + 8 y z - z ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 G := [17 z + 6 z - 2, -2 x + 6 z - 10] > Problem := [F,G]; Problem := 3 2 2 3 2 2 [[-14 x - 2, 5 x y z + 8 y z - z ], [17 z + 6 z - 2, -2 x + 6 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=4.1MB, alloc=32.3MB, time=0.17 memory used=26.1MB, alloc=32.3MB, time=0.51 memory used=46.7MB, alloc=32.3MB, time=0.85 memory used=69.4MB, alloc=56.3MB, time=1.28 memory used=116.9MB, alloc=56.3MB, time=2.02 memory used=155.7MB, alloc=84.3MB, time=2.74 N1 := 1279 > GB := Basis(F, plex(op(vars))); 3 2 2 GB := [7 x + 1, -5 x y z - 8 y z + z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=207.6MB, alloc=84.3MB, time=4.25 memory used=265.8MB, alloc=108.3MB, time=5.21 memory used=354.3MB, alloc=132.3MB, time=6.72 N2 := 1279 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 2 3 2 2 H := [-14 x - 2, 5 x y z + 8 y z - z , 17 z + 6 z - 2, -2 x + 6 z - 10] > J:=[op(GB),op(G)]; 3 2 2 3 2 2 J := [7 x + 1, -5 x y z - 8 y z + z , 17 z + 6 z - 2, -2 x + 6 z - 10] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 7, 11, 3, 3, 2, 3, 3/4, 1/4, 3/4, 3/11, 2/11, 6/11, 4, 7, 11, 3, 3, 2, 3, 3/4, 1/4, 3/4, 3/11, 2/11, 6/11, 0, 0, 0] > save(F, G, cat("ranSet/33", convert(F, string),".txt")); > quit memory used=402.5MB, alloc=132.3MB, time=8.16 |\^/| 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(); 1428507636 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 F := [-12 x z - 15 y z + 17 z, -3 x z + 7 y z + x ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 G := [x z + 13 z + 16 y, -2 x y ] > Problem := [F,G]; 2 2 2 2 Problem := [[-12 x z - 15 y z + 17 z, -3 x z + 7 y z + x ], 2 3 2 [x z + 13 z + 16 y, -2 x y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=26.6MB, alloc=32.3MB, time=0.52 memory used=45.9MB, alloc=56.3MB, time=0.82 memory used=87.1MB, alloc=60.3MB, time=1.44 memory used=130.0MB, alloc=68.3MB, time=2.02 memory used=174.3MB, alloc=68.3MB, time=2.43 memory used=219.4MB, alloc=92.3MB, time=2.99 memory used=290.7MB, alloc=92.3MB, time=3.90 memory used=329.6MB, alloc=92.3MB, time=4.09 memory used=363.2MB, alloc=92.3MB, time=4.20 memory used=390.2MB, alloc=92.3MB, time=4.29 memory used=467.3MB, alloc=92.3MB, time=4.96 memory used=531.5MB, alloc=92.3MB, time=5.69 memory used=603.9MB, alloc=116.3MB, time=6.46 memory used=704.4MB, alloc=116.3MB, time=7.57 memory used=801.8MB, alloc=116.3MB, time=8.37 memory used=895.2MB, alloc=116.3MB, time=9.18 memory used=975.0MB, alloc=140.3MB, time=10.52 memory used=1077.3MB, alloc=140.3MB, time=12.21 memory used=1173.3MB, alloc=164.3MB, time=13.89 memory used=1274.8MB, alloc=188.3MB, time=15.64 memory used=1374.7MB, alloc=444.3MB, time=17.31 memory used=1514.8MB, alloc=468.3MB, time=19.55 memory used=1659.1MB, alloc=492.3MB, time=22.53 memory used=1795.3MB, alloc=516.3MB, time=26.88 memory used=1942.6MB, alloc=540.3MB, time=32.07 memory used=2098.1MB, alloc=564.3MB, time=38.47 memory used=2276.6MB, alloc=588.3MB, time=45.59 memory used=2479.0MB, alloc=588.3MB, time=53.93 memory used=2681.4MB, alloc=612.3MB, time=62.05 memory used=2907.8MB, alloc=612.3MB, time=72.18 memory used=3134.1MB, alloc=636.3MB, time=81.31 memory used=3384.5MB, alloc=660.3MB, time=91.29 N1 := 7577 > GB := Basis(F, plex(op(vars))); 5 4 2 3 4 2 2 GB := [-12 x - 45 x y + 105 x y + 51 x - 119 x y , 3 2 2 2 2 2 2 12 x z + 15 x y - 17 x , -3 x z + 7 y z + x , 12 x z + 15 y z - 17 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=3685.8MB, alloc=660.3MB, time=98.10 memory used=3958.0MB, alloc=660.3MB, time=100.70 memory used=4321.9MB, alloc=660.3MB, time=104.36 memory used=4659.5MB, alloc=684.3MB, time=110.04 memory used=5010.3MB, alloc=708.3MB, time=116.91 memory used=5339.4MB, alloc=732.3MB, time=128.32 memory used=5640.0MB, alloc=756.3MB, time=142.58 memory used=5958.7MB, alloc=780.3MB, time=156.40 memory used=6301.3MB, alloc=804.3MB, time=171.39 memory used=6668.1MB, alloc=828.3MB, time=187.05 N2 := 7577 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 3 2 H := [-12 x z - 15 y z + 17 z, -3 x z + 7 y z + x , 13 z + z x + 16 y, 2 -2 y x] > J:=[op(GB),op(G)]; 5 4 2 3 4 2 2 J := [-12 x - 45 x y + 105 x y + 51 x - 119 x y , 3 2 2 2 2 2 2 12 x z + 15 x y - 17 x , -3 x z + 7 y z + x , 12 x z + 15 y z - 17 z, 3 2 2 13 z + z x + 16 y, -2 y x] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 11, 12, 3, 2, 2, 3, 1, 1, 3/4, 5/12, 1/3, 7/12, 6, 16, 21, 5, 13 5, 3, 3, 1, 1, 2/3, --, 2/5, 2/5, -5, -9, -2] 20 > save(F, G, cat("ranSet/33", convert(F, string),".txt")); > quit memory used=6939.5MB, alloc=828.3MB, time=198.03 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428507855 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 2 2 F := [10 x - 10 z + 7 y, -6 x y + 2 x - 4 z ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 G := [y z - 16 x y - 5 x z, 7 x y z + x z - 8 y z] > Problem := [F,G]; 3 2 2 2 2 Problem := [[10 x - 10 z + 7 y, -6 x y + 2 x - 4 z ], 2 2 2 [y z - 16 x y - 5 x z, 7 x y z + x z - 8 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=26.9MB, alloc=32.3MB, time=0.53 memory used=47.5MB, alloc=56.3MB, time=0.88 memory used=88.5MB, alloc=60.3MB, time=1.58 memory used=128.7MB, alloc=60.3MB, time=2.18 memory used=164.5MB, alloc=60.3MB, time=2.64 memory used=204.0MB, alloc=84.3MB, time=3.17 memory used=237.5MB, alloc=84.3MB, time=3.67 memory used=302.7MB, alloc=92.3MB, time=4.66 memory used=368.8MB, alloc=116.3MB, time=5.56 memory used=436.4MB, alloc=116.3MB, time=6.48 memory used=495.9MB, alloc=372.3MB, time=7.27 memory used=584.7MB, alloc=396.3MB, time=8.44 memory used=694.4MB, alloc=420.3MB, time=9.91 memory used=832.9MB, alloc=420.3MB, time=11.41 memory used=935.0MB, alloc=420.3MB, time=12.08 memory used=1047.9MB, alloc=420.3MB, time=13.53 memory used=1187.2MB, alloc=444.3MB, time=15.05 memory used=1342.1MB, alloc=444.3MB, time=16.57 memory used=1449.8MB, alloc=468.3MB, time=18.13 memory used=1553.8MB, alloc=468.3MB, time=19.74 memory used=1647.6MB, alloc=468.3MB, time=21.26 memory used=1742.1MB, alloc=492.3MB, time=22.60 memory used=1828.2MB, alloc=492.3MB, time=24.01 memory used=1908.0MB, alloc=492.3MB, time=25.45 memory used=1963.0MB, alloc=492.3MB, time=26.47 memory used=2026.9MB, alloc=492.3MB, time=27.63 memory used=2081.3MB, alloc=492.3MB, time=28.66 memory used=2141.7MB, alloc=492.3MB, time=29.70 memory used=2194.1MB, alloc=492.3MB, time=30.58 memory used=2234.4MB, alloc=492.3MB, time=31.34 memory used=2432.8MB, alloc=516.3MB, time=33.70 memory used=2605.8MB, alloc=540.3MB, time=35.91 memory used=2752.2MB, alloc=540.3MB, time=37.13 memory used=2987.8MB, alloc=564.3MB, time=39.98 memory used=3170.2MB, alloc=564.3MB, time=42.87 memory used=3342.5MB, alloc=588.3MB, time=45.78 memory used=3623.2MB, alloc=612.3MB, time=49.55 memory used=3921.2MB, alloc=636.3MB, time=52.63 memory used=4112.3MB, alloc=660.3MB, time=56.50 memory used=4395.6MB, alloc=684.3MB, time=60.77 memory used=4645.5MB, alloc=708.3MB, time=66.10 memory used=4887.6MB, alloc=732.3MB, time=71.01 memory used=5170.0MB, alloc=756.3MB, time=76.04 memory used=5430.6MB, alloc=780.3MB, time=81.05 memory used=5721.0MB, alloc=804.3MB, time=86.11 memory used=5964.1MB, alloc=828.3MB, time=91.83 memory used=6224.6MB, alloc=852.3MB, time=97.59 memory used=6429.4MB, alloc=876.3MB, time=102.26 memory used=6643.8MB, alloc=900.3MB, time=107.39 memory used=6849.5MB, alloc=924.3MB, time=112.42 memory used=7049.9MB, alloc=948.3MB, time=117.69 memory used=7220.7MB, alloc=972.3MB, time=122.39 memory used=7410.0MB, alloc=996.3MB, time=127.23 memory used=7585.3MB, alloc=1020.3MB, time=131.69 memory used=8065.5MB, alloc=1044.3MB, time=142.35 memory used=8571.7MB, alloc=1068.3MB, time=152.56 memory used=9093.9MB, alloc=1092.3MB, time=162.24 memory used=9505.5MB, alloc=1116.3MB, time=177.28 memory used=9892.7MB, alloc=1140.3MB, time=192.93 memory used=10280.1MB, alloc=1164.3MB, time=209.68 memory used=10674.8MB, alloc=1188.3MB, time=226.79 memory used=11079.0MB, alloc=1212.3MB, time=244.70 |\^/| 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(); 1428508155 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 3 3 F := [4 x + 9 z + 14, 3 x + 8 z - 2 y z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 G := [-13 x y - 7 y z - 9 x , -6 y z - 8 x z - 8 y] > Problem := [F,G]; 3 3 3 Problem := [[4 x + 9 z + 14, 3 x + 8 z - 2 y z], 2 2 2 2 [-13 x y - 7 y z - 9 x , -6 y z - 8 x 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=4.3MB, alloc=32.3MB, time=0.17 memory used=25.1MB, alloc=32.3MB, time=0.48 memory used=44.2MB, alloc=56.3MB, time=0.77 memory used=84.5MB, alloc=60.3MB, time=1.35 memory used=126.4MB, alloc=68.3MB, time=1.93 memory used=166.8MB, alloc=68.3MB, time=2.40 memory used=211.6MB, alloc=92.3MB, time=3.01 memory used=276.3MB, alloc=92.3MB, time=3.96 memory used=336.7MB, alloc=92.3MB, time=4.67 memory used=402.6MB, alloc=372.3MB, time=5.61 memory used=491.9MB, alloc=372.3MB, time=6.79 memory used=586.1MB, alloc=396.3MB, time=8.02 memory used=697.5MB, alloc=396.3MB, time=9.28 memory used=808.5MB, alloc=396.3MB, time=10.72 memory used=916.0MB, alloc=420.3MB, time=12.34 memory used=1049.9MB, alloc=420.3MB, time=14.12 memory used=1164.7MB, alloc=444.3MB, time=15.51 memory used=1290.1MB, alloc=444.3MB, time=16.62 memory used=1408.1MB, alloc=444.3MB, time=18.57 memory used=1486.7MB, alloc=444.3MB, time=18.94 memory used=1611.4MB, alloc=444.3MB, time=20.59 memory used=1763.7MB, alloc=444.3MB, time=21.87 memory used=1928.5MB, alloc=444.3MB, time=24.42 memory used=2062.3MB, alloc=444.3MB, time=26.23 memory used=2209.9MB, alloc=444.3MB, time=27.70 memory used=2345.5MB, alloc=468.3MB, time=29.39 memory used=2462.6MB, alloc=468.3MB, time=30.91 memory used=2574.7MB, alloc=468.3MB, time=32.43 memory used=2695.6MB, alloc=468.3MB, time=33.75 memory used=2791.6MB, alloc=468.3MB, time=35.17 memory used=2899.7MB, alloc=492.3MB, time=36.88 memory used=3024.9MB, alloc=492.3MB, time=37.94 memory used=3180.3MB, alloc=492.3MB, time=39.71 memory used=3269.6MB, alloc=492.3MB, time=40.11 memory used=3344.4MB, alloc=492.3MB, time=40.42 memory used=3423.1MB, alloc=492.3MB, time=40.73 memory used=3518.5MB, alloc=492.3MB, time=41.06 memory used=3794.6MB, alloc=492.3MB, time=43.15 memory used=3883.1MB, alloc=492.3MB, time=43.55 memory used=3963.2MB, alloc=492.3MB, time=43.88 memory used=4069.1MB, alloc=492.3MB, time=44.55 memory used=4146.6MB, alloc=492.3MB, time=44.89 memory used=4293.2MB, alloc=492.3MB, time=46.04 memory used=4375.8MB, alloc=492.3MB, time=47.33 memory used=4518.8MB, alloc=492.3MB, time=50.98 memory used=4638.7MB, alloc=492.3MB, time=51.81 memory used=4770.0MB, alloc=492.3MB, time=55.37 memory used=4852.8MB, alloc=492.3MB, time=55.77 memory used=4967.4MB, alloc=492.3MB, time=57.09 memory used=5126.8MB, alloc=492.3MB, time=59.85 memory used=5213.7MB, alloc=492.3MB, time=60.28 memory used=5294.6MB, alloc=492.3MB, time=60.69 memory used=5380.1MB, alloc=492.3MB, time=61.81 memory used=5460.8MB, alloc=492.3MB, time=63.06 memory used=5653.5MB, alloc=516.3MB, time=64.84 memory used=5807.9MB, alloc=516.3MB, time=66.71 memory used=5970.5MB, alloc=516.3MB, time=68.32 memory used=6351.4MB, alloc=516.3MB, time=69.34 memory used=6714.4MB, alloc=516.3MB, time=70.22 memory used=7072.6MB, alloc=516.3MB, time=71.08 memory used=7425.9MB, alloc=516.3MB, time=71.93 memory used=7770.7MB, alloc=516.3MB, time=72.75 memory used=8113.5MB, alloc=516.3MB, time=73.63 memory used=8472.8MB, alloc=516.3MB, time=76.78 memory used=8828.5MB, alloc=516.3MB, time=77.90 memory used=9191.2MB, alloc=516.3MB, time=78.77 memory used=9541.7MB, alloc=516.3MB, time=79.57 memory used=9884.3MB, alloc=516.3MB, time=80.36 memory used=10227.1MB, alloc=516.3MB, time=81.16 memory used=10568.8MB, alloc=516.3MB, time=82.00 memory used=10909.2MB, alloc=516.3MB, time=82.86 memory used=11252.2MB, alloc=516.3MB, time=83.72 memory used=11535.7MB, alloc=516.3MB, time=86.71 memory used=11666.6MB, alloc=516.3MB, time=88.30 memory used=12045.1MB, alloc=516.3MB, time=89.26 memory used=12404.1MB, alloc=516.3MB, time=90.14 memory used=12754.3MB, alloc=516.3MB, time=91.00 memory used=13095.1MB, alloc=516.3MB, time=91.81 memory used=13433.9MB, alloc=516.3MB, time=92.59 memory used=13781.5MB, alloc=516.3MB, time=93.42 memory used=14121.7MB, alloc=516.3MB, time=94.29 memory used=14465.1MB, alloc=516.3MB, time=95.13 memory used=14752.2MB, alloc=516.3MB, time=97.64 memory used=15165.9MB, alloc=516.3MB, time=98.64 memory used=15529.2MB, alloc=516.3MB, time=99.53 memory used=15882.2MB, alloc=516.3MB, time=100.38 memory used=16228.3MB, alloc=516.3MB, time=101.21 memory used=16575.1MB, alloc=516.3MB, time=102.13 memory used=16913.6MB, alloc=516.3MB, time=102.97 memory used=17144.3MB, alloc=516.3MB, time=105.77 memory used=17288.5MB, alloc=540.3MB, time=107.86 memory used=17422.1MB, alloc=540.3MB, time=109.88 memory used=17566.4MB, alloc=564.3MB, time=112.12 memory used=17686.5MB, alloc=564.3MB, time=114.08 memory used=17823.3MB, alloc=588.3MB, time=116.23 memory used=17941.9MB, alloc=588.3MB, time=118.29 memory used=18067.1MB, alloc=588.3MB, time=120.36 memory used=18194.9MB, alloc=612.3MB, time=122.44 memory used=18301.3MB, alloc=612.3MB, time=124.31 memory used=18423.8MB, alloc=612.3MB, time=126.30 memory used=18545.1MB, alloc=636.3MB, time=128.40 memory used=18644.7MB, alloc=636.3MB, time=130.19 memory used=18733.2MB, alloc=636.3MB, time=131.89 memory used=18919.5MB, alloc=660.3MB, time=142.22 |\^/| 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(); 1428508455 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 2 F := [-2 x z + 14 y z + 15 y z , 5 y z - 10 x y - 9 y ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 G := [-18 x - 14 y z - 9, -5 x + 5 x z + 5 x y z] > Problem := [F,G]; 2 2 2 2 2 Problem := [[-2 x z + 14 y z + 15 y z , 5 y z - 10 x y - 9 y ], 2 3 2 [-18 x - 14 y z - 9, -5 x + 5 x z + 5 x y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=26.2MB, alloc=32.3MB, time=0.53 memory used=47.1MB, alloc=32.3MB, time=0.86 memory used=66.0MB, alloc=56.3MB, time=1.19 memory used=105.9MB, alloc=60.3MB, time=1.86 memory used=144.9MB, alloc=84.3MB, time=2.49 memory used=205.9MB, alloc=92.3MB, time=3.51 memory used=265.7MB, alloc=116.3MB, time=4.51 memory used=348.4MB, alloc=140.3MB, time=5.92 memory used=419.6MB, alloc=396.3MB, time=7.18 memory used=523.2MB, alloc=420.3MB, time=9.21 memory used=634.8MB, alloc=444.3MB, time=11.49 memory used=761.9MB, alloc=468.3MB, time=14.10 memory used=905.0MB, alloc=492.3MB, time=17.03 memory used=1061.1MB, alloc=516.3MB, time=20.29 memory used=1226.7MB, alloc=540.3MB, time=24.33 memory used=1386.6MB, alloc=564.3MB, time=29.69 memory used=1554.5MB, alloc=588.3MB, time=35.64 memory used=1735.2MB, alloc=612.3MB, time=42.53 memory used=1923.0MB, alloc=636.3MB, time=50.89 memory used=2134.7MB, alloc=660.3MB, time=60.40 memory used=2370.4MB, alloc=684.3MB, time=70.69 memory used=2630.0MB, alloc=708.3MB, time=82.01 memory used=2913.5MB, alloc=708.3MB, time=94.40 memory used=3197.0MB, alloc=732.3MB, time=107.20 memory used=3504.6MB, alloc=732.3MB, time=121.14 memory used=3812.0MB, alloc=732.3MB, time=135.24 memory used=4119.3MB, alloc=756.3MB, time=149.48 memory used=4450.5MB, alloc=756.3MB, time=163.81 memory used=4781.5MB, alloc=780.3MB, time=177.61 N1 := 11173 > GB := Basis(F, plex(op(vars))); 3 2 2 3 4 2 2 3 GB := [-20 x y - 18 x y + 140 x y + 126 y + 300 x y + 540 x y + 243 y , 5 4 4 3 2 3 3 20 x z - 280 x y - 600 x z - 252 x y + 4200 x y + 4500 x z 3 2 2 4 3 3 - 3402 x y - 7290 x y - 6561 x y , -20 x z + 280 x y + 300 x z 2 2 2 3 2 + 252 x y + 3780 x y + 4050 x y z + 3402 y + 7290 x y + 6561 y , 2 2 4 2 4 3 2 3 5 y z - 10 x y - 9 y , 45 x z - 781 x z - 675 x z + 9800 x y 3 3 2 2 + 10500 x z - 7938 x y - 17010 x y - 15309 x y , 2 2 2 -10 x z + 75 y z + 140 x y + 126 y ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=5151.9MB, alloc=780.3MB, time=190.60 memory used=5274.0MB, alloc=780.3MB, time=193.06 memory used=5382.9MB, alloc=780.3MB, time=195.18 memory used=5475.8MB, alloc=780.3MB, time=197.14 memory used=5576.7MB, alloc=780.3MB, time=199.26 memory used=5661.2MB, alloc=780.3MB, time=201.08 memory used=5732.9MB, alloc=780.3MB, time=202.66 memory used=5812.3MB, alloc=780.3MB, time=204.15 memory used=5895.2MB, alloc=780.3MB, time=206.07 memory used=5967.7MB, alloc=780.3MB, time=207.88 memory used=6028.4MB, alloc=780.3MB, time=209.37 memory used=6089.6MB, alloc=780.3MB, time=210.73 memory used=6161.6MB, alloc=780.3MB, time=212.35 memory used=6216.3MB, alloc=780.3MB, time=213.75 memory used=6460.9MB, alloc=804.3MB, time=218.77 memory used=6671.0MB, alloc=828.3MB, time=222.66 memory used=6874.8MB, alloc=852.3MB, time=226.45 |\^/| 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(); 1428508755 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 F := [-20 x y - 9 x y + 9 y , y z - 3 x - 5] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 G := [7 x z - 18 z, -7 x - 9 x - 6] > Problem := [F,G]; 2 2 2 2 Problem := [[-20 x y - 9 x y + 9 y , y z - 3 x - 5], 2 2 [7 x z - 18 z, -7 x - 9 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=4.1MB, alloc=32.3MB, time=0.18 memory used=26.8MB, alloc=32.3MB, time=0.55 memory used=48.4MB, alloc=56.3MB, time=0.95 N1 := 403 > GB := Basis(F, plex(op(vars))); 3 3 2 GB := [60 x y + 27 x - 27 x y + 100 x y + 45 x - 45 y, 2 2 6 5 4 4 3 20 x y + 9 x y - 9 y , -3600 x + 3240 x + 243 x z - 12729 x + 10800 x 2 2 5 4 3 + 405 x z - 12430 x + 9000 x - 2025, 3600 x - 3240 x - 243 x z 3 2 + 12729 x - 8100 x - 405 x z + 405 y z + 11215 x - 4500] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=87.4MB, alloc=60.3MB, time=1.61 memory used=129.6MB, alloc=60.3MB, time=2.35 N2 := 635 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 2 2 H := [-20 x y - 9 x y + 9 y , y z - 3 x - 5, 7 x z - 18 z, -7 x - 9 x - 6] > J:=[op(GB),op(G)]; 3 3 2 2 2 J := [60 x y + 27 x - 27 x y + 100 x y + 45 x - 45 y, 20 x y + 9 x y - 9 y , 6 5 4 4 3 2 2 -3600 x + 3240 x + 243 x z - 12729 x + 10800 x + 405 x z - 12430 x 5 3 4 3 + 9000 x - 2025, 3600 x - 243 z x - 3240 x + 12729 x + 405 z y 2 2 2 - 405 z x - 8100 x + 11215 x - 4500, 7 x z - 18 z, -7 x - 9 x - 6] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 8, 11, 3, 2, 2, 2, 1, 1/2, 1/2, 6/11, 4/11, 3/11, 6, 12, 23, 25 6, 6, 2, 2, 1, 1/2, 1/2, --, 1/4, 7/32, -4, -12, -3] 32 > save(F, G, cat("ranSet/33", convert(F, string),".txt")); > quit memory used=158.3MB, alloc=60.3MB, time=3.00 |\^/| 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(); 1428508759 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 F := [-5 x y z - 4 y - 13 x, 5 x z + 4 y z - 4 x z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 2 G := [16 x z - 15 y z + 8 y , -7 x z - 2 y z + 4 x z] > Problem := [F,G]; 2 2 2 Problem := [[-5 x y z - 4 y - 13 x, 5 x z + 4 y z - 4 x z], 2 2 2 2 2 [16 x z - 15 y z + 8 y , -7 x z - 2 y z + 4 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=26.0MB, alloc=32.3MB, time=0.52 memory used=46.5MB, alloc=32.3MB, time=0.83 memory used=65.6MB, alloc=56.3MB, time=1.14 memory used=106.2MB, alloc=68.3MB, time=1.76 memory used=146.5MB, alloc=92.3MB, time=2.32 memory used=209.0MB, alloc=92.3MB, time=3.23 memory used=273.5MB, alloc=116.3MB, time=4.13 memory used=343.2MB, alloc=116.3MB, time=5.10 memory used=409.6MB, alloc=396.3MB, time=6.11 memory used=520.6MB, alloc=420.3MB, time=7.72 memory used=653.0MB, alloc=444.3MB, time=9.56 memory used=778.9MB, alloc=444.3MB, time=11.18 memory used=898.6MB, alloc=468.3MB, time=12.80 memory used=1005.2MB, alloc=468.3MB, time=14.29 memory used=1112.7MB, alloc=492.3MB, time=15.85 memory used=1266.4MB, alloc=516.3MB, time=18.07 memory used=1381.4MB, alloc=516.3MB, time=20.15 memory used=1538.4MB, alloc=540.3MB, time=22.91 memory used=1693.1MB, alloc=564.3MB, time=25.61 memory used=1863.1MB, alloc=588.3MB, time=28.48 memory used=2010.4MB, alloc=612.3MB, time=31.11 memory used=2146.5MB, alloc=636.3MB, time=33.80 memory used=2276.3MB, alloc=636.3MB, time=36.81 memory used=2402.0MB, alloc=660.3MB, time=39.39 memory used=2511.3MB, alloc=660.3MB, time=42.00 memory used=2636.9MB, alloc=684.3MB, time=44.80 memory used=2752.3MB, alloc=708.3MB, time=47.34 memory used=2853.4MB, alloc=708.3MB, time=49.64 memory used=2963.5MB, alloc=732.3MB, time=52.24 memory used=3055.5MB, alloc=732.3MB, time=54.51 memory used=3157.0MB, alloc=756.3MB, time=56.68 memory used=3245.7MB, alloc=756.3MB, time=58.73 memory used=3343.0MB, alloc=756.3MB, time=60.91 memory used=3444.5MB, alloc=780.3MB, time=63.14 memory used=3549.2MB, alloc=780.3MB, time=65.50 memory used=3630.9MB, alloc=804.3MB, time=67.51 memory used=3728.0MB, alloc=804.3MB, time=69.80 memory used=3804.1MB, alloc=828.3MB, time=71.67 memory used=3945.8MB, alloc=852.3MB, time=76.44 memory used=4289.8MB, alloc=876.3MB, time=89.15 memory used=4631.3MB, alloc=900.3MB, time=102.59 memory used=4978.3MB, alloc=924.3MB, time=116.57 memory used=5334.7MB, alloc=948.3MB, time=131.44 memory used=5702.6MB, alloc=972.3MB, time=147.45 memory used=6083.3MB, alloc=996.3MB, time=164.00 memory used=6476.5MB, alloc=1020.3MB, time=181.48 memory used=6883.7MB, alloc=1044.3MB, time=200.48 memory used=7299.5MB, alloc=1068.3MB, time=219.42 memory used=7739.4MB, alloc=1092.3MB, time=239.40 memory used=8203.1MB, alloc=1116.3MB, time=261.31 |\^/| 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(); 1428509059 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 F := [20 x z - z + 17, 3 x y z - x + 10 x] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 G := [4 x z - 19 x y - y , 2 x y + 10 x - 4 z] > Problem := [F,G]; 2 2 2 Problem := [[20 x z - z + 17, 3 x y z - x + 10 x], 2 2 2 2 [4 x z - 19 x y - y , 2 x y + 10 x - 4 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.21 memory used=26.1MB, alloc=32.3MB, time=0.56 memory used=46.2MB, alloc=32.3MB, time=0.86 memory used=65.9MB, alloc=60.3MB, time=1.16 memory used=108.9MB, alloc=68.3MB, time=1.81 memory used=150.4MB, alloc=68.3MB, time=2.41 memory used=195.5MB, alloc=92.3MB, time=3.00 memory used=265.9MB, alloc=92.3MB, time=3.97 memory used=329.9MB, alloc=92.3MB, time=4.80 memory used=397.7MB, alloc=372.3MB, time=5.68 memory used=493.4MB, alloc=372.3MB, time=6.98 memory used=581.8MB, alloc=396.3MB, time=8.28 memory used=700.9MB, alloc=420.3MB, time=9.88 memory used=851.0MB, alloc=420.3MB, time=11.80 memory used=985.1MB, alloc=420.3MB, time=12.96 memory used=1125.2MB, alloc=444.3MB, time=15.21 memory used=1289.9MB, alloc=468.3MB, time=17.52 memory used=1482.1MB, alloc=468.3MB, time=19.86 memory used=1672.2MB, alloc=492.3MB, time=22.28 memory used=1890.9MB, alloc=492.3MB, time=25.02 memory used=2097.9MB, alloc=516.3MB, time=27.90 memory used=2304.1MB, alloc=540.3MB, time=31.58 memory used=2506.6MB, alloc=564.3MB, time=35.40 memory used=2731.9MB, alloc=588.3MB, time=39.50 memory used=2970.7MB, alloc=612.3MB, time=43.98 memory used=3198.4MB, alloc=636.3MB, time=48.06 memory used=3424.5MB, alloc=660.3MB, time=51.87 memory used=3728.6MB, alloc=684.3MB, time=56.16 memory used=3927.8MB, alloc=708.3MB, time=59.66 memory used=4091.6MB, alloc=732.3MB, time=63.21 memory used=4382.6MB, alloc=756.3MB, time=73.24 memory used=4665.8MB, alloc=780.3MB, time=83.72 memory used=4955.8MB, alloc=804.3MB, time=95.08 memory used=5257.4MB, alloc=828.3MB, time=107.19 memory used=5571.0MB, alloc=852.3MB, time=119.92 memory used=5893.6MB, alloc=876.3MB, time=133.55 memory used=6228.4MB, alloc=900.3MB, time=148.34 memory used=6581.9MB, alloc=924.3MB, time=164.18 memory used=6959.4MB, alloc=948.3MB, time=181.00 memory used=7360.7MB, alloc=972.3MB, time=198.88 memory used=7786.1MB, alloc=996.3MB, time=217.82 memory used=8235.4MB, alloc=1020.3MB, time=237.93 |\^/| 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(); 1428509359 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 3 2 2 F := [15 x y + 17 y z - 18 z, 9 x - x z - 5 x ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 G := [x y + 2 y z - 7 y z, -8 x y z + x z + y z] > Problem := [F,G]; 2 2 3 2 2 Problem := [[15 x y + 17 y z - 18 z, 9 x - x z - 5 x ], 2 2 2 [x y + 2 y z - 7 y z, -8 x y z + x z + y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.1MB, alloc=32.3MB, time=0.49 memory used=46.1MB, alloc=32.3MB, time=0.78 memory used=63.5MB, alloc=56.3MB, time=1.06 memory used=101.8MB, alloc=60.3MB, time=1.66 memory used=139.1MB, alloc=84.3MB, time=2.24 memory used=198.1MB, alloc=92.3MB, time=3.20 memory used=255.8MB, alloc=116.3MB, time=4.14 memory used=337.0MB, alloc=140.3MB, time=5.62 memory used=432.0MB, alloc=164.3MB, time=7.32 memory used=541.3MB, alloc=188.3MB, time=9.32 memory used=655.8MB, alloc=468.3MB, time=11.39 memory used=795.3MB, alloc=492.3MB, time=13.89 memory used=948.6MB, alloc=516.3MB, time=16.62 memory used=1110.3MB, alloc=540.3MB, time=19.64 memory used=1282.0MB, alloc=564.3MB, time=22.87 memory used=1462.4MB, alloc=588.3MB, time=26.28 memory used=1650.4MB, alloc=612.3MB, time=30.00 memory used=1828.5MB, alloc=636.3MB, time=35.80 memory used=2011.7MB, alloc=660.3MB, time=42.32 memory used=2206.3MB, alloc=684.3MB, time=49.66 memory used=2414.9MB, alloc=708.3MB, time=57.66 memory used=2638.3MB, alloc=732.3MB, time=66.43 memory used=2877.0MB, alloc=756.3MB, time=76.09 memory used=3130.9MB, alloc=780.3MB, time=86.28 memory used=3400.3MB, alloc=804.3MB, time=97.43 memory used=3685.6MB, alloc=828.3MB, time=109.36 memory used=3982.2MB, alloc=852.3MB, time=122.57 memory used=4302.8MB, alloc=876.3MB, time=136.80 memory used=4647.3MB, alloc=900.3MB, time=151.95 memory used=5015.8MB, alloc=924.3MB, time=168.08 memory used=5408.2MB, alloc=948.3MB, time=185.17 memory used=5824.6MB, alloc=972.3MB, time=203.47 memory used=6265.0MB, alloc=972.3MB, time=222.57 memory used=6705.2MB, alloc=996.3MB, time=241.69 memory used=7169.4MB, alloc=996.3MB, time=261.79 |\^/| 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(); 1428509659 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 3 F := [-6 x y + x z + 19 z , 2 x - 9 x y - 6 y] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 G := [-x z - 16 y z - 3 x, 5 x y z + 9 x z + 7 y z] > Problem := [F,G]; 2 2 3 Problem := [[-6 x y + x z + 19 z , 2 x - 9 x y - 6 y], 2 2 [-x z - 16 y z - 3 x, 5 x y z + 9 x z + 7 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=31.6MB, alloc=40.3MB, time=0.60 memory used=59.3MB, alloc=44.3MB, time=1.02 memory used=85.6MB, alloc=68.3MB, time=1.41 memory used=134.4MB, alloc=76.3MB, time=2.22 memory used=183.6MB, alloc=100.3MB, time=3.08 memory used=253.4MB, alloc=100.3MB, time=4.27 memory used=316.2MB, alloc=124.3MB, time=5.46 memory used=389.5MB, alloc=148.3MB, time=7.81 memory used=477.6MB, alloc=172.3MB, time=11.20 N1 := 2279 > GB := Basis(F, plex(op(vars))); 3 GB := [-2 x + 9 x y + 6 y, 5 4 3 2 2 -72 x + 48 x - 32 x + 243 x z + 972 y + 4617 z + 96 y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=585.5MB, alloc=172.3MB, time=13.28 memory used=655.0MB, alloc=428.3MB, time=14.37 memory used=762.2MB, alloc=428.3MB, time=15.36 memory used=825.4MB, alloc=428.3MB, time=15.59 memory used=893.9MB, alloc=428.3MB, time=15.95 memory used=1006.3MB, alloc=428.3MB, time=16.93 memory used=1120.2MB, alloc=428.3MB, time=17.63 memory used=1215.4MB, alloc=428.3MB, time=18.01 memory used=1337.4MB, alloc=428.3MB, time=18.78 memory used=1451.2MB, alloc=428.3MB, time=19.42 memory used=1583.2MB, alloc=452.3MB, time=20.52 memory used=1725.7MB, alloc=452.3MB, time=21.32 memory used=1886.9MB, alloc=452.3MB, time=22.77 memory used=2061.3MB, alloc=452.3MB, time=25.29 memory used=2226.4MB, alloc=476.3MB, time=27.87 memory used=2426.6MB, alloc=500.3MB, time=30.47 memory used=2592.8MB, alloc=524.3MB, time=35.68 memory used=2754.4MB, alloc=548.3MB, time=42.84 memory used=2939.9MB, alloc=572.3MB, time=50.43 N2 := 4415 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 3 2 2 H := [-6 x y + x z + 19 z , 2 x - 9 y x - 6 y, -x z - 16 y z - 3 x, 5 x y z + 9 x z + 7 y z] > J:=[op(GB),op(G)]; 3 J := [-2 x + 9 x y + 6 y, 5 4 3 2 2 -72 x + 48 x - 32 x + 243 x z + 972 y + 4617 z + 96 y, 2 2 -x z - 16 y z - 3 x, 5 x y z + 9 x z + 7 y z] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 11, 12, 3, 3, 2, 2, 1, 1, 3/4, 2/3, 1/2, 7/12, 4, 11, 14, 5, 5, 2, 2, 1, 1, 3/4, 5/8, 7/16, 7/16, 0, -2, -2] > save(F, G, cat("ranSet/33", convert(F, string),".txt")); > quit memory used=3108.0MB, alloc=572.3MB, time=57.30 |\^/| 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(); 1428509729 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 3 2 2 F := [-20 x y + 8 y - 11 z, -5 x - 6 x y + 6 y z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 G := [-17 x + 20 x y + 11 z, 7 + x - 3 y] > Problem := [F,G]; 2 3 3 2 2 Problem := [[-20 x y + 8 y - 11 z, -5 x - 6 x y + 6 y z], 3 2 [-17 x + 20 x y + 11 z, 7 + 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=4.2MB, alloc=32.3MB, time=0.17 memory used=27.0MB, alloc=32.3MB, time=0.58 memory used=46.5MB, alloc=56.3MB, time=0.98 memory used=88.8MB, alloc=60.3MB, time=1.69 memory used=127.2MB, alloc=84.3MB, time=2.41 memory used=180.5MB, alloc=108.3MB, time=3.36 memory used=256.9MB, alloc=140.3MB, time=4.97 memory used=342.9MB, alloc=164.3MB, time=7.88 N1 := 2269 > GB := Basis(F, plex(op(vars))); 2 3 5 3 2 3 2 GB := [-120 x y + 48 y - 55 x - 66 x y, -8 y + 20 y x + 11 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=450.8MB, alloc=164.3MB, time=11.14 N2 := 513 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 3 3 2 2 3 2 H := [-20 x y + 8 y - 11 z, -5 x - 6 x y + 6 y z, -17 x + 20 x y + 11 z, -3 y + x + 7] > J:=[op(GB),op(G)]; 2 3 5 3 2 3 2 J := [-120 x y + 48 y - 55 x - 66 x y, -8 y + 20 y x + 11 z, 3 2 -17 x + 20 x y + 11 z, -3 y + x + 7] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 11, 10, 3, 3, 3, 1, 1, 1, 3/4, 1/2, 1/2, 1/4, 4, 10, 12, 5, 3, 5, 1, 1, 1, 1/2, 7/13, 7/13, 2/13, 1, -2, -2] > save(F, G, cat("ranSet/33", convert(F, string),".txt")); > quit memory used=502.7MB, alloc=164.3MB, time=12.12 |\^/| 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(); 1428509745 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 F := [-11 x z - 9 y z - 12 z, 10 x z + 7 y z + 3 x z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 G := [17 y z + 11 x z - 15 x, -8 x y z - y - 6 y z ] > Problem := [F,G]; 2 2 2 Problem := [[-11 x z - 9 y z - 12 z, 10 x z + 7 y z + 3 x z], 2 3 2 [17 y z + 11 x z - 15 x, -8 x y z - y - 6 y z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.6MB, alloc=32.3MB, time=0.50 memory used=47.6MB, alloc=32.3MB, time=0.80 memory used=65.8MB, alloc=56.3MB, time=1.09 memory used=106.7MB, alloc=60.3MB, time=1.68 memory used=146.7MB, alloc=84.3MB, time=2.25 memory used=208.0MB, alloc=92.3MB, time=3.18 memory used=271.0MB, alloc=116.3MB, time=4.08 memory used=354.2MB, alloc=116.3MB, time=5.22 memory used=427.8MB, alloc=372.3MB, time=6.09 memory used=514.8MB, alloc=396.3MB, time=7.24 memory used=631.3MB, alloc=396.3MB, time=8.70 memory used=744.2MB, alloc=420.3MB, time=10.24 memory used=885.7MB, alloc=444.3MB, time=12.18 memory used=1046.2MB, alloc=444.3MB, time=14.34 memory used=1196.1MB, alloc=468.3MB, time=16.51 memory used=1353.1MB, alloc=492.3MB, time=19.17 memory used=1524.9MB, alloc=516.3MB, time=22.14 memory used=1714.0MB, alloc=540.3MB, time=25.48 memory used=1903.4MB, alloc=564.3MB, time=29.03 memory used=2108.1MB, alloc=588.3MB, time=32.79 memory used=2296.9MB, alloc=612.3MB, time=38.76 memory used=2487.1MB, alloc=636.3MB, time=45.88 memory used=2688.1MB, alloc=660.3MB, time=53.58 memory used=2902.5MB, alloc=684.3MB, time=62.44 memory used=3127.0MB, alloc=708.3MB, time=71.69 memory used=3370.3MB, alloc=732.3MB, time=82.06 memory used=3637.5MB, alloc=756.3MB, time=93.54 memory used=3928.7MB, alloc=780.3MB, time=106.14 memory used=4243.8MB, alloc=804.3MB, time=119.96 memory used=4582.9MB, alloc=804.3MB, time=135.12 memory used=4921.8MB, alloc=828.3MB, time=149.82 memory used=5284.8MB, alloc=828.3MB, time=165.07 memory used=5647.7MB, alloc=828.3MB, time=180.17 memory used=6010.5MB, alloc=852.3MB, time=195.34 memory used=6397.2MB, alloc=852.3MB, time=211.38 memory used=6783.7MB, alloc=876.3MB, time=227.72 |\^/| 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(); 1428510045 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 F := [5 x y + 20 y z - y z , 8 y z - 8 y z + 7 y] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 3 G := [-13 y z - 11 x + 12 y z, -2 x y - 7 x z - 7 y ] > Problem := [F,G]; 2 2 2 2 Problem := [[5 x y + 20 y z - y z , 8 y z - 8 y z + 7 y], 2 2 2 2 3 [-13 y z - 11 x + 12 y z, -2 x y - 7 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=4.2MB, alloc=32.3MB, time=0.17 memory used=26.6MB, alloc=32.3MB, time=0.51 memory used=46.5MB, alloc=60.3MB, time=0.81 memory used=84.4MB, alloc=60.3MB, time=1.28 memory used=129.6MB, alloc=68.3MB, time=1.93 memory used=171.0MB, alloc=68.3MB, time=2.53 memory used=215.3MB, alloc=92.3MB, time=3.12 memory used=283.0MB, alloc=92.3MB, time=3.96 memory used=356.4MB, alloc=92.3MB, time=4.85 memory used=426.8MB, alloc=116.3MB, time=5.62 memory used=495.6MB, alloc=116.3MB, time=6.65 memory used=574.7MB, alloc=372.3MB, time=7.81 memory used=662.8MB, alloc=396.3MB, time=9.17 memory used=772.9MB, alloc=396.3MB, time=10.82 memory used=891.8MB, alloc=420.3MB, time=12.39 memory used=1028.0MB, alloc=420.3MB, time=14.55 memory used=1136.8MB, alloc=420.3MB, time=16.20 memory used=1239.4MB, alloc=420.3MB, time=17.01 memory used=1381.7MB, alloc=444.3MB, time=18.16 memory used=1556.1MB, alloc=444.3MB, time=19.98 memory used=1712.7MB, alloc=444.3MB, time=21.08 memory used=1839.3MB, alloc=468.3MB, time=22.90 memory used=1978.0MB, alloc=468.3MB, time=24.74 memory used=2101.3MB, alloc=468.3MB, time=26.37 memory used=2217.5MB, alloc=492.3MB, time=28.30 memory used=2370.3MB, alloc=492.3MB, time=30.40 memory used=2467.2MB, alloc=516.3MB, time=31.66 memory used=2582.7MB, alloc=516.3MB, time=33.25 memory used=2677.1MB, alloc=516.3MB, time=34.82 memory used=2882.6MB, alloc=540.3MB, time=36.95 memory used=3065.8MB, alloc=564.3MB, time=40.10 memory used=3215.6MB, alloc=588.3MB, time=42.91 memory used=3419.7MB, alloc=612.3MB, time=50.13 memory used=3625.9MB, alloc=636.3MB, time=57.90 N1 := 3703 > GB := Basis(F, plex(op(vars))); 4 2 2 2 3 2 GB := [1600 x y + 6400 x y + 240 x y + 22400 y - 1120 y + 49 y, 2 2 2 2 2 40 x y z - 40 x y - 140 y + 7 y z, 40 x y + 160 y z - 8 y z + 7 y, 2 8 y z - 8 y z + 7 y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=3761.7MB, alloc=636.3MB, time=61.12 memory used=3867.1MB, alloc=636.3MB, time=63.01 memory used=3972.6MB, alloc=636.3MB, time=64.57 memory used=4077.9MB, alloc=636.3MB, time=65.89 memory used=4186.6MB, alloc=636.3MB, time=67.12 memory used=4263.6MB, alloc=636.3MB, time=68.48 memory used=4345.1MB, alloc=636.3MB, time=70.08 memory used=4411.3MB, alloc=636.3MB, time=71.26 memory used=4504.7MB, alloc=636.3MB, time=72.72 memory used=4578.8MB, alloc=636.3MB, time=73.87 memory used=4666.9MB, alloc=636.3MB, time=75.63 memory used=4743.7MB, alloc=636.3MB, time=77.06 memory used=4813.9MB, alloc=636.3MB, time=78.47 memory used=4871.5MB, alloc=636.3MB, time=79.87 memory used=4944.0MB, alloc=636.3MB, time=81.08 memory used=5005.1MB, alloc=636.3MB, time=82.11 memory used=5074.6MB, alloc=636.3MB, time=83.51 memory used=5133.8MB, alloc=636.3MB, time=84.99 memory used=5179.4MB, alloc=636.3MB, time=86.16 memory used=5410.1MB, alloc=636.3MB, time=89.38 memory used=5636.0MB, alloc=660.3MB, time=93.27 memory used=5839.0MB, alloc=660.3MB, time=96.72 memory used=6042.3MB, alloc=684.3MB, time=100.67 memory used=6341.5MB, alloc=684.3MB, time=105.18 memory used=6558.6MB, alloc=708.3MB, time=108.42 memory used=6820.7MB, alloc=708.3MB, time=111.64 memory used=6997.9MB, alloc=708.3MB, time=115.15 memory used=7177.7MB, alloc=708.3MB, time=118.49 memory used=7384.6MB, alloc=732.3MB, time=121.57 memory used=7575.5MB, alloc=732.3MB, time=124.93 memory used=7735.7MB, alloc=732.3MB, time=127.75 memory used=7875.1MB, alloc=756.3MB, time=130.87 memory used=8014.8MB, alloc=756.3MB, time=133.66 memory used=8199.7MB, alloc=756.3MB, time=137.33 memory used=8386.1MB, alloc=780.3MB, time=141.79 memory used=8715.5MB, alloc=804.3MB, time=147.78 memory used=8895.2MB, alloc=828.3MB, time=151.93 memory used=9175.9MB, alloc=852.3MB, time=161.43 memory used=9508.2MB, alloc=876.3MB, time=176.40 memory used=9844.7MB, alloc=900.3MB, time=192.66 memory used=10205.1MB, alloc=924.3MB, time=209.15 memory used=10589.5MB, alloc=948.3MB, time=226.54 memory used=10998.1MB, alloc=972.3MB, time=244.90 N2 := 8365 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 2 2 H := [5 x y + 20 y z - y z , 8 y z - 8 y z + 7 y, -13 y z - 11 x + 12 y z, 2 2 3 -2 x y - 7 x z - 7 y ] > J:=[op(GB),op(G)]; 4 2 2 2 3 2 J := [1600 x y + 6400 x y + 240 x y + 22400 y - 1120 y + 49 y, 2 2 2 2 2 40 x y z - 40 x y - 140 y + 7 y z, 40 x y + 160 y z - 8 y z + 7 y, 2 2 2 2 2 3 8 y z - 8 y z + 7 y, -13 y z - 11 x + 12 y z, -2 x y - 7 x z - 7 y ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 11, 12, 3, 2, 3, 2, 3/4, 1, 1, 1/3, 5/6, 7/12, 6, 16, 21, 5, 21 4, 3, 2, 5/6, 1, 5/6, 9/23, --, 9/23, -5, -9, -2] 23 > save(F, G, cat("ranSet/33", convert(F, string),".txt")); > quit memory used=11210.5MB, alloc=972.3MB, time=254.23 |\^/| 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(); 1428510325 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 3 3 F := [8 y + 20 y z - 12 y, -y - 3 z - 5] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 G := [18 x y + 2 x y z + 19 y, 10 x y z - 7 x] > Problem := [F,G]; 3 2 3 3 Problem := [[8 y + 20 y z - 12 y, -y - 3 z - 5], 2 [18 x y + 2 x y z + 19 y, 10 x y z - 7 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.1MB, alloc=32.3MB, time=0.18 memory used=26.7MB, alloc=32.3MB, time=0.51 memory used=47.1MB, alloc=32.3MB, time=0.82 memory used=65.9MB, alloc=56.3MB, time=1.12 memory used=108.8MB, alloc=60.3MB, time=1.70 memory used=150.5MB, alloc=60.3MB, time=2.11 memory used=194.4MB, alloc=68.3MB, time=2.77 memory used=238.8MB, alloc=92.3MB, time=3.38 memory used=298.0MB, alloc=92.3MB, time=3.91 memory used=361.7MB, alloc=92.3MB, time=4.81 memory used=416.0MB, alloc=92.3MB, time=5.27 memory used=454.8MB, alloc=92.3MB, time=5.50 memory used=503.1MB, alloc=92.3MB, time=5.91 memory used=567.2MB, alloc=92.3MB, time=6.58 memory used=633.8MB, alloc=116.3MB, time=7.56 memory used=718.7MB, alloc=116.3MB, time=8.99 memory used=793.0MB, alloc=140.3MB, time=10.32 memory used=888.1MB, alloc=164.3MB, time=11.99 memory used=989.9MB, alloc=188.3MB, time=13.88 memory used=1092.5MB, alloc=468.3MB, time=15.73 memory used=1229.9MB, alloc=492.3MB, time=19.55 memory used=1370.2MB, alloc=516.3MB, time=24.71 memory used=1518.4MB, alloc=540.3MB, time=31.09 memory used=1688.1MB, alloc=564.3MB, time=37.95 memory used=1881.8MB, alloc=564.3MB, time=45.56 memory used=2075.5MB, alloc=564.3MB, time=53.70 memory used=2269.2MB, alloc=588.3MB, time=61.67 memory used=2487.0MB, alloc=612.3MB, time=70.52 N1 := 6637 > GB := Basis(F, plex(op(vars))); 7 5 4 3 GB := [101 y + 108 y + 625 y - 162 y + 81 y, 6 4 3 2 3 3 101 y + 108 y + 625 y - 108 y + 135 y z, 3 z + y + 5] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=2738.9MB, alloc=612.3MB, time=75.48 memory used=2966.3MB, alloc=612.3MB, time=78.57 memory used=3169.8MB, alloc=612.3MB, time=80.94 memory used=3367.1MB, alloc=612.3MB, time=82.46 memory used=3566.6MB, alloc=612.3MB, time=85.79 memory used=3916.4MB, alloc=627.8MB, time=87.06 memory used=4244.1MB, alloc=627.8MB, time=87.74 memory used=4441.3MB, alloc=627.8MB, time=88.24 memory used=4665.7MB, alloc=627.8MB, time=88.73 memory used=4917.5MB, alloc=627.8MB, time=90.18 memory used=5205.0MB, alloc=627.8MB, time=104.55 memory used=5451.0MB, alloc=627.8MB, time=108.23 memory used=5606.1MB, alloc=627.8MB, time=109.18 memory used=5808.2MB, alloc=627.8MB, time=111.95 memory used=6093.1MB, alloc=627.8MB, time=115.33 memory used=6286.4MB, alloc=627.8MB, time=120.67 memory used=6443.1MB, alloc=627.8MB, time=121.53 memory used=6668.0MB, alloc=627.8MB, time=122.49 memory used=6967.4MB, alloc=627.8MB, time=127.11 memory used=7143.9MB, alloc=627.8MB, time=170.38 memory used=7268.6MB, alloc=627.8MB, time=170.89 memory used=7394.4MB, alloc=627.8MB, time=171.38 memory used=7656.0MB, alloc=627.8MB, time=172.07 memory used=7800.0MB, alloc=627.8MB, time=172.64 memory used=7967.2MB, alloc=627.8MB, time=173.16 memory used=8158.4MB, alloc=627.8MB, time=173.70 memory used=8368.3MB, alloc=627.8MB, time=174.27 memory used=8532.5MB, alloc=627.8MB, time=174.80 memory used=8719.5MB, alloc=627.8MB, time=175.34 memory used=9006.1MB, alloc=627.8MB, time=177.76 memory used=9231.2MB, alloc=627.8MB, time=178.81 memory used=9522.6MB, alloc=627.8MB, time=179.49 memory used=9802.3MB, alloc=627.8MB, time=181.25 memory used=10025.5MB, alloc=627.8MB, time=181.83 memory used=10285.7MB, alloc=627.8MB, time=182.39 memory used=10461.9MB, alloc=627.8MB, time=182.84 memory used=10655.6MB, alloc=627.8MB, time=183.29 memory used=10870.0MB, alloc=627.8MB, time=183.86 memory used=11147.8MB, alloc=627.8MB, time=184.44 memory used=11319.1MB, alloc=627.8MB, time=184.88 memory used=11510.1MB, alloc=627.8MB, time=185.32 memory used=11712.3MB, alloc=627.8MB, time=188.84 memory used=11953.4MB, alloc=627.8MB, time=189.41 memory used=12219.6MB, alloc=627.8MB, time=190.00 memory used=12436.7MB, alloc=627.8MB, time=190.52 memory used=12628.8MB, alloc=627.8MB, time=190.98 memory used=12831.2MB, alloc=627.8MB, time=191.47 memory used=13041.4MB, alloc=627.8MB, time=191.98 memory used=13235.5MB, alloc=627.8MB, time=192.47 memory used=13430.0MB, alloc=627.8MB, time=192.90 memory used=13634.0MB, alloc=627.8MB, time=193.33 memory used=13844.1MB, alloc=627.8MB, time=193.83 memory used=14056.5MB, alloc=627.8MB, time=194.28 memory used=14244.0MB, alloc=627.8MB, time=194.75 memory used=14447.1MB, alloc=627.8MB, time=195.22 memory used=14655.1MB, alloc=627.8MB, time=195.66 memory used=14867.8MB, alloc=627.8MB, time=196.08 memory used=15082.7MB, alloc=627.8MB, time=196.49 memory used=15286.8MB, alloc=627.8MB, time=197.08 memory used=15540.3MB, alloc=627.8MB, time=197.72 memory used=15811.2MB, alloc=627.8MB, time=198.33 memory used=15999.2MB, alloc=627.8MB, time=198.80 memory used=16195.9MB, alloc=627.8MB, time=199.27 memory used=16400.2MB, alloc=627.8MB, time=199.83 memory used=16612.2MB, alloc=627.8MB, time=200.36 memory used=16796.5MB, alloc=627.8MB, time=200.83 memory used=16996.0MB, alloc=627.8MB, time=201.27 memory used=17201.5MB, alloc=627.8MB, time=201.73 memory used=17412.8MB, alloc=627.8MB, time=202.24 memory used=17616.8MB, alloc=627.8MB, time=202.73 memory used=17808.9MB, alloc=627.8MB, time=203.23 memory used=18013.0MB, alloc=627.8MB, time=203.69 memory used=18222.2MB, alloc=627.8MB, time=204.15 memory used=18436.0MB, alloc=627.8MB, time=204.58 memory used=18642.6MB, alloc=627.8MB, time=205.01 memory used=18847.4MB, alloc=627.8MB, time=209.96 memory used=19095.3MB, alloc=627.8MB, time=212.23 memory used=19242.1MB, alloc=627.8MB, time=213.36 memory used=19413.9MB, alloc=627.8MB, time=214.21 memory used=19672.6MB, alloc=627.8MB, time=216.85 memory used=19963.5MB, alloc=627.8MB, time=219.39 memory used=20257.6MB, alloc=627.8MB, time=222.07 memory used=20543.1MB, alloc=651.8MB, time=226.80 memory used=20832.1MB, alloc=675.8MB, time=231.90 memory used=21122.5MB, alloc=699.8MB, time=237.43 memory used=21419.1MB, alloc=723.8MB, time=243.69 memory used=21717.2MB, alloc=747.8MB, time=251.54 |\^/| 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(); 1428510625 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; F := [-3 x z + 9 y z + 3, 6 x y z + 3 x y] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 3 2 2 G := [-18 x + 20 z + 4 x, 10 x z - 7 y - 7] > Problem := [F,G]; Problem := [[-3 x z + 9 y z + 3, 6 x y z + 3 x y], 3 3 2 2 [-18 x + 20 z + 4 x, 10 x z - 7 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=4.2MB, alloc=32.3MB, time=0.18 memory used=26.5MB, alloc=32.3MB, time=0.50 memory used=47.7MB, alloc=32.3MB, time=0.81 memory used=66.1MB, alloc=56.3MB, time=1.11 memory used=104.5MB, alloc=60.3MB, time=1.69 memory used=142.4MB, alloc=84.3MB, time=2.28 memory used=203.4MB, alloc=92.3MB, time=3.19 memory used=261.7MB, alloc=92.3MB, time=4.08 memory used=319.5MB, alloc=116.3MB, time=4.97 memory used=396.5MB, alloc=372.3MB, time=5.96 memory used=489.5MB, alloc=372.3MB, time=7.37 memory used=569.0MB, alloc=396.3MB, time=8.88 memory used=666.7MB, alloc=420.3MB, time=10.61 memory used=780.4MB, alloc=444.3MB, time=12.66 memory used=902.3MB, alloc=468.3MB, time=15.87 memory used=1023.1MB, alloc=492.3MB, time=20.51 memory used=1162.3MB, alloc=516.3MB, time=26.15 memory used=1325.5MB, alloc=516.3MB, time=32.67 memory used=1488.9MB, alloc=540.3MB, time=38.81 N1 := 4543 > GB := Basis(F, plex(op(vars))); 2 2 2 GB := [-x y + 3 x y - 2 x y, 2 x z + 3 x y - 2 x, -x z + 3 y z + 1] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1669.6MB, alloc=540.3MB, time=41.95 memory used=1827.2MB, alloc=540.3MB, time=44.69 memory used=1978.4MB, alloc=540.3MB, time=47.17 memory used=2121.3MB, alloc=540.3MB, time=49.09 memory used=2260.0MB, alloc=564.3MB, time=51.27 memory used=2384.7MB, alloc=564.3MB, time=53.03 memory used=2569.3MB, alloc=588.3MB, time=56.23 memory used=2765.4MB, alloc=612.3MB, time=59.94 memory used=2956.3MB, alloc=636.3MB, time=63.74 memory used=3164.0MB, alloc=660.3MB, time=67.65 memory used=3411.0MB, alloc=684.3MB, time=75.34 memory used=3674.8MB, alloc=708.3MB, time=85.71 memory used=3940.1MB, alloc=732.3MB, time=97.63 memory used=4229.3MB, alloc=756.3MB, time=110.86 memory used=4542.6MB, alloc=780.3MB, time=124.69 memory used=4879.7MB, alloc=804.3MB, time=139.15 memory used=5240.9MB, alloc=828.3MB, time=154.86 memory used=5626.2MB, alloc=852.3MB, time=171.16 N2 := 8947 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 3 H := [-3 x z + 9 y z + 3, 6 x y z + 3 x y, -18 x + 20 z + 4 x, 2 2 10 z x - 7 y - 7] > J:=[op(GB),op(G)]; 2 2 2 J := [-x y + 3 x y - 2 x y, 2 x z + 3 x y - 2 x, -x z + 3 y z + 1, 3 3 2 2 -18 x + 20 z + 4 x, 10 z x - 7 y - 7] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 11, 11, 3, 3, 2, 3, 1, 3/4, 1, 6/11, 4/11, 5/11, 5, 13, 14, 3, 3, 2, 3, 1, 4/5, 4/5, 2/3, 2/5, 1/3, -2, -3, 0] > save(F, G, cat("ranSet/33", convert(F, string),".txt")); > quit memory used=5748.1MB, alloc=852.3MB, time=175.66 |\^/| 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(); 1428510861 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 3 F := [-14 x z - 15 x z - 14 y z, -4 x + 2 x y z + 7] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 3 2 G := [-16 y - 13 z - 18 y z, 7 z ] > Problem := [F,G]; 2 2 2 3 Problem := [[-14 x z - 15 x z - 14 y z, -4 x + 2 x y z + 7], 3 3 2 [-16 y - 13 z - 18 y 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=0.19 memory used=26.0MB, alloc=32.3MB, time=0.52 memory used=47.4MB, alloc=60.3MB, time=0.83 memory used=79.7MB, alloc=60.3MB, time=1.25 memory used=124.2MB, alloc=68.3MB, time=1.77 memory used=162.2MB, alloc=68.3MB, time=2.10 memory used=188.6MB, alloc=68.3MB, time=2.24 memory used=214.1MB, alloc=68.3MB, time=2.39 memory used=259.3MB, alloc=68.3MB, time=2.89 memory used=317.8MB, alloc=68.3MB, time=3.38 memory used=361.6MB, alloc=68.3MB, time=3.87 memory used=393.8MB, alloc=68.3MB, time=4.44 memory used=418.1MB, alloc=68.3MB, time=4.59 memory used=440.2MB, alloc=68.3MB, time=4.70 memory used=477.7MB, alloc=68.3MB, time=5.30 memory used=503.3MB, alloc=68.3MB, time=5.69 memory used=550.2MB, alloc=68.3MB, time=6.16 memory used=573.4MB, alloc=68.3MB, time=6.31 memory used=604.0MB, alloc=68.3MB, time=6.67 memory used=623.6MB, alloc=68.3MB, time=6.79 memory used=641.8MB, alloc=68.3MB, time=6.87 memory used=663.7MB, alloc=68.3MB, time=6.96 memory used=688.6MB, alloc=92.3MB, time=7.07 memory used=716.4MB, alloc=92.3MB, time=7.15 memory used=747.3MB, alloc=92.3MB, time=7.26 memory used=782.8MB, alloc=92.3MB, time=7.34 memory used=822.6MB, alloc=92.3MB, time=7.44 memory used=867.3MB, alloc=92.3MB, time=7.53 memory used=910.0MB, alloc=107.8MB, time=7.63 memory used=920.2MB, alloc=107.8MB, time=7.70 memory used=931.0MB, alloc=107.8MB, time=7.77 memory used=941.7MB, alloc=107.8MB, time=7.83 memory used=952.8MB, alloc=107.8MB, time=7.89 memory used=964.3MB, alloc=107.8MB, time=7.94 memory used=976.5MB, alloc=107.8MB, time=8.00 memory used=988.8MB, alloc=107.8MB, time=8.05 memory used=1001.4MB, alloc=107.8MB, time=8.12 memory used=1014.8MB, alloc=107.8MB, time=8.18 memory used=1028.5MB, alloc=107.8MB, time=8.24 memory used=1042.6MB, alloc=107.8MB, time=8.30 memory used=1057.5MB, alloc=107.8MB, time=8.37 memory used=1117.9MB, alloc=107.8MB, time=9.11 memory used=1155.8MB, alloc=107.8MB, time=9.25 memory used=1197.1MB, alloc=107.8MB, time=9.78 memory used=1246.5MB, alloc=107.8MB, time=9.90 memory used=1283.4MB, alloc=107.8MB, time=9.99 memory used=1299.8MB, alloc=107.8MB, time=10.09 memory used=1341.5MB, alloc=107.8MB, time=10.20 memory used=1374.8MB, alloc=107.8MB, time=11.46 memory used=1390.3MB, alloc=107.8MB, time=11.53 memory used=1406.8MB, alloc=107.8MB, time=11.59 memory used=1426.3MB, alloc=107.8MB, time=11.66 memory used=1454.7MB, alloc=107.8MB, time=11.74 memory used=1485.2MB, alloc=107.8MB, time=11.82 memory used=1517.8MB, alloc=107.8MB, time=11.89 memory used=1552.4MB, alloc=107.8MB, time=11.97 memory used=1589.1MB, alloc=107.8MB, time=12.06 memory used=1607.2MB, alloc=107.8MB, time=12.12 memory used=1618.0MB, alloc=107.8MB, time=12.18 memory used=1629.1MB, alloc=107.8MB, time=12.23 memory used=1640.3MB, alloc=107.8MB, time=12.28 memory used=1656.1MB, alloc=107.8MB, time=12.39 memory used=1671.9MB, alloc=107.8MB, time=12.46 memory used=1688.5MB, alloc=107.8MB, time=12.52 memory used=1713.2MB, alloc=107.8MB, time=12.60 memory used=1742.2MB, alloc=107.8MB, time=12.68 memory used=1773.1MB, alloc=107.8MB, time=12.76 memory used=1805.9MB, alloc=107.8MB, time=12.84 memory used=1840.8MB, alloc=107.8MB, time=12.92 memory used=1873.5MB, alloc=107.8MB, time=13.00 memory used=1884.0MB, alloc=107.8MB, time=13.05 memory used=1894.7MB, alloc=107.8MB, time=13.11 memory used=1905.6MB, alloc=107.8MB, time=13.17 memory used=1919.1MB, alloc=107.8MB, time=13.58 memory used=2027.8MB, alloc=107.8MB, time=15.41 memory used=2101.0MB, alloc=107.8MB, time=15.97 memory used=2161.2MB, alloc=107.8MB, time=16.65 memory used=2249.8MB, alloc=107.8MB, time=17.36 memory used=2343.4MB, alloc=107.8MB, time=18.39 memory used=2407.8MB, alloc=107.8MB, time=19.27 memory used=2475.5MB, alloc=131.8MB, time=20.29 memory used=2551.8MB, alloc=155.8MB, time=21.72 N1 := 1471 > GB := Basis(F, plex(op(vars))); 6 5 3 3 3 2 3 GB := [240 x + 112 x y + 112 x y - 840 x - 196 x y - 196 y + 735, 5 4 3 2 2 2 3 56 x + 60 x z + 56 x y - 98 x - 105 x z - 98 y , -4 x + 2 x y z + 7, 4 3 3 2 2 2 56 x + 60 x z + 28 y z - 98 x - 105 z, 14 x z + 15 x z + 14 y z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=2637.8MB, alloc=155.8MB, time=24.31 memory used=2713.5MB, alloc=411.8MB, time=25.42 memory used=2821.1MB, alloc=411.8MB, time=26.77 memory used=2885.2MB, alloc=411.8MB, time=27.30 memory used=2945.3MB, alloc=435.8MB, time=27.73 memory used=3006.4MB, alloc=435.8MB, time=28.00 memory used=3079.0MB, alloc=435.8MB, time=28.36 memory used=3156.2MB, alloc=435.8MB, time=28.86 memory used=3222.7MB, alloc=435.8MB, time=29.11 memory used=3291.8MB, alloc=435.8MB, time=29.45 memory used=3362.7MB, alloc=435.8MB, time=30.00 memory used=3456.4MB, alloc=435.8MB, time=34.60 memory used=3516.7MB, alloc=435.8MB, time=34.81 memory used=3577.9MB, alloc=435.8MB, time=35.00 memory used=3660.1MB, alloc=435.8MB, time=35.53 memory used=3733.6MB, alloc=435.8MB, time=35.81 memory used=3810.1MB, alloc=435.8MB, time=36.24 memory used=3885.0MB, alloc=435.8MB, time=36.91 memory used=3962.4MB, alloc=435.8MB, time=37.33 memory used=4046.9MB, alloc=435.8MB, time=37.83 memory used=4173.5MB, alloc=435.8MB, time=39.11 memory used=4234.7MB, alloc=435.8MB, time=39.35 memory used=4375.6MB, alloc=435.8MB, time=40.57 memory used=4520.6MB, alloc=435.8MB, time=41.59 memory used=4667.3MB, alloc=435.8MB, time=43.07 memory used=4808.7MB, alloc=435.8MB, time=44.88 memory used=4957.2MB, alloc=435.8MB, time=46.94 memory used=5067.4MB, alloc=435.8MB, time=48.05 memory used=5195.5MB, alloc=459.8MB, time=49.72 memory used=5301.4MB, alloc=459.8MB, time=50.47 memory used=5464.6MB, alloc=459.8MB, time=52.14 memory used=5559.1MB, alloc=459.8MB, time=53.14 memory used=5632.7MB, alloc=459.8MB, time=53.51 memory used=5688.7MB, alloc=459.8MB, time=53.81 memory used=5764.2MB, alloc=459.8MB, time=54.13 memory used=5815.5MB, alloc=459.8MB, time=54.38 memory used=5895.3MB, alloc=459.8MB, time=54.99 memory used=5959.6MB, alloc=459.8MB, time=55.28 memory used=6023.5MB, alloc=459.8MB, time=55.60 memory used=6089.1MB, alloc=459.8MB, time=55.86 memory used=6160.5MB, alloc=459.8MB, time=57.43 memory used=6250.1MB, alloc=459.8MB, time=65.76 memory used=6320.7MB, alloc=459.8MB, time=66.06 memory used=6373.8MB, alloc=459.8MB, time=66.32 memory used=6436.0MB, alloc=459.8MB, time=66.60 memory used=6544.5MB, alloc=459.8MB, time=67.31 memory used=6675.2MB, alloc=483.8MB, time=69.04 memory used=6817.7MB, alloc=483.8MB, time=70.87 memory used=6912.1MB, alloc=483.8MB, time=71.42 memory used=6985.3MB, alloc=483.8MB, time=71.74 memory used=7083.0MB, alloc=483.8MB, time=72.37 memory used=7157.3MB, alloc=483.8MB, time=72.69 memory used=7525.1MB, alloc=483.8MB, time=98.98 memory used=7648.5MB, alloc=483.8MB, time=101.08 memory used=7757.5MB, alloc=483.8MB, time=117.35 memory used=7832.3MB, alloc=483.8MB, time=117.63 memory used=7957.2MB, alloc=483.8MB, time=118.77 memory used=8047.2MB, alloc=483.8MB, time=119.24 memory used=8110.6MB, alloc=483.8MB, time=119.50 memory used=8239.1MB, alloc=483.8MB, time=119.98 memory used=8318.5MB, alloc=483.8MB, time=120.32 memory used=8382.2MB, alloc=483.8MB, time=120.62 memory used=8512.4MB, alloc=483.8MB, time=121.12 memory used=8591.8MB, alloc=483.8MB, time=121.46 memory used=8657.1MB, alloc=483.8MB, time=121.74 memory used=8781.8MB, alloc=483.8MB, time=122.19 memory used=8872.8MB, alloc=507.8MB, time=132.51 memory used=8949.5MB, alloc=531.8MB, time=132.96 memory used=9068.0MB, alloc=531.8MB, time=133.47 memory used=9156.4MB, alloc=555.8MB, time=133.90 memory used=9242.0MB, alloc=555.8MB, time=134.31 memory used=9336.7MB, alloc=555.8MB, time=134.71 memory used=9439.3MB, alloc=555.8MB, time=135.13 memory used=9549.4MB, alloc=555.8MB, time=135.56 memory used=9667.8MB, alloc=555.8MB, time=136.06 memory used=9803.9MB, alloc=555.8MB, time=136.53 memory used=9949.0MB, alloc=555.8MB, time=137.02 memory used=10055.3MB, alloc=579.8MB, time=137.45 memory used=10132.7MB, alloc=603.8MB, time=137.80 memory used=10226.1MB, alloc=603.8MB, time=138.18 memory used=10322.7MB, alloc=603.8MB, time=138.55 memory used=10421.9MB, alloc=603.8MB, time=138.91 memory used=10523.7MB, alloc=603.8MB, time=139.28 memory used=10628.3MB, alloc=603.8MB, time=139.66 memory used=10736.5MB, alloc=603.8MB, time=140.04 memory used=10860.9MB, alloc=603.8MB, time=140.43 memory used=10989.6MB, alloc=603.8MB, time=140.84 memory used=11121.4MB, alloc=603.8MB, time=141.24 memory used=11256.3MB, alloc=603.8MB, time=141.64 memory used=11394.4MB, alloc=603.8MB, time=142.13 memory used=11535.4MB, alloc=603.8MB, time=142.58 memory used=11679.5MB, alloc=603.8MB, time=143.03 memory used=11826.4MB, alloc=603.8MB, time=143.53 memory used=11976.2MB, alloc=603.8MB, time=144.02 memory