|\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428240187 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [15 x y - 3 x y - y z + 10, 6 y z - 9 x + 10 y + 14 x, 2 2 2 -14 x z + 5 x z - 4 y z - 12 y] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 2 G := [-10 x y + 8 x z - 16 x z + 13 y, 5 x z - x - 9 z - 19 z, 2 2 2 -20 x y - 8 y z + 7 x - 10 x y] > Problem := [F,G]; 2 2 2 2 Problem := [[15 x y - 3 x y - y z + 10, 6 y z - 9 x + 10 y + 14 x, 2 2 2 2 2 2 -14 x z + 5 x z - 4 y z - 12 y], [-10 x y + 8 x z - 16 x z + 13 y, 2 2 2 2 2 2 5 x z - x - 9 z - 19 z, -20 x y - 8 y z + 7 x - 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=4.4MB, alloc=32.3MB, time=0.18 memory used=26.8MB, alloc=32.3MB, time=0.55 memory used=47.1MB, alloc=56.3MB, time=0.88 memory used=85.0MB, alloc=60.3MB, time=1.48 memory used=126.7MB, alloc=68.3MB, time=2.14 memory used=165.8MB, alloc=92.3MB, time=2.79 memory used=231.1MB, alloc=92.3MB, time=3.79 memory used=298.2MB, alloc=116.3MB, time=4.77 memory used=370.1MB, alloc=116.3MB, time=5.53 memory used=438.5MB, alloc=372.3MB, time=6.49 memory used=530.4MB, alloc=372.3MB, time=7.62 memory used=621.1MB, alloc=372.3MB, time=8.95 memory used=707.4MB, alloc=396.3MB, time=10.19 memory used=824.2MB, alloc=396.3MB, time=11.70 memory used=937.0MB, alloc=396.3MB, time=13.32 memory used=1045.0MB, alloc=420.3MB, time=15.11 memory used=1177.9MB, alloc=420.3MB, time=17.14 memory used=1265.4MB, alloc=420.3MB, time=17.93 memory used=1358.3MB, alloc=420.3MB, time=18.76 memory used=1464.0MB, alloc=420.3MB, time=19.71 memory used=1617.7MB, alloc=444.3MB, time=22.25 memory used=1753.8MB, alloc=444.3MB, time=23.74 memory used=1884.5MB, alloc=444.3MB, time=24.88 memory used=2030.3MB, alloc=444.3MB, time=26.79 memory used=2157.2MB, alloc=444.3MB, time=28.02 memory used=2290.4MB, alloc=444.3MB, time=29.73 memory used=2393.9MB, alloc=444.3MB, time=30.69 memory used=2528.6MB, alloc=444.3MB, time=32.32 memory used=2683.7MB, alloc=444.3MB, time=34.26 memory used=2753.8MB, alloc=444.3MB, time=34.63 memory used=2853.2MB, alloc=444.3MB, time=35.68 memory used=2936.3MB, alloc=444.3MB, time=36.24 memory used=3009.5MB, alloc=444.3MB, time=36.71 memory used=3069.6MB, alloc=444.3MB, time=36.98 memory used=3146.9MB, alloc=444.3MB, time=37.49 memory used=3247.7MB, alloc=444.3MB, time=38.46 memory used=3361.0MB, alloc=468.3MB, time=40.27 memory used=3493.3MB, alloc=468.3MB, time=42.15 memory used=3603.7MB, alloc=468.3MB, time=43.94 memory used=3697.5MB, alloc=468.3MB, time=44.50 memory used=3796.7MB, alloc=468.3MB, time=45.38 memory used=3928.5MB, alloc=468.3MB, time=46.98 memory used=4047.2MB, alloc=468.3MB, time=48.62 memory used=4171.0MB, alloc=468.3MB, time=50.24 memory used=4310.3MB, alloc=468.3MB, time=52.34 memory used=4444.1MB, alloc=468.3MB, time=53.60 memory used=4540.9MB, alloc=468.3MB, time=55.20 memory used=4639.1MB, alloc=468.3MB, time=56.63 memory used=4721.2MB, alloc=468.3MB, time=58.31 memory used=4810.5MB, alloc=492.3MB, time=60.05 memory used=4879.2MB, alloc=492.3MB, time=61.40 memory used=4953.5MB, alloc=492.3MB, time=63.03 memory used=5038.1MB, alloc=492.3MB, time=64.52 memory used=5167.8MB, alloc=492.3MB, time=65.84 memory used=5244.9MB, alloc=492.3MB, time=67.09 memory used=5357.1MB, alloc=492.3MB, time=67.97 memory used=5473.5MB, alloc=492.3MB, time=69.02 memory used=5582.1MB, alloc=492.3MB, time=69.78 memory used=5714.6MB, alloc=492.3MB, time=71.00 memory used=5796.3MB, alloc=492.3MB, time=72.13 memory used=5900.3MB, alloc=492.3MB, time=73.45 memory used=6010.4MB, alloc=492.3MB, time=74.56 memory used=6078.2MB, alloc=492.3MB, time=75.94 memory used=6132.3MB, alloc=492.3MB, time=76.98 memory used=6179.9MB, alloc=492.3MB, time=77.70 memory used=6255.0MB, alloc=516.3MB, time=78.65 memory used=6313.2MB, alloc=516.3MB, time=79.80 memory used=6375.5MB, alloc=516.3MB, time=80.84 memory used=6444.4MB, alloc=516.3MB, time=81.99 memory used=6540.1MB, alloc=516.3MB, time=83.09 memory used=6628.7MB, alloc=516.3MB, time=84.00 memory used=6673.6MB, alloc=516.3MB, time=85.03 memory used=6715.2MB, alloc=516.3MB, time=85.98 memory used=6760.0MB, alloc=516.3MB, time=86.94 memory used=6800.3MB, alloc=516.3MB, time=87.94 memory used=7004.5MB, alloc=540.3MB, time=92.05 memory used=7210.4MB, alloc=564.3MB, time=96.16 memory used=7422.9MB, alloc=588.3MB, time=100.15 memory used=7613.6MB, alloc=612.3MB, time=104.11 memory used=7803.1MB, alloc=636.3MB, time=107.02 memory used=7988.0MB, alloc=660.3MB, time=109.47 memory used=8167.1MB, alloc=660.3MB, time=113.11 |\^/| 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(); 1428240487 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [6 x z - 2 x + 15 y + 18 z, 20 x z + 18 x y z + 4 x z + 18 y, 2 3 2 -9 x y + 3 y - 9 y z + 2 y] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 3 2 G := [20 x y z - 17 y - 7 y z + 19 y, -2 x + 16 y - 16 y z + 8 z, 2 2 -6 x z + 7 y z + 15 y z - y] > Problem := [F,G]; 2 2 2 Problem := [[6 x z - 2 x + 15 y + 18 z, 20 x z + 18 x y z + 4 x z + 18 y, 2 3 2 3 -9 x y + 3 y - 9 y z + 2 y], [20 x y z - 17 y - 7 y z + 19 y, 3 2 2 2 -2 x + 16 y - 16 y z + 8 z, -6 x z + 7 y z + 15 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=4.4MB, alloc=32.3MB, time=0.17 memory used=26.3MB, alloc=32.3MB, time=0.52 memory used=46.9MB, alloc=32.3MB, time=0.84 memory used=64.8MB, alloc=56.3MB, time=1.12 memory used=104.7MB, alloc=60.3MB, time=1.75 memory used=144.2MB, alloc=84.3MB, time=2.40 memory used=209.7MB, alloc=92.3MB, time=3.41 memory used=273.1MB, alloc=92.3MB, time=4.40 memory used=339.0MB, alloc=116.3MB, time=5.42 memory used=408.5MB, alloc=372.3MB, time=6.54 memory used=494.2MB, alloc=396.3MB, time=7.97 memory used=604.4MB, alloc=396.3MB, time=9.83 memory used=723.3MB, alloc=420.3MB, time=11.62 memory used=862.1MB, alloc=444.3MB, time=13.77 memory used=995.2MB, alloc=444.3MB, time=15.73 memory used=1133.3MB, alloc=468.3MB, time=18.33 memory used=1249.4MB, alloc=468.3MB, time=20.11 memory used=1376.0MB, alloc=492.3MB, time=22.18 memory used=1495.1MB, alloc=492.3MB, time=24.37 memory used=1627.4MB, alloc=492.3MB, time=27.11 memory used=1724.8MB, alloc=516.3MB, time=28.67 memory used=1834.5MB, alloc=516.3MB, time=30.75 memory used=1924.7MB, alloc=516.3MB, time=32.57 memory used=2027.3MB, alloc=516.3MB, time=34.72 memory used=2096.0MB, alloc=516.3MB, time=36.13 memory used=2178.1MB, alloc=540.3MB, time=38.09 memory used=2243.8MB, alloc=540.3MB, time=39.37 memory used=2310.5MB, alloc=540.3MB, time=40.51 memory used=2383.5MB, alloc=540.3MB, time=42.39 memory used=2454.5MB, alloc=540.3MB, time=44.10 memory used=2517.9MB, alloc=540.3MB, time=45.65 memory used=2567.3MB, alloc=540.3MB, time=46.79 memory used=2621.7MB, alloc=540.3MB, time=47.88 memory used=2846.5MB, alloc=564.3MB, time=52.85 memory used=3041.7MB, alloc=588.3MB, time=56.98 memory used=3198.2MB, alloc=612.3MB, time=60.39 memory used=3390.7MB, alloc=636.3MB, time=64.22 memory used=3559.1MB, alloc=660.3MB, time=67.82 memory used=3726.9MB, alloc=660.3MB, time=71.41 memory used=3876.0MB, alloc=660.3MB, time=75.01 memory used=3995.3MB, alloc=660.3MB, time=77.30 memory used=4166.4MB, alloc=684.3MB, time=80.42 memory used=4296.3MB, alloc=684.3MB, time=82.84 memory used=4422.6MB, alloc=684.3MB, time=85.17 memory used=4572.1MB, alloc=684.3MB, time=88.62 memory used=4666.1MB, alloc=684.3MB, time=90.93 memory used=5051.4MB, alloc=708.3MB, time=97.09 memory used=5454.7MB, alloc=732.3MB, time=104.16 |\^/| 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(); 1428240787 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [12 y z - 10 z - 6 y + 8 z, -3 x + 2 y - 3 z, 2 2 -17 x y - 18 x y z + 6 y z + 18 x y] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 G := [5 x + 11 y - 19 x y + 15 y z, -12 x y + 16 y z + 6 z , 2 2 -x z + 6 x + 5 x y - 8 z] > Problem := [F,G]; 2 2 2 2 Problem := [[12 y z - 10 z - 6 y + 8 z, -3 x + 2 y - 3 z, 2 2 3 3 -17 x y - 18 x y z + 6 y z + 18 x y], [5 x + 11 y - 19 x y + 15 y z, 2 2 2 2 -12 x y + 16 y z + 6 z , -x z + 6 x + 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=4.3MB, alloc=32.3MB, time=0.18 memory used=26.1MB, alloc=32.3MB, time=0.50 memory used=45.2MB, alloc=56.3MB, time=0.80 memory used=86.8MB, alloc=60.3MB, time=1.44 memory used=130.8MB, alloc=68.3MB, time=2.07 memory used=174.9MB, alloc=92.3MB, time=2.71 memory used=241.3MB, alloc=92.3MB, time=3.70 memory used=307.2MB, alloc=116.3MB, time=4.68 memory used=373.7MB, alloc=116.3MB, time=5.75 memory used=439.5MB, alloc=372.3MB, time=6.75 memory used=528.9MB, alloc=396.3MB, time=8.16 memory used=636.2MB, alloc=420.3MB, time=9.87 memory used=770.0MB, alloc=444.3MB, time=12.01 memory used=890.7MB, alloc=444.3MB, time=13.72 memory used=1016.2MB, alloc=468.3MB, time=15.66 memory used=1116.6MB, alloc=468.3MB, time=17.16 memory used=1231.6MB, alloc=468.3MB, time=19.12 memory used=1335.7MB, alloc=492.3MB, time=20.89 memory used=1426.2MB, alloc=492.3MB, time=22.29 memory used=1512.8MB, alloc=492.3MB, time=23.58 memory used=1592.8MB, alloc=492.3MB, time=24.73 memory used=1676.4MB, alloc=492.3MB, time=26.34 memory used=1747.4MB, alloc=492.3MB, time=27.56 memory used=1813.1MB, alloc=492.3MB, time=28.70 memory used=1884.5MB, alloc=492.3MB, time=30.08 memory used=1932.1MB, alloc=492.3MB, time=31.07 memory used=1997.7MB, alloc=492.3MB, time=32.39 memory used=2050.2MB, alloc=492.3MB, time=33.52 memory used=2097.3MB, alloc=492.3MB, time=34.51 memory used=2148.9MB, alloc=492.3MB, time=35.56 memory used=2211.3MB, alloc=492.3MB, time=36.69 memory used=2253.8MB, alloc=492.3MB, time=37.57 memory used=2293.4MB, alloc=492.3MB, time=38.43 memory used=2478.5MB, alloc=516.3MB, time=41.85 memory used=2675.2MB, alloc=540.3MB, time=45.46 memory used=2828.3MB, alloc=564.3MB, time=48.30 memory used=2993.0MB, alloc=588.3MB, time=51.29 memory used=3171.0MB, alloc=588.3MB, time=54.33 memory used=3305.7MB, alloc=588.3MB, time=57.06 memory used=3486.0MB, alloc=612.3MB, time=59.72 memory used=3649.9MB, alloc=612.3MB, time=63.08 memory used=3789.2MB, alloc=636.3MB, time=65.86 memory used=3945.3MB, alloc=636.3MB, time=68.08 memory used=4079.6MB, alloc=636.3MB, time=70.65 memory used=4212.6MB, alloc=636.3MB, time=73.38 memory used=4327.2MB, alloc=636.3MB, time=75.94 memory used=4439.3MB, alloc=636.3MB, time=78.32 memory used=4543.7MB, alloc=636.3MB, time=80.68 memory used=4652.1MB, alloc=636.3MB, time=83.20 memory used=4744.1MB, alloc=636.3MB, time=85.47 memory used=4850.2MB, alloc=660.3MB, time=88.17 memory used=5160.9MB, alloc=684.3MB, time=92.94 memory used=5513.0MB, alloc=708.3MB, time=98.71 |\^/| 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(); 1428241087 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 3 F := [6 x y + 9 x z - 3 z - 8 z , -18 y + 17 y z + 9 y - 16 z, 3 2 -5 x + 4 y z - 5 x z - 12 y z] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 G := [-4 y + 18 x + 20 y - 4, 8 x z + 2 x y z + 14 y z - 13, 3 2 2 -9 x - 7 y z + 7 x + 20] > Problem := [F,G]; 2 2 3 2 3 Problem := [[6 x y + 9 x z - 3 z - 8 z , -18 y + 17 y z + 9 y - 16 z, 3 2 3 -5 x + 4 y z - 5 x z - 12 y z], [-4 y + 18 x + 20 y - 4, 2 3 2 2 8 x z + 2 x y z + 14 y z - 13, -9 x - 7 y z + 7 x + 20]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=25.7MB, alloc=32.3MB, time=0.52 memory used=45.5MB, alloc=56.3MB, time=0.82 memory used=89.4MB, alloc=60.3MB, time=1.39 memory used=133.8MB, alloc=68.3MB, time=2.04 memory used=171.7MB, alloc=68.3MB, time=2.34 memory used=215.5MB, alloc=68.3MB, time=2.92 memory used=262.3MB, alloc=92.3MB, time=3.49 memory used=331.7MB, alloc=92.3MB, time=4.47 memory used=376.4MB, alloc=92.3MB, time=4.79 memory used=458.9MB, alloc=93.3MB, time=5.73 memory used=523.4MB, alloc=93.3MB, time=6.47 memory used=559.8MB, alloc=93.3MB, time=6.86 memory used=628.1MB, alloc=117.3MB, time=7.57 memory used=713.1MB, alloc=117.3MB, time=8.95 memory used=782.5MB, alloc=373.3MB, time=10.08 memory used=870.5MB, alloc=397.3MB, time=11.27 memory used=990.0MB, alloc=397.3MB, time=12.90 memory used=1091.2MB, alloc=421.3MB, time=14.29 memory used=1208.9MB, alloc=421.3MB, time=15.86 memory used=1308.8MB, alloc=445.3MB, time=20.08 memory used=1399.5MB, alloc=445.3MB, time=23.84 memory used=1508.9MB, alloc=445.3MB, time=26.26 memory used=1644.8MB, alloc=445.3MB, time=27.52 memory used=1774.7MB, alloc=445.3MB, time=29.21 memory used=1894.2MB, alloc=469.3MB, time=31.23 memory used=2019.4MB, alloc=469.3MB, time=32.82 memory used=2101.6MB, alloc=469.3MB, time=33.19 memory used=2189.2MB, alloc=469.3MB, time=33.69 memory used=2277.8MB, alloc=469.3MB, time=35.03 memory used=2370.9MB, alloc=469.3MB, time=35.59 memory used=2466.6MB, alloc=469.3MB, time=36.08 memory used=2559.4MB, alloc=493.3MB, time=61.06 memory used=2662.1MB, alloc=493.3MB, time=64.60 memory used=2756.5MB, alloc=493.3MB, time=64.94 memory used=2825.3MB, alloc=493.3MB, time=65.24 memory used=2902.6MB, alloc=493.3MB, time=65.55 memory used=2990.6MB, alloc=493.3MB, time=65.85 memory used=3091.5MB, alloc=493.3MB, time=66.15 memory used=3224.0MB, alloc=493.3MB, time=66.88 memory used=3326.9MB, alloc=493.3MB, time=71.31 memory used=3438.2MB, alloc=493.3MB, time=95.44 memory used=3543.0MB, alloc=493.3MB, time=95.80 memory used=3608.5MB, alloc=493.3MB, time=96.09 memory used=3683.0MB, alloc=493.3MB, time=96.39 memory used=3767.0MB, alloc=493.3MB, time=96.69 memory used=3863.0MB, alloc=493.3MB, time=96.99 memory used=3986.6MB, alloc=493.3MB, time=97.52 memory used=4177.0MB, alloc=493.3MB, time=115.62 memory used=4273.4MB, alloc=493.3MB, time=116.01 memory used=4356.7MB, alloc=493.3MB, time=116.37 memory used=4462.0MB, alloc=493.3MB, time=116.73 memory used=4528.9MB, alloc=493.3MB, time=117.03 memory used=4606.7MB, alloc=493.3MB, time=117.34 memory used=4696.0MB, alloc=493.3MB, time=117.65 memory used=4868.9MB, alloc=493.3MB, time=119.04 memory used=4990.9MB, alloc=493.3MB, time=120.40 memory used=5131.8MB, alloc=493.3MB, time=121.78 memory used=5247.9MB, alloc=493.3MB, time=123.38 memory used=5334.2MB, alloc=493.3MB, time=124.70 memory used=5433.6MB, alloc=493.3MB, time=128.31 memory used=5532.5MB, alloc=493.3MB, time=129.33 memory used=5622.7MB, alloc=493.3MB, time=132.54 |\^/| 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(); 1428241387 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 3 2 F := [13 x + 17 x y + 12 y - 18 z, 11 y z - 18 z + 3 x + 3 x, 2 2 -18 x y z + 19 y + 9 z + 2] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 3 2 2 2 G := [-5 x z - 20 y - 6 z - 11, 8 x y - 12 x y - 20 x z + 17 y, 3 2 2 5 x - 10 x z - 13 x - 6 x z] > Problem := [F,G]; 3 2 2 3 2 Problem := [[13 x + 17 x y + 12 y - 18 z, 11 y z - 18 z + 3 x + 3 x, 2 2 2 3 3 -18 x y z + 19 y + 9 z + 2], [-5 x z - 20 y - 6 z - 11, 2 2 2 3 2 2 8 x y - 12 x y - 20 x z + 17 y, 5 x - 10 x z - 13 x - 6 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.17 memory used=25.7MB, alloc=32.3MB, time=0.50 memory used=46.0MB, alloc=60.3MB, time=0.80 memory used=86.0MB, alloc=60.3MB, time=1.31 memory used=126.4MB, alloc=60.3MB, time=1.91 memory used=159.3MB, alloc=60.3MB, time=2.35 memory used=201.5MB, alloc=92.3MB, time=2.91 memory used=270.6MB, alloc=92.3MB, time=3.71 memory used=339.6MB, alloc=92.3MB, time=4.59 memory used=406.3MB, alloc=92.3MB, time=5.23 memory used=465.1MB, alloc=116.3MB, time=6.05 memory used=526.9MB, alloc=372.3MB, time=6.77 memory used=614.0MB, alloc=372.3MB, time=7.75 memory used=706.5MB, alloc=372.3MB, time=8.89 memory used=801.1MB, alloc=396.3MB, time=10.19 memory used=917.5MB, alloc=420.3MB, time=11.84 memory used=1031.3MB, alloc=420.3MB, time=13.42 memory used=1157.5MB, alloc=444.3MB, time=15.08 memory used=1274.5MB, alloc=444.3MB, time=16.94 memory used=1395.0MB, alloc=468.3MB, time=18.36 memory used=1535.6MB, alloc=468.3MB, time=20.18 memory used=1676.0MB, alloc=468.3MB, time=21.85 memory used=1766.6MB, alloc=468.3MB, time=23.30 memory used=1879.4MB, alloc=468.3MB, time=24.70 memory used=1987.6MB, alloc=468.3MB, time=26.40 memory used=2077.5MB, alloc=468.3MB, time=27.78 memory used=2176.1MB, alloc=492.3MB, time=29.13 memory used=2252.0MB, alloc=492.3MB, time=30.36 memory used=2332.5MB, alloc=492.3MB, time=31.60 memory used=2396.8MB, alloc=492.3MB, time=32.67 memory used=2464.3MB, alloc=492.3MB, time=33.88 memory used=2525.8MB, alloc=492.3MB, time=35.05 memory used=2588.3MB, alloc=492.3MB, time=36.19 memory used=2650.9MB, alloc=492.3MB, time=37.25 memory used=2703.3MB, alloc=492.3MB, time=38.29 memory used=2753.4MB, alloc=492.3MB, time=39.38 memory used=2808.1MB, alloc=492.3MB, time=40.42 memory used=2848.5MB, alloc=492.3MB, time=41.30 memory used=2896.1MB, alloc=492.3MB, time=42.20 memory used=2933.5MB, alloc=492.3MB, time=43.02 memory used=2976.2MB, alloc=492.3MB, time=43.90 memory used=3170.4MB, alloc=516.3MB, time=46.57 memory used=3394.6MB, alloc=540.3MB, time=49.97 memory used=3561.5MB, alloc=564.3MB, time=52.37 memory used=3744.1MB, alloc=588.3MB, time=55.67 memory used=3917.6MB, alloc=612.3MB, time=58.20 memory used=4093.1MB, alloc=636.3MB, time=60.65 memory used=4234.8MB, alloc=636.3MB, time=63.35 memory used=4392.8MB, alloc=636.3MB, time=65.73 memory used=4556.8MB, alloc=660.3MB, time=67.94 memory used=4721.6MB, alloc=660.3MB, time=70.00 memory used=4844.1MB, alloc=660.3MB, time=72.48 memory used=4967.4MB, alloc=684.3MB, time=74.86 memory used=5088.7MB, alloc=684.3MB, time=77.09 memory used=5188.8MB, alloc=684.3MB, time=78.86 memory used=5523.0MB, alloc=708.3MB, time=83.09 memory used=5942.5MB, alloc=732.3MB, time=88.61 memory used=6290.3MB, alloc=756.3MB, time=92.94 memory used=6637.6MB, alloc=780.3MB, time=98.76 |\^/| 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(); 1428241687 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 F := [-18 x z - 8 x z - 5 y + 14 z, 9 x + 16 y z - 3 x, 3 2 7 y - 16 x + 16 x y + 11] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 3 2 2 G := [-16 x z - 16 y + 11 y z + 2 z , 4 x - 16 x y - 2 y z + 11 z, 2 12 x z - 16 x y z + z] > Problem := [F,G]; 2 2 3 Problem := [[-18 x z - 8 x z - 5 y + 14 z, 9 x + 16 y z - 3 x, 3 2 2 3 2 2 7 y - 16 x + 16 x y + 11], [-16 x z - 16 y + 11 y z + 2 z , 3 2 2 2 4 x - 16 x y - 2 y z + 11 z, 12 x z - 16 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=4.3MB, 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=66.2MB, alloc=56.3MB, time=1.09 memory used=108.8MB, alloc=68.3MB, time=1.71 memory used=148.9MB, alloc=92.3MB, time=2.31 memory used=212.6MB, alloc=92.3MB, time=3.25 memory used=275.8MB, alloc=92.3MB, time=4.16 memory used=336.1MB, alloc=116.3MB, time=5.08 memory used=403.8MB, alloc=372.3MB, time=6.10 memory used=489.3MB, alloc=396.3MB, time=7.36 memory used=596.9MB, alloc=420.3MB, time=8.94 memory used=727.8MB, alloc=444.3MB, time=10.86 memory used=862.0MB, alloc=468.3MB, time=12.87 memory used=1002.5MB, alloc=468.3MB, time=15.32 memory used=1122.6MB, alloc=492.3MB, time=17.07 memory used=1254.5MB, alloc=492.3MB, time=19.49 memory used=1350.5MB, alloc=492.3MB, time=21.07 memory used=1440.9MB, alloc=492.3MB, time=22.59 memory used=1526.6MB, alloc=492.3MB, time=24.09 memory used=1615.5MB, alloc=516.3MB, time=25.78 memory used=1707.6MB, alloc=516.3MB, time=27.23 memory used=1774.9MB, alloc=516.3MB, time=28.52 memory used=1838.7MB, alloc=516.3MB, time=29.50 memory used=1902.2MB, alloc=516.3MB, time=30.78 memory used=1945.5MB, alloc=516.3MB, time=31.69 memory used=2011.8MB, alloc=516.3MB, time=33.10 memory used=2058.3MB, alloc=516.3MB, time=34.16 memory used=2098.9MB, alloc=516.3MB, time=35.23 memory used=2303.4MB, alloc=540.3MB, time=39.00 memory used=2486.5MB, alloc=564.3MB, time=41.58 memory used=2691.8MB, alloc=588.3MB, time=45.62 memory used=2870.3MB, alloc=612.3MB, time=48.84 memory used=3065.4MB, alloc=636.3MB, time=52.87 memory used=3218.9MB, alloc=636.3MB, time=55.98 memory used=3423.8MB, alloc=660.3MB, time=59.25 memory used=3625.8MB, alloc=660.3MB, time=62.02 memory used=3812.9MB, alloc=660.3MB, time=64.70 memory used=3958.3MB, alloc=660.3MB, time=67.60 memory used=4089.0MB, alloc=660.3MB, time=70.62 memory used=4218.8MB, alloc=660.3MB, time=73.27 memory used=4310.8MB, alloc=660.3MB, time=75.30 memory used=4403.4MB, alloc=684.3MB, time=77.43 memory used=4507.9MB, alloc=684.3MB, time=80.18 memory used=4609.2MB, alloc=684.3MB, time=82.95 memory used=4961.2MB, alloc=708.3MB, time=89.75 memory used=5210.9MB, alloc=732.3MB, time=92.84 memory used=5387.7MB, alloc=732.3MB, time=94.43 memory used=5604.8MB, alloc=756.3MB, time=96.60 memory used=5779.1MB, alloc=756.3MB, time=97.93 memory used=6024.1MB, alloc=756.3MB, time=103.32 memory used=6212.9MB, alloc=756.3MB, time=104.85 |\^/| 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(); 1428241987 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 3 2 F := [4 x y z + 16 z + 15 y z - 3 y, -5 x - x y + 20 y + 3 z, 2 15 x y + 13 x + 10 y + 3 z] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 G := [-16 x z - 3 x y - 2 x y + 10, 6 x z - 8 z + 2 z - 20, 2 2 -2 x z - 19 x z - 19 x] > Problem := [F,G]; 3 3 2 Problem := [[4 x y z + 16 z + 15 y z - 3 y, -5 x - x y + 20 y + 3 z, 2 2 2 15 x y + 13 x + 10 y + 3 z], [-16 x z - 3 x y - 2 x y + 10, 2 3 2 2 2 6 x z - 8 z + 2 z - 20, -2 x z - 19 x z - 19 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.1MB, alloc=32.3MB, time=0.50 memory used=45.7MB, alloc=56.3MB, time=0.81 memory used=86.0MB, alloc=60.3MB, time=1.37 memory used=127.9MB, alloc=68.3MB, time=2.00 memory used=171.4MB, alloc=68.3MB, time=2.58 memory used=212.8MB, alloc=92.3MB, time=3.18 memory used=278.5MB, alloc=92.3MB, time=4.08 memory used=344.7MB, alloc=92.3MB, time=4.88 memory used=411.2MB, alloc=92.3MB, time=5.73 memory used=477.1MB, alloc=116.3MB, time=6.59 memory used=556.3MB, alloc=372.3MB, time=7.81 memory used=649.2MB, alloc=396.3MB, time=9.05 memory used=765.4MB, alloc=420.3MB, time=10.56 memory used=889.0MB, alloc=444.3MB, time=12.01 memory used=1006.3MB, alloc=444.3MB, time=13.62 memory used=1117.1MB, alloc=444.3MB, time=15.00 memory used=1237.0MB, alloc=468.3MB, time=16.78 memory used=1325.9MB, alloc=468.3MB, time=18.23 memory used=1417.8MB, alloc=492.3MB, time=19.42 memory used=1496.0MB, alloc=492.3MB, time=20.68 memory used=1575.5MB, alloc=492.3MB, time=21.97 memory used=1651.8MB, alloc=492.3MB, time=23.11 memory used=1732.1MB, alloc=492.3MB, time=24.22 memory used=1810.5MB, alloc=492.3MB, time=25.54 memory used=1883.3MB, alloc=492.3MB, time=26.63 memory used=1951.9MB, alloc=492.3MB, time=27.77 memory used=2010.3MB, alloc=492.3MB, time=28.77 memory used=2069.4MB, alloc=492.3MB, time=29.67 memory used=2126.4MB, alloc=492.3MB, time=30.61 memory used=2187.6MB, alloc=492.3MB, time=31.93 memory used=2244.8MB, alloc=492.3MB, time=33.12 memory used=2294.5MB, alloc=492.3MB, time=33.98 memory used=2488.3MB, alloc=516.3MB, time=36.55 memory used=2673.6MB, alloc=540.3MB, time=38.58 memory used=2909.5MB, alloc=564.3MB, time=41.35 memory used=3113.4MB, alloc=564.3MB, time=44.00 memory used=3305.0MB, alloc=588.3MB, time=47.19 memory used=3496.6MB, alloc=588.3MB, time=49.74 memory used=3700.7MB, alloc=588.3MB, time=52.28 memory used=3902.1MB, alloc=612.3MB, time=54.56 memory used=4063.3MB, alloc=612.3MB, time=57.67 memory used=4230.5MB, alloc=612.3MB, time=59.95 memory used=4387.0MB, alloc=612.3MB, time=62.31 memory used=4547.2MB, alloc=636.3MB, time=64.23 memory used=4689.8MB, alloc=636.3MB, time=66.63 memory used=4830.8MB, alloc=636.3MB, time=68.50 memory used=4937.4MB, alloc=636.3MB, time=70.45 memory used=5069.2MB, alloc=636.3MB, time=72.35 memory used=5182.3MB, alloc=636.3MB, time=74.47 memory used=5288.7MB, alloc=636.3MB, time=76.85 memory used=5356.2MB, alloc=636.3MB, time=78.57 memory used=5597.7MB, alloc=660.3MB, time=81.53 memory used=5813.6MB, alloc=660.3MB, time=83.78 memory used=6162.8MB, alloc=684.3MB, time=88.20 memory used=6537.1MB, alloc=708.3MB, time=94.37 memory used=6853.1MB, alloc=732.3MB, time=98.62 memory used=7301.1MB, alloc=756.3MB, time=105.46 memory used=7662.1MB, alloc=780.3MB, time=111.52 memory used=8013.4MB, alloc=804.3MB, time=118.49 |\^/| 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(); 1428242287 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 3 2 3 F := [-10 x + 13 x y - 8 y - 17 y z, 13 x - 9 x y z - 2 x z + 13 z , 3 2 -8 y - 18 x + 19 x y - 16 y] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 G := [10 x + 8 x y z + x z - 6 x, -17 x y + 5 x y + 19 z + 5 y, 3 3 y + 16 x y + 17 x z - y z] > Problem := [F,G]; 3 2 3 2 Problem := [[-10 x + 13 x y - 8 y - 17 y z, 3 2 3 3 2 13 x - 9 x y z - 2 x z + 13 z , -8 y - 18 x + 19 x y - 16 y], [ 3 2 2 10 x + 8 x y z + x z - 6 x, -17 x y + 5 x y + 19 z + 5 y, 3 3 y + 16 x y + 17 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=31.6MB, alloc=40.3MB, time=0.57 memory used=58.2MB, alloc=44.3MB, time=0.98 memory used=84.7MB, alloc=68.3MB, time=1.37 memory used=136.1MB, alloc=76.3MB, time=2.09 memory used=186.4MB, alloc=76.3MB, time=2.76 memory used=237.7MB, alloc=100.3MB, time=3.42 memory used=315.4MB, alloc=100.3MB, time=4.33 memory used=394.8MB, alloc=100.3MB, time=5.33 memory used=462.6MB, alloc=380.3MB, time=6.31 memory used=553.9MB, alloc=380.3MB, time=7.62 memory used=650.3MB, alloc=404.3MB, time=9.02 memory used=769.2MB, alloc=404.3MB, time=10.56 memory used=887.9MB, alloc=404.3MB, time=12.05 memory used=993.5MB, alloc=404.3MB, time=13.29 memory used=1094.3MB, alloc=404.3MB, time=14.49 memory used=1167.7MB, alloc=404.3MB, time=15.13 memory used=1236.4MB, alloc=404.3MB, time=15.65 memory used=1352.8MB, alloc=428.3MB, time=17.04 memory used=1476.1MB, alloc=428.3MB, time=18.62 memory used=1597.5MB, alloc=428.3MB, time=20.14 memory used=1729.4MB, alloc=428.3MB, time=21.94 memory used=1856.5MB, alloc=452.3MB, time=23.57 memory used=1982.0MB, alloc=452.3MB, time=25.24 memory used=2089.8MB, alloc=452.3MB, time=27.02 memory used=2193.3MB, alloc=476.3MB, time=28.47 memory used=2330.7MB, alloc=476.3MB, time=30.14 memory used=2453.2MB, alloc=476.3MB, time=31.67 memory used=2549.5MB, alloc=476.3MB, time=33.31 memory used=2685.2MB, alloc=476.3MB, time=34.73 memory used=2765.8MB, alloc=476.3MB, time=36.20 memory used=2878.1MB, alloc=476.3MB, time=37.92 memory used=2968.5MB, alloc=476.3MB, time=38.60 memory used=3052.1MB, alloc=476.3MB, time=39.11 memory used=3202.7MB, alloc=476.3MB, time=39.84 memory used=3358.0MB, alloc=476.3MB, time=40.31 memory used=3497.1MB, alloc=476.3MB, time=41.60 memory used=3585.6MB, alloc=476.3MB, time=42.45 memory used=3683.6MB, alloc=476.3MB, time=43.13 memory used=3788.7MB, alloc=476.3MB, time=44.31 memory used=3914.6MB, alloc=476.3MB, time=46.23 memory used=3993.6MB, alloc=500.3MB, time=47.77 memory used=4098.1MB, alloc=500.3MB, time=48.93 memory used=4208.8MB, alloc=500.3MB, time=49.84 memory used=4332.7MB, alloc=500.3MB, time=51.81 memory used=4397.5MB, alloc=500.3MB, time=52.91 memory used=4468.3MB, alloc=500.3MB, time=53.99 memory used=4543.4MB, alloc=500.3MB, time=55.12 memory used=4610.6MB, alloc=500.3MB, time=56.49 memory used=4719.9MB, alloc=500.3MB, time=58.23 memory used=4791.4MB, alloc=500.3MB, time=59.55 memory used=4850.0MB, alloc=500.3MB, time=60.70 memory used=4904.1MB, alloc=500.3MB, time=61.70 memory used=4959.7MB, alloc=500.3MB, time=62.67 memory used=5158.1MB, alloc=524.3MB, time=65.29 memory used=5372.1MB, alloc=548.3MB, time=68.75 memory used=5573.2MB, alloc=572.3MB, time=72.02 memory used=5754.6MB, alloc=596.3MB, time=74.57 memory used=5956.9MB, alloc=620.3MB, time=76.95 memory used=6154.7MB, alloc=644.3MB, time=80.30 memory used=6330.2MB, alloc=668.3MB, time=83.49 memory used=6449.7MB, alloc=692.3MB, time=85.63 memory used=6589.8MB, alloc=692.3MB, time=87.82 memory used=6718.1MB, alloc=692.3MB, time=89.78 memory used=6837.8MB, alloc=716.3MB, time=91.61 memory used=6936.6MB, alloc=716.3MB, time=93.83 memory used=7073.5MB, alloc=716.3MB, time=96.45 memory used=7180.9MB, alloc=716.3MB, time=98.61 memory used=7277.8MB, alloc=716.3MB, time=100.41 memory used=7682.5MB, alloc=740.3MB, time=105.30 memory used=8008.6MB, alloc=764.3MB, time=110.37 memory used=8416.0MB, alloc=788.3MB, time=116.49 |\^/| 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(); 1428242587 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 F := [-17 x z + 13 x z - 13 x y + 16 y , 4 x y + 17 y - 18 x - 12, 2 2 3 x y + 11 x y z + 14 x + 15 y z] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 3 2 G := [4 x z + 14 z + 2 z , 8 x z + 4 y + 20 y z - 9 x y, 3 2 2 2 -5 x - 19 y z + 13 x - 3 y ] > Problem := [F,G]; 2 2 2 2 2 Problem := [[-17 x z + 13 x z - 13 x y + 16 y , 4 x y + 17 y - 18 x - 12, 2 2 2 3 2 3 x y + 11 x y z + 14 x + 15 y z], [4 x z + 14 z + 2 z , 2 3 2 3 2 2 2 8 x z + 4 y + 20 y z - 9 x y, -5 x - 19 y z + 13 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=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=105.4MB, alloc=60.3MB, time=1.70 memory used=144.6MB, alloc=60.3MB, time=2.28 memory used=183.2MB, alloc=84.3MB, time=2.87 memory used=221.4MB, alloc=84.3MB, time=3.46 memory used=284.6MB, alloc=92.3MB, time=4.41 memory used=343.3MB, alloc=116.3MB, time=5.33 memory used=423.8MB, alloc=116.3MB, time=6.61 memory used=493.0MB, alloc=396.3MB, time=7.73 memory used=603.6MB, alloc=420.3MB, time=9.36 memory used=734.3MB, alloc=444.3MB, time=11.52 memory used=858.3MB, alloc=444.3MB, time=13.39 memory used=983.9MB, alloc=468.3MB, time=15.34 memory used=1098.3MB, alloc=468.3MB, time=17.20 memory used=1206.0MB, alloc=492.3MB, time=19.01 memory used=1313.1MB, alloc=492.3MB, time=20.87 memory used=1410.7MB, alloc=492.3MB, time=22.42 memory used=1502.0MB, alloc=492.3MB, time=23.97 memory used=1601.8MB, alloc=492.3MB, time=25.79 memory used=1677.2MB, alloc=492.3MB, time=27.26 memory used=1748.1MB, alloc=492.3MB, time=28.79 memory used=1827.2MB, alloc=516.3MB, time=30.47 memory used=1905.6MB, alloc=516.3MB, time=32.09 memory used=1962.4MB, alloc=516.3MB, time=33.25 memory used=2025.0MB, alloc=516.3MB, time=34.74 memory used=2081.6MB, alloc=516.3MB, time=35.72 memory used=2141.9MB, alloc=516.3MB, time=37.07 memory used=2186.9MB, alloc=516.3MB, time=38.17 memory used=2383.0MB, alloc=540.3MB, time=41.65 memory used=2593.4MB, alloc=564.3MB, time=45.42 memory used=2823.3MB, alloc=588.3MB, time=50.42 memory used=3002.2MB, alloc=612.3MB, time=53.77 memory used=3184.9MB, alloc=636.3MB, time=57.29 memory used=3358.7MB, alloc=660.3MB, time=61.15 memory used=3481.9MB, alloc=660.3MB, time=63.81 memory used=3620.1MB, alloc=660.3MB, time=66.90 memory used=3766.4MB, alloc=660.3MB, time=69.46 memory used=3884.5MB, alloc=660.3MB, time=72.04 memory used=4019.2MB, alloc=684.3MB, time=75.20 memory used=4125.5MB, alloc=684.3MB, time=77.65 memory used=4296.4MB, alloc=684.3MB, time=80.15 memory used=4410.0MB, alloc=684.3MB, time=82.13 memory used=4518.7MB, alloc=684.3MB, time=85.02 memory used=4854.7MB, alloc=708.3MB, time=91.93 memory used=5210.8MB, alloc=732.3MB, time=98.31 memory used=5576.7MB, alloc=756.3MB, time=104.12 memory used=5934.8MB, alloc=780.3MB, time=109.99 |\^/| 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(); 1428242887 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 F := [2 x y + 13 y z - 18 x + 10, -19 x y + 8 x y z + 3 y z - 6 x z, 3 2 3 2 16 x - x z - 3 y - 3 y z] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 2 G := [-18 x z - x y z + 12 y z + 17 x , -3 x + 19 x y + 14 x z + 9 x, 2 11 y z + 7 x y + 17 x z + 8 x] > Problem := [F,G]; 2 2 2 2 2 Problem := [[2 x y + 13 y z - 18 x + 10, -19 x y + 8 x y z + 3 y z - 6 x z, 3 2 3 2 2 2 2 16 x - x z - 3 y - 3 y z], [-18 x z - x y z + 12 y z + 17 x , 3 2 2 2 -3 x + 19 x y + 14 x z + 9 x, 11 y z + 7 x y + 17 x z + 8 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.17 memory used=24.6MB, alloc=36.3MB, time=0.47 memory used=44.5MB, alloc=36.3MB, time=0.74 memory used=62.5MB, alloc=36.3MB, time=0.87 memory used=79.4MB, alloc=36.3MB, time=1.02 memory used=98.2MB, alloc=36.3MB, time=1.20 memory used=120.5MB, alloc=36.3MB, time=1.78 memory used=130.4MB, alloc=60.3MB, time=1.83 memory used=157.9MB, alloc=60.3MB, time=1.90 memory used=185.4MB, alloc=60.3MB, time=1.95 memory used=214.3MB, alloc=60.3MB, time=2.01 memory used=236.7MB, alloc=60.3MB, time=2.05 memory used=290.3MB, alloc=60.9MB, time=2.61 memory used=330.8MB, alloc=60.9MB, time=3.18 memory used=367.6MB, alloc=60.9MB, time=3.53 memory used=409.8MB, alloc=60.9MB, time=4.60 memory used=434.9MB, alloc=60.9MB, time=4.67 memory used=454.1MB, alloc=60.9MB, time=4.73 memory used=478.6MB, alloc=60.9MB, time=4.79 memory used=504.9MB, alloc=60.9MB, time=4.85 memory used=521.9MB, alloc=60.9MB, time=4.89 memory used=540.9MB, alloc=60.9MB, time=4.94 memory used=562.5MB, alloc=60.9MB, time=4.99 memory used=605.7MB, alloc=60.9MB, time=5.35 memory used=648.1MB, alloc=68.9MB, time=5.86 memory used=704.3MB, alloc=68.9MB, time=6.47 memory used=728.8MB, alloc=68.9MB, time=6.55 memory used=746.8MB, alloc=68.9MB, time=6.63 memory used=768.5MB, alloc=68.9MB, time=6.70 memory used=793.8MB, alloc=68.9MB, time=6.77 memory used=815.4MB, alloc=68.9MB, time=6.85 memory used=832.7MB, alloc=68.9MB, time=6.91 memory used=850.0MB, alloc=68.9MB, time=6.98 memory used=868.9MB, alloc=68.9MB, time=7.04 memory used=890.4MB, alloc=68.9MB, time=7.09 memory used=914.8MB, alloc=68.9MB, time=7.16 memory used=948.1MB, alloc=69.1MB, time=7.51 memory used=972.6MB, alloc=69.1MB, time=7.59 memory used=990.3MB, alloc=69.1MB, time=7.66 memory used=1010.9MB, alloc=69.1MB, time=7.74 memory used=1035.2MB, alloc=69.1MB, time=7.81 memory used=1057.7MB, alloc=69.1MB, time=7.88 memory used=1075.8MB, alloc=69.1MB, time=7.94 memory used=1092.5MB, alloc=69.1MB, time=8.00 memory used=1110.4MB, alloc=69.1MB, time=8.08 memory used=1130.4MB, alloc=69.1MB, time=8.14 memory used=1152.5MB, alloc=69.1MB, time=8.23 memory used=1186.6MB, alloc=69.1MB, time=8.70 memory used=1210.7MB, alloc=69.1MB, time=8.95 memory used=1231.3MB, alloc=69.1MB, time=9.03 memory used=1252.7MB, alloc=69.1MB, time=9.12 memory used=1284.9MB, alloc=81.9MB, time=9.54 memory used=1300.1MB, alloc=83.8MB, time=9.60 memory used=1316.9MB, alloc=83.8MB, time=9.66 memory used=1347.4MB, alloc=83.8MB, time=9.75 memory used=1367.0MB, alloc=83.8MB, time=9.81 memory used=1398.7MB, alloc=83.8MB, time=10.75 memory used=1415.3MB, alloc=83.8MB, time=10.82 memory used=1432.6MB, alloc=83.8MB, time=10.88 memory used=1450.6MB, alloc=83.8MB, time=10.94 memory used=1469.2MB, alloc=83.8MB, time=11.00 memory used=1488.5MB, alloc=83.8MB, time=11.08 memory used=1508.5MB, alloc=83.8MB, time=11.22 memory used=1529.1MB, alloc=83.8MB, time=11.28 memory used=1550.4MB, alloc=83.8MB, time=11.34 memory used=1572.4MB, alloc=83.8MB, time=11.44 memory used=1595.1MB, alloc=83.8MB, time=11.53 memory used=1626.4MB, alloc=83.8MB, time=11.60 memory used=1661.0MB, alloc=83.8MB, time=11.68 memory used=1671.6MB, alloc=83.8MB, time=11.74 memory used=1682.3MB, alloc=83.8MB, time=11.80 memory used=1693.1MB, alloc=83.8MB, time=11.85 memory used=1704.0MB, alloc=83.8MB, time=11.92 memory used=1715.1MB, alloc=83.8MB, time=11.97 memory used=1726.3MB, alloc=83.8MB, time=12.02 memory used=1737.6MB, alloc=83.8MB, time=12.08 memory used=1749.0MB, alloc=83.8MB, time=12.18 memory used=1760.5MB, alloc=83.8MB, time=12.25 memory used=1772.2MB, alloc=83.8MB, time=12.32 memory used=1784.0MB, alloc=83.8MB, time=12.40 memory used=1795.9MB, alloc=83.8MB, time=12.46 memory used=1809.1MB, alloc=83.8MB, time=12.72 memory used=1867.1MB, alloc=83.8MB, time=14.98 memory used=1888.2MB, alloc=83.8MB, time=15.08 memory used=1912.8MB, alloc=83.8MB, time=15.16 memory used=1929.4MB, alloc=83.8MB, time=15.24 memory used=1948.1MB, alloc=83.8MB, time=15.31 memory used=1969.3MB, alloc=83.8MB, time=15.38 memory used=1993.0MB, alloc=83.8MB, time=15.46 memory used=2017.2MB, alloc=83.8MB, time=15.52 memory used=2040.6MB, alloc=83.8MB, time=15.59 memory used=2056.6MB, alloc=83.8MB, time=15.65 memory used=2071.7MB, alloc=83.8MB, time=15.71 memory used=2087.8MB, alloc=83.8MB, time=15.77 memory used=2105.2MB, alloc=83.8MB, time=15.82 memory used=2122.8MB, alloc=83.8MB, time=15.88 memory used=2141.5MB, alloc=83.8MB, time=15.97 memory used=2161.9MB, alloc=83.8MB, time=16.04 memory used=2182.2MB, alloc=83.8MB, time=16.09 memory used=2204.1MB, alloc=83.8MB, time=16.16 memory used=2227.1MB, alloc=83.8MB, time=16.22 memory used=2252.0MB, alloc=83.8MB, time=16.28 memory used=2280.4MB, alloc=83.8MB, time=16.35 memory used=2300.0MB, alloc=83.8MB, time=16.40 memory used=2317.8MB, alloc=83.8MB, time=16.50 memory used=2332.2MB, alloc=83.8MB, time=16.55 memory used=2395.0MB, alloc=83.8MB, time=17.18 memory used=2436.0MB, alloc=83.8MB, time=17.75 memory used=2479.8MB, alloc=107.8MB, time=18.34 memory used=2545.8MB, alloc=107.8MB, time=19.16 memory used=2601.3MB, alloc=107.8MB, time=19.69 memory used=2631.9MB, alloc=107.8MB, time=19.80 memory used=2685.1MB, alloc=107.8MB, time=20.70 memory used=2736.2MB, alloc=107.8MB, time=20.96 memory used=2762.8MB, alloc=107.8MB, time=21.07 memory used=2797.7MB, alloc=107.8MB, time=21.17 memory used=2821.0MB, alloc=107.8MB, time=21.26 memory used=2866.4MB, alloc=107.8MB, time=21.85 memory used=2899.8MB, alloc=131.8MB, time=21.99 memory used=2943.8MB, alloc=131.8MB, time=22.15 memory used=2999.7MB, alloc=131.8MB, time=22.32 memory used=3043.1MB, alloc=131.8MB, time=22.46 memory used=3079.6MB, alloc=131.8MB, time=22.59 memory used=3119.1MB, alloc=131.8MB, time=22.73 memory used=3162.2MB, alloc=131.8MB, time=22.86 memory used=3209.8MB, alloc=131.8MB, time=22.99 memory used=3262.1MB, alloc=131.8MB, time=23.11 memory used=3320.2MB, alloc=131.8MB, time=23.25 memory used=3362.9MB, alloc=131.8MB, time=23.37 memory used=3396.1MB, alloc=131.8MB, time=23.47 memory used=3432.6MB, alloc=131.8MB, time=23.57 memory used=3472.2MB, alloc=131.8MB, time=23.67 memory used=3543.5MB, alloc=131.8MB, time=24.47 memory used=3585.6MB, alloc=131.8MB, time=24.63 memory used=3640.1MB, alloc=131.8MB, time=24.80 memory used=3688.4MB, alloc=131.8MB, time=24.94 memory used=3723.7MB, alloc=131.8MB, time=25.06 memory used=3763.1MB, alloc=131.8MB, time=25.19 memory used=3805.8MB, alloc=131.8MB, time=25.33 memory used=3853.7MB, alloc=131.8MB, time=25.46 memory used=3906.1MB, alloc=131.8MB, time=25.60 memory used=3964.3MB, alloc=131.8MB, time=25.75 memory used=4009.9MB, alloc=131.8MB, time=25.87 memory used=4042.9MB, alloc=131.8MB, time=25.97 memory used=4078.8MB, alloc=131.8MB, time=26.08 memory used=4118.4MB, alloc=131.8MB, time=26.17 memory used=4203.4MB, alloc=131.8MB, time=46.56 memory used=4317.1MB, alloc=131.8MB, time=50.90 memory used=4367.3MB, alloc=131.8MB, time=51.05 memory used=4406.1MB, alloc=131.8MB, time=51.18 memory used=4452.5MB, alloc=131.8MB, time=51.32 memory used=4508.2MB, alloc=131.8MB, time=51.46 memory used=4552.5MB, alloc=131.8MB, time=51.58 memory used=4586.5MB, alloc=131.8MB, time=51.68 memory used=4622.0MB, alloc=131.8MB, time=51.83 memory used=4661.1MB, alloc=131.8MB, time=51.94 memory used=4702.5MB, alloc=131.8MB, time=52.05 memory used=4747.4MB, alloc=131.8MB, time=52.16 memory used=4795.6MB, alloc=131.8MB, time=52.27 memory used=4846.7MB, alloc=131.8MB, time=52.39 memory used=4901.7MB, alloc=131.8MB, time=52.51 memory used=4961.1MB, alloc=131.8MB, time=52.62 memory used=4981.8MB, alloc=131.8MB, time=52.70 memory used=4991.8MB, alloc=131.8MB, time=52.78 memory used=5001.5MB, alloc=131.8MB, time=52.86 memory used=5011.1MB, alloc=131.8MB, time=52.94 memory used=5021.6MB, alloc=131.8MB, time=53.00 memory used=5031.9MB, alloc=131.8MB, time=53.09 memory used=5042.1MB, alloc=131.8MB, time=53.18 memory used=5053.0MB, alloc=131.8MB, time=53.27 memory used=5063.7MB, alloc=131.8MB, time=53.35 memory used=5075.1MB, alloc=131.8MB, time=53.46 memory used=5086.3MB, alloc=131.8MB, time=53.54 memory used=5097.7MB, alloc=131.8MB, time=53.62 memory used=5109.7MB, alloc=131.8MB, time=53.70 memory used=5122.0MB, alloc=131.8MB, time=53.79 memory used=5134.5MB, alloc=131.8MB, time=53.88 memory used=5148.0MB, alloc=131.8MB, time=53.96 memory used=5161.6MB, alloc=131.8MB, time=54.08 memory used=5175.9MB, alloc=131.8MB, time=54.15 memory used=5268.4MB, alloc=131.8MB, time=55.10 memory used=5348.6MB, alloc=131.8MB, time=55.86 memory used=5432.1MB, alloc=387.8MB, time=57.17 memory used=5506.7MB, alloc=387.8MB, time=79.42 memory used=5554.8MB, alloc=387.8MB, time=80.02 memory used=5598.1MB, alloc=387.8MB, time=80.17 memory used=5635.2MB, alloc=387.8MB, time=80.30 memory used=5679.2MB, alloc=387.8MB, time=80.44 memory used=5731.5MB, alloc=387.8MB, time=80.59 memory used=5773.1MB, alloc=387.8MB, time=80.71 memory used=5804.3MB, alloc=387.8MB, time=80.81 memory used=5836.9MB, alloc=387.8MB, time=80.92 memory used=5871.8MB, alloc=387.8MB, time=81.03 memory used=5908.8MB, alloc=387.8MB, time=81.15 memory used=5949.3MB, alloc=387.8MB, time=81.26 memory used=5991.7MB, alloc=387.8MB, time=81.38 memory used=6037.3MB, alloc=387.8MB, time=81.50 memory used=6085.7MB, alloc=387.8MB, time=81.61 memory used=6137.9MB, alloc=387.8MB, time=81.73 memory used=6193.3MB, alloc=387.8MB, time=81.86 memory used=6345.9MB, alloc=387.8MB, time=82.31 memory used=6520.9MB, alloc=387.8MB, time=83.59 memory used=6614.3MB, alloc=387.8MB, time=84.52 memory used=6692.7MB, alloc=387.8MB, time=85.40 memory used=6783.2MB, alloc=387.8MB, time=86.65 memory used=6862.1MB, alloc=411.8MB, time=87.90 memory used=6973.5MB, alloc=435.8MB, time=89.47 memory used=7059.1MB, alloc=435.8MB, time=90.11 memory used=7134.3MB, alloc=435.8MB, time=90.63 memory used=7213.1MB, alloc=435.8MB, time=91.20 memory used=7286.3MB, alloc=435.8MB, time=92.38 memory used=7347.8MB, alloc=435.8MB, time=92.62 memory used=7407.1MB, alloc=435.8MB, time=92.81 memory used=7471.8MB, alloc=435.8MB, time=93.81 memory used=7544.4MB, alloc=435.8MB, time=94.12 memory used=7609.2MB, alloc=435.8MB, time=94.37 memory used=7673.4MB, alloc=435.8MB, time=94.61 memory used=7718.2MB, alloc=435.8MB, time=94.82 memory used=7767.9MB, alloc=435.8MB, time=95.04 memory used=7822.8MB, alloc=435.8MB, time=95.25 memory used=7885.7MB, alloc=435.8MB, time=95.47 memory used=7953.4MB, alloc=435.8MB, time=95.68 memory used=8028.5MB, alloc=435.8MB, time=95.92 memory used=8079.4MB, alloc=435.8MB, time=96.10 memory used=8120.5MB, alloc=435.8MB, time=96.28 memory used=8163.6MB, alloc=435.8MB, time=96.45 memory used=8211.0MB, alloc=435.8MB, time=96.65 memory used=8259.8MB, alloc=435.8MB, time=96.86 memory used=8312.6MB, alloc=435.8MB, time=97.06 memory used=8369.1MB, alloc=435.8MB, time=97.26 memory used=8447.3MB, alloc=435.8MB, time=98.52 memory used=8515.2MB, alloc=435.8MB, time=98.81 memory used=8581.9MB, alloc=435.8MB, time=99.07 memory used=8643.9MB, alloc=435.8MB, time=99.32 memory used=8688.7MB, alloc=435.8MB, time=99.54 memory used=8738.6MB, alloc=435.8MB, time=99.75 memory used=8794.0MB, alloc=435.8MB, time=99.99 memory used=8856.7MB, alloc=435.8MB, time=100.21 memory used=8924.9MB, alloc=435.8MB, time=100.43 memory used=9000.1MB, alloc=435.8MB, time=100.66 memory used=9048.8MB, alloc=435.8MB, time=100.84 memory used=9091.3MB, alloc=435.8MB, time=101.03 memory used=9134.8MB, alloc=435.8MB, time=101.23 memory used=9181.7MB, alloc=435.8MB, time=101.43 memory used=9232.4MB, alloc=435.8MB, time=101.61 memory used=9285.3MB, alloc=435.8MB, time=101.79 memory used=9342.9MB, alloc=435.8MB, time=101.97 memory used=9431.0MB, alloc=435.8MB, time=109.01 memory used=9513.9MB, alloc=459.8MB, time=148.53 memory used=9604.5MB, alloc=459.8MB, time=154.89 memory used=9672.8MB, alloc=459.8MB, time=155.12 memory used=9762.7MB, alloc=459.8MB, time=155.39 memory used=9827.0MB, alloc=459.8MB, time=155.59 memory used=9887.7MB, alloc=459.8MB, time=155.79 memory used=9956.0MB, alloc=459.8MB, time=155.99 memory used=10031.1MB, alloc=459.8MB, time=156.19 memory used=10114.5MB, alloc=459.8MB, time=156.41 memory used=10207.6MB, alloc=459.8MB, time=156.63 memory used=10424.0MB, alloc=459.8MB, time=157.02 memory used=10588.7MB, alloc=459.8MB, time=157.34 memory used=10851.2MB, alloc=459.8MB, time=158.15 |\^/| 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(); 1428243187 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 3 F := [-14 x - 16 y z - 15 y z - 19 y, -16 x y + 16 y - 6 x z - 13 x, 2 2 2 -10 y z - 5 x + 7 z - 17 z] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [-9 x y - 8 x y z - 13 x - 9 y , 20 x y - 5 x y z + 9 x - 17 y, 2 3 2 6 x z - 5 y + y z + 10 x y] > Problem := [F,G]; 3 2 2 3 Problem := [[-14 x - 16 y z - 15 y z - 19 y, -16 x y + 16 y - 6 x z - 13 x, 2 2 2 2 2 2 -10 y z - 5 x + 7 z - 17 z], [-9 x y - 8 x y z - 13 x - 9 y , 2 2 3 2 20 x y - 5 x y z + 9 x - 17 y, 6 x z - 5 y + 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=0.18 memory used=24.9MB, alloc=36.3MB, time=0.48 memory used=45.1MB, alloc=36.3MB, time=0.74 memory used=62.9MB, alloc=60.3MB, time=0.95 memory used=109.8MB, alloc=68.3MB, time=1.55 memory used=154.5MB, alloc=68.3MB, time=2.00 memory used=202.9MB, alloc=68.3MB, time=2.57 memory used=248.0MB, alloc=92.3MB, time=3.19 memory used=314.0MB, alloc=92.3MB, time=4.09 memory used=378.2MB, alloc=92.3MB, time=4.82 memory used=442.7MB, alloc=92.3MB, time=5.70 memory used=504.9MB, alloc=372.3MB, time=6.66 memory used=592.4MB, alloc=372.3MB, time=7.72 memory used=693.6MB, alloc=372.3MB, time=8.94 memory used=783.0MB, alloc=372.3MB, time=10.12 memory used=871.0MB, alloc=396.3MB, time=11.17 memory used=982.6MB, alloc=396.3MB, time=12.56 memory used=1093.1MB, alloc=420.3MB, time=14.09 memory used=1209.7MB, alloc=420.3MB, time=15.65 memory used=1293.6MB, alloc=444.3MB, time=16.83 memory used=1400.0MB, alloc=444.3MB, time=18.05 memory used=1492.5MB, alloc=468.3MB, time=19.37 memory used=1577.2MB, alloc=468.3MB, time=20.46 memory used=1652.7MB, alloc=468.3MB, time=21.52 memory used=1734.8MB, alloc=468.3MB, time=22.89 memory used=1805.6MB, alloc=468.3MB, time=23.96 memory used=1882.3MB, alloc=468.3MB, time=25.12 memory used=1960.3MB, alloc=492.3MB, time=26.53 memory used=2011.5MB, alloc=492.3MB, time=27.40 memory used=2070.1MB, alloc=492.3MB, time=28.46 memory used=2155.4MB, alloc=492.3MB, time=29.63 memory used=2235.8MB, alloc=492.3MB, time=30.71 memory used=2284.8MB, alloc=492.3MB, time=31.61 memory used=2350.4MB, alloc=492.3MB, time=32.68 memory used=2398.6MB, alloc=492.3MB, time=33.49 memory used=2452.0MB, alloc=492.3MB, time=34.61 memory used=2655.0MB, alloc=516.3MB, time=37.06 memory used=2831.7MB, alloc=516.3MB, time=39.25 memory used=3009.6MB, alloc=540.3MB, time=41.59 memory used=3191.8MB, alloc=564.3MB, time=44.43 memory used=3403.2MB, alloc=588.3MB, time=46.99 memory used=3556.7MB, alloc=588.3MB, time=49.43 memory used=3737.1MB, alloc=612.3MB, time=52.16 memory used=3919.7MB, alloc=612.3MB, time=54.43 memory used=4110.5MB, alloc=612.3MB, time=56.77 memory used=4246.2MB, alloc=612.3MB, time=58.92 memory used=4354.2MB, alloc=612.3MB, time=61.21 memory used=4471.7MB, alloc=636.3MB, time=63.29 memory used=4593.0MB, alloc=636.3MB, time=65.40 memory used=4663.7MB, alloc=636.3MB, time=67.01 memory used=4768.1MB, alloc=636.3MB, time=68.70 memory used=4856.9MB, alloc=636.3MB, time=70.51 memory used=4961.6MB, alloc=636.3MB, time=72.40 memory used=5285.0MB, alloc=660.3MB, time=77.20 memory used=5618.5MB, alloc=684.3MB, time=82.45 memory used=5958.3MB, alloc=708.3MB, time=88.17 memory used=6275.8MB, alloc=732.3MB, time=93.11 memory used=6601.0MB, alloc=756.3MB, time=98.26 memory used=6904.4MB, alloc=780.3MB, time=103.12 memory used=7217.0MB, alloc=804.3MB, time=108.80 memory used=7532.6MB, 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(); 1428243487 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 2 F := [-10 y + 13 x y + 6 z + 14 z, 17 x z - 19 y z - 8 y z + 4 y , 3 2 7 y - 15 y z + 13 x + 9] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 3 G := [-13 x y z + 7 y - 7 x y + 8 y , 5 x + 13 y z + 14 z + 17 z, 2 17 x y + 15 x y z - 8 z - 10] > Problem := [F,G]; 3 2 2 2 2 2 Problem := [[-10 y + 13 x y + 6 z + 14 z, 17 x z - 19 y z - 8 y z + 4 y , 3 2 3 2 7 y - 15 y z + 13 x + 9], [-13 x y z + 7 y - 7 x y + 8 y , 3 2 3 2 5 x + 13 y z + 14 z + 17 z, 17 x y + 15 x y 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=4.3MB, alloc=32.3MB, time=0.17 memory used=25.1MB, alloc=32.3MB, time=0.48 memory used=43.6MB, alloc=56.3MB, time=0.74 memory used=82.6MB, alloc=60.3MB, time=1.28 memory used=125.8MB, alloc=68.3MB, time=1.82 memory used=173.1MB, alloc=68.3MB, time=2.44 memory used=212.2MB, alloc=92.3MB, time=2.90 memory used=268.7MB, alloc=92.3MB, time=3.33 memory used=338.3MB, alloc=92.3MB, time=4.13 memory used=398.0MB, alloc=92.3MB, time=4.86 memory used=468.9MB, alloc=92.3MB, time=5.70 memory used=528.8MB, alloc=348.3MB, time=6.55 memory used=596.6MB, alloc=372.3MB, time=7.39 memory used=686.2MB, alloc=372.3MB, time=8.36 memory used=759.5MB, alloc=372.3MB, time=8.98 memory used=826.3MB, alloc=372.3MB, time=9.54 memory used=879.7MB, alloc=372.3MB, time=9.96 memory used=947.5MB, alloc=372.3MB, time=10.50 memory used=1000.1MB, alloc=372.3MB, time=10.80 memory used=1055.7MB, alloc=372.3MB, time=12.17 memory used=1122.2MB, alloc=372.3MB, time=12.68 memory used=1224.3MB, alloc=372.3MB, time=13.87 memory used=1305.9MB, alloc=372.3MB, time=14.97 memory used=1342.7MB, alloc=372.3MB, time=15.14 memory used=1374.1MB, alloc=372.3MB, time=15.29 memory used=1452.5MB, alloc=396.3MB, time=15.97 memory used=1565.5MB, alloc=420.3MB, time=17.60 memory used=1690.1MB, alloc=420.3MB, time=19.21 memory used=1773.6MB, alloc=420.3MB, time=19.97 memory used=1897.2MB, alloc=444.3MB, time=21.38 memory used=2024.6MB, alloc=444.3MB, time=22.50 memory used=2090.5MB, alloc=444.3MB, time=22.77 memory used=2179.3MB, alloc=444.3MB, time=23.22 memory used=2245.6MB, alloc=444.3MB, time=23.49 memory used=2335.4MB, alloc=444.3MB, time=25.94 memory used=2402.2MB, alloc=444.3MB, time=26.19 memory used=2477.9MB, alloc=444.3MB, time=26.60 memory used=2578.6MB, alloc=444.3MB, time=27.92 memory used=2680.7MB, alloc=444.3MB, time=28.72 memory used=2773.1MB, alloc=444.3MB, time=29.44 memory used=2847.5MB, alloc=444.3MB, time=29.83 memory used=2924.0MB, alloc=444.3MB, time=30.61 memory used=3027.2MB, alloc=444.3MB, time=31.41 memory used=3158.8MB, alloc=444.3MB, time=32.62 memory used=3229.9MB, alloc=444.3MB, time=33.03 memory used=3300.7MB, alloc=444.3MB, time=33.34 memory used=3383.9MB, alloc=444.3MB, time=35.77 memory used=3451.0MB, alloc=444.3MB, time=36.07 memory used=3517.3MB, alloc=444.3MB, time=36.51 memory used=3586.9MB, alloc=444.3MB, time=37.00 memory used=3702.3MB, alloc=444.3MB, time=38.31 memory used=3866.5MB, alloc=444.3MB, time=40.12 memory used=3996.8MB, alloc=444.3MB, time=43.01 memory used=4117.7MB, alloc=468.3MB, time=44.43 memory used=4234.7MB, alloc=468.3MB, time=45.30 memory used=4320.9MB, alloc=468.3MB, time=45.73 memory used=4400.7MB, alloc=468.3MB, time=46.09 memory used=4492.5MB, alloc=468.3MB, time=47.51 memory used=4575.2MB, alloc=468.3MB, time=47.96 memory used=4681.7MB, alloc=468.3MB, time=49.05 memory used=4776.1MB, alloc=468.3MB, time=49.45 memory used=4844.6MB, alloc=468.3MB, time=49.80 memory used=4941.0MB, alloc=468.3MB, time=50.48 memory used=5017.2MB, alloc=468.3MB, time=50.82 memory used=5120.5MB, alloc=468.3MB, time=55.92 memory used=5196.4MB, alloc=468.3MB, time=56.26 memory used=5276.7MB, alloc=468.3MB, time=56.60 memory used=5343.9MB, alloc=468.3MB, time=56.89 memory used=5467.7MB, alloc=468.3MB, time=58.05 memory used=5569.5MB, alloc=468.3MB, time=59.51 memory used=5695.1MB, alloc=468.3MB, time=60.45 memory used=5808.4MB, alloc=468.3MB, time=61.66 memory used=5907.2MB, alloc=468.3MB, time=62.46 memory used=5979.3MB, alloc=468.3MB, time=62.83 memory used=6068.7MB, alloc=492.3MB, time=63.33 memory used=6173.4MB, alloc=492.3MB, time=65.75 memory used=6258.7MB, alloc=492.3MB, time=66.10 memory used=6350.8MB, alloc=492.3MB, time=67.12 memory used=6463.6MB, alloc=492.3MB, time=67.93 memory used=6596.8MB, alloc=492.3MB, time=69.62 memory used=6679.7MB, alloc=492.3MB, time=70.01 memory used=6775.4MB, alloc=492.3MB, time=70.65 memory used=6906.6MB, alloc=492.3MB, time=71.28 memory used=7010.3MB, alloc=492.3MB, time=72.46 memory used=7100.6MB, alloc=492.3MB, time=73.51 memory used=7235.5MB, alloc=492.3MB, time=75.76 memory used=7342.6MB, alloc=492.3MB, time=76.79 memory used=7422.1MB, alloc=492.3MB, time=77.99 memory used=7481.0MB, alloc=492.3MB, time=79.15 memory used=7531.2MB, alloc=492.3MB, time=80.08 memory used=7582.6MB, alloc=492.3MB, time=80.96 memory used=7629.3MB, alloc=516.3MB, time=81.74 memory used=7823.6MB, alloc=540.3MB, time=84.53 memory used=7992.7MB, alloc=540.3MB, time=86.06 memory used=8215.2MB, alloc=564.3MB, time=88.95 memory used=8416.5MB, alloc=588.3MB, time=91.35 memory used=8598.0MB, alloc=612.3MB, time=93.66 memory used=8755.8MB, alloc=636.3MB, time=96.43 memory used=8893.8MB, alloc=636.3MB, time=98.68 memory used=9039.7MB, alloc=636.3MB, time=101.19 memory used=9172.3MB, alloc=660.3MB, time=103.38 memory used=9329.2MB, alloc=660.3MB, time=105.49 memory used=9421.4MB, alloc=660.3MB, time=107.42 memory used=9497.6MB, alloc=660.3MB, time=108.97 memory used=9617.2MB, alloc=660.3MB, time=110.88 memory used=9733.5MB, alloc=660.3MB, time=112.73 memory used=9875.2MB, alloc=660.3MB, time=114.54 memory used=10044.2MB, alloc=660.3MB, time=116.55 memory used=10194.9MB, alloc=684.3MB, time=118.21 memory used=10362.2MB, alloc=684.3MB, time=120.59 memory used=10462.4MB, alloc=684.3MB, time=122.72 memory used=10847.7MB, alloc=708.3MB, time=127.50 memory used=11164.4MB, alloc=732.3MB, time=131.86 memory used=11390.0MB, alloc=732.3MB, time=133.87 memory used=11591.0MB, alloc=732.3MB, time=135.29 memory used=11771.3MB, alloc=732.3MB, time=136.64 |\^/| 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(); 1428243787 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 3 F := [-9 x y z - 12 x + 4 x y + x, 15 x - 15 x y - 17 x y - 9 z , 2 2 2 10 x z - 5 x y + 18 x + x] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 G := [-17 x y + 2 y z - 15 z - 16 x, 9 y z - x + 4 z + 5, 3 2 -16 y - 14 y z - 11 y z] > Problem := [F,G]; 2 3 2 2 3 Problem := [[-9 x y z - 12 x + 4 x y + x, 15 x - 15 x y - 17 x y - 9 z , 2 2 2 2 10 x z - 5 x y + 18 x + x], [-17 x y + 2 y z - 15 z - 16 x, 3 2 9 y z - x + 4 z + 5, -16 y - 14 y z - 11 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.17 memory used=26.1MB, alloc=32.3MB, time=0.49 memory used=46.2MB, alloc=32.3MB, time=0.78 memory used=65.1MB, alloc=56.3MB, time=1.08 memory used=104.5MB, alloc=60.3MB, time=1.67 memory used=143.6MB, alloc=84.3MB, time=2.28 memory used=204.7MB, alloc=92.3MB, time=3.24 memory used=266.3MB, alloc=116.3MB, time=4.21 memory used=350.4MB, alloc=116.3MB, time=5.50 memory used=427.8MB, alloc=396.3MB, time=6.74 memory used=528.0MB, alloc=396.3MB, time=8.38 memory used=632.5MB, alloc=420.3MB, time=10.03 memory used=764.8MB, alloc=444.3MB, time=12.08 memory used=909.6MB, alloc=468.3MB, time=14.57 memory used=1048.2MB, alloc=492.3MB, time=16.95 memory used=1187.6MB, alloc=492.3MB, time=19.37 memory used=1304.5MB, alloc=492.3MB, time=21.52 memory used=1418.0MB, alloc=516.3MB, time=23.34 memory used=1516.1MB, alloc=516.3MB, time=25.10 memory used=1639.5MB, alloc=516.3MB, time=27.61 memory used=1738.9MB, alloc=516.3MB, time=29.53 memory used=1830.2MB, alloc=516.3MB, time=31.14 memory used=1912.6MB, alloc=516.3MB, time=32.88 memory used=2020.9MB, alloc=516.3MB, time=35.30 memory used=2111.6MB, alloc=516.3MB, time=37.33 memory used=2204.7MB, alloc=516.3MB, time=39.67 memory used=2278.8MB, alloc=540.3MB, time=41.51 memory used=2335.5MB, alloc=540.3MB, time=42.74 memory used=2369.4MB, alloc=540.3MB, time=43.54 memory used=2441.2MB, alloc=540.3MB, time=45.28 memory used=2488.3MB, alloc=540.3MB, time=46.23 memory used=2552.3MB, alloc=540.3MB, time=47.95 memory used=2785.5MB, alloc=564.3MB, time=52.88 memory used=3004.9MB, alloc=588.3MB, time=57.60 memory used=3220.7MB, alloc=612.3MB, time=61.99 memory used=3433.4MB, alloc=636.3MB, time=66.46 memory used=3639.6MB, alloc=660.3MB, time=70.98 memory used=3823.7MB, alloc=660.3MB, time=75.21 memory used=3970.1MB, alloc=684.3MB, time=78.33 memory used=4145.9MB, alloc=684.3MB, time=82.04 memory used=4300.4MB, alloc=684.3MB, time=85.55 memory used=4435.6MB, alloc=684.3MB, time=88.52 memory used=4560.6MB, alloc=708.3MB, time=91.38 memory used=4698.2MB, alloc=708.3MB, time=94.61 memory used=4809.8MB, alloc=708.3MB, time=97.35 memory used=4936.8MB, alloc=708.3MB, time=100.38 memory used=5054.8MB, alloc=708.3MB, time=103.14 memory used=5170.4MB, alloc=708.3MB, time=106.89 memory used=5530.6MB, alloc=732.3MB, time=114.60 |\^/| 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(); 1428244087 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 3 F := [18 x z - z - 9 x y - 7, 15 x y z + 20 y + 16 x y + 4 y z, 2 2 -15 x z + 16 x y + 16 x z - 3 y] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 2 G := [18 x - 4 y - 8 z + 7 y, 15 x + 20 x y + 19 x y + 2 y, 3 2 2 -9 x + 2 x y - 4 x - 18 y z] > Problem := [F,G]; 2 3 3 Problem := [[18 x z - z - 9 x y - 7, 15 x y z + 20 y + 16 x y + 4 y z, 2 2 2 2 2 -15 x z + 16 x y + 16 x z - 3 y], [18 x - 4 y - 8 z + 7 y, 3 2 2 3 2 2 15 x + 20 x y + 19 x y + 2 y, -9 x + 2 x y - 4 x - 18 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.17 memory used=26.6MB, alloc=32.3MB, time=0.49 memory used=46.9MB, alloc=32.3MB, time=0.80 memory used=66.6MB, alloc=56.3MB, time=1.10 memory used=107.1MB, alloc=60.3MB, time=1.69 memory used=145.4MB, alloc=60.3MB, time=2.25 memory used=187.6MB, alloc=92.3MB, time=2.84 memory used=255.6MB, alloc=92.3MB, time=3.77 memory used=321.7MB, alloc=116.3MB, time=4.71 memory used=389.2MB, alloc=372.3MB, time=5.70 memory used=482.5MB, alloc=372.3MB, time=6.92 memory used=575.7MB, alloc=396.3MB, time=8.14 memory used=691.7MB, alloc=396.3MB, time=9.76 memory used=802.6MB, alloc=420.3MB, time=11.31 memory used=940.4MB, alloc=444.3MB, time=13.29 memory used=1072.1MB, alloc=444.3MB, time=14.95 memory used=1194.9MB, alloc=444.3MB, time=16.65 memory used=1311.0MB, alloc=468.3MB, time=18.29 memory used=1439.2MB, alloc=468.3MB, time=19.73 memory used=1585.1MB, alloc=468.3MB, time=21.35 memory used=1693.1MB, alloc=468.3MB, time=22.81 memory used=1786.8MB, alloc=468.3MB, time=24.20 memory used=1875.8MB, alloc=468.3MB, time=25.52 memory used=1974.5MB, alloc=468.3MB, time=26.70 memory used=2075.3MB, alloc=492.3MB, time=28.06 memory used=2155.1MB, alloc=492.3MB, time=29.25 memory used=2229.9MB, alloc=492.3MB, time=30.35 memory used=2318.8MB, alloc=492.3MB, time=31.65 memory used=2388.0MB, alloc=492.3MB, time=32.74 memory used=2472.1MB, alloc=492.3MB, time=34.33 memory used=2535.4MB, alloc=492.3MB, time=35.43 memory used=2601.6MB, alloc=516.3MB, time=36.46 memory used=2656.1MB, alloc=516.3MB, time=37.36 memory used=2720.0MB, alloc=516.3MB, time=38.43 memory used=2786.6MB, alloc=516.3MB, time=39.81 memory used=2838.1MB, alloc=516.3MB, time=40.85 memory used=2880.1MB, alloc=516.3MB, time=41.72 memory used=2921.1MB, alloc=516.3MB, time=42.63 memory used=3105.8MB, alloc=540.3MB, time=44.91 memory used=3309.2MB, alloc=564.3MB, time=47.96 memory used=3472.5MB, alloc=588.3MB, time=50.30 memory used=3636.5MB, alloc=612.3MB, time=52.40 memory used=3801.3MB, alloc=636.3MB, time=55.49 memory used=3946.6MB, alloc=636.3MB, time=57.68 memory used=4083.9MB, alloc=660.3MB, time=59.72 memory used=4271.6MB, alloc=660.3MB, time=62.34 memory used=4380.9MB, alloc=660.3MB, time=64.45 memory used=4489.6MB, alloc=660.3MB, time=66.48 memory used=4601.5MB, alloc=684.3MB, time=68.34 memory used=4719.8MB, alloc=684.3MB, time=70.06 memory used=4825.6MB, alloc=684.3MB, time=72.35 memory used=4915.8MB, alloc=684.3MB, time=74.25 memory used=5298.5MB, alloc=708.3MB, time=78.97 memory used=5681.0MB, alloc=732.3MB, time=84.44 memory used=6030.3MB, alloc=756.3MB, time=90.11 memory used=6340.0MB, alloc=780.3MB, time=94.60 memory used=6669.3MB, alloc=804.3MB, time=98.91 memory used=7014.8MB, alloc=828.3MB, time=104.93 memory used=7291.0MB, alloc=852.3MB, time=109.17 memory used=7658.4MB, alloc=876.3MB, time=114.44 |\^/| 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(); 1428244387 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 3 2 F := [-5 y z + 5 z - 13 y z + 10 x, -4 y z + 14 z - 11 x z - 10 z , 2 17 y - 5 y z + 6 z] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 G := [-20 x y + 7 y + 15 y z - 5 x, x z + 15 z + 10 z + 20, 2 3 3 x z + 13 x y z - 16 y + 14 x z] > Problem := [F,G]; 2 3 2 3 2 Problem := [[-5 y z + 5 z - 13 y z + 10 x, -4 y z + 14 z - 11 x z - 10 z , 2 2 2 17 y - 5 y z + 6 z], [-20 x y + 7 y + 15 y z - 5 x, 2 3 2 3 x z + 15 z + 10 z + 20, 3 x z + 13 x y z - 16 y + 14 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.0MB, alloc=32.3MB, time=0.48 memory used=45.9MB, alloc=56.3MB, time=0.79 memory used=86.1MB, alloc=60.3MB, time=1.39 memory used=126.7MB, alloc=60.3MB, time=1.99 memory used=164.1MB, alloc=84.3MB, time=2.53 memory used=226.0MB, alloc=92.3MB, time=3.49 memory used=289.8MB, alloc=116.3MB, time=4.41 memory used=366.3MB, alloc=116.3MB, time=5.56 memory used=440.0MB, alloc=372.3MB, time=6.69 memory used=527.0MB, alloc=396.3MB, time=7.97 memory used=636.1MB, alloc=420.3MB, time=9.73 memory used=773.0MB, alloc=420.3MB, time=11.62 memory used=898.1MB, alloc=444.3MB, time=13.77 memory used=1043.5MB, alloc=468.3MB, time=16.01 memory used=1176.2MB, alloc=492.3MB, time=18.23 memory used=1310.5MB, alloc=492.3MB, time=20.36 memory used=1422.4MB, alloc=492.3MB, time=22.00 memory used=1537.3MB, alloc=492.3MB, time=23.68 memory used=1649.1MB, alloc=516.3MB, time=25.55 memory used=1747.1MB, alloc=516.3MB, time=27.05 memory used=1857.1MB, alloc=516.3MB, time=28.81 memory used=1934.9MB, alloc=516.3MB, time=30.26 memory used=2058.8MB, alloc=516.3MB, time=31.96 memory used=2144.5MB, alloc=516.3MB, time=33.33 memory used=2267.4MB, alloc=540.3MB, time=34.93 memory used=2373.4MB, alloc=540.3MB, time=36.46 memory used=2456.5MB, alloc=540.3MB, time=38.09 memory used=2525.1MB, alloc=540.3MB, time=39.53 memory used=2601.5MB, alloc=540.3MB, time=41.06 memory used=2678.9MB, alloc=540.3MB, time=42.68 memory used=2740.8MB, alloc=540.3MB, time=43.95 memory used=2793.5MB, alloc=540.3MB, time=45.18 memory used=2848.7MB, alloc=564.3MB, time=46.26 memory used=3088.0MB, alloc=588.3MB, time=49.66 memory used=3313.2MB, alloc=612.3MB, time=53.20 memory used=3540.2MB, alloc=612.3MB, time=56.23 memory used=3706.1MB, alloc=612.3MB, time=58.31 memory used=3925.8MB, alloc=636.3MB, time=61.77 memory used=4120.7MB, alloc=660.3MB, time=65.01 memory used=4291.4MB, alloc=660.3MB, time=68.43 memory used=4474.0MB, alloc=684.3MB, time=72.26 memory used=4610.6MB, alloc=684.3MB, time=74.90 memory used=4799.4MB, alloc=684.3MB, time=78.86 memory used=4946.1MB, alloc=708.3MB, time=81.68 memory used=5068.9MB, alloc=708.3MB, time=83.99 memory used=5192.9MB, alloc=708.3MB, time=86.32 memory used=5311.6MB, alloc=732.3MB, time=89.27 memory used=5454.6MB, alloc=732.3MB, time=92.74 memory used=5605.7MB, alloc=732.3MB, time=95.85 memory used=5700.0MB, alloc=732.3MB, time=97.97 memory used=5790.8MB, alloc=732.3MB, time=99.94 memory used=5867.7MB, alloc=732.3MB, time=101.60 |\^/| 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(); 1428244687 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 2 2 F := [11 x z + 19 x y - 7 y - 2 z , -19 x z + 5 x + 13 y - 19 y, 2 2 2 8 x z + 20 x y + 7 y z + 3] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 3 G := [-16 x y - 3 y z + 16 y + 19 z, -15 x - 12 x z + 19 z + 5 y z, 2 2 2 2 x z - 18 y z - 16 y z + 16 z ] > Problem := [F,G]; 2 2 3 2 2 2 2 Problem := [[11 x z + 19 x y - 7 y - 2 z , -19 x z + 5 x + 13 y - 19 y, 2 2 2 2 2 8 x z + 20 x y + 7 y z + 3], [-16 x y - 3 y z + 16 y + 19 z, 3 2 3 2 2 2 -15 x - 12 x z + 19 z + 5 y z, 2 x z - 18 y z - 16 y z + 16 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.18 memory used=26.6MB, alloc=32.3MB, time=0.50 memory used=46.7MB, alloc=32.3MB, time=0.80 memory used=65.8MB, alloc=56.3MB, time=1.10 memory used=106.0MB, alloc=60.3MB, time=1.69 memory used=144.7MB, alloc=84.3MB, time=2.29 memory used=205.7MB, alloc=92.3MB, time=3.22 memory used=266.1MB, alloc=116.3MB, time=4.15 memory used=335.4MB, alloc=116.3MB, time=5.11 memory used=413.4MB, alloc=372.3MB, time=6.25 memory used=493.4MB, alloc=396.3MB, time=7.59 memory used=596.4MB, alloc=420.3MB, time=9.25 memory used=730.4MB, alloc=444.3MB, time=11.31 memory used=853.8MB, alloc=444.3MB, time=13.23 memory used=970.7MB, alloc=468.3MB, time=14.97 memory used=1100.8MB, alloc=492.3MB, time=17.29 memory used=1207.6MB, alloc=492.3MB, time=19.05 memory used=1321.3MB, alloc=492.3MB, time=21.14 memory used=1418.1MB, alloc=492.3MB, time=22.73 memory used=1496.6MB, alloc=492.3MB, time=23.98 memory used=1582.8MB, alloc=516.3MB, time=25.30 memory used=1655.4MB, alloc=516.3MB, time=26.68 memory used=1732.7MB, alloc=516.3MB, time=28.29 memory used=1803.6MB, alloc=516.3MB, time=29.80 memory used=1868.7MB, alloc=516.3MB, time=31.15 memory used=1933.9MB, alloc=516.3MB, time=32.41 memory used=1984.0MB, alloc=516.3MB, time=33.42 memory used=2028.9MB, alloc=516.3MB, time=34.41 memory used=2082.1MB, alloc=516.3MB, time=35.82 memory used=2116.7MB, alloc=516.3MB, time=36.76 memory used=2326.6MB, alloc=540.3MB, time=40.71 memory used=2507.4MB, alloc=564.3MB, time=44.21 memory used=2720.7MB, alloc=588.3MB, time=48.84 memory used=2894.5MB, alloc=612.3MB, time=52.53 memory used=3047.7MB, alloc=636.3MB, time=55.52 memory used=3191.1MB, alloc=636.3MB, time=58.46 memory used=3335.5MB, alloc=636.3MB, time=61.64 memory used=3485.9MB, alloc=660.3MB, time=65.50 memory used=3652.8MB, alloc=660.3MB, time=69.97 memory used=3772.0MB, alloc=684.3MB, time=73.01 memory used=3874.0MB, alloc=684.3MB, time=75.55 memory used=3982.4MB, alloc=684.3MB, time=78.69 memory used=4346.3MB, alloc=708.3MB, time=85.16 memory used=4712.2MB, alloc=732.3MB, time=92.37 memory used=5077.6MB, alloc=756.3MB, time=100.33 memory used=5419.2MB, alloc=780.3MB, time=106.91 |\^/| 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(); 1428244987 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 3 2 F := [-8 x z + 2 x z - 20 x - y z, -7 y z + 12 z - 13 y + 4, 2 3 2 -6 x y z + 14 y z + 6 z + 12 x ] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 3 2 2 G := [-17 x y + 8 x y - 6 y z , 9 x y - 7 y - 11 y z + 3 z , 3 2 2 2 -18 x + 12 x y + 17 y z + 13 y ] > Problem := [F,G]; 2 2 2 2 3 2 Problem := [[-8 x z + 2 x z - 20 x - y z, -7 y z + 12 z - 13 y + 4, 2 3 2 2 2 2 -6 x y z + 14 y z + 6 z + 12 x ], [-17 x y + 8 x y - 6 y z , 2 3 2 2 3 2 2 2 9 x y - 7 y - 11 y z + 3 z , -18 x + 12 x y + 17 y z + 13 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.19 memory used=24.5MB, alloc=32.3MB, time=0.47 memory used=42.4MB, alloc=56.3MB, time=0.75 memory used=83.2MB, alloc=56.3MB, time=3.35 memory used=110.6MB, alloc=56.3MB, time=3.42 memory used=146.3MB, alloc=56.3MB, time=5.95 memory used=173.6MB, alloc=56.3MB, time=6.01 memory used=205.3MB, alloc=58.3MB, time=6.24 memory used=238.7MB, alloc=58.3MB, time=6.72 memory used=292.1MB, alloc=72.8MB, time=12.54 memory used=321.0MB, alloc=72.8MB, time=12.59 memory used=365.1MB, alloc=72.8MB, time=13.10 memory used=398.3MB, alloc=72.8MB, time=14.33 memory used=441.3MB, alloc=72.8MB, time=14.86 memory used=473.7MB, alloc=72.8MB, time=15.39 memory used=515.0MB, alloc=72.8MB, time=15.96 memory used=555.9MB, alloc=96.8MB, time=16.56 memory used=622.6MB, alloc=96.8MB, time=17.43 memory used=672.3MB, alloc=96.8MB, time=19.21 memory used=714.1MB, alloc=96.8MB, time=19.47 memory used=750.6MB, alloc=96.8MB, time=19.78 memory used=784.7MB, alloc=96.8MB, time=19.90 memory used=817.6MB, alloc=96.8MB, time=20.00 memory used=858.2MB, alloc=96.8MB, time=20.23 memory used=891.2MB, alloc=96.8MB, time=20.34 memory used=930.7MB, alloc=96.8MB, time=22.87 memory used=982.3MB, alloc=96.8MB, time=26.37 memory used=1013.6MB, alloc=96.8MB, time=26.48 memory used=1041.7MB, alloc=96.8MB, time=26.58 memory used=1074.3MB, alloc=96.8MB, time=26.67 memory used=1117.1MB, alloc=96.8MB, time=27.01 memory used=1171.9MB, alloc=96.8MB, time=27.67 memory used=1219.9MB, alloc=96.8MB, time=28.07 memory used=1293.8MB, alloc=96.8MB, time=29.04 memory used=1343.8MB, alloc=96.8MB, time=29.40 memory used=1374.0MB, alloc=96.8MB, time=29.51 memory used=1407.5MB, alloc=96.8MB, time=29.78 memory used=1440.1MB, alloc=96.8MB, time=29.91 memory used=1472.4MB, alloc=96.8MB, time=30.02 memory used=1513.9MB, alloc=96.8MB, time=35.42 memory used=1559.8MB, alloc=96.8MB, time=36.10 memory used=1588.3MB, alloc=96.8MB, time=36.21 memory used=1615.8MB, alloc=96.8MB, time=36.30 memory used=1646.0MB, alloc=96.8MB, time=36.40 memory used=1686.4MB, alloc=96.8MB, time=36.71 memory used=1739.5MB, alloc=96.8MB, time=37.17 memory used=1799.4MB, alloc=120.8MB, time=37.86 memory used=1853.3MB, alloc=120.8MB, time=38.17 memory used=1902.5MB, alloc=120.8MB, time=38.40 memory used=1956.3MB, alloc=120.8MB, time=38.69 memory used=2001.0MB, alloc=120.8MB, time=38.89 memory used=2077.0MB, alloc=120.8MB, time=39.57 memory used=2134.3MB, alloc=120.8MB, time=40.34 memory used=2195.7MB, alloc=376.8MB, time=41.25 memory used=2281.1MB, alloc=400.8MB, time=42.44 memory used=2388.8MB, alloc=400.8MB, time=43.54 memory used=2471.7MB, alloc=400.8MB, time=47.40 memory used=2575.7MB, alloc=400.8MB, time=51.95 memory used=2624.0MB, alloc=400.8MB, time=52.15 memory used=2683.5MB, alloc=400.8MB, time=52.35 memory used=2725.5MB, alloc=400.8MB, time=52.52 memory used=2779.7MB, alloc=400.8MB, time=52.81 memory used=2844.0MB, alloc=400.8MB, time=53.18 memory used=2907.2MB, alloc=400.8MB, time=53.56 memory used=2964.1MB, alloc=400.8MB, time=53.88 memory used=3028.9MB, alloc=400.8MB, time=58.18 memory used=3125.1MB, alloc=400.8MB, time=62.22 memory used=3176.2MB, alloc=400.8MB, time=62.42 memory used=3220.2MB, alloc=400.8MB, time=62.59 memory used=3275.7MB, alloc=400.8MB, time=62.77 memory used=3325.4MB, alloc=400.8MB, time=62.92 memory used=3362.8MB, alloc=400.8MB, time=63.07 memory used=3404.2MB, alloc=400.8MB, time=63.24 memory used=3449.8MB, alloc=400.8MB, time=63.40 memory used=3500.2MB, alloc=400.8MB, time=63.56 memory used=3555.9MB, alloc=400.8MB, time=63.73 memory used=3731.9MB, alloc=400.8MB, time=67.22 memory used=3836.5MB, alloc=400.8MB, time=68.42 memory used=3924.2MB, alloc=400.8MB, time=68.91 memory used=3971.7MB, alloc=400.8MB, time=69.11 memory used=4026.0MB, alloc=400.8MB, time=69.31 memory used=4083.2MB, alloc=400.8MB, time=69.50 memory used=4126.6MB, alloc=400.8MB, time=69.67 memory used=4166.1MB, alloc=400.8MB, time=69.84 memory used=4208.2MB, alloc=400.8MB, time=70.01 memory used=4254.3MB, alloc=400.8MB, time=70.18 memory used=4304.4MB, alloc=400.8MB, time=70.36 memory used=4360.3MB, alloc=400.8MB, time=70.54 memory used=4418.3MB, alloc=400.8MB, time=70.72 memory used=4500.9MB, alloc=400.8MB, time=71.36 memory used=4576.4MB, alloc=400.8MB, time=71.96 memory used=4680.3MB, alloc=424.8MB, time=73.27 memory used=4757.5MB, alloc=424.8MB, time=77.52 memory used=4837.6MB, alloc=424.8MB, time=77.99 memory used=5003.3MB, alloc=424.8MB, time=88.24 memory used=5125.2MB, alloc=424.8MB, time=89.69 memory used=5206.4MB, alloc=424.8MB, time=93.63 memory used=5330.4MB, alloc=424.8MB, time=95.39 memory used=5458.4MB, alloc=448.8MB, time=96.65 memory used=5595.2MB, alloc=448.8MB, time=98.60 memory used=5729.4MB, alloc=472.8MB, time=100.55 memory used=5861.0MB, alloc=496.8MB, time=102.48 memory used=5983.9MB, alloc=496.8MB, time=104.15 memory used=6129.5MB, alloc=496.8MB, time=106.63 memory used=6230.8MB, alloc=496.8MB, time=107.17 memory used=6339.4MB, alloc=496.8MB, time=107.83 memory used=6422.8MB, alloc=496.8MB, time=108.19 memory used=6517.1MB, alloc=496.8MB, time=108.76 memory used=6598.6MB, alloc=496.8MB, time=109.10 memory used=6719.9MB, alloc=496.8MB, time=115.26 memory used=6822.9MB, alloc=496.8MB, time=116.34 memory used=6935.7MB, alloc=496.8MB, time=117.10 memory used=7030.8MB, alloc=496.8MB, time=117.58 memory used=7139.1MB, alloc=496.8MB, time=118.24 memory used=7229.8MB, alloc=496.8MB, time=118.59 memory used=7334.8MB, alloc=496.8MB, time=119.43 memory used=7414.7MB, alloc=496.8MB, time=119.77 memory used=7513.7MB, alloc=496.8MB, time=120.46 memory used=7595.7MB, alloc=496.8MB, time=120.83 memory used=7704.6MB, alloc=520.8MB, time=137.61 memory used=7816.2MB, alloc=520.8MB, time=138.49 memory used=7926.9MB, alloc=520.8MB, time=138.86 memory used=8006.9MB, alloc=520.8MB, time=139.16 memory used=8102.6MB, alloc=520.8MB, time=139.49 memory used=8232.4MB, alloc=520.8MB, time=141.00 memory used=8339.5MB, alloc=520.8MB, time=141.45 memory used=8428.9MB, alloc=520.8MB, time=141.82 |\^/| 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(); 1428245287 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 F := [15 x y + 18 x y z - 3 x + 6, 6 y - 14 y z - 3 x, 2 -18 x y + 4 y z - 6 x + 12] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; G := [ 3 2 3 2 3 2 11 x - 7 x y - 19 z , -3 x z - 5 x y - y z, -20 x - 12 y z - 8 x y + 4 ] > Problem := [F,G]; 2 2 3 2 Problem := [[15 x y + 18 x y z - 3 x + 6, 6 y - 14 y z - 3 x, 2 -18 x y + 4 y z - 6 x + 12], [ 3 2 3 2 3 2 11 x - 7 x y - 19 z , -3 x z - 5 x y - y z, -20 x - 12 y z - 8 x y + 4 ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=24.0MB, alloc=32.3MB, time=0.47 memory used=42.4MB, alloc=56.3MB, time=0.74 memory used=81.7MB, alloc=60.3MB, time=1.31 memory used=122.6MB, alloc=68.3MB, time=1.88 memory used=163.8MB, alloc=68.3MB, time=2.46 memory used=203.0MB, alloc=92.3MB, time=3.07 memory used=267.6MB, alloc=92.3MB, time=4.02 memory used=331.5MB, alloc=92.3MB, time=5.05 memory used=393.5MB, alloc=116.3MB, time=6.00 memory used=463.4MB, alloc=116.3MB, time=7.04 memory used=531.4MB, alloc=372.3MB, time=8.08 memory used=619.8MB, alloc=396.3MB, time=9.42 memory used=730.8MB, alloc=420.3MB, time=11.03 memory used=863.9MB, alloc=444.3MB, time=13.24 memory used=1006.0MB, alloc=468.3MB, time=15.68 memory used=1117.1MB, alloc=468.3MB, time=17.27 memory used=1220.9MB, alloc=468.3MB, time=18.72 memory used=1320.9MB, alloc=468.3MB, time=20.48 memory used=1420.8MB, alloc=492.3MB, time=22.23 memory used=1515.2MB, alloc=492.3MB, time=23.94 memory used=1594.0MB, alloc=492.3MB, time=25.41 memory used=1649.2MB, alloc=492.3MB, time=26.46 memory used=1712.4MB, alloc=492.3MB, time=27.66 memory used=1777.0MB, alloc=492.3MB, time=28.85 memory used=1841.0MB, alloc=492.3MB, time=30.10 memory used=1902.1MB, alloc=492.3MB, time=31.39 memory used=1964.1MB, alloc=492.3MB, time=32.70 memory used=2017.6MB, alloc=492.3MB, time=33.87 memory used=2069.6MB, alloc=492.3MB, time=35.22 memory used=2123.2MB, alloc=492.3MB, time=36.37 memory used=2177.0MB, alloc=492.3MB, time=37.69 memory used=2222.0MB, alloc=492.3MB, time=38.65 memory used=2411.7MB, alloc=516.3MB, time=42.02 memory used=2602.8MB, alloc=540.3MB, time=45.74 memory used=2786.1MB, alloc=564.3MB, time=49.60 memory used=2947.1MB, alloc=588.3MB, time=52.84 memory used=3100.6MB, alloc=588.3MB, time=55.66 memory used=3246.6MB, alloc=588.3MB, time=58.47 memory used=3396.5MB, alloc=612.3MB, time=61.51 memory used=3518.2MB, alloc=612.3MB, time=63.97 memory used=3635.8MB, alloc=612.3MB, time=66.34 memory used=3734.0MB, alloc=612.3MB, time=68.18 memory used=3852.5MB, alloc=612.3MB, time=70.79 memory used=3966.1MB, alloc=636.3MB, time=73.14 memory used=4045.6MB, alloc=636.3MB, time=75.12 memory used=4141.3MB, alloc=636.3MB, time=77.38 memory used=4235.8MB, alloc=636.3MB, time=79.71 memory used=4330.6MB, alloc=636.3MB, time=82.05 memory used=4618.9MB, alloc=660.3MB, time=87.52 memory used=4932.3MB, alloc=684.3MB, time=91.98 memory used=5243.0MB, alloc=708.3MB, time=98.44 memory used=5565.3MB, alloc=732.3MB, time=104.32 memory used=5841.6MB, alloc=756.3MB, 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(); 1428245587 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 2 F := [x y z + z + 5 x z + 3 y , 16 x - 15 x z + 17 z - 5 z, 2 13 x y - 16 x y - 8 z] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 G := [-3 x y z - 2 y z + 7 y z + 18 y, -19 y - 19 y z + 14 y z - 14, 3 3 -5 x - z + 11 y - 12 z] > Problem := [F,G]; 3 2 3 2 2 Problem := [[x y z + z + 5 x z + 3 y , 16 x - 15 x z + 17 z - 5 z, 2 2 2 13 x y - 16 x y - 8 z], [-3 x y z - 2 y z + 7 y z + 18 y, 3 2 2 3 3 -19 y - 19 y z + 14 y z - 14, -5 x - z + 11 y - 12 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=27.1MB, alloc=32.3MB, time=0.53 memory used=48.1MB, alloc=56.3MB, time=0.87 memory used=90.0MB, alloc=60.3MB, time=1.51 memory used=130.6MB, alloc=60.3MB, time=2.14 memory used=169.1MB, alloc=84.3MB, time=2.73 memory used=235.0MB, alloc=92.3MB, time=3.69 memory used=299.0MB, alloc=116.3MB, time=4.63 memory used=362.4MB, alloc=116.3MB, time=5.46 memory used=425.5MB, alloc=372.3MB, time=6.35 memory used=517.0MB, alloc=396.3MB, time=7.62 memory used=626.1MB, alloc=396.3MB, time=9.26 memory used=737.8MB, alloc=420.3MB, time=10.84 memory used=864.8MB, alloc=420.3MB, time=12.77 memory used=985.1MB, alloc=444.3MB, time=14.41 memory used=1097.4MB, alloc=444.3MB, time=18.29 memory used=1166.3MB, alloc=444.3MB, time=18.56 memory used=1242.5MB, alloc=444.3MB, time=18.82 memory used=1308.9MB, alloc=444.3MB, time=19.30 memory used=1467.9MB, alloc=444.3MB, time=21.26 memory used=1583.0MB, alloc=444.3MB, time=25.25 memory used=1657.3MB, alloc=444.3MB, time=25.70 memory used=1731.6MB, alloc=444.3MB, time=25.96 memory used=1783.7MB, alloc=444.3MB, time=26.21 memory used=1857.3MB, alloc=444.3MB, time=26.63 memory used=1978.6MB, alloc=444.3MB, time=27.81 memory used=2114.7MB, alloc=444.3MB, time=29.68 memory used=2220.6MB, alloc=468.3MB, time=31.26 memory used=2324.1MB, alloc=468.3MB, time=32.90 memory used=2488.9MB, alloc=468.3MB, time=34.46 memory used=2593.5MB, alloc=468.3MB, time=35.26 memory used=2668.0MB, alloc=468.3MB, time=35.58 memory used=2771.1MB, alloc=468.3MB, time=41.39 memory used=2848.2MB, alloc=468.3MB, time=41.73 memory used=2918.4MB, alloc=468.3MB, time=42.05 memory used=2983.7MB, alloc=468.3MB, time=42.34 memory used=3063.5MB, alloc=468.3MB, time=42.69 memory used=3297.0MB, alloc=468.3MB, time=43.39 memory used=3474.1MB, alloc=468.3MB, time=43.83 memory used=3625.9MB, alloc=468.3MB, time=44.40 memory used=3773.8MB, alloc=468.3MB, time=45.70 memory used=3894.8MB, alloc=468.3MB, time=47.39 memory used=3999.6MB, alloc=492.3MB, time=48.78 memory used=4137.2MB, alloc=492.3MB, time=50.05 memory used=4238.0MB, alloc=492.3MB, time=51.21 memory used=4374.2MB, alloc=492.3MB, time=52.58 memory used=4504.2MB, alloc=492.3MB, time=53.60 memory used=4613.6MB, alloc=492.3MB, time=61.49 memory used=4712.1MB, alloc=492.3MB, time=62.21 memory used=4796.5MB, alloc=492.3MB, time=62.61 memory used=4888.6MB, alloc=492.3MB, time=63.01 memory used=4956.4MB, alloc=492.3MB, time=63.40 memory used=5034.9MB, alloc=492.3MB, time=63.75 memory used=5125.3MB, alloc=492.3MB, time=64.11 memory used=5284.4MB, alloc=492.3MB, time=64.55 memory used=5384.7MB, alloc=492.3MB, time=65.17 memory used=5494.5MB, alloc=492.3MB, time=67.23 memory used=5583.4MB, alloc=492.3MB, time=67.62 memory used=5737.1MB, alloc=492.3MB, time=69.64 memory used=5936.2MB, alloc=492.3MB, time=72.39 memory used=6122.8MB, alloc=492.3MB, time=77.16 memory used=6318.6MB, alloc=492.3MB, time=83.64 memory used=6496.8MB, alloc=492.3MB, time=90.99 memory used=6592.7MB, alloc=492.3MB, time=93.43 memory used=6712.3MB, alloc=492.3MB, time=94.28 memory used=6787.3MB, alloc=492.3MB, time=94.66 memory used=6917.8MB, alloc=492.3MB, time=102.78 memory used=6992.0MB, alloc=492.3MB, time=103.16 memory used=7087.7MB, alloc=492.3MB, time=103.55 memory used=7150.2MB, alloc=516.3MB, time=103.90 memory used=7238.4MB, alloc=516.3MB, time=104.26 memory used=7343.2MB, alloc=516.3MB, time=104.64 memory used=7596.3MB, alloc=516.3MB, time=105.47 memory used=7696.2MB, alloc=516.3MB, time=105.87 memory used=7843.1MB, alloc=516.3MB, time=107.32 memory used=7935.2MB, alloc=516.3MB, time=108.66 memory used=8066.5MB, alloc=516.3MB, time=109.83 memory used=8173.3MB, alloc=516.3MB, time=111.08 memory used=8236.0MB, alloc=516.3MB, time=112.29 memory used=8297.6MB, alloc=516.3MB, time=113.40 memory used=8355.5MB, alloc=516.3MB, time=114.97 memory used=8439.2MB, alloc=516.3MB, time=116.03 memory used=8497.8MB, alloc=516.3MB, time=117.27 memory used=8549.0MB, alloc=516.3MB, time=118.26 memory used=8601.3MB, alloc=516.3MB, time=119.45 memory used=8653.7MB, alloc=516.3MB, time=120.34 memory used=8736.1MB, alloc=516.3MB, time=121.18 memory used=8842.2MB, alloc=516.3MB, time=125.66 memory used=8942.8MB, alloc=516.3MB, time=126.32 memory used=9034.4MB, alloc=516.3MB, time=126.76 memory used=9118.6MB, alloc=516.3MB, time=127.16 memory used=9240.7MB, alloc=516.3MB, time=128.21 |\^/| 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(); 1428245887 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 3 2 3 F := [-x + 9 y - 12 y z + 12 x y, -9 y - 16 x y - 13 x z - 17, 2 -17 x y + 10 x y z + 18] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 G := [-6 x y - 11 y z - 18 y + 4 z, 4 x y - 18 y - 9 y z, 3 2 3 2 4 x - 3 y z + 13 z + 9 y ] > Problem := [F,G]; 3 3 2 3 Problem := [[-x + 9 y - 12 y z + 12 x y, -9 y - 16 x y - 13 x z - 17, 2 2 -17 x y + 10 x y z + 18], [-6 x y - 11 y z - 18 y + 4 z, 2 3 3 2 3 2 4 x y - 18 y - 9 y z, 4 x - 3 y z + 13 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=4.3MB, alloc=32.3MB, time=0.17 memory used=25.8MB, alloc=32.3MB, time=0.50 memory used=46.3MB, alloc=56.3MB, time=0.81 memory used=87.8MB, alloc=60.3MB, time=1.41 memory used=129.8MB, alloc=68.3MB, time=2.02 memory used=169.3MB, alloc=92.3MB, time=2.63 memory used=236.6MB, alloc=92.3MB, time=3.55 memory used=302.2MB, alloc=92.3MB, time=4.49 memory used=366.0MB, alloc=92.3MB, time=5.28 memory used=430.0MB, alloc=116.3MB, time=6.30 memory used=498.8MB, alloc=116.3MB, time=7.40 memory used=553.8MB, alloc=396.3MB, time=8.17 memory used=669.5MB, alloc=396.3MB, time=9.69 memory used=776.8MB, alloc=420.3MB, time=11.41 memory used=904.8MB, alloc=444.3MB, time=13.51 memory used=1026.1MB, alloc=444.3MB, time=15.20 memory used=1127.5MB, alloc=444.3MB, time=16.55 memory used=1234.7MB, alloc=468.3MB, time=18.25 memory used=1335.9MB, alloc=468.3MB, time=19.81 memory used=1433.0MB, alloc=468.3MB, time=21.29 memory used=1544.6MB, alloc=468.3MB, time=22.68 memory used=1646.1MB, alloc=468.3MB, time=23.93 memory used=1741.4MB, alloc=468.3MB, time=25.15 memory used=1835.8MB, alloc=492.3MB, time=26.61 memory used=1934.9MB, alloc=492.3MB, time=28.47 memory used=2020.5MB, alloc=492.3MB, time=30.03 memory used=2096.3MB, alloc=492.3MB, time=31.44 memory used=2167.0MB, alloc=492.3MB, time=32.77 memory used=2246.9MB, alloc=492.3MB, time=34.38 memory used=2310.5MB, alloc=492.3MB, time=35.65 memory used=2364.1MB, alloc=492.3MB, time=36.62 memory used=2427.3MB, alloc=492.3MB, time=37.74 memory used=2482.1MB, alloc=492.3MB, time=38.70 memory used=2536.2MB, alloc=492.3MB, time=39.89 memory used=2588.5MB, alloc=492.3MB, time=40.84 memory used=2643.9MB, alloc=492.3MB, time=42.18 memory used=2826.9MB, alloc=516.3MB, time=45.32 memory used=3025.3MB, alloc=540.3MB, time=48.15 memory used=3244.7MB, alloc=564.3MB, time=51.16 memory used=3438.7MB, alloc=564.3MB, time=53.69 memory used=3640.3MB, alloc=588.3MB, time=57.71 memory used=3826.8MB, alloc=612.3MB, time=61.13 memory used=3988.6MB, alloc=612.3MB, time=63.76 memory used=4138.2MB, alloc=612.3MB, time=66.21 memory used=4304.6MB, alloc=612.3MB, time=68.51 memory used=4436.5MB, alloc=612.3MB, time=70.82 memory used=4582.6MB, alloc=636.3MB, time=73.55 memory used=4721.7MB, alloc=636.3MB, time=75.64 memory used=4875.7MB, alloc=636.3MB, time=77.75 memory used=4982.4MB, alloc=636.3MB, time=79.74 memory used=5082.1MB, alloc=636.3MB, time=81.77 memory used=5214.8MB, alloc=636.3MB, time=84.05 memory used=5305.7MB, alloc=636.3MB, time=85.87 memory used=5394.1MB, alloc=636.3MB, time=87.63 memory used=5515.4MB, alloc=660.3MB, time=90.79 memory used=5623.3MB, alloc=660.3MB, time=92.95 memory used=5718.3MB, alloc=660.3MB, time=94.97 memory used=5818.1MB, alloc=660.3MB, time=96.97 memory used=6157.2MB, alloc=684.3MB, time=100.89 |\^/| 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(); 1428246187 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-12 x y z + 17 y z + 7 x z + 17 x, -9 x y + 20 x y + 12 y + 3, 3 3 z + 9 x y + 5 x + 3 z] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [9 x y z - 14 x - 2 x + 4 z, -15 x y - y z + 5 x z - 9 x, 2 5 x y + 2 y z + 8 x + 15 y] > Problem := [F,G]; 2 2 Problem := [[-12 x y z + 17 y z + 7 x z + 17 x, -9 x y + 20 x y + 12 y + 3, 3 2 3 z + 9 x y + 5 x + 3 z], [9 x y z - 14 x - 2 x + 4 z, 2 2 2 -15 x y - y z + 5 x z - 9 x, 5 x y + 2 y z + 8 x + 15 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=25.9MB, alloc=32.3MB, time=0.50 memory used=45.3MB, alloc=56.3MB, time=0.81 memory used=87.2MB, alloc=60.3MB, time=1.43 memory used=127.8MB, alloc=68.3MB, time=2.06 memory used=168.4MB, alloc=92.3MB, time=2.67 memory used=231.8MB, alloc=92.3MB, time=3.61 memory used=293.2MB, alloc=92.3MB, time=4.58 memory used=357.8MB, alloc=116.3MB, time=5.62 memory used=422.0MB, alloc=372.3MB, time=6.65 memory used=507.0MB, alloc=396.3MB, time=8.00 memory used=618.3MB, alloc=420.3MB, time=9.82 memory used=753.9MB, alloc=420.3MB, time=11.85 memory used=882.8MB, alloc=444.3MB, time=14.20 memory used=1006.7MB, alloc=444.3MB, time=16.30 memory used=1139.0MB, alloc=468.3MB, time=20.06 memory used=1299.9MB, alloc=468.3MB, time=23.63 memory used=1433.6MB, alloc=468.3MB, time=26.01 memory used=1532.7MB, alloc=468.3MB, time=27.79 memory used=1644.6MB, alloc=492.3MB, time=29.87 memory used=1758.7MB, alloc=492.3MB, time=32.06 memory used=1845.2MB, alloc=492.3MB, time=33.67 memory used=1930.3MB, alloc=492.3MB, time=35.29 memory used=2020.6MB, alloc=492.3MB, time=37.20 memory used=2106.3MB, alloc=492.3MB, time=39.01 memory used=2180.5MB, alloc=492.3MB, time=40.44 memory used=2254.9MB, alloc=492.3MB, time=41.77 memory used=2333.0MB, alloc=516.3MB, time=43.40 memory used=2401.9MB, alloc=516.3MB, time=44.70 memory used=2459.6MB, alloc=516.3MB, time=45.76 memory used=2515.4MB, alloc=516.3MB, time=47.04 memory used=2579.8MB, alloc=516.3MB, time=48.46 memory used=2636.8MB, alloc=516.3MB, time=49.83 memory used=2686.4MB, alloc=516.3MB, time=51.01 memory used=2728.6MB, alloc=516.3MB, time=52.19 memory used=2787.5MB, alloc=516.3MB, time=53.66 memory used=2997.4MB, alloc=540.3MB, time=57.41 memory used=3222.2MB, alloc=564.3MB, time=61.90 memory used=3422.1MB, alloc=588.3MB, time=66.28 memory used=3610.7MB, alloc=612.3MB, time=70.26 memory used=3756.8MB, alloc=636.3MB, time=72.87 memory used=3944.0MB, alloc=660.3MB, time=77.57 memory used=4089.2MB, alloc=660.3MB, time=80.84 memory used=4217.7MB, alloc=660.3MB, time=83.43 memory used=4364.8MB, alloc=660.3MB, time=86.89 memory used=4473.1MB, alloc=684.3MB, time=89.28 memory used=4560.7MB, alloc=684.3MB, time=91.11 memory used=4684.2MB, alloc=684.3MB, time=94.21 memory used=4780.8MB, alloc=684.3MB, time=96.67 memory used=4881.2MB, alloc=684.3MB, time=99.13 memory used=5001.0MB, alloc=684.3MB, time=102.35 memory used=5353.0MB, alloc=708.3MB, time=110.20 |\^/| 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(); 1428246487 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 2 2 F := [-20 x y + 9 x z - 17 x y - z , -17 x z - 8 x y - 16 y z + 13 y , 3 19 z + 16 x y - 15 y z + 19 y] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 G := [16 x - 2 x y + 16 z + 3 z, -13 x z + 16 y z + 10 y - 13, 2 2 17 x y + 14 x y - 18 x z + 19 y] > Problem := [F,G]; 2 2 2 Problem := [[-20 x y + 9 x z - 17 x y - z , 2 2 2 2 3 -17 x z - 8 x y - 16 y z + 13 y , 19 z + 16 x y - 15 y z + 19 y], [ 2 2 2 2 2 16 x - 2 x y + 16 z + 3 z, -13 x z + 16 y z + 10 y - 13, 2 2 17 x y + 14 x y - 18 x z + 19 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.17 memory used=24.1MB, alloc=32.3MB, time=0.41 memory used=44.9MB, alloc=32.3MB, time=0.65 memory used=64.9MB, alloc=32.3MB, time=0.92 memory used=85.4MB, alloc=36.3MB, time=1.19 memory used=105.2MB, alloc=60.3MB, time=1.48 memory used=147.4MB, alloc=60.3MB, time=2.09 memory used=188.3MB, alloc=60.3MB, time=2.67 memory used=224.3MB, alloc=60.3MB, time=2.98 memory used=258.6MB, alloc=60.3MB, time=3.44 memory used=306.8MB, alloc=92.3MB, time=4.02 memory used=376.4MB, alloc=92.3MB, time=4.92 memory used=439.9MB, alloc=92.3MB, time=5.59 memory used=506.0MB, alloc=372.3MB, time=6.41 memory used=596.5MB, alloc=372.3MB, time=7.36 memory used=687.8MB, alloc=372.3MB, time=8.45 memory used=775.3MB, alloc=372.3MB, time=9.66 memory used=864.4MB, alloc=396.3MB, time=10.89 memory used=978.3MB, alloc=396.3MB, time=12.44 memory used=1086.2MB, alloc=420.3MB, time=13.71 memory used=1213.0MB, alloc=420.3MB, time=15.49 memory used=1336.2MB, alloc=420.3MB, time=16.96 memory used=1437.3MB, alloc=420.3MB, time=18.15 memory used=1501.3MB, alloc=420.3MB, time=18.51 memory used=1648.7MB, alloc=444.3MB, time=20.52 memory used=1819.2MB, alloc=444.3MB, time=22.74 memory used=1911.5MB, alloc=444.3MB, time=23.37 memory used=2054.3MB, alloc=444.3MB, time=24.76 memory used=2125.5MB, alloc=444.3MB, time=25.08 memory used=2192.8MB, alloc=444.3MB, time=25.49 memory used=2323.6MB, alloc=444.3MB, time=27.24 memory used=2393.8MB, alloc=444.3MB, time=27.69 memory used=2456.2MB, alloc=444.3MB, time=27.93 memory used=2586.3MB, alloc=468.3MB, time=29.68 memory used=2689.4MB, alloc=468.3MB, time=31.23 memory used=2798.9MB, alloc=468.3MB, time=32.92 memory used=2888.2MB, alloc=468.3MB, time=34.39 memory used=2970.0MB, alloc=468.3MB, time=35.77 memory used=3063.5MB, alloc=492.3MB, time=37.08 memory used=3150.6MB, alloc=492.3MB, time=38.16 memory used=3268.7MB, alloc=492.3MB, time=39.74 memory used=3425.5MB, alloc=492.3MB, time=41.64 memory used=3556.7MB, alloc=492.3MB, time=42.88 memory used=3691.4MB, alloc=492.3MB, time=44.01 memory used=3774.3MB, alloc=492.3MB, time=45.28 memory used=3880.0MB, alloc=492.3MB, time=46.47 memory used=3956.2MB, alloc=492.3MB, time=47.81 memory used=4049.7MB, alloc=492.3MB, time=49.17 memory used=4131.5MB, alloc=492.3MB, time=49.63 memory used=4228.0MB, alloc=492.3MB, time=50.47 memory used=4326.9MB, alloc=492.3MB, time=51.24 memory used=4447.8MB, alloc=492.3MB, time=52.68 memory used=4529.6MB, alloc=492.3MB, time=53.81 memory used=4584.5MB, alloc=492.3MB, time=54.84 memory used=4683.0MB, alloc=492.3MB, time=55.82 memory used=4754.0MB, alloc=516.3MB, time=57.07 memory used=4849.1MB, alloc=516.3MB, time=58.65 memory used=4925.6MB, alloc=516.3MB, time=59.81 memory used=4994.7MB, alloc=516.3MB, time=60.78 memory used=5049.1MB, alloc=516.3MB, time=61.83 memory used=5121.4MB, alloc=516.3MB, time=62.89 memory used=5174.3MB, alloc=516.3MB, time=64.03 memory used=5248.7MB, alloc=516.3MB, time=65.07 memory used=5347.8MB, alloc=516.3MB, time=66.02 memory used=5466.3MB, alloc=516.3MB, time=67.05 memory used=5517.7MB, alloc=516.3MB, time=67.93 memory used=5578.4MB, alloc=516.3MB, time=68.88 memory used=5651.8MB, alloc=516.3MB, time=70.36 memory used=5750.0MB, alloc=516.3MB, time=70.87 memory used=5859.2MB, alloc=516.3MB, time=71.88 memory used=5952.5MB, alloc=516.3MB, time=72.77 memory used=6063.6MB, alloc=516.3MB, time=73.58 memory used=6158.8MB, alloc=516.3MB, time=74.62 memory used=6349.4MB, alloc=516.3MB, time=76.42 memory used=6438.2MB, alloc=516.3MB, time=76.92 memory used=6574.2MB, alloc=516.3MB, time=78.97 memory used=6668.8MB, alloc=516.3MB, time=79.63 memory used=6878.2MB, alloc=540.3MB, time=82.37 memory used=7081.8MB, alloc=540.3MB, time=84.82 memory used=7278.6MB, alloc=564.3MB, time=86.92 memory used=7498.2MB, alloc=564.3MB, time=89.40 memory used=7687.8MB, alloc=588.3MB, time=92.48 memory used=7872.8MB, alloc=588.3MB, time=95.62 memory used=8076.2MB, alloc=612.3MB, time=98.23 memory used=8299.8MB, alloc=636.3MB, time=101.50 memory used=8474.7MB, alloc=636.3MB, time=104.22 memory used=8631.3MB, alloc=660.3MB, time=106.60 memory used=8779.7MB, alloc=660.3MB, time=109.28 memory used=8921.2MB, alloc=660.3MB, time=111.36 memory used=9098.8MB, alloc=684.3MB, time=113.56 memory used=9231.3MB, alloc=684.3MB, time=115.81 memory used=9352.7MB, alloc=684.3MB, time=118.33 |\^/| 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(); 1428246787 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 F := [-7 x y z + 3 z - 13 x z + 8 z , 11 x y - x y - 15 y z + 15 z, 3 2 2 -x + x y z + 2 x z + 10 z ] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 3 G := [11 x y + 2 x y - 16 y z + 8 z, -19 y + 3 z + 4 x + 10 y, 3 -16 x y z - 8 y - 2 y z - 16 y] > Problem := [F,G]; 3 2 2 Problem := [[-7 x y z + 3 z - 13 x z + 8 z , 11 x y - x y - 15 y z + 15 z, 3 2 2 2 2 2 -x + x y z + 2 x z + 10 z ], [11 x y + 2 x y - 16 y z + 8 z, 3 3 3 -19 y + 3 z + 4 x + 10 y, -16 x y z - 8 y - 2 y z - 16 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=25.4MB, alloc=32.3MB, time=0.48 memory used=44.6MB, alloc=56.3MB, time=0.77 memory used=85.3MB, alloc=60.3MB, time=1.38 memory used=125.2MB, alloc=60.3MB, time=1.94 memory used=165.1MB, alloc=84.3MB, time=2.53 memory used=227.5MB, alloc=92.3MB, time=3.45 memory used=287.6MB, alloc=92.3MB, time=4.35 memory used=349.5MB, alloc=116.3MB, time=5.30 memory used=431.4MB, alloc=116.3MB, time=6.65 memory used=513.0MB, alloc=140.3MB, time=8.06 memory used=580.1MB, alloc=396.3MB, time=8.98 memory used=696.5MB, alloc=396.3MB, time=10.57 memory used=800.2MB, alloc=420.3MB, time=12.31 memory used=934.8MB, alloc=420.3MB, time=14.39 memory used=1063.5MB, alloc=444.3MB, time=16.49 memory used=1209.9MB, alloc=468.3MB, time=19.17 memory used=1351.6MB, alloc=468.3MB, time=21.76 memory used=1511.2MB, alloc=492.3MB, time=24.94 memory used=1628.8MB, alloc=516.3MB, time=26.72 memory used=1761.8MB, alloc=516.3MB, time=29.23 memory used=1906.0MB, alloc=516.3MB, time=32.24 memory used=2022.4MB, alloc=540.3MB, time=34.79 memory used=2142.3MB, alloc=540.3MB, time=37.12 memory used=2234.6MB, alloc=540.3MB, time=38.60 memory used=2354.4MB, alloc=540.3MB, time=40.23 memory used=2450.7MB, alloc=540.3MB, time=42.08 memory used=2543.2MB, alloc=540.3MB, time=43.70 memory used=2627.5MB, alloc=564.3MB, time=45.33 memory used=2700.7MB, alloc=564.3MB, time=46.84 memory used=2765.3MB, alloc=564.3MB, time=48.22 memory used=2845.4MB, alloc=564.3MB, time=50.28 memory used=2915.6MB, alloc=564.3MB, time=51.91 memory used=2995.0MB, alloc=564.3MB, time=53.94 memory used=3059.6MB, alloc=564.3MB, time=55.15 memory used=3142.6MB, alloc=564.3MB, time=56.35 memory used=3202.6MB, alloc=564.3MB, time=57.59 memory used=3261.1MB, alloc=564.3MB, time=58.78 memory used=3331.8MB, alloc=588.3MB, time=60.53 memory used=3386.0MB, alloc=588.3MB, time=61.87 memory used=3429.4MB, alloc=588.3MB, time=62.75 memory used=3478.9MB, alloc=588.3MB, time=64.05 memory used=3702.3MB, alloc=588.3MB, time=67.42 memory used=3917.2MB, alloc=612.3MB, time=71.14 memory used=4190.6MB, alloc=636.3MB, time=78.04 memory used=4415.1MB, alloc=660.3MB, time=83.41 memory used=4607.8MB, alloc=684.3MB, time=88.41 memory used=4807.5MB, alloc=708.3MB, time=93.29 memory used=4971.4MB, alloc=732.3MB, time=96.22 memory used=5118.9MB, alloc=732.3MB, time=98.34 memory used=5298.4MB, alloc=732.3MB, time=103.49 memory used=5466.8MB, alloc=756.3MB, time=107.65 |\^/| 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(); 1428247087 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-17 x y - 12 x z - 8 y z - 3 z, -8 y z - 10 x y + 17 z - 7 y, 2 2 14 x z - 5 y z + 18 z - 17] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 G := [-19 x - 8 z + 12 x - 9 y, 6 x z + 15 x z + 2 x + 10 z, 2 2 -9 x z + 20 x + 9 x z + 13 y z] > Problem := [F,G]; 2 2 2 Problem := [[-17 x y - 12 x z - 8 y z - 3 z, -8 y z - 10 x y + 17 z - 7 y, 2 2 3 2 14 x z - 5 y z + 18 z - 17], [-19 x - 8 z + 12 x - 9 y, 2 2 2 6 x z + 15 x z + 2 x + 10 z, -9 x z + 20 x + 9 x z + 13 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=26.6MB, alloc=32.3MB, time=0.52 memory used=47.4MB, alloc=56.3MB, time=0.86 memory used=89.4MB, alloc=60.3MB, time=1.47 memory used=131.4MB, alloc=68.3MB, time=2.12 memory used=172.0MB, alloc=92.3MB, time=2.77 memory used=235.3MB, alloc=92.3MB, time=3.80 memory used=298.7MB, alloc=116.3MB, time=4.78 memory used=364.6MB, alloc=116.3MB, time=5.71 memory used=431.2MB, alloc=372.3MB, time=6.74 memory used=518.5MB, alloc=396.3MB, time=8.05 memory used=630.2MB, alloc=396.3MB, time=9.75 memory used=738.2MB, alloc=420.3MB, time=11.68 memory used=870.3MB, alloc=444.3MB, time=13.89 memory used=984.1MB, alloc=444.3MB, time=15.78 memory used=1100.9MB, alloc=468.3MB, time=17.68 memory used=1224.6MB, alloc=468.3MB, time=20.01 memory used=1340.6MB, alloc=492.3MB, time=22.12 memory used=1450.6MB, alloc=492.3MB, time=24.43 memory used=1555.9MB, alloc=492.3MB, time=26.22 memory used=1649.2MB, alloc=516.3MB, time=27.55 memory used=1736.4MB, alloc=516.3MB, time=29.42 memory used=1800.1MB, alloc=516.3MB, time=30.65 memory used=1871.5MB, alloc=516.3MB, time=31.93 memory used=1959.0MB, alloc=540.3MB, time=33.56 memory used=2016.0MB, alloc=540.3MB, time=34.81 memory used=2079.8MB, alloc=540.3MB, time=36.12 memory used=2141.1MB, alloc=540.3MB, time=37.33 memory used=2190.5MB, alloc=540.3MB, time=38.70 memory used=2239.3MB, alloc=540.3MB, time=39.73 memory used=2280.7MB, alloc=540.3MB, time=40.73 memory used=2486.0MB, alloc=564.3MB, time=44.16 memory used=2673.1MB, alloc=588.3MB, time=47.55 memory used=2859.2MB, alloc=612.3MB, time=50.25 memory used=3066.8MB, alloc=636.3MB, time=54.54 memory used=3220.6MB, alloc=636.3MB, time=57.42 memory used=3377.4MB, alloc=636.3MB, time=59.95 memory used=3542.2MB, alloc=636.3MB, time=62.65 memory used=3704.5MB, alloc=660.3MB, time=65.29 memory used=3867.4MB, alloc=660.3MB, time=68.40 memory used=4009.5MB, alloc=660.3MB, time=71.74 memory used=4122.8MB, alloc=684.3MB, time=73.99 memory used=4241.3MB, alloc=684.3MB, time=76.79 memory used=4338.3MB, alloc=684.3MB, time=79.15 memory used=4411.0MB, alloc=684.3MB, time=80.97 memory used=4773.9MB, alloc=708.3MB, time=87.91 memory used=5159.0MB, alloc=732.3MB, time=95.03 memory used=5515.5MB, alloc=756.3MB, time=102.26 |\^/| 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(); 1428247387 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 F := [-18 x y - 20 x y + 4 y + 2 y z, -11 x z - 7 x y - y + 12 z, 3 2 2 5 x y z - 16 y + 7 y z + 17 x ] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 2 G := [19 x - 6 x z + 13 y + 15, 19 x + 6 x z - 20 x z + 14 y, 2 2 2 18 x z - 16 y - 19 z + 13 x] > Problem := [F,G]; 2 2 3 2 Problem := [[-18 x y - 20 x y + 4 y + 2 y z, -11 x z - 7 x y - y + 12 z, 3 2 2 3 2 5 x y z - 16 y + 7 y z + 17 x ], [19 x - 6 x z + 13 y + 15, 3 2 2 2 2 2 19 x + 6 x z - 20 x z + 14 y, 18 x z - 16 y - 19 z + 13 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=25.8MB, alloc=32.3MB, time=0.50 memory used=46.6MB, alloc=60.3MB, time=0.77 memory used=87.1MB, alloc=60.3MB, time=1.34 memory used=128.5MB, alloc=60.3MB, time=1.94 memory used=165.1MB, alloc=60.3MB, time=2.38 memory used=209.5MB, alloc=92.3MB, time=2.91 memory used=288.1MB, alloc=92.3MB, time=3.75 memory used=355.0MB, alloc=92.3MB, time=4.70 memory used=420.4MB, alloc=372.3MB, time=5.61 memory used=514.8MB, alloc=372.3MB, time=6.88 memory used=601.6MB, alloc=396.3MB, time=8.16 memory used=718.6MB, alloc=396.3MB, time=9.67 memory used=841.2MB, alloc=420.3MB, time=11.13 memory used=947.0MB, alloc=420.3MB, time=12.12 memory used=1084.6MB, alloc=420.3MB, time=14.16 memory used=1212.2MB, alloc=444.3MB, time=15.73 memory used=1291.8MB, alloc=444.3MB, time=16.31 memory used=1436.1MB, alloc=444.3MB, time=17.70 memory used=1562.1MB, alloc=444.3MB, time=19.31 memory used=1658.8MB, alloc=444.3MB, time=20.82 memory used=1755.8MB, alloc=468.3MB, time=22.24 memory used=1895.8MB, alloc=468.3MB, time=23.49 memory used=1977.8MB, alloc=468.3MB, time=24.75 memory used=2114.1MB, alloc=468.3MB, time=26.25 memory used=2190.1MB, alloc=468.3MB, time=27.49 memory used=2293.8MB, alloc=492.3MB, time=28.95 memory used=2443.1MB, alloc=492.3MB, time=30.90 memory used=2533.5MB, alloc=492.3MB, time=31.32 memory used=2611.2MB, alloc=492.3MB, time=31.67 memory used=2717.1MB, alloc=492.3MB, time=32.30 memory used=2814.6MB, alloc=492.3MB, time=33.61 memory used=2898.0MB, alloc=492.3MB, time=33.98 memory used=2999.2MB, alloc=492.3MB, time=34.45 memory used=3124.6MB, alloc=492.3MB, time=35.74 memory used=3208.3MB, alloc=492.3MB, time=37.21 memory used=3282.6MB, alloc=492.3MB, time=38.54 memory used=3338.9MB, alloc=492.3MB, time=39.49 memory used=3402.4MB, alloc=516.3MB, time=40.39 memory used=3465.9MB, alloc=516.3MB, time=41.39 memory used=3524.1MB, alloc=516.3MB, time=42.53 memory used=3576.7MB, alloc=516.3MB, time=43.45 memory used=3615.4MB, alloc=516.3MB, time=44.35 memory used=3814.2MB, alloc=540.3MB, time=46.74 memory used=4022.5MB, alloc=564.3MB, time=49.84 memory used=4195.4MB, alloc=588.3MB, time=52.63 memory used=4379.7MB, alloc=588.3MB, time=55.52 memory used=4561.9MB, alloc=612.3MB, time=58.86 memory used=4712.2MB, alloc=612.3MB, time=61.05 memory used=4864.5MB, alloc=636.3MB, time=63.76 memory used=4990.4MB, alloc=636.3MB, time=66.01 memory used=5118.1MB, alloc=636.3MB, time=68.60 memory used=5252.6MB, alloc=636.3MB, time=71.14 memory used=5334.9MB, alloc=636.3MB, time=72.90 memory used=5446.8MB, alloc=636.3MB, time=74.87 memory used=5575.8MB, alloc=636.3MB, time=76.81 memory used=5756.5MB, alloc=660.3MB, time=78.93 memory used=5948.0MB, alloc=660.3MB, time=82.72 memory used=6090.2MB, alloc=660.3MB, time=83.68 memory used=6272.9MB, alloc=660.3MB, time=85.20 memory used=6557.8MB, alloc=660.3MB, time=86.98 memory used=6814.9MB, alloc=660.3MB, time=88.12 memory used=7070.7MB, alloc=660.3MB, time=90.33 memory used=7185.1MB, alloc=660.3MB, time=92.56 memory used=7559.4MB, alloc=684.3MB, time=96.65 memory used=7927.1MB, alloc=708.3MB, time=101.70 memory used=8221.4MB, alloc=732.3MB, time=105.34 memory used=8489.1MB, alloc=732.3MB, time=110.34 memory used=8682.7MB, alloc=732.3MB, time=111.92 memory used=9010.6MB, alloc=732.3MB, time=115.91 memory used=9481.5MB, alloc=756.3MB, time=122.36 |\^/| 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(); 1428247687 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 F := [-19 x z + 18 x z - 7 y, 5 x y + 14 y - 9 x y - 6 z , 2 2 20 x z - 2 y + 7 y z - 7] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 3 2 G := [3 x y - 14 x z + 15 y + 7 z, -15 y z - 8 z - 9 y + 13, 3 2 3 -12 x + 2 x z - 2 y - 12 x y] > Problem := [F,G]; 2 2 2 3 2 Problem := [[-19 x z + 18 x z - 7 y, 5 x y + 14 y - 9 x y - 6 z , 2 2 2 2 3 20 x z - 2 y + 7 y z - 7], [3 x y - 14 x z + 15 y + 7 z, 2 3 2 3 2 3 -15 y z - 8 z - 9 y + 13, -12 x + 2 x z - 2 y - 12 x y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.18 memory used=27.0MB, alloc=32.3MB, time=0.41 memory used=48.9MB, alloc=36.3MB, time=0.66 memory used=74.8MB, alloc=36.3MB, time=1.06 memory used=94.9MB, alloc=36.3MB, time=1.21 memory used=121.2MB, alloc=36.3MB, time=3.02 memory used=138.3MB, alloc=37.0MB, time=3.08 memory used=149.6MB, alloc=37.0MB, time=3.12 memory used=164.7MB, alloc=61.0MB, time=4.55 memory used=193.6MB, alloc=85.0MB, time=7.19 memory used=324.3MB, alloc=117.0MB, time=13.03 memory used=411.3MB, alloc=119.8MB, time=14.03 memory used=486.3MB, alloc=120.0MB, time=14.23 memory used=567.7MB, alloc=120.0MB, time=14.55 memory used=621.8MB, alloc=120.0MB, time=14.70 memory used=686.3MB, alloc=120.0MB, time=14.87 memory used=764.0MB, alloc=120.0MB, time=15.04 memory used=812.4MB, alloc=120.0MB, time=15.16 memory used=938.9MB, alloc=120.0MB, time=16.47 memory used=1059.6MB, alloc=120.0MB, time=17.06 memory used=1212.4MB, alloc=120.0MB, time=18.70 memory used=1340.1MB, alloc=120.0MB, time=19.14 memory used=1433.0MB, alloc=120.0MB, time=20.28 memory used=1489.8MB, alloc=120.0MB, time=20.42 memory used=1549.0MB, alloc=120.0MB, time=20.75 memory used=1632.5MB, alloc=120.0MB, time=21.63 memory used=1755.3MB, alloc=122.3MB, time=23.95 memory used=1869.1MB, alloc=378.3MB, time=26.54 memory used=1994.9MB, alloc=378.3MB, time=30.21 memory used=2085.7MB, alloc=378.3MB, time=31.47 memory used=2150.4MB, alloc=378.3MB, time=32.29 memory used=2229.2MB, alloc=378.3MB, time=32.91 memory used=2298.5MB, alloc=378.3MB, time=33.38 memory used=2352.5MB, alloc=378.3MB, time=33.68 memory used=2439.1MB, alloc=378.3MB, time=34.60 memory used=2526.1MB, alloc=378.3MB, time=35.70 memory used=2571.6MB, alloc=378.3MB, time=35.81 memory used=2629.6MB, alloc=378.3MB, time=38.21 memory used=2673.5MB, alloc=378.3MB, time=38.36 memory used=2722.4MB, alloc=378.3MB, time=38.51 memory used=2762.6MB, alloc=378.3MB, time=38.62 memory used=2799.7MB, alloc=378.3MB, time=38.73 memory used=2843.2MB, alloc=378.3MB, time=38.85 memory used=2895.4MB, alloc=378.3MB, time=38.97 memory used=2994.7MB, alloc=378.3MB, time=39.91 memory used=3081.3MB, alloc=378.3MB, time=41.01 memory used=3171.7MB, alloc=402.3MB, time=54.71 memory used=3239.6MB, alloc=426.3MB, time=73.29 memory used=3326.2MB, alloc=426.3MB, time=73.54 memory used=3396.7MB, alloc=426.3MB, time=73.77 memory used=3448.2MB, alloc=426.3MB, time=73.97 memory used=3497.3MB, alloc=426.3MB, time=74.17 memory used=3545.1MB, alloc=426.3MB, time=74.36 memory used=3593.3MB, alloc=426.3MB, time=74.56 memory used=3641.5MB, alloc=426.3MB, time=74.75 memory used=3685.6MB, alloc=426.3MB, time=74.95 memory used=3730.1MB, alloc=426.3MB, time=75.15 memory used=3774.8MB, alloc=426.3MB, time=75.34 memory used=3819.7MB, alloc=426.3MB, time=75.53 memory used=3864.8MB, alloc=426.3MB, time=75.73 memory used=3910.1MB, alloc=426.3MB, time=75.91 memory used=3956.0MB, alloc=426.3MB, time=76.11 memory used=4002.0MB, alloc=426.3MB, time=76.31 memory used=4048.1MB, alloc=426.3MB, time=76.49 memory used=4094.3MB, alloc=426.3MB, time=76.68 memory used=4140.6MB, alloc=426.3MB, time=76.88 memory used=4187.1MB, alloc=426.3MB, time=77.09 memory used=4233.6MB, alloc=426.3MB, time=77.28 memory used=4280.3MB, alloc=450.3MB, time=77.48 memory used=4342.6MB, alloc=450.3MB, time=77.74 memory used=4410.4MB, alloc=450.3MB, time=77.97 memory used=4478.5MB, alloc=450.3MB, time=78.20 memory used=4546.6MB, alloc=450.3MB, time=78.43 memory used=4615.0MB, alloc=450.3MB, time=78.67 memory used=4683.4MB, alloc=450.3MB, time=78.90 memory used=4751.9MB, alloc=450.3MB, time=79.13 memory used=4820.5MB, alloc=450.3MB, time=79.37 memory used=4889.5MB, alloc=450.3MB, time=79.61 memory used=4963.6MB, alloc=450.3MB, time=79.86 memory used=5037.7MB, alloc=450.3MB, time=80.09 memory used=5111.8MB, alloc=450.3MB, time=80.34 memory used=5185.9MB, alloc=450.3MB, time=80.57 memory used=5260.3MB, alloc=450.3MB, time=80.82 memory used=5339.7MB, alloc=450.3MB, time=81.06 memory used=5419.0MB, alloc=450.3MB, time=81.31 memory used=5498.3MB, alloc=450.3MB, time=81.53 memory used=5577.5MB, alloc=450.3MB, time=81.77 memory used=5656.7MB, alloc=450.3MB, time=82.01 memory used=5740.9MB, alloc=450.3MB, time=82.26 memory used=5824.8MB, alloc=450.3MB, time=82.51 memory used=5908.5MB, alloc=450.3MB, time=82.75 memory used=5992.1MB, alloc=450.3MB, time=83.00 memory used=6080.5MB, alloc=450.3MB, time=83.24 memory used=6168.5MB, alloc=450.3MB, time=83.50 memory used=6256.3MB, alloc=450.3MB, time=83.76 memory used=6348.6MB, alloc=450.3MB, time=84.01 memory used=6440.4MB, alloc=450.3MB, time=84.26 memory used=6531.8MB, alloc=450.3MB, time=84.51 memory used=6627.5MB, alloc=450.3MB, time=84.78 memory used=6722.4MB, alloc=450.3MB, time=85.02 memory used=6816.8MB, alloc=450.3MB, time=85.26 memory used=6915.1MB, alloc=450.3MB, time=85.51 memory used=7012.6MB, alloc=450.3MB, time=85.76 memory used=7113.7MB, alloc=450.3MB, time=86.01 memory used=7213.9MB, alloc=450.3MB, time=86.27 memory used=7317.4MB, alloc=450.3MB, time=86.54 memory used=7424.0MB, alloc=450.3MB, time=86.81 memory used=7529.1MB, alloc=450.3MB, time=87.07 memory used=7635.5MB, alloc=450.3MB, time=87.33 memory used=7720.8MB, alloc=450.3MB, time=87.55 memory used=7792.6MB, alloc=450.3MB, time=87.75 memory used=7857.2MB, alloc=450.3MB, time=87.94 memory used=7919.0MB, alloc=450.3MB, time=88.14 memory used=7977.3MB, alloc=450.3MB, time=88.32 memory used=8031.7MB, alloc=450.3MB, time=88.50 memory used=8086.6MB, alloc=450.3MB, time=88.68 memory used=8141.6MB, alloc=450.3MB, time=88.86 memory used=8199.6MB, alloc=450.3MB, time=89.05 memory used=8256.5MB, alloc=450.3MB, time=89.23 memory used=8312.5MB, alloc=450.3MB, time=89.42 memory used=8371.0MB, alloc=450.3MB, time=89.60 memory used=8428.4MB, alloc=450.3MB, time=89.78 memory used=8487.9MB, alloc=450.3MB, time=89.97 memory used=8549.4MB, alloc=450.3MB, time=90.16 memory used=8609.3MB, alloc=450.3MB, time=90.35 memory used=8670.7MB, alloc=450.3MB, time=90.54 memory used=8733.2MB, alloc=450.3MB, time=90.72 memory used=8796.5MB, alloc=450.3MB, time=90.91 memory used=8860.3MB, alloc=450.3MB, time=91.09 memory used=8926.6MB, alloc=450.3MB, time=91.28 memory used=8992.1MB, alloc=450.3MB, time=91.47 memory used=9058.7MB, alloc=450.3MB, time=91.66 memory used=9127.3MB, alloc=450.3MB, time=91.85 memory used=9198.1MB, alloc=450.3MB, time=92.04 memory used=9269.9MB, alloc=450.3MB, time=92.23 memory used=9344.1MB, alloc=450.3MB, time=92.42 memory used=9442.3MB, alloc=450.3MB, time=123.95 memory used=9559.0MB, alloc=450.3MB, time=124.27 memory used=9645.5MB, alloc=450.3MB, time=124.55 memory used=9712.9MB, alloc=450.3MB, time=124.80 memory used=9777.2MB, alloc=450.3MB, time=125.05 memory used=9839.4MB, alloc=450.3MB, time=125.28 memory used=9897.5MB, alloc=450.3MB, time=125.50 memory used=9956.4MB, alloc=450.3MB, time=125.74 memory used=10016.0MB, alloc=450.3MB, time=125.97 memory used=10075.8MB, alloc=450.3MB, time=126.20 memory used=10136.0MB, alloc=450.3MB, time=126.42 memory used=10197.2MB, alloc=450.3MB, time=126.65 memory used=10258.7MB, alloc=450.3MB, time=126.90 memory used=10320.4MB, alloc=450.3MB, time=127.12 memory used=10382.3MB, alloc=450.3MB, time=127.33 memory used=10444.4MB, alloc=450.3MB, time=127.57 memory used=10506.7MB, alloc=450.3MB, time=127.79 memory used=10569.4MB, alloc=450.3MB, time=128.02 memory used=10637.3MB, alloc=450.3MB, time=128.27 memory used=10705.3MB, alloc=450.3MB, time=128.50 memory used=10773.5MB, alloc=450.3MB, time=128.74 memory used=10841.8MB, alloc=450.3MB, time=128.99 memory used=10910.2MB, alloc=450.3MB, time=129.21 memory used=10978.7MB, alloc=450.3MB, time=129.45 memory used=11047.6MB, alloc=450.3MB, time=129.69 memory used=11121.6MB, alloc=450.3MB, time=129.94 memory used=11195.7MB, alloc=450.3MB, time=130.18 memory used=11269.8MB, alloc=450.3MB, time=130.41 memory used=11343.9MB, alloc=450.3MB, time=130.66 memory used=11418.0MB, alloc=450.3MB, time=130.90 memory used=11492.4MB, alloc=450.3MB, time=131.14 memory used=11571.8MB, alloc=450.3MB, time=131.38 memory used=11651.2MB, alloc=450.3MB, time=131.62 memory used=11730.4MB, alloc=450.3MB, time=131.86 memory used=11809.6MB, alloc=450.3MB, time=132.12 memory used=11888.8MB, alloc=450.3MB, time=132.36 memory used=11973.0MB, alloc=450.3MB, time=132.60 memory used=12057.0MB, alloc=450.3MB, time=132.85 memory used=12140.6MB, alloc=450.3MB, time=133.10 memory used=12224.3MB, alloc=450.3MB, time=133.34 memory used=12312.7MB, alloc=450.3MB, time=133.60 memory used=12400.7MB, alloc=450.3MB, time=133.84 memory used=12488.5MB, alloc=450.3MB, time=134.08 memory used=12580.8MB, alloc=450.3MB, time=134.33 memory used=12672.6MB, alloc=450.3MB, time=134.57 memory used=12764.0MB, alloc=450.3MB, time=134.82 memory used=12859.7MB, alloc=450.3MB, time=135.08 memory used=12954.8MB, alloc=450.3MB, time=135.34 memory used=13054.0MB, alloc=450.3MB, time=135.59 memory used=13152.4MB, alloc=450.3MB, time=135.86 memory used=13254.5MB, alloc=450.3MB, time=136.11 memory used=13355.7MB, alloc=450.3MB, time=136.36 memory used=13460.3MB, alloc=450.3MB, time=136.61 memory used=13563.6MB, alloc=450.3MB, time=136.87 memory used=13670.1MB, alloc=450.3MB, time=137.13 memory used=13779.4MB, alloc=450.3MB, time=137.41 memory used=13883.3MB, alloc=450.3MB, time=137.69 memory used=13963.2MB, alloc=450.3MB, time=137.89 memory used=14032.2MB, alloc=450.3MB, time=138.10 memory used=14097.1MB, alloc=450.3MB, time=138.31 memory used=14158.8MB, alloc=450.3MB, time=138.51 memory used=14217.1MB, alloc=450.3MB, time=138.70 memory used=14271.5MB, alloc=450.3MB, time=138.88 memory used=14326.6MB, alloc=450.3MB, time=139.06 memory used=14381.5MB, alloc=450.3MB, time=139.25 memory used=14439.3MB, alloc=450.3MB, time=139.43 memory used=14496.2MB, alloc=450.3MB, time=139.62 memory used=14555.6MB, alloc=450.3MB, time=139.81 memory used=14614.0MB, alloc=450.3MB, time=140.00 memory used=14674.6MB, alloc=450.3MB, time=140.19 memory used=14733.9MB, alloc=450.3MB, time=140.38 memory used=14795.0MB, alloc=450.3MB, time=140.57 memory used=14857.7MB, alloc=450.3MB, time=140.75 memory used=14918.6MB, alloc=450.3MB, time=140.94 memory used=14980.6MB, alloc=450.3MB, time=141.12 memory used=15043.4MB, alloc=450.3MB, time=141.29 memory used=15109.3MB, alloc=450.3MB, time=141.48 memory used=15174.8MB, alloc=450.3MB, time=141.67 memory used=15241.9MB, alloc=450.3MB, time=141.86 memory used=15309.7MB, alloc=450.3MB, time=142.06 memory used=15378.9MB, alloc=450.3MB, time=142.25 memory used=15449.6MB, alloc=450.3MB, time=142.44 memory used=15522.1MB, alloc=450.3MB, time=142.63 memory used=15597.2MB, alloc=450.3MB, time=142.82 memory used=15741.4MB, alloc=450.3MB, time=144.59 memory used=15829.1MB, alloc=450.3MB, time=144.81 memory used=15918.9MB, alloc=450.3MB, time=145.03 memory used=16010.4MB, alloc=450.3MB, time=145.24 memory used=16103.0MB, alloc=450.3MB, time=145.46 memory used=16198.1MB, alloc=450.3MB, time=145.67 memory used=16294.4MB, alloc=450.3MB, time=145.88 memory used=16392.7MB, alloc=450.3MB, time=146.10 memory used=16492.7MB, alloc=450.3MB, time=146.30 memory used=16594.9MB, alloc=450.3MB, time=146.51 memory used=16701.4MB, alloc=450.3MB, time=146.72 memory used=16809.8MB, alloc=450.3MB, time=146.93 memory used=16914.8MB, alloc=450.3MB, time=158.61 memory used=17003.7MB, alloc=450.3MB, time=158.91 memory used=17098.4MB, alloc=450.3MB, time=159.21 memory used=17197.8MB, alloc=450.3MB, time=159.51 memory used=17301.6MB, alloc=450.3MB, time=159.83 memory used=17409.6MB, alloc=450.3MB, time=160.14 memory used=17521.8MB, alloc=450.3MB, time=160.45 memory used=17598.0MB, alloc=450.3MB, time=160.71 memory used=17664.3MB, alloc=450.3MB, time=160.97 memory used=17727.3MB, alloc=450.3MB, time=161.22 memory used=17789.5MB, alloc=450.3MB, time=161.44 memory used=17850.6MB, alloc=450.3MB, time=161.68 memory used=17915.0MB, alloc=450.3MB, time=161.91 memory used=17979.3MB, alloc=450.3MB, time=162.13 memory used=18046.3MB, alloc=450.3MB, time=162.35 memory used=18113.0MB, alloc=450.3MB, time=162.58 memory used=18182.2MB, alloc=450.3MB, time=162.83 memory used=18253.9MB, alloc=450.3MB, time=163.08 memory used=18327.6MB, alloc=450.3MB, time=163.30 memory used=18400.5MB, alloc=450.3MB, time=163.54 memory used=18475.4MB, alloc=450.3MB, time=163.78 memory used=18554.6MB, alloc=450.3MB, time=164.02 memory used=18635.0MB, alloc=450.3MB, time=164.27 memory used=18716.3MB, alloc=450.3MB, time=164.51 memory used=18800.6MB, alloc=450.3MB, time=164.76 memory used=18887.3MB, alloc=450.3MB, time=165.00 memory used=18975.5MB, alloc=450.3MB, time=165.24 memory used=19066.7MB, alloc=450.3MB, time=165.49 memory used=19161.3MB, alloc=450.3MB, time=165.74 memory used=19259.1MB, alloc=450.3MB, time=165.98 memory used=19361.8MB, alloc=450.3MB, time=166.23 memory used=19470.1MB, alloc=450.3MB, time=166.48 |\^/| 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(); 1428247987 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 2 F := [16 x y + 14 y z - 4 x - 15 x y, -5 x z - 5 x y + 2 z + 12, 2 3 3 2 9 x z - 11 y - 14 z + 15 z ] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 2 2 G := [-18 y + 15 y z - 18 x - 17 z , 7 x z - y z - 14 z - 17 x, 2 2 2 -2 x y - 16 y z + 19 y z + 10 x] > Problem := [F,G]; 2 2 2 2 2 2 Problem := [[16 x y + 14 y z - 4 x - 15 x y, -5 x z - 5 x y + 2 z + 12, 2 3 3 2 3 2 2 2 9 x z - 11 y - 14 z + 15 z ], [-18 y + 15 y z - 18 x - 17 z , 2 2 2 2 2 2 7 x z - y z - 14 z - 17 x, -2 x y - 16 y z + 19 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=4.4MB, alloc=32.3MB, time=0.17 memory used=30.1MB, alloc=32.7MB, time=0.41 memory used=43.6MB, alloc=32.7MB, time=0.45 memory used=64.6MB, alloc=32.7MB, time=0.66 memory used=84.6MB, alloc=32.7MB, time=0.93 memory used=104.0MB, alloc=32.8MB, time=1.05 memory used=119.5MB, alloc=32.8MB, time=1.12 memory used=136.2MB, alloc=56.9MB, time=2.52 memory used=179.2MB, alloc=59.4MB, time=3.15 memory used=207.8MB, alloc=59.4MB, time=3.22 memory used=233.5MB, alloc=59.4MB, time=3.27 memory used=266.1MB, alloc=59.4MB, time=3.33 memory used=292.6MB, alloc=59.4MB, time=3.39 memory used=313.9MB, alloc=59.4MB, time=3.43 memory used=337.8MB, alloc=59.4MB, time=3.47 memory used=365.7MB, alloc=59.4MB, time=3.52 memory used=403.6MB, alloc=63.4MB, time=3.71 memory used=431.8MB, alloc=63.4MB, time=3.77 memory used=458.7MB, alloc=63.4MB, time=3.83 memory used=494.8MB, alloc=63.4MB, time=4.00 memory used=520.6MB, alloc=63.4MB, time=4.07 memory used=549.4MB, alloc=63.4MB, time=4.13 memory used=587.1MB, alloc=63.4MB, time=7.84 memory used=634.3MB, alloc=64.1MB, time=8.86 memory used=665.7MB, alloc=64.1MB, time=8.94 memory used=687.8MB, alloc=64.1MB, time=9.01 memory used=714.2MB, alloc=64.1MB, time=9.07 memory used=745.7MB, alloc=64.1MB, time=9.15 memory used=778.0MB, alloc=64.1MB, time=9.22 memory used=797.8MB, alloc=64.1MB, time=9.28 memory used=818.9MB, alloc=64.1MB, time=9.33 memory used=841.7MB, alloc=64.1MB, time=9.38 memory used=865.9MB, alloc=64.1MB, time=9.46 memory used=892.7MB, alloc=64.1MB, time=9.51 memory used=921.4MB, alloc=64.1MB, time=9.56 memory used=954.0MB, alloc=64.1MB, time=9.62 memory used=996.9MB, alloc=64.1MB, time=10.28 memory used=1025.4MB, alloc=64.1MB, time=10.35 memory used=1052.3MB, alloc=64.1MB, time=10.42 memory used=1082.2MB, alloc=64.1MB, time=10.49 memory used=1104.9MB, alloc=64.1MB, time=10.54 memory used=1148.1MB, alloc=64.1MB, time=10.96 memory used=1210.4MB, alloc=64.1MB, time=15.72 memory used=1244.3MB, alloc=64.1MB, time=15.85 memory used=1272.8MB, alloc=64.1MB, time=15.93 memory used=1294.6MB, alloc=64.1MB, time=16.01 memory used=1320.2MB, alloc=64.1MB, time=16.09 memory used=1350.4MB, alloc=64.1MB, time=16.16 memory used=1380.7MB, alloc=64.1MB, time=16.25 memory used=1399.4MB, alloc=64.1MB, time=16.30 memory used=1419.1MB, alloc=64.1MB, time=16.36 memory used=1440.4MB, alloc=64.1MB, time=16.41 memory used=1462.6MB, alloc=64.1MB, time=16.47 memory used=1486.9MB, alloc=64.1MB, time=16.53 memory used=1513.3MB, alloc=64.1MB, time=16.59 memory used=1542.2MB, alloc=64.1MB, time=16.65 memory used=1574.6MB, alloc=64.1MB, time=16.71 memory used=1623.1MB, alloc=64.1MB, time=17.17 memory used=1668.6MB, alloc=72.1MB, time=17.85 memory used=1709.9MB, alloc=72.1MB, time=18.32 memory used=1752.1MB, alloc=72.1MB, time=18.91 memory used=1787.8MB, alloc=72.1MB, time=19.19 memory used=1811.8MB, alloc=72.1MB, time=19.28 memory used=1831.7MB, alloc=72.1MB, time=19.37 memory used=1853.4MB, alloc=72.1MB, time=19.45 memory used=1874.3MB, alloc=72.1MB, time=19.60 memory used=1904.9MB, alloc=72.1MB, time=19.77 memory used=1922.5MB, alloc=72.1MB, time=19.85 memory used=1946.4MB, alloc=72.1MB, time=19.93 memory used=1962.4MB, alloc=72.1MB, time=20.00 memory used=1990.2MB, alloc=72.1MB, time=20.34 memory used=2033.6MB, alloc=72.1MB, time=25.47 memory used=2063.4MB, alloc=96.1MB, time=25.62 memory used=2102.0MB, alloc=96.1MB, time=25.74 memory used=2134.4MB, alloc=96.1MB, time=25.84 memory used=2174.9MB, alloc=96.1MB, time=25.96 memory used=2213.9MB, alloc=96.1MB, time=26.06 memory used=2241.8MB, alloc=96.1MB, time=26.15 memory used=2271.9MB, alloc=96.1MB, time=26.23 memory used=2305.9MB, alloc=96.1MB, time=26.31 memory used=2344.7MB, alloc=96.1MB, time=26.42 memory used=2397.1MB, alloc=96.1MB, time=27.09 memory used=2433.5MB, alloc=96.1MB, time=27.20 memory used=2474.6MB, alloc=96.1MB, time=27.30 memory used=2519.2MB, alloc=96.1MB, time=27.63 memory used=2559.3MB, alloc=96.1MB, time=27.76 memory used=2595.5MB, alloc=96.1MB, time=27.86 memory used=2646.8MB, alloc=96.1MB, time=30.31 memory used=2684.7MB, alloc=96.1MB, time=30.42 memory used=2720.8MB, alloc=96.1MB, time=30.54 memory used=2761.7MB, alloc=96.1MB, time=30.64 memory used=2790.7MB, alloc=96.1MB, time=30.72 memory used=2833.1MB, alloc=96.1MB, time=30.90 memory used=2877.5MB, alloc=96.1MB, time=31.30 memory used=2920.3MB, alloc=96.1MB, time=31.54 memory used=2997.5MB, alloc=96.1MB, time=32.74 memory used=3056.4MB, alloc=96.1MB, time=33.33 memory used=3149.8MB, alloc=96.1MB, time=34.70 memory used=3226.5MB, alloc=96.1MB, time=36.61 memory used=3303.4MB, alloc=96.1MB, time=39.05 memory used=3374.2MB, alloc=96.1MB, time=41.26 memory used=3408.7MB, alloc=96.1MB, time=41.36 memory used=3447.7MB, alloc=96.1MB, time=41.46 memory used=3475.1MB, alloc=96.1MB, time=41.54 memory used=3516.4MB, alloc=96.1MB, time=41.79 memory used=3549.9MB, alloc=96.1MB, time=41.96 memory used=3582.0MB, alloc=107.8MB, time=42.22 memory used=3629.5MB, alloc=107.8MB, time=42.34 memory used=3665.5MB, alloc=107.8MB, time=42.44 memory used=3713.6MB, alloc=107.8MB, time=42.56 memory used=3770.9MB, alloc=107.8MB, time=43.31 memory used=3826.9MB, alloc=107.8MB, time=43.73 memory used=3881.3MB, alloc=107.8MB, time=44.30 memory used=3958.0MB, alloc=107.8MB, time=45.27 memory used=4019.7MB, alloc=107.8MB, time=45.94 memory used=4081.8MB, alloc=107.8MB, time=46.66 memory used=4145.3MB, alloc=107.8MB, time=48.19 memory used=4172.7MB, alloc=107.8MB, time=48.30 memory used=4219.2MB, alloc=107.8MB, time=48.62 memory used=4261.2MB, alloc=107.8MB, time=49.83 memory used=4292.5MB, alloc=107.8MB, time=49.95 memory used=4319.9MB, alloc=107.8MB, time=50.06 memory used=4375.8MB, alloc=107.8MB, time=50.64 memory used=4432.8MB, alloc=131.8MB, time=51.16 memory used=4491.2MB, alloc=131.8MB, time=51.89 memory used=4538.9MB, alloc=131.8MB, time=52.04 memory used=4617.4MB, alloc=131.8MB, time=52.85 memory used=4719.4MB, alloc=387.8MB, time=53.86 memory used=4806.8MB, alloc=387.8MB, time=55.12 memory used=4891.3MB, alloc=387.8MB, time=56.28 memory used=4978.5MB, alloc=411.8MB, time=57.18 memory used=5030.3MB, alloc=411.8MB, time=57.38 memory used=5080.9MB, alloc=411.8MB, time=57.55 memory used=5126.3MB, alloc=411.8MB, time=57.72 memory used=5182.2MB, alloc=411.8MB, time=57.88 memory used=5253.6MB, alloc=411.8MB, time=58.36 memory used=5312.4MB, alloc=411.8MB, time=58.56 memory used=5356.6MB, alloc=411.8MB, time=58.72 memory used=5405.9MB, alloc=411.8MB, time=58.89 memory used=5472.7MB, alloc=411.8MB, time=59.61 memory used=5565.9MB, alloc=411.8MB, time=69.29 memory used=5617.7MB, alloc=411.8MB, time=69.49 memory used=5668.1MB, alloc=411.8MB, time=69.66 memory used=5731.5MB, alloc=411.8MB, time=69.85 memory used=5769.2MB, alloc=411.8MB, time=70.01 memory used=5811.4MB, alloc=411.8MB, time=70.19 memory used=5858.3MB, alloc=411.8MB, time=70.35 memory used=5910.7MB, alloc=411.8MB, time=70.50 memory used=5968.5MB, alloc=411.8MB, time=70.66 memory used=6090.5MB, alloc=411.8MB, time=71.17 memory used=6148.5MB, alloc=411.8MB, time=71.39 memory used=6205.6MB, alloc=411.8MB, time=71.58 memory used=6248.0MB, alloc=411.8MB, time=71.74 memory used=6299.9MB, alloc=411.8MB, time=71.92 memory used=6373.9MB, alloc=411.8MB, time=72.43 memory used=6430.0MB, alloc=411.8MB, time=72.65 memory used=6485.9MB, alloc=411.8MB, time=72.84 memory used=6528.7MB, alloc=411.8MB, time=73.01 memory used=6581.1MB, alloc=411.8MB, time=73.18 memory used=6660.0MB, alloc=411.8MB, time=77.39 memory used=6743.0MB, alloc=411.8MB, time=83.68 memory used=6793.8MB, alloc=411.8MB, time=83.86 memory used=6845.5MB, alloc=411.8MB, time=84.03 memory used=6906.8MB, alloc=411.8MB, time=84.21 memory used=6944.8MB, alloc=411.8MB, time=84.35 memory used=6986.9MB, alloc=411.8MB, time=84.49 memory used=7034.3MB, alloc=411.8MB, time=84.64 memory used=7086.7MB, alloc=411.8MB, time=84.80 memory used=7143.9MB, alloc=411.8MB, time=84.95 memory used=7269.7MB, alloc=411.8MB, time=85.32 memory used=7333.0MB, alloc=411.8MB, time=85.71 memory used=7404.8MB, alloc=411.8MB, time=86.45 memory used=7453.4MB, alloc=411.8MB, time=86.65 memory used=7517.3MB, alloc=411.8MB, time=86.85 memory used=7557.4MB, alloc=411.8MB, time=87.06 memory used=7601.2MB, alloc=411.8MB, time=87.23 memory used=7650.2MB, alloc=411.8MB, time=87.40 memory used=7705.1MB, alloc=411.8MB, time=87.57 memory used=7767.8MB, alloc=411.8MB, time=87.76 memory used=7818.7MB, alloc=411.8MB, time=87.90 memory used=7855.9MB, alloc=411.8MB, time=88.04 memory used=7896.5MB, alloc=411.8MB, time=88.19 memory used=7971.6MB, alloc=411.8MB, time=100.89 memory used=8045.3MB, alloc=411.8MB, time=108.87 memory used=8098.7MB, alloc=411.8MB, time=109.06 memory used=8143.7MB, alloc=411.8MB, time=109.24 memory used=8200.5MB, alloc=411.8MB, time=109.42 memory used=8258.3MB, alloc=411.8MB, time=109.59 memory used=8295.3MB, alloc=411.8MB, time=109.75 memory used=8336.5MB, alloc=411.8MB, time=109.90 memory used=8380.2MB, alloc=411.8MB, time=110.05 memory used=8427.9MB, alloc=411.8MB, time=110.20 memory used=8480.3MB, alloc=411.8MB, time=110.36 memory used=8537.0MB, alloc=411.8MB, time=110.51 memory used=8599.0MB, alloc=411.8MB, time=110.68 memory used=8803.4MB, alloc=411.8MB, time=111.12 memory used=8889.3MB, alloc=411.8MB, time=111.57 memory used=9009.6MB, alloc=411.8MB, time=113.31 memory used=9111.2MB, alloc=411.8MB, time=118.41 memory used=9158.8MB, alloc=411.8MB, time=118.61 memory used=9207.4MB, alloc=411.8MB, time=118.79 memory used=9260.5MB, alloc=411.8MB, time=118.97 memory used=9296.7MB, alloc=411.8MB, time=119.14 memory used=9337.9MB, alloc=411.8MB, time=119.29 memory used=9384.2MB, alloc=411.8MB, time=119.44 memory used=9438.4MB, alloc=411.8MB, time=119.62 memory used=9506.4MB, alloc=411.8MB, time=120.07 memory used=9597.2MB, alloc=411.8MB, time=120.98 memory used=9719.6MB, alloc=435.8MB, time=122.19 memory used=9870.8MB, alloc=459.8MB, time=123.47 memory used=10039.2MB, alloc=459.8MB, time=125.04 memory used=10158.0MB, alloc=459.8MB, time=127.18 memory used=10257.9MB, alloc=459.8MB, time=128.66 memory used=10361.0MB, alloc=483.8MB, time=129.88 memory used=10463.4MB, alloc=507.8MB, time=131.45 memory used=10543.8MB, alloc=507.8MB, time=132.50 memory used=10625.0MB, alloc=507.8MB, time=133.91 memory used=10769.9MB, alloc=507.8MB, time=135.18 memory used=10867.5MB, alloc=507.8MB, time=135.61 memory used=10937.3MB, alloc=507.8MB, time=135.97 memory used=11043.3MB, alloc=507.8MB, time=136.64 memory used=11129.4MB, alloc=507.8MB, time=137.04 memory used=11205.8MB, alloc=507.8MB, time=137.40 memory used=11343.4MB, alloc=507.8MB, time=149.76 memory used=11424.6MB, alloc=507.8MB, time=150.15 memory used=11518.7MB, alloc=531.8MB, time=150.54 memory used=11596.7MB, alloc=531.8MB, time=150.86 memory used=11692.8MB, alloc=531.8MB, time=151.22 memory used=11852.8MB, alloc=531.8MB, time=151.85 memory used=11959.5MB, alloc=531.8MB, time=152.31 memory used=12054.4MB, alloc=531.8MB, time=152.70 memory used=12182.5MB, alloc=531.8MB, time=153.35 memory used=12274.6MB, alloc=531.8MB, time=153.74 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428248287 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 3 2 3 2 F := [9 x y + 14 x z - 13 y z - 11 z , -2 x - 13 x z + 6 z - 2 y , 2 9 x y + 18 x z + 5 y - 7] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 3 G := [7 x y z + 11 x + 19 y - x, 4 x y - 10 x z - 9 x z + 11 z , 3 2 2 11 x - 10 y z + 7 y + 4 y z] > Problem := [F,G]; 2 2 2 3 3 2 3 2 Problem := [[9 x y + 14 x z - 13 y z - 11 z , -2 x - 13 x z + 6 z - 2 y , 2 2 2 9 x y + 18 x z + 5 y - 7], [7 x y z + 11 x + 19 y - x, 2 2 2 3 3 2 2 4 x y - 10 x z - 9 x z + 11 z , 11 x - 10 y z + 7 y + 4 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.20 memory used=24.1MB, alloc=32.3MB, time=0.48 