used=12128.8MB, alloc=603.8MB, time=144.51 memory used=12284.2MB, alloc=603.8MB, time=144.96 memory used=12442.2MB, alloc=603.8MB, time=145.43 memory used=12602.9MB, alloc=603.8MB, time=145.90 memory used=12766.3MB, alloc=603.8MB, time=146.39 memory used=12933.7MB, alloc=603.8MB, time=146.87 memory used=13121.8MB, alloc=603.8MB, time=147.38 memory used=13309.5MB, alloc=603.8MB, time=147.95 memory used=13403.6MB, alloc=603.8MB, time=148.35 memory used=13510.5MB, alloc=603.8MB, time=148.78 memory used=13620.0MB, alloc=603.8MB, time=149.28 memory used=13730.4MB, alloc=603.8MB, time=149.70 memory used=13841.7MB, alloc=603.8MB, time=150.19 memory used=13953.7MB, alloc=603.8MB, time=150.65 memory used=14066.7MB, alloc=603.8MB, time=151.08 memory used=14180.4MB, alloc=603.8MB, time=151.51 memory used=14295.0MB, alloc=603.8MB, time=151.96 memory used=14410.3MB, alloc=603.8MB, time=152.42 memory used=14526.4MB, alloc=603.8MB, time=152.87 memory used=14643.3MB, alloc=603.8MB, time=153.31 memory used=14761.0MB, alloc=603.8MB, time=153.76 memory used=14879.4MB, alloc=603.8MB, time=154.20 memory used=14998.5MB, alloc=603.8MB, time=154.64 memory used=15118.3MB, alloc=603.8MB, time=155.07 memory used=15238.8MB, alloc=603.8MB, time=155.50 memory used=15360.1MB, alloc=603.8MB, time=155.94 memory used=15482.0MB, alloc=603.8MB, time=156.46 memory used=15604.5MB, alloc=603.8MB, time=156.96 memory used=15727.7MB, alloc=603.8MB, time=157.42 memory used=15853.5MB, alloc=603.8MB, time=157.87 memory used=16001.0MB, alloc=603.8MB, time=158.33 memory used=16129.1MB, alloc=603.8MB, time=158.77 memory used=16277.2MB, alloc=603.8MB, time=159.24 memory used=16429.1MB, alloc=603.8MB, time=159.73 memory used=16581.7MB, alloc=603.8MB, time=160.20 memory used=16735.2MB, alloc=603.8MB, time=160.74 memory used=16889.4MB, alloc=603.8MB, time=161.27 memory used=17044.3MB, alloc=603.8MB, time=161.74 memory used=17199.9MB, alloc=603.8MB, time=162.17 memory used=17356.3MB, alloc=603.8MB, time=162.62 memory used=17513.3MB, alloc=603.8MB, time=163.08 memory used=17670.9MB, alloc=603.8MB, time=163.59 memory used=17829.2MB, alloc=603.8MB, time=164.05 memory used=17988.1MB, alloc=603.8MB, time=164.51 memory used=18147.6MB, alloc=603.8MB, time=164.96 memory used=18307.6MB, alloc=603.8MB, time=165.40 memory used=18468.1MB, alloc=603.8MB, time=165.85 memory used=18629.2MB, alloc=603.8MB, time=166.28 memory used=18790.7MB, alloc=603.8MB, time=166.74 memory used=18955.1MB, alloc=603.8MB, time=167.21 memory used=19142.4MB, alloc=603.8MB, time=167.69 memory used=19332.6MB, alloc=603.8MB, time=168.19 memory used=19523.2MB, alloc=603.8MB, time=168.78 memory used=19714.4MB, alloc=603.8MB, time=169.30 memory used=19906.0MB, alloc=603.8MB, time=169.80 memory used=20098.0MB, alloc=603.8MB, time=170.28 memory used=20290.4MB, alloc=603.8MB, time=170.83 memory used=20483.2MB, alloc=603.8MB, time=171.32 memory used=20676.3MB, alloc=603.8MB, time=171.86 memory used=20869.7MB, alloc=603.8MB, time=172.36 memory used=21063.3MB, alloc=603.8MB, time=172.90 memory used=21257.0MB, alloc=603.8MB, time=173.38 memory used=21451.0MB, alloc=603.8MB, time=173.89 memory used=21648.1MB, alloc=603.8MB, time=174.41 memory used=21867.0MB, alloc=603.8MB, time=174.94 memory used=22089.1MB, alloc=603.8MB, time=175.47 memory used=22311.1MB, alloc=603.8MB, time=176.01 memory used=22533.1MB, alloc=603.8MB, time=176.58 memory used=22700.7MB, alloc=603.8MB, time=177.06 memory used=22833.5MB, alloc=603.8MB, time=177.50 memory used=22971.4MB, alloc=603.8MB, time=177.93 memory used=23109.2MB, alloc=603.8MB, time=178.40 memory used=23247.0MB, alloc=603.8MB, time=178.86 memory used=23384.6MB, alloc=603.8MB, time=179.35 memory used=23522.1MB, alloc=603.8MB, time=179.78 memory used=23659.5MB, alloc=603.8MB, time=180.21 memory used=23796.7MB, alloc=603.8MB, time=180.63 memory used=23933.7MB, alloc=603.8MB, time=181.05 memory used=24070.6MB, alloc=603.8MB, time=181.54 memory used=24210.3MB, alloc=603.8MB, time=181.97 memory used=24370.9MB, alloc=603.8MB, time=182.45 memory used=24511.8MB, alloc=603.8MB, time=182.97 memory used=24670.3MB, alloc=603.8MB, time=183.45 memory used=24833.1MB, alloc=603.8MB, time=183.98 memory used=24995.5MB, alloc=603.8MB, time=184.45 memory used=25157.4MB, alloc=603.8MB, time=184.92 memory used=25319.0MB, alloc=603.8MB, time=185.42 memory used=25480.0MB, alloc=603.8MB, time=185.88 memory used=25640.7MB, alloc=603.8MB, time=186.33 memory used=25800.8MB, alloc=603.8MB, time=186.81 memory used=25960.4MB, alloc=603.8MB, time=187.30 memory used=26119.4MB, alloc=603.8MB, time=187.78 memory used=26277.9MB, alloc=603.8MB, time=188.24 memory used=26439.2MB, alloc=603.8MB, time=188.73 memory used=26619.3MB, alloc=603.8MB, time=189.20 memory used=26801.8MB, alloc=603.8MB, time=189.75 memory used=26983.5MB, alloc=603.8MB, time=190.25 memory used=27164.2MB, alloc=603.8MB, time=190.73 memory used=27343.9MB, alloc=603.8MB, time=191.22 memory used=27522.7MB, alloc=603.8MB, time=191.71 memory used=27700.3MB, alloc=603.8MB, time=192.20 memory used=27876.9MB, alloc=603.8MB, time=192.67 memory used=28055.9MB, alloc=603.8MB, time=193.14 memory used=28251.5MB, alloc=603.8MB, time=193.63 memory used=28449.0MB, alloc=603.8MB, time=194.12 memory used=28645.0MB, alloc=603.8MB, time=194.62 memory used=28839.2MB, alloc=603.8MB, time=195.11 memory used=29031.8MB, alloc=603.8MB, time=195.61 memory used=29226.2MB, alloc=603.8MB, time=196.11 memory used=29434.9MB, alloc=603.8MB, time=196.60 memory used=29644.9MB, alloc=603.8MB, time=197.11 memory used=29852.4MB, alloc=603.8MB, time=197.62 memory used=30057.5MB, alloc=603.8MB, time=198.15 memory used=30264.0MB, alloc=603.8MB, time=198.65 memory used=30481.4MB, alloc=603.8MB, time=199.15 memory used=30699.6MB, alloc=603.8MB, time=199.68 memory used=30914.3MB, alloc=603.8MB, time=200.19 memory used=31146.3MB, alloc=603.8MB, time=200.72 memory used=31373.6MB, alloc=603.8MB, time=201.23 memory used=31600.4MB, alloc=603.8MB, time=201.73 memory used=31785.8MB, alloc=603.8MB, time=202.20 memory used=31960.7MB, alloc=603.8MB, time=202.67 memory used=32130.5MB, alloc=603.8MB, time=203.14 memory used=32303.2MB, alloc=603.8MB, time=203.59 memory used=32477.3MB, alloc=603.8MB, time=204.06 memory used=32657.6MB, alloc=603.8MB, time=204.52 memory used=32841.6MB, alloc=603.8MB, time=204.99 memory used=33028.7MB, alloc=603.8MB, time=205.43 memory used=33216.6MB, alloc=603.8MB, time=205.87 memory used=33407.4MB, alloc=603.8MB, time=206.28 memory used=33601.1MB, alloc=603.8MB, time=206.76 memory used=33805.2MB, alloc=603.8MB, time=207.21 memory used=34009.4MB, alloc=603.8MB, time=207.65 memory used=34219.2MB, alloc=603.8MB, time=208.10 memory used=34435.0MB, alloc=603.8MB, time=208.55 memory used=34654.4MB, alloc=603.8MB, time=208.97 memory used=34880.3MB, alloc=603.8MB, time=209.41 memory used=35109.2MB, alloc=603.8MB, time=209.86 memory used=35342.8MB, alloc=603.8MB, time=210.29 memory used=35581.0MB, alloc=603.8MB, time=210.77 memory used=35755.9MB, alloc=605.6MB, time=215.94 memory used=35757.7MB, alloc=607.4MB, time=216.16 memory used=35759.5MB, alloc=609.2MB, time=216.38 memory used=35761.3MB, alloc=611.0MB, time=216.58 memory used=35763.1MB, alloc=605.6MB, time=216.82 memory used=35941.6MB, alloc=603.8MB, time=226.99 memory used=36109.5MB, alloc=603.8MB, time=227.60 memory used=36223.8MB, alloc=603.8MB, time=228.12 memory used=36356.0MB, alloc=603.8MB, time=228.61 memory used=36502.5MB, alloc=603.8MB, time=229.16 memory used=36663.1MB, alloc=603.8MB, time=229.69 memory used=36837.7MB, alloc=603.8MB, time=230.30 memory used=37011.5MB, alloc=603.8MB, time=230.86 memory used=37109.8MB, alloc=603.8MB, time=231.28 memory used=37202.2MB, alloc=603.8MB, time=231.70 memory used=37298.8MB, alloc=603.8MB, time=232.06 memory used=37398.0MB, alloc=603.8MB, time=232.45 memory used=37499.9MB, alloc=603.8MB, time=232.82 memory used=37604.4MB, alloc=603.8MB, time=233.20 memory used=37712.6MB, alloc=603.8MB, time=233.62 memory used=37837.1MB, alloc=603.8MB, time=234.07 memory used=37965.7MB, alloc=603.8MB, time=234.46 memory used=38097.5MB, alloc=603.8MB, time=234.89 memory used=38232.5MB, alloc=603.8MB, time=235.32 memory used=38370.5MB, alloc=603.8MB, time=235.75 memory used=38511.6MB, alloc=603.8MB, time=236.19 memory used=38655.6MB, alloc=603.8MB, time=236.61 memory used=38802.5MB, alloc=603.8MB, time=237.06 memory used=38952.3MB, alloc=603.8MB, time=237.49 memory used=39104.9MB, alloc=603.8MB, time=237.92 memory used=39260.3MB, alloc=603.8MB, time=238.39 memory used=39418.4MB, alloc=603.8MB, time=238.81 memory used=39579.1MB, alloc=603.8MB, time=239.25 memory used=39742.4MB, alloc=603.8MB, time=239.71 memory used=39909.8MB, alloc=603.8MB, time=240.15 memory used=40098.0MB, alloc=603.8MB, time=240.60 memory used=40285.6MB, alloc=603.8MB, time=241.12 memory used=40379.6MB, alloc=603.8MB, time=241.52 memory used=40486.6MB, alloc=603.8MB, time=241.91 memory used=40596.1MB, alloc=603.8MB, time=242.34 memory used=40706.4MB, alloc=603.8MB, time=242.79 memory used=40817.7MB, alloc=603.8MB, time=243.21 memory used=40929.8MB, alloc=603.8MB, time=243.61 memory used=41042.7MB, alloc=603.8MB, time=243.99 memory used=41156.5MB, alloc=603.8MB, time=244.39 memory used=41271.0MB, alloc=603.8MB, time=244.77 memory used=41386.3MB, alloc=603.8MB, time=245.17 memory used=41502.5MB, alloc=603.8MB, time=245.57 memory used=41619.3MB, alloc=603.8MB, time=245.97 memory used=41737.0MB, alloc=603.8MB, time=246.36 memory used=41855.4MB, alloc=603.8MB, time=246.75 memory used=41974.5MB, alloc=603.8MB, time=247.21 memory used=42094.3MB, alloc=603.8MB, time=247.66 memory used=42214.8MB, alloc=603.8MB, time=248.11 memory used=42336.1MB, alloc=603.8MB, time=248.51 memory used=42458.0MB, alloc=603.8MB, time=248.91 memory used=42580.5MB, alloc=603.8MB, time=249.38 memory used=42703.7MB, alloc=603.8MB, time=249.80 memory used=42829.5MB, alloc=603.8MB, time=250.23 memory used=42977.0MB, alloc=603.8MB, time=250.72 memory used=43105.1MB, alloc=603.8MB, time=251.12 memory used=43253.2MB, alloc=603.8MB, time=251.56 memory used=43405.1MB, alloc=603.8MB, time=252.00 memory used=43557.7MB, alloc=603.8MB, time=252.44 memory used=43711.2MB, alloc=603.8MB, time=252.92 memory used=43865.4MB, alloc=603.8MB, time=253.44 memory used=44020.3MB, alloc=603.8MB, time=253.89 memory used=44175.9MB, alloc=603.8MB, time=254.31 memory used=44332.3MB, alloc=603.8MB, time=254.75 memory used=44489.3MB, alloc=603.8MB, time=255.20 memory used=44646.9MB, alloc=603.8MB, time=255.65 memory used=44805.2MB, alloc=603.8MB, time=256.10 memory used=44964.1MB, alloc=603.8MB, time=256.57 memory used=45123.6MB, alloc=603.8MB, time=257.00 memory used=45283.6MB, alloc=603.8MB, time=257.44 memory used=45444.1MB, alloc=603.8MB, time=257.90 memory used=45605.2MB, alloc=603.8MB, time=258.35 memory used=45766.7MB, alloc=603.8MB, time=258.78 memory used=45931.1MB, alloc=603.8MB, time=259.26 memory used=46118.4MB, alloc=603.8MB, time=259.80 memory used=46308.6MB, alloc=603.8MB, time=260.31 memory used=46499.2MB, alloc=603.8MB, time=260.85 memory used=46690.4MB, alloc=603.8MB, time=261.35 memory used=46882.0MB, alloc=603.8MB, time=261.82 memory used=47074.0MB, alloc=603.8MB, time=262.35 memory used=47266.4MB, alloc=603.8MB, time=262.86 memory used=47459.2MB, alloc=603.8MB, time=263.39 memory used=47652.3MB, alloc=603.8MB, time=263.90 memory used=47845.7MB, alloc=603.8MB, time=264.39 memory used=48039.2MB, alloc=603.8MB, time=264.89 memory used=48233.0MB, alloc=603.8MB, time=265.39 memory used=48427.0MB, alloc=603.8MB, time=265.91 memory used=48624.0MB, alloc=603.8MB, time=266.44 memory used=48843.0MB, alloc=603.8MB, time=266.98 memory used=49065.0MB, alloc=603.8MB, time=267.49 memory used=49287.1MB, alloc=603.8MB, time=268.01 memory used=49509.0MB, alloc=603.8MB, time=268.57 memory used=49676.7MB, alloc=603.8MB, time=269.05 memory used=49809.5MB, alloc=603.8MB, time=269.44 memory used=49947.4MB, alloc=603.8MB, time=269.87 memory used=50085.2MB, alloc=603.8MB, time=270.31 memory used=50223.0MB, alloc=603.8MB, time=270.70 memory used=50360.6MB, alloc=603.8MB, time=271.10 memory used=50498.1MB, alloc=603.8MB, time=271.51 memory used=50635.5MB, alloc=603.8MB, time=271.89 memory used=50772.7MB, alloc=603.8MB, time=272.29 memory used=50909.7MB, alloc=603.8MB, time=272.71 memory used=51046.6MB, alloc=603.8MB, time=273.11 memory used=51186.3MB, alloc=603.8MB, time=273.56 memory used=51346.9MB, alloc=603.8MB, time=274.04 memory used=51487.8MB, alloc=603.8MB, time=274.45 memory used=51646.3MB, alloc=603.8MB, time=274.98 memory used=51809.1MB, alloc=603.8MB, time=275.46 memory used=51971.5MB, alloc=603.8MB, time=275.90 memory used=52133.4MB, alloc=603.8MB, time=276.35 memory used=52295.0MB, alloc=603.8MB, time=276.78 memory used=52456.1MB, alloc=603.8MB, time=277.27 memory used=52616.6MB, alloc=603.8MB, time=277.68 memory used=52776.7MB, alloc=603.8MB, time=278.17 memory used=52936.3MB, alloc=603.8MB, time=278.62 memory used=53095.4MB, alloc=603.8MB, time=279.09 memory used=53253.9MB, alloc=603.8MB, time=279.59 memory used=53415.1MB, alloc=603.8MB, time=280.03 memory used=53595.3MB, alloc=603.8MB, time=280.49 memory used=53777.8MB, alloc=603.8MB, time=280.94 memory used=53959.5MB, alloc=603.8MB, time=281.38 memory used=54140.2MB, alloc=603.8MB, time=281.82 memory used=54319.9MB, alloc=603.8MB, time=282.27 memory used=54498.6MB, alloc=603.8MB, time=282.70 memory used=54676.3MB, alloc=603.8MB, time=283.12 memory used=54852.9MB, alloc=603.8MB, time=283.56 memory used=55031.9MB, alloc=603.8MB, time=284.01 memory used=55227.4MB, alloc=603.8MB, time=284.47 memory used=55425.0MB, alloc=603.8MB, time=284.92 memory used=55620.9MB, alloc=603.8MB, time=285.38 memory used=55815.2MB, alloc=603.8MB, time=285.83 memory used=56007.7MB, alloc=603.8MB, time=286.29 memory used=56202.2MB, alloc=603.8MB, time=286.75 memory used=56410.9MB, alloc=603.8MB, time=287.22 memory used=56620.9MB, alloc=603.8MB, time=287.69 memory used=56828.4MB, alloc=603.8MB, time=288.14 memory used=57033.4MB, alloc=603.8MB, time=288.61 memory used=57239.9MB, alloc=603.8MB, time=289.08 memory used=57457.4MB, alloc=603.8MB, time=289.55 memory used=57675.6MB, alloc=603.8MB, time=290.02 memory used=57890.2MB, alloc=603.8MB, time=290.49 memory used=58122.2MB, alloc=603.8MB, time=290.96 memory used=58349.5MB, alloc=603.8MB, time=291.44 memory used=58576.3MB, alloc=603.8MB, time=291.90 memory used=58761.7MB, alloc=603.8MB, time=292.34 memory used=58936.7MB, alloc=603.8MB, time=292.74 memory used=59106.5MB, alloc=603.8MB, time=293.16 memory used=59279.2MB, alloc=603.8MB, time=293.57 memory used=59453.3MB, alloc=603.8MB, time=293.97 memory used=59633.6MB, alloc=603.8MB, time=294.38 memory used=59817.6MB, alloc=603.8MB, time=294.80 memory used=60000.2MB, alloc=603.8MB, time=295.21 memory used=60192.6MB, alloc=603.8MB, time=295.63 memory used=60383.3MB, alloc=603.8MB, time=296.05 memory used=60577.1MB, alloc=603.8MB, time=296.48 memory used=60781.2MB, alloc=603.8MB, time=296.90 memory used=60985.3MB, alloc=603.8MB, time=297.32 memory used=61195.1MB, alloc=603.8MB, time=297.75 memory used=61410.8MB, alloc=603.8MB, time=298.17 memory used=61630.4MB, alloc=603.8MB, time=298.60 memory used=61856.3MB, alloc=603.8MB, time=299.03 memory used=62085.2MB, alloc=603.8MB, time=299.48 memory used=62318.7MB, alloc=603.8MB, time=299.91 memory used=62557.0MB, alloc=603.8MB, time=300.34 memory used=62719.5MB, alloc=605.6MB, time=304.41 memory used=62721.3MB, alloc=607.4MB, time=304.59 memory used=62723.0MB, alloc=609.2MB, time=304.77 memory used=62724.9MB, alloc=611.0MB, time=304.98 memory used=62726.6MB, alloc=605.6MB, time=305.18 |\^/| 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(); 1428511161 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 2 F := [-10 x z - 17 y z - 10 z , -3 x y - 2 z + 7 x] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 2 G := [-12 x - 10 x z - 16 y z, x y + 4 x y - 3 z] > Problem := [F,G]; 2 2 2 2 2 Problem := [[-10 x z - 17 y z - 10 z , -3 x y - 2 z + 7 x], 3 2 2 2 [-12 x - 10 x z - 16 y z, x y + 4 x y - 3 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=26.4MB, alloc=32.3MB, time=0.52 memory used=46.4MB, alloc=60.3MB, time=0.83 memory used=88.5MB, alloc=60.3MB, time=1.43 memory used=128.5MB, alloc=84.3MB, time=2.02 memory used=167.5MB, alloc=84.3MB, time=2.60 memory used=235.3MB, alloc=92.3MB, time=3.56 memory used=295.3MB, alloc=372.3MB, time=4.46 memory used=381.1MB, alloc=372.3MB, time=5.81 memory used=466.7MB, alloc=396.3MB, time=7.10 memory used=575.2MB, alloc=420.3MB, time=8.71 memory used=707.3MB, alloc=420.3MB, time=10.77 memory used=836.4MB, alloc=444.3MB, time=12.74 memory used=962.6MB, alloc=468.3MB, time=14.75 memory used=1088.2MB, alloc=468.3MB, time=16.84 memory used=1197.2MB, alloc=492.3MB, time=18.48 memory used=1304.3MB, alloc=492.3MB, time=20.00 memory used=1448.7MB, alloc=492.3MB, time=22.29 memory used=1599.6MB, alloc=516.3MB, time=25.36 memory used=1750.0MB, alloc=540.3MB, time=28.79 memory used=1925.1MB, alloc=564.3MB, time=35.17 memory used=2095.8MB, alloc=588.3MB, time=42.35 memory used=2290.4MB, alloc=612.3MB, time=50.64 memory used=2509.2MB, alloc=636.3MB, time=60.01 N1 := 4887 > GB := Basis(F, plex(op(vars))); 6 4 3 2 5 4 2 5 3 2 GB := [300 x y + 1020 x y + 867 x y + 450 x y - 700 x - 2380 x y 4 3 2 5 2 3 4 5 - 2023 x y - 2100 x y + 2450 x , -1530 x y - 2601 x y - 1350 x y 5 4 3 2 4 2 + 900 x z + 3150 x + 8330 x + 14161 x y + 8330 x z, -510 x y 2 4 4 4 3 3 3 - 867 x y - 450 x y + 300 x z + 1190 x y + 2023 x y + 1050 x 2 2 2 2 2 + 1190 x y z, -15 x y + 10 x z + 17 y z + 35 x, 3 y x + 2 z - 7 x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=2609.5MB, alloc=636.3MB, time=61.83 memory used=2732.3MB, alloc=636.3MB, time=63.39 memory used=2834.6MB, alloc=636.3MB, time=64.91 memory used=2922.8MB, alloc=636.3MB, time=66.24 memory used=3011.5MB, alloc=636.3MB, time=67.45 memory used=3099.6MB, alloc=636.3MB, time=68.71 memory used=3237.4MB, alloc=636.3MB, time=69.89 memory used=3365.7MB, alloc=636.3MB, time=71.25 memory used=3436.6MB, alloc=636.3MB, time=72.39 memory used=3494.1MB, alloc=636.3MB, time=73.42 memory used=3562.2MB, alloc=636.3MB, time=74.71 memory used=3656.2MB, alloc=636.3MB, time=75.86 memory used=3734.5MB, alloc=636.3MB, time=77.26 memory used=3790.6MB, alloc=636.3MB, time=78.36 memory used=3878.0MB, alloc=636.3MB, time=79.51 memory used=3934.9MB, alloc=636.3MB, time=80.51 memory used=3998.4MB, alloc=636.3MB, time=81.77 memory used=4056.2MB, alloc=636.3MB, time=83.07 memory used=4102.6MB, alloc=636.3MB, time=84.24 memory used=4281.8MB, alloc=636.3MB, time=87.05 memory used=4503.1MB, alloc=660.3MB, time=90.36 memory used=4737.5MB, alloc=660.3MB, time=92.54 memory used=4972.0MB, alloc=660.3MB, time=95.44 memory used=5163.1MB, alloc=660.3MB, time=98.54 memory used=5436.9MB, alloc=684.3MB, time=101.69 memory used=5613.8MB, alloc=684.3MB, time=103.95 memory used=5850.0MB, alloc=708.3MB, time=106.84 memory used=6035.0MB, alloc=708.3MB, time=107.93 memory used=6234.4MB, alloc=708.3MB, time=114.92 memory used=6442.3MB, alloc=708.3MB, time=116.21 memory used=6586.5MB, alloc=708.3MB, time=117.01 memory used=6771.8MB, alloc=708.3MB, time=117.89 memory used=7122.4MB, alloc=708.3MB, time=121.05 memory used=7273.0MB, alloc=708.3MB, time=123.56 memory used=7405.5MB, alloc=732.3MB, time=126.02 memory used=7514.4MB, alloc=732.3MB, time=129.00 memory used=7728.3MB, alloc=732.3MB, time=130.84 memory used=8003.5MB, alloc=732.3MB, time=133.56 memory used=8166.5MB, alloc=732.3MB, time=134.60 memory used=8424.4MB, alloc=732.3MB, time=135.90 memory used=8579.9MB, alloc=732.3MB, time=136.90 memory used=8817.2MB, alloc=732.3MB, time=139.45 memory used=9003.1MB, alloc=732.3MB, time=140.47 memory used=9148.0MB, alloc=732.3MB, time=141.43 memory used=9303.2MB, alloc=732.3MB, time=142.41 memory used=9579.3MB, alloc=732.3MB, time=146.16 memory used=9737.6MB, alloc=756.3MB, time=147.24 memory used=10034.4MB, alloc=756.3MB, time=148.46 memory used=10187.1MB, alloc=756.3MB, time=149.46 memory used=10487.0MB, alloc=756.3MB, time=152.44 memory used=10675.1MB, alloc=756.3MB, time=153.59 memory used=10831.9MB, alloc=756.3MB, time=154.57 memory used=11038.3MB, alloc=756.3MB, time=155.98 memory used=11226.6MB, alloc=756.3MB, time=157.10 memory used=11386.5MB, alloc=756.3MB, time=158.12 memory used=11688.7MB, alloc=756.3MB, time=175.91 memory used=11872.1MB, alloc=756.3MB, time=177.02 memory used=12044.4MB, alloc=756.3MB, time=178.06 memory used=12357.4MB, alloc=756.3MB, time=179.30 memory used=12483.3MB, alloc=756.3MB, time=180.25 memory used=12625.1MB, alloc=756.3MB, time=181.23 memory used=12780.8MB, alloc=756.3MB, time=182.21 memory used=12956.1MB, alloc=756.3MB, time=183.24 memory used=13150.3MB, alloc=756.3MB, time=184.27 memory used=13324.1MB, alloc=756.3MB, time=185.25 memory used=13486.1MB, alloc=756.3MB, time=186.23 memory used=13777.1MB, alloc=756.3MB, time=189.05 memory used=14030.9MB, alloc=756.3MB, time=191.74 memory used=14245.0MB, alloc=756.3MB, time=193.52 memory used=14429.9MB, alloc=756.3MB, time=194.56 memory used=14644.9MB, alloc=756.3MB, time=196.29 |\^/| 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(); 1428511461 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 F := [-6 x + 15 x z - 6 x, -5 x z - 6 x y - 6 y ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 3 2 G := [-6 x - 20 x y z - 15 z , -6 x y - 3 z - 8 x ] > Problem := [F,G]; 3 2 2 Problem := [[-6 x + 15 x z - 6 x, -5 x z - 6 x y - 6 y ], 3 2 2 3 2 [-6 x - 20 x y z - 15 z , -6 x y - 3 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=31.5MB, alloc=44.3MB, time=0.63 memory used=58.6MB, alloc=44.3MB, time=1.06 memory used=84.0MB, alloc=68.3MB, time=1.50 memory used=131.9MB, alloc=76.3MB, time=2.34 memory used=181.0MB, alloc=100.3MB, time=3.09 memory used=254.3MB, alloc=100.3MB, time=4.17 memory used=321.8MB, alloc=356.3MB, time=5.15 memory used=395.0MB, alloc=380.3MB, time=6.14 memory used=494.3MB, alloc=380.3MB, time=7.69 memory used=591.4MB, alloc=404.3MB, time=9.19 memory used=709.3MB, alloc=428.3MB, time=11.16 memory used=842.4MB, alloc=428.3MB, time=13.03 memory used=966.7MB, alloc=428.3MB, time=14.76 memory used=1097.7MB, alloc=452.3MB, time=16.79 memory used=1217.8MB, alloc=452.3MB, time=18.79 memory used=1331.3MB, alloc=476.3MB, time=20.72 memory used=1437.8MB, alloc=476.3MB, time=22.40 memory used=1547.7MB, alloc=476.3MB, time=24.01 memory used=1648.7MB, alloc=476.3MB, time=25.41 memory used=1756.9MB, alloc=476.3MB, time=26.85 memory used=1848.5MB, alloc=476.3MB, time=28.43 memory used=1966.0MB, alloc=500.3MB, time=29.77 memory used=2086.3MB, alloc=500.3MB, time=30.44 memory used=2232.0MB, alloc=500.3MB, time=31.72 memory used=2339.9MB, alloc=500.3MB, time=32.76 memory used=2482.4MB, alloc=500.3MB, time=34.35 memory used=2654.1MB, alloc=500.3MB, time=36.18 memory used=2770.1MB, alloc=500.3MB, time=37.98 memory used=2896.9MB, alloc=500.3MB, time=38.93 memory used=3026.3MB, alloc=500.3MB, time=39.88 memory used=3166.5MB, alloc=500.3MB, time=41.29 memory used=3254.4MB, alloc=500.3MB, time=42.62 memory used=3334.8MB, alloc=500.3MB, time=43.96 memory used=3418.2MB, alloc=500.3MB, time=45.64 memory used=3491.6MB, alloc=500.3MB, time=47.17 memory used=3553.4MB, alloc=500.3MB, time=48.58 memory used=3617.3MB, alloc=524.3MB, time=49.78 memory used=3688.7MB, alloc=524.3MB, time=51.08 memory used=3752.5MB, alloc=524.3MB, time=52.05 memory used=3804.1MB, alloc=524.3MB, time=53.07 memory used=3855.3MB, alloc=524.3MB, time=54.07 memory used=3909.8MB, alloc=524.3MB, time=55.37 memory used=3982.3MB, alloc=524.3MB, time=56.44 memory used=4201.9MB, alloc=548.3MB, time=59.34 memory used=4459.1MB, alloc=572.3MB, time=63.11 memory used=4722.8MB, alloc=572.3MB, time=66.25 memory used=4983.1MB, alloc=596.3MB, time=70.63 memory used=5248.4MB, alloc=620.3MB, time=75.86 memory used=5526.6MB, alloc=644.3MB, time=81.27 memory used=5813.2MB, alloc=668.3MB, time=87.16 memory used=6126.8MB, alloc=692.3MB, time=92.49 memory used=6464.2MB, alloc=716.3MB, time=97.86 memory used=6785.6MB, alloc=740.3MB, time=103.93 memory used=7140.8MB, alloc=764.3MB, time=109.86 memory used=7430.9MB, alloc=788.3MB, time=115.61 memory used=7757.7MB, alloc=812.3MB, time=123.67 memory used=8033.2MB, alloc=836.3MB, time=133.88 memory used=8310.2MB, alloc=860.3MB, time=144.85 memory used=8595.3MB, alloc=884.3MB, time=156.71 memory used=8891.6MB, alloc=908.3MB, time=169.23 memory used=9196.3MB, alloc=932.3MB, time=183.02 |\^/| 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(); 1428511761 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 F := [-5 x y + 17 x z - 12, 6 x - 10 z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 2 G := [9 x y + 9 y - 13 z , 9 x y - 10 x z - 5 y ] > Problem := [F,G]; 2 3 Problem := [[-5 x y + 17 x z - 12, 6 x - 10 z], 2 2 2 2 2 [9 x y + 9 y - 13 z , 9 x y - 10 x z - 5 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=27.4MB, alloc=32.3MB, time=0.54 memory used=48.3MB, alloc=60.3MB, time=0.86 memory used=86.9MB, alloc=60.3MB, time=1.47 memory used=127.6MB, alloc=92.3MB, time=2.12 memory used=191.9MB, alloc=92.3MB, time=3.11 memory used=255.9MB, alloc=116.3MB, time=4.16 memory used=334.7MB, alloc=372.3MB, time=5.45 memory used=419.6MB, alloc=396.3MB, time=6.82 memory used=529.2MB, alloc=420.3MB, time=8.61 memory used=660.8MB, alloc=444.3MB, time=10.90 memory used=800.2MB, alloc=468.3MB, time=13.37 memory used=951.9MB, alloc=492.3MB, time=16.09 memory used=1115.1MB, alloc=516.3MB, time=19.02 memory used=1289.7MB, alloc=540.3MB, time=22.21 memory used=1479.6MB, alloc=564.3MB, time=25.66 memory used=1677.0MB, alloc=588.3MB, time=29.73 memory used=1873.5MB, alloc=612.3MB, time=33.68 memory used=2061.4MB, alloc=636.3MB, time=39.83 memory used=2253.9MB, alloc=660.3MB, time=46.74 memory used=2458.2MB, alloc=684.3MB, time=54.38 memory used=2676.3MB, alloc=708.3MB, time=62.65 memory used=2909.0MB, alloc=732.3MB, time=71.70 memory used=3157.0MB, alloc=756.3MB, time=81.59 memory used=3418.2MB, alloc=780.3MB, time=92.47 memory used=3691.8MB, alloc=804.3MB, time=104.24 memory used=3989.3MB, alloc=828.3MB, time=117.81 memory used=4310.8MB, alloc=852.3MB, time=132.46 memory used=4656.3MB, alloc=876.3MB, time=148.16 memory used=5025.7MB, alloc=900.3MB, time=165.57 memory used=5419.1MB, alloc=924.3MB, time=182.88 memory used=5836.3MB, alloc=924.3MB, time=201.25 memory used=6253.5MB, alloc=948.3MB, time=219.50 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428520535 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 F := [14 x y + 3 x z + 15 y, -10 x z + 6 x y - 2 y ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 2 G := [-8 y - y z - 8 x, 4 y z + 10 y + y z] > Problem := [F,G]; 2 2 2 2 Problem := [[14 x y + 3 x z + 15 y, -10 x z + 6 x y - 2 y ], 3 2 2 2 [-8 y - y z - 8 x, 4 y z + 10 y + y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.8MB, alloc=32.3MB, time=0.52 memory used=46.5MB, alloc=56.3MB, time=0.83 memory used=88.8MB, alloc=60.3MB, time=1.44 memory used=131.1MB, alloc=92.3MB, time=2.09 memory used=197.8MB, alloc=92.3MB, time=3.04 memory used=264.3MB, alloc=116.3MB, time=3.95 memory used=334.5MB, alloc=372.3MB, time=4.93 memory used=422.9MB, alloc=396.3MB, time=6.18 memory used=538.9MB, alloc=420.3MB, time=7.76 memory used=685.6MB, alloc=420.3MB, time=9.92 memory used=800.0MB, alloc=444.3MB, time=11.92 memory used=940.9MB, alloc=468.3MB, time=14.23 memory used=1113.2MB, alloc=492.3MB, time=16.67 memory used=1300.3MB, alloc=516.3MB, time=19.62 memory used=1489.2MB, alloc=540.3MB, time=23.19 memory used=1676.4MB, alloc=564.3MB, time=28.60 memory used=1855.8MB, alloc=588.3MB, time=34.83 memory used=2041.3MB, alloc=612.3MB, time=42.27 memory used=2240.9MB, alloc=636.3MB, time=50.87 memory used=2464.5MB, alloc=660.3MB, time=60.84 memory used=2712.0MB, alloc=684.3MB, time=71.38 memory used=2983.5MB, alloc=684.3MB, time=83.09 memory used=3255.0MB, alloc=708.3MB, time=94.41 memory used=3550.4MB, alloc=708.3MB, time=106.64 memory used=3845.8MB, alloc=732.3MB, time=119.09 N1 := 8757 > GB := Basis(F, plex(op(vars))); 2 2 2 2 GB := [-70 x y - 9 x y + 3 y - 75 y, 3 z x + 14 y x + 15 y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=4105.6MB, alloc=732.3MB, time=126.97 memory used=4285.8MB, alloc=732.3MB, time=130.23 memory used=4469.9MB, alloc=732.3MB, time=133.89 N2 := 2451 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 3 2 H := [3 z x + 14 y x + 15 y, -10 x z + 6 x y - 2 y , -8 y - y z - 8 x, 2 2 4 y z + 10 y + y z] > J:=[op(GB),op(G)]; 2 2 2 2 J := [-70 x y - 9 x y + 3 y - 75 y, 3 z x + 14 y x + 15 y, 3 2 2 2 -8 y - y z - 8 x, 4 y z + 10 y + y z] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 11, 12, 3, 2, 3, 2, 3/4, 1, 1, 5/12, 3/4, 5/12, 4, 10, 12, 3, 11 2, 3, 2, 3/4, 1, 3/4, 5/13, --, 4/13, 1, 0, 0] 13 > save(F, G, cat("ranSet/33", convert(F, string),".txt")); > quit memory used=4670.7MB, alloc=732.3MB, time=141.94 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428520701 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 F := [14 y z + 4 y z + 17, 8 x + 10 z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 3 3 2 G := [-16 x + 11 z - 9 z, 2 x + 10 x y - 9 y ] > Problem := [F,G]; 2 2 Problem := [[14 y z + 4 y z + 17, 8 x + 10 z], 3 3 3 2 [-16 x + 11 z - 9 z, 2 x + 10 x 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=4.3MB, alloc=32.3MB, time=0.18 memory used=26.8MB, alloc=32.3MB, time=0.52 memory used=45.6MB, alloc=56.3MB, time=0.81 memory used=88.4MB, alloc=60.3MB, time=1.44 memory used=129.3MB, alloc=84.3MB, time=2.21 memory used=192.9MB, alloc=84.3MB, time=3.26 memory used=248.5MB, alloc=108.3MB, time=4.29 memory used=319.4MB, alloc=132.3MB, time=5.97 memory used=399.0MB, alloc=156.3MB, time=8.75 memory used=499.8MB, alloc=156.3MB, time=12.35 N1 := 2765 > GB := Basis(F, plex(op(vars))); 2 2 2 2 GB := [56 y x + 16 y x - 85, 4 x + 5 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=596.2MB, alloc=156.3MB, time=14.81 N2 := 803 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 3 3 H := [14 z y + 4 z y + 17, 8 x + 10 z, -16 x + 11 z - 9 z, 3 2 2 x - 9 y + 10 y x] > J:=[op(GB),op(G)]; 2 2 2 2 3 3 J := [56 y x + 16 y x - 85, 4 x + 5 z, -16 x + 11 z - 9 z, 3 2 2 x - 9 y + 10 y x] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 8, 11, 3, 3, 2, 3, 3/4, 1/2, 3/4, 4/11, 4/11, 5/11, 4, 8, 12, 4, 3, 2, 3, 1, 1/2, 1/2, 6/11, 4/11, 3/11, 0, -1, -1] > save(F, G, cat("ranSet/33", convert(F, string),".txt")); > quit memory used=640.8MB, alloc=164.3MB, time=15.83 |\^/| 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(); 1428520719 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 3 F := [-19 y z - 19 x z + 8 y , -9 x y + 9 y ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 2 2 2 G := [-19 x y + 9 z + 11 x , -6 y z + 3 y z - 6 y ] > Problem := [F,G]; 2 2 2 3 Problem := [[-19 y z - 19 x z + 8 y , -9 x y + 9 y ], 2 3 2 2 2 2 [-19 x y + 9 z + 11 x , -6 y z + 3 y z - 6 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.5MB, alloc=32.3MB, time=0.50 memory used=46.7MB, alloc=32.3MB, time=0.81 memory used=64.6MB, alloc=56.3MB, time=1.08 memory used=105.4MB, alloc=60.3MB, time=1.66 memory used=145.4MB, alloc=84.3MB, time=2.26 memory used=209.3MB, alloc=92.3MB, time=3.19 memory used=273.7MB, alloc=92.3MB, time=3.76 memory used=330.4MB, alloc=92.3MB, time=8.04 memory used=364.2MB, alloc=92.3MB, time=8.16 memory used=390.1MB, alloc=92.3MB, time=8.26 memory used=421.9MB, alloc=92.3MB, time=8.37 memory used=451.9MB, alloc=92.3MB, time=8.46 memory used=529.1MB, alloc=92.3MB, time=9.13 memory used=604.8MB, alloc=116.3MB, time=10.09 memory used=712.7MB, alloc=116.3MB, time=10.75 memory used=812.7MB, alloc=116.3MB, time=11.98 memory used=892.6MB, alloc=372.3MB, time=13.12 memory used=972.1MB, alloc=372.3MB, time=13.87 memory used=1054.4MB, alloc=396.3MB, time=15.57 memory used=1134.9MB, alloc=396.3MB, time=17.04 memory used=1221.6MB, alloc=396.3MB, time=17.89 memory used=1333.0MB, alloc=396.3MB, time=18.82 memory used=1412.5MB, alloc=396.3MB, time=19.16 memory used=1493.1MB, alloc=396.3MB, time=19.47 memory used=1614.6MB, alloc=396.3MB, time=21.04 memory used=1709.3MB, alloc=420.3MB, time=22.77 memory used=1828.5MB, alloc=444.3MB, time=24.83 memory used=1979.6MB, alloc=468.3MB, time=27.06 memory used=2144.4MB, alloc=492.3MB, time=29.72 memory used=2318.9MB, alloc=516.3MB, time=32.95 memory used=2478.9MB, alloc=540.3MB, time=38.13 memory used=2646.9MB, alloc=564.3MB, time=44.06 memory used=2820.7MB, alloc=588.3MB, time=51.16 memory used=3018.4MB, alloc=612.3MB, time=59.37 memory used=3240.1MB, alloc=612.3MB, time=68.39 memory used=3461.9MB, alloc=636.3MB, time=77.23 memory used=3707.6MB, alloc=636.3MB, time=86.97 memory used=3953.6MB, alloc=660.3MB, time=96.79 N1 := 7161 > GB := Basis(F, plex(op(vars))); 2 3 3 2 2 2 GB := [-x y + y , 19 x z + 19 x z - 8 x y , -x z + x y z, 2 2 19 z y + 19 z x - 8 y ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=4156.3MB, alloc=660.3MB, time=101.18 memory used=4294.0MB, alloc=660.3MB, time=103.56 memory used=4440.7MB, alloc=660.3MB, time=105.65 memory used=4558.2MB, alloc=660.3MB, time=107.48 memory used=4699.7MB, alloc=660.3MB, time=109.82 memory used=4826.2MB, alloc=660.3MB, time=112.12 memory used=4927.0MB, alloc=660.3MB, time=114.04 memory used=5036.2MB, alloc=660.3MB, time=115.74 memory used=5183.6MB, alloc=660.3MB, time=117.09 memory used=5309.7MB, alloc=660.3MB, time=118.66 memory used=5477.7MB, alloc=660.3MB, time=120.77 memory used=5703.9MB, alloc=660.3MB, time=121.65 memory used=5841.6MB, alloc=660.3MB, time=123.29 memory used=5931.5MB, alloc=684.3MB, time=124.88 memory used=6115.6MB, alloc=684.3MB, time=125.95 memory used=6276.3MB, alloc=684.3MB, time=126.69 memory used=6450.6MB, alloc=684.3MB, time=128.29 memory used=6613.4MB, alloc=684.3MB, time=129.10 memory used=6809.3MB, alloc=684.3MB, time=130.30 memory used=6971.6MB, alloc=684.3MB, time=130.99 memory used=7125.8MB, alloc=684.3MB, time=131.73 memory used=7281.8MB, alloc=684.3MB, time=132.37 memory used=7452.4MB, alloc=684.3MB, time=134.50 memory used=7626.3MB, alloc=684.3MB, time=135.37 memory used=7831.4MB, alloc=684.3MB, time=136.90 memory used=8048.4MB, alloc=684.3MB, time=139.37 memory used=8249.2MB, alloc=684.3MB, time=141.31 memory used=8363.5MB, alloc=684.3MB, time=142.85 memory used=8527.4MB, alloc=684.3MB, time=148.19 memory used=8698.6MB, alloc=708.3MB, time=149.49 memory used=8824.4MB, alloc=708.3MB, time=151.76 memory used=8901.6MB, alloc=708.3MB, time=153.26 memory used=8978.5MB, alloc=708.3MB, time=155.01 memory used=9056.8MB, alloc=708.3MB, time=156.92 memory used=9127.1MB, alloc=708.3MB, time=158.26 memory used=9205.9MB, alloc=708.3MB, time=159.65 memory used=9276.6MB, alloc=708.3MB, time=160.84 memory used=9327.1MB, alloc=708.3MB, time=162.20 memory used=9412.6MB, alloc=708.3MB, time=163.86 memory used=9482.0MB, alloc=708.3MB, time=165.20 memory used=9758.7MB, alloc=708.3MB, time=169.17 memory used=10093.6MB, alloc=732.3MB, time=171.99 memory used=10484.0MB, alloc=732.3MB, time=174.24 memory used=10817.1MB, alloc=732.3MB, time=176.52 memory used=11178.6MB, alloc=756.3MB, time=180.06 memory used=11522.1MB, alloc=780.3MB, time=186.11 memory used=11905.0MB, alloc=804.3MB, time=192.68 memory used=12284.8MB, alloc=828.3MB, time=199.33 memory used=12613.5MB, alloc=852.3MB, time=205.18 memory used=12941.3MB, alloc=876.3MB, time=211.34 memory used=13273.5MB, alloc=900.3MB, time=217.37 memory used=13595.2MB, alloc=924.3MB, time=224.09 memory used=13873.6MB, alloc=948.3MB, time=229.91 memory used=14274.0MB, alloc=972.3MB, time=244.82 memory used=14658.9MB, alloc=996.3MB, time=260.69 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428521019 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 3 F := [-18 x y - 13 x + 6, -3 x y + 3 z - 2 x] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 3 G := [-10 x y + 19 z - 8 x , -3 y + 3 z] > Problem := [F,G]; 2 2 2 3 Problem := [[-18 x y - 13 x + 6, -3 x y + 3 z - 2 x], 2 3 2 3 [-10 x y + 19 z - 8 x , -3 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=4.2MB, alloc=32.3MB, time=0.17 memory used=26.9MB, alloc=32.3MB, time=0.51 memory used=45.2MB, alloc=32.3MB, time=0.72 memory used=65.4MB, alloc=56.3MB, time=1.01 memory used=108.3MB, alloc=68.3MB, time=1.61 memory used=149.2MB, alloc=68.3MB, time=2.17 memory used=190.0MB, alloc=92.3MB, time=2.79 memory used=261.8MB, alloc=92.3MB, time=3.90 memory used=323.5MB, alloc=116.3MB, time=4.94 memory used=405.3MB, alloc=140.3MB, time=6.36 memory used=503.4MB, alloc=164.3MB, time=8.19 memory used=607.1MB, alloc=188.3MB, time=11.41 memory used=718.9MB, alloc=212.3MB, time=15.78 memory used=854.8MB, alloc=212.3MB, time=20.86 N1 := 3393 > GB := Basis(F, plex(op(vars))); 2 2 3 2 GB := [18 y x + 13 x - 6, 18 z + 13 x - 12 x - 6] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=972.0MB, alloc=212.3MB, time=23.52 memory used=1137.4MB, alloc=492.3MB, time=26.18 memory used=1318.6MB, alloc=516.3MB, time=31.14 N2 := 2369 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 3 2 3 2 H := [-18 x y - 13 x + 6, -3 x y + 3 z - 2 x, -10 x y + 19 z - 8 x , 3 -3 y + 3 z] > J:=[op(GB),op(G)]; 2 2 3 2 2 3 2 J := [18 y x + 13 x - 6, 18 z + 13 x - 12 x - 6, -10 x y + 19 z - 8 x , 3 -3 y + 3 z] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 10, 12, 3, 2, 3, 3, 3/4, 1, 3/4, 6/11, 4/11, 3/11, 4, 9, 12, 3, 2, 3, 3, 3/4, 3/4, 3/4, 1/2, 1/4, 1/4, 1, 0, 0] > save(F, G, cat("ranSet/33", convert(F, string),".txt")); > quit memory used=1432.0MB, alloc=516.3MB, time=35.66 |\^/| 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(); 1428521062 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 3 2 F := [-14 x z + 10 z , 8 x + 10 x - 9 x y] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 G := [18 x y + 16 z - 11 x, 3 x y z + 5 x y - 8 z ] > Problem := [F,G]; 2 3 3 2 Problem := [[-14 x z + 10 z , 8 x + 10 x - 9 x y], 2 2 2 [18 x y + 16 z - 11 x, 3 x y z + 5 x y - 8 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=26.6MB, alloc=32.3MB, time=0.53 memory used=47.5MB, alloc=32.3MB, time=0.85 memory used=67.0MB, alloc=56.3MB, time=1.17 memory used=107.2MB, alloc=60.3MB, time=1.83 memory used=145.7MB, alloc=60.3MB, time=2.44 memory used=182.9MB, alloc=84.3MB, time=3.06 memory used=230.1MB, alloc=84.3MB, time=3.96 memory used=286.5MB, alloc=116.3MB, time=5.06 memory used=362.5MB, alloc=140.3MB, time=6.51 memory used=454.0MB, alloc=164.3MB, time=8.23 memory used=561.5MB, alloc=188.3MB, time=10.17 memory used=684.8MB, alloc=212.3MB, time=12.39 memory used=809.5MB, alloc=492.3MB, time=14.66 memory used=952.3MB, alloc=516.3MB, time=17.97 memory used=1089.1MB, alloc=540.3MB, time=22.31 memory used=1237.0MB, alloc=564.3MB, time=27.36 memory used=1399.2MB, alloc=588.3MB, time=33.09 memory used=1575.8MB, alloc=612.3MB, time=39.61 memory used=1765.4MB, alloc=636.3MB, time=47.40 memory used=1979.0MB, alloc=660.3MB, time=56.07 memory used=2216.5MB, alloc=684.3MB, time=65.54 memory used=2477.9MB, alloc=684.3MB, time=75.93 memory used=2739.3MB, alloc=684.3MB, time=86.38 memory used=3000.7MB, alloc=708.3MB, time=96.84 memory used=3286.0MB, alloc=708.3MB, time=108.39 memory used=3571.3MB, alloc=708.3MB, time=120.00 memory used=3856.5MB, alloc=732.3MB, time=131.52 memory used=4165.7MB, alloc=732.3MB, time=143.79 memory used=4474.9MB, alloc=732.3MB, time=156.00 memory used=4784.0MB, alloc=756.3MB, time=168.20 memory used=5117.0MB, alloc=780.3MB, time=181.22 memory used=5473.9MB, alloc=804.3MB, time=195.24 N1 := 12349 > GB := Basis(F, plex(op(vars))); 3 2 2 3 GB := [-8 x - 10 x + 9 x y, -7 x z + 5 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=5861.4MB, alloc=804.3MB, time=205.27 memory used=6295.3MB, alloc=828.3MB, time=213.86 memory used=6725.3MB, alloc=852.3MB, time=225.80 memory used=7105.2MB, alloc=876.3MB, time=239.90 |\^/| 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(); 1428521363 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 F := [-5 y z - 13 z, 4 x z - 8 x z - 6 y z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 G := [18 x z + 15 y z - 6, 7 x y - 9 x - 2 y] > Problem := [F,G]; 2 2 Problem := [[-5 y z - 13 z, 4 x z - 8 x z - 6 y z], 2 2 [18 x z + 15 y z - 6, 7 x y - 9 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=4.2MB, alloc=32.3MB, time=0.19 memory used=26.1MB, alloc=32.3MB, time=0.50 memory used=48.3MB, alloc=32.3MB, time=0.86 memory used=68.5MB, alloc=56.3MB, time=1.22 memory used=110.0MB, alloc=84.3MB, time=2.02 N1 := 813 > GB := Basis(F, plex(op(vars))); 4 3 2 2 GB := [20 x z - 80 x z + 80 x z + 117 z, -2 x z + 4 x z + 3 y z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=169.0MB, alloc=84.3MB, time=3.17 N2 := 715 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 H := [-5 y z - 13 z, 4 x z - 8 x z - 6 y z, 18 x z + 15 y z - 6, 2 7 y x - 2 y - 9 x] > J:=[op(GB),op(G)]; 4 3 2 2 J := [20 x z - 80 x z + 80 x z + 117 z, -2 x z + 4 x z + 3 y z, 2 2 18 x z + 15 y z - 6, 7 y x - 2 y - 9 x] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 10, 12, 3, 2, 2, 2, 3/4, 1, 3/4, 5/11, 5/11, 7/11, 4, 10, 14, 5, 4, 2, 2, 1, 3/4, 3/4, 8/13, 4/13, 9/13, 0, -2, -2] > save(F, G, cat("ranSet/33", convert(F, string),".txt")); > quit memory used=226.3MB, alloc=84.3MB, time=4.36 |\^/| 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(); 1428521367 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 F := [-7 x y - 4 x z - 12 y z, -5 x z - 10 z - 5] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 G := [15 x z + 3 x z + 5, -5 y + 9 y z - 9] > Problem := [F,G]; 2 Problem := [[-7 x y - 4 x z - 12 y z, -5 x z - 10 z - 5], 2 3 2 [15 x z + 3 x z + 5, -5 y + 9 y z - 9]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=24.6MB, alloc=32.3MB, time=0.47 memory used=43.6MB, alloc=56.3MB, time=0.76 memory used=85.4MB, alloc=60.3MB, time=1.37 memory used=125.7MB, alloc=60.3MB, time=1.95 memory used=166.6MB, alloc=60.3MB, time=2.53 memory used=205.0MB, alloc=84.3MB, time=3.11 memory used=247.8MB, alloc=84.3MB, time=3.72 memory used=318.8MB, alloc=92.3MB, time=4.55 memory used=389.8MB, alloc=92.3MB, time=5.25 memory used=459.2MB, alloc=116.3MB, time=6.26 memory used=546.4MB, alloc=116.3MB, time=7.68 memory used=633.6MB, alloc=140.3MB, time=9.01 memory used=743.0MB, alloc=140.3MB, time=10.60 memory used=845.5MB, alloc=164.3MB, time=12.19 memory used=963.5MB, alloc=164.3MB, time=14.20 memory used=1080.1MB, alloc=188.3MB, time=16.03 memory used=1221.2MB, alloc=212.3MB, time=18.12 memory used=1335.2MB, alloc=468.3MB, time=20.12 memory used=1480.9MB, alloc=492.3MB, time=22.49 memory used=1627.5MB, alloc=516.3MB, time=26.40 memory used=1773.7MB, alloc=540.3MB, time=31.13 memory used=1932.0MB, alloc=564.3MB, time=36.61 memory used=2102.5MB, alloc=588.3MB, time=43.07 memory used=2289.1MB, alloc=612.3MB, time=50.56 memory used=2499.7MB, alloc=636.3MB, time=58.98 memory used=2734.1MB, alloc=636.3MB, time=68.26 memory used=2968.5MB, alloc=660.3MB, time=77.67 memory used=3226.9MB, alloc=660.3MB, time=87.94 memory used=3485.2MB, alloc=660.3MB, time=98.31 memory used=3743.6MB, alloc=660.3MB, time=108.70 memory used=4001.8MB, alloc=684.3MB, time=118.98 memory used=4284.0MB, alloc=684.3MB, time=130.38 memory used=4566.0MB, alloc=708.3MB, time=141.87 memory used=4871.9MB, alloc=732.3MB, time=153.91 N1 := 10461 > GB := Basis(F, plex(op(vars))); 2 3 2 2 2 2 GB := [49 y x - 168 y x - 56 y x + 144 y + 96 y x + 16 x , 3 3 49 x y + 28 x z - 168 x y + 48 x + 144 y, 12 z y + 4 z x + 7 y x, 2 z x + 2 z + 1] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=5089.1MB, alloc=732.3MB, time=159.46 memory used=5213.9MB, alloc=732.3MB, time=161.73 memory used=5336.7MB, alloc=732.3MB, time=164.03 memory used=5467.9MB, alloc=732.3MB, time=166.47 memory used=5594.8MB, alloc=732.3MB, time=168.59 memory used=5716.5MB, alloc=732.3MB, time=170.87 memory used=5821.8MB, alloc=732.3MB, time=173.09 memory used=5949.4MB, alloc=732.3MB, time=175.47 memory used=6128.0MB, alloc=732.3MB, time=177.63 memory used=6297.2MB, alloc=732.3MB, time=179.95 memory used=6417.1MB, alloc=732.3MB, time=182.19 memory used=6606.0MB, alloc=732.3MB, time=185.92 memory used=6777.9MB, alloc=756.3MB, time=189.56 memory used=6949.1MB, alloc=780.3MB, time=193.08 memory used=7111.3MB, alloc=804.3MB, time=196.49 memory used=7294.8MB, alloc=804.3MB, time=200.06 memory used=7440.3MB, alloc=828.3MB, time=203.10 memory used=7601.9MB, alloc=828.3MB, time=206.85 memory used=7787.5MB, alloc=852.3MB, time=210.22 memory used=7948.6MB, alloc=876.3MB, time=213.19 memory used=8120.2MB, alloc=876.3MB, time=216.27 memory used=8295.8MB, alloc=900.3MB, time=219.48 memory used=8472.2MB, alloc=900.3MB, time=222.67 memory used=8649.7MB, alloc=924.3MB, time=225.98 memory used=8760.5MB, alloc=924.3MB, time=228.22 memory used=8915.5MB, alloc=924.3MB, time=231.09 memory used=9068.5MB, alloc=948.3MB, time=233.86 memory used=9188.1MB, alloc=948.3MB, time=236.75 memory used=9326.0MB, alloc=972.3MB, time=239.61 memory used=9418.8MB, alloc=972.3MB, time=242.00 memory used=9528.3MB, alloc=996.3MB, time=244.68 memory used=9643.0MB, alloc=1020.3MB, time=248.33 memory used=10139.9MB, alloc=1044.3MB, time=266.98 |\^/| 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(); 1428521668 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 3 2 2 2 F := [20 y + 20 z - 20 x , 7 x - 7 z + 10 z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 2 G := [2 x y - 13 x y z + 13 z , -3 x y + 4 x + 3 z] > Problem := [F,G]; 3 3 2 2 2 Problem := [[20 y + 20 z - 20 x , 7 x - 7 z + 10 z], 2 3 2 2 [2 x y - 13 x y z + 13 z , -3 x y + 4 x + 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=0.17 memory used=26.6MB, alloc=32.3MB, time=0.50 memory used=46.1MB, alloc=32.3MB, time=0.67 memory used=66.9MB, alloc=57.1MB, time=1.02 memory used=101.1MB, alloc=57.4MB, time=1.11 memory used=137.6MB, alloc=61.4MB, time=1.45 memory used=201.0MB, alloc=70.3MB, time=2.07 memory used=264.1MB, alloc=70.3MB, time=2.86 memory used=321.7MB, alloc=70.3MB, time=3.42 memory used=379.8MB, alloc=70.3MB, time=4.00 memory used=424.1MB, alloc=70.3MB, time=4.36 memory used=471.9MB, alloc=71.0MB, time=4.79 memory used=522.0MB, alloc=71.0MB, time=5.31 memory used=572.4MB, alloc=71.6MB, time=5.76 memory used=594.8MB, alloc=71.6MB, time=5.84 memory used=644.0MB, alloc=71.6MB, time=6.34 memory used=675.7MB, alloc=71.6MB, time=6.50 memory used=698.2MB, alloc=71.6MB, time=6.56 memory used=719.8MB, alloc=71.6MB, time=6.63 memory used=745.9MB, alloc=71.6MB, time=6.70 memory used=766.9MB, alloc=71.6MB, time=6.76 memory used=784.8MB, alloc=71.6MB, time=6.80 memory used=805.7MB, alloc=71.6MB, time=6.85 memory used=864.0MB, alloc=71.6MB, time=7.26 memory used=918.1MB, alloc=71.6MB, time=7.67 memory used=972.3MB, alloc=71.6MB, time=7.99 memory used=1021.6MB, alloc=71.6MB, time=8.47 memory used=1061.7MB, alloc=95.6MB, time=8.93 memory used=1124.1MB, alloc=95.6MB, time=9.60 memory used=1177.7MB, alloc=95.6MB, time=9.94 memory used=1223.2MB, alloc=95.6MB, time=10.22 memory used=1279.6MB, alloc=95.6MB, time=10.49 memory used=1314.6MB, alloc=95.6MB, time=10.62 memory used=1344.9MB, alloc=95.6MB, time=10.72 memory used=1381.8MB, alloc=95.6MB, time=10.83 memory used=1412.5MB, alloc=95.6MB, time=10.93 memory used=1451.6MB, alloc=95.6MB, time=13.27 memory used=1477.7MB, alloc=95.6MB, time=13.36 memory used=1511.1MB, alloc=95.6MB, time=13.45 memory used=1548.8MB, alloc=95.6MB, time=13.70 memory used=1588.0MB, alloc=95.6MB, time=13.89 memory used=1629.8MB, alloc=95.6MB, time=14.09 memory used=1670.5MB, alloc=95.6MB, time=14.24 memory used=1711.0MB, alloc=95.6MB, time=14.40 memory used=1753.8MB, alloc=95.6MB, time=14.57 memory used=1792.9MB, alloc=95.6MB, time=14.72 memory used=1833.3MB, alloc=95.6MB, time=14.86 memory used=1874.2MB, alloc=95.6MB, time=15.05 memory used=1917.1MB, alloc=95.6MB, time=15.20 memory used=1962.8MB, alloc=95.6MB, time=15.53 memory used=1998.9MB, alloc=95.6MB, time=15.65 memory used=2028.0MB, alloc=95.6MB, time=15.75 memory used=2063.3MB, alloc=95.6MB, time=15.85 memory used=2101.1MB, alloc=95.6MB, time=15.95 memory used=2124.2MB, alloc=95.6MB, time=16.03 memory used=2149.2MB, alloc=95.6MB, time=16.13 memory used=2177.0MB, alloc=95.6MB, time=16.21 memory used=2206.8MB, alloc=95.6MB, time=16.30 memory used=2240.1MB, alloc=95.6MB, time=16.40 memory used=2277.0MB, alloc=95.6MB, time=16.49 memory used=2317.2MB, alloc=95.6MB, time=16.65 memory used=2366.5MB, alloc=95.6MB, time=16.99 memory used=2398.2MB, alloc=95.6MB, time=17.09 memory used=2441.5MB, alloc=95.6MB, time=17.24 memory used=2488.6MB, alloc=95.6MB, time=18.13 memory used=2521.8MB, alloc=95.6MB, time=18.23 memory used=2551.7MB, alloc=95.6MB, time=18.33 memory used=2581.6MB, alloc=95.6MB, time=18.41 memory used=2620.9MB, alloc=95.6MB, time=18.55 memory used=2673.6MB, alloc=95.6MB, time=19.55 memory used=2709.4MB, alloc=95.6MB, time=19.67 memory used=2743.3MB, alloc=95.6MB, time=19.76 memory used=2770.2MB, alloc=95.6MB, time=19.86 memory used=2810.7MB, alloc=95.6MB, time=20.00 memory used=2863.0MB, alloc=95.6MB, time=20.44 memory used=2899.4MB, alloc=95.6MB, time=20.58 memory used=2924.6MB, alloc=95.6MB, time=20.69 memory used=2953.2MB, alloc=95.6MB, time=20.81 memory used=2985.2MB, alloc=95.6MB, time=20.93 memory used=3020.4MB, alloc=95.6MB, time=21.05 memory used=3058.8MB, alloc=95.6MB, time=21.14 memory used=3094.5MB, alloc=95.6MB, time=21.25 memory used=3116.9MB, alloc=95.6MB, time=21.33 memory used=3139.6MB, alloc=95.6MB, time=21.43 memory used=3162.9MB, alloc=95.6MB, time=21.52 memory used=3187.7MB, alloc=95.6MB, time=21.61 memory used=3212.9MB, alloc=95.6MB, time=21.70 memory used=3239.3MB, alloc=95.6MB, time=21.79 memory used=3267.4MB, alloc=95.6MB, time=21.90 memory used=3296.7MB, alloc=95.6MB, time=22.00 memory used=3327.2MB, alloc=95.6MB, time=22.10 memory used=3360.1MB, alloc=95.6MB, time=22.20 memory used=3395.0MB, alloc=95.6MB, time=22.29 memory used=3431.3MB, alloc=95.6MB, time=22.38 memory used=3469.7MB, alloc=95.6MB, time=22.49 memory used=3508.4MB, alloc=95.6MB, time=22.59 memory used=3530.3MB, alloc=95.6MB, time=22.66 memory used=3552.6MB, alloc=95.6MB, time=22.73 memory used=3577.5MB, alloc=95.6MB, time=22.83 memory used=3627.5MB, alloc=95.6MB, time=23.28 memory used=3707.0MB, alloc=95.6MB, time=24.01 memory used=3783.9MB, alloc=375.6MB, time=24.80 memory used=3896.6MB, alloc=375.6MB, time=25.82 memory used=4014.3MB, alloc=375.6MB, time=26.76 memory used=4093.6MB, alloc=375.6MB, time=27.33 memory used=4164.4MB, alloc=375.6MB, time=28.93 memory used=4206.8MB, alloc=375.6MB, time=29.06 memory used=4269.0MB, alloc=375.6MB, time=30.30 memory used=4314.7MB, alloc=375.6MB, time=30.44 memory used=4361.6MB, alloc=375.6MB, time=30.61 memory used=4473.4MB, alloc=375.6MB, time=31.34 memory used=4578.7MB, alloc=375.6MB, time=31.98 memory used=4689.1MB, alloc=375.6MB, time=33.05 memory used=4791.7MB, alloc=399.6MB, time=33.81 memory used=4917.4MB, alloc=399.6MB, time=35.09 memory used=5000.4MB, alloc=399.6MB, time=35.55 memory used=5068.3MB, alloc=399.6MB, time=35.80 memory used=5131.2MB, alloc=399.6MB, time=36.03 memory used=5200.9MB, alloc=399.6MB, time=36.40 memory used=5268.8MB, alloc=399.6MB, time=36.63 memory used=5332.1MB, alloc=399.6MB, time=36.92 memory used=5396.8MB, alloc=399.6MB, time=37.16 memory used=5471.7MB, alloc=399.6MB, time=37.59 memory used=5529.8MB, alloc=399.6MB, time=37.76 memory used=5580.1MB, alloc=399.6MB, time=37.94 memory used=5625.2MB, alloc=399.6MB, time=38.11 memory used=5678.2MB, alloc=399.6MB, time=38.27 memory used=5740.3MB, alloc=399.6MB, time=38.42 memory used=5795.4MB, alloc=399.6MB, time=38.58 memory used=5835.2MB, alloc=399.6MB, time=38.71 memory used=5893.1MB, alloc=399.6MB, time=38.91 memory used=5963.1MB, alloc=399.6MB, time=39.35 memory used=6024.1MB, alloc=399.6MB, time=39.55 memory used=6098.9MB, alloc=399.6MB, time=40.54 memory used=6151.8MB, alloc=399.6MB, time=40.72 memory used=6209.4MB, alloc=399.6MB, time=40.86 memory used=6271.6MB, alloc=399.6MB, time=41.06 memory used=6346.7MB, alloc=399.6MB, time=42.05 memory used=6399.3MB, alloc=399.6MB, time=42.23 memory used=6456.3MB, alloc=399.6MB, time=42.38 memory used=6530.6MB, alloc=399.6MB, time=42.89 memory used=6588.4MB, alloc=399.6MB, time=43.09 memory used=6641.3MB, alloc=399.6MB, time=43.27 memory used=6706.7MB, alloc=399.6MB, time=43.49 memory used=6753.5MB, alloc=399.6MB, time=43.65 memory used=6793.9MB, alloc=399.6MB, time=43.81 memory used=6837.4MB, alloc=399.6MB, time=43.99 memory used=6886.1MB, alloc=399.6MB, time=44.18 memory used=6938.0MB, alloc=399.6MB, time=44.34 memory used=6994.7MB, alloc=399.6MB, time=44.51 memory used=7056.0MB, alloc=399.6MB, time=44.67 memory used=7123.0MB, alloc=399.6MB, time=44.84 memory used=7172.5MB, alloc=399.6MB, time=44.98 memory used=7208.3MB, alloc=399.6MB, time=45.11 memory used=7245.9MB, alloc=399.6MB, time=45.23 memory used=7285.4MB, alloc=399.6MB, time=45.34 memory used=7327.4MB, alloc=399.6MB, time=45.47 memory used=7372.6MB, alloc=399.6MB, time=45.60 memory used=7420.8MB, alloc=399.6MB, time=45.73 memory used=7477.0MB, alloc=399.6MB, time=46.00 memory used=7608.1MB, alloc=399.6MB, time=47.09 memory used=7729.2MB, alloc=399.6MB, time=48.00 memory used=7796.4MB, alloc=399.6MB, time=49.33 memory used=7845.8MB, alloc=399.6MB, time=49.52 memory used=7898.5MB, alloc=399.6MB, time=49.70 memory used=7999.4MB, alloc=399.6MB, time=50.41 memory used=8130.7MB, alloc=423.6MB, time=51.41 memory used=8257.4MB, alloc=423.6MB, time=52.63 memory used=8343.6MB, alloc=447.6MB, time=53.46 memory used=8440.2MB, alloc=447.6MB, time=54.19 memory used=8543.1MB, alloc=447.6MB, time=55.29 memory used=8658.2MB, alloc=447.6MB, time=56.60 memory used=8793.3MB, alloc=447.6MB, time=58.76 memory used=8896.9MB, alloc=471.6MB, time=59.71 memory used=9022.9MB, alloc=471.6MB, time=60.58 memory used=9125.4MB, alloc=471.6MB, time=60.99 memory used=9203.3MB, alloc=471.6MB, time=61.29 memory used=9353.7MB, alloc=471.6MB, time=66.35 memory used=9440.0MB, alloc=471.6MB, time=66.67 memory used=9511.4MB, alloc=471.6MB, time=67.01 memory used=9598.2MB, alloc=471.6MB, time=67.44 memory used=9706.8MB, alloc=471.6MB, time=68.51 memory used=9851.2MB, alloc=471.6MB, time=70.59 memory used=9964.2MB, alloc=471.6MB, time=71.38 memory used=10082.1MB, alloc=471.6MB, time=72.20 memory used=10167.1MB, alloc=471.6MB, time=72.57 memory used=10255.4MB, alloc=471.6MB, time=73.00 memory used=10345.0MB, alloc=471.6MB, time=73.45 memory used=10429.9MB, alloc=471.6MB, time=73.83 memory used=10522.4MB, alloc=471.6MB, time=74.30 memory used=10602.3MB, alloc=471.6MB, time=74.68 memory used=10682.5MB, alloc=471.6MB, time=75.02 memory used=10802.3MB, alloc=471.6MB, time=81.39 memory used=10884.4MB, alloc=471.6MB, time=81.75 memory used=10953.4MB, alloc=471.6MB, time=82.05 memory used=11044.1MB, alloc=471.6MB, time=82.38 memory used=11101.0MB, alloc=495.6MB, time=82.66 memory used=11175.0MB, alloc=495.6MB, time=82.95 memory used=11259.4MB, alloc=495.6MB, time=83.24 memory used=11355.9MB, alloc=495.6MB, time=83.54 memory used=11465.4MB, alloc=495.6MB, time=83.84 memory used=11671.1MB, alloc=495.6MB, time=84.40 memory used=11833.7MB, alloc=495.6MB, time=84.76 memory used=11974.4MB, alloc=495.6MB, time=85.42 memory used=12064.4MB, alloc=495.6MB, time=85.75 memory used=12192.9MB, alloc=495.6MB, time=89.47 memory used=12278.5MB, alloc=495.6MB, time=89.88 memory