memory used=44.1MB, alloc=56.3MB, time=0.75 memory used=88.8MB, alloc=61.1MB, time=1.09 memory used=148.3MB, alloc=70.2MB, time=1.87 memory used=183.2MB, alloc=70.2MB, time=2.04 memory used=218.0MB, alloc=70.2MB, time=2.30 memory used=243.3MB, alloc=70.2MB, time=2.37 memory used=290.5MB, alloc=70.2MB, time=2.84 memory used=322.9MB, alloc=70.2MB, time=3.05 memory used=369.2MB, alloc=70.2MB, time=3.59 memory used=411.8MB, alloc=70.2MB, time=4.17 memory used=456.1MB, alloc=70.2MB, time=4.71 memory used=504.1MB, alloc=94.2MB, time=5.27 memory used=570.4MB, alloc=94.2MB, time=5.92 memory used=618.5MB, alloc=94.2MB, time=6.20 memory used=669.8MB, alloc=94.2MB, time=6.84 memory used=712.4MB, alloc=94.2MB, time=7.05 memory used=758.8MB, alloc=94.2MB, time=7.69 memory used=800.1MB, alloc=94.2MB, time=7.86 memory used=850.0MB, alloc=94.2MB, time=8.46 memory used=895.2MB, alloc=94.2MB, time=8.71 memory used=934.3MB, alloc=94.2MB, time=8.86 memory used=976.1MB, alloc=94.2MB, time=9.21 memory used=1019.7MB, alloc=94.2MB, time=9.36 memory used=1061.8MB, alloc=94.2MB, time=9.67 memory used=1108.3MB, alloc=94.2MB, time=9.87 memory used=1150.7MB, alloc=94.2MB, time=10.17 memory used=1218.0MB, alloc=94.2MB, time=10.82 memory used=1284.4MB, alloc=350.2MB, time=11.63 memory used=1370.5MB, alloc=350.2MB, time=12.54 memory used=1423.9MB, alloc=350.2MB, time=13.34 memory used=1467.0MB, alloc=350.2MB, time=14.52 memory used=1498.5MB, alloc=350.2MB, time=14.63 memory used=1559.1MB, alloc=350.2MB, time=15.16 memory used=1634.2MB, alloc=350.2MB, time=16.10 memory used=1696.9MB, alloc=374.2MB, time=17.00 memory used=1774.1MB, alloc=374.2MB, time=17.66 memory used=1822.8MB, alloc=374.2MB, time=17.91 memory used=1884.3MB, alloc=374.2MB, time=19.05 memory used=1924.8MB, alloc=374.2MB, time=19.20 memory used=1970.8MB, alloc=374.2MB, time=19.39 memory used=2019.6MB, alloc=374.2MB, time=19.62 memory used=2064.0MB, alloc=374.2MB, time=20.56 memory used=2113.3MB, alloc=374.2MB, time=20.97 memory used=2153.4MB, alloc=374.2MB, time=21.10 memory used=2201.5MB, alloc=374.2MB, time=21.30 memory used=2248.7MB, alloc=374.2MB, time=21.51 memory used=2308.9MB, alloc=374.2MB, time=22.66 memory used=2349.3MB, alloc=374.2MB, time=22.80 memory used=2400.8MB, alloc=374.2MB, time=23.20 memory used=2480.7MB, alloc=374.2MB, time=23.96 memory used=2582.7MB, alloc=374.2MB, time=26.37 memory used=2619.9MB, alloc=374.2MB, time=26.53 memory used=2660.4MB, alloc=374.2MB, time=26.67 memory used=2691.1MB, alloc=374.2MB, time=26.79 memory used=2782.0MB, alloc=398.2MB, time=27.59 memory used=2855.7MB, alloc=398.2MB, time=28.10 memory used=2918.5MB, alloc=398.2MB, time=28.35 memory used=2974.3MB, alloc=398.2MB, time=28.55 memory used=3020.1MB, alloc=398.2MB, time=28.73 memory used=3091.1MB, alloc=398.2MB, time=29.21 memory used=3147.9MB, alloc=398.2MB, time=29.42 memory used=3202.0MB, alloc=398.2MB, time=29.61 memory used=3249.4MB, alloc=398.2MB, time=29.78 memory used=3334.7MB, alloc=398.2MB, time=33.95 memory used=3407.5MB, alloc=398.2MB, time=34.29 memory used=3452.0MB, alloc=398.2MB, time=34.48 memory used=3509.2MB, alloc=398.2MB, time=34.66 memory used=3560.1MB, alloc=398.2MB, time=34.82 memory used=3600.8MB, alloc=398.2MB, time=34.98 memory used=3646.5MB, alloc=398.2MB, time=35.14 memory used=3714.3MB, alloc=398.2MB, time=35.46 memory used=3769.1MB, alloc=398.2MB, time=35.68 memory used=3822.3MB, alloc=398.2MB, time=35.86 memory used=3868.7MB, alloc=398.2MB, time=36.04 memory used=3940.9MB, alloc=398.2MB, time=36.45 memory used=3994.1MB, alloc=398.2MB, time=36.66 memory used=4043.3MB, alloc=398.2MB, time=36.85 memory used=4091.9MB, alloc=398.2MB, time=37.03 memory used=4171.0MB, alloc=398.2MB, time=41.29 memory used=4224.2MB, alloc=398.2MB, time=41.49 memory used=4272.8MB, alloc=398.2MB, time=41.68 memory used=4335.9MB, alloc=398.2MB, time=41.87 memory used=4377.6MB, alloc=398.2MB, time=42.03 memory used=4419.8MB, alloc=398.2MB, time=42.18 memory used=4467.7MB, alloc=398.2MB, time=42.34 memory used=4536.0MB, alloc=398.2MB, time=42.77 memory used=4592.0MB, alloc=398.2MB, time=42.99 memory used=4645.5MB, alloc=398.2MB, time=43.18 memory used=4691.3MB, alloc=398.2MB, time=43.37 memory used=4761.9MB, alloc=398.2MB, time=43.80 memory used=4816.1MB, alloc=398.2MB, time=44.01 memory used=4863.5MB, alloc=398.2MB, time=44.20 memory used=4913.0MB, alloc=398.2MB, time=44.39 memory used=5008.5MB, alloc=398.2MB, time=48.69 memory used=5061.4MB, alloc=398.2MB, time=48.89 memory used=5111.0MB, alloc=398.2MB, time=49.09 memory used=5174.2MB, alloc=398.2MB, time=49.27 memory used=5212.7MB, alloc=398.2MB, time=49.44 memory used=5255.3MB, alloc=398.2MB, time=49.62 memory used=5305.6MB, alloc=398.2MB, time=49.78 memory used=5378.5MB, alloc=398.2MB, time=50.61 memory used=5428.8MB, alloc=398.2MB, time=50.80 memory used=5489.8MB, alloc=398.2MB, time=51.15 memory used=5547.7MB, alloc=398.2MB, time=51.37 memory used=5595.6MB, alloc=398.2MB, time=51.56 memory used=5659.9MB, alloc=398.2MB, time=51.89 memory used=5717.0MB, alloc=398.2MB, time=52.11 memory used=5763.5MB, alloc=398.2MB, time=52.30 memory used=5831.9MB, alloc=398.2MB, time=53.60 memory used=5883.3MB, alloc=398.2MB, time=53.78 memory used=5939.0MB, alloc=398.2MB, time=53.96 memory used=5983.6MB, alloc=398.2MB, time=54.13 memory used=6047.2MB, alloc=398.2MB, time=54.46 memory used=6099.9MB, alloc=398.2MB, time=54.64 memory used=6150.8MB, alloc=398.2MB, time=54.82 memory used=6217.0MB, alloc=398.2MB, time=55.15 memory used=6267.3MB, alloc=398.2MB, time=55.34 memory used=6332.2MB, alloc=398.2MB, time=56.79 memory used=6395.0MB, alloc=398.2MB, time=57.04 memory used=6446.9MB, alloc=398.2MB, time=57.23 memory used=6494.4MB, alloc=398.2MB, time=57.38 memory used=6558.0MB, alloc=398.2MB, time=57.74 memory used=6610.9MB, alloc=398.2MB, time=57.93 memory used=6661.4MB, alloc=398.2MB, time=58.12 memory used=6727.7MB, alloc=398.2MB, time=58.46 memory used=6778.1MB, alloc=398.2MB, time=58.65 memory used=6844.0MB, alloc=398.2MB, time=60.01 memory used=6906.1MB, alloc=398.2MB, time=60.27 memory used=6957.9MB, alloc=398.2MB, time=60.45 memory used=7005.2MB, alloc=398.2MB, time=60.61 memory used=7073.0MB, alloc=398.2MB, time=61.14 memory used=7168.8MB, alloc=398.2MB, time=61.97 memory used=7293.8MB, alloc=398.2MB, time=64.69 memory used=7343.8MB, alloc=398.2MB, time=64.89 memory used=7392.9MB, alloc=398.2MB, time=65.08 memory used=7445.5MB, alloc=398.2MB, time=65.27 memory used=7484.4MB, alloc=398.2MB, time=65.43 memory used=7539.2MB, alloc=398.2MB, time=65.79 memory used=7657.0MB, alloc=398.2MB, time=67.11 memory used=7752.8MB, alloc=398.2MB, time=68.22 memory used=7851.5MB, alloc=422.2MB, time=69.62 memory used=7937.1MB, alloc=422.2MB, time=70.48 memory used=8009.6MB, alloc=422.2MB, time=70.95 memory used=8127.0MB, alloc=422.2MB, time=72.63 memory used=8239.9MB, alloc=446.2MB, time=73.97 memory used=8332.3MB, alloc=446.2MB, time=75.21 memory used=8426.3MB, alloc=446.2MB, time=76.53 memory used=8546.7MB, alloc=446.2MB, time=77.58 memory used=8643.7MB, alloc=446.2MB, time=79.99 memory used=8709.0MB, alloc=446.2MB, time=80.28 memory used=8791.3MB, alloc=446.2MB, time=80.67 memory used=8876.4MB, alloc=446.2MB, time=84.55 memory used=8952.7MB, alloc=446.2MB, time=85.14 memory used=9020.7MB, alloc=446.2MB, time=85.43 memory used=9087.1MB, alloc=446.2MB, time=85.90 memory used=9209.6MB, alloc=446.2MB, time=87.18 memory used=9281.0MB, alloc=446.2MB, time=87.51 memory used=9344.6MB, alloc=446.2MB, time=87.80 memory used=9455.4MB, alloc=446.2MB, time=96.04 memory used=9528.4MB, alloc=446.2MB, time=96.36 memory used=9587.5MB, alloc=446.2MB, time=96.69 memory used=9661.4MB, alloc=446.2MB, time=96.98 memory used=9717.3MB, alloc=446.2MB, time=97.32 memory used=9773.5MB, alloc=446.2MB, time=97.57 memory used=9843.3MB, alloc=446.2MB, time=97.86 memory used=9929.1MB, alloc=446.2MB, time=98.89 memory used=10075.7MB, alloc=446.2MB, time=100.28 memory used=10237.1MB, alloc=446.2MB, time=103.60 memory used=10346.8MB, alloc=470.2MB, time=105.36 memory used=10496.6MB, alloc=470.2MB, time=107.54 memory used=10633.6MB, alloc=470.2MB, time=111.05 memory used=10740.1MB, alloc=470.2MB, time=112.39 memory used=10854.4MB, alloc=470.2MB, time=113.77 memory used=10961.2MB, alloc=470.2MB, time=115.35 memory used=11037.9MB, alloc=470.2MB, time=115.70 memory used=11102.4MB, alloc=470.2MB, time=116.02 memory used=11184.1MB, alloc=470.2MB, time=116.36 memory used=11436.6MB, alloc=470.2MB, time=117.71 memory used=11533.9MB, alloc=470.2MB, time=119.10 memory used=11592.2MB, alloc=470.2MB, time=120.10 memory used=11662.9MB, alloc=470.2MB, time=121.26 memory used=11720.4MB, alloc=470.2MB, time=122.29 memory used=11828.4MB, alloc=494.2MB, time=123.20 memory used=11928.2MB, alloc=494.2MB, time=123.74 memory used=12037.6MB, alloc=494.2MB, time=125.68 memory used=12127.9MB, alloc=494.2MB, time=126.10 memory used=12219.3MB, alloc=494.2MB, time=126.58 memory used=12307.8MB, alloc=494.2MB, time=127.01 memory used=12408.4MB, alloc=494.2MB, time=127.52 memory used=12524.0MB, alloc=494.2MB, time=129.51 memory used=12606.9MB, alloc=494.2MB, time=129.86 memory used=12745.0MB, alloc=494.2MB, time=131.11 memory used=12847.2MB, alloc=494.2MB, time=131.63 memory used=12963.6MB, alloc=494.2MB, time=135.14 memory used=13050.9MB, alloc=494.2MB, time=135.55 memory used=13134.1MB, alloc=494.2MB, time=135.90 memory used=13212.6MB, alloc=494.2MB, time=136.25 memory used=13327.4MB, alloc=494.2MB, time=136.86 memory used=13415.5MB, alloc=494.2MB, time=137.29 memory used=13498.5MB, alloc=494.2MB, time=137.68 memory used=13629.0MB, alloc=494.2MB, time=144.15 memory used=13712.4MB, alloc=494.2MB, time=144.57 memory used=13797.3MB, alloc=494.2MB, time=144.95 memory used=13869.8MB, alloc=494.2MB, time=145.33 memory used=13957.2MB, alloc=494.2MB, time=145.69 memory used=14113.6MB, alloc=494.2MB, time=146.52 memory used=14201.0MB, alloc=494.2MB, time=146.94 memory used=14264.3MB, alloc=494.2MB, time=147.78 memory used=14330.0MB, alloc=494.2MB, time=149.17 memory used=14468.8MB, alloc=494.2MB, time=155.42 memory used=14559.2MB, alloc=494.2MB, time=155.87 memory used=14643.5MB, alloc=494.2MB, time=156.28 memory used=14724.2MB, alloc=494.2MB, time=156.64 memory used=14906.4MB, alloc=494.2MB, time=162.26 memory used=14993.3MB, alloc=494.2MB, time=162.70 memory used=15069.8MB, alloc=494.2MB, time=163.13 memory used=15166.1MB, alloc=494.2MB, time=163.55 memory used=15248.3MB, alloc=518.2MB, time=163.96 memory used=15325.5MB, alloc=518.2MB, time=164.35 memory used=15413.3MB, alloc=518.2MB, time=164.76 memory used=15510.0MB, alloc=518.2MB, time=165.17 memory used=15617.5MB, alloc=518.2MB, time=165.57 memory used=15735.3MB, alloc=518.2MB, time=165.98 memory used=15876.8MB, alloc=518.2MB, time=166.41 memory used=16040.7MB, alloc=518.2MB, time=166.93 memory used=16187.0MB, alloc=518.2MB, time=167.41 memory used=16348.8MB, alloc=518.2MB, time=167.88 memory used=16533.8MB, alloc=518.2MB, time=168.36 |\^/| 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(); 1428248587 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-17 x y z + 12 y z + y z - 7 y, 3 x y + 17 x y + 17 x z - 3 x, 3 20 x y z + y - 3 x z + 9 z] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 G := [19 x y - 19 y z - 20 x y - y, -5 x y z + 5 y + 13 x - 16, 3 -5 z - 2 x y + 5 y + 3 z] > Problem := [F,G]; 2 2 Problem := [[-17 x y z + 12 y z + y z - 7 y, 3 x y + 17 x y + 17 x z - 3 x, 3 2 2 20 x y z + y - 3 x z + 9 z], [19 x y - 19 y z - 20 x y - y, 3 3 -5 x y z + 5 y + 13 x - 16, -5 z - 2 x y + 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=4.3MB, alloc=32.3MB, time=0.17 memory used=25.6MB, alloc=32.3MB, time=0.49 memory used=46.2MB, alloc=32.3MB, time=0.79 memory used=65.0MB, alloc=56.3MB, time=1.09 memory used=105.0MB, alloc=60.3MB, time=1.69 memory used=140.5MB, alloc=84.3MB, time=2.19 memory used=202.9MB, alloc=92.3MB, time=3.17 memory used=266.6MB, alloc=92.3MB, time=4.09 memory used=329.4MB, alloc=116.3MB, time=5.00 memory used=406.2MB, alloc=372.3MB, time=6.19 memory used=486.3MB, alloc=396.3MB, time=7.47 memory used=597.7MB, alloc=420.3MB, time=9.12 memory used=725.1MB, alloc=444.3MB, time=10.95 memory used=865.2MB, alloc=468.3MB, time=13.30 memory used=985.1MB, alloc=468.3MB, time=15.35 memory used=1085.8MB, alloc=468.3MB, time=16.82 memory used=1186.3MB, alloc=492.3MB, time=18.37 memory used=1280.1MB, alloc=492.3MB, time=19.70 memory used=1371.1MB, alloc=492.3MB, time=21.21 memory used=1458.8MB, alloc=492.3MB, time=22.60 memory used=1535.3MB, alloc=492.3MB, time=23.93 memory used=1615.0MB, alloc=492.3MB, time=25.39 memory used=1675.0MB, alloc=516.3MB, time=26.53 memory used=1732.9MB, alloc=516.3MB, time=27.69 memory used=1782.9MB, alloc=516.3MB, time=28.66 memory used=1843.2MB, alloc=516.3MB, time=29.76 memory used=1900.3MB, alloc=516.3MB, time=31.04 memory used=1955.1MB, alloc=516.3MB, time=32.41 memory used=2148.1MB, alloc=540.3MB, time=36.13 memory used=2345.1MB, alloc=564.3MB, time=39.91 memory used=2519.3MB, alloc=588.3MB, time=43.06 memory used=2678.0MB, alloc=612.3MB, time=46.33 memory used=2847.2MB, alloc=612.3MB, time=50.00 memory used=2999.3MB, alloc=636.3MB, time=53.00 memory used=3110.5MB, alloc=636.3MB, time=55.46 memory used=3232.0MB, alloc=636.3MB, time=58.01 memory used=3365.0MB, alloc=636.3MB, time=61.16 memory used=3481.0MB, alloc=636.3MB, time=63.81 memory used=3584.7MB, alloc=636.3MB, time=65.76 memory used=3682.9MB, alloc=660.3MB, time=68.34 memory used=4009.8MB, alloc=684.3MB, time=75.58 memory used=4360.4MB, alloc=708.3MB, time=82.51 memory used=4728.8MB, alloc=732.3MB, time=89.20 memory used=5060.7MB, alloc=756.3MB, time=95.42 memory used=5381.8MB, alloc=780.3MB, time=101.23 memory used=5670.3MB, alloc=804.3MB, time=107.25 memory used=6017.3MB, alloc=828.3MB, time=115.04 |\^/| 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(); 1428248887 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [-19 y z + 18 x - 12 z - 3, 15 y z + 19 y - 20 y z - 13 y, 2 2 -13 x z + 2 z + 11 x - 9 y] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 3 2 G := [11 x y - 12 x y + 16 x z + 14 x, 17 x y z + 18 y + 2 z + 15 x , 2 2 20 x z - 5 y z + 5 x - 7 y] > Problem := [F,G]; 2 2 2 2 Problem := [[-19 y z + 18 x - 12 z - 3, 15 y z + 19 y - 20 y z - 13 y, 2 2 2 2 -13 x z + 2 z + 11 x - 9 y], [11 x y - 12 x y + 16 x z + 14 x, 3 3 2 2 2 17 x y z + 18 y + 2 z + 15 x , 20 x z - 5 y z + 5 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=0.18 memory used=25.3MB, alloc=32.3MB, time=0.49 memory used=44.7MB, alloc=56.3MB, time=0.79 memory used=87.4MB, alloc=60.3MB, time=1.40 memory used=129.0MB, alloc=68.3MB, time=2.00 memory used=168.2MB, alloc=92.3MB, time=2.61 memory used=234.5MB, alloc=92.3MB, time=3.56 memory used=301.1MB, alloc=348.3MB, time=4.43 memory used=365.4MB, alloc=372.3MB, time=5.38 memory used=450.7MB, alloc=372.3MB, time=6.69 memory used=539.1MB, alloc=396.3MB, time=7.88 memory used=648.1MB, alloc=420.3MB, time=9.54 memory used=778.6MB, alloc=444.3MB, time=11.48 memory used=917.2MB, alloc=444.3MB, time=13.58 memory used=1048.9MB, alloc=468.3MB, time=15.60 memory used=1172.6MB, alloc=468.3MB, time=17.17 memory used=1285.0MB, alloc=468.3MB, time=18.84 memory used=1392.8MB, alloc=492.3MB, time=20.50 memory used=1506.6MB, alloc=492.3MB, time=22.52 memory used=1613.0MB, alloc=492.3MB, time=24.44 memory used=1713.0MB, alloc=492.3MB, time=25.77 memory used=1799.7MB, alloc=516.3MB, time=27.14 memory used=1856.0MB, alloc=516.3MB, time=28.09 memory used=1927.4MB, alloc=516.3MB, time=29.32 memory used=1986.5MB, alloc=516.3MB, time=30.37 memory used=2088.6MB, alloc=516.3MB, time=31.54 memory used=2176.0MB, alloc=516.3MB, time=33.24 memory used=2242.1MB, alloc=516.3MB, time=34.48 memory used=2302.0MB, alloc=540.3MB, time=35.51 memory used=2355.0MB, alloc=540.3MB, time=36.50 memory used=2422.4MB, alloc=540.3MB, time=37.75 memory used=2621.6MB, alloc=564.3MB, time=41.22 memory used=2838.6MB, alloc=588.3MB, time=44.34 memory used=3031.1MB, alloc=612.3MB, time=47.98 memory used=3217.9MB, alloc=636.3MB, time=51.48 memory used=3403.2MB, alloc=636.3MB, time=55.07 memory used=3545.8MB, alloc=660.3MB, time=57.39 memory used=3734.6MB, alloc=660.3MB, time=60.31 memory used=3870.0MB, alloc=684.3MB, time=62.74 memory used=4000.4MB, alloc=684.3MB, time=65.57 memory used=4150.6MB, alloc=684.3MB, time=68.89 memory used=4286.7MB, alloc=708.3MB, time=72.08 memory used=4382.6MB, alloc=708.3MB, time=74.38 memory used=4495.3MB, alloc=708.3MB, time=77.35 memory used=4883.8MB, alloc=732.3MB, time=83.41 memory used=5238.8MB, alloc=756.3MB, time=88.59 memory used=5623.3MB, alloc=780.3MB, time=94.87 memory used=5998.7MB, alloc=804.3MB, time=102.73 memory used=6401.1MB, alloc=828.3MB, time=110.39 |\^/| 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(); 1428249187 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 2 F := [-16 x y - 20 z + 16 y z - 19 z, -5 x z - 7 x y z + 4 y z - 2 x , 2 -10 y z + 16 x z + 20 x + 4 z] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 G := [-5 x y z + 20 y - 13 y + 17, -10 x z + 9 x - 8 y z + 19 z , 2 2 2 20 x y - 3 y z - 7 x ] > Problem := [F,G]; 2 3 Problem := [[-16 x y - 20 z + 16 y z - 19 z, 2 2 2 2 -5 x z - 7 x y z + 4 y z - 2 x , -10 y z + 16 x z + 20 x + 4 z], [ 3 2 2 2 -5 x y z + 20 y - 13 y + 17, -10 x z + 9 x - 8 y z + 19 z , 2 2 2 20 x y - 3 y z - 7 x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.17 memory used=25.7MB, alloc=32.3MB, time=0.45 memory used=46.7MB, alloc=36.3MB, time=0.69 memory used=67.4MB, alloc=60.3MB, time=0.98 memory used=113.8MB, alloc=68.3MB, time=1.63 memory used=154.6MB, alloc=68.3MB, time=2.10 memory used=183.3MB, alloc=68.3MB, time=2.28 memory used=207.8MB, alloc=68.3MB, time=2.38 memory used=250.5MB, alloc=68.3MB, time=2.93 memory used=288.0MB, alloc=68.3MB, time=3.36 memory used=331.7MB, alloc=92.3MB, time=3.93 memory used=402.0MB, alloc=92.3MB, time=4.66 memory used=469.5MB, alloc=92.3MB, time=5.46 memory used=519.1MB, alloc=92.3MB, time=6.00 memory used=586.3MB, alloc=92.3MB, time=6.81 memory used=656.6MB, alloc=372.3MB, time=7.61 memory used=743.1MB, alloc=396.3MB, time=8.76 memory used=859.3MB, alloc=396.3MB, time=10.30 memory used=954.6MB, alloc=420.3MB, time=11.25 memory used=1036.5MB, alloc=420.3MB, time=12.20 memory used=1176.8MB, alloc=420.3MB, time=13.75 memory used=1305.1MB, alloc=444.3MB, time=15.69 memory used=1429.9MB, alloc=444.3MB, time=17.60 memory used=1540.3MB, alloc=444.3MB, time=18.73 memory used=1678.1MB, alloc=468.3MB, time=20.30 memory used=1810.3MB, alloc=468.3MB, time=22.02 memory used=1910.8MB, alloc=468.3MB, time=23.42 memory used=1995.0MB, alloc=468.3MB, time=24.70 memory used=2084.1MB, alloc=468.3MB, time=25.93 memory used=2203.1MB, alloc=492.3MB, time=27.58 memory used=2351.0MB, alloc=492.3MB, time=28.92 memory used=2443.6MB, alloc=492.3MB, time=30.29 memory used=2549.5MB, alloc=492.3MB, time=31.63 memory used=2668.1MB, alloc=492.3MB, time=32.86 memory used=2725.7MB, alloc=492.3MB, time=33.79 memory used=2800.5MB, alloc=492.3MB, time=35.04 memory used=2870.3MB, alloc=492.3MB, time=35.96 memory used=2938.4MB, alloc=492.3MB, time=36.98 memory used=2989.6MB, alloc=492.3MB, time=37.92 memory used=3053.4MB, alloc=492.3MB, time=39.05 memory used=3127.5MB, alloc=516.3MB, time=40.10 memory used=3187.9MB, alloc=516.3MB, time=41.08 memory used=3238.9MB, alloc=516.3MB, time=42.07 memory used=3291.9MB, alloc=516.3MB, time=43.06 memory used=3332.9MB, alloc=516.3MB, time=44.04 memory used=3467.4MB, alloc=516.3MB, time=46.60 memory used=3563.4MB, alloc=516.3MB, time=47.10 memory used=3668.5MB, alloc=516.3MB, time=49.20 memory used=3768.3MB, alloc=516.3MB, time=49.71 memory used=3852.1MB, alloc=516.3MB, time=50.16 memory used=3969.4MB, alloc=516.3MB, time=51.25 memory used=4073.5MB, alloc=516.3MB, time=52.25 memory used=4258.1MB, alloc=516.3MB, time=54.08 memory used=4421.6MB, alloc=516.3MB, time=55.86 memory used=4622.6MB, alloc=540.3MB, time=58.11 memory used=4843.0MB, alloc=564.3MB, time=61.17 memory used=5013.0MB, alloc=564.3MB, time=63.67 memory used=5236.7MB, alloc=588.3MB, time=67.06 memory used=5403.6MB, alloc=612.3MB, time=69.37 memory used=5582.2MB, alloc=636.3MB, time=71.45 memory used=5793.4MB, alloc=636.3MB, time=74.22 memory used=5972.2MB, alloc=660.3MB, time=77.02 memory used=6092.0MB, alloc=660.3MB, time=78.86 memory used=6211.0MB, alloc=660.3MB, time=80.72 memory used=6326.1MB, alloc=684.3MB, time=82.60 memory used=6454.6MB, alloc=684.3MB, time=85.07 memory used=6543.3MB, alloc=684.3MB, time=86.94 memory used=6629.3MB, alloc=684.3MB, time=88.67 memory used=6981.1MB, alloc=708.3MB, time=94.01 memory used=7358.1MB, alloc=732.3MB, time=99.49 memory used=7654.1MB, alloc=756.3MB, time=103.14 memory used=8027.8MB, alloc=780.3MB, time=108.31 memory used=8437.4MB, alloc=804.3MB, time=114.07 memory used=8823.9MB, alloc=828.3MB, time=121.63 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428249487 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 3 F := [17 z - 16 x - 3 x y, 15 x - 17 x z + 7 z , 2 3 -5 x z + 16 x y z - 19 z - 14 x y] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 3 3 G := [12 x y - 17 x y z - 10 x y - 10 y , x + 19 y + 12 z + 17 x, 3 2 2 -x y z + 13 y + 16 y z - 17 y ] > Problem := [F,G]; 3 2 3 2 3 Problem := [[17 z - 16 x - 3 x y, 15 x - 17 x z + 7 z , 2 3 2 2 -5 x z + 16 x y z - 19 z - 14 x y], [12 x y - 17 x y z - 10 x y - 10 y , 3 3 3 3 2 2 x + 19 y + 12 z + 17 x, -x y z + 13 y + 16 y z - 17 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.3MB, alloc=32.3MB, time=0.52 memory used=46.4MB, alloc=56.3MB, time=0.84 memory used=88.2MB, alloc=60.3MB, time=1.44 memory used=130.2MB, alloc=60.3MB, time=2.00 memory used=165.3MB, alloc=60.3MB, time=2.38 memory used=213.5MB, alloc=68.3MB, time=2.92 memory used=258.0MB, alloc=92.3MB, time=3.42 memory used=325.3MB, alloc=92.3MB, time=4.33 memory used=387.5MB, alloc=92.3MB, time=5.07 memory used=449.0MB, alloc=92.3MB, time=5.66 memory used=496.1MB, alloc=92.3MB, time=6.02 memory used=612.0MB, alloc=92.3MB, time=7.58 memory used=675.1MB, alloc=116.3MB, time=8.33 memory used=750.8MB, alloc=116.3MB, time=9.45 memory used=816.2MB, alloc=372.3MB, time=10.40 memory used=903.2MB, alloc=396.3MB, time=11.60 memory used=1010.5MB, alloc=396.3MB, time=13.25 memory used=1080.9MB, alloc=420.3MB, time=14.18 memory used=1141.4MB, alloc=420.3MB, time=14.43 memory used=1212.5MB, alloc=420.3MB, time=14.68 memory used=1268.2MB, alloc=420.3MB, time=14.90 memory used=1341.4MB, alloc=420.3MB, time=15.28 memory used=1422.6MB, alloc=420.3MB, time=16.09 memory used=1481.4MB, alloc=420.3MB, time=16.34 memory used=1552.1MB, alloc=420.3MB, time=16.57 memory used=1606.8MB, alloc=420.3MB, time=16.80 memory used=1679.0MB, alloc=420.3MB, time=17.17 memory used=1760.7MB, alloc=420.3MB, time=35.57 memory used=1840.5MB, alloc=420.3MB, time=45.71 memory used=1904.0MB, alloc=420.3MB, time=45.95 memory used=1961.9MB, alloc=420.3MB, time=46.16 memory used=2030.6MB, alloc=420.3MB, time=46.37 memory used=2082.6MB, alloc=420.3MB, time=46.54 memory used=2160.9MB, alloc=420.3MB, time=47.33 memory used=2224.3MB, alloc=420.3MB, time=47.57 memory used=2289.7MB, alloc=420.3MB, time=47.80 memory used=2349.1MB, alloc=420.3MB, time=48.00 memory used=2428.8MB, alloc=420.3MB, time=48.84 memory used=2494.5MB, alloc=420.3MB, time=49.08 memory used=2556.9MB, alloc=420.3MB, time=49.30 memory used=2628.0MB, alloc=420.3MB, time=53.10 memory used=2714.8MB, alloc=420.3MB, time=77.81 memory used=2785.7MB, alloc=420.3MB, time=78.19 memory used=2840.1MB, alloc=420.3MB, time=78.40 memory used=2903.6MB, alloc=420.3MB, time=78.62 memory used=2966.8MB, alloc=420.3MB, time=78.81 memory used=3034.0MB, alloc=420.3MB, time=80.26 memory used=3097.6MB, alloc=420.3MB, time=80.52 memory used=3157.0MB, alloc=420.3MB, time=80.77 memory used=3227.3MB, alloc=420.3MB, time=81.01 memory used=3294.2MB, alloc=420.3MB, time=81.24 memory used=3341.3MB, alloc=420.3MB, time=81.45 memory used=3392.6MB, alloc=420.3MB, time=81.66 memory used=3449.0MB, alloc=420.3MB, time=81.88 memory used=3511.2MB, alloc=420.3MB, time=82.09 memory used=3570.6MB, alloc=420.3MB, time=82.28 memory used=3632.2MB, alloc=420.3MB, time=82.47 memory used=3758.3MB, alloc=420.3MB, time=85.71 memory used=3828.9MB, alloc=420.3MB, time=87.86 memory used=3891.0MB, alloc=420.3MB, time=88.25 memory used=3975.1MB, alloc=420.3MB, time=88.58 memory used=4081.9MB, alloc=420.3MB, time=89.71 memory used=4216.5MB, alloc=420.3MB, time=91.10 memory used=4285.4MB, alloc=444.3MB, time=91.90 memory used=4367.1MB, alloc=444.3MB, time=92.17 memory used=4428.8MB, alloc=444.3MB, time=92.41 memory used=4505.7MB, alloc=444.3MB, time=92.64 memory used=4589.0MB, alloc=444.3MB, time=93.50 memory used=4666.0MB, alloc=444.3MB, time=93.79 memory used=4735.9MB, alloc=444.3MB, time=94.04 memory used=4806.4MB, alloc=444.3MB, time=94.27 memory used=4880.1MB, alloc=444.3MB, time=94.49 memory used=4987.7MB, alloc=444.3MB, time=122.29 memory used=5067.7MB, alloc=444.3MB, time=123.16 memory used=5138.8MB, alloc=444.3MB, time=123.41 memory used=5210.8MB, alloc=444.3MB, time=123.63 memory used=5271.5MB, alloc=444.3MB, time=123.84 memory used=5348.8MB, alloc=444.3MB, time=124.06 memory used=5441.0MB, alloc=444.3MB, time=124.90 memory used=5542.5MB, alloc=444.3MB, time=125.20 memory used=5710.5MB, alloc=444.3MB, time=125.80 memory used=5966.6MB, alloc=444.3MB, time=127.10 memory used=6046.7MB, alloc=444.3MB, time=127.42 memory used=6119.9MB, alloc=444.3MB, time=127.69 memory used=6187.2MB, alloc=444.3MB, time=127.93 memory used=6262.4MB, alloc=444.3MB, time=128.16 memory used=6348.4MB, alloc=444.3MB, time=129.11 memory used=6429.1MB, alloc=444.3MB, time=129.40 memory used=6490.0MB, alloc=444.3MB, time=129.63 memory used=6566.2MB, alloc=444.3MB, time=129.87 memory used=6651.7MB, alloc=444.3MB, time=137.94 memory used=6747.9MB, alloc=444.3MB, time=158.61 memory used=6818.4MB, alloc=444.3MB, time=158.86 memory used=6899.2MB, alloc=444.3MB, time=159.11 memory used=6958.9MB, alloc=444.3MB, time=159.31 memory used=7024.1MB, alloc=444.3MB, time=159.52 memory used=7132.6MB, alloc=444.3MB, time=161.49 memory used=7201.8MB, alloc=444.3MB, time=161.79 memory used=7289.8MB, alloc=444.3MB, time=162.09 memory used=7347.4MB, alloc=444.3MB, time=162.33 memory used=7407.8MB, alloc=444.3MB, time=162.57 memory used=7477.9MB, alloc=444.3MB, time=162.82 memory used=7557.5MB, alloc=444.3MB, time=163.08 memory used=7637.4MB, alloc=444.3MB, time=163.32 memory used=7712.6MB, alloc=444.3MB, time=163.55 memory used=7766.2MB, alloc=444.3MB, time=163.75 memory used=7825.3MB, alloc=444.3MB, time=163.96 memory used=7892.3MB, alloc=444.3MB, time=164.18 memory used=7975.4MB, alloc=444.3MB, time=164.72 memory used=8060.5MB, alloc=444.3MB, time=164.98 memory used=8246.2MB, alloc=444.3MB, time=165.49 memory used=8446.5MB, alloc=444.3MB, time=170.23 memory used=8522.1MB, alloc=444.3MB, time=170.68 memory used=8641.0MB, alloc=444.3MB, time=171.63 memory used=8802.6MB, alloc=444.3MB, time=173.61 memory used=8927.0MB, alloc=468.3MB, time=175.32 |\^/| 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(); 1428249787 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 F := [-5 x y z + 7 x z - 16 x z + 11 y , -20 x y z + 15 y z - 3 x - 5 y , 2 -6 y z + x y + 8] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 3 2 G := [17 x z + 5 y z + 6 z + 16 x, 9 x z - 12 z - 13 x - 7 x z, 2 2 2 x z + 7 y z - 16 x] > Problem := [F,G]; 2 2 Problem := [[-5 x y z + 7 x z - 16 x z + 11 y , 2 2 2 2 -20 x y z + 15 y z - 3 x - 5 y , -6 y z + x y + 8], [ 2 2 3 2 3 2 17 x z + 5 y z + 6 z + 16 x, 9 x z - 12 z - 13 x - 7 x z, 2 2 2 x z + 7 y z - 16 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.18 memory used=24.6MB, alloc=32.3MB, time=0.44 memory used=43.5MB, alloc=56.3MB, time=0.72 memory used=88.3MB, alloc=61.1MB, time=1.11 memory used=122.3MB, alloc=61.1MB, time=1.31 memory used=162.0MB, alloc=61.1MB, time=2.58 memory used=200.5MB, alloc=61.1MB, time=2.91 memory used=240.7MB, alloc=61.1MB, time=4.06 memory used=282.3MB, alloc=61.1MB, time=4.46 memory used=327.0MB, alloc=61.4MB, time=5.21 memory used=369.7MB, alloc=69.4MB, time=5.75 memory used=412.0MB, alloc=93.4MB, time=6.36 memory used=467.8MB, alloc=93.4MB, time=6.75 memory used=523.2MB, alloc=93.4MB, time=8.51 memory used=563.1MB, alloc=93.4MB, time=8.64 memory used=614.7MB, alloc=93.4MB, time=9.19 memory used=698.2MB, alloc=93.4MB, time=10.22 memory used=782.0MB, alloc=93.4MB, time=11.37 memory used=858.6MB, alloc=93.4MB, time=12.20 memory used=923.9MB, alloc=93.4MB, time=13.05 memory used=989.7MB, alloc=117.4MB, time=13.92 memory used=1055.6MB, alloc=373.4MB, time=14.75 memory used=1149.0MB, alloc=373.4MB, time=16.02 memory used=1214.5MB, alloc=373.4MB, time=20.23 memory used=1250.8MB, alloc=373.4MB, time=20.40 memory used=1311.6MB, alloc=373.4MB, time=21.13 memory used=1372.2MB, alloc=373.4MB, time=25.13 memory used=1414.0MB, alloc=373.4MB, time=25.29 memory used=1452.3MB, alloc=373.4MB, time=25.42 memory used=1489.8MB, alloc=373.4MB, time=25.56 memory used=1565.2MB, alloc=373.4MB, time=26.25 memory used=1652.7MB, alloc=397.4MB, time=27.75 memory used=1720.4MB, alloc=397.4MB, time=28.14 memory used=1796.9MB, alloc=397.4MB, time=30.80 memory used=1857.5MB, alloc=397.4MB, time=31.16 memory used=1942.1MB, alloc=397.4MB, time=31.94 memory used=2046.5MB, alloc=397.4MB, time=33.87 memory used=2166.8MB, alloc=397.4MB, time=35.10 memory used=2264.7MB, alloc=421.4MB, time=37.36 memory used=2386.8MB, alloc=445.4MB, time=39.01 memory used=2506.7MB, alloc=445.4MB, time=40.70 memory used=2605.5MB, alloc=469.4MB, time=41.88 memory used=2726.2MB, alloc=469.4MB, time=45.51 memory used=2837.1MB, alloc=469.4MB, time=46.57 memory used=2957.0MB, alloc=469.4MB, time=49.90 memory used=3032.5MB, alloc=469.4MB, time=50.20 memory used=3130.5MB, alloc=469.4MB, time=50.94 memory used=3215.4MB, alloc=469.4MB, time=51.27 memory used=3309.0MB, alloc=469.4MB, time=51.98 memory used=3394.4MB, alloc=469.4MB, time=52.31 memory used=3498.1MB, alloc=469.4MB, time=70.99 memory used=3588.2MB, alloc=469.4MB, time=71.83 memory used=3657.7MB, alloc=469.4MB, time=72.11 memory used=3750.1MB, alloc=469.4MB, time=72.43 memory used=3816.9MB, alloc=469.4MB, time=72.68 memory used=3884.2MB, alloc=469.4MB, time=72.94 memory used=3982.8MB, alloc=469.4MB, time=73.81 memory used=4068.0MB, alloc=469.4MB, time=74.13 memory used=4161.8MB, alloc=469.4MB, time=74.83 memory used=4247.7MB, alloc=469.4MB, time=75.15 memory used=4342.2MB, alloc=469.4MB, time=82.97 memory used=4440.1MB, alloc=469.4MB, time=95.38 memory used=4515.1MB, alloc=469.4MB, time=95.70 memory used=4596.8MB, alloc=469.4MB, time=96.02 memory used=4679.9MB, alloc=469.4MB, time=96.31 memory used=4741.4MB, alloc=469.4MB, time=96.56 memory used=4824.2MB, alloc=469.4MB, time=97.12 memory used=4915.0MB, alloc=469.4MB, time=97.49 memory used=5000.4MB, alloc=469.4MB, time=97.89 memory used=5202.7MB, alloc=469.4MB, time=100.24 memory used=5358.4MB, alloc=469.4MB, time=109.51 memory used=5432.8MB, alloc=469.4MB, time=109.83 memory used=5512.4MB, alloc=469.4MB, time=110.15 memory used=5579.3MB, alloc=469.4MB, time=110.42 memory used=5756.5MB, alloc=469.4MB, time=112.34 memory used=5901.2MB, alloc=493.4MB, time=113.96 memory used=6100.0MB, alloc=493.4MB, time=117.41 memory used=6197.5MB, alloc=493.4MB, time=117.94 memory used=6295.6MB, alloc=493.4MB, time=118.45 memory used=6409.5MB, alloc=493.4MB, time=127.06 memory used=6511.5MB, alloc=493.4MB, time=127.54 memory used=6592.3MB, alloc=493.4MB, time=127.85 memory used=6717.8MB, alloc=493.4MB, time=131.40 memory used=6807.7MB, alloc=493.4MB, time=131.75 memory used=6882.5MB, alloc=493.4MB, time=132.04 memory used=6986.8MB, alloc=493.4MB, time=132.77 memory used=7068.6MB, alloc=493.4MB, time=133.12 memory used=7166.2MB, alloc=493.4MB, time=133.58 memory used=7275.0MB, alloc=493.4MB, time=134.27 memory used=7351.7MB, alloc=493.4MB, time=134.62 memory used=7465.5MB, alloc=493.4MB, time=142.30 memory used=7573.6MB, alloc=493.4MB, time=154.36 memory used=7654.2MB, alloc=493.4MB, time=154.72 memory used=7743.9MB, alloc=493.4MB, time=155.04 memory used=7812.1MB, alloc=493.4MB, time=155.33 memory used=7893.0MB, alloc=493.4MB, time=155.62 memory used=7989.2MB, alloc=493.4MB, time=155.92 memory used=8127.7MB, alloc=493.4MB, time=156.72 memory used=8211.9MB, alloc=493.4MB, time=157.08 memory used=8308.0MB, alloc=493.4MB, time=157.54 memory used=8416.3MB, alloc=493.4MB, time=158.18 memory used=8492.8MB, alloc=493.4MB, time=158.50 memory used=8608.9MB, alloc=517.4MB, time=175.33 |\^/| 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(); 1428250087 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 F := [15 y z - 6 x z - 12 y + 19 z, -x + x y + 3 z - 13, 2 3 2 -7 x z - 13 z + 13 y - 18 y] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [-4 y z + 5 x y + 7 z + 6, -7 x y - 15 y z - 4 x z + 11 y, 2 2 2 -6 x z - 3 x + 3 x z - 19 z ] > Problem := [F,G]; 2 2 3 2 Problem := [[15 y z - 6 x z - 12 y + 19 z, -x + x y + 3 z - 13, 2 3 2 2 2 -7 x z - 13 z + 13 y - 18 y], [-4 y z + 5 x y + 7 z + 6, 2 2 2 2 2 -7 x y - 15 y z - 4 x z + 11 y, -6 x z - 3 x + 3 x z - 19 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.18 memory used=24.5MB, alloc=32.3MB, time=0.47 memory used=43.5MB, alloc=36.3MB, time=0.70 memory used=65.3MB, alloc=60.3MB, time=0.95 memory used=110.2MB, alloc=68.3MB, time=1.49 memory used=154.6MB, alloc=68.3MB, time=1.97 memory used=197.2MB, alloc=68.3MB, time=2.39 memory used=240.9MB, alloc=68.3MB, time=2.84 memory used=282.6MB, alloc=68.3MB, time=3.45 memory used=323.0MB, alloc=92.3MB, time=3.96 memory used=380.2MB, alloc=92.3MB, time=4.41 memory used=433.5MB, alloc=92.5MB, time=4.73 memory used=487.2MB, alloc=92.5MB, time=5.31 memory used=550.6MB, alloc=92.5MB, time=5.96 memory used=619.0MB, alloc=92.5MB, time=6.76 memory used=693.5MB, alloc=348.5MB, time=7.51 memory used=748.3MB, alloc=348.5MB, time=8.04 memory used=794.7MB, alloc=348.5MB, time=8.36 memory used=837.1MB, alloc=348.5MB, time=8.56 memory used=880.6MB, alloc=348.5MB, time=9.16 memory used=927.3MB, alloc=348.5MB, time=9.54 memory used=993.2MB, alloc=348.5MB, time=10.29 memory used=1066.7MB, alloc=372.5MB, time=11.10 memory used=1152.7MB, alloc=372.5MB, time=12.18 memory used=1247.2MB, alloc=372.5MB, time=13.22 memory used=1335.9MB, alloc=396.5MB, time=14.39 memory used=1448.3MB, alloc=396.5MB, time=15.52 memory used=1532.6MB, alloc=396.5MB, time=16.11 memory used=1604.5MB, alloc=396.5MB, time=16.71 memory used=1674.9MB, alloc=396.5MB, time=17.03 memory used=1739.3MB, alloc=396.5MB, time=17.59 memory used=1809.5MB, alloc=396.5MB, time=17.99 memory used=1865.3MB, alloc=396.5MB, time=18.19 memory used=1933.9MB, alloc=396.5MB, time=18.63 memory used=1986.4MB, alloc=396.5MB, time=18.83 memory used=2055.3MB, alloc=396.5MB, time=20.11 memory used=2106.0MB, alloc=396.5MB, time=20.30 memory used=2196.6MB, alloc=396.5MB, time=21.19 memory used=2288.5MB, alloc=396.5MB, time=22.38 memory used=2348.0MB, alloc=396.5MB, time=22.73 memory used=2468.1MB, alloc=396.5MB, time=24.10 memory used=2572.1MB, alloc=420.5MB, time=25.43 memory used=2699.9MB, alloc=420.5MB, time=27.09 memory used=2794.8MB, alloc=420.5MB, time=27.82 memory used=2877.8MB, alloc=420.5MB, time=28.42 memory used=2955.1MB, alloc=420.5MB, time=29.04 memory used=3019.5MB, alloc=420.5MB, time=29.38 memory used=3130.5MB, alloc=420.5MB, time=31.00 memory used=3243.3MB, alloc=420.5MB, time=32.05 memory used=3354.0MB, alloc=444.5MB, time=33.65 memory used=3463.0MB, alloc=444.5MB, time=34.91 memory used=3568.6MB, alloc=444.5MB, time=35.86 memory used=3661.3MB, alloc=444.5MB, time=36.37 memory used=3748.0MB, alloc=444.5MB, time=37.57 memory used=3858.7MB, alloc=444.5MB, time=38.82 memory used=3987.7MB, alloc=444.5MB, time=40.38 memory used=4077.7MB, alloc=468.5MB, time=41.79 memory used=4161.5MB, alloc=468.5MB, time=43.05 memory used=4273.5MB, alloc=468.5MB, time=44.40 memory used=4379.4MB, alloc=468.5MB, time=45.78 memory used=4490.4MB, alloc=468.5MB, time=47.16 memory used=4571.5MB, alloc=468.5MB, time=48.18 memory used=4658.6MB, alloc=468.5MB, time=49.55 memory used=4777.8MB, alloc=468.5MB, time=50.74 memory used=4866.8MB, alloc=468.5MB, time=51.31 memory used=4943.2MB, alloc=468.5MB, time=51.70 memory used=5078.1MB, alloc=468.5MB, time=53.03 memory used=5169.1MB, alloc=468.5MB, time=54.25 memory used=5237.4MB, alloc=492.5MB, time=55.54 memory used=5299.4MB, alloc=492.5MB, time=56.70 memory used=5355.2MB, alloc=492.5MB, time=57.53 memory used=5414.2MB, alloc=492.5MB, time=58.46 memory used=5485.5MB, alloc=492.5MB, time=59.39 memory used=5544.0MB, alloc=492.5MB, time=60.78 memory used=5642.9MB, alloc=492.5MB, time=61.29 memory used=5751.0MB, alloc=492.5MB, time=62.14 memory used=5846.0MB, alloc=492.5MB, time=63.16 memory used=5939.7MB, alloc=492.5MB, time=64.18 memory used=6037.1MB, alloc=492.5MB, time=65.59 memory used=6111.4MB, alloc=492.5MB, time=66.57 memory used=6304.6MB, alloc=492.5MB, time=68.51 memory used=6450.9MB, alloc=516.5MB, time=70.05 memory used=6546.2MB, alloc=516.5MB, time=70.55 memory used=6660.0MB, alloc=516.5MB, time=71.80 memory used=6768.4MB, alloc=516.5MB, time=72.36 memory used=7000.5MB, alloc=516.5MB, time=75.74 memory used=7099.6MB, alloc=516.5MB, time=76.30 memory used=7203.5MB, alloc=516.5MB, time=76.99 memory used=7318.6MB, alloc=516.5MB, time=77.92 memory used=7471.4MB, alloc=516.5MB, time=79.09 memory used=7721.8MB, alloc=540.5MB, time=82.42 memory used=7917.8MB, alloc=540.5MB, time=84.75 memory used=8034.4MB, alloc=540.5MB, time=85.46 memory used=8147.7MB, alloc=540.5MB, time=86.48 memory used=8267.2MB, alloc=540.5MB, time=87.36 memory used=8378.5MB, alloc=540.5MB, time=88.08 memory used=8488.8MB, alloc=540.5MB, time=89.25 memory used=8611.0MB, alloc=540.5MB, time=90.09 memory used=8707.8MB, alloc=564.5MB, time=90.68 memory used=8831.7MB, alloc=564.5MB, time=91.25 memory used=8957.5MB, alloc=564.5MB, time=92.02 memory used=9075.2MB, alloc=564.5MB, time=92.65 memory used=9189.3MB, alloc=564.5MB, time=93.26 memory used=9302.1MB, alloc=564.5MB, time=93.78 memory used=9438.5MB, alloc=564.5MB, time=95.96 memory used=9550.1MB, alloc=564.5MB, time=96.51 memory used=9701.8MB, alloc=564.5MB, time=97.61 memory used=9832.7MB, alloc=564.5MB, time=98.39 memory used=10071.0MB, alloc=564.5MB, time=100.81 memory used=10239.1MB, alloc=564.5MB, time=102.52 memory used=10352.4MB, alloc=564.5MB, time=103.18 memory used=10488.2MB, alloc=564.5MB, time=104.12 memory used=10662.4MB, alloc=564.5MB, time=107.12 memory used=10786.0MB, alloc=564.5MB, time=107.89 memory used=10967.5MB, alloc=564.5MB, time=109.74 memory used=11079.6MB, alloc=564.5MB, time=110.36 memory used=11214.0MB, alloc=564.5MB, time=112.21 memory used=11427.3MB, alloc=564.5MB, time=115.08 memory used=11543.0MB, alloc=564.5MB, time=115.71 memory used=11670.7MB, alloc=564.5MB, time=116.67 memory used=11918.1MB, alloc=564.5MB, time=119.13 memory used=12188.2MB, alloc=564.5MB, time=123.25 |\^/| 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(); 1428250388 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [-7 x y + 17 x z + 17 z - 12 x, 19 x y - x z - 8 x y, 2 2 2 9 x z - 17 y z - 18 x - 8 y] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 G := [-16 x y + 4 y z + 11 x y - 15 y , 5 x z + 13 x y + 16 z, 2 2 3 -12 x z - 15 y z - 7 z ] > Problem := [F,G]; 2 2 2 2 Problem := [[-7 x y + 17 x z + 17 z - 12 x, 19 x y - x z - 8 x y, 2 2 2 2 2 2 9 x z - 17 y z - 18 x - 8 y], [-16 x y + 4 y z + 11 x y - 15 y , 2 2 2 2 3 5 x z + 13 x y + 16 z, -12 x z - 15 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=26.2MB, alloc=32.3MB, time=0.49 memory used=45.8MB, alloc=56.3MB, time=0.79 memory used=86.2MB, alloc=60.3MB, time=1.39 memory used=128.2MB, alloc=92.3MB, time=2.02 memory used=193.5MB, alloc=92.3MB, time=2.96 memory used=258.8MB, alloc=92.3MB, time=3.78 memory used=327.8MB, alloc=116.3MB, time=4.66 memory used=393.1MB, alloc=116.3MB, time=5.59 memory used=472.4MB, alloc=372.3MB, time=6.80 memory used=555.3MB, alloc=396.3MB, time=8.09 memory used=664.6MB, alloc=420.3MB, time=9.78 memory used=796.3MB, alloc=444.3MB, time=11.91 memory used=921.2MB, alloc=444.3MB, time=13.95 memory used=1047.3MB, alloc=468.3MB, time=15.96 memory used=1202.3MB, alloc=468.3MB, time=17.81 memory used=1328.2MB, alloc=468.3MB, time=19.74 memory used=1436.2MB, alloc=468.3MB, time=21.49 memory used=1550.2MB, alloc=492.3MB, time=23.57 memory used=1646.7MB, alloc=492.3MB, time=25.25 memory used=1730.5MB, alloc=492.3MB, time=26.74 memory used=1803.9MB, alloc=492.3MB, time=28.09 memory used=1890.2MB, alloc=516.3MB, time=29.71 memory used=1993.2MB, alloc=516.3MB, time=32.04 memory used=2072.1MB, alloc=516.3MB, time=33.50 memory used=2150.1MB, alloc=516.3MB, time=34.97 memory used=2218.1MB, alloc=516.3MB, time=36.46 memory used=2279.3MB, alloc=540.3MB, time=37.58 memory used=2343.3MB, alloc=540.3MB, time=38.68 memory used=2399.8MB, alloc=540.3MB, time=40.17 memory used=2446.7MB, alloc=540.3MB, time=41.27 memory used=2497.9MB, alloc=540.3MB, time=42.42 memory used=2546.0MB, alloc=540.3MB, time=43.60 memory used=2779.1MB, alloc=564.3MB, time=47.11 memory used=2981.4MB, alloc=588.3MB, time=50.72 memory used=3190.3MB, alloc=612.3MB, time=54.41 memory used=3355.3MB, alloc=612.3MB, time=57.90 memory used=3521.6MB, alloc=636.3MB, time=60.89 memory used=3680.6MB, alloc=636.3MB, time=64.22 memory used=3828.6MB, alloc=660.3MB, time=67.52 memory used=3997.8MB, alloc=660.3MB, time=71.37 memory used=4155.6MB, alloc=660.3MB, time=75.09 memory used=4302.4MB, alloc=684.3MB, time=78.56 memory used=4407.9MB, alloc=684.3MB, time=80.87 memory used=4545.9MB, alloc=684.3MB, time=84.54 memory used=4671.0MB, alloc=684.3MB, time=87.90 memory used=4759.3MB, alloc=684.3MB, time=90.08 memory used=5098.7MB, alloc=708.3MB, time=96.87 memory used=5476.9MB, alloc=732.3MB, time=104.10 |\^/| 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(); 1428250687 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 2 2 F := [8 x z - 7 y + 9 y - 4 z, -8 x z - 10 y z + 14 x z - 15 y , 2 3 10 x z - 9 y - 4 y z + 12 x] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [-17 x y z - 10 x y - 16 x z + 14 y z, 10 x z - 12 x y - 20 y z - 9 x , 3 3 9 x - 11 y + x z + x] > Problem := [F,G]; 2 3 2 2 2 2 Problem := [[8 x z - 7 y + 9 y - 4 z, -8 x z - 10 y z + 14 x z - 15 y , 2 3 10 x z - 9 y - 4 y z + 12 x], [-17 x y z - 10 x y - 16 x z + 14 y z, 2 2 2 2 3 3 10 x z - 12 x y - 20 y z - 9 x , 9 x - 11 y + x z + x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.18 memory used=24.7MB, alloc=32.3MB, time=0.42 memory used=47.6MB, alloc=36.3MB, time=0.70 memory used=70.3MB, alloc=36.3MB, time=0.99 memory used=92.2MB, alloc=36.3MB, time=1.28 memory used=117.2MB, alloc=60.3MB, time=1.58 memory used=160.2MB, alloc=68.3MB, time=2.16 memory used=204.7MB, alloc=68.3MB, time=2.68 memory used=247.2MB, alloc=68.3MB, time=3.14 memory used=293.1MB, alloc=92.3MB, time=3.71 memory used=362.2MB, alloc=92.3MB, time=4.47 memory used=426.5MB, alloc=348.3MB, time=5.33 memory used=510.9MB, alloc=348.3MB, time=6.54 memory used=597.4MB, alloc=372.3MB, time=7.59 memory used=689.7MB, alloc=372.3MB, time=8.52 memory used=753.3MB, alloc=372.3MB, time=8.93 memory used=843.1MB, alloc=372.3MB, time=9.78 memory used=959.1MB, alloc=372.3MB, time=10.90 memory used=1059.1MB, alloc=372.3MB, time=12.14 memory used=1142.1MB, alloc=396.3MB, time=13.30 memory used=1246.0MB, alloc=420.3MB, time=14.65 memory used=1361.4MB, alloc=444.3MB, time=16.04 memory used=1468.4MB, alloc=444.3MB, time=17.47 memory used=1582.5MB, alloc=444.3MB, time=18.86 memory used=1693.3MB, alloc=444.3MB, time=20.34 memory used=1815.6MB, alloc=444.3MB, time=22.43 memory used=1940.4MB, alloc=444.3MB, time=24.56 memory used=2017.1MB, alloc=468.3MB, time=25.90 memory used=2102.9MB, alloc=468.3MB, time=27.28 memory used=2183.5MB, alloc=468.3MB, time=28.63 memory used=2257.1MB, alloc=468.3MB, time=29.96 memory used=2326.0MB, alloc=468.3MB, time=31.19 memory used=2394.0MB, alloc=492.3MB, time=32.38 memory used=2455.5MB, alloc=492.3MB, time=33.43 memory used=2513.7MB, alloc=492.3MB, time=34.42 memory used=2563.3MB, alloc=492.3MB, time=35.38 memory used=2624.4MB, alloc=492.3MB, time=36.33 memory used=2683.0MB, alloc=492.3MB, time=37.23 memory used=2733.4MB, alloc=492.3MB, time=38.32 memory used=2783.7MB, alloc=492.3MB, time=39.13 memory used=2876.4MB, alloc=492.3MB, time=40.06 memory used=2969.4MB, alloc=492.3MB, time=41.23 memory used=3013.5MB, alloc=492.3MB, time=42.03 memory used=3223.2MB, alloc=516.3MB, time=44.85 memory used=3404.1MB, alloc=540.3MB, time=47.84 memory used=3600.7MB, alloc=564.3MB, time=50.50 memory used=3791.1MB, alloc=588.3MB, time=52.97 memory used=3953.4MB, alloc=588.3MB, time=55.49 memory used=4119.4MB, alloc=612.3MB, time=57.99 memory used=4272.6MB, alloc=612.3MB, time=60.29 memory used=4428.1MB, alloc=636.3MB, time=62.47 memory used=4588.7MB, alloc=636.3MB, time=64.84 memory used=4729.7MB, alloc=660.3MB, time=67.20 memory used=4874.6MB, alloc=660.3MB, time=70.38 memory used=5039.8MB, alloc=660.3MB, time=73.02 memory used=5277.9MB, alloc=660.3MB, time=77.79 memory used=5480.5MB, alloc=660.3MB, time=85.20 memory used=5705.6MB, alloc=660.3MB, time=89.66 memory used=5895.8MB, alloc=684.3MB, time=116.42 |\^/| 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(); 1428250988 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 3 F := [5 x z - 8 y z - 15 x y, 5 x - 2 x y z - 10 y z - 12 z , 2 2 -4 x y - 14 x z - 10 z + 17 y] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 G := [20 x z + 13 y z - 13 z, -12 x y z - 19 x + 18 x y + 20 y z, 2 2 -13 x z - 11 y z - 17 x - 8 y] > Problem := [F,G]; 2 2 3 2 3 Problem := [[5 x z - 8 y z - 15 x y, 5 x - 2 x y z - 10 y z - 12 z , 2 2 -4 x y - 14 x z - 10 z + 17 y], [20 x z + 13 y z - 13 z, 2 2 2 -12 x y z - 19 x + 18 x y + 20 y z, -13 x z - 11 y z - 17 x - 8 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.18 memory used=26.7MB, alloc=32.3MB, time=0.51 memory used=47.5MB, alloc=32.3MB, time=0.80 memory used=67.1MB, alloc=56.3MB, time=1.11 memory used=108.5MB, alloc=60.3MB, time=1.71 memory used=146.2MB, alloc=84.3MB, time=2.28 memory used=210.1MB, alloc=92.3MB, time=3.23 memory used=273.2MB, alloc=116.3MB, time=4.20 memory used=352.4MB, alloc=116.3MB, time=5.39 memory used=436.8MB, alloc=116.3MB, time=6.45 memory used=515.4MB, alloc=140.3MB, time=7.70 memory used=584.6MB, alloc=396.3MB, time=8.80 memory used=692.1MB, alloc=420.3MB, time=10.52 memory used=821.7MB, alloc=444.3MB, time=12.69 memory used=972.8MB, alloc=444.3MB, time=15.05 memory used=1099.5MB, alloc=444.3MB, time=16.28 memory used=1216.3MB, alloc=468.3MB, time=17.45 memory used=1361.0MB, alloc=468.3MB, time=19.79 memory used=1490.9MB, alloc=492.3MB, time=21.97 memory used=1617.8MB, alloc=492.3MB, time=23.80 memory used=1763.1MB, alloc=492.3MB, time=26.18 memory used=1870.1MB, alloc=492.3MB, time=26.86 memory used=1972.4MB, alloc=492.3MB, time=27.47 memory used=2075.8MB, alloc=492.3MB, time=28.76 memory used=2156.1MB, alloc=492.3MB, time=29.06 memory used=2236.3MB, alloc=492.3MB, time=29.35 memory used=2391.3MB, alloc=516.3MB, time=30.85 memory used=2517.2MB, alloc=516.3MB, time=32.61 memory used=2634.0MB, alloc=516.3MB, time=34.97 memory used=2734.7MB, alloc=516.3MB, time=36.85 memory used=2832.5MB, alloc=516.3MB, time=38.65 memory used=2912.6MB, alloc=540.3MB, time=40.12 memory used=3020.3MB, alloc=540.3MB, time=42.63 memory used=3122.3MB, alloc=540.3MB, time=44.97 memory used=3202.8MB, alloc=540.3MB, time=46.78 memory used=3286.1MB, alloc=540.3MB, time=48.46 memory used=3360.7MB, alloc=540.3MB, time=49.75 memory used=3439.5MB, alloc=540.3MB, time=50.90 memory used=3523.2MB, alloc=540.3MB, time=52.95 memory used=3586.9MB, alloc=564.3MB, time=54.40 memory used=3660.3MB, alloc=564.3MB, time=56.20 memory used=3724.5MB, alloc=564.3MB, time=58.03 memory used=3932.0MB, alloc=588.3MB, time=62.19 memory used=4166.1MB, alloc=612.3MB, time=67.17 memory used=4360.6MB, alloc=636.3MB, time=71.49 memory used=4577.0MB, alloc=660.3MB, time=76.43 memory used=4773.4MB, alloc=684.3MB, time=81.77 memory used=4947.1MB, alloc=684.3MB, time=85.78 memory used=5111.1MB, alloc=684.3MB, time=89.87 memory used=5273.7MB, alloc=684.3MB, time=93.94 memory used=5402.5MB, alloc=684.3MB, time=97.01 memory used=5612.1MB, alloc=708.3MB, time=99.16 |\^/| 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(); 1428251288 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [10 x y + 19 y z + 11 x z + 6, 6 x z + 5 x + 17 x z - 2 y, 2 2 12 x z + 14 y z - 6 z ] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 3 G := [8 x + 12 x z - 17 y - z, -18 x y + 2 x y z + 5 y + 8 z, 2 2 9 y z + 19 y + 10 y z - 6] > Problem := [F,G]; 2 2 2 2 Problem := [[10 x y + 19 y z + 11 x z + 6, 6 x z + 5 x + 17 x z - 2 y, 2 2 3 2 2 12 x z + 14 y z - 6 z ], [8 x + 12 x z - 17 y - z, 2 3 2 2 -18 x y + 2 x y z + 5 y + 8 z, 9 y z + 19 y + 10 y z - 6]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.5MB, alloc=32.3MB, time=0.18 memory used=26.4MB, alloc=32.3MB, time=0.50 memory used=46.2MB, alloc=32.3MB, time=0.79 memory used=65.3MB, alloc=56.3MB, time=1.09 memory used=105.2MB, alloc=60.3MB, time=1.69 memory used=144.2MB, alloc=84.3MB, time=2.29 memory used=206.0MB, alloc=92.3MB, time=3.22 memory used=265.8MB, alloc=116.3MB, time=4.14 memory used=335.6MB, alloc=116.3MB, time=5.15 memory used=407.6MB, alloc=396.3MB, time=6.30 memory used=520.1MB, alloc=420.3MB, time=7.99 memory used=652.6MB, alloc=444.3MB, time=10.09 memory used=777.4MB, alloc=468.3MB, time=12.08 memory used=900.4MB, alloc=468.3MB, time=14.15 memory used=1018.3MB, alloc=468.3MB, time=16.10 memory used=1119.1MB, alloc=468.3MB, time=17.84 memory used=1207.5MB, alloc=468.3MB, time=19.48 memory used=1294.7MB, alloc=492.3MB, time=21.11 memory used=1377.7MB, alloc=492.3MB, time=22.66 memory used=1464.5MB, alloc=492.3MB, time=24.35 memory used=1527.7MB, alloc=492.3MB, time=25.68 memory used=1597.7MB, alloc=492.3MB, time=27.09 memory used=1656.7MB, alloc=492.3MB, time=28.29 memory used=1706.8MB, alloc=492.3MB, time=29.36 memory used=1757.0MB, alloc=492.3MB, time=30.61 memory used=1813.0MB, alloc=492.3MB, time=31.96 memory used=1988.9MB, alloc=516.3MB, time=35.51 memory used=2182.7MB, alloc=540.3MB, time=39.08 memory used=2392.1MB, alloc=564.3MB, time=42.87 memory used=2560.6MB, alloc=588.3MB, time=45.78 memory used=2731.4MB, alloc=612.3MB, time=49.12 memory used=2899.1MB, alloc=636.3MB, time=52.66 memory used=3031.3MB, alloc=660.3MB, time=55.55 memory used=3183.0MB, alloc=660.3MB, time=58.39 memory used=3337.6MB, alloc=660.3MB, time=61.89 memory used=3476.5MB, alloc=684.3MB, time=65.47 memory used=3571.4MB, alloc=684.3MB, time=67.65 memory used=3658.8MB, alloc=684.3MB, time=69.71 memory used=4005.4MB, alloc=708.3MB, time=77.12 memory used=4381.2MB, alloc=732.3MB, time=83.73 memory used=4760.0MB, alloc=756.3MB, time=92.72 memory used=5113.4MB, alloc=780.3MB, time=100.78 memory used=5415.4MB, alloc=804.3MB, time=105.93 |\^/| 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(); 1428251588 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 2 2 F := [-15 y - 11 z - 8 y + 10 y, -16 x z - 19 x y + 10 z , 2 3 -2 x y z - 8 y z + 20 z - 10] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 3 G := [6 z + x z - 18 z + 16, -5 x y - 12 y z + 2 z - 20 x z, 3 2 3 -19 x + 13 x z + 4 z + 11 x y] > Problem := [F,G]; 3 3 2 2 2 2 Problem := [[-15 y - 11 z - 8 y + 10 y, -16 x z - 19 x y + 10 z , 2 3 3 -2 x y z - 8 y z + 20 z - 10], [6 z + x z - 18 z + 16, 2 2 3 3 2 3 -5 x y - 12 y z + 2 z - 20 x z, -19 x + 13 x z + 4 z + 11 x y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.18 memory used=24.9MB, alloc=32.3MB, time=0.50 memory used=46.2MB, alloc=60.3MB, time=0.79 memory used=106.2MB, alloc=60.3MB, time=1.45 memory used=149.6MB, alloc=60.3MB, time=1.85 memory used=188.1MB, alloc=60.3MB, time=2.12 memory used=230.6MB, alloc=60.3MB, time=2.51 memory used=268.9MB, alloc=62.9MB, time=2.65 memory used=306.9MB, alloc=62.9MB, time=3.00 memory used=343.2MB, alloc=62.9MB, time=3.27 memory used=380.7MB, alloc=62.9MB, time=3.52 memory used=415.9MB, alloc=62.9MB, time=3.61 memory used=444.1MB, alloc=62.9MB, time=3.77 memory used=466.3MB, alloc=62.9MB, time=3.91 memory used=489.5MB, alloc=62.9MB, time=3.98 memory used=514.7MB, alloc=62.9MB, time=4.04 memory used=543.0MB, alloc=62.9MB, time=4.12 memory used=574.1MB, alloc=62.9MB, time=4.19 memory used=605.5MB, alloc=62.9MB, time=4.26 memory used=622.3MB, alloc=62.9MB, time=4.31 memory used=639.9MB, alloc=62.9MB, time=4.37 memory used=658.3MB, alloc=62.9MB, time=4.43 memory used=678.2MB, alloc=62.9MB, time=4.48 memory used=699.2MB, alloc=62.9MB, time=4.54 memory used=721.7MB, alloc=62.9MB, time=4.60 memory used=745.5MB, alloc=62.9MB, time=4.66 memory used=771.5MB, alloc=62.9MB, time=4.71 memory used=810.0MB, alloc=66.7MB, time=6.85 memory used=833.9MB, alloc=66.7MB, time=6.90 memory used=872.4MB, alloc=66.7MB, time=7.42 memory used=920.1MB, alloc=66.7MB, time=9.11 memory used=946.3MB, alloc=66.7MB, time=9.20 memory used=981.6MB, alloc=66.7MB, time=9.50 memory used=1015.7MB, alloc=66.7MB, time=9.75 memory used=1059.3MB, alloc=74.7MB, time=10.30 memory used=1095.1MB, alloc=74.7MB, time=10.56 memory used=1115.8MB, alloc=74.7MB, time=10.63 memory used=1141.9MB, alloc=74.7MB, time=10.72 memory used=1166.8MB, alloc=74.7MB, time=10.79 memory used=1184.1MB, alloc=74.7MB, time=10.87 memory used=1203.0MB, alloc=74.7MB, time=10.94 memory used=1224.2MB, alloc=74.7MB, time=11.01 memory used=1247.6MB, alloc=74.7MB, time=11.08 memory used=1273.3MB, alloc=74.7MB, time=11.16 memory used=1301.5MB, alloc=74.7MB, time=11.23 memory used=1324.3MB, alloc=74.7MB, time=11.29 memory used=1340.4MB, alloc=74.7MB, time=11.35 memory used=1357.6MB, alloc=74.7MB, time=11.40 memory used=1380.0MB, alloc=74.7MB, time=12.69 memory used=1401.6MB, alloc=98.7MB, time=16.78 memory used=1430.7MB, alloc=122.7MB, time=23.61 memory used=1475.6MB, alloc=122.7MB, time=23.75 memory used=1510.3MB, alloc=122.7MB, time=23.88 memory used=1542.3MB, alloc=122.7MB, time=23.99 memory used=1575.4MB, alloc=146.7MB, time=24.11 memory used=1618.8MB, alloc=146.7MB, time=24.24 memory used=1663.8MB, alloc=146.7MB, time=24.38 memory used=1711.0MB, alloc=146.7MB, time=24.51 memory used=1759.3MB, alloc=146.7MB, time=24.66 memory used=1808.4MB, alloc=146.7MB, time=24.81 memory used=1858.5MB, alloc=146.7MB, time=24.95 memory used=1909.5MB, alloc=146.7MB, time=25.11 memory used=1961.3MB, alloc=146.7MB, time=25.24 memory used=2014.0MB, alloc=146.7MB, time=25.39 memory used=2067.5MB, alloc=146.7MB, time=25.53 memory used=2121.9MB, alloc=146.7MB, time=25.67 memory used=2177.3MB, alloc=146.7MB, time=25.81 memory used=2239.6MB, alloc=146.7MB, time=25.95 memory used=2302.8MB, alloc=146.7MB, time=26.11 memory used=2366.9MB, alloc=146.7MB, time=26.28 memory used=2432.0MB, alloc=146.7MB, time=26.42 memory used=2498.0MB, alloc=146.7MB, time=26.58 memory used=2564.8MB, alloc=146.7MB, time=26.74 memory used=2632.5MB, alloc=146.7MB, time=26.89 memory used=2701.0MB, alloc=146.7MB, time=27.03 memory used=2770.4MB, alloc=146.7MB, time=27.18 memory used=2840.5MB, alloc=146.7MB, time=27.32 memory used=2911.4MB, alloc=146.7MB, time=27.48 memory used=2983.3MB, alloc=146.7MB, time=27.64 memory used=3063.1MB, alloc=146.7MB, time=27.81 memory used=3143.6MB, alloc=146.7MB, time=27.96 memory used=3210.5MB, alloc=146.7MB, time=28.12 memory used=3259.3MB, alloc=146.7MB, time=28.24 memory used=3305.5MB, alloc=146.7MB, time=28.34 memory used=3347.7MB, alloc=146.7MB, time=28.44 memory used=3383.4MB, alloc=146.7MB, time=28.54 memory used=3419.9MB, alloc=146.7MB, time=28.64 memory used=3456.9MB, alloc=146.7MB, time=28.74 memory used=3493.9MB, alloc=146.7MB, time=28.83 memory used=3531.9MB, alloc=146.7MB, time=28.93 memory used=3570.2MB, alloc=146.7MB, time=29.02 memory used=3608.7MB, alloc=146.7MB, time=29.12 memory used=3647.3MB, alloc=146.7MB, time=29.22 memory used=3686.0MB, alloc=146.7MB, time=29.32 memory used=3724.9MB, alloc=146.7MB, time=29.42 memory used=3763.8MB, alloc=146.7MB, time=29.52 memory used=3803.0MB, alloc=146.7MB, time=29.61 memory used=3842.2MB, alloc=146.7MB, time=29.71 memory used=3881.6MB, alloc=146.7MB, time=29.80 memory used=3921.0MB, alloc=146.7MB, time=29.90 memory used=3960.6MB, alloc=146.7MB, time=29.99 memory used=4000.3MB, alloc=146.7MB, time=30.09 memory used=4040.2MB, alloc=146.7MB, time=30.18 memory used=4080.1MB, alloc=146.7MB, time=30.29 memory used=4120.1MB, alloc=146.7MB, time=30.39 memory used=4160.3MB, alloc=146.7MB, time=30.48 memory used=4200.5MB, alloc=146.7MB, time=30.58 memory used=4240.8MB, alloc=146.7MB, time=30.68 memory used=4281.3MB, alloc=146.7MB, time=30.77 memory used=4321.8MB, alloc=146.7MB, time=30.87 memory used=4362.6MB, alloc=146.7MB, time=30.97 memory used=4411.5MB, alloc=146.7MB, time=31.08 memory used=4460.5MB, alloc=146.7MB, time=31.19 memory used=4509.6MB, alloc=146.7MB, time=31.29 memory used=4558.8MB, alloc=146.7MB, time=31.41 memory used=4608.1MB, alloc=146.7MB, time=31.52 memory used=4657.6MB, alloc=146.7MB, time=31.63 memory used=4707.1MB, alloc=146.7MB, time=31.74 memory used=4756.7MB, alloc=146.7MB, time=31.84 memory used=4806.5MB, alloc=146.7MB, time=31.95 memory used=4856.3MB, alloc=146.7MB, time=32.05 memory used=4906.2MB, alloc=146.7MB, time=32.15 memory used=4956.1MB, alloc=146.7MB, time=32.25 memory used=5006.2MB, alloc=146.7MB, time=32.36 memory used=5056.3MB, alloc=146.7MB, time=32.47 memory used=5106.5MB, alloc=146.7MB, time=32.57 memory used=5156.7MB, alloc=146.7MB, time=32.67 memory used=5207.0MB, alloc=146.7MB, time=32.78 memory used=5257.4MB, alloc=146.7MB, time=32.87 memory used=5307.8MB, alloc=146.7MB, time=32.98 memory used=5358.2MB, alloc=146.7MB, time=33.08 memory used=5408.7MB, alloc=146.7MB, time=33.19 memory used=5459.3MB, alloc=146.7MB, time=33.29 memory used=5518.3MB, alloc=146.7MB, time=33.40 memory used=5577.3MB, alloc=146.7MB, time=33.52 memory used=5636.4MB, alloc=146.7MB, time=33.64 memory used=5695.4MB, alloc=146.7MB, time=33.75 memory used=5754.5MB, alloc=146.7MB, time=33.86 memory used=5813.6MB, alloc=146.7MB, time=33.97 memory used=5872.6MB, alloc=146.7MB, time=34.09 memory used=5931.7MB, alloc=146.7MB, time=34.20 memory used=5990.8MB, alloc=146.7MB, time=34.32 memory used=6049.8MB, alloc=146.7MB, time=34.44 memory used=6108.8MB, alloc=146.7MB, time=34.55 memory used=6167.7MB, alloc=146.7MB, time=34.66 memory used=6226.6MB, alloc=146.7MB, time=34.77 memory used=6285.5MB, alloc=146.7MB, time=34.89 memory used=6344.5MB, alloc=146.7MB, time=35.01 memory used=6411.6MB, alloc=146.7MB, time=35.13 memory used=6478.7MB, alloc=146.7MB, time=35.25 memory used=6545.6MB, alloc=146.7MB, time=35.36 memory used=6612.4MB, alloc=146.7MB, time=35.48 memory used=6679.1MB, alloc=146.7MB, time=35.59 memory used=6745.7MB, alloc=146.7MB, time=35.71 memory used=6812.1MB, alloc=146.7MB, time=35.83 memory used=6878.3MB, alloc=146.7MB, time=35.95 memory used=6944.4MB, alloc=146.7MB, time=36.07 memory used=7010.3MB, alloc=146.7MB, time=36.18 memory used=7076.2MB, alloc=146.7MB, time=36.30 memory used=7149.9MB, alloc=146.7MB, time=36.42 memory used=7223.3MB, alloc=146.7MB, time=36.55 memory used=7296.5MB, alloc=146.7MB, time=36.67 memory used=7369.4MB, alloc=146.7MB, time=36.79 memory used=7441.9MB, alloc=146.7MB, time=36.91 memory used=7514.1MB, alloc=146.7MB, time=37.02 memory used=7586.1MB, alloc=146.7MB, time=37.15 memory used=7665.6MB, alloc=146.7MB, time=37.27 memory used=7744.6MB, alloc=146.7MB, time=37.40 memory used=7823.1MB, alloc=146.7MB, time=37.52 memory used=7880.8MB, alloc=155.8MB, time=37.63 memory used=7898.1MB, alloc=155.8MB, time=37.69 memory used=7911.8MB, alloc=155.8MB, time=37.75 memory used=7922.3MB, alloc=155.8MB, time=37.81 memory used=7929.5MB, alloc=155.8MB, time=37.86 memory used=7936.7MB, alloc=155.8MB, time=37.95 memory used=7943.9MB, alloc=155.8MB, time=38.01 memory used=7951.1MB, alloc=155.8MB, time=38.06 memory used=7958.3MB, alloc=155.8MB, time=38.11 memory used=7965.6MB, alloc=155.8MB, time=38.21 memory used=7972.8MB, alloc=155.8MB, time=38.26 memory used=7980.1MB, alloc=155.8MB, time=38.32 memory used=7987.4MB, alloc=155.8MB, time=38.38 memory used=7993.0MB, alloc=411.8MB, time=38.46 memory used=8134.8MB, alloc=411.8MB, time=38.86 memory used=8267.5MB, alloc=411.8MB, time=39.09 memory used=8403.2MB, alloc=411.8MB, time=39.32 memory used=8544.1MB, alloc=411.8MB, time=39.56 memory used=8682.6MB, alloc=411.8MB, time=39.79 memory used=8825.6MB, alloc=411.8MB, time=40.02 memory used=8972.7MB, alloc=411.8MB, time=40.27 memory used=9122.7MB, alloc=411.8MB, time=40.50 memory used=9275.3MB, alloc=411.8MB, time=40.74 memory used=9429.6MB, alloc=411.8MB, time=40.99 memory used=9590.6MB, alloc=411.8MB, time=41.24 memory used=9750.6MB, alloc=411.8MB, time=41.50 memory used=9919.6MB, alloc=411.8MB, time=41.75 memory used=10089.0MB, alloc=411.8MB, time=42.00 memory used=10265.0MB, alloc=411.8MB, time=42.26 memory used=10446.2MB, alloc=411.8MB, time=42.53 memory used=10637.1MB, alloc=411.8MB, time=42.79 memory used=10873.8MB, alloc=411.8MB, time=55.38 memory used=10931.0MB, alloc=411.8MB, time=55.53 memory used=10979.4MB, alloc=411.8MB, time=55.69 memory used=11026.8MB, alloc=411.8MB, time=55.83 memory used=11071.2MB, alloc=411.8MB, time=55.97 memory used=11117.8MB, alloc=411.8MB, time=56.12 memory used=11165.8MB, alloc=411.8MB, time=56.28 memory used=11214.7MB, alloc=411.8MB, time=56.42 memory used=11264.5MB, alloc=411.8MB, time=56.57 memory used=11315.2MB, alloc=411.8MB, time=56.72 memory used=11366.7MB, alloc=411.8MB, time=56.85 memory used=11419.1MB, alloc=411.8MB, time=57.00 memory used=11472.4MB, alloc=411.8MB, time=57.14 memory used=11526.4MB, alloc=411.8MB, time=57.27 memory used=11581.6MB, alloc=411.8MB, time=57.42 memory used=11643.5MB, alloc=411.8MB, time=57.59 memory used=11706.5MB, alloc=411.8MB, time=57.73 memory used=11770.3MB, alloc=411.8MB, time=57.87 memory used=11835.1MB, alloc=411.8MB, time=58.03 memory used=11900.8MB, alloc=411.8MB, time=58.20 memory used=11967.4MB, alloc=411.8MB, time=58.36 memory used=12034.9MB, alloc=411.8MB, time=58.52 memory used=12103.2MB, alloc=411.8MB, time=58.67 memory used=12172.3MB, alloc=411.8MB, time=58.82 memory used=12242.2MB, alloc=411.8MB, time=58.96 memory used=12312.9MB, alloc=411.8MB, time=59.11 memory used=12384.5MB, alloc=411.8MB, time=59.28 memory used=12464.0MB, alloc=411.8MB, time=59.43 memory used=12544.3MB, alloc=411.8MB, time=59.61 memory used=12617.8MB, alloc=411.8MB, time=59.75 memory used=12669.3MB, alloc=411.8MB, time=59.87 memory used=12714.4MB, alloc=411.8MB, time=59.97 memory used=12756.4MB, alloc=411.8MB, time=60.09 memory used=12798.9MB, alloc=411.8MB, time=60.20 memory used=12835.3MB, alloc=411.8MB, time=60.30 memory used=12872.1MB, alloc=411.8MB, time=60.39 memory used=12909.0MB, alloc=411.8MB, time=60.50 memory used=12946.8MB, alloc=411.8MB, time=60.59 memory used=12985.1MB, alloc=411.8MB, time=60.69 memory used=13023.5MB, alloc=411.8MB, time=60.79 memory used=13062.0MB, alloc=411.8MB, time=60.89 memory used=13100.7MB, alloc=411.8MB, time=60.99 memory used=13139.6MB, alloc=411.8MB, time=61.09 memory used=13178.5MB, alloc=411.8MB, time=61.18 memory used=13217.6MB, alloc=411.8MB, time=61.28 memory used=13256.8MB, alloc=411.8MB, time=61.37 memory used=13296.2MB, alloc=411.8MB, time=61.47 memory used=13335.6MB, alloc=411.8MB, time=61.56 memory used=13375.2MB, alloc=411.8MB, time=61.66 memory used=13414.9MB, alloc=411.8MB, time=61.76 memory used=13454.7MB, alloc=411.8MB, time=61.85 memory used=13494.6MB, alloc=411.8MB, time=61.95 memory used=13534.6MB, alloc=411.8MB, time=62.05 memory used=13574.7MB, alloc=411.8MB, time=62.15 memory used=13614.9MB, alloc=411.8MB, time=62.24 memory used=13655.2MB, alloc=411.8MB, time=62.33 memory used=13695.7MB, alloc=411.8MB, time=62.42 memory used=13736.2MB, alloc=411.8MB, time=62.52 memory used=13776.8MB, alloc=411.8MB, time=62.61 memory used=13817.6MB, alloc=411.8MB, time=62.71 memory used=13866.6MB, alloc=411.8MB, time=62.83 memory used=13915.7MB, alloc=411.8MB, time=62.93 memory used=13964.8MB, alloc=411.8MB, time=63.03 memory used=14014.1MB, alloc=411.8MB, time=63.15 memory used=14063.5MB, alloc=411.8MB, time=63.25 memory used=14113.0MB, alloc=411.8MB, time=63.35 memory used=14162.6MB, alloc=411.8MB, time=63.46 memory used=14212.3MB, alloc=411.8MB, time=63.57 memory used=14262.1MB, alloc=411.8MB, time=63.67 memory used=14312.0MB, alloc=411.8MB, time=63.77 memory used=14361.9MB, alloc=411.8MB, time=63.88 memory used=14411.9MB, alloc=411.8MB, time=63.98 memory used=14462.0MB, alloc=411.8MB, time=64.09 memory used=14512.2MB, alloc=411.8MB, time=64.21 memory used=14562.4MB, alloc=411.8MB, time=64.31 memory used=14612.7MB, alloc=411.8MB, time=64.41 memory used=14663.0MB, alloc=411.8MB, time=64.51 memory used=14713.4MB, alloc=411.8MB, time=64.61 memory used=14763.8MB, alloc=411.8MB, time=64.71 memory used=14814.3MB, alloc=411.8MB, time=64.81 memory used=14864.8MB, alloc=411.8MB, time=64.92 memory used=14915.3MB, alloc=411.8MB, time=65.03 memory used=14966.1MB, alloc=411.8MB, time=65.13 memory used=15025.1MB, alloc=411.8MB, time=65.24 memory used=15084.1MB, alloc=411.8MB, time=65.35 memory used=15143.2MB, alloc=411.8MB, time=65.46 memory used=15202.2MB, alloc=411.8MB, time=65.57 memory used=15261.3MB, alloc=411.8MB, time=65.68 memory used=15320.4MB, alloc=411.8MB, time=65.79 memory used=15379.4MB, alloc=411.8MB, time=65.90 memory used=15438.5MB, alloc=411.8MB, time=66.01 memory used=15497.5MB, alloc=411.8MB, time=66.12 memory used=15556.5MB, alloc=411.8MB, time=66.24 memory used=15615.4MB, alloc=411.8MB, time=66.35 memory used=15674.3MB, alloc=411.8MB, time=66.46 memory used=15733.1MB, alloc=411.8MB, time=66.57 memory used=15791.9MB, alloc=411.8MB, time=66.68 memory used=15850.8MB, alloc=411.8MB, time=66.80 memory used=15917.8MB, alloc=411.8MB, time=66.92 memory used=15984.7MB, alloc=411.8MB, time=67.03 memory used=16051.5MB, alloc=411.8MB, time=67.15 memory used=16118.1MB, alloc=411.8MB, time=67.26 memory used=16184.7MB, alloc=411.8MB, time=67.38 memory used=16251.0MB, alloc=411.8MB, time=67.49 memory used=16317.2MB, alloc=411.8MB, time=67.61 memory used=16383.3MB, alloc=411.8MB, time=67.72 memory used=16449.1MB, alloc=411.8MB, time=67.84 memory used=16515.0MB, alloc=411.8MB, time=67.96 memory used=16588.6MB, alloc=411.8MB, time=68.08 memory used=16662.0MB, alloc=411.8MB, time=68.21 memory used=16735.1MB, alloc=411.8MB, time=68.33 memory used=16807.9MB, alloc=411.8MB, time=68.44 memory used=16880.4MB, alloc=411.8MB, time=68.56 memory used=16952.5MB, alloc=411.8MB, time=68.67 memory used=17024.3MB, alloc=411.8MB, time=68.80 memory used=17095.9MB, alloc=411.8MB, time=68.92 memory used=17174.8MB, alloc=411.8MB, time=69.05 memory used=17253.4MB, alloc=411.8MB, time=69.17 memory used=17394.0MB, alloc=411.8MB, time=69.41 memory used=17540.8MB, alloc=411.8MB, time=69.72 memory used=17675.0MB, alloc=411.8MB, time=69.94 memory used=17810.9MB, alloc=411.8MB, time=70.17 memory used=17952.1MB, alloc=411.8MB, time=70.40 memory used=18090.9MB, alloc=411.8MB, time=70.64 memory used=18234.2MB, alloc=411.8MB, time=70.88 memory used=18381.5MB, alloc=411.8MB, time=71.12 memory used=18532.0MB, alloc=411.8MB, time=71.37 memory used=18684.9MB, alloc=411.8MB, time=71.62 memory used=18839.6MB, alloc=411.8MB, time=71.86 memory used=19001.2MB, alloc=411.8MB, time=72.11 memory used=19161.7MB, alloc=411.8MB, time=72.36 memory used=19325.9MB, alloc=411.8MB, time=72.62 memory used=19496.3MB, alloc=411.8MB, time=72.87 memory used=19673.7MB, alloc=411.8MB, time=73.13 memory used=19856.5MB, alloc=411.8MB, time=73.39 memory used=20045.8MB, alloc=411.8MB, time=73.65 memory used=20272.1MB, alloc=411.8MB, time=75.99 memory used=20508.6MB, alloc=411.8MB, time=77.33 memory used=20689.2MB, alloc=411.8MB, time=77.60 memory used=20877.1MB, alloc=411.8MB, time=77.86 memory used=21071.1MB, alloc=411.8MB, time=78.12 memory used=21273.7MB, alloc=411.8MB, time=78.40 memory used=21489.1MB, alloc=411.8MB, time=78.68 memory used=21721.7MB, alloc=411.8MB, time=78.98 memory used=21835.6MB, alloc=411.8MB, time=80.47 memory used=21935.6MB, alloc=411.8MB, time=80.72 memory used=22022.9MB, alloc=411.8MB, time=80.91 memory used=22238.8MB, alloc=411.8MB, time=81.45 memory used=22476.5MB, alloc=411.8MB, time=81.81 memory used=22716.1MB, alloc=411.8MB, time=82.63 memory used=23003.1MB, alloc=411.8MB, time=83.03 memory used=23221.1MB, alloc=411.8MB, time=83.31 memory used=23443.1MB, alloc=411.8MB, time=83.57 memory used=23668.9MB, alloc=411.8MB, time=83.82 memory used=23917.5MB, alloc=411.8MB, time=84.19 memory used=24215.9MB, alloc=411.8MB, time=84.57 memory used=24418.1MB, alloc=411.8MB, time=84.82 memory used=24661.6MB, alloc=411.8MB, time=85.10 memory used=24904.9MB, alloc=411.8MB, time=99.10 memory used=24956.6MB, alloc=411.8MB, time=99.25 memory used=25004.9MB, alloc=411.8MB, time=99.41 memory used=25052.4MB, alloc=411.8MB, time=99.57 memory used=25097.3MB, alloc=411.8MB, time=99.71 memory used=25144.1MB, alloc=411.8MB, time=99.87 memory used=25192.0MB, alloc=411.8MB, time=100.03 memory used=25240.9MB, alloc=411.8MB, 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time=149.48 memory used=43902.0MB, alloc=411.8MB, time=152.96 memory used=44070.9MB, alloc=411.8MB, time=153.21 memory used=44245.8MB, alloc=411.8MB, time=153.47 memory used=44429.2MB, alloc=411.8MB, time=153.72 memory used=44620.2MB, alloc=411.8MB, time=153.98 memory used=44820.4MB, alloc=411.8MB, time=154.25 memory used=45029.9MB, alloc=411.8MB, time=154.53 memory used=45316.5MB, alloc=411.8MB, time=155.53 memory used=45394.6MB, alloc=411.8MB, time=155.71 memory used=45480.4MB, alloc=411.8MB, time=156.04 memory used=45670.0MB, alloc=411.8MB, time=156.35 memory used=45861.9MB, alloc=411.8MB, time=156.66 |\^/| 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(); 1428251888 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 F := [9 y z - 15 x y - 13 y z - 4, 17 x z - 6 x y z - 12 x z - 2 z , 2 2 3 -6 x y + 15 x y z + 19 y z + 12 z ] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 3 2 2 3 G := [-15 x + 9 x y - 20 y - 14 y , -14 x + 12 x z + 9 y z - 17 z , 2 2 2 2 17 x y + 18 x y - 14 y z - 9 x ] > Problem := [F,G]; 2 2 2 3 Problem := [[9 y z - 15 x y - 13 y z - 4, 17 x z - 6 x y z - 12 x z - 2 z , 2 2 3 3 2 3 2 -6 x y + 15 x y z + 19 y z + 12 z ], [-15 x + 9 x y - 20 y - 14 y , 3 2 2 3 2 2 2 2 -14 x + 12 x z + 9 y z - 17 z , 17 x y + 18 x y - 14 y z - 9 x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.18 memory used=25.3MB, alloc=32.3MB, time=0.50 memory used=45.1MB, alloc=56.3MB, time=0.79 memory used=86.4MB, alloc=60.3MB, time=1.40 memory used=126.8MB, alloc=60.3MB, time=1.96 memory used=163.5MB, alloc=84.3MB, time=2.45 memory used=228.4MB, alloc=92.3MB, time=3.42 memory used=285.4MB, alloc=92.3MB, time=4.03 memory used=346.0MB, alloc=92.3MB, time=4.71 memory used=409.0MB, alloc=116.3MB, time=5.69 memory used=491.5MB, alloc=116.3MB, time=6.74 memory used=559.0MB, alloc=372.3MB, time=7.76 memory used=640.1MB, alloc=396.3MB, time=8.78 memory used=751.1MB, alloc=396.3MB, time=10.38 memory used=859.3MB, alloc=420.3MB, time=12.00 memory used=987.1MB, alloc=444.3MB, time=14.09 memory used=1110.9MB, alloc=444.3MB, time=15.42 memory used=1268.6MB, alloc=444.3MB, time=17.76 memory used=1404.8MB, alloc=468.3MB, time=19.93 memory used=1535.2MB, alloc=492.3MB, time=22.14 memory used=1650.6MB, alloc=492.3MB, time=23.88 memory used=1747.7MB, alloc=492.3MB, time=25.28 memory used=1852.6MB, alloc=516.3MB, time=27.05 memory used=1933.8MB, alloc=516.3MB, time=28.31 memory used=2034.3MB, alloc=516.3MB, time=30.01 memory used=2121.6MB, alloc=516.3MB, time=31.32 memory used=2207.3MB, alloc=516.3MB, time=32.80 memory used=2343.7MB, alloc=540.3MB, time=34.67 memory used=2473.2MB, alloc=540.3MB, time=36.81 memory used=2575.7MB, alloc=540.3MB, time=38.11 memory used=2645.5MB, alloc=540.3MB, time=39.19 memory used=2709.5MB, alloc=540.3MB, time=40.09 memory used=2778.6MB, alloc=540.3MB, time=41.41 memory used=2845.6MB, alloc=540.3MB, time=42.79 memory used=2973.1MB, alloc=564.3MB, time=44.70 memory used=3054.0MB, alloc=564.3MB, time=46.92 memory used=3119.5MB, alloc=564.3MB, time=48.03 memory used=3197.8MB, alloc=564.3MB, time=49.53 memory used=3255.6MB, alloc=564.3MB, time=50.40 memory used=3313.0MB, alloc=564.3MB, time=51.50 memory used=3371.5MB, alloc=564.3MB, time=53.01 memory used=3604.1MB, alloc=588.3MB, time=56.08 memory used=3765.2MB, alloc=588.3MB, time=57.67 memory used=3980.1MB, alloc=612.3MB, time=60.57 memory used=4216.2MB, alloc=612.3MB, time=63.01 memory used=4369.7MB, alloc=612.3MB, time=64.29 memory used=4528.9MB, alloc=612.3MB, time=65.57 memory used=4750.1MB, alloc=612.3MB, time=68.01 memory used=4963.5MB, alloc=636.3MB, time=71.01 memory used=5125.9MB, alloc=636.3MB, time=73.69 memory used=5285.6MB, alloc=660.3MB, time=76.36 memory used=5471.8MB, alloc=660.3MB, time=79.31 memory used=5597.2MB, alloc=684.3MB, time=81.45 memory used=5752.3MB, alloc=684.3MB, time=84.75 memory used=5899.9MB, alloc=684.3MB, time=87.96 memory used=6036.4MB, alloc=684.3MB, time=90.74 memory used=6124.4MB, alloc=684.3MB, time=92.85 memory used=6254.3MB, alloc=684.3MB, time=95.77 memory used=6356.1MB, alloc=684.3MB, time=98.42 memory used=6443.2MB, alloc=708.3MB, time=100.68 memory used=6674.8MB, alloc=708.3MB, time=102.78 memory used=6869.6MB, alloc=708.3MB, time=107.16 memory used=7052.4MB, alloc=708.3MB, time=108.46 memory used=7249.9MB, alloc=708.3MB, time=112.95 memory used=7436.7MB, alloc=708.3MB, time=114.22 memory used=7641.5MB, alloc=708.3MB, time=117.83 memory used=7833.5MB, alloc=708.3MB, time=119.86 memory used=8037.2MB, alloc=708.3MB, time=121.46 memory used=8240.9MB, alloc=708.3MB, time=123.79 memory used=8426.5MB, alloc=708.3MB, time=125.12 memory used=8615.0MB, alloc=708.3MB, time=127.76 memory used=8800.3MB, alloc=708.3MB, time=129.00 memory used=8996.1MB, alloc=708.3MB, time=130.78 |\^/| 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(); 1428252188 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 3 2 2 F := [-2 x + 20 y z - y - 1, -5 x + 11 x z - 7 y z + 15 z, 3 3 2 19 x - 10 y + 11 y z + 13 x] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-10 y z - 13 x y + 20 x + 19 z, x y z + 3 y z - 8 x z + 3 y, 2 2 2 -8 x y + 19 y z - 3 z - 5 x] > Problem := [F,G]; 3 2 2 3 2 2 Problem := [[-2 x + 20 y z - y - 1, -5 x + 11 x z - 7 y z + 15 z, 3 3 2 2 19 x - 10 y + 11 y z + 13 x], [-10 y z - 13 x y + 20 x + 19 z, 2 2 2 2 x y z + 3 y z - 8 x z + 3 y, -8 x y + 19 y z - 3 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=4.5MB, alloc=32.3MB, time=0.18 memory used=24.3MB, alloc=32.3MB, time=0.49 memory used=44.3MB, alloc=32.3MB, time=0.67 memory used=64.2MB, alloc=32.3MB, time=0.92 memory used=84.3MB, alloc=32.4MB, time=1.10 memory used=104.3MB, alloc=36.4MB, time=1.29 memory used=124.3MB, alloc=60.4MB, time=1.54 memory used=158.4MB, alloc=60.4MB, time=1.69 memory used=200.1MB, alloc=68.4MB, time=2.21 memory used=247.8MB, alloc=68.4MB, time=2.87 memory used=292.8MB, alloc=68.4MB, time=3.28 memory used=331.5MB, alloc=68.4MB, time=3.63 memory used=377.2MB, alloc=68.4MB, time=4.22 memory used=426.5MB, alloc=92.4MB, time=4.80 memory used=487.5MB, alloc=92.4MB, time=5.64 memory used=545.7MB, alloc=92.4MB, time=6.19 memory used=587.4MB, alloc=92.4MB, time=6.40 memory used=630.2MB, alloc=92.4MB, time=6.89 memory used=665.9MB, alloc=92.4MB, time=7.07 memory used=712.5MB, alloc=92.4MB, time=7.48 memory used=759.8MB, alloc=92.4MB, time=7.94 memory used=798.3MB, alloc=92.4MB, time=8.18 memory used=870.0MB, alloc=92.4MB, time=8.96 memory used=937.5MB, alloc=93.4MB, time=10.71 memory used=965.5MB, alloc=93.4MB, time=10.82 memory used=1020.3MB, alloc=117.4MB, time=11.25 memory used=1088.2MB, alloc=117.4MB, time=12.03 memory used=1157.2MB, alloc=117.4MB, time=12.77 memory used=1212.3MB, alloc=117.4MB, time=13.39 memory used=1270.5MB, alloc=373.4MB, time=14.16 memory used=1339.1MB, alloc=373.4MB, time=15.61 memory used=1417.2MB, alloc=373.4MB, time=16.19 memory used=1506.0MB, alloc=397.4MB, time=17.38 memory used=1618.7MB, alloc=397.4MB, time=18.75 memory used=1728.1MB, alloc=421.4MB, time=20.20 memory used=1847.1MB, alloc=421.4MB, time=21.75 memory used=1933.9MB, alloc=421.4MB, time=22.35 memory used=2006.9MB, alloc=421.4MB, time=23.21 memory used=2071.5MB, alloc=421.4MB, time=23.59 memory used=2164.4MB, alloc=421.4MB, time=24.76 memory used=2232.6MB, alloc=421.4MB, time=25.16 memory used=2306.6MB, alloc=421.4MB, time=25.62 memory used=2366.4MB, alloc=421.4MB, time=25.89 memory used=2446.3MB, alloc=421.4MB, time=28.34 memory used=2500.5MB, alloc=421.4MB, time=28.55 memory used=2594.8MB, alloc=421.4MB, time=29.54 memory used=2664.3MB, alloc=421.4MB, time=29.88 memory used=2726.0MB, alloc=421.4MB, time=30.14 memory used=2799.8MB, alloc=421.4MB, time=32.43 memory used=2853.4MB, alloc=421.4MB, time=32.67 memory used=2961.4MB, alloc=421.4MB, time=33.54 memory used=3121.9MB, alloc=445.4MB, time=35.92 memory used=3297.5MB, alloc=445.4MB, time=38.71 memory used=3430.7MB, alloc=445.4MB, time=41.30 memory used=3577.9MB, alloc=445.4MB, time=42.81 memory used=3713.7MB, alloc=445.4MB, time=44.46 memory used=3794.8MB, alloc=469.4MB, time=45.73 memory used=3918.3MB, alloc=469.4MB, time=47.17 memory used=4004.0MB, alloc=469.4MB, time=47.64 memory used=4116.7MB, alloc=469.4MB, time=48.99 memory used=4201.9MB, alloc=469.4MB, time=49.48 memory used=4277.5MB, alloc=469.4MB, time=49.82 memory used=4371.2MB, alloc=469.4MB, time=50.28 memory used=4445.3MB, alloc=469.4MB, time=50.63 memory used=4543.1MB, alloc=469.4MB, time=53.82 memory used=4617.3MB, alloc=469.4MB, time=54.12 memory used=4751.4MB, alloc=469.4MB, time=55.81 memory used=4904.8MB, alloc=469.4MB, time=57.49 memory used=5069.8MB, alloc=469.4MB, time=60.76 memory used=5225.3MB, alloc=469.4MB, time=62.49 memory used=5390.8MB, alloc=469.4MB, time=65.76 memory used=5503.7MB, alloc=469.4MB, time=67.09 memory used=5568.1MB, alloc=493.4MB, time=67.45 memory used=5663.0MB, alloc=493.4MB, time=67.86 memory used=5755.1MB, alloc=493.4MB, time=68.22 memory used=5822.7MB, alloc=493.4MB, time=68.54 memory used=5899.5MB, alloc=493.4MB, time=68.85 memory used=5985.1MB, alloc=493.4MB, time=69.17 memory used=6082.2MB, alloc=493.4MB, time=69.51 memory used=6192.1MB, alloc=493.4MB, time=69.84 memory used=6337.0MB, alloc=493.4MB, time=70.80 memory used=6417.0MB, alloc=493.4MB, time=71.19 memory used=6517.5MB, alloc=493.4MB, time=71.60 memory used=6600.6MB, alloc=493.4MB, time=71.95 memory used=6669.7MB, alloc=493.4MB, time=72.29 memory used=6747.6MB, alloc=493.4MB, time=72.62 memory used=6835.1MB, alloc=493.4MB, time=72.96 memory used=6934.2MB, alloc=493.4MB, time=73.31 memory used=7047.6MB, alloc=493.4MB, time=73.68 memory used=7192.2MB, alloc=493.4MB, time=81.85 memory used=7283.9MB, alloc=493.4MB, time=82.23 memory used=7360.7MB, alloc=493.4MB, time=82.60 memory used=7454.7MB, alloc=493.4MB, time=82.94 memory used=7706.6MB, alloc=493.4MB, time=83.65 memory used=7871.6MB, alloc=493.4MB, time=84.09 memory used=8076.6MB, alloc=493.4MB, time=84.56 memory used=8175.0MB, alloc=493.4MB, time=85.65 memory used=8281.1MB, alloc=493.4MB, time=86.91 memory used=8357.3MB, alloc=493.4MB, time=88.20 memory used=8469.9MB, alloc=493.4MB, time=89.33 memory used=8578.5MB, alloc=493.4MB, time=90.98 memory used=8696.1MB, alloc=493.4MB, time=91.96 memory used=8772.7MB, alloc=493.4MB, time=93.01 memory used=8871.9MB, alloc=493.4MB, time=93.59 memory used=8965.7MB, alloc=493.4MB, time=94.17 memory used=9064.4MB, alloc=493.4MB, time=96.07 memory used=9162.4MB, alloc=493.4MB, time=97.16 memory used=9228.1MB, alloc=493.4MB, time=98.14 memory used=9343.5MB, alloc=493.4MB, time=100.16 memory used=9435.8MB, alloc=517.4MB, time=101.67 memory used=9547.8MB, alloc=517.4MB, time=104.35 memory used=9606.6MB, alloc=517.4MB, time=105.50 memory used=9645.7MB, alloc=517.4MB, time=106.32 memory used=9742.7MB, alloc=517.4MB, time=108.33 memory used=9812.0MB, alloc=517.4MB, time=110.27 memory used=9881.4MB, alloc=517.4MB, time=111.17 memory used=9959.7MB, alloc=517.4MB, time=112.26 memory used=10049.6MB, alloc=517.4MB, time=112.80 memory used=10136.4MB, alloc=517.4MB, time=114.04 memory used=10250.5MB, alloc=517.4MB, time=114.68 memory used=10350.3MB, alloc=517.4MB, time=115.18 memory used=10431.3MB, alloc=517.4MB, time=115.67 memory used=10532.1MB, alloc=517.4MB, time=116.14 memory used=10627.4MB, alloc=517.4MB, time=116.58 memory used=10741.3MB, alloc=517.4MB, time=117.55 memory used=10843.5MB, alloc=517.4MB, time=118.03 memory used=10922.8MB, alloc=517.4MB, time=118.50 memory used=11019.9MB, alloc=517.4MB, time=118.95 memory used=11120.4MB, alloc=517.4MB, time=119.38 memory used=11246.4MB, alloc=517.4MB, time=131.21 memory used=11337.0MB, alloc=517.4MB, time=131.71 memory used=11440.9MB, alloc=517.4MB, time=132.18 memory used=11527.5MB, alloc=517.4MB, time=132.59 memory used=11604.4MB, alloc=517.4MB, time=132.97 memory used=11693.8MB, alloc=517.4MB, time=133.38 memory used=11799.7MB, alloc=517.4MB, time=133.78 memory used=11927.2MB, alloc=517.4MB, time=134.62 memory used=12050.7MB, alloc=517.4MB, time=135.68 memory used=12163.9MB, alloc=517.4MB, time=137.05 memory used=12269.3MB, alloc=517.4MB, time=137.60 memory used=12345.1MB, alloc=517.4MB, time=138.08 memory used=12437.6MB, alloc=517.4MB, time=138.55 memory used=12546.1MB, alloc=517.4MB, time=139.02 memory used=12653.7MB, alloc=517.4MB, time=140.06 memory used=12754.7MB, alloc=517.4MB, time=140.59 memory used=12839.8MB, alloc=517.4MB, time=141.07 memory used=12927.0MB, alloc=517.4MB, time=141.52 memory used=13035.1MB, alloc=517.4MB, time=141.97 memory used=13142.2MB, alloc=517.4MB, time=153.44 memory used=13255.4MB, alloc=517.4MB, time=154.90 memory used=13341.1MB, alloc=517.4MB, time=155.36 memory used=13451.8MB, alloc=517.4MB, time=155.83 memory used=13523.7MB, alloc=517.4MB, time=156.20 memory used=13605.3MB, alloc=517.4MB, time=156.61 memory used=13699.5MB, alloc=517.4MB, time=157.00 memory used=13826.0MB, alloc=517.4MB, time=157.61 memory used=13921.1MB, alloc=517.4MB, time=158.54 memory used=13971.4MB, alloc=517.4MB, time=159.41 |\^/| 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(); 1428252488 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 F := [-9 x y + 6 x + 6 x y - z , -4 y z + 3 x - 19 x z - 6 y z, 2 8 x y + 2 y + 18 z + 10] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 G := [14 x y + 13 x z + 2 y - 9, 5 x y - 6 x + 14 y z - 12 y, 2 3 2 -5 x z + 18 y + 8 x + 10 z] > Problem := [F,G]; 2 2 2 2 2 Problem := [[-9 x y + 6 x + 6 x y - z , -4 y z + 3 x - 19 x z - 6 y z, 2 2 2 2 8 x y + 2 y + 18 z + 10], [14 x y + 13 x z + 2 y - 9, 2 2 2 3 2 5 x y - 6 x + 14 y z - 12 y, -5 x z + 18 y + 8 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=4.4MB, alloc=32.3MB, time=0.18 memory used=25.4MB, alloc=36.3MB, time=0.49 memory used=46.8MB, alloc=60.3MB, time=0.73 memory used=83.7MB, alloc=60.3MB, time=1.23 memory used=130.2MB, alloc=68.3MB, time=1.86 memory used=169.7MB, alloc=68.3MB, time=2.23 memory used=217.0MB, alloc=68.3MB, time=2.66 memory used=270.9MB, alloc=92.3MB, time=3.20 memory used=339.0MB, alloc=92.3MB, time=4.13 memory used=405.0MB, alloc=348.3MB, time=5.00 memory used=471.1MB, alloc=348.3MB, time=5.76 memory used=555.0MB, alloc=372.3MB, time=6.59 memory used=648.4MB, alloc=372.3MB, time=7.94 memory used=742.1MB, alloc=372.3MB, time=9.03 memory used=835.5MB, alloc=396.3MB, time=10.13 memory used=914.5MB, alloc=396.3MB, time=10.72 memory used=1014.9MB, alloc=396.3MB, time=11.52 memory used=1142.3MB, alloc=396.3MB, time=13.28 memory used=1252.2MB, alloc=420.3MB, time=14.71 memory used=1367.9MB, alloc=420.3MB, time=16.19 memory used=1477.1MB, alloc=444.3MB, time=17.72 memory used=1573.2MB, alloc=468.3MB, time=18.88 memory used=1695.0MB, alloc=468.3MB, time=20.26 memory used=1805.8MB, alloc=468.3MB, time=21.63 memory used=1899.4MB, alloc=468.3MB, time=22.86 memory used=1997.4MB, alloc=468.3MB, time=23.98 memory used=2082.2MB, alloc=492.3MB, time=25.06 memory used=2171.9MB, alloc=492.3MB, time=26.50 memory used=2251.0MB, alloc=492.3MB, time=27.87 memory used=2319.8MB, alloc=492.3MB, time=28.93 memory used=2383.4MB, alloc=492.3MB, time=29.80 memory used=2441.4MB, alloc=492.3MB, time=30.74 memory used=2494.9MB, alloc=492.3MB, time=31.76 memory used=2545.0MB, alloc=492.3MB, time=32.68 memory used=2587.8MB, alloc=492.3MB, time=33.48 memory used=2760.0MB, alloc=516.3MB, time=35.31 memory used=2968.0MB, alloc=516.3MB, time=37.88 memory used=3185.0MB, alloc=540.3MB, time=40.83 memory used=3437.7MB, alloc=564.3MB, time=43.84 memory used=3673.4MB, alloc=564.3MB, time=46.75 memory used=3829.4MB, alloc=588.3MB, time=48.92 memory used=3977.1MB, alloc=612.3MB, time=51.47 memory used=4143.8MB, alloc=612.3MB, time=53.90 memory used=4280.8MB, alloc=612.3MB, time=56.06 memory used=4406.4MB, alloc=636.3MB, time=57.89 memory used=4618.8MB, alloc=636.3MB, time=60.55 memory used=4758.2MB, alloc=636.3MB, time=62.83 memory used=4858.3MB, alloc=636.3MB, time=64.58 memory used=5015.5MB, alloc=636.3MB, time=66.84 memory used=5102.8MB, alloc=636.3MB, time=68.81 memory used=5207.0MB, alloc=660.3MB, time=70.78 memory used=5415.5MB, alloc=660.3MB, time=72.64 memory used=5613.2MB, alloc=660.3MB, time=74.52 memory used=5709.0MB, alloc=660.3MB, time=76.54 memory used=5810.9MB, alloc=660.3MB, time=78.56 memory used=6125.5MB, alloc=684.3MB, time=82.22 memory used=6453.1MB, alloc=684.3MB, time=86.26 memory used=6836.6MB, alloc=708.3MB, time=91.46 memory used=7220.6MB, alloc=732.3MB, time=97.41 memory used=7608.6MB, alloc=756.3MB, time=103.34 memory used=7975.0MB, alloc=780.3MB, time=109.08 |\^/| 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(); 1428252788 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 F := [13 x y z - 19 x - 17 y, -4 z + 14 x y + 13 y + 7 y z, 2 2 2 3 -x y + 4 x z - 14 y z - 5 z ] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 G := [11 y - 19 z + 7 y + 3, -7 x y + 12 x y z + 14 y - 5 y z, 3 2 2 8 x + 17 y z - 14 x + 7 x] > Problem := [F,G]; 3 2 Problem := [[13 x y z - 19 x - 17 y, -4 z + 14 x y + 13 y + 7 y z, 2 2 2 3 3 2 -x y + 4 x z - 14 y z - 5 z ], [11 y - 19 z + 7 y + 3, 2 2 3 2 2 -7 x y + 12 x y z + 14 y - 5 y z, 8 x + 17 y z - 14 x + 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=25.7MB, alloc=32.3MB, time=0.49 memory used=45.1MB, alloc=32.3MB, time=0.76 memory used=63.7MB, alloc=56.3MB, time=1.06 memory used=106.0MB, alloc=60.3MB, time=1.62 memory used=137.0MB, alloc=60.3MB, time=2.05 memory used=180.0MB, alloc=92.3MB, time=2.63 memory used=244.9MB, alloc=92.3MB, time=3.26 memory used=293.2MB, alloc=92.3MB, time=4.09 memory used=332.3MB, alloc=92.3MB, time=4.32 memory used=365.1MB, alloc=107.8MB, time=4.50 memory used=412.6MB, alloc=107.8MB, time=4.61 memory used=470.7MB, alloc=107.8MB, time=5.13 memory used=548.9MB, alloc=107.8MB, time=6.05 memory used=621.3MB, alloc=107.8MB, time=6.83 memory used=686.7MB, alloc=107.8MB, time=7.66 memory used=750.3MB, alloc=107.8MB, time=8.38 memory used=820.6MB, alloc=131.8MB, time=9.08 memory used=872.6MB, alloc=131.8MB, time=9.30 memory used=926.1MB, alloc=131.8MB, time=10.14 memory used=981.9MB, alloc=131.8MB, time=11.22 memory used=1031.6MB, alloc=131.8MB, time=11.37 memory used=1067.0MB, alloc=131.8MB, time=11.48 memory used=1117.3MB, alloc=131.8MB, time=11.65 memory used=1196.4MB, alloc=131.8MB, time=12.46 memory used=1262.8MB, alloc=387.8MB, time=13.23 memory used=1341.9MB, alloc=387.8MB, time=13.93 memory used=1393.5MB, alloc=387.8MB, time=14.81 memory used=1492.2MB, alloc=387.8MB, time=15.69 memory used=1594.1MB, alloc=387.8MB, time=17.70 memory used=1672.1MB, alloc=411.8MB, time=18.55 memory used=1754.2MB, alloc=411.8MB, time=19.13 memory used=1828.9MB, alloc=411.8MB, time=21.29 memory used=1882.5MB, alloc=411.8MB, time=21.47 memory used=2007.4MB, alloc=411.8MB, time=23.03 memory used=2102.3MB, alloc=411.8MB, time=23.92 memory used=2165.2MB, alloc=411.8MB, time=25.29 memory used=2295.0MB, alloc=411.8MB, time=26.97 memory used=2417.5MB, alloc=435.8MB, time=28.34 memory used=2491.6MB, alloc=435.8MB, time=28.83 memory used=2569.0MB, alloc=435.8MB, time=30.26 memory used=2627.8MB, alloc=435.8MB, time=30.49 memory used=2745.9MB, alloc=435.8MB, time=31.73 memory used=2857.7MB, alloc=459.8MB, time=33.44 memory used=2982.2MB, alloc=459.8MB, time=35.28 memory used=3082.5MB, alloc=483.8MB, time=36.78 memory used=3167.1MB, alloc=483.8MB, time=37.90 memory used=3270.2MB, alloc=483.8MB, time=39.48 memory used=3380.9MB, alloc=483.8MB, time=40.93 memory used=3484.5MB, alloc=483.8MB, time=41.62 memory used=3589.5MB, alloc=483.8MB, time=43.64 memory used=3688.7MB, alloc=483.8MB, time=44.99 memory used=3765.1MB, alloc=507.8MB, time=46.17 memory used=3891.0MB, alloc=507.8MB, time=48.44 memory used=3987.4MB, alloc=507.8MB, time=50.86 memory used=4082.4MB, alloc=507.8MB, time=51.55 memory used=4228.1MB, alloc=507.8MB, time=52.68 memory used=4369.2MB, alloc=507.8MB, time=53.80 memory used=4488.1MB, alloc=507.8MB, time=54.87 memory used=4600.2MB, alloc=531.8MB, time=57.22 memory used=4698.7MB, alloc=531.8MB, time=57.65 memory used=4786.0MB, alloc=531.8MB, time=58.03 memory used=4932.2MB, alloc=531.8MB, time=58.88 memory used=5037.9MB, alloc=531.8MB, time=59.37 memory used=5126.4MB, alloc=531.8MB, time=59.79 memory used=5250.9MB, alloc=531.8MB, time=60.44 memory used=5347.0MB, alloc=531.8MB, time=60.89 memory used=5448.7MB, alloc=531.8MB, time=61.33 memory used=5619.3MB, alloc=531.8MB, time=82.91 memory used=5714.7MB, alloc=531.8MB, time=83.37 memory used=5823.6MB, alloc=531.8MB, time=83.86 memory used=5897.2MB, alloc=531.8MB, time=84.24 memory used=5983.0MB, alloc=531.8MB, time=84.63 memory used=6082.5MB, alloc=531.8MB, time=85.02 memory used=6196.9MB, alloc=531.8MB, time=85.46 memory used=6409.2MB, alloc=531.8MB, time=86.14 memory used=6576.6MB, alloc=531.8MB, time=86.64 memory used=6865.2MB, alloc=531.8MB, time=87.55 memory used=6950.7MB, alloc=531.8MB, time=87.95 memory used=7075.9MB, alloc=531.8MB, time=88.63 memory used=7173.1MB, alloc=531.8MB, time=89.07 memory used=7271.1MB, alloc=531.8MB, time=89.51 memory used=7444.5MB, alloc=531.8MB, time=111.17 memory used=7538.7MB, alloc=531.8MB, time=111.65 memory used=7649.4MB, alloc=531.8MB, time=112.10 memory used=7722.7MB, alloc=531.8MB, time=112.50 memory used=7806.9MB, alloc=531.8MB, time=112.90 memory used=7903.8MB, alloc=531.8MB, time=113.33 memory used=8015.5MB, alloc=531.8MB, time=113.72 memory used=8243.3MB, alloc=531.8MB, time=114.28 memory used=8410.6MB, alloc=531.8MB, time=114.74 memory used=8658.0MB, alloc=531.8MB, time=115.85 memory used=8749.6MB, alloc=531.8MB, time=117.17 memory used=8850.0MB, alloc=531.8MB, time=118.28 memory used=8927.7MB, alloc=531.8MB, time=119.60 memory used=9039.6MB, alloc=531.8MB, time=123.07 |\^/| 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(); 1428253088 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 F := [2 x y z - 17 x z + 19 x z - 8 z , -13 x y z + 7 y + 6 x y + 16 x, 2 15 x y + 16 x y - 4 y z + 18] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 G := [12 x z + 18 z + 16 x - 5 y, 18 x z + 3 y z + 19 z + 9 y, 2 x y z - 16 x z - 19 y + 4 z] > Problem := [F,G]; 2 2 3 Problem := [[2 x y z - 17 x z + 19 x z - 8 z , -13 x y z + 7 y + 6 x y + 16 x, 2 2 3 15 x y + 16 x y - 4 y z + 18], [12 x z + 18 z + 16 x - 5 y, 2 2 2 18 x z + 3 y z + 19 z + 9 y, x y z - 16 x z - 19 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=26.4MB, alloc=32.3MB, time=0.50 memory used=46.4MB, alloc=32.3MB, time=0.79 memory used=65.3MB, alloc=56.3MB, time=1.08 memory used=106.0MB, alloc=60.3MB, time=1.70 memory used=145.9MB, alloc=60.3MB, time=2.26 memory used=184.3MB, alloc=84.3MB, time=2.84 memory used=227.6MB, alloc=84.3MB, time=3.51 memory used=291.8MB, alloc=116.3MB, time=4.48 memory used=361.8MB, alloc=372.3MB, time=5.53 memory used=451.8MB, alloc=396.3MB, time=6.83 memory used=565.5MB, alloc=420.3MB, time=8.49 memory used=693.3MB, alloc=420.3MB, time=10.34 memory used=825.7MB, alloc=444.3MB, time=12.53 memory used=952.0MB, alloc=468.3MB, time=14.60 memory used=1079.6MB, alloc=468.3MB, time=16.69 memory used=1186.1MB, alloc=492.3MB, time=18.34 memory used=1293.7MB, alloc=492.3MB, time=19.83 memory used=1397.0MB, alloc=492.3MB, time=21.61 memory used=1487.3MB, alloc=492.3MB, time=22.95 memory used=1579.1MB, alloc=492.3MB, time=24.51 memory used=1660.3MB, alloc=492.3MB, time=25.83 memory used=1756.3MB, alloc=516.3MB, time=26.98 memory used=1836.5MB, alloc=516.3MB, time=28.45 memory used=1920.6MB, alloc=516.3MB, time=29.66 memory used=1986.9MB, alloc=516.3MB, time=30.69 memory used=2051.3MB, alloc=516.3MB, time=32.00 memory used=2110.1MB, alloc=516.3MB, time=33.26 memory used=2177.6MB, alloc=516.3MB, time=34.42 memory used=2239.1MB, alloc=516.3MB, time=35.66 memory used=2318.0MB, alloc=540.3MB, time=36.75 memory used=2373.3MB, alloc=540.3MB, time=38.13 memory used=2599.7MB, alloc=540.3MB, time=40.96 memory used=2757.4MB, alloc=540.3MB, time=42.70 memory used=2907.1MB, alloc=540.3MB, time=44.15 memory used=3123.2MB, alloc=564.3MB, time=48.22 memory used=3296.2MB, alloc=588.3MB, time=51.13 memory used=3479.0MB, alloc=612.3MB, time=54.50 memory used=3650.1MB, alloc=636.3MB, time=57.70 memory used=3792.2MB, alloc=660.3MB, time=60.47 memory used=3948.2MB, alloc=660.3MB, time=63.13 memory used=4075.6MB, alloc=684.3MB, time=65.70 memory used=4188.4MB, alloc=684.3MB, time=67.83 memory used=4317.1MB, alloc=684.3MB, time=70.76 memory used=4424.2MB, alloc=684.3MB, time=72.69 memory used=4533.4MB, alloc=684.3MB, time=74.97 memory used=4895.0MB, alloc=708.3MB, time=80.64 memory used=5256.8MB, alloc=732.3MB, time=87.32 memory used=5630.2MB, alloc=756.3MB, time=95.06 memory used=5981.6MB, alloc=780.3MB, time=102.35 |\^/| 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(); 1428253388 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 F := [-8 x z + 8 x + 6 x z - 20 z, 20 x y + 11 y z + 7 y - 7 z, 2 2 14 x + 6 z - 18 x + 3] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; G := [ 3 2 3 2 -x - 3 x z + 10 x - 11, x y - 10 y - 20 x - y, 8 z + 12 y + 18 y - 4 z] > Problem := [F,G]; 2 2 2 2 2 Problem := [[-8 x z + 8 x + 6 x z - 20 z, 20 x y + 11 y z + 7 y - 7 z, 2 2 14 x + 6 z - 18 x + 3], [ 3 2 3 2 -x - 3 x z + 10 x - 11, x y - 10 y - 20 x - y, 8 z + 12 y + 18 y - 4 z] ] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.17 memory used=26.7MB, alloc=32.3MB, time=0.51 memory used=46.8MB, alloc=60.3MB, time=0.84 memory used=88.6MB, alloc=60.3MB, time=1.48 memory used=128.4MB, alloc=60.3MB, time=2.06 memory used=169.7MB, alloc=60.3MB, time=2.70 memory used=207.5MB, alloc=84.3MB, time=3.30 memory used=250.2MB, alloc=84.3MB, time=3.92 memory used=313.4MB, alloc=92.3MB, time=4.90 memory used=376.8MB, alloc=116.3MB, time=5.88 memory used=441.0MB, alloc=116.3MB, time=6.83 memory used=498.8MB, alloc=372.3MB, time=7.62 memory used=590.2MB, alloc=396.3MB, time=8.88 memory used=711.5MB, alloc=420.3MB, time=10.54 memory used=842.8MB, alloc=420.3MB, time=12.70 memory used=962.4MB, alloc=444.3MB, time=14.01 memory used=1034.0MB, alloc=444.3MB, time=14.30 memory used=1123.1MB, alloc=444.3MB, time=14.94 memory used=1217.4MB, alloc=444.3MB, time=15.61 memory used=1288.4MB, alloc=444.3MB, time=15.89 memory used=1379.8MB, alloc=444.3MB, time=16.49 memory used=1484.4MB, alloc=444.3MB, time=17.24 memory used=1631.2MB, alloc=444.3MB, time=18.82 memory used=1713.3MB, alloc=444.3MB, time=26.54 memory used=1872.4MB, alloc=468.3MB, time=32.79 memory used=2032.0MB, alloc=468.3MB, time=35.55 memory used=2133.0MB, alloc=468.3MB, time=44.19 memory used=2254.2MB, alloc=468.3MB, time=44.63 memory used=2353.5MB, alloc=468.3MB, time=44.93 memory used=2458.7MB, alloc=468.3MB, time=45.24 memory used=2546.6MB, alloc=468.3MB, time=45.51 memory used=2604.0MB, alloc=468.3MB, time=45.75 memory used=2662.1MB, alloc=468.3MB, time=45.99 memory used=2723.4MB, alloc=468.3MB, time=46.22 memory used=2786.4MB, alloc=468.3MB, time=46.46 memory used=2852.2MB, alloc=468.3MB, time=46.70 memory used=2920.6MB, alloc=468.3MB, time=46.96 memory used=2992.7MB, alloc=468.3MB, time=47.23 memory used=3081.7MB, alloc=468.3MB, time=47.60 memory used=3177.9MB, alloc=468.3MB, time=56.76 memory used=3285.1MB, alloc=468.3MB, time=82.22 memory used=3366.2MB, alloc=468.3MB, time=82.59 memory used=3435.6MB, alloc=468.3MB, time=82.86 memory used=3508.5MB, alloc=468.3MB, time=83.14 memory used=3585.3MB, alloc=468.3MB, time=83.43 memory used=3667.2MB, alloc=468.3MB, time=83.72 memory used=3752.3MB, alloc=468.3MB, time=84.01 memory used=3843.1MB, alloc=468.3MB, time=84.29 memory used=3939.0MB, alloc=468.3MB, time=84.58 memory used=4040.3MB, alloc=468.3MB, time=84.87 memory used=4128.5MB, alloc=468.3MB, time=85.14 memory used=4184.4MB, alloc=468.3MB, time=85.38 memory used=4240.9MB, alloc=468.3MB, time=85.61 memory used=4299.9MB, alloc=468.3MB, time=85.85 memory used=4361.1MB, alloc=468.3MB, time=86.07 memory used=4424.2MB, alloc=468.3MB, time=86.31 memory used=4490.3MB, alloc=468.3MB, time=86.55 memory used=4560.0MB, alloc=468.3MB, time=86.78 memory used=4775.6MB, alloc=468.3MB, time=88.84 memory used=4926.3MB, alloc=468.3MB, time=90.52 memory used=5074.4MB, alloc=468.3MB, time=91.88 memory used=5227.9MB, alloc=468.3MB, time=93.22 memory used=5373.5MB, alloc=468.3MB, time=94.62 memory used=5524.9MB, alloc=468.3MB, time=96.23 memory used=5673.3MB, alloc=468.3MB, time=98.16 memory used=5820.7MB, alloc=468.3MB, time=100.38 memory used=5976.0MB, alloc=468.3MB, time=104.41 memory used=6079.9MB, alloc=492.3MB, time=138.60 memory used=6188.4MB, alloc=492.3MB, time=143.25 memory used=6269.8MB, alloc=492.3MB, time=143.74 memory used=6356.3MB, alloc=492.3MB, time=144.23 memory used=6448.7MB, alloc=492.3MB, time=144.72 memory used=6546.4MB, alloc=492.3MB, time=145.23 memory used=6650.4MB, alloc=492.3MB, time=145.73 memory used=6762.8MB, alloc=492.3MB, time=146.24 memory used=6882.1MB, alloc=492.3MB, time=146.76 memory used=6980.8MB, alloc=492.3MB, time=147.23 memory used=7047.2MB, alloc=492.3MB, time=147.60 memory used=7115.3MB, alloc=492.3MB, time=148.00 memory used=7186.0MB, alloc=492.3MB, time=148.40 memory used=7260.5MB, alloc=492.3MB, time=148.79 memory used=7339.2MB, alloc=492.3MB, time=149.19 memory used=7422.0MB, alloc=492.3MB, time=149.60 memory used=7677.7MB, alloc=492.3MB, time=154.71 memory used=7860.0MB, alloc=516.3MB, time=157.53 memory used=8059.2MB, alloc=516.3MB, time=160.30 memory used=8261.5MB, alloc=516.3MB, time=163.20 memory used=8461.5MB, alloc=516.3MB, time=166.62 memory used=8667.2MB, alloc=516.3MB, time=170.64 |\^/| 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(); 1428253688 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 2 F := [-9 x y - 6 x z - 12 x + 12 z , 11 x z + 15 x + 13 x y + 11 x z, 2 12 x y z - 15 z - 14 x + 4 y] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; G := [ 2 2 3 2 2 3 2 -2 x z - 16 x z + 15 z - 9 z, -5 y + 2 y + 4 z + 1, -14 y + 6 x + y] > Problem := [F,G]; 2 2 2 2 Problem := [[-9 x y - 6 x z - 12 x + 12 z , 2 2 2 11 x z + 15 x + 13 x y + 11 x z, 12 x y z - 15 z - 14 x + 4 y], [ 2 2 3 2 2 3 2 -2 x z - 16 x z + 15 z - 9 z, -5 y + 2 y + 4 z + 1, -14 y + 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=4.4MB, alloc=32.3MB, time=0.30 memory used=26.5MB, alloc=32.3MB, time=0.86 memory used=46.9MB, alloc=32.3MB, time=1.40 memory used=65.7MB, alloc=56.3MB, time=1.92 memory used=107.2MB, alloc=60.3MB, time=2.99 memory used=146.8MB, alloc=84.3MB, time=4.04 memory used=208.2MB, alloc=92.3MB, time=5.66 memory used=272.9MB, alloc=116.3MB, time=7.19 memory used=348.3MB, alloc=116.3MB, time=9.31 memory used=423.4MB, alloc=396.3MB, time=11.38 memory used=539.5MB, alloc=396.3MB, time=14.19 memory used=654.1MB, alloc=420.3MB, time=16.95 memory used=788.1MB, alloc=444.3MB, time=20.57 memory used=922.8MB, alloc=468.3MB, time=23.99 memory used=1063.0MB, alloc=468.3MB, time=27.96 memory used=1185.2MB, alloc=468.3MB, time=31.27 memory used=1285.5MB, alloc=492.3MB, time=34.23 memory used=1392.2MB, alloc=492.3MB, time=37.52 memory used=1490.6MB, alloc=492.3MB, time=40.36 memory used=1579.5MB, alloc=492.3MB, time=42.93 memory used=1659.0MB, alloc=492.3MB, time=45.63 memory used=1746.9MB, alloc=492.3MB, time=48.54 memory used=1840.9MB, alloc=492.3MB, time=51.71 memory used=1915.6MB, alloc=492.3MB, time=54.31 memory used=1993.8MB, alloc=516.3MB, time=56.90 memory used=2055.6MB, alloc=516.3MB, time=59.15 memory used=2120.7MB, alloc=516.3MB, time=61.46 memory used=2176.0MB, alloc=516.3MB, time=63.61 memory used=2232.7MB, alloc=516.3MB, time=65.80 memory used=2292.2MB, alloc=516.3MB, time=68.06 memory used=2333.8MB, alloc=516.3MB, time=69.88 memory used=2546.7MB, alloc=540.3MB, time=75.85 memory used=2778.2MB, alloc=564.3MB, time=82.60 memory used=3012.7MB, alloc=588.3MB, time=88.06 memory used=3243.2MB, alloc=612.3MB, time=95.54 memory used=3422.6MB, alloc=636.3MB, time=101.43 memory used=3599.5MB, alloc=660.3MB, time=107.11 memory used=3843.3MB, alloc=660.3MB, time=111.64 memory used=4015.8MB, alloc=660.3MB, time=114.00 memory used=4255.4MB, alloc=660.3MB, time=118.47 |\^/| 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(); 1428253988 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 3 2 2 F := [11 y - 12 y z - 12 y z - 20 x z, x y - 6 y + 18 y z + 15 z , 2 3 3 2 -x y + 3 y + 5 z - 2 x ] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 G := [10 y z + 2 z - 8 y + 15 z, -15 y z + 8 y z + 13 x - 19 y, 2 2 -4 x y - 13 x y - 20 x y - 14 y z] > Problem := [F,G]; 3 2 2 2 3 2 2 Problem := [[11 y - 12 y z - 12 y z - 20 x z, x y - 6 y + 18 y z + 15 z , 2 3 3 2 2 2 -x y + 3 y + 5 z - 2 x ], [10 y z + 2 z - 8 y + 15 z, 2 2 2 2 2 -15 y z + 8 y z + 13 x - 19 y, -4 x y - 13 x y - 20 x y - 14 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.5MB, alloc=32.3MB, time=0.30 memory used=25.5MB, alloc=32.3MB, time=0.84 memory used=44.8MB, alloc=56.3MB, time=1.35 memory used=78.5MB, alloc=60.3MB, time=2.12 memory used=123.0MB, alloc=68.3MB, time=3.14 memory used=164.8MB, alloc=68.3MB, time=4.14 memory used=200.1MB, alloc=68.3MB, time=4.62 memory used=237.1MB, alloc=68.3MB, time=5.46 memory used=260.7MB, alloc=92.3MB, time=5.77 memory used=299.9MB, alloc=92.3MB, time=6.03 memory used=339.2MB, alloc=92.3MB, time=6.35 memory used=393.2MB, alloc=92.3MB, time=7.04 memory used=479.1MB, alloc=92.3MB, time=8.36 memory used=542.6MB, alloc=92.3MB, time=9.67 memory used=575.5MB, alloc=92.3MB, time=9.82 memory used=616.6MB, alloc=92.3MB, time=10.18 memory used=697.6MB, alloc=92.3MB, time=11.64 memory used=759.1MB, alloc=92.3MB, time=12.86 memory used=822.0MB, alloc=92.3MB, time=14.24 memory used=885.8MB, alloc=372.3MB, time=15.78 memory used=975.7MB, alloc=372.3MB, time=17.63 memory used=1018.9MB, alloc=372.3MB, time=17.87 memory used=1058.8MB, alloc=372.3MB, time=18.09 memory used=1111.1MB, alloc=372.3MB, time=18.53 memory used=1178.3MB, alloc=372.3MB, time=19.24 memory used=1275.8MB, alloc=372.3MB, time=21.49 memory used=1333.2MB, alloc=372.3MB, time=22.22 memory used=1392.4MB, alloc=372.3MB, time=23.04 memory used=1446.3MB, alloc=372.3MB, time=23.99 memory used=1495.6MB, alloc=372.3MB, time=24.72 memory used=1543.1MB, alloc=372.3MB, time=25.11 memory used=1578.6MB, alloc=372.3MB, time=25.32 memory used=1617.1MB, alloc=372.3MB, time=25.53 memory used=1661.5MB, alloc=372.3MB, time=26.08 memory used=1708.0MB, alloc=372.3MB, time=26.90 memory used=1752.2MB, alloc=372.3MB, time=27.16 memory used=1788.2MB, alloc=372.3MB, time=27.36 memory used=1826.4MB, alloc=372.3MB, time=27.56 memory used=1898.0MB, alloc=396.3MB, time=34.25 memory used=2296.3MB, alloc=396.3MB, time=46.41 memory used=2709.8MB, alloc=420.3MB, time=54.82 memory used=3112.7MB, alloc=420.3MB, time=61.75 memory used=3382.4MB, alloc=420.3MB, time=67.15 memory used=3474.7MB, alloc=420.3MB, time=68.30 memory used=3558.0MB, alloc=420.3MB, time=69.00 memory used=3632.5MB, alloc=420.3MB, time=69.38 memory used=3712.9MB, alloc=420.3MB, time=69.77 memory used=3776.0MB, alloc=420.3MB, time=70.18 memory used=3871.0MB, alloc=420.3MB, time=72.04 memory used=3931.4MB, alloc=420.3MB, time=72.36 memory used=3991.8MB, alloc=420.3MB, time=72.69 memory used=4052.8MB, alloc=420.3MB, time=73.01 memory used=4114.0MB, alloc=420.3MB, time=73.34 memory used=4174.7MB, alloc=420.3MB, time=73.66 memory used=4238.3MB, alloc=420.3MB, time=73.98 memory used=4303.6MB, alloc=420.3MB, time=74.30 memory used=4372.0MB, alloc=420.3MB, time=74.63 memory used=4441.6MB, alloc=420.3MB, time=74.95 memory used=4513.9MB, alloc=420.3MB, time=75.27 memory used=4588.5MB, alloc=420.3MB, time=75.60 memory used=4666.7MB, alloc=420.3MB, time=75.94 memory used=4747.9MB, alloc=420.3MB, time=76.27 memory used=4831.3MB, alloc=420.3MB, time=76.61 memory used=4917.7MB, alloc=420.3MB, time=76.96 memory used=5001.1MB, alloc=420.3MB, time=77.29 memory used=5053.8MB, alloc=420.3MB, time=77.54 memory used=5100.6MB, alloc=420.3MB, time=77.78 memory used=5148.7MB, alloc=420.3MB, time=78.01 memory used=5197.4MB, alloc=420.3MB, time=78.25 memory used=5247.6MB, alloc=420.3MB, time=78.49 memory used=5299.5MB, alloc=420.3MB, time=78.73 memory used=5352.8MB, alloc=420.3MB, time=78.97 memory used=5424.0MB, alloc=420.3MB, time=79.55 memory used=5559.1MB, alloc=420.3MB, time=81.80 memory used=5680.5MB, alloc=420.3MB, time=84.89 memory used=5805.8MB, alloc=420.3MB, time=87.83 memory used=5926.2MB, alloc=444.3MB, time=90.94 memory used=6052.1MB, alloc=444.3MB, time=93.14 memory used=6134.9MB, alloc=444.3MB, time=94.07 memory used=6233.9MB, alloc=444.3MB, time=96.18 memory used=6293.4MB, alloc=468.3MB, time=96.62 memory used=6379.8MB, alloc=468.3MB, time=97.13 memory used=6474.9MB, alloc=468.3MB, time=97.60 memory used=6537.1MB, alloc=468.3MB, time=98.00 memory used=6607.2MB, alloc=468.3MB, time=98.43 memory used=6688.2MB, alloc=468.3MB, time=98.84 memory used=6784.0MB, alloc=468.3MB, time=99.27 memory used=6875.7MB, alloc=468.3MB, time=101.49 memory used=6978.1MB, alloc=468.3MB, time=102.11 memory used=7059.0MB, alloc=468.3MB, time=102.61 memory used=7160.2MB, alloc=468.3MB, time=103.13 memory used=7225.9MB, alloc=468.3MB, time=103.55 memory used=7294.2MB, alloc=468.3MB, time=103.97 memory used=7373.4MB, alloc=468.3MB, time=104.40 memory used=7464.8MB, alloc=468.3MB, time=104.86 memory used=7555.2MB, alloc=468.3MB, time=105.58 |\^/| 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(); 1428254288 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 3 F := [7 x y + 13 x + 17 y z - 10 z , 11 x y + 2 x z - 5 y - 17 y, 2 2 -12 x y - 10 y z - 9 x - 18 y] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 2 G := [-15 y z - 17 y z + 5 z - 14 x, 8 x z + 2 y - 4 y + z , 2 2 2 11 x y + 16 y z + 15 x y + 15 y ] > Problem := [F,G]; 2 2 2 2 2 3 Problem := [[7 x y + 13 x + 17 y z - 10 z , 11 x y + 2 x z - 5 y - 17 y, 2 2 2 2 -12 x y - 10 y z - 9 x - 18 y], [-15 y z - 17 y z + 5 z - 14 x, 2 3 2 2 2 2 2 8 x z + 2 y - 4 y + z , 11 x y + 16 y z + 15 x y + 15 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.0MB, alloc=32.3MB, time=0.86 memory used=47.2MB, alloc=32.3MB, time=1.22 memory used=65.0MB, alloc=32.3MB, time=1.58 memory used=89.7MB, alloc=60.6MB, time=2.13 memory used=137.9MB, alloc=62.3MB, time=3.17 memory used=180.3MB, alloc=62.3MB, time=3.98 memory used=227.9MB, alloc=62.3MB, time=4.75 memory used=269.1MB, alloc=62.3MB, time=5.64 memory used=292.1MB, alloc=62.3MB, time=5.75 memory used=321.3MB, alloc=62.3MB, time=6.02 memory used=345.3MB, alloc=62.3MB, time=6.20 memory used=372.7MB, alloc=62.3MB, time=6.50 memory used=414.9MB, alloc=62.3MB, time=7.30 memory used=455.4MB, alloc=70.3MB, time=8.37 memory used=497.9MB, alloc=94.3MB, time=9.33 memory used=553.7MB, alloc=94.3MB, time=10.18 memory used=600.8MB, alloc=94.3MB, time=10.75 memory used=657.5MB, alloc=94.3MB, time=13.25 memory used=690.2MB, alloc=94.3MB, time=13.41 memory used=733.7MB, alloc=94.3MB, time=13.68 memory used=777.4MB, alloc=94.3MB, time=14.00 memory used=831.8MB, alloc=94.3MB, time=18.41 memory used=865.4MB, alloc=94.3MB, time=18.59 memory used=898.0MB, alloc=94.3MB, time=18.75 memory used=941.1MB, alloc=94.3MB, time=19.33 memory used=1013.9MB, alloc=94.3MB, time=20.84 memory used=1097.5MB, alloc=94.3MB, time=22.85 memory used=1144.8MB, alloc=94.3MB, time=25.45 memory used=1173.9MB, alloc=94.3MB, time=25.61 memory used=1229.4MB, alloc=94.3MB, time=26.46 memory used=1305.8MB, alloc=94.3MB, time=28.18 memory used=1360.1MB, alloc=118.3MB, time=29.35 memory used=1439.8MB, alloc=118.3MB, time=30.65 memory used=1504.4MB, alloc=118.3MB, time=32.05 memory used=1575.5MB, alloc=118.3MB, time=33.10 memory used=1625.8MB, alloc=118.3MB, time=33.47 memory used=1676.1MB, alloc=118.3MB, time=33.84 memory used=1727.8MB, alloc=118.3MB, time=35.02 memory used=1773.3MB, alloc=118.3MB, time=35.44 memory used=1825.0MB, alloc=118.3MB, time=35.87 memory used=1877.3MB, alloc=118.3MB, time=36.73 memory used=1919.7MB, alloc=118.3MB, time=37.08 memory used=1976.0MB, alloc=118.3MB, time=38.45 memory used=2018.8MB, alloc=118.3MB, time=38.70 memory used=2069.0MB, alloc=118.3MB, time=39.19 memory used=2121.4MB, alloc=118.3MB, time=39.63 memory used=2174.1MB, alloc=118.3MB, time=40.04 memory used=2242.3MB, alloc=118.3MB, time=47.36 memory used=2285.5MB, alloc=118.3MB, time=47.60 memory used=2320.2MB, alloc=118.3MB, time=47.82 memory used=2364.7MB, alloc=118.3MB, time=48.04 memory used=2402.7MB, alloc=118.3MB, time=48.24 memory used=2435.7MB, alloc=118.3MB, time=48.41 memory used=2485.9MB, alloc=118.3MB, time=49.09 memory used=2531.0MB, alloc=118.3MB, time=49.71 memory used=2580.2MB, alloc=118.3MB, time=50.01 memory used=2626.8MB, alloc=118.3MB, time=50.26 memory used=2659.7MB, alloc=118.3MB, time=50.46 memory used=2714.2MB, alloc=118.3MB, time=51.09 memory used=2759.0MB, alloc=118.3MB, time=51.34 memory used=2794.8MB, alloc=118.3MB, time=51.55 memory used=2861.7MB, alloc=118.3MB, time=67.89 memory used=2910.0MB, alloc=118.3MB, time=68.21 memory used=2948.5MB, alloc=118.3MB, time=68.43 memory used=2985.9MB, alloc=118.3MB, time=68.65 memory used=3031.6MB, alloc=118.3MB, time=68.87 memory used=3073.8MB, alloc=118.3MB, time=69.07 memory used=3103.7MB, alloc=118.3MB, time=69.25 memory used=3136.5MB, alloc=118.3MB, time=69.43 memory used=3173.9MB, alloc=118.3MB, time=69.61 memory used=3221.1MB, alloc=118.3MB, time=70.18 memory used=3275.8MB, alloc=130.8MB, time=70.60 memory used=3325.6MB, alloc=130.8MB, time=71.81 memory used=3364.5MB, alloc=130.8MB, time=72.04 memory used=3433.3MB, alloc=386.8MB, time=73.30 memory used=3538.7MB, alloc=386.8MB, time=81.72 memory used=3582.3MB, alloc=386.8MB, time=81.97 memory used=3615.6MB, alloc=386.8MB, time=82.19 memory used=3654.9MB, alloc=386.8MB, time=82.41 memory used=3696.5MB, alloc=386.8MB, time=82.62 memory used=3725.4MB, alloc=386.8MB, time=82.80 memory used=3794.5MB, alloc=386.8MB, time=83.84 memory used=3883.1MB, alloc=410.8MB, time=85.78 memory used=3961.4MB, alloc=410.8MB, time=87.12 memory used=4021.9MB, alloc=410.8MB, time=87.67 memory used=4105.0MB, alloc=410.8MB, time=92.20 memory used=4153.1MB, alloc=410.8MB, time=92.49 memory used=4203.4MB, alloc=410.8MB, time=92.76 memory used=4265.4MB, alloc=410.8MB, time=93.53 memory used=4321.3MB, alloc=410.8MB, time=93.84 memory used=4384.7MB, alloc=410.8MB, time=94.53 memory used=4435.0MB, alloc=410.8MB, time=94.82 memory used=4513.4MB, alloc=410.8MB, time=103.68 memory used=4562.2MB, alloc=410.8MB, time=103.98 memory used=4616.2MB, alloc=410.8MB, time=104.27 memory used=4657.6MB, alloc=410.8MB, time=104.51 memory used=4714.4MB, alloc=410.8MB, time=105.27 memory used=4825.1MB, alloc=410.8MB, time=108.07 memory used=4890.4MB, alloc=410.8MB, time=111.79 memory used=4937.6MB, alloc=410.8MB, time=112.06 memory used=4986.0MB, alloc=410.8MB, time=112.47 memory used=5084.0MB, alloc=410.8MB, time=114.10 memory used=5164.9MB, alloc=410.8MB, time=116.61 memory used=5266.0MB, alloc=434.8MB, time=119.17 memory used=5382.4MB, alloc=434.8MB, time=121.41 memory used=5474.5MB, alloc=434.8MB, time=124.40 memory used=5580.3MB, alloc=434.8MB, time=126.27 memory used=5711.4MB, alloc=458.8MB, time=129.23 memory used=5834.5MB, alloc=458.8MB, time=131.83 memory used=5953.7MB, alloc=458.8MB, time=133.84 memory used=6064.9MB, alloc=458.8MB, time=135.69 memory used=6198.8MB, alloc=458.8MB, time=138.55 memory used=6306.3MB, alloc=458.8MB, time=140.49 memory used=6450.3MB, alloc=458.8MB, time=142.79 memory used=6518.1MB, alloc=458.8MB, time=143.29 memory used=6590.4MB, alloc=458.8MB, time=144.21 memory used=6662.3MB, alloc=458.8MB, time=144.91 memory used=6767.5MB, alloc=458.8MB, time=146.58 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428254588 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [13 x z + 17 x + 3 z, -10 x z - 7 y - 17 z - 10 z, 2 3 2 5 x y + 9 y + 15 y z - 2 y z] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [-5 x z - 13 x y z - 8 x + 13 x y, 13 x y z + 8 x - 9 x z + 6 x, 2 2 x z - 11 x y z + 4 x - 12 x] > Problem := [F,G]; 2 2 2 2 Problem := [[13 x z + 17 x + 3 z, -10 x z - 7 y - 17 z - 10 z, 2 3 2 2 2 5 x y + 9 y + 15 y z - 2 y z], [-5 x z - 13 x y z - 8 x + 13 x y, 2 2 2 13 x y z + 8 x - 9 x z + 6 x, x z - 11 x y z + 4 x - 12 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.30 memory used=26.6MB, alloc=32.3MB, time=0.85 memory used=47.2MB, alloc=32.3MB, time=1.38 memory used=66.3MB, alloc=56.3MB, time=1.88 memory used=105.0MB, alloc=60.3MB, time=2.90 memory used=142.6MB, alloc=84.3MB, time=3.90 memory used=201.3MB, alloc=92.3MB, time=5.48 memory used=259.5MB, alloc=116.3MB, time=7.05 memory used=340.2MB, alloc=116.3MB, time=9.22 memory used=419.9MB, alloc=140.3MB, time=11.47 memory used=515.9MB, alloc=164.3MB, time=14.29 memory used=579.7MB, alloc=420.3MB, time=16.00 memory used=707.6MB, alloc=444.3MB, time=19.66 memory used=862.0MB, alloc=468.3MB, time=24.01 memory used=1030.9MB, alloc=492.3MB, time=28.93 memory used=1225.7MB, alloc=516.3MB, time=34.54 memory used=1452.5MB, alloc=540.3MB, time=40.98 memory used=1691.9MB, alloc=564.3MB, time=48.46 memory used=1962.1MB, alloc=588.3MB, time=56.99 memory used=2245.5MB, alloc=612.3MB, time=66.63 memory used=2510.4MB, alloc=636.3MB, time=76.59 memory used=2759.1MB, alloc=660.3MB, time=85.08 memory used=2969.2MB, alloc=684.3MB, time=92.62 memory used=3173.5MB, alloc=708.3MB, time=100.70 |\^/| 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(); 1428254888 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 F := [-20 x y z + 13 y z - 13 x y - 16 x z, -17 x - 12 x y z + 2 y z - 7 z , 3 2 2 x - 13 x z - 17 x z - 3 x] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 G := [-10 x - 5 y + 3 y + 11 z, 19 x z + 2 z + 13 y - 18 z, 2 -13 x z + 20 x z + 16 x - 13] > Problem := [F,G]; 2 Problem := [[-20 x y z + 13 y z - 13 x y - 16 x z, 3 2 2 3 2 2 -17 x - 12 x y z + 2 y z - 7 z , x - 13 x z - 17 x z - 3 x], [ 3 2 2 2 -10 x - 5 y + 3 y + 11 z, 19 x z + 2 z + 13 y - 18 z, 2 -13 x z + 20 x z + 16 x - 13]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.30 memory used=26.0MB, alloc=32.3MB, time=0.87 memory used=45.4MB, alloc=60.3MB, time=1.38 memory used=84.4MB, alloc=60.3MB, time=1.94 memory used=132.7MB, alloc=68.3MB, time=2.81 memory used=192.5MB, alloc=69.5MB, time=3.94 memory used=239.1MB, alloc=69.5MB, time=4.77 memory used=289.5MB, alloc=69.5MB, time=5.75 memory used=333.6MB, alloc=69.5MB, time=6.46 memory used=364.8MB, alloc=69.5MB, time=6.84 memory used=391.9MB, alloc=69.5MB, time=7.11 memory used=432.5MB, alloc=69.5MB, time=7.81 memory used=479.0MB, alloc=69.5MB, time=8.80 memory used=517.7MB, alloc=93.5MB, time=9.85 memory used=585.4MB, alloc=93.5MB, time=11.48 memory used=653.2MB, alloc=93.5MB, time=12.73 memory used=703.2MB, alloc=93.5MB, time=13.46 memory used=750.7MB, alloc=117.5MB, time=14.10 memory used=816.1MB, alloc=117.5MB, time=14.73 memory used=874.4MB, alloc=117.5MB, time=15.21 memory used=933.3MB, alloc=117.5MB, time=15.72 memory used=989.1MB, alloc=117.5MB, time=16.17 memory used=1043.4MB, alloc=117.5MB, time=16.73 memory used=1115.6MB, alloc=117.5MB, time=17.58 memory used=1207.4MB, alloc=117.5MB, time=19.10 memory used=1303.3MB, alloc=373.5MB, time=20.58 memory used=1384.7MB, alloc=373.5MB, time=22.13 memory used=1496.9MB, alloc=373.5MB, time=23.69 memory used=1572.8MB, alloc=373.5MB, time=24.85 memory used=1624.7MB, alloc=373.5MB, time=25.32 memory used=1676.3MB, alloc=373.5MB, time=25.77 memory used=1724.1MB, alloc=373.5MB, time=26.11 memory used=1775.6MB, alloc=373.5MB, time=26.74 memory used=1813.7MB, alloc=373.5MB, time=26.98 memory used=1860.0MB, alloc=373.5MB, time=27.44 memory used=1897.6MB, alloc=373.5MB, time=27.68 memory used=1946.1MB, alloc=373.5MB, time=28.27 memory used=2020.7MB, alloc=373.5MB, time=29.42 memory used=2116.2MB, alloc=397.5MB, time=30.89 memory used=2235.1MB, alloc=397.5MB, time=32.66 memory used=2321.9MB, alloc=397.5MB, time=33.84 memory used=2445.5MB, alloc=397.5MB, time=36.02 memory used=2566.2MB, alloc=421.5MB, time=38.29 memory used=2690.7MB, alloc=421.5MB, time=40.16 memory used=2767.7MB, alloc=421.5MB, time=40.96 memory used=2852.2MB, alloc=421.5MB, time=41.81 memory used=2928.9MB, alloc=421.5MB, time=42.44 memory used=3008.1MB, alloc=421.5MB, time=43.22 memory used=3082.2MB, alloc=421.5MB, time=43.90 memory used=3153.3MB, alloc=421.5MB, time=44.52 memory used=3221.9MB, alloc=421.5MB, time=45.23 memory used=3334.4MB, alloc=421.5MB, time=46.85 memory used=3465.0MB, alloc=421.5MB, time=48.97 memory used=3602.2MB, alloc=421.5MB, time=51.51 memory used=3724.3MB, alloc=445.5MB, time=54.02 memory used=3832.3MB, alloc=445.5MB, time=56.75 memory used=3935.3MB, alloc=469.5MB, time=59.54 memory used=4028.7MB, alloc=469.5MB, time=61.97 memory used=4115.8MB, alloc=469.5MB, time=64.28 memory used=4209.4MB, alloc=469.5MB, time=66.46 memory used=4288.5MB, alloc=469.5MB, time=68.67 memory used=4364.5MB, alloc=469.5MB, time=70.87 memory used=4486.4MB, alloc=469.5MB, time=73.74 memory used=4587.4MB, alloc=493.5MB, time=75.75 memory used=4656.6MB, alloc=493.5MB, time=77.84 memory used=4748.1MB, alloc=493.5MB, time=79.83 memory used=4823.0MB, alloc=493.5MB, time=82.09 memory used=4908.2MB, alloc=493.5MB, time=83.85 memory used=5010.8MB, alloc=493.5MB, time=86.32 memory used=5069.6MB, alloc=493.5MB, time=88.17 memory used=5137.4MB, alloc=493.5MB, time=90.17 memory used=5206.7MB, alloc=493.5MB, time=92.02 memory used=5282.7MB, alloc=493.5MB, time=93.95 memory used=5331.4MB, alloc=493.5MB, time=95.32 memory used=5431.2MB, alloc=493.5MB, time=96.58 memory used=5541.8MB, alloc=493.5MB, time=98.36 memory used=5645.8MB, alloc=493.5MB, time=99.80 memory used=5739.8MB, alloc=493.5MB, time=100.81 memory used=5824.2MB, alloc=493.5MB, time=101.65 memory used=5917.0MB, alloc=493.5MB, time=102.51 memory used=6009.0MB, alloc=493.5MB, time=103.57 memory used=6089.0MB, alloc=517.5MB, time=104.32 memory used=6184.3MB, alloc=517.5MB, time=105.04 memory used=6287.8MB, alloc=517.5MB, time=106.02 memory used=6387.4MB, alloc=517.5MB, time=106.78 memory used=6483.9MB, alloc=517.5MB, time=107.85 memory used=6580.3MB, alloc=517.5MB, time=108.58 memory used=6707.8MB, alloc=517.5MB, time=110.23 memory used=6823.7MB, alloc=517.5MB, time=111.95 memory used=6916.8MB, alloc=517.5MB, time=112.64 memory used=6995.8MB, alloc=517.5MB, time=114.18 memory used=7063.7MB, alloc=517.5MB, time=115.67 memory used=7142.9MB, alloc=517.5MB, time=117.32 memory used=7193.0MB, alloc=517.5MB, time=118.94 memory used=7241.1MB, alloc=517.5MB, time=121.05 memory used=7441.5MB, alloc=517.5MB, time=124.65 memory used=7648.9MB, alloc=517.5MB, time=130.02 |\^/| 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(); 1428255188 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 3 2 2 2 F := [3 x z + 18 x y - 4 y + x , 8 x + x z + 2 x - 2 z , 2 3 2 -4 x z + 8 y - 6 y z - 20 x] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 G := [-13 x z - 12 y - 13 y z + 9 z, 7 x z - 19 y + 12 z + 16, 2 3 17 x y + 4 y - 4] > Problem := [F,G]; 2 2 3 2 3 2 2 2 Problem := [[3 x z + 18 x y - 4 y + x , 8 x + x z + 2 x - 2 z , 2 3 2 2 3 2 -4 x z + 8 y - 6 y z - 20 x], [-13 x z - 12 y - 13 y z + 9 z, 2 2 3 7 x z - 19 y + 12 z + 16, 17 x y + 4 y - 4]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.31 memory used=25.0MB, alloc=32.3MB, time=0.84 memory used=45.0MB, alloc=32.3MB, time=1.22 memory used=64.8MB, alloc=56.3MB, time=1.69 memory used=107.2MB, alloc=60.3MB, time=2.44 memory used=145.0MB, alloc=60.3MB, time=3.29 memory used=193.4MB, alloc=68.3MB, time=4.30 memory used=246.1MB, alloc=70.0MB, time=5.20 memory used=289.0MB, alloc=70.0MB, time=6.23 memory used=336.9MB, alloc=94.0MB, time=7.18 memory used=403.4MB, alloc=94.0MB, time=8.45 memory used=469.7MB, alloc=350.0MB, time=9.87 memory used=547.0MB, alloc=374.0MB, time=11.25 memory used=640.7MB, alloc=374.0MB, time=13.31 memory used=730.9MB, alloc=398.0MB, time=14.64 memory used=847.1MB, alloc=422.0MB, time=17.09 memory used=958.7MB, alloc=422.0MB, time=18.69 memory used=1065.4MB, alloc=422.0MB, time=20.16 memory used=1165.2MB, alloc=422.0MB, time=21.51 memory used=1308.6MB, alloc=422.0MB, time=23.99 memory used=1444.7MB, alloc=446.0MB, time=26.19 memory used=1544.6MB, alloc=446.0MB, time=28.60 memory used=1655.1MB, alloc=446.0MB, time=29.84 memory used=1767.4MB, alloc=446.0MB, time=31.19 memory used=1886.7MB, alloc=446.0MB, time=33.20 memory used=1992.2MB, alloc=446.0MB, time=35.11 memory used=2074.1MB, alloc=446.0MB, time=36.81 memory used=2176.2MB, alloc=446.0MB, time=37.96 memory used=2261.0MB, alloc=446.0MB, time=38.73 memory used=2346.5MB, alloc=446.0MB, time=39.41 memory used=2425.1MB, alloc=446.0MB, time=40.18 memory used=2521.8MB, alloc=446.0MB, time=41.17 memory used=2602.8MB, alloc=446.0MB, time=41.81 memory used=2691.9MB, alloc=446.0MB, time=43.29 memory used=2764.3MB, alloc=446.0MB, time=43.92 memory used=2849.7MB, alloc=446.0MB, time=44.60 memory used=2934.4MB, alloc=446.0MB, time=46.10 memory used=2996.3MB, alloc=446.0MB, time=46.55 memory used=3086.3MB, alloc=446.0MB, time=47.68 memory used=3205.2MB, alloc=470.0MB, time=50.10 memory used=3312.0MB, alloc=470.0MB, time=52.68 memory used=3428.2MB, alloc=470.0MB, time=54.51 memory used=3549.0MB, alloc=470.0MB, time=56.41 memory used=3676.4MB, alloc=470.0MB, time=58.73 memory used=3786.1MB, alloc=470.0MB, time=61.52 memory used=3874.2MB, alloc=470.0MB, time=63.73 memory used=3949.1MB, alloc=470.0MB, time=65.70 memory used=4048.3MB, alloc=470.0MB, time=67.30 memory used=4163.6MB, alloc=470.0MB, time=68.94 memory used=4245.6MB, alloc=494.0MB, time=70.44 memory used=4301.2MB, alloc=494.0MB, time=71.91 memory used=4378.4MB, alloc=494.0MB, time=73.72 memory used=4431.0MB, alloc=494.0MB, time=77.22 memory used=4533.3MB, alloc=494.0MB, time=78.11 memory used=4645.4MB, alloc=494.0MB, time=79.79 memory used=4699.8MB, alloc=494.0MB, time=81.45 memory used=4757.4MB, alloc=494.0MB, time=82.94 memory used=4815.6MB, alloc=494.0MB, time=84.59 memory used=4855.6MB, alloc=494.0MB, time=86.09 memory used=4907.2MB, alloc=494.0MB, time=87.57 memory used=5005.2MB, alloc=494.0MB, time=89.33 memory used=5045.9MB, alloc=494.0MB, time=90.64 memory used=5236.1MB, alloc=518.0MB, time=94.74 memory used=5375.4MB, alloc=518.0MB, time=96.79 memory used=5552.7MB, alloc=542.0MB, time=103.64 memory used=5660.9MB, alloc=542.0MB, time=104.52 memory used=5787.8MB, alloc=542.0MB, time=106.05 memory used=6055.6MB, alloc=542.0MB, time=110.63 memory used=6327.8MB, alloc=542.0MB, time=115.15 memory used=6521.8MB, alloc=542.0MB, time=119.15 memory used=6739.2MB, alloc=566.0MB, time=122.53 memory used=6899.9MB, alloc=590.0MB, time=127.25 memory used=7081.1MB, alloc=590.0MB, time=130.81 memory used=7289.3MB, alloc=590.0MB, time=134.38 memory used=7458.3MB, alloc=590.0MB, time=138.60 |\^/| 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(); 1428255488 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 3 3 2 F := [-20 y z - 9 z - 7 x, 6 y + 18 z + 13 x z + 4 y , 3 -13 y - 7 x y - 11 z - 11] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [18 x y + 14 y - 16 y z + 12 y, 20 y z + 10 x z - 10 y z - 6 x, 2 2 2 -15 x y - 18 x z - 14 y z + 3 x y] > Problem := [F,G]; 2 3 3 3 2 Problem := [[-20 y z - 9 z - 7 x, 6 y + 18 z + 13 x z + 4 y , 3 2 2 -13 y - 7 x y - 11 z - 11], [18 x y + 14 y - 16 y z + 12 y, 2 2 2 2 20 y z + 10 x z - 10 y z - 6 x, -15 x y - 18 x z - 14 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=4.3MB, alloc=32.3MB, time=0.30 memory used=25.3MB, alloc=32.3MB, time=0.84 memory used=44.6MB, alloc=56.3MB, time=1.34 memory used=91.7MB, alloc=60.3MB, time=2.08 memory used=136.1MB, alloc=68.3MB, time=3.08 memory used=174.4MB, alloc=68.3MB, time=3.60 memory used=197.1MB, alloc=68.3MB, time=3.71 memory used=240.9MB, alloc=68.3MB, time=4.35 memory used=274.4MB, alloc=68.3MB, time=4.83 memory used=301.6MB, alloc=68.3MB, time=5.12 memory used=324.3MB, alloc=68.3MB, time=5.24 memory used=354.0MB, alloc=68.3MB, time=5.57 memory used=386.1MB, alloc=68.3MB, time=5.88 memory used=429.6MB, alloc=68.3MB, time=6.95 memory used=471.5MB, alloc=92.3MB, time=7.99 memory used=539.1MB, alloc=92.3MB, time=9.58 memory used=591.9MB, alloc=92.3MB, time=10.30 memory used=634.8MB, alloc=92.3MB, time=10.90 memory used=673.4MB, alloc=92.3MB, time=12.47 memory used=710.1MB, alloc=92.3MB, time=12.75 memory used=757.3MB, alloc=92.3MB, time=14.85 memory used=786.9MB, alloc=92.3MB, time=15.05 memory used=861.0MB, alloc=92.3MB, time=16.59 memory used=915.4MB, alloc=116.3MB, time=18.00 memory used=999.0MB, alloc=116.3MB, time=19.43 memory used=1053.7MB, alloc=372.3MB, time=20.71 memory used=1145.9MB, alloc=396.3MB, time=22.70 memory used=1219.6MB, alloc=396.3MB, time=23.47 memory used=1278.7MB, alloc=396.3MB, time=23.88 memory used=1343.6MB, alloc=396.3MB, time=24.55 memory used=1413.4MB, alloc=396.3MB, time=25.31 memory used=1480.9MB, alloc=396.3MB, time=26.02 memory used=1533.5MB, alloc=396.3MB, time=26.33 memory used=1587.3MB, alloc=396.3MB, time=26.61 memory used=1634.2MB, alloc=396.3MB, time=26.86 memory used=1702.4MB, alloc=396.3MB, time=27.55 memory used=1760.4MB, alloc=396.3MB, time=27.86 memory used=1806.9MB, alloc=396.3MB, time=28.13 memory used=1862.1MB, alloc=396.3MB, time=29.07 memory used=1946.7MB, alloc=396.3MB, time=48.01 memory used=2001.0MB, alloc=396.3MB, time=48.30 memory used=2048.8MB, alloc=396.3MB, time=48.56 memory used=2108.7MB, alloc=396.3MB, time=48.84 memory used=2159.3MB, alloc=396.3MB, time=49.07 memory used=2199.2MB, alloc=396.3MB, time=49.28 memory used=2244.2MB, alloc=396.3MB, time=49.51 memory used=2293.8MB, alloc=396.3MB, time=49.73 memory used=2348.9MB, alloc=396.3MB, time=49.96 memory used=2423.5MB, alloc=396.3MB, time=50.66 memory used=2479.7MB, alloc=396.3MB, time=51.00 memory used=2535.9MB, alloc=396.3MB, time=51.29 memory used=2580.9MB, alloc=396.3MB, time=51.53 memory used=2654.2MB, alloc=396.3MB, time=52.31 memory used=2705.9MB, alloc=396.3MB, time=52.60 memory used=2757.7MB, alloc=396.3MB, time=52.88 memory used=2805.6MB, alloc=396.3MB, time=53.14 memory used=2902.6MB, alloc=396.3MB, time=72.84 memory used=2974.5MB, alloc=396.3MB, time=73.38 memory used=3020.8MB, alloc=396.3MB, time=73.66 memory used=3074.2MB, alloc=396.3MB, time=73.94 memory used=3137.5MB, alloc=396.3MB, time=74.23 memory used=3176.2MB, alloc=396.3MB, time=74.45 memory used=3218.0MB, alloc=396.3MB, time=74.69 memory used=3264.7MB, alloc=396.3MB, time=74.92 memory used=3316.1MB, alloc=396.3MB, time=75.14 memory used=3374.6MB, alloc=396.3MB, time=75.38 memory used=3471.6MB, alloc=396.3MB, time=76.64 memory used=3600.6MB, alloc=396.3MB, time=86.57 memory used=3663.2MB, alloc=396.3MB, time=87.32 memory used=3706.1MB, alloc=396.3MB, time=87.57 memory