used=12366.4MB, alloc=495.6MB, time=90.26 memory used=12472.5MB, alloc=495.6MB, time=90.68 memory used=12570.6MB, alloc=495.6MB, time=91.06 memory used=12633.8MB, alloc=495.6MB, time=91.41 memory used=12700.5MB, alloc=495.6MB, time=91.72 memory used=12770.8MB, alloc=519.6MB, time=92.06 memory used=12860.8MB, alloc=519.6MB, time=92.44 memory used=12952.9MB, alloc=519.6MB, time=92.79 memory used=13056.5MB, alloc=519.6MB, time=93.18 memory used=13164.9MB, alloc=519.6MB, time=93.55 memory used=13277.7MB, alloc=519.6MB, time=93.94 memory used=13395.1MB, alloc=519.6MB, time=94.34 memory used=13525.3MB, alloc=519.6MB, time=94.75 memory used=13660.1MB, alloc=519.6MB, time=95.12 memory used=13744.9MB, alloc=543.6MB, time=95.45 memory used=13818.7MB, alloc=543.6MB, time=95.75 memory used=13894.0MB, alloc=543.6MB, time=96.05 memory used=13971.2MB, alloc=543.6MB, time=96.38 memory used=14058.0MB, alloc=543.6MB, time=96.73 memory used=14146.9MB, alloc=543.6MB, time=97.09 memory used=14237.1MB, alloc=543.6MB, time=97.40 memory used=14328.5MB, alloc=543.6MB, time=97.70 memory used=14421.1MB, alloc=543.6MB, time=98.00 memory used=14514.8MB, alloc=543.6MB, time=98.32 memory used=14609.6MB, alloc=543.6MB, time=98.63 memory used=14705.4MB, alloc=543.6MB, time=98.94 memory used=14803.1MB, alloc=543.6MB, time=99.26 memory used=14911.2MB, alloc=543.6MB, time=99.58 memory used=15021.0MB, alloc=543.6MB, time=99.90 memory used=15131.9MB, alloc=543.6MB, time=100.23 memory used=15243.8MB, alloc=543.6MB, time=100.56 memory used=15356.5MB, alloc=543.6MB, time=100.87 memory used=15470.2MB, alloc=543.6MB, time=101.21 memory used=15585.9MB, alloc=543.6MB, time=101.53 memory used=15711.5MB, alloc=543.6MB, time=101.86 memory used=15839.1MB, alloc=543.6MB, time=102.19 memory used=15967.3MB, alloc=543.6MB, time=102.52 memory used=16096.2MB, alloc=543.6MB, time=102.87 memory used=16226.7MB, alloc=543.6MB, time=103.22 memory used=16367.5MB, alloc=543.6MB, time=103.56 memory used=16509.7MB, alloc=543.6MB, time=103.92 memory used=16652.3MB, alloc=543.6MB, time=104.26 memory used=16796.1MB, alloc=543.6MB, time=104.60 memory used=16950.0MB, alloc=543.6MB, time=104.94 memory used=17188.0MB, alloc=543.6MB, time=105.43 memory used=17308.9MB, alloc=543.6MB, time=105.83 memory used=17426.8MB, alloc=543.6MB, time=106.21 memory used=17544.5MB, alloc=543.6MB, time=106.56 memory used=17661.9MB, alloc=543.6MB, time=106.96 memory used=17790.5MB, alloc=543.6MB, time=107.31 memory used=17918.6MB, alloc=543.6MB, time=107.67 memory used=18045.9MB, alloc=543.6MB, time=108.04 memory used=18173.7MB, alloc=543.6MB, time=108.40 memory used=18309.9MB, alloc=543.6MB, time=108.79 memory used=18446.1MB, alloc=543.6MB, time=109.16 memory used=18582.3MB, alloc=543.6MB, time=109.53 memory used=18725.9MB, alloc=543.6MB, time=109.91 memory used=18869.1MB, alloc=543.6MB, time=110.29 memory used=19021.3MB, alloc=543.6MB, time=110.66 memory used=19171.2MB, alloc=543.6MB, time=111.04 memory used=19329.0MB, alloc=543.6MB, time=111.42 memory used=19484.1MB, alloc=543.6MB, time=111.80 memory used=19645.9MB, alloc=543.6MB, time=112.19 memory used=19813.5MB, alloc=543.6MB, time=112.57 memory used=19985.9MB, alloc=543.6MB, time=112.96 memory used=20161.7MB, alloc=543.6MB, time=113.35 memory used=20339.5MB, alloc=543.6MB, time=113.74 memory used=20526.1MB, alloc=543.6MB, time=114.14 memory used=20717.9MB, alloc=543.6MB, time=114.53 memory used=20918.2MB, alloc=543.6MB, time=114.94 memory used=21126.4MB, alloc=543.6MB, time=115.34 memory used=21344.9MB, alloc=543.6MB, time=115.76 memory used=21637.1MB, alloc=543.6MB, time=300.60 |\^/| 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(); 1428521968 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 2 2 F := [4 x z - 8 z + 16 y , 9 y z - 4 z + 3 z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 G := [2 x - 8 x z + 20 y, -9 x y + 8 x y - 2 y ] > Problem := [F,G]; 2 3 2 2 2 Problem := [[4 x z - 8 z + 16 y , 9 y z - 4 z + 3 z], 2 2 2 [2 x - 8 x z + 20 y, -9 x y + 8 x y - 2 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.3MB, alloc=32.3MB, time=0.48 memory used=47.7MB, alloc=32.3MB, time=0.78 memory used=66.5MB, alloc=56.3MB, time=1.07 memory used=106.9MB, alloc=60.3MB, time=1.67 memory used=145.8MB, alloc=84.3MB, time=2.26 memory used=208.4MB, alloc=92.3MB, time=3.18 memory used=269.3MB, alloc=116.3MB, time=4.10 memory used=337.9MB, alloc=116.3MB, time=5.03 memory used=426.5MB, alloc=116.3MB, time=5.85 memory used=505.6MB, alloc=116.3MB, time=6.89 memory used=595.3MB, alloc=396.3MB, time=8.10 memory used=714.4MB, alloc=396.3MB, time=9.46 memory used=830.1MB, alloc=396.3MB, time=10.36 memory used=925.0MB, alloc=420.3MB, time=12.02 memory used=1034.0MB, alloc=444.3MB, time=13.87 memory used=1158.5MB, alloc=468.3MB, time=15.90 memory used=1297.6MB, alloc=492.3MB, time=18.02 memory used=1450.4MB, alloc=516.3MB, time=20.31 memory used=1617.0MB, alloc=540.3MB, time=23.08 memory used=1789.4MB, alloc=564.3MB, time=26.07 memory used=1964.1MB, alloc=588.3MB, time=29.34 memory used=2124.3MB, alloc=612.3MB, time=34.25 memory used=2292.5MB, alloc=636.3MB, time=39.90 memory used=2473.3MB, alloc=660.3MB, time=46.32 memory used=2669.1MB, alloc=684.3MB, time=52.72 memory used=2879.4MB, alloc=708.3MB, time=60.38 memory used=3104.5MB, alloc=732.3MB, time=68.31 memory used=3343.3MB, alloc=756.3MB, time=77.29 memory used=3595.7MB, alloc=780.3MB, time=87.36 memory used=3872.1MB, alloc=804.3MB, time=98.19 memory used=4172.4MB, alloc=828.3MB, time=109.59 memory used=4496.7MB, alloc=852.3MB, time=121.24 memory used=4844.9MB, alloc=876.3MB, time=133.61 memory used=5217.1MB, alloc=900.3MB, time=146.85 memory used=5613.2MB, alloc=900.3MB, time=160.77 memory used=6009.2MB, alloc=924.3MB, time=174.80 memory used=6429.2MB, alloc=924.3MB, time=189.71 memory used=6849.2MB, alloc=924.3MB, time=204.61 memory used=7269.1MB, alloc=924.3MB, time=219.44 memory used=7688.9MB, alloc=948.3MB, time=234.31 memory used=8132.8MB, alloc=948.3MB, time=250.03 memory used=8576.6MB, alloc=948.3MB, time=265.63 memory used=9020.3MB, alloc=948.3MB, time=281.24 |\^/| 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(); 1428522268 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 2 F := [7 y z - 17 z - 10 x, 8 x z + 8 x y + 2 y z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 3 3 G := [9 x + 10 y z - 11 z , 2 x y z + 5 y + 10 x z] > Problem := [F,G]; 2 2 2 2 2 Problem := [[7 y z - 17 z - 10 x, 8 x z + 8 x y + 2 y z], 3 2 3 3 [9 x + 10 y z - 11 z , 2 x y z + 5 y + 10 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.1MB, alloc=32.3MB, time=0.50 memory used=46.5MB, alloc=56.3MB, time=0.81 memory used=87.3MB, alloc=61.0MB, time=1.30 memory used=139.1MB, alloc=69.0MB, time=1.88 memory used=179.0MB, alloc=69.0MB, time=2.37 memory used=228.9MB, alloc=69.0MB, time=2.92 memory used=272.9MB, alloc=69.0MB, time=3.49 memory used=311.6MB, alloc=93.0MB, time=4.03 memory used=375.7MB, alloc=93.0MB, time=4.88 memory used=443.9MB, alloc=93.0MB, time=5.60 memory used=495.1MB, alloc=94.2MB, time=5.86 memory used=546.2MB, alloc=94.2MB, time=8.26 memory used=583.9MB, alloc=94.2MB, time=8.43 memory used=630.2MB, alloc=94.2MB, time=9.24 memory used=682.4MB, alloc=95.2MB, time=9.48 memory used=739.4MB, alloc=95.2MB, time=11.94 memory used=767.9MB, alloc=95.2MB, time=12.04 memory used=818.3MB, alloc=95.2MB, time=12.52 memory used=872.0MB, alloc=95.2MB, time=12.99 memory used=933.4MB, alloc=95.2MB, time=13.53 memory used=1014.8MB, alloc=95.2MB, time=14.38 memory used=1060.0MB, alloc=119.2MB, time=15.16 memory used=1134.5MB, alloc=375.2MB, time=15.71 memory used=1245.3MB, alloc=375.2MB, time=16.58 memory used=1334.2MB, alloc=375.2MB, time=17.52 memory used=1424.6MB, alloc=399.2MB, time=18.51 memory used=1543.2MB, alloc=399.2MB, time=19.74 memory used=1617.5MB, alloc=423.2MB, time=21.74 memory used=1702.9MB, alloc=423.2MB, time=23.24 memory used=1785.9MB, alloc=423.2MB, time=25.11 memory used=1900.3MB, alloc=423.2MB, time=30.47 memory used=2009.4MB, alloc=423.2MB, time=32.35 memory used=2132.4MB, alloc=423.2MB, time=33.20 memory used=2250.9MB, alloc=423.2MB, time=33.85 memory used=2320.6MB, alloc=423.2MB, time=34.15 memory used=2391.9MB, alloc=423.2MB, time=34.40 memory used=2487.9MB, alloc=423.2MB, time=46.67 memory used=2560.8MB, alloc=423.2MB, time=48.50 memory used=2619.7MB, alloc=423.2MB, time=48.69 memory used=2674.2MB, alloc=423.2MB, time=48.89 memory used=2740.4MB, alloc=423.2MB, time=49.07 memory used=2813.6MB, alloc=423.2MB, time=49.40 memory used=2910.5MB, alloc=423.2MB, time=52.79 memory used=2967.1MB, alloc=423.2MB, time=52.98 memory used=3051.8MB, alloc=423.2MB, time=53.31 memory used=3110.5MB, alloc=423.2MB, time=53.54 memory used=3191.2MB, alloc=423.2MB, time=53.88 memory used=3278.4MB, alloc=423.2MB, time=60.67 memory used=3359.0MB, alloc=423.2MB, time=67.77 memory used=3420.2MB, alloc=423.2MB, time=67.97 memory used=3472.2MB, alloc=423.2MB, time=68.15 memory used=3538.1MB, alloc=423.2MB, time=68.34 memory used=3599.4MB, alloc=423.2MB, time=68.60 memory used=3676.7MB, alloc=423.2MB, time=68.91 memory used=3753.1MB, alloc=423.2MB, time=69.22 memory used=3837.9MB, alloc=423.2MB, time=71.55 memory used=3905.7MB, alloc=423.2MB, time=71.81 memory used=3991.5MB, alloc=423.2MB, time=72.81 memory used=4071.6MB, alloc=423.2MB, time=73.13 memory used=4159.7MB, alloc=423.2MB, time=74.23 memory used=4276.8MB, alloc=423.2MB, time=75.67 memory used=4398.9MB, alloc=447.2MB, time=76.75 memory used=4522.7MB, alloc=447.2MB, time=78.08 memory used=4638.9MB, alloc=447.2MB, time=79.20 memory used=4757.0MB, alloc=471.2MB, time=80.71 memory used=4872.5MB, alloc=471.2MB, time=82.11 memory used=4986.0MB, alloc=471.2MB, time=83.52 memory used=5108.6MB, alloc=495.2MB, time=87.11 memory used=5269.4MB, alloc=495.2MB, time=88.55 memory used=5415.0MB, alloc=495.2MB, time=89.76 memory used=5557.0MB, alloc=495.2MB, time=91.66 memory used=5764.2MB, alloc=495.2MB, time=92.98 memory used=5908.3MB, alloc=495.2MB, time=94.89 memory used=6005.1MB, alloc=495.2MB, time=95.94 memory used=6111.5MB, alloc=519.2MB, time=97.20 memory used=6202.3MB, alloc=519.2MB, time=98.33 memory used=6345.3MB, alloc=519.2MB, time=105.76 memory used=6449.7MB, alloc=519.2MB, time=106.25 memory used=6543.7MB, alloc=519.2MB, time=107.29 memory used=6634.9MB, alloc=519.2MB, time=108.26 memory used=6720.1MB, alloc=519.2MB, time=109.25 memory used=6783.8MB, alloc=519.2MB, time=110.12 memory used=6917.2MB, alloc=543.2MB, time=111.01 memory used=7021.9MB, alloc=543.2MB, time=111.43 memory used=7156.5MB, alloc=543.2MB, time=112.00 memory used=7290.0MB, alloc=543.2MB, time=121.22 memory used=7465.7MB, alloc=543.2MB, time=135.30 memory used=7572.8MB, alloc=543.2MB, time=135.74 memory used=7674.1MB, alloc=543.2MB, time=136.14 memory used=7766.3MB, alloc=543.2MB, time=136.52 memory used=7876.9MB, alloc=543.2MB, time=136.89 memory used=8009.0MB, alloc=543.2MB, time=137.28 memory used=8168.5MB, alloc=543.2MB, time=137.87 memory used=8338.6MB, alloc=543.2MB, time=138.33 memory used=8482.5MB, alloc=543.2MB, time=139.36 memory used=8589.1MB, alloc=543.2MB, time=139.80 memory used=8681.4MB, alloc=543.2MB, time=140.29 memory used=8792.3MB, alloc=543.2MB, time=140.76 memory used=8925.1MB, alloc=543.2MB, time=141.21 memory used=9012.7MB, alloc=543.2MB, time=141.59 memory used=9093.9MB, alloc=543.2MB, time=141.95 memory used=9181.5MB, alloc=543.2MB, time=142.30 memory used=9278.6MB, alloc=543.2MB, time=142.68 memory used=9386.6MB, alloc=543.2MB, time=143.03 memory used=9529.1MB, alloc=543.2MB, time=144.03 memory used=9647.2MB, alloc=543.2MB, time=144.51 memory used=9737.6MB, alloc=543.2MB, time=144.97 memory used=9837.5MB, alloc=543.2MB, time=145.41 memory used=9954.9MB, alloc=543.2MB, time=145.83 memory used=10079.4MB, alloc=543.2MB, time=146.25 memory used=10156.0MB, alloc=543.2MB, time=146.60 memory used=10238.1MB, alloc=543.2MB, time=146.95 memory used=10328.1MB, alloc=543.2MB, time=147.32 memory used=10427.4MB, alloc=543.2MB, time=147.68 memory used=10539.6MB, alloc=543.2MB, time=148.04 memory used=10689.6MB, alloc=567.2MB, time=204.03 memory used=10868.1MB, alloc=567.2MB, time=252.49 memory used=11022.7MB, alloc=567.2MB, time=253.40 memory used=11143.6MB, alloc=567.2MB, time=253.86 memory used=11260.3MB, alloc=567.2MB, time=254.30 memory used=11359.5MB, alloc=567.2MB, time=254.71 memory used=11474.2MB, alloc=567.2MB, time=255.11 memory used=11604.4MB, alloc=567.2MB, time=255.52 memory used=11754.5MB, alloc=567.2MB, time=255.95 memory used=11940.0MB, alloc=567.2MB, time=256.43 memory used=12084.7MB, alloc=567.2MB, time=256.89 memory used=12244.8MB, alloc=567.2MB, time=257.36 memory used=12422.4MB, alloc=567.2MB, time=257.83 memory used=12623.0MB, alloc=567.2MB, time=258.32 memory used=12923.0MB, alloc=567.2MB, time=259.38 memory used=13058.6MB, alloc=567.2MB, time=291.77 memory used=13247.3MB, alloc=567.2MB, time=328.55 memory used=13423.7MB, alloc=567.2MB, time=329.85 memory used=13541.8MB, alloc=567.2MB, time=330.33 memory used=13679.1MB, alloc=567.2MB, time=330.80 memory used=13771.1MB, alloc=567.2MB, time=331.17 memory used=13875.5MB, alloc=567.2MB, time=331.54 memory used=13994.1MB, alloc=567.2MB, time=331.95 memory used=14128.1MB, alloc=567.2MB, time=332.36 memory used=14279.8MB, alloc=567.2MB, time=332.79 memory used=14439.4MB, alloc=567.2MB, time=333.27 memory used=14583.8MB, alloc=567.2MB, time=333.72 memory used=14739.6MB, alloc=567.2MB, time=334.17 memory used=14911.6MB, alloc=567.2MB, time=334.65 memory used=15100.6MB, alloc=567.2MB, time=335.15 memory used=15315.5MB, alloc=567.2MB, time=335.65 memory used=15612.2MB, alloc=567.2MB, time=336.62 memory used=15754.8MB, alloc=567.2MB, time=337.59 memory used=15872.0MB, alloc=567.2MB, time=337.98 memory used=16033.3MB, alloc=567.2MB, time=338.88 memory used=16209.2MB, alloc=567.2MB, time=340.06 memory used=16288.3MB, alloc=567.2MB, time=340.88 memory used=16376.0MB, alloc=567.2MB, time=342.31 memory used=16542.1MB, alloc=591.2MB, time=353.70 memory used=16643.9MB, alloc=591.2MB, time=355.85 memory used=16748.1MB, alloc=591.2MB, time=356.97 memory used=16880.0MB, alloc=591.2MB, time=358.27 memory used=17030.4MB, alloc=591.2MB, time=359.59 memory used=17149.3MB, alloc=591.2MB, time=361.26 memory used=17311.5MB, alloc=591.2MB, time=362.71 memory used=17448.1MB, alloc=591.2MB, time=363.34 memory used=17559.9MB, alloc=591.2MB, time=363.88 memory used=17699.0MB, alloc=591.2MB, time=364.43 memory used=17855.8MB, alloc=591.2MB, time=365.00 memory used=17948.4MB, alloc=591.2MB, time=365.44 memory used=18048.1MB, alloc=591.2MB, time=365.89 memory used=18157.2MB, alloc=591.2MB, time=366.34 memory used=18274.8MB, alloc=591.2MB, time=366.80 memory used=18400.7MB, alloc=591.2MB, time=367.28 memory used=18539.8MB, alloc=591.2MB, time=367.78 memory used=18691.0MB, alloc=591.2MB, time=368.30 memory used=18852.5MB, alloc=591.2MB, time=368.79 memory used=19075.6MB, alloc=591.2MB, time=369.41 memory used=19210.4MB, alloc=591.2MB, time=369.92 memory used=19358.7MB, alloc=591.2MB, time=370.42 memory used=19545.9MB, alloc=591.2MB, time=372.01 memory used=19660.3MB, alloc=591.2MB, time=372.59 memory used=19790.6MB, alloc=591.2MB, time=373.20 memory used=19946.2MB, alloc=591.2MB, time=373.82 memory used=20062.7MB, alloc=591.2MB, time=374.32 memory used=20158.1MB, alloc=591.2MB, time=374.76 memory used=20261.1MB, alloc=591.2MB, time=375.21 memory used=20372.3MB, alloc=591.2MB, time=375.65 memory used=20495.9MB, alloc=591.2MB, time=376.11 memory used=20628.6MB, alloc=591.2MB, time=376.60 memory used=20773.9MB, alloc=591.2MB, time=377.09 memory used=20930.4MB, alloc=591.2MB, time=377.58 memory used=21224.9MB, alloc=591.2MB, time=378.28 memory used=21360.1MB, alloc=591.2MB, time=378.77 memory used=21508.4MB, alloc=591.2MB, time=379.25 |\^/| 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(); 1428522568 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 2 3 F := [12 x + 10 z , 8 x z - 6 y z + 8 z ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 G := [-16 x y z - 18 y z - 16 x, 3 x y z + 6 y z + 4 x ] > Problem := [F,G]; 3 2 2 2 3 Problem := [[12 x + 10 z , 8 x z - 6 y z + 8 z ], 2 2 2 [-16 x y z - 18 y z - 16 x, 3 x y z + 6 y 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=4.2MB, alloc=32.3MB, time=0.17 memory used=26.5MB, alloc=32.3MB, time=0.51 memory used=47.0MB, alloc=32.3MB, time=0.81 memory used=66.5MB, alloc=56.3MB, time=1.11 memory used=105.6MB, alloc=84.3MB, time=1.70 memory used=141.0MB, alloc=84.3MB, time=2.21 memory used=203.8MB, alloc=92.3MB, time=3.15 memory used=265.6MB, alloc=116.3MB, time=4.09 memory used=339.3MB, alloc=116.3MB, time=5.18 memory used=418.9MB, alloc=396.3MB, time=6.48 memory used=527.1MB, alloc=420.3MB, time=8.16 memory used=655.2MB, alloc=420.3MB, time=10.22 memory used=783.9MB, alloc=444.3MB, time=12.20 memory used=905.0MB, alloc=468.3MB, time=14.10 memory used=1031.5MB, alloc=492.3MB, time=16.16 memory used=1158.9MB, alloc=492.3MB, time=18.37 memory used=1281.3MB, alloc=516.3MB, time=20.64 memory used=1465.9MB, alloc=540.3MB, time=23.73 memory used=1661.5MB, alloc=564.3MB, time=27.05 memory used=1830.4MB, alloc=588.3MB, time=30.30 memory used=1996.2MB, alloc=612.3MB, time=33.53 memory used=2149.3MB, alloc=636.3MB, time=36.55 memory used=2311.1MB, alloc=660.3MB, time=39.68 memory used=2438.5MB, alloc=684.3MB, time=42.27 memory used=2590.4MB, alloc=708.3MB, time=45.18 memory used=2711.1MB, alloc=732.3MB, time=47.71 memory used=2868.3MB, alloc=756.3MB, time=50.67 memory used=3004.5MB, alloc=780.3MB, time=53.47 memory used=3140.9MB, alloc=804.3MB, time=56.25 memory used=3267.4MB, alloc=828.3MB, time=59.66 memory used=3449.4MB, alloc=852.3MB, time=65.79 memory used=3677.9MB, alloc=876.3MB, time=74.11 memory used=4031.3MB, alloc=900.3MB, time=87.05 memory used=4388.8MB, alloc=924.3MB, time=99.26 memory used=4754.2MB, alloc=948.3MB, time=111.70 memory used=5128.3MB, alloc=972.3MB, time=124.90 memory used=5517.5MB, alloc=996.3MB, time=138.63 memory used=5917.4MB, alloc=1020.3MB, time=153.39 memory used=6334.1MB, alloc=1044.3MB, time=168.96 memory used=6774.7MB, alloc=1068.3MB, time=185.58 memory used=7239.3MB, alloc=1092.3MB, time=202.79 memory used=7727.8MB, alloc=1116.3MB, time=220.86 memory used=8240.2MB, alloc=1140.3MB, time=239.69 memory used=8776.6MB, alloc=1140.3MB, time=259.31 memory used=9312.9MB, alloc=1140.3MB, time=279.07 |\^/| 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(); 1428522868 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 3 2 F := [-4 x y z - 20 y + 4 y z , -2 z - 7 z ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 3 G := [16 x z + 15 x z - 12 y, 3 y z - 9 y z - 5 z ] > Problem := [F,G]; 3 2 3 2 Problem := [[-4 x y z - 20 y + 4 y z , -2 z - 7 z ], 2 2 2 3 [16 x z + 15 x z - 12 y, 3 y z - 9 y z - 5 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.16 memory used=26.4MB, alloc=32.3MB, time=0.48 memory used=46.6MB, alloc=32.3MB, time=0.77 memory used=65.3MB, alloc=56.3MB, time=1.05 memory used=104.8MB, alloc=60.3MB, time=1.64 memory used=142.9MB, alloc=84.3MB, time=2.20 memory used=202.5MB, alloc=92.3MB, time=3.12 memory used=263.1MB, alloc=116.3MB, time=4.18 memory used=341.4MB, alloc=140.3MB, time=5.53 memory used=436.4MB, alloc=164.3MB, time=7.18 memory used=547.0MB, alloc=188.3MB, time=9.05 memory used=646.1MB, alloc=468.3MB, time=10.81 memory used=785.5MB, alloc=492.3MB, time=13.27 memory used=934.7MB, alloc=516.3MB, time=15.86 memory used=1081.5MB, alloc=540.3MB, time=19.91 memory used=1230.8MB, alloc=564.3MB, time=24.48 memory used=1390.9MB, alloc=588.3MB, time=29.01 memory used=1563.1MB, alloc=612.3MB, time=34.10 memory used=1743.6MB, alloc=636.3MB, time=40.25 memory used=1948.1MB, alloc=660.3MB, time=47.12 memory used=2176.5MB, alloc=684.3MB, time=54.88 memory used=2428.8MB, alloc=708.3MB, time=63.41 memory used=2705.1MB, alloc=708.3MB, time=72.67 memory used=2981.4MB, alloc=732.3MB, time=82.10 memory used=3281.5MB, alloc=732.3MB, time=92.08 memory used=3581.6MB, alloc=732.3MB, time=102.16 memory used=3881.8MB, alloc=732.3MB, time=112.77 memory used=4181.9MB, alloc=756.3MB, time=123.32 memory used=4505.8MB, alloc=756.3MB, time=134.84 memory used=4829.9MB, alloc=756.3MB, time=146.28 memory used=5153.7MB, alloc=780.3MB, time=157.16 memory used=5501.5MB, alloc=780.3MB, time=168.66 memory used=5849.5MB, alloc=804.3MB, time=180.05 memory used=6221.4MB, alloc=828.3MB, time=192.41 memory used=6617.6MB, alloc=852.3MB, time=205.32 N1 := 13765 > GB := Basis(F, plex(op(vars))); 7 5 5 GB := [20 y - 14 x y - 49 y , 3 2 3 5 2 3 3 4 x y z + 20 x y - 100 y + 28 x y z + 140 x y + 49 x y z + 245 y , 2 3 3 3 3 2 2 x y z + 10 x y + 10 y z + 7 x y z + 35 y , -x y z - 5 y + y z , 3 2 2 z + 7 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=6954.5MB, alloc=852.3MB, time=210.47 memory used=7235.5MB, alloc=852.3MB, time=214.55 memory used=7543.4MB, alloc=852.3MB, time=219.43 memory used=7806.9MB, alloc=876.3MB, time=223.44 memory used=8027.5MB, alloc=900.3MB, time=226.92 memory used=8256.0MB, alloc=924.3MB, time=230.69 memory used=8817.3MB, alloc=948.3MB, time=239.33 memory used=9346.1MB, alloc=972.3MB, time=248.40 memory used=9858.6MB, alloc=996.3MB, time=257.09 memory used=10326.7MB, alloc=1020.3MB, time=265.46 memory used=10794.6MB, alloc=1044.3MB, time=273.88 memory used=11467.2MB, alloc=1068.3MB, time=287.05 |\^/| 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(); 1428523168 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 3 2 F := [-x y - 19 x , 7 z + 5 x + 4 y z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 3 3 2 G := [-16 x y - 16 y + 13 z , -8 x - 4 x + 2 x y] > Problem := [F,G]; 2 2 3 2 Problem := [[-x y - 19 x , 7 z + 5 x + 4 y z], 2 3 3 3 2 [-16 x y - 16 y + 13 z , -8 x - 4 x + 2 x y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=25.8MB, alloc=32.3MB, time=0.46 memory used=45.8MB, alloc=56.3MB, time=0.75 memory used=90.4MB, alloc=60.3MB, time=1.28 memory used=133.4MB, alloc=60.3MB, time=1.70 memory used=172.8MB, alloc=60.3MB, time=1.98 memory used=214.0MB, alloc=60.3MB, time=2.36 memory used=238.0MB, alloc=60.3MB, time=2.43 memory used=273.7MB, alloc=60.3MB, time=2.67 memory used=324.5MB, alloc=84.3MB, time=3.17 memory used=398.9MB, alloc=84.3MB, time=3.66 memory used=467.2MB, alloc=84.3MB, time=3.98 memory used=529.9MB, alloc=84.3MB, time=4.23 memory used=593.6MB, alloc=84.3MB, time=4.44 memory used=649.1MB, alloc=84.3MB, time=4.62 memory used=715.8MB, alloc=84.3MB, time=5.00 memory used=790.2MB, alloc=84.3MB, time=5.49 memory used=851.0MB, alloc=84.3MB, time=5.75 memory used=926.7MB, alloc=92.3MB, time=6.33 memory used=998.8MB, alloc=92.3MB, time=6.88 memory used=1070.2MB, alloc=92.3MB, time=7.77 memory used=1141.2MB, alloc=92.3MB, time=8.55 memory used=1204.2MB, alloc=116.3MB, time=9.38 memory used=1287.9MB, alloc=140.3MB, time=10.56 memory used=1374.1MB, alloc=164.3MB, time=12.93 N1 := 2157 > GB := Basis(F, plex(op(vars))); 2 2 3 2 GB := [x y + 19 x , 7 z + 4 z y + 5 x ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1481.0MB, alloc=164.3MB, time=15.42 memory used=1575.7MB, alloc=420.3MB, time=16.38 memory used=1677.7MB, alloc=420.3MB, time=17.07 memory used=1792.9MB, alloc=420.3MB, time=17.88 memory used=1908.4MB, alloc=420.3MB, time=18.48 memory used=2011.1MB, alloc=420.3MB, time=18.84 memory used=2103.6MB, alloc=420.3MB, time=19.13 memory used=2216.8MB, alloc=420.3MB, time=19.72 memory used=2331.4MB, alloc=420.3MB, time=20.34 memory used=2465.5MB, alloc=420.3MB, time=21.40 memory used=2599.8MB, alloc=444.3MB, time=22.95 memory used=2746.7MB, alloc=468.3MB, time=25.25 memory used=2877.6MB, alloc=492.3MB, time=29.23 N2 := 2157 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 3 2 2 3 3 H := [-x y - 19 x , 7 z + 4 z y + 5 x , -16 x y - 16 y + 13 z , 3 2 -8 x - 4 x + 2 x y] > J:=[op(GB),op(G)]; 2 2 3 2 2 3 3 J := [x y + 19 x , 7 z + 4 z y + 5 x , -16 x y - 16 y + 13 z , 3 2 -8 x - 4 x + 2 x y] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 10, 12, 3, 3, 3, 3, 1, 1, 1/2, 7/11, 5/11, 3/11, 4, 10, 12, 3, 3, 3, 3, 1, 1, 1/2, 7/11, 5/11, 3/11, 0, 0, 0] > save(F, G, cat("ranSet/33", convert(F, string),".txt")); > quit memory used=2879.5MB, alloc=492.3MB, time=29.27 |\^/| 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(); 1428523197 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 2 3 F := [-14 x y - 4 y + 19 z , -4 x y + 3 z - x z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 G := [-14 x z + 2 x z + 15 x y, 4 x y - 5 x y + 7 x] > Problem := [F,G]; 2 3 2 2 3 Problem := [[-14 x y - 4 y + 19 z , -4 x y + 3 z - x z], 2 2 2 [-14 x z + 2 x z + 15 x y, 4 x y - 5 x y + 7 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.13 memory used=26.5MB, alloc=32.3MB, time=0.42 memory used=46.7MB, alloc=56.3MB, time=0.69 memory used=87.3MB, alloc=60.3MB, time=1.17 memory used=129.3MB, alloc=68.3MB, time=1.61 memory used=170.6MB, alloc=92.3MB, time=2.08 memory used=226.0MB, alloc=92.3MB, time=2.39 memory used=271.6MB, alloc=92.3MB, time=2.80 memory used=318.3MB, alloc=92.3MB, time=2.95 memory used=366.2MB, alloc=92.3MB, time=3.39 memory used=413.2MB, alloc=92.3MB, time=3.53 memory used=463.1MB, alloc=92.3MB, time=4.13 memory used=518.8MB, alloc=92.3MB, time=4.76 memory used=579.1MB, alloc=92.3MB, time=5.18 memory used=644.6MB, alloc=92.3MB, time=5.90 memory used=709.8MB, alloc=116.3MB, time=6.68 memory used=777.4MB, alloc=116.3MB, time=7.47 memory used=858.3MB, alloc=116.3MB, time=8.16 memory used=910.9MB, alloc=116.3MB, time=8.39 memory used=968.7MB, alloc=116.3MB, time=9.04 memory used=1020.3MB, alloc=116.3MB, time=9.29 memory used=1073.4MB, alloc=116.3MB, time=9.52 memory used=1133.1MB, alloc=116.3MB, time=10.44 memory used=1198.3MB, alloc=116.3MB, time=10.94 memory used=1249.0MB, alloc=116.3MB, time=11.11 memory used=1291.0MB, alloc=116.3MB, time=11.22 memory used=1347.5MB, alloc=116.3MB, time=11.56 memory used=1384.9MB, alloc=116.3MB, time=11.67 memory used=1431.6MB, alloc=116.3MB, time=12.42 memory used=1493.3MB, alloc=116.3MB, time=12.85 memory used=1529.6MB, alloc=116.3MB, time=12.99 memory used=1574.1MB, alloc=116.3MB, time=13.11 memory used=1610.5MB, alloc=116.3MB, time=13.22 memory used=1643.8MB, alloc=116.3MB, time=13.32 memory used=1717.9MB, alloc=116.3MB, time=13.79 memory used=1808.6MB, alloc=116.3MB, time=14.83 memory used=1901.2MB, alloc=116.3MB, time=15.30 memory used=1971.0MB, alloc=116.4MB, time=15.83 memory used=2019.4MB, alloc=116.4MB, time=16.03 memory used=2074.6MB, alloc=116.4MB, time=16.93 memory used=2143.2MB, alloc=116.4MB, time=17.42 memory used=2179.8MB, alloc=116.4MB, time=17.54 memory used=2218.9MB, alloc=116.4MB, time=17.67 memory used=2274.6MB, alloc=116.4MB, time=18.03 memory used=2309.3MB, alloc=116.4MB, time=18.16 memory used=2346.7MB, alloc=116.4MB, time=18.28 memory used=2411.4MB, alloc=116.4MB, time=19.34 memory used=2448.0MB, alloc=116.4MB, time=19.47 memory used=2487.4MB, alloc=116.4MB, time=19.60 memory used=2527.6MB, alloc=116.4MB, time=19.72 memory used=2557.1MB, alloc=116.4MB, time=19.84 memory used=2598.8MB, alloc=116.4MB, time=20.01 memory used=2673.6MB, alloc=140.4MB, time=20.55 memory used=2750.2MB, alloc=396.4MB, time=21.25 memory used=2859.9MB, alloc=396.4MB, time=22.27 memory used=2961.7MB, alloc=420.4MB, time=23.25 memory used=3054.6MB, alloc=420.4MB, time=25.50 memory used=3115.3MB, alloc=420.4MB, time=25.70 memory used=3173.3MB, alloc=420.4MB, time=25.88 memory used=3227.3MB, alloc=420.4MB, time=26.03 memory used=3313.3MB, alloc=420.4MB, time=26.40 memory used=3384.1MB, alloc=420.4MB, time=26.71 memory used=3455.6MB, alloc=420.4MB, time=26.97 memory used=3538.4MB, alloc=420.4MB, time=27.73 memory used=3600.7MB, alloc=420.4MB, time=27.91 memory used=3670.4MB, alloc=420.4MB, time=28.21 memory used=3825.0MB, alloc=420.4MB, time=31.68 memory used=3894.6MB, alloc=420.4MB, time=31.94 memory used=3960.2MB, alloc=420.4MB, time=32.17 memory used=4004.5MB, alloc=420.4MB, time=32.33 memory used=4056.9MB, alloc=420.4MB, time=32.50 memory used=4118.1MB, alloc=420.4MB, time=32.67 memory used=4187.9MB, alloc=420.4MB, time=32.86 memory used=4371.0MB, alloc=420.4MB, time=33.36 memory used=4540.2MB, alloc=420.4MB, time=33.69 memory used=4750.8MB, alloc=420.4MB, time=34.05 memory used=4965.5MB, alloc=420.4MB, time=34.92 memory used=5074.9MB, alloc=420.4MB, time=35.71 memory used=5206.9MB, alloc=444.4MB, time=37.11 memory used=5330.1MB, alloc=444.4MB, time=37.67 memory used=5443.7MB, alloc=444.4MB, time=38.08 memory used=5551.8MB, alloc=444.4MB, time=38.44 memory used=5696.5MB, alloc=444.4MB, time=39.34 memory used=5806.0MB, alloc=444.4MB, time=39.70 memory used=5920.8MB, alloc=444.4MB, time=40.06 memory used=6039.1MB, alloc=444.4MB, time=40.39 memory used=6167.2MB, alloc=444.4MB, time=40.76 memory used=6303.5MB, alloc=444.4MB, time=41.13 memory used=6446.9MB, alloc=444.4MB, time=41.48 memory used=6627.2MB, alloc=444.4MB, time=42.06 memory used=6744.2MB, alloc=444.4MB, time=42.49 memory used=6849.1MB, alloc=444.4MB, time=42.86 memory used=6988.8MB, alloc=444.4MB, time=43.40 memory used=7123.4MB, alloc=444.4MB, time=44.11 memory used=7273.3MB, alloc=444.4MB, time=45.13 memory used=7422.0MB, alloc=444.4MB, time=46.25 memory used=7580.2MB, alloc=444.4MB, time=47.45 memory used=7720.9MB, alloc=468.4MB, time=48.32 memory used=7873.3MB, alloc=468.4MB, time=49.16 memory used=8065.6MB, alloc=468.4MB, time=51.10 memory used=8305.2MB, alloc=468.4MB, time=55.01 memory used=8506.5MB, alloc=492.4MB, time=58.96 memory used=8794.4MB, alloc=492.4MB, time=62.99 memory used=8999.7MB, alloc=516.4MB, time=64.80 memory used=9272.6MB, alloc=516.4MB, time=67.49 memory used=9507.5MB, alloc=516.4MB, time=69.28 memory used=9762.8MB, alloc=540.4MB, time=72.60 memory used=9959.8MB, alloc=540.4MB, time=75.01 memory used=10654.7MB, alloc=564.4MB, time=89.79 memory used=11186.4MB, alloc=564.4MB, time=105.14 memory used=11494.0MB, alloc=588.4MB, time=108.90 memory used=11677.7MB, alloc=588.4MB, time=112.29 memory used=12036.3MB, alloc=612.4MB, time=116.94 memory used=12197.4MB, alloc=636.4MB, time=119.17 memory used=12478.3MB, alloc=636.4MB, time=121.51 memory used=12810.8MB, alloc=636.4MB, time=123.53 memory used=13153.1MB, alloc=636.4MB, time=125.81 memory used=13361.6MB, alloc=660.4MB, time=130.63 memory used=13596.3MB, alloc=684.4MB, time=137.56 memory used=13837.2MB, alloc=708.4MB, time=145.06 memory used=14088.7MB, alloc=732.4MB, time=153.28 memory used=14344.0MB, alloc=756.4MB, time=162.58 memory used=14623.3MB, alloc=780.4MB, time=172.70 memory used=14926.5MB, alloc=804.4MB, time=183.63 memory used=15253.7MB, alloc=828.4MB, time=195.39 memory used=15604.8MB, alloc=828.4MB, time=208.30 memory used=15955.8MB, alloc=852.4MB, time=221.73 memory used=16330.9MB, alloc=852.4MB, time=235.34 memory used=16705.8MB, alloc=852.4MB, time=248.50 memory used=17080.7MB, alloc=876.4MB, time=261.92 memory used=17479.6MB, alloc=876.4MB, time=276.01 memory used=17878.3MB, alloc=900.4MB, time=290.07 |\^/| 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(); 1428523498 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 2 F := [14 z + 20 x - 15 z, 8 x - 9 x z + 2 x z ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 G := [12 x y + 9 z + 14 y, -10 z - 7 x] > Problem := [F,G]; 2 3 2 2 Problem := [[14 z + 20 x - 15 z, 8 x - 9 x z + 2 x z ], 2 3 2 [12 x y + 9 z + 14 y, -10 z - 7 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=25.9MB, alloc=32.3MB, time=0.47 memory used=46.8MB, alloc=56.3MB, time=0.80 memory used=88.5MB, alloc=60.3MB, time=1.41 memory used=129.9MB, alloc=84.3MB, time=2.14 memory used=192.6MB, alloc=84.3MB, time=3.15 memory used=247.6MB, alloc=108.3MB, time=4.08 memory used=316.4MB, alloc=132.3MB, time=5.98 memory used=399.3MB, alloc=156.3MB, time=8.16 N1 := 2257 > GB := Basis(F, plex(op(vars))); 5 4 3 4 3 2 GB := [1568 x - 175 x - 25 x , -4704 x - 595 x - 200 x + 150 x z, 2 14 z - 15 z + 20 x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=509.3MB, alloc=164.3MB, time=9.72 memory used=634.1MB, alloc=444.3MB, time=11.60 N2 := 1325 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 3 2 2 3 2 H := [14 z - 15 z + 20 x, 8 x - 9 x z + 2 x z , 9 z + 12 y x + 14 y, 2 -10 z - 7 x] > J:=[op(GB),op(G)]; 5 4 3 4 3 2 J := [1568 x - 175 x - 25 x , -4704 x - 595 x - 200 x + 150 x z, 2 3 2 2 14 z - 15 z + 20 x, 9 z + 12 y x + 14 y, -10 z - 7 x] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 9, 10, 3, 3, 1, 3, 1, 1/4, 1, 6/11, 2/11, 6/11, 5, 10, 16, 5, 5, 1, 3, 1, 1/5, 4/5, 2/3, 2/15, 1/3, -1, -6, -2] > save(F, G, cat("ranSet/33", convert(F, string),".txt")); > quit memory used=681.3MB, alloc=444.3MB, time=12.68 |\^/| 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(); 1428523511 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 F := [-8 x z + 8 y + 16, -7 x y - 5 y z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 G := [-14 x z + 13 x y + 18 y, -4 x y z - 2 y z - 7 x] > Problem := [F,G]; 2 Problem := [[-8 x z + 8 y + 16, -7 x y - 5 y z], 2 2 [-14 x z + 13 x y + 18 y, -4 x y z - 2 y z - 7 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.14 memory used=25.9MB, alloc=32.3MB, time=0.39 memory used=46.2MB, alloc=32.3MB, time=0.64 memory used=64.9MB, alloc=60.3MB, time=0.90 memory used=108.2MB, alloc=68.3MB, time=1.41 memory used=149.1MB, alloc=92.3MB, time=1.93 memory used=214.6MB, alloc=92.3MB, time=2.71 memory used=278.6MB, alloc=92.3MB, time=3.44 memory used=340.3MB, alloc=116.3MB, time=4.17 memory used=402.0MB, alloc=372.3MB, time=4.88 memory used=490.5MB, alloc=372.3MB, time=6.05 memory used=580.0MB, alloc=396.3MB, time=7.07 memory used=689.4MB, alloc=420.3MB, time=8.51 memory used=811.2MB, alloc=444.3MB, time=10.27 memory used=943.0MB, alloc=468.3MB, time=12.25 memory used=1093.3MB, alloc=492.3MB, time=14.59 memory used=1242.0MB, alloc=516.3MB, time=18.51 memory used=1387.2MB, alloc=540.3MB, time=23.59 memory used=1555.9MB, alloc=564.3MB, time=29.37 memory used=1748.6MB, alloc=588.3MB, time=35.73 memory used=1965.4MB, alloc=588.3MB, time=42.95 N1 := 5473 > GB := Basis(F, plex(op(vars))); 2 3 2 GB := [7 x y + 5 y + 10 y, z x - y - 2, 7 x y + 5 y z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=2180.4MB, alloc=588.3MB, time=47.41 memory used=2319.4MB, alloc=588.3MB, time=49.44 memory used=2437.9MB, alloc=588.3MB, time=51.20 memory used=2552.1MB, alloc=588.3MB, time=52.88 memory used=2666.2MB, alloc=588.3MB, time=54.65 memory used=2844.4MB, alloc=612.3MB, time=57.54 memory used=3016.8MB, alloc=636.3MB, time=60.49 memory used=3291.7MB, alloc=660.3MB, time=68.28 memory used=3536.0MB, alloc=684.3MB, time=77.66 memory used=3804.5MB, alloc=708.3MB, time=88.01 N2 := 5473 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 H := [-8 x z + 8 y + 16, -7 x y - 5 y z, -14 z x + 13 y x + 18 y, 2 -4 x y z - 2 y z - 7 x] > J:=[op(GB),op(G)]; 2 3 2 J := [7 x y + 5 y + 10 y, z x - y - 2, 7 x y + 5 y z, 2 2 -14 z x + 13 y x + 18 y, -4 x y z - 2 y z - 7 x] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 12, 10, 3, 1, 2, 2, 1, 1, 1, 6/11, 7/11, 5/11, 5, 14, 13, 3, 2, 3, 2, 1, 1, 4/5, 1/2, 5/7, 5/14, -2, -3, 0] > save(F, G, cat("ranSet/33", convert(F, string),".txt")); > quit memory used=4057.2MB, alloc=708.3MB, time=97.75 |\^/| 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(); 1428523612 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 F := [17 x y - 2 x y + 17 y z, -2 x y + x y z - 7] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 G := [18 x z + 15 x y + 5 z, 2 y z + 3 y + 5] > Problem := [F,G]; 2 2 Problem := [[17 x y - 2 x y + 17 y z, -2 x y + x y z - 7], 2 2 [18 x z + 15 x y + 5 z, 2 y z + 3 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=4.2MB, alloc=32.3MB, time=0.18 memory used=25.3MB, alloc=32.3MB, time=0.50 memory used=45.1MB, alloc=32.3MB, time=0.80 memory used=64.1MB, alloc=56.3MB, time=1.10 memory used=106.8MB, alloc=68.3MB, time=1.75 memory used=148.1MB, alloc=92.3MB, time=2.37 memory used=214.4MB, alloc=92.3MB, time=3.31 memory used=279.2MB, alloc=92.3MB, time=4.28 memory used=345.9MB, alloc=116.3MB, time=5.23 memory used=416.2MB, alloc=372.3MB, time=6.34 memory used=502.9MB, alloc=396.3MB, time=7.60 memory used=618.9MB, alloc=396.3MB, time=9.24 memory used=729.7MB, alloc=420.3MB, time=10.98 memory used=868.3MB, alloc=444.3MB, time=13.16 memory used=1008.7MB, alloc=468.3MB, time=15.55 memory used=1158.3MB, alloc=492.3MB, time=18.33 memory used=1326.5MB, alloc=516.3MB, time=21.27 memory used=1521.8MB, alloc=540.3MB, time=24.94 memory used=1738.5MB, alloc=564.3MB, time=27.73 memory used=1935.6MB, alloc=588.3MB, time=30.68 memory used=2100.6MB, alloc=612.3MB, time=33.50 memory used=2329.9MB, alloc=636.3MB, time=40.08 memory used=2554.2MB, alloc=660.3MB, time=47.51 memory used=2787.5MB, alloc=684.3MB, time=55.23 memory used=3029.8MB, alloc=708.3MB, time=63.87 memory used=3282.7MB, alloc=732.3MB, time=73.84 memory used=3559.5MB, alloc=756.3MB, time=84.62 memory used=3860.3MB, alloc=780.3MB, time=96.05 memory used=4184.9MB, alloc=804.3MB, time=108.45 memory used=4533.5MB, alloc=804.3MB, time=120.65 memory used=4882.1MB, alloc=804.3MB, time=134.03 memory used=5230.7MB, alloc=828.3MB, time=146.79 memory used=5603.1MB, alloc=828.3MB, time=161.34 memory used=5975.5MB, alloc=828.3MB, time=175.98 memory used=6347.6MB, alloc=852.3MB, time=190.04 memory used=6743.7MB, alloc=852.3MB, time=204.42 memory used=7139.9MB, alloc=876.3MB, time=218.58 memory used=7560.0MB, alloc=900.3MB, time=233.47 N1 := 13643 > GB := Basis(F, plex(op(vars))); 2 2 2 2 GB := [17 y x + 34 y x - 2 y x + 119, 17 y x + 17 z - 2 x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=8013.6MB, alloc=900.3MB, time=247.65 memory used=8102.5MB, alloc=900.3MB, time=249.66 memory used=8202.9MB, alloc=900.3MB, time=251.67 memory used=8333.6MB, alloc=900.3MB, time=254.43 memory used=8488.8MB, alloc=900.3MB, time=257.33 memory used=8657.0MB, alloc=900.3MB, time=261.67 memory used=9136.9MB, alloc=924.3MB, time=279.24 N2 := 4147 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 H := [17 x y - 2 x y + 17 y z, -2 x y + x y z - 7, 18 z x + 15 y x + 5 z, 2 2 z y + 3 y + 5] > J:=[op(GB),op(G)]; 2 2 2 2 J := [17 y x + 34 y x - 2 y x + 119, 17 y x + 17 z - 2 x, 2 2 18 z x + 15 y x + 5 z, 2 z y + 3 y + 5] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 11, 12, 3, 1, 2, 2, 3/4, 1, 1, 1/2, 2/3, 5/12, 4, 10, 12, 4, 2, 2, 2, 3/4, 1, 3/4, 7/13, 7/13, 4/13, 1, 0, -1] > save(F, G, cat("ranSet/33", convert(F, string),".txt")); > quit memory used=9155.0MB, alloc=924.3MB, time=279.69 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428523902 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 2 F := [-17 x z - y z + 2 y, -3 x z + 2 x z - 3 y z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 G := [-4 y z + 14 y + 8, 7 x z + 3 x z + 5 z] > Problem := [F,G]; 2 2 2 2 2 Problem := [[-17 x z - y z + 2 y, -3 x z + 2 x z - 3 y z], 2 2 2 2 [-4 y z + 14 y + 8, 7 x z + 3 x z + 5 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.16 memory used=26.3MB, alloc=32.3MB, time=0.46 memory used=46.8MB, alloc=32.3MB, time=0.73 memory used=66.2MB, alloc=56.3MB, time=0.97 memory used=104.6MB, alloc=60.3MB, time=1.46 memory used=142.5MB, alloc=84.3MB, time=1.93 memory used=204.6MB, alloc=92.3MB, time=2.75 memory used=266.0MB, alloc=116.3MB, time=3.64 memory used=334.2MB, alloc=116.3MB, time=4.50 memory used=409.4MB, alloc=372.3MB, time=5.45 memory used=498.4MB, alloc=396.3MB, time=6.43 memory used=606.0MB, alloc=396.3MB, time=7.80 memory used=712.2MB, alloc=420.3MB, time=9.11 memory used=841.9MB, alloc=444.3MB, time=10.56 memory used=979.9MB, alloc=444.3MB, time=12.10 memory used=1113.4MB, alloc=468.3MB, time=13.51 memory used=1230.2MB, alloc=468.3MB, time=14.79 memory used=1359.0MB, alloc=468.3MB, time=16.05 memory used=1520.2MB, alloc=492.3MB, time=18.35 memory used=1731.1MB, alloc=516.3MB, time=20.31 memory used=1900.7MB, alloc=540.3MB, time=23.88 memory used=2055.6MB, alloc=564.3MB, time=28.90 N1 := 3287 > GB := Basis(F, plex(op(vars))); 4 2 3 5 2 GB := [153 x y + 312 x y + 159 y - 8 x y , 3 2 2 4 2 3 102 x z + 159 x y + 159 y - 8 x y, -3 x y + 2 x y z - 3 y , 2 2 2 2 51 x z + 53 y z - 4 y, -3 x z + 53 x z - 6 y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=2257.6MB, alloc=564.3MB, time=33.34 memory used=2388.8MB, alloc=564.3MB, time=35.14 memory used=2504.8MB, alloc=564.3MB, time=36.80 memory used=2598.0MB, alloc=564.3MB, time=38.12 memory used=2688.3MB, alloc=564.3MB, time=39.51 memory used=2799.5MB, alloc=564.3MB, time=41.21 memory used=2891.0MB, alloc=564.3MB, time=42.68 memory used=2969.8MB, alloc=564.3MB, time=44.04 memory used=3048.1MB, alloc=588.3MB, time=45.37 memory used=3125.7MB, alloc=588.3MB, time=46.64 memory used=3235.3MB, alloc=588.3MB, time=47.72 memory used=3306.4MB, alloc=588.3MB, time=48.92 memory used=3354.5MB, alloc=588.3MB, time=49.77 memory used=3430.2MB, alloc=588.3MB, time=51.24 memory used=3492.4MB, alloc=588.3MB, time=52.17 memory used=3554.1MB, alloc=588.3MB, time=53.27 memory used=3598.4MB, alloc=588.3MB, time=54.20 memory used=3801.8MB, alloc=612.3MB, time=57.21 memory used=3983.1MB, alloc=636.3MB, time=59.84 memory used=4168.7MB, alloc=660.3MB, time=62.24 memory used=4370.1MB, alloc=684.3MB, time=64.48 memory used=4534.8MB, alloc=684.3MB, time=67.31 memory used=4686.4MB, alloc=708.3MB, time=69.90 memory used=4852.0MB, alloc=708.3MB, time=72.28 memory used=4989.7MB, alloc=732.3MB, time=74.55 memory used=5078.7MB, alloc=732.3MB, time=76.59 memory used=5196.3MB, alloc=732.3MB, time=78.73 memory used=5291.9MB, alloc=732.3MB, time=80.65 memory used=5393.0MB, alloc=732.3MB, time=82.50 memory used=5797.0MB, alloc=756.3MB, time=88.17 memory used=6196.6MB, alloc=780.3MB, time=94.28 memory used=6578.2MB, alloc=804.3MB, time=100.25 memory used=6921.5MB, alloc=828.3MB, time=105.76 memory used=7269.8MB, alloc=852.3MB, time=111.23 memory used=7597.1MB, alloc=876.3MB, time=116.46 memory used=7932.3MB, alloc=900.3MB, time=122.23 memory used=8157.3MB, alloc=924.3MB, time=126.58 memory used=8363.9MB, alloc=948.3MB, time=131.04 memory used=8587.4MB, alloc=972.3MB, time=135.71 memory used=8826.3MB, alloc=996.3MB, time=140.61 memory used=8994.2MB, alloc=1020.3MB, time=144.75 memory used=9603.6MB, alloc=1044.3MB, time=154.43 memory used=10272.1MB, alloc=1068.3MB, time=162.52 memory used=10983.1MB, alloc=1092.3MB, time=172.08 memory used=11621.1MB, alloc=1116.3MB, time=184.35 memory used=12302.3MB, alloc=1140.3MB, time=194.99 memory used=12922.7MB, alloc=1164.3MB, time=207.25 memory used=13568.4MB, alloc=1188.3MB, time=219.25 memory used=14245.6MB, alloc=1212.3MB, time=232.47 memory used=14836.9MB, alloc=1236.3MB, time=245.41 memory used=15359.9MB, alloc=1260.3MB, time=255.45 memory used=15816.4MB, alloc=1284.3MB, time=266.51 memory used=16261.6MB, alloc=1308.3MB, time=277.01 memory used=16674.8MB, alloc=1332.3MB, time=286.97 memory used=17073.0MB, alloc=1356.3MB, time=297.59 memory used=17410.7MB, alloc=1380.3MB, time=305.62 memory used=17741.7MB, alloc=1404.3MB, time=315.23 |\^/| 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(); 1428524202 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 2 F := [-14 y z + 16 z - 18, -10 x z - 4 y z + 4 x ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 G := [10 x - 7 x y + 5 z, -8 x z - 6 x ] > Problem := [F,G]; 2 2 2 2 2 Problem := [[-14 y z + 16 z - 18, -10 x z - 4 y z + 4 x ], 2 2 2 [10 x - 7 x y + 5 z, -8 x z - 6 x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=32.5MB, alloc=44.3MB, time=0.60 memory used=58.4MB, alloc=68.3MB, time=0.99 memory used=98.3MB, alloc=68.3MB, time=1.55 memory used=147.5MB, alloc=76.3MB, time=2.29 memory used=199.0MB, alloc=100.3MB, time=2.96 memory used=269.5MB, alloc=100.3MB, time=4.02 memory used=339.7MB, alloc=100.3MB, time=5.06 memory used=408.4MB, alloc=124.3MB, time=6.12 memory used=484.9MB, alloc=380.3MB, time=7.16 memory used=575.5MB, alloc=404.3MB, time=8.51 memory used=694.7MB, alloc=404.3MB, time=10.05 memory used=772.3MB, alloc=404.3MB, time=10.64 memory used=897.8MB, alloc=428.3MB, time=12.29 memory used=1045.3MB, alloc=428.3MB, time=13.87 memory used=1165.8MB, alloc=428.3MB, time=14.63 memory used=1289.3MB, alloc=452.3MB, time=16.56 memory used=1436.8MB, alloc=476.3MB, time=18.86 memory used=1594.6MB, alloc=500.3MB, time=21.29 memory used=1762.6MB, alloc=524.3MB, time=24.10 memory used=1944.2MB, alloc=548.3MB, time=27.05 memory used=2127.7MB, alloc=572.3MB, time=29.99 memory used=2320.1MB, alloc=596.3MB, time=33.23 memory used=2544.2MB, alloc=620.3MB, time=36.11 memory used=2737.1MB, alloc=644.3MB, time=39.23 memory used=2965.5MB, alloc=668.3MB, time=45.25 memory used=3173.6MB, alloc=692.3MB, time=52.21 memory used=3390.5MB, alloc=716.3MB, time=59.69 memory used=3618.5MB, alloc=740.3MB, time=68.07 memory used=3859.1MB, alloc=764.3MB, time=77.11 memory used=4112.8MB, alloc=788.3MB, time=86.73 memory used=4380.9MB, alloc=812.3MB, time=96.89 memory used=4660.0MB, alloc=836.3MB, time=108.29 memory used=4955.1MB, alloc=860.3MB, time=120.56 memory used=5274.2MB, alloc=884.3MB, time=133.77 memory used=5617.2MB, alloc=908.3MB, time=148.15 memory used=5984.0MB, alloc=932.3MB, time=163.34 memory used=6374.9MB, alloc=956.3MB, time=179.38 memory used=6789.7MB, alloc=980.3MB, time=196.45 memory used=7228.4MB, alloc=1004.3MB, time=214.69 memory used=7691.0MB, alloc=1004.3MB, time=234.44 memory used=8153.6MB, alloc=1004.3MB, time=254.23 |\^/| 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(); 1428524502 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 F := [-17 z + 10 z , 10 x z + 6 y z - 2 z ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 2 3 G := [-20 y + 17 y z - 8 x y, 6 x y - 8 y z - 2 z ] > Problem := [F,G]; 3 2 2 Problem := [[-17 z + 10 z , 10 x z + 6 y z - 2 z ], 3 2 2 2 3 [-20 y + 17 y z - 8 x y, 6 x y - 8 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=4.2MB, alloc=32.3MB, time=0.17 memory used=26.5MB, alloc=32.3MB, time=0.48 memory used=47.8MB, alloc=32.3MB, time=0.80 memory used=66.8MB, alloc=56.3MB, time=1.10 memory used=105.6MB, alloc=60.3MB, time=1.70 memory used=142.6MB, alloc=84.3MB, time=2.27 memory used=203.9MB, alloc=92.3MB, time=3.23 memory used=263.5MB, alloc=116.3MB, time=4.16 memory used=346.2MB, alloc=140.3MB, time=5.44 memory used=422.2MB, alloc=396.3MB, time=6.63 memory used=524.5MB, alloc=420.3MB, time=8.32 memory used=662.7MB, alloc=444.3MB, time=10.18 memory used=812.8MB, alloc=468.3MB, time=12.47 memory used=974.3MB, alloc=492.3MB, time=15.30 memory used=1145.7MB, alloc=516.3MB, time=18.39 memory used=1328.3MB, alloc=540.3MB, time=21.70 memory used=1519.1MB, alloc=564.3MB, time=25.19 memory used=1673.9MB, alloc=588.3MB, time=28.09 memory used=1856.1MB, alloc=612.3MB, time=33.56 memory used=2039.5MB, alloc=636.3MB, time=39.74 memory used=2233.2MB, alloc=660.3MB, time=46.64 memory used=2438.0MB, alloc=684.3MB, time=54.29 memory used=2649.3MB, alloc=708.3MB, time=63.12 memory used=2884.5MB, alloc=732.3MB, time=72.92 memory used=3143.6MB, alloc=756.3MB, time=83.54 memory used=3426.7MB, alloc=780.3MB, time=95.19 memory used=3733.8MB, alloc=804.3MB, time=107.83 memory used=4064.8MB, alloc=828.3MB, time=121.51 memory used=4419.7MB, alloc=852.3MB, time=136.18 memory used=4798.6MB, alloc=852.3MB, time=150.72 memory used=5177.4MB, alloc=852.3MB, time=163.61 memory used=5556.1MB, alloc=876.3MB, time=176.77 memory used=5958.7MB, alloc=876.3MB, time=190.83 memory used=6361.1MB, alloc=900.3MB, time=204.94 memory used=6787.5MB, alloc=900.3MB, time=219.81 memory used=7213.8MB, alloc=924.3MB, time=234.68 memory used=7664.2MB, alloc=948.3MB, time=249.98 N1 := 14355 > GB := Basis(F, plex(op(vars))); 2 2 2 GB := [425 x z + 510 x y z + 153 y z - 50 x z - 30 y z, -5 x z - 3 y z + z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428524802 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 F := [-19 x z - 6 z + 19, 6 y z - 4 z + 8 x] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 G := [12 x - 2 y + 9, -9 x y z - 7 x + 8] > Problem := [F,G]; 2 2 Problem := [[-19 x z - 6 z + 19, 6 y z - 4 z + 8 x], 2 2 [12 x - 2 y + 9, -9 x y z - 7 x + 8]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.4MB, alloc=32.3MB, time=0.51 memory used=46.9MB, alloc=56.3MB, time=0.83 memory used=88.0MB, alloc=60.3MB, time=1.42 memory used=127.4MB, alloc=84.3MB, time=1.91 memory used=176.0MB, alloc=84.3MB, time=2.62 memory used=233.7MB, alloc=108.3MB, time=3.59 memory used=312.1MB, alloc=116.3MB, time=4.70 memory used=385.5MB, alloc=140.3MB, time=5.77 memory used=474.5MB, alloc=164.3MB, time=7.34 memory used=570.8MB, alloc=188.3MB, time=9.75 memory used=678.2MB, alloc=212.3MB, time=13.11 memory used=809.5MB, alloc=212.3MB, time=17.13 memory used=941.0MB, alloc=236.3MB, time=21.06 N1 := 3961 > GB := Basis(F, plex(op(vars))); 2 3 2 2 GB := [1083 y x + 1444 x + 342 y + 912 x + 144 x - 722, 2 2 -76 x - 57 y - 24 x + 38 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1057.1MB, alloc=236.3MB, time=23.12 N2 := 825 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 H := [-19 x z - 6 z + 19, 6 y z - 4 z + 8 x, -2 y + 12 x + 9, -9 x y z - 7 x + 8] > J:=[op(GB),op(G)]; 2 3 2 2 J := [1083 y x + 1444 x + 342 y + 912 x + 144 x - 722, 2 2 2 2 -76 x - 57 y - 24 x + 38 z, -2 y + 12 x + 9, -9 x y z - 7 x + 8] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 10, 10, 3, 2, 2, 2, 1, 3/4, 3/4, 5/12, 1/4, 5/12, 4, 10, 10, 3, 3, 2, 1, 1, 1, 1/2, 9/16, 5/16, 1/8, 0, 0, 0] > save(F, G, cat("ranSet/33", convert(F, string),".txt")); > quit memory used=1119.2MB, alloc=492.3MB, time=24.24 |\^/| 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(); 1428524827 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 3 2 F := [-4 x z + 17 x z - 13 x, 10 y z - 6 z + 5 z ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 G := [12 y z + 3 x - 8 x, -4 x y + 10 y - 9 x] > Problem := [F,G]; 2 2 2 3 2 Problem := [[-4 x z + 17 x z - 13 x, 10 y z - 6 z + 5 z ], 2 2 2 2 [12 y z + 3 x - 8 x, -4 x y + 10 y - 9 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.15 memory used=26.6MB, alloc=32.3MB, time=0.44 memory used=47.6MB, alloc=32.3MB, time=0.71 memory used=67.5MB, alloc=56.3MB, time=1.03 memory used=107.7MB, alloc=60.3MB, time=1.54 memory used=146.0MB, alloc=84.3MB, time=2.05 memory used=211.0MB, alloc=92.3MB, time=2.95 memory used=271.7MB, alloc=116.3MB, time=3.84 memory used=350.0MB, alloc=140.3MB, time=4.98 memory used=446.6MB, alloc=164.3MB, time=6.36 memory used=561.1MB, alloc=188.3MB, time=7.96 memory used=687.0MB, alloc=212.3MB, time=9.90 memory used=826.0MB, alloc=236.3MB, time=11.92 memory used=956.7MB, alloc=516.3MB, time=14.11 memory used=1100.5MB, alloc=540.3MB, time=17.63 memory used=1251.9MB, alloc=564.3MB, time=21.66 memory used=1415.1MB, alloc=588.3MB, time=26.24 memory used=1590.5MB, alloc=612.3MB, time=31.53 memory used=1780.1MB, alloc=636.3MB, time=37.90 memory used=1993.6MB, alloc=660.3MB, time=44.79 memory used=2231.1MB, alloc=684.3MB, time=52.56 memory used=2492.5MB, alloc=684.3MB, time=60.99 memory used=2753.9MB, alloc=684.3MB, time=69.52 memory used=3015.2MB, alloc=708.3MB, time=77.99 memory used=3300.5MB, alloc=708.3MB, time=87.26 memory used=3585.8MB, alloc=708.3MB, time=96.65 memory used=3871.1MB, alloc=732.3MB, time=105.76 memory used=4180.2MB, alloc=732.3MB, time=115.76 memory used=4489.4MB, alloc=732.3MB, time=125.85 memory used=4798.5MB, alloc=756.3MB, time=135.76 memory used=5131.5MB, alloc=756.3MB, time=146.59 memory used=5464.4MB, alloc=780.3MB, time=157.36 memory used=5821.3MB, alloc=804.3MB, time=168.63 N1 := 12885 > GB := Basis(F, plex(op(vars))); 3 2 4 2 2 2 2 GB := [-960 x y + 28900 x y + 3400 x y - 26520 x y + 1560 x + 559 x, 2 2 2 2 2 24 x z - 170 x y - 85 x z + 78 x, -40 x y + 170 x y z - 78 x z + 65 x, 2 2 2 3 2 -10 x y + 6 x z - 5 x z, -10 y z + 6 z - 5 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=6202.5MB, alloc=804.3MB, time=176.55 memory used=6562.2MB, alloc=804.3MB, time=181.94 memory used=6982.8MB, alloc=828.3MB, time=190.13 memory used=7393.3MB, alloc=852.3MB, time=197.67 memory used=7788.2MB, alloc=876.3MB, time=204.64 memory used=8167.1MB, alloc=900.3MB, time=211.66 memory used=8556.0MB, alloc=924.3MB, time=222.92 memory used=8912.1MB, alloc=948.3MB, time=235.41 memory used=9271.7MB, alloc=972.3MB, time=248.59 memory used=9638.6MB, alloc=996.3MB, time=261.47 memory used=10015.6MB, alloc=1020.3MB, time=274.95 memory used=10404.5MB, alloc=1044.3MB, time=288.68 |\^/| 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(); 1428525127 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 F := [-x y + 20 z + 18, -3 x - 9 x y + 7 y ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 G := [-17 y z - 15 z - 20, -9 y z + 4 z - 3] > Problem := [F,G]; 3 2 Problem := [[-x y + 20 z + 18, -3 x - 9 x y + 7 y ], 2 [-17 y z - 15 z - 20, -9 y z + 4 z - 3]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.1MB, alloc=32.3MB, time=0.16 memory used=26.3MB, alloc=32.3MB, time=0.48 memory used=47.2MB, alloc=32.3MB, time=0.78 memory used=66.9MB, alloc=56.3MB, time=1.08 memory used=107.2MB, alloc=60.3MB, time=1.65 memory used=146.2MB, alloc=60.3MB, time=2.20 memory used=185.6MB, alloc=84.3MB, time=2.84 memory used=231.7MB, alloc=84.3MB, time=3.61 memory used=285.9MB, alloc=116.3MB, time=4.54 memory used=360.1MB, alloc=140.3MB, time=5.79 memory used=452.7MB, alloc=164.3MB, time=7.38 memory used=562.2MB, alloc=188.3MB, time=9.31 memory used=670.2MB, alloc=468.3MB, time=11.25 memory used=805.1MB, alloc=492.3MB, time=14.88 memory used=945.7MB, alloc=516.3MB, time=18.88 memory used=1101.0MB, alloc=540.3MB, time=23.47 memory used=1267.9MB, alloc=564.3MB, time=29.38 memory used=1456.0MB, alloc=588.3MB, time=36.19 memory used=1668.0MB, alloc=588.3MB, time=43.79 memory used=1879.9MB, alloc=588.3MB, time=51.31 memory used=2091.8MB, alloc=612.3MB, time=58.68 memory used=2327.8MB, alloc=612.3MB, time=67.28 memory used=2563.7MB, alloc=636.3MB, time=75.79 N1 := 7803 > GB := Basis(F, plex(op(vars))); 3 2 GB := [-3 x - 9 x y + 7 y , -x y + 20 z + 18] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=2832.6MB, alloc=636.3MB, time=83.24 memory used=3014.2MB, alloc=636.3MB, time=86.35 memory used=3214.8MB, alloc=636.3MB, time=89.78 memory used=3405.9MB, alloc=660.3MB, time=93.25 memory used=3696.5MB, alloc=684.3MB, time=101.93 memory used=3975.5MB, alloc=708.3MB, time=112.12 memory used=4262.6MB, alloc=732.3MB, time=123.40 memory used=4573.6MB, alloc=756.3MB, time=134.52 memory used=4908.6MB, alloc=780.3MB, time=147.65 memory used=5267.7MB, alloc=804.3MB, time=161.31 N2 := 7803 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 H := [-x y + 20 z + 18, -3 x - 9 x y + 7 y , -17 y z - 15 z - 20, 2 -9 y z + 4 z - 3] > J:=[op(GB),op(G)]; 3 2 J := [-3 x - 9 x y + 7 y , -x y + 20 z + 18, -17 y z - 15 z - 20, 2 -9 y z + 4 z - 3] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 9, 10, 3, 3, 2, 1, 1/2, 1, 3/4, 1/4, 5/12, 5/12, 4, 9, 10, 3, 3, 2, 1, 1/2, 1, 3/4, 1/4, 5/12, 5/12, 0, 0, 0] > save(F, G, cat("ranSet/33", convert(F, string),".txt")); > quit memory used=5521.8MB, alloc=804.3MB, time=170.21 |\^/| 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(); 1428525303 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 3 2 F := [20 x + 15 z + 13 z, -x + 5 x y - 8 x y] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 G := [16 y z - 3 x y + 12 x z, -3 y z - 2 y z ] > Problem := [F,G]; 2 2 3 2 Problem := [[20 x + 15 z + 13 z, -x + 5 x y - 8 x y], 2 2 2 [16 y z - 3 x y + 12 