used=3762.1MB, alloc=396.3MB, time=87.84 memory used=3808.7MB, alloc=396.3MB, time=88.06 memory used=3848.2MB, alloc=396.3MB, time=88.27 memory used=3892.9MB, alloc=396.3MB, time=88.50 memory used=3981.4MB, alloc=396.3MB, time=89.73 memory used=4098.1MB, alloc=396.3MB, time=92.05 memory used=4178.9MB, alloc=396.3MB, time=93.46 memory used=4232.8MB, alloc=420.3MB, time=93.85 memory used=4289.5MB, alloc=420.3MB, time=94.21 memory used=4368.0MB, alloc=420.3MB, time=94.89 memory used=4428.1MB, alloc=420.3MB, time=95.25 memory used=4519.1MB, alloc=420.3MB, time=106.38 memory used=4591.9MB, alloc=420.3MB, time=107.27 memory used=4654.9MB, alloc=420.3MB, time=107.61 memory used=4709.7MB, alloc=420.3MB, time=107.91 memory used=4779.9MB, alloc=420.3MB, time=108.22 memory used=4891.6MB, alloc=420.3MB, time=109.11 memory used=4948.3MB, alloc=420.3MB, time=109.44 memory used=5026.6MB, alloc=420.3MB, time=110.12 memory used=5085.4MB, alloc=420.3MB, time=110.47 memory used=5176.5MB, alloc=420.3MB, time=121.33 memory used=5257.3MB, alloc=420.3MB, time=122.85 memory used=5322.2MB, alloc=420.3MB, time=123.22 memory used=5374.5MB, alloc=420.3MB, time=123.52 memory used=5440.4MB, alloc=420.3MB, time=123.85 memory used=5601.0MB, alloc=420.3MB, time=125.91 memory used=5708.8MB, alloc=420.3MB, time=132.24 memory used=5769.4MB, alloc=420.3MB, time=132.60 memory used=5822.3MB, alloc=420.3MB, time=132.91 memory used=5946.0MB, alloc=420.3MB, time=134.43 memory used=6035.0MB, alloc=420.3MB, time=135.23 memory used=6124.9MB, alloc=420.3MB, time=141.31 memory used=6195.4MB, alloc=420.3MB, time=141.79 memory used=6282.8MB, alloc=420.3MB, time=147.62 memory used=6358.5MB, alloc=420.3MB, time=148.48 memory used=6459.0MB, alloc=420.3MB, time=149.80 memory used=6574.2MB, alloc=444.3MB, time=152.38 memory used=6709.1MB, alloc=444.3MB, time=155.20 memory used=6842.3MB, alloc=444.3MB, time=158.45 memory used=6962.7MB, alloc=444.3MB, time=161.03 memory used=7081.8MB, alloc=468.3MB, time=163.49 memory used=7186.5MB, alloc=468.3MB, time=165.79 memory used=7342.7MB, alloc=468.3MB, time=168.65 |\^/| 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(); 1428255788 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 F := [-20 x y z + 14 x z + 10 x y - 18 z, 19 x z - 4 z - x - 18 y, 2 3 2 12 x z + z - 7 y - 2 y z] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [17 x z + 20 y z - 17 x z + 4 y z, 5 x y + 3 x y z + 17 x + 3 x z, 2 2 3 -5 x y + 5 x y - 19 y - 11 x y] > Problem := [F,G]; 2 2 3 Problem := [[-20 x y z + 14 x z + 10 x y - 18 z, 19 x z - 4 z - x - 18 y, 2 3 2 2 2 12 x z + z - 7 y - 2 y z], [17 x z + 20 y z - 17 x z + 4 y z, 2 2 2 2 3 5 x y + 3 x y z + 17 x + 3 x z, -5 x y + 5 x y - 19 y - 11 x y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.31 memory used=26.3MB, alloc=32.3MB, time=0.85 memory used=47.1MB, alloc=32.3MB, time=1.38 memory used=66.6MB, alloc=56.3MB, time=1.91 memory used=105.9MB, alloc=60.3MB, time=2.97 memory used=142.1MB, alloc=84.3MB, time=3.96 memory used=200.1MB, alloc=92.3MB, time=5.57 memory used=256.1MB, alloc=116.3MB, time=7.13 memory used=337.1MB, alloc=116.3MB, time=9.36 memory used=415.8MB, alloc=140.3MB, time=11.66 memory used=502.4MB, alloc=140.3MB, time=14.19 memory used=586.7MB, alloc=420.3MB, time=16.71 memory used=708.7MB, alloc=420.3MB, time=20.20 memory used=834.8MB, alloc=444.3MB, time=23.94 memory used=979.7MB, alloc=468.3MB, time=28.01 memory used=1135.5MB, alloc=492.3MB, time=32.39 memory used=1286.1MB, alloc=516.3MB, time=37.11 memory used=1424.8MB, alloc=516.3MB, time=41.38 memory used=1542.0MB, alloc=516.3MB, time=44.86 memory used=1653.8MB, alloc=540.3MB, time=48.21 memory used=1760.8MB, alloc=540.3MB, time=51.55 memory used=1875.0MB, alloc=540.3MB, time=55.63 memory used=1983.1MB, alloc=540.3MB, time=59.63 memory used=2084.0MB, alloc=540.3MB, time=63.53 memory used=2179.2MB, alloc=540.3MB, time=67.00 memory used=2267.3MB, alloc=540.3MB, time=70.36 memory used=2343.6MB, alloc=540.3MB, time=73.28 memory used=2410.5MB, alloc=540.3MB, time=75.65 memory used=2466.3MB, alloc=540.3MB, time=77.58 memory used=2545.9MB, alloc=540.3MB, time=80.62 memory used=2595.8MB, alloc=540.3MB, time=82.62 memory used=2666.1MB, alloc=540.3MB, time=85.32 memory used=2720.6MB, alloc=564.3MB, time=87.69 memory used=2789.4MB, alloc=564.3MB, time=90.81 memory used=3002.6MB, alloc=588.3MB, time=97.95 memory used=3236.7MB, alloc=612.3MB, time=104.85 memory used=3450.1MB, alloc=636.3MB, time=112.24 |\^/| 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(); 1428256088 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 3 F := [-x y - 8 x y z - y + 12, -8 x y - 19 y + 12 z - 7 y, 3 2 -4 z - 11 x + 19 x y + 19] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 G := [-8 x y z - 10 z + 11 x y - 11, 9 x y + 5 y z + 4 x - 15, 2 -11 x y z + 16 x y - 14 y z - 6 z ] > Problem := [F,G]; 2 2 2 3 3 Problem := [[-x y - 8 x y z - y + 12, -8 x y - 19 y + 12 z - 7 y, 3 2 3 -4 z - 11 x + 19 x y + 19], [-8 x y z - 10 z + 11 x y - 11, 2 2 2 2 9 x y + 5 y z + 4 x - 15, -11 x y z + 16 x y - 14 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=4.3MB, alloc=32.3MB, time=0.30 memory used=24.5MB, alloc=32.3MB, time=0.81 memory used=45.2MB, alloc=36.3MB, time=1.23 memory used=63.3MB, alloc=36.5MB, time=1.45 memory used=78.4MB, alloc=36.5MB, time=1.63 memory used=99.8MB, alloc=36.5MB, time=2.09 memory used=125.4MB, alloc=36.5MB, time=2.76 memory used=148.6MB, alloc=60.5MB, time=3.36 memory used=193.4MB, alloc=69.5MB, time=4.12 memory used=234.9MB, alloc=69.5MB, time=4.86 memory used=282.9MB, alloc=69.5MB, time=5.85 memory used=324.8MB, alloc=69.5MB, time=6.74 memory used=367.4MB, alloc=69.5MB, time=7.77 memory used=412.1MB, alloc=93.5MB, time=8.78 memory used=475.9MB, alloc=93.5MB, time=9.77 memory used=528.8MB, alloc=93.5MB, time=10.45 memory used=570.5MB, alloc=93.5MB, time=10.94 memory used=618.0MB, alloc=93.5MB, time=11.25 memory used=660.5MB, alloc=93.5MB, time=11.94 memory used=713.9MB, alloc=93.5MB, time=12.57 memory used=758.3MB, alloc=93.5MB, time=12.93 memory used=806.8MB, alloc=93.5MB, time=14.68 memory used=847.3MB, alloc=93.5MB, time=14.93 memory used=890.7MB, alloc=93.5MB, time=15.27 memory used=926.0MB, alloc=93.5MB, time=15.46 memory used=975.7MB, alloc=93.5MB, time=15.86 memory used=1006.7MB, alloc=93.5MB, time=16.05 memory used=1063.2MB, alloc=93.5MB, time=18.98 memory used=1095.6MB, alloc=93.5MB, time=19.16 memory used=1134.4MB, alloc=93.5MB, time=19.69 memory used=1169.6MB, alloc=93.5MB, time=20.03 memory used=1216.0MB, alloc=93.5MB, time=20.66 memory used=1256.9MB, alloc=93.5MB, time=20.88 memory used=1286.5MB, alloc=93.5MB, time=21.05 memory used=1323.0MB, alloc=93.5MB, time=21.23 memory used=1357.3MB, alloc=93.5MB, time=21.40 memory used=1383.4MB, alloc=93.5MB, time=21.55 memory used=1437.3MB, alloc=93.8MB, time=22.20 memory used=1469.5MB, alloc=93.8MB, time=22.38 memory used=1501.4MB, alloc=93.8MB, time=22.56 memory used=1540.7MB, alloc=93.8MB, time=22.74 memory used=1568.6MB, alloc=93.8MB, time=22.89 memory used=1609.4MB, alloc=93.8MB, time=28.10 memory used=1667.3MB, alloc=93.8MB, time=30.10 memory used=1705.2MB, alloc=93.8MB, time=30.29 memory used=1731.5MB, alloc=93.8MB, time=30.45 memory used=1762.8MB, alloc=93.8MB, time=30.61 memory used=1804.8MB, alloc=93.8MB, time=31.09 memory used=1838.6MB, alloc=93.8MB, time=31.39 memory used=1880.0MB, alloc=97.1MB, time=31.81 memory used=1919.7MB, alloc=97.1MB, time=32.00 memory used=1954.0MB, alloc=97.1MB, time=32.17 memory used=2021.1MB, alloc=97.1MB, time=33.89 memory used=2099.7MB, alloc=353.1MB, time=35.76 memory used=2179.4MB, alloc=353.1MB, time=37.88 memory used=2236.6MB, alloc=353.1MB, time=38.90 memory used=2314.0MB, alloc=353.1MB, time=40.63 memory used=2376.9MB, alloc=377.1MB, time=42.17 memory used=2468.1MB, alloc=377.1MB, time=43.81 memory used=2529.7MB, alloc=377.1MB, time=44.83 memory used=2598.7MB, alloc=377.1MB, time=45.94 memory used=2670.5MB, alloc=377.1MB, time=46.97 memory used=2761.1MB, alloc=401.1MB, time=49.01 memory used=2867.1MB, alloc=401.1MB, time=50.67 memory used=2928.4MB, alloc=401.1MB, time=51.03 memory used=3002.7MB, alloc=401.1MB, time=51.69 memory used=3065.4MB, alloc=401.1MB, time=53.51 memory used=3130.0MB, alloc=401.1MB, time=53.90 memory used=3192.7MB, alloc=401.1MB, time=54.71 memory used=3251.2MB, alloc=401.1MB, time=55.08 memory used=3311.2MB, alloc=401.1MB, time=55.39 memory used=3372.6MB, alloc=401.1MB, time=56.12 memory used=3431.3MB, alloc=401.1MB, time=56.48 memory used=3491.7MB, alloc=401.1MB, time=56.80 memory used=3556.1MB, alloc=401.1MB, time=59.71 memory used=3614.1MB, alloc=401.1MB, time=60.05 memory used=3661.2MB, alloc=401.1MB, time=60.35 memory used=3721.0MB, alloc=401.1MB, time=60.89 memory used=3792.0MB, alloc=401.1MB, time=61.62 memory used=3856.8MB, alloc=401.1MB, time=62.27 memory used=3917.5MB, alloc=401.1MB, time=62.64 memory used=4012.4MB, alloc=401.1MB, time=65.29 memory used=4064.3MB, alloc=401.1MB, time=65.60 memory used=4139.1MB, alloc=401.1MB, time=66.37 memory used=4190.4MB, alloc=401.1MB, time=66.68 memory used=4253.9MB, alloc=401.1MB, time=67.28 memory used=4331.5MB, alloc=401.1MB, time=68.05 memory used=4382.5MB, alloc=401.1MB, time=68.37 memory used=4445.5MB, alloc=401.1MB, time=68.97 memory used=4521.2MB, alloc=401.1MB, time=74.59 memory used=4579.6MB, alloc=401.1MB, time=74.91 memory used=4623.9MB, alloc=401.1MB, time=75.19 memory used=4680.0MB, alloc=401.1MB, time=75.47 memory used=4761.8MB, alloc=401.1MB, time=76.55 memory used=4809.4MB, alloc=401.1MB, time=76.88 memory used=4866.3MB, alloc=401.1MB, time=77.19 memory used=4921.0MB, alloc=401.1MB, time=77.48 memory used=4977.5MB, alloc=401.1MB, time=78.37 memory used=5048.7MB, alloc=401.1MB, time=78.80 memory used=5096.8MB, alloc=401.1MB, time=79.12 memory used=5158.9MB, alloc=401.1MB, time=79.44 memory used=5204.8MB, alloc=401.1MB, time=79.71 memory used=5284.1MB, alloc=401.1MB, time=90.70 memory used=5337.3MB, alloc=401.1MB, time=91.02 memory used=5393.5MB, alloc=401.1MB, time=91.32 memory used=5437.3MB, alloc=401.1MB, time=91.60 memory used=5490.0MB, alloc=401.1MB, time=91.88 memory used=5549.3MB, alloc=401.1MB, time=92.18 memory used=5611.3MB, alloc=401.1MB, time=93.77 memory used=5687.4MB, alloc=401.1MB, time=94.20 memory used=5730.4MB, alloc=401.1MB, time=94.51 memory used=5776.9MB, alloc=401.1MB, time=94.81 memory used=5830.1MB, alloc=401.1MB, time=95.14 memory used=5891.0MB, alloc=401.1MB, time=95.47 memory used=5956.1MB, alloc=401.1MB, time=95.79 memory used=5995.3MB, alloc=401.1MB, time=96.05 memory used=6033.6MB, alloc=401.1MB, time=96.31 memory used=6074.3MB, alloc=401.1MB, time=96.58 memory used=6117.9MB, alloc=401.1MB, time=96.85 memory used=6165.2MB, alloc=401.1MB, time=97.12 memory used=6215.4MB, alloc=401.1MB, time=97.39 memory used=6270.1MB, alloc=401.1MB, time=97.67 memory used=6330.6MB, alloc=401.1MB, time=97.96 memory used=6404.5MB, alloc=401.1MB, time=99.87 memory used=6476.5MB, alloc=401.1MB, time=100.28 memory used=6519.4MB, alloc=401.1MB, time=100.60 memory used=6568.7MB, alloc=401.1MB, time=100.91 memory used=6624.0MB, alloc=401.1MB, time=101.25 memory used=6687.5MB, alloc=401.1MB, time=101.58 memory used=6747.2MB, alloc=401.1MB, time=101.90 memory used=6785.0MB, alloc=401.1MB, time=102.17 memory used=6824.3MB, alloc=401.1MB, time=102.44 memory used=6866.6MB, alloc=401.1MB, time=102.71 memory used=6911.6MB, alloc=401.1MB, time=102.99 memory used=6960.2MB, alloc=401.1MB, time=103.27 memory used=7012.8MB, alloc=401.1MB, time=103.55 memory used=7069.5MB, alloc=401.1MB, time=103.84 memory used=7131.4MB, alloc=401.1MB, time=104.12 memory used=7213.6MB, alloc=401.1MB, time=144.12 memory used=7269.5MB, alloc=401.1MB, time=144.48 memory used=7327.5MB, alloc=401.1MB, time=144.81 memory used=7379.0MB, alloc=401.1MB, time=145.12 memory used=7419.8MB, alloc=401.1MB, time=145.42 memory used=7465.4MB, alloc=401.1MB, time=145.70 memory used=7516.3MB, alloc=401.1MB, time=145.99 memory used=7573.2MB, alloc=401.1MB, time=146.28 memory used=7637.0MB, alloc=401.1MB, time=146.57 memory used=7685.3MB, alloc=401.1MB, time=146.83 memory used=7723.1MB, alloc=401.1MB, time=147.07 memory used=7763.2MB, alloc=401.1MB, time=147.31 memory used=7805.7MB, alloc=401.1MB, time=147.54 memory used=7889.9MB, alloc=401.1MB, time=148.81 memory used=8017.0MB, alloc=401.1MB, time=151.54 memory used=8064.4MB, alloc=401.1MB, time=151.83 memory used=8183.7MB, alloc=401.1MB, time=154.09 memory used=8288.5MB, alloc=425.1MB, time=156.65 memory used=8376.9MB, alloc=425.1MB, time=158.25 memory used=8453.2MB, alloc=425.1MB, time=159.50 memory used=8531.8MB, alloc=425.1MB, time=160.70 memory used=8652.9MB, alloc=425.1MB, time=163.78 memory used=8754.1MB, alloc=425.1MB, time=165.99 |\^/| 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(); 1428256388 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 3 F := [-15 x z + 3 y - x y - 11, 8 x z + 6 y z + z + 20 z, 2 2 -8 x z - 13 y + 19 y + 2 z] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 3 2 2 G := [11 x + 18 y z + 15 x + 9 y z, 15 x - 12 y z + 3 y z , 2 2 -19 x y z + 8 y z - 18 y z - z ] > Problem := [F,G]; 2 3 2 2 3 Problem := [[-15 x z + 3 y - x y - 11, 8 x z + 6 y z + z + 20 z, 2 2 3 2 2 -8 x z - 13 y + 19 y + 2 z], [11 x + 18 y z + 15 x + 9 y z, 3 2 2 2 2 15 x - 12 y z + 3 y z , -19 x y z + 8 y z - 18 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=0.31 memory used=25.2MB, alloc=32.3MB, time=0.84 memory used=44.8MB, alloc=56.3MB, time=1.36 memory used=86.8MB, alloc=60.3MB, time=2.14 memory used=131.8MB, alloc=68.3MB, time=3.22 memory used=172.8MB, alloc=68.3MB, time=4.25 memory used=214.9MB, alloc=92.3MB, time=5.07 memory used=286.4MB, alloc=92.3MB, time=6.66 memory used=324.5MB, alloc=92.3MB, time=6.99 memory used=387.5MB, alloc=92.3MB, time=8.08 memory used=451.4MB, alloc=92.3MB, time=9.56 memory used=515.3MB, alloc=116.3MB, time=11.11 memory used=594.8MB, alloc=116.3MB, time=12.90 memory used=658.8MB, alloc=372.3MB, time=14.42 memory used=745.7MB, alloc=396.3MB, time=16.23 memory used=856.6MB, alloc=420.3MB, time=18.95 memory used=988.2MB, alloc=444.3MB, time=22.37 memory used=1123.6MB, alloc=444.3MB, time=25.70 memory used=1216.9MB, alloc=444.3MB, time=27.39 memory used=1350.4MB, alloc=444.3MB, time=30.08 memory used=1497.3MB, alloc=468.3MB, time=32.80 memory used=1612.1MB, alloc=468.3MB, time=36.00 memory used=1729.8MB, alloc=468.3MB, time=39.40 memory used=1832.9MB, alloc=492.3MB, time=42.07 memory used=1950.9MB, alloc=492.3MB, time=44.84 memory used=2087.5MB, alloc=492.3MB, time=46.91 memory used=2220.8MB, alloc=492.3MB, time=49.31 memory used=2354.0MB, alloc=492.3MB, time=51.58 memory used=2470.8MB, alloc=492.3MB, time=57.59 memory used=2551.6MB, alloc=492.3MB, time=58.14 memory used=2658.1MB, alloc=492.3MB, time=59.40 memory used=2775.1MB, alloc=492.3MB, time=65.26 memory used=2856.1MB, alloc=492.3MB, time=65.86 memory used=3007.0MB, alloc=492.3MB, time=68.33 memory used=3094.7MB, alloc=492.3MB, time=70.35 memory used=3180.5MB, alloc=492.3MB, time=72.99 memory used=3260.3MB, alloc=492.3MB, time=75.45 memory used=3326.5MB, alloc=492.3MB, time=77.49 memory used=3402.5MB, alloc=492.3MB, time=79.90 memory used=3470.7MB, alloc=516.3MB, time=82.00 memory used=3542.5MB, alloc=516.3MB, time=84.45 memory used=3606.6MB, alloc=516.3MB, time=86.48 memory used=3667.8MB, alloc=516.3MB, time=88.66 memory used=3733.6MB, alloc=516.3MB, time=90.78 memory used=3783.0MB, alloc=516.3MB, time=92.64 memory used=3983.7MB, alloc=540.3MB, time=98.72 memory used=4203.2MB, alloc=564.3MB, time=103.86 memory used=4415.2MB, alloc=588.3MB, time=110.13 memory used=4645.9MB, alloc=612.3MB, time=117.86 memory used=4874.7MB, alloc=636.3MB, time=123.74 memory used=5114.7MB, alloc=636.3MB, time=130.10 memory used=5345.7MB, alloc=636.3MB, time=133.65 |\^/| 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(); 1428256688 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 2 2 F := [5 x z - 12 y + 5 y z - 3 x z, -20 x z + 19 y z - 14 y z - 5 z, 3 2 3 y - 8 y z + 5 z + 10 y] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [-2 x z - 2 x y + 7 y z - 11 z, 20 y z - 4 x z - 16 y + 19 y z, 3 3 2 2 x - 6 z - 19 x y - 11 z ] > Problem := [F,G]; 2 3 2 Problem := [[5 x z - 12 y + 5 y z - 3 x z, 2 2 2 3 2 3 -20 x z + 19 y z - 14 y z - 5 z, y - 8 y z + 5 z + 10 y], [ 2 2 2 -2 x z - 2 x y + 7 y z - 11 z, 20 y z - 4 x z - 16 y + 19 y z, 3 3 2 2 x - 6 z - 19 x y - 11 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.31 memory used=26.4MB, alloc=32.3MB, time=0.87 memory used=46.6MB, alloc=56.3MB, time=1.34 memory used=85.4MB, alloc=60.3MB, time=2.24 memory used=127.4MB, alloc=68.3MB, time=3.32 memory used=167.3MB, alloc=68.3MB, time=4.36 memory used=206.1MB, alloc=92.3MB, time=5.38 memory used=269.5MB, alloc=92.3MB, time=6.65 memory used=339.6MB, alloc=92.3MB, time=8.22 memory used=403.0MB, alloc=92.3MB, time=9.54 memory used=466.3MB, alloc=116.3MB, time=10.99 memory used=547.9MB, alloc=116.3MB, time=12.65 memory used=619.9MB, alloc=140.3MB, time=14.99 memory used=680.5MB, alloc=140.3MB, time=17.99 memory used=741.9MB, alloc=140.3MB, time=18.30 memory used=815.3MB, alloc=140.3MB, time=18.76 memory used=872.7MB, alloc=140.3MB, time=19.85 memory used=932.6MB, alloc=140.3MB, time=20.27 memory used=999.3MB, alloc=140.3MB, time=21.15 memory used=1121.2MB, alloc=140.3MB, time=26.20 memory used=1184.5MB, alloc=140.3MB, time=27.54 memory used=1300.2MB, alloc=396.3MB, time=29.42 memory used=1373.0MB, alloc=396.3MB, time=34.36 memory used=1487.7MB, alloc=396.3MB, time=35.77 memory used=1617.1MB, alloc=396.3MB, time=37.91 memory used=1714.9MB, alloc=396.3MB, time=43.49 memory used=1791.6MB, alloc=396.3MB, time=44.49 memory used=1889.5MB, alloc=420.3MB, time=47.08 memory used=2011.0MB, alloc=444.3MB, time=49.95 memory used=2145.4MB, alloc=444.3MB, time=53.28 memory used=2271.2MB, alloc=468.3MB, time=56.21 memory used=2401.7MB, alloc=492.3MB, time=59.82 memory used=2525.7MB, alloc=492.3MB, time=63.13 memory used=2640.7MB, alloc=492.3MB, time=65.56 memory used=2775.5MB, alloc=492.3MB, time=67.61 memory used=2894.4MB, alloc=492.3MB, time=69.30 memory used=3065.8MB, alloc=492.3MB, time=72.26 memory used=3180.0MB, alloc=516.3MB, time=74.51 memory used=3289.7MB, alloc=516.3MB, time=76.97 memory used=3385.4MB, alloc=516.3MB, time=79.70 memory used=3472.1MB, alloc=516.3MB, time=82.05 memory used=3547.7MB, alloc=516.3MB, time=84.28 memory used=3627.6MB, alloc=516.3MB, time=86.53 memory used=3693.1MB, alloc=516.3MB, time=88.75 memory used=3774.0MB, alloc=516.3MB, time=91.36 memory used=3864.8MB, alloc=516.3MB, time=93.45 memory used=3913.4MB, alloc=516.3MB, time=95.09 memory used=3966.4MB, alloc=516.3MB, time=96.69 memory used=4027.8MB, alloc=516.3MB, time=98.65 memory used=4123.6MB, alloc=540.3MB, time=100.34 memory used=4212.0MB, alloc=540.3MB, time=102.26 memory used=4334.1MB, alloc=540.3MB, time=104.14 memory used=4396.4MB, alloc=540.3MB, time=106.05 memory used=4449.7MB, alloc=540.3MB, time=107.92 memory used=4487.5MB, alloc=540.3MB, time=109.08 memory used=4531.4MB, alloc=540.3MB, time=110.46 memory used=4750.8MB, alloc=564.3MB, time=116.67 memory used=4947.2MB, alloc=588.3MB, time=121.26 memory used=5121.2MB, alloc=612.3MB, time=126.03 memory used=5316.8MB, alloc=636.3MB, time=132.51 |\^/| 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(); 1428256988 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [-8 x z - x y - 18 y - 12 z, 14 x y z - 17 x - y z - 8 z , 2 2 3 x z + 3 y z - 4 z ] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 2 3 G := [20 x y + 8 y - 15 y z - 14 z , 13 x y + 5 y + 14 x z - 10, 2 -x z + 17 y z - 16 z + 11] > Problem := [F,G]; 2 2 2 2 Problem := [[-8 x z - x y - 18 y - 12 z, 14 x y z - 17 x - y z - 8 z , 2 2 2 3 2 2 3 x z + 3 y z - 4 z ], [20 x y + 8 y - 15 y z - 14 z , 2 3 2 13 x y + 5 y + 14 x z - 10, -x z + 17 y z - 16 z + 11]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.31 memory used=25.2MB, alloc=32.3MB, time=0.85 memory used=45.5MB, alloc=56.3MB, time=1.38 memory used=86.4MB, alloc=60.3MB, time=2.43 memory used=126.1MB, alloc=60.3MB, time=3.42 memory used=165.2MB, alloc=84.3MB, time=4.39 memory used=233.0MB, alloc=92.3MB, time=5.84 memory used=278.3MB, alloc=92.3MB, time=6.52 memory used=343.5MB, alloc=92.3MB, time=8.11 memory used=407.5MB, alloc=372.3MB, time=9.78 memory used=495.5MB, alloc=396.3MB, time=12.04 memory used=609.2MB, alloc=420.3MB, time=14.95 memory used=738.0MB, alloc=420.3MB, time=18.33 memory used=864.0MB, alloc=444.3MB, time=21.40 memory used=994.1MB, alloc=444.3MB, time=24.53 memory used=1148.3MB, alloc=468.3MB, time=29.52 memory used=1256.7MB, alloc=468.3MB, time=32.19 memory used=1411.6MB, alloc=468.3MB, time=34.94 memory used=1569.7MB, alloc=468.3MB, time=38.65 memory used=1659.1MB, alloc=468.3MB, time=41.07 memory used=1742.8MB, alloc=468.3MB, time=41.75 memory used=1839.3MB, alloc=468.3MB, time=45.26 memory used=1911.1MB, alloc=468.3MB, time=45.73 memory used=2038.0MB, alloc=468.3MB, time=48.39 memory used=2174.5MB, alloc=468.3MB, time=52.01 memory used=2273.6MB, alloc=492.3MB, time=54.75 memory used=2377.1MB, alloc=492.3MB, time=57.99 memory used=2454.1MB, alloc=492.3MB, time=60.47 memory used=2537.9MB, alloc=492.3MB, time=62.98 memory used=2611.8MB, alloc=492.3MB, time=65.20 memory used=2687.6MB, alloc=492.3MB, time=67.51 memory used=2755.0MB, alloc=492.3MB, time=69.66 memory used=2820.7MB, alloc=492.3MB, time=71.83 memory used=2872.8MB, alloc=492.3MB, time=73.61 memory used=2950.6MB, alloc=492.3MB, time=75.44 memory used=3025.8MB, alloc=516.3MB, time=77.54 memory used=3085.4MB, alloc=516.3MB, time=79.44 memory used=3131.3MB, alloc=516.3MB, time=81.19 memory used=3255.4MB, alloc=516.3MB, time=83.93 memory used=3361.4MB, alloc=516.3MB, time=84.83 memory used=3470.9MB, alloc=516.3MB, time=87.14 memory used=3550.7MB, alloc=516.3MB, time=89.16 memory used=3610.8MB, alloc=516.3MB, time=90.65 memory used=3728.0MB, alloc=516.3MB, time=93.52 memory used=3926.2MB, alloc=516.3MB, time=98.46 memory used=4125.4MB, alloc=540.3MB, time=104.48 memory used=4313.0MB, alloc=564.3MB, time=109.68 memory used=4516.2MB, alloc=588.3MB, time=115.33 memory used=4725.3MB, alloc=612.3MB, time=122.81 memory used=4864.8MB, alloc=612.3MB, time=124.16 memory used=5010.8MB, alloc=612.3MB, time=125.50 memory used=5225.2MB, alloc=612.3MB, time=130.52 |\^/| 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(); 1428257288 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 F := [-8 x + 16 y z + 5 x y, -9 z + 14 x + 18 y z - 6 y, 3 2 -19 x + 6 x y z + 20 y z + z] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 2 G := [16 x z - 17 y z - 2 y z + 6 y, -2 x - 9 x z - 4 x y + 9, 2 2 x y + 2 z + 7 x + 18 y] > Problem := [F,G]; 3 2 3 2 Problem := [[-8 x + 16 y z + 5 x y, -9 z + 14 x + 18 y z - 6 y, 3 2 2 2 2 -19 x + 6 x y z + 20 y z + z], [16 x z - 17 y z - 2 y z + 6 y, 3 2 2 2 2 -2 x - 9 x z - 4 x y + 9, x y + 2 z + 7 x + 18 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.31 memory used=24.3MB, alloc=32.3MB, time=0.74 memory used=44.6MB, alloc=36.3MB, time=1.21 memory used=65.3MB, alloc=36.3MB, time=1.69 memory used=83.5MB, alloc=60.3MB, time=2.12 memory used=126.2MB, alloc=60.3MB, time=2.91 memory used=173.2MB, alloc=68.3MB, time=3.98 memory used=218.2MB, alloc=68.3MB, time=5.14 memory used=246.4MB, alloc=68.3MB, time=5.46 memory used=292.9MB, alloc=92.3MB, time=6.48 memory used=356.9MB, alloc=92.3MB, time=7.75 memory used=419.7MB, alloc=348.3MB, time=9.13 memory used=490.0MB, alloc=372.3MB, time=10.64 memory used=579.5MB, alloc=372.3MB, time=12.40 memory used=652.3MB, alloc=372.3MB, time=13.57 memory used=714.1MB, alloc=372.3MB, time=14.46 memory used=816.6MB, alloc=372.3MB, time=16.58 memory used=917.4MB, alloc=396.3MB, time=18.42 memory used=1030.1MB, alloc=396.3MB, time=21.21 memory used=1146.7MB, alloc=420.3MB, time=23.87 memory used=1263.1MB, alloc=420.3MB, time=26.13 memory used=1348.5MB, alloc=420.3MB, time=27.36 memory used=1479.1MB, alloc=444.3MB, time=29.95 memory used=1587.2MB, alloc=444.3MB, time=32.52 memory used=1714.7MB, alloc=444.3MB, time=35.11 memory used=1826.7MB, alloc=444.3MB, time=38.06 memory used=1966.5MB, alloc=468.3MB, time=40.19 memory used=2083.7MB, alloc=468.3MB, time=43.48 memory used=2191.6MB, alloc=468.3MB, time=47.50 memory used=2308.7MB, alloc=468.3MB, time=49.99 memory used=2406.9MB, alloc=468.3MB, time=51.87 memory used=2503.8MB, alloc=468.3MB, time=54.24 memory used=2592.7MB, alloc=468.3MB, time=56.52 memory used=2668.4MB, alloc=468.3MB, time=58.60 memory used=2737.1MB, alloc=468.3MB, time=60.64 memory used=2805.2MB, alloc=468.3MB, time=62.58 memory used=2866.2MB, alloc=468.3MB, time=64.54 memory used=2948.4MB, alloc=492.3MB, time=66.39 memory used=3020.8MB, alloc=492.3MB, time=68.27 memory used=3083.4MB, alloc=492.3MB, time=70.36 memory used=3158.5MB, alloc=492.3MB, time=71.96 memory used=3252.0MB, alloc=492.3MB, time=73.96 memory used=3363.3MB, alloc=492.3MB, time=75.38 memory used=3439.2MB, alloc=492.3MB, time=76.04 memory used=3537.6MB, alloc=492.3MB, time=76.72 memory used=3644.6MB, alloc=492.3MB, time=77.78 memory used=3718.4MB, alloc=492.3MB, time=78.47 memory used=3836.7MB, alloc=492.3MB, time=83.44 memory used=3934.1MB, alloc=492.3MB, time=84.64 memory used=4031.6MB, alloc=492.3MB, time=85.36 memory used=4097.4MB, alloc=492.3MB, time=85.94 memory used=4175.2MB, alloc=492.3MB, time=86.57 memory used=4267.1MB, alloc=492.3MB, time=87.20 memory used=4376.3MB, alloc=492.3MB, time=87.85 memory used=4519.1MB, alloc=492.3MB, time=88.89 memory used=4696.5MB, alloc=492.3MB, time=91.23 memory used=4802.4MB, alloc=492.3MB, time=93.16 memory used=4894.9MB, alloc=492.3MB, time=94.08 memory used=4963.3MB, alloc=492.3MB, time=95.92 memory used=5028.9MB, alloc=492.3MB, time=97.41 memory used=5085.1MB, alloc=492.3MB, time=98.90 memory used=5137.5MB, alloc=492.3MB, time=100.80 memory used=5324.3MB, alloc=516.3MB, time=105.24 memory used=5533.9MB, alloc=540.3MB, time=109.73 memory used=5694.9MB, alloc=564.3MB, time=114.05 memory used=5855.0MB, alloc=564.3MB, time=118.77 |\^/| 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(); 1428257588 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 2 2 F := [-11 x z - 9 y z - 12 x z - 15 z , -12 x - 10 x y - 11 x z + 8 y z, 2 2 2 14 x y + 13 y z + 7 y - 17 x] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 G := [-19 x + 12 x z - 7 x z + 11 x z, 17 x y - 19 x y + 11 z - 14, 2 2 2 2 19 x z - 6 x z - 7 y + 9 z ] > Problem := [F,G]; 2 2 2 Problem := [[-11 x z - 9 y z - 12 x z - 15 z , 3 2 2 2 2 2 2 -12 x - 10 x y - 11 x z + 8 y z, 14 x y + 13 y z + 7 y - 17 x], [ 3 2 2 2 2 -19 x + 12 x z - 7 x z + 11 x z, 17 x y - 19 x y + 11 z - 14, 2 2 2 2 19 x z - 6 x 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=4.4MB, alloc=32.3MB, time=0.32 memory used=25.9MB, alloc=32.3MB, time=0.87 memory used=45.4MB, alloc=56.3MB, time=1.39 memory used=86.5MB, alloc=60.3MB, time=2.40 memory used=128.0MB, alloc=60.3MB, time=3.43 memory used=168.1MB, alloc=60.3MB, time=4.12 memory used=207.6MB, alloc=60.3MB, time=4.87 memory used=233.9MB, alloc=60.3MB, time=5.22 memory used=275.9MB, alloc=92.3MB, time=6.42 memory used=343.9MB, alloc=92.3MB, time=7.84 memory used=386.0MB, alloc=92.3MB, time=8.25 memory used=427.6MB, alloc=92.3MB, time=8.82 memory used=462.1MB, alloc=92.3MB, time=9.02 memory used=493.5MB, alloc=92.3MB, time=9.18 memory used=539.7MB, alloc=92.3MB, time=10.50 memory used=571.2MB, alloc=92.3MB, time=10.69 memory used=603.5MB, alloc=92.3MB, time=10.85 memory used=631.6MB, alloc=92.3MB, time=11.00 memory used=666.5MB, alloc=92.3MB, time=11.15 memory used=727.3MB, alloc=92.3MB, time=12.52 memory used=789.1MB, alloc=116.3MB, time=14.15 memory used=851.0MB, alloc=372.3MB, time=15.67 memory used=935.6MB, alloc=372.3MB, time=17.53 memory used=1028.8MB, alloc=372.3MB, time=19.47 memory used=1116.0MB, alloc=396.3MB, time=21.52 memory used=1215.7MB, alloc=396.3MB, time=23.64 memory used=1278.7MB, alloc=396.3MB, time=24.71 memory used=1386.5MB, alloc=396.3MB, time=26.94 memory used=1516.4MB, alloc=396.3MB, time=30.31 memory used=1596.7MB, alloc=396.3MB, time=31.98 memory used=1705.5MB, alloc=420.3MB, time=34.62 memory used=1792.2MB, alloc=420.3MB, time=35.84 memory used=1861.2MB, alloc=420.3MB, time=37.19 memory used=1926.9MB, alloc=420.3MB, time=37.73 memory used=1996.5MB, alloc=420.3MB, time=39.08 memory used=2109.9MB, alloc=420.3MB, time=40.77 memory used=2227.9MB, alloc=420.3MB, time=43.29 memory used=2280.9MB, alloc=420.3MB, time=43.61 memory used=2341.3MB, alloc=420.3MB, time=44.28 memory used=2427.3MB, alloc=420.3MB, time=46.58 memory used=2486.8MB, alloc=420.3MB, time=46.98 memory used=2533.4MB, alloc=420.3MB, time=47.33 memory used=2611.7MB, alloc=420.3MB, time=48.94 memory used=2671.1MB, alloc=420.3MB, time=49.34 memory used=2718.2MB, alloc=420.3MB, time=49.66 memory used=2838.3MB, alloc=420.3MB, time=51.41 memory used=2957.9MB, alloc=444.3MB, time=54.19 memory used=3025.5MB, alloc=444.3MB, time=54.60 memory used=3122.3MB, alloc=444.3MB, time=55.82 memory used=3238.8MB, alloc=468.3MB, time=59.09 memory used=3349.2MB, alloc=468.3MB, time=62.23 memory used=3433.3MB, alloc=468.3MB, time=64.53 memory used=3532.6MB, alloc=468.3MB, time=67.35 memory used=3637.2MB, alloc=492.3MB, time=70.53 memory used=3700.6MB, alloc=492.3MB, time=72.47 memory used=3768.6MB, alloc=492.3MB, time=74.41 memory used=3858.6MB, alloc=492.3MB, time=76.73 memory used=3989.3MB, alloc=492.3MB, time=78.90 memory used=4082.7MB, alloc=492.3MB, time=81.29 memory used=4203.5MB, alloc=492.3MB, time=83.46 memory used=4315.0MB, alloc=516.3MB, time=85.46 memory used=4423.4MB, alloc=516.3MB, time=87.63 memory used=4500.2MB, alloc=516.3MB, time=90.72 memory used=4571.4MB, alloc=516.3MB, time=93.19 memory used=4633.6MB, alloc=516.3MB, time=94.93 memory used=4684.0MB, alloc=516.3MB, time=96.66 memory used=4743.9MB, alloc=516.3MB, time=98.65 memory used=4793.8MB, alloc=516.3MB, time=100.31 memory used=4848.1MB, alloc=516.3MB, time=102.44 memory used=4924.8MB, alloc=516.3MB, time=105.22 memory used=4969.8MB, alloc=516.3MB, time=107.04 memory used=5170.8MB, alloc=540.3MB, time=113.12 memory used=5357.0MB, alloc=564.3MB, time=118.52 |\^/| 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(); 1428257888 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [-13 y z + 19 y z - 17 z - 19, 15 x y + 14 z + 15 y - 3 z, 2 2 2 -16 x z + 3 x z - 7 y - 8 z] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 2 G := [12 x - 2 x y - 8 y z - 11, -15 x - 13 y z + 14 y z + 9, 2 2 -7 x y - 17 x y + 6 z - 20 x] > Problem := [F,G]; 2 2 2 2 Problem := [[-13 y z + 19 y z - 17 z - 19, 15 x y + 14 z + 15 y - 3 z, 2 2 2 3 2 -16 x z + 3 x z - 7 y - 8 z], [12 x - 2 x y - 8 y z - 11, 3 2 2 2 2 -15 x - 13 y z + 14 y z + 9, -7 x y - 17 x y + 6 z - 20 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.30 memory used=24.6MB, alloc=32.3MB, time=0.82 memory used=44.8MB, alloc=32.3MB, time=1.18 memory used=65.4MB, alloc=32.3MB, time=1.56 memory used=87.6MB, alloc=60.3MB, time=2.01 memory used=129.5MB, alloc=60.3MB, time=2.97 memory used=163.5MB, alloc=60.3MB, time=3.39 memory used=199.5MB, alloc=60.3MB, time=3.91 memory used=257.8MB, alloc=70.5MB, time=5.34 memory used=307.3MB, alloc=70.5MB, time=6.42 memory used=349.0MB, alloc=70.5MB, time=7.45 memory used=389.5MB, alloc=94.5MB, time=8.39 memory used=460.2MB, alloc=94.5MB, time=9.71 memory used=523.5MB, alloc=94.5MB, time=11.17 memory used=583.2MB, alloc=94.5MB, time=12.39 memory used=645.8MB, alloc=374.5MB, time=13.91 memory used=744.2MB, alloc=374.5MB, time=15.96 memory used=833.9MB, alloc=398.5MB, time=18.09 memory used=923.9MB, alloc=398.5MB, time=19.54 memory used=1000.1MB, alloc=398.5MB, time=20.59 memory used=1066.4MB, alloc=398.5MB, time=21.46 memory used=1133.6MB, alloc=398.5MB, time=22.22 memory used=1197.9MB, alloc=398.5MB, time=22.90 memory used=1263.4MB, alloc=398.5MB, time=23.74 memory used=1335.2MB, alloc=398.5MB, time=24.58 memory used=1425.6MB, alloc=398.5MB, time=26.07 memory used=1545.8MB, alloc=398.5MB, time=29.14 memory used=1665.3MB, alloc=398.5MB, time=31.82 memory used=1753.9MB, alloc=398.5MB, time=33.15 memory used=1873.8MB, alloc=398.5MB, time=36.03 memory used=1952.4MB, alloc=398.5MB, time=37.28 memory used=2018.3MB, alloc=398.5MB, time=37.99 memory used=2088.6MB, alloc=398.5MB, time=38.92 memory used=2189.4MB, alloc=398.5MB, time=40.81 memory used=2238.5MB, alloc=398.5MB, time=41.28 memory used=2359.1MB, alloc=422.5MB, time=43.40 memory used=2472.6MB, alloc=422.5MB, time=46.03 memory used=2586.5MB, alloc=446.5MB, time=48.70 memory used=2712.5MB, alloc=470.5MB, time=52.13 memory used=2823.7MB, alloc=470.5MB, time=54.47 memory used=2973.0MB, alloc=470.5MB, time=56.81 memory used=3068.0MB, alloc=470.5MB, time=57.90 memory used=3172.5MB, alloc=470.5MB, time=59.31 memory used=3268.8MB, alloc=470.5MB, time=60.43 memory used=3360.3MB, alloc=470.5MB, time=61.49 memory used=3504.9MB, alloc=470.5MB, time=63.91 memory used=3635.1MB, alloc=470.5MB, time=65.80 memory used=3757.1MB, alloc=470.5MB, time=68.68 memory used=3855.5MB, alloc=470.5MB, time=70.96 memory used=3945.7MB, alloc=470.5MB, time=73.02 memory used=4053.9MB, alloc=494.5MB, time=75.56 memory used=4140.6MB, alloc=494.5MB, time=77.79 memory used=4211.7MB, alloc=494.5MB, time=80.05 memory used=4297.9MB, alloc=494.5MB, time=82.55 memory used=4370.9MB, alloc=494.5MB, time=84.68 memory used=4456.0MB, alloc=494.5MB, time=86.62 memory used=4535.6MB, alloc=494.5MB, time=88.00 memory used=4614.7MB, alloc=494.5MB, time=90.00 memory used=4705.1MB, alloc=494.5MB, time=91.97 memory used=4791.3MB, alloc=494.5MB, time=94.58 memory used=4892.6MB, alloc=494.5MB, time=96.18 memory used=4966.6MB, alloc=494.5MB, time=98.40 memory used=5018.0MB, alloc=518.5MB, time=100.06 memory used=5087.7MB, alloc=518.5MB, time=101.48 memory used=5156.4MB, alloc=518.5MB, time=103.21 memory used=5231.5MB, alloc=518.5MB, time=105.03 memory used=5290.2MB, alloc=518.5MB, time=107.06 memory used=5343.4MB, alloc=518.5MB, time=108.82 memory used=5402.5MB, alloc=518.5MB, time=110.66 memory used=5447.7MB, alloc=518.5MB, time=112.26 memory used=5640.0MB, alloc=542.5MB, time=117.54 |\^/| 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(); 1428258188 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 F := [-13 x + 10 x z + 11 y + 5 y z, 12 y - 9 y z + 19 z + 6, 2 2 3 2 -5 x y - 6 x z - 17 y + 17 z ] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 3 3 2 G := [13 x - 16 x z + 4 x y z + 7 x y, 20 x - 19 y - 19 x + 20 x y, 3 2 2 18 x + 11 x y + 16 x y z + 9 y z] > Problem := [F,G]; 2 2 3 2 2 Problem := [[-13 x + 10 x z + 11 y + 5 y z, 12 y - 9 y z + 19 z + 6, 2 2 3 2 3 2 -5 x y - 6 x z - 17 y + 17 z ], [13 x - 16 x z + 4 x y z + 7 x y, 3 3 2 3 2 2 20 x - 19 y - 19 x + 20 x y, 18 x + 11 x y + 16 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=4.4MB, alloc=32.3MB, time=0.31 memory used=26.1MB, alloc=32.3MB, time=0.88 memory used=47.1MB, alloc=32.3MB, time=1.41 memory used=67.4MB, alloc=60.3MB, time=1.93 memory used=109.7MB, alloc=68.3MB, time=2.97 memory used=151.2MB, alloc=92.3MB, time=4.02 memory used=219.1MB, alloc=92.3MB, time=5.64 memory used=287.5MB, alloc=92.3MB, time=7.24 memory used=349.6MB, alloc=116.3MB, time=8.81 memory used=415.0MB, alloc=372.3MB, time=10.40 memory used=500.9MB, alloc=372.3MB, time=12.38 memory used=590.2MB, alloc=396.3MB, time=14.37 memory used=703.9MB, alloc=420.3MB, time=16.95 memory used=836.3MB, alloc=420.3MB, time=19.75 memory used=957.5MB, alloc=444.3MB, time=22.36 memory used=1092.9MB, alloc=444.3MB, time=25.20 memory used=1234.9MB, alloc=468.3MB, time=28.42 memory used=1349.7MB, alloc=468.3MB, time=31.15 memory used=1474.6MB, alloc=468.3MB, time=34.02 memory used=1576.3MB, alloc=492.3MB, time=36.60 memory used=1714.2MB, alloc=492.3MB, time=39.09 memory used=1864.9MB, alloc=492.3MB, time=42.27 memory used=1981.6MB, alloc=492.3MB, time=44.58 memory used=2119.1MB, alloc=492.3MB, time=47.45 memory used=2197.0MB, alloc=492.3MB, time=49.27 memory used=2284.7MB, alloc=516.3MB, time=51.60 memory used=2419.6MB, alloc=516.3MB, time=53.55 memory used=2482.5MB, alloc=516.3MB, time=55.58 memory used=2549.5MB, alloc=516.3MB, time=57.43 memory used=2615.7MB, alloc=516.3MB, time=59.52 memory used=2677.7MB, alloc=516.3MB, time=61.36 memory used=2791.0MB, alloc=516.3MB, time=63.98 memory used=2872.4MB, alloc=516.3MB, time=66.42 memory used=2920.7MB, alloc=516.3MB, time=68.01 memory used=2991.4MB, alloc=516.3MB, time=69.75 memory used=3054.5MB, alloc=540.3MB, time=71.81 memory used=3110.0MB, alloc=540.3MB, time=73.24 memory used=3160.2MB, alloc=540.3MB, time=74.96 memory used=3204.9MB, alloc=540.3MB, time=76.63 memory used=3419.4MB, alloc=564.3MB, time=82.11 memory used=3573.3MB, alloc=564.3MB, time=86.20 memory used=3803.8MB, alloc=588.3MB, time=90.64 memory used=4081.4MB, alloc=588.3MB, time=97.48 memory used=4316.4MB, alloc=612.3MB, time=102.28 memory used=4485.9MB, alloc=612.3MB, time=105.12 memory used=4717.3MB, alloc=612.3MB, time=110.83 memory used=4916.5MB, alloc=612.3MB, time=115.35 |\^/| 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(); 1428258488 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [8 x z + 8 x y z + 20 x, -14 x z - y z + 6 z + 11 x, 2 -x z + 9 x y + 11 y + 11] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [4 x z + 10 x y + 13 x y + x z, 17 x y z - 4 z + 14 y + 9, 2 2 2 7 x y - 15 y z - y - 7 x] > Problem := [F,G]; 2 2 2 2 Problem := [[8 x z + 8 x y z + 20 x, -14 x z - y z + 6 z + 11 x, 2 2 2 -x z + 9 x y + 11 y + 11], [4 x z + 10 x y + 13 x y + x z, 2 2 2 2 17 x y z - 4 z + 14 y + 9, 7 x y - 15 y z - 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=4.3MB, alloc=32.3MB, time=0.30 memory used=25.0MB, alloc=32.3MB, time=0.83 memory used=44.9MB, alloc=60.3MB, time=1.33 memory used=86.6MB, alloc=60.3MB, time=2.35 memory used=130.7MB, alloc=92.3MB, time=3.43 memory used=196.4MB, alloc=92.3MB, time=4.82 memory used=265.9MB, alloc=92.3MB, time=6.42 memory used=327.5MB, alloc=372.3MB, time=7.91 memory used=420.3MB, alloc=372.3MB, time=10.11 memory used=512.8MB, alloc=372.3MB, time=12.28 memory used=600.5MB, alloc=396.3MB, time=14.58 memory used=707.9MB, alloc=396.3MB, time=16.74 memory used=830.3MB, alloc=420.3MB, time=19.58 memory used=964.8MB, alloc=420.3MB, time=22.36 memory used=1078.1MB, alloc=420.3MB, time=25.00 memory used=1196.0MB, alloc=444.3MB, time=27.74 memory used=1306.5MB, alloc=444.3MB, time=30.33 memory used=1415.7MB, alloc=444.3MB, time=32.95 memory used=1536.5MB, alloc=444.3MB, time=35.02 memory used=1613.4MB, alloc=444.3MB, time=35.96 memory used=1714.0MB, alloc=468.3MB, time=37.58 memory used=1833.9MB, alloc=468.3MB, time=40.74 memory used=1906.9MB, alloc=468.3MB, time=42.62 memory used=1986.0MB, alloc=492.3MB, time=44.48 memory used=2069.8MB, alloc=492.3MB, time=47.01 memory used=2145.1MB, alloc=492.3MB, time=48.93 memory used=2211.5MB, alloc=492.3MB, time=50.57 memory used=2290.7MB, alloc=492.3MB, time=52.69 memory used=2354.2MB, alloc=492.3MB, time=54.81 memory used=2410.1MB, alloc=492.3MB, time=56.48 memory used=2476.7MB, alloc=492.3MB, time=58.80 memory used=2519.8MB, alloc=492.3MB, time=60.16 memory used=2564.3MB, alloc=492.3MB, time=61.61 memory used=2752.0MB, alloc=516.3MB, time=66.40 memory used=2925.4MB, alloc=540.3MB, time=70.98 memory used=3097.7MB, alloc=564.3MB, time=75.42 memory used=3295.1MB, alloc=588.3MB, time=79.39 memory used=3505.8MB, alloc=612.3MB, time=84.29 memory used=3668.9MB, alloc=612.3MB, time=88.23 memory used=3819.9MB, alloc=636.3MB, time=92.98 memory used=3965.4MB, alloc=636.3MB, time=97.54 memory used=4073.4MB, alloc=636.3MB, time=101.07 memory used=4195.4MB, alloc=660.3MB, time=105.47 memory used=4271.1MB, alloc=660.3MB, time=108.62 memory used=4352.3MB, alloc=660.3MB, time=111.64 |\^/| 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(); 1428258789 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 F := [10 x y - 7 x z + 14 x y - 14 x z, 3 x y + 12 x y z - 20 x + 20 x, 2 2 3 11 x z + y z + 19 z - 5 x] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 G := [-4 x + 3 x - 5 x z + 12 z, 20 x y + 17 x z + 12 y z + 4 z, 3 2 4 y - 6 y + 11 z - 16] > Problem := [F,G]; 2 2 2 Problem := [[10 x y - 7 x z + 14 x y - 14 x z, 2 2 2 2 3 3 x y + 12 x y z - 20 x + 20 x, 11 x z + y z + 19 z - 5 x], [ 3 2 2 2 2 -4 x + 3 x - 5 x z + 12 z, 20 x y + 17 x z + 12 y z + 4 z, 3 2 4 y - 6 y + 11 z - 16]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.31 memory used=24.9MB, alloc=32.3MB, time=0.85 memory used=43.9MB, alloc=32.3MB, time=1.33 memory used=62.4MB, alloc=56.3MB, time=1.83 memory used=104.9MB, alloc=60.3MB, time=2.90 memory used=141.4MB, alloc=60.3MB, time=3.80 memory used=182.5MB, alloc=92.3MB, time=4.91 memory used=251.1MB, alloc=92.3MB, time=6.59 memory used=318.3MB, alloc=116.3MB, time=8.24 memory used=382.1MB, alloc=372.3MB, time=9.94 memory used=468.2MB, alloc=396.3MB, time=12.19 memory used=579.6MB, alloc=420.3MB, time=15.06 memory used=693.2MB, alloc=420.3MB, time=17.75 memory used=816.5MB, alloc=444.3MB, time=20.77 memory used=942.0MB, alloc=468.3MB, time=24.18 memory used=1036.9MB, alloc=468.3MB, time=26.49 memory used=1134.1MB, alloc=468.3MB, time=29.04 memory used=1220.6MB, alloc=468.3MB, time=31.19 memory used=1308.5MB, alloc=468.3MB, time=33.38 memory used=1381.2MB, alloc=468.3MB, time=35.34 memory used=1464.2MB, alloc=468.3MB, time=37.63 memory used=1540.8MB, alloc=492.3MB, time=40.01 memory used=1620.4MB, alloc=492.3MB, time=41.96 memory used=1686.1MB, alloc=492.3MB, time=43.85 memory used=1751.8MB, alloc=492.3MB, time=45.91 memory used=1797.3MB, alloc=492.3MB, time=47.45 memory used=1845.9MB, alloc=492.3MB, time=49.05 memory used=1908.4MB, alloc=492.3MB, time=51.24 memory used=1960.0MB, alloc=492.3MB, time=52.84 memory used=2147.6MB, alloc=516.3MB, time=58.29 memory used=2342.9MB, alloc=540.3MB, time=63.59 memory used=2531.2MB, alloc=564.3MB, time=68.55 memory used=2689.0MB, alloc=588.3MB, time=73.36 memory used=2847.9MB, alloc=588.3MB, time=78.47 memory used=3019.8MB, alloc=612.3MB, time=82.96 memory used=3208.4MB, alloc=612.3MB, time=87.58 memory used=3361.4MB, alloc=636.3MB, time=92.84 memory used=3481.6MB, alloc=636.3MB, time=96.88 memory used=3664.4MB, alloc=636.3MB, time=101.01 memory used=3802.7MB, alloc=636.3MB, time=104.51 memory used=3919.5MB, alloc=636.3MB, time=108.44 memory used=4031.4MB, alloc=636.3MB, time=112.49 memory used=4118.7MB, alloc=660.3MB, time=115.83 memory used=4201.2MB, alloc=660.3MB, time=119.03 memory used=4310.2MB, alloc=660.3MB, time=122.87 |\^/| 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(); 1428259089 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 3 3 F := [-8 y + 12 y z - 9 z - 16 y z, -3 z + 5 x z - 8 y, 2 3 2 -7 x z - 9 z + 15 z - 9] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [4 x - 17 z - 7 x + 3 y, -7 x z - 14 x z - 15 x + 15, 2 2 2 12 x y + 11 x z + 15 y z + 17 z ] > Problem := [F,G]; 3 2 3 3 Problem := [[-8 y + 12 y z - 9 z - 16 y z, -3 z + 5 x z - 8 y, 2 3 2 2 2 -7 x z - 9 z + 15 z - 9], [4 x - 17 z - 7 x + 3 y, 2 2 2 2 -7 x z - 14 x z - 15 x + 15, 12 x y + 11 x z + 15 y z + 17 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.31 memory used=26.3MB, alloc=32.3MB, time=0.88 memory used=45.7MB, alloc=56.3MB, time=1.42 memory used=87.6MB, alloc=60.3MB, time=2.50 memory used=131.9MB, alloc=68.3MB, time=3.56 memory used=173.6MB, alloc=92.3MB, time=4.62 memory used=239.8MB, alloc=92.3MB, time=6.26 memory used=302.1MB, alloc=92.3MB, time=7.84 memory used=361.5MB, alloc=116.3MB, time=9.42 memory used=441.8MB, alloc=372.3MB, time=11.36 memory used=525.2MB, alloc=372.3MB, time=13.15 memory used=622.9MB, alloc=396.3MB, time=15.16 memory used=736.4MB, alloc=396.3MB, time=17.62 memory used=853.5MB, alloc=420.3MB, time=20.22 memory used=990.5MB, alloc=420.3MB, time=23.70 memory used=1131.7MB, alloc=444.3MB, time=26.88 memory used=1259.7MB, alloc=444.3MB, time=28.75 memory used=1399.4MB, alloc=444.3MB, time=32.43 memory used=1534.5MB, alloc=468.3MB, time=36.15 memory used=1655.0MB, alloc=468.3MB, time=39.42 memory used=1778.3MB, alloc=468.3MB, time=42.94 memory used=1893.8MB, alloc=492.3MB, time=46.16 memory used=2005.2MB, alloc=492.3MB, time=49.24 memory used=2100.5MB, alloc=492.3MB, time=51.93 memory used=2198.8MB, alloc=492.3MB, time=54.83 memory used=2304.8MB, alloc=492.3MB, time=57.72 memory used=2410.9MB, alloc=492.3MB, time=60.16 memory used=2525.8MB, alloc=492.3MB, time=62.87 memory used=2635.3MB, alloc=516.3MB, time=65.63 memory used=2768.8MB, alloc=516.3MB, time=68.37 memory used=2857.2MB, alloc=516.3MB, time=70.89 memory used=2919.9MB, alloc=516.3MB, time=72.59 memory used=3000.2MB, alloc=516.3MB, time=75.09 memory used=3130.1MB, alloc=516.3MB, time=77.53 memory used=3217.7MB, alloc=516.3MB, time=79.75 memory used=3290.7MB, alloc=516.3MB, time=82.14 memory used=3378.3MB, alloc=516.3MB, time=84.54 memory used=3456.6MB, alloc=516.3MB, time=87.01 memory used=3530.5MB, alloc=516.3MB, time=89.20 memory used=3600.7MB, alloc=516.3MB, time=91.45 memory used=3679.7MB, alloc=516.3MB, time=94.24 memory used=3734.8MB, alloc=516.3MB, time=96.33 memory used=3794.2MB, alloc=516.3MB, time=98.43 memory used=3859.0MB, alloc=516.3MB, time=100.75 memory used=3911.4MB, alloc=540.3MB, time=102.84 memory used=3966.5MB, alloc=540.3MB, time=105.15 memory used=4186.3MB, alloc=564.3MB, time=111.17 memory used=4378.3MB, alloc=588.3MB, time=117.42 |\^/| 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(); 1428259389 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [3 x y - 20 x y z + 19 y z - 20 x y, 2 x z + 3 x y + 17 z + y, 3 3 2 2 20 x + 19 z - 17 y + 7 z ] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 3 3 2 3 G := [4 x y - 12 y + 11 y z + 18 z , -14 x - 15 x y - 18 z , 3 2 2 2 -8 x + 2 x y + 10 x - 7 z ] > Problem := [F,G]; 2 2 2 2 Problem := [[3 x y - 20 x y z + 19 y z - 20 x y, 2 x z + 3 x y + 17 z + y, 3 3 2 2 2 3 2 3 20 x + 19 z - 17 y + 7 z ], [4 x y - 12 y + 11 y z + 18 z , 3 2 3 3 2 2 2 -14 x - 15 x y - 18 z , -8 x + 2 x y + 10 x - 7 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.31 memory used=26.4MB, alloc=32.3MB, time=0.88 memory used=46.5MB, alloc=56.3MB, time=1.42 memory used=85.2MB, alloc=60.3MB, time=2.38 memory used=127.8MB, alloc=92.3MB, time=3.50 memory used=194.0MB, alloc=92.3MB, time=5.04 memory used=264.9MB, alloc=92.3MB, time=6.55 memory used=328.4MB, alloc=116.3MB, time=8.20 memory used=395.9MB, alloc=116.3MB, time=9.82 memory used=465.8MB, alloc=372.3MB, time=11.55 memory used=555.2MB, alloc=396.3MB, time=13.62 memory used=666.8MB, alloc=396.3MB, time=16.24 memory used=788.7MB, alloc=420.3MB, time=18.54 memory used=919.4MB, alloc=444.3MB, time=21.92 memory used=1044.2MB, alloc=444.3MB, time=24.48 memory used=1155.1MB, alloc=468.3MB, time=27.28 memory used=1295.4MB, alloc=468.3MB, time=29.74 memory used=1410.8MB, alloc=468.3MB, time=31.24 memory used=1524.9MB, alloc=468.3MB, time=32.89 memory used=1662.2MB, alloc=468.3MB, time=35.74 memory used=1793.6MB, alloc=468.3MB, time=37.98 memory used=1922.9MB, alloc=468.3MB, time=40.20 memory used=2034.3MB, alloc=468.3MB, time=42.08 memory used=2142.3MB, alloc=468.3MB, time=43.27 memory used=2286.7MB, alloc=468.3MB, time=46.54 memory used=2391.6MB, alloc=468.3MB, time=48.40 memory used=2504.5MB, alloc=492.3MB, time=51.00 memory used=2598.0MB, alloc=492.3MB, time=53.53 memory used=2687.2MB, alloc=492.3MB, time=55.54 memory used=2774.8MB, alloc=492.3MB, time=58.16 memory used=2844.8MB, alloc=492.3MB, time=60.25 memory used=2917.4MB, alloc=492.3MB, time=62.32 memory used=3025.9MB, alloc=492.3MB, time=64.30 memory used=3141.5MB, alloc=492.3MB, time=65.76 memory used=3246.7MB, alloc=516.3MB, time=67.52 memory used=3378.6MB, alloc=516.3MB, time=69.42 memory used=3502.0MB, alloc=516.3MB, time=71.11 memory used=3624.4MB, alloc=516.3MB, time=72.12 memory used=3777.4MB, alloc=516.3MB, time=74.21 memory used=3871.8MB, alloc=516.3MB, time=76.50 memory used=3951.3MB, alloc=516.3MB, time=78.41 memory used=4017.4MB, alloc=516.3MB, time=80.50 memory used=4076.3MB, alloc=516.3MB, time=82.25 memory used=4164.5MB, alloc=516.3MB, time=83.81 memory used=4227.9MB, alloc=516.3MB, time=85.61 memory used=4290.8MB, alloc=516.3MB, time=87.37 memory used=4357.0MB, alloc=516.3MB, time=89.34 memory used=4407.4MB, alloc=516.3MB, time=91.08 memory used=4464.2MB, alloc=516.3MB, time=93.07 memory used=4673.6MB, alloc=540.3MB, time=98.77 memory used=4875.4MB, alloc=564.3MB, time=103.97 memory used=5075.9MB, alloc=588.3MB, time=109.34 memory used=5278.6MB, alloc=612.3MB, time=114.54 memory used=5587.5MB, alloc=612.3MB, time=119.81 memory used=5907.4MB, alloc=636.3MB, time=125.50 memory used=6154.8MB, alloc=636.3MB, time=130.17 |\^/| 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(); 1428259689 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 3 2 F := [3 x z + 5 x - 12 z + 17, 7 x - 18 x y - 9 z - 16 x , 2 2 3 2 2 x y + 7 x y + 5 y + 11 y ] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 3 G := [18 y z - 18 z - 3 x y - 10 y z, -12 x y z + 3 x z + 5 z - 20 y, 3 3 3 x + 13 y - 7 x - 7 y] > Problem := [F,G]; 2 2 2 3 2 3 2 Problem := [[3 x z + 5 x - 12 z + 17, 7 x - 18 x y - 9 z - 16 x , 2 2 3 2 2 3 2 x y + 7 x y + 5 y + 11 y ], [18 y z - 18 z - 3 x y - 10 y z, 2 3 3 3 -12 x y z + 3 x z + 5 z - 20 y, 3 x + 13 y - 7 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=4.4MB, alloc=32.3MB, time=0.32 memory used=27.1MB, alloc=32.3MB, time=0.89 memory used=48.0MB, alloc=32.3MB, time=1.43 memory used=67.2MB, alloc=56.3MB, time=1.92 memory used=108.4MB, alloc=60.3MB, time=2.98 memory used=147.2MB, alloc=60.3MB, time=3.87 memory used=187.4MB, alloc=84.3MB, time=4.86 memory used=228.6MB, alloc=84.3MB, time=5.93 memory used=296.7MB, alloc=92.3MB, time=7.49 memory used=362.3MB, alloc=116.3MB, time=9.12 memory used=436.2MB, alloc=116.3MB, time=11.03 memory used=502.7MB, alloc=372.3MB, time=12.35 memory used=584.3MB, alloc=372.3MB, time=13.77 memory used=674.4MB, alloc=396.3MB, time=15.62 memory used=756.2MB, alloc=396.3MB, time=16.54 memory used=833.6MB, alloc=396.3MB, time=17.21 memory used=907.9MB, alloc=396.3MB, time=17.80 memory used=963.2MB, alloc=396.3MB, time=18.19 memory used=1079.9MB, alloc=396.3MB, time=20.34 memory used=1192.5MB, alloc=396.3MB, time=23.14 memory used=1301.7MB, alloc=420.3MB, time=25.88 memory used=1430.7MB, alloc=420.3MB, time=29.10 memory used=1567.6MB, alloc=420.3MB, time=32.11 memory used=1686.3MB, alloc=444.3MB, time=34.34 memory used=1815.1MB, alloc=444.3MB, time=36.61 memory used=1951.1MB, alloc=444.3MB, time=39.30 memory used=2063.2MB, alloc=444.3MB, time=40.76 memory used=2185.6MB, alloc=444.3MB, time=43.31 memory used=2303.6MB, alloc=444.3MB, time=44.87 memory used=2465.3MB, alloc=444.3MB, time=47.24 memory used=2604.3MB, alloc=444.3MB, time=49.66 memory used=2726.7MB, alloc=444.3MB, time=52.17 memory used=2791.8MB, alloc=444.3MB, time=52.55 memory used=2868.0MB, alloc=444.3MB, time=53.16 memory used=2983.1MB, alloc=444.3MB, time=54.49 memory used=3117.2MB, alloc=468.3MB, time=57.66 memory used=3235.0MB, alloc=468.3MB, time=61.14 memory used=3356.6MB, alloc=468.3MB, time=63.35 memory used=3427.5MB, alloc=468.3MB, time=63.80 memory used=3513.1MB, alloc=468.3MB, time=64.58 memory used=3584.7MB, alloc=468.3MB, time=65.02 memory used=3731.0MB, alloc=468.3MB, time=67.63 memory used=3855.0MB, alloc=492.3MB, time=70.13 memory used=3975.1MB, alloc=492.3MB, time=72.60 memory used=4074.6MB, alloc=492.3MB, time=73.47 memory used=4187.5MB, alloc=492.3MB, time=74.75 memory used=4285.7MB, alloc=492.3MB, time=75.53 memory used=4391.6MB, alloc=492.3MB, time=76.68 memory used=4501.2MB, alloc=492.3MB, time=79.13 memory used=4596.3MB, alloc=492.3MB, time=79.67 memory used=4776.1MB, alloc=492.3MB, time=86.16 memory used=4944.2MB, alloc=492.3MB, time=90.50 memory used=5055.0MB, alloc=492.3MB, time=91.69 memory used=5147.9MB, alloc=492.3MB, time=92.30 memory used=5240.6MB, alloc=492.3MB, time=92.88 memory used=5312.0MB, alloc=492.3MB, time=93.39 memory used=5394.0MB, alloc=492.3MB, time=93.94 memory used=5486.5MB, alloc=492.3MB, time=94.47 memory used=5592.4MB, alloc=492.3MB, time=95.03 memory used=5685.2MB, alloc=492.3MB, time=95.54 memory used=5750.6MB, alloc=492.3MB, time=95.98 memory used=5821.6MB, alloc=492.3MB, time=96.41 memory used=5951.9MB, alloc=492.3MB, time=98.01 memory used=6095.5MB, alloc=492.3MB, time=100.48 memory used=6211.9MB, alloc=492.3MB, time=103.72 memory used=6321.3MB, alloc=516.3MB, time=107.17 memory used=6420.2MB, alloc=516.3MB, time=110.38 memory used=6515.9MB, alloc=516.3MB, time=113.19 memory used=6612.2MB, alloc=516.3MB, time=115.22 memory used=6699.1MB, alloc=516.3MB, time=117.85 memory used=6768.0MB, alloc=516.3MB, time=119.94 memory used=6846.6MB, alloc=540.3MB, time=121.79 memory used=6942.8MB, alloc=540.3MB, time=125.24 |\^/| 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(); 1428259989 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [2 y z - 4 x y - 3 y z - 13, 9 x z + 3 x z + 17 z - 17, 2 2 10 x y + 20 x z + 10 y + 16] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 2 G := [-15 x y - 13 y - 19 z - 9 z, 5 x y - 12 y z - y - 4, 3 2 2 3 7 x + 2 x y + 13 y z - 17 z ] > Problem := [F,G]; 2 2 2 Problem := [[2 y z - 4 x y - 3 y z - 13, 9 x z + 3 x z + 17 z - 17, 2 2 2 3 2 10 x y + 20 x z + 10 y + 16], [-15 x y - 13 y - 19 z - 9 z, 2 2 3 2 2 3 5 x y - 12 y z - y - 4, 7 x + 2 x y + 13 y z - 17 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.31 memory used=24.3MB, alloc=32.3MB, time=0.80 memory used=44.6MB, alloc=36.3MB, time=1.21 memory used=66.7MB, alloc=36.3MB, time=1.71 memory used=87.4MB, alloc=60.3MB, time=2.22 memory used=128.1MB, alloc=60.3MB, time=2.95 memory used=186.4MB, alloc=69.0MB, time=3.88 memory used=248.8MB, alloc=69.0MB, time=4.75 memory used=302.2MB, alloc=69.0MB, time=5.68 memory used=347.2MB, alloc=69.0MB, time=6.73 memory used=400.1MB, alloc=69.0MB, time=7.60 memory used=443.5MB, alloc=69.0MB, time=8.46 memory used=485.2MB, alloc=93.0MB, time=9.38 memory used=552.4MB, alloc=93.0MB, time=10.58 memory used=619.5MB, alloc=93.0MB, time=11.78 memory used=679.4MB, alloc=349.0MB, time=13.13 memory used=756.8MB, alloc=373.0MB, time=14.57 memory used=850.3MB, alloc=373.0MB, time=16.72 memory used=933.2MB, alloc=373.0MB, time=18.10 memory used=981.3MB, alloc=373.0MB, time=18.57 memory used=1018.6MB, alloc=373.0MB, time=18.82 memory used=1064.2MB, alloc=397.0MB, time=19.29 memory used=1117.4MB, alloc=397.0MB, time=19.58 memory used=1181.7MB, alloc=397.0MB, time=20.21 memory used=1245.5MB, alloc=397.0MB, time=20.73 memory used=1298.6MB, alloc=397.0MB, time=21.02 memory used=1366.9MB, alloc=397.0MB, time=21.49 memory used=1426.3MB, alloc=397.0MB, time=22.06 memory used=1479.6MB, alloc=397.0MB, time=22.35 memory used=1549.0MB, alloc=397.0MB, time=22.88 memory used=1608.6MB, alloc=397.0MB, time=23.33 memory used=1661.9MB, alloc=397.0MB, time=23.61 memory used=1726.5MB, alloc=397.0MB, time=24.22 memory used=1795.1MB, alloc=397.0MB, time=24.89 memory used=1861.4MB, alloc=397.0MB, time=25.35 memory used=1926.7MB, alloc=397.0MB, time=25.84 memory used=2005.0MB, alloc=397.0MB, time=28.95 memory used=2059.5MB, alloc=397.0MB, time=29.26 memory used=2113.4MB, alloc=397.0MB, time=29.53 memory used=2167.7MB, alloc=397.0MB, time=29.78 memory used=2226.1MB, alloc=397.0MB, time=30.25 memory used=2289.7MB, alloc=397.0MB, time=30.70 memory used=2351.1MB, alloc=397.0MB, time=32.55 memory used=2429.6MB, alloc=397.0MB, time=34.07 memory used=2478.4MB, alloc=397.0MB, time=34.33 memory used=2540.1MB, alloc=397.0MB, time=34.63 memory used=2584.5MB, alloc=397.0MB, time=34.86 memory used=2647.9MB, alloc=397.0MB, time=35.35 memory used=2713.1MB, alloc=397.0MB, time=35.81 memory used=2800.5MB, alloc=397.0MB, time=39.05 memory used=2855.9MB, alloc=397.0MB, time=39.37 memory used=2908.7MB, alloc=397.0MB, time=39.66 memory used=2964.7MB, alloc=397.0MB, time=39.93 memory used=3030.5MB, alloc=397.0MB, time=40.72 memory used=3173.5MB, alloc=397.0MB, time=43.62 memory used=3278.1MB, alloc=397.0MB, time=45.90 memory used=3328.0MB, alloc=397.0MB, time=46.17 memory used=3406.6MB, alloc=397.0MB, time=51.24 memory used=3461.4MB, alloc=397.0MB, time=51.55 memory used=3509.3MB, alloc=397.0MB, time=51.84 memory used=3570.3MB, alloc=397.0MB, time=52.14 memory used=3617.6MB, alloc=397.0MB, time=52.40 memory used=3659.1MB, alloc=397.0MB, time=52.66 memory used=3733.6MB, alloc=397.0MB, time=53.61 memory used=3865.0MB, alloc=397.0MB, time=55.63 memory used=3953.2MB, alloc=397.0MB, time=57.38 memory used=4044.5MB, alloc=397.0MB, time=58.65 memory used=4173.4MB, alloc=397.0MB, time=61.40 memory used=4301.7MB, alloc=397.0MB, time=63.96 memory used=4377.5MB, alloc=421.0MB, time=65.05 memory used=4448.1MB, alloc=421.0MB, time=65.61 memory used=4512.6MB, alloc=421.0MB, time=65.94 memory used=4582.2MB, alloc=421.0MB, time=66.45 memory used=4647.3MB, alloc=421.0MB, time=66.80 memory used=4715.2MB, alloc=421.0MB, time=67.43 memory used=4783.3MB, alloc=421.0MB, time=67.94 memory used=4845.5MB, alloc=421.0MB, time=68.31 memory used=4908.4MB, alloc=421.0MB, time=68.63 memory used=4978.6MB, alloc=421.0MB, time=69.15 memory used=5042.8MB, alloc=421.0MB, time=69.47 memory used=5112.5MB, alloc=421.0MB, time=70.13 memory used=5182.3MB, alloc=421.0MB, time=70.65 memory used=5243.0MB, alloc=421.0MB, time=71.01 memory used=5311.7MB, alloc=421.0MB, time=71.50 memory used=5377.2MB, alloc=421.0MB, time=71.89 memory used=5441.1MB, alloc=421.0MB, time=72.21 memory used=5512.1MB, alloc=421.0MB, time=72.87 memory used=5582.1MB, alloc=421.0MB, time=73.43 memory used=5665.2MB, alloc=421.0MB, time=74.41 memory used=5729.9MB, alloc=421.0MB, time=74.79 memory used=5805.1MB, alloc=421.0MB, time=75.35 memory used=5878.8MB, alloc=421.0MB, time=78.31 memory used=5953.2MB, alloc=421.0MB, time=78.83 memory used=6024.3MB, alloc=421.0MB, time=79.19 memory used=6074.2MB, alloc=421.0MB, time=79.48 memory used=6131.5MB, alloc=421.0MB, time=79.76 memory used=6202.6MB, alloc=421.0MB, time=80.05 memory used=6288.0MB, alloc=421.0MB, time=80.65 memory used=6358.5MB, alloc=421.0MB, time=81.14 memory used=6419.8MB, alloc=421.0MB, time=81.49 memory used=6509.0MB, alloc=421.0MB, time=84.61 memory used=6573.3MB, alloc=421.0MB, time=84.95 memory used=6629.9MB, alloc=421.0MB, time=85.25 memory used=6684.7MB, alloc=421.0MB, time=85.53 memory used=6750.3MB, alloc=421.0MB, time=85.83 memory used=6837.7MB, alloc=421.0MB, time=86.60 memory used=6910.4MB, alloc=421.0MB, time=87.27 memory used=6979.8MB, alloc=421.0MB, time=87.77 memory used=7040.9MB, alloc=421.0MB, time=88.11 memory used=7137.0MB, alloc=421.0MB, time=91.38 memory used=7196.8MB, alloc=421.0MB, time=91.73 memory used=7259.9MB, alloc=421.0MB, time=92.05 memory used=7311.4MB, alloc=421.0MB, time=92.33 memory used=7372.9MB, alloc=421.0MB, time=92.62 memory used=7491.3MB, alloc=421.0MB, time=94.10 memory used=7660.0MB, alloc=421.0MB, time=98.73 memory used=7720.4MB, alloc=421.0MB, time=99.08 memory used=7776.5MB, alloc=421.0MB, time=99.36 memory used=7849.3MB, alloc=421.0MB, time=102.92 memory used=7924.5MB, alloc=421.0MB, time=105.06 memory used=7984.6MB, alloc=421.0MB, time=105.41 memory used=8046.6MB, alloc=421.0MB, time=105.74 memory used=8094.3MB, alloc=421.0MB, time=106.03 memory used=8149.7MB, alloc=421.0MB, time=106.34 memory used=8213.6MB, alloc=421.0MB, time=106.65 memory used=8348.0MB, alloc=421.0MB, time=107.20 memory used=8515.4MB, alloc=421.0MB, time=110.16 memory used=8593.1MB, alloc=421.0MB, time=111.25 memory used=8650.8MB, alloc=421.0MB, time=111.59 memory used=8777.5MB, alloc=421.0MB, time=113.48 memory used=8917.7MB, alloc=421.0MB, time=116.41 memory used=9077.3MB, alloc=421.0MB, time=119.36 memory used=9194.3MB, alloc=445.0MB, time=121.93 memory used=9297.0MB, alloc=445.0MB, time=124.31 memory used=9389.2MB, alloc=445.0MB, time=126.51 memory used=9495.2MB, alloc=469.0MB, time=129.27 memory used=9607.6MB, alloc=469.0MB, time=130.54 memory used=9697.6MB, alloc=469.0MB, time=131.38 memory used=9783.1MB, alloc=469.0MB, time=132.07 memory used=9873.4MB, alloc=469.0MB, time=132.88 memory used=9963.0MB, alloc=469.0MB, time=133.70 memory used=10071.8MB, alloc=469.0MB, time=135.32 memory used=10161.6MB, alloc=469.0MB, time=136.37 memory used=10260.7MB, alloc=469.0MB, time=137.31 memory used=10355.9MB, alloc=469.0MB, time=139.01 memory used=10441.7MB, alloc=469.0MB, time=139.62 memory used=10550.8MB, alloc=469.0MB, time=141.60 memory used=10634.8MB, alloc=469.0MB, time=142.43 memory used=10731.7MB, alloc=469.0MB, time=144.92 memory used=10838.3MB, alloc=469.0MB, time=147.63 memory used=10913.7MB, alloc=469.0MB, time=148.18 memory used=11051.7MB, alloc=469.0MB, time=150.57 memory used=11166.6MB, alloc=469.0MB, time=152.52 memory used=11264.1MB, alloc=493.0MB, time=154.63 memory used=11343.5MB, alloc=493.0MB, time=156.89 memory used=11434.1MB, alloc=493.0MB, time=158.73 memory used=11549.2MB, alloc=493.0MB, time=160.46 memory used=11667.2MB, alloc=493.0MB, time=162.52 |\^/| 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(); 1428260289 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 2 2 F := [-19 x z + 6 x y z - 13 z - z , -11 x y - 13 x y - 9 y z - 11 x y, 3 2 2 2 7 x + 11 x z + 12 x z + 11 y z ] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 2 G := [14 y z - 15 z - 18 z + 2, 19 x y - 13 z + 11 z - 1, 2 2 12 x y - 18 x z + 17 y - 13 y] > Problem := [F,G]; 2 3 2 Problem := [[-19 x z + 6 x y z - 13 z - z , 2 2 2 3 2 2 2 -11 x y - 13 x y - 9 y z - 11 x y, 7 x + 11 x z + 12 x z + 11 y z ], 2 3 2 2 2 [14 y z - 15 z - 18 z + 2, 19 x y - 13 z + 11 z - 1, 2 2 12 x y - 18 x z + 17 y - 13 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.7MB, alloc=32.3MB, time=0.88 memory used=47.3MB, alloc=56.3MB, time=1.45 memory used=86.2MB, alloc=60.3MB, time=2.43 memory used=127.9MB, alloc=60.3MB, time=3.48 memory used=167.7MB, alloc=84.3MB, time=4.54 memory used=231.9MB, alloc=92.3MB, time=6.17 memory used=294.9MB, alloc=116.3MB, time=7.75 memory used=372.5MB, alloc=116.3MB, time=9.82 memory used=447.9MB, alloc=396.3MB, time=11.93 memory used=562.0MB, alloc=420.3MB, time=14.65 memory used=695.0MB, alloc=444.3MB, time=18.11 memory used=815.5MB, alloc=468.3MB, time=21.30 memory used=931.4MB, alloc=468.3MB, time=24.56 memory used=1038.4MB, alloc=468.3MB, time=27.42 memory used=1152.7MB, alloc=492.3MB, time=30.77 memory used=1250.9MB, alloc=492.3MB, time=33.23 memory used=1358.9MB, alloc=492.3MB, time=36.12 memory used=1457.1MB, alloc=492.3MB, time=39.07 memory used=1548.9MB, alloc=492.3MB, time=41.59 memory used=1623.4MB, alloc=492.3MB, time=43.74 memory used=1703.5MB, alloc=516.3MB, time=45.73 memory used=1788.0MB, alloc=516.3MB, time=47.68 memory used=1854.8MB, alloc=516.3MB, time=49.63 memory used=1917.9MB, alloc=516.3MB, time=51.65 memory used=1979.9MB, alloc=516.3MB, time=53.78 memory used=2050.5MB, alloc=516.3MB, time=56.35 memory used=2103.2MB, alloc=516.3MB, time=58.01 memory used=2161.9MB, alloc=516.3MB, time=60.33 memory used=2219.6MB, alloc=516.3MB, time=62.58 memory used=2425.8MB, alloc=540.3MB, time=68.93 memory used=2640.2MB, alloc=564.3MB, time=75.89 memory used=2838.4MB, alloc=588.3MB, time=82.19 memory used=3005.8MB, alloc=612.3MB, time=88.03 memory used=3160.9MB, alloc=636.3MB, time=93.21 memory used=3299.7MB, alloc=636.3MB, time=97.53 memory used=3447.3MB, alloc=660.3MB, time=102.26 memory used=3576.3MB, alloc=660.3MB, time=106.76 memory used=3692.1MB, alloc=660.3MB, time=110.99 memory used=3821.1MB, alloc=660.3MB, time=116.20 memory used=3922.3MB, alloc=660.3MB, time=120.27 |\^/| 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(); 1428260589 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 3 2 F := [-5 x y - 10 x y + 16 z - 15 x z, 7 x y + 3 y + 6 y z + 6 x y, 3 2 x - 19 x z + 3 y z + 16 z] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 G := [16 x + 14 x y + 17 y z - 5, -19 x y z - 18 y + 10 x z + 9 z , 2 2 2 -5 x z + 18 x y - 12 x z - 5 x y] > Problem := [F,G]; 2 2 3 2 3 2 Problem := [[-5 x y - 10 x y + 16 z - 15 x z, 7 x y + 3 y + 6 y z + 6 x y, 3 2 3 2 x - 19 x z + 3 y z + 16 z], [16 x + 14 x y + 17 y z - 5, 3 2 2 2 2 -19 x y z - 18 y + 10 x z + 9 z , -5 x z + 18 x y - 12 x 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=4.4MB, alloc=32.3MB, time=0.31 memory used=26.5MB, alloc=32.3MB, time=0.88 memory used=47.1MB, alloc=56.3MB, time=1.43 memory used=91.9MB, alloc=60.3MB, time=2.33 memory used=130.4MB, alloc=60.3MB, time=2.81 memory used=172.2MB, alloc=60.3MB, time=3.63 memory used=213.3MB, alloc=60.3MB, time=4.67 memory used=253.6MB, alloc=84.3MB, time=5.70 memory used=320.8MB, alloc=92.3MB, time=7.32 memory used=383.3MB, alloc=92.3MB, time=8.50 memory used=431.6MB, alloc=92.3MB, time=9.16 memory used=503.9MB, alloc=116.3MB, time=10.58 memory used=577.4MB, alloc=116.3MB, time=11.80 memory used=639.0MB, alloc=372.3MB, time=13.33 memory used=701.7MB, alloc=372.3MB, time=14.22 memory used=752.0MB, alloc=372.3MB, time=14.87 memory used=803.4MB, alloc=372.3MB, time=15.57 memory used=890.7MB, alloc=396.3MB, time=17.32 memory used=948.7MB, alloc=396.3MB, time=17.87 memory used=1049.4MB, alloc=396.3MB, time=19.27 memory used=1119.0MB, alloc=396.3MB, time=20.07 memory used=1188.8MB, alloc=396.3MB, time=20.83 memory used=1255.4MB, alloc=396.3MB, time=21.69 memory used=1326.1MB, alloc=396.3MB, time=22.60 memory used=1395.1MB, alloc=396.3MB, time=23.35 memory used=1466.9MB, alloc=396.3MB, time=24.30 memory used=1557.9MB, alloc=396.3MB, time=25.68 memory used=1649.5MB, alloc=396.3MB, time=27.28 memory used=1762.5MB, alloc=396.3MB, time=29.60 memory used=1877.1MB, alloc=420.3MB, time=32.09 memory used=2001.8MB, alloc=444.3MB, time=35.15 memory used=2137.6MB, alloc=444.3MB, time=37.87 memory used=2272.7MB, alloc=444.3MB, time=41.41 memory used=2374.3MB, alloc=444.3MB, time=43.69 memory used=2485.5MB, alloc=468.3MB, time=46.24 memory used=2593.8MB, alloc=468.3MB, time=47.64 memory used=2687.8MB, alloc=468.3MB, time=48.55 memory used=2788.6MB, alloc=468.3MB, time=49.77 memory used=2915.5MB, alloc=468.3MB, time=52.65 memory used=3001.0MB, alloc=468.3MB, time=53.19 memory used=3090.5MB, alloc=468.3MB, time=53.95 memory used=3182.3MB, alloc=468.3MB, time=55.92 memory used=3305.3MB, alloc=468.3MB, time=57.55 memory used=3445.4MB, alloc=468.3MB, time=60.69 memory used=3639.4MB, alloc=468.3MB, time=63.65 memory used=3827.1MB, alloc=468.3MB, time=70.38 memory used=3908.5MB, alloc=468.3MB, time=70.94 memory used=3991.2MB, alloc=468.3MB, time=71.65 memory used=4075.8MB, alloc=468.3MB, time=72.86 memory used=4156.6MB, alloc=468.3MB, time=73.55 memory used=4275.5MB, alloc=468.3MB, time=75.50 memory used=4352.2MB, alloc=468.3MB, time=76.02 memory used=4419.5MB, alloc=468.3MB, time=76.48 memory used=4515.5MB, alloc=468.3MB, time=79.07 memory used=4580.2MB, alloc=468.3MB, time=79.53 memory used=4686.2MB, alloc=468.3MB, time=80.37 memory used=4834.6MB, alloc=468.3MB, time=82.38 memory used=4954.2MB, alloc=468.3MB, time=84.58 memory used=5080.7MB, alloc=492.3MB, time=87.01 memory used=5179.5MB, alloc=492.3MB, time=89.48 memory used=5285.3MB, alloc=492.3MB, time=90.89 memory used=5391.8MB, alloc=492.3MB, time=92.35 memory used=5509.1MB, alloc=492.3MB, time=93.93 memory used=5615.0MB, alloc=492.3MB, time=96.06 memory used=5711.1MB, alloc=492.3MB, time=97.08 memory used=5814.3MB, alloc=492.3MB, time=99.08 memory used=5902.1MB, alloc=492.3MB, time=99.85 memory used=5998.2MB, alloc=492.3MB, time=101.76 memory used=6083.6MB, alloc=492.3MB, time=103.77 memory used=6163.6MB, alloc=492.3MB, time=105.74 memory used=6271.6MB, alloc=492.3MB, time=108.02 memory used=6327.3MB, alloc=492.3MB, time=109.74 memory used=6402.8MB, alloc=492.3MB, time=111.46 memory used=6459.7MB, alloc=492.3MB, time=113.16 memory used=6538.7MB, alloc=492.3MB, time=115.01 memory used=6595.3MB, alloc=492.3MB, time=116.56 memory used=6642.8MB, alloc=492.3MB, time=118.19 memory used=6685.3MB, alloc=492.3MB, time=119.41 memory used=6735.6MB, alloc=516.3MB, time=121.10 memory used=6769.8MB, alloc=516.3MB, time=122.36 memory used=6808.6MB, alloc=516.3MB, time=123.84 memory used=6946.2MB, alloc=516.3MB, time=126.00 memory used=7075.6MB, alloc=516.3MB, time=128.38 memory used=7175.2MB, alloc=516.3MB, time=129.55 memory used=7304.7MB, alloc=516.3MB, time=131.19 |\^/| 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(); 1428260889 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 3 2 F := [12 x + 11 x y + 4 x y - 8 y, -2 x z + 8 y + 19 y z + 8 z, 3 3 2 y - 4 z - 18 x + 2] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-4 x y - 8 x z - 5 x + 16, 12 x y z - 10 y z + 3 x + 11, 2 2 3 2 7 x z + 2 x y - 8 y - 8 y z ] > Problem := [F,G]; 3 2 2 2 3 2 Problem := [[12 x + 11 x y + 4 x y - 8 y, -2 x z + 8 y + 19 y z + 8 z, 3 3 2 2 2 y - 4 z - 18 x + 2], [-4 x y - 8 x z - 5 x + 16, 2 2 3 2 12 x y z - 10 y z + 3 x + 11, 7 x z + 2 x y - 8 y - 8 y z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.31 memory used=25.9MB, alloc=32.3MB, time=0.90 memory used=45.1MB, alloc=32.3MB, time=1.39 memory used=62.8MB, alloc=60.3MB, time=1.86 memory used=103.7MB, alloc=60.3MB, time=2.69 memory used=138.9MB, alloc=60.3MB, time=3.44 memory used=180.5MB, alloc=68.3MB, time=4.49 memory used=224.5MB, alloc=68.3MB, time=5.47 memory used=267.4MB, alloc=92.3MB, time=6.35 memory used=333.0MB, alloc=92.3MB, time=7.61 memory used=398.2MB, alloc=92.3MB, time=8.75 memory used=454.4MB, alloc=92.3MB, time=9.48 memory used=520.4MB, alloc=92.6MB, time=11.28 memory used=560.0MB, alloc=92.6MB, time=11.49 memory used=597.4MB, alloc=92.6MB, time=11.67 memory used=623.6MB, alloc=92.6MB, time=11.82 memory used=654.9MB, alloc=92.6MB, time=11.98 memory used=714.5MB, alloc=92.6MB, time=12.74 memory used=790.8MB, alloc=93.0MB, time=14.12 memory used=858.3MB, alloc=93.0MB, time=15.96 memory used=897.5MB, alloc=93.0MB, time=16.19 memory used=934.6MB, alloc=93.0MB, time=16.38 memory used=959.7MB, alloc=93.0MB, time=16.53 memory used=989.6MB, alloc=93.0MB, time=16.68 memory used=1041.8MB, alloc=93.0MB, time=17.19 memory used=1105.5MB, alloc=349.0MB, time=18.74 memory used=1165.4MB, alloc=373.0MB, time=20.34 memory used=1252.5MB, alloc=373.0MB, time=21.79 memory used=1310.0MB, alloc=373.0MB, time=23.31 memory used=1355.8MB, alloc=373.0MB, time=23.56 memory used=1391.9MB, alloc=373.0MB, time=23.78 memory used=1437.0MB, alloc=373.0MB, time=24.02 memory used=1481.2MB, alloc=373.0MB, time=24.23 memory used=1514.3MB, alloc=373.0MB, time=24.41 memory used=1607.8MB, alloc=373.0MB, time=26.31 memory used=1651.0MB, alloc=373.0MB, time=26.57 memory used=1696.3MB, alloc=373.0MB, time=27.11 memory used=1745.7MB, alloc=373.0MB, time=27.64 memory used=1813.8MB, alloc=373.0MB, time=28.90 memory used=1854.8MB, alloc=373.0MB, time=29.14 memory used=1930.5MB, alloc=373.0MB, time=30.64 memory used=2015.7MB, alloc=397.0MB, time=32.81 memory used=2122.0MB, alloc=397.0MB, time=35.22 memory used=2231.7MB, alloc=421.0MB, time=37.77 memory used=2354.8MB, alloc=445.0MB, time=39.95 memory used=2456.8MB, alloc=445.0MB, time=42.62 memory used=2565.1MB, alloc=469.0MB, time=45.21 memory used=2656.9MB, alloc=469.0MB, time=47.70 memory used=2746.2MB, alloc=469.0MB, time=49.65 memory used=2853.7MB, alloc=493.0MB, time=51.75 memory used=2943.8MB, alloc=493.0MB, time=53.89 memory used=3021.3MB, alloc=493.0MB, time=55.80 memory used=3099.1MB, alloc=493.0MB, time=57.37 memory used=3185.5MB, alloc=493.0MB, time=59.29 memory used=3292.3MB, alloc=493.0MB, time=61.09 memory used=3431.6MB, alloc=493.0MB, time=63.99 memory used=3526.3MB, alloc=493.0MB, time=65.03 memory used=3642.2MB, alloc=493.0MB, time=66.15 memory used=3760.4MB, alloc=493.0MB, time=71.37 memory used=3860.1MB, alloc=493.0MB, time=72.55 memory used=3956.9MB, alloc=493.0MB, time=73.70 memory used=4031.8MB, alloc=493.0MB, time=75.75 memory used=4129.2MB, alloc=493.0MB, time=77.86 memory used=4213.1MB, alloc=493.0MB, time=80.18 memory used=4279.2MB, alloc=493.0MB, time=81.66 memory used=4338.1MB, alloc=493.0MB, time=83.08 memory used=4398.8MB, alloc=493.0MB, time=84.96 memory used=4440.3MB, alloc=493.0MB, time=86.33 memory used=4494.0MB, alloc=493.0MB, time=87.93 memory used=4536.6MB, alloc=493.0MB, time=89.27 memory used=4706.7MB, alloc=517.0MB, time=91.90 memory used=4853.4MB, alloc=517.0MB, time=93.94 memory used=5002.1MB, alloc=517.0MB, time=98.22 memory used=5093.9MB, alloc=517.0MB, time=99.03 memory used=5199.2MB, alloc=517.0MB, time=99.83 memory used=5314.6MB, alloc=517.0MB, time=101.13 memory used=5420.0MB, alloc=517.0MB, time=102.02 memory used=5516.4MB, alloc=517.0MB, time=103.23 memory used=5629.0MB, alloc=517.0MB, time=104.19 memory used=5724.8MB, alloc=517.0MB, time=104.99 memory used=5868.1MB, alloc=517.0MB, time=113.82 memory used=5966.3MB, alloc=517.0MB, time=114.66 memory used=6059.5MB, alloc=517.0MB, time=115.45 memory used=6169.9MB, alloc=517.0MB, time=116.25 memory used=6243.7MB, alloc=517.0MB, time=116.92 memory used=6358.9MB, alloc=517.0MB, time=118.32 memory used=6463.7MB, alloc=517.0MB, time=119.24 memory used=6556.3MB, alloc=517.0MB, time=120.03 memory used=6678.5MB, alloc=517.0MB, time=121.34 memory used=6780.3MB, alloc=517.0MB, time=122.18 memory used=6918.2MB, alloc=517.0MB, time=130.98 memory used=7021.3MB, alloc=517.0MB, time=131.88 memory used=7105.5MB, alloc=517.0MB, time=132.67 memory used=7216.9MB, alloc=517.0MB, time=133.49 memory used=7297.3MB, alloc=517.0MB, time=134.20 memory used=7379.9MB, alloc=517.0MB, time=134.89 memory used=7523.2MB, alloc=517.0MB, time=136.96 memory used=7614.0MB, alloc=517.0MB, time=137.83 memory used=7733.4MB, alloc=517.0MB, time=138.73 memory used=7808.7MB, alloc=517.0MB, time=139.53 memory used=7891.2MB, alloc=517.0MB, time=140.31 memory used=7986.6MB, alloc=517.0MB, time=141.10 memory used=8118.1MB, alloc=517.0MB, time=142.76 memory used=8235.2MB, alloc=517.0MB, time=143.75 memory used=8334.1MB, alloc=517.0MB, time=144.64 memory used=8443.2MB, alloc=517.0MB, time=145.51 memory used=8517.9MB, alloc=517.0MB, time=146.30 memory used=8604.0MB, alloc=517.0MB, time=147.07 memory used=8704.4MB, alloc=517.0MB, time=147.88 |\^/| 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(); 1428261189 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 3 2 F := [-17 x y - 11 x z - 16 z - 8, 19 x z - 3 y - 2 y z - 12 y z, 2 3 3 -17 x y - 20 y + 15 z + 7 x] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 3 2 2 3 2 G := [-15 x y + 15 y + 20 z + 5 y , 16 y z + 8 z + 6 y + 10 y, 3 -11 z + 2 x y + 9 x + 14] > Problem := [F,G]; 2 2 3 2 3 2 Problem := [[-17 x y - 11 x z - 16 z - 8, 19 x z - 3 y - 2 y z - 12 y z, 2 3 3 2 3 3 2 -17 x y - 20 y + 15 z + 7 x], [-15 x y + 15 y + 20 z + 5 y , 2 3 2 3 16 y z + 8 z + 6 y + 10 y, -11 z + 2 x y + 9 x + 14]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.5MB, alloc=32.3MB, time=0.30 memory used=24.5MB, alloc=32.3MB, time=0.80 memory used=66.8MB, alloc=37.2MB, time=1.76 memory used=91.7MB, alloc=38.4MB, time=2.02 memory used=101.7MB, alloc=62.4MB, time=2.11 memory used=129.3MB, alloc=62.4MB, time=2.23 memory used=156.4MB, alloc=62.4MB, time=2.35 memory used=190.6MB, alloc=62.4MB, time=2.47 memory used=212.6MB, alloc=62.4MB, time=2.56 memory used=233.8MB, alloc=62.4MB, time=2.64 memory used=257.0MB, alloc=62.4MB, time=2.73 memory used=282.6MB, alloc=62.4MB, time=2.82 memory used=311.0MB, alloc=62.4MB, time=2.92 memory used=341.6MB, alloc=62.4MB, time=3.01 memory used=374.7MB, alloc=62.4MB, time=3.12 memory used=408.2MB, alloc=81.9MB, time=3.25 memory used=419.9MB, alloc=83.8MB, time=3.32 memory used=432.1MB, alloc=83.8MB, time=3.40 memory used=444.8MB, alloc=83.8MB, time=3.47 memory used=458.3MB, alloc=83.8MB, time=3.54 memory used=472.3MB, alloc=83.8MB, time=3.61 memory used=487.3MB, alloc=83.8MB, time=3.69 memory used=529.6MB, alloc=83.8MB, time=4.28 memory used=558.4MB, alloc=83.8MB, time=4.43 memory used=615.5MB, alloc=83.8MB, time=5.50 memory used=643.9MB, alloc=83.8MB, time=5.63 memory used=670.4MB, alloc=83.8MB, time=5.74 memory used=720.4MB, alloc=83.8MB, time=6.61 memory used=779.2MB, alloc=83.8MB, time=7.68 memory used=825.5MB, alloc=83.8MB, time=10.06 memory used=856.4MB, alloc=83.8MB, time=10.24 memory used=877.9MB, alloc=107.8MB, time=10.40 memory used=908.2MB, alloc=107.8MB, time=10.60 memory used=945.4MB, alloc=107.8MB, time=10.81 memory used=987.6MB, alloc=107.8MB, time=11.02 memory used=1034.2MB, alloc=107.8MB, time=11.24 memory used=1069.2MB, alloc=107.8MB, time=11.42 memory used=1092.4MB, alloc=107.8MB, time=11.56 memory used=1116.8MB, alloc=107.8MB, time=11.72 memory used=1142.0MB, alloc=107.8MB, time=11.87 memory used=1168.0MB, alloc=107.8MB, time=12.02 memory used=1194.7MB, alloc=107.8MB, time=12.17 memory used=1222.2MB, alloc=107.8MB, time=12.34 memory used=1251.1MB, alloc=107.8MB, time=12.50 memory used=1285.2MB, alloc=107.8MB, time=12.68 memory used=1320.8MB, alloc=107.8MB, time=12.86 memory used=1357.4MB, alloc=107.8MB, time=13.03 memory used=1394.8MB, alloc=107.8MB, time=13.21 memory used=1433.1MB, alloc=107.8MB, time=13.40 memory used=1472.3MB, alloc=107.8MB, time=13.59 memory used=1512.2MB, alloc=107.8MB, time=13.77 memory used=1553.0MB, alloc=107.8MB, time=13.96 memory used=1594.4MB, alloc=107.8MB, time=14.14 memory used=1636.6MB, alloc=107.8MB, time=14.32 memory used=1672.7MB, alloc=107.8MB, time=14.48 memory used=1694.7MB, alloc=107.8MB, time=14.59 memory used=1715.4MB, alloc=107.8MB, time=14.71 memory used=1737.1MB, alloc=107.8MB, time=14.83 memory used=1758.9MB, alloc=107.8MB, time=14.95 memory used=1780.9MB, alloc=107.8MB, time=15.06 memory used=1803.0MB, alloc=107.8MB, time=15.18 memory used=1825.3MB, alloc=107.8MB, time=15.30 memory used=1847.7MB, alloc=107.8MB, time=15.42 memory used=1870.1MB, alloc=107.8MB, time=15.53 memory used=1892.8MB, alloc=107.8MB, time=15.64 memory used=1915.5MB, alloc=131.8MB, time=15.79 memory used=1952.9MB, alloc=131.8MB, time=15.94 memory used=1991.5MB, alloc=131.8MB, time=16.10 memory used=2030.3MB, alloc=131.8MB, time=16.26 memory used=2069.4MB, alloc=131.8MB, time=16.42 memory used=2108.8MB, alloc=131.8MB, time=16.58 memory used=2148.4MB, alloc=131.8MB, time=16.74 memory used=2188.2MB, alloc=131.8MB, time=16.90 memory used=2229.4MB, alloc=131.8MB, time=17.06 memory used=2276.4MB, alloc=131.8MB, time=17.24 memory used=2324.8MB, alloc=131.8MB, time=17.42 memory used=2373.3MB, alloc=131.8MB, time=17.59 memory used=2422.0MB, alloc=131.8MB, time=17.76 memory used=2470.8MB, alloc=131.8MB, time=17.94 memory used=2519.6MB, alloc=131.8MB, time=18.11 memory used=2568.6MB, alloc=131.8MB, time=18.29 memory used=2618.9MB, alloc=131.8MB, time=18.46 memory used=2674.6MB, alloc=131.8MB, time=18.64 memory used=2731.5MB, alloc=131.8MB, time=18.83 memory used=2788.4MB, alloc=131.8MB, time=19.01 memory used=2845.0MB, alloc=131.8MB, time=19.20 memory used=2903.0MB, alloc=131.8MB, time=19.38 memory used=2965.6MB, alloc=131.8MB, time=19.58 memory used=3029.3MB, alloc=131.8MB, time=19.78 memory used=3092.4MB, alloc=131.8MB, time=19.98 memory used=3156.9MB, alloc=131.8MB, time=20.17 memory used=3229.7MB, alloc=131.8MB, time=20.38 memory used=3247.6MB, alloc=131.8MB, time=20.48 memory used=3263.9MB, alloc=131.8MB, time=20.58 memory used=3279.3MB, alloc=131.8MB, time=20.67 memory used=3288.7MB, alloc=131.8MB, time=20.75 memory used=3292.4MB, alloc=131.8MB, time=20.82 memory used=3294.6MB, alloc=131.8MB, time=20.91 memory used=3298.1MB, alloc=387.8MB, time=21.00 memory used=3432.0MB, alloc=387.8MB, time=21.69 memory used=3574.9MB, alloc=387.8MB, time=22.11 memory used=3725.1MB, alloc=387.8MB, time=22.54 memory used=3887.8MB, alloc=387.8MB, time=22.98 memory used=4085.4MB, alloc=387.8MB, time=25.40 memory used=4135.3MB, alloc=387.8MB, time=25.67 memory used=4196.5MB, alloc=387.8MB, time=25.98 memory used=4262.2MB, alloc=387.8MB, time=26.27 memory used=4301.3MB, alloc=387.8MB, time=26.48 memory used=4339.8MB, alloc=387.8MB, time=26.70 memory used=4381.6MB, alloc=387.8MB, time=26.93 memory used=4425.5MB, alloc=387.8MB, time=27.16 memory used=4471.9MB, alloc=387.8MB, time=27.39 memory used=4524.7MB, alloc=387.8MB, time=27.65 memory used=4580.2MB, alloc=387.8MB, time=27.89 memory used=4637.8MB, alloc=387.8MB, time=28.14 memory used=4697.3MB, alloc=387.8MB, time=28.37 memory used=4759.5MB, alloc=387.8MB, time=28.62 memory used=4828.8MB, alloc=387.8MB, time=28.89 memory used=4884.4MB, alloc=387.8MB, time=29.10 memory used=4917.0MB, alloc=387.8MB, time=29.25 memory used=4947.0MB, alloc=387.8MB, time=29.39 memory used=4982.6MB, alloc=387.8MB, time=29.55 memory used=5013.8MB, alloc=387.8MB, time=29.69 memory used=5049.8MB, alloc=387.8MB, time=29.84 memory used=5087.5MB, alloc=387.8MB, time=30.01 memory used=5125.5MB, alloc=387.8MB, time=30.17 memory used=5163.9MB, alloc=387.8MB, time=30.33 memory used=5202.5MB, alloc=387.8MB, time=30.49 memory used=5241.4MB, alloc=387.8MB, time=30.65 memory used=5280.6MB, alloc=387.8MB, time=30.80 memory used=5320.0MB, alloc=387.8MB, time=30.96 memory used=5359.6MB, alloc=387.8MB, time=31.12 memory used=5399.4MB, alloc=387.8MB, time=31.29 memory used=5440.7MB, alloc=387.8MB, time=31.46 memory used=5487.8MB, alloc=387.8MB, time=31.64 memory used=5536.1MB, alloc=387.8MB, time=31.81 memory used=5584.7MB, alloc=387.8MB, time=31.99 memory used=5633.4MB, alloc=387.8MB, time=32.17 memory used=5682.2MB, alloc=387.8MB, time=32.34 memory used=5731.1MB, alloc=387.8MB, time=32.51 memory used=5780.0MB, alloc=387.8MB, time=32.69 memory used=5830.5MB, alloc=387.8MB, time=32.87 memory used=5886.0MB, alloc=387.8MB, time=33.06 memory used=5943.0MB, alloc=387.8MB, time=33.25 memory used=5999.8MB, alloc=387.8MB, time=33.44 memory used=6056.4MB, alloc=387.8MB, time=33.63 memory used=6114.4MB, alloc=387.8MB, time=33.82 memory used=6176.9MB, alloc=387.8MB, time=34.02 memory used=6240.5MB, alloc=387.8MB, time=34.22 memory used=6303.6MB, alloc=387.8MB, time=34.42 memory used=6368.6MB, alloc=387.8MB, time=34.62 memory used=6447.4MB, alloc=387.8MB, time=34.85 memory used=6607.5MB, alloc=387.8MB, time=35.32 memory used=6748.8MB, alloc=387.8MB, time=35.73 memory used=6897.4MB, alloc=387.8MB, time=36.16 memory used=7058.9MB, alloc=387.8MB, time=36.60 memory used=7274.0MB, alloc=387.8MB, time=37.52 memory used=7355.9MB, alloc=387.8MB, time=82.78 memory used=7432.3MB, alloc=387.8MB, time=167.09 |\^/| 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(); 1428261489 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 3 2 F := [12 y z - z + 9 x + 3 z , -14 z + 7 y + 16 y z + 20 x, 2 3 13 x y + 11 z - 2 x z - 7 z] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 3 3 2 G := [-12 x - 10 x y + 5 y z + 12 z , 17 x + 12 x y z + 14 y z - 16 y, 2 2 2 13 x y + 11 y z + 14 x y + 6 z ] > Problem := [F,G]; 2 3 2 2 3 2 Problem := [[12 y z - z + 9 x + 3 z , -14 z + 7 y + 16 y z + 20 x, 2 3 3 2 2 3 13 x y + 11 z - 2 x z - 7 z], [-12 x - 10 x y + 5 y z + 12 z , 3 2 2 2 2 17 x + 12 x y z + 14 y z - 16 y, 13 x y + 11 y z + 14 x y + 6 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.30 memory used=24.3MB, alloc=32.3MB, time=0.77 memory used=46.7MB, alloc=36.5MB, time=1.16 memory used=63.5MB, alloc=37.0MB, time=1.41 memory used=75.3MB, alloc=37.0MB, time=1.47 memory used=87.4MB, alloc=37.0MB, time=1.53 memory used=97.6MB, alloc=37.0MB, time=1.58 memory used=119.3MB, alloc=37.0MB, time=2.05 memory used=139.0MB, alloc=37.0MB, time=2.36 memory used=156.8MB, alloc=37.0MB, time=2.68 memory used=171.9MB, alloc=37.0MB, time=2.77 memory used=192.8MB, alloc=61.0MB, time=3.10 memory used=228.2MB, alloc=61.0MB, time=4.55 memory used=263.0MB, alloc=61.0MB, time=5.38 memory used=305.3MB, alloc=61.0MB, time=6.46 memory used=327.9MB, alloc=61.0MB, time=6.58 memory used=350.5MB, alloc=61.0MB, time=6.69 memory used=375.1MB, alloc=61.0MB, time=6.80 memory used=403.4MB, alloc=61.0MB, time=11.54 memory used=441.9MB, alloc=61.0MB, time=17.16 memory used=472.6MB, alloc=61.0MB, time=17.26 memory used=490.4MB, alloc=61.0MB, time=17.33 memory used=518.1MB, alloc=61.0MB, time=18.83 memory used=566.6MB, alloc=61.0MB, time=19.42 memory used=620.2MB, alloc=61.0MB, time=21.09 memory used=652.9MB, alloc=85.0MB, time=33.19 memory used=701.7MB, alloc=85.0MB, time=54.45 memory used=751.8MB, alloc=85.0MB, time=55.70 memory used=783.5MB, alloc=85.0MB, time=55.84 memory used=837.3MB, alloc=85.0MB, time=56.49 memory used=920.8MB, alloc=85.0MB, time=57.69 memory used=988.8MB, alloc=93.0MB, time=59.72 memory used=1040.6MB, alloc=93.0MB, time=59.98 memory used=1072.5MB, alloc=93.0MB, time=60.16 memory used=1111.3MB, alloc=93.0MB, time=60.34 memory used=1152.3MB, alloc=93.0MB, time=60.53 memory used=1188.1MB, alloc=93.0MB, time=60.70 memory used=1215.4MB, alloc=93.0MB, time=60.84 memory used=1245.7MB, alloc=93.0MB, time=60.99 memory used=1278.4MB, alloc=93.0MB, time=61.15 memory used=1313.7MB, alloc=93.0MB, time=61.30 memory used=1351.5MB, alloc=93.0MB, time=61.46 memory used=1389.5MB, alloc=93.0MB, time=61.62 memory used=1423.3MB, alloc=93.0MB, time=61.75 memory used=1458.0MB, alloc=93.0MB, time=61.89 memory used=1494.6MB, alloc=93.0MB, time=62.03 memory used=1528.7MB, alloc=93.0MB, time=62.17 memory used=1558.0MB, alloc=93.0MB, time=62.29 memory used=1589.2MB, alloc=93.0MB, time=62.41 memory used=1624.3MB, alloc=93.0MB, time=62.53 memory used=1686.5MB, alloc=93.6MB, time=64.40 memory used=1720.9MB, alloc=93.6MB, time=64.58 memory used=1757.3MB, alloc=93.6MB, time=64.77 memory used=1798.2MB, alloc=93.6MB, time=64.96 memory used=1838.4MB, alloc=93.6MB, time=65.14 memory used=1866.3MB, alloc=93.6MB, time=65.29 memory used=1896.2MB, alloc=93.6MB, time=65.44 memory used=1928.8MB, alloc=93.6MB, time=65.60 memory used=1963.8MB, alloc=93.6MB, time=65.77 memory used=2001.4MB, alloc=93.6MB, time=65.94 memory used=2041.7MB, alloc=93.6MB, time=66.10 memory used=2074.8MB, alloc=93.6MB, time=66.25 memory used=2110.6MB, alloc=93.6MB, time=66.39 memory used=2147.3MB, alloc=93.6MB, time=66.54 memory used=2182.6MB, alloc=93.6MB, time=66.67 memory used=2211.2MB, alloc=93.6MB, time=66.79 memory used=2241.9MB, alloc=93.6MB, time=66.91 memory used=2275.8MB, alloc=93.6MB, time=67.03 memory used=2341.9MB, alloc=93.6MB, time=86.76 memory used=2506.7MB, alloc=94.0MB, time=90.44 memory used=2544.9MB, alloc=94.0MB, time=90.63 memory used=2584.0MB, alloc=94.0MB, time=90.80 memory used=2614.1MB, alloc=94.0MB, time=90.97 memory used=2648.9MB, alloc=94.0MB, time=91.12 memory used=2688.0MB, alloc=94.0MB, time=91.30 memory used=2727.9MB, alloc=94.0MB, time=91.47 memory used=2765.2MB, alloc=94.0MB, time=91.62 memory used=2791.7MB, alloc=94.0MB, time=91.74 memory used=2820.5MB, alloc=94.0MB, time=91.86 memory used=2850.6MB, alloc=94.0MB, time=91.98 memory used=2883.5MB, alloc=94.0MB, time=92.11 memory used=2918.2MB, alloc=94.0MB, time=92.24 memory used=2955.5MB, alloc=94.0MB, time=92.36 memory used=3004.2MB, alloc=104.8MB, time=92.53 memory used=3032.0MB, alloc=107.8MB, time=92.65 memory used=3055.7MB, alloc=107.8MB, time=92.76 memory used=3075.0MB, alloc=107.8MB, time=92.87 memory used=3143.3MB, alloc=107.8MB, time=98.12 memory used=3182.3MB, alloc=107.8MB, time=98.33 memory used=3210.1MB, alloc=107.8MB, time=98.50 memory used=3240.2MB, alloc=107.8MB, time=98.68 memory used=3272.9MB, alloc=107.8MB, time=98.86 memory used=3308.2MB, alloc=107.8MB, time=99.05 memory used=3348.5MB, alloc=107.8MB, time=99.24 memory used=3389.3MB, alloc=107.8MB, time=99.43 memory used=3431.7MB, alloc=107.8MB, time=99.62 memory used=3458.8MB, alloc=107.8MB, time=99.79 memory used=3480.7MB, alloc=107.8MB, time=99.93 memory used=3504.6MB, alloc=107.8MB, time=100.07 memory used=3529.4MB, alloc=107.8MB, time=100.21 memory used=3554.7MB, alloc=107.8MB, time=100.36 memory used=3580.5MB, alloc=107.8MB, time=100.51 memory used=3606.8MB, alloc=107.8MB, time=100.66 memory used=3633.6MB, alloc=107.8MB, time=100.81 memory used=3660.8MB, alloc=107.8MB, time=100.95 memory used=3688.4MB, alloc=107.8MB, time=101.10 memory used=3716.5MB, alloc=107.8MB, time=101.24 memory used=3745.2MB, alloc=107.8MB, time=101.39 memory used=3774.5MB, alloc=107.8MB, time=101.55 memory used=3807.8MB, alloc=107.8MB, time=101.71 memory used=3841.8MB, alloc=107.8MB, time=101.86 memory used=3876.3MB, alloc=107.8MB, time=102.02 memory used=3911.3MB, alloc=107.8MB, time=102.18 memory used=3946.7MB, alloc=107.8MB, time=102.34 memory used=3978.9MB, alloc=107.8MB, time=102.49 memory used=4010.2MB, alloc=107.8MB, time=102.64 memory used=4042.3MB, alloc=107.8MB, time=102.78 memory used=4078.3MB, alloc=107.8MB, time=102.94 memory used=4115.4MB, alloc=107.8MB, time=103.10 memory used=4152.8MB, alloc=107.8MB, time=103.25 memory used=4190.5MB, alloc=107.8MB, time=103.41 memory used=4228.5MB, alloc=107.8MB, time=103.56 memory used=4265.9MB, alloc=107.8MB, time=103.73 memory used=4292.9MB, alloc=107.8MB, time=103.86 memory used=4314.7MB, alloc=131.8MB, time=104.02 memory used=4345.7MB, alloc=131.8MB, time=104.16 memory used=4379.6MB, alloc=131.8MB, time=104.31 memory used=4413.6MB, alloc=131.8MB, time=104.45 memory used=4447.8MB, alloc=131.8MB, time=104.60 memory used=4482.1MB, alloc=131.8MB, time=104.74 memory used=4516.5MB, alloc=131.8MB, time=104.88 memory used=4551.2MB, alloc=131.8MB, time=105.02 memory used=4586.4MB, alloc=131.8MB, time=105.15 memory used=4625.4MB, alloc=131.8MB, time=105.30 memory used=4665.1MB, alloc=131.8MB, time=105.44 memory used=4704.7MB, alloc=131.8MB, time=105.59 memory used=4744.4MB, alloc=131.8MB, time=105.74 memory used=4784.1MB, alloc=131.8MB, time=105.88 memory used=4824.4MB, alloc=131.8MB, time=106.03 memory used=4868.6MB, alloc=131.8MB, time=106.18 memory used=4913.1MB, alloc=131.8MB, time=106.34 memory used=4957.5MB, alloc=131.8MB, time=106.49 memory used=5001.8MB, alloc=131.8MB, time=106.65 memory used=5046.5MB, alloc=131.8MB, time=106.80 memory used=5094.8MB, alloc=131.8MB, time=106.95 memory used=5143.1MB, alloc=131.8MB, time=107.11 memory used=5191.6MB, alloc=131.8MB, time=107.27 memory used=5244.1MB, alloc=131.8MB, time=107.44 memory used=5296.2MB, alloc=131.8MB, time=107.59 memory used=5348.1MB, alloc=131.8MB, time=107.76 memory used=5404.3MB, alloc=131.8MB, time=107.93 memory used=5440.7MB, alloc=131.8MB, time=108.08 memory used=5479.2MB, alloc=131.8MB, time=108.22 memory used=5514.3MB, alloc=131.8MB, time=108.35 memory used=5551.9MB, alloc=131.8MB, time=108.48 memory used=5589.0MB, alloc=131.8MB, time=108.61 memory used=5623.0MB, alloc=131.8MB, time=108.74 memory used=5658.9MB, alloc=131.8MB, time=108.88 memory used=5694.1MB, alloc=131.8MB, time=109.01 memory used=5726.5MB, alloc=131.8MB, time=109.14 memory used=5760.4MB, alloc=131.8MB, time=109.26 memory used=5793.6MB, alloc=131.8MB, time=109.39 memory used=5826.5MB, alloc=131.8MB, time=109.52 memory used=5858.7MB, alloc=131.8MB, time=109.65 memory used=5890.1MB, alloc=131.8MB, time=109.77 memory used=5920.6MB, alloc=131.8MB, time=109.90 memory used=5950.2MB, alloc=131.8MB, time=110.02 memory used=5979.0MB, alloc=131.8MB, time=110.13 memory used=6006.9MB, alloc=131.8MB, time=110.25 memory used=6033.8MB, alloc=131.8MB, time=110.36 memory used=6057.0MB, alloc=131.8MB, time=110.48 memory used=6067.7MB, alloc=131.8MB, time=110.58 memory used=6076.1MB, alloc=131.8MB, time=110.67 memory used=6084.5MB, alloc=131.8MB, time=110.79 memory used=6093.6MB, alloc=131.8MB, time=110.88 memory used=6102.2MB, alloc=131.8MB, time=110.97 memory used=6112.0MB, alloc=131.8MB, time=111.08 memory used=6120.9MB, alloc=131.8MB, time=111.16 memory used=6130.4MB, alloc=131.8MB, time=111.25 memory used=6140.5MB, alloc=131.8MB, time=111.35 memory used=6150.5MB, alloc=131.8MB, time=111.44 memory used=6161.1MB, alloc=131.8MB, time=111.52 memory used=6172.4MB, alloc=131.8MB, time=111.63 memory used=6184.0MB, alloc=131.8MB, time=111.73 memory used=6195.2MB, alloc=131.8MB, time=111.82 memory used=6206.9MB, alloc=131.8MB, time=111.91 memory used=6218.8MB, alloc=131.8MB, time=112.00 memory used=6231.8MB, alloc=131.8MB, time=112.10 memory used=6245.4MB, alloc=131.8MB, time=112.19 memory used=6260.9MB, alloc=131.8MB, time=112.44 memory used=6356.6MB, alloc=131.8MB, time=117.38 memory used=6399.5MB, alloc=131.8MB, time=117.62 memory used=6448.1MB, alloc=131.8MB, time=117.86 memory used=6503.0MB, alloc=131.8MB, time=118.10 memory used=6564.9MB, alloc=131.8MB, time=118.36 memory used=6624.0MB, alloc=131.8MB, time=118.59 memory used=6661.6MB, alloc=131.8MB, time=118.78 memory used=6697.9MB, alloc=131.8MB, time=118.99 memory used=6737.6MB, alloc=131.8MB, time=119.18 memory used=6778.6MB, alloc=131.8MB, time=119.37 memory used=6820.8MB, alloc=131.8MB, time=119.59 memory used=6864.4MB, alloc=131.8MB, time=119.80 memory used=6912.9MB, alloc=131.8MB, time=120.00 memory used=6962.7MB, alloc=131.8MB, time=120.22 memory used=7013.6MB, alloc=131.8MB, time=120.42 memory used=7065.7MB, alloc=131.8MB, time=120.65 memory used=7119.3MB, alloc=131.8MB, time=120.87 memory used=7172.9MB, alloc=131.8MB, time=121.07 memory used=7225.9MB, alloc=131.8MB, time=121.29 memory used=7281.5MB, alloc=131.8MB, time=121.48 memory used=7337.9MB, alloc=131.8MB, time=121.70 memory used=7394.5MB, alloc=131.8MB, time=121.91 memory used=7451.8MB, alloc=131.8MB, time=122.11 memory used=7491.8MB, alloc=131.8MB, time=122.26 memory used=7523.6MB, alloc=131.8MB, time=122.39 memory used=7557.3MB, alloc=131.8MB, time=122.53 memory used=7591.4MB, alloc=131.8MB, time=122.66 memory used=7625.6MB, alloc=131.8MB, time=122.80 memory used=7659.9MB, alloc=131.8MB, time=122.95 memory used=7694.3MB, alloc=131.8MB, time=123.09 memory used=7728.8MB, alloc=131.8MB, time=123.23 memory used=7763.9MB, alloc=131.8MB, time=123.38 memory used=7803.1MB, alloc=131.8MB, time=123.52 memory used=7842.8MB, alloc=131.8MB, time=123.67 memory used=7882.4MB, alloc=131.8MB, time=123.82 memory used=7922.1MB, alloc=131.8MB, time=123.97 memory used=7961.8MB, alloc=131.8MB, time=124.11 memory used=8001.7MB, alloc=131.8MB, time=124.26 memory used=8046.3MB, alloc=131.8MB, time=124.41 memory used=8090.8MB, alloc=131.8MB, time=124.57 memory used=8135.2MB, alloc=131.8MB, time=124.73 memory used=8179.3MB, alloc=131.8MB, time=124.87 memory used=8223.6MB, alloc=131.8MB, time=125.03 memory used=8272.4MB, alloc=131.8MB, time=125.19 memory used=8320.9MB, alloc=131.8MB, time=125.35 memory used=8369.3MB, alloc=131.8MB, time=125.50 memory used=8417.9MB, alloc=131.8MB, time=125.66 memory used=8469.4MB, alloc=131.8MB, time=125.82 memory used=8521.4MB, alloc=131.8MB, time=125.99 memory used=8577.1MB, alloc=131.8MB, time=126.15 memory used=8623.2MB, alloc=131.8MB, time=126.32 memory used=8661.9MB, alloc=131.8MB, time=126.45 memory used=8697.0MB, alloc=131.8MB, time=126.59 memory used=8734.5MB, alloc=131.8MB, time=126.73 memory used=8768.7MB, alloc=131.8MB, time=126.86 memory used=8805.1MB, alloc=131.8MB, time=126.99 memory used=8841.0MB, alloc=131.8MB, time=127.13 memory used=8874.0MB, alloc=131.8MB, time=127.26 memory used=8908.6MB, alloc=131.8MB, time=127.39 memory used=8942.5MB, alloc=131.8MB, time=127.52 memory used=8973.8MB, alloc=131.8MB, time=127.65 memory used=9006.2MB, alloc=131.8MB, time=127.76 memory used=9038.0MB, alloc=131.8MB, time=127.89 memory used=9067.2MB, alloc=131.8MB, time=128.01 memory used=9097.2MB, alloc=131.8MB, time=128.13 memory used=9126.6MB, alloc=131.8MB, time=128.25 memory used=9153.6MB, alloc=131.8MB, time=128.37 memory used=9181.1MB, alloc=131.8MB, time=128.49 memory used=9208.0MB, alloc=131.8MB, time=128.60 memory used=9233.9MB, alloc=131.8MB, time=128.74 memory used=9247.8MB, alloc=131.8MB, time=128.84 memory used=9256.0MB, alloc=131.8MB, time=128.94 memory used=9264.4MB, alloc=131.8MB, time=129.03 memory used=9272.8MB, alloc=131.8MB, time=129.12 memory used=9281.8MB, alloc=131.8MB, time=129.23 memory used=9291.9MB, alloc=131.8MB, time=129.31 memory used=9300.9MB, alloc=131.8MB, time=129.39 memory used=9310.4MB, alloc=131.8MB, time=129.47 memory used=9320.7MB, alloc=131.8MB, time=129.56 memory used=9330.7MB, alloc=131.8MB, time=129.64 memory used=9340.5MB, alloc=131.8MB, time=129.75 memory used=9351.0MB, alloc=131.8MB, time=129.84 memory used=9362.1MB, alloc=131.8MB, time=129.92 memory used=9373.4MB, alloc=131.8MB, time=130.02 memory used=9385.3MB, alloc=131.8MB, time=130.11 memory used=9397.4MB, alloc=131.8MB, time=130.21 memory used=9409.7MB, alloc=131.8MB, time=130.31 memory used=9422.5MB, alloc=131.8MB, time=130.40 memory used=9435.9MB, alloc=131.8MB, time=130.50 |\^/| 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(); 1428261789 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 F := [19 x z + 15 y z - 10 x - 19 z , 12 x z - 3 x y z + 11 y - 6, 3 2 2 17 x + 16 x z + 16 y z + 7 z] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [13 x y + 17 x y + 9 x y z + 13 x y, -4 x z - 2 x z + 6 z , 3 2 2 4 x + 13 y z + 7 x - 5 x z] > Problem := [F,G]; 2 2 2 2 2 Problem := [[19 x z + 15 y z - 10 x - 19 z , 12 x z - 3 x y z + 11 y - 6, 3 2 2 2 2 17 x + 16 x z + 16 y z + 7 z], [13 x y + 17 x y + 9 x y z + 13 x y, 2 2 3 2 2 -4 x z - 2 x z + 6 z , 4 x + 13 y z + 7 x - 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=4.4MB, alloc=32.3MB, time=0.31 memory used=25.9MB, alloc=32.3MB, time=0.85 memory used=45.9MB, alloc=32.3MB, time=1.37 memory used=64.7MB, alloc=56.3MB, time=1.89 memory used=103.9MB, alloc=60.3MB, time=2.94 memory used=141.5MB, alloc=84.3MB, time=3.99 memory used=202.2MB, alloc=92.3MB, time=5.64 memory used=261.2MB, alloc=116.3MB, time=7.28 memory used=345.1MB, alloc=116.3MB, time=9.60 memory used=426.5MB, alloc=140.3MB, time=11.99 memory used=504.8MB, alloc=140.3MB, time=14.23 memory used=580.0MB, alloc=420.3MB, time=16.55 memory used=709.4MB, alloc=444.3MB, time=20.32 memory used=860.8MB, alloc=468.3MB, time=24.86 memory used=997.6MB, alloc=468.3MB, time=28.77 memory used=1144.4MB, alloc=492.3MB, time=33.20 memory used=1257.9MB, alloc=516.3MB, time=36.80 memory used=1377.9MB, alloc=516.3MB, time=40.05 memory used=1476.9MB, alloc=516.3MB, time=42.92 memory used=1600.0MB, alloc=516.3MB, time=46.22 memory used=1715.2MB, alloc=540.3MB, time=50.24 memory used=1809.7MB, alloc=540.3MB, time=53.30 memory used=1915.0MB, alloc=540.3MB, time=57.01 memory used=1997.0MB, alloc=540.3MB, time=59.72 memory used=2089.5MB, alloc=540.3MB, time=63.25 memory used=2160.8MB, alloc=540.3MB, time=65.53 memory used=2243.9MB, alloc=540.3MB, time=68.89 memory used=2329.8MB, alloc=540.3MB, time=72.16 memory used=2391.9MB, alloc=540.3MB, time=74.44 memory used=2457.8MB, alloc=564.3MB, time=76.59 memory used=2536.3MB, alloc=564.3MB, time=79.45 memory used=2598.6MB, alloc=564.3MB, time=82.10 memory used=2674.6MB, alloc=564.3MB, time=85.31 memory used=2730.5MB, alloc=564.3MB, time=87.58 memory used=2948.9MB, alloc=588.3MB, time=94.54 memory used=3159.5MB, alloc=612.3MB, time=101.43 memory used=3394.1MB, alloc=636.3MB, time=110.45 memory used=3588.0MB, alloc=660.3MB, time=117.33 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428262089 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 2 F := [-5 x - 18 y z - 14 x y - 16 z , -13 x z + 17 x z + y z + z , 3 3 3 -11 x + 10 y + 9 z - 14 y z] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [7 x z - 18 y z + 6 z + 12 x, -17 y - 19 x + 17, 2 -4 x y z - 6 y - 12 y - 2 z] > Problem := [F,G]; 3 2 2 2 2 2 Problem := [[-5 x - 18 y z - 14 x y - 16 z , -13 x z + 17 x z + y z + z , 3 3 3 2 2 -11 x + 10 y + 9 z - 14 y z], [7 x z - 18 y z + 6 z + 12 x, 2 2 -17 y - 19 x + 17, -4 x y z - 6 y - 12 y - 2 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.31 memory used=26.8MB, alloc=32.3MB, time=0.89 memory used=47.8MB, alloc=32.3MB, time=1.43 memory used=66.8MB, alloc=56.3MB, time=1.96 memory used=105.4MB, alloc=60.3MB, time=2.97 memory used=142.7MB, alloc=84.3MB, time=3.98 memory used=204.8MB, alloc=92.3MB, time=5.61 memory used=264.7MB, alloc=92.3MB, time=7.24 memory used=324.8MB, alloc=116.3MB, time=8.89 memory used=401.4MB, alloc=372.3MB, time=10.81 memory used=484.9MB, alloc=396.3MB, time=13.04 memory used=589.6MB, alloc=420.3MB, time=16.19 memory used=721.0MB, alloc=420.3MB, time=19.13 memory used=847.8MB, alloc=444.3MB, time=22.78 memory used=970.4MB, alloc=444.3MB, time=25.10 memory used=1092.2MB, alloc=444.3MB, time=27.18 memory used=1182.0MB, alloc=444.3MB, time=28.47 memory used=1318.4MB, alloc=468.3MB, time=31.77 memory used=1443.8MB, alloc=468.3MB, time=35.22 memory used=1558.9MB, alloc=492.3MB, time=38.27 memory used=1683.9MB, alloc=492.3MB, time=42.11 memory used=1811.1MB, alloc=516.3MB, time=46.18 memory used=1897.0MB, alloc=516.3MB, time=48.77 memory used=1987.0MB, alloc=516.3MB, time=51.52 memory used=2071.9MB, alloc=516.3MB, time=54.29 memory used=2140.6MB, alloc=516.3MB, time=56.48 memory used=2224.1MB, alloc=516.3MB, time=58.86 memory used=2280.2MB, alloc=516.3MB, time=60.77 memory used=2330.5MB, alloc=516.3MB, time=62.33 memory used=2404.8MB, alloc=516.3MB, time=64.75 memory used=2461.3MB, alloc=516.3MB, time=66.52 memory used=2519.7MB, alloc=540.3MB, time=68.30 memory used=2576.8MB, alloc=540.3MB, time=70.68 memory used=2627.6MB, alloc=540.3MB, time=72.64 memory used=2850.7MB, alloc=564.3MB, time=79.35 memory used=3068.5MB, alloc=588.3MB, time=86.75 memory used=3281.2MB, alloc=612.3MB, time=94.26 memory used=3484.8MB, alloc=636.3MB, time=98.69 memory used=3683.2MB, alloc=660.3MB, time=103.58 memory used=3862.8MB, alloc=660.3MB, time=109.00 memory used=4037.1MB, alloc=660.3MB, time=114.48 memory used=4217.7MB, alloc=684.3MB, time=121.14 |\^/| 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(); 1428262389 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [20 x y + 6 y z + 9 x y - 11 x z, -5 x y z + 9 z + 10 z, 3 2 2 -2 y + 4 x - 3 x z + 16 z ] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 G := [-10 x + 9 x y z + 9 x + 13 x y, 16 x y z + 12 y z + 8 y - 10 x, 3 4 x + 8 y - 16] > Problem := [F,G]; 2 2 2 Problem := [[20 x y + 6 y z + 9 x y - 11 x z, -5 x y z + 9 z + 10 z, 3 2 2 3 2 -2 y + 4 x - 3 x z + 16 z ], [-10 x + 9 x y z + 9 x + 13 x y, 2 2 3 16 x y z + 12 y z + 8 y - 10 x, 4 x + 8 y - 16]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.31 memory used=25.9MB, alloc=32.3MB, time=0.86 memory used=46.2MB, alloc=32.3MB, time=1.39 memory used=65.0MB, alloc=56.3MB, time=1.90 memory used=105.3MB, alloc=60.3MB, time=2.95 memory used=144.0MB, alloc=60.3MB, time=3.97 memory used=181.8MB, alloc=84.3MB, time=4.98 memory used=227.0MB, alloc=84.3MB, time=6.19 memory used=287.6MB, alloc=92.3MB, time=7.84 memory used=346.7MB, alloc=116.3MB, time=9.42 memory used=415.0MB, alloc=116.3MB, time=11.18 memory used=481.5MB, alloc=396.3MB, time=12.96 memory used=591.6MB, alloc=420.3MB, time=15.78 memory used=721.2MB, alloc=444.3MB, time=19.37 memory used=841.2MB, alloc=444.3MB, time=22.58 memory used=955.8MB, alloc=468.3MB, time=25.48 memory used=1074.8MB, alloc=468.3MB, time=28.91 memory used=1165.7MB, alloc=468.3MB, time=31.56 memory used=1259.0MB, alloc=468.3MB, time=34.40 memory used=1340.3MB, alloc=492.3MB, time=36.92 memory used=1402.7MB, alloc=492.3MB, time=38.85 memory used=1479.1MB, alloc=492.3MB, time=41.38 memory used=1546.2MB, alloc=492.3MB, time=43.45 memory used=1604.5MB, alloc=492.3MB, time=45.44 memory used=1672.9MB, alloc=492.3MB, time=47.87 memory used=1721.7MB, alloc=492.3MB, time=49.51 memory used=1780.6MB, alloc=492.3MB, time=51.79 memory used=1968.6MB, alloc=516.3MB, time=56.97 memory used=2174.4MB, alloc=540.3MB, time=63.06 memory used=2370.2MB, alloc=564.3MB, time=69.29 memory used=2536.6MB, alloc=588.3MB, time=74.77 memory used=2669.0MB, alloc=612.3MB, time=78.86 memory used=2829.2MB, alloc=636.3MB, time=84.35 memory used=2946.8MB, alloc=636.3MB, time=88.43 memory used=3082.1MB, alloc=636.3MB, time=92.92 memory used=3181.6MB, alloc=636.3MB, time=96.79 memory used=3317.7MB, alloc=660.3MB, time=101.13 memory used=3420.4MB, alloc=660.3MB, time=104.48 memory used=3516.7MB, alloc=660.3MB, time=108.01 |\^/| 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(); 1428262689 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-20 x z + 16 y z + 20 x y - 17 x, -7 y z - 20 x y - 6 x + 8, 2 3 3 18 x z - y + 14 z + 2 x y] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 3 G := [-11 y z + 4 x y + 9 z + 13 y, 3 x + 8 x y z - 12 y z - 7 z , 3 -14 y - 8 x z - 8] > Problem := [F,G]; 2 2 2 Problem := [[-20 x z + 16 y z + 20 x y - 17 x, -7 y z - 20 x y - 6 x + 8, 2 3 3 2 2 18 x z - y + 14 z + 2 x y], [-11 y z + 4 x y + 9 z + 13 y, 3 2 3 3 3 x + 8 x y z - 12 y z - 7 z , -14 y - 8 x 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=4.4MB, alloc=32.3MB, time=0.31 memory used=27.8MB, alloc=34.3MB, time=0.78 memory used=49.3MB, alloc=38.3MB, time=1.17 memory used=69.9MB, alloc=38.3MB, time=1.59 memory used=90.4MB, alloc=62.3MB, time=2.29 memory used=128.7MB, alloc=62.3MB, time=2.82 memory used=185.1MB, alloc=70.3MB, time=4.00 memory used=240.1MB, alloc=70.3MB, time=6.19 memory used=267.6MB, alloc=70.3MB, time=6.39 memory used=304.2MB, alloc=70.3MB, time=7.38 memory used=336.5MB, alloc=70.3MB, time=7.71 memory used=379.9MB, alloc=70.3MB, time=8.49 memory used=417.0MB, alloc=70.3MB, time=8.97 memory used=466.5MB, alloc=70.3MB, time=10.14 memory used=495.8MB, alloc=70.3MB, time=11.41 memory used=522.4MB, alloc=70.3MB, time=11.72 memory used=558.0MB, alloc=70.3MB, time=12.25 memory used=601.2MB, alloc=70.3MB, time=13.14 memory used=643.0MB, alloc=70.3MB, time=14.06 memory used=689.4MB, alloc=94.3MB, time=15.00 memory used=754.0MB, alloc=94.3MB, time=16.33 memory used=799.1MB, alloc=94.3MB, time=17.65 memory used=840.6MB, alloc=94.3MB, time=18.39 memory used=888.0MB, alloc=94.3MB, time=18.90 memory used=931.6MB, alloc=94.3MB, time=21.45 memory used=966.7MB, alloc=94.3MB, time=21.76 memory used=1010.8MB, alloc=94.3MB, time=22.12 memory used=1054.3MB, alloc=94.3MB, time=24.39 memory used=1092.4MB, alloc=94.3MB, time=24.73 memory used=1126.4MB, alloc=94.3MB, time=24.92 memory used=1167.9MB, alloc=94.3MB, time=25.25 memory used=1200.1MB, alloc=94.3MB, time=25.46 memory used=1245.9MB, alloc=94.3MB, time=28.27 memory used=1273.5MB, alloc=94.3MB, time=28.43 memory used=1321.3MB, alloc=94.3MB, time=28.98 memory used=1365.5MB, alloc=94.3MB, time=29.62 memory used=1400.7MB, alloc=94.3MB, time=29.83 memory used=1433.1MB, alloc=94.3MB, time=30.01 memory used=1465.0MB, alloc=94.3MB, time=30.18 memory used=1490.0MB, alloc=94.3MB, time=30.34 memory used=1524.7MB, alloc=94.3MB, time=30.61 memory used=1565.9MB, alloc=94.3MB, time=31.18 memory used=1601.7MB, alloc=94.3MB, time=31.39 memory used=1632.6MB, alloc=94.3MB, time=31.57 memory used=1665.3MB, alloc=94.3MB, time=31.75 memory used=1689.3MB, alloc=94.3MB, time=31.89 memory used=1717.8MB, alloc=94.3MB, time=32.05 memory used=1756.4MB, alloc=94.3MB, time=32.43 memory used=1817.6MB, alloc=94.3MB, time=37.36 memory used=1847.0MB, alloc=94.3MB, time=37.54 memory used=1877.1MB, alloc=94.3MB, time=37.71 memory used=1914.1MB, alloc=94.3MB, time=38.06 memory used=1993.6MB, alloc=94.3MB, time=40.26 memory used=2075.0MB, alloc=94.3MB, time=42.37 memory used=2151.5MB, alloc=118.3MB, time=44.03 memory used=2236.9MB, alloc=118.3MB, time=46.91 memory used=2289.5MB, alloc=118.3MB, time=48.67 memory used=2372.1MB, alloc=374.3MB, time=49.90 memory used=2467.3MB, alloc=374.3MB, time=52.76 memory used=2553.2MB, alloc=398.3MB, time=54.63 memory used=2622.9MB, alloc=398.3MB, time=55.27 memory used=2692.5MB, alloc=398.3MB, time=59.10 memory used=2762.5MB, alloc=398.3MB, time=59.85 memory used=2838.0MB, alloc=398.3MB, time=63.37 memory used=2890.1MB, alloc=398.3MB, time=63.67 memory used=3011.4MB, alloc=398.3MB, time=67.69 memory used=3063.4MB, alloc=398.3MB, time=68.16 memory used=3163.5MB, alloc=398.3MB, time=69.70 memory used=3233.4MB, alloc=422.3MB, time=70.58 memory used=3309.2MB, alloc=422.3MB, time=71.40 memory used=3382.1MB, alloc=422.3MB, time=71.84 memory used=3477.1MB, alloc=422.3MB, time=88.90 memory used=3547.2MB, alloc=422.3MB, time=89.31 memory used=3601.4MB, alloc=422.3MB, time=89.65 memory used=3667.3MB, alloc=422.3MB, time=90.00 memory used=3749.3MB, alloc=422.3MB, time=91.29 memory used=3828.6MB, alloc=422.3MB, time=92.01 memory used=3907.4MB, alloc=422.3MB, time=92.94 memory used=3977.4MB, alloc=422.3MB, time=93.34 memory used=4073.1MB, alloc=422.3MB, time=108.34 memory used=4139.0MB, alloc=422.3MB, time=108.71 memory used=4193.3MB, alloc=422.3MB, time=109.03 memory used=4259.8MB, alloc=422.3MB, time=109.38 memory used=4326.9MB, alloc=422.3MB, time=110.04 memory used=4403.5MB, alloc=422.3MB, time=110.56 memory used=4481.2MB, alloc=422.3MB, time=111.14 memory used=4561.4MB, alloc=422.3MB, time=111.89 memory used=4644.7MB, alloc=422.3MB, time=112.62 memory used=4705.8MB, alloc=422.3MB, time=112.98 memory used=4793.0MB, alloc=422.3MB, time=120.19 memory used=4850.6MB, alloc=422.3MB, time=120.51 memory used=4938.4MB, alloc=422.3MB, time=121.67 memory used=5022.7MB, alloc=422.3MB, time=122.90 memory used=5083.4MB, alloc=422.3MB, time=123.29 memory used=5156.0MB, alloc=422.3MB, time=123.68 memory used=5205.5MB, alloc=422.3MB, time=124.00 memory used=5275.1MB, alloc=422.3MB, time=125.19 memory used=5348.6MB, alloc=422.3MB, time=125.64 memory used=5412.0MB, alloc=422.3MB, time=126.01 memory used=5480.7MB, alloc=422.3MB, time=126.38 memory used=5530.6MB, alloc=422.3MB, time=126.71 memory used=5610.0MB, alloc=422.3MB, time=138.97 memory used=5684.6MB, alloc=422.3MB, time=140.32 memory used=5741.4MB, alloc=422.3MB, time=140.69 memory used=5810.3MB, alloc=422.3MB, time=141.18 memory used=5879.6MB, alloc=422.3MB, time=141.80 memory used=6019.1MB, alloc=422.3MB, time=147.61 memory used=6075.9MB, alloc=422.3MB, time=147.99 memory used=6203.8MB, alloc=422.3MB, time=150.74 memory used=6287.2MB, alloc=422.3MB, time=152.08 memory used=6398.8MB, alloc=446.3MB, time=154.77 memory used=6490.3MB, alloc=446.3MB, time=156.17 memory used=6581.0MB, alloc=446.3MB, time=158.36 memory used=6663.4MB, alloc=446.3MB, time=159.02 memory used=6740.9MB, alloc=446.3MB, time=159.66 memory used=6807.5MB, alloc=446.3MB, time=160.10 memory used=6906.2MB, alloc=446.3MB, time=164.21 memory used=7040.3MB, alloc=446.3MB, time=167.32 memory used=7137.6MB, alloc=446.3MB, time=168.71 memory used=7274.0MB, alloc=470.3MB, time=171.64 |\^/| 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(); 1428262989 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 2 F := [x z + 4 y - 13 y z - 7 z, 5 x z - 8 y z - 9 x + 8 z , 2 2 10 y z - 11 x z - 15 z + 20] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 3 G := [4 x + 6 y - 2 y z + 20 x y, -14 x y + 10 x y z - 3 z - 5 z, 2 2 3 2 x z + 13 x y - 14 y - z] > Problem := [F,G]; 2 2 2 2 2 2 Problem := [[x z + 4 y - 13 y z - 7 z, 5 x z - 8 y z - 9 x + 8 z , 2 2 3 3 2 10 y z - 11 x z - 15 z + 20], [4 x + 6 y - 2 y z + 20 x y, 2 3 2 2 3 -14 x y + 10 x y z - 3 z - 5 z, 2 x z + 13 x y - 14 y - z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=31.4MB, alloc=45.0MB, time=0.90 memory used=57.2MB, alloc=45.0MB, time=1.43 memory used=78.9MB, alloc=45.0MB, time=1.67 memory used=104.0MB, alloc=45.0MB, time=1.99 memory used=134.0MB, alloc=45.0MB, time=3.01 memory used=161.1MB, alloc=45.0MB, time=3.45 memory used=184.7MB, alloc=45.0MB, time=3.82 memory used=200.6MB, alloc=45.0MB, time=3.89 memory used=229.3MB, alloc=45.0MB, time=4.40 memory used=253.1MB, alloc=45.0MB, time=4.50 memory used=267.8MB, alloc=45.0MB, time=4.58 memory used=282.0MB, alloc=45.0MB, time=4.65 memory used=298.4MB, alloc=45.0MB, time=4.73 memory used=317.3MB, alloc=45.0MB, time=4.81 memory used=333.8MB, alloc=45.0MB, time=4.88 memory used=346.1MB, alloc=45.0MB, time=4.94 memory used=373.5MB, alloc=45.8MB, time=5.32 memory used=395.1MB, alloc=45.8MB, time=5.42 memory used=408.1MB, alloc=45.8MB, time=5.49 memory used=423.0MB, alloc=45.8MB, time=5.56 memory used=440.1MB, alloc=45.8MB, time=5.64 memory used=460.1MB, alloc=45.8MB, time=5.72 memory used=474.3MB, alloc=45.8MB, time=5.79 memory used=493.5MB, alloc=45.8MB, time=7.11 memory used=524.4MB, alloc=45.8MB, time=13.84 memory used=542.6MB, alloc=45.8MB, time=13.94 memory used=556.8MB, alloc=45.8MB, time=14.01 memory used=573.9MB, alloc=45.8MB, time=14.09 memory used=590.7MB, alloc=45.8MB, time=14.16 memory used=601.9MB, alloc=45.8MB, time=14.22 memory used=614.1MB, alloc=45.8MB, time=14.29 memory used=627.1MB, alloc=45.8MB, time=14.35 memory used=641.2MB, alloc=45.8MB, time=14.41 memory used=656.1MB, alloc=45.8MB, time=14.48 memory used=672.4MB, alloc=45.8MB, time=14.55 memory used=689.6MB, alloc=45.8MB, time=14.62 memory used=707.3MB, alloc=45.8MB, time=14.68 memory used=721.2MB, alloc=45.8MB, time=14.74 memory used=731.9MB, alloc=45.8MB, time=14.79 memory used=742.5MB, alloc=45.8MB, time=14.84 memory used=754.0MB, alloc=45.8MB, time=14.90 memory used=766.1MB, alloc=45.8MB, time=14.95 memory used=779.2MB, alloc=45.8MB, time=15.00 memory used=801.2MB, alloc=45.8MB, time=15.54 memory used=817.1MB, alloc=45.8MB, time=15.63 memory used=833.6MB, alloc=45.8MB, time=15.70 memory used=846.0MB, alloc=45.8MB, time=15.76 memory used=872.5MB, alloc=45.8MB, time=16.14 memory used=906.2MB, alloc=46.7MB, time=18.05 memory used=920.2MB, alloc=46.7MB, time=18.13 memory used=936.7MB, alloc=46.7MB, time=18.20 memory used=953.5MB, alloc=46.7MB, time=18.28 memory used=964.9MB, alloc=46.7MB, time=18.34 memory used=977.6MB, alloc=46.7MB, time=18.41 memory used=991.5MB, alloc=46.7MB, time=18.48 memory used=1006.3MB, alloc=46.7MB, time=18.54 memory used=1022.5MB, alloc=46.7MB, time=18.61 memory used=1040.6MB, alloc=46.7MB, time=18.68 memory used=1054.3MB, alloc=46.7MB, time=18.75 memory used=1065.2MB, alloc=46.7MB, time=18.80 memory used=1077.3MB, alloc=46.7MB, time=18.85 memory used=1116.4MB, alloc=46.7MB, time=19.64 memory used=1150.3MB, alloc=46.7MB, time=20.17 memory used=1183.9MB, alloc=46.7MB, time=20.77 memory used=1217.9MB, alloc=46.7MB, time=21.51 memory used=1252.3MB, alloc=46.7MB, time=22.43 memory used=1287.3MB, alloc=46.7MB, time=23.50 memory used=1321.0MB, alloc=46.7MB, time=24.80 memory used=1355.1MB, alloc=46.7MB, time=26.28 memory used=1390.1MB, alloc=46.7MB, time=27.85 memory used=1424.8MB, alloc=46.7MB, time=29.53 memory used=1459.9MB, alloc=46.7MB, time=31.38 memory used=1489.8MB, alloc=46.7MB, time=32.72 memory used=1519.0MB, alloc=70.7MB, time=33.92 memory used=1569.7MB, alloc=70.7MB, time=35.68 memory used=1594.9MB, alloc=70.7MB, time=35.80 memory used=1627.6MB, alloc=70.7MB, time=35.94 memory used=1650.1MB, alloc=70.7MB, time=36.03 memory used=1685.1MB, alloc=70.7MB, time=36.39 memory used=1726.3MB, alloc=70.9MB, time=36.89 memory used=1756.8MB, alloc=70.9MB, time=37.02 memory used=1786.6MB, alloc=70.9MB, time=37.15 memory used=1811.2MB, alloc=70.9MB, time=37.27 memory used=1846.8MB, alloc=70.9MB, time=37.65 memory used=1879.8MB, alloc=70.9MB, time=37.82 memory used=1913.0MB, alloc=70.9MB, time=37.96 memory used=1939.0MB, alloc=70.9MB, time=38.09 memory used=1964.7MB, alloc=70.9MB, time=38.21 memory used=2009.3MB, alloc=70.9MB, time=47.09 memory used=2045.6MB, alloc=70.9MB, time=49.08 memory used=2075.5MB, alloc=70.9MB, time=49.22 memory used=2101.6MB, alloc=70.9MB, time=49.33 memory used=2133.6MB, alloc=70.9MB, time=49.45 memory used=2167.7MB, alloc=70.9MB, time=49.59 memory used=2188.7MB, alloc=70.9MB, time=49.69 memory used=2212.0MB, alloc=70.9MB, time=49.78 memory used=2236.8MB, alloc=70.9MB, time=49.87 memory used=2263.9MB, alloc=70.9MB, time=49.97 memory used=2294.6MB, alloc=70.9MB, time=50.08 memory used=2336.2MB, alloc=70.9MB, time=50.76 memory used=2367.1MB, alloc=70.9MB, time=50.91 memory used=2397.4MB, alloc=70.9MB, time=51.03 memory used=2439.4MB, alloc=70.9MB, time=51.81 memory used=2496.5MB, alloc=78.9MB, time=55.03 memory used=2525.8MB, alloc=78.9MB, time=55.20 memory used=2559.3MB, alloc=78.9MB, time=55.35 memory used=2581.6MB, alloc=78.9MB, time=55.48 memory used=2606.2MB, alloc=78.9MB, time=55.61 memory used=2634.8MB, alloc=78.9MB, time=55.74 memory used=2666.4MB, alloc=78.9MB, time=55.88 memory used=2702.2MB, alloc=78.9MB, time=56.03 memory used=2727.2MB, alloc=78.9MB, time=56.15 memory used=2747.6MB, alloc=78.9MB, time=56.25 memory used=2769.3MB, alloc=78.9MB, time=56.35 memory used=2791.6MB, alloc=78.9MB, time=56.44 memory used=2815.2MB, alloc=78.9MB, time=56.53 memory used=2841.3MB, alloc=78.9MB, time=56.64 memory used=2870.6MB, alloc=78.9MB, time=56.77 memory used=2923.1MB, alloc=78.9MB, time=57.88 memory used=2968.9MB, alloc=78.9MB, time=61.99 memory used=2995.2MB, alloc=78.9MB, time=62.13 memory used=3028.1MB, alloc=78.9MB, time=62.29 memory used=3049.8MB, alloc=78.9MB, time=62.41 memory used=3071.7MB, alloc=78.9MB, time=62.53 memory used=3096.1MB, alloc=78.9MB, time=62.66 memory used=3122.7MB, alloc=78.9MB, time=62.79 memory used=3151.7MB, alloc=78.9MB, time=62.93 memory used=3183.9MB, alloc=78.9MB, time=63.06 memory used=3218.1MB, alloc=78.9MB, time=63.19 memory used=3242.1MB, alloc=78.9MB, time=63.30 memory used=3261.7MB, alloc=78.9MB, time=63.40 memory used=3281.0MB, alloc=78.9MB, time=63.50 memory used=3301.1MB, alloc=78.9MB, time=63.60 memory used=3322.2MB, alloc=78.9MB, time=63.70 memory used=3344.4MB, alloc=78.9MB, time=63.80 memory used=3367.5MB, alloc=78.9MB, time=63.93 memory used=3391.5MB, alloc=78.9MB, time=64.04 memory used=3417.2MB, alloc=78.9MB, time=64.13 memory used=3443.2MB, alloc=78.9MB, time=64.24 memory used=3469.6MB, alloc=78.9MB, time=64.36 memory used=3497.8MB, alloc=78.9MB, time=64.51 memory used=3527.3MB, alloc=78.9MB, time=64.61 memory used=3559.2MB, alloc=78.9MB, time=64.72 memory used=3591.9MB, alloc=91.8MB, time=64.85 memory used=3607.9MB, alloc=91.8MB, time=65.03 memory used=3675.7MB, alloc=91.8MB, time=66.25 memory used=3730.6MB, alloc=91.8MB, time=72.27 memory used=3767.3MB, alloc=91.8MB, time=73.50 memory used=3795.0MB, alloc=91.8MB, time=73.64 memory used=3815.8MB, alloc=91.8MB, time=73.77 memory used=3836.7MB, alloc=91.8MB, time=73.89 memory used=3860.8MB, alloc=91.8MB, time=74.01 memory used=3887.9MB, alloc=91.8MB, time=74.14 memory used=3918.9MB, alloc=91.8MB, time=74.28 memory used=3940.3MB, alloc=91.8MB, time=74.40 memory used=3957.6MB, alloc=91.8MB, time=74.50 memory used=3976.1MB, alloc=91.8MB, time=74.60 memory used=3994.9MB, alloc=91.8MB, time=74.70 memory used=4015.0MB, alloc=91.8MB, time=74.81 memory used=4036.3MB, alloc=91.8MB, time=74.91 memory used=4058.9MB, alloc=91.8MB, time=75.03 memory used=4082.5MB, alloc=91.8MB, time=75.13 memory used=4107.2MB, alloc=91.8MB, time=75.25 memory used=4133.5MB, alloc=91.8MB, time=75.35 memory used=4160.5MB, alloc=91.8MB, time=75.46 memory used=4188.6MB, alloc=91.8MB, time=75.59 memory used=4218.5MB, alloc=91.8MB, time=75.70 memory used=4236.1MB, alloc=91.8MB, time=75.80 memory used=4246.4MB, alloc=91.8MB, time=75.90 memory used=4257.0MB, alloc=91.8MB, time=75.98 memory used=4268.2MB, alloc=91.8MB, time=76.11 memory used=4279.9MB, alloc=91.8MB, time=76.21 memory used=4292.1MB, alloc=91.8MB, time=76.31 memory used=4344.1MB, alloc=91.8MB, time=95.36 memory used=4373.7MB, alloc=91.8MB, time=97.08 memory used=4399.4MB, alloc=91.8MB, time=97.22 memory used=4424.3MB, alloc=91.8MB, time=97.35 memory used=4443.2MB, alloc=91.8MB, time=97.48 memory used=4463.7MB, alloc=91.8MB, time=97.60 memory used=4487.0MB, alloc=91.8MB, time=97.73 memory used=4513.1MB, alloc=91.8MB, time=97.86 memory used=4540.9MB, alloc=91.8MB, time=97.99 memory used=4571.3MB, alloc=91.8MB, time=98.14 memory used=4590.9MB, alloc=115.8MB, time=98.28 memory used=4620.5MB, alloc=115.8MB, time=98.40 memory used=4652.6MB, alloc=115.8MB, time=98.54 memory used=4685.8MB, alloc=115.8MB, time=98.67 memory used=4722.5MB, alloc=115.8MB, time=98.81 memory used=4760.3MB, alloc=115.8MB, time=98.96 memory used=4801.5MB, alloc=115.8MB, time=99.10 memory used=4845.0MB, alloc=115.8MB, time=99.24 memory used=4891.9MB, alloc=115.8MB, time=99.40 memory used=4941.8MB, alloc=115.8MB, time=99.56 memory used=4994.5MB, alloc=115.8MB, time=99.72 memory used=5023.6MB, alloc=115.8MB, time=99.83 memory used=5033.4MB, alloc=115.8MB, time=99.92 memory used=5043.0MB, alloc=115.8MB, time=100.03 memory used=5052.9MB, alloc=115.8MB, time=100.12 memory used=5062.7MB, alloc=115.8MB, time=100.23 memory used=5072.4MB, alloc=115.8MB, time=100.32 memory used=5081.9MB, alloc=115.8MB, time=100.41 memory used=5091.7MB, alloc=115.8MB, time=100.50 memory used=5102.1MB, alloc=115.8MB, time=100.59 memory used=5112.6MB, alloc=115.8MB, time=100.68 memory used=5123.0MB, alloc=115.8MB, time=100.77 memory used=5133.5MB, alloc=115.8MB, time=100.86 memory used=5144.4MB, alloc=115.8MB, time=100.96 memory used=5155.5MB, alloc=115.8MB, time=101.05 memory used=5167.4MB, alloc=115.8MB, time=101.14 memory used=5179.1MB, alloc=115.8MB, time=101.23 memory used=5191.6MB, alloc=115.8MB, time=101.32 memory used=5203.7MB, alloc=115.8MB, time=101.42 memory used=5216.4MB, alloc=115.8MB, time=101.51 memory used=5229.6MB, alloc=115.8MB, time=101.61 memory used=5243.1MB, alloc=115.8MB, time=101.70 memory used=5256.7MB, alloc=115.8MB, time=101.82 memory used=5271.0MB, alloc=115.8MB, time=101.90 memory used=5285.8MB, alloc=115.8MB, time=102.03 memory used=5345.8MB, alloc=115.8MB, time=102.92 memory used=5387.6MB, alloc=115.8MB, time=103.11 memory used=5450.3MB, alloc=115.8MB, time=105.44 memory used=5487.9MB, alloc=115.8MB, time=105.63 memory used=5536.1MB, alloc=115.8MB, time=105.82 memory used=5572.7MB, alloc=115.8MB, time=105.96 memory used=5605.7MB, alloc=115.8MB, time=106.09 memory used=5643.9MB, alloc=115.8MB, time=106.23 memory used=5689.0MB, alloc=115.8MB, time=106.37 memory used=5773.2MB, alloc=115.8MB, time=107.62 memory used=5841.2MB, alloc=115.8MB, time=109.20 memory used=5906.8MB, alloc=115.8MB, time=110.48 memory used=5972.7MB, alloc=115.8MB, time=111.94 memory used=6040.3MB, alloc=115.8MB, time=113.12 memory used=6115.6MB, alloc=139.8MB, time=114.18 memory used=6177.8MB, alloc=139.8MB, time=114.65 memory used=6239.3MB, alloc=139.8MB, time=115.10 memory used=6312.2MB, alloc=139.8MB, time=117.59 memory used=6356.4MB, alloc=139.8MB, time=117.81 memory used=6422.9MB, alloc=139.8MB, time=118.87 memory used=6485.0MB, alloc=139.8MB, time=119.29 memory used=6544.4MB, alloc=139.8MB, time=119.70 memory used=6626.6MB, alloc=139.8MB, time=124.47 memory used=6672.9MB, alloc=139.8MB, time=124.71 memory used=6720.6MB, alloc=139.8MB, time=124.92 memory used=6775.4MB, alloc=139.8MB, time=125.48 memory used=6829.4MB, alloc=139.8MB, time=125.77 memory used=6881.2MB, alloc=139.8MB, time=126.01 memory used=6945.3MB, alloc=139.8MB, time=126.62 memory used=6992.3MB, alloc=139.8MB, time=126.87 memory used=7052.7MB, alloc=139.8MB, time=131.90 memory used=7115.3MB, alloc=139.8MB, time=135.41 memory used=7160.6MB, alloc=139.8MB, time=135.64 memory used=7205.9MB, alloc=139.8MB, time=135.86 memory used=7260.7MB, alloc=139.8MB, time=136.09 memory used=7297.7MB, alloc=139.8MB, time=136.27 memory used=7346.8MB, alloc=139.8MB, time=136.66 memory used=7411.9MB, alloc=139.8MB, time=137.18 memory used=7497.0MB, alloc=139.8MB, time=142.11 memory used=7548.4MB, alloc=139.8MB, time=142.38 memory used=7589.6MB, alloc=139.8MB, time=142.60 memory used=7639.0MB, alloc=139.8MB, time=142.81 memory used=7691.3MB, alloc=139.8MB, time=143.50 memory used=7736.8MB, alloc=139.8MB, time=143.78 memory used=7769.5MB, alloc=139.8MB, time=144.46 memory used=7825.9MB, alloc=139.8MB, time=144.71 memory used=7851.1MB, alloc=139.8MB, time=144.88 memory used=7906.8MB, alloc=139.8MB, time=145.12 memory used=7930.4MB, alloc=139.8MB, time=145.31 memory used=7986.5MB, alloc=139.8MB, time=145.56 memory used=8046.6MB, alloc=139.8MB, time=146.94 memory used=8107.7MB, alloc=139.8MB, time=147.35 memory used=8193.1MB, alloc=139.8MB, time=159.93 memory used=8243.2MB, alloc=139.8MB, time=160.22 memory used=8290.9MB, alloc=139.8MB, time=160.48 memory used=8330.4MB, alloc=139.8MB, time=160.70 memory used=8376.9MB, alloc=139.8MB, time=160.94 memory used=8430.6MB, alloc=139.8MB, time=161.18 memory used=8481.7MB, alloc=139.8MB, time=161.41 memory used=8515.2MB, alloc=139.8MB, time=161.60 memory used=8550.7MB, alloc=139.8MB, time=161.78 memory used=8589.2MB, alloc=139.8MB, time=161.97 memory used=8631.1MB, alloc=139.8MB, time=162.16 memory used=8676.2MB, alloc=139.8MB, time=162.37 memory used=8727.3MB, alloc=139.8MB, time=162.58 memory used=8791.8MB, alloc=139.8MB, time=163.41 memory used=8844.3MB, alloc=139.8MB, time=163.97 memory used=8893.1MB, alloc=139.8MB, time=164.25 memory used=8937.2MB, alloc=139.8MB, time=165.21 memory used=8960.3MB, alloc=139.8MB, time=165.38 memory used=8985.7MB, alloc=139.8MB, time=165.56 memory used=9013.5MB, alloc=139.8MB, time=165.73 memory used=9043.6MB, alloc=139.8MB, time=165.89 memory used=9075.8MB, alloc=139.8MB, time=166.10 memory used=9116.7MB, alloc=139.8MB, time=166.33 memory used=9139.3MB, alloc=139.8MB, time=166.51 memory used=9164.1MB, alloc=139.8MB, time=166.71 memory used=9191.2MB, alloc=139.8MB, time=166.90 memory used=9220.6MB, alloc=139.8MB, time=167.10 memory used=9252.3MB, alloc=139.8MB, time=167.29 memory used=9332.9MB, alloc=139.8MB, time=168.71 memory used=9378.3MB, alloc=139.8MB, time=168.98 memory used=9432.4MB, alloc=139.8MB, time=169.24 memory used=9484.1MB, alloc=139.8MB, time=169.77 memory used=9539.1MB, alloc=139.8MB, time=170.09 memory used=9587.7MB, alloc=139.8MB, time=170.36 memory used=9632.3MB, alloc=139.8MB, time=170.60 |\^/| 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(); 1428263289 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 3 2 2 F := [14 x - 12 x y - 15 x z + 8 x y z, -5 x + 12 x y - 7 x y z - 10 x z , 3 2 3 -17 x + 18 x y z - 14 x z + 6 y ] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 G := [11 x z - 9 x y z - 15 y z - 2 y z, -9 y - 10 x z + 19 z + 17 x, 2 2 15 x y + 10 x z + 6 x] > Problem := [F,G]; 3 2 2 Problem := [[14 x - 12 x y - 15 x z + 8 x y z, 3 2 2 3 2 3 -5 x + 12 x y - 7 x y z - 10 x z , -17 x + 18 x y z - 14 x z + 6 y ], [ 2 2 3 2 11 x z - 9 x y z - 15 y z - 2 y z, -9 y - 10 x z + 19 z + 17 x, 2 2 15 x y + 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=0.31 memory used=26.7MB, alloc=32.3MB, time=0.89 memory used=48.1MB, alloc=32.3MB, time=1.43 memory used=67.9MB, alloc=56.3MB, time=1.98 memory used=107.0MB, alloc=60.3MB, time=3.00 memory used=144.9MB, alloc=84.3MB, time=4.03 memory used=206.9MB, alloc=92.3MB, time=5.55 memory used=269.2MB, alloc=92.3MB, time=7.09 memory used=327.2MB, alloc=116.3MB, time=8.67 memory used=403.8MB, alloc=372.3MB, time=10.72 memory used=491.4MB, alloc=396.3MB, time=12.92 memory used=602.8MB, alloc=420.3MB, time=15.67 memory used=734.4MB, alloc=444.3MB, time=19.14 memory used=872.7MB, alloc=468.3MB, time=22.88 memory used=986.5MB, alloc=468.3MB, time=25.86 memory used=1107.6MB, alloc=492.3MB, time=28.59 memory used=1217.1MB, alloc=492.3MB, time=31.00 memory used=1327.6MB, alloc=492.3MB, time=33.71 memory used=1441.7MB, alloc=492.3MB, time=36.89 memory used=1535.5MB, alloc=516.3MB, time=39.29 memory used=1627.9MB, alloc=516.3MB, time=41.55 memory used=1747.7MB, alloc=516.3MB, time=43.93 memory used=1855.3MB, alloc=516.3MB, time=46.09 memory used=1935.3MB, alloc=516.3MB, time=48.03 memory used=2034.0MB, alloc=516.3MB, time=50.35 memory used=2104.3MB, alloc=516.3MB, time=52.34 memory used=2178.4MB, alloc=516.3MB, time=54.62 memory used=2238.9MB, alloc=516.3MB, time=56.56 memory used=2300.0MB, alloc=516.3MB, time=58.56 memory used=2341.8MB, alloc=516.3MB, time=60.15 memory used=2377.2MB, alloc=516.3MB, time=61.41 memory used=2424.1MB, alloc=516.3MB, time=63.37 memory used=2627.6MB, alloc=540.3MB, time=69.31 memory used=2847.0MB, alloc=564.3MB, time=76.29 memory used=3011.1MB, alloc=588.3MB, time=81.35 memory used=3189.8MB, alloc=612.3MB, time=87.35 memory used=3421.0MB, alloc=636.3MB, time=92.43 memory used=3605.6MB, alloc=660.3MB, time=97.08 memory used=3803.1MB, alloc=660.3MB, time=102.23 memory used=3952.7MB, alloc=660.3MB, time=106.69 memory used=4104.1MB, alloc=684.3MB, time=111.99 memory