x z, -3 y z - 2 y z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.3MB, alloc=32.3MB, time=0.48 memory used=47.7MB, alloc=32.3MB, time=0.79 memory used=67.5MB, alloc=56.3MB, time=1.09 memory used=107.3MB, alloc=60.3MB, time=1.68 memory used=149.2MB, alloc=84.3MB, time=2.36 memory used=210.0MB, alloc=84.3MB, time=3.33 memory used=272.3MB, alloc=108.3MB, time=4.14 memory used=346.9MB, alloc=140.3MB, time=5.44 memory used=430.2MB, alloc=164.3MB, time=7.81 memory used=527.0MB, alloc=164.3MB, time=11.10 memory used=623.9MB, alloc=188.3MB, time=14.44 N1 := 2997 > GB := Basis(F, plex(op(vars))); 3 2 2 2 GB := [-x + 5 x y - 8 x y, 15 z + 20 x + 13 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=731.6MB, alloc=188.3MB, time=16.32 memory used=879.3MB, alloc=444.3MB, time=18.74 memory used=1013.8MB, alloc=468.3MB, time=21.39 memory used=1137.2MB, alloc=492.3MB, time=25.99 N2 := 2997 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 3 2 2 H := [15 z + 20 x + 13 z, -x + 5 x y - 8 x y, 16 y z - 3 x y + 12 x z, 2 2 -3 y z - 2 y z ] > J:=[op(GB),op(G)]; 3 2 2 2 2 J := [-x + 5 x y - 8 x y, 15 z + 20 x + 13 z, 16 y z - 3 x y + 12 x z, 2 2 -3 y z - 2 y z ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 9, 11, 3, 3, 2, 2, 3/4, 3/4, 3/4, 6/11, 6/11, 6/11, 4, 9, 11, 3, 3, 2, 2, 3/4, 3/4, 3/4, 6/11, 6/11, 6/11, 0, 0, 0] > save(F, G, cat("ranSet/33", convert(F, string),".txt")); > quit memory used=1273.6MB, alloc=492.3MB, time=30.73 |\^/| 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(); 1428525339 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 3 2 F := [11 x y + 16 x y z + 15 z , -5 x y + 9 z + 8 x ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 G := [7 x y z - 14 y z + 17 x y, 3 y + 9 x] > Problem := [F,G]; 2 3 2 3 2 Problem := [[11 x y + 16 x y z + 15 z , -5 x y + 9 z + 8 x ], 2 3 [7 x y z - 14 y z + 17 x y, 3 y + 9 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=25.9MB, alloc=32.3MB, time=0.49 memory used=46.1MB, alloc=32.3MB, time=0.78 memory used=64.3MB, alloc=56.3MB, time=1.05 memory used=107.5MB, alloc=60.3MB, time=1.50 memory used=149.9MB, alloc=60.3MB, time=2.05 memory used=192.0MB, alloc=68.3MB, time=2.66 memory used=235.3MB, alloc=92.3MB, time=3.23 memory used=302.1MB, alloc=92.3MB, time=4.08 memory used=362.3MB, alloc=92.3MB, time=4.70 memory used=394.0MB, alloc=92.3MB, time=4.80 memory used=425.6MB, alloc=116.3MB, time=6.50 memory used=476.2MB, alloc=116.3MB, time=7.55 memory used=544.7MB, alloc=116.3MB, time=8.22 memory used=607.3MB, alloc=116.3MB, time=14.09 memory used=650.2MB, alloc=116.3MB, time=14.23 memory used=692.9MB, alloc=116.3MB, time=14.33 memory used=790.0MB, alloc=116.3MB, time=15.53 memory used=892.3MB, alloc=116.3MB, time=16.21 memory used=994.9MB, alloc=116.3MB, time=17.53 memory used=1104.1MB, alloc=116.3MB, time=19.36 memory used=1192.2MB, alloc=116.3MB, time=20.43 memory used=1263.6MB, alloc=116.3MB, time=21.26 memory used=1347.3MB, alloc=140.3MB, time=22.26 memory used=1453.6MB, alloc=140.3MB, time=23.41 memory used=1562.0MB, alloc=396.3MB, time=24.48 memory used=1680.0MB, alloc=420.3MB, time=26.12 memory used=1823.0MB, alloc=420.3MB, time=28.11 memory used=1955.1MB, alloc=420.3MB, time=29.75 memory used=2072.3MB, alloc=444.3MB, time=31.62 memory used=2222.4MB, alloc=468.3MB, time=33.87 memory used=2389.3MB, alloc=492.3MB, time=36.40 memory used=2563.3MB, alloc=516.3MB, time=39.50 memory used=2758.4MB, alloc=540.3MB, time=42.65 memory used=2946.1MB, alloc=564.3MB, time=47.71 memory used=3124.0MB, alloc=588.3MB, time=53.61 memory used=3314.3MB, alloc=612.3MB, time=60.36 memory used=3511.0MB, alloc=636.3MB, time=68.29 memory used=3731.1MB, alloc=660.3MB, time=77.76 memory used=3975.2MB, alloc=684.3MB, time=86.85 memory used=4243.2MB, alloc=684.3MB, time=97.19 memory used=4511.2MB, alloc=708.3MB, time=107.55 memory used=4803.2MB, alloc=708.3MB, time=118.90 memory used=5095.0MB, alloc=732.3MB, time=129.34 memory used=5411.0MB, alloc=732.3MB, time=141.06 memory used=5727.1MB, alloc=756.3MB, time=152.85 N1 := 9507 > GB := Basis(F, plex(op(vars))); 4 3 3 4 2 5 6 4 2 GB := [15625 x y + 123315 x y + 81675 x y + 35937 x y - 75000 x y 3 3 2 4 4 3 2 4 - 296304 x y - 130680 x y + 120000 x y + 158400 x y - 64000 x , 4 2 3 3 2 4 5 4 -15625 x y - 123315 x y - 81675 x y - 35937 x y + 75000 x y 3 2 2 3 4 3 3 + 296304 x y + 130680 x y - 80000 x - 105600 x y + 76800 x z, 2 2 2 4 2 3 3 25 x y + 33 x y + 48 x y z - 40 x , -78125 x y - 616575 x y 2 4 5 4 3 2 4 - 408375 x y - 179685 x y + 250000 x y + 495000 x y - 287496 x y 4 3 2 2 2 2 3 - 200000 x + 1050432 x y + 696960 x y + 737280 x z - 422400 x , 2 3 2 -5 x y + 9 z + 8 x ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=5847.5MB, alloc=756.3MB, time=155.26 memory used=6006.2MB, alloc=756.3MB, time=157.76 memory used=6281.0MB, alloc=756.3MB, time=160.27 memory used=6604.1MB, alloc=756.3MB, time=165.12 memory used=6791.3MB, alloc=756.3MB, time=167.09 memory used=7007.5MB, alloc=756.3MB, time=172.97 memory used=7262.9MB, alloc=756.3MB, time=175.06 memory used=7490.9MB, alloc=756.3MB, time=186.34 memory used=7704.1MB, alloc=756.3MB, time=188.65 memory used=7882.6MB, alloc=756.3MB, time=190.34 memory used=8075.8MB, alloc=756.3MB, time=192.19 memory used=8343.5MB, alloc=780.3MB, time=208.30 memory used=9555.5MB, alloc=780.3MB, time=212.74 memory used=10541.8MB, alloc=780.3MB, time=217.40 memory used=11325.3MB, alloc=780.3MB, time=222.14 memory used=12932.1MB, alloc=780.3MB, time=229.31 memory used=13368.8MB, alloc=780.3MB, time=232.76 memory used=13473.0MB, alloc=812.5MB, time=238.85 memory used=13481.2MB, alloc=820.7MB, time=239.33 memory used=13489.4MB, alloc=828.9MB, time=239.94 memory used=13497.6MB, alloc=837.1MB, time=240.46 memory used=13505.8MB, alloc=812.5MB, time=241.06 memory used=13730.0MB, alloc=804.3MB, time=242.17 memory used=13997.0MB, alloc=804.3MB, time=243.24 memory used=14227.4MB, alloc=804.3MB, time=244.16 |\^/| 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(); 1428525639 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 2 F := [-5 x y - 20 x y z - 18 x z , 9 x y - 7 x z - 6 y ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 3 G := [3 z + 10 z + 6, -10 y + 10 x + z] > Problem := [F,G]; 2 2 2 2 2 Problem := [[-5 x y - 20 x y z - 18 x z , 9 x y - 7 x z - 6 y ], 3 2 3 [3 z + 10 z + 6, -10 y + 10 x + z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=24.5MB, alloc=32.3MB, time=0.45 memory used=46.3MB, alloc=36.3MB, time=0.70 memory used=66.6MB, alloc=60.3MB, time=0.99 memory used=111.7MB, alloc=68.3MB, time=1.53 memory used=152.1MB, alloc=68.3MB, time=1.78 memory used=183.8MB, alloc=68.3MB, time=1.94 memory used=222.8MB, alloc=68.3MB, time=2.12 memory used=245.6MB, alloc=68.3MB, time=2.20 memory used=277.3MB, alloc=68.3MB, time=2.35 memory used=311.1MB, alloc=68.3MB, time=2.45 memory used=334.8MB, alloc=68.3MB, time=2.52 memory used=369.1MB, alloc=68.3MB, time=3.72 memory used=407.3MB, alloc=68.3MB, time=5.35 memory used=433.9MB, alloc=68.3MB, time=5.42 memory used=453.4MB, alloc=68.3MB, time=5.48 memory used=478.2MB, alloc=68.3MB, time=5.55 memory used=510.9MB, alloc=68.3MB, time=5.70 memory used=552.4MB, alloc=68.3MB, time=6.23 memory used=581.1MB, alloc=68.3MB, time=6.37 memory used=613.4MB, alloc=68.3MB, time=6.48 memory used=637.6MB, alloc=68.3MB, time=6.56 memory used=671.3MB, alloc=68.3MB, time=6.70 memory used=700.2MB, alloc=68.3MB, time=6.79 memory used=725.9MB, alloc=68.3MB, time=6.86 memory used=765.5MB, alloc=68.3MB, time=9.63 memory used=798.4MB, alloc=68.3MB, time=9.94 memory used=823.4MB, alloc=68.3MB, time=10.01 memory used=843.9MB, alloc=68.3MB, time=10.06 memory used=870.7MB, alloc=68.3MB, time=10.13 memory used=918.7MB, alloc=68.3MB, time=10.68 memory used=963.1MB, alloc=68.3MB, time=11.28 memory used=989.5MB, alloc=68.3MB, time=11.44 memory used=1031.6MB, alloc=68.3MB, time=11.70 memory used=1074.2MB, alloc=68.3MB, time=12.36 memory used=1119.8MB, alloc=68.3MB, time=12.89 memory used=1157.2MB, alloc=68.3MB, time=13.10 memory used=1175.5MB, alloc=68.3MB, time=13.17 memory used=1197.1MB, alloc=68.3MB, time=13.25 memory used=1220.2MB, alloc=68.3MB, time=13.39 memory used=1253.1MB, alloc=68.3MB, time=13.51 memory used=1270.5MB, alloc=68.3MB, time=13.58 memory used=1292.6MB, alloc=68.3MB, time=13.66 memory used=1317.1MB, alloc=92.3MB, time=14.23 memory used=1377.8MB, alloc=92.3MB, time=18.61 memory used=1415.4MB, alloc=92.3MB, time=18.71 memory used=1450.9MB, alloc=92.3MB, time=18.82 memory used=1488.4MB, alloc=92.3MB, time=18.91 memory used=1548.6MB, alloc=93.2MB, time=19.69 memory used=1594.6MB, alloc=93.2MB, time=19.92 memory used=1637.6MB, alloc=93.2MB, time=20.05 memory used=1682.5MB, alloc=93.2MB, time=20.23 memory used=1727.7MB, alloc=93.2MB, time=20.37 memory used=1766.8MB, alloc=93.2MB, time=20.48 memory used=1833.0MB, alloc=93.2MB, time=25.38 memory used=1871.0MB, alloc=93.2MB, time=25.49 memory used=1905.3MB, alloc=93.2MB, time=25.60 memory used=1943.5MB, alloc=93.2MB, time=25.70 memory used=2004.5MB, alloc=93.2MB, time=26.28 memory used=2050.9MB, alloc=93.2MB, time=26.51 memory used=2123.3MB, alloc=93.2MB, time=27.09 memory used=2165.4MB, alloc=93.2MB, time=27.30 memory used=2206.5MB, alloc=93.2MB, time=27.46 memory used=2253.6MB, alloc=93.2MB, time=27.69 memory used=2316.9MB, alloc=93.3MB, time=29.99 memory used=2351.7MB, alloc=93.3MB, time=30.10 memory used=2381.6MB, alloc=93.3MB, time=30.20 memory used=2411.9MB, alloc=93.3MB, time=30.30 memory used=2447.5MB, alloc=93.3MB, time=30.41 memory used=2486.0MB, alloc=93.3MB, time=30.51 memory used=2513.3MB, alloc=93.3MB, time=30.59 memory used=2538.7MB, alloc=93.3MB, time=30.66 memory used=2565.8MB, alloc=93.3MB, time=30.74 memory used=2594.9MB, alloc=93.3MB, time=30.81 memory used=2626.5MB, alloc=93.3MB, time=30.89 memory used=2662.6MB, alloc=93.3MB, time=30.97 memory used=2723.9MB, alloc=93.3MB, time=33.32 memory used=2766.2MB, alloc=93.3MB, time=33.48 memory used=2799.7MB, alloc=93.3MB, time=33.58 memory used=2828.8MB, alloc=93.3MB, time=33.68 memory used=2863.7MB, alloc=93.3MB, time=33.78 memory used=2901.8MB, alloc=93.3MB, time=33.89 memory used=2929.5MB, alloc=93.3MB, time=33.98 memory used=2954.6MB, alloc=93.3MB, time=34.06 memory used=2981.9MB, alloc=93.3MB, time=34.13 memory used=3011.8MB, alloc=93.3MB, time=34.21 memory used=3046.1MB, alloc=93.3MB, time=34.30 memory used=3122.9MB, alloc=93.3MB, time=34.87 memory used=3196.8MB, alloc=95.1MB, time=35.60 memory used=3231.0MB, alloc=95.1MB, time=35.70 memory used=3269.4MB, alloc=95.1MB, time=35.91 memory used=3318.5MB, alloc=95.1MB, time=36.57 memory used=3351.6MB, alloc=95.1MB, time=36.67 memory used=3380.4MB, alloc=95.1MB, time=36.76 memory used=3414.1MB, alloc=95.1MB, time=36.85 memory used=3450.8MB, alloc=95.1MB, time=37.10 memory used=3484.5MB, alloc=95.1MB, time=37.28 memory used=3508.9MB, alloc=107.8MB, time=37.50 memory used=3544.3MB, alloc=107.8MB, time=37.59 memory used=3589.0MB, alloc=107.8MB, time=37.71 memory used=3623.4MB, alloc=107.8MB, time=37.80 memory used=3700.5MB, alloc=107.8MB, time=38.50 memory used=3781.5MB, alloc=107.8MB, time=39.10 memory used=3858.4MB, alloc=107.8MB, time=39.84 memory used=3934.7MB, alloc=107.8MB, time=40.66 memory used=4012.6MB, alloc=107.8MB, time=41.60 memory used=4075.9MB, alloc=131.8MB, time=42.25 memory used=4137.2MB, alloc=131.8MB, time=42.60 memory used=4219.8MB, alloc=131.8MB, time=43.94 memory used=4301.6MB, alloc=131.8MB, time=44.89 memory used=4378.3MB, alloc=155.8MB, time=45.63 memory used=4446.7MB, alloc=155.8MB, time=45.98 memory used=4508.2MB, alloc=155.8MB, time=46.15 memory used=4570.9MB, alloc=155.8MB, time=46.33 memory used=4649.2MB, alloc=155.8MB, time=47.41 memory used=4704.0MB, alloc=155.8MB, time=47.61 memory used=4774.3MB, alloc=155.8MB, time=47.81 memory used=4820.2MB, alloc=155.8MB, time=47.97 memory used=4865.3MB, alloc=155.8MB, time=48.13 memory used=4911.6MB, alloc=155.8MB, time=48.31 memory used=4961.6MB, alloc=155.8MB, time=48.48 memory used=5018.9MB, alloc=155.8MB, time=48.68 memory used=5080.2MB, alloc=155.8MB, time=48.84 memory used=5144.7MB, alloc=155.8MB, time=49.02 memory used=5212.4MB, alloc=155.8MB, time=49.20 memory used=5267.8MB, alloc=155.8MB, time=49.34 memory used=5303.6MB, alloc=155.8MB, time=49.46 memory used=5339.4MB, alloc=179.8MB, time=49.59 memory used=5386.3MB, alloc=179.8MB, time=49.72 memory used=5434.9MB, alloc=179.8MB, time=49.87 memory used=5485.4MB, alloc=179.8MB, time=50.01 memory used=5542.7MB, alloc=179.8MB, time=50.15 memory used=5601.9MB, alloc=179.8MB, time=50.29 memory used=5662.3MB, alloc=179.8MB, time=50.45 memory used=5723.8MB, alloc=179.8MB, time=50.59 memory used=5786.5MB, alloc=179.8MB, time=50.74 memory used=5850.1MB, alloc=179.8MB, time=50.89 memory used=5914.8MB, alloc=179.8MB, time=51.05 memory used=5981.6MB, alloc=179.8MB, time=51.20 memory used=6055.5MB, alloc=179.8MB, time=51.37 memory used=6131.3MB, alloc=179.8MB, time=51.54 memory used=6208.2MB, alloc=179.8MB, time=51.71 memory used=6285.9MB, alloc=179.8MB, time=51.86 memory used=6364.5MB, alloc=179.8MB, time=52.03 memory used=6445.6MB, alloc=179.8MB, time=52.19 memory used=6532.8MB, alloc=179.8MB, time=52.35 memory used=6630.3MB, alloc=179.8MB, time=52.53 memory used=6659.2MB, alloc=179.8MB, time=52.63 memory used=6686.9MB, alloc=179.8MB, time=52.73 memory used=6720.8MB, alloc=179.8MB, time=52.84 memory used=6741.9MB, alloc=179.8MB, time=52.93 memory used=6751.8MB, alloc=179.8MB, time=53.01 memory used=6757.6MB, alloc=179.8MB, time=53.09 memory used=6764.5MB, alloc=179.8MB, time=53.16 memory used=6765.8MB, alloc=179.8MB, time=53.23 memory used=6766.5MB, alloc=179.8MB, time=53.30 memory used=6770.5MB, alloc=435.8MB, time=53.37 memory used=6908.9MB, alloc=435.8MB, time=53.77 memory used=7050.0MB, alloc=435.8MB, time=54.04 memory used=7198.1MB, alloc=435.8MB, time=54.32 memory used=7346.3MB, alloc=435.8MB, time=54.60 memory used=7503.3MB, alloc=435.8MB, time=54.90 memory used=7668.4MB, alloc=435.8MB, time=55.19 memory used=7840.8MB, alloc=435.8MB, time=55.50 memory used=8019.6MB, alloc=435.8MB, time=55.79 memory used=8211.9MB, alloc=435.8MB, time=56.10 memory used=8409.7MB, alloc=435.8MB, time=56.40 memory used=8620.9MB, alloc=435.8MB, time=56.72 memory used=8844.8MB, alloc=435.8MB, time=57.05 memory used=9086.7MB, alloc=435.8MB, time=57.36 memory used=9287.1MB, alloc=435.8MB, time=58.87 memory used=9375.5MB, alloc=435.8MB, time=59.13 memory used=9436.3MB, alloc=435.8MB, time=59.34 memory used=9496.2MB, alloc=435.8MB, time=59.55 memory used=9564.6MB, alloc=435.8MB, time=59.73 memory used=9638.9MB, alloc=435.8MB, time=59.94 memory used=9719.5MB, alloc=435.8MB, time=60.15 memory used=9810.5MB, alloc=435.8MB, time=60.37 memory used=9883.8MB, alloc=435.8MB, time=60.55 memory used=9933.7MB, alloc=435.8MB, time=60.69 memory used=9979.6MB, alloc=435.8MB, time=60.83 memory used=10027.6MB, alloc=435.8MB, time=60.97 memory used=10077.1MB, alloc=435.8MB, time=61.10 memory used=10134.1MB, alloc=435.8MB, time=61.25 memory used=10192.9MB, alloc=435.8MB, time=61.40 memory used=10253.1MB, alloc=435.8MB, time=61.55 memory used=10314.3MB, alloc=435.8MB, time=61.69 memory used=10376.7MB, alloc=435.8MB, time=61.84 memory used=10440.1MB, alloc=435.8MB, time=61.98 memory used=10504.5MB, alloc=435.8MB, time=62.14 memory used=10571.0MB, alloc=435.8MB, time=62.28 memory used=10644.7MB, alloc=435.8MB, time=62.44 memory used=10720.3MB, alloc=435.8MB, time=62.60 memory used=10797.0MB, alloc=435.8MB, time=62.76 memory used=10874.5MB, alloc=435.8MB, time=62.92 memory used=10952.9MB, alloc=435.8MB, time=63.08 memory used=11033.4MB, alloc=435.8MB, time=63.24 memory used=11120.9MB, alloc=435.8MB, time=63.42 memory used=11211.4MB, alloc=435.8MB, time=63.59 memory used=11334.4MB, alloc=435.8MB, time=63.81 memory used=11495.7MB, alloc=435.8MB, time=64.11 memory used=11630.4MB, alloc=435.8MB, time=64.37 memory used=11776.4MB, alloc=435.8MB, time=64.63 memory used=11924.7MB, alloc=435.8MB, time=64.90 memory used=12081.8MB, alloc=435.8MB, time=65.19 memory used=12247.2MB, alloc=435.8MB, time=65.49 memory used=12419.9MB, alloc=435.8MB, time=65.79 memory used=12599.1MB, alloc=435.8MB, time=66.08 memory used=12785.5MB, alloc=435.8MB, time=66.38 memory used=12981.9MB, alloc=435.8MB, time=66.69 memory used=13193.1MB, alloc=435.8MB, time=67.01 memory used=13418.4MB, alloc=435.8MB, time=67.34 memory used=13658.2MB, alloc=435.8MB, time=67.65 memory used=13883.9MB, alloc=435.8MB, time=68.23 memory used=14000.2MB, alloc=435.8MB, time=123.59 memory used=14110.2MB, alloc=435.8MB, time=152.08 memory used=14182.4MB, alloc=435.8MB, time=152.30 memory used=14255.9MB, alloc=435.8MB, time=152.49 memory used=14338.4MB, alloc=435.8MB, time=152.70 memory used=14391.7MB, alloc=435.8MB, time=152.86 memory used=14449.9MB, alloc=435.8MB, time=153.01 memory used=14511.4MB, alloc=435.8MB, time=153.17 memory used=14580.0MB, alloc=435.8MB, time=153.34 memory used=14652.9MB, alloc=435.8MB, time=153.51 memory used=14733.4MB, alloc=435.8MB, time=153.68 memory used=14818.1MB, alloc=435.8MB, time=153.85 memory used=14912.7MB, alloc=435.8MB, time=154.05 memory used=15100.9MB, alloc=435.8MB, time=154.39 memory used=15255.1MB, alloc=435.8MB, time=154.67 memory used=15418.4MB, alloc=435.8MB, time=154.96 memory used=15597.1MB, alloc=435.8MB, time=155.28 memory used=15787.7MB, alloc=435.8MB, time=155.66 memory used=15994.6MB, alloc=435.8MB, time=155.99 memory used=16216.9MB, alloc=435.8MB, time=156.33 memory used=16454.0MB, alloc=435.8MB, time=156.69 memory used=16703.0MB, alloc=435.8MB, time=157.07 memory used=16913.8MB, alloc=435.8MB, time=157.40 memory used=17101.3MB, alloc=435.8MB, time=157.70 memory used=17300.4MB, alloc=435.8MB, time=158.02 memory used=17508.0MB, alloc=435.8MB, time=158.34 memory used=17730.0MB, alloc=435.8MB, time=158.68 memory used=17965.2MB, alloc=435.8MB, time=159.03 memory used=18213.0MB, alloc=435.8MB, time=159.36 memory used=18460.1MB, alloc=435.8MB, time=159.69 memory used=18682.6MB, alloc=435.8MB, time=160.00 memory used=18985.8MB, alloc=435.8MB, time=160.91 memory used=19083.0MB, alloc=435.8MB, time=161.44 memory used=19181.7MB, alloc=435.8MB, time=161.66 memory used=19367.9MB, alloc=435.8MB, time=162.79 memory used=19629.9MB, alloc=435.8MB, time=163.19 memory used=19871.5MB, alloc=435.8MB, time=164.61 memory used=20007.1MB, alloc=435.8MB, time=165.63 memory used=20099.1MB, alloc=435.8MB, time=165.99 memory used=20166.0MB, alloc=435.8MB, time=166.18 memory used=20250.5MB, alloc=435.8MB, time=166.40 memory used=20316.4MB, alloc=435.8MB, time=166.56 memory used=20376.8MB, alloc=435.8MB, time=166.71 memory used=20446.2MB, alloc=435.8MB, time=166.86 memory used=20525.8MB, alloc=435.8MB, time=167.02 memory used=20638.9MB, alloc=435.8MB, time=170.54 memory used=20715.5MB, alloc=435.8MB, time=170.76 memory used=20782.8MB, alloc=435.8MB, time=170.93 memory used=20849.5MB, alloc=435.8MB, time=171.09 memory used=20928.8MB, alloc=435.8MB, time=171.27 memory used=21028.6MB, alloc=435.8MB, time=171.46 memory used=21186.0MB, alloc=435.8MB, time=171.74 memory used=21373.5MB, alloc=435.8MB, time=172.05 memory used=21672.4MB, alloc=435.8MB, time=173.60 memory used=21790.6MB, alloc=435.8MB, time=174.44 memory used=21915.5MB, alloc=435.8MB, time=175.11 memory used=21992.9MB, alloc=435.8MB, time=175.34 memory used=22068.2MB, alloc=435.8MB, time=175.55 memory used=22144.8MB, alloc=435.8MB, time=175.81 memory used=22247.3MB, alloc=435.8MB, time=179.55 memory used=22317.3MB, alloc=435.8MB, time=179.76 memory used=22373.5MB, alloc=435.8MB, time=179.92 memory used=22442.9MB, alloc=435.8MB, time=180.10 memory used=22681.0MB, alloc=435.8MB, time=180.52 memory used=22874.8MB, alloc=435.8MB, time=180.87 memory used=23099.3MB, alloc=435.8MB, time=181.28 memory used=23233.8MB, alloc=435.8MB, time=184.89 memory used=23303.4MB, alloc=435.8MB, time=185.08 memory used=23361.1MB, alloc=435.8MB, time=185.24 memory used=23432.0MB, alloc=435.8MB, time=185.42 memory used=23661.0MB, alloc=435.8MB, time=185.81 memory used=23857.3MB, alloc=435.8MB, time=186.16 memory used=24079.9MB, alloc=435.8MB, time=186.49 memory used=24256.6MB, alloc=435.8MB, time=187.68 memory used=24409.8MB, alloc=435.8MB, time=188.80 memory used=24544.8MB, alloc=435.8MB, time=190.22 memory used=24701.6MB, alloc=435.8MB, time=190.85 memory used=24858.5MB, alloc=435.8MB, time=191.55 memory used=25013.3MB, alloc=435.8MB, time=192.38 memory used=25167.9MB, alloc=435.8MB, time=193.40 memory used=25316.3MB, alloc=435.8MB, time=194.60 memory used=25380.1MB, alloc=435.8MB, time=194.83 memory used=25438.6MB, alloc=435.8MB, time=195.00 memory used=25506.3MB, alloc=435.8MB, time=195.22 memory used=25562.1MB, alloc=435.8MB, time=195.40 memory used=25635.0MB, alloc=435.8MB, time=195.67 memory used=25694.8MB, alloc=435.8MB, time=195.89 memory used=25775.7MB, alloc=435.8MB, time=196.27 memory used=25831.8MB, alloc=435.8MB, time=196.48 memory used=25901.7MB, alloc=435.8MB, time=196.71 memory used=25956.3MB, alloc=435.8MB, time=196.89 memory used=26003.3MB, alloc=435.8MB, time=197.07 memory used=26055.8MB, alloc=435.8MB, time=197.24 memory used=26115.2MB, alloc=435.8MB, time=197.42 memory used=26180.6MB, alloc=435.8MB, time=197.61 memory used=26252.7MB, alloc=435.8MB, time=197.78 memory used=26460.1MB, alloc=435.8MB, time=198.14 memory used=26664.2MB, alloc=435.8MB, time=198.86 memory used=26730.2MB, alloc=435.8MB, time=199.07 memory used=26778.4MB, alloc=435.8MB, time=199.24 memory used=26835.9MB, alloc=435.8MB, time=199.42 memory used=26904.4MB, alloc=435.8MB, time=199.60 memory used=27125.2MB, alloc=435.8MB, time=199.99 memory used=27379.6MB, alloc=435.8MB, time=200.86 memory used=27473.0MB, alloc=435.8MB, time=201.63 memory used=27557.1MB, alloc=435.8MB, time=201.87 memory used=27642.6MB, alloc=435.8MB, time=202.78 memory used=27707.0MB, alloc=435.8MB, time=203.02 memory used=27757.8MB, alloc=435.8MB, time=203.23 memory used=27819.8MB, alloc=435.8MB, time=203.43 memory used=27892.3MB, alloc=435.8MB, time=203.63 memory used=27938.1MB, alloc=435.8MB, time=203.80 memory used=27983.2MB, alloc=435.8MB, time=203.97 memory used=28032.8MB, alloc=435.8MB, time=204.13 memory used=28087.2MB, alloc=435.8MB, time=204.30 memory used=28146.5MB, alloc=435.8MB, time=204.46 memory used=28242.6MB, alloc=459.8MB, time=232.38 memory used=28342.6MB, alloc=459.8MB, time=295.24 memory used=28442.8MB, alloc=459.8MB, time=296.94 memory used=28511.2MB, alloc=459.8MB, time=297.18 memory used=28580.0MB, alloc=459.8MB, time=297.41 memory used=28663.2MB, alloc=459.8MB, time=297.68 memory used=28740.4MB, alloc=459.8MB, time=297.93 memory used=28793.6MB, alloc=459.8MB, time=298.13 memory used=28848.3MB, alloc=459.8MB, time=298.33 memory used=28905.3MB, alloc=459.8MB, time=298.53 memory used=28965.3MB, alloc=459.8MB, time=298.74 memory used=29028.2MB, alloc=459.8MB, time=298.93 memory used=29093.9MB, alloc=459.8MB, time=299.13 memory used=29162.4MB, alloc=459.8MB, time=299.33 memory used=29234.0MB, alloc=459.8MB, time=299.54 memory used=29313.3MB, alloc=459.8MB, time=299.75 memory used=29396.0MB, alloc=459.8MB, time=299.96 memory used=29481.7MB, alloc=459.8MB, time=300.18 memory used=29570.2MB, alloc=459.8MB, time=300.39 memory used=29748.8MB, alloc=459.8MB, time=300.75 memory used=29883.7MB, alloc=459.8MB, time=301.07 memory used=30024.6MB, alloc=459.8MB, time=301.40 memory used=30174.6MB, alloc=459.8MB, time=301.73 memory used=30329.6MB, alloc=459.8MB, time=302.05 memory used=30489.6MB, alloc=459.8MB, time=302.40 memory used=30655.2MB, alloc=459.8MB, time=302.74 memory used=30832.5MB, alloc=459.8MB, time=303.09 memory used=31015.4MB, alloc=459.8MB, time=303.46 memory used=31203.0MB, alloc=459.8MB, time=303.82 memory used=31404.4MB, alloc=459.8MB, time=304.20 memory used=31610.3MB, alloc=459.8MB, time=304.59 memory used=31821.6MB, alloc=459.8MB, time=304.97 memory used=32045.7MB, alloc=459.8MB, time=305.35 memory used=32274.8MB, alloc=459.8MB, time=305.80 memory used=32516.1MB, alloc=459.8MB, time=306.20 memory used=32750.1MB, alloc=459.8MB, time=306.58 memory used=32940.9MB, alloc=459.8MB, time=306.94 memory used=33115.4MB, alloc=459.8MB, time=307.29 memory used=33294.1MB, alloc=459.8MB, time=307.63 memory used=33475.6MB, alloc=459.8MB, time=307.98 memory used=33658.6MB, alloc=459.8MB, time=308.33 memory used=33842.9MB, alloc=459.8MB, time=308.66 memory used=34029.5MB, alloc=459.8MB, time=309.02 memory used=34226.4MB, alloc=459.8MB, time=309.36 memory used=34425.4MB, alloc=459.8MB, time=309.72 memory used=34625.6MB, alloc=459.8MB, time=310.08 memory used=34837.7MB, alloc=459.8MB, time=310.46 memory used=35050.8MB, alloc=459.8MB, time=310.82 memory used=35264.6MB, alloc=459.8MB, time=311.19 memory used=35490.2MB, alloc=459.8MB, time=311.58 memory used=35716.4MB, alloc=459.8MB, time=311.98 memory used=35954.1MB, alloc=459.8MB, time=312.36 memory used=36192.0MB, alloc=459.8MB, time=312.73 memory used=36428.2MB, alloc=459.8MB, time=313.11 memory used=36664.4MB, alloc=459.8MB, time=313.47 memory used=36876.0MB, alloc=459.8MB, time=313.82 memory used=37063.9MB, alloc=459.8MB, time=314.14 memory used=37261.7MB, alloc=459.8MB, time=314.48 memory used=37461.9MB, alloc=459.8MB, time=314.84 memory used=37661.3MB, alloc=459.8MB, time=315.18 memory used=37870.6MB, alloc=459.8MB, time=315.55 memory used=38078.7MB, alloc=459.8MB, time=315.89 memory used=38287.0MB, alloc=459.8MB, time=316.23 memory used=38501.2MB, alloc=459.8MB, time=316.61 memory used=38725.7MB, alloc=459.8MB, time=316.98 memory used=38948.1MB, alloc=459.8MB, time=317.36 memory used=39178.4MB, alloc=459.8MB, time=317.74 memory used=39415.9MB, alloc=459.8MB, time=318.12 memory used=39651.2MB, alloc=459.8MB, time=318.49 memory used=39888.5MB, alloc=459.8MB, time=318.85 memory used=40119.7MB, alloc=459.8MB, time=319.23 memory used=40359.4MB, alloc=459.8MB, time=319.61 memory used=40591.7MB, alloc=459.8MB, time=319.99 memory used=40804.1MB, alloc=459.8MB, time=320.33 memory used=41017.0MB, alloc=459.8MB, time=320.68 memory used=41232.8MB, alloc=459.8MB, time=321.04 memory used=41458.1MB, alloc=459.8MB, time=321.40 memory used=41683.2MB, alloc=459.8MB, time=321.74 memory used=41915.4MB, alloc=459.8MB, time=322.10 memory used=42155.4MB, alloc=459.8MB, time=322.47 memory used=42401.8MB, alloc=459.8MB, time=322.81 memory used=42641.4MB, alloc=459.8MB, time=323.17 memory used=42874.1MB, alloc=459.8MB, time=323.56 memory used=43178.0MB, alloc=459.8MB, time=325.44 memory used=43275.5MB, alloc=459.8MB, time=326.33 memory used=43380.5MB, alloc=459.8MB, time=326.58 memory used=43485.2MB, alloc=459.8MB, time=326.85 memory used=43710.2MB, alloc=459.8MB, time=328.96 memory used=43938.9MB, alloc=459.8MB, time=329.36 memory used=44125.2MB, alloc=459.8MB, time=329.67 memory used=44461.9MB, alloc=459.8MB, time=334.38 memory used=44588.2MB, alloc=459.8MB, time=335.02 memory used=44657.8MB, alloc=459.8MB, time=335.22 memory used=44739.6MB, alloc=459.8MB, time=335.53 memory used=44812.1MB, alloc=459.8MB, time=335.73 memory used=44908.7MB, alloc=459.8MB, time=336.45 memory used=44986.7MB, alloc=459.8MB, time=336.71 memory used=45048.3MB, alloc=459.8MB, time=336.98 memory used=45120.3MB, alloc=459.8MB, time=337.25 memory used=45204.8MB, alloc=459.8MB, time=337.51 memory used=45296.1MB, alloc=459.8MB, time=337.76 memory used=45353.1MB, alloc=459.8MB, time=337.96 memory used=45405.0MB, alloc=459.8MB, time=338.15 memory used=45458.4MB, alloc=459.8MB, time=338.34 memory used=45516.5MB, alloc=459.8MB, time=338.54 memory used=45577.4MB, alloc=459.8MB, time=338.73 memory used=45640.1MB, alloc=459.8MB, time=338.92 memory used=45705.8MB, alloc=459.8MB, time=339.13 memory used=45776.0MB, alloc=459.8MB, time=339.34 memory used=45849.3MB, alloc=459.8MB, time=339.55 memory used=45925.6MB, alloc=459.8MB, time=339.76 memory used=46006.3MB, alloc=459.8MB, time=339.97 memory used=46090.1MB, alloc=459.8MB, time=340.18 memory used=46181.3MB, alloc=459.8MB, time=340.40 memory used=46286.9MB, alloc=459.8MB, time=340.63 memory used=46472.4MB, alloc=459.8MB, time=341.00 memory used=46613.3MB, alloc=459.8MB, time=341.33 memory used=46763.1MB, alloc=459.8MB, time=341.65 memory used=46919.1MB, alloc=459.8MB, time=341.96 memory used=47086.6MB, alloc=459.8MB, time=342.29 memory used=47265.6MB, alloc=459.8MB, time=342.60 memory used=47459.8MB, alloc=459.8MB, time=342.94 memory used=47669.9MB, alloc=459.8MB, time=343.30 memory used=47852.9MB, alloc=459.8MB, time=362.16 memory used=47924.8MB, alloc=459.8MB, time=362.40 memory used=48006.1MB, alloc=459.8MB, time=362.65 memory used=48080.6MB, alloc=459.8MB, time=362.87 memory used=48135.5MB, alloc=459.8MB, time=363.06 memory used=48197.5MB, alloc=459.8MB, time=363.26 memory used=48264.6MB, alloc=459.8MB, time=363.46 memory used=48336.3MB, alloc=459.8MB, time=363.67 memory used=48415.8MB, alloc=459.8MB, time=363.91 memory used=48499.9MB, alloc=459.8MB, time=364.14 memory used=48592.2MB, alloc=459.8MB, time=364.37 memory used=48798.7MB, alloc=459.8MB, time=364.76 memory used=48943.9MB, alloc=459.8MB, time=365.09 memory used=49103.1MB, alloc=459.8MB, time=365.42 memory used=49274.4MB, alloc=459.8MB, time=365.78 memory used=49457.2MB, alloc=459.8MB, time=366.12 memory used=49656.5MB, alloc=459.8MB, time=366.52 memory used=49871.9MB, alloc=459.8MB, time=366.91 memory used=50098.2MB, alloc=459.8MB, time=367.31 memory used=50338.9MB, alloc=459.8MB, time=367.71 memory used=50553.3MB, alloc=459.8MB, time=368.08 memory used=50731.9MB, alloc=459.8MB, time=368.40 memory used=50922.4MB, alloc=459.8MB, time=368.74 memory used=51122.9MB, alloc=459.8MB, time=369.11 memory used=51331.4MB, alloc=459.8MB, time=369.45 memory used=51551.4MB, alloc=459.8MB, time=369.82 memory used=51785.2MB, alloc=459.8MB, time=370.19 memory used=52030.4MB, alloc=459.8MB, time=370.56 memory used=52257.9MB, alloc=459.8MB, time=370.91 memory used=52467.4MB, alloc=459.8MB, time=371.24 memory used=52692.4MB, alloc=459.8MB, time=371.59 memory used=52880.2MB, alloc=459.8MB, time=373.18 memory used=53048.2MB, alloc=459.8MB, time=374.60 memory used=53226.0MB, alloc=459.8MB, time=376.40 memory used=53365.1MB, alloc=459.8MB, time=377.47 memory used=53512.3MB, alloc=459.8MB, time=378.45 memory used=53672.0MB, alloc=459.8MB, time=379.85 memory used=53821.1MB, alloc=459.8MB, time=380.82 memory used=53975.3MB, alloc=459.8MB, time=382.12 memory used=54125.3MB, alloc=459.8MB, time=383.17 memory used=54281.9MB, alloc=459.8MB, time=384.54 memory used=54437.0MB, alloc=483.8MB, time=385.97 memory used=54606.4MB, alloc=483.8MB, time=387.63 memory used=54759.4MB, alloc=507.8MB, time=389.77 memory used=54923.8MB, alloc=531.8MB, time=392.30 memory used=55093.2MB, alloc=555.8MB, time=395.50 memory used=55266.8MB, alloc=579.8MB, time=398.52 memory used=55418.2MB, alloc=603.8MB, time=401.18 memory used=55583.5MB, alloc=627.8MB, time=403.80 memory used=55743.2MB, alloc=651.8MB, time=406.21 memory used=55891.5MB, alloc=675.8MB, time=409.08 |\^/| 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(); 1428525939 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 2 F := [-15 x y - 5 y z + 12 x y, -8 x z - 10 y z + 4 z ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 2 2 G := [4 x + 17 x + 15 x, -x y - 2 y + 4 z ] > Problem := [F,G]; 2 2 2 2 2 Problem := [[-15 x y - 5 y z + 12 x y, -8 x z - 10 y z + 4 z ], 3 2 2 2 2 [4 x + 17 x + 15 x, -x y - 2 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=4.2MB, alloc=32.3MB, time=0.16 memory used=26.4MB, alloc=32.3MB, time=0.45 memory used=47.7MB, alloc=32.3MB, time=0.73 memory used=67.7MB, alloc=56.3MB, time=1.03 memory used=108.8MB, alloc=60.3MB, time=1.68 memory used=148.0MB, alloc=84.3MB, time=2.34 memory used=207.8MB, alloc=108.3MB, time=3.37 memory used=288.6MB, alloc=116.3MB, time=4.63 memory used=362.7MB, alloc=140.3MB, time=5.66 memory used=453.5MB, alloc=164.3MB, time=7.06 memory used=552.8MB, alloc=188.3MB, time=9.18 memory used=660.3MB, alloc=212.3MB, time=11.98 memory used=775.8MB, alloc=236.3MB, time=15.74 memory used=914.1MB, alloc=260.3MB, time=20.29 memory used=1076.4MB, alloc=260.3MB, time=25.49 memory used=1238.6MB, alloc=260.3MB, time=30.62 memory used=1400.8MB, alloc=284.3MB, time=36.01 memory used=1587.2MB, alloc=284.3MB, time=42.48 N1 := 6201 > GB := Basis(F, plex(op(vars))); 4 2 5 4 4 3 2 GB := [400 x y + 1875 x y - 320 x y - 4500 x y + 3900 x y - 1440 x y 2 3 2 + 192 x y, 20 x y z - 75 x y + 90 x y - 24 x y, 3 2 3 3 2 20 x y + 25 x y z - 16 x y - 30 x y z + 8 x y z, 2 2 2 -4 x z + 15 x y - 12 x y + 2 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1768.9MB, alloc=284.3MB, time=47.09 memory used=1940.0MB, alloc=540.3MB, time=49.56 memory used=2079.4MB, alloc=540.3MB, time=51.63 memory used=2231.3MB, alloc=564.3MB, time=54.16 memory used=2421.8MB, alloc=588.3MB, time=56.78 memory used=2620.2MB, alloc=612.3MB, time=60.16 memory used=2815.3MB, alloc=636.3MB, time=63.56 memory used=3005.6MB, alloc=660.3MB, time=66.86 memory used=3199.3MB, alloc=684.3MB, time=70.17 memory used=3382.3MB, alloc=708.3MB, time=73.17 memory used=3561.1MB, alloc=732.3MB, time=76.11 memory used=3749.8MB, alloc=756.3MB, time=79.48 memory used=3898.3MB, alloc=780.3MB, time=82.15 memory used=4048.5MB, alloc=804.3MB, time=84.93 memory used=4199.3MB, alloc=828.3MB, time=87.81 memory used=4346.1MB, alloc=852.3MB, time=90.57 memory used=4499.2MB, alloc=876.3MB, time=93.46 memory used=4631.4MB, alloc=876.3MB, time=95.88 memory used=4794.1MB, alloc=900.3MB, time=100.25 memory used=5115.0MB, alloc=924.3MB, time=111.17 memory used=5437.4MB, alloc=948.3MB, time=122.73 memory used=5837.0MB, alloc=972.3MB, time=137.98 memory used=6242.8MB, alloc=996.3MB, time=153.45 memory used=6658.1MB, alloc=1020.3MB, time=169.68 memory used=7084.7MB, alloc=1044.3MB, time=186.47 memory used=7524.7MB, alloc=1068.3MB, time=204.10 memory used=7972.4MB, alloc=1092.3MB, time=222.78 memory used=8435.3MB, alloc=1116.3MB, time=242.59 memory used=8922.3MB, alloc=1140.3MB, time=263.45 memory used=9433.2MB, alloc=1164.3MB, time=285.08 |\^/| 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(); 1428526239 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 F := [9 x z + 2 x y + 16, 7 x y + 5 z + 8] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 3 G := [12 x y - 15 y + 4 z, 6 x y + 7 z + 3 x] > Problem := [F,G]; 2 2 2 2 Problem := [[9 x z + 2 x y + 16, 7 x y + 5 z + 8], 2 2 2 3 [12 x y - 15 y + 4 z, 6 x y + 7 z + 3 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=24.8MB, alloc=32.3MB, time=0.41 memory used=47.9MB, alloc=37.6MB, time=0.70 memory used=68.0MB, alloc=61.6MB, time=0.98 memory used=114.9MB, alloc=69.7MB, time=1.58 memory used=159.2MB, alloc=69.7MB, time=2.10 memory used=191.7MB, alloc=69.7MB, time=2.29 memory used=225.8MB, alloc=69.7MB, time=2.50 memory used=259.4MB, alloc=69.7MB, time=2.68 memory used=308.4MB, alloc=69.7MB, time=3.21 memory used=358.2MB, alloc=69.7MB, time=3.69 memory used=406.1MB, alloc=93.7MB, time=4.20 memory used=472.5MB, alloc=93.7MB, time=5.09 memory used=538.5MB, alloc=93.7MB, time=5.64 memory used=585.0MB, alloc=93.7MB, time=5.87 memory used=638.4MB, alloc=93.7MB, time=6.56 memory used=672.2MB, alloc=93.7MB, time=6.68 memory used=702.1MB, alloc=93.7MB, time=6.84 memory used=743.1MB, alloc=93.7MB, time=7.00 memory used=786.0MB, alloc=93.7MB, time=7.19 memory used=819.1MB, alloc=93.7MB, time=7.32 memory used=869.4MB, alloc=93.7MB, time=7.90 memory used=903.1MB, alloc=93.7MB, time=8.02 memory used=933.7MB, alloc=93.7MB, time=8.15 memory used=978.6MB, alloc=93.7MB, time=8.33 memory used=1030.1MB, alloc=93.7MB, time=8.99 memory used=1062.9MB, alloc=93.7MB, time=9.11 memory used=1094.4MB, alloc=93.7MB, time=9.26 memory used=1141.7MB, alloc=93.7MB, time=9.52 memory used=1172.5MB, alloc=93.7MB, time=9.63 memory used=1214.8MB, alloc=93.7MB, time=9.81 memory used=1259.6MB, alloc=93.7MB, time=10.32 memory used=1293.3MB, alloc=93.7MB, time=10.44 memory used=1321.7MB, alloc=93.7MB, time=10.55 memory used=1365.5MB, alloc=93.7MB, time=10.73 memory used=1400.2MB, alloc=93.7MB, time=10.90 memory used=1438.9MB, alloc=93.7MB, time=11.05 memory used=1488.8MB, alloc=93.7MB, time=11.61 memory used=1522.1MB, alloc=93.7MB, time=11.74 memory used=1549.8MB, alloc=93.7MB, time=11.84 memory used=1593.1MB, alloc=93.7MB, time=12.04 memory used=1633.0MB, alloc=93.7MB, time=12.22 memory used=1667.1MB, alloc=93.7MB, time=12.36 memory used=1717.9MB, alloc=93.7MB, time=12.93 memory used=1751.4MB, alloc=93.7MB, time=13.06 memory used=1778.4MB, alloc=93.7MB, time=13.17 memory used=1844.5MB, alloc=93.7MB, time=13.97 memory used=1897.7MB, alloc=93.7MB, time=14.34 memory used=1967.0MB, alloc=93.7MB, time=15.06 memory used=2020.8MB, alloc=117.7MB, time=15.53 memory used=2078.0MB, alloc=117.7MB, time=16.26 memory used=2138.9MB, alloc=373.7MB, time=17.18 memory used=2229.5MB, alloc=397.7MB, time=18.46 memory used=2343.7MB, alloc=397.7MB, time=19.78 memory used=2414.9MB, alloc=397.7MB, time=20.32 memory used=2516.6MB, alloc=397.7MB, time=21.28 memory used=2639.5MB, alloc=421.7MB, time=22.86 memory used=2801.7MB, alloc=421.7MB, time=24.07 memory used=2868.2MB, alloc=421.7MB, time=24.37 memory used=2943.1MB, alloc=421.7MB, time=24.75 memory used=2998.8MB, alloc=421.7MB, time=25.00 memory used=3059.1MB, alloc=421.7MB, time=25.23 memory used=3108.2MB, alloc=421.7MB, time=25.44 memory used=3175.6MB, alloc=421.7MB, time=25.73 memory used=3233.8MB, alloc=421.7MB, time=26.00 memory used=3302.5MB, alloc=421.7MB, time=26.22 memory used=3348.0MB, alloc=421.7MB, time=26.41 memory used=3401.9MB, alloc=421.7MB, time=26.60 memory used=3500.4MB, alloc=421.7MB, time=28.27 memory used=3565.0MB, alloc=421.7MB, time=28.48 memory used=3612.2MB, alloc=421.7MB, time=28.66 memory used=3668.2MB, alloc=421.7MB, time=28.86 memory used=3735.6MB, alloc=421.7MB, time=29.06 memory used=3927.3MB, alloc=421.7MB, time=29.59 memory used=4191.7MB, alloc=421.7MB, time=30.95 memory used=4265.3MB, alloc=421.7MB, time=31.30 memory used=4341.4MB, alloc=421.7MB, time=32.11 memory used=4400.3MB, alloc=421.7MB, time=32.32 memory used=4452.1MB, alloc=421.7MB, time=32.52 memory used=4515.8MB, alloc=421.7MB, time=32.71 memory used=4722.7MB, alloc=421.7MB, time=33.07 memory used=4913.9MB, alloc=421.7MB, time=34.48 memory used=5040.9MB, alloc=445.7MB, time=35.70 memory used=5142.9MB, alloc=445.7MB, time=36.83 memory used=5240.7MB, alloc=445.7MB, time=37.42 memory used=5316.4MB, alloc=445.7MB, time=37.74 memory used=5392.3MB, alloc=445.7MB, time=38.03 memory used=5465.5MB, alloc=445.7MB, time=38.33 memory used=5554.7MB, alloc=445.7MB, time=38.84 memory used=5620.2MB, alloc=445.7MB, time=39.13 memory used=5690.2MB, alloc=445.7MB, time=39.38 memory used=5765.4MB, alloc=445.7MB, time=39.64 memory used=5815.4MB, alloc=445.7MB, time=39.85 memory used=5871.9MB, alloc=445.7MB, time=40.05 memory used=5934.1MB, alloc=445.7MB, time=40.26 memory used=6003.4MB, alloc=445.7MB, time=40.49 memory used=6080.3MB, alloc=445.7MB, time=40.72 memory used=6165.6MB, alloc=445.7MB, time=40.96 memory used=6324.3MB, alloc=445.7MB, time=41.31 memory used=6429.2MB, alloc=445.7MB, time=41.79 memory used=6491.0MB, alloc=445.7MB, time=42.05 memory used=6572.0MB, alloc=445.7MB, time=42.32 memory used=6628.9MB, alloc=445.7MB, time=42.54 memory used=6682.0MB, alloc=445.7MB, time=42.77 memory used=6742.1MB, alloc=445.7MB, time=42.99 memory used=6808.0MB, alloc=445.7MB, time=43.22 memory used=6881.7MB, alloc=445.7MB, time=43.45 memory used=6963.4MB, alloc=445.7MB, time=43.68 memory used=7162.0MB, alloc=445.7MB, time=44.04 memory used=7284.3MB, alloc=445.7MB, time=45.88 memory used=7361.7MB, alloc=445.7MB, time=46.14 memory used=7414.1MB, alloc=445.7MB, time=46.36 memory used=7474.7MB, alloc=445.7MB, time=46.60 memory used=7545.9MB, alloc=445.7MB, time=46.81 memory used=7628.7MB, alloc=445.7MB, time=47.07 memory used=7807.8MB, alloc=445.7MB, time=47.49 memory used=7973.0MB, alloc=445.7MB, time=47.87 memory used=8174.0MB, alloc=445.7MB, time=48.28 memory used=8311.4MB, alloc=445.7MB, time=48.80 memory used=8371.2MB, alloc=445.7MB, time=49.06 memory used=8450.1MB, alloc=445.7MB, time=49.32 memory used=8508.9MB, alloc=445.7MB, time=49.55 memory used=8561.5MB, alloc=445.7MB, time=49.76 memory used=8619.9MB, alloc=445.7MB, time=49.98 memory used=8684.8MB, alloc=445.7MB, time=50.22 memory used=8757.4MB, alloc=445.7MB, time=50.44 memory used=8837.5MB, alloc=445.7MB, time=50.67 memory used=9044.9MB, alloc=445.7MB, time=51.06 memory used=9149.5MB, alloc=445.7MB, time=51.51 memory used=9209.6MB, alloc=445.7MB, time=51.79 memory used=9289.6MB, alloc=445.7MB, time=52.05 memory used=9347.6MB, alloc=445.7MB, time=52.25 memory used=9401.2MB, alloc=445.7MB, time=52.46 memory used=9459.7MB, alloc=445.7MB, time=52.67 memory used=9525.4MB, alloc=445.7MB, time=52.90 memory used=9598.1MB, alloc=445.7MB, time=53.11 memory used=9679.5MB, alloc=445.7MB, time=53.35 memory used=9882.6MB, alloc=445.7MB, time=53.73 memory used=10005.1MB, alloc=445.7MB, time=55.61 memory used=10082.7MB, alloc=445.7MB, time=55.89 memory used=10135.1MB, alloc=445.7MB, time=56.10 memory used=10196.0MB, alloc=445.7MB, time=56.32 memory used=10267.0MB, alloc=445.7MB, time=56.56 memory used=10349.8MB, alloc=445.7MB, time=56.79 memory used=10528.6MB, alloc=445.7MB, time=57.21 memory used=10693.7MB, alloc=445.7MB, time=57.55 memory used=10894.7MB, alloc=445.7MB, time=57.92 memory used=11060.6MB, alloc=445.7MB, time=58.79 memory used=11160.4MB, alloc=445.7MB, time=59.31 memory used=11240.0MB, alloc=445.7MB, time=59.71 memory used=11316.7MB, alloc=445.7MB, time=60.11 memory used=11386.8MB, alloc=445.7MB, time=60.40 memory used=11445.3MB, alloc=445.7MB, time=60.63 memory used=11520.9MB, alloc=445.7MB, time=60.95 memory used=11593.2MB, alloc=445.7MB, time=61.25 memory used=11648.4MB, alloc=445.7MB, time=61.48 memory used=11812.0MB, alloc=445.7MB, time=64.46 memory used=11886.2MB, alloc=445.7MB, time=64.76 memory used=11942.1MB, alloc=445.7MB, time=64.98 memory used=12012.3MB, alloc=445.7MB, time=65.23 memory used=12169.7MB, alloc=445.7MB, time=65.64 memory used=12263.6MB, alloc=445.7MB, time=66.61 memory used=12332.5MB, alloc=445.7MB, time=66.89 memory used=12396.7MB, alloc=445.7MB, time=67.15 memory used=12455.0MB, alloc=445.7MB, time=67.38 memory used=12524.5MB, alloc=445.7MB, time=67.61 memory used=12607.5MB, alloc=445.7MB, time=67.87 memory used=12772.5MB, alloc=445.7MB, time=68.26 memory used=12950.4MB, alloc=445.7MB, time=68.61 memory used=13149.2MB, alloc=445.7MB, time=69.91 memory used=13326.6MB, alloc=445.7MB, time=71.24 memory used=13504.4MB, alloc=445.7MB, time=72.20 memory used=13638.8MB, alloc=445.7MB, time=73.22 memory used=13753.1MB, alloc=445.7MB, time=74.71 memory used=13864.0MB, alloc=469.7MB, time=75.86 memory used=13956.5MB, alloc=469.7MB, time=76.93 memory used=14042.3MB, alloc=469.7MB, time=77.81 memory used=14125.7MB, alloc=469.7MB, time=78.92 memory used=14190.0MB, alloc=469.7MB, time=79.95 memory used=14256.8MB, alloc=469.7MB, time=80.97 memory used=14336.3MB, alloc=493.7MB, time=81.98 memory used=14407.1MB, alloc=493.7MB, time=82.88 memory used=14506.9MB, alloc=493.7MB, time=83.91 memory used=14619.1MB, alloc=493.7MB, time=85.44 memory used=14695.9MB, alloc=493.7MB, time=86.47 memory used=14753.9MB, alloc=493.7MB, time=87.41 memory used=14848.5MB, alloc=493.7MB, time=88.35 memory used=14956.1MB, alloc=493.7MB, time=89.75 memory used=15020.7MB, alloc=493.7MB, time=90.51 memory used=15090.7MB, alloc=493.7MB, time=91.31 memory used=15155.6MB, alloc=493.7MB, time=92.14 memory used=15217.8MB, alloc=493.7MB, time=93.04 memory used=15297.0MB, alloc=493.7MB, time=94.21 memory used=15488.2MB, alloc=517.7MB, time=96.71 memory used=15695.0MB, alloc=517.7MB, time=98.54 memory used=15873.6MB, alloc=517.7MB, time=99.14 memory used=16103.6MB, alloc=517.7MB, time=99.75 memory used=16370.4MB, alloc=517.7MB, time=101.18 memory used=16538.1MB, alloc=517.7MB, time=101.90 memory used=16733.8MB, alloc=517.7MB, time=102.64 memory used=16948.1MB, alloc=517.7MB, time=103.93 memory used=17117.7MB, alloc=517.7MB, time=104.71 memory used=17318.9MB, alloc=517.7MB, time=105.75 memory used=17505.6MB, alloc=541.7MB, time=108.71 memory used=17702.2MB, alloc=565.7MB, time=112.09 memory used=17926.9MB, alloc=589.7MB, time=115.58 memory used=18181.2MB, alloc=613.7MB, time=119.36 memory used=18466.6MB, alloc=637.7MB, time=122.98 memory used=18787.2MB, alloc=661.7MB, time=126.55 memory used=19098.9MB, alloc=685.7MB, time=131.16 memory used=19366.8MB, alloc=709.7MB, time=138.97 memory used=19614.0MB, alloc=733.7MB, time=147.74 memory used=19869.1MB, alloc=757.7MB, time=157.24 memory used=20125.6MB, alloc=781.7MB, time=167.86 memory used=20403.1MB, alloc=805.7MB, time=179.48 memory used=20704.6MB, alloc=829.7MB, time=192.02 memory used=21030.1MB, alloc=853.7MB, time=204.40 memory used=21379.4MB, alloc=877.7MB, time=218.99 memory used=21752.7MB, alloc=901.7MB, time=234.63 memory used=22150.0MB, alloc=925.7MB, time=250.88 memory used=22571.1MB, alloc=949.7MB, time=268.00 memory used=23016.1MB, alloc=949.7MB, time=285.90 memory used=23461.2MB, alloc=973.7MB, time=303.64 |\^/| 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(); 1428526539 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 F := [3 x y - 8 y z - 15 x, 3 x z + 9 y z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 2 G := [10 x y z - 18 z + 16 y , -8 x y + y z + 5 y] > Problem := [F,G]; 2 Problem := [[3 x y - 8 y z - 15 x, 3 x z + 9 y z], 3 2 2 2 [10 x y z - 18 z + 16 y , -8 x y + y z + 5 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.9MB, alloc=32.3MB, time=0.50 memory used=47.9MB, alloc=32.3MB, time=0.81 memory used=67.2MB, alloc=56.3MB, time=1.10 memory used=108.4MB, alloc=68.3MB, time=1.73 memory used=148.4MB, alloc=92.3MB, time=2.32 memory used=215.6MB, alloc=92.3MB, time=3.08 memory used=299.7MB, alloc=92.3MB, time=4.00 memory used=373.7MB, alloc=92.3MB, time=5.06 memory used=444.6MB, alloc=92.3MB, time=5.91 memory used=512.0MB, alloc=116.3MB, time=6.79 memory used=598.8MB, alloc=372.3MB, time=8.04 memory used=679.5MB, alloc=372.3MB, time=8.60 memory used=773.1MB, alloc=396.3MB, time=9.43 memory used=892.8MB, alloc=396.3MB, time=10.60 memory used=1011.0MB, alloc=396.3MB, time=11.61 memory used=1107.4MB, alloc=396.3MB, time=12.14 memory used=1216.0MB, alloc=420.3MB, time=13.68 memory used=1339.1MB, alloc=444.3MB, time=15.59 memory used=1478.5MB, alloc=468.3MB, time=17.86 memory used=1633.9MB, alloc=492.3MB, time=20.41 memory used=1803.3MB, alloc=516.3MB, time=23.19 memory used=2003.8MB, alloc=540.3MB, time=26.01 memory used=2220.8MB, alloc=564.3MB, time=29.25 memory used=2455.8MB, alloc=588.3MB, time=32.63 memory used=2705.7MB, alloc=612.3MB, time=35.99 memory used=2972.8MB, alloc=636.3MB, time=39.82 memory used=3246.7MB, alloc=660.3MB, time=43.76 memory used=3472.2MB, alloc=684.3MB, time=47.46 memory used=3699.5MB, alloc=708.3MB, time=51.10 memory used=3923.8MB, alloc=732.3MB, time=55.85 memory used=4166.4MB, alloc=756.3MB, time=63.70 memory used=4411.2MB, alloc=780.3MB, time=72.26 memory used=4667.1MB, alloc=804.3MB, time=81.46 memory used=4935.2MB, alloc=828.3MB, time=91.56 memory used=5218.5MB, alloc=852.3MB, time=102.20 memory used=5515.9MB, alloc=876.3MB, time=113.49 memory used=5828.7MB, alloc=900.3MB, time=125.49 memory used=6157.3MB, alloc=924.3MB, time=138.22 memory used=6501.1MB, alloc=948.3MB, time=151.55 memory used=6859.4MB, alloc=972.3MB, time=165.71 memory used=7225.4MB, alloc=996.3MB, time=180.80 memory used=7615.4MB, alloc=1020.3MB, time=196.80 memory used=8029.3MB, alloc=1044.3MB, time=212.33 memory used=8467.2MB, alloc=1068.3MB, time=228.32 memory used=8929.0MB, alloc=1092.3MB, time=246.23 memory used=9414.8MB, alloc=1116.3MB, time=264.68 memory used=9924.5MB, alloc=1140.3MB, time=282.56 |\^/| 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(); 1428526839 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 3 2 F := [-11 x - 12 x y - 3 x z, 3 x - 5 z ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 3 3 G := [-3 x y + 16 y z + 11 x , 7 x + 10 y - 6 z] > Problem := [F,G]; 3 3 2 Problem := [[-11 x - 12 x y - 3 x z, 3 x - 5 z ], 2 2 2 3 3 [-3 x y + 16 y z + 11 x , 7 x + 10 y - 6 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=24.1MB, alloc=32.3MB, time=0.45 memory used=43.8MB, alloc=32.3MB, time=0.70 memory used=62.4MB, alloc=56.3MB, time=0.97 memory used=109.5MB, alloc=68.6MB, time=1.53 memory used=158.5MB, alloc=68.6MB, time=2.08 memory used=209.4MB, alloc=92.6MB, time=2.56 memory used=277.8MB, alloc=92.6MB, time=3.24 memory used=354.7MB, alloc=92.6MB, time=3.92 memory used=421.4MB, alloc=116.6MB, time=4.70 memory used=490.8MB, alloc=116.6MB, time=5.34 memory used=565.0MB, alloc=372.6MB, time=6.06 memory used=658.5MB, alloc=396.6MB, time=7.25 memory used=777.3MB, alloc=396.6MB, time=8.70 memory used=904.9MB, alloc=420.6MB, time=10.11 memory used=994.9MB, alloc=420.6MB, time=10.71 memory used=1065.6MB, alloc=420.6MB, time=11.26 memory used=1121.4MB, alloc=420.6MB, time=11.47 memory used=1194.2MB, alloc=420.6MB, time=11.86 memory used=1257.3MB, alloc=420.6MB, time=12.17 memory used=1379.9MB, alloc=444.6MB, time=13.67 memory used=1486.3MB, alloc=444.6MB, time=15.13 memory used=1645.3MB, alloc=444.6MB, time=16.45 memory used=1778.5MB, alloc=444.6MB, time=17.33 memory used=1855.9MB, alloc=444.6MB, time=17.78 memory used=1992.8MB, alloc=468.6MB, time=18.67 memory used=2099.8MB, alloc=468.6MB, time=19.71 memory used=2279.8MB, alloc=492.6MB, time=21.29 memory used=2468.6MB, alloc=492.6MB, time=22.70 memory used=2617.3MB, alloc=492.6MB, time=24.20 memory used=2781.5MB, alloc=516.6MB, time=26.74 memory used=2927.8MB, alloc=540.6MB, time=29.01 memory used=3105.0MB, alloc=564.6MB, time=31.58 memory used=3241.9MB, alloc=588.6MB, time=33.63 memory used=3390.8MB, alloc=612.6MB, time=36.44 memory used=3547.9MB, alloc=636.6MB, time=39.43 memory used=3716.6MB, alloc=660.6MB, time=43.54 memory used=3950.7MB, alloc=684.6MB, time=50.83 memory used=4185.2MB, alloc=708.6MB, time=59.04 memory used=4425.4MB, alloc=732.6MB, time=68.13 memory used=4670.0MB, alloc=756.6MB, time=77.94 memory used=4938.5MB, alloc=780.6MB, time=89.12 memory used=5230.9MB, alloc=804.6MB, time=100.82 memory used=5547.2MB, alloc=828.6MB, time=113.02 memory used=5887.5MB, alloc=852.6MB, time=126.54 memory used=6251.8MB, alloc=852.6MB, time=141.08 memory used=6616.0MB, alloc=876.6MB, time=155.64 memory used=7004.2MB, alloc=876.6MB, time=170.82 memory used=7392.3MB, alloc=900.6MB, time=185.86 memory used=7804.1MB, alloc=900.6MB, time=201.82 memory used=8215.9MB, alloc=900.6MB, time=216.91 memory used=8627.6MB, alloc=924.6MB, time=231.51 memory used=9063.4MB, alloc=948.6MB, time=246.94 memory used=9523.0MB, alloc=972.6MB, time=262.96 N1 := 14279 > GB := Basis(F, plex(op(vars))); GB := [ 5 4 3 2 3 3 2 605 x - 27 x + 1320 x y + 720 x y , 11 x + 12 x y + 3 x z, -3 x + 5 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=9865.0MB, alloc=972.6MB, time=273.31 memory used=9931.7MB, alloc=972.6MB, time=275.29 memory used=9996.7MB, alloc=972.6MB, time=276.83 memory used=10062.8MB, alloc=972.6MB, time=278.55 memory used=10127.7MB, alloc=972.6MB, time=280.34 memory used=10188.0MB, alloc=972.6MB, time=281.85 memory used=10241.2MB, alloc=972.6MB, time=283.51 memory used=10306.4MB, alloc=972.6MB, time=285.24 memory used=10530.9MB, alloc=972.6MB, time=288.72 memory used=10763.8MB, alloc=972.6MB, time=291.99 memory used=11112.3MB, alloc=972.6MB, time=294.42 |\^/| 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(); 1428527139 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 3 2 F := [x y - 17 x z - 7 x z, 6 x + 4 x + 2 x] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 G := [8 x - 19 x + 19, -6 x z - 2 x z - 8 y ] > Problem := [F,G]; 2 2 3 2 Problem := [[x y - 17 x z - 7 x z, 6 x + 4 x + 2 x], 3 2 2 [8 x - 19 x + 19, -6 x z - 2 x 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=4.2MB, alloc=32.3MB, time=0.16 memory used=27.1MB, alloc=32.3MB, time=0.50 memory used=49.5MB, alloc=32.3MB, time=0.86 memory used=70.2MB, alloc=56.3MB, time=1.20 N1 := 681 > GB := Basis(F, plex(op(vars))); 3 2 2 2 GB := [3 x + 2 x + x, -x y + 17 x z + 7 x z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=111.6MB, alloc=60.3MB, time=1.86 memory used=153.5MB, alloc=60.3MB, time=2.41 memory used=193.0MB, alloc=84.3MB, time=3.03 N2 := 681 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 3 2 3 H := [x y - 17 x z - 7 x z, 6 x + 4 x + 2 x, 8 x - 19 x + 19, 2 2 -6 x z - 2 x z - 8 y ] > J:=[op(GB),op(G)]; 3 2 2 2 3 J := [3 x + 2 x + x, -x y + 17 x z + 7 x z, 8 x - 19 x + 19, 2 2 -6 x z - 2 x z - 8 y ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 8, 12, 3, 3, 2, 2, 1, 1/2, 1/2, 5/6, 1/6, 1/3, 4, 8, 12, 3, 3, 2, 2, 1, 1/2, 1/2, 5/6, 1/6, 1/3, 0, 0, 0] > save(F, G, cat("ranSet/33", convert(F, string),".txt")); > quit memory used=194.5MB, alloc=84.3MB, time=3.07 |\^/| 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(); 1428527143 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 3 2 2 F := [-4 x + 7 z + 9 x y, x y - 6 x z + 5 y ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 3 2 G := [x z + 2 y z + 9 z , -9 x y + 8 y - 9 y z] > Problem := [F,G]; 3 3 2 2 Problem := [[-4 x + 7 z + 9 x y, x y - 6 x z + 5 y ], 2 2 2 3 2 [x z + 2 y z + 9 z , -9 x y + 8 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=4.2MB, alloc=32.3MB, time=0.16 memory used=26.4MB, alloc=32.3MB, time=0.47 memory used=47.7MB, alloc=32.3MB, time=0.76 memory used=66.4MB, alloc=56.3MB, time=1.01 memory used=108.6MB, alloc=68.3MB, time=1.53 memory used=149.5MB, alloc=92.3MB, time=2.03 memory used=214.9MB, alloc=92.3MB, time=2.81 memory used=280.0MB, alloc=92.3MB, time=3.59 memory used=342.6MB, alloc=116.3MB, time=4.32 memory used=413.0MB, alloc=372.3MB, time=5.10 memory used=500.3MB, alloc=372.3MB, time=6.06 memory used=587.5MB, alloc=396.3MB, time=6.87 memory used=694.9MB, alloc=396.3MB, time=7.92 memory used=806.7MB, alloc=396.3MB, time=9.11 memory used=933.5MB, alloc=420.3MB, time=13.67 memory used=1089.4MB, alloc=420.3MB, time=15.04 memory used=1229.0MB, alloc=444.3MB, time=16.66 memory used=1393.5MB, alloc=468.3MB, time=18.70 memory used=1554.7MB, alloc=468.3MB, time=20.70 memory used=1704.0MB, alloc=492.3MB, time=22.95 memory used=1868.1MB, alloc=516.3MB, time=25.34 memory used=2046.3MB, alloc=540.3MB, time=28.09 memory used=2209.6MB, alloc=564.3MB, time=30.40 memory used=2383.2MB, alloc=588.3MB, time=33.63 memory used=2549.2MB, alloc=612.3MB, time=36.29 memory used=2718.9MB, alloc=636.3MB, time=39.02 memory used=2885.5MB, alloc=660.3MB, time=41.69 memory used=3041.1MB, alloc=684.3MB, time=44.14 memory used=3173.5MB, alloc=708.3MB, time=46.45 memory used=3310.1MB, alloc=732.3MB, time=48.84 memory used=3591.9MB, alloc=756.3MB, time=56.97 memory used=3867.7MB, alloc=780.3MB, time=65.87 memory used=4152.0MB, alloc=804.3MB, time=75.18 memory used=4447.0MB, alloc=828.3MB, time=85.27 memory used=4754.5MB, alloc=852.3MB, time=95.90 memory used=5060.6MB, alloc=876.3MB, time=106.56 memory used=5396.0MB, alloc=900.3MB, time=118.06 memory used=5738.1MB, alloc=924.3MB, time=130.46 memory used=6103.3MB, alloc=948.3MB, time=144.15 memory used=6492.4MB, alloc=972.3MB, time=158.48 memory used=6905.5MB, alloc=996.3MB, time=173.47 memory used=7342.5MB, alloc=1020.3MB, time=189.22 memory used=7803.5MB, alloc=1044.3MB, time=205.79 memory used=8288.4MB, alloc=1044.3MB, time=223.01 