used=4230.2MB, alloc=684.3MB, time=116.61 |\^/| 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(); 1428263589 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 2 2 F := [7 x z - 11 x y - 11 y - 6 y , 15 x z + 15 x y - 8 x - 15, 3 -2 x y z + 2 y + 16 x - 15 y] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 3 2 G := [16 x z + 17 x z + 15 z + 6 x z, -12 x + x y z + 10 x - 19 y z, 2 2 3 2 6 x y - 5 x z - 4 z + 5 z ] > Problem := [F,G]; 2 2 3 2 2 2 2 Problem := [[7 x z - 11 x y - 11 y - 6 y , 15 x z + 15 x y - 8 x - 15, 3 2 2 3 -2 x y z + 2 y + 16 x - 15 y], [16 x z + 17 x z + 15 z + 6 x z, 3 2 2 2 3 2 -12 x + x y z + 10 x - 19 y z, 6 x y - 5 x z - 4 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=0.31 memory used=26.0MB, alloc=32.3MB, time=0.87 memory used=45.5MB, alloc=56.3MB, time=1.40 memory used=86.1MB, alloc=60.3MB, time=2.44 memory used=127.0MB, alloc=60.3MB, time=3.43 memory used=165.5MB, alloc=84.3MB, time=4.49 memory used=232.1MB, alloc=92.3MB, time=6.15 memory used=297.9MB, alloc=92.3MB, time=7.71 memory used=365.5MB, alloc=116.3MB, time=9.27 memory used=433.8MB, alloc=372.3MB, time=10.91 memory used=528.1MB, alloc=372.3MB, time=12.88 memory used=615.4MB, alloc=396.3MB, time=15.13 memory used=726.1MB, alloc=420.3MB, time=17.96 memory used=851.0MB, alloc=444.3MB, time=21.23 memory used=974.3MB, alloc=444.3MB, time=24.55 memory used=1083.3MB, alloc=468.3MB, time=27.37 memory used=1184.0MB, alloc=468.3MB, time=30.04 memory used=1274.6MB, alloc=468.3MB, time=32.32 memory used=1367.8MB, alloc=468.3MB, time=34.66 memory used=1464.0MB, alloc=468.3MB, time=37.00 memory used=1544.5MB, alloc=468.3MB, time=39.30 memory used=1614.3MB, alloc=492.3MB, time=41.41 memory used=1703.1MB, alloc=492.3MB, time=44.23 memory used=1791.4MB, alloc=492.3MB, time=46.89 memory used=1854.9MB, alloc=492.3MB, time=48.61 memory used=1936.2MB, alloc=492.3MB, time=51.30 memory used=2005.9MB, alloc=492.3MB, time=53.35 memory used=2066.9MB, alloc=516.3MB, time=55.16 memory used=2141.7MB, alloc=516.3MB, time=57.41 memory used=2193.0MB, alloc=516.3MB, time=59.18 memory used=2243.6MB, alloc=516.3MB, time=60.70 memory used=2292.1MB, alloc=516.3MB, time=62.30 memory used=2503.9MB, alloc=540.3MB, time=67.63 memory used=2723.8MB, alloc=564.3MB, time=72.28 memory used=2906.0MB, alloc=588.3MB, time=76.31 memory used=3079.2MB, alloc=612.3MB, time=80.98 memory used=3232.7MB, alloc=612.3MB, time=85.53 memory used=3390.5MB, alloc=636.3MB, time=90.22 memory used=3502.9MB, alloc=636.3MB, time=93.35 memory used=3664.1MB, alloc=636.3MB, time=97.47 memory used=3782.2MB, alloc=660.3MB, time=100.94 memory used=3901.6MB, alloc=660.3MB, time=104.93 memory used=4005.5MB, alloc=660.3MB, time=108.04 memory used=4119.4MB, alloc=660.3MB, time=111.88 memory used=4208.1MB, alloc=660.3MB, time=115.17 memory used=4534.6MB, alloc=684.3MB, time=124.71 |\^/| 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(); 1428263889 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 F := [-17 x z - 11 x y + 2 x + 2 y, 9 x y z + 12 y + 5 y z - 10 y z, 2 3 2 2 -13 x y + 11 y - 3 x - 19 y ] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 3 2 G := [3 x y z - z - 12 x - 2 y, -2 x + 15 x z + y z - x, 2 12 x z - 7 x z - 12 z + 7] > Problem := [F,G]; 2 2 3 2 Problem := [[-17 x z - 11 x y + 2 x + 2 y, 9 x y z + 12 y + 5 y z - 10 y z, 2 3 2 2 3 -13 x y + 11 y - 3 x - 19 y ], [3 x y z - z - 12 x - 2 y, 3 2 2 -2 x + 15 x z + y z - x, 12 x z - 7 x z - 12 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=25.5MB, alloc=32.3MB, time=0.85 memory used=44.6MB, alloc=32.3MB, time=1.34 memory used=62.6MB, alloc=56.3MB, time=1.85 memory used=102.2MB, alloc=60.3MB, time=2.89 memory used=141.5MB, alloc=60.3MB, time=3.92 memory used=179.5MB, alloc=84.3MB, time=4.94 memory used=217.4MB, alloc=84.3MB, time=5.96 memory used=278.3MB, alloc=92.3MB, time=7.63 memory used=337.6MB, alloc=116.3MB, time=9.27 memory used=415.8MB, alloc=116.3MB, time=11.40 memory used=480.7MB, alloc=396.3MB, time=13.06 memory used=589.6MB, alloc=420.3MB, time=15.88 memory used=723.5MB, alloc=444.3MB, time=19.38 memory used=873.5MB, alloc=468.3MB, time=23.68 memory used=988.3MB, alloc=468.3MB, time=26.67 memory used=1111.1MB, alloc=468.3MB, time=30.03 memory used=1210.9MB, alloc=492.3MB, time=33.01 memory used=1311.4MB, alloc=492.3MB, time=36.14 memory used=1409.0MB, alloc=492.3MB, time=39.07 memory used=1502.1MB, alloc=492.3MB, time=41.97 memory used=1598.0MB, alloc=492.3MB, time=45.06 memory used=1686.0MB, alloc=492.3MB, time=48.00 memory used=1781.8MB, alloc=492.3MB, time=51.31 memory used=1879.2MB, alloc=516.3MB, time=55.10 memory used=1931.4MB, alloc=516.3MB, time=57.05 memory used=2023.1MB, alloc=516.3MB, time=60.58 memory used=2123.2MB, alloc=516.3MB, time=64.61 memory used=2191.3MB, alloc=516.3MB, time=67.38 memory used=2255.7MB, alloc=516.3MB, time=70.23 memory used=2319.2MB, alloc=516.3MB, time=72.98 memory used=2521.7MB, alloc=540.3MB, time=79.27 memory used=2727.7MB, alloc=564.3MB, time=86.26 memory used=2923.4MB, alloc=588.3MB, time=93.16 memory used=3154.9MB, alloc=612.3MB, time=101.73 memory used=3342.1MB, alloc=636.3MB, time=108.37 memory used=3496.1MB, alloc=660.3MB, time=113.94 |\^/| 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(); 1428264189 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 2 F := [-20 x z + 7 y - 14 x z + 5 z, -9 x z - 7 y + 11 z - 14 y, 2 2 17 y z - 3 y ] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 G := [2 x z - 16 x y + 13 x z + 19 y , -17 x + 2 x y - 18 x z + 10 y z, 2 10 x y z - 2 x z + 20 y - 4] > Problem := [F,G]; 2 3 2 2 2 Problem := [[-20 x z + 7 y - 14 x z + 5 z, -9 x z - 7 y + 11 z - 14 y, 2 2 2 2 2 17 y z - 3 y ], [2 x z - 16 x y + 13 x z + 19 y , 3 2 -17 x + 2 x y - 18 x z + 10 y z, 10 x y z - 2 x z + 20 y - 4]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.29 memory used=24.5MB, alloc=32.3MB, time=0.81 memory used=44.0MB, alloc=56.3MB, time=1.33 memory used=84.9MB, alloc=60.3MB, time=2.38 memory used=129.2MB, alloc=68.3MB, time=3.40 memory used=172.9MB, alloc=92.3MB, time=4.47 memory used=242.1MB, alloc=92.3MB, time=6.01 memory used=310.1MB, alloc=92.3MB, time=7.56 memory used=372.9MB, alloc=116.3MB, time=8.94 memory used=453.4MB, alloc=116.3MB, time=10.08 memory used=500.6MB, alloc=116.3MB, time=10.37 memory used=545.7MB, alloc=116.3MB, time=10.92 memory used=624.5MB, alloc=116.3MB, time=12.10 memory used=686.2MB, alloc=372.3MB, time=13.64 memory used=776.1MB, alloc=372.3MB, time=15.73 memory used=857.7MB, alloc=396.3MB, time=17.89 memory used=969.4MB, alloc=420.3MB, time=20.57 memory used=1102.1MB, alloc=444.3MB, time=23.20 memory used=1208.1MB, alloc=444.3MB, time=25.61 memory used=1352.6MB, alloc=468.3MB, time=28.65 memory used=1501.6MB, alloc=468.3MB, time=31.68 memory used=1597.7MB, alloc=468.3MB, time=33.89 memory used=1706.2MB, alloc=492.3MB, time=36.16 memory used=1794.8MB, alloc=492.3MB, time=38.42 memory used=1872.7MB, alloc=492.3MB, time=40.08 memory used=1953.7MB, alloc=492.3MB, time=42.38 memory used=2021.7MB, alloc=492.3MB, time=43.97 memory used=2100.7MB, alloc=492.3MB, time=45.82 memory used=2177.7MB, alloc=516.3MB, time=47.88 memory used=2238.7MB, alloc=516.3MB, time=49.58 memory used=2306.6MB, alloc=516.3MB, time=51.20 memory used=2380.7MB, alloc=516.3MB, time=52.73 memory used=2499.5MB, alloc=516.3MB, time=54.02 memory used=2608.5MB, alloc=516.3MB, time=55.80 memory used=2683.6MB, alloc=516.3MB, time=57.62 memory used=2787.3MB, alloc=516.3MB, time=59.46 memory used=2841.8MB, alloc=516.3MB, time=60.87 memory used=2873.9MB, alloc=516.3MB, time=62.09 memory used=3074.2MB, alloc=540.3MB, time=65.23 memory used=3198.1MB, alloc=540.3MB, time=66.76 memory used=3408.9MB, alloc=564.3MB, time=71.72 memory used=3652.6MB, alloc=564.3MB, time=76.26 memory used=3873.0MB, alloc=588.3MB, time=80.51 memory used=4101.1MB, alloc=612.3MB, time=85.78 memory used=4272.9MB, alloc=636.3MB, time=90.52 memory used=4455.5MB, alloc=636.3MB, time=94.92 memory used=4623.8MB, alloc=636.3MB, time=98.66 memory used=4773.9MB, alloc=660.3MB, time=102.62 memory used=4909.9MB, alloc=660.3MB, time=106.23 memory used=5097.3MB, alloc=660.3MB, time=110.02 memory used=5261.6MB, alloc=660.3MB, time=113.56 memory used=5380.0MB, alloc=660.3MB, time=116.73 |\^/| 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(); 1428264489 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 F := [2 x y z - 19 y - 14 x z + 2 z, -7 x z + 17 y - 3 z + 7, 2 2 -17 x z + 4 y + 2 y z] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 G := [-7 x + 6 x z - 12 y, -2 x z - 9 x y z - 14 y z + 2 z , 3 2 2 -9 x + 18 y z + 10 y - 2 y] > Problem := [F,G]; 3 2 3 2 Problem := [[2 x y z - 19 y - 14 x z + 2 z, -7 x z + 17 y - 3 z + 7, 2 2 3 -17 x z + 4 y + 2 y z], [-7 x + 6 x z - 12 y, 2 2 3 2 2 -2 x z - 9 x y z - 14 y z + 2 z , -9 x + 18 y z + 10 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=26.1MB, alloc=32.3MB, time=0.88 memory used=46.3MB, alloc=56.3MB, time=1.42 memory used=87.6MB, alloc=60.3MB, time=2.50 memory used=126.8MB, alloc=84.3MB, time=3.55 memory used=170.5MB, alloc=84.3MB, time=4.75 memory used=232.3MB, alloc=116.3MB, time=6.43 memory used=314.1MB, alloc=372.3MB, time=8.54 memory used=398.8MB, alloc=396.3MB, time=10.79 memory used=507.6MB, alloc=420.3MB, time=13.67 memory used=640.6MB, alloc=444.3MB, time=17.24 memory used=795.6MB, alloc=444.3MB, time=21.55 memory used=927.3MB, alloc=468.3MB, time=25.09 memory used=1050.4MB, alloc=468.3MB, time=28.40 memory used=1149.5MB, alloc=492.3MB, time=31.18 memory used=1267.5MB, alloc=492.3MB, time=34.64 memory used=1387.0MB, alloc=492.3MB, time=38.29 memory used=1493.9MB, alloc=516.3MB, time=41.91 memory used=1594.4MB, alloc=516.3MB, time=45.15 memory used=1687.3MB, alloc=540.3MB, time=47.10 memory used=1791.3MB, alloc=540.3MB, time=50.38 memory used=1867.7MB, alloc=540.3MB, time=52.68 memory used=1956.0MB, alloc=540.3MB, time=55.57 memory used=2019.2MB, alloc=540.3MB, time=57.61 memory used=2070.4MB, alloc=540.3MB, time=59.25 memory used=2133.7MB, alloc=540.3MB, time=61.73 memory used=2189.6MB, alloc=540.3MB, time=63.79 memory used=2258.8MB, alloc=540.3MB, time=66.68 memory used=2311.5MB, alloc=540.3MB, time=68.75 memory used=2533.2MB, alloc=564.3MB, time=75.94 memory used=2754.2MB, alloc=588.3MB, time=82.60 memory used=2925.5MB, alloc=612.3MB, time=88.02 memory used=3124.5MB, alloc=636.3MB, time=94.43 memory used=3314.6MB, alloc=660.3MB, time=100.44 memory used=3470.4MB, alloc=660.3MB, time=105.72 memory used=3616.7MB, alloc=684.3MB, time=111.22 memory used=3741.7MB, alloc=684.3MB, time=115.16 |\^/| 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(); 1428264789 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 3 F := [x y - 2 y z - 17 x - 11 x, -12 x + 7 x z + 9 y + 3 z, 2 2 -12 x y - 2 y z + 17 y z + 19 y] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 G := [3 x y - 16 y z + 16 y z + 13 z , -15 y + 4 x z - 5 z - 3 z, 3 3 3 2 -5 x - 19 y - 3 z - 20 x ] > Problem := [F,G]; 2 2 2 3 2 3 Problem := [[x y - 2 y z - 17 x - 11 x, -12 x + 7 x z + 9 y + 3 z, 2 2 2 2 2 -12 x y - 2 y z + 17 y z + 19 y], [3 x y - 16 y z + 16 y z + 13 z , 3 2 3 3 3 2 -15 y + 4 x z - 5 z - 3 z, -5 x - 19 y - 3 z - 20 x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.31 memory used=26.0MB, alloc=32.3MB, time=0.88 memory used=45.9MB, alloc=56.3MB, time=1.44 memory used=88.5MB, alloc=60.3MB, time=2.56 memory used=130.2MB, alloc=68.3MB, time=3.68 memory used=170.0MB, alloc=92.3MB, time=4.75 memory used=237.8MB, alloc=92.3MB, time=6.37 memory used=303.6MB, alloc=116.3MB, time=7.99 memory used=368.6MB, alloc=116.3MB, time=9.52 memory used=450.3MB, alloc=372.3MB, time=11.57 memory used=538.7MB, alloc=396.3MB, time=13.77 memory used=657.1MB, alloc=396.3MB, time=16.47 memory used=774.2MB, alloc=420.3MB, time=19.25 memory used=914.3MB, alloc=420.3MB, time=22.47 memory used=1035.6MB, alloc=444.3MB, time=25.35 memory used=1162.9MB, alloc=444.3MB, time=28.44 memory used=1268.6MB, alloc=444.3MB, time=29.90 memory used=1351.5MB, alloc=444.3MB, time=30.86 memory used=1432.0MB, alloc=444.3MB, time=31.85 memory used=1506.5MB, alloc=444.3MB, time=32.71 memory used=1607.6MB, alloc=444.3MB, time=34.45 memory used=1688.2MB, alloc=444.3MB, time=35.12 memory used=1774.0MB, alloc=444.3MB, time=38.63 memory used=1840.9MB, alloc=444.3MB, time=39.04 memory used=1925.8MB, alloc=444.3MB, time=40.18 memory used=2054.9MB, alloc=468.3MB, time=45.28 memory used=2142.8MB, alloc=468.3MB, time=45.79 memory used=2213.5MB, alloc=468.3MB, time=46.25 memory used=2305.1MB, alloc=468.3MB, time=46.72 memory used=2365.8MB, alloc=468.3MB, time=47.07 memory used=2460.0MB, alloc=468.3MB, time=50.09 memory used=2540.6MB, alloc=468.3MB, time=50.52 memory used=2612.5MB, alloc=468.3MB, time=50.89 memory used=2741.7MB, alloc=468.3MB, time=52.69 memory used=2930.6MB, alloc=468.3MB, time=57.42 memory used=3129.0MB, alloc=468.3MB, time=60.79 memory used=3286.7MB, alloc=468.3MB, time=64.90 memory used=3378.2MB, alloc=468.3MB, time=66.00 memory used=3466.0MB, alloc=468.3MB, time=67.03 memory used=3557.7MB, alloc=468.3MB, time=69.77 memory used=3665.4MB, alloc=468.3MB, time=71.84 memory used=3737.6MB, alloc=468.3MB, time=72.33 memory used=3812.3MB, alloc=468.3MB, time=72.81 memory used=3888.9MB, alloc=492.3MB, time=73.28 memory used=3963.6MB, alloc=492.3MB, time=73.70 memory used=4072.2MB, alloc=492.3MB, time=76.93 memory used=4156.3MB, alloc=492.3MB, time=77.39 memory used=4263.3MB, alloc=492.3MB, time=78.41 memory used=4413.5MB, alloc=492.3MB, time=80.33 memory used=4537.9MB, alloc=492.3MB, time=82.68 memory used=4695.5MB, alloc=492.3MB, time=84.25 memory used=4785.8MB, alloc=492.3MB, time=84.95 memory used=4872.9MB, alloc=492.3MB, time=85.54 memory used=4957.4MB, alloc=492.3MB, time=86.30 memory used=5066.2MB, alloc=492.3MB, time=87.55 memory used=5191.8MB, alloc=492.3MB, time=90.41 memory used=5339.4MB, alloc=492.3MB, time=94.39 memory used=5434.2MB, alloc=492.3MB, time=95.32 memory used=5513.9MB, alloc=492.3MB, time=95.90 memory used=5772.7MB, alloc=492.3MB, time=97.97 memory used=5897.5MB, alloc=492.3MB, time=100.24 memory used=5970.1MB, alloc=492.3MB, time=102.03 memory used=6084.5MB, alloc=492.3MB, time=103.91 memory used=6192.8MB, alloc=492.3MB, time=105.32 memory used=6307.3MB, alloc=492.3MB, time=107.26 memory used=6422.3MB, alloc=516.3MB, time=111.06 memory used=6526.1MB, alloc=516.3MB, time=111.92 memory used=6686.8MB, alloc=516.3MB, time=114.15 memory used=6807.0MB, alloc=516.3MB, time=120.43 memory used=6921.7MB, alloc=516.3MB, time=121.84 memory used=7111.9MB, alloc=516.3MB, time=124.68 memory used=7283.2MB, alloc=516.3MB, time=127.66 memory used=7451.0MB, alloc=516.3MB, time=134.13 memory used=7614.5MB, alloc=516.3MB, time=136.00 memory used=7715.1MB, alloc=516.3MB, time=136.73 memory used=7807.1MB, alloc=516.3MB, time=137.52 memory used=7898.3MB, alloc=516.3MB, time=138.19 memory used=7992.7MB, alloc=516.3MB, time=139.13 memory used=8083.6MB, alloc=516.3MB, time=139.75 |\^/| 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(); 1428265089 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 F := [-6 y z - 15 x - 15 y z, -13 x y - 3 y z - 13 z , 2 2 2 16 x y - 16 y z + 14 y z + 3 y] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 G := [-9 x z + 6 y z + 13 y z - 8 y, -15 x z - 19 y z - 10 x - 11 x y, 2 2 2 2 -6 x y + 3 x z + 19 x z + 12 y ] > Problem := [F,G]; 2 2 2 2 2 Problem := [[-6 y z - 15 x - 15 y z, -13 x y - 3 y z - 13 z , 2 2 2 2 2 16 x y - 16 y z + 14 y z + 3 y], [-9 x z + 6 y z + 13 y z - 8 y, 2 2 2 2 2 2 2 -15 x z - 19 y z - 10 x - 11 x y, -6 x y + 3 x z + 19 x z + 12 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.30 memory used=26.2MB, alloc=32.3MB, time=0.88 memory used=46.6MB, alloc=56.3MB, time=1.44 memory used=87.7MB, alloc=60.3MB, time=2.47 memory used=128.1MB, alloc=84.3MB, time=3.55 memory used=164.5MB, alloc=84.3MB, time=4.52 memory used=231.5MB, alloc=92.3MB, time=6.18 memory used=297.2MB, alloc=372.3MB, time=7.80 memory used=389.1MB, alloc=372.3MB, time=9.88 memory used=484.8MB, alloc=396.3MB, time=11.99 memory used=601.0MB, alloc=420.3MB, time=14.82 memory used=735.8MB, alloc=420.3MB, time=18.20 memory used=868.7MB, alloc=444.3MB, time=21.71 memory used=984.0MB, alloc=468.3MB, time=24.90 memory used=1109.8MB, alloc=468.3MB, time=27.96 memory used=1219.1MB, alloc=468.3MB, time=30.40 memory used=1321.9MB, alloc=468.3MB, time=33.17 memory used=1411.8MB, alloc=468.3MB, time=35.76 memory used=1500.3MB, alloc=492.3MB, time=38.39 memory used=1606.7MB, alloc=492.3MB, time=41.20 memory used=1689.6MB, alloc=492.3MB, time=43.24 memory used=1774.0MB, alloc=492.3MB, time=45.34 memory used=1847.6MB, alloc=492.3MB, time=47.43 memory used=1941.3MB, alloc=516.3MB, time=49.49 memory used=2005.8MB, alloc=516.3MB, time=51.34 memory used=2066.2MB, alloc=516.3MB, time=53.01 memory used=2127.5MB, alloc=516.3MB, time=54.97 memory used=2192.1MB, alloc=516.3MB, time=56.86 memory used=2254.2MB, alloc=516.3MB, time=58.82 memory used=2310.3MB, alloc=516.3MB, time=60.73 memory used=2346.2MB, alloc=516.3MB, time=62.09 memory used=2406.0MB, alloc=516.3MB, time=64.14 memory used=2449.3MB, alloc=516.3MB, time=65.64 memory used=2488.3MB, alloc=516.3MB, time=67.06 memory used=2657.5MB, alloc=516.3MB, time=69.81 memory used=2880.6MB, alloc=540.3MB, time=74.97 memory used=3060.5MB, alloc=564.3MB, time=79.51 memory used=3264.3MB, alloc=588.3MB, time=85.97 memory used=3443.9MB, alloc=612.3MB, time=90.51 memory used=3634.1MB, alloc=636.3MB, time=95.51 memory used=3789.2MB, alloc=636.3MB, time=99.82 memory used=3955.7MB, alloc=660.3MB, time=105.02 memory used=4100.1MB, alloc=660.3MB, time=109.81 memory used=4260.0MB, alloc=660.3MB, time=113.96 memory used=4411.6MB, alloc=684.3MB, time=117.44 memory used=4563.4MB, alloc=684.3MB, time=122.68 memory used=4688.5MB, alloc=684.3MB, time=126.32 |\^/| 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(); 1428265389 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 F := [16 x y - 11 x z + 17 x y - 20 y z, 8 y z - 7 z + 10 x y + 13 y , 3 2 3 16 x + 11 y z + 2 z + 8 z] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 G := [18 y z + 8 y + 3 z - 8 x, 5 x y - x z - 15 x y z - 18 x y, 2 2 3 2 -4 x z + 15 x y + 12 y - 6 y ] > Problem := [F,G]; 2 2 Problem := [[16 x y - 11 x z + 17 x y - 20 y z, 2 3 2 3 2 3 8 y z - 7 z + 10 x y + 13 y , 16 x + 11 y z + 2 z + 8 z], [ 2 2 2 2 2 18 y z + 8 y + 3 z - 8 x, 5 x y - x z - 15 x y z - 18 x y, 2 2 3 2 -4 x z + 15 x y + 12 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=4.4MB, alloc=32.3MB, time=0.30 memory used=25.9MB, alloc=32.3MB, time=0.86 memory used=45.8MB, alloc=32.3MB, time=1.38 memory used=64.1MB, alloc=60.3MB, time=1.88 memory used=104.6MB, alloc=60.3MB, time=2.89 memory used=139.6MB, alloc=84.3MB, time=3.70 memory used=207.4MB, alloc=92.3MB, time=5.27 memory used=275.1MB, alloc=116.3MB, time=6.93 memory used=342.4MB, alloc=116.3MB, time=8.66 memory used=407.3MB, alloc=372.3MB, time=10.20 memory used=491.5MB, alloc=396.3MB, time=12.35 memory used=619.7MB, alloc=396.3MB, time=14.59 memory used=734.4MB, alloc=420.3MB, time=17.06 memory used=870.6MB, alloc=444.3MB, time=20.32 memory used=997.9MB, alloc=444.3MB, time=23.41 memory used=1127.2MB, alloc=468.3MB, time=25.83 memory used=1268.7MB, alloc=468.3MB, time=28.90 memory used=1366.6MB, alloc=468.3MB, time=31.30 memory used=1461.6MB, alloc=468.3MB, time=33.58 memory used=1550.4MB, alloc=492.3MB, time=35.98 memory used=1645.8MB, alloc=492.3MB, time=38.45 memory used=1742.5MB, alloc=492.3MB, time=40.55 memory used=1847.8MB, alloc=492.3MB, time=41.98 memory used=1952.7MB, alloc=492.3MB, time=44.18 memory used=2075.5MB, alloc=492.3MB, time=46.87 memory used=2186.7MB, alloc=492.3MB, time=48.78 memory used=2291.6MB, alloc=492.3MB, time=51.19 memory used=2396.2MB, alloc=516.3MB, time=52.83 memory used=2471.7MB, alloc=516.3MB, time=54.16 memory used=2539.5MB, alloc=516.3MB, time=56.01 memory used=2620.3MB, alloc=516.3MB, time=57.91 memory used=2678.6MB, alloc=516.3MB, time=59.51 memory used=2735.5MB, alloc=516.3MB, time=60.94 memory used=2787.7MB, alloc=516.3MB, time=62.32 memory used=2838.9MB, alloc=516.3MB, time=63.92 memory used=2915.0MB, alloc=516.3MB, time=66.02 memory used=2987.4MB, alloc=516.3MB, time=67.54 memory used=3183.6MB, alloc=540.3MB, time=72.02 memory used=3395.5MB, alloc=564.3MB, time=76.69 memory used=3629.6MB, alloc=588.3MB, time=80.99 memory used=3823.4MB, alloc=612.3MB, time=86.33 memory used=3995.4MB, alloc=636.3MB, time=90.34 memory used=4151.7MB, alloc=660.3MB, time=94.05 memory used=4298.2MB, alloc=684.3MB, time=98.65 memory used=4430.3MB, alloc=684.3MB, time=102.21 memory used=4584.5MB, alloc=684.3MB, time=106.77 memory used=4732.7MB, alloc=684.3MB, time=110.80 memory used=4865.3MB, alloc=684.3MB, time=115.09 memory used=4986.9MB, alloc=684.3MB, time=118.43 memory used=5091.1MB, alloc=708.3MB, time=121.62 memory used=5208.1MB, alloc=708.3MB, time=124.77 memory used=5341.4MB, alloc=732.3MB, time=127.88 |\^/| 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(); 1428265689 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 2 F := [2 x y - 4 y + 2 x y + 13 y z, -13 x y + 5 x y + 18 z - 17 z, 2 2 -7 y z + 18 y z - 14 x y - 10 x] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 3 2 3 2 G := [18 x - 2 z - 3 y + 3 y z, 17 y - 3 y z - 3 z + 8 y, 2 2 x y - 6 y z - 3 x - 9 y] > Problem := [F,G]; 2 3 2 2 2 Problem := [[2 x y - 4 y + 2 x y + 13 y z, -13 x y + 5 x y + 18 z - 17 z, 2 2 3 3 2 -7 y z + 18 y z - 14 x y - 10 x], [18 x - 2 z - 3 y + 3 y z, 3 2 2 17 y - 3 y z - 3 z + 8 y, 2 x y - 6 y z - 3 x - 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=0.31 memory used=24.4MB, alloc=32.3MB, time=0.82 memory used=43.4MB, alloc=56.3MB, time=1.32 memory used=82.3MB, alloc=60.8MB, time=2.20 memory used=127.5MB, alloc=68.8MB, time=3.19 memory used=169.6MB, alloc=68.8MB, time=4.13 memory used=212.4MB, alloc=92.8MB, time=5.21 memory used=279.0MB, alloc=92.8MB, time=6.82 memory used=335.1MB, alloc=92.8MB, time=7.80 memory used=403.0MB, alloc=348.8MB, time=9.03 memory used=479.1MB, alloc=372.8MB, time=10.45 memory used=570.8MB, alloc=372.8MB, time=12.61 memory used=662.6MB, alloc=396.8MB, time=14.63 memory used=746.9MB, alloc=396.8MB, time=15.76 memory used=830.8MB, alloc=396.8MB, time=16.96 memory used=946.4MB, alloc=396.8MB, time=19.15 memory used=1058.0MB, alloc=396.8MB, time=21.52 memory used=1136.2MB, alloc=396.8MB, time=22.65 memory used=1250.0MB, alloc=420.8MB, time=25.13 memory used=1369.4MB, alloc=420.8MB, time=28.13 memory used=1487.9MB, alloc=444.8MB, time=30.67 memory used=1606.1MB, alloc=444.8MB, time=33.26 memory used=1720.8MB, alloc=444.8MB, time=35.87 memory used=1839.5MB, alloc=444.8MB, time=38.33 memory used=1968.9MB, alloc=468.8MB, time=40.53 memory used=2121.5MB, alloc=468.8MB, time=43.41 memory used=2225.4MB, alloc=468.8MB, time=45.72 memory used=2336.6MB, alloc=468.8MB, time=48.16 memory used=2457.8MB, alloc=468.8MB, time=49.68 memory used=2584.7MB, alloc=468.8MB, time=51.66 memory used=2698.3MB, alloc=468.8MB, time=53.75 memory used=2824.9MB, alloc=468.8MB, time=56.38 memory used=2939.8MB, alloc=468.8MB, time=58.93 memory used=3078.0MB, alloc=468.8MB, time=61.93 memory used=3195.2MB, alloc=468.8MB, time=66.95 memory used=3289.8MB, alloc=492.8MB, time=69.19 memory used=3374.7MB, alloc=492.8MB, time=71.34 memory used=3447.5MB, alloc=492.8MB, time=73.33 memory used=3520.7MB, alloc=492.8MB, time=75.14 memory used=3585.5MB, alloc=492.8MB, time=76.98 memory used=3652.2MB, alloc=492.8MB, time=78.88 memory used=3714.2MB, alloc=492.8MB, time=80.57 memory used=3773.5MB, alloc=492.8MB, time=81.95 memory used=3849.4MB, alloc=492.8MB, time=84.31 memory used=3924.5MB, alloc=492.8MB, time=85.69 memory used=3987.0MB, alloc=492.8MB, time=87.29 memory used=4037.3MB, alloc=492.8MB, time=88.94 memory used=4097.9MB, alloc=492.8MB, time=90.67 memory used=4161.7MB, alloc=492.8MB, time=92.16 memory used=4228.2MB, alloc=492.8MB, time=93.71 memory used=4315.8MB, alloc=492.8MB, time=95.41 memory used=4358.7MB, alloc=492.8MB, time=96.83 memory used=4405.1MB, alloc=492.8MB, time=98.31 memory used=4456.5MB, alloc=516.8MB, time=99.87 memory used=4643.7MB, alloc=516.8MB, time=103.97 memory used=4749.7MB, alloc=516.8MB, time=105.50 memory used=4859.2MB, alloc=516.8MB, time=107.43 |\^/| 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(); 1428265989 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 F := [-14 x y + 17 y + 14 y z + 6 x, 4 x y z - 8 y z - 19 y + 19, 2 3 2 -13 x z + 16 y - 17 y z - 6 y] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 3 2 G := [-12 x y + 14 y z + 13 x - 18 x z, 10 x y + 5 y + 12 y z - 12 x, 2 2 2 11 x z - 15 y z + 8 y - 14 y] > Problem := [F,G]; 2 3 2 2 Problem := [[-14 x y + 17 y + 14 y z + 6 x, 4 x y z - 8 y z - 19 y + 19, 2 3 2 2 2 2 -13 x z + 16 y - 17 y z - 6 y], [-12 x y + 14 y z + 13 x - 18 x z, 2 3 2 2 2 2 10 x y + 5 y + 12 y z - 12 x, 11 x z - 15 y z + 8 y - 14 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.31 memory used=25.3MB, alloc=32.3MB, time=0.84 memory used=47.9MB, alloc=36.3MB, time=1.25 memory used=67.1MB, alloc=60.3MB, time=1.67 memory used=110.1MB, alloc=68.3MB, time=2.68 memory used=156.8MB, alloc=68.3MB, time=3.69 memory used=194.9MB, alloc=68.3MB, time=4.21 memory used=228.5MB, alloc=68.3MB, time=4.72 memory used=261.5MB, alloc=68.3MB, time=5.19 memory used=307.4MB, alloc=68.3MB, time=6.18 memory used=357.3MB, alloc=92.3MB, time=7.12 memory used=432.7MB, alloc=92.3MB, time=8.62 memory used=495.1MB, alloc=92.3MB, time=9.70 memory used=552.9MB, alloc=372.3MB, time=10.96 memory used=638.7MB, alloc=372.3MB, time=12.61 memory used=733.7MB, alloc=372.3MB, time=14.42 memory used=801.3MB, alloc=372.3MB, time=15.40 memory used=861.3MB, alloc=372.3MB, time=22.13 memory used=906.8MB, alloc=372.3MB, time=22.90 memory used=944.4MB, alloc=372.3MB, time=23.12 memory used=979.5MB, alloc=372.3MB, time=23.32 memory used=1037.5MB, alloc=372.3MB, time=26.81 memory used=1073.8MB, alloc=372.3MB, time=27.05 memory used=1111.5MB, alloc=372.3MB, time=27.27 memory used=1187.5MB, alloc=372.3MB, time=29.94 memory used=1233.8MB, alloc=372.3MB, time=31.80 memory used=1271.4MB, alloc=372.3MB, time=32.03 memory used=1350.2MB, alloc=396.3MB, time=33.17 memory used=1484.0MB, alloc=396.3MB, time=37.30 memory used=1631.0MB, alloc=396.3MB, time=40.25 memory used=1767.3MB, alloc=396.3MB, time=45.25 memory used=1885.4MB, alloc=420.3MB, time=47.54 memory used=2000.6MB, alloc=420.3MB, time=49.15 memory used=2068.4MB, alloc=420.3MB, time=49.64 memory used=2127.9MB, alloc=420.3MB, time=50.00 memory used=2201.4MB, alloc=420.3MB, time=51.45 memory used=2291.2MB, alloc=420.3MB, time=52.44 memory used=2356.4MB, alloc=420.3MB, time=52.84 memory used=2426.6MB, alloc=420.3MB, time=53.39 memory used=2498.6MB, alloc=420.3MB, time=57.01 memory used=2607.2MB, alloc=420.3MB, time=74.25 memory used=2666.1MB, alloc=420.3MB, time=74.60 memory used=2730.5MB, alloc=420.3MB, time=74.96 memory used=2788.8MB, alloc=420.3MB, time=75.26 memory used=2836.2MB, alloc=420.3MB, time=75.55 memory used=2890.8MB, alloc=420.3MB, time=75.82 memory used=2953.0MB, alloc=420.3MB, time=76.12 memory used=3024.1MB, alloc=420.3MB, time=76.41 memory used=3184.4MB, alloc=420.3MB, time=84.36 memory used=3263.5MB, alloc=420.3MB, time=85.69 memory used=3324.5MB, alloc=420.3MB, time=86.04 memory used=3382.3MB, alloc=420.3MB, time=86.35 memory used=3432.8MB, alloc=420.3MB, time=86.65 memory used=3491.5MB, alloc=420.3MB, time=86.93 memory used=3580.9MB, alloc=420.3MB, time=87.62 memory used=3679.2MB, alloc=420.3MB, time=88.81 memory used=3825.9MB, alloc=420.3MB, time=91.85 memory used=3973.0MB, alloc=420.3MB, time=94.06 memory used=4124.1MB, alloc=420.3MB, time=99.42 memory used=4234.5MB, alloc=420.3MB, time=101.28 memory used=4323.4MB, alloc=420.3MB, time=111.68 memory used=4403.4MB, alloc=420.3MB, time=114.56 memory used=4453.1MB, alloc=420.3MB, time=114.91 memory used=4519.8MB, alloc=420.3MB, time=115.27 memory used=4563.7MB, alloc=420.3MB, time=115.58 memory used=4610.3MB, alloc=420.3MB, time=115.88 memory used=4663.5MB, alloc=420.3MB, time=116.19 memory used=4723.0MB, alloc=420.3MB, time=116.51 memory used=4790.0MB, alloc=420.3MB, time=116.84 memory used=4937.8MB, alloc=420.3MB, time=117.98 memory used=5045.2MB, alloc=420.3MB, time=119.40 memory used=5171.1MB, alloc=444.3MB, time=121.95 memory used=5263.9MB, alloc=444.3MB, time=122.96 memory used=5332.1MB, alloc=444.3MB, time=123.42 memory used=5406.1MB, alloc=444.3MB, time=124.08 memory used=5476.1MB, alloc=444.3MB, time=124.53 memory used=5550.5MB, alloc=444.3MB, time=126.43 memory used=5612.2MB, alloc=444.3MB, time=126.85 memory used=5697.6MB, alloc=444.3MB, time=128.05 memory used=5769.6MB, alloc=444.3MB, time=128.51 memory used=5867.4MB, alloc=444.3MB, time=130.08 memory used=5932.8MB, alloc=444.3MB, time=130.54 memory used=5999.2MB, alloc=444.3MB, time=130.98 memory used=6080.7MB, alloc=444.3MB, time=131.65 memory used=6140.3MB, alloc=444.3MB, time=132.07 memory used=6255.2MB, alloc=444.3MB, time=163.25 memory used=6339.1MB, alloc=444.3MB, time=163.97 memory used=6407.3MB, alloc=444.3MB, time=164.44 memory used=6467.3MB, alloc=468.3MB, time=164.88 memory used=6536.3MB, alloc=468.3MB, time=165.30 memory used=6619.2MB, alloc=468.3MB, time=165.77 memory used=6717.5MB, alloc=468.3MB, time=166.25 memory used=6890.6MB, alloc=468.3MB, time=167.06 memory used=7174.5MB, alloc=468.3MB, time=180.66 memory used=7257.3MB, alloc=468.3MB, time=181.20 memory used=7336.1MB, alloc=468.3MB, time=181.65 memory used=7411.4MB, alloc=468.3MB, time=182.09 memory used=7504.7MB, alloc=468.3MB, time=182.58 |\^/| 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(); 1428266289 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 F := [9 x y + 5 x z + 19 z - 19 x, 2 x y + 4 z + 3 y, 2 2 3 8 y z - 19 y z + 6 z + 9] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 G := [-3 y - 11 y z - 20 x + z, 12 x y + 8 y z - 8 x, 2 2 2 -10 y z - 5 y z - 17 y z - 14 z ] > Problem := [F,G]; 2 2 3 2 2 Problem := [[9 x y + 5 x z + 19 z - 19 x, 2 x y + 4 z + 3 y, 2 2 3 3 2 2 8 y z - 19 y z + 6 z + 9], [-3 y - 11 y z - 20 x + z, 2 2 2 2 2 12 x y + 8 y z - 8 x, -10 y z - 5 y z - 17 y z - 14 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.31 memory used=26.5MB, alloc=32.3MB, time=0.90 memory used=46.4MB, alloc=32.3MB, time=1.42 memory used=64.6MB, alloc=56.3MB, time=1.93 memory used=114.4MB, alloc=68.3MB, time=2.95 memory used=146.7MB, alloc=68.3MB, time=4.44 memory used=175.8MB, alloc=92.3MB, time=12.87 memory used=210.9MB, alloc=92.3MB, time=27.33 memory used=236.6MB, alloc=92.3MB, time=31.88 memory used=274.8MB, alloc=116.3MB, time=33.29 memory used=339.4MB, alloc=140.3MB, time=33.82 memory used=390.4MB, alloc=164.3MB, time=75.48 memory used=410.6MB, alloc=188.3MB, time=75.61 memory used=426.0MB, alloc=212.3MB, time=75.78 memory used=441.0MB, alloc=236.3MB, time=75.93 memory used=579.2MB, alloc=493.0MB, time=78.32 memory used=894.1MB, alloc=493.0MB, time=85.52 memory used=1098.1MB, alloc=493.0MB, time=90.23 memory used=1240.4MB, alloc=493.0MB, time=91.88 memory used=1390.8MB, alloc=493.0MB, time=93.67 memory used=1571.3MB, alloc=493.0MB, time=95.88 memory used=1674.9MB, alloc=493.0MB, time=96.34 memory used=1798.4MB, alloc=493.0MB, time=96.81 memory used=1946.6MB, alloc=493.0MB, time=97.33 memory used=2044.0MB, alloc=493.0MB, time=97.68 memory used=2156.3MB, alloc=493.0MB, time=114.14 memory used=2298.7MB, alloc=493.0MB, time=114.75 memory used=2436.8MB, alloc=493.0MB, time=115.32 memory used=2538.0MB, alloc=493.0MB, time=115.80 memory used=2633.4MB, alloc=493.0MB, time=116.27 memory used=2726.6MB, alloc=493.0MB, time=116.71 memory used=2822.4MB, alloc=493.0MB, time=117.16 memory used=2922.0MB, alloc=493.0MB, time=117.61 memory used=3026.5MB, alloc=493.0MB, time=118.07 memory used=3135.5MB, alloc=493.0MB, time=118.53 memory used=3248.9MB, alloc=493.0MB, time=119.01 memory used=3370.0MB, alloc=493.0MB, time=119.50 memory used=3498.1MB, alloc=493.0MB, time=119.98 memory used=3632.5MB, alloc=493.0MB, time=120.49 memory used=3772.1MB, alloc=493.0MB, time=120.99 memory used=3919.2MB, alloc=493.0MB, time=121.51 memory used=4057.8MB, alloc=493.0MB, time=122.01 memory used=4159.4MB, alloc=493.0MB, time=122.39 memory used=4245.5MB, alloc=493.0MB, time=122.73 memory used=4329.9MB, alloc=493.0MB, time=123.07 memory used=4417.4MB, alloc=493.0MB, time=123.40 memory used=4508.2MB, alloc=493.0MB, time=123.74 memory used=4604.6MB, alloc=493.0MB, time=124.09 memory used=4706.2MB, alloc=493.0MB, time=124.45 memory used=4843.1MB, alloc=493.0MB, time=141.21 memory used=4990.0MB, alloc=493.0MB, time=141.81 memory used=5099.0MB, alloc=493.0MB, time=142.32 memory used=5195.3MB, alloc=493.0MB, time=142.79 memory used=5287.2MB, alloc=493.0MB, time=143.25 memory used=5380.1MB, alloc=493.0MB, time=143.69 memory used=5478.6MB, alloc=493.0MB, time=144.17 memory used=5579.0MB, alloc=493.0MB, time=144.64 memory used=5687.8MB, alloc=493.0MB, time=145.12 memory used=5801.0MB, alloc=493.0MB, time=145.59 memory used=5918.2MB, alloc=493.0MB, time=146.07 memory used=6042.8MB, alloc=493.0MB, time=146.57 memory used=6174.0MB, alloc=493.0MB, time=147.08 memory used=6311.0MB, alloc=493.0MB, time=147.58 memory used=6456.1MB, alloc=493.0MB, time=148.10 memory used=6605.2MB, alloc=493.0MB, time=148.63 memory used=6717.6MB, alloc=493.0MB, time=149.05 memory used=6808.3MB, alloc=493.0MB, time=149.41 memory used=6891.7MB, alloc=493.0MB, time=149.73 memory used=6979.0MB, alloc=493.0MB, time=150.07 memory used=7067.9MB, alloc=493.0MB, time=150.40 memory used=7160.4MB, alloc=493.0MB, time=150.75 memory used=7259.1MB, alloc=493.0MB, time=151.10 |\^/| 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(); 1428266589 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 F := [-13 x y - 18 x z + 6 y + 12 x, -20 x - 5 x y + 8 x z - 5 y, 2 2 17 x z + 4 y - 6 x + 17] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 G := [-13 z + 5 y z + 18 z - 18 y, 13 x y + 17 x + 17 x y - 14 z , 2 2 x z + 19 x y - 14 x - 13] > Problem := [F,G]; 2 3 2 Problem := [[-13 x y - 18 x z + 6 y + 12 x, -20 x - 5 x y + 8 x z - 5 y, 2 2 3 2 17 x z + 4 y - 6 x + 17], [-13 z + 5 y z + 18 z - 18 y, 2 2 2 2 13 x y + 17 x + 17 x y - 14 z , 2 x z + 19 x y - 14 x - 13]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.3MB, alloc=32.3MB, time=0.88 memory used=47.6MB, alloc=36.3MB, time=1.43 memory used=67.0MB, alloc=60.3MB, time=1.96 memory used=108.9MB, alloc=60.3MB, time=3.02 memory used=149.5MB, alloc=60.3MB, time=4.06 memory used=189.3MB, alloc=84.3MB, time=5.10 memory used=229.0MB, alloc=84.3MB, time=6.17 memory used=300.7MB, alloc=116.3MB, time=7.73 memory used=360.3MB, alloc=372.3MB, time=9.26 memory used=447.5MB, alloc=396.3MB, time=11.52 memory used=563.1MB, alloc=420.3MB, time=14.34 memory used=680.7MB, alloc=444.3MB, time=17.28 memory used=802.0MB, alloc=444.3MB, time=20.32 memory used=907.8MB, alloc=468.3MB, time=23.13 memory used=1016.6MB, alloc=468.3MB, time=26.01 memory used=1127.5MB, alloc=468.3MB, time=29.01 memory used=1221.9MB, alloc=468.3MB, time=31.68 memory used=1314.2MB, alloc=468.3MB, time=34.44 memory used=1395.3MB, alloc=492.3MB, time=36.91 memory used=1466.5MB, alloc=492.3MB, time=39.16 memory used=1543.5MB, alloc=492.3MB, time=41.53 memory used=1611.2MB, alloc=492.3MB, time=43.40 memory used=1674.9MB, alloc=492.3MB, time=45.61 memory used=1726.2MB, alloc=492.3MB, time=47.14 memory used=1788.5MB, alloc=492.3MB, time=49.47 memory used=1830.0MB, alloc=492.3MB, time=50.93 memory used=1890.4MB, alloc=492.3MB, time=52.93 memory used=1938.9MB, alloc=492.3MB, time=54.76 memory used=2133.8MB, alloc=516.3MB, time=60.22 memory used=2334.3MB, alloc=540.3MB, time=66.04 memory used=2514.0MB, alloc=564.3MB, time=71.37 memory used=2655.5MB, alloc=588.3MB, time=75.77 memory used=2830.6MB, alloc=612.3MB, time=81.25 memory used=2974.8MB, alloc=612.3MB, time=85.53 memory used=3116.5MB, alloc=612.3MB, time=89.83 memory used=3243.1MB, alloc=612.3MB, time=94.14 memory used=3374.3MB, alloc=636.3MB, time=98.56 memory used=3499.3MB, alloc=636.3MB, time=102.55 memory used=3614.9MB, alloc=636.3MB, time=106.47 memory used=3707.7MB, alloc=636.3MB, time=110.23 |\^/| 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(); 1428266889 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 2 2 2 2 F := [-20 x y - 20 y + 15 y z - 20 y z , 18 x y + 19 x y + 14 x - 10 z , 3 2 2 16 x + 9 x z - 10 y ] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 G := [-20 x - 19 x y + 15 x y z + 13 x y, 3 x - 9 y z - 20 x y + 15, 2 4 x y z - 4 y z + 5 x y - z] > Problem := [F,G]; 2 3 2 2 Problem := [[-20 x y - 20 y + 15 y z - 20 y z , 2 2 2 2 3 2 2 18 x y + 19 x y + 14 x - 10 z , 16 x + 9 x z - 10 y ], [ 3 2 3 2 -20 x - 19 x y + 15 x y z + 13 x y, 3 x - 9 y z - 20 x y + 15, 2 4 x y z - 4 y 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=4.3MB, alloc=32.3MB, time=0.30 memory used=25.2MB, alloc=32.3MB, time=0.82 memory used=45.2MB, alloc=32.3MB, time=1.22 memory used=67.9MB, alloc=60.3MB, time=1.83 memory used=114.3MB, alloc=68.3MB, time=2.85 memory used=160.2MB, alloc=68.3MB, time=3.75 memory used=204.0MB, alloc=68.3MB, time=4.77 memory used=251.0MB, alloc=92.3MB, time=5.74 memory used=316.0MB, alloc=92.3MB, time=6.69 memory used=391.8MB, alloc=92.3MB, time=8.12 memory used=467.7MB, alloc=92.3MB, time=9.58 memory used=529.5MB, alloc=372.3MB, time=11.04 memory used=624.9MB, alloc=372.3MB, time=12.92 memory used=694.4MB, alloc=372.3MB, time=13.90 memory used=748.7MB, alloc=372.3MB, time=14.56 memory used=802.2MB, alloc=372.3MB, time=15.15 memory used=857.8MB, alloc=372.3MB, time=15.73 memory used=906.5MB, alloc=372.3MB, time=16.27 memory used=961.6MB, alloc=372.3MB, time=16.93 memory used=1044.0MB, alloc=372.3MB, time=18.38 memory used=1132.3MB, alloc=396.3MB, time=20.22 memory used=1238.1MB, alloc=396.3MB, time=22.24 memory used=1356.7MB, alloc=396.3MB, time=24.80 memory used=1461.8MB, alloc=420.3MB, time=27.16 memory used=1590.9MB, alloc=420.3MB, time=29.76 memory used=1707.6MB, alloc=420.3MB, time=32.54 memory used=1841.2MB, alloc=444.3MB, time=35.13 memory used=1981.0MB, alloc=444.3MB, time=37.55 memory used=2086.3MB, alloc=444.3MB, time=40.07 memory used=2210.0MB, alloc=444.3MB, time=42.13 memory used=2300.0MB, alloc=444.3MB, time=43.57 memory used=2375.6MB, alloc=444.3MB, time=44.54 memory used=2452.7MB, alloc=444.3MB, time=45.48 memory used=2561.7MB, alloc=444.3MB, time=47.96 memory used=2666.1MB, alloc=468.3MB, time=50.42 memory used=2757.4MB, alloc=468.3MB, time=52.77 memory used=2848.6MB, alloc=468.3MB, time=55.03 memory used=2924.8MB, alloc=468.3MB, time=57.12 memory used=3007.0MB, alloc=468.3MB, time=59.42 memory used=3097.9MB, alloc=492.3MB, time=61.29 memory used=3181.1MB, alloc=492.3MB, time=63.25 memory used=3251.5MB, alloc=492.3MB, time=65.18 memory used=3323.4MB, alloc=492.3MB, time=67.03 memory used=3396.5MB, alloc=492.3MB, time=68.85 memory used=3461.5MB, alloc=492.3MB, time=70.78 memory used=3522.6MB, alloc=492.3MB, time=72.61 memory used=3588.4MB, alloc=492.3MB, time=74.68 memory used=3654.4MB, alloc=516.3MB, time=76.55 memory used=3711.7MB, alloc=516.3MB, time=78.08 memory used=3775.9MB, alloc=516.3MB, time=79.65 memory used=3829.3MB, alloc=516.3MB, time=81.02 memory used=4000.1MB, alloc=540.3MB, time=83.88 memory used=4248.2MB, alloc=564.3MB, time=89.41 memory used=4471.1MB, alloc=588.3MB, time=93.60 memory used=4671.8MB, alloc=612.3MB, time=98.72 memory used=4868.1MB, alloc=636.3MB, time=102.63 memory used=5038.2MB, alloc=636.3MB, time=107.30 memory used=5171.7MB, alloc=636.3MB, time=110.53 memory used=5416.2MB, alloc=660.3MB, time=114.49 memory used=5601.6MB, alloc=660.3MB, time=117.40 memory used=5801.2MB, alloc=660.3MB, time=120.69 memory used=5966.4MB, alloc=660.3MB, time=125.20 memory used=6100.8MB, alloc=660.3MB, time=128.42 |\^/| 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(); 1428267189 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 F := [-4 x y + 20 y z + 17, -3 x - 10 y z - 2 x z + 6 x, 3 2 y - 10 x + 18 x + 20 z] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 2 2 G := [4 x y + 17 x z - 16 x y z + 4 y z, 18 x y + 18 x z - 3 y z - 19 z , 2 2 -10 y z + 14 x + 20] > Problem := [F,G]; 2 2 3 2 Problem := [[-4 x y + 20 y z + 17, -3 x - 10 y z - 2 x z + 6 x, 3 2 2 2 2 y - 10 x + 18 x + 20 z], [4 x y + 17 x z - 16 x y z + 4 y z, 2 2 2 2 2 2 18 x y + 18 x z - 3 y z - 19 z , -10 y z + 14 x + 20]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.5MB, alloc=32.3MB, time=0.32 memory used=25.8MB, alloc=36.3MB, time=0.79 memory used=46.0MB, alloc=36.3MB, time=1.20 memory used=66.2MB, alloc=36.3MB, time=1.67 memory used=87.2MB, alloc=60.3MB, time=2.13 memory used=121.4MB, alloc=60.3MB, time=2.96 memory used=166.8MB, alloc=68.3MB, time=4.07 memory used=214.5MB, alloc=68.3MB, time=5.04 memory used=256.3MB, alloc=92.3MB, time=6.10 memory used=324.4MB, alloc=92.3MB, time=7.70 memory used=388.6MB, alloc=92.3MB, time=9.28 memory used=442.9MB, alloc=372.3MB, time=10.69 memory used=534.2MB, alloc=372.3MB, time=13.01 memory used=622.2MB, alloc=396.3MB, time=15.20 memory used=733.9MB, alloc=396.3MB, time=17.96 memory used=845.9MB, alloc=420.3MB, time=20.62 memory used=961.7MB, alloc=444.3MB, time=22.82 memory used=1066.1MB, alloc=444.3MB, time=25.52 memory used=1171.8MB, alloc=468.3MB, time=27.85 memory used=1266.8MB, alloc=468.3MB, time=29.99 memory used=1348.7MB, alloc=468.3MB, time=31.90 memory used=1447.1MB, alloc=468.3MB, time=34.22 memory used=1520.5MB, alloc=468.3MB, time=36.30 memory used=1590.7MB, alloc=492.3MB, time=38.26 memory used=1638.8MB, alloc=492.3MB, time=39.57 memory used=1704.7MB, alloc=492.3MB, time=41.15 memory used=1817.4MB, alloc=492.3MB, time=42.90 memory used=1882.2MB, alloc=492.3MB, time=44.62 memory used=1934.3MB, alloc=492.3MB, time=46.23 memory used=1979.9MB, alloc=492.3MB, time=47.59 memory used=2017.0MB, alloc=492.3MB, time=48.88 memory used=2063.4MB, alloc=492.3MB, time=50.70 memory used=2256.0MB, alloc=516.3MB, time=55.69 memory used=2440.4MB, alloc=540.3MB, time=59.95 memory used=2614.6MB, alloc=564.3MB, time=64.31 memory used=2767.8MB, alloc=588.3MB, time=68.42 memory used=2909.6MB, alloc=588.3MB, time=72.60 memory used=3050.9MB, alloc=612.3MB, time=76.89 memory used=3183.1MB, alloc=612.3MB, time=80.88 memory used=3285.4MB, alloc=612.3MB, time=84.35 memory used=3379.3MB, alloc=612.3MB, time=87.66 memory used=3494.8MB, alloc=612.3MB, time=91.58 memory used=3571.4MB, alloc=612.3MB, time=94.27 memory used=3697.8MB, alloc=636.3MB, time=98.83 memory used=4000.9MB, alloc=660.3MB, time=107.43 memory used=4341.7MB, alloc=684.3MB, time=115.87 |\^/| 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(); 1428267489 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [-14 x y - 3 x y z - 5 x + 9 y z, 10 x z - 7 x y z - 7 x z + 16 y, 2 2 2 -8 x y + x z - 11 y z - 2 z ] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 G := [3 x z - 11 x + 14 x z - 9, x - y - 20 y z - 9 z, 2 2 3 2 16 x z - 2 x y + 6 y - 4 z ] > Problem := [F,G]; 2 2 Problem := [[-14 x y - 3 x y z - 5 x + 9 y z, 2 2 2 2 2 10 x z - 7 x y z - 7 x z + 16 y, -8 x y + x z - 11 y z - 2 z ], [ 2 2 3 2 3 x z - 11 x + 14 x z - 9, x - y - 20 y z - 9 z, 2 2 3 2 16 x z - 2 x y + 6 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=0.31 memory used=26.5MB, alloc=32.3MB, time=0.89 memory used=46.2MB, alloc=32.3MB, time=1.39 memory used=65.3MB, alloc=56.3MB, time=1.90 memory used=106.2MB, alloc=68.3MB, time=2.99 memory used=148.9MB, alloc=92.3MB, time=4.05 memory used=216.7MB, alloc=92.3MB, time=5.59 memory used=284.5MB, alloc=348.3MB, time=7.36 memory used=350.0MB, alloc=348.3MB, time=8.98 memory used=417.8MB, alloc=372.3MB, time=10.54 memory used=502.9MB, alloc=372.3MB, time=12.16 memory used=602.3MB, alloc=372.3MB, time=14.25 memory used=697.7MB, alloc=372.3MB, time=16.52 memory used=788.1MB, alloc=396.3MB, time=18.74 memory used=898.9MB, alloc=396.3MB, time=21.61 memory used=1010.7MB, alloc=420.3MB, time=24.06 memory used=1143.4MB, alloc=420.3MB, time=26.95 memory used=1295.2MB, alloc=420.3MB, time=30.53 memory used=1424.7MB, alloc=444.3MB, time=34.32 memory used=1561.6MB, alloc=444.3MB, time=36.59 memory used=1658.7MB, alloc=444.3MB, time=38.62 memory used=1764.1MB, alloc=444.3MB, time=39.82 memory used=1890.0MB, alloc=444.3MB, time=42.27 memory used=2022.1MB, alloc=444.3MB, time=44.71 memory used=2106.5MB, alloc=444.3MB, time=46.06 memory used=2239.7MB, alloc=444.3MB, time=48.36 memory used=2332.5MB, alloc=444.3MB, time=49.91 memory used=2458.1MB, alloc=444.3MB, time=51.93 memory used=2583.5MB, alloc=468.3MB, time=54.60 memory used=2694.4MB, alloc=468.3MB, time=57.69 memory used=2792.4MB, alloc=468.3MB, time=59.99 memory used=2878.6MB, alloc=492.3MB, time=62.52 memory used=2964.5MB, alloc=492.3MB, time=65.14 memory used=3035.2MB, alloc=492.3MB, time=66.95 memory used=3101.5MB, alloc=492.3MB, time=68.79 memory used=3178.4MB, alloc=492.3MB, time=71.32 memory used=3256.9MB, alloc=492.3MB, time=73.73 memory used=3326.6MB, alloc=492.3MB, time=75.89 memory used=3383.5MB, alloc=492.3MB, time=77.76 memory used=3451.1MB, alloc=492.3MB, time=80.00 memory used=3509.7MB, alloc=492.3MB, time=81.75 memory used=3574.4MB, alloc=492.3MB, time=84.03 memory used=3628.4MB, alloc=492.3MB, time=85.69 memory used=3682.1MB, alloc=492.3MB, time=87.16 memory used=3739.0MB, alloc=492.3MB, time=89.17 memory used=3803.1MB, alloc=516.3MB, time=90.81 memory used=3867.1MB, alloc=516.3MB, time=92.64 memory used=4087.4MB, alloc=540.3MB, time=97.38 memory used=4306.2MB, alloc=540.3MB, time=101.91 memory used=4515.5MB, alloc=540.3MB, time=106.52 memory used=4726.6MB, alloc=540.3MB, time=111.84 memory used=4882.7MB, alloc=564.3MB, time=115.96 memory used=5046.8MB, alloc=588.3MB, time=120.83 memory used=5221.6MB, alloc=588.3MB, time=126.25 memory used=5398.4MB, alloc=612.3MB, time=131.39 memory used=5560.1MB, alloc=612.3MB, time=136.38 |\^/| 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(); 1428267789 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 2 2 F := [7 x z + 16 y z - 19 y z + 16 x , -16 x y + 18 x y z - 16 y z - 13 x , 2 2 3 2 6 x y - 13 x z + 19 y + 9 y z] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 G := [2 y z - x z + 9 y z + 4 x, -8 x z + 2 y - x z - 18 z , 3 3 2 -4 x - 20 x y z - 12 y + 5 y z ] > Problem := [F,G]; 2 2 2 2 Problem := [[7 x z + 16 y z - 19 y z + 16 x , 2 2 2 2 2 3 2 -16 x y + 18 x y z - 16 y z - 13 x , 6 x y - 13 x z + 19 y + 9 y z], 2 2 3 2 [2 y z - x z + 9 y z + 4 x, -8 x z + 2 y - x z - 18 z , 3 3 2 -4 x - 20 x y z - 12 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=4.5MB, alloc=32.3MB, time=0.32 memory used=24.8MB, alloc=32.3MB, time=0.80 memory used=44.5MB, alloc=56.3MB, time=1.30 memory used=96.8MB, alloc=60.3MB, time=2.29 memory used=133.1MB, alloc=60.6MB, time=2.58 memory used=170.7MB, alloc=60.6MB, time=2.95 memory used=216.0MB, alloc=68.6MB, time=3.86 memory used=254.1MB, alloc=68.6MB, time=4.45 memory used=291.4MB, alloc=68.6MB, time=5.00 memory used=327.7MB, alloc=68.6MB, time=5.65 memory used=368.0MB, alloc=68.6MB, time=7.19 memory used=413.1MB, alloc=68.6MB, time=8.95 memory used=454.8MB, alloc=68.6MB, time=9.76 memory used=499.5MB, alloc=68.6MB, time=10.57 memory used=524.5MB, alloc=92.6MB, time=14.17 memory used=561.7MB, alloc=92.6MB, time=14.37 memory used=593.3MB, alloc=92.6MB, time=14.55 memory used=623.7MB, alloc=92.6MB, time=14.72 memory used=655.6MB, alloc=92.6MB, time=14.89 memory used=688.8MB, alloc=92.6MB, time=15.08 memory used=723.5MB, alloc=92.6MB, time=15.25 memory used=759.5MB, alloc=92.6MB, time=15.43 memory used=797.9MB, alloc=92.6MB, time=15.61 memory used=838.4MB, alloc=92.6MB, time=15.80 memory used=880.6MB, alloc=92.6MB, time=15.99 memory used=925.4MB, alloc=92.6MB, time=16.19 memory used=972.1MB, alloc=92.6MB, time=16.40 memory used=1021.8MB, alloc=92.6MB, time=16.60 memory used=1058.0MB, alloc=92.6MB, time=16.77 memory used=1084.7MB, alloc=92.6MB, time=16.94 memory used=1112.8MB, alloc=92.6MB, time=17.08 memory used=1142.3MB, alloc=92.6MB, time=17.23 memory used=1177.8MB, alloc=92.6MB, time=20.79 memory used=1215.7MB, alloc=92.6MB, time=21.00 memory used=1247.8MB, alloc=92.6MB, time=21.18 memory used=1279.1MB, alloc=92.6MB, time=21.37 memory used=1311.0MB, alloc=92.6MB, time=21.57 memory used=1344.2MB, alloc=92.6MB, time=21.77 memory used=1379.0MB, alloc=92.6MB, time=21.95 memory used=1416.2MB, alloc=92.6MB, time=22.15 memory used=1454.6MB, alloc=92.6MB, time=22.35 memory used=1495.2MB, alloc=92.6MB, time=22.55 memory used=1538.6MB, alloc=92.6MB, time=22.76 memory used=1584.5MB, alloc=92.6MB, time=22.97 memory used=1632.1MB, alloc=92.6MB, time=23.17 memory used=1682.6MB, alloc=92.6MB, time=23.39 memory used=1715.8MB, alloc=92.6MB, time=23.55 memory used=1742.9MB, alloc=92.6MB, time=23.69 memory used=1771.3MB, alloc=92.6MB, time=23.85 memory used=1801.4MB, alloc=92.6MB, time=24.02 memory used=1836.4MB, alloc=92.6MB, time=24.70 memory used=1871.8MB, alloc=92.6MB, time=24.87 memory used=1901.4MB, alloc=92.6MB, time=24.99 memory used=1931.2MB, alloc=92.6MB, time=25.11 memory used=1963.1MB, alloc=92.6MB, time=25.24 memory used=2005.0MB, alloc=92.6MB, time=29.02 memory used=2036.6MB, alloc=92.6MB, time=29.19 memory used=2066.4MB, alloc=92.6MB, time=29.38 memory used=2096.7MB, alloc=92.6MB, time=29.57 memory used=2128.6MB, alloc=92.6MB, time=29.76 memory used=2162.1MB, alloc=92.6MB, time=29.93 memory used=2196.8MB, alloc=92.6MB, time=30.11 memory used=2232.9MB, alloc=92.6MB, time=30.29 memory used=2271.1MB, alloc=92.6MB, time=30.49 memory used=2311.4MB, alloc=92.6MB, time=30.68 memory used=2353.2MB, alloc=92.6MB, time=30.87 memory used=2397.5MB, alloc=92.6MB, time=31.06 memory used=2444.4MB, alloc=92.6MB, time=31.25 memory used=2492.1MB, alloc=92.6MB, time=31.46 memory used=2518.9MB, alloc=92.6MB, time=31.61 memory used=2545.1MB, alloc=92.6MB, time=31.76 memory used=2572.4MB, alloc=92.6MB, time=31.91 memory used=2601.5MB, alloc=92.6MB, time=32.05 memory used=2638.9MB, alloc=92.6MB, time=35.67 memory used=2672.5MB, alloc=92.6MB, time=35.87 memory used=2703.7MB, alloc=92.6MB, time=36.05 memory used=2734.1MB, alloc=92.6MB, time=36.23 memory used=2764.9MB, alloc=92.6MB, time=36.41 memory used=2797.0MB, alloc=92.6MB, time=36.60 memory used=2830.5MB, alloc=92.6MB, time=36.79 memory used=2865.3MB, alloc=92.6MB, time=36.96 memory used=2902.5MB, alloc=92.6MB, time=37.16 memory used=2940.7MB, alloc=92.6MB, time=37.35 memory used=2982.0MB, alloc=92.6MB, time=37.52 memory used=3024.8MB, alloc=92.6MB, time=37.73 memory used=3069.7MB, alloc=92.6MB, time=37.91 memory used=3117.1MB, alloc=92.6MB, time=38.10 memory used=3159.4MB, alloc=92.6MB, time=38.28 memory used=3185.3MB, alloc=92.6MB, time=38.43 memory used=3211.7MB, alloc=92.6MB, time=38.58 memory used=3239.6MB, alloc=92.6MB, time=38.73 memory used=3269.0MB, alloc=92.6MB, time=38.87 memory used=3309.9MB, alloc=92.6MB, time=39.61 memory used=3339.3MB, alloc=92.6MB, time=39.73 memory used=3367.6MB, alloc=92.6MB, time=39.85 memory used=3396.2MB, alloc=92.6MB, time=39.96 memory used=3430.3MB, alloc=92.6MB, time=42.33 memory used=3467.3MB, alloc=92.6MB, time=49.37 memory used=3496.5MB, alloc=92.6MB, time=49.54 memory used=3527.3MB, alloc=92.6MB, time=49.71 memory used=3558.5MB, alloc=92.6MB, time=49.88 memory used=3590.1MB, alloc=92.6MB, time=50.04 memory used=3623.9MB, alloc=92.6MB, time=50.23 memory used=3658.1MB, alloc=92.6MB, time=50.41 memory used=3692.5MB, alloc=92.6MB, time=50.59 memory used=3727.2MB, alloc=92.6MB, time=50.77 memory used=3764.2MB, alloc=92.6MB, time=50.96 memory used=3801.4MB, alloc=92.6MB, time=51.13 memory used=3838.9MB, alloc=92.6MB, time=51.30 memory used=3878.6MB, alloc=92.6MB, time=51.49 memory used=3918.4MB, alloc=92.6MB, time=51.67 memory used=3958.3MB, alloc=92.6MB, time=51.85 memory used=4000.5MB, alloc=92.6MB, time=52.03 memory used=4042.7MB, alloc=92.6MB, time=52.22 memory used=4085.0MB, alloc=92.6MB, time=52.40 memory used=4113.5MB, alloc=92.6MB, time=52.55 memory used=4138.4MB, alloc=92.6MB, time=52.70 memory used=4161.2MB, alloc=92.6MB, time=52.85 memory used=4182.7MB, alloc=92.6MB, time=52.98 memory used=4204.9MB, alloc=92.6MB, time=53.13 memory used=4227.5MB, alloc=92.6MB, time=53.26 memory used=4249.9MB, alloc=92.6MB, time=53.40 memory used=4272.3MB, alloc=92.6MB, time=53.55 memory used=4294.5MB, alloc=116.6MB, time=53.70 memory used=4330.8MB, alloc=116.6MB, time=53.88 memory used=4368.5MB, alloc=116.6MB, time=54.06 memory used=4407.8MB, alloc=116.6MB, time=54.24 memory used=4446.7MB, alloc=116.6MB, time=54.43 memory used=4487.1MB, alloc=116.6MB, time=54.61 memory used=4529.0MB, alloc=116.6MB, time=54.80 memory used=4570.1MB, alloc=116.6MB, time=54.99 memory used=4612.4MB, alloc=116.6MB, time=55.19 memory used=4655.7MB, alloc=116.6MB, time=55.41 memory used=4699.8MB, alloc=116.6MB, time=55.61 memory used=4746.2MB, alloc=116.6MB, time=55.80 memory used=4792.7MB, alloc=116.6MB, time=55.99 memory used=4840.6MB, alloc=116.6MB, time=56.20 memory used=4889.4MB, alloc=116.6MB, time=56.40 memory used=4939.7MB, alloc=116.6MB, time=56.61 memory used=4991.7MB, alloc=116.6MB, time=56.82 memory used=5045.8MB, alloc=116.6MB, time=57.04 memory used=5103.4MB, alloc=116.6MB, time=57.26 memory used=5163.3MB, alloc=116.6MB, time=66.64 memory used=5213.5MB, alloc=116.6MB, time=66.88 memory used=5262.4MB, alloc=116.6MB, time=67.13 memory used=5314.5MB, alloc=116.6MB, time=67.36 memory used=5367.4MB, alloc=116.6MB, time=67.62 memory used=5423.1MB, alloc=116.6MB, time=67.89 memory used=5481.5MB, alloc=116.6MB, time=68.14 memory used=5540.4MB, alloc=116.6MB, time=68.41 memory used=5602.0MB, alloc=116.6MB, time=68.67 memory used=5666.1MB, alloc=116.6MB, time=68.92 memory used=5732.5MB, alloc=116.6MB, time=69.16 memory used=5798.5MB, alloc=116.6MB, time=69.42 memory used=5841.7MB, alloc=116.6MB, time=69.63 memory used=5878.3MB, alloc=116.6MB, time=69.81 memory used=5912.2MB, alloc=116.6MB, time=69.98 memory used=5948.4MB, alloc=116.6MB, time=70.18 memory used=5984.5MB, alloc=116.6MB, time=70.38 memory used=6020.4MB, alloc=116.6MB, time=70.58 memory used=6058.1MB, alloc=116.6MB, time=70.77 memory used=6095.6MB, alloc=116.6MB, time=70.95 memory used=6134.7MB, alloc=116.6MB, time=71.16 memory used=6173.4MB, alloc=116.6MB, time=71.34 memory used=6213.6MB, alloc=116.6MB, time=71.53 memory used=6255.2MB, alloc=116.6MB, time=71.72 memory used=6298.0MB, alloc=116.6MB, time=71.91 memory used=6341.9MB, alloc=116.6MB, time=72.10 memory used=6386.6MB, alloc=116.6MB, time=72.29 memory used=6431.9MB, alloc=116.6MB, time=72.48 memory used=6477.5MB, alloc=116.6MB, time=72.67 memory used=6524.9MB, alloc=116.6MB, time=72.86 memory used=6573.4MB, alloc=116.6MB, time=73.08 memory used=6623.8MB, alloc=116.6MB, time=73.29 memory used=6675.2MB, alloc=116.6MB, time=73.50 memory used=6728.6MB, alloc=116.6MB, time=73.72 memory used=6784.6MB, alloc=116.6MB, time=73.93 memory used=6843.5MB, alloc=116.6MB, time=74.18 memory used=6918.3MB, alloc=123.3MB, time=75.25 memory used=6972.7MB, alloc=123.3MB, time=75.41 memory used=7029.3MB, alloc=123.3MB, time=75.57 memory used=7122.7MB, alloc=123.3MB, time=81.77 memory used=7203.9MB, alloc=123.3MB, time=88.10 memory used=7280.7MB, alloc=123.3MB, time=88.92 memory used=7345.3MB, alloc=123.3MB, time=89.44 memory used=7408.3MB, alloc=123.3MB, time=90.23 memory used=7506.2MB, alloc=123.3MB, time=94.00 memory used=7569.4MB, alloc=123.3MB, time=94.48 memory used=7630.1MB, alloc=123.3MB, time=94.89 memory used=7685.3MB, alloc=123.3MB, time=96.09 memory used=7738.1MB, alloc=123.3MB, time=97.96 memory used=7799.0MB, alloc=123.3MB, time=98.66 memory used=7854.6MB, alloc=123.3MB, time=99.25 memory used=7911.9MB, alloc=123.3MB, time=99.54 memory used=7964.9MB, alloc=123.3MB, time=99.76 memory used=8011.3MB, alloc=123.3MB, time=99.95 memory used=8079.3MB, alloc=123.3MB, time=100.70 memory used=8131.6MB, alloc=123.3MB, time=100.94 memory used=8180.8MB, alloc=123.3MB, time=101.15 memory used=8233.6MB, alloc=123.3MB, time=101.48 memory used=8297.9MB, alloc=123.3MB, time=106.26 memory used=8344.9MB, alloc=123.3MB, time=106.42 memory used=8403.6MB, alloc=123.3MB, time=107.15 memory used=8457.8MB, alloc=123.3MB, time=107.39 memory used=8500.9MB, alloc=131.8MB, time=107.77 memory used=8527.3MB, alloc=131.8MB, time=107.91 memory used=8556.3MB, alloc=131.8MB, time=108.05 memory used=8588.0MB, alloc=131.8MB, time=108.19 memory used=8622.4MB, alloc=131.8MB, time=108.33 memory used=8659.3MB, alloc=131.8MB, time=108.46 memory used=8696.4MB, alloc=131.8MB, time=108.60 memory used=8781.6MB, alloc=131.8MB, time=114.98 memory used=8829.6MB, alloc=131.8MB, time=115.20 memory used=8883.8MB, alloc=131.8MB, time=115.57 memory used=8969.2MB, alloc=131.8MB, time=121.73 memory used=9017.0MB, alloc=131.8MB, time=121.96 memory used=9092.1MB, alloc=131.8MB, time=122.86 memory used=9168.7MB, alloc=387.8MB, time=124.38 memory used=9255.8MB, alloc=387.8MB, time=133.81 memory used=9298.6MB, alloc=387.8MB, time=134.03 memory used=9376.5MB, alloc=387.8MB, time=135.07 memory used=9464.5MB, alloc=387.8MB, time=136.85 memory used=9552.1MB, alloc=387.8MB, time=138.68 memory used=9603.0MB, alloc=411.8MB, time=139.32 memory used=9672.8MB, alloc=411.8MB, time=140.22 memory used=9733.2MB, alloc=411.8MB, time=140.53 memory used=9776.9MB, alloc=411.8MB, time=140.79 memory used=9833.7MB, alloc=411.8MB, time=141.05 memory used=9902.5MB, alloc=411.8MB, time=141.89 memory used=9961.2MB, alloc=411.8MB, time=142.19 memory used=10007.2MB, alloc=411.8MB, time=142.45 memory used=10073.1MB, alloc=411.8MB, time=144.73 memory used=10260.2MB, alloc=411.8MB, time=157.80 memory used=10312.3MB, alloc=411.8MB, time=158.08 memory used=10369.6MB, alloc=411.8MB, time=158.34 memory used=10419.1MB, alloc=411.8MB, time=158.57 memory used=10462.9MB, alloc=411.8MB, time=158.77 memory used=10530.5MB, alloc=411.8MB, time=160.38 memory used=10582.3MB, alloc=411.8MB, time=160.70 memory used=10643.8MB, alloc=411.8MB, time=161.01 memory used=10693.4MB, alloc=411.8MB, time=161.29 memory used=10735.9MB, alloc=411.8MB, time=161.54 memory used=10782.6MB, alloc=411.8MB, time=161.80 memory used=10834.6MB, alloc=411.8MB, time=162.06 memory used=10893.2MB, alloc=411.8MB, time=162.32 memory used=10959.5MB, alloc=411.8MB, time=162.59 memory used=11007.2MB, alloc=411.8MB, time=162.82 memory used=11045.3MB, alloc=411.8MB, time=163.01 memory used=11087.0MB, alloc=411.8MB, time=163.22 memory used=11132.5MB, alloc=411.8MB, time=163.42 memory used=11196.9MB, alloc=411.8MB, time=164.01 memory used=11261.3MB, alloc=411.8MB, time=165.65 memory used=11316.4MB, alloc=411.8MB, time=165.97 memory used=11376.7MB, alloc=411.8MB, time=166.29 memory used=11429.2MB, alloc=411.8MB, time=166.58 memory used=11471.6MB, alloc=411.8MB, time=166.83 memory used=11518.3MB, alloc=411.8MB, time=167.09 memory used=11570.2MB, alloc=411.8MB, time=167.35 memory used=11628.9MB, alloc=411.8MB, time=167.63 memory used=11695.2MB, alloc=411.8MB, time=167.91 memory used=11744.8MB, alloc=411.8MB, time=168.14 memory used=11783.2MB, alloc=411.8MB, time=168.34 memory used=11825.1MB, alloc=411.8MB, time=168.54 memory used=11870.8MB, alloc=411.8MB, time=168.74 memory used=11934.9MB, alloc=411.8MB, time=169.33 memory used=11997.7MB, alloc=411.8MB, time=179.88 |\^/| 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(); 1428268089 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 2 F := [-8 x z - 17 x z - 3 y z + 16 z , -3 x y + 12 x y - 16 x y z + y, 2 3 16 y z - 12 z + 3 y z - 16 x] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 3 2 2 G := [2 x z - 20 x y z - 3 y z + 13 z , 14 x y + 15 y - 7 y - 7 z , 3 2 12 y + 20 x - x y - 11 y z] > Problem := [F,G]; 2 2 2 3 Problem := [[-8 x z - 17 x z - 3 y z + 16 z , 2 2 2 3 -3 x y + 12 x y - 16 x y z + y, 16 y z - 12 z + 3 y z - 16 x], [ 2 2 2 2 3 2 2 2 x z - 20 x y z - 3 y z + 13 z , 14 x y + 15 y - 7 y - 7 z , 3 2 12 y + 20 x - x y - 11 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.30 memory used=26.9MB, alloc=32.3MB, time=0.89 memory used=47.0MB, alloc=32.3MB, time=1.41 memory used=66.7MB, alloc=56.3MB, time=1.95 memory used=108.4MB, alloc=60.3MB, time=3.04 memory used=148.3MB, alloc=60.3MB, time=4.05 memory used=187.0MB, alloc=92.3MB, time=5.13 memory used=248.5MB, alloc=92.3MB, time=6.77 memory used=311.9MB, alloc=116.3MB, time=8.37 memory used=385.7MB, alloc=372.3MB, time=10.38 memory used=475.3MB, alloc=396.3MB, time=12.58 memory used=588.1MB, alloc=420.3MB, time=15.51 memory used=724.7MB, alloc=420.3MB, time=18.97 memory used=853.7MB, alloc=444.3MB, time=22.33 memory used=972.5MB, alloc=444.3MB, time=25.56 memory used=1085.4MB, alloc=468.3MB, time=28.49 memory used=1195.2MB, alloc=468.3MB, time=31.53 memory used=1302.9MB, alloc=468.3MB, time=34.61 memory used=1396.7MB, alloc=468.3MB, time=37.39 memory used=1489.3MB, alloc=492.3MB, time=39.84 memory used=1583.8MB, alloc=492.3MB, time=42.63 memory used=1666.3MB, alloc=492.3MB, time=45.08 memory used=1748.3MB, alloc=492.3MB, time=47.36 memory used=1826.4MB, alloc=492.3MB, time=49.57 memory used=1910.7MB, alloc=492.3MB, time=51.90 memory used=1982.6MB, alloc=492.3MB, time=54.09 memory used=2049.3MB, alloc=492.3MB, time=55.93 memory used=2106.6MB, alloc=492.3MB, time=57.84 memory used=2189.2MB, alloc=516.3MB, time=59.67 memory used=2254.2MB, alloc=516.3MB, time=61.53 memory used=2322.1MB, alloc=516.3MB, time=63.90 memory used=2379.5MB, alloc=516.3MB, time=65.66 memory used=2437.3MB, alloc=516.3MB, time=67.18 memory used=2503.5MB, alloc=516.3MB, time=68.66 memory used=2553.6MB, alloc=516.3MB, time=70.33 memory used=2606.9MB, alloc=516.3MB, time=72.21 memory used=2634.6MB, alloc=516.3MB, time=73.45 memory used=2784.1MB, alloc=516.3MB, time=76.28 memory used=2973.7MB, alloc=540.3MB, time=82.56 memory used=3184.9MB, alloc=564.3MB, time=88.57 memory used=3354.2MB, alloc=588.3MB, time=92.99 memory used=3531.4MB, alloc=612.3MB, time=98.49 memory used=3693.0MB, alloc=636.3MB, time=103.14 memory used=3835.6MB, alloc=660.3MB, time=107.63 memory used=3992.9MB, alloc=684.3MB, time=111.73 memory used=4154.2MB, alloc=684.3MB, time=116.93 memory used=4262.6MB, alloc=708.3MB, time=120.34 memory used=4366.8MB, alloc=708.3MB, time=123.33 memory used=4473.8MB, alloc=708.3MB, time=126.33 memory used=4585.7MB, alloc=708.3MB, time=131.06 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428268390 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 3 2 F := [14 x z + 12 z + 9 x + 11 z, -13 x z - 15 z - 13 y + 6 y, 2 2 -9 x y + 6 x y z - 13 y ] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 3 3 2 G := [-15 x + 4 x y + x y z + 2 z , -15 x + 2 x y + 7 y z - z , 2 2 -19 x y - 9 x y z + 17 y z + 15 x] > Problem := [F,G]; 2 3 2 2 3 2 Problem := [[14 x z + 12 z + 9 x + 11 z, -13 x z - 15 z - 13 y + 6 y, 2 2 3 2 3 -9 x y + 6 x y z - 13 y ], [-15 x + 4 x y + x y z + 2 z , 3 2 2 2 -15 x + 2 x y + 7 y z - z , -19 x y - 9 x y z + 17 y z + 15 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.31 memory used=25.9MB, alloc=32.3MB, time=0.86 memory used=47.0MB, alloc=60.3MB, time=1.36 memory used=133.7MB, alloc=60.5MB, time=4.03 memory used=160.8MB, alloc=60.5MB, time=4.15 memory used=212.6MB, alloc=60.5MB, time=4.84 memory used=256.4MB, alloc=60.5MB, time=5.33 memory used=301.0MB, alloc=60.5MB, time=6.32 memory used=342.6MB, alloc=60.5MB, time=7.34 memory used=377.1MB, alloc=84.5MB, time=8.04 memory used=424.8MB, alloc=84.5MB, time=8.55 memory used=491.0MB, alloc=92.5MB, time=10.14 memory used=551.8MB, alloc=116.5MB, time=11.24 memory used=603.4MB, alloc=116.5MB, time=11.51 memory used=651.4MB, alloc=140.5MB, time=24.22 memory used=703.7MB, alloc=140.5MB, time=24.48 memory used=753.0MB, alloc=140.5MB, time=24.70 memory used=803.9MB, alloc=140.5MB, time=24.94 memory used=856.1MB, alloc=140.5MB, time=25.20 memory used=909.3MB, alloc=140.5MB, time=25.41 memory used=963.2MB, alloc=140.5MB, time=25.65 memory used=1017.6MB, alloc=140.5MB, time=25.90 memory used=1074.1MB, alloc=140.5MB, time=26.13 memory used=1132.1MB, alloc=140.5MB, time=26.39 memory used=1191.0MB, alloc=140.5MB, time=26.64 memory used=1253.0MB, alloc=140.5MB, time=26.89 memory used=1316.5MB, alloc=140.5MB, time=27.15 memory used=1381.9MB, alloc=140.5MB, time=27.41 memory used=1450.9MB, alloc=140.5MB, time=27.66 memory used=1541.0MB, alloc=148.7MB, time=28.89 memory used=1619.1MB, alloc=148.7MB, time=29.16 memory used=1690.3MB, alloc=148.7MB, time=29.37 memory used=1760.2MB, alloc=148.7MB, time=85.89 memory used=1804.6MB, alloc=148.7MB, time=118.06 memory used=1854.9MB, alloc=172.7MB, time=118.32 memory used=1893.3MB, alloc=172.7MB, time=118.50 memory used=1934.4MB, alloc=196.7MB, time=118.71 memory used=1988.6MB, alloc=196.7MB, time=118.92 memory used=2043.1MB, alloc=196.7MB, time=119.14 memory used=2097.4MB, alloc=196.7MB, time=119.35 memory used=2151.5MB, alloc=196.7MB, time=119.55 memory used=2205.5MB, alloc=196.7MB, time=119.76 memory used=2259.2MB, alloc=196.7MB, time=119.97 memory used=2312.6MB, alloc=196.7MB, time=120.17 memory used=2365.9MB, alloc=196.7MB, time=120.38 memory used=2419.0MB, alloc=196.7MB, time=120.59 memory used=2471.8MB, alloc=196.7MB, time=120.79 memory used=2524.4MB, alloc=196.7MB, time=120.99 memory used=2576.8MB, alloc=196.7MB, time=121.19 memory used=2629.1MB, alloc=196.7MB, time=121.41 memory used=2687.5MB, alloc=196.7MB, time=121.63 memory used=2745.6MB, alloc=196.7MB, time=121.85 memory used=2803.4MB, alloc=196.7MB, time=122.06 memory used=2860.9MB, alloc=196.7MB, time=122.27 memory used=2918.0MB, alloc=196.7MB, time=122.48 memory used=2974.8MB, alloc=196.7MB, time=122.70 memory used=3031.3MB, alloc=196.7MB, time=122.91 memory used=3087.5MB, alloc=196.7MB, time=123.12 memory used=3143.3MB, alloc=196.7MB, time=123.32 memory used=3198.9MB, alloc=196.7MB, time=123.54 memory used=3260.2MB, alloc=196.7MB, time=123.76 memory used=3321.0MB, alloc=196.7MB, time=123.98 memory used=3381.3MB, alloc=196.7MB, time=124.21 memory used=3441.2MB, alloc=196.7MB, time=124.41 memory used=3500.7MB, alloc=196.7MB, time=124.63 memory used=3559.7MB, alloc=196.7MB, time=124.84 memory used=3618.3MB, alloc=196.7MB, time=125.07 memory used=3682.1MB, alloc=196.7MB, time=125.29 memory used=3745.3MB, alloc=196.7MB, time=125.51 memory used=3808.0MB, alloc=196.7MB, time=125.72 memory used=3870.0MB, alloc=196.7MB, time=125.95 memory used=3931.4MB, alloc=196.7MB, time=126.16 memory used=3992.3MB, alloc=196.7MB, time=126.39 memory used=4057.9MB, alloc=196.7MB, time=126.61 memory used=4122.7MB, alloc=196.7MB, time=126.84 memory used=4186.7MB, alloc=196.7MB, time=127.06 memory used=4250.1MB, alloc=196.7MB, time=127.29 memory used=4317.7MB, alloc=196.7MB, time=127.51 memory used=4384.4MB, alloc=196.7MB, time=127.74 memory used=4450.1MB, alloc=196.7MB, time=127.96 memory used=4514.9MB, alloc=196.7MB, time=128.18 memory used=4583.5MB, alloc=196.7MB, time=128.41 memory used=4651.0MB, alloc=196.7MB, time=128.64 memory used=4721.9MB, alloc=196.7MB, time=128.87 memory used=4791.4MB, alloc=196.7MB, time=129.10 memory used=4859.6MB, alloc=196.7MB, time=129.33 memory used=4930.7MB, alloc=196.7MB, time=129.56 memory used=5000.2MB, alloc=196.7MB, time=129.79 memory used=5072.1MB, alloc=196.7MB, time=130.02 memory used=5146.1MB, alloc=196.7MB, time=130.25 memory used=5218.0MB, alloc=196.7MB, time=130.49 memory used=5291.5MB, alloc=196.7MB, time=130.72 memory used=5366.0MB, alloc=196.7MB, time=130.96 memory used=5441.2MB, alloc=196.7MB, time=131.19 memory used=5516.6MB, alloc=196.7MB, time=131.43 memory used=5594.7MB, alloc=196.7MB, time=131.67 memory used=5674.4MB, alloc=196.7MB, time=131.92 memory used=5754.3MB, alloc=196.7MB, time=132.16 memory used=5835.6MB, alloc=196.7MB, time=132.41 memory used=5918.0MB, alloc=196.7MB, time=132.66 memory used=6001.6MB, alloc=196.7MB, time=132.91 memory used=6086.9MB, alloc=196.7MB, time=133.16 memory used=6142.3MB, alloc=203.8MB, time=134.70 memory used=6158.3MB, alloc=203.8MB, time=135.31 memory used=6189.5MB, alloc=203.8MB, time=135.61 memory used=6208.2MB, alloc=203.8MB, time=135.77 memory used=6217.1MB, alloc=203.8MB, time=135.88 memory used=6226.9MB, alloc=203.8MB, time=135.99 memory used=6236.5MB, alloc=203.8MB, time=136.12 memory used=6245.9MB, alloc=203.8MB, time=136.23 memory used=6255.2MB, alloc=203.8MB, time=136.34 memory used=6265.7MB, alloc=203.8MB, time=136.46 memory used=6276.0MB, alloc=203.8MB, time=136.58 memory used=6286.2MB, alloc=203.8MB, time=136.69 memory used=6296.0MB, alloc=203.8MB, time=136.81 memory used=6306.9MB, alloc=203.8MB, time=136.93 memory used=6317.5MB, alloc=203.8MB, time=137.07 memory used=6327.7MB, alloc=203.8MB, time=137.18 memory used=6338.8MB, alloc=203.8MB, time=137.29 memory used=6349.5MB, alloc=203.8MB, time=137.42 memory used=6360.8MB, alloc=203.8MB, time=137.53 memory used=6371.7MB, alloc=203.8MB, time=137.64 memory used=6383.0MB, alloc=203.8MB, time=137.75 memory used=6394.6MB, alloc=203.8MB, time=137.86 memory used=6406.2MB, alloc=203.8MB, time=137.98 memory used=6417.8MB, alloc=203.8MB, time=138.11 memory used=6429.8MB, alloc=203.8MB, time=138.21 memory used=6441.5MB, alloc=203.8MB, time=138.32 memory used=6453.5MB, alloc=203.8MB, time=138.46 memory used=6576.7MB, alloc=459.8MB, time=140.05 memory used=6699.6MB, alloc=459.8MB, time=143.93 memory used=6829.0MB, alloc=459.8MB, time=145.27 memory used=6974.8MB, alloc=459.8MB, time=170.58 memory used=7089.2MB, alloc=459.8MB, time=171.09 memory used=7195.2MB, alloc=459.8MB, time=171.48 memory used=7310.9MB, alloc=459.8MB, time=171.85 |\^/| 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(); 1428268690 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 F := [9 x z + 18 x y z - 5 z + 15 y , x y - 16 x y z - 19 x z - 19, 2 3 11 x y + 15 x y z - 12 z - y z] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 3 2 G := [x y + 7 y z - 20 y - 12, 12 x z + 19 y + 20 z - 8 x, 3 2 7 y - 20 y z - 15 y z + 10 y] > Problem := [F,G]; 2 3 2 2 Problem := [[9 x z + 18 x y z - 5 z + 15 y , x y - 16 x y z - 19 x z - 19, 2 3 2 2 2 11 x y + 15 x y z - 12 z - y z], [x y + 7 y z - 20 y - 12, 2 3 2 3 2 12 x z + 19 y + 20 z - 8 x, 7 y - 20 y z - 15 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=4.4MB, alloc=32.3MB, time=0.31 memory used=24.9MB, alloc=32.3MB, time=0.82 memory used=43.4MB, alloc=56.3MB, time=1.31 memory used=85.3MB, alloc=60.3MB, time=2.32 memory used=126.5MB, alloc=68.3MB, time=3.35 memory used=171.0MB, alloc=92.3MB, time=4.41 memory used=236.2MB, alloc=92.3MB, time=5.84 memory used=294.5MB, alloc=92.3MB, time=6.77 memory used=359.5MB, alloc=92.3MB, time=8.16 memory used=426.1MB, alloc=92.3MB, time=9.56 memory used=485.6MB, alloc=116.3MB, time=10.99 memory used=553.9MB, alloc=372.3MB, time=12.70 memory used=640.2MB, alloc=372.3MB, time=14.91 memory used=722.5MB, alloc=396.3MB, time=17.15 memory used=832.8MB, alloc=396.3MB, time=19.95 memory used=912.8MB, alloc=420.3MB, time=21.45 memory used=995.3MB, alloc=420.3MB, time=22.19 memory used=1096.9MB, alloc=420.3MB, time=25.39 memory used=1182.9MB, alloc=420.3MB, time=27.76 memory used=1251.3MB, alloc=420.3MB, time=28.32 memory used=1389.5MB, alloc=420.3MB, time=31.05 memory used=1520.2MB, alloc=420.3MB, time=34.09 memory used=1593.3MB, alloc=420.3MB, time=34.92 memory used=1732.2MB, alloc=420.3MB, time=38.02 memory used=1860.7MB, alloc=444.3MB, time=41.23 memory used=1960.7MB, alloc=444.3MB, time=42.89 memory used=2050.4MB, alloc=444.3MB, time=45.69 memory used=2172.8MB, alloc=444.3MB, time=48.08 memory used=2310.3MB, alloc=444.3MB, time=51.06 memory used=2428.0MB, alloc=444.3MB, time=53.54 memory used=2489.5MB, alloc=444.3MB, time=53.92 memory used=2566.5MB, alloc=444.3MB, time=54.66 memory used=2641.5MB, alloc=444.3MB, time=55.69 memory used=2704.9MB, alloc=444.3MB, time=56.14 memory used=2778.2MB, alloc=444.3MB, time=56.76 memory used=2855.5MB, alloc=444.3MB, time=61.27 memory used=2928.3MB, alloc=444.3MB, time=62.71 memory used=2990.5MB, alloc=444.3MB, time=63.07 memory used=3051.0MB, alloc=444.3MB, time=63.39 memory used=3186.8MB, alloc=468.3MB, time=66.43 memory used=3312.2MB, alloc=468.3MB, time=68.61 memory used=3403.7MB, alloc=468.3MB, time=69.33 memory used=3493.3MB, alloc=468.3MB, time=70.10 memory used=3590.8MB, alloc=468.3MB, time=73.64 memory used=3664.5MB, alloc=468.3MB, time=74.07 memory used=3805.4MB, alloc=468.3MB, time=76.82 memory used=3890.5MB, alloc=468.3MB, time=77.35 memory used=3976.3MB, alloc=468.3MB, time=78.14 memory used=4068.2MB, alloc=468.3MB, time=82.77 memory used=4146.8MB, alloc=468.3MB, time=83.28 memory used=4219.8MB, alloc=468.3MB, time=83.69 memory used=4347.7MB, alloc=468.3MB, time=86.42 memory used=4468.2MB, alloc=468.3MB, time=88.24 memory used=4648.9MB, alloc=468.3MB, time=92.23 memory used=4792.5MB, alloc=468.3MB, time=97.87 memory used=4908.9MB, alloc=468.3MB, time=99.81 memory used=5001.1MB, alloc=492.3MB, time=102.34 memory used=5153.8MB, alloc=492.3MB, time=105.05 memory used=5268.6MB, alloc=492.3MB, time=106.39 memory used=5352.3MB, alloc=492.3MB, time=106.96 memory used=5466.1MB, alloc=492.3MB, time=108.33 memory used=5556.4MB, alloc=492.3MB, time=108.93 memory used=5635.7MB, alloc=492.3MB, time=109.44 memory used=5758.7MB, alloc=492.3MB, time=119.16 memory used=5843.6MB, alloc=492.3MB, time=119.69 memory used=5923.6MB, alloc=492.3MB, time=120.15 memory used=6019.3MB, alloc=492.3MB, time=120.95 memory used=6139.5MB, alloc=492.3MB, time=122.72 memory used=6226.9MB, alloc=492.3MB, time=123.28 memory used=6329.7MB, alloc=492.3MB, time=124.33 memory used=6424.7MB, alloc=492.3MB, time=124.94 memory used=6500.8MB, alloc=492.3MB, time=125.45 memory used=6619.4MB, alloc=492.3MB, time=134.90 memory used=6703.5MB, alloc=492.3MB, time=135.44 memory used=6782.3MB, alloc=492.3MB, time=135.93 memory used=6907.1MB, alloc=492.3MB, time=137.51 memory used=7044.1MB, alloc=492.3MB, time=140.33 memory used=7143.5MB, alloc=492.3MB, time=141.42 memory used=7256.7MB, alloc=492.3MB, time=144.01 memory used=7385.9MB, alloc=492.3MB, time=146.65 memory used=7491.7MB, alloc=492.3MB, time=148.00 memory used=7589.2MB, alloc=492.3MB, time=148.65 memory used=7683.4MB, alloc=492.3MB, time=149.42 memory used=7785.5MB, alloc=492.3MB, time=154.00 memory used=7868.5MB, alloc=492.3MB, time=154.56 memory used=8010.8MB, alloc=492.3MB, time=156.72 memory used=8107.1MB, alloc=492.3MB, time=157.73 |\^/| 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(); 1428268989 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 F := [4 x z + 6 y z + 6 x + 9 z, 8 x + 19 x z - 4 x - 4, 2 -10 x - 2 x z - 11 z - 13] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 3 G := [-17 x + 3 y z - 17 y + 8 x, 19 x y z + 16 z - 19, 2 2 2 2 -4 x y + 2 x z - 7 y z + 9 y z ] > Problem := [F,G]; 2 2 3 2 2 Problem := [[4 x z + 6 y z + 6 x + 9 z, 8 x + 19 x z - 4 x - 4, 2 3 2 2 -10 x - 2 x z - 11 z - 13], [-17 x + 3 y z - 17 y + 8 x, 3 2 2 2 2 19 x y z + 16 z - 19, -4 x y + 2 x z - 7 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=0.30 memory used=26.1MB, alloc=32.3MB, time=0.89 memory used=45.3MB, alloc=56.3MB, time=1.41 memory used=87.6MB, alloc=60.3MB, time=2.49 memory used=126.9MB, alloc=92.3MB, time=3.60 memory used=194.8MB, alloc=92.3MB, time=5.26 memory used=259.4MB, alloc=92.3MB, time=6.92 memory used=323.0MB, alloc=92.3MB, time=8.48 memory used=379.4MB, alloc=92.3MB, time=9.36 memory used=447.4MB, alloc=372.3MB, time=10.95 memory used=537.9MB, alloc=372.3MB, time=13.22 memory used=629.6MB, alloc=396.3MB, time=15.38 memory used=739.8MB, alloc=396.3MB, time=18.30 memory used=845.8MB, alloc=420.3MB, time=21.39 memory used=984.4MB, alloc=444.3MB, time=25.04 memory used=1118.1MB, alloc=468.3MB, time=28.74 memory used=1240.5MB, alloc=468.3MB, time=31.55 memory used=1369.1MB, alloc=468.3MB, time=34.44 memory used=1486.2MB, alloc=468.3MB, time=37.29 memory used=1603.3MB, alloc=468.3MB, time=40.38 memory used=1706.2MB, alloc=492.3MB, time=42.87 memory used=1813.7MB, alloc=492.3MB, time=46.02 memory used=1909.7MB, alloc=492.3MB, time=48.91 memory used=1998.3MB, alloc=492.3MB, time=51.06 memory used=2088.8MB, alloc=492.3MB, time=53.89 memory used=2185.2MB, alloc=492.3MB, time=56.80 memory used=2267.4MB, alloc=492.3MB, time=59.16 memory used=2373.6MB, alloc=516.3MB, time=61.19 memory used=2505.2MB, alloc=516.3MB, time=62.77 memory used=2630.9MB, alloc=516.3MB, time=64.54 memory used=2735.1MB, alloc=516.3MB, time=66.45 memory used=2815.0MB, alloc=516.3MB, time=68.47 memory used=2881.2MB, alloc=516.3MB, time=70.20 memory used=2952.3MB, alloc=516.3MB, time=72.06 memory used=3040.2MB, alloc=516.3MB, time=74.00 memory used=3162.5MB, alloc=516.3MB, time=75.92 memory used=3242.3MB, alloc=516.3MB, time=78.30 memory used=3311.3MB, alloc=516.3MB, time=80.11 memory used=3377.0MB, alloc=516.3MB, time=81.77 memory used=3428.0MB, alloc=516.3MB, time=83.76 memory used=3484.0MB, alloc=516.3MB, time=85.68 memory used=3532.0MB, alloc=516.3MB, time=87.32 memory used=3594.6MB, alloc=516.3MB, time=89.50 memory used=3810.7MB, alloc=540.3MB, time=95.12 memory used=4017.1MB, alloc=564.3MB, time=100.72 memory used=4192.9MB, alloc=564.3MB, time=105.99 memory used=4394.3MB, alloc=588.3MB, time=110.97 memory used=4600.7MB, alloc=588.3MB, time=115.63 memory used=4791.8MB, alloc=588.3MB, time=118.52 memory used=5017.2MB, alloc=588.3MB, time=123.10 memory used=5187.1MB, alloc=612.3MB, time=128.00 memory used=5350.7MB, alloc=612.3MB, time=133.31 memory used=5500.8MB, alloc=612.3MB, time=137.91 memory used=5634.0MB, alloc=612.3MB, time=142.05 memory used=5766.8MB, alloc=612.3MB, time=145.78 |\^/| 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(); 1428269290 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 3 2 3 F := [12 x z + 3 y z + 6 z - 14, -x - 7 x y - 12 z + 3 y, 2 15 x y z - 9 x - 20 x y + 16 y z] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [-8 x y + 6 y z - 14 x y - 17 y z, -9 y z - 13 y + 8 x - 5, 2 2 2 -13 x z + 6 y z - 12 x y + 20 z ] > Problem := [F,G]; 2 2 3 3 2 3 Problem := [[12 x z + 3 y z + 6 z - 14, -x - 7 x y - 12 z + 3 y, 2 2 2 15 x y z - 9 x - 20 x y + 16 y z], [-8 x y + 6 y z - 14 x y - 17 y z, 2 2 2 2 2 -9 y z - 13 y + 8 x - 5, -13 x z + 6 y z - 12 x y + 20 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.1MB, alloc=32.3MB, time=0.87 memory used=45.5MB, alloc=56.3MB, time=1.37 memory used=86.8MB, alloc=60.3MB, time=2.43 memory used=129.5MB, alloc=68.3MB, time=3.53 memory used=170.6MB, alloc=92.3MB, time=4.53 memory used=242.8MB, alloc=92.3MB, time=6.06 memory used=311.5MB, alloc=92.3MB, time=7.54 memory used=364.5MB, alloc=92.3MB, time=8.33 memory used=431.6MB, alloc=372.3MB, time=9.76 memory used=516.3MB, alloc=372.3MB, time=11.92 memory used=611.9MB, alloc=372.3MB, time=14.05 memory used=699.6MB, alloc=396.3MB, time=16.27 memory used=819.3MB, alloc=396.3MB, time=18.72 memory used=929.3MB, alloc=420.3MB, time=21.29 memory used=1006.3MB, alloc=420.3MB, time=21.95 memory used=1117.8MB, alloc=420.3MB, time=23.67 memory used=1256.3MB, alloc=420.3MB, time=26.87 memory used=1387.2MB, alloc=444.3MB, time=30.45 memory used=1520.6MB, alloc=444.3MB, time=33.38 memory used=1623.3MB, alloc=468.3MB, time=36.04 memory used=1751.1MB, alloc=468.3MB, time=39.75 memory used=1856.8MB, alloc=468.3MB, time=42.28 memory used=1976.3MB, alloc=492.3MB, time=45.34 memory used=2085.4MB, alloc=492.3MB, time=48.02 memory used=2185.5MB, alloc=492.3MB, time=50.35 memory used=2291.6MB, alloc=516.3MB, time=52.45 memory used=2387.4MB, alloc=516.3MB, time=54.49 memory used=2504.4MB, alloc=516.3MB, time=56.99 memory used=2576.5MB, alloc=516.3MB, time=59.22 memory used=2639.6MB, alloc=516.3MB, time=61.03 memory used=2723.7MB, alloc=516.3MB, time=62.72 memory used=2833.6MB, alloc=516.3MB, time=64.83 memory used=2890.4MB, alloc=516.3MB, time=66.45 memory used=2966.5MB, alloc=516.3MB, time=68.32 memory used=3031.8MB, alloc=516.3MB, time=69.90 memory used=3099.3MB, alloc=540.3MB, time=71.35 memory used=3160.8MB, alloc=540.3MB, time=73.01 memory used=3235.7MB, alloc=540.3MB, time=74.53 memory used=3287.7MB, alloc=540.3MB, time=75.97 memory used=3336.6MB, alloc=540.3MB, time=78.14 memory used=3554.1MB, alloc=564.3MB, time=83.70 memory used=3726.5MB, alloc=564.3MB, time=87.72 memory used=3948.0MB, alloc=564.3MB, time=92.55 memory used=4190.4MB, alloc=588.3MB, time=97.73 memory used=4365.6MB, alloc=612.3MB, time=102.34 memory used=4560.9MB, alloc=636.3MB, time=107.83 memory used=4733.6MB, alloc=636.3MB, time=112.78 memory used=4893.7MB, alloc=636.3MB, time=116.54 memory used=5116.7MB, alloc=660.3MB, time=120.50 memory used=5284.1MB, alloc=660.3MB, time=122.12 memory used=5453.1MB, alloc=660.3MB, time=123.72 memory used=5617.6MB, alloc=660.3MB, time=129.11 memory used=5787.8MB, alloc=660.3MB, time=130.70 memory used=5961.5MB, alloc=660.3MB, time=132.47 memory used=6142.2MB, alloc=660.3MB, time=138.19 memory used=6308.6MB, alloc=660.3MB, time=140.04 memory used=6479.1MB, alloc=660.3MB, time=144.29 |\^/| 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(); 1428269590 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [-2 y z + 12 y + 8 x - 3 z, 5 y z - 4 x + 3 x + 9 y, 2 2 -16 x z - 14 x z - 7 y z - 4 z ] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 G := [18 y + y + 19 y z - 6 z , 6 x y + 12 x z - 7 x + 5 z, 2 2 2 -3 x y - 7 x z + 14 y z + 15 x y] > Problem := [F,G]; 2 2 2 2 Problem := [[-2 y z + 12 y + 8 x - 3 z, 5 y z - 4 x + 3 x + 9 y, 2 2 3 2 2 -16 x z - 14 x z - 7 y z - 4 z ], [18 y + y + 19 y z - 6 z , 2 2 2 2 2 6 x y + 12 x z - 7 x + 5 z, -3 x y - 7 x z + 14 y z + 15 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=0.29 memory used=26.2MB, alloc=32.3MB, time=0.87 memory used=46.6MB, alloc=56.3MB, time=1.41 memory used=88.2MB, alloc=60.3MB, time=2.48 memory used=128.4MB, alloc=84.3MB, time=3.52 memory used=171.5MB, alloc=84.3MB, time=4.62 memory used=231.0MB, alloc=92.3MB, time=6.25 memory used=292.3MB, alloc=116.3MB, time=7.87 memory used=365.5MB, alloc=116.3MB, time=9.81 memory used=432.9MB, alloc=372.3MB, time=11.64 memory used=518.7MB, alloc=396.3MB, time=13.88 memory used=627.9MB, alloc=420.3MB, time=16.82 memory used=761.5MB, alloc=420.3MB, time=20.44 memory used=891.7MB, alloc=444.3MB, time=24.01 memory used=1029.4MB, alloc=468.3MB, time=27.95 memory used=1148.8MB, alloc=468.3MB, time=31.28 memory used=1257.4MB, alloc=468.3MB, time=34.57 memory used=1361.1MB, alloc=492.3MB, time=37.38 memory used=1486.5MB, alloc=492.3MB, time=41.27 memory used=1583.1MB, alloc=492.3MB, time=44.16 memory used=1684.3MB, alloc=516.3MB, time=47.61 memory used=1773.0MB, alloc=516.3MB, time=49.92 memory used=1865.5MB, alloc=516.3MB, time=52.07 memory used=1995.3MB, alloc=516.3MB, time=54.40 memory used=2072.3MB, alloc=516.3MB, time=56.88 memory used=2142.4MB, alloc=516.3MB, time=59.42 memory used=2226.4MB, alloc=516.3MB, time=61.23 memory used=2287.2MB, alloc=516.3MB, time=63.05 memory used=2407.4MB, alloc=516.3MB, time=65.02 memory used=2463.5MB, alloc=516.3MB, time=67.05 memory used=2544.2MB, alloc=540.3MB, time=68.79 memory used=2632.6MB, alloc=540.3MB, time=71.58 memory used=2683.5MB, alloc=540.3MB, time=73.59 memory used=2746.6MB, alloc=540.3MB, time=76.19 memory used=2802.3MB, alloc=540.3MB, time=78.52 memory used=3012.2MB, alloc=564.3MB, time=83.30 memory used=3244.8MB, alloc=588.3MB, time=88.57 memory used=3513.6MB, alloc=588.3MB, time=94.39 memory used=3668.3MB, alloc=588.3MB, time=96.41 memory used=3800.7MB, alloc=588.3MB, time=98.04 memory used=3965.8MB, alloc=588.3MB, time=100.48 memory used=4224.2MB, alloc=612.3MB, time=109.03 memory used=4431.3MB, alloc=636.3MB, time=116.62 memory used=4618.0MB, alloc=660.3MB, time=123.26 memory used=4791.4MB, alloc=684.3MB, time=129.55 memory used=4926.5MB, alloc=684.3MB, time=134.71 |\^/| 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(); 1428269890 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 2 3 F := [x z - 9 y - 9 y , 8 x y + 15 y z - 20 z - 7 z, 3 2 2 18 z + 8 x - 11 z - 6] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 2 G := [-13 x + 7 y + 3 y z + 4, -15 x y z + 14 x z - 17 y z + 7 x , 2 3 -20 x z + 14 y - 18 x] > Problem := [F,G]; 2 3 2 2 2 3 Problem := [[x z - 9 y - 9 y , 8 x y + 15 y z - 20 z - 7 z, 3 2 2 3 3 18 z + 8 x - 11 z - 6], [-13 x + 7 y + 3 y z + 4, 2 2 2 2 3 -15 x y z + 14 x z - 17 y z + 7 x , -20 x z + 14 y - 18 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.32 memory used=28.7MB, alloc=33.0MB, time=0.83 memory used=53.7MB, alloc=37.0MB, time=1.33 memory used=75.8MB, alloc=37.0MB, time=1.79 memory used=91.7MB, alloc=37.0MB, time=1.87 memory used=100.6MB, alloc=37.0MB, time=1.93 memory used=110.7MB, alloc=61.0MB, time=2.01 memory used=144.1MB, alloc=61.0MB, time=2.12 memory used=165.9MB, alloc=61.0MB, time=2.21 memory used=191.4MB, alloc=61.0MB, time=2.30 memory used=230.6MB, alloc=61.2MB, time=2.55 memory used=258.6MB, alloc=61.2MB, time=2.66 memory used=289.7MB, alloc=61.2MB, time=2.77 memory used=313.3MB, alloc=61.2MB, time=2.86 memory used=341.6MB, alloc=61.2MB, time=2.95 memory used=423.9MB, alloc=64.8MB, time=11.39 memory used=453.3MB, alloc=64.8MB, time=11.51 memory used=477.9MB, alloc=64.8MB, time=11.62 memory used=503.1MB, alloc=64.8MB, time=11.72 memory used=533.1MB, alloc=64.8MB, time=11.84 memory used=568.1MB, alloc=64.8MB, time=11.98 memory used=591.0MB, alloc=64.8MB, time=12.07 memory used=611.1MB, alloc=64.8MB, time=12.14 memory used=632.3MB, alloc=64.8MB, time=12.22 memory used=655.0MB, alloc=64.8MB, time=12.30 memory used=679.1MB, alloc=64.8MB, time=12.39 memory used=704.8MB, alloc=64.8MB, time=12.48 memory used=732.6MB, alloc=64.8MB, time=12.56 memory used=761.9MB, alloc=64.8MB, time=12.66 memory used=793.2MB, alloc=64.8MB, time=12.75 memory used=826.7MB, alloc=64.8MB, time=12.84 memory used=871.0MB, alloc=81.9MB, time=12.98 memory used=882.6MB, alloc=81.9MB, time=13.04 memory used=894.7MB, alloc=81.9MB, time=13.12 memory used=907.2MB, alloc=81.9MB, time=13.19 memory used=920.2MB, alloc=81.9MB, time=13.29 memory used=933.8MB, alloc=81.9MB, time=13.35 memory used=948.1MB, alloc=81.9MB, time=13.41 memory used=989.4MB, alloc=81.9MB, time=13.69 memory used=1019.6MB, alloc=81.9MB, time=13.82 memory used=1045.8MB, alloc=81.9MB, time=13.92 memory used=1069.8MB, alloc=81.9MB, time=14.04 memory used=1105.2MB, alloc=81.9MB, time=14.38 memory used=1156.6MB, alloc=81.9MB, time=15.14 memory used=1182.3MB, alloc=81.9MB, time=15.25 memory used=1211.5MB, alloc=81.9MB, time=15.35 memory used=1256.8MB, alloc=81.9MB, time=15.96 memory used=1297.6MB, alloc=81.9MB, time=16.61 memory used=1331.7MB, alloc=81.9MB, time=17.72 memory used=1364.6MB, alloc=81.9MB, time=18.66 memory used=1387.2MB, alloc=81.9MB, time=18.78 memory used=1412.9MB, alloc=81.9MB, time=18.89 memory used=1446.3MB, alloc=81.9MB, time=19.39 memory used=1473.4MB, alloc=81.9MB, time=19.59 memory used=1519.3MB, alloc=81.9MB, time=20.44 memory used=1566.6MB, alloc=81.9MB, time=21.09 memory used=1598.5MB, alloc=81.9MB, time=21.79 memory used=1632.2MB, alloc=81.9MB, time=22.44 memory used=1665.4MB, alloc=81.9MB, time=23.70 memory used=1686.3MB, alloc=81.9MB, time=23.82 memory used=1722.9MB, alloc=81.9MB, time=24.48 memory used=1760.9MB, alloc=105.9MB, time=25.42 memory used=1793.2MB, alloc=105.9MB, time=26.24 memory used=1836.1MB, alloc=105.9MB, time=26.57 memory used=1874.1MB, alloc=105.9MB, time=26.75 memory used=1900.3MB, alloc=105.9MB, time=26.91 memory used=1936.3MB, alloc=105.9MB, time=27.20 memory used=1977.7MB, alloc=105.9MB, time=27.44 memory used=2015.6MB, alloc=105.9MB, time=27.61 memory used=2042.2MB, alloc=105.9MB, time=27.77 memory used=2081.0MB, alloc=105.9MB, time=28.83 memory used=2162.1MB, alloc=105.9MB, time=36.54 memory used=2196.8MB, alloc=105.9MB, time=36.72 memory used=2224.9MB, alloc=105.9MB, time=36.88 memory used=2259.3MB, alloc=105.9MB, time=37.04 memory used=2299.8MB, alloc=105.9MB, time=37.22 memory used=2325.4MB, alloc=105.9MB, time=37.35 memory used=2349.2MB, alloc=105.9MB, time=37.48 memory used=2375.4MB, alloc=105.9MB, time=37.61 memory used=2403.1MB, alloc=105.9MB, time=37.74 memory used=2433.7MB, alloc=105.9MB, time=37.87 memory used=2466.8MB, alloc=105.9MB, time=38.00 memory used=2502.2MB, alloc=105.9MB, time=38.14 memory used=2539.2MB, alloc=105.9MB, time=38.29 memory used=2579.4MB, alloc=105.9MB, time=38.43 memory used=2603.1MB, alloc=107.8MB, time=38.56 memory used=2615.6MB, alloc=107.8MB, time=38.67 memory used=2628.8MB, alloc=107.8MB, time=38.77 memory used=2642.3MB, alloc=107.8MB, time=38.87 memory used=2656.4MB, alloc=107.8MB, time=38.98 memory used=2671.2MB, alloc=107.8MB, time=39.10 memory used=2688.9MB, alloc=107.8MB, time=39.29 memory used=2730.3MB, alloc=107.8MB, time=39.51 memory used=2768.3MB, alloc=107.8MB, time=39.68 memory used=2794.7MB, alloc=107.8MB, time=39.84 memory used=2831.5MB, alloc=107.8MB, time=40.10 memory used=2870.6MB, alloc=107.8MB, time=40.31 memory used=2908.3MB, alloc=107.8MB, time=40.50 memory used=2934.9MB, alloc=107.8MB, time=40.63 memory used=2975.5MB, alloc=107.8MB, time=42.39 memory used=3054.0MB, alloc=107.8MB, time=49.40 memory used=3088.3MB, alloc=107.8MB, time=49.57 memory used=3116.7MB, alloc=107.8MB, time=49.73 memory used=3151.5MB, alloc=107.8MB, time=49.89 memory used=3192.8MB, alloc=107.8MB, time=50.08 memory used=3217.1MB, alloc=107.8MB, time=50.21 memory used=3241.5MB, alloc=107.8MB, time=50.33 memory used=3267.7MB, alloc=107.8MB, time=50.47 memory used=3296.8MB, alloc=107.8MB, time=50.59 memory used=3327.4MB, alloc=107.8MB, time=50.72 memory used=3360.5MB, alloc=107.8MB, time=50.88 memory used=3396.0MB, alloc=107.8MB, time=51.01 memory used=3433.9MB, alloc=107.8MB, time=51.16 memory used=3475.4MB, alloc=107.8MB, time=51.30 memory used=3492.9MB, alloc=107.8MB, time=51.41 memory used=3505.4MB, alloc=107.8MB, time=51.52 memory used=3518.6MB, alloc=107.8MB, time=51.64 memory used=3532.0MB, alloc=107.8MB, time=51.76 memory used=3546.2MB, alloc=107.8MB, time=51.86 memory used=3561.0MB, alloc=107.8MB, time=51.96 memory used=3581.3MB, alloc=107.8MB, time=52.35 memory used=3624.5MB, alloc=107.8MB, time=52.58 memory used=3656.9MB, alloc=107.8MB, time=52.75 memory used=3696.5MB, alloc=107.8MB, time=52.94 memory used=3720.8MB, alloc=107.8MB, time=53.09 memory used=3747.5MB, alloc=107.8MB, time=53.26 memory used=3776.8MB, alloc=107.8MB, time=53.41 memory used=3809.5MB, alloc=107.8MB, time=53.58 memory used=3846.4MB, alloc=107.8MB, time=53.74 memory used=3887.1MB, alloc=107.8MB, time=53.91 memory used=3917.1MB, alloc=107.8MB, time=54.04 memory used=3940.4MB, alloc=107.8MB, time=54.17 memory used=3975.6MB, alloc=107.8MB, time=56.71 memory used=4037.5MB, alloc=107.8MB, time=71.12 memory used=4072.4MB, alloc=107.8MB, time=71.30 memory used=4100.6MB, alloc=107.8MB, time=71.46 memory used=4129.6MB, alloc=107.8MB, time=71.61 memory used=4163.9MB, alloc=107.8MB, time=71.78 memory used=4203.2MB, alloc=107.8MB, time=71.95 memory used=4231.9MB, alloc=107.8MB, time=72.08 memory used=4255.2MB, alloc=107.8MB, time=72.21 memory used=4279.7MB, alloc=107.8MB, time=72.33 memory used=4306.3MB, alloc=107.8MB, time=72.48 memory used=4333.5MB, alloc=107.8MB, time=72.61 memory used=4362.5MB, alloc=107.8MB, time=72.73 memory used=4393.6MB, alloc=107.8MB, time=72.86 memory used=4426.6MB, alloc=107.8MB, time=72.99 memory used=4461.3MB, alloc=107.8MB, time=73.13 memory used=4497.7MB, alloc=107.8MB, time=73.27 memory used=4537.0MB, alloc=107.8MB, time=73.41 memory used=4578.8MB, alloc=107.8MB, time=73.55 memory used=4599.2MB, alloc=107.8MB, time=73.67 memory used=4606.7MB, alloc=107.8MB, time=73.77 memory used=4614.5MB, alloc=107.8MB, time=73.88 memory used=4622.6MB, alloc=107.8MB, time=73.98 memory used=4630.6MB, alloc=107.8MB, time=74.10 memory used=4638.5MB, alloc=107.8MB, time=74.21 memory used=4646.4MB, alloc=107.8MB, time=74.30 memory used=4654.2MB, alloc=107.8MB, time=74.39 memory used=4662.1MB, alloc=107.8MB, time=74.50 memory used=4670.8MB, alloc=107.8MB, time=74.60 memory used=4679.6MB, alloc=107.8MB, time=74.70 memory used=4688.2MB, alloc=107.8MB, time=74.79 memory used=4696.7MB, alloc=107.8MB, time=74.89 memory used=4705.5MB, alloc=107.8MB, time=75.00 memory used=4714.6MB, alloc=107.8MB, time=75.10 memory used=4723.8MB, alloc=107.8MB, time=75.20 memory used=4733.1MB, alloc=107.8MB, time=75.31 memory used=4742.8MB, alloc=107.8MB, time=75.40 memory used=4752.6MB, alloc=107.8MB, time=75.51 memory used=4763.0MB, alloc=107.8MB, time=75.61 memory used=4773.4MB, alloc=107.8MB, time=75.70 memory used=4783.8MB, alloc=107.8MB, time=75.79 memory used=4795.0MB, alloc=107.8MB, time=75.89 memory used=4806.5MB, alloc=107.8MB, time=76.02 memory used=4818.0MB, alloc=107.8MB, time=76.11 memory used=4829.9MB, alloc=107.8MB, time=76.20 memory used=4858.7MB, alloc=107.8MB, time=77.25 memory used=4892.4MB, alloc=107.8MB, time=77.43 memory used=4924.3MB, alloc=107.8MB, time=77.59 memory used=4959.1MB, alloc=107.8MB, time=77.75 memory used=4984.5MB, alloc=107.8MB, time=77.88 memory used=5014.6MB, alloc=107.8MB, time=78.01 memory used=5080.6MB, alloc=107.8MB, time=79.23 memory used=5163.3MB, alloc=107.8MB, time=89.75 memory used=5212.1MB, alloc=107.8MB, time=96.84 memory used=5246.4MB, alloc=107.8MB, time=97.03 memory used=5270.6MB, alloc=107.8MB, time=97.19 memory used=5298.2MB, alloc=107.8MB, time=97.34 memory used=5330.3MB, alloc=107.8MB, time=97.50 memory used=5366.6MB, alloc=107.8MB, time=97.66 memory used=5396.0MB, alloc=107.8MB, time=97.80 memory used=5417.0MB, alloc=107.8MB, time=97.93 memory used=5439.7MB, alloc=107.8MB, time=98.05 memory used=5463.2MB, alloc=107.8MB, time=98.18 memory used=5488.7MB, alloc=131.8MB, time=98.33 memory used=5531.6MB, alloc=131.8MB, time=98.50 memory used=5578.6MB, alloc=131.8MB, time=98.68 memory used=5629.4MB, alloc=131.8MB, time=98.85 memory used=5685.3MB, alloc=131.8MB, time=99.03 memory used=5745.7MB, alloc=131.8MB, time=99.22 memory used=5768.8MB, alloc=131.8MB, time=99.35 memory used=5778.3MB, alloc=131.8MB, time=99.46 memory used=5787.7MB, alloc=131.8MB, time=99.57 memory used=5797.3MB, alloc=131.8MB, time=99.68 memory used=5807.7MB, alloc=131.8MB, time=99.80 memory used=5818.2MB, alloc=131.8MB, time=99.91 memory used=5828.5MB, alloc=131.8MB, time=100.02 memory used=5839.0MB, alloc=131.8MB, time=100.14 memory used=5850.0MB, alloc=131.8MB, time=100.26 memory used=5861.1MB, alloc=131.8MB, time=100.37 memory used=5872.3MB, alloc=131.8MB, time=100.48 memory used=5883.9MB, alloc=131.8MB, time=100.60 memory used=5895.5MB, alloc=131.8MB, time=100.72 memory used=5907.8MB, alloc=131.8MB, time=100.82 memory used=5920.1MB, alloc=131.8MB, time=100.93 memory used=5932.5MB, alloc=131.8MB, time=101.06 memory used=5945.6MB, alloc=131.8MB, time=101.18 memory used=5959.0MB, alloc=131.8MB, time=101.31 memory used=5972.8MB, alloc=131.8MB, time=101.41 memory used=5987.1MB, alloc=131.8MB, time=101.54 memory used=6002.1MB, alloc=131.8MB, time=101.66 memory used=6077.9MB, alloc=387.8MB, time=102.93 memory used=6189.4MB, alloc=387.8MB, time=104.67 memory used=6277.4MB, alloc=387.8MB, time=106.76 memory used=6335.8MB, alloc=387.8MB, time=107.32 memory used=6386.8MB, alloc=387.8MB, time=109.35 memory used=6424.9MB, alloc=387.8MB, time=109.57 memory used=6469.8MB, alloc=387.8MB, time=109.88 memory used=6523.4MB, alloc=387.8MB, time=112.04 memory used=6559.1MB, alloc=387.8MB, time=112.26 memory used=6603.1MB, alloc=387.8MB, time=112.65 memory used=6644.6MB, alloc=387.8MB, time=112.90 memory used=6698.9MB, alloc=387.8MB, time=116.97 memory used=6734.5MB, alloc=387.8MB, time=117.18 memory used=6770.8MB, alloc=387.8MB, time=117.38 memory used=6812.5MB, alloc=387.8MB, time=117.73 memory used=6863.2MB, alloc=387.8MB, time=118.42 memory used=6903.0MB, alloc=387.8MB, time=118.66 memory used=6952.4MB, alloc=387.8MB, time=119.04 memory used=7011.1MB, alloc=411.8MB, time=123.13 memory used=7064.4MB, alloc=411.8MB, time=123.40 memory used=7117.1MB, alloc=411.8MB, time=123.65 memory used=7163.8MB, alloc=411.8MB, time=123.86 memory used=7235.2MB, alloc=411.8MB, time=124.31 memory used=7292.6MB, alloc=411.8MB, time=124.62 memory used=7341.0MB, alloc=411.8MB, time=124.87 memory used=7427.1MB, alloc=411.8MB, time=132.81 memory used=7477.9MB, alloc=411.8MB, time=133.06 memory used=7534.2MB, alloc=411.8MB, time=133.32 memory used=7578.4MB, alloc=411.8MB, time=133.53 memory used=7629.8MB, alloc=411.8MB, time=133.75 memory used=7691.8MB, alloc=411.8MB, time=133.99 memory used=7778.4MB, alloc=411.8MB, time=134.78 memory used=7844.8MB, alloc=411.8MB, time=135.18 memory used=7921.8MB, alloc=411.8MB, time=139.15 memory used=7975.7MB, alloc=411.8MB, time=139.44 memory used=8029.6MB, alloc=411.8MB, time=139.69 memory used=8076.0MB, alloc=411.8MB, time=139.90 memory used=8141.0MB, alloc=411.8MB, time=140.31 memory used=8204.0MB, alloc=411.8MB, time=141.15 memory used=8269.3MB, alloc=411.8MB, time=141.69 memory used=8389.2MB, alloc=411.8MB, time=143.65 memory used=8524.9MB, alloc=411.8MB, time=145.81 memory used=8623.0MB, alloc=411.8MB, time=154.11 memory used=8671.3MB, alloc=411.8MB, time=154.39 memory used=8729.7MB, alloc=411.8MB, time=154.67 memory used=8767.7MB, alloc=411.8MB, time=154.90 memory used=8811.0MB, alloc=411.8MB, time=155.14 memory used=8860.7MB, alloc=411.8MB, time=155.36 memory used=8936.1MB, alloc=411.8MB, time=155.63 memory used=9063.5MB, alloc=411.8MB, time=157.91 memory used=9172.4MB, alloc=435.8MB, time=160.33 memory used=9265.6MB, alloc=435.8MB, time=161.84 memory used=9394.8MB, alloc=435.8MB, time=164.69 memory used=9525.1MB, alloc=435.8MB, time=167.97 memory used=9614.9MB, alloc=435.8MB, time=171.25 memory used=9675.7MB, alloc=435.8MB, time=171.70 memory used=9762.9MB, alloc=435.8MB, time=173.70 memory used=9869.3MB, alloc=435.8MB, time=175.84 memory used=9954.8MB, alloc=435.8MB, time=179.08 memory used=10066.9MB, alloc=459.8MB, time=181.38 memory used=10168.6MB, alloc=459.8MB, time=183.86 memory used=10272.3MB, alloc=483.8MB, time=185.32 memory used=10365.3MB, alloc=483.8MB, time=186.00 memory used=10473.7MB, alloc=483.8MB, time=192.28 memory used=10554.3MB, alloc=483.8MB, time=192.77 memory used=10633.8MB, alloc=483.8MB, time=193.20 memory used=10705.5MB, alloc=483.8MB, time=193.60 memory used=10808.4MB, alloc=483.8MB, time=194.03 memory used=10916.1MB, alloc=483.8MB, time=195.22 memory used=10985.5MB, alloc=483.8MB, time=195.65 memory used=11085.9MB, alloc=483.8MB, time=196.41 memory used=11197.9MB, alloc=483.8MB, time=197.43 |\^/| 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(); 1428270190 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 F := [3 x y z - 3 y z - 10 z + 3 x, 2 x y + 10 x z - 11 x - 17 z , 2 2 3 2 -9 x z + 19 y z + 4 z - 9 y ] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 G := [-10 z + 17 y z - 7 z - 10 z, 6 y + 12 y z - 16 y, 2 2 8 x y + 18 x y z + 2 z + 4 y] > Problem := [F,G]; 2 2 2 2 2 Problem := [[3 x y z - 3 y z - 10 z + 3 x, 2 x y + 10 x z - 11 x - 17 z , 2 2 3 2 3 2 -9 x z + 19 y z + 4 z - 9 y ], [-10 z + 17 y z - 7 z - 10 z, 2 2 2 6 y + 12 y z - 16 y, 8 x y + 18 x y z + 2 z + 4 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.30 memory used=26.9MB, alloc=32.3MB, time=0.89 memory used=47.3MB, alloc=32.3MB, time=1.41 memory used=66.2MB, alloc=56.3MB, time=1.92 memory used=104.8MB, alloc=60.3MB, time=2.94 memory used=140.1MB, alloc=84.3MB, time=3.90 memory used=195.0MB, alloc=108.3MB, time=5.38 memory used=270.2MB, alloc=116.3MB, time=7.59 memory used=345.7MB, alloc=140.3MB, time=9.81 memory used=443.4MB, alloc=140.3MB, time=13.00 memory used=544.8MB, alloc=164.3MB, time=16.28 memory used=652.7MB, alloc=420.3MB, time=20.04 memory used=776.8MB, alloc=444.3MB, time=24.69 memory used=926.7MB, alloc=468.3MB, time=30.28 memory used=1099.5MB, alloc=468.3MB, time=37.10 memory used=1270.4MB, alloc=492.3MB, time=44.06 memory used=1459.6MB, alloc=516.3MB, time=51.79 memory used=1677.6MB, alloc=540.3MB, time=61.30 memory used=1910.4MB, alloc=564.3MB, time=70.97 memory used=2170.2MB, alloc=588.3MB, time=82.58 memory used=2453.2MB, alloc=612.3MB, time=93.58 memory used=2748.3MB, alloc=636.3MB, time=107.15 |\^/| 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(); 1428270490 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 3 F := [3 x + 7 y - 9 x - 12 x y, 8 x z - 2 y - x y - 9 x, 2 2 2 2 20 x y + 2 x z - 7 y z + 20 z ] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 G := [9 x z - 10 x y z - 2 x z + 8 y , -10 x z - 4 x y - 13 y z, 2 3 -5 x y - 7 y - 13 x y - 15 x z] > Problem := [F,G]; 3 3 2 2 3 Problem := [[3 x + 7 y - 9 x - 12 x y, 8 x z - 2 y - x y - 9 x, 2 2 2 2 2 2 3 20 x y + 2 x z - 7 y z + 20 z ], [9 x z - 10 x y z - 2 x z + 8 y , 2 2 2 3 -10 x z - 4 x y - 13 y z, -5 x y - 7 y - 13 x y - 15 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.31 memory used=25.8MB, alloc=32.3MB, time=0.89 memory used=45.3MB, alloc=56.3MB, time=1.41 memory used=85.0MB, alloc=60.3MB, time=2.34 memory used=128.6MB, alloc=68.3MB, time=3.39 memory used=171.4MB, alloc=68.3MB, time=4.36 memory used=212.2MB, alloc=68.3MB, time=5.23 memory used=257.9MB, alloc=92.3MB, time=6.23 memory used=328.5MB, alloc=92.3MB, time=7.96 memory used=367.8MB, alloc=92.3MB, time=8.35 memory used=449.3MB, alloc=92.3MB, time=9.70 memory used=526.7MB, alloc=92.3MB, time=11.71 memory used=585.1MB, alloc=92.3MB, time=12.74 memory used=622.1MB, alloc=92.3MB, time=13.59 memory used=686.0MB, alloc=116.3MB, time=14.69 memory used=737.8MB, alloc=116.3MB, time=15.13 memory used=805.8MB, alloc=116.3MB, time=16.17 memory used=890.9MB, alloc=116.3MB, time=17.41 memory used=962.9MB, alloc=116.3MB, time=21.06 memory used=1009.0MB, alloc=116.3MB, time=21.30 memory used=1047.1MB, alloc=116.3MB, time=21.51 memory used=1089.6MB, alloc=116.3MB, time=21.70 memory used=1160.5MB, alloc=116.3MB, time=22.67 memory used=1218.4MB, alloc=372.3MB, time=24.22 memory used=1302.5MB, alloc=396.3MB, time=26.27 memory used=1417.5MB, alloc=420.3MB, time=28.83 memory used=1538.2MB, alloc=444.3MB, time=32.05 memory used=1647.6MB, alloc=444.3MB, time=34.62 memory used=1769.9MB, alloc=444.3MB, time=37.27 memory used=1875.9MB, alloc=468.3MB, time=39.73 memory used=1983.3MB, alloc=468.3MB, time=41.87 memory used=2104.2MB, alloc=468.3MB, time=43.97 memory used=2210.4MB, alloc=468.3MB, time=46.41 memory used=2308.9MB, alloc=468.3MB, time=48.78 memory used=2376.8MB, alloc=492.3MB, time=50.66 memory used=2480.3MB, alloc=492.3MB, time=52.36 memory used=2605.9MB, alloc=492.3MB, time=54.02 memory used=2735.5MB, alloc=492.3MB, time=55.89 memory used=2848.8MB, alloc=492.3MB, time=58.22 memory used=2962.1MB, alloc=492.3MB, time=60.82 memory used=3064.5MB, alloc=492.3MB, time=63.06 memory used=3171.9MB, alloc=492.3MB, time=66.39 memory used=3313.7MB, alloc=492.3MB, time=69.17 memory used=3414.9MB, alloc=492.3MB, time=71.36 memory used=3486.1MB, alloc=492.3MB, time=73.62 memory used=3548.2MB, alloc=492.3MB, time=75.37 memory used=3610.7MB, alloc=492.3MB, time=77.19 memory used=3668.5MB, alloc=492.3MB, time=78.89 memory used=3723.6MB, alloc=492.3MB, time=80.83 memory used=3895.5MB, alloc=516.3MB, time=84.82 memory used=4076.2MB, alloc=540.3MB, time=88.45 memory used=4300.7MB, alloc=540.3MB, time=93.86 memory used=4440.4MB, alloc=564.3MB, time=95.76 memory used=4597.3MB, alloc=564.3MB, time=101.31 memory used=4716.7MB, alloc=564.3MB, time=102.31 memory used=4850.6MB, alloc=564.3MB, time=103.75 memory used=5006.7MB, alloc=564.3MB, time=105.41 memory used=5158.7MB, alloc=564.3MB, time=111.07 memory used=5279.4MB, alloc=564.3MB, time=112.01 memory used=5410.3MB, alloc=564.3MB, time=113.52 memory used=5547.4MB, alloc=564.3MB, time=114.84 memory used=5686.5MB, alloc=564.3MB, time=118.55 memory used=5810.6MB, alloc=564.3MB, time=119.77 memory used=5958.2MB, alloc=564.3MB, time=121.42 memory used=6178.7MB, alloc=564.3MB, time=125.05 memory used=6376.5MB, alloc=564.3MB, time=132.99 memory used=6494.6MB, alloc=564.3MB, time=134.12 memory used=6705.8MB, alloc=588.3MB, time=139.12 memory used=6904.0MB, alloc=588.3MB, time=142.10 memory used=7047.3MB, alloc=588.3MB, time=144.95 memory used=7211.7MB, alloc=588.3MB, time=146.82 memory used=7446.3MB, alloc=588.3MB, time=154.31 memory used=7564.8MB, alloc=588.3MB, time=155.35 memory used=7749.0MB, alloc=612.3MB, time=159.57 |\^/| 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(); 1428270790 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 3 2 F := [-12 x z + 11 y z - 18 y - 9 y, -16 x y - 9 z + 2 z , 2 3 x y + 7 x y z - 7 x z + y z] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 3 2 2 2 2 G := [-7 x z + 14 y - z + 7 x , 13 x z - 7 y + 20 z + 12 y, 2 2 2 13 y z + 14 x + 16 x z + 16 y ] > Problem := [F,G]; 2 2 2 2 3 2 Problem := [[-12 x z + 11 y z - 18 y - 9 y, -16 x y - 9 z + 2 z , 2 2 3 3 2 3 x y + 7 x y z - 7 x z + y z], [-7 x z + 14 y - z + 7 x , 2 2 2 2 2 2 13 x z - 7 y + 20 z + 12 y, 13 y z + 14 x + 16 x z + 16 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.31 memory used=26.5MB, alloc=32.3MB, time=0.89 memory used=46.2MB, alloc=56.3MB, time=1.41 memory used=87.4MB, alloc=60.3MB, time=2.47 memory used=127.9MB, alloc=60.3MB, time=3.48 memory used=165.9MB, alloc=84.3MB, time=4.25 memory used=235.8MB, alloc=92.3MB, time=5.84 memory used=304.1MB, alloc=348.3MB, time=7.36 memory used=367.1MB, alloc=348.3MB, time=8.60 memory used=429.4MB, alloc=372.3MB, time=10.19 memory used=518.5MB, alloc=372.3MB, time=12.37 memory used=608.7MB, alloc=396.3MB, time=14.51 memory used=718.6MB, alloc=420.3MB, time=17.39 memory used=846.8MB, alloc=420.3MB, time=19.95 memory used=943.6MB, alloc=420.3MB, time=21.57 memory used=1073.6MB, alloc=420.3MB, time=24.32 memory used=1199.7MB, alloc=420.3MB, time=26.79 memory used=1334.0MB, alloc=444.3MB, time=30.28 memory used=1460.6MB, alloc=468.3MB, time=33.55 memory used=1561.8MB, alloc=468.3MB, time=36.02 memory used=1686.4MB, alloc=468.3MB, time=37.55 memory used=1791.9MB, alloc=468.3MB, time=38.61 memory used=1912.3MB, alloc=468.3MB, time=40.30 memory used=2016.9MB, alloc=468.3MB, time=41.12 memory used=2121.1MB, alloc=468.3MB, time=44.85 memory used=2212.9MB, alloc=468.3MB, time=45.63 memory used=2327.2MB, alloc=468.3MB, time=49.64 memory used=2410.3MB, alloc=468.3MB, time=50.23 memory used=2503.4MB, alloc=468.3MB, time=51.24 memory used=2610.6MB, alloc=468.3MB, time=53.54 memory used=2717.8MB, alloc=468.3MB, time=57.55 memory used=2854.3MB, alloc=468.3MB, time=59.94 memory used=2962.6MB, alloc=468.3MB, time=61.92 memory used=3085.1MB, alloc=468.3MB, time=64.87 memory used=3198.0MB, alloc=492.3MB, time=67.88 memory used=3281.7MB, alloc=492.3MB, time=70.42 memory used=3370.0MB, alloc=492.3MB, time=72.98 memory used=3455.8MB, alloc=492.3MB, time=75.54 memory used=3529.8MB, alloc=492.3MB, time=77.57 memory used=3653.4MB, alloc=492.3MB, time=79.29 memory used=3737.1MB, alloc=492.3MB, time=83.36 memory used=3835.6MB, alloc=492.3MB, time=84.30 memory used=3923.9MB, alloc=492.3MB, time=85.97 memory used=4023.1MB, alloc=492.3MB, time=88.14 memory used=4110.4MB, alloc=492.3MB, time=90.67 memory used=4169.2MB, alloc=492.3MB, time=92.70 memory used=4240.5MB, alloc=492.3MB, time=94.23 memory used=4316.9MB, alloc=492.3MB, time=96.27 memory used=4372.6MB, alloc=516.3MB, time=98.06 memory used=4430.9MB, alloc=516.3MB, time=99.95 memory used=4478.8MB, alloc=516.3MB, time=101.53 memory used=4533.6MB, alloc=516.3MB, time=103.31 memory used=4575.0MB, alloc=516.3MB, time=104.81 memory used=4633.5MB, alloc=516.3MB, time=106.60 memory used=4838.8MB, alloc=516.3MB, time=110.67 memory used=4986.1MB, alloc=516.3MB, time=113.08 memory used=5171.7MB, alloc=540.3MB, time=117.54 memory used=5389.9MB, alloc=540.3MB, time=120.51 memory used=5568.7MB, alloc=540.3MB, time=123.59 memory used=5733.1MB, alloc=540.3MB, time=126.36 memory used=5828.8MB, alloc=540.3MB, time=127.20 memory used=5982.0MB, alloc=540.3MB, time=140.44 memory used=6087.7MB, alloc=540.3MB, time=141.30 memory used=6173.5MB, alloc=540.3MB, time=142.09 memory used=6268.7MB, alloc=540.3MB, time=142.87 memory used=6384.3MB, alloc=540.3MB, time=143.68 memory used=6575.4MB, alloc=540.3MB, time=144.86 memory used=6772.6MB, alloc=540.3MB, time=146.41 memory used=7018.5MB, alloc=564.3MB, time=151.78 memory used=7268.8MB, alloc=564.3MB, time=156.91 |\^/| 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(); 1428271090 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 3 F := [17 x - 13 x + 17 y z + 9 z, 7 x + 2 x y - 7 z - 17 x y, 2 2 19 x z - 6 y z + 16 x y + z] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [-18 x y - 8 x + 9 y z + 5 x, 3 x z + 4 x y z - 18 x z - 13 y z, 3 2 6 x y z + 13 z + 16 x + 16 x y] > Problem := [F,G]; 3 2 3 2 3 Problem := [[17 x - 13 x + 17 y z + 9 z, 7 x + 2 x y - 7 z - 17 x y, 2 2 2 2 19 x z - 6 y z + 16 x y + z], [-18 x y - 8 x + 9 y z + 5 x, 2 2 3 2 3 x z + 4 x y z - 18 x z - 13 y z, 6 x y z + 13 z + 16 x + 16 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=0.30 memory used=26.1MB, alloc=32.3MB, time=0.86 memory used=46.8MB, alloc=32.3MB, time=1.41 memory used=65.9MB, alloc=56.3MB, time=1.94 memory used=106.6MB, alloc=60.3MB, time=2.99 memory used=145.5MB, alloc=84.3MB, time=4.05 memory used=205.7MB, alloc=92.3MB, time=5.67 memory used=268.2MB, alloc=116.3MB, time=7.33 memory used=343.7MB, alloc=116.3MB, time=9.35 memory used=412.6MB, alloc=372.3MB, time=11.20 memory used=495.5MB, alloc=396.3MB, time=13.57 memory used=604.9MB, alloc=420.3MB, time=16.55 memory used=737.3MB, alloc=444.3MB, time=20.40 memory used=881.7MB, alloc=444.3MB, time=24.46 memory used=1025.1MB, alloc=468.3MB, time=28.94 memory used=1151.4MB, alloc=468.3MB, time=32.75 memory used=1265.4MB, alloc=492.3MB, time=36.15 memory used=1368.2MB, alloc=492.3MB, time=39.25 memory used=1471.1MB, alloc=492.3MB, time=42.59 memory used=1573.3MB, alloc=492.3MB, time=45.81 memory used=1686.1MB, alloc=516.3MB, time=49.63 memory used=1794.3MB, alloc=516.3MB, time=53.26 memory used=1864.5MB, alloc=516.3MB, time=55.41 memory used=1940.9MB, alloc=540.3MB, time=57.49 memory used=2033.9MB, alloc=540.3MB, time=60.53 memory used=2095.8MB, alloc=540.3MB, time=62.70 memory used=2168.3MB, alloc=540.3MB, time=65.26 memory used=2232.2MB, alloc=540.3MB, time=67.71 memory used=2285.9MB, alloc=540.3MB, time=69.66 memory used=2342.4MB, alloc=540.3MB, time=71.59 memory used=2397.1MB, alloc=540.3MB, time=73.29 memory used=2459.6MB, alloc=540.3MB, time=76.12 memory used=2659.0MB, alloc=564.3MB, time=82.17 memory used=2866.1MB, alloc=588.3MB, time=87.72 memory used=3050.6MB, alloc=612.3MB, time=93.61 memory used=3247.0MB, alloc=636.3MB, time=100.46 memory used=3450.0MB, alloc=660.3MB, time=107.35 memory used=3651.2MB, alloc=660.3MB, time=113.87 memory used=3790.6MB, alloc=684.3MB, time=118.51 memory used=3959.8MB, alloc=684.3MB, time=124.56 memory used=4123.7MB, alloc=684.3MB, time=130.33 memory used=4244.0MB, alloc=684.3MB, time=134.33 memory used=4405.0MB, alloc=684.3MB, time=140.83 |\^/| 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(); 1428271390 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [2 x y + 18 y - 17 x - 6, 12 x y - 16 y z + 19 x z + 15 y z, 2 3 18 y z - 10 z + 11 y + 19] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 3 3 2 2 G := [-10 x + 4 x y z - 13 z - 10 x, 13 x + 3 y z - 9 y + 2 z, 2 3 -12 x y + 19 y + 20 y] > Problem := [F,G]; 2 2 2 2 Problem := [[2 x y + 18 y - 17 x - 6, 12 x y - 16 y z + 19 x z + 15 y z, 2 3 3 3 18 y z - 10 z + 11 y + 19], [-10 x + 4 x y z - 13 z - 10 x, 3 2 2 2 3 13 x + 3 y z - 9 y + 2 z, -12 x y + 19 y + 20 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.31 memory used=26.2MB, alloc=32.3MB, time=0.89 memory used=46.2MB, alloc=56.3MB, time=1.44 memory used=86.5MB, alloc=60.3MB, time=2.50 memory used=130.6MB, alloc=68.3MB, time=3.53 memory used=174.8MB, alloc=68.3MB, time=4.43 memory used=197.2MB, alloc=68.3MB, time=4.59 memory used=220.1MB, alloc=68.3MB, time=4.75 memory used=241.5MB, alloc=68.3MB, time=4.91 memory used=271.2MB, alloc=68.3MB, time=5.31 memory used=292.4MB, alloc=68.3MB, time=5.43 memory used=310.8MB, alloc=68.3MB, time=5.55 memory used=332.1MB, alloc=68.3MB, time=5.66 memory used=373.0MB, alloc=68.3MB, time=6.44 memory used=412.7MB, alloc=92.3MB, time=7.49 memory used=479.1MB, alloc=92.3MB, time=9.06 memory used=543.5MB, alloc=116.3MB, time=10.69 memory used=608.2MB, alloc=372.3MB, time=12.29 memory used=693.1MB, alloc=372.3MB, time=13.98 memory used=747.6MB, alloc=372.3MB, time=15.56 memory used=796.6MB, alloc=372.3MB, time=15.86 memory used=851.1MB, alloc=372.3MB, time=16.30 memory used=892.6MB, alloc=372.3MB, time=16.55 memory used=956.0MB, alloc=372.3MB, time=21.39 memory used=994.5MB, alloc=372.3MB, time=21.61 memory used=1075.9MB, alloc=372.3MB, time=23.31 memory used=1121.0MB, alloc=372.3MB, time=23.75 memory used=1208.0MB, alloc=372.3MB, time=25.61 memory used=1293.0MB, alloc=372.3MB, time=27.01 memory used=1357.1MB, alloc=372.3MB, time=28.31 memory used=1411.5MB, alloc=372.3MB, time=30.10 memory used=1462.2MB, alloc=372.3MB, time=30.66 memory used=1521.1MB, alloc=372.3MB, time=31.01 memory used=1554.2MB, alloc=372.3MB, time=31.24 memory used=1592.2MB, alloc=372.3MB, time=31.48 memory used=1634.6MB, alloc=372.3MB, time=31.71 memory used=1701.8MB, alloc=372.3MB, time=32.33 memory used=1740.8MB, alloc=372.3MB, time=32.58 memory used=1776.5MB, alloc=372.3MB, time=32.82 memory used=1820.7MB, alloc=372.3MB, time=33.09 memory used=1893.8MB, alloc=372.3MB, time=42.44 memory used=1934.8MB, alloc=396.3MB, time=42.74 memory used=1992.4MB, alloc=396.3MB, time=43.04 memory used=2041.2MB, alloc=396.3MB, time=43.30 memory used=2147.6MB, alloc=396.3MB, time=45.90 memory used=2252.6MB, alloc=396.3MB, time=47.76 memory used=2367.7MB, alloc=396.3MB, time=50.70 memory used=2426.5MB, alloc=396.3MB, time=51.08 memory used=2479.9MB, alloc=396.3MB, time=51.40 memory used=2517.4MB, alloc=396.3MB, time=51.68 memory used=2562.5MB, alloc=396.3MB, time=51.97 memory used=2615.9MB, alloc=396.3MB, time=52.26 memory used=2666.0MB, alloc=396.3MB, time=52.53 memory used=2719.3MB, alloc=396.3MB, time=53.13 memory used=2768.1MB, alloc=396.3MB, time=53.47 memory used=2817.9MB, alloc=420.3MB, time=53.82 memory used=2873.3MB, alloc=420.3MB, time=54.16 memory used=2944.1MB, alloc=420.3MB, time=54.50 memory used=3007.6MB, alloc=420.3MB, time=54.80 memory used=3109.5MB, alloc=420.3MB, time=69.16 memory used=3173.4MB, alloc=420.3MB, time=69.52 memory used=3247.4MB, alloc=420.3MB, time=69.88 memory used=3304.0MB, alloc=420.3MB, time=70.17 memory used=3357.9MB, alloc=420.3MB, time=70.45 memory used=3418.9MB, alloc=420.3MB, time=70.74 memory used=3487.8MB, alloc=420.3MB, time=71.04 memory used=3566.6MB, alloc=420.3MB, time=71.35 memory used=3752.1MB, alloc=420.3MB, time=72.14 memory used=3892.6MB, alloc=420.3MB, time=74.35 memory used=3958.6MB, alloc=420.3MB, time=74.75 memory used=4036.1MB, alloc=420.3MB, time=75.14 memory used=4083.7MB, alloc=420.3MB, time=75.47 memory used=4134.4MB, alloc=420.3MB, time=75.80 memory used=4188.9MB, alloc=420.3MB, time=76.15 memory used=4250.2MB, alloc=420.3MB, time=76.48 memory used=4314.6MB, alloc=420.3MB, time=76.84 memory used=4386.1MB, alloc=420.3MB, time=77.19 memory used=4464.6MB, alloc=420.3MB, time=77.56 memory used=4540.1MB, alloc=420.3MB, time=77.91 memory used=4583.0MB, alloc=420.3MB, time=78.19 memory used=4626.5MB, alloc=420.3MB, time=78.48 memory used=4668.4MB, alloc=420.3MB, time=78.74 memory used=4714.3MB, alloc=420.3MB, time=79.01 memory used=4761.0MB, alloc=420.3MB, time=79.28 memory used=4808.1MB, alloc=420.3MB, time=79.56 memory used=4860.0MB, alloc=420.3MB, time=79.83 memory used=4912.0MB, alloc=420.3MB, time=80.11 memory used=4964.2MB, alloc=420.3MB, time=80.39 memory used=5021.0MB, alloc=420.3MB, time=80.66 memory used=5077.7MB, alloc=420.3MB, time=80.95 memory used=5138.7MB, alloc=420.3MB, time=81.24 memory used=5199.9MB, alloc=420.3MB, time=81.52 memory used=5263.7MB, alloc=420.3MB, time=81.81 memory used=5331.7MB, alloc=420.3MB, time=82.10 memory used=5402.7MB, alloc=420.3MB, time=82.40 memory used=5476.1MB, alloc=420.3MB, time=82.70 memory used=5551.8MB, alloc=420.3MB, time=83.00 memory used=5631.6MB, alloc=420.3MB, time=83.29 memory used=5815.3MB, alloc=420.3MB, time=83.82 memory used=5988.7MB, alloc=420.3MB, time=86.15 memory used=6052.8MB, alloc=420.3MB, time=86.53 memory used=6129.8MB, alloc=420.3MB, time=86.93 memory used=6175.2MB, alloc=420.3MB, time=87.26 memory used=6224.5MB, alloc=420.3MB, time=87.59 memory used=6278.6MB, alloc=420.3MB, time=87.93 memory used=6339.4MB, alloc=420.3MB, time=88.27 memory used=6403.5MB, alloc=420.3MB, time=88.62 memory used=6474.4MB, alloc=420.3MB, time=88.97 memory used=6548.3MB, alloc=420.3MB, time=89.32 memory used=6628.1MB, alloc=420.3MB, time=89.67 memory used=6674.5MB, alloc=444.3MB, time=89.96 memory used=6727.7MB, alloc=444.3MB, time=90.25 memory used=6783.5MB, alloc=444.3MB, time=90.55 memory used=6844.4MB, alloc=444.3MB, time=90.85 memory used=6906.0MB, alloc=444.3MB, time=91.17 memory used=6972.6MB, alloc=444.3MB, time=91.47 memory used=7039.6MB, alloc=444.3MB, time=91.78 memory used=7111.4MB, alloc=444.3MB, time=92.09 memory used=7187.7MB, alloc=444.3MB, time=92.41 memory used=7264.4MB, alloc=444.3MB, time=92.72 memory used=7347.9MB, alloc=444.3MB, time=93.05 memory used=7435.3MB, alloc=444.3MB, time=93.37 memory used=7525.1MB, alloc=444.3MB, time=93.70 memory used=7620.5MB, alloc=444.3MB, time=94.03 memory used=7723.7MB, alloc=444.3MB, time=94.37 memory used=7912.7MB, alloc=444.3MB, time=94.92 memory used=8127.6MB, alloc=444.3MB, time=191.27 memory used=8249.1MB, alloc=444.3MB, time=193.37 memory used=8322.2MB, alloc=444.3MB, time=193.76 memory used=8412.8MB, alloc=444.3MB, time=194.15 memory used=8490.5MB, alloc=444.3MB, time=194.51 memory used=8550.9MB, alloc=444.3MB, time=194.80 memory used=8617.8MB, alloc=444.3MB, time=195.12 memory used=8693.0MB, alloc=444.3MB, time=195.43 memory used=8774.2MB, alloc=444.3MB, time=195.75 memory used=8863.8MB, alloc=444.3MB, time=196.09 memory used=8959.3MB, alloc=444.3MB, time=196.43 memory used=9195.7MB, alloc=444.3MB, time=197.08 memory used=9337.9MB, alloc=444.3MB, time=197.55 memory used=9496.6MB, alloc=444.3MB, time=198.04 memory used=9670.5MB, alloc=444.3MB, time=198.55 memory used=9864.2MB, alloc=444.3MB, time=199.08 memory used=10087.8MB, alloc=444.3MB, time=199.64 memory used=10225.7MB, alloc=444.3MB, time=200.85 memory used=10385.7MB, alloc=444.3MB, time=208.99 memory used=10468.6MB, alloc=444.3MB, time=209.37 memory used=10539.0MB, alloc=444.3MB, time=209.66 memory used=10614.2MB, alloc=444.3MB, time=209.95 memory used=10706.3MB, alloc=444.3MB, time=210.26 memory used=10922.9MB, alloc=444.3MB, time=212.44 memory used=11022.0MB, alloc=444.3MB, time=213.14 |\^/| 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(); 1428271690 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 F := [-8 x z - 12 y + 11 y z + 6, 20 x y - 11 x y z - 9 x - 19 z, 2 -18 x + 16 x y - 4 x + 10] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 3 2 2 G := [-3 y z + 7 z + 19 x z - 9 y, -6 x + 20 x y + 8 x z - 9 y z, 2 2 5 x y + 19 z - 13] > Problem := [F,G]; 2 3 2 2 Problem := [[-8 x z - 12 y + 11 y z + 6, 20 x y - 11 x y z - 9 x - 19 z, 2 2 3 -18 x + 16 x y - 4 x + 10], [-3 y z + 7 z + 19 x z - 9 y, 3 2 2 2 2 -6 x + 20 x y + 8 x z - 9 y z, 5 x y + 19 z - 13]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.30 memory used=26.5MB, alloc=32.3MB, time=0.88 memory used=45.2MB, alloc=56.3MB, time=1.36 memory used=89.4MB, alloc=61.7MB, time=2.40 memory used=128.7MB, alloc=61.7MB, time=2.85 memory used=171.2MB, alloc=61.7MB, time=3.56 memory used=216.1MB, alloc=69.7MB, time=4.62 memory used=252.1MB, alloc=69.7MB, time=5.12 memory used=280.1MB, alloc=69.7MB, time=5.57 memory used=325.0MB, alloc=93.7MB, time=6.57 memory used=391.6MB, alloc=93.7MB, time=8.16 memory used=460.0MB, alloc=93.7MB, time=9.60 memory used=488.2MB, alloc=93.7MB, time=9.76 memory used=517.4MB, alloc=93.7MB, time=9.94 memory used=590.7MB, alloc=117.7MB, time=11.54 memory used=681.9MB, alloc=373.7MB, time=13.37 memory used=765.2MB, alloc=373.7MB, time=15.58 memory used=807.7MB, alloc=373.7MB, time=15.81 memory used=857.7MB, alloc=373.7MB, time=16.04 memory used=892.3MB, alloc=373.7MB, time=16.23 memory used=932.3MB, alloc=373.7MB, time=16.42 memory used=987.2MB, alloc=373.7MB, time=17.01 memory used=1031.4MB, alloc=373.7MB, time=17.24 memory used=1125.4MB, alloc=373.7MB, time=18.71 memory used=1213.6MB, alloc=373.7MB, time=20.76 memory used=1301.7MB, alloc=397.7MB, time=22.68 memory used=1396.0MB, alloc=397.7MB, time=27.77 memory used=1455.5MB, alloc=397.7MB, time=28.15 memory used=1533.2MB, alloc=397.7MB, time=29.36 memory used=1624.6MB, alloc=397.7MB, time=34.15 memory used=1688.7MB, alloc=397.7MB, time=34.83 memory used=1790.8MB, alloc=397.7MB, time=36.49 memory used=1867.8MB, alloc=397.7MB, time=37.32 memory used=1944.1MB, alloc=397.7MB, time=50.32 memory used=2004.4MB, alloc=397.7MB, time=50.73 memory used=2050.6MB, alloc=397.7MB, time=51.05 memory used=2104.0MB, alloc=397.7MB, time=51.37 memory used=2165.5MB, alloc=397.7MB, time=51.70 memory used=2227.7MB, alloc=397.7MB, time=52.03 memory used=2266.7MB, alloc=397.7MB, time=52.31 memory used=2308.1MB, alloc=397.7MB, time=52.61 memory used=2353.7MB, alloc=397.7MB, time=52.89 memory used=2402.9MB, alloc=397.7MB, time=53.17 memory used=2496.1MB, alloc=397.7MB, time=55.49 memory used=2561.5MB, alloc=397.7MB, time=56.47 memory used=2672.5MB, alloc=397.7MB, time=58.33 memory used=2788.5MB, alloc=397.7MB, time=59.94 memory used=2905.2MB, alloc=397.7MB, time=63.22 memory used=3027.4MB, alloc=397.7MB, time=68.94 memory used=3163.0MB, alloc=421.7MB, time=71.51 memory used=3315.3MB, alloc=421.7MB, time=74.21 memory used=3470.8MB, alloc=421.7MB, time=80.43 memory used=3583.5MB, alloc=421.7MB, time=84.35 memory used=3745.0MB, alloc=421.7MB, time=86.63 memory used=3894.3MB, alloc=421.7MB, time=88.86 memory used=4044.8MB, alloc=421.7MB, time=94.03 memory used=4194.1MB, alloc=445.7MB, time=99.22 memory used=4301.0MB, alloc=445.7MB, time=101.87 memory used=4434.4MB, alloc=469.7MB, time=104.47 memory used=4540.4MB, alloc=469.7MB, time=106.66 memory used=4647.0MB, alloc=469.7MB, time=109.38 memory used=4731.1MB, alloc=469.7MB, time=111.51 memory used=4802.4MB, alloc=469.7MB, time=113.38 memory used=4883.6MB, alloc=493.7MB, time=115.62 memory used=4947.5MB, alloc=493.7MB, time=117.55 memory used=5020.5MB, alloc=493.7MB, time=119.53 memory used=5090.0MB, alloc=493.7MB, time=121.67 memory used=5205.4MB, alloc=493.7MB, time=122.95 memory used=5299.0MB, alloc=493.7MB, time=123.86 memory used=5399.6MB, alloc=493.7MB, time=125.84 memory used=5494.5MB, alloc=493.7MB, time=126.86 memory used=5607.7MB, alloc=493.7MB, time=128.22 memory used=5708.8MB, alloc=493.7MB, time=129.17 memory used=5804.1MB, alloc=493.7MB, time=133.11 memory used=5946.4MB, alloc=493.7MB, time=142.09 memory used=6028.8MB, alloc=493.7MB, time=142.78 memory used=6116.6MB, alloc=493.7MB, time=143.44 memory used=6195.9MB, alloc=493.7MB, time=144.05 memory used=6266.1MB, alloc=493.7MB, time=144.63 memory used=6350.3MB, alloc=493.7MB, time=145.22 memory used=6458.6MB, alloc=493.7MB, time=147.19 memory used=6540.0MB, alloc=493.7MB, time=147.81 memory used=6644.1MB, alloc=493.7MB, time=148.80 memory used=6745.0MB, alloc=493.7MB, time=149.77 memory used=6897.2MB, alloc=493.7MB, time=161.78 memory used=6994.3MB, alloc=493.7MB, time=162.73 memory used=7075.4MB, alloc=493.7MB, time=163.40 memory used=7162.5MB, alloc=493.7MB, time=164.02 memory used=7229.8MB, alloc=493.7MB, time=164.59 memory used=7308.9MB, alloc=493.7MB, time=165.15 memory used=7411.6MB, alloc=493.7MB, time=166.12 memory used=7519.2MB, alloc=493.7MB, time=167.84 memory used=7618.4MB, alloc=493.7MB, time=170.26 |\^/| 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(); 1428271990 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 2 2 F := [-6 x y + 11 y + 5 y + 14 y, -5 x z + 6 y z + 6 x - 12 x z, 2 2 -8 y z - 3 x z + 3 z + 13] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 2 2 2 G := [8 x z - 11 x y + 4 y - 2 z , -20 x z - 2 x y + 12 y z + 19 y , 3 2 2 -8 x - 12 x y - 2 x z - 6 x z] > Problem := [F,G]; 2 3 2 2 2 2 Problem := [[-6 x y + 11 y + 5 y + 14 y, -5 x z + 6 y z + 6 x - 12 x z, 2 2 2 2 3 2 -8 y z - 3 x z + 3 z + 13], [8 x z - 11 x y + 4 y - 2 z , 2 2 2 2 3 2 2 -20 x z - 2 x y + 12 y z + 19 y , -8 x - 12 x y - 2 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=4.5MB, alloc=32.3MB, time=0.32 memory used=27.0MB, alloc=32.3MB, time=0.92 memory used=47.5MB, alloc=56.3MB, time=1.48 memory used=89.3MB, alloc=60.3MB, time=2.53 memory used=129.2MB, alloc=60.3MB, time=3.55 memory used=169.4MB, alloc=84.3MB, time=4.56 memory used=234.9MB, alloc=92.3MB, time=5.83 memory used=297.3MB, alloc=92.3MB, time=6.93 memory used=365.7MB, alloc=92.3MB, time=8.41 memory used=430.3MB, alloc=116.3MB, time=9.80 memory used=494.7MB, alloc=116.3MB, time=11.37 memory used=560.4MB, alloc=372.3MB, time=12.88 memory used=650.5MB, alloc=372.3MB, time=15.01 memory used=742.4MB, alloc=396.3MB, time=17.04 memory used=819.0MB, alloc=396.3MB, time=18.12 memory used=884.8MB, alloc=396.3MB, time=18.71 memory used=946.0MB, alloc=396.3MB, time=19.30 memory used=1007.6MB, alloc=396.3MB, time=20.49 memory used=1076.1MB, alloc=396.3MB, time=22.77 memory used=1135.9MB, alloc=396.3MB, time=23.42 memory used=1202.8MB, alloc=396.3MB, time=23.91 memory used=1267.4MB, alloc=396.3MB, time=24.23 memory used=1334.8MB, alloc=396.3MB, time=25.09 memory used=1402.6MB, alloc=396.3MB, time=26.32 memory used=1476.2MB, alloc=396.3MB, time=26.89 memory used=1551.1MB, alloc=396.3MB, time=28.10 memory used=1614.9MB, alloc=396.3MB, time=28.88 memory used=1668.1MB, alloc=396.3MB, time=29.34 memory used=1802.6MB, alloc=396.3MB, time=31.73 memory used=1897.8MB, alloc=396.3MB, time=33.40 memory used=2009.4MB, alloc=396.3MB, time=35.45 memory used=2119.7MB, alloc=420.3MB, time=37.92 memory used=2208.4MB, alloc=420.3MB, time=40.08 memory used=2329.7MB, alloc=420.3MB, time=42.20 memory used=2399.4MB, alloc=420.3MB, time=43.17 memory used=2528.3MB, alloc=420.3MB, time=45.63 memory used=2596.7MB, alloc=420.3MB, time=46.54 memory used=2666.5MB, alloc=420.3MB, time=47.02 memory used=2742.1MB, alloc=420.3MB, time=49.27 memory used=2829.1MB, alloc=420.3MB, time=50.68 memory used=2954.9MB, alloc=444.3MB, time=54.04 memory used=3073.6MB, alloc=468.3MB, time=57.20 memory used=3185.1MB, alloc=468.3MB, time=59.88 memory used=3315.6MB, alloc=468.3MB, time=63.22 memory used=3422.7MB, alloc=468.3MB, time=65.67 memory used=3529.6MB, alloc=492.3MB, time=67.77 memory used=3659.8MB, alloc=516.3MB, time=70.07 memory used=3733.5MB, alloc=516.3MB, time=72.11 memory used=3824.3MB, alloc=516.3MB, time=74.70 memory used=3908.7MB, alloc=516.3MB, time=77.11 memory used=3979.9MB, alloc=516.3MB, time=79.09 memory used=4060.7MB, alloc=516.3MB, time=81.06 memory used=4144.5MB, alloc=516.3MB, time=82.93 memory used=4215.0MB, alloc=516.3MB, time=85.15 memory used=4280.9MB, alloc=540.3MB, time=87.44 memory used=4329.5MB, alloc=540.3MB, time=89.20 memory used=4397.5MB, alloc=540.3MB, time=91.24 memory used=4464.4MB, alloc=540.3MB, time=93.19 memory used=4517.6MB, alloc=540.3MB, time=94.89 memory used=4563.7MB, alloc=540.3MB, time=96.26 memory used=4786.3MB, alloc=564.3MB, time=101.24 memory used=4945.5MB, alloc=564.3MB, time=104.13 memory used=5173.5MB, alloc=588.3MB, time=109.74 memory used=5338.7MB, alloc=588.3MB, time=114.34 memory used=5572.2MB, alloc=612.3MB, time=120.83 memory used=5828.5MB, alloc=612.3MB, time=125.85 memory used=6084.3MB, alloc=636.3MB, time=131.59 memory used=6267.9MB, alloc=636.3MB, time=136.03 memory used=6464.2MB, alloc=636.3MB, time=139.37 memory used=6657.4MB, alloc=636.3MB, time=144.38 memory used=6862.6MB, alloc=636.3MB, time=148.73 memory used=7039.9MB, alloc=636.3MB, time=150.80 |\^/| 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(); 1428272290 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 2 F := [-2 x z + 8 x y - 5 y - 3, -18 x z - 7 y + 13 y z + 3 y , 3 2 -9 x y z + 5 y + 19 x + 11 y z] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 G := [16 x y + 5 x z + 16 z + 7 x y, 9 x y - 14 x z + 6 x y + y z, 2 3 -14 y z + 10 z - 15 y z] > Problem := [F,G]; 2 2 2 3 2 2 Problem := [[-2 x z + 8 x y - 5 y - 3, -18 x z - 7 y + 13 y z + 3 y , 3 2 2 2 3 -9 x y z + 5 y + 19 x + 11 y z], [16 x y + 5 x z + 16 z + 7 x y, 2 2 2 3 9 x y - 14 x z + 6 x y + y z, -14 y z + 10 z - 15 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=24.6MB, alloc=32.3MB, time=0.81 memory used=43.5MB, alloc=56.3MB, time=1.32 memory used=84.9MB, alloc=60.3MB, time=2.31 memory used=128.9MB, alloc=68.3MB, time=3.38 memory used=170.7MB, alloc=92.3MB, time=4.45 memory used=235.9MB, alloc=92.3MB, time=6.02 memory used=301.9MB, alloc=92.3MB, time=7.45 memory used=364.7MB, alloc=116.3MB, time=8.97 memory used=443.1MB, alloc=372.3MB, time=10.80 memory used=528.3MB, alloc=372.3MB, time=12.54 memory used=617.7MB, alloc=396.3MB, time=14.62 memory used=724.9MB, alloc=420.3MB, time=17.41 memory used=854.9MB, alloc=420.3MB, time=20.75 memory used=986.3MB, alloc=444.3MB, time=24.10 memory used=1094.1MB, alloc=444.3MB, time=25.74 memory used=1230.4MB, alloc=444.3MB, time=28.39 memory used=1369.1MB, alloc=444.3MB, time=31.20 memory used=1493.6MB, alloc=468.3MB, time=34.60 memory used=1623.5MB, alloc=468.3MB, time=37.65 memory used=1733.2MB, alloc=468.3MB, time=40.37 memory used=1829.7MB, alloc=468.3MB, time=43.00 memory used=1926.2MB, alloc=492.3MB, time=45.88 memory used=2021.3MB, alloc=492.3MB, time=48.36 memory used=2112.6MB, alloc=492.3MB, time=50.87 memory used=2194.2MB, alloc=492.3MB, time=53.24 memory used=2319.2MB, alloc=492.3MB, time=55.29 memory used=2436.6MB, alloc=492.3MB, time=57.68 memory used=2531.4MB, alloc=492.3MB, time=59.58 memory used=2596.7MB, alloc=492.3MB, time=61.59 memory used=2674.2MB, alloc=492.3MB, time=64.01 memory used=2751.4MB, alloc=516.3MB, time=66.58 memory used=2812.0MB, alloc=516.3MB, time=68.56 memory used=2861.3MB, alloc=516.3MB, time=70.11 memory used=2913.4MB, alloc=516.3MB, time=71.83 memory used=2961.2MB, alloc=516.3MB, time=73.54 memory used=3080.2MB, alloc=516.3MB, time=75.61 memory used=3202.8MB, alloc=516.3MB, time=77.33 memory used=3260.4MB, alloc=516.3MB, time=79.36 memory used=3404.3MB, alloc=516.3MB, time=81.46 memory used=3509.0MB, alloc=516.3MB, time=83.83 memory used=3632.4MB, alloc=516.3MB, time=85.81 memory used=3811.2MB, alloc=516.3MB, time=89.54 memory used=4011.9MB, alloc=540.3MB, time=95.12 memory used=4207.6MB, alloc=564.3MB, time=99.26 memory used=4384.7MB, alloc=564.3MB, time=103.84 memory used=4505.5MB, alloc=564.3MB, time=105.08 memory used=4679.9MB, alloc=564.3MB, time=107.77 memory used=4865.1MB, alloc=564.3MB, time=111.46 memory used=5058.1MB, alloc=588.3MB, time=115.40 memory used=5289.1MB, alloc=588.3MB, time=122.34 memory used=5450.8MB, alloc=612.3MB, time=126.46 memory used=5627.6MB, alloc=636.3MB, time=131.56 memory used=5767.5MB, alloc=636.3MB, time=135.41 memory used=5899.6MB, alloc=660.3MB, time=138.61 memory used=6051.1MB, alloc=660.3MB, time=143.55 memory used=6168.9MB, alloc=660.3MB, time=147.90 |\^/| 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(); 1428272590 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 3 2 3 F := [-15 x - 7 x z - 14 y z - 7 z , 4 x y - 15 x y z + 9 y , 3 2 2 2 -7 x - 4 x y - 15 x z + 6 z ] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 3 2 G := [-15 x y + 3 x y - 11 x y z - 7 y , 11 x z - 9 z - 19 y z - 20 z , 2 3 2 12 x z + 19 y - 15 z + 18 x] > Problem := [F,G]; 3 2 2 3 2 3 Problem := [[-15 x - 7 x z - 14 y z - 7 z , 4 x y - 15 x y z + 9 y , 3 2 2 2 2 2 2 -7 x - 4 x y - 15 x z + 6 z ], [-15 x y + 3 x y - 11 x y z - 7 y , 2 3 2 2 3 2 11 x z - 9 z - 19 y z - 20 z , 12 x z + 19 y - 15 z + 18 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.9MB, alloc=32.3MB, time=0.88 memory used=48.0MB, alloc=56.3MB, time=1.46 memory used=89.1MB, alloc=60.3MB, time=2.54 memory used=128.5MB, alloc=84.3MB, time=3.57 memory used=168.4MB, alloc=84.3MB, time=4.65 memory used=229.5MB, alloc=116.3MB, time=6.35 memory used=311.2MB, alloc=116.3MB, time=8.52 memory used=389.3MB, alloc=140.3MB, time=10.52 memory used=470.5MB, alloc=396.3MB, time=12.85 memory used=584.0MB, alloc=420.3MB, time=15.50 memory used=712.6MB, alloc=444.3MB, time=19.03 memory used=858.7MB, alloc=468.3MB, time=23.14 memory used=993.9MB, alloc=492.3MB, time=26.50 memory used=1125.4MB, alloc=492.3MB, time=29.67 memory used=1251.7MB, alloc=516.3MB, time=33.61 memory used=1350.2MB, alloc=516.3MB, time=36.46 memory used=1455.4MB, alloc=516.3MB, time=39.34 memory used=1547.0MB, alloc=516.3MB, time=41.97 memory used=1646.4MB, alloc=516.3MB, time=44.76 memory used=1732.2MB, alloc=516.3MB, time=47.69 memory used=1803.6MB, alloc=516.3MB, time=49.88 memory used=1878.1MB, alloc=516.3MB, time=52.36 memory used=1936.4MB, alloc=540.3MB, time=54.46 memory used=2003.4MB, alloc=540.3MB, time=57.11 memory used=2070.8MB, alloc=540.3MB, time=59.76 memory used=2122.4MB, alloc=540.3MB, time=61.66 memory used=2179.0MB, alloc=540.3MB, time=64.18 memory used=2373.9MB, alloc=564.3MB, time=70.86 memory used=2575.9MB, alloc=588.3MB, time=77.75 memory used=2776.0MB, alloc=612.3MB, time=84.64 memory used=2964.2MB, alloc=636.3MB, time=91.39 memory used=3110.8MB, alloc=660.3MB, time=96.85 memory used=3246.2MB, alloc=660.3MB, time=101.56 memory used=3378.7MB, alloc=660.3MB, time=106.31 memory used=3520.2MB, alloc=660.3MB, time=110.95 memory used=3644.9MB, alloc=660.3MB, time=115.72 memory used=3780.7MB, alloc=684.3MB, time=120.86 memory used=3882.7MB, alloc=684.3MB, time=125.12 memory used=3978.8MB, alloc=684.3MB, time=129.38 memory used=4081.2MB, alloc=684.3MB, time=134.08 |\^/| 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(); 1428272890 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 F := [16 x y + 13 x z - 18 x + 17, 12 x z - 3 y z - 9 x z + 6 y, 3 2 2 20 y - 8 y z - 17 y - 18 x] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [-9 x y - 13 x z - 12 x y + 2, 4 x z - 16 y z - 3 z - 4 x, 3 2 3 2 -19 x + 2 x z - 8 y + 16 y z] > Problem := [F,G]; 2 2 2 2 2 Problem := [[16 x y + 13 x z - 18 x + 17, 12 x z - 3 y z - 9 x z + 6 y, 3 2 2 2 2 20 y - 8 y z - 17 y - 18 x], [-9 x y - 13 x z - 12 x y + 2, 2 2 3 2 3 2 4 x z - 16 y z - 3 z - 4 x, -19 x + 2 x z - 8 y + 16 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.8MB, alloc=32.3MB, time=0.73 memory used=48.4MB, alloc=32.6MB, time=1.08 memory used=68.7MB, alloc=36.6MB, time=1.59 memory used=91.5MB, alloc=60.6MB, time=2.07 memory used=128.2MB, alloc=61.9MB, time=2.31 memory used=169.4MB, alloc=61.9MB, time=6.11 memory used=206.9MB, alloc=61.9MB, time=6.65 memory used=236.4MB, alloc=61.9MB, time=6.76 memory used=257.4MB, alloc=61.9MB, time=6.86 memory used=283.8MB, alloc=61.9MB, time=6.95 memory used=320.0MB, alloc=61.9MB, time=7.18 memory used=357.5MB, alloc=61.9MB, time=7.74 memory used=406.8MB, alloc=62.9MB, time=11.74 memory used=435.8MB, alloc=62.9MB, time=11.85 memory used=458.9MB, alloc=62.9MB, time=11.95 memory used=484.0MB, alloc=62.9MB, time=12.05 memory used=525.2MB, alloc=62.9MB, time=12.52 memory used=574.5MB, alloc=70.9MB, time=13.53 memory used=599.3MB, alloc=70.9MB, time=13.65 memory used=635.9MB, alloc=70.9MB, time=14.22 memory used=691.0MB, alloc=70.9MB, time=15.19 memory used=737.4MB, alloc=70.9MB, time=16.31 memory used=784.7MB, alloc=70.9MB, time=17.41 memory used=830.9MB, alloc=94.9MB, time=18.40 memory used=884.8MB, alloc=94.9MB, time=18.87 memory used=920.2MB, alloc=94.9MB, time=19.06 memory used=972.9MB, alloc=94.9MB, time=19.39 memory used=1008.5MB, alloc=94.9MB, time=19.57 memory used=1088.1MB, alloc=94.9MB, time=27.62 memory used=1125.5MB, alloc=94.9MB, time=27.81 memory used=1161.3MB, alloc=94.9MB, time=27.98 memory used=1190.7MB, alloc=94.9MB, time=28.15 memory used=1225.7MB, alloc=94.9MB, time=28.32 memory used=1267.2MB, alloc=94.9MB, time=28.51 memory used=1301.0MB, alloc=94.9MB, time=28.65 memory used=1326.5MB, alloc=94.9MB, time=28.77 memory used=1354.5MB, alloc=94.9MB, time=28.89 memory used=1386.1MB, alloc=94.9MB, time=29.02 memory used=1429.6MB, alloc=94.9MB, time=29.36 memory used=1489.5MB, alloc=94.9MB, time=30.64 memory used=1522.7MB, alloc=94.9MB, time=30.80 memory used=1559.3MB, alloc=94.9MB, time=30.95 memory used=1599.5MB, alloc=94.9MB, time=31.21 memory used=1683.0MB, alloc=94.9MB, time=33.95 memory used=1774.0MB, alloc=94.9MB, time=35.69 memory used=1852.2MB, alloc=94.9MB, time=37.07 memory used=1931.2MB, alloc=94.9MB, time=39.44 memory used=2010.8MB, alloc=94.9MB, time=43.10 memory used=2092.0MB, alloc=94.9MB, time=47.70 memory used=2151.7MB, alloc=94.9MB, time=49.50 memory used=2219.1MB, alloc=94.9MB, time=51.20 memory used=2284.5MB, alloc=94.9MB, time=52.41 memory used=2346.6MB, alloc=374.9MB, time=53.65 memory used=2443.8MB, alloc=374.9MB, time=60.49 memory used=2515.6MB, alloc=374.9MB, time=62.26 memory used=2556.2MB, alloc=374.9MB, time=62.53 memory used=2610.4MB, alloc=374.9MB, time=63.00 memory used=2687.9MB, alloc=374.9MB, time=69.98 memory used=2730.7MB, alloc=374.9MB, time=70.23 memory used=2769.5MB, alloc=374.9MB, time=70.47 memory used=2820.2MB, alloc=374.9MB, time=70.71 memory used=2852.9MB, alloc=374.9MB, time=70.90 memory used=2886.9MB, alloc=374.9MB, time=71.09 memory used=2926.6MB, alloc=374.9MB, time=71.29 memory used=2982.1MB, alloc=374.9MB, time=72.55 memory used=3026.0MB, alloc=374.9MB, time=73.08 memory used=3075.6MB, alloc=374.9MB, time=73.35 memory used=3125.5MB, alloc=374.9MB, time=73.63 memory used=3168.9MB, alloc=374.9MB, time=74.15 memory used=3297.8MB, alloc=374.9MB, time=75.12 memory used=3374.4MB, alloc=374.9MB, time=75.38 memory used=3523.4MB, alloc=374.9MB, time=75.91 memory used=3598.4MB, alloc=374.9MB, time=76.18 memory used=3700.0MB, alloc=374.9MB, time=78.51 memory used=3793.0MB, alloc=374.9MB, time=80.37 memory used=3841.6MB, alloc=374.9MB, time=80.85 memory used=3882.2MB, alloc=374.9MB, time=81.07 memory used=3929.4MB, alloc=374.9MB, time=81.61 memory used=4004.7MB, alloc=374.9MB, time=82.81 memory used=4093.7MB, alloc=374.9MB, time=84.10 memory used=4136.8MB, alloc=374.9MB, time=84.48 memory used=4237.6MB, alloc=374.9MB, time=86.54 memory used=4316.1MB, alloc=374.9MB, time=87.99 memory used=4396.9MB, alloc=398.9MB, time=89.81 memory used=4513.5MB, alloc=422.9MB, time=92.20 memory used=4611.6MB, alloc=422.9MB, time=96.93 memory used=4668.9MB, alloc=422.9MB, time=97.32 memory used=4749.5MB, alloc=422.9MB, time=97.88 memory used=4839.5MB, alloc=422.9MB, time=102.54 memory used=4895.3MB, alloc=422.9MB, time=102.89 memory used=4983.8MB, alloc=422.9MB, time=104.31 memory used=5141.2MB, alloc=422.9MB, time=107.25 memory used=5248.0MB, alloc=446.9MB, time=108.61 memory used=5412.3MB, alloc=446.9MB, time=111.25 memory used=5506.6MB, alloc=446.9MB, time=113.64 memory used=5602.4MB, alloc=470.9MB, time=115.83 memory used=5699.6MB, alloc=470.9MB, time=117.89 memory used=5814.7MB, alloc=470.9MB, time=120.08 memory used=5919.4MB, alloc=470.9MB, time=122.21 memory used=6021.1MB, alloc=470.9MB, time=123.05 memory used=6125.2MB, alloc=470.9MB, time=131.01 memory used=6225.9MB, alloc=494.9MB, time=131.95 memory used=6314.5MB, alloc=494.9MB, time=132.52 memory used=6397.1MB, alloc=494.9MB, time=133.05 memory used=6488.1MB, alloc=494.9MB, time=133.95 memory used=6605.0MB, alloc=494.9MB, time=134.99 memory used=6751.5MB, alloc=494.9MB, time=143.59 memory used=6841.0MB, alloc=494.9MB, time=144.23 memory used=6941.4MB, alloc=494.9MB, time=144.84 memory used=7012.7MB, alloc=494.9MB, time=145.34 memory used=7120.1MB, alloc=494.9MB, time=146.32 memory used=7245.4MB, alloc=494.9MB, time=147.32 memory used=7382.5MB, alloc=494.9MB, time=155.45 memory used=7470.2MB, alloc=494.9MB, time=156.06 memory used=7566.2MB, alloc=494.9MB, time=156.65 memory used=7639.2MB, alloc=494.9MB, time=157.14 memory used=7746.9MB, alloc=494.9MB, time=158.66 memory used=7862.3MB, alloc=494.9MB, time=159.82 memory used=7980.3MB, alloc=494.9MB, time=160.94 memory used=8075.8MB, alloc=494.9MB, time=161.58 memory used=8155.5MB, alloc=494.9MB, time=162.14 memory used=8269.9MB, alloc=494.9MB, time=163.15 memory used=8359.7MB, alloc=494.9MB, time=163.77 memory used=8448.8MB, alloc=494.9MB, time=164.34 memory used=8573.5MB, alloc=494.9MB, time=167.73 memory used=8662.6MB, alloc=494.9MB, time=168.30 memory used=8745.1MB, alloc=494.9MB, time=168.80 memory used=8841.2MB, alloc=494.9MB, time=169.46 memory used=8960.5MB, alloc=494.9MB, time=170.77 memory used=9065.8MB, alloc=494.9MB, time=171.55 memory used=9180.3MB, alloc=494.9MB, time=172.89 memory used=9287.9MB, alloc=494.9MB, time=173.88 memory used=9421.7MB, alloc=494.9MB, time=175.96 memory used=9610.7MB, alloc=494.9MB, time=180.00 memory used=9777.4MB, alloc=494.9MB, time=188.56 memory used=9899.4MB, alloc=494.9MB, time=193.36 memory used=10116.2MB, alloc=494.9MB, time=197.29 memory used=10317.4MB, alloc=494.9MB, time=204.44 |\^/| 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(); 1428273190 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 3 F := [20 x y + 20 x + 20 x y + 6 y , 8 x y + 16 x z + 20 z + 15 y, 3 2 13 x + x y - 13 x y z - 11] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 2 G := [16 x y + z + 9 x + 8 y, -15 x y - 2 x y z - 18 x z + 17 z, 3 2 3 2 x + 12 x y - 4 z ] > Problem := [F,G]; 2 2 2 2 2 3 Problem := [[20 x y + 20 x + 20 x y + 6 y , 8 x y + 16 x z + 20 z + 15 y, 3 2 2 3 2 13 x + x y - 13 x y z - 11], [16 x y + z + 9 x + 8 y, 2 2 3 2 3 -15 x y - 2 x y z - 18 x z + 17 z, 2 x + 12 x y - 4 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=25.5MB, alloc=32.3MB, time=0.87 memory used=45.0MB, alloc=56.3MB, time=1.35 memory used=87.2MB, alloc=60.3MB, time=2.38 memory used=131.1MB, alloc=68.3MB, time=3.24 memory used=164.2MB, alloc=68.3MB, time=3.56 memory used=206.3MB, alloc=68.3MB, time=4.41 memory used=251.6MB, alloc=68.3MB, time=5.39 memory used=294.4MB, alloc=68.3MB, time=6.14 memory used=322.2MB, alloc=68.3MB, time=6.36 memory used=355.0MB, alloc=68.3MB, time=6.94 memory used=384.7MB, alloc=68.3MB, time=7.37 memory used=417.9MB, alloc=68.3MB, time=7.97 memory used=460.5MB, alloc=68.3MB, time=8.68 memory used=503.2MB, alloc=92.3MB, time=9.54 memory used=568.1MB, alloc=92.3MB, time=10.71 memory used=631.3MB, alloc=92.3MB, time=11.86 memory used=699.9MB, alloc=348.3MB, time=13.24 memory used=764.1MB, alloc=348.3MB, time=14.48 memory used=800.1MB, alloc=348.3MB, time=14.77 memory used=847.7MB, alloc=348.3MB, time=15.63 memory used=888.7MB, alloc=348.3MB, time=16.13 memory used=928.1MB, alloc=348.3MB, time=16.79 memory used=956.3MB, alloc=348.3MB, time=16.97 memory used=994.1MB, alloc=348.3MB, time=17.46 memory used=1051.2MB, alloc=348.3MB, time=19.01 memory used=1079.1MB, alloc=348.3MB, time=19.19 memory used=1147.8MB, alloc=372.3MB, time=20.52 memory used=1251.1MB, alloc=372.3MB, time=22.42 memory used=1335.4MB, alloc=372.3MB, time=24.36 memory used=1386.5MB, alloc=372.3MB, time=24.80 memory used=1486.7MB, alloc=372.3MB, time=26.72 memory used=1566.7MB, alloc=372.3MB, time=28.21 memory used=1659.2MB, alloc=396.3MB, time=30.21 memory used=1774.5MB, alloc=396.3MB, time=33.02 memory used=1829.2MB, alloc=396.3MB, time=33.35 memory used=1871.2MB, alloc=396.3MB, time=33.60 memory used=1935.2MB, alloc=396.3MB, time=34.15 memory used=2051.7MB, alloc=396.3MB, time=36.02 memory used=2134.6MB, alloc=396.3MB, time=38.53 memory used=2185.5MB, alloc=396.3MB, time=38.84 memory used=2234.8MB, alloc=396.3MB, time=39.13 memory used=2303.5MB, alloc=396.3MB, time=41.19 memory used=2352.4MB, alloc=396.3MB, time=41.50 memory used=2404.8MB, alloc=396.3MB, time=41.79 memory used=2470.3MB, alloc=396.3MB, time=42.57 memory used=2541.8MB, alloc=396.3MB, time=44.93 memory used=2590.3MB, alloc=396.3MB, time=45.23 memory used=2646.2MB, alloc=396.3MB, time=45.52 memory used=2684.4MB, alloc=396.3MB, time=45.75 memory used=2752.3MB, alloc=396.3MB, time=47.92 memory used=2799.8MB, alloc=396.3MB, time=48.21 memory used=2854.5MB, alloc=396.3MB, time=48.50 memory used=2893.8MB, alloc=396.3MB, time=48.74 memory used=3058.2MB, alloc=396.3MB, time=53.52 memory used=3148.5MB, alloc=396.3MB, time=54.66 memory used=3246.8MB, alloc=420.3MB, time=57.06 memory used=3370.7MB, alloc=420.3MB, time=59.35 memory used=3492.1MB, alloc=420.3MB, time=62.03 memory used=3612.7MB, alloc=444.3MB, time=64.53 memory used=3720.6MB, alloc=444.3MB, time=66.86 memory used=3847.4MB, alloc=444.3MB, time=68.81 memory used=3973.5MB, alloc=444.3MB, time=71.41 memory used=4086.0MB, alloc=468.3MB, time=73.56 memory used=4196.9MB, alloc=468.3MB, time=75.73 memory used=4289.9MB, alloc=468.3MB, time=78.03 memory used=4380.1MB, alloc=468.3MB, time=79.88 memory used=4500.4MB, alloc=492.3MB, time=81.90 memory used=4593.1MB, alloc=492.3MB, time=84.03 memory used=4675.3MB, alloc=492.3MB, time=85.83 memory used=4758.8MB, alloc=492.3MB, time=87.42 memory used=4894.7MB, alloc=492.3MB, time=89.61 memory used=4984.9MB, alloc=492.3MB, time=90.30 memory used=5063.7MB, alloc=492.3MB, time=90.94 memory used=5175.3MB, alloc=492.3MB, time=91.91 memory used=5256.1MB, alloc=492.3MB, time=92.52 memory used=5391.9MB, alloc=492.3MB, time=103.91 memory used=5478.6MB, alloc=492.3MB, time=104.58 memory used=5560.0MB, alloc=492.3MB, time=105.17 memory used=5666.6MB, alloc=492.3MB, time=106.09 memory used=5756.9MB, alloc=492.3MB, time=106.77 memory used=5835.6MB, alloc=492.3MB, time=107.38 memory used=5947.7MB, alloc=492.3MB, time=108.38 memory used=6030.1MB, alloc=492.3MB, time=109.01 memory used=6167.5MB, alloc=492.3MB, time=121.06 memory used=6252.9MB, alloc=492.3MB, time=121.68 memory used=6339.3MB, alloc=492.3MB, time=122.29 memory used=6417.4MB, alloc=492.3MB, time=122.82 memory used=6530.5MB, alloc=492.3MB, time=124.19 memory used=6627.2MB, alloc=492.3MB, time=124.88 memory used=6697.6MB, alloc=492.3MB, time=125.51 memory used=6782.3MB, alloc=492.3MB, time=126.13 memory used=6879.3MB, alloc=492.3MB, time=126.76 memory used=6950.6MB, alloc=492.3MB, time=127.29 memory used=7029.5MB, alloc=492.3MB, time=129.21 memory used=7158.2MB, alloc=492.3MB, time=132.12 memory used=7246.6MB, alloc=492.3MB, time=133.95 memory used=7314.8MB, alloc=492.3MB, time=135.54 memory used=7384.6MB, alloc=492.3MB, time=137.50 memory used=7437.4MB, alloc=492.3MB, time=139.32 memory used=7489.2MB, alloc=492.3MB, time=140.91 memory used=7560.8MB, alloc=492.3MB, time=142.47 memory used=7673.7MB, alloc=492.3MB, time=143.87 memory used=7786.1MB, alloc=492.3MB, time=146.00 memory used=7891.7MB, alloc=492.3MB, time=147.45 memory used=8006.9MB, alloc=516.3MB, time=151.46 memory used=8121.1MB, alloc=516.3MB, time=156.37 memory used=8229.6MB, alloc=516.3MB, time=157.10 memory used=8308.5MB, alloc=516.3MB, time=157.72 memory used=8406.5MB, alloc=516.3MB, time=158.37 memory used=8539.7MB, alloc=516.3MB, time=161.73 memory used=8635.7MB, alloc=516.3MB, time=162.55 memory used=8750.6MB, alloc=516.3MB, time=163.39 memory used=8824.8MB, alloc=516.3MB, time=164.14 memory used=8907.7MB, alloc=516.3MB, time=164.88 memory used=8999.9MB, alloc=516.3MB, time=165.66 memory used=9100.9MB, alloc=516.3MB, time=166.39 memory used=9214.1MB, alloc=516.3MB, time=167.15 memory used=9339.3MB, alloc=516.3MB, time=167.94 memory used=9420.8MB, alloc=516.3MB, time=168.62 memory used=9488.7MB, alloc=540.3MB, time=169.26 memory used=9572.4MB, alloc=540.3MB, time=169.93 memory used=9662.8MB, alloc=540.3MB, time=170.61 memory used=9760.1MB, alloc=540.3MB, time=171.28 memory used=9863.1MB, alloc=540.3MB, time=171.94 memory used=9970.9MB, alloc=540.3MB, time=172.63 memory used=10086.7MB, alloc=540.3MB, time=173.33 |\^/| 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(); 1428273490 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 3 F := [13 x y - 12 x y z - 16 z - 7 x, 13 x y - 16 y - 4 y z + 3 z, 2 9 y z + 8 x z + 10 x + 5] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 G := [-17 x y + 17 y + 3 y + 17 z, -5 x y + 19 y + 4 y z - 4 z, 2 3 -6 x y + 10 z + 6 z - 18] > Problem := [F,G]; 2 3 2 3 Problem := [[13 x y - 12 x y z - 16 z - 7 x, 13 x y - 16 y - 4 y z + 3 z, 2 2 2 9 y z + 8 x z + 10 x + 5], [-17 x y + 17 y + 3 y + 17 z, 2 3 2 3 -5 x y + 19 y + 4 y z - 4 z, -6 x y + 10 z + 6 z - 18]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=31.6MB, alloc=40.3MB, time=1.04 memory used=57.7MB, alloc=44.3MB, time=1.74 memory used=82.4MB, alloc=68.3MB, time=2.40 memory used=131.1MB, alloc=76.3MB, time=3.70 memory used=178.7MB, alloc=100.3MB, time=4.94 memory used=251.9MB, alloc=100.3MB, time=6.81 memory used=322.4MB, alloc=100.3MB, time=8.69 memory used=392.0MB, alloc=124.3MB, time=10.49 memory used=473.5MB, alloc=380.3MB, time=12.02 memory used=578.1MB, alloc=380.3MB, time=14.46 memory used=667.2MB, alloc=404.3MB, time=16.70 memory used=791.3MB, alloc=404.3MB, time=19.35 memory used=902.4MB, alloc=404.3MB, time=21.54 memory used=1027.6MB, alloc=404.3MB, time=24.56 memory used=1137.7MB, alloc=428.3MB, time=27.57 memory used=1254.5MB, alloc=428.3MB, time=29.54 memory used=1361.7MB, alloc=428.3MB, time=31.38 memory used=1492.6MB, alloc=452.3MB, time=34.55 memory used=1601.5MB, alloc=452.3MB, time=37.06 memory used=1736.5MB, alloc=476.3MB, time=40.80 memory used=1850.5MB, alloc=476.3MB, time=43.95 memory used=1944.3MB, alloc=500.3MB, time=46.10 memory used=2032.6MB, alloc=500.3MB, time=48.14 memory used=2116.6MB, alloc=500.3MB, time=49.78 memory used=2223.5MB, alloc=524.3MB, time=53.25 memory used=2313.0MB, alloc=524.3MB, time=55.62 memory used=2406.0MB, alloc=524.3MB, time=58.30 memory used=2466.8MB, alloc=524.3MB, time=60.13 memory used=2539.6MB, alloc=524.3MB, time=62.04 memory used=2617.3MB, alloc=524.3MB, time=64.39 memory used=2682.4MB, alloc=524.3MB, time=66.61 memory used=2744.3MB, alloc=524.3MB, time=68.83 memory used=2810.4MB, alloc=524.3MB, time=71.02 memory used=2869.3MB, alloc=524.3MB, time=72.74 memory used=2927.7MB, alloc=524.3MB, time=74.40 memory used=2992.1MB, alloc=524.3MB, time=75.98 memory used=3065.5MB, alloc=524.3MB, time=78.46 memory used=3190.4MB, alloc=548.3MB, time=80.50 memory used=3341.6MB, alloc=548.3MB, time=82.50 memory used=3487.6MB, alloc=548.3MB, time=85.85 memory used=3713.0MB, alloc=548.3MB, time=92.05 memory used=3959.8MB, alloc=572.3MB, time=97.27 memory used=4190.1MB, alloc=596.3MB, time=101.85 memory used=4354.6MB, alloc=596.3MB, time=103.99 memory used=4510.7MB, alloc=596.3MB, time=107.75 memory used=4726.1MB, alloc=596.3MB, time=113.20 memory used=4923.6MB, alloc=620.3MB, time=118.06 memory used=5089.9MB, alloc=620.3MB, time=122.48 memory used=5240.7MB, alloc=644.3MB, time=126.49 |\^/| 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(); 1428273790 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [20 x y - 12 x + 3 z - 20, -15 x z + 18 y z + 7 x y, 2 2 -12 y - z - 10 y - 3] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 G := [-19 x y - 3 x y z - 7 x - 2 x z, -11 x y - 17 x - 8 y + 7, 2 2 2 -17 y z + 14 x - 13 y - 13] > Problem := [F,G]; 2 2 2 2 Problem := [[20 x y - 12 x + 3 z - 20, -15 x z + 18 y z + 7 x y, 2 2 2 2 -12 y - z - 10 y - 3], [-19 x y - 3 x y z - 7 x - 2 x z, 2 2 2 2 2 2 -11 x y - 17 x - 8 y + 7, -17 y z + 14 x - 13 y - 13]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.31 memory used=26.2MB, alloc=32.3MB, time=0.88 memory used=46.3MB, alloc=32.3MB, time=1.39 memory used=64.5MB, alloc=56.3MB, time=1.91 memory used=105.5MB, alloc=60.3MB, time=2.99 memory used=146.5MB, alloc=60.3MB, time=4.04 memory used=186.4MB, alloc=84.3MB, time=5.10 memory used=222.5MB, alloc=84.3MB, time=6.02 memory used=282.5MB, alloc=92.3MB, time=7.64 memory used=346.4MB, alloc=116.3MB, time=9.33 memory used=427.0MB, alloc=116.3MB, time=11.47 memory used=497.0MB, alloc=396.3MB, time=13.44 memory used=609.1MB, alloc=396.3MB, time=16.28 memory used=721.5MB, alloc=420.3MB, time=19.09 memory used=856.4MB, alloc=420.3MB, time=22.30 memory used=989.7MB, alloc=444.3MB, time=25.57 memory used=1122.6MB, alloc=468.3MB, time=29.30 memory used=1248.8MB, alloc=468.3MB, time=32.78 memory used=1381.7MB, alloc=468.3MB, time=35.26 memory used=1503.9MB, alloc=468.3MB, time=38.32 memory used=1611.2MB, alloc=492.3MB, time=41.34 memory used=1717.5MB, alloc=492.3MB, time=44.41 memory used=1811.0MB, alloc=492.3MB, time=47.12 memory used=1914.4MB, alloc=492.3MB, time=49.82 memory used=1983.1MB, alloc=492.3MB, time=51.81 memory used=2062.0MB, alloc=492.3MB, time=54.08 memory used=2150.7MB, alloc=492.3MB, time=56.72 memory used=2234.2MB, alloc=492.3MB, time=58.87 memory used=2337.2MB, alloc=492.3MB, time=61.16 memory used=2410.3MB, alloc=492.3MB, time=62.91 memory used=2510.7MB, alloc=492.3MB, time=65.55 memory used=2599.9MB, alloc=516.3MB, time=67.93 memory used=2679.7MB, alloc=516.3MB, time=70.87 memory used=2743.1MB, alloc=516.3MB, time=73.17 memory used=2812.1MB, alloc=516.3MB, time=75.80 memory used=2869.1MB, alloc=516.3MB, time=78.00 memory used=2937.3MB, alloc=516.3MB, time=79.66 memory used=3001.6MB, alloc=516.3MB, time=81.64 memory used=3079.6MB, alloc=516.3MB, time=83.01 memory used=3149.7MB, alloc=516.3MB, time=84.60 memory used=3243.2MB, alloc=516.3MB, time=86.39 memory used=3344.6MB, alloc=516.3MB, time=88.30 memory used=3451.6MB, alloc=516.3MB, time=91.45 memory used=3541.5MB, alloc=516.3MB, time=92.20 memory used=3641.4MB, alloc=516.3MB, time=93.20 memory used=3717.6MB, alloc=516.3MB, time=94.84 memory used=3771.5MB, alloc=516.3MB, time=96.46 memory used=3824.4MB, alloc=516.3MB, time=98.43 memory used=3905.3MB, alloc=516.3MB, time=100.12 memory used=4131.9MB, alloc=540.3MB, time=105.82 memory used=4254.4MB, alloc=564.3MB, time=107.51 memory used=4391.0MB, alloc=564.3MB, time=108.89 memory used=4542.4MB, alloc=564.3MB, time=110.89 memory used=4762.2MB, alloc=564.3MB, time=115.75 memory used=5015.2MB, alloc=564.3MB, time=120.78 memory used=5260.6MB, alloc=588.3MB, time=127.65 memory used=5452.5MB, alloc=612.3MB, time=133.83 memory used=5661.7MB, alloc=612.3MB, time=138.15 memory used=5835.4MB, alloc=612.3MB, time=140.40 memory used=5984.2MB, alloc=612.3MB, time=145.38 |\^/| 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(); 1428274090 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [20 x y z + 3 x z + x - 3 y z, 2 x z + 7 y z - 16 z , 2 2 2 5 x y - 19 x y + 14 z - 7 y] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 G := [11 y z + 9 y z + 4 y z - 9 x, -7 y + 2 y z + 17 x - 1, 2 -x y z + 12 z - 14 z] > Problem := [F,G]; 2 2 2 2 Problem := [[20 x y z + 3 x z + x - 3 y z, 2 x z + 7 y z - 16 z , 2 2 2 2 2 5 x y - 19 x y + 14 z - 7 y], [11 y z + 9 y z + 4 y z - 9 x, 3 2 2 2 -7 y + 2 y z + 17 x - 1, -x y z + 12 z - 14 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.31 memory used=27.0MB, alloc=32.3MB, time=0.90 memory used=48.2MB, alloc=32.3MB, time=1.46 memory used=68.4MB, alloc=56.3MB, time=2.02 memory used=109.3MB, alloc=60.3MB, time=3.13 memory used=148.3MB, alloc=84.3MB, time=4.20 memory used=208.1MB, alloc=92.3MB, time=5.86 memory used=270.2MB, alloc=116.3MB, time=7.49 memory used=353.6MB, alloc=116.3MB, time=9.83 memory used=429.0MB, alloc=396.3MB, time=12.09 memory used=535.6MB, alloc=420.3MB, time=15.22 memory used=668.9MB, alloc=444.3MB, time=19.07 memory used=817.4MB, alloc=468.3MB, time=23.63 memory used=963.6MB, alloc=468.3MB, time=28.16 memory used=1108.0MB, alloc=492.3MB, time=32.76 memory used=1248.1MB, alloc=492.3MB, time=37.35 memory used=1352.6MB, alloc=492.3MB, time=40.73 memory used=1461.2MB, alloc=516.3MB, time=44.12 memory used=1562.3MB, alloc=516.3MB, time=47.39 memory used=1662.6MB, alloc=516.3MB, time=50.66 memory used=1755.1MB, alloc=516.3MB, time=53.72 memory used=1848.1MB, alloc=516.3MB, time=56.92 memory used=1929.0MB, alloc=540.3MB, time=59.86 memory used=2001.9MB, alloc=540.3MB, time=62.63 memory used=2072.0MB, alloc=540.3MB, time=65.23 memory used=2141.9MB, alloc=540.3MB, time=67.30 memory used=2219.5MB, alloc=540.3MB, time=70.38 memory used=2280.6MB, alloc=540.3MB, time=72.70 memory used=2355.9MB, alloc=540.3MB, time=75.44 memory used=2423.7MB, alloc=564.3MB, time=78.10 memory used=2473.8MB, alloc=564.3MB, time=80.01 memory used=2512.9MB, alloc=564.3MB, time=81.90 memory used=2721.5MB, alloc=588.3MB, time=88.64 memory used=2925.1MB, alloc=612.3MB, time=95.71 memory used=3146.8MB, alloc=636.3MB, time=104.28 memory used=3323.2MB, alloc=660.3MB, time=110.56 memory used=3493.8MB, alloc=684.3MB, time=116.92 memory used=3633.7MB, alloc=684.3MB, time=122.61 memory used=3792.6MB, alloc=684.3MB, time=128.51 memory used=3919.2MB, alloc=684.3MB, time=133.10 |\^/| 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(); 1428274390 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 F := [-18 x y + 9 x z - 15 x z + 14 z , y + 19 y z - 16 x - 3 z, 2 2 3 2 x y + 11 x z + 15 y + 7 x y] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 2 G := [-14 x + 6 x z - 18 z + 13 y, 10 x y z + 8 x z + 13 x - 5 y z, 2 2 3 2 20 x z - 20 x y + 4 y - 4 x ] > Problem := [F,G]; 2 2 2 3 2 Problem := [[-18 x y + 9 x z - 15 x z + 14 z , y + 19 y z - 16 x - 3 z, 2 2 3 3 2 3 2 x y + 11 x z + 15 y + 7 x y], [-14 x + 6 x z - 18 z + 13 y, 2 2 2 2 3 2 10 x y z + 8 x z + 13 x - 5 y z, 20 x z - 20 x y + 4 y - 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=0.30 memory used=24.1MB, alloc=32.3MB, time=0.73 memory used=46.9MB, alloc=32.3MB, time=1.44 memory used=62.3MB, alloc=32.3MB, time=1.59 memory used=76.5MB, alloc=32.3MB, time=1.72 memory used=88.5MB, alloc=32.3MB, time=1.78 memory used=102.2MB, alloc=32.3MB, time=1.90 memory used=126.1MB, alloc=32.3MB, time=2.58 memory used=143.5MB, alloc=32.3MB, time=2.86 memory used=168.5MB, alloc=36.3MB, time=3.56 memory used=184.1MB, alloc=36.3MB, time=3.71 memory used=197.9MB, alloc=36.3MB, time=3.82 memory used=218.7MB, alloc=36.3MB, time=4.15 memory used=239.2MB, alloc=60.3MB, time=4.60 memory used=284.3MB, alloc=68.3MB, time=5.44 memory used=326.7MB, alloc=69.6MB, time=7.32 memory used=356.5MB, alloc=69.6MB, time=7.49 memory used=380.2MB, alloc=69.6MB, time=7.61 memory used=419.0MB, alloc=69.6MB, time=8.09 memory used=469.4MB, alloc=69.6MB, time=9.43 memory used=498.2MB, alloc=69.6MB, time=9.65 memory used=547.3MB, alloc=69.6MB, time=10.85 memory used=575.9MB, alloc=69.6MB, time=11.16 memory used=629.3MB, alloc=69.6MB, time=11.86 memory used=684.6MB, alloc=69.6MB, time=12.74 memory used=740.8MB, alloc=69.6MB, time=14.38 memory used=790.0MB, alloc=69.6MB, time=15.87 memory used=837.7MB, alloc=69.6MB, time=16.76 memory used=885.4MB, alloc=69.6MB, time=17.64 memory used=926.2MB, alloc=69.6MB, time=18.53 memory used=968.6MB, alloc=93.6MB, time=19.49 memory used=1016.5MB, alloc=93.6MB, time=20.77 memory used=1070.7MB, alloc=93.6MB, time=21.77 memory used=1146.7MB, alloc=93.6MB, time=23.16 memory used=1184.1MB, alloc=93.6MB, time=23.49 memory used=1243.4MB, alloc=93.6MB, time=24.51 memory used=1312.3MB, alloc=93.6MB, time=25.65 memory used=1357.0MB, alloc=93.6MB, time=27.07 memory used=1407.3MB, alloc=93.6MB, time=28.78 memory used=1447.5MB, alloc=93.6MB, time=29.11 memory used=1513.9MB, alloc=93.6MB, time=30.82 memory used=1550.8MB, alloc=93.6MB, time=31.24 memory used=1581.7MB, alloc=93.6MB, time=31.44 memory used=1627.9MB, alloc=93.6MB, time=32.59 memory used=1692.3MB, alloc=117.6MB, time=34.04 memory used=1773.7MB, alloc=373.6MB, time=36.01 memory used=1859.7MB, alloc=373.6MB, time=37.40 memory used=1952.4MB, alloc=397.6MB, time=39.02 memory used=2067.3MB, alloc=421.6MB, time=41.62 memory used=2165.6MB, alloc=421.6MB, time=44.45 memory used=2236.3MB, alloc=421.6MB, time=45.08 memory used=2329.2MB, alloc=421.6MB, time=47.79 memory used=2401.0MB, alloc=421.6MB, time=48.44 memory used=2497.3MB, alloc=421.6MB, time=51.27 memory used=2585.0MB, alloc=421.6MB, time=54.10 memory used=2654.7MB, alloc=421.6MB, time=54.56 memory used=2761.4MB, alloc=421.6MB, time=57.76 memory used=2839.1MB, alloc=421.6MB, time=58.50 memory used=2900.6MB, alloc=421.6MB, time=58.83 memory used=2976.4MB, alloc=421.6MB, time=59.52 memory used=3035.7MB, alloc=421.6MB, time=59.84 memory used=3134.1MB, alloc=421.6MB, time=66.70 memory used=3194.6MB, alloc=421.6MB, time=67.03 memory used=3253.0MB, alloc=421.6MB, time=67.30 memory used=3317.9MB, alloc=421.6MB, time=67.91 memory used=3389.5MB, alloc=421.6MB, time=68.30 memory used=3459.5MB, alloc=421.6MB, time=68.90 memory used=3523.7MB, alloc=421.6MB, time=69.24 memory used=3630.4MB, alloc=421.6MB, time=76.77 memory used=3748.2MB, alloc=421.6MB, time=77.94 memory used=3815.4MB, alloc=421.6MB, time=78.27 memory used=3864.3MB, alloc=421.6MB, time=78.52 memory used=3936.8MB, alloc=421.6MB, time=79.14 memory used=3997.7MB, alloc=421.6MB, time=79.48 memory used=4072.0MB, alloc=421.6MB, time=80.20 memory used=4132.0MB, alloc=421.6MB, time=80.55 memory used=4298.3MB, alloc=421.6MB, time=88.89 memory used=4358.9MB, alloc=421.6MB, time=89.21 memory used=4418.7MB, alloc=421.6MB, time=89.49 memory used=4474.0MB, alloc=421.6MB, time=89.75 memory used=4551.7MB, alloc=421.6MB, time=90.47 memory used=4614.2MB, alloc=421.6MB, time=91.15 memory used=4686.2MB, alloc=421.6MB, time=91.54 memory used=4755.8MB, alloc=421.6MB, time=96.96 memory used=4913.8MB, alloc=421.6MB, time=100.59 memory used=4977.6MB, alloc=421.6MB, time=100.91 memory used=5029.0MB, alloc=421.6MB, time=101.17 memory used=5116.6MB, alloc=421.6MB, time=102.24 memory used=5273.9MB, alloc=421.6MB, time=106.24 memory used=5437.4MB, alloc=421.6MB, time=109.38 memory used=5574.8MB, alloc=421.6MB, time=119.14 memory used=5632.1MB, alloc=421.6MB, time=119.48 memory used=5694.1MB, alloc=421.6MB, time=119.81 memory used=5741.3MB, alloc=421.6MB, time=120.08 memory used=5861.1MB, alloc=421.6MB, time=121.71 memory used=6002.6MB, alloc=421.6MB, time=124.28 memory used=6111.2MB, alloc=421.6MB, time=127.84 memory used=6167.2MB, alloc=421.6MB, time=128.17 memory used=6302.0MB, alloc=445.6MB, time=130.42 memory used=6477.9MB, alloc=445.6MB, time=134.46 memory used=6601.9MB, alloc=445.6MB, time=138.05 memory used=6700.1MB, alloc=445.6MB, time=140.59 memory used=6775.6MB, alloc=445.6MB, time=141.27 memory used=6875.8MB, alloc=445.6MB, time=142.74 memory used=6942.9MB, alloc=445.6MB, time=143.14 memory used=7029.8MB, alloc=445.6MB, time=143.88 memory used=7106.0MB, alloc=445.6MB, time=149.04 memory used=7196.1MB, alloc=445.6MB, time=151.15 memory used=7269.3MB, alloc=445.6MB, time=151.54 memory used=7325.0MB, alloc=445.6MB, time=151.84 memory used=7408.8MB, alloc=445.6MB, time=152.48 memory used=7475.4MB, alloc=445.6MB, time=152.87 memory used=7563.3MB, alloc=445.6MB, time=153.94 memory used=7632.0MB, alloc=445.6MB, time=154.35 memory used=7708.8MB, alloc=445.6MB, time=155.01 memory used=7880.4MB, alloc=445.6MB, time=163.59 memory used=7948.9MB, alloc=445.6MB, time=163.98 memory used=8011.3MB, alloc=445.6MB, time=164.31 memory used=8090.9MB, alloc=445.6MB, time=165.17 memory used=8158.4MB, alloc=445.6MB, time=165.59 memory used=8240.5MB, alloc=445.6MB, time=166.39 memory used=8307.6MB, alloc=445.6MB, time=166.78 memory used=8484.5MB, alloc=445.6MB, time=175.21 memory used=8552.8MB, alloc=445.6MB, time=175.60 memory used=8610.7MB, alloc=445.6MB, time=175.92 |\^/| 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(); 1428274690 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 F := [11 x y - 8 x z + 20 y z + 13 y, 8 x y z - 8 y + 6 y z + 13 x y, 3 2 2 11 x - 3 y z + x + 4 x y] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 3 G := [19 x z + 13 y z + 14 z + 7 z , -17 x y z + y + 2 z + 17, 2 2 2 2 2 x y + 7 y z - 4 x - 9 y ] > Problem := [F,G]; 2 2 2 Problem := [[11 x y - 8 x z + 20 y z + 13 y, 3 2 3 2 2 8 x y z - 8 y + 6 y z + 13 x y, 11 x - 3 y z + x + 4 x y], [ 2 2 3 2 3 19 x z + 13 y z + 14 z + 7 z , -17 x y z + y + 2 z + 17, 2 2 2 2 2 x y + 7 y z - 4 x - 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=0.31 memory used=25.6MB, alloc=32.3MB, time=0.87 memory used=45.0MB, alloc=32.3MB, time=1.38 memory used=63.4MB, alloc=56.3MB, time=1.88 memory used=103.7MB, alloc=60.3MB, time=2.91 memory used=142.1MB, alloc=60.3MB, time=3.90 memory used=180.1MB, alloc=84.3MB, time=4.89 memory used=223.9MB, alloc=84.3MB, time=6.03 memory used=275.7MB, alloc=92.3MB, time=6.80 memory used=335.7MB, alloc=116.3MB, time=8.34 memory used=410.3MB, alloc=116.3MB, time=10.19 memory used=481.2MB, alloc=372.3MB, time=11.63 memory used=565.5MB, alloc=396.3MB, time=13.75 memory used=670.6MB, alloc=420.3MB, time=16.59 memory used=795.7MB, alloc=444.3MB, time=19.63 memory used=946.7MB, alloc=444.3MB, time=23.13 memory used=1072.3MB, alloc=444.3MB, time=26.34 memory used=1215.8MB, alloc=468.3MB, time=29.61 memory used=1344.9MB, alloc=468.3MB, time=32.34 memory used=1452.3MB, alloc=468.3MB, time=35.66 memory used=1543.8MB, alloc=468.3MB, time=38.25 memory used=1641.3MB, alloc=492.3MB, time=41.30 memory used=1735.9MB, alloc=492.3MB, time=44.20 memory used=1812.7MB, alloc=492.3MB, time=46.31 memory used=1886.1MB, alloc=492.3MB, time=48.67 memory used=1964.0MB, alloc=492.3MB, time=51.29 memory used=2044.0MB, alloc=492.3MB, time=54.07 memory used=2115.4MB, alloc=516.3MB, time=56.61 memory used=2179.4MB, alloc=516.3MB, time=58.75 memory used=2233.7MB, alloc=516.3MB, time=60.77 memory used=2278.3MB, alloc=516.3MB, time=62.49 memory used=2329.8MB, alloc=516.3MB, time=64.11 memory used=2386.4MB, alloc=516.3MB, time=65.93 memory used=2448.8MB, alloc=516.3MB, time=67.87 memory used=2652.3MB, alloc=540.3MB, time=73.62 memory used=2848.3MB, alloc=564.3MB, time=78.09 memory used=3046.2MB, alloc=588.3MB, time=84.11 memory used=3252.1MB, alloc=612.3MB, time=90.19 memory used=3442.6MB, alloc=636.3MB, time=95.90 memory used=3709.5MB, alloc=660.3MB, time=102.47 |\^/| 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(); 1428274990 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 3 F := [11 x y + 13 y - 17 z + 16 y, -6 x z + 3 x y z + 2 z - 12 x, 2 2 19 x y - y z + 18 x z - 5 y z] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 G := [-8 x y - 13 y - 17 x z + 12, y z + 12 y - 7 z, 3 2 2 12 z - 16 x + 8 y + 17 x] > Problem := [F,G]; 2 2 2 2 3 Problem := [[11 x y + 13 y - 17 z + 16 y, -6 x z + 3 x y z + 2 z - 12 x, 2 2 2 3 19 x y - y z + 18 x z - 5 y z], [-8 x y - 13 y - 17 x z + 12, 2 3 2 2 y z + 12 y - 7 z, 12 z - 16 x + 8 y + 17 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.31 memory used=27.3MB, alloc=34.3MB, time=0.78 memory used=45.8MB, alloc=34.3MB, time=1.18 memory used=62.4MB, alloc=34.3MB, time=1.36 memory used=85.2MB, alloc=38.3MB, time=1.96 memory used=108.3MB, alloc=38.3MB, time=2.45 memory used=125.2MB, alloc=38.3MB, time=2.55 memory used=143.5MB, alloc=38.3MB, time=2.69 memory used=165.8MB, alloc=38.3MB, time=3.67 memory used=175.6MB, alloc=38.3MB, time=3.73 memory used=186.5MB, alloc=62.3MB, time=3.81 memory used=229.8MB, alloc=62.3MB, time=4.70 memory used=288.3MB, alloc=70.3MB, time=6.78 memory used=332.2MB, alloc=70.3MB, time=7.75 memory used=364.4MB, alloc=70.3MB, time=8.16 memory used=397.8MB, alloc=70.3MB, time=9.62 memory used=419.3MB, alloc=70.3MB, time=9.72 memory used=444.2MB, alloc=70.3MB, time=9.83 memory used=475.4MB, alloc=70.3MB, time=10.08 memory used=504.5MB, alloc=70.3MB, time=10.30 memory used=530.1MB, alloc=70.3MB, time=10.43 memory used=565.0MB, alloc=70.3MB, time=11.91 memory used=586.7MB, alloc=70.3MB, time=12.02 memory used=610.7MB, alloc=70.3MB, time=12.12 memory used=646.7MB, alloc=70.3MB, time=12.68 memory used=695.3MB, alloc=70.3MB, time=13.65 memory used=738.3MB, alloc=70.3MB, time=14.57 memory used=776.1MB, alloc=70.3MB, time=15.49 memory used=814.4MB, alloc=70.3MB, time=16.55 memory used=844.0MB, alloc=70.3MB, time=17.16 memory used=883.5MB, alloc=70.3MB, time=18.01 memory used=927.8MB, alloc=94.3MB, time=19.00 memory used=997.5MB, alloc=94.3MB, time=20.16 memory used=1035.9MB, alloc=94.3MB, time=20.46 memory used=1078.5MB, alloc=94.3MB, time=20.83 memory used=1124.4MB, alloc=94.3MB, time=22.91 memory used=1161.2MB, alloc=94.3MB, time=23.16 memory used=1203.1MB, alloc=94.3MB, time=23.84 memory used=1260.9MB, alloc=94.3MB, time=25.21 memory used=1307.5MB, alloc=94.3MB, time=28.33 memory used=1339.4MB, alloc=94.3MB, time=28.50 memory used=1367.4MB, alloc=94.3MB, time=28.67 memory used=1421.8MB, alloc=94.7MB, time=29.82 memory used=1454.7MB, alloc=94.7MB, time=30.01 memory used=1507.6MB, alloc=94.7MB, time=31.33 memory used=1554.2MB, alloc=94.7MB, time=34.40 memory used=1586.0MB, alloc=94.7MB, time=34.58 memory used=1613.2MB, alloc=94.7MB, time=34.74 memory used=1661.4MB, alloc=94.7MB, time=35.25 memory used=1703.8MB, alloc=94.7MB, time=35.64 memory used=1749.0MB, alloc=94.7MB, time=37.69 memory used=1778.2MB, alloc=94.7MB, time=37.86 memory used=1821.1MB, alloc=94.7MB, time=38.31 memory used=1866.5MB, alloc=94.7MB, time=39.08 memory used=1917.8MB, alloc=94.7MB, time=39.88 memory used=1976.6MB, alloc=94.7MB, time=40.78 memory used=2041.6MB, alloc=94.7MB, time=42.99 memory used=2114.1MB, alloc=350.7MB, time=45.31 memory used=2194.1MB, alloc=350.7MB, time=48.12 memory used=2236.2MB, alloc=374.7MB, time=49.30 memory used=2309.8MB, alloc=374.7MB, time=50.38 memory used=2411.5MB, alloc=374.7MB, time=53.28 memory used=2496.8MB, alloc=374.7MB, time=55.43 memory used=2582.3MB, alloc=398.7MB, time=57.41 memory used=2670.9MB, alloc=398.7MB, time=58.63 memory used=2748.4MB, alloc=398.7MB, time=64.92 memory used=2796.9MB, alloc=398.7MB, time=65.20 memory used=2849.0MB, alloc=398.7MB, time=65.47 memory used=2893.1MB, alloc=398.7MB, time=65.70 memory used=2964.8MB, alloc=398.7MB, time=66.31 memory used=3029.2MB, alloc=398.7MB, time=67.86 memory used=3078.6MB, alloc=398.7MB, time=68.15 memory used=3149.3MB, alloc=398.7MB, time=69.51 memory used=3221.9MB, alloc=398.7MB, time=75.01 memory used=3270.8MB, alloc=398.7MB, time=75.29 memory used=3319.2MB, alloc=398.7MB, time=75.54 memory used=3372.0MB, alloc=398.7MB, time=75.96 memory used=3430.7MB, alloc=398.7MB, time=76.54 memory used=3492.7MB, alloc=398.7MB, time=77.13 memory used=3552.7MB, alloc=398.7MB, time=77.45 memory used=3650.1MB, alloc=398.7MB, time=79.61 memory used=3732.5MB, alloc=398.7MB, time=81.67 memory used=3808.3MB, alloc=398.7MB, time=82.65 memory used=3894.4MB, alloc=398.7MB, time=83.90 memory used=3950.7MB, alloc=398.7MB, time=84.28 memory used=4014.5MB, alloc=398.7MB, time=84.84 memory used=4071.7MB, alloc=398.7MB, time=85.22 memory used=4138.1MB, alloc=422.7MB, time=92.63 memory used=4234.7MB, alloc=422.7MB, time=121.56 memory used=4304.2MB, alloc=422.7MB, time=121.96 memory used=4361.5MB, alloc=422.7MB, time=122.31 memory used=4418.3MB, alloc=422.7MB, time=122.65 memory used=4484.4MB, alloc=422.7MB, time=123.00 memory used=4561.2MB, alloc=422.7MB, time=123.35 memory used=4624.0MB, alloc=422.7MB, time=123.66 memory used=4671.4MB, alloc=422.7MB, time=123.95 memory used=4722.1MB, alloc=422.7MB, time=124.22 memory used=4777.6MB, alloc=422.7MB, time=124.50 memory used=4837.6MB, alloc=422.7MB, time=124.78 memory used=4902.5MB, alloc=422.7MB, time=125.08 memory used=4993.2MB, alloc=422.7MB, time=125.68 memory used=5059.6MB, alloc=422.7MB, time=126.05 memory used=5143.6MB, alloc=422.7MB, time=126.65 memory used=5238.6MB, alloc=422.7MB, time=132.22 memory used=5306.3MB, alloc=422.7MB, time=132.61 memory used=5363.7MB, alloc=422.7MB, time=132.95 memory used=5438.7MB, alloc=422.7MB, time=133.31 memory used=5490.3MB, alloc=422.7MB, time=133.58 memory used=5577.3MB, alloc=422.7MB, time=134.40 memory used=5658.2MB, alloc=422.7MB, time=135.01 memory used=5730.1MB, alloc=422.7MB, time=135.44 memory used=5837.6MB, alloc=422.7MB, time=171.32 memory used=5908.9MB, alloc=422.7MB, time=171.80 memory used=5976.3MB, alloc=422.7MB, time=172.17 memory used=6029.0MB, alloc=422.7MB, time=172.51 memory used=6089.9MB, alloc=422.7MB, time=172.86 memory used=6161.5MB, alloc=422.7MB, time=173.21 memory used=6238.6MB, alloc=422.7MB, time=173.57 memory used=6283.4MB, alloc=422.7MB, time=173.84 memory used=6331.7MB, alloc=422.7MB, time=174.11 memory used=6383.9MB, alloc=422.7MB, time=174.39 memory used=6440.1MB, alloc=422.7MB, time=174.68 memory used=6501.1MB, alloc=422.7MB, time=174.97 memory used=6569.1MB, alloc=422.7MB, time=175.25 memory used=6645.0MB, alloc=422.7MB, time=175.95 memory used=6735.3MB, alloc=422.7MB, time=176.96 memory used=6799.7MB, alloc=422.7MB, time=177.35 memory used=6861.3MB, alloc=422.7MB, time=177.71 memory used=6946.1MB, alloc=422.7MB, time=178.55 memory used=7008.7MB, alloc=422.7MB, time=178.95 memory used=7072.2MB, alloc=422.7MB, time=179.31 memory used=7160.3MB, alloc=422.7MB, time=188.03 memory used=7226.5MB, alloc=422.7MB, time=188.41 memory used=7283.4MB, alloc=422.7MB, time=188.76 memory used=7355.1MB, alloc=422.7MB, time=189.11 memory used=7416.3MB, alloc=422.7MB, time=189.67 memory used=7496.7MB, alloc=422.7MB, time=190.41 memory used=7581.5MB, alloc=422.7MB, time=191.03 memory used=7647.9MB, alloc=422.7MB, time=191.42 memory used=7729.4MB, alloc=422.7MB, time=193.76 memory used=7810.4MB, alloc=422.7MB, time=194.41 memory used=7894.9MB, alloc=422.7MB, time=195.12 memory used=7965.4MB, alloc=422.7MB, time=195.52 memory used=8050.6MB, alloc=422.7MB, time=197.89 memory used=8124.7MB, alloc=422.7MB, time=198.45 memory used=8267.0MB, alloc=422.7MB, time=202.74 memory used=8324.7MB, alloc=422.7MB, time=203.11 |\^/| 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(); 1428275290 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 F := [-11 x z + 15 x y z + 5 x z - 5 y , -19 x y + 12 y + 19 y + 12, 2 2 2 2 x y - 5 y z + 18 y + 3 y z] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 3 G := [6 x y z - 14 x z + y - 4 y, -11 x y - 6 y - 13 x z - 16 y, 2 2 2 x - 19 y + 13 y z + 6 z ] > Problem := [F,G]; 2 2 3 2 2 Problem := [[-11 x z + 15 x y z + 5 x z - 5 y , -19 x y + 12 y + 19 y + 12, 2 2 2 2 3 2 x y - 5 y z + 18 y + 3 y z], [6 x y z - 14 x z + y - 4 y, 2 3 2 2 2 -11 x y - 6 y - 13 x z - 16 y, x - 19 y + 13 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=4.3MB, alloc=32.3MB, time=0.31 memory used=25.9MB, alloc=32.3MB, time=0.89 memory used=47.6MB, alloc=60.3MB, time=1.39 memory used=90.8MB, alloc=60.3MB, time=2.35 memory used=133.7MB, alloc=60.3MB, time=3.06 memory used=172.7MB, alloc=63.2MB, time=4.20 memory used=195.4MB, alloc=63.2MB, time=4.30 memory used=227.5MB, alloc=63.2MB, time=4.50 memory used=262.8MB, alloc=63.2MB, time=5.73 memory used=285.3MB, alloc=63.2MB, time=5.83 memory used=328.6MB, alloc=71.2MB, time=6.66 memory used=371.3MB, alloc=71.2MB, time=7.45 memory used=405.1MB, alloc=71.2MB, time=7.85 memory used=436.0MB, alloc=71.2MB, time=8.75 memory used=466.0MB, alloc=71.2MB, time=10.43 memory used=487.2MB, alloc=71.2MB, time=10.55 memory used=505.2MB, alloc=71.2MB, time=10.67 memory used=528.5MB, alloc=71.2MB, time=10.79 memory used=554.7MB, alloc=71.2MB, time=10.97 memory used=583.1MB, alloc=71.2MB, time=11.20 memory used=619.6MB, alloc=71.2MB, time=13.57 memory used=641.8MB, alloc=71.2MB, time=13.70 memory used=658.7MB, alloc=71.2MB, time=13.80 memory used=680.7MB, alloc=71.2MB, time=13.92 memory used=716.9MB, alloc=71.2MB, time=14.51 memory used=749.8MB, alloc=71.2MB, time=14.95 memory used=788.0MB, alloc=71.2MB, time=15.57 memory used=828.8MB, alloc=95.2MB, time=16.60 memory used=901.2MB, alloc=95.2MB, time=17.96 memory used=966.6MB, alloc=95.2MB, time=19.40 memory used=1009.1MB, alloc=95.2MB, time=20.71 memory used=1068.6MB, alloc=95.2MB, time=21.99 memory used=1144.2MB, alloc=119.2MB, time=23.22 memory used=1220.4MB, alloc=375.2MB, time=24.90 memory used=1309.3MB, alloc=375.2MB, time=27.01 memory used=1399.6MB, alloc=399.2MB, time=28.82 memory used=1503.4MB, alloc=399.2MB, time=31.43 memory used=1603.9MB, alloc=423.2MB, time=33.92 memory used=1700.5MB, alloc=423.2MB, time=35.13 memory used=1789.1MB, alloc=423.2MB, time=37.53 memory used=1897.1MB, alloc=423.2MB, time=39.31 memory used=1998.5MB, alloc=423.2MB, time=41.53 memory used=2137.9MB, alloc=447.2MB, time=44.40 memory used=2274.2MB, alloc=447.2MB, time=47.09 memory used=2360.4MB, alloc=447.2MB, time=47.74 memory used=2449.3MB, alloc=447.2MB, time=50.61 memory used=2545.7MB, alloc=447.2MB, time=53.67 memory used=2613.9MB, alloc=447.2MB, time=54.07 memory used=2751.9MB, alloc=447.2MB, time=58.94 memory used=2819.3MB, alloc=447.2MB, time=59.37 memory used=2977.1MB, alloc=471.2MB, time=61.69 memory used=3081.7MB, alloc=471.2MB, time=64.26 memory used=3199.2MB, alloc=471.2MB, time=67.09 memory used=3316.8MB, alloc=471.2MB, time=69.08 memory used=3426.6MB, alloc=471.2MB, time=71.44 memory used=3553.3MB, alloc=495.2MB, time=73.82 memory used=3681.9MB, alloc=495.2MB, time=76.13 memory used=3775.0MB, alloc=495.2MB, time=78.27 memory used=3872.2MB, alloc=495.2MB, time=80.60 memory used=3938.7MB, alloc=495.2MB, time=82.43 memory used=4040.7MB, alloc=495.2MB, time=84.47 memory used=4139.1MB, alloc=495.2MB, time=86.29 memory used=4265.2MB, alloc=495.2MB, time=89.62 memory used=4372.3MB, alloc=495.2MB, time=90.86 memory used=4469.1MB, alloc=495.2MB, time=92.31 memory used=4574.2MB, alloc=495.2MB, time=94.20 memory used=4691.8MB, alloc=495.2MB, time=96.21 memory used=4814.4MB, alloc=519.2MB, time=98.39 memory used=4954.1MB, alloc=519.2MB, time=101.24 memory used=5092.1MB, alloc=519.2MB, time=104.33 memory used=5203.5MB, alloc=519.2MB, time=105.99 memory used=5356.3MB, alloc=519.2MB, time=108.12 memory used=5485.5MB, alloc=543.2MB, time=110.84 memory used=5613.8MB, alloc=543.2MB, time=113.39 memory used=5738.2MB, alloc=543.2MB, time=114.97 memory used=5870.7MB, alloc=543.2MB, time=117.11 memory used=6006.8MB, alloc=543.2MB, time=119.31 memory used=6113.2MB, alloc=543.2MB, time=121.81 memory used=6232.2MB, alloc=543.2MB, time=124.42 memory used=6304.1MB, alloc=543.2MB, time=125.81 memory used=6386.9MB, alloc=543.2MB, time=127.99 memory used=6433.8MB, alloc=543.2MB, time=129.61 memory used=6472.7MB, alloc=543.2MB, time=130.89 memory used=6680.2MB, alloc=567.2MB, time=136.14 memory used=6870.5MB, alloc=591.2MB, time=141.14 memory used=7045.5MB, alloc=615.2MB, time=145.76 memory used=7227.6MB, alloc=615.2MB, time=149.40 memory used=7370.6MB, alloc=615.2MB, time=153.81 memory used=7525.6MB, alloc=615.2MB, time=156.72 memory used=7676.5MB, alloc=615.2MB, time=159.39 memory used=7823.7MB, alloc=615.2MB, time=161.60 |\^/| 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(); 1428275590 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; F := 3 2 2 2 [-18 x y z - 19 y + 7, -18 y z + 2 y z, -5 x y - 20 y z - 14 x z + 5 y] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 3 2 2 G := [-17 x y + 3 z + 7 y - y z, 13 x z + 15 y - 5 y z - 17 y , 3 3 10 x + 6 z + 17 x z + 7 y z] > Problem := [F,G]; Problem := [ 3 2 2 2 [-18 x y z - 19 y + 7, -18 y z + 2 y z, -5 x y - 20 y z - 14 x z + 5 y] 2 3 2 2 3 2 2 , [-17 x y + 3 z + 7 y - y z, 13 x z + 15 y - 5 y z - 17 y , 3 3 10 x + 6 z + 17 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=4.4MB, alloc=32.3MB, time=0.30 memory used=25.6MB, alloc=32.3MB, time=0.85 memory used=46.0MB, alloc=32.3MB, time=1.37 memory used=64.2MB, alloc=56.3MB, time=1.85 memory used=105.0MB, alloc=60.3MB, time=2.86 memory used=146.8MB, alloc=60.3MB, time=3.68 memory used=187.3MB, alloc=84.3MB, time=4.67 memory used=224.2MB, alloc=84.3MB, time=5.54 memory used=287.3MB, alloc=92.3MB, time=7.17 memory used=349.8MB, alloc=116.3MB, time=8.72 memory used=431.2MB, alloc=116.3MB, time=10.75 memory used=504.5MB, alloc=372.3MB, time=12.74 memory used=592.5MB, alloc=396.3MB, time=14.86 memory used=694.5MB, alloc=396.3MB, time=18.93 memory used=784.7MB, alloc=396.3MB, time=22.26 memory used=894.9MB, alloc=396.3MB, time=25.56 memory used=972.1MB, alloc=420.3MB, time=27.89 memory used=1075.3MB, alloc=420.3MB, time=30.49 memory used=1208.0MB, alloc=420.3MB, time=34.16 memory used=1309.6MB, alloc=420.3MB, time=38.26 memory used=1433.3MB, alloc=444.3MB, time=41.73 memory used=1580.4MB, alloc=444.3MB, time=45.35 memory used=1726.1MB, alloc=468.3MB, time=49.66 memory used=1834.5MB, alloc=468.3MB, time=52.43 memory used=1972.8MB, alloc=468.3MB, time=55.17 memory used=2114.4MB, alloc=492.3MB, time=59.37 memory used=2283.2MB, alloc=516.3MB, time=65.03 memory used=2412.6MB, alloc=516.3MB, time=68.56 memory used=2560.0MB, alloc=540.3MB, time=72.57 memory used=2667.4MB, alloc=540.3MB, time=75.51 memory used=2764.3MB, alloc=540.3MB, time=78.21 memory used=2893.1MB, alloc=540.3MB, time=82.16 memory used=3019.3MB, alloc=540.3MB, time=84.59 memory used=3124.8MB, alloc=540.3MB, time=87.27 memory used=3247.6MB, alloc=540.3MB, time=88.30 memory used=3365.7MB, alloc=540.3MB, time=93.16 memory used=3476.0MB, alloc=540.3MB, time=94.25 memory used=3661.6MB, alloc=540.3MB, time=95.80 memory used=3803.3MB, alloc=540.3MB, time=97.99 memory used=3924.2MB, alloc=540.3MB, time=102.52 memory used=4076.7MB, alloc=564.3MB, time=107.13 memory used=4199.6MB, alloc=564.3MB, time=109.65 memory used=4324.6MB, alloc=564.3MB, time=110.78 memory used=4570.2MB, alloc=564.3MB, time=113.55 memory used=4765.0MB, alloc=564.3MB, time=118.00 memory used=4913.6MB, alloc=564.3MB, time=123.62 memory used=5077.2MB, alloc=564.3MB, time=126.82 memory used=5234.7MB, alloc=564.3MB, time=129.35 memory used=5331.5MB, alloc=564.3MB, time=132.25 memory used=5441.4MB, alloc=564.3MB, time=136.20 |\^/| 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(); 1428275890 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 3 F := [-14 x y + 12 y + 13 y z + 8, -15 x y + y z + 17 z + 11 y, 2 2 2 -15 x y + 7 y z + 14 x y - 2 y ] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-18 x y - 14 x - 5 y - 16, -15 y z - 4 y z - 14 x - 4 y, 2 2 2 -13 x y - 5 y z - 13 y + 4] > Problem := [F,G]; 2 2 2 2 3 Problem := [[-14 x y + 12 y + 13 y z + 8, -15 x y + y z + 17 z + 11 y, 2 2 2 2 -15 x y + 7 y z + 14 x y - 2 y ], [-18 x y - 14 x - 5 y - 16, 2 2 2 2 -15 y z - 4 y z - 14 x - 4 y, -13 x y - 5 y z - 13 y + 4]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=32.1MB, alloc=40.3MB, time=1.03 memory used=59.7MB, alloc=44.3MB, time=1.72 memory used=85.4MB, alloc=68.3MB, time=2.38 memory used=137.4MB, alloc=76.3MB, time=3.64 memory used=189.1MB, alloc=76.3MB, time=4.78 memory used=241.7MB, alloc=76.3MB, time=5.97 memory used=287.9MB, alloc=100.3MB, time=7.06 memory used=359.1MB, alloc=100.3MB, time=8.94 memory used=429.6MB, alloc=380.3MB, time=10.80 memory used=527.0MB, alloc=380.3MB, time=13.12 memory used=620.6MB, alloc=380.3MB, time=15.05 memory used=719.0MB, alloc=404.3MB, time=17.52 memory used=795.9MB, alloc=404.3MB, time=19.04 memory used=922.3MB, alloc=404.3MB, time=21.84 memory used=1035.0MB, alloc=428.3MB, time=24.72 memory used=1153.5MB, alloc=428.3MB, time=27.43 memory used=1233.4MB, alloc=428.3MB, time=29.59 memory used=1363.8MB, alloc=428.3MB, time=32.23 memory used=1492.8MB, alloc=428.3MB, time=35.17 memory used=1618.7MB, alloc=452.3MB, time=38.43 memory used=1736.6MB, alloc=452.3MB, time=41.62 memory used=1853.0MB, alloc=476.3MB, time=45.08 memory used=1976.1MB, alloc=476.3MB, time=47.71 memory used=2077.4MB, alloc=476.3MB, time=50.34 memory used=2200.2MB, alloc=476.3MB, time=53.28 memory used=2312.0MB, alloc=476.3MB, time=56.03 memory used=2415.6MB, alloc=476.3MB, time=58.79 memory used=2513.1MB, alloc=500.3MB, time=61.54 memory used=2630.1MB, alloc=500.3MB, time=63.08 memory used=2773.4MB, alloc=500.3MB, time=65.61 memory used=2864.9MB, alloc=500.3MB, time=67.93 memory used=2958.2MB, alloc=500.3MB, time=70.47 memory used=3044.0MB, alloc=500.3MB, time=72.99 memory used=3121.8MB, alloc=500.3MB, time=75.56 memory used=3199.4MB, alloc=500.3MB, time=77.96 memory used=3276.1MB, alloc=500.3MB, time=80.07 memory used=3343.9MB, alloc=524.3MB, time=82.12 memory used=3412.8MB, alloc=524.3MB, time=84.09 memory used=3474.5MB, alloc=524.3MB, time=86.27 memory used=3540.4MB, alloc=524.3MB, time=88.26 memory used=3591.0MB, alloc=524.3MB, time=89.93 memory used=3640.0MB, alloc=524.3MB, time=91.57 memory used=3695.7MB, alloc=524.3MB, time=93.57 memory used=3767.2MB, alloc=524.3MB, time=96.27 memory used=3823.1MB, alloc=524.3MB, time=98.39 memory used=3871.9MB, alloc=524.3MB, time=100.11 memory used=4074.7MB, alloc=548.3MB, time=106.20 memory used=4243.4MB, alloc=572.3MB, time=111.02 memory used=4450.6MB, alloc=596.3MB, time=117.15 memory used=4664.1MB, alloc=620.3MB, time=122.93 memory used=4813.2MB, alloc=644.3MB, time=126.99 memory used=4959.3MB, alloc=644.3MB, time=131.02 memory used=5163.8MB, alloc=644.3MB, time=136.50 memory used=5299.6MB, alloc=644.3MB, time=140.39 memory used=5411.4MB, alloc=668.3MB, time=143.40 |\^/| 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(); 1428276190 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [6 x z - 4 x y - 11 y + 7, 13 y z + 13 x y - 9 x z + 19 x, 2 2 2 8 y z - 16 y z - 12 x y + 12 z ] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 3 2 G := [-19 x z + 20 x z - 5 y z - 4 y, x y - 19 y - 17 y z + 12 x z, 2 2 -8 x y - 20 x z + 14 y z - 3] > Problem := [F,G]; 2 2 Problem := [[6 x z - 4 x y - 11 y + 7, 13 y z + 13 x y - 9 x z + 19 x, 2 2 2 2 2 2 8 y z - 16 y z - 12 x y + 12 z ], [-19 x z + 20 x z - 5 y z - 4 y, 2 3 2 2 2 x y - 19 y - 17 y z + 12 x z, -8 x y - 20 x z + 14 y z - 3]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.30 memory used=24.0MB, alloc=32.3MB, time=0.81 memory used=42.9MB, alloc=60.3MB, time=1.33 memory used=81.4MB, alloc=60.3MB, time=2.01 memory used=125.5MB, alloc=68.3MB, time=3.11 memory used=168.8MB, alloc=68.3MB, time=4.07 memory used=209.8MB, alloc=92.3MB, time=5.09 memory used=267.8MB, alloc=92.3MB, time=6.35 memory used=327.6MB, alloc=92.3MB, time=7.35 memory used=382.2MB, alloc=92.3MB, time=8.26 memory used=450.6MB, alloc=92.3MB, time=9.60 memory used=493.1MB, alloc=116.3MB, time=10.67 memory used=561.1MB, alloc=116.3MB, time=11.99 memory used=612.5MB, alloc=372.3MB, time=13.27 memory used=703.6MB, alloc=396.3MB, time=15.44 memory used=818.4MB, alloc=420.3MB, time=18.21 memory used=948.2MB, alloc=420.3MB, time=21.39 memory used=1079.1MB, alloc=420.3MB, time=23.55 memory used=1157.8MB, alloc=420.3MB, time=25.30 memory used=1280.5MB, alloc=444.3MB, time=27.68 memory used=1399.9MB, alloc=444.3MB, time=30.17 memory used=1515.2MB, alloc=444.3MB, time=32.97 memory used=1613.2MB, alloc=444.3MB, time=35.57 memory used=1716.1MB, alloc=468.3MB, time=37.96 memory used=1816.9MB, alloc=468.3MB, time=40.45 memory used=1922.3MB, alloc=468.3MB, time=42.86 memory used=2019.5MB, alloc=468.3MB, time=43.65 memory used=2113.8MB, alloc=468.3MB, time=46.73 memory used=2192.7MB, alloc=468.3MB, time=47.26 memory used=2314.4MB, alloc=468.3MB, time=49.38 memory used=2406.3MB, alloc=468.3MB, time=51.59 memory used=2510.0MB, alloc=468.3MB, time=53.50 memory used=2583.9MB, alloc=468.3MB, time=54.04 memory used=2675.7MB, alloc=468.3MB, time=55.06 memory used=2768.2MB, alloc=468.3MB, time=57.14 memory used=2887.7MB, alloc=468.3MB, time=60.32 memory used=2996.7MB, alloc=468.3MB, time=62.43 memory used=3092.0MB, alloc=492.3MB, time=64.31 memory used=3248.4MB, alloc=492.3MB, time=68.41 memory used=3314.6MB, alloc=492.3MB, time=70.29 memory used=3381.9MB, alloc=492.3MB, time=72.22 memory used=3446.5MB, alloc=492.3MB, time=74.11 memory used=3509.2MB, alloc=492.3MB, time=75.98 memory used=3559.8MB, alloc=492.3MB, time=77.71 memory used=3630.4MB, alloc=492.3MB, time=79.26 memory used=3703.7MB, alloc=492.3MB, time=80.54 memory used=3814.1MB, alloc=492.3MB, time=81.64 memory used=3898.8MB, alloc=492.3MB, time=85.73 memory used=3981.5MB, alloc=492.3MB, time=86.45 memory used=4099.8MB, alloc=492.3MB, time=87.99 memory used=4143.1MB, alloc=492.3MB, time=89.49 memory used=4322.7MB, alloc=492.3MB, time=93.11 memory used=4509.2MB, alloc=516.3MB, time=97.22 memory used=4626.7MB, alloc=516.3MB, time=98.74 memory used=4749.4MB, alloc=516.3MB, time=101.52 memory used=4954.6MB, alloc=516.3MB, time=105.79 memory used=5159.8MB, alloc=540.3MB, time=109.63 memory used=5290.1MB, alloc=540.3MB, time=111.46 memory used=5404.3MB, alloc=540.3MB, time=113.04 memory used=5532.2MB, alloc=540.3MB, time=117.50 memory used=5636.8MB, alloc=540.3MB, time=118.48 memory used=5771.6MB, alloc=540.3MB, time=123.47 memory used=5873.2MB, alloc=540.3MB, time=124.35 memory used=6009.6MB, alloc=540.3MB, time=126.17 memory used=6212.8MB, alloc=564.3MB, time=130.96 memory used=6365.4MB, alloc=588.3MB, time=135.66 memory used=6506.9MB, alloc=612.3MB, time=139.10 memory used=6652.6MB, alloc=636.3MB, time=142.55 memory used=6835.4MB, alloc=636.3MB, time=147.14 memory used=6993.6MB, alloc=636.3MB, time=151.36 memory used=7119.8MB, alloc=660.3MB, time=154.93 |\^/| 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(); 1428276490 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 3 2 F := [18 x + 20 x z + 5 x y + 5, -20 x y + 17 x y z + 16 y + 6 y z, 3 3 2 6 x + 11 y - 5 y z - 18 z] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 3 2 2 G := [-14 y z - 19 z - 20 x y + 12 x, 13 x - 7 x y + 12 x z + 16 z, 2 2 -4 x z - 19 y ] > Problem := [F,G]; 3 2 2 2 3 2 Problem := [[18 x + 20 x z + 5 x y + 5, -20 x y + 17 x y z + 16 y + 6 y z, 3 3 2 2 3 6 x + 11 y - 5 y z - 18 z], [-14 y z - 19 z - 20 x y + 12 x, 3 2 2 2 2 13 x - 7 x y + 12 x z + 16 z, -4 x z - 19 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.5MB, alloc=32.3MB, time=0.90 memory used=46.5MB, alloc=32.3MB, time=1.41 memory used=65.7MB, alloc=60.3MB, time=1.94 memory used=107.4MB, alloc=68.3MB, time=3.06 memory used=149.3MB, alloc=92.3MB, time=4.11 memory used=215.8MB, alloc=92.3MB, time=5.72 memory used=282.7MB, alloc=348.3MB, time=7.35 memory used=348.5MB, alloc=372.3MB, time=9.04 memory used=438.8MB, alloc=396.3MB, time=11.33 memory used=557.0MB, alloc=396.3MB, time=13.87 memory used=668.5MB, alloc=420.3MB, time=16.73 memory used=803.1MB, alloc=420.3MB, time=19.70 memory used=933.8MB, alloc=444.3MB, time=22.57 memory used=1040.5MB, alloc=444.3MB, time=25.42 memory used=1142.3MB, alloc=444.3MB, time=28.11 memory used=1243.4MB, alloc=468.3MB, time=30.41 memory used=1341.7MB, alloc=468.3MB, time=32.69 memory used=1437.8MB, alloc=468.3MB, time=35.40 memory used=1535.3MB, alloc=468.3MB, time=37.96 memory used=1614.7MB, alloc=468.3MB, time=40.22 memory used=1715.7MB, alloc=492.3MB, time=43.09 memory used=1804.8MB, alloc=492.3MB, time=45.65 memory used=1879.0MB, alloc=492.3MB, time=47.44 memory used=1940.8MB, alloc=492.3MB, time=49.58 memory used=2022.7MB, alloc=492.3MB, time=51.97 memory used=2081.2MB, alloc=492.3MB, time=53.99 memory used=2149.1MB, alloc=492.3MB, time=56.13 memory used=2220.8MB, alloc=492.3MB, time=58.48 memory used=2275.7MB, alloc=492.3MB, time=60.18 memory used=2334.6MB, alloc=492.3MB, time=62.27 memory used=2375.4MB, alloc=492.3MB, time=63.91 memory used=2431.9MB, alloc=492.3MB, time=66.17 memory used=2623.9MB, alloc=516.3MB, time=71.20 memory used=2807.7MB, alloc=516.3MB, time=75.57 memory used=3012.4MB, alloc=540.3MB, time=80.78 memory used=3194.7MB, alloc=564.3MB, time=86.01 memory used=3360.0MB, alloc=564.3MB, time=90.22 memory used=3542.7MB, alloc=588.3MB, time=94.73 memory used=3707.2MB, alloc=588.3MB, time=99.53 memory used=3880.8MB, alloc=612.3MB, time=104.13 memory used=4041.0MB, alloc=612.3MB, time=108.35 memory used=4157.9MB, alloc=612.3MB, time=111.72 memory used=4302.5MB, alloc=612.3MB, time=115.21 memory used=4476.9MB, alloc=612.3MB, time=119.76 memory used=4619.4MB, alloc=636.3MB, time=124.85 memory used=4726.4MB, alloc=636.3MB, time=128.55 memory used=4855.8MB, alloc=636.3MB, time=133.66 memory used=4966.2MB, alloc=636.3MB, time=138.17 memory used=5038.3MB, alloc=636.3MB, time=141.24 memory used=5375.2MB, alloc=660.3MB, time=149.59 |\^/| 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(); 1428276790 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 F := [5 y z + 16 y z + 19 y, -4 y - 7 z - x, -8 y + 18 y z - 5 x + 5] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 3 2 3 G := [11 x + 17 y - 5 x y - 16 x z, 2 x y - 18 y - 2 x y - 16, 3 2 3 2 20 x + 8 x y + 6 y - 3 z ] > Problem := [F,G]; Problem := [ 2 2 2 3 [5 y z + 16 y z + 19 y, -4 y - 7 z - x, -8 y + 18 y z - 5 x + 5], [ 3 3 2 3 11 x + 17 y - 5 x y - 16 x z, 2 x y - 18 y - 2 x y - 16, 3 2 3 2 20 x + 8 x y + 6 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=0.31 memory used=24.4MB, alloc=32.3MB, time=0.81 memory used=43.9MB, alloc=60.3MB, time=1.32 memory used=87.6MB, alloc=60.3MB, time=2.14 memory used=129.8MB, alloc=68.3MB, time=2.91 memory used=173.5MB, alloc=68.3MB, time=3.72 memory used=212.5MB, alloc=68.3MB, time=4.25 memory used=249.2MB, alloc=68.3MB, time=5.78 memory used=270.9MB, alloc=68.3MB, time=5.90 memory used=297.4MB, alloc=68.3MB, time=6.11 memory used=321.8MB, alloc=68.3MB, time=6.42 memory used=345.1MB, alloc=68.3MB, time=6.56 memory used=387.2MB, alloc=68.3MB, time=7.39 memory used=432.2MB, alloc=68.3MB, time=8.40 memory used=463.7MB, alloc=68.3MB, time=8.76 memory used=494.0MB, alloc=92.3MB, time=10.57 memory used=534.5MB, alloc=92.3MB, time=10.87 memory used=573.2MB, alloc=92.3MB, time=11.02 memory used=635.4MB, alloc=92.3MB, time=12.13 memory used=720.6MB, alloc=92.3MB, time=13.42 memory used=809.1MB, alloc=93.3MB, time=16.31 memory used=868.3MB, alloc=93.3MB, time=17.70 memory used=929.3MB, alloc=93.3MB, time=18.59 memory used=981.2MB, alloc=93.3MB, time=19.31 memory used=1043.1MB, alloc=93.3MB, time=20.08 memory used=1105.3MB, alloc=93.3MB, time=21.43 memory used=1165.3MB, alloc=93.3MB, time=22.78 memory used=1228.4MB, alloc=117.3MB, time=24.28 memory used=1284.4MB, alloc=117.3MB, time=25.47 memory used=1335.8MB, alloc=373.3MB, time=26.57 memory used=1425.9MB, alloc=397.3MB, time=28.41 memory used=1540.4MB, alloc=421.3MB, time=30.80 memory used=1650.6MB, alloc=421.3MB, time=33.13 memory used=1734.9MB, alloc=421.3MB, time=34.87 memory used=1805.2MB, alloc=421.3MB, time=35.39 memory used=1919.5MB, alloc=421.3MB, time=37.66 memory used=2053.2MB, alloc=421.3MB, time=40.71 memory used=2168.4MB, alloc=445.3MB, time=42.92 memory used=2288.7MB, alloc=445.3MB, time=45.46 memory used=2371.4MB, alloc=445.3MB, time=46.52 memory used=2452.6MB, alloc=445.3MB, time=48.31 memory used=2539.8MB, alloc=445.3MB, time=50.56 memory used=2611.0MB, alloc=445.3MB, time=51.18 memory used=2690.4MB, alloc=445.3MB, time=51.87 memory used=2789.6MB, alloc=469.3MB, time=56.47 memory used=2878.1MB, alloc=469.3MB, time=57.03 memory used=2952.9MB, alloc=469.3MB, time=57.48 memory used=3057.7MB, alloc=469.3MB, time=58.28 memory used=3175.5MB, alloc=469.3MB, time=62.92 memory used=3251.1MB, alloc=469.3MB, time=63.35 memory used=3354.5MB, alloc=469.3MB, time=64.30 memory used=3517.2MB, alloc=469.3MB, time=67.42 memory used=3699.3MB, alloc=469.3MB, time=71.51 memory used=3843.5MB, alloc=469.3MB, time=75.80 memory used=4027.2MB, alloc=469.3MB, time=79.53 memory used=4173.2MB, alloc=469.3MB, time=82.15 memory used=4365.0MB, alloc=469.3MB, time=85.55 memory used=4460.0MB, alloc=469.3MB, time=88.77 memory used=4593.7MB, alloc=469.3MB, time=91.91 memory used=4675.6MB, alloc=493.3MB, time=93.76 memory used=4822.1MB, alloc=493.3MB, time=95.51 memory used=4921.3MB, alloc=493.3MB, time=96.29 memory used=5034.9MB, alloc=493.3MB, time=109.00 memory used=5119.7MB, alloc=493.3MB, time=109.60 memory used=5219.9MB, alloc=493.3MB, time=110.19 memory used=5285.1MB, alloc=493.3MB, time=110.68 memory used=5361.7MB, alloc=493.3MB, time=111.18 memory used=5451.3MB, alloc=493.3MB, time=111.70 memory used=5556.9MB, alloc=493.3MB, time=112.25 memory used=5746.9MB, alloc=493.3MB, time=113.50 memory used=5846.3MB, alloc=493.3MB, time=114.45 memory used=5931.7MB, alloc=493.3MB, time=115.06 memory used=6060.5MB, alloc=493.3MB, time=131.97 memory used=6142.6MB, alloc=493.3MB, time=132.57 memory used=6238.0MB, alloc=493.3MB, time=133.21 memory used=6305.0MB, alloc=493.3MB, time=133.71 memory used=6383.7MB, alloc=493.3MB, time=134.22 memory used=6475.8MB, alloc=493.3MB, time=134.74 memory used=6676.3MB, alloc=493.3MB, time=135.78 memory used=6774.0MB, alloc=493.3MB, time=136.69 memory used=6873.2MB, alloc=493.3MB, time=137.67 memory used=6967.6MB, alloc=493.3MB, time=138.36 memory used=7068.9MB, alloc=493.3MB, time=139.23 memory used=7165.8MB, alloc=493.3MB, time=144.75 memory used=7277.1MB, alloc=493.3MB, time=156.26 memory used=7362.9MB, alloc=493.3MB, time=156.87 memory used=7449.3MB, alloc=493.3MB, time=157.46 memory used=7520.3MB, alloc=493.3MB, time=157.99 memory used=7603.7MB, alloc=493.3MB, time=158.54 memory used=7700.9MB, alloc=493.3MB, time=159.10 memory used=7899.0MB, alloc=493.3MB, time=160.23 memory used=7983.8MB, alloc=493.3MB, time=160.85 memory used=8089.3MB, alloc=493.3MB, time=161.69 memory used=8206.8MB, alloc=493.3MB, time=177.92 memory used=8290.4MB, alloc=493.3MB, time=178.56 memory used=8385.1MB, alloc=493.3MB, time=179.18 memory used=8459.1MB, alloc=493.3MB, time=179.71 memory used=8532.2MB, alloc=493.3MB, time=180.24 memory used=8617.2MB, alloc=493.3MB, time=180.78 memory used=8717.0MB, alloc=493.3MB, time=181.35 memory used=8910.8MB, alloc=493.3MB, time=182.39 memory used=9003.9MB, alloc=493.3MB, time=183.29 memory used=9117.6MB, alloc=493.3MB, time=184.57 memory used=9236.5MB, alloc=493.3MB, time=186.88 memory used=9346.8MB, alloc=493.3MB, time=188.60 memory used=9439.0MB, alloc=493.3MB, time=189.44 memory used=9531.9MB, alloc=517.3MB, time=191.34 memory used=9656.7MB, alloc=517.3MB, time=193.57 memory used=9713.5MB, alloc=517.3MB, time=195.27 memory used=9796.7MB, alloc=517.3MB, time=197.58 memory used=9860.7MB, alloc=517.3MB, time=199.21 memory used=9911.8MB, alloc=517.3MB, time=200.64 memory used=9958.7MB, alloc=517.3MB, time=202.26 memory used=10003.1MB, alloc=517.3MB, time=203.88 memory used=10190.8MB, alloc=541.3MB, time=208.80 memory used=10410.0MB, alloc=541.3MB, time=213.03 |\^/| 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(); 1428277090 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 3 2 3 F := [-8 x y + 4 y - 20 z + 2 x z, 9 y z - 12 z + 5 x + 10 z, 3 2 13 x - 11 x y z - 9 y + 10 z] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 3 2 3 G := [-17 x + 5 x z - 6 y z + 3 z, 18 x - 11 x z - 13 z - 12, 3 3 3 2 -x + 11 y - 13 z - 18 x ] > Problem := [F,G]; 2 3 3 2 3 Problem := [[-8 x y + 4 y - 20 z + 2 x z, 9 y z - 12 z + 5 x + 10 z, 3 2 3 2 2 13 x - 11 x y z - 9 y + 10 z], [-17 x + 5 x z - 6 y z + 3 z, 3 2 3 3 3 3 2 18 x - 11 x z - 13 z - 12, -x + 11 y - 13 z - 18 x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.5MB, alloc=32.3MB, time=0.31 memory used=29.2MB, alloc=32.7MB, time=0.81 memory used=49.7MB, alloc=36.8MB, time=1.31 memory used=73.8MB, alloc=36.8MB, time=1.81 memory used=96.6MB, alloc=36.8MB, time=2.26 memory used=113.0MB, alloc=36.8MB, time=2.42 memory used=131.3MB, alloc=38.1MB, time=2.53 memory used=147.3MB, alloc=62.1MB, time=3.02 memory used=190.5MB, alloc=64.9MB, time=3.26 memory used=225.7MB, alloc=64.9MB, time=3.42 memory used=248.9MB, alloc=64.9MB, time=3.54 memory used=291.0MB, alloc=64.9MB, time=4.11 memory used=330.6MB, alloc=64.9MB, time=4.29 memory used=354.0MB, alloc=64.9MB, time=4.41 memory used=389.8MB, alloc=64.9MB, time=4.94 memory used=442.0MB, alloc=64.9MB, time=6.34 memory used=465.8MB, alloc=64.9MB, time=6.47 memory used=493.0MB, alloc=64.9MB, time=6.60 memory used=540.6MB, alloc=65.6MB, time=7.85 memory used=580.4MB, alloc=65.6MB, time=8.70 memory used=615.8MB, alloc=65.6MB, time=8.86 memory used=637.0MB, alloc=65.6MB, time=9.00 memory used=659.2MB, alloc=65.6MB, time=9.12 memory used=683.1MB, alloc=65.6MB, time=9.25 memory used=709.3MB, alloc=65.6MB, time=9.37 memory used=737.9MB, alloc=65.6MB, time=9.49 memory used=770.7MB, alloc=65.6MB, time=9.73 memory used=819.9MB, alloc=65.6MB, time=10.47 memory used=881.2MB, alloc=65.6MB, time=11.43 memory used=938.3MB, alloc=65.6MB, time=15.66 memory used=978.2MB, alloc=65.6MB, time=17.81 memory used=1004.1MB, alloc=65.6MB, time=17.95 memory used=1029.2MB, alloc=65.6MB, time=18.07 memory used=1064.3MB, alloc=65.6MB, time=26.53 memory used=1103.2MB, alloc=65.6MB, time=32.06 memory used=1125.2MB, alloc=65.6MB, time=32.19 memory used=1148.3MB, alloc=65.6MB, time=32.30 memory used=1174.8MB, alloc=65.6MB, time=32.45 memory used=1205.1MB, alloc=65.6MB, time=32.59 memory used=1234.5MB, alloc=65.6MB, time=32.72 memory used=1253.3MB, alloc=65.6MB, time=32.82 memory used=1291.6MB, alloc=65.6MB, time=33.58 memory used=1348.3MB, alloc=65.6MB, time=34.18 memory used=1405.0MB, alloc=65.6MB, time=35.31 memory used=1455.5MB, alloc=73.6MB, time=36.74 memory used=1499.2MB, alloc=73.6MB, time=37.78 memory used=1526.1MB, alloc=73.6MB, time=37.93 memory used=1546.9MB, alloc=73.6MB, time=38.05 memory used=1572.1MB, alloc=73.6MB, time=38.19 memory used=1588.6MB, alloc=73.6MB, time=38.29 memory used=1607.6MB, alloc=73.6MB, time=38.41 memory used=1638.0MB, alloc=73.6MB, time=38.77 memory used=1661.2MB, alloc=73.6MB, time=38.91 memory used=1683.9MB, alloc=73.6MB, time=39.04 memory used=1706.8MB, alloc=73.6MB, time=39.17 memory used=1723.7MB, alloc=73.6MB, time=39.29 memory used=1743.2MB, alloc=73.6MB, time=39.40 memory used=1809.9MB, alloc=73.6MB, time=43.44 memory used=1832.3MB, alloc=73.6MB, time=43.58 memory used=1854.3MB, alloc=73.6MB, time=43.70 memory used=1871.0MB, alloc=73.6MB, time=43.81 memory used=1890.7MB, alloc=73.6MB, time=43.93 memory used=1913.6MB, alloc=73.6MB, time=44.05 memory used=1937.3MB, alloc=73.6MB, time=44.17 memory used=1951.9MB, alloc=73.6MB, time=44.26 memory used=1967.1MB, alloc=73.6MB, time=44.35 memory used=1983.9MB, alloc=73.6MB, time=44.45 memory used=2002.5MB, alloc=73.6MB, time=44.54 memory used=2029.6MB, alloc=73.6MB, time=44.89 memory used=2052.5MB, alloc=73.6MB, time=45.15 memory used=2073.6MB, alloc=73.6MB, time=45.29 memory used=2089.9MB, alloc=81.9MB, time=45.67 memory used=2113.1MB, alloc=81.9MB, time=45.79 memory used=2135.5MB, alloc=81.9MB, time=45.91 memory used=2164.0MB, alloc=83.8MB, time=46.68 memory used=2181.7MB, alloc=83.8MB, time=46.78 memory used=2201.4MB, alloc=83.8MB, time=46.89 memory used=2232.0MB, alloc=83.8MB, time=47.03 memory used=2265.0MB, alloc=83.8MB, time=47.16 memory used=2300.6MB, alloc=83.8MB, time=47.29 memory used=2338.5MB, alloc=83.8MB, time=47.41 memory used=2378.7MB, alloc=83.8MB, time=47.54 memory used=2391.0MB, alloc=83.8MB, time=47.62 memory used=2402.9MB, alloc=83.8MB, time=47.70 memory used=2415.0MB, alloc=83.8MB, time=47.78 memory used=2459.9MB, alloc=83.8MB, time=49.24 memory used=2483.0MB, alloc=107.8MB, time=49.40 memory used=2516.3MB, alloc=107.8MB, time=49.59 memory used=2557.3MB, alloc=107.8MB, time=49.77 memory used=2601.0MB, alloc=107.8MB, time=49.95 memory used=2627.7MB, alloc=107.8MB, time=50.11 memory used=2656.1MB, alloc=107.8MB, time=50.26 memory used=2687.8MB, alloc=107.8MB, time=50.42 memory used=2721.1MB, alloc=107.8MB, time=50.56 memory used=2757.1MB, alloc=107.8MB, time=50.72 memory used=2796.1MB, alloc=107.8MB, time=50.89 memory used=2839.6MB, alloc=107.8MB, time=51.07 memory used=2885.9MB, alloc=107.8MB, time=51.23 memory used=2927.5MB, alloc=107.8MB, time=51.39 memory used=2952.7MB, alloc=107.8MB, time=51.50 memory used=2978.0MB, alloc=107.8MB, time=51.61 memory used=3004.6MB, alloc=107.8MB, time=51.73 memory used=3032.5MB, alloc=107.8MB, time=51.84 memory used=3062.5MB, alloc=107.8MB, time=51.97 memory used=3093.5MB, alloc=107.8MB, time=52.09 memory used=3126.4MB, alloc=107.8MB, time=52.21 memory used=3161.6MB, alloc=107.8MB, time=52.33 memory used=3207.0MB, alloc=107.8MB, time=53.21 memory used=3261.0MB, alloc=107.8MB, time=53.66 memory used=3294.6MB, alloc=107.8MB, time=53.85 memory used=3335.6MB, alloc=107.8MB, time=54.04 memory used=3379.1MB, alloc=107.8MB, time=54.23 memory used=3405.7MB, alloc=107.8MB, time=54.37 memory used=3434.1MB, alloc=107.8MB, time=54.52 memory used=3466.0MB, alloc=107.8MB, time=54.68 memory used=3499.3MB, alloc=107.8MB, time=54.84 memory used=3535.2MB, alloc=107.8MB, time=55.02 memory used=3574.2MB, alloc=107.8MB, time=55.19 memory used=3617.8MB, alloc=107.8MB, time=55.36 memory used=3664.1MB, alloc=107.8MB, time=55.52 memory used=3705.8MB, alloc=107.8MB, time=55.68 memory used=3731.0MB, alloc=107.8MB, time=55.79 memory used=3756.3MB, alloc=107.8MB, time=55.90 memory used=3782.9MB, alloc=107.8MB, time=56.02 memory used=3810.6MB, alloc=107.8MB, time=56.13 memory used=3840.6MB, alloc=107.8MB, time=56.25 memory used=3871.8MB, alloc=107.8MB, time=56.36 memory used=3904.7MB, alloc=107.8MB, time=56.48 memory used=3939.7MB, alloc=107.8MB, time=56.59 memory used=3986.4MB, alloc=107.8MB, time=57.73 memory used=4086.2MB, alloc=107.8MB, time=75.19 memory used=4126.5MB, alloc=107.8MB, time=75.37 memory used=4158.7MB, alloc=107.8MB, time=75.54 memory used=4192.8MB, alloc=107.8MB, time=75.69 memory used=4232.1MB, alloc=107.8MB, time=75.88 memory used=4278.2MB, alloc=107.8MB, time=76.05 memory used=4309.7MB, alloc=107.8MB, time=76.18 memory used=4336.7MB, alloc=107.8MB, time=76.30 memory used=4365.3MB, alloc=107.8MB, time=76.42 memory used=4395.7MB, alloc=107.8MB, time=76.54 memory used=4428.6MB, alloc=107.8MB, time=76.67 memory used=4464.0MB, alloc=107.8MB, time=76.80 memory used=4501.7MB, alloc=107.8MB, time=76.93 memory used=4542.4MB, alloc=107.8MB, time=77.07 memory used=4585.0MB, alloc=107.8MB, time=77.20 memory used=4632.6MB, alloc=107.8MB, time=77.34 memory used=4653.9MB, alloc=107.8MB, time=77.44 memory used=4664.5MB, alloc=107.8MB, time=77.52 memory used=4675.6MB, alloc=107.8MB, time=77.60 memory used=4686.8MB, alloc=107.8MB, time=77.68 memory used=4698.7MB, alloc=107.8MB, time=77.77 memory used=4710.8MB, alloc=107.8MB, time=77.85 memory used=4723.8MB, alloc=107.8MB, time=77.95 memory used=4777.8MB, alloc=107.8MB, time=78.67 memory used=4861.5MB, alloc=107.8MB, time=95.04 memory used=4909.4MB, alloc=107.8MB, time=95.84 memory used=4948.2MB, alloc=107.8MB, time=96.02 memory used=4978.1MB, alloc=107.8MB, time=96.18 memory used=5014.1MB, alloc=107.8MB, time=96.33 memory used=5055.8MB, alloc=107.8MB, time=96.50 memory used=5098.8MB, alloc=107.8MB, time=96.66 memory used=5124.4MB, alloc=107.8MB, time=96.78 memory used=5152.1MB, alloc=107.8MB, time=96.91 memory used=5180.8MB, alloc=107.8MB, time=97.03 memory used=5212.1MB, alloc=107.8MB, time=97.15 memory used=5244.8MB, alloc=107.8MB, time=97.28 memory used=5280.0MB, alloc=107.8MB, time=97.41 memory used=5318.4MB, alloc=107.8MB, time=97.54 memory used=5359.4MB, alloc=107.8MB, time=97.68 memory used=5402.1MB, alloc=107.8MB, time=97.82 memory used=5453.6MB, alloc=107.8MB, time=97.97 memory used=5463.9MB, alloc=107.8MB, time=98.06 memory used=5474.7MB, alloc=107.8MB, time=98.15 memory used=5485.8MB, alloc=107.8MB, time=98.24 memory used=5497.6MB, alloc=107.8MB, time=98.33 memory used=5509.8MB, alloc=107.8MB, time=98.42 memory used=5522.7MB, alloc=107.8MB, time=98.53 memory used=5570.7MB, alloc=107.8MB, time=99.45 memory used=5605.6MB, alloc=107.8MB, time=99.67 memory used=5645.3MB, alloc=107.8MB, time=100.16 memory used=5674.3MB, alloc=107.8MB, time=100.31 memory used=5721.5MB, alloc=107.8MB, time=100.50 memory used=5753.7MB, alloc=107.8MB, time=100.67 memory used=5800.5MB, alloc=107.8MB, time=100.86 memory used=5837.1MB, alloc=107.8MB, time=101.90 memory used=5855.2MB, alloc=107.8MB, time=102.02 memory used=5874.3MB, alloc=107.8MB, time=102.13 memory used=5894.4MB, alloc=107.8MB, time=102.25 memory used=5916.0MB, alloc=107.8MB, time=102.36 memory used=5950.0MB, alloc=107.8MB, time=102.50 memory used=5986.2MB, alloc=107.8MB, time=102.64 memory used=6024.8MB, alloc=107.8MB, time=102.77 memory used=6065.6MB, alloc=107.8MB, time=102.91 memory used=6077.6MB, alloc=107.8MB, time=102.99 memory used=6089.6MB, alloc=107.8MB, time=103.08 memory used=6101.8MB, alloc=107.8MB, time=103.17 memory used=6114.1MB, alloc=107.8MB, time=103.26 memory used=6126.6MB, alloc=107.8MB, time=103.34 memory used=6140.8MB, alloc=107.8MB, time=103.48 memory used=6158.3MB, alloc=107.8MB, time=103.59 memory used=6176.8MB, alloc=107.8MB, time=103.70 memory used=6196.3MB, alloc=107.8MB, time=103.82 memory used=6216.8MB, alloc=107.8MB, time=103.93 memory used=6244.0MB, alloc=107.8MB, time=104.07 memory used=6278.8MB, alloc=107.8MB, time=104.21 memory used=6315.9MB, alloc=107.8MB, time=104.34 memory used=6355.3MB, alloc=107.8MB, time=104.48 memory used=6383.0MB, alloc=107.8MB, time=104.59 memory used=6394.8MB, alloc=107.8MB, time=104.68 memory used=6406.8MB, alloc=107.8MB, time=104.77 memory used=6418.9MB, alloc=107.8MB, time=104.86 memory used=6431.2MB, alloc=107.8MB, time=104.95 memory used=6443.7MB, alloc=107.8MB, time=105.04 memory used=6526.0MB, alloc=107.8MB, time=107.54 memory used=6591.4MB, alloc=107.8MB, time=108.84 memory used=6654.8MB, alloc=107.8MB, time=110.28 memory used=6712.2MB, alloc=387.8MB, time=111.66 memory used=6767.1MB, alloc=387.8MB, time=112.20 memory used=6814.4MB, alloc=387.8MB, time=112.76 memory used=6863.6MB, alloc=387.8MB, time=113.39 memory used=6912.9MB, alloc=387.8MB, time=113.69 memory used=6970.3MB, alloc=387.8MB, time=116.70 memory used=7018.3MB, alloc=387.8MB, time=117.02 memory used=7059.9MB, alloc=387.8MB, time=117.28 memory used=7110.9MB, alloc=387.8MB, time=117.58 memory used=7149.5MB, alloc=411.8MB, time=117.86 memory used=7192.5MB, alloc=411.8MB, time=118.17 memory used=7242.3MB, alloc=411.8MB, time=118.45 memory used=7295.9MB, alloc=411.8MB, time=118.73 memory used=7353.3MB, alloc=411.8MB, time=119.05 memory used=7418.3MB, alloc=411.8MB, time=119.35 memory used=7487.1MB, alloc=411.8MB, time=119.67 memory used=7559.4MB, alloc=411.8MB, time=120.01 memory used=7608.2MB, alloc=411.8MB, time=120.26 memory used=7645.9MB, alloc=411.8MB, time=120.47 memory used=7682.3MB, alloc=411.8MB, time=120.68 memory used=7723.6MB, alloc=411.8MB, time=120.90 memory used=7766.0MB, alloc=411.8MB, time=121.13 memory used=7809.1MB, alloc=411.8MB, time=121.36 memory used=7852.9MB, alloc=411.8MB, time=121.58 memory used=7897.3MB, alloc=411.8MB, time=121.80 memory used=7942.3MB, alloc=411.8MB, time=122.02 memory used=7988.0MB, alloc=411.8MB, time=122.25 memory used=8039.9MB, alloc=411.8MB, time=122.50 memory used=8092.3MB, alloc=411.8MB, time=122.74 memory used=8145.4MB, alloc=411.8MB, time=122.98 memory used=8198.9MB, alloc=411.8MB, time=123.22 memory used=8252.9MB, alloc=411.8MB, time=123.47 memory used=8308.2MB, alloc=411.8MB, time=123.70 memory used=8368.1MB, alloc=411.8MB, time=123.96 memory used=8429.3MB, alloc=411.8MB, time=124.21 memory used=8490.8MB, alloc=411.8MB, time=124.47 memory used=8553.3MB, alloc=411.8MB, time=124.72 memory used=8620.6MB, alloc=411.8MB, time=124.99 memory used=8688.8MB, alloc=411.8MB, time=125.26 memory used=8757.7MB, alloc=411.8MB, time=125.53 memory used=8835.8MB, alloc=411.8MB, time=125.83 memory used=8997.0MB, alloc=411.8MB, time=126.62 memory used=9133.8MB, alloc=411.8MB, time=127.12 memory used=9281.0MB, alloc=411.8MB, time=127.63 memory used=9436.4MB, alloc=411.8MB, time=128.15 memory used=9599.0MB, alloc=411.8MB, time=128.68 memory used=9773.6MB, alloc=411.8MB, time=129.22 memory used=9961.8MB, alloc=411.8MB, time=129.77 memory used=10169.9MB, alloc=411.8MB, time=130.34 memory used=10310.0MB, alloc=411.8MB, time=135.59 memory used=10374.3MB, alloc=411.8MB, time=135.96 memory used=10434.8MB, alloc=411.8MB, time=136.29 memory used=10478.8MB, alloc=411.8MB, time=136.56 memory used=10528.9MB, alloc=411.8MB, time=136.87 memory used=10582.8MB, alloc=411.8MB, time=137.17 memory used=10640.4MB, alloc=411.8MB, time=137.48 memory used=10705.8MB, alloc=411.8MB, time=137.80 memory used=10774.7MB, alloc=411.8MB, time=138.12 memory used=10847.6MB, alloc=411.8MB, time=138.46 memory used=10893.5MB, alloc=411.8MB, time=138.69 memory used=10928.8MB, alloc=411.8MB, time=138.90 memory used=10965.2MB, alloc=411.8MB, time=139.11 memory used=11006.5MB, alloc=411.8MB, time=139.33 memory used=11048.9MB, alloc=411.8MB, time=139.55 memory used=11092.1MB, alloc=411.8MB, time=139.77 memory used=11135.9MB, alloc=411.8MB, time=140.00 memory used=11180.3MB, alloc=411.8MB, time=140.22 memory used=11225.3MB, alloc=411.8MB, time=140.44 memory used=11271.4MB, alloc=411.8MB, time=140.66 memory used=11322.8MB, alloc=411.8MB, time=140.90 memory used=11375.3MB, alloc=411.8MB, time=141.15 memory used=11428.3MB, alloc=411.8MB, time=141.39 memory used=11481.8MB, alloc=411.8MB, time=141.63 memory used=11535.8MB, alloc=411.8MB, time=141.88 memory used=11591.2MB, alloc=411.8MB, time=142.12 memory used=11651.1MB, alloc=411.8MB, time=142.37 memory used=11712.3MB, alloc=411.8MB, time=142.63 memory used=11773.8MB, alloc=411.8MB, time=142.88 memory used=11836.5MB, alloc=411.8MB, time=143.13 memory used=11903.6MB, alloc=411.8MB, time=143.40 memory used=11971.8MB, alloc=411.8MB, time=143.67 memory used=12040.8MB, alloc=411.8MB, time=143.94 memory used=12118.8MB, alloc=411.8MB, time=144.23 memory used=12279.8MB, alloc=411.8MB, time=144.77 memory used=12416.6MB, alloc=411.8MB, time=145.26 memory used=12563.7MB, alloc=411.8MB, time=145.76 memory used=12719.2MB, alloc=411.8MB, time=146.28 memory used=12881.8MB, alloc=411.8MB, time=146.80 memory used=13056.4MB, alloc=411.8MB, time=147.34 memory used=13244.5MB, alloc=411.8MB, time=147.89 memory used=13452.6MB, alloc=411.8MB, time=148.44 |\^/| 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(); 1428277390 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 3 2 F := [6 x y - 17 x y - 16 y z - 7 z, -x + 11 z + 15 x + 6, 2 19 y z - 15 x + 3 y - 5] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 2 G := [-18 x - 18 x y - 13 y z + 19, 17 x y + 8 y z - x y + 10 z , 2 2 -x y z - 15 y z + 16 x - 18 x] > Problem := [F,G]; 2 2 2 3 3 2 Problem := [[6 x y - 17 x y - 16 y z - 7 z, -x + 11 z + 15 x + 6, 2 3 2 2 19 y z - 15 x + 3 y - 5], [-18 x - 18 x y - 13 y z + 19, 2 2 2 2 2 17 x y + 8 y z - x y + 10 z , -x y z - 15 y z + 16 x - 18 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.0MB, alloc=32.3MB, time=0.87 memory used=45.9MB, alloc=56.3MB, time=1.37 memory used=83.3MB, alloc=60.3MB, time=2.17 memory used=128.8MB, alloc=68.3MB, time=3.08 memory used=170.1MB, alloc=68.3MB, time=4.12 memory used=212.1MB, alloc=92.3MB, time=5.21 memory used=287.1MB, alloc=92.3MB, time=6.74 memory used=360.9MB, alloc=92.3MB, time=8.26 memory used=429.8MB, alloc=348.3MB, time=9.83 memory used=501.6MB, alloc=372.3MB, time=11.49 memory used=599.7MB, alloc=372.3MB, time=13.49 memory used=684.9MB, alloc=372.3MB, time=15.73 memory used=771.8MB, alloc=396.3MB, time=17.87 memory used=886.9MB, alloc=396.3MB, time=20.59 memory used=1001.6MB, alloc=420.3MB, time=23.29 memory used=1130.1MB, alloc=444.3MB, time=26.94 memory used=1255.2MB, alloc=444.3MB, time=30.37 memory used=1379.5MB, alloc=468.3MB, time=33.96 memory used=1476.6MB, alloc=468.3MB, time=36.39 memory used=1574.1MB, alloc=468.3MB, time=39.33 memory used=1695.3MB, alloc=468.3MB, time=41.66 memory used=1791.2MB, alloc=468.3MB, time=44.22 memory used=1876.4MB, alloc=492.3MB, time=46.12 memory used=1959.4MB, alloc=492.3MB, time=47.91 memory used=2061.7MB, alloc=492.3MB, time=50.35 memory used=2132.7MB, alloc=492.3MB, time=52.37 memory used=2197.1MB, alloc=492.3MB, time=54.08 memory used=2286.3MB, alloc=516.3MB, time=56.31 memory used=2344.8MB, alloc=516.3MB, time=58.14 memory used=2387.1MB, alloc=516.3MB, time=59.51 memory used=2444.0MB, alloc=516.3MB, time=61.15 memory used=2509.3MB, alloc=516.3MB, time=62.67 memory used=2580.6MB, alloc=516.3MB, time=64.61 memory used=2649.0MB, alloc=516.3MB, time=66.59 memory used=2720.7MB, alloc=516.3MB, time=68.71 memory used=2780.6MB, alloc=516.3MB, time=70.17 memory used=2895.6MB, alloc=540.3MB, time=80.35 memory used=2986.0MB, alloc=540.3MB, time=87.93 memory used=3195.2MB, alloc=564.3MB, time=102.35 memory used=3259.2MB, alloc=588.3MB, time=113.41 memory used=3279.4MB, alloc=612.3MB, time=114.06 memory used=3304.4MB, alloc=612.3MB, time=115.99 memory used=3605.0MB, alloc=612.3MB, time=120.01 memory used=3891.6MB, alloc=612.3MB, time=127.12 memory used=4207.9MB, alloc=612.3MB, time=132.45 memory used=4417.3MB, alloc=612.3MB, time=137.51 memory used=4617.9MB, alloc=612.3MB, time=143.05 |\^/| 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(); 1428277690 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 3 3 F := [7 z + 5 x z - z + 9 x, -17 y - 9 z + 20 z, 3 -14 x y z + 5 y - 20 x z + 2 x] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 G := [8 z - 12 y z - 10 y - 11 z, -17 x + 10 x y - 11 x - 13 y, 2 2 -11 x z - 8 x z + 15 y + 15 z] > Problem := [F,G]; 3 2 3 3 Problem := [[7 z + 5 x z - z + 9 x, -17 y - 9 z + 20 z, 3 3 -14 x y z + 5 y - 20 x z + 2 x], [8 z - 12 y z - 10 y - 11 z, 3 2 2 2 2 -17 x + 10 x y - 11 x - 13 y, -11 x z - 8 x z + 15 y + 15 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.31 memory used=24.3MB, alloc=32.3MB, time=0.82 memory used=44.5MB, alloc=56.3MB, time=1.30 memory used=89.6MB, alloc=60.3MB, time=2.09 memory used=136.7MB, alloc=68.3MB, time=3.21 memory used=180.8MB, alloc=68.3MB, time=4.19 memory used=218.4MB, alloc=68.3MB, time=4.68 memory used=256.7MB, alloc=68.3MB, time=5.07 memory used=278.2MB, alloc=68.3MB, time=5.20 memory used=297.0MB, alloc=68.3MB, time=5.32 memory used=320.4MB, alloc=68.3MB, time=5.44 memory used=344.3MB, alloc=68.3MB, time=5.66 memory used=377.9MB, alloc=68.3MB, time=5.96 memory used=398.8MB, alloc=68.3MB, time=6.09 memory used=417.5MB, alloc=68.3MB, time=6.20 memory used=440.9MB, alloc=68.3MB, time=6.32 memory used=472.3MB, alloc=68.3MB, time=9.55 memory used=509.0MB, alloc=68.3MB, time=11.54 memory used=529.3MB, alloc=68.3MB, time=11.66 memory used=550.6MB, alloc=68.3MB, time=11.78 memory used=566.7MB, alloc=68.3MB, time=11.88 memory used=585.2MB, alloc=68.3MB, time=12.01 memory used=607.0MB, alloc=68.3MB, time=12.12 memory used=627.3MB, alloc=68.3MB, time=12.23 memory used=661.9MB, alloc=68.3MB, time=12.53 memory used=682.6MB, alloc=68.3MB, time=12.65 memory used=702.6MB, alloc=68.3MB, time=12.78 memory used=727.2MB, alloc=68.3MB, time=12.90 memory used=754.0MB, alloc=68.3MB, time=13.25 memory used=785.3MB, alloc=68.3MB, time=13.42 memory used=804.1MB, alloc=68.3MB, time=13.54 memory used=824.2MB, alloc=68.3MB, time=13.65 memory used=849.0MB, alloc=68.3MB, time=13.77 memory used=875.2MB, alloc=68.3MB, time=14.65 memory used=919.0MB, alloc=68.3MB, time=19.17 memory used=939.4MB, alloc=68.3MB, time=19.30 memory used=962.8MB, alloc=68.3MB, time=19.43 memory used=978.8MB, alloc=68.3MB, time=19.54 memory used=997.0MB, alloc=68.3MB, time=19.64 memory used=1018.5MB, alloc=68.3MB, time=19.76 memory used=1040.2MB, alloc=68.3MB, time=19.87 memory used=1076.7MB, alloc=68.3MB, time=20.93 memory used=1096.7MB, alloc=68.3MB, time=21.05 memory used=1114.4MB, alloc=68.3MB, time=21.15 memory used=1164.0MB, alloc=92.3MB, time=22.24 memory used=1212.4MB, alloc=92.3MB, time=22.94 memory used=1281.2MB, alloc=92.3MB, time=24.47 memory used=1349.6MB, alloc=92.3MB, time=25.96 memory used=1381.5MB, alloc=92.3MB, time=26.14 memory used=1410.7MB, alloc=92.3MB, time=26.32 memory used=1445.7MB, alloc=92.3MB, time=26.50 memory used=1486.3MB, alloc=92.3MB, time=26.68 memory used=1512.1MB, alloc=92.3MB, time=26.83 memory used=1535.5MB, alloc=92.3MB, time=26.96 memory used=1561.2MB, alloc=92.3MB, time=27.11 memory used=1588.7MB, alloc=92.3MB, time=27.24 memory used=1618.4MB, alloc=92.3MB, time=27.40 memory used=1650.9MB, alloc=92.3MB, time=27.54 memory used=1686.7MB, alloc=92.3MB, time=27.69 memory used=1726.6MB, alloc=92.3MB, time=27.85 memory used=1779.1MB, alloc=92.3MB, time=28.71 memory used=1809.6MB, alloc=92.3MB, time=28.88 memory used=1839.4MB, alloc=92.3MB, time=29.06 memory used=1874.7MB, alloc=92.3MB, time=29.24 memory used=1916.5MB, alloc=92.3MB, time=29.42 memory used=1940.1MB, alloc=92.3MB, time=29.56 memory used=1964.1MB, alloc=92.3MB, time=29.70 memory used=1989.9MB, alloc=92.3MB, time=29.84 memory used=2018.7MB, alloc=92.3MB, time=30.00 memory used=2048.9MB, alloc=92.3MB, time=30.15 memory used=2082.1MB, alloc=92.3MB, time=30.31 memory used=2118.7MB, alloc=92.3MB, time=30.48 memory used=2162.2MB, alloc=92.3MB, time=31.19 memory used=2219.2MB, alloc=116.3MB, time=60.86 memory used=2328.5MB, alloc=116.7MB, time=67.38 memory used=2379.9MB, alloc=116.7MB, time=67.61 memory used=2423.5MB, alloc=116.7MB, time=67.82 memory used=2477.2MB, alloc=116.7MB, time=68.03 memory used=2533.9MB, alloc=116.7MB, time=68.23 memory used=2570.0MB, alloc=116.7MB, time=68.38 memory used=2609.8MB, alloc=116.7MB, time=68.53 memory used=2653.6MB, alloc=116.7MB, time=68.69 memory used=2701.7MB, alloc=116.7MB, time=68.85 memory used=2764.5MB, alloc=116.7MB, time=69.77 memory used=2825.5MB, alloc=117.3MB, time=70.06 memory used=2874.7MB, alloc=117.3MB, time=70.31 memory used=2937.1MB, alloc=117.3MB, time=70.57 memory used=2974.6MB, alloc=117.3MB, time=70.77 memory used=3015.7MB, alloc=117.3MB, time=70.98 memory used=3062.8MB, alloc=117.3MB, time=71.18 memory used=3116.6MB, alloc=117.3MB, time=71.38 memory used=3182.0MB, alloc=117.3MB, time=71.72 memory used=3251.4MB, alloc=118.4MB, time=72.77 memory used=3297.0MB, alloc=118.4MB, time=73.00 memory used=3356.3MB, alloc=118.4MB, time=73.23 memory used=3399.6MB, alloc=118.4MB, time=73.44 memory used=3439.6MB, alloc=118.4MB, time=73.64 memory used=3484.2MB, alloc=118.4MB, time=73.85 memory used=3535.2MB, alloc=118.4MB, time=74.07 memory used=3593.6MB, alloc=118.4MB, time=74.27 memory used=3677.0MB, alloc=118.4MB, time=105.28 memory used=3788.2MB, alloc=118.4MB, time=111.84 memory used=3840.4MB, alloc=118.4MB, time=112.06 memory used=3882.6MB, alloc=118.4MB, time=112.27 memory used=3934.3MB, alloc=118.4MB, time=112.49 memory used=3994.2MB, alloc=118.4MB, time=112.71 memory used=4029.8MB, alloc=118.4MB, time=112.87 memory used=4069.0MB, alloc=118.4MB, time=113.03 memory used=4112.1MB, alloc=118.4MB, time=113.18 memory used=4159.1MB, alloc=118.4MB, time=113.34 memory used=4213.4MB, alloc=118.4MB, time=113.50 memory used=4282.1MB, alloc=118.4MB, time=116.48 memory used=4344.3MB, alloc=118.4MB, time=118.48 memory used=4390.2MB, alloc=118.4MB, time=118.70 memory used=4438.1MB, alloc=118.4MB, time=118.88 memory used=4527.3MB, alloc=374.4MB, time=122.07 memory used=4576.4MB, alloc=374.4MB, time=122.32 memory used=4625.2MB, alloc=374.4MB, time=122.54 memory used=4723.9MB, alloc=374.4MB, time=124.36 memory used=4795.0MB, alloc=374.4MB, time=125.41 memory used=4884.0MB, alloc=374.4MB, time=131.44 memory used=4942.6MB, alloc=374.4MB, time=132.10 memory used=4981.5MB, alloc=374.4MB, time=132.31 memory used=5030.5MB, alloc=374.4MB, time=132.53 memory used=5079.8MB, alloc=374.4MB, time=132.74 memory used=5113.2MB, alloc=374.4MB, time=132.90 memory used=5150.8MB, alloc=374.4MB, time=133.07 memory used=5192.1MB, alloc=374.4MB, time=133.25 memory used=5236.8MB, alloc=374.4MB, time=133.43 memory used=5286.5MB, alloc=374.4MB, time=133.61 memory used=5340.8MB, alloc=374.4MB, time=133.81 memory used=5534.1MB, alloc=374.4MB, time=142.96 memory used=5598.8MB, alloc=374.4MB, time=148.65 memory used=5642.1MB, alloc=374.4MB, time=148.88 memory used=5683.1MB, alloc=374.4MB, time=149.12 memory used=5733.4MB, alloc=374.4MB, time=149.33 memory used=5782.2MB, alloc=374.4MB, time=149.54 memory used=5814.0MB, alloc=374.4MB, time=149.71 memory used=5849.0MB, alloc=374.4MB, time=149.88 memory used=5886.7MB, alloc=374.4MB, time=150.05 memory used=5927.0MB, alloc=374.4MB, time=150.22 memory used=5969.8MB, alloc=374.4MB, time=150.40 memory used=6016.3MB, alloc=374.4MB, time=150.58 memory used=6065.1MB, alloc=374.4MB, time=150.77 memory used=6117.7MB, alloc=374.4MB, time=150.96 memory used=6175.0MB, alloc=374.4MB, time=151.15 memory used=6322.6MB, alloc=374.4MB, time=151.60 memory used=6589.3MB, alloc=374.4MB, time=153.93 memory used=6682.2MB, alloc=374.4MB, time=155.77 memory used=6746.8MB, alloc=374.4MB, time=157.05 memory used=6836.9MB, alloc=374.4MB, time=158.92 memory used=6913.4MB, alloc=374.4MB, time=160.49 memory used=6959.2MB, alloc=374.4MB, time=161.09 memory used=7007.9MB, alloc=398.4MB, time=163.68 memory used=7064.2MB, alloc=398.4MB, time=164.09 memory used=7119.1MB, alloc=398.4MB, time=164.46 memory used=7181.0MB, alloc=398.4MB, time=164.83 memory used=7219.8MB, alloc=398.4MB, time=165.11 memory used=7261.2MB, alloc=398.4MB, time=165.40 memory used=7305.2MB, alloc=398.4MB, time=165.71 memory used=7355.1MB, alloc=398.4MB, time=166.02 memory used=7407.4MB, alloc=398.4MB, time=166.33 memory used=7462.4MB, alloc=398.4MB, time=166.67 memory used=7522.6MB, alloc=398.4MB, time=167.00 memory used=7589.5MB, alloc=398.4MB, time=167.33 memory used=7639.7MB, alloc=422.4MB, time=167.65 memory used=7684.3MB, alloc=422.4MB, time=167.93 memory used=7731.7MB, alloc=422.4MB, time=168.21 memory used=7780.3MB, alloc=422.4MB, time=168.49 memory used=7833.7MB, alloc=422.4MB, time=168.78 memory used=7887.7MB, alloc=422.4MB, time=169.08 memory used=7946.3MB, alloc=422.4MB, time=169.38 memory used=8005.1MB, alloc=422.4MB, time=169.69 memory used=8068.5MB, alloc=422.4MB, time=170.00 memory used=8132.6MB, alloc=422.4MB, time=170.30 memory used=8199.7MB, alloc=422.4MB, time=170.62 memory used=8270.4MB, alloc=422.4MB, time=170.94 memory used=8344.6MB, alloc=422.4MB, time=171.26 memory used=8424.3MB, alloc=422.4MB, time=171.60 memory used=8507.3MB, alloc=422.4MB, time=171.93 memory used=8596.7MB, alloc=422.4MB, time=172.28 memory used=8767.6MB, alloc=422.4MB, time=172.84 memory used=8917.2MB, alloc=422.4MB, time=175.88 memory used=8997.3MB, alloc=422.4MB, time=176.34 memory used=9059.2MB, alloc=422.4MB, time=176.72 memory used=9115.1MB, alloc=422.4MB, time=177.07 memory used=9177.9MB, alloc=422.4MB, time=177.46 memory used=9248.9MB, alloc=422.4MB, time=177.85 memory used=9328.1MB, alloc=422.4MB, time=178.24 memory used=9412.0MB, alloc=422.4MB, time=178.65 memory used=9486.5MB, alloc=422.4MB, time=179.01 memory used=9533.1MB, alloc=422.4MB, time=179.29 memory used=9581.1MB, alloc=422.4MB, time=179.56 memory used=9630.2MB, alloc=422.4MB, time=179.83 memory used=9683.2MB, alloc=422.4MB, time=180.12 memory used=9737.1MB, alloc=422.4MB, time=180.41 memory used=9795.8MB, alloc=422.4MB, time=180.70 memory used=9854.7MB, alloc=422.4MB, time=181.00 memory used=9917.9MB, alloc=422.4MB, time=181.30 memory used=9985.5MB, alloc=422.4MB, time=181.60 memory used=10053.2MB, alloc=422.4MB, time=181.90 memory used=10124.2MB, alloc=422.4MB, time=182.22 memory used=10201.5MB, alloc=422.4MB, time=182.55 memory used=10281.9MB, alloc=422.4MB, time=182.87 memory used=10367.6MB, alloc=422.4MB, time=183.21 memory used=10456.9MB, alloc=422.4MB, time=183.54 memory used=10612.5MB, alloc=422.4MB, time=184.08 |\^/| 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(); 1428277990 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [9 y z + 20 x z - 3 y - 19 y, 2 x z - 3 y - 3 x - 16, 3 3 2 -3 x + 19 y + 3 y + 11 x] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 G := [6 y - 14 x - 4 z, -14 x y - 11 y + 15 x y + 15 x z, 3 2 2 -5 y + 19 x - 7 y + 7 x] > Problem := [F,G]; 2 2 2 Problem := [[9 y z + 20 x z - 3 y - 19 y, 2 x z - 3 y - 3 x - 16, 3 3 2 2 -3 x + 19 y + 3 y + 11 x], [6 y - 14 x - 4 z, 2 3 3 2 2 -14 x y - 11 y + 15 x y + 15 x z, -5 y + 19 x - 7 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=4.4MB, alloc=32.3MB, time=0.31 memory used=26.0MB, alloc=32.3MB, time=0.86 memory used=45.9MB, alloc=32.3MB, time=1.37 memory used=65.4MB, alloc=56.3MB, time=1.90 memory used=107.1MB, alloc=60.3MB, time=2.96 memory used=147.1MB, alloc=60.3MB, time=3.98 memory used=186.7MB, alloc=84.3MB, time=5.00 memory used=225.1MB, alloc=84.3MB, time=6.02 memory used=291.9MB, alloc=92.3MB, time=7.59 memory used=357.3MB, alloc=116.3MB, time=9.25 memory used=427.4MB, alloc=116.3MB, time=11.04 memory used=490.5MB, alloc=372.3MB, time=12.67 memory used=577.7MB, alloc=396.3MB, time=14.86 memory used=684.4MB, alloc=396.3MB, time=17.64 memory used=796.3MB, alloc=420.3MB, time=20.44 memory used=904.8MB, alloc=420.3MB, time=23.08 memory used=1016.1MB, alloc=444.3MB, time=25.90 memory used=1125.1MB, alloc=444.3MB, time=28.58 memory used=1243.6MB, alloc=444.3MB, time=31.78 memory used=1355.9MB, alloc=468.3MB, time=34.28 memory used=1449.2MB, alloc=468.3MB, time=36.48 memory used=1571.4MB, alloc=468.3MB, time=39.06 memory used=1661.1MB, alloc=468.3MB, time=41.52 memory used=1760.7MB, alloc=468.3MB, time=44.02 memory used=1851.3MB, alloc=468.3MB, time=46.26 memory used=1966.0MB, alloc=492.3MB, time=48.62 memory used=2048.4MB, alloc=492.3MB, time=50.62 memory used=2146.8MB, alloc=492.3MB, time=52.82 memory used=2225.3MB, alloc=492.3MB, time=54.98 memory used=2290.5MB, alloc=492.3MB, time=56.66 memory used=2358.6MB, alloc=492.3MB, time=58.87 memory used=2425.3MB, alloc=492.3MB, time=60.91 memory used=2486.9MB, alloc=492.3MB, time=62.86 memory used=2552.2MB, alloc=492.3MB, time=64.76 memory used=2618.6MB, alloc=492.3MB, time=66.93 memory used=2681.3MB, alloc=492.3MB, time=68.56 memory used=2773.1MB, alloc=492.3MB, time=70.48 memory used=2829.5MB, alloc=492.3MB, time=72.16 memory used=2898.9MB, alloc=492.3MB, time=73.93 memory used=2981.1MB, alloc=492.3MB, time=76.06 memory used=3043.7MB, alloc=492.3MB, time=77.63 memory used=3099.2MB, alloc=492.3MB, time=79.36 memory used=3155.6MB, alloc=492.3MB, time=81.26 memory used=3310.6MB, alloc=516.3MB, time=84.51 memory used=3505.8MB, alloc=516.3MB, time=88.68 memory used=3712.5MB, alloc=540.3MB, time=94.25 memory used=3935.3MB, alloc=540.3MB, time=99.36 memory used=4149.9MB, alloc=564.3MB, time=104.07 memory used=4366.1MB, alloc=564.3MB, time=108.56 memory used=4589.0MB, alloc=564.3MB, time=113.20 memory used=4801.9MB, alloc=564.3MB, time=117.64 memory used=5003.4MB, alloc=588.3MB, time=122.99 memory used=5255.8MB, alloc=612.3MB, time=129.04 memory used=5457.8MB, alloc=612.3MB, time=134.59 |\^/| 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(); 1428278290 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 3 F := [10 y - 20 x z - 12 z + 6 z, 12 x z - 4 y + 7 x y - 17 x z, 3 2 2 -10 x y z - 12 z - 18 x - 6 z ] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 3 3 G := [-9 x z + 16 x y - 4 z - 3, -4 x - 13 z + 11 x + 7, 2 2 -3 x z - 16 y z - 14 x + 13] > Problem := [F,G]; 3 2 2 3 Problem := [[10 y - 20 x z - 12 z + 6 z, 12 x z - 4 y + 7 x y - 17 x z, 3 2 2 2 2 3 -10 x y z - 12 z - 18 x - 6 z ], [-9 x z + 16 x y - 4 z - 3, 3 3 2 2 -4 x - 13 z + 11 x + 7, -3 x z - 16 y z - 14 x + 13]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.31 memory used=26.1MB, alloc=32.3MB, time=0.81 memory used=46.0MB, alloc=60.3MB, time=1.30 memory used=89.8MB, alloc=60.3MB, time=2.33 memory used=130.5MB, alloc=61.7MB, time=2.78 memory used=173.8MB, alloc=61.7MB, time=3.49 memory used=216.7MB, alloc=61.7MB, time=4.49 memory used=258.1MB, alloc=61.7MB, time=5.52 memory used=303.8MB, alloc=69.7MB, time=6.53 memory used=345.8MB, alloc=93.7MB, time=7.60 memory used=407.9MB, alloc=93.7MB, time=8.65 memory used=466.8MB, alloc=93.7MB, time=9.55 memory used=534.5MB, alloc=93.7MB, time=11.45 memory used=591.6MB, alloc=93.7MB, time=12.74 memory used=634.7MB, alloc=93.7MB, time=13.09 memory used=695.3MB, alloc=93.7MB, time=14.40 memory used=760.5MB, alloc=93.7MB, time=15.84 memory used=825.8MB, alloc=93.7MB, time=17.08 memory used=879.9MB, alloc=93.7MB, time=22.19 memory used=910.9MB, alloc=93.7MB, time=22.37 memory used=945.6MB, alloc=93.7MB, time=22.67 memory used=1010.2MB, alloc=93.7MB, time=23.79 memory used=1079.5MB, alloc=93.7MB, time=25.26 memory used=1113.4MB, alloc=93.7MB, time=25.60 memory used=1172.0MB, alloc=117.7MB, time=26.63 memory used=1238.2MB, alloc=373.7MB, time=28.36 memory used=1311.4MB, alloc=373.7MB, time=29.36 memory used=1366.9MB, alloc=373.7MB, time=30.66 memory used=1421.2MB, alloc=373.7MB, time=31.10 memory used=1478.7MB, alloc=373.7MB, time=32.50 memory used=1549.4MB, alloc=373.7MB, time=33.61 memory used=1586.8MB, alloc=373.7MB, time=33.83 memory used=1645.1MB, alloc=373.7MB, time=34.70 memory used=1682.8MB, alloc=373.7MB, time=34.96 memory used=1721.4MB, alloc=373.7MB, time=35.19 memory used=1766.9MB, alloc=373.7MB, time=35.44 memory used=1802.3MB, alloc=373.7MB, time=35.67 memory used=1833.1MB, alloc=373.7MB, time=35.88 memory used=1867.3MB, alloc=373.7MB, time=36.09 memory used=1905.5MB, alloc=373.7MB, time=36.30 memory used=1949.5MB, alloc=373.7MB, time=36.52 memory used=1996.0MB, alloc=373.7MB, time=39.83 memory used=2054.8MB, alloc=397.7MB, time=73.37 memory used=2119.8MB, alloc=421.7MB, time=169.98 memory used=2213.2MB, alloc=421.7MB, time=191.23 memory used=2290.7MB, alloc=421.7MB, time=191.60 memory used=2348.5MB, alloc=421.7MB, time=191.91 memory used=2415.9MB, alloc=421.7MB, time=192.23 memory used=2494.4MB, alloc=421.7MB, time=192.58 memory used=2582.7MB, alloc=421.7MB, time=192.92 memory used=2639.6MB, alloc=421.7MB, time=193.18 memory used=2691.2MB, alloc=421.7MB, time=193.42 memory used=2745.1MB, alloc=421.7MB, time=193.66 memory used=2803.0MB, alloc=421.7MB, time=193.90 memory used=2862.3MB, alloc=421.7MB, time=194.15 memory used=2925.3MB, alloc=421.7MB, time=194.40 memory used=2991.8MB, alloc=421.7MB, time=194.65 memory used=3061.7MB, alloc=421.7MB, time=194.91 memory used=3134.9MB, alloc=421.7MB, time=195.18 memory used=3213.7MB, alloc=421.7MB, time=195.44 memory used=3295.8MB, alloc=421.7MB, time=195.72 memory used=3390.9MB, alloc=421.7MB, time=196.03 memory used=3504.7MB, alloc=421.7MB, time=196.38 memory used=3645.5MB, alloc=421.7MB, time=197.04 memory used=3788.4MB, alloc=421.7MB, time=197.47 memory used=3944.6MB, alloc=421.7MB, time=197.92 memory used=4115.9MB, alloc=421.7MB, time=198.39 memory used=4381.2MB, alloc=421.7MB, time=199.90 memory used=4457.9MB, alloc=421.7MB, time=200.26 memory used=4593.0MB, alloc=421.7MB, time=201.23 memory used=4720.1MB, alloc=421.7MB, time=201.60 memory used=4900.6MB, alloc=421.7MB, time=202.17 memory used=5025.5MB, alloc=421.7MB, time=206.87 memory used=5096.7MB, alloc=421.7MB, time=207.19 memory used=5178.5MB, alloc=421.7MB, time=207.52 memory used=5243.7MB, alloc=421.7MB, time=207.78 memory used=5307.0MB, alloc=421.7MB, time=208.03 memory used=5382.0MB, alloc=421.7MB, time=208.29 memory used=5547.4MB, alloc=421.7MB, time=212.84 memory used=5637.2MB, alloc=421.7MB, time=215.66 memory used=5707.5MB, alloc=421.7MB, time=216.00 memory used=5780.5MB, alloc=421.7MB, time=216.30 memory used=5903.9MB, alloc=421.7MB, time=217.86 memory used=6053.6MB, alloc=421.7MB, time=220.80 memory used=6207.5MB, alloc=421.7MB, time=222.96 memory used=6361.4MB, alloc=421.7MB, time=226.43 memory used=6514.0MB, alloc=421.7MB, time=231.12 |\^/| 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(); 1428278590 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [6 x z - 9 x z + 11 y z - 6 x, -11 x y - 16 x y z + 9 y z + 8 y, 2 3 -11 x z - 8 z + 4 x z + 7 z] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [-8 y z - 20 x y - 10 x - z, -4 x y + 19 x z + 20 x z - 16, 3 2 2 8 x - 4 x y - 8 y z - 16 x z] > Problem := [F,G]; 2 2 2 2 Problem := [[6 x z - 9 x z + 11 y z - 6 x, -11 x y - 16 x y z + 9 y z + 8 y, 2 3 2 -11 x z - 8 z + 4 x z + 7 z], [-8 y z - 20 x y - 10 x - z, 2 2 3 2 2 -4 x y + 19 x z + 20 x z - 16, 8 x - 4 x y - 8 y z - 16 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.31 memory used=27.0MB, alloc=32.3MB, time=0.89 memory used=47.7MB, alloc=56.3MB, time=1.46 memory used=89.0MB, alloc=60.3MB, time=2.57 memory used=128.0MB, alloc=84.3MB, time=3.63 memory used=174.4MB, alloc=84.3MB, time=4.89 memory used=234.2MB, alloc=116.3MB, time=6.59 memory used=313.7MB, alloc=116.3MB, time=8.77 memory used=395.8MB, alloc=140.3MB, time=11.13 memory used=471.1MB, alloc=396.3MB, time=13.35 memory used=575.0MB, alloc=420.3MB, time=16.34 memory used=704.6MB, alloc=444.3MB, time=20.09 memory used=860.1MB, alloc=444.3MB, time=24.62 memory used=1010.6MB, alloc=468.3MB, time=29.34 memory used=1166.1MB, alloc=492.3MB, time=34.22 memory used=1325.7MB, alloc=516.3MB, time=39.60 memory used=1482.7MB, alloc=516.3MB, time=45.21 memory used=1626.0MB, alloc=540.3MB, time=50.29 memory used=1747.6MB, alloc=540.3MB, time=54.53 memory used=1855.0MB, alloc=540.3MB, time=58.26 memory used=1964.2MB, alloc=540.3MB, time=62.27 memory used=2053.0MB, alloc=540.3MB, time=65.38 memory used=2173.1MB, alloc=540.3MB, time=70.01 memory used=2276.4MB, alloc=540.3MB, time=74.11 memory used=2378.1MB, alloc=540.3MB, time=78.18 memory used=2495.7MB, alloc=564.3MB, time=83.28 memory used=2579.0MB, alloc=564.3MB, time=86.66 memory used=2659.8MB, alloc=564.3MB, time=89.78 memory used=2739.3MB, alloc=564.3MB, time=92.88 memory used=2809.0MB, alloc=564.3MB, time=95.66 memory used=2889.7MB, alloc=564.3MB, time=99.10 memory used=2952.4MB, alloc=564.3MB, time=101.72 memory used=3019.9MB, alloc=564.3MB, time=104.38 memory used=3092.8MB, alloc=564.3MB, time=107.45 memory used=3159.7MB, alloc=564.3MB, time=110.04 memory used=3208.8MB, alloc=564.3MB, time=112.16 memory used=3268.7MB, alloc=564.3MB, time=114.95 memory used=3332.2MB, alloc=588.3MB, time=117.66 memory used=3388.4MB, alloc=588.3MB, time=120.26 memory used=3447.2MB, alloc=588.3MB, time=123.26 memory used=3709.1MB, alloc=612.3MB, time=133.72 |\^/| 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(); 1428278890 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [5 x y - 8 x - 8 z - 11 y, 6 x y z + 18 x y + 10 y + 6, 2 2 14 x z + 3 y z + 14 x z + 14 y] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 2 G := [20 y - 6 y z - 4 x z + 3, -17 x - x z - 15 y z + 6 x, 2 2 3 -13 x y + 20 y z - 5 z + 19 x] > Problem := [F,G]; 2 2 2 Problem := [[5 x y - 8 x - 8 z - 11 y, 6 x y z + 18 x y + 10 y + 6, 2 2 3 2 14 x z + 3 y z + 14 x z + 14 y], [20 y - 6 y z - 4 x z + 3, 3 2 2 2 2 3 -17 x - x z - 15 y z + 6 x, -13 x y + 20 y z - 5 z + 19 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.30 memory used=24.3MB, alloc=32.3MB, time=0.82 memory used=46.6MB, alloc=36.3MB, time=1.29 memory used=70.4MB, alloc=60.3MB, time=1.92 memory used=112.3MB, alloc=60.6MB, time=3.14 memory used=164.9MB, alloc=60.6MB, time=5.23 memory used=200.2MB, alloc=60.6MB, time=19.16 memory used=220.9MB, alloc=60.6MB, time=25.97 memory used=239.2MB, alloc=84.6MB, time=26.61 memory used=286.8MB, alloc=108.6MB, time=60.74 memory used=473.8MB, alloc=133.8MB, time=64.19 memory used=694.7MB, alloc=422.7MB, time=68.74 memory used=726.7MB, alloc=447.9MB, time=69.73 memory used=727.9MB, alloc=449.1MB, time=69.80 memory used=729.1MB, alloc=450.3MB, time=69.87 memory used=730.3MB, alloc=451.5MB, time=69.94 memory used=731.5MB, alloc=447.9MB, time=70.05 memory used=814.0MB, alloc=446.7MB, time=70.70 memory used=930.8MB, alloc=446.7MB, time=71.11 memory used=1029.3MB, alloc=446.7MB, time=71.52 memory used=1361.0MB, alloc=446.7MB, time=77.53 memory used=1465.2MB, alloc=446.7MB, time=78.11 memory used=1572.5MB, alloc=446.7MB, time=79.10 memory used=1692.3MB, alloc=446.7MB, time=79.69 memory used=1799.7MB, alloc=446.7MB, time=80.28 memory used=1821.3MB, alloc=447.9MB, time=80.79 memory used=1822.5MB, alloc=449.1MB, time=80.87 memory used=1823.7MB, alloc=450.3MB, time=80.95 memory used=1824.9MB, alloc=451.5MB, time=81.02 memory used=1826.1MB, alloc=447.9MB, time=81.13 memory used=1986.0MB, alloc=446.7MB, time=83.32 memory used=2140.8MB, alloc=446.7MB, time=86.57 memory used=2256.1MB, alloc=446.7MB, time=88.36 memory used=2346.8MB, alloc=446.7MB, time=88.94 memory used=2474.0MB, alloc=446.7MB, time=90.95 memory used=2608.5MB, alloc=446.7MB, time=93.25 memory used=2676.3MB, alloc=446.7MB, time=93.63 memory used=2750.0MB, alloc=446.7MB, time=94.02 memory used=2829.3MB, alloc=446.7MB, time=94.41 memory used=2915.5MB, alloc=446.7MB, time=94.81 memory used=3009.7MB, alloc=446.7MB, time=95.26 memory used=3103.9MB, alloc=446.7MB, time=95.69 memory used=3157.0MB, alloc=446.7MB, time=96.02 memory used=3211.5MB, alloc=446.7MB, time=96.36 memory used=3267.0MB, alloc=446.7MB, time=96.69 memory used=3326.4MB, alloc=446.7MB, time=97.03 memory used=3389.3MB, alloc=446.7MB, time=97.38 memory used=3455.7MB, alloc=446.7MB, time=97.72 memory used=3527.2MB, alloc=446.7MB, time=98.08 memory used=3599.4MB, alloc=446.7MB, time=98.52 memory used=3670.7MB, alloc=446.7MB, time=98.93 memory used=3747.2MB, alloc=446.7MB, time=99.35 memory used=3830.9MB, alloc=446.7MB, time=99.76 memory used=3921.2MB, alloc=446.7MB, time=100.19 memory used=4019.1MB, alloc=446.7MB, time=100.63 memory used=4094.2MB, alloc=446.7MB, time=101.02 memory used=4147.4MB, alloc=446.7MB, time=101.34 memory used=4202.4MB, alloc=446.7MB, time=101.69 memory used=4260.1MB, alloc=446.7MB, time=102.02 memory used=4320.9MB, alloc=446.7MB, time=102.36 memory used=4384.3MB, alloc=446.7MB, time=102.72 memory used=4453.2MB, alloc=446.7MB, time=103.08 memory used=4525.0MB, alloc=470.7MB, time=104.10 |\^/| 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(); 1428279191 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 2 3 2 F := [-17 y z + 7 z - 8 z - 11 x, -5 x y - 11 x z + 10 z - 17 x , 2 2 -17 x y - 9 z + z - 14] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 G := [-5 x y - 8 y z - 14 x y - 18 y, -13 x + 6 x - 2 x z - 14 z , 3 2 -3 x + 19 x z + 2 x z - 20 z] > Problem := [F,G]; 2 3 2 2 2 3 2 Problem := [[-17 y z + 7 z - 8 z - 11 x, -5 x y - 11 x z + 10 z - 17 x , 2 2 2 2 -17 x y - 9 z + z - 14], [-5 x y - 8 y z - 14 x y - 18 y, 3 2 2 3 2 -13 x + 6 x - 2 x z - 14 z , -3 x + 19 x z + 2 x z - 20 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.30 memory used=26.6MB, alloc=32.3MB, time=0.89 memory used=46.8MB, alloc=56.3MB, time=1.43 memory used=87.4MB, alloc=60.3MB, time=2.50 memory used=127.5MB, alloc=60.3MB, time=3.56 memory used=165.9MB, alloc=84.3MB, time=4.59 memory used=226.0MB, alloc=92.3MB, time=6.22 memory used=283.6MB, alloc=116.3MB, time=7.82 memory used=365.9MB, alloc=116.3MB, time=10.14 memory used=447.7MB, alloc=140.3MB, time=12.46 memory used=532.5MB, alloc=140.3MB, time=14.83 memory used=619.6MB, alloc=396.3MB, time=17.34 memory used=725.4MB, alloc=396.3MB, time=20.35 memory used=830.1MB, alloc=420.3MB, time=23.52 memory used=956.7MB, alloc=420.3MB, time=27.40 memory used=1081.7MB, alloc=444.3MB, time=31.32 memory used=1223.6MB, alloc=468.3MB, time=35.53 memory used=1386.0MB, alloc=492.3MB, time=40.81 memory used=1538.5MB, alloc=492.3MB, time=45.77 memory used=1692.6MB, alloc=516.3MB, time=50.52 memory used=1822.6MB, alloc=516.3MB, time=54.27 memory used=1967.5MB, alloc=516.3MB, time=58.83 memory used=2075.4MB, alloc=540.3MB, time=62.26 memory used=2191.5MB, alloc=540.3MB, time=65.22 memory used=2295.9MB, alloc=540.3MB, time=68.66 memory used=2403.7MB, alloc=564.3MB, time=71.23 memory used=2522.1MB, alloc=564.3MB, time=75.53 memory used=2608.1MB, alloc=564.3MB, time=78.47 memory used=2699.5MB, alloc=564.3MB, time=80.84 memory used=2796.6MB, alloc=564.3MB, time=84.24 memory used=2869.2MB, alloc=564.3MB, time=86.76 memory used=2944.5MB, alloc=564.3MB, time=88.81 memory used=3040.0MB, alloc=564.3MB, time=92.06 memory used=3109.9MB, alloc=564.3MB, time=94.46 memory used=3186.6MB, alloc=564.3MB, time=96.87 memory used=3269.4MB, alloc=564.3MB, time=99.67 memory used=3329.5MB, alloc=564.3MB, time=101.94 memory used=3388.8MB, alloc=564.3MB, time=104.24 memory used=3441.5MB, alloc=564.3MB, time=106.08 memory used=3516.9MB, alloc=564.3MB, time=108.71 memory used=3576.8MB, alloc=564.3MB, time=111.12 memory used=3626.6MB, alloc=564.3MB, time=113.22 memory used=3669.9MB, alloc=564.3MB, time=114.99 memory used=3695.6MB, alloc=564.3MB, time=116.22 memory used=3911.2MB, alloc=588.3MB, time=123.63 memory used=4115.7MB, alloc=612.3MB, time=130.45 memory used=4326.7MB, alloc=636.3MB, time=137.83 memory used=4534.7MB, alloc=660.3MB, time=144.80 |\^/| 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(); 1428279491 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 F := [-10 x z - 8 y z - 9 z - 7 y, 4 x y z + 5 z - 4 y + 10 x, 2 3 2 -x z - 3 z - 6 y + y z] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 G := [2 x y - 10 x z - 4 y + 4, 18 y z + 13 x y + 5 x - 17, 2 2 -6 x y - y z + 6 y z + 8 y] > Problem := [F,G]; 2 2 2 3 2 Problem := [[-10 x z - 8 y z - 9 z - 7 y, 4 x y z + 5 z - 4 y + 10 x, 2 3 2 2 2 3 -x z - 3 z - 6 y + y z], [2 x y - 10 x z - 4 y + 4, 2 2 2 18 y z + 13 x y + 5 x - 17, -6 x y - y z + 6 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=4.5MB, alloc=32.3MB, time=0.32 memory used=26.3MB, alloc=32.3MB, time=0.89 memory used=45.3MB, alloc=56.3MB, time=1.39 memory used=86.4MB, alloc=60.3MB, time=2.41 memory used=128.6MB, alloc=60.3MB, time=3.27 memory used=174.3MB, alloc=60.3MB, time=4.09 memory used=213.6MB, alloc=60.3MB, time=4.68 memory used=247.5MB, alloc=60.3MB, time=5.32 memory used=276.9MB, alloc=60.3MB, time=5.69 memory used=309.5MB, alloc=60.3MB, time=6.27 memory used=345.7MB, alloc=60.3MB, time=6.82 memory used=378.7MB, alloc=60.3MB, time=7.28 memory used=406.5MB, alloc=60.3MB, time=7.65 memory used=432.7MB, alloc=60.3MB, time=7.96 memory used=460.0MB, alloc=60.3MB, time=8.34 memory used=491.2MB, alloc=60.3MB, time=8.80 memory used=528.7MB, alloc=84.3MB, time=9.80 memory used=564.6MB, alloc=84.3MB, time=10.72 memory used=635.8MB, alloc=92.3MB, time=12.27 memory used=696.9MB, alloc=116.3MB, time=13.86 memory used=764.5MB, alloc=116.3MB, time=15.55 memory used=819.9MB, alloc=372.3MB, time=16.74 memory used=883.8MB, alloc=372.3MB, time=17.72 memory used=946.9MB, alloc=372.3MB, time=18.53 memory used=1003.0MB, alloc=372.3MB, time=19.23 memory used=1064.2MB, alloc=372.3MB, time=21.53 memory used=1113.6MB, alloc=372.3MB, time=21.97 memory used=1165.2MB, alloc=372.3MB, time=22.37 memory used=1218.2MB, alloc=372.3MB, time=22.80 memory used=1283.4MB, alloc=372.3MB, time=26.20 memory used=1327.9MB, alloc=372.3MB, time=26.57 memory used=1422.8MB, alloc=372.3MB, time=28.34 memory used=1516.9MB, alloc=372.3MB, time=30.18 memory used=1564.1MB, alloc=372.3MB, time=32.10 memory used=1655.7MB, alloc=396.3MB, time=33.55 memory used=1755.3MB, alloc=396.3MB, time=35.09 memory used=1846.5MB, alloc=396.3MB, time=36.52 memory used=1958.4MB, alloc=396.3MB, time=38.54 memory used=2028.4MB, alloc=396.3MB, time=39.40 memory used=2131.1MB, alloc=396.3MB, time=41.26 memory used=2237.7MB, alloc=420.3MB, time=43.34 memory used=2324.7MB, alloc=420.3MB, time=44.52 memory used=2404.8MB, alloc=420.3MB, time=45.08 memory used=2479.4MB, alloc=420.3MB, time=46.56 memory used=2555.9MB, alloc=420.3MB, time=47.25 memory used=2635.8MB, alloc=420.3MB, time=48.39 memory used=2723.6MB, alloc=420.3MB, time=50.03 memory used=2797.5MB, alloc=420.3MB, time=50.79 memory used=2871.6MB, alloc=420.3MB, time=51.41 memory used=2948.5MB, alloc=420.3MB, time=52.04 memory used=3011.1MB, alloc=420.3MB, time=52.40 memory used=3093.2MB, alloc=420.3MB, time=57.35 memory used=3151.8MB, alloc=420.3MB, time=57.67 memory used=3226.1MB, alloc=420.3MB, time=58.72 memory used=3296.1MB, alloc=420.3MB, time=59.15 memory used=3356.6MB, alloc=420.3MB, time=59.50 memory used=3433.8MB, alloc=420.3MB, time=60.26 memory used=3501.0MB, alloc=420.3MB, time=60.65 memory used=3555.0MB, alloc=420.3MB, time=61.03 memory used=3645.3MB, alloc=420.3MB, time=69.38 memory used=3702.1MB, alloc=420.3MB, time=69.71 memory used=3766.8MB, alloc=420.3MB, time=70.16 memory used=3913.4MB, alloc=420.3MB, time=76.86 memory used=3970.2MB, alloc=420.3MB, time=77.23 memory used=4088.9MB, alloc=420.3MB, time=78.92 memory used=4185.7MB, alloc=420.3MB, time=80.30 memory used=4282.2MB, alloc=420.3MB, time=81.77 memory used=4377.6MB, alloc=420.3MB, time=83.83 memory used=4495.6MB, alloc=444.3MB, time=85.95 memory used=4587.6MB, alloc=444.3MB, time=87.57 memory used=4666.7MB, alloc=444.3MB, time=88.07 memory used=4745.9MB, alloc=444.3MB, time=88.78 memory used=4816.1MB, alloc=444.3MB, time=89.26 memory used=4921.2MB, alloc=444.3MB, time=94.30 memory used=4991.2MB, alloc=444.3MB, time=94.73 memory used=5074.2MB, alloc=444.3MB, time=95.45 memory used=5150.4MB, alloc=444.3MB, time=95.93 memory used=5210.2MB, alloc=444.3MB, time=96.34 memory used=5298.9MB, alloc=444.3MB, time=97.15 memory used=5376.9MB, alloc=444.3MB, time=97.67 memory used=5440.6MB, alloc=444.3MB, time=98.10 memory used=5512.7MB, alloc=444.3MB, time=98.52 memory used=5630.6MB, alloc=444.3MB, time=106.77 memory used=5702.5MB, alloc=444.3MB, time=107.19 memory used=5763.1MB, alloc=444.3MB, time=107.55 memory used=5839.3MB, alloc=444.3MB, time=108.28 memory used=5973.3MB, alloc=444.3MB, time=111.72 memory used=6055.8MB, alloc=444.3MB, time=115.20 memory used=6125.3MB, alloc=444.3MB, time=115.61 memory used=6196.3MB, alloc=444.3MB, time=116.37 memory used=6328.4MB, alloc=444.3MB, time=118.69 memory used=6429.6MB, alloc=444.3MB, time=120.01 memory used=6523.1MB, alloc=444.3MB, time=123.09 memory used=6608.8MB, alloc=444.3MB, time=123.81 memory used=6698.6MB, alloc=444.3MB, time=124.54 memory used=6795.1MB, alloc=444.3MB, time=129.09 memory used=6865.4MB, alloc=444.3MB, time=129.76 memory used=6965.7MB, alloc=444.3MB, time=130.94 memory used=7090.8MB, alloc=444.3MB, time=133.21 memory used=7201.2MB, alloc=444.3MB, time=135.52 memory used=7287.3MB, alloc=468.3MB, time=137.82 memory used=7380.7MB, alloc=468.3MB, time=140.53 memory used=7458.4MB, alloc=468.3MB, time=142.72 memory used=7537.6MB, alloc=468.3MB, time=145.00 memory used=7638.9MB, alloc=492.3MB, time=147.37 memory used=7756.4MB, alloc=492.3MB, time=149.18 memory used=7869.7MB, alloc=492.3MB, time=151.95 memory used=7999.3MB, alloc=492.3MB, time=154.81 memory used=8134.9MB, alloc=492.3MB, time=168.31 memory used=8222.4MB, alloc=492.3MB, time=168.95 memory used=8303.2MB, alloc=492.3MB, time=169.51 memory used=8419.9MB, alloc=492.3MB, time=171.31 memory used=8544.8MB, alloc=492.3MB, time=174.06 memory used=8646.7MB, alloc=492.3MB, time=176.11 memory used=8766.3MB, alloc=492.3MB, time=178.80 memory used=8845.6MB, alloc=492.3MB, time=180.97 memory used=8954.5MB, alloc=492.3MB, time=182.47 memory used=9031.9MB, alloc=492.3MB, time=183.11 memory used=9114.2MB, alloc=516.3MB, time=184.78 memory used=9184.9MB, alloc=516.3MB, time=186.74 memory used=9230.8MB, alloc=516.3MB, time=188.14 memory used=9355.6MB, alloc=516.3MB, time=189.52 memory used=9479.3MB, alloc=516.3MB, time=191.15 memory used=9602.8MB, alloc=516.3MB, time=193.18 memory used=9721.6MB, alloc=516.3MB, time=194.36 memory used=9839.3MB, alloc=516.3MB, time=197.53 memory used=9957.0MB, alloc=516.3MB, time=198.46 memory used=10075.0MB, alloc=516.3MB, time=201.83 memory used=10151.8MB, alloc=516.3MB, time=203.53 memory used=10214.2MB, alloc=516.3MB, time=205.61 memory used=10338.9MB, alloc=516.3MB, time=208.90 memory used=10439.9MB, alloc=516.3MB, time=210.43 memory used=10537.1MB, alloc=516.3MB, time=212.11 |\^/| 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(); 1428279791 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 3 2 3 F := [-3 x y + 14 x y z + 16 y + 4 y z , -x - 14 x z - 6 z - 13 x, 2 -19 x - 6 z] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [5 x y - 2 y z + 8 x - 13 y, 19 y z - 3 x y - 4 x z - 19 y , 3 2 7 z + 5 x z - 18 y - 7 x] > Problem := [F,G]; 2 3 2 3 2 3 Problem := [[-3 x y + 14 x y z + 16 y + 4 y z , -x - 14 x z - 6 z - 13 x, 2 2 2 -19 x - 6 z], [5 x y - 2 y z + 8 x - 13 y, 19 y z - 3 x y - 4 x z - 19 y , 3 2 7 z + 5 x z - 18 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=4.3MB, alloc=32.3MB, time=0.30 memory used=26.1MB, alloc=32.3MB, time=0.88 memory used=45.8MB, alloc=56.3MB, time=1.41 memory used=91.3MB, alloc=92.3MB, time=2.63 memory used=164.5MB, alloc=100.3MB, time=4.53 memory used=237.7MB, alloc=100.3MB, time=6.36 memory used=308.7MB, alloc=100.3MB, time=8.01 memory used=380.0MB, alloc=380.3MB, time=9.84 memory used=474.1MB, alloc=380.3MB, time=12.30 memory used=566.5MB, alloc=404.3MB, time=14.83 memory used=687.5MB, alloc=428.3MB, time=17.79 memory used=821.4MB, alloc=428.3MB, time=20.48 memory used=966.6MB, alloc=428.3MB, time=23.82 memory used=1096.2MB, alloc=452.3MB, time=27.21 memory used=1230.5MB, alloc=476.3MB, time=30.96 memory used=1354.5MB, alloc=476.3MB, time=34.05 memory used=1479.2MB, alloc=476.3MB, time=37.15 memory used=1603.8MB, alloc=500.3MB, time=40.35 memory used=1725.5MB, alloc=500.3MB, time=44.15 memory used=1817.8MB, alloc=500.3MB, time=47.04 memory used=1905.7MB, alloc=524.3MB, time=49.24 memory used=1993.3MB, alloc=524.3MB, time=51.19 memory used=2075.7MB, alloc=524.3MB, time=54.03 memory used=2143.0MB, alloc=524.3MB, time=55.89 memory used=2216.7MB, alloc=524.3MB, time=58.19 memory used=2290.3MB, alloc=524.3MB, time=60.73 memory used=2354.2MB, alloc=548.3MB, time=62.80 memory used=2423.2MB, alloc=548.3MB, time=65.21 memory used=2478.3MB, alloc=548.3MB, time=66.81 memory used=2527.0MB, alloc=548.3MB, time=68.41 memory used=2588.8MB, alloc=548.3MB, time=70.17 memory used=2639.6MB, alloc=548.3MB, time=71.55 memory used=2878.0MB, alloc=572.3MB, time=77.53 memory used=3132.8MB, alloc=596.3MB, time=83.24 memory used=3334.4MB, alloc=620.3MB, time=89.44 memory used=3476.1MB, alloc=644.3MB, time=93.48 memory used=3671.3MB, alloc=668.3MB, time=98.69 memory used=3812.4MB, alloc=668.3MB, time=102.64 memory used=3964.2MB, alloc=692.3MB, time=107.76 memory used=4108.3MB, alloc=692.3MB, time=111.93 memory used=4336.0MB, alloc=716.3MB, time=116.13 memory used=4500.1MB, alloc=716.3MB, time=119.86 memory used=4649.7MB, alloc=716.3MB, time=124.21 memory used=4783.6MB, alloc=716.3MB, time=128.50 memory used=4900.4MB, alloc=716.3MB, time=132.91 memory used=5018.5MB, alloc=716.3MB, time=136.29 memory used=5322.6MB, alloc=740.3MB, time=141.93 memory used=5726.1MB, alloc=764.3MB, time=150.74 memory used=6118.8MB, alloc=788.3MB, time=161.07 |\^/| 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(); 1428280091 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 3 F := [-17 x y - 13 x z - 2 y + 8 z, -18 x + 2 y z - 2 y + 16 z, 3 2 -7 z + 13 x y + 17 z - 10] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 G := [4 x + 5 x y + 4 x y z + 10 z , 7 x y + 11 x z + 5 y - 3 z, 2 2 10 x y + 9 y + 4 y + 6 z] > Problem := [F,G]; 2 2 3 3 Problem := [[-17 x y - 13 x z - 2 y + 8 z, -18 x + 2 y z - 2 y + 16 z, 3 2 3 2 2 -7 z + 13 x y + 17 z - 10], [4 x + 5 x y + 4 x y z + 10 z , 2 2 2 7 x y + 11 x z + 5 y - 3 z, 10 x y + 9 y + 4 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=30.6MB, alloc=40.3MB, time=0.98 memory used=56.4MB, alloc=68.3MB, time=1.70 memory used=103.9MB, alloc=68.3MB, time=2.91 memory used=154.7MB, alloc=76.3MB, time=4.19 memory used=202.8MB, alloc=100.3MB, time=5.46 memory used=276.0MB, alloc=100.3MB, time=7.30 memory used=348.7MB, alloc=100.3MB, time=9.11 memory used=418.7MB, alloc=124.3MB, time=10.85 memory used=481.9MB, alloc=380.3MB, time=12.24 memory used=587.5MB, alloc=380.3MB, time=14.46 memory used=681.2MB, alloc=404.3MB, time=16.40 memory used=786.9MB, alloc=404.3MB, time=18.06 memory used=910.3MB, alloc=404.3MB, time=21.03 memory used=1024.3MB, alloc=428.3MB, time=23.99 memory used=1151.8MB, alloc=428.3MB, time=26.25 memory used=1272.6MB, alloc=452.3MB, time=29.03 memory used=1380.0MB, alloc=452.3MB, time=31.48 memory used=1504.1MB, alloc=452.3MB, time=34.62 memory used=1632.3MB, alloc=476.3MB, time=38.40 memory used=1726.3MB, alloc=476.3MB, time=41.00 memory used=1804.9MB, alloc=500.3MB, time=42.80 memory used=1910.7MB, alloc=500.3MB, time=46.21 memory used=2007.3MB, alloc=500.3MB, time=49.28 memory used=2086.5MB, alloc=500.3MB, time=51.46 memory used=2159.6MB, alloc=500.3MB, time=53.20 memory used=2253.4MB, alloc=500.3MB, time=56.06 memory used=2316.8MB, alloc=500.3MB, time=58.18 memory used=2383.8MB, alloc=524.3MB, time=60.60 memory used=2442.0MB, alloc=524.3MB, time=62.41 memory used=2495.6MB, alloc=524.3MB, time=64.02 memory used=2560.6MB, alloc=524.3MB, time=66.04 memory used=2614.4MB, alloc=524.3MB, time=68.26 memory used=2822.7MB, alloc=548.3MB, time=74.09 memory used=2995.4MB, alloc=572.3MB, time=78.80 memory used=3162.1MB, alloc=596.3MB, time=83.04 memory used=3330.9MB, alloc=596.3MB, time=88.36 memory used=3511.9MB, alloc=620.3MB, time=92.53 memory used=3712.2MB, alloc=620.3MB, time=96.66 memory