memory used=8773.2MB, alloc=1044.3MB, time=240.28 memory used=9258.0MB, alloc=1068.3MB, time=257.69 memory used=9766.7MB, alloc=1068.3MB, time=276.05 memory used=10275.4MB, alloc=1068.3MB, time=294.39 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428527443 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 3 2 F := [-16 x y + 14 x z - 16 z , -y - 10 y z ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 G := [4 x y - 16 x y z + 3 y z, -7 x - 2 x z + 2 x y] > Problem := [F,G]; 2 2 2 3 2 Problem := [[-16 x y + 14 x z - 16 z , -y - 10 y z ], 2 3 2 [4 x y - 16 x y z + 3 y z, -7 x - 2 x z + 2 x y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.6MB, alloc=32.3MB, time=0.48 memory used=46.0MB, alloc=56.3MB, time=0.78 memory used=86.4MB, alloc=60.3MB, time=1.37 memory used=126.5MB, alloc=84.3MB, time=1.97 memory used=171.8MB, alloc=84.3MB, time=2.65 memory used=232.2MB, alloc=116.3MB, time=3.63 memory used=315.4MB, alloc=140.3MB, time=5.03 memory used=417.8MB, alloc=140.3MB, time=6.75 memory used=508.6MB, alloc=164.3MB, time=9.16 N1 := 2007 > GB := Basis(F, plex(op(vars))); 4 3 2 4 5 2 2 2 3 GB := [3445 x y - 640 x y + 32 y , -40 x y + 35 x y z + 4 y , 2 3 4 3 2 2 2 -689 x y + 64 y + 56 y z, -7 z x + 8 y x + 8 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=605.9MB, alloc=164.3MB, time=12.46 memory used=709.8MB, alloc=420.3MB, time=14.08 memory used=827.6MB, alloc=444.3MB, time=15.93 memory used=972.9MB, alloc=468.3MB, time=18.31 memory used=1140.1MB, alloc=492.3MB, time=21.19 memory used=1329.7MB, alloc=516.3MB, time=24.27 memory used=1539.4MB, alloc=540.3MB, time=27.52 memory used=1750.1MB, alloc=564.3MB, time=30.94 memory used=1975.3MB, alloc=588.3MB, time=34.38 memory used=2204.7MB, alloc=612.3MB, time=38.09 memory used=2437.6MB, alloc=636.3MB, time=43.06 memory used=2650.2MB, alloc=660.3MB, time=49.60 memory used=2868.4MB, alloc=684.3MB, time=56.71 memory used=3094.6MB, alloc=708.3MB, time=65.13 memory used=3330.4MB, alloc=732.3MB, time=74.70 memory used=3590.2MB, alloc=756.3MB, time=84.69 memory used=3873.9MB, alloc=780.3MB, time=95.95 memory used=4181.6MB, alloc=804.3MB, time=108.42 memory used=4513.2MB, alloc=828.3MB, time=120.98 memory used=4868.7MB, alloc=852.3MB, time=135.46 memory used=5248.3MB, alloc=876.3MB, time=151.64 memory used=5651.7MB, alloc=900.3MB, time=168.32 memory used=6079.1MB, alloc=900.3MB, time=184.55 memory used=6506.6MB, alloc=924.3MB, time=200.50 memory used=6958.0MB, alloc=948.3MB, time=217.52 N2 := 12499 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 3 2 2 H := [-16 x y + 14 x z - 16 z , -y - 10 y z , 4 x y - 16 x y z + 3 y z, 3 2 -7 x - 2 x z + 2 x y] > J:=[op(GB),op(G)]; 4 3 2 4 5 2 2 2 3 J := [3445 x y - 640 x y + 32 y , -40 x y + 35 x y z + 4 y , 2 3 4 3 2 2 2 -689 x y + 64 y + 56 y z, -7 z x + 8 y x + 8 z , 2 3 2 4 x y - 16 x y z + 3 y z, -7 x - 2 x z + 2 x y] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 11, 12, 3, 3, 3, 2, 3/4, 1, 1, 7/11, 7/11, 6/11, 6, 17, 25, 7, 4, 5, 2, 1, 1, 5/6, 2/3, 7/9, 7/18, -6, -13, -4] > save(F, G, cat("ranSet/33", convert(F, string),".txt")); > quit memory used=7204.8MB, alloc=948.3MB, time=225.49 |\^/| 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(); 1428527684 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 3 F := [-12 x + 14 y z + 9 y, 10 x - 6 x - 5 z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 G := [-15 x z + 12 y - 18, 5 y z + 6 y - 9 x] > Problem := [F,G]; 3 3 Problem := [[-12 x + 14 y z + 9 y, 10 x - 6 x - 5 z], 2 2 [-15 x z + 12 y - 18, 5 y z + 6 y - 9 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.3MB, alloc=32.3MB, time=0.48 memory used=46.0MB, alloc=56.3MB, time=0.77 memory used=87.2MB, alloc=60.3MB, time=1.35 memory used=127.2MB, alloc=60.3MB, time=1.88 memory used=166.2MB, alloc=84.3MB, time=2.32 memory used=229.8MB, alloc=92.3MB, time=3.22 memory used=285.4MB, alloc=116.3MB, time=3.99 memory used=360.1MB, alloc=140.3MB, time=5.05 memory used=453.8MB, alloc=164.3MB, time=6.37 memory used=561.5MB, alloc=188.3MB, time=8.65 memory used=673.6MB, alloc=212.3MB, time=11.93 memory used=800.7MB, alloc=236.3MB, time=15.93 memory used=951.8MB, alloc=236.3MB, time=20.61 memory used=1103.1MB, alloc=260.3MB, time=25.34 N1 := 4345 > GB := Basis(F, plex(op(vars))); 3 3 3 GB := [140 y x - 60 x - 84 y x + 45 y, -10 x + 6 x + 5 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1207.7MB, alloc=260.3MB, time=27.18 N2 := 1229 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 3 H := [-12 x + 14 y z + 9 y, 10 x - 5 z - 6 x, -15 x z + 12 y - 18, 2 2 5 y z + 6 y - 9 x] > J:=[op(GB),op(G)]; 3 3 3 J := [140 y x - 60 x - 84 y x + 45 y, -10 x + 6 x + 5 z, -15 x z + 12 y - 18, 2 2 5 y z + 6 y - 9 x] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 11, 11, 3, 3, 2, 1, 1, 3/4, 1, 5/12, 5/12, 1/3, 4, 10, 12, 4, 3, 2, 1, 1, 3/4, 3/4, 7/13, 6/13, 3/13, 1, -1, -1] > save(F, G, cat("ranSet/33", convert(F, string),".txt")); > quit memory used=1338.0MB, alloc=516.3MB, time=29.85 |\^/| 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(); 1428527715 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 3 2 F := [19 x y z - 14 y + 2 z , 6 x - 5 z + 5 x] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 G := [-19 x y + 14 x y z + 20 z , -10 x z - 3 x + 10 x] > Problem := [F,G]; 2 2 3 2 Problem := [[19 x y z - 14 y + 2 z , 6 x - 5 z + 5 x], 2 2 2 2 [-19 x y + 14 x y z + 20 z , -10 x z - 3 x + 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=0.15 memory used=26.5MB, alloc=32.3MB, time=0.44 memory used=46.5MB, alloc=32.3MB, time=0.72 memory used=65.6MB, alloc=56.3MB, time=1.02 memory used=106.2MB, alloc=60.3MB, time=1.51 memory used=145.1MB, alloc=84.3MB, time=2.04 memory used=208.2MB, alloc=92.3MB, time=2.88 memory used=270.1MB, alloc=92.3MB, time=3.67 memory used=333.6MB, alloc=92.3MB, time=4.40 memory used=395.1MB, alloc=116.3MB, time=5.26 memory used=476.1MB, alloc=116.3MB, time=6.49 memory used=557.9MB, alloc=396.3MB, time=7.76 memory used=665.3MB, alloc=420.3MB, time=9.31 memory used=790.5MB, alloc=444.3MB, time=11.20 memory used=935.7MB, alloc=468.3MB, time=13.19 memory used=1089.8MB, alloc=492.3MB, time=15.49 memory used=1256.3MB, alloc=516.3MB, time=17.98 memory used=1433.8MB, alloc=540.3MB, time=21.01 memory used=1631.8MB, alloc=564.3MB, time=24.33 memory used=1843.7MB, alloc=588.3MB, time=27.55 memory used=2068.6MB, alloc=612.3MB, time=31.24 memory used=2265.8MB, alloc=636.3MB, time=36.96 memory used=2463.3MB, alloc=660.3MB, time=43.36 memory used=2670.0MB, alloc=684.3MB, time=50.44 memory used=2889.5MB, alloc=708.3MB, time=58.17 memory used=3121.7MB, alloc=732.3MB, time=66.48 memory used=3364.8MB, alloc=756.3MB, time=75.64 memory used=3620.5MB, alloc=780.3MB, time=85.95 memory used=3900.2MB, alloc=804.3MB, time=97.04 memory used=4203.9MB, alloc=828.3MB, time=108.12 memory used=4531.5MB, alloc=852.3MB, time=119.79 memory used=4883.0MB, alloc=876.3MB, time=133.55 memory used=5258.5MB, alloc=900.3MB, time=148.33 memory used=5657.9MB, alloc=900.3MB, time=164.09 memory used=6057.2MB, alloc=924.3MB, time=179.80 memory used=6480.5MB, alloc=924.3MB, time=196.62 memory used=6903.8MB, alloc=924.3MB, time=213.28 memory used=7326.9MB, alloc=924.3MB, time=229.73 memory used=7750.1MB, alloc=948.3MB, time=246.34 memory used=8197.2MB, alloc=948.3MB, time=263.95 memory used=8644.3MB, alloc=948.3MB, time=281.52 |\^/| 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(); 1428528015 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 3 2 F := [10 x y + 13 y z - 2 z , 6 z + 9 x - 4 x] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 G := [-16 x y - 20 z , 9 x y - 8 y] > Problem := [F,G]; 2 2 2 3 2 Problem := [[10 x y + 13 y z - 2 z , 6 z + 9 x - 4 x], 2 3 [-16 x y - 20 z , 9 x y - 8 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.8MB, alloc=32.3MB, time=0.51 memory used=45.9MB, alloc=32.3MB, time=0.77 memory used=65.2MB, alloc=56.3MB, time=1.06 memory used=107.9MB, alloc=60.3MB, time=1.63 memory used=149.4MB, alloc=60.3MB, time=2.13 memory used=188.4MB, alloc=60.3MB, time=2.53 memory used=232.7MB, alloc=60.3MB, time=2.96 memory used=259.4MB, alloc=60.3MB, time=3.09 memory used=282.3MB, alloc=60.3MB, time=3.15 memory used=303.6MB, alloc=60.3MB, time=3.20 memory used=329.2MB, alloc=60.3MB, time=3.31 memory used=356.5MB, alloc=60.3MB, time=3.45 memory used=378.1MB, alloc=60.3MB, time=3.50 memory used=401.6MB, alloc=60.3MB, time=3.56 memory used=427.0MB, alloc=60.3MB, time=3.71 memory used=451.6MB, alloc=60.3MB, time=3.84 memory used=474.4MB, alloc=60.3MB, time=3.91 memory used=511.0MB, alloc=83.8MB, time=4.10 memory used=542.4MB, alloc=83.8MB, time=4.17 memory used=565.5MB, alloc=83.8MB, time=4.23 memory used=594.1MB, alloc=83.8MB, time=4.31 memory used=625.1MB, alloc=83.8MB, time=4.40 memory used=647.9MB, alloc=83.8MB, time=4.47 memory used=674.0MB, alloc=83.8MB, time=4.67 memory used=696.1MB, alloc=83.8MB, time=4.75 memory used=723.2MB, alloc=107.8MB, time=7.97 memory used=773.7MB, alloc=107.8MB, time=11.73 memory used=802.9MB, alloc=107.8MB, time=11.83 memory used=827.8MB, alloc=131.8MB, time=11.92 memory used=863.3MB, alloc=131.8MB, time=12.06 memory used=900.9MB, alloc=131.8MB, time=12.20 memory used=937.1MB, alloc=131.8MB, time=12.32 memory used=974.7MB, alloc=131.8MB, time=12.44 memory used=1013.5MB, alloc=131.8MB, time=12.54 memory used=1053.7MB, alloc=131.8MB, time=12.67 memory used=1095.3MB, alloc=131.8MB, time=12.78 memory used=1144.0MB, alloc=131.8MB, time=12.91 memory used=1194.3MB, alloc=131.8MB, time=13.01 memory used=1246.2MB, alloc=131.8MB, time=13.11 memory used=1299.6MB, alloc=131.8MB, time=13.20 memory used=1354.4MB, alloc=131.8MB, time=13.31 memory used=1410.7MB, alloc=131.8MB, time=13.43 memory used=1468.4MB, alloc=131.8MB, time=13.55 memory used=1527.2MB, alloc=131.8MB, time=13.66 memory used=1573.6MB, alloc=155.8MB, time=13.77 memory used=1616.3MB, alloc=155.8MB, time=13.86 memory used=1657.7MB, alloc=155.8MB, time=13.94 memory used=1695.2MB, alloc=155.8MB, time=14.04 memory used=1734.3MB, alloc=155.8MB, time=14.12 memory used=1774.4MB, alloc=155.8MB, time=14.22 memory used=1815.0MB, alloc=155.8MB, time=14.32 memory used=1856.1MB, alloc=155.8MB, time=14.41 memory used=1897.7MB, alloc=155.8MB, time=14.50 memory used=1939.6MB, alloc=155.8MB, time=14.58 memory used=1982.1MB, alloc=155.8MB, time=14.66 memory used=2024.9MB, alloc=155.8MB, time=14.76 memory used=2068.2MB, alloc=155.8MB, time=14.84 memory used=2112.1MB, alloc=155.8MB, time=14.93 memory used=2165.1MB, alloc=155.8MB, time=15.02 memory used=2218.7MB, alloc=155.8MB, time=15.12 memory used=2272.9MB, alloc=155.8MB, time=15.21 memory used=2327.6MB, alloc=155.8MB, time=15.30 memory used=2382.8MB, alloc=155.8MB, time=15.41 memory used=2438.6MB, alloc=155.8MB, time=15.51 memory used=2494.9MB, alloc=155.8MB, time=15.61 memory used=2551.6MB, alloc=155.8MB, time=15.73 memory used=2608.9MB, alloc=155.8MB, time=15.84 memory used=2666.7MB, alloc=155.8MB, time=15.94 memory used=2724.9MB, alloc=155.8MB, time=16.07 memory used=2783.5MB, alloc=155.8MB, time=16.16 memory used=2842.6MB, alloc=155.8MB, time=16.26 memory used=2902.1MB, alloc=155.8MB, time=16.36 memory used=2962.0MB, alloc=155.8MB, time=16.48 memory used=3022.3MB, alloc=155.8MB, time=16.57 memory used=3083.0MB, alloc=155.8MB, time=16.66 memory used=3144.3MB, alloc=155.8MB, time=16.76 memory used=3216.0MB, alloc=155.8MB, time=16.86 memory used=3288.2MB, alloc=155.8MB, time=16.96 memory used=3360.8MB, alloc=155.8MB, time=17.06 memory used=3433.9MB, alloc=155.8MB, time=17.16 memory used=3507.9MB, alloc=155.8MB, time=17.26 memory used=3585.6MB, alloc=155.8MB, time=17.37 memory used=3660.8MB, alloc=155.8MB, time=17.48 memory used=3746.1MB, alloc=155.8MB, time=17.59 memory used=3831.8MB, alloc=155.8MB, time=17.70 memory used=3917.9MB, alloc=155.8MB, time=17.81 memory used=4005.4MB, alloc=155.8MB, time=17.92 memory used=4033.2MB, alloc=155.8MB, time=17.99 memory used=4044.1MB, alloc=155.8MB, time=18.03 memory used=4053.2MB, alloc=155.8MB, time=18.07 memory used=4062.7MB, alloc=155.8MB, time=18.11 memory used=4063.2MB, alloc=155.8MB, time=18.15 memory used=4069.5MB, alloc=411.8MB, time=18.18 memory used=4218.1MB, alloc=411.8MB, time=18.57 memory used=4351.7MB, alloc=411.8MB, time=18.77 memory used=4484.4MB, alloc=411.8MB, time=18.99 memory used=4628.3MB, alloc=411.8MB, time=19.20 memory used=4772.7MB, alloc=411.8MB, time=19.42 memory used=4917.3MB, alloc=411.8MB, time=19.67 memory used=5073.0MB, alloc=411.8MB, time=19.92 memory used=5228.6MB, alloc=411.8MB, time=20.14 memory used=5384.0MB, alloc=411.8MB, time=20.35 memory used=5550.0MB, alloc=411.8MB, time=20.56 memory used=5715.5MB, alloc=411.8MB, time=20.78 memory used=5890.8MB, alloc=411.8MB, time=21.01 memory used=6065.0MB, alloc=411.8MB, time=21.25 memory used=6248.3MB, alloc=411.8MB, time=21.49 memory used=6430.3MB, alloc=411.8MB, time=21.71 memory used=6619.5MB, alloc=411.8MB, time=21.97 memory used=6816.5MB, alloc=411.8MB, time=22.23 memory used=7020.1MB, alloc=411.8MB, time=22.49 memory used=7228.9MB, alloc=411.8MB, time=22.75 memory used=7441.9MB, alloc=411.8MB, time=23.01 memory used=7666.8MB, alloc=411.8MB, time=23.26 memory used=7899.2MB, alloc=411.8MB, time=23.52 memory used=8122.7MB, alloc=411.8MB, time=23.77 memory used=8352.4MB, alloc=411.8MB, time=24.04 memory used=8593.2MB, alloc=411.8MB, time=24.29 memory used=8839.1MB, alloc=411.8MB, time=24.56 memory used=9040.9MB, alloc=411.8MB, time=24.78 memory used=9256.3MB, alloc=411.8MB, time=27.96 memory used=9332.3MB, alloc=411.8MB, time=28.14 memory used=9386.5MB, alloc=411.8MB, time=28.26 memory used=9445.0MB, alloc=411.8MB, time=28.41 memory used=9508.1MB, alloc=411.8MB, time=28.55 memory used=9579.5MB, alloc=411.8MB, time=28.67 memory used=9655.2MB, alloc=411.8MB, time=28.82 memory used=9739.4MB, alloc=411.8MB, time=28.98 memory used=9822.7MB, alloc=411.8MB, time=29.12 memory used=9876.6MB, alloc=411.8MB, time=29.23 memory used=9923.3MB, alloc=411.8MB, time=29.32 memory used=9969.7MB, alloc=411.8MB, time=29.42 memory used=10016.9MB, alloc=411.8MB, time=29.51 memory used=10065.1MB, alloc=411.8MB, time=29.61 memory used=10119.2MB, alloc=411.8MB, time=29.72 memory used=10174.0MB, alloc=411.8MB, time=29.83 memory used=10229.5MB, alloc=411.8MB, time=29.93 memory used=10285.6MB, alloc=411.8MB, time=30.04 memory used=10342.4MB, alloc=411.8MB, time=30.14 memory used=10405.4MB, alloc=411.8MB, time=30.25 memory used=10468.8MB, alloc=411.8MB, time=30.36 memory used=10532.9MB, alloc=411.8MB, time=30.46 memory used=10603.1MB, alloc=411.8MB, time=30.57 memory used=10673.6MB, alloc=411.8MB, time=30.69 memory used=10744.4MB, alloc=411.8MB, time=30.81 memory used=10821.2MB, alloc=411.8MB, time=30.92 memory used=10898.1MB, alloc=411.8MB, time=31.04 memory used=10986.9MB, alloc=411.8MB, time=31.17 memory used=11079.7MB, alloc=411.8MB, time=31.31 memory used=11179.3MB, alloc=411.8MB, time=31.45 memory used=11289.0MB, alloc=411.8MB, time=31.62 memory used=11437.2MB, alloc=411.8MB, time=31.86 memory used=11585.9MB, alloc=411.8MB, time=32.09 memory used=11744.4MB, alloc=411.8MB, time=32.31 memory used=11911.2MB, alloc=411.8MB, time=32.53 memory used=12094.5MB, alloc=411.8MB, time=32.78 memory used=12293.8MB, alloc=411.8MB, time=33.02 memory used=12571.6MB, alloc=411.8MB, time=64.11 memory used=12838.0MB, alloc=411.8MB, time=84.45 memory used=13065.4MB, alloc=411.8MB, time=84.71 memory used=13345.3MB, alloc=411.8MB, time=88.51 memory used=13451.8MB, alloc=411.8MB, time=88.84 memory used=13619.3MB, alloc=411.8MB, time=89.09 memory used=13826.5MB, alloc=411.8MB, time=89.43 memory used=14091.2MB, alloc=411.8MB, time=90.15 memory used=14297.9MB, alloc=411.8MB, time=90.38 memory used=14526.2MB, alloc=411.8MB, time=90.62 memory used=14782.1MB, alloc=411.8MB, time=91.00 memory used=15049.9MB, alloc=411.8MB, time=91.30 memory used=15259.8MB, alloc=411.8MB, time=91.52 memory used=15485.5MB, alloc=411.8MB, time=91.74 memory used=15731.2MB, alloc=411.8MB, time=93.67 memory used=16022.0MB, alloc=411.8MB, time=94.05 memory used=16308.3MB, alloc=411.8MB, time=94.40 memory used=16519.8MB, alloc=411.8MB, time=94.66 memory used=16748.2MB, alloc=411.8MB, time=94.94 memory used=16996.4MB, alloc=411.8MB, time=95.23 memory used=17219.2MB, alloc=411.8MB, time=95.48 memory used=17438.6MB, alloc=411.8MB, time=95.73 memory used=17676.2MB, alloc=411.8MB, time=95.99 memory used=17927.1MB, alloc=411.8MB, time=96.25 memory used=18153.2MB, alloc=411.8MB, time=96.49 memory used=18376.3MB, alloc=411.8MB, time=96.70 memory used=18612.0MB, alloc=411.8MB, time=96.91 memory used=18862.0MB, alloc=411.8MB, time=97.12 memory used=19105.8MB, alloc=411.8MB, time=97.33 memory used=19372.3MB, alloc=411.8MB, time=99.80 memory used=19499.0MB, alloc=411.8MB, time=100.75 memory used=19608.5MB, alloc=411.8MB, time=101.05 memory used=19737.3MB, alloc=411.8MB, time=101.86 memory used=19862.0MB, alloc=411.8MB, time=103.54 memory used=19989.8MB, alloc=411.8MB, time=104.87 memory used=20115.2MB, alloc=411.8MB, time=106.55 memory used=20227.7MB, alloc=435.8MB, time=108.47 memory used=20325.3MB, alloc=459.8MB, time=111.59 N1 := 2603 > GB := Basis(F, plex(op(vars))); 3 6 2 6 3 4 6 2 4 GB := [18000 x y - 59319 x y - 21060 x y + 26364 x y + 9360 x y 4 3 2 4 4 3 4 4 2 - 324 x + 288 x - 64 x , 1800000 x y - 5931900 x y - 1404000 x y 2 4 4 3 2 4 3 + 2636400 x y + 108000 x z - 1689441 x y - 273780 x + 307914 x z 2 2 3 2 2 2 + 2056392 x y + 243360 x - 316368 x z - 456976 x y - 54080 x 3 4 2 4 3 2 4 + 70304 x z, -600000 x y + 1977300 x y + 468000 x y - 878800 x y 3 2 2 2 3 2 - 36000 x z + 563147 x y + 135200 x y z + 91260 x - 102638 x z 2 2 3 4 2 4 - 342732 x y - 40560 x + 52728 x z, 1800000 x y - 5931900 x y 3 2 4 4 3 - 1404000 x y + 5272800 x y + 3427320 y z + 108000 x z 2 2 3 2 2 2 - 1689441 x y - 273780 x + 307914 x z + 1028196 x y + 243360 x 2 2 2 - 158184 x z - 54080 x, -10 x y - 13 y z + 2 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=20448.0MB, alloc=459.8MB, time=114.94 memory used=20595.6MB, alloc=459.8MB, time=117.08 memory used=20849.7MB, alloc=459.8MB, time=119.88 memory used=21157.0MB, alloc=483.8MB, time=122.88 memory used=21897.3MB, alloc=483.8MB, time=135.22 memory used=22244.9MB, alloc=483.8MB, time=138.78 memory used=22459.5MB, alloc=483.8MB, time=141.75 memory used=22610.2MB, alloc=507.8MB, time=143.81 memory used=22746.9MB, alloc=507.8MB, time=145.62 memory used=22891.9MB, alloc=507.8MB, time=147.70 memory used=23036.2MB, alloc=531.8MB, time=149.77 memory used=23169.9MB, alloc=531.8MB, time=151.71 memory used=23304.5MB, alloc=555.8MB, time=153.56 memory used=23424.8MB, alloc=555.8MB, time=155.00 memory used=23607.8MB, alloc=555.8MB, time=156.50 memory used=23719.2MB, alloc=555.8MB, time=157.73 memory used=23818.5MB, alloc=555.8MB, time=158.34 memory used=23936.4MB, alloc=579.8MB, time=160.35 memory used=24044.8MB, alloc=579.8MB, time=160.77 memory used=24160.2MB, alloc=579.8MB, time=161.76 memory used=24270.1MB, alloc=579.8MB, time=162.15 memory used=24510.5MB, alloc=579.8MB, time=165.15 memory used=25052.0MB, alloc=579.8MB, time=167.66 memory used=25178.4MB, alloc=579.8MB, time=168.31 memory used=25309.1MB, alloc=603.8MB, time=175.63 memory used=25548.4MB, alloc=603.8MB, time=235.44 memory used=25685.2MB, alloc=603.8MB, time=235.83 memory used=25828.6MB, alloc=603.8MB, time=236.23 memory used=25980.2MB, alloc=603.8MB, time=236.62 memory used=26184.5MB, alloc=603.8MB, time=249.58 memory used=26300.4MB, alloc=627.8MB, time=304.63 memory used=26455.1MB, alloc=651.8MB, time=335.90 memory used=26616.1MB, alloc=675.8MB, time=336.32 memory used=26802.9MB, alloc=699.8MB, time=336.78 memory used=27003.0MB, alloc=699.8MB, time=337.25 memory used=27207.4MB, alloc=699.8MB, time=337.70 memory used=27408.9MB, alloc=699.8MB, time=338.18 memory used=27621.1MB, alloc=699.8MB, time=338.65 memory used=27829.7MB, alloc=699.8MB, time=339.11 memory used=28047.8MB, alloc=699.8MB, time=339.58 memory used=28261.8MB, alloc=699.8MB, time=340.07 memory used=28484.1MB, alloc=699.8MB, time=340.56 memory used=28701.3MB, alloc=699.8MB, time=341.04 memory used=28925.5MB, alloc=699.8MB, time=341.52 memory used=29144.0MB, alloc=699.8MB, time=341.99 memory used=29367.9MB, alloc=699.8MB, time=342.46 memory used=29685.1MB, alloc=699.8MB, time=343.07 memory used=29863.5MB, alloc=699.8MB, time=343.56 memory used=30016.8MB, alloc=699.8MB, time=344.00 memory used=30151.2MB, alloc=699.8MB, time=344.43 memory used=30277.6MB, alloc=699.8MB, time=344.86 memory used=30397.3MB, alloc=699.8MB, time=345.27 memory used=30517.3MB, alloc=699.8MB, time=345.69 memory used=30642.5MB, alloc=699.8MB, time=346.11 memory used=30763.6MB, alloc=699.8MB, time=346.53 memory used=30888.4MB, alloc=699.8MB, time=346.95 memory used=31016.3MB, alloc=699.8MB, time=347.37 memory used=31145.7MB, alloc=699.8MB, time=347.81 memory used=31275.7MB, alloc=699.8MB, time=348.22 memory used=31404.9MB, alloc=699.8MB, time=348.65 memory used=31537.8MB, alloc=699.8MB, time=349.08 memory used=31671.5MB, alloc=699.8MB, time=349.51 memory used=31807.3MB, alloc=699.8MB, time=349.94 memory used=31947.7MB, alloc=699.8MB, time=350.38 memory used=32090.5MB, alloc=699.8MB, time=350.82 |\^/| 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(); 1428528315 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 3 F := [9 x y - 3 z - 7 z, -7 x z + 5 z - y] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 3 G := [5 x z - 4 x y z + 11 z , -9 x z + 3 y + 4 z] > Problem := [F,G]; 2 2 2 3 Problem := [[9 x y - 3 z - 7 z, -7 x z + 5 z - y], 2 2 2 3 [5 x z - 4 x y z + 11 z , -9 x z + 3 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=4.2MB, alloc=32.3MB, time=0.17 memory used=26.5MB, alloc=32.3MB, time=0.48 memory used=46.7MB, alloc=56.3MB, time=0.77 memory used=88.1MB, alloc=60.3MB, time=1.34 memory used=129.8MB, alloc=92.3MB, time=1.92 memory used=192.7MB, alloc=92.3MB, time=2.77 memory used=259.8MB, alloc=116.3MB, time=3.66 memory used=329.1MB, alloc=372.3MB, time=4.64 memory used=402.0MB, alloc=372.3MB, time=5.68 memory used=445.1MB, alloc=372.3MB, time=5.89 memory used=494.0MB, alloc=372.3MB, time=6.07 memory used=541.6MB, alloc=372.3MB, time=6.22 memory used=592.0MB, alloc=372.3MB, time=6.49 memory used=640.7MB, alloc=372.3MB, time=7.17 memory used=688.2MB, alloc=372.3MB, time=7.37 memory used=758.9MB, alloc=372.3MB, time=8.10 memory used=852.9MB, alloc=396.3MB, time=9.20 memory used=967.2MB, alloc=420.3MB, time=10.71 memory used=1071.1MB, alloc=420.3MB, time=11.96 memory used=1151.8MB, alloc=420.3MB, time=12.42 memory used=1242.5MB, alloc=420.3MB, time=14.06 memory used=1374.0MB, alloc=420.3MB, time=15.69 memory used=1504.4MB, alloc=444.3MB, time=17.46 memory used=1625.8MB, alloc=444.3MB, time=19.19 memory used=1749.2MB, alloc=468.3MB, time=20.97 memory used=1856.7MB, alloc=468.3MB, time=22.62 memory used=1967.1MB, alloc=468.3MB, time=23.48 memory used=2081.8MB, alloc=492.3MB, time=24.78 memory used=2228.5MB, alloc=492.3MB, time=26.45 memory used=2326.8MB, alloc=492.3MB, time=28.00 memory used=2414.5MB, alloc=492.3MB, time=29.44 memory used=2486.9MB, alloc=492.3MB, time=30.65 memory used=2623.1MB, alloc=492.3MB, time=32.30 memory used=2737.7MB, alloc=492.3MB, time=33.59 memory used=2841.0MB, alloc=516.3MB, time=34.88 memory used=2910.2MB, alloc=516.3MB, time=36.05 memory used=2979.3MB, alloc=516.3MB, time=37.06 memory used=3081.0MB, alloc=516.3MB, time=37.65 memory used=3195.5MB, alloc=516.3MB, time=38.42 memory used=3285.7MB, alloc=516.3MB, time=38.89 memory used=3376.3MB, alloc=516.3MB, time=39.34 memory used=3490.1MB, alloc=516.3MB, time=39.82 memory used=3559.5MB, alloc=516.3MB, time=40.20 memory used=3634.2MB, alloc=516.3MB, time=40.59 memory used=3718.4MB, alloc=516.3MB, time=40.98 memory used=3814.7MB, alloc=516.3MB, time=41.38 memory used=3931.4MB, alloc=516.3MB, time=42.14 memory used=4020.3MB, alloc=516.3MB, time=42.61 memory used=4111.6MB, alloc=516.3MB, time=43.07 memory used=4223.9MB, alloc=516.3MB, time=43.54 memory used=4292.8MB, alloc=540.3MB, time=43.93 memory used=4382.4MB, alloc=540.3MB, time=44.34 memory used=4485.9MB, alloc=540.3MB, time=44.75 memory used=4637.0MB, alloc=540.3MB, time=50.97 memory used=4750.7MB, alloc=540.3MB, time=51.50 memory used=4852.1MB, alloc=540.3MB, time=51.94 memory used=4956.7MB, alloc=540.3MB, time=52.36 memory used=5087.6MB, alloc=540.3MB, time=52.80 memory used=5257.1MB, alloc=540.3MB, time=53.49 memory used=5471.3MB, alloc=540.3MB, time=55.11 memory used=5608.8MB, alloc=540.3MB, time=55.63 memory used=5742.5MB, alloc=540.3MB, time=56.97 memory used=5846.4MB, alloc=540.3MB, time=57.46 memory used=5964.2MB, alloc=540.3MB, time=57.97 memory used=6074.1MB, alloc=540.3MB, time=58.41 memory used=6159.7MB, alloc=540.3MB, time=58.81 memory used=6258.2MB, alloc=540.3MB, time=59.21 memory used=6373.0MB, alloc=540.3MB, time=59.62 memory used=6513.8MB, alloc=540.3MB, time=60.54 memory used=6609.2MB, alloc=540.3MB, time=61.04 memory used=6731.2MB, alloc=540.3MB, time=61.54 memory used=6831.1MB, alloc=540.3MB, time=61.97 memory used=6918.4MB, alloc=540.3MB, time=62.37 memory used=7018.8MB, alloc=540.3MB, time=62.78 memory used=7147.3MB, alloc=540.3MB, time=63.71 memory used=7287.5MB, alloc=540.3MB, time=74.67 memory used=7405.5MB, alloc=540.3MB, time=75.23 memory used=7495.2MB, alloc=540.3MB, time=75.68 memory used=7604.1MB, alloc=540.3MB, time=76.17 memory used=7735.2MB, alloc=540.3MB, time=76.64 memory used=7916.8MB, alloc=540.3MB, time=77.26 memory used=8079.1MB, alloc=540.3MB, time=77.79 memory used=8306.9MB, alloc=540.3MB, time=79.04 memory used=8442.7MB, alloc=540.3MB, time=80.19 memory used=8553.0MB, alloc=540.3MB, time=80.66 memory used=8668.7MB, alloc=540.3MB, time=81.23 memory used=8779.7MB, alloc=540.3MB, time=81.72 memory used=8889.6MB, alloc=540.3MB, time=82.31 memory used=8998.6MB, alloc=540.3MB, time=82.79 memory used=9073.5MB, alloc=540.3MB, time=83.95 memory used=9118.0MB, alloc=540.3MB, time=84.70 memory used=9215.8MB, alloc=540.3MB, time=86.31 memory used=9285.9MB, alloc=540.3MB, time=87.31 memory used=9345.4MB, alloc=540.3MB, time=88.50 memory used=9427.8MB, alloc=540.3MB, time=89.37 memory used=9482.4MB, alloc=540.3MB, time=90.52 memory used=9539.6MB, alloc=540.3MB, time=91.49 memory used=9587.2MB, alloc=540.3MB, time=92.62 memory used=9631.8MB, alloc=540.3MB, time=93.56 memory used=9681.1MB, alloc=540.3MB, time=94.57 memory used=9855.3MB, alloc=564.3MB, time=97.44 memory used=10050.5MB, alloc=564.3MB, time=99.56 memory used=10289.0MB, alloc=564.3MB, time=101.85 memory used=10396.6MB, alloc=564.3MB, time=102.43 memory used=10523.4MB, alloc=564.3MB, time=103.30 memory used=10768.2MB, alloc=588.3MB, time=105.26 memory used=11082.7MB, alloc=588.3MB, time=108.35 memory used=11306.9MB, alloc=612.3MB, time=111.40 memory used=11467.9MB, alloc=612.3MB, time=114.06 memory used=11671.5MB, alloc=612.3MB, time=117.07 memory used=11852.0MB, alloc=636.3MB, time=120.07 memory used=12124.9MB, alloc=636.3MB, time=122.87 memory used=12394.9MB, alloc=660.3MB, time=125.19 memory used=12655.8MB, alloc=660.3MB, time=127.37 memory used=12955.6MB, alloc=660.3MB, time=130.22 memory used=13232.8MB, alloc=660.3MB, time=133.39 memory used=13491.2MB, alloc=684.3MB, time=135.00 memory used=13754.6MB, alloc=684.3MB, time=136.04 memory used=14072.7MB, alloc=684.3MB, time=139.71 memory used=14409.0MB, alloc=684.3MB, time=142.87 memory used=14686.8MB, alloc=708.3MB, time=146.19 memory used=14911.0MB, alloc=708.3MB, time=149.33 memory used=15117.8MB, alloc=732.3MB, time=152.87 memory used=15396.5MB, alloc=756.3MB, time=156.71 memory used=15576.9MB, alloc=780.3MB, time=160.09 memory used=15757.7MB, alloc=804.3MB, time=163.56 memory used=15963.4MB, alloc=828.3MB, time=167.03 memory used=16200.7MB, alloc=852.3MB, time=170.70 memory used=16329.1MB, alloc=876.3MB, time=173.45 memory used=16516.7MB, alloc=900.3MB, time=177.11 memory used=16686.1MB, alloc=924.3MB, time=180.54 memory used=16869.4MB, alloc=948.3MB, time=184.17 memory used=17019.3MB, alloc=972.3MB, time=187.33 memory used=17184.7MB, alloc=996.3MB, time=190.74 memory used=17681.4MB, alloc=1020.3MB, time=198.24 memory used=18181.5MB, alloc=1044.3MB, time=205.87 memory used=18674.0MB, alloc=1068.3MB, time=213.74 memory used=19156.7MB, alloc=1092.3MB, time=221.80 memory used=19638.8MB, alloc=1116.3MB, time=229.75 memory used=20122.0MB, alloc=1140.3MB, time=237.70 memory used=20577.7MB, alloc=1164.3MB, time=246.03 memory used=21020.5MB, alloc=1188.3MB, time=254.23 memory used=21462.3MB, alloc=1212.3MB, time=262.61 memory used=21900.5MB, alloc=1236.3MB, time=270.84 memory used=22378.1MB, alloc=1260.3MB, time=278.51 memory used=22817.6MB, alloc=1284.3MB, time=288.44 memory used=23148.6MB, alloc=1308.3MB, time=300.16 |\^/| 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(); 1428528615 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 3 2 F := [13 y + 13 x - 14, -10 x y z + z - 10 x ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 G := [5 x y z - 20 y - 19 z, -y + y z - 2 y z] > Problem := [F,G]; 3 3 2 Problem := [[13 y + 13 x - 14, -10 x y z + z - 10 x ], 2 3 2 [5 x y z - 20 y - 19 z, -y + y z - 2 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.3MB, alloc=32.3MB, time=0.47 memory used=46.2MB, alloc=32.3MB, time=0.76 memory used=64.0MB, alloc=56.3MB, time=1.02 memory used=103.9MB, alloc=60.3MB, time=1.57 memory used=145.3MB, alloc=60.3MB, time=2.02 memory used=188.8MB, alloc=60.3MB, time=2.51 memory used=230.1MB, alloc=60.3MB, time=3.09 memory used=270.8MB, alloc=92.3MB, time=3.67 memory used=336.3MB, alloc=92.3MB, time=4.54 memory used=387.2MB, alloc=92.3MB, time=4.95 memory used=416.1MB, alloc=92.3MB, time=5.04 memory used=473.7MB, alloc=92.3MB, time=5.46 memory used=536.6MB, alloc=92.3MB, time=7.25 memory used=577.3MB, alloc=92.3MB, time=7.49 memory used=609.0MB, alloc=92.3MB, time=7.61 memory used=635.2MB, alloc=92.3MB, time=7.72 memory used=694.7MB, alloc=116.3MB, time=8.37 memory used=806.1MB, alloc=116.3MB, time=9.17 memory used=901.7MB, alloc=116.3MB, time=9.73 memory used=969.6MB, alloc=116.3MB, time=9.97 memory used=1038.2MB, alloc=116.3MB, time=10.19 memory used=1115.5MB, alloc=119.8MB, time=10.42 memory used=1186.9MB, alloc=131.8MB, time=10.61 memory used=1255.6MB, alloc=131.8MB, time=10.81 memory used=1323.2MB, alloc=131.8MB, time=10.99 memory used=1386.5MB, alloc=131.8MB, time=11.17 memory used=1481.8MB, alloc=131.8MB, time=12.06 memory used=1558.4MB, alloc=131.8MB, time=12.58 memory used=1648.8MB, alloc=131.8MB, time=13.12 memory used=1741.3MB, alloc=131.8MB, time=13.97 memory used=1835.4MB, alloc=155.8MB, time=14.60 memory used=1944.9MB, alloc=155.8MB, time=15.29 memory used=2053.2MB, alloc=155.8MB, time=15.80 memory used=2167.4MB, alloc=155.8MB, time=16.49 memory used=2258.3MB, alloc=155.8MB, time=16.83 memory used=2362.3MB, alloc=155.8MB, time=17.53 memory used=2456.0MB, alloc=155.8MB, time=17.89 memory used=2541.6MB, alloc=155.8MB, time=18.20 memory used=2654.5MB, alloc=155.8MB, time=19.30 memory used=2771.2MB, alloc=155.8MB, time=20.58 memory used=2885.0MB, alloc=155.8MB, time=21.82 memory used=3006.9MB, alloc=155.8MB, time=23.25 memory used=3113.0MB, alloc=435.8MB, time=24.53 memory used=3260.1MB, alloc=435.8MB, time=26.61 memory used=3382.7MB, alloc=459.8MB, time=28.39 memory used=3537.6MB, alloc=483.8MB, time=30.89 memory used=3697.6MB, alloc=507.8MB, time=33.40 memory used=3884.5MB, alloc=531.8MB, time=35.87 memory used=4101.7MB, alloc=555.8MB, time=39.29 memory used=4308.1MB, alloc=579.8MB, time=41.94 memory used=4569.5MB, alloc=603.8MB, time=44.97 memory used=4784.3MB, alloc=627.8MB, time=47.80 memory used=4983.1MB, alloc=651.8MB, time=50.41 memory used=5227.2MB, alloc=675.8MB, time=56.87 memory used=5464.1MB, alloc=699.8MB, time=63.89 memory used=5709.6MB, alloc=723.8MB, time=71.57 memory used=5967.6MB, alloc=747.8MB, time=79.88 memory used=6238.8MB, alloc=771.8MB, time=89.13 memory used=6517.9MB, alloc=795.8MB, time=99.44 memory used=6821.0MB, alloc=819.8MB, time=110.39 memory used=7148.0MB, alloc=843.8MB, time=122.08 memory used=7498.9MB, alloc=867.8MB, time=134.71 memory used=7873.8MB, alloc=867.8MB, time=148.20 memory used=8248.7MB, alloc=867.8MB, time=161.69 memory used=8623.5MB, alloc=891.8MB, time=175.21 memory used=9022.3MB, alloc=891.8MB, time=189.52 memory used=9421.0MB, alloc=891.8MB, time=203.74 memory used=9819.7MB, alloc=891.8MB, time=218.04 memory used=10218.4MB, alloc=915.8MB, time=232.00 memory used=10641.1MB, alloc=915.8MB, time=246.75 memory used=11063.6MB, alloc=939.8MB, time=261.67 memory used=11510.3MB, alloc=939.8MB, time=277.32 |\^/| 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(); 1428528915 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 2 2 2 F := [-15 x - 13 y z - 19 z , 2 x + 5 y + 5 z ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 3 G := [-9 x z + 18 z + 3 x, -9 z - 3] > Problem := [F,G]; 3 2 2 2 2 2 Problem := [[-15 x - 13 y z - 19 z , 2 x + 5 y + 5 z ], 2 2 3 [-9 x z + 18 z + 3 x, -9 z - 3]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.2MB, alloc=32.3MB, time=0.42 memory used=46.0MB, alloc=56.3MB, time=0.65 memory used=85.4MB, alloc=60.3MB, time=1.11 memory used=129.3MB, alloc=68.3MB, time=1.62 memory used=172.2MB, alloc=92.3MB, time=2.10 memory used=238.1MB, alloc=92.3MB, time=2.90 memory used=303.9MB, alloc=92.3MB, time=3.71 memory used=372.8MB, alloc=116.3MB, time=4.50 memory used=443.3MB, alloc=372.3MB, time=5.24 memory used=537.4MB, alloc=372.3MB, time=6.45 memory used=643.2MB, alloc=372.3MB, time=7.57 memory used=753.1MB, alloc=396.3MB, time=8.71 memory used=864.2MB, alloc=396.3MB, time=10.10 memory used=975.9MB, alloc=420.3MB, time=11.52 memory used=1123.5MB, alloc=420.3MB, time=13.17 memory used=1258.8MB, alloc=444.3MB, time=14.81 memory used=1417.2MB, alloc=468.3MB, time=17.51 memory used=1588.8MB, alloc=468.3MB, time=20.53 memory used=1749.1MB, alloc=492.3MB, time=23.38 memory used=1916.9MB, alloc=516.3MB, time=26.90 memory used=2068.3MB, alloc=540.3MB, time=31.57 memory used=2226.4MB, alloc=564.3MB, time=36.95 memory used=2408.6MB, alloc=588.3MB, time=42.94 memory used=2614.9MB, alloc=612.3MB, time=49.70 N1 := 4971 > GB := Basis(F, plex(op(vars))); 6 4 2 6 2 3 5 4 GB := [4225 y + 1690 y x + 5625 x - 14250 y x - 5700 x + 9025 y 2 2 4 + 7220 y x + 1444 x , 3 2 2 4 3 2 2 2 975 x z - 338 x y - 845 y + 1425 x - 494 x z - 722 x - 1805 y , 2 3 2 2 2 2 2 65 z y + 75 x - 95 y - 38 x , 5 z + 5 y + 2 x ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=2853.9MB, alloc=612.3MB, time=53.53 memory used=2990.1MB, alloc=612.3MB, time=55.45 memory used=3121.0MB, alloc=612.3MB, time=57.35 memory used=3257.5MB, alloc=612.3MB, time=59.27 memory used=3425.3MB, alloc=612.3MB, time=61.50 memory used=3623.3MB, alloc=612.3MB, time=63.73 memory used=3740.4MB, alloc=612.3MB, time=65.24 memory used=3984.5MB, alloc=612.3MB, time=67.66 memory used=4262.0MB, alloc=612.3MB, time=73.05 memory used=4396.8MB, alloc=612.3MB, time=74.56 memory used=4499.3MB, alloc=612.3MB, time=76.19 memory used=4606.3MB, alloc=612.3MB, time=77.91 memory used=4704.9MB, alloc=612.3MB, time=79.55 memory used=4807.0MB, alloc=612.3MB, time=81.22 memory used=4916.6MB, alloc=612.3MB, time=82.94 memory used=5017.3MB, alloc=612.3MB, time=84.59 memory used=5107.8MB, alloc=612.3MB, time=85.90 memory used=5203.0MB, alloc=612.3MB, time=87.42 memory used=5295.2MB, alloc=612.3MB, time=88.76 memory used=5403.1MB, alloc=612.3MB, time=90.33 memory used=5484.3MB, alloc=612.3MB, time=91.58 memory used=5568.1MB, alloc=612.3MB, time=92.82 memory used=5652.9MB, alloc=612.3MB, time=94.09 memory used=5736.4MB, alloc=612.3MB, time=95.71 memory used=5813.7MB, alloc=612.3MB, time=97.13 memory used=5886.8MB, alloc=612.3MB, time=98.58 memory used=5967.1MB, alloc=612.3MB, time=99.76 memory used=6103.9MB, alloc=612.3MB, time=101.27 memory used=6177.6MB, alloc=612.3MB, time=102.68 memory used=6235.8MB, alloc=612.3MB, time=103.77 memory used=6294.1MB, alloc=612.3MB, time=104.99 memory used=6396.6MB, alloc=636.3MB, time=107.32 memory used=6457.2MB, alloc=636.3MB, time=108.32 memory used=6542.7MB, alloc=636.3MB, time=109.48 memory used=6601.9MB, alloc=636.3MB, time=110.72 memory used=6650.5MB, alloc=636.3MB, time=111.85 memory used=6708.7MB, alloc=636.3MB, time=113.08 memory used=6768.9MB, alloc=636.3MB, time=114.32 memory used=6832.4MB, alloc=636.3MB, time=115.62 memory used=7117.1MB, alloc=660.3MB, time=119.27 memory used=7388.8MB, alloc=660.3MB, time=122.40 memory used=7682.4MB, alloc=660.3MB, time=125.81 memory used=8029.9MB, alloc=684.3MB, time=128.76 memory used=8352.5MB, alloc=684.3MB, time=132.24 memory used=8579.6MB, alloc=708.3MB, time=135.22 memory used=8809.1MB, alloc=708.3MB, time=138.57 memory used=9085.6MB, alloc=708.3MB, time=141.85 memory used=9347.3MB, alloc=708.3MB, time=145.21 memory used=9572.6MB, alloc=732.3MB, time=148.47 memory used=9860.4MB, alloc=732.3MB, time=152.23 memory used=10126.3MB, alloc=732.3MB, time=155.90 memory used=10496.3MB, alloc=756.3MB, time=161.33 memory used=10889.7MB, alloc=780.3MB, time=167.59 memory used=11294.3MB, alloc=804.3MB, time=174.37 memory used=11639.0MB, alloc=828.3MB, time=185.73 memory used=11951.1MB, alloc=852.3MB, time=198.25 memory used=12277.1MB, alloc=876.3MB, time=211.43 memory used=12627.2MB, alloc=900.3MB, time=225.40 memory used=13001.1MB, alloc=924.3MB, time=240.45 memory used=13399.1MB, alloc=948.3MB, time=256.27 memory used=13821.2MB, alloc=972.3MB, time=272.40 N2 := 9323 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 2 2 2 2 2 2 H := [-15 x - 13 y z - 19 z , 5 z + 5 y + 2 x , -9 x z + 18 z + 3 x, 3 -9 z - 3] > J:=[op(GB),op(G)]; 6 4 2 6 2 3 5 4 J := [4225 y + 1690 y x + 5625 x - 14250 y x - 5700 x + 9025 y 2 2 4 + 7220 y x + 1444 x , 3 4 2 2 2 3 2 2 975 z x - 845 y - 338 y x - 494 z x + 1425 x - 1805 y - 722 x , 2 3 2 2 2 2 2 2 2 65 z y + 75 x - 95 y - 38 x , 5 z + 5 y + 2 x , -9 x z + 18 z + 3 x, 3 -9 z - 3] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 9, 11, 3, 3, 2, 3, 3/4, 1/2, 1, 4/11, 2/11, 6/11, 6, 14, 21, 16 11 6, 6, 6, 3, 5/6, 2/3, 5/6, --, --, 7/27, -5, -10, -3] 27 27 > save(F, G, cat("ranSet/33", convert(F, string),".txt")); > quit memory used=14055.7MB, alloc=972.3MB, time=279.98 |\^/| 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(); 1428529195 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 F := [-9 x y + 12 y z - 10 y , 3 x z + 4 x z + 3 x] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 G := [5 x y + 20, -8 x z - y z] > Problem := [F,G]; 2 2 2 2 Problem := [[-9 x y + 12 y z - 10 y , 3 x z + 4 x z + 3 x], 2 2 [5 x y + 20, -8 x z - y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.4MB, alloc=32.3MB, time=0.48 N1 := 127 > GB := Basis(F, plex(op(vars))); 5 3 2 3 3 3 2 GB := [81 x y + 324 x y + 404 x y , 54 x y z + 117 x y + 202 x y , 2 2 2 2 -9 x y + 12 y z - 10 y , 3 x z + 4 x z + 3 x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=76.6MB, alloc=68.3MB, time=1.18 memory used=124.3MB, alloc=68.3MB, time=1.86 N2 := 327 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; H := [ 2 2 2 2 2 2 -9 x y + 12 y z - 10 y , 3 x z + 4 x z + 3 x, 5 x y + 20, -8 x z - y z ] > J:=[op(GB),op(G)]; 5 3 2 3 3 3 2 J := [81 x y + 324 x y + 404 x y , 54 x y z + 117 x y + 202 x y , 2 2 2 2 2 2 -9 x y + 12 y z - 10 y , 3 x z + 4 x z + 3 x, 5 x y + 20, -8 x z - y z ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 10, 11, 3, 2, 2, 2, 1, 3/4, 3/4, 3/5, 1/2, 1/2, 6, 15, 22, 6, 11 5, 3, 2, 1, 5/6, 2/3, 3/4, --, 3/8, -5, -11, -3] 16 > save(F, G, cat("ranSet/33", convert(F, string),".txt")); > quit memory used=169.3MB, alloc=68.3MB, time=2.55 |\^/| 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(); 1428529197 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 2 2 F := [10 x y - z + 9 z , 10 x z + 6 x z + 9 z ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 G := [5 y + 20 x - 15, 8 y + 8 y z - 9 z] > Problem := [F,G]; 2 3 2 2 2 Problem := [[10 x y - z + 9 z , 10 x z + 6 x z + 9 z ], 2 3 2 [5 y + 20 x - 15, 8 y + 8 y z - 9 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=25.6MB, alloc=32.3MB, time=0.47 memory used=45.5MB, alloc=32.3MB, time=0.76 memory used=64.1MB, alloc=56.3MB, time=1.04 memory used=102.8MB, alloc=60.3MB, time=1.61 memory used=141.3MB, alloc=60.3MB, time=2.12 memory used=179.6MB, alloc=84.3MB, time=2.67 memory used=227.3MB, alloc=84.3MB, time=3.37 memory used=289.5MB, alloc=92.3MB, time=4.15 memory used=350.8MB, alloc=92.3MB, time=5.05 memory used=413.2MB, alloc=116.3MB, time=6.82 memory used=459.4MB, alloc=116.3MB, time=6.95 memory used=505.7MB, alloc=116.3MB, time=7.08 memory used=545.7MB, alloc=116.3MB, time=7.21 memory used=593.0MB, alloc=116.3MB, time=7.32 memory used=649.0MB, alloc=116.3MB, time=7.46 memory used=685.9MB, alloc=116.3MB, time=7.55 memory used=744.2MB, alloc=116.3MB, time=7.82 memory used=845.5MB, alloc=117.5MB, time=9.67 memory used=894.1MB, alloc=117.5MB, time=9.80 memory used=930.2MB, alloc=117.5MB, time=9.92 memory used=975.5MB, alloc=117.5MB, time=10.05 memory used=1029.6MB, alloc=117.5MB, time=10.19 memory used=1066.6MB, alloc=117.5MB, time=10.30 memory used=1100.1MB, alloc=117.5MB, time=10.39 memory used=1136.9MB, alloc=117.5MB, time=10.50 memory used=1177.6MB, alloc=117.5MB, time=10.61 memory used=1221.6MB, alloc=117.5MB, time=10.71 memory used=1269.8MB, alloc=117.5MB, time=10.81 memory used=1336.7MB, alloc=126.1MB, time=10.97 memory used=1431.6MB, alloc=126.1MB, time=11.81 memory used=1507.9MB, alloc=126.1MB, time=13.00 memory used=1584.5MB, alloc=150.1MB, time=13.96 memory used=1679.8MB, alloc=150.1MB, time=14.60 memory used=1748.4MB, alloc=150.1MB, time=15.12 memory used=1802.6MB, alloc=150.1MB, time=15.29 memory used=1844.1MB, alloc=150.1MB, time=15.42 memory used=1909.7MB, alloc=150.1MB, time=15.73 memory used=1964.8MB, alloc=150.1MB, time=15.93 memory used=2030.3MB, alloc=150.1MB, time=16.25 memory used=2097.4MB, alloc=150.1MB, time=16.76 memory used=2145.3MB, alloc=150.1MB, time=16.91 memory used=2196.8MB, alloc=150.1MB, time=17.07 memory used=2244.3MB, alloc=150.1MB, time=17.19 memory used=2284.6MB, alloc=150.1MB, time=17.31 memory used=2360.1MB, alloc=150.1MB, time=18.44 memory used=2406.8MB, alloc=150.1MB, time=18.60 memory used=2496.3MB, alloc=174.1MB, time=29.56 memory used=2570.5MB, alloc=198.1MB, time=49.86 memory used=2654.4MB, alloc=198.1MB, time=50.09 memory used=3375.0MB, alloc=478.1MB, time=53.41 memory used=3454.8MB, alloc=478.1MB, time=55.54 memory used=4311.2MB, alloc=478.1MB, time=61.18 memory used=4691.7MB, alloc=502.1MB, time=64.05 memory used=5411.3MB, alloc=502.1MB, time=68.36 memory used=5937.3MB, alloc=502.1MB, time=72.29 memory used=7033.3MB, alloc=502.1MB, time=78.88 memory used=7069.5MB, alloc=526.1MB, time=80.67 memory used=7252.4MB, alloc=526.1MB, time=83.73 memory used=7939.7MB, alloc=526.1MB, time=88.07 memory used=8159.7MB, alloc=526.1MB, time=95.11 memory used=8200.9MB, alloc=529.6MB, time=95.55 memory used=8204.4MB, alloc=533.1MB, time=95.67 memory used=8207.9MB, alloc=536.5MB, time=95.76 memory used=8211.3MB, alloc=540.0MB, time=95.86 memory used=8214.8MB, alloc=529.6MB, time=96.04 memory used=8361.5MB, alloc=526.1MB, time=97.15 memory used=8517.7MB, alloc=526.1MB, time=97.68 memory used=8624.3MB, alloc=526.1MB, time=97.96 memory used=8749.9MB, alloc=526.1MB, time=98.25 memory used=8899.6MB, alloc=526.1MB, time=98.55 memory used=9030.4MB, alloc=526.1MB, time=98.84 memory used=9124.4MB, alloc=526.1MB, time=99.06 memory used=9225.6MB, alloc=526.1MB, time=99.28 memory used=9335.2MB, alloc=526.1MB, time=99.50 memory used=9454.2MB, alloc=526.1MB, time=99.72 memory used=9583.8MB, alloc=526.1MB, time=99.95 memory used=9725.9MB, alloc=526.1MB, time=100.19 memory used=9883.0MB, alloc=526.1MB, time=100.42 memory used=10178.0MB, alloc=526.1MB, time=102.13 memory used=10373.3MB, alloc=526.1MB, time=102.64 memory used=10581.6MB, alloc=526.1MB, time=103.16 memory used=10811.9MB, alloc=526.1MB, time=103.67 memory used=11063.7MB, alloc=526.1MB, time=104.20 memory used=11338.0MB, alloc=526.1MB, time=104.73 memory used=11577.9MB, alloc=526.1MB, time=105.63 memory used=11779.5MB, alloc=526.1MB, time=106.18 memory used=11993.8MB, alloc=526.1MB, time=106.70 memory used=12231.2MB, alloc=526.1MB, time=107.22 memory used=12477.3MB, alloc=526.1MB, time=108.45 memory used=12664.6MB, alloc=526.1MB, time=109.07 memory used=12871.4MB, alloc=526.1MB, time=110.13 memory used=13054.5MB, alloc=526.1MB, time=110.67 memory used=13267.3MB, alloc=526.1MB, time=111.86 memory used=13481.4MB, alloc=526.1MB, time=112.89 memory used=13676.7MB, alloc=526.1MB, time=113.87 memory used=13899.5MB, alloc=526.1MB, time=116.23 memory used=14253.7MB, alloc=526.1MB, time=148.93 memory used=14453.4MB, alloc=526.1MB, time=151.33 memory used=14615.4MB, alloc=526.1MB, time=153.12 memory used=14766.4MB, alloc=526.1MB, time=154.46 memory used=14911.5MB, alloc=526.1MB, time=157.52 memory used=15031.4MB, alloc=526.1MB, time=158.97 memory used=15139.0MB, alloc=526.1MB, time=160.27 memory used=15277.3MB, alloc=526.1MB, time=163.04 memory used=16400.3MB, alloc=526.1MB, time=167.61 memory used=16614.8MB, alloc=526.1MB, time=168.15 memory used=16976.3MB, alloc=526.1MB, time=199.47 memory used=17145.8MB, alloc=526.1MB, time=201.57 memory used=17294.8MB, alloc=526.1MB, time=203.60 memory used=17430.9MB, alloc=550.1MB, time=205.16 memory used=17592.1MB, alloc=550.1MB, time=208.96 memory used=17722.8MB, alloc=550.1MB, time=210.73 memory used=17842.2MB, alloc=550.1MB, time=212.49 memory used=18610.4MB, alloc=550.1MB, time=218.04 memory used=18975.7MB, alloc=550.1MB, time=258.68 memory used=19163.5MB, alloc=550.1MB, time=263.38 memory used=19319.6MB, alloc=550.1MB, time=265.79 memory used=19480.7MB, alloc=550.1MB, time=272.05 memory used=19623.7MB, alloc=550.1MB, time=274.58 memory used=19743.7MB, alloc=574.1MB, time=276.73 memory used=19901.7MB, alloc=574.1MB, time=282.64 memory used=20704.5MB, alloc=574.1MB, time=292.65 memory used=20956.7MB, alloc=574.1MB, time=298.09 |\^/| 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(); 1428529498 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 F := [x y - 20 z - 12 x, 4 y z - x] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 G := [13 x z + 19 y z - 20 y z , 3 x + 4 y z - 5 z] > Problem := [F,G]; 2 3 2 Problem := [[x y - 20 z - 12 x, 4 y z - x], 2 2 2 2 [13 x z + 19 y z - 20 y z , 3 x + 4 y z - 5 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.59 memory used=26.5MB, alloc=32.3MB, time=1.72 memory used=46.4MB, alloc=32.3MB, time=2.16 memory used=66.1MB, alloc=56.3MB, time=2.46 memory used=106.4MB, alloc=60.3MB, time=3.73 memory used=147.0MB, alloc=84.3MB, time=5.58 memory used=213.8MB, alloc=92.3MB, time=8.60 memory used=280.4MB, alloc=92.3MB, time=9.47 memory used=341.8MB, alloc=116.3MB, time=10.38 memory used=413.0MB, alloc=372.3MB, time=12.38 memory used=498.4MB, alloc=396.3MB, time=16.47 memory used=608.0MB, alloc=396.3MB, time=18.69 memory used=699.0MB, alloc=396.3MB, time=19.57 memory used=782.4MB, alloc=396.3MB, time=22.63 memory used=848.7MB, alloc=396.3MB, time=24.70 memory used=962.8MB, alloc=420.3MB, time=29.99 memory used=1091.4MB, alloc=420.3MB, time=33.54 memory used=1173.2MB, alloc=420.3MB, time=34.91 memory used=1231.1MB, alloc=420.3MB, time=35.59 memory used=1346.6MB, alloc=420.3MB, time=39.69 memory used=1458.8MB, alloc=444.3MB, time=43.68 memory used=1592.0MB, alloc=444.3MB, time=48.54 memory used=1673.7MB, alloc=444.3MB, time=49.78 memory used=1741.2MB, alloc=444.3MB, time=50.09 memory used=1806.2MB, alloc=444.3MB, time=50.32 memory used=1881.3MB, alloc=444.3MB, time=50.75 memory used=1946.4MB, alloc=444.3MB, time=51.02 memory used=2017.7MB, alloc=444.3MB, time=51.27 memory used=2095.8MB, alloc=444.3MB, time=53.44 memory used=2169.9MB, alloc=444.3MB, time=54.37 memory used=2227.4MB, alloc=444.3MB, time=55.11 memory used=2327.4MB, alloc=444.3MB, time=58.19 memory used=2407.3MB, alloc=444.3MB, time=59.18 memory used=2465.8MB, alloc=444.3MB, time=59.99 memory used=2538.4MB, alloc=444.3MB, time=60.84 memory used=2608.7MB, alloc=444.3MB, time=61.61 memory used=2662.2MB, alloc=444.3MB, time=62.24 memory used=2742.5MB, alloc=444.3MB, time=64.26 memory used=2809.1MB, alloc=444.3MB, time=65.15 memory used=2875.5MB, alloc=444.3MB, time=66.02 memory used=2955.2MB, alloc=444.3MB, time=66.91 memory used=3006.4MB, alloc=444.3MB, time=67.59 memory used=3090.2MB, alloc=444.3MB, time=121.69 memory used=3168.9MB, alloc=444.3MB, time=132.92 memory used=3235.3MB, alloc=444.3MB, time=133.81 memory used=3303.2MB, alloc=444.3MB, time=134.64 memory used=3357.0MB, alloc=444.3MB, time=135.37 memory used=3419.2MB, alloc=444.3MB, time=136.12 memory used=3490.0MB, alloc=444.3MB, time=136.92 memory used=3570.4MB, alloc=444.3MB, time=137.75 memory used=3757.9MB, alloc=444.3MB, time=139.68 memory used=3929.8MB, alloc=444.3MB, time=140.97 memory used=4089.5MB, alloc=444.3MB, time=146.27 memory used=4215.3MB, alloc=444.3MB, time=150.89 memory used=4365.4MB, alloc=468.3MB, time=158.39 memory used=4529.2MB, alloc=492.3MB, time=166.89 memory used=4701.2MB, alloc=516.3MB, time=176.77 memory used=4859.3MB, alloc=540.3MB, time=192.40 memory used=5017.9MB, alloc=564.3MB, time=210.96 memory used=5200.9MB, alloc=588.3MB, time=232.00 N1 := 3971 > GB := Basis(F, plex(op(vars))); 2 7 6 3 2 5 4 2 2 GB := [16 x y - 192 x y - 5 x , -4 x y + 48 x y + 5 x z, 4 y z - x, 2 3 2 2 2 3 -x y + 12 x y + 5 x z , -x y + 20 z + 12 x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=5344.7MB, alloc=588.3MB, time=240.81 |\^/| 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(); 1428529798 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 2 3 F := [18 x - 8 x z + 8 y z , 2 x y + z + 5 x z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 G := [3 + 6 x - 14 y, 7 x y - x z - 4 x z] > Problem := [F,G]; 3 2 2 2 3 Problem := [[18 x - 8 x z + 8 y z , 2 x y + z + 5 x z], 2 2 [3 + 6 x - 14 y, 7 x y - x z - 4 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.59 memory used=26.9MB, alloc=32.3MB, time=1.76 memory used=45.7MB, alloc=56.3MB, time=2.72 memory used=86.7MB, alloc=60.3MB, time=4.77 memory used=127.9MB, alloc=60.3MB, time=6.75 memory used=166.1MB, alloc=84.3MB, time=8.58 memory used=231.0MB, alloc=92.3MB, time=10.95 memory used=293.2MB, alloc=92.3MB, time=13.31 memory used=355.5MB, alloc=92.3MB, time=16.34 memory used=419.7MB, alloc=92.3MB, time=19.12 memory used=457.5MB, alloc=116.3MB, time=21.64 memory used=508.3MB, alloc=116.3MB, time=22.18 memory used=555.9MB, alloc=116.3MB, time=22.56 memory used=594.3MB, alloc=116.3MB, time=22.87 memory used=644.4MB, alloc=116.3MB, time=24.11 memory used=701.6MB, alloc=129.7MB, time=25.18 memory used=758.8MB, alloc=129.7MB, time=25.62 memory used=791.9MB, alloc=131.8MB, time=27.22 memory used=811.6MB, alloc=131.8MB, time=27.47 memory used=832.3MB, alloc=131.8MB, time=27.73 memory used=854.2MB, alloc=131.8MB, time=27.99 memory used=877.1MB, alloc=131.8MB, time=28.26 memory used=911.4MB, alloc=131.8MB, time=28.56 memory used=950.4MB, alloc=131.8MB, time=28.86 memory used=991.9MB, alloc=131.8MB, time=29.17 memory used=1026.5MB, alloc=131.8MB, time=29.44 memory used=1039.1MB, alloc=131.8MB, time=29.64 memory used=1051.8MB, alloc=131.8MB, time=29.85 memory used=1064.8MB, alloc=131.8MB, time=30.05 memory used=1077.9MB, alloc=131.8MB, time=30.26 memory used=1091.3MB, alloc=131.8MB, time=30.46 memory used=1121.8MB, alloc=131.8MB, time=32.74 memory used=1206.5MB, alloc=131.8MB, time=35.64 memory used=1275.1MB, alloc=131.8MB, time=37.93 memory used=1370.1MB, alloc=131.8MB, time=41.78 memory used=1448.2MB, alloc=131.8MB, time=43.31 memory used=1523.6MB, alloc=131.8MB, time=44.50 memory used=1615.8MB, alloc=131.8MB, time=47.13 memory used=1689.3MB, alloc=155.8MB, time=48.53 memory used=1802.2MB, alloc=155.8MB, time=51.30 memory used=1920.6MB, alloc=155.8MB, time=54.83 memory used=2037.2MB, alloc=155.8MB, time=57.92 memory used=2125.2MB, alloc=155.8MB, time=59.17 memory used=2234.7MB, alloc=155.8MB, time=61.57 memory used=2327.8MB, alloc=155.8MB, time=62.97 memory used=2453.3MB, alloc=155.8MB, time=66.70 memory used=2559.2MB, alloc=155.8MB, time=69.50 memory used=2640.5MB, alloc=435.8MB, time=74.42 memory used=2761.2MB, alloc=435.8MB, time=81.09 memory used=2886.5MB, alloc=459.8MB, time=86.77 memory used=3046.0MB, alloc=459.8MB, time=93.77 memory used=3193.5MB, alloc=483.8MB, time=98.68 memory used=3370.4MB, alloc=483.8MB, time=106.95 memory used=3526.5MB, alloc=507.8MB, time=115.25 memory used=3698.4MB, alloc=531.8MB, time=124.97 memory used=3904.2MB, alloc=555.8MB, time=134.79 memory used=4132.4MB, alloc=579.8MB, time=146.57 memory used=4377.2MB, alloc=603.8MB, time=155.59 memory used=4660.3MB, alloc=603.8MB, time=166.62 memory used=4940.8MB, alloc=627.8MB, time=175.83 memory used=5252.0MB, alloc=627.8MB, time=185.27 memory used=5455.1MB, alloc=651.8MB, time=197.24 memory used=5677.1MB, alloc=675.8MB, time=215.31 memory used=5902.1MB, alloc=699.8MB, time=234.90 memory used=6136.5MB, alloc=723.8MB, time=256.05 |\^/| 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(); 1428530098 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 2 F := [-15 x z - 3 y + 3 y z, -9 x y z + 3 y z + 5 z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 G := [-6 x y - 8 x y, 9 y + 8 z] > Problem := [F,G]; 2 3 2 2 Problem := [[-15 x z - 3 y + 3 y z, -9 x y z + 3 y z + 5 z], 2 2 [-6 x y - 8 x y, 9 y + 8 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.55 memory used=26.4MB, alloc=32.3MB, time=1.63 memory used=48.7MB, alloc=32.3MB, time=2.94 memory used=69.2MB, alloc=56.3MB, time=4.18 N1 := 683 > GB := Basis(F, plex(op(vars))); 4 5 3 2 GB := [-9 x y + 3 y + 5 y , -9 x y z + 3 y z + 5 z, 2 3 -9 x y z + 15 x z + 3 y + 5 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=110.3MB, alloc=60.3MB, time=7.18 memory used=149.4MB, alloc=84.3MB, time=9.29 memory used=212.3MB, alloc=92.3MB, time=13.09 memory used=268.1MB, alloc=116.3MB, time=17.58 N2 := 1317 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 3 2 2 2 H := [-15 x z - 3 y + 3 y z, -9 x y z + 3 y z + 5 z, -6 x y - 8 x y, 2 9 y + 8 z] > J:=[op(GB),op(G)]; 4 5 3 2 J := [-9 x y + 3 y + 5 y , -9 x y z + 3 y z + 5 z, 2 3 2 2 -9 x y z + 15 x z + 3 y + 5 z, -6 x y - 8 x y, 9 y + 8 z] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 10, 11, 3, 2, 3, 2, 3/4, 1, 3/4, 2/5, 7/10, 3/5, 5, 12, 16, 5, 2, 5, 2, 4/5, 1, 3/5, 3/7, 5/7, 1/2, -2, -5, -2] > save(F, G, cat("ranSet/33", convert(F, string),".txt")); > quit memory used=304.7MB, alloc=116.3MB, time=20.91 |\^/| 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(); 1428530121 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 3 F := [4 x y + 2 x y + 14 y, 9 x z + 6 y + 7 x y] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 3 G := [14 x y + 20 z + 11, 8 z - 4 x - z] > Problem := [F,G]; 2 2 2 3 Problem := [[4 x y + 2 x y + 14 y, 9 x z + 6 y + 7 x y], 2 3 3 [14 x y + 20 z + 11, 8 z - 4 x - z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.54 memory used=25.2MB, alloc=32.3MB, time=1.49 memory used=44.5MB, alloc=56.3MB, time=2.38 memory used=93.5MB, alloc=60.6MB, time=3.56 memory used=143.6MB, alloc=60.6MB, time=4.96 memory used=174.3MB, alloc=60.6MB, time=5.25 memory used=199.9MB, alloc=60.6MB, time=5.40 memory used=247.1MB, alloc=60.6MB, time=6.52 memory used=290.8MB, alloc=68.6MB, time=8.20 memory used=333.5MB, alloc=68.6MB, time=9.46 memory used=378.1MB, alloc=68.6MB, time=12.12 