used=3871.8MB, alloc=620.3MB, time=100.66 memory used=4043.9MB, alloc=644.3MB, time=104.55 memory used=4243.7MB, alloc=644.3MB, time=109.11 memory used=4361.9MB, alloc=644.3MB, time=112.83 memory used=4507.4MB, alloc=644.3MB, time=116.15 memory used=4638.8MB, alloc=668.3MB, time=121.01 memory used=4724.5MB, alloc=668.3MB, time=124.02 memory used=4854.1MB, alloc=668.3MB, time=127.16 memory used=4987.2MB, alloc=668.3MB, time=130.41 memory used=5078.0MB, alloc=668.3MB, time=133.61 memory used=5193.6MB, alloc=668.3MB, time=137.14 memory used=5531.5MB, alloc=692.3MB, time=145.22 memory used=5917.0MB, alloc=716.3MB, time=155.40 |\^/| 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(); 1428280391 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 2 F := [17 x y + 8 x z - 15 x y + 5 y z , -2 y z + 7 y - 3 y z, 3 2 2 -19 y + 10 y z + y z + 17 y z] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 G := [-17 x z - 13 y + 11 x - 11 y, -19 y z - 6 z - x + y z, 2 2 7 x - 12 x y + 18 y + 18 y z] > Problem := [F,G]; 2 2 2 2 2 2 Problem := [[17 x y + 8 x z - 15 x y + 5 y z , -2 y z + 7 y - 3 y z, 3 2 2 2 2 -19 y + 10 y z + y z + 17 y z], [-17 x z - 13 y + 11 x - 11 y, 2 3 2 2 2 -19 y z - 6 z - x + y z, 7 x - 12 x y + 18 y + 18 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=24.9MB, alloc=32.3MB, time=0.85 memory used=43.8MB, alloc=56.3MB, time=1.34 memory used=84.2MB, alloc=60.3MB, time=2.37 memory used=128.4MB, alloc=68.3MB, time=3.40 memory used=172.9MB, alloc=68.3MB, time=4.46 memory used=214.9MB, alloc=92.3MB, time=5.54 memory used=280.7MB, alloc=92.3MB, time=7.12 memory used=345.1MB, alloc=92.3MB, time=8.57 memory used=411.3MB, alloc=116.3MB, time=10.26 memory used=481.0MB, alloc=116.3MB, time=11.94 memory used=534.3MB, alloc=372.3MB, time=13.30 memory used=620.4MB, alloc=372.3MB, time=15.07 memory used=709.5MB, alloc=396.3MB, time=17.11 memory used=818.3MB, alloc=396.3MB, time=19.30 memory used=933.0MB, alloc=420.3MB, time=22.00 memory used=1062.9MB, alloc=420.3MB, time=25.36 memory used=1182.9MB, alloc=444.3MB, time=27.97 memory used=1306.0MB, alloc=468.3MB, time=31.07 memory used=1413.0MB, alloc=468.3MB, time=33.21 memory used=1516.7MB, alloc=468.3MB, time=36.11 memory used=1618.2MB, alloc=468.3MB, time=38.93 memory used=1711.0MB, alloc=492.3MB, time=41.24 memory used=1811.5MB, alloc=492.3MB, time=43.97 memory used=1894.3MB, alloc=492.3MB, time=46.27 memory used=1973.5MB, alloc=492.3MB, time=48.55 memory used=2068.1MB, alloc=492.3MB, time=50.58 memory used=2147.4MB, alloc=492.3MB, time=52.88 memory used=2219.7MB, alloc=492.3MB, time=54.55 memory used=2274.4MB, alloc=492.3MB, time=56.14 memory used=2347.4MB, alloc=516.3MB, time=57.77 memory used=2415.8MB, alloc=516.3MB, time=59.40 memory used=2499.6MB, alloc=516.3MB, time=61.57 memory used=2576.3MB, alloc=516.3MB, time=63.41 memory used=2633.5MB, alloc=516.3MB, time=65.13 memory used=2691.9MB, alloc=516.3MB, time=66.73 memory used=2752.2MB, alloc=516.3MB, time=68.18 memory used=2812.5MB, alloc=516.3MB, time=70.33 memory used=2855.8MB, alloc=516.3MB, time=71.93 memory used=2904.7MB, alloc=516.3MB, time=73.47 memory used=2947.0MB, alloc=516.3MB, time=74.94 memory used=3149.5MB, alloc=540.3MB, time=81.41 memory used=3363.2MB, alloc=564.3MB, time=86.48 memory used=3545.2MB, alloc=564.3MB, time=90.94 memory used=3764.5MB, alloc=588.3MB, time=96.18 memory used=3911.0MB, alloc=588.3MB, time=100.16 memory used=4078.6MB, alloc=612.3MB, time=105.15 memory used=4272.4MB, alloc=612.3MB, time=109.54 memory used=4454.9MB, alloc=612.3MB, time=114.04 memory used=4579.4MB, alloc=636.3MB, time=117.20 memory used=4727.6MB, alloc=636.3MB, time=122.06 memory used=4854.9MB, alloc=636.3MB, time=125.59 memory used=5007.9MB, alloc=636.3MB, time=130.52 memory used=5168.0MB, alloc=636.3MB, time=134.67 memory used=5284.4MB, alloc=636.3MB, time=138.63 memory used=5394.3MB, alloc=660.3MB, time=141.83 memory used=5533.9MB, alloc=660.3MB, time=145.69 |\^/| 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(); 1428280691 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [16 x y z - 2 y z - 6 x y + 2, -7 x z + 5 x y z + 20 x z - 20 y z, 3 2 10 x + 11 y z + 13 x y - 2 x z] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 G := [15 y + 12 x z + 12 z - 6 y, -5 x y + 13 x z - 13 y + 19, 2 3 2 2 -5 x z - 8 z + 13 x - 2 y ] > Problem := [F,G]; 2 2 Problem := [[16 x y z - 2 y z - 6 x y + 2, -7 x z + 5 x y z + 20 x z - 20 y z, 3 2 3 2 10 x + 11 y z + 13 x y - 2 x z], [15 y + 12 x z + 12 z - 6 y, 2 2 3 2 2 -5 x y + 13 x z - 13 y + 19, -5 x z - 8 z + 13 x - 2 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.31 memory used=26.6MB, alloc=32.3MB, time=0.90 memory used=47.3MB, alloc=32.3MB, time=1.43 memory used=67.2MB, alloc=60.3MB, time=1.98 memory used=108.0MB, alloc=60.3MB, time=2.98 memory used=143.1MB, alloc=84.3MB, time=3.87 memory used=206.6MB, alloc=92.3MB, time=5.57 memory used=272.0MB, alloc=92.3MB, time=7.20 memory used=335.3MB, alloc=116.3MB, time=8.85 memory used=423.6MB, alloc=116.3MB, time=11.21 memory used=484.9MB, alloc=116.3MB, time=12.13 memory used=571.3MB, alloc=372.3MB, time=13.80 memory used=655.2MB, alloc=372.3MB, time=15.68 memory used=737.9MB, alloc=396.3MB, time=17.87 memory used=847.0MB, alloc=420.3MB, time=20.65 memory used=979.9MB, alloc=420.3MB, time=23.74 memory used=1107.0MB, alloc=444.3MB, time=27.28 memory used=1240.7MB, alloc=444.3MB, time=29.59 memory used=1340.6MB, alloc=444.3MB, time=31.49 memory used=1440.4MB, alloc=444.3MB, time=32.84 memory used=1614.7MB, alloc=444.3MB, time=36.80 memory used=1751.2MB, alloc=468.3MB, time=40.50 memory used=1881.4MB, alloc=492.3MB, time=43.25 memory used=2024.1MB, alloc=492.3MB, time=46.24 memory used=2109.8MB, alloc=492.3MB, time=46.77 memory used=2258.0MB, alloc=492.3MB, time=49.30 memory used=2361.4MB, alloc=492.3MB, time=50.37 memory used=2465.6MB, alloc=492.3MB, time=52.38 memory used=2546.8MB, alloc=492.3MB, time=52.95 memory used=2625.6MB, alloc=492.3MB, time=53.45 memory used=2731.1MB, alloc=492.3MB, time=55.65 memory used=2812.2MB, alloc=492.3MB, time=56.22 memory used=2905.7MB, alloc=492.3MB, time=57.03 memory used=2999.6MB, alloc=492.3MB, time=58.01 memory used=3128.1MB, alloc=492.3MB, time=60.10 memory used=3231.9MB, alloc=516.3MB, time=63.32 memory used=3308.5MB, alloc=516.3MB, time=65.57 memory used=3401.5MB, alloc=516.3MB, time=68.47 memory used=3496.4MB, alloc=516.3MB, time=71.59 memory used=3569.8MB, alloc=516.3MB, time=73.92 memory used=3626.3MB, alloc=516.3MB, time=75.49 memory used=3699.6MB, alloc=516.3MB, time=77.89 memory used=3747.1MB, alloc=516.3MB, time=79.67 memory used=3792.1MB, alloc=516.3MB, time=81.17 memory used=3857.4MB, alloc=516.3MB, time=83.75 memory used=3896.8MB, alloc=516.3MB, time=85.43 memory used=4094.9MB, alloc=540.3MB, time=91.14 memory used=4233.9MB, alloc=564.3MB, time=98.11 memory used=4410.4MB, alloc=588.3MB, time=102.94 memory used=4661.0MB, alloc=588.3MB, time=110.86 memory used=4804.4MB, alloc=588.3MB, time=117.07 memory used=5055.7MB, alloc=612.3MB, time=121.62 memory used=5257.7MB, alloc=612.3MB, time=164.80 memory used=5429.9MB, alloc=612.3MB, time=166.67 memory used=5748.0MB, alloc=636.3MB, time=172.60 memory used=5949.7MB, alloc=636.3MB, time=177.38 |\^/| 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(); 1428280991 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 F := [-10 x y - 19 z - 2 x y - 16 x z, -19 y z + 8 x z - 4 y - 13 y z, 2 2 15 x y z - 13 y z + 16 x + 14 y] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-11 x y + 9 x y z + 10 y + 1, -8 x y - 9 y + 15 y z + 4 y, 2 2 2 -4 x z - 8 y z - 3 x - x] > Problem := [F,G]; 2 3 Problem := [[-10 x y - 19 z - 2 x y - 16 x z, 2 2 2 2 -19 y z + 8 x z - 4 y - 13 y z, 15 x y z - 13 y z + 16 x + 14 y], [ 2 2 -11 x y + 9 x y z + 10 y + 1, -8 x y - 9 y + 15 y z + 4 y, 2 2 2 -4 x z - 8 y 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=4.3MB, alloc=32.3MB, time=0.30 memory used=24.9MB, alloc=32.3MB, time=0.84 memory used=44.1MB, alloc=56.3MB, time=1.35 memory used=81.4MB, alloc=60.3MB, time=2.19 memory used=125.2MB, alloc=68.3MB, time=3.15 memory used=167.9MB, alloc=68.3MB, time=3.93 memory used=207.4MB, alloc=68.3MB, time=4.73 memory used=251.6MB, alloc=92.3MB, time=5.81 memory used=316.5MB, alloc=92.3MB, time=7.49 memory used=372.0MB, alloc=92.3MB, time=8.31 memory used=440.4MB, alloc=92.3MB, time=9.74 memory used=509.0MB, alloc=116.3MB, time=11.21 memory used=569.6MB, alloc=116.3MB, time=12.56 memory used=635.1MB, alloc=372.3MB, time=14.10 memory used=720.6MB, alloc=372.3MB, time=15.72 memory used=779.2MB, alloc=372.3MB, time=16.43 memory used=865.9MB, alloc=372.3MB, time=18.41 memory used=959.8MB, alloc=396.3MB, time=20.41 memory used=1071.1MB, alloc=396.3MB, time=22.83 memory used=1136.5MB, alloc=396.3MB, time=23.40 memory used=1196.3MB, alloc=396.3MB, time=24.13 memory used=1300.6MB, alloc=396.3MB, time=26.37 memory used=1381.3MB, alloc=396.3MB, time=27.47 memory used=1469.2MB, alloc=396.3MB, time=28.63 memory used=1564.1MB, alloc=420.3MB, time=30.24 memory used=1689.1MB, alloc=420.3MB, time=32.76 memory used=1794.2MB, alloc=420.3MB, time=35.13 memory used=1894.1MB, alloc=444.3MB, time=37.02 memory used=2042.0MB, alloc=444.3MB, time=39.72 memory used=2138.2MB, alloc=444.3MB, time=42.06 memory used=2236.7MB, alloc=444.3MB, time=43.43 memory used=2378.9MB, alloc=444.3MB, time=45.74 memory used=2489.0MB, alloc=468.3MB, time=47.95 memory used=2615.1MB, alloc=468.3MB, time=50.10 memory used=2730.4MB, alloc=468.3MB, time=52.62 memory used=2829.6MB, alloc=468.3MB, time=53.65 memory used=2916.8MB, alloc=468.3MB, time=54.77 memory used=3034.1MB, alloc=468.3MB, time=56.98 memory used=3160.8MB, alloc=468.3MB, time=58.39 memory used=3243.2MB, alloc=468.3MB, time=59.07 memory used=3326.4MB, alloc=468.3MB, time=60.27 memory used=3417.5MB, alloc=468.3MB, time=61.14 memory used=3532.1MB, alloc=468.3MB, time=62.67 memory used=3659.5MB, alloc=468.3MB, time=65.60 memory used=3732.9MB, alloc=468.3MB, time=66.13 memory used=3808.5MB, alloc=468.3MB, time=66.62 memory used=3886.4MB, alloc=468.3MB, time=67.45 memory used=3976.7MB, alloc=468.3MB, time=68.62 memory used=4052.6MB, alloc=468.3MB, time=69.17 memory used=4117.5MB, alloc=468.3MB, time=69.63 memory used=4290.2MB, alloc=468.3MB, time=71.98 memory used=4423.0MB, alloc=468.3MB, time=74.73 memory used=4541.9MB, alloc=492.3MB, time=77.16 memory used=4632.8MB, alloc=492.3MB, time=77.73 memory used=4721.5MB, alloc=492.3MB, time=78.56 memory used=4823.0MB, alloc=492.3MB, time=79.75 memory used=4910.4MB, alloc=492.3MB, time=80.29 memory used=5079.8MB, alloc=492.3MB, time=82.83 memory used=5166.9MB, alloc=492.3MB, time=85.02 memory used=5246.5MB, alloc=492.3MB, time=86.94 memory used=5359.5MB, alloc=492.3MB, time=88.66 memory used=5430.3MB, alloc=492.3MB, time=90.69 memory used=5564.8MB, alloc=492.3MB, time=93.63 memory used=5685.8MB, alloc=492.3MB, time=95.82 memory used=5747.5MB, alloc=492.3MB, time=97.67 memory used=5819.7MB, alloc=516.3MB, time=99.18 memory used=5888.6MB, alloc=516.3MB, time=100.77 memory used=5976.8MB, alloc=516.3MB, time=102.83 memory used=6065.5MB, alloc=516.3MB, time=104.41 memory used=6125.3MB, alloc=516.3MB, time=106.21 memory used=6192.8MB, alloc=516.3MB, time=107.94 memory used=6242.0MB, alloc=516.3MB, time=109.42 memory used=6337.1MB, alloc=516.3MB, time=111.04 memory used=6393.1MB, alloc=516.3MB, time=113.45 memory used=6490.1MB, alloc=516.3MB, time=114.21 memory used=6571.7MB, alloc=516.3MB, time=114.84 memory used=6682.8MB, alloc=516.3MB, time=116.07 memory used=6783.0MB, alloc=516.3MB, time=116.81 memory used=6859.5MB, alloc=516.3MB, time=117.45 memory used=6981.9MB, alloc=516.3MB, time=119.20 memory used=7187.3MB, alloc=540.3MB, time=123.30 memory used=7329.5MB, alloc=540.3MB, time=126.16 memory used=7457.4MB, alloc=540.3MB, time=128.29 memory used=7856.7MB, alloc=540.3MB, time=146.85 memory used=8492.1MB, alloc=564.3MB, time=159.37 memory used=8511.6MB, alloc=566.2MB, time=161.23 memory used=8513.5MB, alloc=568.1MB, time=161.81 memory used=8515.3MB, alloc=570.0MB, time=162.36 memory used=8517.2MB, alloc=571.9MB, time=162.91 memory used=8519.1MB, alloc=566.2MB, time=163.53 memory used=8661.2MB, alloc=564.3MB, time=165.36 |\^/| 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(); 1428281291 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 3 2 2 F := [4 x y - 8 y - 17 z + 14 z, 15 x y + 13 x z - 18 x y - y z, 3 2 -6 x - 17 x y z - 11 x z + 20 y] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 G := [-3 y - y z + 10 x - 7 y, 10 x y - 5 x y + x z - 11 x, 2 2 2 8 x y - 5 x z - 2 x z - 2] > Problem := [F,G]; 2 3 3 2 2 Problem := [[4 x y - 8 y - 17 z + 14 z, 15 x y + 13 x z - 18 x y - y z, 3 2 3 -6 x - 17 x y z - 11 x z + 20 y], [-3 y - y z + 10 x - 7 y, 2 2 2 2 2 10 x y - 5 x y + x z - 11 x, 8 x y - 5 x z - 2 x z - 2]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=25.7MB, alloc=32.3MB, time=0.85 memory used=45.4MB, alloc=60.3MB, time=1.33 memory used=88.3MB, alloc=60.3MB, time=2.23 memory used=131.5MB, alloc=60.3MB, time=3.25 memory used=171.2MB, alloc=84.3MB, time=4.20 memory used=239.5MB, alloc=92.3MB, time=5.53 memory used=303.6MB, alloc=348.3MB, time=7.01 memory used=370.3MB, alloc=372.3MB, time=8.54 memory used=458.5MB, alloc=372.3MB, time=10.19 memory used=550.8MB, alloc=372.3MB, time=12.05 memory used=655.9MB, alloc=396.3MB, time=14.48 memory used=769.5MB, alloc=420.3MB, time=17.33 memory used=897.5MB, alloc=420.3MB, time=20.05 memory used=998.9MB, alloc=420.3MB, time=21.69 memory used=1135.8MB, alloc=444.3MB, time=24.41 memory used=1232.3MB, alloc=444.3MB, time=25.57 memory used=1319.6MB, alloc=444.3MB, time=26.51 memory used=1453.0MB, alloc=444.3MB, time=29.16 memory used=1561.2MB, alloc=444.3MB, time=32.31 memory used=1661.1MB, alloc=468.3MB, time=34.98 memory used=1754.2MB, alloc=468.3MB, time=37.34 memory used=1878.2MB, alloc=468.3MB, time=39.76 memory used=1957.3MB, alloc=468.3MB, time=41.90 memory used=2066.5MB, alloc=468.3MB, time=43.52 memory used=2156.0MB, alloc=468.3MB, time=44.72 memory used=2266.7MB, alloc=492.3MB, time=46.82 memory used=2343.6MB, alloc=492.3MB, time=49.01 memory used=2412.9MB, alloc=492.3MB, time=50.82 memory used=2488.4MB, alloc=492.3MB, time=53.11 memory used=2565.9MB, alloc=492.3MB, time=55.38 memory used=2640.2MB, alloc=492.3MB, time=57.97 memory used=2703.8MB, alloc=492.3MB, time=59.83 memory used=2772.8MB, alloc=492.3MB, time=61.99 memory used=2824.9MB, alloc=492.3MB, time=63.47 memory used=2868.5MB, alloc=492.3MB, time=64.92 memory used=2920.8MB, alloc=492.3MB, time=66.46 memory used=2970.9MB, alloc=492.3MB, time=68.01 memory used=3157.5MB, alloc=516.3MB, time=72.65 memory used=3338.7MB, alloc=540.3MB, time=77.40 memory used=3486.2MB, alloc=564.3MB, time=80.62 memory used=3670.8MB, alloc=588.3MB, time=85.59 memory used=3807.1MB, alloc=612.3MB, time=89.39 memory used=4019.6MB, alloc=612.3MB, time=95.03 memory used=4181.8MB, alloc=612.3MB, time=99.15 memory used=4327.3MB, alloc=636.3MB, time=102.89 memory used=4485.1MB, alloc=660.3MB, time=106.62 memory used=4648.0MB, alloc=660.3MB, time=110.60 memory used=4766.3MB, alloc=660.3MB, time=114.05 memory used=4862.3MB, alloc=660.3MB, time=116.86 memory used=4978.3MB, alloc=660.3MB, time=120.28 memory used=5065.7MB, alloc=660.3MB, time=123.70 memory used=5156.6MB, alloc=660.3MB, time=127.16 memory used=5477.8MB, alloc=684.3MB, time=136.89 |\^/| 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(); 1428281591 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 F := [5 z - 13 x + 16 x z - 8 y z, -20 x y z - 14 y - 17 y z + 12 x, 2 3 2 19 x z + 12 x y z - 4 y + 11 x ] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 2 3 2 G := [3 x z + 6 y z + 10 y z - 11 z , -18 x y - 13 x y + 8 y - 16 x , 2 2 16 x z - 10 x - 7 x z] > Problem := [F,G]; 3 2 3 2 Problem := [[5 z - 13 x + 16 x z - 8 y z, -20 x y z - 14 y - 17 y z + 12 x, 2 3 2 2 2 2 2 19 x z + 12 x y z - 4 y + 11 x ], [3 x z + 6 y z + 10 y z - 11 z , 2 2 3 2 2 2 -18 x y - 13 x y + 8 y - 16 x , 16 x z - 10 x - 7 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.30 memory used=25.7MB, alloc=32.3MB, time=0.86 memory used=45.9MB, alloc=32.3MB, time=1.38 memory used=63.6MB, alloc=56.3MB, time=1.87 memory used=104.2MB, alloc=60.3MB, time=2.90 memory used=140.6MB, alloc=84.3MB, time=3.86 memory used=204.4MB, alloc=92.3MB, time=5.55 memory used=268.0MB, alloc=92.3MB, time=7.13 memory used=328.9MB, alloc=116.3MB, time=8.82 memory used=395.7MB, alloc=372.3MB, time=10.53 memory used=477.4MB, alloc=396.3MB, time=12.85 memory used=589.9MB, alloc=420.3MB, time=15.73 memory used=729.8MB, alloc=444.3MB, time=19.22 memory used=859.4MB, alloc=468.3MB, time=22.59 memory used=980.0MB, alloc=468.3MB, time=25.65 memory used=1127.8MB, alloc=492.3MB, time=30.17 memory used=1242.1MB, alloc=492.3MB, time=33.59 memory used=1342.9MB, alloc=516.3MB, time=36.34 memory used=1448.1MB, alloc=516.3MB, time=39.50 memory used=1528.2MB, alloc=516.3MB, time=41.88 memory used=1609.0MB, alloc=516.3MB, time=43.79 memory used=1688.7MB, alloc=516.3MB, time=46.55 memory used=1754.3MB, alloc=516.3MB, time=48.46 memory used=1827.0MB, alloc=540.3MB, time=50.18 memory used=1895.1MB, alloc=540.3MB, time=52.40 memory used=1959.1MB, alloc=540.3MB, time=54.97 memory used=2036.1MB, alloc=540.3MB, time=57.91 memory used=2087.1MB, alloc=540.3MB, time=59.76 memory used=2126.1MB, alloc=540.3MB, time=61.17 memory used=2327.7MB, alloc=564.3MB, time=67.00 memory used=2523.8MB, alloc=588.3MB, time=72.51 memory used=2718.3MB, alloc=612.3MB, time=78.56 memory used=2917.5MB, alloc=636.3MB, time=85.54 memory used=3082.5MB, alloc=660.3MB, time=91.52 memory used=3253.4MB, alloc=660.3MB, time=97.20 memory used=3394.4MB, alloc=684.3MB, time=100.90 memory used=3538.4MB, alloc=684.3MB, time=106.48 memory used=3667.7MB, alloc=684.3MB, time=111.21 memory used=3766.4MB, alloc=684.3MB, time=114.57 memory used=3897.7MB, alloc=684.3MB, time=118.28 memory used=4038.4MB, alloc=684.3MB, time=123.17 memory used=4134.5MB, alloc=708.3MB, time=126.24 memory used=4527.0MB, alloc=732.3MB, time=137.11 |\^/| 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(); 1428281891 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 F := [17 x y z - 19 x z + y - 7 z , 6 x z + 4 x y z + 3 y z + 19 z , 2 3 2 15 x z + 12 y - 16 y ] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 3 3 2 G := [15 x z + 6 y z - 13 x + z , -10 y + 7 z - 8 x - 10, 3 -10 x - 20 x y z - 15 y z - 3 x] > Problem := [F,G]; 2 2 2 2 2 Problem := [[17 x y z - 19 x z + y - 7 z , 6 x z + 4 x y z + 3 y z + 19 z , 2 3 2 2 2 2 2 15 x z + 12 y - 16 y ], [15 x z + 6 y z - 13 x + z , 3 3 2 3 -10 y + 7 z - 8 x - 10, -10 x - 20 x y z - 15 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=4.4MB, alloc=32.3MB, time=0.31 memory used=25.5MB, alloc=32.3MB, time=0.86 memory used=44.4MB, alloc=56.3MB, time=1.36 memory used=84.7MB, alloc=60.3MB, time=2.34 memory used=124.7MB, alloc=60.3MB, time=3.38 memory used=161.6MB, alloc=84.3MB, time=4.32 memory used=232.0MB, alloc=92.3MB, time=5.98 memory used=297.3MB, alloc=348.3MB, time=7.40 memory used=364.6MB, alloc=372.3MB, time=8.98 memory used=457.0MB, alloc=372.3MB, time=10.83 memory used=552.0MB, alloc=396.3MB, time=13.00 memory used=664.5MB, alloc=396.3MB, time=15.83 memory used=779.7MB, alloc=420.3MB, time=18.68 memory used=913.2MB, alloc=444.3MB, time=22.08 memory used=1035.8MB, alloc=444.3MB, time=25.09 memory used=1156.7MB, alloc=444.3MB, time=27.88 memory used=1258.2MB, alloc=468.3MB, time=30.36 memory used=1365.2MB, alloc=468.3MB, time=32.77 memory used=1477.6MB, alloc=468.3MB, time=35.28 memory used=1608.1MB, alloc=468.3MB, time=37.76 memory used=1726.5MB, alloc=468.3MB, time=40.05 memory used=1818.6MB, alloc=468.3MB, time=42.27 memory used=1904.4MB, alloc=492.3MB, time=44.58 memory used=1991.8MB, alloc=492.3MB, time=46.66 memory used=2082.8MB, alloc=492.3MB, time=48.77 memory used=2173.7MB, alloc=492.3MB, time=50.91 memory used=2250.9MB, alloc=492.3MB, time=52.91 memory used=2320.6MB, alloc=492.3MB, time=54.85 memory used=2396.8MB, alloc=492.3MB, time=56.80 memory used=2454.2MB, alloc=492.3MB, time=58.48 memory used=2508.6MB, alloc=492.3MB, time=60.10 memory used=2591.1MB, alloc=516.3MB, time=62.85 memory used=2658.7MB, alloc=516.3MB, time=65.22 memory used=2732.5MB, alloc=516.3MB, time=67.76 memory used=2787.9MB, alloc=516.3MB, time=69.62 memory used=2834.0MB, alloc=516.3MB, time=71.16 memory used=2895.0MB, alloc=516.3MB, time=72.77 memory used=2960.6MB, alloc=516.3MB, time=74.33 memory used=3174.9MB, alloc=540.3MB, time=79.01 memory used=3378.1MB, alloc=564.3MB, time=84.32 memory used=3625.3MB, alloc=588.3MB, time=88.83 memory used=3837.1MB, alloc=612.3MB, time=95.02 memory used=4040.6MB, alloc=636.3MB, time=100.37 memory used=4207.4MB, alloc=660.3MB, time=104.47 memory used=4366.4MB, alloc=684.3MB, time=107.75 memory used=4574.7MB, alloc=684.3MB, time=113.06 memory used=4704.1MB, alloc=708.3MB, time=117.00 memory used=4837.1MB, alloc=708.3MB, time=121.36 memory used=4958.5MB, alloc=708.3MB, time=125.21 memory used=5092.3MB, alloc=708.3MB, time=129.71 memory used=5203.5MB, alloc=708.3MB, time=133.61 memory used=5305.7MB, alloc=708.3MB, time=136.61 memory used=5411.0MB, alloc=708.3MB, time=139.47 memory used=5558.7MB, alloc=732.3MB, time=142.55 memory used=5965.5MB, alloc=756.3MB, time=152.19 |\^/| 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(); 1428282191 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 F := [2 x z - 14 x z + 5 y z + 17 x z, -4 x z - 2 x y - 10 x z + 9, 2 3 2 -2 x y - 10 z - 5 x + 14 z] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [6 x y - 15 x y z + 8 z + 9, -12 y z + 13 x + 10 y + 17, 3 2 -4 x y z + 11 y + 10 x - 5] > Problem := [F,G]; 2 2 2 2 2 Problem := [[2 x z - 14 x z + 5 y z + 17 x z, -4 x z - 2 x y - 10 x z + 9, 2 3 2 2 -2 x y - 10 z - 5 x + 14 z], [6 x y - 15 x y z + 8 z + 9, 2 2 2 3 2 -12 y z + 13 x + 10 y + 17, -4 x y z + 11 y + 10 x - 5]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.30 memory used=26.1MB, alloc=32.3MB, time=0.86 memory used=46.7MB, alloc=32.3MB, time=1.39 memory used=65.2MB, alloc=56.3MB, time=1.91 memory used=105.7MB, alloc=60.3MB, time=2.94 memory used=145.8MB, alloc=84.3MB, time=3.98 memory used=209.5MB, alloc=92.3MB, time=5.60 memory used=270.6MB, alloc=116.3MB, time=7.19 memory used=345.3MB, alloc=116.3MB, time=9.16 memory used=416.8MB, alloc=396.3MB, time=11.10 memory used=530.4MB, alloc=420.3MB, time=13.97 memory used=659.0MB, alloc=444.3MB, time=17.12 memory used=786.3MB, alloc=444.3MB, time=20.59 memory used=881.2MB, alloc=468.3MB, time=23.10 memory used=978.2MB, alloc=468.3MB, time=25.86 memory used=1068.9MB, alloc=468.3MB, time=28.36 memory used=1152.6MB, alloc=468.3MB, time=30.77 memory used=1240.8MB, alloc=468.3MB, time=33.34 memory used=1323.7MB, alloc=468.3MB, time=35.83 memory used=1400.4MB, alloc=492.3MB, time=38.12 memory used=1465.1MB, alloc=492.3MB, time=40.31 memory used=1520.7MB, alloc=492.3MB, time=42.10 memory used=1579.6MB, alloc=492.3MB, time=44.18 memory used=1645.6MB, alloc=492.3MB, time=46.48 memory used=1698.3MB, alloc=492.3MB, time=48.35 memory used=1736.4MB, alloc=492.3MB, time=49.80 memory used=1785.8MB, alloc=492.3MB, time=51.66 memory used=1971.2MB, alloc=516.3MB, time=56.80 memory used=2159.9MB, alloc=540.3MB, time=62.23 memory used=2332.4MB, alloc=564.3MB, time=67.17 memory used=2476.4MB, alloc=588.3MB, time=71.49 memory used=2610.1MB, alloc=612.3MB, time=75.51 memory used=2743.5MB, alloc=612.3MB, time=79.61 memory used=2895.7MB, alloc=636.3MB, time=84.62 memory used=3008.5MB, alloc=636.3MB, time=88.74 memory used=3113.2MB, alloc=636.3MB, time=92.36 memory used=3206.0MB, alloc=636.3MB, time=95.27 memory used=3330.1MB, alloc=636.3MB, time=99.87 memory used=3460.1MB, alloc=636.3MB, time=104.83 memory used=3556.4MB, alloc=660.3MB, time=108.82 memory used=3884.8MB, alloc=684.3MB, time=119.74 memory used=4237.1MB, alloc=708.3MB, time=130.42 memory used=4511.8MB, alloc=732.3MB, time=139.08 |\^/| 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(); 1428282491 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 3 3 F := [12 x - 11 y z - 18 x z - 7, -x - 10 y - 7 x z, 2 3 2 -8 x z + 11 z + 9 y + 13] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 2 G := [16 x y + 7 y z - 20 z + 12 x, 20 x z - 12 x z + 7 x - 20 x y, 2 2 3 12 x y - 17 y z - 11 z ] > Problem := [F,G]; 3 2 3 3 Problem := [[12 x - 11 y z - 18 x z - 7, -x - 10 y - 7 x z, 2 3 2 2 2 2 -8 x z + 11 z + 9 y + 13], [16 x y + 7 y z - 20 z + 12 x, 2 2 2 2 2 3 20 x z - 12 x z + 7 x - 20 x y, 12 x y - 17 y z - 11 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.31 memory used=26.4MB, alloc=36.3MB, time=0.75 memory used=48.7MB, alloc=36.3MB, time=1.39 memory used=72.4MB, alloc=36.3MB, time=1.92 memory used=93.4MB, alloc=36.3MB, time=2.44 memory used=107.1MB, alloc=36.3MB, time=2.55 memory used=129.8MB, alloc=36.3MB, time=3.16 memory used=150.2MB, alloc=36.3MB, time=3.41 memory used=172.2MB, alloc=60.3MB, time=3.90 memory used=220.9MB, alloc=62.0MB, time=5.31 memory used=246.0MB, alloc=62.0MB, time=5.42 memory used=272.3MB, alloc=62.0MB, time=5.52 memory used=317.2MB, alloc=62.0MB, time=6.38 memory used=372.2MB, alloc=62.5MB, time=7.27 memory used=433.3MB, alloc=71.5MB, time=9.04 memory used=477.4MB, alloc=71.5MB, time=9.98 memory used=517.2MB, alloc=71.5MB, time=10.68 memory used=557.8MB, alloc=71.5MB, time=11.47 memory used=605.8MB, alloc=71.5MB, time=12.39 memory used=654.1MB, alloc=95.5MB, time=13.24 memory used=705.6MB, alloc=95.5MB, time=14.47 memory used=762.0MB, alloc=95.5MB, time=15.21 memory used=830.4MB, alloc=95.5MB, time=16.92 memory used=890.0MB, alloc=351.5MB, time=18.10 memory used=962.9MB, alloc=375.5MB, time=19.36 memory used=1037.8MB, alloc=375.5MB, time=20.65 memory used=1128.2MB, alloc=375.5MB, time=22.32 memory used=1232.7MB, alloc=399.5MB, time=24.03 memory used=1356.6MB, alloc=399.5MB, time=26.08 memory used=1483.1MB, alloc=423.5MB, time=28.30 memory used=1576.8MB, alloc=423.5MB, time=29.23 memory used=1644.6MB, alloc=423.5MB, time=29.77 memory used=1725.3MB, alloc=423.5MB, time=32.31 memory used=1782.2MB, alloc=423.5MB, time=32.63 memory used=1863.0MB, alloc=423.5MB, time=33.50 memory used=1935.1MB, alloc=423.5MB, time=34.05 memory used=2014.4MB, alloc=423.5MB, time=39.00 memory used=2085.8MB, alloc=423.5MB, time=39.52 memory used=2144.6MB, alloc=423.5MB, time=39.85 memory used=2218.8MB, alloc=423.5MB, time=41.20 memory used=2278.5MB, alloc=423.5MB, time=41.55 memory used=2351.2MB, alloc=423.5MB, time=42.06 memory used=2423.7MB, alloc=423.5MB, time=42.75 memory used=2502.9MB, alloc=423.5MB, time=47.69 memory used=2574.7MB, alloc=423.5MB, time=48.21 memory used=2634.1MB, alloc=423.5MB, time=48.52 memory used=2704.9MB, alloc=423.5MB, time=49.13 memory used=2762.1MB, alloc=423.5MB, time=49.48 memory used=2836.0MB, alloc=423.5MB, time=50.06 memory used=2909.5MB, alloc=423.5MB, time=53.08 memory used=2970.5MB, alloc=423.5MB, time=53.43 memory used=3032.1MB, alloc=423.5MB, time=53.82 memory used=3106.6MB, alloc=423.5MB, time=54.99 memory used=3185.3MB, alloc=423.5MB, time=56.12 memory used=3326.9MB, alloc=423.5MB, time=58.87 memory used=3497.1MB, alloc=423.5MB, time=62.70 memory used=3646.6MB, alloc=447.5MB, time=65.82 memory used=3792.4MB, alloc=447.5MB, time=69.17 memory used=3955.8MB, alloc=447.5MB, time=71.34 memory used=4092.8MB, alloc=447.5MB, time=74.73 memory used=4278.4MB, alloc=447.5MB, time=78.26 memory used=4377.8MB, alloc=447.5MB, time=81.17 memory used=4475.9MB, alloc=471.5MB, time=83.31 memory used=4572.0MB, alloc=471.5MB, time=85.33 memory used=4660.3MB, alloc=471.5MB, time=87.13 memory used=4756.3MB, alloc=471.5MB, time=89.03 memory used=4887.0MB, alloc=471.5MB, time=92.90 memory used=4986.8MB, alloc=471.5MB, time=94.69 memory used=5069.8MB, alloc=471.5MB, time=96.43 memory used=5145.7MB, alloc=495.5MB, time=97.94 memory used=5277.6MB, alloc=495.5MB, time=100.14 memory used=5376.8MB, alloc=495.5MB, time=100.91 memory used=5458.3MB, alloc=495.5MB, time=101.56 memory used=5539.9MB, alloc=495.5MB, time=102.20 memory used=5641.8MB, alloc=495.5MB, time=102.86 memory used=5715.8MB, alloc=495.5MB, time=103.42 memory used=5787.1MB, alloc=495.5MB, time=103.95 memory used=5898.3MB, alloc=495.5MB, time=105.61 memory used=6000.3MB, alloc=495.5MB, time=106.38 memory used=6082.4MB, alloc=495.5MB, time=107.01 memory used=6162.8MB, alloc=495.5MB, time=107.65 memory used=6264.3MB, alloc=495.5MB, time=108.29 memory used=6340.0MB, alloc=495.5MB, time=108.85 memory used=6410.9MB, alloc=495.5MB, time=109.39 memory used=6518.9MB, alloc=495.5MB, time=110.39 memory used=6665.0MB, alloc=495.5MB, time=156.87 memory used=6749.5MB, alloc=495.5MB, time=157.52 memory used=6841.6MB, alloc=495.5MB, time=158.17 memory used=6924.5MB, alloc=495.5MB, time=158.76 memory used=6991.1MB, alloc=495.5MB, time=159.30 memory used=7066.3MB, alloc=495.5MB, time=159.84 memory used=7151.9MB, alloc=495.5MB, time=160.39 memory used=7247.8MB, alloc=495.5MB, time=160.99 memory used=7354.6MB, alloc=495.5MB, time=161.57 memory used=7520.4MB, alloc=495.5MB, time=162.55 memory used=7679.5MB, alloc=495.5MB, time=163.27 memory used=7910.2MB, alloc=495.5MB, time=170.59 memory used=7996.2MB, alloc=495.5MB, time=171.25 memory used=8086.1MB, alloc=495.5MB, time=171.87 memory used=8157.5MB, alloc=495.5MB, time=172.41 memory used=8245.5MB, alloc=495.5MB, time=172.96 memory used=8412.6MB, alloc=495.5MB, time=174.68 memory used=8505.9MB, alloc=495.5MB, time=175.37 memory used=8580.5MB, alloc=495.5MB, time=175.99 memory used=8664.4MB, alloc=495.5MB, time=176.61 memory used=8768.6MB, alloc=495.5MB, time=177.23 memory used=8836.3MB, alloc=495.5MB, time=177.75 memory used=8922.8MB, alloc=495.5MB, time=179.01 memory used=9021.4MB, alloc=495.5MB, time=179.76 memory used=9101.7MB, alloc=495.5MB, time=180.42 memory used=9182.9MB, alloc=495.5MB, time=181.05 memory used=9284.8MB, alloc=495.5MB, time=181.68 memory used=9359.0MB, alloc=495.5MB, time=182.21 memory used=9430.2MB, alloc=495.5MB, time=182.72 |\^/| 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(); 1428282791 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 F := [-6 x z - 12 y - 16 y z - 16 x, 17 y + 6 y z + 2 y, 3 2 2 10 x + 16 y z - 15 x z + 12 y ] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 2 2 G := [-2 x y + 14 y - 5 x + 9 x z, 9 x y + 6 x z - 6 y z + x, 2 13 x - 17 x y - 2 x + 3] > Problem := [F,G]; 2 3 Problem := [[-6 x z - 12 y - 16 y z - 16 x, 17 y + 6 y z + 2 y, 3 2 2 2 3 2 10 x + 16 y z - 15 x z + 12 y ], [-2 x y + 14 y - 5 x + 9 x z, 2 2 2 2 9 x y + 6 x z - 6 y z + x, 13 x - 17 x y - 2 x + 3]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.31 memory used=26.1MB, alloc=32.3MB, time=0.87 memory used=46.6MB, alloc=32.3MB, time=1.40 memory used=66.6MB, alloc=56.3MB, time=1.93 memory used=108.1MB, alloc=60.3MB, time=2.97 memory used=147.7MB, alloc=84.3MB, time=3.99 memory used=211.3MB, alloc=92.3MB, time=5.64 memory used=279.5MB, alloc=116.3MB, time=7.16 memory used=354.3MB, alloc=116.3MB, time=8.98 memory used=419.4MB, alloc=372.3MB, time=10.58 memory used=507.5MB, alloc=396.3MB, time=12.64 memory used=622.0MB, alloc=396.3MB, time=15.13 memory used=732.2MB, alloc=420.3MB, time=17.88 memory used=864.3MB, alloc=444.3MB, time=21.09 memory used=983.5MB, alloc=468.3MB, time=24.27 memory used=1099.1MB, alloc=468.3MB, time=27.30 memory used=1209.3MB, alloc=468.3MB, time=29.90 memory used=1314.8MB, alloc=468.3MB, time=32.19 memory used=1464.4MB, alloc=468.3MB, time=35.21 memory used=1585.3MB, alloc=492.3MB, time=37.86 memory used=1694.9MB, alloc=492.3MB, time=40.72 memory used=1806.0MB, alloc=492.3MB, time=43.23 memory used=1891.3MB, alloc=492.3MB, time=45.28 memory used=2016.8MB, alloc=492.3MB, time=48.96 memory used=2105.7MB, alloc=492.3MB, time=49.89 memory used=2208.0MB, alloc=492.3MB, time=51.80 memory used=2288.4MB, alloc=492.3MB, time=53.90 memory used=2404.2MB, alloc=516.3MB, time=55.85 memory used=2535.6MB, alloc=516.3MB, time=57.27 memory used=2659.7MB, alloc=516.3MB, time=60.77 memory used=2776.5MB, alloc=516.3MB, time=62.19 memory used=2877.0MB, alloc=516.3MB, time=64.12 memory used=2964.8MB, alloc=516.3MB, time=66.48 memory used=3057.0MB, alloc=516.3MB, time=68.44 memory used=3151.5MB, alloc=516.3MB, time=70.55 memory used=3209.0MB, alloc=516.3MB, time=72.22 memory used=3273.4MB, alloc=516.3MB, time=74.32 memory used=3335.6MB, alloc=516.3MB, time=76.45 memory used=3434.7MB, alloc=516.3MB, time=79.04 memory used=3484.6MB, alloc=516.3MB, time=80.43 memory used=3536.7MB, alloc=516.3MB, time=81.92 memory used=3654.9MB, alloc=540.3MB, time=85.61 memory used=3763.8MB, alloc=540.3MB, time=86.44 memory used=3940.6MB, alloc=540.3MB, time=95.58 memory used=4048.0MB, alloc=540.3MB, time=96.40 memory used=4144.7MB, alloc=540.3MB, time=97.13 memory used=4268.9MB, alloc=540.3MB, time=98.47 memory used=4380.9MB, alloc=540.3MB, time=99.56 memory used=4620.5MB, alloc=564.3MB, time=104.10 memory used=4850.4MB, alloc=564.3MB, time=108.14 memory used=4995.1MB, alloc=564.3MB, time=111.81 memory used=5140.9MB, alloc=564.3MB, time=115.27 memory used=5267.2MB, alloc=564.3MB, time=116.56 memory used=5483.5MB, alloc=564.3MB, time=120.57 memory used=5639.7MB, alloc=564.3MB, time=122.97 memory used=5866.4MB, alloc=564.3MB, time=128.58 memory used=6082.0MB, alloc=588.3MB, time=133.60 memory used=6281.5MB, alloc=612.3MB, time=139.67 memory used=6436.9MB, alloc=636.3MB, time=143.74 |\^/| 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(); 1428283091 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 F := [11 x - 15 x z + 14 y - 19, -18 y + 4 x + 15 x y - 13, 2 2 5 x y - 17 x y z - 19 y z - 4 x y] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 3 2 2 2 G := [3 x + 2 z + 5 x - 19 z , -10 x - 6 x y + 5 x z - 15 y z , 3 2 2 -19 x - 2 x z + 19 y z - 2 y z] > Problem := [F,G]; 3 2 3 2 Problem := [[11 x - 15 x z + 14 y - 19, -18 y + 4 x + 15 x y - 13, 2 2 3 3 2 2 5 x y - 17 x y z - 19 y z - 4 x y], [3 x + 2 z + 5 x - 19 z , 3 2 2 2 3 2 2 -10 x - 6 x y + 5 x z - 15 y z , -19 x - 2 x z + 19 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=4.3MB, alloc=32.3MB, time=0.31 memory used=26.3MB, alloc=32.3MB, time=0.89 memory used=45.7MB, alloc=56.3MB, time=1.41 memory used=87.4MB, alloc=60.3MB, time=2.47 memory used=129.8MB, alloc=92.3MB, time=3.57 memory used=189.6MB, alloc=92.3MB, time=4.36 memory used=249.9MB, alloc=92.3MB, time=5.25 memory used=318.4MB, alloc=92.3MB, time=6.60 memory used=386.7MB, alloc=92.3MB, time=8.18 memory used=452.0MB, alloc=92.3MB, time=9.63 memory used=496.7MB, alloc=92.3MB, time=10.15 memory used=562.8MB, alloc=372.3MB, time=11.64 memory used=647.2MB, alloc=372.3MB, time=13.25 memory used=751.7MB, alloc=372.3MB, time=15.78 memory used=841.0MB, alloc=396.3MB, time=17.76 memory used=931.2MB, alloc=396.3MB, time=19.14 memory used=992.4MB, alloc=396.3MB, time=19.90 memory used=1055.8MB, alloc=396.3MB, time=20.82 memory used=1116.8MB, alloc=396.3MB, time=21.45 memory used=1221.4MB, alloc=396.3MB, time=23.39 memory used=1330.5MB, alloc=396.3MB, time=25.46 memory used=1435.9MB, alloc=420.3MB, time=28.31 memory used=1573.0MB, alloc=444.3MB, time=30.51 memory used=1690.6MB, alloc=444.3MB, time=32.36 memory used=1799.8MB, alloc=468.3MB, time=33.80 memory used=1919.6MB, alloc=468.3MB, time=34.84 memory used=2046.6MB, alloc=468.3MB, time=36.51 memory used=2157.0MB, alloc=492.3MB, time=37.83 memory used=2271.5MB, alloc=492.3MB, time=39.50 memory used=2379.9MB, alloc=492.3MB, time=40.86 memory used=2474.0MB, alloc=492.3MB, time=42.35 memory used=2551.4MB, alloc=492.3MB, time=43.47 memory used=2642.3MB, alloc=492.3MB, time=44.83 memory used=2718.0MB, alloc=516.3MB, time=46.05 memory used=2800.1MB, alloc=516.3MB, time=47.43 memory used=2855.6MB, alloc=516.3MB, time=48.47 memory used=2920.3MB, alloc=516.3MB, time=49.60 memory used=3005.0MB, alloc=516.3MB, time=50.76 memory used=3108.2MB, alloc=516.3MB, time=51.81 memory used=3224.9MB, alloc=516.3MB, time=52.67 memory used=3336.1MB, alloc=516.3MB, time=53.49 memory used=3446.1MB, alloc=516.3MB, time=54.81 memory used=3503.4MB, alloc=516.3MB, time=55.97 memory used=3569.8MB, alloc=516.3MB, time=56.98 memory used=3689.9MB, alloc=516.3MB, time=58.41 memory used=3762.8MB, alloc=516.3MB, time=59.35 memory used=3973.4MB, alloc=540.3MB, time=61.73 memory used=4117.1MB, alloc=540.3MB, time=63.03 memory used=4340.3MB, alloc=564.3MB, time=65.84 memory used=4540.6MB, alloc=588.3MB, time=68.89 memory used=4763.4MB, alloc=588.3MB, time=71.46 memory used=4923.5MB, alloc=588.3MB, time=73.17 memory used=5082.3MB, alloc=588.3MB, time=74.60 memory used=5228.0MB, alloc=588.3MB, time=75.64 memory used=5370.8MB, alloc=588.3MB, time=77.28 memory used=5629.0MB, alloc=588.3MB, time=80.42 memory used=5865.8MB, alloc=612.3MB, time=83.44 memory used=6084.5MB, alloc=612.3MB, time=85.97 memory used=6354.7MB, alloc=612.3MB, time=88.96 memory used=6513.4MB, alloc=612.3MB, time=90.38 memory used=6667.6MB, alloc=612.3MB, time=91.69 memory used=6818.4MB, alloc=612.3MB, time=93.45 memory used=7011.8MB, alloc=636.3MB, time=95.86 memory used=7213.9MB, alloc=636.3MB, time=98.41 memory used=7434.9MB, alloc=636.3MB, time=100.95 memory used=7549.1MB, alloc=636.3MB, time=103.02 memory used=7674.1MB, alloc=636.3MB, time=105.37 memory used=7788.7MB, alloc=636.3MB, time=107.39 memory used=7937.4MB, alloc=660.3MB, time=109.85 memory used=8070.5MB, alloc=660.3MB, time=112.23 memory used=8166.8MB, alloc=660.3MB, time=114.30 memory used=8281.2MB, alloc=684.3MB, time=116.25 memory used=8486.9MB, alloc=684.3MB, time=118.04 memory used=8659.7MB, alloc=684.3MB, time=119.32 memory used=8846.0MB, alloc=684.3MB, time=122.08 memory used=9019.2MB, alloc=684.3MB, time=124.54 memory used=9342.8MB, alloc=684.3MB, time=128.39 memory used=9584.2MB, alloc=708.3MB, time=131.72 memory used=9784.5MB, alloc=708.3MB, time=133.70 memory used=9979.4MB, alloc=708.3MB, time=135.15 memory used=10148.9MB, alloc=708.3MB, time=136.27 memory used=10332.7MB, alloc=708.3MB, time=137.70 memory used=10501.4MB, alloc=708.3MB, time=138.80 memory used=10711.1MB, alloc=708.3MB, time=146.39 memory used=10867.9MB, alloc=708.3MB, time=147.41 memory used=11082.4MB, alloc=708.3MB, time=148.99 memory used=11277.0MB, alloc=708.3MB, time=150.77 memory used=11474.3MB, alloc=708.3MB, time=152.45 memory used=11673.7MB, alloc=708.3MB, time=154.49 memory used=11848.6MB, alloc=708.3MB, time=155.64 memory used=12027.3MB, alloc=708.3MB, time=156.95 memory used=12230.1MB, alloc=708.3MB, time=159.59 memory used=12493.0MB, alloc=708.3MB, time=162.53 memory used=12770.6MB, alloc=708.3MB, time=165.94 memory used=13138.0MB, alloc=732.3MB, time=170.72 memory used=13524.4MB, alloc=756.3MB, time=177.03 |\^/| 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(); 1428283391 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 F := [-7 x y - 10 y - 19 y z - 7 y, -4 x y - 3 x z - 5 x y + 18 z, 2 2 3 -6 y z + 12 y z + 4 z - 7 x z] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 2 G := [10 x z + 3 y z - 18 x y - 6 z , -6 x y + 6 y z - 7 x - 11 x, 3 2 y - 18 y z + 14 z + 7 z] > Problem := [F,G]; 2 3 2 2 Problem := [[-7 x y - 10 y - 19 y z - 7 y, -4 x y - 3 x z - 5 x y + 18 z, 2 2 3 2 2 2 -6 y z + 12 y z + 4 z - 7 x z], [10 x z + 3 y z - 18 x y - 6 z , 2 2 2 3 2 -6 x y + 6 y z - 7 x - 11 x, y - 18 y z + 14 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=4.4MB, alloc=32.3MB, time=0.18 memory used=26.5MB, alloc=32.3MB, time=0.52 memory used=47.0MB, alloc=32.3MB, time=0.84 memory used=66.1MB, alloc=56.3MB, time=1.15 memory used=107.7MB, alloc=60.3MB, time=1.79 memory used=147.2MB, alloc=60.3MB, time=2.39 memory used=188.2MB, alloc=92.3MB, time=3.03 memory used=251.0MB, alloc=92.3MB, time=3.97 memory used=309.8MB, alloc=116.3MB, time=4.93 memory used=382.0MB, alloc=396.3MB, time=6.05 memory used=489.3MB, alloc=396.3MB, time=7.78 memory used=597.4MB, alloc=420.3MB, time=9.57 memory used=722.2MB, alloc=420.3MB, time=11.48 memory used=832.4MB, alloc=444.3MB, time=13.12 memory used=967.9MB, alloc=468.3MB, time=15.46 memory used=1079.6MB, alloc=468.3MB, time=17.03 memory used=1191.5MB, alloc=468.3MB, time=18.95 memory used=1315.2MB, alloc=492.3MB, time=21.32 memory used=1427.5MB, alloc=492.3MB, time=23.36 memory used=1522.9MB, alloc=492.3MB, time=25.09 memory used=1606.2MB, alloc=492.3MB, time=26.51 memory used=1694.7MB, alloc=516.3MB, time=28.21 memory used=1783.6MB, alloc=516.3MB, time=29.51 memory used=1864.5MB, alloc=516.3MB, time=31.09 memory used=1937.8MB, alloc=516.3MB, time=32.51 memory used=2004.0MB, alloc=516.3MB, time=33.88 memory used=2068.5MB, alloc=516.3MB, time=35.20 memory used=2124.7MB, alloc=516.3MB, time=36.41 memory used=2181.3MB, alloc=516.3MB, time=37.60 memory used=2249.4MB, alloc=516.3MB, time=38.58 memory used=2340.7MB, alloc=516.3MB, time=39.73 memory used=2403.6MB, alloc=516.3MB, time=40.92 memory used=2448.7MB, alloc=516.3MB, time=42.02 memory used=2482.4MB, alloc=540.3MB, time=42.82 memory used=2534.1MB, alloc=540.3MB, time=43.66 memory used=2594.8MB, alloc=540.3MB, time=45.06 memory used=2810.9MB, alloc=564.3MB, time=48.38 memory used=3026.8MB, alloc=588.3MB, time=51.76 memory used=3229.6MB, alloc=612.3MB, time=55.86 memory used=3434.7MB, alloc=612.3MB, time=58.82 memory used=3633.3MB, alloc=636.3MB, time=62.05 memory used=3826.3MB, alloc=636.3MB, time=65.21 memory used=4027.0MB, alloc=660.3MB, time=68.23 memory used=4223.7MB, alloc=684.3MB, time=72.36 memory used=4398.9MB, alloc=684.3MB, time=76.57 memory used=4524.1MB, alloc=708.3MB, time=79.04 memory used=4660.1MB, alloc=708.3MB, time=81.91 memory used=4788.2MB, alloc=708.3MB, time=85.40 memory used=4917.4MB, alloc=708.3MB, time=88.84 memory used=5026.4MB, alloc=708.3MB, time=91.73 memory used=5114.4MB, alloc=708.3MB, time=93.89 memory used=5472.8MB, alloc=732.3MB, time=102.40 memory used=5858.5MB, alloc=756.3MB, time=109.47 memory used=6254.4MB, alloc=780.3MB, time=117.17 memory used=6652.8MB, alloc=804.3MB, time=125.86 memory used=7028.5MB, alloc=828.3MB, time=134.34 |\^/| 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(); 1428283691 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 2 2 F := [-7 x y - 5 x y z + 13 z - y , 17 x z - 7 y z - 3 z - 11 z, 2 2 6 x y + x + 8 y z - 12 y] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 2 G := [15 x y - 18 x + 8 z - 8, -3 x y - 12 y z + 9 y - 4 z, 2 2 -8 y z - 4 z + 2 x - 19] > Problem := [F,G]; 2 3 2 2 2 2 Problem := [[-7 x y - 5 x y z + 13 z - y , 17 x z - 7 y z - 3 z - 11 z, 2 2 2 2 2 6 x y + x + 8 y z - 12 y], [15 x y - 18 x + 8 z - 8, 2 2 2 2 2 -3 x y - 12 y z + 9 y - 4 z, -8 y z - 4 z + 2 x - 19]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.18 memory used=26.5MB, alloc=32.3MB, time=0.53 memory used=46.0MB, alloc=56.3MB, time=0.83 memory used=87.8MB, alloc=60.3MB, time=1.47 memory used=128.0MB, alloc=60.3MB, time=2.07 memory used=165.7MB, alloc=84.3MB, time=2.61 memory used=231.0MB, alloc=92.3MB, time=3.59 memory used=292.4MB, alloc=92.3MB, time=4.46 memory used=359.8MB, alloc=116.3MB, time=5.37 memory used=436.0MB, alloc=372.3MB, time=6.56 memory used=528.4MB, alloc=396.3MB, time=7.84 memory used=645.5MB, alloc=420.3MB, time=9.37 memory used=775.1MB, alloc=420.3MB, time=11.29 memory used=896.5MB, alloc=444.3MB, time=12.95 memory used=1018.3MB, alloc=444.3MB, time=14.37 memory used=1138.9MB, alloc=444.3MB, time=15.88 memory used=1254.8MB, alloc=468.3MB, time=17.79 memory used=1382.6MB, alloc=468.3MB, time=19.25 memory used=1500.4MB, alloc=468.3MB, time=20.66 memory used=1624.2MB, alloc=468.3MB, time=22.09 memory used=1701.8MB, alloc=468.3MB, time=23.17 memory used=1787.7MB, alloc=468.3MB, time=24.41 memory used=1869.1MB, alloc=468.3MB, time=25.73 memory used=1958.3MB, alloc=492.3MB, time=27.24 memory used=2032.5MB, alloc=492.3MB, time=28.63 memory used=2103.1MB, alloc=492.3MB, time=30.00 memory used=2173.7MB, alloc=492.3MB, time=31.32 memory used=2231.2MB, alloc=492.3MB, time=32.53 memory used=2290.5MB, alloc=492.3MB, time=33.68 memory used=2361.8MB, alloc=492.3MB, time=34.75 memory used=2423.0MB, alloc=492.3MB, time=35.80 memory used=2485.2MB, alloc=492.3MB, time=36.86 memory used=2525.5MB, alloc=492.3MB, time=37.73 memory used=2585.4MB, alloc=492.3MB, time=38.76 memory used=2667.9MB, alloc=516.3MB, time=39.98 memory used=2715.9MB, alloc=516.3MB, time=41.05 memory used=2915.4MB, alloc=540.3MB, time=44.69 memory used=3104.6MB, alloc=564.3MB, time=47.93 memory used=3305.9MB, alloc=588.3MB, time=50.32 memory used=3536.8MB, alloc=612.3MB, time=53.06 memory used=3752.0MB, alloc=612.3MB, time=55.68 memory used=3920.4MB, alloc=612.3MB, time=57.94 memory used=4113.5MB, alloc=612.3MB, time=60.17 memory used=4289.2MB, alloc=636.3MB, time=62.81 memory used=4463.1MB, alloc=636.3MB, time=65.66 memory used=4642.8MB, alloc=636.3MB, time=67.91 memory used=4779.6MB, alloc=636.3MB, time=70.52 memory used=4948.0MB, alloc=636.3MB, time=72.80 memory used=5053.6MB, alloc=636.3MB, time=74.84 memory used=5168.3MB, alloc=636.3MB, time=77.03 memory used=5292.2MB, alloc=660.3MB, time=78.88 memory used=5448.7MB, alloc=660.3MB, time=80.90 memory used=5571.0MB, alloc=660.3MB, time=82.78 memory used=5649.8MB, alloc=660.3MB, time=84.40 memory used=5758.5MB, alloc=660.3MB, time=86.67 memory used=5909.1MB, alloc=660.3MB, time=90.58 memory used=6005.1MB, alloc=684.3MB, time=92.62 memory used=6103.8MB, alloc=684.3MB, time=94.59 memory used=6448.2MB, alloc=708.3MB, time=100.60 memory used=6809.6MB, alloc=732.3MB, time=106.75 memory used=7171.5MB, alloc=756.3MB, time=113.00 memory used=7511.7MB, alloc=780.3MB, time=119.51 memory used=7788.1MB, alloc=804.3MB, time=124.28 memory used=8036.9MB, alloc=828.3MB, time=129.46 memory used=8264.4MB, alloc=852.3MB, time=133.89 memory used=8512.3MB, alloc=876.3MB, time=139.51 memory used=8722.0MB, alloc=900.3MB, time=143.59 memory used=8930.2MB, alloc=924.3MB, time=148.50 memory used=9089.5MB, alloc=948.3MB, time=153.22 |\^/| 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(); 1428283991 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 3 2 F := [16 y z + 18 x + 19 y z, 20 x - 15 x y + 9 z - 4 y , 2 2 -20 x z - 4 y z - x + 2 z] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 G := [18 x z + 8 y z + 15 y, -6 x - 5 x y - 10 y z - 14 z, 2 2 2 2 5 x y - 18 y z - 5 x - 10 y ] > Problem := [F,G]; 2 2 3 2 3 2 Problem := [[16 y z + 18 x + 19 y z, 20 x - 15 x y + 9 z - 4 y , 2 2 2 2 -20 x z - 4 y z - x + 2 z], [18 x z + 8 y z + 15 y, 3 2 2 2 2 2 2 -6 x - 5 x y - 10 y z - 14 z, 5 x y - 18 y z - 5 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=4.6MB, alloc=32.3MB, time=0.18 memory used=24.7MB, alloc=32.3MB, time=0.48 memory used=42.5MB, alloc=32.3MB, time=0.64 memory used=56.9MB, alloc=32.3MB, time=0.72 memory used=67.7MB, alloc=32.3MB, time=0.75 memory used=87.0MB, alloc=56.3MB, time=1.03 memory used=128.3MB, alloc=68.3MB, time=1.64 memory used=170.6MB, alloc=68.3MB, time=2.06 memory used=215.4MB, alloc=68.3MB, time=2.58 memory used=240.7MB, alloc=68.3MB, time=2.66 memory used=259.4MB, alloc=68.3MB, time=2.74 memory used=288.1MB, alloc=68.3MB, time=2.84 memory used=319.5MB, alloc=68.3MB, time=3.16 memory used=356.7MB, alloc=68.3MB, time=3.40 memory used=376.8MB, alloc=68.3MB, time=3.47 memory used=399.7MB, alloc=68.3MB, time=3.54 memory used=431.5MB, alloc=68.3MB, time=3.68 memory used=459.0MB, alloc=68.3MB, time=3.78 memory used=485.9MB, alloc=68.3MB, time=3.87 memory used=525.6MB, alloc=68.3MB, time=4.80 memory used=552.0MB, alloc=68.3MB, time=4.89 memory used=574.3MB, alloc=68.3MB, time=4.96 memory used=594.5MB, alloc=68.3MB, time=5.03 memory used=619.5MB, alloc=68.3MB, time=5.10 memory used=640.1MB, alloc=68.3MB, time=5.16 memory used=683.1MB, alloc=68.3MB, time=5.69 memory used=707.2MB, alloc=68.3MB, time=5.77 memory used=725.5MB, alloc=68.3MB, time=5.84 memory used=757.7MB, alloc=68.3MB, time=6.05 memory used=799.1MB, alloc=68.3MB, time=6.55 memory used=820.8MB, alloc=68.3MB, time=6.62 memory used=841.2MB, alloc=68.3MB, time=6.68 memory used=886.5MB, alloc=68.3MB, time=7.01 memory used=930.7MB, alloc=68.3MB, time=7.49 memory used=960.2MB, alloc=68.3MB, time=7.76 memory used=992.3MB, alloc=68.3MB, time=8.01 memory used=1029.4MB, alloc=68.6MB, time=8.16 memory used=1069.0MB, alloc=68.6MB, time=8.83 memory used=1096.5MB, alloc=68.6MB, time=8.96 memory used=1140.5MB, alloc=68.6MB, time=9.43 memory used=1183.5MB, alloc=92.6MB, time=10.02 memory used=1251.3MB, alloc=92.6MB, time=10.94 memory used=1314.6MB, alloc=92.6MB, time=11.56 memory used=1367.3MB, alloc=92.6MB, time=12.01 memory used=1408.1MB, alloc=92.6MB, time=12.18 memory used=1449.9MB, alloc=92.6MB, time=12.36 memory used=1497.8MB, alloc=92.6MB, time=13.20 memory used=1533.2MB, alloc=92.6MB, time=13.33 memory used=1561.2MB, alloc=92.6MB, time=13.43 memory used=1623.3MB, alloc=92.6MB, time=14.01 memory used=1654.1MB, alloc=92.6MB, time=14.13 memory used=1688.9MB, alloc=92.6MB, time=14.23 memory used=1743.7MB, alloc=92.6MB, time=16.54 memory used=1775.5MB, alloc=92.6MB, time=16.67 memory used=1807.3MB, alloc=92.6MB, time=16.78 memory used=1833.6MB, alloc=92.6MB, time=16.89 memory used=1864.8MB, alloc=92.6MB, time=16.99 memory used=1901.2MB, alloc=92.6MB, time=17.10 memory used=1935.9MB, alloc=92.6MB, time=17.20 memory used=1958.5MB, alloc=92.6MB, time=17.27 memory used=1983.4MB, alloc=92.6MB, time=17.36 memory used=2020.0MB, alloc=92.6MB, time=17.56 memory used=2078.1MB, alloc=92.6MB, time=18.12 memory used=2123.2MB, alloc=92.6MB, time=19.38 memory used=2205.5MB, alloc=92.7MB, time=20.11 memory used=2270.2MB, alloc=92.7MB, time=20.58 memory used=2337.1MB, alloc=92.7MB, time=21.25 memory used=2403.6MB, alloc=92.7MB, time=22.31 memory used=2470.0MB, alloc=92.7MB, time=23.81 memory used=2537.8MB, alloc=92.7MB, time=25.79 memory used=2605.5MB, alloc=92.7MB, time=28.23 memory used=2672.9MB, alloc=92.7MB, time=31.15 memory used=2741.5MB, alloc=92.7MB, time=34.29 memory used=2807.8MB, alloc=92.7MB, time=36.68 memory used=2848.8MB, alloc=92.7MB, time=36.87 memory used=2889.1MB, alloc=92.7MB, time=37.07 memory used=2937.3MB, alloc=92.7MB, time=37.89 memory used=2966.0MB, alloc=92.7MB, time=38.00 memory used=3004.9MB, alloc=92.7MB, time=38.33 memory used=3060.9MB, alloc=93.2MB, time=38.79 memory used=3088.8MB, alloc=93.2MB, time=38.90 memory used=3123.7MB, alloc=93.2MB, time=39.08 memory used=3156.5MB, alloc=93.2MB, time=39.33 memory used=3187.9MB, alloc=93.2MB, time=39.68 memory used=3238.3MB, alloc=93.2MB, time=41.78 memory used=3269.6MB, alloc=93.2MB, time=41.91 memory used=3298.2MB, alloc=93.2MB, time=42.03 memory used=3322.8MB, alloc=93.2MB, time=42.13 memory used=3351.7MB, alloc=93.2MB, time=42.23 memory used=3384.9MB, alloc=93.2MB, time=42.34 memory used=3420.8MB, alloc=93.2MB, time=42.46 memory used=3441.6MB, alloc=93.2MB, time=42.55 memory used=3464.2MB, alloc=93.2MB, time=42.64 memory used=3489.1MB, alloc=93.2MB, time=42.74 memory used=3526.2MB, alloc=93.2MB, time=43.01 memory used=3601.2MB, alloc=373.2MB, time=43.72 memory used=3685.8MB, alloc=373.2MB, time=44.84 memory used=3762.7MB, alloc=373.2MB, time=45.42 memory used=3847.8MB, alloc=373.2MB, time=46.31 memory used=3901.5MB, alloc=373.2MB, time=46.80 memory used=3946.3MB, alloc=373.2MB, time=46.99 memory used=4036.8MB, alloc=373.2MB, time=48.07 memory used=4111.5MB, alloc=373.2MB, time=48.94 memory used=4168.4MB, alloc=373.2MB, time=49.49 memory used=4249.2MB, alloc=397.2MB, time=50.32 memory used=4319.4MB, alloc=397.2MB, time=50.80 memory used=4375.9MB, alloc=397.2MB, time=51.14 memory used=4432.4MB, alloc=397.2MB, time=51.34 memory used=4530.4MB, alloc=397.2MB, time=52.57 memory used=4642.8MB, alloc=397.2MB, time=54.14 memory used=4705.2MB, alloc=397.2MB, time=54.77 memory used=4780.9MB, alloc=397.2MB, time=55.38 memory used=4883.0MB, alloc=397.2MB, time=56.86 memory used=4992.9MB, alloc=421.2MB, time=58.31 memory used=5120.0MB, alloc=421.2MB, time=59.84 memory used=5174.4MB, alloc=421.2MB, time=60.08 memory used=5264.1MB, alloc=421.2MB, time=60.83 memory used=5326.0MB, alloc=421.2MB, time=61.13 memory used=5393.3MB, alloc=421.2MB, time=61.41 memory used=5456.3MB, alloc=421.2MB, time=61.74 memory used=5538.2MB, alloc=421.2MB, time=62.92 memory used=5599.0MB, alloc=421.2MB, time=63.20 memory used=5654.5MB, alloc=421.2MB, time=63.44 memory used=5768.7MB, alloc=445.2MB, time=64.72 memory used=5892.3MB, alloc=445.2MB, time=65.91 memory used=6039.1MB, alloc=445.2MB, time=67.21 memory used=6196.2MB, alloc=445.2MB, time=68.80 memory used=6310.1MB, alloc=445.2MB, time=69.56 memory used=6430.4MB, alloc=445.2MB, time=71.12 memory used=6519.2MB, alloc=445.2MB, time=72.38 memory used=6586.5MB, alloc=469.2MB, time=73.29 memory used=6662.3MB, alloc=469.2MB, time=74.60 memory used=6714.7MB, alloc=469.2MB, time=75.48 memory used=6805.6MB, alloc=469.2MB, time=76.70 memory used=6937.9MB, alloc=469.2MB, time=77.82 memory used=7009.3MB, alloc=469.2MB, time=78.94 memory used=7073.5MB, alloc=469.2MB, time=79.82 memory used=7141.8MB, alloc=493.2MB, time=81.07 memory used=7211.4MB, alloc=493.2MB, time=82.09 memory used=7341.0MB, alloc=493.2MB, time=83.27 memory used=7461.3MB, alloc=493.2MB, time=84.26 memory used=7571.8MB, alloc=493.2MB, time=84.92 memory used=7698.9MB, alloc=493.2MB, time=86.29 memory used=7811.4MB, alloc=493.2MB, time=87.05 memory used=7918.1MB, alloc=493.2MB, time=87.63 memory used=8065.8MB, alloc=493.2MB, time=90.70 memory used=8164.1MB, alloc=493.2MB, time=91.23 memory used=8259.0MB, alloc=493.2MB, time=91.66 memory used=8341.7MB, alloc=493.2MB, time=92.14 memory used=8453.6MB, alloc=493.2MB, time=92.75 memory used=8621.3MB, alloc=493.2MB, time=95.99 memory used=8713.0MB, alloc=493.2MB, time=96.45 memory used=8808.4MB, alloc=493.2MB, time=96.89 memory used=8890.6MB, alloc=493.2MB, time=97.35 memory used=8992.5MB, alloc=493.2MB, time=98.00 memory used=9108.3MB, alloc=493.2MB, time=100.75 memory used=9190.3MB, alloc=493.2MB, time=101.19 memory used=9278.8MB, alloc=493.2MB, time=101.59 memory used=9380.4MB, alloc=493.2MB, time=102.46 memory used=9468.5MB, alloc=493.2MB, time=102.93 memory used=9566.9MB, alloc=493.2MB, time=103.39 memory used=9635.3MB, alloc=493.2MB, time=103.85 memory used=9717.0MB, alloc=493.2MB, time=104.28 memory used=9813.3MB, alloc=493.2MB, time=104.72 memory used=9901.5MB, alloc=493.2MB, time=105.11 memory used=10005.2MB, alloc=493.2MB, time=106.23 memory used=10107.8MB, alloc=493.2MB, time=106.76 memory used=10210.0MB, alloc=493.2MB, time=107.23 memory used=10278.2MB, alloc=493.2MB, time=107.66 memory used=10354.5MB, alloc=493.2MB, time=108.07 memory used=10445.1MB, alloc=493.2MB, time=108.50 memory used=10544.3MB, alloc=493.2MB, time=108.91 memory used=10632.2MB, alloc=493.2MB, time=109.60 memory used=10793.1MB, alloc=493.2MB, time=115.97 memory used=10889.7MB, alloc=493.2MB, time=116.46 memory used=10971.2MB, alloc=493.2MB, time=116.90 memory used=11065.5MB, alloc=493.2MB, time=117.31 memory used=11133.4MB, alloc=493.2MB, time=117.67 memory used=11218.6MB, alloc=493.2MB, time=118.11 memory used=11328.7MB, alloc=493.2MB, time=118.69 memory used=11432.0MB, alloc=493.2MB, time=119.90 memory used=11521.7MB, alloc=493.2MB, time=120.33 memory used=11619.8MB, alloc=493.2MB, time=120.87 memory used=11724.3MB, alloc=493.2MB, time=121.47 memory used=11844.5MB, alloc=493.2MB, time=124.44 memory used=11929.3MB, alloc=493.2MB, time=124.88 memory used=12024.8MB, alloc=493.2MB, time=125.32 memory used=12096.2MB, alloc=493.2MB, time=125.70 memory used=12203.3MB, alloc=493.2MB, time=126.52 memory used=12288.8MB, alloc=493.2MB, time=127.00 memory used=12391.0MB, alloc=493.2MB, time=127.49 memory used=12456.5MB, alloc=493.2MB, time=127.91 memory used=12533.0MB, alloc=493.2MB, time=128.34 memory used=12621.3MB, alloc=493.2MB, time=128.79 memory used=12725.6MB, alloc=493.2MB, time=129.23 memory used=12800.6MB, alloc=493.2MB, time=129.62 memory used=12909.1MB, alloc=493.2MB, time=130.64 memory used=12990.5MB, alloc=493.2MB, time=131.12 memory used=13088.9MB, alloc=493.2MB, time=131.60 memory used=13155.9MB, alloc=493.2MB, time=132.03 memory used=13233.4MB, alloc=493.2MB, time=132.46 memory used=13323.2MB, alloc=493.2MB, time=132.91 memory used=13429.1MB, alloc=493.2MB, time=133.35 memory used=13498.3MB, alloc=493.2MB, time=133.73 memory used=13626.1MB, alloc=493.2MB, time=140.32 memory used=13712.6MB, alloc=493.2MB, time=140.77 memory used=13794.7MB, alloc=493.2MB, time=141.19 memory used=13895.2MB, alloc=493.2MB, time=141.63 memory used=13959.1MB, alloc=493.2MB, time=142.01 memory used=14033.4MB, alloc=493.2MB, time=142.38 memory used=14118.8MB, alloc=493.2MB, time=142.77 memory used=14236.3MB, alloc=493.2MB, time=143.73 memory used=14324.7MB, alloc=493.2MB, time=144.21 memory used=14413.9MB, alloc=493.2MB, time=144.65 memory used=14484.3MB, alloc=493.2MB, time=145.07 memory used=14565.8MB, alloc=493.2MB, time=145.49 memory used=14659.7MB, alloc=493.2MB, time=145.92 memory used=14761.8MB, alloc=493.2MB, time=146.35 memory used=14824.3MB, alloc=493.2MB, time=146.69 memory used=14934.4MB, alloc=493.2MB, time=147.78 memory used=15025.9MB, alloc=493.2MB, time=148.26 memory used=15110.5MB, alloc=493.2MB, time=148.70 memory used=15180.9MB, alloc=493.2MB, time=149.12 memory used=15262.6MB, alloc=493.2MB, time=149.53 memory used=15358.4MB, alloc=493.2MB, time=149.97 memory used=15456.8MB, alloc=493.2MB, time=150.38 memory used=15520.6MB, alloc=493.2MB, time=150.74 memory used=15654.7MB, alloc=493.2MB, time=157.23 memory used=15735.5MB, alloc=493.2MB, time=157.66 memory used=15828.2MB, alloc=493.2MB, time=158.07 memory used=15914.1MB, alloc=493.2MB, time=158.45 memory used=15982.5MB, alloc=493.2MB, time=158.83 memory used=16061.7MB, alloc=493.2MB, time=159.20 memory used=16187.1MB, alloc=493.2MB, time=160.14 memory used=16290.0MB, alloc=493.2MB, time=161.36 memory used=16445.0MB, alloc=493.2MB, time=163.33 memory used=16560.4MB, alloc=493.2MB, time=166.07 memory used=16673.6MB, alloc=493.2MB, time=170.12 memory used=16796.2MB, alloc=493.2MB, time=175.70 memory used=16884.4MB, alloc=493.2MB, time=179.16 memory used=16975.0MB, alloc=493.2MB, time=179.63 memory used=17094.6MB, alloc=493.2MB, time=180.80 memory used=17263.5MB, alloc=493.2MB, time=182.53 memory used=17408.3MB, alloc=493.2MB, time=184.58 memory used=17528.5MB, alloc=493.2MB, time=187.67 memory used=17640.0MB, alloc=493.2MB, time=191.91 memory used=17750.4MB, alloc=493.2MB, time=197.00 memory used=17865.3MB, alloc=493.2MB, time=203.50 memory used=17949.6MB, alloc=493.2MB, time=203.97 memory used=18032.8MB, alloc=493.2MB, time=204.41 memory used=18113.0MB, alloc=493.2MB, time=204.81 memory used=18184.5MB, alloc=493.2MB, time=205.21 memory used=18246.8MB, alloc=493.2MB, time=206.31 memory used=18318.7MB, alloc=517.2MB, time=207.18 memory used=18549.6MB, alloc=517.2MB, time=209.54 memory used=18780.5MB, alloc=517.2MB, time=215.81 memory used=19010.8MB, alloc=517.2MB, time=225.19 memory used=19121.2MB, alloc=517.2MB, time=225.85 memory used=19227.6MB, alloc=517.2MB, time=226.58 memory used=19476.0MB, alloc=541.2MB, time=229.43 memory used=19740.9MB, alloc=541.2MB, time=232.79 |\^/| 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(); 1428284291 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 3 3 3 2 F := [-x y - 3 x z + 19 y - 14 z , 19 x + 3 y - 3 z + z, 2 2 -9 x z - 7 y z + 4 z - 20 x] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 3 2 G := [11 x z + 3 y z + 19 z + 10, 15 z + 20 x y + 8 x z - 19 z , 2 2 2 3 -2 x z + 14 x y + 11 x z + 20 y ] > Problem := [F,G]; 2 2 3 3 3 3 2 Problem := [[-x y - 3 x z + 19 y - 14 z , 19 x + 3 y - 3 z + z, 2 2 2 2 3 -9 x z - 7 y z + 4 z - 20 x], [11 x z + 3 y z + 19 z + 10, 3 2 2 2 2 3 15 z + 20 x y + 8 x z - 19 z , -2 x z + 14 x y + 11 x z + 20 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.18 memory used=26.6MB, alloc=32.3MB, time=0.43 memory used=48.1MB, alloc=36.3MB, time=0.72 memory used=70.2MB, alloc=36.5MB, time=0.98 memory used=88.2MB, alloc=36.6MB, time=1.18 memory used=99.5MB, alloc=36.6MB, time=1.21 memory used=108.1MB, alloc=36.6MB, time=1.25 memory used=119.1MB, alloc=36.6MB, time=1.28 memory used=130.6MB, alloc=36.6MB, time=1.31 memory used=146.2MB, alloc=36.6MB, time=1.48 memory used=158.2MB, alloc=36.6MB, time=1.54 memory used=168.6MB, alloc=36.6MB, time=1.63 memory used=179.8MB, alloc=36.6MB, time=1.67 memory used=190.7MB, alloc=36.6MB, time=1.72 memory used=201.4MB, alloc=36.6MB, time=1.76 memory used=222.8MB, alloc=51.0MB, time=1.97 memory used=246.2MB, alloc=56.9MB, time=2.02 memory used=258.5MB, alloc=56.9MB, time=2.06 memory used=271.8MB, alloc=56.9MB, time=2.09 memory used=281.7MB, alloc=56.9MB, time=2.12 memory used=291.1MB, alloc=56.9MB, time=2.15 memory used=312.2MB, alloc=59.8MB, time=2.22 memory used=330.5MB, alloc=59.8MB, time=2.26 memory used=342.5MB, alloc=59.8MB, time=2.30 memory used=355.6MB, alloc=59.8MB, time=2.33 memory used=365.2MB, alloc=59.8MB, time=2.36 memory used=374.4MB, alloc=59.8MB, time=2.39 memory used=395.1MB, alloc=59.8MB, time=2.77 memory used=411.4MB, alloc=59.8MB, time=2.88 memory used=436.0MB, alloc=83.8MB, time=3.14 memory used=461.7MB, alloc=83.8MB, time=3.22 memory used=504.0MB, alloc=83.8MB, time=3.64 memory used=540.9MB, alloc=83.8MB, time=4.07 memory used=592.3MB, alloc=83.8MB, time=4.96 memory used=617.5MB, alloc=83.8MB, time=5.04 memory used=651.5MB, alloc=83.8MB, time=5.19 memory used=702.8MB, alloc=83.8MB, time=6.06 memory used=731.8MB, alloc=83.8MB, time=6.20 memory used=788.0MB, alloc=83.8MB, time=7.16 memory used=811.0MB, alloc=83.8MB, time=7.23 memory used=858.5MB, alloc=83.8MB, time=8.17 memory used=881.6MB, alloc=83.8MB, time=8.25 memory used=920.7MB, alloc=83.8MB, time=8.92 memory used=955.8MB, alloc=83.8MB, time=9.36 memory used=981.7MB, alloc=83.8MB, time=9.50 memory used=1012.6MB, alloc=83.8MB, time=9.82 memory used=1045.9MB, alloc=83.8MB, time=10.25 memory used=1073.6MB, alloc=83.8MB, time=10.63 memory used=1101.5MB, alloc=83.8MB, time=11.01 memory used=1132.3MB, alloc=83.8MB, time=11.51 memory used=1172.8MB, alloc=83.8MB, time=11.70 memory used=1201.4MB, alloc=107.8MB, time=16.47 memory used=1244.7MB, alloc=107.8MB, time=17.85 memory used=1278.4MB, alloc=107.8MB, time=17.94 memory used=1313.8MB, alloc=107.8MB, time=18.05 memory used=1365.8MB, alloc=107.8MB, time=18.29 memory used=1420.3MB, alloc=107.8MB, time=23.84 memory used=1459.1MB, alloc=107.8MB, time=24.58 memory used=1492.8MB, alloc=107.8MB, time=24.68 memory used=1527.7MB, alloc=107.8MB, time=24.79 memory used=1584.8MB, alloc=107.8MB, time=25.02 memory used=1641.4MB, alloc=107.8MB, time=31.04 memory used=1673.1MB, alloc=107.8MB, time=31.14 memory used=1706.6MB, alloc=107.8MB, time=31.24 memory used=1742.6MB, alloc=107.8MB, time=31.34 memory used=1817.7MB, alloc=107.8MB, time=35.64 memory used=1857.6MB, alloc=107.8MB, time=35.78 memory used=1891.8MB, alloc=107.8MB, time=35.89 memory used=1968.7MB, alloc=107.8MB, time=40.05 memory used=2013.1MB, alloc=107.8MB, time=40.20 memory used=2045.6MB, alloc=107.8MB, time=40.32 memory used=2111.5MB, alloc=107.8MB, time=40.85 memory used=2146.7MB, alloc=107.8MB, time=40.97 memory used=2174.6MB, alloc=107.8MB, time=41.08 memory used=2220.8MB, alloc=107.8MB, time=41.41 memory used=2256.8MB, alloc=107.8MB, time=41.56 memory used=2286.9MB, alloc=107.8MB, time=41.67 memory used=2325.6MB, alloc=107.8MB, time=41.92 memory used=2443.3MB, alloc=107.8MB, time=46.28 memory used=2484.1MB, alloc=107.8MB, time=46.45 memory used=2512.3MB, alloc=107.8MB, time=46.56 memory used=2549.0MB, alloc=107.8MB, time=46.68 memory used=2580.9MB, alloc=107.8MB, time=46.78 memory used=2605.5MB, alloc=107.8MB, time=46.87 memory used=2632.9MB, alloc=107.8MB, time=46.96 memory used=2663.7MB, alloc=107.8MB, time=47.06 memory used=2698.0MB, alloc=107.8MB, time=47.16 memory used=2737.1MB, alloc=107.8MB, time=47.27 memory used=2761.5MB, alloc=107.8MB, time=47.35 memory used=2773.0MB, alloc=107.8MB, time=47.43 memory used=2821.9MB, alloc=107.8MB, time=47.77 memory used=2853.7MB, alloc=107.8MB, time=47.88 memory used=2896.2MB, alloc=107.8MB, time=48.14 memory used=2931.7MB, alloc=107.8MB, time=48.27 memory used=2959.3MB, alloc=107.8MB, time=48.38 memory used=3086.0MB, alloc=107.8MB, time=53.06 memory used=3118.9MB, alloc=107.8MB, time=53.19 memory used=3148.9MB, alloc=107.8MB, time=53.31 memory used=3187.2MB, alloc=107.8MB, time=53.44 memory used=3214.2MB, alloc=107.8MB, time=53.54 memory used=3239.5MB, alloc=107.8MB, time=53.63 memory used=3267.7MB, alloc=107.8MB, time=53.72 memory used=3298.6MB, alloc=107.8MB, time=53.83 memory used=3333.4MB, alloc=107.8MB, time=53.93 memory used=3373.3MB, alloc=107.8MB, time=54.03 memory used=3388.0MB, alloc=107.8MB, time=54.12 memory used=3399.5MB, alloc=107.8MB, time=54.22 memory used=3449.5MB, alloc=107.8MB, time=54.83 memory used=3481.3MB, alloc=107.8MB, time=54.95 memory used=3520.8MB, alloc=107.8MB, time=55.19 memory used=3555.4MB, alloc=107.8MB, time=55.33 memory used=3597.4MB, alloc=107.8MB, time=55.55 memory used=3632.2MB, alloc=107.8MB, time=55.67 memory used=3669.1MB, alloc=107.8MB, time=56.46 memory used=3788.9MB, alloc=107.8MB, time=60.24 memory used=3821.1MB, alloc=107.8MB, time=60.36 memory used=3851.5MB, alloc=107.8MB, time=60.47 memory used=3890.2MB, alloc=107.8MB, time=60.60 memory used=3915.3MB, alloc=107.8MB, time=60.69 memory used=3940.5MB, alloc=107.8MB, time=60.79 memory used=3968.8MB, alloc=107.8MB, time=60.88 memory used=3999.7MB, alloc=107.8MB, time=60.98 memory used=4034.5MB, alloc=107.8MB, time=61.09 memory used=4073.9MB, alloc=107.8MB, time=61.19 memory used=4088.1MB, alloc=107.8MB, time=61.26 memory used=4099.5MB, alloc=107.8MB, time=61.35 memory used=4169.1MB, alloc=107.8MB, time=64.60 memory used=4219.2MB, alloc=107.8MB, time=65.43 memory used=4249.0MB, alloc=107.8MB, time=65.55 memory used=4281.6MB, alloc=107.8MB, time=65.65 memory used=4318.6MB, alloc=107.8MB, time=65.76 memory used=4342.4MB, alloc=107.8MB, time=65.84 memory used=4368.2MB, alloc=107.8MB, time=65.94 memory used=4397.1MB, alloc=107.8MB, time=66.03 memory used=4428.5MB, alloc=107.8MB, time=66.13 memory used=4463.9MB, alloc=107.8MB, time=66.23 memory used=4513.4MB, alloc=107.8MB, time=66.35 memory used=4524.7MB, alloc=107.8MB, time=66.42 memory used=4596.8MB, alloc=107.8MB, time=68.34 memory used=4656.9MB, alloc=107.8MB, time=70.61 memory used=4688.1MB, alloc=107.8MB, time=70.73 memory used=4718.3MB, alloc=107.8MB, time=70.85 memory used=4756.5MB, alloc=107.8MB, time=70.97 memory used=4780.7MB, alloc=107.8MB, time=71.07 memory used=4805.5MB, alloc=107.8MB, time=71.16 memory used=4832.7MB, alloc=107.8MB, time=71.25 memory used=4862.6MB, alloc=107.8MB, time=71.36 memory used=4896.2MB, alloc=107.8MB, time=71.46 memory used=4934.2MB, alloc=107.8MB, time=71.58 memory used=4951.4MB, alloc=107.8MB, time=71.66 memory used=4962.8MB, alloc=107.8MB, time=71.73 memory used=5042.7MB, alloc=107.8MB, time=72.72 memory used=5083.9MB, alloc=107.8MB, time=75.74 memory used=5109.7MB, alloc=107.8MB, time=75.84 memory used=5145.8MB, alloc=107.8MB, time=76.12 memory used=5184.0MB, alloc=107.8MB, time=76.29 memory used=5214.0MB, alloc=107.8MB, time=76.39 memory used=5235.9MB, alloc=107.8MB, time=76.55 memory used=5258.6MB, alloc=107.8MB, time=76.63 memory used=5287.0MB, alloc=107.8MB, time=76.75 memory used=5318.0MB, alloc=107.8MB, time=76.86 memory used=5351.5MB, alloc=107.8MB, time=76.96 memory used=5387.5MB, alloc=107.8MB, time=77.06 memory used=5425.9MB, alloc=107.8MB, time=77.16 memory used=5446.6MB, alloc=107.8MB, time=77.25 memory used=5458.1MB, alloc=107.8MB, time=77.35 memory used=5507.3MB, alloc=107.8MB, time=80.74 memory used=5535.5MB, alloc=107.8MB, time=80.82 memory used=5576.1MB, alloc=131.8MB, time=82.91 memory used=5625.3MB, alloc=131.8MB, time=84.23 memory used=5698.6MB, alloc=387.8MB, time=85.13 memory used=5785.6MB, alloc=387.8MB, time=86.54 memory used=5833.5MB, alloc=387.8MB, time=88.60 memory used=5900.3MB, alloc=387.8MB, time=89.04 memory used=5977.4MB, alloc=387.8MB, time=98.83 memory used=6206.7MB, alloc=387.8MB, time=102.32 memory used=6242.3MB, alloc=387.8MB, time=102.46 memory used=6285.9MB, alloc=387.8MB, time=102.60 memory used=6359.5MB, alloc=387.8MB, time=103.19 memory used=6452.3MB, alloc=387.8MB, time=104.02 memory used=6539.1MB, alloc=387.8MB, time=104.95 memory used=6624.3MB, alloc=411.8MB, time=105.97 memory used=6692.8MB, alloc=411.8MB, time=106.31 memory used=6754.2MB, alloc=411.8MB, time=106.59 memory used=6843.8MB, alloc=411.8MB, time=109.49 memory used=6894.7MB, alloc=411.8MB, time=109.70 memory used=6941.7MB, alloc=411.8MB, time=109.87 memory used=6987.9MB, alloc=411.8MB, time=110.02 memory used=7052.1MB, alloc=411.8MB, time=110.27 memory used=7113.8MB, alloc=411.8MB, time=110.69 memory used=7175.0MB, alloc=411.8MB, time=110.94 memory used=7262.6MB, alloc=411.8MB, time=113.89 memory used=7313.4MB, alloc=411.8MB, time=114.08 memory used=7366.7MB, alloc=411.8MB, time=114.25 memory used=7409.5MB, alloc=411.8MB, time=114.40 memory used=7463.6MB, alloc=411.8MB, time=114.55 memory used=7552.4MB, alloc=411.8MB, time=115.63 memory used=7615.3MB, alloc=411.8MB, time=115.87 memory used=7671.2MB, alloc=411.8MB, time=116.07 memory used=7711.8MB, alloc=411.8MB, time=116.23 memory used=7760.1MB, alloc=411.8MB, time=116.40 memory used=7817.3MB, alloc=411.8MB, time=116.59 memory used=7878.4MB, alloc=411.8MB, time=116.77 memory used=7914.2MB, alloc=411.8MB, time=116.89 memory used=7953.9MB, alloc=411.8MB, time=117.02 memory used=7997.5MB, alloc=411.8MB, time=117.16 memory used=8079.4MB, alloc=411.8MB, time=141.07 memory used=8266.1MB, alloc=411.8MB, time=145.15 memory used=8314.7MB, alloc=411.8MB, time=145.34 memory used=8360.8MB, alloc=411.8MB, time=145.52 memory used=8416.7MB, alloc=411.8MB, time=145.71 memory used=8472.8MB, alloc=411.8MB, time=145.90 memory used=8509.0MB, alloc=411.8MB, time=146.04 memory used=8545.7MB, alloc=411.8MB, time=146.18 memory used=8585.3MB, alloc=411.8MB, time=146.33 memory used=8628.6MB, alloc=411.8MB, time=146.48 memory used=8673.6MB, alloc=411.8MB, time=146.64 memory used=8722.5MB, alloc=411.8MB, time=146.79 memory used=8772.9MB, alloc=411.8MB, time=146.95 memory used=8827.1MB, alloc=411.8MB, time=147.11 memory used=8885.2MB, alloc=411.8MB, time=147.28 memory used=8944.6MB, alloc=411.8MB, time=147.46 memory used=9008.2MB, alloc=411.8MB, time=147.63 memory used=9160.3MB, alloc=411.8MB, time=148.13 memory used=9316.5MB, alloc=411.8MB, time=148.47 memory used=9488.9MB, alloc=411.8MB, time=148.83 memory used=9681.2MB, alloc=411.8MB, time=149.21 memory used=9898.0MB, alloc=411.8MB, time=149.60 memory used=10132.8MB, alloc=411.8MB, time=150.00 memory used=10214.6MB, alloc=411.8MB, time=150.42 memory used=10292.1MB, alloc=411.8MB, time=150.98 memory used=10407.3MB, alloc=411.8MB, time=155.07 memory used=10461.6MB, alloc=411.8MB, time=155.32 memory used=10509.2MB, alloc=411.8MB, time=155.49 memory used=10632.6MB, alloc=411.8MB, time=157.01 memory used=10746.2MB, alloc=435.8MB, time=157.96 memory used=10896.6MB, alloc=435.8MB, time=159.18 memory used=11047.4MB, alloc=435.8MB, time=161.26 memory used=11195.7MB, alloc=435.8MB, time=164.36 memory used=11343.7MB, alloc=435.8MB, time=168.00 memory used=11492.1MB, alloc=435.8MB, time=172.16 memory used=11638.3MB, alloc=435.8MB, time=177.24 memory used=11785.5MB, alloc=435.8MB, time=182.86 memory used=11932.0MB, alloc=435.8MB, time=189.22 memory used=12078.1MB, alloc=435.8MB, time=196.37 memory used=12225.9MB, alloc=435.8MB, time=203.71 memory used=12371.8MB, alloc=435.8MB, time=211.67 |\^/| 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(); 1428284591 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 2 F := [-10 x y + 5 x z + 2 y z - 17 x z, -7 y - 9 y z - y z + 12 x y, 2 -8 y z - 6 x z - 8 x + 15 y] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 3 2 G := [-19 y z - 15 x + 17 x z - 9 y , -16 x z + 13 x z + 6 y + 19 x , 3 -8 x y z - 15 y + 3 y z - 17 y] > Problem := [F,G]; 2 2 2 Problem := [[-10 x y + 5 x z + 2 y z - 17 x z, 3 2 2 2 -7 y - 9 y z - y z + 12 x y, -8 y z - 6 x z - 8 x + 15 y], [ 2 2 2 2 2 3 2 -19 y z - 15 x + 17 x z - 9 y , -16 x z + 13 x z + 6 y + 19 x , 3 -8 x y z - 15 y + 3 y z - 17 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.18 memory used=26.2MB, alloc=32.3MB, time=0.50 memory used=46.1MB, alloc=56.3MB, time=0.80 memory used=89.0MB, alloc=60.3MB, time=1.35 memory used=135.7MB, alloc=68.3MB, time=1.90 memory used=180.9MB, alloc=68.3MB, time=2.45 memory used=225.9MB, alloc=68.3MB, time=2.97 memory used=269.0MB, alloc=92.3MB, time=3.43 memory used=312.2MB, alloc=92.3MB, time=3.71 memory used=350.6MB, alloc=92.3MB, time=3.95 memory used=416.1MB, alloc=92.3MB, time=4.84 memory used=482.9MB, alloc=116.3MB, time=5.75 memory used=552.1MB, alloc=116.3MB, time=6.75 memory used=624.0MB, alloc=372.3MB, time=7.70 memory used=682.5MB, alloc=372.3MB, time=8.24 memory used=743.8MB, alloc=372.3MB, time=10.25 memory used=785.2MB, alloc=372.3MB, time=10.43 memory used=846.3MB, alloc=372.3MB, time=12.47 memory used=887.4MB, alloc=372.3MB, time=12.62 memory used=986.8MB, alloc=372.3MB, time=13.61 memory used=1081.8MB, alloc=396.3MB, time=14.72 memory used=1180.8MB, alloc=396.3MB, time=16.09 memory used=1299.0MB, alloc=396.3MB, time=17.53 memory used=1407.1MB, alloc=420.3MB, time=18.93 memory used=1530.2MB, alloc=444.3MB, time=20.47 memory used=1626.3MB, alloc=444.3MB, time=21.17 memory used=1710.1MB, alloc=444.3MB, time=22.32 memory used=1795.2MB, alloc=444.3MB, time=22.81 memory used=1878.8MB, alloc=444.3MB, time=23.58 memory used=1965.5MB, alloc=444.3MB, time=23.93 memory used=2045.5MB, alloc=444.3MB, time=24.19 memory used=2128.1MB, alloc=444.3MB, time=24.66 memory used=2210.9MB, alloc=444.3MB, time=25.12 memory used=2303.2MB, alloc=444.3MB, time=33.55 memory used=2372.2MB, alloc=444.3MB, time=33.80 memory used=2436.4MB, alloc=444.3MB, time=34.02 memory used=2509.7MB, alloc=444.3MB, time=34.37 memory used=2595.0MB, alloc=444.3MB, time=34.87 memory used=2675.5MB, alloc=444.3MB, time=35.19 memory used=2758.3MB, alloc=444.3MB, time=35.59 memory used=2850.4MB, alloc=444.3MB, time=44.18 memory used=2919.5MB, alloc=444.3MB, time=44.45 memory used=2984.2MB, alloc=444.3MB, time=44.67 memory used=3095.5MB, alloc=444.3MB, time=45.69 memory used=3245.3MB, alloc=444.3MB, time=50.54 memory used=3311.8MB, alloc=444.3MB, time=50.78 memory used=3422.3MB, alloc=444.3MB, time=51.66 memory used=3549.8MB, alloc=468.3MB, time=53.22 memory used=3667.0MB, alloc=468.3MB, time=56.09 memory used=3772.5MB, alloc=468.3MB, time=58.68 memory used=3905.5MB, alloc=468.3MB, time=60.12 memory used=4066.3MB, alloc=492.3MB, time=62.53 memory used=4181.5MB, alloc=492.3MB, time=64.22 memory used=4291.2MB, alloc=492.3MB, time=65.98 memory used=4425.5MB, alloc=516.3MB, time=67.38 memory used=4583.0MB, alloc=516.3MB, time=70.43 memory used=4736.1MB, alloc=516.3MB, time=71.94 memory used=4843.8MB, alloc=516.3MB, time=73.12 memory used=4953.8MB, alloc=516.3MB, time=74.83 memory used=5077.9MB, alloc=516.3MB, time=76.24 memory used=5162.8MB, alloc=516.3MB, time=77.57 memory used=5228.4MB, alloc=516.3MB, time=78.62 memory used=5293.3MB, alloc=516.3MB, time=79.64 memory used=5387.0MB, alloc=516.3MB, time=81.08 memory used=5473.9MB, alloc=540.3MB, time=82.24 memory used=5544.2MB, alloc=540.3MB, time=83.42 memory used=5651.5MB, alloc=540.3MB, time=84.75 memory used=5701.3MB, alloc=540.3MB, time=85.64 memory used=5811.6MB, alloc=540.3MB, time=87.07 memory used=5934.3MB, alloc=540.3MB, time=87.65 memory used=6020.7MB, alloc=540.3MB, time=88.64 memory used=6120.1MB, alloc=540.3MB, time=89.72 memory used=6250.0MB, alloc=540.3MB, time=91.05 memory used=6360.5MB, alloc=540.3MB, time=92.46 memory used=6487.0MB, alloc=540.3MB, time=102.25 memory used=6576.0MB, alloc=540.3MB, time=102.71 memory used=6688.6MB, alloc=540.3MB, time=103.20 memory used=6864.1MB, alloc=540.3MB, time=103.94 memory used=7050.1MB, alloc=540.3MB, time=104.54 memory used=7286.8MB, alloc=540.3MB, time=105.78 memory used=7380.5MB, alloc=540.3MB, time=106.83 memory used=7436.7MB, alloc=540.3MB, time=107.81 memory used=7534.9MB, alloc=540.3MB, time=108.77 memory used=7764.3MB, alloc=564.3MB, time=111.54 memory used=7962.3MB, alloc=564.3MB, time=113.68 memory used=8073.0MB, alloc=588.3MB, time=114.27 memory used=8183.9MB, alloc=588.3MB, time=114.84 memory used=8322.7MB, alloc=588.3MB, time=115.79 memory used=8449.0MB, alloc=588.3MB, time=116.41 memory used=8561.8MB, alloc=588.3MB, time=116.98 memory used=8735.1MB, alloc=588.3MB, time=130.29 memory used=8849.9MB, alloc=588.3MB, time=130.86 memory used=9088.3MB, alloc=588.3MB, time=131.60 memory used=9266.1MB, alloc=588.3MB, time=132.23 memory used=9475.5MB, alloc=588.3MB, time=133.69 memory used=9780.6MB, alloc=588.3MB, time=135.00 memory used=10010.3MB, alloc=588.3MB, time=136.46 memory used=10125.3MB, alloc=588.3MB, time=137.02 memory used=10264.7MB, alloc=588.3MB, time=137.93 memory used=10391.1MB, alloc=588.3MB, time=138.53 memory used=10498.6MB, alloc=588.3MB, time=139.09 memory used=10667.7MB, alloc=588.3MB, time=152.57 memory used=10785.1MB, alloc=588.3MB, time=153.15 memory used=11044.1MB, alloc=588.3MB, time=153.95 memory used=11222.5MB, alloc=588.3MB, time=154.60 memory used=11420.7MB, alloc=588.3MB, time=156.19 memory used=11539.1MB, alloc=588.3MB, time=156.81 memory used=11679.4MB, alloc=588.3MB, time=157.58 memory used=11811.0MB, alloc=588.3MB, time=159.38 memory used=11937.4MB, alloc=588.3MB, time=159.96 memory used=12106.2MB, alloc=588.3MB, time=161.46 memory used=12242.3MB, alloc=588.3MB, time=162.21 memory used=12495.5MB, alloc=588.3MB, time=167.25 memory used=12696.4MB, alloc=588.3MB, time=171.53 memory used=12908.7MB, alloc=612.3MB, time=174.23 memory used=13146.1MB, alloc=612.3MB, time=176.72 memory used=13484.5MB, alloc=612.3MB, time=181.52 |\^/| 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(); 1428284891 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 2 2 F := [-15 x y + 19 y - 13 y z - 18, 17 x z - 4 x - 3 y , 2 3 2 -16 x z + 15 y + 5 y z + 13] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 3 G := [12 x y - 14 y - 4 z + 4 z, -7 y z + 18 z + 11 y + 19 z, 2 2 3 -11 x y + 15 x z + 5 y + 13] > Problem := [F,G]; 2 3 2 2 2 2 Problem := [[-15 x y + 19 y - 13 y z - 18, 17 x z - 4 x - 3 y , 2 3 2 2 2 2 -16 x z + 15 y + 5 y z + 13], [12 x y - 14 y - 4 z + 4 z, 2 3 2 2 3 -7 y z + 18 z + 11 y + 19 z, -11 x y + 15 x z + 5 y + 13]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=25.9MB, alloc=36.3MB, time=0.50 memory used=44.7MB, alloc=36.3MB, time=0.65 memory used=69.3MB, alloc=36.3MB, time=0.95 memory used=92.5MB, alloc=60.3MB, time=1.23 memory used=128.7MB, alloc=60.3MB, time=1.69 memory used=174.9MB, alloc=60.3MB, time=2.09 memory used=215.3MB, alloc=60.3MB, time=2.52 memory used=250.1MB, alloc=60.3MB, time=2.79 memory used=290.3MB, alloc=60.3MB, time=3.19 memory used=335.8MB, alloc=68.3MB, time=3.82 memory used=383.6MB, alloc=92.3MB, time=4.34 memory used=442.6MB, alloc=92.3MB, time=4.74 memory used=486.8MB, alloc=92.3MB, time=4.97 memory used=531.9MB, alloc=92.3MB, time=5.27 memory used=568.9MB, alloc=92.3MB, time=5.42 memory used=620.4MB, alloc=92.3MB, time=6.01 memory used=651.4MB, alloc=92.3MB, time=6.12 memory used=705.3MB, alloc=92.3MB, time=7.85 memory used=747.8MB, alloc=92.3MB, time=7.99 memory used=776.5MB, alloc=92.3MB, time=8.09 memory used=813.3MB, alloc=92.3MB, time=8.20 memory used=853.6MB, alloc=92.3MB, time=8.39 memory used=907.0MB, alloc=92.3MB, time=10.11 memory used=939.5MB, alloc=92.3MB, time=10.23 memory used=972.9MB, alloc=92.3MB, time=10.34 memory used=1009.5MB, alloc=92.3MB, time=10.50 memory used=1086.0MB, alloc=348.3MB, time=11.29 memory used=1171.3MB, alloc=348.3MB, time=12.19 memory used=1219.9MB, alloc=348.3MB, time=13.49 memory used=1254.5MB, alloc=348.3MB, time=13.62 memory used=1280.8MB, alloc=348.3MB, time=13.72 memory used=1342.1MB, alloc=348.3MB, time=14.14 memory used=1420.9MB, alloc=372.3MB, time=15.02 memory used=1522.7MB, alloc=372.3MB, time=16.26 memory used=1616.6MB, alloc=396.3MB, time=17.22 memory used=1732.9MB, alloc=396.3MB, time=18.54 memory used=1806.8MB, alloc=396.3MB, time=19.03 memory used=1867.9MB, alloc=396.3MB, time=19.33 memory used=1923.8MB, alloc=396.3MB, time=19.57 memory used=1990.6MB, alloc=396.3MB, time=20.18 memory used=2032.6MB, alloc=396.3MB, time=20.36 memory used=2094.5MB, alloc=396.3MB, time=20.65 memory used=2144.2MB, alloc=396.3MB, time=20.85 memory used=2185.7MB, alloc=396.3MB, time=21.05 memory used=2231.2MB, alloc=396.3MB, time=21.24 memory used=2282.5MB, alloc=396.3MB, time=21.41 memory used=2338.6MB, alloc=396.3MB, time=21.69 memory used=2389.9MB, alloc=420.3MB, time=21.91 memory used=2446.8MB, alloc=420.3MB, time=22.13 memory used=2514.9MB, alloc=420.3MB, time=22.35 memory used=2604.3MB, alloc=420.3MB, time=23.88 memory used=2660.9MB, alloc=420.3MB, time=24.11 memory used=2734.5MB, alloc=420.3MB, time=24.33 memory used=2784.5MB, alloc=420.3MB, time=24.51 memory used=2840.0MB, alloc=420.3MB, time=24.70 memory used=2919.2MB, alloc=420.3MB, time=25.07 memory used=3001.5MB, alloc=420.3MB, time=25.78 memory used=3069.0MB, alloc=420.3MB, time=26.05 memory used=3144.3MB, alloc=420.3MB, time=26.42 memory used=3247.7MB, alloc=420.3MB, time=29.63 memory used=3316.9MB, alloc=420.3MB, time=29.89 memory used=3371.5MB, alloc=420.3MB, time=30.09 memory used=3441.8MB, alloc=420.3MB, time=30.33 memory used=3506.1MB, alloc=420.3MB, time=30.56 memory used=3555.4MB, alloc=420.3MB, time=30.73 memory used=3611.0MB, alloc=420.3MB, time=30.91 memory used=3672.6MB, alloc=420.3MB, time=31.09 memory used=3759.3MB, alloc=420.3MB, time=31.39 memory used=3824.1MB, alloc=420.3MB, time=31.63 memory used=3898.9MB, alloc=420.3MB, time=31.93 memory used=3970.9MB, alloc=420.3MB, time=33.57 memory used=4072.9MB, alloc=420.3MB, time=48.51 memory used=4143.2MB, alloc=420.3MB, time=48.77 memory used=4194.9MB, alloc=420.3MB, time=48.99 memory used=4252.3MB, alloc=420.3MB, time=49.21 memory used=4319.5MB, alloc=420.3MB, time=49.44 memory used=4397.3MB, alloc=420.3MB, time=49.69 memory used=4452.6MB, alloc=420.3MB, time=49.88 memory used=4497.6MB, alloc=420.3MB, time=50.09 memory used=4544.6MB, alloc=420.3MB, time=50.27 memory used=4595.7MB, alloc=420.3MB, time=50.45 memory used=4649.3MB, alloc=420.3MB, time=50.65 memory used=4706.9MB, alloc=420.3MB, time=50.84 memory used=4768.1MB, alloc=420.3MB, time=51.03 memory used=4832.7MB, alloc=420.3MB, time=51.23 memory used=4901.8MB, alloc=420.3MB, time=51.43 memory used=4974.7MB, alloc=420.3MB, time=51.65 memory used=5053.3MB, alloc=420.3MB, time=51.87 memory used=5222.2MB, alloc=420.3MB, time=52.37 memory used=5411.8MB, alloc=420.3MB, time=52.85 memory used=5485.7MB, alloc=420.3MB, time=53.20 memory used=5548.0MB, alloc=420.3MB, time=53.43 memory used=5657.9MB, alloc=420.3MB, time=69.67 memory used=5724.0MB, alloc=420.3MB, time=69.93 memory used=5781.9MB, alloc=420.3MB, time=70.17 memory used=5836.1MB, alloc=420.3MB, time=70.39 memory used=5900.0MB, alloc=420.3MB, time=70.61 memory used=5974.3MB, alloc=420.3MB, time=70.83 memory used=6041.1MB, alloc=420.3MB, time=71.05 memory used=6085.7MB, alloc=420.3MB, time=71.23 memory used=6131.9MB, alloc=420.3MB, time=71.42 memory used=6181.1MB, alloc=420.3MB, time=71.61 memory used=6234.5MB, alloc=420.3MB, time=71.80 memory used=6290.2MB, alloc=420.3MB, time=71.98 memory used=6349.7MB, alloc=420.3MB, time=72.17 memory used=6412.6MB, alloc=420.3MB, time=72.36 memory used=6480.3MB, alloc=420.3MB, time=72.55 memory used=6551.9MB, alloc=420.3MB, time=72.74 memory used=6628.2MB, alloc=420.3MB, time=72.94 memory used=6824.5MB, alloc=420.3MB, time=73.30 memory used=7009.5MB, alloc=420.3MB, time=73.91 memory used=7108.1MB, alloc=420.3MB, time=74.68 memory used=7268.3MB, alloc=420.3MB, time=84.44 memory used=7333.3MB, alloc=420.3MB, time=84.70 memory used=7386.2MB, alloc=420.3MB, time=84.95 memory used=7442.9MB, alloc=420.3MB, time=85.19 memory used=7510.4MB, alloc=420.3MB, time=85.41 memory used=7580.8MB, alloc=420.3MB, time=85.64 memory used=7623.8MB, alloc=420.3MB, time=85.84 memory used=7669.8MB, alloc=420.3MB, time=86.03 memory used=7718.8MB, alloc=420.3MB, time=86.21 memory used=7771.9MB, alloc=420.3MB, time=86.40 memory used=7830.1MB, alloc=420.3MB, time=86.60 memory used=7892.5MB, alloc=420.3MB, time=86.79 memory used=7961.0MB, alloc=420.3MB, time=87.00 memory used=8036.7MB, alloc=420.3MB, time=87.20 memory used=8262.2MB, alloc=420.3MB, time=88.56 memory used=8385.5MB, alloc=444.3MB, time=90.22 memory used=8507.0MB, alloc=444.3MB, time=91.74 memory used=8572.4MB, alloc=444.3MB, time=91.98 memory used=8670.5MB, alloc=444.3MB, time=93.66 memory used=8759.2MB, alloc=444.3MB, time=96.33 memory used=8834.8MB, alloc=444.3MB, time=96.61 memory used=8891.8MB, alloc=444.3MB, time=96.89 memory used=8955.0MB, alloc=444.3MB, time=97.13 memory used=9045.1MB, alloc=444.3MB, time=97.52 memory used=9150.9MB, alloc=444.3MB, time=101.41 memory used=9218.2MB, alloc=444.3MB, time=101.67 memory used=9289.4MB, alloc=444.3MB, time=101.93 memory used=9346.8MB, alloc=444.3MB, time=102.15 memory used=9418.1MB, alloc=444.3MB, time=102.40 memory used=9501.3MB, alloc=444.3MB, time=103.01 memory used=9587.5MB, alloc=444.3MB, time=103.58 memory used=9681.4MB, alloc=444.3MB, time=103.89 memory used=9766.2MB, alloc=444.3MB, time=104.64 memory used=9901.6MB, alloc=444.3MB, time=107.99 memory used=9967.6MB, alloc=444.3MB, time=108.27 memory used=10034.6MB, alloc=444.3MB, time=108.54 memory used=10095.0MB, alloc=444.3MB, time=108.76 memory used=10171.9MB, alloc=444.3MB, time=109.34 memory used=10307.0MB, alloc=444.3MB, time=111.69 memory used=10404.7MB, alloc=444.3MB, time=113.07 memory used=10487.6MB, alloc=444.3MB, time=114.17 memory used=10580.1MB, alloc=468.3MB, time=115.53 memory used=10678.1MB, alloc=468.3MB, time=116.70 memory used=10774.2MB, alloc=468.3MB, time=117.24 memory used=10866.9MB, alloc=468.3MB, time=119.07 memory used=10942.2MB, alloc=468.3MB, time=119.41 memory used=11052.3MB, alloc=468.3MB, time=120.20 memory used=11146.2MB, alloc=468.3MB, time=121.34 memory used=11252.6MB, alloc=468.3MB, time=122.07 memory used=11364.1MB, alloc=468.3MB, time=125.41 memory used=11437.6MB, alloc=468.3MB, time=125.72 memory used=11515.7MB, alloc=468.3MB, time=126.14 memory used=11647.0MB, alloc=468.3MB, time=127.57 memory used=11742.5MB, alloc=468.3MB, time=129.24 memory used=11877.1MB, alloc=468.3MB, time=130.62 memory used=11982.7MB, alloc=492.3MB, time=132.20 memory used=12125.3MB, alloc=492.3MB, time=133.95 memory used=12207.6MB, alloc=492.3MB, time=135.41 memory used=12314.6MB, alloc=492.3MB, time=136.60 memory used=12421.4MB, alloc=492.3MB, time=137.69 memory used=12490.0MB, alloc=492.3MB, time=138.77 memory used=12556.2MB, alloc=492.3MB, time=139.95 memory used=12603.2MB, alloc=492.3MB, time=140.77 memory used=12710.3MB, alloc=492.3MB, time=141.44 memory used=12802.5MB, alloc=492.3MB, time=142.23 memory used=12906.2MB, alloc=492.3MB, time=142.93 memory used=13020.6MB, alloc=516.3MB, time=143.86 memory used=13130.3MB, alloc=516.3MB, time=144.45 memory used=13247.8MB, alloc=516.3MB, time=146.42 memory used=13368.9MB, alloc=516.3MB, time=147.64 memory used=13501.7MB, alloc=516.3MB, time=148.67 memory used=13556.7MB, alloc=516.3MB, time=149.79 memory used=13634.9MB, alloc=516.3MB, time=151.63 memory used=13747.5MB, alloc=516.3MB, time=152.24 memory used=13839.5MB, alloc=516.3MB, time=153.18 memory used=13905.2MB, alloc=516.3MB, time=153.93 memory used=14150.1MB, alloc=516.3MB, time=156.57 memory used=14408.7MB, alloc=516.3MB, time=159.78 memory used=14639.8MB, alloc=516.3MB, time=163.11 memory used=14750.8MB, alloc=516.3MB, time=163.94 memory used=14842.9MB, alloc=516.3MB, time=164.49 memory used=14927.9MB, alloc=540.3MB, time=165.04 memory used=15027.2MB, alloc=540.3MB, time=165.50 memory used=15177.5MB, alloc=540.3MB, time=166.14 memory used=15293.0MB, alloc=540.3MB, time=166.74 memory used=15392.2MB, alloc=540.3MB, time=167.26 memory used=15497.5MB, alloc=540.3MB, time=167.76 memory used=15667.1MB, alloc=540.3MB, time=169.41 memory used=15772.6MB, alloc=540.3MB, time=169.95 memory used=15885.1MB, alloc=540.3MB, time=170.44 memory used=16070.8MB, alloc=540.3MB, time=171.04 memory used=16248.4MB, alloc=540.3MB, time=171.64 memory used=16384.5MB, alloc=540.3MB, time=172.42 memory used=16576.0MB, alloc=540.3MB, time=174.33 memory used=16682.3MB, alloc=540.3MB, time=174.89 memory used=16787.6MB, alloc=540.3MB, time=175.37 memory used=16932.7MB, alloc=540.3MB, time=211.22 memory used=17049.1MB, alloc=540.3MB, time=212.78 memory used=17167.3MB, alloc=540.3MB, time=213.37 memory used=17248.9MB, alloc=540.3MB, time=213.84 memory used=17343.3MB, alloc=540.3MB, time=214.35 memory used=17450.6MB, alloc=540.3MB, time=214.87 memory used=17573.2MB, alloc=540.3MB, time=215.40 memory used=17831.4MB, alloc=540.3MB, time=216.13 memory used=17956.0MB, alloc=540.3MB, time=216.70 memory used=18092.6MB, alloc=540.3MB, time=217.27 memory used=18235.8MB, alloc=540.3MB, time=217.84 memory used=18390.2MB, alloc=540.3MB, time=218.42 memory used=18557.2MB, alloc=540.3MB, time=219.05 memory used=18730.9MB, alloc=540.3MB, time=219.66 memory used=18915.3MB, alloc=540.3MB, time=220.26 memory used=19112.5MB, alloc=540.3MB, time=220.89 memory used=19321.8MB, alloc=540.3MB, time=221.52 memory used=19524.9MB, alloc=540.3MB, time=222.15 |\^/| 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(); 1428285191 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 2 3 2 F := [8 x + 12 z + 17 z + 5 z, 10 x y + 2 x y + 4 z + 18 x , 3 2 3 10 x - 14 x y + 4 y + 2 y z] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 3 G := [19 x y + 6 x y - 7 y - 2 x y, 19 x y - 6 y - 7 y z - 17 x, 2 3 -5 x z - 12 z - 8 y z - 18 z] > Problem := [F,G]; 3 3 2 2 2 3 2 Problem := [[8 x + 12 z + 17 z + 5 z, 10 x y + 2 x y + 4 z + 18 x , 3 2 3 2 2 3 10 x - 14 x y + 4 y + 2 y z], [19 x y + 6 x y - 7 y - 2 x y, 2 3 2 3 19 x y - 6 y - 7 y z - 17 x, -5 x z - 12 z - 8 y z - 18 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.17 memory used=26.6MB, 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=105.3MB, alloc=60.3MB, time=1.71 memory used=145.2MB, alloc=84.3MB, time=2.30 memory used=208.8MB, alloc=92.3MB, time=3.21 memory used=273.4MB, alloc=116.3MB, time=4.15 memory used=355.1MB, alloc=116.3MB, time=5.37 memory used=435.2MB, alloc=372.3MB, time=6.62 memory used=522.3MB, alloc=396.3MB, time=7.97 memory used=629.4MB, alloc=396.3MB, time=9.60 memory used=725.2MB, alloc=420.3MB, time=10.86 memory used=828.9MB, alloc=420.3MB, time=11.74 memory used=908.0MB, alloc=420.3MB, time=12.19 memory used=1003.1MB, alloc=420.3MB, time=14.80 memory used=1065.3MB, alloc=420.3MB, time=15.03 memory used=1132.0MB, alloc=420.3MB, time=15.23 memory used=1215.8MB, alloc=420.3MB, time=15.92 memory used=1320.0MB, alloc=420.3MB, time=16.90 memory used=1407.3MB, alloc=420.3MB, time=18.62 memory used=1470.7MB, alloc=420.3MB, time=18.98 memory used=1575.2MB, alloc=420.3MB, time=20.28 memory used=1692.6MB, alloc=444.3MB, time=22.01 memory used=1814.0MB, alloc=444.3MB, time=23.76 memory used=1926.9MB, alloc=468.3MB, time=25.39 memory used=2067.3MB, alloc=468.3MB, time=27.27 memory used=2177.8MB, alloc=468.3MB, time=28.89 memory used=2284.8MB, alloc=492.3MB, time=30.46 memory used=2384.0MB, alloc=492.3MB, time=32.14 memory used=2474.8MB, alloc=492.3MB, time=33.70 memory used=2549.4MB, alloc=492.3MB, time=34.95 memory used=2635.1MB, alloc=492.3MB, time=36.44 memory used=2720.2MB, alloc=492.3MB, time=38.00 memory used=2791.8MB, alloc=492.3MB, time=39.46 memory used=2857.4MB, alloc=492.3MB, time=40.67 memory used=2962.4MB, alloc=492.3MB, time=42.80 memory used=3088.0MB, alloc=492.3MB, time=45.39 memory used=3156.3MB, alloc=492.3MB, time=46.41 memory used=3212.2MB, alloc=492.3MB, time=47.45 memory used=3263.1MB, alloc=516.3MB, time=48.20 memory used=3321.1MB, alloc=516.3MB, time=49.14 memory used=3377.7MB, alloc=516.3MB, time=50.24 memory used=3535.1MB, alloc=516.3MB, time=52.87 memory used=3734.9MB, alloc=540.3MB, time=55.74 memory used=3958.1MB, alloc=564.3MB, time=58.63 memory used=4151.0MB, alloc=564.3MB, time=62.54 memory used=4371.8MB, alloc=564.3MB, time=64.75 memory used=4532.9MB, alloc=564.3MB, time=68.30 memory used=4668.2MB, alloc=564.3MB, time=69.16 memory used=4803.8MB, alloc=564.3MB, time=70.01 memory used=4948.1MB, alloc=564.3MB, time=73.33 memory used=5103.9MB, alloc=564.3MB, time=74.38 memory used=5241.8MB, alloc=564.3MB, time=77.74 memory used=5443.8MB, alloc=564.3MB, time=79.81 memory used=5646.5MB, alloc=588.3MB, time=82.68 memory used=5804.0MB, alloc=612.3MB, time=85.65 memory used=5965.1MB, alloc=612.3MB, time=88.14 memory used=6120.5MB, alloc=612.3MB, time=92.32 memory used=6283.9MB, alloc=636.3MB, time=94.89 memory used=6431.0MB, alloc=636.3MB, time=97.50 memory used=6548.7MB, alloc=636.3MB, time=99.54 memory used=6673.2MB, alloc=636.3MB, time=102.02 memory used=6806.7MB, alloc=636.3MB, time=104.27 memory used=7010.7MB, alloc=636.3MB, time=107.69 memory used=7182.2MB, alloc=636.3MB, time=108.93 memory used=7355.5MB, alloc=636.3MB, time=112.03 memory used=7541.6MB, alloc=636.3MB, time=113.51 memory used=7736.4MB, alloc=636.3MB, time=117.02 memory used=7920.4MB, alloc=660.3MB, time=120.22 memory used=8118.8MB, alloc=660.3MB, time=121.63 memory used=8319.9MB, alloc=660.3MB, time=124.84 memory used=8519.6MB, alloc=660.3MB, time=128.04 memory used=8678.0MB, alloc=660.3MB, time=130.39 memory used=8808.6MB, alloc=660.3MB, time=132.73 memory used=8941.4MB, alloc=660.3MB, time=135.25 memory used=9105.7MB, alloc=660.3MB, time=137.41 memory used=9235.2MB, alloc=660.3MB, time=139.80 memory used=9393.9MB, alloc=684.3MB, time=140.89 memory used=9539.1MB, alloc=684.3MB, time=141.89 memory used=9729.8MB, alloc=684.3MB, time=143.21 memory used=9909.3MB, alloc=684.3MB, time=144.32 memory used=10059.4MB, alloc=684.3MB, time=145.38 memory used=10266.2MB, alloc=684.3MB, time=161.35 memory used=10447.9MB, alloc=684.3MB, time=163.10 memory used=10599.0MB, alloc=684.3MB, time=164.06 memory used=10765.0MB, alloc=684.3MB, time=164.99 memory used=10976.7MB, alloc=684.3MB, time=166.66 memory used=11131.8MB, alloc=684.3MB, time=167.73 memory used=11312.0MB, alloc=684.3MB, time=168.76 memory used=11494.8MB, alloc=684.3MB, time=170.15 memory used=11647.9MB, alloc=684.3MB, time=171.19 memory used=11826.1MB, alloc=684.3MB, time=172.22 memory used=12037.6MB, alloc=684.3MB, time=188.96 memory used=12203.0MB, alloc=684.3MB, time=189.96 memory used=12343.9MB, alloc=684.3MB, time=190.85 memory used=12566.9MB, alloc=684.3MB, time=192.29 memory used=12730.2MB, alloc=684.3MB, time=193.36 memory used=12892.3MB, alloc=684.3MB, time=194.38 memory used=13081.3MB, alloc=684.3MB, time=195.76 |\^/| 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(); 1428285491 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 3 F := [9 x y z - 20 x z + 6 z - 11 x z, 15 x z - 5 y - 20 x z + 8 y z, 2 2 2 5 x y - 3 y z - 20 x - 19 x] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 G := [-3 x + 3 x y - 6 z + 2 y, -12 x z + 3 x y + 19 x z - 14 y, 2 2 5 x z + 13 x z - 7 y + 12] > Problem := [F,G]; 2 3 2 3 Problem := [[9 x y z - 20 x z + 6 z - 11 x z, 15 x z - 5 y - 20 x z + 8 y z, 2 2 2 2 2 5 x y - 3 y z - 20 x - 19 x], [-3 x + 3 x y - 6 z + 2 y, 2 2 2 2 2 -12 x z + 3 x y + 19 x z - 14 y, 5 x z + 13 x z - 7 y + 12]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.18 memory used=26.7MB, alloc=32.3MB, time=0.50 memory used=46.7MB, alloc=56.3MB, time=0.81 memory used=86.9MB, alloc=60.3MB, time=1.43 memory used=125.6MB, alloc=84.3MB, time=2.02 memory used=168.4MB, alloc=84.3MB, time=2.66 memory used=230.9MB, alloc=92.3MB, time=3.63 memory used=291.8MB, alloc=116.3MB, time=4.62 memory used=361.0MB, alloc=116.3MB, time=5.53 memory used=437.1MB, alloc=372.3MB, time=6.64 memory used=522.0MB, alloc=396.3MB, time=7.95 memory used=628.9MB, alloc=396.3MB, time=9.56 memory used=737.7MB, alloc=420.3MB, time=11.10 memory used=859.3MB, alloc=444.3MB, time=13.26 memory used=1009.1MB, alloc=468.3MB, time=15.93 memory used=1158.4MB, alloc=492.3MB, time=18.79 memory used=1287.1MB, alloc=492.3MB, time=21.14 memory used=1406.6MB, alloc=516.3MB, time=23.22 memory used=1527.4MB, alloc=516.3MB, time=25.34 memory used=1629.6MB, alloc=516.3MB, time=27.04 memory used=1727.5MB, alloc=516.3MB, time=29.18 memory used=1831.1MB, alloc=516.3MB, time=31.30 memory used=1919.2MB, alloc=516.3MB, time=33.02 memory used=2007.7MB, alloc=516.3MB, time=35.04 memory used=2076.7MB, alloc=516.3MB, time=36.40 memory used=2160.6MB, alloc=540.3MB, time=37.97 memory used=2234.4MB, alloc=540.3MB, time=39.11 memory used=2324.0MB, alloc=540.3MB, time=40.63 memory used=2402.8MB, alloc=540.3MB, time=42.04 memory used=2484.7MB, alloc=540.3MB, time=43.23 memory used=2574.7MB, alloc=540.3MB, time=44.65 memory used=2675.9MB, alloc=540.3MB, time=45.97 memory used=2742.3MB, alloc=540.3MB, time=47.33 memory used=2818.9MB, alloc=540.3MB, time=48.76 memory used=2878.0MB, alloc=540.3MB, time=49.88 memory used=2936.6MB, alloc=540.3MB, time=50.95 memory used=2999.4MB, alloc=540.3MB, time=52.53 memory used=3075.3MB, alloc=564.3MB, time=53.59 memory used=3131.7MB, alloc=564.3MB, time=54.89 memory used=3183.6MB, alloc=564.3MB, time=55.95 memory used=3420.5MB, alloc=588.3MB, time=60.25 memory used=3660.3MB, alloc=612.3MB, time=65.78 memory used=3867.0MB, alloc=636.3MB, time=70.40 memory used=4102.9MB, alloc=660.3MB, time=76.20 memory used=4310.5MB, alloc=684.3MB, time=80.75 memory used=4469.7MB, alloc=684.3MB, time=84.19 memory used=4660.3MB, alloc=684.3MB, time=87.70 memory used=4876.1MB, alloc=684.3MB, time=91.06 memory used=5065.8MB, alloc=684.3MB, time=95.04 memory used=5217.6MB, alloc=684.3MB, time=98.41 memory used=5358.0MB, alloc=684.3MB, time=102.07 memory used=5504.3MB, alloc=708.3MB, time=105.55 memory used=5641.4MB, alloc=708.3MB, time=109.12 memory used=5776.1MB, alloc=708.3MB, time=113.17 memory used=5898.2MB, alloc=708.3MB, time=116.87 memory used=5981.9MB, alloc=708.3MB, time=119.20 memory used=6114.5MB, alloc=708.3MB, time=123.27 |\^/| 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(); 1428285791 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 3 2 2 F := [13 x y z + 20 x z - 2 z + 2 x z, -16 x + 11 x z - x z - 10 z, 2 12 x y - 7 x z - 16 y z - 5] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 3 G := [-14 y + 15 z , -z + 2 x z + 19 y z, 5 x y z - 15 z - x + 15 y] > Problem := [F,G]; 2 3 3 2 2 Problem := [[13 x y z + 20 x z - 2 z + 2 x z, -16 x + 11 x z - x z - 10 z, 2 12 x y - 7 x z - 16 y z - 5], 2 2 3 3 [-14 y + 15 z , -z + 2 x z + 19 y z, 5 x y z - 15 z - x + 15 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.5MB, alloc=32.3MB, time=0.18 memory used=26.8MB, alloc=32.3MB, time=0.51 memory used=46.7MB, alloc=56.3MB, time=0.82 memory used=88.1MB, alloc=60.3MB, time=1.41 memory used=129.6MB, alloc=68.3MB, time=1.98 memory used=168.9MB, alloc=92.3MB, time=2.58 memory used=235.8MB, alloc=92.3MB, time=3.56 memory used=301.4MB, alloc=116.3MB, time=4.52 memory used=373.0MB, alloc=116.3MB, time=5.62 memory used=447.3MB, alloc=372.3MB, time=6.83 memory used=531.9MB, alloc=396.3MB, time=8.17 memory used=646.6MB, alloc=396.3MB, time=9.62 memory used=761.5MB, alloc=420.3MB, time=11.33 memory used=890.5MB, alloc=444.3MB, time=13.46 memory used=1028.3MB, alloc=468.3MB, time=15.83 memory used=1160.9MB, alloc=468.3MB, time=18.05 memory used=1273.3MB, alloc=492.3MB, time=20.01 memory used=1384.5MB, alloc=492.3MB, time=21.95 memory used=1479.8MB, alloc=492.3MB, time=23.59 memory used=1569.0MB, alloc=492.3MB, time=25.12 memory used=1655.0MB, alloc=492.3MB, time=26.73 memory used=1743.7MB, alloc=516.3MB, time=28.38 memory used=1838.1MB, alloc=516.3MB, time=30.20 memory used=1910.0MB, alloc=516.3MB, time=31.52 memory used=1977.1MB, alloc=516.3MB, time=32.72 memory used=2058.0MB, alloc=516.3MB, time=34.05 memory used=2120.7MB, alloc=516.3MB, time=35.29 memory used=2189.8MB, alloc=516.3MB, time=36.60 memory used=2243.7MB, alloc=516.3MB, time=37.76 memory used=2295.5MB, alloc=516.3MB, time=38.91 memory used=2343.8MB, alloc=516.3MB, time=40.01 memory used=2395.7MB, alloc=516.3MB, time=41.23 memory used=2448.5MB, alloc=540.3MB, time=42.51 memory used=2508.0MB, alloc=540.3MB, time=44.02 memory used=2696.0MB, alloc=564.3MB, time=47.47 memory used=2891.2MB, alloc=588.3MB, time=51.02 memory used=3093.5MB, alloc=612.3MB, time=55.19 memory used=3297.0MB, alloc=636.3MB, time=60.10 memory used=3483.8MB, alloc=660.3MB, time=63.87 memory used=3643.8MB, alloc=684.3MB, time=67.21 memory used=3801.1MB, alloc=684.3MB, time=70.68 memory used=3947.2MB, alloc=684.3MB, time=74.18 memory used=4093.3MB, alloc=684.3MB, time=77.64 memory used=4214.1MB, alloc=708.3MB, time=80.03 memory used=4343.2MB, alloc=708.3MB, time=83.22 memory used=4456.3MB, alloc=708.3MB, time=85.54 memory used=4582.6MB, alloc=708.3MB, time=88.54 memory used=4696.7MB, alloc=708.3MB, time=91.72 memory used=5062.9MB, alloc=732.3MB, time=99.57 memory used=5442.1MB, alloc=756.3MB, time=108.85 memory used=5835.7MB, alloc=780.3MB, time=118.12 memory used=6251.0MB, alloc=804.3MB, time=128.10 memory used=6630.4MB, alloc=828.3MB, time=136.38 |\^/| 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(); 1428286091 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 3 F := [-17 x + 9 x y z + 20 x z - 13, -5 x - 19 x y - 10 y z - 14 z, 2 2 2 -10 x y + 19 x z + z - 2 z] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 2 2 2 G := [-10 x - 17 x y - 18 y + 4 x, 19 x y - 2 x z - 4 y - 3 z , 2 3 -17 y z + 9 z - 12 x y - 4 y z] > Problem := [F,G]; 3 3 Problem := [[-17 x + 9 x y z + 20 x z - 13, -5 x - 19 x y - 10 y z - 14 z, 2 2 2 3 2 3 -10 x y + 19 x z + z - 2 z], [-10 x - 17 x y - 18 y + 4 x, 2 2 2 2 2 3 19 x y - 2 x z - 4 y - 3 z , -17 y z + 9 z - 12 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=25.6MB, alloc=32.3MB, time=0.50 memory used=44.7MB, alloc=56.3MB, time=0.79 memory used=81.9MB, alloc=60.3MB, time=1.33 memory used=123.3MB, alloc=68.3MB, time=1.87 memory used=165.4MB, alloc=68.3MB, time=2.49 memory used=206.2MB, alloc=68.3MB, time=3.01 memory used=250.2MB, alloc=68.3MB, time=3.55 memory used=293.5MB, alloc=92.3MB, time=4.16 memory used=357.2MB, alloc=92.3MB, time=4.93 memory used=431.1MB, alloc=92.3MB, time=6.00 memory used=488.4MB, alloc=92.3MB, time=6.65 memory used=555.6MB, alloc=92.3MB, time=7.51 memory used=606.3MB, alloc=116.3MB, time=8.05 memory used=683.3MB, alloc=116.3MB, time=9.14 memory used=740.9MB, alloc=372.3MB, time=10.00 memory used=829.5MB, alloc=396.3MB, time=11.38 memory used=937.7MB, alloc=396.3MB, time=13.09 memory used=1057.8MB, alloc=420.3MB, time=14.88 memory used=1183.3MB, alloc=444.3MB, time=16.82 memory used=1315.6MB, alloc=444.3MB, time=18.66 memory used=1431.1MB, alloc=444.3MB, time=20.11 memory used=1526.5MB, alloc=468.3MB, time=21.31 memory used=1662.5MB, alloc=468.3MB, time=22.71 memory used=1765.5MB, alloc=468.3MB, time=24.15 memory used=1861.5MB, alloc=468.3MB, time=25.70 memory used=1956.9MB, alloc=468.3MB, time=27.22 memory used=2042.3MB, alloc=468.3MB, time=28.63 memory used=2138.8MB, alloc=468.3MB, time=30.20 memory used=2230.0MB, alloc=492.3MB, time=31.61 memory used=2328.1MB, alloc=492.3MB, time=32.63 memory used=2416.4MB, alloc=492.3MB, time=33.97 memory used=2499.1MB, alloc=492.3MB, time=35.10 memory used=2585.9MB, alloc=492.3MB, time=36.34 memory used=2680.9MB, alloc=492.3MB, time=37.50 memory used=2759.5MB, alloc=492.3MB, time=39.06 memory used=2831.3MB, alloc=492.3MB, time=40.39 memory used=2901.1MB, alloc=492.3MB, time=41.82 memory used=2960.3MB, alloc=492.3MB, time=42.89 memory used=3021.0MB, alloc=492.3MB, time=44.27 memory used=3079.5MB, alloc=492.3MB, time=45.54 memory used=3143.3MB, alloc=492.3MB, time=46.51 memory used=3195.1MB, alloc=492.3MB, time=47.48 memory used=3258.5MB, alloc=492.3MB, time=48.56 memory used=3418.1MB, alloc=492.3MB, time=50.17 memory used=3531.8MB, alloc=492.3MB, time=51.10 memory used=3645.6MB, alloc=492.3MB, time=52.03 memory used=3838.0MB, alloc=516.3MB, time=54.32 memory used=4053.6MB, alloc=540.3MB, time=57.44 memory used=4282.4MB, alloc=564.3MB, time=60.36 memory used=4473.0MB, alloc=564.3MB, time=63.48 memory used=4669.8MB, alloc=588.3MB, time=66.51 memory used=4856.6MB, alloc=588.3MB, time=69.75 memory used=5038.3MB, alloc=612.3MB, time=73.82 memory used=5197.1MB, alloc=612.3MB, time=76.95 memory used=5352.6MB, alloc=636.3MB, time=80.17 memory used=5510.6MB, alloc=636.3MB, time=83.32 memory used=5656.8MB, alloc=636.3MB, time=86.64 memory used=5777.2MB, alloc=636.3MB, time=88.58 memory used=5936.1MB, alloc=660.3MB, time=91.04 memory used=6073.5MB, alloc=660.3MB, time=94.08 memory used=6197.4MB, alloc=660.3MB, time=96.84 memory used=6328.7MB, alloc=660.3MB, time=99.61 memory used=6429.6MB, alloc=660.3MB, time=102.26 memory used=6526.7MB, alloc=660.3MB, time=104.64 memory used=6628.7MB, alloc=660.3MB, time=107.11 memory used=6721.9MB, alloc=660.3MB, time=109.42 memory used=6845.1MB, alloc=660.3MB, time=111.87 memory used=7158.4MB, alloc=684.3MB, time=116.06 memory used=7389.8MB, alloc=684.3MB, time=118.77 memory used=7768.7MB, alloc=708.3MB, time=124.87 memory used=8045.1MB, alloc=708.3MB, time=128.08 memory used=8250.3MB, alloc=708.3MB, time=129.99 memory used=8629.1MB, alloc=732.3MB, time=135.23 memory used=9060.5MB, alloc=756.3MB, time=143.06 memory used=9446.4MB, alloc=780.3MB, time=150.18 |\^/| 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(); 1428286391 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 F := [12 x z + 15 x y - 18 y z + 6 x, -8 x z - 12 x y z - y - 6, 2 -14 x y z + 17 y z + 9 x z] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 2 G := [4 x z - 19 y + 18 y z - 18 y, -15 y z + 2 x y - 3 x z + 7 y , 2 -16 x y z + 14 y + 8 y z + 19] > Problem := [F,G]; 2 2 2 2 2 Problem := [[12 x z + 15 x y - 18 y z + 6 x, -8 x z - 12 x y z - y - 6, 2 2 3 2 -14 x y z + 17 y z + 9 x z], [4 x z - 19 y + 18 y z - 18 y, 2 2 2 -15 y z + 2 x y - 3 x z + 7 y , -16 x y z + 14 y + 8 y z + 19]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.18 memory used=26.4MB, alloc=32.3MB, time=0.49 memory used=46.4MB, alloc=32.3MB, time=0.80 memory used=65.1MB, alloc=56.3MB, time=1.10 memory used=104.9MB, alloc=60.3MB, time=1.71 memory used=144.1MB, alloc=84.3MB, time=2.31 memory used=203.6MB, alloc=92.3MB, time=3.26 memory used=263.6MB, alloc=116.3MB, time=4.24 memory used=341.8MB, alloc=116.3MB, time=5.51 memory used=424.0MB, alloc=372.3MB, time=6.85 memory used=512.0MB, alloc=396.3MB, time=8.14 memory used=617.1MB, alloc=396.3MB, time=10.00 memory used=724.7MB, alloc=420.3MB, time=11.89 memory used=851.6MB, alloc=444.3MB, time=14.28 memory used=999.7MB, alloc=468.3MB, time=16.98 memory used=1133.4MB, alloc=468.3MB, time=19.26 memory used=1275.5MB, alloc=492.3MB, time=21.88 memory used=1406.9MB, alloc=492.3MB, time=24.27 memory used=1523.3MB, alloc=492.3MB, time=26.05 memory used=1648.2MB, alloc=516.3MB, time=28.32 memory used=1752.4MB, alloc=516.3MB, time=30.10 memory used=1867.7MB, alloc=516.3MB, time=32.43 memory used=1977.6MB, alloc=516.3MB, time=34.76 memory used=2066.3MB, alloc=540.3MB, time=36.40 memory used=2149.5MB, alloc=540.3MB, time=38.17 memory used=2237.4MB, alloc=540.3MB, time=40.09 memory used=2302.8MB, alloc=540.3MB, time=41.37 memory used=2404.5MB, alloc=540.3MB, time=44.01 memory used=2493.3MB, alloc=540.3MB, time=46.20 memory used=2557.5MB, alloc=540.3MB, time=47.86 memory used=2625.0MB, alloc=540.3MB, time=49.31 memory used=2683.4MB, alloc=564.3MB, time=50.70 memory used=2752.7MB, alloc=564.3MB, time=52.60 memory used=2805.6MB, alloc=564.3MB, time=53.86 memory used=2854.4MB, alloc=564.3MB, time=54.91 memory used=3099.6MB, alloc=588.3MB, time=60.50 memory used=3285.7MB, alloc=612.3MB, time=64.02 memory used=3476.8MB, alloc=636.3MB, time=68.22 memory used=3691.4MB, alloc=660.3MB, time=72.37 memory used=3907.7MB, alloc=684.3MB, time=77.55 memory used=4133.7MB, alloc=708.3MB, time=83.03 memory used=4368.2MB, alloc=708.3MB, time=89.54 memory used=4592.8MB, alloc=708.3MB, time=93.54 memory used=4724.7MB, alloc=708.3MB, time=96.26 memory used=4875.7MB, alloc=708.3MB, time=100.06 memory used=4994.4MB, alloc=732.3MB, time=102.87 memory used=5134.9MB, alloc=732.3MB, time=106.60 memory used=5276.1MB, alloc=732.3MB, time=110.52 memory used=5403.4MB, alloc=732.3MB, time=114.49 memory used=5500.6MB, alloc=732.3MB, time=117.06 memory used=5879.9MB, alloc=756.3MB, time=127.36 memory used=6293.0MB, alloc=780.3MB, time=137.19 memory used=6720.5MB, alloc=804.3MB, time=148.85 |\^/| 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(); 1428286691 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 F := [-11 x y z - 3 z - 2 z, -12 x y z - 4 y z + 3 y z - 15 y , 2 2 -14 x z - 13 y - 14 x + 9] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 G := [4 x z - 2 x y z + 12 x z + 11 y, -17 y + 17 y z + 13 y - 13, 3 18 z + 20 x y + 8 y + 10 z] > Problem := [F,G]; 3 2 2 2 Problem := [[-11 x y z - 3 z - 2 z, -12 x y z - 4 y z + 3 y z - 15 y , 2 2 2 2 -14 x z - 13 y - 14 x + 9], [4 x z - 2 x y z + 12 x z + 11 y, 3 3 -17 y + 17 y z + 13 y - 13, 18 z + 20 x y + 8 y + 10 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.1MB, alloc=32.3MB, time=0.50 memory used=46.0MB, alloc=56.3MB, time=0.80 memory used=87.1MB, alloc=60.3MB, time=1.40 memory used=127.3MB, alloc=60.3MB, time=1.97 memory used=161.7MB, alloc=60.3MB, time=2.23 memory used=186.7MB, alloc=60.3MB, time=2.43 memory used=222.1MB, alloc=60.3MB, time=2.80 memory used=248.1MB, alloc=60.3MB, time=2.93 memory used=272.9MB, alloc=60.3MB, time=3.02 memory used=298.0MB, alloc=60.3MB, time=3.27 memory used=325.1MB, alloc=60.3MB, time=3.49 memory used=366.2MB, alloc=92.3MB, time=4.08 memory used=432.0MB, alloc=92.3MB, time=4.94 memory used=499.1MB, alloc=92.3MB, time=5.84 memory used=558.9MB, alloc=116.3MB, time=6.78 memory used=628.5MB, alloc=116.3MB, time=7.75 memory used=693.9MB, alloc=396.3MB, time=8.73 memory used=809.9MB, alloc=396.3MB, time=10.26 memory used=922.3MB, alloc=420.3MB, time=11.72 memory used=1004.3MB, alloc=420.3MB, time=12.29 memory used=1134.8MB, alloc=420.3MB, time=14.05 memory used=1235.1MB, alloc=444.3MB, time=14.95 memory used=1328.8MB, alloc=444.3MB, time=15.56 memory used=1422.3MB, alloc=444.3MB, time=16.11 memory used=1513.0MB, alloc=444.3MB, time=17.97 memory used=1610.8MB, alloc=444.3MB, time=19.88 memory used=1688.2MB, alloc=444.3MB, time=20.14 memory used=1841.1MB, alloc=444.3MB, time=21.81 memory used=2019.3MB, alloc=444.3MB, time=24.07 memory used=2178.4MB, alloc=444.3MB, time=26.12 memory used=2306.7MB, alloc=444.3MB, time=27.57 memory used=2395.1MB, alloc=444.3MB, time=28.16 memory used=2471.0MB, alloc=444.3MB, time=28.60 memory used=2534.7MB, alloc=444.3MB, time=28.90 memory used=2616.7MB, alloc=444.3MB, time=29.31 memory used=2682.4MB, alloc=444.3MB, time=29.61 memory used=2746.3MB, alloc=444.3MB, time=29.90 memory used=2829.0MB, alloc=444.3MB, time=31.25 memory used=2896.3MB, alloc=444.3MB, time=31.53 memory used=2960.2MB, alloc=444.3MB, time=31.83 memory used=3040.6MB, alloc=444.3MB, time=32.36 memory used=3129.4MB, alloc=444.3MB, time=33.59 memory used=3193.6MB, alloc=444.3MB, time=33.87 memory used=3256.4MB, alloc=444.3MB, time=34.15 memory used=3315.2MB, alloc=444.3MB, time=34.40 memory used=3397.7MB, alloc=444.3MB, time=34.81 memory used=3457.2MB, alloc=444.3MB, time=35.08 memory used=3537.0MB, alloc=444.3MB, time=35.50 memory used=3600.6MB, alloc=444.3MB, time=35.79 memory used=3701.9MB, alloc=444.3MB, time=45.06 memory used=3766.8MB, alloc=468.3MB, time=45.38 memory used=3845.7MB, alloc=468.3MB, time=45.69 memory used=3929.7MB, alloc=468.3MB, time=45.98 memory used=3993.5MB, alloc=468.3MB, time=46.24 memory used=4067.5MB, alloc=468.3MB, time=46.51 memory used=4154.5MB, alloc=468.3MB, time=46.77 memory used=4334.1MB, alloc=468.3MB, time=47.34 memory used=4422.5MB, alloc=468.3MB, time=47.70 memory used=4514.1MB, alloc=468.3MB, time=48.15 memory used=4595.0MB, alloc=468.3MB, time=48.47 memory used=4711.4MB, alloc=468.3MB, time=57.62 memory used=4790.4MB, alloc=468.3MB, time=57.95 memory used=4879.9MB, alloc=468.3MB, time=58.26 memory used=4949.8MB, alloc=468.3MB, time=58.53 memory used=5016.8MB, alloc=468.3MB, time=58.78 memory used=5094.9MB, alloc=468.3MB, time=59.04 memory used=5186.1MB, alloc=468.3MB, time=59.30 memory used=5371.0MB, alloc=468.3MB, time=60.01 memory used=5506.1MB, alloc=468.3MB, time=61.44 memory used=5613.9MB, alloc=468.3MB, time=62.08 memory used=5772.4MB, alloc=468.3MB, time=63.68 memory used=5884.6MB, alloc=468.3MB, time=65.58 memory used=5988.9MB, alloc=492.3MB, time=67.11 memory used=6091.1MB, alloc=492.3MB, time=68.89 memory used=6183.5MB, alloc=492.3MB, time=70.38 memory used=6269.8MB, alloc=492.3MB, time=71.83 memory used=6368.5MB, alloc=516.3MB, time=73.10 memory used=6442.6MB, alloc=516.3MB, time=74.35 memory used=6506.3MB, alloc=516.3MB, time=75.51 memory used=6576.6MB, alloc=516.3MB, time=76.85 memory used=6678.8MB, alloc=516.3MB, time=78.09 memory used=6752.4MB, alloc=516.3MB, time=79.17 memory used=6834.6MB, alloc=516.3MB, time=80.38 memory used=6927.7MB, alloc=516.3MB, time=81.76 memory used=6978.5MB, alloc=516.3MB, time=82.75 memory used=7017.9MB, alloc=516.3MB, time=83.67 memory used=7072.5MB, alloc=516.3MB, time=84.74 memory used=7275.9MB, alloc=540.3MB, time=87.97 memory used=7480.6MB, alloc=564.3MB, time=90.47 memory used=7601.7MB, alloc=564.3MB, time=91.34 memory used=7716.3MB, alloc=564.3MB, time=91.93 memory used=7887.4MB, alloc=564.3MB, time=93.88 memory used=8045.5MB, alloc=564.3MB, time=94.56 memory used=8255.0MB, alloc=588.3MB, time=96.45 memory used=8515.6MB, alloc=588.3MB, time=99.56 memory used=8637.7MB, alloc=588.3MB, time=100.27 memory used=8757.4MB, alloc=588.3MB, time=101.13 memory used=8871.6MB, alloc=588.3MB, time=101.80 memory used=9025.6MB, alloc=588.3MB, time=109.28 memory used=9132.8MB, alloc=588.3MB, time=109.95 memory used=9398.7MB, alloc=588.3MB, time=110.90 memory used=9567.8MB, alloc=588.3MB, time=111.65 memory used=9818.4MB, alloc=588.3MB, time=112.76 memory used=9942.3MB, alloc=588.3MB, time=113.60 memory used=10056.5MB, alloc=588.3MB, time=114.31 memory used=10207.0MB, alloc=588.3MB, time=121.76 memory used=10313.7MB, alloc=588.3MB, time=122.41 memory used=10576.0MB, alloc=588.3MB, time=123.28 memory used=10745.0MB, alloc=588.3MB, time=124.02 memory used=11011.6MB, alloc=588.3MB, time=125.56 memory used=11122.2MB, alloc=588.3MB, time=126.20 memory used=11255.2MB, alloc=588.3MB, time=127.01 memory used=11376.8MB, alloc=588.3MB, time=128.48 memory used=11491.9MB, alloc=588.3MB, time=129.13 memory used=11685.7MB, alloc=588.3MB, time=130.50 memory used=11827.1MB, alloc=588.3MB, time=131.62 memory used=12053.5MB, alloc=612.3MB, time=134.75 memory used=12276.5MB, alloc=612.3MB, time=138.39 memory used=12467.3MB, alloc=612.3MB, time=141.31 memory used=12687.1MB, alloc=636.3MB, time=143.87 memory used=12919.8MB, alloc=636.3MB, time=146.50 memory used=13094.5MB, alloc=636.3MB, time=149.64 memory used=13269.0MB, alloc=636.3MB, time=151.98 memory used=13411.7MB, alloc=660.3MB, time=154.67 memory used=13551.8MB, alloc=660.3MB, time=157.90 memory used=13695.1MB, alloc=660.3MB, time=160.39 memory used=13837.0MB, alloc=684.3MB, time=163.45 memory used=13971.5MB, alloc=684.3MB, time=166.76 memory used=14083.6MB, alloc=684.3MB, time=168.90 memory used=14184.9MB, alloc=708.3MB, time=170.99 memory used=14553.9MB, alloc=732.3MB, time=177.95 |\^/| 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(); 1428286991 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [x y + 7 x + 3 y + 19 z, 12 x y - 8 x y z - 3 y - 6 z, 3 2 2 -4 y - 11 y z + 5 z - 11] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [2 x z + 2 y z - 13 x z + 7 z , 18 x z + 3 z + 7 x, 2 2 2 -4 x z - 5 x y z - 6 y z - 16 y ] > Problem := [F,G]; 2 2 Problem := [[x y + 7 x + 3 y + 19 z, 12 x y - 8 x y z - 3 y - 6 z, 3 2 2 2 2 2 -4 y - 11 y z + 5 z - 11], [2 x z + 2 y z - 13 x z + 7 z , 2 2 2 2 18 x z + 3 z + 7 x, -4 x z - 5 x y z - 6 y z - 16 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.18 memory used=26.3MB, alloc=32.3MB, time=0.51 memory used=46.5MB, alloc=32.3MB, time=0.82 memory used=65.2MB, alloc=56.3MB, time=1.12 memory used=105.1MB, alloc=60.3MB, time=1.74 memory used=144.6MB, alloc=60.3MB, time=2.35 memory used=181.7MB, alloc=84.3MB, time=2.94 memory used=229.5MB, alloc=84.3MB, time=3.71 memory used=287.3MB, alloc=116.3MB, time=4.69 memory used=369.1MB, alloc=116.3MB, time=5.98 memory used=449.1MB, alloc=116.3MB, time=7.27 memory used=521.4MB, alloc=396.3MB, time=8.49 memory used=623.3MB, alloc=396.3MB, time=10.21 memory used=725.4MB, alloc=420.3MB, time=11.90 memory used=848.2MB, alloc=444.3MB, time=14.02 memory used=992.0MB, alloc=468.3MB, time=16.59 memory used=1147.3MB, alloc=492.3MB, time=19.29 memory used=1292.2MB, alloc=492.3MB, time=22.01 memory used=1428.1MB, alloc=516.3MB, time=24.70 memory used=1544.5MB, alloc=516.3MB, time=27.00 memory used=1633.1MB, alloc=540.3MB, time=28.42 memory used=1752.1MB, alloc=540.3MB, time=30.92 memory used=1852.5MB, alloc=540.3MB, time=33.05 memory used=1931.9MB, alloc=540.3MB, time=34.44 memory used=2015.8MB, alloc=540.3MB, time=35.93 memory used=2096.5MB, alloc=540.3MB, time=37.64 memory used=2172.0MB, alloc=540.3MB, time=39.43 memory used=2241.2MB, alloc=540.3MB, time=40.79 memory used=2318.9MB, alloc=540.3MB, time=42.59 memory used=2387.3MB, alloc=564.3MB, time=44.36 memory used=2440.3MB, alloc=564.3MB, time=45.54 memory used=2491.1MB, alloc=564.3MB, time=46.56 memory used=2539.0MB, alloc=564.3MB, time=47.52 memory used=2610.6MB, alloc=564.3MB, time=49.30 memory used=2815.5MB, alloc=588.3MB, time=53.08 memory used=3034.3MB, alloc=612.3MB, time=57.73 memory used=3265.7MB, alloc=636.3MB, time=63.17 memory used=3410.2MB, alloc=660.3MB, time=66.25 memory used=3570.2MB, alloc=684.3MB, time=69.52 memory used=3733.6MB, alloc=684.3MB, time=73.15 memory used=3872.8MB, alloc=684.3MB, time=76.44 memory used=3979.0MB, alloc=684.3MB, time=78.92 memory used=4111.9MB, alloc=684.3MB, time=81.86 memory used=4241.1MB, alloc=684.3MB, time=85.22 memory used=4359.4MB, alloc=708.3MB, time=87.82 memory used=4507.7MB, alloc=708.3MB, time=90.67 memory used=4603.9MB, alloc=708.3MB, time=93.05 memory used=4697.8MB, alloc=708.3MB, time=95.30 memory used=5073.5MB, alloc=732.3MB, time=103.90 memory used=5462.0MB, alloc=756.3MB, time=112.86 memory used=5867.1MB, alloc=780.3MB, time=122.56 memory used=6240.1MB, alloc=804.3MB, time=129.81 memory used=6606.1MB, alloc=828.3MB, time=138.75 memory used=6944.5MB, alloc=852.3MB, time=146.31 memory used=7260.8MB, alloc=876.3MB, time=153.72 |\^/| 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(); 1428287291 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 F := [-16 x y - 5 x + 11 z + 12, -10 x y z - 7 y z + 9 y + 16 y z, 3 3 3 -13 x + 4 y + 4 z + 2 x] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 G := [-11 x y + 9 x y z + 19 y z + 6 x, 17 x y + 5 x y z - 18 x z + 19 y , 2 2 3 2 x y - 20 x z - 4 y + 16 y] > Problem := [F,G]; 2 2 2 2 2 Problem := [[-16 x y - 5 x + 11 z + 12, -10 x y z - 7 y z + 9 y + 16 y z, 3 3 3 2 2 -13 x + 4 y + 4 z + 2 x], [-11 x y + 9 x y z + 19 y z + 6 x, 2 2 2 2 2 3 17 x y + 5 x y z - 18 x z + 19 y , 2 x y - 20 x z - 4 y + 16 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.18 memory used=26.2MB, alloc=32.3MB, time=0.50 memory used=45.5MB, alloc=56.3MB, time=0.79 memory used=93.8MB, alloc=60.3MB, time=1.77 memory used=121.4MB, alloc=60.3MB, time=4.72 memory used=154.1MB, alloc=84.3MB, time=8.29 memory used=346.7MB, alloc=116.3MB, time=10.32 memory used=419.1MB, alloc=117.1MB, time=10.79 memory used=464.1MB, alloc=117.1MB, time=10.91 memory used=510.1MB, alloc=117.1MB, time=11.03 memory used=560.7MB, alloc=117.1MB, time=11.16 memory used=671.5MB, alloc=117.1MB, time=11.67 memory used=790.9MB, alloc=117.1MB, time=12.54 memory used=864.7MB, alloc=117.1MB, time=12.98 memory used=945.3MB, alloc=117.1MB, time=13.59 memory used=1023.0MB, alloc=117.1MB, time=14.37 memory used=1113.5MB, alloc=117.1MB, time=15.44 memory used=1196.0MB, alloc=117.1MB, time=16.42 memory used=1276.0MB, alloc=117.1MB, time=17.29 memory used=1325.0MB, alloc=117.1MB, time=17.54 memory used=1382.5MB, alloc=117.1MB, time=18.13 memory used=1420.4MB, alloc=117.1MB, time=18.25 memory used=1488.1MB, alloc=117.1MB, time=18.72 memory used=1564.6MB, alloc=373.1MB, time=19.93 memory used=1648.8MB, alloc=397.1MB, time=23.49 memory used=1718.2MB, alloc=421.1MB, time=25.61 memory used=1776.4MB, alloc=421.1MB, time=25.83 memory used=1827.9MB, alloc=421.1MB, time=26.02 memory used=1876.9MB, alloc=421.1MB, time=26.22 memory used=1922.6MB, alloc=421.1MB, time=26.41 memory used=1968.3MB, alloc=421.1MB, time=26.60 memory used=2015.9MB, alloc=421.1MB, time=26.80 memory used=2064.3MB, alloc=421.1MB, time=26.98 memory used=2113.2MB, alloc=421.1MB, time=27.17 memory used=2164.2MB, alloc=421.1MB, time=27.36 memory used=2216.6MB, alloc=421.1MB, time=27.56 memory used=2269.8MB, alloc=421.1MB, time=27.75 memory used=2325.8MB, alloc=421.1MB, time=27.94 memory used=2382.9MB, alloc=421.1MB, time=28.14 memory used=2443.5MB, alloc=421.1MB, time=28.33 memory used=2507.3MB, alloc=421.1MB, time=28.52 memory used=2594.3MB, alloc=421.1MB, time=33.18 memory used=2649.7MB, alloc=421.1MB, time=33.39 memory used=2699.0MB, alloc=421.1MB, time=33.59 memory used=2746.2MB, alloc=421.1MB, time=33.80 memory used=2791.8MB, alloc=421.1MB, time=34.00 memory used=2837.7MB, alloc=421.1MB, time=34.19 memory used=2885.1MB, alloc=421.1MB, time=34.38 memory used=2933.3MB, alloc=421.1MB, time=34.58 memory used=2982.0MB, alloc=421.1MB, time=34.77 memory used=3032.8MB, alloc=421.1MB, time=34.96 memory used=3085.0MB, alloc=421.1MB, time=35.16 memory used=3139.4MB, alloc=421.1MB, time=35.37 memory used=3195.0MB, alloc=421.1MB, time=35.58 memory used=3252.8MB, alloc=421.1MB, time=35.78 memory used=3313.6MB, alloc=421.1MB, time=36.00 memory used=3381.2MB, alloc=421.1MB, time=36.27 memory used=3472.5MB, alloc=445.1MB, time=55.04 memory used=3665.3MB, alloc=445.1MB, time=62.31 memory used=3750.8MB, alloc=445.1MB, time=62.50 memory used=3835.9MB, alloc=445.1MB, time=62.69 memory used=3922.0MB, alloc=445.1MB, time=62.89 memory used=4008.8MB, alloc=445.1MB, time=63.08 memory used=4098.7MB, alloc=445.1MB, time=63.27 memory used=4188.5MB, alloc=445.1MB, time=63.47 memory used=4280.3MB, alloc=445.1MB, time=63.67 memory used=4373.4MB, alloc=445.1MB, time=63.86 memory used=4467.1MB, alloc=445.1MB, time=64.06 memory used=4562.7MB, alloc=445.1MB, time=64.25 memory used=4658.9MB, alloc=445.1MB, time=64.44 memory used=4757.9MB, alloc=445.1MB, time=64.65 memory used=4911.0MB, alloc=445.1MB, time=65.06 memory used=5043.0MB, alloc=445.1MB, time=65.34 memory used=5228.5MB, alloc=445.1MB, time=133.20 memory used=5311.3MB, alloc=469.1MB, time=133.45 memory used=5413.7MB, alloc=469.1MB, time=133.71 memory used=5511.0MB, alloc=469.1MB, time=133.97 memory used=5616.4MB, alloc=469.1MB, time=134.22 memory used=5721.6MB, alloc=469.1MB, time=134.50 memory used=5826.6MB, alloc=469.1MB, time=134.75 memory used=5931.2MB, alloc=469.1MB, time=135.02 memory used=6018.8MB, alloc=493.1MB, time=135.26 memory used=6108.3MB, alloc=493.1MB, time=135.49 memory used=6195.3MB, alloc=493.1MB, time=135.71 memory used=6275.4MB, alloc=493.1MB, time=135.94 memory used=6349.6MB, alloc=493.1MB, time=136.15 memory used=6424.1MB, alloc=493.1MB, time=136.37 memory used=6498.3MB, alloc=493.1MB, time=136.59 memory used=6572.4MB, alloc=493.1MB, time=136.80 memory used=6645.9MB, alloc=493.1MB, time=137.00 memory used=6711.9MB, alloc=493.1MB, time=137.20 memory used=6777.8MB, alloc=493.1MB, time=137.40 memory used=6843.4MB, alloc=493.1MB, time=137.59 memory used=6908.9MB, alloc=493.1MB, time=137.80 memory used=6974.1MB, alloc=493.1MB, time=137.99 memory used=7039.0MB, alloc=493.1MB, time=138.18 memory used=7103.8MB, alloc=493.1MB, time=138.38 memory used=7168.3MB, alloc=493.1MB, time=138.57 memory used=7232.5MB, alloc=493.1MB, time=138.77 memory used=7297.1MB, alloc=493.1MB, time=138.97 memory used=7361.7MB, alloc=493.1MB, time=139.17 memory used=7425.9MB, alloc=493.1MB, time=139.37 memory used=7489.9MB, alloc=493.1MB, time=139.56 memory used=7553.6MB, alloc=493.1MB, time=139.75 memory used=7617.1MB, alloc=493.1MB, time=139.95 memory used=7688.0MB, alloc=493.1MB, time=140.15 memory used=7758.6MB, alloc=493.1MB, time=140.35 memory used=7828.7MB, alloc=493.1MB, time=140.55 memory used=7898.4MB, alloc=493.1MB, time=140.75 memory used=7967.7MB, alloc=493.1MB, time=140.95 memory used=8036.6MB, alloc=493.1MB, time=141.15 memory used=8105.0MB, alloc=493.1MB, time=141.35 memory used=8173.0MB, alloc=493.1MB, time=141.54 memory used=8240.7MB, alloc=493.1MB, time=141.75 memory used=8315.2MB, alloc=493.1MB, time=141.96 memory used=8389.2MB, alloc=493.1MB, time=142.15 memory used=8462.5MB, alloc=493.1MB, time=142.36 memory used=8535.3MB, alloc=493.1MB, time=142.56 memory used=8607.5MB, alloc=493.1MB, time=142.75 memory used=8679.1MB, alloc=493.1MB, time=142.95 memory used=8750.2MB, alloc=493.1MB, time=143.16 memory used=8827.5MB, alloc=493.1MB, time=143.38 memory used=8904.1MB, alloc=493.1MB, time=143.58 memory used=8979.9MB, alloc=493.1MB, time=143.78 memory used=9054.9MB, alloc=493.1MB, time=143.99 memory used=9129.2MB, alloc=493.1MB, time=144.19 memory used=9209.2MB, alloc=493.1MB, time=144.39 memory used=9288.2MB, alloc=493.1MB, time=144.60 memory used=9366.3MB, alloc=493.1MB, time=144.81 memory used=9443.4MB, alloc=493.1MB, time=145.02 memory used=9525.6MB, alloc=493.1MB, time=145.23 memory used=9606.6MB, alloc=493.1MB, time=145.44 memory used=9686.4MB, alloc=493.1MB, time=145.64 memory used=9765.0MB, alloc=493.1MB, time=145.85 memory used=9848.1MB, alloc=493.1MB, time=146.06 memory used=9929.8MB, alloc=493.1MB, time=146.26 memory used=10015.5MB, alloc=493.1MB, time=146.48 memory used=10099.6MB, alloc=493.1MB, time=146.70 memory used=10187.1MB, alloc=493.1MB, time=146.91 memory used=10272.6MB, alloc=493.1MB, time=147.12 memory used=10360.9MB, alloc=493.1MB, time=147.33 memory used=10446.9MB, alloc=493.1MB, time=147.54 memory used=10535.3MB, alloc=493.1MB, time=147.75 memory used=10625.4MB, alloc=493.1MB, time=147.97 memory used=10716.8MB, alloc=493.1MB, time=148.18 memory used=10808.9MB, alloc=493.1MB, time=148.40 memory used=10901.0MB, alloc=493.1MB, time=148.62 memory used=10996.1MB, alloc=493.1MB, time=148.83 memory used=11089.4MB, alloc=493.1MB, time=149.06 memory used=11186.6MB, alloc=493.1MB, time=149.28 memory used=11284.9MB, alloc=493.1MB, time=149.50 memory used=11384.1MB, alloc=493.1MB, time=149.72 memory used=11486.0MB, alloc=493.1MB, time=149.94 memory used=11591.9MB, alloc=493.1MB, time=152.66 memory used=11752.4MB, alloc=493.1MB, time=217.98 memory used=11876.6MB, alloc=493.1MB, time=218.28 memory used=12000.3MB, alloc=493.1MB, time=218.57 memory used=12123.7MB, alloc=493.1MB, time=218.87 memory used=12246.7MB, alloc=493.1MB, time=219.15 memory used=12377.9MB, alloc=493.1MB, time=219.47 memory used=12491.1MB, alloc=493.1MB, time=219.73 memory used=12581.8MB, alloc=493.1MB, time=219.99 memory used=12669.4MB, alloc=493.1MB, time=220.22 memory used=12749.5MB, alloc=493.1MB, time=220.44 memory used=12823.8MB, alloc=493.1MB, time=220.66 memory used=12898.2MB, alloc=493.1MB, time=220.88 memory used=12972.5MB, alloc=493.1MB, time=221.09 memory used=13046.8MB, alloc=493.1MB, time=221.30 memory used=13120.2MB, alloc=493.1MB, time=221.50 memory used=13186.1MB, alloc=493.1MB, time=221.70 memory used=13252.0MB, alloc=493.1MB, time=221.89 memory used=13317.7MB, alloc=493.1MB, time=222.09 memory used=13383.1MB, alloc=493.1MB, time=222.29 memory used=13448.2MB, alloc=493.1MB, time=222.49 memory used=13513.1MB, alloc=493.1MB, time=222.69 memory used=13577.9MB, alloc=493.1MB, time=222.88 memory