memory used=402.0MB, alloc=68.6MB, time=12.37 memory used=444.2MB, alloc=68.6MB, time=13.88 memory used=486.7MB, alloc=68.6MB, time=15.58 memory used=523.3MB, alloc=92.6MB, time=16.62 memory used=562.8MB, alloc=92.6MB, time=16.98 memory used=598.5MB, alloc=92.6MB, time=17.30 memory used=642.0MB, alloc=92.6MB, time=17.61 memory used=676.7MB, alloc=92.6MB, time=17.88 memory used=703.6MB, alloc=92.6MB, time=18.14 memory used=733.9MB, alloc=92.6MB, time=18.38 memory used=766.4MB, alloc=92.6MB, time=18.68 memory used=802.8MB, alloc=92.6MB, time=18.93 memory used=842.7MB, alloc=92.6MB, time=19.20 memory used=888.8MB, alloc=92.6MB, time=19.47 memory used=920.3MB, alloc=92.6MB, time=19.70 memory used=970.2MB, alloc=92.6MB, time=20.66 memory used=1007.3MB, alloc=92.6MB, time=21.01 memory used=1043.4MB, alloc=92.6MB, time=21.34 memory used=1087.1MB, alloc=92.6MB, time=21.68 memory used=1120.1MB, alloc=92.6MB, time=21.95 memory used=1146.9MB, alloc=92.6MB, time=22.19 memory used=1177.2MB, alloc=92.6MB, time=22.48 memory used=1209.8MB, alloc=92.6MB, time=22.74 memory used=1246.2MB, alloc=92.6MB, time=23.01 memory used=1287.4MB, alloc=92.6MB, time=23.28 memory used=1333.6MB, alloc=92.6MB, time=23.57 memory used=1363.4MB, alloc=92.6MB, time=23.78 memory used=1421.1MB, alloc=92.6MB, time=61.00 memory used=1469.6MB, alloc=116.6MB, time=125.50 memory used=1528.1MB, alloc=116.6MB, time=219.34 memory used=1580.5MB, alloc=116.6MB, time=393.25 |\^/| 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(); 1428530421 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 3 2 F := [9 x z - 8 x y z - 15 z, -2 x y + y - 7 y z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 G := [-12 y z + 19 x y + 10 z , -2 x y - 2 x z - 5 y z] > Problem := [F,G]; 2 2 3 2 Problem := [[9 x z - 8 x y z - 15 z, -2 x y + y - 7 y z], 2 2 [-12 y z + 19 x y + 10 z , -2 x y - 2 x z - 5 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.60 memory used=26.5MB, alloc=32.3MB, time=1.72 memory used=47.7MB, alloc=32.3MB, time=2.79 memory used=67.2MB, alloc=56.3MB, time=3.82 memory used=107.8MB, alloc=60.3MB, time=5.83 memory used=145.9MB, alloc=60.3MB, time=7.65 memory used=185.4MB, alloc=84.3MB, time=9.65 memory used=224.7MB, alloc=84.3MB, time=11.36 memory used=291.6MB, alloc=92.3MB, time=14.47 memory used=359.1MB, alloc=116.3MB, time=17.17 memory used=439.8MB, alloc=116.3MB, time=21.07 memory used=532.0MB, alloc=140.3MB, time=24.89 memory used=628.8MB, alloc=140.3MB, time=29.62 memory used=704.0MB, alloc=420.3MB, time=34.52 memory used=828.9MB, alloc=444.3MB, time=41.46 memory used=973.7MB, alloc=468.3MB, time=48.96 memory used=1122.6MB, alloc=492.3MB, time=58.00 memory used=1283.3MB, alloc=516.3MB, time=67.86 memory used=1479.4MB, alloc=540.3MB, time=77.51 memory used=1692.2MB, alloc=564.3MB, time=87.96 memory used=1896.0MB, alloc=588.3MB, time=98.38 memory used=2078.5MB, alloc=612.3MB, time=108.27 memory used=2243.8MB, alloc=636.3MB, time=117.35 memory used=2471.4MB, alloc=660.3MB, time=135.21 memory used=2681.5MB, alloc=684.3MB, time=156.44 memory used=2900.9MB, alloc=708.3MB, time=179.70 memory used=3134.1MB, alloc=732.3MB, time=203.49 memory used=3381.2MB, alloc=756.3MB, time=230.52 |\^/| 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(); 1428530721 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 F := [20 x + 20 x z - 1, -5 x y + 3 x z - 6 z ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 3 G := [-4 y z + 3 z , 7 x - 5 x y z - z] > Problem := [F,G]; 3 2 2 Problem := [[20 x + 20 x z - 1, -5 x y + 3 x z - 6 z ], 2 3 3 [-4 y z + 3 z , 7 x - 5 x y z - z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.59 memory used=26.7MB, alloc=32.3MB, time=1.76 memory used=47.7MB, alloc=32.3MB, time=2.82 memory used=67.5MB, alloc=56.3MB, time=3.88 memory used=105.9MB, alloc=84.3MB, time=5.91 memory used=151.6MB, alloc=84.3MB, time=8.26 memory used=212.6MB, alloc=92.3MB, time=11.75 memory used=271.9MB, alloc=116.3MB, time=15.02 memory used=353.8MB, alloc=116.3MB, time=19.49 memory used=433.5MB, alloc=140.3MB, time=24.14 memory used=511.4MB, alloc=140.3MB, time=28.77 memory used=584.1MB, alloc=396.3MB, time=32.82 memory used=684.7MB, alloc=420.3MB, time=37.97 memory used=801.4MB, alloc=444.3MB, time=44.23 memory used=932.3MB, alloc=468.3MB, time=51.03 memory used=1082.5MB, alloc=492.3MB, time=58.41 memory used=1244.2MB, alloc=516.3MB, time=63.14 memory used=1414.6MB, alloc=540.3MB, time=65.84 memory used=1595.3MB, alloc=564.3MB, time=68.73 memory used=1785.3MB, alloc=588.3MB, time=71.70 memory used=1983.2MB, alloc=612.3MB, time=74.88 memory used=2180.6MB, alloc=636.3MB, time=79.27 memory used=2363.5MB, alloc=660.3MB, time=84.79 memory used=2553.0MB, alloc=684.3MB, time=90.98 memory used=2753.7MB, alloc=708.3MB, time=97.77 memory used=2967.0MB, alloc=732.3MB, time=104.96 memory used=3193.6MB, alloc=756.3MB, time=112.60 memory used=3433.6MB, alloc=780.3MB, time=120.96 memory used=3685.9MB, alloc=804.3MB, time=130.84 memory used=3953.9MB, alloc=828.3MB, time=141.81 memory used=4245.8MB, alloc=852.3MB, time=153.06 memory used=4561.6MB, alloc=876.3MB, time=165.07 memory used=4901.4MB, alloc=900.3MB, time=178.92 memory used=5265.1MB, alloc=924.3MB, time=193.16 memory used=5652.8MB, alloc=948.3MB, time=207.57 memory used=6064.4MB, alloc=972.3MB, time=223.04 memory used=6499.9MB, alloc=996.3MB, time=239.26 memory used=6959.4MB, alloc=996.3MB, time=256.65 memory used=7418.9MB, alloc=996.3MB, time=273.94 |\^/| 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(); 1428531020 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 F := [-8 x y z - x + 16, -9 x y - 2 z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 G := [-7 x y - x z - 11 z, 2 x z - y - 2 z] > Problem := [F,G]; 2 2 Problem := [[-8 x y z - x + 16, -9 x y - 2 z], 2 2 [-7 x y - x z - 11 z, 2 x z - y - 2 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.2MB, alloc=32.3MB, time=0.48 memory used=46.8MB, alloc=32.3MB, time=0.77 memory used=66.3MB, alloc=56.3MB, time=1.06 memory used=107.0MB, alloc=60.3MB, time=1.67 memory used=146.5MB, alloc=84.3MB, time=2.27 memory used=209.1MB, alloc=92.3MB, time=3.27 memory used=269.0MB, alloc=116.3MB, time=4.35 memory used=349.7MB, alloc=140.3MB, time=5.68 memory used=447.3MB, alloc=140.3MB, time=7.30 memory used=536.6MB, alloc=164.3MB, time=8.93 memory used=640.0MB, alloc=444.3MB, time=10.82 memory used=766.2MB, alloc=468.3MB, time=12.69 memory used=912.9MB, alloc=492.3MB, time=14.74 memory used=1074.8MB, alloc=516.3MB, time=17.02 memory used=1242.8MB, alloc=540.3MB, time=19.74 memory used=1412.0MB, alloc=564.3MB, time=24.13 memory used=1585.9MB, alloc=588.3MB, time=29.27 memory used=1771.7MB, alloc=612.3MB, time=35.38 memory used=1972.0MB, alloc=636.3MB, time=42.38 memory used=2180.5MB, alloc=660.3MB, time=50.39 memory used=2413.0MB, alloc=684.3MB, time=59.52 memory used=2669.3MB, alloc=708.3MB, time=69.34 memory used=2949.6MB, alloc=732.3MB, time=80.17 memory used=3253.9MB, alloc=732.3MB, time=91.95 memory used=3558.1MB, alloc=732.3MB, time=103.78 memory used=3862.2MB, alloc=732.3MB, time=114.37 memory used=4166.3MB, alloc=756.3MB, time=125.27 memory used=4494.3MB, alloc=756.3MB, time=137.51 memory used=4822.3MB, alloc=756.3MB, time=149.88 memory used=5150.3MB, alloc=780.3MB, time=162.55 memory used=5502.2MB, alloc=780.3MB, time=175.78 memory used=5854.1MB, alloc=804.3MB, time=189.22 memory used=6229.9MB, alloc=828.3MB, time=203.10 N1 := 12859 > GB := Basis(F, plex(op(vars))); 2 3 2 2 GB := [36 y x - x + 16, 9 y x + 2 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=6639.6MB, alloc=828.3MB, time=212.10 N2 := 2849 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; H := 2 2 2 2 [-8 x y z - x + 16, -9 x y - 2 z, -7 x y - x z - 11 z, 2 z x - 2 z - y] > J:=[op(GB),op(G)]; 2 3 2 2 2 2 J := [36 y x - x + 16, 9 y x + 2 z, -7 x y - x z - 11 z, 2 z x - 2 z - y] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 12, 11, 3, 2, 1, 2, 1, 1, 1, 6/11, 4/11, 6/11, 4, 11, 13, 5, 3, 2, 2, 1, 1, 3/4, 6/11, 4/11, 5/11, 1, -2, -2] > save(F, G, cat("ranSet/33", convert(F, string),".txt")); > quit memory used=6965.5MB, alloc=828.3MB, time=222.80 |\^/| 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(); 1428531252 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 2 F := [-5 x y + 14 z + 7 x , 6 x + 10 y z - 1] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 3 3 3 2 G := [-15 x - y - 4 z , 7 x - 9 x z - y z] > Problem := [F,G]; 2 3 2 2 Problem := [[-5 x y + 14 z + 7 x , 6 x + 10 y z - 1], 3 3 3 3 2 [-15 x - y - 4 z , 7 x - 9 x z - y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=25.5MB, alloc=32.3MB, time=0.48 memory used=44.6MB, alloc=56.3MB, time=0.74 memory used=87.9MB, alloc=60.3MB, time=1.27 memory used=133.7MB, alloc=68.3MB, time=1.71 memory used=183.8MB, alloc=68.4MB, time=2.28 memory used=230.7MB, alloc=68.4MB, time=2.83 memory used=264.4MB, alloc=68.4MB, time=3.09 memory used=311.9MB, alloc=68.4MB, time=3.60 memory used=354.9MB, alloc=92.4MB, time=4.11 memory used=420.7MB, alloc=92.4MB, time=4.69 memory used=464.1MB, alloc=92.4MB, time=4.93 memory used=543.4MB, alloc=92.4MB, time=5.96 memory used=580.7MB, alloc=92.4MB, time=6.08 memory used=626.1MB, alloc=92.4MB, time=6.33 memory used=676.0MB, alloc=92.4MB, time=6.96 memory used=706.6MB, alloc=92.4MB, time=7.06 memory used=742.5MB, alloc=92.4MB, time=7.15 memory used=787.3MB, alloc=92.4MB, time=7.49 memory used=867.3MB, alloc=92.4MB, time=8.37 memory used=906.0MB, alloc=92.4MB, time=8.50 memory used=946.0MB, alloc=92.4MB, time=8.71 memory used=1016.0MB, alloc=92.4MB, time=9.52 memory used=1080.5MB, alloc=116.4MB, time=10.36 memory used=1149.0MB, alloc=116.4MB, time=11.23 memory used=1221.8MB, alloc=372.4MB, time=12.03 memory used=1280.5MB, alloc=372.4MB, time=12.43 memory used=1342.6MB, alloc=372.4MB, time=12.91 memory used=1395.5MB, alloc=372.4MB, time=13.18 memory used=1436.4MB, alloc=372.4MB, time=13.33 memory used=1475.7MB, alloc=372.4MB, time=13.46 memory used=1531.3MB, alloc=372.4MB, time=13.77 memory used=1574.4MB, alloc=372.4MB, time=13.90 memory used=1645.5MB, alloc=372.4MB, time=15.28 memory used=1684.7MB, alloc=372.4MB, time=15.42 memory used=1725.1MB, alloc=372.4MB, time=15.54 memory used=1780.0MB, alloc=372.4MB, time=15.85 memory used=1823.4MB, alloc=372.4MB, time=15.98 memory used=1867.9MB, alloc=372.4MB, time=16.31 memory used=1923.8MB, alloc=372.4MB, time=16.67 memory used=1964.7MB, alloc=372.4MB, time=16.82 memory used=2003.9MB, alloc=372.4MB, time=16.95 memory used=2052.3MB, alloc=372.4MB, time=17.30 memory used=2132.1MB, alloc=372.4MB, time=23.51 memory used=2266.4MB, alloc=372.4MB, time=23.98 memory used=2310.1MB, alloc=372.4MB, time=24.13 memory used=2351.9MB, alloc=372.4MB, time=24.28 memory used=2391.8MB, alloc=372.4MB, time=24.41 memory used=2423.9MB, alloc=372.4MB, time=24.54 memory used=2462.3MB, alloc=372.4MB, time=24.67 memory used=2533.8MB, alloc=372.4MB, time=25.31 memory used=2642.1MB, alloc=372.4MB, time=26.47 memory used=2701.7MB, alloc=396.4MB, time=26.92 memory used=2826.7MB, alloc=396.4MB, time=28.05 memory used=2960.6MB, alloc=396.4MB, time=29.24 memory used=3036.4MB, alloc=396.4MB, time=29.86 memory used=3100.5MB, alloc=396.4MB, time=30.17 memory used=3149.9MB, alloc=396.4MB, time=30.35 memory used=3215.3MB, alloc=396.4MB, time=30.69 memory used=3274.7MB, alloc=396.4MB, time=32.91 memory used=3480.7MB, alloc=396.4MB, time=37.27 memory used=3542.7MB, alloc=396.4MB, time=37.62 memory used=3598.9MB, alloc=396.4MB, time=37.82 memory used=3807.4MB, alloc=396.4MB, time=44.42 memory used=3865.6MB, alloc=396.4MB, time=44.72 memory used=3918.7MB, alloc=396.4MB, time=44.91 memory used=3977.9MB, alloc=396.4MB, time=45.25 memory used=4120.0MB, alloc=396.4MB, time=45.55 memory used=4260.3MB, alloc=396.4MB, time=46.27 memory used=4456.9MB, alloc=396.4MB, time=46.61 memory used=4689.3MB, alloc=396.4MB, time=46.94 memory used=4884.5MB, alloc=396.4MB, time=47.21 memory used=5091.8MB, alloc=396.4MB, time=47.47 memory used=5169.8MB, alloc=396.4MB, time=48.23 memory used=5225.2MB, alloc=396.4MB, time=48.41 memory used=5266.9MB, alloc=396.4MB, time=48.57 memory used=5320.7MB, alloc=396.4MB, time=48.83 memory used=5429.5MB, alloc=396.4MB, time=49.95 memory used=5515.4MB, alloc=396.4MB, time=50.57 memory used=5637.4MB, alloc=420.4MB, time=51.76 memory used=5754.2MB, alloc=420.4MB, time=52.81 memory used=5867.9MB, alloc=420.4MB, time=53.85 memory used=6000.1MB, alloc=444.4MB, time=55.13 memory used=6105.6MB, alloc=444.4MB, time=55.88 memory used=6208.8MB, alloc=444.4MB, time=56.50 memory used=6305.0MB, alloc=444.4MB, time=56.96 memory used=6408.9MB, alloc=444.4MB, time=57.59 memory used=6517.7MB, alloc=444.4MB, time=58.48 memory used=6667.0MB, alloc=444.4MB, time=60.00 memory used=6785.7MB, alloc=444.4MB, time=61.43 memory used=6881.6MB, alloc=468.4MB, time=62.61 memory used=7028.1MB, alloc=468.4MB, time=63.78 memory used=7112.8MB, alloc=468.4MB, time=64.25 memory used=7200.3MB, alloc=468.4MB, time=64.76 memory used=7283.0MB, alloc=468.4MB, time=65.12 memory used=7372.9MB, alloc=468.4MB, time=65.58 memory used=7445.6MB, alloc=468.4MB, time=65.90 memory used=7532.2MB, alloc=468.4MB, time=66.33 memory used=7611.9MB, alloc=468.4MB, time=66.72 memory used=7685.4MB, alloc=468.4MB, time=67.01 memory used=7786.3MB, alloc=468.4MB, time=67.57 memory used=7853.1MB, alloc=468.4MB, time=67.92 memory used=7943.9MB, alloc=468.4MB, time=68.28 memory used=8005.1MB, alloc=468.4MB, time=68.57 memory used=8070.0MB, alloc=468.4MB, time=68.86 memory used=8164.6MB, alloc=468.4MB, time=69.47 memory used=8238.1MB, alloc=468.4MB, time=69.80 memory used=8320.2MB, alloc=468.4MB, time=70.14 memory used=8394.7MB, alloc=468.4MB, time=70.45 memory used=8457.2MB, alloc=468.4MB, time=70.74 memory used=8561.4MB, alloc=468.4MB, time=73.22 memory used=8639.4MB, alloc=468.4MB, time=73.58 memory used=8714.7MB, alloc=468.4MB, time=73.91 memory used=8780.4MB, alloc=468.4MB, time=74.21 memory used=8859.1MB, alloc=468.4MB, time=74.52 memory used=8952.8MB, alloc=468.4MB, time=74.84 memory used=9112.8MB, alloc=468.4MB, time=75.27 memory used=9311.6MB, alloc=468.4MB, time=76.00 memory used=9378.9MB, alloc=468.4MB, time=76.34 memory used=9469.6MB, alloc=468.4MB, time=76.69 memory used=9530.2MB, alloc=468.4MB, time=76.97 memory used=9595.2MB, alloc=468.4MB, time=77.26 memory used=9705.5MB, alloc=468.4MB, time=79.77 memory used=9782.7MB, alloc=468.4MB, time=80.14 memory used=9852.8MB, alloc=468.4MB, time=80.46 memory used=9919.4MB, alloc=468.4MB, time=80.77 memory 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time=309.69 memory used=48162.8MB, alloc=516.4MB, time=310.19 memory used=48268.4MB, alloc=516.4MB, time=310.66 memory used=48377.7MB, alloc=516.4MB, time=311.14 memory used=48491.4MB, alloc=516.4MB, time=311.61 memory used=48595.7MB, alloc=516.4MB, time=312.06 memory used=48692.7MB, alloc=516.4MB, time=312.48 memory used=48783.8MB, alloc=516.4MB, time=312.90 memory used=48870.0MB, alloc=516.4MB, time=313.30 memory used=48955.4MB, alloc=516.4MB, time=313.67 memory used=49038.7MB, alloc=516.4MB, time=314.08 memory used=49124.0MB, alloc=516.4MB, time=314.48 memory used=49206.4MB, alloc=516.4MB, time=314.85 memory used=49290.4MB, alloc=516.4MB, time=315.22 memory used=49372.7MB, alloc=516.4MB, time=315.58 memory used=49457.5MB, alloc=516.4MB, time=315.96 memory used=49549.2MB, alloc=516.4MB, time=316.37 memory used=49642.2MB, alloc=516.4MB, time=316.74 memory used=49736.5MB, alloc=516.4MB, time=317.15 memory used=49832.1MB, alloc=516.4MB, time=317.60 memory used=49929.4MB, alloc=516.4MB, time=318.05 memory used=50033.7MB, alloc=516.4MB, time=318.47 memory used=50139.3MB, alloc=516.4MB, time=318.90 memory used=50246.0MB, alloc=516.4MB, time=319.35 memory used=50354.2MB, alloc=516.4MB, time=319.79 memory used=50469.8MB, alloc=516.4MB, time=320.23 memory used=50586.3MB, alloc=516.4MB, time=320.68 memory used=50704.1MB, alloc=516.4MB, time=321.16 memory used=50829.2MB, alloc=516.4MB, time=321.60 memory used=50943.8MB, alloc=516.4MB, time=322.06 memory used=51043.0MB, alloc=516.4MB, time=322.51 memory used=51138.2MB, alloc=516.4MB, time=322.92 memory used=51224.7MB, alloc=516.4MB, time=323.30 memory used=51307.1MB, alloc=516.4MB, time=323.68 memory used=51389.5MB, alloc=516.4MB, time=324.06 memory used=51466.7MB, alloc=540.4MB, time=324.46 memory used=51551.7MB, alloc=540.4MB, time=324.84 memory used=51636.0MB, alloc=540.4MB, time=325.18 memory used=51720.4MB, alloc=540.4MB, time=325.51 memory used=51799.8MB, alloc=540.4MB, time=325.86 memory used=51881.0MB, alloc=540.4MB, time=326.19 memory used=51962.8MB, alloc=540.4MB, time=326.54 memory used=52051.3MB, alloc=540.4MB, time=326.88 memory used=52139.9MB, alloc=540.4MB, time=327.24 memory used=52228.3MB, alloc=540.4MB, time=327.58 memory used=52316.7MB, alloc=540.4MB, time=327.92 memory used=52405.1MB, alloc=540.4MB, time=328.26 memory used=52500.1MB, alloc=540.4MB, time=328.60 memory used=52595.0MB, alloc=540.4MB, time=328.96 memory used=52689.5MB, alloc=540.4MB, time=329.31 memory used=52783.8MB, alloc=540.4MB, time=329.65 memory used=52878.2MB, alloc=540.4MB, time=330.00 memory used=52978.5MB, alloc=540.4MB, time=330.35 memory used=53078.4MB, alloc=540.4MB, time=330.70 memory used=53178.1MB, alloc=540.4MB, time=331.05 memory used=53283.7MB, alloc=540.4MB, time=331.40 memory used=53388.6MB, alloc=540.4MB, time=331.74 memory used=53492.9MB, alloc=540.4MB, time=332.13 memory used=53602.8MB, alloc=540.4MB, time=332.47 memory used=53711.9MB, alloc=540.4MB, time=332.84 memory used=53826.2MB, alloc=540.4MB, time=333.18 memory used=53939.4MB, alloc=540.4MB, time=333.54 memory used=54057.4MB, alloc=540.4MB, time=333.89 memory used=54174.0MB, alloc=540.4MB, time=334.26 memory used=54294.9MB, alloc=540.4MB, time=334.63 memory used=54419.8MB, alloc=540.4MB, time=335.00 memory used=54542.5MB, alloc=540.4MB, time=335.37 memory used=54668.5MB, alloc=540.4MB, time=335.74 memory used=54797.4MB, alloc=540.4MB, time=336.11 memory used=54928.4MB, alloc=540.4MB, time=336.48 memory used=55061.2MB, alloc=540.4MB, time=336.86 memory used=55199.8MB, alloc=540.4MB, time=337.24 memory used=55338.2MB, alloc=540.4MB, time=337.61 memory used=55480.1MB, alloc=540.4MB, time=337.99 memory used=55628.1MB, alloc=540.4MB, time=338.38 memory used=55779.3MB, alloc=540.4MB, time=338.76 memory used=55934.1MB, alloc=540.4MB, time=339.16 memory used=56136.4MB, alloc=540.4MB, time=339.60 memory used=56263.0MB, alloc=540.4MB, time=339.98 memory used=56511.0MB, alloc=540.4MB, time=351.46 memory used=56637.0MB, alloc=540.4MB, time=351.97 memory used=56765.9MB, alloc=540.4MB, time=352.45 memory used=56898.8MB, alloc=540.4MB, time=352.93 memory used=57016.5MB, alloc=540.4MB, time=353.39 memory used=57126.6MB, alloc=540.4MB, time=353.84 memory used=57231.9MB, alloc=540.4MB, time=354.29 memory used=57334.4MB, alloc=540.4MB, time=354.75 memory used=57436.1MB, alloc=540.4MB, time=355.17 memory used=57536.2MB, alloc=540.4MB, time=355.57 memory used=57634.4MB, alloc=540.4MB, time=356.00 memory used=57736.1MB, alloc=540.4MB, time=356.40 memory used=57837.1MB, alloc=540.4MB, time=356.81 memory used=57940.6MB, alloc=540.4MB, time=357.23 memory used=58051.4MB, alloc=540.4MB, time=357.68 memory used=58164.1MB, alloc=540.4MB, time=358.10 memory used=58278.9MB, alloc=540.4MB, time=358.55 memory used=58401.5MB, alloc=540.4MB, time=358.97 memory used=58525.7MB, alloc=540.4MB, time=359.42 memory used=58651.9MB, alloc=540.4MB, time=359.85 memory used=58786.0MB, alloc=540.4MB, time=360.32 memory used=58921.6MB, alloc=540.4MB, time=360.78 memory used=59059.0MB, alloc=540.4MB, time=361.19 memory used=59204.1MB, alloc=540.4MB, time=361.67 memory used=59337.9MB, alloc=540.4MB, time=362.10 memory used=59458.2MB, alloc=540.4MB, time=362.51 memory used=59565.7MB, alloc=540.4MB, time=362.88 memory used=59663.8MB, alloc=540.4MB, time=363.26 memory used=59758.4MB, alloc=540.4MB, time=363.61 memory used=59847.2MB, alloc=540.4MB, time=363.96 memory used=59936.8MB, alloc=540.4MB, time=364.33 memory used=60021.2MB, alloc=540.4MB, time=364.71 memory used=60105.4MB, alloc=540.4MB, time=365.05 memory used=60184.8MB, alloc=540.4MB, time=365.42 memory used=60265.9MB, alloc=540.4MB, time=365.78 memory used=60347.7MB, alloc=540.4MB, time=366.15 memory used=60436.2MB, alloc=540.4MB, time=366.51 memory used=60524.7MB, alloc=540.4MB, time=366.88 memory used=60613.2MB, alloc=540.4MB, time=367.25 memory used=60701.6MB, alloc=540.4MB, time=367.63 memory used=60789.9MB, alloc=540.4MB, time=368.00 memory used=60878.3MB, alloc=540.4MB, time=368.37 memory used=60973.1MB, alloc=540.4MB, time=368.75 memory used=61067.7MB, alloc=540.4MB, time=369.13 memory used=61162.0MB, alloc=540.4MB, time=369.51 memory used=61256.3MB, alloc=540.4MB, time=369.88 memory used=61356.8MB, alloc=540.4MB, time=370.24 memory used=61456.8MB, alloc=540.4MB, time=370.63 memory used=61556.5MB, alloc=540.4MB, time=371.02 memory used=61662.2MB, alloc=540.4MB, time=371.41 memory used=61767.2MB, alloc=540.4MB, time=371.80 memory used=61871.6MB, alloc=540.4MB, time=372.20 memory used=61981.6MB, alloc=540.4MB, time=372.59 memory used=62090.8MB, alloc=540.4MB, time=372.98 memory used=62205.3MB, alloc=540.4MB, time=373.32 memory used=62318.6MB, alloc=540.4MB, time=373.69 memory used=62436.7MB, alloc=540.4MB, time=374.05 |\^/| 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(); 1428531552 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 2 F := [-12 x y + 16 y z + 9 x , -3 y z - 5 x z - 6 z ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 G := [2 x y z - 7 z + 17 x z, -6 y z + x + y] > Problem := [F,G]; 2 2 2 2 2 Problem := [[-12 x y + 16 y z + 9 x , -3 y z - 5 x z - 6 z ], 3 [2 x y z - 7 z + 17 x z, -6 y z + x + y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=26.5MB, alloc=32.3MB, time=0.51 memory used=46.8MB, alloc=56.3MB, time=0.80 memory used=87.0MB, alloc=60.3MB, time=1.36 memory used=124.0MB, alloc=84.3MB, time=1.91 memory used=170.0MB, alloc=84.3MB, time=2.59 memory used=229.9MB, alloc=92.3MB, time=3.50 memory used=292.7MB, alloc=116.3MB, time=4.40 memory used=375.7MB, alloc=116.3MB, time=5.57 memory used=457.6MB, alloc=140.3MB, time=6.75 memory used=539.1MB, alloc=140.3MB, time=7.98 memory used=603.4MB, alloc=420.3MB, time=8.94 memory used=729.3MB, alloc=444.3MB, time=10.84 memory used=881.7MB, alloc=444.3MB, time=13.15 memory used=1026.7MB, alloc=468.3MB, time=15.36 memory used=1166.1MB, alloc=492.3MB, time=17.44 memory used=1372.8MB, alloc=492.3MB, time=19.44 memory used=1566.1MB, alloc=516.3MB, time=21.80 memory used=1694.0MB, alloc=540.3MB, time=23.97 memory used=1856.0MB, alloc=564.3MB, time=26.80 memory used=2039.7MB, alloc=588.3MB, time=29.77 memory used=2247.2MB, alloc=612.3MB, time=32.55 memory used=2436.4MB, alloc=636.3MB, time=35.37 memory used=2618.3MB, alloc=660.3MB, time=38.04 memory used=2768.4MB, alloc=684.3MB, time=40.35 memory used=2913.8MB, alloc=684.3MB, time=42.91 memory used=3116.5MB, alloc=708.3MB, time=45.49 memory used=3268.5MB, alloc=732.3MB, time=47.93 memory used=3398.2MB, alloc=756.3MB, time=50.26 memory used=3534.4MB, alloc=780.3MB, time=52.82 memory used=3660.5MB, alloc=780.3MB, time=55.14 memory used=3785.1MB, alloc=804.3MB, time=57.37 memory used=3891.5MB, alloc=804.3MB, time=59.59 memory used=3997.3MB, alloc=828.3MB, time=61.71 memory used=4103.3MB, alloc=852.3MB, time=63.82 memory used=4215.7MB, alloc=852.3MB, time=66.06 memory used=4313.7MB, alloc=876.3MB, time=68.23 memory used=4412.8MB, alloc=876.3MB, time=70.28 memory used=4514.4MB, alloc=900.3MB, time=72.41 memory used=4605.1MB, alloc=900.3MB, time=74.34 memory used=4728.7MB, alloc=924.3MB, time=77.90 memory used=5112.1MB, alloc=948.3MB, time=91.90 memory used=5492.5MB, alloc=972.3MB, time=106.60 memory used=5875.6MB, alloc=996.3MB, time=120.79 memory used=6266.0MB, alloc=1020.3MB, time=135.67 memory used=6666.1MB, alloc=1044.3MB, time=151.82 memory used=7077.3MB, alloc=1068.3MB, time=168.94 memory used=7500.8MB, alloc=1092.3MB, time=186.77 memory used=7936.9MB, alloc=1116.3MB, time=204.64 memory used=8386.1MB, alloc=1140.3MB, time=222.85 memory used=8849.0MB, alloc=1164.3MB, time=241.72 memory used=9320.2MB, alloc=1188.3MB, time=261.63 memory used=9810.2MB, alloc=1212.3MB, time=282.42 |\^/| 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(); 1428531852 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 F := [-12 x z - 2 z + 6, -4 x z + z ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 2 2 G := [15 x y - 8 y - y, -6 x y - 4 y z + 7 y z ] > Problem := [F,G]; 2 2 2 2 Problem := [[-12 x z - 2 z + 6, -4 x z + z ], 2 3 2 2 2 [15 x y - 8 y - y, -6 x y - 4 y z + 7 y z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.6MB, alloc=32.3MB, time=0.50 memory used=47.6MB, alloc=32.3MB, time=0.81 memory used=66.7MB, alloc=56.3MB, time=1.10 memory used=107.2MB, alloc=60.3MB, time=1.75 memory used=146.7MB, alloc=84.3MB, time=2.44 memory used=206.0MB, alloc=108.3MB, time=3.49 memory used=284.0MB, alloc=140.3MB, time=4.84 memory used=374.9MB, alloc=164.3MB, time=6.59 memory used=471.5MB, alloc=188.3MB, time=9.27 memory used=575.5MB, alloc=212.3MB, time=13.15 memory used=703.6MB, alloc=212.3MB, time=17.88 memory used=831.7MB, alloc=236.3MB, time=22.43 memory used=983.8MB, alloc=236.3MB, time=27.74 N1 := 4707 > GB := Basis(F, plex(op(vars))); 4 2 GB := [40 x - 3, -4 x + z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1144.2MB, alloc=236.3MB, time=31.51 N2 := 785 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 2 3 H := [-12 x z - 2 z + 6, -4 x z + z , 15 x y - 8 y - y, 2 2 2 -6 x y - 4 y z + 7 y z ] > J:=[op(GB),op(G)]; 4 2 2 3 2 2 2 J := [40 x - 3, -4 x + z, 15 x y - 8 y - y, -6 x y - 4 y z + 7 y z ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 9, 12, 3, 2, 3, 2, 1, 1/2, 3/4, 4/11, 6/11, 6/11, 4, 8, 12, 4, 4, 3, 2, 1, 1/2, 1/2, 2/5, 3/5, 3/10, 1, 0, -1] > save(F, G, cat("ranSet/33", convert(F, string),".txt")); > quit memory used=1164.3MB, alloc=236.3MB, time=32.01 |\^/| 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(); 1428531889 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 3 2 F := [-8 x z - 18 y z + 13 x z, -2 x z - 2 y + 4 y ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 G := [20 x z - 10 y + 9 y, 5 x y + 10 y z + 4 x y] > Problem := [F,G]; 2 2 2 3 2 Problem := [[-8 x z - 18 y z + 13 x z, -2 x z - 2 y + 4 y ], 2 2 2 [20 x z - 10 y + 9 y, 5 x y + 10 y z + 4 x y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.3MB, alloc=32.3MB, time=0.47 memory used=45.4MB, alloc=56.3MB, time=0.76 memory used=84.8MB, alloc=60.3MB, time=1.33 memory used=123.7MB, alloc=60.3MB, time=1.89 memory used=163.5MB, alloc=84.3MB, time=2.40 memory used=224.5MB, alloc=92.3MB, time=3.28 memory used=284.6MB, alloc=92.3MB, time=4.14 memory used=344.1MB, alloc=116.3MB, time=5.02 memory used=413.1MB, alloc=372.3MB, time=5.85 memory used=501.8MB, alloc=372.3MB, time=6.97 memory used=586.0MB, alloc=396.3MB, time=7.94 memory used=711.5MB, alloc=396.3MB, time=9.25 memory used=821.0MB, alloc=420.3MB, time=10.71 memory used=961.3MB, alloc=444.3MB, time=12.48 memory used=1090.9MB, alloc=468.3MB, time=14.60 memory used=1250.7MB, alloc=492.3MB, time=17.03 memory used=1418.6MB, alloc=516.3MB, time=19.71 memory used=1606.8MB, alloc=540.3MB, time=22.59 memory used=1815.7MB, alloc=564.3MB, time=25.61 memory used=2004.2MB, alloc=588.3MB, time=30.45 memory used=2185.1MB, alloc=612.3MB, time=36.08 memory used=2374.4MB, alloc=636.3MB, time=42.49 memory used=2570.9MB, alloc=660.3MB, time=50.18 memory used=2783.5MB, alloc=684.3MB, time=58.91 memory used=3020.0MB, alloc=708.3MB, time=68.55 memory used=3280.4MB, alloc=732.3MB, time=79.12 memory used=3564.8MB, alloc=756.3MB, time=89.14 memory used=3873.1MB, alloc=780.3MB, time=99.62 memory used=4205.3MB, alloc=780.3MB, time=110.98 memory used=4537.5MB, alloc=780.3MB, time=122.23 memory used=4869.7MB, alloc=804.3MB, time=133.46 memory used=5225.7MB, alloc=804.3MB, time=145.56 memory used=5581.9MB, alloc=828.3MB, time=157.54 memory used=5961.9MB, alloc=828.3MB, time=170.40 memory used=6341.8MB, alloc=852.3MB, time=183.05 N1 := 12593 > GB := Basis(F, plex(op(vars))); 4 3 7 4 2 3 3 6 3 2 5 GB := [-8 x y + 18 y + 16 x y + 13 x y - 72 y - 26 x y + 72 y , 2 3 2 z x + y - 2 y , 2 3 4 2 2 3 3 2 8 x y + 18 y z - 16 x y - 13 x y - 36 y z + 26 x y , 3 2 2 -8 y + 18 y z - 13 x z + 16 y ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=6749.4MB, alloc=852.3MB, time=195.77 memory used=6888.8MB, alloc=852.3MB, time=198.21 memory used=7006.6MB, alloc=852.3MB, time=200.21 memory used=7095.0MB, alloc=852.3MB, time=201.97 memory used=7189.3MB, alloc=852.3MB, time=203.75 memory used=7296.6MB, alloc=852.3MB, time=205.45 memory used=7402.4MB, alloc=852.3MB, time=207.15 memory used=7506.5MB, alloc=852.3MB, time=208.96 memory used=7606.3MB, alloc=852.3MB, time=210.41 memory used=7714.1MB, alloc=852.3MB, time=212.26 memory used=7801.5MB, alloc=852.3MB, time=214.32 memory used=7887.4MB, alloc=852.3MB, time=216.35 memory used=7977.9MB, alloc=852.3MB, time=218.36 memory used=8052.2MB, alloc=852.3MB, time=219.97 memory used=8111.7MB, alloc=852.3MB, time=221.41 memory used=8182.2MB, alloc=852.3MB, time=223.08 memory used=8249.7MB, alloc=852.3MB, time=224.32 memory used=8339.7MB, alloc=852.3MB, time=225.55 memory used=8420.7MB, alloc=852.3MB, time=227.01 memory used=8477.0MB, alloc=852.3MB, time=228.40 memory used=8524.5MB, alloc=852.3MB, time=229.64 memory used=8762.7MB, alloc=876.3MB, time=233.02 memory used=8969.8MB, alloc=876.3MB, time=236.29 memory used=9177.1MB, alloc=876.3MB, time=239.38 memory used=9451.5MB, alloc=900.3MB, time=242.06 memory used=9702.2MB, alloc=900.3MB, time=245.07 memory used=9885.5MB, alloc=900.3MB, time=248.38 memory used=10411.9MB, alloc=924.3MB, time=255.46 memory used=10950.4MB, alloc=948.3MB, time=263.16 memory used=11461.7MB, alloc=972.3MB, time=268.82 memory used=11806.6MB, alloc=996.3MB, time=271.96 memory used=12274.8MB, alloc=1020.3MB, time=277.99 memory used=12923.6MB, alloc=1044.3MB, time=286.65 |\^/| 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(); 1428532189 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 3 F := [-4 x + 19 x z - 14 x y, 9 x z - 3 z - 8 x] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 3 G := [13 y z - 4 x y + 7 y z, 2 x y + y z + 4 z ] > Problem := [F,G]; 3 2 2 3 Problem := [[-4 x + 19 x z - 14 x y, 9 x z - 3 z - 8 x], 2 2 2 3 [13 y z - 4 x y + 7 y z, 2 x y + y z + 4 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=26.7MB, alloc=32.3MB, time=0.52 memory used=46.9MB, alloc=32.3MB, time=0.82 memory used=65.6MB, alloc=56.3MB, time=1.10 memory used=106.8MB, alloc=60.3MB, time=1.70 memory used=145.3MB, alloc=84.3MB, time=2.32 memory used=209.2MB, alloc=92.3MB, time=3.23 memory used=278.5MB, alloc=348.3MB, time=4.18 memory used=340.8MB, alloc=348.3MB, time=4.75 memory used=403.3MB, alloc=348.3MB, time=5.33 memory used=469.0MB, alloc=372.3MB, time=6.09 memory used=560.5MB, alloc=372.3MB, time=7.15 memory used=647.3MB, alloc=396.3MB, time=8.17 memory used=757.4MB, alloc=396.3MB, time=9.49 memory used=840.1MB, alloc=396.3MB, time=10.05 memory used=952.3MB, alloc=420.3MB, time=11.24 memory used=1082.0MB, alloc=420.3MB, time=12.53 memory used=1179.0MB, alloc=420.3MB, time=13.24 memory used=1301.8MB, alloc=420.3MB, time=14.66 memory used=1427.9MB, alloc=444.3MB, time=16.27 memory used=1556.3MB, alloc=444.3MB, time=17.64 memory used=1669.5MB, alloc=468.3MB, time=19.05 memory used=1793.1MB, alloc=468.3MB, time=20.66 memory used=1919.4MB, alloc=492.3MB, time=22.43 memory used=2064.8MB, alloc=516.3MB, time=24.26 memory used=2249.9MB, alloc=516.3MB, time=26.32 memory used=2403.9MB, alloc=540.3MB, time=28.07 memory used=2581.6MB, alloc=564.3MB, time=30.72 memory used=2739.1MB, alloc=564.3MB, time=32.98 memory used=2887.3MB, alloc=588.3MB, time=35.30 memory used=3030.5MB, alloc=612.3MB, time=37.55 memory used=3179.0MB, alloc=636.3MB, time=39.76 memory used=3326.3MB, alloc=660.3MB, time=42.14 memory used=3457.1MB, alloc=660.3MB, time=44.80 memory used=3584.1MB, alloc=684.3MB, time=47.06 memory used=3713.3MB, alloc=708.3MB, time=49.35 memory used=3847.7MB, alloc=708.3MB, time=51.70 memory used=3974.3MB, alloc=732.3MB, time=54.09 memory used=4095.6MB, alloc=756.3MB, time=56.27 memory used=4223.1MB, alloc=756.3MB, time=58.49 memory used=4420.1MB, alloc=780.3MB, time=60.94 memory used=4566.2MB, alloc=780.3MB, time=63.05 memory used=4670.8MB, alloc=780.3MB, time=65.18 memory used=4772.5MB, alloc=804.3MB, time=67.36 memory used=4949.5MB, alloc=804.3MB, time=69.62 memory used=5048.6MB, alloc=828.3MB, time=71.61 memory used=5145.1MB, alloc=828.3MB, time=73.61 memory used=5274.7MB, alloc=852.3MB, time=75.51 memory used=5421.1MB, alloc=852.3MB, time=77.65 memory used=5505.5MB, alloc=876.3MB, time=79.59 memory used=5583.7MB, alloc=876.3MB, time=81.41 memory used=5676.6MB, alloc=876.3MB, time=83.32 memory used=5774.5MB, alloc=900.3MB, time=85.19 memory used=5862.8MB, alloc=900.3MB, time=86.89 memory used=5962.4MB, alloc=900.3MB, time=88.76 memory used=6058.3MB, alloc=924.3MB, time=90.44 memory used=6472.8MB, alloc=948.3MB, time=100.41 memory used=6826.4MB, alloc=972.3MB, time=111.32 memory used=7182.2MB, alloc=996.3MB, time=123.07 memory used=7544.5MB, alloc=1020.3MB, time=135.31 memory used=7914.7MB, alloc=1044.3MB, time=148.23 memory used=8298.4MB, alloc=1068.3MB, time=161.73 memory used=8698.2MB, alloc=1092.3MB, time=176.05 memory used=9116.6MB, alloc=1116.3MB, time=190.84 memory used=9548.4MB, alloc=1140.3MB, time=206.13 memory used=9992.4MB, alloc=1164.3MB, time=221.78 memory used=10449.7MB, alloc=1188.3MB, time=238.33 memory used=10921.1MB, alloc=1212.3MB, time=255.85 memory used=11403.4MB, alloc=1236.3MB, time=274.11 memory used=11896.9MB, alloc=1260.3MB, time=293.70 |\^/| 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(); 1428532489 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 3 3 2 2 F := [10 y + 12 z , -x + 10 x y + 8 y z ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 G := [8 x y - 3 y z - 14 x y, 6 x z - 4 y z + 7 y] > Problem := [F,G]; 3 3 3 2 2 Problem := [[10 y + 12 z , -x + 10 x y + 8 y z ], 2 2 2 2 [8 x y - 3 y z - 14 x y, 6 x z - 4 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=4.2MB, alloc=32.3MB, time=0.18 memory used=26.0MB, alloc=32.3MB, time=0.49 memory used=47.4MB, alloc=32.3MB, time=0.82 memory used=66.6MB, alloc=56.3MB, time=1.11 memory used=106.6MB, alloc=60.3MB, time=1.72 memory used=145.8MB, alloc=84.3MB, time=2.29 memory used=210.6MB, alloc=92.3MB, time=3.16 memory used=274.4MB, alloc=92.3MB, time=4.01 memory used=336.6MB, alloc=116.3MB, time=4.91 memory used=415.0MB, alloc=372.3MB, time=6.05 memory used=498.6MB, alloc=372.3MB, time=7.03 memory used=556.9MB, alloc=372.3MB, time=8.57 memory used=602.2MB, alloc=372.3MB, time=8.89 memory used=638.6MB, alloc=372.3MB, time=9.03 memory used=709.8MB, alloc=396.3MB, time=11.07 memory used=769.6MB, alloc=396.3MB, time=11.44 memory used=839.5MB, alloc=396.3MB, time=11.68 memory used=921.1MB, alloc=396.3MB, time=18.19 memory used=977.7MB, alloc=396.3MB, time=18.37 memory used=1035.9MB, alloc=396.3MB, time=18.54 memory used=1089.5MB, alloc=396.3MB, time=18.78 memory used=1216.9MB, alloc=396.3MB, time=19.99 memory used=1325.8MB, alloc=396.3MB, time=21.49 memory used=1404.0MB, alloc=420.3MB, time=22.12 memory used=1528.5MB, alloc=420.3MB, time=27.40 memory used=1589.0MB, alloc=420.3MB, time=27.59 memory used=1673.9MB, alloc=420.3MB, time=28.36 memory used=1771.7MB, alloc=420.3MB, time=31.71 memory used=1854.3MB, alloc=420.3MB, time=33.75 memory used=1912.5MB, alloc=420.3MB, time=33.94 memory used=2062.8MB, alloc=420.3MB, time=42.74 memory used=2137.3MB, alloc=420.3MB, time=44.69 memory used=2190.2MB, alloc=420.3MB, time=44.89 memory used=2252.0MB, alloc=420.3MB, time=45.10 memory used=2316.9MB, alloc=420.3MB, time=45.31 memory used=2359.8MB, alloc=420.3MB, time=45.50 memory used=2407.6MB, alloc=420.3MB, time=45.66 memory used=2460.4MB, alloc=420.3MB, time=45.85 memory used=2517.8MB, alloc=420.3MB, time=46.02 memory used=2580.8MB, alloc=420.3MB, time=46.20 memory used=2650.4MB, alloc=420.3MB, time=46.37 memory used=2852.1MB, alloc=420.3MB, time=46.84 memory used=3091.0MB, alloc=420.3MB, time=47.93 memory used=3152.9MB, alloc=420.3MB, time=48.14 memory used=3228.4MB, alloc=420.3MB, time=52.04 memory used=3306.7MB, alloc=420.3MB, time=54.41 memory used=3357.6MB, alloc=420.3MB, time=54.58 memory used=3423.9MB, alloc=420.3MB, time=54.77 memory used=3468.2MB, alloc=420.3MB, time=54.92 memory used=3531.1MB, alloc=420.3MB, time=55.20 memory used=3596.8MB, alloc=420.3MB, time=55.49 memory used=3728.0MB, alloc=420.3MB, time=55.99 memory used=3827.9MB, alloc=420.3MB, time=56.22 memory used=3920.9MB, alloc=420.3MB, time=56.79 memory used=3997.7MB, alloc=420.3MB, time=57.88 memory used=4120.0MB, alloc=420.3MB, time=59.00 memory used=4202.0MB, alloc=420.3MB, time=61.26 memory used=4327.5MB, alloc=444.3MB, time=62.51 memory used=4470.6MB, alloc=444.3MB, time=63.95 memory used=4541.4MB, alloc=444.3MB, time=64.21 memory used=4601.0MB, alloc=444.3MB, time=64.46 memory used=4678.3MB, alloc=444.3MB, time=64.72 memory used=4733.3MB, alloc=444.3MB, time=64.93 memory used=4787.3MB, alloc=444.3MB, time=65.15 memory used=4851.2MB, alloc=444.3MB, time=65.36 memory used=4956.3MB, alloc=444.3MB, time=76.53 memory used=5023.0MB, alloc=444.3MB, time=76.80 memory used=5086.9MB, alloc=444.3MB, time=77.04 memory used=5144.7MB, alloc=444.3MB, time=77.25 memory used=5215.1MB, alloc=444.3MB, time=77.48 memory used=5437.9MB, alloc=444.3MB, time=77.92 memory used=5644.2MB, alloc=444.3MB, time=78.95 memory used=5720.5MB, alloc=444.3MB, time=79.20 memory used=5796.2MB, alloc=444.3MB, time=79.45 memory used=5952.8MB, alloc=444.3MB, time=80.05 memory used=6100.9MB, alloc=444.3MB, time=80.34 memory used=6295.9MB, alloc=444.3MB, time=80.73 memory used=6571.6MB, alloc=444.3MB, time=82.08 memory used=6772.6MB, alloc=444.3MB, time=82.43 memory used=6954.9MB, alloc=444.3MB, time=82.77 memory used=7163.5MB, alloc=444.3MB, time=83.11 memory used=7367.7MB, alloc=444.3MB, time=83.46 memory used=7658.9MB, alloc=444.3MB, time=83.92 memory used=7868.4MB, alloc=444.3MB, time=84.28 memory used=8073.3MB, alloc=444.3MB, time=84.61 memory used=8283.1MB, alloc=444.3MB, time=84.92 memory used=8455.9MB, alloc=468.3MB, time=117.75 memory used=8559.5MB, alloc=468.3MB, time=148.26 memory used=8635.6MB, alloc=468.3MB, time=148.58 memory used=8720.5MB, alloc=468.3MB, time=148.87 memory used=8782.4MB, alloc=468.3MB, time=149.12 memory used=8851.4MB, alloc=468.3MB, time=149.37 memory used=8931.1MB, alloc=468.3MB, time=149.62 memory used=9019.8MB, alloc=468.3MB, time=149.91 memory used=9117.2MB, alloc=468.3MB, time=150.18 memory used=9288.5MB, alloc=468.3MB, time=150.61 memory used=9433.7MB, alloc=468.3MB, time=150.98 memory used=9595.5MB, alloc=468.3MB, time=151.37 memory used=9775.2MB, alloc=468.3MB, time=151.78 memory used=9976.9MB, alloc=468.3MB, time=152.20 memory used=10203.3MB, alloc=468.3MB, time=152.66 memory used=10398.3MB, alloc=468.3MB, time=153.07 memory used=10583.2MB, alloc=468.3MB, time=153.47 memory used=10923.9MB, alloc=468.3MB, time=155.37 memory used=11059.0MB, alloc=468.3MB, time=156.83 memory used=11225.8MB, alloc=468.3MB, time=158.49 memory used=11367.1MB, alloc=468.3MB, time=159.19 memory used=11493.5MB, alloc=468.3MB, time=159.74 memory used=11670.6MB, alloc=492.3MB, time=161.47 memory used=11869.3MB, alloc=492.3MB, time=163.30 memory used=12050.3MB, alloc=492.3MB, time=165.68 memory used=12235.2MB, alloc=516.3MB, time=168.27 memory used=12443.4MB, alloc=540.3MB, time=171.02 memory used=12646.4MB, alloc=564.3MB, time=174.37 memory used=12826.8MB, alloc=564.3MB, time=177.27 memory used=12995.7MB, alloc=588.3MB, time=180.02 memory used=13182.3MB, alloc=612.3MB, time=183.16 memory used=13357.1MB, alloc=636.3MB, time=186.02 memory used=13553.8MB, alloc=660.3MB, time=190.56 memory used=13794.9MB, alloc=684.3MB, time=198.62 memory used=14046.0MB, alloc=708.3MB, time=207.20 memory used=14300.3MB, alloc=732.3MB, time=216.35 memory used=14573.0MB, alloc=756.3MB, time=226.84 memory used=14869.6MB, alloc=780.3MB, time=238.63 memory used=15190.3MB, alloc=780.3MB, time=251.09 memory used=15510.8MB, alloc=804.3MB, time=263.67 memory used=15855.3MB, alloc=804.3MB, time=277.24 memory used=16199.8MB, alloc=828.3MB, time=290.74 memory used=16568.3MB, alloc=852.3MB, time=305.06 memory used=16961.2MB, alloc=876.3MB, time=319.74 N1 := 10389 > GB := Basis(F, plex(op(vars))); 9 8 7 2 6 3 9 8 GB := [-9 x + 270 x y - 2700 x y + 9000 x y + 3200 y , 5625 x 7 7 6 2 4 4 3 5 2 6 - 112500 x y + 3 x z + 562500 x y + 20 x y + 200 x y + 2000 x y 7 8 3 2 4 + 20000 x y + 200000 y , -3 x z + 30 x y z - 20 y , 6 5 4 2 5 3 x - 60 x y + 300 x y + 160 y z, 5 4 3 2 4 3 2 2 3 3 -15 x + 150 x y + 12 x z + 80 y z, -x + 10 x y + 8 y z , 6 z + 5 y ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=17081.2MB, alloc=876.3MB, time=322.97 |\^/| 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(); 1428532789 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 F := [-5 x z + 16 y + 10 z , -4 y - y z + 2 x] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 G := [-4 x y + x - 12 z, 10 y z - 8 x ] > Problem := [F,G]; 2 2 2 2 Problem := [[-5 x z + 16 y + 10 z , -4 y - y z + 2 x], 2 2 2 2 [-4 x y + x - 12 z, 10 y z - 8 x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=24.9MB, alloc=32.3MB, time=0.46 memory used=44.3MB, alloc=32.3MB, time=0.73 memory used=64.3MB, alloc=60.3MB, time=1.02 memory used=108.1MB, alloc=68.3MB, time=1.64 memory used=150.4MB, alloc=68.3MB, time=2.16 memory used=194.9MB, alloc=92.3MB, time=2.73 memory used=258.0MB, alloc=92.3MB, time=3.57 memory used=327.0MB, alloc=92.3MB, time=4.47 memory used=391.2MB, alloc=116.3MB, time=5.45 memory used=480.8MB, alloc=140.3MB, time=6.82 memory used=585.1MB, alloc=396.3MB, time=8.51 memory used=686.4MB, alloc=420.3MB, time=10.08 memory used=803.5MB, alloc=444.3MB, time=12.01 memory used=935.0MB, alloc=468.3MB, time=14.22 memory used=1082.1MB, alloc=492.3MB, time=16.69 memory used=1233.1MB, alloc=516.3MB, time=20.78 memory used=1386.6MB, alloc=540.3MB, time=25.68 memory used=1548.2MB, alloc=564.3MB, time=31.66 memory used=1726.0MB, alloc=588.3MB, time=38.35 memory used=1927.7MB, alloc=612.3MB, time=45.96 memory used=2153.3MB, alloc=612.3MB, time=54.79 memory used=2378.9MB, alloc=636.3MB, time=63.72 memory used=2628.4MB, alloc=636.3MB, time=73.65 memory used=2878.0MB, alloc=636.3MB, time=83.61 memory used=3127.7MB, alloc=660.3MB, time=93.61 N1 := 8405 > GB := Basis(F, plex(op(vars))); 4 4 2 2 2 3 2 GB := [20 y x - 44 y - 20 y x + 40 y x + 5 x - 10 x , 3 2 2 3 2 40 x y - 20 x y + 5 x z - 88 y + 40 x y - 10 x z, 4 y + y z - 2 x, 2 2 2 5 z x - 10 z - 16 y ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=3414.4MB, alloc=660.3MB, time=102.90 memory used=3526.1MB, alloc=660.3MB, time=104.83 memory used=3643.5MB, alloc=660.3MB, time=106.67 memory used=3763.6MB, alloc=660.3MB, time=108.78 memory used=3871.2MB, alloc=660.3MB, time=110.50 memory used=3972.4MB, alloc=660.3MB, time=112.30 memory used=4064.0MB, alloc=660.3MB, time=113.87 memory used=4159.7MB, alloc=660.3MB, time=115.21 memory used=4259.5MB, alloc=660.3MB, time=116.67 memory used=4342.4MB, alloc=684.3MB, time=118.38 memory used=4417.6MB, alloc=684.3MB, time=119.76 memory used=4505.6MB, alloc=684.3MB, time=121.38 memory used=4583.2MB, alloc=684.3MB, time=122.96 memory used=4670.0MB, alloc=684.3MB, time=124.69 memory used=4743.8MB, alloc=684.3MB, time=126.05 memory used=4849.6MB, alloc=684.3MB, time=127.18 memory used=4935.4MB, alloc=684.3MB, time=128.39 memory used=5002.7MB, alloc=684.3MB, time=129.61 memory used=5064.4MB, alloc=708.3MB, time=131.04 memory used=5131.1MB, alloc=708.3MB, time=132.42 memory used=5368.0MB, alloc=708.3MB, time=134.19 memory used=5630.2MB, alloc=708.3MB, time=136.04 memory used=5712.0MB, alloc=708.3MB, time=137.56 memory used=5817.1MB, alloc=708.3MB, time=139.24 memory used=5890.0MB, alloc=708.3MB, time=141.05 memory used=5997.5MB, alloc=732.3MB, time=143.22 memory used=6098.9MB, alloc=732.3MB, time=145.28 memory used=6193.9MB, alloc=732.3MB, time=147.26 memory used=6275.0MB, alloc=756.3MB, time=149.27 memory used=6373.9MB, alloc=756.3MB, time=151.48 memory used=6490.6MB, alloc=756.3MB, time=153.48 memory used=6627.2MB, alloc=756.3MB, time=155.42 memory used=6732.1MB, alloc=756.3MB, time=157.08 memory used=6852.3MB, alloc=780.3MB, time=159.18 memory used=6989.4MB, alloc=780.3MB, time=161.21 memory used=7104.4MB, alloc=780.3MB, time=162.95 memory used=7216.9MB, alloc=780.3MB, time=165.01 memory used=7632.0MB, alloc=804.3MB, time=171.00 memory used=7988.6MB, alloc=828.3MB, time=176.94 memory used=8315.5MB, alloc=852.3MB, time=182.49 memory used=8662.6MB, alloc=876.3MB, time=188.14 memory used=8997.2MB, alloc=900.3MB, time=193.92 memory used=9413.7MB, alloc=924.3MB, time=205.48 memory used=9792.8MB, alloc=948.3MB, time=218.30 memory used=10171.7MB, alloc=972.3MB, time=231.90 memory used=10557.0MB, alloc=996.3MB, time=245.74 memory used=10951.8MB, alloc=1020.3MB, time=260.19 |\^/| 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(); 1428533089 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 F := [-12 y z + 8 x y + 8 z, 3 x z - 3 y - 10 z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 G := [-15 x + 7 x y z, -6 y z - 7 x z - 9 y] > Problem := [F,G]; 2 2 Problem := [[-12 y z + 8 x y + 8 z, 3 x z - 3 y - 10 z], 3 2 [-15 x + 7 x y z, -6 y z - 7 x z - 9 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.6MB, alloc=32.3MB, time=0.49 memory used=47.3MB, alloc=32.3MB, time=0.78 memory used=65.5MB, alloc=56.3MB, time=1.08 memory used=104.4MB, alloc=60.3MB, time=1.64 memory used=142.2MB, alloc=84.3MB, time=2.19 memory used=208.3MB, alloc=92.3MB, time=3.08 memory used=271.2MB, alloc=116.3MB, time=3.99 memory used=347.5MB, alloc=116.3MB, time=5.10 memory used=420.1MB, alloc=372.3MB, time=6.11 memory used=503.6MB, alloc=396.3MB, time=7.32 memory used=611.1MB, alloc=420.3MB, time=8.91 memory used=739.5MB, alloc=420.3MB, time=10.78 memory used=871.3MB, alloc=444.3MB, time=12.71 memory used=1014.2MB, alloc=468.3MB, time=15.08 memory used=1162.9MB, alloc=492.3MB, time=17.78 memory used=1324.1MB, alloc=516.3MB, time=20.30 memory used=1496.2MB, alloc=540.3MB, time=23.11 memory used=1665.3MB, alloc=564.3MB, time=26.03 memory used=1795.5MB, alloc=588.3MB, time=28.13 memory used=1958.7MB, alloc=612.3MB, time=30.94 memory used=2102.8MB, alloc=636.3MB, time=33.30 memory used=2253.4MB, alloc=660.3MB, time=35.76 memory used=2403.7MB, alloc=684.3MB, time=38.23 memory used=2548.2MB, alloc=708.3MB, time=40.60 memory used=2666.0MB, alloc=708.3MB, time=42.65 memory used=2791.2MB, alloc=732.3MB, time=44.89 memory used=2912.7MB, alloc=732.3MB, time=47.03 memory used=3033.4MB, alloc=756.3MB, time=49.23 memory used=3154.5MB, alloc=780.3MB, time=51.45 memory used=3263.5MB, alloc=780.3MB, time=53.40 memory used=3373.9MB, alloc=780.3MB, time=55.37 memory used=3492.5MB, alloc=804.3MB, time=57.48 memory used=3603.9MB, alloc=804.3MB, time=59.57 memory used=3709.8MB, alloc=828.3MB, time=61.63 memory used=3808.3MB, alloc=828.3MB, time=63.92 memory used=3907.3MB, alloc=852.3MB, time=66.18 memory used=3996.4MB, alloc=852.3MB, time=68.37 memory used=4083.5MB, alloc=876.3MB, time=70.52 memory used=4190.2MB, alloc=900.3MB, time=73.63 memory used=4428.2MB, alloc=924.3MB, time=82.40 memory used=4811.0MB, alloc=948.3MB, time=96.27 memory used=5196.8MB, alloc=972.3MB, time=110.93 memory used=5590.5MB, alloc=996.3MB, time=126.09 memory used=5994.2MB, alloc=1020.3MB, time=141.86 memory used=6410.1MB, alloc=1044.3MB, time=158.41 memory used=6839.1MB, alloc=1068.3MB, time=175.72 memory used=7281.6MB, alloc=1092.3MB, time=193.97 memory used=7738.9MB, alloc=1116.3MB, time=212.80 memory used=8210.2MB, alloc=1140.3MB, time=231.96 memory used=8696.2MB, alloc=1164.3MB, time=251.36 memory used=9193.1MB, alloc=1188.3MB, time=272.39 memory used=9706.5MB, alloc=1212.3MB, time=294.36 |\^/| 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(); 1428533389 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 F := [12 x y - 18 y z + 9 x y, -5 y z - 9 x z - 3 y z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 G := [-16 x + 7 x y - 5 y z, -8 x z + 9 y z + 9 z] > Problem := [F,G]; 2 2 2 Problem := [[12 x y - 18 y z + 9 x y, -5 y z - 9 x z - 3 y z], 2 2 2 [-16 x + 7 x y - 5 y z, -8 x z + 9 y z + 9 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.0MB, alloc=32.3MB, time=0.47 memory used=46.6MB, alloc=32.3MB, time=0.76 memory used=65.4MB, alloc=56.3MB, time=1.04 memory used=105.2MB, alloc=60.3MB, time=1.63 memory used=143.4MB, alloc=84.3MB, time=2.21 memory used=204.4MB, alloc=92.3MB, time=3.19 memory used=261.3MB, alloc=116.3MB, time=4.17 memory used=336.4MB, alloc=140.3MB, time=5.45 memory used=428.1MB, alloc=164.3MB, time=7.04 memory used=531.6MB, alloc=188.3MB, time=9.88 memory used=640.7MB, alloc=212.3MB, time=13.99 memory used=772.0MB, alloc=212.3MB, time=19.00 memory used=903.5MB, alloc=236.3MB, time=24.09 N1 := 3919 > GB := Basis(F, plex(op(vars))); 4 2 2 3 2 2 GB := [20 x y + 36 x y + 27 x y + 27 x y + 9 x y , 2 2 3 2 2 2 60 x y - 20 x y + 45 x y + 162 x z - 27 x y - 9 x y, 2 20 x y + 15 x y + 54 x z + 18 y z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1044.6MB, alloc=236.3MB, time=27.00 memory used=1217.4MB, alloc=492.3MB, time=29.58 memory used=1384.9MB, alloc=516.3MB, time=32.14 memory used=1550.4MB, alloc=540.3MB, time=34.73 memory used=1678.1MB, alloc=540.3MB, time=36.74 memory used=1813.0MB, alloc=564.3MB, time=38.83 memory used=1945.8MB, alloc=564.3MB, time=41.00 memory used=2084.2MB, alloc=564.3MB, time=43.41 memory used=2201.5MB, alloc=588.3MB, time=45.36 memory used=2281.2MB, alloc=588.3MB, time=46.87 memory used=2373.6MB, alloc=588.3MB, time=48.58 memory used=2485.3MB, alloc=612.3MB, time=50.84 memory used=2613.8MB, alloc=612.3MB, time=53.32 memory used=2731.2MB, alloc=636.3MB, time=55.62 memory used=2847.3MB, alloc=660.3MB, time=58.08 memory used=2956.1MB, alloc=660.3MB, time=60.41 memory used=3063.5MB, alloc=684.3MB, time=62.80 memory used=3185.6MB, alloc=708.3MB, time=65.42 memory used=3296.8MB, alloc=708.3MB, time=67.86 memory used=3406.0MB, alloc=732.3MB, time=70.16 memory used=3513.7MB, alloc=756.3MB, time=72.43 memory used=3600.9MB, alloc=756.3MB, time=74.20 memory used=3697.3MB, alloc=780.3MB, time=76.17 memory used=3794.0MB, alloc=780.3MB, time=77.96 memory used=3887.8MB, alloc=804.3MB, time=80.42 memory used=4050.5MB, alloc=828.3MB, time=85.50 memory used=4395.5MB, alloc=852.3MB, time=97.08 memory used=4742.1MB, alloc=876.3MB, time=110.03 memory used=5097.2MB, alloc=900.3MB, time=123.28 memory used=5462.4MB, alloc=924.3MB, time=137.42 memory used=5829.6MB, alloc=948.3MB, time=151.76 memory used=6220.7MB, alloc=972.3MB, time=167.17 memory used=6635.8MB, alloc=996.3MB, time=183.04 memory used=7074.7MB, alloc=1020.3MB, time=200.69 memory used=7537.7MB, alloc=1044.3MB, time=219.47 memory used=8024.5MB, alloc=1044.3MB, time=238.62 memory used=8511.2MB, alloc=1044.3MB, time=258.43 memory used=8998.0MB, alloc=1044.3MB, time=277.96 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428533689 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 3 F := [-17 z - 10 x y - 12 z , -3 x z - 10 y + 4 x] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 G := [-14 x y z - x y + 10 y z, -7 x z - 3 y + 5 x] > Problem := [F,G]; 3 2 2 3 Problem := [[-17 z - 10 x y - 12 z , -3 x z - 10 y + 4 x], 2 2 [-14 x y z - x y + 10 y z, -7 x z - 3 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=4.2MB, alloc=32.3MB, time=0.17 memory used=26.8MB, alloc=32.3MB, time=0.53 memory used=47.6MB, alloc=32.3MB, time=0.84 memory used=67.2MB, alloc=56.3MB, time=1.14 memory used=107.8MB, alloc=60.3MB, time=1.76 memory used=148.2MB, alloc=84.3MB, time=2.33 memory used=216.0MB, alloc=92.3MB, time=3.26 memory used=282.9MB, alloc=92.3MB, time=4.14 memory used=350.5MB, alloc=116.3MB, time=5.09 memory used=413.7MB, alloc=372.3MB, time=5.99 memory used=498.4MB, alloc=372.3MB, time=7.19 memory used=567.9MB, alloc=372.3MB, time=9.01 memory used=641.7MB, alloc=372.3MB, time=9.74 memory used=715.7MB, alloc=396.3MB, time=10.96 memory used=821.0MB, alloc=396.3MB, time=12.70 memory used=928.9MB, alloc=396.3MB, time=13.85 memory used=1046.3MB, alloc=420.3MB, time=15.00 memory used=1177.4MB, alloc=444.3MB, time=16.64 memory used=1306.7MB, alloc=444.3MB, time=18.12 memory used=1390.0MB, alloc=468.3MB, time=18.71 memory used=1464.1MB, alloc=468.3MB, time=19.01 memory used=1549.6MB, alloc=468.3MB, time=19.34 memory used=1611.1MB, alloc=468.3MB, time=19.60 memory used=1683.3MB, alloc=468.3MB, time=19.86 memory used=1768.8MB, alloc=468.3MB, time=20.14 memory used=1884.9MB, alloc=468.3MB, time=34.24 memory used=1977.6MB, alloc=468.3MB, time=35.12 memory used=2047.7MB, alloc=468.3MB, time=35.41 memory used=2131.9MB, alloc=468.3MB, time=35.69 memory used=2339.9MB, alloc=468.3MB, time=36.31 memory used=2536.4MB, alloc=468.3MB, time=36.76 memory used=2699.1MB, alloc=468.3MB, time=38.14 memory used=2814.0MB, alloc=468.3MB, time=39.52 memory used=2953.6MB, alloc=468.3MB, time=41.19 memory used=3045.9MB, alloc=468.3MB, time=44.70 memory used=3204.3MB, alloc=492.3MB, time=45.98 memory used=3375.1MB, alloc=492.3MB, time=47.80 memory used=3511.0MB, alloc=492.3MB, time=50.72 memory used=3648.5MB, alloc=492.3MB, time=51.91 memory used=3751.3MB, alloc=492.3MB, time=53.15 memory used=3828.6MB, alloc=492.3MB, time=54.18 memory used=3923.2MB, alloc=516.3MB, time=55.27 memory used=4061.2MB, alloc=516.3MB, time=61.39 memory used=4161.7MB, alloc=516.3MB, time=61.81 memory used=4288.8MB, alloc=516.3MB, time=62.84 memory used=4447.4MB, alloc=540.3MB, time=64.79 memory used=4618.5MB, alloc=540.3MB, time=65.92 memory used=4708.9MB, alloc=540.3MB, time=66.90 memory used=4920.1MB, alloc=540.3MB, time=68.26 memory used=5004.7MB, alloc=540.3MB, time=69.22 memory used=5131.7MB, alloc=540.3MB, time=69.96 memory used=5275.5MB, alloc=540.3MB, time=78.65 memory used=5387.9MB, alloc=540.3MB, time=79.08 memory used=5472.6MB, alloc=540.3MB, time=79.45 memory used=5579.4MB, alloc=540.3MB, time=79.84 memory used=5696.2MB, alloc=540.3MB, time=80.76 memory used=5773.1MB, alloc=540.3MB, time=81.56 memory used=5892.4MB, alloc=540.3MB, time=82.51 memory used=5968.0MB, alloc=540.3MB, time=83.55 memory used=6067.7MB, alloc=540.3MB, time=84.61 memory used=6155.3MB, alloc=540.3MB, time=85.81 memory used=6273.7MB, alloc=564.3MB, time=86.95 memory used=6482.5MB, alloc=564.3MB, time=87.63 memory used=6763.3MB, alloc=564.3MB, time=88.39 memory used=7076.8MB, alloc=564.3MB, time=89.33 memory used=7275.5MB, alloc=564.3MB, time=90.36 memory used=7473.8MB, alloc=564.3MB, time=91.12 memory used=7689.5MB, alloc=564.3MB, time=92.06 memory used=7892.3MB, alloc=564.3MB, time=93.27 memory used=8086.2MB, alloc=564.3MB, time=94.36 memory used=8287.8MB, alloc=564.3MB, time=95.49 memory used=8485.6MB, alloc=564.3MB, time=96.31 memory used=8682.9MB, alloc=564.3MB, time=97.05 memory used=8922.3MB, alloc=564.3MB, time=98.33 memory used=9146.3MB, alloc=564.3MB, time=99.06 memory used=9429.2MB, alloc=564.3MB, time=99.83 memory used=9703.1MB, alloc=564.3MB, time=101.34 memory used=9956.7MB, alloc=588.3MB, time=105.11 memory used=10204.6MB, alloc=612.3MB, time=108.63 memory used=10469.4MB, alloc=636.3MB, time=112.04 memory used=10750.9MB, alloc=660.3MB, time=115.78 memory used=11044.2MB, alloc=684.3MB, time=119.77 memory used=11343.0MB, alloc=708.3MB, time=124.23 memory used=11684.6MB, alloc=732.3MB, time=128.75 memory used=12106.0MB, alloc=756.3MB, time=131.88 memory used=12532.7MB, alloc=780.3MB, time=135.97 memory used=12978.0MB, alloc=804.3MB, time=140.39 memory used=13435.5MB, alloc=828.3MB, time=145.35 memory used=13914.0MB, alloc=852.3MB, time=150.68 memory used=14352.7MB, alloc=876.3MB, time=156.25 memory used=14867.7MB, alloc=900.3MB, time=161.77 memory used=15436.9MB, alloc=924.3MB, time=166.76 memory used=15976.3MB, alloc=948.3MB, time=172.55 memory used=16637.2MB, alloc=972.3MB, time=181.92 memory used=17074.9MB, alloc=996.3MB, time=193.98 memory used=17470.3MB, alloc=1020.3MB, time=206.73 memory used=17865.9MB, alloc=1044.3MB, time=220.27 memory used=18268.4MB, alloc=1068.3MB, time=235.14 memory used=18680.9MB, alloc=1092.3MB, time=250.38 memory used=19106.0MB, alloc=1116.3MB, time=266.00 memory used=19543.1MB, alloc=1140.3MB, time=283.18 memory used=19991.6MB, alloc=1164.3MB, time=301.50 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428533989 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 F := [x y - 7 y z + 12 x y, 5 y - 4 z - 4] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 G := [-18 x - x y + 11 y, 7 x y z - 3 x + 6 x y] > Problem := [F,G]; 2 2 2 Problem := [[x y - 7 y z + 12 x y, 5 y - 4 z - 4], 3 2 2 [-18 x - x y + 11 y, 7 x y z - 3 x + 6 x y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=26.2MB, alloc=32.3MB, time=0.49 memory used=46.4MB, alloc=60.3MB, time=0.79 memory used=88.5MB, alloc=60.3MB, time=1.36 memory used=128.5MB, alloc=60.3MB, time=1.92 memory used=168.3MB, alloc=84.3MB, time=2.53 memory used=235.7MB, alloc=116.3MB, time=3.59 memory used=317.2MB, alloc=116.3MB, time=4.93 memory used=396.5MB, alloc=140.3MB, time=6.19 memory used=491.8MB, alloc=164.3MB, time=7.80 memory used=597.2MB, alloc=188.3MB, time=9.54 memory used=718.5MB, alloc=212.3MB, time=12.35 memory used=841.9MB, alloc=236.3MB, time=16.05 memory used=977.2MB, alloc=260.3MB, time=20.62 memory used=1126.2MB, alloc=284.3MB, time=26.23 memory used=1299.1MB, alloc=308.3MB, time=32.61 memory used=1496.0MB, alloc=308.3MB, time=39.97 memory used=1693.0MB, alloc=308.3MB, time=47.32 memory used=1889.9MB, alloc=332.3MB, time=54.62 memory used=2110.8MB, alloc=356.3MB, time=62.34 N1 := 6771 > GB := Basis(F, plex(op(vars))); 5 2 3 2 GB := [175 y - 16 x y - 280 y - 192 x y + 112 y, -5 y + 4 z + 4] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=2219.9MB, alloc=356.3MB, time=64.82 N2 := 1635 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 3 2 H := [x y - 7 y z + 12 x y, 5 y - 4 z - 4, -18 x - x y + 11 y, 2 7 x y z - 3 x + 6 x y] > J:=[op(GB),op(G)]; 5 2 3 2 J := [175 y - 16 x y - 280 y - 192 x y + 112 y, -5 y + 4 z + 4, 3 2 2 -18 x - x y + 11 y, 7 x y z - 3 x + 6 x y] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 10, 11, 3, 3, 2, 2, 3/4, 1, 3/4, 7/12, 2/3, 1/4, 4, 9, 13, 5, 3, 5, 1, 3/4, 1, 1/2, 1/2, 5/7, 1/7, 1, -2, -2] > save(F, G, cat("ranSet/33", convert(F, string),".txt")); > quit memory used=2446.9MB, alloc=612.3MB, time=70.11 |\^/| 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(); 1428534062 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 3 2 2 F := [-16 y + 13 y - 6 y z, -8 x + 3 x y + x ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 G := [-12 x z + 6 x y - 8 y, 3 x y z + 5 z + 4 y z] > Problem := [F,G]; 3 2 3 2 2 Problem := [[-16 y + 13 y - 6 y z, -8 x + 3 x y + x ], 2 3 [-12 x z + 6 x y - 8 y, 3 x y z + 5 z + 4 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.16 memory used=26.0MB, alloc=32.3MB, time=0.44 memory used=47.3MB, alloc=32.3MB, time=0.71 memory used=67.8MB, alloc=32.3MB, time=0.99 memory used=85.9MB, alloc=56.3MB, time=1.25 memory used=128.1MB, alloc=60.3MB, time=1.95 memory used=165.8MB, alloc=84.3MB, time=2.56 memory used=223.2MB, alloc=108.3MB, time=3.51 memory used=297.0MB, alloc=140.3MB, time=4.95 memory used=380.2MB, alloc=164.3MB, time=7.52 memory used=479.1MB, alloc=164.3MB, time=10.95 memory used=578.2MB, alloc=188.3MB, time=13.98 N1 := 3031 > GB := Basis(F, plex(op(vars))); 3 2 2 GB := [-8 x + 3 x y + x , 5 4 3 3 2 2 8192 x - 5568 x + 432 x z + 1008 x - 54 x z - 55 x , 3 2 16 y - 13 y + 6 y z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=696.5MB, alloc=188.3MB, time=15.78 memory used=829.4MB, alloc=444.3MB, time=17.73 memory used=964.7MB, alloc=468.3MB, time=19.85 memory used=1115.4MB, alloc=492.3MB, time=22.34 memory used=1275.4MB, alloc=516.3MB, time=25.04 memory used=1445.5MB, alloc=540.3MB, time=27.89 memory used=1612.9MB, alloc=564.3MB, time=32.58 memory used=1781.7MB, alloc=588.3MB, time=38.11 memory used=1961.8MB, alloc=612.3MB, time=44.43 memory used=2151.5MB, alloc=636.3MB, time=51.81 memory used=2365.2MB, alloc=660.3MB, time=60.03 memory used=2602.8MB, alloc=684.3MB, time=69.13 memory used=2864.3MB, alloc=708.3MB, time=79.10 memory used=3149.8MB, alloc=732.3MB, time=89.82 memory used=3459.3MB, alloc=732.3MB, time=101.61 memory used=3768.7MB, alloc=756.3MB, time=113.27 memory used=4102.1MB, alloc=756.3MB, time=125.75 memory used=4435.3MB, alloc=780.3MB, time=138.85 N2 := 10153 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 3 2 2 2 H := [-16 y + 13 y - 6 y z, -8 x + 3 x y + x , -12 x z + 6 x y - 8 y, 3 3 x y z + 5 z + 4 y z] > J:=[op(GB),op(G)]; 3 2 2 J := [-8 x + 3 x y + x , 5 4 3 3 2 2 8192 x - 5568 x + 432 x z + 1008 x - 54 x z - 55 x , 3 2 2 3 16 y - 13 y + 6 y z, -12 x z + 6 x y - 8 y, 3 x y z + 5 z + 4 y z] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 10, 12, 3, 3, 3, 3, 3/4, 1, 3/4, 1/2, 2/3, 5/12, 5, 12, 17, 5, 5, 3, 3, 4/5, 4/5, 4/5, 2/3, 4/9, 7/18, -2, -5, -2] > save(F, G, cat("ranSet/33", convert(F, string),".txt")); > quit memory used=4696.1MB, alloc=780.3MB, time=148.63 |\^/| 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(); 1428534222 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 3 F := [-16 x z - 13 y + 15 x, 9 x y z - 8 y ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 G := [19 x z - 15 x z + 4 y , 5 x y + 4 x y - 6 x z] > Problem := [F,G]; 2 2 3 Problem := [[-16 x z - 13 y + 15 x, 9 x y z - 8 y ], 2 2 2 2 [19 x z - 15 x z + 4 y , 5 x y + 4 x y - 6 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.5MB, alloc=32.3MB, time=0.49 memory used=48.1MB, alloc=32.3MB, time=0.81 memory used=67.9MB, alloc=56.3MB, time=1.09 memory used=109.5MB, alloc=60.3MB, time=1.67 memory used=149.0MB, alloc=60.3MB, time=2.21 memory used=189.4MB, alloc=92.3MB, time=2.79 memory used=256.7MB, alloc=92.3MB, time=3.65 memory used=322.1MB, alloc=116.3MB, time=4.62 memory used=419.5MB, alloc=116.3MB, time=5.84 memory used=494.3MB, alloc=140.3MB, time=7.16 memory used=599.8MB, alloc=140.3MB, time=8.70 memory used=691.6MB, alloc=164.3MB, time=10.25 memory used=801.8MB, alloc=188.3MB, time=12.12 memory used=906.5MB, alloc=468.3MB, time=13.90 memory used=1047.5MB, alloc=492.3MB, time=16.57 memory used=1191.4MB, alloc=516.3MB, time=20.87 memory used=1343.5MB, alloc=540.3MB, time=25.97 memory used=1502.2MB, alloc=564.3MB, time=32.38 memory used=1685.0MB, alloc=588.3MB, time=39.57 memory used=1891.7MB, alloc=588.3MB, time=47.36 memory used=2098.4MB, alloc=612.3MB, time=55.17 memory used=2329.1MB, alloc=612.3MB, time=63.76 memory used=2559.7MB, alloc=636.3MB, time=72.08 memory used=2814.5MB, alloc=636.3MB, time=81.36 N1 := 7789 > GB := Basis(F, plex(op(vars))); 5 3 2 3 GB := [1024 y + 1053 x y - 1215 x y, 9 x y z - 8 y , 3 3 2 2 128 y z + 117 y - 135 x y, 16 z x + 13 y - 15 x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=3081.7MB, alloc=636.3MB, time=88.22 memory used=3218.6MB, alloc=636.3MB, time=90.27 memory used=3347.0MB, alloc=636.3MB, time=92.26 memory used=3473.9MB, alloc=636.3MB, time=94.16 memory used=3586.1MB, alloc=636.3MB, time=96.00 memory used=3688.7MB, alloc=660.3MB, time=97.59 memory used=3799.1MB, alloc=660.3MB, time=99.13 memory used=3902.2MB, alloc=660.3MB, time=100.63 memory used=4013.3MB, alloc=684.3MB, time=102.19 memory used=4124.6MB, alloc=684.3MB, time=104.04 memory used=4239.8MB, alloc=684.3MB, time=106.00 memory used=4371.4MB, alloc=708.3MB, time=108.58 memory used=4492.3MB, alloc=708.3MB, time=110.86 memory used=4629.7MB, alloc=732.3MB, time=113.38 memory used=4763.4MB, alloc=732.3MB, time=115.89 memory used=4887.5MB, alloc=756.3MB, time=118.30 memory used=5004.1MB, alloc=756.3MB, time=120.79 memory used=5113.4MB, alloc=780.3MB, time=123.08 memory used=5243.2MB, alloc=780.3MB, time=125.43 memory used=5333.2MB, alloc=804.3MB, time=127.49 memory used=5451.4MB, alloc=828.3MB, time=130.07 memory used=5567.3MB, alloc=828.3MB, time=132.60 memory used=5668.9MB, alloc=852.3MB, time=134.85 memory used=5830.3MB, alloc=876.3MB, time=139.99 memory used=6011.2MB, alloc=900.3MB, time=146.63 memory used=6423.9MB, alloc=924.3MB, time=161.93 memory used=6836.5MB, alloc=948.3MB, time=178.06 memory used=7244.3MB, alloc=972.3MB, time=195.59 memory used=7676.0MB, alloc=996.3MB, time=214.11 memory used=8131.6MB, alloc=1020.3MB, time=233.67 memory used=8611.2MB, alloc=1044.3MB, time=253.26 |\^/| 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(); 1428534522 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 3 2 2 F := [-8 x z + 6 x y + 17 z, 5 x - 10 x z + x y ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 2 G := [9 x z - 4 x y - 20 x , x z - 10 x - 3] > Problem := [F,G]; 2 2 3 2 2 Problem := [[-8 x z + 6 x y + 17 z, 5 x - 10 x z + x y ], 2 2 2 2 2 [9 x z - 4 x y - 20 x , x z - 10 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=4.2MB, alloc=32.3MB, time=0.17 memory used=26.5MB, alloc=32.3MB, time=0.49 memory used=46.8MB, alloc=32.3MB, time=0.80 memory used=66.2MB, alloc=56.3MB, time=1.11 memory used=106.6MB, alloc=60.3MB, time=1.73 memory used=148.9MB, alloc=84.3MB, time=2.43 memory used=209.0MB, alloc=84.3MB, time=3.28 memory used=265.4MB, alloc=108.3MB, time=4.13 memory used=341.5MB, alloc=116.3MB, time=5.36 memory used=411.4MB, alloc=140.3MB, time=6.61 memory used=494.4MB, alloc=164.3MB, time=8.80 memory used=587.0MB, alloc=188.3MB, time=11.90 memory used=703.6MB, alloc=188.3MB, time=15.88 memory used=820.4MB, alloc=212.3MB, time=19.90 N1 := 3639 > GB := Basis(F, plex(op(vars))); 5 3 2 3 2 3 2 GB := [-40 x + 52 x y + 85 x + 17 x y , -20 x + 26 x y + 85 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=948.5MB, alloc=212.3MB, time=22.36 N2 := 1427 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 3 2 2 2 2 2 H := [-8 x z + 6 x y + 17 z, 5 x - 10 x z + x y , 9 x z - 4 x y - 20 x , 2 2 z x - 10 x - 3] > J:=[op(GB),op(G)]; 5 3 2 3 2 3 2 J := [-40 x + 52 x y + 85 x + 17 x y , -20 x + 26 x y + 85 z, 2 2 2 2 2 9 x z - 4 x y - 20 x , z x - 10 x - 3] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 11, 12, 3, 3, 2, 1, 1, 3/4, 1, 5/6, 1/4, 5/12, 4, 10, 14, 5, 11 5, 2, 1, 1, 3/4, 3/4, --, 4/13, 3/13, 1, -2, -2] 13 > save(F, G, cat("ranSet/33", convert(F, string),".txt")); > quit memory used=1093.0MB, alloc=468.3MB, time=25.61 |\^/| 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(); 1428534550 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 2 F := [-19 x z - 16 y - 12 z , 7 x y + x - 9 y] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 3 2 2 G := [-16 x y - 20 y + 2 x, -9 y + x - 5 y ] > Problem := [F,G]; 2 3 2 2 Problem := [[-19 x z - 16 y - 12 z , 7 x y + x - 9 y], 2 3 3 2 2 [-16 x y - 20 y + 2 x, -9 y + x - 5 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=24.7MB, alloc=32.3MB, time=0.47 memory used=43.5MB, alloc=56.3MB, time=0.75 memory used=86.4MB, alloc=60.3MB, time=1.42 memory used=126.9MB, alloc=84.3MB, time=2.09 memory used=186.5MB, alloc=108.3MB, time=3.13 memory used=258.0MB, alloc=132.3MB, time=5.16 N1 := 1405 > GB := Basis(F, plex(op(vars))); 2 2 3 2 GB := [7 y x - 9 y + x, 19 z x + 16 y + 12 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=356.0MB, alloc=140.3MB, time=6.59 memory used=459.1MB, alloc=164.3MB, time=8.39 N2 := 1405 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 3 2 2 2 3 H := [-19 x z - 16 y - 12 z , 7 y x - 9 y + x, -16 x y - 20 y + 2 x, 3 2 2 -9 y - 5 y + x ] > J:=[op(GB),op(G)]; 2 2 3 2 2 3 J := [7 y x - 9 y + x, 19 z x + 16 y + 12 z , -16 x y - 20 y + 2 x, 3 2 2 -9 y - 5 y + x ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 9, 12, 3, 2, 3, 2, 1, 1, 1/4, 1/2, 7/12, 1/6, 4, 9, 12, 3, 2, 3, 2, 1, 1, 1/4, 1/2, 7/12, 1/6, 0, 0, 0] > save(F, G, cat("ranSet/33", convert(F, string),".txt")); > quit memory used=521.5MB, alloc=164.3MB, time=10.25 |\^/| 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(); 1428534561 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 2 F := [8 y - 11 y z - 15 z, -10 y z - y z - 2 z ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 G := [-13 x + 16 y z - 7 z, -x y - 8 x + 2 z] > Problem := [F,G]; 3 2 2 2 Problem := [[8 y - 11 y z - 15 z, -10 y z - y z - 2 z ], 3 2 [-13 x + 16 y z - 7 z, -x y - 8 x + 2 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=31.1MB, alloc=40.3MB, time=0.53 memory used=57.7MB, alloc=40.3MB, time=0.88 memory used=82.7MB, alloc=64.3MB, time=1.22 memory used=130.4MB, alloc=76.3MB, time=1.87 memory used=176.3MB, alloc=100.3MB, time=2.53 memory used=243.6MB, alloc=100.3MB, time=3.46 memory used=315.0MB, alloc=100.3MB, time=4.33 memory used=387.7MB, alloc=124.3MB, time=5.26 memory used=474.8MB, alloc=124.3MB, time=6.48 memory used=542.1MB, alloc=124.3MB, time=7.30 memory used=625.4MB, alloc=148.3MB, time=8.26 memory used=695.7MB, alloc=148.3MB, time=9.27 memory used=775.6MB, alloc=404.3MB, time=10.49 memory used=883.9MB, alloc=428.3MB, time=11.54 memory used=1024.1MB, alloc=428.3MB, time=13.41 memory used=1153.0MB, alloc=428.3MB, time=14.75 memory used=1270.9MB, alloc=428.3MB, time=15.78 memory used=1339.0MB, alloc=428.3MB, time=16.21 memory used=1401.3MB, alloc=428.3MB, time=16.80 memory used=1545.3MB, alloc=452.3MB, time=18.09 memory used=1696.1MB, alloc=452.3MB, time=19.04 memory used=1860.0MB, alloc=452.3MB, time=20.57 memory used=2008.4MB, alloc=476.3MB, time=21.70 memory used=2195.0MB, alloc=476.3MB, time=23.59 memory used=2369.2MB, alloc=500.3MB, time=24.99 memory used=2554.8MB, alloc=500.3MB, time=26.37 memory used=2745.2MB, alloc=524.3MB, time=28.72 memory used=2958.4MB, alloc=548.3MB, time=31.31 memory used=3168.3MB, alloc=572.3MB, time=33.92 memory used=3389.1MB, alloc=596.3MB, time=36.62 memory used=3540.2MB, alloc=620.3MB, time=39.21 memory used=3705.2MB, alloc=644.3MB, time=42.18 memory used=3884.7MB, alloc=668.3MB, time=45.20 memory used=4034.3MB, alloc=692.3MB, time=47.79 memory used=4206.3MB, alloc=716.3MB, time=50.36 memory used=4345.9MB, alloc=716.3MB, time=52.99 memory used=4478.8MB, alloc=740.3MB, time=55.56 memory used=4633.0MB, alloc=764.3MB, time=58.27 memory used=4763.3MB, alloc=788.3MB, time=60.66 memory used=4894.9MB, alloc=788.3MB, time=63.11 memory used=5016.5MB, alloc=812.3MB, time=65.42 memory used=5144.3MB, alloc=836.3MB, time=67.89 memory used=5286.4MB, alloc=836.3MB, time=70.47 memory used=5419.7MB, alloc=860.3MB, time=72.78 memory used=5534.0MB, alloc=860.3MB, time=74.71 memory used=5637.2MB, alloc=884.3MB, time=76.75 memory used=5761.6MB, alloc=884.3MB, time=79.09 memory used=5912.5MB, alloc=908.3MB, time=81.15 memory used=6014.9MB, alloc=932.3MB, time=83.24 memory used=6101.1MB, alloc=932.3MB, time=85.13 memory used=6205.4MB, alloc=932.3MB, time=87.39 memory used=6305.8MB, alloc=956.3MB, time=89.62 memory used=6402.9MB, alloc=980.3MB, time=91.54 memory used=6507.4MB, alloc=1004.3MB, time=94.58 memory used=6934.4MB, alloc=1028.3MB, time=108.61 memory used=7350.7MB, alloc=1052.3MB, time=124.12 memory used=7769.8MB, alloc=1076.3MB, time=139.78 memory used=8196.2MB, alloc=1100.3MB, time=155.19 memory used=8632.3MB, alloc=1124.3MB, time=171.34 memory used=9079.7MB, alloc=1148.3MB, time=188.47 memory used=9539.0MB, alloc=1172.3MB, time=205.70 memory used=10010.2MB, alloc=1196.3MB, time=224.19 memory used=10494.8MB, alloc=1220.3MB, time=243.44 memory used=10992.6MB, alloc=1244.3MB, time=262.41 memory used=11504.1MB, alloc=1268.3MB, time=282.10 |\^/| 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(); 1428534861 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 F := [4 x z + 20 x z + 13 z , -8 z - 9 y + 4] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 3 2 2 2 G := [10 x y + 9 x z - 17 y , 5 x y + 6 x z - 10 y z ] > Problem := [F,G]; 2 2 2 Problem := [[4 x z + 20 x z + 13 z , -8 z - 9 y + 4], 2 2 3 2 2 2 [10 x y + 9 x z - 17 y , 5 x y + 6 x z - 10 y z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.7MB, alloc=32.3MB, time=0.50 memory used=47.6MB, alloc=32.3MB, time=0.80 memory used=66.2MB, alloc=56.3MB, time=1.08 memory used=105.2MB, alloc=60.3MB, time=1.66 memory used=143.5MB, alloc=84.3MB, time=2.22 memory used=208.9MB, alloc=92.3MB, time=3.12 memory used=275.1MB, alloc=116.3MB, time=4.00 memory used=350.7MB, alloc=116.3MB, time=5.08 memory used=426.0MB, alloc=396.3MB, time=6.28 memory used=533.5MB, alloc=396.3MB, time=7.87 memory used=638.6MB, alloc=420.3MB, time=9.52 memory used=766.4MB, alloc=420.3MB, time=11.03 memory used=897.8MB, alloc=444.3MB, time=12.57 memory used=1031.7MB, alloc=444.3MB, time=14.08 memory used=1162.9MB, alloc=468.3MB, time=15.76 memory used=1272.8MB, alloc=468.3MB, time=17.30 memory used=1414.5MB, alloc=492.3MB, time=18.70 memory used=1532.5MB, alloc=492.3MB, time=20.29 memory used=1707.7MB, alloc=516.3MB, time=22.14 memory used=1872.0MB, alloc=516.3MB, time=24.13 memory used=2079.6MB, alloc=516.3MB, time=26.11 memory used=2275.8MB, alloc=540.3MB, time=28.23 memory used=2441.1MB, alloc=564.3MB, time=30.81 memory used=2582.8MB, alloc=588.3MB, time=33.04 memory used=2702.3MB, alloc=612.3MB, time=35.25 memory used=2874.5MB, alloc=636.3MB, time=38.23 memory used=3019.8MB, alloc=660.3MB, time=41.04 memory used=3177.8MB, alloc=660.3MB, time=43.72 memory used=3312.9MB, alloc=684.3MB, time=46.33 memory used=3450.6MB, alloc=708.3MB, time=49.02 memory used=3571.9MB, alloc=732.3MB, time=51.38 memory used=3707.6MB, alloc=756.3MB, time=54.04 memory used=3816.1MB, alloc=756.3MB, time=56.16 memory used=3945.0MB, alloc=780.3MB, time=58.46 memory used=4067.0MB, alloc=780.3MB, time=60.77 memory used=4164.4MB, alloc=804.3MB, time=62.73 memory used=4265.5MB, alloc=804.3MB, time=64.86 memory used=4368.2MB, alloc=828.3MB, time=67.02 memory used=4481.8MB, alloc=852.3MB, time=69.34 memory used=4589.2MB, alloc=852.3MB, time=71.67 memory used=4685.2MB, alloc=876.3MB, time=73.71 memory used=4767.1MB, alloc=876.3MB, time=75.53 memory used=4859.5MB, alloc=876.3MB, time=77.55 memory used=5271.8MB, alloc=900.3MB, time=84.78 memory used=5641.7MB, alloc=924.3MB, time=91.59 memory used=5990.4MB, alloc=948.3MB, time=102.39 memory used=6317.4MB, alloc=972.3MB, time=113.83 memory used=6647.7MB, alloc=996.3MB, time=125.95 memory used=6985.5MB, alloc=1020.3MB, time=138.44 memory used=7334.0MB, alloc=1044.3MB, time=151.53 memory used=7692.7MB, alloc=1068.3MB, time=165.40 memory used=8063.3MB, alloc=1092.3MB, time=179.91 memory used=8446.6MB, alloc=1116.3MB, time=195.34 memory used=8842.5MB, alloc=1140.3MB, time=211.04 memory used=9252.8MB, alloc=1164.3MB, time=227.55 memory used=9676.7MB, alloc=1188.3MB, time=243.72 memory used=10114.3MB, alloc=1212.3MB, time=259.74 memory used=10565.7MB, alloc=1236.3MB, time=276.81 memory used=11031.5MB, alloc=1260.3MB, time=296.23 |\^/| 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(); 1428535161 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 3 F := [15 x z + 13 y z + 5 x, 2 x - 5 y z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 G := [10 y z - 11 y z, x y z + 7 y z + y z] > Problem := [F,G]; 2 2 3 Problem := [[15 x z + 13 y z + 5 x, 2 x - 5 y z], 2 2 [10 y z - 11 y z, x y z + 7 y z + y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.4MB, alloc=32.3MB, time=0.47 memory used=46.6MB, alloc=56.3MB, time=0.78 memory used=87.3MB, alloc=60.3MB, time=1.38 memory used=126.9MB, alloc=84.3MB, time=2.02 memory used=188.7MB, alloc=84.3MB, time=3.12 memory used=244.5MB, alloc=108.3MB, time=4.13 memory used=315.7MB, alloc=140.3MB, time=5.71 memory used=393.9MB, alloc=164.3MB, time=8.44 memory used=493.0MB, alloc=188.3MB, time=12.16 N1 := 2691 > GB := Basis(F, plex(op(vars))); 5 3 2 3 2 3 GB := [30 x + 26 x y + 25 x y, 26 x y + 75 x z + 25 x, -2 x + 5 y z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=617.5MB, alloc=188.3MB, time=14.64 memory used=726.8MB, alloc=444.3MB, time=16.54 memory used=854.7MB, alloc=468.3MB, time=18.78 memory used=993.8MB, alloc=492.3MB, time=22.65 memory used=1131.3MB, alloc=516.3MB, time=27.64 memory used=1293.0MB, alloc=540.3MB, time=33.50 memory used=1478.8MB, alloc=564.3MB, time=39.73 N2 := 4335 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 3 2 H := [13 z y + 15 z x + 5 x, 2 x - 5 z y, 10 y z - 11 y z, 2 x y z + 7 y z + y z] > J:=[op(GB),op(G)]; 5 3 2 3 2 3 J := [30 x + 26 x y + 25 x y, 26 x y + 75 x z + 25 x, -2 x + 5 y z, 2 2 10 y z - 11 y z, x y z + 7 y z + y z] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 11, 12, 3, 3, 2, 2, 3/4, 1, 1, 2/5, 7/10, 4/5, 5, 13, 18, 5, 5, 2, 2, 4/5, 1, 4/5, 8/13, 9/13, 7/13, -2, -6, -2] > save(F, G, cat("ranSet/33", convert(F, string),".txt")); > quit memory used=1491.4MB, alloc=564.3MB, time=40.01 |\^/| 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(); 1428535204 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 F := [-20 x y + 14 x z + 3 y, 6 x y - 10 z - 1] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 G := [-4 y z - 16 y z - 20 x y, -3 y z - 2 z - 8] > Problem := [F,G]; 2 2 2 2 Problem := [[-20 x y + 14 x z + 3 y, 6 x y - 10 z - 1], 2 2 [-4 y z - 16 y z - 20 x y, -3 y z - 2 z - 8]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.16 memory used=26.7MB, alloc=32.3MB, time=0.48 memory used=46.7MB, alloc=56.3MB, time=0.77 memory used=86.4MB, alloc=60.3MB, time=1.34 memory used=125.8MB, alloc=60.3MB, time=1.89 memory used=163.8MB, alloc=84.3MB, time=2.43 memory used=223.5MB, alloc=92.3MB, time=3.22 memory used=285.5MB, alloc=116.3MB, time=4.05 memory used=367.9MB, alloc=116.3MB, time=5.09 memory used=440.1MB, alloc=372.3MB, time=6.00 memory used=525.2MB, alloc=396.3MB, time=7.11 memory used=631.8MB, alloc=420.3MB, time=8.65 memory used=759.7MB, alloc=444.3MB, time=10.52 memory used=902.3MB, alloc=444.3MB, time=12.65 memory used=1040.7MB, alloc=468.3MB, time=14.83 memory used=1169.5MB, alloc=492.3MB, time=16.82 memory used=1298.5MB, alloc=492.3MB, time=18.81 memory used=1401.5MB, alloc=492.3MB, time=20.42 memory used=1517.4MB, alloc=492.3MB, time=22.06 memory used=1623.4MB, alloc=492.3MB, time=23.19 memory used=1708.1MB, alloc=516.3MB, time=24.32 memory used=1796.2MB, alloc=516.3MB, time=25.61 memory used=1886.4MB, alloc=516.3MB, time=27.15 memory used=1982.0MB, alloc=516.3MB, time=28.81 memory used=2050.9MB, alloc=516.3MB, time=30.02 memory used=2121.4MB, alloc=516.3MB, time=31.32 memory used=2183.3MB, alloc=516.3MB, time=32.38 memory used=2278.4MB, alloc=540.3MB, time=33.83 memory used=2365.9MB, alloc=540.3MB, time=35.30 memory used=2453.7MB, alloc=540.3MB, time=36.82 memory used=2557.6MB, alloc=540.3MB, time=38.41 memory used=2631.1MB, alloc=564.3MB, time=39.95 memory used=2735.7MB, alloc=564.3MB, time=41.75 memory used=2831.1MB, alloc=588.3MB, time=43.58 memory used=2909.7MB, alloc=588.3MB, time=45.05 memory used=2997.0MB, alloc=588.3MB, time=46.69 memory used=3083.7MB, alloc=612.3MB, time=48.35 memory used=3181.0MB, alloc=612.3MB, time=50.23 memory used=3263.1MB, alloc=636.3MB, time=51.97 memory used=3534.0MB, alloc=660.3MB, time=56.74 memory used=3816.8MB, alloc=684.3MB, time=61.65 memory used=4099.0MB, alloc=708.3MB, time=66.96 memory used=4379.0MB, alloc=732.3MB, time=72.11 memory used=4680.8MB, alloc=756.3MB, time=77.44 memory used=4990.5MB, alloc=780.3MB, time=82.27 memory used=5269.6MB, alloc=804.3MB, time=86.97 memory used=5574.5MB, alloc=828.3MB, time=92.16 memory used=5884.7MB, alloc=852.3MB, time=98.21 memory used=6116.7MB, alloc=876.3MB, time=102.99 memory used=6460.3MB, alloc=900.3MB, time=110.64 memory used=6743.8MB, alloc=924.3MB, time=120.55 memory used=7031.1MB, alloc=948.3MB, time=131.22 memory used=7327.2MB, alloc=972.3MB, time=142.98 memory used=7633.7MB, alloc=996.3MB, time=155.25 memory used=7952.3MB, alloc=1020.3MB, time=168.23 memory used=8283.6MB, alloc=1044.3MB, time=182.03 memory used=8629.5MB, alloc=1068.3MB, time=196.53 memory used=8990.8MB, alloc=1092.3MB, time=212.24 memory used=9368.3MB, alloc=1116.3MB, time=228.76 memory used=9762.5MB, alloc=1140.3MB, time=246.27 memory used=10174.0MB, alloc=1164.3MB, time=263.98 |\^/| 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(); 1428535504 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 F := [19 x y - 7 z - 15, 10 x y - 4 x y + 6 y ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 G := [-13 - 12 y + 15 z, 3 x - 4 x - 10 y z] > Problem := [F,G]; 2 2 2 2 Problem := [[19 x y - 7 z - 15, 10 x y - 4 x y + 6 y ], 3 2 [-13 - 12 y + 15 z, 3 x - 4 x - 10 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.5MB, alloc=32.3MB, time=0.48 memory used=48.0MB, alloc=32.3MB, time=0.80 memory used=68.4MB, alloc=56.3MB, time=1.12 memory used=110.4MB, alloc=60.3MB, time=1.76 memory used=150.5MB, alloc=84.3MB, time=2.37 memory used=213.4MB, alloc=116.3MB, time=3.50 memory used=293.3MB, alloc=116.3MB, time=4.87 memory used=367.3MB, alloc=140.3MB, time=6.18 memory used=458.9MB, alloc=164.3MB, time=7.78 memory used=561.3MB, alloc=188.3MB, time=10.66 memory used=673.3MB, alloc=212.3MB, time=14.49 memory used=798.7MB, alloc=236.3MB, time=19.50 memory used=948.1MB, alloc=236.3MB, time=25.81 memory used=1097.4MB, alloc=260.3MB, time=32.21 N1 := 4645 > GB := Basis(F, plex(op(vars))); 2 2 3 2 2 GB := [5 x y - 2 x y + 3 y , 95 x y - 38 x y + 21 z + 45] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1279.1MB, alloc=260.3MB, time=37.65 memory used=1348.2MB, alloc=516.3MB, time=38.85 memory used=1544.6MB, alloc=540.3MB, time=42.28 memory used=1754.5MB, alloc=564.3MB, time=49.00 memory used=1958.4MB, alloc=588.3MB, time=57.11 N2 := 3229 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 H := [19 y x - 7 z - 15, 10 x y - 4 x y + 6 y , -13 - 12 y + 15 z, 3 2 3 x - 10 z y - 4 x ] > J:=[op(GB),op(G)]; 2 2 3 2 2 J := [5 x y - 2 x y + 3 y , 95 y x - 38 y x + 21 z + 45, -13 - 12 y + 15 z, 3 2 3 x - 10 z y - 4 x ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 10, 10, 3, 3, 2, 2, 3/4, 1, 3/4, 5/12, 1/2, 1/4, 4, 10, 11, 4, 3, 2, 2, 3/4, 1, 3/4, 6/13, 7/13, 3/13, 0, -1, -1] > save(F, G, cat("ranSet/33", convert(F, string),".txt")); > quit memory used=1968.1MB, alloc=588.3MB, time=57.40 |\^/| 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(); 1428535588 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 2 2 F := [8 x - 3 x z + 6 x , -4 x z - 7 y z - 6 y] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 G := [12 x y + 9 x, 6 y z + 7 y + 2 z] > Problem := [F,G]; 3 2 2 2 2 Problem := [[8 x - 3 x z + 6 x , -4 x z - 7 y z - 6 y], 2 2 2 [12 x y + 9 x, 6 y z + 7 y + 2 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.4MB, alloc=32.3MB, time=0.49 memory used=45.7MB, alloc=56.3MB, time=0.79 memory used=87.7MB, alloc=60.3MB, time=1.39 memory used=130.6MB, alloc=68.3MB, time=1.99 memory used=171.0MB, alloc=92.3MB, time=2.56 memory used=236.5MB, alloc=92.3MB, time=3.22 memory used=316.9MB, alloc=348.3MB, time=4.09 memory used=386.2MB, alloc=348.3MB, time=4.83 memory used=450.2MB, alloc=348.3MB, time=5.43 memory used=518.0MB, alloc=348.3MB, time=6.19 memory used=585.9MB, alloc=348.3MB, time=6.78 memory used=653.4MB, alloc=372.3MB, time=7.41 memory used=754.6MB, alloc=372.3MB, time=8.65 memory used=851.2MB, alloc=372.3MB, time=9.92 memory used=931.8MB, alloc=396.3MB, time=11.18 memory used=1034.9MB, alloc=420.3MB, time=12.83 memory used=1158.4MB, alloc=444.3MB, time=14.87 memory used=1307.6MB, alloc=444.3MB, time=17.30 memory used=1448.2MB, alloc=468.3MB, time=19.57 memory used=1600.7MB, alloc=492.3MB, time=22.21 memory used=1745.0MB, alloc=516.3MB, time=26.29 memory used=1895.8MB, alloc=540.3MB, time=31.07 memory used=2056.9MB, alloc=564.3MB, time=36.91 memory used=2232.3MB, alloc=588.3MB, time=43.73 memory used=2431.6MB, alloc=612.3MB, time=51.47 memory used=2654.7MB, alloc=612.3MB, time=60.12 memory used=2878.0MB, alloc=612.3MB, time=68.81 memory used=3101.1MB, alloc=636.3MB, time=77.49 memory used=3348.1MB, alloc=636.3MB, time=87.10 memory used=3595.0MB, alloc=660.3MB, time=96.81 memory used=3866.2MB, alloc=684.3MB, time=107.45 N1 := 8569 > GB := Basis(F, plex(op(vars))); 7 5 2 3 4 6 4 2 2 4 2 GB := [64 x + 224 x y + 196 x y + 48 x + 168 x y + 147 x y - 54 x y , 5 3 3 4 2 3 3 -112 x y - 196 x y - 84 x y - 147 x y + 36 x z + 54 x y, 5 3 2 4 2 2 2 2 16 x + 28 x y + 12 x + 21 x y + 9 x y z, 7 z y + 4 z x + 6 y, 3 2 2 -8 x + 3 x z - 6 x ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=4085.7MB, alloc=684.3MB, time=112.69 memory used=4200.3MB, alloc=684.3MB, time=114.73 memory used=4326.2MB, alloc=684.3MB, time=116.90 memory used=4462.4MB, alloc=684.3MB, time=118.89 memory used=4580.0MB, alloc=684.3MB, time=120.44 memory used=4682.8MB, alloc=684.3MB, time=122.13 memory used=4770.6MB, alloc=684.3MB, time=123.71 memory used=4856.5MB, alloc=684.3MB, time=125.23 memory used=4942.7MB, alloc=684.3MB, time=126.78 memory used=5031.5MB, alloc=684.3MB, time=128.12 memory used=5129.4MB, alloc=684.3MB, time=129.60 memory used=5215.4MB, alloc=684.3MB, time=131.38 memory used=5409.1MB, alloc=684.3MB, time=133.41 memory used=5550.4MB, alloc=684.3MB, time=135.99 memory used=5624.5MB, alloc=684.3MB, time=137.39 memory used=5700.0MB, alloc=684.3MB, time=138.68 memory used=5751.3MB, alloc=684.3MB, time=139.92 memory used=5821.2MB, alloc=684.3MB, time=141.16 memory used=5884.5MB, alloc=684.3MB, time=142.44 memory used=5959.7MB, alloc=684.3MB, time=143.82 memory used=6012.5MB, alloc=684.3MB, time=145.01 memory used=6068.4MB, alloc=684.3MB, time=146.39 memory used=6133.6MB, alloc=684.3MB, time=147.67 memory used=6192.8MB, alloc=684.3MB, time=148.69 memory used=6247.5MB, alloc=684.3MB, time=149.79 memory used=6310.1MB, alloc=684.3MB, time=150.86 memory used=6361.1MB, alloc=708.3MB, time=151.98 memory used=6404.4MB, alloc=708.3MB, time=152.99 memory used=6592.8MB, alloc=708.3MB, time=156.12 memory used=6825.1MB, alloc=732.3MB, time=158.96 memory used=7037.5MB, alloc=732.3MB, time=160.41 memory used=7260.1MB, alloc=732.3MB, time=162.02 memory used=7424.2MB, alloc=732.3MB, time=162.86 memory used=7608.1MB, alloc=732.3MB, time=163.80 memory used=7802.7MB, alloc=732.3MB, time=165.67 memory used=7985.0MB, alloc=732.3MB, time=166.63 memory used=8148.9MB, alloc=732.3MB, time=167.45 memory used=8367.9MB, alloc=732.3MB, time=168.69 memory used=8543.0MB, alloc=732.3MB, time=169.67 memory used=8799.0MB, alloc=756.3MB, time=172.85 memory used=9088.1MB, alloc=756.3MB, time=175.79 memory used=9285.3MB, alloc=756.3MB, time=176.80 memory used=9487.8MB, alloc=756.3MB, time=178.19 memory used=9714.7MB, alloc=756.3MB, time=179.45 memory used=9935.8MB, alloc=756.3MB, time=180.94 memory used=10181.6MB, alloc=756.3MB, time=183.49 memory used=10397.8MB, alloc=756.3MB, time=185.70 memory used=10667.0MB, alloc=756.3MB, time=187.65 memory used=10862.3MB, alloc=780.3MB, time=190.34 memory used=11034.4MB, alloc=780.3MB, time=193.01 memory used=11185.3MB, alloc=780.3MB, time=195.10 memory used=11369.5MB, alloc=780.3MB, time=197.49 memory used=11496.1MB, alloc=780.3MB, time=199.43 memory used=11649.6MB, alloc=804.3MB, time=201.54 memory used=11787.8MB, alloc=804.3MB, time=203.73 memory used=11924.7MB, alloc=804.3MB, time=206.04 memory used=12038.4MB, alloc=804.3MB, time=207.96 memory used=12162.1MB, alloc=804.3MB, time=209.98 memory used=12308.7MB, alloc=804.3MB, time=212.45 memory used=12667.4MB, alloc=828.3MB, time=214.70 memory used=13129.0MB, alloc=828.3MB, time=216.47 memory used=13581.8MB, alloc=828.3MB, time=219.05 memory used=14080.9MB, alloc=828.3MB, time=220.88 memory used=14630.9MB, alloc=828.3MB, time=223.41 memory used=15063.6MB, alloc=828.3MB, time=225.96 memory used=15481.6MB, alloc=828.3MB, time=229.18 memory used=15864.2MB, alloc=828.3MB, time=231.29 memory used=16049.4MB, alloc=828.3MB, time=233.86 memory used=16470.0MB, alloc=828.3MB, time=236.90 memory used=16767.4MB, alloc=828.3MB, time=240.00 |\^/| 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(); 1428535888 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 F := [-8 x z - 11 z + 17, -9 x + 3 x - 7] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 3 G := [13 x z - 3 y - 9 y , -6 x y z + 2 y + 4 x z] > Problem := [F,G]; 2 3 Problem := [[-8 x z - 11 z + 17, -9 x + 3 x - 7], 2 3 2 3 [13 x z - 3 y - 9 y , -6 x y z + 2 y + 4 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=24.4MB, alloc=32.3MB, time=0.46 memory used=42.5MB, alloc=56.3MB, time=0.72 memory used=87.1MB, alloc=60.3MB, time=1.36 memory used=123.8MB, alloc=60.3MB, time=1.71 memory used=158.7MB, alloc=60.3MB, time=1.94 memory used=220.0MB, alloc=69.1MB, time=2.44 memory used=274.3MB, alloc=69.1MB, time=2.98 memory used=331.1MB, alloc=69.1MB, time=3.45 memory used=375.4MB, alloc=69.1MB, time=4.00 memory used=423.2MB, alloc=69.1MB, time=4.51 memory used=470.4MB, alloc=93.1MB, time=5.12 memory used=547.0MB, alloc=93.1MB, time=5.90 memory used=615.8MB, alloc=93.1MB, time=6.31 memory used=692.1MB, alloc=93.1MB, time=7.08 memory used=761.4MB, alloc=93.1MB, time=7.45 memory used=834.5MB, alloc=93.1MB, time=8.05 memory used=904.5MB, alloc=93.1MB, time=8.55 memory used=971.9MB, alloc=117.1MB, time=9.51 memory used=1057.5MB, alloc=117.1MB, time=10.70 memory used=1141.1MB, alloc=141.1MB, time=11.87 memory used=1252.9MB, alloc=141.1MB, time=13.39 memory used=1345.5MB, alloc=165.1MB, time=14.90 memory used=1478.9MB, alloc=165.1MB, time=16.60 memory used=1591.7MB, alloc=189.1MB, time=18.37 memory used=1733.0MB, alloc=469.1MB, time=20.39 memory used=1911.5MB, alloc=469.1MB, time=22.27 memory used=2067.1MB, alloc=493.1MB, time=24.58 memory used=2258.0MB, alloc=517.1MB, time=26.87 memory used=2460.3MB, alloc=541.1MB, time=29.82 memory used=2645.3MB, alloc=565.1MB, time=34.65 memory used=2824.2MB, alloc=589.1MB, time=40.22 memory used=3013.5MB, alloc=613.1MB, time=46.55 memory used=3215.1MB, alloc=637.1MB, time=53.64 memory used=3427.6MB, alloc=661.1MB, time=61.91 memory used=3664.1MB, alloc=685.1MB, time=71.10 memory used=3924.6MB, alloc=709.1MB, time=81.09 memory used=4208.9MB, alloc=709.1MB, time=92.08 memory used=4493.3MB, alloc=709.1MB, time=103.06 memory used=4777.6MB, alloc=709.1MB, time=113.98 memory used=5061.9MB, alloc=733.1MB, time=125.15 memory used=5370.1MB, alloc=733.1MB, time=137.36 memory used=5678.3MB, alloc=733.1MB, time=149.55 memory used=5986.5MB, alloc=757.1MB, time=161.72 memory used=6318.6MB, alloc=757.1MB, time=174.76 memory used=6650.7MB, alloc=781.1MB, time=187.85 memory used=7006.5MB, alloc=805.1MB, time=201.83 N1 := 12383 > GB := Basis(F, plex(op(vars))); 3 2 GB := [9 x - 3 x + 7, 11 z + 8 z x - 17] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=7400.7MB, alloc=805.1MB, time=213.12 memory used=7759.3MB, alloc=805.1MB, time=217.03 memory used=8258.1MB, alloc=805.1MB, time=221.60 memory used=8728.7MB, alloc=805.1MB, time=228.12 memory used=9193.6MB, alloc=829.1MB, time=234.09 memory used=9672.8MB, alloc=853.1MB, time=240.65 memory used=10084.3MB, alloc=877.1MB, time=252.80 memory used=10479.5MB, alloc=901.1MB, time=265.93 |\^/| 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(); 1428536188 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 F := [17 x - 4 x + 16 x z, 8 y z + 3 x y - 2] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 G := [-3 x z - 8 x z - 5 y z, -3 y + 4 z + 5] > Problem := [F,G]; 3 2 2 Problem := [[17 x - 4 x + 16 x z, 8 y z + 3 x y - 2], 2 2 2 2 [-3 x z - 8 x z - 5 y z, -3 y + 4 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=4.2MB, alloc=32.3MB, time=0.17 memory used=26.4MB, alloc=32.3MB, time=0.46 memory used=47.4MB, alloc=32.3MB, time=0.76 memory used=65.3MB, alloc=56.3MB, time=1.03 memory used=104.9MB, alloc=60.3MB, time=1.60 memory used=143.6MB, alloc=84.3MB, time=2.19 memory used=203.5MB, alloc=92.3MB, time=3.14 memory used=265.4MB, alloc=116.3MB, time=4.05 memory used=331.4MB, alloc=116.3MB, time=5.00 memory used=403.0MB, alloc=372.3MB, time=6.08 memory used=484.4MB, alloc=396.3MB, time=7.30 memory used=591.9MB, alloc=420.3MB, time=8.83 memory used=723.0MB, alloc=444.3MB, time=10.54 memory used=848.4MB, alloc=468.3MB, time=12.09 memory used=1032.5MB, alloc=492.3MB, time=14.46 memory used=1198.3MB, alloc=516.3MB, time=17.02 memory used=1378.3MB, alloc=540.3MB, time=19.75 memory used=1568.1MB, alloc=564.3MB, time=22.70 memory used=1758.0MB, alloc=588.3MB, time=25.70 memory used=1960.0MB, alloc=612.3MB, time=28.95 memory used=2169.4MB, alloc=636.3MB, time=32.38 memory used=2351.4MB, alloc=660.3MB, time=36.74 memory used=2551.9MB, alloc=684.3MB, time=42.58 memory used=2760.0MB, alloc=708.3MB, time=49.23 memory used=2980.4MB, alloc=732.3MB, time=56.25 memory used=3213.6MB, alloc=756.3MB, time=64.06 memory used=3462.1MB, alloc=780.3MB, time=72.42 memory used=3725.6MB, alloc=804.3MB, time=81.35 memory used=4002.9MB, alloc=828.3MB, time=90.93 memory used=4294.2MB, alloc=852.3MB, time=101.41 memory used=4609.5MB, alloc=876.3MB, time=112.83 memory used=4948.8MB, alloc=900.3MB, time=126.35 memory used=5311.9MB, alloc=924.3MB, time=139.56 memory used=5699.1MB, alloc=948.3MB, time=154.21 memory used=6110.2MB, alloc=972.3MB, time=169.98 memory used=6545.1MB, alloc=996.3MB, time=186.09 memory used=7004.0MB, alloc=996.3MB, time=203.61 memory used=7462.9MB, alloc=1020.3MB, time=220.70 memory used=7945.7MB, alloc=1020.3MB, time=238.70 memory used=8428.5MB, alloc=1020.3MB, time=256.41 memory used=8911.2MB, alloc=1020.3MB, time=273.29 memory used=9393.9MB, alloc=1044.3MB, time=290.44 |\^/| 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(); 1428536488 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 3 F := [-9 y z + 12 x y + 18 y , 10 x y - 4 y z - 4 z ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 G := [15 x y z + 10 z + 13 z, -5 x y - z + 3 x] > Problem := [F,G]; 2 2 2 2 3 Problem := [[-9 y z + 12 x y + 18 y , 10 x y - 4 y z - 4 z ], 2 2 2 [15 x y z + 10 z + 13 z, -5 x y - z + 3 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.16 memory used=27.0MB, alloc=32.3MB, time=0.48 memory used=47.7MB, alloc=32.3MB, time=0.78 memory used=67.0MB, alloc=56.3MB, time=1.07 memory used=106.1MB, alloc=60.3MB, time=1.65 memory used=143.6MB, alloc=84.3MB, time=2.22 memory used=205.2MB, alloc=92.3MB, time=3.19 memory used=267.9MB, alloc=116.3MB, time=4.11 memory used=351.9MB, alloc=116.3MB, time=5.36 memory used=428.5MB, alloc=396.3MB, time=6.50 memory used=541.7MB, alloc=396.3MB, time=8.15 memory used=648.5MB, alloc=420.3MB, time=9.75 memory used=777.2MB, alloc=444.3MB, time=11.79 memory used=905.4MB, alloc=444.3MB, time=13.49 memory used=1040.2MB, alloc=468.3MB, time=15.56 memory used=1165.3MB, alloc=468.3MB, time=17.56 memory used=1291.1MB, alloc=492.3MB, time=19.13 memory used=1397.7MB, alloc=492.3MB, time=20.61 memory used=1521.3MB, alloc=492.3MB, time=21.96 memory used=1619.7MB, alloc=492.3MB, time=23.12 memory used=1731.4MB, alloc=492.3MB, time=24.41 memory used=1832.1MB, alloc=492.3MB, time=25.83 memory used=1920.3MB, alloc=492.3MB, time=27.19 memory used=2044.8MB, alloc=516.3MB, time=28.38 memory used=2190.9MB, alloc=516.3MB, time=29.31 memory used=2282.9MB, alloc=516.3MB, time=30.35 memory used=2367.7MB, alloc=516.3MB, time=31.56 memory used=2450.3MB, alloc=516.3MB, time=32.67 memory used=2560.0MB, alloc=516.3MB, time=33.68 memory used=2635.8MB, alloc=540.3MB, time=34.73 memory used=2726.1MB, alloc=540.3MB, time=35.72 memory used=2798.1MB, alloc=540.3MB, time=36.65 memory used=2869.8MB, alloc=540.3MB, time=37.84 memory used=2982.7MB, alloc=540.3MB, time=39.08 memory used=3060.0MB, alloc=540.3MB, time=40.31 memory used=3159.9MB, alloc=564.3MB, time=41.90 memory used=3224.4MB, alloc=564.3MB, time=43.07 memory used=3311.0MB, alloc=588.3MB, time=44.51 memory used=3397.7MB, alloc=588.3MB, time=45.99 memory used=3485.4MB, alloc=612.3MB, time=47.55 memory used=3572.3MB, alloc=612.3MB, time=49.26 memory used=3839.9MB, alloc=636.3MB, time=52.53 memory used=4118.4MB, alloc=660.3MB, time=56.24 memory used=4407.1MB, alloc=684.3MB, time=60.19 memory used=4659.0MB, alloc=708.3MB, time=66.40 memory used=4894.6MB, alloc=732.3MB, time=73.59 memory used=5136.2MB, alloc=756.3MB, time=81.46 memory used=5385.1MB, alloc=780.3MB, time=90.00 memory used=5642.0MB, alloc=804.3MB, time=99.61 memory used=5922.9MB, alloc=828.3MB, time=110.04 memory used=6227.7MB, alloc=852.3MB, time=121.28 memory used=6556.4MB, alloc=876.3MB, time=134.41 memory used=6909.1MB, alloc=900.3MB, time=147.50 memory used=7285.7MB, alloc=924.3MB, time=161.82 memory used=7686.2MB, alloc=948.3MB, time=176.88 memory used=8110.8MB, alloc=972.3MB, time=192.94 memory used=8559.2MB, alloc=972.3MB, time=211.08 memory used=9007.6MB, alloc=996.3MB, time=229.44 memory used=9479.9MB, alloc=996.3MB, time=248.50 memory used=9952.2MB, alloc=1020.3MB, time=267.49 memory used=10448.4MB, alloc=1020.3MB, time=287.41 |\^/| 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(); 1428536788 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 F := [x y + 10 x z + 13, 4 x - 2 z + 3] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 3 2 G := [x + 10 x y - 13 y , -9 x + 2 x z + 5 x] > Problem := [F,G]; 2 2 Problem := [[x y + 10 x z + 13, 4 x - 2 z + 3], 3 2 2 3 2 [x + 10 x y - 13 y , -9 x + 2 x z + 5 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.5MB, alloc=32.3MB, time=0.51 memory used=48.3MB, alloc=32.3MB, time=0.87 memory used=68.4MB, alloc=56.3MB, time=1.22 N1 := 699 > GB := Basis(F, plex(op(vars))); 2 3 2 GB := [y x + 20 x + 15 x + 13, -4 x + 2 z - 3] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=109.3MB, alloc=56.3MB, time=2.03 N2 := 149 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 3 2 H := [y x + 10 z x + 13, 4 x - 2 z + 3, 10 y x + x - 13 y , 3 2 -9 x + 2 x z + 5 x] > J:=[op(GB),op(G)]; 2 3 2 2 3 2 J := [y x + 20 x + 15 x + 13, -4 x + 2 z - 3, 10 y x + x - 13 y , 3 2 -9 x + 2 x z + 5 x] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 9, 11, 3, 3, 2, 1, 1, 1/2, 3/4, 2/3, 1/4, 1/4, 4, 8, 11, 3, 3, 2, 1, 1, 1/2, 1/2, 9/13, 3/13, 2/13, 1, 0, 0] > save(F, G, cat("ranSet/33", convert(F, string),".txt")); > quit memory used=126.3MB, alloc=56.3MB, time=2.29 |\^/| 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(); 1428536791 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 2 F := [16 x y - 17 x y - y , -9 x y + 10 x z + 10 y z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 2 2 G := [8 x + x + 6 y z, 8 x z - y z - 4 x ] > Problem := [F,G]; 2 2 2 2 2 Problem := [[16 x y - 17 x y - y , -9 x y + 10 x z + 10 y z], 3 2 2 2 2 [8 x + x + 6 y z, 8 x z - y 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=4.2MB, alloc=32.3MB, time=0.17 memory used=26.4MB, alloc=32.3MB, time=0.49 memory used=46.3MB, alloc=56.3MB, time=0.80 memory used=87.8MB, alloc=60.3MB, time=1.42 memory used=129.9MB, alloc=92.3MB, time=2.05 memory used=197.0MB, alloc=92.3MB, time=2.92 memory used=264.7MB, alloc=92.3MB, time=3.75 memory used=334.4MB, alloc=116.3MB, time=4.78 memory used=435.0MB, alloc=116.3MB, time=5.68 memory used=529.5MB, alloc=372.3MB, time=7.00 memory used=614.4MB, alloc=396.3MB, time=8.33 memory used=726.3MB, alloc=396.3MB, time=9.81 memory used=822.2MB, alloc=420.3MB, time=11.44 memory used=953.6MB, alloc=444.3MB, time=13.13 memory used=1096.3MB, alloc=444.3MB, time=15.28 memory used=1236.0MB, alloc=468.3MB, time=17.35 memory used=1391.6MB, alloc=492.3MB, time=19.75 memory used=1569.5MB, alloc=516.3MB, time=22.40 memory used=1755.1MB, alloc=540.3MB, time=25.52 memory used=1952.7MB, alloc=564.3MB, time=28.64 memory used=2166.9MB, alloc=588.3MB, time=33.10 memory used=2355.5MB, alloc=612.3MB, time=39.19 memory used=2554.7MB, alloc=636.3MB, time=45.95 memory used=2767.3MB, alloc=660.3MB, time=53.46 memory used=2995.6MB, alloc=684.3MB, time=61.64 memory used=3234.5MB, alloc=708.3MB, time=70.88 memory used=3491.6MB, alloc=732.3MB, time=81.16 memory used=3772.7MB, alloc=756.3MB, time=92.34 memory used=4077.7MB, alloc=780.3MB, time=104.51 memory used=4406.7MB, alloc=780.3MB, time=117.72 memory used=4735.6MB, alloc=780.3MB, time=130.89 memory used=5064.5MB, alloc=804.3MB, time=142.76 memory used=5417.3MB, alloc=804.3MB, time=156.04 memory used=5770.1MB, alloc=804.3MB, time=169.98 memory used=6122.8MB, alloc=828.3MB, time=183.88 memory used=6499.5MB, alloc=828.3MB, time=198.53 memory used=6876.1MB, alloc=852.3MB, time=213.23 memory used=7276.8MB, alloc=852.3MB, time=228.72 memory used=7677.5MB, alloc=876.3MB, time=243.99 memory used=8102.5MB, alloc=900.3MB, time=260.18 N1 := 13739 > GB := Basis(F, plex(op(vars))); 2 2 2 2 2 GB := [16 x y - 17 x y - y , -9 x y + 10 x z + 10 y z, 4 3 2 2 3 2 40960 y z - 43520 y z + 2560 y z - 144 y - 2601 x y - 153 y ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=8241.7MB, alloc=900.3MB, time=263.46 memory used=8358.2MB, alloc=900.3MB, time=265.59 memory used=8471.7MB, alloc=900.3MB, time=267.76 memory used=8571.9MB, alloc=900.3MB, time=269.61 memory used=8667.3MB, alloc=900.3MB, time=271.49 memory used=8750.7MB, alloc=900.3MB, time=273.20 memory used=8830.1MB, alloc=900.3MB, time=274.72 memory used=8913.2MB, alloc=900.3MB, time=276.54 memory used=8981.8MB, alloc=900.3MB, time=278.30 memory used=9078.9MB, alloc=900.3MB, time=279.81 memory used=9154.4MB, alloc=900.3MB, time=281.27 memory used=9209.5MB, alloc=900.3MB, time=282.57 memory used=9267.3MB, alloc=900.3MB, time=284.19 memory used=9307.4MB, alloc=900.3MB, time=285.44 memory used=9370.7MB, alloc=900.3MB, time=287.10 memory used=9413.3MB, alloc=900.3MB, time=288.41 |\^/| 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(); 1428537091 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 F := [-x z + 5 x z + 2 z, 6 x z - x + 8] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 G := [-19 x y + 6 x - 11 y z, 2 x z - 2 x + 6 y] > Problem := [F,G]; 2 2 Problem := [[-x z + 5 x z + 2 z, 6 x z - x + 8], 2 2 2 2 [-19 x y + 6 x - 11 y z, 2 x z - 2 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=4.2MB, alloc=32.3MB, time=0.17 memory used=26.3MB, alloc=32.3MB, time=0.49 memory used=46.9MB, alloc=32.3MB, time=0.79 memory used=66.3MB, alloc=56.3MB, time=1.07 memory used=106.7MB, alloc=60.3MB, time=1.64 memory used=145.3MB, alloc=84.3MB, time=2.19 memory used=204.2MB, alloc=92.3MB, time=3.08 memory used=263.9MB, alloc=116.3MB, time=4.04 memory used=346.6MB, alloc=140.3MB, time=5.35 memory used=442.0MB, alloc=140.3MB, time=6.88 memory used=529.1MB, alloc=164.3MB, time=8.32 memory used=634.4MB, alloc=188.3MB, time=10.01 memory used=753.3MB, alloc=212.3MB, time=11.99 memory used=886.2MB, alloc=492.3MB, time=14.22 memory used=1032.2MB, alloc=516.3MB, time=16.65 memory used=1204.4MB, alloc=540.3MB, time=19.36 memory used=1404.8MB, alloc=564.3MB, time=22.19 memory used=1584.2MB, alloc=588.3MB, time=26.98 memory used=1762.6MB, alloc=612.3MB, time=32.54 memory used=1951.4MB, alloc=636.3MB, time=38.79 memory used=2153.1MB, alloc=660.3MB, time=45.65 memory used=2368.2MB, alloc=684.3MB, time=53.22 memory used=2592.7MB, alloc=708.3MB, time=61.89 memory used=2839.5MB, alloc=732.3MB, time=71.45 memory used=3110.3MB, alloc=756.3MB, time=81.94 memory used=3405.0MB, alloc=780.3MB, time=93.31 memory used=3723.6MB, alloc=804.3MB, time=105.68 memory used=4066.2MB, alloc=804.3MB, time=119.03 memory used=4408.8MB, alloc=804.3MB, time=132.82 memory used=4751.3MB, alloc=804.3MB, time=146.60 memory used=5093.7MB, alloc=828.3MB, time=160.36 memory used=5460.2MB, alloc=828.3MB, time=174.94 memory used=5826.5MB, alloc=828.3MB, time=189.53 memory used=6192.9MB, alloc=828.3MB, time=204.10 memory used=6559.3MB, alloc=852.3MB, time=217.48 memory used=6949.5MB, alloc=852.3MB, time=230.55 memory used=7339.6MB, alloc=852.3MB, time=243.72 memory used=7729.9MB, alloc=876.3MB, time=256.91 memory used=8144.0MB, alloc=876.3MB, time=270.78 |\^/| 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(); 1428537391 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 3 2 2 F := [-15 y + 3 z + 20 x z, 9 x y + 7 x z + x] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 G := [2 x z - 7 y + 17, -3 y z - 7 x + 6 y z] > Problem := [F,G]; 3 3 2 2 Problem := [[-15 y + 3 z + 20 x z, 9 x y + 7 x z + x], 2 2 2 2 [2 x z - 7 y + 17, -3 y z - 7 x + 6 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=26.6MB, alloc=32.3MB, time=0.51 memory used=46.7MB, alloc=60.3MB, time=0.80 memory used=92.0MB, alloc=60.3MB, time=1.31 memory used=156.9MB, alloc=70.4MB, time=1.78 memory used=210.0MB, alloc=70.4MB, time=2.34 memory used=253.6MB, alloc=70.4MB, time=2.94 memory used=294.9MB, alloc=70.4MB, time=3.40 memory used=346.2MB, alloc=70.4MB, time=3.99 memory used=394.1MB, alloc=94.4MB, time=4.57 memory used=461.1MB, alloc=94.4MB, time=5.44 memory used=528.9MB, alloc=94.4MB, time=6.28 memory used=593.7MB, alloc=118.4MB, time=6.93 memory used=667.2MB, alloc=118.4MB, time=7.52 memory used=723.7MB, alloc=118.4MB, time=7.90 memory used=784.3MB, alloc=118.4MB, time=8.28 memory used=840.1MB, alloc=118.4MB, time=8.59 memory used=911.9MB, alloc=118.4MB, time=10.50 memory used=957.0MB, alloc=118.4MB, time=10.64 memory used=999.2MB, alloc=118.4MB, time=10.78 memory used=1038.0MB, alloc=118.4MB, time=10.91 memory used=1084.5MB, alloc=118.4MB, time=11.05 memory used=1135.8MB, alloc=118.4MB, time=11.18 memory used=1167.1MB, alloc=118.4MB, time=11.28 memory used=1202.9MB, alloc=118.4MB, time=11.38 memory used=1265.3MB, alloc=118.4MB, time=11.62 memory used=1303.5MB, alloc=118.4MB, time=11.76 memory used=1350.0MB, alloc=118.4MB, time=11.92 memory used=1402.5MB, alloc=118.4MB, time=12.07 memory used=1434.6MB, alloc=118.4MB, time=12.22 memory used=1470.2MB, alloc=118.4MB, time=12.35 memory used=1510.6MB, alloc=118.4MB, time=12.49 memory used=1556.4MB, alloc=118.4MB, time=12.63 memory used=1609.8MB, alloc=118.4MB, time=12.84 memory used=1671.5MB, alloc=118.4MB, time=13.10 memory used=1709.6MB, alloc=118.4MB, time=13.25 memory used=1757.4MB, alloc=118.4MB, time=13.40 memory used=1805.4MB, alloc=118.4MB, time=13.55 memory used=1838.3MB, alloc=118.4MB, time=13.68 memory used=1875.0MB, alloc=118.4MB, time=13.82 memory used=1916.1MB, alloc=118.4MB, time=13.96 memory used=1963.6MB, alloc=118.4MB, time=14.09 memory used=2025.8MB, alloc=118.4MB, time=18.78 memory used=2081.8MB, alloc=142.4MB, time=42.55 memory used=2151.8MB, alloc=142.4MB, time=44.10 memory used=2218.1MB, alloc=142.4MB, time=44.27 memory used=2271.7MB, alloc=142.4MB, time=44.42 memory used=2322.4MB, alloc=142.4MB, time=44.56 memory used=2380.0MB, alloc=142.4MB, time=44.72 memory used=2445.6MB, alloc=142.4MB, time=44.86 memory used=2519.1MB, alloc=142.4MB, time=45.02 memory used=2576.3MB, alloc=142.4MB, time=45.15 memory used=2617.8MB, alloc=142.4MB, time=45.27 memory used=2662.3MB, alloc=142.4MB, time=45.39 memory used=2709.9MB, alloc=142.4MB, time=45.50 memory used=2760.1MB, alloc=142.4MB, time=45.62 memory used=2812.8MB, alloc=142.4MB, time=45.74 memory used=2868.6MB, alloc=142.4MB, time=45.86 memory used=2928.3MB, alloc=142.4MB, time=45.98 memory used=2991.8MB, alloc=142.4MB, time=46.11 memory used=3060.4MB, alloc=142.4MB, time=46.24 memory used=3132.9MB, alloc=142.4MB, time=46.36 memory used=3156.4MB, alloc=155.8MB, time=46.45 memory used=3167.5MB, alloc=155.8MB, time=46.52 memory used=3178.9MB, alloc=155.8MB, time=46.60 memory used=3259.8MB, alloc=155.8MB, time=46.86 memory used=3322.1MB, alloc=155.8MB, time=47.04 memory used=3386.8MB, alloc=155.8MB, time=47.21 memory used=3435.8MB, alloc=155.8MB, time=47.36 memory used=3493.3MB, alloc=155.8MB, time=47.51 memory used=3562.7MB, alloc=155.8MB, time=47.66 memory used=3641.4MB, alloc=155.8MB, time=47.92 memory used=3702.3MB, alloc=155.8MB, time=48.08 memory used=3769.9MB, alloc=155.8MB, time=48.24 memory used=3818.7MB, alloc=155.8MB, time=48.39 memory used=3875.2MB, alloc=155.8MB, time=48.55 memory used=3943.7MB, alloc=155.8MB, time=48.70 memory used=4031.5MB, alloc=155.8MB, time=73.84 memory used=4106.9MB, alloc=155.8MB, time=78.44 memory used=4169.5MB, alloc=155.8MB, time=78.60 memory used=4226.4MB, alloc=155.8MB, time=78.77 memory used=4275.4MB, alloc=155.8MB, time=78.91 memory used=4331.1MB, alloc=155.8MB, time=79.07 memory used=4394.7MB, alloc=155.8MB, time=79.23 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used=6770.5MB, alloc=155.8MB, time=114.60 memory used=6828.1MB, alloc=155.8MB, time=114.72 memory used=6890.1MB, alloc=155.8MB, time=114.83 memory used=6956.0MB, alloc=155.8MB, time=114.96 memory used=7027.4MB, alloc=155.8MB, time=115.08 memory used=7078.1MB, alloc=155.8MB, time=115.19 memory used=7089.2MB, alloc=155.8MB, time=115.27 memory used=7100.6MB, alloc=155.8MB, time=115.35 memory used=7186.8MB, alloc=155.8MB, time=116.50 memory used=7248.3MB, alloc=155.8MB, time=116.67 memory used=7303.8MB, alloc=155.8MB, time=116.84 memory used=7375.9MB, alloc=155.8MB, time=116.99 memory used=7421.7MB, alloc=155.8MB, time=117.11 memory used=7523.3MB, alloc=155.8MB, time=117.75 memory used=7621.1MB, alloc=411.8MB, time=118.35 memory used=7725.4MB, alloc=411.8MB, time=121.74 memory used=7786.2MB, alloc=411.8MB, time=121.91 memory used=7836.0MB, alloc=411.8MB, time=122.06 memory used=7898.9MB, alloc=411.8MB, time=122.22 memory used=7955.8MB, alloc=411.8MB, time=122.36 memory used=8000.0MB, 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time=237.04 memory used=14898.1MB, alloc=411.8MB, time=237.21 memory used=14970.3MB, alloc=411.8MB, time=240.47 memory used=15042.8MB, alloc=411.8MB, time=267.10 memory used=15105.3MB, alloc=411.8MB, time=268.01 memory used=15163.2MB, alloc=411.8MB, time=268.21 memory used=15210.8MB, alloc=411.8MB, time=268.43 memory used=15252.8MB, alloc=411.8MB, time=268.59 memory used=15299.9MB, alloc=411.8MB, time=268.77 memory used=15352.6MB, alloc=411.8MB, time=268.97 memory used=15410.8MB, alloc=411.8MB, time=269.18 memory used=15474.4MB, alloc=411.8MB, time=269.37 memory used=15521.8MB, alloc=411.8MB, time=269.53 memory used=15557.9MB, alloc=411.8MB, time=269.68 memory used=15595.0MB, alloc=411.8MB, time=269.82 memory used=15635.0MB, alloc=411.8MB, time=269.98 memory used=15676.4MB, alloc=411.8MB, time=270.12 memory used=15720.4MB, alloc=411.8MB, time=270.25 memory used=15766.7MB, alloc=411.8MB, time=270.40 memory used=15814.9MB, alloc=411.8MB, time=270.55 memory used=15865.8MB, alloc=411.8MB, time=270.72 memory used=15920.0MB, alloc=411.8MB, time=270.87 memory used=15977.2MB, alloc=411.8MB, time=271.03 memory used=16037.9MB, alloc=411.8MB, time=271.19 memory used=16144.3MB, alloc=411.8MB, time=271.43 memory used=16218.5MB, alloc=411.8MB, time=272.69 memory used=16272.6MB, alloc=411.8MB, time=272.87 memory used=16319.4MB, alloc=411.8MB, time=273.08 memory used=16378.8MB, alloc=411.8MB, time=273.28 memory used=16427.8MB, alloc=411.8MB, time=273.45 memory used=16469.8MB, alloc=411.8MB, time=273.59 memory used=16579.8MB, alloc=411.8MB, time=274.99 memory used=16651.3MB, alloc=411.8MB, time=277.58 memory used=16704.0MB, alloc=411.8MB, time=277.76 memory used=16746.6MB, alloc=411.8MB, time=277.95 