used=13642.3MB, alloc=493.1MB, time=223.07 memory used=13706.6MB, alloc=493.1MB, time=223.26 memory used=13771.2MB, alloc=493.1MB, time=223.45 memory used=13835.8MB, alloc=493.1MB, time=223.64 memory used=13900.0MB, alloc=493.1MB, time=223.84 memory used=13963.9MB, alloc=493.1MB, time=224.04 memory used=14027.8MB, alloc=493.1MB, time=224.24 memory used=14099.0MB, alloc=493.1MB, time=224.44 memory used=14169.8MB, alloc=493.1MB, time=224.64 memory used=14240.2MB, alloc=493.1MB, time=224.84 memory used=14310.3MB, alloc=493.1MB, time=225.04 memory used=14379.9MB, alloc=493.1MB, time=225.23 memory used=14449.1MB, alloc=493.1MB, time=225.43 |\^/| 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(); 1428287591 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 3 2 2 F := [-6 x y z + 18 y z + 6 z + 2 y , -x - 7 x y + 18 x z + 10 x, 3 2 2 -16 x + 3 x y - 19 x y z - 20 z ] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 2 2 G := [-8 x y + 18 x - 14 y + 15 z, -15 x y - 8 y z + 7 y z - 7 y , 2 2 3 x y - 7 y + 5 y z + 15 x] > Problem := [F,G]; 2 3 2 3 2 2 Problem := [[-6 x y z + 18 y z + 6 z + 2 y , -x - 7 x y + 18 x z + 10 x, 3 2 2 2 2 2 -16 x + 3 x y - 19 x y z - 20 z ], [-8 x y + 18 x - 14 y + 15 z, 2 2 2 2 2 2 -15 x y - 8 y z + 7 y z - 7 y , 3 x y - 7 y + 5 y z + 15 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.18 memory used=24.6MB, alloc=32.3MB, time=0.49 memory used=43.9MB, alloc=56.3MB, time=0.78 memory used=80.7MB, alloc=60.3MB, time=1.26 memory used=126.6MB, alloc=68.3MB, time=1.86 memory used=171.5MB, alloc=68.3MB, time=2.32 memory used=211.9MB, alloc=68.3MB, time=2.92 memory used=257.9MB, alloc=92.3MB, time=3.52 memory used=323.6MB, alloc=92.3MB, time=4.45 memory used=382.7MB, alloc=92.3MB, time=5.06 memory used=432.8MB, alloc=116.3MB, time=5.49 memory used=505.1MB, alloc=372.3MB, time=6.33 memory used=603.1MB, alloc=372.3MB, time=7.49 memory used=691.1MB, alloc=396.3MB, time=8.60 memory used=772.3MB, alloc=396.3MB, time=9.10 memory used=851.9MB, alloc=396.3MB, time=9.63 memory used=940.2MB, alloc=396.3MB, time=10.32 memory used=1062.8MB, alloc=396.3MB, time=11.58 memory used=1171.0MB, alloc=396.3MB, time=12.84 memory used=1287.8MB, alloc=420.3MB, time=14.35 memory used=1407.1MB, alloc=420.3MB, time=15.82 memory used=1530.5MB, alloc=444.3MB, time=17.59 memory used=1642.5MB, alloc=444.3MB, time=19.02 memory used=1793.7MB, alloc=444.3MB, time=20.60 memory used=1901.2MB, alloc=444.3MB, time=21.62 memory used=2011.7MB, alloc=444.3MB, time=23.01 memory used=2124.7MB, alloc=468.3MB, time=24.50 memory used=2235.8MB, alloc=468.3MB, time=25.28 memory used=2341.8MB, alloc=468.3MB, time=25.98 memory used=2433.8MB, alloc=468.3MB, time=26.55 memory used=2554.2MB, alloc=468.3MB, time=27.85 memory used=2642.8MB, alloc=468.3MB, time=29.31 memory used=2753.9MB, alloc=468.3MB, time=30.76 memory used=2839.7MB, alloc=468.3MB, time=32.04 memory used=2915.7MB, alloc=468.3MB, time=33.25 memory used=3000.9MB, alloc=492.3MB, time=34.69 memory used=3073.3MB, alloc=492.3MB, time=35.81 memory used=3150.4MB, alloc=492.3MB, time=36.85 memory used=3226.0MB, alloc=492.3MB, time=37.79 memory used=3286.4MB, alloc=492.3MB, time=38.88 memory used=3352.5MB, alloc=492.3MB, time=39.89 memory used=3416.1MB, alloc=492.3MB, time=40.89 memory used=3471.5MB, alloc=492.3MB, time=41.90 memory used=3532.9MB, alloc=492.3MB, time=42.93 memory used=3583.2MB, alloc=492.3MB, time=43.87 memory used=3641.7MB, alloc=492.3MB, time=44.95 memory used=3682.4MB, alloc=492.3MB, time=45.96 memory used=3737.7MB, alloc=516.3MB, time=47.08 memory used=3784.8MB, alloc=516.3MB, time=48.00 memory used=3985.1MB, alloc=540.3MB, time=50.92 memory used=4181.7MB, alloc=564.3MB, time=53.94 memory used=4404.2MB, alloc=588.3MB, time=57.44 memory used=4605.2MB, alloc=612.3MB, time=60.12 memory used=4785.3MB, alloc=612.3MB, time=62.52 memory used=4980.9MB, alloc=636.3MB, time=65.49 memory used=5134.4MB, alloc=660.3MB, time=67.84 memory used=5265.7MB, alloc=660.3MB, time=70.47 memory used=5369.1MB, alloc=660.3MB, time=72.46 memory used=5556.9MB, alloc=660.3MB, time=74.64 memory used=5764.4MB, alloc=660.3MB, time=77.07 memory used=5898.0MB, alloc=660.3MB, time=79.24 memory used=6025.5MB, alloc=684.3MB, time=81.15 memory used=6150.5MB, alloc=684.3MB, time=83.01 memory used=6298.8MB, alloc=684.3MB, time=85.11 memory used=6643.0MB, alloc=708.3MB, time=91.06 memory used=7038.6MB, alloc=732.3MB, time=97.23 memory used=7430.6MB, alloc=756.3MB, time=103.04 memory used=7836.7MB, alloc=780.3MB, time=108.67 memory used=8208.4MB, alloc=804.3MB, time=114.25 memory used=8581.8MB, alloc=828.3MB, time=121.09 memory used=9007.4MB, alloc=852.3MB, time=126.41 memory used=9427.2MB, alloc=876.3MB, time=131.29 memory used=9822.2MB, alloc=900.3MB, time=135.76 memory used=10136.1MB, alloc=924.3MB, time=139.01 memory used=10473.9MB, alloc=948.3MB, time=143.90 |\^/| 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(); 1428287891 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-16 x z + 7 y z - 19 x - 7, -6 x y + 7 x z - 14 y + 13 z, 2 2 18 x y z + 6 x z + 11 x - 3 z] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 3 2 G := [5 x z - 18 x z - 12 z - 4 z, 20 x y + 6 x z - 12 y + 4 x , 2 2 -11 x y - 20 z + 4 y + 11] > Problem := [F,G]; 2 2 Problem := [[-16 x z + 7 y z - 19 x - 7, -6 x y + 7 x z - 14 y + 13 z, 2 2 2 2 3 18 x y z + 6 x z + 11 x - 3 z], [5 x z - 18 x z - 12 z - 4 z, 2 2 3 2 2 2 20 x y + 6 x z - 12 y + 4 x , -11 x y - 20 z + 4 y + 11]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=25.6MB, alloc=32.3MB, time=0.49 memory used=45.3MB, alloc=56.3MB, time=0.80 memory used=87.0MB, alloc=60.3MB, time=1.42 memory used=127.9MB, alloc=68.3MB, time=2.03 memory used=169.8MB, alloc=92.3MB, time=2.59 memory used=233.6MB, alloc=92.3MB, time=3.52 memory used=299.8MB, alloc=116.3MB, time=4.43 memory used=375.2MB, alloc=116.3MB, time=5.56 memory used=441.8MB, alloc=372.3MB, time=6.56 memory used=528.7MB, alloc=396.3MB, time=7.83 memory used=640.9MB, alloc=420.3MB, time=9.36 memory used=769.5MB, alloc=420.3MB, time=10.91 memory used=898.6MB, alloc=444.3MB, time=12.78 memory used=1002.8MB, alloc=444.3MB, time=14.28 memory used=1119.8MB, alloc=468.3MB, time=16.14 memory used=1218.0MB, alloc=468.3MB, time=17.71 memory used=1312.8MB, alloc=468.3MB, time=19.19 memory used=1423.2MB, alloc=468.3MB, time=20.45 memory used=1519.1MB, alloc=492.3MB, time=21.76 memory used=1597.3MB, alloc=492.3MB, time=23.11 memory used=1677.3MB, alloc=492.3MB, time=24.32 memory used=1793.7MB, alloc=492.3MB, time=25.49 memory used=1900.8MB, alloc=492.3MB, time=26.78 memory used=1999.7MB, alloc=492.3MB, time=28.54 memory used=2057.0MB, alloc=492.3MB, time=29.60 memory used=2127.6MB, alloc=492.3MB, time=30.76 memory used=2201.9MB, alloc=492.3MB, time=31.84 memory used=2256.7MB, alloc=492.3MB, time=32.72 memory used=2314.7MB, alloc=516.3MB, time=33.88 memory used=2432.1MB, alloc=516.3MB, time=34.92 memory used=2490.2MB, alloc=516.3MB, time=35.84 memory used=2534.5MB, alloc=516.3MB, time=36.76 memory used=2584.9MB, alloc=516.3MB, time=37.53 memory used=2694.5MB, alloc=516.3MB, time=38.44 memory used=2823.2MB, alloc=516.3MB, time=39.45 memory used=2930.2MB, alloc=516.3MB, time=40.25 memory used=3127.6MB, alloc=540.3MB, time=42.62 memory used=3318.0MB, alloc=564.3MB, time=45.79 memory used=3501.3MB, alloc=564.3MB, time=48.23 memory used=3680.4MB, alloc=588.3MB, time=50.88 memory used=3806.5MB, alloc=588.3MB, time=51.59 memory used=4045.7MB, alloc=588.3MB, time=54.31 memory used=4229.3MB, alloc=588.3MB, time=56.25 memory used=4438.9MB, alloc=588.3MB, time=59.45 memory used=4612.7MB, alloc=612.3MB, time=62.45 memory used=4775.4MB, alloc=636.3MB, time=65.53 memory used=4920.1MB, alloc=660.3MB, time=67.93 memory used=5065.8MB, alloc=660.3MB, time=70.19 memory used=5192.4MB, alloc=660.3MB, time=72.84 memory used=5297.5MB, alloc=684.3MB, time=74.60 memory used=5407.0MB, alloc=684.3MB, time=76.50 memory used=5517.4MB, alloc=684.3MB, time=79.09 memory used=5864.0MB, alloc=708.3MB, time=83.94 memory used=6257.1MB, alloc=732.3MB, time=89.24 memory used=6641.5MB, alloc=756.3MB, time=95.92 memory used=6985.2MB, alloc=780.3MB, time=101.27 memory used=7336.9MB, alloc=804.3MB, time=107.77 memory used=7608.7MB, alloc=828.3MB, time=112.86 memory used=7918.0MB, alloc=852.3MB, time=118.41 memory used=8174.0MB, alloc=876.3MB, time=123.35 memory used=8452.7MB, alloc=900.3MB, time=127.77 memory used=8699.8MB, alloc=924.3MB, time=132.62 memory used=8963.5MB, alloc=948.3MB, time=136.83 memory used=9179.6MB, alloc=972.3MB, time=141.59 memory used=9363.9MB, alloc=996.3MB, time=145.55 memory used=9936.2MB, alloc=1020.3MB, time=154.77 memory used=10399.3MB, alloc=1044.3MB, time=161.88 |\^/| 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(); 1428288191 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 F := [-3 x y - 7 z + 7 x y + 3 y z, -15 x y + 16 x y z + 15 x - 3 y, 3 2 2 18 x - 16 x y - 19 y z + 6 y] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [x y - 7 x z - 14 y z - 15 z, 18 y z + 16 x y + 8 x - z, 2 3 6 y z + 16 z - 17 z + 9] > Problem := [F,G]; 2 3 2 Problem := [[-3 x y - 7 z + 7 x y + 3 y z, -15 x y + 16 x y z + 15 x - 3 y, 3 2 2 2 2 18 x - 16 x y - 19 y z + 6 y], [x y - 7 x z - 14 y z - 15 z, 2 2 3 18 y z + 16 x y + 8 x - z, 6 y z + 16 z - 17 z + 9]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=25.4MB, alloc=32.3MB, time=0.48 memory used=46.8MB, alloc=60.3MB, time=0.77 memory used=82.3MB, alloc=61.3MB, time=1.04 memory used=120.7MB, alloc=61.3MB, time=1.33 memory used=174.2MB, alloc=62.5MB, time=2.06 memory used=218.8MB, alloc=70.5MB, time=2.46 memory used=250.9MB, alloc=70.5MB, time=2.59 memory used=285.3MB, alloc=70.5MB, time=2.94 memory used=329.4MB, alloc=70.5MB, time=3.36 memory used=367.7MB, alloc=70.5MB, time=3.63 memory used=410.3MB, alloc=70.5MB, time=4.00 memory used=452.1MB, alloc=70.5MB, time=4.33 memory used=475.2MB, alloc=70.5MB, time=4.40 memory used=516.2MB, alloc=70.5MB, time=5.19 memory used=543.9MB, alloc=70.5MB, time=5.28 memory used=563.0MB, alloc=70.5MB, time=5.35 memory used=584.9MB, alloc=70.5MB, time=5.43 memory used=610.9MB, alloc=70.5MB, time=5.50 memory used=638.8MB, alloc=70.5MB, time=5.57 memory used=657.1MB, alloc=70.5MB, time=5.63 memory used=675.3MB, alloc=70.5MB, time=5.69 memory used=695.4MB, alloc=70.5MB, time=5.75 memory used=717.8MB, alloc=70.5MB, time=5.81 memory used=748.9MB, alloc=70.5MB, time=6.00 memory used=777.4MB, alloc=70.5MB, time=6.32 memory used=804.1MB, alloc=70.5MB, time=6.39 memory used=828.6MB, alloc=70.5MB, time=6.47 memory used=861.1MB, alloc=70.5MB, time=6.79 memory used=889.5MB, alloc=70.5MB, time=6.95 memory used=936.6MB, alloc=70.5MB, time=7.53 memory used=978.3MB, alloc=94.5MB, time=8.14 memory used=1045.2MB, alloc=94.5MB, time=8.95 memory used=1096.3MB, alloc=94.5MB, time=9.29 memory used=1142.9MB, alloc=94.5MB, time=9.66 memory used=1194.0MB, alloc=94.5MB, time=10.15 memory used=1231.6MB, alloc=94.5MB, time=10.30 memory used=1267.4MB, alloc=94.5MB, time=10.44 memory used=1301.7MB, alloc=94.5MB, time=10.55 memory used=1341.7MB, alloc=94.5MB, time=10.80 memory used=1377.8MB, alloc=94.5MB, time=10.94 memory used=1412.2MB, alloc=94.5MB, time=11.05 memory used=1468.0MB, alloc=94.5MB, time=13.03 memory used=1501.4MB, alloc=94.5MB, time=13.14 memory used=1530.2MB, alloc=94.5MB, time=13.24 memory used=1564.6MB, alloc=94.5MB, time=13.35 memory used=1601.1MB, alloc=94.5MB, time=13.63 memory used=1635.3MB, alloc=94.5MB, time=13.81 memory used=1693.8MB, alloc=94.5MB, time=14.43 memory used=1778.0MB, alloc=94.5MB, time=15.41 memory used=1859.7MB, alloc=94.5MB, time=16.37 memory used=1916.4MB, alloc=94.5MB, time=17.05 memory used=1955.4MB, alloc=94.5MB, time=17.72 memory used=1998.3MB, alloc=94.5MB, time=19.00 memory used=2027.1MB, alloc=94.5MB, time=19.10 memory used=2054.2MB, alloc=94.5MB, time=19.20 memory used=2086.3MB, alloc=94.5MB, time=19.29 memory used=2116.1MB, alloc=94.5MB, time=19.49 memory used=2161.7MB, alloc=94.5MB, time=19.95 memory used=2240.0MB, alloc=94.5MB, time=20.89 memory used=2294.6MB, alloc=118.5MB, time=21.71 memory used=2375.0MB, alloc=374.5MB, time=22.43 memory used=2462.1MB, alloc=374.5MB, time=23.27 memory used=2549.1MB, alloc=374.5MB, time=24.17 memory used=2622.1MB, alloc=374.5MB, time=24.78 memory used=2670.8MB, alloc=374.5MB, time=24.96 memory used=2715.2MB, alloc=374.5MB, time=25.18 memory used=2753.9MB, alloc=374.5MB, time=25.34 memory used=2801.7MB, alloc=374.5MB, time=25.73 memory used=2848.4MB, alloc=374.5MB, time=25.98 memory used=2889.5MB, alloc=374.5MB, time=26.14 memory used=2933.9MB, alloc=374.5MB, time=26.37 memory used=2972.4MB, alloc=374.5MB, time=26.52 memory used=3020.3MB, alloc=374.5MB, time=26.90 memory used=3071.8MB, alloc=374.5MB, time=27.17 memory used=3118.4MB, alloc=374.5MB, time=27.38 memory used=3173.4MB, alloc=374.5MB, time=28.34 memory used=3226.8MB, alloc=374.5MB, time=28.78 memory used=3261.4MB, alloc=374.5MB, time=28.94 memory used=3301.6MB, alloc=374.5MB, time=29.09 memory used=3340.2MB, alloc=374.5MB, time=29.23 memory used=3369.7MB, alloc=374.5MB, time=29.36 memory used=3412.4MB, alloc=374.5MB, time=29.74 memory used=3462.9MB, alloc=398.5MB, time=29.98 memory used=3517.9MB, alloc=398.5MB, time=30.20 memory used=3579.6MB, alloc=398.5MB, time=30.43 memory used=3623.9MB, alloc=398.5MB, time=30.62 memory used=3674.4MB, alloc=398.5MB, time=30.80 memory used=3733.6MB, alloc=398.5MB, time=30.99 memory used=3799.4MB, alloc=398.5MB, time=31.17 memory used=3860.3MB, alloc=398.5MB, time=31.64 memory used=3919.2MB, alloc=398.5MB, time=31.88 memory used=3984.6MB, alloc=398.5MB, time=32.11 memory used=4033.3MB, alloc=398.5MB, time=32.30 memory used=4080.8MB, alloc=398.5MB, time=32.49 memory used=4135.0MB, alloc=398.5MB, time=32.69 memory used=4198.6MB, alloc=398.5MB, time=32.88 memory used=4252.9MB, alloc=398.5MB, time=33.05 memory used=4347.5MB, alloc=398.5MB, time=43.02 memory used=4408.6MB, alloc=398.5MB, time=43.24 memory used=4454.7MB, alloc=398.5MB, time=43.42 memory used=4512.7MB, alloc=398.5MB, time=43.60 memory used=4579.5MB, alloc=398.5MB, time=43.79 memory used=4619.7MB, alloc=398.5MB, time=43.94 memory used=4663.4MB, alloc=398.5MB, time=44.10 memory used=4711.9MB, alloc=398.5MB, time=44.25 memory used=4765.0MB, alloc=398.5MB, time=44.40 memory used=4823.6MB, alloc=398.5MB, time=44.55 memory used=4887.5MB, alloc=398.5MB, time=44.71 memory used=5002.3MB, alloc=398.5MB, time=45.22 memory used=5132.6MB, alloc=398.5MB, time=46.74 memory used=5241.0MB, alloc=398.5MB, time=56.71 memory used=5296.9MB, alloc=398.5MB, time=56.91 memory used=5340.0MB, alloc=398.5MB, time=57.13 memory used=5393.2MB, alloc=398.5MB, time=57.32 memory used=5456.6MB, alloc=398.5MB, time=57.52 memory used=5497.6MB, alloc=398.5MB, time=57.67 memory used=5537.1MB, alloc=398.5MB, time=57.82 memory used=5580.0MB, alloc=398.5MB, time=57.98 memory used=5626.8MB, alloc=398.5MB, time=58.13 memory used=5677.9MB, alloc=398.5MB, time=58.30 memory used=5734.0MB, alloc=398.5MB, time=58.46 memory used=5795.3MB, alloc=398.5MB, time=58.63 memory used=5915.3MB, alloc=398.5MB, time=59.18 memory used=6009.5MB, alloc=398.5MB, time=59.65 memory used=6095.6MB, alloc=398.5MB, time=59.87 memory used=6206.2MB, alloc=398.5MB, time=60.96 memory used=6317.5MB, alloc=398.5MB, time=62.30 memory used=6398.8MB, alloc=398.5MB, time=63.03 memory used=6464.2MB, alloc=398.5MB, time=63.38 memory used=6538.3MB, alloc=422.5MB, time=64.31 memory used=6598.2MB, alloc=422.5MB, time=64.55 memory used=6659.9MB, alloc=422.5MB, time=64.78 memory used=6715.7MB, alloc=422.5MB, time=64.96 memory used=6788.5MB, alloc=422.5MB, time=65.52 memory used=6872.6MB, alloc=422.5MB, time=66.17 memory used=6936.5MB, alloc=422.5MB, time=66.43 memory used=7001.2MB, alloc=422.5MB, time=66.68 memory used=7051.7MB, alloc=422.5MB, time=66.89 memory used=7110.7MB, alloc=422.5MB, time=67.12 memory used=7180.2MB, alloc=422.5MB, time=67.36 memory used=7251.9MB, alloc=422.5MB, time=67.58 memory used=7300.4MB, alloc=422.5MB, time=67.76 memory used=7384.4MB, alloc=422.5MB, time=68.47 memory used=7448.8MB, alloc=422.5MB, time=68.73 memory used=7523.4MB, alloc=422.5MB, time=69.01 memory used=7573.0MB, alloc=422.5MB, time=69.24 memory used=7629.2MB, alloc=422.5MB, time=69.47 memory used=7693.3MB, alloc=422.5MB, time=69.70 memory used=7768.6MB, alloc=422.5MB, time=69.93 memory used=7823.9MB, alloc=422.5MB, time=70.12 memory used=7884.2MB, alloc=422.5MB, time=70.50 memory used=8007.1MB, alloc=422.5MB, time=77.92 memory used=8071.0MB, alloc=422.5MB, time=78.17 memory used=8129.1MB, alloc=422.5MB, time=78.41 memory used=8203.6MB, alloc=422.5MB, time=78.65 memory used=8256.0MB, alloc=422.5MB, time=78.85 memory used=8305.6MB, alloc=422.5MB, time=79.05 memory used=8360.8MB, alloc=422.5MB, time=79.24 memory used=8421.8MB, alloc=422.5MB, time=79.43 memory used=8490.0MB, alloc=422.5MB, time=79.63 memory used=8568.9MB, alloc=422.5MB, time=79.82 memory used=8751.9MB, alloc=422.5MB, time=80.92 memory used=8917.5MB, alloc=422.5MB, time=89.17 memory used=8981.5MB, alloc=422.5MB, time=89.42 memory used=9033.6MB, alloc=422.5MB, time=89.65 memory used=9100.4MB, alloc=422.5MB, time=89.88 memory used=9161.9MB, alloc=422.5MB, time=90.08 memory used=9206.6MB, alloc=422.5MB, time=90.26 memory used=9256.3MB, alloc=422.5MB, time=90.45 memory used=9312.1MB, alloc=422.5MB, time=90.64 memory used=9373.2MB, alloc=422.5MB, time=90.83 memory used=9441.8MB, alloc=422.5MB, time=91.03 memory used=9610.4MB, alloc=422.5MB, time=91.58 memory used=9680.0MB, alloc=422.5MB, time=92.09 memory used=9742.4MB, alloc=422.5MB, time=92.46 memory used=9880.8MB, alloc=422.5MB, time=93.11 memory used=10011.4MB, alloc=422.5MB, time=93.43 memory used=10141.7MB, alloc=422.5MB, time=94.79 memory used=10258.3MB, alloc=422.5MB, time=95.81 memory used=10350.5MB, alloc=422.5MB, time=96.22 memory used=10444.5MB, alloc=422.5MB, time=98.14 memory used=10550.8MB, alloc=422.5MB, time=99.22 memory used=10660.2MB, alloc=446.5MB, time=101.01 memory used=10762.1MB, alloc=446.5MB, time=102.40 memory used=10860.3MB, alloc=446.5MB, time=103.81 memory used=10979.1MB, alloc=446.5MB, time=105.13 memory used=11073.7MB, alloc=470.5MB, time=106.56 memory used=11196.1MB, alloc=470.5MB, time=107.49 memory used=11286.9MB, alloc=470.5MB, time=108.73 memory used=11414.7MB, alloc=470.5MB, time=110.26 memory used=11550.8MB, alloc=470.5MB, time=111.53 memory used=11640.0MB, alloc=470.5MB, time=112.10 memory used=11725.9MB, alloc=470.5MB, time=112.53 memory used=11809.1MB, alloc=470.5MB, time=113.07 memory used=11931.2MB, alloc=470.5MB, time=114.20 memory used=12002.9MB, alloc=470.5MB, time=114.54 memory used=12094.3MB, alloc=470.5MB, time=115.47 memory used=12164.4MB, alloc=470.5MB, time=115.78 memory used=12271.5MB, alloc=470.5MB, time=116.97 memory used=12345.6MB, alloc=470.5MB, time=118.26 memory used=12453.3MB, alloc=470.5MB, time=119.34 memory used=12563.4MB, alloc=494.5MB, time=120.42 memory used=12633.0MB, alloc=494.5MB, time=121.63 memory used=12765.0MB, alloc=494.5MB, time=122.63 memory used=12878.3MB, alloc=494.5MB, time=123.85 memory used=12967.2MB, alloc=494.5MB, time=124.29 memory used=13041.5MB, alloc=494.5MB, time=124.67 memory used=13140.8MB, alloc=494.5MB, time=125.10 memory used=13326.6MB, alloc=494.5MB, time=125.94 memory used=13399.4MB, alloc=494.5MB, time=126.37 memory used=13488.5MB, alloc=494.5MB, time=126.84 memory used=13582.2MB, alloc=494.5MB, time=127.27 memory used=13643.9MB, alloc=494.5MB, time=127.62 memory used=13712.7MB, alloc=494.5MB, time=127.99 memory used=13790.4MB, alloc=494.5MB, time=128.34 memory used=13878.3MB, alloc=494.5MB, time=128.71 memory used=13983.9MB, alloc=494.5MB, time=129.39 memory used=14066.9MB, alloc=494.5MB, time=129.85 memory used=14149.5MB, alloc=494.5MB, time=130.29 memory used=14254.1MB, alloc=494.5MB, time=130.74 memory used=14318.5MB, alloc=494.5MB, time=131.11 memory used=14385.2MB, alloc=494.5MB, time=131.47 memory used=14460.1MB, alloc=494.5MB, time=131.84 memory used=14544.4MB, alloc=494.5MB, time=132.23 memory used=14677.8MB, alloc=494.5MB, time=139.49 memory used=14762.6MB, alloc=494.5MB, time=139.92 memory used=14848.6MB, alloc=494.5MB, time=140.33 memory used=14919.9MB, alloc=494.5MB, time=140.71 memory used=15006.2MB, alloc=494.5MB, time=141.08 memory used=15107.9MB, alloc=494.5MB, time=141.46 memory used=15295.1MB, alloc=494.5MB, time=142.06 memory used=15457.8MB, alloc=494.5MB, time=142.54 memory used=15656.1MB, alloc=494.5MB, time=143.05 memory used=15816.9MB, alloc=494.5MB, time=144.04 memory used=15930.5MB, alloc=494.5MB, time=145.06 memory used=16003.3MB, alloc=494.5MB, time=146.07 memory used=16112.8MB, alloc=494.5MB, time=146.72 memory used=16194.3MB, alloc=494.5MB, time=147.16 memory used=16279.6MB, alloc=494.5MB, time=147.54 memory used=16389.2MB, alloc=494.5MB, time=148.16 memory used=16480.7MB, alloc=494.5MB, time=148.59 memory used=16551.9MB, alloc=494.5MB, time=148.98 memory used=16646.8MB, alloc=494.5MB, time=149.36 memory used=16783.9MB, alloc=494.5MB, time=155.59 memory used=16866.8MB, alloc=494.5MB, time=155.99 memory used=16957.1MB, alloc=494.5MB, time=156.38 memory used=17026.1MB, alloc=494.5MB, time=156.72 memory used=17109.6MB, alloc=494.5MB, time=157.06 memory used=17232.9MB, alloc=494.5MB, time=157.65 memory used=17323.8MB, alloc=494.5MB, time=158.66 memory used=17423.3MB, alloc=494.5MB, time=159.85 memory used=17509.5MB, alloc=494.5MB, time=160.25 memory used=17614.2MB, alloc=494.5MB, time=161.43 memory used=17741.8MB, alloc=494.5MB, time=163.71 memory used=17875.5MB, alloc=494.5MB, time=164.83 memory used=18039.2MB, alloc=494.5MB, time=166.09 memory used=18204.8MB, alloc=494.5MB, time=168.04 memory used=18334.3MB, alloc=494.5MB, time=170.79 memory used=18449.5MB, alloc=494.5MB, time=171.91 memory used=18508.0MB, alloc=494.5MB, time=173.18 memory used=18633.3MB, alloc=494.5MB, time=174.85 memory used=18719.0MB, alloc=494.5MB, time=175.33 memory used=18815.8MB, alloc=518.5MB, time=176.25 memory used=18902.1MB, alloc=518.5MB, time=177.21 memory used=18950.5MB, alloc=518.5MB, time=178.22 memory used=18997.5MB, alloc=518.5MB, time=179.16 memory used=19042.5MB, alloc=518.5MB, time=180.13 memory used=19239.4MB, alloc=542.5MB, time=182.80 memory used=19449.5MB, alloc=566.5MB, time=186.03 memory used=19664.4MB, alloc=590.5MB, time=188.50 memory used=19867.3MB, alloc=590.5MB, time=191.11 memory used=20081.6MB, alloc=590.5MB, time=193.79 memory used=20315.9MB, alloc=590.5MB, time=196.58 memory used=20556.2MB, alloc=614.5MB, time=199.02 memory used=20765.6MB, alloc=614.5MB, time=205.13 memory used=20937.9MB, alloc=614.5MB, time=207.06 memory used=21089.3MB, alloc=614.5MB, time=211.83 |\^/| 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(); 1428288491 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [-15 x - 8 y + 2 y z + 2 y, -4 x y - 7 x y z - 16 y , 3 3 3 5 x - 9 x y z + 8 y - 6 z ] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 2 G := [9 x y + y - 15 x + 19 x, -17 x z - 20 y z + 17 y - 13, 2 2 2 -12 x y - 15 x z + 2 x y - 18 z ] > Problem := [F,G]; 2 2 2 2 Problem := [[-15 x - 8 y + 2 y z + 2 y, -4 x y - 7 x y z - 16 y , 3 3 3 2 3 2 5 x - 9 x y z + 8 y - 6 z ], [9 x y + y - 15 x + 19 x, 2 2 2 2 2 -17 x z - 20 y z + 17 y - 13, -12 x y - 15 x z + 2 x y - 18 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.2MB, alloc=32.3MB, time=0.50 memory used=46.1MB, alloc=56.3MB, time=0.80 memory used=87.0MB, alloc=60.3MB, time=1.42 memory used=129.6MB, alloc=68.3MB, time=2.05 memory used=171.4MB, alloc=92.3MB, time=2.67 memory used=236.0MB, alloc=92.3MB, time=3.61 memory used=301.0MB, alloc=92.3MB, time=4.56 memory used=365.7MB, alloc=116.3MB, time=5.50 memory used=439.0MB, alloc=372.3MB, time=6.60 memory used=528.7MB, alloc=372.3MB, time=7.76 memory used=617.5MB, alloc=396.3MB, time=9.03 memory used=732.2MB, alloc=396.3MB, time=10.64 memory used=843.2MB, alloc=420.3MB, time=12.31 memory used=977.0MB, alloc=420.3MB, time=14.10 memory used=1110.3MB, alloc=444.3MB, time=16.11 memory used=1238.1MB, alloc=444.3MB, time=18.00 memory used=1385.4MB, alloc=444.3MB, time=19.75 memory used=1524.1MB, alloc=468.3MB, time=21.59 memory used=1628.0MB, alloc=468.3MB, time=23.34 memory used=1742.1MB, alloc=468.3MB, time=24.72 memory used=1840.9MB, alloc=468.3MB, time=26.16 memory used=1959.4MB, alloc=468.3MB, time=27.66 memory used=2058.4MB, alloc=468.3MB, time=28.47 memory used=2174.6MB, alloc=468.3MB, time=30.34 memory used=2259.4MB, alloc=492.3MB, time=31.68 memory used=2335.2MB, alloc=492.3MB, time=32.91 memory used=2413.2MB, alloc=492.3MB, time=34.01 memory used=2488.6MB, alloc=492.3MB, time=35.40 memory used=2567.2MB, alloc=492.3MB, time=36.57 memory used=2640.7MB, alloc=492.3MB, time=37.68 memory used=2712.1MB, alloc=516.3MB, time=38.68 memory used=2785.2MB, alloc=516.3MB, time=39.69 memory used=2881.1MB, alloc=540.3MB, time=40.61 memory used=2924.7MB, alloc=540.3MB, time=41.54 memory used=2984.7MB, alloc=540.3MB, time=42.87 memory used=3040.9MB, alloc=540.3MB, time=44.01 memory used=3110.1MB, alloc=540.3MB, time=45.16 memory used=3327.2MB, alloc=564.3MB, time=48.58 memory used=3533.9MB, alloc=588.3MB, time=51.81 memory used=3707.6MB, alloc=612.3MB, time=54.20 memory used=3940.0MB, alloc=636.3MB, time=56.65 memory used=4113.5MB, alloc=660.3MB, time=59.42 memory used=4275.2MB, alloc=660.3MB, time=61.71 memory used=4458.9MB, alloc=684.3MB, time=63.94 memory used=4615.0MB, alloc=684.3MB, time=66.69 memory used=4744.3MB, alloc=684.3MB, time=68.89 memory used=4861.0MB, alloc=684.3MB, time=71.05 memory used=5001.7MB, alloc=708.3MB, time=73.53 memory used=5106.5MB, alloc=708.3MB, time=75.50 memory used=5212.2MB, alloc=708.3MB, time=77.45 memory used=5316.9MB, alloc=708.3MB, time=79.39 memory used=5428.7MB, alloc=708.3MB, time=81.73 memory used=5565.5MB, alloc=708.3MB, time=84.28 memory used=5950.8MB, alloc=732.3MB, time=90.09 memory used=6338.7MB, alloc=756.3MB, time=96.99 memory used=6710.1MB, alloc=780.3MB, time=102.49 memory used=7048.0MB, alloc=804.3MB, time=108.12 memory used=7481.1MB, alloc=828.3MB, time=113.74 memory used=7884.0MB, alloc=852.3MB, time=119.17 memory used=8298.4MB, alloc=876.3MB, time=123.58 memory used=8593.1MB, alloc=900.3MB, time=127.41 memory used=8828.1MB, alloc=924.3MB, time=129.39 memory used=9093.5MB, alloc=948.3MB, time=131.46 memory used=9386.7MB, alloc=972.3MB, time=136.52 memory used=9683.1MB, alloc=972.3MB, time=138.66 memory used=9980.6MB, alloc=972.3MB, time=143.42 memory used=10366.3MB, alloc=972.3MB, time=148.29 memory used=10779.1MB, alloc=996.3MB, time=153.83 memory used=11198.9MB, alloc=1020.3MB, time=160.07 |\^/| 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(); 1428288791 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 F := [4 x - 3 x y - 16 x z + 4 y , 15 x - x z + 14 x y - 3 y , 3 2 14 y + 12 y z - 3 z] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 G := [-11 x y z + 13 y + 10 x - 16 z, -19 x z - 12 x y - x - 7 y, 2 2 -5 x y z + 14 y z - 10 x z - 6 y ] > Problem := [F,G]; 2 2 3 2 2 Problem := [[4 x - 3 x y - 16 x z + 4 y , 15 x - x z + 14 x y - 3 y , 3 2 3 2 14 y + 12 y z - 3 z], [-11 x y z + 13 y + 10 x - 16 z, 2 2 2 -19 x z - 12 x y - x - 7 y, -5 x y z + 14 y z - 10 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=24.6MB, alloc=32.3MB, time=0.49 memory used=43.9MB, alloc=60.3MB, time=0.79 memory used=82.9MB, alloc=60.3MB, time=1.36 memory used=126.4MB, alloc=68.3MB, time=1.97 memory used=172.0MB, alloc=68.3MB, time=2.54 memory used=217.0MB, alloc=92.3MB, time=3.16 memory used=285.3MB, alloc=92.3MB, time=4.04 memory used=343.9MB, alloc=92.3MB, time=4.82 memory used=407.8MB, alloc=348.3MB, time=5.78 memory used=474.0MB, alloc=372.3MB, time=6.64 memory used=566.5MB, alloc=372.3MB, time=7.91 memory used=656.0MB, alloc=396.3MB, time=9.12 memory used=775.7MB, alloc=396.3MB, time=10.55 memory used=879.7MB, alloc=396.3MB, time=11.79 memory used=955.8MB, alloc=396.3MB, time=12.38 memory used=1063.5MB, alloc=396.3MB, time=13.60 memory used=1191.2MB, alloc=420.3MB, time=15.46 memory used=1297.4MB, alloc=444.3MB, time=17.09 memory used=1406.6MB, alloc=444.3MB, time=18.58 memory used=1523.3MB, alloc=444.3MB, time=19.96 memory used=1630.7MB, alloc=468.3MB, time=21.69 memory used=1735.2MB, alloc=468.3MB, time=23.24 memory used=1831.8MB, alloc=468.3MB, time=24.47 memory used=1917.9MB, alloc=468.3MB, time=25.62 memory used=2007.6MB, alloc=492.3MB, time=26.72 memory used=2082.3MB, alloc=492.3MB, time=27.99 memory used=2153.1MB, alloc=492.3MB, time=29.09 memory used=2209.9MB, alloc=492.3MB, time=30.02 memory used=2269.0MB, alloc=492.3MB, time=31.12 memory used=2316.0MB, alloc=492.3MB, time=32.01 memory used=2368.7MB, alloc=492.3MB, time=32.86 memory used=2420.1MB, alloc=492.3MB, time=33.69 memory used=2487.2MB, alloc=516.3MB, time=34.73 memory used=2549.5MB, alloc=516.3MB, time=35.69 memory used=2596.9MB, alloc=516.3MB, time=36.61 memory used=2800.1MB, alloc=516.3MB, time=39.66 memory used=2936.6MB, alloc=516.3MB, time=41.81 memory used=3054.9MB, alloc=516.3MB, time=45.05 memory used=3166.2MB, alloc=540.3MB, time=56.66 memory used=3273.9MB, alloc=564.3MB, time=129.33 memory used=3339.8MB, alloc=588.3MB, time=158.46 memory used=3393.5MB, alloc=612.3MB, time=193.32 |\^/| 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(); 1428289091 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 2 F := [6 y z - 3 z + 8 y - 17, -9 x y + 11 x z - 2 z - 19 z, 2 3 2 2 12 x y - 2 y + 8 y z + 8 y ] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 3 2 G := [-8 x + 12 x z - 3 y + 15 z, -19 x + 3 x z + 9 x z - 6 x, 2 3 2 15 x z - 19 y - y z + 4 z] > Problem := [F,G]; 2 3 2 2 2 Problem := [[6 y z - 3 z + 8 y - 17, -9 x y + 11 x z - 2 z - 19 z, 2 3 2 2 3 12 x y - 2 y + 8 y z + 8 y ], [-8 x + 12 x z - 3 y + 15 z, 3 2 2 3 2 -19 x + 3 x z + 9 x z - 6 x, 15 x z - 19 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=4.3MB, alloc=32.3MB, time=0.17 memory used=26.2MB, alloc=32.3MB, time=0.48 memory used=46.3MB, alloc=56.3MB, time=0.78 memory used=86.6MB, alloc=60.3MB, time=1.36 memory used=125.7MB, alloc=84.3MB, time=1.92 memory used=168.6MB, alloc=84.3MB, time=2.55 memory used=234.0MB, alloc=92.3MB, time=3.49 memory used=297.1MB, alloc=116.3MB, time=4.40 memory used=378.2MB, alloc=116.3MB, time=5.56 memory used=449.1MB, alloc=396.3MB, time=6.65 memory used=557.1MB, alloc=420.3MB, time=8.28 memory used=693.2MB, alloc=444.3MB, time=10.29 memory used=844.1MB, alloc=468.3MB, time=12.79 memory used=963.2MB, alloc=468.3MB, time=14.67 memory used=1075.5MB, alloc=468.3MB, time=16.45 memory used=1191.3MB, alloc=492.3MB, time=18.25 memory used=1301.7MB, alloc=492.3MB, time=20.01 memory used=1399.8MB, alloc=492.3MB, time=21.59 memory used=1496.6MB, alloc=492.3MB, time=23.23 memory used=1574.2MB, alloc=492.3MB, time=24.56 memory used=1655.9MB, alloc=492.3MB, time=26.11 memory used=1732.7MB, alloc=492.3MB, time=27.55 memory used=1803.1MB, alloc=492.3MB, time=28.91 memory used=1868.4MB, alloc=492.3MB, time=30.22 memory used=1933.1MB, alloc=516.3MB, time=31.43 memory used=1992.3MB, alloc=516.3MB, time=32.71 memory used=2050.5MB, alloc=516.3MB, time=33.79 memory used=2105.9MB, alloc=516.3MB, time=35.16 memory used=2146.7MB, alloc=516.3MB, time=36.16 memory used=2358.6MB, alloc=540.3MB, time=40.01 memory used=2553.3MB, alloc=564.3MB, time=43.79 memory used=2722.2MB, alloc=588.3MB, time=47.08 memory used=2892.3MB, alloc=612.3MB, time=50.70 memory used=3045.2MB, alloc=612.3MB, time=53.69 memory used=3206.6MB, alloc=636.3MB, time=57.31 memory used=3345.2MB, alloc=636.3MB, time=60.42 memory used=3478.7MB, alloc=636.3MB, time=63.36 memory used=3598.3MB, alloc=636.3MB, time=66.01 memory used=3717.3MB, alloc=660.3MB, time=68.79 memory used=3802.4MB, alloc=660.3MB, time=71.14 memory used=3907.9MB, alloc=660.3MB, time=73.67 memory used=4010.2MB, alloc=660.3MB, time=76.24 memory used=4350.5MB, alloc=684.3MB, time=82.93 memory used=4702.6MB, alloc=708.3MB, time=90.14 memory used=5067.9MB, alloc=732.3MB, time=97.88 memory used=5442.8MB, alloc=756.3MB, time=106.12 memory used=5799.3MB, alloc=780.3MB, time=114.09 memory used=6131.6MB, alloc=804.3MB, time=122.07 |\^/| 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(); 1428289391 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 F := [-3 x z + 17 y + 10 z + 3, -5 x y + 17 y + 15 y z + 19 x , 3 5 z + 4 x y + 9 y] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 3 2 2 G := [-4 y z + 15 z + 11 y z + 18 y, -9 x + 10 x y + 11 z , 2 3 2 20 x y - 15 y + 4 x - 9 y] > Problem := [F,G]; 2 2 3 2 2 Problem := [[-3 x z + 17 y + 10 z + 3, -5 x y + 17 y + 15 y z + 19 x , 3 2 3 5 z + 4 x y + 9 y], [-4 y z + 15 z + 11 y z + 18 y, 3 2 2 2 3 2 -9 x + 10 x y + 11 z , 20 x y - 15 y + 4 x - 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=4.5MB, alloc=32.3MB, time=0.18 memory used=24.8MB, alloc=32.3MB, time=0.49 memory used=43.3MB, alloc=56.3MB, time=0.78 memory used=83.4MB, alloc=60.3MB, time=1.36 memory used=126.3MB, alloc=68.3MB, time=1.91 memory used=170.4MB, alloc=68.3MB, time=2.56 memory used=211.3MB, alloc=92.3MB, time=3.20 memory used=277.7MB, alloc=92.3MB, time=4.03 memory used=343.2MB, alloc=92.3MB, time=4.96 memory used=409.0MB, alloc=348.3MB, time=5.91 memory used=478.6MB, alloc=348.3MB, time=6.92 memory used=542.6MB, alloc=372.3MB, time=7.96 memory used=631.2MB, alloc=396.3MB, time=9.26 memory used=745.2MB, alloc=396.3MB, time=10.83 memory used=823.7MB, alloc=396.3MB, time=11.46 memory used=923.9MB, alloc=420.3MB, time=12.54 memory used=1061.8MB, alloc=420.3MB, time=14.51 memory used=1176.5MB, alloc=444.3MB, time=16.22 memory used=1298.7MB, alloc=444.3MB, time=17.43 memory used=1436.0MB, alloc=444.3MB, time=18.93 memory used=1561.6MB, alloc=444.3MB, time=20.42 memory used=1680.5MB, alloc=444.3MB, time=22.03 memory used=1806.6MB, alloc=468.3MB, time=23.36 memory used=1910.8MB, alloc=468.3MB, time=24.61 memory used=2033.9MB, alloc=468.3MB, time=26.07 memory used=2143.2MB, alloc=468.3MB, time=27.38 memory used=2248.3MB, alloc=468.3MB, time=28.72 memory used=2338.1MB, alloc=468.3MB, time=30.02 memory used=2450.0MB, alloc=468.3MB, time=31.90 memory used=2524.8MB, alloc=468.3MB, time=33.05 memory used=2616.5MB, alloc=468.3MB, time=34.44 memory used=2704.0MB, alloc=468.3MB, time=36.01 memory used=2777.7MB, alloc=492.3MB, time=37.35 memory used=2853.6MB, alloc=492.3MB, time=38.30 memory used=2964.8MB, alloc=492.3MB, time=39.38 memory used=3079.8MB, alloc=492.3MB, time=40.31 memory used=3143.6MB, alloc=492.3MB, time=41.36 memory used=3258.2MB, alloc=492.3MB, time=42.18 memory used=3378.1MB, alloc=492.3MB, time=43.28 memory used=3466.3MB, alloc=492.3MB, time=44.36 memory used=3557.1MB, alloc=492.3MB, time=44.84 memory used=3631.5MB, alloc=492.3MB, time=45.28 memory used=3725.7MB, alloc=492.3MB, time=45.70 memory used=3833.8MB, alloc=492.3MB, time=51.74 memory used=3920.4MB, alloc=492.3MB, time=52.18 memory used=4010.1MB, alloc=492.3MB, time=52.59 memory used=4079.5MB, alloc=492.3MB, time=52.96 memory used=4164.7MB, alloc=492.3MB, time=53.33 memory used=4361.9MB, alloc=492.3MB, time=54.55 memory used=4432.9MB, alloc=492.3MB, time=55.85 memory used=4498.5MB, alloc=492.3MB, time=57.01 memory used=4552.1MB, alloc=492.3MB, time=57.87 memory used=4606.5MB, alloc=492.3MB, time=58.72 memory used=4687.2MB, alloc=492.3MB, time=59.52 memory used=4756.7MB, alloc=492.3MB, time=60.58 memory used=4847.7MB, alloc=516.3MB, time=61.45 memory used=4949.0MB, alloc=516.3MB, time=62.02 memory used=5066.7MB, alloc=516.3MB, time=62.57 memory used=5147.8MB, alloc=516.3MB, time=63.05 memory used=5297.8MB, alloc=516.3MB, time=79.14 memory used=5404.4MB, alloc=516.3MB, time=79.64 memory used=5494.0MB, alloc=516.3MB, time=80.12 memory used=5583.2MB, alloc=516.3MB, time=80.62 memory used=5688.7MB, alloc=516.3MB, time=81.14 memory used=5814.4MB, alloc=516.3MB, time=81.63 memory used=5887.5MB, alloc=516.3MB, time=82.04 memory used=5966.0MB, alloc=516.3MB, time=82.44 memory used=6067.9MB, alloc=516.3MB, time=83.04 memory used=6135.5MB, alloc=516.3MB, time=84.00 memory used=6234.3MB, alloc=516.3MB, time=85.37 memory used=6285.7MB, alloc=516.3MB, time=86.29 memory used=6336.1MB, alloc=516.3MB, time=87.41 memory used=6422.2MB, alloc=516.3MB, time=88.52 memory used=6539.2MB, alloc=516.3MB, time=89.16 memory used=6636.8MB, alloc=516.3MB, time=89.70 memory used=6736.0MB, alloc=516.3MB, time=90.23 memory used=6854.3MB, alloc=516.3MB, time=105.71 memory used=6971.1MB, alloc=516.3MB, time=106.89 memory used=7079.6MB, alloc=516.3MB, time=107.42 memory used=7158.7MB, alloc=516.3MB, time=107.88 memory used=7252.0MB, alloc=516.3MB, time=108.37 memory used=7362.2MB, alloc=516.3MB, time=108.85 memory used=7468.3MB, alloc=516.3MB, time=109.32 memory used=7540.8MB, alloc=516.3MB, time=109.74 memory used=7620.3MB, alloc=516.3MB, time=110.18 memory used=7712.5MB, alloc=516.3MB, time=110.99 memory used=7776.9MB, alloc=516.3MB, time=111.87 memory used=7841.2MB, alloc=516.3MB, time=113.05 memory used=8095.9MB, alloc=516.3MB, time=119.43 memory used=8299.1MB, alloc=540.3MB, time=122.28 memory used=8456.2MB, alloc=540.3MB, time=123.64 memory used=8639.6MB, alloc=540.3MB, time=125.66 memory used=8823.7MB, alloc=540.3MB, time=129.78 memory used=8974.8MB, alloc=564.3MB, time=131.85 memory used=9136.9MB, alloc=564.3MB, time=133.05 memory used=9260.4MB, alloc=564.3MB, time=133.75 memory used=9391.4MB, alloc=564.3MB, time=135.37 memory used=9512.0MB, alloc=564.3MB, time=136.10 memory used=9610.2MB, alloc=564.3MB, time=136.76 memory used=9726.5MB, alloc=564.3MB, time=137.43 memory used=9863.6MB, alloc=564.3MB, time=138.11 memory used=9969.9MB, alloc=588.3MB, time=138.72 memory used=10062.3MB, alloc=588.3MB, time=139.28 memory used=10162.2MB, alloc=588.3MB, time=139.82 memory used=10268.9MB, alloc=588.3MB, time=140.43 memory used=10384.3MB, alloc=588.3MB, time=141.04 memory used=10506.4MB, alloc=588.3MB, time=141.64 memory used=10637.5MB, alloc=588.3MB, time=142.26 memory used=10781.3MB, alloc=588.3MB, time=142.88 memory used=10929.0MB, alloc=588.3MB, time=143.52 memory used=11088.0MB, alloc=588.3MB, time=144.15 memory used=11258.2MB, alloc=588.3MB, time=144.81 memory used=11411.6MB, alloc=588.3MB, time=145.56 memory used=11524.9MB, alloc=588.3MB, time=146.18 memory used=11646.2MB, alloc=588.3MB, time=146.77 memory used=11769.4MB, alloc=588.3MB, time=147.38 memory used=11900.8MB, alloc=588.3MB, time=148.03 memory used=12032.0MB, alloc=588.3MB, time=148.65 memory used=12170.9MB, alloc=588.3MB, time=149.27 memory used=12316.8MB, alloc=588.3MB, time=149.92 memory used=12468.9MB, alloc=588.3MB, time=150.58 memory used=12626.6MB, alloc=588.3MB, time=151.20 memory used=12788.9MB, alloc=588.3MB, time=151.81 memory used=12961.5MB, alloc=588.3MB, time=152.44 memory used=13142.4MB, alloc=588.3MB, time=153.05 memory used=13332.0MB, alloc=588.3MB, time=153.69 memory used=13534.5MB, alloc=588.3MB, time=154.32 |\^/| 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(); 1428289691 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 F := [-15 x - 3 x y z - 16 y z - 13 y z, -16 x y + 12 x z + 3 x y + 20 y z, 2 -3 x y - 15 y z - 12 y + 13] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 2 G := [-6 x y z - 15 x - 20 x z - 17 x, -14 x - 9 x y - 3 y z + 19 x , 2 2 2 2 19 x z + 6 x y + y - 20 z ] > Problem := [F,G]; 3 2 Problem := [[-15 x - 3 x y z - 16 y z - 13 y z, 2 2 2 -16 x y + 12 x z + 3 x y + 20 y z, -3 x y - 15 y z - 12 y + 13], [ 2 3 2 2 2 -6 x y z - 15 x - 20 x z - 17 x, -14 x - 9 x y - 3 y z + 19 x , 2 2 2 2 19 x z + 6 x y + y - 20 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.0MB, alloc=32.3MB, time=0.50 memory used=46.3MB, alloc=56.3MB, time=0.82 memory used=86.8MB, alloc=60.3MB, time=1.37 memory used=133.7MB, alloc=68.3MB, time=2.02 memory used=177.4MB, alloc=68.3MB, time=2.57 memory used=220.6MB, alloc=68.3MB, time=3.08 memory used=258.7MB, alloc=92.3MB, time=3.68 memory used=325.4MB, alloc=92.3MB, time=4.65 memory used=391.1MB, alloc=116.3MB, time=5.63 memory used=462.2MB, alloc=116.3MB, time=6.64 memory used=528.4MB, alloc=372.3MB, time=7.50 memory used=636.2MB, alloc=372.3MB, time=8.75 memory used=723.2MB, alloc=396.3MB, time=10.05 memory used=838.6MB, alloc=396.3MB, time=11.76 memory used=918.7MB, alloc=396.3MB, time=12.52 memory used=1033.6MB, alloc=420.3MB, time=13.92 memory used=1167.7MB, alloc=420.3MB, time=15.78 memory used=1285.5MB, alloc=420.3MB, time=17.49 memory used=1392.8MB, alloc=444.3MB, time=19.27 memory used=1511.0MB, alloc=444.3MB, time=21.38 memory used=1622.8MB, alloc=468.3MB, time=23.09 memory used=1721.7MB, alloc=468.3MB, time=24.69 memory used=1817.6MB, alloc=468.3MB, time=26.16 memory used=1918.6MB, alloc=468.3MB, time=27.46 memory used=2015.9MB, alloc=468.3MB, time=28.75 memory used=2113.5MB, alloc=468.3MB, time=30.40 memory used=2232.4MB, alloc=468.3MB, time=31.81 memory used=2322.0MB, alloc=468.3MB, time=33.15 memory used=2401.3MB, alloc=468.3MB, time=34.38 memory used=2494.8MB, alloc=468.3MB, time=35.76 memory used=2585.1MB, alloc=492.3MB, time=37.20 memory used=2660.9MB, alloc=492.3MB, time=38.50 memory used=2735.2MB, alloc=492.3MB, time=39.85 memory used=2812.7MB, alloc=492.3MB, time=41.32 memory used=2880.0MB, alloc=492.3MB, time=42.60 memory used=2937.1MB, alloc=492.3MB, time=43.66 memory used=2993.0MB, alloc=492.3MB, time=44.77 memory used=3058.5MB, alloc=492.3MB, time=45.95 memory used=3116.7MB, alloc=492.3MB, time=47.13 memory used=3168.3MB, alloc=492.3MB, time=48.21 memory used=3216.5MB, alloc=492.3MB, time=49.24 memory used=3258.1MB, alloc=492.3MB, time=50.14 memory used=3444.9MB, alloc=516.3MB, time=53.37 memory used=3635.3MB, alloc=540.3MB, time=57.33 memory used=3823.1MB, alloc=564.3MB, time=60.34 memory used=4005.9MB, alloc=588.3MB, time=63.56 memory used=4183.5MB, alloc=612.3MB, time=66.62 memory used=4363.6MB, alloc=636.3MB, time=70.11 memory used=4557.5MB, alloc=636.3MB, time=73.36 memory used=4693.5MB, alloc=636.3MB, time=75.61 memory used=4906.1MB, alloc=660.3MB, time=78.26 memory used=5099.3MB, alloc=684.3MB, time=80.75 memory used=5248.5MB, alloc=684.3MB, time=83.97 memory used=5375.9MB, alloc=684.3MB, time=86.19 memory used=5517.3MB, alloc=708.3MB, time=89.08 memory used=5638.3MB, alloc=708.3MB, time=92.26 memory used=5747.0MB, alloc=708.3MB, time=95.18 memory used=5853.9MB, alloc=708.3MB, time=97.51 memory used=5953.2MB, alloc=708.3MB, time=99.57 memory used=6270.6MB, alloc=708.3MB, time=103.08 memory used=6632.9MB, alloc=732.3MB, time=108.59 memory used=7062.3MB, alloc=756.3MB, time=115.11 memory used=7473.6MB, alloc=780.3MB, time=121.67 memory used=7906.5MB, alloc=804.3MB, time=128.44 memory used=8276.0MB, alloc=828.3MB, time=135.47 memory used=8589.2MB, alloc=852.3MB, time=141.90 memory used=8943.2MB, alloc=876.3MB, time=149.64 |\^/| 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(); 1428289991 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 2 2 F := [13 x y + 13 x z + 13 y z - 5 z , 16 x y + 20 x + 4 x y + 9 z , 2 3 2 -19 x z + 5 y - 14 y ] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 2 G := [12 x + 13 x y - 3 y z + 4 y, 5 x y + 10 y z + 9 y z - 6, 2 2 -15 x z + 19 y z + 9 y + 5 z] > Problem := [F,G]; 2 2 2 2 2 2 2 Problem := [[13 x y + 13 x z + 13 y z - 5 z , 16 x y + 20 x + 4 x y + 9 z , 2 3 2 3 2 2 -19 x z + 5 y - 14 y ], [12 x + 13 x y - 3 y z + 4 y, 2 2 2 2 2 5 x y + 10 y z + 9 y z - 6, -15 x z + 19 y z + 9 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=4.4MB, alloc=32.3MB, time=0.18 memory used=26.2MB, alloc=32.3MB, time=0.51 memory used=46.6MB, alloc=32.3MB, time=0.82 memory used=65.5MB, alloc=56.3MB, time=1.12 memory used=107.2MB, alloc=60.3MB, time=1.73 memory used=146.2MB, alloc=84.3MB, time=2.34 memory used=208.1MB, alloc=92.3MB, time=3.30 memory used=276.1MB, alloc=92.3MB, time=4.22 memory used=343.6MB, alloc=116.3MB, time=5.10 memory used=408.2MB, alloc=372.3MB, time=6.05 memory used=496.6MB, alloc=372.3MB, time=7.05 memory used=592.6MB, alloc=396.3MB, time=8.28 memory used=703.9MB, alloc=420.3MB, time=9.88 memory used=836.5MB, alloc=444.3MB, time=11.99 memory used=955.1MB, alloc=444.3MB, time=13.71 memory used=1068.6MB, alloc=444.3MB, time=15.39 memory used=1186.6MB, alloc=468.3MB, time=17.21 memory used=1281.7MB, alloc=468.3MB, time=18.75 memory used=1419.1MB, alloc=468.3MB, time=20.13 memory used=1508.6MB, alloc=468.3MB, time=20.62 memory used=1596.6MB, alloc=468.3MB, time=21.38 memory used=1669.9MB, alloc=468.3MB, time=21.71 memory used=1755.2MB, alloc=468.3MB, time=22.13 memory used=1875.1MB, alloc=468.3MB, time=23.33 memory used=1967.4MB, alloc=468.3MB, time=24.39 memory used=2092.7MB, alloc=468.3MB, time=25.62 memory used=2219.6MB, alloc=468.3MB, time=27.61 memory used=2332.6MB, alloc=492.3MB, time=29.60 memory used=2437.1MB, alloc=492.3MB, time=30.96 memory used=2508.5MB, alloc=492.3MB, time=32.18 memory used=2591.4MB, alloc=492.3MB, time=33.69 memory used=2664.1MB, alloc=492.3MB, time=35.02 memory used=2737.4MB, alloc=492.3MB, time=36.35 memory used=2801.4MB, alloc=492.3MB, time=37.42 memory used=2915.9MB, alloc=492.3MB, time=38.45 memory used=2981.4MB, alloc=492.3MB, time=39.62 memory used=3059.9MB, alloc=492.3MB, time=40.78 memory used=3123.9MB, alloc=492.3MB, time=42.19 memory used=3216.6MB, alloc=492.3MB, time=42.97 memory used=3306.9MB, alloc=492.3MB, time=43.93 memory used=3369.8MB, alloc=516.3MB, time=44.88 memory used=3414.3MB, alloc=516.3MB, time=45.83 memory used=3516.6MB, alloc=516.3MB, time=46.78 memory used=3615.5MB, alloc=516.3MB, time=47.33 memory used=3707.8MB, alloc=516.3MB, time=47.85 memory used=3798.7MB, alloc=516.3MB, time=48.38 memory used=3904.3MB, alloc=516.3MB, time=49.44 memory used=4031.5MB, alloc=516.3MB, time=50.29 memory used=4134.8MB, alloc=516.3MB, time=50.89 memory used=4236.1MB, alloc=516.3MB, time=51.41 memory used=4314.2MB, alloc=516.3MB, time=51.83 memory used=4427.0MB, alloc=516.3MB, time=52.99 memory used=4516.9MB, alloc=516.3MB, time=53.47 memory used=4648.8MB, alloc=516.3MB, time=54.11 memory used=4750.9MB, alloc=516.3MB, time=54.60 memory used=4844.4MB, alloc=516.3MB, time=55.39 memory used=4936.3MB, alloc=516.3MB, time=55.85 memory used=5047.9MB, alloc=516.3MB, time=57.04 memory used=5089.7MB, alloc=516.3MB, time=57.81 memory used=5147.9MB, alloc=516.3MB, time=58.83 memory used=5303.2MB, alloc=516.3MB, time=61.16 memory used=5437.8MB, alloc=516.3MB, time=62.34 memory used=5652.4MB, alloc=516.3MB, time=66.65 memory used=5845.6MB, alloc=540.3MB, time=69.55 memory used=6050.8MB, alloc=540.3MB, time=72.33 memory used=6237.8MB, alloc=564.3MB, time=74.68 memory used=6443.8MB, alloc=564.3MB, time=76.82 memory used=6587.7MB, alloc=564.3MB, time=78.07 memory used=6687.6MB, alloc=564.3MB, time=78.73 memory used=6819.0MB, alloc=564.3MB, time=79.40 memory used=6905.7MB, alloc=564.3MB, time=79.97 memory used=7000.5MB, alloc=564.3MB, time=80.54 memory used=7110.0MB, alloc=564.3MB, time=81.13 memory used=7239.1MB, alloc=564.3MB, time=81.72 memory used=7493.7MB, alloc=564.3MB, time=85.42 memory used=7605.9MB, alloc=564.3MB, time=86.11 memory used=7707.8MB, alloc=564.3MB, time=86.76 memory used=7965.9MB, alloc=564.3MB, time=87.78 memory used=8132.4MB, alloc=564.3MB, time=89.80 memory used=8280.4MB, alloc=564.3MB, time=98.49 memory used=8391.4MB, alloc=564.3MB, time=99.20 memory used=8498.0MB, alloc=564.3MB, time=99.81 memory used=8592.2MB, alloc=564.3MB, time=100.42 memory used=8704.9MB, alloc=564.3MB, time=101.00 memory used=8837.0MB, alloc=564.3MB, time=101.61 memory used=9034.2MB, alloc=564.3MB, time=102.36 memory used=9173.1MB, alloc=564.3MB, time=103.02 memory used=9331.4MB, alloc=564.3MB, time=103.70 memory used=9518.5MB, alloc=564.3MB, time=104.38 memory used=9681.6MB, alloc=564.3MB, time=105.16 memory used=9967.2MB, alloc=564.3MB, time=108.06 memory used=10148.5MB, alloc=588.3MB, time=110.51 memory used=10377.3MB, alloc=588.3MB, time=113.04 memory used=10600.6MB, alloc=588.3MB, time=115.59 memory used=10781.4MB, alloc=612.3MB, time=117.44 memory used=10998.0MB, alloc=612.3MB, time=120.12 memory used=11180.9MB, alloc=612.3MB, time=122.35 memory used=11362.5MB, alloc=612.3MB, time=125.16 memory used=11498.7MB, alloc=612.3MB, time=126.14 memory used=11675.2MB, alloc=612.3MB, time=128.22 memory used=11813.7MB, alloc=636.3MB, time=130.80 memory used=11937.8MB, alloc=636.3MB, time=133.33 memory used=12062.2MB, alloc=636.3MB, time=135.25 memory used=12188.9MB, alloc=660.3MB, time=137.20 memory used=12316.3MB, alloc=684.3MB, time=139.09 memory used=12466.3MB, alloc=684.3MB, time=141.57 memory used=12551.2MB, alloc=684.3MB, time=143.41 memory used=12625.7MB, alloc=684.3MB, time=145.03 memory used=12980.3MB, alloc=708.3MB, time=150.44 memory used=13356.7MB, alloc=732.3MB, time=154.98 memory used=13734.0MB, alloc=756.3MB, time=160.44 memory used=14129.4MB, alloc=780.3MB, time=165.88 |\^/| 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(); 1428290291 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 3 2 2 F := [14 y z - 3 z + 9 x y - 12 x, 12 x - 5 x y + 12 z - 17 z, 2 2 2 11 x y - 4 y z + 11 x - 19] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [19 x z - 4 z - 18 y + 13, 11 x y z - 13 x + 14 x y + 15 y, 2 2 -15 x y z + 4 y + 7 z - 16 z] > Problem := [F,G]; 2 3 3 2 2 Problem := [[14 y z - 3 z + 9 x y - 12 x, 12 x - 5 x y + 12 z - 17 z, 2 2 2 2 11 x y - 4 y z + 11 x - 19], [19 x z - 4 z - 18 y + 13, 2 2 2 11 x y z - 13 x + 14 x y + 15 y, -15 x y z + 4 y + 7 z - 16 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=25.4MB, alloc=32.3MB, time=0.48 memory used=45.3MB, alloc=56.3MB, time=0.72 memory used=82.9MB, alloc=60.3MB, time=1.27 memory used=126.4MB, alloc=68.3MB, time=1.87 memory used=169.1MB, alloc=68.3MB, time=2.47 memory used=210.0MB, alloc=92.3MB, time=3.09 memory used=274.4MB, alloc=92.3MB, time=4.05 memory used=338.4MB, alloc=116.3MB, time=4.86 memory used=405.7MB, alloc=372.3MB, time=5.77 memory used=501.4MB, alloc=372.3MB, time=7.03 memory used=590.1MB, alloc=396.3MB, time=8.35 memory used=688.2MB, alloc=396.3MB, time=9.42 memory used=805.6MB, alloc=396.3MB, time=10.79 memory used=914.3MB, alloc=420.3MB, time=12.07 memory used=1041.3MB, alloc=420.3MB, time=13.85 memory used=1171.6MB, alloc=444.3MB, time=15.85 memory used=1290.0MB, alloc=444.3MB, time=17.67 memory used=1415.2MB, alloc=444.3MB, time=19.18 memory used=1530.7MB, alloc=468.3MB, time=21.02 memory used=1639.3MB, alloc=468.3MB, time=22.89 memory used=1730.0MB, alloc=468.3MB, time=24.41 memory used=1833.6MB, alloc=468.3MB, time=26.17 memory used=1940.3MB, alloc=492.3MB, time=27.52 memory used=2065.2MB, alloc=492.3MB, time=28.69 memory used=2191.9MB, alloc=492.3MB, time=30.15 memory used=2304.7MB, alloc=492.3MB, time=31.84 memory used=2423.6MB, alloc=492.3MB, time=33.61 memory used=2521.8MB, alloc=492.3MB, time=35.22 memory used=2630.1MB, alloc=492.3MB, time=36.34 memory used=2725.1MB, alloc=492.3MB, time=37.88 memory used=2822.4MB, alloc=492.3MB, time=39.27 memory used=2880.3MB, alloc=492.3MB, time=40.44 memory used=2950.2MB, alloc=492.3MB, time=41.76 memory used=3002.1MB, alloc=492.3MB, time=42.90 memory used=3067.3MB, alloc=492.3MB, time=44.20 memory used=3125.8MB, alloc=492.3MB, time=45.54 memory used=3190.5MB, alloc=516.3MB, time=46.94 memory used=3256.0MB, alloc=516.3MB, time=48.03 memory used=3325.2MB, alloc=516.3MB, time=49.12 memory used=3381.9MB, alloc=516.3MB, time=50.16 memory used=3445.6MB, alloc=516.3MB, time=51.27 memory used=3628.1MB, alloc=516.3MB, time=53.30 memory used=3842.4MB, alloc=540.3MB, time=56.10 memory used=4038.8MB, alloc=540.3MB, time=58.57 memory used=4266.7MB, alloc=564.3MB, time=61.59 memory used=4518.9MB, alloc=564.3MB, time=64.73 memory used=4743.0MB, alloc=588.3MB, time=67.88 memory used=4931.8MB, alloc=588.3MB, time=71.18 memory used=5111.4MB, alloc=612.3MB, time=74.42 memory used=5306.5MB, alloc=612.3MB, time=77.02 memory used=5473.6MB, alloc=612.3MB, time=78.66 memory used=5677.5MB, alloc=636.3MB, time=81.48 memory used=5853.1MB, alloc=636.3MB, time=84.07 memory used=6073.1MB, alloc=636.3MB, time=86.55 memory used=6258.0MB, alloc=636.3MB, time=89.26 memory used=6419.2MB, alloc=660.3MB, time=91.88 memory used=6563.9MB, alloc=660.3MB, time=95.20 memory used=6691.3MB, alloc=660.3MB, time=97.65 memory used=6823.5MB, alloc=660.3MB, time=100.59 memory used=6938.6MB, alloc=684.3MB, time=102.73 memory used=7028.6MB, alloc=684.3MB, time=104.41 memory used=7165.8MB, alloc=708.3MB, time=106.53 memory used=7543.4MB, alloc=732.3MB, time=113.32 memory used=7933.8MB, alloc=756.3MB, time=120.25 memory used=8322.0MB, alloc=780.3MB, time=126.61 memory used=8729.1MB, alloc=804.3MB, time=132.07 memory used=9036.7MB, alloc=828.3MB, time=137.89 memory used=9341.4MB, alloc=852.3MB, time=144.11 memory used=9646.2MB, alloc=876.3MB, time=150.34 |\^/| 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(); 1428290591 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 F := [17 x y + 10 z - 17 y + 15, -18 x y + 19 x z + y - 2 y z, 3 2 2 -9 y - 4 x + 4 x z - 17 y ] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 2 2 G := [10 x - 4 x y - 19 y z + 13 x , -11 x y + 3 x z + 6 y z - 20 x, 2 2 2 -x z - 2 x z - 15 x z - 15 z ] > Problem := [F,G]; 2 3 2 Problem := [[17 x y + 10 z - 17 y + 15, -18 x y + 19 x z + y - 2 y z, 3 2 2 3 2 2 2 -9 y - 4 x + 4 x z - 17 y ], [10 x - 4 x y - 19 y z + 13 x , 2 2 2 2 2 2 -11 x y + 3 x z + 6 y z - 20 x, -x z - 2 x z - 15 x z - 15 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.1MB, alloc=32.3MB, time=0.50 memory used=46.8MB, alloc=56.3MB, time=0.81 memory used=88.8MB, alloc=60.3MB, time=1.43 memory used=128.7MB, alloc=60.3MB, time=2.01 memory used=165.7MB, alloc=84.3MB, time=2.56 memory used=228.8MB, alloc=116.3MB, time=3.49 memory used=308.0MB, alloc=372.3MB, time=4.62 memory used=393.5MB, alloc=396.3MB, time=5.91 memory used=504.9MB, alloc=420.3MB, time=7.53 memory used=642.4MB, alloc=444.3MB, time=9.52 memory used=779.7MB, alloc=444.3MB, time=11.68 memory used=899.6MB, alloc=468.3MB, time=13.56 memory used=1027.6MB, alloc=468.3MB, time=15.69 memory used=1141.7MB, alloc=492.3MB, time=17.64 memory used=1244.3MB, alloc=492.3MB, time=19.29 memory used=1347.1MB, alloc=492.3MB, time=21.02 memory used=1444.6MB, alloc=516.3MB, time=22.82 memory used=1540.4MB, alloc=516.3MB, time=24.54 memory used=1630.8MB, alloc=516.3MB, time=26.25 memory used=1725.5MB, alloc=516.3MB, time=28.06 memory used=1791.4MB, alloc=516.3MB, time=29.14 memory used=1877.5MB, alloc=516.3MB, time=31.02 memory used=1938.6MB, alloc=516.3MB, time=32.16 memory used=2003.7MB, alloc=540.3MB, time=33.26 memory used=2067.1MB, alloc=540.3MB, time=34.33 memory used=2116.8MB, alloc=540.3MB, time=35.09 memory used=2168.5MB, alloc=540.3MB, time=36.15 memory used=2210.1MB, alloc=540.3MB, time=37.16 memory used=2258.3MB, alloc=540.3MB, time=38.49 memory used=2295.2MB, alloc=540.3MB, time=39.37 memory used=2481.2MB, alloc=564.3MB, time=42.04 memory used=2700.4MB, alloc=588.3MB, time=45.67 memory used=2901.4MB, alloc=612.3MB, time=49.02 memory used=3057.1MB, alloc=636.3MB, time=51.60 memory used=3206.9MB, alloc=660.3MB, time=53.71 memory used=3382.6MB, alloc=660.3MB, time=57.07 memory used=3541.8MB, alloc=684.3MB, time=60.24 memory used=3716.0MB, alloc=684.3MB, time=63.72 memory used=3845.0MB, alloc=684.3MB, time=66.15 memory used=3970.2MB, alloc=708.3MB, time=68.24 memory used=4081.4MB, alloc=708.3MB, time=70.25 memory used=4233.5MB, alloc=732.3MB, time=73.36 memory used=4333.6MB, alloc=732.3MB, time=75.62 memory used=4733.2MB, alloc=756.3MB, time=82.47 memory used=5128.8MB, alloc=780.3MB, time=89.10 memory used=5527.0MB, alloc=804.3MB, time=95.87 memory used=5866.8MB, alloc=828.3MB, time=102.40 memory used=6209.0MB, alloc=852.3MB, time=108.39 memory used=6482.8MB, alloc=876.3MB, time=112.94 memory used=6803.8MB, alloc=900.3MB, time=119.88 memory used=7057.3MB, alloc=924.3MB, time=125.88 memory used=7326.4MB, alloc=948.3MB, time=132.24 memory used=7561.8MB, alloc=972.3MB, time=138.08 memory used=7791.6MB, alloc=996.3MB, time=142.70 memory used=8039.5MB, alloc=1020.3MB, time=148.57 |\^/| 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(); 1428290891 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 2 2 F := [-19 x y - 14 y z - 17 x - 6 y, -11 x + 11 x z - 3 y - 11 z , 3 2 -3 x - y z - 15 z + 8] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 3 G := [10 z + 2 y z - 12 x - 15 z, 18 x z + 6 x y z + 4 y + 17 y z, 2 2 3 11 x y + 11 x z + 7 z - 4 x] > Problem := [F,G]; 2 2 2 3 2 2 2 Problem := [[-19 x y - 14 y z - 17 x - 6 y, -11 x + 11 x z - 3 y - 11 z , 3 2 3 -3 x - y z - 15 z + 8], [10 z + 2 y z - 12 x - 15 z, 2 3 2 2 3 18 x z + 6 x y z + 4 y + 17 y z, 11 x y + 11 x z + 7 z - 4 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=25.8MB, alloc=32.3MB, time=0.48 memory used=45.4MB, alloc=33.5MB, time=0.60 memory used=55.8MB, alloc=33.5MB, time=0.63 memory used=71.6MB, alloc=33.5MB, time=0.72 memory used=87.3MB, alloc=33.5MB, time=0.76 memory used=99.9MB, alloc=33.5MB, time=0.80 memory used=122.6MB, alloc=33.5MB, time=1.58 memory used=135.1MB, alloc=33.5MB, time=1.62 memory used=146.6MB, alloc=33.5MB, time=1.66 memory used=156.1MB, alloc=33.5MB, time=1.69 memory used=168.1MB, alloc=33.5MB, time=1.72 memory used=180.1MB, alloc=33.5MB, time=1.75 memory used=235.1MB, alloc=72.0MB, time=2.94 memory used=267.6MB, alloc=72.0MB, time=3.02 memory used=306.5MB, alloc=72.0MB, time=3.25 memory used=339.8MB, alloc=72.0MB, time=3.35 memory used=388.6MB, alloc=72.0MB, time=3.90 memory used=443.5MB, alloc=80.0MB, time=4.46 memory used=473.9MB, alloc=80.0MB, time=4.55 memory used=503.1MB, alloc=80.0MB, time=4.63 memory used=528.9MB, alloc=80.0MB, time=4.71 memory used=565.7MB, alloc=80.0MB, time=4.89 memory used=598.0MB, alloc=80.0MB, time=4.99 memory used=621.7MB, alloc=80.0MB, time=5.06 memory used=666.8MB, alloc=80.0MB, time=10.53 memory used=717.2MB, alloc=80.0MB, time=11.21 memory used=748.0MB, alloc=80.0MB, time=11.29 memory used=773.0MB, alloc=80.0MB, time=11.38 memory used=804.4MB, alloc=80.0MB, time=11.47 memory used=840.3MB, alloc=80.0MB, time=11.56 memory used=861.5MB, alloc=80.0MB, time=11.63 memory used=884.2MB, alloc=80.0MB, time=11.70 memory used=908.6MB, alloc=80.0MB, time=11.78 memory used=935.2MB, alloc=80.0MB, time=11.84 memory used=963.8MB, alloc=80.0MB, time=11.91 memory used=993.8MB, alloc=80.0MB, time=11.97 memory used=1026.8MB, alloc=80.0MB, time=12.04 memory used=1071.0MB, alloc=91.8MB, time=12.13 memory used=1079.8MB, alloc=91.8MB, time=12.18 memory used=1089.0MB, alloc=91.8MB, time=12.23 memory used=1098.7MB, alloc=91.8MB, time=12.28 memory used=1109.0MB, alloc=91.8MB, time=12.34 memory used=1155.0MB, alloc=91.8MB, time=12.62 memory used=1197.3MB, alloc=91.8MB, time=13.32 memory used=1256.0MB, alloc=91.8MB, time=13.86 memory used=1319.9MB, alloc=91.8MB, time=14.36 memory used=1382.7MB, alloc=91.8MB, time=15.03 memory used=1445.6MB, alloc=91.8MB, time=16.09 memory used=1509.0MB, alloc=91.8MB, time=17.57 memory used=1572.5MB, alloc=91.8MB, time=19.41 memory used=1636.3MB, alloc=91.8MB, time=21.73 memory used=1700.6MB, alloc=91.8MB, time=24.31 memory used=1757.9MB, alloc=91.8MB, time=25.76 memory used=1815.6MB, alloc=91.8MB, time=27.71 memory used=1843.3MB, alloc=91.8MB, time=27.80 memory used=1864.2MB, alloc=91.8MB, time=27.90 memory used=1891.2MB, alloc=91.8MB, time=27.99 memory used=1919.6MB, alloc=91.8MB, time=28.07 memory used=1938.3MB, alloc=91.8MB, time=28.14 memory used=1959.5MB, alloc=91.8MB, time=28.22 memory used=1984.6MB, alloc=91.8MB, time=28.29 memory used=2022.4MB, alloc=91.8MB, time=28.51 memory used=2049.2MB, alloc=91.8MB, time=28.62 memory used=2071.3MB, alloc=91.8MB, time=28.69 memory used=2105.5MB, alloc=91.8MB, time=28.86 memory used=2133.1MB, alloc=91.8MB, time=28.95 memory used=2155.0MB, alloc=91.8MB, time=29.02 memory used=2200.4MB, alloc=91.8MB, time=34.12 memory used=2246.1MB, alloc=91.8MB, time=34.53 memory used=2274.3MB, alloc=91.8MB, time=34.62 memory used=2294.6MB, alloc=91.8MB, time=34.71 memory used=2318.0MB, alloc=91.8MB, time=34.80 memory used=2345.6MB, alloc=91.8MB, time=34.88 memory used=2375.8MB, alloc=91.8MB, time=34.97 memory used=2393.6MB, alloc=91.8MB, time=35.03 memory used=2412.4MB, alloc=91.8MB, time=35.09 memory used=2432.6MB, alloc=91.8MB, time=35.16 memory used=2453.5MB, alloc=91.8MB, time=35.22 memory used=2476.1MB, alloc=91.8MB, time=35.30 memory used=2501.3MB, alloc=91.8MB, time=35.39 memory used=2529.4MB, alloc=91.8MB, time=35.47 memory used=2572.4MB, alloc=91.8MB, time=35.72 memory used=2600.3MB, alloc=91.8MB, time=35.91 memory used=2625.4MB, alloc=91.8MB, time=35.99 memory used=2652.8MB, alloc=91.8MB, time=36.08 memory used=2676.9MB, alloc=91.8MB, time=36.16 memory used=2709.1MB, alloc=91.8MB, time=36.40 memory used=2764.9MB, alloc=91.8MB, time=36.96 memory used=2807.9MB, alloc=91.8MB, time=37.26 memory used=2829.9MB, alloc=91.8MB, time=37.34 memory used=2858.0MB, alloc=91.8MB, time=37.53 memory used=2891.9MB, alloc=91.8MB, time=37.83 memory used=2928.8MB, alloc=91.8MB, time=38.13 memory used=2951.2MB, alloc=91.8MB, time=38.20 memory used=2994.5MB, alloc=91.8MB, time=38.53 memory used=3049.1MB, alloc=115.8MB, time=39.04 memory used=3113.2MB, alloc=115.8MB, time=41.53 memory used=3151.9MB, alloc=115.8MB, time=41.64 memory used=3189.9MB, alloc=115.8MB, time=41.76 memory used=3237.5MB, alloc=115.8MB, time=41.87 memory used=3267.7MB, alloc=115.8MB, time=41.96 memory used=3298.5MB, alloc=115.8MB, time=42.05 memory used=3332.8MB, alloc=115.8MB, time=42.13 memory used=3370.9MB, alloc=115.8MB, time=42.23 memory used=3412.3MB, alloc=115.8MB, time=42.33 memory used=3460.4MB, alloc=115.8MB, time=42.43 memory used=3477.8MB, alloc=115.8MB, time=42.51 memory used=3488.9MB, alloc=115.8MB, time=42.57 memory used=3551.3MB, alloc=115.8MB, time=49.05 memory used=3596.5MB, alloc=115.8MB, time=49.20 memory used=3631.1MB, alloc=115.8MB, time=49.32 memory used=3668.2MB, alloc=115.8MB, time=49.43 memory used=3712.4MB, alloc=115.8MB, time=49.56 memory used=3753.6MB, alloc=115.8MB, time=49.67 memory used=3781.2MB, alloc=115.8MB, time=49.76 memory used=3811.6MB, alloc=115.8MB, time=49.86 memory used=3844.1MB, alloc=115.8MB, time=49.97 memory used=3878.7MB, alloc=115.8MB, time=50.07 memory used=3916.5MB, alloc=115.8MB, time=50.16 memory used=3957.2MB, alloc=115.8MB, time=50.26 memory used=4000.5MB, alloc=115.8MB, time=50.37 memory used=4047.4MB, alloc=115.8MB, time=50.47 memory used=4100.1MB, alloc=115.8MB, time=50.58 memory used=4110.3MB, alloc=115.8MB, time=50.64 memory used=4120.3MB, alloc=115.8MB, time=50.71 memory used=4130.2MB, alloc=115.8MB, time=50.80 memory used=4140.6MB, alloc=115.8MB, time=50.89 memory used=4151.1MB, alloc=115.8MB, time=50.95 memory used=4162.0MB, alloc=115.8MB, time=51.03 memory used=4173.0MB, alloc=115.8MB, time=51.13 memory used=4184.9MB, alloc=115.8MB, time=51.21 memory used=4196.8MB, alloc=115.8MB, time=51.28 memory used=4209.4MB, alloc=115.8MB, time=51.37 memory used=4222.2MB, alloc=115.8MB, time=51.44 memory used=4235.7MB, alloc=115.8MB, time=51.50 memory used=4250.0MB, alloc=115.8MB, time=51.56 memory used=4301.4MB, alloc=115.8MB, time=51.84 memory used=4381.2MB, alloc=115.8MB, time=52.73 memory used=4426.4MB, alloc=115.8MB, time=52.91 memory used=4473.3MB, alloc=115.8MB, time=53.74 memory used=4507.9MB, alloc=115.8MB, time=53.85 memory used=4550.6MB, alloc=115.8MB, time=54.13 memory used=4595.0MB, alloc=115.8MB, time=54.41 memory used=4663.9MB, alloc=115.8MB, time=55.23 memory used=4723.9MB, alloc=115.8MB, time=55.80 memory used=4796.6MB, alloc=115.8MB, time=56.41 memory used=4857.6MB, alloc=395.8MB, time=57.05 memory used=4955.0MB, alloc=419.8MB, time=58.38 memory used=5073.2MB, alloc=419.8MB, time=59.72 memory used=5129.0MB, alloc=419.8MB, time=59.96 memory used=5188.2MB, alloc=419.8MB, time=60.24 memory used=5253.9MB, alloc=419.8MB, time=61.62 memory used=5302.7MB, alloc=419.8MB, time=61.81 memory used=5368.0MB, alloc=419.8MB, time=62.23 memory used=5434.6MB, alloc=419.8MB, time=62.57 memory used=5487.0MB, alloc=419.8MB, time=62.87 memory used=5543.7MB, alloc=419.8MB, time=63.08 memory used=5605.2MB, alloc=419.8MB, time=65.64 memory used=5691.8MB, alloc=419.8MB, time=69.45 memory used=5737.8MB, alloc=419.8MB, time=69.65 memory used=5795.1MB, alloc=419.8MB, time=69.84 memory used=5833.1MB, alloc=419.8MB, time=70.00 memory used=5876.6MB, alloc=419.8MB, time=70.17 memory used=5926.8MB, alloc=419.8MB, time=70.35 memory used=5984.2MB, alloc=419.8MB, time=70.53 memory used=6101.4MB, alloc=419.8MB, time=71.88 memory used=6171.7MB, alloc=419.8MB, time=73.46 memory used=6225.3MB, alloc=419.8MB, time=73.66 memory used=6268.8MB, alloc=419.8MB, time=73.82 memory used=6312.5MB, alloc=419.8MB, time=73.98 memory used=6367.8MB, alloc=419.8MB, time=74.18 memory used=6434.2MB, alloc=419.8MB, time=74.45 memory used=6480.6MB, alloc=419.8MB, time=74.64 memory used=6546.3MB, alloc=419.8MB, time=75.01 memory used=6593.4MB, alloc=419.8MB, time=75.19 memory used=6694.4MB, alloc=419.8MB, time=81.44 memory used=6745.3MB, alloc=419.8MB, time=81.64 memory used=6797.9MB, alloc=419.8MB, time=81.84 memory used=6846.4MB, alloc=419.8MB, time=82.03 memory used=6886.9MB, alloc=419.8MB, time=82.20 memory used=6934.2MB, alloc=419.8MB, time=82.37 memory used=6987.3MB, alloc=419.8MB, time=82.56 memory used=7098.4MB, alloc=419.8MB, time=82.86 memory used=7160.1MB, alloc=419.8MB, time=83.17 memory used=7208.8MB, alloc=419.8MB, time=83.36 memory used=7274.5MB, alloc=419.8MB, time=83.80 memory used=7325.1MB, alloc=419.8MB, time=84.01 memory used=7386.9MB, alloc=419.8MB, time=85.27 memory used=7463.2MB, alloc=419.8MB, time=89.76 memory used=7508.2MB, alloc=419.8MB, time=89.96 memory used=7567.1MB, alloc=419.8MB, time=90.15 memory used=7604.4MB, alloc=443.8MB, time=90.33 memory used=7662.9MB, alloc=443.8MB, time=90.52 memory used=7733.2MB, alloc=443.8MB, time=90.71 memory used=7894.4MB, alloc=443.8MB, time=91.12 memory used=7992.1MB, alloc=443.8MB, time=93.54 memory used=8060.6MB, alloc=443.8MB, time=93.77 memory used=8118.2MB, alloc=443.8MB, time=93.96 memory used=8182.5MB, alloc=443.8MB, time=94.13 memory used=8276.2MB, alloc=443.8MB, time=94.41 memory used=8366.4MB, alloc=443.8MB, time=96.78 memory used=8438.5MB, alloc=443.8MB, time=97.01 memory used=8493.8MB, alloc=443.8MB, time=97.19 memory used=8563.4MB, alloc=443.8MB, time=97.37 memory used=8654.8MB, alloc=443.8MB, time=97.78 memory used=8787.2MB, alloc=443.8MB, time=99.07 memory used=8948.5MB, alloc=443.8MB, time=101.20 memory used=9111.1MB, alloc=443.8MB, time=105.77 memory used=9293.6MB, alloc=443.8MB, time=110.27 memory used=9446.8MB, alloc=443.8MB, time=111.56 memory used=9603.7MB, alloc=443.8MB, time=114.64 memory used=9761.4MB, alloc=443.8MB, time=120.37 memory used=9917.8MB, alloc=443.8MB, time=123.13 memory used=10066.0MB, alloc=443.8MB, time=124.24 memory used=10214.0MB, alloc=443.8MB, time=126.90 memory used=10362.7MB, alloc=443.8MB, time=131.92 memory used=10507.8MB, alloc=443.8MB, time=137.68 memory used=10571.9MB, alloc=443.8MB, time=137.90 memory used=10625.1MB, alloc=443.8MB, time=138.13 memory used=10698.7MB, alloc=443.8MB, time=138.90 memory used=10760.1MB, alloc=443.8MB, time=139.12 memory used=10822.5MB, alloc=443.8MB, time=139.43 memory used=10973.0MB, alloc=467.8MB, time=141.08 memory used=11163.7MB, alloc=467.8MB, time=143.11 memory used=11342.9MB, alloc=467.8MB, time=145.97 memory used=11524.5MB, alloc=467.8MB, time=152.31 memory used=11711.1MB, alloc=467.8MB, time=158.10 memory used=11810.4MB, alloc=467.8MB, time=159.48 memory used=11888.1MB, alloc=467.8MB, time=159.90 memory used=11967.6MB, alloc=467.8MB, time=160.42 memory used=12085.1MB, alloc=467.8MB, time=165.73 memory used=12155.6MB, alloc=467.8MB, time=166.00 memory used=12216.2MB, alloc=467.8MB, time=166.26 memory used=12278.0MB, alloc=467.8MB, time=166.50 memory used=12375.0MB, alloc=467.8MB, time=167.05 memory used=12472.6MB, alloc=467.8MB, time=169.13 memory used=12541.8MB, alloc=467.8MB, time=169.40 memory used=12603.9MB, alloc=467.8MB, time=169.63 memory used=12686.5MB, alloc=467.8MB, time=170.03 memory used=12772.8MB, alloc=467.8MB, time=170.50 memory used=12894.4MB, alloc=467.8MB, time=176.16 memory used=12961.2MB, alloc=467.8MB, time=176.44 memory used=13034.0MB, alloc=467.8MB, time=176.70 memory used=13089.4MB, alloc=467.8MB, time=176.93 memory used=13158.4MB, alloc=467.8MB, time=177.17 memory used=13316.5MB, alloc=467.8MB, time=178.57 memory used=13455.0MB, alloc=491.8MB, time=180.02 memory used=13560.4MB, alloc=491.8MB, time=180.74 memory used=13711.3MB, alloc=491.8MB, time=181.84 memory used=13815.9MB, alloc=491.8MB, time=182.42 memory used=13887.5MB, alloc=491.8MB, time=182.73 memory used=13978.2MB, alloc=491.8MB, time=183.04 memory used=14069.8MB, alloc=491.8MB, time=183.65 memory used=14150.6MB, alloc=491.8MB, time=183.99 memory used=14227.2MB, alloc=491.8MB, time=184.30 memory used=14326.5MB, alloc=491.8MB, time=189.91 memory used=14451.5MB, alloc=491.8MB, time=201.62 memory used=14526.6MB, alloc=491.8MB, time=201.94 memory used=14620.7MB, alloc=491.8MB, time=202.26 memory used=14680.0MB, alloc=491.8MB, time=202.54 memory used=14746.7MB, alloc=491.8MB, time=202.80 memory used=14820.8MB, alloc=491.8MB, time=203.08 memory used=14905.8MB, alloc=491.8MB, time=203.37 memory used=14999.7MB, alloc=491.8MB, time=203.67 memory used=15211.4MB, alloc=491.8MB, time=204.20 memory used=15379.1MB, alloc=491.8MB, time=204.58 memory used=15654.5MB, alloc=491.8MB, time=207.54 memory used=15762.9MB, alloc=491.8MB, time=211.23 memory used=15846.4MB, alloc=491.8MB, time=211.56 memory used=15916.7MB, alloc=491.8MB, time=211.84 memory used=15984.5MB, alloc=491.8MB, time=212.15 memory used=16064.4MB, alloc=491.8MB, time=212.43 memory used=16157.3MB, alloc=491.8MB, time=212.71 memory used=16354.8MB, alloc=491.8MB, time=213.13 memory used=16494.0MB, alloc=491.8MB, time=213.70 memory used=16562.0MB, alloc=491.8MB, time=214.00 memory used=16650.0MB, alloc=491.8MB, time=214.31 memory used=16742.3MB, alloc=491.8MB, time=214.80 memory used=16817.0MB, alloc=491.8MB, time=215.11 memory used=16906.0MB, alloc=491.8MB, time=215.42 memory used=17011.8MB, alloc=515.8MB, time=232.08 memory used=17129.6MB, alloc=515.8MB, time=232.68 memory used=17234.6MB, alloc=515.8MB, time=233.02 memory used=17315.7MB, alloc=515.8MB, time=233.34 memory used=17398.3MB, alloc=515.8MB, time=233.64 memory used=17493.4MB, alloc=515.8MB, time=233.94 memory used=17603.5MB, alloc=515.8MB, time=234.26 memory used=17847.8MB, alloc=515.8MB, time=234.73 memory used=18014.2MB, alloc=515.8MB, time=235.13 memory used=18305.9MB, alloc=515.8MB, time=236.01 memory used=18522.2MB, alloc=515.8MB, time=236.79 memory used=18716.7MB, alloc=515.8MB, time=237.82 memory used=18811.1MB, alloc=515.8MB, time=238.19 memory used=18911.2MB, alloc=515.8MB, time=238.53 memory used=19021.8MB, alloc=515.8MB, time=239.20 memory used=19114.6MB, alloc=515.8MB, time=239.55 memory used=19217.4MB, alloc=515.8MB, time=239.88 |\^/| 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(); 1428291191 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 3 3 2 F := [-2 x y + 6 y - z - 12, 12 z + 19 x - 17 x y + 5, 3 2 3 -12 x - 9 x y - 10 x y z - 11 y ] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 G := [5 x + 12 y z - 18 z - 12, x y + 15 y z - 10 x + 12, 2 2 3 y z - 3 y + 5 y z - 2 x] > Problem := [F,G]; 2 3 3 3 2 Problem := [[-2 x y + 6 y - z - 12, 12 z + 19 x - 17 x y + 5, 3 2 3 3 2 2 -12 x - 9 x y - 10 x y z - 11 y ], [5 x + 12 y z - 18 z - 12, 2 2 2 2 x y + 15 y z - 10 x + 12, 3 y z - 3 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=4.4MB, alloc=32.3MB, time=0.18 memory used=24.5MB, alloc=32.3MB, time=0.45 memory used=44.1MB, alloc=36.3MB, time=0.71 memory used=64.8MB, alloc=60.3MB, time=0.98 memory used=106.1MB, alloc=60.3MB, time=1.56 memory used=146.1MB, alloc=60.3MB, time=2.08 memory used=192.8MB, alloc=92.3MB, time=2.61 memory used=251.9MB, alloc=92.3MB, time=3.16 memory used=309.3MB, alloc=92.3MB, time=3.57 memory used=379.1MB, alloc=348.3MB, time=4.40 memory used=451.4MB, alloc=348.3MB, time=5.23 memory used=519.9MB, alloc=348.3MB, time=6.08 memory used=588.0MB, alloc=348.3MB, time=6.87 memory used=650.8MB, alloc=372.3MB, time=7.79 memory used=740.8MB, alloc=372.3MB, time=8.94 memory used=788.1MB, alloc=372.3MB, time=9.17 memory used=834.3MB, alloc=372.3MB, time=9.56 memory used=886.0MB, alloc=372.3MB, time=9.94 memory used=942.6MB, alloc=372.3MB, time=10.31 memory used=1000.7MB, alloc=372.3MB, time=11.90 memory used=1040.0MB, alloc=372.3MB, time=12.06 memory used=1076.8MB, alloc=372.3MB, time=12.18 memory used=1115.5MB, alloc=372.3MB, time=12.32 memory used=1146.8MB, alloc=372.3MB, time=12.43 memory used=1198.3MB, alloc=372.3MB, time=12.67 memory used=1254.9MB, alloc=372.3MB, time=14.31 memory used=1292.8MB, alloc=372.3MB, time=14.46 memory used=1328.4MB, alloc=372.3MB, time=14.60 memory used=1367.4MB, alloc=372.3MB, time=14.73 memory used=1397.4MB, alloc=372.3MB, time=14.84 memory used=1442.0MB, alloc=372.3MB, time=15.32 memory used=1512.5MB, alloc=372.3MB, time=16.06 memory used=1562.0MB, alloc=396.3MB, time=16.32 memory used=1624.8MB, alloc=396.3MB, time=16.57 memory used=1692.2MB, alloc=396.3MB, time=17.80 memory used=1745.4MB, alloc=396.3MB, time=17.98 memory used=1799.7MB, alloc=396.3MB, time=18.14 memory used=1898.6MB, alloc=396.3MB, time=19.04 memory used=2022.7MB, alloc=396.3MB, time=20.48 memory used=2157.0MB, alloc=396.3MB, time=22.23 memory used=2281.8MB, alloc=396.3MB, time=24.17 memory used=2370.6MB, alloc=396.3MB, time=25.10 memory used=2453.7MB, alloc=396.3MB, time=25.96 memory used=2549.4MB, alloc=396.3MB, time=26.76 memory used=2645.8MB, alloc=396.3MB, time=27.62 memory used=2722.5MB, alloc=396.3MB, time=28.27 memory used=2795.5MB, alloc=396.3MB, time=29.95 memory used=2840.5MB, alloc=396.3MB, time=30.14 memory used=2899.1MB, alloc=396.3MB, time=30.56 memory used=2973.8MB, alloc=396.3MB, time=32.21 memory used=3018.9MB, alloc=396.3MB, time=32.38 memory used=3078.4MB, alloc=396.3MB, time=32.77 memory used=3187.0MB, alloc=396.3MB, time=34.31 memory used=3238.2MB, alloc=396.3MB, time=34.58 memory used=3360.4MB, alloc=420.3MB, time=36.07 memory used=3499.0MB, alloc=420.3MB, time=38.89 memory used=3605.3MB, alloc=420.3MB, time=39.75 memory used=3665.3MB, alloc=420.3MB, time=39.96 memory used=3732.1MB, alloc=420.3MB, time=40.36 memory used=3807.9MB, alloc=420.3MB, time=40.73 memory used=3868.8MB, alloc=420.3MB, time=41.05 memory used=3948.7MB, alloc=420.3MB, time=43.12 memory used=4010.4MB, alloc=420.3MB, time=43.33 memory used=4062.0MB, alloc=420.3MB, time=43.50 memory used=4132.8MB, alloc=420.3MB, time=43.97 memory used=4212.8MB, alloc=420.3MB, time=44.62 memory used=4299.4MB, alloc=420.3MB, time=44.90 memory used=4375.8MB, alloc=420.3MB, time=45.63 memory used=4510.5MB, alloc=420.3MB, time=47.02 memory used=4619.2MB, alloc=420.3MB, time=47.94 memory used=4708.0MB, alloc=420.3MB, time=48.60 memory used=4797.0MB, alloc=420.3MB, time=51.54 memory used=4857.0MB, alloc=420.3MB, time=51.80 memory used=4911.8MB, alloc=420.3MB, time=52.02 memory used=4966.0MB, alloc=420.3MB, time=52.24 memory used=5042.2MB, alloc=420.3MB, time=52.62 memory used=5126.1MB, alloc=420.3MB, time=55.46 memory used=5182.5MB, alloc=420.3MB, time=55.70 memory used=5241.1MB, alloc=420.3MB, time=55.93 memory used=5291.3MB, alloc=420.3MB, time=56.12 memory used=5358.2MB, alloc=420.3MB, time=56.61 memory used=5480.1MB, alloc=444.3MB, time=58.04 memory used=5620.9MB, alloc=444.3MB, time=59.66 memory used=5729.5MB, alloc=444.3MB, time=60.99 memory used=5870.8MB, alloc=444.3MB, time=63.14 memory used=5965.1MB, alloc=444.3MB, time=64.60 memory used=6086.3MB, alloc=468.3MB, time=65.98 memory used=6181.4MB, alloc=468.3MB, time=66.68 memory used=6272.1MB, alloc=468.3MB, time=67.42 memory used=6381.3MB, alloc=468.3MB, time=68.14 memory used=6479.7MB, alloc=468.3MB, time=68.84 memory used=6568.9MB, alloc=468.3MB, time=69.38 memory used=6671.2MB, alloc=468.3MB, time=73.37 memory used=6755.6MB, alloc=468.3MB, time=73.69 memory used=6820.2MB, alloc=468.3MB, time=73.95 memory used=6916.0MB, alloc=468.3MB, time=74.64 memory used=6995.5MB, alloc=468.3MB, time=75.16 memory used=7101.4MB, alloc=468.3MB, time=75.67 memory used=7207.4MB, alloc=468.3MB, time=76.03 memory used=7438.4MB, alloc=468.3MB, time=77.22 memory used=7644.3MB, alloc=468.3MB, time=77.73 memory used=7823.1MB, alloc=468.3MB, time=78.13 memory used=8038.0MB, alloc=468.3MB, time=79.50 memory used=8143.6MB, alloc=468.3MB, time=83.52 memory used=8222.2MB, alloc=468.3MB, time=83.84 memory used=8297.6MB, alloc=468.3MB, time=84.12 memory used=8370.9MB, alloc=468.3MB, time=84.41 memory used=8470.5MB, alloc=468.3MB, time=85.26 memory used=8554.2MB, alloc=468.3MB, time=85.58 memory used=8709.5MB, alloc=468.3MB, time=86.46 memory used=8892.0MB, alloc=468.3MB, time=86.89 memory used=9045.1MB, alloc=468.3MB, time=87.26 memory used=9155.3MB, alloc=468.3MB, time=88.48 memory used=9258.4MB, alloc=468.3MB, time=89.93 memory used=9380.2MB, alloc=468.3MB, time=90.93 memory used=9462.8MB, alloc=468.3MB, time=91.30 memory used=9535.1MB, alloc=468.3MB, time=91.62 memory used=9605.5MB, alloc=468.3MB, time=91.95 memory used=9709.2MB, alloc=468.3MB, time=92.47 memory used=9792.0MB, alloc=468.3MB, time=92.85 memory used=9864.2MB, alloc=468.3MB, time=93.18 memory used=9935.3MB, alloc=468.3MB, time=93.49 memory used=10044.8MB, alloc=468.3MB, time=99.23 memory used=10141.4MB, alloc=468.3MB, time=111.37 memory used=10215.7MB, alloc=468.3MB, time=111.71 memory used=10287.1MB, alloc=468.3MB, time=112.04 memory used=10376.3MB, alloc=468.3MB, time=112.39 memory used=10448.6MB, alloc=468.3MB, time=112.69 memory used=10504.4MB, alloc=468.3MB, time=112.96 memory used=10564.9MB, alloc=468.3MB, time=113.23 memory used=10631.5MB, alloc=468.3MB, time=113.52 memory used=10704.0MB, alloc=468.3MB, time=113.82 memory used=10782.4MB, alloc=468.3MB, time=114.10 memory used=10866.2MB, alloc=468.3MB, time=114.38 memory used=10956.9MB, alloc=468.3MB, time=114.68 memory used=11053.9MB, alloc=468.3MB, time=114.97 memory used=11202.7MB, alloc=468.3MB, time=115.36 memory used=11347.8MB, alloc=468.3MB, time=115.74 memory used=11514.0MB, alloc=468.3MB, time=116.13 memory used=11683.4MB, alloc=468.3MB, time=118.03 memory used=11757.8MB, alloc=468.3MB, time=118.34 memory used=11834.9MB, alloc=468.3MB, time=118.65 memory used=11895.8MB, alloc=468.3MB, time=118.94 memory used=11967.3MB, alloc=468.3MB, time=119.23 memory used=12052.2MB, alloc=468.3MB, time=119.52 memory used=12154.4MB, alloc=468.3MB, time=120.15 memory used=12248.6MB, alloc=468.3MB, time=120.71 memory used=12333.8MB, alloc=468.3MB, time=121.07 memory used=12474.1MB, alloc=468.3MB, time=122.91 memory used=12568.2MB, alloc=468.3MB, time=123.52 memory used=12650.5MB, alloc=468.3MB, time=123.87 memory used=12710.3MB, alloc=468.3MB, time=124.17 memory used=12785.0MB, alloc=468.3MB, time=124.48 memory used=12869.7MB, alloc=468.3MB, time=124.80 memory used=12942.8MB, alloc=468.3MB, time=125.26 memory used=13024.7MB, alloc=468.3MB, time=125.65 memory used=13095.2MB, alloc=468.3MB, time=125.98 memory used=13164.2MB, alloc=468.3MB, time=126.30 memory used=13251.2MB, alloc=468.3MB, time=126.63 memory used=13314.6MB, alloc=468.3MB, time=126.90 memory used=13416.3MB, alloc=468.3MB, time=133.77 memory used=13488.3MB, alloc=468.3MB, time=134.11 memory used=13567.6MB, alloc=468.3MB, time=134.44 memory used=13645.9MB, alloc=468.3MB, time=134.74 memory used=13703.3MB, alloc=468.3MB, time=135.02 memory used=13767.8MB, alloc=468.3MB, time=135.29 memory used=13839.6MB, alloc=468.3MB, time=135.57 memory used=13920.2MB, alloc=468.3MB, time=135.86 memory used=14011.2MB, alloc=468.3MB, time=136.15 memory used=14240.8MB, alloc=468.3MB, time=137.26 memory used=14371.2MB, alloc=468.3MB, time=138.42 memory used=14460.5MB, alloc=468.3MB, time=139.54 memory used=14596.9MB, alloc=492.3MB, time=141.52 memory used=14681.8MB, alloc=492.3MB, time=141.88 memory used=14765.0MB, alloc=492.3MB, time=142.20 memory used=14894.4MB, alloc=492.3MB, time=143.83 memory used=14999.1MB, alloc=492.3MB, time=145.17 memory used=15097.6MB, alloc=492.3MB, time=145.52 memory used=15168.9MB, alloc=492.3MB, time=145.82 memory used=15281.6MB, alloc=492.3MB, time=146.87 memory used=15349.1MB, alloc=492.3MB, time=147.92 memory used=15411.8MB, alloc=492.3MB, time=148.93 memory used=15515.3MB, alloc=492.3MB, time=150.32 memory used=15637.4MB, alloc=492.3MB, time=152.03 memory used=15723.6MB, alloc=492.3MB, time=152.41 memory used=15826.0MB, alloc=492.3MB, time=153.36 memory used=15915.1MB, alloc=492.3MB, time=154.35 memory used=16010.3MB, alloc=492.3MB, time=155.09 memory used=16110.0MB, alloc=492.3MB, time=155.86 memory used=16230.2MB, alloc=492.3MB, time=159.77 memory used=16306.4MB, alloc=492.3MB, time=160.16 memory used=16392.1MB, alloc=492.3MB, time=160.55 memory used=16503.4MB, alloc=492.3MB, time=164.59 memory used=16584.8MB, alloc=492.3MB, time=164.99 memory used=16675.7MB, alloc=492.3MB, time=165.40 memory used=16744.5MB, alloc=492.3MB, time=165.74 memory used=16847.8MB, alloc=492.3MB, time=166.71 memory used=16918.3MB, alloc=492.3MB, time=167.54 memory used=16984.1MB, alloc=492.3MB, time=168.62 memory used=17045.2MB, alloc=492.3MB, time=169.62 memory used=17102.5MB, alloc=492.3MB, time=170.72 memory used=17142.0MB, alloc=492.3MB, time=171.46 memory used=17187.7MB, alloc=516.3MB, time=172.23 memory used=17232.0MB, alloc=516.3MB, time=173.05 memory used=17282.7MB, alloc=516.3MB, time=173.84 memory used=17318.6MB, alloc=516.3MB, time=174.52 memory used=17541.8MB, alloc=540.3MB, time=176.80 memory used=17721.9MB, alloc=540.3MB, time=178.47 memory used=17913.3MB, alloc=564.3MB, time=180.82 memory used=18096.6MB, alloc=564.3MB, time=183.18 memory used=18279.0MB, alloc=588.3MB, time=185.54 memory used=18448.9MB, alloc=588.3MB, time=187.93 memory used=18611.7MB, alloc=588.3MB, time=190.47 memory used=18789.5MB, alloc=612.3MB, time=193.26 memory used=18951.0MB, alloc=612.3MB, time=195.68 memory used=19086.5MB, alloc=636.3MB, time=197.69 memory used=19245.0MB, alloc=636.3MB, time=199.92 |\^/| 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(); 1428291492 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 3 2 F := [-2 x + 14 x z + 4 z - 8 y, 3 x z - 19 y z + 4 z + 20 y , 3 -17 z + 19 y z - 10 z] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 3 2 2 G := [4 x y + 5 z - 18 y z - 9 y, 16 x - 11 x z - 3 z + 3 z, 3 -2 y + 6 x y - 2 y z - 14 y] > Problem := [F,G]; 3 2 2 2 3 2 Problem := [[-2 x + 14 x z + 4 z - 8 y, 3 x z - 19 y z + 4 z + 20 y , 3 2 3 -17 z + 19 y z - 10 z], [4 x y + 5 z - 18 y z - 9 y, 3 2 2 3 16 x - 11 x z - 3 z + 3 z, -2 y + 6 x y - 2 y z - 14 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.6MB, alloc=32.3MB, time=0.50 memory used=46.8MB, alloc=56.3MB, time=0.81 memory used=88.4MB, alloc=60.3MB, time=1.42 memory used=127.5MB, alloc=84.3MB, time=2.01 memory used=169.7MB, alloc=84.3MB, time=2.66 memory used=230.8MB, alloc=92.3MB, time=3.62 memory used=293.1MB, alloc=116.3MB, time=4.52 memory used=366.1MB, alloc=116.3MB, time=5.62 memory used=443.6MB, alloc=140.3MB, time=6.86 memory used=508.8MB, alloc=140.3MB, time=7.82 memory used=581.3MB, alloc=396.3MB, time=9.00 memory used=683.6MB, alloc=420.3MB, time=10.63 memory used=810.6MB, alloc=444.3MB, time=12.68 memory used=958.2MB, alloc=468.3MB, time=15.21 memory used=1090.0MB, alloc=468.3MB, time=17.12 memory used=1232.9MB, alloc=492.3MB, time=19.48 memory used=1346.4MB, alloc=492.3MB, time=21.46 memory used=1448.7MB, alloc=492.3MB, time=23.01 memory used=1562.5MB, alloc=492.3MB, time=25.16 memory used=1683.1MB, alloc=516.3MB, time=27.46 memory used=1787.5MB, alloc=516.3MB, time=29.42 memory used=1891.2MB, alloc=516.3MB, time=31.47 memory used=1980.4MB, alloc=516.3MB, time=33.18 memory used=2071.4MB, alloc=516.3MB, time=35.06 memory used=2145.8MB, alloc=540.3MB, time=36.52 memory used=2219.1MB, alloc=540.3MB, time=37.91 memory used=2287.3MB, alloc=540.3MB, time=39.33 memory used=2338.9MB, alloc=540.3MB, time=40.54 memory used=2401.7MB, alloc=540.3MB, time=41.93 memory used=2463.8MB, alloc=540.3MB, time=43.50 memory used=2513.2MB, alloc=540.3MB, time=44.73 memory used=2555.2MB, alloc=540.3MB, time=45.78 memory used=2775.3MB, alloc=564.3MB, time=49.37 memory used=2997.1MB, alloc=588.3MB, time=53.66 memory used=3196.5MB, alloc=612.3MB, time=57.46 memory used=3415.7MB, alloc=636.3MB, time=62.25 memory used=3614.0MB, alloc=660.3MB, time=66.30 memory used=3808.2MB, alloc=684.3MB, time=69.30 memory used=4021.4MB, alloc=708.3MB, time=73.16 memory used=4197.5MB, alloc=708.3MB, time=77.01 memory used=4363.0MB, alloc=732.3MB, time=80.92 memory used=4481.6MB, alloc=732.3MB, time=83.26 memory used=4596.3MB, alloc=756.3MB, time=85.38 memory used=4729.7MB, alloc=756.3MB, time=89.18 memory used=4828.4MB, alloc=756.3MB, time=91.74 memory used=4904.9MB, alloc=756.3MB, time=93.79 memory used=5314.7MB, alloc=780.3MB, time=101.78 memory used=5727.8MB, alloc=804.3MB, time=110.72 memory used=6131.5MB, alloc=828.3MB, time=120.03 |\^/| 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(); 1428291792 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 3 2 F := [19 x z + 4 y - 3 x - 6 y, -20 x z + 4 y - 16 z + 7 y , 2 2 19 x z + 10 y z + 5 x - 15 y] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 G := [-3 x + 5 x + 10 y z - 12 z, 3 y z - 17 x y - 8 z - 17, 2 2 2 -8 x y + 7 x z - z - 16 z] > Problem := [F,G]; 2 2 3 3 2 Problem := [[19 x z + 4 y - 3 x - 6 y, -20 x z + 4 y - 16 z + 7 y , 2 2 3 2 19 x z + 10 y z + 5 x - 15 y], [-3 x + 5 x + 10 y z - 12 z, 2 2 2 2 3 y z - 17 x y - 8 z - 17, -8 x y + 7 x z - z - 16 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=24.2MB, alloc=32.3MB, time=0.47 memory used=44.4MB, alloc=60.3MB, time=0.75 memory used=84.5MB, alloc=60.3MB, time=1.30 memory used=125.3MB, alloc=60.3MB, time=1.88 memory used=161.4MB, alloc=60.3MB, time=2.36 memory used=202.1MB, alloc=92.3MB, time=2.87 memory used=273.9MB, alloc=92.3MB, time=3.72 memory used=341.9MB, alloc=92.3MB, time=4.67 memory used=409.5MB, alloc=116.3MB, time=5.61 memory used=478.4MB, alloc=116.3MB, time=7.18 memory used=532.8MB, alloc=140.3MB, time=10.53 memory used=632.2MB, alloc=140.3MB, time=11.57 memory used=739.6MB, alloc=396.3MB, time=12.74 memory used=854.2MB, alloc=396.3MB, time=14.27 memory used=968.8MB, alloc=396.3MB, time=15.88 memory used=1075.8MB, alloc=420.3MB, time=17.54 memory used=1203.6MB, alloc=420.3MB, time=19.23 memory used=1332.8MB, alloc=444.3MB, time=20.84 memory used=1469.4MB, alloc=444.3MB, time=22.32 memory used=1580.4MB, alloc=444.3MB, time=23.85 memory used=1702.7MB, alloc=444.3MB, time=25.50 memory used=1811.6MB, alloc=468.3MB, time=27.12 memory used=1918.1MB, alloc=468.3MB, time=28.45 memory used=2005.1MB, alloc=468.3MB, time=29.80 memory used=2095.2MB, alloc=468.3MB, time=31.07 memory used=2203.3MB, alloc=468.3MB, time=32.52 memory used=2328.6MB, alloc=492.3MB, time=33.79 memory used=2422.9MB, alloc=492.3MB, time=35.52 memory used=2496.4MB, alloc=492.3MB, time=36.62 memory used=2562.6MB, alloc=492.3MB, time=37.61 memory used=2641.4MB, alloc=516.3MB, time=38.56 memory used=2731.6MB, alloc=516.3MB, time=39.87 memory used=2797.5MB, alloc=516.3MB, time=41.23 memory used=2860.4MB, alloc=516.3MB, time=42.24 memory used=2922.5MB, alloc=516.3MB, time=43.22 memory used=2973.8MB, alloc=516.3MB, time=44.08 memory used=3025.5MB, alloc=516.3MB, time=45.04 memory used=3255.9MB, alloc=540.3MB, time=47.74 memory used=3441.8MB, alloc=564.3MB, time=50.24 memory used=3654.4MB, alloc=588.3MB, time=53.32 memory used=3832.2MB, alloc=612.3MB, time=56.46 memory used=4001.6MB, alloc=636.3MB, time=59.05 memory used=4160.3MB, alloc=660.3MB, time=61.10 memory used=4325.9MB, alloc=660.3MB, time=63.83 memory used=4512.0MB, alloc=660.3MB, time=65.05 memory used=4649.2MB, alloc=660.3MB, time=66.83 memory used=4820.2MB, alloc=660.3MB, time=68.97 memory used=4947.7MB, alloc=660.3MB, time=69.90 memory used=5139.8MB, alloc=660.3MB, time=71.20 memory used=5414.0MB, alloc=684.3MB, time=84.90 memory used=5673.2MB, alloc=684.3MB, time=86.78 memory used=5931.9MB, alloc=684.3MB, time=89.86 memory used=6201.8MB, alloc=684.3MB, time=96.30 memory used=6397.6MB, alloc=708.3MB, time=108.33 memory used=6536.9MB, alloc=732.3MB, time=124.06 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428292092 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 F := [17 x + 9 x y - x y + 12 y, -11 y z - 2 y - 2 y z + 19 x, 2 2 2 -x z + 5 y z - 5 z + y] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [6 x z - 7 y + 4 z + 11 x, 18 x y - 15 x + 3 x z + 3 z, 2 2 2 18 x y - x z - x + 20 x z] > Problem := [F,G]; 3 2 2 2 Problem := [[17 x + 9 x y - x y + 12 y, -11 y z - 2 y - 2 y z + 19 x, 2 2 2 2 2 -x z + 5 y z - 5 z + y], [6 x z - 7 y + 4 z + 11 x, 2 2 2 2 2 18 x y - 15 x + 3 x z + 3 z, 18 x y - x z - x + 20 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=25.3MB, alloc=32.3MB, time=0.47 memory used=44.6MB, alloc=56.3MB, time=0.76 memory used=85.9MB, alloc=60.3MB, time=1.35 memory used=127.6MB, alloc=68.3MB, time=1.93 memory used=168.8MB, alloc=68.3MB, time=2.48 memory used=212.7MB, alloc=68.3MB, time=2.92 memory used=252.1MB, alloc=92.3MB, time=3.51 memory used=314.8MB, alloc=92.3MB, time=4.23 memory used=378.3MB, alloc=92.3MB, time=4.88 memory used=441.0MB, alloc=116.3MB, time=5.80 memory used=509.7MB, alloc=372.3MB, time=6.76 memory used=595.8MB, alloc=396.3MB, time=8.02 memory used=707.6MB, alloc=396.3MB, time=9.62 memory used=819.7MB, alloc=420.3MB, time=11.14 memory used=942.7MB, alloc=420.3MB, time=12.75 memory used=1035.0MB, alloc=420.3MB, time=14.44 memory used=1125.2MB, alloc=420.3MB, time=16.25 memory used=1248.4MB, alloc=444.3MB, time=17.70 memory used=1390.0MB, alloc=444.3MB, time=19.33 memory used=1524.3MB, alloc=468.3MB, time=21.51 memory used=1658.7MB, alloc=468.3MB, time=23.68 memory used=1779.8MB, alloc=468.3MB, time=24.54 memory used=1891.9MB, alloc=468.3MB, time=27.47 memory used=1966.1MB, alloc=468.3MB, time=27.81 memory used=2069.9MB, alloc=468.3MB, time=28.35 memory used=2180.5MB, alloc=468.3MB, time=31.37 memory used=2254.7MB, alloc=468.3MB, time=31.70 memory used=2408.9MB, alloc=492.3MB, time=33.26 memory used=2524.1MB, alloc=492.3MB, time=34.23 memory used=2623.6MB, alloc=492.3MB, time=34.67 memory used=2766.0MB, alloc=492.3MB, time=36.58 memory used=2963.9MB, alloc=492.3MB, time=40.62 memory used=3073.8MB, alloc=492.3MB, time=41.94 memory used=3197.5MB, alloc=516.3MB, time=43.47 memory used=3288.4MB, alloc=516.3MB, time=45.16 memory used=3373.8MB, alloc=516.3MB, time=46.70 memory used=3441.9MB, alloc=516.3MB, time=48.07 memory used=3519.2MB, alloc=516.3MB, time=49.61 memory used=3590.3MB, alloc=516.3MB, time=50.93 memory used=3687.8MB, alloc=516.3MB, time=52.05 memory used=3749.7MB, alloc=516.3MB, time=52.96 memory used=3817.7MB, alloc=516.3MB, time=54.34 memory used=3872.7MB, alloc=516.3MB, time=55.30 memory used=3927.8MB, alloc=516.3MB, time=56.52 memory used=4003.8MB, alloc=516.3MB, time=58.39 memory used=4074.7MB, alloc=516.3MB, time=60.12 memory used=4133.2MB, alloc=516.3MB, time=61.51 memory used=4344.8MB, alloc=540.3MB, time=65.39 memory used=4501.2MB, alloc=564.3MB, time=67.30 memory used=4707.2MB, alloc=564.3MB, time=69.41 memory used=4937.1MB, alloc=588.3MB, time=72.50 memory used=5071.9MB, alloc=588.3MB, time=73.35 memory used=5227.9MB, alloc=588.3MB, time=77.29 memory used=5351.1MB, alloc=588.3MB, time=77.97 memory used=5457.1MB, alloc=588.3MB, time=78.55 memory used=5674.4MB, alloc=588.3MB, time=79.46 memory used=5803.4MB, alloc=588.3MB, time=80.38 memory used=5936.8MB, alloc=588.3MB, time=81.28 memory used=6097.9MB, alloc=588.3MB, time=85.45 memory used=6219.8MB, alloc=588.3MB, time=86.10 memory used=6326.7MB, alloc=588.3MB, time=86.72 memory used=6538.8MB, alloc=588.3MB, time=87.66 memory used=6795.0MB, alloc=588.3MB, time=91.55 memory used=7035.0MB, alloc=612.3MB, time=94.76 memory used=7237.5MB, alloc=612.3MB, time=97.98 memory used=7384.2MB, alloc=612.3MB, time=100.87 memory used=7545.9MB, alloc=636.3MB, time=104.35 memory used=7764.5MB, alloc=636.3MB, time=107.18 memory used=7921.4MB, alloc=636.3MB, time=109.78 memory used=8175.8MB, alloc=660.3MB, time=113.84 memory used=8338.7MB, alloc=660.3MB, time=116.49 memory used=8514.1MB, alloc=684.3MB, time=120.55 memory used=8659.8MB, alloc=684.3MB, time=124.12 memory used=8769.5MB, alloc=684.3MB, time=126.54 memory used=8867.8MB, alloc=708.3MB, time=128.47 memory used=8987.6MB, alloc=708.3MB, time=131.42 memory used=9088.4MB, alloc=708.3MB, time=133.95 memory used=9449.3MB, alloc=732.3MB, time=140.24 memory used=9822.0MB, alloc=756.3MB, time=147.11 memory used=10147.1MB, alloc=780.3MB, time=153.17 |\^/| 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(); 1428292392 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 3 2 F := [5 y + 4 y z + z + 17 z , -5 x + 5 y z - 10 x z - 8 z, 2 2 -20 y z + 18 y z + 12 x z + y z] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 G := [-4 x y - 8 y z + 13 x + 16 z, 3 x + 17 x y - 20 x z + 19 z, 2 2 2 14 x z + 7 y z + 11 z - 8 z] > Problem := [F,G]; 3 2 3 2 3 2 Problem := [[5 y + 4 y z + z + 17 z , -5 x + 5 y z - 10 x z - 8 z, 2 2 2 2 -20 y z + 18 y z + 12 x z + y z], [-4 x y - 8 y z + 13 x + 16 z, 3 2 2 2 3 x + 17 x y - 20 x z + 19 z, 14 x z + 7 y z + 11 z - 8 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.17 memory used=26.8MB, alloc=32.3MB, time=0.50 memory used=48.0MB, alloc=32.3MB, time=0.82 memory used=67.0MB, alloc=56.3MB, time=1.12 memory used=108.8MB, alloc=60.3MB, time=1.76 memory used=148.2MB, alloc=84.3MB, time=2.36 memory used=208.9MB, alloc=92.3MB, time=3.29 memory used=268.4MB, alloc=116.3MB, time=4.26 memory used=340.8MB, alloc=116.3MB, time=5.40 memory used=408.4MB, alloc=396.3MB, time=6.48 memory used=519.2MB, alloc=396.3MB, time=8.29 memory used=633.1MB, alloc=420.3MB, time=10.01 memory used=763.4MB, alloc=444.3MB, time=12.18 memory used=901.8MB, alloc=468.3MB, time=14.60 memory used=1034.3MB, alloc=468.3MB, time=16.96 memory used=1173.4MB, alloc=492.3MB, time=19.55 memory used=1285.7MB, alloc=492.3MB, time=21.58 memory used=1390.9MB, alloc=492.3MB, time=23.25 memory used=1503.7MB, alloc=492.3MB, time=25.23 memory used=1608.6MB, alloc=492.3MB, time=27.47 memory used=1706.9MB, alloc=516.3MB, time=29.50 memory used=1792.6MB, alloc=516.3MB, time=31.19 memory used=1889.1MB, alloc=516.3MB, time=33.14 memory used=1960.4MB, alloc=516.3MB, time=34.76 memory used=2031.3MB, alloc=516.3MB, time=36.31 memory used=2093.1MB, alloc=516.3MB, time=37.60 memory used=2152.2MB, alloc=516.3MB, time=38.82 memory used=2220.9MB, alloc=516.3MB, time=39.85 memory used=2283.5MB, alloc=516.3MB, time=41.29 memory used=2340.0MB, alloc=516.3MB, time=42.71 memory used=2403.2MB, alloc=516.3MB, time=44.05 memory used=2466.6MB, alloc=540.3MB, time=45.15 memory used=2519.8MB, alloc=540.3MB, time=46.38 memory used=2561.0MB, alloc=540.3MB, time=47.15 memory used=2615.2MB, alloc=540.3MB, time=48.26 memory used=2839.7MB, alloc=564.3MB, time=53.34 memory used=3076.4MB, alloc=588.3MB, time=57.70 memory used=3302.9MB, alloc=612.3MB, time=60.89 memory used=3489.1MB, alloc=636.3MB, time=63.84 memory used=3694.3MB, alloc=660.3MB, time=68.32 memory used=3914.2MB, alloc=660.3MB, time=74.26 memory used=4068.2MB, alloc=684.3MB, time=77.37 memory used=4251.5MB, alloc=708.3MB, time=81.61 memory used=4414.9MB, alloc=708.3MB, time=85.78 memory used=4531.9MB, alloc=708.3MB, time=88.44 memory used=4669.7MB, alloc=708.3MB, time=91.90 memory used=4785.3MB, alloc=708.3MB, time=94.77 memory used=4874.9MB, alloc=732.3MB, time=96.93 memory used=5276.4MB, alloc=756.3MB, time=105.20 memory used=5689.1MB, alloc=780.3MB, time=114.60 memory used=6078.7MB, alloc=804.3MB, time=122.99 memory used=6454.0MB, alloc=828.3MB, time=131.46 memory used=6804.3MB, alloc=852.3MB, time=140.07 memory used=7101.7MB, alloc=876.3MB, time=147.53 memory used=7363.6MB, alloc=900.3MB, time=154.42 memory used=7632.8MB, alloc=924.3MB, time=161.63 |\^/| 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(); 1428292692 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 2 F := [16 x + 19 x y + y z + 14 x z, -20 x y - 12 y z - 17 x + 9, 2 2 19 x z - 11 y z - 11 x z + 20 z] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 3 2 G := [15 x y z - y z - 8 z - 5, -5 x z + 2 y - 6 x + 6 x z, 2 2 2 -12 x y + 17 y + 12 z - 14] > Problem := [F,G]; 3 2 2 2 2 2 Problem := [[16 x + 19 x y + y z + 14 x z, -20 x y - 12 y z - 17 x + 9, 2 2 2 3 19 x z - 11 y z - 11 x z + 20 z], [15 x y z - y z - 8 z - 5, 2 3 2 2 2 2 -5 x z + 2 y - 6 x + 6 x z, -12 x y + 17 y + 12 z - 14]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.18 memory used=25.8MB, alloc=32.3MB, time=0.51 memory used=46.4MB, alloc=36.3MB, time=0.82 memory used=66.0MB, alloc=60.3MB, time=1.11 memory used=109.4MB, alloc=60.3MB, time=1.68 memory used=142.4MB, alloc=60.3MB, time=2.13 memory used=183.6MB, alloc=92.3MB, time=2.76 memory used=253.7MB, alloc=92.3MB, time=3.67 memory used=320.1MB, alloc=92.3MB, time=4.57 memory used=384.7MB, alloc=92.3MB, time=5.22 memory used=451.1MB, alloc=116.3MB, time=6.17 memory used=505.5MB, alloc=372.3MB, time=6.96 memory used=590.9MB, alloc=396.3MB, time=8.28 memory used=702.5MB, alloc=396.3MB, time=9.91 memory used=804.7MB, alloc=420.3MB, time=11.28 memory used=940.8MB, alloc=420.3MB, time=13.11 memory used=1064.0MB, alloc=420.3MB, time=14.66 memory used=1172.9MB, alloc=444.3MB, time=15.90 memory used=1290.5MB, alloc=444.3MB, time=17.75 memory used=1383.6MB, alloc=468.3MB, time=19.01 memory used=1481.7MB, alloc=468.3MB, time=20.69 memory used=1586.2MB, alloc=468.3MB, time=22.21 memory used=1672.8MB, alloc=468.3MB, time=23.39 memory used=1762.4MB, alloc=492.3MB, time=24.64 memory used=1835.7MB, alloc=492.3MB, time=25.88 memory used=1919.8MB, alloc=492.3MB, time=27.21 memory used=2031.6MB, alloc=492.3MB, time=28.70 memory used=2105.1MB, alloc=492.3MB, time=29.88 memory used=2175.4MB, alloc=492.3MB, time=30.83 memory used=2256.2MB, alloc=516.3MB, time=31.90 memory used=2318.6MB, alloc=516.3MB, time=32.98 memory used=2374.7MB, alloc=516.3MB, time=34.05 memory used=2437.5MB, alloc=516.3MB, time=35.23 memory used=2493.3MB, alloc=516.3MB, time=36.36 memory used=2530.6MB, alloc=516.3MB, time=37.12 memory used=2721.7MB, alloc=540.3MB, time=39.96 memory used=2923.7MB, alloc=564.3MB, time=43.26 memory used=3109.8MB, alloc=588.3MB, time=46.45 memory used=3282.5MB, alloc=588.3MB, time=49.24 memory used=3456.8MB, alloc=612.3MB, time=52.04 memory used=3602.6MB, alloc=612.3MB, time=54.46 memory used=3715.3MB, alloc=636.3MB, time=56.67 memory used=3840.5MB, alloc=636.3MB, time=59.23 memory used=4053.5MB, alloc=636.3MB, time=61.81 memory used=4230.3MB, alloc=636.3MB, time=63.71 memory used=4402.6MB, alloc=636.3MB, time=65.09 memory used=4582.3MB, alloc=636.3MB, time=67.29 memory used=4698.6MB, alloc=636.3MB, time=69.43 memory used=4821.1MB, alloc=636.3MB, time=71.49 memory used=4957.3MB, alloc=660.3MB, time=73.28 memory used=5113.8MB, alloc=660.3MB, time=75.84 memory used=5208.3MB, alloc=660.3MB, time=77.91 memory used=5300.3MB, alloc=660.3MB, time=80.13 memory used=5412.0MB, alloc=660.3MB, time=82.76 memory used=5732.0MB, alloc=684.3MB, time=87.29 memory used=6079.9MB, alloc=708.3MB, time=92.81 memory used=6434.5MB, alloc=732.3MB, time=98.34 memory used=6791.3MB, alloc=756.3MB, time=104.32 memory used=7071.6MB, alloc=780.3MB, time=109.11 memory used=7352.5MB, alloc=804.3MB, time=114.46 memory used=7649.7MB, alloc=828.3MB, time=120.08 memory used=7922.3MB, alloc=852.3MB, time=124.84 memory used=8248.0MB, alloc=876.3MB, time=129.26 memory used=8505.8MB, alloc=900.3MB, time=132.76 memory used=8808.4MB, alloc=924.3MB, time=136.81 memory used=9232.0MB, alloc=924.3MB, time=145.61 memory used=9490.2MB, alloc=948.3MB, time=147.49 memory used=9839.9MB, alloc=948.3MB, time=150.77 memory used=10244.3MB, alloc=948.3MB, time=159.99 memory used=10483.4MB, alloc=972.3MB, time=165.58 memory used=10707.7MB, alloc=972.3MB, time=170.99 |\^/| 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(); 1428292992 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 F := [-2 x y - 4 x y - 15 y z - 5 y, -19 y - 8 y z + 14 x - 11 y, 2 2 2 10 x y - 18 y + 20 z + 19 x] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 3 G := [x + 11 x y + 4 y - 4 z, 15 x z + 6 y z - 13 y z - 11 z , 3 2 12 x - 16 x y z + 10 y z] > Problem := [F,G]; 2 3 2 Problem := [[-2 x y - 4 x y - 15 y z - 5 y, -19 y - 8 y z + 14 x - 11 y, 2 2 2 3 10 x y - 18 y + 20 z + 19 x], [x + 11 x y + 4 y - 4 z, 2 2 2 3 3 2 15 x z + 6 y z - 13 y z - 11 z , 12 x - 16 x y z + 10 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.16 memory used=26.2MB, alloc=32.3MB, time=0.48 memory used=46.9MB, alloc=32.3MB, time=0.80 memory used=66.6MB, alloc=56.3MB, time=1.11 memory used=106.9MB, alloc=60.3MB, time=1.70 memory used=145.9MB, alloc=84.3MB, time=2.29 memory used=207.8MB, alloc=92.3MB, time=3.21 memory used=267.9MB, alloc=116.3MB, time=4.15 memory used=344.4MB, alloc=116.3MB, time=5.30 memory used=420.5MB, alloc=372.3MB, time=6.50 memory used=505.3MB, alloc=396.3MB, time=7.81 memory used=612.0MB, alloc=420.3MB, time=9.49 memory used=739.9MB, alloc=420.3MB, time=11.59 memory used=866.6MB, alloc=444.3MB, time=13.67 memory used=1010.5MB, alloc=468.3MB, time=16.08 memory used=1141.8MB, alloc=468.3MB, time=18.25 memory used=1260.2MB, alloc=492.3MB, time=20.31 memory used=1381.9MB, alloc=492.3MB, time=22.64 memory used=1492.4MB, alloc=516.3MB, time=24.71 memory used=1578.3MB, alloc=516.3MB, time=26.24 memory used=1711.5MB, alloc=516.3MB, time=27.76 memory used=1806.3MB, alloc=516.3MB, time=29.78 memory used=1893.2MB, alloc=516.3MB, time=31.59 memory used=1965.5MB, alloc=516.3MB, time=33.00 memory used=2027.7MB, alloc=540.3MB, time=34.15 memory used=2088.6MB, alloc=540.3MB, time=35.36 memory used=2171.6MB, alloc=540.3MB, time=37.32 memory used=2223.8MB, alloc=540.3MB, time=38.45 memory used=2272.0MB, alloc=540.3MB, time=39.46 memory used=2317.9MB, alloc=540.3MB, time=40.45 memory used=2543.2MB, alloc=564.3MB, time=45.00 memory used=2723.7MB, alloc=588.3MB, time=48.00 memory used=2913.0MB, alloc=612.3MB, time=51.80 memory used=3071.5MB, alloc=636.3MB, time=55.33 memory used=3199.6MB, alloc=660.3MB, time=57.67 memory used=3343.7MB, alloc=660.3MB, time=60.99 memory used=3452.1MB, alloc=660.3MB, time=63.24 memory used=3586.8MB, alloc=684.3MB, time=66.66 memory used=3684.0MB, alloc=684.3MB, time=68.80 memory used=3780.3MB, alloc=684.3MB, time=71.23 memory used=4133.7MB, alloc=708.3MB, time=78.19 memory used=4503.5MB, alloc=732.3MB, time=85.59 memory used=4888.2MB, alloc=756.3MB, time=93.92 memory used=5221.4MB, alloc=780.3MB, time=100.65 memory used=5515.2MB, alloc=804.3MB, time=106.99 memory used=5789.0MB, alloc=828.3MB, time=113.28 memory used=6051.6MB, alloc=852.3MB, time=119.20 memory used=6196.6MB, alloc=876.3MB, time=123.10 memory used=6418.2MB, alloc=900.3MB, time=128.91 memory used=6590.8MB, alloc=924.3MB, time=133.72 memory used=7130.0MB, alloc=948.3MB, time=145.41 memory used=7671.2MB, alloc=972.3MB, time=157.36 |\^/| 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(); 1428293292 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 F := [-17 x z - 9 x - 20 x y - 6 x, -4 x + 11 x z - 15 x y, 2 2 2 2 x y z + 13 y z + 16 y z - 4 y ] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 2 G := [17 x y - 9 y z + 11 x + 6, -15 x z - 8 x - 3 y + 13 y z, 2 2 2 x y + 14 z - 17 x - 2 z] > Problem := [F,G]; 2 2 3 2 Problem := [[-17 x z - 9 x - 20 x y - 6 x, -4 x + 11 x z - 15 x y, 2 2 2 2 2 2 2 x y z + 13 y z + 16 y z - 4 y ], [17 x y - 9 y z + 11 x + 6, 2 2 2 2 2 -15 x z - 8 x - 3 y + 13 y z, 2 x y + 14 z - 17 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=4.3MB, alloc=32.3MB, time=0.18 memory used=26.0MB, alloc=32.3MB, time=0.50 memory used=46.1MB, alloc=56.3MB, time=0.83 memory used=86.2MB, alloc=60.3MB, time=1.45 memory used=125.3MB, alloc=84.3MB, time=2.07 memory used=165.6MB, alloc=84.3MB, time=2.69 memory used=227.8MB, alloc=92.3MB, time=3.70 memory used=289.6MB, alloc=116.3MB, time=4.67 memory used=371.5MB, alloc=116.3MB, time=5.98 memory used=441.1MB, alloc=396.3MB, time=7.14 memory used=552.3MB, alloc=396.3MB, time=8.84 memory used=660.1MB, alloc=420.3MB, time=10.57 memory used=789.7MB, alloc=444.3MB, time=12.73 memory used=924.1MB, alloc=468.3MB, time=15.02 memory used=1056.5MB, alloc=468.3MB, time=17.27 memory used=1181.5MB, alloc=492.3MB, time=19.59 memory used=1286.9MB, alloc=492.3MB, time=21.25 memory used=1412.2MB, alloc=516.3MB, time=23.72 memory used=1523.4MB, alloc=516.3MB, time=25.90 memory used=1626.6MB, alloc=516.3MB, time=27.74 memory used=1744.4MB, alloc=516.3MB, time=30.48 memory used=1846.4MB, alloc=540.3MB, time=32.79 memory used=1932.9MB, alloc=540.3MB, time=34.49 memory used=2007.3MB, alloc=540.3MB, time=35.91 memory used=2093.0MB, alloc=540.3MB, time=37.90 memory used=2167.6MB, alloc=540.3MB, time=39.35 memory used=2236.9MB, alloc=540.3MB, time=40.55 memory used=2308.7MB, alloc=540.3MB, time=42.36 memory used=2363.1MB, alloc=540.3MB, time=43.44 memory used=2425.2MB, alloc=540.3MB, time=44.92 memory used=2484.1MB, alloc=540.3MB, time=46.54 memory used=2696.4MB, alloc=564.3MB, time=50.38 memory used=2897.6MB, alloc=588.3MB, time=54.02 memory used=3100.6MB, alloc=612.3MB, time=58.05 memory used=3293.6MB, alloc=612.3MB, time=61.96 memory used=3457.3MB, alloc=636.3MB, time=64.98 memory used=3618.8MB, alloc=636.3MB, time=67.95 memory used=3777.5MB, alloc=636.3MB, time=71.32 memory used=3935.9MB, alloc=660.3MB, time=74.97 memory used=4089.9MB, alloc=660.3MB, time=78.41 memory used=4223.6MB, alloc=660.3MB, time=81.51 memory used=4289.6MB, alloc=660.3MB, time=83.56 memory used=4411.9MB, alloc=660.3MB, time=86.70 memory used=4520.8MB, alloc=684.3MB, time=89.45 memory used=4880.0MB, alloc=708.3MB, time=96.85 memory used=5254.8MB, alloc=732.3MB, time=103.76 memory used=5654.9MB, alloc=756.3MB, time=113.68 memory used=6077.2MB, alloc=780.3MB, time=122.73 memory used=6483.6MB, alloc=804.3MB, time=130.96 memory used=6838.4MB, alloc=828.3MB, time=138.55 memory used=7186.4MB, alloc=852.3MB, time=147.99 |\^/| 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(); 1428293592 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 F := [-11 x - 17 x z + 10 y + 12 z, 5 x + 6 y z + 17 x z + 7 y z, 3 2 -x + 15 x y - 12 y - z] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 G := [11 x z + 13 x y + 16 x z , -2 x y + 5 y z + 11 x y - 6 x, 2 2 2 3 19 x y - 8 x z - 11 y z - 6 z ] > Problem := [F,G]; 3 2 3 2 Problem := [[-11 x - 17 x z + 10 y + 12 z, 5 x + 6 y z + 17 x z + 7 y z, 3 2 2 2 2 -x + 15 x y - 12 y - z], [11 x z + 13 x y + 16 x z , 2 2 2 2 2 3 -2 x y + 5 y z + 11 x y - 6 x, 19 x y - 8 x z - 11 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=4.3MB, alloc=32.3MB, time=0.17 memory used=25.7MB, alloc=32.3MB, time=0.50 memory used=47.8MB, alloc=36.3MB, time=0.76 memory used=67.0MB, alloc=60.3MB, time=1.03 memory used=109.9MB, alloc=68.3MB, time=1.67 memory used=154.4MB, alloc=68.3MB, time=2.15 memory used=204.1MB, alloc=68.3MB, time=2.72 memory used=250.0MB, alloc=68.3MB, time=3.16 memory used=301.1MB, alloc=68.3MB, time=3.77 memory used=346.2MB, alloc=92.3MB, time=4.42 memory used=413.2MB, alloc=92.3MB, time=5.35 memory used=480.6MB, alloc=92.3MB, time=6.14 memory used=546.6MB, alloc=92.3MB, time=7.02 memory used=603.5MB, alloc=92.3MB, time=7.58 memory used=669.2MB, alloc=92.3MB, time=8.23 memory used=723.0MB, alloc=372.3MB, time=9.06 memory used=807.3MB, alloc=372.3MB, time=9.91 memory used=920.0MB, alloc=372.3MB, time=11.30 memory used=1005.9MB, alloc=372.3MB, time=12.49 memory used=1073.0MB, alloc=372.3MB, time=13.04 memory used=1125.1MB, alloc=372.3MB, time=13.48 memory used=1163.5MB, alloc=372.3MB, time=13.65 memory used=1254.7MB, alloc=396.3MB, time=14.83 memory used=1375.5MB, alloc=396.3MB, time=16.35 memory used=1482.0MB, alloc=396.3MB, time=17.77 memory used=1565.4MB, alloc=420.3MB, time=18.52 memory used=1682.4MB, alloc=420.3MB, time=19.79 memory used=1822.5MB, alloc=420.3MB, time=21.23 memory used=1950.2MB, alloc=420.3MB, time=22.88 memory used=2078.5MB, alloc=444.3MB, time=24.43 memory used=2188.0MB, alloc=444.3MB, time=26.30 memory used=2270.8MB, alloc=468.3MB, time=27.54 memory used=2351.5MB, alloc=468.3MB, time=28.50 memory used=2457.7MB, alloc=468.3MB, time=29.89 memory used=2561.3MB, alloc=468.3MB, time=31.22 memory used=2655.0MB, alloc=468.3MB, time=32.37 memory used=2725.0MB, alloc=468.3MB, time=33.42 memory used=2839.9MB, alloc=492.3MB, time=34.45 memory used=2921.4MB, alloc=492.3MB, time=36.05 memory used=2994.8MB, alloc=492.3MB, time=37.28 memory used=3064.1MB, alloc=492.3MB, time=38.40 memory used=3118.9MB, alloc=492.3MB, time=39.29 memory used=3174.9MB, alloc=492.3MB, time=40.08 memory used=3238.0MB, alloc=492.3MB, time=41.03 memory used=3295.4MB, alloc=492.3MB, time=42.15 memory used=3341.0MB, alloc=492.3MB, time=43.13 memory used=3391.6MB, alloc=492.3MB, time=44.02 memory used=3580.2MB, alloc=516.3MB, time=46.44 memory used=3761.7MB, alloc=540.3MB, time=49.08 memory used=3983.4MB, alloc=564.3MB, time=51.23 memory used=4158.7MB, alloc=564.3MB, time=53.81 memory used=4265.8MB, alloc=564.3MB, time=54.39 memory used=4402.9MB, alloc=564.3MB, time=55.24 memory used=4530.9MB, alloc=564.3MB, time=56.12 memory used=4673.5MB, alloc=564.3MB, time=57.24 memory used=4797.3MB, alloc=564.3MB, time=58.34 memory used=5012.8MB, alloc=588.3MB, time=61.15 memory used=5291.1MB, alloc=588.3MB, time=67.19 memory used=5411.6MB, alloc=588.3MB, time=67.87 memory used=5523.7MB, alloc=612.3MB, time=68.47 memory used=5669.8MB, alloc=612.3MB, time=69.47 memory used=5955.2MB, alloc=612.3MB, time=72.06 memory used=6106.6MB, alloc=636.3MB, time=74.92 memory used=6270.6MB, alloc=636.3MB, time=77.14 memory used=6491.7MB, alloc=636.3MB, time=79.89 memory used=6709.0MB, alloc=636.3MB, time=82.59 memory used=6867.8MB, alloc=636.3MB, time=85.21 memory used=7060.8MB, alloc=636.3MB, time=87.82 memory used=7246.0MB, alloc=660.3MB, time=90.49 memory used=7450.2MB, alloc=660.3MB, time=93.69 memory used=7612.3MB, alloc=660.3MB, time=96.02 memory used=7823.5MB, alloc=660.3MB, time=98.13 memory used=7935.6MB, alloc=660.3MB, time=100.26 memory used=8035.8MB, alloc=660.3MB, time=102.03 memory used=8159.0MB, alloc=660.3MB, time=104.49 memory used=8242.7MB, alloc=684.3MB, time=106.38 memory used=8529.7MB, alloc=684.3MB, time=109.37 memory used=8847.4MB, alloc=684.3MB, time=112.98 memory used=9191.7MB, alloc=708.3MB, time=117.27 memory used=9471.2MB, alloc=708.3MB, time=120.88 memory used=9889.5MB, alloc=732.3MB, time=127.11 memory used=10268.2MB, alloc=756.3MB, time=132.01 memory used=10651.1MB, alloc=780.3MB, time=139.24 memory used=11000.5MB, alloc=804.3MB, time=144.63 memory used=11373.0MB, alloc=828.3MB, time=149.78 memory used=11655.1MB, alloc=852.3MB, time=153.20 memory used=11921.2MB, alloc=876.3MB, time=155.76 memory used=12211.7MB, alloc=900.3MB, time=160.99 memory used=12454.5MB, alloc=900.3MB, time=162.78 memory used=12757.5MB, alloc=900.3MB, time=165.73 memory used=13215.6MB, alloc=924.3MB, time=171.02 |\^/| 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(); 1428293892 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 F := [8 x y - 6 x z - 9 x + 19, 14 y - 3 y z + 7 x - 10 y, 2 2 x y z - 7 y + 6 x + 15 z] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 3 2 G := [-x - 4 y z + 9 z + 5, 12 x z + 15 x z + 13 z + 6 y , 2 2 2 -19 y z - 17 x + 12 y - 15 y] > Problem := [F,G]; 2 2 3 2 2 Problem := [[8 x y - 6 x z - 9 x + 19, 14 y - 3 y z + 7 x - 10 y, 2 3 2 2 x y z - 7 y + 6 x + 15 z], [-x - 4 y z + 9 z + 5, 2 2 3 2 2 2 2 12 x z + 15 x z + 13 z + 6 y , -19 y z - 17 x + 12 y - 15 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.5MB, alloc=32.3MB, time=0.18 memory used=25.8MB, alloc=32.3MB, time=0.49 memory used=46.5MB, alloc=60.3MB, time=0.80 memory used=82.1MB, alloc=61.1MB, time=1.23 memory used=123.7MB, alloc=61.1MB, time=1.82 memory used=162.9MB, alloc=85.1MB, time=2.38 memory used=229.1MB, alloc=93.1MB, time=3.35 memory used=296.9MB, alloc=349.1MB, time=4.21 memory used=366.8MB, alloc=349.1MB, time=5.02 memory used=442.9MB, alloc=373.1MB, time=5.91 memory used=531.5MB, alloc=373.1MB, time=7.31 memory used=618.6MB, alloc=397.1MB, time=8.63 memory used=733.2MB, alloc=397.1MB, time=10.28 memory used=856.3MB, alloc=421.1MB, time=11.77 memory used=988.2MB, alloc=445.1MB, time=13.78 memory used=1109.3MB, alloc=445.1MB, time=15.35 memory used=1236.9MB, alloc=445.1MB, time=16.80 memory used=1350.8MB, alloc=445.1MB, time=18.33 memory used=1471.0MB, alloc=469.1MB, time=20.16 memory used=1573.6MB, alloc=469.1MB, time=21.98 memory used=1665.6MB, alloc=469.1MB, time=23.37 memory used=1761.3MB, alloc=493.1MB, time=24.76 memory used=1847.2MB, alloc=493.1MB, time=26.33 memory used=1919.6MB, alloc=493.1MB, time=27.52 memory used=1993.4MB, alloc=493.1MB, time=28.65 memory used=2078.1MB, alloc=493.1MB, time=29.99 memory used=2198.9MB, alloc=517.1MB, time=35.95 memory used=2353.6MB, alloc=541.1MB, time=40.93 memory used=2469.3MB, alloc=541.1MB, time=49.98 memory used=2579.7MB, alloc=541.1MB, time=50.54 memory used=2683.3MB, alloc=541.1MB, time=51.10 memory used=2790.8MB, alloc=541.1MB, time=51.64 memory used=2906.3MB, alloc=541.1MB, time=52.17 memory used=3031.1MB, alloc=541.1MB, time=52.69 memory used=3166.5MB, alloc=541.1MB, time=55.98 memory used=3275.1MB, alloc=541.1MB, time=56.55 memory used=3377.8MB, alloc=541.1MB, time=57.11 memory used=3485.5MB, alloc=541.1MB, time=57.64 memory used=3600.7MB, alloc=541.1MB, time=58.19 memory used=3726.2MB, alloc=541.1MB, time=58.75 memory used=3864.2MB, alloc=541.1MB, time=59.47 memory used=3987.6MB, alloc=541.1MB, time=62.40 memory used=4093.5MB, alloc=541.1MB, time=62.93 memory used=4197.0MB, alloc=541.1MB, time=63.47 memory used=4307.8MB, alloc=541.1MB, time=64.01 memory used=4426.7MB, alloc=541.1MB, time=64.54 memory used=4557.2MB, alloc=541.1MB, time=65.08 memory used=4680.4MB, alloc=541.1MB, time=68.01 memory used=4784.7MB, alloc=541.1MB, time=68.56 memory used=4889.3MB, alloc=541.1MB, time=69.09 memory used=5001.4MB, alloc=541.1MB, time=69.62 memory used=5121.6MB, alloc=541.1MB, time=70.17 memory used=5254.3MB, alloc=541.1MB, time=70.71 memory used=5408.8MB, alloc=541.1MB, time=71.98 memory used=5508.9MB, alloc=541.1MB, time=73.12 memory used=5735.0MB, alloc=541.1MB, time=75.59 memory used=5895.1MB, alloc=541.1MB, time=113.72 memory used=6021.3MB, alloc=541.1MB, time=114.25 memory used=6160.1MB, alloc=541.1MB, time=114.80 memory used=6314.7MB, alloc=541.1MB, time=115.39 memory used=6409.8MB, alloc=541.1MB, time=115.87 memory used=6548.6MB, alloc=541.1MB, time=117.14 memory used=6723.6MB, alloc=541.1MB, time=118.41 memory used=6930.9MB, alloc=541.1MB, time=138.23 memory used=7040.3MB, alloc=541.1MB, time=138.77 memory used=7164.7MB, alloc=541.1MB, time=139.31 memory used=7315.1MB, alloc=541.1MB, time=139.99 memory used=7404.0MB, alloc=541.1MB, time=141.13 memory used=7536.4MB, alloc=541.1MB, time=142.26 memory used=7704.2MB, alloc=541.1MB, time=143.57 memory used=7805.4MB, alloc=541.1MB, time=145.03 memory used=7875.3MB, alloc=541.1MB, time=145.86 memory used=7940.4MB, alloc=541.1MB, time=147.12 memory used=8000.6MB, alloc=541.1MB, time=148.14 memory used=8069.6MB, alloc=541.1MB, time=149.16 memory used=8122.3MB, alloc=541.1MB, time=149.93 memory used=8168.2MB, alloc=541.1MB, time=150.88 memory used=8376.3MB, alloc=565.1MB, time=154.10 memory used=8574.8MB, alloc=589.1MB, time=157.93 memory used=8760.0MB, alloc=613.1MB, time=160.84 memory used=8922.9MB, alloc=637.1MB, time=163.76 memory used=9096.9MB, alloc=637.1MB, time=166.59 memory used=9246.4MB, alloc=637.1MB, time=169.38 memory used=9369.7MB, alloc=661.1MB, time=171.35 memory used=9528.6MB, alloc=661.1MB, time=173.54 memory used=9672.9MB, alloc=661.1MB, time=175.86 memory used=9829.4MB, alloc=685.1MB, time=178.03 memory used=9961.2MB, alloc=685.1MB, time=180.18 memory used=10094.1MB, alloc=685.1MB, time=182.47 memory used=10201.0MB, alloc=685.1MB, time=184.45 memory used=10322.0MB, alloc=709.1MB, time=186.34 memory used=10423.0MB, alloc=709.1MB, time=188.86 memory used=10528.3MB, alloc=709.1MB, time=191.46 |\^/| 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(); 1428294192 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 F := [y z - 8 y z - 8 z + 6, -14 x z + 19 y z - 19 y z - 10 x y, 2 3 17 x y - 5 x y z + 18 z + 15 z] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 2 G := [-7 x y + 10 x z + 11 x z + 3 z , -16 y z + 6 x z + 11 y + z, 2 3 2 2 x y - 15 y - 13 x - 19 x z] > Problem := [F,G]; 2 2 2 2 2 Problem := [[y z - 8 y z - 8 z + 6, -14 x z + 19 y z - 19 y z - 10 x y, 2 3 2 2 2 2 17 x y - 5 x y z + 18 z + 15 z], [-7 x y + 10 x z + 11 x z + 3 z , 2 2 2 3 2 -16 y z + 6 x z + 11 y + z, 2 x y - 15 y - 13 x - 19 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=25.4MB, alloc=32.9MB, time=0.44 memory used=46.9MB, alloc=32.9MB, time=1.05 memory used=69.2MB, alloc=36.9MB, time=1.22 memory used=88.8MB, alloc=37.2MB, time=1.43 memory used=105.5MB, alloc=37.2MB, time=1.74 memory used=121.0MB, alloc=37.2MB, time=1.84 memory used=141.6MB, alloc=37.2MB, time=2.05 memory used=167.1MB, alloc=37.2MB, time=2.58 memory used=178.0MB, alloc=37.2MB, time=2.62 memory used=201.7MB, alloc=61.2MB, time=2.92 memory used=244.8MB, alloc=61.6MB, time=3.16 memory used=289.2MB, alloc=62.9MB, time=4.45 memory used=316.2MB, alloc=62.9MB, time=4.52 memory used=344.5MB, alloc=62.9MB, time=4.66 memory used=373.1MB, alloc=62.9MB, time=4.83 memory used=406.2MB, alloc=62.9MB, time=5.06 memory used=449.6MB, alloc=62.9MB, time=5.59 memory used=508.0MB, alloc=70.9MB, time=6.24 memory used=562.7MB, alloc=70.9MB, time=7.49 memory used=608.1MB, alloc=70.9MB, time=8.01 memory used=648.3MB, alloc=70.9MB, time=8.42 memory used=681.8MB, alloc=70.9MB, time=9.32 memory used=703.4MB, alloc=70.9MB, time=9.39 memory used=727.0MB, alloc=70.9MB, time=9.57 memory used=750.6MB, alloc=70.9MB, time=9.74 memory used=770.8MB, alloc=70.9MB, time=9.82 memory used=802.6MB, alloc=70.9MB, time=10.03 memory used=837.3MB, alloc=70.9MB, time=10.28 memory used=865.7MB, alloc=70.9MB, time=10.54 memory used=900.7MB, alloc=70.9MB, time=12.86 memory used=924.6MB, alloc=70.9MB, time=12.95 memory used=941.8MB, alloc=70.9MB, time=13.01 memory used=961.0MB, alloc=70.9MB, time=13.08 memory used=988.6MB, alloc=70.9MB, time=13.26 memory used=1011.1MB, alloc=70.9MB, time=13.42 memory used=1044.7MB, alloc=83.8MB, time=13.64 memory used=1073.8MB, alloc=83.8MB, time=13.73 memory used=1096.0MB, alloc=83.8MB, time=13.80 memory used=1122.3MB, alloc=83.8MB, time=14.19 memory used=1144.0MB, alloc=83.8MB, time=14.27 memory used=1190.0MB, alloc=83.8MB, time=14.75 memory used=1224.7MB, alloc=83.8MB, time=15.72 memory used=1247.2MB, alloc=83.8MB, time=15.80 memory used=1264.3MB, alloc=83.8MB, time=15.87 memory used=1282.0MB, alloc=83.8MB, time=15.94 memory used=1303.0MB, alloc=83.8MB, time=16.02 memory used=1323.1MB, alloc=83.8MB, time=16.09 memory used=1358.7MB, alloc=83.8MB, time=17.12 memory used=1383.7MB, alloc=83.8MB, time=17.38 memory used=1406.2MB, alloc=83.8MB, time=17.46 memory used=1422.4MB, alloc=83.8MB, time=17.53 memory used=1440.9MB, alloc=83.8MB, time=17.60 memory used=1463.1MB, alloc=83.8MB, time=17.67 memory used=1480.9MB, alloc=83.8MB, time=17.73 memory used=1525.9MB, alloc=107.8MB, time=18.14 memory used=1597.6MB, alloc=107.8MB, time=19.21 memory used=1664.6MB, alloc=107.8MB, time=20.41 memory used=1719.1MB, alloc=107.8MB, time=21.11 memory used=1762.8MB, alloc=107.8MB, time=21.48 memory used=1824.5MB, alloc=107.8MB, time=22.24 memory used=1888.7MB, alloc=387.8MB, time=22.98 memory used=1988.8MB, alloc=387.8MB, time=23.99 memory used=2059.3MB, alloc=387.8MB, time=24.98 memory used=2106.7MB, alloc=387.8MB, time=25.27 memory used=2163.2MB, alloc=387.8MB, time=25.83 memory used=2221.9MB, alloc=387.8MB, time=26.26 memory used=2289.8MB, alloc=387.8MB, time=27.86 memory used=2343.3MB, alloc=387.8MB, time=28.22 memory used=2406.6MB, alloc=387.8MB, time=29.17 memory used=2462.1MB, alloc=387.8MB, time=30.07 memory used=2523.8MB, alloc=387.8MB, time=30.45 memory used=2584.3MB, alloc=387.8MB, time=32.34 memory used=2637.1MB, alloc=387.8MB, time=32.78 memory used=2694.1MB, alloc=387.8MB, time=33.06 memory used=2733.9MB, alloc=387.8MB, time=33.23 memory used=2787.2MB, alloc=387.8MB, time=33.60 memory used=2833.2MB, alloc=387.8MB, time=33.78 memory used=2881.2MB, alloc=387.8MB, time=34.02 memory used=2942.0MB, alloc=387.8MB, time=37.30 memory used=2980.3MB, alloc=387.8MB, time=37.44 memory used=3028.8MB, alloc=387.8MB, time=37.72 memory used=3074.8MB, alloc=387.8MB, time=37.95 memory used=3170.9MB, alloc=387.8MB, time=39.19 memory used=3285.4MB, alloc=387.8MB, time=41.09 memory used=3398.4MB, alloc=387.8MB, time=43.21 memory used=3505.7MB, alloc=387.8MB, time=44.92 memory used=3610.8MB, alloc=411.8MB, time=46.48 memory used=3746.1MB, alloc=411.8MB, time=49.54 memory used=3808.9MB, alloc=411.8MB, time=50.28 memory used=3924.9MB, alloc=411.8MB, time=51.35 memory used=4045.6MB, alloc=411.8MB, time=54.17 memory used=4132.6MB, alloc=411.8MB, time=55.04 memory used=4248.4MB, alloc=435.8MB, time=56.32 memory used=4369.7MB, alloc=459.8MB, time=57.66 memory used=4482.4MB, alloc=459.8MB, time=59.16 memory used=4580.5MB, alloc=483.8MB, time=60.52 memory used=4697.0MB, alloc=483.8MB, time=61.73 memory used=4817.7MB, alloc=483.8MB, time=64.84 memory used=4914.9MB, alloc=483.8MB, time=65.65 memory used=5007.0MB, alloc=483.8MB, time=66.28 memory used=5126.6MB, alloc=483.8MB, time=69.33 memory used=5267.1MB, alloc=483.8MB, time=70.70 memory used=5371.4MB, alloc=483.8MB, time=72.74 memory used=5503.3MB, alloc=483.8MB, time=73.86 memory used=5604.6MB, alloc=507.8MB, time=74.57 memory used=5714.0MB, alloc=507.8MB, time=75.18 memory used=5838.2MB, alloc=507.8MB, time=84.48 memory used=5925.1MB, alloc=507.8MB, time=84.85 memory used=6025.3MB, alloc=507.8MB, time=85.23 memory used=6095.9MB, alloc=507.8MB, time=85.55 memory used=6179.7MB, alloc=507.8MB, time=85.85 memory used=6303.9MB, alloc=507.8MB, time=87.25 memory used=6393.8MB, alloc=507.8MB, time=87.69 memory used=6500.9MB, alloc=507.8MB, time=88.20 memory used=6615.5MB, alloc=507.8MB, time=91.56 memory used=6727.2MB, alloc=507.8MB, time=97.99 memory used=6814.1MB, alloc=507.8MB, time=98.35 memory used=6900.7MB, alloc=507.8MB, time=98.68 memory used=6976.9MB, alloc=507.8MB, time=98.98 memory used=7088.4MB, alloc=507.8MB, time=99.52 memory used=7199.8MB, alloc=507.8MB, time=100.13 memory used=7316.1MB, alloc=507.8MB, time=109.09 memory used=7411.7MB, alloc=507.8MB, time=109.90 memory used=7505.9MB, alloc=507.8MB, time=110.26 memory used=7585.1MB, alloc=507.8MB, time=110.59 memory used=7664.1MB, alloc=507.8MB, time=110.90 memory used=7769.8MB, alloc=507.8MB, time=111.48 memory used=7876.3MB, alloc=507.8MB, time=111.96 memory used=7999.6MB, alloc=507.8MB, time=113.48 memory used=8083.3MB, alloc=507.8MB, time=113.84 memory used=8197.3MB, alloc=507.8MB, time=115.12 memory used=8286.7MB, alloc=507.8MB, time=115.52 memory used=8375.3MB, alloc=507.8MB, time=115.89 memory used=8448.6MB, alloc=507.8MB, time=116.24 memory used=8535.9MB, alloc=507.8MB, time=116.61 memory used=8634.0MB, alloc=507.8MB, time=116.97 memory used=8710.2MB, alloc=507.8MB, time=117.28 memory used=8824.3MB, alloc=507.8MB, time=118.52 memory used=8923.5MB, alloc=507.8MB, time=118.94 memory used=9001.3MB, alloc=507.8MB, time=119.31 memory used=9079.8MB, alloc=507.8MB, time=119.67 memory used=9173.2MB, alloc=507.8MB, time=120.03 memory used=9267.2MB, alloc=507.8MB, time=120.36 memory used=9364.6MB, alloc=507.8MB, time=123.53 memory used=9481.0MB, alloc=507.8MB, time=142.20 memory used=9563.3MB, alloc=507.8MB, time=142.60 memory used=9662.1MB, alloc=507.8MB, time=142.97 memory used=9738.4MB, alloc=507.8MB, time=143.29 memory used=9810.8MB, alloc=507.8MB, time=143.60 memory used=9895.4MB, alloc=507.8MB, time=143.91 memory used=10004.6MB, alloc=507.8MB, time=144.25 memory used=10116.5MB, alloc=507.8MB, time=145.54 memory used=10218.8MB, alloc=507.8MB, time=146.82 memory used=10375.7MB, alloc=507.8MB, time=150.81 memory used=10462.6MB, alloc=507.8MB, time=151.17 memory used=10535.7MB, alloc=507.8MB, time=151.48 memory used=10647.7MB, alloc=507.8MB, time=152.59 memory used=10742.6MB, alloc=507.8MB, time=155.18 memory used=10873.1MB, alloc=507.8MB, time=157.99 memory used=10980.9MB, alloc=507.8MB, time=158.98 memory used=11044.7MB, alloc=507.8MB, time=159.92 memory used=11101.9MB, alloc=507.8MB, time=160.74 memory used=11169.3MB, alloc=531.8MB, time=161.69 memory used=11242.0MB, alloc=531.8MB, time=163.09 memory used=11321.3MB, alloc=531.8MB, time=164.84 memory used=11375.9MB, alloc=531.8MB, time=165.75 memory used=11425.1MB, alloc=531.8MB, time=166.61 memory used=11481.5MB, alloc=531.8MB, time=167.53 memory used=11541.8MB, alloc=531.8MB, time=168.55 memory used=11581.6MB, alloc=531.8MB, time=169.36 memory used=11781.0MB, alloc=555.8MB, time=171.83 memory used=11982.2MB, alloc=555.8MB, time=174.29 memory used=12239.5MB, alloc=579.8MB, time=177.68 |\^/| 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(); 1428294492 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [10 y z - 4 x y + z - 14, -12 x y - 7 x z - 19 y - 7, 2 2 2 18 x y + 6 x z - 15 y z ] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 G := [18 x y - 18 x y z - 10 x + z , -2 y z + y z - 6 x z + 7, 2 2 -18 x z - 16 x y z - 16 x + 17 z] > Problem := [F,G]; 2 2 Problem := [[10 y z - 4 x y + z - 14, -12 x y - 7 x z - 19 y - 7, 2 2 2 2 2 2 18 x y + 6 x z - 15 y z ], [18 x y - 18 x y z - 10 x + z , 2 2 2 2 -2 y z + y z - 6 x z + 7, -18 x z - 16 x y z - 16 x + 17 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=25.2MB, alloc=32.3MB, time=0.49 memory used=45.6MB, alloc=36.3MB, time=0.78 memory used=64.9MB, alloc=60.3MB, time=1.05 memory used=107.2MB, alloc=60.3MB, time=1.66 memory used=143.9MB, alloc=60.3MB, time=2.13 memory used=185.1MB, alloc=92.3MB, time=2.75 memory used=255.4MB, alloc=92.3MB, time=3.68 memory used=320.7MB, alloc=116.3MB, time=4.47 memory used=390.6MB, alloc=372.3MB, time=5.25 memory used=487.9MB, alloc=372.3MB, time=6.48 memory used=580.5MB, alloc=396.3MB, time=7.74 memory used=695.4MB, alloc=420.3MB, time=9.40 memory used=814.1MB, alloc=444.3MB, time=11.14 memory used=952.8MB, alloc=444.3MB, time=12.55 memory used=1088.5MB, alloc=444.3MB, time=14.15 memory used=1190.3MB, alloc=444.3MB, time=15.80 memory used=1294.9MB, alloc=468.3MB, time=17.27 memory used=1380.8MB, alloc=468.3MB, time=18.64 memory used=1474.0MB, alloc=468.3MB, time=20.21 memory used=1554.5MB, alloc=468.3MB, time=21.45 memory used=1616.0MB, alloc=468.3MB, time=22.57 memory used=1693.6MB, alloc=468.3MB, time=23.77 memory used=1796.2MB, alloc=468.3MB, time=24.97 memory used=1859.3MB, alloc=468.3MB, time=26.21 memory used=1930.6MB, alloc=468.3MB, time=27.57 memory used=1983.9MB, alloc=492.3MB, time=28.70 memory used=2045.5MB, alloc=492.3MB, time=29.89 memory used=2094.5MB, alloc=492.3MB, time=30.85 memory used=2152.9MB, alloc=492.3MB, time=32.08 memory used=2211.5MB, alloc=492.3MB, time=33.39 memory used=2419.7MB, alloc=516.3MB, time=36.32 memory used=2658.5MB, alloc=516.3MB, time=39.16 memory used=2862.9MB, alloc=540.3MB, time=42.10 memory used=3041.0MB, alloc=564.3MB, time=45.13 memory used=3210.4MB, alloc=564.3MB, time=46.73 memory used=3357.0MB, alloc=564.3MB, time=47.99 memory used=3560.9MB, alloc=564.3MB, time=50.73 memory used=3776.5MB, alloc=588.3MB, time=53.79 memory used=3934.2MB, alloc=588.3MB, time=56.30 memory used=4127.3MB, alloc=588.3MB, time=58.84 memory used=4263.3MB, alloc=612.3MB, time=61.67 memory used=4401.7MB, alloc=612.3MB, time=64.43 memory used=4530.3MB, alloc=612.3MB, time=66.87 memory used=4655.4MB, alloc=636.3MB, time=69.45 memory