memory used=16799.2MB, alloc=411.8MB, time=278.11 memory used=16857.4MB, alloc=411.8MB, time=278.28 memory used=16893.0MB, alloc=411.8MB, time=278.41 memory used=16934.6MB, alloc=411.8MB, time=278.55 memory used=17047.0MB, alloc=435.8MB, time=284.49 memory used=17139.4MB, alloc=435.8MB, time=311.07 memory used=17205.8MB, alloc=435.8MB, time=311.34 memory used=17273.5MB, alloc=435.8MB, time=311.56 memory used=17326.0MB, alloc=435.8MB, time=311.78 memory used=17387.0MB, alloc=435.8MB, time=312.00 memory used=17456.9MB, alloc=435.8MB, time=312.25 memory used=17536.8MB, alloc=435.8MB, time=312.49 memory used=17596.7MB, alloc=435.8MB, time=312.69 memory used=17643.5MB, alloc=435.8MB, time=312.85 memory used=17692.9MB, alloc=435.8MB, time=313.03 memory used=17745.3MB, alloc=435.8MB, time=313.20 memory used=17800.5MB, alloc=435.8MB, time=313.39 memory used=17860.4MB, alloc=435.8MB, time=313.56 memory used=17923.3MB, alloc=435.8MB, time=313.71 memory used=17991.7MB, alloc=435.8MB, time=313.88 memory used=18064.9MB, alloc=435.8MB, time=314.05 memory used=18143.5MB, alloc=435.8MB, time=314.22 memory used=18311.3MB, alloc=435.8MB, time=315.01 memory used=18442.1MB, alloc=435.8MB, time=316.39 memory used=18566.7MB, alloc=459.8MB, time=317.70 memory used=18706.2MB, alloc=459.8MB, time=319.19 memory used=18826.5MB, alloc=459.8MB, time=320.17 memory used=18959.0MB, alloc=459.8MB, time=321.72 memory used=19083.8MB, alloc=459.8MB, time=322.61 memory used=19179.8MB, alloc=459.8MB, time=323.12 memory used=19262.6MB, alloc=459.8MB, time=323.48 memory used=19375.8MB, alloc=459.8MB, time=325.80 memory used=19446.9MB, alloc=459.8MB, time=326.11 memory used=19511.7MB, alloc=459.8MB, time=326.39 memory used=19596.8MB, alloc=459.8MB, time=326.73 memory used=19664.9MB, alloc=459.8MB, time=326.99 memory used=19761.1MB, alloc=459.8MB, time=329.60 memory used=19822.9MB, alloc=459.8MB, time=329.85 memory used=19892.5MB, alloc=459.8MB, time=330.13 memory used=19977.4MB, alloc=459.8MB, time=330.63 memory used=20065.8MB, alloc=459.8MB, time=331.04 memory used=20151.3MB, alloc=459.8MB, time=332.94 memory used=20259.1MB, alloc=459.8MB, time=333.77 memory used=20319.8MB, alloc=459.8MB, time=334.03 memory used=20387.0MB, alloc=459.8MB, time=334.27 memory used=20473.2MB, alloc=459.8MB, time=334.68 memory used=20567.7MB, alloc=459.8MB, time=336.46 memory used=20628.0MB, alloc=459.8MB, time=336.73 memory used=20696.0MB, alloc=459.8MB, time=336.99 memory used=20787.0MB, alloc=459.8MB, time=337.40 memory used=20891.3MB, alloc=459.8MB, time=342.93 memory used=20964.8MB, alloc=459.8MB, time=343.24 memory used=21019.9MB, alloc=459.8MB, time=343.50 memory used=21089.1MB, alloc=459.8MB, time=343.78 memory used=21160.5MB, alloc=459.8MB, time=344.04 memory used=21211.1MB, alloc=459.8MB, time=344.26 memory used=21269.7MB, alloc=459.8MB, time=344.49 memory used=21372.0MB, alloc=483.8MB, time=345.12 memory used=21446.2MB, alloc=483.8MB, time=345.49 memory used=21538.6MB, alloc=483.8MB, time=345.82 memory used=21636.4MB, alloc=483.8MB, time=346.20 memory used=21697.4MB, alloc=483.8MB, time=346.55 memory used=21764.3MB, alloc=483.8MB, time=346.86 memory used=21838.0MB, alloc=483.8MB, time=347.15 memory used=21919.6MB, alloc=483.8MB, time=347.49 memory used=22008.2MB, alloc=483.8MB, time=347.83 memory used=22106.7MB, alloc=483.8MB, time=348.17 memory used=22202.8MB, alloc=483.8MB, time=348.45 memory used=22262.2MB, alloc=483.8MB, time=348.66 memory used=22327.6MB, alloc=483.8MB, time=348.87 memory used=22449.7MB, alloc=483.8MB, time=349.60 memory used=22524.3MB, alloc=483.8MB, time=349.92 memory used=22618.0MB, alloc=483.8MB, time=350.26 memory used=22710.8MB, alloc=483.8MB, time=350.57 memory used=22772.5MB, alloc=483.8MB, time=350.83 memory used=22839.9MB, alloc=483.8MB, time=351.10 memory used=22913.5MB, alloc=483.8MB, time=351.36 memory used=22995.1MB, alloc=483.8MB, time=351.66 memory used=23083.5MB, alloc=483.8MB, time=351.99 memory used=23181.7MB, alloc=483.8MB, time=352.31 memory used=23274.2MB, alloc=483.8MB, time=352.60 memory used=23333.7MB, alloc=483.8MB, time=352.83 memory used=23398.6MB, alloc=483.8MB, time=353.06 memory used=23525.4MB, alloc=483.8MB, time=412.80 memory used=23639.8MB, alloc=483.8MB, time=414.82 memory used=23729.0MB, alloc=483.8MB, time=415.15 memory used=23796.6MB, alloc=483.8MB, time=415.44 memory used=23877.4MB, alloc=483.8MB, time=415.74 memory used=23973.1MB, alloc=483.8MB, time=416.06 memory used=24063.0MB, alloc=483.8MB, time=416.38 memory used=24121.4MB, alloc=483.8MB, time=416.63 memory used=24185.4MB, alloc=483.8MB, time=416.90 memory used=24253.0MB, alloc=483.8MB, time=417.16 memory used=24326.6MB, alloc=483.8MB, time=417.43 memory used=24405.5MB, alloc=483.8MB, time=417.70 memory used=24491.2MB, alloc=483.8MB, time=417.98 memory used=24584.1MB, alloc=483.8MB, time=418.25 memory used=24686.5MB, alloc=483.8MB, time=418.49 memory used=24876.8MB, alloc=483.8MB, time=419.22 memory used=24949.5MB, alloc=483.8MB, time=419.54 memory used=25040.8MB, alloc=483.8MB, time=419.86 memory used=25138.0MB, alloc=483.8MB, time=420.18 memory used=25197.7MB, alloc=483.8MB, time=420.47 memory used=25264.6MB, alloc=483.8MB, time=420.76 memory used=25338.0MB, alloc=483.8MB, time=421.07 memory used=25417.0MB, alloc=483.8MB, time=421.36 memory used=25505.5MB, alloc=483.8MB, time=421.65 memory used=25601.5MB, alloc=483.8MB, time=421.97 memory used=25699.9MB, alloc=483.8MB, time=422.26 memory used=25757.3MB, alloc=483.8MB, time=422.48 memory used=25820.5MB, alloc=483.8MB, time=422.71 memory used=25942.3MB, alloc=483.8MB, time=423.50 memory used=26019.3MB, alloc=483.8MB, time=423.86 memory used=26105.5MB, alloc=483.8MB, time=424.22 memory used=26209.7MB, alloc=483.8MB, time=424.59 memory used=26273.4MB, alloc=483.8MB, time=424.87 memory used=26339.4MB, alloc=483.8MB, time=425.16 memory used=26410.3MB, alloc=483.8MB, time=425.45 memory used=26489.2MB, alloc=483.8MB, time=425.73 memory used=26575.6MB, alloc=483.8MB, time=426.05 memory used=26672.2MB, alloc=483.8MB, time=426.34 memory used=26777.9MB, alloc=483.8MB, time=426.65 memory used=26837.3MB, alloc=483.8MB, time=426.88 memory used=26900.5MB, alloc=483.8MB, time=427.10 |\^/| 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(); 1428537691 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 3 F := [-10 x z + 15 y z + 7 x y, -7 y z - 8 z + 5 x y] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 G := [-20 x z + 10 x z - 9 y z, -x y z - 10 y z - 5 y z] > Problem := [F,G]; 2 2 2 3 Problem := [[-10 x z + 15 y z + 7 x y, -7 y z - 8 z + 5 x y], 2 2 [-20 x z + 10 x z - 9 y z, -x y z - 10 y z - 5 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.6MB, alloc=32.3MB, time=0.48 memory used=47.0MB, alloc=56.3MB, time=0.79 memory used=86.5MB, alloc=60.3MB, time=1.36 memory used=130.5MB, alloc=60.3MB, time=1.91 memory used=175.4MB, alloc=84.3MB, time=2.36 memory used=244.8MB, alloc=92.3MB, time=3.23 memory used=313.0MB, alloc=92.3MB, time=4.02 memory used=383.6MB, alloc=92.3MB, time=4.84 memory used=447.4MB, alloc=116.3MB, time=5.61 memory used=533.9MB, alloc=116.3MB, time=6.70 memory used=617.7MB, alloc=140.3MB, time=7.92 memory used=709.9MB, alloc=140.3MB, time=8.92 memory used=787.1MB, alloc=396.3MB, time=9.88 memory used=893.0MB, alloc=420.3MB, time=11.26 memory used=1034.0MB, alloc=420.3MB, time=12.93 memory used=1099.3MB, alloc=444.3MB, time=33.21 memory used=1155.8MB, alloc=468.3MB, time=57.52 memory used=1239.8MB, alloc=492.3MB, time=67.74 memory used=1361.0MB, alloc=516.3MB, time=68.16 memory used=1404.3MB, alloc=540.3MB, time=149.28 memory used=1550.3MB, alloc=540.3MB, time=150.52 memory used=1715.9MB, alloc=540.3MB, time=152.92 memory used=1870.3MB, alloc=540.3MB, time=153.24 memory used=2254.3MB, alloc=540.3MB, time=155.97 memory used=2464.7MB, alloc=540.3MB, time=156.97 memory used=2669.0MB, alloc=540.3MB, time=158.52 memory used=2831.4MB, alloc=540.3MB, time=159.22 memory used=3006.3MB, alloc=540.3MB, time=207.12 memory used=3134.6MB, alloc=564.3MB, time=227.87 memory used=3318.7MB, alloc=588.3MB, time=326.23 memory used=3539.3MB, alloc=588.3MB, time=327.67 memory used=3681.6MB, alloc=588.3MB, time=329.27 memory used=3879.6MB, alloc=588.3MB, time=329.81 memory used=4229.9MB, alloc=588.3MB, time=331.76 memory used=4439.7MB, alloc=588.3MB, time=332.89 memory used=4687.5MB, alloc=588.3MB, time=334.66 memory used=4976.8MB, alloc=588.3MB, time=338.41 memory used=5269.7MB, alloc=588.3MB, time=341.71 memory used=5541.3MB, alloc=588.3MB, time=343.65 memory used=5756.9MB, alloc=588.3MB, time=344.44 memory used=6023.4MB, alloc=588.3MB, time=345.94 memory used=6219.6MB, alloc=588.3MB, time=346.62 memory used=6486.9MB, alloc=588.3MB, time=347.30 memory used=6891.6MB, alloc=588.3MB, time=348.26 memory used=7307.6MB, alloc=603.8MB, time=349.19 memory used=7689.6MB, alloc=603.8MB, time=350.03 memory used=8066.2MB, alloc=603.8MB, time=350.81 memory used=8436.1MB, alloc=603.8MB, time=351.58 memory used=8798.5MB, alloc=603.8MB, time=352.36 memory used=9158.0MB, alloc=603.8MB, time=353.10 memory used=9519.6MB, alloc=603.8MB, time=353.90 memory used=9882.5MB, alloc=603.8MB, time=354.71 memory used=10238.9MB, alloc=603.8MB, time=355.50 memory used=10599.5MB, alloc=603.8MB, time=356.29 memory used=10964.6MB, alloc=603.8MB, time=357.06 memory used=11321.3MB, alloc=603.8MB, time=357.86 memory used=11683.4MB, alloc=603.8MB, time=358.68 memory used=12040.6MB, alloc=603.8MB, time=359.49 memory used=12399.4MB, alloc=603.8MB, time=360.31 memory used=12757.9MB, alloc=603.8MB, time=361.11 memory used=13116.9MB, alloc=603.8MB, time=361.90 memory used=13476.7MB, alloc=603.8MB, time=362.77 memory used=13836.4MB, alloc=603.8MB, time=363.62 memory used=14199.8MB, alloc=603.8MB, time=364.46 memory used=14559.8MB, alloc=603.8MB, time=365.29 memory used=14923.1MB, alloc=603.8MB, time=366.12 memory used=15285.2MB, alloc=603.8MB, time=366.96 memory used=15647.3MB, alloc=603.8MB, time=367.82 memory used=16008.4MB, alloc=603.8MB, time=368.67 memory used=16373.1MB, alloc=603.8MB, time=369.55 memory used=16733.7MB, alloc=603.8MB, time=370.37 memory used=17095.6MB, alloc=603.8MB, time=371.19 memory used=17459.4MB, alloc=603.8MB, time=371.99 memory used=17822.0MB, alloc=603.8MB, time=372.82 memory used=18185.1MB, alloc=603.8MB, time=373.68 memory used=18549.2MB, alloc=603.8MB, time=374.55 memory used=18914.0MB, alloc=603.8MB, time=375.37 memory used=19279.2MB, alloc=603.8MB, time=376.22 memory used=19644.6MB, alloc=603.8MB, time=377.03 memory used=20010.8MB, alloc=603.8MB, time=377.92 memory used=20377.0MB, alloc=603.8MB, time=378.80 memory used=20743.8MB, alloc=603.8MB, time=379.68 memory used=21113.5MB, alloc=603.8MB, time=380.54 memory used=21470.8MB, alloc=603.8MB, time=381.38 memory used=21831.2MB, alloc=603.8MB, time=382.37 memory used=22191.9MB, alloc=603.8MB, time=383.39 memory used=22665.5MB, alloc=603.8MB, time=385.42 memory used=22970.2MB, alloc=627.8MB, time=387.34 memory used=23182.5MB, alloc=627.8MB, time=388.09 memory used=23491.5MB, alloc=627.8MB, time=388.98 memory used=23978.0MB, alloc=627.8MB, time=390.50 memory used=24275.6MB, alloc=651.8MB, time=393.36 memory used=24599.4MB, alloc=675.8MB, time=397.04 memory used=24916.7MB, alloc=699.8MB, time=401.37 memory used=25318.0MB, alloc=723.8MB, time=404.36 memory used=25746.3MB, alloc=747.8MB, time=407.85 memory used=26210.7MB, alloc=747.8MB, time=411.12 memory used=26669.0MB, alloc=747.8MB, time=414.17 memory used=27137.4MB, alloc=747.8MB, time=416.71 |\^/| 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(); 1428537991 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 F := [6 x y + 8 y z - 2 y, 8 x y + 7 x z - 10 y ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 G := [-9 x y - 14 x y z + 20 y, 7 x y - 8 x + 4 y] > Problem := [F,G]; 2 2 2 2 Problem := [[6 x y + 8 y z - 2 y, 8 x y + 7 x z - 10 y ], 2 [-9 x y - 14 x y z + 20 y, 7 x y - 8 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=4.2MB, alloc=32.3MB, time=0.17 memory used=26.5MB, alloc=32.3MB, time=0.42 memory used=47.5MB, alloc=32.3MB, time=0.68 memory used=66.8MB, alloc=56.3MB, time=0.94 memory used=107.9MB, alloc=60.3MB, time=1.48 memory used=148.2MB, alloc=84.3MB, time=2.08 memory used=209.0MB, alloc=92.3MB, time=2.99 memory used=263.7MB, alloc=116.3MB, time=3.81 memory used=338.6MB, alloc=140.3MB, time=4.85 memory used=432.0MB, alloc=164.3MB, time=6.19 memory used=539.9MB, alloc=188.3MB, time=8.13 memory used=654.7MB, alloc=212.3MB, time=11.12 memory used=780.4MB, alloc=236.3MB, time=14.92 memory used=922.8MB, alloc=236.3MB, time=19.40 memory used=1065.0MB, alloc=260.3MB, time=23.90 memory used=1231.4MB, alloc=260.3MB, time=29.11 memory used=1397.8MB, alloc=284.3MB, time=34.21 N1 := 5309 > GB := Basis(F, plex(op(vars))); 3 3 2 2 3 2 GB := [63 x y + 86 x y - 160 y + 7 x y, 3 x y + 4 y z - y, 2 2 2 7 z x + 8 y x - 10 y ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1543.0MB, alloc=284.3MB, time=37.00 memory used=1759.1MB, alloc=540.3MB, time=40.13 memory used=1960.9MB, alloc=564.3MB, time=43.25 memory used=2179.1MB, alloc=588.3MB, time=48.77 memory used=2386.6MB, alloc=612.3MB, time=55.51 memory used=2616.2MB, alloc=636.3MB, time=63.25 memory used=2869.9MB, alloc=660.3MB, time=71.69 N2 := 5309 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 2 H := [6 x y + 8 y z - 2 y, 7 z x + 8 y x - 10 y , -9 x y - 14 x y z + 20 y, 7 y x + 4 y - 8 x] > J:=[op(GB),op(G)]; 3 3 2 2 3 2 J := [63 x y + 86 x y - 160 y + 7 x y, 3 x y + 4 y z - y, 2 2 2 2 7 z x + 8 y x - 10 y , -9 x y - 14 x y z + 20 y, 7 y x + 4 y - 8 x] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 11, 11, 3, 2, 2, 2, 1, 1, 3/4, 7/12, 5/6, 1/4, 5, 13, 17, 6, 3, 3, 2, 1, 1, 3/5, 5/8, 7/8, 3/16, -2, -6, -3] > save(F, G, cat("ranSet/33", convert(F, string),".txt")); > quit memory used=2956.0MB, alloc=660.3MB, time=73.97 |\^/| 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(); 1428538067 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 F := [14 x z - 12 x y z - 3 z, -3 x - y z + 2 z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 3 3 2 G := [2 x - 9 x y + 14, -6 y - z - 8 x ] > Problem := [F,G]; 2 2 Problem := [[14 x z - 12 x y z - 3 z, -3 x - y z + 2 z], 3 2 3 3 2 [2 x - 9 x y + 14, -6 y - z - 8 x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.16 memory used=25.9MB, alloc=32.3MB, time=0.45 memory used=45.8MB, alloc=32.3MB, time=0.72 memory used=64.6MB, alloc=56.3MB, time=0.97 memory used=110.2MB, alloc=68.3MB, time=1.58 memory used=150.0MB, alloc=92.3MB, time=2.21 memory used=213.0MB, alloc=92.3MB, time=3.03 memory used=270.1MB, alloc=116.3MB, time=3.82 memory used=341.7MB, alloc=140.3MB, time=5.28 memory used=422.1MB, alloc=164.3MB, time=7.75 N1 := 2469 > GB := Basis(F, plex(op(vars))); GB := 4 3 2 3 2 2 [-14 x + 12 x y + 3 x , 36 x + 14 x z - 24 x z - 3 z, z y + 3 x - 2 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=528.3MB, alloc=164.3MB, time=10.26 memory used=607.8MB, alloc=420.3MB, time=11.31 memory used=736.5MB, alloc=444.3MB, time=12.82 memory used=888.6MB, alloc=468.3MB, time=14.85 memory used=1060.1MB, alloc=492.3MB, time=17.15 memory used=1224.9MB, alloc=516.3MB, time=21.84 memory used=1392.0MB, alloc=540.3MB, time=27.12 N2 := 3283 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 3 H := [14 x z - 12 x y z - 3 z, -3 x - y z + 2 z, -9 y x + 2 x + 14, 3 3 2 -6 y - z - 8 x ] > J:=[op(GB),op(G)]; 4 3 2 2 3 2 J := [-14 x + 12 x y + 3 x , 14 z x + 36 x - 24 z x - 3 z, z y + 3 x - 2 z, 2 3 3 3 2 -9 y x + 2 x + 14, -6 y - z - 8 x ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 11, 11, 3, 3, 3, 3, 1, 1, 3/4, 1/2, 1/3, 1/2, 5, 12, 15, 4, 4, 3, 3, 1, 4/5, 3/5, 5/8, 1/4, 3/8, -1, -4, -1] > save(F, G, cat("ranSet/33", convert(F, string),".txt")); > quit memory used=1467.3MB, alloc=540.3MB, time=28.87 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428538097 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 3 2 2 2 F := [19 x y + 10 y z - 8 z , 5 x y + 10 y z + 5 z ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 G := [19 x y z - 4 y z - 19 y, -3 x y z + 10 y + 6 y ] > Problem := [F,G]; 2 2 3 2 2 2 Problem := [[19 x y + 10 y z - 8 z , 5 x y + 10 y z + 5 z ], 2 3 2 [19 x y z - 4 y z - 19 y, -3 x y z + 10 y + 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=4.2MB, alloc=32.3MB, time=0.16 memory used=25.8MB, alloc=32.3MB, time=0.41 memory used=45.0MB, alloc=56.3MB, time=0.64 memory used=86.1MB, alloc=60.3MB, time=1.14 memory used=126.3MB, alloc=84.3MB, time=1.60 memory used=163.5MB, alloc=84.3MB, time=2.02 memory used=229.1MB, alloc=92.3MB, time=2.57 memory used=287.5MB, alloc=92.3MB, time=3.06 memory used=355.2MB, alloc=116.3MB, time=3.87 memory used=430.2MB, alloc=372.3MB, time=4.81 memory used=514.1MB, alloc=396.3MB, time=5.95 memory used=625.4MB, alloc=396.3MB, time=6.93 memory used=741.1MB, alloc=420.3MB, time=8.19 memory used=878.4MB, alloc=420.3MB, time=9.66 memory used=1007.2MB, alloc=420.3MB, time=11.03 memory used=1131.3MB, alloc=444.3MB, time=12.77 memory used=1257.0MB, alloc=444.3MB, time=14.61 memory used=1370.4MB, alloc=468.3MB, time=16.37 memory used=1484.3MB, alloc=468.3MB, time=17.81 memory used=1607.9MB, alloc=468.3MB, time=19.31 memory used=1710.8MB, alloc=468.3MB, time=20.81 memory used=1851.6MB, alloc=492.3MB, time=22.31 memory used=1957.4MB, alloc=492.3MB, time=22.91 memory used=2035.5MB, alloc=492.3MB, time=23.29 memory used=2126.2MB, alloc=492.3MB, time=23.64 memory used=2215.2MB, alloc=492.3MB, time=24.17 memory used=2300.7MB, alloc=492.3MB, time=24.58 memory used=2398.2MB, alloc=492.3MB, time=24.98 memory used=2469.2MB, alloc=492.3MB, time=25.29 memory used=2572.6MB, alloc=492.3MB, time=27.05 memory used=2654.6MB, alloc=492.3MB, time=27.39 memory used=2778.1MB, alloc=492.3MB, time=28.43 memory used=2886.3MB, alloc=492.3MB, time=28.97 memory used=2981.8MB, alloc=492.3MB, time=29.80 memory used=3115.1MB, alloc=492.3MB, time=31.02 memory used=3228.9MB, alloc=492.3MB, time=32.30 memory used=3324.4MB, alloc=492.3MB, time=33.53 memory used=3393.3MB, alloc=492.3MB, time=34.72 memory used=3478.1MB, alloc=492.3MB, time=36.21 memory used=3539.4MB, alloc=492.3MB, time=37.37 memory used=3591.1MB, alloc=492.3MB, time=38.34 memory used=3667.6MB, alloc=492.3MB, time=39.73 memory used=3732.9MB, alloc=516.3MB, time=40.73 memory used=3853.2MB, alloc=516.3MB, time=41.38 memory used=3962.9MB, alloc=516.3MB, time=42.48 memory used=4065.2MB, alloc=516.3MB, time=43.05 memory used=4189.5MB, alloc=516.3MB, time=43.80 memory used=4296.7MB, alloc=516.3MB, time=44.50 memory used=4367.4MB, alloc=516.3MB, time=45.46 memory used=4427.6MB, alloc=516.3MB, time=46.45 memory used=4491.1MB, alloc=516.3MB, time=47.33 memory used=4558.8MB, alloc=516.3MB, time=48.48 memory used=4622.9MB, alloc=516.3MB, time=49.64 memory used=4672.7MB, alloc=516.3MB, time=50.58 memory used=4723.9MB, alloc=516.3MB, time=51.35 memory used=4927.1MB, alloc=540.3MB, time=53.73 memory used=5175.1MB, alloc=564.3MB, time=56.87 memory used=5426.6MB, alloc=588.3MB, time=60.80 memory used=5679.9MB, alloc=612.3MB, time=64.78 memory used=5956.7MB, alloc=636.3MB, time=68.35 memory used=6249.1MB, alloc=660.3MB, time=72.85 memory used=6501.5MB, alloc=684.3MB, time=77.40 memory used=6783.6MB, alloc=708.3MB, time=82.45 memory used=7051.5MB, alloc=732.3MB, time=87.00 memory used=7304.3MB, alloc=756.3MB, time=91.62 memory used=7540.1MB, alloc=780.3MB, time=96.08 memory used=7853.9MB, alloc=804.3MB, time=104.82 memory used=8131.1MB, alloc=828.3MB, time=114.80 memory used=8413.9MB, alloc=852.3MB, time=125.48 memory used=8705.6MB, alloc=876.3MB, time=136.89 memory used=9009.5MB, alloc=900.3MB, time=148.98 memory used=9327.5MB, alloc=924.3MB, time=161.74 memory used=9658.8MB, alloc=948.3MB, time=175.32 memory used=10000.5MB, alloc=972.3MB, time=189.98 memory used=10366.2MB, alloc=996.3MB, time=205.58 memory used=10755.8MB, alloc=1020.3MB, time=222.18 memory used=11169.4MB, alloc=1044.3MB, time=239.80 memory used=11606.9MB, alloc=1068.3MB, time=258.31 memory used=12068.4MB, alloc=1092.3MB, time=277.78 |\^/| 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(); 1428538397 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 3 F := [-x z - 16 z - x, 9 x y z + 2 x z + 2 z ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 3 2 G := [-7 x + 12 x z - 3 y z , 9 x + 9 x y - 7] > Problem := [F,G]; 2 2 2 3 Problem := [[-x z - 16 z - x, 9 x y z + 2 x z + 2 z ], 3 2 2 3 2 [-7 x + 12 x z - 3 y z , 9 x + 9 x 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=4.2MB, alloc=32.3MB, time=0.17 memory used=26.5MB, alloc=32.3MB, time=0.49 memory used=47.8MB, alloc=32.3MB, time=0.79 memory used=67.6MB, alloc=56.3MB, time=1.11 memory used=108.5MB, alloc=60.3MB, time=1.70 memory used=147.8MB, alloc=84.3MB, time=2.27 memory used=209.3MB, alloc=92.3MB, time=3.12 memory used=270.0MB, alloc=116.3MB, time=4.00 memory used=344.0MB, alloc=116.3MB, time=5.04 memory used=427.6MB, alloc=396.3MB, time=6.33 memory used=546.3MB, alloc=396.3MB, time=7.88 memory used=660.4MB, alloc=420.3MB, time=9.39 memory used=787.0MB, alloc=444.3MB, time=11.41 memory used=932.2MB, alloc=468.3MB, time=13.83 memory used=1094.4MB, alloc=492.3MB, time=16.44 memory used=1274.0MB, alloc=516.3MB, time=19.34 memory used=1485.5MB, alloc=540.3MB, time=22.07 memory used=1689.7MB, alloc=564.3MB, time=24.63 memory used=1864.8MB, alloc=564.3MB, time=25.61 memory used=2053.4MB, alloc=564.3MB, time=26.49 memory used=2233.6MB, alloc=564.3MB, time=27.27 memory used=2391.6MB, alloc=564.3MB, time=27.98 memory used=2567.1MB, alloc=564.3MB, time=28.76 memory used=2774.2MB, alloc=564.3MB, time=29.66 memory used=3001.0MB, alloc=564.3MB, time=30.53 memory used=3247.4MB, alloc=564.3MB, time=31.46 memory used=3513.6MB, alloc=564.3MB, time=32.44 memory used=3893.8MB, alloc=564.3MB, time=33.94 memory used=4171.1MB, alloc=564.3MB, time=34.97 memory used=4461.0MB, alloc=564.3MB, time=35.95 memory used=4766.0MB, alloc=564.3MB, time=36.93 memory used=5085.9MB, alloc=564.3MB, time=38.01 memory used=5412.9MB, alloc=564.3MB, time=39.15 memory used=5748.1MB, alloc=564.3MB, time=40.32 memory used=6097.2MB, alloc=564.3MB, time=41.52 memory used=6450.7MB, alloc=564.3MB, time=42.64 memory used=6815.6MB, alloc=564.3MB, time=43.82 memory used=7193.6MB, alloc=564.3MB, time=44.98 memory used=7584.9MB, alloc=564.3MB, time=46.28 memory used=7988.9MB, alloc=564.3MB, time=47.52 memory used=8406.5MB, alloc=564.3MB, time=49.00 memory used=8837.3MB, alloc=564.3MB, time=50.49 memory used=9281.0MB, alloc=564.3MB, time=52.11 memory used=9619.9MB, alloc=564.3MB, time=53.35 memory used=9848.6MB, alloc=564.3MB, time=54.25 memory used=10079.2MB, alloc=564.3MB, time=55.20 memory used=10312.0MB, alloc=564.3MB, time=56.14 memory used=10547.6MB, alloc=564.3MB, time=57.07 memory used=10786.0MB, alloc=564.3MB, time=58.04 memory used=11027.1MB, alloc=564.3MB, time=59.02 memory used=11271.2MB, alloc=564.3MB, time=60.01 memory used=11518.3MB, alloc=564.3MB, time=61.03 memory used=11768.4MB, alloc=564.3MB, time=62.04 memory used=12021.8MB, alloc=564.3MB, time=63.05 memory used=12278.2MB, alloc=564.3MB, time=64.10 memory used=12537.8MB, alloc=564.3MB, time=65.12 memory used=12800.5MB, alloc=564.3MB, time=66.10 memory used=13066.3MB, alloc=564.3MB, time=66.96 memory used=13335.2MB, alloc=564.3MB, time=67.89 memory used=13607.1MB, alloc=564.3MB, time=68.76 memory used=13882.2MB, alloc=564.3MB, time=69.69 memory used=14156.6MB, alloc=564.3MB, time=70.65 memory used=14433.7MB, alloc=564.3MB, time=71.71 memory used=14713.7MB, alloc=564.3MB, time=72.85 memory used=14996.5MB, alloc=564.3MB, time=73.94 memory used=15282.6MB, alloc=564.3MB, time=75.04 memory used=15571.2MB, alloc=564.3MB, time=76.21 memory used=15857.9MB, alloc=564.3MB, time=77.32 memory used=16147.5MB, alloc=564.3MB, time=78.47 memory used=16440.1MB, alloc=564.3MB, time=79.64 memory used=16735.6MB, alloc=564.3MB, time=80.78 memory used=17034.0MB, alloc=564.3MB, time=82.01 memory used=17335.2MB, alloc=564.3MB, time=83.19 memory used=17639.5MB, alloc=564.3MB, time=84.38 memory used=17946.8MB, alloc=564.3MB, time=85.62 memory used=18256.9MB, alloc=564.3MB, time=86.80 memory used=18569.9MB, alloc=564.3MB, time=88.04 memory used=18885.8MB, alloc=564.3MB, time=89.29 memory used=19196.3MB, alloc=564.3MB, time=90.56 memory used=19467.1MB, alloc=564.3MB, time=91.68 memory used=19739.2MB, alloc=564.3MB, time=92.81 memory used=20012.6MB, alloc=564.3MB, time=93.94 memory used=20287.4MB, alloc=564.3MB, time=95.03 memory used=20563.6MB, alloc=564.3MB, time=96.15 memory used=20841.6MB, alloc=564.3MB, time=97.28 memory used=21121.6MB, alloc=564.3MB, time=98.47 memory used=21403.6MB, alloc=564.3MB, time=99.65 memory used=21687.6MB, alloc=564.3MB, time=100.85 memory used=21973.4MB, alloc=564.3MB, time=102.05 memory used=22261.3MB, alloc=564.3MB, time=103.22 memory used=22551.1MB, alloc=564.3MB, time=104.45 memory used=22843.0MB, alloc=564.3MB, time=105.66 memory used=23136.7MB, alloc=564.3MB, time=106.92 memory used=23429.6MB, alloc=564.3MB, time=108.19 memory used=23723.4MB, alloc=564.3MB, time=109.43 memory used=24019.2MB, alloc=564.3MB, time=110.73 memory used=24316.8MB, alloc=564.3MB, time=112.00 memory used=24616.7MB, alloc=564.3MB, time=113.26 memory used=24918.4MB, alloc=564.3MB, time=114.49 memory used=25222.1MB, alloc=564.3MB, time=115.80 memory used=25526.4MB, alloc=564.3MB, time=117.09 memory used=25830.4MB, alloc=564.3MB, time=118.40 memory used=26136.2MB, alloc=564.3MB, time=119.67 memory used=26444.0MB, alloc=564.3MB, time=120.88 memory used=26753.7MB, alloc=564.3MB, time=122.22 memory used=27065.4MB, alloc=564.3MB, time=123.59 memory used=27378.9MB, alloc=564.3MB, time=124.93 memory used=27694.6MB, alloc=564.3MB, time=126.26 memory used=28012.0MB, alloc=564.3MB, time=127.60 memory used=28331.5MB, alloc=564.3MB, time=128.98 memory used=28652.6MB, alloc=564.3MB, time=130.35 memory used=28975.9MB, alloc=564.3MB, time=131.75 memory used=29301.0MB, alloc=564.3MB, time=133.15 memory used=29628.2MB, alloc=564.3MB, time=134.58 memory used=29957.1MB, alloc=564.3MB, time=136.02 memory used=30288.1MB, alloc=564.3MB, time=137.44 memory used=30620.8MB, alloc=564.3MB, time=138.89 memory used=30955.6MB, alloc=564.3MB, time=140.34 memory used=31292.2MB, alloc=564.3MB, time=141.83 memory used=31630.5MB, alloc=564.3MB, time=143.27 memory used=31971.0MB, alloc=564.3MB, time=144.68 memory used=32313.3MB, alloc=564.3MB, time=146.18 memory used=32616.1MB, alloc=564.3MB, time=147.50 memory used=32876.8MB, alloc=564.3MB, time=148.66 memory used=33137.9MB, alloc=564.3MB, time=149.83 memory used=33399.7MB, alloc=564.3MB, time=151.00 memory used=33662.0MB, alloc=564.3MB, time=152.16 memory used=33924.7MB, alloc=564.3MB, time=153.37 memory used=34188.6MB, alloc=564.3MB, time=154.55 memory used=34453.2MB, alloc=564.3MB, time=155.72 memory used=34718.7MB, alloc=564.3MB, time=156.88 memory used=34984.9MB, alloc=564.3MB, time=158.08 memory used=35252.0MB, alloc=564.3MB, time=159.28 memory used=35520.2MB, alloc=564.3MB, time=160.48 memory used=35789.1MB, alloc=564.3MB, time=161.70 memory used=36059.0MB, alloc=564.3MB, time=162.87 memory used=36329.8MB, alloc=564.3MB, time=164.10 memory used=36601.6MB, alloc=564.3MB, time=165.37 memory used=36874.8MB, alloc=564.3MB, time=166.59 memory used=37149.1MB, alloc=564.3MB, time=167.80 memory used=37424.2MB, alloc=564.3MB, time=169.08 memory used=37700.4MB, alloc=564.3MB, time=170.37 memory used=37977.4MB, alloc=564.3MB, time=171.64 memory used=38255.6MB, alloc=564.3MB, time=172.92 memory used=38534.9MB, alloc=564.3MB, time=174.13 memory used=38815.5MB, alloc=564.3MB, time=175.38 memory used=39096.6MB, alloc=564.3MB, time=176.61 memory used=39379.0MB, alloc=564.3MB, time=177.89 memory used=39662.7MB, alloc=564.3MB, time=179.20 memory used=39947.4MB, alloc=564.3MB, time=180.44 memory used=40232.8MB, alloc=564.3MB, time=181.69 memory used=40519.4MB, alloc=564.3MB, time=182.97 memory used=40806.0MB, alloc=564.3MB, time=184.27 memory used=41092.0MB, alloc=564.3MB, time=185.53 memory used=41378.8MB, alloc=564.3MB, time=186.78 memory used=41666.9MB, alloc=564.3MB, time=188.04 memory used=41956.2MB, alloc=564.3MB, time=189.27 memory used=42246.4MB, alloc=564.3MB, time=190.54 memory used=42537.7MB, alloc=564.3MB, time=191.85 memory used=42830.1MB, alloc=564.3MB, time=193.21 memory used=43123.2MB, alloc=564.3MB, time=194.58 memory used=43417.4MB, alloc=564.3MB, time=195.95 memory used=43710.9MB, alloc=564.3MB, time=197.29 memory used=44004.2MB, alloc=564.3MB, time=198.65 memory used=44298.1MB, alloc=564.3MB, time=199.99 memory used=44593.3MB, alloc=564.3MB, time=201.29 memory used=44889.9MB, alloc=564.3MB, time=202.62 memory used=45187.0MB, alloc=564.3MB, time=203.97 memory used=45485.2MB, alloc=564.3MB, time=205.32 memory used=45784.5MB, alloc=564.3MB, time=206.67 memory used=46084.8MB, alloc=564.3MB, time=208.06 memory used=46386.1MB, alloc=564.3MB, time=209.43 memory used=46688.6MB, alloc=564.3MB, time=210.80 memory used=46992.0MB, alloc=564.3MB, time=212.18 memory used=47296.5MB, alloc=564.3MB, time=213.56 memory used=47602.0MB, alloc=564.3MB, time=214.96 memory used=47908.4MB, alloc=564.3MB, time=216.37 memory used=48216.1MB, alloc=564.3MB, time=217.73 memory used=48524.3MB, alloc=564.3MB, time=219.12 memory used=48834.1MB, alloc=564.3MB, time=220.53 memory used=49145.0MB, alloc=564.3MB, time=222.00 memory used=49456.6MB, alloc=564.3MB, time=223.51 memory used=49759.0MB, alloc=564.3MB, time=224.96 memory used=50040.8MB, alloc=564.3MB, time=226.28 memory used=50323.1MB, alloc=564.3MB, time=227.61 memory used=50606.2MB, alloc=564.3MB, time=228.96 memory used=50889.5MB, alloc=564.3MB, time=230.31 memory used=51174.0MB, alloc=564.3MB, time=231.63 memory used=51458.5MB, alloc=564.3MB, time=232.93 memory used=51744.0MB, alloc=564.3MB, time=234.22 memory used=52030.3MB, alloc=564.3MB, time=235.54 memory used=52316.9MB, alloc=564.3MB, time=236.80 memory used=52604.3MB, alloc=564.3MB, time=238.15 memory used=52892.6MB, alloc=564.3MB, time=239.50 memory used=53181.7MB, alloc=564.3MB, time=240.88 memory used=53471.8MB, alloc=564.3MB, time=242.26 memory used=53762.5MB, alloc=564.3MB, time=243.65 memory used=54053.9MB, alloc=564.3MB, time=245.01 memory used=54345.8MB, alloc=564.3MB, time=246.34 memory used=54638.8MB, alloc=564.3MB, time=247.71 memory used=54932.5MB, alloc=564.3MB, time=249.10 memory used=55226.8MB, alloc=564.3MB, time=250.49 memory used=55522.5MB, alloc=564.3MB, time=251.89 memory used=55818.5MB, alloc=564.3MB, time=253.31 memory used=56115.2MB, alloc=564.3MB, time=254.74 memory used=56411.6MB, alloc=564.3MB, time=256.13 memory used=56708.1MB, alloc=564.3MB, time=257.53 memory used=57005.6MB, alloc=564.3MB, time=258.94 memory used=57303.8MB, alloc=564.3MB, time=260.40 memory used=57603.0MB, alloc=564.3MB, time=261.85 memory used=57902.9MB, alloc=564.3MB, time=263.29 memory used=58203.3MB, alloc=564.3MB, time=264.71 memory used=58504.8MB, alloc=564.3MB, time=266.13 memory used=58807.3MB, alloc=564.3MB, time=267.58 memory used=59110.2MB, alloc=564.3MB, time=269.02 memory used=59413.9MB, alloc=564.3MB, time=270.48 memory used=59718.4MB, alloc=564.3MB, time=271.89 memory used=60022.0MB, alloc=564.3MB, time=273.36 memory used=60326.6MB, alloc=564.3MB, time=274.80 memory used=60631.5MB, alloc=564.3MB, time=276.21 memory used=60937.4MB, alloc=564.3MB, time=277.70 memory used=61244.3MB, alloc=564.3MB, time=279.20 memory used=61551.7MB, alloc=564.3MB, time=280.65 memory used=61860.1MB, alloc=564.3MB, time=282.14 memory used=62169.2MB, alloc=564.3MB, time=283.64 memory used=62479.3MB, alloc=564.3MB, time=285.11 memory used=62790.1MB, alloc=564.3MB, time=286.60 memory used=63101.7MB, alloc=564.3MB, time=288.07 memory used=63414.3MB, alloc=564.3MB, time=289.58 memory used=63727.2MB, alloc=564.3MB, time=291.03 memory used=64041.2MB, alloc=564.3MB, time=292.51 memory used=64356.0MB, alloc=564.3MB, time=293.99 memory used=64671.7MB, alloc=564.3MB, time=295.50 memory used=64988.2MB, alloc=564.3MB, time=297.00 memory used=65305.0MB, alloc=564.3MB, time=298.55 memory used=65622.9MB, alloc=564.3MB, time=300.12 memory used=65941.6MB, alloc=564.3MB, time=301.67 memory used=66261.3MB, alloc=564.3MB, time=303.23 |\^/| 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(); 1428538697 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 2 2 3 F := [7 x - 13 x y - 3 y, 6 x z - 2 x z + 9 y ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 2 2 2 G := [-5 x y z + 14 x - 13 z, 4 x y + 6 x + 9 z ] > Problem := [F,G]; 3 2 2 3 Problem := [[7 x - 13 x y - 3 y, 6 x z - 2 x z + 9 y ], 2 2 2 2 [-5 x y z + 14 x - 13 z, 4 x y + 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=4.2MB, alloc=32.3MB, time=0.17 memory used=25.5MB, alloc=32.3MB, time=0.49 memory used=44.9MB, alloc=56.3MB, time=0.77 memory used=87.2MB, alloc=60.3MB, time=1.33 memory used=131.3MB, alloc=68.3MB, time=1.91 memory used=174.0MB, alloc=68.3MB, time=2.38 memory used=219.2MB, alloc=92.3MB, time=2.93 memory used=287.3MB, alloc=92.3MB, time=3.81 memory used=353.3MB, alloc=92.3MB, time=4.59 memory used=405.0MB, alloc=116.3MB, time=5.12 memory used=461.1MB, alloc=116.3MB, time=5.47 memory used=532.6MB, alloc=116.3MB, time=6.09 memory used=583.5MB, alloc=116.3MB, time=6.37 memory used=673.0MB, alloc=116.3MB, time=7.05 memory used=756.7MB, alloc=116.3MB, time=8.12 memory used=805.7MB, alloc=116.3MB, time=8.36 memory used=880.5MB, alloc=116.3MB, time=9.10 memory used=935.9MB, alloc=372.3MB, time=9.84 memory used=1021.7MB, alloc=372.3MB, time=10.76 memory used=1082.1MB, alloc=372.3MB, time=11.23 memory used=1148.7MB, alloc=396.3MB, time=11.86 memory used=1228.9MB, alloc=396.3MB, time=12.37 memory used=1347.4MB, alloc=396.3MB, time=13.77 memory used=1435.9MB, alloc=396.3MB, time=14.22 memory used=1518.5MB, alloc=396.3MB, time=14.57 memory used=1593.6MB, alloc=396.3MB, time=14.88 memory used=1680.1MB, alloc=396.3MB, time=15.34 memory used=1785.8MB, alloc=396.3MB, time=16.60 memory used=1869.2MB, alloc=396.3MB, time=16.98 memory used=1945.7MB, alloc=396.3MB, time=17.31 memory used=2020.7MB, alloc=396.3MB, time=17.59 memory used=2137.5MB, alloc=396.3MB, time=19.07 memory used=2249.4MB, alloc=420.3MB, time=20.34 memory used=2391.1MB, alloc=420.3MB, time=22.71 memory used=2531.7MB, alloc=444.3MB, time=23.99 memory used=2703.2MB, alloc=444.3MB, time=26.09 memory used=2870.8MB, alloc=444.3MB, time=28.46 memory used=3016.6MB, alloc=468.3MB, time=30.88 memory used=3178.8MB, alloc=492.3MB, time=33.61 memory used=3342.9MB, alloc=516.3MB, time=36.55 memory used=3534.0MB, alloc=540.3MB, time=39.67 memory used=3743.3MB, alloc=564.3MB, time=43.06 memory used=3940.3MB, alloc=588.3MB, time=48.80 memory used=4131.3MB, alloc=612.3MB, time=55.42 memory used=4334.3MB, alloc=636.3MB, time=62.85 memory used=4548.1MB, alloc=660.3MB, time=71.32 memory used=4779.5MB, alloc=684.3MB, time=80.78 memory used=5034.8MB, alloc=708.3MB, time=91.18 memory used=5314.1MB, alloc=732.3MB, time=102.53 memory used=5617.3MB, alloc=732.3MB, time=114.85 memory used=5920.5MB, alloc=732.3MB, time=127.13 memory used=6223.7MB, alloc=756.3MB, time=139.07 memory used=6550.7MB, alloc=756.3MB, time=150.15 memory used=6877.9MB, alloc=780.3MB, time=161.25 memory used=7228.8MB, alloc=804.3MB, time=172.80 N1 := 10633 > GB := Basis(F, plex(op(vars))); 3 2 2 3 8 GB := [-7 x + 13 x y + 3 y, -6 x z + 2 x z - 9 y , -2674423479 x 7 6 5 4 + 1851523947 x - 712124595 x + 230071023 x - 53093313 x 3 4 3 3 - 2635437714 x z + 31813498119 y + 12252303 x - 912266901 y 2 2 + 1631461442 y z - 52319358 y + 1129473306 y z - 5250987 y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=7548.1MB, alloc=804.3MB, time=181.35 memory used=7648.1MB, alloc=804.3MB, time=183.25 memory used=7750.7MB, alloc=804.3MB, time=185.18 memory used=7886.9MB, alloc=804.3MB, time=186.98 memory used=8064.4MB, alloc=804.3MB, time=188.81 memory used=8181.3MB, alloc=804.3MB, time=190.42 memory used=8321.1MB, alloc=804.3MB, time=192.14 memory used=8414.3MB, alloc=804.3MB, time=193.73 memory used=8535.8MB, alloc=804.3MB, time=195.24 memory used=8694.1MB, alloc=804.3MB, time=196.81 memory used=8789.4MB, alloc=804.3MB, time=198.50 memory used=8901.3MB, alloc=804.3MB, time=200.44 memory used=9078.5MB, alloc=804.3MB, time=202.34 memory used=9335.5MB, alloc=804.3MB, time=206.59 memory used=9580.6MB, alloc=804.3MB, time=207.60 memory used=9901.7MB, alloc=804.3MB, time=248.52 memory used=10087.7MB, alloc=804.3MB, time=249.33 memory used=10248.5MB, alloc=804.3MB, time=250.12 memory used=10406.8MB, alloc=804.3MB, time=250.88 memory used=10570.0MB, alloc=804.3MB, time=251.65 |\^/| 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(); 1428538997 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 2 F := [16 x y z + 18 x z + 13 y , -7 x z - 3 y - 7 z] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 3 2 G := [14 x y - 2 y - 17 z , -y z + 10 x z + 4 x] > Problem := [F,G]; 2 3 2 2 Problem := [[16 x y z + 18 x z + 13 y , -7 x z - 3 y - 7 z], 2 3 3 2 [14 x y - 2 y - 17 z , -y z + 10 x z + 4 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=26.3MB, alloc=32.3MB, time=0.52 memory used=44.9MB, alloc=56.3MB, time=0.78 memory used=86.9MB, alloc=60.3MB, time=1.36 memory used=129.1MB, alloc=68.3MB, time=1.94 memory used=171.5MB, alloc=68.3MB, time=2.45 memory used=216.3MB, alloc=92.3MB, time=3.08 memory used=284.6MB, alloc=92.3MB, time=3.91 memory used=331.5MB, alloc=92.3MB, time=4.23 memory used=373.1MB, alloc=92.3MB, time=4.46 memory used=423.7MB, alloc=92.3MB, time=4.84 memory used=461.5MB, alloc=92.3MB, time=5.03 memory used=495.5MB, alloc=92.3MB, time=5.18 memory used=539.2MB, alloc=92.3MB, time=12.78 memory used=576.9MB, alloc=92.3MB, time=14.23 memory used=607.0MB, alloc=92.3MB, time=14.33 memory used=641.0MB, alloc=92.3MB, time=14.43 memory used=669.8MB, alloc=92.3MB, time=14.52 memory used=696.6MB, alloc=92.3MB, time=14.60 memory used=772.2MB, alloc=92.3MB, time=15.58 memory used=852.0MB, alloc=92.3MB, time=16.23 memory used=923.8MB, alloc=92.3MB, time=16.94 memory used=995.2MB, alloc=92.3MB, time=18.12 memory used=1057.5MB, alloc=92.3MB, time=19.32 memory used=1104.6MB, alloc=92.3MB, time=19.67 memory used=1146.8MB, alloc=92.3MB, time=24.05 memory used=1185.0MB, alloc=92.3MB, time=28.38 memory used=1215.6MB, alloc=92.3MB, time=28.47 memory used=1242.2MB, alloc=92.3MB, time=28.56 memory used=1275.2MB, alloc=92.3MB, time=28.64 memory used=1299.0MB, alloc=92.3MB, time=28.70 memory used=1334.8MB, alloc=92.3MB, time=28.90 memory used=1372.8MB, alloc=96.0MB, time=29.06 memory used=1404.4MB, alloc=96.0MB, time=29.15 memory used=1440.8MB, alloc=96.0MB, time=29.24 memory used=1471.4MB, alloc=96.0MB, time=29.33 memory used=1525.8MB, alloc=96.0MB, time=29.78 memory used=1603.8MB, alloc=96.0MB, time=30.60 memory used=1671.8MB, alloc=120.0MB, time=31.37 memory used=1744.5MB, alloc=376.0MB, time=32.15 memory used=1835.2MB, alloc=376.0MB, time=34.58 memory used=1908.4MB, alloc=376.0MB, time=35.03 memory used=1980.5MB, alloc=376.0MB, time=37.16 memory used=2021.1MB, alloc=376.0MB, time=37.31 memory used=2087.6MB, alloc=376.0MB, time=37.85 memory used=2184.1MB, alloc=376.0MB, time=38.79 memory used=2267.6MB, alloc=376.0MB, time=39.91 memory used=2348.2MB, alloc=400.0MB, time=40.85 memory used=2458.1MB, alloc=400.0MB, time=42.16 memory used=2562.8MB, alloc=424.0MB, time=43.51 memory used=2700.1MB, alloc=448.0MB, time=45.19 memory used=2841.6MB, alloc=448.0MB, time=46.66 memory used=2952.1MB, alloc=448.0MB, time=48.03 memory used=3095.8MB, alloc=472.0MB, time=49.33 memory used=3218.5MB, alloc=472.0MB, time=50.35 memory used=3300.1MB, alloc=472.0MB, time=50.63 memory used=3401.6MB, alloc=472.0MB, time=51.00 memory used=3526.9MB, alloc=472.0MB, time=63.44 memory used=3631.0MB, alloc=472.0MB, time=71.46 memory used=3706.6MB, alloc=472.0MB, time=71.74 memory used=3783.9MB, alloc=472.0MB, time=72.02 memory used=3847.1MB, alloc=472.0MB, time=72.26 memory used=3922.2MB, alloc=472.0MB, time=72.50 memory used=4011.2MB, alloc=472.0MB, time=72.73 memory used=4184.7MB, alloc=472.0MB, time=73.29 memory used=4265.6MB, alloc=472.0MB, time=73.55 memory used=4360.2MB, alloc=472.0MB, time=73.97 memory used=4438.9MB, alloc=472.0MB, time=74.25 memory used=4528.5MB, alloc=472.0MB, time=75.17 memory used=4661.5MB, alloc=472.0MB, time=95.53 memory used=4738.3MB, alloc=472.0MB, time=95.82 memory used=4827.1MB, alloc=472.0MB, time=96.09 memory used=4886.6MB, alloc=472.0MB, time=96.31 memory used=4956.1MB, alloc=472.0MB, time=96.54 memory used=5038.8MB, alloc=472.0MB, time=96.77 memory used=5221.1MB, alloc=472.0MB, time=97.28 memory used=5310.3MB, alloc=472.0MB, time=97.63 memory used=5382.9MB, alloc=472.0MB, time=97.92 memory used=5467.5MB, alloc=472.0MB, time=98.19 memory used=5531.9MB, alloc=472.0MB, time=98.40 memory used=5631.6MB, alloc=472.0MB, time=98.83 memory used=5718.1MB, alloc=472.0MB, time=99.14 memory used=5788.3MB, alloc=472.0MB, time=99.44 memory used=5873.9MB, alloc=472.0MB, time=99.73 memory used=5936.3MB, alloc=472.0MB, time=99.94 memory used=6037.1MB, alloc=472.0MB, time=105.88 memory used=6145.4MB, alloc=472.0MB, time=142.70 memory used=6246.6MB, alloc=472.0MB, time=155.52 memory used=6318.6MB, alloc=472.0MB, time=155.80 memory used=6402.6MB, alloc=472.0MB, time=156.07 memory used=6475.4MB, alloc=472.0MB, time=156.31 memory used=6534.7MB, alloc=472.0MB, time=156.53 memory used=6599.8MB, alloc=472.0MB, time=156.75 memory used=6672.5MB, alloc=472.0MB, time=156.98 memory used=6753.9MB, alloc=472.0MB, time=157.23 memory used=6844.8MB, alloc=472.0MB, time=157.47 memory used=7052.1MB, alloc=472.0MB, time=157.95 memory used=7219.5MB, alloc=472.0MB, time=158.31 memory used=7329.6MB, alloc=472.0MB, time=158.97 memory used=7429.7MB, alloc=472.0MB, time=159.29 memory used=7522.2MB, alloc=472.0MB, time=159.57 memory used=7655.6MB, alloc=472.0MB, time=161.96 memory used=7736.0MB, alloc=472.0MB, time=162.24 memory used=7884.4MB, alloc=472.0MB, time=166.96 memory used=7962.3MB, alloc=472.0MB, time=167.24 memory used=8036.2MB, alloc=472.0MB, time=167.49 memory used=8106.3MB, alloc=472.0MB, time=167.71 memory used=8241.4MB, alloc=496.0MB, time=169.15 memory used=8399.4MB, alloc=496.0MB, time=170.61 memory used=8513.6MB, alloc=496.0MB, time=171.35 memory used=8625.0MB, alloc=496.0MB, time=172.03 memory used=8727.1MB, alloc=496.0MB, time=172.54 memory used=8828.0MB, alloc=496.0MB, time=173.03 memory used=8944.3MB, alloc=496.0MB, time=189.12 memory used=9037.1MB, alloc=496.0MB, time=189.46 memory used=9108.5MB, alloc=496.0MB, time=189.73 memory used=9220.4MB, alloc=496.0MB, time=190.28 memory used=9397.9MB, alloc=496.0MB, time=190.87 memory used=9602.0MB, alloc=496.0MB, time=191.67 memory used=9688.5MB, alloc=496.0MB, time=192.02 memory used=9787.2MB, alloc=496.0MB, time=192.52 memory used=9893.4MB, alloc=496.0MB, time=193.16 memory used=9971.3MB, alloc=496.0MB, time=193.48 memory used=10083.2MB, alloc=496.0MB, time=208.34 memory used=10177.8MB, alloc=496.0MB, time=210.90 memory used=10261.8MB, alloc=496.0MB, time=211.19 memory used=10342.8MB, alloc=496.0MB, time=211.45 memory used=10447.2MB, alloc=496.0MB, time=212.17 memory used=10638.2MB, alloc=496.0MB, time=212.75 memory used=10794.9MB, alloc=496.0MB, time=217.38 memory used=10887.5MB, alloc=496.0MB, time=217.90 memory used=10980.5MB, alloc=496.0MB, time=218.45 memory used=11095.8MB, alloc=496.0MB, time=218.90 memory used=11195.0MB, alloc=496.0MB, time=219.77 memory used=11285.4MB, alloc=496.0MB, time=220.12 memory used=11359.7MB, alloc=496.0MB, time=220.43 memory used=11454.0MB, alloc=496.0MB, time=220.76 memory used=11536.2MB, alloc=496.0MB, time=221.05 memory used=11619.7MB, alloc=496.0MB, time=221.53 memory used=11726.6MB, alloc=496.0MB, time=222.37 memory used=11821.5MB, alloc=496.0MB, time=222.78 memory used=11893.0MB, alloc=496.0MB, time=223.12 memory used=11978.4MB, alloc=496.0MB, time=223.47 memory used=12076.4MB, alloc=496.0MB, time=223.81 memory used=12142.1MB, alloc=496.0MB, time=224.07 memory used=12242.8MB, alloc=496.0MB, time=224.63 memory used=12376.5MB, alloc=520.0MB, time=281.29 memory used=12477.9MB, alloc=520.0MB, time=287.77 memory used=12587.4MB, alloc=520.0MB, time=288.18 memory used=12667.5MB, alloc=520.0MB, time=288.49 memory used=12767.2MB, alloc=520.0MB, time=288.82 memory used=12937.6MB, alloc=520.0MB, time=289.33 memory used=13089.8MB, alloc=520.0MB, time=289.95 memory used=13293.6MB, alloc=520.0MB, time=291.23 memory used=13412.6MB, alloc=520.0MB, time=294.54 memory used=13507.4MB, alloc=520.0MB, time=294.85 memory used=13621.2MB, alloc=520.0MB, time=295.42 memory used=13837.5MB, alloc=520.0MB, time=296.10 memory used=14052.3MB, alloc=520.0MB, time=297.98 memory used=14164.5MB, alloc=520.0MB, time=298.47 memory used=14258.1MB, alloc=520.0MB, time=298.88 memory used=14341.4MB, alloc=520.0MB, time=299.30 memory used=14437.4MB, alloc=520.0MB, time=299.69 memory used=14548.3MB, alloc=520.0MB, time=300.12 memory used=14675.7MB, alloc=520.0MB, time=300.57 memory used=14753.5MB, alloc=520.0MB, time=300.86 memory used=14827.8MB, alloc=520.0MB, time=301.16 memory used=14908.3MB, alloc=520.0MB, time=301.48 memory used=14997.0MB, alloc=520.0MB, time=301.77 memory used=15098.9MB, alloc=520.0MB, time=302.08 memory used=15214.9MB, alloc=520.0MB, time=303.97 memory used=15334.5MB, alloc=520.0MB, time=304.39 memory used=15411.9MB, alloc=520.0MB, time=304.78 memory used=15499.6MB, alloc=520.0MB, time=305.15 memory used=15600.6MB, alloc=520.0MB, time=305.52 memory used=15716.4MB, alloc=520.0MB, time=305.92 memory used=15832.5MB, alloc=520.0MB, time=306.30 memory used=15903.5MB, alloc=520.0MB, time=306.60 memory used=15980.4MB, alloc=520.0MB, time=306.88 memory used=16065.0MB, alloc=520.0MB, time=307.18 memory used=16158.2MB, alloc=520.0MB, time=307.50 memory used=16278.8MB, alloc=520.0MB, time=311.29 memory used=16384.2MB, alloc=544.0MB, time=384.93 |\^/| 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(); 1428539297 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 2 3 2 2 2 F := [-8 x z - 2 z + 6 x, -5 x z + 8 y z + 7 y ] > G := [ randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=3, coeffs=rand(-10 .. 10)) > ]; 3 3 3 G := [14 x y z + 14 z - 10 y z, -6 x + z + 9 y] > Problem := [F,G]; 2 3 2 2 2 Problem := [[-8 x z - 2 z + 6 x, -5 x z + 8 y z + 7 y ], 3 3 3 [14 x y z + 14 z - 10 y z, -6 x + z + 9 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=25.5MB, alloc=32.3MB, time=0.50 memory used=44.9MB, alloc=60.3MB, time=0.78 memory used=85.9MB, alloc=60.3MB, time=1.32 memory used=126.6MB, alloc=60.3MB, time=1.65 memory used=167.0MB, alloc=60.3MB, time=2.00 memory used=208.3MB, alloc=60.3MB, time=2.36 memory used=236.2MB, alloc=60.3MB, time=2.52 memory used=271.6MB, alloc=60.3MB, time=2.80 memory used=307.6MB, alloc=60.3MB, time=3.12 memory used=353.7MB, alloc=68.3MB, time=3.69 memory used=378.5MB, alloc=68.3MB, time=3.85 memory used=419.6MB, alloc=68.3MB, time=4.45 memory used=459.8MB, alloc=92.3MB, time=4.99 memory used=524.4MB, alloc=92.3MB, time=5.55 memory used=557.9MB, alloc=92.3MB, time=5.65 memory used=612.7MB, alloc=92.3MB, time=6.10 memory used=657.0MB, alloc=92.3MB, time=6.28 memory used=706.2MB, alloc=92.3MB, time=6.79 memory used=751.9MB, alloc=92.3MB, time=6.98 memory used=790.0MB, alloc=92.3MB, time=7.10 memory used=821.6MB, alloc=92.3MB, time=7.21 memory used=851.4MB, alloc=92.3MB, time=7.31 memory used=886.3MB, alloc=92.3MB, time=7.42 memory used=952.7MB, alloc=92.3MB, time=8.03 memory used=987.8MB, alloc=92.3MB, time=8.16 memory used=1029.1MB, alloc=92.3MB, time=8.28 memory used=1056.1MB, alloc=92.3MB, time=8.37 memory used=1087.4MB, alloc=92.3MB, time=8.47 memory used=1124.5MB, alloc=92.3MB, time=8.58 memory used=1181.2MB, alloc=92.3MB, time=8.94 memory used=1214.6MB, alloc=92.3MB, time=9.05 memory used=1246.9MB, alloc=92.3MB, time=9.15 memory used=1307.9MB, alloc=92.3MB, time=9.71 memory used=1341.2MB, alloc=92.3MB, time=9.83 memory used=1374.6MB, alloc=92.3MB, time=9.94 memory used=1403.1MB, alloc=92.3MB, time=10.03 memory used=1437.1MB, alloc=92.3MB, time=10.14 memory used=1476.7MB, alloc=92.3MB, time=10.24 memory used=1506.1MB, alloc=92.3MB, time=10.32 memory used=1531.0MB, alloc=92.3MB, time=10.40 memory used=1559.6MB, alloc=92.3MB, time=10.48 memory used=1624.0MB, alloc=92.3MB, time=11.12 memory used=1658.8MB, alloc=92.3MB, time=11.24 memory used=1691.0MB, alloc=92.3MB, time=11.35 memory used=1720.7MB, alloc=92.3MB, time=11.45 memory used=1756.0MB, alloc=92.3MB, time=11.55 memory used=1797.5MB, alloc=92.3MB, time=11.67 memory used=1824.9MB, alloc=92.3MB, time=11.76 memory used=1850.5MB, alloc=92.3MB, time=11.84 memory used=1879.9MB, alloc=92.3MB, time=11.92 memory used=1934.2MB, alloc=92.3MB, time=12.26 memory used=1973.1MB, alloc=92.3MB, time=13.39 memory used=2193.0MB, alloc=92.6MB, time=23.84 memory used=2306.8MB, alloc=92.6MB, time=26.51 memory used=2471.7MB, alloc=372.6MB, time=30.48 memory used=2506.6MB, alloc=373.8MB, time=31.33 memory used=2507.8MB, alloc=375.0MB, time=31.39 memory used=2509.0MB, alloc=376.2MB, time=31.45 memory used=2510.2MB, alloc=377.3MB, time=31.52 memory used=2511.3MB, alloc=373.8MB, time=31.59 memory used=2577.4MB, alloc=372.6MB, time=31.88 memory used=2632.4MB, alloc=372.6MB, time=32.19 memory used=2717.7MB, alloc=372.6MB, time=33.26 memory used=2801.2MB, alloc=372.6MB, time=34.35 memory used=2883.2MB, alloc=372.6MB, time=35.57 memory used=2960.7MB, alloc=396.6MB, time=36.33 memory used=3038.9MB, alloc=396.6MB, time=36.87 memory used=3089.2MB, alloc=396.6MB, time=37.03 memory used=3148.3MB, alloc=420.6MB, time=44.28 memory used=3217.7MB, alloc=420.6MB, time=44.52 memory used=3281.9MB, alloc=420.6MB, time=44.75 memory used=3352.3MB, alloc=420.6MB, time=44.97 memory used=3427.2MB, alloc=420.6MB, time=45.20 memory used=3506.6MB, alloc=420.6MB, time=45.45 memory used=3564.6MB, alloc=444.6MB, time=45.68 memory used=3620.1MB, alloc=444.6MB, time=45.91 memory used=3678.5MB, alloc=444.6MB, time=46.15 memory used=3740.0MB, alloc=444.6MB, time=46.37 memory used=3803.2MB, alloc=444.6MB, time=46.60 memory used=3867.9MB, alloc=444.6MB, time=46.85 memory used=3934.0MB, alloc=444.6MB, time=47.06 memory used=4001.6MB, alloc=444.6MB, time=47.28 memory used=4070.7MB, alloc=444.6MB, time=47.51 memory used=4147.3MB, alloc=444.6MB, time=47.77 memory used=4225.3MB, alloc=444.6MB, time=48.01 memory used=4304.6MB, alloc=444.6MB, time=48.25 memory used=4385.3MB, alloc=444.6MB, time=48.51 memory used=4473.8MB, alloc=444.6MB, time=48.76 memory used=4563.6MB, alloc=444.6MB, time=48.99 memory used=4654.4MB, alloc=444.6MB, time=49.23 memory used=4746.5MB, alloc=444.6MB, time=49.49 memory used=4846.3MB, alloc=444.6MB, time=49.74 memory used=4947.0MB, alloc=444.6MB, time=50.00 memory used=5007.7MB, alloc=444.6MB, time=50.17 memory used=5057.3MB, alloc=444.6MB, time=50.35 memory used=5105.2MB, alloc=444.6MB, time=50.51 memory used=5155.6MB, alloc=444.6MB, time=50.68 memory used=5206.1MB, alloc=444.6MB, time=50.83 memory used=5256.7MB, alloc=444.6MB, time=50.97 memory used=5307.3MB, alloc=444.6MB, time=51.12 memory used=5357.9MB, alloc=444.6MB, time=51.29 memory used=5408.8MB, alloc=444.6MB, time=51.46 memory used=5466.7MB, alloc=444.6MB, time=51.61 memory used=5524.6MB, alloc=444.6MB, time=51.79 memory used=5582.5MB, alloc=444.6MB, time=51.95 memory used=5640.2MB, alloc=444.6MB, time=52.13 memory used=5697.9MB, alloc=444.6MB, time=52.29 memory used=5755.4MB, alloc=444.6MB, time=52.46 memory used=5813.0MB, alloc=444.6MB, time=52.64 memory used=5877.3MB, alloc=444.6MB, time=52.81 memory used=5941.4MB, alloc=444.6MB, time=52.99 memory used=6005.2MB, alloc=444.6MB, time=53.16 memory used=6068.6MB, alloc=444.6MB, time=53.34 memory used=6132.1MB, alloc=444.6MB, time=53.52 memory used=6201.4MB, alloc=444.6MB, time=53.70 memory used=6270.4MB, alloc=444.6MB, time=53.88 memory used=6338.9MB, alloc=444.6MB, time=54.06 memory used=6413.3MB, alloc=444.6MB, time=54.24 memory used=6486.9MB, alloc=444.6MB, time=54.43 memory used=6559.7MB, alloc=444.6MB, time=54.62 memory used=6637.7MB, alloc=444.6MB, time=54.80 memory used=6714.6MB, alloc=444.6MB, time=54.99 memory used=6796.3MB, alloc=444.6MB, time=55.19 memory used=6876.3MB, alloc=444.6MB, time=55.38 memory used=6960.4MB, alloc=444.6MB, time=55.57 memory used=7047.9MB, alloc=444.6MB, time=55.76 memory used=7138.3MB, alloc=444.6MB, time=55.93 memory used=7230.5MB, alloc=444.6MB, time=56.10 memory used=7323.8MB, alloc=444.6MB, time=56.28 memory used=7421.8MB, alloc=444.6MB, time=56.46 memory used=7522.2MB, alloc=444.6MB, time=56.65 memory used=7626.3MB, alloc=444.6MB, time=56.82 memory used=7805.9MB, alloc=444.6MB, time=57.24 memory used=7937.9MB, alloc=444.6MB, time=64.49 memory used=8017.1MB, alloc=444.6MB, time=64.77 memory used=8105.6MB, alloc=444.6MB, time=65.07 memory used=8205.9MB, alloc=444.6MB, time=65.35 memory used=8295.3MB, alloc=444.6MB, time=65.63 memory used=8350.8MB, alloc=444.6MB, time=65.85 memory used=8406.8MB, alloc=444.6MB, time=66.07 memory used=8462.6MB, alloc=444.6MB, time=66.32 memory used=8525.1MB, alloc=444.6MB, time=66.55 memory used=8589.3MB, alloc=444.6MB, time=66.75 memory used=8654.9MB, alloc=444.6MB, time=66.94 memory used=8721.9MB, alloc=444.6MB, time=67.14 memory used=8790.6MB, alloc=444.6MB, time=67.35 memory used=8866.7MB, alloc=444.6MB, time=67.57 memory used=8944.2MB, alloc=444.6MB, time=67.80 memory used=9023.0MB, alloc=444.6MB, time=68.01 memory used=9103.1MB, alloc=444.6MB, time=68.20 memory used=9184.7MB, alloc=444.6MB, time=68.43 memory used=9273.9MB, alloc=444.6MB, time=68.67 memory used=9364.3MB, alloc=444.6MB, time=68.89 memory used=9456.0MB, alloc=444.6MB, time=69.13 memory used=9555.5MB, alloc=444.6MB, time=69.38 memory used=9656.0MB, alloc=444.6MB, time=69.63 memory used=9732.3MB, alloc=444.6MB, time=69.80 memory used=9783.4MB, alloc=468.6MB, time=69.96 memory used=9842.2MB, alloc=468.6MB, time=70.12 memory used=9906.7MB, alloc=468.6MB, time=70.30 memory used=9971.8MB, alloc=468.6MB, time=70.46 memory used=10037.1MB, alloc=468.6MB, time=70.63 memory used=10102.4MB, alloc=468.6MB, time=70.79 memory used=10167.8MB, alloc=468.6MB, time=70.95 memory used=10233.6MB, alloc=468.6MB, time=71.14 memory used=10306.0MB, alloc=468.6MB, time=71.32 memory used=10378.5MB, alloc=468.6MB, time=71.51 memory used=10450.9MB, alloc=468.6MB, time=71.69 memory used=10523.2MB, alloc=468.6MB, time=71.88 memory used=10602.4MB, alloc=468.6MB, time=72.06 memory used=10681.1MB, alloc=468.6MB, time=72.25 memory used=10759.5MB, alloc=468.6MB, time=72.43 memory used=10844.4MB, alloc=468.6MB, time=72.63 memory used=10928.6MB, alloc=468.6MB, time=72.81 memory used=11012.1MB, alloc=468.6MB, time=73.01 memory used=11101.4MB, alloc=468.6MB, time=73.20 memory used=11189.8MB, alloc=468.6MB, time=73.40 memory used=11283.4MB, alloc=468.6MB, time=73.60 memory used=11375.6MB, alloc=468.6MB, time=73.80 memory used=11472.4MB, alloc=468.6MB, time=74.00 memory used=11573.3MB, alloc=468.6MB, time=74.19 memory used=11677.6MB, alloc=468.6MB, time=74.40 memory used=11784.5MB, alloc=468.6MB, time=74.60 memory used=11893.1MB, alloc=468.6MB, time=74.81 memory used=12003.0MB, alloc=468.6MB, time=75.02 memory used=12121.1MB, alloc=468.6MB, time=75.23 memory used=12241.0MB, alloc=468.6MB, time=75.45 memory used=12367.1MB, alloc=468.6MB, time=75.67 memory used=12551.1MB, alloc=468.6MB, time=75.99 memory used=12860.5MB, alloc=468.6MB, time=214.68