used=4769.9MB, alloc=636.3MB, time=71.77 memory used=4886.9MB, alloc=636.3MB, time=73.74 memory used=5008.2MB, alloc=636.3MB, time=76.14 memory used=5124.0MB, alloc=636.3MB, time=78.07 memory used=5191.9MB, alloc=636.3MB, time=79.87 memory used=5296.6MB, alloc=636.3MB, time=82.13 memory used=5593.0MB, alloc=660.3MB, time=85.77 memory used=5759.2MB, alloc=660.3MB, time=87.31 memory used=6061.4MB, alloc=684.3MB, time=91.66 memory used=6407.5MB, alloc=708.3MB, time=97.58 memory used=6773.1MB, alloc=732.3MB, time=103.96 memory used=7135.9MB, alloc=756.3MB, time=110.28 memory used=7431.0MB, alloc=780.3MB, time=116.19 memory used=7686.7MB, alloc=804.3MB, time=120.90 memory used=7932.2MB, alloc=828.3MB, time=127.01 memory used=8169.0MB, alloc=852.3MB, time=132.32 memory used=8406.7MB, alloc=876.3MB, time=138.32 memory used=8630.1MB, alloc=900.3MB, time=143.46 memory used=8914.1MB, alloc=924.3MB, time=148.25 memory used=9137.2MB, alloc=948.3MB, time=153.31 memory used=9363.4MB, alloc=972.3MB, time=157.82 |\^/| 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(); 1428294792 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 F := [-14 x z - 3 z + 14 y z + 14, 6 x y - 10 x + 20 z + 12, 2 2 12 x z - 13 x z + 5 z] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 G := [11 x y - 16 y - 8 y - 5, 14 x z - 3 y + 4 x z + 17 z, 2 2 17 x - 20 x y - 7 z - 17 x] > Problem := [F,G]; 2 3 2 Problem := [[-14 x z - 3 z + 14 y z + 14, 6 x y - 10 x + 20 z + 12, 2 2 2 2 12 x z - 13 x z + 5 z], [11 x y - 16 y - 8 y - 5, 2 3 2 2 14 x z - 3 y + 4 x z + 17 z, 17 x - 20 x y - 7 z - 17 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.5MB, alloc=32.3MB, time=0.48 memory used=47.3MB, alloc=32.3MB, time=0.78 memory used=67.1MB, alloc=56.3MB, time=1.09 memory used=106.7MB, alloc=60.3MB, time=1.68 memory used=144.9MB, alloc=60.3MB, time=2.23 memory used=184.0MB, alloc=84.3MB, time=2.81 memory used=229.6MB, alloc=84.3MB, time=3.48 memory used=294.5MB, alloc=92.3MB, time=4.40 memory used=356.2MB, alloc=116.3MB, time=5.27 memory used=433.8MB, alloc=116.3MB, time=6.41 memory used=506.4MB, alloc=396.3MB, time=7.55 memory used=612.7MB, alloc=396.3MB, time=9.17 memory used=716.8MB, alloc=420.3MB, time=10.84 memory used=843.1MB, alloc=444.3MB, time=12.92 memory used=992.6MB, alloc=468.3MB, time=15.35 memory used=1146.2MB, alloc=468.3MB, time=17.79 memory used=1291.5MB, alloc=492.3MB, time=20.22 memory used=1399.4MB, alloc=516.3MB, time=21.91 memory used=1513.1MB, alloc=516.3MB, time=23.69 memory used=1621.2MB, alloc=516.3MB, time=25.56 memory used=1715.9MB, alloc=516.3MB, time=26.89 memory used=1817.1MB, alloc=540.3MB, time=28.27 memory used=1887.7MB, alloc=540.3MB, time=29.67 memory used=1965.2MB, alloc=540.3MB, time=30.90 memory used=2039.2MB, alloc=540.3MB, time=32.00 memory used=2125.4MB, alloc=564.3MB, time=33.10 memory used=2189.8MB, alloc=564.3MB, time=34.57 memory used=2250.5MB, alloc=564.3MB, time=35.66 memory used=2289.4MB, alloc=564.3MB, time=36.49 memory used=2350.8MB, alloc=564.3MB, time=37.43 memory used=2385.4MB, alloc=564.3MB, time=38.17 memory used=2637.4MB, alloc=588.3MB, time=42.29 memory used=2855.6MB, alloc=612.3MB, time=45.68 memory used=3023.8MB, alloc=636.3MB, time=48.78 memory used=3199.4MB, alloc=660.3MB, time=51.17 memory used=3355.0MB, alloc=684.3MB, time=54.22 memory used=3489.9MB, alloc=684.3MB, time=56.61 memory used=3625.4MB, alloc=684.3MB, time=59.21 memory used=3765.5MB, alloc=684.3MB, time=62.24 memory used=3874.8MB, alloc=684.3MB, time=64.25 memory used=4015.1MB, alloc=684.3MB, time=67.03 memory used=4110.2MB, alloc=708.3MB, time=69.03 memory used=4215.4MB, alloc=708.3MB, time=70.96 memory used=4473.5MB, alloc=708.3MB, time=78.28 memory used=4676.5MB, alloc=708.3MB, time=84.42 memory used=4917.8MB, alloc=708.3MB, time=86.73 memory used=5330.9MB, alloc=732.3MB, time=92.34 memory used=5711.4MB, alloc=756.3MB, time=99.40 memory used=6081.0MB, alloc=780.3MB, time=105.53 memory used=6427.7MB, alloc=804.3MB, time=111.50 memory used=6799.4MB, alloc=828.3MB, time=117.42 memory used=7171.9MB, alloc=852.3MB, time=125.10 memory used=7461.4MB, alloc=876.3MB, time=131.33 memory used=7841.1MB, alloc=900.3MB, time=139.58 memory used=8245.3MB, alloc=924.3MB, time=147.43 memory used=8550.0MB, alloc=948.3MB, time=152.79 |\^/| 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(); 1428295092 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 2 F := [12 x y + 17 x + 7 x z + 20 y , 10 y z + x - 20 z + 18 x, 2 3 2 -15 y z - 8 z + 2 y - 8 z] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 2 G := [-20 x y + 9 x y + 10 z - 2 z, 12 y z - 17 x + 9 z - 17 x, 3 2 2 -10 x + 19 x y - 11 x y z + 14 x z ] > Problem := [F,G]; 2 2 2 2 2 2 Problem := [[12 x y + 17 x + 7 x z + 20 y , 10 y z + x - 20 z + 18 x, 2 3 2 2 2 3 -15 y z - 8 z + 2 y - 8 z], [-20 x y + 9 x y + 10 z - 2 z, 2 2 2 3 2 2 12 y z - 17 x + 9 z - 17 x, -10 x + 19 x y - 11 x y z + 14 x z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.17 memory used=26.5MB, alloc=32.3MB, time=0.44 memory used=48.0MB, alloc=60.3MB, time=0.74 memory used=89.2MB, alloc=60.3MB, time=1.20 memory used=130.6MB, alloc=60.3MB, time=1.58 memory used=173.8MB, alloc=60.3MB, time=2.07 memory used=202.9MB, alloc=60.3MB, time=2.21 memory used=252.8MB, alloc=60.3MB, time=2.55 memory used=299.5MB, alloc=68.3MB, time=3.07 memory used=328.6MB, alloc=68.3MB, time=3.35 memory used=355.2MB, alloc=68.3MB, time=3.49 memory used=403.5MB, alloc=68.3MB, time=4.07 memory used=448.0MB, alloc=68.3MB, time=4.65 memory used=492.5MB, alloc=92.3MB, time=5.22 memory used=558.9MB, alloc=92.3MB, time=5.94 memory used=601.3MB, alloc=92.3MB, time=6.25 memory used=654.8MB, alloc=92.3MB, time=6.78 memory used=711.7MB, alloc=92.3MB, time=7.26 memory used=774.5MB, alloc=92.3MB, time=7.78 memory used=836.3MB, alloc=92.3MB, time=8.47 memory used=897.0MB, alloc=92.3MB, time=9.09 memory used=959.5MB, alloc=116.3MB, time=9.93 memory used=1021.3MB, alloc=116.3MB, time=10.66 memory used=1087.8MB, alloc=372.3MB, time=11.48 memory used=1174.1MB, alloc=372.3MB, time=12.31 memory used=1243.0MB, alloc=372.3MB, time=12.91 memory used=1299.2MB, alloc=372.3MB, time=13.95 memory used=1334.7MB, alloc=372.3MB, time=14.10 memory used=1387.3MB, alloc=372.3MB, time=14.57 memory used=1435.9MB, alloc=372.3MB, time=14.95 memory used=1477.1MB, alloc=372.3MB, time=15.12 memory used=1517.0MB, alloc=372.3MB, time=15.27 memory used=1559.2MB, alloc=372.3MB, time=15.57 memory used=1601.4MB, alloc=372.3MB, time=15.74 memory used=1641.8MB, alloc=372.3MB, time=15.89 memory used=1684.2MB, alloc=372.3MB, time=17.17 memory used=1738.6MB, alloc=372.3MB, time=19.87 memory used=1773.6MB, alloc=372.3MB, time=20.02 memory used=1814.5MB, alloc=372.3MB, time=20.16 memory used=1847.2MB, alloc=372.3MB, time=20.28 memory used=1889.1MB, alloc=372.3MB, time=20.55 memory used=1928.5MB, alloc=372.3MB, time=20.82 memory used=1981.0MB, alloc=396.3MB, time=21.29 memory used=2039.2MB, alloc=396.3MB, time=21.50 memory used=2093.8MB, alloc=396.3MB, time=21.68 memory used=2141.3MB, alloc=396.3MB, time=21.84 memory used=2197.4MB, alloc=396.3MB, time=22.03 memory used=2264.4MB, alloc=396.3MB, time=22.21 memory used=2326.8MB, alloc=396.3MB, time=22.76 memory used=2381.6MB, alloc=396.3MB, time=22.99 memory used=2445.1MB, alloc=396.3MB, time=23.20 memory used=2488.8MB, alloc=396.3MB, time=23.38 memory used=2540.3MB, alloc=396.3MB, time=23.56 memory used=2601.4MB, alloc=396.3MB, time=23.74 memory used=2657.2MB, alloc=396.3MB, time=23.90 memory used=2737.9MB, alloc=396.3MB, time=35.28 memory used=2793.4MB, alloc=396.3MB, time=35.48 memory used=2845.7MB, alloc=396.3MB, time=35.65 memory used=2908.8MB, alloc=396.3MB, time=35.83 memory used=2950.3MB, alloc=396.3MB, time=35.97 memory used=2998.1MB, alloc=396.3MB, time=36.12 memory used=3061.5MB, alloc=396.3MB, time=36.44 memory used=3149.5MB, alloc=396.3MB, time=37.08 memory used=3272.5MB, alloc=396.3MB, time=38.39 memory used=3390.2MB, alloc=396.3MB, time=39.40 memory used=3464.7MB, alloc=396.3MB, time=40.67 memory used=3553.9MB, alloc=396.3MB, time=41.40 memory used=3679.8MB, alloc=396.3MB, time=42.43 memory used=3764.4MB, alloc=396.3MB, time=43.11 memory used=3825.4MB, alloc=396.3MB, time=44.26 memory used=3881.9MB, alloc=396.3MB, time=44.55 memory used=3944.6MB, alloc=396.3MB, time=45.10 memory used=4007.7MB, alloc=396.3MB, time=45.52 memory used=4059.8MB, alloc=396.3MB, time=45.71 memory used=4100.6MB, alloc=396.3MB, time=45.88 memory used=4163.0MB, alloc=396.3MB, time=46.30 memory used=4211.1MB, alloc=396.3MB, time=46.50 memory used=4280.3MB, alloc=396.3MB, time=50.47 memory used=4328.0MB, alloc=396.3MB, time=50.66 memory used=4381.5MB, alloc=396.3MB, time=50.84 memory used=4420.5MB, alloc=396.3MB, time=50.99 memory used=4483.6MB, alloc=396.3MB, time=51.58 memory used=4536.1MB, alloc=396.3MB, time=51.78 memory used=4583.8MB, alloc=396.3MB, time=51.97 memory used=4623.0MB, alloc=396.3MB, time=52.15 memory used=4668.4MB, alloc=396.3MB, time=52.34 memory used=4721.6MB, alloc=396.3MB, time=52.52 memory used=4777.2MB, alloc=396.3MB, time=52.70 memory used=4832.1MB, alloc=396.3MB, time=53.35 memory used=4881.1MB, alloc=396.3MB, time=53.56 memory used=4941.3MB, alloc=396.3MB, time=53.78 memory used=4979.3MB, alloc=396.3MB, time=53.97 memory used=5021.6MB, alloc=396.3MB, time=54.15 memory used=5071.2MB, alloc=396.3MB, time=54.33 memory used=5129.5MB, alloc=396.3MB, time=54.52 memory used=5173.5MB, alloc=396.3MB, time=54.67 memory used=5246.8MB, alloc=396.3MB, time=66.14 memory used=5300.0MB, alloc=396.3MB, time=66.35 memory used=5342.3MB, alloc=396.3MB, time=66.52 memory used=5397.7MB, alloc=396.3MB, time=66.71 memory used=5441.5MB, alloc=396.3MB, time=66.87 memory used=5480.0MB, alloc=396.3MB, time=67.02 memory used=5523.5MB, alloc=396.3MB, time=67.17 memory used=5583.5MB, alloc=396.3MB, time=67.47 memory used=5664.1MB, alloc=396.3MB, time=68.22 memory used=5758.2MB, alloc=396.3MB, time=69.19 memory used=5853.2MB, alloc=396.3MB, time=70.61 memory used=5942.4MB, alloc=396.3MB, time=71.34 memory used=6040.7MB, alloc=420.3MB, time=72.20 memory used=6164.5MB, alloc=420.3MB, time=73.60 memory used=6291.0MB, alloc=444.3MB, time=75.03 memory used=6398.3MB, alloc=444.3MB, time=76.46 memory used=6520.0MB, alloc=444.3MB, time=78.45 memory used=6673.9MB, alloc=468.3MB, time=80.22 memory used=6791.0MB, alloc=468.3MB, time=81.70 memory used=6895.4MB, alloc=492.3MB, time=82.96 memory used=7001.0MB, alloc=492.3MB, time=84.43 memory used=7087.2MB, alloc=492.3MB, time=85.65 memory used=7235.2MB, alloc=492.3MB, time=87.01 memory used=7344.7MB, alloc=492.3MB, time=87.99 memory used=7468.4MB, alloc=492.3MB, time=89.49 memory used=7570.5MB, alloc=492.3MB, time=90.20 memory used=7670.8MB, alloc=492.3MB, time=90.85 memory used=7755.4MB, alloc=492.3MB, time=91.20 memory used=7863.8MB, alloc=492.3MB, time=91.92 memory used=7954.1MB, alloc=492.3MB, time=92.40 memory used=8061.7MB, alloc=492.3MB, time=96.58 memory used=8144.1MB, alloc=492.3MB, time=96.93 memory used=8244.0MB, alloc=492.3MB, time=97.67 memory used=8329.9MB, alloc=492.3MB, time=98.07 memory used=8408.9MB, alloc=492.3MB, time=98.42 memory used=8510.0MB, alloc=492.3MB, time=98.80 memory used=8575.2MB, alloc=492.3MB, time=99.11 memory used=8680.6MB, alloc=492.3MB, time=100.02 memory used=8761.1MB, alloc=492.3MB, time=100.40 memory used=8845.9MB, alloc=492.3MB, time=100.77 memory used=8940.2MB, alloc=492.3MB, time=101.14 memory used=9027.8MB, alloc=492.3MB, time=107.46 memory used=9123.6MB, alloc=492.3MB, time=113.51 memory used=9217.8MB, alloc=492.3MB, time=113.88 memory used=9285.9MB, alloc=492.3MB, time=114.21 memory used=9368.6MB, alloc=492.3MB, time=114.55 memory used=9479.7MB, alloc=492.3MB, time=115.23 memory used=9616.8MB, alloc=492.3MB, time=116.70 memory used=9762.8MB, alloc=492.3MB, time=117.90 memory used=9916.5MB, alloc=492.3MB, time=119.78 memory used=10016.3MB, alloc=492.3MB, time=121.21 memory used=10087.0MB, alloc=492.3MB, time=122.30 memory used=10150.7MB, alloc=492.3MB, time=123.21 memory used=10223.0MB, alloc=492.3MB, time=124.17 memory used=10300.1MB, alloc=492.3MB, time=125.61 memory used=10396.0MB, alloc=492.3MB, time=127.07 memory used=10489.9MB, alloc=492.3MB, time=128.85 memory used=10602.5MB, alloc=492.3MB, time=130.78 memory used=10734.9MB, alloc=516.3MB, time=131.96 memory used=10848.4MB, alloc=516.3MB, time=132.68 memory used=11033.2MB, alloc=516.3MB, time=137.87 memory used=11139.8MB, alloc=516.3MB, time=138.92 memory used=11224.8MB, alloc=516.3MB, time=139.99 memory used=11291.6MB, alloc=516.3MB, time=141.15 memory used=11372.9MB, alloc=516.3MB, time=142.30 memory used=11507.2MB, alloc=516.3MB, time=143.94 memory used=11554.9MB, alloc=516.3MB, time=144.80 memory used=11607.5MB, alloc=516.3MB, time=145.77 memory used=11660.5MB, alloc=516.3MB, time=146.71 memory used=11855.5MB, alloc=516.3MB, time=149.43 memory used=12069.4MB, alloc=540.3MB, time=151.73 memory used=12295.7MB, alloc=540.3MB, time=154.63 memory used=12494.1MB, alloc=564.3MB, time=157.56 memory used=12707.5MB, alloc=588.3MB, time=160.61 memory used=12904.5MB, alloc=612.3MB, time=163.64 memory used=13089.4MB, alloc=612.3MB, time=166.50 memory used=13273.7MB, alloc=636.3MB, time=169.31 memory used=13467.1MB, alloc=636.3MB, time=172.51 memory used=13738.7MB, alloc=636.3MB, time=174.98 memory used=13940.7MB, alloc=636.3MB, time=177.10 memory used=14116.3MB, alloc=636.3MB, time=179.68 memory used=14290.4MB, alloc=660.3MB, time=182.31 memory used=14527.7MB, alloc=660.3MB, time=184.70 memory used=14704.8MB, alloc=660.3MB, time=186.06 memory used=14860.4MB, alloc=660.3MB, time=186.92 memory used=14985.4MB, alloc=660.3MB, time=187.67 memory used=15165.7MB, alloc=660.3MB, time=188.70 memory used=15317.7MB, alloc=660.3MB, time=189.55 memory used=15446.1MB, alloc=660.3MB, time=190.28 |\^/| 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(); 1428295392 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 3 2 3 2 F := [3 x y + 14 y + 12 z - 10 z , -z - 2 y + 17 y z + 1, 2 2 2 x z - 18 x + 18 y z + 1] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 G := [20 x y + 4 y z + 6 y z + 2 y z, -12 x y z - 3 y + 3 x - 7 x, 2 2 6 x y - 7 x y z + 5 y z + 11 x z] > Problem := [F,G]; 2 3 3 2 3 2 Problem := [[3 x y + 14 y + 12 z - 10 z , -z - 2 y + 17 y z + 1, 2 2 2 2 2 2 x z - 18 x + 18 y z + 1], [20 x y + 4 y z + 6 y z + 2 y z, 3 2 2 2 -12 x y z - 3 y + 3 x - 7 x, 6 x y - 7 x y z + 5 y z + 11 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.17 memory used=25.2MB, alloc=32.3MB, time=0.48 memory used=44.4MB, alloc=56.3MB, time=0.76 memory used=85.8MB, alloc=60.3MB, time=1.34 memory used=128.4MB, alloc=68.3MB, time=1.90 memory used=174.2MB, alloc=68.3MB, time=2.44 memory used=216.3MB, alloc=68.3MB, time=2.90 memory used=265.5MB, alloc=92.3MB, time=3.50 memory used=305.6MB, alloc=92.3MB, time=3.69 memory used=369.4MB, alloc=92.3MB, time=4.46 memory used=432.2MB, alloc=92.3MB, time=5.33 memory used=491.0MB, alloc=348.3MB, time=6.09 memory used=558.7MB, alloc=372.3MB, time=7.00 memory used=645.8MB, alloc=372.3MB, time=8.28 memory used=732.8MB, alloc=396.3MB, time=9.54 memory used=840.6MB, alloc=396.3MB, time=10.75 memory used=922.8MB, alloc=396.3MB, time=11.47 memory used=1000.3MB, alloc=396.3MB, time=11.88 memory used=1080.8MB, alloc=396.3MB, time=13.35 memory used=1142.8MB, alloc=396.3MB, time=13.69 memory used=1220.1MB, alloc=396.3MB, time=14.05 memory used=1295.8MB, alloc=396.3MB, time=15.53 memory used=1383.6MB, alloc=396.3MB, time=16.35 memory used=1490.5MB, alloc=396.3MB, time=17.74 memory used=1603.9MB, alloc=420.3MB, time=19.15 memory used=1708.0MB, alloc=420.3MB, time=20.73 memory used=1833.3MB, alloc=444.3MB, time=22.32 memory used=1936.1MB, alloc=444.3MB, time=23.27 memory used=2039.1MB, alloc=444.3MB, time=23.79 memory used=2133.1MB, alloc=444.3MB, time=24.30 memory used=2213.5MB, alloc=444.3MB, time=24.64 memory used=2321.7MB, alloc=444.3MB, time=28.65 memory used=2397.7MB, alloc=444.3MB, time=28.95 memory used=2469.0MB, alloc=444.3MB, time=29.33 memory used=2557.1MB, alloc=444.3MB, time=30.00 memory used=2643.0MB, alloc=444.3MB, time=30.36 memory used=2748.6MB, alloc=444.3MB, time=30.91 memory used=2842.0MB, alloc=444.3MB, time=34.62 memory used=2932.0MB, alloc=444.3MB, time=35.33 memory used=3002.8MB, alloc=444.3MB, time=35.62 memory used=3084.2MB, alloc=444.3MB, time=36.01 memory used=3210.1MB, alloc=444.3MB, time=37.84 memory used=3301.3MB, alloc=444.3MB, time=39.16 memory used=3432.9MB, alloc=444.3MB, time=40.40 memory used=3561.0MB, alloc=468.3MB, time=41.97 memory used=3661.0MB, alloc=468.3MB, time=42.48 memory used=3765.2MB, alloc=468.3MB, time=43.96 memory used=3864.7MB, alloc=468.3MB, time=44.50 memory used=3969.8MB, alloc=468.3MB, time=45.93 memory used=4063.2MB, alloc=468.3MB, time=46.35 memory used=4173.1MB, alloc=468.3MB, time=47.74 memory used=4315.6MB, alloc=468.3MB, time=49.37 memory used=4417.8MB, alloc=468.3MB, time=50.82 memory used=4503.3MB, alloc=468.3MB, time=52.28 memory used=4575.0MB, alloc=468.3MB, time=53.54 memory used=4636.9MB, alloc=468.3MB, time=54.69 memory used=4707.2MB, alloc=492.3MB, time=55.96 memory used=4766.5MB, alloc=492.3MB, time=56.77 memory used=4860.7MB, alloc=492.3MB, time=57.79 memory used=4977.3MB, alloc=492.3MB, time=58.73 memory used=5073.5MB, alloc=492.3MB, time=60.30 memory used=5157.7MB, alloc=492.3MB, time=61.25 memory used=5247.7MB, alloc=492.3MB, time=62.92 memory used=5302.2MB, alloc=492.3MB, time=63.73 memory used=5388.9MB, alloc=492.3MB, time=65.33 memory used=5443.5MB, alloc=492.3MB, time=66.45 memory used=5512.9MB, alloc=492.3MB, time=67.39 memory used=5569.1MB, alloc=492.3MB, time=68.54 memory used=5612.9MB, alloc=492.3MB, time=69.38 memory used=5664.7MB, alloc=492.3MB, time=70.32 memory used=5735.5MB, alloc=492.3MB, time=71.03 memory used=5786.1MB, alloc=492.3MB, time=71.92 memory used=5837.7MB, alloc=492.3MB, time=72.90 memory used=5882.6MB, alloc=492.3MB, time=73.70 memory used=6086.5MB, alloc=516.3MB, time=77.40 memory used=6187.5MB, alloc=516.3MB, time=77.94 memory used=6285.2MB, alloc=516.3MB, time=78.41 memory used=6387.6MB, alloc=516.3MB, time=79.04 memory used=6616.4MB, alloc=516.3MB, time=81.88 memory used=6789.8MB, alloc=540.3MB, time=84.35 memory used=6914.9MB, alloc=540.3MB, time=85.23 memory used=7057.3MB, alloc=540.3MB, time=86.50 memory used=7170.1MB, alloc=540.3MB, time=87.11 memory used=7253.3MB, alloc=540.3MB, time=87.66 memory used=7350.7MB, alloc=540.3MB, time=88.22 memory used=7466.5MB, alloc=540.3MB, time=88.78 memory used=7570.6MB, alloc=540.3MB, time=89.30 memory used=7647.5MB, alloc=540.3MB, time=89.80 memory used=7730.8MB, alloc=540.3MB, time=90.29 memory used=7862.5MB, alloc=540.3MB, time=91.37 memory used=7968.9MB, alloc=540.3MB, time=92.01 memory used=8061.7MB, alloc=540.3MB, time=92.61 memory used=8153.4MB, alloc=540.3MB, time=93.19 memory used=8262.1MB, alloc=540.3MB, time=93.78 memory used=8379.1MB, alloc=540.3MB, time=94.34 memory used=8460.3MB, alloc=540.3MB, time=94.85 memory used=8540.3MB, alloc=540.3MB, time=95.36 memory used=8633.4MB, alloc=540.3MB, time=95.91 memory used=8807.0MB, alloc=540.3MB, time=104.04 memory used=8903.4MB, alloc=540.3MB, time=104.66 memory used=9014.3MB, alloc=540.3MB, time=105.23 memory used=9093.9MB, alloc=540.3MB, time=105.77 memory used=9182.6MB, alloc=540.3MB, time=106.32 memory used=9283.9MB, alloc=540.3MB, time=106.82 memory used=9399.5MB, alloc=540.3MB, time=107.35 memory used=9634.3MB, alloc=540.3MB, time=108.20 memory used=9781.2MB, alloc=540.3MB, time=108.78 memory used=9949.4MB, alloc=540.3MB, time=110.13 memory used=10055.7MB, alloc=540.3MB, time=110.77 memory used=10140.7MB, alloc=540.3MB, time=111.35 memory used=10242.7MB, alloc=540.3MB, time=111.94 memory used=10363.9MB, alloc=540.3MB, time=112.55 memory used=10454.6MB, alloc=564.3MB, time=113.08 memory used=10545.8MB, alloc=564.3MB, time=113.62 memory used=10650.4MB, alloc=564.3MB, time=114.15 memory used=10804.5MB, alloc=564.3MB, time=115.41 memory used=10920.8MB, alloc=564.3MB, time=116.10 memory used=11028.5MB, alloc=564.3MB, time=116.73 memory used=11160.7MB, alloc=564.3MB, time=117.37 memory used=11282.7MB, alloc=564.3MB, time=117.97 memory used=11373.3MB, alloc=564.3MB, time=118.51 memory used=11476.2MB, alloc=564.3MB, time=119.00 memory used=11668.7MB, alloc=564.3MB, time=127.35 memory used=11784.1MB, alloc=564.3MB, time=128.00 memory used=11902.2MB, alloc=564.3MB, time=128.59 memory used=11999.0MB, alloc=564.3MB, time=129.16 memory used=12110.9MB, alloc=564.3MB, time=129.73 memory used=12241.5MB, alloc=564.3MB, time=130.28 memory used=12496.7MB, alloc=564.3MB, time=131.02 memory used=12643.5MB, alloc=564.3MB, time=131.61 memory used=12818.6MB, alloc=564.3MB, time=132.90 memory used=13114.9MB, alloc=564.3MB, time=135.92 memory used=13231.2MB, alloc=564.3MB, time=136.50 memory used=13393.5MB, alloc=564.3MB, time=137.88 memory used=13500.3MB, alloc=564.3MB, time=138.50 memory used=13634.8MB, alloc=564.3MB, time=139.13 memory used=13729.9MB, alloc=564.3MB, time=139.66 memory used=13861.4MB, alloc=564.3MB, time=140.64 memory used=13979.0MB, alloc=564.3MB, time=141.29 memory used=14096.9MB, alloc=564.3MB, time=141.94 memory used=14217.4MB, alloc=564.3MB, time=142.52 memory used=14315.1MB, alloc=564.3MB, time=143.02 memory used=14453.0MB, alloc=564.3MB, time=144.85 memory used=14568.9MB, alloc=564.3MB, time=145.41 memory used=14706.1MB, alloc=564.3MB, time=146.11 memory used=14822.9MB, alloc=564.3MB, time=146.70 memory used=14963.6MB, alloc=564.3MB, time=147.86 memory used=15094.2MB, alloc=564.3MB, time=148.70 memory used=15329.6MB, alloc=564.3MB, time=151.04 memory used=15479.9MB, alloc=564.3MB, time=152.88 memory used=15673.8MB, alloc=564.3MB, time=155.76 memory used=15900.1MB, alloc=564.3MB, time=159.13 memory used=16079.1MB, alloc=564.3MB, time=161.73 memory used=16213.5MB, alloc=588.3MB, time=163.87 memory used=16372.7MB, alloc=588.3MB, time=166.41 memory used=16503.6MB, alloc=588.3MB, time=168.64 memory used=16628.4MB, alloc=612.3MB, time=170.46 memory used=16832.1MB, alloc=612.3MB, time=172.82 memory used=16985.6MB, alloc=612.3MB, time=174.55 memory used=17176.5MB, alloc=612.3MB, time=176.32 memory used=17363.4MB, alloc=612.3MB, time=180.40 memory used=17495.9MB, alloc=612.3MB, time=181.16 memory used=17638.1MB, alloc=612.3MB, time=182.18 memory used=17827.4MB, alloc=612.3MB, time=184.11 memory used=17966.0MB, alloc=612.3MB, time=186.14 memory used=18151.8MB, alloc=612.3MB, time=188.42 memory used=18295.7MB, alloc=636.3MB, time=191.09 memory used=18444.8MB, alloc=636.3MB, time=193.28 memory used=18571.0MB, alloc=636.3MB, time=195.44 memory used=18700.6MB, alloc=636.3MB, time=197.59 memory used=18843.6MB, alloc=636.3MB, time=200.13 |\^/| 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(); 1428295692 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 2 2 F := [2 x z + 5 y z + 16 x + 8 y, 5 x z - 10 y z - 10 x + 18 z , 2 2 6 x y - 10 y - 20 y + 9 z] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [-11 x + 8 x z + 12 y + 2 z , 10 x y z - 15 x z + 8 x - 8 z, 2 2 2 2 5 x z + 2 y z + 17 y z + 13 y ] > Problem := [F,G]; 2 2 2 2 2 2 2 Problem := [[2 x z + 5 y z + 16 x + 8 y, 5 x z - 10 y z - 10 x + 18 z , 2 2 2 2 2 6 x y - 10 y - 20 y + 9 z], [-11 x + 8 x z + 12 y + 2 z , 2 2 2 2 10 x y z - 15 x z + 8 x - 8 z, 5 x z + 2 y z + 17 y z + 13 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.18 memory used=24.4MB, alloc=32.3MB, time=0.45 memory used=44.3MB, alloc=36.3MB, time=0.70 memory used=67.2MB, alloc=36.3MB, time=0.97 memory used=91.5MB, alloc=36.3MB, time=1.24 memory used=111.2MB, alloc=60.3MB, time=1.54 memory used=156.1MB, alloc=68.3MB, time=2.09 memory used=201.7MB, alloc=68.3MB, time=2.60 memory used=243.7MB, alloc=68.3MB, time=3.17 memory used=291.5MB, alloc=92.3MB, time=3.78 memory used=357.0MB, alloc=92.3MB, time=4.38 memory used=419.4MB, alloc=348.3MB, time=5.00 memory used=502.3MB, alloc=348.3MB, time=5.92 memory used=559.9MB, alloc=348.3MB, time=6.56 memory used=632.8MB, alloc=372.3MB, time=7.46 memory used=725.3MB, alloc=372.3MB, time=8.74 memory used=814.4MB, alloc=396.3MB, time=9.91 memory used=915.4MB, alloc=396.3MB, time=11.20 memory used=996.5MB, alloc=420.3MB, time=11.90 memory used=1089.7MB, alloc=420.3MB, time=12.55 memory used=1198.3MB, alloc=420.3MB, time=13.46 memory used=1328.1MB, alloc=420.3MB, time=14.90 memory used=1449.5MB, alloc=444.3MB, time=16.54 memory used=1558.6MB, alloc=444.3MB, time=17.90 memory used=1665.8MB, alloc=444.3MB, time=19.47 memory used=1752.6MB, alloc=444.3MB, time=20.73 memory used=1857.4MB, alloc=468.3MB, time=22.08 memory used=1964.1MB, alloc=468.3MB, time=23.36 memory used=2059.8MB, alloc=468.3MB, time=24.72 memory used=2130.9MB, alloc=468.3MB, time=25.88 memory used=2213.9MB, alloc=468.3MB, time=27.30 memory used=2284.5MB, alloc=492.3MB, time=28.56 memory used=2356.4MB, alloc=492.3MB, time=29.61 memory used=2433.6MB, alloc=492.3MB, time=30.58 memory used=2498.2MB, alloc=492.3MB, time=31.70 memory used=2566.4MB, alloc=492.3MB, time=32.80 memory used=2673.4MB, alloc=492.3MB, time=33.98 memory used=2753.6MB, alloc=492.3MB, time=35.09 memory used=2819.4MB, alloc=492.3MB, time=36.06 memory used=2873.7MB, alloc=492.3MB, time=36.94 memory used=2929.2MB, alloc=492.3MB, time=38.01 memory used=2990.0MB, alloc=492.3MB, time=39.01 memory used=3042.4MB, alloc=492.3MB, time=39.94 memory used=3120.7MB, alloc=492.3MB, time=40.83 memory used=3179.4MB, alloc=492.3MB, time=41.95 memory used=3218.5MB, alloc=516.3MB, time=42.84 memory used=3367.4MB, alloc=516.3MB, time=44.15 memory used=3493.7MB, alloc=516.3MB, time=45.05 memory used=3604.1MB, alloc=516.3MB, time=45.88 memory used=3810.5MB, alloc=516.3MB, time=48.22 memory used=4065.4MB, alloc=540.3MB, time=51.24 memory used=4290.9MB, alloc=540.3MB, time=54.13 memory used=4475.1MB, alloc=564.3MB, time=57.16 memory used=4647.3MB, alloc=588.3MB, time=59.76 memory used=4811.9MB, alloc=612.3MB, time=62.08 memory used=4999.1MB, alloc=612.3MB, time=64.54 memory used=5182.9MB, alloc=612.3MB, time=67.14 memory used=5378.4MB, alloc=636.3MB, time=69.56 memory used=5542.6MB, alloc=636.3MB, time=72.53 memory used=5668.9MB, alloc=636.3MB, time=75.23 memory used=5781.6MB, alloc=660.3MB, time=77.19 memory used=5919.4MB, alloc=684.3MB, time=79.12 memory used=6035.5MB, alloc=708.3MB, time=81.09 memory used=6146.4MB, alloc=708.3MB, time=83.03 memory used=6257.6MB, alloc=708.3MB, time=85.39 memory used=6356.5MB, alloc=708.3MB, time=87.28 memory used=6772.7MB, alloc=732.3MB, time=92.40 memory used=7203.1MB, alloc=756.3MB, time=98.21 memory used=7510.0MB, alloc=780.3MB, time=103.64 memory used=7842.3MB, alloc=804.3MB, time=109.60 memory used=8186.7MB, alloc=828.3MB, time=115.56 memory used=8485.6MB, alloc=852.3MB, time=120.23 memory used=8777.4MB, alloc=876.3MB, time=123.71 memory used=9121.1MB, alloc=900.3MB, time=129.06 memory used=9473.7MB, alloc=924.3MB, time=134.13 memory used=9755.3MB, alloc=948.3MB, time=139.67 memory used=9995.1MB, alloc=972.3MB, time=144.47 memory used=10241.5MB, alloc=996.3MB, time=149.43 memory used=10511.3MB, alloc=1020.3MB, time=153.89 memory used=10741.2MB, alloc=1044.3MB, time=159.12 memory used=11417.9MB, alloc=1068.3MB, time=170.52 |\^/| 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(); 1428295992 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 2 F := [14 x y - 5 x y - 4 y - 2 y z, -14 y z + 6 y z - 10 y z + 8 z , 2 2 2 -4 x y - 13 y z - 18 z - 4] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 G := [20 x y + 8 y z - 10 z - 12 x y, -16 x z + 10 x z - 11 x - 11 z, 2 12 x y z - 16 y z - 12 x y - 17] > Problem := [F,G]; 2 2 3 2 2 2 Problem := [[14 x y - 5 x y - 4 y - 2 y z, -14 y z + 6 y z - 10 y z + 8 z , 2 2 2 2 2 3 -4 x y - 13 y z - 18 z - 4], [20 x y + 8 y z - 10 z - 12 x y, 2 2 2 -16 x z + 10 x z - 11 x - 11 z, 12 x y z - 16 y z - 12 x y - 17]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.3MB, alloc=32.3MB, time=0.52 memory used=45.3MB, alloc=56.3MB, time=0.83 memory used=86.8MB, alloc=60.3MB, time=1.46 memory used=127.1MB, alloc=60.3MB, time=2.06 memory used=161.5MB, alloc=84.3MB, time=2.58 memory used=223.2MB, alloc=92.3MB, time=3.58 memory used=287.1MB, alloc=92.3MB, time=4.47 memory used=352.9MB, alloc=116.3MB, time=5.40 memory used=430.4MB, alloc=372.3MB, time=6.55 memory used=502.1MB, alloc=372.3MB, time=7.38 memory used=571.1MB, alloc=372.3MB, time=8.10 memory used=651.8MB, alloc=396.3MB, time=9.29 memory used=755.0MB, alloc=420.3MB, time=10.94 memory used=883.3MB, alloc=420.3MB, time=12.96 memory used=1009.1MB, alloc=444.3MB, time=14.74 memory used=1142.5MB, alloc=468.3MB, time=16.71 memory used=1282.3MB, alloc=468.3MB, time=19.09 memory used=1425.1MB, alloc=468.3MB, time=20.80 memory used=1531.4MB, alloc=492.3MB, time=22.18 memory used=1642.6MB, alloc=492.3MB, time=23.73 memory used=1755.8MB, alloc=492.3MB, time=25.65 memory used=1854.7MB, alloc=492.3MB, time=27.37 memory used=1959.2MB, alloc=492.3MB, time=29.19 memory used=2034.5MB, alloc=492.3MB, time=30.42 memory used=2168.9MB, alloc=492.3MB, time=31.91 memory used=2283.0MB, alloc=492.3MB, time=33.51 memory used=2401.1MB, alloc=492.3MB, time=34.74 memory used=2524.7MB, alloc=516.3MB, time=36.19 memory used=2614.1MB, alloc=516.3MB, time=37.47 memory used=2692.3MB, alloc=516.3MB, time=38.78 memory used=2767.1MB, alloc=516.3MB, time=40.05 memory used=2850.1MB, alloc=516.3MB, time=41.45 memory used=2916.4MB, alloc=516.3MB, time=42.67 memory used=2996.8MB, alloc=516.3MB, time=44.45 memory used=3075.0MB, alloc=516.3MB, time=46.10 memory used=3142.5MB, alloc=516.3MB, time=47.62 memory used=3201.2MB, alloc=516.3MB, time=49.02 memory used=3242.7MB, alloc=516.3MB, time=49.95 memory used=3297.8MB, alloc=516.3MB, time=51.32 memory used=3499.1MB, alloc=540.3MB, time=55.20 memory used=3714.2MB, alloc=564.3MB, time=58.70 memory used=3920.7MB, alloc=588.3MB, time=62.99 memory used=4126.5MB, alloc=612.3MB, time=66.78 memory used=4332.2MB, alloc=636.3MB, time=70.00 memory used=4544.9MB, alloc=660.3MB, time=73.44 memory used=4731.7MB, alloc=660.3MB, time=75.01 memory used=4900.1MB, alloc=660.3MB, time=76.11 memory used=5081.7MB, alloc=660.3MB, time=78.77 memory used=5282.6MB, alloc=660.3MB, time=80.37 memory used=5488.6MB, alloc=660.3MB, time=83.45 memory used=5708.0MB, alloc=660.3MB, time=87.70 memory used=5881.3MB, alloc=660.3MB, time=90.34 memory used=6039.4MB, alloc=660.3MB, time=93.75 memory used=6180.4MB, alloc=684.3MB, time=96.18 memory used=6343.1MB, alloc=684.3MB, time=99.09 memory used=6494.8MB, alloc=684.3MB, time=102.26 memory used=6664.0MB, alloc=684.3MB, time=106.56 memory used=6806.6MB, alloc=684.3MB, time=110.34 memory used=6948.3MB, alloc=708.3MB, time=113.97 memory used=7045.4MB, alloc=708.3MB, time=116.24 memory used=7137.3MB, alloc=708.3MB, time=118.41 memory used=7513.1MB, alloc=732.3MB, time=125.40 memory used=7871.5MB, alloc=756.3MB, time=132.54 memory used=8272.0MB, alloc=780.3MB, time=139.90 memory used=8599.5MB, alloc=804.3MB, time=145.79 memory used=8921.4MB, alloc=828.3MB, time=152.83 memory used=9240.7MB, alloc=852.3MB, time=157.95 |\^/| 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(); 1428296292 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 F := [-5 x y + 15 y z - 12 z + x, 13 x z - 5 y z - 4 x, 2 2 -8 x y - 4 y z + 2 x z] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 G := [6 x z - 18 y - 14 x z + 4 y z, -13 x y - 14 y z - 10 x + 12, 2 3 2 2 -17 x z - 13 y - 15 x + 9 y ] > Problem := [F,G]; 2 2 2 2 2 Problem := [[-5 x y + 15 y z - 12 z + x, 13 x z - 5 y z - 4 x, 2 2 2 3 -8 x y - 4 y z + 2 x z], [6 x z - 18 y - 14 x z + 4 y z, 2 2 2 3 2 2 -13 x y - 14 y z - 10 x + 12, -17 x z - 13 y - 15 x + 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=24.4MB, alloc=32.3MB, time=0.37 memory used=47.3MB, alloc=36.3MB, time=0.65 memory used=68.3MB, alloc=36.3MB, time=0.89 memory used=86.3MB, alloc=36.3MB, time=1.07 memory used=106.9MB, alloc=60.3MB, time=1.35 memory used=164.6MB, alloc=69.0MB, time=1.97 memory used=209.7MB, alloc=69.0MB, time=2.50 memory used=253.1MB, alloc=69.0MB, time=2.96 memory used=296.0MB, alloc=69.0MB, time=3.39 memory used=337.3MB, alloc=69.0MB, time=3.78 memory used=379.8MB, alloc=69.0MB, time=4.27 memory used=424.1MB, alloc=93.0MB, time=4.77 memory used=494.4MB, alloc=93.0MB, time=5.54 memory used=542.6MB, alloc=93.0MB, time=5.93 memory used=593.2MB, alloc=93.0MB, time=6.39 memory used=638.2MB, alloc=93.0MB, time=6.80 memory used=677.7MB, alloc=93.0MB, time=7.01 memory used=715.6MB, alloc=93.0MB, time=7.19 memory used=760.6MB, alloc=93.0MB, time=7.90 memory used=793.0MB, alloc=93.0MB, time=8.05 memory used=830.1MB, alloc=93.0MB, time=8.24 memory used=870.7MB, alloc=93.0MB, time=8.48 memory used=918.0MB, alloc=93.0MB, time=9.31 memory used=947.0MB, alloc=93.0MB, time=9.41 memory used=989.7MB, alloc=93.0MB, time=9.74 memory used=1058.8MB, alloc=93.0MB, time=10.37 memory used=1138.9MB, alloc=349.0MB, time=11.28 memory used=1217.2MB, alloc=373.0MB, time=11.88 memory used=1287.6MB, alloc=373.0MB, time=12.63 memory used=1404.1MB, alloc=373.0MB, time=13.50 memory used=1495.8MB, alloc=397.0MB, time=14.76 memory used=1609.7MB, alloc=421.0MB, time=16.19 memory used=1745.6MB, alloc=421.0MB, time=18.19 memory used=1877.0MB, alloc=421.0MB, time=19.61 memory used=2008.7MB, alloc=445.0MB, time=21.03 memory used=2127.5MB, alloc=445.0MB, time=22.39 memory used=2259.9MB, alloc=445.0MB, time=23.60 memory used=2349.9MB, alloc=445.0MB, time=25.04 memory used=2436.9MB, alloc=445.0MB, time=25.80 memory used=2561.6MB, alloc=445.0MB, time=27.11 memory used=2661.8MB, alloc=445.0MB, time=29.01 memory used=2731.5MB, alloc=445.0MB, time=29.29 memory used=2797.1MB, alloc=445.0MB, time=29.83 memory used=2872.0MB, alloc=445.0MB, time=30.15 memory used=3013.7MB, alloc=445.0MB, time=31.30 memory used=3193.2MB, alloc=445.0MB, time=33.83 memory used=3339.5MB, alloc=469.0MB, time=35.22 memory used=3522.7MB, alloc=469.0MB, time=38.02 memory used=3651.4MB, alloc=469.0MB, time=39.44 memory used=3755.9MB, alloc=469.0MB, time=40.38 memory used=3858.8MB, alloc=469.0MB, time=41.60 memory used=3927.0MB, alloc=493.0MB, time=42.64 memory used=3998.8MB, alloc=493.0MB, time=43.78 memory used=4076.1MB, alloc=493.0MB, time=45.02 memory used=4141.4MB, alloc=493.0MB, time=46.12 memory used=4214.2MB, alloc=493.0MB, time=47.09 memory used=4322.4MB, alloc=493.0MB, time=48.23 memory used=4445.2MB, alloc=493.0MB, time=49.15 memory used=4548.2MB, alloc=493.0MB, time=50.93 memory used=4650.6MB, alloc=493.0MB, time=51.89 memory used=4741.6MB, alloc=493.0MB, time=52.50 memory used=4807.6MB, alloc=493.0MB, time=53.46 memory used=4880.2MB, alloc=493.0MB, time=54.67 memory used=4937.2MB, alloc=493.0MB, time=55.43 memory used=5030.8MB, alloc=493.0MB, time=56.71 memory used=5146.0MB, alloc=493.0MB, time=58.05 memory used=5221.1MB, alloc=517.0MB, time=59.22 memory used=5344.3MB, alloc=517.0MB, time=61.50 memory used=5436.3MB, alloc=517.0MB, time=61.97 memory used=5581.1MB, alloc=517.0MB, time=62.92 memory used=5678.0MB, alloc=517.0MB, time=63.41 memory used=5768.6MB, alloc=517.0MB, time=64.17 memory used=5813.1MB, alloc=517.0MB, time=64.96 memory used=5890.4MB, alloc=517.0MB, time=65.84 memory used=6077.5MB, alloc=541.0MB, time=67.97 memory used=6184.8MB, alloc=541.0MB, time=68.54 memory used=6282.3MB, alloc=541.0MB, time=69.03 memory used=6398.1MB, alloc=541.0MB, time=69.72 memory used=6502.4MB, alloc=541.0MB, time=70.24 memory used=6637.2MB, alloc=541.0MB, time=73.58 memory used=6736.0MB, alloc=541.0MB, time=74.09 memory used=6974.6MB, alloc=541.0MB, time=75.04 memory used=7102.0MB, alloc=541.0MB, time=76.24 memory used=7237.4MB, alloc=541.0MB, time=77.25 memory used=7344.2MB, alloc=541.0MB, time=77.81 memory used=7469.5MB, alloc=541.0MB, time=78.49 memory used=7578.8MB, alloc=541.0MB, time=79.05 memory used=7726.1MB, alloc=541.0MB, time=86.07 memory used=7830.5MB, alloc=541.0MB, time=86.62 memory used=7928.6MB, alloc=541.0MB, time=87.13 memory used=8055.9MB, alloc=541.0MB, time=87.66 memory used=8197.3MB, alloc=541.0MB, time=88.27 memory used=8362.3MB, alloc=541.0MB, time=88.88 memory used=8559.0MB, alloc=541.0MB, time=91.92 memory used=8661.0MB, alloc=541.0MB, time=92.44 memory used=8772.3MB, alloc=541.0MB, time=92.94 memory used=8962.0MB, alloc=541.0MB, time=93.60 memory used=9101.9MB, alloc=541.0MB, time=94.64 memory used=9229.8MB, alloc=541.0MB, time=96.02 memory used=9332.0MB, alloc=541.0MB, time=96.52 memory used=9495.1MB, alloc=541.0MB, time=97.55 memory used=9739.5MB, alloc=541.0MB, time=99.93 memory used=9945.5MB, alloc=541.0MB, time=103.04 memory used=10064.4MB, alloc=541.0MB, time=103.87 memory used=10176.7MB, alloc=541.0MB, time=104.84 memory used=10352.3MB, alloc=541.0MB, time=106.66 memory used=10608.9MB, alloc=565.0MB, time=109.37 memory used=10807.1MB, alloc=565.0MB, time=112.58 memory used=11021.6MB, alloc=565.0MB, time=115.65 memory used=11184.4MB, alloc=589.0MB, time=118.06 memory used=11340.7MB, alloc=589.0MB, time=119.50 memory used=11493.1MB, alloc=589.0MB, time=121.74 memory used=11603.3MB, alloc=589.0MB, time=122.40 memory used=11772.5MB, alloc=613.0MB, time=124.67 memory used=11946.7MB, alloc=613.0MB, time=125.61 memory used=12091.1MB, alloc=613.0MB, time=126.45 memory used=12264.4MB, alloc=613.0MB, time=131.39 memory used=12389.1MB, alloc=613.0MB, time=132.07 memory used=12672.9MB, alloc=613.0MB, time=134.69 memory used=12797.6MB, alloc=613.0MB, time=135.38 memory used=12984.1MB, alloc=613.0MB, time=136.56 memory used=13233.0MB, alloc=613.0MB, time=138.83 memory used=13461.4MB, alloc=613.0MB, time=144.92 memory used=13590.8MB, alloc=613.0MB, time=145.67 memory used=13711.8MB, alloc=613.0MB, time=146.38 memory used=13832.0MB, alloc=613.0MB, time=147.03 memory used=14080.1MB, alloc=613.0MB, time=147.96 memory used=14230.8MB, alloc=613.0MB, time=150.02 memory used=14352.1MB, alloc=613.0MB, time=150.71 memory used=14537.1MB, alloc=613.0MB, time=152.49 memory used=14716.2MB, alloc=613.0MB, time=158.07 memory used=14852.2MB, alloc=613.0MB, time=158.82 memory used=14956.0MB, alloc=613.0MB, time=159.53 memory used=15089.9MB, alloc=613.0MB, time=160.21 memory used=15348.0MB, alloc=613.0MB, time=162.21 memory used=15474.0MB, alloc=613.0MB, time=162.95 memory used=15602.6MB, alloc=613.0MB, time=163.62 memory used=15842.0MB, alloc=637.0MB, time=166.02 memory used=16080.4MB, alloc=637.0MB, time=168.52 memory used=16209.1MB, alloc=637.0MB, time=169.25 memory used=16449.6MB, alloc=637.0MB, time=172.50 memory used=16597.4MB, alloc=637.0MB, time=173.49 memory used=16798.9MB, alloc=637.0MB, time=175.02 memory used=16943.2MB, alloc=637.0MB, time=176.98 memory used=17186.6MB, alloc=637.0MB, time=179.66 memory used=17356.3MB, alloc=637.0MB, time=182.67 memory used=17499.8MB, alloc=637.0MB, time=183.48 memory used=17624.3MB, alloc=637.0MB, time=184.15 memory used=17852.6MB, alloc=637.0MB, time=187.88 memory used=17980.0MB, alloc=637.0MB, time=188.62 memory used=18172.8MB, alloc=637.0MB, time=195.49 memory used=18318.1MB, alloc=637.0MB, time=196.32 memory used=18431.4MB, alloc=637.0MB, time=197.05 memory used=18577.7MB, alloc=637.0MB, time=197.74 memory used=18802.9MB, alloc=637.0MB, time=201.19 memory used=18938.5MB, alloc=637.0MB, time=201.94 memory used=19094.4MB, alloc=637.0MB, time=203.23 memory used=19231.1MB, alloc=637.0MB, time=204.04 memory used=19415.1MB, alloc=637.0MB, time=205.98 memory used=19635.8MB, alloc=637.0MB, time=208.41 memory used=19821.8MB, alloc=637.0MB, time=210.62 memory used=19975.5MB, alloc=637.0MB, time=211.93 memory used=20132.1MB, alloc=637.0MB, time=213.83 memory used=20309.9MB, alloc=661.0MB, time=216.04 memory used=20444.1MB, alloc=661.0MB, time=217.78 |\^/| 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(); 1428296592 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 F := [-4 x y z - 5 y z - 10, 5 x - 19 y - 13 y - 10, 2 2 2 9 x z - 7 y z - 8 x - 13] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 G := [20 x y - 3 x z + 19 y z - 19, -8 z + 14 x z - 9 z - 13 y, 2 2 2 -4 x y + 17 x z + y z - 6 y z] > Problem := [F,G]; 2 3 2 Problem := [[-4 x y z - 5 y z - 10, 5 x - 19 y - 13 y - 10, 2 2 2 2 2 2 9 x z - 7 y z - 8 x - 13], [20 x y - 3 x z + 19 y z - 19, 3 2 2 2 2 -8 z + 14 x z - 9 z - 13 y, -4 x y + 17 x z + y 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=4.5MB, alloc=32.3MB, time=0.18 memory used=26.3MB, alloc=32.3MB, time=0.51 memory used=46.3MB, alloc=60.3MB, time=0.83 memory used=88.4MB, alloc=60.3MB, time=1.42 memory used=131.0MB, alloc=68.3MB, time=2.04 memory used=173.7MB, alloc=92.3MB, time=2.63 memory used=240.1MB, alloc=92.3MB, time=3.34 memory used=306.2MB, alloc=348.3MB, time=4.19 memory used=371.3MB, alloc=372.3MB, time=5.18 memory used=448.0MB, alloc=372.3MB, time=5.78 memory used=536.3MB, alloc=372.3MB, time=6.73 memory used=629.7MB, alloc=372.3MB, time=7.90 memory used=682.6MB, alloc=372.3MB, time=8.68 memory used=760.7MB, alloc=396.3MB, time=9.49 memory used=891.1MB, alloc=396.3MB, time=11.04 memory used=1003.7MB, alloc=420.3MB, time=12.65 memory used=1129.0MB, alloc=420.3MB, time=13.81 memory used=1195.7MB, alloc=420.3MB, time=14.29 memory used=1304.5MB, alloc=420.3MB, time=16.89 memory used=1360.4MB, alloc=420.3MB, time=17.13 memory used=1418.4MB, alloc=420.3MB, time=17.34 memory used=1530.1MB, alloc=420.3MB, time=19.18 memory used=1601.3MB, alloc=420.3MB, time=19.58 memory used=1689.7MB, alloc=420.3MB, time=20.39 memory used=1830.4MB, alloc=420.3MB, time=21.49 memory used=1963.9MB, alloc=420.3MB, time=23.20 memory used=2098.0MB, alloc=420.3MB, time=26.06 memory used=2242.4MB, alloc=444.3MB, time=29.15 memory used=2410.7MB, alloc=444.3MB, time=30.52 memory used=2574.0MB, alloc=444.3MB, time=33.63 memory used=2746.6MB, alloc=444.3MB, time=38.36 memory used=2864.7MB, alloc=444.3MB, time=39.51 memory used=3029.3MB, alloc=444.3MB, time=41.11 memory used=3136.1MB, alloc=468.3MB, time=42.72 memory used=3233.8MB, alloc=468.3MB, time=44.24 memory used=3357.4MB, alloc=468.3MB, time=45.64 memory used=3438.4MB, alloc=468.3MB, time=46.00 memory used=3502.2MB, alloc=468.3MB, time=46.33 memory used=3603.9MB, alloc=468.3MB, time=47.20 memory used=3679.6MB, alloc=468.3MB, time=47.58 memory used=3791.2MB, alloc=468.3MB, time=52.45 memory used=3866.0MB, alloc=468.3MB, time=52.83 memory used=3937.1MB, alloc=468.3MB, time=53.17 memory used=4002.1MB, alloc=468.3MB, time=53.51 memory used=4080.9MB, alloc=468.3MB, time=53.86 memory used=4320.7MB, alloc=468.3MB, time=54.88 memory used=4420.9MB, alloc=468.3MB, time=55.68 memory used=4519.2MB, alloc=468.3MB, time=56.05 memory used=4668.6MB, alloc=468.3MB, time=57.78 memory used=4779.0MB, alloc=468.3MB, time=59.01 memory used=4891.0MB, alloc=492.3MB, time=65.35 memory used=5025.0MB, alloc=492.3MB, time=66.24 memory used=5208.2MB, alloc=516.3MB, time=85.69 |\^/| 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(); 1428296892 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 2 F := [-x y - 2 x z - x y z - 9 y, 8 x z + 4 x + 20 y + 5 z , 2 3 x y - 8 x y z + 11 x z + 4 z] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 3 G := [12 x y + 9 x z + 16 z + 16 z, 8 x z - 12 x z - 6 y - 13, 2 2 -19 y z - 20 x - 20 x z - 20 z] > Problem := [F,G]; 2 2 2 2 2 2 Problem := [[-x y - 2 x z - x y z - 9 y, 8 x z + 4 x + 20 y + 5 z , 2 2 2 3 3 x y - 8 x y z + 11 x z + 4 z], [12 x y + 9 x z + 16 z + 16 z, 2 2 3 2 2 8 x z - 12 x z - 6 y - 13, -19 y z - 20 x - 20 x z - 20 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.18 memory used=26.6MB, alloc=32.3MB, time=0.50 memory used=46.5MB, alloc=56.3MB, time=0.81 memory used=88.0MB, alloc=60.3MB, time=1.42 memory used=129.2MB, alloc=60.3MB, time=1.99 memory used=169.1MB, alloc=84.3MB, time=2.57 memory used=235.5MB, alloc=92.3MB, time=3.27 memory used=303.9MB, alloc=92.3MB, time=4.12 memory used=366.9MB, alloc=92.3MB, time=5.08 memory used=429.6MB, alloc=116.3MB, time=6.03 memory used=499.8MB, alloc=116.3MB, time=7.07 memory used=556.2MB, alloc=372.3MB, time=7.88 memory used=646.3MB, alloc=396.3MB, time=9.13 memory used=755.3MB, alloc=396.3MB, time=10.71 memory used=871.6MB, alloc=420.3MB, time=12.29 memory used=990.2MB, alloc=444.3MB, time=13.99 memory used=1142.6MB, alloc=444.3MB, time=15.66 memory used=1265.4MB, alloc=444.3MB, time=17.19 memory used=1404.2MB, alloc=444.3MB, time=18.45 memory used=1500.6MB, alloc=444.3MB, time=19.12 memory used=1602.8MB, alloc=444.3MB, time=19.83 memory used=1704.7MB, alloc=444.3MB, time=20.56 memory used=1805.2MB, alloc=444.3MB, time=21.36 memory used=1919.0MB, alloc=444.3MB, time=22.78 memory used=2041.8MB, alloc=468.3MB, time=24.25 memory used=2139.9MB, alloc=468.3MB, time=25.66 memory used=2246.8MB, alloc=468.3MB, time=26.76 memory used=2338.5MB, alloc=468.3MB, time=27.99 memory used=2414.5MB, alloc=468.3MB, time=28.97 memory used=2503.7MB, alloc=468.3MB, time=30.43 memory used=2579.8MB, alloc=468.3MB, time=31.72 memory used=2661.9MB, alloc=468.3MB, time=33.10 memory used=2730.8MB, alloc=468.3MB, time=34.18 memory used=2788.6MB, alloc=468.3MB, time=35.38 memory used=2853.3MB, alloc=492.3MB, time=36.51 memory used=2914.6MB, alloc=492.3MB, time=37.69 memory used=2978.3MB, alloc=492.3MB, time=39.02 memory used=3024.8MB, alloc=492.3MB, time=40.00 memory used=3069.2MB, alloc=492.3MB, time=40.81 memory used=3127.2MB, alloc=492.3MB, time=41.98 memory used=3166.8MB, alloc=492.3MB, time=42.83 memory used=3210.2MB, alloc=492.3MB, time=43.76 memory used=3400.5MB, alloc=516.3MB, time=46.94 memory used=3599.0MB, alloc=540.3MB, time=49.58 memory used=3733.3MB, alloc=540.3MB, time=50.77 memory used=3889.3MB, alloc=540.3MB, time=52.55 memory used=4015.6MB, alloc=540.3MB, time=53.99 memory used=4132.6MB, alloc=540.3MB, time=55.10 memory used=4356.9MB, alloc=540.3MB, time=59.63 memory used=4457.6MB, alloc=540.3MB, time=60.21 memory used=4626.9MB, alloc=564.3MB, time=61.99 memory used=4900.0MB, alloc=564.3MB, time=65.85 memory used=5095.4MB, alloc=564.3MB, time=69.12 memory used=5230.8MB, alloc=564.3MB, time=70.35 memory used=5405.8MB, alloc=564.3MB, time=72.35 memory used=5522.1MB, alloc=564.3MB, time=73.01 memory used=5661.7MB, alloc=564.3MB, time=76.39 memory used=5778.7MB, alloc=564.3MB, time=77.01 memory used=5871.8MB, alloc=564.3MB, time=77.54 memory used=6055.5MB, alloc=564.3MB, time=79.07 memory used=6252.0MB, alloc=588.3MB, time=81.85 memory used=6400.1MB, alloc=588.3MB, time=83.72 memory used=6575.5MB, alloc=588.3MB, time=85.03 memory used=6768.2MB, alloc=588.3MB, time=87.56 memory used=6921.3MB, alloc=588.3MB, time=88.72 memory used=7057.0MB, alloc=588.3MB, time=89.90 memory used=7188.3MB, alloc=588.3MB, time=90.93 memory used=7332.2MB, alloc=588.3MB, time=91.96 memory used=7468.4MB, alloc=588.3MB, time=93.08 memory used=7599.5MB, alloc=588.3MB, time=93.89 memory used=7777.6MB, alloc=588.3MB, time=95.48 memory used=7924.3MB, alloc=588.3MB, time=97.48 memory used=8045.6MB, alloc=588.3MB, time=98.15 memory used=8181.6MB, alloc=588.3MB, time=99.09 memory used=8300.5MB, alloc=588.3MB, time=99.85 memory used=8453.1MB, alloc=588.3MB, time=103.27 memory used=8575.7MB, alloc=588.3MB, time=103.98 memory used=8692.3MB, alloc=588.3MB, time=104.65 memory used=8807.1MB, alloc=588.3MB, time=105.27 memory used=8952.2MB, alloc=588.3MB, time=106.19 memory used=9129.9MB, alloc=588.3MB, time=108.34 memory used=9355.1MB, alloc=588.3MB, time=110.60 memory used=9543.2MB, alloc=588.3MB, time=113.60 memory used=9735.3MB, alloc=588.3MB, time=116.24 memory used=9886.7MB, alloc=588.3MB, time=117.67 memory used=10183.5MB, alloc=612.3MB, time=120.48 memory used=10472.2MB, alloc=612.3MB, time=127.19 memory used=10643.1MB, alloc=612.3MB, time=130.62 memory used=10794.4MB, alloc=612.3MB, time=132.00 memory used=11055.5MB, alloc=612.3MB, time=134.48 memory used=11180.6MB, alloc=612.3MB, time=136.65 memory used=11338.7MB, alloc=612.3MB, time=138.82 memory used=11459.9MB, alloc=636.3MB, time=141.09 memory used=11571.0MB, alloc=636.3MB, time=143.27 memory used=11667.3MB, alloc=636.3MB, time=145.26 memory used=11865.1MB, alloc=636.3MB, time=147.43 memory used=12045.1MB, alloc=636.3MB, time=149.70 memory used=12213.8MB, alloc=636.3MB, time=151.81 memory used=12355.5MB, alloc=636.3MB, time=153.61 memory used=12523.9MB, alloc=636.3MB, time=157.60 memory used=12658.2MB, alloc=636.3MB, time=158.54 memory used=12840.5MB, alloc=636.3MB, time=160.18 |\^/| 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(); 1428297192 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 2 3 F := [2 x y - 19 z + 8 y - 13 y, 2 x y + x y + 13 y + 4 y, 2 -2 x y - 20 z - 11 y + 10] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 3 2 G := [-3 x y + 3 x z + 14 y + 3 z , 20 x y - 2 x z + 6 x, 2 2 2 -17 x y z + 20 x z + 4 y z + 10 z ] > Problem := [F,G]; 2 3 2 2 2 3 Problem := [[2 x y - 19 z + 8 y - 13 y, 2 x y + x y + 13 y + 4 y, 2 2 2 3 3 -2 x y - 20 z - 11 y + 10], [-3 x y + 3 x z + 14 y + 3 z , 2 2 2 2 20 x y - 2 x z + 6 x, -17 x y z + 20 x z + 4 y z + 10 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.18 memory used=26.6MB, alloc=32.3MB, time=0.50 memory used=47.1MB, 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=146.2MB, alloc=60.3MB, time=2.34 memory used=184.3MB, alloc=84.3MB, time=2.96 memory used=241.9MB, alloc=84.3MB, time=3.89 memory used=299.9MB, alloc=116.3MB, time=4.88 memory used=379.3MB, alloc=116.3MB, time=6.20 memory used=459.2MB, alloc=140.3MB, time=7.52 memory used=533.7MB, alloc=396.3MB, time=8.76 memory used=636.1MB, alloc=420.3MB, time=10.50 memory used=766.9MB, alloc=444.3MB, time=12.68 memory used=917.5MB, alloc=444.3MB, time=15.20 memory used=1054.3MB, alloc=468.3MB, time=17.54 memory used=1212.5MB, alloc=492.3MB, time=20.54 memory used=1326.4MB, alloc=492.3MB, time=22.53 memory used=1456.9MB, alloc=492.3MB, time=24.96 memory used=1581.4MB, alloc=492.3MB, time=27.32 memory used=1703.4MB, alloc=516.3MB, time=29.65 memory used=1810.6MB, alloc=516.3MB, time=31.88 memory used=1912.4MB, alloc=516.3MB, time=33.91 memory used=2017.1MB, alloc=516.3MB, time=36.12 memory used=2116.2MB, alloc=516.3MB, time=38.24 memory used=2204.3MB, alloc=540.3MB, time=40.12 memory used=2294.0MB, alloc=540.3MB, time=42.26 memory used=2378.8MB, alloc=540.3MB, time=44.19 memory used=2451.3MB, alloc=540.3MB, time=45.53 memory used=2532.1MB, alloc=540.3MB, time=47.43 memory used=2632.2MB, alloc=540.3MB, time=48.68 memory used=2722.3MB, alloc=540.3MB, time=49.82 memory used=2784.6MB, alloc=540.3MB, time=51.13 memory used=2850.3MB, alloc=540.3MB, time=52.61 memory used=2904.9MB, alloc=540.3MB, time=53.90 memory used=2965.2MB, alloc=564.3MB, time=55.39 memory used=3053.8MB, alloc=564.3MB, time=56.43 memory used=3110.9MB, alloc=564.3MB, time=57.62 memory used=3159.6MB, alloc=564.3MB, time=58.78 memory used=3393.0MB, alloc=588.3MB, time=63.72 memory used=3626.4MB, alloc=612.3MB, time=69.09 memory used=3849.9MB, alloc=636.3MB, time=74.09 memory used=4039.1MB, alloc=660.3MB, time=77.75 memory used=4208.2MB, alloc=684.3MB, time=81.65 memory used=4365.7MB, alloc=708.3MB, time=84.38 memory used=4564.4MB, alloc=732.3MB, time=89.10 memory used=4730.5MB, alloc=732.3MB, time=92.82 memory used=4893.7MB, alloc=732.3MB, time=97.18 memory used=5011.2MB, alloc=732.3MB, time=99.89 memory used=5165.6MB, alloc=732.3MB, time=104.11 memory used=5280.8MB, alloc=732.3MB, time=107.12 memory used=5367.6MB, alloc=732.3MB, time=109.35 memory used=5478.6MB, alloc=732.3MB, time=112.84 memory used=5584.5MB, alloc=756.3MB, time=115.86 memory used=6004.6MB, alloc=780.3MB, time=123.93 memory used=6428.0MB, alloc=804.3MB, time=132.50 memory used=6747.3MB, alloc=828.3MB, time=139.45 memory used=7106.3MB, alloc=852.3MB, time=149.03 memory used=7393.2MB, alloc=876.3MB, time=155.35 |\^/| 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(); 1428297492 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 2 F := [-16 x z + 3 y - 12 y z - 8 x, 14 x y - 7 y z + 17 x z, 2 2 2 15 x z - 11 y z + x + 9 x] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 G := [18 x z + 20 x z + 18 y z - 19 y z , -15 y z - 16 x z + 14 x + 2, 2 2 2 -16 x y + 12 y + 3 z - 16 z] > Problem := [F,G]; 2 3 2 2 2 Problem := [[-16 x z + 3 y - 12 y z - 8 x, 14 x y - 7 y z + 17 x z, 2 2 2 2 2 2 2 15 x z - 11 y z + x + 9 x], [18 x z + 20 x z + 18 y z - 19 y z , 2 2 2 2 -15 y z - 16 x z + 14 x + 2, -16 x y + 12 y + 3 z - 16 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.18 memory used=24.5MB, alloc=32.3MB, time=0.47 memory used=42.6MB, alloc=56.3MB, time=0.77 memory used=77.9MB, alloc=60.3MB, time=1.22 memory used=120.1MB, alloc=60.3MB, time=1.81 memory used=159.2MB, alloc=84.3MB, time=2.39 memory used=230.9MB, alloc=92.3MB, time=3.22 memory used=297.4MB, alloc=92.3MB, time=4.10 memory used=356.9MB, alloc=116.3MB, time=5.03 memory used=431.3MB, alloc=372.3MB, time=6.05 memory used=526.7MB, alloc=396.3MB, time=7.17 memory used=636.4MB, alloc=420.3MB, time=8.78 memory used=766.9MB, alloc=444.3MB, time=10.65 memory used=910.2MB, alloc=444.3MB, time=12.46 memory used=1000.8MB, alloc=444.3MB, time=13.24 memory used=1146.0MB, alloc=468.3MB, time=14.81 memory used=1274.0MB, alloc=468.3MB, time=16.24 memory used=1401.9MB, alloc=492.3MB, time=17.76 memory used=1489.3MB, alloc=492.3MB, time=19.20 memory used=1585.8MB, alloc=492.3MB, time=20.59 memory used=1685.3MB, alloc=492.3MB, time=22.06 memory used=1760.9MB, alloc=492.3MB, time=23.19 memory used=1846.3MB, alloc=516.3MB, time=24.70 memory used=1921.6MB, alloc=516.3MB, time=26.14 memory used=1993.4MB, alloc=516.3MB, time=27.57 memory used=2045.6MB, alloc=516.3MB, time=28.51 memory used=2096.8MB, alloc=516.3MB, time=29.39 memory used=2160.1MB, alloc=516.3MB, time=30.62 memory used=2201.7MB, alloc=516.3MB, time=31.56 memory used=2402.3MB, alloc=540.3MB, time=35.13 memory used=2604.9MB, alloc=564.3MB, time=38.58 memory used=2828.2MB, alloc=588.3MB, time=41.79 memory used=2988.6MB, alloc=612.3MB, time=43.46 memory used=3233.2MB, alloc=612.3MB, time=46.24 memory used=3434.9MB, alloc=612.3MB, time=49.25 memory used=3620.0MB, alloc=636.3MB, time=52.14 memory used=3747.1MB, alloc=636.3MB, time=54.54 memory used=3904.4MB, alloc=660.3MB, time=57.82 memory used=4052.3MB, alloc=660.3MB, time=60.72 memory used=4184.1MB, alloc=660.3MB, time=63.21 memory used=4312.1MB, alloc=684.3MB, time=66.04 memory used=4446.7MB, alloc=684.3MB, time=68.34 memory used=4585.3MB, alloc=684.3MB, time=70.44 memory used=4684.4MB, alloc=684.3MB, time=72.39 memory used=4914.0MB, alloc=684.3MB, time=74.84 memory used=5079.3MB, alloc=684.3MB, time=76.91 memory used=5279.4MB, alloc=684.3MB, time=79.00 memory used=5371.6MB, alloc=684.3MB, time=81.06 memory used=5656.9MB, alloc=708.3MB, time=85.07 memory used=5867.0MB, alloc=708.3MB, time=87.33 memory used=6080.0MB, alloc=708.3MB, time=89.23 memory used=6277.0MB, alloc=708.3MB, time=90.90 memory used=6601.3MB, alloc=732.3MB, time=95.03 memory used=7025.2MB, alloc=756.3MB, time=101.89 memory used=7428.8MB, alloc=780.3MB, time=109.53 memory used=7814.0MB, alloc=804.3MB, time=116.48 memory used=8073.3MB, alloc=828.3MB, time=119.12 memory used=8326.3MB, alloc=852.3MB, time=122.38 memory used=8573.9MB, alloc=876.3MB, time=126.64 memory used=8787.7MB, alloc=876.3MB, time=128.25 memory used=9195.3MB, alloc=900.3MB, time=133.80 memory used=9595.1MB, alloc=924.3MB, time=138.51 memory used=9912.2MB, alloc=924.3MB, time=141.52 memory used=10364.1MB, alloc=924.3MB, time=147.38 memory used=10689.1MB, alloc=948.3MB, time=153.26 memory used=10983.4MB, alloc=972.3MB, time=160.19 memory used=11240.9MB, alloc=996.3MB, time=164.69 memory used=11557.4MB, alloc=1020.3MB, time=169.07 |\^/| 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(); 1428297792 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-13 x y - 12 y - 16 z - 1, 10 x y + 8 x y z - 20 y + 18 z, 3 2 7 x + 12 y z - 19 x - 20 y] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 G := [16 x y - 16 x z - 20 y - 17 z, -4 x y + 13 y - 5 z + 18 y, 2 2 2 -7 x z + 12 x z + 10 y + 13] > Problem := [F,G]; 2 2 2 Problem := [[-13 x y - 12 y - 16 z - 1, 10 x y + 8 x y z - 20 y + 18 z, 3 2 7 x + 12 y z - 19 x - 20 y], [16 x y - 16 x z - 20 y - 17 z, 2 3 2 2 2 2 -4 x y + 13 y - 5 z + 18 y, -7 x z + 12 x z + 10 y + 13]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.4MB, alloc=32.3MB, time=0.52 memory used=47.2MB, alloc=56.3MB, time=0.84 memory used=88.5MB, alloc=60.3MB, time=1.45 memory used=126.6MB, alloc=84.3MB, time=2.03 memory used=168.5MB, alloc=84.3MB, time=2.66 memory used=233.4MB, alloc=92.3MB, time=3.66 memory used=295.4MB, alloc=116.3MB, time=4.64 memory used=378.7MB, alloc=116.3MB, time=5.69 memory used=443.9MB, alloc=372.3MB, time=6.56 memory used=530.9MB, alloc=396.3MB, time=7.73 memory used=639.8MB, alloc=396.3MB, time=9.46 memory used=744.2MB, alloc=420.3MB, time=11.26 memory used=876.7MB, alloc=444.3MB, time=13.47 memory used=1014.5MB, alloc=444.3MB, time=14.99 memory used=1148.1MB, alloc=468.3MB, time=16.81 memory used=1263.2MB, alloc=468.3MB, time=18.77 memory used=1366.4MB, alloc=468.3MB, time=20.53 memory used=1451.0MB, alloc=492.3MB, time=21.87 memory used=1575.2MB, alloc=492.3MB, time=24.19 memory used=1654.4MB, alloc=492.3MB, time=25.59 memory used=1720.3MB, alloc=516.3MB, time=26.64 memory used=1807.2MB, alloc=516.3MB, time=28.39 memory used=1880.5MB, alloc=516.3MB, time=29.61 memory used=1953.6MB, alloc=516.3MB, time=31.03 memory used=2013.0MB, alloc=516.3MB, time=32.28 memory used=2064.4MB, alloc=516.3MB, time=33.37 memory used=2113.5MB, alloc=516.3MB, time=34.19 memory used=2173.5MB, alloc=516.3MB, time=35.75 memory used=2220.0MB, alloc=516.3MB, time=36.91 memory used=2421.8MB, alloc=540.3MB, time=41.08 memory used=2623.2MB, alloc=564.3MB, time=43.71 memory used=2808.7MB, alloc=588.3MB, time=47.05 memory used=2998.9MB, alloc=612.3MB, time=50.40 memory used=3123.5MB, alloc=612.3MB, time=52.62 memory used=3271.1MB, alloc=612.3MB, time=55.59 memory used=3441.6MB, alloc=636.3MB, time=59.48 memory used=3587.2MB, alloc=636.3MB, time=62.77 memory used=3725.7MB, alloc=660.3MB, time=65.92 memory used=3840.2MB, alloc=660.3MB, time=68.25 memory used=3973.9MB, alloc=660.3MB, time=71.37 memory used=4091.0MB, alloc=660.3MB, time=74.02 memory used=4200.4MB, alloc=660.3MB, time=76.88 memory used=4529.4MB, alloc=684.3MB, time=83.90 memory used=4880.2MB, alloc=708.3MB, time=90.73 memory used=5210.3MB, alloc=732.3MB, time=96.04 memory used=5579.0MB, alloc=756.3MB, time=102.79 memory used=5946.9MB, alloc=780.3MB, time=109.40 memory used=6273.8MB, alloc=804.3MB, time=115.21 memory used=6592.2MB, alloc=828.3MB, time=123.16 memory used=6897.8MB, alloc=852.3MB, time=130.28 memory used=7228.4MB, alloc=876.3MB, time=138.66 memory used=7446.5MB, alloc=900.3MB, time=144.67 memory used=7682.1MB, alloc=924.3MB, time=150.18 memory used=7955.1MB, alloc=948.3MB, time=156.38 memory used=8165.7MB, alloc=972.3MB, time=162.40 |\^/| 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(); 1428298092 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 2 F := [14 x + 5 x y - 3 x z - 7 y z, -5 y z + 17 y z + 17 z - 17 x, 2 3 2 -12 x y + 14 z + 11 x + 8 y] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [-9 x y + 4 x z - 9 y z - 9, -3 y z - 6 x + 20 y z + 18 z, 2 2 20 x z - 3 x y + 18 x y - 9 y z] > Problem := [F,G]; 3 2 2 2 2 2 Problem := [[14 x + 5 x y - 3 x z - 7 y z, -5 y z + 17 y z + 17 z - 17 x, 2 3 2 2 -12 x y + 14 z + 11 x + 8 y], [-9 x y + 4 x z - 9 y z - 9, 2 2 2 2 -3 y z - 6 x + 20 y z + 18 z, 20 x z - 3 x y + 18 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=4.5MB, alloc=32.3MB, time=0.18 memory used=26.2MB, alloc=32.3MB, time=0.50 memory used=44.8MB, alloc=56.3MB, time=0.77 memory used=84.8MB, alloc=60.3MB, time=1.33 memory used=133.6MB, alloc=68.3MB, time=1.82 memory used=177.7MB, alloc=68.3MB, time=2.52 memory used=220.6MB, alloc=92.3MB, time=3.09 memory used=287.8MB, alloc=92.3MB, time=3.83 memory used=353.8MB, alloc=92.3MB, time=4.79 memory used=416.2MB, alloc=348.3MB, time=5.56 memory used=484.4MB, alloc=372.3MB, time=6.51 memory used=574.3MB, alloc=372.3MB, time=7.74 memory used=637.4MB, alloc=372.3MB, time=8.19 memory used=693.7MB, alloc=372.3MB, time=8.54 memory used=751.5MB, alloc=372.3MB, time=8.96 memory used=848.0MB, alloc=396.3MB, time=10.11 memory used=968.7MB, alloc=396.3MB, time=11.49 memory used=1093.7MB, alloc=396.3MB, time=13.05 memory used=1189.1MB, alloc=420.3MB, time=14.34 memory used=1314.1MB, alloc=420.3MB, time=16.00 memory used=1415.8MB, alloc=444.3MB, time=17.42 memory used=1502.3MB, alloc=444.3MB, time=18.61 memory used=1602.5MB, alloc=444.3MB, time=20.11 memory used=1704.1MB, alloc=468.3MB, time=21.66 memory used=1800.0MB, alloc=468.3MB, time=22.81 memory used=1928.0MB, alloc=468.3MB, time=24.25 memory used=2055.8MB, alloc=468.3MB, time=25.45 memory used=2160.8MB, alloc=468.3MB, time=26.45 memory used=2270.7MB, alloc=468.3MB, time=27.93 memory used=2369.0MB, alloc=468.3MB, time=29.74 memory used=2481.0MB, alloc=468.3MB, time=31.69 memory used=2566.0MB, alloc=468.3MB, time=32.94 memory used=2680.8MB, alloc=468.3MB, time=34.02 memory used=2744.1MB, alloc=468.3MB, time=35.10 memory used=2800.4MB, alloc=492.3MB, time=36.05 memory used=2861.6MB, alloc=492.3MB, time=37.18 memory used=2910.6MB, alloc=492.3MB, time=38.13 memory used=2955.6MB, alloc=492.3MB, time=39.04 memory used=3006.6MB, alloc=492.3MB, time=40.11 memory used=3050.5MB, alloc=492.3MB, time=41.00 memory used=3173.3MB, alloc=492.3MB, time=42.20 memory used=3283.7MB, alloc=492.3MB, time=43.34 memory used=3473.2MB, alloc=516.3MB, time=45.71 memory used=3668.5MB, alloc=516.3MB, time=48.12 memory used=3775.0MB, alloc=516.3MB, time=49.11 memory used=3890.4MB, alloc=516.3MB, time=50.15 memory used=4099.8MB, alloc=540.3MB, time=52.91 memory used=4226.4MB, alloc=540.3MB, time=53.97 memory used=4355.4MB, alloc=540.3MB, time=55.22 memory used=4481.5MB, alloc=540.3MB, time=56.45 memory used=4606.6MB, alloc=540.3MB, time=57.69 memory used=4718.4MB, alloc=540.3MB, time=58.49 memory used=4913.3MB, alloc=564.3MB, time=60.81 memory used=5119.9MB, alloc=564.3MB, time=63.31 memory used=5310.1MB, alloc=564.3MB, time=66.28 memory used=5451.6MB, alloc=564.3MB, time=68.57 memory used=5585.0MB, alloc=588.3MB, time=70.85 memory used=5751.7MB, alloc=588.3MB, time=72.72 memory used=5901.2MB, alloc=588.3MB, time=74.27 memory used=6009.4MB, alloc=588.3MB, time=76.02 memory used=6213.5MB, alloc=612.3MB, time=78.57 memory used=6389.3MB, alloc=612.3MB, time=80.14 memory used=6558.5MB, alloc=612.3MB, time=82.10 memory used=6715.5MB, alloc=612.3MB, time=83.50 memory used=6863.0MB, alloc=612.3MB, time=85.37 memory used=7056.3MB, alloc=612.3MB, time=88.01 memory used=7228.9MB, alloc=612.3MB, time=90.17 memory used=7401.1MB, alloc=612.3MB, time=92.28 memory used=7574.7MB, alloc=612.3MB, time=94.36 memory used=7722.4MB, alloc=612.3MB, time=96.29 memory used=7886.6MB, alloc=636.3MB, time=98.82 memory used=8001.8MB, alloc=636.3MB, time=100.64 memory used=8184.5MB, alloc=636.3MB, time=103.37 memory used=8308.2MB, alloc=636.3MB, time=105.22 memory used=8447.1MB, alloc=636.3MB, time=107.74 memory used=8535.5MB, alloc=636.3MB, time=109.75 memory used=8624.8MB, alloc=636.3MB, time=111.47 memory used=8951.1MB, alloc=660.3MB, time=115.54 memory used=9299.9MB, alloc=684.3MB, time=119.55 memory used=9620.6MB, alloc=708.3MB, time=124.80 memory used=9961.2MB, alloc=732.3MB, time=129.57 memory used=10279.8MB, alloc=756.3MB, time=135.47 memory used=10534.8MB, alloc=780.3MB, time=138.90 memory used=10892.0MB, alloc=804.3MB, time=144.11 memory used=11212.1MB, alloc=828.3MB, time=148.93 memory used=11613.1MB, alloc=852.3MB, time=153.62 memory used=11865.9MB, alloc=876.3MB, time=158.74 memory used=12120.3MB, alloc=900.3MB, time=163.10 |\^/| 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(); 1428298392 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 F := [-11 x + 5 y - 10 x + 6 z, -16 x + 7 y z - 17 x y + 18, 3 3 7 x + 14 x y z - 4 z + 10 x y] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 G := [19 x + y z - 7 y + 9 y, -6 x y - 15 x y + 17 x z - 3 y , 2 3 2 3 -17 x z - 14 y + 12 y z - z ] > Problem := [F,G]; 2 2 3 2 Problem := [[-11 x + 5 y - 10 x + 6 z, -16 x + 7 y z - 17 x y + 18, 3 3 3 2 2 7 x + 14 x y z - 4 z + 10 x y], [19 x + y z - 7 y + 9 y, 2 2 2 3 2 3 -6 x y - 15 x y + 17 x z - 3 y , -17 x z - 14 y + 12 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=0.17 memory used=25.8MB, alloc=32.3MB, time=0.49 memory used=47.0MB, alloc=32.3MB, time=0.72 memory used=61.6MB, alloc=32.3MB, time=0.81 memory used=75.5MB, alloc=32.3MB, time=0.92 memory used=98.8MB, alloc=60.3MB, time=1.23 memory used=156.5MB, alloc=72.3MB, time=1.87 memory used=200.5MB, alloc=72.3MB, time=2.30 memory used=247.8MB, alloc=72.3MB, time=2.84 memory used=298.0MB, alloc=72.3MB, time=3.42 memory used=338.6MB, alloc=72.3MB, time=3.85 memory used=378.7MB, alloc=96.3MB, time=4.45 memory used=443.0MB, alloc=96.3MB, time=5.08 memory used=496.7MB, alloc=96.3MB, time=5.55 memory used=556.3MB, alloc=96.3MB, time=6.10 memory used=632.1MB, alloc=352.3MB, time=7.01 memory used=712.6MB, alloc=352.3MB, time=8.03 memory used=774.8MB, alloc=376.3MB, time=8.87 memory used=859.1MB, alloc=376.3MB, time=9.69 memory used=960.4MB, alloc=376.3MB, time=10.56 memory used=1035.0MB, alloc=376.3MB, time=11.50 memory used=1108.0MB, alloc=376.3MB, time=12.15 memory used=1168.2MB, alloc=376.3MB, time=13.28 memory used=1216.2MB, alloc=376.3MB, time=13.46 memory used=1252.2MB, alloc=376.3MB, time=13.59 memory used=1300.6MB, alloc=376.3MB, time=13.82 memory used=1354.4MB, alloc=376.3MB, time=14.10 memory used=1407.6MB, alloc=376.3MB, time=14.35 memory used=1468.0MB, alloc=376.3MB, time=15.88 memory used=1506.8MB, alloc=376.3MB, time=16.02 memory used=1551.7MB, alloc=376.3MB, time=16.17 memory used=1599.2MB, alloc=376.3MB, time=16.42 memory used=1657.6MB, alloc=376.3MB, time=16.75 memory used=1709.7MB, alloc=376.3MB, time=16.98 memory used=1767.9MB, alloc=376.3MB, time=18.50 memory used=1810.0MB, alloc=376.3MB, time=18.65 memory used=1850.3MB, alloc=376.3MB, time=18.79 memory used=1896.2MB, alloc=376.3MB, time=19.04 memory used=1945.5MB, alloc=376.3MB, time=19.31 memory used=2005.7MB, alloc=376.3MB, time=20.44 memory used=2053.5MB, alloc=376.3MB, time=20.61 memory used=2088.6MB, alloc=376.3MB, time=20.75 memory used=2132.2MB, alloc=376.3MB, time=20.89 memory used=2178.3MB, alloc=376.3MB, time=21.22 memory used=2227.5MB, alloc=376.3MB, time=21.51 memory used=2310.6MB, alloc=376.3MB, time=22.31 memory used=2393.5MB, alloc=376.3MB, time=23.06 memory used=2484.4MB, alloc=400.3MB, time=24.19 memory used=2590.8MB, alloc=400.3MB, time=25.40 memory used=2703.0MB, alloc=400.3MB, time=26.94 memory used=2829.0MB, alloc=424.3MB, time=28.41 memory used=2962.0MB, alloc=424.3MB, time=30.25 memory used=3085.3MB, alloc=448.3MB, time=31.73 memory used=3176.1MB, alloc=448.3MB, time=32.33 memory used=3251.9MB, alloc=448.3MB, time=32.66 memory used=3335.7MB, alloc=448.3MB, time=33.78 memory used=3405.9MB, alloc=448.3MB, time=34.06 memory used=3466.5MB, alloc=448.3MB, time=34.30 memory used=3546.2MB, alloc=448.3MB, time=34.55 memory used=3658.2MB, alloc=448.3MB, time=35.29 memory used=3762.8MB, alloc=448.3MB, time=36.47 memory used=3910.4MB, alloc=448.3MB, time=37.77 memory used=4034.1MB, alloc=448.3MB, time=38.94 memory used=4105.4MB, alloc=448.3MB, time=39.29 memory used=4190.9MB, alloc=448.3MB, time=40.41 memory used=4259.1MB, alloc=448.3MB, time=40.71 memory used=4323.0MB, alloc=448.3MB, time=40.97 memory used=4384.1MB, alloc=448.3MB, time=41.21 memory used=4467.0MB, alloc=448.3MB, time=41.47 memory used=4562.8MB, alloc=448.3MB, time=41.88 memory used=4654.6MB, alloc=448.3MB, time=42.57 memory used=4718.7MB, alloc=448.3MB, time=42.86 memory used=4798.0MB, alloc=448.3MB, time=43.24 memory used=4878.3MB, alloc=448.3MB, time=44.72 memory used=4946.9MB, alloc=448.3MB, time=45.01 memory used=5008.8MB, alloc=448.3MB, time=45.28 memory used=5070.1MB, alloc=448.3MB, time=45.54 memory used=5148.0MB, alloc=448.3MB, time=45.79 memory used=5271.2MB, alloc=448.3MB, time=46.40 memory used=5378.5MB, alloc=448.3MB, time=47.63 memory used=5485.0MB, alloc=472.3MB, time=49.01 memory used=5565.5MB, alloc=472.3MB, time=50.25 memory used=5645.0MB, alloc=472.3MB, time=51.48 memory used=5775.0MB, alloc=472.3MB, time=52.87 memory used=5881.6MB, alloc=472.3MB, time=54.01 memory used=5976.4MB, alloc=472.3MB, time=55.20 memory used=6063.7MB, alloc=496.3MB, time=56.38 memory used=6160.0MB, alloc=496.3MB, time=57.51 memory used=6224.5MB, alloc=496.3MB, time=58.56 memory used=6278.6MB, alloc=496.3MB, time=59.53 memory used=6340.3MB, alloc=496.3MB, time=60.71 memory used=6415.0MB, alloc=496.3MB, time=62.15 memory used=6483.2MB, alloc=496.3MB, time=63.23 memory used=6564.1MB, alloc=496.3MB, time=64.30 memory used=6636.1MB, alloc=520.3MB, time=65.27 memory used=6752.6MB, alloc=520.3MB, time=66.41 memory used=6845.1MB, alloc=520.3MB, time=67.45 memory used=6974.7MB, alloc=520.3MB, time=68.88 memory used=7045.9MB, alloc=520.3MB, time=70.11 memory used=7113.5MB, alloc=520.3MB, time=71.09 memory used=7167.4MB, alloc=520.3MB, time=72.00 memory used=7230.4MB, alloc=520.3MB, time=73.04 memory used=7283.0MB, alloc=520.3MB, time=73.92 memory used=7506.7MB, alloc=544.3MB, time=76.41 memory used=7759.3MB, alloc=568.3MB, time=79.00 memory used=7960.1MB, alloc=592.3MB, time=82.29 memory used=8130.1MB, alloc=616.3MB, time=84.58 memory used=8343.0MB, alloc=616.3MB, time=86.92 memory used=8519.3MB, alloc=640.3MB, time=89.67 memory used=8676.5MB, alloc=640.3MB, time=91.75 memory used=8821.2MB, alloc=664.3MB, time=93.74 memory used=9064.3MB, alloc=664.3MB, time=96.87 memory used=9274.9MB, alloc=664.3MB, time=99.41 memory used=9426.3MB, alloc=664.3MB, time=102.31 memory used=9619.0MB, alloc=664.3MB, time=103.84 memory used=9805.8MB, alloc=688.3MB, time=107.63 memory used=9968.3MB, alloc=688.3MB, time=108.50 memory used=10165.1MB, alloc=688.3MB, time=109.81 memory used=10365.0MB, alloc=688.3MB, time=113.77 memory used=10518.2MB, alloc=688.3MB, time=114.60 memory used=10713.9MB, alloc=688.3MB, time=115.91 memory used=10913.7MB, alloc=688.3MB, time=119.83 memory used=11077.5MB, alloc=688.3MB, time=120.68 memory used=11280.8MB, alloc=688.3MB, time=124.80 memory used=11448.9MB, alloc=688.3MB, time=125.70 memory used=11637.9MB, alloc=688.3MB, time=127.13 memory used=11828.5MB, alloc=688.3MB, time=128.26 memory used=12015.6MB, alloc=688.3MB, time=132.16 memory used=12185.3MB, alloc=688.3MB, time=133.23 memory used=12381.5MB, alloc=688.3MB, time=134.41 memory used=12572.5MB, alloc=688.3MB, time=138.28 memory used=12753.7MB, alloc=688.3MB, time=139.28 memory used=12941.0MB, alloc=688.3MB, time=140.35 memory used=13129.6MB, alloc=688.3MB, time=144.16 memory used=13314.7MB, alloc=688.3MB, time=145.16 memory used=13498.6MB, alloc=688.3MB, time=149.13 memory used=13708.1MB, alloc=688.3MB, time=151.16 memory used=13880.6MB, alloc=688.3MB, time=153.73 memory used=14133.2MB, alloc=688.3MB, time=156.83 memory used=14279.9MB, alloc=688.3MB, time=158.98 memory used=14402.2MB, alloc=688.3MB, time=161.06 memory used=14526.3MB, alloc=688.3MB, time=162.85 memory used=14620.6MB, alloc=688.3MB, time=165.04 memory used=14704.7MB, alloc=688.3MB, time=166.84 memory used=14768.9MB, alloc=688.3MB, time=168.32 memory used=14945.6MB, alloc=712.3MB, time=170.78 memory used=15305.5MB, alloc=736.3MB, time=175.83 memory used=15728.5MB, alloc=760.3MB, time=182.09 memory used=16031.9MB, alloc=784.3MB, time=186.16 memory used=16479.6MB, alloc=808.3MB, time=192.52 memory used=16882.2MB, alloc=832.3MB, time=198.85 memory used=17199.1MB, alloc=856.3MB, time=204.16 |\^/| 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(); 1428298692 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 2 3 F := [18 x y + 10 x z - 8 z - 18 x , -10 x y + 8 x z - 13 y + 17 x z, 3 2 -10 x - 17 x z + 11 z - 6 z] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 3 G := [-5 y z - 16 y + 5 y z - 17, 12 x y + 2 x z - 11 y , 2 2 5 x y + 12 y z - 8 z - 13] > Problem := [F,G]; 2 2 3 2 Problem := [[18 x y + 10 x z - 8 z - 18 x , 2 2 3 3 2 -10 x y + 8 x z - 13 y + 17 x z, -10 x - 17 x z + 11 z - 6 z], [ 2 2 2 2 3 -5 y z - 16 y + 5 y z - 17, 12 x y + 2 x z - 11 y , 2 2 5 x y + 12 y z - 8 z - 13]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.17 memory used=23.8MB, alloc=32.3MB, time=0.45 memory used=42.4MB, alloc=56.3MB, time=0.73 memory used=81.9MB, alloc=60.3MB, time=1.21 memory used=128.7MB, alloc=68.3MB, time=1.68 memory used=174.9MB, alloc=68.3MB, time=2.23 memory used=220.0MB, alloc=68.3MB, time=2.62 memory used=265.0MB, alloc=68.3MB, time=3.19 memory used=307.9MB, alloc=68.3MB, time=3.56 memory used=330.7MB, alloc=68.3MB, time=3.63 memory used=360.5MB, alloc=68.3MB, time=3.78 memory used=386.9MB, alloc=68.3MB, time=4.16 memory used=423.1MB, alloc=68.3MB, time=4.38 memory used=443.4MB, alloc=68.3MB, time=4.44 memory used=473.7MB, alloc=68.3MB, time=4.63 memory used=494.1MB, alloc=68.3MB, time=4.71 memory used=523.2MB, alloc=68.3MB, time=4.83 memory used=565.7MB, alloc=68.3MB, time=5.35 memory used=586.4MB, alloc=68.3MB, time=5.44 memory used=605.3MB, alloc=68.3MB, time=5.51 memory used=653.0MB, alloc=68.3MB, time=5.98 memory used=705.7MB, alloc=68.3MB, time=6.29 memory used=756.4MB, alloc=68.3MB, time=6.63 memory used=787.0MB, alloc=68.3MB, time=6.80 memory used=805.9MB, alloc=68.3MB, time=6.88 memory used=828.1MB, alloc=68.3MB, time=6.96 memory used=844.3MB, alloc=68.3MB, time=7.03 memory used=873.4MB, alloc=68.3MB, time=7.25 memory used=894.8MB, alloc=68.3MB, time=7.33 memory used=911.6MB, alloc=68.3MB, time=7.40 memory used=944.0MB, alloc=68.3MB, time=7.70 memory used=975.7MB, alloc=68.3MB, time=7.81 memory used=993.5MB, alloc=92.3MB, time=7.90 memory used=1031.6MB, alloc=92.3MB, time=8.01 memory used=1071.5MB, alloc=92.3MB, time=8.12 memory used=1102.1MB, alloc=92.3MB, time=8.22 memory used=1143.0MB, alloc=92.3MB, time=9.18 memory used=1192.3MB, alloc=92.3MB, time=9.90 memory used=1232.5MB, alloc=92.3MB, time=10.02 memory used=1264.3MB, alloc=92.3MB, time=10.11 memory used=1303.3MB, alloc=92.3MB, time=10.22 memory used=1343.2MB, alloc=92.3MB, time=10.31 memory used=1379.6MB, alloc=92.3MB, time=10.49 memory used=1473.0MB, alloc=92.3MB, time=11.55 memory used=1555.8MB, alloc=92.3MB, time=13.59 memory used=1639.9MB, alloc=92.3MB, time=14.78 memory used=1724.7MB, alloc=92.3MB, time=15.97 memory used=1808.5MB, alloc=92.3MB, time=17.48 memory used=1891.6MB, alloc=92.3MB, time=19.54 memory used=1972.6MB, alloc=92.3MB, time=22.09 memory used=2054.5MB, alloc=92.3MB, time=24.89 memory used=2136.5MB, alloc=92.3MB, time=28.07 memory used=2218.5MB, alloc=92.3MB, time=30.18 memory used=2318.9MB, alloc=92.3MB, time=32.57 memory used=2402.1MB, alloc=92.3MB, time=33.65 memory used=2487.5MB, alloc=92.3MB, time=34.53 memory used=2572.4MB, alloc=92.3MB, time=35.76 memory used=2655.8MB, alloc=92.3MB, time=37.26 memory used=2739.1MB, alloc=92.3MB, time=39.15 memory used=2822.7MB, alloc=92.3MB, time=41.34 memory used=2904.1MB, alloc=92.3MB, time=43.04 memory used=2984.5MB, alloc=92.3MB, time=44.80 memory used=3024.8MB, alloc=92.3MB, time=44.92 memory used=3064.1MB, alloc=92.3MB, time=45.09 memory used=3122.2MB, alloc=92.3MB, time=45.69 memory used=3154.0MB, alloc=92.3MB, time=45.79 memory used=3220.4MB, alloc=92.3MB, time=46.28 memory used=3306.2MB, alloc=94.9MB, time=46.82 memory used=3352.5MB, alloc=94.9MB, time=47.10 memory used=3387.5MB, alloc=94.9MB, time=47.21 memory used=3417.6MB, alloc=94.9MB, time=47.31 memory used=3461.9MB, alloc=94.9MB, time=47.57 memory used=3493.5MB, alloc=94.9MB, time=47.68 memory used=3528.4MB, alloc=94.9MB, time=47.78 memory used=3580.5MB, alloc=94.9MB, time=48.21 memory used=3617.3MB, alloc=94.9MB, time=48.34 memory used=3654.1MB, alloc=94.9MB, time=48.46 memory used=3684.6MB, alloc=94.9MB, time=48.56 memory used=3711.8MB, alloc=94.9MB, time=48.65 memory used=3743.3MB, alloc=94.9MB, time=48.75 memory used=3780.0MB, alloc=94.9MB, time=48.85 memory used=3815.2MB, alloc=94.9MB, time=48.94 memory used=3861.4MB, alloc=94.9MB, time=50.42 memory used=3897.9MB, alloc=94.9MB, time=50.54 memory used=3924.5MB, alloc=94.9MB, time=50.65 memory used=3957.1MB, alloc=94.9MB, time=50.75 memory used=3997.2MB, alloc=94.9MB, time=50.86 memory used=4023.9MB, alloc=94.9MB, time=50.95 memory used=4049.1MB, alloc=94.9MB, time=51.03 memory used=4077.5MB, alloc=94.9MB, time=51.11 memory used=4110.2MB, alloc=94.9MB, time=51.20 memory used=4185.5MB, alloc=94.9MB, time=51.88 memory used=4274.2MB, alloc=94.9MB, time=53.02 memory used=4360.4MB, alloc=94.9MB, time=54.03 memory used=4444.5MB, alloc=94.9MB, time=54.95 memory used=4521.8MB, alloc=94.9MB, time=56.11 memory used=4592.1MB, alloc=94.9MB, time=56.98 memory used=4676.8MB, alloc=94.9MB, time=57.69 memory used=4736.7MB, alloc=118.9MB, time=58.55 memory used=4806.7MB, alloc=374.9MB, time=59.19 memory used=4900.8MB, alloc=374.9MB, time=60.34 memory used=4988.4MB, alloc=398.9MB, time=61.46 memory used=5130.3MB, alloc=398.9MB, time=62.56 memory used=5254.4MB, alloc=398.9MB, time=63.79 memory used=5370.9MB, alloc=398.9MB, time=65.00 memory used=5418.2MB, alloc=398.9MB, time=65.18 memory used=5488.5MB, alloc=398.9MB, time=69.26 memory used=5557.3MB, alloc=398.9MB, time=69.60 memory used=5599.8MB, alloc=398.9MB, time=69.77 memory used=5656.8MB, alloc=398.9MB, time=69.96 memory used=5697.8MB, alloc=398.9MB, time=70.12 memory used=5739.2MB, alloc=398.9MB, time=70.26 memory used=5835.4MB, alloc=398.9MB, time=71.09 memory used=5942.2MB, alloc=422.9MB, time=72.52 memory used=6070.3MB, alloc=422.9MB, time=74.20 memory used=6195.7MB, alloc=446.9MB, time=75.62 memory used=6303.5MB, alloc=446.9MB, time=77.00 memory used=6414.8MB, alloc=446.9MB, time=78.21 memory used=6508.5MB, alloc=470.9MB, time=79.56 memory used=6613.6MB, alloc=470.9MB, time=80.76 memory used=6736.9MB, alloc=470.9MB, time=81.76 memory used=6834.6MB, alloc=470.9MB, time=82.23 memory used=6953.4MB, alloc=470.9MB, time=83.21 memory used=7067.0MB, alloc=470.9MB, time=84.14 memory used=7163.1MB, alloc=470.9MB, time=84.60 memory used=7269.4MB, alloc=470.9MB, time=85.46 memory used=7358.7MB, alloc=470.9MB, time=85.88 memory used=7448.5MB, alloc=470.9MB, time=86.38 memory used=7539.2MB, alloc=470.9MB, time=86.82 memory used=7631.1MB, alloc=470.9MB, time=87.24 memory used=7718.7MB, alloc=470.9MB, time=87.73 memory used=7824.5MB, alloc=470.9MB, time=88.28 memory used=7909.6MB, alloc=470.9MB, time=88.76 memory used=8008.1MB, alloc=470.9MB, time=89.36 memory used=8097.0MB, alloc=470.9MB, time=89.78 memory used=8183.7MB, alloc=470.9MB, time=90.26 memory used=8286.5MB, alloc=470.9MB, time=90.81 memory used=8384.7MB, alloc=470.9MB, time=92.17 memory used=8462.4MB, alloc=470.9MB, time=92.51 memory used=8543.8MB, alloc=470.9MB, time=92.81 memory used=8635.9MB, alloc=470.9MB, time=93.27 memory used=8735.2MB, alloc=470.9MB, time=94.55 memory used=8812.9MB, alloc=470.9MB, time=94.89 memory used=8894.6MB, alloc=470.9MB, time=95.20 memory used=8991.4MB, alloc=470.9MB, time=95.70 memory used=9071.1MB, alloc=470.9MB, time=96.05 memory used=9166.5MB, alloc=470.9MB, time=97.79 memory used=9243.4MB, alloc=470.9MB, time=98.11 memory used=9326.5MB, alloc=470.9MB, time=98.44 memory used=9410.6MB, alloc=470.9MB, time=98.82 memory used=9515.2MB, alloc=470.9MB, time=100.23 memory used=9591.8MB, alloc=470.9MB, time=100.58 memory used=9674.7MB, alloc=470.9MB, time=100.89 memory used=9770.5MB, alloc=470.9MB, time=101.45 memory used=9855.3MB, alloc=470.9MB, time=101.83 memory used=9933.9MB, alloc=470.9MB, time=102.15 memory used=10054.6MB, alloc=470.9MB, time=115.84 memory used=10141.2MB, alloc=470.9MB, time=116.21 memory used=10204.7MB, alloc=470.9MB, time=116.51 memory used=10279.2MB, alloc=470.9MB, time=116.82 memory used=10369.1MB, alloc=470.9MB, time=117.15 memory used=10448.8MB, alloc=470.9MB, time=117.46 memory used=10505.9MB, alloc=470.9MB, time=117.74 memory used=10567.8MB, alloc=470.9MB, time=118.01 memory used=10635.7MB, alloc=470.9MB, time=118.31 memory used=10709.7MB, alloc=470.9MB, time=118.59 memory used=10791.2MB, alloc=470.9MB, time=118.86 memory used=10886.9MB, alloc=470.9MB, time=119.15 memory used=11004.5MB, alloc=470.9MB, time=119.73 memory used=11086.9MB, alloc=470.9MB, time=120.06 memory used=11187.4MB, alloc=470.9MB, time=120.62 memory used=11266.6MB, alloc=470.9MB, time=120.97 memory used=11338.0MB, alloc=470.9MB, time=121.28 memory used=11462.3MB, alloc=470.9MB, time=134.85 memory used=11545.5MB, alloc=470.9MB, time=135.19 memory used=11610.7MB, alloc=470.9MB, time=135.52 memory used=11688.8MB, alloc=470.9MB, time=135.83 memory used=11783.1MB, alloc=470.9MB, time=136.16 memory used=11850.1MB, alloc=470.9MB, time=136.43 memory used=11908.6MB, alloc=470.9MB, time=136.70 memory used=11971.7MB, alloc=470.9MB, time=136.96 memory used=12040.6MB, alloc=470.9MB, time=137.23 memory used=12117.1MB, alloc=470.9MB, time=137.51 memory used=12201.1MB, alloc=470.9MB, time=137.78 memory used=12319.9MB, alloc=470.9MB, time=138.24 memory used=12417.4MB, alloc=470.9MB, time=138.94 memory used=12499.1MB, alloc=470.9MB, time=139.31 memory used=12576.3MB, alloc=470.9MB, time=139.62 memory used=12676.9MB, alloc=470.9MB, time=140.15 memory used=12762.0MB, alloc=470.9MB, time=140.49 memory used=12860.7MB, alloc=470.9MB, time=153.00 memory used=12954.7MB, alloc=470.9MB, time=154.34 memory used=13031.5MB, alloc=470.9MB, time=154.69 memory used=13100.7MB, alloc=470.9MB, time=155.03 memory used=13183.7MB, alloc=470.9MB, time=155.40 memory used=13279.2MB, alloc=470.9MB, time=155.73 memory used=13335.3MB, alloc=470.9MB, time=156.01 memory used=13395.2MB, alloc=470.9MB, time=156.30 memory used=13460.7MB, alloc=470.9MB, time=156.58 memory used=13532.8MB, alloc=470.9MB, time=156.87 memory used=13611.8MB, alloc=470.9MB, time=157.17 memory used=13699.0MB, alloc=470.9MB, time=157.45 memory used=13828.1MB, alloc=470.9MB, time=158.01 memory used=13910.3MB, alloc=470.9MB, time=158.37 memory used=13992.0MB, alloc=470.9MB, time=158.85 memory used=14080.4MB, alloc=470.9MB, time=159.25 memory used=14160.0MB, alloc=470.9MB, time=159.59 memory used=14280.1MB, alloc=470.9MB, time=173.05 memory used=14364.0MB, alloc=470.9MB, time=173.41 memory used=14429.9MB, alloc=470.9MB, time=173.73 memory used=14503.0MB, alloc=470.9MB, time=174.06 memory used=14590.8MB, alloc=470.9MB, time=174.39 memory used=14673.8MB, alloc=470.9MB, time=174.71 memory used=14730.2MB, alloc=470.9MB, time=174.99 memory used=14792.0MB, alloc=470.9MB, time=175.26 memory used=14858.6MB, alloc=470.9MB, time=175.55 memory used=14931.5MB, alloc=470.9MB, time=175.83 memory used=15012.2MB, alloc=470.9MB, time=176.11 memory used=15102.8MB, alloc=470.9MB, time=176.40 memory used=15217.5MB, alloc=470.9MB, time=177.00 memory used=15358.3MB, alloc=470.9MB, time=178.36 memory used=15541.8MB, alloc=470.9MB, time=179.90 memory used=15726.3MB, alloc=470.9MB, time=182.37 memory used=15910.6MB, alloc=470.9MB, time=186.06 memory used=16096.4MB, alloc=470.9MB, time=189.97 memory used=16257.4MB, alloc=470.9MB, time=192.91 memory used=16356.3MB, alloc=470.9MB, time=194.79 memory used=16431.0MB, alloc=470.9MB, time=195.12 memory used=16511.3MB, alloc=470.9MB, time=195.43 memory used=16685.4MB, alloc=494.9MB, time=197.14 memory used=16894.9MB, alloc=494.9MB, time=198.83 memory used=17104.0MB, alloc=494.9MB, time=201.19 memory used=17314.6MB, alloc=494.9MB, time=204.97 memory used=17527.1MB, alloc=494.9MB, time=209.59 memory used=17720.9MB, alloc=494.9MB, time=225.54 memory used=17829.1MB, alloc=494.9MB, time=227.03 memory used=17913.7MB, alloc=494.9MB, time=227.39 memory used=17999.8MB, alloc=494.9MB, time=227.76 memory used=18106.4MB, alloc=494.9MB, time=228.15 memory used=18187.3MB, alloc=494.9MB, time=228.46 memory used=18256.6MB, alloc=494.9MB, time=228.76 memory used=18333.9MB, alloc=494.9MB, time=229.06 memory used=18418.9MB, alloc=494.9MB, time=229.36 memory used=18514.1MB, alloc=494.9MB, time=229.67 memory used=18647.5MB, alloc=494.9MB, time=230.18 memory used=18780.3MB, alloc=494.9MB, time=231.93 memory used=19000.2MB, alloc=494.9MB, time=234.70 memory used=19210.2MB, alloc=494.9MB, time=237.48 memory used=19424.4MB, alloc=494.9MB, time=241.14 memory used=19639.5MB, alloc=494.9MB, time=247.25 memory used=19830.9MB, alloc=494.9MB, time=250.82 memory used=19931.9MB, alloc=494.9MB, time=251.85 memory used=20053.4MB, alloc=494.9MB, time=256.73 memory used=20141.4MB, alloc=494.9MB, time=257.12 memory used=20221.8MB, alloc=494.9MB, time=257.48 memory used=20324.7MB, alloc=494.9MB, time=257.87 memory used=20391.7MB, alloc=494.9MB, time=258.18 memory used=20465.3MB, alloc=494.9MB, time=258.49 memory used=20577.6MB, alloc=494.9MB, time=259.13 memory used=20656.1MB, alloc=494.9MB, time=260.52 memory used=20864.7MB, alloc=518.9MB, time=263.05 memory used=21054.5MB, alloc=518.9MB, time=265.49 memory used=21298.6MB, alloc=518.9MB, time=268.76 memory used=21538.8MB, alloc=518.9MB, time=274.22 memory used=21745.9MB, alloc=518.9MB, time=278.88 memory used=21843.1MB, alloc=518.9MB, time=280.27 memory used=21985.8MB, alloc=518.9MB, time=281.40 memory used=22101.0MB, alloc=518.9MB, time=282.04 memory used=22233.2MB, alloc=518.9MB, time=283.02 memory used=22358.4MB, alloc=518.9MB, time=283.71 memory used=22491.1MB, alloc=518.9MB, time=284.83 memory used=22611.5MB, alloc=518.9MB, time=285.70 memory used=22728.7MB, alloc=518.9MB, time=286.38 |\^/| 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(); 1428298992 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 F := [-3 x + 2 x y + 12 z + 7 z, 19 x z - 9 x y z - 5 y z + 2 y, 2 3 2 2 9 x y - 5 y - 18 y z - 7 x ] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 3 G := [20 x y - 10 x y - 10, -x + 20 y z - 13 x, 6 z - 20 x + 9] > Problem := [F,G]; 3 2 2 2 2 Problem := [[-3 x + 2 x y + 12 z + 7 z, 19 x z - 9 x y z - 5 y z + 2 y, 2 3 2 2 9 x y - 5 y - 18 y z - 7 x ], 2 3 3 [20 x y - 10 x y - 10, -x + 20 y z - 13 x, 6 z - 20 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=26.4MB, alloc=32.3MB, time=0.53 memory used=46.8MB, alloc=32.3MB, time=0.83 memory used=65.3MB, alloc=56.3MB, time=1.11 memory used=106.6MB, alloc=68.3MB, time=1.73 memory used=146.5MB, alloc=92.3MB, time=2.32 memory used=214.8MB, alloc=92.3MB, time=3.23 memory used=279.8MB, alloc=92.3MB, time=4.18 memory used=346.2MB, alloc=116.3MB, time=4.99 memory used=423.8MB, alloc=116.3MB, time=5.76 memory used=496.3MB, alloc=116.3MB, time=6.85 memory used=550.2MB, alloc=396.3MB, time=7.53 memory used=665.2MB, alloc=420.3MB, time=9.13 memory used=788.2MB, alloc=420.3MB, time=11.01 memory used=903.3MB, alloc=444.3MB, time=12.62 memory used=991.6MB, alloc=444.3MB, time=13.85 memory used=1103.7MB, alloc=444.3MB, time=15.56 memory used=1198.2MB, alloc=468.3MB, time=16.91 memory used=1340.0MB, alloc=468.3MB, time=18.31 memory used=1458.5MB, alloc=468.3MB, time=20.04 memory used=1563.6MB, alloc=468.3MB, time=21.46 memory used=1682.5MB, alloc=468.3MB, time=22.90 memory used=1762.0MB, alloc=468.3MB, time=24.18 memory used=1829.6MB, alloc=468.3MB, time=25.33 memory used=1906.5MB, alloc=468.3MB, time=26.60 memory used=1975.1MB, alloc=492.3MB, time=27.74 memory used=2039.2MB, alloc=492.3MB, time=28.94 memory used=2103.8MB, alloc=492.3MB, time=29.98 memory used=2190.0MB, alloc=492.3MB, time=30.89 memory used=2252.1MB, alloc=492.3MB, time=31.69 memory used=2328.9MB, alloc=492.3MB, time=32.48 memory used=2429.4MB, alloc=492.3MB, time=34.92 memory used=2526.2MB, alloc=492.3MB, time=35.62 memory used=2615.3MB, alloc=492.3MB, time=36.91 memory used=2734.6MB, alloc=492.3MB, time=38.69 memory used=2802.9MB, alloc=492.3MB, time=39.76 memory used=2865.9MB, alloc=492.3MB, time=40.81 memory used=2936.7MB, alloc=492.3MB, time=42.26 memory used=3009.0MB, alloc=492.3MB, time=43.11 memory used=3060.2MB, alloc=492.3MB, time=44.26 memory used=3091.1MB, alloc=492.3MB, time=45.05 memory used=3144.1MB, alloc=492.3MB, time=46.10 memory used=3248.0MB, alloc=492.3MB, time=46.97 memory used=3347.2MB, alloc=492.3MB, time=47.51 memory used=3443.1MB, alloc=492.3MB, time=48.15 memory used=3525.0MB, alloc=492.3MB, time=48.66 memory used=3634.3MB, alloc=492.3MB, time=51.19 memory used=3717.8MB, alloc=492.3MB, time=51.67 memory used=3807.7MB, alloc=492.3MB, time=52.25 memory used=3889.6MB, alloc=492.3MB, time=52.76 memory used=3986.1MB, alloc=492.3MB, time=53.39 memory used=4066.7MB, alloc=492.3MB, time=53.88 memory used=4172.9MB, alloc=492.3MB, time=56.43 memory used=4255.7MB, alloc=492.3MB, time=56.91 memory used=4395.5MB, alloc=492.3MB, time=58.38 memory used=4534.4MB, alloc=492.3MB, time=60.56 memory used=4692.8MB, alloc=516.3MB, time=62.21 memory used=4879.4MB, alloc=540.3MB, time=65.19 memory used=5059.1MB, alloc=564.3MB, time=68.33 memory used=5201.3MB, alloc=588.3MB, time=70.69 memory used=5370.1MB, alloc=588.3MB, time=73.09 memory used=5542.5MB, alloc=588.3MB, time=77.43 memory used=5756.2MB, alloc=588.3MB, time=80.09 memory used=6000.8MB, alloc=612.3MB, time=82.79 memory used=6168.5MB, alloc=612.3MB, time=85.38 memory used=6315.6MB, alloc=612.3MB, time=87.60 memory used=6410.2MB, alloc=612.3MB, time=89.46 memory used=6509.4MB, alloc=612.3MB, time=91.29 memory used=6581.1MB, alloc=612.3MB, time=93.01 memory used=6698.8MB, alloc=636.3MB, time=95.12 memory used=6792.7MB, alloc=636.3MB, time=96.81 memory used=6904.9MB, alloc=636.3MB, time=98.51 memory used=7004.1MB, alloc=636.3MB, time=100.15 memory used=7104.8MB, alloc=636.3MB, time=102.23 memory used=7239.6MB, alloc=636.3MB, time=104.36 memory used=7354.5MB, alloc=636.3MB, time=106.29 memory used=7584.4MB, alloc=636.3MB, time=115.06 memory used=7721.7MB, alloc=636.3MB, time=116.02 memory used=7847.7MB, alloc=636.3MB, time=116.93 memory used=8028.0MB, alloc=636.3MB, time=118.66 memory used=8286.0MB, alloc=660.3MB, time=121.69 memory used=8658.8MB, alloc=684.3MB, time=126.91 memory used=8890.3MB, alloc=684.3MB, time=128.80 memory used=9087.2MB, alloc=684.3MB, time=130.52 memory used=9290.1MB, alloc=684.3MB, time=135.09 memory used=9444.7MB, alloc=684.3MB, time=136.23 memory used=9642.7MB, alloc=684.3MB, time=137.62 memory used=9834.2MB, alloc=684.3MB, time=139.01 memory used=10033.1MB, alloc=684.3MB, time=143.35 memory used=10197.4MB, alloc=684.3MB, time=144.60 memory used=10420.6MB, alloc=684.3MB, time=146.31 memory used=10622.0MB, alloc=684.3MB, time=148.34 memory used=10927.8MB, alloc=684.3MB, time=151.81 memory used=11125.8MB, alloc=708.3MB, time=153.50 memory used=11332.6MB, alloc=708.3MB, time=155.17 memory used=11539.0MB, alloc=708.3MB, time=159.61 memory used=11708.4MB, alloc=708.3MB, time=160.87 memory used=11967.8MB, alloc=708.3MB, time=168.54 memory used=12142.6MB, alloc=708.3MB, time=169.73 memory used=12302.5MB, alloc=708.3MB, time=171.03 memory used=12528.6MB, alloc=708.3MB, time=172.84 memory used=12830.7MB, alloc=708.3MB, time=178.40 memory used=13152.3MB, alloc=732.3MB, time=182.55 memory used=13566.3MB, alloc=732.3MB, time=190.43 memory used=13984.1MB, alloc=732.3MB, time=207.77 memory used=14341.8MB, alloc=732.3MB, time=216.86 memory used=14729.7MB, alloc=756.3MB, time=221.53 |\^/| 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(); 1428299292 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 3 2 F := [18 x y + 15 y z + 19 x z - 20 x, -20 x + 4 x y + 4 z + 10 y , 2 3 2 12 x y + 8 x y z - 18 z + x ] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 G := [12 x - 15 y z + 2 x - 9, 6 x y + 2 x y - 19 x - 18, 2 2 3 -19 x y - 16 x y - 8 z - 7 x y] > Problem := [F,G]; 2 2 3 2 3 2 Problem := [[18 x y + 15 y z + 19 x z - 20 x, -20 x + 4 x y + 4 z + 10 y , 2 3 2 3 2 2 12 x y + 8 x y z - 18 z + x ], [12 x - 15 y z + 2 x - 9, 2 2 2 2 3 6 x y + 2 x y - 19 x - 18, -19 x y - 16 x y - 8 z - 7 x y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.17 memory used=25.4MB, alloc=32.3MB, time=0.48 memory used=45.6MB, alloc=36.3MB, time=0.75 memory used=65.3MB, alloc=60.3MB, time=0.97 memory used=110.6MB, alloc=68.3MB, time=1.62 memory used=154.5MB, alloc=68.3MB, time=2.05 memory used=191.4MB, alloc=68.3MB, time=2.46 memory used=225.2MB, alloc=68.3MB, time=2.62 memory used=258.6MB, alloc=68.3MB, time=3.04 memory used=300.9MB, alloc=68.3MB, time=3.53 memory used=343.5MB, alloc=68.3MB, time=3.98 memory used=388.4MB, alloc=68.3MB, time=4.55 memory used=428.8MB, alloc=92.3MB, time=4.85 memory used=475.2MB, alloc=92.3MB, time=5.03 memory used=534.2MB, alloc=92.3MB, time=6.11 memory used=570.7MB, alloc=92.3MB, time=6.24 memory used=620.1MB, alloc=92.3MB, time=6.48 memory used=667.5MB, alloc=92.3MB, time=6.67 memory used=727.7MB, alloc=92.3MB, time=7.69 memory used=765.5MB, alloc=92.3MB, time=7.83 memory used=831.5MB, alloc=92.3MB, time=8.72 memory used=893.9MB, alloc=92.3MB, time=9.17 memory used=945.7MB, alloc=92.3MB, time=9.72 memory used=1003.6MB, alloc=93.3MB, time=10.33 memory used=1064.3MB, alloc=93.3MB, time=10.84 memory used=1124.9MB, alloc=349.3MB, time=11.59 memory used=1193.6MB, alloc=349.3MB, time=12.29 memory used=1234.6MB, alloc=349.3MB, time=12.50 memory used=1290.1MB, alloc=349.3MB, time=16.07 memory used=1326.1MB, alloc=349.3MB, time=16.22 memory used=1356.3MB, alloc=349.3MB, time=16.36 memory used=1381.9MB, alloc=349.3MB, time=16.47 memory used=1412.3MB, alloc=349.3MB, time=16.58 memory used=1448.3MB, alloc=349.3MB, time=16.68 memory used=1472.7MB, alloc=349.3MB, time=16.77 memory used=1494.4MB, alloc=349.3MB, time=16.86 memory used=1518.2MB, alloc=349.3MB, time=16.96 memory used=1545.0MB, alloc=349.3MB, time=17.08 memory used=1607.1MB, alloc=349.3MB, time=17.73 memory used=1681.8MB, alloc=373.3MB, time=18.65 memory used=1772.2MB, alloc=373.3MB, time=19.50 memory used=1862.0MB, alloc=373.3MB, time=20.73 memory used=1906.3MB, alloc=373.3MB, time=21.02 memory used=1962.1MB, alloc=397.3MB, time=21.55 memory used=2016.7MB, alloc=397.3MB, time=21.80 memory used=2070.9MB, alloc=397.3MB, time=22.02 memory used=2116.6MB, alloc=397.3MB, time=22.24 memory used=2169.0MB, alloc=397.3MB, time=22.45 memory used=2229.7MB, alloc=397.3MB, time=22.67 memory used=2298.4MB, alloc=397.3MB, time=22.88 memory used=2341.2MB, alloc=397.3MB, time=23.04 memory used=2380.7MB, alloc=397.3MB, time=23.20 memory used=2422.1MB, alloc=397.3MB, time=23.35 memory used=2466.8MB, alloc=397.3MB, time=23.50 memory used=2515.7MB, alloc=397.3MB, time=23.65 memory used=2567.4MB, alloc=397.3MB, time=23.81 memory used=2624.5MB, alloc=397.3MB, time=23.97 memory used=2696.5MB, alloc=397.3MB, time=24.62 memory used=2761.4MB, alloc=397.3MB, time=24.89 memory used=2823.3MB, alloc=397.3MB, time=25.11 memory used=2866.0MB, alloc=397.3MB, time=25.31 memory used=2914.6MB, alloc=397.3MB, time=25.51 memory used=2971.5MB, alloc=397.3MB, time=25.73 memory used=3036.5MB, alloc=397.3MB, time=25.94 memory used=3092.4MB, alloc=397.3MB, time=26.12 memory used=3129.9MB, alloc=397.3MB, time=26.28 memory used=3170.4MB, alloc=397.3MB, time=26.44 memory used=3213.5MB, alloc=397.3MB, time=26.61 memory used=3260.6MB, alloc=397.3MB, time=26.78 memory used=3310.8MB, alloc=397.3MB, time=26.95 memory used=3365.4MB, alloc=397.3MB, time=27.11 memory used=3424.7MB, alloc=397.3MB, time=27.29 memory used=3598.8MB, alloc=397.3MB, time=36.40 memory used=3655.0MB, alloc=397.3MB, time=36.62 memory used=3706.6MB, alloc=397.3MB, time=36.81 memory used=3771.1MB, alloc=397.3MB, time=37.02 memory used=3811.3MB, alloc=397.3MB, time=37.17 memory used=3855.4MB, alloc=397.3MB, time=37.33 memory used=3904.8MB, alloc=397.3MB, time=37.49 memory used=3959.0MB, alloc=397.3MB, time=37.66 memory used=4019.4MB, alloc=397.3MB, time=37.83 memory used=4086.4MB, alloc=397.3MB, time=38.01 memory used=4254.9MB, alloc=397.3MB, time=38.50 memory used=4424.2MB, alloc=397.3MB, time=39.27 memory used=4479.3MB, alloc=397.3MB, time=39.73 memory used=4573.2MB, alloc=397.3MB, time=39.99 memory used=4753.9MB, alloc=397.3MB, time=41.18 memory used=4989.1MB, alloc=397.3MB, time=41.52 memory used=5123.0MB, alloc=397.3MB, time=43.07 memory used=5186.5MB, alloc=397.3MB, time=43.57 memory used=5249.5MB, alloc=397.3MB, time=44.05 memory used=5308.0MB, alloc=397.3MB, time=44.47 memory used=5379.6MB, alloc=397.3MB, time=44.95 memory used=5433.8MB, alloc=397.3MB, time=45.16 memory used=5485.2MB, alloc=397.3MB, time=45.37 memory used=5532.6MB, alloc=397.3MB, time=45.55 memory used=5590.0MB, alloc=397.3MB, time=45.74 memory used=5651.2MB, alloc=397.3MB, time=45.92 memory used=5743.2MB, alloc=397.3MB, time=66.76 memory used=5807.7MB, alloc=397.3MB, time=67.47 memory used=5856.0MB, alloc=397.3MB, time=67.67 memory used=5907.6MB, alloc=397.3MB, time=67.86 memory used=5970.6MB, alloc=397.3MB, time=68.07 memory used=6021.1MB, alloc=397.3MB, time=68.23 memory used=6059.2MB, alloc=397.3MB, time=68.39 memory used=6100.5MB, alloc=397.3MB, time=68.54 memory used=6145.5MB, alloc=397.3MB, time=68.70 memory used=6192.4MB, alloc=397.3MB, time=68.85 memory used=6243.1MB, alloc=397.3MB, time=69.02 memory used=6297.7MB, alloc=397.3MB, time=69.18 memory used=6354.1MB, alloc=397.3MB, time=69.35 memory used=6416.1MB, alloc=397.3MB, time=69.52 memory used=6480.0MB, alloc=397.3MB, time=69.69 memory used=6675.8MB, alloc=397.3MB, time=70.09 memory used=6822.1MB, alloc=397.3MB, time=70.42 memory used=6985.4MB, alloc=397.3MB, time=70.75 memory used=7167.1MB, alloc=397.3MB, time=71.11 memory used=7377.5MB, alloc=397.3MB, time=71.48 memory used=7559.6MB, alloc=397.3MB, time=72.32 memory used=7615.7MB, alloc=397.3MB, time=72.64 memory used=7669.0MB, alloc=397.3MB, time=72.83 memory used=7723.7MB, alloc=397.3MB, time=73.02 memory used=7828.2MB, alloc=397.3MB, time=73.89 memory used=7926.7MB, alloc=397.3MB, time=74.11 memory used=8045.8MB, alloc=397.3MB, time=74.39 memory used=8146.2MB, alloc=397.3MB, time=74.63 memory used=8245.2MB, alloc=397.3MB, time=74.86 memory used=8446.2MB, alloc=397.3MB, time=76.97 memory used=8580.7MB, alloc=397.3MB, time=77.21 memory used=8761.1MB, alloc=397.3MB, time=77.50 memory used=8971.5MB, alloc=397.3MB, time=77.85 memory used=9144.8MB, alloc=397.3MB, time=78.17 memory used=9364.1MB, alloc=397.3MB, time=78.51 memory used=9564.5MB, alloc=397.3MB, time=78.85 memory used=9767.9MB, alloc=397.3MB, time=79.21 memory used=9991.8MB, alloc=397.3MB, time=79.56 memory used=10191.8MB, alloc=397.3MB, time=81.27 memory used=10342.3MB, alloc=397.3MB, time=85.96 memory used=10428.7MB, alloc=397.3MB, time=87.07 memory used=10474.2MB, alloc=397.3MB, time=87.26 memory used=10535.4MB, alloc=397.3MB, time=87.45 memory used=10578.7MB, alloc=397.3MB, time=87.61 memory used=10620.9MB, alloc=397.3MB, time=87.77 memory used=10667.7MB, alloc=397.3MB, time=87.93 memory used=10720.2MB, alloc=397.3MB, time=88.10 memory used=10779.3MB, alloc=397.3MB, time=88.26 memory used=10845.2MB, alloc=397.3MB, time=88.43 memory used=11002.9MB, alloc=397.3MB, time=88.76 memory used=11104.1MB, alloc=397.3MB, time=89.55 memory used=11156.6MB, alloc=397.3MB, time=89.74 memory used=11210.3MB, alloc=397.3MB, time=89.94 memory used=11337.0MB, alloc=397.3MB, time=90.70 memory used=11452.4MB, alloc=397.3MB, time=90.98 memory used=11529.1MB, alloc=397.3MB, time=91.18 memory used=11613.4MB, alloc=397.3MB, time=92.41 memory used=11744.3MB, alloc=397.3MB, time=93.73 memory used=11859.5MB, alloc=397.3MB, time=95.56 memory used=11982.9MB, alloc=397.3MB, time=96.99 memory used=12103.6MB, alloc=397.3MB, time=98.47 memory used=12218.9MB, alloc=397.3MB, time=99.99 memory used=12334.8MB, alloc=397.3MB, time=101.95 memory used=12452.3MB, alloc=397.3MB, time=104.17 memory used=12567.5MB, alloc=397.3MB, time=106.88 memory used=12682.8MB, alloc=397.3MB, time=110.00 memory used=12796.4MB, alloc=397.3MB, time=113.56 memory used=12909.9MB, alloc=397.3MB, time=117.31 memory used=13022.7MB, alloc=397.3MB, time=121.35 memory used=13136.3MB, alloc=397.3MB, time=125.77 memory used=13252.4MB, alloc=397.3MB, time=130.29 memory used=13342.5MB, alloc=397.3MB, time=132.69 memory used=13455.4MB, alloc=397.3MB, time=134.80 memory used=13503.8MB, alloc=397.3MB, time=135.00 memory used=13547.7MB, alloc=397.3MB, time=135.19 memory used=13604.9MB, alloc=397.3MB, time=135.37 memory used=13644.4MB, alloc=397.3MB, time=135.54 memory used=13682.5MB, alloc=397.3MB, time=135.70 memory used=13724.7MB, alloc=397.3MB, time=135.87 memory used=13770.8MB, alloc=397.3MB, time=136.05 memory used=13822.7MB, alloc=397.3MB, time=136.22 memory used=13879.7MB, alloc=397.3MB, time=136.39 memory used=14092.1MB, alloc=397.3MB, time=137.06 memory used=14146.6MB, alloc=397.3MB, time=137.62 memory used=14200.4MB, alloc=397.3MB, time=137.82 memory used=14255.1MB, alloc=397.3MB, time=138.03 memory used=14352.7MB, alloc=397.3MB, time=138.95 memory used=14452.0MB, alloc=397.3MB, time=139.20 memory used=14590.8MB, alloc=397.3MB, time=139.54 memory used=14683.4MB, alloc=397.3MB, time=139.77 memory used=14801.5MB, alloc=397.3MB, time=141.30 memory used=14892.1MB, alloc=397.3MB, time=142.12 memory used=15011.4MB, alloc=397.3MB, time=142.90 memory used=15103.2MB, alloc=397.3MB, time=143.82 memory used=15173.5MB, alloc=421.3MB, time=144.26 memory used=15247.0MB, alloc=421.3MB, time=146.66 memory used=15353.7MB, alloc=421.3MB, time=152.72 memory used=15418.5MB, alloc=421.3MB, time=152.98 memory used=15470.7MB, alloc=421.3MB, time=153.19 memory used=15529.3MB, alloc=421.3MB, time=153.39 memory used=15599.7MB, alloc=421.3MB, time=153.61 memory used=15880.8MB, alloc=421.3MB, time=154.97 memory used=16006.2MB, alloc=421.3MB, time=156.31 memory used=16134.1MB, alloc=445.3MB, time=157.91 memory used=16336.0MB, alloc=445.3MB, time=159.59 memory used=16508.5MB, alloc=445.3MB, time=160.39 memory used=16681.3MB, alloc=445.3MB, time=161.28 memory used=16774.8MB, alloc=445.3MB, time=161.89 memory used=16936.6MB, alloc=445.3MB, time=164.38 memory used=17114.5MB, alloc=445.3MB, time=169.15 memory used=17181.4MB, alloc=445.3MB, time=169.48 memory used=17258.4MB, alloc=445.3MB, time=169.81 memory used=17310.8MB, alloc=469.3MB, time=170.07 memory used=17381.1MB, alloc=469.3MB, time=170.36 memory used=17464.4MB, alloc=469.3MB, time=170.65 memory used=17557.7MB, alloc=469.3MB, time=170.97 memory used=17665.3MB, alloc=469.3MB, time=171.31 memory used=17803.6MB, alloc=469.3MB, time=171.75 memory used=17947.8MB, alloc=469.3MB, time=172.19 memory used=18108.4MB, alloc=469.3MB, time=172.64 memory used=18284.5MB, alloc=469.3MB, time=173.11 memory used=18476.7MB, alloc=469.3MB, time=173.60 memory used=18687.5MB, alloc=469.3MB, time=174.13 memory used=18920.2MB, alloc=469.3MB, time=174.68 memory used=19106.3MB, alloc=469.3MB, time=175.14 memory used=19280.4MB, alloc=469.3MB, time=175.60 memory used=19460.8MB, alloc=469.3MB, time=176.06 memory used=19654.1MB, alloc=469.3MB, time=176.53 memory used=19856.0MB, alloc=469.3MB, time=177.02 memory used=20071.3MB, alloc=469.3MB, time=177.53 memory used=20298.8MB, alloc=469.3MB, time=178.04 memory used=20532.9MB, alloc=469.3MB, time=178.56 memory used=20719.3MB, alloc=469.3MB, time=179.00 memory used=20913.2MB, alloc=469.3MB, time=179.45 memory used=21116.9MB, alloc=469.3MB, time=179.90 memory used=21333.7MB, alloc=469.3MB, time=180.37 memory used=21562.3MB, alloc=469.3MB, time=180.84 memory used=21801.4MB, alloc=469.3MB, time=181.30 memory used=22161.3MB, alloc=469.3MB, time=188.28 memory used=22243.1MB, alloc=469.3MB, time=188.54 memory used=22451.3MB, alloc=469.3MB, time=189.02 memory used=22583.2MB, alloc=469.3MB, time=190.59 memory used=22693.3MB, alloc=469.3MB, time=192.14 memory used=22843.1MB, alloc=469.3MB, time=192.55 memory used=23078.8MB, alloc=469.3MB, time=196.43 memory used=23317.1MB, alloc=469.3MB, time=196.84 memory used=23592.5MB, alloc=469.3MB, time=197.40 memory used=23788.4MB, alloc=469.3MB, time=198.21 memory used=24030.9MB, alloc=469.3MB, time=203.67 memory used=24240.2MB, alloc=469.3MB, time=205.28 memory used=24331.8MB, alloc=469.3MB, time=205.65 memory used=24432.4MB, alloc=469.3MB, time=206.64 memory used=24513.5MB, alloc=469.3MB, time=206.95 memory used=24596.3MB, alloc=469.3MB, time=207.21 memory used=24667.0MB, alloc=469.3MB, time=207.45 memory used=24763.6MB, alloc=469.3MB, time=209.04 |\^/| 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(); 1428299592 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 F := [-12 x y z - 12 x - 10 y, -13 x + 11 x z + 6 y z - 17 y, x + 6 x - 16] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [-12 x y + 14 y z + 17 y - 17, 17 x y z - 11 x y - 9 x z - 3, 2 4 x y - 5 x y - 14 y z] > Problem := [F,G]; Problem := [ 2 3 2 2 [-12 x y z - 12 x - 10 y, -13 x + 11 x z + 6 y z - 17 y, x + 6 x - 16], 2 2 2 [-12 x y + 14 y z + 17 y - 17, 17 x y z - 11 x y - 9 x z - 3, 2 4 x y - 5 x y - 14 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.4MB, alloc=32.3MB, time=0.49 memory used=47.1MB, alloc=32.3MB, time=0.80 memory used=66.3MB, alloc=56.3MB, time=1.09 memory used=105.7MB, alloc=60.3MB, time=1.67 memory used=144.1MB, alloc=84.3MB, time=2.25 memory used=207.6MB, alloc=92.3MB, time=3.20 memory used=269.8MB, alloc=116.3MB, time=4.15 memory used=342.9MB, alloc=116.3MB, time=5.27 memory used=417.6MB, alloc=372.3MB, time=6.46 memory used=501.2MB, alloc=396.3MB, time=7.77 memory used=609.0MB, alloc=396.3MB, time=9.45 memory used=712.2MB, alloc=420.3MB, time=11.07 memory used=844.0MB, alloc=444.3MB, time=13.07 memory used=969.7MB, alloc=468.3MB, time=15.06 memory used=1089.6MB, alloc=468.3MB, time=16.95 memory used=1206.0MB, alloc=468.3MB, time=18.86 memory used=1325.9MB, alloc=492.3MB, time=20.92 memory used=1431.5MB, alloc=492.3MB, time=22.73 memory used=1528.1MB, alloc=492.3MB, time=24.41 memory used=1628.9MB, alloc=492.3MB, time=26.19 memory used=1716.0MB, alloc=492.3MB, time=27.79 memory used=1791.7MB, alloc=492.3MB, time=29.18 memory used=1873.7MB, alloc=492.3MB, time=30.75 memory used=1948.9MB, alloc=492.3MB, time=32.22 memory used=2013.4MB, alloc=492.3MB, time=33.61 memory used=2084.8MB, alloc=516.3MB, time=35.01 memory used=2141.0MB, alloc=516.3MB, time=36.23 memory used=2210.9MB, alloc=516.3MB, time=37.68 memory used=2274.3MB, alloc=516.3MB, time=38.92 memory used=2340.2MB, alloc=516.3MB, time=40.48 memory used=2387.1MB, alloc=516.3MB, time=41.51 memory used=2436.3MB, alloc=516.3MB, time=42.57 memory used=2639.8MB, alloc=540.3MB, time=46.29 memory used=2849.8MB, alloc=564.3MB, time=50.13 memory used=3038.6MB, alloc=588.3MB, time=53.85 memory used=3232.4MB, alloc=612.3MB, time=57.84 memory used=3407.1MB, alloc=636.3MB, time=61.36 memory used=3588.5MB, alloc=636.3MB, time=65.54 memory used=3753.1MB, alloc=636.3MB, time=68.14 memory used=3880.9MB, alloc=636.3MB, time=70.97 memory used=4032.2MB, alloc=660.3MB, time=74.22 memory used=4170.9MB, alloc=660.3MB, time=77.21 memory used=4288.4MB, alloc=660.3MB, time=80.02 memory used=4430.8MB, alloc=660.3MB, time=83.35 memory used=4537.6MB, alloc=660.3MB, time=86.06 memory used=4638.0MB, alloc=660.3MB, time=88.51 memory used=4721.7MB, alloc=660.3MB, time=90.84 memory used=4810.9MB, alloc=660.3MB, time=93.14 memory used=4892.2MB, alloc=660.3MB, time=95.19 memory used=5224.6MB, alloc=684.3MB, time=101.23 memory used=5584.6MB, alloc=708.3MB, time=108.11 memory used=5972.6MB, alloc=732.3MB, time=114.92 memory used=6366.8MB, alloc=756.3MB, time=122.87 memory used=6769.5MB, alloc=780.3MB, time=130.96 memory used=7084.5MB, alloc=804.3MB, time=136.33 memory used=7444.6MB, alloc=828.3MB, time=143.63 memory used=7683.5MB, alloc=852.3MB, time=148.45 memory used=7996.4MB, alloc=876.3MB, time=155.13 memory used=8291.9MB, alloc=900.3MB, time=162.98 memory used=8541.7MB, alloc=924.3MB, time=168.67 memory used=8820.3MB, alloc=948.3MB, time=173.44 memory used=9077.3MB, alloc=948.3MB, time=179.34 memory used=9377.1MB, alloc=972.3MB, time=184.29 memory used=9675.9MB, alloc=972.3MB, time=189.43 memory used=9904.8MB, alloc=996.3MB, time=194.70 memory used=10151.9MB, alloc=996.3MB, time=200.16 memory used=10354.8MB, alloc=996.3MB, time=204.75 |\^/| 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(); 1428299892 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 F := [x z + 6 z - 20 x z + 4 x, 13 x y z - 8 x y - 6 y + 19, 2 2 3 -4 x y + 2 x z - 8 y - 2 y z] > G := [ randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 2 2 G := [-19 x z - 14 y - z + 9 x, 4 x y + 2 x z - 9 x z - 3 y , 2 -5 x y z + 10 x z - 3 x y - 19 y z] > Problem := [F,G]; 2 3 2 Problem := [[x z + 6 z - 20 x z + 4 x, 13 x y z - 8 x y - 6 y + 19, 2 2 3 2 3 2 -4 x y + 2 x z - 8 y - 2 y z], [-19 x z - 14 y - z + 9 x, 2 2 2 2 4 x y + 2 x z - 9 x z - 3 y , -5 x y z + 10 x z - 3 x y - 19 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.6MB, alloc=32.3MB, time=0.40 memory used=44.7MB, alloc=32.3MB, time=0.58 memory used=65.3MB, alloc=32.3MB, time=0.81 memory used=77.2MB, alloc=32.3MB, time=0.84 memory used=87.6MB, alloc=32.3MB, time=0.87 memory used=105.9MB, alloc=32.3MB, time=1.07 memory used=119.0MB, alloc=32.3MB, time=1.11 memory used=130.2MB, alloc=32.3MB, time=1.14 memory used=146.3MB, alloc=32.3MB, time=1.24 memory used=169.0MB, alloc=36.3MB, time=1.54 memory used=212.4MB, alloc=61.2MB, time=2.95 memory used=243.5MB, alloc=62.5MB, time=3.04 memory used=268.5MB, alloc=62.5MB, time=3.10 memory used=295.3MB, alloc=62.5MB, time=3.15 memory used=339.7MB, alloc=62.5MB, time=3.61 memory used=383.7MB, alloc=70.5MB, time=4.21 memory used=420.7MB, alloc=70.5MB, time=4.52 memory used=441.9MB, alloc=70.5MB, time=4.59 memory used=477.4MB, alloc=70.5MB, time=4.82 memory used=500.5MB, alloc=70.5MB, time=4.89 memory used=526.7MB, alloc=70.5MB, time=5.26 memory used=547.3MB, alloc=70.5MB, time=5.34 memory used=569.1MB, alloc=70.5MB, time=5.41 memory used=598.2MB, alloc=70.5MB, time=5.66 memory used=620.6MB, alloc=70.5MB, time=5.74 memory used=646.5MB, alloc=70.5MB, time=5.93 memory used=694.4MB, alloc=70.5MB, time=6.59 memory used=714.0MB, alloc=70.5MB, time=6.65 memory used=741.7MB, alloc=70.5MB, time=6.91 memory used=764.4MB, alloc=70.5MB, time=7.06 memory used=784.6MB, alloc=70.5MB, time=7.15 memory used=805.4MB, alloc=70.5MB, time=7.22 memory used=850.5MB, alloc=70.5MB, time=7.74 memory used=897.3MB, alloc=70.5MB, time=8.07 memory used=945.2MB, alloc=70.5MB, time=8.40 memory used=993.3MB, alloc=70.5MB, time=8.83 memory used=1039.4MB, alloc=70.5MB, time=9.54 memory used=1080.1MB, alloc=70.5MB, time=9.95 memory used=1099.2MB, alloc=70.5MB, time=10.02 memory used=1138.7MB, alloc=94.5MB, time=10.38 memory used=1207.1MB, alloc=94.5MB, time=11.08 memory used=1269.5MB, alloc=94.5MB, time=11.84 memory used=1327.5MB, alloc=94.5MB, time=12.40 memory used=1388.2MB, alloc=94.5MB, time=13.03 memory used=1444.5MB, alloc=94.5MB, time=13.55 memory used=1474.9MB, alloc=94.5MB, time=13.66 memory used=1513.3MB, alloc=94.5MB, time=13.99 memory used=1541.5MB, alloc=94.5MB, time=14.09 memory used=1614.4MB, alloc=94.5MB, time=14.85 memory used=1650.0MB, alloc=94.5MB, time=15.06 memory used=1684.8MB, alloc=94.5MB, time=15.39 memory used=1719.4MB, alloc=94.5MB, time=15.56 memory used=1745.6MB, alloc=94.5MB, time=15.68 memory used=1776.2MB, alloc=94.5MB, time=15.78 memory used=1798.8MB, alloc=94.5MB, time=15.86 memory used=1843.5MB, alloc=94.5MB, time=16.93 memory used=1873.5MB, alloc=118.5MB, time=17.07 memory used=1917.3MB, alloc=118.5MB, time=17.20 memory used=1963.0MB, alloc=118.5MB, time=17.32 memory used=2000.5MB, alloc=118.5MB, time=17.43 memory used=2046.5MB, alloc=118.5MB, time=17.54 memory used=2115.8MB, alloc=118.5MB, time=17.99 memory used=2197.0MB, alloc=118.5MB, time=18.88 memory used=2245.4MB, alloc=118.5MB, time=19.10 memory used=2305.7MB, alloc=118.5MB, time=19.69 memory used=2348.7MB, alloc=118.5MB, time=19.83 memory used=2405.1MB, alloc=118.5MB, time=20.21 memory used=2477.7MB, alloc=118.5MB, time=21.06 memory used=2566.0MB, alloc=118.5MB, time=22.58 memory used=2606.5MB, alloc=118.5MB, time=22.71 memory used=2677.3MB, alloc=374.5MB, time=23.33 memory used=2772.7MB, alloc=398.5MB, time=24.33 memory used=2878.9MB, alloc=422.5MB, time=25.79 memory used=3006.2MB, alloc=422.5MB, time=27.23 memory used=3079.6MB, alloc=422.5MB, time=27.87 memory used=3152.0MB, alloc=422.5MB, time=28.20 memory used=3223.7MB, alloc=422.5MB, time=28.83 memory used=3296.0MB, alloc=422.5MB, time=29.28 memory used=3364.6MB, alloc=422.5MB, time=29.76 memory used=3441.6MB, alloc=422.5MB, time=30.27 memory used=3513.7MB, alloc=422.5MB, time=30.76 memory used=3578.9MB, alloc=422.5MB, time=31.25 memory used=3656.0MB, alloc=422.5MB, time=31.72 memory used=3721.4MB, alloc=422.5MB, time=32.13 memory used=3795.9MB, alloc=422.5MB, time=32.62 memory used=3889.7MB, alloc=422.5MB, time=36.82 memory used=3953.9MB, alloc=422.5MB, time=37.07 memory used=4007.8MB, alloc=422.5MB, time=37.27 memory used=4077.9MB, alloc=422.5MB, time=37.50 memory used=4123.6MB, alloc=422.5MB, time=37.69 memory used=4171.4MB, alloc=422.5MB, time=37.86 memory used=4224.9MB, alloc=422.5MB, time=38.06 memory used=4285.3MB, alloc=422.5MB, time=38.25 memory used=4352.1MB, alloc=422.5MB, time=38.43 memory used=4488.9MB, alloc=422.5MB, time=39.02 memory used=4553.0MB, alloc=422.5MB, time=39.26 memory used=4601.9MB, alloc=422.5MB, time=39.46 memory used=4674.0MB, alloc=422.5MB, time=39.83 memory used=4741.3MB, alloc=422.5MB, time=40.22 memory used=4805.6MB, alloc=422.5MB, time=40.45 memory used=4880.0MB, alloc=422.5MB, time=40.97 memory used=4942.3MB, alloc=422.5MB, time=41.20 memory used=4992.9MB, alloc=422.5MB, time=41.39 memory used=5065.0MB, alloc=422.5MB, time=41.80 memory used=5131.2MB, alloc=422.5MB, time=42.15 memory used=5196.2MB, alloc=422.5MB, time=42.37 memory used=5309.9MB, alloc=422.5MB, time=54.33 memory used=5373.0MB, alloc=422.5MB, time=54.58 memory used=5422.5MB, alloc=422.5MB, time=54.79 memory used=5483.1MB, alloc=422.5MB, time=55.00 memory used=5550.0MB, alloc=422.5MB, time=55.22 memory used=5592.5MB, alloc=422.5MB, time=55.41 memory used=5637.1MB, alloc=422.5MB, time=55.58 memory used=5686.5MB, alloc=422.5MB, time=55.76 memory used=5740.2MB, alloc=422.5MB, time=55.94 memory used=5797.8MB, alloc=422.5MB, time=56.13 memory used=5860.4MB, alloc=422.5MB, time=56.31 memory used=5928.6MB, alloc=422.5MB, time=56.50 memory used=6134.1MB, alloc=422.5MB, time=56.97 memory used=6285.7MB, alloc=422.5MB, time=57.74 memory used=6349.2MB, alloc=422.5MB, time=57.99 memory used=6491.5MB, alloc=422.5MB, time=58.59 memory used=6611.0MB, alloc=422.5MB, time=59.25 memory used=6674.9MB, alloc=422.5MB, time=59.49 memory used=6729.3MB, alloc=422.5MB, time=59.70 memory used=6786.7MB, alloc=422.5MB, time=59.92 memory used=6861.7MB, alloc=422.5MB, time=60.47 memory used=6927.1MB, alloc=422.5MB, time=60.69 memory used=6992.8MB, alloc=422.5MB, time=61.14 memory used=7064.2MB, alloc=422.5MB, time=61.52 memory used=7124.8MB, alloc=422.5MB, time=61.75 memory used=7175.5MB, alloc=422.5MB, time=61.95 memory used=7247.3MB, alloc=422.5MB, time=62.37 memory used=7313.9MB, alloc=422.5MB, time=62.71 memory used=7379.0MB, alloc=422.5MB, time=62.92 memory used=7494.1MB, alloc=422.5MB, time=74.99 memory used=7555.4MB, alloc=422.5MB, time=75.22 memory used=7605.2MB, alloc=422.5MB, time=75.43 memory used=7666.8MB, alloc=422.5MB, time=75.64 memory used=7732.2MB, alloc=422.5MB, time=75.86 memory used=7774.8MB, alloc=422.5MB, time=76.03 memory used=7819.9MB, alloc=422.5MB, time=76.22 memory used=7869.4MB, alloc=422.5MB, time=76.40 memory used=7923.2MB, alloc=422.5MB, time=76.58 memory used=7980.8MB, alloc=422.5MB, time=76.76 memory used=8043.5MB, alloc=422.5MB, time=76.95 memory used=8113.1MB, alloc=422.5MB, time=77.13 memory used=8313.9MB, alloc=422.5MB, time=77.49 memory used=8467.2MB, alloc=422.5MB, time=78.26 memory used=8530.3MB, alloc=422.5MB, time=78.50 memory used=8593.4MB, alloc=422.5MB, time=78.73 memory used=8726.0MB, alloc=422.5MB, time=79.37 memory used=8826.8MB, alloc=422.5MB, time=79.61 memory used=8986.7MB, alloc=422.5MB, time=79.98 memory used=9106.0MB, alloc=422.5MB, time=80.77 memory used=9167.5MB, alloc=422.5MB, time=81.01 memory used=9219.0MB, alloc=422.5MB, time=81.23 memory used=9278.4MB, alloc=422.5MB, time=81.44 memory used=9353.8MB, alloc=422.5MB, time=81.99 memory used=9418.0MB, alloc=422.5MB, time=82.24 memory used=9493.3MB, alloc=422.5MB, time=82.70 memory used=9555.6MB, alloc=422.5MB, time=82.96 memory used=9605.8MB, alloc=422.5MB, time=83.19 memory used=9667.3MB, alloc=422.5MB, time=83.40 memory used=9742.3MB, alloc=422.5MB, time=83.93 memory used=9806.4MB, alloc=422.5MB, time=84.15 memory used=9871.3MB, alloc=422.5MB, time=84.63 memory used=9948.7MB, alloc=422.5MB, time=86.55 memory used=10050.5MB, alloc=422.5MB, time=96.48 memory used=10109.8MB, alloc=422.5MB, time=96.72 memory used=10160.3MB, alloc=422.5MB, time=96.94 memory used=10223.0MB, alloc=422.5MB, time=97.15 memory used=10284.4MB, alloc=422.5MB, time=97.36 memory used=10327.2MB, alloc=422.5MB, time=97.57 memory used=10373.3MB, alloc=422.5MB, time=97.75 memory used=10423.0MB, alloc=422.5MB, time=97.94 memory used=10476.9MB, alloc=422.5MB, time=98.13 memory used=10536.2MB, alloc=422.5MB, time=98.34 memory used=10600.2MB, alloc=422.5MB, time=98.53 memory used=10669.7MB, alloc=422.5MB, time=98.74 memory used=10860.4MB, alloc=422.5MB, time=99.10 memory used=11074.9MB, alloc=422.5MB, time=100.67 memory used=11230.1MB, alloc=446.5MB, time=102.44 memory used=11405.0MB, alloc=446.5MB, time=103.94 memory used=11521.4MB, alloc=446.5MB, time=116.37 memory used=11588.7MB, alloc=446.5MB, time=116.64 memory used=11664.7MB, alloc=446.5MB, time=116.93 memory used=11740.4MB, alloc=446.5MB, time=117.20 memory used=11794.6MB, alloc=446.5MB, time=117.41 memory used=11854.5MB, alloc=446.5MB, time=117.62 memory used=11920.0MB, alloc=446.5MB, time=117.83 memory used=11992.1MB, alloc=446.5MB, time=118.05 memory used=12072.9MB, alloc=446.5MB, time=118.25 memory used=12162.9MB, alloc=446.5MB, time=118.47 memory used=12328.2MB, alloc=446.5MB, time=118.79 memory used=12627.6MB, alloc=446.5MB, time=121.21 memory used=12773.2MB, alloc=446.5MB, time=123.27 memory used=12840.0MB, alloc=446.5MB, time=123.54 memory used=12915.5MB, alloc=446.5MB, time=123.77 memory used=12970.1MB, alloc=446.5MB, time=123.96 memory used=13037.5MB, alloc=446.5MB, time=124.17 memory used=13196.8MB, alloc=446.5MB, time=125.44 memory used=13364.6MB, alloc=446.5MB, time=126.67 memory used=13495.1MB, alloc=446.5MB, time=127.96 memory used=13578.2MB, alloc=446.5MB, time=128.59 memory used=13659.6MB, alloc=446.5MB, time=129.23 memory used=13743.0MB, alloc=446.5MB, time=129.73 memory used=13842.1MB, alloc=446.5MB, time=130.59 memory used=13938.1MB, alloc=446.5MB, time=134.14 memory used=13995.5MB, alloc=446.5MB, time=134.40 memory used=14072.1MB, alloc=446.5MB, time=134.68 memory used=14125.4MB, alloc=446.5MB, time=134.91 memory used=14178.6MB, alloc=446.5MB, time=135.13 memory used=14239.2MB, alloc=446.5MB, time=135.35 memory used=14308.9MB, alloc=446.5MB, time=135.57 memory used=14426.1MB, alloc=446.5MB, time=135.97 memory used=14496.4MB, alloc=446.5MB, time=136.27 memory used=14553.7MB, alloc=446.5MB, time=136.51 memory used=14639.0MB, alloc=446.5MB, time=136.98 memory used=14708.6MB, alloc=446.5MB, time=137.26 memory used=14763.2MB, alloc=446.5MB, time=137.52 memory used=14876.7MB, alloc=446.5MB, time=148.73 memory used=14961.4MB, alloc=446.5MB, time=149.12 memory used=15017.2MB, alloc=446.5MB, time=149.37 memory used=15086.2MB, alloc=446.5MB, time=149.61 memory used=15159.3MB, alloc=470.5MB, time=149.89 memory used=15221.2MB, alloc=470.5MB, time=150.12 memory used=15289.5MB, alloc=470.5MB, time=150.36 memory used=15367.0MB, alloc=470.5MB, time=150.59 memory used=15454.3MB, alloc=470.5MB, time=150.83 memory used=15553.7MB, alloc=470.5MB, time=151.07 memory used=15740.4MB, alloc=470.5MB, time=151.43 memory used=15853.5MB, alloc=470.5MB, time=152.03 memory used=15926.8MB, alloc=470.5MB, time=152.32 memory used=16031.0MB, alloc=470.5MB, time=152.85 memory used=16108.9MB, alloc=470.5MB, time=153.14 memory used=16250.2MB, alloc=470.5MB, time=164.44 memory used=16335.7MB, alloc=470.5MB, time=164.76 memory used=16414.5MB, alloc=470.5MB, time=165.06 memory used=16509.4MB, alloc=470.5MB, time=165.34 memory used=16571.7MB, alloc=470.5MB, time=165.57 memory used=16641.1MB, alloc=470.5MB, time=165.80 memory used=16718.8MB, alloc=470.5MB, time=166.04 memory used=16806.2MB, alloc=470.5MB, time=166.29 memory used=16905.6MB, alloc=470.5MB, time=166.55 memory used=17091.8MB, alloc=470.5MB, time=166.88 memory used=17204.5MB, alloc=470.5MB, time=167.49 memory used=17277.7MB, alloc=470.5MB, time=167.77 memory used=17380.7MB, alloc=470.5MB, time=168.33 memory used=17476.2MB, alloc=470.5MB, time=168.69 memory used=17548.7MB, alloc=470.5MB, time=168.98 memory used=17690.3MB, alloc=470.5MB, time=180.48 memory used=17770.6MB, alloc=470.5MB, time=180.77 memory used=17853.3MB, alloc=470.5MB, time=181.04 memory used=17941.4MB, alloc=470.5MB, time=181.33 memory used=18003.6MB, alloc=470.5MB, time=181.56 memory used=18073.2MB, alloc=470.5MB, time=181.79 memory used=18151.1MB, alloc=470.5MB, time=182.01 memory used=18239.8MB, alloc=470.5MB, time=182.26 memory used=18339.9MB, alloc=470.5MB, time=182.50 memory used=18511.7MB, alloc=470.5MB, time=182.89 memory used=18676.9MB, alloc=470.5MB, time=184.75 memory used=18792.8MB, alloc=470.5MB, time=196.82 memory used=18864.2MB, alloc=470.5MB, time=197.12 memory used=18949.6MB, alloc=470.5MB, time=197.43 memory used=19027.6MB, alloc=470.5MB, time=197.71 memory used=19088.0MB, alloc=470.5MB, time=197.97 memory used=19155.5MB, alloc=470.5MB, time=198.22 memory used=19230.8MB, alloc=470.5MB, time=198.50 memory used=19314.4MB, alloc=470.5MB, time=198.75 memory used=19409.2MB, alloc=470.5MB, time=199.03 memory used=19604.7MB, alloc=470.5MB, time=199.43 memory used=19771.0MB, alloc=470.5MB, time=201.69 memory used=19848.4MB, alloc=470.5MB, time=202.03 memory used=19931.3MB, alloc=470.5MB, time=202.32 memory used=19992.1MB, alloc=470.5MB, time=202.55 memory used=20124.3MB, alloc=470.5MB, time=203.68 memory used=20289.4MB, alloc=470.5MB, time=205.04 memory used=20423.5MB, alloc=470.5MB, time=206.41 memory used=20502.5MB, alloc=494.5MB, time=207.59 memory used=20606.0MB, alloc=494.5MB, time=208.96 memory used=20684.4MB, alloc=494.5MB, time=210.11 memory used=20777.6MB, alloc=494.5MB, time=211.38 memory used=20879.8MB, alloc=494.5MB, time=212.97 memory used=20970.6MB, alloc=494.5MB, time=214.62 memory used=21045.3MB, alloc=494.5MB, time=215.68 memory used=21117.2MB, alloc=518.5MB, time=216.79 memory used=21179.7MB, alloc=518.5MB, time=218.03 memory used=21247.4MB, alloc=518.5MB, time=219.28 memory used=21337.1MB, alloc=518.5MB, time=220.31 memory used=21397.0MB, alloc=518.5MB, time=221.39 memory used=21451.6MB, alloc=518.5MB, time=222.24 memory used=21556.3MB, alloc=518.5MB, time=223.29 memory used=21664.3MB, alloc=518.5MB, time=224.21 memory used=21775.4MB, alloc=518.5MB, time=225.05 memory used=21883.2MB, alloc=518.5MB, time=225.82 memory used=21991.4MB, alloc=518.5MB, time=226.52 memory used=22096.5MB, alloc=518.5MB, time=227.10 memory used=22211.2MB, alloc=518.5MB, time=228.10 memory used=22307.1MB, alloc=518.5MB, time=228.76 memory used=22425.2MB, alloc=518.5MB, time=229.43 memory used=22556.9MB, alloc=518.5MB, time=230.27 memory used=22646.9MB, alloc=518.5MB, time=230.72 memory used=22741.0MB, alloc=518.5MB, time=231.14 memory used=22847.5MB, alloc=518.5MB, time=232.62 memory used=22935.2MB, alloc=518.5MB, time=233.02 memory used=23041.7MB, alloc=518.5MB, time=233.69 memory used=23207.4MB, alloc=518.5MB, time=234.59 memory used=23381.7MB, alloc=518.5MB, time=235.43 memory used=23486.6MB, alloc=518.5MB, time=235.96 memory used=23596.7MB, alloc=518.5MB, time=236.96 memory used=23687.4MB, alloc=518.5MB, time=237.45 memory used=23798.3MB, alloc=518.5MB, time=238.24 memory used=23901.5MB, alloc=518.5MB, time=238.89 memory used=24045.3MB, alloc=518.5MB, time=243.00 memory used=24136.9MB, alloc=518.5MB, time=243.50 memory used=24228.2MB, alloc=542.5MB, time=243.93 memory used=24322.9MB, alloc=542.5MB, time=244.36 memory used=24443.1MB, alloc=542.5MB, time=244.78 memory used=24670.8MB, alloc=542.5MB, time=245.79 memory used=24845.4MB, alloc=542.5MB, time=246.62 memory used=25047.4MB, alloc=542.5MB, time=247.21 memory used=25155.7MB, alloc=542.5MB, time=248.11 memory used=25262.5MB, alloc=542.5MB, time=248.61 memory used=25406.7MB, alloc=542.5MB, time=249.58 memory used=25515.6MB, alloc=542.5MB, time=250.09 memory used=25647.7MB, alloc=542.5MB, time=250.84 memory used=25813.4MB, alloc=542.5MB, time=261.89 memory used=25921.5MB, alloc=542.5MB, time=262.42 memory used=26027.9MB, alloc=542.5MB, time=262.87 memory used=26120.4MB, alloc=542.5MB, time=263.29 memory used=26231.0MB, alloc=542.5MB, time=263.73 memory used=26362.4MB, alloc=542.5MB, time=264.16 memory used=26535.8MB, alloc=542.5MB, time=264.66 memory used=26813.6MB, alloc=542.5MB, time=265.81 memory used=27052.7MB, alloc=542.5MB, time=266.77 memory used=27311.9MB, alloc=542.5MB, time=267.87 memory used=27416.9MB, alloc=542.5MB, time=268.33 memory used=27561.1MB, alloc=542.5MB, time=269.31 memory used=27666.0MB, alloc=542.5MB, time=269.81 memory used=27798.6MB, alloc=542.5MB, time=270.58 memory used=27964.6MB, alloc=542.5MB, time=281.47 memory used=28071.9MB, alloc=542.5MB, time=281.94 memory used=28176.2MB, alloc=542.5MB, time=282.41 memory used=28269.7MB, alloc=542.5MB, time=282.82 memory used=28380.5MB, alloc=542.5MB, time=283.24 memory used=28511.9MB, alloc=542.5MB, time=283.68 memory used=28680.4MB, alloc=542.5MB, time=284.17 memory used=28957.4MB, alloc=542.5MB, time=285.36 memory used=29108.9MB, alloc=542.5MB, time=285.91 memory used=29350.2MB, alloc=542.5MB, time=286.92 memory used=29570.0MB, alloc=542.5MB, time=287.50 memory used=29859.3MB, alloc=542.5MB, time=288.78 memory used=29965.8MB, alloc=542.5MB, time=289.28 memory used=30097.9MB, alloc=542.5MB, time=290.00 memory used=30226.6MB, alloc=542.5MB, time=290.71 memory used=30347.1MB, alloc=542.5MB, time=291.35 memory used=30517.8MB, alloc=542.5MB, time=302.39 memory used=30629.8MB, alloc=542.5MB, time=302.95 memory used=30747.3MB, alloc=542.5MB, time=303.48 memory used=30834.0MB, alloc=542.5MB, time=303.87 memory used=30936.9MB, alloc=542.5MB, time=304.24 memory used=31059.6MB, alloc=542.5MB, time=304.63 memory used=31283.0MB, alloc=542.5MB, time=305.13 memory used=31559.2MB, alloc=542.5MB, time=306.12 memory used=31688.8MB, alloc=542.5MB, time=306.69 memory used=31839.5MB, alloc=542.5MB, time=307.18 memory used=32137.1MB, alloc=542.5MB, time=308.19 memory used=32422.1MB, alloc=542.5MB, time=308.81 memory used=32667.4MB, alloc=542.5MB, time=309.37 memory used=32847.5MB, alloc=542.5MB, time=310.71 memory used=32916.0MB, alloc=542.5MB, time=311.58 memory used=33080.6MB, alloc=542.5MB, time=322.24 memory used=33195.2MB, alloc=542.5MB, time=322.66 memory used=33284.2MB, alloc=542.5MB, time=323.09 memory used=33377.8MB, alloc=542.5MB, time=323.48 memory used=33488.7MB, alloc=542.5MB, time=323.91 memory used=33618.4MB, alloc=542.5MB, time=324.30 memory used=33764.8MB, alloc=542.5MB, time=324.75 memory used=33903.4MB, alloc=542.5MB, time=325.21 memory used=34101.1MB, alloc=542.5MB, time=326.13 memory used=34317.1MB, alloc=542.5MB, time=326.84 memory used=34547.8MB, alloc=542.5MB, time=329.24 memory used=34651.8MB, alloc=542.5MB, time=329.63 memory used=34751.1MB, alloc=542.5MB, time=330.04 memory used=34991.4MB, alloc=542.5MB, time=332.19 memory used=35186.2MB, alloc=566.5MB, time=334.75 memory used=35293.4MB, alloc=566.5MB, time=335.20 memory used=35428.5MB, alloc=566.5MB, time=335.89 memory used=35558.7MB, alloc=566.5MB, time=336.53 memory used=35719.0MB, alloc=566.5MB, time=339.70 memory used=35828.1MB, alloc=566.5MB, time=340.18 memory used=35946.7MB, alloc=566.5MB, time=340.65 memory used=36106.2MB, alloc=566.5MB, time=341.40 memory used=36271.5MB, alloc=566.5MB, time=344.73 memory used=36384.4MB, alloc=566.5MB, time=345.24 memory used=36487.5MB, alloc=566.5MB, time=345.69 memory used=36652.6MB, alloc=566.5MB, time=346.54 memory used=36785.0MB, alloc=566.5MB, time=347.19